Newspace parameters
Level: | \( N \) | \(=\) | \( 787 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 787.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(6.28422663907\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 787.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.54331 | −1.09128 | −0.545641 | − | 0.838019i | \(-0.683714\pi\) | ||||
−0.545641 | + | 0.838019i | \(0.683714\pi\) | |||||||
\(3\) | 2.10249 | 1.21387 | 0.606937 | − | 0.794750i | \(-0.292398\pi\) | ||||
0.606937 | + | 0.794750i | \(0.292398\pi\) | |||||||
\(4\) | 0.381797 | 0.190898 | ||||||||
\(5\) | 1.25926 | 0.563156 | 0.281578 | − | 0.959538i | \(-0.409142\pi\) | ||||
0.281578 | + | 0.959538i | \(0.409142\pi\) | |||||||
\(6\) | −3.24479 | −1.32468 | ||||||||
\(7\) | 3.14448 | 1.18850 | 0.594250 | − | 0.804280i | \(-0.297449\pi\) | ||||
0.594250 | + | 0.804280i | \(0.297449\pi\) | |||||||
\(8\) | 2.49738 | 0.882959 | ||||||||
\(9\) | 1.42047 | 0.473490 | ||||||||
\(10\) | −1.94342 | −0.614563 | ||||||||
\(11\) | −0.917999 | −0.276787 | −0.138394 | − | 0.990377i | \(-0.544194\pi\) | ||||
−0.138394 | + | 0.990377i | \(0.544194\pi\) | |||||||
\(12\) | 0.802724 | 0.231727 | ||||||||
\(13\) | 2.37731 | 0.659346 | 0.329673 | − | 0.944095i | \(-0.393061\pi\) | ||||
0.329673 | + | 0.944095i | \(0.393061\pi\) | |||||||
\(14\) | −4.85289 | −1.29699 | ||||||||
\(15\) | 2.64757 | 0.683600 | ||||||||
\(16\) | −4.61782 | −1.15446 | ||||||||
\(17\) | 4.67298 | 1.13336 | 0.566681 | − | 0.823937i | \(-0.308227\pi\) | ||||
0.566681 | + | 0.823937i | \(0.308227\pi\) | |||||||
\(18\) | −2.19222 | −0.516712 | ||||||||
\(19\) | 0.491776 | 0.112821 | 0.0564105 | − | 0.998408i | \(-0.482034\pi\) | ||||
0.0564105 | + | 0.998408i | \(0.482034\pi\) | |||||||
\(20\) | 0.480780 | 0.107506 | ||||||||
\(21\) | 6.61124 | 1.44269 | ||||||||
\(22\) | 1.41675 | 0.302053 | ||||||||
\(23\) | −1.93961 | −0.404436 | −0.202218 | − | 0.979341i | \(-0.564815\pi\) | ||||
−0.202218 | + | 0.979341i | \(0.564815\pi\) | |||||||
\(24\) | 5.25073 | 1.07180 | ||||||||
\(25\) | −3.41428 | −0.682855 | ||||||||
\(26\) | −3.66892 | −0.719533 | ||||||||
\(27\) | −3.32095 | −0.639117 | ||||||||
\(28\) | 1.20055 | 0.226883 | ||||||||
\(29\) | 5.54398 | 1.02949 | 0.514746 | − | 0.857343i | \(-0.327886\pi\) | ||||
0.514746 | + | 0.857343i | \(0.327886\pi\) | |||||||
\(30\) | −4.08602 | −0.746002 | ||||||||
\(31\) | −4.99990 | −0.898009 | −0.449005 | − | 0.893529i | \(-0.648221\pi\) | ||||
−0.449005 | + | 0.893529i | \(0.648221\pi\) | |||||||
\(32\) | 2.13195 | 0.376880 | ||||||||
\(33\) | −1.93008 | −0.335985 | ||||||||
\(34\) | −7.21184 | −1.23682 | ||||||||
\(35\) | 3.95970 | 0.669311 | ||||||||
\(36\) | 0.542331 | 0.0903885 | ||||||||
\(37\) | 0.00995484 | 0.00163657 | 0.000818283 | − | 1.00000i | \(-0.499740\pi\) | ||||
0.000818283 | 1.00000i | \(0.499740\pi\) | ||||||||
\(38\) | −0.758961 | −0.123120 | ||||||||
\(39\) | 4.99827 | 0.800364 | ||||||||
\(40\) | 3.14484 | 0.497244 | ||||||||
\(41\) | 7.33823 | 1.14604 | 0.573020 | − | 0.819541i | \(-0.305772\pi\) | ||||
0.573020 | + | 0.819541i | \(0.305772\pi\) | |||||||
\(42\) | −10.2032 | −1.57438 | ||||||||
\(43\) | 2.73113 | 0.416494 | 0.208247 | − | 0.978076i | \(-0.433224\pi\) | ||||
0.208247 | + | 0.978076i | \(0.433224\pi\) | |||||||
\(44\) | −0.350489 | −0.0528382 | ||||||||
\(45\) | 1.78874 | 0.266649 | ||||||||
\(46\) | 2.99341 | 0.441354 | ||||||||
\(47\) | −5.69556 | −0.830783 | −0.415392 | − | 0.909643i | \(-0.636355\pi\) | ||||
−0.415392 | + | 0.909643i | \(0.636355\pi\) | |||||||
\(48\) | −9.70894 | −1.40136 | ||||||||
\(49\) | 2.88774 | 0.412534 | ||||||||
\(50\) | 5.26928 | 0.745188 | ||||||||
\(51\) | 9.82489 | 1.37576 | ||||||||
\(52\) | 0.907648 | 0.125868 | ||||||||
\(53\) | −3.42166 | −0.470002 | −0.235001 | − | 0.971995i | \(-0.575509\pi\) | ||||
−0.235001 | + | 0.971995i | \(0.575509\pi\) | |||||||
\(54\) | 5.12524 | 0.697457 | ||||||||
\(55\) | −1.15599 | −0.155874 | ||||||||
\(56\) | 7.85297 | 1.04940 | ||||||||
\(57\) | 1.03395 | 0.136951 | ||||||||
\(58\) | −8.55607 | −1.12347 | ||||||||
\(59\) | 1.55022 | 0.201821 | 0.100911 | − | 0.994895i | \(-0.467824\pi\) | ||||
0.100911 | + | 0.994895i | \(0.467824\pi\) | |||||||
\(60\) | 1.01083 | 0.130498 | ||||||||
\(61\) | 0.660781 | 0.0846043 | 0.0423022 | − | 0.999105i | \(-0.486531\pi\) | ||||
0.0423022 | + | 0.999105i | \(0.486531\pi\) | |||||||
\(62\) | 7.71639 | 0.979982 | ||||||||
\(63\) | 4.46664 | 0.562743 | ||||||||
\(64\) | 5.94539 | 0.743174 | ||||||||
\(65\) | 2.99364 | 0.371315 | ||||||||
\(66\) | 2.97871 | 0.366654 | ||||||||
\(67\) | −6.25946 | −0.764715 | −0.382357 | − | 0.924014i | \(-0.624888\pi\) | ||||
−0.382357 | + | 0.924014i | \(0.624888\pi\) | |||||||
\(68\) | 1.78413 | 0.216357 | ||||||||
\(69\) | −4.07801 | −0.490935 | ||||||||
\(70\) | −6.11103 | −0.730408 | ||||||||
\(71\) | 6.33818 | 0.752204 | 0.376102 | − | 0.926578i | \(-0.377264\pi\) | ||||
0.376102 | + | 0.926578i | \(0.377264\pi\) | |||||||
\(72\) | 3.54746 | 0.418072 | ||||||||
\(73\) | −6.27766 | −0.734744 | −0.367372 | − | 0.930074i | \(-0.619742\pi\) | ||||
−0.367372 | + | 0.930074i | \(0.619742\pi\) | |||||||
\(74\) | −0.0153634 | −0.00178596 | ||||||||
\(75\) | −7.17849 | −0.828900 | ||||||||
\(76\) | 0.187758 | 0.0215374 | ||||||||
\(77\) | −2.88663 | −0.328962 | ||||||||
\(78\) | −7.71386 | −0.873423 | ||||||||
\(79\) | 8.41425 | 0.946677 | 0.473338 | − | 0.880881i | \(-0.343049\pi\) | ||||
0.473338 | + | 0.880881i | \(0.343049\pi\) | |||||||
\(80\) | −5.81502 | −0.650139 | ||||||||
\(81\) | −11.2437 | −1.24930 | ||||||||
\(82\) | −11.3251 | −1.25065 | ||||||||
\(83\) | −2.75585 | −0.302494 | −0.151247 | − | 0.988496i | \(-0.548329\pi\) | ||||
−0.151247 | + | 0.988496i | \(0.548329\pi\) | |||||||
\(84\) | 2.52415 | 0.275407 | ||||||||
\(85\) | 5.88447 | 0.638260 | ||||||||
\(86\) | −4.21498 | −0.454513 | ||||||||
\(87\) | 11.6562 | 1.24967 | ||||||||
\(88\) | −2.29260 | −0.244392 | ||||||||
\(89\) | 12.8586 | 1.36301 | 0.681505 | − | 0.731813i | \(-0.261326\pi\) | ||||
0.681505 | + | 0.731813i | \(0.261326\pi\) | |||||||
\(90\) | −2.76057 | −0.290989 | ||||||||
\(91\) | 7.47539 | 0.783634 | ||||||||
\(92\) | −0.740536 | −0.0772062 | ||||||||
\(93\) | −10.5123 | −1.09007 | ||||||||
\(94\) | 8.79000 | 0.906620 | ||||||||
\(95\) | 0.619271 | 0.0635358 | ||||||||
\(96\) | 4.48241 | 0.457484 | ||||||||
\(97\) | 14.0438 | 1.42593 | 0.712963 | − | 0.701201i | \(-0.247353\pi\) | ||||
0.712963 | + | 0.701201i | \(0.247353\pi\) | |||||||
\(98\) | −4.45666 | −0.450191 | ||||||||
\(99\) | −1.30399 | −0.131056 | ||||||||
\(100\) | −1.30356 | −0.130356 | ||||||||
\(101\) | −7.55228 | −0.751480 | −0.375740 | − | 0.926725i | \(-0.622611\pi\) | ||||
−0.375740 | + | 0.926725i | \(0.622611\pi\) | |||||||
\(102\) | −15.1628 | −1.50134 | ||||||||
\(103\) | −9.07007 | −0.893701 | −0.446850 | − | 0.894609i | \(-0.647454\pi\) | ||||
−0.446850 | + | 0.894609i | \(0.647454\pi\) | |||||||
\(104\) | 5.93705 | 0.582176 | ||||||||
\(105\) | 8.32523 | 0.812460 | ||||||||
\(106\) | 5.28068 | 0.512905 | ||||||||
\(107\) | 18.0943 | 1.74924 | 0.874619 | − | 0.484811i | \(-0.161112\pi\) | ||||
0.874619 | + | 0.484811i | \(0.161112\pi\) | |||||||
\(108\) | −1.26793 | −0.122006 | ||||||||
\(109\) | −0.101668 | −0.00973802 | −0.00486901 | − | 0.999988i | \(-0.501550\pi\) | ||||
−0.00486901 | + | 0.999988i | \(0.501550\pi\) | |||||||
\(110\) | 1.78405 | 0.170103 | ||||||||
\(111\) | 0.0209300 | 0.00198658 | ||||||||
\(112\) | −14.5206 | −1.37207 | ||||||||
\(113\) | 11.4722 | 1.07921 | 0.539606 | − | 0.841918i | \(-0.318573\pi\) | ||||
0.539606 | + | 0.841918i | \(0.318573\pi\) | |||||||
\(114\) | −1.59571 | −0.149452 | ||||||||
\(115\) | −2.44246 | −0.227761 | ||||||||
\(116\) | 2.11668 | 0.196528 | ||||||||
\(117\) | 3.37690 | 0.312194 | ||||||||
\(118\) | −2.39246 | −0.220244 | ||||||||
\(119\) | 14.6941 | 1.34700 | ||||||||
\(120\) | 6.61201 | 0.603591 | ||||||||
\(121\) | −10.1573 | −0.923389 | ||||||||
\(122\) | −1.01979 | −0.0923273 | ||||||||
\(123\) | 15.4286 | 1.39115 | ||||||||
\(124\) | −1.90895 | −0.171429 | ||||||||
\(125\) | −10.5957 | −0.947710 | ||||||||
\(126\) | −6.89339 | −0.614112 | ||||||||
\(127\) | 4.12393 | 0.365939 | 0.182970 | − | 0.983119i | \(-0.441429\pi\) | ||||
0.182970 | + | 0.983119i | \(0.441429\pi\) | |||||||
\(128\) | −13.4395 | −1.18789 | ||||||||
\(129\) | 5.74219 | 0.505571 | ||||||||
\(130\) | −4.62010 | −0.405210 | ||||||||
\(131\) | 13.2555 | 1.15814 | 0.579068 | − | 0.815279i | \(-0.303417\pi\) | ||||
0.579068 | + | 0.815279i | \(0.303417\pi\) | |||||||
\(132\) | −0.736900 | −0.0641389 | ||||||||
\(133\) | 1.54638 | 0.134088 | ||||||||
\(134\) | 9.66027 | 0.834520 | ||||||||
\(135\) | −4.18192 | −0.359922 | ||||||||
\(136\) | 11.6702 | 1.00071 | ||||||||
\(137\) | −12.3555 | −1.05560 | −0.527800 | − | 0.849369i | \(-0.676983\pi\) | ||||
−0.527800 | + | 0.849369i | \(0.676983\pi\) | |||||||
\(138\) | 6.29362 | 0.535749 | ||||||||
\(139\) | −20.2775 | −1.71991 | −0.859957 | − | 0.510366i | \(-0.829510\pi\) | ||||
−0.859957 | + | 0.510366i | \(0.829510\pi\) | |||||||
\(140\) | 1.51180 | 0.127770 | ||||||||
\(141\) | −11.9749 | −1.00847 | ||||||||
\(142\) | −9.78176 | −0.820867 | ||||||||
\(143\) | −2.18236 | −0.182499 | ||||||||
\(144\) | −6.55948 | −0.546624 | ||||||||
\(145\) | 6.98129 | 0.579765 | ||||||||
\(146\) | 9.68836 | 0.801814 | ||||||||
\(147\) | 6.07144 | 0.500764 | ||||||||
\(148\) | 0.00380073 | 0.000312418 0 | ||||||||
\(149\) | −2.91309 | −0.238650 | −0.119325 | − | 0.992855i | \(-0.538073\pi\) | ||||
−0.119325 | + | 0.992855i | \(0.538073\pi\) | |||||||
\(150\) | 11.0786 | 0.904565 | ||||||||
\(151\) | −5.82211 | −0.473796 | −0.236898 | − | 0.971534i | \(-0.576131\pi\) | ||||
−0.236898 | + | 0.971534i | \(0.576131\pi\) | |||||||
\(152\) | 1.22815 | 0.0996163 | ||||||||
\(153\) | 6.63782 | 0.536636 | ||||||||
\(154\) | 4.45495 | 0.358990 | ||||||||
\(155\) | −6.29616 | −0.505719 | ||||||||
\(156\) | 1.90832 | 0.152788 | ||||||||
\(157\) | 6.85944 | 0.547443 | 0.273721 | − | 0.961809i | \(-0.411745\pi\) | ||||
0.273721 | + | 0.961809i | \(0.411745\pi\) | |||||||
\(158\) | −12.9858 | −1.03309 | ||||||||
\(159\) | −7.19402 | −0.570523 | ||||||||
\(160\) | 2.68467 | 0.212242 | ||||||||
\(161\) | −6.09905 | −0.480673 | ||||||||
\(162\) | 17.3524 | 1.36334 | ||||||||
\(163\) | −9.63668 | −0.754803 | −0.377402 | − | 0.926050i | \(-0.623182\pi\) | ||||
−0.377402 | + | 0.926050i | \(0.623182\pi\) | |||||||
\(164\) | 2.80171 | 0.218777 | ||||||||
\(165\) | −2.43047 | −0.189212 | ||||||||
\(166\) | 4.25312 | 0.330106 | ||||||||
\(167\) | −6.38436 | −0.494037 | −0.247018 | − | 0.969011i | \(-0.579451\pi\) | ||||
−0.247018 | + | 0.969011i | \(0.579451\pi\) | |||||||
\(168\) | 16.5108 | 1.27384 | ||||||||
\(169\) | −7.34841 | −0.565262 | ||||||||
\(170\) | −9.08154 | −0.696522 | ||||||||
\(171\) | 0.698553 | 0.0534197 | ||||||||
\(172\) | 1.04274 | 0.0795081 | ||||||||
\(173\) | −10.1853 | −0.774376 | −0.387188 | − | 0.922001i | \(-0.626553\pi\) | ||||
−0.387188 | + | 0.922001i | \(0.626553\pi\) | |||||||
\(174\) | −17.9891 | −1.36375 | ||||||||
\(175\) | −10.7361 | −0.811574 | ||||||||
\(176\) | 4.23916 | 0.319538 | ||||||||
\(177\) | 3.25932 | 0.244986 | ||||||||
\(178\) | −19.8448 | −1.48743 | ||||||||
\(179\) | −6.30119 | −0.470973 | −0.235487 | − | 0.971878i | \(-0.575668\pi\) | ||||
−0.235487 | + | 0.971878i | \(0.575668\pi\) | |||||||
\(180\) | 0.682933 | 0.0509028 | ||||||||
\(181\) | −2.30314 | −0.171191 | −0.0855954 | − | 0.996330i | \(-0.527279\pi\) | ||||
−0.0855954 | + | 0.996330i | \(0.527279\pi\) | |||||||
\(182\) | −11.5368 | −0.855166 | ||||||||
\(183\) | 1.38929 | 0.102699 | ||||||||
\(184\) | −4.84395 | −0.357100 | ||||||||
\(185\) | 0.0125357 | 0.000921642 0 | ||||||||
\(186\) | 16.2236 | 1.18958 | ||||||||
\(187\) | −4.28978 | −0.313700 | ||||||||
\(188\) | −2.17455 | −0.158595 | ||||||||
\(189\) | −10.4426 | −0.759590 | ||||||||
\(190\) | −0.955725 | −0.0693356 | ||||||||
\(191\) | 19.0312 | 1.37705 | 0.688526 | − | 0.725212i | \(-0.258258\pi\) | ||||
0.688526 | + | 0.725212i | \(0.258258\pi\) | |||||||
\(192\) | 12.5001 | 0.902120 | ||||||||
\(193\) | −18.3716 | −1.32241 | −0.661207 | − | 0.750204i | \(-0.729955\pi\) | ||||
−0.661207 | + | 0.750204i | \(0.729955\pi\) | |||||||
\(194\) | −21.6738 | −1.55609 | ||||||||
\(195\) | 6.29410 | 0.450730 | ||||||||
\(196\) | 1.10253 | 0.0787520 | ||||||||
\(197\) | −14.6513 | −1.04386 | −0.521930 | − | 0.852989i | \(-0.674788\pi\) | ||||
−0.521930 | + | 0.852989i | \(0.674788\pi\) | |||||||
\(198\) | 2.01246 | 0.143019 | ||||||||
\(199\) | −11.3317 | −0.803282 | −0.401641 | − | 0.915797i | \(-0.631560\pi\) | ||||
−0.401641 | + | 0.915797i | \(0.631560\pi\) | |||||||
\(200\) | −8.52676 | −0.602933 | ||||||||
\(201\) | −13.1605 | −0.928268 | ||||||||
\(202\) | 11.6555 | 0.820078 | ||||||||
\(203\) | 17.4329 | 1.22355 | ||||||||
\(204\) | 3.75111 | 0.262630 | ||||||||
\(205\) | 9.24071 | 0.645399 | ||||||||
\(206\) | 13.9979 | 0.975280 | ||||||||
\(207\) | −2.75516 | −0.191497 | ||||||||
\(208\) | −10.9780 | −0.761187 | ||||||||
\(209\) | −0.451449 | −0.0312274 | ||||||||
\(210\) | −12.8484 | −0.886623 | ||||||||
\(211\) | −24.1080 | −1.65967 | −0.829833 | − | 0.558013i | \(-0.811564\pi\) | ||||
−0.829833 | + | 0.558013i | \(0.811564\pi\) | |||||||
\(212\) | −1.30638 | −0.0897225 | ||||||||
\(213\) | 13.3260 | 0.913081 | ||||||||
\(214\) | −27.9250 | −1.90891 | ||||||||
\(215\) | 3.43920 | 0.234551 | ||||||||
\(216\) | −8.29368 | −0.564314 | ||||||||
\(217\) | −15.7221 | −1.06728 | ||||||||
\(218\) | 0.156905 | 0.0106269 | ||||||||
\(219\) | −13.1987 | −0.891887 | ||||||||
\(220\) | −0.441355 | −0.0297561 | ||||||||
\(221\) | 11.1091 | 0.747279 | ||||||||
\(222\) | −0.0323014 | −0.00216793 | ||||||||
\(223\) | −25.3974 | −1.70073 | −0.850367 | − | 0.526191i | \(-0.823620\pi\) | ||||
−0.850367 | + | 0.526191i | \(0.823620\pi\) | |||||||
\(224\) | 6.70388 | 0.447922 | ||||||||
\(225\) | −4.84988 | −0.323325 | ||||||||
\(226\) | −17.7051 | −1.17772 | ||||||||
\(227\) | 3.56104 | 0.236354 | 0.118177 | − | 0.992993i | \(-0.462295\pi\) | ||||
0.118177 | + | 0.992993i | \(0.462295\pi\) | |||||||
\(228\) | 0.394760 | 0.0261436 | ||||||||
\(229\) | 1.97251 | 0.130347 | 0.0651735 | − | 0.997874i | \(-0.479240\pi\) | ||||
0.0651735 | + | 0.997874i | \(0.479240\pi\) | |||||||
\(230\) | 3.76947 | 0.248551 | ||||||||
\(231\) | −6.06911 | −0.399318 | ||||||||
\(232\) | 13.8455 | 0.908999 | ||||||||
\(233\) | −8.85144 | −0.579877 | −0.289939 | − | 0.957045i | \(-0.593635\pi\) | ||||
−0.289939 | + | 0.957045i | \(0.593635\pi\) | |||||||
\(234\) | −5.21159 | −0.340692 | ||||||||
\(235\) | −7.17217 | −0.467861 | ||||||||
\(236\) | 0.591869 | 0.0385274 | ||||||||
\(237\) | 17.6909 | 1.14915 | ||||||||
\(238\) | −22.6775 | −1.46996 | ||||||||
\(239\) | −8.00959 | −0.518097 | −0.259049 | − | 0.965864i | \(-0.583409\pi\) | ||||
−0.259049 | + | 0.965864i | \(0.583409\pi\) | |||||||
\(240\) | −12.2260 | −0.789187 | ||||||||
\(241\) | −10.1593 | −0.654415 | −0.327208 | − | 0.944952i | \(-0.606108\pi\) | ||||
−0.327208 | + | 0.944952i | \(0.606108\pi\) | |||||||
\(242\) | 15.6758 | 1.00768 | ||||||||
\(243\) | −13.6769 | −0.877373 | ||||||||
\(244\) | 0.252284 | 0.0161508 | ||||||||
\(245\) | 3.63640 | 0.232321 | ||||||||
\(246\) | −23.8110 | −1.51814 | ||||||||
\(247\) | 1.16910 | 0.0743881 | ||||||||
\(248\) | −12.4867 | −0.792905 | ||||||||
\(249\) | −5.79415 | −0.367189 | ||||||||
\(250\) | 16.3525 | 1.03422 | ||||||||
\(251\) | −9.64964 | −0.609080 | −0.304540 | − | 0.952500i | \(-0.598503\pi\) | ||||
−0.304540 | + | 0.952500i | \(0.598503\pi\) | |||||||
\(252\) | 1.70535 | 0.107427 | ||||||||
\(253\) | 1.78056 | 0.111943 | ||||||||
\(254\) | −6.36449 | −0.399343 | ||||||||
\(255\) | 12.3720 | 0.774767 | ||||||||
\(256\) | 8.85045 | 0.553153 | ||||||||
\(257\) | 19.3494 | 1.20698 | 0.603491 | − | 0.797370i | \(-0.293776\pi\) | ||||
0.603491 | + | 0.797370i | \(0.293776\pi\) | |||||||
\(258\) | −8.86196 | −0.551721 | ||||||||
\(259\) | 0.0313028 | 0.00194506 | ||||||||
\(260\) | 1.14296 | 0.0708834 | ||||||||
\(261\) | 7.87507 | 0.487454 | ||||||||
\(262\) | −20.4573 | −1.26385 | ||||||||
\(263\) | −3.53940 | −0.218249 | −0.109124 | − | 0.994028i | \(-0.534805\pi\) | ||||
−0.109124 | + | 0.994028i | \(0.534805\pi\) | |||||||
\(264\) | −4.82016 | −0.296661 | ||||||||
\(265\) | −4.30875 | −0.264684 | ||||||||
\(266\) | −2.38653 | −0.146328 | ||||||||
\(267\) | 27.0351 | 1.65452 | ||||||||
\(268\) | −2.38984 | −0.145983 | ||||||||
\(269\) | 21.2672 | 1.29669 | 0.648343 | − | 0.761348i | \(-0.275462\pi\) | ||||
0.648343 | + | 0.761348i | \(0.275462\pi\) | |||||||
\(270\) | 6.45399 | 0.392777 | ||||||||
\(271\) | 10.6255 | 0.645453 | 0.322726 | − | 0.946492i | \(-0.395401\pi\) | ||||
0.322726 | + | 0.946492i | \(0.395401\pi\) | |||||||
\(272\) | −21.5790 | −1.30842 | ||||||||
\(273\) | 15.7169 | 0.951233 | ||||||||
\(274\) | 19.0683 | 1.15196 | ||||||||
\(275\) | 3.13430 | 0.189005 | ||||||||
\(276\) | −1.55697 | −0.0937186 | ||||||||
\(277\) | −6.19742 | −0.372367 | −0.186183 | − | 0.982515i | \(-0.559612\pi\) | ||||
−0.186183 | + | 0.982515i | \(0.559612\pi\) | |||||||
\(278\) | 31.2944 | 1.87691 | ||||||||
\(279\) | −7.10222 | −0.425199 | ||||||||
\(280\) | 9.88889 | 0.590974 | ||||||||
\(281\) | −0.403247 | −0.0240557 | −0.0120278 | − | 0.999928i | \(-0.503829\pi\) | ||||
−0.0120278 | + | 0.999928i | \(0.503829\pi\) | |||||||
\(282\) | 18.4809 | 1.10052 | ||||||||
\(283\) | −3.24956 | −0.193167 | −0.0965833 | − | 0.995325i | \(-0.530791\pi\) | ||||
−0.0965833 | + | 0.995325i | \(0.530791\pi\) | |||||||
\(284\) | 2.41990 | 0.143595 | ||||||||
\(285\) | 1.30201 | 0.0771245 | ||||||||
\(286\) | 3.36806 | 0.199158 | ||||||||
\(287\) | 23.0749 | 1.36207 | ||||||||
\(288\) | 3.02838 | 0.178449 | ||||||||
\(289\) | 4.83670 | 0.284512 | ||||||||
\(290\) | −10.7743 | −0.632687 | ||||||||
\(291\) | 29.5269 | 1.73090 | ||||||||
\(292\) | −2.39679 | −0.140262 | ||||||||
\(293\) | 5.58232 | 0.326123 | 0.163061 | − | 0.986616i | \(-0.447863\pi\) | ||||
0.163061 | + | 0.986616i | \(0.447863\pi\) | |||||||
\(294\) | −9.37010 | −0.546475 | ||||||||
\(295\) | 1.95212 | 0.113657 | ||||||||
\(296\) | 0.0248611 | 0.00144502 | ||||||||
\(297\) | 3.04862 | 0.176899 | ||||||||
\(298\) | 4.49579 | 0.260434 | ||||||||
\(299\) | −4.61104 | −0.266664 | ||||||||
\(300\) | −2.74072 | −0.158236 | ||||||||
\(301\) | 8.58799 | 0.495004 | ||||||||
\(302\) | 8.98530 | 0.517046 | ||||||||
\(303\) | −15.8786 | −0.912202 | ||||||||
\(304\) | −2.27093 | −0.130247 | ||||||||
\(305\) | 0.832092 | 0.0476454 | ||||||||
\(306\) | −10.2442 | −0.585622 | ||||||||
\(307\) | 10.8518 | 0.619345 | 0.309673 | − | 0.950843i | \(-0.399781\pi\) | ||||
0.309673 | + | 0.950843i | \(0.399781\pi\) | |||||||
\(308\) | −1.10210 | −0.0627982 | ||||||||
\(309\) | −19.0697 | −1.08484 | ||||||||
\(310\) | 9.71690 | 0.551883 | ||||||||
\(311\) | −21.3609 | −1.21127 | −0.605633 | − | 0.795744i | \(-0.707080\pi\) | ||||
−0.605633 | + | 0.795744i | \(0.707080\pi\) | |||||||
\(312\) | 12.4826 | 0.706688 | ||||||||
\(313\) | 8.53183 | 0.482248 | 0.241124 | − | 0.970494i | \(-0.422484\pi\) | ||||
0.241124 | + | 0.970494i | \(0.422484\pi\) | |||||||
\(314\) | −10.5862 | −0.597415 | ||||||||
\(315\) | 5.62464 | 0.316912 | ||||||||
\(316\) | 3.21253 | 0.180719 | ||||||||
\(317\) | −7.28886 | −0.409383 | −0.204692 | − | 0.978827i | \(-0.565619\pi\) | ||||
−0.204692 | + | 0.978827i | \(0.565619\pi\) | |||||||
\(318\) | 11.1026 | 0.622602 | ||||||||
\(319\) | −5.08937 | −0.284950 | ||||||||
\(320\) | 7.48677 | 0.418523 | ||||||||
\(321\) | 38.0430 | 2.12335 | ||||||||
\(322\) | 9.41271 | 0.524550 | ||||||||
\(323\) | 2.29805 | 0.127867 | ||||||||
\(324\) | −4.29280 | −0.238489 | ||||||||
\(325\) | −8.11678 | −0.450238 | ||||||||
\(326\) | 14.8724 | 0.823704 | ||||||||
\(327\) | −0.213756 | −0.0118207 | ||||||||
\(328\) | 18.3264 | 1.01191 | ||||||||
\(329\) | −17.9096 | −0.987387 | ||||||||
\(330\) | 3.75096 | 0.206484 | ||||||||
\(331\) | 3.46556 | 0.190484 | 0.0952422 | − | 0.995454i | \(-0.469637\pi\) | ||||
0.0952422 | + | 0.995454i | \(0.469637\pi\) | |||||||
\(332\) | −1.05217 | −0.0577456 | ||||||||
\(333\) | 0.0141406 | 0.000774898 0 | ||||||||
\(334\) | 9.85303 | 0.539134 | ||||||||
\(335\) | −7.88226 | −0.430654 | ||||||||
\(336\) | −30.5295 | −1.66552 | ||||||||
\(337\) | 12.2351 | 0.666489 | 0.333244 | − | 0.942840i | \(-0.391857\pi\) | ||||
0.333244 | + | 0.942840i | \(0.391857\pi\) | |||||||
\(338\) | 11.3409 | 0.616861 | ||||||||
\(339\) | 24.1201 | 1.31003 | ||||||||
\(340\) | 2.24667 | 0.121843 | ||||||||
\(341\) | 4.58991 | 0.248557 | ||||||||
\(342\) | −1.07808 | −0.0582960 | ||||||||
\(343\) | −12.9309 | −0.698204 | ||||||||
\(344\) | 6.82069 | 0.367747 | ||||||||
\(345\) | −5.13525 | −0.276473 | ||||||||
\(346\) | 15.7191 | 0.845063 | ||||||||
\(347\) | 15.5937 | 0.837111 | 0.418556 | − | 0.908191i | \(-0.362536\pi\) | ||||
0.418556 | + | 0.908191i | \(0.362536\pi\) | |||||||
\(348\) | 4.45029 | 0.238561 | ||||||||
\(349\) | 9.55242 | 0.511329 | 0.255665 | − | 0.966766i | \(-0.417706\pi\) | ||||
0.255665 | + | 0.966766i | \(0.417706\pi\) | |||||||
\(350\) | 16.5691 | 0.885657 | ||||||||
\(351\) | −7.89491 | −0.421399 | ||||||||
\(352\) | −1.95713 | −0.104315 | ||||||||
\(353\) | −9.09226 | −0.483932 | −0.241966 | − | 0.970285i | \(-0.577792\pi\) | ||||
−0.241966 | + | 0.970285i | \(0.577792\pi\) | |||||||
\(354\) | −5.03014 | −0.267349 | ||||||||
\(355\) | 7.98139 | 0.423608 | ||||||||
\(356\) | 4.90938 | 0.260196 | ||||||||
\(357\) | 30.8941 | 1.63509 | ||||||||
\(358\) | 9.72468 | 0.513965 | ||||||||
\(359\) | 17.2094 | 0.908277 | 0.454139 | − | 0.890931i | \(-0.349947\pi\) | ||||
0.454139 | + | 0.890931i | \(0.349947\pi\) | |||||||
\(360\) | 4.46716 | 0.235440 | ||||||||
\(361\) | −18.7582 | −0.987271 | ||||||||
\(362\) | 3.55445 | 0.186818 | ||||||||
\(363\) | −21.3556 | −1.12088 | ||||||||
\(364\) | 2.85408 | 0.149594 | ||||||||
\(365\) | −7.90518 | −0.413776 | ||||||||
\(366\) | −2.14410 | −0.112074 | ||||||||
\(367\) | 8.17947 | 0.426965 | 0.213483 | − | 0.976947i | \(-0.431519\pi\) | ||||
0.213483 | + | 0.976947i | \(0.431519\pi\) | |||||||
\(368\) | 8.95677 | 0.466904 | ||||||||
\(369\) | 10.4237 | 0.542639 | ||||||||
\(370\) | −0.0193464 | −0.00100577 | ||||||||
\(371\) | −10.7593 | −0.558597 | ||||||||
\(372\) | −4.01355 | −0.208093 | ||||||||
\(373\) | 3.65734 | 0.189370 | 0.0946850 | − | 0.995507i | \(-0.469816\pi\) | ||||
0.0946850 | + | 0.995507i | \(0.469816\pi\) | |||||||
\(374\) | 6.62046 | 0.342336 | ||||||||
\(375\) | −22.2774 | −1.15040 | ||||||||
\(376\) | −14.2240 | −0.733547 | ||||||||
\(377\) | 13.1798 | 0.678792 | ||||||||
\(378\) | 16.1162 | 0.828928 | ||||||||
\(379\) | −13.6390 | −0.700589 | −0.350294 | − | 0.936640i | \(-0.613918\pi\) | ||||
−0.350294 | + | 0.936640i | \(0.613918\pi\) | |||||||
\(380\) | 0.236436 | 0.0121289 | ||||||||
\(381\) | 8.67052 | 0.444204 | ||||||||
\(382\) | −29.3710 | −1.50275 | ||||||||
\(383\) | −32.5444 | −1.66294 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(384\) | −28.2564 | −1.44195 | ||||||||
\(385\) | −3.63500 | −0.185257 | ||||||||
\(386\) | 28.3530 | 1.44313 | ||||||||
\(387\) | 3.87950 | 0.197206 | ||||||||
\(388\) | 5.36186 | 0.272207 | ||||||||
\(389\) | 5.60065 | 0.283964 | 0.141982 | − | 0.989869i | \(-0.454652\pi\) | ||||
0.141982 | + | 0.989869i | \(0.454652\pi\) | |||||||
\(390\) | −9.71372 | −0.491873 | ||||||||
\(391\) | −9.06374 | −0.458373 | ||||||||
\(392\) | 7.21179 | 0.364250 | ||||||||
\(393\) | 27.8695 | 1.40583 | ||||||||
\(394\) | 22.6114 | 1.13915 | ||||||||
\(395\) | 10.5957 | 0.533127 | ||||||||
\(396\) | −0.497859 | −0.0250184 | ||||||||
\(397\) | 12.8170 | 0.643264 | 0.321632 | − | 0.946865i | \(-0.395769\pi\) | ||||
0.321632 | + | 0.946865i | \(0.395769\pi\) | |||||||
\(398\) | 17.4883 | 0.876608 | ||||||||
\(399\) | 3.25124 | 0.162766 | ||||||||
\(400\) | 15.7665 | 0.788327 | ||||||||
\(401\) | 39.6940 | 1.98222 | 0.991111 | − | 0.133037i | \(-0.0424728\pi\) | ||||
0.991111 | + | 0.133037i | \(0.0424728\pi\) | |||||||
\(402\) | 20.3106 | 1.01300 | ||||||||
\(403\) | −11.8863 | −0.592099 | ||||||||
\(404\) | −2.88344 | −0.143456 | ||||||||
\(405\) | −14.1587 | −0.703549 | ||||||||
\(406\) | −26.9044 | −1.33524 | ||||||||
\(407\) | −0.00913853 | −0.000452980 0 | ||||||||
\(408\) | 24.5365 | 1.21474 | ||||||||
\(409\) | −9.10948 | −0.450435 | −0.225217 | − | 0.974309i | \(-0.572309\pi\) | ||||
−0.225217 | + | 0.974309i | \(0.572309\pi\) | |||||||
\(410\) | −14.2613 | −0.704313 | ||||||||
\(411\) | −25.9773 | −1.28137 | ||||||||
\(412\) | −3.46292 | −0.170606 | ||||||||
\(413\) | 4.87463 | 0.239865 | ||||||||
\(414\) | 4.25205 | 0.208977 | ||||||||
\(415\) | −3.47032 | −0.170351 | ||||||||
\(416\) | 5.06831 | 0.248494 | ||||||||
\(417\) | −42.6333 | −2.08776 | ||||||||
\(418\) | 0.696725 | 0.0340779 | ||||||||
\(419\) | −1.62496 | −0.0793847 | −0.0396924 | − | 0.999212i | \(-0.512638\pi\) | ||||
−0.0396924 | + | 0.999212i | \(0.512638\pi\) | |||||||
\(420\) | 3.17855 | 0.155097 | ||||||||
\(421\) | 14.4927 | 0.706330 | 0.353165 | − | 0.935561i | \(-0.385105\pi\) | ||||
0.353165 | + | 0.935561i | \(0.385105\pi\) | |||||||
\(422\) | 37.2061 | 1.81116 | ||||||||
\(423\) | −8.09038 | −0.393368 | ||||||||
\(424\) | −8.54521 | −0.414992 | ||||||||
\(425\) | −15.9548 | −0.773923 | ||||||||
\(426\) | −20.5661 | −0.996429 | ||||||||
\(427\) | 2.07781 | 0.100552 | ||||||||
\(428\) | 6.90833 | 0.333927 | ||||||||
\(429\) | −4.58840 | −0.221530 | ||||||||
\(430\) | −5.30773 | −0.255962 | ||||||||
\(431\) | −14.0946 | −0.678913 | −0.339457 | − | 0.940622i | \(-0.610243\pi\) | ||||
−0.339457 | + | 0.940622i | \(0.610243\pi\) | |||||||
\(432\) | 15.3356 | 0.737832 | ||||||||
\(433\) | −15.4666 | −0.743280 | −0.371640 | − | 0.928377i | \(-0.621204\pi\) | ||||
−0.371640 | + | 0.928377i | \(0.621204\pi\) | |||||||
\(434\) | 24.2640 | 1.16471 | ||||||||
\(435\) | 14.6781 | 0.703761 | ||||||||
\(436\) | −0.0388165 | −0.00185897 | ||||||||
\(437\) | −0.953852 | −0.0456289 | ||||||||
\(438\) | 20.3697 | 0.973301 | ||||||||
\(439\) | 20.3349 | 0.970530 | 0.485265 | − | 0.874367i | \(-0.338723\pi\) | ||||
0.485265 | + | 0.874367i | \(0.338723\pi\) | |||||||
\(440\) | −2.88696 | −0.137631 | ||||||||
\(441\) | 4.10194 | 0.195331 | ||||||||
\(442\) | −17.1447 | −0.815493 | ||||||||
\(443\) | −36.0512 | −1.71285 | −0.856423 | − | 0.516275i | \(-0.827318\pi\) | ||||
−0.856423 | + | 0.516275i | \(0.827318\pi\) | |||||||
\(444\) | 0.00799099 | 0.000379236 0 | ||||||||
\(445\) | 16.1923 | 0.767587 | ||||||||
\(446\) | 39.1959 | 1.85598 | ||||||||
\(447\) | −6.12475 | −0.289691 | ||||||||
\(448\) | 18.6951 | 0.883263 | ||||||||
\(449\) | −22.8583 | −1.07875 | −0.539376 | − | 0.842065i | \(-0.681340\pi\) | ||||
−0.539376 | + | 0.842065i | \(0.681340\pi\) | |||||||
\(450\) | 7.48485 | 0.352839 | ||||||||
\(451\) | −6.73649 | −0.317209 | ||||||||
\(452\) | 4.38004 | 0.206020 | ||||||||
\(453\) | −12.2409 | −0.575129 | ||||||||
\(454\) | −5.49578 | −0.257930 | ||||||||
\(455\) | 9.41342 | 0.441308 | ||||||||
\(456\) | 2.58218 | 0.120922 | ||||||||
\(457\) | 27.9339 | 1.30669 | 0.653346 | − | 0.757059i | \(-0.273365\pi\) | ||||
0.653346 | + | 0.757059i | \(0.273365\pi\) | |||||||
\(458\) | −3.04419 | −0.142246 | ||||||||
\(459\) | −15.5187 | −0.724351 | ||||||||
\(460\) | −0.932524 | −0.0434791 | ||||||||
\(461\) | 21.1066 | 0.983033 | 0.491516 | − | 0.870868i | \(-0.336443\pi\) | ||||
0.491516 | + | 0.870868i | \(0.336443\pi\) | |||||||
\(462\) | 9.36649 | 0.435769 | ||||||||
\(463\) | 28.0736 | 1.30469 | 0.652345 | − | 0.757922i | \(-0.273785\pi\) | ||||
0.652345 | + | 0.757922i | \(0.273785\pi\) | |||||||
\(464\) | −25.6011 | −1.18850 | ||||||||
\(465\) | −13.2376 | −0.613880 | ||||||||
\(466\) | 13.6605 | 0.632810 | ||||||||
\(467\) | −4.91492 | −0.227435 | −0.113718 | − | 0.993513i | \(-0.536276\pi\) | ||||
−0.113718 | + | 0.993513i | \(0.536276\pi\) | |||||||
\(468\) | 1.28929 | 0.0595973 | ||||||||
\(469\) | −19.6827 | −0.908864 | ||||||||
\(470\) | 11.0689 | 0.510568 | ||||||||
\(471\) | 14.4219 | 0.664527 | ||||||||
\(472\) | 3.87149 | 0.178200 | ||||||||
\(473\) | −2.50718 | −0.115280 | ||||||||
\(474\) | −27.3025 | −1.25404 | ||||||||
\(475\) | −1.67906 | −0.0770404 | ||||||||
\(476\) | 5.61015 | 0.257141 | ||||||||
\(477\) | −4.86037 | −0.222541 | ||||||||
\(478\) | 12.3613 | 0.565391 | ||||||||
\(479\) | 31.5688 | 1.44241 | 0.721207 | − | 0.692720i | \(-0.243588\pi\) | ||||
0.721207 | + | 0.692720i | \(0.243588\pi\) | |||||||
\(480\) | 5.64450 | 0.257635 | ||||||||
\(481\) | 0.0236657 | 0.00107906 | ||||||||
\(482\) | 15.6789 | 0.714152 | ||||||||
\(483\) | −12.8232 | −0.583476 | ||||||||
\(484\) | −3.87802 | −0.176273 | ||||||||
\(485\) | 17.6847 | 0.803019 | ||||||||
\(486\) | 21.1076 | 0.957462 | ||||||||
\(487\) | 26.3909 | 1.19588 | 0.597942 | − | 0.801540i | \(-0.295985\pi\) | ||||
0.597942 | + | 0.801540i | \(0.295985\pi\) | |||||||
\(488\) | 1.65022 | 0.0747021 | ||||||||
\(489\) | −20.2610 | −0.916236 | ||||||||
\(490\) | −5.61208 | −0.253528 | ||||||||
\(491\) | 33.9322 | 1.53134 | 0.765669 | − | 0.643235i | \(-0.222408\pi\) | ||||
0.765669 | + | 0.643235i | \(0.222408\pi\) | |||||||
\(492\) | 5.89058 | 0.265568 | ||||||||
\(493\) | 25.9069 | 1.16679 | ||||||||
\(494\) | −1.80428 | −0.0811785 | ||||||||
\(495\) | −1.64206 | −0.0738049 | ||||||||
\(496\) | 23.0887 | 1.03671 | ||||||||
\(497\) | 19.9303 | 0.893995 | ||||||||
\(498\) | 8.94215 | 0.400707 | ||||||||
\(499\) | 4.42373 | 0.198033 | 0.0990167 | − | 0.995086i | \(-0.468430\pi\) | ||||
0.0990167 | + | 0.995086i | \(0.468430\pi\) | |||||||
\(500\) | −4.04541 | −0.180916 | ||||||||
\(501\) | −13.4231 | −0.599698 | ||||||||
\(502\) | 14.8924 | 0.664678 | ||||||||
\(503\) | 22.7962 | 1.01643 | 0.508216 | − | 0.861230i | \(-0.330305\pi\) | ||||
0.508216 | + | 0.861230i | \(0.330305\pi\) | |||||||
\(504\) | 11.1549 | 0.496879 | ||||||||
\(505\) | −9.51025 | −0.423201 | ||||||||
\(506\) | −2.74795 | −0.122161 | ||||||||
\(507\) | −15.4500 | −0.686157 | ||||||||
\(508\) | 1.57450 | 0.0698572 | ||||||||
\(509\) | −14.4925 | −0.642369 | −0.321185 | − | 0.947017i | \(-0.604081\pi\) | ||||
−0.321185 | + | 0.947017i | \(0.604081\pi\) | |||||||
\(510\) | −19.0939 | −0.845490 | ||||||||
\(511\) | −19.7400 | −0.873244 | ||||||||
\(512\) | 13.2200 | 0.584246 | ||||||||
\(513\) | −1.63316 | −0.0721058 | ||||||||
\(514\) | −29.8621 | −1.31716 | ||||||||
\(515\) | −11.4215 | −0.503293 | ||||||||
\(516\) | 2.19235 | 0.0965128 | ||||||||
\(517\) | 5.22852 | 0.229950 | ||||||||
\(518\) | −0.0483098 | −0.00212261 | ||||||||
\(519\) | −21.4145 | −0.939994 | ||||||||
\(520\) | 7.47626 | 0.327856 | ||||||||
\(521\) | −16.3460 | −0.716131 | −0.358065 | − | 0.933697i | \(-0.616564\pi\) | ||||
−0.358065 | + | 0.933697i | \(0.616564\pi\) | |||||||
\(522\) | −12.1536 | −0.531951 | ||||||||
\(523\) | 11.3842 | 0.497795 | 0.248897 | − | 0.968530i | \(-0.419932\pi\) | ||||
0.248897 | + | 0.968530i | \(0.419932\pi\) | |||||||
\(524\) | 5.06090 | 0.221086 | ||||||||
\(525\) | −22.5726 | −0.985149 | ||||||||
\(526\) | 5.46238 | 0.238171 | ||||||||
\(527\) | −23.3644 | −1.01777 | ||||||||
\(528\) | 8.91279 | 0.387879 | ||||||||
\(529\) | −19.2379 | −0.836431 | ||||||||
\(530\) | 6.64972 | 0.288845 | ||||||||
\(531\) | 2.20204 | 0.0955605 | ||||||||
\(532\) | 0.590402 | 0.0255972 | ||||||||
\(533\) | 17.4452 | 0.755637 | ||||||||
\(534\) | −41.7235 | −1.80555 | ||||||||
\(535\) | 22.7853 | 0.985094 | ||||||||
\(536\) | −15.6323 | −0.675212 | ||||||||
\(537\) | −13.2482 | −0.571702 | ||||||||
\(538\) | −32.8219 | −1.41505 | ||||||||
\(539\) | −2.65094 | −0.114184 | ||||||||
\(540\) | −1.59664 | −0.0687086 | ||||||||
\(541\) | 14.1027 | 0.606322 | 0.303161 | − | 0.952939i | \(-0.401958\pi\) | ||||
0.303161 | + | 0.952939i | \(0.401958\pi\) | |||||||
\(542\) | −16.3984 | −0.704371 | ||||||||
\(543\) | −4.84233 | −0.207804 | ||||||||
\(544\) | 9.96256 | 0.427141 | ||||||||
\(545\) | −0.128026 | −0.00548403 | ||||||||
\(546\) | −24.2561 | −1.03806 | ||||||||
\(547\) | 15.9165 | 0.680541 | 0.340270 | − | 0.940328i | \(-0.389481\pi\) | ||||
0.340270 | + | 0.940328i | \(0.389481\pi\) | |||||||
\(548\) | −4.71728 | −0.201512 | ||||||||
\(549\) | 0.938620 | 0.0400593 | ||||||||
\(550\) | −4.83719 | −0.206258 | ||||||||
\(551\) | 2.72640 | 0.116148 | ||||||||
\(552\) | −10.1844 | −0.433475 | ||||||||
\(553\) | 26.4584 | 1.12513 | ||||||||
\(554\) | 9.56452 | 0.406358 | ||||||||
\(555\) | 0.0263562 | 0.00111876 | ||||||||
\(556\) | −7.74188 | −0.328329 | ||||||||
\(557\) | 19.8147 | 0.839574 | 0.419787 | − | 0.907623i | \(-0.362105\pi\) | ||||
0.419787 | + | 0.907623i | \(0.362105\pi\) | |||||||
\(558\) | 10.9609 | 0.464012 | ||||||||
\(559\) | 6.49275 | 0.274614 | ||||||||
\(560\) | −18.2852 | −0.772691 | ||||||||
\(561\) | −9.01924 | −0.380792 | ||||||||
\(562\) | 0.622334 | 0.0262516 | ||||||||
\(563\) | −36.3627 | −1.53250 | −0.766252 | − | 0.642540i | \(-0.777881\pi\) | ||||
−0.766252 | + | 0.642540i | \(0.777881\pi\) | |||||||
\(564\) | −4.57197 | −0.192515 | ||||||||
\(565\) | 14.4464 | 0.607764 | ||||||||
\(566\) | 5.01507 | 0.210799 | ||||||||
\(567\) | −35.3555 | −1.48479 | ||||||||
\(568\) | 15.8289 | 0.664165 | ||||||||
\(569\) | −23.0447 | −0.966085 | −0.483043 | − | 0.875597i | \(-0.660468\pi\) | ||||
−0.483043 | + | 0.875597i | \(0.660468\pi\) | |||||||
\(570\) | −2.00940 | −0.0841647 | ||||||||
\(571\) | −32.5529 | −1.36229 | −0.681147 | − | 0.732146i | \(-0.738519\pi\) | ||||
−0.681147 | + | 0.732146i | \(0.738519\pi\) | |||||||
\(572\) | −0.833220 | −0.0348387 | ||||||||
\(573\) | 40.0130 | 1.67157 | ||||||||
\(574\) | −35.6117 | −1.48640 | ||||||||
\(575\) | 6.62236 | 0.276171 | ||||||||
\(576\) | 8.44525 | 0.351886 | ||||||||
\(577\) | 23.8906 | 0.994579 | 0.497289 | − | 0.867585i | \(-0.334329\pi\) | ||||
0.497289 | + | 0.867585i | \(0.334329\pi\) | |||||||
\(578\) | −7.46451 | −0.310483 | ||||||||
\(579\) | −38.6261 | −1.60524 | ||||||||
\(580\) | 2.66543 | 0.110676 | ||||||||
\(581\) | −8.66570 | −0.359514 | ||||||||
\(582\) | −45.5690 | −1.88890 | ||||||||
\(583\) | 3.14108 | 0.130090 | ||||||||
\(584\) | −15.6777 | −0.648749 | ||||||||
\(585\) | 4.25237 | 0.175814 | ||||||||
\(586\) | −8.61524 | −0.355892 | ||||||||
\(587\) | −13.1090 | −0.541066 | −0.270533 | − | 0.962711i | \(-0.587200\pi\) | ||||
−0.270533 | + | 0.962711i | \(0.587200\pi\) | |||||||
\(588\) | 2.31806 | 0.0955950 | ||||||||
\(589\) | −2.45883 | −0.101314 | ||||||||
\(590\) | −3.01272 | −0.124032 | ||||||||
\(591\) | −30.8042 | −1.26711 | ||||||||
\(592\) | −0.0459697 | −0.00188934 | ||||||||
\(593\) | −0.00581924 | −0.000238967 0 | −0.000119484 | − | 1.00000i | \(-0.500038\pi\) | ||||
−0.000119484 | 1.00000i | \(0.500038\pi\) | ||||||||
\(594\) | −4.70496 | −0.193047 | ||||||||
\(595\) | 18.5036 | 0.758573 | ||||||||
\(596\) | −1.11221 | −0.0455578 | ||||||||
\(597\) | −23.8248 | −0.975083 | ||||||||
\(598\) | 7.11626 | 0.291005 | ||||||||
\(599\) | −36.4163 | −1.48793 | −0.743965 | − | 0.668219i | \(-0.767057\pi\) | ||||
−0.743965 | + | 0.668219i | \(0.767057\pi\) | |||||||
\(600\) | −17.9274 | −0.731885 | ||||||||
\(601\) | −15.5649 | −0.634907 | −0.317454 | − | 0.948274i | \(-0.602828\pi\) | ||||
−0.317454 | + | 0.948274i | \(0.602828\pi\) | |||||||
\(602\) | −13.2539 | −0.540189 | ||||||||
\(603\) | −8.89138 | −0.362085 | ||||||||
\(604\) | −2.22286 | −0.0904469 | ||||||||
\(605\) | −12.7906 | −0.520012 | ||||||||
\(606\) | 24.5056 | 0.995471 | ||||||||
\(607\) | −33.2538 | −1.34973 | −0.674865 | − | 0.737941i | \(-0.735798\pi\) | ||||
−0.674865 | + | 0.737941i | \(0.735798\pi\) | |||||||
\(608\) | 1.04844 | 0.0425199 | ||||||||
\(609\) | 36.6526 | 1.48524 | ||||||||
\(610\) | −1.28417 | −0.0519946 | ||||||||
\(611\) | −13.5401 | −0.547774 | ||||||||
\(612\) | 2.53430 | 0.102443 | ||||||||
\(613\) | 14.6747 | 0.592705 | 0.296353 | − | 0.955079i | \(-0.404230\pi\) | ||||
0.296353 | + | 0.955079i | \(0.404230\pi\) | |||||||
\(614\) | −16.7477 | −0.675881 | ||||||||
\(615\) | 19.4285 | 0.783433 | ||||||||
\(616\) | −7.20901 | −0.290459 | ||||||||
\(617\) | −2.79841 | −0.112660 | −0.0563298 | − | 0.998412i | \(-0.517940\pi\) | ||||
−0.0563298 | + | 0.998412i | \(0.517940\pi\) | |||||||
\(618\) | 29.4305 | 1.18387 | ||||||||
\(619\) | −25.0599 | −1.00724 | −0.503622 | − | 0.863924i | \(-0.668000\pi\) | ||||
−0.503622 | + | 0.863924i | \(0.668000\pi\) | |||||||
\(620\) | −2.40385 | −0.0965410 | ||||||||
\(621\) | 6.44134 | 0.258482 | ||||||||
\(622\) | 32.9665 | 1.32183 | ||||||||
\(623\) | 40.4336 | 1.61994 | ||||||||
\(624\) | −23.0811 | −0.923985 | ||||||||
\(625\) | 3.72867 | 0.149147 | ||||||||
\(626\) | −13.1672 | −0.526269 | ||||||||
\(627\) | −0.949168 | −0.0379061 | ||||||||
\(628\) | 2.61891 | 0.104506 | ||||||||
\(629\) | 0.0465187 | 0.00185482 | ||||||||
\(630\) | −8.68054 | −0.345841 | ||||||||
\(631\) | 5.16456 | 0.205598 | 0.102799 | − | 0.994702i | \(-0.467220\pi\) | ||||
0.102799 | + | 0.994702i | \(0.467220\pi\) | |||||||
\(632\) | 21.0136 | 0.835876 | ||||||||
\(633\) | −50.6869 | −2.01462 | ||||||||
\(634\) | 11.2489 | 0.446753 | ||||||||
\(635\) | 5.19308 | 0.206081 | ||||||||
\(636\) | −2.74665 | −0.108912 | ||||||||
\(637\) | 6.86504 | 0.272003 | ||||||||
\(638\) | 7.85446 | 0.310961 | ||||||||
\(639\) | 9.00320 | 0.356161 | ||||||||
\(640\) | −16.9237 | −0.668969 | ||||||||
\(641\) | 7.13556 | 0.281838 | 0.140919 | − | 0.990021i | \(-0.454994\pi\) | ||||
0.140919 | + | 0.990021i | \(0.454994\pi\) | |||||||
\(642\) | −58.7121 | −2.31718 | ||||||||
\(643\) | −33.7559 | −1.33120 | −0.665601 | − | 0.746307i | \(-0.731825\pi\) | ||||
−0.665601 | + | 0.746307i | \(0.731825\pi\) | |||||||
\(644\) | −2.32860 | −0.0917596 | ||||||||
\(645\) | 7.23088 | 0.284716 | ||||||||
\(646\) | −3.54660 | −0.139539 | ||||||||
\(647\) | 5.75214 | 0.226140 | 0.113070 | − | 0.993587i | \(-0.463932\pi\) | ||||
0.113070 | + | 0.993587i | \(0.463932\pi\) | |||||||
\(648\) | −28.0798 | −1.10308 | ||||||||
\(649\) | −1.42310 | −0.0558615 | ||||||||
\(650\) | 12.5267 | 0.491337 | ||||||||
\(651\) | −33.0556 | −1.29555 | ||||||||
\(652\) | −3.67925 | −0.144091 | ||||||||
\(653\) | −48.0198 | −1.87916 | −0.939581 | − | 0.342327i | \(-0.888785\pi\) | ||||
−0.939581 | + | 0.342327i | \(0.888785\pi\) | |||||||
\(654\) | 0.329891 | 0.0128998 | ||||||||
\(655\) | 16.6920 | 0.652211 | ||||||||
\(656\) | −33.8867 | −1.32305 | ||||||||
\(657\) | −8.91723 | −0.347894 | ||||||||
\(658\) | 27.6400 | 1.07752 | ||||||||
\(659\) | −24.1192 | −0.939552 | −0.469776 | − | 0.882786i | \(-0.655665\pi\) | ||||
−0.469776 | + | 0.882786i | \(0.655665\pi\) | |||||||
\(660\) | −0.927945 | −0.0361202 | ||||||||
\(661\) | 45.0095 | 1.75067 | 0.875333 | − | 0.483520i | \(-0.160642\pi\) | ||||
0.875333 | + | 0.483520i | \(0.160642\pi\) | |||||||
\(662\) | −5.34842 | −0.207872 | ||||||||
\(663\) | 23.3568 | 0.907102 | ||||||||
\(664\) | −6.88241 | −0.267089 | ||||||||
\(665\) | 1.94728 | 0.0755124 | ||||||||
\(666\) | −0.0218232 | −0.000845633 0 | ||||||||
\(667\) | −10.7532 | −0.416364 | ||||||||
\(668\) | −2.43753 | −0.0943108 | ||||||||
\(669\) | −53.3977 | −2.06448 | ||||||||
\(670\) | 12.1647 | 0.469965 | ||||||||
\(671\) | −0.606596 | −0.0234174 | ||||||||
\(672\) | 14.0948 | 0.543720 | ||||||||
\(673\) | 50.0165 | 1.92799 | 0.963997 | − | 0.265915i | \(-0.0856740\pi\) | ||||
0.963997 | + | 0.265915i | \(0.0856740\pi\) | |||||||
\(674\) | −18.8825 | −0.727328 | ||||||||
\(675\) | 11.3386 | 0.436424 | ||||||||
\(676\) | −2.80560 | −0.107908 | ||||||||
\(677\) | 11.4711 | 0.440871 | 0.220436 | − | 0.975402i | \(-0.429252\pi\) | ||||
0.220436 | + | 0.975402i | \(0.429252\pi\) | |||||||
\(678\) | −37.2248 | −1.42961 | ||||||||
\(679\) | 44.1603 | 1.69472 | ||||||||
\(680\) | 14.6958 | 0.563557 | ||||||||
\(681\) | 7.48705 | 0.286905 | ||||||||
\(682\) | −7.08363 | −0.271246 | ||||||||
\(683\) | 11.1992 | 0.428525 | 0.214262 | − | 0.976776i | \(-0.431265\pi\) | ||||
0.214262 | + | 0.976776i | \(0.431265\pi\) | |||||||
\(684\) | 0.266705 | 0.0101977 | ||||||||
\(685\) | −15.5587 | −0.594468 | ||||||||
\(686\) | 19.9564 | 0.761938 | ||||||||
\(687\) | 4.14718 | 0.158225 | ||||||||
\(688\) | −12.6119 | −0.480824 | ||||||||
\(689\) | −8.13435 | −0.309894 | ||||||||
\(690\) | 7.92527 | 0.301710 | ||||||||
\(691\) | 8.42528 | 0.320513 | 0.160256 | − | 0.987075i | \(-0.448768\pi\) | ||||
0.160256 | + | 0.987075i | \(0.448768\pi\) | |||||||
\(692\) | −3.88872 | −0.147827 | ||||||||
\(693\) | −4.10037 | −0.155760 | ||||||||
\(694\) | −24.0658 | −0.913525 | ||||||||
\(695\) | −25.5345 | −0.968580 | ||||||||
\(696\) | 29.1100 | 1.10341 | ||||||||
\(697\) | 34.2914 | 1.29888 | ||||||||
\(698\) | −14.7423 | −0.558005 | ||||||||
\(699\) | −18.6101 | −0.703898 | ||||||||
\(700\) | −4.09901 | −0.154928 | ||||||||
\(701\) | 29.4021 | 1.11050 | 0.555250 | − | 0.831683i | \(-0.312622\pi\) | ||||
0.555250 | + | 0.831683i | \(0.312622\pi\) | |||||||
\(702\) | 12.1843 | 0.459866 | ||||||||
\(703\) | 0.00489555 | 0.000184639 0 | ||||||||
\(704\) | −5.45786 | −0.205701 | ||||||||
\(705\) | −15.0794 | −0.567924 | ||||||||
\(706\) | 14.0322 | 0.528107 | ||||||||
\(707\) | −23.7480 | −0.893135 | ||||||||
\(708\) | 1.24440 | 0.0467674 | ||||||||
\(709\) | −26.8200 | −1.00725 | −0.503624 | − | 0.863923i | \(-0.668000\pi\) | ||||
−0.503624 | + | 0.863923i | \(0.668000\pi\) | |||||||
\(710\) | −12.3177 | −0.462276 | ||||||||
\(711\) | 11.9522 | 0.448242 | ||||||||
\(712\) | 32.1129 | 1.20348 | ||||||||
\(713\) | 9.69785 | 0.363188 | ||||||||
\(714\) | −47.6792 | −1.78435 | ||||||||
\(715\) | −2.74815 | −0.102775 | ||||||||
\(716\) | −2.40578 | −0.0899080 | ||||||||
\(717\) | −16.8401 | −0.628905 | ||||||||
\(718\) | −26.5594 | −0.991188 | ||||||||
\(719\) | 35.9642 | 1.34124 | 0.670620 | − | 0.741801i | \(-0.266028\pi\) | ||||
0.670620 | + | 0.741801i | \(0.266028\pi\) | |||||||
\(720\) | −8.26006 | −0.307834 | ||||||||
\(721\) | −28.5206 | −1.06216 | ||||||||
\(722\) | 28.9496 | 1.07739 | ||||||||
\(723\) | −21.3598 | −0.794378 | ||||||||
\(724\) | −0.879330 | −0.0326801 | ||||||||
\(725\) | −18.9287 | −0.702994 | ||||||||
\(726\) | 32.9582 | 1.22319 | ||||||||
\(727\) | −1.77216 | −0.0657256 | −0.0328628 | − | 0.999460i | \(-0.510462\pi\) | ||||
−0.0328628 | + | 0.999460i | \(0.510462\pi\) | |||||||
\(728\) | 18.6689 | 0.691916 | ||||||||
\(729\) | 4.97548 | 0.184277 | ||||||||
\(730\) | 12.2001 | 0.451546 | ||||||||
\(731\) | 12.7625 | 0.472039 | ||||||||
\(732\) | 0.530425 | 0.0196051 | ||||||||
\(733\) | 42.9239 | 1.58543 | 0.792715 | − | 0.609592i | \(-0.208667\pi\) | ||||
0.792715 | + | 0.609592i | \(0.208667\pi\) | |||||||
\(734\) | −12.6234 | −0.465940 | ||||||||
\(735\) | 7.64549 | 0.282008 | ||||||||
\(736\) | −4.13515 | −0.152424 | ||||||||
\(737\) | 5.74618 | 0.211663 | ||||||||
\(738\) | −16.0870 | −0.592172 | ||||||||
\(739\) | −40.1728 | −1.47778 | −0.738891 | − | 0.673825i | \(-0.764650\pi\) | ||||
−0.738891 | + | 0.673825i | \(0.764650\pi\) | |||||||
\(740\) | 0.00478608 | 0.000175940 0 | ||||||||
\(741\) | 2.45803 | 0.0902978 | ||||||||
\(742\) | 16.6050 | 0.609588 | ||||||||
\(743\) | −37.6445 | −1.38104 | −0.690521 | − | 0.723313i | \(-0.742619\pi\) | ||||
−0.690521 | + | 0.723313i | \(0.742619\pi\) | |||||||
\(744\) | −26.2531 | −0.962487 | ||||||||
\(745\) | −3.66832 | −0.134397 | ||||||||
\(746\) | −5.64440 | −0.206656 | ||||||||
\(747\) | −3.91460 | −0.143228 | ||||||||
\(748\) | −1.63783 | −0.0598848 | ||||||||
\(749\) | 56.8970 | 2.07897 | ||||||||
\(750\) | 34.3809 | 1.25541 | ||||||||
\(751\) | 10.5774 | 0.385973 | 0.192987 | − | 0.981201i | \(-0.438183\pi\) | ||||
0.192987 | + | 0.981201i | \(0.438183\pi\) | |||||||
\(752\) | 26.3011 | 0.959103 | ||||||||
\(753\) | −20.2883 | −0.739346 | ||||||||
\(754\) | −20.3404 | −0.740754 | ||||||||
\(755\) | −7.33152 | −0.266821 | ||||||||
\(756\) | −3.98697 | −0.145005 | ||||||||
\(757\) | 6.11713 | 0.222331 | 0.111165 | − | 0.993802i | \(-0.464542\pi\) | ||||
0.111165 | + | 0.993802i | \(0.464542\pi\) | |||||||
\(758\) | 21.0492 | 0.764541 | ||||||||
\(759\) | 3.74361 | 0.135884 | ||||||||
\(760\) | 1.54656 | 0.0560995 | ||||||||
\(761\) | −42.3024 | −1.53346 | −0.766730 | − | 0.641969i | \(-0.778118\pi\) | ||||
−0.766730 | + | 0.641969i | \(0.778118\pi\) | |||||||
\(762\) | −13.3813 | −0.484753 | ||||||||
\(763\) | −0.319692 | −0.0115736 | ||||||||
\(764\) | 7.26606 | 0.262877 | ||||||||
\(765\) | 8.35871 | 0.302210 | ||||||||
\(766\) | 50.2259 | 1.81474 | ||||||||
\(767\) | 3.68535 | 0.133070 | ||||||||
\(768\) | 18.6080 | 0.671458 | ||||||||
\(769\) | 9.78310 | 0.352787 | 0.176394 | − | 0.984320i | \(-0.443557\pi\) | ||||
0.176394 | + | 0.984320i | \(0.443557\pi\) | |||||||
\(770\) | 5.60992 | 0.202167 | ||||||||
\(771\) | 40.6819 | 1.46512 | ||||||||
\(772\) | −7.01420 | −0.252447 | ||||||||
\(773\) | 50.6466 | 1.82163 | 0.910815 | − | 0.412815i | \(-0.135454\pi\) | ||||
0.910815 | + | 0.412815i | \(0.135454\pi\) | |||||||
\(774\) | −5.98725 | −0.215207 | ||||||||
\(775\) | 17.0711 | 0.613210 | ||||||||
\(776\) | 35.0726 | 1.25903 | ||||||||
\(777\) | 0.0658138 | 0.00236106 | ||||||||
\(778\) | −8.64353 | −0.309886 | ||||||||
\(779\) | 3.60876 | 0.129297 | ||||||||
\(780\) | 2.40307 | 0.0860435 | ||||||||
\(781\) | −5.81844 | −0.208200 | ||||||||
\(782\) | 13.9881 | 0.500215 | ||||||||
\(783\) | −18.4113 | −0.657965 | ||||||||
\(784\) | −13.3351 | −0.476252 | ||||||||
\(785\) | 8.63778 | 0.308296 | ||||||||
\(786\) | −43.0112 | −1.53416 | ||||||||
\(787\) | 1.00000 | 0.0356462 | ||||||||
\(788\) | −5.59380 | −0.199271 | ||||||||
\(789\) | −7.44156 | −0.264927 | ||||||||
\(790\) | −16.3524 | −0.581792 | ||||||||
\(791\) | 36.0740 | 1.28264 | ||||||||
\(792\) | −3.25656 | −0.115717 | ||||||||
\(793\) | 1.57088 | 0.0557836 | ||||||||
\(794\) | −19.7805 | −0.701983 | ||||||||
\(795\) | −9.05910 | −0.321293 | ||||||||
\(796\) | −4.32640 | −0.153345 | ||||||||
\(797\) | 18.1740 | 0.643755 | 0.321877 | − | 0.946781i | \(-0.395686\pi\) | ||||
0.321877 | + | 0.946781i | \(0.395686\pi\) | |||||||
\(798\) | −5.01767 | −0.177624 | ||||||||
\(799\) | −26.6152 | −0.941579 | ||||||||
\(800\) | −7.27908 | −0.257354 | ||||||||
\(801\) | 18.2653 | 0.645372 | ||||||||
\(802\) | −61.2600 | −2.16317 | ||||||||
\(803\) | 5.76288 | 0.203368 | ||||||||
\(804\) | −5.02462 | −0.177205 | ||||||||
\(805\) | −7.68026 | −0.270694 | ||||||||
\(806\) | 18.3442 | 0.646148 | ||||||||
\(807\) | 44.7142 | 1.57401 | ||||||||
\(808\) | −18.8610 | −0.663526 | ||||||||
\(809\) | 19.5962 | 0.688966 | 0.344483 | − | 0.938793i | \(-0.388054\pi\) | ||||
0.344483 | + | 0.938793i | \(0.388054\pi\) | |||||||
\(810\) | 21.8512 | 0.767771 | ||||||||
\(811\) | 47.5922 | 1.67119 | 0.835594 | − | 0.549348i | \(-0.185124\pi\) | ||||
0.835594 | + | 0.549348i | \(0.185124\pi\) | |||||||
\(812\) | 6.65584 | 0.233574 | ||||||||
\(813\) | 22.3400 | 0.783498 | ||||||||
\(814\) | 0.0141036 | 0.000494330 0 | ||||||||
\(815\) | −12.1350 | −0.425072 | ||||||||
\(816\) | −45.3696 | −1.58825 | ||||||||
\(817\) | 1.34311 | 0.0469893 | ||||||||
\(818\) | 14.0587 | 0.491552 | ||||||||
\(819\) | 10.6186 | 0.371043 | ||||||||
\(820\) | 3.52807 | 0.123206 | ||||||||
\(821\) | −53.1186 | −1.85385 | −0.926927 | − | 0.375243i | \(-0.877559\pi\) | ||||
−0.926927 | + | 0.375243i | \(0.877559\pi\) | |||||||
\(822\) | 40.0909 | 1.39833 | ||||||||
\(823\) | −25.6754 | −0.894989 | −0.447494 | − | 0.894287i | \(-0.647684\pi\) | ||||
−0.447494 | + | 0.894287i | \(0.647684\pi\) | |||||||
\(824\) | −22.6515 | −0.789101 | ||||||||
\(825\) | 6.58984 | 0.229429 | ||||||||
\(826\) | −7.52305 | −0.261760 | ||||||||
\(827\) | −11.0337 | −0.383680 | −0.191840 | − | 0.981426i | \(-0.561446\pi\) | ||||
−0.191840 | + | 0.981426i | \(0.561446\pi\) | |||||||
\(828\) | −1.05191 | −0.0365564 | ||||||||
\(829\) | 33.3089 | 1.15687 | 0.578433 | − | 0.815730i | \(-0.303664\pi\) | ||||
0.578433 | + | 0.815730i | \(0.303664\pi\) | |||||||
\(830\) | 5.35576 | 0.185901 | ||||||||
\(831\) | −13.0300 | −0.452006 | ||||||||
\(832\) | 14.1340 | 0.490009 | ||||||||
\(833\) | 13.4943 | 0.467550 | ||||||||
\(834\) | 65.7962 | 2.27834 | ||||||||
\(835\) | −8.03954 | −0.278220 | ||||||||
\(836\) | −0.172362 | −0.00596126 | ||||||||
\(837\) | 16.6044 | 0.573933 | ||||||||
\(838\) | 2.50782 | 0.0866312 | ||||||||
\(839\) | 30.7148 | 1.06039 | 0.530197 | − | 0.847875i | \(-0.322118\pi\) | ||||
0.530197 | + | 0.847875i | \(0.322118\pi\) | |||||||
\(840\) | 20.7913 | 0.717368 | ||||||||
\(841\) | 1.73576 | 0.0598539 | ||||||||
\(842\) | −22.3667 | −0.770806 | ||||||||
\(843\) | −0.847823 | −0.0292006 | ||||||||
\(844\) | −9.20437 | −0.316827 | ||||||||
\(845\) | −9.25352 | −0.318331 | ||||||||
\(846\) | 12.4859 | 0.429276 | ||||||||
\(847\) | −31.9393 | −1.09745 | ||||||||
\(848\) | 15.8006 | 0.542596 | ||||||||
\(849\) | −6.83218 | −0.234480 | ||||||||
\(850\) | 24.6232 | 0.844569 | ||||||||
\(851\) | −0.0193085 | −0.000661886 0 | ||||||||
\(852\) | 5.08781 | 0.174306 | ||||||||
\(853\) | 32.9507 | 1.12821 | 0.564104 | − | 0.825703i | \(-0.309222\pi\) | ||||
0.564104 | + | 0.825703i | \(0.309222\pi\) | |||||||
\(854\) | −3.20670 | −0.109731 | ||||||||
\(855\) | 0.879656 | 0.0300836 | ||||||||
\(856\) | 45.1883 | 1.54451 | ||||||||
\(857\) | −27.1765 | −0.928332 | −0.464166 | − | 0.885748i | \(-0.653646\pi\) | ||||
−0.464166 | + | 0.885748i | \(0.653646\pi\) | |||||||
\(858\) | 7.08132 | 0.241752 | ||||||||
\(859\) | 14.7938 | 0.504757 | 0.252379 | − | 0.967629i | \(-0.418787\pi\) | ||||
0.252379 | + | 0.967629i | \(0.418787\pi\) | |||||||
\(860\) | 1.31307 | 0.0447754 | ||||||||
\(861\) | 48.5148 | 1.65338 | ||||||||
\(862\) | 21.7523 | 0.740886 | ||||||||
\(863\) | −37.2987 | −1.26966 | −0.634832 | − | 0.772650i | \(-0.718931\pi\) | ||||
−0.634832 | + | 0.772650i | \(0.718931\pi\) | |||||||
\(864\) | −7.08010 | −0.240870 | ||||||||
\(865\) | −12.8259 | −0.436094 | ||||||||
\(866\) | 23.8698 | 0.811128 | ||||||||
\(867\) | 10.1691 | 0.345361 | ||||||||
\(868\) | −6.00264 | −0.203743 | ||||||||
\(869\) | −7.72427 | −0.262028 | ||||||||
\(870\) | −22.6528 | −0.768003 | ||||||||
\(871\) | −14.8807 | −0.504212 | ||||||||
\(872\) | −0.253904 | −0.00859827 | ||||||||
\(873\) | 19.9487 | 0.675162 | ||||||||
\(874\) | 1.47209 | 0.0497941 | ||||||||
\(875\) | −33.3180 | −1.12635 | ||||||||
\(876\) | −5.03923 | −0.170260 | ||||||||
\(877\) | −39.6680 | −1.33949 | −0.669747 | − | 0.742589i | \(-0.733597\pi\) | ||||
−0.669747 | + | 0.742589i | \(0.733597\pi\) | |||||||
\(878\) | −31.3830 | −1.05912 | ||||||||
\(879\) | 11.7368 | 0.395872 | ||||||||
\(880\) | 5.33818 | 0.179950 | ||||||||
\(881\) | 41.7817 | 1.40766 | 0.703830 | − | 0.710369i | \(-0.251472\pi\) | ||||
0.703830 | + | 0.710369i | \(0.251472\pi\) | |||||||
\(882\) | −6.33056 | −0.213161 | ||||||||
\(883\) | −37.7142 | −1.26918 | −0.634592 | − | 0.772847i | \(-0.718832\pi\) | ||||
−0.634592 | + | 0.772847i | \(0.718832\pi\) | |||||||
\(884\) | 4.24142 | 0.142654 | ||||||||
\(885\) | 4.10432 | 0.137965 | ||||||||
\(886\) | 55.6381 | 1.86920 | ||||||||
\(887\) | 25.7369 | 0.864162 | 0.432081 | − | 0.901835i | \(-0.357779\pi\) | ||||
0.432081 | + | 0.901835i | \(0.357779\pi\) | |||||||
\(888\) | 0.0522702 | 0.00175407 | ||||||||
\(889\) | 12.9676 | 0.434919 | ||||||||
\(890\) | −24.9897 | −0.837655 | ||||||||
\(891\) | 10.3217 | 0.345789 | ||||||||
\(892\) | −9.69663 | −0.324667 | ||||||||
\(893\) | −2.80094 | −0.0937298 | ||||||||
\(894\) | 9.45236 | 0.316134 | ||||||||
\(895\) | −7.93481 | −0.265231 | ||||||||
\(896\) | −42.2601 | −1.41181 | ||||||||
\(897\) | −9.69468 | −0.323696 | ||||||||
\(898\) | 35.2774 | 1.17722 | ||||||||
\(899\) | −27.7194 | −0.924494 | ||||||||
\(900\) | −1.85167 | −0.0617223 | ||||||||
\(901\) | −15.9893 | −0.532682 | ||||||||
\(902\) | 10.3965 | 0.346165 | ||||||||
\(903\) | 18.0562 | 0.600872 | ||||||||
\(904\) | 28.6504 | 0.952899 | ||||||||
\(905\) | −2.90024 | −0.0964072 | ||||||||
\(906\) | 18.8915 | 0.627628 | ||||||||
\(907\) | −52.6909 | −1.74957 | −0.874787 | − | 0.484508i | \(-0.838999\pi\) | ||||
−0.874787 | + | 0.484508i | \(0.838999\pi\) | |||||||
\(908\) | 1.35959 | 0.0451197 | ||||||||
\(909\) | −10.7278 | −0.355819 | ||||||||
\(910\) | −14.5278 | −0.481592 | ||||||||
\(911\) | 0.00578822 | 0.000191772 0 | 9.58861e−5 | − | 1.00000i | \(-0.499969\pi\) | ||||
9.58861e−5 | 1.00000i | \(0.499969\pi\) | ||||||||
\(912\) | −4.77462 | −0.158103 | ||||||||
\(913\) | 2.52987 | 0.0837263 | ||||||||
\(914\) | −43.1106 | −1.42597 | ||||||||
\(915\) | 1.74947 | 0.0578356 | ||||||||
\(916\) | 0.753098 | 0.0248830 | ||||||||
\(917\) | 41.6815 | 1.37645 | ||||||||
\(918\) | 23.9501 | 0.790472 | ||||||||
\(919\) | 51.0704 | 1.68466 | 0.842328 | − | 0.538965i | \(-0.181184\pi\) | ||||
0.842328 | + | 0.538965i | \(0.181184\pi\) | |||||||
\(920\) | −6.09976 | −0.201103 | ||||||||
\(921\) | 22.8158 | 0.751807 | ||||||||
\(922\) | −32.5740 | −1.07277 | ||||||||
\(923\) | 15.0678 | 0.495963 | ||||||||
\(924\) | −2.31717 | −0.0762291 | ||||||||
\(925\) | −0.0339886 | −0.00111754 | ||||||||
\(926\) | −43.3262 | −1.42379 | ||||||||
\(927\) | −12.8838 | −0.423158 | ||||||||
\(928\) | 11.8195 | 0.387994 | ||||||||
\(929\) | −1.83007 | −0.0600426 | −0.0300213 | − | 0.999549i | \(-0.509558\pi\) | ||||
−0.0300213 | + | 0.999549i | \(0.509558\pi\) | |||||||
\(930\) | 20.4297 | 0.669916 | ||||||||
\(931\) | 1.42012 | 0.0465425 | ||||||||
\(932\) | −3.37945 | −0.110698 | ||||||||
\(933\) | −44.9112 | −1.47033 | ||||||||
\(934\) | 7.58523 | 0.248196 | ||||||||
\(935\) | −5.40193 | −0.176662 | ||||||||
\(936\) | 8.43341 | 0.275655 | ||||||||
\(937\) | −0.504327 | −0.0164757 | −0.00823783 | − | 0.999966i | \(-0.502622\pi\) | ||||
−0.00823783 | + | 0.999966i | \(0.502622\pi\) | |||||||
\(938\) | 30.3765 | 0.991828 | ||||||||
\(939\) | 17.9381 | 0.585388 | ||||||||
\(940\) | −2.73831 | −0.0893138 | ||||||||
\(941\) | 34.3603 | 1.12011 | 0.560056 | − | 0.828455i | \(-0.310780\pi\) | ||||
0.560056 | + | 0.828455i | \(0.310780\pi\) | |||||||
\(942\) | −22.2574 | −0.725187 | ||||||||
\(943\) | −14.2333 | −0.463500 | ||||||||
\(944\) | −7.15864 | −0.232994 | ||||||||
\(945\) | −13.1500 | −0.427768 | ||||||||
\(946\) | 3.86935 | 0.125803 | ||||||||
\(947\) | 24.7169 | 0.803192 | 0.401596 | − | 0.915817i | \(-0.368456\pi\) | ||||
0.401596 | + | 0.915817i | \(0.368456\pi\) | |||||||
\(948\) | 6.75432 | 0.219370 | ||||||||
\(949\) | −14.9239 | −0.484451 | ||||||||
\(950\) | 2.59130 | 0.0840729 | ||||||||
\(951\) | −15.3248 | −0.496939 | ||||||||
\(952\) | 36.6967 | 1.18935 | ||||||||
\(953\) | 13.2820 | 0.430245 | 0.215122 | − | 0.976587i | \(-0.430985\pi\) | ||||
0.215122 | + | 0.976587i | \(0.430985\pi\) | |||||||
\(954\) | 7.50105 | 0.242855 | ||||||||
\(955\) | 23.9652 | 0.775495 | ||||||||
\(956\) | −3.05804 | −0.0989039 | ||||||||
\(957\) | −10.7004 | −0.345893 | ||||||||
\(958\) | −48.7203 | −1.57408 | ||||||||
\(959\) | −38.8515 | −1.25458 | ||||||||
\(960\) | 15.7409 | 0.508034 | ||||||||
\(961\) | −6.00095 | −0.193579 | ||||||||
\(962\) | −0.0365235 | −0.00117756 | ||||||||
\(963\) | 25.7024 | 0.828247 | ||||||||
\(964\) | −3.87877 | −0.124927 | ||||||||
\(965\) | −23.1345 | −0.744725 | ||||||||
\(966\) | 19.7901 | 0.636737 | ||||||||
\(967\) | −1.03353 | −0.0332361 | −0.0166181 | − | 0.999862i | \(-0.505290\pi\) | ||||
−0.0166181 | + | 0.999862i | \(0.505290\pi\) | |||||||
\(968\) | −25.3666 | −0.815314 | ||||||||
\(969\) | 4.83164 | 0.155215 | ||||||||
\(970\) | −27.2929 | −0.876321 | ||||||||
\(971\) | −61.0345 | −1.95869 | −0.979344 | − | 0.202199i | \(-0.935191\pi\) | ||||
−0.979344 | + | 0.202199i | \(0.935191\pi\) | |||||||
\(972\) | −5.22179 | −0.167489 | ||||||||
\(973\) | −63.7621 | −2.04412 | ||||||||
\(974\) | −40.7292 | −1.30505 | ||||||||
\(975\) | −17.0655 | −0.546532 | ||||||||
\(976\) | −3.05137 | −0.0976720 | ||||||||
\(977\) | 4.88191 | 0.156186 | 0.0780931 | − | 0.996946i | \(-0.475117\pi\) | ||||
0.0780931 | + | 0.996946i | \(0.475117\pi\) | |||||||
\(978\) | 31.2690 | 0.999873 | ||||||||
\(979\) | −11.8042 | −0.377264 | ||||||||
\(980\) | 1.38836 | 0.0443497 | ||||||||
\(981\) | −0.144416 | −0.00461086 | ||||||||
\(982\) | −52.3678 | −1.67112 | ||||||||
\(983\) | −18.3456 | −0.585133 | −0.292567 | − | 0.956245i | \(-0.594509\pi\) | ||||
−0.292567 | + | 0.956245i | \(0.594509\pi\) | |||||||
\(984\) | 38.5311 | 1.22833 | ||||||||
\(985\) | −18.4497 | −0.587856 | ||||||||
\(986\) | −39.9823 | −1.27330 | ||||||||
\(987\) | −37.6547 | −1.19856 | ||||||||
\(988\) | 0.446359 | 0.0142006 | ||||||||
\(989\) | −5.29733 | −0.168445 | ||||||||
\(990\) | 2.53420 | 0.0805421 | ||||||||
\(991\) | −34.0250 | −1.08084 | −0.540420 | − | 0.841396i | \(-0.681735\pi\) | ||||
−0.540420 | + | 0.841396i | \(0.681735\pi\) | |||||||
\(992\) | −10.6596 | −0.338441 | ||||||||
\(993\) | 7.28631 | 0.231224 | ||||||||
\(994\) | −30.7585 | −0.975601 | ||||||||
\(995\) | −14.2695 | −0.452373 | ||||||||
\(996\) | −2.21219 | −0.0700958 | ||||||||
\(997\) | 2.02210 | 0.0640406 | 0.0320203 | − | 0.999487i | \(-0.489806\pi\) | ||||
0.0320203 | + | 0.999487i | \(0.489806\pi\) | |||||||
\(998\) | −6.82718 | −0.216111 | ||||||||
\(999\) | −0.0330595 | −0.00104596 |
(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 | 787.2.a.b.1.9 | ✓ | 37 | |
3.2 | odd | 2 | 7083.2.a.g.1.29 | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
787.2.a.b.1.9 | ✓ | 37 | 1.1 | even | 1 | trivial | |
7083.2.a.g.1.29 | 37 | 3.2 | odd | 2 |