Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.554958 | 0.392415 | 0.196207 | − | 0.980562i | \(-0.437137\pi\) | ||||
0.196207 | + | 0.980562i | \(0.437137\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.69202 | −0.846011 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | −0.554958 | −0.226561 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.04892 | −0.724402 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.445042 | 0.134185 | 0.0670926 | − | 0.997747i | \(-0.478628\pi\) | ||||
0.0670926 | + | 0.997747i | \(0.478628\pi\) | |||||||
\(12\) | 1.69202 | 0.488445 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.554958 | −0.148319 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.24698 | 0.561745 | ||||||||
\(17\) | 3.60388 | 0.874068 | 0.437034 | − | 0.899445i | \(-0.356029\pi\) | ||||
0.437034 | + | 0.899445i | \(0.356029\pi\) | |||||||
\(18\) | 0.554958 | 0.130805 | ||||||||
\(19\) | 4.09783 | 0.940108 | 0.470054 | − | 0.882638i | \(-0.344234\pi\) | ||||
0.470054 | + | 0.882638i | \(0.344234\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0.246980 | 0.0526562 | ||||||||
\(23\) | −7.00969 | −1.46162 | −0.730811 | − | 0.682580i | \(-0.760858\pi\) | ||||
−0.730811 | + | 0.682580i | \(0.760858\pi\) | |||||||
\(24\) | 2.04892 | 0.418234 | ||||||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.69202 | 0.319762 | ||||||||
\(29\) | 1.74094 | 0.323284 | 0.161642 | − | 0.986849i | \(-0.448321\pi\) | ||||
0.161642 | + | 0.986849i | \(0.448321\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.49396 | −1.16635 | −0.583175 | − | 0.812347i | \(-0.698190\pi\) | ||||
−0.583175 | + | 0.812347i | \(0.698190\pi\) | |||||||
\(32\) | 5.34481 | 0.944839 | ||||||||
\(33\) | −0.445042 | −0.0774718 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.69202 | −0.282004 | ||||||||
\(37\) | 7.18598 | 1.18137 | 0.590684 | − | 0.806903i | \(-0.298858\pi\) | ||||
0.590684 | + | 0.806903i | \(0.298858\pi\) | |||||||
\(38\) | 2.27413 | 0.368912 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.89008 | 1.07605 | 0.538025 | − | 0.842929i | \(-0.319171\pi\) | ||||
0.538025 | + | 0.842929i | \(0.319171\pi\) | |||||||
\(42\) | 0.554958 | 0.0856319 | ||||||||
\(43\) | 8.85086 | 1.34974 | 0.674871 | − | 0.737935i | \(-0.264199\pi\) | ||||
0.674871 | + | 0.737935i | \(0.264199\pi\) | |||||||
\(44\) | −0.753020 | −0.113522 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.89008 | −0.573562 | ||||||||
\(47\) | −9.48188 | −1.38307 | −0.691537 | − | 0.722341i | \(-0.743066\pi\) | ||||
−0.691537 | + | 0.722341i | \(0.743066\pi\) | |||||||
\(48\) | −2.24698 | −0.324324 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.77479 | −0.392415 | ||||||||
\(51\) | −3.60388 | −0.504644 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.28382 | 1.27523 | 0.637615 | − | 0.770355i | \(-0.279921\pi\) | ||||
0.637615 | + | 0.770355i | \(0.279921\pi\) | |||||||
\(54\) | −0.554958 | −0.0755202 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.04892 | 0.273798 | ||||||||
\(57\) | −4.09783 | −0.542771 | ||||||||
\(58\) | 0.966148 | 0.126861 | ||||||||
\(59\) | −4.98792 | −0.649372 | −0.324686 | − | 0.945822i | \(-0.605259\pi\) | ||||
−0.324686 | + | 0.945822i | \(0.605259\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.933624 | −0.119538 | −0.0597692 | − | 0.998212i | \(-0.519036\pi\) | ||||
−0.0597692 | + | 0.998212i | \(0.519036\pi\) | |||||||
\(62\) | −3.60388 | −0.457693 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −1.52781 | −0.190976 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.246980 | −0.0304011 | ||||||||
\(67\) | −1.70410 | −0.208189 | −0.104095 | − | 0.994567i | \(-0.533194\pi\) | ||||
−0.104095 | + | 0.994567i | \(0.533194\pi\) | |||||||
\(68\) | −6.09783 | −0.739471 | ||||||||
\(69\) | 7.00969 | 0.843867 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.80194 | 0.451207 | 0.225603 | − | 0.974219i | \(-0.427565\pi\) | ||||
0.225603 | + | 0.974219i | \(0.427565\pi\) | |||||||
\(72\) | −2.04892 | −0.241467 | ||||||||
\(73\) | −7.30559 | −0.855054 | −0.427527 | − | 0.904003i | \(-0.640615\pi\) | ||||
−0.427527 | + | 0.904003i | \(0.640615\pi\) | |||||||
\(74\) | 3.98792 | 0.463586 | ||||||||
\(75\) | 5.00000 | 0.577350 | ||||||||
\(76\) | −6.93362 | −0.795341 | ||||||||
\(77\) | −0.445042 | −0.0507172 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.621334 | −0.0699055 | −0.0349528 | − | 0.999389i | \(-0.511128\pi\) | ||||
−0.0349528 | + | 0.999389i | \(0.511128\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.82371 | 0.422258 | ||||||||
\(83\) | 4.27413 | 0.469146 | 0.234573 | − | 0.972098i | \(-0.424631\pi\) | ||||
0.234573 | + | 0.972098i | \(0.424631\pi\) | |||||||
\(84\) | −1.69202 | −0.184615 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.91185 | 0.529659 | ||||||||
\(87\) | −1.74094 | −0.186648 | ||||||||
\(88\) | −0.911854 | −0.0972040 | ||||||||
\(89\) | −8.81163 | −0.934031 | −0.467015 | − | 0.884249i | \(-0.654671\pi\) | ||||
−0.467015 | + | 0.884249i | \(0.654671\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 11.8605 | 1.23655 | ||||||||
\(93\) | 6.49396 | 0.673392 | ||||||||
\(94\) | −5.26205 | −0.542739 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.34481 | −0.545503 | ||||||||
\(97\) | 6.59179 | 0.669295 | 0.334648 | − | 0.942343i | \(-0.391383\pi\) | ||||
0.334648 | + | 0.942343i | \(0.391383\pi\) | |||||||
\(98\) | 0.554958 | 0.0560592 | ||||||||
\(99\) | 0.445042 | 0.0447284 | ||||||||
\(100\) | 8.46011 | 0.846011 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | −2.00000 | −0.198030 | ||||||||
\(103\) | −15.3056 | −1.50810 | −0.754052 | − | 0.656815i | \(-0.771903\pi\) | ||||
−0.754052 | + | 0.656815i | \(0.771903\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.15213 | 0.500419 | ||||||||
\(107\) | −14.6649 | −1.41771 | −0.708853 | − | 0.705356i | \(-0.750787\pi\) | ||||
−0.708853 | + | 0.705356i | \(0.750787\pi\) | |||||||
\(108\) | 1.69202 | 0.162815 | ||||||||
\(109\) | −14.8605 | −1.42338 | −0.711691 | − | 0.702493i | \(-0.752070\pi\) | ||||
−0.711691 | + | 0.702493i | \(0.752070\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.18598 | −0.682063 | ||||||||
\(112\) | −2.24698 | −0.212320 | ||||||||
\(113\) | −13.7071 | −1.28945 | −0.644727 | − | 0.764413i | \(-0.723029\pi\) | ||||
−0.644727 | + | 0.764413i | \(0.723029\pi\) | |||||||
\(114\) | −2.27413 | −0.212991 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.94571 | −0.273502 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.76809 | −0.254823 | ||||||||
\(119\) | −3.60388 | −0.330367 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8019 | −0.981994 | ||||||||
\(122\) | −0.518122 | −0.0469086 | ||||||||
\(123\) | −6.89008 | −0.621258 | ||||||||
\(124\) | 10.9879 | 0.986744 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.554958 | −0.0494396 | ||||||||
\(127\) | −16.1371 | −1.43193 | −0.715966 | − | 0.698135i | \(-0.754014\pi\) | ||||
−0.715966 | + | 0.698135i | \(0.754014\pi\) | |||||||
\(128\) | −11.5375 | −1.01978 | ||||||||
\(129\) | −8.85086 | −0.779274 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.3177 | −1.42568 | −0.712841 | − | 0.701326i | \(-0.752592\pi\) | ||||
−0.712841 | + | 0.701326i | \(0.752592\pi\) | |||||||
\(132\) | 0.753020 | 0.0655420 | ||||||||
\(133\) | −4.09783 | −0.355327 | ||||||||
\(134\) | −0.945706 | −0.0816965 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.38404 | −0.633176 | ||||||||
\(137\) | −0.719169 | −0.0614427 | −0.0307214 | − | 0.999528i | \(-0.509780\pi\) | ||||
−0.0307214 | + | 0.999528i | \(0.509780\pi\) | |||||||
\(138\) | 3.89008 | 0.331146 | ||||||||
\(139\) | 2.12200 | 0.179986 | 0.0899928 | − | 0.995942i | \(-0.471316\pi\) | ||||
0.0899928 | + | 0.995942i | \(0.471316\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.48188 | 0.798518 | ||||||||
\(142\) | 2.10992 | 0.177060 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.24698 | 0.187248 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.05429 | −0.335536 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −12.1588 | −0.999450 | ||||||||
\(149\) | 3.16852 | 0.259575 | 0.129788 | − | 0.991542i | \(-0.458570\pi\) | ||||
0.129788 | + | 0.991542i | \(0.458570\pi\) | |||||||
\(150\) | 2.77479 | 0.226561 | ||||||||
\(151\) | 0.929312 | 0.0756264 | 0.0378132 | − | 0.999285i | \(-0.487961\pi\) | ||||
0.0378132 | + | 0.999285i | \(0.487961\pi\) | |||||||
\(152\) | −8.39612 | −0.681016 | ||||||||
\(153\) | 3.60388 | 0.291356 | ||||||||
\(154\) | −0.246980 | −0.0199022 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.15346 | 0.411291 | 0.205645 | − | 0.978627i | \(-0.434071\pi\) | ||||
0.205645 | + | 0.978627i | \(0.434071\pi\) | |||||||
\(158\) | −0.344814 | −0.0274320 | ||||||||
\(159\) | −9.28382 | −0.736254 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.00969 | 0.552441 | ||||||||
\(162\) | 0.554958 | 0.0436016 | ||||||||
\(163\) | −15.0707 | −1.18043 | −0.590214 | − | 0.807247i | \(-0.700957\pi\) | ||||
−0.590214 | + | 0.807247i | \(0.700957\pi\) | |||||||
\(164\) | −11.6582 | −0.910350 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.37196 | 0.184100 | ||||||||
\(167\) | 11.9323 | 0.923349 | 0.461674 | − | 0.887049i | \(-0.347249\pi\) | ||||
0.461674 | + | 0.887049i | \(0.347249\pi\) | |||||||
\(168\) | −2.04892 | −0.158077 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.09783 | 0.313369 | ||||||||
\(172\) | −14.9758 | −1.14190 | ||||||||
\(173\) | 3.03146 | 0.230478 | 0.115239 | − | 0.993338i | \(-0.463237\pi\) | ||||
0.115239 | + | 0.993338i | \(0.463237\pi\) | |||||||
\(174\) | −0.966148 | −0.0732435 | ||||||||
\(175\) | 5.00000 | 0.377964 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 4.98792 | 0.374915 | ||||||||
\(178\) | −4.89008 | −0.366527 | ||||||||
\(179\) | −9.87263 | −0.737915 | −0.368957 | − | 0.929446i | \(-0.620285\pi\) | ||||
−0.368957 | + | 0.929446i | \(0.620285\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.5362 | −0.857477 | −0.428738 | − | 0.903429i | \(-0.641042\pi\) | ||||
−0.428738 | + | 0.903429i | \(0.641042\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.933624 | 0.0690155 | ||||||||
\(184\) | 14.3623 | 1.05880 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.60388 | 0.264249 | ||||||||
\(187\) | 1.60388 | 0.117287 | ||||||||
\(188\) | 16.0435 | 1.17010 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.12498 | −0.226116 | −0.113058 | − | 0.993588i | \(-0.536065\pi\) | ||||
−0.113058 | + | 0.993588i | \(0.536065\pi\) | |||||||
\(192\) | 1.52781 | 0.110260 | ||||||||
\(193\) | −21.0030 | −1.51183 | −0.755914 | − | 0.654671i | \(-0.772807\pi\) | ||||
−0.755914 | + | 0.654671i | \(0.772807\pi\) | |||||||
\(194\) | 3.65817 | 0.262641 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.69202 | −0.120859 | ||||||||
\(197\) | 11.6233 | 0.828122 | 0.414061 | − | 0.910249i | \(-0.364110\pi\) | ||||
0.414061 | + | 0.910249i | \(0.364110\pi\) | |||||||
\(198\) | 0.246980 | 0.0175521 | ||||||||
\(199\) | 6.86592 | 0.486712 | 0.243356 | − | 0.969937i | \(-0.421752\pi\) | ||||
0.243356 | + | 0.969937i | \(0.421752\pi\) | |||||||
\(200\) | 10.2446 | 0.724402 | ||||||||
\(201\) | 1.70410 | 0.120198 | ||||||||
\(202\) | −3.32975 | −0.234280 | ||||||||
\(203\) | −1.74094 | −0.122190 | ||||||||
\(204\) | 6.09783 | 0.426934 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.49396 | −0.591802 | ||||||||
\(207\) | −7.00969 | −0.487207 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.82371 | 0.126149 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.88769 | 0.474168 | 0.237084 | − | 0.971489i | \(-0.423808\pi\) | ||||
0.237084 | + | 0.971489i | \(0.423808\pi\) | |||||||
\(212\) | −15.7084 | −1.07886 | ||||||||
\(213\) | −3.80194 | −0.260504 | ||||||||
\(214\) | −8.13839 | −0.556329 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.04892 | 0.139411 | ||||||||
\(217\) | 6.49396 | 0.440839 | ||||||||
\(218\) | −8.24698 | −0.558556 | ||||||||
\(219\) | 7.30559 | 0.493666 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.98792 | −0.267652 | ||||||||
\(223\) | 17.7017 | 1.18539 | 0.592697 | − | 0.805425i | \(-0.298063\pi\) | ||||
0.592697 | + | 0.805425i | \(0.298063\pi\) | |||||||
\(224\) | −5.34481 | −0.357115 | ||||||||
\(225\) | −5.00000 | −0.333333 | ||||||||
\(226\) | −7.60686 | −0.506001 | ||||||||
\(227\) | 25.0315 | 1.66140 | 0.830698 | − | 0.556723i | \(-0.187942\pi\) | ||||
0.830698 | + | 0.556723i | \(0.187942\pi\) | |||||||
\(228\) | 6.93362 | 0.459190 | ||||||||
\(229\) | 24.4940 | 1.61861 | 0.809303 | − | 0.587391i | \(-0.199845\pi\) | ||||
0.809303 | + | 0.587391i | \(0.199845\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.445042 | 0.0292816 | ||||||||
\(232\) | −3.56704 | −0.234188 | ||||||||
\(233\) | 9.19269 | 0.602233 | 0.301116 | − | 0.953587i | \(-0.402641\pi\) | ||||
0.301116 | + | 0.953587i | \(0.402641\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.43967 | 0.549375 | ||||||||
\(237\) | 0.621334 | 0.0403600 | ||||||||
\(238\) | −2.00000 | −0.129641 | ||||||||
\(239\) | −7.91723 | −0.512123 | −0.256062 | − | 0.966660i | \(-0.582425\pi\) | ||||
−0.256062 | + | 0.966660i | \(0.582425\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.51679 | −0.0977053 | −0.0488527 | − | 0.998806i | \(-0.515556\pi\) | ||||
−0.0488527 | + | 0.998806i | \(0.515556\pi\) | |||||||
\(242\) | −5.99462 | −0.385349 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.57971 | 0.101131 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.82371 | −0.243791 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 13.3056 | 0.844906 | ||||||||
\(249\) | −4.27413 | −0.270862 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.0978 | −1.64728 | −0.823640 | − | 0.567112i | \(-0.808060\pi\) | ||||
−0.823640 | + | 0.567112i | \(0.808060\pi\) | |||||||
\(252\) | 1.69202 | 0.106587 | ||||||||
\(253\) | −3.11960 | −0.196128 | ||||||||
\(254\) | −8.95539 | −0.561911 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.34721 | −0.209200 | ||||||||
\(257\) | −5.42758 | −0.338563 | −0.169282 | − | 0.985568i | \(-0.554145\pi\) | ||||
−0.169282 | + | 0.985568i | \(0.554145\pi\) | |||||||
\(258\) | −4.91185 | −0.305799 | ||||||||
\(259\) | −7.18598 | −0.446515 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.74094 | 0.107761 | ||||||||
\(262\) | −9.05562 | −0.559458 | ||||||||
\(263\) | −12.8955 | −0.795168 | −0.397584 | − | 0.917566i | \(-0.630151\pi\) | ||||
−0.397584 | + | 0.917566i | \(0.630151\pi\) | |||||||
\(264\) | 0.911854 | 0.0561207 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.27413 | −0.139436 | ||||||||
\(267\) | 8.81163 | 0.539263 | ||||||||
\(268\) | 2.88338 | 0.176130 | ||||||||
\(269\) | 0.141375 | 0.00861980 | 0.00430990 | − | 0.999991i | \(-0.498628\pi\) | ||||
0.00430990 | + | 0.999991i | \(0.498628\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.90946 | −0.419720 | −0.209860 | − | 0.977731i | \(-0.567301\pi\) | ||||
−0.209860 | + | 0.977731i | \(0.567301\pi\) | |||||||
\(272\) | 8.09783 | 0.491003 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.399108 | −0.0241110 | ||||||||
\(275\) | −2.22521 | −0.134185 | ||||||||
\(276\) | −11.8605 | −0.713921 | ||||||||
\(277\) | 3.35929 | 0.201840 | 0.100920 | − | 0.994895i | \(-0.467821\pi\) | ||||
0.100920 | + | 0.994895i | \(0.467821\pi\) | |||||||
\(278\) | 1.17762 | 0.0706290 | ||||||||
\(279\) | −6.49396 | −0.388783 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.7439 | −1.59541 | −0.797704 | − | 0.603049i | \(-0.793952\pi\) | ||||
−0.797704 | + | 0.603049i | \(0.793952\pi\) | |||||||
\(282\) | 5.26205 | 0.313350 | ||||||||
\(283\) | 14.6655 | 0.871771 | 0.435886 | − | 0.900002i | \(-0.356435\pi\) | ||||
0.435886 | + | 0.900002i | \(0.356435\pi\) | |||||||
\(284\) | −6.43296 | −0.381726 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.89008 | −0.406709 | ||||||||
\(288\) | 5.34481 | 0.314946 | ||||||||
\(289\) | −4.01208 | −0.236005 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.59179 | −0.386418 | ||||||||
\(292\) | 12.3612 | 0.723385 | ||||||||
\(293\) | −5.15346 | −0.301068 | −0.150534 | − | 0.988605i | \(-0.548099\pi\) | ||||
−0.150534 | + | 0.988605i | \(0.548099\pi\) | |||||||
\(294\) | −0.554958 | −0.0323658 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −14.7235 | −0.855785 | ||||||||
\(297\) | −0.445042 | −0.0258239 | ||||||||
\(298\) | 1.75840 | 0.101861 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −8.46011 | −0.488445 | ||||||||
\(301\) | −8.85086 | −0.510155 | ||||||||
\(302\) | 0.515729 | 0.0296769 | ||||||||
\(303\) | 6.00000 | 0.344691 | ||||||||
\(304\) | 9.20775 | 0.528101 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.00000 | 0.114332 | ||||||||
\(307\) | 15.4276 | 0.880499 | 0.440249 | − | 0.897876i | \(-0.354890\pi\) | ||||
0.440249 | + | 0.897876i | \(0.354890\pi\) | |||||||
\(308\) | 0.753020 | 0.0429073 | ||||||||
\(309\) | 15.3056 | 0.870704 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −34.9638 | −1.98261 | −0.991306 | − | 0.131574i | \(-0.957997\pi\) | ||||
−0.991306 | + | 0.131574i | \(0.957997\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.5569 | −1.50108 | −0.750542 | − | 0.660823i | \(-0.770207\pi\) | ||||
−0.750542 | + | 0.660823i | \(0.770207\pi\) | |||||||
\(314\) | 2.85995 | 0.161396 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.05131 | 0.0591408 | ||||||||
\(317\) | 13.9511 | 0.783571 | 0.391785 | − | 0.920057i | \(-0.371858\pi\) | ||||
0.391785 | + | 0.920057i | \(0.371858\pi\) | |||||||
\(318\) | −5.15213 | −0.288917 | ||||||||
\(319\) | 0.774791 | 0.0433799 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.6649 | 0.818513 | ||||||||
\(322\) | 3.89008 | 0.216786 | ||||||||
\(323\) | 14.7681 | 0.821718 | ||||||||
\(324\) | −1.69202 | −0.0940012 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.36360 | −0.463217 | ||||||||
\(327\) | 14.8605 | 0.821790 | ||||||||
\(328\) | −14.1172 | −0.779493 | ||||||||
\(329\) | 9.48188 | 0.522753 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.46011 | 0.300115 | 0.150057 | − | 0.988677i | \(-0.452054\pi\) | ||||
0.150057 | + | 0.988677i | \(0.452054\pi\) | |||||||
\(332\) | −7.23191 | −0.396903 | ||||||||
\(333\) | 7.18598 | 0.393789 | ||||||||
\(334\) | 6.62192 | 0.362336 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.24698 | 0.122583 | ||||||||
\(337\) | −18.6262 | −1.01464 | −0.507318 | − | 0.861759i | \(-0.669363\pi\) | ||||
−0.507318 | + | 0.861759i | \(0.669363\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.7071 | 0.744467 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.89008 | −0.156507 | ||||||||
\(342\) | 2.27413 | 0.122971 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −18.1347 | −0.977756 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.68233 | 0.0904428 | ||||||||
\(347\) | −36.4373 | −1.95606 | −0.978028 | − | 0.208475i | \(-0.933150\pi\) | ||||
−0.978028 | + | 0.208475i | \(0.933150\pi\) | |||||||
\(348\) | 2.94571 | 0.157906 | ||||||||
\(349\) | 14.5810 | 0.780505 | 0.390253 | − | 0.920708i | \(-0.372388\pi\) | ||||
0.390253 | + | 0.920708i | \(0.372388\pi\) | |||||||
\(350\) | 2.77479 | 0.148319 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.37867 | 0.126783 | ||||||||
\(353\) | −15.4276 | −0.821127 | −0.410564 | − | 0.911832i | \(-0.634668\pi\) | ||||
−0.410564 | + | 0.911832i | \(0.634668\pi\) | |||||||
\(354\) | 2.76809 | 0.147122 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.9095 | 0.790200 | ||||||||
\(357\) | 3.60388 | 0.190737 | ||||||||
\(358\) | −5.47889 | −0.289569 | ||||||||
\(359\) | 24.5894 | 1.29778 | 0.648889 | − | 0.760883i | \(-0.275234\pi\) | ||||
0.648889 | + | 0.760883i | \(0.275234\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.20775 | −0.116197 | ||||||||
\(362\) | −6.40209 | −0.336487 | ||||||||
\(363\) | 10.8019 | 0.566955 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.518122 | 0.0270827 | ||||||||
\(367\) | 28.3370 | 1.47918 | 0.739591 | − | 0.673057i | \(-0.235019\pi\) | ||||
0.739591 | + | 0.673057i | \(0.235019\pi\) | |||||||
\(368\) | −15.7506 | −0.821058 | ||||||||
\(369\) | 6.89008 | 0.358683 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.28382 | −0.481992 | ||||||||
\(372\) | −10.9879 | −0.569697 | ||||||||
\(373\) | 20.9661 | 1.08559 | 0.542793 | − | 0.839867i | \(-0.317367\pi\) | ||||
0.542793 | + | 0.839867i | \(0.317367\pi\) | |||||||
\(374\) | 0.890084 | 0.0460251 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19.4276 | 1.00190 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.554958 | 0.0285440 | ||||||||
\(379\) | 15.7845 | 0.810794 | 0.405397 | − | 0.914141i | \(-0.367133\pi\) | ||||
0.405397 | + | 0.914141i | \(0.367133\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.1371 | 0.826727 | ||||||||
\(382\) | −1.73423 | −0.0887311 | ||||||||
\(383\) | 31.2814 | 1.59841 | 0.799203 | − | 0.601061i | \(-0.205255\pi\) | ||||
0.799203 | + | 0.601061i | \(0.205255\pi\) | |||||||
\(384\) | 11.5375 | 0.588771 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.6558 | −0.593263 | ||||||||
\(387\) | 8.85086 | 0.449914 | ||||||||
\(388\) | −11.1535 | −0.566231 | ||||||||
\(389\) | −8.07308 | −0.409321 | −0.204661 | − | 0.978833i | \(-0.565609\pi\) | ||||
−0.204661 | + | 0.978833i | \(0.565609\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.2620 | −1.27756 | ||||||||
\(392\) | −2.04892 | −0.103486 | ||||||||
\(393\) | 16.3177 | 0.823117 | ||||||||
\(394\) | 6.45042 | 0.324967 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.753020 | −0.0378407 | ||||||||
\(397\) | 17.5496 | 0.880788 | 0.440394 | − | 0.897805i | \(-0.354839\pi\) | ||||
0.440394 | + | 0.897805i | \(0.354839\pi\) | |||||||
\(398\) | 3.81030 | 0.190993 | ||||||||
\(399\) | 4.09783 | 0.205148 | ||||||||
\(400\) | −11.2349 | −0.561745 | ||||||||
\(401\) | 7.68664 | 0.383853 | 0.191926 | − | 0.981409i | \(-0.438527\pi\) | ||||
0.191926 | + | 0.981409i | \(0.438527\pi\) | |||||||
\(402\) | 0.945706 | 0.0471675 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 10.1521 | 0.505087 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.966148 | −0.0479491 | ||||||||
\(407\) | 3.19806 | 0.158522 | ||||||||
\(408\) | 7.38404 | 0.365565 | ||||||||
\(409\) | −36.3129 | −1.79556 | −0.897778 | − | 0.440448i | \(-0.854820\pi\) | ||||
−0.897778 | + | 0.440448i | \(0.854820\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.719169 | 0.0354740 | ||||||||
\(412\) | 25.8974 | 1.27587 | ||||||||
\(413\) | 4.98792 | 0.245439 | ||||||||
\(414\) | −3.89008 | −0.191187 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.12200 | −0.103915 | ||||||||
\(418\) | 1.01208 | 0.0495025 | ||||||||
\(419\) | 2.75733 | 0.134704 | 0.0673522 | − | 0.997729i | \(-0.478545\pi\) | ||||
0.0673522 | + | 0.997729i | \(0.478545\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.8552 | −1.21137 | −0.605683 | − | 0.795706i | \(-0.707100\pi\) | ||||
−0.605683 | + | 0.795706i | \(0.707100\pi\) | |||||||
\(422\) | 3.82238 | 0.186071 | ||||||||
\(423\) | −9.48188 | −0.461025 | ||||||||
\(424\) | −19.0218 | −0.923779 | ||||||||
\(425\) | −18.0194 | −0.874068 | ||||||||
\(426\) | −2.10992 | −0.102226 | ||||||||
\(427\) | 0.933624 | 0.0451812 | ||||||||
\(428\) | 24.8133 | 1.19940 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.6515 | −1.18742 | −0.593710 | − | 0.804679i | \(-0.702337\pi\) | ||||
−0.593710 | + | 0.804679i | \(0.702337\pi\) | |||||||
\(432\) | −2.24698 | −0.108108 | ||||||||
\(433\) | 29.6233 | 1.42360 | 0.711801 | − | 0.702381i | \(-0.247880\pi\) | ||||
0.711801 | + | 0.702381i | \(0.247880\pi\) | |||||||
\(434\) | 3.60388 | 0.172992 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 25.1444 | 1.20420 | ||||||||
\(437\) | −28.7245 | −1.37408 | ||||||||
\(438\) | 4.05429 | 0.193722 | ||||||||
\(439\) | 28.6219 | 1.36605 | 0.683025 | − | 0.730395i | \(-0.260664\pi\) | ||||
0.683025 | + | 0.730395i | \(0.260664\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.3690 | −1.11029 | −0.555147 | − | 0.831752i | \(-0.687338\pi\) | ||||
−0.555147 | + | 0.831752i | \(0.687338\pi\) | |||||||
\(444\) | 12.1588 | 0.577033 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.82371 | 0.465166 | ||||||||
\(447\) | −3.16852 | −0.149866 | ||||||||
\(448\) | 1.52781 | 0.0721823 | ||||||||
\(449\) | −9.44073 | −0.445536 | −0.222768 | − | 0.974872i | \(-0.571509\pi\) | ||||
−0.222768 | + | 0.974872i | \(0.571509\pi\) | |||||||
\(450\) | −2.77479 | −0.130805 | ||||||||
\(451\) | 3.06638 | 0.144390 | ||||||||
\(452\) | 23.1927 | 1.09089 | ||||||||
\(453\) | −0.929312 | −0.0436629 | ||||||||
\(454\) | 13.8914 | 0.651956 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.39612 | 0.393185 | ||||||||
\(457\) | −19.3110 | −0.903329 | −0.451664 | − | 0.892188i | \(-0.649170\pi\) | ||||
−0.451664 | + | 0.892188i | \(0.649170\pi\) | |||||||
\(458\) | 13.5931 | 0.635165 | ||||||||
\(459\) | −3.60388 | −0.168215 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.9215 | 1.57988 | 0.789942 | − | 0.613182i | \(-0.210111\pi\) | ||||
0.789942 | + | 0.613182i | \(0.210111\pi\) | |||||||
\(462\) | 0.246980 | 0.0114905 | ||||||||
\(463\) | −20.3773 | −0.947015 | −0.473508 | − | 0.880790i | \(-0.657012\pi\) | ||||
−0.473508 | + | 0.880790i | \(0.657012\pi\) | |||||||
\(464\) | 3.91185 | 0.181603 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.10156 | 0.236325 | ||||||||
\(467\) | 27.5448 | 1.27462 | 0.637311 | − | 0.770607i | \(-0.280047\pi\) | ||||
0.637311 | + | 0.770607i | \(0.280047\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.70410 | 0.0786882 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.15346 | −0.237459 | ||||||||
\(472\) | 10.2198 | 0.470406 | ||||||||
\(473\) | 3.93900 | 0.181115 | ||||||||
\(474\) | 0.344814 | 0.0158378 | ||||||||
\(475\) | −20.4892 | −0.940108 | ||||||||
\(476\) | 6.09783 | 0.279494 | ||||||||
\(477\) | 9.28382 | 0.425077 | ||||||||
\(478\) | −4.39373 | −0.200965 | ||||||||
\(479\) | −2.05429 | −0.0938631 | −0.0469315 | − | 0.998898i | \(-0.514944\pi\) | ||||
−0.0469315 | + | 0.998898i | \(0.514944\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.841757 | −0.0383410 | ||||||||
\(483\) | −7.00969 | −0.318952 | ||||||||
\(484\) | 18.2771 | 0.830778 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.554958 | −0.0251734 | ||||||||
\(487\) | −7.08516 | −0.321059 | −0.160530 | − | 0.987031i | \(-0.551320\pi\) | ||||
−0.160530 | + | 0.987031i | \(0.551320\pi\) | |||||||
\(488\) | 1.91292 | 0.0865938 | ||||||||
\(489\) | 15.0707 | 0.681520 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.8984 | −1.66520 | −0.832602 | − | 0.553872i | \(-0.813150\pi\) | ||||
−0.832602 | + | 0.553872i | \(0.813150\pi\) | |||||||
\(492\) | 11.6582 | 0.525591 | ||||||||
\(493\) | 6.27413 | 0.282572 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.5918 | −0.655191 | ||||||||
\(497\) | −3.80194 | −0.170540 | ||||||||
\(498\) | −2.37196 | −0.106290 | ||||||||
\(499\) | 16.6069 | 0.743425 | 0.371713 | − | 0.928348i | \(-0.378771\pi\) | ||||
0.371713 | + | 0.928348i | \(0.378771\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.9323 | −0.533096 | ||||||||
\(502\) | −14.4832 | −0.646417 | ||||||||
\(503\) | −4.39612 | −0.196014 | −0.0980068 | − | 0.995186i | \(-0.531247\pi\) | ||||
−0.0980068 | + | 0.995186i | \(0.531247\pi\) | |||||||
\(504\) | 2.04892 | 0.0912660 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.73125 | −0.0769635 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 27.3043 | 1.21143 | ||||||||
\(509\) | −28.9444 | −1.28294 | −0.641468 | − | 0.767149i | \(-0.721674\pi\) | ||||
−0.641468 | + | 0.767149i | \(0.721674\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.30559 | 0.323180 | ||||||||
\(512\) | 21.2174 | 0.937687 | ||||||||
\(513\) | −4.09783 | −0.180924 | ||||||||
\(514\) | −3.01208 | −0.132857 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 14.9758 | 0.659274 | ||||||||
\(517\) | −4.21983 | −0.185588 | ||||||||
\(518\) | −3.98792 | −0.175219 | ||||||||
\(519\) | −3.03146 | −0.133066 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.6547 | −1.34301 | −0.671504 | − | 0.741001i | \(-0.734351\pi\) | ||||
−0.671504 | + | 0.741001i | \(0.734351\pi\) | |||||||
\(522\) | 0.966148 | 0.0422872 | ||||||||
\(523\) | −15.8866 | −0.694674 | −0.347337 | − | 0.937740i | \(-0.612914\pi\) | ||||
−0.347337 | + | 0.937740i | \(0.612914\pi\) | |||||||
\(524\) | 27.6098 | 1.20614 | ||||||||
\(525\) | −5.00000 | −0.218218 | ||||||||
\(526\) | −7.15644 | −0.312036 | ||||||||
\(527\) | −23.4034 | −1.01947 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | 26.1357 | 1.13634 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.98792 | −0.216457 | ||||||||
\(532\) | 6.93362 | 0.300611 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 4.89008 | 0.211615 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.49157 | 0.150813 | ||||||||
\(537\) | 9.87263 | 0.426035 | ||||||||
\(538\) | 0.0784573 | 0.00338254 | ||||||||
\(539\) | 0.445042 | 0.0191693 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.1062 | 1.46634 | 0.733170 | − | 0.680045i | \(-0.238040\pi\) | ||||
0.733170 | + | 0.680045i | \(0.238040\pi\) | |||||||
\(542\) | −3.83446 | −0.164704 | ||||||||
\(543\) | 11.5362 | 0.495065 | ||||||||
\(544\) | 19.2620 | 0.825853 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.0597 | 0.943203 | 0.471602 | − | 0.881812i | \(-0.343676\pi\) | ||||
0.471602 | + | 0.881812i | \(0.343676\pi\) | |||||||
\(548\) | 1.21685 | 0.0519812 | ||||||||
\(549\) | −0.933624 | −0.0398461 | ||||||||
\(550\) | −1.23490 | −0.0526562 | ||||||||
\(551\) | 7.13408 | 0.303922 | ||||||||
\(552\) | −14.3623 | −0.611299 | ||||||||
\(553\) | 0.621334 | 0.0264218 | ||||||||
\(554\) | 1.86426 | 0.0792050 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.59047 | −0.152270 | ||||||||
\(557\) | 43.6558 | 1.84975 | 0.924877 | − | 0.380266i | \(-0.124167\pi\) | ||||
0.924877 | + | 0.380266i | \(0.124167\pi\) | |||||||
\(558\) | −3.60388 | −0.152564 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.60388 | −0.0677157 | ||||||||
\(562\) | −14.8418 | −0.626062 | ||||||||
\(563\) | −34.4698 | −1.45273 | −0.726364 | − | 0.687310i | \(-0.758791\pi\) | ||||
−0.726364 | + | 0.687310i | \(0.758791\pi\) | |||||||
\(564\) | −16.0435 | −0.675555 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.13872 | 0.342096 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −7.78986 | −0.326855 | ||||||||
\(569\) | −5.69633 | −0.238803 | −0.119401 | − | 0.992846i | \(-0.538098\pi\) | ||||
−0.119401 | + | 0.992846i | \(0.538098\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.00777 | −0.209569 | −0.104784 | − | 0.994495i | \(-0.533415\pi\) | ||||
−0.104784 | + | 0.994495i | \(0.533415\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.12498 | 0.130548 | ||||||||
\(574\) | −3.82371 | −0.159598 | ||||||||
\(575\) | 35.0484 | 1.46162 | ||||||||
\(576\) | −1.52781 | −0.0636588 | ||||||||
\(577\) | 18.3370 | 0.763381 | 0.381691 | − | 0.924290i | \(-0.375342\pi\) | ||||
0.381691 | + | 0.924290i | \(0.375342\pi\) | |||||||
\(578\) | −2.22654 | −0.0926117 | ||||||||
\(579\) | 21.0030 | 0.872854 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.27413 | −0.177321 | ||||||||
\(582\) | −3.65817 | −0.151636 | ||||||||
\(583\) | 4.13169 | 0.171117 | ||||||||
\(584\) | 14.9685 | 0.619403 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.85995 | −0.118144 | ||||||||
\(587\) | −38.8745 | −1.60452 | −0.802262 | − | 0.596972i | \(-0.796370\pi\) | ||||
−0.802262 | + | 0.596972i | \(0.796370\pi\) | |||||||
\(588\) | 1.69202 | 0.0697778 | ||||||||
\(589\) | −26.6112 | −1.09649 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.6233 | −0.478117 | ||||||||
\(592\) | 16.1468 | 0.663627 | ||||||||
\(593\) | 47.3551 | 1.94464 | 0.972320 | − | 0.233652i | \(-0.0750676\pi\) | ||||
0.972320 | + | 0.233652i | \(0.0750676\pi\) | |||||||
\(594\) | −0.246980 | −0.0101337 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.36121 | −0.219604 | ||||||||
\(597\) | −6.86592 | −0.281003 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.4534 | 1.04000 | 0.519999 | − | 0.854167i | \(-0.325932\pi\) | ||||
0.519999 | + | 0.854167i | \(0.325932\pi\) | |||||||
\(600\) | −10.2446 | −0.418234 | ||||||||
\(601\) | 30.7982 | 1.25629 | 0.628143 | − | 0.778098i | \(-0.283815\pi\) | ||||
0.628143 | + | 0.778098i | \(0.283815\pi\) | |||||||
\(602\) | −4.91185 | −0.200192 | ||||||||
\(603\) | −1.70410 | −0.0693964 | ||||||||
\(604\) | −1.57242 | −0.0639807 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.32975 | 0.135262 | ||||||||
\(607\) | −20.0000 | −0.811775 | −0.405887 | − | 0.913923i | \(-0.633038\pi\) | ||||
−0.405887 | + | 0.913923i | \(0.633038\pi\) | |||||||
\(608\) | 21.9022 | 0.888250 | ||||||||
\(609\) | 1.74094 | 0.0705464 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −6.09783 | −0.246490 | ||||||||
\(613\) | 17.5297 | 0.708019 | 0.354010 | − | 0.935242i | \(-0.384818\pi\) | ||||
0.354010 | + | 0.935242i | \(0.384818\pi\) | |||||||
\(614\) | 8.56166 | 0.345521 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.911854 | 0.0367396 | ||||||||
\(617\) | −46.6741 | −1.87903 | −0.939514 | − | 0.342510i | \(-0.888723\pi\) | ||||
−0.939514 | + | 0.342510i | \(0.888723\pi\) | |||||||
\(618\) | 8.49396 | 0.341677 | ||||||||
\(619\) | −14.1086 | −0.567072 | −0.283536 | − | 0.958962i | \(-0.591508\pi\) | ||||
−0.283536 | + | 0.958962i | \(0.591508\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.00969 | 0.281289 | ||||||||
\(622\) | −19.4034 | −0.778006 | ||||||||
\(623\) | 8.81163 | 0.353030 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | −14.7380 | −0.589047 | ||||||||
\(627\) | −1.82371 | −0.0728319 | ||||||||
\(628\) | −8.71976 | −0.347956 | ||||||||
\(629\) | 25.8974 | 1.03260 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.0140005 | 0.000557353 0 | 0.000278676 | − | 1.00000i | \(-0.499911\pi\) | ||||
0.000278676 | 1.00000i | \(0.499911\pi\) | ||||||||
\(632\) | 1.27306 | 0.0506397 | ||||||||
\(633\) | −6.88769 | −0.273761 | ||||||||
\(634\) | 7.74227 | 0.307485 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 15.7084 | 0.622879 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.429976 | 0.0170229 | ||||||||
\(639\) | 3.80194 | 0.150402 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.1148 | −1.18946 | −0.594732 | − | 0.803924i | \(-0.702742\pi\) | ||||
−0.594732 | + | 0.803924i | \(0.702742\pi\) | |||||||
\(642\) | 8.13839 | 0.321197 | ||||||||
\(643\) | 14.5617 | 0.574256 | 0.287128 | − | 0.957892i | \(-0.407300\pi\) | ||||
0.287128 | + | 0.957892i | \(0.407300\pi\) | |||||||
\(644\) | −11.8605 | −0.467371 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.19567 | 0.322454 | ||||||||
\(647\) | −47.7840 | −1.87858 | −0.939292 | − | 0.343120i | \(-0.888516\pi\) | ||||
−0.939292 | + | 0.343120i | \(0.888516\pi\) | |||||||
\(648\) | −2.04892 | −0.0804891 | ||||||||
\(649\) | −2.21983 | −0.0871360 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.49396 | −0.254518 | ||||||||
\(652\) | 25.4999 | 0.998654 | ||||||||
\(653\) | 34.0452 | 1.33229 | 0.666146 | − | 0.745822i | \(-0.267943\pi\) | ||||
0.666146 | + | 0.745822i | \(0.267943\pi\) | |||||||
\(654\) | 8.24698 | 0.322482 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 15.4819 | 0.604466 | ||||||||
\(657\) | −7.30559 | −0.285018 | ||||||||
\(658\) | 5.26205 | 0.205136 | ||||||||
\(659\) | −46.4801 | −1.81061 | −0.905303 | − | 0.424766i | \(-0.860356\pi\) | ||||
−0.905303 | + | 0.424766i | \(0.860356\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.3551 | 1.37515 | 0.687577 | − | 0.726112i | \(-0.258674\pi\) | ||||
0.687577 | + | 0.726112i | \(0.258674\pi\) | |||||||
\(662\) | 3.03013 | 0.117769 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.75733 | −0.339850 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.98792 | 0.154529 | ||||||||
\(667\) | −12.2034 | −0.472519 | ||||||||
\(668\) | −20.1897 | −0.781163 | ||||||||
\(669\) | −17.7017 | −0.684388 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.415502 | −0.0160403 | ||||||||
\(672\) | 5.34481 | 0.206181 | ||||||||
\(673\) | 43.0562 | 1.65970 | 0.829848 | − | 0.557990i | \(-0.188427\pi\) | ||||
0.829848 | + | 0.557990i | \(0.188427\pi\) | |||||||
\(674\) | −10.3368 | −0.398158 | ||||||||
\(675\) | 5.00000 | 0.192450 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.1715 | −0.928986 | −0.464493 | − | 0.885577i | \(-0.653763\pi\) | ||||
−0.464493 | + | 0.885577i | \(0.653763\pi\) | |||||||
\(678\) | 7.60686 | 0.292140 | ||||||||
\(679\) | −6.59179 | −0.252970 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.0315 | −0.959208 | ||||||||
\(682\) | −1.60388 | −0.0614156 | ||||||||
\(683\) | 10.1715 | 0.389202 | 0.194601 | − | 0.980882i | \(-0.437659\pi\) | ||||
0.194601 | + | 0.980882i | \(0.437659\pi\) | |||||||
\(684\) | −6.93362 | −0.265114 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.554958 | −0.0211884 | ||||||||
\(687\) | −24.4940 | −0.934503 | ||||||||
\(688\) | 19.8877 | 0.758211 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.8176 | −1.32452 | −0.662262 | − | 0.749272i | \(-0.730403\pi\) | ||||
−0.662262 | + | 0.749272i | \(0.730403\pi\) | |||||||
\(692\) | −5.12929 | −0.194986 | ||||||||
\(693\) | −0.445042 | −0.0169057 | ||||||||
\(694\) | −20.2212 | −0.767585 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.56704 | 0.135208 | ||||||||
\(697\) | 24.8310 | 0.940541 | ||||||||
\(698\) | 8.09187 | 0.306282 | ||||||||
\(699\) | −9.19269 | −0.347699 | ||||||||
\(700\) | −8.46011 | −0.319762 | ||||||||
\(701\) | −12.7571 | −0.481828 | −0.240914 | − | 0.970546i | \(-0.577447\pi\) | ||||
−0.240914 | + | 0.970546i | \(0.577447\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29.4470 | 1.11061 | ||||||||
\(704\) | −0.679940 | −0.0256262 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.56166 | −0.322222 | ||||||||
\(707\) | 6.00000 | 0.225653 | ||||||||
\(708\) | −8.43967 | −0.317182 | ||||||||
\(709\) | 33.9909 | 1.27656 | 0.638278 | − | 0.769806i | \(-0.279647\pi\) | ||||
0.638278 | + | 0.769806i | \(0.279647\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.621334 | −0.0233018 | ||||||||
\(712\) | 18.0543 | 0.676613 | ||||||||
\(713\) | 45.5206 | 1.70476 | ||||||||
\(714\) | 2.00000 | 0.0748481 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.7047 | 0.624284 | ||||||||
\(717\) | 7.91723 | 0.295674 | ||||||||
\(718\) | 13.6461 | 0.509267 | ||||||||
\(719\) | −4.59658 | −0.171423 | −0.0857117 | − | 0.996320i | \(-0.527316\pi\) | ||||
−0.0857117 | + | 0.996320i | \(0.527316\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3056 | 0.570010 | ||||||||
\(722\) | −1.22521 | −0.0455976 | ||||||||
\(723\) | 1.51679 | 0.0564102 | ||||||||
\(724\) | 19.5195 | 0.725435 | ||||||||
\(725\) | −8.70469 | −0.323284 | ||||||||
\(726\) | 5.99462 | 0.222481 | ||||||||
\(727\) | 40.4349 | 1.49965 | 0.749823 | − | 0.661638i | \(-0.230138\pi\) | ||||
0.749823 | + | 0.661638i | \(0.230138\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.8974 | 1.17977 | ||||||||
\(732\) | −1.57971 | −0.0583878 | ||||||||
\(733\) | −17.0207 | −0.628674 | −0.314337 | − | 0.949311i | \(-0.601782\pi\) | ||||
−0.314337 | + | 0.949311i | \(0.601782\pi\) | |||||||
\(734\) | 15.7259 | 0.580453 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −37.4655 | −1.38100 | ||||||||
\(737\) | −0.758397 | −0.0279359 | ||||||||
\(738\) | 3.82371 | 0.140753 | ||||||||
\(739\) | −28.5483 | −1.05016 | −0.525082 | − | 0.851051i | \(-0.675965\pi\) | ||||
−0.525082 | + | 0.851051i | \(0.675965\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.15213 | −0.189141 | ||||||||
\(743\) | 11.6732 | 0.428249 | 0.214125 | − | 0.976806i | \(-0.431310\pi\) | ||||
0.214125 | + | 0.976806i | \(0.431310\pi\) | |||||||
\(744\) | −13.3056 | −0.487806 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11.6353 | 0.426000 | ||||||||
\(747\) | 4.27413 | 0.156382 | ||||||||
\(748\) | −2.71379 | −0.0992261 | ||||||||
\(749\) | 14.6649 | 0.535843 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.9898 | 1.53223 | 0.766115 | − | 0.642703i | \(-0.222187\pi\) | ||||
0.766115 | + | 0.642703i | \(0.222187\pi\) | |||||||
\(752\) | −21.3056 | −0.776935 | ||||||||
\(753\) | 26.0978 | 0.951058 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.69202 | −0.0615382 | ||||||||
\(757\) | 44.9245 | 1.63281 | 0.816405 | − | 0.577480i | \(-0.195964\pi\) | ||||
0.816405 | + | 0.577480i | \(0.195964\pi\) | |||||||
\(758\) | 8.75973 | 0.318168 | ||||||||
\(759\) | 3.11960 | 0.113234 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.1207 | 0.838124 | 0.419062 | − | 0.907958i | \(-0.362359\pi\) | ||||
0.419062 | + | 0.907958i | \(0.362359\pi\) | |||||||
\(762\) | 8.95539 | 0.324420 | ||||||||
\(763\) | 14.8605 | 0.537988 | ||||||||
\(764\) | 5.28754 | 0.191296 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.3599 | 0.627238 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 3.34721 | 0.120782 | ||||||||
\(769\) | −10.4590 | −0.377163 | −0.188581 | − | 0.982058i | \(-0.560389\pi\) | ||||
−0.188581 | + | 0.982058i | \(0.560389\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.42758 | 0.195470 | ||||||||
\(772\) | 35.5375 | 1.27902 | ||||||||
\(773\) | −28.7525 | −1.03416 | −0.517079 | − | 0.855938i | \(-0.672981\pi\) | ||||
−0.517079 | + | 0.855938i | \(0.672981\pi\) | |||||||
\(774\) | 4.91185 | 0.176553 | ||||||||
\(775\) | 32.4698 | 1.16635 | ||||||||
\(776\) | −13.5060 | −0.484839 | ||||||||
\(777\) | 7.18598 | 0.257796 | ||||||||
\(778\) | −4.48022 | −0.160624 | ||||||||
\(779\) | 28.2344 | 1.01160 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.69202 | 0.0605453 | ||||||||
\(782\) | −14.0194 | −0.501332 | ||||||||
\(783\) | −1.74094 | −0.0622161 | ||||||||
\(784\) | 2.24698 | 0.0802493 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.05562 | 0.323003 | ||||||||
\(787\) | 34.2392 | 1.22050 | 0.610248 | − | 0.792210i | \(-0.291070\pi\) | ||||
0.610248 | + | 0.792210i | \(0.291070\pi\) | |||||||
\(788\) | −19.6668 | −0.700601 | ||||||||
\(789\) | 12.8955 | 0.459091 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.7071 | 0.487368 | ||||||||
\(792\) | −0.911854 | −0.0324013 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 9.73928 | 0.345634 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.6173 | −0.411764 | ||||||||
\(797\) | −19.1750 | −0.679212 | −0.339606 | − | 0.940568i | \(-0.610294\pi\) | ||||
−0.339606 | + | 0.940568i | \(0.610294\pi\) | |||||||
\(798\) | 2.27413 | 0.0805032 | ||||||||
\(799\) | −34.1715 | −1.20890 | ||||||||
\(800\) | −26.7241 | −0.944839 | ||||||||
\(801\) | −8.81163 | −0.311344 | ||||||||
\(802\) | 4.26577 | 0.150629 | ||||||||
\(803\) | −3.25129 | −0.114736 | ||||||||
\(804\) | −2.88338 | −0.101689 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.141375 | −0.00497664 | ||||||||
\(808\) | 12.2935 | 0.432484 | ||||||||
\(809\) | −12.3394 | −0.433832 | −0.216916 | − | 0.976190i | \(-0.569600\pi\) | ||||
−0.216916 | + | 0.976190i | \(0.569600\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.2078 | −0.393557 | −0.196779 | − | 0.980448i | \(-0.563048\pi\) | ||||
−0.196779 | + | 0.980448i | \(0.563048\pi\) | |||||||
\(812\) | 2.94571 | 0.103374 | ||||||||
\(813\) | 6.90946 | 0.242325 | ||||||||
\(814\) | 1.77479 | 0.0622064 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.09783 | −0.283481 | ||||||||
\(817\) | 36.2693 | 1.26890 | ||||||||
\(818\) | −20.1521 | −0.704603 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.5666 | −1.72989 | −0.864943 | − | 0.501871i | \(-0.832645\pi\) | ||||
−0.864943 | + | 0.501871i | \(0.832645\pi\) | |||||||
\(822\) | 0.399108 | 0.0139205 | ||||||||
\(823\) | −20.0761 | −0.699808 | −0.349904 | − | 0.936786i | \(-0.613786\pi\) | ||||
−0.349904 | + | 0.936786i | \(0.613786\pi\) | |||||||
\(824\) | 31.3599 | 1.09247 | ||||||||
\(825\) | 2.22521 | 0.0774718 | ||||||||
\(826\) | 2.76809 | 0.0963140 | ||||||||
\(827\) | −50.8743 | −1.76907 | −0.884536 | − | 0.466472i | \(-0.845525\pi\) | ||||
−0.884536 | + | 0.466472i | \(0.845525\pi\) | |||||||
\(828\) | 11.8605 | 0.412182 | ||||||||
\(829\) | 1.19700 | 0.0415734 | 0.0207867 | − | 0.999784i | \(-0.493383\pi\) | ||||
0.0207867 | + | 0.999784i | \(0.493383\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.35929 | −0.116532 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.60388 | 0.124867 | ||||||||
\(834\) | −1.17762 | −0.0407776 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.08575 | −0.106723 | ||||||||
\(837\) | 6.49396 | 0.224464 | ||||||||
\(838\) | 1.53020 | 0.0528600 | ||||||||
\(839\) | 33.5905 | 1.15967 | 0.579836 | − | 0.814733i | \(-0.303117\pi\) | ||||
0.579836 | + | 0.814733i | \(0.303117\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.9691 | −0.895487 | ||||||||
\(842\) | −13.7936 | −0.475358 | ||||||||
\(843\) | 26.7439 | 0.921110 | ||||||||
\(844\) | −11.6541 | −0.401151 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.26205 | −0.180913 | ||||||||
\(847\) | 10.8019 | 0.371159 | ||||||||
\(848\) | 20.8605 | 0.716354 | ||||||||
\(849\) | −14.6655 | −0.503317 | ||||||||
\(850\) | −10.0000 | −0.342997 | ||||||||
\(851\) | −50.3715 | −1.72671 | ||||||||
\(852\) | 6.43296 | 0.220390 | ||||||||
\(853\) | 38.7525 | 1.32686 | 0.663431 | − | 0.748238i | \(-0.269100\pi\) | ||||
0.663431 | + | 0.748238i | \(0.269100\pi\) | |||||||
\(854\) | 0.518122 | 0.0177298 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 30.0471 | 1.02699 | ||||||||
\(857\) | −7.48188 | −0.255576 | −0.127788 | − | 0.991802i | \(-0.540788\pi\) | ||||
−0.127788 | + | 0.991802i | \(0.540788\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.45042 | −0.0836072 | −0.0418036 | − | 0.999126i | \(-0.513310\pi\) | ||||
−0.0418036 | + | 0.999126i | \(0.513310\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.89008 | 0.234813 | ||||||||
\(862\) | −13.6805 | −0.465961 | ||||||||
\(863\) | −15.0175 | −0.511200 | −0.255600 | − | 0.966783i | \(-0.582273\pi\) | ||||
−0.255600 | + | 0.966783i | \(0.582273\pi\) | |||||||
\(864\) | −5.34481 | −0.181834 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.4397 | 0.558643 | ||||||||
\(867\) | 4.01208 | 0.136257 | ||||||||
\(868\) | −10.9879 | −0.372954 | ||||||||
\(869\) | −0.276520 | −0.00938028 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 30.4480 | 1.03110 | ||||||||
\(873\) | 6.59179 | 0.223098 | ||||||||
\(874\) | −15.9409 | −0.539210 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.3612 | −0.417647 | ||||||||
\(877\) | −25.7372 | −0.869084 | −0.434542 | − | 0.900652i | \(-0.643090\pi\) | ||||
−0.434542 | + | 0.900652i | \(0.643090\pi\) | |||||||
\(878\) | 15.8840 | 0.536058 | ||||||||
\(879\) | 5.15346 | 0.173822 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.8939 | 1.24299 | 0.621494 | − | 0.783419i | \(-0.286526\pi\) | ||||
0.621494 | + | 0.783419i | \(0.286526\pi\) | |||||||
\(882\) | 0.554958 | 0.0186864 | ||||||||
\(883\) | −50.5273 | −1.70038 | −0.850190 | − | 0.526476i | \(-0.823513\pi\) | ||||
−0.850190 | + | 0.526476i | \(0.823513\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.9688 | −0.435695 | ||||||||
\(887\) | −28.1957 | −0.946718 | −0.473359 | − | 0.880870i | \(-0.656959\pi\) | ||||
−0.473359 | + | 0.880870i | \(0.656959\pi\) | |||||||
\(888\) | 14.7235 | 0.494088 | ||||||||
\(889\) | 16.1371 | 0.541220 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.445042 | 0.0149095 | ||||||||
\(892\) | −29.9517 | −1.00286 | ||||||||
\(893\) | −38.8552 | −1.30024 | ||||||||
\(894\) | −1.75840 | −0.0588096 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11.5375 | 0.385441 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.23921 | −0.174835 | ||||||||
\(899\) | −11.3056 | −0.377062 | ||||||||
\(900\) | 8.46011 | 0.282004 | ||||||||
\(901\) | 33.4577 | 1.11464 | ||||||||
\(902\) | 1.70171 | 0.0566608 | ||||||||
\(903\) | 8.85086 | 0.294538 | ||||||||
\(904\) | 28.0847 | 0.934083 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.515729 | −0.0171340 | ||||||||
\(907\) | −42.6389 | −1.41580 | −0.707901 | − | 0.706312i | \(-0.750358\pi\) | ||||
−0.707901 | + | 0.706312i | \(0.750358\pi\) | |||||||
\(908\) | −42.3538 | −1.40556 | ||||||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.2825 | 0.870778 | 0.435389 | − | 0.900243i | \(-0.356611\pi\) | ||||
0.435389 | + | 0.900243i | \(0.356611\pi\) | |||||||
\(912\) | −9.20775 | −0.304899 | ||||||||
\(913\) | 1.90217 | 0.0629525 | ||||||||
\(914\) | −10.7168 | −0.354479 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −41.4443 | −1.36936 | ||||||||
\(917\) | 16.3177 | 0.538857 | ||||||||
\(918\) | −2.00000 | −0.0660098 | ||||||||
\(919\) | −20.9071 | −0.689661 | −0.344830 | − | 0.938665i | \(-0.612064\pi\) | ||||
−0.344830 | + | 0.938665i | \(0.612064\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.4276 | −0.508356 | ||||||||
\(922\) | 18.8250 | 0.619970 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.753020 | −0.0247726 | ||||||||
\(925\) | −35.9299 | −1.18137 | ||||||||
\(926\) | −11.3086 | −0.371623 | ||||||||
\(927\) | −15.3056 | −0.502701 | ||||||||
\(928\) | 9.30499 | 0.305451 | ||||||||
\(929\) | −24.3526 | −0.798982 | −0.399491 | − | 0.916737i | \(-0.630813\pi\) | ||||
−0.399491 | + | 0.916737i | \(0.630813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.09783 | 0.134301 | ||||||||
\(932\) | −15.5542 | −0.509495 | ||||||||
\(933\) | 34.9638 | 1.14466 | ||||||||
\(934\) | 15.2862 | 0.500180 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.7560 | −0.841412 | −0.420706 | − | 0.907197i | \(-0.638218\pi\) | ||||
−0.420706 | + | 0.907197i | \(0.638218\pi\) | |||||||
\(938\) | 0.945706 | 0.0308784 | ||||||||
\(939\) | 26.5569 | 0.866651 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.1258 | −1.43846 | −0.719231 | − | 0.694771i | \(-0.755506\pi\) | ||||
−0.719231 | + | 0.694771i | \(0.755506\pi\) | |||||||
\(942\) | −2.85995 | −0.0931823 | ||||||||
\(943\) | −48.2973 | −1.57278 | ||||||||
\(944\) | −11.2078 | −0.364781 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.18598 | 0.0710724 | ||||||||
\(947\) | −29.8165 | −0.968907 | −0.484454 | − | 0.874817i | \(-0.660982\pi\) | ||||
−0.484454 | + | 0.874817i | \(0.660982\pi\) | |||||||
\(948\) | −1.05131 | −0.0341450 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −11.3706 | −0.368912 | ||||||||
\(951\) | −13.9511 | −0.452395 | ||||||||
\(952\) | 7.38404 | 0.239318 | ||||||||
\(953\) | 3.46489 | 0.112239 | 0.0561194 | − | 0.998424i | \(-0.482127\pi\) | ||||
0.0561194 | + | 0.998424i | \(0.482127\pi\) | |||||||
\(954\) | 5.15213 | 0.166806 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.3961 | 0.433262 | ||||||||
\(957\) | −0.774791 | −0.0250454 | ||||||||
\(958\) | −1.14005 | −0.0368333 | ||||||||
\(959\) | 0.719169 | 0.0232232 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.1715 | 0.360371 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.6649 | −0.472569 | ||||||||
\(964\) | 2.56645 | 0.0826597 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.89008 | −0.125161 | ||||||||
\(967\) | −9.94810 | −0.319909 | −0.159955 | − | 0.987124i | \(-0.551135\pi\) | ||||
−0.159955 | + | 0.987124i | \(0.551135\pi\) | |||||||
\(968\) | 22.1323 | 0.711358 | ||||||||
\(969\) | −14.7681 | −0.474419 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.7754 | 0.506256 | 0.253128 | − | 0.967433i | \(-0.418541\pi\) | ||||
0.253128 | + | 0.967433i | \(0.418541\pi\) | |||||||
\(972\) | 1.69202 | 0.0542716 | ||||||||
\(973\) | −2.12200 | −0.0680281 | ||||||||
\(974\) | −3.93197 | −0.125988 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.09783 | −0.0671501 | ||||||||
\(977\) | 21.7178 | 0.694815 | 0.347408 | − | 0.937714i | \(-0.387062\pi\) | ||||
0.347408 | + | 0.937714i | \(0.387062\pi\) | |||||||
\(978\) | 8.36360 | 0.267438 | ||||||||
\(979\) | −3.92154 | −0.125333 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.8605 | −0.474461 | ||||||||
\(982\) | −20.4771 | −0.653450 | ||||||||
\(983\) | 4.99654 | 0.159365 | 0.0796825 | − | 0.996820i | \(-0.474609\pi\) | ||||
0.0796825 | + | 0.996820i | \(0.474609\pi\) | |||||||
\(984\) | 14.1172 | 0.450040 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.48188 | 0.110886 | ||||||||
\(987\) | −9.48188 | −0.301811 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −62.0417 | −1.97281 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.98015 | 0.253498 | 0.126749 | − | 0.991935i | \(-0.459546\pi\) | ||||
0.126749 | + | 0.991935i | \(0.459546\pi\) | |||||||
\(992\) | −34.7090 | −1.10201 | ||||||||
\(993\) | −5.46011 | −0.173271 | ||||||||
\(994\) | −2.10992 | −0.0669225 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.23191 | 0.229152 | ||||||||
\(997\) | −33.9952 | −1.07664 | −0.538320 | − | 0.842741i | \(-0.680941\pi\) | ||||
−0.538320 | + | 0.842741i | \(0.680941\pi\) | |||||||
\(998\) | 9.21611 | 0.291731 | ||||||||
\(999\) | −7.18598 | −0.227354 |
(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 | 3549.2.a.r.1.2 | yes | 3 | |
13.12 | even | 2 | 3549.2.a.g.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.g.1.2 | ✓ | 3 | 13.12 | even | 2 | ||
3549.2.a.r.1.2 | yes | 3 | 1.1 | even | 1 | trivial |