Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [520,2,Mod(1,520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("520.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 520 = 2^{3} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 520.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: | \(4.15222090511\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 520.1 |
$q$-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 | ||||||||
\(3\) | −2.44949 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.44949 | −1.34157 | −0.670786 | − | 0.741651i | \(-0.734043\pi\) | ||||
−0.670786 | + | 0.741651i | \(0.734043\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.44949 | −0.632456 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.89898 | 1.67325 | 0.836624 | − | 0.547777i | \(-0.184526\pi\) | ||||
0.836624 | + | 0.547777i | \(0.184526\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.449490 | 0.103120 | 0.0515600 | − | 0.998670i | \(-0.483581\pi\) | ||||
0.0515600 | + | 0.998670i | \(0.483581\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.89898 | −1.06904 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.44949 | 1.34481 | 0.672406 | − | 0.740183i | \(-0.265261\pi\) | ||||
0.672406 | + | 0.740183i | \(0.265261\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.44949 | −0.799152 | −0.399576 | − | 0.916700i | \(-0.630843\pi\) | ||||
−0.399576 | + | 0.916700i | \(0.630843\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.8990 | 1.89727 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | 0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.89898 | 0.805387 | 0.402694 | − | 0.915335i | \(-0.368074\pi\) | ||||
0.402694 | + | 0.915335i | \(0.368074\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.44949 | 0.392232 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.8990 | 1.70213 | 0.851067 | − | 0.525057i | \(-0.175956\pi\) | ||||
0.851067 | + | 0.525057i | \(0.175956\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.3485 | 1.73063 | 0.865313 | − | 0.501232i | \(-0.167120\pi\) | ||||
0.865313 | + | 0.501232i | \(0.167120\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00000 | 0.447214 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.00000 | −0.291730 | −0.145865 | − | 0.989305i | \(-0.546597\pi\) | ||||
−0.145865 | + | 0.989305i | \(0.546597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.8990 | −2.36633 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.10102 | 0.151237 | 0.0756184 | − | 0.997137i | \(-0.475907\pi\) | ||||
0.0756184 | + | 0.997137i | \(0.475907\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.44949 | −0.599969 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.10102 | −0.145834 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.34847 | 1.21707 | 0.608534 | − | 0.793528i | \(-0.291758\pi\) | ||||
0.608534 | + | 0.793528i | \(0.291758\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.79796 | −0.742353 | −0.371176 | − | 0.928562i | \(-0.621045\pi\) | ||||
−0.371176 | + | 0.928562i | \(0.621045\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.00000 | 0.755929 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.10102 | −0.623189 | −0.311594 | − | 0.950215i | \(-0.600863\pi\) | ||||
−0.311594 | + | 0.950215i | \(0.600863\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −15.7980 | −1.90185 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.55051 | −0.421368 | −0.210684 | − | 0.977554i | \(-0.567569\pi\) | ||||
−0.210684 | + | 0.977554i | \(0.567569\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.6969 | −1.72015 | −0.860073 | − | 0.510171i | \(-0.829582\pi\) | ||||
−0.860073 | + | 0.510171i | \(0.829582\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.44949 | −0.282843 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.89898 | −1.01413 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.89898 | 0.551178 | 0.275589 | − | 0.961276i | \(-0.411127\pi\) | ||||
0.275589 | + | 0.961276i | \(0.411127\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.00000 | 0.219529 | 0.109764 | − | 0.993958i | \(-0.464990\pi\) | ||||
0.109764 | + | 0.993958i | \(0.464990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.89898 | 0.748299 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.79796 | −1.05045 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.8990 | 1.13017 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.449490 | 0.0461167 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.79796 | 0.791763 | 0.395881 | − | 0.918302i | \(-0.370439\pi\) | ||||
0.395881 | + | 0.918302i | \(0.370439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.3485 | −1.34157 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.7980 | −1.57196 | −0.785978 | − | 0.618255i | \(-0.787840\pi\) | ||||
−0.785978 | + | 0.618255i | \(0.787840\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.3485 | 1.11820 | 0.559099 | − | 0.829101i | \(-0.311147\pi\) | ||||
0.559099 | + | 0.829101i | \(0.311147\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.89898 | −0.478091 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.2474 | −1.18401 | −0.592003 | − | 0.805936i | \(-0.701663\pi\) | ||||
−0.592003 | + | 0.805936i | \(0.701663\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.0000 | −1.13899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.10102 | 0.103575 | 0.0517876 | − | 0.998658i | \(-0.483508\pi\) | ||||
0.0517876 | + | 0.998658i | \(0.483508\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.44949 | 0.601418 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.00000 | −0.277350 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.7980 | 1.26486 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.79796 | 0.799814 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −26.6969 | −2.40718 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.65153 | 0.412757 | 0.206378 | − | 0.978472i | \(-0.433832\pi\) | ||||
0.206378 | + | 0.978472i | \(0.433832\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −27.7980 | −2.44747 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.5959 | 1.71210 | 0.856052 | − | 0.516890i | \(-0.172910\pi\) | ||||
0.856052 | + | 0.516890i | \(0.172910\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.898979 | 0.0779514 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.0000 | −1.19610 | −0.598050 | − | 0.801459i | \(-0.704058\pi\) | ||||
−0.598050 | + | 0.801459i | \(0.704058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.8990 | −1.43335 | −0.716676 | − | 0.697406i | \(-0.754338\pi\) | ||||
−0.716676 | + | 0.697406i | \(0.754338\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.89898 | 0.412568 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.44949 | 0.372085 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.00000 | 0.332182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.34847 | 0.606092 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.7980 | 0.966526 | 0.483263 | − | 0.875475i | \(-0.339451\pi\) | ||||
0.483263 | + | 0.875475i | \(0.339451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.65153 | −0.215779 | −0.107889 | − | 0.994163i | \(-0.534409\pi\) | ||||
−0.107889 | + | 0.994163i | \(0.534409\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.6969 | 1.67325 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.44949 | −0.357392 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.69694 | −0.213881 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.8990 | 1.01658 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.10102 | −0.712847 | −0.356423 | − | 0.934325i | \(-0.616004\pi\) | ||||
−0.356423 | + | 0.934325i | \(0.616004\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.8990 | 0.848484 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.0000 | 1.39288 | 0.696441 | − | 0.717614i | \(-0.254766\pi\) | ||||
0.696441 | + | 0.717614i | \(0.254766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.34847 | 0.103120 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.89898 | 0.524520 | 0.262260 | − | 0.964997i | \(-0.415532\pi\) | ||||
0.262260 | + | 0.964997i | \(0.415532\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | 0.151186 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −22.8990 | −1.72119 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.00000 | 0.597948 | 0.298974 | − | 0.954261i | \(-0.403356\pi\) | ||||
0.298974 | + | 0.954261i | \(0.403356\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.79796 | 0.430959 | 0.215479 | − | 0.976508i | \(-0.430869\pi\) | ||||
0.215479 | + | 0.976508i | \(0.430869\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.2020 | 1.04985 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.89898 | 0.360180 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −30.6969 | −2.24478 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.79796 | −0.130096 | −0.0650479 | − | 0.997882i | \(-0.520720\pi\) | ||||
−0.0650479 | + | 0.997882i | \(0.520720\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.202041 | 0.0145432 | 0.00727162 | − | 0.999974i | \(-0.497685\pi\) | ||||
0.00727162 | + | 0.999974i | \(0.497685\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.44949 | 0.175412 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.7980 | −1.69553 | −0.847767 | − | 0.530369i | \(-0.822054\pi\) | ||||
−0.847767 | + | 0.530369i | \(0.822054\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.79796 | 0.411006 | 0.205503 | − | 0.978656i | \(-0.434117\pi\) | ||||
0.205503 | + | 0.978656i | \(0.434117\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.4949 | 0.881322 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.00000 | 0.561490 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.8990 | 0.761218 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19.3485 | 1.34481 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.00000 | −0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.7980 | −1.77600 | −0.888002 | − | 0.459839i | \(-0.847907\pi\) | ||||
−0.888002 | + | 0.459839i | \(0.847907\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.69694 | 0.595904 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.3485 | 0.773959 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.89898 | −0.604102 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 36.0000 | 2.43265 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.89898 | −0.464076 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.5959 | −1.17831 | −0.589155 | − | 0.808020i | \(-0.700539\pi\) | ||||
−0.589155 | + | 0.808020i | \(0.700539\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.8990 | 1.51986 | 0.759929 | − | 0.650006i | \(-0.225234\pi\) | ||||
0.759929 | + | 0.650006i | \(0.225234\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.8990 | −1.24888 | −0.624440 | − | 0.781073i | \(-0.714673\pi\) | ||||
−0.624440 | + | 0.781073i | \(0.714673\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.7980 | 1.43420 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.5959 | −1.67684 | −0.838422 | − | 0.545021i | \(-0.816522\pi\) | ||||
−0.838422 | + | 0.545021i | \(0.816522\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.00000 | −0.130466 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.0000 | −0.779484 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.1464 | −0.721003 | −0.360501 | − | 0.932759i | \(-0.617394\pi\) | ||||
−0.360501 | + | 0.932759i | \(0.617394\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.696938 | −0.0448938 | −0.0224469 | − | 0.999748i | \(-0.507146\pi\) | ||||
−0.0224469 | + | 0.999748i | \(0.507146\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.0454 | 1.41421 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00000 | −0.191663 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.449490 | −0.0286003 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.89898 | −0.310460 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.6969 | −0.927663 | −0.463831 | − | 0.885924i | \(-0.653526\pi\) | ||||
−0.463831 | + | 0.885924i | \(0.653526\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.6969 | −1.80416 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.8990 | −1.05826 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.79796 | −0.236910 | −0.118455 | − | 0.992959i | \(-0.537794\pi\) | ||||
−0.118455 | + | 0.992959i | \(0.537794\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.79796 | 0.608816 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.0000 | 0.742781 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.4495 | 1.63095 | 0.815473 | − | 0.578796i | \(-0.196477\pi\) | ||||
0.815473 | + | 0.578796i | \(0.196477\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.10102 | 0.0676352 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.6969 | −0.899438 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.0000 | 1.58525 | 0.792624 | − | 0.609711i | \(-0.208714\pi\) | ||||
0.792624 | + | 0.609711i | \(0.208714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.55051 | 0.215678 | 0.107839 | − | 0.994168i | \(-0.465607\pi\) | ||||
0.107839 | + | 0.994168i | \(0.465607\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.89898 | 0.296500 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.44949 | −0.268314 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.4949 | −1.35159 | −0.675794 | − | 0.737091i | \(-0.736199\pi\) | ||||
−0.675794 | + | 0.737091i | \(0.736199\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.3485 | −0.799152 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.89898 | −0.411559 | −0.205779 | − | 0.978598i | \(-0.565973\pi\) | ||||
−0.205779 | + | 0.978598i | \(0.565973\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.44949 | −0.383382 | −0.191691 | − | 0.981455i | \(-0.561397\pi\) | ||||
−0.191691 | + | 0.981455i | \(0.561397\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.10102 | −0.0652188 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.7980 | 1.28669 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.5959 | 1.79976 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.1010 | −1.11972 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.4949 | 1.66469 | 0.832345 | − | 0.554258i | \(-0.186998\pi\) | ||||
0.832345 | + | 0.554258i | \(0.186998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.34847 | 0.544289 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.44949 | −0.372984 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.6969 | 1.30823 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 38.6969 | 2.22308 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.79796 | −0.331990 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.79796 | 0.445053 | 0.222527 | − | 0.974927i | \(-0.428570\pi\) | ||||
0.222527 | + | 0.974927i | \(0.428570\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −27.7980 | −1.58137 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.10102 | 0.175843 | 0.0879214 | − | 0.996127i | \(-0.471978\pi\) | ||||
0.0879214 | + | 0.996127i | \(0.471978\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.4949 | −1.27149 | −0.635743 | − | 0.771900i | \(-0.719306\pi\) | ||||
−0.635743 | + | 0.771900i | \(0.719306\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.00000 | 0.338062 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.6969 | 1.49945 | 0.749725 | − | 0.661750i | \(-0.230186\pi\) | ||||
0.749725 | + | 0.661750i | \(0.230186\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.7980 | −0.996494 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 30.0000 | 1.67444 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.10102 | 0.172545 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.4949 | 1.35457 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.00000 | −0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.55051 | −0.195154 | −0.0975768 | − | 0.995228i | \(-0.531109\pi\) | ||||
−0.0975768 | + | 0.995228i | \(0.531109\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.6969 | 0.805387 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.10102 | −0.278699 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.6969 | −0.909540 | −0.454770 | − | 0.890609i | \(-0.650279\pi\) | ||||
−0.454770 | + | 0.890609i | \(0.650279\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.69694 | −0.146478 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.7980 | 1.07212 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.7980 | −0.850534 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.2474 | 1.08694 | 0.543470 | − | 0.839429i | \(-0.317110\pi\) | ||||
0.543470 | + | 0.839429i | \(0.317110\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.6969 | 1.10788 | 0.553941 | − | 0.832556i | \(-0.313123\pi\) | ||||
0.553941 | + | 0.832556i | \(0.313123\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.4949 | −1.51663 | −0.758315 | − | 0.651888i | \(-0.773977\pi\) | ||||
−0.758315 | + | 0.651888i | \(0.773977\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.55051 | −0.188442 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −33.7980 | −1.78878 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.75255 | −0.303608 | −0.151804 | − | 0.988411i | \(-0.548508\pi\) | ||||
−0.151804 | + | 0.988411i | \(0.548508\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7980 | −0.989366 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.5505 | −1.13111 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.6969 | −0.769273 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.9444 | 1.82408 | 0.912041 | − | 0.410099i | \(-0.134506\pi\) | ||||
0.912041 | + | 0.410099i | \(0.134506\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 32.6969 | 1.70213 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.20204 | 0.114324 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.5959 | 1.53242 | 0.766209 | − | 0.642591i | \(-0.222141\pi\) | ||||
0.766209 | + | 0.642591i | \(0.222141\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.44949 | −0.126491 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.00000 | −0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.4495 | −0.844954 | −0.422477 | − | 0.906374i | \(-0.638839\pi\) | ||||
−0.422477 | + | 0.906374i | \(0.638839\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.3939 | −0.583726 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.5959 | −1.30789 | −0.653945 | − | 0.756542i | \(-0.726887\pi\) | ||||
−0.653945 | + | 0.756542i | \(0.726887\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.89898 | −0.453534 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 34.0454 | 1.73063 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.59592 | 0.0809163 | 0.0404581 | − | 0.999181i | \(-0.487118\pi\) | ||||
0.0404581 | + | 0.999181i | \(0.487118\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44.4949 | 2.25020 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −48.0000 | −2.42128 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.89898 | 0.246494 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.6969 | 1.54064 | 0.770318 | − | 0.637660i | \(-0.220098\pi\) | ||||
0.770318 | + | 0.637660i | \(0.220098\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.20204 | −0.110240 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.00000 | 0.299626 | 0.149813 | − | 0.988714i | \(-0.452133\pi\) | ||||
0.149813 | + | 0.988714i | \(0.452133\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.44949 | 0.221645 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.00000 | −0.447214 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.7980 | −1.08048 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.89898 | −0.341133 | −0.170566 | − | 0.985346i | \(-0.554560\pi\) | ||||
−0.170566 | + | 0.985346i | \(0.554560\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 34.2929 | 1.69154 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.6969 | 0.920016 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.00000 | 0.0981761 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 41.3939 | 2.02707 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.6969 | 1.89047 | 0.945235 | − | 0.326392i | \(-0.105833\pi\) | ||||
0.945235 | + | 0.326392i | \(0.105833\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.79796 | −0.185101 | −0.0925506 | − | 0.995708i | \(-0.529502\pi\) | ||||
−0.0925506 | + | 0.995708i | \(0.529502\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.00000 | −0.291730 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.89898 | 0.334650 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.5959 | −0.561166 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.8990 | −0.526208 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.0454 | −1.54357 | −0.771786 | − | 0.635882i | \(-0.780637\pi\) | ||||
−0.771786 | + | 0.635882i | \(0.780637\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.7980 | 0.566974 | 0.283487 | − | 0.958976i | \(-0.408509\pi\) | ||||
0.283487 | + | 0.958976i | \(0.408509\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.79796 | −0.469776 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.89898 | 0.138677 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.7980 | −0.849450 | −0.424725 | − | 0.905322i | \(-0.639629\pi\) | ||||
−0.424725 | + | 0.905322i | \(0.639629\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.00000 | −0.428571 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.0454 | −1.04741 | −0.523704 | − | 0.851900i | \(-0.675450\pi\) | ||||
−0.523704 | + | 0.851900i | \(0.675450\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | 0.284427 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −28.8990 | −1.36687 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.6969 | −0.976749 | −0.488374 | − | 0.872634i | \(-0.662410\pi\) | ||||
−0.488374 | + | 0.872634i | \(0.662410\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −48.4949 | −2.28354 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.49490 | 0.305157 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.00000 | −0.0937614 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0000 | 1.02912 | 0.514558 | − | 0.857455i | \(-0.327956\pi\) | ||||
0.514558 | + | 0.857455i | \(0.327956\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.6969 | −1.52285 | −0.761424 | − | 0.648254i | \(-0.775499\pi\) | ||||
−0.761424 | + | 0.648254i | \(0.775499\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.8990 | −1.06421 | −0.532103 | − | 0.846680i | \(-0.678598\pi\) | ||||
−0.532103 | + | 0.846680i | \(0.678598\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.8990 | 0.505428 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.9444 | 1.06174 | 0.530870 | − | 0.847453i | \(-0.321865\pi\) | ||||
0.530870 | + | 0.847453i | \(0.321865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.2020 | −0.471086 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.4949 | −1.12867 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −50.4949 | −2.32176 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.449490 | 0.0206240 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.30306 | 0.151237 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.34847 | −0.427142 | −0.213571 | − | 0.976927i | \(-0.568510\pi\) | ||||
−0.213571 | + | 0.976927i | \(0.568510\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.89898 | −0.223374 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −31.5959 | −1.43766 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.79796 | 0.354087 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.89898 | −0.312623 | −0.156311 | − | 0.987708i | \(-0.549960\pi\) | ||||
−0.156311 | + | 0.987708i | \(0.549960\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.2929 | 1.00812 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.2929 | −1.54761 | −0.773807 | − | 0.633421i | \(-0.781650\pi\) | ||||
−0.773807 | + | 0.633421i | \(0.781650\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.5959 | 1.24286 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.3485 | −0.599969 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.10102 | −0.318524 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.65153 | 0.297763 | 0.148882 | − | 0.988855i | \(-0.452433\pi\) | ||||
0.148882 | + | 0.988855i | \(0.452433\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −44.0908 | −1.96983 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.9444 | 1.20139 | 0.600695 | − | 0.799478i | \(-0.294890\pi\) | ||||
0.600695 | + | 0.799478i | \(0.294890\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.7980 | −0.703000 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.44949 | −0.108786 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.1010 | 0.757989 | 0.378995 | − | 0.925399i | \(-0.376270\pi\) | ||||
0.378995 | + | 0.925399i | \(0.376270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.3939 | −1.30031 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.3485 | 0.500073 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.89898 | 0.391377 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.8990 | −0.741783 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.7980 | 1.13023 | 0.565115 | − | 0.825012i | \(-0.308832\pi\) | ||||
0.565115 | + | 0.825012i | \(0.308832\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.6515 | −1.07794 | −0.538968 | − | 0.842326i | \(-0.681186\pi\) | ||||
−0.538968 | + | 0.842326i | \(0.681186\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.89898 | −0.213809 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −30.6969 | −1.33718 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.5959 | 0.808518 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.0454 | 1.21707 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.8990 | −0.472087 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.2474 | −0.529503 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.5959 | −0.845626 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.3485 | 0.574959 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.8990 | 0.640557 | 0.320279 | − | 0.947323i | \(-0.396223\pi\) | ||||
0.320279 | + | 0.947323i | \(0.396223\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.2020 | −0.609468 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.0000 | −0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.3485 | 0.656253 | 0.328127 | − | 0.944634i | \(-0.393583\pi\) | ||||
0.328127 | + | 0.944634i | \(0.393583\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.3939 | −0.742353 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.79796 | 0.0765956 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.79796 | 0.416652 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.0000 | −0.509372 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.6969 | −1.30067 | −0.650336 | − | 0.759647i | \(-0.725372\pi\) | ||||
−0.650336 | + | 0.759647i | \(0.725372\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.3485 | −0.479989 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 75.1918 | 3.17460 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.2474 | −1.35907 | −0.679534 | − | 0.733644i | \(-0.737818\pi\) | ||||
−0.679534 | + | 0.733644i | \(0.737818\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.10102 | 0.0463203 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.0000 | −0.755929 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.7980 | 1.24920 | 0.624598 | − | 0.780947i | \(-0.285263\pi\) | ||||
0.624598 | + | 0.780947i | \(0.285263\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.4949 | −0.857685 | −0.428842 | − | 0.903379i | \(-0.641078\pi\) | ||||
−0.428842 | + | 0.903379i | \(0.641078\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.40408 | 0.183983 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.44949 | 0.268962 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.8990 | 1.53612 | 0.768062 | − | 0.640375i | \(-0.221221\pi\) | ||||
0.768062 | + | 0.640375i | \(0.221221\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.494897 | −0.0205672 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.00000 | 0.165948 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.89898 | −0.202895 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.00000 | −0.124035 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.10102 | −0.0454440 | −0.0227220 | − | 0.999742i | \(-0.507233\pi\) | ||||
−0.0227220 | + | 0.999742i | \(0.507233\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | −0.0824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 58.2929 | 2.39785 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.00000 | 0.246390 | 0.123195 | − | 0.992382i | \(-0.460686\pi\) | ||||
0.123195 | + | 0.992382i | \(0.460686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.7980 | 0.565661 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.2020 | −0.581251 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.1010 | −0.780447 | −0.390223 | − | 0.920720i | \(-0.627602\pi\) | ||||
−0.390223 | + | 0.920720i | \(0.627602\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.59592 | 0.228262 | 0.114131 | − | 0.993466i | \(-0.463592\pi\) | ||||
0.114131 | + | 0.993466i | \(0.463592\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.3031 | −0.623189 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.79796 | 0.357688 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.4495 | 1.07355 | 0.536776 | − | 0.843725i | \(-0.319642\pi\) | ||||
0.536776 | + | 0.843725i | \(0.319642\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −19.5959 | −0.794067 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.00000 | 0.0809113 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.1918 | −1.34061 | −0.670303 | − | 0.742088i | \(-0.733836\pi\) | ||||
−0.670303 | + | 0.742088i | \(0.733836\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −26.6969 | −1.07652 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.3939 | 0.941802 | 0.470901 | − | 0.882186i | \(-0.343929\pi\) | ||||
0.470901 | + | 0.882186i | \(0.343929\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.34847 | 0.375747 | 0.187873 | − | 0.982193i | \(-0.439841\pi\) | ||||
0.187873 | + | 0.982193i | \(0.439841\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0000 | 0.480770 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.89898 | 0.195646 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.7980 | 1.34761 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.5505 | −0.459819 | −0.229909 | − | 0.973212i | \(-0.573843\pi\) | ||||
−0.229909 | + | 0.973212i | \(0.573843\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 63.1918 | 2.51165 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.65153 | 0.184590 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00000 | 0.118864 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.6515 | −0.421368 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.3939 | 0.924003 | 0.462001 | − | 0.886879i | \(-0.347132\pi\) | ||||
0.462001 | + | 0.886879i | \(0.347132\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.0000 | −1.18308 | −0.591542 | − | 0.806274i | \(-0.701481\pi\) | ||||
−0.591542 | + | 0.806274i | \(0.701481\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27.7980 | −1.09454 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.9444 | −1.53106 | −0.765531 | − | 0.643399i | \(-0.777524\pi\) | ||||
−0.765531 | + | 0.643399i | \(0.777524\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41.5959 | −1.63278 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.7980 | 0.854329 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.2020 | −0.947099 | −0.473550 | − | 0.880767i | \(-0.657028\pi\) | ||||
−0.473550 | + | 0.880767i | \(0.657028\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.5959 | 0.765676 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −44.0908 | −1.72015 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.6969 | −0.572511 | −0.286256 | − | 0.958153i | \(-0.592411\pi\) | ||||
−0.286256 | + | 0.958153i | \(0.592411\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.2020 | 0.785768 | 0.392884 | − | 0.919588i | \(-0.371477\pi\) | ||||
0.392884 | + | 0.919588i | \(0.371477\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.8990 | 0.656302 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.898979 | 0.0348609 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.7980 | 0.998901 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 43.1010 | 1.66638 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.7980 | 0.995919 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.8990 | −0.420125 | −0.210062 | − | 0.977688i | \(-0.567367\pi\) | ||||
−0.210062 | + | 0.977688i | \(0.567367\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.3031 | −0.434412 | −0.217206 | − | 0.976126i | \(-0.569694\pi\) | ||||
−0.217206 | + | 0.976126i | \(0.569694\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.5959 | 0.598516 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −56.0908 | −2.14940 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.49490 | 0.248520 | 0.124260 | − | 0.992250i | \(-0.460344\pi\) | ||||
0.124260 | + | 0.992250i | \(0.460344\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.0000 | −0.534913 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 46.2929 | 1.76618 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.10102 | −0.0419455 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.3485 | −1.11647 | −0.558234 | − | 0.829683i | \(-0.688521\pi\) | ||||
−0.558234 | + | 0.829683i | \(0.688521\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −26.6969 | −1.01413 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.8990 | −0.641015 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 75.1918 | 2.84809 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 62.6969 | 2.37142 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.1918 | 1.55579 | 0.777897 | − | 0.628392i | \(-0.216286\pi\) | ||||
0.777897 | + | 0.628392i | \(0.216286\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.20204 | 0.0830516 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.89898 | 0.184506 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −31.5959 | −1.18829 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.2929 | 1.36301 | 0.681503 | − | 0.731815i | \(-0.261326\pi\) | ||||
0.681503 | + | 0.731815i | \(0.261326\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.6969 | 0.551178 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.6969 | −1.07471 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.44949 | 0.166401 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27.3031 | 1.01965 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.0000 | −0.745874 | −0.372937 | − | 0.927857i | \(-0.621649\pi\) | ||||
−0.372937 | + | 0.927857i | \(0.621649\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.6969 | 0.845278 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.70714 | 0.0634894 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.00000 | 0.148556 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.0454 | −0.965971 | −0.482985 | − | 0.875628i | \(-0.660448\pi\) | ||||
−0.482985 | + | 0.875628i | \(0.660448\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 78.2929 | 2.89577 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.00000 | −0.221615 | −0.110808 | − | 0.993842i | \(-0.535344\pi\) | ||||
−0.110808 | + | 0.993842i | \(0.535344\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.34847 | 0.271052 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.6969 | 0.836052 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.2474 | 0.671243 | 0.335622 | − | 0.941997i | \(-0.391054\pi\) | ||||
0.335622 | + | 0.941997i | \(0.391054\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.10102 | 0.0404470 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.3939 | 0.858238 | 0.429119 | − | 0.903248i | \(-0.358824\pi\) | ||||
0.429119 | + | 0.903248i | \(0.358824\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.7980 | 0.432244 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.00000 | 0.219529 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.4949 | −0.895024 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.8990 | 1.49242 | 0.746212 | − | 0.665708i | \(-0.231870\pi\) | ||||
0.746212 | + | 0.665708i | \(0.231870\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36.0000 | 1.31191 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.65153 | −0.0964991 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.4949 | −0.817591 | −0.408795 | − | 0.912626i | \(-0.634051\pi\) | ||||
−0.408795 | + | 0.912626i | \(0.634051\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 70.2929 | 2.55147 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −49.5959 | −1.79785 | −0.898925 | − | 0.438102i | \(-0.855651\pi\) | ||||
−0.898925 | + | 0.438102i | \(0.855651\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.0000 | −0.724049 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20.6969 | 0.748299 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.34847 | −0.337554 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.3939 | −0.699361 | −0.349681 | − | 0.936869i | \(-0.613710\pi\) | ||||
−0.349681 | + | 0.936869i | \(0.613710\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.30306 | 0.335042 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −44.0908 | −1.58584 | −0.792918 | − | 0.609328i | \(-0.791439\pi\) | ||||
−0.792918 | + | 0.609328i | \(0.791439\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.44949 | −0.159830 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.0000 | −0.860995 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.89898 | 0.175524 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.7980 | 0.565295 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.0000 | 0.356915 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.0000 | 1.35455 | 0.677277 | − | 0.735728i | \(-0.263160\pi\) | ||||
0.677277 | + | 0.735728i | \(0.263160\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −64.7878 | −2.30651 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.20204 | 0.0782956 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.79796 | 0.205892 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.69694 | −0.0956506 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.20204 | 0.290531 | 0.145266 | − | 0.989393i | \(-0.453596\pi\) | ||||
0.145266 | + | 0.989393i | \(0.453596\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.7980 | −0.488137 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.0000 | 0.635999 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 65.3939 | 2.30770 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.8990 | 0.454629 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −63.6867 | −2.24188 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.0000 | 0.421898 | 0.210949 | − | 0.977497i | \(-0.432345\pi\) | ||||
0.210949 | + | 0.977497i | \(0.432345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.84337 | 0.345647 | 0.172824 | − | 0.984953i | \(-0.444711\pi\) | ||||
0.172824 | + | 0.984953i | \(0.444711\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.69694 | −0.305015 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.10102 | −0.318795 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.10102 | 0.178462 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.00000 | −0.209657 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.1918 | 0.879201 | 0.439601 | − | 0.898193i | \(-0.355120\pi\) | ||||
0.439601 | + | 0.898193i | \(0.355120\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.5505 | 0.890635 | 0.445317 | − | 0.895373i | \(-0.353091\pi\) | ||||
0.445317 | + | 0.895373i | \(0.353091\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.8990 | 0.379454 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.1918 | −0.736912 | −0.368456 | − | 0.929645i | \(-0.620114\pi\) | ||||
−0.368456 | + | 0.929645i | \(0.620114\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.0000 | −0.694629 | −0.347314 | − | 0.937749i | \(-0.612906\pi\) | ||||
−0.347314 | + | 0.937749i | \(0.612906\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 55.1010 | 1.91143 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.6969 | −0.717106 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0000 | 0.622916 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.4495 | −0.844090 | −0.422045 | − | 0.906575i | \(-0.638688\pi\) | ||||
−0.422045 | + | 0.906575i | \(0.638688\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.8990 | 0.582032 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.5959 | 0.604603 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.7980 | 0.542185 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.5959 | 1.08309 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.6969 | 0.366256 | 0.183128 | − | 0.983089i | \(-0.441378\pi\) | ||||
0.183128 | + | 0.983089i | \(0.441378\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.34847 | 0.0461167 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.3939 | −0.799120 | −0.399560 | − | 0.916707i | \(-0.630837\pi\) | ||||
−0.399560 | + | 0.916707i | \(0.630837\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.30306 | −0.0444599 | −0.0222299 | − | 0.999753i | \(-0.507077\pi\) | ||||
−0.0222299 | + | 0.999753i | \(0.507077\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −53.3939 | −1.81966 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.3939 | −1.20482 | −0.602411 | − | 0.798186i | \(-0.705793\pi\) | ||||
−0.602411 | + | 0.798186i | \(0.705793\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.89898 | 0.234572 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −74.9444 | −2.54524 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.7980 | −0.739445 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.10102 | 0.172841 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.3939 | 0.791763 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.00000 | 0.0676123 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.5959 | −0.729242 | −0.364621 | − | 0.931156i | \(-0.618802\pi\) | ||||
−0.364621 | + | 0.931156i | \(0.618802\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −69.7980 | −2.35423 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.79796 | −0.330102 | −0.165051 | − | 0.986285i | \(-0.552779\pi\) | ||||
−0.165051 | + | 0.986285i | \(0.552779\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.34847 | 0.112685 | 0.0563425 | − | 0.998412i | \(-0.482056\pi\) | ||||
0.0563425 | + | 0.998412i | \(0.482056\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −22.8990 | −0.769741 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.2474 | −0.679843 | −0.339921 | − | 0.940454i | \(-0.610400\pi\) | ||||
−0.339921 | + | 0.940454i | \(0.610400\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.30306 | 0.312015 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 40.0454 | 1.34157 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.898979 | −0.0300832 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.00000 | 0.267411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.7980 | 0.527478 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.7980 | −0.593595 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.59592 | 0.253057 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −55.5959 | −1.85012 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.79796 | 0.192731 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.8434 | −0.658888 | −0.329444 | − | 0.944175i | \(-0.606861\pi\) | ||||
−0.329444 | + | 0.944175i | \(0.606861\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −47.3939 | −1.57196 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.39388 | 0.311233 | 0.155617 | − | 0.987818i | \(-0.450264\pi\) | ||||
0.155617 | + | 0.987818i | \(0.450264\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.89898 | −0.294513 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.2020 | 0.469505 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 39.1918 | 1.29423 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.8990 | −0.689394 | −0.344697 | − | 0.938714i | \(-0.612018\pi\) | ||||
−0.344697 | + | 0.938714i | \(0.612018\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.1010 | −0.629400 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.55051 | 0.116866 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.89898 | 0.161077 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 34.0454 | 1.11820 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.69694 | −0.154102 | −0.0770508 | − | 0.997027i | \(-0.524550\pi\) | ||||
−0.0770508 | + | 0.997027i | \(0.524550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.34847 | −0.0441943 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.59592 | −0.248679 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −30.6969 | −1.00390 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.3939 | 1.28694 | 0.643471 | − | 0.765471i | \(-0.277494\pi\) | ||||
0.643471 | + | 0.765471i | \(0.277494\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 55.1010 | 1.79815 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −52.6969 | −1.71787 | −0.858936 | − | 0.512084i | \(-0.828874\pi\) | ||||
−0.858936 | + | 0.512084i | \(0.828874\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 70.2929 | 2.28905 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.2020 | −0.916443 | −0.458222 | − | 0.888838i | \(-0.651513\pi\) | ||||
−0.458222 | + | 0.888838i | \(0.651513\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.6969 | 0.477083 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −65.3939 | −2.12054 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.1918 | 0.686471 | 0.343235 | − | 0.939249i | \(-0.388477\pi\) | ||||
0.343235 | + | 0.939249i | \(0.388477\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.79796 | −0.0581806 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 43.5959 | 1.40926 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.0000 | −0.904167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.2020 | −0.361356 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −36.7423 | −1.18401 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.202041 | 0.00650393 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.8990 | 1.12228 | 0.561138 | − | 0.827722i | \(-0.310364\pi\) | ||||
0.561138 | + | 0.827722i | \(0.310364\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.59592 | −0.244016 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.5959 | −0.372131 | −0.186065 | − | 0.982537i | \(-0.559574\pi\) | ||||
−0.186065 | + | 0.982537i | \(0.559574\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.7980 | −1.08351 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.44949 | 0.0784465 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.6969 | −0.982082 | −0.491041 | − | 0.871136i | \(-0.663383\pi\) | ||||
−0.491041 | + | 0.871136i | \(0.663383\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.6969 | −0.853238 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.0000 | −0.957826 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49.1010 | 1.56608 | 0.783040 | − | 0.621972i | \(-0.213668\pi\) | ||||
0.783040 | + | 0.621972i | \(0.213668\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.7980 | −0.758266 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.79796 | 0.311872 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 73.1918 | 2.32736 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.7980 | −1.58188 | −0.790942 | − | 0.611891i | \(-0.790409\pi\) | ||||
−0.790942 | + | 0.611891i | \(0.790409\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.69694 | 0.275989 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.79796 | 0.183808 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.8990 | 1.10526 | 0.552631 | − | 0.833426i | \(-0.313624\pi\) | ||||
0.552631 | + | 0.833426i | \(0.313624\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 520.2.a.f.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 4680.2.a.z.1.2 | 2 | |||
4.3 | odd | 2 | 1040.2.a.k.1.2 | 2 | |||
5.2 | odd | 4 | 2600.2.d.h.1249.4 | 4 | |||
5.3 | odd | 4 | 2600.2.d.h.1249.1 | 4 | |||
5.4 | even | 2 | 2600.2.a.q.1.2 | 2 | |||
8.3 | odd | 2 | 4160.2.a.ba.1.1 | 2 | |||
8.5 | even | 2 | 4160.2.a.bg.1.2 | 2 | |||
12.11 | even | 2 | 9360.2.a.cc.1.1 | 2 | |||
13.12 | even | 2 | 6760.2.a.s.1.1 | 2 | |||
20.19 | odd | 2 | 5200.2.a.bv.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
520.2.a.f.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1040.2.a.k.1.2 | 2 | 4.3 | odd | 2 | |||
2600.2.a.q.1.2 | 2 | 5.4 | even | 2 | |||
2600.2.d.h.1249.1 | 4 | 5.3 | odd | 4 | |||
2600.2.d.h.1249.4 | 4 | 5.2 | odd | 4 | |||
4160.2.a.ba.1.1 | 2 | 8.3 | odd | 2 | |||
4160.2.a.bg.1.2 | 2 | 8.5 | even | 2 | |||
4680.2.a.z.1.2 | 2 | 3.2 | odd | 2 | |||
5200.2.a.bv.1.1 | 2 | 20.19 | odd | 2 | |||
6760.2.a.s.1.1 | 2 | 13.12 | even | 2 | |||
9360.2.a.cc.1.1 | 2 | 12.11 | even | 2 |