Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} - 8 x^{10} + 94 x^{9} - 7 x^{8} - 580 x^{7} + 180 x^{6} + 1787 x^{5} - 308 x^{4} + \cdots + 768 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.02386\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.812175 | −0.363216 | −0.181608 | − | 0.983371i | \(-0.558130\pi\) | ||||
−0.181608 | + | 0.983371i | \(0.558130\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.80411 | −1.05985 | −0.529927 | − | 0.848043i | \(-0.677781\pi\) | ||||
−0.529927 | + | 0.848043i | \(0.677781\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.812175 | 0.256832 | ||||||||
\(11\) | 4.04933 | 1.22092 | 0.610459 | − | 0.792048i | \(-0.290985\pi\) | ||||
0.610459 | + | 0.792048i | \(0.290985\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 2.80411 | 0.749429 | ||||||||
\(15\) | −0.812175 | −0.209703 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.29591 | 0.556841 | 0.278420 | − | 0.960459i | \(-0.410189\pi\) | ||||
0.278420 | + | 0.960459i | \(0.410189\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.01847 | −0.233654 | −0.116827 | − | 0.993152i | \(-0.537272\pi\) | ||||
−0.116827 | + | 0.993152i | \(0.537272\pi\) | |||||||
\(20\) | −0.812175 | −0.181608 | ||||||||
\(21\) | −2.80411 | −0.611907 | ||||||||
\(22\) | −4.04933 | −0.863319 | ||||||||
\(23\) | −8.19340 | −1.70844 | −0.854221 | − | 0.519910i | \(-0.825965\pi\) | ||||
−0.854221 | + | 0.519910i | \(0.825965\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.34037 | −0.868074 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.80411 | −0.529927 | ||||||||
\(29\) | 6.94281 | 1.28925 | 0.644624 | − | 0.764500i | \(-0.277014\pi\) | ||||
0.644624 | + | 0.764500i | \(0.277014\pi\) | |||||||
\(30\) | 0.812175 | 0.148282 | ||||||||
\(31\) | 1.13390 | 0.203655 | 0.101827 | − | 0.994802i | \(-0.467531\pi\) | ||||
0.101827 | + | 0.994802i | \(0.467531\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.04933 | 0.704897 | ||||||||
\(34\) | −2.29591 | −0.393746 | ||||||||
\(35\) | 2.27743 | 0.384955 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.96324 | 0.980351 | 0.490175 | − | 0.871624i | \(-0.336933\pi\) | ||||
0.490175 | + | 0.871624i | \(0.336933\pi\) | |||||||
\(38\) | 1.01847 | 0.165218 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0.812175 | 0.128416 | ||||||||
\(41\) | −10.6535 | −1.66379 | −0.831896 | − | 0.554932i | \(-0.812744\pi\) | ||||
−0.831896 | + | 0.554932i | \(0.812744\pi\) | |||||||
\(42\) | 2.80411 | 0.432683 | ||||||||
\(43\) | −8.47462 | −1.29237 | −0.646184 | − | 0.763182i | \(-0.723636\pi\) | ||||
−0.646184 | + | 0.763182i | \(0.723636\pi\) | |||||||
\(44\) | 4.04933 | 0.610459 | ||||||||
\(45\) | −0.812175 | −0.121072 | ||||||||
\(46\) | 8.19340 | 1.20805 | ||||||||
\(47\) | −4.10776 | −0.599179 | −0.299589 | − | 0.954068i | \(-0.596850\pi\) | ||||
−0.299589 | + | 0.954068i | \(0.596850\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0.863023 | 0.123289 | ||||||||
\(50\) | 4.34037 | 0.613821 | ||||||||
\(51\) | 2.29591 | 0.321492 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 12.4604 | 1.71157 | 0.855784 | − | 0.517334i | \(-0.173075\pi\) | ||||
0.855784 | + | 0.517334i | \(0.173075\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −3.28876 | −0.443456 | ||||||||
\(56\) | 2.80411 | 0.374715 | ||||||||
\(57\) | −1.01847 | −0.134900 | ||||||||
\(58\) | −6.94281 | −0.911636 | ||||||||
\(59\) | 0.884938 | 0.115209 | 0.0576045 | − | 0.998339i | \(-0.481654\pi\) | ||||
0.0576045 | + | 0.998339i | \(0.481654\pi\) | |||||||
\(60\) | −0.812175 | −0.104851 | ||||||||
\(61\) | −4.79433 | −0.613851 | −0.306926 | − | 0.951733i | \(-0.599300\pi\) | ||||
−0.306926 | + | 0.951733i | \(0.599300\pi\) | |||||||
\(62\) | −1.13390 | −0.144006 | ||||||||
\(63\) | −2.80411 | −0.353284 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.812175 | −0.100738 | ||||||||
\(66\) | −4.04933 | −0.498438 | ||||||||
\(67\) | 0.580237 | 0.0708873 | 0.0354436 | − | 0.999372i | \(-0.488716\pi\) | ||||
0.0354436 | + | 0.999372i | \(0.488716\pi\) | |||||||
\(68\) | 2.29591 | 0.278420 | ||||||||
\(69\) | −8.19340 | −0.986369 | ||||||||
\(70\) | −2.27743 | −0.272204 | ||||||||
\(71\) | −8.92029 | −1.05864 | −0.529322 | − | 0.848421i | \(-0.677554\pi\) | ||||
−0.529322 | + | 0.848421i | \(0.677554\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 15.9992 | 1.87256 | 0.936282 | − | 0.351249i | \(-0.114243\pi\) | ||||
0.936282 | + | 0.351249i | \(0.114243\pi\) | |||||||
\(74\) | −5.96324 | −0.693213 | ||||||||
\(75\) | −4.34037 | −0.501183 | ||||||||
\(76\) | −1.01847 | −0.116827 | ||||||||
\(77\) | −11.3547 | −1.29399 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −9.00058 | −1.01264 | −0.506322 | − | 0.862344i | \(-0.668995\pi\) | ||||
−0.506322 | + | 0.862344i | \(0.668995\pi\) | |||||||
\(80\) | −0.812175 | −0.0908039 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.6535 | 1.17648 | ||||||||
\(83\) | −4.73672 | −0.519923 | −0.259962 | − | 0.965619i | \(-0.583710\pi\) | ||||
−0.259962 | + | 0.965619i | \(0.583710\pi\) | |||||||
\(84\) | −2.80411 | −0.305953 | ||||||||
\(85\) | −1.86468 | −0.202253 | ||||||||
\(86\) | 8.47462 | 0.913842 | ||||||||
\(87\) | 6.94281 | 0.744348 | ||||||||
\(88\) | −4.04933 | −0.431660 | ||||||||
\(89\) | 10.1598 | 1.07694 | 0.538469 | − | 0.842645i | \(-0.319003\pi\) | ||||
0.538469 | + | 0.842645i | \(0.319003\pi\) | |||||||
\(90\) | 0.812175 | 0.0856107 | ||||||||
\(91\) | −2.80411 | −0.293950 | ||||||||
\(92\) | −8.19340 | −0.854221 | ||||||||
\(93\) | 1.13390 | 0.117580 | ||||||||
\(94\) | 4.10776 | 0.423683 | ||||||||
\(95\) | 0.827178 | 0.0848667 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 4.77835 | 0.485168 | 0.242584 | − | 0.970130i | \(-0.422005\pi\) | ||||
0.242584 | + | 0.970130i | \(0.422005\pi\) | |||||||
\(98\) | −0.863023 | −0.0871785 | ||||||||
\(99\) | 4.04933 | 0.406973 | ||||||||
\(100\) | −4.34037 | −0.434037 | ||||||||
\(101\) | −15.0451 | −1.49704 | −0.748522 | − | 0.663110i | \(-0.769236\pi\) | ||||
−0.748522 | + | 0.663110i | \(0.769236\pi\) | |||||||
\(102\) | −2.29591 | −0.227329 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 2.27743 | 0.222254 | ||||||||
\(106\) | −12.4604 | −1.21026 | ||||||||
\(107\) | 0.0930370 | 0.00899423 | 0.00449712 | − | 0.999990i | \(-0.498569\pi\) | ||||
0.00449712 | + | 0.999990i | \(0.498569\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −7.16487 | −0.686270 | −0.343135 | − | 0.939286i | \(-0.611489\pi\) | ||||
−0.343135 | + | 0.939286i | \(0.611489\pi\) | |||||||
\(110\) | 3.28876 | 0.313571 | ||||||||
\(111\) | 5.96324 | 0.566006 | ||||||||
\(112\) | −2.80411 | −0.264963 | ||||||||
\(113\) | −5.38039 | −0.506145 | −0.253072 | − | 0.967447i | \(-0.581441\pi\) | ||||
−0.253072 | + | 0.967447i | \(0.581441\pi\) | |||||||
\(114\) | 1.01847 | 0.0953888 | ||||||||
\(115\) | 6.65447 | 0.620533 | ||||||||
\(116\) | 6.94281 | 0.644624 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −0.884938 | −0.0814651 | ||||||||
\(119\) | −6.43799 | −0.590170 | ||||||||
\(120\) | 0.812175 | 0.0741411 | ||||||||
\(121\) | 5.39704 | 0.490640 | ||||||||
\(122\) | 4.79433 | 0.434058 | ||||||||
\(123\) | −10.6535 | −0.960591 | ||||||||
\(124\) | 1.13390 | 0.101827 | ||||||||
\(125\) | 7.58601 | 0.678514 | ||||||||
\(126\) | 2.80411 | 0.249810 | ||||||||
\(127\) | −10.4196 | −0.924593 | −0.462296 | − | 0.886725i | \(-0.652974\pi\) | ||||
−0.462296 | + | 0.886725i | \(0.652974\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −8.47462 | −0.746148 | ||||||||
\(130\) | 0.812175 | 0.0712324 | ||||||||
\(131\) | 10.0961 | 0.882104 | 0.441052 | − | 0.897482i | \(-0.354605\pi\) | ||||
0.441052 | + | 0.897482i | \(0.354605\pi\) | |||||||
\(132\) | 4.04933 | 0.352449 | ||||||||
\(133\) | 2.85591 | 0.247639 | ||||||||
\(134\) | −0.580237 | −0.0501249 | ||||||||
\(135\) | −0.812175 | −0.0699009 | ||||||||
\(136\) | −2.29591 | −0.196873 | ||||||||
\(137\) | 6.33088 | 0.540883 | 0.270442 | − | 0.962736i | \(-0.412830\pi\) | ||||
0.270442 | + | 0.962736i | \(0.412830\pi\) | |||||||
\(138\) | 8.19340 | 0.697468 | ||||||||
\(139\) | −7.51896 | −0.637750 | −0.318875 | − | 0.947797i | \(-0.603305\pi\) | ||||
−0.318875 | + | 0.947797i | \(0.603305\pi\) | |||||||
\(140\) | 2.27743 | 0.192478 | ||||||||
\(141\) | −4.10776 | −0.345936 | ||||||||
\(142\) | 8.92029 | 0.748574 | ||||||||
\(143\) | 4.04933 | 0.338622 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −5.63878 | −0.468275 | ||||||||
\(146\) | −15.9992 | −1.32410 | ||||||||
\(147\) | 0.863023 | 0.0711810 | ||||||||
\(148\) | 5.96324 | 0.490175 | ||||||||
\(149\) | 5.49662 | 0.450300 | 0.225150 | − | 0.974324i | \(-0.427713\pi\) | ||||
0.225150 | + | 0.974324i | \(0.427713\pi\) | |||||||
\(150\) | 4.34037 | 0.354390 | ||||||||
\(151\) | 6.71314 | 0.546308 | 0.273154 | − | 0.961970i | \(-0.411933\pi\) | ||||
0.273154 | + | 0.961970i | \(0.411933\pi\) | |||||||
\(152\) | 1.01847 | 0.0826091 | ||||||||
\(153\) | 2.29591 | 0.185614 | ||||||||
\(154\) | 11.3547 | 0.914992 | ||||||||
\(155\) | −0.920926 | −0.0739706 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −8.77574 | −0.700381 | −0.350190 | − | 0.936679i | \(-0.613883\pi\) | ||||
−0.350190 | + | 0.936679i | \(0.613883\pi\) | |||||||
\(158\) | 9.00058 | 0.716048 | ||||||||
\(159\) | 12.4604 | 0.988174 | ||||||||
\(160\) | 0.812175 | 0.0642080 | ||||||||
\(161\) | 22.9752 | 1.81070 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 19.3491 | 1.51554 | 0.757769 | − | 0.652523i | \(-0.226289\pi\) | ||||
0.757769 | + | 0.652523i | \(0.226289\pi\) | |||||||
\(164\) | −10.6535 | −0.831896 | ||||||||
\(165\) | −3.28876 | −0.256030 | ||||||||
\(166\) | 4.73672 | 0.367641 | ||||||||
\(167\) | −10.1438 | −0.784952 | −0.392476 | − | 0.919762i | \(-0.628381\pi\) | ||||
−0.392476 | + | 0.919762i | \(0.628381\pi\) | |||||||
\(168\) | 2.80411 | 0.216342 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 1.86468 | 0.143015 | ||||||||
\(171\) | −1.01847 | −0.0778846 | ||||||||
\(172\) | −8.47462 | −0.646184 | ||||||||
\(173\) | −15.1679 | −1.15319 | −0.576596 | − | 0.817029i | \(-0.695619\pi\) | ||||
−0.576596 | + | 0.817029i | \(0.695619\pi\) | |||||||
\(174\) | −6.94281 | −0.526333 | ||||||||
\(175\) | 12.1709 | 0.920032 | ||||||||
\(176\) | 4.04933 | 0.305229 | ||||||||
\(177\) | 0.884938 | 0.0665160 | ||||||||
\(178\) | −10.1598 | −0.761510 | ||||||||
\(179\) | −20.7858 | −1.55360 | −0.776802 | − | 0.629745i | \(-0.783159\pi\) | ||||
−0.776802 | + | 0.629745i | \(0.783159\pi\) | |||||||
\(180\) | −0.812175 | −0.0605359 | ||||||||
\(181\) | 8.49683 | 0.631565 | 0.315782 | − | 0.948832i | \(-0.397733\pi\) | ||||
0.315782 | + | 0.948832i | \(0.397733\pi\) | |||||||
\(182\) | 2.80411 | 0.207854 | ||||||||
\(183\) | −4.79433 | −0.354407 | ||||||||
\(184\) | 8.19340 | 0.604025 | ||||||||
\(185\) | −4.84319 | −0.356079 | ||||||||
\(186\) | −1.13390 | −0.0831417 | ||||||||
\(187\) | 9.29690 | 0.679857 | ||||||||
\(188\) | −4.10776 | −0.299589 | ||||||||
\(189\) | −2.80411 | −0.203969 | ||||||||
\(190\) | −0.827178 | −0.0600098 | ||||||||
\(191\) | −24.5573 | −1.77690 | −0.888452 | − | 0.458970i | \(-0.848218\pi\) | ||||
−0.888452 | + | 0.458970i | \(0.848218\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 20.6351 | 1.48535 | 0.742675 | − | 0.669652i | \(-0.233557\pi\) | ||||
0.742675 | + | 0.669652i | \(0.233557\pi\) | |||||||
\(194\) | −4.77835 | −0.343066 | ||||||||
\(195\) | −0.812175 | −0.0581610 | ||||||||
\(196\) | 0.863023 | 0.0616445 | ||||||||
\(197\) | 12.8639 | 0.916515 | 0.458258 | − | 0.888819i | \(-0.348474\pi\) | ||||
0.458258 | + | 0.888819i | \(0.348474\pi\) | |||||||
\(198\) | −4.04933 | −0.287773 | ||||||||
\(199\) | 23.5266 | 1.66776 | 0.833879 | − | 0.551948i | \(-0.186115\pi\) | ||||
0.833879 | + | 0.551948i | \(0.186115\pi\) | |||||||
\(200\) | 4.34037 | 0.306911 | ||||||||
\(201\) | 0.580237 | 0.0409268 | ||||||||
\(202\) | 15.0451 | 1.05857 | ||||||||
\(203\) | −19.4684 | −1.36641 | ||||||||
\(204\) | 2.29591 | 0.160746 | ||||||||
\(205\) | 8.65247 | 0.604315 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | −8.19340 | −0.569481 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −4.12413 | −0.285272 | ||||||||
\(210\) | −2.27743 | −0.157157 | ||||||||
\(211\) | 5.66546 | 0.390027 | 0.195013 | − | 0.980801i | \(-0.437525\pi\) | ||||
0.195013 | + | 0.980801i | \(0.437525\pi\) | |||||||
\(212\) | 12.4604 | 0.855784 | ||||||||
\(213\) | −8.92029 | −0.611208 | ||||||||
\(214\) | −0.0930370 | −0.00635988 | ||||||||
\(215\) | 6.88287 | 0.469408 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −3.17958 | −0.215844 | ||||||||
\(218\) | 7.16487 | 0.485266 | ||||||||
\(219\) | 15.9992 | 1.08113 | ||||||||
\(220\) | −3.28876 | −0.221728 | ||||||||
\(221\) | 2.29591 | 0.154440 | ||||||||
\(222\) | −5.96324 | −0.400227 | ||||||||
\(223\) | 2.11119 | 0.141376 | 0.0706878 | − | 0.997498i | \(-0.477481\pi\) | ||||
0.0706878 | + | 0.997498i | \(0.477481\pi\) | |||||||
\(224\) | 2.80411 | 0.187357 | ||||||||
\(225\) | −4.34037 | −0.289358 | ||||||||
\(226\) | 5.38039 | 0.357898 | ||||||||
\(227\) | 16.6256 | 1.10348 | 0.551739 | − | 0.834017i | \(-0.313964\pi\) | ||||
0.551739 | + | 0.834017i | \(0.313964\pi\) | |||||||
\(228\) | −1.01847 | −0.0674500 | ||||||||
\(229\) | −22.6417 | −1.49620 | −0.748101 | − | 0.663585i | \(-0.769034\pi\) | ||||
−0.748101 | + | 0.663585i | \(0.769034\pi\) | |||||||
\(230\) | −6.65447 | −0.438783 | ||||||||
\(231\) | −11.3547 | −0.747088 | ||||||||
\(232\) | −6.94281 | −0.455818 | ||||||||
\(233\) | −0.805363 | −0.0527611 | −0.0263806 | − | 0.999652i | \(-0.508398\pi\) | ||||
−0.0263806 | + | 0.999652i | \(0.508398\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 3.33622 | 0.217631 | ||||||||
\(236\) | 0.884938 | 0.0576045 | ||||||||
\(237\) | −9.00058 | −0.584651 | ||||||||
\(238\) | 6.43799 | 0.417313 | ||||||||
\(239\) | −27.6450 | −1.78821 | −0.894103 | − | 0.447861i | \(-0.852186\pi\) | ||||
−0.894103 | + | 0.447861i | \(0.852186\pi\) | |||||||
\(240\) | −0.812175 | −0.0524257 | ||||||||
\(241\) | 5.25526 | 0.338521 | 0.169260 | − | 0.985571i | \(-0.445862\pi\) | ||||
0.169260 | + | 0.985571i | \(0.445862\pi\) | |||||||
\(242\) | −5.39704 | −0.346935 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.79433 | −0.306926 | ||||||||
\(245\) | −0.700926 | −0.0447805 | ||||||||
\(246\) | 10.6535 | 0.679240 | ||||||||
\(247\) | −1.01847 | −0.0648039 | ||||||||
\(248\) | −1.13390 | −0.0720028 | ||||||||
\(249\) | −4.73672 | −0.300178 | ||||||||
\(250\) | −7.58601 | −0.479782 | ||||||||
\(251\) | −11.7511 | −0.741721 | −0.370860 | − | 0.928689i | \(-0.620937\pi\) | ||||
−0.370860 | + | 0.928689i | \(0.620937\pi\) | |||||||
\(252\) | −2.80411 | −0.176642 | ||||||||
\(253\) | −33.1777 | −2.08587 | ||||||||
\(254\) | 10.4196 | 0.653786 | ||||||||
\(255\) | −1.86468 | −0.116771 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.55065 | 0.283862 | 0.141931 | − | 0.989877i | \(-0.454669\pi\) | ||||
0.141931 | + | 0.989877i | \(0.454669\pi\) | |||||||
\(258\) | 8.47462 | 0.527607 | ||||||||
\(259\) | −16.7216 | −1.03903 | ||||||||
\(260\) | −0.812175 | −0.0503689 | ||||||||
\(261\) | 6.94281 | 0.429749 | ||||||||
\(262\) | −10.0961 | −0.623742 | ||||||||
\(263\) | 2.07134 | 0.127724 | 0.0638620 | − | 0.997959i | \(-0.479658\pi\) | ||||
0.0638620 | + | 0.997959i | \(0.479658\pi\) | |||||||
\(264\) | −4.04933 | −0.249219 | ||||||||
\(265\) | −10.1200 | −0.621668 | ||||||||
\(266\) | −2.85591 | −0.175107 | ||||||||
\(267\) | 10.1598 | 0.621771 | ||||||||
\(268\) | 0.580237 | 0.0354436 | ||||||||
\(269\) | −16.0087 | −0.976067 | −0.488034 | − | 0.872825i | \(-0.662286\pi\) | ||||
−0.488034 | + | 0.872825i | \(0.662286\pi\) | |||||||
\(270\) | 0.812175 | 0.0494274 | ||||||||
\(271\) | −22.3206 | −1.35588 | −0.677940 | − | 0.735118i | \(-0.737127\pi\) | ||||
−0.677940 | + | 0.735118i | \(0.737127\pi\) | |||||||
\(272\) | 2.29591 | 0.139210 | ||||||||
\(273\) | −2.80411 | −0.169712 | ||||||||
\(274\) | −6.33088 | −0.382462 | ||||||||
\(275\) | −17.5756 | −1.05985 | ||||||||
\(276\) | −8.19340 | −0.493185 | ||||||||
\(277\) | 1.43459 | 0.0861962 | 0.0430981 | − | 0.999071i | \(-0.486277\pi\) | ||||
0.0430981 | + | 0.999071i | \(0.486277\pi\) | |||||||
\(278\) | 7.51896 | 0.450958 | ||||||||
\(279\) | 1.13390 | 0.0678849 | ||||||||
\(280\) | −2.27743 | −0.136102 | ||||||||
\(281\) | −27.6330 | −1.64845 | −0.824223 | − | 0.566266i | \(-0.808388\pi\) | ||||
−0.824223 | + | 0.566266i | \(0.808388\pi\) | |||||||
\(282\) | 4.10776 | 0.244614 | ||||||||
\(283\) | −29.2077 | −1.73621 | −0.868107 | − | 0.496376i | \(-0.834664\pi\) | ||||
−0.868107 | + | 0.496376i | \(0.834664\pi\) | |||||||
\(284\) | −8.92029 | −0.529322 | ||||||||
\(285\) | 0.827178 | 0.0489978 | ||||||||
\(286\) | −4.04933 | −0.239442 | ||||||||
\(287\) | 29.8735 | 1.76338 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −11.7288 | −0.689928 | ||||||||
\(290\) | 5.63878 | 0.331120 | ||||||||
\(291\) | 4.77835 | 0.280112 | ||||||||
\(292\) | 15.9992 | 0.936282 | ||||||||
\(293\) | −25.8130 | −1.50801 | −0.754005 | − | 0.656868i | \(-0.771881\pi\) | ||||
−0.754005 | + | 0.656868i | \(0.771881\pi\) | |||||||
\(294\) | −0.863023 | −0.0503325 | ||||||||
\(295\) | −0.718724 | −0.0418457 | ||||||||
\(296\) | −5.96324 | −0.346606 | ||||||||
\(297\) | 4.04933 | 0.234966 | ||||||||
\(298\) | −5.49662 | −0.318410 | ||||||||
\(299\) | −8.19340 | −0.473837 | ||||||||
\(300\) | −4.34037 | −0.250592 | ||||||||
\(301\) | 23.7637 | 1.36972 | ||||||||
\(302\) | −6.71314 | −0.386298 | ||||||||
\(303\) | −15.0451 | −0.864319 | ||||||||
\(304\) | −1.01847 | −0.0584134 | ||||||||
\(305\) | 3.89384 | 0.222960 | ||||||||
\(306\) | −2.29591 | −0.131249 | ||||||||
\(307\) | −4.20527 | −0.240008 | −0.120004 | − | 0.992773i | \(-0.538291\pi\) | ||||
−0.120004 | + | 0.992773i | \(0.538291\pi\) | |||||||
\(308\) | −11.3547 | −0.646997 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 0.920926 | 0.0523051 | ||||||||
\(311\) | 6.72177 | 0.381156 | 0.190578 | − | 0.981672i | \(-0.438964\pi\) | ||||
0.190578 | + | 0.981672i | \(0.438964\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −20.8705 | −1.17967 | −0.589835 | − | 0.807524i | \(-0.700807\pi\) | ||||
−0.589835 | + | 0.807524i | \(0.700807\pi\) | |||||||
\(314\) | 8.77574 | 0.495244 | ||||||||
\(315\) | 2.27743 | 0.128318 | ||||||||
\(316\) | −9.00058 | −0.506322 | ||||||||
\(317\) | −11.3847 | −0.639431 | −0.319715 | − | 0.947514i | \(-0.603587\pi\) | ||||
−0.319715 | + | 0.947514i | \(0.603587\pi\) | |||||||
\(318\) | −12.4604 | −0.698745 | ||||||||
\(319\) | 28.1137 | 1.57407 | ||||||||
\(320\) | −0.812175 | −0.0454019 | ||||||||
\(321\) | 0.0930370 | 0.00519282 | ||||||||
\(322\) | −22.9752 | −1.28036 | ||||||||
\(323\) | −2.33833 | −0.130108 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.34037 | −0.240761 | ||||||||
\(326\) | −19.3491 | −1.07165 | ||||||||
\(327\) | −7.16487 | −0.396218 | ||||||||
\(328\) | 10.6535 | 0.588239 | ||||||||
\(329\) | 11.5186 | 0.635042 | ||||||||
\(330\) | 3.28876 | 0.181040 | ||||||||
\(331\) | −1.90596 | −0.104761 | −0.0523805 | − | 0.998627i | \(-0.516681\pi\) | ||||
−0.0523805 | + | 0.998627i | \(0.516681\pi\) | |||||||
\(332\) | −4.73672 | −0.259962 | ||||||||
\(333\) | 5.96324 | 0.326784 | ||||||||
\(334\) | 10.1438 | 0.555045 | ||||||||
\(335\) | −0.471254 | −0.0257474 | ||||||||
\(336\) | −2.80411 | −0.152977 | ||||||||
\(337\) | 22.3056 | 1.21506 | 0.607532 | − | 0.794295i | \(-0.292159\pi\) | ||||
0.607532 | + | 0.794295i | \(0.292159\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −5.38039 | −0.292223 | ||||||||
\(340\) | −1.86468 | −0.101127 | ||||||||
\(341\) | 4.59154 | 0.248646 | ||||||||
\(342\) | 1.01847 | 0.0550727 | ||||||||
\(343\) | 17.2087 | 0.929185 | ||||||||
\(344\) | 8.47462 | 0.456921 | ||||||||
\(345\) | 6.65447 | 0.358265 | ||||||||
\(346\) | 15.1679 | 0.815430 | ||||||||
\(347\) | −34.3314 | −1.84301 | −0.921503 | − | 0.388371i | \(-0.873038\pi\) | ||||
−0.921503 | + | 0.388371i | \(0.873038\pi\) | |||||||
\(348\) | 6.94281 | 0.372174 | ||||||||
\(349\) | −25.3383 | −1.35633 | −0.678165 | − | 0.734910i | \(-0.737224\pi\) | ||||
−0.678165 | + | 0.734910i | \(0.737224\pi\) | |||||||
\(350\) | −12.1709 | −0.650561 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −4.04933 | −0.215830 | ||||||||
\(353\) | −9.54966 | −0.508277 | −0.254139 | − | 0.967168i | \(-0.581792\pi\) | ||||
−0.254139 | + | 0.967168i | \(0.581792\pi\) | |||||||
\(354\) | −0.884938 | −0.0470339 | ||||||||
\(355\) | 7.24483 | 0.384516 | ||||||||
\(356\) | 10.1598 | 0.538469 | ||||||||
\(357\) | −6.43799 | −0.340735 | ||||||||
\(358\) | 20.7858 | 1.09856 | ||||||||
\(359\) | −3.57808 | −0.188844 | −0.0944218 | − | 0.995532i | \(-0.530100\pi\) | ||||
−0.0944218 | + | 0.995532i | \(0.530100\pi\) | |||||||
\(360\) | 0.812175 | 0.0428054 | ||||||||
\(361\) | −17.9627 | −0.945406 | ||||||||
\(362\) | −8.49683 | −0.446584 | ||||||||
\(363\) | 5.39704 | 0.283271 | ||||||||
\(364\) | −2.80411 | −0.146975 | ||||||||
\(365\) | −12.9941 | −0.680145 | ||||||||
\(366\) | 4.79433 | 0.250604 | ||||||||
\(367\) | −3.17092 | −0.165521 | −0.0827604 | − | 0.996569i | \(-0.526374\pi\) | ||||
−0.0827604 | + | 0.996569i | \(0.526374\pi\) | |||||||
\(368\) | −8.19340 | −0.427110 | ||||||||
\(369\) | −10.6535 | −0.554597 | ||||||||
\(370\) | 4.84319 | 0.251786 | ||||||||
\(371\) | −34.9403 | −1.81401 | ||||||||
\(372\) | 1.13390 | 0.0587901 | ||||||||
\(373\) | 26.5049 | 1.37237 | 0.686185 | − | 0.727427i | \(-0.259284\pi\) | ||||
0.686185 | + | 0.727427i | \(0.259284\pi\) | |||||||
\(374\) | −9.29690 | −0.480731 | ||||||||
\(375\) | 7.58601 | 0.391740 | ||||||||
\(376\) | 4.10776 | 0.211842 | ||||||||
\(377\) | 6.94281 | 0.357573 | ||||||||
\(378\) | 2.80411 | 0.144228 | ||||||||
\(379\) | −26.3016 | −1.35102 | −0.675512 | − | 0.737349i | \(-0.736078\pi\) | ||||
−0.675512 | + | 0.737349i | \(0.736078\pi\) | |||||||
\(380\) | 0.827178 | 0.0424333 | ||||||||
\(381\) | −10.4196 | −0.533814 | ||||||||
\(382\) | 24.5573 | 1.25646 | ||||||||
\(383\) | −10.3778 | −0.530279 | −0.265140 | − | 0.964210i | \(-0.585418\pi\) | ||||
−0.265140 | + | 0.964210i | \(0.585418\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 9.22204 | 0.469999 | ||||||||
\(386\) | −20.6351 | −1.05030 | ||||||||
\(387\) | −8.47462 | −0.430789 | ||||||||
\(388\) | 4.77835 | 0.242584 | ||||||||
\(389\) | −11.6907 | −0.592743 | −0.296372 | − | 0.955073i | \(-0.595777\pi\) | ||||
−0.296372 | + | 0.955073i | \(0.595777\pi\) | |||||||
\(390\) | 0.812175 | 0.0411261 | ||||||||
\(391\) | −18.8113 | −0.951330 | ||||||||
\(392\) | −0.863023 | −0.0435893 | ||||||||
\(393\) | 10.0961 | 0.509283 | ||||||||
\(394\) | −12.8639 | −0.648074 | ||||||||
\(395\) | 7.31005 | 0.367808 | ||||||||
\(396\) | 4.04933 | 0.203486 | ||||||||
\(397\) | −10.2444 | −0.514151 | −0.257075 | − | 0.966391i | \(-0.582759\pi\) | ||||
−0.257075 | + | 0.966391i | \(0.582759\pi\) | |||||||
\(398\) | −23.5266 | −1.17928 | ||||||||
\(399\) | 2.85591 | 0.142974 | ||||||||
\(400\) | −4.34037 | −0.217019 | ||||||||
\(401\) | −29.0137 | −1.44887 | −0.724437 | − | 0.689341i | \(-0.757900\pi\) | ||||
−0.724437 | + | 0.689341i | \(0.757900\pi\) | |||||||
\(402\) | −0.580237 | −0.0289396 | ||||||||
\(403\) | 1.13390 | 0.0564837 | ||||||||
\(404\) | −15.0451 | −0.748522 | ||||||||
\(405\) | −0.812175 | −0.0403573 | ||||||||
\(406\) | 19.4684 | 0.966200 | ||||||||
\(407\) | 24.1471 | 1.19693 | ||||||||
\(408\) | −2.29591 | −0.113665 | ||||||||
\(409\) | 29.3234 | 1.44995 | 0.724973 | − | 0.688777i | \(-0.241852\pi\) | ||||
0.724973 | + | 0.688777i | \(0.241852\pi\) | |||||||
\(410\) | −8.65247 | −0.427315 | ||||||||
\(411\) | 6.33088 | 0.312279 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | −2.48146 | −0.122105 | ||||||||
\(414\) | 8.19340 | 0.402684 | ||||||||
\(415\) | 3.84705 | 0.188844 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −7.51896 | −0.368205 | ||||||||
\(418\) | 4.12413 | 0.201718 | ||||||||
\(419\) | −10.6366 | −0.519632 | −0.259816 | − | 0.965658i | \(-0.583662\pi\) | ||||
−0.259816 | + | 0.965658i | \(0.583662\pi\) | |||||||
\(420\) | 2.27743 | 0.111127 | ||||||||
\(421\) | −6.31510 | −0.307779 | −0.153889 | − | 0.988088i | \(-0.549180\pi\) | ||||
−0.153889 | + | 0.988088i | \(0.549180\pi\) | |||||||
\(422\) | −5.66546 | −0.275790 | ||||||||
\(423\) | −4.10776 | −0.199726 | ||||||||
\(424\) | −12.4604 | −0.605131 | ||||||||
\(425\) | −9.96512 | −0.483379 | ||||||||
\(426\) | 8.92029 | 0.432190 | ||||||||
\(427\) | 13.4438 | 0.650592 | ||||||||
\(428\) | 0.0930370 | 0.00449712 | ||||||||
\(429\) | 4.04933 | 0.195503 | ||||||||
\(430\) | −6.88287 | −0.331921 | ||||||||
\(431\) | −32.7901 | −1.57944 | −0.789721 | − | 0.613466i | \(-0.789775\pi\) | ||||
−0.789721 | + | 0.613466i | \(0.789775\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −23.0398 | −1.10722 | −0.553611 | − | 0.832776i | \(-0.686750\pi\) | ||||
−0.553611 | + | 0.832776i | \(0.686750\pi\) | |||||||
\(434\) | 3.17958 | 0.152625 | ||||||||
\(435\) | −5.63878 | −0.270359 | ||||||||
\(436\) | −7.16487 | −0.343135 | ||||||||
\(437\) | 8.34476 | 0.399184 | ||||||||
\(438\) | −15.9992 | −0.764471 | ||||||||
\(439\) | 37.5925 | 1.79419 | 0.897096 | − | 0.441837i | \(-0.145673\pi\) | ||||
0.897096 | + | 0.441837i | \(0.145673\pi\) | |||||||
\(440\) | 3.28876 | 0.156785 | ||||||||
\(441\) | 0.863023 | 0.0410963 | ||||||||
\(442\) | −2.29591 | −0.109205 | ||||||||
\(443\) | 34.6459 | 1.64607 | 0.823037 | − | 0.567988i | \(-0.192278\pi\) | ||||
0.823037 | + | 0.567988i | \(0.192278\pi\) | |||||||
\(444\) | 5.96324 | 0.283003 | ||||||||
\(445\) | −8.25154 | −0.391161 | ||||||||
\(446\) | −2.11119 | −0.0999676 | ||||||||
\(447\) | 5.49662 | 0.259981 | ||||||||
\(448\) | −2.80411 | −0.132482 | ||||||||
\(449\) | −11.6519 | −0.549888 | −0.274944 | − | 0.961460i | \(-0.588659\pi\) | ||||
−0.274944 | + | 0.961460i | \(0.588659\pi\) | |||||||
\(450\) | 4.34037 | 0.204607 | ||||||||
\(451\) | −43.1394 | −2.03135 | ||||||||
\(452\) | −5.38039 | −0.253072 | ||||||||
\(453\) | 6.71314 | 0.315411 | ||||||||
\(454\) | −16.6256 | −0.780277 | ||||||||
\(455\) | 2.27743 | 0.106767 | ||||||||
\(456\) | 1.01847 | 0.0476944 | ||||||||
\(457\) | 26.5669 | 1.24275 | 0.621374 | − | 0.783514i | \(-0.286575\pi\) | ||||
0.621374 | + | 0.783514i | \(0.286575\pi\) | |||||||
\(458\) | 22.6417 | 1.05797 | ||||||||
\(459\) | 2.29591 | 0.107164 | ||||||||
\(460\) | 6.65447 | 0.310266 | ||||||||
\(461\) | −10.3671 | −0.482844 | −0.241422 | − | 0.970420i | \(-0.577614\pi\) | ||||
−0.241422 | + | 0.970420i | \(0.577614\pi\) | |||||||
\(462\) | 11.3547 | 0.528271 | ||||||||
\(463\) | 29.0583 | 1.35046 | 0.675228 | − | 0.737609i | \(-0.264045\pi\) | ||||
0.675228 | + | 0.737609i | \(0.264045\pi\) | |||||||
\(464\) | 6.94281 | 0.322312 | ||||||||
\(465\) | −0.920926 | −0.0427069 | ||||||||
\(466\) | 0.805363 | 0.0373077 | ||||||||
\(467\) | 5.95392 | 0.275514 | 0.137757 | − | 0.990466i | \(-0.456011\pi\) | ||||
0.137757 | + | 0.990466i | \(0.456011\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −1.62705 | −0.0751301 | ||||||||
\(470\) | −3.33622 | −0.153888 | ||||||||
\(471\) | −8.77574 | −0.404365 | ||||||||
\(472\) | −0.884938 | −0.0407326 | ||||||||
\(473\) | −34.3165 | −1.57787 | ||||||||
\(474\) | 9.00058 | 0.413411 | ||||||||
\(475\) | 4.42055 | 0.202829 | ||||||||
\(476\) | −6.43799 | −0.295085 | ||||||||
\(477\) | 12.4604 | 0.570523 | ||||||||
\(478\) | 27.6450 | 1.26445 | ||||||||
\(479\) | −2.33530 | −0.106703 | −0.0533513 | − | 0.998576i | \(-0.516990\pi\) | ||||
−0.0533513 | + | 0.998576i | \(0.516990\pi\) | |||||||
\(480\) | 0.812175 | 0.0370705 | ||||||||
\(481\) | 5.96324 | 0.271900 | ||||||||
\(482\) | −5.25526 | −0.239370 | ||||||||
\(483\) | 22.9752 | 1.04541 | ||||||||
\(484\) | 5.39704 | 0.245320 | ||||||||
\(485\) | −3.88086 | −0.176221 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 17.3845 | 0.787769 | 0.393884 | − | 0.919160i | \(-0.371131\pi\) | ||||
0.393884 | + | 0.919160i | \(0.371131\pi\) | |||||||
\(488\) | 4.79433 | 0.217029 | ||||||||
\(489\) | 19.3491 | 0.874996 | ||||||||
\(490\) | 0.700926 | 0.0316646 | ||||||||
\(491\) | −19.7595 | −0.891733 | −0.445867 | − | 0.895099i | \(-0.647104\pi\) | ||||
−0.445867 | + | 0.895099i | \(0.647104\pi\) | |||||||
\(492\) | −10.6535 | −0.480295 | ||||||||
\(493\) | 15.9401 | 0.717906 | ||||||||
\(494\) | 1.01847 | 0.0458233 | ||||||||
\(495\) | −3.28876 | −0.147819 | ||||||||
\(496\) | 1.13390 | 0.0509137 | ||||||||
\(497\) | 25.0135 | 1.12201 | ||||||||
\(498\) | 4.73672 | 0.212258 | ||||||||
\(499\) | −0.921867 | −0.0412684 | −0.0206342 | − | 0.999787i | \(-0.506569\pi\) | ||||
−0.0206342 | + | 0.999787i | \(0.506569\pi\) | |||||||
\(500\) | 7.58601 | 0.339257 | ||||||||
\(501\) | −10.1438 | −0.453192 | ||||||||
\(502\) | 11.7511 | 0.524476 | ||||||||
\(503\) | −12.8080 | −0.571078 | −0.285539 | − | 0.958367i | \(-0.592173\pi\) | ||||
−0.285539 | + | 0.958367i | \(0.592173\pi\) | |||||||
\(504\) | 2.80411 | 0.124905 | ||||||||
\(505\) | 12.2193 | 0.543750 | ||||||||
\(506\) | 33.1777 | 1.47493 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −10.4196 | −0.462296 | ||||||||
\(509\) | 5.13942 | 0.227801 | 0.113900 | − | 0.993492i | \(-0.463666\pi\) | ||||
0.113900 | + | 0.993492i | \(0.463666\pi\) | |||||||
\(510\) | 1.86468 | 0.0825696 | ||||||||
\(511\) | −44.8635 | −1.98464 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.01847 | −0.0449667 | ||||||||
\(514\) | −4.55065 | −0.200721 | ||||||||
\(515\) | 0.812175 | 0.0357887 | ||||||||
\(516\) | −8.47462 | −0.373074 | ||||||||
\(517\) | −16.6337 | −0.731548 | ||||||||
\(518\) | 16.7216 | 0.734704 | ||||||||
\(519\) | −15.1679 | −0.665796 | ||||||||
\(520\) | 0.812175 | 0.0356162 | ||||||||
\(521\) | 6.97500 | 0.305580 | 0.152790 | − | 0.988259i | \(-0.451174\pi\) | ||||
0.152790 | + | 0.988259i | \(0.451174\pi\) | |||||||
\(522\) | −6.94281 | −0.303879 | ||||||||
\(523\) | −0.406703 | −0.0177839 | −0.00889194 | − | 0.999960i | \(-0.502830\pi\) | ||||
−0.00889194 | + | 0.999960i | \(0.502830\pi\) | |||||||
\(524\) | 10.0961 | 0.441052 | ||||||||
\(525\) | 12.1709 | 0.531180 | ||||||||
\(526\) | −2.07134 | −0.0903145 | ||||||||
\(527\) | 2.60334 | 0.113403 | ||||||||
\(528\) | 4.04933 | 0.176224 | ||||||||
\(529\) | 44.1318 | 1.91877 | ||||||||
\(530\) | 10.1200 | 0.439586 | ||||||||
\(531\) | 0.884938 | 0.0384030 | ||||||||
\(532\) | 2.85591 | 0.123819 | ||||||||
\(533\) | −10.6535 | −0.461453 | ||||||||
\(534\) | −10.1598 | −0.439658 | ||||||||
\(535\) | −0.0755623 | −0.00326684 | ||||||||
\(536\) | −0.580237 | −0.0250624 | ||||||||
\(537\) | −20.7858 | −0.896973 | ||||||||
\(538\) | 16.0087 | 0.690184 | ||||||||
\(539\) | 3.49466 | 0.150526 | ||||||||
\(540\) | −0.812175 | −0.0349504 | ||||||||
\(541\) | 43.1680 | 1.85594 | 0.927969 | − | 0.372657i | \(-0.121553\pi\) | ||||
0.927969 | + | 0.372657i | \(0.121553\pi\) | |||||||
\(542\) | 22.3206 | 0.958751 | ||||||||
\(543\) | 8.49683 | 0.364634 | ||||||||
\(544\) | −2.29591 | −0.0984365 | ||||||||
\(545\) | 5.81913 | 0.249264 | ||||||||
\(546\) | 2.80411 | 0.120005 | ||||||||
\(547\) | −31.5402 | −1.34856 | −0.674280 | − | 0.738476i | \(-0.735546\pi\) | ||||
−0.674280 | + | 0.738476i | \(0.735546\pi\) | |||||||
\(548\) | 6.33088 | 0.270442 | ||||||||
\(549\) | −4.79433 | −0.204617 | ||||||||
\(550\) | 17.5756 | 0.749425 | ||||||||
\(551\) | −7.07107 | −0.301238 | ||||||||
\(552\) | 8.19340 | 0.348734 | ||||||||
\(553\) | 25.2386 | 1.07325 | ||||||||
\(554\) | −1.43459 | −0.0609499 | ||||||||
\(555\) | −4.84319 | −0.205582 | ||||||||
\(556\) | −7.51896 | −0.318875 | ||||||||
\(557\) | −1.08304 | −0.0458899 | −0.0229449 | − | 0.999737i | \(-0.507304\pi\) | ||||
−0.0229449 | + | 0.999737i | \(0.507304\pi\) | |||||||
\(558\) | −1.13390 | −0.0480019 | ||||||||
\(559\) | −8.47462 | −0.358438 | ||||||||
\(560\) | 2.27743 | 0.0962388 | ||||||||
\(561\) | 9.29690 | 0.392516 | ||||||||
\(562\) | 27.6330 | 1.16563 | ||||||||
\(563\) | 19.7982 | 0.834393 | 0.417196 | − | 0.908816i | \(-0.363013\pi\) | ||||
0.417196 | + | 0.908816i | \(0.363013\pi\) | |||||||
\(564\) | −4.10776 | −0.172968 | ||||||||
\(565\) | 4.36982 | 0.183840 | ||||||||
\(566\) | 29.2077 | 1.22769 | ||||||||
\(567\) | −2.80411 | −0.117761 | ||||||||
\(568\) | 8.92029 | 0.374287 | ||||||||
\(569\) | −27.6820 | −1.16049 | −0.580246 | − | 0.814442i | \(-0.697043\pi\) | ||||
−0.580246 | + | 0.814442i | \(0.697043\pi\) | |||||||
\(570\) | −0.827178 | −0.0346467 | ||||||||
\(571\) | 20.4317 | 0.855042 | 0.427521 | − | 0.904005i | \(-0.359387\pi\) | ||||
0.427521 | + | 0.904005i | \(0.359387\pi\) | |||||||
\(572\) | 4.04933 | 0.169311 | ||||||||
\(573\) | −24.5573 | −1.02590 | ||||||||
\(574\) | −29.8735 | −1.24689 | ||||||||
\(575\) | 35.5624 | 1.48305 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −6.45607 | −0.268770 | −0.134385 | − | 0.990929i | \(-0.542906\pi\) | ||||
−0.134385 | + | 0.990929i | \(0.542906\pi\) | |||||||
\(578\) | 11.7288 | 0.487853 | ||||||||
\(579\) | 20.6351 | 0.857567 | ||||||||
\(580\) | −5.63878 | −0.234137 | ||||||||
\(581\) | 13.2823 | 0.551042 | ||||||||
\(582\) | −4.77835 | −0.198069 | ||||||||
\(583\) | 50.4562 | 2.08968 | ||||||||
\(584\) | −15.9992 | −0.662052 | ||||||||
\(585\) | −0.812175 | −0.0335793 | ||||||||
\(586\) | 25.8130 | 1.06632 | ||||||||
\(587\) | −7.18362 | −0.296500 | −0.148250 | − | 0.988950i | \(-0.547364\pi\) | ||||
−0.148250 | + | 0.988950i | \(0.547364\pi\) | |||||||
\(588\) | 0.863023 | 0.0355905 | ||||||||
\(589\) | −1.15485 | −0.0475847 | ||||||||
\(590\) | 0.718724 | 0.0295894 | ||||||||
\(591\) | 12.8639 | 0.529150 | ||||||||
\(592\) | 5.96324 | 0.245088 | ||||||||
\(593\) | 43.5311 | 1.78761 | 0.893804 | − | 0.448458i | \(-0.148027\pi\) | ||||
0.893804 | + | 0.448458i | \(0.148027\pi\) | |||||||
\(594\) | −4.04933 | −0.166146 | ||||||||
\(595\) | 5.22877 | 0.214359 | ||||||||
\(596\) | 5.49662 | 0.225150 | ||||||||
\(597\) | 23.5266 | 0.962880 | ||||||||
\(598\) | 8.19340 | 0.335053 | ||||||||
\(599\) | −11.6674 | −0.476716 | −0.238358 | − | 0.971177i | \(-0.576609\pi\) | ||||
−0.238358 | + | 0.971177i | \(0.576609\pi\) | |||||||
\(600\) | 4.34037 | 0.177195 | ||||||||
\(601\) | 43.9848 | 1.79418 | 0.897090 | − | 0.441849i | \(-0.145677\pi\) | ||||
0.897090 | + | 0.441849i | \(0.145677\pi\) | |||||||
\(602\) | −23.7637 | −0.968538 | ||||||||
\(603\) | 0.580237 | 0.0236291 | ||||||||
\(604\) | 6.71314 | 0.273154 | ||||||||
\(605\) | −4.38334 | −0.178208 | ||||||||
\(606\) | 15.0451 | 0.611166 | ||||||||
\(607\) | 6.80863 | 0.276354 | 0.138177 | − | 0.990408i | \(-0.455876\pi\) | ||||
0.138177 | + | 0.990408i | \(0.455876\pi\) | |||||||
\(608\) | 1.01847 | 0.0413045 | ||||||||
\(609\) | −19.4684 | −0.788899 | ||||||||
\(610\) | −3.89384 | −0.157657 | ||||||||
\(611\) | −4.10776 | −0.166182 | ||||||||
\(612\) | 2.29591 | 0.0928068 | ||||||||
\(613\) | −34.8280 | −1.40669 | −0.703344 | − | 0.710850i | \(-0.748311\pi\) | ||||
−0.703344 | + | 0.710850i | \(0.748311\pi\) | |||||||
\(614\) | 4.20527 | 0.169711 | ||||||||
\(615\) | 8.65247 | 0.348901 | ||||||||
\(616\) | 11.3547 | 0.457496 | ||||||||
\(617\) | 36.1839 | 1.45671 | 0.728354 | − | 0.685201i | \(-0.240286\pi\) | ||||
0.728354 | + | 0.685201i | \(0.240286\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | −13.4757 | −0.541632 | −0.270816 | − | 0.962631i | \(-0.587294\pi\) | ||||
−0.270816 | + | 0.962631i | \(0.587294\pi\) | |||||||
\(620\) | −0.920926 | −0.0369853 | ||||||||
\(621\) | −8.19340 | −0.328790 | ||||||||
\(622\) | −6.72177 | −0.269518 | ||||||||
\(623\) | −28.4892 | −1.14140 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 15.5407 | 0.621628 | ||||||||
\(626\) | 20.8705 | 0.834153 | ||||||||
\(627\) | −4.12413 | −0.164702 | ||||||||
\(628\) | −8.77574 | −0.350190 | ||||||||
\(629\) | 13.6911 | 0.545899 | ||||||||
\(630\) | −2.27743 | −0.0907348 | ||||||||
\(631\) | 15.6495 | 0.622998 | 0.311499 | − | 0.950246i | \(-0.399169\pi\) | ||||
0.311499 | + | 0.950246i | \(0.399169\pi\) | |||||||
\(632\) | 9.00058 | 0.358024 | ||||||||
\(633\) | 5.66546 | 0.225182 | ||||||||
\(634\) | 11.3847 | 0.452146 | ||||||||
\(635\) | 8.46256 | 0.335827 | ||||||||
\(636\) | 12.4604 | 0.494087 | ||||||||
\(637\) | 0.863023 | 0.0341942 | ||||||||
\(638\) | −28.1137 | −1.11303 | ||||||||
\(639\) | −8.92029 | −0.352881 | ||||||||
\(640\) | 0.812175 | 0.0321040 | ||||||||
\(641\) | −17.3158 | −0.683934 | −0.341967 | − | 0.939712i | \(-0.611093\pi\) | ||||
−0.341967 | + | 0.939712i | \(0.611093\pi\) | |||||||
\(642\) | −0.0930370 | −0.00367188 | ||||||||
\(643\) | 44.8856 | 1.77011 | 0.885057 | − | 0.465483i | \(-0.154119\pi\) | ||||
0.885057 | + | 0.465483i | \(0.154119\pi\) | |||||||
\(644\) | 22.9752 | 0.905349 | ||||||||
\(645\) | 6.88287 | 0.271013 | ||||||||
\(646\) | 2.33833 | 0.0920002 | ||||||||
\(647\) | 34.9463 | 1.37388 | 0.686940 | − | 0.726715i | \(-0.258954\pi\) | ||||
0.686940 | + | 0.726715i | \(0.258954\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 3.58340 | 0.140661 | ||||||||
\(650\) | 4.34037 | 0.170243 | ||||||||
\(651\) | −3.17958 | −0.124618 | ||||||||
\(652\) | 19.3491 | 0.757769 | ||||||||
\(653\) | −36.4184 | −1.42516 | −0.712581 | − | 0.701590i | \(-0.752474\pi\) | ||||
−0.712581 | + | 0.701590i | \(0.752474\pi\) | |||||||
\(654\) | 7.16487 | 0.280169 | ||||||||
\(655\) | −8.19983 | −0.320394 | ||||||||
\(656\) | −10.6535 | −0.415948 | ||||||||
\(657\) | 15.9992 | 0.624188 | ||||||||
\(658\) | −11.5186 | −0.449042 | ||||||||
\(659\) | −27.5734 | −1.07411 | −0.537053 | − | 0.843549i | \(-0.680462\pi\) | ||||
−0.537053 | + | 0.843549i | \(0.680462\pi\) | |||||||
\(660\) | −3.28876 | −0.128015 | ||||||||
\(661\) | −32.6336 | −1.26930 | −0.634651 | − | 0.772799i | \(-0.718856\pi\) | ||||
−0.634651 | + | 0.772799i | \(0.718856\pi\) | |||||||
\(662\) | 1.90596 | 0.0740773 | ||||||||
\(663\) | 2.29591 | 0.0891659 | ||||||||
\(664\) | 4.73672 | 0.183821 | ||||||||
\(665\) | −2.31950 | −0.0899462 | ||||||||
\(666\) | −5.96324 | −0.231071 | ||||||||
\(667\) | −56.8852 | −2.20261 | ||||||||
\(668\) | −10.1438 | −0.392476 | ||||||||
\(669\) | 2.11119 | 0.0816232 | ||||||||
\(670\) | 0.471254 | 0.0182061 | ||||||||
\(671\) | −19.4138 | −0.749462 | ||||||||
\(672\) | 2.80411 | 0.108171 | ||||||||
\(673\) | −41.2898 | −1.59161 | −0.795803 | − | 0.605556i | \(-0.792951\pi\) | ||||
−0.795803 | + | 0.605556i | \(0.792951\pi\) | |||||||
\(674\) | −22.3056 | −0.859181 | ||||||||
\(675\) | −4.34037 | −0.167061 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −8.12620 | −0.312315 | −0.156158 | − | 0.987732i | \(-0.549911\pi\) | ||||
−0.156158 | + | 0.987732i | \(0.549911\pi\) | |||||||
\(678\) | 5.38039 | 0.206633 | ||||||||
\(679\) | −13.3990 | −0.514207 | ||||||||
\(680\) | 1.86468 | 0.0715073 | ||||||||
\(681\) | 16.6256 | 0.637094 | ||||||||
\(682\) | −4.59154 | −0.175819 | ||||||||
\(683\) | −2.65217 | −0.101482 | −0.0507412 | − | 0.998712i | \(-0.516158\pi\) | ||||
−0.0507412 | + | 0.998712i | \(0.516158\pi\) | |||||||
\(684\) | −1.01847 | −0.0389423 | ||||||||
\(685\) | −5.14178 | −0.196457 | ||||||||
\(686\) | −17.2087 | −0.657033 | ||||||||
\(687\) | −22.6417 | −0.863833 | ||||||||
\(688\) | −8.47462 | −0.323092 | ||||||||
\(689\) | 12.4604 | 0.474703 | ||||||||
\(690\) | −6.65447 | −0.253331 | ||||||||
\(691\) | −5.60099 | −0.213072 | −0.106536 | − | 0.994309i | \(-0.533976\pi\) | ||||
−0.106536 | + | 0.994309i | \(0.533976\pi\) | |||||||
\(692\) | −15.1679 | −0.576596 | ||||||||
\(693\) | −11.3547 | −0.431331 | ||||||||
\(694\) | 34.3314 | 1.30320 | ||||||||
\(695\) | 6.10671 | 0.231641 | ||||||||
\(696\) | −6.94281 | −0.263167 | ||||||||
\(697\) | −24.4594 | −0.926467 | ||||||||
\(698\) | 25.3383 | 0.959070 | ||||||||
\(699\) | −0.805363 | −0.0304616 | ||||||||
\(700\) | 12.1709 | 0.460016 | ||||||||
\(701\) | −3.74962 | −0.141621 | −0.0708106 | − | 0.997490i | \(-0.522559\pi\) | ||||
−0.0708106 | + | 0.997490i | \(0.522559\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −6.07340 | −0.229063 | ||||||||
\(704\) | 4.04933 | 0.152615 | ||||||||
\(705\) | 3.33622 | 0.125649 | ||||||||
\(706\) | 9.54966 | 0.359406 | ||||||||
\(707\) | 42.1881 | 1.58665 | ||||||||
\(708\) | 0.884938 | 0.0332580 | ||||||||
\(709\) | 18.7137 | 0.702809 | 0.351405 | − | 0.936224i | \(-0.385704\pi\) | ||||
0.351405 | + | 0.936224i | \(0.385704\pi\) | |||||||
\(710\) | −7.24483 | −0.271894 | ||||||||
\(711\) | −9.00058 | −0.337548 | ||||||||
\(712\) | −10.1598 | −0.380755 | ||||||||
\(713\) | −9.29051 | −0.347932 | ||||||||
\(714\) | 6.43799 | 0.240936 | ||||||||
\(715\) | −3.28876 | −0.122993 | ||||||||
\(716\) | −20.7858 | −0.776802 | ||||||||
\(717\) | −27.6450 | −1.03242 | ||||||||
\(718\) | 3.57808 | 0.133533 | ||||||||
\(719\) | −49.5279 | −1.84708 | −0.923540 | − | 0.383501i | \(-0.874718\pi\) | ||||
−0.923540 | + | 0.383501i | \(0.874718\pi\) | |||||||
\(720\) | −0.812175 | −0.0302680 | ||||||||
\(721\) | 2.80411 | 0.104430 | ||||||||
\(722\) | 17.9627 | 0.668503 | ||||||||
\(723\) | 5.25526 | 0.195445 | ||||||||
\(724\) | 8.49683 | 0.315782 | ||||||||
\(725\) | −30.1344 | −1.11916 | ||||||||
\(726\) | −5.39704 | −0.200303 | ||||||||
\(727\) | 25.3400 | 0.939807 | 0.469904 | − | 0.882718i | \(-0.344289\pi\) | ||||
0.469904 | + | 0.882718i | \(0.344289\pi\) | |||||||
\(728\) | 2.80411 | 0.103927 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.9941 | 0.480935 | ||||||||
\(731\) | −19.4570 | −0.719643 | ||||||||
\(732\) | −4.79433 | −0.177204 | ||||||||
\(733\) | −47.0633 | −1.73832 | −0.869162 | − | 0.494528i | \(-0.835341\pi\) | ||||
−0.869162 | + | 0.494528i | \(0.835341\pi\) | |||||||
\(734\) | 3.17092 | 0.117041 | ||||||||
\(735\) | −0.700926 | −0.0258540 | ||||||||
\(736\) | 8.19340 | 0.302013 | ||||||||
\(737\) | 2.34957 | 0.0865475 | ||||||||
\(738\) | 10.6535 | 0.392159 | ||||||||
\(739\) | −48.7133 | −1.79195 | −0.895973 | − | 0.444108i | \(-0.853521\pi\) | ||||
−0.895973 | + | 0.444108i | \(0.853521\pi\) | |||||||
\(740\) | −4.84319 | −0.178039 | ||||||||
\(741\) | −1.01847 | −0.0374145 | ||||||||
\(742\) | 34.9403 | 1.28270 | ||||||||
\(743\) | 3.11576 | 0.114306 | 0.0571530 | − | 0.998365i | \(-0.481798\pi\) | ||||
0.0571530 | + | 0.998365i | \(0.481798\pi\) | |||||||
\(744\) | −1.13390 | −0.0415709 | ||||||||
\(745\) | −4.46421 | −0.163556 | ||||||||
\(746\) | −26.5049 | −0.970412 | ||||||||
\(747\) | −4.73672 | −0.173308 | ||||||||
\(748\) | 9.29690 | 0.339928 | ||||||||
\(749\) | −0.260886 | −0.00953257 | ||||||||
\(750\) | −7.58601 | −0.277002 | ||||||||
\(751\) | −10.5836 | −0.386200 | −0.193100 | − | 0.981179i | \(-0.561854\pi\) | ||||
−0.193100 | + | 0.981179i | \(0.561854\pi\) | |||||||
\(752\) | −4.10776 | −0.149795 | ||||||||
\(753\) | −11.7511 | −0.428233 | ||||||||
\(754\) | −6.94281 | −0.252842 | ||||||||
\(755\) | −5.45224 | −0.198428 | ||||||||
\(756\) | −2.80411 | −0.101984 | ||||||||
\(757\) | −44.7518 | −1.62653 | −0.813266 | − | 0.581893i | \(-0.802312\pi\) | ||||
−0.813266 | + | 0.581893i | \(0.802312\pi\) | |||||||
\(758\) | 26.3016 | 0.955319 | ||||||||
\(759\) | −33.1777 | −1.20428 | ||||||||
\(760\) | −0.827178 | −0.0300049 | ||||||||
\(761\) | −32.1122 | −1.16407 | −0.582034 | − | 0.813164i | \(-0.697743\pi\) | ||||
−0.582034 | + | 0.813164i | \(0.697743\pi\) | |||||||
\(762\) | 10.4196 | 0.377464 | ||||||||
\(763\) | 20.0911 | 0.727346 | ||||||||
\(764\) | −24.5573 | −0.888452 | ||||||||
\(765\) | −1.86468 | −0.0674178 | ||||||||
\(766\) | 10.3778 | 0.374964 | ||||||||
\(767\) | 0.884938 | 0.0319532 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −10.9588 | −0.395185 | −0.197593 | − | 0.980284i | \(-0.563312\pi\) | ||||
−0.197593 | + | 0.980284i | \(0.563312\pi\) | |||||||
\(770\) | −9.22204 | −0.332339 | ||||||||
\(771\) | 4.55065 | 0.163888 | ||||||||
\(772\) | 20.6351 | 0.742675 | ||||||||
\(773\) | 2.54269 | 0.0914540 | 0.0457270 | − | 0.998954i | \(-0.485440\pi\) | ||||
0.0457270 | + | 0.998954i | \(0.485440\pi\) | |||||||
\(774\) | 8.47462 | 0.304614 | ||||||||
\(775\) | −4.92156 | −0.176788 | ||||||||
\(776\) | −4.77835 | −0.171533 | ||||||||
\(777\) | −16.7216 | −0.599883 | ||||||||
\(778\) | 11.6907 | 0.419133 | ||||||||
\(779\) | 10.8503 | 0.388751 | ||||||||
\(780\) | −0.812175 | −0.0290805 | ||||||||
\(781\) | −36.1212 | −1.29252 | ||||||||
\(782\) | 18.8113 | 0.672692 | ||||||||
\(783\) | 6.94281 | 0.248116 | ||||||||
\(784\) | 0.863023 | 0.0308223 | ||||||||
\(785\) | 7.12744 | 0.254389 | ||||||||
\(786\) | −10.0961 | −0.360117 | ||||||||
\(787\) | −29.6963 | −1.05856 | −0.529279 | − | 0.848448i | \(-0.677538\pi\) | ||||
−0.529279 | + | 0.848448i | \(0.677538\pi\) | |||||||
\(788\) | 12.8639 | 0.458258 | ||||||||
\(789\) | 2.07134 | 0.0737415 | ||||||||
\(790\) | −7.31005 | −0.260080 | ||||||||
\(791\) | 15.0872 | 0.536439 | ||||||||
\(792\) | −4.04933 | −0.143887 | ||||||||
\(793\) | −4.79433 | −0.170252 | ||||||||
\(794\) | 10.2444 | 0.363559 | ||||||||
\(795\) | −10.1200 | −0.358920 | ||||||||
\(796\) | 23.5266 | 0.833879 | ||||||||
\(797\) | 12.2889 | 0.435294 | 0.217647 | − | 0.976028i | \(-0.430162\pi\) | ||||
0.217647 | + | 0.976028i | \(0.430162\pi\) | |||||||
\(798\) | −2.85591 | −0.101098 | ||||||||
\(799\) | −9.43107 | −0.333647 | ||||||||
\(800\) | 4.34037 | 0.153455 | ||||||||
\(801\) | 10.1598 | 0.358979 | ||||||||
\(802\) | 29.0137 | 1.02451 | ||||||||
\(803\) | 64.7860 | 2.28625 | ||||||||
\(804\) | 0.580237 | 0.0204634 | ||||||||
\(805\) | −18.6599 | −0.657674 | ||||||||
\(806\) | −1.13390 | −0.0399400 | ||||||||
\(807\) | −16.0087 | −0.563533 | ||||||||
\(808\) | 15.0451 | 0.529285 | ||||||||
\(809\) | 38.1455 | 1.34112 | 0.670562 | − | 0.741854i | \(-0.266053\pi\) | ||||
0.670562 | + | 0.741854i | \(0.266053\pi\) | |||||||
\(810\) | 0.812175 | 0.0285369 | ||||||||
\(811\) | 34.7872 | 1.22154 | 0.610771 | − | 0.791807i | \(-0.290860\pi\) | ||||
0.610771 | + | 0.791807i | \(0.290860\pi\) | |||||||
\(812\) | −19.4684 | −0.683207 | ||||||||
\(813\) | −22.3206 | −0.782817 | ||||||||
\(814\) | −24.1471 | −0.846356 | ||||||||
\(815\) | −15.7148 | −0.550467 | ||||||||
\(816\) | 2.29591 | 0.0803731 | ||||||||
\(817\) | 8.63117 | 0.301966 | ||||||||
\(818\) | −29.3234 | −1.02527 | ||||||||
\(819\) | −2.80411 | −0.0979835 | ||||||||
\(820\) | 8.65247 | 0.302158 | ||||||||
\(821\) | 15.0268 | 0.524438 | 0.262219 | − | 0.965008i | \(-0.415546\pi\) | ||||
0.262219 | + | 0.965008i | \(0.415546\pi\) | |||||||
\(822\) | −6.33088 | −0.220815 | ||||||||
\(823\) | 38.1909 | 1.33125 | 0.665626 | − | 0.746286i | \(-0.268165\pi\) | ||||
0.665626 | + | 0.746286i | \(0.268165\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | −17.5756 | −0.611903 | ||||||||
\(826\) | 2.48146 | 0.0863411 | ||||||||
\(827\) | −19.1560 | −0.666121 | −0.333060 | − | 0.942905i | \(-0.608081\pi\) | ||||
−0.333060 | + | 0.942905i | \(0.608081\pi\) | |||||||
\(828\) | −8.19340 | −0.284740 | ||||||||
\(829\) | −4.32580 | −0.150241 | −0.0751207 | − | 0.997174i | \(-0.523934\pi\) | ||||
−0.0751207 | + | 0.997174i | \(0.523934\pi\) | |||||||
\(830\) | −3.84705 | −0.133533 | ||||||||
\(831\) | 1.43459 | 0.0497654 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 1.98143 | 0.0686524 | ||||||||
\(834\) | 7.51896 | 0.260360 | ||||||||
\(835\) | 8.23855 | 0.285107 | ||||||||
\(836\) | −4.12413 | −0.142636 | ||||||||
\(837\) | 1.13390 | 0.0391934 | ||||||||
\(838\) | 10.6366 | 0.367435 | ||||||||
\(839\) | 4.61218 | 0.159230 | 0.0796151 | − | 0.996826i | \(-0.474631\pi\) | ||||
0.0796151 | + | 0.996826i | \(0.474631\pi\) | |||||||
\(840\) | −2.27743 | −0.0785787 | ||||||||
\(841\) | 19.2026 | 0.662160 | ||||||||
\(842\) | 6.31510 | 0.217633 | ||||||||
\(843\) | −27.6330 | −0.951730 | ||||||||
\(844\) | 5.66546 | 0.195013 | ||||||||
\(845\) | −0.812175 | −0.0279397 | ||||||||
\(846\) | 4.10776 | 0.141228 | ||||||||
\(847\) | −15.1339 | −0.520007 | ||||||||
\(848\) | 12.4604 | 0.427892 | ||||||||
\(849\) | −29.2077 | −1.00240 | ||||||||
\(850\) | 9.96512 | 0.341801 | ||||||||
\(851\) | −48.8592 | −1.67487 | ||||||||
\(852\) | −8.92029 | −0.305604 | ||||||||
\(853\) | 7.79993 | 0.267065 | 0.133532 | − | 0.991044i | \(-0.457368\pi\) | ||||
0.133532 | + | 0.991044i | \(0.457368\pi\) | |||||||
\(854\) | −13.4438 | −0.460038 | ||||||||
\(855\) | 0.827178 | 0.0282889 | ||||||||
\(856\) | −0.0930370 | −0.00317994 | ||||||||
\(857\) | −1.80417 | −0.0616293 | −0.0308146 | − | 0.999525i | \(-0.509810\pi\) | ||||
−0.0308146 | + | 0.999525i | \(0.509810\pi\) | |||||||
\(858\) | −4.04933 | −0.138242 | ||||||||
\(859\) | −35.2598 | −1.20305 | −0.601525 | − | 0.798854i | \(-0.705440\pi\) | ||||
−0.601525 | + | 0.798854i | \(0.705440\pi\) | |||||||
\(860\) | 6.88287 | 0.234704 | ||||||||
\(861\) | 29.8735 | 1.01809 | ||||||||
\(862\) | 32.7901 | 1.11683 | ||||||||
\(863\) | −43.8890 | −1.49400 | −0.747000 | − | 0.664824i | \(-0.768506\pi\) | ||||
−0.747000 | + | 0.664824i | \(0.768506\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 12.3190 | 0.418857 | ||||||||
\(866\) | 23.0398 | 0.782924 | ||||||||
\(867\) | −11.7288 | −0.398330 | ||||||||
\(868\) | −3.17958 | −0.107922 | ||||||||
\(869\) | −36.4463 | −1.23636 | ||||||||
\(870\) | 5.63878 | 0.191172 | ||||||||
\(871\) | 0.580237 | 0.0196606 | ||||||||
\(872\) | 7.16487 | 0.242633 | ||||||||
\(873\) | 4.77835 | 0.161723 | ||||||||
\(874\) | −8.34476 | −0.282266 | ||||||||
\(875\) | −21.2720 | −0.719125 | ||||||||
\(876\) | 15.9992 | 0.540563 | ||||||||
\(877\) | 12.7397 | 0.430191 | 0.215095 | − | 0.976593i | \(-0.430994\pi\) | ||||
0.215095 | + | 0.976593i | \(0.430994\pi\) | |||||||
\(878\) | −37.5925 | −1.26868 | ||||||||
\(879\) | −25.8130 | −0.870650 | ||||||||
\(880\) | −3.28876 | −0.110864 | ||||||||
\(881\) | −32.4436 | −1.09305 | −0.546526 | − | 0.837442i | \(-0.684050\pi\) | ||||
−0.546526 | + | 0.837442i | \(0.684050\pi\) | |||||||
\(882\) | −0.863023 | −0.0290595 | ||||||||
\(883\) | 1.56011 | 0.0525018 | 0.0262509 | − | 0.999655i | \(-0.491643\pi\) | ||||
0.0262509 | + | 0.999655i | \(0.491643\pi\) | |||||||
\(884\) | 2.29591 | 0.0772199 | ||||||||
\(885\) | −0.718724 | −0.0241596 | ||||||||
\(886\) | −34.6459 | −1.16395 | ||||||||
\(887\) | −42.1818 | −1.41633 | −0.708163 | − | 0.706049i | \(-0.750476\pi\) | ||||
−0.708163 | + | 0.706049i | \(0.750476\pi\) | |||||||
\(888\) | −5.96324 | −0.200113 | ||||||||
\(889\) | 29.2178 | 0.979933 | ||||||||
\(890\) | 8.25154 | 0.276592 | ||||||||
\(891\) | 4.04933 | 0.135658 | ||||||||
\(892\) | 2.11119 | 0.0706878 | ||||||||
\(893\) | 4.18365 | 0.140000 | ||||||||
\(894\) | −5.49662 | −0.183834 | ||||||||
\(895\) | 16.8817 | 0.564293 | ||||||||
\(896\) | 2.80411 | 0.0936787 | ||||||||
\(897\) | −8.19340 | −0.273570 | ||||||||
\(898\) | 11.6519 | 0.388829 | ||||||||
\(899\) | 7.87247 | 0.262562 | ||||||||
\(900\) | −4.34037 | −0.144679 | ||||||||
\(901\) | 28.6080 | 0.953071 | ||||||||
\(902\) | 43.1394 | 1.43638 | ||||||||
\(903\) | 23.7637 | 0.790808 | ||||||||
\(904\) | 5.38039 | 0.178949 | ||||||||
\(905\) | −6.90091 | −0.229394 | ||||||||
\(906\) | −6.71314 | −0.223029 | ||||||||
\(907\) | 6.97762 | 0.231688 | 0.115844 | − | 0.993267i | \(-0.463043\pi\) | ||||
0.115844 | + | 0.993267i | \(0.463043\pi\) | |||||||
\(908\) | 16.6256 | 0.551739 | ||||||||
\(909\) | −15.0451 | −0.499015 | ||||||||
\(910\) | −2.27743 | −0.0754959 | ||||||||
\(911\) | 45.6638 | 1.51291 | 0.756454 | − | 0.654047i | \(-0.226930\pi\) | ||||
0.756454 | + | 0.654047i | \(0.226930\pi\) | |||||||
\(912\) | −1.01847 | −0.0337250 | ||||||||
\(913\) | −19.1805 | −0.634783 | ||||||||
\(914\) | −26.5669 | −0.878755 | ||||||||
\(915\) | 3.89384 | 0.128726 | ||||||||
\(916\) | −22.6417 | −0.748101 | ||||||||
\(917\) | −28.3107 | −0.934901 | ||||||||
\(918\) | −2.29591 | −0.0757764 | ||||||||
\(919\) | −38.2955 | −1.26325 | −0.631625 | − | 0.775274i | \(-0.717612\pi\) | ||||
−0.631625 | + | 0.775274i | \(0.717612\pi\) | |||||||
\(920\) | −6.65447 | −0.219391 | ||||||||
\(921\) | −4.20527 | −0.138569 | ||||||||
\(922\) | 10.3671 | 0.341423 | ||||||||
\(923\) | −8.92029 | −0.293615 | ||||||||
\(924\) | −11.3547 | −0.373544 | ||||||||
\(925\) | −25.8827 | −0.851018 | ||||||||
\(926\) | −29.0583 | −0.954916 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −6.94281 | −0.227909 | ||||||||
\(929\) | 21.2377 | 0.696787 | 0.348394 | − | 0.937348i | \(-0.386727\pi\) | ||||
0.348394 | + | 0.937348i | \(0.386727\pi\) | |||||||
\(930\) | 0.920926 | 0.0301984 | ||||||||
\(931\) | −0.878966 | −0.0288069 | ||||||||
\(932\) | −0.805363 | −0.0263806 | ||||||||
\(933\) | 6.72177 | 0.220061 | ||||||||
\(934\) | −5.95392 | −0.194818 | ||||||||
\(935\) | −7.55071 | −0.246935 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 15.2350 | 0.497706 | 0.248853 | − | 0.968541i | \(-0.419946\pi\) | ||||
0.248853 | + | 0.968541i | \(0.419946\pi\) | |||||||
\(938\) | 1.62705 | 0.0531250 | ||||||||
\(939\) | −20.8705 | −0.681083 | ||||||||
\(940\) | 3.33622 | 0.108816 | ||||||||
\(941\) | 10.3780 | 0.338315 | 0.169157 | − | 0.985589i | \(-0.445895\pi\) | ||||
0.169157 | + | 0.985589i | \(0.445895\pi\) | |||||||
\(942\) | 8.77574 | 0.285929 | ||||||||
\(943\) | 87.2881 | 2.84249 | ||||||||
\(944\) | 0.884938 | 0.0288023 | ||||||||
\(945\) | 2.27743 | 0.0740847 | ||||||||
\(946\) | 34.3165 | 1.11573 | ||||||||
\(947\) | −14.8925 | −0.483943 | −0.241971 | − | 0.970283i | \(-0.577794\pi\) | ||||
−0.241971 | + | 0.970283i | \(0.577794\pi\) | |||||||
\(948\) | −9.00058 | −0.292325 | ||||||||
\(949\) | 15.9992 | 0.519356 | ||||||||
\(950\) | −4.42055 | −0.143422 | ||||||||
\(951\) | −11.3847 | −0.369176 | ||||||||
\(952\) | 6.43799 | 0.208656 | ||||||||
\(953\) | −13.2268 | −0.428458 | −0.214229 | − | 0.976783i | \(-0.568724\pi\) | ||||
−0.214229 | + | 0.976783i | \(0.568724\pi\) | |||||||
\(954\) | −12.4604 | −0.403420 | ||||||||
\(955\) | 19.9448 | 0.645399 | ||||||||
\(956\) | −27.6450 | −0.894103 | ||||||||
\(957\) | 28.1137 | 0.908787 | ||||||||
\(958\) | 2.33530 | 0.0754501 | ||||||||
\(959\) | −17.7525 | −0.573257 | ||||||||
\(960\) | −0.812175 | −0.0262128 | ||||||||
\(961\) | −29.7143 | −0.958525 | ||||||||
\(962\) | −5.96324 | −0.192263 | ||||||||
\(963\) | 0.0930370 | 0.00299808 | ||||||||
\(964\) | 5.25526 | 0.169260 | ||||||||
\(965\) | −16.7593 | −0.539502 | ||||||||
\(966\) | −22.9752 | −0.739214 | ||||||||
\(967\) | −23.5141 | −0.756162 | −0.378081 | − | 0.925772i | \(-0.623416\pi\) | ||||
−0.378081 | + | 0.925772i | \(0.623416\pi\) | |||||||
\(968\) | −5.39704 | −0.173467 | ||||||||
\(969\) | −2.33833 | −0.0751179 | ||||||||
\(970\) | 3.88086 | 0.124607 | ||||||||
\(971\) | 13.0234 | 0.417941 | 0.208971 | − | 0.977922i | \(-0.432989\pi\) | ||||
0.208971 | + | 0.977922i | \(0.432989\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 21.0840 | 0.675922 | ||||||||
\(974\) | −17.3845 | −0.557036 | ||||||||
\(975\) | −4.34037 | −0.139003 | ||||||||
\(976\) | −4.79433 | −0.153463 | ||||||||
\(977\) | 38.2541 | 1.22386 | 0.611928 | − | 0.790913i | \(-0.290394\pi\) | ||||
0.611928 | + | 0.790913i | \(0.290394\pi\) | |||||||
\(978\) | −19.3491 | −0.618716 | ||||||||
\(979\) | 41.1404 | 1.31485 | ||||||||
\(980\) | −0.700926 | −0.0223902 | ||||||||
\(981\) | −7.16487 | −0.228757 | ||||||||
\(982\) | 19.7595 | 0.630551 | ||||||||
\(983\) | 14.4742 | 0.461656 | 0.230828 | − | 0.972995i | \(-0.425857\pi\) | ||||
0.230828 | + | 0.972995i | \(0.425857\pi\) | |||||||
\(984\) | 10.6535 | 0.339620 | ||||||||
\(985\) | −10.4477 | −0.332893 | ||||||||
\(986\) | −15.9401 | −0.507636 | ||||||||
\(987\) | 11.5186 | 0.366641 | ||||||||
\(988\) | −1.01847 | −0.0324019 | ||||||||
\(989\) | 69.4359 | 2.20793 | ||||||||
\(990\) | 3.28876 | 0.104524 | ||||||||
\(991\) | 55.8050 | 1.77270 | 0.886351 | − | 0.463013i | \(-0.153232\pi\) | ||||
0.886351 | + | 0.463013i | \(0.153232\pi\) | |||||||
\(992\) | −1.13390 | −0.0360014 | ||||||||
\(993\) | −1.90596 | −0.0604838 | ||||||||
\(994\) | −25.0135 | −0.793379 | ||||||||
\(995\) | −19.1077 | −0.605755 | ||||||||
\(996\) | −4.73672 | −0.150089 | ||||||||
\(997\) | −24.8981 | −0.788530 | −0.394265 | − | 0.918997i | \(-0.629001\pi\) | ||||
−0.394265 | + | 0.918997i | \(0.629001\pi\) | |||||||
\(998\) | 0.921867 | 0.0291812 | ||||||||
\(999\) | 5.96324 | 0.188669 |
(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 | 8034.2.a.w.1.7 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.w.1.7 | ✓ | 12 | 1.1 | even | 1 | trivial |