Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, 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("4020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.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: | \(32.0998616126\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{15})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.95630\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.44512 | −1.30213 | −0.651067 | − | 0.759020i | \(-0.725678\pi\) | ||||
−0.651067 | + | 0.759020i | \(0.725678\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.102193 | −0.0308124 | −0.0154062 | − | 0.999881i | \(-0.504904\pi\) | ||||
−0.0154062 | + | 0.999881i | \(0.504904\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.50361 | 0.417027 | 0.208514 | − | 0.978019i | \(-0.433137\pi\) | ||||
0.208514 | + | 0.978019i | \(0.433137\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.84187 | −1.65940 | −0.829699 | − | 0.558211i | \(-0.811488\pi\) | ||||
−0.829699 | + | 0.558211i | \(0.811488\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.86889 | 1.11700 | 0.558499 | − | 0.829505i | \(-0.311377\pi\) | ||||
0.558499 | + | 0.829505i | \(0.311377\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.44512 | −0.751788 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.49448 | −1.35419 | −0.677096 | − | 0.735895i | \(-0.736762\pi\) | ||||
−0.677096 | + | 0.735895i | \(0.736762\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.53976 | 0.657317 | 0.328659 | − | 0.944449i | \(-0.393403\pi\) | ||||
0.328659 | + | 0.944449i | \(0.393403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.02859 | 0.723556 | 0.361778 | − | 0.932264i | \(-0.382170\pi\) | ||||
0.361778 | + | 0.932264i | \(0.382170\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.102193 | −0.0177896 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.44512 | −0.582332 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.49448 | −1.39648 | −0.698242 | − | 0.715862i | \(-0.746034\pi\) | ||||
−0.698242 | + | 0.715862i | \(0.746034\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.50361 | 0.240771 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.72023 | −0.424828 | −0.212414 | − | 0.977180i | \(-0.568133\pi\) | ||||
−0.212414 | + | 0.977180i | \(0.568133\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.71734 | −1.02438 | −0.512192 | − | 0.858871i | \(-0.671167\pi\) | ||||
−0.512192 | + | 0.858871i | \(0.671167\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.84943 | −0.269767 | −0.134884 | − | 0.990861i | \(-0.543066\pi\) | ||||
−0.134884 | + | 0.990861i | \(0.543066\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.86889 | 0.695555 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.84187 | −0.958054 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.79252 | −1.07039 | −0.535193 | − | 0.844730i | \(-0.679761\pi\) | ||||
−0.535193 | + | 0.844730i | \(0.679761\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.102193 | −0.0137797 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.86889 | 0.644900 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.9534 | 1.42601 | 0.713006 | − | 0.701158i | \(-0.247333\pi\) | ||||
0.713006 | + | 0.701158i | \(0.247333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.796590 | 0.101993 | 0.0509964 | − | 0.998699i | \(-0.483760\pi\) | ||||
0.0509964 | + | 0.998699i | \(0.483760\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.44512 | −0.434045 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.50361 | 0.186500 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000 | 0.122169 | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.49448 | −0.781843 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.59727 | −0.782952 | −0.391476 | − | 0.920188i | \(-0.628035\pi\) | ||||
−0.391476 | + | 0.920188i | \(0.628035\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.3791 | −1.44886 | −0.724431 | − | 0.689347i | \(-0.757897\pi\) | ||||
−0.724431 | + | 0.689347i | \(0.757897\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.352068 | 0.0401219 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.29923 | −0.933736 | −0.466868 | − | 0.884327i | \(-0.654618\pi\) | ||||
−0.466868 | + | 0.884327i | \(0.654618\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.0528416 | −0.00580012 | −0.00290006 | − | 0.999996i | \(-0.500923\pi\) | ||||
−0.00290006 | + | 0.999996i | \(0.500923\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.84187 | −0.742105 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.53976 | 0.379502 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.48436 | 0.581341 | 0.290671 | − | 0.956823i | \(-0.406122\pi\) | ||||
0.290671 | + | 0.956823i | \(0.406122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.18014 | −0.543026 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.02859 | 0.417745 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.86889 | 0.499537 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.284239 | −0.0288601 | −0.0144301 | − | 0.999896i | \(-0.504593\pi\) | ||||
−0.0144301 | + | 0.999896i | \(0.504593\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.102193 | −0.0102708 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.5240 | −1.44520 | −0.722598 | − | 0.691268i | \(-0.757052\pi\) | ||||
−0.722598 | + | 0.691268i | \(0.757052\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.84536 | 0.181829 | 0.0909146 | − | 0.995859i | \(-0.471021\pi\) | ||||
0.0909146 | + | 0.995859i | \(0.471021\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.44512 | −0.336210 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.3803 | −1.19684 | −0.598422 | − | 0.801181i | \(-0.704206\pi\) | ||||
−0.598422 | + | 0.801181i | \(0.704206\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.81507 | −0.556982 | −0.278491 | − | 0.960439i | \(-0.589834\pi\) | ||||
−0.278491 | + | 0.960439i | \(0.589834\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.49448 | −0.806260 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.42474 | 0.228100 | 0.114050 | − | 0.993475i | \(-0.463618\pi\) | ||||
0.114050 | + | 0.993475i | \(0.463618\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.49448 | −0.605613 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.50361 | 0.139009 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 23.5711 | 2.16076 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9896 | −0.999051 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.72023 | −0.245275 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.1238 | 1.34202 | 0.671010 | − | 0.741448i | \(-0.265861\pi\) | ||||
0.671010 | + | 0.741448i | \(0.265861\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.71734 | −0.591429 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.80126 | 0.681599 | 0.340800 | − | 0.940136i | \(-0.389302\pi\) | ||||
0.340800 | + | 0.940136i | \(0.389302\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.7739 | −1.45448 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.13387 | −0.353181 | −0.176590 | − | 0.984284i | \(-0.556507\pi\) | ||||
−0.176590 | + | 0.984284i | \(0.556507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.7311 | 0.995023 | 0.497511 | − | 0.867457i | \(-0.334247\pi\) | ||||
0.497511 | + | 0.867457i | \(0.334247\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.84943 | −0.155750 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.153659 | −0.0128496 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.53976 | 0.293961 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.86889 | 0.401579 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.2089 | −1.40981 | −0.704905 | − | 0.709301i | \(-0.749011\pi\) | ||||
−0.704905 | + | 0.709301i | \(0.749011\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.5456 | −1.10233 | −0.551163 | − | 0.834398i | \(-0.685816\pi\) | ||||
−0.551163 | + | 0.834398i | \(0.685816\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.84187 | −0.553133 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.02859 | 0.323584 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.42278 | 0.273168 | 0.136584 | − | 0.990628i | \(-0.456388\pi\) | ||||
0.136584 | + | 0.990628i | \(0.456388\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.79252 | −0.617987 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.3743 | 1.76334 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.16442 | −0.639487 | −0.319743 | − | 0.947504i | \(-0.603597\pi\) | ||||
−0.319743 | + | 0.947504i | \(0.603597\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.102193 | −0.00795573 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.99342 | 0.541167 | 0.270584 | − | 0.962697i | \(-0.412783\pi\) | ||||
0.270584 | + | 0.962697i | \(0.412783\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.7391 | −0.826088 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.86889 | 0.372333 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.15345 | −0.315781 | −0.157891 | − | 0.987457i | \(-0.550469\pi\) | ||||
−0.157891 | + | 0.987457i | \(0.550469\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.44512 | −0.260427 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.9534 | 0.823309 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.9018 | −1.41279 | −0.706394 | − | 0.707819i | \(-0.749679\pi\) | ||||
−0.706394 | + | 0.707819i | \(0.749679\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.63651 | −0.121641 | −0.0608205 | − | 0.998149i | \(-0.519372\pi\) | ||||
−0.0608205 | + | 0.998149i | \(0.519372\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.796590 | 0.0588856 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.49448 | −0.624526 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.699193 | 0.0511301 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.44512 | −0.250596 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.41247 | −0.319275 | −0.159637 | − | 0.987176i | \(-0.551033\pi\) | ||||
−0.159637 | + | 0.987176i | \(0.551033\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.83485 | −0.204057 | −0.102029 | − | 0.994781i | \(-0.532533\pi\) | ||||
−0.102029 | + | 0.994781i | \(0.532533\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.50361 | 0.107676 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.2785 | −0.946052 | −0.473026 | − | 0.881049i | \(-0.656838\pi\) | ||||
−0.473026 | + | 0.881049i | \(0.656838\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.4658 | 0.954562 | 0.477281 | − | 0.878751i | \(-0.341622\pi\) | ||||
0.477281 | + | 0.878751i | \(0.341622\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | 0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.1949 | −0.855916 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.72023 | −0.189989 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.49448 | −0.451397 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.497567 | −0.0344174 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.1568 | 0.768067 | 0.384034 | − | 0.923319i | \(-0.374535\pi\) | ||||
0.384034 | + | 0.923319i | \(0.374535\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.59727 | −0.452038 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.71734 | −0.458119 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.8790 | −0.942168 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.3791 | −0.836501 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.2875 | −0.692014 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.28911 | −0.220255 | −0.110128 | − | 0.993917i | \(-0.535126\pi\) | ||||
−0.110128 | + | 0.993917i | \(0.535126\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.582490 | −0.0386612 | −0.0193306 | − | 0.999813i | \(-0.506154\pi\) | ||||
−0.0193306 | + | 0.999813i | \(0.506154\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.0911463 | −0.00602312 | −0.00301156 | − | 0.999995i | \(-0.500959\pi\) | ||||
−0.00301156 | + | 0.999995i | \(0.500959\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.352068 | 0.0231644 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.61482 | 0.564375 | 0.282188 | − | 0.959359i | \(-0.408940\pi\) | ||||
0.282188 | + | 0.959359i | \(0.408940\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.84943 | −0.120644 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.29923 | −0.539093 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.2902 | 0.989038 | 0.494519 | − | 0.869167i | \(-0.335344\pi\) | ||||
0.494519 | + | 0.869167i | \(0.335344\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.08839 | −0.521019 | −0.260509 | − | 0.965471i | \(-0.583890\pi\) | ||||
−0.260509 | + | 0.965471i | \(0.583890\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.86889 | 0.311062 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.32092 | 0.465819 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.0528416 | −0.00334870 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.18887 | −0.453758 | −0.226879 | − | 0.973923i | \(-0.572852\pi\) | ||||
−0.226879 | + | 0.973923i | \(0.572852\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.663692 | 0.0417259 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.84187 | −0.428455 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.2474 | 0.888726 | 0.444363 | − | 0.895847i | \(-0.353430\pi\) | ||||
0.444363 | + | 0.895847i | \(0.353430\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.2645 | 1.81841 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.53976 | 0.219106 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.8631 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314344\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314344\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.79252 | −0.478691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.48436 | 0.335638 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.16791 | −0.315093 | −0.157546 | − | 0.987512i | \(-0.550358\pi\) | ||||
−0.157546 | + | 0.987512i | \(0.550358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.1095 | 1.70753 | 0.853765 | − | 0.520658i | \(-0.174313\pi\) | ||||
0.853765 | + | 0.520658i | \(0.174313\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.18014 | −0.313516 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.102193 | −0.00616248 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.8573 | 1.19311 | 0.596554 | − | 0.802573i | \(-0.296536\pi\) | ||||
0.596554 | + | 0.802573i | \(0.296536\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.02859 | 0.241185 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.38973 | −0.321524 | −0.160762 | − | 0.986993i | \(-0.551395\pi\) | ||||
−0.160762 | + | 0.986993i | \(0.551395\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.0292 | 0.655616 | 0.327808 | − | 0.944744i | \(-0.393690\pi\) | ||||
0.327808 | + | 0.944744i | \(0.393690\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.86889 | 0.288408 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.37152 | 0.553183 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.8112 | 1.75360 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.284239 | −0.0166624 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.1050 | −1.58349 | −0.791744 | − | 0.610853i | \(-0.790827\pi\) | ||||
−0.791744 | + | 0.610853i | \(0.790827\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.9534 | 0.637732 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.102193 | −0.00592985 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.76518 | −0.564735 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.1421 | 1.33389 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.5240 | −0.834385 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.796590 | 0.0456126 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.5608 | 1.40176 | 0.700879 | − | 0.713280i | \(-0.252791\pi\) | ||||
0.700879 | + | 0.713280i | \(0.252791\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.84536 | 0.104979 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.5985 | −1.16803 | −0.584017 | − | 0.811742i | \(-0.698520\pi\) | ||||
−0.584017 | + | 0.811742i | \(0.698520\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.7980 | 1.68429 | 0.842143 | − | 0.539255i | \(-0.181294\pi\) | ||||
0.842143 | + | 0.539255i | \(0.181294\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.44512 | −0.194111 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.174862 | −0.00982122 | −0.00491061 | − | 0.999988i | \(-0.501563\pi\) | ||||
−0.00491061 | + | 0.999988i | \(0.501563\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.361740 | −0.0202535 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.3803 | −0.690999 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.3123 | −1.85355 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.50361 | 0.0834055 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.81507 | −0.321574 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.37152 | 0.351273 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.36816 | 0.130166 | 0.0650829 | − | 0.997880i | \(-0.479269\pi\) | ||||
0.0650829 | + | 0.997880i | \(0.479269\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.49448 | −0.465494 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.00000 | 0.0546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.08997 | 0.113848 | 0.0569238 | − | 0.998379i | \(-0.481871\pi\) | ||||
0.0569238 | + | 0.998379i | \(0.481871\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.42474 | 0.131694 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.411695 | −0.0222945 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.34196 | 0.396428 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.49448 | −0.349651 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.8864 | −0.960194 | −0.480097 | − | 0.877215i | \(-0.659399\pi\) | ||||
−0.480097 | + | 0.877215i | \(0.659399\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.5298 | −1.84834 | −0.924170 | − | 0.381982i | \(-0.875242\pi\) | ||||
−0.924170 | + | 0.381982i | \(0.875242\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.50361 | 0.0802569 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.9949 | 0.957770 | 0.478885 | − | 0.877878i | \(-0.341041\pi\) | ||||
0.478885 | + | 0.877878i | \(0.341041\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.59727 | −0.350147 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 23.5711 | 1.24752 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.9871 | −1.47710 | −0.738552 | − | 0.674197i | \(-0.764490\pi\) | ||||
−0.738552 | + | 0.674197i | \(0.764490\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.70605 | 0.247687 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.9896 | −0.576802 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.3791 | −0.647951 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.4131 | 1.06556 | 0.532778 | − | 0.846255i | \(-0.321148\pi\) | ||||
0.532778 | + | 0.846255i | \(0.321148\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.72023 | −0.141609 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.8462 | 1.39379 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.0922842 | 0.00477829 | 0.00238915 | − | 0.999997i | \(-0.499240\pi\) | ||||
0.00238915 | + | 0.999997i | \(0.499240\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.32243 | 0.274119 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.9406 | −0.767446 | −0.383723 | − | 0.923448i | \(-0.625358\pi\) | ||||
−0.383723 | + | 0.923448i | \(0.625358\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.1238 | 0.774816 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.1996 | −1.54313 | −0.771563 | − | 0.636152i | \(-0.780525\pi\) | ||||
−0.771563 | + | 0.636152i | \(0.780525\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.352068 | 0.0179431 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.71734 | −0.341462 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.4739 | 0.784559 | 0.392279 | − | 0.919846i | \(-0.371687\pi\) | ||||
0.392279 | + | 0.919846i | \(0.371687\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44.4344 | 2.24714 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.80126 | 0.393522 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.29923 | −0.417579 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.7452 | 1.49287 | 0.746434 | − | 0.665459i | \(-0.231764\pi\) | ||||
0.746434 | + | 0.665459i | \(0.231764\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.7739 | −0.839746 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.69866 | −0.134765 | −0.0673823 | − | 0.997727i | \(-0.521465\pi\) | ||||
−0.0673823 | + | 0.997727i | \(0.521465\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.05744 | 0.301743 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.868078 | 0.0430290 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.1955 | −0.553580 | −0.276790 | − | 0.960930i | \(-0.589271\pi\) | ||||
−0.276790 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.13387 | −0.203909 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −37.7359 | −1.85686 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0528416 | −0.00259389 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.7311 | 0.574477 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.27275 | −0.208738 | −0.104369 | − | 0.994539i | \(-0.533282\pi\) | ||||
−0.104369 | + | 0.994539i | \(0.533282\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.92599 | 0.142604 | 0.0713020 | − | 0.997455i | \(-0.477285\pi\) | ||||
0.0713020 | + | 0.997455i | \(0.477285\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.84943 | −0.0899224 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.84187 | −0.331880 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.74435 | −0.132808 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.153659 | −0.00741873 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.8707 | −1.00531 | −0.502654 | − | 0.864488i | \(-0.667643\pi\) | ||||
−0.502654 | + | 0.864488i | \(0.667643\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.6840 | 0.753726 | 0.376863 | − | 0.926269i | \(-0.377003\pi\) | ||||
0.376863 | + | 0.926269i | \(0.377003\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.53976 | 0.169719 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −31.6209 | −1.51263 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.41556 | −0.353925 | −0.176963 | − | 0.984218i | \(-0.556627\pi\) | ||||
−0.176963 | + | 0.984218i | \(0.556627\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.86889 | 0.231852 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.8336 | 0.562231 | 0.281115 | − | 0.959674i | \(-0.409296\pi\) | ||||
0.281115 | + | 0.959674i | \(0.409296\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.48436 | 0.259984 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.2089 | −0.813954 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.5338 | 1.39379 | 0.696893 | − | 0.717175i | \(-0.254565\pi\) | ||||
0.696893 | + | 0.717175i | \(0.254565\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.277989 | 0.0130900 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.5456 | −0.636428 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.18014 | −0.242849 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −39.0155 | −1.82507 | −0.912534 | − | 0.409000i | \(-0.865877\pi\) | ||||
−0.912534 | + | 0.409000i | \(0.865877\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.84187 | −0.319351 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.08708 | −0.283504 | −0.141752 | − | 0.989902i | \(-0.545273\pi\) | ||||
−0.141752 | + | 0.989902i | \(0.545273\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.85954 | −0.225842 | −0.112921 | − | 0.993604i | \(-0.536021\pi\) | ||||
−0.112921 | + | 0.993604i | \(0.536021\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.02859 | 0.186821 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.5083 | −0.578816 | −0.289408 | − | 0.957206i | \(-0.593458\pi\) | ||||
−0.289408 | + | 0.957206i | \(0.593458\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.44512 | −0.159081 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.42278 | 0.157714 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.686467 | 0.0315638 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.86889 | 0.223400 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.79252 | −0.356795 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.6997 | −0.808722 | −0.404361 | − | 0.914600i | \(-0.632506\pi\) | ||||
−0.404361 | + | 0.914600i | \(0.632506\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.7724 | −0.582372 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.3743 | 1.01807 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.284239 | −0.0129066 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.845295 | 0.0383040 | 0.0191520 | − | 0.999817i | \(-0.493903\pi\) | ||||
0.0191520 | + | 0.999817i | \(0.493903\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.16442 | −0.369208 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.02485 | −0.136510 | −0.0682549 | − | 0.997668i | \(-0.521743\pi\) | ||||
−0.0682549 | + | 0.997668i | \(0.521743\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.2186 | −1.09075 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.102193 | −0.00459324 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.7284 | 1.01951 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.10824 | 0.273442 | 0.136721 | − | 0.990610i | \(-0.456344\pi\) | ||||
0.136721 | + | 0.990610i | \(0.456344\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.99342 | 0.312443 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.3757 | 1.30980 | 0.654898 | − | 0.755717i | \(-0.272712\pi\) | ||||
0.654898 | + | 0.755717i | \(0.272712\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.5240 | −0.646311 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.7391 | −0.476942 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.5752 | 0.601709 | 0.300855 | − | 0.953670i | \(-0.402728\pi\) | ||||
0.300855 | + | 0.953670i | \(0.402728\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 42.6475 | 1.88661 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.86889 | 0.214967 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.84536 | 0.0813165 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.188999 | 0.00831218 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.15345 | −0.182316 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.5900 | 1.51542 | 0.757708 | − | 0.652593i | \(-0.226319\pi\) | ||||
0.757708 | + | 0.652593i | \(0.226319\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.0201 | −0.744237 | −0.372119 | − | 0.928185i | \(-0.621369\pi\) | ||||
−0.372119 | + | 0.928185i | \(0.621369\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.44512 | −0.150358 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −27.5631 | −1.20067 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.1782 | 0.833836 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.9534 | 0.475337 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.09017 | −0.177165 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.3803 | −0.535245 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.9018 | −0.815674 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.497567 | −0.0214317 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.4214 | −1.60887 | −0.804436 | − | 0.594040i | \(-0.797532\pi\) | ||||
−0.804436 | + | 0.594040i | \(0.797532\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.63651 | −0.0702294 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.81507 | −0.249090 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.9358 | 1.49375 | 0.746874 | − | 0.664966i | \(-0.231554\pi\) | ||||
0.746874 | + | 0.664966i | \(0.231554\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.796590 | 0.0339976 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.2347 | 0.734223 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.5919 | 1.21585 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.49448 | −0.360570 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.45768 | −0.231249 | −0.115625 | − | 0.993293i | \(-0.536887\pi\) | ||||
−0.115625 | + | 0.993293i | \(0.536887\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.1003 | −0.427196 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.699193 | 0.0295200 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.1141 | 0.510548 | 0.255274 | − | 0.966869i | \(-0.417834\pi\) | ||||
0.255274 | + | 0.966869i | \(0.417834\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.42474 | 0.102009 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.44512 | −0.144682 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.1461 | 1.13803 | 0.569013 | − | 0.822329i | \(-0.307325\pi\) | ||||
0.569013 | + | 0.822329i | \(0.307325\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.12408 | −0.339982 | −0.169991 | − | 0.985446i | \(-0.554374\pi\) | ||||
−0.169991 | + | 0.985446i | \(0.554374\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.41247 | −0.184333 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.49448 | −0.270838 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.5321 | 1.35433 | 0.677166 | − | 0.735831i | \(-0.263208\pi\) | ||||
0.677166 | + | 0.735831i | \(0.263208\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.83485 | −0.117812 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.182046 | 0.00755254 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.796343 | 0.0329812 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.50361 | 0.0621668 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.03476 | 0.207807 | 0.103903 | − | 0.994587i | \(-0.466867\pi\) | ||||
0.103903 | + | 0.994587i | \(0.466867\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.6147 | 0.808212 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.2785 | −0.546203 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.4273 | −0.756716 | −0.378358 | − | 0.925659i | \(-0.623511\pi\) | ||||
−0.378358 | + | 0.925659i | \(0.623511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.5711 | 0.966321 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.4658 | 0.551117 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −47.1055 | −1.92468 | −0.962339 | − | 0.271853i | \(-0.912363\pi\) | ||||
−0.962339 | + | 0.271853i | \(0.912363\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.5631 | −0.594040 | −0.297020 | − | 0.954871i | \(-0.595993\pi\) | ||||
−0.297020 | + | 0.954871i | \(0.595993\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000 | 0.0407231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.9896 | −0.446789 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.48825 | 0.344528 | 0.172264 | − | 0.985051i | \(-0.444892\pi\) | ||||
0.172264 | + | 0.985051i | \(0.444892\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.1949 | −0.494163 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.78083 | −0.112500 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.1137 | 0.610436 | 0.305218 | − | 0.952282i | \(-0.401271\pi\) | ||||
0.305218 | + | 0.952282i | \(0.401271\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.72023 | −0.109690 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.94054 | 0.239157 | 0.119578 | − | 0.992825i | \(-0.461846\pi\) | ||||
0.119578 | + | 0.992825i | \(0.461846\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.3925 | −0.658870 | −0.329435 | − | 0.944178i | \(-0.606858\pi\) | ||||
−0.329435 | + | 0.944178i | \(0.606858\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.49448 | −0.260614 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.8943 | −0.756985 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.497567 | −0.0198709 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 58.1181 | 2.31732 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.1231 | −0.920518 | −0.460259 | − | 0.887785i | \(-0.652243\pi\) | ||||
−0.460259 | + | 0.887785i | \(0.652243\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.1568 | 0.443444 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.1238 | 0.600170 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.32092 | 0.290065 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.59727 | −0.260984 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.52758 | −0.297321 | −0.148661 | − | 0.988888i | \(-0.547496\pi\) | ||||
−0.148661 | + | 0.988888i | \(0.547496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.39679 | 0.0945203 | 0.0472601 | − | 0.998883i | \(-0.484951\pi\) | ||||
0.0472601 | + | 0.998883i | \(0.484951\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.71734 | −0.264495 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.13014 | −0.0837444 | −0.0418722 | − | 0.999123i | \(-0.513332\pi\) | ||||
−0.0418722 | + | 0.999123i | \(0.513332\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.11936 | −0.0439389 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.8790 | −0.543961 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.6084 | −1.27606 | −0.638032 | − | 0.770010i | \(-0.720251\pi\) | ||||
−0.638032 | + | 0.770010i | \(0.720251\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.80126 | 0.304820 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.3791 | −0.482954 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.0047 | 0.896136 | 0.448068 | − | 0.893999i | \(-0.352112\pi\) | ||||
0.448068 | + | 0.893999i | \(0.352112\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.8359 | 0.654839 | 0.327420 | − | 0.944879i | \(-0.393821\pi\) | ||||
0.327420 | + | 0.944879i | \(0.393821\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.2875 | −0.399535 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.7739 | −0.650465 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.9889 | −0.890134 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.28911 | −0.127164 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0814061 | −0.00314265 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.7569 | 0.568837 | 0.284418 | − | 0.958700i | \(-0.408200\pi\) | ||||
0.284418 | + | 0.958700i | \(0.408200\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −47.2075 | −1.81433 | −0.907165 | − | 0.420775i | \(-0.861758\pi\) | ||||
−0.907165 | + | 0.420775i | \(0.861758\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.979239 | 0.0375798 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.582490 | −0.0223210 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.12953 | −0.0814844 | −0.0407422 | − | 0.999170i | \(-0.512972\pi\) | ||||
−0.0407422 | + | 0.999170i | \(0.512972\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.13387 | −0.157947 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.0911463 | −0.00347745 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.7169 | −0.446380 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.0569 | 1.63796 | 0.818980 | − | 0.573822i | \(-0.194540\pi\) | ||||
0.818980 | + | 0.573822i | \(0.194540\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.352068 | 0.0133740 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.7311 | 0.444988 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.6115 | 0.704959 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.61482 | 0.325842 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.8575 | 0.447850 | 0.223925 | − | 0.974606i | \(-0.428113\pi\) | ||||
0.223925 | + | 0.974606i | \(0.428113\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −41.3586 | −1.55987 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.84943 | −0.0696536 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 50.0371 | 1.88184 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.25735 | −0.310111 | −0.155056 | − | 0.987906i | \(-0.549556\pi\) | ||||
−0.155056 | + | 0.987906i | \(0.549556\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.29923 | −0.311245 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.1636 | −0.979834 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.153659 | −0.00574652 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.2902 | 0.571021 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.6745 | 0.547266 | 0.273633 | − | 0.961834i | \(-0.411775\pi\) | ||||
0.273633 | + | 0.961834i | \(0.411775\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.35751 | −0.236766 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.08839 | −0.300810 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.53976 | 0.131463 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.2460 | 1.19594 | 0.597969 | − | 0.801519i | \(-0.295975\pi\) | ||||
0.597969 | + | 0.801519i | \(0.295975\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.9592 | 1.69986 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.6390 | −0.910064 | −0.455032 | − | 0.890475i | \(-0.650372\pi\) | ||||
−0.455032 | + | 0.890475i | \(0.650372\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.86889 | 0.179592 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.102193 | −0.00376434 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.5893 | −1.71382 | −0.856908 | − | 0.515469i | \(-0.827618\pi\) | ||||
−0.856908 | + | 0.515469i | \(0.827618\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.32092 | 0.268941 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 50.0981 | 1.83792 | 0.918961 | − | 0.394349i | \(-0.129030\pi\) | ||||
0.918961 | + | 0.394349i | \(0.129030\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.2089 | −0.630486 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.0528416 | −0.00193337 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 42.6515 | 1.55845 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.7406 | 1.30419 | 0.652097 | − | 0.758136i | \(-0.273890\pi\) | ||||
0.652097 | + | 0.758136i | \(0.273890\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.18887 | −0.261977 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.5456 | −0.492975 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.0721 | −0.729534 | −0.364767 | − | 0.931099i | \(-0.618851\pi\) | ||||
−0.364767 | + | 0.931099i | \(0.618851\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.663692 | 0.0240905 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.72859 | −0.280161 | −0.140081 | − | 0.990140i | \(-0.544736\pi\) | ||||
−0.140081 | + | 0.990140i | \(0.544736\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.0336 | 0.725266 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.84187 | −0.247368 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.4697 | 0.594686 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.90069 | −0.212784 | −0.106392 | − | 0.994324i | \(-0.533930\pi\) | ||||
−0.106392 | + | 0.994324i | \(0.533930\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.2474 | 0.513106 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.4425 | −1.09494 | −0.547470 | − | 0.836825i | \(-0.684409\pi\) | ||||
−0.547470 | + | 0.836825i | \(0.684409\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.02859 | 0.144711 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 29.2645 | 1.04986 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.2445 | −0.474533 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.674197 | 0.0241247 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.53976 | 0.126501 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.42278 | 0.122164 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.1832 | 1.28979 | 0.644896 | − | 0.764270i | \(-0.276901\pi\) | ||||
0.644896 | + | 0.764270i | \(0.276901\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.8631 | 0.635944 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.35352 | −0.297017 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.19776 | 0.0425338 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.79252 | −0.276372 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.8037 | 0.807750 | 0.403875 | − | 0.914814i | \(-0.367663\pi\) | ||||
0.403875 | + | 0.914814i | \(0.367663\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.6536 | 0.447651 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.48436 | 0.193780 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.26506 | 0.0446429 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.3743 | 0.788590 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.16791 | −0.181919 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.4671 | 1.31727 | 0.658637 | − | 0.752461i | \(-0.271133\pi\) | ||||
0.658637 | + | 0.752461i | \(0.271133\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.1110 | 1.09246 | 0.546228 | − | 0.837636i | \(-0.316063\pi\) | ||||
0.546228 | + | 0.837636i | \(0.316063\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.1095 | 0.985843 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.16442 | −0.285987 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.7060 | −1.14424 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.18014 | −0.181009 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.9473 | −0.696165 | −0.348082 | − | 0.937464i | \(-0.613167\pi\) | ||||
−0.348082 | + | 0.937464i | \(0.613167\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.6234 | 0.440022 | 0.220011 | − | 0.975497i | \(-0.429391\pi\) | ||||
0.220011 | + | 0.975497i | \(0.429391\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.102193 | −0.00355791 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.5312 | 1.51373 | 0.756864 | − | 0.653572i | \(-0.226730\pi\) | ||||
0.756864 | + | 0.653572i | \(0.226730\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.7891 | 1.83344 | 0.916721 | − | 0.399529i | \(-0.130826\pi\) | ||||
0.916721 | + | 0.399529i | \(0.130826\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.8573 | 0.688841 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.3123 | −1.15420 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.99342 | 0.242017 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.02859 | 0.139248 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.2287 | 0.732898 | 0.366449 | − | 0.930438i | \(-0.380574\pi\) | ||||
0.366449 | + | 0.930438i | \(0.380574\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.4701 | −0.567934 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.38973 | −0.185632 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.7391 | −0.369438 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.8604 | 1.30090 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.0292 | 0.378520 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 55.1672 | 1.89111 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.6325 | 1.22003 | 0.610017 | − | 0.792389i | \(-0.291163\pi\) | ||||
0.610017 | + | 0.792389i | \(0.291163\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.86889 | 0.166512 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.0360 | 0.445301 | 0.222650 | − | 0.974898i | \(-0.428529\pi\) | ||||
0.222650 | + | 0.974898i | \(0.428529\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.98082 | 0.238182 | 0.119091 | − | 0.992883i | \(-0.462002\pi\) | ||||
0.119091 | + | 0.992883i | \(0.462002\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.37152 | 0.319381 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.47708 | −0.322604 | −0.161302 | − | 0.986905i | \(-0.551569\pi\) | ||||
−0.161302 | + | 0.986905i | \(0.551569\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.15345 | −0.141222 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.8112 | 1.01244 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.848125 | 0.0287707 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.50361 | 0.0509480 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.284239 | −0.00962004 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.44512 | −0.116466 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.7906 | 1.24233 | 0.621164 | − | 0.783680i | \(-0.286660\pi\) | ||||
0.621164 | + | 0.783680i | \(0.286660\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.1050 | −0.914227 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.3062 | −1.82962 | −0.914811 | − | 0.403882i | \(-0.867661\pi\) | ||||
−0.914811 | + | 0.403882i | \(0.867661\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.5094 | −0.622891 | −0.311446 | − | 0.950264i | \(-0.600813\pi\) | ||||
−0.311446 | + | 0.950264i | \(0.600813\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.9534 | 0.368195 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.6772 | −0.828579 | −0.414290 | − | 0.910145i | \(-0.635970\pi\) | ||||
−0.414290 | + | 0.910145i | \(0.635970\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −52.1034 | −1.74749 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.102193 | −0.00342360 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.00467 | −0.301330 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.9018 | −0.631818 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.76518 | −0.326050 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.2602 | 0.475606 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53.3155 | 1.77620 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23.1421 | 0.770120 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.63651 | −0.0543995 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.7308 | 1.58487 | 0.792437 | − | 0.609953i | \(-0.208812\pi\) | ||||
0.792437 | + | 0.609953i | \(0.208812\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.5240 | −0.481732 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.41520 | −0.0800192 | −0.0400096 | − | 0.999199i | \(-0.512739\pi\) | ||||
−0.0400096 | + | 0.999199i | \(0.512739\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.00540005 | 0.000178716 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.796590 | 0.0263345 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −26.8763 | −0.887534 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.6947 | −1.54032 | −0.770158 | − | 0.637853i | \(-0.779823\pi\) | ||||
−0.770158 | + | 0.637853i | \(0.779823\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.5608 | 0.809306 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.91975 | −0.326512 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.49448 | −0.279297 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.84536 | 0.0606097 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.95289 | 0.228117 | 0.114058 | − | 0.993474i | \(-0.463615\pi\) | ||||
0.114058 | + | 0.993474i | \(0.463615\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.7060 | 0.776934 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.5985 | −0.674364 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.699193 | 0.0228661 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −58.0892 | −1.89769 | −0.948845 | − | 0.315741i | \(-0.897747\pi\) | ||||
−0.948845 | + | 0.315741i | \(0.897747\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.7980 | 0.972422 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.9560 | −0.715745 | −0.357872 | − | 0.933770i | \(-0.616498\pi\) | ||||
−0.357872 | + | 0.933770i | \(0.616498\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.6665 | 0.575299 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.44512 | −0.112070 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.2497 | 0.788011 | 0.394005 | − | 0.919108i | \(-0.371089\pi\) | ||||
0.394005 | + | 0.919108i | \(0.371089\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.6133 | −0.604215 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.174862 | −0.00567028 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −59.4174 | −1.92472 | −0.962359 | − | 0.271783i | \(-0.912387\pi\) | ||||
−0.962359 | + | 0.271783i | \(0.912387\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.41247 | −0.142784 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.361740 | −0.0116934 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.2417 | 0.459889 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.7705 | −0.476466 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.3803 | −0.398948 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.83485 | −0.0912571 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.0448 | 1.15912 | 0.579561 | − | 0.814929i | \(-0.303224\pi\) | ||||
0.579561 | + | 0.814929i | \(0.303224\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −33.3123 | −1.07015 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.2763 | 0.811155 | 0.405578 | − | 0.914061i | \(-0.367070\pi\) | ||||
0.405578 | + | 0.914061i | \(0.367070\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40.4153 | −1.29565 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.50361 | 0.0481542 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.3632 | 0.907418 | 0.453709 | − | 0.891150i | \(-0.350101\pi\) | ||||
0.453709 | + | 0.891150i | \(0.350101\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.560465 | −0.0179125 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.81507 | −0.185661 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.9588 | 1.65723 | 0.828614 | − | 0.559821i | \(-0.189130\pi\) | ||||
0.828614 | + | 0.559821i | \(0.189130\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.2785 | −0.423087 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.37152 | 0.202808 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 43.6256 | 1.38721 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.1770 | 0.863305 | 0.431653 | − | 0.902040i | \(-0.357931\pi\) | ||||
0.431653 | + | 0.902040i | \(0.357931\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.36816 | 0.0751512 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.4658 | 0.426893 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.7593 | 0.784136 | 0.392068 | − | 0.919936i | \(-0.371760\pi\) | ||||
0.392068 | + | 0.919936i | \(0.371760\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.49448 | −0.268753 |
(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 | 4020.2.a.d.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.a.d.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial |