Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.6988960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 22x^{4} - 11x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 693) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.80692\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.80692 | −1.27769 | −0.638844 | − | 0.769336i | \(-0.720587\pi\) | ||||
−0.638844 | + | 0.769336i | \(0.720587\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.26498 | 0.632489 | ||||||||
\(5\) | 2.14896 | 0.961045 | 0.480522 | − | 0.876982i | \(-0.340447\pi\) | ||||
0.480522 | + | 0.876982i | \(0.340447\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.32813 | 0.469565 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.88301 | −1.22792 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.66481 | 1.01644 | 0.508218 | − | 0.861229i | \(-0.330305\pi\) | ||||
0.508218 | + | 0.861229i | \(0.330305\pi\) | |||||||
\(14\) | −1.80692 | −0.482921 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.92979 | −1.23245 | ||||||||
\(17\) | −1.89145 | −0.458743 | −0.229371 | − | 0.973339i | \(-0.573667\pi\) | ||||
−0.229371 | + | 0.973339i | \(0.573667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.44661 | −1.02012 | −0.510061 | − | 0.860138i | \(-0.670377\pi\) | ||||
−0.510061 | + | 0.860138i | \(0.670377\pi\) | |||||||
\(20\) | 2.71839 | 0.607850 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.20938 | −1.08623 | −0.543116 | − | 0.839658i | \(-0.682756\pi\) | ||||
−0.543116 | + | 0.839658i | \(0.682756\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.381966 | −0.0763932 | ||||||||
\(26\) | −6.62204 | −1.29869 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.26498 | 0.239058 | ||||||||
\(29\) | 3.76049 | 0.698306 | 0.349153 | − | 0.937066i | \(-0.386469\pi\) | ||||
0.349153 | + | 0.937066i | \(0.386469\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.21054 | 0.397025 | 0.198512 | − | 0.980098i | \(-0.436389\pi\) | ||||
0.198512 | + | 0.980098i | \(0.436389\pi\) | |||||||
\(32\) | 6.25149 | 1.10512 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.41770 | 0.586131 | ||||||||
\(35\) | 2.14896 | 0.363241 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.31175 | −1.36644 | −0.683222 | − | 0.730211i | \(-0.739422\pi\) | ||||
−0.683222 | + | 0.730211i | \(0.739422\pi\) | |||||||
\(38\) | 8.03469 | 1.30340 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.85410 | 0.451273 | ||||||||
\(41\) | −0.0621247 | −0.00970224 | −0.00485112 | − | 0.999988i | \(-0.501544\pi\) | ||||
−0.00485112 | + | 0.999988i | \(0.501544\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.99443 | 1.37164 | 0.685819 | − | 0.727772i | \(-0.259444\pi\) | ||||
0.685819 | + | 0.727772i | \(0.259444\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.41297 | 1.38787 | ||||||||
\(47\) | 12.3547 | 1.80212 | 0.901061 | − | 0.433693i | \(-0.142790\pi\) | ||||
0.901061 | + | 0.433693i | \(0.142790\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.690184 | 0.0976067 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.63590 | 0.642884 | ||||||||
\(53\) | −7.01020 | −0.962925 | −0.481462 | − | 0.876467i | \(-0.659894\pi\) | ||||
−0.481462 | + | 0.876467i | \(0.659894\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.32813 | 0.177479 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.79493 | −0.892218 | ||||||||
\(59\) | −12.0268 | −1.56576 | −0.782879 | − | 0.622174i | \(-0.786249\pi\) | ||||
−0.782879 | + | 0.622174i | \(0.786249\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.13486 | −0.657451 | −0.328725 | − | 0.944426i | \(-0.606619\pi\) | ||||
−0.328725 | + | 0.944426i | \(0.606619\pi\) | |||||||
\(62\) | −3.99428 | −0.507274 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.43640 | −0.179550 | ||||||||
\(65\) | 7.87553 | 0.976840 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.38744 | −1.14686 | −0.573429 | − | 0.819255i | \(-0.694387\pi\) | ||||
−0.573429 | + | 0.819255i | \(0.694387\pi\) | |||||||
\(68\) | −2.39264 | −0.290150 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.88301 | −0.464109 | ||||||||
\(71\) | −4.35232 | −0.516525 | −0.258262 | − | 0.966075i | \(-0.583150\pi\) | ||||
−0.258262 | + | 0.966075i | \(0.583150\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.65242 | −0.895647 | −0.447824 | − | 0.894122i | \(-0.647801\pi\) | ||||
−0.447824 | + | 0.894122i | \(0.647801\pi\) | |||||||
\(74\) | 15.0187 | 1.74589 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.62486 | −0.645216 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.1679 | −1.81904 | −0.909518 | − | 0.415665i | \(-0.863549\pi\) | ||||
−0.909518 | + | 0.415665i | \(0.863549\pi\) | |||||||
\(80\) | −10.5939 | −1.18444 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.112255 | 0.0123964 | ||||||||
\(83\) | 7.24748 | 0.795514 | 0.397757 | − | 0.917491i | \(-0.369789\pi\) | ||||
0.397757 | + | 0.917491i | \(0.369789\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.06464 | −0.440872 | ||||||||
\(86\) | −16.2523 | −1.75253 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.68300 | −0.708397 | −0.354198 | − | 0.935170i | \(-0.615246\pi\) | ||||
−0.354198 | + | 0.935170i | \(0.615246\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.66481 | 0.384176 | ||||||||
\(92\) | −6.58975 | −0.687029 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −22.3240 | −2.30255 | ||||||||
\(95\) | −9.55559 | −0.980383 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.1033 | −1.33044 | −0.665219 | − | 0.746648i | \(-0.731662\pi\) | ||||
−0.665219 | + | 0.746648i | \(0.731662\pi\) | |||||||
\(98\) | −1.80692 | −0.182527 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.483178 | −0.0483178 | ||||||||
\(101\) | −1.24739 | −0.124120 | −0.0620598 | − | 0.998072i | \(-0.519767\pi\) | ||||
−0.0620598 | + | 0.998072i | \(0.519767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.9689 | −1.47493 | −0.737465 | − | 0.675385i | \(-0.763977\pi\) | ||||
−0.737465 | + | 0.675385i | \(0.763977\pi\) | |||||||
\(104\) | 4.86735 | 0.477283 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.6669 | 1.23032 | ||||||||
\(107\) | 10.2458 | 0.990496 | 0.495248 | − | 0.868752i | \(-0.335077\pi\) | ||||
0.495248 | + | 0.868752i | \(0.335077\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.39172 | −0.324868 | −0.162434 | − | 0.986719i | \(-0.551934\pi\) | ||||
−0.162434 | + | 0.986719i | \(0.551934\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.92979 | −0.465821 | ||||||||
\(113\) | 8.21990 | 0.773264 | 0.386632 | − | 0.922234i | \(-0.373638\pi\) | ||||
0.386632 | + | 0.922234i | \(0.373638\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.1948 | −1.04392 | ||||||||
\(116\) | 4.75694 | 0.441671 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 21.7315 | 2.00055 | ||||||||
\(119\) | −1.89145 | −0.173389 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 9.27830 | 0.840018 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.79628 | 0.251114 | ||||||||
\(125\) | −11.5656 | −1.03446 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.25941 | 0.289226 | 0.144613 | − | 0.989488i | \(-0.453806\pi\) | ||||
0.144613 | + | 0.989488i | \(0.453806\pi\) | |||||||
\(128\) | −9.90751 | −0.875709 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −14.2305 | −1.24810 | ||||||||
\(131\) | −0.349304 | −0.0305189 | −0.0152594 | − | 0.999884i | \(-0.504857\pi\) | ||||
−0.0152594 | + | 0.999884i | \(0.504857\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.44661 | −0.385570 | ||||||||
\(134\) | 16.9624 | 1.46533 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.51209 | −0.215410 | ||||||||
\(137\) | −0.776324 | −0.0663258 | −0.0331629 | − | 0.999450i | \(-0.510558\pi\) | ||||
−0.0331629 | + | 0.999450i | \(0.510558\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.76940 | −0.743811 | −0.371906 | − | 0.928271i | \(-0.621295\pi\) | ||||
−0.371906 | + | 0.928271i | \(0.621295\pi\) | |||||||
\(140\) | 2.71839 | 0.229746 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.86431 | 0.659958 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.08116 | 0.671104 | ||||||||
\(146\) | 13.8273 | 1.14436 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.5142 | −0.864260 | ||||||||
\(149\) | 2.71490 | 0.222413 | 0.111206 | − | 0.993797i | \(-0.464529\pi\) | ||||
0.111206 | + | 0.993797i | \(0.464529\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.67720 | 0.299247 | 0.149623 | − | 0.988743i | \(-0.452194\pi\) | ||||
0.149623 | + | 0.988743i | \(0.452194\pi\) | |||||||
\(152\) | −5.90568 | −0.479014 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.75037 | 0.381559 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.0688 | 1.68148 | 0.840738 | − | 0.541443i | \(-0.182122\pi\) | ||||
0.840738 | + | 0.541443i | \(0.182122\pi\) | |||||||
\(158\) | 29.2143 | 2.32416 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 13.4342 | 1.06207 | ||||||||
\(161\) | −5.20938 | −0.410557 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.9490 | −1.32755 | −0.663774 | − | 0.747933i | \(-0.731046\pi\) | ||||
−0.663774 | + | 0.747933i | \(0.731046\pi\) | |||||||
\(164\) | −0.0785863 | −0.00613656 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.0956 | −1.01642 | ||||||||
\(167\) | 15.7297 | 1.21720 | 0.608599 | − | 0.793478i | \(-0.291732\pi\) | ||||
0.608599 | + | 0.793478i | \(0.291732\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.430832 | 0.0331409 | ||||||||
\(170\) | 7.34450 | 0.563298 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.3777 | 0.867545 | ||||||||
\(173\) | −9.79142 | −0.744428 | −0.372214 | − | 0.928147i | \(-0.621401\pi\) | ||||
−0.372214 | + | 0.928147i | \(0.621401\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.381966 | −0.0288739 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.0757 | 0.905111 | ||||||||
\(179\) | 13.4597 | 1.00603 | 0.503013 | − | 0.864279i | \(-0.332225\pi\) | ||||
0.503013 | + | 0.864279i | \(0.332225\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.7516 | −1.17081 | −0.585404 | − | 0.810742i | \(-0.699064\pi\) | ||||
−0.585404 | + | 0.810742i | \(0.699064\pi\) | |||||||
\(182\) | −6.62204 | −0.490858 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.91874 | −0.510057 | ||||||||
\(185\) | −17.8616 | −1.31321 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 15.6284 | 1.13982 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.2662 | 1.25262 | ||||||||
\(191\) | −9.10153 | −0.658563 | −0.329282 | − | 0.944232i | \(-0.606807\pi\) | ||||
−0.329282 | + | 0.944232i | \(0.606807\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.3475 | −1.03275 | −0.516377 | − | 0.856361i | \(-0.672720\pi\) | ||||
−0.516377 | + | 0.856361i | \(0.672720\pi\) | |||||||
\(194\) | 23.6767 | 1.69989 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.26498 | 0.0903555 | ||||||||
\(197\) | 20.6333 | 1.47006 | 0.735029 | − | 0.678035i | \(-0.237168\pi\) | ||||
0.735029 | + | 0.678035i | \(0.237168\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.5733 | 1.38751 | 0.693755 | − | 0.720211i | \(-0.255955\pi\) | ||||
0.693755 | + | 0.720211i | \(0.255955\pi\) | |||||||
\(200\) | −0.507301 | −0.0358716 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.25393 | 0.158586 | ||||||||
\(203\) | 3.76049 | 0.263935 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.133503 | −0.00932429 | ||||||||
\(206\) | 27.0477 | 1.88450 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −18.0667 | −1.25270 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.1880 | −0.701371 | −0.350685 | − | 0.936493i | \(-0.614051\pi\) | ||||
−0.350685 | + | 0.936493i | \(0.614051\pi\) | |||||||
\(212\) | −8.86774 | −0.609039 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.5133 | −1.26555 | ||||||||
\(215\) | 19.3287 | 1.31821 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.21054 | 0.150061 | ||||||||
\(218\) | 6.12858 | 0.415080 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.93179 | −0.466283 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.5903 | −1.64669 | −0.823345 | − | 0.567542i | \(-0.807895\pi\) | ||||
−0.823345 | + | 0.567542i | \(0.807895\pi\) | |||||||
\(224\) | 6.25149 | 0.417695 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.8527 | −0.987990 | ||||||||
\(227\) | −23.2865 | −1.54558 | −0.772789 | − | 0.634663i | \(-0.781139\pi\) | ||||
−0.772789 | + | 0.634663i | \(0.781139\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.48746 | −0.428703 | −0.214352 | − | 0.976757i | \(-0.568764\pi\) | ||||
−0.214352 | + | 0.976757i | \(0.568764\pi\) | |||||||
\(230\) | 20.2281 | 1.33380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.99443 | 0.327900 | ||||||||
\(233\) | 23.0166 | 1.50787 | 0.753935 | − | 0.656949i | \(-0.228154\pi\) | ||||
0.753935 | + | 0.656949i | \(0.228154\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 26.5498 | 1.73192 | ||||||||
\(236\) | −15.2136 | −0.990324 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.41770 | 0.221537 | ||||||||
\(239\) | −9.08553 | −0.587694 | −0.293847 | − | 0.955852i | \(-0.594936\pi\) | ||||
−0.293847 | + | 0.955852i | \(0.594936\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.60908 | −0.425728 | −0.212864 | − | 0.977082i | \(-0.568279\pi\) | ||||
−0.212864 | + | 0.977082i | \(0.568279\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.49548 | −0.415830 | ||||||||
\(245\) | 2.14896 | 0.137292 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.2960 | −1.03689 | ||||||||
\(248\) | 2.93589 | 0.186429 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 20.8982 | 1.32172 | ||||||||
\(251\) | 3.59669 | 0.227021 | 0.113511 | − | 0.993537i | \(-0.463790\pi\) | ||||
0.113511 | + | 0.993537i | \(0.463790\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.88950 | −0.369540 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.7749 | 1.29843 | ||||||||
\(257\) | −8.69374 | −0.542301 | −0.271150 | − | 0.962537i | \(-0.587404\pi\) | ||||
−0.271150 | + | 0.962537i | \(0.587404\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.31175 | −0.516467 | ||||||||
\(260\) | 9.96237 | 0.617840 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.631167 | 0.0389936 | ||||||||
\(263\) | 23.6423 | 1.45785 | 0.728925 | − | 0.684594i | \(-0.240020\pi\) | ||||
0.728925 | + | 0.684594i | \(0.240020\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.0646 | −0.925414 | ||||||||
\(266\) | 8.03469 | 0.492638 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.8749 | −0.725375 | ||||||||
\(269\) | 11.9533 | 0.728808 | 0.364404 | − | 0.931241i | \(-0.381273\pi\) | ||||
0.364404 | + | 0.931241i | \(0.381273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.7131 | 1.74420 | 0.872099 | − | 0.489330i | \(-0.162758\pi\) | ||||
0.872099 | + | 0.489330i | \(0.162758\pi\) | |||||||
\(272\) | 9.32442 | 0.565376 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.40276 | 0.0847438 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.6358 | −0.939464 | −0.469732 | − | 0.882809i | \(-0.655650\pi\) | ||||
−0.469732 | + | 0.882809i | \(0.655650\pi\) | |||||||
\(278\) | 15.8457 | 0.950359 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.85410 | 0.170565 | ||||||||
\(281\) | −16.2703 | −0.970607 | −0.485304 | − | 0.874346i | \(-0.661291\pi\) | ||||
−0.485304 | + | 0.874346i | \(0.661291\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.18428 | 0.129842 | 0.0649209 | − | 0.997890i | \(-0.479321\pi\) | ||||
0.0649209 | + | 0.997890i | \(0.479321\pi\) | |||||||
\(284\) | −5.50558 | −0.326696 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.0621247 | −0.00366710 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.4224 | −0.789555 | ||||||||
\(290\) | −14.6020 | −0.857462 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.68013 | −0.566487 | ||||||||
\(293\) | −12.3305 | −0.720353 | −0.360176 | − | 0.932884i | \(-0.617283\pi\) | ||||
−0.360176 | + | 0.932884i | \(0.617283\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −25.8451 | −1.50476 | ||||||||
\(296\) | −11.0391 | −0.641634 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.90561 | −0.284174 | ||||||||
\(299\) | −19.0914 | −1.10408 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.99443 | 0.518430 | ||||||||
\(302\) | −6.64443 | −0.382344 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 21.9208 | 1.25725 | ||||||||
\(305\) | −11.0346 | −0.631840 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.73840 | 0.0992160 | 0.0496080 | − | 0.998769i | \(-0.484203\pi\) | ||||
0.0496080 | + | 0.998769i | \(0.484203\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.58355 | −0.487513 | ||||||||
\(311\) | 11.2208 | 0.636273 | 0.318137 | − | 0.948045i | \(-0.396943\pi\) | ||||
0.318137 | + | 0.948045i | \(0.396943\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.5442 | 1.66994 | 0.834970 | − | 0.550296i | \(-0.185485\pi\) | ||||
0.834970 | + | 0.550296i | \(0.185485\pi\) | |||||||
\(314\) | −38.0698 | −2.14840 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.4521 | −1.15052 | ||||||||
\(317\) | 8.53297 | 0.479259 | 0.239630 | − | 0.970864i | \(-0.422974\pi\) | ||||
0.239630 | + | 0.970864i | \(0.422974\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −3.08677 | −0.172556 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.41297 | 0.524564 | ||||||||
\(323\) | 8.41052 | 0.467974 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.39983 | −0.0776488 | ||||||||
\(326\) | 30.6256 | 1.69619 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.0825097 | −0.00455583 | ||||||||
\(329\) | 12.3547 | 0.681138 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.22164 | 0.177078 | 0.0885388 | − | 0.996073i | \(-0.471780\pi\) | ||||
0.0885388 | + | 0.996073i | \(0.471780\pi\) | |||||||
\(332\) | 9.16789 | 0.503153 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −28.4223 | −1.55520 | ||||||||
\(335\) | −20.1732 | −1.10218 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.52393 | 0.191961 | 0.0959803 | − | 0.995383i | \(-0.469401\pi\) | ||||
0.0959803 | + | 0.995383i | \(0.469401\pi\) | |||||||
\(338\) | −0.778481 | −0.0423438 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.14168 | −0.278847 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 11.9458 | 0.644073 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.6924 | 0.951148 | ||||||||
\(347\) | 4.90171 | 0.263138 | 0.131569 | − | 0.991307i | \(-0.457999\pi\) | ||||
0.131569 | + | 0.991307i | \(0.457999\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.5598 | 0.618780 | 0.309390 | − | 0.950935i | \(-0.399875\pi\) | ||||
0.309390 | + | 0.950935i | \(0.399875\pi\) | |||||||
\(350\) | 0.690184 | 0.0368919 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.5076 | −1.57053 | −0.785264 | − | 0.619161i | \(-0.787473\pi\) | ||||
−0.785264 | + | 0.619161i | \(0.787473\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.35296 | −0.496404 | ||||||||
\(356\) | −8.45385 | −0.448053 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −24.3207 | −1.28539 | ||||||||
\(359\) | −7.57351 | −0.399715 | −0.199857 | − | 0.979825i | \(-0.564048\pi\) | ||||
−0.199857 | + | 0.979825i | \(0.564048\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.772330 | 0.0406490 | ||||||||
\(362\) | 28.4620 | 1.49593 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.63590 | 0.242987 | ||||||||
\(365\) | −16.4447 | −0.860757 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.52922 | −0.497421 | −0.248711 | − | 0.968578i | \(-0.580007\pi\) | ||||
−0.248711 | + | 0.968578i | \(0.580007\pi\) | |||||||
\(368\) | 25.6812 | 1.33872 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 32.2746 | 1.67788 | ||||||||
\(371\) | −7.01020 | −0.363951 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.3921 | −0.900527 | −0.450264 | − | 0.892896i | \(-0.648670\pi\) | ||||
−0.450264 | + | 0.892896i | \(0.648670\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.4087 | 0.846213 | ||||||||
\(377\) | 13.7815 | 0.709783 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.3456 | 0.942349 | 0.471175 | − | 0.882040i | \(-0.343830\pi\) | ||||
0.471175 | + | 0.882040i | \(0.343830\pi\) | |||||||
\(380\) | −12.0876 | −0.620081 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.4458 | 0.841439 | ||||||||
\(383\) | 2.83652 | 0.144940 | 0.0724698 | − | 0.997371i | \(-0.476912\pi\) | ||||
0.0724698 | + | 0.997371i | \(0.476912\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.9248 | 1.31954 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.5754 | −0.841487 | ||||||||
\(389\) | 20.6813 | 1.04858 | 0.524291 | − | 0.851539i | \(-0.324330\pi\) | ||||
0.524291 | + | 0.851539i | \(0.324330\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.85327 | 0.498301 | ||||||||
\(392\) | 1.32813 | 0.0670807 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −37.2827 | −1.87828 | ||||||||
\(395\) | −34.7443 | −1.74817 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.6868 | 1.33937 | 0.669685 | − | 0.742645i | \(-0.266429\pi\) | ||||
0.669685 | + | 0.742645i | \(0.266429\pi\) | |||||||
\(398\) | −35.3674 | −1.77281 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.88301 | 0.0941506 | ||||||||
\(401\) | 12.6012 | 0.629272 | 0.314636 | − | 0.949212i | \(-0.398117\pi\) | ||||
0.314636 | + | 0.949212i | \(0.398117\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.10121 | 0.403550 | ||||||||
\(404\) | −1.57792 | −0.0785043 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.79493 | −0.337227 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.0123946 | 0.000612872 0 | 0.000306436 | − | 1.00000i | \(-0.499902\pi\) | ||||
0.000306436 | 1.00000i | \(0.499902\pi\) | ||||||||
\(410\) | 0.241231 | 0.0119135 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −18.9353 | −0.932876 | ||||||||
\(413\) | −12.0268 | −0.591801 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.5745 | 0.764524 | ||||||||
\(416\) | 22.9105 | 1.12328 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.9560 | 1.61001 | 0.805003 | − | 0.593271i | \(-0.202164\pi\) | ||||
0.805003 | + | 0.593271i | \(0.202164\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.3708 | −1.33397 | −0.666986 | − | 0.745070i | \(-0.732416\pi\) | ||||
−0.666986 | + | 0.745070i | \(0.732416\pi\) | |||||||
\(422\) | 18.4089 | 0.896134 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.31046 | −0.452156 | ||||||||
\(425\) | 0.722468 | 0.0350448 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.13486 | −0.248493 | ||||||||
\(428\) | 12.9607 | 0.626478 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −34.9255 | −1.68426 | ||||||||
\(431\) | 24.7125 | 1.19036 | 0.595180 | − | 0.803593i | \(-0.297081\pi\) | ||||
0.595180 | + | 0.803593i | \(0.297081\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.4299 | −1.31820 | −0.659099 | − | 0.752056i | \(-0.729062\pi\) | ||||
−0.659099 | + | 0.752056i | \(0.729062\pi\) | |||||||
\(434\) | −3.99428 | −0.191732 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.29044 | −0.205475 | ||||||||
\(437\) | 23.1641 | 1.10809 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.36929 | −0.160807 | −0.0804037 | − | 0.996762i | \(-0.525621\pi\) | ||||
−0.0804037 | + | 0.996762i | \(0.525621\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.5252 | 0.595764 | ||||||||
\(443\) | −7.97012 | −0.378672 | −0.189336 | − | 0.981912i | \(-0.560634\pi\) | ||||
−0.189336 | + | 0.981912i | \(0.560634\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.3615 | −0.680801 | ||||||||
\(446\) | 44.4329 | 2.10396 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.43640 | −0.0678636 | ||||||||
\(449\) | −5.55142 | −0.261988 | −0.130994 | − | 0.991383i | \(-0.541817\pi\) | ||||
−0.130994 | + | 0.991383i | \(0.541817\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 10.3980 | 0.489080 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 42.0769 | 1.97477 | ||||||||
\(455\) | 7.87553 | 0.369211 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.7915 | 0.785471 | 0.392735 | − | 0.919651i | \(-0.371529\pi\) | ||||
0.392735 | + | 0.919651i | \(0.371529\pi\) | |||||||
\(458\) | 11.7223 | 0.547749 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14.1611 | −0.660266 | ||||||||
\(461\) | −17.3351 | −0.807376 | −0.403688 | − | 0.914897i | \(-0.632272\pi\) | ||||
−0.403688 | + | 0.914897i | \(0.632272\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.9175 | 1.15801 | 0.579006 | − | 0.815323i | \(-0.303441\pi\) | ||||
0.579006 | + | 0.815323i | \(0.303441\pi\) | |||||||
\(464\) | −18.5384 | −0.860625 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −41.5893 | −1.92659 | ||||||||
\(467\) | 22.4093 | 1.03698 | 0.518490 | − | 0.855083i | \(-0.326494\pi\) | ||||
0.518490 | + | 0.855083i | \(0.326494\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.38744 | −0.433472 | ||||||||
\(470\) | −47.9735 | −2.21285 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.9732 | −0.735225 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.69845 | 0.0779304 | ||||||||
\(476\) | −2.39264 | −0.109666 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16.4169 | 0.750890 | ||||||||
\(479\) | −3.20429 | −0.146408 | −0.0732039 | − | 0.997317i | \(-0.523322\pi\) | ||||
−0.0732039 | + | 0.997317i | \(0.523322\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.4610 | −1.38890 | ||||||||
\(482\) | 11.9421 | 0.543948 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −28.1585 | −1.27861 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.39844 | 0.380570 | 0.190285 | − | 0.981729i | \(-0.439059\pi\) | ||||
0.190285 | + | 0.981729i | \(0.439059\pi\) | |||||||
\(488\) | −6.81976 | −0.308716 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.88301 | −0.175417 | ||||||||
\(491\) | −34.7888 | −1.57000 | −0.784998 | − | 0.619498i | \(-0.787336\pi\) | ||||
−0.784998 | + | 0.619498i | \(0.787336\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.11277 | −0.320343 | ||||||||
\(494\) | 29.4456 | 1.32482 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.8975 | −0.489312 | ||||||||
\(497\) | −4.35232 | −0.195228 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.1305 | 0.677333 | 0.338667 | − | 0.940906i | \(-0.390024\pi\) | ||||
0.338667 | + | 0.940906i | \(0.390024\pi\) | |||||||
\(500\) | −14.6303 | −0.654285 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.49895 | −0.290063 | ||||||||
\(503\) | −36.7358 | −1.63797 | −0.818985 | − | 0.573815i | \(-0.805463\pi\) | ||||
−0.818985 | + | 0.573815i | \(0.805463\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.68059 | −0.119285 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.12308 | 0.182932 | ||||||||
\(509\) | −31.2822 | −1.38656 | −0.693279 | − | 0.720669i | \(-0.743835\pi\) | ||||
−0.693279 | + | 0.720669i | \(0.743835\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.65242 | −0.338523 | ||||||||
\(512\) | −17.7237 | −0.783285 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.7089 | 0.692892 | ||||||||
\(515\) | −32.1676 | −1.41747 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 15.0187 | 0.659884 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.4597 | 0.458690 | ||||||||
\(521\) | −41.5773 | −1.82153 | −0.910767 | − | 0.412921i | \(-0.864509\pi\) | ||||
−0.910767 | + | 0.412921i | \(0.864509\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.4520 | 0.763122 | 0.381561 | − | 0.924344i | \(-0.375387\pi\) | ||||
0.381561 | + | 0.924344i | \(0.375387\pi\) | |||||||
\(524\) | −0.441862 | −0.0193028 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −42.7199 | −1.86268 | ||||||||
\(527\) | −4.18112 | −0.182132 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.13768 | 0.179899 | ||||||||
\(530\) | 27.2207 | 1.18239 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.62486 | −0.243869 | ||||||||
\(533\) | −0.227675 | −0.00986170 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.0178 | 0.951911 | ||||||||
\(536\) | −12.4677 | −0.538525 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −21.5988 | −0.931189 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.3372 | −1.17532 | −0.587659 | − | 0.809109i | \(-0.699950\pi\) | ||||
−0.587659 | + | 0.809109i | \(0.699950\pi\) | |||||||
\(542\) | −51.8825 | −2.22854 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −11.8244 | −0.506965 | ||||||||
\(545\) | −7.28867 | −0.312212 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.1721 | 1.33282 | 0.666411 | − | 0.745585i | \(-0.267830\pi\) | ||||
0.666411 | + | 0.745585i | \(0.267830\pi\) | |||||||
\(548\) | −0.982032 | −0.0419503 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.7214 | −0.712358 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.1679 | −0.687531 | ||||||||
\(554\) | 28.2527 | 1.20034 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.0931 | −0.470452 | ||||||||
\(557\) | −4.18066 | −0.177140 | −0.0885700 | − | 0.996070i | \(-0.528230\pi\) | ||||
−0.0885700 | + | 0.996070i | \(0.528230\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.9629 | 1.39418 | ||||||||
\(560\) | −10.5939 | −0.447675 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 29.3993 | 1.24013 | ||||||||
\(563\) | −24.7878 | −1.04468 | −0.522340 | − | 0.852737i | \(-0.674941\pi\) | ||||
−0.522340 | + | 0.852737i | \(0.674941\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.6643 | 0.743141 | ||||||||
\(566\) | −3.94682 | −0.165897 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.78045 | −0.242542 | ||||||||
\(569\) | 35.0889 | 1.47100 | 0.735502 | − | 0.677522i | \(-0.236946\pi\) | ||||
0.735502 | + | 0.677522i | \(0.236946\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.83359 | −0.285977 | −0.142988 | − | 0.989724i | \(-0.545671\pi\) | ||||
−0.142988 | + | 0.989724i | \(0.545671\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.112255 | 0.00468542 | ||||||||
\(575\) | 1.98981 | 0.0829807 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.3214 | −1.88675 | −0.943377 | − | 0.331721i | \(-0.892371\pi\) | ||||
−0.943377 | + | 0.331721i | \(0.892371\pi\) | |||||||
\(578\) | 24.2533 | 1.00881 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.2225 | 0.424465 | ||||||||
\(581\) | 7.24748 | 0.300676 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −10.1634 | −0.420565 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.2802 | 0.920387 | ||||||||
\(587\) | 44.8902 | 1.85282 | 0.926409 | − | 0.376518i | \(-0.122879\pi\) | ||||
0.926409 | + | 0.376518i | \(0.122879\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.82941 | −0.405014 | ||||||||
\(590\) | 46.7002 | 1.92262 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 40.9752 | 1.68407 | ||||||||
\(593\) | −38.8436 | −1.59512 | −0.797558 | − | 0.603242i | \(-0.793875\pi\) | ||||
−0.797558 | + | 0.603242i | \(0.793875\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.06464 | −0.166634 | ||||||||
\(596\) | 3.43428 | 0.140674 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 34.4967 | 1.41068 | ||||||||
\(599\) | −17.2289 | −0.703954 | −0.351977 | − | 0.936009i | \(-0.614490\pi\) | ||||
−0.351977 | + | 0.936009i | \(0.614490\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.0667 | 1.18565 | 0.592827 | − | 0.805330i | \(-0.298012\pi\) | ||||
0.592827 | + | 0.805330i | \(0.298012\pi\) | |||||||
\(602\) | −16.2523 | −0.662393 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.65158 | 0.189270 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.0011 | 0.974174 | 0.487087 | − | 0.873353i | \(-0.338059\pi\) | ||||
0.487087 | + | 0.873353i | \(0.338059\pi\) | |||||||
\(608\) | −27.7979 | −1.12736 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 19.9387 | 0.807294 | ||||||||
\(611\) | 45.2777 | 1.83174 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.4567 | 1.91676 | 0.958379 | − | 0.285498i | \(-0.0921589\pi\) | ||||
0.958379 | + | 0.285498i | \(0.0921589\pi\) | |||||||
\(614\) | −3.14117 | −0.126767 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.0679 | −0.566354 | −0.283177 | − | 0.959068i | \(-0.591388\pi\) | ||||
−0.283177 | + | 0.959068i | \(0.591388\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.1265 | 1.41185 | 0.705927 | − | 0.708284i | \(-0.250530\pi\) | ||||
0.705927 | + | 0.708284i | \(0.250530\pi\) | |||||||
\(620\) | 6.00910 | 0.241331 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −20.2751 | −0.812959 | ||||||||
\(623\) | −6.68300 | −0.267749 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.9443 | −0.917771 | ||||||||
\(626\) | −53.3842 | −2.13366 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 26.6516 | 1.06351 | ||||||||
\(629\) | 15.7212 | 0.626846 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.2530 | −1.40340 | −0.701700 | − | 0.712473i | \(-0.747575\pi\) | ||||
−0.701700 | + | 0.712473i | \(0.747575\pi\) | |||||||
\(632\) | −21.4731 | −0.854156 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.4184 | −0.612344 | ||||||||
\(635\) | 7.00434 | 0.277959 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.66481 | 0.145205 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21.2909 | −0.841595 | ||||||||
\(641\) | 36.1668 | 1.42850 | 0.714252 | − | 0.699889i | \(-0.246767\pi\) | ||||
0.714252 | + | 0.699889i | \(0.246767\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.33953 | −0.0922620 | −0.0461310 | − | 0.998935i | \(-0.514689\pi\) | ||||
−0.0461310 | + | 0.998935i | \(0.514689\pi\) | |||||||
\(644\) | −6.58975 | −0.259673 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.1972 | −0.597925 | ||||||||
\(647\) | 28.6902 | 1.12793 | 0.563965 | − | 0.825799i | \(-0.309275\pi\) | ||||
0.563965 | + | 0.825799i | \(0.309275\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.52939 | 0.0992109 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −21.4401 | −0.839659 | ||||||||
\(653\) | −35.8827 | −1.40420 | −0.702099 | − | 0.712079i | \(-0.747754\pi\) | ||||
−0.702099 | + | 0.712079i | \(0.747754\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.750641 | −0.0293300 | ||||||||
\(656\) | 0.306261 | 0.0119575 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −22.3240 | −0.870282 | ||||||||
\(659\) | −48.1529 | −1.87577 | −0.937885 | − | 0.346945i | \(-0.887219\pi\) | ||||
−0.937885 | + | 0.346945i | \(0.887219\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.9186 | −1.04701 | −0.523506 | − | 0.852022i | \(-0.675376\pi\) | ||||
−0.523506 | + | 0.852022i | \(0.675376\pi\) | |||||||
\(662\) | −5.82127 | −0.226250 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.62560 | 0.373546 | ||||||||
\(665\) | −9.55559 | −0.370550 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.5899 | −0.758523 | ||||||||
\(668\) | 19.8977 | 0.769864 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 36.4515 | 1.40825 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.53324 | 0.251838 | 0.125919 | − | 0.992041i | \(-0.459812\pi\) | ||||
0.125919 | + | 0.992041i | \(0.459812\pi\) | |||||||
\(674\) | −6.36747 | −0.245266 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.544993 | 0.0209613 | ||||||||
\(677\) | −41.9065 | −1.61060 | −0.805299 | − | 0.592869i | \(-0.797995\pi\) | ||||
−0.805299 | + | 0.592869i | \(0.797995\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.1033 | −0.502859 | ||||||||
\(680\) | −5.39838 | −0.207018 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.5429 | 0.671259 | 0.335630 | − | 0.941994i | \(-0.391051\pi\) | ||||
0.335630 | + | 0.941994i | \(0.391051\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.66829 | −0.0637421 | ||||||||
\(686\) | −1.80692 | −0.0689887 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −44.3406 | −1.69047 | ||||||||
\(689\) | −25.6910 | −0.978751 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.6341 | −1.39363 | −0.696813 | − | 0.717253i | \(-0.745399\pi\) | ||||
−0.696813 | + | 0.717253i | \(0.745399\pi\) | |||||||
\(692\) | −12.3859 | −0.470842 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.85703 | −0.336208 | ||||||||
\(695\) | −18.8451 | −0.714836 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.117505 | 0.00445083 | ||||||||
\(698\) | −20.8876 | −0.790608 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.483178 | −0.0182624 | ||||||||
\(701\) | −16.5248 | −0.624132 | −0.312066 | − | 0.950060i | \(-0.601021\pi\) | ||||
−0.312066 | + | 0.950060i | \(0.601021\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.9591 | 1.39394 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 53.3179 | 2.00665 | ||||||||
\(707\) | −1.24739 | −0.0469128 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.8668 | −0.671002 | −0.335501 | − | 0.942040i | \(-0.608906\pi\) | ||||
−0.335501 | + | 0.942040i | \(0.608906\pi\) | |||||||
\(710\) | 16.9001 | 0.634249 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.87590 | −0.332639 | ||||||||
\(713\) | −11.5156 | −0.431261 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 17.0262 | 0.636300 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.6848 | 0.510711 | ||||||||
\(719\) | 19.7323 | 0.735891 | 0.367945 | − | 0.929847i | \(-0.380061\pi\) | ||||
0.367945 | + | 0.929847i | \(0.380061\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.9689 | −0.557471 | ||||||||
\(722\) | −1.39554 | −0.0519367 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.9254 | −0.740522 | ||||||||
\(725\) | −1.43638 | −0.0533459 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.6895 | −1.06403 | −0.532017 | − | 0.846733i | \(-0.678566\pi\) | ||||
−0.532017 | + | 0.846733i | \(0.678566\pi\) | |||||||
\(728\) | 4.86735 | 0.180396 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 29.7144 | 1.09978 | ||||||||
\(731\) | −17.0125 | −0.629229 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.36355 | 0.198107 | 0.0990535 | − | 0.995082i | \(-0.468418\pi\) | ||||
0.0990535 | + | 0.995082i | \(0.468418\pi\) | |||||||
\(734\) | 17.2186 | 0.635549 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −32.5664 | −1.20041 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.1733 | −1.66173 | −0.830864 | − | 0.556476i | \(-0.812153\pi\) | ||||
−0.830864 | + | 0.556476i | \(0.812153\pi\) | |||||||
\(740\) | −22.5946 | −0.830593 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.6669 | 0.465017 | ||||||||
\(743\) | −19.8716 | −0.729020 | −0.364510 | − | 0.931199i | \(-0.618764\pi\) | ||||
−0.364510 | + | 0.931199i | \(0.618764\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.83421 | 0.213749 | ||||||||
\(746\) | 31.4262 | 1.15059 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.2458 | 0.374372 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.72318 | 0.135861 | 0.0679304 | − | 0.997690i | \(-0.478360\pi\) | ||||
0.0679304 | + | 0.997690i | \(0.478360\pi\) | |||||||
\(752\) | −60.9061 | −2.22102 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −24.9021 | −0.906882 | ||||||||
\(755\) | 7.90217 | 0.287589 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.2656 | 1.35444 | 0.677220 | − | 0.735780i | \(-0.263184\pi\) | ||||
0.677220 | + | 0.735780i | \(0.263184\pi\) | |||||||
\(758\) | −33.1491 | −1.20403 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.6911 | −0.460354 | ||||||||
\(761\) | −21.3908 | −0.775416 | −0.387708 | − | 0.921782i | \(-0.626733\pi\) | ||||
−0.387708 | + | 0.921782i | \(0.626733\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.39172 | −0.122788 | ||||||||
\(764\) | −11.5132 | −0.416534 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.12539 | −0.185188 | ||||||||
\(767\) | −44.0760 | −1.59149 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.2160 | 0.729006 | 0.364503 | − | 0.931202i | \(-0.381239\pi\) | ||||
0.364503 | + | 0.931202i | \(0.381239\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18.1492 | −0.653206 | ||||||||
\(773\) | −39.5108 | −1.42111 | −0.710553 | − | 0.703644i | \(-0.751555\pi\) | ||||
−0.710553 | + | 0.703644i | \(0.751555\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.844351 | −0.0303300 | ||||||||
\(776\) | −17.4029 | −0.624728 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −37.3695 | −1.33976 | ||||||||
\(779\) | 0.276244 | 0.00989747 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −17.8041 | −0.636674 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.92979 | −0.176064 | ||||||||
\(785\) | 45.2761 | 1.61597 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.2457 | 1.22073 | 0.610364 | − | 0.792121i | \(-0.291023\pi\) | ||||
0.610364 | + | 0.792121i | \(0.291023\pi\) | |||||||
\(788\) | 26.1006 | 0.929795 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 62.7803 | 2.23362 | ||||||||
\(791\) | 8.21990 | 0.292266 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.8183 | −0.668256 | ||||||||
\(794\) | −48.2210 | −1.71130 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.7597 | 0.877585 | ||||||||
\(797\) | 16.1138 | 0.570779 | 0.285390 | − | 0.958412i | \(-0.407877\pi\) | ||||
0.285390 | + | 0.958412i | \(0.407877\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.3683 | −0.826710 | ||||||||
\(800\) | −2.38786 | −0.0844235 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22.7694 | −0.804014 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.1948 | −0.394564 | ||||||||
\(806\) | −14.6383 | −0.515611 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.65669 | −0.0582823 | ||||||||
\(809\) | 7.67619 | 0.269880 | 0.134940 | − | 0.990854i | \(-0.456916\pi\) | ||||
0.134940 | + | 0.990854i | \(0.456916\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.03802 | 0.0364498 | 0.0182249 | − | 0.999834i | \(-0.494199\pi\) | ||||
0.0182249 | + | 0.999834i | \(0.494199\pi\) | |||||||
\(812\) | 4.75694 | 0.166936 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −36.4228 | −1.27583 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −39.9947 | −1.39924 | ||||||||
\(818\) | −0.0223961 | −0.000783060 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.168879 | −0.00589750 | ||||||||
\(821\) | −7.44620 | −0.259874 | −0.129937 | − | 0.991522i | \(-0.541478\pi\) | ||||
−0.129937 | + | 0.991522i | \(0.541478\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.94956 | 0.102815 | 0.0514076 | − | 0.998678i | \(-0.483629\pi\) | ||||
0.0514076 | + | 0.998678i | \(0.483629\pi\) | |||||||
\(824\) | −19.8807 | −0.692576 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 21.7315 | 0.756137 | ||||||||
\(827\) | 42.6293 | 1.48237 | 0.741183 | − | 0.671303i | \(-0.234265\pi\) | ||||
0.741183 | + | 0.671303i | \(0.234265\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.02334 | 0.209199 | 0.104600 | − | 0.994514i | \(-0.466644\pi\) | ||||
0.104600 | + | 0.994514i | \(0.466644\pi\) | |||||||
\(830\) | −28.1420 | −0.976824 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.26414 | −0.182501 | ||||||||
\(833\) | −1.89145 | −0.0655347 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.8025 | 1.16978 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −59.5490 | −2.05709 | ||||||||
\(839\) | 2.90271 | 0.100213 | 0.0501064 | − | 0.998744i | \(-0.484044\pi\) | ||||
0.0501064 | + | 0.998744i | \(0.484044\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.8587 | −0.512368 | ||||||||
\(842\) | 49.4570 | 1.70440 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.8876 | −0.443609 | ||||||||
\(845\) | 0.925842 | 0.0318499 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 34.5588 | 1.18675 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.30545 | −0.0447764 | ||||||||
\(851\) | 43.2991 | 1.48427 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.92232 | 0.0658191 | 0.0329095 | − | 0.999458i | \(-0.489523\pi\) | ||||
0.0329095 | + | 0.999458i | \(0.489523\pi\) | |||||||
\(854\) | 9.27830 | 0.317497 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.6077 | 0.465103 | ||||||||
\(857\) | −55.9198 | −1.91019 | −0.955093 | − | 0.296308i | \(-0.904245\pi\) | ||||
−0.955093 | + | 0.296308i | \(0.904245\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.723243 | 0.0246767 | 0.0123384 | − | 0.999924i | \(-0.496072\pi\) | ||||
0.0123384 | + | 0.999924i | \(0.496072\pi\) | |||||||
\(860\) | 24.4503 | 0.833750 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −44.6536 | −1.52091 | ||||||||
\(863\) | 41.6422 | 1.41752 | 0.708759 | − | 0.705451i | \(-0.249256\pi\) | ||||
0.708759 | + | 0.705451i | \(0.249256\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.0414 | −0.715429 | ||||||||
\(866\) | 49.5638 | 1.68425 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.79628 | 0.0949121 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.4032 | −1.16571 | ||||||||
\(872\) | −4.50464 | −0.152546 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −41.8558 | −1.41579 | ||||||||
\(875\) | −11.5656 | −0.390990 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.1509 | −1.35580 | −0.677900 | − | 0.735154i | \(-0.737110\pi\) | ||||
−0.677900 | + | 0.735154i | \(0.737110\pi\) | |||||||
\(878\) | 6.08805 | 0.205462 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.28404 | 0.110642 | 0.0553210 | − | 0.998469i | \(-0.482382\pi\) | ||||
0.0553210 | + | 0.998469i | \(0.482382\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.76427 | −0.160331 | −0.0801653 | − | 0.996782i | \(-0.525545\pi\) | ||||
−0.0801653 | + | 0.996782i | \(0.525545\pi\) | |||||||
\(884\) | −8.76855 | −0.294918 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.4014 | 0.483825 | ||||||||
\(887\) | −8.82252 | −0.296231 | −0.148116 | − | 0.988970i | \(-0.547321\pi\) | ||||
−0.148116 | + | 0.988970i | \(0.547321\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.25941 | 0.109317 | ||||||||
\(890\) | 25.9502 | 0.869852 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −31.1062 | −1.04151 | ||||||||
\(893\) | −54.9366 | −1.83838 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.9244 | 0.966835 | ||||||||
\(896\) | −9.90751 | −0.330987 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.0310 | 0.334739 | ||||||||
\(899\) | 8.31273 | 0.277245 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.2594 | 0.441735 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.9171 | 0.363098 | ||||||||
\(905\) | −33.8496 | −1.12520 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.1246 | −0.601816 | −0.300908 | − | 0.953653i | \(-0.597290\pi\) | ||||
−0.300908 | + | 0.953653i | \(0.597290\pi\) | |||||||
\(908\) | −29.4569 | −0.977560 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −14.2305 | −0.471736 | ||||||||
\(911\) | 40.4176 | 1.33910 | 0.669548 | − | 0.742769i | \(-0.266488\pi\) | ||||
0.669548 | + | 0.742769i | \(0.266488\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −30.3409 | −1.00359 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.20648 | −0.271150 | ||||||||
\(917\) | −0.349304 | −0.0115350 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.0293 | −0.957587 | −0.478794 | − | 0.877928i | \(-0.658926\pi\) | ||||
−0.478794 | + | 0.877928i | \(0.658926\pi\) | |||||||
\(920\) | −14.8681 | −0.490187 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 31.3232 | 1.03158 | ||||||||
\(923\) | −15.9504 | −0.525014 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.17481 | 0.104387 | ||||||||
\(926\) | −45.0240 | −1.47958 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 23.5087 | 0.771711 | ||||||||
\(929\) | 21.6963 | 0.711832 | 0.355916 | − | 0.934518i | \(-0.384169\pi\) | ||||
0.355916 | + | 0.934518i | \(0.384169\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.44661 | −0.145732 | ||||||||
\(932\) | 29.1155 | 0.953710 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −40.4920 | −1.32494 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.4997 | 1.61709 | 0.808543 | − | 0.588438i | \(-0.200257\pi\) | ||||
0.808543 | + | 0.588438i | \(0.200257\pi\) | |||||||
\(938\) | 16.9624 | 0.553842 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 33.5849 | 1.09542 | ||||||||
\(941\) | 59.9530 | 1.95441 | 0.977206 | − | 0.212293i | \(-0.0680930\pi\) | ||||
0.977206 | + | 0.212293i | \(0.0680930\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.323631 | 0.0105389 | ||||||||
\(944\) | 59.2896 | 1.92971 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −59.3880 | −1.92985 | −0.964925 | − | 0.262526i | \(-0.915445\pi\) | ||||
−0.964925 | + | 0.262526i | \(0.915445\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.0446 | −0.910368 | ||||||||
\(950\) | −3.06898 | −0.0995708 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.51209 | −0.0814172 | ||||||||
\(953\) | 56.6435 | 1.83486 | 0.917432 | − | 0.397893i | \(-0.130258\pi\) | ||||
0.917432 | + | 0.397893i | \(0.130258\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.5588 | −0.632909 | ||||||||
\(956\) | −11.4930 | −0.371710 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.78992 | 0.187064 | ||||||||
\(959\) | −0.776324 | −0.0250688 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.1135 | −0.842371 | ||||||||
\(962\) | 55.0407 | 1.77458 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.36034 | −0.269268 | ||||||||
\(965\) | −30.8322 | −0.992523 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.51193 | −0.273725 | −0.136863 | − | 0.990590i | \(-0.543702\pi\) | ||||
−0.136863 | + | 0.990590i | \(0.543702\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 50.8803 | 1.63367 | ||||||||
\(971\) | −8.61967 | −0.276618 | −0.138309 | − | 0.990389i | \(-0.544167\pi\) | ||||
−0.138309 | + | 0.990389i | \(0.544167\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.76940 | −0.281134 | ||||||||
\(974\) | −15.1754 | −0.486250 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 25.3137 | 0.810273 | ||||||||
\(977\) | 34.3030 | 1.09745 | 0.548726 | − | 0.836002i | \(-0.315113\pi\) | ||||
0.548726 | + | 0.836002i | \(0.315113\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 2.71839 | 0.0868357 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 62.8607 | 2.00597 | ||||||||
\(983\) | −55.0178 | −1.75479 | −0.877397 | − | 0.479765i | \(-0.840722\pi\) | ||||
−0.877397 | + | 0.479765i | \(0.840722\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 44.3401 | 1.41279 | ||||||||
\(986\) | 12.8522 | 0.409299 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20.6140 | −0.655820 | ||||||||
\(989\) | −46.8554 | −1.48992 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.7838 | 1.35907 | 0.679536 | − | 0.733642i | \(-0.262181\pi\) | ||||
0.679536 | + | 0.733642i | \(0.262181\pi\) | |||||||
\(992\) | 13.8192 | 0.438759 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.86431 | 0.249441 | ||||||||
\(995\) | 42.0622 | 1.33346 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.5608 | −1.37958 | −0.689792 | − | 0.724007i | \(-0.742298\pi\) | ||||
−0.689792 | + | 0.724007i | \(0.742298\pi\) | |||||||
\(998\) | −27.3396 | −0.865421 | ||||||||
\(999\) | 0 | 0 |
(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 | 7623.2.a.cv.1.2 | 8 | ||
3.2 | odd | 2 | inner | 7623.2.a.cv.1.7 | 8 | ||
11.2 | odd | 10 | 693.2.m.h.631.1 | yes | 16 | ||
11.6 | odd | 10 | 693.2.m.h.190.1 | ✓ | 16 | ||
11.10 | odd | 2 | 7623.2.a.cu.1.7 | 8 | |||
33.2 | even | 10 | 693.2.m.h.631.4 | yes | 16 | ||
33.17 | even | 10 | 693.2.m.h.190.4 | yes | 16 | ||
33.32 | even | 2 | 7623.2.a.cu.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
693.2.m.h.190.1 | ✓ | 16 | 11.6 | odd | 10 | ||
693.2.m.h.190.4 | yes | 16 | 33.17 | even | 10 | ||
693.2.m.h.631.1 | yes | 16 | 11.2 | odd | 10 | ||
693.2.m.h.631.4 | yes | 16 | 33.2 | even | 10 | ||
7623.2.a.cu.1.2 | 8 | 33.32 | even | 2 | |||
7623.2.a.cu.1.7 | 8 | 11.10 | odd | 2 | |||
7623.2.a.cv.1.2 | 8 | 1.1 | even | 1 | trivial | ||
7623.2.a.cv.1.7 | 8 | 3.2 | odd | 2 | inner |