Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.87945 | −1.32897 | −0.664485 | − | 0.747301i | \(-0.731349\pi\) | ||||
−0.664485 | + | 0.747301i | \(0.731349\pi\) | |||||||
\(3\) | −2.61165 | −1.50784 | −0.753920 | − | 0.656967i | \(-0.771839\pi\) | ||||
−0.753920 | + | 0.656967i | \(0.771839\pi\) | |||||||
\(4\) | 1.53233 | 0.766163 | ||||||||
\(5\) | −1.23543 | −0.552503 | −0.276252 | − | 0.961085i | \(-0.589092\pi\) | ||||
−0.276252 | + | 0.961085i | \(0.589092\pi\) | |||||||
\(6\) | 4.90847 | 2.00387 | ||||||||
\(7\) | −3.71692 | −1.40486 | −0.702432 | − | 0.711751i | \(-0.747902\pi\) | ||||
−0.702432 | + | 0.711751i | \(0.747902\pi\) | |||||||
\(8\) | 0.878969 | 0.310762 | ||||||||
\(9\) | 3.82074 | 1.27358 | ||||||||
\(10\) | 2.32194 | 0.734260 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −4.00191 | −1.15525 | ||||||||
\(13\) | −4.16760 | −1.15589 | −0.577943 | − | 0.816077i | \(-0.696144\pi\) | ||||
−0.577943 | + | 0.816077i | \(0.696144\pi\) | |||||||
\(14\) | 6.98576 | 1.86702 | ||||||||
\(15\) | 3.22653 | 0.833086 | ||||||||
\(16\) | −4.71663 | −1.17916 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −7.18088 | −1.69255 | ||||||||
\(19\) | −5.54379 | −1.27183 | −0.635916 | − | 0.771758i | \(-0.719378\pi\) | ||||
−0.635916 | + | 0.771758i | \(0.719378\pi\) | |||||||
\(20\) | −1.89309 | −0.423307 | ||||||||
\(21\) | 9.70731 | 2.11831 | ||||||||
\(22\) | 1.87945 | 0.400700 | ||||||||
\(23\) | −0.942351 | −0.196494 | −0.0982468 | − | 0.995162i | \(-0.531323\pi\) | ||||
−0.0982468 | + | 0.995162i | \(0.531323\pi\) | |||||||
\(24\) | −2.29556 | −0.468580 | ||||||||
\(25\) | −3.47370 | −0.694740 | ||||||||
\(26\) | 7.83280 | 1.53614 | ||||||||
\(27\) | −2.14348 | −0.412512 | ||||||||
\(28\) | −5.69553 | −1.07635 | ||||||||
\(29\) | −2.45710 | −0.456271 | −0.228136 | − | 0.973629i | \(-0.573263\pi\) | ||||
−0.228136 | + | 0.973629i | \(0.573263\pi\) | |||||||
\(30\) | −6.06409 | −1.10715 | ||||||||
\(31\) | −3.17078 | −0.569489 | −0.284745 | − | 0.958603i | \(-0.591909\pi\) | ||||
−0.284745 | + | 0.958603i | \(0.591909\pi\) | |||||||
\(32\) | 7.10672 | 1.25630 | ||||||||
\(33\) | 2.61165 | 0.454631 | ||||||||
\(34\) | −1.87945 | −0.322323 | ||||||||
\(35\) | 4.59201 | 0.776192 | ||||||||
\(36\) | 5.85461 | 0.975769 | ||||||||
\(37\) | 9.01121 | 1.48143 | 0.740717 | − | 0.671818i | \(-0.234486\pi\) | ||||
0.740717 | + | 0.671818i | \(0.234486\pi\) | |||||||
\(38\) | 10.4193 | 1.69023 | ||||||||
\(39\) | 10.8843 | 1.74289 | ||||||||
\(40\) | −1.08591 | −0.171697 | ||||||||
\(41\) | 1.96599 | 0.307036 | 0.153518 | − | 0.988146i | \(-0.450940\pi\) | ||||
0.153518 | + | 0.988146i | \(0.450940\pi\) | |||||||
\(42\) | −18.2444 | −2.81517 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −1.53233 | −0.231007 | ||||||||
\(45\) | −4.72027 | −0.703656 | ||||||||
\(46\) | 1.77110 | 0.261134 | ||||||||
\(47\) | −4.72284 | −0.688897 | −0.344448 | − | 0.938805i | \(-0.611934\pi\) | ||||
−0.344448 | + | 0.938805i | \(0.611934\pi\) | |||||||
\(48\) | 12.3182 | 1.77798 | ||||||||
\(49\) | 6.81550 | 0.973642 | ||||||||
\(50\) | 6.52864 | 0.923289 | ||||||||
\(51\) | −2.61165 | −0.365705 | ||||||||
\(52\) | −6.38613 | −0.885597 | ||||||||
\(53\) | −7.71299 | −1.05946 | −0.529730 | − | 0.848166i | \(-0.677707\pi\) | ||||
−0.529730 | + | 0.848166i | \(0.677707\pi\) | |||||||
\(54\) | 4.02855 | 0.548217 | ||||||||
\(55\) | 1.23543 | 0.166586 | ||||||||
\(56\) | −3.26706 | −0.436579 | ||||||||
\(57\) | 14.4785 | 1.91772 | ||||||||
\(58\) | 4.61799 | 0.606371 | ||||||||
\(59\) | 9.28151 | 1.20835 | 0.604175 | − | 0.796852i | \(-0.293503\pi\) | ||||
0.604175 | + | 0.796852i | \(0.293503\pi\) | |||||||
\(60\) | 4.94409 | 0.638280 | ||||||||
\(61\) | −14.6966 | −1.88171 | −0.940855 | − | 0.338809i | \(-0.889976\pi\) | ||||
−0.940855 | + | 0.338809i | \(0.889976\pi\) | |||||||
\(62\) | 5.95932 | 0.756834 | ||||||||
\(63\) | −14.2014 | −1.78920 | ||||||||
\(64\) | −3.92346 | −0.490432 | ||||||||
\(65\) | 5.14880 | 0.638630 | ||||||||
\(66\) | −4.90847 | −0.604191 | ||||||||
\(67\) | −10.9358 | −1.33602 | −0.668010 | − | 0.744152i | \(-0.732854\pi\) | ||||
−0.668010 | + | 0.744152i | \(0.732854\pi\) | |||||||
\(68\) | 1.53233 | 0.185822 | ||||||||
\(69\) | 2.46109 | 0.296281 | ||||||||
\(70\) | −8.63045 | −1.03154 | ||||||||
\(71\) | −1.56038 | −0.185184 | −0.0925918 | − | 0.995704i | \(-0.529515\pi\) | ||||
−0.0925918 | + | 0.995704i | \(0.529515\pi\) | |||||||
\(72\) | 3.35831 | 0.395780 | ||||||||
\(73\) | 0.378831 | 0.0443388 | 0.0221694 | − | 0.999754i | \(-0.492943\pi\) | ||||
0.0221694 | + | 0.999754i | \(0.492943\pi\) | |||||||
\(74\) | −16.9361 | −1.96878 | ||||||||
\(75\) | 9.07211 | 1.04756 | ||||||||
\(76\) | −8.49490 | −0.974431 | ||||||||
\(77\) | 3.71692 | 0.423582 | ||||||||
\(78\) | −20.4565 | −2.31625 | ||||||||
\(79\) | −4.75181 | −0.534620 | −0.267310 | − | 0.963611i | \(-0.586135\pi\) | ||||
−0.267310 | + | 0.963611i | \(0.586135\pi\) | |||||||
\(80\) | 5.82709 | 0.651488 | ||||||||
\(81\) | −5.86419 | −0.651576 | ||||||||
\(82\) | −3.69497 | −0.408042 | ||||||||
\(83\) | 17.6463 | 1.93693 | 0.968466 | − | 0.249147i | \(-0.0801501\pi\) | ||||
0.968466 | + | 0.249147i | \(0.0801501\pi\) | |||||||
\(84\) | 14.8748 | 1.62297 | ||||||||
\(85\) | −1.23543 | −0.134002 | ||||||||
\(86\) | −1.87945 | −0.202666 | ||||||||
\(87\) | 6.41709 | 0.687984 | ||||||||
\(88\) | −0.878969 | −0.0936984 | ||||||||
\(89\) | −1.26378 | −0.133960 | −0.0669802 | − | 0.997754i | \(-0.521336\pi\) | ||||
−0.0669802 | + | 0.997754i | \(0.521336\pi\) | |||||||
\(90\) | 8.87150 | 0.935138 | ||||||||
\(91\) | 15.4907 | 1.62386 | ||||||||
\(92\) | −1.44399 | −0.150546 | ||||||||
\(93\) | 8.28098 | 0.858698 | ||||||||
\(94\) | 8.87633 | 0.915524 | ||||||||
\(95\) | 6.84899 | 0.702692 | ||||||||
\(96\) | −18.5603 | −1.89430 | ||||||||
\(97\) | 4.07807 | 0.414065 | 0.207033 | − | 0.978334i | \(-0.433619\pi\) | ||||
0.207033 | + | 0.978334i | \(0.433619\pi\) | |||||||
\(98\) | −12.8094 | −1.29394 | ||||||||
\(99\) | −3.82074 | −0.383998 | ||||||||
\(100\) | −5.32284 | −0.532284 | ||||||||
\(101\) | −4.19158 | −0.417078 | −0.208539 | − | 0.978014i | \(-0.566871\pi\) | ||||
−0.208539 | + | 0.978014i | \(0.566871\pi\) | |||||||
\(102\) | 4.90847 | 0.486011 | ||||||||
\(103\) | 6.79926 | 0.669951 | 0.334975 | − | 0.942227i | \(-0.391272\pi\) | ||||
0.334975 | + | 0.942227i | \(0.391272\pi\) | |||||||
\(104\) | −3.66319 | −0.359206 | ||||||||
\(105\) | −11.9927 | −1.17037 | ||||||||
\(106\) | 14.4962 | 1.40799 | ||||||||
\(107\) | 5.08133 | 0.491230 | 0.245615 | − | 0.969367i | \(-0.421010\pi\) | ||||
0.245615 | + | 0.969367i | \(0.421010\pi\) | |||||||
\(108\) | −3.28451 | −0.316052 | ||||||||
\(109\) | −12.7028 | −1.21671 | −0.608353 | − | 0.793666i | \(-0.708170\pi\) | ||||
−0.608353 | + | 0.793666i | \(0.708170\pi\) | |||||||
\(110\) | −2.32194 | −0.221388 | ||||||||
\(111\) | −23.5342 | −2.23376 | ||||||||
\(112\) | 17.5313 | 1.65656 | ||||||||
\(113\) | −1.29250 | −0.121588 | −0.0607941 | − | 0.998150i | \(-0.519363\pi\) | ||||
−0.0607941 | + | 0.998150i | \(0.519363\pi\) | |||||||
\(114\) | −27.2115 | −2.54859 | ||||||||
\(115\) | 1.16421 | 0.108563 | ||||||||
\(116\) | −3.76507 | −0.349578 | ||||||||
\(117\) | −15.9233 | −1.47211 | ||||||||
\(118\) | −17.4441 | −1.60586 | ||||||||
\(119\) | −3.71692 | −0.340730 | ||||||||
\(120\) | 2.83602 | 0.258892 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 27.6216 | 2.50074 | ||||||||
\(123\) | −5.13448 | −0.462961 | ||||||||
\(124\) | −4.85867 | −0.436322 | ||||||||
\(125\) | 10.4687 | 0.936349 | ||||||||
\(126\) | 26.6907 | 2.37780 | ||||||||
\(127\) | −15.5239 | −1.37752 | −0.688762 | − | 0.724987i | \(-0.741846\pi\) | ||||
−0.688762 | + | 0.724987i | \(0.741846\pi\) | |||||||
\(128\) | −6.83951 | −0.604533 | ||||||||
\(129\) | −2.61165 | −0.229943 | ||||||||
\(130\) | −9.67691 | −0.848721 | ||||||||
\(131\) | −0.248366 | −0.0216999 | −0.0108499 | − | 0.999941i | \(-0.503454\pi\) | ||||
−0.0108499 | + | 0.999941i | \(0.503454\pi\) | |||||||
\(132\) | 4.00191 | 0.348321 | ||||||||
\(133\) | 20.6058 | 1.78675 | ||||||||
\(134\) | 20.5533 | 1.77553 | ||||||||
\(135\) | 2.64813 | 0.227914 | ||||||||
\(136\) | 0.878969 | 0.0753710 | ||||||||
\(137\) | 10.0029 | 0.854603 | 0.427302 | − | 0.904109i | \(-0.359464\pi\) | ||||
0.427302 | + | 0.904109i | \(0.359464\pi\) | |||||||
\(138\) | −4.62550 | −0.393749 | ||||||||
\(139\) | −20.1663 | −1.71048 | −0.855241 | − | 0.518231i | \(-0.826591\pi\) | ||||
−0.855241 | + | 0.518231i | \(0.826591\pi\) | |||||||
\(140\) | 7.03646 | 0.594689 | ||||||||
\(141\) | 12.3344 | 1.03875 | ||||||||
\(142\) | 2.93266 | 0.246104 | ||||||||
\(143\) | 4.16760 | 0.348513 | ||||||||
\(144\) | −18.0210 | −1.50175 | ||||||||
\(145\) | 3.03558 | 0.252091 | ||||||||
\(146\) | −0.711993 | −0.0589249 | ||||||||
\(147\) | −17.7997 | −1.46810 | ||||||||
\(148\) | 13.8081 | 1.13502 | ||||||||
\(149\) | 22.7000 | 1.85966 | 0.929830 | − | 0.367989i | \(-0.119954\pi\) | ||||
0.929830 | + | 0.367989i | \(0.119954\pi\) | |||||||
\(150\) | −17.0506 | −1.39217 | ||||||||
\(151\) | 15.4469 | 1.25705 | 0.628524 | − | 0.777790i | \(-0.283659\pi\) | ||||
0.628524 | + | 0.777790i | \(0.283659\pi\) | |||||||
\(152\) | −4.87282 | −0.395238 | ||||||||
\(153\) | 3.82074 | 0.308888 | ||||||||
\(154\) | −6.98576 | −0.562929 | ||||||||
\(155\) | 3.91729 | 0.314645 | ||||||||
\(156\) | 16.6784 | 1.33534 | ||||||||
\(157\) | 13.6005 | 1.08544 | 0.542719 | − | 0.839914i | \(-0.317395\pi\) | ||||
0.542719 | + | 0.839914i | \(0.317395\pi\) | |||||||
\(158\) | 8.93077 | 0.710494 | ||||||||
\(159\) | 20.1437 | 1.59750 | ||||||||
\(160\) | −8.77989 | −0.694111 | ||||||||
\(161\) | 3.50264 | 0.276047 | ||||||||
\(162\) | 11.0214 | 0.865926 | ||||||||
\(163\) | −6.91743 | −0.541815 | −0.270907 | − | 0.962605i | \(-0.587324\pi\) | ||||
−0.270907 | + | 0.962605i | \(0.587324\pi\) | |||||||
\(164\) | 3.01254 | 0.235240 | ||||||||
\(165\) | −3.22653 | −0.251185 | ||||||||
\(166\) | −33.1653 | −2.57413 | ||||||||
\(167\) | 4.95994 | 0.383811 | 0.191906 | − | 0.981413i | \(-0.438533\pi\) | ||||
0.191906 | + | 0.981413i | \(0.438533\pi\) | |||||||
\(168\) | 8.53242 | 0.658291 | ||||||||
\(169\) | 4.36892 | 0.336071 | ||||||||
\(170\) | 2.32194 | 0.178084 | ||||||||
\(171\) | −21.1814 | −1.61978 | ||||||||
\(172\) | 1.53233 | 0.116839 | ||||||||
\(173\) | 20.9972 | 1.59639 | 0.798193 | − | 0.602402i | \(-0.205789\pi\) | ||||
0.798193 | + | 0.602402i | \(0.205789\pi\) | |||||||
\(174\) | −12.0606 | −0.914310 | ||||||||
\(175\) | 12.9115 | 0.976016 | ||||||||
\(176\) | 4.71663 | 0.355529 | ||||||||
\(177\) | −24.2401 | −1.82200 | ||||||||
\(178\) | 2.37521 | 0.178030 | ||||||||
\(179\) | −2.74331 | −0.205045 | −0.102522 | − | 0.994731i | \(-0.532691\pi\) | ||||
−0.102522 | + | 0.994731i | \(0.532691\pi\) | |||||||
\(180\) | −7.23299 | −0.539115 | ||||||||
\(181\) | 24.6365 | 1.83122 | 0.915610 | − | 0.402068i | \(-0.131708\pi\) | ||||
0.915610 | + | 0.402068i | \(0.131708\pi\) | |||||||
\(182\) | −29.1139 | −2.15806 | ||||||||
\(183\) | 38.3825 | 2.83732 | ||||||||
\(184\) | −0.828297 | −0.0610629 | ||||||||
\(185\) | −11.1328 | −0.818496 | ||||||||
\(186\) | −15.5637 | −1.14118 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | −7.23693 | −0.527807 | ||||||||
\(189\) | 7.96713 | 0.579524 | ||||||||
\(190\) | −12.8723 | −0.933857 | ||||||||
\(191\) | 12.6808 | 0.917549 | 0.458775 | − | 0.888553i | \(-0.348289\pi\) | ||||
0.458775 | + | 0.888553i | \(0.348289\pi\) | |||||||
\(192\) | 10.2467 | 0.739493 | ||||||||
\(193\) | 13.8459 | 0.996649 | 0.498325 | − | 0.866991i | \(-0.333949\pi\) | ||||
0.498325 | + | 0.866991i | \(0.333949\pi\) | |||||||
\(194\) | −7.66452 | −0.550280 | ||||||||
\(195\) | −13.4469 | −0.962952 | ||||||||
\(196\) | 10.4436 | 0.745969 | ||||||||
\(197\) | 13.8384 | 0.985942 | 0.492971 | − | 0.870046i | \(-0.335911\pi\) | ||||
0.492971 | + | 0.870046i | \(0.335911\pi\) | |||||||
\(198\) | 7.18088 | 0.510323 | ||||||||
\(199\) | 7.08749 | 0.502419 | 0.251210 | − | 0.967933i | \(-0.419172\pi\) | ||||
0.251210 | + | 0.967933i | \(0.419172\pi\) | |||||||
\(200\) | −3.05328 | −0.215899 | ||||||||
\(201\) | 28.5605 | 2.01450 | ||||||||
\(202\) | 7.87786 | 0.554284 | ||||||||
\(203\) | 9.13283 | 0.640999 | ||||||||
\(204\) | −4.00191 | −0.280189 | ||||||||
\(205\) | −2.42885 | −0.169638 | ||||||||
\(206\) | −12.7789 | −0.890345 | ||||||||
\(207\) | −3.60047 | −0.250250 | ||||||||
\(208\) | 19.6570 | 1.36297 | ||||||||
\(209\) | 5.54379 | 0.383472 | ||||||||
\(210\) | 22.5397 | 1.55539 | ||||||||
\(211\) | 23.4891 | 1.61706 | 0.808528 | − | 0.588458i | \(-0.200265\pi\) | ||||
0.808528 | + | 0.588458i | \(0.200265\pi\) | |||||||
\(212\) | −11.8188 | −0.811719 | ||||||||
\(213\) | 4.07518 | 0.279227 | ||||||||
\(214\) | −9.55009 | −0.652831 | ||||||||
\(215\) | −1.23543 | −0.0842559 | ||||||||
\(216\) | −1.88405 | −0.128193 | ||||||||
\(217\) | 11.7855 | 0.800055 | ||||||||
\(218\) | 23.8742 | 1.61697 | ||||||||
\(219\) | −0.989374 | −0.0668557 | ||||||||
\(220\) | 1.89309 | 0.127632 | ||||||||
\(221\) | −4.16760 | −0.280343 | ||||||||
\(222\) | 44.2312 | 2.96861 | ||||||||
\(223\) | 5.71676 | 0.382823 | 0.191411 | − | 0.981510i | \(-0.438694\pi\) | ||||
0.191411 | + | 0.981510i | \(0.438694\pi\) | |||||||
\(224\) | −26.4151 | −1.76493 | ||||||||
\(225\) | −13.2721 | −0.884806 | ||||||||
\(226\) | 2.42919 | 0.161587 | ||||||||
\(227\) | −9.48892 | −0.629802 | −0.314901 | − | 0.949125i | \(-0.601971\pi\) | ||||
−0.314901 | + | 0.949125i | \(0.601971\pi\) | |||||||
\(228\) | 22.1857 | 1.46929 | ||||||||
\(229\) | −1.20499 | −0.0796278 | −0.0398139 | − | 0.999207i | \(-0.512677\pi\) | ||||
−0.0398139 | + | 0.999207i | \(0.512677\pi\) | |||||||
\(230\) | −2.18808 | −0.144278 | ||||||||
\(231\) | −9.70731 | −0.638694 | ||||||||
\(232\) | −2.15971 | −0.141792 | ||||||||
\(233\) | 5.85795 | 0.383767 | 0.191884 | − | 0.981418i | \(-0.438540\pi\) | ||||
0.191884 | + | 0.981418i | \(0.438540\pi\) | |||||||
\(234\) | 29.9270 | 1.95639 | ||||||||
\(235\) | 5.83476 | 0.380618 | ||||||||
\(236\) | 14.2223 | 0.925792 | ||||||||
\(237\) | 12.4101 | 0.806121 | ||||||||
\(238\) | 6.98576 | 0.452820 | ||||||||
\(239\) | −13.3843 | −0.865756 | −0.432878 | − | 0.901452i | \(-0.642502\pi\) | ||||
−0.432878 | + | 0.901452i | \(0.642502\pi\) | |||||||
\(240\) | −15.2183 | −0.982339 | ||||||||
\(241\) | −13.5993 | −0.876010 | −0.438005 | − | 0.898973i | \(-0.644315\pi\) | ||||
−0.438005 | + | 0.898973i | \(0.644315\pi\) | |||||||
\(242\) | −1.87945 | −0.120816 | ||||||||
\(243\) | 21.7457 | 1.39498 | ||||||||
\(244\) | −22.5200 | −1.44170 | ||||||||
\(245\) | −8.42010 | −0.537940 | ||||||||
\(246\) | 9.64999 | 0.615261 | ||||||||
\(247\) | 23.1043 | 1.47009 | ||||||||
\(248\) | −2.78702 | −0.176976 | ||||||||
\(249\) | −46.0860 | −2.92058 | ||||||||
\(250\) | −19.6754 | −1.24438 | ||||||||
\(251\) | −24.7495 | −1.56217 | −0.781087 | − | 0.624422i | \(-0.785335\pi\) | ||||
−0.781087 | + | 0.624422i | \(0.785335\pi\) | |||||||
\(252\) | −21.7611 | −1.37082 | ||||||||
\(253\) | 0.942351 | 0.0592451 | ||||||||
\(254\) | 29.1764 | 1.83069 | ||||||||
\(255\) | 3.22653 | 0.202053 | ||||||||
\(256\) | 20.7014 | 1.29384 | ||||||||
\(257\) | 19.8535 | 1.23842 | 0.619212 | − | 0.785224i | \(-0.287452\pi\) | ||||
0.619212 | + | 0.785224i | \(0.287452\pi\) | |||||||
\(258\) | 4.90847 | 0.305588 | ||||||||
\(259\) | −33.4939 | −2.08121 | ||||||||
\(260\) | 7.88964 | 0.489295 | ||||||||
\(261\) | −9.38792 | −0.581097 | ||||||||
\(262\) | 0.466792 | 0.0288385 | ||||||||
\(263\) | −27.7326 | −1.71007 | −0.855034 | − | 0.518572i | \(-0.826464\pi\) | ||||
−0.855034 | + | 0.518572i | \(0.826464\pi\) | |||||||
\(264\) | 2.29556 | 0.141282 | ||||||||
\(265\) | 9.52889 | 0.585355 | ||||||||
\(266\) | −38.7276 | −2.37454 | ||||||||
\(267\) | 3.30056 | 0.201991 | ||||||||
\(268\) | −16.7572 | −1.02361 | ||||||||
\(269\) | 7.62916 | 0.465158 | 0.232579 | − | 0.972577i | \(-0.425284\pi\) | ||||
0.232579 | + | 0.972577i | \(0.425284\pi\) | |||||||
\(270\) | −4.97702 | −0.302892 | ||||||||
\(271\) | −17.1206 | −1.04000 | −0.520002 | − | 0.854165i | \(-0.674069\pi\) | ||||
−0.520002 | + | 0.854165i | \(0.674069\pi\) | |||||||
\(272\) | −4.71663 | −0.285988 | ||||||||
\(273\) | −40.4562 | −2.44852 | ||||||||
\(274\) | −18.7999 | −1.13574 | ||||||||
\(275\) | 3.47370 | 0.209472 | ||||||||
\(276\) | 3.77120 | 0.226999 | ||||||||
\(277\) | 1.54921 | 0.0930827 | 0.0465414 | − | 0.998916i | \(-0.485180\pi\) | ||||
0.0465414 | + | 0.998916i | \(0.485180\pi\) | |||||||
\(278\) | 37.9015 | 2.27318 | ||||||||
\(279\) | −12.1147 | −0.725289 | ||||||||
\(280\) | 4.03624 | 0.241211 | ||||||||
\(281\) | −6.98042 | −0.416417 | −0.208209 | − | 0.978084i | \(-0.566763\pi\) | ||||
−0.208209 | + | 0.978084i | \(0.566763\pi\) | |||||||
\(282\) | −23.1819 | −1.38046 | ||||||||
\(283\) | 9.21245 | 0.547623 | 0.273812 | − | 0.961783i | \(-0.411715\pi\) | ||||
0.273812 | + | 0.961783i | \(0.411715\pi\) | |||||||
\(284\) | −2.39102 | −0.141881 | ||||||||
\(285\) | −17.8872 | −1.05955 | ||||||||
\(286\) | −7.83280 | −0.463163 | ||||||||
\(287\) | −7.30742 | −0.431344 | ||||||||
\(288\) | 27.1529 | 1.60000 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −5.70522 | −0.335022 | ||||||||
\(291\) | −10.6505 | −0.624343 | ||||||||
\(292\) | 0.580492 | 0.0339707 | ||||||||
\(293\) | 29.7459 | 1.73777 | 0.868887 | − | 0.495011i | \(-0.164836\pi\) | ||||
0.868887 | + | 0.495011i | \(0.164836\pi\) | |||||||
\(294\) | 33.4537 | 1.95106 | ||||||||
\(295\) | −11.4667 | −0.667617 | ||||||||
\(296\) | 7.92057 | 0.460374 | ||||||||
\(297\) | 2.14348 | 0.124377 | ||||||||
\(298\) | −42.6636 | −2.47143 | ||||||||
\(299\) | 3.92734 | 0.227124 | ||||||||
\(300\) | 13.9014 | 0.802599 | ||||||||
\(301\) | −3.71692 | −0.214240 | ||||||||
\(302\) | −29.0316 | −1.67058 | ||||||||
\(303\) | 10.9470 | 0.628886 | ||||||||
\(304\) | 26.1480 | 1.49969 | ||||||||
\(305\) | 18.1567 | 1.03965 | ||||||||
\(306\) | −7.18088 | −0.410503 | ||||||||
\(307\) | −5.66235 | −0.323167 | −0.161584 | − | 0.986859i | \(-0.551660\pi\) | ||||
−0.161584 | + | 0.986859i | \(0.551660\pi\) | |||||||
\(308\) | 5.69553 | 0.324533 | ||||||||
\(309\) | −17.7573 | −1.01018 | ||||||||
\(310\) | −7.36235 | −0.418153 | ||||||||
\(311\) | 5.05158 | 0.286449 | 0.143224 | − | 0.989690i | \(-0.454253\pi\) | ||||
0.143224 | + | 0.989690i | \(0.454253\pi\) | |||||||
\(312\) | 9.56700 | 0.541624 | ||||||||
\(313\) | 20.3204 | 1.14858 | 0.574290 | − | 0.818652i | \(-0.305278\pi\) | ||||
0.574290 | + | 0.818652i | \(0.305278\pi\) | |||||||
\(314\) | −25.5614 | −1.44252 | ||||||||
\(315\) | 17.5449 | 0.988541 | ||||||||
\(316\) | −7.28132 | −0.409606 | ||||||||
\(317\) | −0.490531 | −0.0275510 | −0.0137755 | − | 0.999905i | \(-0.504385\pi\) | ||||
−0.0137755 | + | 0.999905i | \(0.504385\pi\) | |||||||
\(318\) | −37.8590 | −2.12303 | ||||||||
\(319\) | 2.45710 | 0.137571 | ||||||||
\(320\) | 4.84718 | 0.270965 | ||||||||
\(321\) | −13.2707 | −0.740696 | ||||||||
\(322\) | −6.58303 | −0.366858 | ||||||||
\(323\) | −5.54379 | −0.308465 | ||||||||
\(324\) | −8.98585 | −0.499214 | ||||||||
\(325\) | 14.4770 | 0.803040 | ||||||||
\(326\) | 13.0009 | 0.720056 | ||||||||
\(327\) | 33.1753 | 1.83460 | ||||||||
\(328\) | 1.72804 | 0.0954152 | ||||||||
\(329\) | 17.5544 | 0.967806 | ||||||||
\(330\) | 6.06409 | 0.333817 | ||||||||
\(331\) | 14.6330 | 0.804303 | 0.402151 | − | 0.915573i | \(-0.368263\pi\) | ||||
0.402151 | + | 0.915573i | \(0.368263\pi\) | |||||||
\(332\) | 27.0399 | 1.48401 | ||||||||
\(333\) | 34.4294 | 1.88672 | ||||||||
\(334\) | −9.32194 | −0.510074 | ||||||||
\(335\) | 13.5105 | 0.738155 | ||||||||
\(336\) | −45.7858 | −2.49782 | ||||||||
\(337\) | −2.49971 | −0.136168 | −0.0680840 | − | 0.997680i | \(-0.521689\pi\) | ||||
−0.0680840 | + | 0.997680i | \(0.521689\pi\) | |||||||
\(338\) | −8.21116 | −0.446628 | ||||||||
\(339\) | 3.37556 | 0.183335 | ||||||||
\(340\) | −1.89309 | −0.102667 | ||||||||
\(341\) | 3.17078 | 0.171707 | ||||||||
\(342\) | 39.8093 | 2.15264 | ||||||||
\(343\) | 0.685784 | 0.0370289 | ||||||||
\(344\) | 0.878969 | 0.0473908 | ||||||||
\(345\) | −3.04052 | −0.163696 | ||||||||
\(346\) | −39.4631 | −2.12155 | ||||||||
\(347\) | 12.7918 | 0.686698 | 0.343349 | − | 0.939208i | \(-0.388439\pi\) | ||||
0.343349 | + | 0.939208i | \(0.388439\pi\) | |||||||
\(348\) | 9.83307 | 0.527108 | ||||||||
\(349\) | 10.2188 | 0.546999 | 0.273499 | − | 0.961872i | \(-0.411819\pi\) | ||||
0.273499 | + | 0.961872i | \(0.411819\pi\) | |||||||
\(350\) | −24.2664 | −1.29710 | ||||||||
\(351\) | 8.93316 | 0.476817 | ||||||||
\(352\) | −7.10672 | −0.378790 | ||||||||
\(353\) | 18.6457 | 0.992413 | 0.496206 | − | 0.868205i | \(-0.334726\pi\) | ||||
0.496206 | + | 0.868205i | \(0.334726\pi\) | |||||||
\(354\) | 45.5580 | 2.42138 | ||||||||
\(355\) | 1.92775 | 0.102314 | ||||||||
\(356\) | −1.93652 | −0.102636 | ||||||||
\(357\) | 9.70731 | 0.513765 | ||||||||
\(358\) | 5.15592 | 0.272499 | ||||||||
\(359\) | −12.1451 | −0.640996 | −0.320498 | − | 0.947249i | \(-0.603850\pi\) | ||||
−0.320498 | + | 0.947249i | \(0.603850\pi\) | |||||||
\(360\) | −4.14897 | −0.218670 | ||||||||
\(361\) | 11.7336 | 0.617559 | ||||||||
\(362\) | −46.3031 | −2.43364 | ||||||||
\(363\) | −2.61165 | −0.137076 | ||||||||
\(364\) | 23.7367 | 1.24414 | ||||||||
\(365\) | −0.468020 | −0.0244973 | ||||||||
\(366\) | −72.1379 | −3.77071 | ||||||||
\(367\) | −6.71172 | −0.350349 | −0.175175 | − | 0.984537i | \(-0.556049\pi\) | ||||
−0.175175 | + | 0.984537i | \(0.556049\pi\) | |||||||
\(368\) | 4.44472 | 0.231697 | ||||||||
\(369\) | 7.51152 | 0.391034 | ||||||||
\(370\) | 20.9234 | 1.08776 | ||||||||
\(371\) | 28.6686 | 1.48840 | ||||||||
\(372\) | 12.6892 | 0.657903 | ||||||||
\(373\) | −19.3351 | −1.00113 | −0.500566 | − | 0.865699i | \(-0.666875\pi\) | ||||
−0.500566 | + | 0.865699i | \(0.666875\pi\) | |||||||
\(374\) | 1.87945 | 0.0971840 | ||||||||
\(375\) | −27.3406 | −1.41186 | ||||||||
\(376\) | −4.15123 | −0.214083 | ||||||||
\(377\) | 10.2402 | 0.527397 | ||||||||
\(378\) | −14.9738 | −0.770170 | ||||||||
\(379\) | −5.49769 | −0.282397 | −0.141199 | − | 0.989981i | \(-0.545096\pi\) | ||||
−0.141199 | + | 0.989981i | \(0.545096\pi\) | |||||||
\(380\) | 10.4949 | 0.538376 | ||||||||
\(381\) | 40.5431 | 2.07709 | ||||||||
\(382\) | −23.8329 | −1.21940 | ||||||||
\(383\) | −19.2787 | −0.985098 | −0.492549 | − | 0.870285i | \(-0.663935\pi\) | ||||
−0.492549 | + | 0.870285i | \(0.663935\pi\) | |||||||
\(384\) | 17.8624 | 0.911538 | ||||||||
\(385\) | −4.59201 | −0.234031 | ||||||||
\(386\) | −26.0226 | −1.32452 | ||||||||
\(387\) | 3.82074 | 0.194219 | ||||||||
\(388\) | 6.24893 | 0.317241 | ||||||||
\(389\) | −12.6496 | −0.641362 | −0.320681 | − | 0.947187i | \(-0.603912\pi\) | ||||
−0.320681 | + | 0.947187i | \(0.603912\pi\) | |||||||
\(390\) | 25.2727 | 1.27973 | ||||||||
\(391\) | −0.942351 | −0.0476567 | ||||||||
\(392\) | 5.99061 | 0.302572 | ||||||||
\(393\) | 0.648647 | 0.0327199 | ||||||||
\(394\) | −26.0085 | −1.31029 | ||||||||
\(395\) | 5.87054 | 0.295379 | ||||||||
\(396\) | −5.85461 | −0.294205 | ||||||||
\(397\) | 11.4929 | 0.576812 | 0.288406 | − | 0.957508i | \(-0.406875\pi\) | ||||
0.288406 | + | 0.957508i | \(0.406875\pi\) | |||||||
\(398\) | −13.3206 | −0.667700 | ||||||||
\(399\) | −53.8153 | −2.69413 | ||||||||
\(400\) | 16.3842 | 0.819208 | ||||||||
\(401\) | 8.82987 | 0.440943 | 0.220471 | − | 0.975393i | \(-0.429240\pi\) | ||||
0.220471 | + | 0.975393i | \(0.429240\pi\) | |||||||
\(402\) | −53.6780 | −2.67722 | ||||||||
\(403\) | 13.2146 | 0.658264 | ||||||||
\(404\) | −6.42287 | −0.319550 | ||||||||
\(405\) | 7.24482 | 0.359998 | ||||||||
\(406\) | −17.1647 | −0.851869 | ||||||||
\(407\) | −9.01121 | −0.446669 | ||||||||
\(408\) | −2.29556 | −0.113647 | ||||||||
\(409\) | −18.5658 | −0.918020 | −0.459010 | − | 0.888431i | \(-0.651796\pi\) | ||||
−0.459010 | + | 0.888431i | \(0.651796\pi\) | |||||||
\(410\) | 4.56490 | 0.225444 | ||||||||
\(411\) | −26.1240 | −1.28860 | ||||||||
\(412\) | 10.4187 | 0.513291 | ||||||||
\(413\) | −34.4986 | −1.69757 | ||||||||
\(414\) | 6.76690 | 0.332575 | ||||||||
\(415\) | −21.8008 | −1.07016 | ||||||||
\(416\) | −29.6180 | −1.45214 | ||||||||
\(417\) | 52.6673 | 2.57913 | ||||||||
\(418\) | −10.4193 | −0.509623 | ||||||||
\(419\) | 39.3049 | 1.92017 | 0.960085 | − | 0.279708i | \(-0.0902376\pi\) | ||||
0.960085 | + | 0.279708i | \(0.0902376\pi\) | |||||||
\(420\) | −18.3768 | −0.896696 | ||||||||
\(421\) | 27.7544 | 1.35267 | 0.676333 | − | 0.736596i | \(-0.263568\pi\) | ||||
0.676333 | + | 0.736596i | \(0.263568\pi\) | |||||||
\(422\) | −44.1465 | −2.14902 | ||||||||
\(423\) | −18.0447 | −0.877364 | ||||||||
\(424\) | −6.77948 | −0.329241 | ||||||||
\(425\) | −3.47370 | −0.168499 | ||||||||
\(426\) | −7.65910 | −0.371084 | ||||||||
\(427\) | 54.6262 | 2.64355 | ||||||||
\(428\) | 7.78625 | 0.376363 | ||||||||
\(429\) | −10.8843 | −0.525501 | ||||||||
\(430\) | 2.32194 | 0.111974 | ||||||||
\(431\) | −25.4371 | −1.22526 | −0.612631 | − | 0.790369i | \(-0.709889\pi\) | ||||
−0.612631 | + | 0.790369i | \(0.709889\pi\) | |||||||
\(432\) | 10.1100 | 0.486417 | ||||||||
\(433\) | 19.4336 | 0.933921 | 0.466961 | − | 0.884278i | \(-0.345349\pi\) | ||||
0.466961 | + | 0.884278i | \(0.345349\pi\) | |||||||
\(434\) | −22.1503 | −1.06325 | ||||||||
\(435\) | −7.92789 | −0.380113 | ||||||||
\(436\) | −19.4648 | −0.932195 | ||||||||
\(437\) | 5.22419 | 0.249907 | ||||||||
\(438\) | 1.85948 | 0.0888493 | ||||||||
\(439\) | −18.7491 | −0.894847 | −0.447423 | − | 0.894322i | \(-0.647658\pi\) | ||||
−0.447423 | + | 0.894322i | \(0.647658\pi\) | |||||||
\(440\) | 1.08591 | 0.0517687 | ||||||||
\(441\) | 26.0402 | 1.24001 | ||||||||
\(442\) | 7.83280 | 0.372568 | ||||||||
\(443\) | −23.4840 | −1.11576 | −0.557880 | − | 0.829922i | \(-0.688385\pi\) | ||||
−0.557880 | + | 0.829922i | \(0.688385\pi\) | |||||||
\(444\) | −36.0620 | −1.71143 | ||||||||
\(445\) | 1.56132 | 0.0740136 | ||||||||
\(446\) | −10.7444 | −0.508760 | ||||||||
\(447\) | −59.2847 | −2.80407 | ||||||||
\(448\) | 14.5832 | 0.688991 | ||||||||
\(449\) | 23.5069 | 1.10936 | 0.554681 | − | 0.832063i | \(-0.312840\pi\) | ||||
0.554681 | + | 0.832063i | \(0.312840\pi\) | |||||||
\(450\) | 24.9442 | 1.17588 | ||||||||
\(451\) | −1.96599 | −0.0925748 | ||||||||
\(452\) | −1.98053 | −0.0931563 | ||||||||
\(453\) | −40.3418 | −1.89543 | ||||||||
\(454\) | 17.8339 | 0.836988 | ||||||||
\(455\) | −19.1377 | −0.897188 | ||||||||
\(456\) | 12.7261 | 0.595955 | ||||||||
\(457\) | 33.3341 | 1.55930 | 0.779651 | − | 0.626215i | \(-0.215397\pi\) | ||||
0.779651 | + | 0.626215i | \(0.215397\pi\) | |||||||
\(458\) | 2.26471 | 0.105823 | ||||||||
\(459\) | −2.14348 | −0.100049 | ||||||||
\(460\) | 1.78395 | 0.0831772 | ||||||||
\(461\) | 13.1322 | 0.611629 | 0.305815 | − | 0.952091i | \(-0.401071\pi\) | ||||
0.305815 | + | 0.952091i | \(0.401071\pi\) | |||||||
\(462\) | 18.2444 | 0.848806 | ||||||||
\(463\) | −9.55467 | −0.444043 | −0.222022 | − | 0.975042i | \(-0.571266\pi\) | ||||
−0.222022 | + | 0.975042i | \(0.571266\pi\) | |||||||
\(464\) | 11.5892 | 0.538016 | ||||||||
\(465\) | −10.2306 | −0.474433 | ||||||||
\(466\) | −11.0097 | −0.510015 | ||||||||
\(467\) | −31.1091 | −1.43956 | −0.719780 | − | 0.694202i | \(-0.755757\pi\) | ||||
−0.719780 | + | 0.694202i | \(0.755757\pi\) | |||||||
\(468\) | −24.3997 | −1.12788 | ||||||||
\(469\) | 40.6475 | 1.87693 | ||||||||
\(470\) | −10.9661 | −0.505830 | ||||||||
\(471\) | −35.5198 | −1.63667 | ||||||||
\(472\) | 8.15816 | 0.375510 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −23.3241 | −1.07131 | ||||||||
\(475\) | 19.2575 | 0.883594 | ||||||||
\(476\) | −5.69553 | −0.261054 | ||||||||
\(477\) | −29.4693 | −1.34931 | ||||||||
\(478\) | 25.1550 | 1.15056 | ||||||||
\(479\) | −7.96866 | −0.364097 | −0.182049 | − | 0.983290i | \(-0.558273\pi\) | ||||
−0.182049 | + | 0.983290i | \(0.558273\pi\) | |||||||
\(480\) | 22.9300 | 1.04661 | ||||||||
\(481\) | −37.5551 | −1.71237 | ||||||||
\(482\) | 25.5592 | 1.16419 | ||||||||
\(483\) | −9.14769 | −0.416234 | ||||||||
\(484\) | 1.53233 | 0.0696512 | ||||||||
\(485\) | −5.03819 | −0.228772 | ||||||||
\(486\) | −40.8698 | −1.85389 | ||||||||
\(487\) | −0.595390 | −0.0269797 | −0.0134898 | − | 0.999909i | \(-0.504294\pi\) | ||||
−0.0134898 | + | 0.999909i | \(0.504294\pi\) | |||||||
\(488\) | −12.9179 | −0.584765 | ||||||||
\(489\) | 18.0659 | 0.816970 | ||||||||
\(490\) | 15.8251 | 0.714907 | ||||||||
\(491\) | −4.19963 | −0.189527 | −0.0947634 | − | 0.995500i | \(-0.530209\pi\) | ||||
−0.0947634 | + | 0.995500i | \(0.530209\pi\) | |||||||
\(492\) | −7.86770 | −0.354703 | ||||||||
\(493\) | −2.45710 | −0.110662 | ||||||||
\(494\) | −43.4234 | −1.95371 | ||||||||
\(495\) | 4.72027 | 0.212160 | ||||||||
\(496\) | 14.9554 | 0.671517 | ||||||||
\(497\) | 5.79982 | 0.260158 | ||||||||
\(498\) | 86.6162 | 3.88137 | ||||||||
\(499\) | 3.16092 | 0.141502 | 0.0707511 | − | 0.997494i | \(-0.477460\pi\) | ||||
0.0707511 | + | 0.997494i | \(0.477460\pi\) | |||||||
\(500\) | 16.0415 | 0.717396 | ||||||||
\(501\) | −12.9536 | −0.578726 | ||||||||
\(502\) | 46.5154 | 2.07608 | ||||||||
\(503\) | −21.9706 | −0.979621 | −0.489810 | − | 0.871829i | \(-0.662934\pi\) | ||||
−0.489810 | + | 0.871829i | \(0.662934\pi\) | |||||||
\(504\) | −12.4826 | −0.556018 | ||||||||
\(505\) | 5.17842 | 0.230437 | ||||||||
\(506\) | −1.77110 | −0.0787350 | ||||||||
\(507\) | −11.4101 | −0.506740 | ||||||||
\(508\) | −23.7877 | −1.05541 | ||||||||
\(509\) | 10.2971 | 0.456413 | 0.228206 | − | 0.973613i | \(-0.426714\pi\) | ||||
0.228206 | + | 0.973613i | \(0.426714\pi\) | |||||||
\(510\) | −6.06409 | −0.268522 | ||||||||
\(511\) | −1.40808 | −0.0622899 | ||||||||
\(512\) | −25.2282 | −1.11494 | ||||||||
\(513\) | 11.8830 | 0.524647 | ||||||||
\(514\) | −37.3136 | −1.64583 | ||||||||
\(515\) | −8.40004 | −0.370150 | ||||||||
\(516\) | −4.00191 | −0.176174 | ||||||||
\(517\) | 4.72284 | 0.207710 | ||||||||
\(518\) | 62.9501 | 2.76587 | ||||||||
\(519\) | −54.8374 | −2.40709 | ||||||||
\(520\) | 4.52564 | 0.198462 | ||||||||
\(521\) | 3.34953 | 0.146746 | 0.0733729 | − | 0.997305i | \(-0.476624\pi\) | ||||
0.0733729 | + | 0.997305i | \(0.476624\pi\) | |||||||
\(522\) | 17.6441 | 0.772261 | ||||||||
\(523\) | 10.0729 | 0.440458 | 0.220229 | − | 0.975448i | \(-0.429320\pi\) | ||||
0.220229 | + | 0.975448i | \(0.429320\pi\) | |||||||
\(524\) | −0.380578 | −0.0166256 | ||||||||
\(525\) | −33.7203 | −1.47167 | ||||||||
\(526\) | 52.1221 | 2.27263 | ||||||||
\(527\) | −3.17078 | −0.138121 | ||||||||
\(528\) | −12.3182 | −0.536081 | ||||||||
\(529\) | −22.1120 | −0.961390 | ||||||||
\(530\) | −17.9091 | −0.777920 | ||||||||
\(531\) | 35.4622 | 1.53893 | ||||||||
\(532\) | 31.5748 | 1.36894 | ||||||||
\(533\) | −8.19346 | −0.354898 | ||||||||
\(534\) | −6.20323 | −0.268440 | ||||||||
\(535\) | −6.27765 | −0.271406 | ||||||||
\(536\) | −9.61222 | −0.415185 | ||||||||
\(537\) | 7.16458 | 0.309175 | ||||||||
\(538\) | −14.3386 | −0.618181 | ||||||||
\(539\) | −6.81550 | −0.293564 | ||||||||
\(540\) | 4.05779 | 0.174620 | ||||||||
\(541\) | −42.1401 | −1.81175 | −0.905873 | − | 0.423549i | \(-0.860784\pi\) | ||||
−0.905873 | + | 0.423549i | \(0.860784\pi\) | |||||||
\(542\) | 32.1774 | 1.38214 | ||||||||
\(543\) | −64.3421 | −2.76118 | ||||||||
\(544\) | 7.10672 | 0.304698 | ||||||||
\(545\) | 15.6935 | 0.672234 | ||||||||
\(546\) | 76.0354 | 3.25401 | ||||||||
\(547\) | 38.6103 | 1.65086 | 0.825429 | − | 0.564506i | \(-0.190933\pi\) | ||||
0.825429 | + | 0.564506i | \(0.190933\pi\) | |||||||
\(548\) | 15.3277 | 0.654765 | ||||||||
\(549\) | −56.1519 | −2.39651 | ||||||||
\(550\) | −6.52864 | −0.278382 | ||||||||
\(551\) | 13.6216 | 0.580301 | ||||||||
\(552\) | 2.16322 | 0.0920730 | ||||||||
\(553\) | 17.6621 | 0.751068 | ||||||||
\(554\) | −2.91165 | −0.123704 | ||||||||
\(555\) | 29.0749 | 1.23416 | ||||||||
\(556\) | −30.9013 | −1.31051 | ||||||||
\(557\) | 22.9269 | 0.971444 | 0.485722 | − | 0.874113i | \(-0.338557\pi\) | ||||
0.485722 | + | 0.874113i | \(0.338557\pi\) | |||||||
\(558\) | 22.7690 | 0.963888 | ||||||||
\(559\) | −4.16760 | −0.176271 | ||||||||
\(560\) | −21.6588 | −0.915252 | ||||||||
\(561\) | 2.61165 | 0.110264 | ||||||||
\(562\) | 13.1193 | 0.553406 | ||||||||
\(563\) | −22.0885 | −0.930919 | −0.465460 | − | 0.885069i | \(-0.654111\pi\) | ||||
−0.465460 | + | 0.885069i | \(0.654111\pi\) | |||||||
\(564\) | 18.9003 | 0.795848 | ||||||||
\(565\) | 1.59680 | 0.0671778 | ||||||||
\(566\) | −17.3143 | −0.727775 | ||||||||
\(567\) | 21.7967 | 0.915376 | ||||||||
\(568\) | −1.37153 | −0.0575481 | ||||||||
\(569\) | −18.1352 | −0.760265 | −0.380133 | − | 0.924932i | \(-0.624122\pi\) | ||||
−0.380133 | + | 0.924932i | \(0.624122\pi\) | |||||||
\(570\) | 33.6181 | 1.40811 | ||||||||
\(571\) | 33.4079 | 1.39808 | 0.699039 | − | 0.715083i | \(-0.253611\pi\) | ||||
0.699039 | + | 0.715083i | \(0.253611\pi\) | |||||||
\(572\) | 6.38613 | 0.267017 | ||||||||
\(573\) | −33.1178 | −1.38352 | ||||||||
\(574\) | 13.7339 | 0.573243 | ||||||||
\(575\) | 3.27344 | 0.136512 | ||||||||
\(576\) | −14.9905 | −0.624604 | ||||||||
\(577\) | 35.7416 | 1.48794 | 0.743972 | − | 0.668211i | \(-0.232940\pi\) | ||||
0.743972 | + | 0.668211i | \(0.232940\pi\) | |||||||
\(578\) | −1.87945 | −0.0781747 | ||||||||
\(579\) | −36.1607 | −1.50279 | ||||||||
\(580\) | 4.65150 | 0.193143 | ||||||||
\(581\) | −65.5898 | −2.72113 | ||||||||
\(582\) | 20.0171 | 0.829734 | ||||||||
\(583\) | 7.71299 | 0.319439 | ||||||||
\(584\) | 0.332980 | 0.0137788 | ||||||||
\(585\) | 19.6722 | 0.813346 | ||||||||
\(586\) | −55.9059 | −2.30945 | ||||||||
\(587\) | −46.7204 | −1.92836 | −0.964180 | − | 0.265250i | \(-0.914545\pi\) | ||||
−0.964180 | + | 0.265250i | \(0.914545\pi\) | |||||||
\(588\) | −27.2750 | −1.12480 | ||||||||
\(589\) | 17.5782 | 0.724295 | ||||||||
\(590\) | 21.5511 | 0.887243 | ||||||||
\(591\) | −36.1410 | −1.48664 | ||||||||
\(592\) | −42.5025 | −1.74684 | ||||||||
\(593\) | −8.83285 | −0.362722 | −0.181361 | − | 0.983417i | \(-0.558050\pi\) | ||||
−0.181361 | + | 0.983417i | \(0.558050\pi\) | |||||||
\(594\) | −4.02855 | −0.165294 | ||||||||
\(595\) | 4.59201 | 0.188254 | ||||||||
\(596\) | 34.7839 | 1.42480 | ||||||||
\(597\) | −18.5101 | −0.757567 | ||||||||
\(598\) | −7.38124 | −0.301841 | ||||||||
\(599\) | 0.447343 | 0.0182779 | 0.00913897 | − | 0.999958i | \(-0.497091\pi\) | ||||
0.00913897 | + | 0.999958i | \(0.497091\pi\) | |||||||
\(600\) | 7.97410 | 0.325541 | ||||||||
\(601\) | 32.5502 | 1.32775 | 0.663874 | − | 0.747844i | \(-0.268911\pi\) | ||||
0.663874 | + | 0.747844i | \(0.268911\pi\) | |||||||
\(602\) | 6.98576 | 0.284718 | ||||||||
\(603\) | −41.7828 | −1.70153 | ||||||||
\(604\) | 23.6696 | 0.963103 | ||||||||
\(605\) | −1.23543 | −0.0502276 | ||||||||
\(606\) | −20.5742 | −0.835771 | ||||||||
\(607\) | 45.5242 | 1.84777 | 0.923886 | − | 0.382669i | \(-0.124995\pi\) | ||||
0.923886 | + | 0.382669i | \(0.124995\pi\) | |||||||
\(608\) | −39.3982 | −1.59781 | ||||||||
\(609\) | −23.8518 | −0.966523 | ||||||||
\(610\) | −34.1246 | −1.38167 | ||||||||
\(611\) | 19.6829 | 0.796286 | ||||||||
\(612\) | 5.85461 | 0.236659 | ||||||||
\(613\) | −31.9346 | −1.28983 | −0.644913 | − | 0.764256i | \(-0.723106\pi\) | ||||
−0.644913 | + | 0.764256i | \(0.723106\pi\) | |||||||
\(614\) | 10.6421 | 0.429480 | ||||||||
\(615\) | 6.34332 | 0.255787 | ||||||||
\(616\) | 3.26706 | 0.131634 | ||||||||
\(617\) | −0.866433 | −0.0348813 | −0.0174406 | − | 0.999848i | \(-0.505552\pi\) | ||||
−0.0174406 | + | 0.999848i | \(0.505552\pi\) | |||||||
\(618\) | 33.3739 | 1.34250 | ||||||||
\(619\) | 6.64791 | 0.267202 | 0.133601 | − | 0.991035i | \(-0.457346\pi\) | ||||
0.133601 | + | 0.991035i | \(0.457346\pi\) | |||||||
\(620\) | 6.00257 | 0.241069 | ||||||||
\(621\) | 2.01991 | 0.0810561 | ||||||||
\(622\) | −9.49417 | −0.380682 | ||||||||
\(623\) | 4.69737 | 0.188196 | ||||||||
\(624\) | −51.3374 | −2.05514 | ||||||||
\(625\) | 4.43511 | 0.177404 | ||||||||
\(626\) | −38.1912 | −1.52643 | ||||||||
\(627\) | −14.4785 | −0.578214 | ||||||||
\(628\) | 20.8404 | 0.831623 | ||||||||
\(629\) | 9.01121 | 0.359300 | ||||||||
\(630\) | −32.9747 | −1.31374 | ||||||||
\(631\) | 34.9282 | 1.39047 | 0.695235 | − | 0.718782i | \(-0.255300\pi\) | ||||
0.695235 | + | 0.718782i | \(0.255300\pi\) | |||||||
\(632\) | −4.17669 | −0.166140 | ||||||||
\(633\) | −61.3454 | −2.43826 | ||||||||
\(634\) | 0.921928 | 0.0366144 | ||||||||
\(635\) | 19.1788 | 0.761087 | ||||||||
\(636\) | 30.8666 | 1.22394 | ||||||||
\(637\) | −28.4043 | −1.12542 | ||||||||
\(638\) | −4.61799 | −0.182828 | ||||||||
\(639\) | −5.96182 | −0.235846 | ||||||||
\(640\) | 8.44976 | 0.334006 | ||||||||
\(641\) | −43.0709 | −1.70120 | −0.850599 | − | 0.525815i | \(-0.823760\pi\) | ||||
−0.850599 | + | 0.525815i | \(0.823760\pi\) | |||||||
\(642\) | 24.9415 | 0.984364 | ||||||||
\(643\) | −3.85352 | −0.151968 | −0.0759840 | − | 0.997109i | \(-0.524210\pi\) | ||||
−0.0759840 | + | 0.997109i | \(0.524210\pi\) | |||||||
\(644\) | 5.36719 | 0.211497 | ||||||||
\(645\) | 3.22653 | 0.127044 | ||||||||
\(646\) | 10.4193 | 0.409941 | ||||||||
\(647\) | −24.1068 | −0.947735 | −0.473867 | − | 0.880596i | \(-0.657142\pi\) | ||||
−0.473867 | + | 0.880596i | \(0.657142\pi\) | |||||||
\(648\) | −5.15444 | −0.202485 | ||||||||
\(649\) | −9.28151 | −0.364331 | ||||||||
\(650\) | −27.2088 | −1.06722 | ||||||||
\(651\) | −30.7798 | −1.20635 | ||||||||
\(652\) | −10.5998 | −0.415118 | ||||||||
\(653\) | 22.4035 | 0.876717 | 0.438359 | − | 0.898800i | \(-0.355560\pi\) | ||||
0.438359 | + | 0.898800i | \(0.355560\pi\) | |||||||
\(654\) | −62.3512 | −2.43813 | ||||||||
\(655\) | 0.306840 | 0.0119892 | ||||||||
\(656\) | −9.27284 | −0.362044 | ||||||||
\(657\) | 1.44741 | 0.0564689 | ||||||||
\(658\) | −32.9926 | −1.28619 | ||||||||
\(659\) | −30.7181 | −1.19661 | −0.598303 | − | 0.801270i | \(-0.704158\pi\) | ||||
−0.598303 | + | 0.801270i | \(0.704158\pi\) | |||||||
\(660\) | −4.94409 | −0.192449 | ||||||||
\(661\) | −11.8599 | −0.461295 | −0.230648 | − | 0.973037i | \(-0.574084\pi\) | ||||
−0.230648 | + | 0.973037i | \(0.574084\pi\) | |||||||
\(662\) | −27.5020 | −1.06890 | ||||||||
\(663\) | 10.8843 | 0.422713 | ||||||||
\(664\) | 15.5105 | 0.601926 | ||||||||
\(665\) | −25.4572 | −0.987186 | ||||||||
\(666\) | −64.7083 | −2.50740 | ||||||||
\(667\) | 2.31545 | 0.0896544 | ||||||||
\(668\) | 7.60024 | 0.294062 | ||||||||
\(669\) | −14.9302 | −0.577235 | ||||||||
\(670\) | −25.3922 | −0.980987 | ||||||||
\(671\) | 14.6966 | 0.567357 | ||||||||
\(672\) | 68.9872 | 2.66124 | ||||||||
\(673\) | 1.93666 | 0.0746526 | 0.0373263 | − | 0.999303i | \(-0.488116\pi\) | ||||
0.0373263 | + | 0.999303i | \(0.488116\pi\) | |||||||
\(674\) | 4.69808 | 0.180963 | ||||||||
\(675\) | 7.44580 | 0.286589 | ||||||||
\(676\) | 6.69461 | 0.257485 | ||||||||
\(677\) | 18.5223 | 0.711871 | 0.355935 | − | 0.934511i | \(-0.384162\pi\) | ||||
0.355935 | + | 0.934511i | \(0.384162\pi\) | |||||||
\(678\) | −6.34419 | −0.243647 | ||||||||
\(679\) | −15.1579 | −0.581705 | ||||||||
\(680\) | −1.08591 | −0.0416427 | ||||||||
\(681\) | 24.7818 | 0.949640 | ||||||||
\(682\) | −5.95932 | −0.228194 | ||||||||
\(683\) | −30.3340 | −1.16070 | −0.580349 | − | 0.814368i | \(-0.697084\pi\) | ||||
−0.580349 | + | 0.814368i | \(0.697084\pi\) | |||||||
\(684\) | −32.4567 | −1.24101 | ||||||||
\(685\) | −12.3579 | −0.472171 | ||||||||
\(686\) | −1.28890 | −0.0492103 | ||||||||
\(687\) | 3.14701 | 0.120066 | ||||||||
\(688\) | −4.71663 | −0.179820 | ||||||||
\(689\) | 32.1447 | 1.22461 | ||||||||
\(690\) | 5.71450 | 0.217547 | ||||||||
\(691\) | −36.4084 | −1.38504 | −0.692521 | − | 0.721398i | \(-0.743500\pi\) | ||||
−0.692521 | + | 0.721398i | \(0.743500\pi\) | |||||||
\(692\) | 32.1745 | 1.22309 | ||||||||
\(693\) | 14.2014 | 0.539465 | ||||||||
\(694\) | −24.0415 | −0.912602 | ||||||||
\(695\) | 24.9141 | 0.945047 | ||||||||
\(696\) | 5.64042 | 0.213800 | ||||||||
\(697\) | 1.96599 | 0.0744671 | ||||||||
\(698\) | −19.2057 | −0.726945 | ||||||||
\(699\) | −15.2989 | −0.578659 | ||||||||
\(700\) | 19.7846 | 0.747787 | ||||||||
\(701\) | −32.4436 | −1.22538 | −0.612690 | − | 0.790324i | \(-0.709912\pi\) | ||||
−0.612690 | + | 0.790324i | \(0.709912\pi\) | |||||||
\(702\) | −16.7894 | −0.633676 | ||||||||
\(703\) | −49.9562 | −1.88414 | ||||||||
\(704\) | 3.92346 | 0.147871 | ||||||||
\(705\) | −15.2384 | −0.573910 | ||||||||
\(706\) | −35.0437 | −1.31889 | ||||||||
\(707\) | 15.5798 | 0.585937 | ||||||||
\(708\) | −37.1437 | −1.39595 | ||||||||
\(709\) | 4.86710 | 0.182788 | 0.0913940 | − | 0.995815i | \(-0.470868\pi\) | ||||
0.0913940 | + | 0.995815i | \(0.470868\pi\) | |||||||
\(710\) | −3.62311 | −0.135973 | ||||||||
\(711\) | −18.1554 | −0.680880 | ||||||||
\(712\) | −1.11082 | −0.0416299 | ||||||||
\(713\) | 2.98799 | 0.111901 | ||||||||
\(714\) | −18.2444 | −0.682779 | ||||||||
\(715\) | −5.14880 | −0.192554 | ||||||||
\(716\) | −4.20365 | −0.157098 | ||||||||
\(717\) | 34.9551 | 1.30542 | ||||||||
\(718\) | 22.8262 | 0.851864 | ||||||||
\(719\) | −29.3259 | −1.09367 | −0.546837 | − | 0.837239i | \(-0.684168\pi\) | ||||
−0.546837 | + | 0.837239i | \(0.684168\pi\) | |||||||
\(720\) | 22.2638 | 0.829721 | ||||||||
\(721\) | −25.2723 | −0.941190 | ||||||||
\(722\) | −22.0527 | −0.820718 | ||||||||
\(723\) | 35.5167 | 1.32088 | ||||||||
\(724\) | 37.7512 | 1.40301 | ||||||||
\(725\) | 8.53522 | 0.316990 | ||||||||
\(726\) | 4.90847 | 0.182170 | ||||||||
\(727\) | −22.2199 | −0.824090 | −0.412045 | − | 0.911163i | \(-0.635185\pi\) | ||||
−0.412045 | + | 0.911163i | \(0.635185\pi\) | |||||||
\(728\) | 13.6158 | 0.504635 | ||||||||
\(729\) | −39.1996 | −1.45184 | ||||||||
\(730\) | 0.879620 | 0.0325562 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 58.8145 | 2.17385 | ||||||||
\(733\) | −11.1130 | −0.410469 | −0.205235 | − | 0.978713i | \(-0.565796\pi\) | ||||
−0.205235 | + | 0.978713i | \(0.565796\pi\) | |||||||
\(734\) | 12.6143 | 0.465604 | ||||||||
\(735\) | 21.9904 | 0.811128 | ||||||||
\(736\) | −6.69702 | −0.246856 | ||||||||
\(737\) | 10.9358 | 0.402825 | ||||||||
\(738\) | −14.1175 | −0.519673 | ||||||||
\(739\) | 17.2563 | 0.634782 | 0.317391 | − | 0.948295i | \(-0.397193\pi\) | ||||
0.317391 | + | 0.948295i | \(0.397193\pi\) | |||||||
\(740\) | −17.0590 | −0.627102 | ||||||||
\(741\) | −60.3405 | −2.21666 | ||||||||
\(742\) | −53.8811 | −1.97804 | ||||||||
\(743\) | 38.8946 | 1.42690 | 0.713452 | − | 0.700704i | \(-0.247131\pi\) | ||||
0.713452 | + | 0.700704i | \(0.247131\pi\) | |||||||
\(744\) | 7.27873 | 0.266851 | ||||||||
\(745\) | −28.0444 | −1.02747 | ||||||||
\(746\) | 36.3392 | 1.33047 | ||||||||
\(747\) | 67.4218 | 2.46683 | ||||||||
\(748\) | −1.53233 | −0.0560274 | ||||||||
\(749\) | −18.8869 | −0.690112 | ||||||||
\(750\) | 51.3853 | 1.87633 | ||||||||
\(751\) | −3.30930 | −0.120758 | −0.0603790 | − | 0.998176i | \(-0.519231\pi\) | ||||
−0.0603790 | + | 0.998176i | \(0.519231\pi\) | |||||||
\(752\) | 22.2759 | 0.812318 | ||||||||
\(753\) | 64.6371 | 2.35551 | ||||||||
\(754\) | −19.2459 | −0.700896 | ||||||||
\(755\) | −19.0836 | −0.694523 | ||||||||
\(756\) | 12.2082 | 0.444010 | ||||||||
\(757\) | −50.4906 | −1.83511 | −0.917557 | − | 0.397605i | \(-0.869841\pi\) | ||||
−0.917557 | + | 0.397605i | \(0.869841\pi\) | |||||||
\(758\) | 10.3326 | 0.375298 | ||||||||
\(759\) | −2.46109 | −0.0893320 | ||||||||
\(760\) | 6.02005 | 0.218370 | ||||||||
\(761\) | −30.6135 | −1.10974 | −0.554870 | − | 0.831937i | \(-0.687232\pi\) | ||||
−0.554870 | + | 0.831937i | \(0.687232\pi\) | |||||||
\(762\) | −76.1986 | −2.76039 | ||||||||
\(763\) | 47.2153 | 1.70931 | ||||||||
\(764\) | 19.4311 | 0.702992 | ||||||||
\(765\) | −4.72027 | −0.170662 | ||||||||
\(766\) | 36.2334 | 1.30917 | ||||||||
\(767\) | −38.6816 | −1.39671 | ||||||||
\(768\) | −54.0649 | −1.95090 | ||||||||
\(769\) | −3.34187 | −0.120511 | −0.0602554 | − | 0.998183i | \(-0.519192\pi\) | ||||
−0.0602554 | + | 0.998183i | \(0.519192\pi\) | |||||||
\(770\) | 8.63045 | 0.311020 | ||||||||
\(771\) | −51.8504 | −1.86735 | ||||||||
\(772\) | 21.2164 | 0.763596 | ||||||||
\(773\) | −44.1888 | −1.58936 | −0.794681 | − | 0.607028i | \(-0.792362\pi\) | ||||
−0.794681 | + | 0.607028i | \(0.792362\pi\) | |||||||
\(774\) | −7.18088 | −0.258111 | ||||||||
\(775\) | 11.0143 | 0.395647 | ||||||||
\(776\) | 3.58449 | 0.128676 | ||||||||
\(777\) | 87.4746 | 3.13813 | ||||||||
\(778\) | 23.7743 | 0.852352 | ||||||||
\(779\) | −10.8990 | −0.390498 | ||||||||
\(780\) | −20.6050 | −0.737778 | ||||||||
\(781\) | 1.56038 | 0.0558349 | ||||||||
\(782\) | 1.77110 | 0.0633344 | ||||||||
\(783\) | 5.26673 | 0.188218 | ||||||||
\(784\) | −32.1462 | −1.14808 | ||||||||
\(785\) | −16.8025 | −0.599708 | ||||||||
\(786\) | −1.21910 | −0.0434838 | ||||||||
\(787\) | 25.6510 | 0.914360 | 0.457180 | − | 0.889374i | \(-0.348860\pi\) | ||||
0.457180 | + | 0.889374i | \(0.348860\pi\) | |||||||
\(788\) | 21.2049 | 0.755392 | ||||||||
\(789\) | 72.4281 | 2.57851 | ||||||||
\(790\) | −11.0334 | −0.392550 | ||||||||
\(791\) | 4.80412 | 0.170815 | ||||||||
\(792\) | −3.35831 | −0.119332 | ||||||||
\(793\) | 61.2497 | 2.17504 | ||||||||
\(794\) | −21.6003 | −0.766567 | ||||||||
\(795\) | −24.8862 | −0.882621 | ||||||||
\(796\) | 10.8604 | 0.384935 | ||||||||
\(797\) | 9.65198 | 0.341891 | 0.170945 | − | 0.985280i | \(-0.445318\pi\) | ||||
0.170945 | + | 0.985280i | \(0.445318\pi\) | |||||||
\(798\) | 101.143 | 3.58043 | ||||||||
\(799\) | −4.72284 | −0.167082 | ||||||||
\(800\) | −24.6866 | −0.872804 | ||||||||
\(801\) | −4.82857 | −0.170609 | ||||||||
\(802\) | −16.5953 | −0.586000 | ||||||||
\(803\) | −0.378831 | −0.0133686 | ||||||||
\(804\) | 43.7640 | 1.54344 | ||||||||
\(805\) | −4.32728 | −0.152517 | ||||||||
\(806\) | −24.8361 | −0.874814 | ||||||||
\(807\) | −19.9247 | −0.701384 | ||||||||
\(808\) | −3.68427 | −0.129612 | ||||||||
\(809\) | 4.72435 | 0.166099 | 0.0830496 | − | 0.996545i | \(-0.473534\pi\) | ||||
0.0830496 | + | 0.996545i | \(0.473534\pi\) | |||||||
\(810\) | −13.6163 | −0.478427 | ||||||||
\(811\) | −16.4749 | −0.578511 | −0.289256 | − | 0.957252i | \(-0.593408\pi\) | ||||
−0.289256 | + | 0.957252i | \(0.593408\pi\) | |||||||
\(812\) | 13.9945 | 0.491110 | ||||||||
\(813\) | 44.7132 | 1.56816 | ||||||||
\(814\) | 16.9361 | 0.593610 | ||||||||
\(815\) | 8.54603 | 0.299354 | ||||||||
\(816\) | 12.3182 | 0.431223 | ||||||||
\(817\) | −5.54379 | −0.193953 | ||||||||
\(818\) | 34.8935 | 1.22002 | ||||||||
\(819\) | 59.1857 | 2.06811 | ||||||||
\(820\) | −3.72179 | −0.129971 | ||||||||
\(821\) | −13.7131 | −0.478592 | −0.239296 | − | 0.970947i | \(-0.576917\pi\) | ||||
−0.239296 | + | 0.970947i | \(0.576917\pi\) | |||||||
\(822\) | 49.0988 | 1.71252 | ||||||||
\(823\) | 34.3716 | 1.19812 | 0.599060 | − | 0.800704i | \(-0.295541\pi\) | ||||
0.599060 | + | 0.800704i | \(0.295541\pi\) | |||||||
\(824\) | 5.97634 | 0.208196 | ||||||||
\(825\) | −9.07211 | −0.315850 | ||||||||
\(826\) | 64.8384 | 2.25602 | ||||||||
\(827\) | 32.4075 | 1.12692 | 0.563460 | − | 0.826144i | \(-0.309470\pi\) | ||||
0.563460 | + | 0.826144i | \(0.309470\pi\) | |||||||
\(828\) | −5.51710 | −0.191732 | ||||||||
\(829\) | −23.5988 | −0.819620 | −0.409810 | − | 0.912171i | \(-0.634405\pi\) | ||||
−0.409810 | + | 0.912171i | \(0.634405\pi\) | |||||||
\(830\) | 40.9735 | 1.42221 | ||||||||
\(831\) | −4.04599 | −0.140354 | ||||||||
\(832\) | 16.3514 | 0.566884 | ||||||||
\(833\) | 6.81550 | 0.236143 | ||||||||
\(834\) | −98.9856 | −3.42759 | ||||||||
\(835\) | −6.12768 | −0.212057 | ||||||||
\(836\) | 8.49490 | 0.293802 | ||||||||
\(837\) | 6.79650 | 0.234921 | ||||||||
\(838\) | −73.8715 | −2.55185 | ||||||||
\(839\) | −42.2398 | −1.45828 | −0.729141 | − | 0.684364i | \(-0.760080\pi\) | ||||
−0.729141 | + | 0.684364i | \(0.760080\pi\) | |||||||
\(840\) | −10.5413 | −0.363708 | ||||||||
\(841\) | −22.9627 | −0.791816 | ||||||||
\(842\) | −52.1630 | −1.79765 | ||||||||
\(843\) | 18.2305 | 0.627890 | ||||||||
\(844\) | 35.9929 | 1.23893 | ||||||||
\(845\) | −5.39751 | −0.185680 | ||||||||
\(846\) | 33.9141 | 1.16599 | ||||||||
\(847\) | −3.71692 | −0.127715 | ||||||||
\(848\) | 36.3793 | 1.24927 | ||||||||
\(849\) | −24.0597 | −0.825728 | ||||||||
\(850\) | 6.52864 | 0.223931 | ||||||||
\(851\) | −8.49171 | −0.291092 | ||||||||
\(852\) | 6.24451 | 0.213933 | ||||||||
\(853\) | 35.3128 | 1.20909 | 0.604544 | − | 0.796572i | \(-0.293355\pi\) | ||||
0.604544 | + | 0.796572i | \(0.293355\pi\) | |||||||
\(854\) | −102.667 | −3.51320 | ||||||||
\(855\) | 26.1682 | 0.894933 | ||||||||
\(856\) | 4.46633 | 0.152656 | ||||||||
\(857\) | −7.95792 | −0.271837 | −0.135919 | − | 0.990720i | \(-0.543399\pi\) | ||||
−0.135919 | + | 0.990720i | \(0.543399\pi\) | |||||||
\(858\) | 20.4565 | 0.698375 | ||||||||
\(859\) | 7.50464 | 0.256055 | 0.128028 | − | 0.991771i | \(-0.459135\pi\) | ||||
0.128028 | + | 0.991771i | \(0.459135\pi\) | |||||||
\(860\) | −1.89309 | −0.0645538 | ||||||||
\(861\) | 19.0845 | 0.650397 | ||||||||
\(862\) | 47.8077 | 1.62834 | ||||||||
\(863\) | −36.8899 | −1.25575 | −0.627874 | − | 0.778315i | \(-0.716075\pi\) | ||||
−0.627874 | + | 0.778315i | \(0.716075\pi\) | |||||||
\(864\) | −15.2331 | −0.518241 | ||||||||
\(865\) | −25.9406 | −0.882008 | ||||||||
\(866\) | −36.5245 | −1.24115 | ||||||||
\(867\) | −2.61165 | −0.0886964 | ||||||||
\(868\) | 18.0593 | 0.612972 | ||||||||
\(869\) | 4.75181 | 0.161194 | ||||||||
\(870\) | 14.9001 | 0.505159 | ||||||||
\(871\) | 45.5761 | 1.54429 | ||||||||
\(872\) | −11.1654 | −0.378107 | ||||||||
\(873\) | 15.5812 | 0.527344 | ||||||||
\(874\) | −9.81860 | −0.332119 | ||||||||
\(875\) | −38.9113 | −1.31544 | ||||||||
\(876\) | −1.51604 | −0.0512224 | ||||||||
\(877\) | −17.2652 | −0.583006 | −0.291503 | − | 0.956570i | \(-0.594155\pi\) | ||||
−0.291503 | + | 0.956570i | \(0.594155\pi\) | |||||||
\(878\) | 35.2380 | 1.18922 | ||||||||
\(879\) | −77.6860 | −2.62028 | ||||||||
\(880\) | −5.82709 | −0.196431 | ||||||||
\(881\) | −15.6675 | −0.527852 | −0.263926 | − | 0.964543i | \(-0.585017\pi\) | ||||
−0.263926 | + | 0.964543i | \(0.585017\pi\) | |||||||
\(882\) | −48.9412 | −1.64794 | ||||||||
\(883\) | 34.5296 | 1.16201 | 0.581006 | − | 0.813899i | \(-0.302659\pi\) | ||||
0.581006 | + | 0.813899i | \(0.302659\pi\) | |||||||
\(884\) | −6.38613 | −0.214789 | ||||||||
\(885\) | 29.9470 | 1.00666 | ||||||||
\(886\) | 44.1370 | 1.48281 | ||||||||
\(887\) | −18.1439 | −0.609213 | −0.304607 | − | 0.952478i | \(-0.598525\pi\) | ||||
−0.304607 | + | 0.952478i | \(0.598525\pi\) | |||||||
\(888\) | −20.6858 | −0.694170 | ||||||||
\(889\) | 57.7012 | 1.93523 | ||||||||
\(890\) | −2.93442 | −0.0983619 | ||||||||
\(891\) | 5.86419 | 0.196458 | ||||||||
\(892\) | 8.75995 | 0.293305 | ||||||||
\(893\) | 26.1824 | 0.876161 | ||||||||
\(894\) | 111.422 | 3.72652 | ||||||||
\(895\) | 3.38918 | 0.113288 | ||||||||
\(896\) | 25.4219 | 0.849286 | ||||||||
\(897\) | −10.2569 | −0.342467 | ||||||||
\(898\) | −44.1801 | −1.47431 | ||||||||
\(899\) | 7.79092 | 0.259842 | ||||||||
\(900\) | −20.3372 | −0.677906 | ||||||||
\(901\) | −7.71299 | −0.256957 | ||||||||
\(902\) | 3.69497 | 0.123029 | ||||||||
\(903\) | 9.70731 | 0.323039 | ||||||||
\(904\) | −1.13607 | −0.0377850 | ||||||||
\(905\) | −30.4368 | −1.01175 | ||||||||
\(906\) | 75.8204 | 2.51896 | ||||||||
\(907\) | 10.5620 | 0.350704 | 0.175352 | − | 0.984506i | \(-0.443894\pi\) | ||||
0.175352 | + | 0.984506i | \(0.443894\pi\) | |||||||
\(908\) | −14.5401 | −0.482531 | ||||||||
\(909\) | −16.0149 | −0.531181 | ||||||||
\(910\) | 35.9683 | 1.19234 | ||||||||
\(911\) | −14.9802 | −0.496317 | −0.248159 | − | 0.968719i | \(-0.579825\pi\) | ||||
−0.248159 | + | 0.968719i | \(0.579825\pi\) | |||||||
\(912\) | −68.2895 | −2.26129 | ||||||||
\(913\) | −17.6463 | −0.584007 | ||||||||
\(914\) | −62.6496 | −2.07227 | ||||||||
\(915\) | −47.4191 | −1.56763 | ||||||||
\(916\) | −1.84643 | −0.0610078 | ||||||||
\(917\) | 0.923158 | 0.0304854 | ||||||||
\(918\) | 4.02855 | 0.132962 | ||||||||
\(919\) | −5.55199 | −0.183143 | −0.0915717 | − | 0.995798i | \(-0.529189\pi\) | ||||
−0.0915717 | + | 0.995798i | \(0.529189\pi\) | |||||||
\(920\) | 1.02331 | 0.0337374 | ||||||||
\(921\) | 14.7881 | 0.487284 | ||||||||
\(922\) | −24.6814 | −0.812838 | ||||||||
\(923\) | 6.50306 | 0.214051 | ||||||||
\(924\) | −14.8748 | −0.489344 | ||||||||
\(925\) | −31.3022 | −1.02921 | ||||||||
\(926\) | 17.9575 | 0.590120 | ||||||||
\(927\) | 25.9782 | 0.853235 | ||||||||
\(928\) | −17.4619 | −0.573215 | ||||||||
\(929\) | 3.40408 | 0.111684 | 0.0558420 | − | 0.998440i | \(-0.482216\pi\) | ||||
0.0558420 | + | 0.998440i | \(0.482216\pi\) | |||||||
\(930\) | 19.2279 | 0.630508 | ||||||||
\(931\) | −37.7837 | −1.23831 | ||||||||
\(932\) | 8.97629 | 0.294028 | ||||||||
\(933\) | −13.1930 | −0.431918 | ||||||||
\(934\) | 58.4680 | 1.91313 | ||||||||
\(935\) | 1.23543 | 0.0404030 | ||||||||
\(936\) | −13.9961 | −0.457477 | ||||||||
\(937\) | 28.8206 | 0.941527 | 0.470763 | − | 0.882260i | \(-0.343979\pi\) | ||||
0.470763 | + | 0.882260i | \(0.343979\pi\) | |||||||
\(938\) | −76.3948 | −2.49438 | ||||||||
\(939\) | −53.0700 | −1.73187 | ||||||||
\(940\) | 8.94075 | 0.291615 | ||||||||
\(941\) | 9.36860 | 0.305408 | 0.152704 | − | 0.988272i | \(-0.451202\pi\) | ||||
0.152704 | + | 0.988272i | \(0.451202\pi\) | |||||||
\(942\) | 66.7576 | 2.17508 | ||||||||
\(943\) | −1.85265 | −0.0603306 | ||||||||
\(944\) | −43.7774 | −1.42483 | ||||||||
\(945\) | −9.84287 | −0.320189 | ||||||||
\(946\) | 1.87945 | 0.0611061 | ||||||||
\(947\) | −17.8830 | −0.581120 | −0.290560 | − | 0.956857i | \(-0.593842\pi\) | ||||
−0.290560 | + | 0.956857i | \(0.593842\pi\) | |||||||
\(948\) | 19.0163 | 0.617620 | ||||||||
\(949\) | −1.57882 | −0.0512505 | ||||||||
\(950\) | −36.1934 | −1.17427 | ||||||||
\(951\) | 1.28110 | 0.0415424 | ||||||||
\(952\) | −3.26706 | −0.105886 | ||||||||
\(953\) | −20.7617 | −0.672538 | −0.336269 | − | 0.941766i | \(-0.609165\pi\) | ||||
−0.336269 | + | 0.941766i | \(0.609165\pi\) | |||||||
\(954\) | 55.3860 | 1.79319 | ||||||||
\(955\) | −15.6663 | −0.506949 | ||||||||
\(956\) | −20.5091 | −0.663310 | ||||||||
\(957\) | −6.41709 | −0.207435 | ||||||||
\(958\) | 14.9767 | 0.483875 | ||||||||
\(959\) | −37.1799 | −1.20060 | ||||||||
\(960\) | −12.6591 | −0.408572 | ||||||||
\(961\) | −20.9461 | −0.675682 | ||||||||
\(962\) | 70.5829 | 2.27569 | ||||||||
\(963\) | 19.4144 | 0.625620 | ||||||||
\(964\) | −20.8386 | −0.671166 | ||||||||
\(965\) | −17.1057 | −0.550652 | ||||||||
\(966\) | 17.1926 | 0.553163 | ||||||||
\(967\) | −7.39961 | −0.237956 | −0.118978 | − | 0.992897i | \(-0.537962\pi\) | ||||
−0.118978 | + | 0.992897i | \(0.537962\pi\) | |||||||
\(968\) | 0.878969 | 0.0282511 | ||||||||
\(969\) | 14.4785 | 0.465115 | ||||||||
\(970\) | 9.46901 | 0.304032 | ||||||||
\(971\) | 60.0242 | 1.92627 | 0.963134 | − | 0.269021i | \(-0.0867000\pi\) | ||||
0.963134 | + | 0.269021i | \(0.0867000\pi\) | |||||||
\(972\) | 33.3214 | 1.06879 | ||||||||
\(973\) | 74.9565 | 2.40299 | ||||||||
\(974\) | 1.11900 | 0.0358552 | ||||||||
\(975\) | −37.8089 | −1.21086 | ||||||||
\(976\) | 69.3185 | 2.21883 | ||||||||
\(977\) | −18.6170 | −0.595610 | −0.297805 | − | 0.954627i | \(-0.596255\pi\) | ||||
−0.297805 | + | 0.954627i | \(0.596255\pi\) | |||||||
\(978\) | −33.9540 | −1.08573 | ||||||||
\(979\) | 1.26378 | 0.0403906 | ||||||||
\(980\) | −12.9023 | −0.412150 | ||||||||
\(981\) | −48.5340 | −1.54957 | ||||||||
\(982\) | 7.89300 | 0.251876 | ||||||||
\(983\) | 51.8626 | 1.65416 | 0.827080 | − | 0.562084i | \(-0.190000\pi\) | ||||
0.827080 | + | 0.562084i | \(0.190000\pi\) | |||||||
\(984\) | −4.51305 | −0.143871 | ||||||||
\(985\) | −17.0964 | −0.544736 | ||||||||
\(986\) | 4.61799 | 0.147067 | ||||||||
\(987\) | −45.8460 | −1.45930 | ||||||||
\(988\) | 35.4034 | 1.12633 | ||||||||
\(989\) | −0.942351 | −0.0299650 | ||||||||
\(990\) | −8.87150 | −0.281955 | ||||||||
\(991\) | −51.4948 | −1.63579 | −0.817894 | − | 0.575370i | \(-0.804858\pi\) | ||||
−0.817894 | + | 0.575370i | \(0.804858\pi\) | |||||||
\(992\) | −22.5339 | −0.715451 | ||||||||
\(993\) | −38.2164 | −1.21276 | ||||||||
\(994\) | −10.9005 | −0.345742 | ||||||||
\(995\) | −8.75613 | −0.277588 | ||||||||
\(996\) | −70.6188 | −2.23764 | ||||||||
\(997\) | 28.9337 | 0.916340 | 0.458170 | − | 0.888865i | \(-0.348505\pi\) | ||||
0.458170 | + | 0.888865i | \(0.348505\pi\) | |||||||
\(998\) | −5.94079 | −0.188052 | ||||||||
\(999\) | −19.3153 | −0.611110 |
(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 | 8041.2.a.g.1.15 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.g.1.15 | ✓ | 69 | 1.1 | even | 1 | trivial |