Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7600,2,Mod(1,7600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7600.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: | \(60.6863055362\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.993.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 950) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.77339\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7600.1 |
$q$-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 | 0 | ||||||||
\(3\) | −1.77339 | −1.02387 | −0.511933 | − | 0.859025i | \(-0.671070\pi\) | ||||
−0.511933 | + | 0.859025i | \(0.671070\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.69168 | −1.01736 | −0.508679 | − | 0.860956i | \(-0.669866\pi\) | ||||
−0.508679 | + | 0.860956i | \(0.669866\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.144903 | 0.0483010 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.54677 | −1.67242 | −0.836208 | − | 0.548413i | \(-0.815232\pi\) | ||||
−0.836208 | + | 0.548413i | \(0.815232\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.91829 | 0.809388 | 0.404694 | − | 0.914452i | \(-0.367378\pi\) | ||||
0.404694 | + | 0.914452i | \(0.367378\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.91829 | −1.19286 | −0.596430 | − | 0.802665i | \(-0.703415\pi\) | ||||
−0.596430 | + | 0.802665i | \(0.703415\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.77339 | 1.04164 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.60997 | 0.752730 | 0.376365 | − | 0.926471i | \(-0.377174\pi\) | ||||
0.376365 | + | 0.926471i | \(0.377174\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.06319 | 0.974412 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.08171 | 0.200868 | 0.100434 | − | 0.994944i | \(-0.467977\pi\) | ||||
0.100434 | + | 0.994944i | \(0.467977\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.54677 | −1.35544 | −0.677720 | − | 0.735320i | \(-0.737032\pi\) | ||||
−0.677720 | + | 0.735320i | \(0.737032\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.83658 | 1.71233 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.54677 | −0.747485 | −0.373743 | − | 0.927532i | \(-0.621926\pi\) | ||||
−0.373743 | + | 0.927532i | \(0.621926\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.17526 | −0.828705 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.54677 | −1.45587 | −0.727935 | − | 0.685646i | \(-0.759520\pi\) | ||||
−0.727935 | + | 0.685646i | \(0.759520\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.836581 | −0.122028 | −0.0610139 | − | 0.998137i | \(-0.519433\pi\) | ||||
−0.0610139 | + | 0.998137i | \(0.519433\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.245129 | 0.0350184 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.72203 | 1.22133 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.78523 | −1.34410 | −0.672052 | − | 0.740504i | \(-0.734587\pi\) | ||||
−0.672052 | + | 0.740504i | \(0.734587\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.77339 | 0.234891 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.9933 | −1.69159 | −0.845793 | − | 0.533511i | \(-0.820872\pi\) | ||||
−0.845793 | + | 0.533511i | \(0.820872\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.38336 | −0.945342 | −0.472671 | − | 0.881239i | \(-0.656710\pi\) | ||||
−0.472671 | + | 0.881239i | \(0.656710\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.390032 | −0.0491394 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.85510 | 0.348806 | 0.174403 | − | 0.984674i | \(-0.444201\pi\) | ||||
0.174403 | + | 0.984674i | \(0.444201\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.40187 | −0.770695 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.4769 | −1.71809 | −0.859046 | − | 0.511898i | \(-0.828943\pi\) | ||||
−0.859046 | + | 0.511898i | \(0.828943\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.15674 | −0.603551 | −0.301776 | − | 0.953379i | \(-0.597579\pi\) | ||||
−0.301776 | + | 0.953379i | \(0.597579\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.9301 | 1.70145 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.09355 | 0.348052 | 0.174026 | − | 0.984741i | \(-0.444322\pi\) | ||||
0.174026 | + | 0.984741i | \(0.444322\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.41371 | −1.04597 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.71019 | 0.187718 | 0.0938591 | − | 0.995585i | \(-0.470080\pi\) | ||||
0.0938591 | + | 0.995585i | \(0.470080\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.91829 | −0.205662 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.09355 | −0.539915 | −0.269958 | − | 0.962872i | \(-0.587010\pi\) | ||||
−0.269958 | + | 0.962872i | \(0.587010\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.85510 | −0.823438 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.3834 | 1.38779 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.2570 | 1.75218 | 0.876090 | − | 0.482148i | \(-0.160143\pi\) | ||||
0.876090 | + | 0.482148i | \(0.160143\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.803744 | −0.0807793 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.38336 | −0.933679 | −0.466839 | − | 0.884342i | \(-0.654607\pi\) | ||||
−0.466839 | + | 0.884342i | \(0.654607\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.9301 | −1.27404 | −0.637022 | − | 0.770846i | \(-0.719834\pi\) | ||||
−0.637022 | + | 0.770846i | \(0.719834\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.9420 | 1.83119 | 0.915595 | − | 0.402102i | \(-0.131720\pi\) | ||||
0.915595 | + | 0.402102i | \(0.131720\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.69168 | −0.257816 | −0.128908 | − | 0.991657i | \(-0.541147\pi\) | ||||
−0.128908 | + | 0.991657i | \(0.541147\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.06319 | 0.765324 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.422869 | 0.0390942 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.2385 | 1.21357 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.7667 | 1.79697 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.87361 | −0.166256 | −0.0831282 | − | 0.996539i | \(-0.526491\pi\) | ||||
−0.0831282 | + | 0.996539i | \(0.526491\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.9301 | 1.49061 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.5468 | 1.00885 | 0.504423 | − | 0.863457i | \(-0.331705\pi\) | ||||
0.504423 | + | 0.863457i | \(0.331705\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.69168 | 0.233398 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.23845 | −0.362115 | −0.181058 | − | 0.983472i | \(-0.557952\pi\) | ||||
−0.181058 | + | 0.983472i | \(0.557952\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.21994 | −0.782025 | −0.391012 | − | 0.920385i | \(-0.627875\pi\) | ||||
−0.391012 | + | 0.920385i | \(0.627875\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.48358 | 0.124940 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.1871 | −1.35363 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.434709 | −0.0358542 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.25697 | −0.594514 | −0.297257 | − | 0.954797i | \(-0.596072\pi\) | ||||
−0.297257 | + | 0.954797i | \(0.596072\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.0000 | −1.62758 | −0.813788 | − | 0.581161i | \(-0.802599\pi\) | ||||
−0.813788 | + | 0.581161i | \(0.802599\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.712675 | −0.0576163 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.54677 | 0.761916 | 0.380958 | − | 0.924592i | \(-0.375594\pi\) | ||||
0.380958 | + | 0.924592i | \(0.375594\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 17.3530 | 1.37618 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.71687 | −0.765797 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.7102 | 1.23052 | 0.615259 | − | 0.788325i | \(-0.289052\pi\) | ||||
0.615259 | + | 0.788325i | \(0.289052\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.45323 | 0.499366 | 0.249683 | − | 0.968328i | \(-0.419674\pi\) | ||||
0.249683 | + | 0.968328i | \(0.419674\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.48358 | −0.344891 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.144903 | −0.0110810 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.873614 | 0.0664196 | 0.0332098 | − | 0.999448i | \(-0.489427\pi\) | ||||
0.0332098 | + | 0.999448i | \(0.489427\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23.0422 | 1.73196 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.3834 | 0.925575 | 0.462788 | − | 0.886469i | \(-0.346849\pi\) | ||||
0.462788 | + | 0.886469i | \(0.346849\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.6403 | −1.31119 | −0.655597 | − | 0.755111i | \(-0.727583\pi\) | ||||
−0.655597 | + | 0.755111i | \(0.727583\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.0935 | 0.967903 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.2806 | 1.99496 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.6285 | −0.991326 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.1567 | 1.09670 | 0.548352 | − | 0.836248i | \(-0.315256\pi\) | ||||
0.548352 | + | 0.836248i | \(0.315256\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.3834 | −1.68317 | −0.841585 | − | 0.540124i | \(-0.818377\pi\) | ||||
−0.841585 | + | 0.540124i | \(0.818377\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.0935 | 1.64535 | 0.822674 | − | 0.568514i | \(-0.192481\pi\) | ||||
0.822674 | + | 0.568514i | \(0.192481\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.7852 | 1.82787 | 0.913933 | − | 0.405865i | \(-0.133030\pi\) | ||||
0.913933 | + | 0.405865i | \(0.133030\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.06319 | −0.357130 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.91161 | −0.204355 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.523095 | 0.0363576 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.54677 | 0.383678 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.2266 | −0.979400 | −0.489700 | − | 0.871891i | \(-0.662894\pi\) | ||||
−0.489700 | + | 0.871891i | \(0.662894\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 25.6732 | 1.75910 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.3135 | 1.37897 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.14490 | 0.617955 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.3530 | −0.965487 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.45323 | −0.298210 | −0.149105 | − | 0.988821i | \(-0.547639\pi\) | ||||
−0.149105 | + | 0.988821i | \(0.547639\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.94865 | 0.394826 | 0.197413 | − | 0.980320i | \(-0.436746\pi\) | ||||
0.197413 | + | 0.980320i | \(0.436746\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.09355 | 0.0722638 | 0.0361319 | − | 0.999347i | \(-0.488496\pi\) | ||||
0.0361319 | + | 0.999347i | \(0.488496\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −26.4769 | −1.74205 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.0935 | −0.923299 | −0.461650 | − | 0.887062i | \(-0.652742\pi\) | ||||
−0.461650 | + | 0.887062i | \(0.652742\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.48606 | −0.356358 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.6100 | −1.00972 | −0.504862 | − | 0.863200i | \(-0.668457\pi\) | ||||
−0.504862 | + | 0.863200i | \(0.668457\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.21994 | −0.336246 | −0.168123 | − | 0.985766i | \(-0.553771\pi\) | ||||
−0.168123 | + | 0.985766i | \(0.553771\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.50458 | 0.0965188 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.91829 | −0.185686 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.03284 | −0.192198 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.6403 | 1.80776 | 0.903881 | − | 0.427785i | \(-0.140706\pi\) | ||||
0.903881 | + | 0.427785i | \(0.140706\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.0237 | −1.25888 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.45323 | −0.402541 | −0.201271 | − | 0.979536i | \(-0.564507\pi\) | ||||
−0.201271 | + | 0.979536i | \(0.564507\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.2385 | 0.760460 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.156743 | 0.00970214 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.1871 | 1.36812 | 0.684058 | − | 0.729428i | \(-0.260214\pi\) | ||||
0.684058 | + | 0.729428i | \(0.260214\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.03284 | 0.552801 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.4070 | −1.24424 | −0.622119 | − | 0.782922i | \(-0.713728\pi\) | ||||
−0.622119 | + | 0.782922i | \(0.713728\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.9368 | −0.968092 | −0.484046 | − | 0.875043i | \(-0.660833\pi\) | ||||
−0.484046 | + | 0.875043i | \(0.660833\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.9301 | 0.843090 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.02368 | −0.241759 | −0.120880 | − | 0.992667i | \(-0.538572\pi\) | ||||
−0.120880 | + | 0.992667i | \(0.538572\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.09355 | −0.0654691 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.67316 | 0.0998124 | 0.0499062 | − | 0.998754i | \(-0.484108\pi\) | ||||
0.0499062 | + | 0.998754i | \(0.484108\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.8931 | 1.00419 | 0.502095 | − | 0.864812i | \(-0.332563\pi\) | ||||
0.502095 | + | 0.864812i | \(0.332563\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.18958 | 0.422916 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −30.6033 | −1.79400 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.08171 | 0.0631942 | 0.0315971 | − | 0.999501i | \(-0.489941\pi\) | ||||
0.0315971 | + | 0.999501i | \(0.489941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −28.0844 | −1.62962 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.5349 | 0.609251 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.6968 | 1.48114 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.6403 | 0.955962 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.38336 | 0.136025 | 0.0680126 | − | 0.997684i | \(-0.478334\pi\) | ||||
0.0680126 | + | 0.997684i | \(0.478334\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.9301 | 1.30445 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.4584 | 1.67043 | 0.835216 | − | 0.549922i | \(-0.185343\pi\) | ||||
0.835216 | + | 0.549922i | \(0.185343\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.0355 | −1.81075 | −0.905377 | − | 0.424608i | \(-0.860412\pi\) | ||||
−0.905377 | + | 0.424608i | \(0.860412\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.6665 | 1.49774 | 0.748870 | − | 0.662717i | \(-0.230597\pi\) | ||||
0.748870 | + | 0.662717i | \(0.230597\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00000 | −0.335936 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −33.5915 | −1.87489 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.91829 | 0.273661 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.77339 | 0.263969 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.25181 | 0.124146 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.8721 | 1.09227 | 0.546135 | − | 0.837697i | \(-0.316099\pi\) | ||||
0.546135 | + | 0.837697i | \(0.316099\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.658841 | −0.0361043 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.5705 | −1.50186 | −0.750929 | − | 0.660383i | \(-0.770394\pi\) | ||||
−0.750929 | + | 0.660383i | \(0.770394\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.6403 | −0.577903 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 41.8603 | 2.26686 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.1819 | 0.981732 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.2806 | −1.46450 | −0.732251 | − | 0.681035i | \(-0.761530\pi\) | ||||
−0.732251 | + | 0.681035i | \(0.761530\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.9538 | 1.65692 | 0.828460 | − | 0.560049i | \(-0.189218\pi\) | ||||
0.828460 | + | 0.560049i | \(0.189218\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.7759 | 0.788677 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.1819 | −0.595154 | −0.297577 | − | 0.954698i | \(-0.596179\pi\) | ||||
−0.297577 | + | 0.954698i | \(0.596179\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −23.4769 | −1.24253 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.3387 | −1.07343 | −0.536717 | − | 0.843762i | \(-0.680336\pi\) | ||||
−0.536717 | + | 0.843762i | \(0.680336\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −35.0540 | −1.83986 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.9538 | −1.72017 | −0.860087 | − | 0.510147i | \(-0.829591\pi\) | ||||
−0.860087 | + | 0.510147i | \(0.829591\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.3387 | 1.36744 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0869 | 0.522278 | 0.261139 | − | 0.965301i | \(-0.415902\pi\) | ||||
0.261139 | + | 0.965301i | \(0.415902\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.15674 | 0.162581 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.4256 | 0.946457 | 0.473229 | − | 0.880940i | \(-0.343088\pi\) | ||||
0.473229 | + | 0.880940i | \(0.343088\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.32264 | 0.170224 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.1871 | 1.44029 | 0.720147 | − | 0.693822i | \(-0.244074\pi\) | ||||
0.720147 | + | 0.693822i | \(0.244074\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.38336 | −0.0703199 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.0237 | 1.01524 | 0.507620 | − | 0.861581i | \(-0.330525\pi\) | ||||
0.507620 | + | 0.861581i | \(0.330525\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.7549 | −0.897902 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.4769 | −1.03292 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.32684 | 0.417912 | 0.208956 | − | 0.977925i | \(-0.432993\pi\) | ||||
0.208956 | + | 0.977925i | \(0.432993\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.77339 | −0.238968 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.1501 | −1.10612 | −0.553061 | − | 0.833141i | \(-0.686540\pi\) | ||||
−0.553061 | + | 0.833141i | \(0.686540\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.0237 | −1.09708 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.2199 | 1.25011 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.0237 | 1.68236 | 0.841181 | − | 0.540753i | \(-0.181861\pi\) | ||||
0.841181 | + | 0.540753i | \(0.181861\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.51642 | 0.370758 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 34.9738 | 1.72095 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.3505 | 0.800688 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −37.5334 | −1.83363 | −0.916814 | − | 0.399315i | \(-0.869248\pi\) | ||||
−0.916814 | + | 0.399315i | \(0.869248\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.8341 | 1.64897 | 0.824487 | − | 0.565882i | \(-0.191464\pi\) | ||||
0.824487 | + | 0.565882i | \(0.191464\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.121223 | −0.00589406 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.8736 | 0.961752 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 28.7060 | 1.38594 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.8037 | −1.19475 | −0.597377 | − | 0.801960i | \(-0.703790\pi\) | ||||
−0.597377 | + | 0.801960i | \(0.703790\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.68651 | −0.0810487 | −0.0405244 | − | 0.999179i | \(-0.512903\pi\) | ||||
−0.0405244 | + | 0.999179i | \(0.512903\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.60997 | −0.172688 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.326839 | −0.0155992 | −0.00779958 | − | 0.999970i | \(-0.502483\pi\) | ||||
−0.00779958 | + | 0.999970i | \(0.502483\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0355199 | 0.00169142 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.490258 | 0.0232929 | 0.0116464 | − | 0.999932i | \(-0.496293\pi\) | ||||
0.0116464 | + | 0.999932i | \(0.496293\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.8694 | 0.608703 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.5468 | 1.11124 | 0.555621 | − | 0.831436i | \(-0.312481\pi\) | ||||
0.555621 | + | 0.831436i | \(0.312481\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 35.4677 | 1.66642 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.01184 | 0.374778 | 0.187389 | − | 0.982286i | \(-0.439997\pi\) | ||||
0.187389 | + | 0.982286i | \(0.439997\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −24.9023 | −1.16234 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.83658 | 0.178687 | 0.0893437 | − | 0.996001i | \(-0.471523\pi\) | ||||
0.0893437 | + | 0.996001i | \(0.471523\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.58381 | −0.305975 | −0.152988 | − | 0.988228i | \(-0.548890\pi\) | ||||
−0.152988 | + | 0.988228i | \(0.548890\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.6033 | 1.04596 | 0.522978 | − | 0.852346i | \(-0.324821\pi\) | ||||
0.522978 | + | 0.852346i | \(0.324821\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.68500 | −0.354860 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.9301 | −0.780099 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 52.9538 | 2.43482 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.41791 | −0.0649215 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.7904 | 1.63530 | 0.817652 | − | 0.575712i | \(-0.195275\pi\) | ||||
0.817652 | + | 0.575712i | \(0.195275\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.2688 | −0.605006 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.2318 | 0.784073 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.4070 | −0.970045 | −0.485023 | − | 0.874502i | \(-0.661189\pi\) | ||||
−0.485023 | + | 0.874502i | \(0.661189\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −27.8603 | −1.25988 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.32684 | 0.195267 | 0.0976337 | − | 0.995222i | \(-0.468873\pi\) | ||||
0.0976337 | + | 0.995222i | \(0.468873\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.32016 | −0.239608 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 38.9672 | 1.74792 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.6968 | 1.68754 | 0.843771 | − | 0.536703i | \(-0.180330\pi\) | ||||
0.843771 | + | 0.536703i | \(0.180330\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.4441 | −0.511283 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.9183 | −0.754349 | −0.377175 | − | 0.926142i | \(-0.623104\pi\) | ||||
−0.377175 | + | 0.926142i | \(0.623104\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.95113 | 0.353122 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.79955 | −0.301385 | −0.150692 | − | 0.988581i | \(-0.548150\pi\) | ||||
−0.150692 | + | 0.988581i | \(0.548150\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.8803 | 0.614028 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.06319 | −0.223545 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.64032 | 0.204081 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.54926 | −0.0680048 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.35968 | −0.0595685 | −0.0297842 | − | 0.999556i | \(-0.509482\pi\) | ||||
−0.0297842 | + | 0.999556i | \(0.509482\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.9486 | −0.959747 | −0.479874 | − | 0.877338i | \(-0.659318\pi\) | ||||
−0.479874 | + | 0.877338i | \(0.659318\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 37.1172 | 1.61685 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.96813 | −0.433397 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.88277 | −0.0817053 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.9605 | −0.947665 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.35968 | −0.0585654 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.8973 | −1.71532 | −0.857659 | − | 0.514218i | \(-0.828082\pi\) | ||||
−0.857659 | + | 0.514218i | \(0.828082\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 31.2831 | 1.34249 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.34632 | −0.314106 | −0.157053 | − | 0.987590i | \(-0.550199\pi\) | ||||
−0.157053 | + | 0.987590i | \(0.550199\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.06987 | −0.0456609 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.08171 | −0.0460824 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.32684 | −0.354093 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.9672 | 1.14264 | 0.571318 | − | 0.820729i | \(-0.306432\pi\) | ||||
0.571318 | + | 0.820729i | \(0.306432\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.8603 | −1.17836 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −48.3792 | −2.04257 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −44.8973 | −1.89220 | −0.946098 | − | 0.323881i | \(-0.895012\pi\) | ||||
−0.946098 | + | 0.323881i | \(0.895012\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 25.3387 | 1.06412 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.1172 | 1.30450 | 0.652251 | − | 0.758003i | \(-0.273825\pi\) | ||||
0.652251 | + | 0.758003i | \(0.273825\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.2570 | −1.39176 | −0.695880 | − | 0.718158i | \(-0.744986\pi\) | ||||
−0.695880 | + | 0.718158i | \(0.744986\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.8788 | −1.12288 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.4702 | −0.977078 | −0.488539 | − | 0.872542i | \(-0.662470\pi\) | ||||
−0.488539 | + | 0.872542i | \(0.662470\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 41.4677 | 1.72334 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.60329 | −0.190977 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 54.2765 | 2.24790 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.1501 | −0.418938 | −0.209469 | − | 0.977815i | \(-0.567174\pi\) | ||||
−0.209469 | + | 0.977815i | \(0.567174\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.54677 | 0.310959 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −40.9538 | −1.68461 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.6732 | 0.684685 | 0.342342 | − | 0.939575i | \(-0.388780\pi\) | ||||
0.342342 | + | 0.939575i | \(0.388780\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −45.7272 | −1.87149 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.2765 | −0.746756 | −0.373378 | − | 0.927679i | \(-0.621800\pi\) | ||||
−0.373378 | + | 0.927679i | \(0.621800\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.96297 | 0.324816 | 0.162408 | − | 0.986724i | \(-0.448074\pi\) | ||||
0.162408 | + | 0.986724i | \(0.448074\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.413712 | 0.0168477 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.93013 | −0.281285 | −0.140643 | − | 0.990060i | \(-0.544917\pi\) | ||||
−0.140643 | + | 0.990060i | \(0.544917\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.16342 | 0.209232 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.44139 | −0.0987679 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.2765 | 1.38441 | 0.692206 | − | 0.721700i | \(-0.256639\pi\) | ||||
0.692206 | + | 0.721700i | \(0.256639\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.5139 | −1.42974 | −0.714869 | − | 0.699259i | \(-0.753514\pi\) | ||||
−0.714869 | + | 0.699259i | \(0.753514\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.5334 | 1.18705 | 0.593524 | − | 0.804816i | \(-0.297736\pi\) | ||||
0.593524 | + | 0.804816i | \(0.297736\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.2780 | 0.733470 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.7102 | 0.549287 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.83658 | −0.392835 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.3624 | 0.891646 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.1634 | 0.603646 | 0.301823 | − | 0.953364i | \(-0.402405\pi\) | ||||
0.301823 | + | 0.953364i | \(0.402405\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.2293 | 1.00277 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.715358 | 0.0283435 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.09775 | −0.0829855 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.0802 | −0.990608 | −0.495304 | − | 0.868720i | \(-0.664943\pi\) | ||||
−0.495304 | + | 0.868720i | \(0.664943\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.1306 | 0.754437 | 0.377218 | − | 0.926124i | \(-0.376881\pi\) | ||||
0.377218 | + | 0.926124i | \(0.376881\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.4019 | 0.487568 | 0.243784 | − | 0.969830i | \(-0.421611\pi\) | ||||
0.243784 | + | 0.969830i | \(0.421611\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 72.0710 | 2.82904 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −36.0237 | −1.41188 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.7801 | 0.421856 | 0.210928 | − | 0.977502i | \(-0.432351\pi\) | ||||
0.210928 | + | 0.977502i | \(0.432351\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.747227 | −0.0291521 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.56529 | −0.333656 | −0.166828 | − | 0.985986i | \(-0.553353\pi\) | ||||
−0.166828 | + | 0.985986i | \(0.553353\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.2883 | −1.02250 | −0.511248 | − | 0.859433i | \(-0.670817\pi\) | ||||
−0.511248 | + | 0.859433i | \(0.670817\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 25.4534 | 0.988529 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.90494 | 0.151200 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.89729 | 0.305327 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 40.9538 | 1.58100 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.9301 | 0.498420 | 0.249210 | − | 0.968449i | \(-0.419829\pi\) | ||||
0.249210 | + | 0.968449i | \(0.419829\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.9250 | 0.612046 | 0.306023 | − | 0.952024i | \(-0.401002\pi\) | ||||
0.306023 | + | 0.952024i | \(0.401002\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −46.4502 | −1.78260 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.5493 | −0.404248 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.2898 | 0.508520 | 0.254260 | − | 0.967136i | \(-0.418168\pi\) | ||||
0.254260 | + | 0.967136i | \(0.418168\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.93929 | −0.0739884 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.5561 | −1.08790 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.2570 | −1.03690 | −0.518452 | − | 0.855107i | \(-0.673492\pi\) | ||||
−0.518452 | + | 0.855107i | \(0.673492\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.16342 | 0.0821815 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.9933 | 0.945334 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.4441 | −1.56532 | −0.782660 | − | 0.622449i | \(-0.786138\pi\) | ||||
−0.782660 | + | 0.622449i | \(0.786138\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.54677 | 0.171485 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.2570 | 0.949886 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.7904 | −1.38169 | −0.690846 | − | 0.723002i | \(-0.742762\pi\) | ||||
−0.690846 | + | 0.723002i | \(0.742762\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.448264 | 0.0168112 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.2436 | −1.02028 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27.6825 | 1.03382 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.13726 | 0.154294 | 0.0771469 | − | 0.997020i | \(-0.475419\pi\) | ||||
0.0771469 | + | 0.997020i | \(0.475419\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.8037 | 1.29616 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.25697 | 0.344270 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.4374 | −1.49974 | −0.749870 | − | 0.661585i | \(-0.769884\pi\) | ||||
−0.749870 | + | 0.661585i | \(0.769884\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.5729 | 0.947146 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.9538 | 1.73665 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.1264 | −1.03887 | −0.519436 | − | 0.854509i | \(-0.673858\pi\) | ||||
−0.519436 | + | 0.854509i | \(0.673858\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.8366 | −0.583348 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.1501 | 1.40337 | 0.701686 | − | 0.712486i | \(-0.252431\pi\) | ||||
0.701686 | + | 0.712486i | \(0.252431\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.17526 | 0.190118 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.8232 | −0.653871 | −0.326935 | − | 0.945047i | \(-0.606016\pi\) | ||||
−0.326935 | + | 0.945047i | \(0.606016\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.247812 | 0.00906697 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −50.9857 | −1.86298 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.6968 | −0.864710 | −0.432355 | − | 0.901703i | \(-0.642317\pi\) | ||||
−0.432355 | + | 0.901703i | \(0.642317\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −50.7904 | −1.85090 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.51394 | 0.236753 | 0.118377 | − | 0.992969i | \(-0.462231\pi\) | ||||
0.118377 | + | 0.992969i | \(0.462231\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 35.5097 | 1.28892 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.7786 | 1.26072 | 0.630361 | − | 0.776302i | \(-0.282907\pi\) | ||||
0.630361 | + | 0.776302i | \(0.282907\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.24513 | 0.262291 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37.9183 | −1.36915 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.6850 | −0.998347 | −0.499173 | − | 0.866502i | \(-0.666363\pi\) | ||||
−0.499173 | + | 0.866502i | \(0.666363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.4441 | 0.412148 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.9738 | 0.718409 | 0.359205 | − | 0.933259i | \(-0.383048\pi\) | ||||
0.359205 | + | 0.933259i | \(0.383048\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −21.7035 | −0.778609 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 80.3001 | 2.87336 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.47691 | 0.195729 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.0118 | 1.49756 | 0.748780 | − | 0.662818i | \(-0.230640\pi\) | ||||
0.748780 | + | 0.662818i | \(0.230640\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −39.3463 | −1.40077 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.1501 | −0.574230 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.5468 | −0.765148 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 45.1054 | 1.59771 | 0.798857 | − | 0.601520i | \(-0.205438\pi\) | ||||
0.798857 | + | 0.601520i | \(0.205438\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.11455 | 0.145562 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.738070 | −0.0260784 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.6033 | 1.00939 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 36.1896 | 1.27393 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.85510 | 0.241012 | 0.120506 | − | 0.992713i | \(-0.461548\pi\) | ||||
0.120506 | + | 0.992713i | \(0.461548\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.1819 | 0.533110 | 0.266555 | − | 0.963820i | \(-0.414115\pi\) | ||||
0.266555 | + | 0.963820i | \(0.414115\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.2621 | 0.991196 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.54677 | 0.333999 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.13823 | −0.0397729 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.5006 | 0.785276 | 0.392638 | − | 0.919693i | \(-0.371563\pi\) | ||||
0.392638 | + | 0.919693i | \(0.371563\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.1896 | −0.564333 | −0.282167 | − | 0.959365i | \(-0.591053\pi\) | ||||
−0.282167 | + | 0.959365i | \(0.591053\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.0817 | −0.872177 | −0.436088 | − | 0.899904i | \(-0.643636\pi\) | ||||
−0.436088 | + | 0.899904i | \(0.643636\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.3068 | 0.740016 | 0.370008 | − | 0.929029i | \(-0.379355\pi\) | ||||
0.370008 | + | 0.929029i | \(0.379355\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.13554 | 0.247529 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.20562 | −0.0417721 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −38.2108 | −1.32076 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.4727 | 0.396082 | 0.198041 | − | 0.980194i | \(-0.436542\pi\) | ||||
0.198041 | + | 0.980194i | \(0.436542\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.8299 | −0.959652 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.96716 | −0.102195 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −53.2056 | −1.82817 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.9580 | −1.02816 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.4137 | −0.562655 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.9908 | 1.33502 | 0.667511 | − | 0.744600i | \(-0.267360\pi\) | ||||
0.667511 | + | 0.744600i | \(0.267360\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.8973 | 1.02127 | 0.510636 | − | 0.859797i | \(-0.329410\pi\) | ||||
0.510636 | + | 0.859797i | \(0.329410\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.47691 | 0.220989 | 0.110495 | − | 0.993877i | \(-0.464757\pi\) | ||||
0.110495 | + | 0.993877i | \(0.464757\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.09355 | −0.173386 | −0.0866932 | − | 0.996235i | \(-0.527630\pi\) | ||||
−0.0866932 | + | 0.996235i | \(0.527630\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.7499 | −0.433010 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.1592 | −0.582087 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.33200 | 0.282319 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.50059 | 0.0846320 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.8341 | 1.00743 | 0.503713 | − | 0.863871i | \(-0.331967\pi\) | ||||
0.503713 | + | 0.863871i | \(0.331967\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.91829 | −0.0647023 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.5796 | −0.390127 | −0.195064 | − | 0.980791i | \(-0.562491\pi\) | ||||
−0.195064 | + | 0.980791i | \(0.562491\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.0237 | −1.61613 | −0.808063 | − | 0.589096i | \(-0.799484\pi\) | ||||
−0.808063 | + | 0.589096i | \(0.799484\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.38336 | 0.315062 | 0.157531 | − | 0.987514i | \(-0.449647\pi\) | ||||
0.157531 | + | 0.987514i | \(0.449647\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.04316 | 0.169142 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 52.2157 | 1.74929 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.836581 | 0.0279951 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.6825 | −0.623791 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.16342 | −0.272265 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48.1266 | 1.60333 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −45.5705 | −1.51649 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.4347 | −0.645319 | −0.322659 | − | 0.946515i | \(-0.604577\pi\) | ||||
−0.322659 | + | 0.946515i | \(0.604577\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.35968 | −0.0450976 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.9866 | 0.662187 | 0.331094 | − | 0.943598i | \(-0.392582\pi\) | ||||
0.331094 | + | 0.943598i | \(0.392582\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.48606 | −0.313943 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −31.0802 | −1.02636 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.15158 | −0.202922 | −0.101461 | − | 0.994840i | \(-0.532352\pi\) | ||||
−0.101461 | + | 0.994840i | \(0.532352\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.22661 | −0.139272 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −42.2478 | −1.39060 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.87361 | −0.0615375 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.17010 | −0.235243 | −0.117622 | − | 0.993058i | \(-0.537527\pi\) | ||||
−0.117622 | + | 0.993058i | \(0.537527\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.245129 | −0.00803378 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −52.2411 | −1.71030 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.2646 | 0.792690 | 0.396345 | − | 0.918102i | \(-0.370278\pi\) | ||||
0.396345 | + | 0.918102i | \(0.370278\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 56.8114 | 1.85397 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.44806 | −0.242800 | −0.121400 | − | 0.992604i | \(-0.538738\pi\) | ||||
−0.121400 | + | 0.992604i | \(0.538738\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −52.9538 | −1.72077 | −0.860384 | − | 0.509647i | \(-0.829776\pi\) | ||||
−0.860384 | + | 0.509647i | \(0.829776\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.0489 | −0.488507 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −47.2900 | −1.53348 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.8694 | 0.416881 | 0.208441 | − | 0.978035i | \(-0.433161\pi\) | ||||
0.208441 | + | 0.978035i | \(0.433161\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.6403 | 0.343953 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.4085 | 0.368401 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.9538 | 0.837220 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.74475 | 0.0884482 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.8603 | 0.831610 | 0.415805 | − | 0.909454i | \(-0.363500\pi\) | ||||
0.415805 | + | 0.909454i | \(0.363500\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.72203 | −0.280192 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.0935 | −1.12621 | −0.563103 | − | 0.826387i | \(-0.690392\pi\) | ||||
−0.563103 | + | 0.826387i | \(0.690392\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.8171 | 0.795600 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.1737 | 1.34926 | 0.674629 | − | 0.738157i | \(-0.264304\pi\) | ||||
0.674629 | + | 0.738157i | \(0.264304\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.2528 | 0.902963 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.390032 | −0.0124528 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.6270 | −1.35959 | −0.679795 | − | 0.733403i | \(-0.737931\pi\) | ||||
−0.679795 | + | 0.733403i | \(0.737931\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.99332 | −0.127109 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −34.4636 | −1.09588 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.1737 | 1.08556 | 0.542782 | − | 0.839873i | \(-0.317371\pi\) | ||||
0.542782 | + | 0.839873i | \(0.317371\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −35.2409 | −1.11834 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.3834 | −0.930580 | −0.465290 | − | 0.885158i | \(-0.654050\pi\) | ||||
−0.465290 | + | 0.885158i | \(0.654050\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23.0212 | −0.728359 |
(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 | 7600.2.a.bz.1.1 | 3 | ||
4.3 | odd | 2 | 950.2.a.j.1.3 | ✓ | 3 | ||
5.4 | even | 2 | 7600.2.a.bk.1.3 | 3 | |||
12.11 | even | 2 | 8550.2.a.cp.1.3 | 3 | |||
20.3 | even | 4 | 950.2.b.h.799.6 | 6 | |||
20.7 | even | 4 | 950.2.b.h.799.1 | 6 | |||
20.19 | odd | 2 | 950.2.a.l.1.1 | yes | 3 | ||
60.59 | even | 2 | 8550.2.a.ci.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.a.j.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
950.2.a.l.1.1 | yes | 3 | 20.19 | odd | 2 | ||
950.2.b.h.799.1 | 6 | 20.7 | even | 4 | |||
950.2.b.h.799.6 | 6 | 20.3 | even | 4 | |||
7600.2.a.bk.1.3 | 3 | 5.4 | even | 2 | |||
7600.2.a.bz.1.1 | 3 | 1.1 | even | 1 | trivial | ||
8550.2.a.ci.1.1 | 3 | 60.59 | even | 2 | |||
8550.2.a.cp.1.3 | 3 | 12.11 | even | 2 |