Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6030,2,Mod(1,6030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6030, 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("6030.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6030 = 2 \cdot 3^{2} \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6030.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: | \(48.1497924188\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.70292.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + 10x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2010) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.59676\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6030.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.45037 | −0.548189 | −0.274094 | − | 0.961703i | \(-0.588378\pi\) | ||||
−0.274094 | + | 0.961703i | \(0.588378\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.50940 | 1.05812 | 0.529062 | − | 0.848583i | \(-0.322544\pi\) | ||||
0.529062 | + | 0.848583i | \(0.322544\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.95977 | 1.37559 | 0.687797 | − | 0.725903i | \(-0.258578\pi\) | ||||
0.687797 | + | 0.725903i | \(0.258578\pi\) | |||||||
\(14\) | −1.45037 | −0.387628 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.19351 | 0.774540 | 0.387270 | − | 0.921966i | \(-0.373418\pi\) | ||||
0.387270 | + | 0.921966i | \(0.373418\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.19351 | 0.732642 | 0.366321 | − | 0.930489i | \(-0.380617\pi\) | ||||
0.366321 | + | 0.930489i | \(0.380617\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.50940 | 0.748207 | ||||||||
\(23\) | −4.15328 | −0.866019 | −0.433010 | − | 0.901389i | \(-0.642548\pi\) | ||||
−0.433010 | + | 0.901389i | \(0.642548\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.95977 | 0.972691 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.45037 | −0.274094 | ||||||||
\(29\) | 3.25254 | 0.603981 | 0.301991 | − | 0.953311i | \(-0.402349\pi\) | ||||
0.301991 | + | 0.953311i | \(0.402349\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.95977 | 1.25001 | 0.625006 | − | 0.780620i | \(-0.285097\pi\) | ||||
0.625006 | + | 0.780620i | \(0.285097\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.19351 | 0.547683 | ||||||||
\(35\) | −1.45037 | −0.245158 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.70291 | −0.773154 | −0.386577 | − | 0.922257i | \(-0.626343\pi\) | ||||
−0.386577 | + | 0.922257i | \(0.626343\pi\) | |||||||
\(38\) | 3.19351 | 0.518056 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −8.21231 | −1.28255 | −0.641274 | − | 0.767312i | \(-0.721594\pi\) | ||||
−0.641274 | + | 0.767312i | \(0.721594\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.01880 | −1.07036 | −0.535178 | − | 0.844739i | \(-0.679756\pi\) | ||||
−0.535178 | + | 0.844739i | \(0.679756\pi\) | |||||||
\(44\) | 3.50940 | 0.529062 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.15328 | −0.612368 | ||||||||
\(47\) | 8.66700 | 1.26421 | 0.632106 | − | 0.774882i | \(-0.282191\pi\) | ||||
0.632106 | + | 0.774882i | \(0.282191\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.89642 | −0.699489 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.95977 | 0.687797 | ||||||||
\(53\) | −0.900743 | −0.123727 | −0.0618633 | − | 0.998085i | \(-0.519704\pi\) | ||||
−0.0618633 | + | 0.998085i | \(0.519704\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.50940 | 0.473207 | ||||||||
\(56\) | −1.45037 | −0.193814 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.25254 | 0.427079 | ||||||||
\(59\) | −8.21231 | −1.06915 | −0.534576 | − | 0.845120i | \(-0.679529\pi\) | ||||
−0.534576 | + | 0.845120i | \(0.679529\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.549629 | 0.0703727 | 0.0351864 | − | 0.999381i | \(-0.488798\pi\) | ||||
0.0351864 | + | 0.999381i | \(0.488798\pi\) | |||||||
\(62\) | 6.95977 | 0.883892 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.95977 | 0.615184 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | −0.122169 | ||||||||
\(68\) | 3.19351 | 0.387270 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.45037 | −0.173353 | ||||||||
\(71\) | 6.64388 | 0.788484 | 0.394242 | − | 0.919007i | \(-0.371007\pi\) | ||||
0.394242 | + | 0.919007i | \(0.371007\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.40582 | 0.866786 | 0.433393 | − | 0.901205i | \(-0.357316\pi\) | ||||
0.433393 | + | 0.901205i | \(0.357316\pi\) | |||||||
\(74\) | −4.70291 | −0.546702 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.19351 | 0.366321 | ||||||||
\(77\) | −5.08993 | −0.580052 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.3656 | −1.39124 | −0.695619 | − | 0.718411i | \(-0.744870\pi\) | ||||
−0.695619 | + | 0.718411i | \(0.744870\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.21231 | −0.906898 | ||||||||
\(83\) | 17.0899 | 1.87586 | 0.937932 | − | 0.346819i | \(-0.112738\pi\) | ||||
0.937932 | + | 0.346819i | \(0.112738\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.19351 | 0.346385 | ||||||||
\(86\) | −7.01880 | −0.756857 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.50940 | 0.374103 | ||||||||
\(89\) | −14.1087 | −1.49552 | −0.747761 | − | 0.663968i | \(-0.768871\pi\) | ||||
−0.747761 | + | 0.663968i | \(0.768871\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.19351 | −0.754085 | ||||||||
\(92\) | −4.15328 | −0.433010 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.66700 | 0.893933 | ||||||||
\(95\) | 3.19351 | 0.327647 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.50940 | −0.356326 | −0.178163 | − | 0.984001i | \(-0.557015\pi\) | ||||
−0.178163 | + | 0.984001i | \(0.557015\pi\) | |||||||
\(98\) | −4.89642 | −0.494613 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 1.68411 | 0.167575 | 0.0837877 | − | 0.996484i | \(-0.473298\pi\) | ||||
0.0837877 | + | 0.996484i | \(0.473298\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.0188 | −1.08571 | −0.542857 | − | 0.839825i | \(-0.682658\pi\) | ||||
−0.542857 | + | 0.839825i | \(0.682658\pi\) | |||||||
\(104\) | 4.95977 | 0.486346 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.900743 | −0.0874879 | ||||||||
\(107\) | 17.9195 | 1.73235 | 0.866174 | − | 0.499743i | \(-0.166572\pi\) | ||||
0.866174 | + | 0.499743i | \(0.166572\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.83739 | 0.559121 | 0.279560 | − | 0.960128i | \(-0.409811\pi\) | ||||
0.279560 | + | 0.960128i | \(0.409811\pi\) | |||||||
\(110\) | 3.50940 | 0.334608 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.45037 | −0.137047 | ||||||||
\(113\) | 8.99568 | 0.846242 | 0.423121 | − | 0.906073i | \(-0.360934\pi\) | ||||
0.423121 | + | 0.906073i | \(0.360934\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.15328 | −0.387296 | ||||||||
\(116\) | 3.25254 | 0.301991 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.21231 | −0.756005 | ||||||||
\(119\) | −4.63178 | −0.424594 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.31589 | 0.119626 | ||||||||
\(122\) | 0.549629 | 0.0497610 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.95977 | 0.625006 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.3254 | 1.35991 | 0.679953 | − | 0.733256i | \(-0.262000\pi\) | ||||
0.679953 | + | 0.733256i | \(0.262000\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.95977 | 0.435001 | ||||||||
\(131\) | 0.886946 | 0.0774928 | 0.0387464 | − | 0.999249i | \(-0.487664\pi\) | ||||
0.0387464 | + | 0.999249i | \(0.487664\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.63178 | −0.401626 | ||||||||
\(134\) | −1.00000 | −0.0863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.19351 | 0.273841 | ||||||||
\(137\) | 8.70291 | 0.743540 | 0.371770 | − | 0.928325i | \(-0.378751\pi\) | ||||
0.371770 | + | 0.928325i | \(0.378751\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.6456 | 1.58150 | 0.790749 | − | 0.612141i | \(-0.209692\pi\) | ||||
0.790749 | + | 0.612141i | \(0.209692\pi\) | |||||||
\(140\) | −1.45037 | −0.122579 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.64388 | 0.557542 | ||||||||
\(143\) | 17.4058 | 1.45555 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.25254 | 0.270109 | ||||||||
\(146\) | 7.40582 | 0.612910 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.70291 | −0.386577 | ||||||||
\(149\) | 3.25254 | 0.266458 | 0.133229 | − | 0.991085i | \(-0.457465\pi\) | ||||
0.133229 | + | 0.991085i | \(0.457465\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.2354 | −1.15846 | −0.579232 | − | 0.815163i | \(-0.696647\pi\) | ||||
−0.579232 | + | 0.815163i | \(0.696647\pi\) | |||||||
\(152\) | 3.19351 | 0.259028 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.08993 | −0.410159 | ||||||||
\(155\) | 6.95977 | 0.559022 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.58554 | −0.206348 | −0.103174 | − | 0.994663i | \(-0.532900\pi\) | ||||
−0.103174 | + | 0.994663i | \(0.532900\pi\) | |||||||
\(158\) | −12.3656 | −0.983754 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 6.02380 | 0.474742 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.7029 | −1.15162 | −0.575810 | − | 0.817583i | \(-0.695313\pi\) | ||||
−0.575810 | + | 0.817583i | \(0.695313\pi\) | |||||||
\(164\) | −8.21231 | −0.641274 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.0899 | 1.32644 | ||||||||
\(167\) | 22.0728 | 1.70805 | 0.854023 | − | 0.520235i | \(-0.174156\pi\) | ||||
0.854023 | + | 0.520235i | \(0.174156\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5993 | 0.892256 | ||||||||
\(170\) | 3.19351 | 0.244931 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.01880 | −0.535178 | ||||||||
\(173\) | 6.77058 | 0.514758 | 0.257379 | − | 0.966311i | \(-0.417141\pi\) | ||||
0.257379 | + | 0.966311i | \(0.417141\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.45037 | −0.109638 | ||||||||
\(176\) | 3.50940 | 0.264531 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.1087 | −1.05749 | ||||||||
\(179\) | 13.6268 | 1.01851 | 0.509256 | − | 0.860615i | \(-0.329920\pi\) | ||||
0.509256 | + | 0.860615i | \(0.329920\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.2073 | −1.57633 | −0.788163 | − | 0.615466i | \(-0.788968\pi\) | ||||
−0.788163 | + | 0.615466i | \(0.788968\pi\) | |||||||
\(182\) | −7.19351 | −0.533219 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.15328 | −0.306184 | ||||||||
\(185\) | −4.70291 | −0.345765 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.2073 | 0.819560 | ||||||||
\(188\) | 8.66700 | 0.632106 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.19351 | 0.231682 | ||||||||
\(191\) | 4.98120 | 0.360427 | 0.180213 | − | 0.983628i | \(-0.442321\pi\) | ||||
0.180213 | + | 0.983628i | \(0.442321\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.92455 | 0.210513 | 0.105257 | − | 0.994445i | \(-0.466434\pi\) | ||||
0.105257 | + | 0.994445i | \(0.466434\pi\) | |||||||
\(194\) | −3.50940 | −0.251960 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.89642 | −0.349744 | ||||||||
\(197\) | −7.91954 | −0.564244 | −0.282122 | − | 0.959379i | \(-0.591038\pi\) | ||||
−0.282122 | + | 0.959379i | \(0.591038\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.08993 | 0.644368 | 0.322184 | − | 0.946677i | \(-0.395583\pi\) | ||||
0.322184 | + | 0.946677i | \(0.395583\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.68411 | 0.118494 | ||||||||
\(203\) | −4.71739 | −0.331096 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.21231 | −0.573573 | ||||||||
\(206\) | −11.0188 | −0.767716 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.95977 | 0.343898 | ||||||||
\(209\) | 11.2073 | 0.775226 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.41083 | −0.579025 | −0.289513 | − | 0.957174i | \(-0.593493\pi\) | ||||
−0.289513 | + | 0.957174i | \(0.593493\pi\) | |||||||
\(212\) | −0.900743 | −0.0618633 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 17.9195 | 1.22495 | ||||||||
\(215\) | −7.01880 | −0.478678 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.0943 | −0.685243 | ||||||||
\(218\) | 5.83739 | 0.395358 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.50940 | 0.236604 | ||||||||
\(221\) | 15.8391 | 1.06545 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.5513 | −0.974429 | −0.487214 | − | 0.873282i | \(-0.661987\pi\) | ||||
−0.487214 | + | 0.873282i | \(0.661987\pi\) | |||||||
\(224\) | −1.45037 | −0.0969070 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.99568 | 0.598384 | ||||||||
\(227\) | 14.2690 | 0.947064 | 0.473532 | − | 0.880776i | \(-0.342979\pi\) | ||||
0.473532 | + | 0.880776i | \(0.342979\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.56843 | −0.500136 | −0.250068 | − | 0.968228i | \(-0.580453\pi\) | ||||
−0.250068 | + | 0.968228i | \(0.580453\pi\) | |||||||
\(230\) | −4.15328 | −0.273859 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.25254 | 0.213540 | ||||||||
\(233\) | −23.9102 | −1.56641 | −0.783205 | − | 0.621763i | \(-0.786417\pi\) | ||||
−0.783205 | + | 0.621763i | \(0.786417\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.66700 | 0.565373 | ||||||||
\(236\) | −8.21231 | −0.534576 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.63178 | −0.300234 | ||||||||
\(239\) | 15.3254 | 0.991316 | 0.495658 | − | 0.868518i | \(-0.334927\pi\) | ||||
0.495658 | + | 0.868518i | \(0.334927\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.9340 | 1.15523 | 0.577616 | − | 0.816309i | \(-0.303983\pi\) | ||||
0.577616 | + | 0.816309i | \(0.303983\pi\) | |||||||
\(242\) | 1.31589 | 0.0845885 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.549629 | 0.0351864 | ||||||||
\(245\) | −4.89642 | −0.312821 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.8391 | 1.00782 | ||||||||
\(248\) | 6.95977 | 0.441946 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 14.7029 | 0.928040 | 0.464020 | − | 0.885825i | \(-0.346407\pi\) | ||||
0.464020 | + | 0.885825i | \(0.346407\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.5755 | −0.916356 | ||||||||
\(254\) | 15.3254 | 0.961599 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.0856 | 1.00339 | 0.501696 | − | 0.865044i | \(-0.332709\pi\) | ||||
0.501696 | + | 0.865044i | \(0.332709\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.82097 | 0.423834 | ||||||||
\(260\) | 4.95977 | 0.307592 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.886946 | 0.0547957 | ||||||||
\(263\) | −8.27134 | −0.510033 | −0.255016 | − | 0.966937i | \(-0.582081\pi\) | ||||
−0.255016 | + | 0.966937i | \(0.582081\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.900743 | −0.0553322 | ||||||||
\(266\) | −4.63178 | −0.283993 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.00000 | −0.0610847 | ||||||||
\(269\) | −12.8655 | −0.784424 | −0.392212 | − | 0.919875i | \(-0.628290\pi\) | ||||
−0.392212 | + | 0.919875i | \(0.628290\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.2475 | −1.22995 | −0.614975 | − | 0.788546i | \(-0.710834\pi\) | ||||
−0.614975 | + | 0.788546i | \(0.710834\pi\) | |||||||
\(272\) | 3.19351 | 0.193635 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.70291 | 0.525762 | ||||||||
\(275\) | 3.50940 | 0.211625 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.6413 | −1.05996 | −0.529980 | − | 0.848010i | \(-0.677801\pi\) | ||||
−0.529980 | + | 0.848010i | \(0.677801\pi\) | |||||||
\(278\) | 18.6456 | 1.11829 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.45037 | −0.0866763 | ||||||||
\(281\) | 17.8391 | 1.06419 | 0.532095 | − | 0.846684i | \(-0.321405\pi\) | ||||
0.532095 | + | 0.846684i | \(0.321405\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.1550 | 1.19809 | 0.599044 | − | 0.800716i | \(-0.295547\pi\) | ||||
0.599044 | + | 0.800716i | \(0.295547\pi\) | |||||||
\(284\) | 6.64388 | 0.394242 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 17.4058 | 1.02923 | ||||||||
\(287\) | 11.9109 | 0.703078 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.80149 | −0.400087 | ||||||||
\(290\) | 3.25254 | 0.190996 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.40582 | 0.433393 | ||||||||
\(293\) | 10.6815 | 0.624019 | 0.312009 | − | 0.950079i | \(-0.398998\pi\) | ||||
0.312009 | + | 0.950079i | \(0.398998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.21231 | −0.478139 | ||||||||
\(296\) | −4.70291 | −0.273351 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.25254 | 0.188415 | ||||||||
\(299\) | −20.5993 | −1.19129 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.1799 | 0.586758 | ||||||||
\(302\) | −14.2354 | −0.819157 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.19351 | 0.183160 | ||||||||
\(305\) | 0.549629 | 0.0314716 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.75957 | −0.385789 | −0.192894 | − | 0.981220i | \(-0.561787\pi\) | ||||
−0.192894 | + | 0.981220i | \(0.561787\pi\) | |||||||
\(308\) | −5.08993 | −0.290026 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.95977 | 0.395288 | ||||||||
\(311\) | 12.1181 | 0.687152 | 0.343576 | − | 0.939125i | \(-0.388362\pi\) | ||||
0.343576 | + | 0.939125i | \(0.388362\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.9427 | 0.788086 | 0.394043 | − | 0.919092i | \(-0.371076\pi\) | ||||
0.394043 | + | 0.919092i | \(0.371076\pi\) | |||||||
\(314\) | −2.58554 | −0.145910 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.3656 | −0.695619 | ||||||||
\(317\) | −22.1584 | −1.24454 | −0.622271 | − | 0.782802i | \(-0.713790\pi\) | ||||
−0.622271 | + | 0.782802i | \(0.713790\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.4145 | 0.639087 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.02380 | 0.335693 | ||||||||
\(323\) | 10.1985 | 0.567461 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.95977 | 0.275119 | ||||||||
\(326\) | −14.7029 | −0.814319 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.21231 | −0.453449 | ||||||||
\(329\) | −12.5704 | −0.693027 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.0607 | 0.882777 | 0.441389 | − | 0.897316i | \(-0.354486\pi\) | ||||
0.441389 | + | 0.897316i | \(0.354486\pi\) | |||||||
\(332\) | 17.0899 | 0.937932 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 22.0728 | 1.20777 | ||||||||
\(335\) | −1.00000 | −0.0546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.7636 | −0.695279 | −0.347640 | − | 0.937628i | \(-0.613017\pi\) | ||||
−0.347640 | + | 0.937628i | \(0.613017\pi\) | |||||||
\(338\) | 11.5993 | 0.630921 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.19351 | 0.173192 | ||||||||
\(341\) | 24.4246 | 1.32267 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.2542 | 0.931641 | ||||||||
\(344\) | −7.01880 | −0.378428 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.77058 | 0.363989 | ||||||||
\(347\) | −35.2929 | −1.89462 | −0.947312 | − | 0.320313i | \(-0.896212\pi\) | ||||
−0.947312 | + | 0.320313i | \(0.896212\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.03760 | −0.430243 | −0.215121 | − | 0.976587i | \(-0.569015\pi\) | ||||
−0.215121 | + | 0.976587i | \(0.569015\pi\) | |||||||
\(350\) | −1.45037 | −0.0775256 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.50940 | 0.187052 | ||||||||
\(353\) | −24.0943 | −1.28241 | −0.641204 | − | 0.767371i | \(-0.721565\pi\) | ||||
−0.641204 | + | 0.767371i | \(0.721565\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.64388 | 0.352621 | ||||||||
\(356\) | −14.1087 | −0.747761 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.6268 | 0.720197 | ||||||||
\(359\) | −28.8700 | −1.52370 | −0.761850 | − | 0.647754i | \(-0.775709\pi\) | ||||
−0.761850 | + | 0.647754i | \(0.775709\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.80149 | −0.463236 | ||||||||
\(362\) | −21.2073 | −1.11463 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.19351 | −0.377042 | ||||||||
\(365\) | 7.40582 | 0.387638 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.4873 | 1.33043 | 0.665213 | − | 0.746654i | \(-0.268341\pi\) | ||||
0.665213 | + | 0.746654i | \(0.268341\pi\) | |||||||
\(368\) | −4.15328 | −0.216505 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.70291 | −0.244493 | ||||||||
\(371\) | 1.30641 | 0.0678255 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.7613 | −0.557197 | −0.278598 | − | 0.960408i | \(-0.589870\pi\) | ||||
−0.278598 | + | 0.960408i | \(0.589870\pi\) | |||||||
\(374\) | 11.2073 | 0.579516 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.66700 | 0.446967 | ||||||||
\(377\) | 16.1319 | 0.830833 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.4471 | −1.25576 | −0.627881 | − | 0.778310i | \(-0.716077\pi\) | ||||
−0.627881 | + | 0.778310i | \(0.716077\pi\) | |||||||
\(380\) | 3.19351 | 0.163824 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.98120 | 0.254860 | ||||||||
\(383\) | 4.50440 | 0.230164 | 0.115082 | − | 0.993356i | \(-0.463287\pi\) | ||||
0.115082 | + | 0.993356i | \(0.463287\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.08993 | −0.259407 | ||||||||
\(386\) | 2.92455 | 0.148855 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.50940 | −0.178163 | ||||||||
\(389\) | −19.8125 | −1.00453 | −0.502267 | − | 0.864713i | \(-0.667500\pi\) | ||||
−0.502267 | + | 0.864713i | \(0.667500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.2636 | −0.670767 | ||||||||
\(392\) | −4.89642 | −0.247307 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.91954 | −0.398981 | ||||||||
\(395\) | −12.3656 | −0.622181 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.92023 | −0.297128 | −0.148564 | − | 0.988903i | \(-0.547465\pi\) | ||||
−0.148564 | + | 0.988903i | \(0.547465\pi\) | |||||||
\(398\) | 9.08993 | 0.455637 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −10.3784 | −0.518272 | −0.259136 | − | 0.965841i | \(-0.583438\pi\) | ||||
−0.259136 | + | 0.965841i | \(0.583438\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.5189 | 1.71951 | ||||||||
\(404\) | 1.68411 | 0.0837877 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.71739 | −0.234120 | ||||||||
\(407\) | −16.5044 | −0.818093 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.0804569 | 0.00397834 | 0.00198917 | − | 0.999998i | \(-0.499367\pi\) | ||||
0.00198917 | + | 0.999998i | \(0.499367\pi\) | |||||||
\(410\) | −8.21231 | −0.405577 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11.0188 | −0.542857 | ||||||||
\(413\) | 11.9109 | 0.586097 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.0899 | 0.838912 | ||||||||
\(416\) | 4.95977 | 0.243173 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11.2073 | 0.548167 | ||||||||
\(419\) | −28.9145 | −1.41257 | −0.706284 | − | 0.707929i | \(-0.749630\pi\) | ||||
−0.706284 | + | 0.707929i | \(0.749630\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.21731 | 0.351750 | 0.175875 | − | 0.984412i | \(-0.443724\pi\) | ||||
0.175875 | + | 0.984412i | \(0.443724\pi\) | |||||||
\(422\) | −8.41083 | −0.409433 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.900743 | −0.0437439 | ||||||||
\(425\) | 3.19351 | 0.154908 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.797166 | −0.0385775 | ||||||||
\(428\) | 17.9195 | 0.866174 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.01880 | −0.338477 | ||||||||
\(431\) | −14.8324 | −0.714451 | −0.357226 | − | 0.934018i | \(-0.616277\pi\) | ||||
−0.357226 | + | 0.934018i | \(0.616277\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.83393 | 0.0881330 | 0.0440665 | − | 0.999029i | \(-0.485969\pi\) | ||||
0.0440665 | + | 0.999029i | \(0.485969\pi\) | |||||||
\(434\) | −10.0943 | −0.484540 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.83739 | 0.279560 | ||||||||
\(437\) | −13.2636 | −0.634482 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.07113 | 0.289759 | 0.144880 | − | 0.989449i | \(-0.453720\pi\) | ||||
0.144880 | + | 0.989449i | \(0.453720\pi\) | |||||||
\(440\) | 3.50940 | 0.167304 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.8391 | 0.753389 | ||||||||
\(443\) | 10.3870 | 0.493502 | 0.246751 | − | 0.969079i | \(-0.420637\pi\) | ||||
0.246751 | + | 0.969079i | \(0.420637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.1087 | −0.668818 | ||||||||
\(446\) | −14.5513 | −0.689025 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.45037 | −0.0685236 | ||||||||
\(449\) | −18.3877 | −0.867769 | −0.433885 | − | 0.900968i | \(-0.642857\pi\) | ||||
−0.433885 | + | 0.900968i | \(0.642857\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.8203 | −1.35709 | ||||||||
\(452\) | 8.99568 | 0.423121 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.2690 | 0.669676 | ||||||||
\(455\) | −7.19351 | −0.337237 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.31157 | −0.435577 | −0.217788 | − | 0.975996i | \(-0.569884\pi\) | ||||
−0.217788 | + | 0.975996i | \(0.569884\pi\) | |||||||
\(458\) | −7.56843 | −0.353649 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.15328 | −0.193648 | ||||||||
\(461\) | 24.2627 | 1.13003 | 0.565013 | − | 0.825082i | \(-0.308871\pi\) | ||||
0.565013 | + | 0.825082i | \(0.308871\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.8193 | 0.502814 | 0.251407 | − | 0.967881i | \(-0.419107\pi\) | ||||
0.251407 | + | 0.967881i | \(0.419107\pi\) | |||||||
\(464\) | 3.25254 | 0.150995 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.9102 | −1.10762 | ||||||||
\(467\) | 19.5232 | 0.903426 | 0.451713 | − | 0.892163i | \(-0.350813\pi\) | ||||
0.451713 | + | 0.892163i | \(0.350813\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.45037 | 0.0669719 | ||||||||
\(470\) | 8.66700 | 0.399779 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.21231 | −0.378002 | ||||||||
\(473\) | −24.6318 | −1.13257 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.19351 | 0.146528 | ||||||||
\(476\) | −4.63178 | −0.212297 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.3254 | 0.700966 | ||||||||
\(479\) | 23.8888 | 1.09151 | 0.545753 | − | 0.837946i | \(-0.316244\pi\) | ||||
0.545753 | + | 0.837946i | \(0.316244\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.3254 | −1.06355 | ||||||||
\(482\) | 17.9340 | 0.816872 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.31589 | 0.0598131 | ||||||||
\(485\) | −3.50940 | −0.159354 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.4263 | −0.925605 | −0.462802 | − | 0.886462i | \(-0.653156\pi\) | ||||
−0.462802 | + | 0.886462i | \(0.653156\pi\) | |||||||
\(488\) | 0.549629 | 0.0248805 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.89642 | −0.221198 | ||||||||
\(491\) | 8.04801 | 0.363202 | 0.181601 | − | 0.983372i | \(-0.441872\pi\) | ||||
0.181601 | + | 0.983372i | \(0.441872\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.3870 | 0.467808 | ||||||||
\(494\) | 15.8391 | 0.712634 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.95977 | 0.312503 | ||||||||
\(497\) | −9.63610 | −0.432238 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.5284 | −1.59047 | −0.795234 | − | 0.606303i | \(-0.792652\pi\) | ||||
−0.795234 | + | 0.606303i | \(0.792652\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.7029 | 0.656223 | ||||||||
\(503\) | −27.2456 | −1.21482 | −0.607410 | − | 0.794388i | \(-0.707792\pi\) | ||||
−0.607410 | + | 0.794388i | \(0.707792\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.68411 | 0.0749420 | ||||||||
\(506\) | −14.5755 | −0.647961 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15.3254 | 0.679953 | ||||||||
\(509\) | −7.64820 | −0.339001 | −0.169500 | − | 0.985530i | \(-0.554215\pi\) | ||||
−0.169500 | + | 0.985530i | \(0.554215\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.7412 | −0.475162 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.0856 | 0.709506 | ||||||||
\(515\) | −11.0188 | −0.485546 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.4160 | 1.33769 | ||||||||
\(518\) | 6.82097 | 0.299696 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.95977 | 0.217500 | ||||||||
\(521\) | −39.6557 | −1.73735 | −0.868675 | − | 0.495383i | \(-0.835028\pi\) | ||||
−0.868675 | + | 0.495383i | \(0.835028\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.5882 | −1.51244 | −0.756219 | − | 0.654319i | \(-0.772956\pi\) | ||||
−0.756219 | + | 0.654319i | \(0.772956\pi\) | |||||||
\(524\) | 0.886946 | 0.0387464 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.27134 | −0.360648 | ||||||||
\(527\) | 22.2261 | 0.968185 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.75024 | −0.250011 | ||||||||
\(530\) | −0.900743 | −0.0391258 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.63178 | −0.200813 | ||||||||
\(533\) | −40.7312 | −1.76426 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.9195 | 0.774729 | ||||||||
\(536\) | −1.00000 | −0.0431934 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.8655 | −0.554672 | ||||||||
\(539\) | −17.1835 | −0.740146 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.0025 | 1.50488 | 0.752438 | − | 0.658663i | \(-0.228878\pi\) | ||||
0.752438 | + | 0.658663i | \(0.228878\pi\) | |||||||
\(542\) | −20.2475 | −0.869706 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.19351 | 0.136921 | ||||||||
\(545\) | 5.83739 | 0.250046 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.3972 | 1.34245 | 0.671223 | − | 0.741255i | \(-0.265769\pi\) | ||||
0.671223 | + | 0.741255i | \(0.265769\pi\) | |||||||
\(548\) | 8.70291 | 0.371770 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.50940 | 0.149641 | ||||||||
\(551\) | 10.3870 | 0.442502 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.9347 | 0.762661 | ||||||||
\(554\) | −17.6413 | −0.749505 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.6456 | 0.790749 | ||||||||
\(557\) | −36.6635 | −1.55348 | −0.776742 | − | 0.629819i | \(-0.783129\pi\) | ||||
−0.776742 | + | 0.629819i | \(0.783129\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −34.8116 | −1.47238 | ||||||||
\(560\) | −1.45037 | −0.0612894 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.8391 | 0.752496 | ||||||||
\(563\) | 4.98120 | 0.209933 | 0.104966 | − | 0.994476i | \(-0.466527\pi\) | ||||
0.104966 | + | 0.994476i | \(0.466527\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.99568 | 0.378451 | ||||||||
\(566\) | 20.1550 | 0.847177 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.64388 | 0.278771 | ||||||||
\(569\) | 13.8298 | 0.579774 | 0.289887 | − | 0.957061i | \(-0.406382\pi\) | ||||
0.289887 | + | 0.957061i | \(0.406382\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.38702 | −0.267289 | −0.133644 | − | 0.991029i | \(-0.542668\pi\) | ||||
−0.133644 | + | 0.991029i | \(0.542668\pi\) | |||||||
\(572\) | 17.4058 | 0.727774 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.9109 | 0.497151 | ||||||||
\(575\) | −4.15328 | −0.173204 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.3117 | 1.09537 | 0.547686 | − | 0.836684i | \(-0.315509\pi\) | ||||
0.547686 | + | 0.836684i | \(0.315509\pi\) | |||||||
\(578\) | −6.80149 | −0.282905 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.25254 | 0.135054 | ||||||||
\(581\) | −24.7868 | −1.02833 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.16107 | −0.130918 | ||||||||
\(584\) | 7.40582 | 0.306455 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.6815 | 0.441248 | ||||||||
\(587\) | −15.7362 | −0.649502 | −0.324751 | − | 0.945800i | \(-0.605281\pi\) | ||||
−0.324751 | + | 0.945800i | \(0.605281\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.2261 | 0.915811 | ||||||||
\(590\) | −8.21231 | −0.338096 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.70291 | −0.193288 | ||||||||
\(593\) | 33.1275 | 1.36038 | 0.680192 | − | 0.733034i | \(-0.261896\pi\) | ||||
0.680192 | + | 0.733034i | \(0.261896\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.63178 | −0.189884 | ||||||||
\(596\) | 3.25254 | 0.133229 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −20.5993 | −0.842369 | ||||||||
\(599\) | −32.3528 | −1.32190 | −0.660950 | − | 0.750430i | \(-0.729846\pi\) | ||||
−0.660950 | + | 0.750430i | \(0.729846\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.53684 | 0.266643 | 0.133322 | − | 0.991073i | \(-0.457436\pi\) | ||||
0.133322 | + | 0.991073i | \(0.457436\pi\) | |||||||
\(602\) | 10.1799 | 0.414900 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.2354 | −0.579232 | ||||||||
\(605\) | 1.31589 | 0.0534985 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.7398 | 1.57240 | 0.786201 | − | 0.617971i | \(-0.212045\pi\) | ||||
0.786201 | + | 0.617971i | \(0.212045\pi\) | |||||||
\(608\) | 3.19351 | 0.129514 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.549629 | 0.0222538 | ||||||||
\(611\) | 42.9864 | 1.73904 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.6030 | 0.710977 | 0.355489 | − | 0.934681i | \(-0.384314\pi\) | ||||
0.355489 | + | 0.934681i | \(0.384314\pi\) | |||||||
\(614\) | −6.75957 | −0.272794 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.08993 | −0.205079 | ||||||||
\(617\) | −7.26533 | −0.292491 | −0.146246 | − | 0.989248i | \(-0.546719\pi\) | ||||
−0.146246 | + | 0.989248i | \(0.546719\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.8065 | −0.675510 | −0.337755 | − | 0.941234i | \(-0.609667\pi\) | ||||
−0.337755 | + | 0.941234i | \(0.609667\pi\) | |||||||
\(620\) | 6.95977 | 0.279511 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.1181 | 0.485890 | ||||||||
\(623\) | 20.4629 | 0.819829 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 13.9427 | 0.557261 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.58554 | −0.103174 | ||||||||
\(629\) | −15.0188 | −0.598839 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.65321 | −0.264860 | −0.132430 | − | 0.991192i | \(-0.542278\pi\) | ||||
−0.132430 | + | 0.991192i | \(0.542278\pi\) | |||||||
\(632\) | −12.3656 | −0.491877 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −22.1584 | −0.880024 | ||||||||
\(635\) | 15.3254 | 0.608169 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.2851 | −0.962212 | ||||||||
\(638\) | 11.4145 | 0.451903 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 33.4421 | 1.32088 | 0.660441 | − | 0.750878i | \(-0.270369\pi\) | ||||
0.660441 | + | 0.750878i | \(0.270369\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.3029 | −1.31334 | −0.656670 | − | 0.754178i | \(-0.728035\pi\) | ||||
−0.656670 | + | 0.754178i | \(0.728035\pi\) | |||||||
\(644\) | 6.02380 | 0.237371 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.1985 | 0.401255 | ||||||||
\(647\) | 44.0645 | 1.73235 | 0.866177 | − | 0.499737i | \(-0.166570\pi\) | ||||
0.866177 | + | 0.499737i | \(0.166570\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.8203 | −1.13130 | ||||||||
\(650\) | 4.95977 | 0.194538 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.7029 | −0.575810 | ||||||||
\(653\) | −20.8835 | −0.817233 | −0.408616 | − | 0.912706i | \(-0.633989\pi\) | ||||
−0.408616 | + | 0.912706i | \(0.633989\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.886946 | 0.0346558 | ||||||||
\(656\) | −8.21231 | −0.320637 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.5704 | −0.490044 | ||||||||
\(659\) | −25.9676 | −1.01155 | −0.505776 | − | 0.862665i | \(-0.668794\pi\) | ||||
−0.505776 | + | 0.862665i | \(0.668794\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.0352 | −0.545907 | −0.272954 | − | 0.962027i | \(-0.588001\pi\) | ||||
−0.272954 | + | 0.962027i | \(0.588001\pi\) | |||||||
\(662\) | 16.0607 | 0.624218 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.0899 | 0.663218 | ||||||||
\(665\) | −4.63178 | −0.179613 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.5087 | −0.523060 | ||||||||
\(668\) | 22.0728 | 0.854023 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.00000 | −0.0386334 | ||||||||
\(671\) | 1.92887 | 0.0744631 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.8066 | 0.763490 | 0.381745 | − | 0.924268i | \(-0.375323\pi\) | ||||
0.381745 | + | 0.924268i | \(0.375323\pi\) | |||||||
\(674\) | −12.7636 | −0.491637 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.5993 | 0.446128 | ||||||||
\(677\) | −21.8391 | −0.839344 | −0.419672 | − | 0.907676i | \(-0.637855\pi\) | ||||
−0.419672 | + | 0.907676i | \(0.637855\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.08993 | 0.195334 | ||||||||
\(680\) | 3.19351 | 0.122466 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 24.4246 | 0.935267 | ||||||||
\(683\) | 13.5943 | 0.520173 | 0.260086 | − | 0.965585i | \(-0.416249\pi\) | ||||
0.260086 | + | 0.965585i | \(0.416249\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.70291 | 0.332521 | ||||||||
\(686\) | 17.2542 | 0.658770 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.01880 | −0.267589 | ||||||||
\(689\) | −4.46748 | −0.170197 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.4060 | −1.68928 | −0.844641 | − | 0.535332i | \(-0.820186\pi\) | ||||
−0.844641 | + | 0.535332i | \(0.820186\pi\) | |||||||
\(692\) | 6.77058 | 0.257379 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −35.2929 | −1.33970 | ||||||||
\(695\) | 18.6456 | 0.707267 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.2261 | −0.993385 | ||||||||
\(698\) | −8.03760 | −0.304228 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.45037 | −0.0548189 | ||||||||
\(701\) | 2.38634 | 0.0901308 | 0.0450654 | − | 0.998984i | \(-0.485650\pi\) | ||||
0.0450654 | + | 0.998984i | \(0.485650\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.0188 | −0.566445 | ||||||||
\(704\) | 3.50940 | 0.132265 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.0943 | −0.906799 | ||||||||
\(707\) | −2.44259 | −0.0918629 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.1543 | 0.456464 | 0.228232 | − | 0.973607i | \(-0.426706\pi\) | ||||
0.228232 | + | 0.973607i | \(0.426706\pi\) | |||||||
\(710\) | 6.64388 | 0.249340 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14.1087 | −0.528747 | ||||||||
\(713\) | −28.9059 | −1.08253 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.4058 | 0.650941 | ||||||||
\(716\) | 13.6268 | 0.509256 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28.8700 | −1.07742 | ||||||||
\(719\) | 1.62576 | 0.0606308 | 0.0303154 | − | 0.999540i | \(-0.490349\pi\) | ||||
0.0303154 | + | 0.999540i | \(0.490349\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.9814 | 0.595177 | ||||||||
\(722\) | −8.80149 | −0.327557 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −21.2073 | −0.788163 | ||||||||
\(725\) | 3.25254 | 0.120796 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.18072 | 0.340494 | 0.170247 | − | 0.985401i | \(-0.445543\pi\) | ||||
0.170247 | + | 0.985401i | \(0.445543\pi\) | |||||||
\(728\) | −7.19351 | −0.266609 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.40582 | 0.274102 | ||||||||
\(731\) | −22.4146 | −0.829035 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.4220 | −1.16060 | −0.580299 | − | 0.814404i | \(-0.697064\pi\) | ||||
−0.580299 | + | 0.814404i | \(0.697064\pi\) | |||||||
\(734\) | 25.4873 | 0.940753 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.15328 | −0.153092 | ||||||||
\(737\) | −3.50940 | −0.129270 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.0326 | −1.06798 | −0.533991 | − | 0.845490i | \(-0.679308\pi\) | ||||
−0.533991 | + | 0.845490i | \(0.679308\pi\) | |||||||
\(740\) | −4.70291 | −0.172882 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.30641 | 0.0479599 | ||||||||
\(743\) | 40.3452 | 1.48012 | 0.740060 | − | 0.672540i | \(-0.234797\pi\) | ||||
0.740060 | + | 0.672540i | \(0.234797\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.25254 | 0.119164 | ||||||||
\(746\) | −10.7613 | −0.393998 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.2073 | 0.409780 | ||||||||
\(749\) | −25.9900 | −0.949654 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0376 | 0.366277 | 0.183139 | − | 0.983087i | \(-0.441374\pi\) | ||||
0.183139 | + | 0.983087i | \(0.441374\pi\) | |||||||
\(752\) | 8.66700 | 0.316053 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.1319 | 0.587487 | ||||||||
\(755\) | −14.2354 | −0.518080 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.71825 | 0.280524 | 0.140262 | − | 0.990114i | \(-0.455205\pi\) | ||||
0.140262 | + | 0.990114i | \(0.455205\pi\) | |||||||
\(758\) | −24.4471 | −0.887957 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.19351 | 0.115841 | ||||||||
\(761\) | 37.4341 | 1.35699 | 0.678493 | − | 0.734607i | \(-0.262634\pi\) | ||||
0.678493 | + | 0.734607i | \(0.262634\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.46639 | −0.306504 | ||||||||
\(764\) | 4.98120 | 0.180213 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.50440 | 0.162750 | ||||||||
\(767\) | −40.7312 | −1.47072 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.1645 | 1.19594 | 0.597970 | − | 0.801518i | \(-0.295974\pi\) | ||||
0.597970 | + | 0.801518i | \(0.295974\pi\) | |||||||
\(770\) | −5.08993 | −0.183428 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.92455 | 0.105257 | ||||||||
\(773\) | 54.1967 | 1.94932 | 0.974660 | − | 0.223690i | \(-0.0718104\pi\) | ||||
0.974660 | + | 0.223690i | \(0.0718104\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.95977 | 0.250002 | ||||||||
\(776\) | −3.50940 | −0.125980 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19.8125 | −0.710313 | ||||||||
\(779\) | −26.2261 | −0.939648 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.3160 | 0.834314 | ||||||||
\(782\) | −13.2636 | −0.474304 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.89642 | −0.174872 | ||||||||
\(785\) | −2.58554 | −0.0922818 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −53.2021 | −1.89645 | −0.948224 | − | 0.317602i | \(-0.897122\pi\) | ||||
−0.948224 | + | 0.317602i | \(0.897122\pi\) | |||||||
\(788\) | −7.91954 | −0.282122 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.3656 | −0.439948 | ||||||||
\(791\) | −13.0471 | −0.463901 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.72603 | 0.0968042 | ||||||||
\(794\) | −5.92023 | −0.210101 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.08993 | 0.322184 | ||||||||
\(797\) | 17.8183 | 0.631158 | 0.315579 | − | 0.948899i | \(-0.397801\pi\) | ||||
0.315579 | + | 0.948899i | \(0.397801\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.6782 | 0.979183 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.3784 | −0.366473 | ||||||||
\(803\) | 25.9900 | 0.917167 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.02380 | 0.212311 | ||||||||
\(806\) | 34.5189 | 1.21588 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.68411 | 0.0592468 | ||||||||
\(809\) | −26.0000 | −0.914111 | −0.457056 | − | 0.889438i | \(-0.651096\pi\) | ||||
−0.457056 | + | 0.889438i | \(0.651096\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.7819 | 1.92365 | 0.961826 | − | 0.273660i | \(-0.0882344\pi\) | ||||
0.961826 | + | 0.273660i | \(0.0882344\pi\) | |||||||
\(812\) | −4.71739 | −0.165548 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.5044 | −0.578479 | ||||||||
\(815\) | −14.7029 | −0.515021 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.4146 | −0.784188 | ||||||||
\(818\) | 0.0804569 | 0.00281311 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.21231 | −0.286786 | ||||||||
\(821\) | 33.6672 | 1.17499 | 0.587496 | − | 0.809227i | \(-0.300114\pi\) | ||||
0.587496 | + | 0.809227i | \(0.300114\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.4434 | 1.37491 | 0.687456 | − | 0.726226i | \(-0.258728\pi\) | ||||
0.687456 | + | 0.726226i | \(0.258728\pi\) | |||||||
\(824\) | −11.0188 | −0.383858 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.9109 | 0.414433 | ||||||||
\(827\) | 40.2268 | 1.39882 | 0.699411 | − | 0.714719i | \(-0.253446\pi\) | ||||
0.699411 | + | 0.714719i | \(0.253446\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.2878 | −0.669892 | −0.334946 | − | 0.942237i | \(-0.608718\pi\) | ||||
−0.334946 | + | 0.942237i | \(0.608718\pi\) | |||||||
\(830\) | 17.0899 | 0.593200 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.95977 | 0.171949 | ||||||||
\(833\) | −15.6368 | −0.541782 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.0728 | 0.763862 | ||||||||
\(836\) | 11.2073 | 0.387613 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −28.9145 | −0.998836 | ||||||||
\(839\) | −20.5079 | −0.708010 | −0.354005 | − | 0.935244i | \(-0.615180\pi\) | ||||
−0.354005 | + | 0.935244i | \(0.615180\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.4210 | −0.635206 | ||||||||
\(842\) | 7.21731 | 0.248725 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.41083 | −0.289513 | ||||||||
\(845\) | 11.5993 | 0.399029 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.90853 | −0.0655778 | ||||||||
\(848\) | −0.900743 | −0.0309316 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.19351 | 0.109537 | ||||||||
\(851\) | 19.5325 | 0.669566 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −54.3342 | −1.86037 | −0.930183 | − | 0.367096i | \(-0.880352\pi\) | ||||
−0.930183 | + | 0.367096i | \(0.880352\pi\) | |||||||
\(854\) | −0.797166 | −0.0272784 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.9195 | 0.612477 | ||||||||
\(857\) | 6.35526 | 0.217092 | 0.108546 | − | 0.994091i | \(-0.465381\pi\) | ||||
0.108546 | + | 0.994091i | \(0.465381\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.7602 | −0.708331 | −0.354165 | − | 0.935183i | \(-0.615235\pi\) | ||||
−0.354165 | + | 0.935183i | \(0.615235\pi\) | |||||||
\(860\) | −7.01880 | −0.239339 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.8324 | −0.505193 | ||||||||
\(863\) | 41.0916 | 1.39878 | 0.699388 | − | 0.714743i | \(-0.253456\pi\) | ||||
0.699388 | + | 0.714743i | \(0.253456\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.77058 | 0.230207 | ||||||||
\(866\) | 1.83393 | 0.0623195 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.0943 | −0.342621 | ||||||||
\(869\) | −43.3958 | −1.47210 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.95977 | −0.168055 | ||||||||
\(872\) | 5.83739 | 0.197679 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13.2636 | −0.448646 | ||||||||
\(875\) | −1.45037 | −0.0490315 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.5803 | −1.23523 | −0.617614 | − | 0.786481i | \(-0.711901\pi\) | ||||
−0.617614 | + | 0.786481i | \(0.711901\pi\) | |||||||
\(878\) | 6.07113 | 0.204891 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.50940 | 0.118302 | ||||||||
\(881\) | −18.8828 | −0.636177 | −0.318088 | − | 0.948061i | \(-0.603041\pi\) | ||||
−0.318088 | + | 0.948061i | \(0.603041\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.1181 | −0.811637 | −0.405819 | − | 0.913954i | \(-0.633014\pi\) | ||||
−0.405819 | + | 0.913954i | \(0.633014\pi\) | |||||||
\(884\) | 15.8391 | 0.532726 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.3870 | 0.348959 | ||||||||
\(887\) | −40.1104 | −1.34678 | −0.673388 | − | 0.739289i | \(-0.735162\pi\) | ||||
−0.673388 | + | 0.739289i | \(0.735162\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.2275 | −0.745486 | ||||||||
\(890\) | −14.1087 | −0.472926 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.5513 | −0.487214 | ||||||||
\(893\) | 27.6782 | 0.926215 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.6268 | 0.455493 | ||||||||
\(896\) | −1.45037 | −0.0484535 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.3877 | −0.613606 | ||||||||
\(899\) | 22.6369 | 0.754984 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.87653 | −0.0958312 | ||||||||
\(902\) | −28.8203 | −0.959611 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.99568 | 0.299192 | ||||||||
\(905\) | −21.2073 | −0.704955 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.5423 | −0.449663 | −0.224832 | − | 0.974398i | \(-0.572183\pi\) | ||||
−0.224832 | + | 0.974398i | \(0.572183\pi\) | |||||||
\(908\) | 14.2690 | 0.473532 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.19351 | −0.238463 | ||||||||
\(911\) | 47.4931 | 1.57352 | 0.786759 | − | 0.617261i | \(-0.211758\pi\) | ||||
0.786759 | + | 0.617261i | \(0.211758\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 59.9754 | 1.98490 | ||||||||
\(914\) | −9.31157 | −0.307999 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.56843 | −0.250068 | ||||||||
\(917\) | −1.28640 | −0.0424807 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.48365 | 0.147902 | 0.0739510 | − | 0.997262i | \(-0.476439\pi\) | ||||
0.0739510 | + | 0.997262i | \(0.476439\pi\) | |||||||
\(920\) | −4.15328 | −0.136930 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 24.2627 | 0.799049 | ||||||||
\(923\) | 32.9521 | 1.08463 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.70291 | −0.154631 | ||||||||
\(926\) | 10.8193 | 0.355543 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.25254 | 0.106770 | ||||||||
\(929\) | −6.01516 | −0.197351 | −0.0986755 | − | 0.995120i | \(-0.531461\pi\) | ||||
−0.0986755 | + | 0.995120i | \(0.531461\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.6368 | −0.512475 | ||||||||
\(932\) | −23.9102 | −0.783205 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19.5232 | 0.638819 | ||||||||
\(935\) | 11.2073 | 0.366518 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.4017 | 1.28720 | 0.643598 | − | 0.765364i | \(-0.277441\pi\) | ||||
0.643598 | + | 0.765364i | \(0.277441\pi\) | |||||||
\(938\) | 1.45037 | 0.0473563 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.66700 | 0.282686 | ||||||||
\(941\) | 31.9900 | 1.04284 | 0.521422 | − | 0.853299i | \(-0.325402\pi\) | ||||
0.521422 | + | 0.853299i | \(0.325402\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.1081 | 1.11071 | ||||||||
\(944\) | −8.21231 | −0.267288 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.6318 | −0.800848 | ||||||||
\(947\) | 17.7680 | 0.577381 | 0.288690 | − | 0.957422i | \(-0.406780\pi\) | ||||
0.288690 | + | 0.957422i | \(0.406780\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.7312 | 1.19234 | ||||||||
\(950\) | 3.19351 | 0.103611 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.63178 | −0.150117 | ||||||||
\(953\) | −41.0226 | −1.32885 | −0.664426 | − | 0.747354i | \(-0.731324\pi\) | ||||
−0.664426 | + | 0.747354i | \(0.731324\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.98120 | 0.161188 | ||||||||
\(956\) | 15.3254 | 0.495658 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.8888 | 0.771812 | ||||||||
\(959\) | −12.6225 | −0.407600 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.4384 | 0.562530 | ||||||||
\(962\) | −23.3254 | −0.752040 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.9340 | 0.577616 | ||||||||
\(965\) | 2.92455 | 0.0941445 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.3081 | 1.52133 | 0.760663 | − | 0.649147i | \(-0.224874\pi\) | ||||
0.760663 | + | 0.649147i | \(0.224874\pi\) | |||||||
\(968\) | 1.31589 | 0.0422943 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.50940 | −0.112680 | ||||||||
\(971\) | −0.494667 | −0.0158746 | −0.00793731 | − | 0.999968i | \(-0.502527\pi\) | ||||
−0.00793731 | + | 0.999968i | \(0.502527\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27.0430 | −0.866959 | ||||||||
\(974\) | −20.4263 | −0.654501 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.549629 | 0.0175932 | ||||||||
\(977\) | 29.2760 | 0.936622 | 0.468311 | − | 0.883564i | \(-0.344863\pi\) | ||||
0.468311 | + | 0.883564i | \(0.344863\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −49.5132 | −1.58245 | ||||||||
\(980\) | −4.89642 | −0.156410 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.04801 | 0.256822 | ||||||||
\(983\) | −16.9626 | −0.541021 | −0.270511 | − | 0.962717i | \(-0.587193\pi\) | ||||
−0.270511 | + | 0.962717i | \(0.587193\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.91954 | −0.252338 | ||||||||
\(986\) | 10.3870 | 0.330790 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.8391 | 0.503908 | ||||||||
\(989\) | 29.1511 | 0.926950 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.6996 | 1.19757 | 0.598784 | − | 0.800911i | \(-0.295651\pi\) | ||||
0.598784 | + | 0.800911i | \(0.295651\pi\) | |||||||
\(992\) | 6.95977 | 0.220973 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.63610 | −0.305638 | ||||||||
\(995\) | 9.08993 | 0.288170 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.4427 | 0.869120 | 0.434560 | − | 0.900643i | \(-0.356904\pi\) | ||||
0.434560 | + | 0.900643i | \(0.356904\pi\) | |||||||
\(998\) | −35.5284 | −1.12463 | ||||||||
\(999\) | 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 | 6030.2.a.bu.1.2 | 4 | ||
3.2 | odd | 2 | 2010.2.a.r.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2010.2.a.r.1.2 | ✓ | 4 | 3.2 | odd | 2 | ||
6030.2.a.bu.1.2 | 4 | 1.1 | even | 1 | trivial |