Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, 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("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-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 | ||||||||
\(3\) | −0.934245 | −0.539387 | −0.269693 | − | 0.962946i | \(-0.586922\pi\) | ||||
−0.269693 | + | 0.962946i | \(0.586922\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.17073 | −1.86521 | −0.932604 | − | 0.360902i | \(-0.882469\pi\) | ||||
−0.932604 | + | 0.360902i | \(0.882469\pi\) | |||||||
\(6\) | 0.934245 | 0.381404 | ||||||||
\(7\) | 1.30479 | 0.493163 | 0.246581 | − | 0.969122i | \(-0.420693\pi\) | ||||
0.246581 | + | 0.969122i | \(0.420693\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.12719 | −0.709062 | ||||||||
\(10\) | 4.17073 | 1.31890 | ||||||||
\(11\) | −6.29050 | −1.89666 | −0.948329 | − | 0.317288i | \(-0.897228\pi\) | ||||
−0.948329 | + | 0.317288i | \(0.897228\pi\) | |||||||
\(12\) | −0.934245 | −0.269693 | ||||||||
\(13\) | −3.79704 | −1.05311 | −0.526555 | − | 0.850141i | \(-0.676517\pi\) | ||||
−0.526555 | + | 0.850141i | \(0.676517\pi\) | |||||||
\(14\) | −1.30479 | −0.348719 | ||||||||
\(15\) | 3.89648 | 1.00607 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.77842 | 0.916402 | 0.458201 | − | 0.888849i | \(-0.348494\pi\) | ||||
0.458201 | + | 0.888849i | \(0.348494\pi\) | |||||||
\(18\) | 2.12719 | 0.501383 | ||||||||
\(19\) | 8.63642 | 1.98133 | 0.990665 | − | 0.136320i | \(-0.0435277\pi\) | ||||
0.990665 | + | 0.136320i | \(0.0435277\pi\) | |||||||
\(20\) | −4.17073 | −0.932604 | ||||||||
\(21\) | −1.21899 | −0.266005 | ||||||||
\(22\) | 6.29050 | 1.34114 | ||||||||
\(23\) | −0.896615 | −0.186957 | −0.0934786 | − | 0.995621i | \(-0.529799\pi\) | ||||
−0.0934786 | + | 0.995621i | \(0.529799\pi\) | |||||||
\(24\) | 0.934245 | 0.190702 | ||||||||
\(25\) | 12.3950 | 2.47900 | ||||||||
\(26\) | 3.79704 | 0.744661 | ||||||||
\(27\) | 4.79005 | 0.921845 | ||||||||
\(28\) | 1.30479 | 0.246581 | ||||||||
\(29\) | −5.01155 | −0.930622 | −0.465311 | − | 0.885147i | \(-0.654058\pi\) | ||||
−0.465311 | + | 0.885147i | \(0.654058\pi\) | |||||||
\(30\) | −3.89648 | −0.711397 | ||||||||
\(31\) | 4.64754 | 0.834723 | 0.417362 | − | 0.908740i | \(-0.362955\pi\) | ||||
0.417362 | + | 0.908740i | \(0.362955\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.87687 | 1.02303 | ||||||||
\(34\) | −3.77842 | −0.647994 | ||||||||
\(35\) | −5.44191 | −0.919851 | ||||||||
\(36\) | −2.12719 | −0.354531 | ||||||||
\(37\) | 0.395367 | 0.0649979 | 0.0324990 | − | 0.999472i | \(-0.489653\pi\) | ||||
0.0324990 | + | 0.999472i | \(0.489653\pi\) | |||||||
\(38\) | −8.63642 | −1.40101 | ||||||||
\(39\) | 3.54737 | 0.568033 | ||||||||
\(40\) | 4.17073 | 0.659451 | ||||||||
\(41\) | 11.0085 | 1.71924 | 0.859618 | − | 0.510937i | \(-0.170701\pi\) | ||||
0.859618 | + | 0.510937i | \(0.170701\pi\) | |||||||
\(42\) | 1.21899 | 0.188094 | ||||||||
\(43\) | −5.38636 | −0.821412 | −0.410706 | − | 0.911768i | \(-0.634718\pi\) | ||||
−0.410706 | + | 0.911768i | \(0.634718\pi\) | |||||||
\(44\) | −6.29050 | −0.948329 | ||||||||
\(45\) | 8.87192 | 1.32255 | ||||||||
\(46\) | 0.896615 | 0.132199 | ||||||||
\(47\) | 6.22519 | 0.908037 | 0.454018 | − | 0.890992i | \(-0.349990\pi\) | ||||
0.454018 | + | 0.890992i | \(0.349990\pi\) | |||||||
\(48\) | −0.934245 | −0.134847 | ||||||||
\(49\) | −5.29754 | −0.756791 | ||||||||
\(50\) | −12.3950 | −1.75292 | ||||||||
\(51\) | −3.52997 | −0.494295 | ||||||||
\(52\) | −3.79704 | −0.526555 | ||||||||
\(53\) | 5.28252 | 0.725610 | 0.362805 | − | 0.931865i | \(-0.381819\pi\) | ||||
0.362805 | + | 0.931865i | \(0.381819\pi\) | |||||||
\(54\) | −4.79005 | −0.651843 | ||||||||
\(55\) | 26.2360 | 3.53766 | ||||||||
\(56\) | −1.30479 | −0.174359 | ||||||||
\(57\) | −8.06853 | −1.06870 | ||||||||
\(58\) | 5.01155 | 0.658049 | ||||||||
\(59\) | 8.08279 | 1.05229 | 0.526145 | − | 0.850395i | \(-0.323637\pi\) | ||||
0.526145 | + | 0.850395i | \(0.323637\pi\) | |||||||
\(60\) | 3.89648 | 0.503034 | ||||||||
\(61\) | 7.71779 | 0.988162 | 0.494081 | − | 0.869416i | \(-0.335505\pi\) | ||||
0.494081 | + | 0.869416i | \(0.335505\pi\) | |||||||
\(62\) | −4.64754 | −0.590239 | ||||||||
\(63\) | −2.77552 | −0.349683 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 15.8364 | 1.96427 | ||||||||
\(66\) | −5.87687 | −0.723393 | ||||||||
\(67\) | −5.28401 | −0.645544 | −0.322772 | − | 0.946477i | \(-0.604615\pi\) | ||||
−0.322772 | + | 0.946477i | \(0.604615\pi\) | |||||||
\(68\) | 3.77842 | 0.458201 | ||||||||
\(69\) | 0.837658 | 0.100842 | ||||||||
\(70\) | 5.44191 | 0.650433 | ||||||||
\(71\) | −13.2315 | −1.57029 | −0.785145 | − | 0.619312i | \(-0.787412\pi\) | ||||
−0.785145 | + | 0.619312i | \(0.787412\pi\) | |||||||
\(72\) | 2.12719 | 0.250691 | ||||||||
\(73\) | 5.22398 | 0.611420 | 0.305710 | − | 0.952125i | \(-0.401106\pi\) | ||||
0.305710 | + | 0.952125i | \(0.401106\pi\) | |||||||
\(74\) | −0.395367 | −0.0459605 | ||||||||
\(75\) | −11.5800 | −1.33714 | ||||||||
\(76\) | 8.63642 | 0.990665 | ||||||||
\(77\) | −8.20776 | −0.935361 | ||||||||
\(78\) | −3.54737 | −0.401660 | ||||||||
\(79\) | −7.87903 | −0.886460 | −0.443230 | − | 0.896408i | \(-0.646168\pi\) | ||||
−0.443230 | + | 0.896408i | \(0.646168\pi\) | |||||||
\(80\) | −4.17073 | −0.466302 | ||||||||
\(81\) | 1.90648 | 0.211831 | ||||||||
\(82\) | −11.0085 | −1.21568 | ||||||||
\(83\) | −4.95162 | −0.543511 | −0.271755 | − | 0.962366i | \(-0.587604\pi\) | ||||
−0.271755 | + | 0.962366i | \(0.587604\pi\) | |||||||
\(84\) | −1.21899 | −0.133003 | ||||||||
\(85\) | −15.7588 | −1.70928 | ||||||||
\(86\) | 5.38636 | 0.580826 | ||||||||
\(87\) | 4.68202 | 0.501965 | ||||||||
\(88\) | 6.29050 | 0.670570 | ||||||||
\(89\) | −15.5420 | −1.64745 | −0.823725 | − | 0.566989i | \(-0.808108\pi\) | ||||
−0.823725 | + | 0.566989i | \(0.808108\pi\) | |||||||
\(90\) | −8.87192 | −0.935183 | ||||||||
\(91\) | −4.95433 | −0.519354 | ||||||||
\(92\) | −0.896615 | −0.0934786 | ||||||||
\(93\) | −4.34194 | −0.450239 | ||||||||
\(94\) | −6.22519 | −0.642079 | ||||||||
\(95\) | −36.0202 | −3.69559 | ||||||||
\(96\) | 0.934245 | 0.0953510 | ||||||||
\(97\) | 4.55797 | 0.462792 | 0.231396 | − | 0.972860i | \(-0.425671\pi\) | ||||
0.231396 | + | 0.972860i | \(0.425671\pi\) | |||||||
\(98\) | 5.29754 | 0.535132 | ||||||||
\(99\) | 13.3811 | 1.34485 | ||||||||
\(100\) | 12.3950 | 1.23950 | ||||||||
\(101\) | −8.68916 | −0.864603 | −0.432302 | − | 0.901729i | \(-0.642298\pi\) | ||||
−0.432302 | + | 0.901729i | \(0.642298\pi\) | |||||||
\(102\) | 3.52997 | 0.349519 | ||||||||
\(103\) | −2.54539 | −0.250805 | −0.125402 | − | 0.992106i | \(-0.540022\pi\) | ||||
−0.125402 | + | 0.992106i | \(0.540022\pi\) | |||||||
\(104\) | 3.79704 | 0.372331 | ||||||||
\(105\) | 5.08408 | 0.496155 | ||||||||
\(106\) | −5.28252 | −0.513083 | ||||||||
\(107\) | −6.96570 | −0.673400 | −0.336700 | − | 0.941612i | \(-0.609311\pi\) | ||||
−0.336700 | + | 0.941612i | \(0.609311\pi\) | |||||||
\(108\) | 4.79005 | 0.460923 | ||||||||
\(109\) | −9.52787 | −0.912605 | −0.456302 | − | 0.889825i | \(-0.650826\pi\) | ||||
−0.456302 | + | 0.889825i | \(0.650826\pi\) | |||||||
\(110\) | −26.2360 | −2.50151 | ||||||||
\(111\) | −0.369369 | −0.0350590 | ||||||||
\(112\) | 1.30479 | 0.123291 | ||||||||
\(113\) | −2.68341 | −0.252434 | −0.126217 | − | 0.992003i | \(-0.540284\pi\) | ||||
−0.126217 | + | 0.992003i | \(0.540284\pi\) | |||||||
\(114\) | 8.06853 | 0.755687 | ||||||||
\(115\) | 3.73954 | 0.348714 | ||||||||
\(116\) | −5.01155 | −0.465311 | ||||||||
\(117\) | 8.07702 | 0.746721 | ||||||||
\(118\) | −8.08279 | −0.744081 | ||||||||
\(119\) | 4.93003 | 0.451935 | ||||||||
\(120\) | −3.89648 | −0.355699 | ||||||||
\(121\) | 28.5705 | 2.59731 | ||||||||
\(122\) | −7.71779 | −0.698736 | ||||||||
\(123\) | −10.2846 | −0.927333 | ||||||||
\(124\) | 4.64754 | 0.417362 | ||||||||
\(125\) | −30.8426 | −2.75864 | ||||||||
\(126\) | 2.77552 | 0.247263 | ||||||||
\(127\) | −13.4700 | −1.19527 | −0.597634 | − | 0.801769i | \(-0.703892\pi\) | ||||
−0.597634 | + | 0.801769i | \(0.703892\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.03218 | 0.443059 | ||||||||
\(130\) | −15.8364 | −1.38895 | ||||||||
\(131\) | 18.2790 | 1.59705 | 0.798523 | − | 0.601964i | \(-0.205615\pi\) | ||||
0.798523 | + | 0.601964i | \(0.205615\pi\) | |||||||
\(132\) | 5.87687 | 0.511516 | ||||||||
\(133\) | 11.2687 | 0.977118 | ||||||||
\(134\) | 5.28401 | 0.456469 | ||||||||
\(135\) | −19.9780 | −1.71943 | ||||||||
\(136\) | −3.77842 | −0.323997 | ||||||||
\(137\) | 12.2643 | 1.04781 | 0.523904 | − | 0.851777i | \(-0.324475\pi\) | ||||
0.523904 | + | 0.851777i | \(0.324475\pi\) | |||||||
\(138\) | −0.837658 | −0.0713062 | ||||||||
\(139\) | 14.0948 | 1.19551 | 0.597754 | − | 0.801680i | \(-0.296060\pi\) | ||||
0.597754 | + | 0.801680i | \(0.296060\pi\) | |||||||
\(140\) | −5.44191 | −0.459925 | ||||||||
\(141\) | −5.81585 | −0.489783 | ||||||||
\(142\) | 13.2315 | 1.11036 | ||||||||
\(143\) | 23.8853 | 1.99739 | ||||||||
\(144\) | −2.12719 | −0.177266 | ||||||||
\(145\) | 20.9018 | 1.73580 | ||||||||
\(146\) | −5.22398 | −0.432339 | ||||||||
\(147\) | 4.94919 | 0.408203 | ||||||||
\(148\) | 0.395367 | 0.0324990 | ||||||||
\(149\) | −1.23075 | −0.100827 | −0.0504136 | − | 0.998728i | \(-0.516054\pi\) | ||||
−0.0504136 | + | 0.998728i | \(0.516054\pi\) | |||||||
\(150\) | 11.5800 | 0.945500 | ||||||||
\(151\) | 6.00890 | 0.488997 | 0.244499 | − | 0.969650i | \(-0.421377\pi\) | ||||
0.244499 | + | 0.969650i | \(0.421377\pi\) | |||||||
\(152\) | −8.63642 | −0.700506 | ||||||||
\(153\) | −8.03740 | −0.649786 | ||||||||
\(154\) | 8.20776 | 0.661400 | ||||||||
\(155\) | −19.3837 | −1.55693 | ||||||||
\(156\) | 3.54737 | 0.284017 | ||||||||
\(157\) | 22.5972 | 1.80345 | 0.901727 | − | 0.432305i | \(-0.142300\pi\) | ||||
0.901727 | + | 0.432305i | \(0.142300\pi\) | |||||||
\(158\) | 7.87903 | 0.626822 | ||||||||
\(159\) | −4.93516 | −0.391384 | ||||||||
\(160\) | 4.17073 | 0.329725 | ||||||||
\(161\) | −1.16989 | −0.0922003 | ||||||||
\(162\) | −1.90648 | −0.149787 | ||||||||
\(163\) | −6.27626 | −0.491595 | −0.245797 | − | 0.969321i | \(-0.579050\pi\) | ||||
−0.245797 | + | 0.969321i | \(0.579050\pi\) | |||||||
\(164\) | 11.0085 | 0.859618 | ||||||||
\(165\) | −24.5109 | −1.90817 | ||||||||
\(166\) | 4.95162 | 0.384320 | ||||||||
\(167\) | 8.07593 | 0.624934 | 0.312467 | − | 0.949929i | \(-0.398845\pi\) | ||||
0.312467 | + | 0.949929i | \(0.398845\pi\) | |||||||
\(168\) | 1.21899 | 0.0940470 | ||||||||
\(169\) | 1.41753 | 0.109041 | ||||||||
\(170\) | 15.7588 | 1.20864 | ||||||||
\(171\) | −18.3713 | −1.40489 | ||||||||
\(172\) | −5.38636 | −0.410706 | ||||||||
\(173\) | −12.9187 | −0.982193 | −0.491096 | − | 0.871105i | \(-0.663404\pi\) | ||||
−0.491096 | + | 0.871105i | \(0.663404\pi\) | |||||||
\(174\) | −4.68202 | −0.354943 | ||||||||
\(175\) | 16.1728 | 1.22255 | ||||||||
\(176\) | −6.29050 | −0.474165 | ||||||||
\(177\) | −7.55130 | −0.567591 | ||||||||
\(178\) | 15.5420 | 1.16492 | ||||||||
\(179\) | −23.2192 | −1.73548 | −0.867742 | − | 0.497014i | \(-0.834430\pi\) | ||||
−0.867742 | + | 0.497014i | \(0.834430\pi\) | |||||||
\(180\) | 8.87192 | 0.661274 | ||||||||
\(181\) | −5.10569 | −0.379503 | −0.189751 | − | 0.981832i | \(-0.560768\pi\) | ||||
−0.189751 | + | 0.981832i | \(0.560768\pi\) | |||||||
\(182\) | 4.95433 | 0.367239 | ||||||||
\(183\) | −7.21030 | −0.533001 | ||||||||
\(184\) | 0.896615 | 0.0660993 | ||||||||
\(185\) | −1.64897 | −0.121235 | ||||||||
\(186\) | 4.34194 | 0.318367 | ||||||||
\(187\) | −23.7682 | −1.73810 | ||||||||
\(188\) | 6.22519 | 0.454018 | ||||||||
\(189\) | 6.24998 | 0.454619 | ||||||||
\(190\) | 36.0202 | 2.61318 | ||||||||
\(191\) | 20.2505 | 1.46527 | 0.732637 | − | 0.680619i | \(-0.238289\pi\) | ||||
0.732637 | + | 0.680619i | \(0.238289\pi\) | |||||||
\(192\) | −0.934245 | −0.0674233 | ||||||||
\(193\) | 7.76495 | 0.558933 | 0.279467 | − | 0.960155i | \(-0.409842\pi\) | ||||
0.279467 | + | 0.960155i | \(0.409842\pi\) | |||||||
\(194\) | −4.55797 | −0.327243 | ||||||||
\(195\) | −14.7951 | −1.05950 | ||||||||
\(196\) | −5.29754 | −0.378395 | ||||||||
\(197\) | 15.6146 | 1.11249 | 0.556246 | − | 0.831018i | \(-0.312241\pi\) | ||||
0.556246 | + | 0.831018i | \(0.312241\pi\) | |||||||
\(198\) | −13.3811 | −0.950952 | ||||||||
\(199\) | −15.3893 | −1.09092 | −0.545461 | − | 0.838136i | \(-0.683645\pi\) | ||||
−0.545461 | + | 0.838136i | \(0.683645\pi\) | |||||||
\(200\) | −12.3950 | −0.876459 | ||||||||
\(201\) | 4.93656 | 0.348198 | ||||||||
\(202\) | 8.68916 | 0.611367 | ||||||||
\(203\) | −6.53900 | −0.458948 | ||||||||
\(204\) | −3.52997 | −0.247147 | ||||||||
\(205\) | −45.9134 | −3.20673 | ||||||||
\(206\) | 2.54539 | 0.177346 | ||||||||
\(207\) | 1.90727 | 0.132564 | ||||||||
\(208\) | −3.79704 | −0.263278 | ||||||||
\(209\) | −54.3274 | −3.75791 | ||||||||
\(210\) | −5.08408 | −0.350835 | ||||||||
\(211\) | 27.6277 | 1.90197 | 0.950986 | − | 0.309235i | \(-0.100073\pi\) | ||||
0.950986 | + | 0.309235i | \(0.100073\pi\) | |||||||
\(212\) | 5.28252 | 0.362805 | ||||||||
\(213\) | 12.3615 | 0.846993 | ||||||||
\(214\) | 6.96570 | 0.476166 | ||||||||
\(215\) | 22.4651 | 1.53210 | ||||||||
\(216\) | −4.79005 | −0.325921 | ||||||||
\(217\) | 6.06405 | 0.411654 | ||||||||
\(218\) | 9.52787 | 0.645309 | ||||||||
\(219\) | −4.88047 | −0.329792 | ||||||||
\(220\) | 26.2360 | 1.76883 | ||||||||
\(221\) | −14.3468 | −0.965072 | ||||||||
\(222\) | 0.369369 | 0.0247905 | ||||||||
\(223\) | −2.83303 | −0.189714 | −0.0948570 | − | 0.995491i | \(-0.530239\pi\) | ||||
−0.0948570 | + | 0.995491i | \(0.530239\pi\) | |||||||
\(224\) | −1.30479 | −0.0871796 | ||||||||
\(225\) | −26.3665 | −1.75777 | ||||||||
\(226\) | 2.68341 | 0.178498 | ||||||||
\(227\) | −16.4681 | −1.09303 | −0.546513 | − | 0.837451i | \(-0.684045\pi\) | ||||
−0.546513 | + | 0.837451i | \(0.684045\pi\) | |||||||
\(228\) | −8.06853 | −0.534351 | ||||||||
\(229\) | 1.54283 | 0.101953 | 0.0509765 | − | 0.998700i | \(-0.483767\pi\) | ||||
0.0509765 | + | 0.998700i | \(0.483767\pi\) | |||||||
\(230\) | −3.73954 | −0.246578 | ||||||||
\(231\) | 7.66806 | 0.504521 | ||||||||
\(232\) | 5.01155 | 0.329025 | ||||||||
\(233\) | 22.7015 | 1.48722 | 0.743612 | − | 0.668611i | \(-0.233111\pi\) | ||||
0.743612 | + | 0.668611i | \(0.233111\pi\) | |||||||
\(234\) | −8.07702 | −0.528011 | ||||||||
\(235\) | −25.9636 | −1.69368 | ||||||||
\(236\) | 8.08279 | 0.526145 | ||||||||
\(237\) | 7.36094 | 0.478145 | ||||||||
\(238\) | −4.93003 | −0.319566 | ||||||||
\(239\) | 1.25406 | 0.0811183 | 0.0405592 | − | 0.999177i | \(-0.487086\pi\) | ||||
0.0405592 | + | 0.999177i | \(0.487086\pi\) | |||||||
\(240\) | 3.89648 | 0.251517 | ||||||||
\(241\) | 0.519454 | 0.0334610 | 0.0167305 | − | 0.999860i | \(-0.494674\pi\) | ||||
0.0167305 | + | 0.999860i | \(0.494674\pi\) | |||||||
\(242\) | −28.5705 | −1.83658 | ||||||||
\(243\) | −16.1513 | −1.03610 | ||||||||
\(244\) | 7.71779 | 0.494081 | ||||||||
\(245\) | 22.0946 | 1.41157 | ||||||||
\(246\) | 10.2846 | 0.655724 | ||||||||
\(247\) | −32.7928 | −2.08656 | ||||||||
\(248\) | −4.64754 | −0.295119 | ||||||||
\(249\) | 4.62603 | 0.293163 | ||||||||
\(250\) | 30.8426 | 1.95066 | ||||||||
\(251\) | 23.4513 | 1.48023 | 0.740117 | − | 0.672478i | \(-0.234770\pi\) | ||||
0.740117 | + | 0.672478i | \(0.234770\pi\) | |||||||
\(252\) | −2.77552 | −0.174841 | ||||||||
\(253\) | 5.64016 | 0.354594 | ||||||||
\(254\) | 13.4700 | 0.845182 | ||||||||
\(255\) | 14.7226 | 0.921962 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.960802 | −0.0599332 | −0.0299666 | − | 0.999551i | \(-0.509540\pi\) | ||||
−0.0299666 | + | 0.999551i | \(0.509540\pi\) | |||||||
\(258\) | −5.03218 | −0.313290 | ||||||||
\(259\) | 0.515869 | 0.0320545 | ||||||||
\(260\) | 15.8364 | 0.982135 | ||||||||
\(261\) | 10.6605 | 0.659869 | ||||||||
\(262\) | −18.2790 | −1.12928 | ||||||||
\(263\) | −18.8333 | −1.16131 | −0.580655 | − | 0.814150i | \(-0.697203\pi\) | ||||
−0.580655 | + | 0.814150i | \(0.697203\pi\) | |||||||
\(264\) | −5.87687 | −0.361696 | ||||||||
\(265\) | −22.0320 | −1.35341 | ||||||||
\(266\) | −11.2687 | −0.690926 | ||||||||
\(267\) | 14.5200 | 0.888612 | ||||||||
\(268\) | −5.28401 | −0.322772 | ||||||||
\(269\) | −13.2221 | −0.806167 | −0.403084 | − | 0.915163i | \(-0.632062\pi\) | ||||
−0.403084 | + | 0.915163i | \(0.632062\pi\) | |||||||
\(270\) | 19.9780 | 1.21582 | ||||||||
\(271\) | −4.48027 | −0.272157 | −0.136079 | − | 0.990698i | \(-0.543450\pi\) | ||||
−0.136079 | + | 0.990698i | \(0.543450\pi\) | |||||||
\(272\) | 3.77842 | 0.229100 | ||||||||
\(273\) | 4.62855 | 0.280133 | ||||||||
\(274\) | −12.2643 | −0.740912 | ||||||||
\(275\) | −77.9708 | −4.70182 | ||||||||
\(276\) | 0.837658 | 0.0504211 | ||||||||
\(277\) | −15.8791 | −0.954082 | −0.477041 | − | 0.878881i | \(-0.658291\pi\) | ||||
−0.477041 | + | 0.878881i | \(0.658291\pi\) | |||||||
\(278\) | −14.0948 | −0.845352 | ||||||||
\(279\) | −9.88619 | −0.591871 | ||||||||
\(280\) | 5.44191 | 0.325216 | ||||||||
\(281\) | −0.405076 | −0.0241648 | −0.0120824 | − | 0.999927i | \(-0.503846\pi\) | ||||
−0.0120824 | + | 0.999927i | \(0.503846\pi\) | |||||||
\(282\) | 5.81585 | 0.346329 | ||||||||
\(283\) | −6.16780 | −0.366638 | −0.183319 | − | 0.983053i | \(-0.558684\pi\) | ||||
−0.183319 | + | 0.983053i | \(0.558684\pi\) | |||||||
\(284\) | −13.2315 | −0.785145 | ||||||||
\(285\) | 33.6517 | 1.99335 | ||||||||
\(286\) | −23.8853 | −1.41237 | ||||||||
\(287\) | 14.3637 | 0.847863 | ||||||||
\(288\) | 2.12719 | 0.125346 | ||||||||
\(289\) | −2.72354 | −0.160208 | ||||||||
\(290\) | −20.9018 | −1.22740 | ||||||||
\(291\) | −4.25826 | −0.249624 | ||||||||
\(292\) | 5.22398 | 0.305710 | ||||||||
\(293\) | 9.66195 | 0.564457 | 0.282229 | − | 0.959347i | \(-0.408926\pi\) | ||||
0.282229 | + | 0.959347i | \(0.408926\pi\) | |||||||
\(294\) | −4.94919 | −0.288643 | ||||||||
\(295\) | −33.7111 | −1.96274 | ||||||||
\(296\) | −0.395367 | −0.0229802 | ||||||||
\(297\) | −30.1318 | −1.74843 | ||||||||
\(298\) | 1.23075 | 0.0712956 | ||||||||
\(299\) | 3.40449 | 0.196887 | ||||||||
\(300\) | −11.5800 | −0.668570 | ||||||||
\(301\) | −7.02804 | −0.405090 | ||||||||
\(302\) | −6.00890 | −0.345773 | ||||||||
\(303\) | 8.11780 | 0.466355 | ||||||||
\(304\) | 8.63642 | 0.495332 | ||||||||
\(305\) | −32.1888 | −1.84313 | ||||||||
\(306\) | 8.03740 | 0.459468 | ||||||||
\(307\) | −20.2896 | −1.15799 | −0.578994 | − | 0.815331i | \(-0.696555\pi\) | ||||
−0.578994 | + | 0.815331i | \(0.696555\pi\) | |||||||
\(308\) | −8.20776 | −0.467680 | ||||||||
\(309\) | 2.37802 | 0.135281 | ||||||||
\(310\) | 19.3837 | 1.10092 | ||||||||
\(311\) | 14.9639 | 0.848527 | 0.424263 | − | 0.905539i | \(-0.360533\pi\) | ||||
0.424263 | + | 0.905539i | \(0.360533\pi\) | |||||||
\(312\) | −3.54737 | −0.200830 | ||||||||
\(313\) | 33.8135 | 1.91125 | 0.955627 | − | 0.294578i | \(-0.0951792\pi\) | ||||
0.955627 | + | 0.294578i | \(0.0951792\pi\) | |||||||
\(314\) | −22.5972 | −1.27524 | ||||||||
\(315\) | 11.5760 | 0.652231 | ||||||||
\(316\) | −7.87903 | −0.443230 | ||||||||
\(317\) | −22.0889 | −1.24064 | −0.620319 | − | 0.784350i | \(-0.712997\pi\) | ||||
−0.620319 | + | 0.784350i | \(0.712997\pi\) | |||||||
\(318\) | 4.93516 | 0.276750 | ||||||||
\(319\) | 31.5252 | 1.76507 | ||||||||
\(320\) | −4.17073 | −0.233151 | ||||||||
\(321\) | 6.50767 | 0.363223 | ||||||||
\(322\) | 1.16989 | 0.0651954 | ||||||||
\(323\) | 32.6320 | 1.81569 | ||||||||
\(324\) | 1.90648 | 0.105916 | ||||||||
\(325\) | −47.0644 | −2.61066 | ||||||||
\(326\) | 6.27626 | 0.347610 | ||||||||
\(327\) | 8.90137 | 0.492247 | ||||||||
\(328\) | −11.0085 | −0.607842 | ||||||||
\(329\) | 8.12253 | 0.447810 | ||||||||
\(330\) | 24.5109 | 1.34928 | ||||||||
\(331\) | −18.2309 | −1.00206 | −0.501031 | − | 0.865429i | \(-0.667046\pi\) | ||||
−0.501031 | + | 0.865429i | \(0.667046\pi\) | |||||||
\(332\) | −4.95162 | −0.271755 | ||||||||
\(333\) | −0.841019 | −0.0460876 | ||||||||
\(334\) | −8.07593 | −0.441895 | ||||||||
\(335\) | 22.0382 | 1.20407 | ||||||||
\(336\) | −1.21899 | −0.0665013 | ||||||||
\(337\) | −0.521940 | −0.0284319 | −0.0142159 | − | 0.999899i | \(-0.504525\pi\) | ||||
−0.0142159 | + | 0.999899i | \(0.504525\pi\) | |||||||
\(338\) | −1.41753 | −0.0771037 | ||||||||
\(339\) | 2.50696 | 0.136159 | ||||||||
\(340\) | −15.7588 | −0.854640 | ||||||||
\(341\) | −29.2354 | −1.58319 | ||||||||
\(342\) | 18.3713 | 0.993404 | ||||||||
\(343\) | −16.0456 | −0.866383 | ||||||||
\(344\) | 5.38636 | 0.290413 | ||||||||
\(345\) | −3.49365 | −0.188092 | ||||||||
\(346\) | 12.9187 | 0.694515 | ||||||||
\(347\) | −16.6049 | −0.891399 | −0.445699 | − | 0.895183i | \(-0.647045\pi\) | ||||
−0.445699 | + | 0.895183i | \(0.647045\pi\) | |||||||
\(348\) | 4.68202 | 0.250983 | ||||||||
\(349\) | −2.71319 | −0.145234 | −0.0726169 | − | 0.997360i | \(-0.523135\pi\) | ||||
−0.0726169 | + | 0.997360i | \(0.523135\pi\) | |||||||
\(350\) | −16.1728 | −0.864473 | ||||||||
\(351\) | −18.1880 | −0.970805 | ||||||||
\(352\) | 6.29050 | 0.335285 | ||||||||
\(353\) | 13.9911 | 0.744674 | 0.372337 | − | 0.928098i | \(-0.378557\pi\) | ||||
0.372337 | + | 0.928098i | \(0.378557\pi\) | |||||||
\(354\) | 7.55130 | 0.401347 | ||||||||
\(355\) | 55.1850 | 2.92892 | ||||||||
\(356\) | −15.5420 | −0.823725 | ||||||||
\(357\) | −4.60585 | −0.243768 | ||||||||
\(358\) | 23.2192 | 1.22717 | ||||||||
\(359\) | 28.3376 | 1.49560 | 0.747801 | − | 0.663923i | \(-0.231110\pi\) | ||||
0.747801 | + | 0.663923i | \(0.231110\pi\) | |||||||
\(360\) | −8.87192 | −0.467591 | ||||||||
\(361\) | 55.5877 | 2.92567 | ||||||||
\(362\) | 5.10569 | 0.268349 | ||||||||
\(363\) | −26.6918 | −1.40096 | ||||||||
\(364\) | −4.95433 | −0.259677 | ||||||||
\(365\) | −21.7878 | −1.14043 | ||||||||
\(366\) | 7.21030 | 0.376889 | ||||||||
\(367\) | −29.5228 | −1.54108 | −0.770538 | − | 0.637395i | \(-0.780012\pi\) | ||||
−0.770538 | + | 0.637395i | \(0.780012\pi\) | |||||||
\(368\) | −0.896615 | −0.0467393 | ||||||||
\(369\) | −23.4171 | −1.21905 | ||||||||
\(370\) | 1.64897 | 0.0857258 | ||||||||
\(371\) | 6.89255 | 0.357843 | ||||||||
\(372\) | −4.34194 | −0.225119 | ||||||||
\(373\) | −26.9628 | −1.39608 | −0.698040 | − | 0.716058i | \(-0.745944\pi\) | ||||
−0.698040 | + | 0.716058i | \(0.745944\pi\) | |||||||
\(374\) | 23.7682 | 1.22902 | ||||||||
\(375\) | 28.8145 | 1.48797 | ||||||||
\(376\) | −6.22519 | −0.321039 | ||||||||
\(377\) | 19.0291 | 0.980048 | ||||||||
\(378\) | −6.24998 | −0.321465 | ||||||||
\(379\) | −28.1649 | −1.44674 | −0.723368 | − | 0.690463i | \(-0.757407\pi\) | ||||
−0.723368 | + | 0.690463i | \(0.757407\pi\) | |||||||
\(380\) | −36.0202 | −1.84780 | ||||||||
\(381\) | 12.5843 | 0.644711 | ||||||||
\(382\) | −20.2505 | −1.03611 | ||||||||
\(383\) | 4.76207 | 0.243330 | 0.121665 | − | 0.992571i | \(-0.461177\pi\) | ||||
0.121665 | + | 0.992571i | \(0.461177\pi\) | |||||||
\(384\) | 0.934245 | 0.0476755 | ||||||||
\(385\) | 34.2324 | 1.74464 | ||||||||
\(386\) | −7.76495 | −0.395226 | ||||||||
\(387\) | 11.4578 | 0.582432 | ||||||||
\(388\) | 4.55797 | 0.231396 | ||||||||
\(389\) | −23.8263 | −1.20804 | −0.604021 | − | 0.796969i | \(-0.706436\pi\) | ||||
−0.604021 | + | 0.796969i | \(0.706436\pi\) | |||||||
\(390\) | 14.7951 | 0.749180 | ||||||||
\(391\) | −3.38779 | −0.171328 | ||||||||
\(392\) | 5.29754 | 0.267566 | ||||||||
\(393\) | −17.0771 | −0.861426 | ||||||||
\(394\) | −15.6146 | −0.786651 | ||||||||
\(395\) | 32.8613 | 1.65343 | ||||||||
\(396\) | 13.3811 | 0.672424 | ||||||||
\(397\) | 8.11106 | 0.407082 | 0.203541 | − | 0.979066i | \(-0.434755\pi\) | ||||
0.203541 | + | 0.979066i | \(0.434755\pi\) | |||||||
\(398\) | 15.3893 | 0.771398 | ||||||||
\(399\) | −10.5277 | −0.527044 | ||||||||
\(400\) | 12.3950 | 0.619750 | ||||||||
\(401\) | −11.8831 | −0.593416 | −0.296708 | − | 0.954968i | \(-0.595889\pi\) | ||||
−0.296708 | + | 0.954968i | \(0.595889\pi\) | |||||||
\(402\) | −4.93656 | −0.246213 | ||||||||
\(403\) | −17.6469 | −0.879056 | ||||||||
\(404\) | −8.68916 | −0.432302 | ||||||||
\(405\) | −7.95142 | −0.395109 | ||||||||
\(406\) | 6.53900 | 0.324525 | ||||||||
\(407\) | −2.48706 | −0.123279 | ||||||||
\(408\) | 3.52997 | 0.174760 | ||||||||
\(409\) | −21.0442 | −1.04057 | −0.520283 | − | 0.853994i | \(-0.674174\pi\) | ||||
−0.520283 | + | 0.853994i | \(0.674174\pi\) | |||||||
\(410\) | 45.9134 | 2.26750 | ||||||||
\(411\) | −11.4578 | −0.565174 | ||||||||
\(412\) | −2.54539 | −0.125402 | ||||||||
\(413\) | 10.5463 | 0.518950 | ||||||||
\(414\) | −1.90727 | −0.0937371 | ||||||||
\(415\) | 20.6519 | 1.01376 | ||||||||
\(416\) | 3.79704 | 0.186165 | ||||||||
\(417\) | −13.1680 | −0.644841 | ||||||||
\(418\) | 54.3274 | 2.65724 | ||||||||
\(419\) | −6.59641 | −0.322256 | −0.161128 | − | 0.986934i | \(-0.551513\pi\) | ||||
−0.161128 | + | 0.986934i | \(0.551513\pi\) | |||||||
\(420\) | 5.08408 | 0.248078 | ||||||||
\(421\) | 5.15248 | 0.251117 | 0.125558 | − | 0.992086i | \(-0.459928\pi\) | ||||
0.125558 | + | 0.992086i | \(0.459928\pi\) | |||||||
\(422\) | −27.6277 | −1.34490 | ||||||||
\(423\) | −13.2421 | −0.643854 | ||||||||
\(424\) | −5.28252 | −0.256542 | ||||||||
\(425\) | 46.8335 | 2.27176 | ||||||||
\(426\) | −12.3615 | −0.598915 | ||||||||
\(427\) | 10.0701 | 0.487324 | ||||||||
\(428\) | −6.96570 | −0.336700 | ||||||||
\(429\) | −22.3147 | −1.07737 | ||||||||
\(430\) | −22.4651 | −1.08336 | ||||||||
\(431\) | 15.9709 | 0.769289 | 0.384645 | − | 0.923065i | \(-0.374324\pi\) | ||||
0.384645 | + | 0.923065i | \(0.374324\pi\) | |||||||
\(432\) | 4.79005 | 0.230461 | ||||||||
\(433\) | −10.3062 | −0.495285 | −0.247642 | − | 0.968852i | \(-0.579656\pi\) | ||||
−0.247642 | + | 0.968852i | \(0.579656\pi\) | |||||||
\(434\) | −6.06405 | −0.291084 | ||||||||
\(435\) | −19.5274 | −0.936269 | ||||||||
\(436\) | −9.52787 | −0.456302 | ||||||||
\(437\) | −7.74354 | −0.370424 | ||||||||
\(438\) | 4.88047 | 0.233198 | ||||||||
\(439\) | 17.0755 | 0.814967 | 0.407483 | − | 0.913213i | \(-0.366406\pi\) | ||||
0.407483 | + | 0.913213i | \(0.366406\pi\) | |||||||
\(440\) | −26.2360 | −1.25075 | ||||||||
\(441\) | 11.2688 | 0.536612 | ||||||||
\(442\) | 14.3468 | 0.682409 | ||||||||
\(443\) | −2.09547 | −0.0995586 | −0.0497793 | − | 0.998760i | \(-0.515852\pi\) | ||||
−0.0497793 | + | 0.998760i | \(0.515852\pi\) | |||||||
\(444\) | −0.369369 | −0.0175295 | ||||||||
\(445\) | 64.8216 | 3.07284 | ||||||||
\(446\) | 2.83303 | 0.134148 | ||||||||
\(447\) | 1.14982 | 0.0543848 | ||||||||
\(448\) | 1.30479 | 0.0616453 | ||||||||
\(449\) | −32.2664 | −1.52275 | −0.761373 | − | 0.648314i | \(-0.775474\pi\) | ||||
−0.761373 | + | 0.648314i | \(0.775474\pi\) | |||||||
\(450\) | 26.3665 | 1.24293 | ||||||||
\(451\) | −69.2489 | −3.26081 | ||||||||
\(452\) | −2.68341 | −0.126217 | ||||||||
\(453\) | −5.61378 | −0.263759 | ||||||||
\(454\) | 16.4681 | 0.772886 | ||||||||
\(455\) | 20.6632 | 0.968704 | ||||||||
\(456\) | 8.06853 | 0.377843 | ||||||||
\(457\) | −2.59763 | −0.121512 | −0.0607560 | − | 0.998153i | \(-0.519351\pi\) | ||||
−0.0607560 | + | 0.998153i | \(0.519351\pi\) | |||||||
\(458\) | −1.54283 | −0.0720917 | ||||||||
\(459\) | 18.0988 | 0.844780 | ||||||||
\(460\) | 3.73954 | 0.174357 | ||||||||
\(461\) | −14.9302 | −0.695368 | −0.347684 | − | 0.937612i | \(-0.613032\pi\) | ||||
−0.347684 | + | 0.937612i | \(0.613032\pi\) | |||||||
\(462\) | −7.66806 | −0.356750 | ||||||||
\(463\) | 13.4971 | 0.627265 | 0.313633 | − | 0.949544i | \(-0.398454\pi\) | ||||
0.313633 | + | 0.949544i | \(0.398454\pi\) | |||||||
\(464\) | −5.01155 | −0.232656 | ||||||||
\(465\) | 18.1091 | 0.839789 | ||||||||
\(466\) | −22.7015 | −1.05163 | ||||||||
\(467\) | −20.2483 | −0.936982 | −0.468491 | − | 0.883468i | \(-0.655202\pi\) | ||||
−0.468491 | + | 0.883468i | \(0.655202\pi\) | |||||||
\(468\) | 8.07702 | 0.373360 | ||||||||
\(469\) | −6.89450 | −0.318358 | ||||||||
\(470\) | 25.9636 | 1.19761 | ||||||||
\(471\) | −21.1113 | −0.972759 | ||||||||
\(472\) | −8.08279 | −0.372041 | ||||||||
\(473\) | 33.8829 | 1.55794 | ||||||||
\(474\) | −7.36094 | −0.338099 | ||||||||
\(475\) | 107.048 | 4.91172 | ||||||||
\(476\) | 4.93003 | 0.225967 | ||||||||
\(477\) | −11.2369 | −0.514502 | ||||||||
\(478\) | −1.25406 | −0.0573593 | ||||||||
\(479\) | −38.1793 | −1.74446 | −0.872229 | − | 0.489097i | \(-0.837326\pi\) | ||||
−0.872229 | + | 0.489097i | \(0.837326\pi\) | |||||||
\(480\) | −3.89648 | −0.177849 | ||||||||
\(481\) | −1.50122 | −0.0684500 | ||||||||
\(482\) | −0.519454 | −0.0236605 | ||||||||
\(483\) | 1.09296 | 0.0497316 | ||||||||
\(484\) | 28.5705 | 1.29866 | ||||||||
\(485\) | −19.0101 | −0.863203 | ||||||||
\(486\) | 16.1513 | 0.732636 | ||||||||
\(487\) | −24.2739 | −1.09995 | −0.549977 | − | 0.835180i | \(-0.685363\pi\) | ||||
−0.549977 | + | 0.835180i | \(0.685363\pi\) | |||||||
\(488\) | −7.71779 | −0.349368 | ||||||||
\(489\) | 5.86356 | 0.265159 | ||||||||
\(490\) | −22.0946 | −0.998132 | ||||||||
\(491\) | −11.5479 | −0.521150 | −0.260575 | − | 0.965454i | \(-0.583912\pi\) | ||||
−0.260575 | + | 0.965454i | \(0.583912\pi\) | |||||||
\(492\) | −10.2846 | −0.463667 | ||||||||
\(493\) | −18.9358 | −0.852824 | ||||||||
\(494\) | 32.7928 | 1.47542 | ||||||||
\(495\) | −55.8089 | −2.50842 | ||||||||
\(496\) | 4.64754 | 0.208681 | ||||||||
\(497\) | −17.2643 | −0.774408 | ||||||||
\(498\) | −4.62603 | −0.207297 | ||||||||
\(499\) | −14.7381 | −0.659770 | −0.329885 | − | 0.944021i | \(-0.607010\pi\) | ||||
−0.329885 | + | 0.944021i | \(0.607010\pi\) | |||||||
\(500\) | −30.8426 | −1.37932 | ||||||||
\(501\) | −7.54490 | −0.337081 | ||||||||
\(502\) | −23.4513 | −1.04668 | ||||||||
\(503\) | 31.8620 | 1.42066 | 0.710328 | − | 0.703871i | \(-0.248547\pi\) | ||||
0.710328 | + | 0.703871i | \(0.248547\pi\) | |||||||
\(504\) | 2.77552 | 0.123632 | ||||||||
\(505\) | 36.2401 | 1.61266 | ||||||||
\(506\) | −5.64016 | −0.250736 | ||||||||
\(507\) | −1.32432 | −0.0588153 | ||||||||
\(508\) | −13.4700 | −0.597634 | ||||||||
\(509\) | 26.1479 | 1.15899 | 0.579493 | − | 0.814977i | \(-0.303251\pi\) | ||||
0.579493 | + | 0.814977i | \(0.303251\pi\) | |||||||
\(510\) | −14.7226 | −0.651926 | ||||||||
\(511\) | 6.81617 | 0.301530 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 41.3688 | 1.82648 | ||||||||
\(514\) | 0.960802 | 0.0423792 | ||||||||
\(515\) | 10.6161 | 0.467803 | ||||||||
\(516\) | 5.03218 | 0.221529 | ||||||||
\(517\) | −39.1596 | −1.72224 | ||||||||
\(518\) | −0.515869 | −0.0226660 | ||||||||
\(519\) | 12.0693 | 0.529782 | ||||||||
\(520\) | −15.8364 | −0.694474 | ||||||||
\(521\) | 4.61006 | 0.201970 | 0.100985 | − | 0.994888i | \(-0.467801\pi\) | ||||
0.100985 | + | 0.994888i | \(0.467801\pi\) | |||||||
\(522\) | −10.6605 | −0.466598 | ||||||||
\(523\) | 25.0913 | 1.09716 | 0.548582 | − | 0.836097i | \(-0.315168\pi\) | ||||
0.548582 | + | 0.836097i | \(0.315168\pi\) | |||||||
\(524\) | 18.2790 | 0.798523 | ||||||||
\(525\) | −15.1094 | −0.659427 | ||||||||
\(526\) | 18.8333 | 0.821169 | ||||||||
\(527\) | 17.5604 | 0.764942 | ||||||||
\(528\) | 5.87687 | 0.255758 | ||||||||
\(529\) | −22.1961 | −0.965047 | ||||||||
\(530\) | 22.0320 | 0.957007 | ||||||||
\(531\) | −17.1936 | −0.746139 | ||||||||
\(532\) | 11.2687 | 0.488559 | ||||||||
\(533\) | −41.7997 | −1.81055 | ||||||||
\(534\) | −14.5200 | −0.628344 | ||||||||
\(535\) | 29.0521 | 1.25603 | ||||||||
\(536\) | 5.28401 | 0.228234 | ||||||||
\(537\) | 21.6924 | 0.936097 | ||||||||
\(538\) | 13.2221 | 0.570046 | ||||||||
\(539\) | 33.3242 | 1.43537 | ||||||||
\(540\) | −19.9780 | −0.859716 | ||||||||
\(541\) | −11.3338 | −0.487278 | −0.243639 | − | 0.969866i | \(-0.578341\pi\) | ||||
−0.243639 | + | 0.969866i | \(0.578341\pi\) | |||||||
\(542\) | 4.48027 | 0.192444 | ||||||||
\(543\) | 4.76996 | 0.204699 | ||||||||
\(544\) | −3.77842 | −0.161998 | ||||||||
\(545\) | 39.7382 | 1.70220 | ||||||||
\(546\) | −4.62855 | −0.198084 | ||||||||
\(547\) | 29.0927 | 1.24391 | 0.621957 | − | 0.783051i | \(-0.286338\pi\) | ||||
0.621957 | + | 0.783051i | \(0.286338\pi\) | |||||||
\(548\) | 12.2643 | 0.523904 | ||||||||
\(549\) | −16.4172 | −0.700668 | ||||||||
\(550\) | 77.9708 | 3.32469 | ||||||||
\(551\) | −43.2819 | −1.84387 | ||||||||
\(552\) | −0.837658 | −0.0356531 | ||||||||
\(553\) | −10.2804 | −0.437169 | ||||||||
\(554\) | 15.8791 | 0.674638 | ||||||||
\(555\) | 1.54054 | 0.0653923 | ||||||||
\(556\) | 14.0948 | 0.597754 | ||||||||
\(557\) | −24.3539 | −1.03191 | −0.515954 | − | 0.856616i | \(-0.672563\pi\) | ||||
−0.515954 | + | 0.856616i | \(0.672563\pi\) | |||||||
\(558\) | 9.88619 | 0.418516 | ||||||||
\(559\) | 20.4522 | 0.865037 | ||||||||
\(560\) | −5.44191 | −0.229963 | ||||||||
\(561\) | 22.2053 | 0.937508 | ||||||||
\(562\) | 0.405076 | 0.0170871 | ||||||||
\(563\) | 34.9975 | 1.47497 | 0.737485 | − | 0.675363i | \(-0.236013\pi\) | ||||
0.737485 | + | 0.675363i | \(0.236013\pi\) | |||||||
\(564\) | −5.81585 | −0.244891 | ||||||||
\(565\) | 11.1918 | 0.470841 | ||||||||
\(566\) | 6.16780 | 0.259252 | ||||||||
\(567\) | 2.48755 | 0.104467 | ||||||||
\(568\) | 13.2315 | 0.555181 | ||||||||
\(569\) | −10.6294 | −0.445607 | −0.222804 | − | 0.974863i | \(-0.571521\pi\) | ||||
−0.222804 | + | 0.974863i | \(0.571521\pi\) | |||||||
\(570\) | −33.6517 | −1.40951 | ||||||||
\(571\) | 8.04737 | 0.336772 | 0.168386 | − | 0.985721i | \(-0.446144\pi\) | ||||
0.168386 | + | 0.985721i | \(0.446144\pi\) | |||||||
\(572\) | 23.8853 | 0.998695 | ||||||||
\(573\) | −18.9189 | −0.790350 | ||||||||
\(574\) | −14.3637 | −0.599530 | ||||||||
\(575\) | −11.1135 | −0.463467 | ||||||||
\(576\) | −2.12719 | −0.0886328 | ||||||||
\(577\) | 24.5992 | 1.02408 | 0.512039 | − | 0.858962i | \(-0.328890\pi\) | ||||
0.512039 | + | 0.858962i | \(0.328890\pi\) | |||||||
\(578\) | 2.72354 | 0.113284 | ||||||||
\(579\) | −7.25436 | −0.301481 | ||||||||
\(580\) | 20.9018 | 0.867902 | ||||||||
\(581\) | −6.46080 | −0.268039 | ||||||||
\(582\) | 4.25826 | 0.176511 | ||||||||
\(583\) | −33.2297 | −1.37623 | ||||||||
\(584\) | −5.22398 | −0.216170 | ||||||||
\(585\) | −33.6871 | −1.39279 | ||||||||
\(586\) | −9.66195 | −0.399132 | ||||||||
\(587\) | 45.1241 | 1.86247 | 0.931236 | − | 0.364416i | \(-0.118731\pi\) | ||||
0.931236 | + | 0.364416i | \(0.118731\pi\) | |||||||
\(588\) | 4.94919 | 0.204101 | ||||||||
\(589\) | 40.1381 | 1.65386 | ||||||||
\(590\) | 33.7111 | 1.38787 | ||||||||
\(591\) | −14.5878 | −0.600063 | ||||||||
\(592\) | 0.395367 | 0.0162495 | ||||||||
\(593\) | −11.4214 | −0.469022 | −0.234511 | − | 0.972113i | \(-0.575349\pi\) | ||||
−0.234511 | + | 0.972113i | \(0.575349\pi\) | |||||||
\(594\) | 30.1318 | 1.23632 | ||||||||
\(595\) | −20.5618 | −0.842953 | ||||||||
\(596\) | −1.23075 | −0.0504136 | ||||||||
\(597\) | 14.3774 | 0.588429 | ||||||||
\(598\) | −3.40449 | −0.139220 | ||||||||
\(599\) | −2.57802 | −0.105335 | −0.0526676 | − | 0.998612i | \(-0.516772\pi\) | ||||
−0.0526676 | + | 0.998612i | \(0.516772\pi\) | |||||||
\(600\) | 11.5800 | 0.472750 | ||||||||
\(601\) | −1.87053 | −0.0763004 | −0.0381502 | − | 0.999272i | \(-0.512147\pi\) | ||||
−0.0381502 | + | 0.999272i | \(0.512147\pi\) | |||||||
\(602\) | 7.02804 | 0.286442 | ||||||||
\(603\) | 11.2401 | 0.457731 | ||||||||
\(604\) | 6.00890 | 0.244499 | ||||||||
\(605\) | −119.160 | −4.84453 | ||||||||
\(606\) | −8.11780 | −0.329763 | ||||||||
\(607\) | 35.1472 | 1.42658 | 0.713290 | − | 0.700869i | \(-0.247204\pi\) | ||||
0.713290 | + | 0.700869i | \(0.247204\pi\) | |||||||
\(608\) | −8.63642 | −0.350253 | ||||||||
\(609\) | 6.10903 | 0.247550 | ||||||||
\(610\) | 32.1888 | 1.30329 | ||||||||
\(611\) | −23.6373 | −0.956263 | ||||||||
\(612\) | −8.03740 | −0.324893 | ||||||||
\(613\) | 3.70585 | 0.149678 | 0.0748389 | − | 0.997196i | \(-0.476156\pi\) | ||||
0.0748389 | + | 0.997196i | \(0.476156\pi\) | |||||||
\(614\) | 20.2896 | 0.818822 | ||||||||
\(615\) | 42.8944 | 1.72967 | ||||||||
\(616\) | 8.20776 | 0.330700 | ||||||||
\(617\) | −19.9943 | −0.804940 | −0.402470 | − | 0.915433i | \(-0.631848\pi\) | ||||
−0.402470 | + | 0.915433i | \(0.631848\pi\) | |||||||
\(618\) | −2.37802 | −0.0956580 | ||||||||
\(619\) | −30.3747 | −1.22086 | −0.610430 | − | 0.792070i | \(-0.709003\pi\) | ||||
−0.610430 | + | 0.792070i | \(0.709003\pi\) | |||||||
\(620\) | −19.3837 | −0.778466 | ||||||||
\(621\) | −4.29483 | −0.172346 | ||||||||
\(622\) | −14.9639 | −0.599999 | ||||||||
\(623\) | −20.2790 | −0.812461 | ||||||||
\(624\) | 3.54737 | 0.142008 | ||||||||
\(625\) | 66.6611 | 2.66644 | ||||||||
\(626\) | −33.8135 | −1.35146 | ||||||||
\(627\) | 50.7551 | 2.02696 | ||||||||
\(628\) | 22.5972 | 0.901727 | ||||||||
\(629\) | 1.49386 | 0.0595642 | ||||||||
\(630\) | −11.5760 | −0.461197 | ||||||||
\(631\) | 31.0024 | 1.23419 | 0.617093 | − | 0.786890i | \(-0.288310\pi\) | ||||
0.617093 | + | 0.786890i | \(0.288310\pi\) | |||||||
\(632\) | 7.87903 | 0.313411 | ||||||||
\(633\) | −25.8111 | −1.02590 | ||||||||
\(634\) | 22.0889 | 0.877264 | ||||||||
\(635\) | 56.1797 | 2.22942 | ||||||||
\(636\) | −4.93516 | −0.195692 | ||||||||
\(637\) | 20.1150 | 0.796984 | ||||||||
\(638\) | −31.5252 | −1.24809 | ||||||||
\(639\) | 28.1459 | 1.11343 | ||||||||
\(640\) | 4.17073 | 0.164863 | ||||||||
\(641\) | 36.7042 | 1.44973 | 0.724864 | − | 0.688892i | \(-0.241902\pi\) | ||||
0.724864 | + | 0.688892i | \(0.241902\pi\) | |||||||
\(642\) | −6.50767 | −0.256837 | ||||||||
\(643\) | 20.7356 | 0.817733 | 0.408867 | − | 0.912594i | \(-0.365924\pi\) | ||||
0.408867 | + | 0.912594i | \(0.365924\pi\) | |||||||
\(644\) | −1.16989 | −0.0461001 | ||||||||
\(645\) | −20.9879 | −0.826396 | ||||||||
\(646\) | −32.6320 | −1.28389 | ||||||||
\(647\) | −5.71625 | −0.224729 | −0.112364 | − | 0.993667i | \(-0.535842\pi\) | ||||
−0.112364 | + | 0.993667i | \(0.535842\pi\) | |||||||
\(648\) | −1.90648 | −0.0748937 | ||||||||
\(649\) | −50.8448 | −1.99583 | ||||||||
\(650\) | 47.0644 | 1.84602 | ||||||||
\(651\) | −5.66530 | −0.222041 | ||||||||
\(652\) | −6.27626 | −0.245797 | ||||||||
\(653\) | 47.7908 | 1.87020 | 0.935099 | − | 0.354388i | \(-0.115311\pi\) | ||||
0.935099 | + | 0.354388i | \(0.115311\pi\) | |||||||
\(654\) | −8.90137 | −0.348071 | ||||||||
\(655\) | −76.2370 | −2.97882 | ||||||||
\(656\) | 11.0085 | 0.429809 | ||||||||
\(657\) | −11.1124 | −0.433535 | ||||||||
\(658\) | −8.12253 | −0.316649 | ||||||||
\(659\) | −2.76816 | −0.107832 | −0.0539161 | − | 0.998545i | \(-0.517170\pi\) | ||||
−0.0539161 | + | 0.998545i | \(0.517170\pi\) | |||||||
\(660\) | −24.5109 | −0.954084 | ||||||||
\(661\) | −21.9511 | −0.853799 | −0.426900 | − | 0.904299i | \(-0.640394\pi\) | ||||
−0.426900 | + | 0.904299i | \(0.640394\pi\) | |||||||
\(662\) | 18.2309 | 0.708565 | ||||||||
\(663\) | 13.4034 | 0.520547 | ||||||||
\(664\) | 4.95162 | 0.192160 | ||||||||
\(665\) | −46.9986 | −1.82253 | ||||||||
\(666\) | 0.841019 | 0.0325888 | ||||||||
\(667\) | 4.49343 | 0.173986 | ||||||||
\(668\) | 8.07593 | 0.312467 | ||||||||
\(669\) | 2.64675 | 0.102329 | ||||||||
\(670\) | −22.0382 | −0.851409 | ||||||||
\(671\) | −48.5488 | −1.87421 | ||||||||
\(672\) | 1.21899 | 0.0470235 | ||||||||
\(673\) | −41.9868 | −1.61847 | −0.809237 | − | 0.587483i | \(-0.800119\pi\) | ||||
−0.809237 | + | 0.587483i | \(0.800119\pi\) | |||||||
\(674\) | 0.521940 | 0.0201044 | ||||||||
\(675\) | 59.3726 | 2.28525 | ||||||||
\(676\) | 1.41753 | 0.0545206 | ||||||||
\(677\) | 9.83797 | 0.378104 | 0.189052 | − | 0.981967i | \(-0.439459\pi\) | ||||
0.189052 | + | 0.981967i | \(0.439459\pi\) | |||||||
\(678\) | −2.50696 | −0.0962792 | ||||||||
\(679\) | 5.94717 | 0.228232 | ||||||||
\(680\) | 15.7588 | 0.604322 | ||||||||
\(681\) | 15.3852 | 0.589563 | ||||||||
\(682\) | 29.2354 | 1.11948 | ||||||||
\(683\) | 2.13712 | 0.0817747 | 0.0408874 | − | 0.999164i | \(-0.486982\pi\) | ||||
0.0408874 | + | 0.999164i | \(0.486982\pi\) | |||||||
\(684\) | −18.3713 | −0.702443 | ||||||||
\(685\) | −51.1510 | −1.95438 | ||||||||
\(686\) | 16.0456 | 0.612626 | ||||||||
\(687\) | −1.44138 | −0.0549921 | ||||||||
\(688\) | −5.38636 | −0.205353 | ||||||||
\(689\) | −20.0579 | −0.764147 | ||||||||
\(690\) | 3.49365 | 0.133001 | ||||||||
\(691\) | −7.26539 | −0.276388 | −0.138194 | − | 0.990405i | \(-0.544130\pi\) | ||||
−0.138194 | + | 0.990405i | \(0.544130\pi\) | |||||||
\(692\) | −12.9187 | −0.491096 | ||||||||
\(693\) | 17.4594 | 0.663229 | ||||||||
\(694\) | 16.6049 | 0.630314 | ||||||||
\(695\) | −58.7858 | −2.22987 | ||||||||
\(696\) | −4.68202 | −0.177471 | ||||||||
\(697\) | 41.5947 | 1.57551 | ||||||||
\(698\) | 2.71319 | 0.102696 | ||||||||
\(699\) | −21.2088 | −0.802189 | ||||||||
\(700\) | 16.1728 | 0.611275 | ||||||||
\(701\) | 12.7895 | 0.483052 | 0.241526 | − | 0.970394i | \(-0.422352\pi\) | ||||
0.241526 | + | 0.970394i | \(0.422352\pi\) | |||||||
\(702\) | 18.1880 | 0.686462 | ||||||||
\(703\) | 3.41455 | 0.128782 | ||||||||
\(704\) | −6.29050 | −0.237082 | ||||||||
\(705\) | 24.2563 | 0.913547 | ||||||||
\(706\) | −13.9911 | −0.526564 | ||||||||
\(707\) | −11.3375 | −0.426390 | ||||||||
\(708\) | −7.55130 | −0.283795 | ||||||||
\(709\) | −29.2608 | −1.09891 | −0.549455 | − | 0.835523i | \(-0.685165\pi\) | ||||
−0.549455 | + | 0.835523i | \(0.685165\pi\) | |||||||
\(710\) | −55.1850 | −2.07106 | ||||||||
\(711\) | 16.7602 | 0.628555 | ||||||||
\(712\) | 15.5420 | 0.582462 | ||||||||
\(713\) | −4.16706 | −0.156058 | ||||||||
\(714\) | 4.60585 | 0.172370 | ||||||||
\(715\) | −99.6192 | −3.72555 | ||||||||
\(716\) | −23.2192 | −0.867742 | ||||||||
\(717\) | −1.17160 | −0.0437541 | ||||||||
\(718\) | −28.3376 | −1.05755 | ||||||||
\(719\) | 0.382835 | 0.0142773 | 0.00713867 | − | 0.999975i | \(-0.497728\pi\) | ||||
0.00713867 | + | 0.999975i | \(0.497728\pi\) | |||||||
\(720\) | 8.87192 | 0.330637 | ||||||||
\(721\) | −3.32119 | −0.123688 | ||||||||
\(722\) | −55.5877 | −2.06876 | ||||||||
\(723\) | −0.485297 | −0.0180484 | ||||||||
\(724\) | −5.10569 | −0.189751 | ||||||||
\(725\) | −62.1182 | −2.30701 | ||||||||
\(726\) | 26.6918 | 0.990626 | ||||||||
\(727\) | −5.33183 | −0.197747 | −0.0988734 | − | 0.995100i | \(-0.531524\pi\) | ||||
−0.0988734 | + | 0.995100i | \(0.531524\pi\) | |||||||
\(728\) | 4.95433 | 0.183620 | ||||||||
\(729\) | 9.36979 | 0.347029 | ||||||||
\(730\) | 21.7878 | 0.806403 | ||||||||
\(731\) | −20.3519 | −0.752743 | ||||||||
\(732\) | −7.21030 | −0.266501 | ||||||||
\(733\) | −37.8541 | −1.39817 | −0.699087 | − | 0.715037i | \(-0.746410\pi\) | ||||
−0.699087 | + | 0.715037i | \(0.746410\pi\) | |||||||
\(734\) | 29.5228 | 1.08970 | ||||||||
\(735\) | −20.6418 | −0.761383 | ||||||||
\(736\) | 0.896615 | 0.0330497 | ||||||||
\(737\) | 33.2391 | 1.22438 | ||||||||
\(738\) | 23.4171 | 0.861995 | ||||||||
\(739\) | 6.28613 | 0.231239 | 0.115620 | − | 0.993294i | \(-0.463115\pi\) | ||||
0.115620 | + | 0.993294i | \(0.463115\pi\) | |||||||
\(740\) | −1.64897 | −0.0606173 | ||||||||
\(741\) | 30.6365 | 1.12546 | ||||||||
\(742\) | −6.89255 | −0.253034 | ||||||||
\(743\) | −41.8927 | −1.53689 | −0.768447 | − | 0.639913i | \(-0.778970\pi\) | ||||
−0.768447 | + | 0.639913i | \(0.778970\pi\) | |||||||
\(744\) | 4.34194 | 0.159183 | ||||||||
\(745\) | 5.13314 | 0.188064 | ||||||||
\(746\) | 26.9628 | 0.987178 | ||||||||
\(747\) | 10.5330 | 0.385383 | ||||||||
\(748\) | −23.7682 | −0.869050 | ||||||||
\(749\) | −9.08875 | −0.332096 | ||||||||
\(750\) | −28.8145 | −1.05216 | ||||||||
\(751\) | −4.92682 | −0.179782 | −0.0898911 | − | 0.995952i | \(-0.528652\pi\) | ||||
−0.0898911 | + | 0.995952i | \(0.528652\pi\) | |||||||
\(752\) | 6.22519 | 0.227009 | ||||||||
\(753\) | −21.9093 | −0.798418 | ||||||||
\(754\) | −19.0291 | −0.692998 | ||||||||
\(755\) | −25.0615 | −0.912082 | ||||||||
\(756\) | 6.24998 | 0.227310 | ||||||||
\(757\) | 3.54979 | 0.129019 | 0.0645097 | − | 0.997917i | \(-0.479452\pi\) | ||||
0.0645097 | + | 0.997917i | \(0.479452\pi\) | |||||||
\(758\) | 28.1649 | 1.02300 | ||||||||
\(759\) | −5.26929 | −0.191263 | ||||||||
\(760\) | 36.0202 | 1.30659 | ||||||||
\(761\) | 18.2164 | 0.660346 | 0.330173 | − | 0.943921i | \(-0.392893\pi\) | ||||
0.330173 | + | 0.943921i | \(0.392893\pi\) | |||||||
\(762\) | −12.5843 | −0.455880 | ||||||||
\(763\) | −12.4318 | −0.450062 | ||||||||
\(764\) | 20.2505 | 0.732637 | ||||||||
\(765\) | 33.5219 | 1.21199 | ||||||||
\(766\) | −4.76207 | −0.172061 | ||||||||
\(767\) | −30.6907 | −1.10818 | ||||||||
\(768\) | −0.934245 | −0.0337117 | ||||||||
\(769\) | −13.3668 | −0.482021 | −0.241010 | − | 0.970523i | \(-0.577479\pi\) | ||||
−0.241010 | + | 0.970523i | \(0.577479\pi\) | |||||||
\(770\) | −34.2324 | −1.23365 | ||||||||
\(771\) | 0.897624 | 0.0323272 | ||||||||
\(772\) | 7.76495 | 0.279467 | ||||||||
\(773\) | 37.1140 | 1.33490 | 0.667450 | − | 0.744655i | \(-0.267386\pi\) | ||||
0.667450 | + | 0.744655i | \(0.267386\pi\) | |||||||
\(774\) | −11.4578 | −0.411842 | ||||||||
\(775\) | 57.6063 | 2.06928 | ||||||||
\(776\) | −4.55797 | −0.163622 | ||||||||
\(777\) | −0.481948 | −0.0172898 | ||||||||
\(778\) | 23.8263 | 0.854214 | ||||||||
\(779\) | 95.0739 | 3.40637 | ||||||||
\(780\) | −14.7951 | −0.529750 | ||||||||
\(781\) | 83.2328 | 2.97830 | ||||||||
\(782\) | 3.38779 | 0.121147 | ||||||||
\(783\) | −24.0056 | −0.857889 | ||||||||
\(784\) | −5.29754 | −0.189198 | ||||||||
\(785\) | −94.2470 | −3.36382 | ||||||||
\(786\) | 17.0771 | 0.609120 | ||||||||
\(787\) | 12.8219 | 0.457051 | 0.228525 | − | 0.973538i | \(-0.426610\pi\) | ||||
0.228525 | + | 0.973538i | \(0.426610\pi\) | |||||||
\(788\) | 15.6146 | 0.556246 | ||||||||
\(789\) | 17.5949 | 0.626394 | ||||||||
\(790\) | −32.8613 | −1.16915 | ||||||||
\(791\) | −3.50127 | −0.124491 | ||||||||
\(792\) | −13.3811 | −0.475476 | ||||||||
\(793\) | −29.3048 | −1.04064 | ||||||||
\(794\) | −8.11106 | −0.287851 | ||||||||
\(795\) | 20.5832 | 0.730013 | ||||||||
\(796\) | −15.3893 | −0.545461 | ||||||||
\(797\) | −42.5698 | −1.50790 | −0.753951 | − | 0.656931i | \(-0.771854\pi\) | ||||
−0.753951 | + | 0.656931i | \(0.771854\pi\) | |||||||
\(798\) | 10.5277 | 0.372676 | ||||||||
\(799\) | 23.5214 | 0.832126 | ||||||||
\(800\) | −12.3950 | −0.438229 | ||||||||
\(801\) | 33.0608 | 1.16814 | ||||||||
\(802\) | 11.8831 | 0.419608 | ||||||||
\(803\) | −32.8615 | −1.15966 | ||||||||
\(804\) | 4.93656 | 0.174099 | ||||||||
\(805\) | 4.87930 | 0.171973 | ||||||||
\(806\) | 17.6469 | 0.621586 | ||||||||
\(807\) | 12.3527 | 0.434836 | ||||||||
\(808\) | 8.68916 | 0.305683 | ||||||||
\(809\) | −4.66593 | −0.164045 | −0.0820227 | − | 0.996630i | \(-0.526138\pi\) | ||||
−0.0820227 | + | 0.996630i | \(0.526138\pi\) | |||||||
\(810\) | 7.95142 | 0.279385 | ||||||||
\(811\) | −22.3456 | −0.784660 | −0.392330 | − | 0.919824i | \(-0.628331\pi\) | ||||
−0.392330 | + | 0.919824i | \(0.628331\pi\) | |||||||
\(812\) | −6.53900 | −0.229474 | ||||||||
\(813\) | 4.18567 | 0.146798 | ||||||||
\(814\) | 2.48706 | 0.0871713 | ||||||||
\(815\) | 26.1766 | 0.916926 | ||||||||
\(816\) | −3.52997 | −0.123574 | ||||||||
\(817\) | −46.5188 | −1.62749 | ||||||||
\(818\) | 21.0442 | 0.735792 | ||||||||
\(819\) | 10.5388 | 0.368255 | ||||||||
\(820\) | −45.9134 | −1.60337 | ||||||||
\(821\) | 17.8228 | 0.622021 | 0.311011 | − | 0.950406i | \(-0.399333\pi\) | ||||
0.311011 | + | 0.950406i | \(0.399333\pi\) | |||||||
\(822\) | 11.4578 | 0.399638 | ||||||||
\(823\) | 5.48252 | 0.191109 | 0.0955543 | − | 0.995424i | \(-0.469538\pi\) | ||||
0.0955543 | + | 0.995424i | \(0.469538\pi\) | |||||||
\(824\) | 2.54539 | 0.0886729 | ||||||||
\(825\) | 72.8438 | 2.53610 | ||||||||
\(826\) | −10.5463 | −0.366953 | ||||||||
\(827\) | 53.7308 | 1.86840 | 0.934202 | − | 0.356744i | \(-0.116113\pi\) | ||||
0.934202 | + | 0.356744i | \(0.116113\pi\) | |||||||
\(828\) | 1.90727 | 0.0662821 | ||||||||
\(829\) | −9.63718 | −0.334713 | −0.167357 | − | 0.985896i | \(-0.553523\pi\) | ||||
−0.167357 | + | 0.985896i | \(0.553523\pi\) | |||||||
\(830\) | −20.6519 | −0.716837 | ||||||||
\(831\) | 14.8350 | 0.514619 | ||||||||
\(832\) | −3.79704 | −0.131639 | ||||||||
\(833\) | −20.0163 | −0.693524 | ||||||||
\(834\) | 13.1680 | 0.455971 | ||||||||
\(835\) | −33.6825 | −1.16563 | ||||||||
\(836\) | −54.3274 | −1.87895 | ||||||||
\(837\) | 22.2620 | 0.769486 | ||||||||
\(838\) | 6.59641 | 0.227869 | ||||||||
\(839\) | −15.0986 | −0.521260 | −0.260630 | − | 0.965439i | \(-0.583930\pi\) | ||||
−0.260630 | + | 0.965439i | \(0.583930\pi\) | |||||||
\(840\) | −5.08408 | −0.175417 | ||||||||
\(841\) | −3.88433 | −0.133942 | ||||||||
\(842\) | −5.15248 | −0.177566 | ||||||||
\(843\) | 0.378440 | 0.0130342 | ||||||||
\(844\) | 27.6277 | 0.950986 | ||||||||
\(845\) | −5.91216 | −0.203384 | ||||||||
\(846\) | 13.2421 | 0.455274 | ||||||||
\(847\) | 37.2783 | 1.28090 | ||||||||
\(848\) | 5.28252 | 0.181402 | ||||||||
\(849\) | 5.76224 | 0.197760 | ||||||||
\(850\) | −46.8335 | −1.60638 | ||||||||
\(851\) | −0.354492 | −0.0121518 | ||||||||
\(852\) | 12.3615 | 0.423497 | ||||||||
\(853\) | 0.329799 | 0.0112921 | 0.00564606 | − | 0.999984i | \(-0.498203\pi\) | ||||
0.00564606 | + | 0.999984i | \(0.498203\pi\) | |||||||
\(854\) | −10.0701 | −0.344590 | ||||||||
\(855\) | 76.6216 | 2.62040 | ||||||||
\(856\) | 6.96570 | 0.238083 | ||||||||
\(857\) | −27.8084 | −0.949918 | −0.474959 | − | 0.880008i | \(-0.657537\pi\) | ||||
−0.474959 | + | 0.880008i | \(0.657537\pi\) | |||||||
\(858\) | 22.3147 | 0.761812 | ||||||||
\(859\) | 9.14814 | 0.312130 | 0.156065 | − | 0.987747i | \(-0.450119\pi\) | ||||
0.156065 | + | 0.987747i | \(0.450119\pi\) | |||||||
\(860\) | 22.4651 | 0.766052 | ||||||||
\(861\) | −13.4192 | −0.457326 | ||||||||
\(862\) | −15.9709 | −0.543970 | ||||||||
\(863\) | −25.5236 | −0.868834 | −0.434417 | − | 0.900712i | \(-0.643046\pi\) | ||||
−0.434417 | + | 0.900712i | \(0.643046\pi\) | |||||||
\(864\) | −4.79005 | −0.162961 | ||||||||
\(865\) | 53.8805 | 1.83199 | ||||||||
\(866\) | 10.3062 | 0.350219 | ||||||||
\(867\) | 2.54445 | 0.0864142 | ||||||||
\(868\) | 6.06405 | 0.205827 | ||||||||
\(869\) | 49.5631 | 1.68131 | ||||||||
\(870\) | 19.5274 | 0.662042 | ||||||||
\(871\) | 20.0636 | 0.679829 | ||||||||
\(872\) | 9.52787 | 0.322655 | ||||||||
\(873\) | −9.69565 | −0.328148 | ||||||||
\(874\) | 7.74354 | 0.261929 | ||||||||
\(875\) | −40.2429 | −1.36046 | ||||||||
\(876\) | −4.88047 | −0.164896 | ||||||||
\(877\) | 44.8226 | 1.51355 | 0.756775 | − | 0.653675i | \(-0.226774\pi\) | ||||
0.756775 | + | 0.653675i | \(0.226774\pi\) | |||||||
\(878\) | −17.0755 | −0.576269 | ||||||||
\(879\) | −9.02663 | −0.304461 | ||||||||
\(880\) | 26.2360 | 0.884416 | ||||||||
\(881\) | −19.4925 | −0.656718 | −0.328359 | − | 0.944553i | \(-0.606496\pi\) | ||||
−0.328359 | + | 0.944553i | \(0.606496\pi\) | |||||||
\(882\) | −11.2688 | −0.379442 | ||||||||
\(883\) | 40.1851 | 1.35234 | 0.676169 | − | 0.736747i | \(-0.263639\pi\) | ||||
0.676169 | + | 0.736747i | \(0.263639\pi\) | |||||||
\(884\) | −14.3468 | −0.482536 | ||||||||
\(885\) | 31.4945 | 1.05867 | ||||||||
\(886\) | 2.09547 | 0.0703986 | ||||||||
\(887\) | 33.1379 | 1.11266 | 0.556330 | − | 0.830961i | \(-0.312209\pi\) | ||||
0.556330 | + | 0.830961i | \(0.312209\pi\) | |||||||
\(888\) | 0.369369 | 0.0123952 | ||||||||
\(889\) | −17.5754 | −0.589461 | ||||||||
\(890\) | −64.8216 | −2.17282 | ||||||||
\(891\) | −11.9927 | −0.401772 | ||||||||
\(892\) | −2.83303 | −0.0948570 | ||||||||
\(893\) | 53.7633 | 1.79912 | ||||||||
\(894\) | −1.14982 | −0.0384559 | ||||||||
\(895\) | 96.8411 | 3.23704 | ||||||||
\(896\) | −1.30479 | −0.0435898 | ||||||||
\(897\) | −3.18062 | −0.106198 | ||||||||
\(898\) | 32.2664 | 1.07674 | ||||||||
\(899\) | −23.2914 | −0.776812 | ||||||||
\(900\) | −26.3665 | −0.878883 | ||||||||
\(901\) | 19.9596 | 0.664950 | ||||||||
\(902\) | 69.2489 | 2.30574 | ||||||||
\(903\) | 6.56591 | 0.218500 | ||||||||
\(904\) | 2.68341 | 0.0892488 | ||||||||
\(905\) | 21.2944 | 0.707851 | ||||||||
\(906\) | 5.61378 | 0.186505 | ||||||||
\(907\) | −14.9243 | −0.495552 | −0.247776 | − | 0.968817i | \(-0.579700\pi\) | ||||
−0.247776 | + | 0.968817i | \(0.579700\pi\) | |||||||
\(908\) | −16.4681 | −0.546513 | ||||||||
\(909\) | 18.4835 | 0.613057 | ||||||||
\(910\) | −20.6632 | −0.684977 | ||||||||
\(911\) | −40.1885 | −1.33150 | −0.665752 | − | 0.746173i | \(-0.731889\pi\) | ||||
−0.665752 | + | 0.746173i | \(0.731889\pi\) | |||||||
\(912\) | −8.06853 | −0.267176 | ||||||||
\(913\) | 31.1482 | 1.03085 | ||||||||
\(914\) | 2.59763 | 0.0859219 | ||||||||
\(915\) | 30.0722 | 0.994158 | ||||||||
\(916\) | 1.54283 | 0.0509765 | ||||||||
\(917\) | 23.8502 | 0.787604 | ||||||||
\(918\) | −18.0988 | −0.597350 | ||||||||
\(919\) | −30.4167 | −1.00335 | −0.501677 | − | 0.865055i | \(-0.667283\pi\) | ||||
−0.501677 | + | 0.865055i | \(0.667283\pi\) | |||||||
\(920\) | −3.73954 | −0.123289 | ||||||||
\(921\) | 18.9555 | 0.624604 | ||||||||
\(922\) | 14.9302 | 0.491700 | ||||||||
\(923\) | 50.2406 | 1.65369 | ||||||||
\(924\) | 7.66806 | 0.252261 | ||||||||
\(925\) | 4.90057 | 0.161130 | ||||||||
\(926\) | −13.4971 | −0.443543 | ||||||||
\(927\) | 5.41452 | 0.177836 | ||||||||
\(928\) | 5.01155 | 0.164512 | ||||||||
\(929\) | −36.2526 | −1.18941 | −0.594705 | − | 0.803944i | \(-0.702731\pi\) | ||||
−0.594705 | + | 0.803944i | \(0.702731\pi\) | |||||||
\(930\) | −18.1091 | −0.593820 | ||||||||
\(931\) | −45.7517 | −1.49945 | ||||||||
\(932\) | 22.7015 | 0.743612 | ||||||||
\(933\) | −13.9800 | −0.457684 | ||||||||
\(934\) | 20.2483 | 0.662546 | ||||||||
\(935\) | 99.1307 | 3.24192 | ||||||||
\(936\) | −8.07702 | −0.264006 | ||||||||
\(937\) | −23.4015 | −0.764493 | −0.382246 | − | 0.924060i | \(-0.624849\pi\) | ||||
−0.382246 | + | 0.924060i | \(0.624849\pi\) | |||||||
\(938\) | 6.89450 | 0.225113 | ||||||||
\(939\) | −31.5901 | −1.03091 | ||||||||
\(940\) | −25.9636 | −0.846839 | ||||||||
\(941\) | −18.2026 | −0.593388 | −0.296694 | − | 0.954973i | \(-0.595884\pi\) | ||||
−0.296694 | + | 0.954973i | \(0.595884\pi\) | |||||||
\(942\) | 21.1113 | 0.687845 | ||||||||
\(943\) | −9.87038 | −0.321424 | ||||||||
\(944\) | 8.08279 | 0.263072 | ||||||||
\(945\) | −26.0670 | −0.847960 | ||||||||
\(946\) | −33.8829 | −1.10163 | ||||||||
\(947\) | −39.9245 | −1.29737 | −0.648686 | − | 0.761056i | \(-0.724681\pi\) | ||||
−0.648686 | + | 0.761056i | \(0.724681\pi\) | |||||||
\(948\) | 7.36094 | 0.239072 | ||||||||
\(949\) | −19.8357 | −0.643893 | ||||||||
\(950\) | −107.048 | −3.47311 | ||||||||
\(951\) | 20.6365 | 0.669184 | ||||||||
\(952\) | −4.93003 | −0.159783 | ||||||||
\(953\) | 33.5945 | 1.08823 | 0.544117 | − | 0.839009i | \(-0.316865\pi\) | ||||
0.544117 | + | 0.839009i | \(0.316865\pi\) | |||||||
\(954\) | 11.2369 | 0.363808 | ||||||||
\(955\) | −84.4594 | −2.73304 | ||||||||
\(956\) | 1.25406 | 0.0405592 | ||||||||
\(957\) | −29.4523 | −0.952056 | ||||||||
\(958\) | 38.1793 | 1.23352 | ||||||||
\(959\) | 16.0023 | 0.516740 | ||||||||
\(960\) | 3.89648 | 0.125758 | ||||||||
\(961\) | −9.40034 | −0.303237 | ||||||||
\(962\) | 1.50122 | 0.0484014 | ||||||||
\(963\) | 14.8173 | 0.477482 | ||||||||
\(964\) | 0.519454 | 0.0167305 | ||||||||
\(965\) | −32.3855 | −1.04253 | ||||||||
\(966\) | −1.09296 | −0.0351655 | ||||||||
\(967\) | 12.7735 | 0.410769 | 0.205385 | − | 0.978681i | \(-0.434155\pi\) | ||||
0.205385 | + | 0.978681i | \(0.434155\pi\) | |||||||
\(968\) | −28.5705 | −0.918289 | ||||||||
\(969\) | −30.4863 | −0.979361 | ||||||||
\(970\) | 19.0101 | 0.610377 | ||||||||
\(971\) | 8.13004 | 0.260905 | 0.130453 | − | 0.991455i | \(-0.458357\pi\) | ||||
0.130453 | + | 0.991455i | \(0.458357\pi\) | |||||||
\(972\) | −16.1513 | −0.518052 | ||||||||
\(973\) | 18.3907 | 0.589580 | ||||||||
\(974\) | 24.2739 | 0.777785 | ||||||||
\(975\) | 43.9696 | 1.40816 | ||||||||
\(976\) | 7.71779 | 0.247040 | ||||||||
\(977\) | 49.8159 | 1.59375 | 0.796876 | − | 0.604143i | \(-0.206485\pi\) | ||||
0.796876 | + | 0.604143i | \(0.206485\pi\) | |||||||
\(978\) | −5.86356 | −0.187496 | ||||||||
\(979\) | 97.7671 | 3.12465 | ||||||||
\(980\) | 22.0946 | 0.705786 | ||||||||
\(981\) | 20.2676 | 0.647094 | ||||||||
\(982\) | 11.5479 | 0.368509 | ||||||||
\(983\) | −19.4029 | −0.618858 | −0.309429 | − | 0.950923i | \(-0.600138\pi\) | ||||
−0.309429 | + | 0.950923i | \(0.600138\pi\) | |||||||
\(984\) | 10.2846 | 0.327862 | ||||||||
\(985\) | −65.1242 | −2.07503 | ||||||||
\(986\) | 18.9358 | 0.603037 | ||||||||
\(987\) | −7.58843 | −0.241542 | ||||||||
\(988\) | −32.7928 | −1.04328 | ||||||||
\(989\) | 4.82949 | 0.153569 | ||||||||
\(990\) | 55.8089 | 1.77372 | ||||||||
\(991\) | 12.4473 | 0.395401 | 0.197701 | − | 0.980262i | \(-0.436653\pi\) | ||||
0.197701 | + | 0.980262i | \(0.436653\pi\) | |||||||
\(992\) | −4.64754 | −0.147560 | ||||||||
\(993\) | 17.0321 | 0.540499 | ||||||||
\(994\) | 17.2643 | 0.547589 | ||||||||
\(995\) | 64.1848 | 2.03480 | ||||||||
\(996\) | 4.62603 | 0.146581 | ||||||||
\(997\) | −22.7094 | −0.719213 | −0.359607 | − | 0.933104i | \(-0.617089\pi\) | ||||
−0.359607 | + | 0.933104i | \(0.617089\pi\) | |||||||
\(998\) | 14.7381 | 0.466528 | ||||||||
\(999\) | 1.89383 | 0.0599180 |
(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 | 4006.2.a.g.1.16 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.g.1.16 | ✓ | 40 | 1.1 | even | 1 | trivial |