Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.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: | \(34.6071642360\) |
Analytic rank: | \(1\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 5 x^{16} - 19 x^{15} + 121 x^{14} + 112 x^{13} - 1172 x^{12} - 25 x^{11} + 5845 x^{10} - 2233 x^{9} - 16035 x^{8} + 9174 x^{7} + 23882 x^{6} - 15232 x^{5} - 17609 x^{4} + \cdots + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.22229\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.22229 | −0.705692 | −0.352846 | − | 0.935681i | \(-0.614786\pi\) | ||||
−0.352846 | + | 0.935681i | \(0.614786\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.12347 | 1.84407 | 0.922036 | − | 0.387105i | \(-0.126525\pi\) | ||||
0.922036 | + | 0.387105i | \(0.126525\pi\) | |||||||
\(6\) | 1.22229 | 0.498999 | ||||||||
\(7\) | −0.673376 | −0.254512 | −0.127256 | − | 0.991870i | \(-0.540617\pi\) | ||||
−0.127256 | + | 0.991870i | \(0.540617\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.50600 | −0.501999 | ||||||||
\(10\) | −4.12347 | −1.30396 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.22229 | −0.352846 | ||||||||
\(13\) | −1.15175 | −0.319439 | −0.159720 | − | 0.987162i | \(-0.551059\pi\) | ||||
−0.159720 | + | 0.987162i | \(0.551059\pi\) | |||||||
\(14\) | 0.673376 | 0.179967 | ||||||||
\(15\) | −5.04009 | −1.30135 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.09398 | −1.23547 | −0.617736 | − | 0.786386i | \(-0.711950\pi\) | ||||
−0.617736 | + | 0.786386i | \(0.711950\pi\) | |||||||
\(18\) | 1.50600 | 0.354967 | ||||||||
\(19\) | −6.95848 | −1.59638 | −0.798192 | − | 0.602403i | \(-0.794210\pi\) | ||||
−0.798192 | + | 0.602403i | \(0.794210\pi\) | |||||||
\(20\) | 4.12347 | 0.922036 | ||||||||
\(21\) | 0.823063 | 0.179607 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 4.97526 | 1.03741 | 0.518706 | − | 0.854953i | \(-0.326414\pi\) | ||||
0.518706 | + | 0.854953i | \(0.326414\pi\) | |||||||
\(24\) | 1.22229 | 0.249500 | ||||||||
\(25\) | 12.0030 | 2.40060 | ||||||||
\(26\) | 1.15175 | 0.225878 | ||||||||
\(27\) | 5.50765 | 1.05995 | ||||||||
\(28\) | −0.673376 | −0.127256 | ||||||||
\(29\) | 4.08775 | 0.759076 | 0.379538 | − | 0.925176i | \(-0.376083\pi\) | ||||
0.379538 | + | 0.925176i | \(0.376083\pi\) | |||||||
\(30\) | 5.04009 | 0.920191 | ||||||||
\(31\) | 8.14953 | 1.46370 | 0.731850 | − | 0.681466i | \(-0.238657\pi\) | ||||
0.731850 | + | 0.681466i | \(0.238657\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.22229 | 0.212774 | ||||||||
\(34\) | 5.09398 | 0.873611 | ||||||||
\(35\) | −2.77664 | −0.469339 | ||||||||
\(36\) | −1.50600 | −0.251000 | ||||||||
\(37\) | 1.53165 | 0.251802 | 0.125901 | − | 0.992043i | \(-0.459818\pi\) | ||||
0.125901 | + | 0.992043i | \(0.459818\pi\) | |||||||
\(38\) | 6.95848 | 1.12881 | ||||||||
\(39\) | 1.40778 | 0.225426 | ||||||||
\(40\) | −4.12347 | −0.651978 | ||||||||
\(41\) | −10.1937 | −1.59198 | −0.795992 | − | 0.605307i | \(-0.793050\pi\) | ||||
−0.795992 | + | 0.605307i | \(0.793050\pi\) | |||||||
\(42\) | −0.823063 | −0.127001 | ||||||||
\(43\) | −2.45640 | −0.374598 | −0.187299 | − | 0.982303i | \(-0.559973\pi\) | ||||
−0.187299 | + | 0.982303i | \(0.559973\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −6.20994 | −0.925723 | ||||||||
\(46\) | −4.97526 | −0.733561 | ||||||||
\(47\) | 7.13004 | 1.04002 | 0.520012 | − | 0.854159i | \(-0.325928\pi\) | ||||
0.520012 | + | 0.854159i | \(0.325928\pi\) | |||||||
\(48\) | −1.22229 | −0.176423 | ||||||||
\(49\) | −6.54656 | −0.935224 | ||||||||
\(50\) | −12.0030 | −1.69748 | ||||||||
\(51\) | 6.22634 | 0.871862 | ||||||||
\(52\) | −1.15175 | −0.159720 | ||||||||
\(53\) | −5.31830 | −0.730525 | −0.365263 | − | 0.930905i | \(-0.619021\pi\) | ||||
−0.365263 | + | 0.930905i | \(0.619021\pi\) | |||||||
\(54\) | −5.50765 | −0.749497 | ||||||||
\(55\) | −4.12347 | −0.556008 | ||||||||
\(56\) | 0.673376 | 0.0899836 | ||||||||
\(57\) | 8.50530 | 1.12655 | ||||||||
\(58\) | −4.08775 | −0.536748 | ||||||||
\(59\) | 10.9112 | 1.42052 | 0.710258 | − | 0.703942i | \(-0.248578\pi\) | ||||
0.710258 | + | 0.703942i | \(0.248578\pi\) | |||||||
\(60\) | −5.04009 | −0.650673 | ||||||||
\(61\) | 2.64210 | 0.338287 | 0.169143 | − | 0.985591i | \(-0.445900\pi\) | ||||
0.169143 | + | 0.985591i | \(0.445900\pi\) | |||||||
\(62\) | −8.14953 | −1.03499 | ||||||||
\(63\) | 1.01410 | 0.127765 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.74922 | −0.589069 | ||||||||
\(66\) | −1.22229 | −0.150454 | ||||||||
\(67\) | −6.43050 | −0.785610 | −0.392805 | − | 0.919622i | \(-0.628495\pi\) | ||||
−0.392805 | + | 0.919622i | \(0.628495\pi\) | |||||||
\(68\) | −5.09398 | −0.617736 | ||||||||
\(69\) | −6.08122 | −0.732093 | ||||||||
\(70\) | 2.77664 | 0.331873 | ||||||||
\(71\) | −9.86795 | −1.17111 | −0.585555 | − | 0.810633i | \(-0.699123\pi\) | ||||
−0.585555 | + | 0.810633i | \(0.699123\pi\) | |||||||
\(72\) | 1.50600 | 0.177484 | ||||||||
\(73\) | −8.78991 | −1.02878 | −0.514391 | − | 0.857556i | \(-0.671982\pi\) | ||||
−0.514391 | + | 0.857556i | \(0.671982\pi\) | |||||||
\(74\) | −1.53165 | −0.178051 | ||||||||
\(75\) | −14.6712 | −1.69408 | ||||||||
\(76\) | −6.95848 | −0.798192 | ||||||||
\(77\) | 0.673376 | 0.0767383 | ||||||||
\(78\) | −1.40778 | −0.159400 | ||||||||
\(79\) | 10.3482 | 1.16426 | 0.582131 | − | 0.813095i | \(-0.302219\pi\) | ||||
0.582131 | + | 0.813095i | \(0.302219\pi\) | |||||||
\(80\) | 4.12347 | 0.461018 | ||||||||
\(81\) | −2.21398 | −0.245997 | ||||||||
\(82\) | 10.1937 | 1.12570 | ||||||||
\(83\) | −5.79609 | −0.636204 | −0.318102 | − | 0.948057i | \(-0.603045\pi\) | ||||
−0.318102 | + | 0.948057i | \(0.603045\pi\) | |||||||
\(84\) | 0.823063 | 0.0898036 | ||||||||
\(85\) | −21.0049 | −2.27830 | ||||||||
\(86\) | 2.45640 | 0.264880 | ||||||||
\(87\) | −4.99643 | −0.535674 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −2.26285 | −0.239862 | −0.119931 | − | 0.992782i | \(-0.538267\pi\) | ||||
−0.119931 | + | 0.992782i | \(0.538267\pi\) | |||||||
\(90\) | 6.20994 | 0.654585 | ||||||||
\(91\) | 0.775564 | 0.0813012 | ||||||||
\(92\) | 4.97526 | 0.518706 | ||||||||
\(93\) | −9.96112 | −1.03292 | ||||||||
\(94\) | −7.13004 | −0.735408 | ||||||||
\(95\) | −28.6931 | −2.94385 | ||||||||
\(96\) | 1.22229 | 0.124750 | ||||||||
\(97\) | −19.3581 | −1.96551 | −0.982757 | − | 0.184901i | \(-0.940803\pi\) | ||||
−0.982757 | + | 0.184901i | \(0.940803\pi\) | |||||||
\(98\) | 6.54656 | 0.661303 | ||||||||
\(99\) | 1.50600 | 0.151358 | ||||||||
\(100\) | 12.0030 | 1.20030 | ||||||||
\(101\) | −17.2864 | −1.72006 | −0.860029 | − | 0.510245i | \(-0.829555\pi\) | ||||
−0.860029 | + | 0.510245i | \(0.829555\pi\) | |||||||
\(102\) | −6.22634 | −0.616500 | ||||||||
\(103\) | 5.18480 | 0.510873 | 0.255437 | − | 0.966826i | \(-0.417781\pi\) | ||||
0.255437 | + | 0.966826i | \(0.417781\pi\) | |||||||
\(104\) | 1.15175 | 0.112939 | ||||||||
\(105\) | 3.39388 | 0.331208 | ||||||||
\(106\) | 5.31830 | 0.516559 | ||||||||
\(107\) | −4.31733 | −0.417372 | −0.208686 | − | 0.977983i | \(-0.566919\pi\) | ||||
−0.208686 | + | 0.977983i | \(0.566919\pi\) | |||||||
\(108\) | 5.50765 | 0.529974 | ||||||||
\(109\) | −5.07937 | −0.486515 | −0.243258 | − | 0.969962i | \(-0.578216\pi\) | ||||
−0.243258 | + | 0.969962i | \(0.578216\pi\) | |||||||
\(110\) | 4.12347 | 0.393157 | ||||||||
\(111\) | −1.87213 | −0.177695 | ||||||||
\(112\) | −0.673376 | −0.0636280 | ||||||||
\(113\) | −8.78693 | −0.826605 | −0.413303 | − | 0.910594i | \(-0.635625\pi\) | ||||
−0.413303 | + | 0.910594i | \(0.635625\pi\) | |||||||
\(114\) | −8.50530 | −0.796595 | ||||||||
\(115\) | 20.5153 | 1.91306 | ||||||||
\(116\) | 4.08775 | 0.379538 | ||||||||
\(117\) | 1.73454 | 0.160358 | ||||||||
\(118\) | −10.9112 | −1.00446 | ||||||||
\(119\) | 3.43016 | 0.314443 | ||||||||
\(120\) | 5.04009 | 0.460095 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.64210 | −0.239205 | ||||||||
\(123\) | 12.4597 | 1.12345 | ||||||||
\(124\) | 8.14953 | 0.731850 | ||||||||
\(125\) | 28.8767 | 2.58281 | ||||||||
\(126\) | −1.01410 | −0.0903434 | ||||||||
\(127\) | 13.4600 | 1.19439 | 0.597193 | − | 0.802098i | \(-0.296283\pi\) | ||||
0.597193 | + | 0.802098i | \(0.296283\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 3.00244 | 0.264350 | ||||||||
\(130\) | 4.74922 | 0.416534 | ||||||||
\(131\) | 2.93923 | 0.256802 | 0.128401 | − | 0.991722i | \(-0.459016\pi\) | ||||
0.128401 | + | 0.991722i | \(0.459016\pi\) | |||||||
\(132\) | 1.22229 | 0.106387 | ||||||||
\(133\) | 4.68567 | 0.406299 | ||||||||
\(134\) | 6.43050 | 0.555510 | ||||||||
\(135\) | 22.7106 | 1.95462 | ||||||||
\(136\) | 5.09398 | 0.436805 | ||||||||
\(137\) | −6.88035 | −0.587828 | −0.293914 | − | 0.955832i | \(-0.594958\pi\) | ||||
−0.293914 | + | 0.955832i | \(0.594958\pi\) | |||||||
\(138\) | 6.08122 | 0.517668 | ||||||||
\(139\) | −4.21524 | −0.357532 | −0.178766 | − | 0.983892i | \(-0.557211\pi\) | ||||
−0.178766 | + | 0.983892i | \(0.557211\pi\) | |||||||
\(140\) | −2.77664 | −0.234669 | ||||||||
\(141\) | −8.71500 | −0.733936 | ||||||||
\(142\) | 9.86795 | 0.828100 | ||||||||
\(143\) | 1.15175 | 0.0963145 | ||||||||
\(144\) | −1.50600 | −0.125500 | ||||||||
\(145\) | 16.8557 | 1.39979 | ||||||||
\(146\) | 8.78991 | 0.727458 | ||||||||
\(147\) | 8.00183 | 0.659979 | ||||||||
\(148\) | 1.53165 | 0.125901 | ||||||||
\(149\) | −14.8554 | −1.21700 | −0.608500 | − | 0.793554i | \(-0.708228\pi\) | ||||
−0.608500 | + | 0.793554i | \(0.708228\pi\) | |||||||
\(150\) | 14.6712 | 1.19790 | ||||||||
\(151\) | −23.9206 | −1.94663 | −0.973315 | − | 0.229472i | \(-0.926300\pi\) | ||||
−0.973315 | + | 0.229472i | \(0.926300\pi\) | |||||||
\(152\) | 6.95848 | 0.564407 | ||||||||
\(153\) | 7.67153 | 0.620206 | ||||||||
\(154\) | −0.673376 | −0.0542622 | ||||||||
\(155\) | 33.6043 | 2.69917 | ||||||||
\(156\) | 1.40778 | 0.112713 | ||||||||
\(157\) | −3.88069 | −0.309713 | −0.154856 | − | 0.987937i | \(-0.549492\pi\) | ||||
−0.154856 | + | 0.987937i | \(0.549492\pi\) | |||||||
\(158\) | −10.3482 | −0.823257 | ||||||||
\(159\) | 6.50053 | 0.515526 | ||||||||
\(160\) | −4.12347 | −0.325989 | ||||||||
\(161\) | −3.35022 | −0.264034 | ||||||||
\(162\) | 2.21398 | 0.173946 | ||||||||
\(163\) | 15.7845 | 1.23633 | 0.618167 | − | 0.786047i | \(-0.287876\pi\) | ||||
0.618167 | + | 0.786047i | \(0.287876\pi\) | |||||||
\(164\) | −10.1937 | −0.795992 | ||||||||
\(165\) | 5.04009 | 0.392371 | ||||||||
\(166\) | 5.79609 | 0.449864 | ||||||||
\(167\) | 9.48967 | 0.734333 | 0.367166 | − | 0.930155i | \(-0.380328\pi\) | ||||
0.367166 | + | 0.930155i | \(0.380328\pi\) | |||||||
\(168\) | −0.823063 | −0.0635007 | ||||||||
\(169\) | −11.6735 | −0.897959 | ||||||||
\(170\) | 21.0049 | 1.61100 | ||||||||
\(171\) | 10.4794 | 0.801384 | ||||||||
\(172\) | −2.45640 | −0.187299 | ||||||||
\(173\) | 3.55523 | 0.270299 | 0.135150 | − | 0.990825i | \(-0.456848\pi\) | ||||
0.135150 | + | 0.990825i | \(0.456848\pi\) | |||||||
\(174\) | 4.99643 | 0.378779 | ||||||||
\(175\) | −8.08253 | −0.610982 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −13.3367 | −1.00245 | ||||||||
\(178\) | 2.26285 | 0.169608 | ||||||||
\(179\) | −23.0257 | −1.72102 | −0.860511 | − | 0.509431i | \(-0.829856\pi\) | ||||
−0.860511 | + | 0.509431i | \(0.829856\pi\) | |||||||
\(180\) | −6.20994 | −0.462861 | ||||||||
\(181\) | 1.67191 | 0.124272 | 0.0621360 | − | 0.998068i | \(-0.480209\pi\) | ||||
0.0621360 | + | 0.998068i | \(0.480209\pi\) | |||||||
\(182\) | −0.775564 | −0.0574886 | ||||||||
\(183\) | −3.22943 | −0.238726 | ||||||||
\(184\) | −4.97526 | −0.366781 | ||||||||
\(185\) | 6.31573 | 0.464342 | ||||||||
\(186\) | 9.96112 | 0.730385 | ||||||||
\(187\) | 5.09398 | 0.372509 | ||||||||
\(188\) | 7.13004 | 0.520012 | ||||||||
\(189\) | −3.70872 | −0.269770 | ||||||||
\(190\) | 28.6931 | 2.08161 | ||||||||
\(191\) | −21.4595 | −1.55275 | −0.776376 | − | 0.630270i | \(-0.782944\pi\) | ||||
−0.776376 | + | 0.630270i | \(0.782944\pi\) | |||||||
\(192\) | −1.22229 | −0.0882115 | ||||||||
\(193\) | 12.4401 | 0.895456 | 0.447728 | − | 0.894170i | \(-0.352233\pi\) | ||||
0.447728 | + | 0.894170i | \(0.352233\pi\) | |||||||
\(194\) | 19.3581 | 1.38983 | ||||||||
\(195\) | 5.80495 | 0.415701 | ||||||||
\(196\) | −6.54656 | −0.467612 | ||||||||
\(197\) | −1.00000 | −0.0712470 | ||||||||
\(198\) | −1.50600 | −0.107027 | ||||||||
\(199\) | −11.2537 | −0.797751 | −0.398875 | − | 0.917005i | \(-0.630599\pi\) | ||||
−0.398875 | + | 0.917005i | \(0.630599\pi\) | |||||||
\(200\) | −12.0030 | −0.848740 | ||||||||
\(201\) | 7.85996 | 0.554398 | ||||||||
\(202\) | 17.2864 | 1.21626 | ||||||||
\(203\) | −2.75259 | −0.193194 | ||||||||
\(204\) | 6.22634 | 0.435931 | ||||||||
\(205\) | −42.0333 | −2.93573 | ||||||||
\(206\) | −5.18480 | −0.361242 | ||||||||
\(207\) | −7.49272 | −0.520780 | ||||||||
\(208\) | −1.15175 | −0.0798598 | ||||||||
\(209\) | 6.95848 | 0.481328 | ||||||||
\(210\) | −3.39388 | −0.234200 | ||||||||
\(211\) | 4.83153 | 0.332616 | 0.166308 | − | 0.986074i | \(-0.446815\pi\) | ||||
0.166308 | + | 0.986074i | \(0.446815\pi\) | |||||||
\(212\) | −5.31830 | −0.365263 | ||||||||
\(213\) | 12.0615 | 0.826442 | ||||||||
\(214\) | 4.31733 | 0.295127 | ||||||||
\(215\) | −10.1289 | −0.690785 | ||||||||
\(216\) | −5.50765 | −0.374748 | ||||||||
\(217\) | −5.48770 | −0.372529 | ||||||||
\(218\) | 5.07937 | 0.344018 | ||||||||
\(219\) | 10.7439 | 0.726002 | ||||||||
\(220\) | −4.12347 | −0.278004 | ||||||||
\(221\) | 5.86702 | 0.394658 | ||||||||
\(222\) | 1.87213 | 0.125649 | ||||||||
\(223\) | −21.1240 | −1.41456 | −0.707282 | − | 0.706931i | \(-0.750079\pi\) | ||||
−0.707282 | + | 0.706931i | \(0.750079\pi\) | |||||||
\(224\) | 0.673376 | 0.0449918 | ||||||||
\(225\) | −18.0765 | −1.20510 | ||||||||
\(226\) | 8.78693 | 0.584498 | ||||||||
\(227\) | −14.6606 | −0.973061 | −0.486530 | − | 0.873664i | \(-0.661738\pi\) | ||||
−0.486530 | + | 0.873664i | \(0.661738\pi\) | |||||||
\(228\) | 8.50530 | 0.563277 | ||||||||
\(229\) | 2.79269 | 0.184546 | 0.0922730 | − | 0.995734i | \(-0.470587\pi\) | ||||
0.0922730 | + | 0.995734i | \(0.470587\pi\) | |||||||
\(230\) | −20.5153 | −1.35274 | ||||||||
\(231\) | −0.823063 | −0.0541536 | ||||||||
\(232\) | −4.08775 | −0.268374 | ||||||||
\(233\) | 7.45053 | 0.488101 | 0.244050 | − | 0.969763i | \(-0.421524\pi\) | ||||
0.244050 | + | 0.969763i | \(0.421524\pi\) | |||||||
\(234\) | −1.73454 | −0.113390 | ||||||||
\(235\) | 29.4005 | 1.91788 | ||||||||
\(236\) | 10.9112 | 0.710258 | ||||||||
\(237\) | −12.6485 | −0.821609 | ||||||||
\(238\) | −3.43016 | −0.222345 | ||||||||
\(239\) | 2.13371 | 0.138018 | 0.0690091 | − | 0.997616i | \(-0.478016\pi\) | ||||
0.0690091 | + | 0.997616i | \(0.478016\pi\) | |||||||
\(240\) | −5.04009 | −0.325336 | ||||||||
\(241\) | −7.12792 | −0.459150 | −0.229575 | − | 0.973291i | \(-0.573734\pi\) | ||||
−0.229575 | + | 0.973291i | \(0.573734\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −13.8168 | −0.886350 | ||||||||
\(244\) | 2.64210 | 0.169143 | ||||||||
\(245\) | −26.9946 | −1.72462 | ||||||||
\(246\) | −12.4597 | −0.794399 | ||||||||
\(247\) | 8.01445 | 0.509948 | ||||||||
\(248\) | −8.14953 | −0.517496 | ||||||||
\(249\) | 7.08453 | 0.448964 | ||||||||
\(250\) | −28.8767 | −1.82632 | ||||||||
\(251\) | 26.5391 | 1.67513 | 0.837566 | − | 0.546337i | \(-0.183978\pi\) | ||||
0.837566 | + | 0.546337i | \(0.183978\pi\) | |||||||
\(252\) | 1.01410 | 0.0638825 | ||||||||
\(253\) | −4.97526 | −0.312792 | ||||||||
\(254\) | −13.4600 | −0.844558 | ||||||||
\(255\) | 25.6741 | 1.60778 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −30.0195 | −1.87257 | −0.936283 | − | 0.351247i | \(-0.885758\pi\) | ||||
−0.936283 | + | 0.351247i | \(0.885758\pi\) | |||||||
\(258\) | −3.00244 | −0.186924 | ||||||||
\(259\) | −1.03138 | −0.0640868 | ||||||||
\(260\) | −4.74922 | −0.294534 | ||||||||
\(261\) | −6.15614 | −0.381056 | ||||||||
\(262\) | −2.93923 | −0.181586 | ||||||||
\(263\) | 28.7291 | 1.77151 | 0.885757 | − | 0.464149i | \(-0.153640\pi\) | ||||
0.885757 | + | 0.464149i | \(0.153640\pi\) | |||||||
\(264\) | −1.22229 | −0.0752270 | ||||||||
\(265\) | −21.9299 | −1.34714 | ||||||||
\(266\) | −4.68567 | −0.287297 | ||||||||
\(267\) | 2.76587 | 0.169268 | ||||||||
\(268\) | −6.43050 | −0.392805 | ||||||||
\(269\) | −1.92518 | −0.117380 | −0.0586901 | − | 0.998276i | \(-0.518692\pi\) | ||||
−0.0586901 | + | 0.998276i | \(0.518692\pi\) | |||||||
\(270\) | −22.7106 | −1.38213 | ||||||||
\(271\) | 7.33014 | 0.445275 | 0.222637 | − | 0.974901i | \(-0.428533\pi\) | ||||
0.222637 | + | 0.974901i | \(0.428533\pi\) | |||||||
\(272\) | −5.09398 | −0.308868 | ||||||||
\(273\) | −0.947967 | −0.0573735 | ||||||||
\(274\) | 6.88035 | 0.415657 | ||||||||
\(275\) | −12.0030 | −0.723808 | ||||||||
\(276\) | −6.08122 | −0.366047 | ||||||||
\(277\) | −6.73088 | −0.404420 | −0.202210 | − | 0.979342i | \(-0.564812\pi\) | ||||
−0.202210 | + | 0.979342i | \(0.564812\pi\) | |||||||
\(278\) | 4.21524 | 0.252813 | ||||||||
\(279\) | −12.2732 | −0.734776 | ||||||||
\(280\) | 2.77664 | 0.165936 | ||||||||
\(281\) | 9.12854 | 0.544563 | 0.272281 | − | 0.962218i | \(-0.412222\pi\) | ||||
0.272281 | + | 0.962218i | \(0.412222\pi\) | |||||||
\(282\) | 8.71500 | 0.518971 | ||||||||
\(283\) | −7.30638 | −0.434319 | −0.217160 | − | 0.976136i | \(-0.569679\pi\) | ||||
−0.217160 | + | 0.976136i | \(0.569679\pi\) | |||||||
\(284\) | −9.86795 | −0.585555 | ||||||||
\(285\) | 35.0714 | 2.07745 | ||||||||
\(286\) | −1.15175 | −0.0681047 | ||||||||
\(287\) | 6.86417 | 0.405179 | ||||||||
\(288\) | 1.50600 | 0.0887418 | ||||||||
\(289\) | 8.94865 | 0.526391 | ||||||||
\(290\) | −16.8557 | −0.989802 | ||||||||
\(291\) | 23.6612 | 1.38705 | ||||||||
\(292\) | −8.78991 | −0.514391 | ||||||||
\(293\) | 1.70904 | 0.0998434 | 0.0499217 | − | 0.998753i | \(-0.484103\pi\) | ||||
0.0499217 | + | 0.998753i | \(0.484103\pi\) | |||||||
\(294\) | −8.00183 | −0.466676 | ||||||||
\(295\) | 44.9920 | 2.61953 | ||||||||
\(296\) | −1.53165 | −0.0890256 | ||||||||
\(297\) | −5.50765 | −0.319586 | ||||||||
\(298\) | 14.8554 | 0.860549 | ||||||||
\(299\) | −5.73027 | −0.331390 | ||||||||
\(300\) | −14.6712 | −0.847042 | ||||||||
\(301\) | 1.65408 | 0.0953396 | ||||||||
\(302\) | 23.9206 | 1.37648 | ||||||||
\(303\) | 21.1290 | 1.21383 | ||||||||
\(304\) | −6.95848 | −0.399096 | ||||||||
\(305\) | 10.8946 | 0.623825 | ||||||||
\(306\) | −7.67153 | −0.438552 | ||||||||
\(307\) | −29.7495 | −1.69789 | −0.848947 | − | 0.528479i | \(-0.822763\pi\) | ||||
−0.848947 | + | 0.528479i | \(0.822763\pi\) | |||||||
\(308\) | 0.673376 | 0.0383692 | ||||||||
\(309\) | −6.33735 | −0.360519 | ||||||||
\(310\) | −33.6043 | −1.90860 | ||||||||
\(311\) | −26.8202 | −1.52084 | −0.760418 | − | 0.649434i | \(-0.775006\pi\) | ||||
−0.760418 | + | 0.649434i | \(0.775006\pi\) | |||||||
\(312\) | −1.40778 | −0.0797000 | ||||||||
\(313\) | 20.3744 | 1.15163 | 0.575816 | − | 0.817579i | \(-0.304685\pi\) | ||||
0.575816 | + | 0.817579i | \(0.304685\pi\) | |||||||
\(314\) | 3.88069 | 0.219000 | ||||||||
\(315\) | 4.18162 | 0.235608 | ||||||||
\(316\) | 10.3482 | 0.582131 | ||||||||
\(317\) | 8.97894 | 0.504308 | 0.252154 | − | 0.967687i | \(-0.418861\pi\) | ||||
0.252154 | + | 0.967687i | \(0.418861\pi\) | |||||||
\(318\) | −6.50053 | −0.364532 | ||||||||
\(319\) | −4.08775 | −0.228870 | ||||||||
\(320\) | 4.12347 | 0.230509 | ||||||||
\(321\) | 5.27705 | 0.294536 | ||||||||
\(322\) | 3.35022 | 0.186700 | ||||||||
\(323\) | 35.4463 | 1.97229 | ||||||||
\(324\) | −2.21398 | −0.122999 | ||||||||
\(325\) | −13.8245 | −0.766846 | ||||||||
\(326\) | −15.7845 | −0.874220 | ||||||||
\(327\) | 6.20848 | 0.343330 | ||||||||
\(328\) | 10.1937 | 0.562851 | ||||||||
\(329\) | −4.80120 | −0.264699 | ||||||||
\(330\) | −5.04009 | −0.277448 | ||||||||
\(331\) | 3.66781 | 0.201601 | 0.100801 | − | 0.994907i | \(-0.467860\pi\) | ||||
0.100801 | + | 0.994907i | \(0.467860\pi\) | |||||||
\(332\) | −5.79609 | −0.318102 | ||||||||
\(333\) | −2.30667 | −0.126405 | ||||||||
\(334\) | −9.48967 | −0.519252 | ||||||||
\(335\) | −26.5160 | −1.44872 | ||||||||
\(336\) | 0.823063 | 0.0449018 | ||||||||
\(337\) | 27.7733 | 1.51291 | 0.756455 | − | 0.654046i | \(-0.226930\pi\) | ||||
0.756455 | + | 0.654046i | \(0.226930\pi\) | |||||||
\(338\) | 11.6735 | 0.634953 | ||||||||
\(339\) | 10.7402 | 0.583328 | ||||||||
\(340\) | −21.0049 | −1.13915 | ||||||||
\(341\) | −8.14953 | −0.441322 | ||||||||
\(342\) | −10.4794 | −0.566664 | ||||||||
\(343\) | 9.12193 | 0.492538 | ||||||||
\(344\) | 2.45640 | 0.132440 | ||||||||
\(345\) | −25.0757 | −1.35003 | ||||||||
\(346\) | −3.55523 | −0.191131 | ||||||||
\(347\) | −4.48980 | −0.241025 | −0.120513 | − | 0.992712i | \(-0.538454\pi\) | ||||
−0.120513 | + | 0.992712i | \(0.538454\pi\) | |||||||
\(348\) | −4.99643 | −0.267837 | ||||||||
\(349\) | 9.48557 | 0.507751 | 0.253876 | − | 0.967237i | \(-0.418295\pi\) | ||||
0.253876 | + | 0.967237i | \(0.418295\pi\) | |||||||
\(350\) | 8.08253 | 0.432029 | ||||||||
\(351\) | −6.34346 | −0.338589 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −35.7101 | −1.90066 | −0.950329 | − | 0.311247i | \(-0.899253\pi\) | ||||
−0.950329 | + | 0.311247i | \(0.899253\pi\) | |||||||
\(354\) | 13.3367 | 0.708836 | ||||||||
\(355\) | −40.6902 | −2.15961 | ||||||||
\(356\) | −2.26285 | −0.119931 | ||||||||
\(357\) | −4.19267 | −0.221900 | ||||||||
\(358\) | 23.0257 | 1.21695 | ||||||||
\(359\) | 23.3915 | 1.23456 | 0.617279 | − | 0.786744i | \(-0.288235\pi\) | ||||
0.617279 | + | 0.786744i | \(0.288235\pi\) | |||||||
\(360\) | 6.20994 | 0.327292 | ||||||||
\(361\) | 29.4204 | 1.54844 | ||||||||
\(362\) | −1.67191 | −0.0878736 | ||||||||
\(363\) | −1.22229 | −0.0641538 | ||||||||
\(364\) | 0.775564 | 0.0406506 | ||||||||
\(365\) | −36.2449 | −1.89715 | ||||||||
\(366\) | 3.22943 | 0.168805 | ||||||||
\(367\) | −37.1698 | −1.94025 | −0.970123 | − | 0.242612i | \(-0.921996\pi\) | ||||
−0.970123 | + | 0.242612i | \(0.921996\pi\) | |||||||
\(368\) | 4.97526 | 0.259353 | ||||||||
\(369\) | 15.3516 | 0.799175 | ||||||||
\(370\) | −6.31573 | −0.328339 | ||||||||
\(371\) | 3.58122 | 0.185928 | ||||||||
\(372\) | −9.96112 | −0.516460 | ||||||||
\(373\) | 21.2940 | 1.10256 | 0.551280 | − | 0.834321i | \(-0.314140\pi\) | ||||
0.551280 | + | 0.834321i | \(0.314140\pi\) | |||||||
\(374\) | −5.09398 | −0.263404 | ||||||||
\(375\) | −35.2958 | −1.82266 | ||||||||
\(376\) | −7.13004 | −0.367704 | ||||||||
\(377\) | −4.70808 | −0.242479 | ||||||||
\(378\) | 3.70872 | 0.190756 | ||||||||
\(379\) | −21.1655 | −1.08720 | −0.543600 | − | 0.839345i | \(-0.682939\pi\) | ||||
−0.543600 | + | 0.839345i | \(0.682939\pi\) | |||||||
\(380\) | −28.6931 | −1.47192 | ||||||||
\(381\) | −16.4521 | −0.842868 | ||||||||
\(382\) | 21.4595 | 1.09796 | ||||||||
\(383\) | −24.0635 | −1.22959 | −0.614793 | − | 0.788689i | \(-0.710760\pi\) | ||||
−0.614793 | + | 0.788689i | \(0.710760\pi\) | |||||||
\(384\) | 1.22229 | 0.0623749 | ||||||||
\(385\) | 2.77664 | 0.141511 | ||||||||
\(386\) | −12.4401 | −0.633183 | ||||||||
\(387\) | 3.69933 | 0.188048 | ||||||||
\(388\) | −19.3581 | −0.982757 | ||||||||
\(389\) | 6.92942 | 0.351336 | 0.175668 | − | 0.984449i | \(-0.443792\pi\) | ||||
0.175668 | + | 0.984449i | \(0.443792\pi\) | |||||||
\(390\) | −5.80495 | −0.293945 | ||||||||
\(391\) | −25.3439 | −1.28169 | ||||||||
\(392\) | 6.54656 | 0.330651 | ||||||||
\(393\) | −3.59260 | −0.181223 | ||||||||
\(394\) | 1.00000 | 0.0503793 | ||||||||
\(395\) | 42.6704 | 2.14698 | ||||||||
\(396\) | 1.50600 | 0.0756792 | ||||||||
\(397\) | −2.47881 | −0.124408 | −0.0622039 | − | 0.998063i | \(-0.519813\pi\) | ||||
−0.0622039 | + | 0.998063i | \(0.519813\pi\) | |||||||
\(398\) | 11.2537 | 0.564095 | ||||||||
\(399\) | −5.72727 | −0.286722 | ||||||||
\(400\) | 12.0030 | 0.600150 | ||||||||
\(401\) | −14.5549 | −0.726835 | −0.363417 | − | 0.931626i | \(-0.618390\pi\) | ||||
−0.363417 | + | 0.931626i | \(0.618390\pi\) | |||||||
\(402\) | −7.85996 | −0.392019 | ||||||||
\(403\) | −9.38626 | −0.467563 | ||||||||
\(404\) | −17.2864 | −0.860029 | ||||||||
\(405\) | −9.12927 | −0.453637 | ||||||||
\(406\) | 2.75259 | 0.136609 | ||||||||
\(407\) | −1.53165 | −0.0759213 | ||||||||
\(408\) | −6.22634 | −0.308250 | ||||||||
\(409\) | −8.66702 | −0.428557 | −0.214278 | − | 0.976773i | \(-0.568740\pi\) | ||||
−0.214278 | + | 0.976773i | \(0.568740\pi\) | |||||||
\(410\) | 42.0333 | 2.07588 | ||||||||
\(411\) | 8.40982 | 0.414826 | ||||||||
\(412\) | 5.18480 | 0.255437 | ||||||||
\(413\) | −7.34733 | −0.361539 | ||||||||
\(414\) | 7.49272 | 0.368247 | ||||||||
\(415\) | −23.9000 | −1.17321 | ||||||||
\(416\) | 1.15175 | 0.0564694 | ||||||||
\(417\) | 5.15226 | 0.252307 | ||||||||
\(418\) | −6.95848 | −0.340350 | ||||||||
\(419\) | −25.8782 | −1.26423 | −0.632117 | − | 0.774873i | \(-0.717814\pi\) | ||||
−0.632117 | + | 0.774873i | \(0.717814\pi\) | |||||||
\(420\) | 3.39388 | 0.165604 | ||||||||
\(421\) | −7.93816 | −0.386882 | −0.193441 | − | 0.981112i | \(-0.561965\pi\) | ||||
−0.193441 | + | 0.981112i | \(0.561965\pi\) | |||||||
\(422\) | −4.83153 | −0.235195 | ||||||||
\(423\) | −10.7378 | −0.522091 | ||||||||
\(424\) | 5.31830 | 0.258280 | ||||||||
\(425\) | −61.1431 | −2.96587 | ||||||||
\(426\) | −12.0615 | −0.584383 | ||||||||
\(427\) | −1.77913 | −0.0860981 | ||||||||
\(428\) | −4.31733 | −0.208686 | ||||||||
\(429\) | −1.40778 | −0.0679684 | ||||||||
\(430\) | 10.1289 | 0.488458 | ||||||||
\(431\) | 28.7579 | 1.38522 | 0.692610 | − | 0.721312i | \(-0.256461\pi\) | ||||
0.692610 | + | 0.721312i | \(0.256461\pi\) | |||||||
\(432\) | 5.50765 | 0.264987 | ||||||||
\(433\) | 36.1236 | 1.73599 | 0.867995 | − | 0.496572i | \(-0.165408\pi\) | ||||
0.867995 | + | 0.496572i | \(0.165408\pi\) | |||||||
\(434\) | 5.48770 | 0.263418 | ||||||||
\(435\) | −20.6026 | −0.987821 | ||||||||
\(436\) | −5.07937 | −0.243258 | ||||||||
\(437\) | −34.6202 | −1.65611 | ||||||||
\(438\) | −10.7439 | −0.513361 | ||||||||
\(439\) | −15.7448 | −0.751458 | −0.375729 | − | 0.926730i | \(-0.622608\pi\) | ||||
−0.375729 | + | 0.926730i | \(0.622608\pi\) | |||||||
\(440\) | 4.12347 | 0.196579 | ||||||||
\(441\) | 9.85911 | 0.469482 | ||||||||
\(442\) | −5.86702 | −0.279065 | ||||||||
\(443\) | 1.08946 | 0.0517616 | 0.0258808 | − | 0.999665i | \(-0.491761\pi\) | ||||
0.0258808 | + | 0.999665i | \(0.491761\pi\) | |||||||
\(444\) | −1.87213 | −0.0888474 | ||||||||
\(445\) | −9.33080 | −0.442322 | ||||||||
\(446\) | 21.1240 | 1.00025 | ||||||||
\(447\) | 18.1576 | 0.858827 | ||||||||
\(448\) | −0.673376 | −0.0318140 | ||||||||
\(449\) | 38.4864 | 1.81629 | 0.908144 | − | 0.418659i | \(-0.137500\pi\) | ||||
0.908144 | + | 0.418659i | \(0.137500\pi\) | |||||||
\(450\) | 18.0765 | 0.852134 | ||||||||
\(451\) | 10.1937 | 0.480001 | ||||||||
\(452\) | −8.78693 | −0.413303 | ||||||||
\(453\) | 29.2380 | 1.37372 | ||||||||
\(454\) | 14.6606 | 0.688058 | ||||||||
\(455\) | 3.19801 | 0.149925 | ||||||||
\(456\) | −8.50530 | −0.398297 | ||||||||
\(457\) | 8.25625 | 0.386211 | 0.193105 | − | 0.981178i | \(-0.438144\pi\) | ||||
0.193105 | + | 0.981178i | \(0.438144\pi\) | |||||||
\(458\) | −2.79269 | −0.130494 | ||||||||
\(459\) | −28.0559 | −1.30954 | ||||||||
\(460\) | 20.5153 | 0.956531 | ||||||||
\(461\) | 16.1195 | 0.750762 | 0.375381 | − | 0.926871i | \(-0.377512\pi\) | ||||
0.375381 | + | 0.926871i | \(0.377512\pi\) | |||||||
\(462\) | 0.823063 | 0.0382924 | ||||||||
\(463\) | −11.3407 | −0.527046 | −0.263523 | − | 0.964653i | \(-0.584884\pi\) | ||||
−0.263523 | + | 0.964653i | \(0.584884\pi\) | |||||||
\(464\) | 4.08775 | 0.189769 | ||||||||
\(465\) | −41.0744 | −1.90478 | ||||||||
\(466\) | −7.45053 | −0.345139 | ||||||||
\(467\) | 10.0432 | 0.464742 | 0.232371 | − | 0.972627i | \(-0.425352\pi\) | ||||
0.232371 | + | 0.972627i | \(0.425352\pi\) | |||||||
\(468\) | 1.73454 | 0.0801791 | ||||||||
\(469\) | 4.33014 | 0.199947 | ||||||||
\(470\) | −29.4005 | −1.35614 | ||||||||
\(471\) | 4.74335 | 0.218562 | ||||||||
\(472\) | −10.9112 | −0.502228 | ||||||||
\(473\) | 2.45640 | 0.112945 | ||||||||
\(474\) | 12.6485 | 0.580966 | ||||||||
\(475\) | −83.5226 | −3.83228 | ||||||||
\(476\) | 3.43016 | 0.157221 | ||||||||
\(477\) | 8.00935 | 0.366723 | ||||||||
\(478\) | −2.13371 | −0.0975936 | ||||||||
\(479\) | 18.2396 | 0.833388 | 0.416694 | − | 0.909047i | \(-0.363189\pi\) | ||||
0.416694 | + | 0.909047i | \(0.363189\pi\) | |||||||
\(480\) | 5.04009 | 0.230048 | ||||||||
\(481\) | −1.76409 | −0.0804355 | ||||||||
\(482\) | 7.12792 | 0.324668 | ||||||||
\(483\) | 4.09495 | 0.186327 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −79.8224 | −3.62455 | ||||||||
\(486\) | 13.8168 | 0.626744 | ||||||||
\(487\) | 10.1976 | 0.462098 | 0.231049 | − | 0.972942i | \(-0.425784\pi\) | ||||
0.231049 | + | 0.972942i | \(0.425784\pi\) | |||||||
\(488\) | −2.64210 | −0.119602 | ||||||||
\(489\) | −19.2932 | −0.872470 | ||||||||
\(490\) | 26.9946 | 1.21949 | ||||||||
\(491\) | 3.23379 | 0.145939 | 0.0729694 | − | 0.997334i | \(-0.476752\pi\) | ||||
0.0729694 | + | 0.997334i | \(0.476752\pi\) | |||||||
\(492\) | 12.4597 | 0.561725 | ||||||||
\(493\) | −20.8229 | −0.937817 | ||||||||
\(494\) | −8.01445 | −0.360587 | ||||||||
\(495\) | 6.20994 | 0.279116 | ||||||||
\(496\) | 8.14953 | 0.365925 | ||||||||
\(497\) | 6.64484 | 0.298062 | ||||||||
\(498\) | −7.08453 | −0.317465 | ||||||||
\(499\) | −42.2098 | −1.88957 | −0.944785 | − | 0.327691i | \(-0.893729\pi\) | ||||
−0.944785 | + | 0.327691i | \(0.893729\pi\) | |||||||
\(500\) | 28.8767 | 1.29140 | ||||||||
\(501\) | −11.5992 | −0.518212 | ||||||||
\(502\) | −26.5391 | −1.18450 | ||||||||
\(503\) | 41.0664 | 1.83106 | 0.915530 | − | 0.402251i | \(-0.131772\pi\) | ||||
0.915530 | + | 0.402251i | \(0.131772\pi\) | |||||||
\(504\) | −1.01410 | −0.0451717 | ||||||||
\(505\) | −71.2798 | −3.17191 | ||||||||
\(506\) | 4.97526 | 0.221177 | ||||||||
\(507\) | 14.2684 | 0.633682 | ||||||||
\(508\) | 13.4600 | 0.597193 | ||||||||
\(509\) | −27.0798 | −1.20029 | −0.600146 | − | 0.799890i | \(-0.704891\pi\) | ||||
−0.600146 | + | 0.799890i | \(0.704891\pi\) | |||||||
\(510\) | −25.6741 | −1.13687 | ||||||||
\(511\) | 5.91891 | 0.261837 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −38.3249 | −1.69208 | ||||||||
\(514\) | 30.0195 | 1.32410 | ||||||||
\(515\) | 21.3794 | 0.942087 | ||||||||
\(516\) | 3.00244 | 0.132175 | ||||||||
\(517\) | −7.13004 | −0.313579 | ||||||||
\(518\) | 1.03138 | 0.0453162 | ||||||||
\(519\) | −4.34554 | −0.190748 | ||||||||
\(520\) | 4.74922 | 0.208267 | ||||||||
\(521\) | 22.0852 | 0.967570 | 0.483785 | − | 0.875187i | \(-0.339262\pi\) | ||||
0.483785 | + | 0.875187i | \(0.339262\pi\) | |||||||
\(522\) | 6.15614 | 0.269447 | ||||||||
\(523\) | 1.49629 | 0.0654283 | 0.0327141 | − | 0.999465i | \(-0.489585\pi\) | ||||
0.0327141 | + | 0.999465i | \(0.489585\pi\) | |||||||
\(524\) | 2.93923 | 0.128401 | ||||||||
\(525\) | 9.87923 | 0.431165 | ||||||||
\(526\) | −28.7291 | −1.25265 | ||||||||
\(527\) | −41.5136 | −1.80836 | ||||||||
\(528\) | 1.22229 | 0.0531935 | ||||||||
\(529\) | 1.75317 | 0.0762248 | ||||||||
\(530\) | 21.9299 | 0.952572 | ||||||||
\(531\) | −16.4322 | −0.713098 | ||||||||
\(532\) | 4.68567 | 0.203150 | ||||||||
\(533\) | 11.7406 | 0.508542 | ||||||||
\(534\) | −2.76587 | −0.119691 | ||||||||
\(535\) | −17.8024 | −0.769664 | ||||||||
\(536\) | 6.43050 | 0.277755 | ||||||||
\(537\) | 28.1442 | 1.21451 | ||||||||
\(538\) | 1.92518 | 0.0830003 | ||||||||
\(539\) | 6.54656 | 0.281981 | ||||||||
\(540\) | 22.7106 | 0.977310 | ||||||||
\(541\) | −20.4706 | −0.880100 | −0.440050 | − | 0.897973i | \(-0.645039\pi\) | ||||
−0.440050 | + | 0.897973i | \(0.645039\pi\) | |||||||
\(542\) | −7.33014 | −0.314857 | ||||||||
\(543\) | −2.04356 | −0.0876978 | ||||||||
\(544\) | 5.09398 | 0.218403 | ||||||||
\(545\) | −20.9446 | −0.897169 | ||||||||
\(546\) | 0.947967 | 0.0405692 | ||||||||
\(547\) | −3.28950 | −0.140649 | −0.0703243 | − | 0.997524i | \(-0.522403\pi\) | ||||
−0.0703243 | + | 0.997524i | \(0.522403\pi\) | |||||||
\(548\) | −6.88035 | −0.293914 | ||||||||
\(549\) | −3.97900 | −0.169820 | ||||||||
\(550\) | 12.0030 | 0.511810 | ||||||||
\(551\) | −28.4445 | −1.21178 | ||||||||
\(552\) | 6.08122 | 0.258834 | ||||||||
\(553\) | −6.96821 | −0.296319 | ||||||||
\(554\) | 6.73088 | 0.285968 | ||||||||
\(555\) | −7.71968 | −0.327682 | ||||||||
\(556\) | −4.21524 | −0.178766 | ||||||||
\(557\) | 3.37251 | 0.142898 | 0.0714489 | − | 0.997444i | \(-0.477238\pi\) | ||||
0.0714489 | + | 0.997444i | \(0.477238\pi\) | |||||||
\(558\) | 12.2732 | 0.519565 | ||||||||
\(559\) | 2.82917 | 0.119661 | ||||||||
\(560\) | −2.77664 | −0.117335 | ||||||||
\(561\) | −6.22634 | −0.262876 | ||||||||
\(562\) | −9.12854 | −0.385064 | ||||||||
\(563\) | 19.1962 | 0.809022 | 0.404511 | − | 0.914533i | \(-0.367442\pi\) | ||||
0.404511 | + | 0.914533i | \(0.367442\pi\) | |||||||
\(564\) | −8.71500 | −0.366968 | ||||||||
\(565\) | −36.2327 | −1.52432 | ||||||||
\(566\) | 7.30638 | 0.307110 | ||||||||
\(567\) | 1.49084 | 0.0626093 | ||||||||
\(568\) | 9.86795 | 0.414050 | ||||||||
\(569\) | −32.9852 | −1.38281 | −0.691406 | − | 0.722467i | \(-0.743008\pi\) | ||||
−0.691406 | + | 0.722467i | \(0.743008\pi\) | |||||||
\(570\) | −35.0714 | −1.46898 | ||||||||
\(571\) | 33.3904 | 1.39735 | 0.698673 | − | 0.715441i | \(-0.253774\pi\) | ||||
0.698673 | + | 0.715441i | \(0.253774\pi\) | |||||||
\(572\) | 1.15175 | 0.0481573 | ||||||||
\(573\) | 26.2298 | 1.09576 | ||||||||
\(574\) | −6.86417 | −0.286505 | ||||||||
\(575\) | 59.7180 | 2.49041 | ||||||||
\(576\) | −1.50600 | −0.0627499 | ||||||||
\(577\) | −13.9148 | −0.579280 | −0.289640 | − | 0.957136i | \(-0.593536\pi\) | ||||
−0.289640 | + | 0.957136i | \(0.593536\pi\) | |||||||
\(578\) | −8.94865 | −0.372215 | ||||||||
\(579\) | −15.2054 | −0.631916 | ||||||||
\(580\) | 16.8557 | 0.699895 | ||||||||
\(581\) | 3.90295 | 0.161922 | ||||||||
\(582\) | −23.6612 | −0.980790 | ||||||||
\(583\) | 5.31830 | 0.220262 | ||||||||
\(584\) | 8.78991 | 0.363729 | ||||||||
\(585\) | 7.15232 | 0.295712 | ||||||||
\(586\) | −1.70904 | −0.0705999 | ||||||||
\(587\) | −38.3362 | −1.58230 | −0.791152 | − | 0.611620i | \(-0.790518\pi\) | ||||
−0.791152 | + | 0.611620i | \(0.790518\pi\) | |||||||
\(588\) | 8.00183 | 0.329990 | ||||||||
\(589\) | −56.7083 | −2.33663 | ||||||||
\(590\) | −44.9920 | −1.85229 | ||||||||
\(591\) | 1.22229 | 0.0502784 | ||||||||
\(592\) | 1.53165 | 0.0629506 | ||||||||
\(593\) | 23.0526 | 0.946656 | 0.473328 | − | 0.880886i | \(-0.343053\pi\) | ||||
0.473328 | + | 0.880886i | \(0.343053\pi\) | |||||||
\(594\) | 5.50765 | 0.225982 | ||||||||
\(595\) | 14.1442 | 0.579855 | ||||||||
\(596\) | −14.8554 | −0.608500 | ||||||||
\(597\) | 13.7553 | 0.562966 | ||||||||
\(598\) | 5.73027 | 0.234328 | ||||||||
\(599\) | 22.4220 | 0.916138 | 0.458069 | − | 0.888917i | \(-0.348541\pi\) | ||||
0.458069 | + | 0.888917i | \(0.348541\pi\) | |||||||
\(600\) | 14.6712 | 0.598949 | ||||||||
\(601\) | 12.3455 | 0.503584 | 0.251792 | − | 0.967781i | \(-0.418980\pi\) | ||||
0.251792 | + | 0.967781i | \(0.418980\pi\) | |||||||
\(602\) | −1.65408 | −0.0674153 | ||||||||
\(603\) | 9.68431 | 0.394376 | ||||||||
\(604\) | −23.9206 | −0.973315 | ||||||||
\(605\) | 4.12347 | 0.167643 | ||||||||
\(606\) | −21.1290 | −0.858308 | ||||||||
\(607\) | 18.4267 | 0.747917 | 0.373958 | − | 0.927446i | \(-0.378000\pi\) | ||||
0.373958 | + | 0.927446i | \(0.378000\pi\) | |||||||
\(608\) | 6.95848 | 0.282203 | ||||||||
\(609\) | 3.36448 | 0.136335 | ||||||||
\(610\) | −10.8946 | −0.441111 | ||||||||
\(611\) | −8.21206 | −0.332224 | ||||||||
\(612\) | 7.67153 | 0.310103 | ||||||||
\(613\) | −0.931220 | −0.0376116 | −0.0188058 | − | 0.999823i | \(-0.505986\pi\) | ||||
−0.0188058 | + | 0.999823i | \(0.505986\pi\) | |||||||
\(614\) | 29.7495 | 1.20059 | ||||||||
\(615\) | 51.3770 | 2.07172 | ||||||||
\(616\) | −0.673376 | −0.0271311 | ||||||||
\(617\) | 12.2372 | 0.492650 | 0.246325 | − | 0.969187i | \(-0.420777\pi\) | ||||
0.246325 | + | 0.969187i | \(0.420777\pi\) | |||||||
\(618\) | 6.33735 | 0.254926 | ||||||||
\(619\) | −33.4532 | −1.34460 | −0.672298 | − | 0.740281i | \(-0.734693\pi\) | ||||
−0.672298 | + | 0.740281i | \(0.734693\pi\) | |||||||
\(620\) | 33.6043 | 1.34958 | ||||||||
\(621\) | 27.4020 | 1.09960 | ||||||||
\(622\) | 26.8202 | 1.07539 | ||||||||
\(623\) | 1.52375 | 0.0610477 | ||||||||
\(624\) | 1.40778 | 0.0563564 | ||||||||
\(625\) | 59.0570 | 2.36228 | ||||||||
\(626\) | −20.3744 | −0.814327 | ||||||||
\(627\) | −8.50530 | −0.339669 | ||||||||
\(628\) | −3.88069 | −0.154856 | ||||||||
\(629\) | −7.80222 | −0.311095 | ||||||||
\(630\) | −4.18162 | −0.166600 | ||||||||
\(631\) | −31.3216 | −1.24689 | −0.623447 | − | 0.781866i | \(-0.714268\pi\) | ||||
−0.623447 | + | 0.781866i | \(0.714268\pi\) | |||||||
\(632\) | −10.3482 | −0.411628 | ||||||||
\(633\) | −5.90555 | −0.234725 | ||||||||
\(634\) | −8.97894 | −0.356599 | ||||||||
\(635\) | 55.5020 | 2.20253 | ||||||||
\(636\) | 6.50053 | 0.257763 | ||||||||
\(637\) | 7.54003 | 0.298747 | ||||||||
\(638\) | 4.08775 | 0.161836 | ||||||||
\(639\) | 14.8611 | 0.587896 | ||||||||
\(640\) | −4.12347 | −0.162994 | ||||||||
\(641\) | −3.80763 | −0.150392 | −0.0751962 | − | 0.997169i | \(-0.523958\pi\) | ||||
−0.0751962 | + | 0.997169i | \(0.523958\pi\) | |||||||
\(642\) | −5.27705 | −0.208268 | ||||||||
\(643\) | 20.8352 | 0.821661 | 0.410831 | − | 0.911712i | \(-0.365239\pi\) | ||||
0.410831 | + | 0.911712i | \(0.365239\pi\) | |||||||
\(644\) | −3.35022 | −0.132017 | ||||||||
\(645\) | 12.3805 | 0.487481 | ||||||||
\(646\) | −35.4463 | −1.39462 | ||||||||
\(647\) | 18.4623 | 0.725828 | 0.362914 | − | 0.931823i | \(-0.381782\pi\) | ||||
0.362914 | + | 0.931823i | \(0.381782\pi\) | |||||||
\(648\) | 2.21398 | 0.0869732 | ||||||||
\(649\) | −10.9112 | −0.428302 | ||||||||
\(650\) | 13.8245 | 0.542242 | ||||||||
\(651\) | 6.70758 | 0.262891 | ||||||||
\(652\) | 15.7845 | 0.618167 | ||||||||
\(653\) | 42.7436 | 1.67268 | 0.836342 | − | 0.548208i | \(-0.184690\pi\) | ||||
0.836342 | + | 0.548208i | \(0.184690\pi\) | |||||||
\(654\) | −6.20848 | −0.242771 | ||||||||
\(655\) | 12.1198 | 0.473561 | ||||||||
\(656\) | −10.1937 | −0.397996 | ||||||||
\(657\) | 13.2376 | 0.516447 | ||||||||
\(658\) | 4.80120 | 0.187170 | ||||||||
\(659\) | 10.3164 | 0.401871 | 0.200935 | − | 0.979605i | \(-0.435602\pi\) | ||||
0.200935 | + | 0.979605i | \(0.435602\pi\) | |||||||
\(660\) | 5.04009 | 0.196185 | ||||||||
\(661\) | −36.2688 | −1.41069 | −0.705346 | − | 0.708863i | \(-0.749208\pi\) | ||||
−0.705346 | + | 0.708863i | \(0.749208\pi\) | |||||||
\(662\) | −3.66781 | −0.142553 | ||||||||
\(663\) | −7.17122 | −0.278507 | ||||||||
\(664\) | 5.79609 | 0.224932 | ||||||||
\(665\) | 19.3212 | 0.749245 | ||||||||
\(666\) | 2.30667 | 0.0893816 | ||||||||
\(667\) | 20.3376 | 0.787475 | ||||||||
\(668\) | 9.48967 | 0.367166 | ||||||||
\(669\) | 25.8197 | 0.998246 | ||||||||
\(670\) | 26.5160 | 1.02440 | ||||||||
\(671\) | −2.64210 | −0.101997 | ||||||||
\(672\) | −0.823063 | −0.0317504 | ||||||||
\(673\) | 12.1381 | 0.467888 | 0.233944 | − | 0.972250i | \(-0.424837\pi\) | ||||
0.233944 | + | 0.972250i | \(0.424837\pi\) | |||||||
\(674\) | −27.7733 | −1.06979 | ||||||||
\(675\) | 66.1084 | 2.54451 | ||||||||
\(676\) | −11.6735 | −0.448979 | ||||||||
\(677\) | 32.0543 | 1.23195 | 0.615973 | − | 0.787767i | \(-0.288763\pi\) | ||||
0.615973 | + | 0.787767i | \(0.288763\pi\) | |||||||
\(678\) | −10.7402 | −0.412475 | ||||||||
\(679\) | 13.0353 | 0.500247 | ||||||||
\(680\) | 21.0049 | 0.805500 | ||||||||
\(681\) | 17.9196 | 0.686681 | ||||||||
\(682\) | 8.14953 | 0.312062 | ||||||||
\(683\) | 41.5937 | 1.59154 | 0.795770 | − | 0.605599i | \(-0.207066\pi\) | ||||
0.795770 | + | 0.605599i | \(0.207066\pi\) | |||||||
\(684\) | 10.4794 | 0.400692 | ||||||||
\(685\) | −28.3709 | −1.08400 | ||||||||
\(686\) | −9.12193 | −0.348277 | ||||||||
\(687\) | −3.41348 | −0.130233 | ||||||||
\(688\) | −2.45640 | −0.0936494 | ||||||||
\(689\) | 6.12538 | 0.233358 | ||||||||
\(690\) | 25.0757 | 0.954617 | ||||||||
\(691\) | 34.3074 | 1.30511 | 0.652557 | − | 0.757740i | \(-0.273696\pi\) | ||||
0.652557 | + | 0.757740i | \(0.273696\pi\) | |||||||
\(692\) | 3.55523 | 0.135150 | ||||||||
\(693\) | −1.01410 | −0.0385226 | ||||||||
\(694\) | 4.48980 | 0.170430 | ||||||||
\(695\) | −17.3814 | −0.659315 | ||||||||
\(696\) | 4.99643 | 0.189389 | ||||||||
\(697\) | 51.9264 | 1.96685 | ||||||||
\(698\) | −9.48557 | −0.359034 | ||||||||
\(699\) | −9.10674 | −0.344449 | ||||||||
\(700\) | −8.08253 | −0.305491 | ||||||||
\(701\) | −44.9691 | −1.69846 | −0.849229 | − | 0.528025i | \(-0.822933\pi\) | ||||
−0.849229 | + | 0.528025i | \(0.822933\pi\) | |||||||
\(702\) | 6.34346 | 0.239419 | ||||||||
\(703\) | −10.6580 | −0.401973 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −35.9361 | −1.35343 | ||||||||
\(706\) | 35.7101 | 1.34397 | ||||||||
\(707\) | 11.6402 | 0.437776 | ||||||||
\(708\) | −13.3367 | −0.501223 | ||||||||
\(709\) | −39.8948 | −1.49828 | −0.749141 | − | 0.662411i | \(-0.769533\pi\) | ||||
−0.749141 | + | 0.662411i | \(0.769533\pi\) | |||||||
\(710\) | 40.6902 | 1.52708 | ||||||||
\(711\) | −15.5843 | −0.584458 | ||||||||
\(712\) | 2.26285 | 0.0848039 | ||||||||
\(713\) | 40.5460 | 1.51846 | ||||||||
\(714\) | 4.19267 | 0.156907 | ||||||||
\(715\) | 4.74922 | 0.177611 | ||||||||
\(716\) | −23.0257 | −0.860511 | ||||||||
\(717\) | −2.60802 | −0.0973983 | ||||||||
\(718\) | −23.3915 | −0.872964 | ||||||||
\(719\) | 3.20406 | 0.119491 | 0.0597456 | − | 0.998214i | \(-0.480971\pi\) | ||||
0.0597456 | + | 0.998214i | \(0.480971\pi\) | |||||||
\(720\) | −6.20994 | −0.231431 | ||||||||
\(721\) | −3.49132 | −0.130024 | ||||||||
\(722\) | −29.4204 | −1.09491 | ||||||||
\(723\) | 8.71241 | 0.324018 | ||||||||
\(724\) | 1.67191 | 0.0621360 | ||||||||
\(725\) | 49.0653 | 1.82224 | ||||||||
\(726\) | 1.22229 | 0.0453636 | ||||||||
\(727\) | 0.822265 | 0.0304961 | 0.0152481 | − | 0.999884i | \(-0.495146\pi\) | ||||
0.0152481 | + | 0.999884i | \(0.495146\pi\) | |||||||
\(728\) | −0.775564 | −0.0287443 | ||||||||
\(729\) | 23.5302 | 0.871487 | ||||||||
\(730\) | 36.2449 | 1.34148 | ||||||||
\(731\) | 12.5129 | 0.462805 | ||||||||
\(732\) | −3.22943 | −0.119363 | ||||||||
\(733\) | −15.2451 | −0.563092 | −0.281546 | − | 0.959548i | \(-0.590847\pi\) | ||||
−0.281546 | + | 0.959548i | \(0.590847\pi\) | |||||||
\(734\) | 37.1698 | 1.37196 | ||||||||
\(735\) | 32.9953 | 1.21705 | ||||||||
\(736\) | −4.97526 | −0.183390 | ||||||||
\(737\) | 6.43050 | 0.236870 | ||||||||
\(738\) | −15.3516 | −0.565102 | ||||||||
\(739\) | −15.3207 | −0.563581 | −0.281790 | − | 0.959476i | \(-0.590928\pi\) | ||||
−0.281790 | + | 0.959476i | \(0.590928\pi\) | |||||||
\(740\) | 6.31573 | 0.232171 | ||||||||
\(741\) | −9.79602 | −0.359866 | ||||||||
\(742\) | −3.58122 | −0.131471 | ||||||||
\(743\) | −30.1120 | −1.10470 | −0.552350 | − | 0.833612i | \(-0.686269\pi\) | ||||
−0.552350 | + | 0.833612i | \(0.686269\pi\) | |||||||
\(744\) | 9.96112 | 0.365192 | ||||||||
\(745\) | −61.2557 | −2.24423 | ||||||||
\(746\) | −21.2940 | −0.779627 | ||||||||
\(747\) | 8.72890 | 0.319374 | ||||||||
\(748\) | 5.09398 | 0.186254 | ||||||||
\(749\) | 2.90719 | 0.106226 | ||||||||
\(750\) | 35.2958 | 1.28882 | ||||||||
\(751\) | −40.4198 | −1.47494 | −0.737470 | − | 0.675380i | \(-0.763980\pi\) | ||||
−0.737470 | + | 0.675380i | \(0.763980\pi\) | |||||||
\(752\) | 7.13004 | 0.260006 | ||||||||
\(753\) | −32.4385 | −1.18213 | ||||||||
\(754\) | 4.70808 | 0.171458 | ||||||||
\(755\) | −98.6358 | −3.58973 | ||||||||
\(756\) | −3.70872 | −0.134885 | ||||||||
\(757\) | 10.1324 | 0.368269 | 0.184134 | − | 0.982901i | \(-0.441052\pi\) | ||||
0.184134 | + | 0.982901i | \(0.441052\pi\) | |||||||
\(758\) | 21.1655 | 0.768766 | ||||||||
\(759\) | 6.08122 | 0.220734 | ||||||||
\(760\) | 28.6931 | 1.04081 | ||||||||
\(761\) | −17.5957 | −0.637844 | −0.318922 | − | 0.947781i | \(-0.603321\pi\) | ||||
−0.318922 | + | 0.947781i | \(0.603321\pi\) | |||||||
\(762\) | 16.4521 | 0.595997 | ||||||||
\(763\) | 3.42032 | 0.123824 | ||||||||
\(764\) | −21.4595 | −0.776376 | ||||||||
\(765\) | 31.6333 | 1.14370 | ||||||||
\(766\) | 24.0635 | 0.869448 | ||||||||
\(767\) | −12.5670 | −0.453768 | ||||||||
\(768\) | −1.22229 | −0.0441057 | ||||||||
\(769\) | −41.0784 | −1.48133 | −0.740663 | − | 0.671877i | \(-0.765488\pi\) | ||||
−0.740663 | + | 0.671877i | \(0.765488\pi\) | |||||||
\(770\) | −2.77664 | −0.100063 | ||||||||
\(771\) | 36.6927 | 1.32145 | ||||||||
\(772\) | 12.4401 | 0.447728 | ||||||||
\(773\) | 39.1151 | 1.40687 | 0.703437 | − | 0.710758i | \(-0.251648\pi\) | ||||
0.703437 | + | 0.710758i | \(0.251648\pi\) | |||||||
\(774\) | −3.69933 | −0.132970 | ||||||||
\(775\) | 97.8188 | 3.51376 | ||||||||
\(776\) | 19.3581 | 0.694914 | ||||||||
\(777\) | 1.26065 | 0.0452255 | ||||||||
\(778\) | −6.92942 | −0.248432 | ||||||||
\(779\) | 70.9324 | 2.54142 | ||||||||
\(780\) | 5.80495 | 0.207850 | ||||||||
\(781\) | 9.86795 | 0.353103 | ||||||||
\(782\) | 25.3439 | 0.906295 | ||||||||
\(783\) | 22.5139 | 0.804582 | ||||||||
\(784\) | −6.54656 | −0.233806 | ||||||||
\(785\) | −16.0019 | −0.571133 | ||||||||
\(786\) | 3.59260 | 0.128144 | ||||||||
\(787\) | 24.1034 | 0.859195 | 0.429597 | − | 0.903021i | \(-0.358656\pi\) | ||||
0.429597 | + | 0.903021i | \(0.358656\pi\) | |||||||
\(788\) | −1.00000 | −0.0356235 | ||||||||
\(789\) | −35.1154 | −1.25014 | ||||||||
\(790\) | −42.6704 | −1.51814 | ||||||||
\(791\) | 5.91691 | 0.210381 | ||||||||
\(792\) | −1.50600 | −0.0535133 | ||||||||
\(793\) | −3.04305 | −0.108062 | ||||||||
\(794\) | 2.47881 | 0.0879696 | ||||||||
\(795\) | 26.8047 | 0.950666 | ||||||||
\(796\) | −11.2537 | −0.398875 | ||||||||
\(797\) | 28.3313 | 1.00355 | 0.501774 | − | 0.864999i | \(-0.332681\pi\) | ||||
0.501774 | + | 0.864999i | \(0.332681\pi\) | |||||||
\(798\) | 5.72727 | 0.202743 | ||||||||
\(799\) | −36.3203 | −1.28492 | ||||||||
\(800\) | −12.0030 | −0.424370 | ||||||||
\(801\) | 3.40785 | 0.120410 | ||||||||
\(802\) | 14.5549 | 0.513950 | ||||||||
\(803\) | 8.78991 | 0.310189 | ||||||||
\(804\) | 7.85996 | 0.277199 | ||||||||
\(805\) | −13.8145 | −0.486898 | ||||||||
\(806\) | 9.38626 | 0.330617 | ||||||||
\(807\) | 2.35313 | 0.0828342 | ||||||||
\(808\) | 17.2864 | 0.608132 | ||||||||
\(809\) | 17.6178 | 0.619409 | 0.309704 | − | 0.950833i | \(-0.399770\pi\) | ||||
0.309704 | + | 0.950833i | \(0.399770\pi\) | |||||||
\(810\) | 9.12927 | 0.320770 | ||||||||
\(811\) | −30.0729 | −1.05600 | −0.528001 | − | 0.849244i | \(-0.677058\pi\) | ||||
−0.528001 | + | 0.849244i | \(0.677058\pi\) | |||||||
\(812\) | −2.75259 | −0.0965971 | ||||||||
\(813\) | −8.95959 | −0.314227 | ||||||||
\(814\) | 1.53165 | 0.0536845 | ||||||||
\(815\) | 65.0867 | 2.27989 | ||||||||
\(816\) | 6.22634 | 0.217966 | ||||||||
\(817\) | 17.0928 | 0.598001 | ||||||||
\(818\) | 8.66702 | 0.303035 | ||||||||
\(819\) | −1.16800 | −0.0408131 | ||||||||
\(820\) | −42.0333 | −1.46787 | ||||||||
\(821\) | −55.6644 | −1.94270 | −0.971350 | − | 0.237652i | \(-0.923622\pi\) | ||||
−0.971350 | + | 0.237652i | \(0.923622\pi\) | |||||||
\(822\) | −8.40982 | −0.293326 | ||||||||
\(823\) | 0.710759 | 0.0247755 | 0.0123877 | − | 0.999923i | \(-0.496057\pi\) | ||||
0.0123877 | + | 0.999923i | \(0.496057\pi\) | |||||||
\(824\) | −5.18480 | −0.180621 | ||||||||
\(825\) | 14.6712 | 0.510785 | ||||||||
\(826\) | 7.34733 | 0.255646 | ||||||||
\(827\) | 30.6740 | 1.06664 | 0.533320 | − | 0.845913i | \(-0.320944\pi\) | ||||
0.533320 | + | 0.845913i | \(0.320944\pi\) | |||||||
\(828\) | −7.49272 | −0.260390 | ||||||||
\(829\) | 5.14186 | 0.178584 | 0.0892921 | − | 0.996005i | \(-0.471540\pi\) | ||||
0.0892921 | + | 0.996005i | \(0.471540\pi\) | |||||||
\(830\) | 23.9000 | 0.829581 | ||||||||
\(831\) | 8.22712 | 0.285395 | ||||||||
\(832\) | −1.15175 | −0.0399299 | ||||||||
\(833\) | 33.3481 | 1.15544 | ||||||||
\(834\) | −5.15226 | −0.178408 | ||||||||
\(835\) | 39.1304 | 1.35416 | ||||||||
\(836\) | 6.95848 | 0.240664 | ||||||||
\(837\) | 44.8848 | 1.55145 | ||||||||
\(838\) | 25.8782 | 0.893948 | ||||||||
\(839\) | 8.81758 | 0.304417 | 0.152208 | − | 0.988348i | \(-0.451362\pi\) | ||||
0.152208 | + | 0.988348i | \(0.451362\pi\) | |||||||
\(840\) | −3.39388 | −0.117100 | ||||||||
\(841\) | −12.2903 | −0.423803 | ||||||||
\(842\) | 7.93816 | 0.273567 | ||||||||
\(843\) | −11.1578 | −0.384294 | ||||||||
\(844\) | 4.83153 | 0.166308 | ||||||||
\(845\) | −48.1352 | −1.65590 | ||||||||
\(846\) | 10.7378 | 0.369174 | ||||||||
\(847\) | −0.673376 | −0.0231375 | ||||||||
\(848\) | −5.31830 | −0.182631 | ||||||||
\(849\) | 8.93055 | 0.306496 | ||||||||
\(850\) | 61.1431 | 2.09719 | ||||||||
\(851\) | 7.62037 | 0.261223 | ||||||||
\(852\) | 12.0615 | 0.413221 | ||||||||
\(853\) | −40.1406 | −1.37439 | −0.687194 | − | 0.726474i | \(-0.741158\pi\) | ||||
−0.687194 | + | 0.726474i | \(0.741158\pi\) | |||||||
\(854\) | 1.77913 | 0.0608805 | ||||||||
\(855\) | 43.2117 | 1.47781 | ||||||||
\(856\) | 4.31733 | 0.147563 | ||||||||
\(857\) | 10.0182 | 0.342216 | 0.171108 | − | 0.985252i | \(-0.445265\pi\) | ||||
0.171108 | + | 0.985252i | \(0.445265\pi\) | |||||||
\(858\) | 1.40778 | 0.0480609 | ||||||||
\(859\) | 57.3877 | 1.95804 | 0.979022 | − | 0.203756i | \(-0.0653150\pi\) | ||||
0.979022 | + | 0.203756i | \(0.0653150\pi\) | |||||||
\(860\) | −10.1289 | −0.345392 | ||||||||
\(861\) | −8.39003 | −0.285932 | ||||||||
\(862\) | −28.7579 | −0.979499 | ||||||||
\(863\) | 30.7325 | 1.04615 | 0.523074 | − | 0.852287i | \(-0.324785\pi\) | ||||
0.523074 | + | 0.852287i | \(0.324785\pi\) | |||||||
\(864\) | −5.50765 | −0.187374 | ||||||||
\(865\) | 14.6599 | 0.498451 | ||||||||
\(866\) | −36.1236 | −1.22753 | ||||||||
\(867\) | −10.9379 | −0.371470 | ||||||||
\(868\) | −5.48770 | −0.186265 | ||||||||
\(869\) | −10.3482 | −0.351038 | ||||||||
\(870\) | 20.6026 | 0.698495 | ||||||||
\(871\) | 7.40635 | 0.250955 | ||||||||
\(872\) | 5.07937 | 0.172009 | ||||||||
\(873\) | 29.1532 | 0.986687 | ||||||||
\(874\) | 34.6202 | 1.17105 | ||||||||
\(875\) | −19.4448 | −0.657356 | ||||||||
\(876\) | 10.7439 | 0.363001 | ||||||||
\(877\) | −12.0207 | −0.405909 | −0.202955 | − | 0.979188i | \(-0.565054\pi\) | ||||
−0.202955 | + | 0.979188i | \(0.565054\pi\) | |||||||
\(878\) | 15.7448 | 0.531361 | ||||||||
\(879\) | −2.08895 | −0.0704586 | ||||||||
\(880\) | −4.12347 | −0.139002 | ||||||||
\(881\) | −19.2054 | −0.647047 | −0.323524 | − | 0.946220i | \(-0.604868\pi\) | ||||
−0.323524 | + | 0.946220i | \(0.604868\pi\) | |||||||
\(882\) | −9.85911 | −0.331974 | ||||||||
\(883\) | 30.5119 | 1.02681 | 0.513403 | − | 0.858147i | \(-0.328385\pi\) | ||||
0.513403 | + | 0.858147i | \(0.328385\pi\) | |||||||
\(884\) | 5.86702 | 0.197329 | ||||||||
\(885\) | −54.9934 | −1.84858 | ||||||||
\(886\) | −1.08946 | −0.0366010 | ||||||||
\(887\) | 36.4429 | 1.22363 | 0.611817 | − | 0.790999i | \(-0.290439\pi\) | ||||
0.611817 | + | 0.790999i | \(0.290439\pi\) | |||||||
\(888\) | 1.87213 | 0.0628246 | ||||||||
\(889\) | −9.06366 | −0.303986 | ||||||||
\(890\) | 9.33080 | 0.312769 | ||||||||
\(891\) | 2.21398 | 0.0741710 | ||||||||
\(892\) | −21.1240 | −0.707282 | ||||||||
\(893\) | −49.6142 | −1.66028 | ||||||||
\(894\) | −18.1576 | −0.607282 | ||||||||
\(895\) | −94.9458 | −3.17369 | ||||||||
\(896\) | 0.673376 | 0.0224959 | ||||||||
\(897\) | 7.00408 | 0.233859 | ||||||||
\(898\) | −38.4864 | −1.28431 | ||||||||
\(899\) | 33.3133 | 1.11106 | ||||||||
\(900\) | −18.0765 | −0.602550 | ||||||||
\(901\) | 27.0913 | 0.902543 | ||||||||
\(902\) | −10.1937 | −0.339412 | ||||||||
\(903\) | −2.02177 | −0.0672804 | ||||||||
\(904\) | 8.78693 | 0.292249 | ||||||||
\(905\) | 6.89407 | 0.229167 | ||||||||
\(906\) | −29.2380 | −0.971367 | ||||||||
\(907\) | −33.6974 | −1.11890 | −0.559451 | − | 0.828863i | \(-0.688988\pi\) | ||||
−0.559451 | + | 0.828863i | \(0.688988\pi\) | |||||||
\(908\) | −14.6606 | −0.486530 | ||||||||
\(909\) | 26.0332 | 0.863468 | ||||||||
\(910\) | −3.19801 | −0.106013 | ||||||||
\(911\) | −19.0867 | −0.632370 | −0.316185 | − | 0.948698i | \(-0.602402\pi\) | ||||
−0.316185 | + | 0.948698i | \(0.602402\pi\) | |||||||
\(912\) | 8.50530 | 0.281639 | ||||||||
\(913\) | 5.79609 | 0.191823 | ||||||||
\(914\) | −8.25625 | −0.273092 | ||||||||
\(915\) | −13.3164 | −0.440228 | ||||||||
\(916\) | 2.79269 | 0.0922730 | ||||||||
\(917\) | −1.97921 | −0.0653592 | ||||||||
\(918\) | 28.0559 | 0.925982 | ||||||||
\(919\) | −30.3199 | −1.00016 | −0.500080 | − | 0.865979i | \(-0.666696\pi\) | ||||
−0.500080 | + | 0.865979i | \(0.666696\pi\) | |||||||
\(920\) | −20.5153 | −0.676370 | ||||||||
\(921\) | 36.3626 | 1.19819 | ||||||||
\(922\) | −16.1195 | −0.530869 | ||||||||
\(923\) | 11.3655 | 0.374098 | ||||||||
\(924\) | −0.823063 | −0.0270768 | ||||||||
\(925\) | 18.3844 | 0.604477 | ||||||||
\(926\) | 11.3407 | 0.372678 | ||||||||
\(927\) | −7.80830 | −0.256458 | ||||||||
\(928\) | −4.08775 | −0.134187 | ||||||||
\(929\) | 14.3780 | 0.471727 | 0.235863 | − | 0.971786i | \(-0.424208\pi\) | ||||
0.235863 | + | 0.971786i | \(0.424208\pi\) | |||||||
\(930\) | 41.0744 | 1.34688 | ||||||||
\(931\) | 45.5541 | 1.49298 | ||||||||
\(932\) | 7.45053 | 0.244050 | ||||||||
\(933\) | 32.7822 | 1.07324 | ||||||||
\(934\) | −10.0432 | −0.328622 | ||||||||
\(935\) | 21.0049 | 0.686933 | ||||||||
\(936\) | −1.73454 | −0.0566952 | ||||||||
\(937\) | −27.2551 | −0.890387 | −0.445193 | − | 0.895435i | \(-0.646865\pi\) | ||||
−0.445193 | + | 0.895435i | \(0.646865\pi\) | |||||||
\(938\) | −4.33014 | −0.141384 | ||||||||
\(939\) | −24.9036 | −0.812697 | ||||||||
\(940\) | 29.4005 | 0.958939 | ||||||||
\(941\) | 38.9972 | 1.27127 | 0.635636 | − | 0.771989i | \(-0.280738\pi\) | ||||
0.635636 | + | 0.771989i | \(0.280738\pi\) | |||||||
\(942\) | −4.74335 | −0.154547 | ||||||||
\(943\) | −50.7161 | −1.65154 | ||||||||
\(944\) | 10.9112 | 0.355129 | ||||||||
\(945\) | −15.2928 | −0.497475 | ||||||||
\(946\) | −2.45640 | −0.0798645 | ||||||||
\(947\) | −10.4985 | −0.341157 | −0.170578 | − | 0.985344i | \(-0.554564\pi\) | ||||
−0.170578 | + | 0.985344i | \(0.554564\pi\) | |||||||
\(948\) | −12.6485 | −0.410805 | ||||||||
\(949\) | 10.1238 | 0.328633 | ||||||||
\(950\) | 83.5226 | 2.70983 | ||||||||
\(951\) | −10.9749 | −0.355886 | ||||||||
\(952\) | −3.43016 | −0.111172 | ||||||||
\(953\) | −59.2223 | −1.91840 | −0.959199 | − | 0.282731i | \(-0.908760\pi\) | ||||
−0.959199 | + | 0.282731i | \(0.908760\pi\) | |||||||
\(954\) | −8.00935 | −0.259312 | ||||||||
\(955\) | −88.4874 | −2.86339 | ||||||||
\(956\) | 2.13371 | 0.0690091 | ||||||||
\(957\) | 4.99643 | 0.161512 | ||||||||
\(958\) | −18.2396 | −0.589294 | ||||||||
\(959\) | 4.63307 | 0.149609 | ||||||||
\(960\) | −5.04009 | −0.162668 | ||||||||
\(961\) | 35.4149 | 1.14242 | ||||||||
\(962\) | 1.76409 | 0.0568765 | ||||||||
\(963\) | 6.50189 | 0.209520 | ||||||||
\(964\) | −7.12792 | −0.229575 | ||||||||
\(965\) | 51.2963 | 1.65128 | ||||||||
\(966\) | −4.09495 | −0.131753 | ||||||||
\(967\) | 44.4173 | 1.42836 | 0.714182 | − | 0.699960i | \(-0.246799\pi\) | ||||
0.714182 | + | 0.699960i | \(0.246799\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −43.3259 | −1.39183 | ||||||||
\(970\) | 79.8224 | 2.56294 | ||||||||
\(971\) | 7.97497 | 0.255929 | 0.127965 | − | 0.991779i | \(-0.459156\pi\) | ||||
0.127965 | + | 0.991779i | \(0.459156\pi\) | |||||||
\(972\) | −13.8168 | −0.443175 | ||||||||
\(973\) | 2.83844 | 0.0909963 | ||||||||
\(974\) | −10.1976 | −0.326752 | ||||||||
\(975\) | 16.8976 | 0.541157 | ||||||||
\(976\) | 2.64210 | 0.0845717 | ||||||||
\(977\) | −22.2031 | −0.710341 | −0.355171 | − | 0.934802i | \(-0.615577\pi\) | ||||
−0.355171 | + | 0.934802i | \(0.615577\pi\) | |||||||
\(978\) | 19.2932 | 0.616930 | ||||||||
\(979\) | 2.26285 | 0.0723210 | ||||||||
\(980\) | −26.9946 | −0.862310 | ||||||||
\(981\) | 7.64952 | 0.244230 | ||||||||
\(982\) | −3.23379 | −0.103194 | ||||||||
\(983\) | −3.91753 | −0.124950 | −0.0624749 | − | 0.998047i | \(-0.519899\pi\) | ||||
−0.0624749 | + | 0.998047i | \(0.519899\pi\) | |||||||
\(984\) | −12.4597 | −0.397199 | ||||||||
\(985\) | −4.12347 | −0.131385 | ||||||||
\(986\) | 20.8229 | 0.663137 | ||||||||
\(987\) | 5.86847 | 0.186796 | ||||||||
\(988\) | 8.01445 | 0.254974 | ||||||||
\(989\) | −12.2212 | −0.388612 | ||||||||
\(990\) | −6.20994 | −0.197365 | ||||||||
\(991\) | −5.75332 | −0.182760 | −0.0913801 | − | 0.995816i | \(-0.529128\pi\) | ||||
−0.0913801 | + | 0.995816i | \(0.529128\pi\) | |||||||
\(992\) | −8.14953 | −0.258748 | ||||||||
\(993\) | −4.48314 | −0.142268 | ||||||||
\(994\) | −6.64484 | −0.210761 | ||||||||
\(995\) | −46.4041 | −1.47111 | ||||||||
\(996\) | 7.08453 | 0.224482 | ||||||||
\(997\) | −26.1214 | −0.827272 | −0.413636 | − | 0.910442i | \(-0.635741\pi\) | ||||
−0.413636 | + | 0.910442i | \(0.635741\pi\) | |||||||
\(998\) | 42.2098 | 1.33613 | ||||||||
\(999\) | 8.43582 | 0.266898 |
(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 | 4334.2.a.c.1.6 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.c.1.6 | ✓ | 17 | 1.1 | even | 1 | trivial |