Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,4,Mod(107,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.107");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.f (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(26.5508595026\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 107.1 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.107 |
Dual form | 450.4.f.f.143.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | + | 1.41421i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 4.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.123724 | − | 0.123724i | −0.00668049 | − | 0.00668049i | 0.703759 | − | 0.710439i | \(-0.251504\pi\) |
−0.710439 | + | 0.703759i | \(0.751504\pi\) | |||||||
\(8\) | 5.65685 | + | 5.65685i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.24264i | − | 0.116291i | −0.998308 | − | 0.0581456i | \(-0.981481\pi\) | ||
0.998308 | − | 0.0581456i | \(-0.0185188\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.62883 | − | 5.62883i | 0.120089 | − | 0.120089i | −0.644508 | − | 0.764597i | \(-0.722938\pi\) |
0.764597 | + | 0.644508i | \(0.222938\pi\) | |||||||
\(14\) | 0.349945 | 0.00668049 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16.0000 | −0.250000 | ||||||||
\(17\) | −34.4660 | + | 34.4660i | −0.491720 | + | 0.491720i | −0.908848 | − | 0.417128i | \(-0.863037\pi\) |
0.417128 | + | 0.908848i | \(0.363037\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 110.485i | − | 1.33405i | −0.745036 | − | 0.667024i | \(-0.767568\pi\) | ||
0.745036 | − | 0.667024i | \(-0.232432\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.00000 | + | 6.00000i | 0.0581456 | + | 0.0581456i | ||||
\(23\) | 111.883 | + | 111.883i | 1.01432 | + | 1.01432i | 0.999896 | + | 0.0144216i | \(0.00459069\pi\) |
0.0144216 | + | 0.999896i | \(0.495409\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 15.9207i | 0.120089i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.494897 | + | 0.494897i | −0.00334024 | + | 0.00334024i | ||||
\(29\) | −53.0547 | −0.339724 | −0.169862 | − | 0.985468i | \(-0.554332\pi\) | ||||
−0.169862 | + | 0.985468i | \(0.554332\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −201.454 | −1.16717 | −0.583584 | − | 0.812053i | \(-0.698350\pi\) | ||||
−0.583584 | + | 0.812053i | \(0.698350\pi\) | |||||||
\(32\) | 22.6274 | − | 22.6274i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 97.4847i | − | 0.491720i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −169.732 | − | 169.732i | −0.754157 | − | 0.754157i | 0.221096 | − | 0.975252i | \(-0.429037\pi\) |
−0.975252 | + | 0.221096i | \(0.929037\pi\) | |||||||
\(38\) | 156.249 | + | 156.249i | 0.667024 | + | 0.667024i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 371.166i | − | 1.41381i | −0.707306 | − | 0.706907i | \(-0.750090\pi\) | ||
0.707306 | − | 0.706907i | \(-0.249910\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 202.639 | − | 202.639i | 0.718655 | − | 0.718655i | −0.249675 | − | 0.968330i | \(-0.580324\pi\) |
0.968330 | + | 0.249675i | \(0.0803237\pi\) | |||||||
\(44\) | −16.9706 | −0.0581456 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −316.454 | −1.01432 | ||||||||
\(47\) | −106.548 | + | 106.548i | −0.330672 | + | 0.330672i | −0.852842 | − | 0.522170i | \(-0.825123\pi\) |
0.522170 | + | 0.852842i | \(0.325123\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 342.969i | − | 0.999911i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −22.5153 | − | 22.5153i | −0.0600445 | − | 0.0600445i | ||||
\(53\) | 243.973 | + | 243.973i | 0.632308 | + | 0.632308i | 0.948646 | − | 0.316338i | \(-0.102453\pi\) |
−0.316338 | + | 0.948646i | \(0.602453\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 1.39978i | − | 0.00334024i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 75.0306 | − | 75.0306i | 0.169862 | − | 0.169862i | ||||
\(59\) | 57.2540 | 0.126336 | 0.0631681 | − | 0.998003i | \(-0.479880\pi\) | ||||
0.0631681 | + | 0.998003i | \(0.479880\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −609.847 | −1.28005 | −0.640024 | − | 0.768355i | \(-0.721076\pi\) | ||||
−0.640024 | + | 0.768355i | \(0.721076\pi\) | |||||||
\(62\) | 284.899 | − | 284.899i | 0.583584 | − | 0.583584i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −340.825 | − | 340.825i | −0.621469 | − | 0.621469i | 0.324438 | − | 0.945907i | \(-0.394825\pi\) |
−0.945907 | + | 0.324438i | \(0.894825\pi\) | |||||||
\(68\) | 137.864 | + | 137.864i | 0.245860 | + | 0.245860i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 990.505i | − | 1.65565i | −0.560985 | − | 0.827826i | \(-0.689577\pi\) | ||
0.560985 | − | 0.827826i | \(-0.310423\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 847.176 | − | 847.176i | 1.35828 | − | 1.35828i | 0.482242 | − | 0.876038i | \(-0.339822\pi\) |
0.876038 | − | 0.482242i | \(-0.160178\pi\) | |||||||
\(74\) | 480.075 | 0.754157 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −441.939 | −0.667024 | ||||||||
\(77\) | −0.524918 | + | 0.524918i | −0.000776883 | + | 0.000776883i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 436.847i | − | 0.622141i | −0.950387 | − | 0.311070i | \(-0.899313\pi\) | ||
0.950387 | − | 0.311070i | \(-0.100687\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 524.908 | + | 524.908i | 0.706907 | + | 0.706907i | ||||
\(83\) | −127.718 | − | 127.718i | −0.168901 | − | 0.168901i | 0.617595 | − | 0.786496i | \(-0.288107\pi\) |
−0.786496 | + | 0.617595i | \(0.788107\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 573.150i | 0.718655i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 24.0000 | − | 24.0000i | 0.0290728 | − | 0.0290728i | ||||
\(89\) | 1230.19 | 1.46517 | 0.732585 | − | 0.680675i | \(-0.238314\pi\) | ||||
0.732585 | + | 0.680675i | \(0.238314\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.39285 | −0.00160450 | ||||||||
\(92\) | 447.534 | − | 447.534i | 0.507159 | − | 0.507159i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 301.362i | − | 0.330672i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 202.578 | + | 202.578i | 0.212048 | + | 0.212048i | 0.805137 | − | 0.593089i | \(-0.202092\pi\) |
−0.593089 | + | 0.805137i | \(0.702092\pi\) | |||||||
\(98\) | 485.032 | + | 485.032i | 0.499955 | + | 0.499955i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 952.538i | − | 0.938426i | −0.883085 | − | 0.469213i | \(-0.844538\pi\) | ||
0.883085 | − | 0.469213i | \(-0.155462\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 862.640 | − | 862.640i | 0.825228 | − | 0.825228i | −0.161624 | − | 0.986852i | \(-0.551673\pi\) |
0.986852 | + | 0.161624i | \(0.0516733\pi\) | |||||||
\(104\) | 63.6829 | 0.0600445 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −690.061 | −0.632308 | ||||||||
\(107\) | −594.933 | + | 594.933i | −0.537517 | + | 0.537517i | −0.922799 | − | 0.385282i | \(-0.874104\pi\) |
0.385282 | + | 0.922799i | \(0.374104\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 46.0918i | 0.0405027i | 0.999795 | + | 0.0202514i | \(0.00644665\pi\) | ||||
−0.999795 | + | 0.0202514i | \(0.993553\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.97959 | + | 1.97959i | 0.00167012 | + | 0.00167012i | ||||
\(113\) | −1140.00 | − | 1140.00i | −0.949049 | − | 0.949049i | 0.0497143 | − | 0.998763i | \(-0.484169\pi\) |
−0.998763 | + | 0.0497143i | \(0.984169\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 212.219i | 0.169862i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −80.9694 | + | 80.9694i | −0.0631681 | + | 0.0631681i | ||||
\(119\) | 8.52858 | 0.00656986 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1313.00 | 0.986476 | ||||||||
\(122\) | 862.454 | − | 862.454i | 0.640024 | − | 0.640024i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 805.816i | 0.583584i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −629.816 | − | 629.816i | −0.440056 | − | 0.440056i | 0.451974 | − | 0.892031i | \(-0.350720\pi\) |
−0.892031 | + | 0.451974i | \(0.850720\pi\) | |||||||
\(128\) | −90.5097 | − | 90.5097i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 744.605i | − | 0.496614i | −0.968681 | − | 0.248307i | \(-0.920126\pi\) | ||
0.968681 | − | 0.248307i | \(-0.0798742\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.6696 | + | 13.6696i | −0.00891210 | + | 0.00891210i | ||||
\(134\) | 963.999 | 0.621469 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −389.939 | −0.245860 | ||||||||
\(137\) | −629.399 | + | 629.399i | −0.392505 | + | 0.392505i | −0.875579 | − | 0.483074i | \(-0.839520\pi\) |
0.483074 | + | 0.875579i | \(0.339520\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 229.755i | 0.140198i | 0.997540 | + | 0.0700992i | \(0.0223316\pi\) | ||||
−0.997540 | + | 0.0700992i | \(0.977668\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1400.79 | + | 1400.79i | 0.827826 | + | 0.827826i | ||||
\(143\) | −23.8811 | − | 23.8811i | −0.0139653 | − | 0.0139653i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2396.18i | 1.35828i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −678.929 | + | 678.929i | −0.377078 | + | 0.377078i | ||||
\(149\) | −1887.54 | −1.03781 | −0.518904 | − | 0.854832i | \(-0.673660\pi\) | ||||
−0.518904 | + | 0.854832i | \(0.673660\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 803.209 | 0.432876 | 0.216438 | − | 0.976296i | \(-0.430556\pi\) | ||||
0.216438 | + | 0.976296i | \(0.430556\pi\) | |||||||
\(152\) | 624.996 | − | 624.996i | 0.333512 | − | 0.333512i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 1.48469i | − | 0.000776883i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1066.46 | − | 1066.46i | −0.542117 | − | 0.542117i | 0.382032 | − | 0.924149i | \(-0.375224\pi\) |
−0.924149 | + | 0.382032i | \(0.875224\pi\) | |||||||
\(158\) | 617.795 | + | 617.795i | 0.311070 | + | 0.311070i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 27.6854i | − | 0.0135523i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2084.54 | + | 2084.54i | −1.00168 | + | 1.00168i | −0.00167955 | + | 0.999999i | \(0.500535\pi\) |
−0.999999 | + | 0.00167955i | \(0.999465\pi\) | |||||||
\(164\) | −1484.66 | −0.706907 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 361.240 | 0.168901 | ||||||||
\(167\) | −734.724 | + | 734.724i | −0.340447 | + | 0.340447i | −0.856535 | − | 0.516088i | \(-0.827388\pi\) |
0.516088 | + | 0.856535i | \(0.327388\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2133.63i | 0.971157i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −810.556 | − | 810.556i | −0.359327 | − | 0.359327i | ||||
\(173\) | −1563.92 | − | 1563.92i | −0.687297 | − | 0.687297i | 0.274337 | − | 0.961634i | \(-0.411542\pi\) |
−0.961634 | + | 0.274337i | \(0.911542\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 67.8823i | 0.0290728i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1739.76 | + | 1739.76i | −0.732585 | + | 0.732585i | ||||
\(179\) | −2662.41 | −1.11172 | −0.555860 | − | 0.831276i | \(-0.687611\pi\) | ||||
−0.555860 | + | 0.831276i | \(0.687611\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3228.45 | 1.32579 | 0.662897 | − | 0.748711i | \(-0.269327\pi\) | ||||
0.662897 | + | 0.748711i | \(0.269327\pi\) | |||||||
\(182\) | 1.96978 | − | 1.96978i | 0.000802252 | − | 0.000802252i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1265.82i | 0.507159i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 146.227 | + | 146.227i | 0.0571828 | + | 0.0571828i | ||||
\(188\) | 426.191 | + | 426.191i | 0.165336 | + | 0.165336i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2901.40i | 1.09915i | 0.835443 | + | 0.549576i | \(0.185211\pi\) | ||||
−0.835443 | + | 0.549576i | \(0.814789\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1073.38 | + | 1073.38i | −0.400329 | + | 0.400329i | −0.878349 | − | 0.478020i | \(-0.841355\pi\) |
0.478020 | + | 0.878349i | \(0.341355\pi\) | |||||||
\(194\) | −572.977 | −0.212048 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1371.88 | −0.499955 | ||||||||
\(197\) | −1689.97 | + | 1689.97i | −0.611196 | + | 0.611196i | −0.943258 | − | 0.332062i | \(-0.892256\pi\) |
0.332062 | + | 0.943258i | \(0.392256\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1221.82i | − | 0.435239i | −0.976034 | − | 0.217620i | \(-0.930171\pi\) | ||
0.976034 | − | 0.217620i | \(-0.0698292\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1347.09 | + | 1347.09i | 0.469213 | + | 0.469213i | ||||
\(203\) | 6.56415 | + | 6.56415i | 0.00226952 | + | 0.00226952i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2439.92i | 0.825228i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −90.0612 | + | 90.0612i | −0.0300222 | + | 0.0300222i | ||||
\(209\) | −468.747 | −0.155138 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4685.99 | 1.52890 | 0.764448 | − | 0.644685i | \(-0.223011\pi\) | ||||
0.764448 | + | 0.644685i | \(0.223011\pi\) | |||||||
\(212\) | 975.894 | − | 975.894i | 0.316154 | − | 0.316154i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 1682.72i | − | 0.537517i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.9248 | + | 24.9248i | 0.00779725 | + | 0.00779725i | ||||
\(218\) | −65.1837 | − | 65.1837i | −0.0202514 | − | 0.0202514i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 388.007i | 0.118100i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3745.86 | + | 3745.86i | −1.12485 | + | 1.12485i | −0.133847 | + | 0.991002i | \(0.542733\pi\) |
−0.991002 | + | 0.133847i | \(0.957267\pi\) | |||||||
\(224\) | −5.59913 | −0.00167012 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3224.42 | 0.949049 | ||||||||
\(227\) | −3266.66 | + | 3266.66i | −0.955136 | + | 0.955136i | −0.999036 | − | 0.0439000i | \(-0.986022\pi\) |
0.0439000 | + | 0.999036i | \(0.486022\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1051.91i | 0.303546i | 0.988415 | + | 0.151773i | \(0.0484983\pi\) | ||||
−0.988415 | + | 0.151773i | \(0.951502\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −300.122 | − | 300.122i | −0.0849311 | − | 0.0849311i | ||||
\(233\) | −972.311 | − | 972.311i | −0.273383 | − | 0.273383i | 0.557077 | − | 0.830461i | \(-0.311923\pi\) |
−0.830461 | + | 0.557077i | \(0.811923\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 229.016i | − | 0.0631681i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.0612 | + | 12.0612i | −0.00328493 | + | 0.00328493i | ||||
\(239\) | −5521.04 | −1.49425 | −0.747126 | − | 0.664682i | \(-0.768567\pi\) | ||||
−0.747126 | + | 0.664682i | \(0.768567\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −115.735 | −0.0309342 | −0.0154671 | − | 0.999880i | \(-0.504924\pi\) | ||||
−0.0154671 | + | 0.999880i | \(0.504924\pi\) | |||||||
\(242\) | −1856.86 | + | 1856.86i | −0.493238 | + | 0.493238i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2439.39i | 0.640024i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −621.899 | − | 621.899i | −0.160204 | − | 0.160204i | ||||
\(248\) | −1139.60 | − | 1139.60i | −0.291792 | − | 0.291792i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2230.94i | 0.561018i | 0.959851 | + | 0.280509i | \(0.0905032\pi\) | ||||
−0.959851 | + | 0.280509i | \(0.909497\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 474.681 | − | 474.681i | 0.117956 | − | 0.117956i | ||||
\(254\) | 1781.39 | 0.440056 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 4373.86 | − | 4373.86i | 1.06161 | − | 1.06161i | 0.0636372 | − | 0.997973i | \(-0.479730\pi\) |
0.997973 | − | 0.0636372i | \(-0.0202701\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 42.0000i | 0.0100763i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1053.03 | + | 1053.03i | 0.248307 | + | 0.248307i | ||||
\(263\) | 1040.02 | + | 1040.02i | 0.243842 | + | 0.243842i | 0.818437 | − | 0.574596i | \(-0.194841\pi\) |
−0.574596 | + | 0.818437i | \(0.694841\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 38.6636i | − | 0.00891210i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1363.30 | + | 1363.30i | −0.310735 | + | 0.310735i | ||||
\(269\) | 8334.34 | 1.88905 | 0.944524 | − | 0.328443i | \(-0.106524\pi\) | ||||
0.944524 | + | 0.328443i | \(0.106524\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −417.878 | −0.0936688 | −0.0468344 | − | 0.998903i | \(-0.514913\pi\) | ||||
−0.0468344 | + | 0.998903i | \(0.514913\pi\) | |||||||
\(272\) | 551.457 | − | 551.457i | 0.122930 | − | 0.122930i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 1780.21i | − | 0.392505i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5795.08 | + | 5795.08i | 1.25701 | + | 1.25701i | 0.952512 | + | 0.304502i | \(0.0984900\pi\) |
0.304502 | + | 0.952512i | \(0.401510\pi\) | |||||||
\(278\) | −324.923 | − | 324.923i | −0.0700992 | − | 0.0700992i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1678.12i | 0.356256i | 0.984007 | + | 0.178128i | \(0.0570042\pi\) | ||||
−0.984007 | + | 0.178128i | \(0.942996\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1934.72 | − | 1934.72i | 0.406386 | − | 0.406386i | −0.474090 | − | 0.880476i | \(-0.657223\pi\) |
0.880476 | + | 0.474090i | \(0.157223\pi\) | |||||||
\(284\) | −3962.02 | −0.827826 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 67.5459 | 0.0139653 | ||||||||
\(287\) | −45.9223 | + | 45.9223i | −0.00944497 | + | 0.00944497i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2537.18i | 0.516422i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3388.70 | − | 3388.70i | −0.679140 | − | 0.679140i | ||||
\(293\) | −3782.25 | − | 3782.25i | −0.754135 | − | 0.754135i | 0.221113 | − | 0.975248i | \(-0.429031\pi\) |
−0.975248 | + | 0.221113i | \(0.929031\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 1920.30i | − | 0.377078i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2669.39 | − | 2669.39i | 0.518904 | − | 0.518904i | ||||
\(299\) | 1259.54 | 0.243617 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −50.1428 | −0.00960193 | ||||||||
\(302\) | −1135.91 | + | 1135.91i | −0.216438 | + | 0.216438i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1767.76i | 0.333512i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3354.68 | − | 3354.68i | −0.623654 | − | 0.623654i | 0.322810 | − | 0.946464i | \(-0.395373\pi\) |
−0.946464 | + | 0.322810i | \(0.895373\pi\) | |||||||
\(308\) | 2.09967 | + | 2.09967i | 0.000388441 | + | 0.000388441i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 4277.43i | − | 0.779905i | −0.920835 | − | 0.389953i | \(-0.872491\pi\) | ||
0.920835 | − | 0.389953i | \(-0.127509\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2311.37 | − | 2311.37i | 0.417400 | − | 0.417400i | −0.466907 | − | 0.884307i | \(-0.654632\pi\) |
0.884307 | + | 0.466907i | \(0.154632\pi\) | |||||||
\(314\) | 3016.39 | 0.542117 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1747.39 | −0.311070 | ||||||||
\(317\) | 4202.41 | − | 4202.41i | 0.744577 | − | 0.744577i | −0.228878 | − | 0.973455i | \(-0.573506\pi\) |
0.973455 | + | 0.228878i | \(0.0735057\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 225.092i | 0.0395070i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 39.1531 | + | 39.1531i | 0.00677614 | + | 0.00677614i | ||||
\(323\) | 3807.97 | + | 3807.97i | 0.655979 | + | 0.655979i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 5895.96i | − | 1.00168i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2099.63 | − | 2099.63i | 0.353454 | − | 0.353454i | ||||
\(329\) | 26.3651 | 0.00441810 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11631.0 | −1.93141 | −0.965703 | − | 0.259650i | \(-0.916393\pi\) | ||||
−0.965703 | + | 0.259650i | \(0.916393\pi\) | |||||||
\(332\) | −510.870 | + | 510.870i | −0.0844507 | + | 0.0844507i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 2078.11i | − | 0.340447i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1086.00 | − | 1086.00i | −0.175543 | − | 0.175543i | 0.613867 | − | 0.789410i | \(-0.289613\pi\) |
−0.789410 | + | 0.613867i | \(0.789613\pi\) | |||||||
\(338\) | −3017.41 | − | 3017.41i | −0.485579 | − | 0.485579i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 854.697i | 0.135732i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −84.8711 | + | 84.8711i | −0.0133604 | + | 0.0133604i | ||||
\(344\) | 2292.60 | 0.359327 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4423.42 | 0.687297 | ||||||||
\(347\) | 6152.44 | − | 6152.44i | 0.951816 | − | 0.951816i | −0.0470749 | − | 0.998891i | \(-0.514990\pi\) |
0.998891 | + | 0.0470749i | \(0.0149899\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4514.31i | 0.692393i | 0.938162 | + | 0.346197i | \(0.112527\pi\) | ||||
−0.938162 | + | 0.346197i | \(0.887473\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −96.0000 | − | 96.0000i | −0.0145364 | − | 0.0145364i | ||||
\(353\) | 216.759 | + | 216.759i | 0.0326825 | + | 0.0326825i | 0.723259 | − | 0.690577i | \(-0.242643\pi\) |
−0.690577 | + | 0.723259i | \(0.742643\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 4920.77i | − | 0.732585i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3765.21 | − | 3765.21i | 0.555860 | − | 0.555860i | ||||
\(359\) | 3746.84 | 0.550837 | 0.275418 | − | 0.961324i | \(-0.411184\pi\) | ||||
0.275418 | + | 0.961324i | \(0.411184\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5347.87 | −0.779686 | ||||||||
\(362\) | −4565.72 | + | 4565.72i | −0.662897 | + | 0.662897i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.57138i | 0.000802252i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4491.23 | + | 4491.23i | 0.638801 | + | 0.638801i | 0.950260 | − | 0.311458i | \(-0.100817\pi\) |
−0.311458 | + | 0.950260i | \(0.600817\pi\) | |||||||
\(368\) | −1790.13 | − | 1790.13i | −0.253579 | − | 0.253579i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 60.3709i | − | 0.00844825i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8308.64 | − | 8308.64i | 1.15337 | − | 1.15337i | 0.167492 | − | 0.985873i | \(-0.446433\pi\) |
0.985873 | − | 0.167492i | \(-0.0535668\pi\) | |||||||
\(374\) | −413.593 | −0.0571828 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1205.45 | −0.165336 | ||||||||
\(377\) | −298.635 | + | 298.635i | −0.0407971 | + | 0.0407971i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 11962.7i | − | 1.62133i | −0.585511 | − | 0.810664i | \(-0.699106\pi\) | ||
0.585511 | − | 0.810664i | \(-0.300894\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4103.20 | − | 4103.20i | −0.549576 | − | 0.549576i | ||||
\(383\) | 9845.04 | + | 9845.04i | 1.31347 | + | 1.31347i | 0.918842 | + | 0.394625i | \(0.129125\pi\) |
0.394625 | + | 0.918842i | \(0.370875\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 3035.97i | − | 0.400329i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 810.311 | − | 810.311i | 0.106024 | − | 0.106024i | ||||
\(389\) | 13835.9 | 1.80337 | 0.901683 | − | 0.432398i | \(-0.142333\pi\) | ||||
0.901683 | + | 0.432398i | \(0.142333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7712.36 | −0.997521 | ||||||||
\(392\) | 1940.13 | − | 1940.13i | 0.249978 | − | 0.249978i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 4779.96i | − | 0.611196i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1250.91 | + | 1250.91i | 0.158139 | + | 0.158139i | 0.781742 | − | 0.623602i | \(-0.214332\pi\) |
−0.623602 | + | 0.781742i | \(0.714332\pi\) | |||||||
\(398\) | 1727.92 | + | 1727.92i | 0.217620 | + | 0.217620i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 9240.23i | − | 1.15071i | −0.817903 | − | 0.575356i | \(-0.804864\pi\) | ||
0.817903 | − | 0.575356i | \(-0.195136\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1133.95 | + | 1133.95i | −0.140164 | + | 0.140164i | ||||
\(404\) | −3810.15 | −0.469213 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.5662 | −0.00226952 | ||||||||
\(407\) | −720.112 | + | 720.112i | −0.0877018 | + | 0.0877018i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3920.81i | − | 0.474013i | −0.971508 | − | 0.237007i | \(-0.923834\pi\) | ||
0.971508 | − | 0.237007i | \(-0.0761663\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3450.56 | − | 3450.56i | −0.412614 | − | 0.412614i | ||||
\(413\) | −7.08371 | − | 7.08371i | −0.000843987 | − | 0.000843987i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 254.732i | − | 0.0300222i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 662.908 | − | 662.908i | 0.0775691 | − | 0.0775691i | ||||
\(419\) | −11909.4 | −1.38858 | −0.694288 | − | 0.719698i | \(-0.744280\pi\) | ||||
−0.694288 | + | 0.719698i | \(0.744280\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10605.7 | −1.22777 | −0.613886 | − | 0.789394i | \(-0.710395\pi\) | ||||
−0.613886 | + | 0.789394i | \(0.710395\pi\) | |||||||
\(422\) | −6627.00 | + | 6627.00i | −0.764448 | + | 0.764448i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2760.24i | 0.316154i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 75.4529 | + | 75.4529i | 0.00855134 | + | 0.00855134i | ||||
\(428\) | 2379.73 | + | 2379.73i | 0.268759 | + | 0.268759i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17058.9i | 1.90649i | 0.302198 | + | 0.953245i | \(0.402280\pi\) | ||||
−0.302198 | + | 0.953245i | \(0.597720\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4011.77 | − | 4011.77i | 0.445250 | − | 0.445250i | −0.448522 | − | 0.893772i | \(-0.648049\pi\) |
0.893772 | + | 0.448522i | \(0.148049\pi\) | |||||||
\(434\) | −70.4979 | −0.00779725 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 184.367 | 0.0202514 | ||||||||
\(437\) | 12361.4 | − | 12361.4i | 1.35315 | − | 1.35315i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 6626.17i | − | 0.720387i | −0.932878 | − | 0.360193i | \(-0.882711\pi\) | ||
0.932878 | − | 0.360193i | \(-0.117289\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −548.724 | − | 548.724i | −0.0590501 | − | 0.0590501i | ||||
\(443\) | 12510.8 | + | 12510.8i | 1.34178 | + | 1.34178i | 0.894291 | + | 0.447486i | \(0.147680\pi\) |
0.447486 | + | 0.894291i | \(0.352320\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 10594.9i | − | 1.12485i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.91836 | − | 7.91836i | 0.000835061 | − | 0.000835061i | ||||
\(449\) | 9955.27 | 1.04637 | 0.523183 | − | 0.852220i | \(-0.324744\pi\) | ||||
0.523183 | + | 0.852220i | \(0.324744\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1574.72 | −0.164414 | ||||||||
\(452\) | −4560.02 | + | 4560.02i | −0.474525 | + | 0.474525i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 9239.51i | − | 0.955136i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4696.35 | + | 4696.35i | 0.480713 | + | 0.480713i | 0.905359 | − | 0.424646i | \(-0.139602\pi\) |
−0.424646 | + | 0.905359i | \(0.639602\pi\) | |||||||
\(458\) | −1487.62 | − | 1487.62i | −0.151773 | − | 0.151773i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1831.59i | − | 0.185044i | −0.995711 | − | 0.0925222i | \(-0.970507\pi\) | ||
0.995711 | − | 0.0925222i | \(-0.0294929\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8401.13 | + | 8401.13i | −0.843269 | + | 0.843269i | −0.989283 | − | 0.146014i | \(-0.953356\pi\) |
0.146014 | + | 0.989283i | \(0.453356\pi\) | |||||||
\(464\) | 848.875 | 0.0849311 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2750.11 | 0.273383 | ||||||||
\(467\) | −12419.2 | + | 12419.2i | −1.23061 | + | 1.23061i | −0.266876 | + | 0.963731i | \(0.585992\pi\) |
−0.963731 | + | 0.266876i | \(0.914008\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 84.3368i | 0.00830343i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 323.878 | + | 323.878i | 0.0315841 | + | 0.0315841i | ||||
\(473\) | −859.725 | − | 859.725i | −0.0835733 | − | 0.0835733i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 34.1143i | − | 0.00328493i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7807.93 | − | 7807.93i | 0.747126 | − | 0.747126i | ||||
\(479\) | −6740.76 | −0.642992 | −0.321496 | − | 0.946911i | \(-0.604186\pi\) | ||||
−0.321496 | + | 0.946911i | \(0.604186\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1910.79 | −0.181132 | ||||||||
\(482\) | 163.674 | − | 163.674i | 0.0154671 | − | 0.0154671i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 5252.00i | − | 0.493238i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7297.37 | − | 7297.37i | −0.679005 | − | 0.679005i | 0.280770 | − | 0.959775i | \(-0.409410\pi\) |
−0.959775 | + | 0.280770i | \(0.909410\pi\) | |||||||
\(488\) | −3449.82 | − | 3449.82i | −0.320012 | − | 0.320012i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 8669.79i | − | 0.796868i | −0.917197 | − | 0.398434i | \(-0.869554\pi\) | ||
0.917197 | − | 0.398434i | \(-0.130446\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1828.58 | − | 1828.58i | 0.167049 | − | 0.167049i | ||||
\(494\) | 1759.00 | 0.160204 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3223.27 | 0.291792 | ||||||||
\(497\) | −122.550 | + | 122.550i | −0.0110606 | + | 0.0110606i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 6159.27i | − | 0.552559i | −0.961077 | − | 0.276279i | \(-0.910898\pi\) | ||
0.961077 | − | 0.276279i | \(-0.0891015\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3155.02 | − | 3155.02i | −0.280509 | − | 0.280509i | ||||
\(503\) | 6743.55 | + | 6743.55i | 0.597773 | + | 0.597773i | 0.939719 | − | 0.341946i | \(-0.111086\pi\) |
−0.341946 | + | 0.939719i | \(0.611086\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1342.60i | 0.117956i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2519.27 | + | 2519.27i | −0.220028 | + | 0.220028i | ||||
\(509\) | −14485.3 | −1.26140 | −0.630698 | − | 0.776028i | \(-0.717231\pi\) | ||||
−0.630698 | + | 0.776028i | \(0.717231\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −209.633 | −0.0181479 | ||||||||
\(512\) | −362.039 | + | 362.039i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12371.1i | 1.06161i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 452.043 | + | 452.043i | 0.0384542 | + | 0.0384542i | ||||
\(518\) | −59.3970 | − | 59.3970i | −0.00503813 | − | 0.00503813i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13211.2i | 1.11093i | 0.831540 | + | 0.555464i | \(0.187459\pi\) | ||||
−0.831540 | + | 0.555464i | \(0.812541\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8899.56 | + | 8899.56i | −0.744074 | + | 0.744074i | −0.973359 | − | 0.229285i | \(-0.926361\pi\) |
0.229285 | + | 0.973359i | \(0.426361\pi\) | |||||||
\(524\) | −2978.42 | −0.248307 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2941.62 | −0.243842 | ||||||||
\(527\) | 6943.32 | − | 6943.32i | 0.573920 | − | 0.573920i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12868.8i | 1.05768i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 54.6786 | + | 54.6786i | 0.00445605 | + | 0.00445605i | ||||
\(533\) | −2089.23 | − | 2089.23i | −0.169783 | − | 0.169783i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 3856.00i | − | 0.310735i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11786.5 | + | 11786.5i | −0.944524 | + | 0.944524i | ||||
\(539\) | −1455.10 | −0.116281 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2620.33 | 0.208238 | 0.104119 | − | 0.994565i | \(-0.466798\pi\) | ||||
0.104119 | + | 0.994565i | \(0.466798\pi\) | |||||||
\(542\) | 590.968 | − | 590.968i | 0.0468344 | − | 0.0468344i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1559.76i | 0.122930i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3267.35 | − | 3267.35i | −0.255396 | − | 0.255396i | 0.567782 | − | 0.823179i | \(-0.307802\pi\) |
−0.823179 | + | 0.567782i | \(0.807802\pi\) | |||||||
\(548\) | 2517.60 | + | 2517.60i | 0.196252 | + | 0.196252i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5861.73i | 0.453209i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −54.0486 | + | 54.0486i | −0.00415620 | + | 0.00415620i | ||||
\(554\) | −16391.0 | −1.25701 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 919.020 | 0.0700992 | ||||||||
\(557\) | 981.246 | − | 981.246i | 0.0746440 | − | 0.0746440i | −0.668799 | − | 0.743443i | \(-0.733191\pi\) |
0.743443 | + | 0.668799i | \(0.233191\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2281.24i | − | 0.172605i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2373.21 | − | 2373.21i | −0.178128 | − | 0.178128i | ||||
\(563\) | −9237.32 | − | 9237.32i | −0.691486 | − | 0.691486i | 0.271073 | − | 0.962559i | \(-0.412622\pi\) |
−0.962559 | + | 0.271073i | \(0.912622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5472.22i | 0.406386i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5603.14 | − | 5603.14i | 0.413913 | − | 0.413913i | ||||
\(569\) | 20917.7 | 1.54115 | 0.770575 | − | 0.637349i | \(-0.219969\pi\) | ||||
0.770575 | + | 0.637349i | \(0.219969\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7734.94 | 0.566895 | 0.283448 | − | 0.958988i | \(-0.408522\pi\) | ||||
0.283448 | + | 0.958988i | \(0.408522\pi\) | |||||||
\(572\) | −95.5244 | + | 95.5244i | −0.00698265 | + | 0.00698265i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 129.888i | − | 0.00944497i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10178.7 | + | 10178.7i | 0.734391 | + | 0.734391i | 0.971486 | − | 0.237096i | \(-0.0761955\pi\) |
−0.237096 | + | 0.971486i | \(0.576196\pi\) | |||||||
\(578\) | −3588.12 | − | 3588.12i | −0.258211 | − | 0.258211i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.6035i | 0.00225669i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1035.09 | − | 1035.09i | 0.0735319 | − | 0.0735319i | ||||
\(584\) | 9584.70 | 0.679140 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10697.8 | 0.754135 | ||||||||
\(587\) | −7041.14 | + | 7041.14i | −0.495092 | + | 0.495092i | −0.909906 | − | 0.414814i | \(-0.863847\pi\) |
0.414814 | + | 0.909906i | \(0.363847\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22257.6i | 1.55706i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2715.71 | + | 2715.71i | 0.188539 | + | 0.188539i | ||||
\(593\) | −15972.6 | − | 15972.6i | −1.10610 | − | 1.10610i | −0.993659 | − | 0.112437i | \(-0.964134\pi\) |
−0.112437 | − | 0.993659i | \(-0.535866\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7550.17i | 0.518904i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1781.27 | + | 1781.27i | −0.121808 | + | 0.121808i | ||||
\(599\) | −26647.8 | −1.81769 | −0.908847 | − | 0.417131i | \(-0.863036\pi\) | ||||
−0.908847 | + | 0.417131i | \(0.863036\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23514.8 | 1.59599 | 0.797993 | − | 0.602666i | \(-0.205895\pi\) | ||||
0.797993 | + | 0.602666i | \(0.205895\pi\) | |||||||
\(602\) | 70.9126 | − | 70.9126i | 0.00480097 | − | 0.00480097i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 3212.84i | − | 0.216438i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1843.31 | + | 1843.31i | 0.123258 | + | 0.123258i | 0.766045 | − | 0.642787i | \(-0.222222\pi\) |
−0.642787 | + | 0.766045i | \(0.722222\pi\) | |||||||
\(608\) | −2499.98 | − | 2499.98i | −0.166756 | − | 0.166756i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1199.48i | 0.0794200i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14527.5 | + | 14527.5i | −0.957197 | + | 0.957197i | −0.999121 | − | 0.0419235i | \(-0.986651\pi\) |
0.0419235 | + | 0.999121i | \(0.486651\pi\) | |||||||
\(614\) | 9488.47 | 0.623654 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.93877 | −0.000388441 | ||||||||
\(617\) | 13639.0 | − | 13639.0i | 0.889928 | − | 0.889928i | −0.104588 | − | 0.994516i | \(-0.533352\pi\) |
0.994516 | + | 0.104588i | \(0.0333524\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11981.4i | 0.777985i | 0.921241 | + | 0.388993i | \(0.127177\pi\) | ||||
−0.921241 | + | 0.388993i | \(0.872823\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6049.19 | + | 6049.19i | 0.389953 | + | 0.389953i | ||||
\(623\) | −152.205 | − | 152.205i | −0.00978805 | − | 0.00978805i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6537.53i | 0.417400i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4265.82 | + | 4265.82i | −0.271059 | + | 0.271059i | ||||
\(629\) | 11700.0 | 0.741668 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −373.658 | −0.0235739 | −0.0117869 | − | 0.999931i | \(-0.503752\pi\) | ||||
−0.0117869 | + | 0.999931i | \(0.503752\pi\) | |||||||
\(632\) | 2471.18 | − | 2471.18i | 0.155535 | − | 0.155535i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11886.2i | 0.744577i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1930.52 | − | 1930.52i | −0.120078 | − | 0.120078i | ||||
\(638\) | −318.328 | − | 318.328i | −0.0197535 | − | 0.0197535i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6251.83i | 0.385230i | 0.981274 | + | 0.192615i | \(0.0616969\pi\) | ||||
−0.981274 | + | 0.192615i | \(0.938303\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3502.38 | + | 3502.38i | −0.214806 | + | 0.214806i | −0.806305 | − | 0.591499i | \(-0.798536\pi\) |
0.591499 | + | 0.806305i | \(0.298536\pi\) | |||||||
\(644\) | −110.742 | −0.00677614 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10770.6 | −0.655979 | ||||||||
\(647\) | −13374.2 | + | 13374.2i | −0.812665 | + | 0.812665i | −0.985033 | − | 0.172368i | \(-0.944858\pi\) |
0.172368 | + | 0.985033i | \(0.444858\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 242.908i | − | 0.0146918i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8338.15 | + | 8338.15i | 0.500839 | + | 0.500839i | ||||
\(653\) | −20892.8 | − | 20892.8i | −1.25207 | − | 1.25207i | −0.954793 | − | 0.297272i | \(-0.903923\pi\) |
−0.297272 | − | 0.954793i | \(-0.596077\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5938.66i | 0.353454i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −37.2858 | + | 37.2858i | −0.00220905 | + | 0.00220905i | ||||
\(659\) | −8493.05 | −0.502037 | −0.251018 | − | 0.967982i | \(-0.580765\pi\) | ||||
−0.251018 | + | 0.967982i | \(0.580765\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27756.2 | 1.63327 | 0.816635 | − | 0.577155i | \(-0.195837\pi\) | ||||
0.816635 | + | 0.577155i | \(0.195837\pi\) | |||||||
\(662\) | 16448.7 | − | 16448.7i | 0.965703 | − | 0.965703i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 1444.96i | − | 0.0844507i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5935.94 | − | 5935.94i | −0.344588 | − | 0.344588i | ||||
\(668\) | 2938.89 | + | 2938.89i | 0.170223 | + | 0.170223i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2587.36i | 0.148858i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13533.3 | − | 13533.3i | 0.775143 | − | 0.775143i | −0.203858 | − | 0.979001i | \(-0.565348\pi\) |
0.979001 | + | 0.203858i | \(0.0653480\pi\) | |||||||
\(674\) | 3071.66 | 0.175543 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8534.53 | 0.485579 | ||||||||
\(677\) | −16217.2 | + | 16217.2i | −0.920647 | + | 0.920647i | −0.997075 | − | 0.0764277i | \(-0.975649\pi\) |
0.0764277 | + | 0.997075i | \(0.475649\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 50.1276i | − | 0.00283317i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1208.72 | − | 1208.72i | −0.0678658 | − | 0.0678658i | ||||
\(683\) | 1055.14 | + | 1055.14i | 0.0591125 | + | 0.0591125i | 0.736045 | − | 0.676933i | \(-0.236691\pi\) |
−0.676933 | + | 0.736045i | \(0.736691\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 240.052i | − | 0.0133604i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3242.22 | + | 3242.22i | −0.179664 | + | 0.179664i | ||||
\(689\) | 2746.57 | 0.151866 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32208.2 | 1.77316 | 0.886582 | − | 0.462571i | \(-0.153073\pi\) | ||||
0.886582 | + | 0.462571i | \(0.153073\pi\) | |||||||
\(692\) | −6255.67 | + | 6255.67i | −0.343648 | + | 0.343648i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17401.7i | 0.951816i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12792.6 | + | 12792.6i | 0.695201 | + | 0.695201i | ||||
\(698\) | −6384.19 | − | 6384.19i | −0.346197 | − | 0.346197i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 7585.34i | − | 0.408694i | −0.978899 | − | 0.204347i | \(-0.934493\pi\) | ||
0.978899 | − | 0.204347i | \(-0.0655071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18752.8 | + | 18752.8i | −1.00608 | + | 1.00608i | ||||
\(704\) | 271.529 | 0.0145364 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −613.087 | −0.0326825 | ||||||||
\(707\) | −117.852 | + | 117.852i | −0.00626914 | + | 0.00626914i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1207.97i | 0.0639862i | 0.999488 | + | 0.0319931i | \(0.0101855\pi\) | ||||
−0.999488 | + | 0.0319931i | \(0.989815\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6959.02 | + | 6959.02i | 0.366293 | + | 0.366293i | ||||
\(713\) | −22539.4 | − | 22539.4i | −1.18388 | − | 1.18388i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10649.6i | 0.555860i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5298.83 | + | 5298.83i | −0.275418 | + | 0.275418i | ||||
\(719\) | 20470.8 | 1.06180 | 0.530898 | − | 0.847436i | \(-0.321855\pi\) | ||||
0.530898 | + | 0.847436i | \(0.321855\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −213.459 | −0.0110258 | ||||||||
\(722\) | 7563.03 | − | 7563.03i | 0.389843 | − | 0.389843i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 12913.8i | − | 0.662897i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3850.51 | + | 3850.51i | 0.196434 | + | 0.196434i | 0.798469 | − | 0.602036i | \(-0.205643\pi\) |
−0.602036 | + | 0.798469i | \(0.705643\pi\) | |||||||
\(728\) | −7.87913 | − | 7.87913i | −0.000401126 | − | 0.000401126i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13968.3i | 0.706754i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18950.5 | − | 18950.5i | 0.954914 | − | 0.954914i | −0.0441122 | − | 0.999027i | \(-0.514046\pi\) |
0.999027 | + | 0.0441122i | \(0.0140459\pi\) | |||||||
\(734\) | −12703.1 | −0.638801 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5063.27 | 0.253579 | ||||||||
\(737\) | −1446.00 | + | 1446.00i | −0.0722715 | + | 0.0722715i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 8217.11i | − | 0.409028i | −0.978864 | − | 0.204514i | \(-0.934439\pi\) | ||
0.978864 | − | 0.204514i | \(-0.0655613\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 85.3774 | + | 85.3774i | 0.00422413 | + | 0.00422413i | ||||
\(743\) | 6551.87 | + | 6551.87i | 0.323506 | + | 0.323506i | 0.850110 | − | 0.526605i | \(-0.176535\pi\) |
−0.526605 | + | 0.850110i | \(0.676535\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 23500.4i | 1.15337i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 584.908 | − | 584.908i | 0.0285914 | − | 0.0285914i | ||||
\(749\) | 147.215 | 0.00718175 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12001.4 | −0.583138 | −0.291569 | − | 0.956550i | \(-0.594177\pi\) | ||||
−0.291569 | + | 0.956550i | \(0.594177\pi\) | |||||||
\(752\) | 1704.76 | − | 1704.76i | 0.0826679 | − | 0.0826679i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 844.669i | − | 0.0407971i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15831.8 | − | 15831.8i | −0.760127 | − | 0.760127i | 0.216218 | − | 0.976345i | \(-0.430628\pi\) |
−0.976345 | + | 0.216218i | \(0.930628\pi\) | |||||||
\(758\) | 16917.8 | + | 16917.8i | 0.810664 | + | 0.810664i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 38246.7i | − | 1.82187i | −0.412553 | − | 0.910933i | \(-0.635363\pi\) | ||
0.412553 | − | 0.910933i | \(-0.364637\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.70268 | − | 5.70268i | 0.000270578 | − | 0.000270578i | ||||
\(764\) | 11605.6 | 0.549576 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27846.0 | −1.31347 | ||||||||
\(767\) | 322.273 | − | 322.273i | 0.0151716 | − | 0.0151716i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24315.9i | 1.14025i | 0.821557 | + | 0.570126i | \(0.193106\pi\) | ||||
−0.821557 | + | 0.570126i | \(0.806894\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4293.52 | + | 4293.52i | 0.200165 | + | 0.200165i | ||||
\(773\) | 5549.98 | + | 5549.98i | 0.258239 | + | 0.258239i | 0.824338 | − | 0.566098i | \(-0.191548\pi\) |
−0.566098 | + | 0.824338i | \(0.691548\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2291.91i | 0.106024i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19566.9 | + | 19566.9i | −0.901683 | + | 0.901683i | ||||
\(779\) | −41008.2 | −1.88610 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4202.36 | −0.192538 | ||||||||
\(782\) | 10906.9 | − | 10906.9i | 0.498760 | − | 0.498760i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5487.51i | 0.249978i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12044.5 | − | 12044.5i | −0.545542 | − | 0.545542i | 0.379606 | − | 0.925148i | \(-0.376059\pi\) |
−0.925148 | + | 0.379606i | \(0.876059\pi\) | |||||||
\(788\) | 6759.89 | + | 6759.89i | 0.305598 | + | 0.305598i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 282.093i | 0.0126802i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3432.72 | + | 3432.72i | −0.153719 | + | 0.153719i | ||||
\(794\) | −3538.11 | −0.158139 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4887.29 | −0.217620 | ||||||||
\(797\) | 446.462 | − | 446.462i | 0.0198425 | − | 0.0198425i | −0.697116 | − | 0.716958i | \(-0.745534\pi\) |
0.716958 | + | 0.697116i | \(0.245534\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 7344.55i | − | 0.325196i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13067.7 | + | 13067.7i | 0.575356 | + | 0.575356i | ||||
\(803\) | −3594.26 | − | 3594.26i | −0.157956 | − | 0.157956i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 3207.30i | − | 0.140164i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5388.37 | − | 5388.37i | 0.234607 | − | 0.234607i | ||||
\(809\) | −5823.00 | −0.253060 | −0.126530 | − | 0.991963i | \(-0.540384\pi\) | ||||
−0.126530 | + | 0.991963i | \(0.540384\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9681.83 | 0.419205 | 0.209602 | − | 0.977787i | \(-0.432783\pi\) | ||||
0.209602 | + | 0.977787i | \(0.432783\pi\) | |||||||
\(812\) | 26.2566 | − | 26.2566i | 0.00113476 | − | 0.00113476i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 2036.79i | − | 0.0877018i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22388.5 | − | 22388.5i | −0.958721 | − | 0.958721i | ||||
\(818\) | 5544.86 | + | 5544.86i | 0.237007 | + | 0.237007i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 613.797i | − | 0.0260922i | −0.999915 | − | 0.0130461i | \(-0.995847\pi\) | ||
0.999915 | − | 0.0130461i | \(-0.00415282\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4884.02 | + | 4884.02i | −0.206861 | + | 0.206861i | −0.802932 | − | 0.596071i | \(-0.796728\pi\) |
0.596071 | + | 0.802932i | \(0.296728\pi\) | |||||||
\(824\) | 9759.66 | 0.412614 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20.0358 | 0.000843987 | ||||||||
\(827\) | −31687.2 | + | 31687.2i | −1.33237 | + | 1.33237i | −0.429126 | + | 0.903245i | \(0.641178\pi\) |
−0.903245 | + | 0.429126i | \(0.858822\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 31717.5i | − | 1.32882i | −0.747367 | − | 0.664411i | \(-0.768682\pi\) | ||
0.747367 | − | 0.664411i | \(-0.231318\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 360.245 | + | 360.245i | 0.0150111 | + | 0.0150111i | ||||
\(833\) | 11820.8 | + | 11820.8i | 0.491676 | + | 0.491676i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1874.99i | 0.0775691i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16842.5 | − | 16842.5i | 0.694288 | − | 0.694288i | ||||
\(839\) | −1336.26 | −0.0549854 | −0.0274927 | − | 0.999622i | \(-0.508752\pi\) | ||||
−0.0274927 | + | 0.999622i | \(0.508752\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21574.2 | −0.884587 | ||||||||
\(842\) | 14998.8 | − | 14998.8i | 0.613886 | − | 0.613886i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 18744.0i | − | 0.764448i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −162.450 | − | 162.450i | −0.00659014 | − | 0.00659014i | ||||
\(848\) | −3903.58 | − | 3903.58i | −0.158077 | − | 0.158077i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 37980.4i | − | 1.52991i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7849.59 | − | 7849.59i | 0.315082 | − | 0.315082i | −0.531793 | − | 0.846875i | \(-0.678481\pi\) |
0.846875 | + | 0.531793i | \(0.178481\pi\) | |||||||
\(854\) | −213.413 | −0.00855134 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6730.90 | −0.268759 | ||||||||
\(857\) | −5652.60 | + | 5652.60i | −0.225308 | + | 0.225308i | −0.810729 | − | 0.585421i | \(-0.800929\pi\) |
0.585421 | + | 0.810729i | \(0.300929\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 22449.7i | − | 0.891706i | −0.895106 | − | 0.445853i | \(-0.852900\pi\) | ||
0.895106 | − | 0.445853i | \(-0.147100\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24124.9 | − | 24124.9i | −0.953245 | − | 0.953245i | ||||
\(863\) | 19455.8 | + | 19455.8i | 0.767420 | + | 0.767420i | 0.977652 | − | 0.210231i | \(-0.0674217\pi\) |
−0.210231 | + | 0.977652i | \(0.567422\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11347.0i | 0.445250i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 99.6991 | − | 99.6991i | 0.00389863 | − | 0.00389863i | ||||
\(869\) | −1853.38 | −0.0723496 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3836.89 | −0.149263 | ||||||||
\(872\) | −260.735 | + | 260.735i | −0.0101257 | + | 0.0101257i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 34963.3i | 1.35315i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15660.5 | + | 15660.5i | 0.602983 | + | 0.602983i | 0.941103 | − | 0.338120i | \(-0.109791\pi\) |
−0.338120 | + | 0.941103i | \(0.609791\pi\) | |||||||
\(878\) | 9370.82 | + | 9370.82i | 0.360193 | + | 0.360193i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 23.8106i | − | 0.000910554i | −1.00000 | 0.000455277i | \(-0.999855\pi\) | |||
1.00000 | 0.000455277i | \(-0.000144919\pi\) | ||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19225.0 | − | 19225.0i | 0.732698 | − | 0.732698i | −0.238456 | − | 0.971153i | \(-0.576641\pi\) |
0.971153 | + | 0.238456i | \(0.0766412\pi\) | |||||||
\(884\) | 1552.03 | 0.0590501 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −35385.9 | −1.34178 | ||||||||
\(887\) | 13803.0 | − | 13803.0i | 0.522502 | − | 0.522502i | −0.395824 | − | 0.918326i | \(-0.629541\pi\) |
0.918326 | + | 0.395824i | \(0.129541\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 155.847i | 0.00587958i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14983.4 | + | 14983.4i | 0.562425 | + | 0.562425i | ||||
\(893\) | 11771.9 | + | 11771.9i | 0.441132 | + | 0.441132i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 22.3965i | 0.000835061i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14078.9 | + | 14078.9i | −0.523183 | + | 0.523183i | ||||
\(899\) | 10688.1 | 0.396515 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16817.6 | −0.621837 | ||||||||
\(902\) | 2227.00 | − | 2227.00i | 0.0822072 | − | 0.0822072i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 12897.7i | − | 0.474525i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28217.1 | − | 28217.1i | −1.03300 | − | 1.03300i | −0.999436 | − | 0.0335664i | \(-0.989313\pi\) |
−0.0335664 | − | 0.999436i | \(-0.510687\pi\) | |||||||
\(908\) | 13066.6 | + | 13066.6i | 0.477568 | + | 0.477568i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 24262.0i | − | 0.882368i | −0.897417 | − | 0.441184i | \(-0.854559\pi\) | ||
0.897417 | − | 0.441184i | \(-0.145441\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −541.860 | + | 541.860i | −0.0196418 | + | 0.0196418i | ||||
\(914\) | −13283.3 | −0.480713 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4207.63 | 0.151773 | ||||||||
\(917\) | −92.1258 | + | 92.1258i | −0.00331762 | + | 0.00331762i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 23354.5i | − | 0.838295i | −0.907918 | − | 0.419148i | \(-0.862329\pi\) | ||
0.907918 | − | 0.419148i | \(-0.137671\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2590.26 | + | 2590.26i | 0.0925222 | + | 0.0925222i | ||||
\(923\) | −5575.38 | − | 5575.38i | −0.198825 | − | 0.198825i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 23762.0i | − | 0.843269i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1200.49 | + | 1200.49i | −0.0424655 | + | 0.0424655i | ||||
\(929\) | −2534.31 | −0.0895026 | −0.0447513 | − | 0.998998i | \(-0.514250\pi\) | ||||
−0.0447513 | + | 0.998998i | \(0.514250\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37892.9 | −1.33393 | ||||||||
\(932\) | −3889.25 | + | 3889.25i | −0.136692 | + | 0.136692i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 35126.9i | − | 1.23061i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21606.6 | − | 21606.6i | −0.753316 | − | 0.753316i | 0.221780 | − | 0.975097i | \(-0.428813\pi\) |
−0.975097 | + | 0.221780i | \(0.928813\pi\) | |||||||
\(938\) | −119.270 | − | 119.270i | −0.00415172 | − | 0.00415172i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 2386.44i | − | 0.0826735i | −0.999145 | − | 0.0413368i | \(-0.986838\pi\) | ||
0.999145 | − | 0.0413368i | \(-0.0131616\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41527.3 | − | 41527.3i | 1.43406 | − | 1.43406i | ||||
\(944\) | −916.064 | −0.0315841 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2431.67 | 0.0835733 | ||||||||
\(947\) | −26386.0 | + | 26386.0i | −0.905417 | + | 0.905417i | −0.995898 | − | 0.0904815i | \(-0.971159\pi\) |
0.0904815 | + | 0.995898i | \(0.471159\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 9537.21i | − | 0.326229i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 48.2449 | + | 48.2449i | 0.00164247 | + | 0.00164247i | ||||
\(953\) | 7162.80 | + | 7162.80i | 0.243469 | + | 0.243469i | 0.818284 | − | 0.574815i | \(-0.194926\pi\) |
−0.574815 | + | 0.818284i | \(0.694926\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 22084.2i | 0.747126i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9532.87 | − | 9532.87i | 0.321496 | − | 0.321496i | ||||
\(959\) | 155.744 | 0.00524425 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10792.7 | 0.362282 | ||||||||
\(962\) | 2702.26 | − | 2702.26i | 0.0905658 | − | 0.0905658i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 462.939i | 0.0154671i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11164.0 | + | 11164.0i | 0.371262 | + | 0.371262i | 0.867937 | − | 0.496675i | \(-0.165446\pi\) |
−0.496675 | + | 0.867937i | \(0.665446\pi\) | |||||||
\(968\) | 7427.45 | + | 7427.45i | 0.246619 | + | 0.246619i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 39205.7i | − | 1.29575i | −0.761747 | − | 0.647874i | \(-0.775658\pi\) | ||
0.761747 | − | 0.647874i | \(-0.224342\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.4263 | − | 28.4263i | 0.000936593 | − | 0.000936593i | ||||
\(974\) | 20640.1 | 0.679005 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9757.55 | 0.320012 | ||||||||
\(977\) | 3864.86 | − | 3864.86i | 0.126559 | − | 0.126559i | −0.640990 | − | 0.767549i | \(-0.721476\pi\) |
0.767549 | + | 0.640990i | \(0.221476\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 5219.27i | − | 0.170387i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12260.9 | + | 12260.9i | 0.398434 | + | 0.398434i | ||||
\(983\) | 21793.2 | + | 21793.2i | 0.707116 | + | 0.707116i | 0.965928 | − | 0.258812i | \(-0.0833310\pi\) |
−0.258812 | + | 0.965928i | \(0.583331\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5172.02i | 0.167049i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2487.60 | + | 2487.60i | −0.0801022 | + | 0.0801022i | ||||
\(989\) | 45343.9 | 1.45789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33283.2 | −1.06688 | −0.533439 | − | 0.845839i | \(-0.679101\pi\) | ||||
−0.533439 | + | 0.845839i | \(0.679101\pi\) | |||||||
\(992\) | −4558.39 | + | 4558.39i | −0.145896 | + | 0.145896i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 346.623i | − | 0.0110606i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36019.7 | + | 36019.7i | 1.14419 | + | 1.14419i | 0.987676 | + | 0.156511i | \(0.0500246\pi\) |
0.156511 | + | 0.987676i | \(0.449975\pi\) | |||||||
\(998\) | 8710.52 | + | 8710.52i | 0.276279 | + | 0.276279i | ||||
\(999\) | 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 | 450.4.f.f.107.1 | yes | 8 | |
3.2 | odd | 2 | inner | 450.4.f.f.107.3 | yes | 8 | |
5.2 | odd | 4 | 450.4.f.d.143.2 | yes | 8 | ||
5.3 | odd | 4 | inner | 450.4.f.f.143.3 | yes | 8 | |
5.4 | even | 2 | 450.4.f.d.107.4 | yes | 8 | ||
15.2 | even | 4 | 450.4.f.d.143.4 | yes | 8 | ||
15.8 | even | 4 | inner | 450.4.f.f.143.1 | yes | 8 | |
15.14 | odd | 2 | 450.4.f.d.107.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.4.f.d.107.2 | ✓ | 8 | 15.14 | odd | 2 | ||
450.4.f.d.107.4 | yes | 8 | 5.4 | even | 2 | ||
450.4.f.d.143.2 | yes | 8 | 5.2 | odd | 4 | ||
450.4.f.d.143.4 | yes | 8 | 15.2 | even | 4 | ||
450.4.f.f.107.1 | yes | 8 | 1.1 | even | 1 | trivial | |
450.4.f.f.107.3 | yes | 8 | 3.2 | odd | 2 | inner | |
450.4.f.f.143.1 | yes | 8 | 15.8 | even | 4 | inner | |
450.4.f.f.143.3 | yes | 8 | 5.3 | odd | 4 | inner |