Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-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 | ||||||||
\(3\) | −1.53830 | −0.888139 | −0.444069 | − | 0.895992i | \(-0.646466\pi\) | ||||
−0.444069 | + | 0.895992i | \(0.646466\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.94371 | 1.76368 | 0.881841 | − | 0.471546i | \(-0.156304\pi\) | ||||
0.881841 | + | 0.471546i | \(0.156304\pi\) | |||||||
\(6\) | −1.53830 | −0.628009 | ||||||||
\(7\) | −3.54174 | −1.33865 | −0.669325 | − | 0.742970i | \(-0.733417\pi\) | ||||
−0.669325 | + | 0.742970i | \(0.733417\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.633629 | −0.211210 | ||||||||
\(10\) | 3.94371 | 1.24711 | ||||||||
\(11\) | 4.54195 | 1.36945 | 0.684725 | − | 0.728802i | \(-0.259922\pi\) | ||||
0.684725 | + | 0.728802i | \(0.259922\pi\) | |||||||
\(12\) | −1.53830 | −0.444069 | ||||||||
\(13\) | 3.47054 | 0.962556 | 0.481278 | − | 0.876568i | \(-0.340173\pi\) | ||||
0.481278 | + | 0.876568i | \(0.340173\pi\) | |||||||
\(14\) | −3.54174 | −0.946569 | ||||||||
\(15\) | −6.06662 | −1.56639 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.19553 | 0.775030 | 0.387515 | − | 0.921863i | \(-0.373334\pi\) | ||||
0.387515 | + | 0.921863i | \(0.373334\pi\) | |||||||
\(18\) | −0.633629 | −0.149348 | ||||||||
\(19\) | 1.14712 | 0.263168 | 0.131584 | − | 0.991305i | \(-0.457994\pi\) | ||||
0.131584 | + | 0.991305i | \(0.457994\pi\) | |||||||
\(20\) | 3.94371 | 0.881841 | ||||||||
\(21\) | 5.44826 | 1.18891 | ||||||||
\(22\) | 4.54195 | 0.968347 | ||||||||
\(23\) | −3.21056 | −0.669448 | −0.334724 | − | 0.942316i | \(-0.608643\pi\) | ||||
−0.334724 | + | 0.942316i | \(0.608643\pi\) | |||||||
\(24\) | −1.53830 | −0.314004 | ||||||||
\(25\) | 10.5529 | 2.11058 | ||||||||
\(26\) | 3.47054 | 0.680630 | ||||||||
\(27\) | 5.58962 | 1.07572 | ||||||||
\(28\) | −3.54174 | −0.669325 | ||||||||
\(29\) | 4.23477 | 0.786378 | 0.393189 | − | 0.919458i | \(-0.371372\pi\) | ||||
0.393189 | + | 0.919458i | \(0.371372\pi\) | |||||||
\(30\) | −6.06662 | −1.10761 | ||||||||
\(31\) | −8.64344 | −1.55241 | −0.776204 | − | 0.630482i | \(-0.782857\pi\) | ||||
−0.776204 | + | 0.630482i | \(0.782857\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −6.98689 | −1.21626 | ||||||||
\(34\) | 3.19553 | 0.548029 | ||||||||
\(35\) | −13.9676 | −2.36095 | ||||||||
\(36\) | −0.633629 | −0.105605 | ||||||||
\(37\) | −4.09499 | −0.673213 | −0.336606 | − | 0.941645i | \(-0.609279\pi\) | ||||
−0.336606 | + | 0.941645i | \(0.609279\pi\) | |||||||
\(38\) | 1.14712 | 0.186088 | ||||||||
\(39\) | −5.33874 | −0.854883 | ||||||||
\(40\) | 3.94371 | 0.623556 | ||||||||
\(41\) | −5.96700 | −0.931889 | −0.465944 | − | 0.884814i | \(-0.654285\pi\) | ||||
−0.465944 | + | 0.884814i | \(0.654285\pi\) | |||||||
\(42\) | 5.44826 | 0.840684 | ||||||||
\(43\) | 7.60529 | 1.15980 | 0.579898 | − | 0.814689i | \(-0.303092\pi\) | ||||
0.579898 | + | 0.814689i | \(0.303092\pi\) | |||||||
\(44\) | 4.54195 | 0.684725 | ||||||||
\(45\) | −2.49885 | −0.372507 | ||||||||
\(46\) | −3.21056 | −0.473372 | ||||||||
\(47\) | 4.18276 | 0.610118 | 0.305059 | − | 0.952333i | \(-0.401324\pi\) | ||||
0.305059 | + | 0.952333i | \(0.401324\pi\) | |||||||
\(48\) | −1.53830 | −0.222035 | ||||||||
\(49\) | 5.54389 | 0.791985 | ||||||||
\(50\) | 10.5529 | 1.49240 | ||||||||
\(51\) | −4.91569 | −0.688334 | ||||||||
\(52\) | 3.47054 | 0.481278 | ||||||||
\(53\) | −0.668336 | −0.0918031 | −0.0459015 | − | 0.998946i | \(-0.514616\pi\) | ||||
−0.0459015 | + | 0.998946i | \(0.514616\pi\) | |||||||
\(54\) | 5.58962 | 0.760650 | ||||||||
\(55\) | 17.9122 | 2.41527 | ||||||||
\(56\) | −3.54174 | −0.473284 | ||||||||
\(57\) | −1.76462 | −0.233729 | ||||||||
\(58\) | 4.23477 | 0.556053 | ||||||||
\(59\) | −0.928020 | −0.120818 | −0.0604090 | − | 0.998174i | \(-0.519240\pi\) | ||||
−0.0604090 | + | 0.998174i | \(0.519240\pi\) | |||||||
\(60\) | −6.06662 | −0.783197 | ||||||||
\(61\) | 8.93473 | 1.14397 | 0.571987 | − | 0.820262i | \(-0.306173\pi\) | ||||
0.571987 | + | 0.820262i | \(0.306173\pi\) | |||||||
\(62\) | −8.64344 | −1.09772 | ||||||||
\(63\) | 2.24415 | 0.282736 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 13.6868 | 1.69764 | ||||||||
\(66\) | −6.98689 | −0.860027 | ||||||||
\(67\) | −4.43454 | −0.541765 | −0.270883 | − | 0.962612i | \(-0.587316\pi\) | ||||
−0.270883 | + | 0.962612i | \(0.587316\pi\) | |||||||
\(68\) | 3.19553 | 0.387515 | ||||||||
\(69\) | 4.93881 | 0.594563 | ||||||||
\(70\) | −13.9676 | −1.66945 | ||||||||
\(71\) | −11.0025 | −1.30575 | −0.652877 | − | 0.757464i | \(-0.726438\pi\) | ||||
−0.652877 | + | 0.757464i | \(0.726438\pi\) | |||||||
\(72\) | −0.633629 | −0.0746739 | ||||||||
\(73\) | −14.9609 | −1.75104 | −0.875521 | − | 0.483180i | \(-0.839482\pi\) | ||||
−0.875521 | + | 0.483180i | \(0.839482\pi\) | |||||||
\(74\) | −4.09499 | −0.476033 | ||||||||
\(75\) | −16.2335 | −1.87448 | ||||||||
\(76\) | 1.14712 | 0.131584 | ||||||||
\(77\) | −16.0864 | −1.83321 | ||||||||
\(78\) | −5.33874 | −0.604493 | ||||||||
\(79\) | 13.8183 | 1.55467 | 0.777337 | − | 0.629084i | \(-0.216570\pi\) | ||||
0.777337 | + | 0.629084i | \(0.216570\pi\) | |||||||
\(80\) | 3.94371 | 0.440921 | ||||||||
\(81\) | −6.69763 | −0.744181 | ||||||||
\(82\) | −5.96700 | −0.658945 | ||||||||
\(83\) | 9.97381 | 1.09477 | 0.547384 | − | 0.836882i | \(-0.315624\pi\) | ||||
0.547384 | + | 0.836882i | \(0.315624\pi\) | |||||||
\(84\) | 5.44826 | 0.594454 | ||||||||
\(85\) | 12.6023 | 1.36691 | ||||||||
\(86\) | 7.60529 | 0.820100 | ||||||||
\(87\) | −6.51436 | −0.698412 | ||||||||
\(88\) | 4.54195 | 0.484174 | ||||||||
\(89\) | 8.67852 | 0.919921 | 0.459961 | − | 0.887939i | \(-0.347863\pi\) | ||||
0.459961 | + | 0.887939i | \(0.347863\pi\) | |||||||
\(90\) | −2.49885 | −0.263402 | ||||||||
\(91\) | −12.2917 | −1.28853 | ||||||||
\(92\) | −3.21056 | −0.334724 | ||||||||
\(93\) | 13.2962 | 1.37875 | ||||||||
\(94\) | 4.18276 | 0.431419 | ||||||||
\(95\) | 4.52392 | 0.464144 | ||||||||
\(96\) | −1.53830 | −0.157002 | ||||||||
\(97\) | 14.3327 | 1.45526 | 0.727632 | − | 0.685968i | \(-0.240621\pi\) | ||||
0.727632 | + | 0.685968i | \(0.240621\pi\) | |||||||
\(98\) | 5.54389 | 0.560018 | ||||||||
\(99\) | −2.87791 | −0.289241 | ||||||||
\(100\) | 10.5529 | 1.05529 | ||||||||
\(101\) | 16.2470 | 1.61664 | 0.808320 | − | 0.588744i | \(-0.200377\pi\) | ||||
0.808320 | + | 0.588744i | \(0.200377\pi\) | |||||||
\(102\) | −4.91569 | −0.486726 | ||||||||
\(103\) | −2.47083 | −0.243458 | −0.121729 | − | 0.992563i | \(-0.538844\pi\) | ||||
−0.121729 | + | 0.992563i | \(0.538844\pi\) | |||||||
\(104\) | 3.47054 | 0.340315 | ||||||||
\(105\) | 21.4864 | 2.09685 | ||||||||
\(106\) | −0.668336 | −0.0649146 | ||||||||
\(107\) | −3.62630 | −0.350567 | −0.175284 | − | 0.984518i | \(-0.556084\pi\) | ||||
−0.175284 | + | 0.984518i | \(0.556084\pi\) | |||||||
\(108\) | 5.58962 | 0.537861 | ||||||||
\(109\) | 11.4090 | 1.09278 | 0.546391 | − | 0.837530i | \(-0.316001\pi\) | ||||
0.546391 | + | 0.837530i | \(0.316001\pi\) | |||||||
\(110\) | 17.9122 | 1.70786 | ||||||||
\(111\) | 6.29933 | 0.597906 | ||||||||
\(112\) | −3.54174 | −0.334663 | ||||||||
\(113\) | 5.67163 | 0.533542 | 0.266771 | − | 0.963760i | \(-0.414043\pi\) | ||||
0.266771 | + | 0.963760i | \(0.414043\pi\) | |||||||
\(114\) | −1.76462 | −0.165272 | ||||||||
\(115\) | −12.6615 | −1.18069 | ||||||||
\(116\) | 4.23477 | 0.393189 | ||||||||
\(117\) | −2.19904 | −0.203301 | ||||||||
\(118\) | −0.928020 | −0.0854312 | ||||||||
\(119\) | −11.3177 | −1.03749 | ||||||||
\(120\) | −6.06662 | −0.553804 | ||||||||
\(121\) | 9.62932 | 0.875393 | ||||||||
\(122\) | 8.93473 | 0.808912 | ||||||||
\(123\) | 9.17904 | 0.827646 | ||||||||
\(124\) | −8.64344 | −0.776204 | ||||||||
\(125\) | 21.8990 | 1.95870 | ||||||||
\(126\) | 2.24415 | 0.199924 | ||||||||
\(127\) | 0.710995 | 0.0630906 | 0.0315453 | − | 0.999502i | \(-0.489957\pi\) | ||||
0.0315453 | + | 0.999502i | \(0.489957\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −11.6992 | −1.03006 | ||||||||
\(130\) | 13.6868 | 1.20041 | ||||||||
\(131\) | 15.7031 | 1.37199 | 0.685995 | − | 0.727606i | \(-0.259367\pi\) | ||||
0.685995 | + | 0.727606i | \(0.259367\pi\) | |||||||
\(132\) | −6.98689 | −0.608131 | ||||||||
\(133\) | −4.06280 | −0.352290 | ||||||||
\(134\) | −4.43454 | −0.383086 | ||||||||
\(135\) | 22.0438 | 1.89723 | ||||||||
\(136\) | 3.19553 | 0.274014 | ||||||||
\(137\) | 7.06102 | 0.603264 | 0.301632 | − | 0.953424i | \(-0.402469\pi\) | ||||
0.301632 | + | 0.953424i | \(0.402469\pi\) | |||||||
\(138\) | 4.93881 | 0.420420 | ||||||||
\(139\) | −13.0236 | −1.10465 | −0.552325 | − | 0.833629i | \(-0.686259\pi\) | ||||
−0.552325 | + | 0.833629i | \(0.686259\pi\) | |||||||
\(140\) | −13.9676 | −1.18048 | ||||||||
\(141\) | −6.43434 | −0.541869 | ||||||||
\(142\) | −11.0025 | −0.923308 | ||||||||
\(143\) | 15.7630 | 1.31817 | ||||||||
\(144\) | −0.633629 | −0.0528024 | ||||||||
\(145\) | 16.7007 | 1.38692 | ||||||||
\(146\) | −14.9609 | −1.23817 | ||||||||
\(147\) | −8.52818 | −0.703392 | ||||||||
\(148\) | −4.09499 | −0.336606 | ||||||||
\(149\) | 11.5078 | 0.942757 | 0.471379 | − | 0.881931i | \(-0.343756\pi\) | ||||
0.471379 | + | 0.881931i | \(0.343756\pi\) | |||||||
\(150\) | −16.2335 | −1.32546 | ||||||||
\(151\) | −4.74768 | −0.386361 | −0.193180 | − | 0.981163i | \(-0.561880\pi\) | ||||
−0.193180 | + | 0.981163i | \(0.561880\pi\) | |||||||
\(152\) | 1.14712 | 0.0930438 | ||||||||
\(153\) | −2.02478 | −0.163694 | ||||||||
\(154\) | −16.0864 | −1.29628 | ||||||||
\(155\) | −34.0872 | −2.73795 | ||||||||
\(156\) | −5.33874 | −0.427441 | ||||||||
\(157\) | −18.4666 | −1.47380 | −0.736898 | − | 0.676004i | \(-0.763710\pi\) | ||||
−0.736898 | + | 0.676004i | \(0.763710\pi\) | |||||||
\(158\) | 13.8183 | 1.09932 | ||||||||
\(159\) | 1.02810 | 0.0815339 | ||||||||
\(160\) | 3.94371 | 0.311778 | ||||||||
\(161\) | 11.3710 | 0.896157 | ||||||||
\(162\) | −6.69763 | −0.526215 | ||||||||
\(163\) | −22.9352 | −1.79642 | −0.898211 | − | 0.439564i | \(-0.855133\pi\) | ||||
−0.898211 | + | 0.439564i | \(0.855133\pi\) | |||||||
\(164\) | −5.96700 | −0.465944 | ||||||||
\(165\) | −27.5543 | −2.14510 | ||||||||
\(166\) | 9.97381 | 0.774118 | ||||||||
\(167\) | −9.37258 | −0.725272 | −0.362636 | − | 0.931931i | \(-0.618123\pi\) | ||||
−0.362636 | + | 0.931931i | \(0.618123\pi\) | |||||||
\(168\) | 5.44826 | 0.420342 | ||||||||
\(169\) | −0.955327 | −0.0734867 | ||||||||
\(170\) | 12.6023 | 0.966549 | ||||||||
\(171\) | −0.726849 | −0.0555836 | ||||||||
\(172\) | 7.60529 | 0.579898 | ||||||||
\(173\) | 6.83501 | 0.519656 | 0.259828 | − | 0.965655i | \(-0.416334\pi\) | ||||
0.259828 | + | 0.965655i | \(0.416334\pi\) | |||||||
\(174\) | −6.51436 | −0.493852 | ||||||||
\(175\) | −37.3755 | −2.82532 | ||||||||
\(176\) | 4.54195 | 0.342362 | ||||||||
\(177\) | 1.42757 | 0.107303 | ||||||||
\(178\) | 8.67852 | 0.650483 | ||||||||
\(179\) | 2.24249 | 0.167611 | 0.0838056 | − | 0.996482i | \(-0.473293\pi\) | ||||
0.0838056 | + | 0.996482i | \(0.473293\pi\) | |||||||
\(180\) | −2.49885 | −0.186253 | ||||||||
\(181\) | 3.30251 | 0.245474 | 0.122737 | − | 0.992439i | \(-0.460833\pi\) | ||||
0.122737 | + | 0.992439i | \(0.460833\pi\) | |||||||
\(182\) | −12.2917 | −0.911125 | ||||||||
\(183\) | −13.7443 | −1.01601 | ||||||||
\(184\) | −3.21056 | −0.236686 | ||||||||
\(185\) | −16.1495 | −1.18733 | ||||||||
\(186\) | 13.2962 | 0.974925 | ||||||||
\(187\) | 14.5139 | 1.06136 | ||||||||
\(188\) | 4.18276 | 0.305059 | ||||||||
\(189\) | −19.7969 | −1.44002 | ||||||||
\(190\) | 4.52392 | 0.328200 | ||||||||
\(191\) | −2.01137 | −0.145537 | −0.0727687 | − | 0.997349i | \(-0.523183\pi\) | ||||
−0.0727687 | + | 0.997349i | \(0.523183\pi\) | |||||||
\(192\) | −1.53830 | −0.111017 | ||||||||
\(193\) | 13.1695 | 0.947962 | 0.473981 | − | 0.880535i | \(-0.342817\pi\) | ||||
0.473981 | + | 0.880535i | \(0.342817\pi\) | |||||||
\(194\) | 14.3327 | 1.02903 | ||||||||
\(195\) | −21.0545 | −1.50774 | ||||||||
\(196\) | 5.54389 | 0.395992 | ||||||||
\(197\) | 15.5252 | 1.10612 | 0.553062 | − | 0.833140i | \(-0.313459\pi\) | ||||
0.553062 | + | 0.833140i | \(0.313459\pi\) | |||||||
\(198\) | −2.87791 | −0.204524 | ||||||||
\(199\) | −5.96083 | −0.422552 | −0.211276 | − | 0.977426i | \(-0.567762\pi\) | ||||
−0.211276 | + | 0.977426i | \(0.567762\pi\) | |||||||
\(200\) | 10.5529 | 0.746201 | ||||||||
\(201\) | 6.82166 | 0.481163 | ||||||||
\(202\) | 16.2470 | 1.14314 | ||||||||
\(203\) | −14.9984 | −1.05268 | ||||||||
\(204\) | −4.91569 | −0.344167 | ||||||||
\(205\) | −23.5321 | −1.64356 | ||||||||
\(206\) | −2.47083 | −0.172151 | ||||||||
\(207\) | 2.03431 | 0.141394 | ||||||||
\(208\) | 3.47054 | 0.240639 | ||||||||
\(209\) | 5.21017 | 0.360395 | ||||||||
\(210\) | 21.4864 | 1.48270 | ||||||||
\(211\) | 2.41890 | 0.166524 | 0.0832619 | − | 0.996528i | \(-0.473466\pi\) | ||||
0.0832619 | + | 0.996528i | \(0.473466\pi\) | |||||||
\(212\) | −0.668336 | −0.0459015 | ||||||||
\(213\) | 16.9251 | 1.15969 | ||||||||
\(214\) | −3.62630 | −0.247889 | ||||||||
\(215\) | 29.9931 | 2.04551 | ||||||||
\(216\) | 5.58962 | 0.380325 | ||||||||
\(217\) | 30.6128 | 2.07813 | ||||||||
\(218\) | 11.4090 | 0.772713 | ||||||||
\(219\) | 23.0144 | 1.55517 | ||||||||
\(220\) | 17.9122 | 1.20764 | ||||||||
\(221\) | 11.0902 | 0.746009 | ||||||||
\(222\) | 6.29933 | 0.422784 | ||||||||
\(223\) | −12.9507 | −0.867240 | −0.433620 | − | 0.901096i | \(-0.642764\pi\) | ||||
−0.433620 | + | 0.901096i | \(0.642764\pi\) | |||||||
\(224\) | −3.54174 | −0.236642 | ||||||||
\(225\) | −6.68661 | −0.445774 | ||||||||
\(226\) | 5.67163 | 0.377271 | ||||||||
\(227\) | 7.68669 | 0.510183 | 0.255092 | − | 0.966917i | \(-0.417894\pi\) | ||||
0.255092 | + | 0.966917i | \(0.417894\pi\) | |||||||
\(228\) | −1.76462 | −0.116865 | ||||||||
\(229\) | −30.1383 | −1.99160 | −0.995798 | − | 0.0915756i | \(-0.970810\pi\) | ||||
−0.995798 | + | 0.0915756i | \(0.970810\pi\) | |||||||
\(230\) | −12.6615 | −0.834877 | ||||||||
\(231\) | 24.7457 | 1.62815 | ||||||||
\(232\) | 4.23477 | 0.278026 | ||||||||
\(233\) | 16.6289 | 1.08939 | 0.544697 | − | 0.838633i | \(-0.316645\pi\) | ||||
0.544697 | + | 0.838633i | \(0.316645\pi\) | |||||||
\(234\) | −2.19904 | −0.143756 | ||||||||
\(235\) | 16.4956 | 1.07605 | ||||||||
\(236\) | −0.928020 | −0.0604090 | ||||||||
\(237\) | −21.2566 | −1.38077 | ||||||||
\(238\) | −11.3177 | −0.733619 | ||||||||
\(239\) | 2.46990 | 0.159765 | 0.0798824 | − | 0.996804i | \(-0.474546\pi\) | ||||
0.0798824 | + | 0.996804i | \(0.474546\pi\) | |||||||
\(240\) | −6.06662 | −0.391599 | ||||||||
\(241\) | 29.0581 | 1.87179 | 0.935897 | − | 0.352273i | \(-0.114591\pi\) | ||||
0.935897 | + | 0.352273i | \(0.114591\pi\) | |||||||
\(242\) | 9.62932 | 0.618996 | ||||||||
\(243\) | −6.46588 | −0.414786 | ||||||||
\(244\) | 8.93473 | 0.571987 | ||||||||
\(245\) | 21.8635 | 1.39681 | ||||||||
\(246\) | 9.17904 | 0.585234 | ||||||||
\(247\) | 3.98113 | 0.253314 | ||||||||
\(248\) | −8.64344 | −0.548859 | ||||||||
\(249\) | −15.3427 | −0.972306 | ||||||||
\(250\) | 21.8990 | 1.38501 | ||||||||
\(251\) | 12.6754 | 0.800065 | 0.400032 | − | 0.916501i | \(-0.368999\pi\) | ||||
0.400032 | + | 0.916501i | \(0.368999\pi\) | |||||||
\(252\) | 2.24415 | 0.141368 | ||||||||
\(253\) | −14.5822 | −0.916776 | ||||||||
\(254\) | 0.710995 | 0.0446118 | ||||||||
\(255\) | −19.3861 | −1.21400 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.8375 | −0.676024 | −0.338012 | − | 0.941142i | \(-0.609754\pi\) | ||||
−0.338012 | + | 0.941142i | \(0.609754\pi\) | |||||||
\(258\) | −11.6992 | −0.728362 | ||||||||
\(259\) | 14.5034 | 0.901196 | ||||||||
\(260\) | 13.6868 | 0.848821 | ||||||||
\(261\) | −2.68328 | −0.166091 | ||||||||
\(262\) | 15.7031 | 0.970143 | ||||||||
\(263\) | −6.89673 | −0.425271 | −0.212635 | − | 0.977132i | \(-0.568205\pi\) | ||||
−0.212635 | + | 0.977132i | \(0.568205\pi\) | |||||||
\(264\) | −6.98689 | −0.430013 | ||||||||
\(265\) | −2.63573 | −0.161911 | ||||||||
\(266\) | −4.06280 | −0.249106 | ||||||||
\(267\) | −13.3502 | −0.817018 | ||||||||
\(268\) | −4.43454 | −0.270883 | ||||||||
\(269\) | −18.2225 | −1.11104 | −0.555521 | − | 0.831502i | \(-0.687481\pi\) | ||||
−0.555521 | + | 0.831502i | \(0.687481\pi\) | |||||||
\(270\) | 22.0438 | 1.34155 | ||||||||
\(271\) | −11.8484 | −0.719738 | −0.359869 | − | 0.933003i | \(-0.617179\pi\) | ||||
−0.359869 | + | 0.933003i | \(0.617179\pi\) | |||||||
\(272\) | 3.19553 | 0.193757 | ||||||||
\(273\) | 18.9084 | 1.14439 | ||||||||
\(274\) | 7.06102 | 0.426572 | ||||||||
\(275\) | 47.9307 | 2.89033 | ||||||||
\(276\) | 4.93881 | 0.297282 | ||||||||
\(277\) | −15.4431 | −0.927886 | −0.463943 | − | 0.885865i | \(-0.653566\pi\) | ||||
−0.463943 | + | 0.885865i | \(0.653566\pi\) | |||||||
\(278\) | −13.0236 | −0.781106 | ||||||||
\(279\) | 5.47673 | 0.327883 | ||||||||
\(280\) | −13.9676 | −0.834723 | ||||||||
\(281\) | 17.7149 | 1.05678 | 0.528390 | − | 0.849002i | \(-0.322796\pi\) | ||||
0.528390 | + | 0.849002i | \(0.322796\pi\) | |||||||
\(282\) | −6.43434 | −0.383160 | ||||||||
\(283\) | −14.4636 | −0.859770 | −0.429885 | − | 0.902884i | \(-0.641446\pi\) | ||||
−0.429885 | + | 0.902884i | \(0.641446\pi\) | |||||||
\(284\) | −11.0025 | −0.652877 | ||||||||
\(285\) | −6.95915 | −0.412224 | ||||||||
\(286\) | 15.7630 | 0.932088 | ||||||||
\(287\) | 21.1335 | 1.24747 | ||||||||
\(288\) | −0.633629 | −0.0373369 | ||||||||
\(289\) | −6.78859 | −0.399329 | ||||||||
\(290\) | 16.7007 | 0.980701 | ||||||||
\(291\) | −22.0480 | −1.29248 | ||||||||
\(292\) | −14.9609 | −0.875521 | ||||||||
\(293\) | −31.4451 | −1.83704 | −0.918520 | − | 0.395374i | \(-0.870615\pi\) | ||||
−0.918520 | + | 0.395374i | \(0.870615\pi\) | |||||||
\(294\) | −8.52818 | −0.497374 | ||||||||
\(295\) | −3.65985 | −0.213084 | ||||||||
\(296\) | −4.09499 | −0.238017 | ||||||||
\(297\) | 25.3878 | 1.47315 | ||||||||
\(298\) | 11.5078 | 0.666630 | ||||||||
\(299\) | −11.1424 | −0.644381 | ||||||||
\(300\) | −16.2335 | −0.937242 | ||||||||
\(301\) | −26.9359 | −1.55256 | ||||||||
\(302\) | −4.74768 | −0.273198 | ||||||||
\(303\) | −24.9928 | −1.43580 | ||||||||
\(304\) | 1.14712 | 0.0657919 | ||||||||
\(305\) | 35.2360 | 2.01761 | ||||||||
\(306\) | −2.02478 | −0.115749 | ||||||||
\(307\) | 25.5046 | 1.45562 | 0.727812 | − | 0.685776i | \(-0.240537\pi\) | ||||
0.727812 | + | 0.685776i | \(0.240537\pi\) | |||||||
\(308\) | −16.0864 | −0.916607 | ||||||||
\(309\) | 3.80088 | 0.216224 | ||||||||
\(310\) | −34.0872 | −1.93603 | ||||||||
\(311\) | 12.6107 | 0.715086 | 0.357543 | − | 0.933897i | \(-0.383615\pi\) | ||||
0.357543 | + | 0.933897i | \(0.383615\pi\) | |||||||
\(312\) | −5.33874 | −0.302247 | ||||||||
\(313\) | 25.7813 | 1.45724 | 0.728621 | − | 0.684917i | \(-0.240161\pi\) | ||||
0.728621 | + | 0.684917i | \(0.240161\pi\) | |||||||
\(314\) | −18.4666 | −1.04213 | ||||||||
\(315\) | 8.85027 | 0.498656 | ||||||||
\(316\) | 13.8183 | 0.777337 | ||||||||
\(317\) | 34.2888 | 1.92585 | 0.962924 | − | 0.269772i | \(-0.0869482\pi\) | ||||
0.962924 | + | 0.269772i | \(0.0869482\pi\) | |||||||
\(318\) | 1.02810 | 0.0576531 | ||||||||
\(319\) | 19.2341 | 1.07690 | ||||||||
\(320\) | 3.94371 | 0.220460 | ||||||||
\(321\) | 5.57834 | 0.311352 | ||||||||
\(322\) | 11.3710 | 0.633679 | ||||||||
\(323\) | 3.66566 | 0.203963 | ||||||||
\(324\) | −6.69763 | −0.372090 | ||||||||
\(325\) | 36.6242 | 2.03155 | ||||||||
\(326\) | −22.9352 | −1.27026 | ||||||||
\(327\) | −17.5504 | −0.970541 | ||||||||
\(328\) | −5.96700 | −0.329472 | ||||||||
\(329\) | −14.8142 | −0.816735 | ||||||||
\(330\) | −27.5543 | −1.51681 | ||||||||
\(331\) | 0.306690 | 0.0168572 | 0.00842860 | − | 0.999964i | \(-0.497317\pi\) | ||||
0.00842860 | + | 0.999964i | \(0.497317\pi\) | |||||||
\(332\) | 9.97381 | 0.547384 | ||||||||
\(333\) | 2.59471 | 0.142189 | ||||||||
\(334\) | −9.37258 | −0.512845 | ||||||||
\(335\) | −17.4886 | −0.955502 | ||||||||
\(336\) | 5.44826 | 0.297227 | ||||||||
\(337\) | −9.17661 | −0.499882 | −0.249941 | − | 0.968261i | \(-0.580411\pi\) | ||||
−0.249941 | + | 0.968261i | \(0.580411\pi\) | |||||||
\(338\) | −0.955327 | −0.0519629 | ||||||||
\(339\) | −8.72468 | −0.473860 | ||||||||
\(340\) | 12.6023 | 0.683453 | ||||||||
\(341\) | −39.2581 | −2.12594 | ||||||||
\(342\) | −0.726849 | −0.0393035 | ||||||||
\(343\) | 5.15714 | 0.278460 | ||||||||
\(344\) | 7.60529 | 0.410050 | ||||||||
\(345\) | 19.4773 | 1.04862 | ||||||||
\(346\) | 6.83501 | 0.367453 | ||||||||
\(347\) | 9.75999 | 0.523944 | 0.261972 | − | 0.965075i | \(-0.415627\pi\) | ||||
0.261972 | + | 0.965075i | \(0.415627\pi\) | |||||||
\(348\) | −6.51436 | −0.349206 | ||||||||
\(349\) | 21.7395 | 1.16369 | 0.581845 | − | 0.813300i | \(-0.302331\pi\) | ||||
0.581845 | + | 0.813300i | \(0.302331\pi\) | |||||||
\(350\) | −37.3755 | −1.99781 | ||||||||
\(351\) | 19.3990 | 1.03544 | ||||||||
\(352\) | 4.54195 | 0.242087 | ||||||||
\(353\) | −16.7254 | −0.890201 | −0.445100 | − | 0.895481i | \(-0.646832\pi\) | ||||
−0.445100 | + | 0.895481i | \(0.646832\pi\) | |||||||
\(354\) | 1.42757 | 0.0758747 | ||||||||
\(355\) | −43.3906 | −2.30294 | ||||||||
\(356\) | 8.67852 | 0.459961 | ||||||||
\(357\) | 17.4101 | 0.921439 | ||||||||
\(358\) | 2.24249 | 0.118519 | ||||||||
\(359\) | −8.80493 | −0.464707 | −0.232353 | − | 0.972631i | \(-0.574643\pi\) | ||||
−0.232353 | + | 0.972631i | \(0.574643\pi\) | |||||||
\(360\) | −2.49885 | −0.131701 | ||||||||
\(361\) | −17.6841 | −0.930743 | ||||||||
\(362\) | 3.30251 | 0.173576 | ||||||||
\(363\) | −14.8128 | −0.777470 | ||||||||
\(364\) | −12.2917 | −0.644263 | ||||||||
\(365\) | −59.0016 | −3.08828 | ||||||||
\(366\) | −13.7443 | −0.718426 | ||||||||
\(367\) | 8.30729 | 0.433637 | 0.216819 | − | 0.976212i | \(-0.430432\pi\) | ||||
0.216819 | + | 0.976212i | \(0.430432\pi\) | |||||||
\(368\) | −3.21056 | −0.167362 | ||||||||
\(369\) | 3.78086 | 0.196824 | ||||||||
\(370\) | −16.1495 | −0.839571 | ||||||||
\(371\) | 2.36707 | 0.122892 | ||||||||
\(372\) | 13.2962 | 0.689376 | ||||||||
\(373\) | −21.1733 | −1.09631 | −0.548155 | − | 0.836377i | \(-0.684670\pi\) | ||||
−0.548155 | + | 0.836377i | \(0.684670\pi\) | |||||||
\(374\) | 14.5139 | 0.750498 | ||||||||
\(375\) | −33.6872 | −1.73960 | ||||||||
\(376\) | 4.18276 | 0.215709 | ||||||||
\(377\) | 14.6970 | 0.756932 | ||||||||
\(378\) | −19.7969 | −1.01825 | ||||||||
\(379\) | 11.4427 | 0.587772 | 0.293886 | − | 0.955840i | \(-0.405051\pi\) | ||||
0.293886 | + | 0.955840i | \(0.405051\pi\) | |||||||
\(380\) | 4.52392 | 0.232072 | ||||||||
\(381\) | −1.09373 | −0.0560332 | ||||||||
\(382\) | −2.01137 | −0.102910 | ||||||||
\(383\) | 24.9349 | 1.27411 | 0.637056 | − | 0.770818i | \(-0.280152\pi\) | ||||
0.637056 | + | 0.770818i | \(0.280152\pi\) | |||||||
\(384\) | −1.53830 | −0.0785011 | ||||||||
\(385\) | −63.4401 | −3.23321 | ||||||||
\(386\) | 13.1695 | 0.670310 | ||||||||
\(387\) | −4.81893 | −0.244960 | ||||||||
\(388\) | 14.3327 | 0.727632 | ||||||||
\(389\) | −7.95651 | −0.403411 | −0.201706 | − | 0.979446i | \(-0.564648\pi\) | ||||
−0.201706 | + | 0.979446i | \(0.564648\pi\) | |||||||
\(390\) | −21.0545 | −1.06613 | ||||||||
\(391\) | −10.2594 | −0.518842 | ||||||||
\(392\) | 5.54389 | 0.280009 | ||||||||
\(393\) | −24.1562 | −1.21852 | ||||||||
\(394\) | 15.5252 | 0.782148 | ||||||||
\(395\) | 54.4952 | 2.74195 | ||||||||
\(396\) | −2.87791 | −0.144621 | ||||||||
\(397\) | −3.17224 | −0.159210 | −0.0796052 | − | 0.996826i | \(-0.525366\pi\) | ||||
−0.0796052 | + | 0.996826i | \(0.525366\pi\) | |||||||
\(398\) | −5.96083 | −0.298790 | ||||||||
\(399\) | 6.24981 | 0.312882 | ||||||||
\(400\) | 10.5529 | 0.527644 | ||||||||
\(401\) | 23.2436 | 1.16073 | 0.580364 | − | 0.814357i | \(-0.302910\pi\) | ||||
0.580364 | + | 0.814357i | \(0.302910\pi\) | |||||||
\(402\) | 6.82166 | 0.340233 | ||||||||
\(403\) | −29.9974 | −1.49428 | ||||||||
\(404\) | 16.2470 | 0.808320 | ||||||||
\(405\) | −26.4135 | −1.31250 | ||||||||
\(406\) | −14.9984 | −0.744361 | ||||||||
\(407\) | −18.5993 | −0.921931 | ||||||||
\(408\) | −4.91569 | −0.243363 | ||||||||
\(409\) | −3.26133 | −0.161263 | −0.0806313 | − | 0.996744i | \(-0.525694\pi\) | ||||
−0.0806313 | + | 0.996744i | \(0.525694\pi\) | |||||||
\(410\) | −23.5321 | −1.16217 | ||||||||
\(411\) | −10.8620 | −0.535782 | ||||||||
\(412\) | −2.47083 | −0.121729 | ||||||||
\(413\) | 3.28680 | 0.161733 | ||||||||
\(414\) | 2.03431 | 0.0999806 | ||||||||
\(415\) | 39.3339 | 1.93082 | ||||||||
\(416\) | 3.47054 | 0.170157 | ||||||||
\(417\) | 20.0343 | 0.981083 | ||||||||
\(418\) | 5.21017 | 0.254838 | ||||||||
\(419\) | 19.1123 | 0.933698 | 0.466849 | − | 0.884337i | \(-0.345389\pi\) | ||||
0.466849 | + | 0.884337i | \(0.345389\pi\) | |||||||
\(420\) | 21.4864 | 1.04843 | ||||||||
\(421\) | −32.5597 | −1.58686 | −0.793432 | − | 0.608658i | \(-0.791708\pi\) | ||||
−0.793432 | + | 0.608658i | \(0.791708\pi\) | |||||||
\(422\) | 2.41890 | 0.117750 | ||||||||
\(423\) | −2.65032 | −0.128863 | ||||||||
\(424\) | −0.668336 | −0.0324573 | ||||||||
\(425\) | 33.7220 | 1.63576 | ||||||||
\(426\) | 16.9251 | 0.820025 | ||||||||
\(427\) | −31.6444 | −1.53138 | ||||||||
\(428\) | −3.62630 | −0.175284 | ||||||||
\(429\) | −24.2483 | −1.17072 | ||||||||
\(430\) | 29.9931 | 1.44640 | ||||||||
\(431\) | 18.4181 | 0.887171 | 0.443585 | − | 0.896232i | \(-0.353706\pi\) | ||||
0.443585 | + | 0.896232i | \(0.353706\pi\) | |||||||
\(432\) | 5.58962 | 0.268931 | ||||||||
\(433\) | −5.93243 | −0.285094 | −0.142547 | − | 0.989788i | \(-0.545529\pi\) | ||||
−0.142547 | + | 0.989788i | \(0.545529\pi\) | |||||||
\(434\) | 30.6128 | 1.46946 | ||||||||
\(435\) | −25.6908 | −1.23178 | ||||||||
\(436\) | 11.4090 | 0.546391 | ||||||||
\(437\) | −3.68290 | −0.176177 | ||||||||
\(438\) | 23.0144 | 1.09967 | ||||||||
\(439\) | 11.5859 | 0.552967 | 0.276483 | − | 0.961019i | \(-0.410831\pi\) | ||||
0.276483 | + | 0.961019i | \(0.410831\pi\) | |||||||
\(440\) | 17.9122 | 0.853929 | ||||||||
\(441\) | −3.51277 | −0.167275 | ||||||||
\(442\) | 11.0902 | 0.527508 | ||||||||
\(443\) | −9.60530 | −0.456361 | −0.228181 | − | 0.973619i | \(-0.573278\pi\) | ||||
−0.228181 | + | 0.973619i | \(0.573278\pi\) | |||||||
\(444\) | 6.29933 | 0.298953 | ||||||||
\(445\) | 34.2256 | 1.62245 | ||||||||
\(446\) | −12.9507 | −0.613231 | ||||||||
\(447\) | −17.7025 | −0.837299 | ||||||||
\(448\) | −3.54174 | −0.167331 | ||||||||
\(449\) | −35.5928 | −1.67973 | −0.839864 | − | 0.542796i | \(-0.817366\pi\) | ||||
−0.839864 | + | 0.542796i | \(0.817366\pi\) | |||||||
\(450\) | −6.68661 | −0.315210 | ||||||||
\(451\) | −27.1018 | −1.27617 | ||||||||
\(452\) | 5.67163 | 0.266771 | ||||||||
\(453\) | 7.30336 | 0.343142 | ||||||||
\(454\) | 7.68669 | 0.360754 | ||||||||
\(455\) | −48.4751 | −2.27255 | ||||||||
\(456\) | −1.76462 | −0.0826358 | ||||||||
\(457\) | −39.0420 | −1.82631 | −0.913154 | − | 0.407616i | \(-0.866360\pi\) | ||||
−0.913154 | + | 0.407616i | \(0.866360\pi\) | |||||||
\(458\) | −30.1383 | −1.40827 | ||||||||
\(459\) | 17.8618 | 0.833717 | ||||||||
\(460\) | −12.6615 | −0.590347 | ||||||||
\(461\) | 15.9153 | 0.741249 | 0.370624 | − | 0.928783i | \(-0.379144\pi\) | ||||
0.370624 | + | 0.928783i | \(0.379144\pi\) | |||||||
\(462\) | 24.7457 | 1.15127 | ||||||||
\(463\) | −5.96915 | −0.277410 | −0.138705 | − | 0.990334i | \(-0.544294\pi\) | ||||
−0.138705 | + | 0.990334i | \(0.544294\pi\) | |||||||
\(464\) | 4.23477 | 0.196594 | ||||||||
\(465\) | 52.4365 | 2.43168 | ||||||||
\(466\) | 16.6289 | 0.770318 | ||||||||
\(467\) | −39.0600 | −1.80748 | −0.903741 | − | 0.428080i | \(-0.859190\pi\) | ||||
−0.903741 | + | 0.428080i | \(0.859190\pi\) | |||||||
\(468\) | −2.19904 | −0.101651 | ||||||||
\(469\) | 15.7060 | 0.725234 | ||||||||
\(470\) | 16.4956 | 0.760885 | ||||||||
\(471\) | 28.4072 | 1.30893 | ||||||||
\(472\) | −0.928020 | −0.0427156 | ||||||||
\(473\) | 34.5429 | 1.58828 | ||||||||
\(474\) | −21.2566 | −0.976349 | ||||||||
\(475\) | 12.1054 | 0.555435 | ||||||||
\(476\) | −11.3177 | −0.518747 | ||||||||
\(477\) | 0.423477 | 0.0193897 | ||||||||
\(478\) | 2.46990 | 0.112971 | ||||||||
\(479\) | −38.1035 | −1.74099 | −0.870497 | − | 0.492174i | \(-0.836202\pi\) | ||||
−0.870497 | + | 0.492174i | \(0.836202\pi\) | |||||||
\(480\) | −6.06662 | −0.276902 | ||||||||
\(481\) | −14.2118 | −0.648005 | ||||||||
\(482\) | 29.0581 | 1.32356 | ||||||||
\(483\) | −17.4920 | −0.795912 | ||||||||
\(484\) | 9.62932 | 0.437696 | ||||||||
\(485\) | 56.5240 | 2.56662 | ||||||||
\(486\) | −6.46588 | −0.293298 | ||||||||
\(487\) | −17.7659 | −0.805049 | −0.402524 | − | 0.915409i | \(-0.631867\pi\) | ||||
−0.402524 | + | 0.915409i | \(0.631867\pi\) | |||||||
\(488\) | 8.93473 | 0.404456 | ||||||||
\(489\) | 35.2812 | 1.59547 | ||||||||
\(490\) | 21.8635 | 0.987694 | ||||||||
\(491\) | 11.8118 | 0.533058 | 0.266529 | − | 0.963827i | \(-0.414123\pi\) | ||||
0.266529 | + | 0.963827i | \(0.414123\pi\) | |||||||
\(492\) | 9.17904 | 0.413823 | ||||||||
\(493\) | 13.5323 | 0.609466 | ||||||||
\(494\) | 3.98113 | 0.179120 | ||||||||
\(495\) | −11.3497 | −0.510129 | ||||||||
\(496\) | −8.64344 | −0.388102 | ||||||||
\(497\) | 38.9679 | 1.74795 | ||||||||
\(498\) | −15.3427 | −0.687524 | ||||||||
\(499\) | −34.9022 | −1.56244 | −0.781218 | − | 0.624259i | \(-0.785401\pi\) | ||||
−0.781218 | + | 0.624259i | \(0.785401\pi\) | |||||||
\(500\) | 21.8990 | 0.979352 | ||||||||
\(501\) | 14.4179 | 0.644142 | ||||||||
\(502\) | 12.6754 | 0.565731 | ||||||||
\(503\) | 13.7370 | 0.612501 | 0.306250 | − | 0.951951i | \(-0.400926\pi\) | ||||
0.306250 | + | 0.951951i | \(0.400926\pi\) | |||||||
\(504\) | 2.24415 | 0.0999622 | ||||||||
\(505\) | 64.0736 | 2.85124 | ||||||||
\(506\) | −14.5822 | −0.648259 | ||||||||
\(507\) | 1.46958 | 0.0652664 | ||||||||
\(508\) | 0.710995 | 0.0315453 | ||||||||
\(509\) | −37.3000 | −1.65329 | −0.826647 | − | 0.562720i | \(-0.809755\pi\) | ||||
−0.826647 | + | 0.562720i | \(0.809755\pi\) | |||||||
\(510\) | −19.3861 | −0.858429 | ||||||||
\(511\) | 52.9876 | 2.34403 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 6.41197 | 0.283095 | ||||||||
\(514\) | −10.8375 | −0.478021 | ||||||||
\(515\) | −9.74424 | −0.429382 | ||||||||
\(516\) | −11.6992 | −0.515030 | ||||||||
\(517\) | 18.9979 | 0.835526 | ||||||||
\(518\) | 14.5034 | 0.637242 | ||||||||
\(519\) | −10.5143 | −0.461527 | ||||||||
\(520\) | 13.6868 | 0.600207 | ||||||||
\(521\) | 7.62525 | 0.334068 | 0.167034 | − | 0.985951i | \(-0.446581\pi\) | ||||
0.167034 | + | 0.985951i | \(0.446581\pi\) | |||||||
\(522\) | −2.68328 | −0.117444 | ||||||||
\(523\) | −24.4204 | −1.06783 | −0.533915 | − | 0.845538i | \(-0.679280\pi\) | ||||
−0.533915 | + | 0.845538i | \(0.679280\pi\) | |||||||
\(524\) | 15.7031 | 0.685995 | ||||||||
\(525\) | 57.4948 | 2.50928 | ||||||||
\(526\) | −6.89673 | −0.300712 | ||||||||
\(527\) | −27.6204 | −1.20316 | ||||||||
\(528\) | −6.98689 | −0.304065 | ||||||||
\(529\) | −12.6923 | −0.551839 | ||||||||
\(530\) | −2.63573 | −0.114489 | ||||||||
\(531\) | 0.588020 | 0.0255179 | ||||||||
\(532\) | −4.06280 | −0.176145 | ||||||||
\(533\) | −20.7087 | −0.896995 | ||||||||
\(534\) | −13.3502 | −0.577719 | ||||||||
\(535\) | −14.3011 | −0.618289 | ||||||||
\(536\) | −4.43454 | −0.191543 | ||||||||
\(537\) | −3.44962 | −0.148862 | ||||||||
\(538\) | −18.2225 | −0.785626 | ||||||||
\(539\) | 25.1801 | 1.08458 | ||||||||
\(540\) | 22.0438 | 0.948616 | ||||||||
\(541\) | −3.86417 | −0.166134 | −0.0830668 | − | 0.996544i | \(-0.526471\pi\) | ||||
−0.0830668 | + | 0.996544i | \(0.526471\pi\) | |||||||
\(542\) | −11.8484 | −0.508932 | ||||||||
\(543\) | −5.08026 | −0.218015 | ||||||||
\(544\) | 3.19553 | 0.137007 | ||||||||
\(545\) | 44.9937 | 1.92732 | ||||||||
\(546\) | 18.9084 | 0.809205 | ||||||||
\(547\) | −0.334902 | −0.0143194 | −0.00715968 | − | 0.999974i | \(-0.502279\pi\) | ||||
−0.00715968 | + | 0.999974i | \(0.502279\pi\) | |||||||
\(548\) | 7.06102 | 0.301632 | ||||||||
\(549\) | −5.66130 | −0.241619 | ||||||||
\(550\) | 47.9307 | 2.04377 | ||||||||
\(551\) | 4.85780 | 0.206949 | ||||||||
\(552\) | 4.93881 | 0.210210 | ||||||||
\(553\) | −48.9406 | −2.08117 | ||||||||
\(554\) | −15.4431 | −0.656114 | ||||||||
\(555\) | 24.8428 | 1.05452 | ||||||||
\(556\) | −13.0236 | −0.552325 | ||||||||
\(557\) | −14.8858 | −0.630731 | −0.315365 | − | 0.948970i | \(-0.602127\pi\) | ||||
−0.315365 | + | 0.948970i | \(0.602127\pi\) | |||||||
\(558\) | 5.47673 | 0.231849 | ||||||||
\(559\) | 26.3945 | 1.11637 | ||||||||
\(560\) | −13.9676 | −0.590239 | ||||||||
\(561\) | −22.3268 | −0.942639 | ||||||||
\(562\) | 17.7149 | 0.747257 | ||||||||
\(563\) | −28.9218 | −1.21891 | −0.609454 | − | 0.792821i | \(-0.708611\pi\) | ||||
−0.609454 | + | 0.792821i | \(0.708611\pi\) | |||||||
\(564\) | −6.43434 | −0.270935 | ||||||||
\(565\) | 22.3673 | 0.940999 | ||||||||
\(566\) | −14.4636 | −0.607949 | ||||||||
\(567\) | 23.7212 | 0.996198 | ||||||||
\(568\) | −11.0025 | −0.461654 | ||||||||
\(569\) | 38.7476 | 1.62438 | 0.812191 | − | 0.583391i | \(-0.198275\pi\) | ||||
0.812191 | + | 0.583391i | \(0.198275\pi\) | |||||||
\(570\) | −6.95915 | −0.291487 | ||||||||
\(571\) | 14.9236 | 0.624532 | 0.312266 | − | 0.949995i | \(-0.398912\pi\) | ||||
0.312266 | + | 0.949995i | \(0.398912\pi\) | |||||||
\(572\) | 15.7630 | 0.659086 | ||||||||
\(573\) | 3.09409 | 0.129257 | ||||||||
\(574\) | 21.1335 | 0.882097 | ||||||||
\(575\) | −33.8807 | −1.41292 | ||||||||
\(576\) | −0.633629 | −0.0264012 | ||||||||
\(577\) | −25.6331 | −1.06712 | −0.533560 | − | 0.845762i | \(-0.679146\pi\) | ||||
−0.533560 | + | 0.845762i | \(0.679146\pi\) | |||||||
\(578\) | −6.78859 | −0.282368 | ||||||||
\(579\) | −20.2587 | −0.841921 | ||||||||
\(580\) | 16.7007 | 0.693460 | ||||||||
\(581\) | −35.3246 | −1.46551 | ||||||||
\(582\) | −22.0480 | −0.913918 | ||||||||
\(583\) | −3.03555 | −0.125720 | ||||||||
\(584\) | −14.9609 | −0.619087 | ||||||||
\(585\) | −8.67237 | −0.358559 | ||||||||
\(586\) | −31.4451 | −1.29898 | ||||||||
\(587\) | −12.2524 | −0.505713 | −0.252856 | − | 0.967504i | \(-0.581370\pi\) | ||||
−0.252856 | + | 0.967504i | \(0.581370\pi\) | |||||||
\(588\) | −8.52818 | −0.351696 | ||||||||
\(589\) | −9.91507 | −0.408543 | ||||||||
\(590\) | −3.65985 | −0.150673 | ||||||||
\(591\) | −23.8824 | −0.982392 | ||||||||
\(592\) | −4.09499 | −0.168303 | ||||||||
\(593\) | −8.85636 | −0.363687 | −0.181844 | − | 0.983327i | \(-0.558206\pi\) | ||||
−0.181844 | + | 0.983327i | \(0.558206\pi\) | |||||||
\(594\) | 25.3878 | 1.04167 | ||||||||
\(595\) | −44.6339 | −1.82981 | ||||||||
\(596\) | 11.5078 | 0.471379 | ||||||||
\(597\) | 9.16956 | 0.375285 | ||||||||
\(598\) | −11.1424 | −0.455646 | ||||||||
\(599\) | 36.9916 | 1.51144 | 0.755718 | − | 0.654897i | \(-0.227288\pi\) | ||||
0.755718 | + | 0.654897i | \(0.227288\pi\) | |||||||
\(600\) | −16.2335 | −0.662730 | ||||||||
\(601\) | 10.3581 | 0.422516 | 0.211258 | − | 0.977430i | \(-0.432244\pi\) | ||||
0.211258 | + | 0.977430i | \(0.432244\pi\) | |||||||
\(602\) | −26.9359 | −1.09783 | ||||||||
\(603\) | 2.80985 | 0.114426 | ||||||||
\(604\) | −4.74768 | −0.193180 | ||||||||
\(605\) | 37.9753 | 1.54391 | ||||||||
\(606\) | −24.9928 | −1.01526 | ||||||||
\(607\) | −9.37971 | −0.380711 | −0.190355 | − | 0.981715i | \(-0.560964\pi\) | ||||
−0.190355 | + | 0.981715i | \(0.560964\pi\) | |||||||
\(608\) | 1.14712 | 0.0465219 | ||||||||
\(609\) | 23.0721 | 0.934930 | ||||||||
\(610\) | 35.2360 | 1.42666 | ||||||||
\(611\) | 14.5164 | 0.587273 | ||||||||
\(612\) | −2.02478 | −0.0818469 | ||||||||
\(613\) | −40.5790 | −1.63897 | −0.819486 | − | 0.573100i | \(-0.805741\pi\) | ||||
−0.819486 | + | 0.573100i | \(0.805741\pi\) | |||||||
\(614\) | 25.5046 | 1.02928 | ||||||||
\(615\) | 36.1995 | 1.45971 | ||||||||
\(616\) | −16.0864 | −0.648139 | ||||||||
\(617\) | −32.2426 | −1.29804 | −0.649020 | − | 0.760771i | \(-0.724821\pi\) | ||||
−0.649020 | + | 0.760771i | \(0.724821\pi\) | |||||||
\(618\) | 3.80088 | 0.152894 | ||||||||
\(619\) | −22.7199 | −0.913190 | −0.456595 | − | 0.889675i | \(-0.650931\pi\) | ||||
−0.456595 | + | 0.889675i | \(0.650931\pi\) | |||||||
\(620\) | −34.0872 | −1.36898 | ||||||||
\(621\) | −17.9458 | −0.720141 | ||||||||
\(622\) | 12.6107 | 0.505642 | ||||||||
\(623\) | −30.7370 | −1.23145 | ||||||||
\(624\) | −5.33874 | −0.213721 | ||||||||
\(625\) | 33.5989 | 1.34396 | ||||||||
\(626\) | 25.7813 | 1.03043 | ||||||||
\(627\) | −8.01481 | −0.320081 | ||||||||
\(628\) | −18.4666 | −0.736898 | ||||||||
\(629\) | −13.0857 | −0.521760 | ||||||||
\(630\) | 8.85027 | 0.352603 | ||||||||
\(631\) | −6.41711 | −0.255461 | −0.127731 | − | 0.991809i | \(-0.540769\pi\) | ||||
−0.127731 | + | 0.991809i | \(0.540769\pi\) | |||||||
\(632\) | 13.8183 | 0.549660 | ||||||||
\(633\) | −3.72100 | −0.147896 | ||||||||
\(634\) | 34.2888 | 1.36178 | ||||||||
\(635\) | 2.80396 | 0.111272 | ||||||||
\(636\) | 1.02810 | 0.0407669 | ||||||||
\(637\) | 19.2403 | 0.762329 | ||||||||
\(638\) | 19.2341 | 0.761487 | ||||||||
\(639\) | 6.97149 | 0.275788 | ||||||||
\(640\) | 3.94371 | 0.155889 | ||||||||
\(641\) | 20.6424 | 0.815326 | 0.407663 | − | 0.913133i | \(-0.366344\pi\) | ||||
0.407663 | + | 0.913133i | \(0.366344\pi\) | |||||||
\(642\) | 5.57834 | 0.220159 | ||||||||
\(643\) | −1.92636 | −0.0759684 | −0.0379842 | − | 0.999278i | \(-0.512094\pi\) | ||||
−0.0379842 | + | 0.999278i | \(0.512094\pi\) | |||||||
\(644\) | 11.3710 | 0.448079 | ||||||||
\(645\) | −46.1384 | −1.81670 | ||||||||
\(646\) | 3.66566 | 0.144223 | ||||||||
\(647\) | −6.10757 | −0.240113 | −0.120057 | − | 0.992767i | \(-0.538308\pi\) | ||||
−0.120057 | + | 0.992767i | \(0.538308\pi\) | |||||||
\(648\) | −6.69763 | −0.263108 | ||||||||
\(649\) | −4.21502 | −0.165454 | ||||||||
\(650\) | 36.6242 | 1.43652 | ||||||||
\(651\) | −47.0917 | −1.84567 | ||||||||
\(652\) | −22.9352 | −0.898211 | ||||||||
\(653\) | −4.57799 | −0.179151 | −0.0895753 | − | 0.995980i | \(-0.528551\pi\) | ||||
−0.0895753 | + | 0.995980i | \(0.528551\pi\) | |||||||
\(654\) | −17.5504 | −0.686276 | ||||||||
\(655\) | 61.9287 | 2.41975 | ||||||||
\(656\) | −5.96700 | −0.232972 | ||||||||
\(657\) | 9.47967 | 0.369837 | ||||||||
\(658\) | −14.8142 | −0.577519 | ||||||||
\(659\) | 17.9011 | 0.697328 | 0.348664 | − | 0.937248i | \(-0.386635\pi\) | ||||
0.348664 | + | 0.937248i | \(0.386635\pi\) | |||||||
\(660\) | −27.5543 | −1.07255 | ||||||||
\(661\) | −17.3864 | −0.676251 | −0.338125 | − | 0.941101i | \(-0.609793\pi\) | ||||
−0.338125 | + | 0.941101i | \(0.609793\pi\) | |||||||
\(662\) | 0.306690 | 0.0119198 | ||||||||
\(663\) | −17.0601 | −0.662560 | ||||||||
\(664\) | 9.97381 | 0.387059 | ||||||||
\(665\) | −16.0225 | −0.621327 | ||||||||
\(666\) | 2.59471 | 0.100543 | ||||||||
\(667\) | −13.5960 | −0.526439 | ||||||||
\(668\) | −9.37258 | −0.362636 | ||||||||
\(669\) | 19.9220 | 0.770230 | ||||||||
\(670\) | −17.4886 | −0.675642 | ||||||||
\(671\) | 40.5811 | 1.56662 | ||||||||
\(672\) | 5.44826 | 0.210171 | ||||||||
\(673\) | 34.7247 | 1.33854 | 0.669269 | − | 0.743021i | \(-0.266608\pi\) | ||||
0.669269 | + | 0.743021i | \(0.266608\pi\) | |||||||
\(674\) | −9.17661 | −0.353470 | ||||||||
\(675\) | 58.9866 | 2.27039 | ||||||||
\(676\) | −0.955327 | −0.0367433 | ||||||||
\(677\) | −10.7236 | −0.412142 | −0.206071 | − | 0.978537i | \(-0.566068\pi\) | ||||
−0.206071 | + | 0.978537i | \(0.566068\pi\) | |||||||
\(678\) | −8.72468 | −0.335069 | ||||||||
\(679\) | −50.7626 | −1.94809 | ||||||||
\(680\) | 12.6023 | 0.483274 | ||||||||
\(681\) | −11.8244 | −0.453114 | ||||||||
\(682\) | −39.2581 | −1.50327 | ||||||||
\(683\) | 9.72173 | 0.371992 | 0.185996 | − | 0.982551i | \(-0.440449\pi\) | ||||
0.185996 | + | 0.982551i | \(0.440449\pi\) | |||||||
\(684\) | −0.726849 | −0.0277918 | ||||||||
\(685\) | 27.8467 | 1.06397 | ||||||||
\(686\) | 5.15714 | 0.196901 | ||||||||
\(687\) | 46.3618 | 1.76881 | ||||||||
\(688\) | 7.60529 | 0.289949 | ||||||||
\(689\) | −2.31949 | −0.0883656 | ||||||||
\(690\) | 19.4773 | 0.741487 | ||||||||
\(691\) | 20.8484 | 0.793109 | 0.396554 | − | 0.918011i | \(-0.370206\pi\) | ||||
0.396554 | + | 0.918011i | \(0.370206\pi\) | |||||||
\(692\) | 6.83501 | 0.259828 | ||||||||
\(693\) | 10.1928 | 0.387193 | ||||||||
\(694\) | 9.75999 | 0.370484 | ||||||||
\(695\) | −51.3615 | −1.94825 | ||||||||
\(696\) | −6.51436 | −0.246926 | ||||||||
\(697\) | −19.0677 | −0.722242 | ||||||||
\(698\) | 21.7395 | 0.822852 | ||||||||
\(699\) | −25.5802 | −0.967533 | ||||||||
\(700\) | −37.3755 | −1.41266 | ||||||||
\(701\) | 14.7538 | 0.557245 | 0.278623 | − | 0.960401i | \(-0.410122\pi\) | ||||
0.278623 | + | 0.960401i | \(0.410122\pi\) | |||||||
\(702\) | 19.3990 | 0.732168 | ||||||||
\(703\) | −4.69745 | −0.177168 | ||||||||
\(704\) | 4.54195 | 0.171181 | ||||||||
\(705\) | −25.3752 | −0.955686 | ||||||||
\(706\) | −16.7254 | −0.629467 | ||||||||
\(707\) | −57.5427 | −2.16411 | ||||||||
\(708\) | 1.42757 | 0.0536515 | ||||||||
\(709\) | −26.0324 | −0.977666 | −0.488833 | − | 0.872377i | \(-0.662577\pi\) | ||||
−0.488833 | + | 0.872377i | \(0.662577\pi\) | |||||||
\(710\) | −43.3906 | −1.62842 | ||||||||
\(711\) | −8.75564 | −0.328362 | ||||||||
\(712\) | 8.67852 | 0.325241 | ||||||||
\(713\) | 27.7503 | 1.03926 | ||||||||
\(714\) | 17.4101 | 0.651555 | ||||||||
\(715\) | 62.1649 | 2.32484 | ||||||||
\(716\) | 2.24249 | 0.0838056 | ||||||||
\(717\) | −3.79946 | −0.141893 | ||||||||
\(718\) | −8.80493 | −0.328597 | ||||||||
\(719\) | 5.33942 | 0.199127 | 0.0995634 | − | 0.995031i | \(-0.468255\pi\) | ||||
0.0995634 | + | 0.995031i | \(0.468255\pi\) | |||||||
\(720\) | −2.49885 | −0.0931267 | ||||||||
\(721\) | 8.75102 | 0.325905 | ||||||||
\(722\) | −17.6841 | −0.658135 | ||||||||
\(723\) | −44.7001 | −1.66241 | ||||||||
\(724\) | 3.30251 | 0.122737 | ||||||||
\(725\) | 44.6891 | 1.65971 | ||||||||
\(726\) | −14.8128 | −0.549754 | ||||||||
\(727\) | −34.4170 | −1.27646 | −0.638228 | − | 0.769848i | \(-0.720332\pi\) | ||||
−0.638228 | + | 0.769848i | \(0.720332\pi\) | |||||||
\(728\) | −12.2917 | −0.455563 | ||||||||
\(729\) | 30.0394 | 1.11257 | ||||||||
\(730\) | −59.0016 | −2.18375 | ||||||||
\(731\) | 24.3029 | 0.898877 | ||||||||
\(732\) | −13.7443 | −0.508004 | ||||||||
\(733\) | −51.6198 | −1.90662 | −0.953310 | − | 0.301995i | \(-0.902348\pi\) | ||||
−0.953310 | + | 0.301995i | \(0.902348\pi\) | |||||||
\(734\) | 8.30729 | 0.306628 | ||||||||
\(735\) | −33.6327 | −1.24056 | ||||||||
\(736\) | −3.21056 | −0.118343 | ||||||||
\(737\) | −20.1415 | −0.741920 | ||||||||
\(738\) | 3.78086 | 0.139176 | ||||||||
\(739\) | −9.38370 | −0.345185 | −0.172592 | − | 0.984993i | \(-0.555214\pi\) | ||||
−0.172592 | + | 0.984993i | \(0.555214\pi\) | |||||||
\(740\) | −16.1495 | −0.593667 | ||||||||
\(741\) | −6.12419 | −0.224978 | ||||||||
\(742\) | 2.36707 | 0.0868979 | ||||||||
\(743\) | −28.7225 | −1.05373 | −0.526863 | − | 0.849950i | \(-0.676632\pi\) | ||||
−0.526863 | + | 0.849950i | \(0.676632\pi\) | |||||||
\(744\) | 13.2962 | 0.487463 | ||||||||
\(745\) | 45.3836 | 1.66272 | ||||||||
\(746\) | −21.1733 | −0.775208 | ||||||||
\(747\) | −6.31970 | −0.231226 | ||||||||
\(748\) | 14.5139 | 0.530682 | ||||||||
\(749\) | 12.8434 | 0.469287 | ||||||||
\(750\) | −33.6872 | −1.23008 | ||||||||
\(751\) | −8.95709 | −0.326849 | −0.163425 | − | 0.986556i | \(-0.552254\pi\) | ||||
−0.163425 | + | 0.986556i | \(0.552254\pi\) | |||||||
\(752\) | 4.18276 | 0.152530 | ||||||||
\(753\) | −19.4986 | −0.710569 | ||||||||
\(754\) | 14.6970 | 0.535232 | ||||||||
\(755\) | −18.7235 | −0.681417 | ||||||||
\(756\) | −19.7969 | −0.720008 | ||||||||
\(757\) | 27.2589 | 0.990740 | 0.495370 | − | 0.868682i | \(-0.335032\pi\) | ||||
0.495370 | + | 0.868682i | \(0.335032\pi\) | |||||||
\(758\) | 11.4427 | 0.415618 | ||||||||
\(759\) | 22.4318 | 0.814224 | ||||||||
\(760\) | 4.52392 | 0.164100 | ||||||||
\(761\) | 6.03567 | 0.218793 | 0.109396 | − | 0.993998i | \(-0.465108\pi\) | ||||
0.109396 | + | 0.993998i | \(0.465108\pi\) | |||||||
\(762\) | −1.09373 | −0.0396215 | ||||||||
\(763\) | −40.4076 | −1.46285 | ||||||||
\(764\) | −2.01137 | −0.0727687 | ||||||||
\(765\) | −7.98515 | −0.288704 | ||||||||
\(766\) | 24.9349 | 0.900933 | ||||||||
\(767\) | −3.22073 | −0.116294 | ||||||||
\(768\) | −1.53830 | −0.0555087 | ||||||||
\(769\) | −40.8408 | −1.47276 | −0.736378 | − | 0.676571i | \(-0.763465\pi\) | ||||
−0.736378 | + | 0.676571i | \(0.763465\pi\) | |||||||
\(770\) | −63.4401 | −2.28622 | ||||||||
\(771\) | 16.6713 | 0.600403 | ||||||||
\(772\) | 13.1695 | 0.473981 | ||||||||
\(773\) | 36.1085 | 1.29873 | 0.649365 | − | 0.760477i | \(-0.275035\pi\) | ||||
0.649365 | + | 0.760477i | \(0.275035\pi\) | |||||||
\(774\) | −4.81893 | −0.173213 | ||||||||
\(775\) | −91.2132 | −3.27647 | ||||||||
\(776\) | 14.3327 | 0.514513 | ||||||||
\(777\) | −22.3106 | −0.800387 | ||||||||
\(778\) | −7.95651 | −0.285255 | ||||||||
\(779\) | −6.84487 | −0.245243 | ||||||||
\(780\) | −21.0545 | −0.753871 | ||||||||
\(781\) | −49.9727 | −1.78817 | ||||||||
\(782\) | −10.2594 | −0.366877 | ||||||||
\(783\) | 23.6708 | 0.845924 | ||||||||
\(784\) | 5.54389 | 0.197996 | ||||||||
\(785\) | −72.8270 | −2.59931 | ||||||||
\(786\) | −24.1562 | −0.861622 | ||||||||
\(787\) | −24.2501 | −0.864423 | −0.432212 | − | 0.901772i | \(-0.642267\pi\) | ||||
−0.432212 | + | 0.901772i | \(0.642267\pi\) | |||||||
\(788\) | 15.5252 | 0.553062 | ||||||||
\(789\) | 10.6093 | 0.377700 | ||||||||
\(790\) | 54.4952 | 1.93885 | ||||||||
\(791\) | −20.0874 | −0.714227 | ||||||||
\(792\) | −2.87791 | −0.102262 | ||||||||
\(793\) | 31.0084 | 1.10114 | ||||||||
\(794\) | −3.17224 | −0.112579 | ||||||||
\(795\) | 4.05454 | 0.143800 | ||||||||
\(796\) | −5.96083 | −0.211276 | ||||||||
\(797\) | −55.4003 | −1.96238 | −0.981189 | − | 0.193050i | \(-0.938162\pi\) | ||||
−0.981189 | + | 0.193050i | \(0.938162\pi\) | |||||||
\(798\) | 6.24981 | 0.221241 | ||||||||
\(799\) | 13.3661 | 0.472860 | ||||||||
\(800\) | 10.5529 | 0.373101 | ||||||||
\(801\) | −5.49896 | −0.194296 | ||||||||
\(802\) | 23.2436 | 0.820758 | ||||||||
\(803\) | −67.9517 | −2.39796 | ||||||||
\(804\) | 6.82166 | 0.240581 | ||||||||
\(805\) | 44.8438 | 1.58054 | ||||||||
\(806\) | −29.9974 | −1.05661 | ||||||||
\(807\) | 28.0316 | 0.986760 | ||||||||
\(808\) | 16.2470 | 0.571568 | ||||||||
\(809\) | −21.6575 | −0.761437 | −0.380718 | − | 0.924691i | \(-0.624323\pi\) | ||||
−0.380718 | + | 0.924691i | \(0.624323\pi\) | |||||||
\(810\) | −26.4135 | −0.928077 | ||||||||
\(811\) | 26.1574 | 0.918512 | 0.459256 | − | 0.888304i | \(-0.348116\pi\) | ||||
0.459256 | + | 0.888304i | \(0.348116\pi\) | |||||||
\(812\) | −14.9984 | −0.526342 | ||||||||
\(813\) | 18.2264 | 0.639227 | ||||||||
\(814\) | −18.5993 | −0.651904 | ||||||||
\(815\) | −90.4498 | −3.16832 | ||||||||
\(816\) | −4.91569 | −0.172083 | ||||||||
\(817\) | 8.72419 | 0.305221 | ||||||||
\(818\) | −3.26133 | −0.114030 | ||||||||
\(819\) | 7.78841 | 0.272149 | ||||||||
\(820\) | −23.5321 | −0.821778 | ||||||||
\(821\) | −39.0897 | −1.36424 | −0.682120 | − | 0.731240i | \(-0.738942\pi\) | ||||
−0.682120 | + | 0.731240i | \(0.738942\pi\) | |||||||
\(822\) | −10.8620 | −0.378855 | ||||||||
\(823\) | 23.5206 | 0.819878 | 0.409939 | − | 0.912113i | \(-0.365550\pi\) | ||||
0.409939 | + | 0.912113i | \(0.365550\pi\) | |||||||
\(824\) | −2.47083 | −0.0860754 | ||||||||
\(825\) | −73.7318 | −2.56701 | ||||||||
\(826\) | 3.28680 | 0.114362 | ||||||||
\(827\) | 37.2711 | 1.29604 | 0.648022 | − | 0.761622i | \(-0.275597\pi\) | ||||
0.648022 | + | 0.761622i | \(0.275597\pi\) | |||||||
\(828\) | 2.03431 | 0.0706970 | ||||||||
\(829\) | 2.33787 | 0.0811975 | 0.0405988 | − | 0.999176i | \(-0.487073\pi\) | ||||
0.0405988 | + | 0.999176i | \(0.487073\pi\) | |||||||
\(830\) | 39.3339 | 1.36530 | ||||||||
\(831\) | 23.7561 | 0.824091 | ||||||||
\(832\) | 3.47054 | 0.120319 | ||||||||
\(833\) | 17.7157 | 0.613812 | ||||||||
\(834\) | 20.0343 | 0.693730 | ||||||||
\(835\) | −36.9628 | −1.27915 | ||||||||
\(836\) | 5.21017 | 0.180197 | ||||||||
\(837\) | −48.3135 | −1.66996 | ||||||||
\(838\) | 19.1123 | 0.660224 | ||||||||
\(839\) | 16.1157 | 0.556377 | 0.278188 | − | 0.960527i | \(-0.410266\pi\) | ||||
0.278188 | + | 0.960527i | \(0.410266\pi\) | |||||||
\(840\) | 21.4864 | 0.741350 | ||||||||
\(841\) | −11.0667 | −0.381610 | ||||||||
\(842\) | −32.5597 | −1.12208 | ||||||||
\(843\) | −27.2508 | −0.938568 | ||||||||
\(844\) | 2.41890 | 0.0832619 | ||||||||
\(845\) | −3.76754 | −0.129607 | ||||||||
\(846\) | −2.65032 | −0.0911198 | ||||||||
\(847\) | −34.1045 | −1.17184 | ||||||||
\(848\) | −0.668336 | −0.0229508 | ||||||||
\(849\) | 22.2493 | 0.763595 | ||||||||
\(850\) | 33.7220 | 1.15666 | ||||||||
\(851\) | 13.1472 | 0.450681 | ||||||||
\(852\) | 16.9251 | 0.579846 | ||||||||
\(853\) | −22.8859 | −0.783599 | −0.391800 | − | 0.920051i | \(-0.628147\pi\) | ||||
−0.391800 | + | 0.920051i | \(0.628147\pi\) | |||||||
\(854\) | −31.6444 | −1.08285 | ||||||||
\(855\) | −2.86649 | −0.0980318 | ||||||||
\(856\) | −3.62630 | −0.123944 | ||||||||
\(857\) | −20.7919 | −0.710238 | −0.355119 | − | 0.934821i | \(-0.615560\pi\) | ||||
−0.355119 | + | 0.934821i | \(0.615560\pi\) | |||||||
\(858\) | −24.2483 | −0.827823 | ||||||||
\(859\) | −12.5793 | −0.429201 | −0.214600 | − | 0.976702i | \(-0.568845\pi\) | ||||
−0.214600 | + | 0.976702i | \(0.568845\pi\) | |||||||
\(860\) | 29.9931 | 1.02276 | ||||||||
\(861\) | −32.5097 | −1.10793 | ||||||||
\(862\) | 18.4181 | 0.627325 | ||||||||
\(863\) | 38.7324 | 1.31847 | 0.659233 | − | 0.751939i | \(-0.270881\pi\) | ||||
0.659233 | + | 0.751939i | \(0.270881\pi\) | |||||||
\(864\) | 5.58962 | 0.190163 | ||||||||
\(865\) | 26.9553 | 0.916509 | ||||||||
\(866\) | −5.93243 | −0.201592 | ||||||||
\(867\) | 10.4429 | 0.354659 | ||||||||
\(868\) | 30.6128 | 1.03907 | ||||||||
\(869\) | 62.7618 | 2.12905 | ||||||||
\(870\) | −25.6908 | −0.870998 | ||||||||
\(871\) | −15.3903 | −0.521479 | ||||||||
\(872\) | 11.4090 | 0.386357 | ||||||||
\(873\) | −9.08160 | −0.307366 | ||||||||
\(874\) | −3.68290 | −0.124576 | ||||||||
\(875\) | −77.5604 | −2.62202 | ||||||||
\(876\) | 23.0144 | 0.777584 | ||||||||
\(877\) | 4.33349 | 0.146331 | 0.0731657 | − | 0.997320i | \(-0.476690\pi\) | ||||
0.0731657 | + | 0.997320i | \(0.476690\pi\) | |||||||
\(878\) | 11.5859 | 0.391006 | ||||||||
\(879\) | 48.3720 | 1.63155 | ||||||||
\(880\) | 17.9122 | 0.603819 | ||||||||
\(881\) | −6.87192 | −0.231521 | −0.115760 | − | 0.993277i | \(-0.536930\pi\) | ||||
−0.115760 | + | 0.993277i | \(0.536930\pi\) | |||||||
\(882\) | −3.51277 | −0.118281 | ||||||||
\(883\) | −31.0302 | −1.04425 | −0.522125 | − | 0.852869i | \(-0.674861\pi\) | ||||
−0.522125 | + | 0.852869i | \(0.674861\pi\) | |||||||
\(884\) | 11.0902 | 0.373005 | ||||||||
\(885\) | 5.62995 | 0.189249 | ||||||||
\(886\) | −9.60530 | −0.322696 | ||||||||
\(887\) | −13.7576 | −0.461936 | −0.230968 | − | 0.972961i | \(-0.574189\pi\) | ||||
−0.230968 | + | 0.972961i | \(0.574189\pi\) | |||||||
\(888\) | 6.29933 | 0.211392 | ||||||||
\(889\) | −2.51816 | −0.0844563 | ||||||||
\(890\) | 34.2256 | 1.14724 | ||||||||
\(891\) | −30.4203 | −1.01912 | ||||||||
\(892\) | −12.9507 | −0.433620 | ||||||||
\(893\) | 4.79813 | 0.160563 | ||||||||
\(894\) | −17.7025 | −0.592060 | ||||||||
\(895\) | 8.84372 | 0.295613 | ||||||||
\(896\) | −3.54174 | −0.118321 | ||||||||
\(897\) | 17.1404 | 0.572300 | ||||||||
\(898\) | −35.5928 | −1.18775 | ||||||||
\(899\) | −36.6030 | −1.22078 | ||||||||
\(900\) | −6.68661 | −0.222887 | ||||||||
\(901\) | −2.13569 | −0.0711501 | ||||||||
\(902\) | −27.1018 | −0.902392 | ||||||||
\(903\) | 41.4356 | 1.37889 | ||||||||
\(904\) | 5.67163 | 0.188636 | ||||||||
\(905\) | 13.0242 | 0.432938 | ||||||||
\(906\) | 7.30336 | 0.242638 | ||||||||
\(907\) | −24.3310 | −0.807897 | −0.403949 | − | 0.914782i | \(-0.632363\pi\) | ||||
−0.403949 | + | 0.914782i | \(0.632363\pi\) | |||||||
\(908\) | 7.68669 | 0.255092 | ||||||||
\(909\) | −10.2946 | −0.341450 | ||||||||
\(910\) | −48.4751 | −1.60694 | ||||||||
\(911\) | −51.9475 | −1.72110 | −0.860548 | − | 0.509370i | \(-0.829879\pi\) | ||||
−0.860548 | + | 0.509370i | \(0.829879\pi\) | |||||||
\(912\) | −1.76462 | −0.0584324 | ||||||||
\(913\) | 45.3006 | 1.49923 | ||||||||
\(914\) | −39.0420 | −1.29139 | ||||||||
\(915\) | −54.2036 | −1.79192 | ||||||||
\(916\) | −30.1383 | −0.995798 | ||||||||
\(917\) | −55.6164 | −1.83661 | ||||||||
\(918\) | 17.8618 | 0.589527 | ||||||||
\(919\) | −47.1052 | −1.55386 | −0.776929 | − | 0.629588i | \(-0.783224\pi\) | ||||
−0.776929 | + | 0.629588i | \(0.783224\pi\) | |||||||
\(920\) | −12.6615 | −0.417439 | ||||||||
\(921\) | −39.2338 | −1.29280 | ||||||||
\(922\) | 15.9153 | 0.524142 | ||||||||
\(923\) | −38.1846 | −1.25686 | ||||||||
\(924\) | 24.7457 | 0.814074 | ||||||||
\(925\) | −43.2140 | −1.42087 | ||||||||
\(926\) | −5.96915 | −0.196158 | ||||||||
\(927\) | 1.56559 | 0.0514207 | ||||||||
\(928\) | 4.23477 | 0.139013 | ||||||||
\(929\) | 47.8679 | 1.57050 | 0.785248 | − | 0.619182i | \(-0.212536\pi\) | ||||
0.785248 | + | 0.619182i | \(0.212536\pi\) | |||||||
\(930\) | 52.4365 | 1.71946 | ||||||||
\(931\) | 6.35952 | 0.208425 | ||||||||
\(932\) | 16.6289 | 0.544697 | ||||||||
\(933\) | −19.3990 | −0.635095 | ||||||||
\(934\) | −39.0600 | −1.27808 | ||||||||
\(935\) | 57.2388 | 1.87191 | ||||||||
\(936\) | −2.19904 | −0.0718778 | ||||||||
\(937\) | −29.4302 | −0.961442 | −0.480721 | − | 0.876874i | \(-0.659625\pi\) | ||||
−0.480721 | + | 0.876874i | \(0.659625\pi\) | |||||||
\(938\) | 15.7060 | 0.512818 | ||||||||
\(939\) | −39.6593 | −1.29423 | ||||||||
\(940\) | 16.4956 | 0.538027 | ||||||||
\(941\) | 16.6307 | 0.542146 | 0.271073 | − | 0.962559i | \(-0.412621\pi\) | ||||
0.271073 | + | 0.962559i | \(0.412621\pi\) | |||||||
\(942\) | 28.4072 | 0.925557 | ||||||||
\(943\) | 19.1574 | 0.623851 | ||||||||
\(944\) | −0.928020 | −0.0302045 | ||||||||
\(945\) | −78.0735 | −2.53973 | ||||||||
\(946\) | 34.5429 | 1.12309 | ||||||||
\(947\) | −6.20208 | −0.201541 | −0.100770 | − | 0.994910i | \(-0.532131\pi\) | ||||
−0.100770 | + | 0.994910i | \(0.532131\pi\) | |||||||
\(948\) | −21.2566 | −0.690383 | ||||||||
\(949\) | −51.9225 | −1.68548 | ||||||||
\(950\) | 12.1054 | 0.392752 | ||||||||
\(951\) | −52.7464 | −1.71042 | ||||||||
\(952\) | −11.3177 | −0.366810 | ||||||||
\(953\) | −8.44933 | −0.273701 | −0.136850 | − | 0.990592i | \(-0.543698\pi\) | ||||
−0.136850 | + | 0.990592i | \(0.543698\pi\) | |||||||
\(954\) | 0.423477 | 0.0137106 | ||||||||
\(955\) | −7.93226 | −0.256682 | ||||||||
\(956\) | 2.46990 | 0.0798824 | ||||||||
\(957\) | −29.5879 | −0.956441 | ||||||||
\(958\) | −38.1035 | −1.23107 | ||||||||
\(959\) | −25.0083 | −0.807559 | ||||||||
\(960\) | −6.06662 | −0.195799 | ||||||||
\(961\) | 43.7090 | 1.40997 | ||||||||
\(962\) | −14.2118 | −0.458208 | ||||||||
\(963\) | 2.29773 | 0.0740432 | ||||||||
\(964\) | 29.0581 | 0.935897 | ||||||||
\(965\) | 51.9368 | 1.67190 | ||||||||
\(966\) | −17.4920 | −0.562795 | ||||||||
\(967\) | −30.5271 | −0.981687 | −0.490843 | − | 0.871248i | \(-0.663311\pi\) | ||||
−0.490843 | + | 0.871248i | \(0.663311\pi\) | |||||||
\(968\) | 9.62932 | 0.309498 | ||||||||
\(969\) | −5.63889 | −0.181147 | ||||||||
\(970\) | 56.5240 | 1.81488 | ||||||||
\(971\) | 41.0564 | 1.31756 | 0.658781 | − | 0.752335i | \(-0.271072\pi\) | ||||
0.658781 | + | 0.752335i | \(0.271072\pi\) | |||||||
\(972\) | −6.46588 | −0.207393 | ||||||||
\(973\) | 46.1263 | 1.47874 | ||||||||
\(974\) | −17.7659 | −0.569256 | ||||||||
\(975\) | −56.3391 | −1.80430 | ||||||||
\(976\) | 8.93473 | 0.285994 | ||||||||
\(977\) | 28.4888 | 0.911438 | 0.455719 | − | 0.890124i | \(-0.349382\pi\) | ||||
0.455719 | + | 0.890124i | \(0.349382\pi\) | |||||||
\(978\) | 35.2812 | 1.12817 | ||||||||
\(979\) | 39.4174 | 1.25979 | ||||||||
\(980\) | 21.8635 | 0.698405 | ||||||||
\(981\) | −7.22906 | −0.230806 | ||||||||
\(982\) | 11.8118 | 0.376929 | ||||||||
\(983\) | −0.0729452 | −0.00232659 | −0.00116330 | − | 0.999999i | \(-0.500370\pi\) | ||||
−0.00116330 | + | 0.999999i | \(0.500370\pi\) | |||||||
\(984\) | 9.17904 | 0.292617 | ||||||||
\(985\) | 61.2269 | 1.95085 | ||||||||
\(986\) | 13.5323 | 0.430958 | ||||||||
\(987\) | 22.7887 | 0.725374 | ||||||||
\(988\) | 3.98113 | 0.126657 | ||||||||
\(989\) | −24.4173 | −0.776424 | ||||||||
\(990\) | −11.3497 | −0.360716 | ||||||||
\(991\) | 23.8192 | 0.756641 | 0.378320 | − | 0.925675i | \(-0.376502\pi\) | ||||
0.378320 | + | 0.925675i | \(0.376502\pi\) | |||||||
\(992\) | −8.64344 | −0.274429 | ||||||||
\(993\) | −0.471782 | −0.0149715 | ||||||||
\(994\) | 38.9679 | 1.23599 | ||||||||
\(995\) | −23.5078 | −0.745248 | ||||||||
\(996\) | −15.3427 | −0.486153 | ||||||||
\(997\) | 32.6055 | 1.03263 | 0.516313 | − | 0.856400i | \(-0.327304\pi\) | ||||
0.516313 | + | 0.856400i | \(0.327304\pi\) | |||||||
\(998\) | −34.9022 | −1.10481 | ||||||||
\(999\) | −22.8894 | −0.724190 |
(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 | 4034.2.a.d.1.12 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.d.1.12 | ✓ | 52 | 1.1 | even | 1 | trivial |