Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6160,2,Mod(1,6160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6160.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6160 = 2^{4} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6160.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: | \(49.1878476451\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3080) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.65544\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6160.1 |
$q$-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 | ||||||||
\(3\) | −2.65544 | −1.53312 | −0.766560 | − | 0.642172i | \(-0.778033\pi\) | ||||
−0.766560 | + | 0.642172i | \(0.778033\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.05137 | 1.35046 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.65544 | −0.736487 | −0.368244 | − | 0.929729i | \(-0.620041\pi\) | ||||
−0.368244 | + | 0.929729i | \(0.620041\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.65544 | 0.685632 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.44731 | −1.32117 | −0.660583 | − | 0.750753i | \(-0.729691\pi\) | ||||
−0.660583 | + | 0.750753i | \(0.729691\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.10275 | 0.941235 | 0.470618 | − | 0.882337i | \(-0.344031\pi\) | ||||
0.470618 | + | 0.882337i | \(0.344031\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.65544 | −0.579465 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.259511 | 0.0541117 | 0.0270558 | − | 0.999634i | \(-0.491387\pi\) | ||||
0.0270558 | + | 0.999634i | \(0.491387\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.79186 | −0.537294 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.91495 | 0.882752 | 0.441376 | − | 0.897322i | \(-0.354491\pi\) | ||||
0.441376 | + | 0.897322i | \(0.354491\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.65544 | −0.462253 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.25951 | −0.371461 | −0.185731 | − | 0.982601i | \(-0.559465\pi\) | ||||
−0.185731 | + | 0.982601i | \(0.559465\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.05137 | 1.12912 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.08505 | −0.169456 | −0.0847279 | − | 0.996404i | \(-0.527002\pi\) | ||||
−0.0847279 | + | 0.996404i | \(0.527002\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.53235 | 0.691177 | 0.345589 | − | 0.938386i | \(-0.387679\pi\) | ||||
0.345589 | + | 0.938386i | \(0.387679\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.05137 | −0.603943 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.13642 | −0.603359 | −0.301680 | − | 0.953409i | \(-0.597547\pi\) | ||||
−0.301680 | + | 0.953409i | \(0.597547\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.4650 | 2.02551 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.36226 | −0.599202 | −0.299601 | − | 0.954065i | \(-0.596854\pi\) | ||||
−0.299601 | + | 0.954065i | \(0.596854\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.8946 | −1.44303 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.97966 | −0.778485 | −0.389243 | − | 0.921135i | \(-0.627263\pi\) | ||||
−0.389243 | + | 0.921135i | \(0.627263\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.80957 | 0.487765 | 0.243882 | − | 0.969805i | \(-0.421579\pi\) | ||||
0.243882 | + | 0.969805i | \(0.421579\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.05137 | 0.510425 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.65544 | 0.329367 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.15412 | −0.874015 | −0.437008 | − | 0.899458i | \(-0.643962\pi\) | ||||
−0.437008 | + | 0.899458i | \(0.643962\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.689115 | −0.0829597 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.2055 | 1.92324 | 0.961619 | − | 0.274387i | \(-0.0884750\pi\) | ||||
0.961619 | + | 0.274387i | \(0.0884750\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.55269 | −0.298770 | −0.149385 | − | 0.988779i | \(-0.547729\pi\) | ||||
−0.149385 | + | 0.988779i | \(0.547729\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.65544 | −0.306624 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.63774 | 0.409278 | 0.204639 | − | 0.978838i | \(-0.434398\pi\) | ||||
0.204639 | + | 0.978838i | \(0.434398\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.74049 | −0.526721 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.79186 | −0.745504 | −0.372752 | − | 0.927931i | \(-0.621586\pi\) | ||||
−0.372752 | + | 0.927931i | \(0.621586\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.44731 | 0.590843 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.31088 | 0.569387 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.31088 | 0.562953 | 0.281476 | − | 0.959568i | \(-0.409176\pi\) | ||||
0.281476 | + | 0.959568i | \(0.409176\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.65544 | −0.278366 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.0514 | −1.35336 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.10275 | −0.420933 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.5164 | 1.77852 | 0.889260 | − | 0.457403i | \(-0.151220\pi\) | ||||
0.889260 | + | 0.457403i | \(0.151220\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.05137 | 0.407178 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.43397 | −0.739708 | −0.369854 | − | 0.929090i | \(-0.620592\pi\) | ||||
−0.369854 | + | 0.929090i | \(0.620592\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.23917 | −0.417698 | −0.208849 | − | 0.977948i | \(-0.566972\pi\) | ||||
−0.208849 | + | 0.977948i | \(0.566972\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.65544 | 0.259145 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.519021 | 0.0501757 | 0.0250878 | − | 0.999685i | \(-0.492013\pi\) | ||||
0.0250878 | + | 0.999685i | \(0.492013\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.31088 | 0.317125 | 0.158563 | − | 0.987349i | \(-0.449314\pi\) | ||||
0.158563 | + | 0.987349i | \(0.449314\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.5164 | 1.08337 | 0.541685 | − | 0.840582i | \(-0.317787\pi\) | ||||
0.541685 | + | 0.840582i | \(0.317787\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.259511 | −0.0241995 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.7582 | −0.994595 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.44731 | −0.499354 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.88128 | 0.259796 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.9974 | 1.86321 | 0.931607 | − | 0.363467i | \(-0.118407\pi\) | ||||
0.931607 | + | 0.363467i | \(0.118407\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.0354 | −1.05966 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.58373 | 0.138371 | 0.0691855 | − | 0.997604i | \(-0.477960\pi\) | ||||
0.0691855 | + | 0.997604i | \(0.477960\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.10275 | 0.355753 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.79186 | 0.240285 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.15676 | 0.696879 | 0.348440 | − | 0.937331i | \(-0.386712\pi\) | ||||
0.348440 | + | 0.937331i | \(0.386712\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.9327 | −1.01211 | −0.506057 | − | 0.862500i | \(-0.668898\pi\) | ||||
−0.506057 | + | 0.862500i | \(0.668898\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.9840 | 0.925022 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.65544 | −0.222059 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.65544 | −0.219017 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.17009 | −0.341627 | −0.170814 | − | 0.985303i | \(-0.554640\pi\) | ||||
−0.170814 | + | 0.985303i | \(0.554640\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.8786 | 1.78046 | 0.890229 | − | 0.455513i | \(-0.150544\pi\) | ||||
0.890229 | + | 0.455513i | \(0.150544\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −22.0691 | −1.78418 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.91495 | −0.394779 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.2055 | −0.974105 | −0.487052 | − | 0.873373i | \(-0.661928\pi\) | ||||
−0.487052 | + | 0.873373i | \(0.661928\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.5837 | 0.918649 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.259511 | 0.0204523 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.1541 | 1.50027 | 0.750133 | − | 0.661287i | \(-0.229989\pi\) | ||||
0.750133 | + | 0.661287i | \(0.229989\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.65544 | 0.206726 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.03804 | −0.235091 | −0.117545 | − | 0.993068i | \(-0.537503\pi\) | ||||
−0.117545 | + | 0.993068i | \(0.537503\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.94863 | −0.457587 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.6218 | 1.27110 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.07171 | −0.233538 | −0.116769 | − | 0.993159i | \(-0.537254\pi\) | ||||
−0.116769 | + | 0.993159i | \(0.537254\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.8786 | 1.19351 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.7626 | −1.62661 | −0.813305 | − | 0.581838i | \(-0.802334\pi\) | ||||
−0.813305 | + | 0.581838i | \(0.802334\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.3082 | −1.06352 | −0.531762 | − | 0.846894i | \(-0.678470\pi\) | ||||
−0.531762 | + | 0.846894i | \(0.678470\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.1161 | −0.747802 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.25951 | 0.166123 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.44731 | −0.398346 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.79186 | −0.203078 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.3109 | 1.25257 | 0.626286 | − | 0.779594i | \(-0.284574\pi\) | ||||
0.626286 | + | 0.779594i | \(0.284574\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.42960 | −0.318850 | −0.159425 | − | 0.987210i | \(-0.550964\pi\) | ||||
−0.159425 | + | 0.987210i | \(0.550964\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.05137 | −0.504959 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.57040 | 0.254380 | 0.127190 | − | 0.991878i | \(-0.459404\pi\) | ||||
0.127190 | + | 0.991878i | \(0.459404\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0824 | 0.714723 | 0.357361 | − | 0.933966i | \(-0.383676\pi\) | ||||
0.357361 | + | 0.933966i | \(0.383676\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.9974 | 1.33997 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.00000 | −0.140372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.08505 | 0.0757830 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.05137 | 0.0730756 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.10275 | 0.283793 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9593 | −1.09868 | −0.549342 | − | 0.835597i | \(-0.685122\pi\) | ||||
−0.549342 | + | 0.835597i | \(0.685122\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −43.0328 | −2.94856 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.53235 | −0.309104 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.91495 | 0.333649 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.77853 | 0.458051 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.4650 | 0.973022 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.2772 | −1.42483 | −0.712414 | − | 0.701760i | \(-0.752398\pi\) | ||||
−0.712414 | + | 0.701760i | \(0.752398\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.05137 | 0.270092 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.82727 | 0.187652 | 0.0938261 | − | 0.995589i | \(-0.470090\pi\) | ||||
0.0938261 | + | 0.995589i | \(0.470090\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.24618 | 0.148432 | 0.0742158 | − | 0.997242i | \(-0.476355\pi\) | ||||
0.0742158 | + | 0.997242i | \(0.476355\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.65544 | −0.174715 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.9840 | −1.76778 | −0.883891 | − | 0.467692i | \(-0.845085\pi\) | ||||
−0.883891 | + | 0.467692i | \(0.845085\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.13642 | 0.269830 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.65981 | −0.627472 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.6191 | −1.01032 | −0.505159 | − | 0.863026i | \(-0.668566\pi\) | ||||
−0.505159 | + | 0.863026i | \(0.668566\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.60143 | 0.167573 | 0.0837864 | − | 0.996484i | \(-0.473299\pi\) | ||||
0.0837864 | + | 0.996484i | \(0.473299\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.9637 | 1.34482 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.8946 | −0.693208 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.0354 | 1.14295 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.1878 | −1.33736 | −0.668681 | − | 0.743549i | \(-0.733141\pi\) | ||||
−0.668681 | + | 0.743549i | \(0.733141\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.259511 | 0.0163153 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.4650 | −0.905834 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.06471 | −0.0664146 | −0.0332073 | − | 0.999448i | \(-0.510572\pi\) | ||||
−0.0332073 | + | 0.999448i | \(0.510572\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.25951 | −0.140399 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.10275 | −0.501548 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.6572 | −1.52043 | −0.760213 | − | 0.649674i | \(-0.774906\pi\) | ||||
−0.760213 | + | 0.649674i | \(0.774906\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.36226 | 0.267971 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.1027 | −0.863074 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.4110 | 1.00060 | 0.500298 | − | 0.865853i | \(-0.333224\pi\) | ||||
0.500298 | + | 0.865853i | \(0.333224\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.4783 | −1.00099 | −0.500494 | − | 0.865740i | \(-0.666848\pi\) | ||||
−0.500494 | + | 0.865740i | \(0.666848\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.05137 | 0.426769 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.74049 | 0.344913 | 0.172456 | − | 0.985017i | \(-0.444830\pi\) | ||||
0.172456 | + | 0.985017i | \(0.444830\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.9123 | 1.19212 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.6865 | −0.816467 | −0.408233 | − | 0.912878i | \(-0.633855\pi\) | ||||
−0.408233 | + | 0.912878i | \(0.633855\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.1408 | −0.662251 | −0.331126 | − | 0.943587i | \(-0.607428\pi\) | ||||
−0.331126 | + | 0.943587i | \(0.607428\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.8946 | 0.645341 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.08505 | −0.0640483 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.6731 | 0.745479 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −46.5137 | −2.72668 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.9663 | −1.51697 | −0.758485 | − | 0.651691i | \(-0.774060\pi\) | ||||
−0.758485 | + | 0.651691i | \(0.774060\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.97966 | 0.348149 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.79186 | −0.162000 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.689115 | −0.0398526 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.53235 | 0.261240 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.7405 | 1.13406 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.80957 | −0.218135 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.5571 | −0.887888 | −0.443944 | − | 0.896054i | \(-0.646421\pi\) | ||||
−0.443944 | + | 0.896054i | \(0.646421\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.2569 | 0.640381 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.53936 | −0.257404 | −0.128702 | − | 0.991683i | \(-0.541081\pi\) | ||||
−0.128702 | + | 0.991683i | \(0.541081\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.7626 | −1.34314 | −0.671570 | − | 0.740941i | \(-0.734380\pi\) | ||||
−0.671570 | + | 0.740941i | \(0.734380\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.05137 | −0.228269 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.5837 | 0.650607 | 0.325303 | − | 0.945610i | \(-0.394534\pi\) | ||||
0.325303 | + | 0.945610i | \(0.394534\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.00000 | −0.111979 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.37823 | −0.0769253 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.3489 | −1.24353 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.65544 | −0.147297 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.79186 | −0.486191 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.13642 | −0.228048 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.0354 | 1.43104 | 0.715518 | − | 0.698595i | \(-0.246191\pi\) | ||||
0.715518 | + | 0.698595i | \(0.246191\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.15412 | −0.501643 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.15412 | 0.390871 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.36490 | −0.183298 | −0.0916488 | − | 0.995791i | \(-0.529214\pi\) | ||||
−0.0916488 | + | 0.995791i | \(0.529214\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −30.5811 | −1.66094 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.91495 | 0.266160 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.689115 | 0.0371007 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.0514 | −0.915366 | −0.457683 | − | 0.889116i | \(-0.651320\pi\) | ||||
−0.457683 | + | 0.889116i | \(0.651320\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.4987 | −0.776097 | −0.388048 | − | 0.921639i | \(-0.626851\pi\) | ||||
−0.388048 | + | 0.921639i | \(0.626851\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.41363 | 0.395710 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.14079 | −0.0607182 | −0.0303591 | − | 0.999539i | \(-0.509665\pi\) | ||||
−0.0303591 | + | 0.999539i | \(0.509665\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.2055 | −0.860098 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.4650 | 0.765569 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.5297 | 0.608515 | 0.304258 | − | 0.952590i | \(-0.401592\pi\) | ||||
0.304258 | + | 0.952590i | \(0.401592\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.16745 | −0.114077 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.65544 | −0.139375 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.55269 | 0.133614 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.2392 | −1.36967 | −0.684837 | − | 0.728697i | \(-0.740127\pi\) | ||||
−0.684837 | + | 0.728697i | \(0.740127\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.39593 | −0.228843 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.36226 | −0.226477 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.1922 | −1.56329 | −0.781646 | − | 0.623723i | \(-0.785619\pi\) | ||||
−0.781646 | + | 0.623723i | \(0.785619\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.65544 | 0.137126 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.31088 | 0.273524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.62177 | 0.340137 | 0.170069 | − | 0.985432i | \(-0.445601\pi\) | ||||
0.170069 | + | 0.985432i | \(0.445601\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −55.7573 | −2.85653 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.7910 | 1.62444 | 0.812221 | − | 0.583350i | \(-0.198258\pi\) | ||||
0.812221 | + | 0.583350i | \(0.198258\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.3623 | 0.933406 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.9707 | −1.16466 | −0.582330 | − | 0.812952i | \(-0.697859\pi\) | ||||
−0.582330 | + | 0.812952i | \(0.697859\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.41363 | −0.0714905 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.20550 | −0.212139 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.63774 | −0.183035 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.7245 | −1.04013 | −0.520067 | − | 0.854126i | \(-0.674093\pi\) | ||||
−0.520067 | + | 0.854126i | \(0.674093\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.8946 | −0.545413 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.24354 | 0.161975 | 0.0809873 | − | 0.996715i | \(-0.474193\pi\) | ||||
0.0809873 | + | 0.996715i | \(0.474193\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.0514 | −0.650135 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.74049 | 0.235557 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.25951 | −0.112000 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.77152 | −0.137043 | −0.0685215 | − | 0.997650i | \(-0.521828\pi\) | ||||
−0.0685215 | + | 0.997650i | \(0.521828\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.6598 | −1.06840 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.97966 | −0.294240 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.79186 | 0.333399 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 31.6865 | 1.55169 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.2586 | −1.33167 | −0.665835 | − | 0.746099i | \(-0.731924\pi\) | ||||
−0.665835 | + | 0.746099i | \(0.731924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.63774 | −0.274767 | −0.137383 | − | 0.990518i | \(-0.543869\pi\) | ||||
−0.137383 | + | 0.990518i | \(0.543869\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.7582 | −0.814811 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.44731 | −0.264233 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.80957 | 0.184358 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.05137 | 0.340444 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.1515 | −0.681653 | −0.340826 | − | 0.940126i | \(-0.610707\pi\) | ||||
−0.340826 | + | 0.940126i | \(0.610707\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.7272 | −0.659685 | −0.329843 | − | 0.944036i | \(-0.606996\pi\) | ||||
−0.329843 | + | 0.944036i | \(0.606996\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.31088 | −0.254637 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.06471 | 0.0509318 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.8246 | −0.946178 | −0.473089 | − | 0.881015i | \(-0.656861\pi\) | ||||
−0.473089 | + | 0.881015i | \(0.656861\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.05137 | 0.192923 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.74049 | −0.367762 | −0.183881 | − | 0.982949i | \(-0.558866\pi\) | ||||
−0.183881 | + | 0.982949i | \(0.558866\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.31088 | −0.251760 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.0734 | 0.523756 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.7785 | 0.603056 | 0.301528 | − | 0.953457i | \(-0.402503\pi\) | ||||
0.301528 | + | 0.953457i | \(0.402503\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.08505 | −0.0510929 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −58.0975 | −2.72966 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.65544 | 0.124489 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.19216 | 0.102545 | 0.0512726 | − | 0.998685i | \(-0.483672\pi\) | ||||
0.0512726 | + | 0.998685i | \(0.483672\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15.2081 | 0.709855 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0824 | 0.655883 | 0.327942 | − | 0.944698i | \(-0.393645\pi\) | ||||
0.327942 | + | 0.944698i | \(0.393645\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.6032 | −1.32930 | −0.664651 | − | 0.747154i | \(-0.731420\pi\) | ||||
−0.664651 | + | 0.747154i | \(0.731420\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.0514 | 0.605243 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.13906 | −0.237807 | −0.118904 | − | 0.992906i | \(-0.537938\pi\) | ||||
−0.118904 | + | 0.992906i | \(0.537938\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.15412 | −0.330347 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.4110 | 1.49342 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.53235 | 0.208398 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.10275 | 0.188247 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.6731 | −0.809198 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.6218 | 0.942233 | 0.471116 | − | 0.882071i | \(-0.343851\pi\) | ||||
0.471116 | + | 0.882071i | \(0.343851\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.00000 | 0.273576 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.689115 | −0.0313558 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.5164 | −0.795378 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.0221 | −0.454143 | −0.227072 | − | 0.973878i | \(-0.572915\pi\) | ||||
−0.227072 | + | 0.973878i | \(0.572915\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −50.8627 | −2.30009 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.2276 | 1.09337 | 0.546687 | − | 0.837337i | \(-0.315889\pi\) | ||||
0.546687 | + | 0.837337i | \(0.315889\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.8946 | 0.490669 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.05137 | −0.182096 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.2055 | 0.726916 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.3463 | 1.40325 | 0.701626 | − | 0.712545i | \(-0.252458\pi\) | ||||
0.701626 | + | 0.712545i | \(0.252458\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.06735 | 0.360422 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.4136 | −1.66819 | −0.834096 | − | 0.551620i | \(-0.814010\pi\) | ||||
−0.834096 | + | 0.551620i | \(0.814010\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.43397 | 0.330807 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.7962 | 0.701535 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.7219 | −1.05145 | −0.525727 | − | 0.850653i | \(-0.676207\pi\) | ||||
−0.525727 | + | 0.850653i | \(0.676207\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.55269 | −0.112925 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11.4543 | −0.505720 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.23917 | 0.186800 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.13642 | −0.181920 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.15676 | 0.358042 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.97334 | −0.174075 | −0.0870375 | − | 0.996205i | \(-0.527740\pi\) | ||||
−0.0870375 | + | 0.996205i | \(0.527740\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.7626 | 1.21397 | 0.606986 | − | 0.794713i | \(-0.292378\pi\) | ||||
0.606986 | + | 0.794713i | \(0.292378\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.65544 | −0.115893 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.7733 | −1.16626 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9327 | −0.997072 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.2258 | −1.05131 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.88128 | 0.124802 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.519021 | −0.0224392 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 57.7892 | 2.49379 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.79186 | 0.120032 | 0.0600158 | − | 0.998197i | \(-0.480885\pi\) | ||||
0.0600158 | + | 0.998197i | \(0.480885\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 37.9947 | 1.63051 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.31088 | −0.141823 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.48362 | −0.106192 | −0.0530959 | − | 0.998589i | \(-0.516909\pi\) | ||||
−0.0530959 | + | 0.998589i | \(0.516909\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.4340 | 0.658706 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.20550 | −0.349566 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.63774 | 0.154692 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.00000 | −0.254686 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.4650 | 0.612902 | 0.306451 | − | 0.951886i | \(-0.400858\pi\) | ||||
0.306451 | + | 0.951886i | \(0.400858\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0354 | −0.509043 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.4650 | 0.610713 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.6572 | 0.702016 | 0.351008 | − | 0.936372i | \(-0.385839\pi\) | ||||
0.351008 | + | 0.936372i | \(0.385839\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.5164 | −0.484498 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.74049 | −0.199082 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.72716 | −0.240095 | −0.120047 | − | 0.992768i | \(-0.538305\pi\) | ||||
−0.120047 | + | 0.992768i | \(0.538305\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.1648 | 1.17866 | 0.589330 | − | 0.807892i | \(-0.299392\pi\) | ||||
0.589330 | + | 0.807892i | \(0.299392\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −45.9681 | −1.92034 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.259511 | 0.0108223 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.1701 | 0.589909 | 0.294954 | − | 0.955511i | \(-0.404696\pi\) | ||||
0.294954 | + | 0.955511i | \(0.404696\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.7626 | 0.488835 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.79186 | −0.281774 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.36226 | −0.180666 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.7582 | 0.444796 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.1071 | −0.623537 | −0.311769 | − | 0.950158i | \(-0.600921\pi\) | ||||
−0.311769 | + | 0.950158i | \(0.600921\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.1648 | 0.830877 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.48098 | −0.389995 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.96633 | 0.162878 | 0.0814388 | − | 0.996678i | \(-0.474048\pi\) | ||||
0.0814388 | + | 0.996678i | \(0.474048\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.44731 | 0.223318 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26.7733 | −1.09576 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.1027 | −0.576223 | −0.288111 | − | 0.957597i | \(-0.593027\pi\) | ||||
−0.288111 | + | 0.957597i | \(0.593027\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.22584 | −0.172376 | −0.0861878 | − | 0.996279i | \(-0.527468\pi\) | ||||
−0.0861878 | + | 0.996279i | \(0.527468\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −28.9840 | −1.18032 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.4110 | 1.55905 | 0.779527 | − | 0.626369i | \(-0.215459\pi\) | ||||
0.779527 | + | 0.626369i | \(0.215459\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.31088 | 0.215208 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.9840 | 0.444366 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.8052 | 0.759535 | 0.379767 | − | 0.925082i | \(-0.376004\pi\) | ||||
0.379767 | + | 0.925082i | \(0.376004\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.88128 | −0.116184 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.77853 | 0.272893 | 0.136447 | − | 0.990647i | \(-0.456432\pi\) | ||||
0.136447 | + | 0.990647i | \(0.456432\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.5341 | 0.744948 | 0.372474 | − | 0.928043i | \(-0.378510\pi\) | ||||
0.372474 | + | 0.928043i | \(0.378510\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.724518 | −0.0290739 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.31088 | 0.212776 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.8946 | −0.435089 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.3082 | 0.490762 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.9947 | −0.557121 | −0.278561 | − | 0.960419i | \(-0.589857\pi\) | ||||
−0.278561 | + | 0.960419i | \(0.589857\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 42.3791 | 1.68442 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.9974 | −0.833255 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.65544 | −0.105212 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 65.6545 | 2.59725 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.9840 | −1.14480 | −0.572400 | − | 0.819974i | \(-0.693988\pi\) | ||||
−0.572400 | + | 0.819974i | \(0.693988\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.2011 | 0.678346 | 0.339173 | − | 0.940724i | \(-0.389853\pi\) | ||||
0.339173 | + | 0.940724i | \(0.389853\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.0354 | 0.473894 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.38260 | −0.329554 | −0.164777 | − | 0.986331i | \(-0.552690\pi\) | ||||
−0.164777 | + | 0.986331i | \(0.552690\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.97966 | −0.234722 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.0514 | −0.511524 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.348927 | 0.0136546 | 0.00682728 | − | 0.999977i | \(-0.497827\pi\) | ||||
0.00682728 | + | 0.999977i | \(0.497827\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.58373 | −0.0618814 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.3419 | −0.403477 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.7492 | −0.769321 | −0.384660 | − | 0.923058i | \(-0.625681\pi\) | ||||
−0.384660 | + | 0.923058i | \(0.625681\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.33755 | −0.0520246 | −0.0260123 | − | 0.999662i | \(-0.508281\pi\) | ||||
−0.0260123 | + | 0.999662i | \(0.508281\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −38.4110 | −1.49176 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.10275 | −0.159098 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.519021 | −0.0200966 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 56.5004 | 2.18443 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.80957 | 0.147067 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −51.1488 | −1.97164 | −0.985822 | − | 0.167797i | \(-0.946335\pi\) | ||||
−0.985822 | + | 0.167797i | \(0.946335\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.79186 | −0.107459 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.9016 | 0.880181 | 0.440090 | − | 0.897953i | \(-0.354946\pi\) | ||||
0.440090 | + | 0.897953i | \(0.354946\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.5164 | 0.672217 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.50764 | −0.287694 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.8520 | −1.67795 | −0.838975 | − | 0.544171i | \(-0.816844\pi\) | ||||
−0.838975 | + | 0.544171i | \(0.816844\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.15676 | −0.311654 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.96460 | −0.227564 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.5837 | 0.441305 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.9504 | −0.644822 | −0.322411 | − | 0.946600i | \(-0.604493\pi\) | ||||
−0.322411 | + | 0.946600i | \(0.604493\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.05137 | 0.153899 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.9327 | 0.452631 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.91058 | 0.223879 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 71.6545 | 2.71022 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.96460 | 0.300819 | 0.150409 | − | 0.988624i | \(-0.451941\pi\) | ||||
0.150409 | + | 0.988624i | \(0.451941\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.27020 | −0.349632 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.9840 | −0.413682 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.43397 | −0.279583 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.3349 | 1.21436 | 0.607182 | − | 0.794563i | \(-0.292300\pi\) | ||||
0.607182 | + | 0.794563i | \(0.292300\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.7379 | 0.552713 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.27548 | 0.0477672 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.65544 | 0.0993079 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 41.4757 | 1.54894 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.2206 | 1.27621 | 0.638106 | − | 0.769949i | \(-0.279718\pi\) | ||||
0.638106 | + | 0.769949i | \(0.279718\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.23917 | −0.157875 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.90794 | −0.256909 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00000 | −0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.2772 | 1.01166 | 0.505828 | − | 0.862634i | \(-0.331187\pi\) | ||||
0.505828 | + | 0.862634i | \(0.331187\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.4464 | −1.53505 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.6891 | −0.913160 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.9256 | 0.957586 | 0.478793 | − | 0.877928i | \(-0.341075\pi\) | ||||
0.478793 | + | 0.877928i | \(0.341075\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.65544 | 0.0979475 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.15412 | −0.263525 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.5457 | 0.755785 | 0.377893 | − | 0.925849i | \(-0.376649\pi\) | ||||
0.377893 | + | 0.925849i | \(0.376649\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.9300 | 1.06277 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −42.3082 | −1.55214 | −0.776069 | − | 0.630647i | \(-0.782789\pi\) | ||||
−0.776069 | + | 0.630647i | \(0.782789\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.17009 | 0.152780 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −27.5164 | −1.00677 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.519021 | 0.0189646 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.9274 | −1.38399 | −0.691995 | − | 0.721902i | \(-0.743268\pi\) | ||||
−0.691995 | + | 0.721902i | \(0.743268\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 56.2630 | 2.05034 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.8786 | −0.796245 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.3756 | 1.32209 | 0.661047 | − | 0.750345i | \(-0.270113\pi\) | ||||
0.661047 | + | 0.750345i | \(0.270113\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.689115 | −0.0250133 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.6661 | 1.07540 | 0.537698 | − | 0.843137i | \(-0.319294\pi\) | ||||
0.537698 | + | 0.843137i | \(0.319294\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.31088 | 0.119862 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 22.0691 | 0.797909 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.8786 | 0.573344 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.9797 | −1.29746 | −0.648730 | − | 0.761019i | \(-0.724699\pi\) | ||||
−0.648730 | + | 0.761019i | \(0.724699\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.82727 | 0.101822 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.3436 | 1.30719 | 0.653595 | − | 0.756844i | \(-0.273260\pi\) | ||||
0.653595 | + | 0.756844i | \(0.273260\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.91495 | 0.176550 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.00000 | 0.215249 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.45168 | −0.159498 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.2055 | 0.579878 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.58373 | 0.199546 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.2055 | 0.435633 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.1648 | −0.861383 | −0.430691 | − | 0.902499i | \(-0.641730\pi\) | ||||
−0.430691 | + | 0.902499i | \(0.641730\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 65.4757 | 2.33100 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.5164 | 0.409475 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.1161 | −0.359233 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.5837 | −0.410832 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.79450 | −0.134408 | −0.0672041 | − | 0.997739i | \(-0.521408\pi\) | ||||
−0.0672041 | + | 0.997739i | \(0.521408\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.5324 | 0.797137 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.5164 | 0.760244 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.55269 | −0.0900826 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.259511 | −0.00914654 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −43.5784 | −1.53403 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.9300 | −0.384279 | −0.192139 | − | 0.981368i | \(-0.561543\pi\) | ||||
−0.192139 | + | 0.981368i | \(0.561543\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.31088 | −0.116261 | −0.0581304 | − | 0.998309i | \(-0.518514\pi\) | ||||
−0.0581304 | + | 0.998309i | \(0.518514\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 43.7573 | 1.53463 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.1541 | −0.670940 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.5951 | 0.650560 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.7582 | −0.375922 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.8566 | −1.39100 | −0.695502 | − | 0.718524i | \(-0.744818\pi\) | ||||
−0.695502 | + | 0.718524i | \(0.744818\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.18079 | −0.110875 | −0.0554376 | − | 0.998462i | \(-0.517655\pi\) | ||||
−0.0554376 | + | 0.998462i | \(0.517655\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.65544 | −0.0924506 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.7059 | 1.62412 | 0.812062 | − | 0.583571i | \(-0.198345\pi\) | ||||
0.812062 | + | 0.583571i | \(0.198345\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.0328 | −1.14728 | −0.573638 | − | 0.819109i | \(-0.694468\pi\) | ||||
−0.573638 | + | 0.819109i | \(0.694468\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.2435 | −0.528793 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.44731 | −0.188738 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.03804 | 0.105136 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.7219 | −0.474298 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.0505 | −1.38270 | −0.691348 | − | 0.722522i | \(-0.742983\pi\) | ||||
−0.691348 | + | 0.722522i | \(0.742983\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 36.3436 | 1.25174 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.94863 | 0.204639 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.5837 | 1.01531 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.586367 | −0.0201004 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.2099 | 0.726212 | 0.363106 | − | 0.931748i | \(-0.381716\pi\) | ||||
0.363106 | + | 0.931748i | \(0.381716\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.6218 | −0.568453 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.3686 | −0.695778 | −0.347889 | − | 0.937536i | \(-0.613101\pi\) | ||||
−0.347889 | + | 0.937536i | \(0.613101\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.9910 | 0.511488 | 0.255744 | − | 0.966745i | \(-0.417680\pi\) | ||||
0.255744 | + | 0.966745i | \(0.417680\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.88128 | 0.0981938 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.9840 | −0.441981 | −0.220991 | − | 0.975276i | \(-0.570929\pi\) | ||||
−0.220991 | + | 0.975276i | \(0.570929\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.07171 | 0.104441 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −33.6528 | −1.14291 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.63774 | 0.123402 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.9974 | 0.643701 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 70.9654 | 2.40182 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −52.1462 | −1.76085 | −0.880426 | − | 0.474183i | \(-0.842743\pi\) | ||||
−0.880426 | + | 0.474183i | \(0.842743\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 68.9521 | 2.32570 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.6865 | −0.798018 | −0.399009 | − | 0.916947i | \(-0.630646\pi\) | ||||
−0.399009 | + | 0.916947i | \(0.630646\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.5004 | −0.757199 | −0.378600 | − | 0.925561i | \(-0.623594\pi\) | ||||
−0.378600 | + | 0.925561i | \(0.623594\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.8786 | −0.533755 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.1382 | 0.407559 | 0.203780 | − | 0.979017i | \(-0.434677\pi\) | ||||
0.203780 | + | 0.979017i | \(0.434677\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.9974 | 0.704229 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.74049 | −0.158812 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.9707 | −0.567903 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.7626 | 0.727442 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.82991 | 0.0610988 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.82991 | −0.327846 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.7626 | 0.791646 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.0354 | −0.400513 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.3082 | 0.475622 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.6058 | −0.651000 | −0.325500 | − | 0.945542i | \(-0.605533\pi\) | ||||
−0.325500 | + | 0.945542i | \(0.605533\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −30.1178 | −0.998945 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.5251 | 1.57458 | 0.787289 | − | 0.616584i | \(-0.211484\pi\) | ||||
0.787289 | + | 0.616584i | \(0.211484\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.79186 | −0.224778 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.1161 | 0.334427 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.58373 | 0.0522993 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.38087 | 0.276459 | 0.138230 | − | 0.990400i | \(-0.455859\pi\) | ||||
0.138230 | + | 0.990400i | \(0.455859\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 41.3109 | 1.36124 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −43.0328 | −1.41644 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.25951 | −0.0742922 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.1745 | −0.564083 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.61039 | 0.184071 | 0.0920355 | − | 0.995756i | \(-0.470663\pi\) | ||||
0.0920355 | + | 0.995756i | \(0.470663\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.10275 | 0.134462 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.0540 | 0.394631 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.44731 | 0.178146 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.5448 | 1.42255 | 0.711273 | − | 0.702916i | \(-0.248119\pi\) | ||||
0.711273 | + | 0.702916i | \(0.248119\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 63.1001 | 2.05919 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.3959 | −0.404096 | −0.202048 | − | 0.979376i | \(-0.564760\pi\) | ||||
−0.202048 | + | 0.979376i | \(0.564760\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.281581 | −0.00916954 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.79186 | 0.0908193 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.4917 | 0.535907 | 0.267954 | − | 0.963432i | \(-0.413653\pi\) | ||||
0.267954 | + | 0.963432i | \(0.413653\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.77853 | 0.220040 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.7599 | −0.997459 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.5944 | −0.407973 | −0.203987 | − | 0.978974i | \(-0.565390\pi\) | ||||
−0.203987 | + | 0.978974i | \(0.565390\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.3109 | −0.560167 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.31088 | 0.171677 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.15676 | 0.263396 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.84324 | −0.220750 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.10275 | 0.0677601 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.42960 | 0.142594 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.42960 | −0.206762 | −0.103381 | − | 0.994642i | \(-0.532966\pi\) | ||||
−0.103381 | + | 0.994642i | \(0.532966\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 59.3463 | 1.90648 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.3959 | −0.975452 | −0.487726 | − | 0.872997i | \(-0.662173\pi\) | ||||
−0.487726 | + | 0.872997i | \(0.662173\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.9327 | −0.382543 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.05137 | 0.225825 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.5597 | 0.337835 | 0.168917 | − | 0.985630i | \(-0.445973\pi\) | ||||
0.168917 | + | 0.985630i | \(0.445973\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.31088 | 0.169737 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.4136 | 0.428264 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −55.8670 | −1.78188 | −0.890941 | − | 0.454119i | \(-0.849954\pi\) | ||||
−0.890941 | + | 0.454119i | \(0.849954\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.57040 | −0.113762 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.9840 | 0.349625 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.17619 | 0.0374008 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.0354 | 1.58943 | 0.794713 | − | 0.606985i | \(-0.207621\pi\) | ||||
0.794713 | + | 0.606985i | \(0.207621\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −69.1355 | −2.19395 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.0824 | −0.319634 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.5474 | −1.15747 | −0.578734 | − | 0.815516i | \(-0.696453\pi\) | ||||
−0.578734 | + | 0.815516i | \(0.696453\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.30825 | 0.199584 |
(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 | 6160.2.a.bd.1.1 | 3 | ||
4.3 | odd | 2 | 3080.2.a.m.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3080.2.a.m.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
6160.2.a.bd.1.1 | 3 | 1.1 | even | 1 | trivial |