Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(218,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.j (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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 407.1 | ||
Character | \(\chi\) | \(=\) | 525.407 |
Dual form | 525.2.j.c.218.1 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.90099 | + | 1.90099i | −1.34421 | + | 1.34421i | −0.452381 | + | 0.891825i | \(0.649425\pi\) |
−0.891825 | + | 0.452381i | \(0.850575\pi\) | |||||||
\(3\) | 0.394708 | + | 1.68648i | 0.227885 | + | 0.973688i | ||||
\(4\) | − | 5.22756i | − | 2.61378i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.95632 | − | 2.45565i | −1.61516 | − | 1.00251i | ||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | 6.13557 | + | 6.13557i | 2.16925 | + | 2.16925i | ||||
\(9\) | −2.68841 | + | 1.33133i | −0.896137 | + | 0.443777i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.76571i | 1.13541i | 0.823234 | + | 0.567703i | \(0.192168\pi\) | ||||
−0.823234 | + | 0.567703i | \(0.807832\pi\) | |||||||
\(12\) | 8.81616 | − | 2.06336i | 2.54501 | − | 0.595640i | ||||
\(13\) | −3.48012 | + | 3.48012i | −0.965210 | + | 0.965210i | −0.999415 | − | 0.0342046i | \(-0.989110\pi\) |
0.0342046 | + | 0.999415i | \(0.489110\pi\) | |||||||
\(14\) | 2.68841 | 0.718508 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12.8723 | −3.21806 | ||||||||
\(17\) | 0.131909 | − | 0.131909i | 0.0319926 | − | 0.0319926i | −0.690930 | − | 0.722922i | \(-0.742799\pi\) |
0.722922 | + | 0.690930i | \(0.242799\pi\) | |||||||
\(18\) | 2.57980 | − | 7.64151i | 0.608066 | − | 1.80112i | ||||
\(19\) | − | 3.89623i | − | 0.893856i | −0.894570 | − | 0.446928i | \(-0.852518\pi\) | ||
0.894570 | − | 0.446928i | \(-0.147482\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.913419 | − | 1.47162i | 0.199324 | − | 0.321134i | ||||
\(22\) | −7.15860 | − | 7.15860i | −1.52622 | − | 1.52622i | ||||
\(23\) | −3.35232 | − | 3.35232i | −0.699007 | − | 0.699007i | 0.265189 | − | 0.964196i | \(-0.414566\pi\) |
−0.964196 | + | 0.265189i | \(0.914566\pi\) | |||||||
\(24\) | −7.92574 | + | 12.7693i | −1.61784 | + | 2.60651i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 13.2314i | − | 2.59488i | ||||||
\(27\) | −3.30640 | − | 4.00846i | −0.636316 | − | 0.771428i | ||||
\(28\) | −3.69644 | + | 3.69644i | −0.698562 | + | 0.698562i | ||||
\(29\) | −4.27537 | −0.793916 | −0.396958 | − | 0.917837i | \(-0.629934\pi\) | ||||
−0.396958 | + | 0.917837i | \(0.629934\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.35375 | 0.602352 | 0.301176 | − | 0.953569i | \(-0.402621\pi\) | ||||
0.301176 | + | 0.953569i | \(0.402621\pi\) | |||||||
\(32\) | 12.1989 | − | 12.1989i | 2.15649 | − | 2.15649i | ||||
\(33\) | −6.35079 | + | 1.48636i | −1.10553 | + | 0.258741i | ||||
\(34\) | 0.501515i | 0.0860092i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.95961 | + | 14.0538i | 1.15993 | + | 2.34231i | ||||
\(37\) | −4.98611 | − | 4.98611i | −0.819711 | − | 0.819711i | 0.166355 | − | 0.986066i | \(-0.446800\pi\) |
−0.986066 | + | 0.166355i | \(0.946800\pi\) | |||||||
\(38\) | 7.40671 | + | 7.40671i | 1.20153 | + | 1.20153i | ||||
\(39\) | −7.24276 | − | 4.49551i | −1.15977 | − | 0.719857i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.16173i | − | 0.181432i | −0.995877 | − | 0.0907161i | \(-0.971084\pi\) | ||
0.995877 | − | 0.0907161i | \(-0.0289156\pi\) | |||||||
\(42\) | 1.06114 | + | 4.53395i | 0.163737 | + | 0.699603i | ||||
\(43\) | 2.05955 | − | 2.05955i | 0.314078 | − | 0.314078i | −0.532409 | − | 0.846487i | \(-0.678713\pi\) |
0.846487 | + | 0.532409i | \(0.178713\pi\) | |||||||
\(44\) | 19.6855 | 2.96770 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.7455 | 1.87922 | ||||||||
\(47\) | −7.97686 | + | 7.97686i | −1.16354 | + | 1.16354i | −0.179851 | + | 0.983694i | \(0.557562\pi\) |
−0.983694 | + | 0.179851i | \(0.942438\pi\) | |||||||
\(48\) | −5.08077 | − | 21.7088i | −0.733347 | − | 3.13339i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.274526 | + | 0.170396i | 0.0384414 | + | 0.0238602i | ||||
\(52\) | 18.1925 | + | 18.1925i | 2.52285 | + | 2.52285i | ||||
\(53\) | 3.80199 | + | 3.80199i | 0.522243 | + | 0.522243i | 0.918248 | − | 0.396005i | \(-0.129604\pi\) |
−0.396005 | + | 0.918248i | \(0.629604\pi\) | |||||||
\(54\) | 13.9055 | + | 1.33462i | 1.89230 | + | 0.181619i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 8.67701i | − | 1.15951i | ||||||
\(57\) | 6.57090 | − | 1.53787i | 0.870337 | − | 0.203696i | ||||
\(58\) | 8.12745 | − | 8.12745i | 1.06719 | − | 1.06719i | ||||
\(59\) | −7.06590 | −0.919901 | −0.459951 | − | 0.887945i | \(-0.652133\pi\) | ||||
−0.459951 | + | 0.887945i | \(0.652133\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.11035 | −0.526276 | −0.263138 | − | 0.964758i | \(-0.584758\pi\) | ||||
−0.263138 | + | 0.964758i | \(0.584758\pi\) | |||||||
\(62\) | −6.37546 | + | 6.37546i | −0.809685 | + | 0.809685i | ||||
\(63\) | 2.84239 | + | 0.959601i | 0.358107 | + | 0.120898i | ||||
\(64\) | 20.6357i | 2.57946i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9.24726 | − | 14.8984i | 1.13826 | − | 1.83386i | ||||
\(67\) | 0.153550 | + | 0.153550i | 0.0187591 | + | 0.0187591i | 0.716424 | − | 0.697665i | \(-0.245778\pi\) |
−0.697665 | + | 0.716424i | \(0.745778\pi\) | |||||||
\(68\) | −0.689561 | − | 0.689561i | −0.0836215 | − | 0.0836215i | ||||
\(69\) | 4.33043 | − | 6.97680i | 0.521322 | − | 0.839908i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.12077i | 0.251689i | 0.992050 | + | 0.125844i | \(0.0401640\pi\) | ||||
−0.992050 | + | 0.125844i | \(0.959836\pi\) | |||||||
\(72\) | −24.6634 | − | 8.32647i | −2.90661 | − | 0.981283i | ||||
\(73\) | 9.79331 | − | 9.79331i | 1.14622 | − | 1.14622i | 0.158930 | − | 0.987290i | \(-0.449196\pi\) |
0.987290 | − | 0.158930i | \(-0.0508045\pi\) | |||||||
\(74\) | 18.9571 | 2.20372 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −20.3678 | −2.33634 | ||||||||
\(77\) | 2.66276 | − | 2.66276i | 0.303450 | − | 0.303450i | ||||
\(78\) | 22.3144 | − | 5.22252i | 2.52661 | − | 0.591334i | ||||
\(79\) | − | 0.147763i | − | 0.0166247i | −0.999965 | − | 0.00831234i | \(-0.997354\pi\) | ||
0.999965 | − | 0.00831234i | \(-0.00264593\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.45512 | − | 7.15833i | 0.606124 | − | 0.795370i | ||||
\(82\) | 2.20845 | + | 2.20845i | 0.243882 | + | 0.243882i | ||||
\(83\) | −2.58598 | − | 2.58598i | −0.283848 | − | 0.283848i | 0.550794 | − | 0.834642i | \(-0.314325\pi\) |
−0.834642 | + | 0.550794i | \(0.814325\pi\) | |||||||
\(84\) | −7.69298 | − | 4.77495i | −0.839373 | − | 0.520990i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.83038i | 0.844372i | ||||||||
\(87\) | −1.68752 | − | 7.21031i | −0.180921 | − | 0.773027i | ||||
\(88\) | −23.1048 | + | 23.1048i | −2.46298 | + | 2.46298i | ||||
\(89\) | 1.17942 | 0.125018 | 0.0625089 | − | 0.998044i | \(-0.480090\pi\) | ||||
0.0625089 | + | 0.998044i | \(0.480090\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.92163 | 0.515927 | ||||||||
\(92\) | −17.5245 | + | 17.5245i | −1.82705 | + | 1.82705i | ||||
\(93\) | 1.32375 | + | 5.65603i | 0.137267 | + | 0.586503i | ||||
\(94\) | − | 30.3279i | − | 3.12809i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 25.3882 | + | 15.7582i | 2.59118 | + | 1.60832i | ||||
\(97\) | −1.52395 | − | 1.52395i | −0.154734 | − | 0.154734i | 0.625495 | − | 0.780228i | \(-0.284897\pi\) |
−0.780228 | + | 0.625495i | \(0.784897\pi\) | |||||||
\(98\) | −1.90099 | − | 1.90099i | −0.192029 | − | 0.192029i | ||||
\(99\) | −5.01341 | − | 10.1238i | −0.503867 | − | 1.01748i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.2192i | 1.11635i | 0.829723 | + | 0.558175i | \(0.188498\pi\) | ||||
−0.829723 | + | 0.558175i | \(0.811502\pi\) | |||||||
\(102\) | −0.845794 | + | 0.197952i | −0.0837461 | + | 0.0196002i | ||||
\(103\) | −13.7215 | + | 13.7215i | −1.35202 | + | 1.35202i | −0.468625 | + | 0.883397i | \(0.655251\pi\) |
−0.883397 | + | 0.468625i | \(0.844749\pi\) | |||||||
\(104\) | −42.7050 | −4.18757 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.4551 | −1.40401 | ||||||||
\(107\) | −7.86779 | + | 7.86779i | −0.760608 | + | 0.760608i | −0.976432 | − | 0.215824i | \(-0.930756\pi\) |
0.215824 | + | 0.976432i | \(0.430756\pi\) | |||||||
\(108\) | −20.9545 | + | 17.2844i | −2.01634 | + | 1.66319i | ||||
\(109\) | 17.0460i | 1.63271i | 0.577551 | + | 0.816354i | \(0.304008\pi\) | ||||
−0.577551 | + | 0.816354i | \(0.695992\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.44090 | − | 10.3770i | 0.611343 | − | 0.984942i | ||||
\(112\) | 9.10206 | + | 9.10206i | 0.860063 | + | 0.860063i | ||||
\(113\) | −12.4798 | − | 12.4798i | −1.17400 | − | 1.17400i | −0.981246 | − | 0.192757i | \(-0.938257\pi\) |
−0.192757 | − | 0.981246i | \(-0.561743\pi\) | |||||||
\(114\) | −9.56776 | + | 15.4147i | −0.896103 | + | 1.44372i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 22.3497i | 2.07512i | ||||||||
\(117\) | 4.72280 | − | 13.9892i | 0.436623 | − | 1.29330i | ||||
\(118\) | 13.4322 | − | 13.4322i | 1.23654 | − | 1.23654i | ||||
\(119\) | −0.186547 | −0.0171007 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.18059 | −0.289145 | ||||||||
\(122\) | 7.81375 | − | 7.81375i | 0.707424 | − | 0.707424i | ||||
\(123\) | 1.95924 | − | 0.458545i | 0.176658 | − | 0.0413456i | ||||
\(124\) | − | 17.5319i | − | 1.57441i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.22756 | + | 3.57917i | −0.643882 | + | 0.318857i | ||||
\(127\) | 8.66204 | + | 8.66204i | 0.768632 | + | 0.768632i | 0.977866 | − | 0.209234i | \(-0.0670969\pi\) |
−0.209234 | + | 0.977866i | \(0.567097\pi\) | |||||||
\(128\) | −14.8305 | − | 14.8305i | −1.31084 | − | 1.31084i | ||||
\(129\) | 4.28630 | + | 2.66046i | 0.377388 | + | 0.234241i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 3.23990i | − | 0.283072i | −0.989933 | − | 0.141536i | \(-0.954796\pi\) | ||
0.989933 | − | 0.141536i | \(-0.0452041\pi\) | |||||||
\(132\) | 7.77001 | + | 33.1991i | 0.676292 | + | 2.88961i | ||||
\(133\) | −2.75505 | + | 2.75505i | −0.238893 | + | 0.238893i | ||||
\(134\) | −0.583796 | −0.0504323 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.61867 | 0.138800 | ||||||||
\(137\) | 5.54149 | − | 5.54149i | 0.473442 | − | 0.473442i | −0.429585 | − | 0.903026i | \(-0.641340\pi\) |
0.903026 | + | 0.429585i | \(0.141340\pi\) | |||||||
\(138\) | 5.03074 | + | 21.4950i | 0.428245 | + | 1.82977i | ||||
\(139\) | 18.9037i | 1.60339i | 0.597735 | + | 0.801694i | \(0.296067\pi\) | ||||
−0.597735 | + | 0.801694i | \(0.703933\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.6013 | − | 10.3043i | −1.39808 | − | 0.867776i | ||||
\(142\) | −4.03157 | − | 4.03157i | −0.338322 | − | 0.338322i | ||||
\(143\) | −13.1051 | − | 13.1051i | −1.09590 | − | 1.09590i | ||||
\(144\) | 34.6059 | − | 17.1372i | 2.88383 | − | 1.42810i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 37.2340i | 3.08151i | ||||||||
\(147\) | −1.68648 | + | 0.394708i | −0.139098 | + | 0.0325549i | ||||
\(148\) | −26.0652 | + | 26.0652i | −2.14254 | + | 2.14254i | ||||
\(149\) | 4.47960 | 0.366983 | 0.183491 | − | 0.983021i | \(-0.441260\pi\) | ||||
0.183491 | + | 0.983021i | \(0.441260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.07180 | 0.168600 | 0.0843002 | − | 0.996440i | \(-0.473135\pi\) | ||||
0.0843002 | + | 0.996440i | \(0.473135\pi\) | |||||||
\(152\) | 23.9056 | − | 23.9056i | 1.93900 | − | 1.93900i | ||||
\(153\) | −0.179011 | + | 0.530239i | −0.0144722 | + | 0.0428673i | ||||
\(154\) | 10.1238i | 0.815798i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −23.5005 | + | 37.8620i | −1.88155 | + | 3.03138i | ||||
\(157\) | 5.17869 | + | 5.17869i | 0.413304 | + | 0.413304i | 0.882888 | − | 0.469584i | \(-0.155596\pi\) |
−0.469584 | + | 0.882888i | \(0.655596\pi\) | |||||||
\(158\) | 0.280897 | + | 0.280897i | 0.0223470 | + | 0.0223470i | ||||
\(159\) | −4.91129 | + | 7.91264i | −0.389491 | + | 0.627513i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.74090i | 0.373635i | ||||||||
\(162\) | 3.23780 | + | 23.9781i | 0.254386 | + | 1.88390i | ||||
\(163\) | 1.14611 | − | 1.14611i | 0.0897706 | − | 0.0897706i | −0.660795 | − | 0.750566i | \(-0.729781\pi\) |
0.750566 | + | 0.660795i | \(0.229781\pi\) | |||||||
\(164\) | −6.07303 | −0.474224 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.83186 | 0.763100 | ||||||||
\(167\) | −1.04994 | + | 1.04994i | −0.0812469 | + | 0.0812469i | −0.746562 | − | 0.665315i | \(-0.768297\pi\) |
0.665315 | + | 0.746562i | \(0.268297\pi\) | |||||||
\(168\) | 14.6336 | − | 3.42488i | 1.12900 | − | 0.264235i | ||||
\(169\) | − | 11.2224i | − | 0.863262i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.18717 | + | 10.4747i | 0.396673 | + | 0.801018i | ||||
\(172\) | −10.7664 | − | 10.7664i | −0.820931 | − | 0.820931i | ||||
\(173\) | 3.39494 | + | 3.39494i | 0.258113 | + | 0.258113i | 0.824286 | − | 0.566173i | \(-0.191577\pi\) |
−0.566173 | + | 0.824286i | \(0.691577\pi\) | |||||||
\(174\) | 16.9147 | + | 10.4988i | 1.28230 | + | 0.795912i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 48.4732i | − | 3.65380i | ||||||
\(177\) | −2.78896 | − | 11.9165i | −0.209631 | − | 0.895697i | ||||
\(178\) | −2.24206 | + | 2.24206i | −0.168050 | + | 0.168050i | ||||
\(179\) | −15.7574 | −1.17776 | −0.588881 | − | 0.808220i | \(-0.700431\pi\) | ||||
−0.588881 | + | 0.808220i | \(0.700431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.06040 | −0.376137 | −0.188068 | − | 0.982156i | \(-0.560223\pi\) | ||||
−0.188068 | + | 0.982156i | \(0.560223\pi\) | |||||||
\(182\) | −9.35598 | + | 9.35598i | −0.693512 | + | 0.693512i | ||||
\(183\) | −1.62239 | − | 6.93201i | −0.119930 | − | 0.512429i | ||||
\(184\) | − | 41.1368i | − | 3.03265i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −13.2685 | − | 8.23563i | −0.972895 | − | 0.603866i | ||||
\(187\) | 0.496730 | + | 0.496730i | 0.0363245 | + | 0.0363245i | ||||
\(188\) | 41.6995 | + | 41.6995i | 3.04125 | + | 3.04125i | ||||
\(189\) | −0.496434 | + | 5.17238i | −0.0361103 | + | 0.376236i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.726830i | 0.0525916i | 0.999654 | + | 0.0262958i | \(0.00837117\pi\) | ||||
−0.999654 | + | 0.0262958i | \(0.991629\pi\) | |||||||
\(192\) | −34.8017 | + | 8.14507i | −2.51159 | + | 0.587820i | ||||
\(193\) | 11.8926 | − | 11.8926i | 0.856050 | − | 0.856050i | −0.134820 | − | 0.990870i | \(-0.543046\pi\) |
0.990870 | + | 0.134820i | \(0.0430458\pi\) | |||||||
\(194\) | 5.79404 | 0.415988 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.22756 | 0.373397 | ||||||||
\(197\) | 12.6242 | − | 12.6242i | 0.899440 | − | 0.899440i | −0.0959464 | − | 0.995387i | \(-0.530588\pi\) |
0.995387 | + | 0.0959464i | \(0.0305877\pi\) | |||||||
\(198\) | 28.7757 | + | 9.71480i | 2.04500 | + | 0.690401i | ||||
\(199\) | − | 1.56130i | − | 0.110677i | −0.998468 | − | 0.0553387i | \(-0.982376\pi\) | ||
0.998468 | − | 0.0553387i | \(-0.0176239\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.198351 | + | 0.319566i | −0.0139906 | + | 0.0225405i | ||||
\(202\) | −21.3276 | − | 21.3276i | −1.50060 | − | 1.50060i | ||||
\(203\) | 3.02314 | + | 3.02314i | 0.212183 | + | 0.212183i | ||||
\(204\) | 0.890753 | − | 1.43510i | 0.0623652 | − | 0.100477i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 52.1691i | − | 3.63479i | ||||||
\(207\) | 13.4755 | + | 4.54937i | 0.936610 | + | 0.316203i | ||||
\(208\) | 44.7969 | − | 44.7969i | 3.10611 | − | 3.10611i | ||||
\(209\) | 14.6721 | 1.01489 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.06281 | −0.279696 | −0.139848 | − | 0.990173i | \(-0.544661\pi\) | ||||
−0.139848 | + | 0.990173i | \(0.544661\pi\) | |||||||
\(212\) | 19.8751 | − | 19.8751i | 1.36503 | − | 1.36503i | ||||
\(213\) | −3.57663 | + | 0.837083i | −0.245066 | + | 0.0573560i | ||||
\(214\) | − | 29.9133i | − | 2.04483i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.30756 | − | 44.8808i | 0.293092 | − | 3.05375i | ||||
\(217\) | −2.37146 | − | 2.37146i | −0.160985 | − | 0.160985i | ||||
\(218\) | −32.4043 | − | 32.4043i | −2.19470 | − | 2.19470i | ||||
\(219\) | 20.3817 | + | 12.6507i | 1.37727 | + | 0.854855i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.918115i | 0.0617591i | ||||||||
\(222\) | 7.48252 | + | 31.9708i | 0.502194 | + | 2.14574i | ||||
\(223\) | −19.2652 | + | 19.2652i | −1.29010 | + | 1.29010i | −0.355370 | + | 0.934726i | \(0.615645\pi\) |
−0.934726 | + | 0.355370i | \(0.884355\pi\) | |||||||
\(224\) | −17.2519 | −1.15269 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 47.4482 | 3.15621 | ||||||||
\(227\) | −15.5808 | + | 15.5808i | −1.03414 | + | 1.03414i | −0.0347402 | + | 0.999396i | \(0.511060\pi\) |
−0.999396 | + | 0.0347402i | \(0.988940\pi\) | |||||||
\(228\) | −8.03931 | − | 34.3498i | −0.532416 | − | 2.27487i | ||||
\(229\) | 25.2714i | 1.66998i | 0.550264 | + | 0.834991i | \(0.314527\pi\) | ||||
−0.550264 | + | 0.834991i | \(0.685473\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.54170 | + | 3.43967i | 0.364617 | + | 0.226314i | ||||
\(232\) | −26.2318 | − | 26.2318i | −1.72220 | − | 1.72220i | ||||
\(233\) | −8.15021 | − | 8.15021i | −0.533938 | − | 0.533938i | 0.387804 | − | 0.921742i | \(-0.373234\pi\) |
−0.921742 | + | 0.387804i | \(0.873234\pi\) | |||||||
\(234\) | 17.6153 | + | 35.5713i | 1.15155 | + | 2.32537i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 36.9374i | 2.40442i | ||||||||
\(237\) | 0.249200 | − | 0.0583233i | 0.0161872 | − | 0.00378851i | ||||
\(238\) | 0.354625 | − | 0.354625i | 0.0229869 | − | 0.0229869i | ||||
\(239\) | 20.4397 | 1.32213 | 0.661066 | − | 0.750328i | \(-0.270104\pi\) | ||||
0.661066 | + | 0.750328i | \(0.270104\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.2544 | −0.853790 | −0.426895 | − | 0.904301i | \(-0.640393\pi\) | ||||
−0.426895 | + | 0.904301i | \(0.640393\pi\) | |||||||
\(242\) | 6.04628 | − | 6.04628i | 0.388670 | − | 0.388670i | ||||
\(243\) | 14.2255 | + | 6.37448i | 0.912569 | + | 0.408923i | ||||
\(244\) | 21.4871i | 1.37557i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.85281 | + | 4.59619i | −0.181888 | + | 0.293042i | ||||
\(247\) | 13.5593 | + | 13.5593i | 0.862759 | + | 0.862759i | ||||
\(248\) | 20.5772 | + | 20.5772i | 1.30665 | + | 1.30665i | ||||
\(249\) | 3.34049 | − | 5.38190i | 0.211695 | − | 0.341064i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.9297i | 1.13171i | 0.824505 | + | 0.565855i | \(0.191454\pi\) | ||||
−0.824505 | + | 0.565855i | \(0.808546\pi\) | |||||||
\(252\) | 5.01637 | − | 14.8587i | 0.316002 | − | 0.936013i | ||||
\(253\) | 12.6239 | − | 12.6239i | 0.793656 | − | 0.793656i | ||||
\(254\) | −32.9330 | −2.06640 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.1139 | 0.944622 | ||||||||
\(257\) | 1.92762 | − | 1.92762i | 0.120242 | − | 0.120242i | −0.644425 | − | 0.764667i | \(-0.722903\pi\) |
0.764667 | + | 0.644425i | \(0.222903\pi\) | |||||||
\(258\) | −13.2058 | + | 3.09071i | −0.822155 | + | 0.192419i | ||||
\(259\) | 7.05142i | 0.438154i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.4940 | − | 5.69193i | 0.711458 | − | 0.352322i | ||||
\(262\) | 6.15904 | + | 6.15904i | 0.380507 | + | 0.380507i | ||||
\(263\) | −11.8215 | − | 11.8215i | −0.728943 | − | 0.728943i | 0.241466 | − | 0.970409i | \(-0.422372\pi\) |
−0.970409 | + | 0.241466i | \(0.922372\pi\) | |||||||
\(264\) | −48.0853 | − | 29.8461i | −2.95945 | − | 1.83690i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 10.4747i | − | 0.642243i | ||||||
\(267\) | 0.465524 | + | 1.98906i | 0.0284896 | + | 0.121728i | ||||
\(268\) | 0.802692 | − | 0.802692i | 0.0490322 | − | 0.0490322i | ||||
\(269\) | −14.6150 | −0.891092 | −0.445546 | − | 0.895259i | \(-0.646991\pi\) | ||||
−0.445546 | + | 0.895259i | \(0.646991\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.12917 | −0.190084 | −0.0950418 | − | 0.995473i | \(-0.530298\pi\) | ||||
−0.0950418 | + | 0.995473i | \(0.530298\pi\) | |||||||
\(272\) | −1.69796 | + | 1.69796i | −0.102954 | + | 0.102954i | ||||
\(273\) | 1.94260 | + | 8.30021i | 0.117572 | + | 0.502352i | ||||
\(274\) | 21.0687i | 1.27281i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −36.4716 | − | 22.6376i | −2.19533 | − | 1.36262i | ||||
\(277\) | 9.61019 | + | 9.61019i | 0.577421 | + | 0.577421i | 0.934192 | − | 0.356771i | \(-0.116122\pi\) |
−0.356771 | + | 0.934192i | \(0.616122\pi\) | |||||||
\(278\) | −35.9357 | − | 35.9357i | −2.15528 | − | 2.15528i | ||||
\(279\) | −9.01627 | + | 4.46495i | −0.539790 | + | 0.267310i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.72113i | − | 0.520259i | −0.965574 | − | 0.260130i | \(-0.916235\pi\) | ||
0.965574 | − | 0.260130i | \(-0.0837653\pi\) | |||||||
\(282\) | 51.1474 | − | 11.9707i | 3.04578 | − | 0.712843i | ||||
\(283\) | 11.6672 | − | 11.6672i | 0.693545 | − | 0.693545i | −0.269465 | − | 0.963010i | \(-0.586847\pi\) |
0.963010 | + | 0.269465i | \(0.0868469\pi\) | |||||||
\(284\) | 11.0864 | 0.657859 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 49.8255 | 2.94624 | ||||||||
\(287\) | −0.821469 | + | 0.821469i | −0.0484898 | + | 0.0484898i | ||||
\(288\) | −16.5549 | + | 49.0366i | −0.975509 | + | 2.88951i | ||||
\(289\) | 16.9652i | 0.997953i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.96859 | − | 3.17162i | 0.115401 | − | 0.185924i | ||||
\(292\) | −51.1951 | − | 51.1951i | −2.99597 | − | 2.99597i | ||||
\(293\) | 14.4218 | + | 14.4218i | 0.842532 | + | 0.842532i | 0.989188 | − | 0.146655i | \(-0.0468508\pi\) |
−0.146655 | + | 0.989188i | \(0.546851\pi\) | |||||||
\(294\) | 2.45565 | − | 3.95632i | 0.143216 | − | 0.230737i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 61.1852i | − | 3.55632i | ||||||
\(297\) | 15.0947 | − | 12.4509i | 0.875884 | − | 0.722477i | ||||
\(298\) | −8.51569 | + | 8.51569i | −0.493301 | + | 0.493301i | ||||
\(299\) | 23.3329 | 1.34938 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.91264 | −0.167882 | ||||||||
\(302\) | −3.93847 | + | 3.93847i | −0.226634 | + | 0.226634i | ||||
\(303\) | −18.9209 | + | 4.42829i | −1.08698 | + | 0.254399i | ||||
\(304\) | 50.1532i | 2.87648i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.667683 | − | 1.34828i | −0.0381689 | − | 0.0770760i | ||||
\(307\) | 6.03004 | + | 6.03004i | 0.344153 | + | 0.344153i | 0.857926 | − | 0.513773i | \(-0.171753\pi\) |
−0.513773 | + | 0.857926i | \(0.671753\pi\) | |||||||
\(308\) | −13.9197 | − | 13.9197i | −0.793151 | − | 0.793151i | ||||
\(309\) | −28.5570 | − | 17.7251i | −1.62455 | − | 1.00834i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.3414i | 1.15345i | 0.816937 | + | 0.576727i | \(0.195670\pi\) | ||||
−0.816937 | + | 0.576727i | \(0.804330\pi\) | |||||||
\(312\) | −16.8560 | − | 72.0210i | −0.954282 | − | 4.07739i | ||||
\(313\) | 13.6095 | − | 13.6095i | 0.769254 | − | 0.769254i | −0.208721 | − | 0.977975i | \(-0.566930\pi\) |
0.977975 | + | 0.208721i | \(0.0669302\pi\) | |||||||
\(314\) | −19.6893 | −1.11113 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.772442 | −0.0434532 | ||||||||
\(317\) | −13.3563 | + | 13.3563i | −0.750166 | + | 0.750166i | −0.974510 | − | 0.224344i | \(-0.927976\pi\) |
0.224344 | + | 0.974510i | \(0.427976\pi\) | |||||||
\(318\) | −5.70554 | − | 24.3782i | −0.319951 | − | 1.36706i | ||||
\(319\) | − | 16.0998i | − | 0.901416i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.3743 | − | 10.1634i | −0.913926 | − | 0.567265i | ||||
\(322\) | −9.01242 | − | 9.01242i | −0.502243 | − | 0.502243i | ||||
\(323\) | −0.513946 | − | 0.513946i | −0.0285967 | − | 0.0285967i | ||||
\(324\) | −37.4206 | − | 28.5169i | −2.07892 | − | 1.58427i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.35751i | 0.241340i | ||||||||
\(327\) | −28.7477 | + | 6.72818i | −1.58975 | + | 0.372069i | ||||
\(328\) | 7.12789 | − | 7.12789i | 0.393572 | − | 0.393572i | ||||
\(329\) | 11.2810 | 0.621941 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.5981 | −1.57189 | −0.785946 | − | 0.618295i | \(-0.787824\pi\) | ||||
−0.785946 | + | 0.618295i | \(0.787824\pi\) | |||||||
\(332\) | −13.5184 | + | 13.5184i | −0.741916 | + | 0.741916i | ||||
\(333\) | 20.0429 | + | 6.76655i | 1.09834 | + | 0.370805i | ||||
\(334\) | − | 3.99187i | − | 0.218425i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −11.7578 | + | 18.9431i | −0.641438 | + | 1.03343i | ||||
\(337\) | 17.2226 | + | 17.2226i | 0.938172 | + | 0.938172i | 0.998197 | − | 0.0600247i | \(-0.0191180\pi\) |
−0.0600247 | + | 0.998197i | \(0.519118\pi\) | |||||||
\(338\) | 21.3337 | + | 21.3337i | 1.16040 | + | 1.16040i | ||||
\(339\) | 16.1211 | − | 25.9728i | 0.875576 | − | 1.41065i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.6293i | 0.683913i | ||||||||
\(342\) | −29.7731 | − | 10.0515i | −1.60994 | − | 0.543523i | ||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | 25.2730 | 1.36263 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.9075 | −0.693914 | ||||||||
\(347\) | −0.679325 | + | 0.679325i | −0.0364681 | + | 0.0364681i | −0.725106 | − | 0.688638i | \(-0.758209\pi\) |
0.688638 | + | 0.725106i | \(0.258209\pi\) | |||||||
\(348\) | −37.6923 | + | 8.82161i | −2.02052 | + | 0.472888i | ||||
\(349\) | − | 6.95006i | − | 0.372028i | −0.982547 | − | 0.186014i | \(-0.940443\pi\) | ||
0.982547 | − | 0.186014i | \(-0.0595570\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.4565 | + | 2.44326i | 1.35877 | + | 0.130412i | ||||
\(352\) | 45.9377 | + | 45.9377i | 2.44849 | + | 2.44849i | ||||
\(353\) | 21.2979 | + | 21.2979i | 1.13358 | + | 1.13358i | 0.989578 | + | 0.143997i | \(0.0459956\pi\) |
0.143997 | + | 0.989578i | \(0.454004\pi\) | |||||||
\(354\) | 27.9549 | + | 17.3513i | 1.48579 | + | 0.922214i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 6.16546i | − | 0.326769i | ||||||
\(357\) | −0.0736316 | − | 0.314607i | −0.00389699 | − | 0.0166508i | ||||
\(358\) | 29.9547 | − | 29.9547i | 1.58315 | − | 1.58315i | ||||
\(359\) | −5.03756 | −0.265872 | −0.132936 | − | 0.991125i | \(-0.542441\pi\) | ||||
−0.132936 | + | 0.991125i | \(0.542441\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.81941 | 0.201022 | ||||||||
\(362\) | 9.61980 | − | 9.61980i | 0.505605 | − | 0.505605i | ||||
\(363\) | −1.25540 | − | 5.36399i | −0.0658916 | − | 0.281537i | ||||
\(364\) | − | 25.7281i | − | 1.34852i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 16.2619 | + | 10.0936i | 0.850021 | + | 0.527599i | ||||
\(367\) | 0.135150 | + | 0.135150i | 0.00705477 | + | 0.00705477i | 0.710625 | − | 0.703571i | \(-0.248412\pi\) |
−0.703571 | + | 0.710625i | \(0.748412\pi\) | |||||||
\(368\) | 43.1519 | + | 43.1519i | 2.24945 | + | 2.24945i | ||||
\(369\) | 1.54665 | + | 3.12322i | 0.0805154 | + | 0.162588i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 5.37682i | − | 0.279151i | ||||||
\(372\) | 29.5672 | − | 6.91999i | 1.53299 | − | 0.358785i | ||||
\(373\) | −14.5624 | + | 14.5624i | −0.754012 | + | 0.754012i | −0.975225 | − | 0.221213i | \(-0.928998\pi\) |
0.221213 | + | 0.975225i | \(0.428998\pi\) | |||||||
\(374\) | −1.88856 | −0.0976553 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −97.8852 | −5.04804 | ||||||||
\(377\) | 14.8788 | − | 14.8788i | 0.766296 | − | 0.766296i | ||||
\(378\) | −8.88895 | − | 10.7764i | −0.457198 | − | 0.554278i | ||||
\(379\) | − | 33.5148i | − | 1.72154i | −0.508994 | − | 0.860770i | \(-0.669982\pi\) | ||
0.508994 | − | 0.860770i | \(-0.330018\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.1894 | + | 18.0273i | −0.573249 | + | 0.923567i | ||||
\(382\) | −1.38170 | − | 1.38170i | −0.0706939 | − | 0.0706939i | ||||
\(383\) | 24.3438 | + | 24.3438i | 1.24391 | + | 1.24391i | 0.958365 | + | 0.285546i | \(0.0921751\pi\) |
0.285546 | + | 0.958365i | \(0.407825\pi\) | |||||||
\(384\) | 19.1576 | − | 30.8650i | 0.977631 | − | 1.57507i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 45.2156i | 2.30141i | ||||||||
\(387\) | −2.79497 | + | 8.27885i | −0.142077 | + | 0.420838i | ||||
\(388\) | −7.96654 | + | 7.96654i | −0.404440 | + | 0.404440i | ||||
\(389\) | 9.70050 | 0.491835 | 0.245917 | − | 0.969291i | \(-0.420911\pi\) | ||||
0.245917 | + | 0.969291i | \(0.420911\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.884401 | −0.0447261 | ||||||||
\(392\) | −6.13557 | + | 6.13557i | −0.309893 | + | 0.309893i | ||||
\(393\) | 5.46403 | − | 1.27881i | 0.275624 | − | 0.0645077i | ||||
\(394\) | 47.9972i | 2.41807i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −52.9227 | + | 26.2079i | −2.65946 | + | 1.31700i | ||||
\(397\) | 3.59901 | + | 3.59901i | 0.180629 | + | 0.180629i | 0.791630 | − | 0.611001i | \(-0.209233\pi\) |
−0.611001 | + | 0.791630i | \(0.709233\pi\) | |||||||
\(398\) | 2.96802 | + | 2.96802i | 0.148773 | + | 0.148773i | ||||
\(399\) | −5.73377 | − | 3.55889i | −0.287047 | − | 0.178167i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 38.9834i | − | 1.94674i | −0.229244 | − | 0.973369i | \(-0.573625\pi\) | ||
0.229244 | − | 0.973369i | \(-0.426375\pi\) | |||||||
\(402\) | −0.230429 | − | 0.984558i | −0.0114927 | − | 0.0491053i | ||||
\(403\) | −11.6714 | + | 11.6714i | −0.581396 | + | 0.581396i | ||||
\(404\) | 58.6489 | 2.91789 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.4940 | −0.570435 | ||||||||
\(407\) | 18.7762 | − | 18.7762i | 0.930704 | − | 0.930704i | ||||
\(408\) | 0.638901 | + | 2.72985i | 0.0316303 | + | 0.135148i | ||||
\(409\) | − | 1.53194i | − | 0.0757493i | −0.999282 | − | 0.0378747i | \(-0.987941\pi\) | ||
0.999282 | − | 0.0378747i | \(-0.0120588\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.5329 | + | 7.15833i | 0.568874 | + | 0.353094i | ||||
\(412\) | 71.7301 | + | 71.7301i | 3.53389 | + | 3.53389i | ||||
\(413\) | 4.99634 | + | 4.99634i | 0.245854 | + | 0.245854i | ||||
\(414\) | −34.2651 | + | 16.9685i | −1.68404 | + | 0.833954i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 84.9074i | 4.16293i | ||||||||
\(417\) | −31.8806 | + | 7.46142i | −1.56120 | + | 0.365387i | ||||
\(418\) | −27.8915 | + | 27.8915i | −1.36422 | + | 1.36422i | ||||
\(419\) | 25.9795 | 1.26918 | 0.634591 | − | 0.772848i | \(-0.281169\pi\) | ||||
0.634591 | + | 0.772848i | \(0.281169\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.34632 | −0.163090 | −0.0815449 | − | 0.996670i | \(-0.525985\pi\) | ||||
−0.0815449 | + | 0.996670i | \(0.525985\pi\) | |||||||
\(422\) | 7.72338 | − | 7.72338i | 0.375968 | − | 0.375968i | ||||
\(423\) | 10.8252 | − | 32.0649i | 0.526342 | − | 1.55905i | ||||
\(424\) | 46.6547i | 2.26575i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.20786 | − | 8.39044i | 0.252321 | − | 0.406518i | ||||
\(427\) | 2.90646 | + | 2.90646i | 0.140653 | + | 0.140653i | ||||
\(428\) | 41.1294 | + | 41.1294i | 1.98806 | + | 1.98806i | ||||
\(429\) | 16.9288 | − | 27.2742i | 0.817330 | − | 1.31681i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.5955i | 1.04022i | 0.854099 | + | 0.520110i | \(0.174109\pi\) | ||||
−0.854099 | + | 0.520110i | \(0.825891\pi\) | |||||||
\(432\) | 42.5608 | + | 51.5979i | 2.04771 | + | 2.48250i | ||||
\(433\) | −10.0406 | + | 10.0406i | −0.482523 | + | 0.482523i | −0.905936 | − | 0.423414i | \(-0.860832\pi\) |
0.423414 | + | 0.905936i | \(0.360832\pi\) | |||||||
\(434\) | 9.01627 | 0.432795 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 89.1089 | 4.26754 | ||||||||
\(437\) | −13.0614 | + | 13.0614i | −0.624812 | + | 0.624812i | ||||
\(438\) | −62.7944 | + | 14.6966i | −3.00043 | + | 0.702229i | ||||
\(439\) | 24.0394i | 1.14734i | 0.819087 | + | 0.573669i | \(0.194480\pi\) | ||||
−0.819087 | + | 0.573669i | \(0.805520\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.33133 | − | 2.68841i | −0.0633967 | − | 0.128020i | ||||
\(442\) | −1.74533 | − | 1.74533i | −0.0830170 | − | 0.0830170i | ||||
\(443\) | −4.25893 | − | 4.25893i | −0.202348 | − | 0.202348i | 0.598657 | − | 0.801005i | \(-0.295701\pi\) |
−0.801005 | + | 0.598657i | \(0.795701\pi\) | |||||||
\(444\) | −54.2464 | − | 33.6702i | −2.57442 | − | 1.59792i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 73.2462i | − | 3.46831i | ||||||
\(447\) | 1.76813 | + | 7.55474i | 0.0836297 | + | 0.357327i | ||||
\(448\) | 14.5916 | − | 14.5916i | 0.689391 | − | 0.689391i | ||||
\(449\) | −30.2607 | −1.42809 | −0.714046 | − | 0.700099i | \(-0.753139\pi\) | ||||
−0.714046 | + | 0.700099i | \(0.753139\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.37475 | 0.205999 | ||||||||
\(452\) | −65.2390 | + | 65.2390i | −3.06859 | + | 3.06859i | ||||
\(453\) | 0.817754 | + | 3.49404i | 0.0384214 | + | 0.164164i | ||||
\(454\) | − | 59.2382i | − | 2.78019i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 49.7519 | + | 30.8805i | 2.32985 | + | 1.44611i | ||||
\(457\) | −10.5131 | − | 10.5131i | −0.491783 | − | 0.491783i | 0.417085 | − | 0.908868i | \(-0.363052\pi\) |
−0.908868 | + | 0.417085i | \(0.863052\pi\) | |||||||
\(458\) | −48.0408 | − | 48.0408i | −2.24480 | − | 2.24480i | ||||
\(459\) | −0.964893 | − | 0.0926083i | −0.0450374 | − | 0.00432259i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 39.7882i | − | 1.85312i | −0.376146 | − | 0.926560i | \(-0.622751\pi\) | ||
0.376146 | − | 0.926560i | \(-0.377249\pi\) | |||||||
\(462\) | −17.0735 | + | 3.99593i | −0.794333 | + | 0.185908i | ||||
\(463\) | 24.1384 | − | 24.1384i | 1.12181 | − | 1.12181i | 0.130335 | − | 0.991470i | \(-0.458395\pi\) |
0.991470 | − | 0.130335i | \(-0.0416053\pi\) | |||||||
\(464\) | 55.0336 | 2.55487 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 30.9870 | 1.43544 | ||||||||
\(467\) | −13.5195 | + | 13.5195i | −0.625610 | + | 0.625610i | −0.946960 | − | 0.321351i | \(-0.895863\pi\) |
0.321351 | + | 0.946960i | \(0.395863\pi\) | |||||||
\(468\) | −73.1292 | − | 24.6887i | −3.38040 | − | 1.14124i | ||||
\(469\) | − | 0.217153i | − | 0.0100272i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.68967 | + | 10.7778i | −0.308244 | + | 0.496615i | ||||
\(472\) | −43.3533 | − | 43.3533i | −1.99550 | − | 1.99550i | ||||
\(473\) | 7.75567 | + | 7.75567i | 0.356606 | + | 0.356606i | ||||
\(474\) | −0.362855 | + | 0.584599i | −0.0166665 | + | 0.0268515i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.975186i | 0.0446976i | ||||||||
\(477\) | −15.2830 | − | 5.15961i | −0.699761 | − | 0.236242i | ||||
\(478\) | −38.8557 | + | 38.8557i | −1.77722 | + | 1.77722i | ||||
\(479\) | −37.0916 | −1.69476 | −0.847380 | − | 0.530987i | \(-0.821821\pi\) | ||||
−0.847380 | + | 0.530987i | \(0.821821\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.7045 | 1.58239 | ||||||||
\(482\) | 25.1965 | − | 25.1965i | 1.14767 | − | 1.14767i | ||||
\(483\) | −7.99542 | + | 1.87127i | −0.363804 | + | 0.0851457i | ||||
\(484\) | 16.6267i | 0.755760i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −39.1605 | + | 14.9248i | −1.77636 | + | 0.677003i | ||||
\(487\) | −12.3041 | − | 12.3041i | −0.557551 | − | 0.557551i | 0.371059 | − | 0.928609i | \(-0.378995\pi\) |
−0.928609 | + | 0.371059i | \(0.878995\pi\) | |||||||
\(488\) | −25.2193 | − | 25.2193i | −1.14163 | − | 1.14163i | ||||
\(489\) | 2.38527 | + | 1.48052i | 0.107866 | + | 0.0669512i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.1173i | 0.682233i | 0.940021 | + | 0.341116i | \(0.110805\pi\) | ||||
−0.940021 | + | 0.341116i | \(0.889195\pi\) | |||||||
\(492\) | −2.39707 | − | 10.2420i | −0.108068 | − | 0.461746i | ||||
\(493\) | −0.563958 | + | 0.563958i | −0.0253994 | + | 0.0253994i | ||||
\(494\) | −51.5524 | −2.31945 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −43.1703 | −1.93841 | ||||||||
\(497\) | 1.49961 | − | 1.49961i | 0.0672667 | − | 0.0672667i | ||||
\(498\) | 3.88071 | + | 16.5812i | 0.173899 | + | 0.743022i | ||||
\(499\) | − | 23.2266i | − | 1.03976i | −0.854238 | − | 0.519882i | \(-0.825976\pi\) | ||
0.854238 | − | 0.519882i | \(-0.174024\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.18512 | − | 1.35628i | −0.0976241 | − | 0.0605943i | ||||
\(502\) | −34.0842 | − | 34.0842i | −1.52125 | − | 1.52125i | ||||
\(503\) | −1.88391 | − | 1.88391i | −0.0839996 | − | 0.0839996i | 0.663859 | − | 0.747858i | \(-0.268918\pi\) |
−0.747858 | + | 0.663859i | \(0.768918\pi\) | |||||||
\(504\) | 11.5520 | + | 23.3274i | 0.514565 | + | 1.03908i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 47.9958i | 2.13368i | ||||||||
\(507\) | 18.9263 | − | 4.42957i | 0.840548 | − | 0.196724i | ||||
\(508\) | 45.2813 | − | 45.2813i | 2.00903 | − | 2.00903i | ||||
\(509\) | −34.4950 | −1.52897 | −0.764483 | − | 0.644644i | \(-0.777006\pi\) | ||||
−0.764483 | + | 0.644644i | \(0.777006\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.8498 | −0.612680 | ||||||||
\(512\) | 0.929454 | − | 0.929454i | 0.0410764 | − | 0.0410764i | ||||
\(513\) | −15.6179 | + | 12.8825i | −0.689546 | + | 0.568775i | ||||
\(514\) | 7.32879i | 0.323259i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 13.9077 | − | 22.4069i | 0.612253 | − | 0.986408i | ||||
\(517\) | −30.0386 | − | 30.0386i | −1.32109 | − | 1.32109i | ||||
\(518\) | −13.4047 | − | 13.4047i | −0.588969 | − | 0.588969i | ||||
\(519\) | −4.38549 | + | 7.06551i | −0.192501 | + | 0.310141i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 40.9966i | − | 1.79609i | −0.439902 | − | 0.898046i | \(-0.644987\pi\) | ||
0.439902 | − | 0.898046i | \(-0.355013\pi\) | |||||||
\(522\) | −11.0296 | + | 32.6703i | −0.482753 | + | 1.42994i | ||||
\(523\) | −8.92643 | + | 8.92643i | −0.390326 | + | 0.390326i | −0.874803 | − | 0.484478i | \(-0.839010\pi\) |
0.484478 | + | 0.874803i | \(0.339010\pi\) | |||||||
\(524\) | −16.9368 | −0.739887 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 44.9451 | 1.95970 | ||||||||
\(527\) | 0.442389 | − | 0.442389i | 0.0192708 | − | 0.0192708i | ||||
\(528\) | 81.7489 | − | 19.1327i | 3.55767 | − | 0.832645i | ||||
\(529\) | − | 0.523883i | − | 0.0227775i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.9960 | − | 9.40704i | 0.824358 | − | 0.408231i | ||||
\(532\) | 14.4022 | + | 14.4022i | 0.624414 | + | 0.624414i | ||||
\(533\) | 4.04296 | + | 4.04296i | 0.175120 | + | 0.175120i | ||||
\(534\) | −4.66615 | − | 2.89623i | −0.201924 | − | 0.125332i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.88424i | 0.0813866i | ||||||||
\(537\) | −6.21956 | − | 26.5745i | −0.268394 | − | 1.14677i | ||||
\(538\) | 27.7830 | − | 27.7830i | 1.19781 | − | 1.19781i | ||||
\(539\) | −3.76571 | −0.162201 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.75064 | −0.247239 | −0.123620 | − | 0.992330i | \(-0.539450\pi\) | ||||
−0.123620 | + | 0.992330i | \(0.539450\pi\) | |||||||
\(542\) | 5.94854 | − | 5.94854i | 0.255511 | − | 0.255511i | ||||
\(543\) | −1.99738 | − | 8.53426i | −0.0857158 | − | 0.366240i | ||||
\(544\) | − | 3.21829i | − | 0.137983i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −19.4715 | − | 12.0858i | −0.833305 | − | 0.517223i | ||||
\(547\) | 6.93451 | + | 6.93451i | 0.296498 | + | 0.296498i | 0.839641 | − | 0.543142i | \(-0.182766\pi\) |
−0.543142 | + | 0.839641i | \(0.682766\pi\) | |||||||
\(548\) | −28.9685 | − | 28.9685i | −1.23747 | − | 1.23747i | ||||
\(549\) | 11.0503 | − | 5.47223i | 0.471616 | − | 0.233549i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.6578i | 0.709647i | ||||||||
\(552\) | 69.3763 | − | 16.2370i | 2.95285 | − | 0.691093i | ||||
\(553\) | −0.104484 | + | 0.104484i | −0.00444313 | + | 0.00444313i | ||||
\(554\) | −36.5378 | −1.55234 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 98.8200 | 4.19090 | ||||||||
\(557\) | 23.5163 | − | 23.5163i | 0.996416 | − | 0.996416i | −0.00357756 | − | 0.999994i | \(-0.501139\pi\) |
0.999994 | + | 0.00357756i | \(0.00113878\pi\) | |||||||
\(558\) | 8.65202 | − | 25.6277i | 0.366269 | − | 1.08491i | ||||
\(559\) | 14.3349i | 0.606303i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.641661 | + | 1.03379i | −0.0270910 | + | 0.0436465i | ||||
\(562\) | 16.5788 | + | 16.5788i | 0.699335 | + | 0.699335i | ||||
\(563\) | 16.6973 | + | 16.6973i | 0.703708 | + | 0.703708i | 0.965205 | − | 0.261496i | \(-0.0842158\pi\) |
−0.261496 | + | 0.965205i | \(0.584216\pi\) | |||||||
\(564\) | −53.8662 | + | 86.7844i | −2.26817 | + | 3.65428i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 44.3587i | 1.86453i | ||||||||
\(567\) | −8.91905 | + | 1.20435i | −0.374565 | + | 0.0505781i | ||||
\(568\) | −13.0121 | + | 13.0121i | −0.545976 | + | 0.545976i | ||||
\(569\) | 32.5519 | 1.36465 | 0.682323 | − | 0.731051i | \(-0.260970\pi\) | ||||
0.682323 | + | 0.731051i | \(0.260970\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.4341 | −0.855141 | −0.427571 | − | 0.903982i | \(-0.640630\pi\) | ||||
−0.427571 | + | 0.903982i | \(0.640630\pi\) | |||||||
\(572\) | −68.5077 | + | 68.5077i | −2.86445 | + | 2.86445i | ||||
\(573\) | −1.22578 | + | 0.286885i | −0.0512078 | + | 0.0119848i | ||||
\(574\) | − | 3.12322i | − | 0.130361i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −27.4730 | − | 55.4773i | −1.14471 | − | 2.31155i | ||||
\(577\) | −30.6497 | − | 30.6497i | −1.27596 | − | 1.27596i | −0.942907 | − | 0.333056i | \(-0.891920\pi\) |
−0.333056 | − | 0.942907i | \(-0.608080\pi\) | |||||||
\(578\) | −32.2507 | − | 32.2507i | −1.34145 | − | 1.34145i | ||||
\(579\) | 24.7507 | + | 15.3625i | 1.02861 | + | 0.638445i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.65713i | 0.151723i | ||||||||
\(582\) | 2.28695 | + | 9.77152i | 0.0947973 | + | 0.405043i | ||||
\(583\) | −14.3172 | + | 14.3172i | −0.592958 | + | 0.592958i | ||||
\(584\) | 120.175 | 4.97288 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −54.8316 | −2.26507 | ||||||||
\(587\) | −33.7010 | + | 33.7010i | −1.39099 | + | 1.39099i | −0.567872 | + | 0.823117i | \(0.692233\pi\) |
−0.823117 | + | 0.567872i | \(0.807767\pi\) | |||||||
\(588\) | 2.06336 | + | 8.81616i | 0.0850914 | + | 0.363572i | ||||
\(589\) | − | 13.0670i | − | 0.538416i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.2734 | + | 16.3076i | 1.08074 | + | 0.670806i | ||||
\(592\) | 64.1824 | + | 64.1824i | 2.63788 | + | 2.63788i | ||||
\(593\) | −8.74429 | − | 8.74429i | −0.359085 | − | 0.359085i | 0.504391 | − | 0.863476i | \(-0.331717\pi\) |
−0.863476 | + | 0.504391i | \(0.831717\pi\) | |||||||
\(594\) | −5.02579 | + | 52.3641i | −0.206211 | + | 2.14853i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 23.4174i | − | 0.959212i | ||||||
\(597\) | 2.63309 | − | 0.616256i | 0.107765 | − | 0.0252217i | ||||
\(598\) | −44.3558 | + | 44.3558i | −1.81384 | + | 1.81384i | ||||
\(599\) | 21.6454 | 0.884407 | 0.442203 | − | 0.896915i | \(-0.354197\pi\) | ||||
0.442203 | + | 0.896915i | \(0.354197\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.8086 | 1.33829 | 0.669146 | − | 0.743131i | \(-0.266660\pi\) | ||||
0.669146 | + | 0.743131i | \(0.266660\pi\) | |||||||
\(602\) | 5.53691 | − | 5.53691i | 0.225668 | − | 0.225668i | ||||
\(603\) | −0.617232 | − | 0.208380i | −0.0251356 | − | 0.00848589i | ||||
\(604\) | − | 10.8304i | − | 0.440684i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 27.5503 | − | 44.3867i | 1.11916 | − | 1.80308i | ||||
\(607\) | 0.943000 | + | 0.943000i | 0.0382752 | + | 0.0382752i | 0.725985 | − | 0.687710i | \(-0.241384\pi\) |
−0.687710 | + | 0.725985i | \(0.741384\pi\) | |||||||
\(608\) | −47.5298 | − | 47.5298i | −1.92759 | − | 1.92759i | ||||
\(609\) | −3.90520 | + | 6.29172i | −0.158247 | + | 0.254953i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 55.5208i | − | 2.24613i | ||||||
\(612\) | 2.77186 | + | 0.935790i | 0.112046 | + | 0.0378271i | ||||
\(613\) | 10.2906 | − | 10.2906i | 0.415635 | − | 0.415635i | −0.468061 | − | 0.883696i | \(-0.655047\pi\) |
0.883696 | + | 0.468061i | \(0.155047\pi\) | |||||||
\(614\) | −22.9261 | −0.925224 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 32.6751 | 1.31652 | ||||||||
\(617\) | −18.2623 | + | 18.2623i | −0.735212 | + | 0.735212i | −0.971647 | − | 0.236435i | \(-0.924021\pi\) |
0.236435 | + | 0.971647i | \(0.424021\pi\) | |||||||
\(618\) | 87.9820 | − | 20.5915i | 3.53916 | − | 0.828313i | ||||
\(619\) | − | 1.95142i | − | 0.0784343i | −0.999231 | − | 0.0392171i | \(-0.987514\pi\) | ||
0.999231 | − | 0.0392171i | \(-0.0124864\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.35354 | + | 24.5217i | −0.0944445 | + | 0.984024i | ||||
\(622\) | −38.6688 | − | 38.6688i | −1.55048 | − | 1.55048i | ||||
\(623\) | −0.833973 | − | 0.833973i | −0.0334124 | − | 0.0334124i | ||||
\(624\) | 93.2307 | + | 57.8673i | 3.73221 | + | 2.31655i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 51.7431i | 2.06807i | ||||||||
\(627\) | 5.79118 | + | 24.7441i | 0.231277 | + | 0.988185i | ||||
\(628\) | 27.0719 | − | 27.0719i | 1.08029 | − | 1.08029i | ||||
\(629\) | −1.31542 | −0.0524493 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.02214 | −0.160119 | −0.0800594 | − | 0.996790i | \(-0.525511\pi\) | ||||
−0.0800594 | + | 0.996790i | \(0.525511\pi\) | |||||||
\(632\) | 0.906612 | − | 0.906612i | 0.0360631 | − | 0.0360631i | ||||
\(633\) | −1.60362 | − | 6.85184i | −0.0637383 | − | 0.272336i | ||||
\(634\) | − | 50.7806i | − | 2.01675i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 41.3638 | + | 25.6741i | 1.64018 | + | 1.01804i | ||||
\(637\) | −3.48012 | − | 3.48012i | −0.137887 | − | 0.137887i | ||||
\(638\) | 30.6056 | + | 30.6056i | 1.21169 | + | 1.21169i | ||||
\(639\) | −2.82344 | − | 5.70150i | −0.111694 | − | 0.225548i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 20.9832i | − | 0.828785i | −0.910098 | − | 0.414393i | \(-0.863994\pi\) | ||
0.910098 | − | 0.414393i | \(-0.136006\pi\) | |||||||
\(642\) | 50.4480 | − | 11.8070i | 1.99103 | − | 0.465985i | ||||
\(643\) | 10.7521 | − | 10.7521i | 0.424021 | − | 0.424021i | −0.462564 | − | 0.886586i | \(-0.653071\pi\) |
0.886586 | + | 0.462564i | \(0.153071\pi\) | |||||||
\(644\) | 24.7833 | 0.976600 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.95402 | 0.0768798 | ||||||||
\(647\) | 11.3490 | − | 11.3490i | 0.446174 | − | 0.446174i | −0.447907 | − | 0.894080i | \(-0.647830\pi\) |
0.894080 | + | 0.447907i | \(0.147830\pi\) | |||||||
\(648\) | 77.3907 | − | 10.4502i | 3.04019 | − | 0.410522i | ||||
\(649\) | − | 26.6081i | − | 1.04446i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.06338 | − | 4.93545i | 0.120063 | − | 0.193435i | ||||
\(652\) | −5.99138 | − | 5.99138i | −0.234640 | − | 0.234640i | ||||
\(653\) | 9.15252 | + | 9.15252i | 0.358166 | + | 0.358166i | 0.863136 | − | 0.504971i | \(-0.168497\pi\) |
−0.504971 | + | 0.863136i | \(0.668497\pi\) | |||||||
\(654\) | 41.8589 | − | 67.4394i | 1.63681 | − | 2.63709i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.9541i | 0.583860i | ||||||||
\(657\) | −13.2903 | + | 39.3666i | −0.518505 | + | 1.53584i | ||||
\(658\) | −21.4451 | + | 21.4451i | −0.836017 | + | 0.836017i | ||||
\(659\) | 35.5908 | 1.38642 | 0.693210 | − | 0.720736i | \(-0.256196\pi\) | ||||
0.693210 | + | 0.720736i | \(0.256196\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.77542 | 0.0690558 | 0.0345279 | − | 0.999404i | \(-0.489007\pi\) | ||||
0.0345279 | + | 0.999404i | \(0.489007\pi\) | |||||||
\(662\) | 54.3648 | − | 54.3648i | 2.11295 | − | 2.11295i | ||||
\(663\) | −1.54838 | + | 0.362387i | −0.0601341 | + | 0.0140739i | ||||
\(664\) | − | 31.7329i | − | 1.23148i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −50.9645 | + | 25.2382i | −1.97484 | + | 0.977960i | ||||
\(667\) | 14.3324 | + | 14.3324i | 0.554953 | + | 0.554953i | ||||
\(668\) | 5.48863 | + | 5.48863i | 0.212362 | + | 0.212362i | ||||
\(669\) | −40.0945 | − | 24.8863i | −1.55014 | − | 0.962158i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 15.4784i | − | 0.597537i | ||||||
\(672\) | −6.80945 | − | 29.0949i | −0.262680 | − | 1.12236i | ||||
\(673\) | 18.9037 | − | 18.9037i | 0.728683 | − | 0.728683i | −0.241675 | − | 0.970357i | \(-0.577697\pi\) |
0.970357 | + | 0.241675i | \(0.0776967\pi\) | |||||||
\(674\) | −65.4799 | −2.52219 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −58.6658 | −2.25638 | ||||||||
\(677\) | 9.88243 | − | 9.88243i | 0.379813 | − | 0.379813i | −0.491222 | − | 0.871035i | \(-0.663450\pi\) |
0.871035 | + | 0.491222i | \(0.163450\pi\) | |||||||
\(678\) | 18.7282 | + | 80.0203i | 0.719250 | + | 3.07316i | ||||
\(679\) | 2.15519i | 0.0827087i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −32.4266 | − | 20.1269i | −1.24259 | − | 0.771263i | ||||
\(682\) | −24.0082 | − | 24.0082i | −0.919320 | − | 0.919320i | ||||
\(683\) | 4.96110 | + | 4.96110i | 0.189831 | + | 0.189831i | 0.795623 | − | 0.605792i | \(-0.207144\pi\) |
−0.605792 | + | 0.795623i | \(0.707144\pi\) | |||||||
\(684\) | 54.7569 | − | 27.1162i | 2.09368 | − | 1.03681i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.68841i | 0.102644i | ||||||||
\(687\) | −42.6197 | + | 9.97482i | −1.62604 | + | 0.380563i | ||||
\(688\) | −26.5110 | + | 26.5110i | −1.01072 | + | 1.01072i | ||||
\(689\) | −26.4627 | −1.00815 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.8476 | 1.63000 | 0.814999 | − | 0.579462i | \(-0.196737\pi\) | ||||
0.814999 | + | 0.579462i | \(0.196737\pi\) | |||||||
\(692\) | 17.7473 | − | 17.7473i | 0.674650 | − | 0.674650i | ||||
\(693\) | −3.61358 | + | 10.7036i | −0.137269 | + | 0.406597i | ||||
\(694\) | − | 2.58279i | − | 0.0980412i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 33.8855 | − | 54.5933i | 1.28443 | − | 2.06935i | ||||
\(697\) | −0.153243 | − | 0.153243i | −0.00580448 | − | 0.00580448i | ||||
\(698\) | 13.2120 | + | 13.2120i | 0.500082 | + | 0.500082i | ||||
\(699\) | 10.5282 | − | 16.9621i | 0.398213 | − | 0.641565i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6.14360i | − | 0.232040i | −0.993247 | − | 0.116020i | \(-0.962986\pi\) | ||
0.993247 | − | 0.116020i | \(-0.0370137\pi\) | |||||||
\(702\) | −53.0374 | + | 43.7481i | −2.00177 | + | 1.65117i | ||||
\(703\) | −19.4270 | + | 19.4270i | −0.732703 | + | 0.732703i | ||||
\(704\) | −77.7081 | −2.92874 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −80.9745 | −3.04752 | ||||||||
\(707\) | 7.93316 | − | 7.93316i | 0.298357 | − | 0.298357i | ||||
\(708\) | −62.2941 | + | 14.5795i | −2.34115 | + | 0.547930i | ||||
\(709\) | − | 18.2416i | − | 0.685078i | −0.939504 | − | 0.342539i | \(-0.888713\pi\) | ||
0.939504 | − | 0.342539i | \(-0.111287\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.196722 | + | 0.397249i | 0.00737765 | + | 0.0148980i | ||||
\(712\) | 7.23639 | + | 7.23639i | 0.271195 | + | 0.271195i | ||||
\(713\) | −11.2429 | − | 11.2429i | −0.421048 | − | 0.421048i | ||||
\(714\) | 0.738040 | + | 0.458094i | 0.0276205 | + | 0.0171437i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 82.3726i | 3.07841i | ||||||||
\(717\) | 8.06769 | + | 34.4710i | 0.301294 | + | 1.28734i | ||||
\(718\) | 9.57638 | − | 9.57638i | 0.357387 | − | 0.357387i | ||||
\(719\) | −34.6302 | −1.29149 | −0.645744 | − | 0.763554i | \(-0.723453\pi\) | ||||
−0.645744 | + | 0.763554i | \(0.723453\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.4052 | 0.722686 | ||||||||
\(722\) | −7.26068 | + | 7.26068i | −0.270214 | + | 0.270214i | ||||
\(723\) | −5.23160 | − | 22.3532i | −0.194565 | − | 0.831325i | ||||
\(724\) | 26.4536i | 0.983139i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 12.5834 | + | 7.81041i | 0.467015 | + | 0.289871i | ||||
\(727\) | 13.6940 | + | 13.6940i | 0.507883 | + | 0.507883i | 0.913876 | − | 0.405993i | \(-0.133074\pi\) |
−0.405993 | + | 0.913876i | \(0.633074\pi\) | |||||||
\(728\) | 30.1970 | + | 30.1970i | 1.11917 | + | 1.11917i | ||||
\(729\) | −5.13550 | + | 26.5071i | −0.190204 | + | 0.981745i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 0.543345i | − | 0.0200963i | ||||||
\(732\) | −36.2375 | + | 8.48112i | −1.33938 | + | 0.313471i | ||||
\(733\) | 27.6570 | − | 27.6570i | 1.02154 | − | 1.02154i | 0.0217732 | − | 0.999763i | \(-0.493069\pi\) |
0.999763 | − | 0.0217732i | \(-0.00693118\pi\) | |||||||
\(734\) | −0.513839 | −0.0189661 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −81.7895 | −3.01480 | ||||||||
\(737\) | −0.578226 | + | 0.578226i | −0.0212992 | + | 0.0212992i | ||||
\(738\) | −8.87739 | − | 2.99704i | −0.326781 | − | 0.110323i | ||||
\(739\) | − | 34.9352i | − | 1.28511i | −0.766238 | − | 0.642556i | \(-0.777874\pi\) | ||
0.766238 | − | 0.642556i | \(-0.222126\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.5155 | + | 28.2195i | −0.643449 | + | 1.03667i | ||||
\(742\) | 10.2213 | + | 10.2213i | 0.375236 | + | 0.375236i | ||||
\(743\) | −30.9489 | − | 30.9489i | −1.13541 | − | 1.13541i | −0.989263 | − | 0.146143i | \(-0.953314\pi\) |
−0.146143 | − | 0.989263i | \(-0.546686\pi\) | |||||||
\(744\) | −26.5810 | + | 42.8249i | −0.974506 | + | 1.57004i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 55.3660i | − | 2.02709i | ||||||
\(747\) | 10.3950 | + | 3.50938i | 0.380332 | + | 0.128402i | ||||
\(748\) | 2.59669 | − | 2.59669i | 0.0949443 | − | 0.0949443i | ||||
\(749\) | 11.1267 | 0.406562 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.98931 | 0.109082 | 0.0545408 | − | 0.998512i | \(-0.482631\pi\) | ||||
0.0545408 | + | 0.998512i | \(0.482631\pi\) | |||||||
\(752\) | 102.680 | − | 102.680i | 3.74436 | − | 3.74436i | ||||
\(753\) | −30.2380 | + | 7.07697i | −1.10193 | + | 0.257899i | ||||
\(754\) | 56.5689i | 2.06012i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 27.0389 | + | 2.59514i | 0.983397 | + | 0.0943843i | ||||
\(757\) | 19.4775 | + | 19.4775i | 0.707921 | + | 0.707921i | 0.966098 | − | 0.258177i | \(-0.0831217\pi\) |
−0.258177 | + | 0.966098i | \(0.583122\pi\) | |||||||
\(758\) | 63.7115 | + | 63.7115i | 2.31411 | + | 2.31411i | ||||
\(759\) | 26.2726 | + | 16.3071i | 0.953636 | + | 0.591912i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 17.8797i | − | 0.648138i | −0.946033 | − | 0.324069i | \(-0.894949\pi\) | ||
0.946033 | − | 0.324069i | \(-0.105051\pi\) | |||||||
\(762\) | −12.9989 | − | 55.5407i | −0.470900 | − | 2.01203i | ||||
\(763\) | 12.0533 | − | 12.0533i | 0.436360 | − | 0.436360i | ||||
\(764\) | 3.79955 | 0.137463 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −92.5549 | −3.34415 | ||||||||
\(767\) | 24.5901 | − | 24.5901i | 0.887898 | − | 0.887898i | ||||
\(768\) | 5.96559 | + | 25.4893i | 0.215265 | + | 0.919767i | ||||
\(769\) | 29.7657i | 1.07338i | 0.843780 | + | 0.536690i | \(0.180325\pi\) | ||||
−0.843780 | + | 0.536690i | \(0.819675\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.01173 | + | 2.49004i | 0.144479 | + | 0.0896766i | ||||
\(772\) | −62.1694 | − | 62.1694i | −2.23752 | − | 2.23752i | ||||
\(773\) | −4.25392 | − | 4.25392i | −0.153003 | − | 0.153003i | 0.626455 | − | 0.779458i | \(-0.284505\pi\) |
−0.779458 | + | 0.626455i | \(0.784505\pi\) | |||||||
\(774\) | −10.4248 | − | 21.0513i | −0.374713 | − | 0.756673i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 18.7006i | − | 0.671313i | ||||||
\(777\) | −11.8921 | + | 2.78325i | −0.426625 | + | 0.0998485i | ||||
\(778\) | −18.4406 | + | 18.4406i | −0.661127 | + | 0.661127i | ||||
\(779\) | −4.52638 | −0.162174 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.98620 | −0.285769 | ||||||||
\(782\) | 1.68124 | − | 1.68124i | 0.0601211 | − | 0.0601211i | ||||
\(783\) | 14.1361 | + | 17.1376i | 0.505182 | + | 0.612449i | ||||
\(784\) | − | 12.8723i | − | 0.459723i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7.95606 | + | 12.8181i | −0.283783 | + | 0.457207i | ||||
\(787\) | 25.4846 | + | 25.4846i | 0.908427 | + | 0.908427i | 0.996145 | − | 0.0877179i | \(-0.0279574\pi\) |
−0.0877179 | + | 0.996145i | \(0.527957\pi\) | |||||||
\(788\) | −65.9940 | − | 65.9940i | −2.35094 | − | 2.35094i | ||||
\(789\) | 15.2706 | − | 24.6027i | 0.543649 | − | 0.875878i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.6491i | 0.627531i | ||||||||
\(792\) | 31.3551 | − | 92.8753i | 1.11415 | − | 3.30018i | ||||
\(793\) | 14.3045 | − | 14.3045i | 0.507967 | − | 0.507967i | ||||
\(794\) | −13.6834 | −0.485605 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.16177 | −0.289286 | ||||||||
\(797\) | 33.4559 | − | 33.4559i | 1.18507 | − | 1.18507i | 0.206654 | − | 0.978414i | \(-0.433743\pi\) |
0.978414 | − | 0.206654i | \(-0.0662574\pi\) | |||||||
\(798\) | 17.6653 | − | 4.13443i | 0.625344 | − | 0.146357i | ||||
\(799\) | 2.10444i | 0.0744496i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.17075 | + | 1.57019i | −0.112033 | + | 0.0554800i | ||||
\(802\) | 74.1072 | + | 74.1072i | 2.61682 | + | 2.61682i | ||||
\(803\) | 36.8788 | + | 36.8788i | 1.30142 | + | 1.30142i | ||||
\(804\) | 1.67055 | + | 1.03689i | 0.0589158 | + | 0.0365684i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 44.3747i | − | 1.56303i | ||||||
\(807\) | −5.76865 | − | 24.6479i | −0.203066 | − | 0.867646i | ||||
\(808\) | −68.8360 | + | 68.8360i | −2.42164 | + | 2.42164i | ||||
\(809\) | 17.3685 | 0.610644 | 0.305322 | − | 0.952249i | \(-0.401236\pi\) | ||||
0.305322 | + | 0.952249i | \(0.401236\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.6279 | −1.14572 | −0.572860 | − | 0.819654i | \(-0.694166\pi\) | ||||
−0.572860 | + | 0.819654i | \(0.694166\pi\) | |||||||
\(812\) | 15.8037 | − | 15.8037i | 0.554599 | − | 0.554599i | ||||
\(813\) | −1.23511 | − | 5.27728i | −0.0433171 | − | 0.185082i | ||||
\(814\) | 71.3871i | 2.50212i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.53377 | − | 2.19338i | −0.123707 | − | 0.0767835i | ||||
\(817\) | −8.02447 | − | 8.02447i | −0.280741 | − | 0.280741i | ||||
\(818\) | 2.91220 | + | 2.91220i | 0.101823 | + | 0.101823i | ||||
\(819\) | −13.2314 | + | 6.55231i | −0.462341 | + | 0.228956i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.4956i | 0.715302i | 0.933855 | + | 0.357651i | \(0.116422\pi\) | ||||
−0.933855 | + | 0.357651i | \(0.883578\pi\) | |||||||
\(822\) | −35.5319 | + | 8.31597i | −1.23932 | + | 0.290053i | ||||
\(823\) | −7.29225 | + | 7.29225i | −0.254192 | + | 0.254192i | −0.822687 | − | 0.568495i | \(-0.807526\pi\) |
0.568495 | + | 0.822687i | \(0.307526\pi\) | |||||||
\(824\) | −168.379 | −5.86575 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.9960 | −0.660957 | ||||||||
\(827\) | 34.4662 | − | 34.4662i | 1.19851 | − | 1.19851i | 0.223891 | − | 0.974614i | \(-0.428124\pi\) |
0.974614 | − | 0.223891i | \(-0.0718761\pi\) | |||||||
\(828\) | 23.7821 | − | 70.4438i | 0.826485 | − | 2.44809i | ||||
\(829\) | 31.3135i | 1.08756i | 0.839227 | + | 0.543782i | \(0.183008\pi\) | ||||
−0.839227 | + | 0.543782i | \(0.816992\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.4142 | + | 20.0006i | −0.430642 | + | 0.693813i | ||||
\(832\) | −71.8146 | − | 71.8146i | −2.48972 | − | 2.48972i | ||||
\(833\) | 0.131909 | + | 0.131909i | 0.00457037 | + | 0.00457037i | ||||
\(834\) | 46.4207 | − | 74.7889i | 1.60742 | − | 2.58973i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 76.6991i | − | 2.65269i | ||||||
\(837\) | −11.0888 | − | 13.4434i | −0.383286 | − | 0.464671i | ||||
\(838\) | −49.3869 | + | 49.3869i | −1.70604 | + | 1.70604i | ||||
\(839\) | −0.518418 | −0.0178978 | −0.00894889 | − | 0.999960i | \(-0.502849\pi\) | ||||
−0.00894889 | + | 0.999960i | \(0.502849\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.7212 | −0.369697 | ||||||||
\(842\) | 6.36134 | − | 6.36134i | 0.219226 | − | 0.219226i | ||||
\(843\) | 14.7080 | − | 3.44230i | 0.506570 | − | 0.118559i | ||||
\(844\) | 21.2386i | 0.731062i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 40.3765 | + | 81.5340i | 1.38817 | + | 2.80320i | ||||
\(847\) | 2.24902 | + | 2.24902i | 0.0772771 | + | 0.0772771i | ||||
\(848\) | −48.9401 | − | 48.9401i | −1.68061 | − | 1.68061i | ||||
\(849\) | 24.2817 | + | 15.0714i | 0.833345 | + | 0.517248i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.4301i | 1.14597i | ||||||||
\(852\) | 4.37590 | + | 18.6970i | 0.149916 | + | 0.640549i | ||||
\(853\) | −13.6122 | + | 13.6122i | −0.466071 | + | 0.466071i | −0.900639 | − | 0.434568i | \(-0.856901\pi\) |
0.434568 | + | 0.900639i | \(0.356901\pi\) | |||||||
\(854\) | −11.0503 | −0.378134 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −96.5468 | −3.29990 | ||||||||
\(857\) | −14.6366 | + | 14.6366i | −0.499977 | + | 0.499977i | −0.911431 | − | 0.411454i | \(-0.865021\pi\) |
0.411454 | + | 0.911431i | \(0.365021\pi\) | |||||||
\(858\) | 19.6665 | + | 84.0296i | 0.671403 | + | 2.86872i | ||||
\(859\) | 18.2644i | 0.623173i | 0.950218 | + | 0.311587i | \(0.100860\pi\) | ||||
−0.950218 | + | 0.311587i | \(0.899140\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.70963 | − | 1.06115i | −0.0582640 | − | 0.0361639i | ||||
\(862\) | −41.0530 | − | 41.0530i | −1.39827 | − | 1.39827i | ||||
\(863\) | −31.7103 | − | 31.7103i | −1.07943 | − | 1.07943i | −0.996560 | − | 0.0828701i | \(-0.973591\pi\) |
−0.0828701 | − | 0.996560i | \(-0.526409\pi\) | |||||||
\(864\) | −89.2334 | − | 8.56443i | −3.03578 | − | 0.291368i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 38.1744i | − | 1.29722i | ||||||
\(867\) | −28.6114 | + | 6.69629i | −0.971695 | + | 0.227418i | ||||
\(868\) | −12.3970 | + | 12.3970i | −0.420780 | + | 0.420780i | ||||
\(869\) | 0.556434 | 0.0188757 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.06874 | −0.0362130 | ||||||||
\(872\) | −104.587 | + | 104.587i | −3.54176 | + | 3.54176i | ||||
\(873\) | 6.12589 | + | 2.06813i | 0.207330 | + | 0.0699954i | ||||
\(874\) | − | 49.6593i | − | 1.67975i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 66.1323 | − | 106.546i | 2.23440 | − | 3.59987i | ||||
\(877\) | −10.9530 | − | 10.9530i | −0.369855 | − | 0.369855i | 0.497569 | − | 0.867424i | \(-0.334226\pi\) |
−0.867424 | + | 0.497569i | \(0.834226\pi\) | |||||||
\(878\) | −45.6988 | − | 45.6988i | −1.54226 | − | 1.54226i | ||||
\(879\) | −18.6297 | + | 30.0145i | −0.628364 | + | 1.01236i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.9978i | 1.54970i | 0.632142 | + | 0.774852i | \(0.282176\pi\) | ||||
−0.632142 | + | 0.774852i | \(0.717824\pi\) | |||||||
\(882\) | 7.64151 | + | 2.57980i | 0.257303 | + | 0.0868665i | ||||
\(883\) | −41.0408 | + | 41.0408i | −1.38113 | + | 1.38113i | −0.538521 | + | 0.842612i | \(0.681017\pi\) |
−0.842612 | + | 0.538521i | \(0.818983\pi\) | |||||||
\(884\) | 4.79950 | 0.161425 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.1924 | 0.543995 | ||||||||
\(887\) | 3.68081 | − | 3.68081i | 0.123590 | − | 0.123590i | −0.642607 | − | 0.766196i | \(-0.722147\pi\) |
0.766196 | + | 0.642607i | \(0.222147\pi\) | |||||||
\(888\) | 103.187 | − | 24.1503i | 3.46275 | − | 0.810430i | ||||
\(889\) | − | 12.2500i | − | 0.410851i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.9562 | + | 20.5424i | 0.903067 | + | 0.688196i | ||||
\(892\) | 100.710 | + | 100.710i | 3.37203 | + | 3.37203i | ||||
\(893\) | 31.0797 | + | 31.0797i | 1.04004 | + | 1.04004i | ||||
\(894\) | −17.7227 | − | 11.0003i | −0.592737 | − | 0.367905i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 20.9735i | 0.700675i | ||||||||
\(897\) | 9.20968 | + | 39.3505i | 0.307502 | + | 1.31387i | ||||
\(898\) | 57.5255 | − | 57.5255i | 1.91965 | − | 1.91965i | ||||
\(899\) | −14.3385 | −0.478217 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.00303 | 0.0334158 | ||||||||
\(902\) | −8.31638 | + | 8.31638i | −0.276905 | + | 0.276905i | ||||
\(903\) | −1.14964 | − | 4.91210i | −0.0382577 | − | 0.163465i | ||||
\(904\) | − | 153.142i | − | 5.09342i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.19669 | − | 5.08760i | −0.272317 | − | 0.169024i | ||||
\(907\) | 2.57083 | + | 2.57083i | 0.0853631 | + | 0.0853631i | 0.748499 | − | 0.663136i | \(-0.230775\pi\) |
−0.663136 | + | 0.748499i | \(0.730775\pi\) | |||||||
\(908\) | 81.4497 | + | 81.4497i | 2.70300 | + | 2.70300i | ||||
\(909\) | −14.9364 | − | 30.1618i | −0.495410 | − | 1.00040i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.65152i | 0.154112i | 0.997027 | + | 0.0770559i | \(0.0245520\pi\) | ||||
−0.997027 | + | 0.0770559i | \(0.975448\pi\) | |||||||
\(912\) | −84.5823 | + | 19.7959i | −2.80080 | + | 0.655506i | ||||
\(913\) | 9.73805 | − | 9.73805i | 0.322282 | − | 0.322282i | ||||
\(914\) | 39.9708 | 1.32212 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 132.108 | 4.36496 | ||||||||
\(917\) | −2.29096 | + | 2.29096i | −0.0756541 | + | 0.0756541i | ||||
\(918\) | 2.01030 | − | 1.65821i | 0.0663499 | − | 0.0547290i | ||||
\(919\) | 0.422209i | 0.0139274i | 0.999976 | + | 0.00696370i | \(0.00221663\pi\) | ||||
−0.999976 | + | 0.00696370i | \(0.997783\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.78942 | + | 12.5496i | −0.256670 | + | 0.413524i | ||||
\(922\) | 75.6371 | + | 75.6371i | 2.49098 | + | 2.49098i | ||||
\(923\) | −7.38051 | − | 7.38051i | −0.242933 | − | 0.242933i | ||||
\(924\) | 17.9811 | − | 28.9695i | 0.591535 | − | 0.953028i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 91.7738i | 3.01587i | ||||||||
\(927\) | 18.6212 | − | 55.1570i | 0.611601 | − | 1.81159i | ||||
\(928\) | −52.1549 | + | 52.1549i | −1.71207 | + | 1.71207i | ||||
\(929\) | −2.97387 | −0.0975694 | −0.0487847 | − | 0.998809i | \(-0.515535\pi\) | ||||
−0.0487847 | + | 0.998809i | \(0.515535\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.89623 | 0.127694 | ||||||||
\(932\) | −42.6057 | + | 42.6057i | −1.39560 | + | 1.39560i | ||||
\(933\) | −34.3053 | + | 8.02890i | −1.12310 | + | 0.262854i | ||||
\(934\) | − | 51.4011i | − | 1.68190i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 114.809 | − | 56.8545i | 3.75264 | − | 1.85835i | ||||
\(937\) | 0.345323 | + | 0.345323i | 0.0112812 | + | 0.0112812i | 0.712725 | − | 0.701444i | \(-0.247461\pi\) |
−0.701444 | + | 0.712725i | \(0.747461\pi\) | |||||||
\(938\) | 0.412806 | + | 0.412806i | 0.0134786 | + | 0.0134786i | ||||
\(939\) | 28.3239 | + | 17.5803i | 0.924314 | + | 0.573712i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 35.5643i | − | 1.15936i | −0.814843 | − | 0.579682i | \(-0.803177\pi\) | ||
0.814843 | − | 0.579682i | \(-0.196823\pi\) | |||||||
\(942\) | −7.77152 | − | 33.2056i | −0.253210 | − | 1.08190i | ||||
\(943\) | −3.89450 | + | 3.89450i | −0.126822 | + | 0.126822i | ||||
\(944\) | 90.9540 | 2.96030 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29.4870 | −0.958704 | ||||||||
\(947\) | −1.40196 | + | 1.40196i | −0.0455577 | + | 0.0455577i | −0.729519 | − | 0.683961i | \(-0.760256\pi\) |
0.683961 | + | 0.729519i | \(0.260256\pi\) | |||||||
\(948\) | −0.304889 | − | 1.30271i | −0.00990232 | − | 0.0423099i | ||||
\(949\) | 68.1637i | 2.21269i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.7970 | − | 17.2533i | −0.901379 | − | 0.559476i | ||||
\(952\) | −1.14457 | − | 1.14457i | −0.0370958 | − | 0.0370958i | ||||
\(953\) | −14.2215 | − | 14.2215i | −0.460680 | − | 0.460680i | 0.438199 | − | 0.898878i | \(-0.355617\pi\) |
−0.898878 | + | 0.438199i | \(0.855617\pi\) | |||||||
\(954\) | 38.8613 | − | 19.2445i | 1.25818 | − | 0.623065i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 106.850i | − | 3.45576i | ||||||
\(957\) | 27.1520 | − | 6.35472i | 0.877698 | − | 0.205419i | ||||
\(958\) | 70.5110 | − | 70.5110i | 2.27811 | − | 2.27811i | ||||
\(959\) | −7.83685 | −0.253065 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.7523 | −0.637172 | ||||||||
\(962\) | −65.9730 | + | 65.9730i | −2.12705 | + | 2.12705i | ||||
\(963\) | 10.6772 | − | 31.6265i | 0.344069 | − | 1.01915i | ||||
\(964\) | 69.2880i | 2.23162i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 11.6420 | − | 18.7565i | 0.374574 | − | 0.603481i | ||||
\(967\) | −20.8267 | − | 20.8267i | −0.669740 | − | 0.669740i | 0.287916 | − | 0.957656i | \(-0.407038\pi\) |
−0.957656 | + | 0.287916i | \(0.907038\pi\) | |||||||
\(968\) | −19.5147 | − | 19.5147i | −0.627227 | − | 0.627227i | ||||
\(969\) | 0.663900 | − | 1.06962i | 0.0213276 | − | 0.0343611i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 21.8627i | − | 0.701608i | −0.936449 | − | 0.350804i | \(-0.885908\pi\) | ||
0.936449 | − | 0.350804i | \(-0.114092\pi\) | |||||||
\(972\) | 33.3230 | − | 74.3648i | 1.06884 | − | 2.38525i | ||||
\(973\) | 13.3669 | − | 13.3669i | 0.428523 | − | 0.428523i | ||||
\(974\) | 46.7799 | 1.49893 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 52.9094 | 1.69359 | ||||||||
\(977\) | −20.2336 | + | 20.2336i | −0.647331 | + | 0.647331i | −0.952347 | − | 0.305016i | \(-0.901338\pi\) |
0.305016 | + | 0.952347i | \(0.401338\pi\) | |||||||
\(978\) | −7.34884 | + | 1.71994i | −0.234990 | + | 0.0549977i | ||||
\(979\) | 4.44134i | 0.141946i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22.6938 | − | 45.8266i | −0.724559 | − | 1.46313i | ||||
\(982\) | −28.7378 | − | 28.7378i | −0.917061 | − | 0.917061i | ||||
\(983\) | 5.04301 | + | 5.04301i | 0.160847 | + | 0.160847i | 0.782942 | − | 0.622095i | \(-0.213718\pi\) |
−0.622095 | + | 0.782942i | \(0.713718\pi\) | |||||||
\(984\) | 14.8345 | + | 9.20760i | 0.472906 | + | 0.293528i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 2.14416i | − | 0.0682841i | ||||||
\(987\) | 4.45269 | + | 19.0251i | 0.141731 | + | 0.605576i | ||||
\(988\) | 70.8821 | − | 70.8821i | 2.25506 | − | 2.25506i | ||||
\(989\) | −13.8085 | −0.439086 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.6595 | 0.688038 | 0.344019 | − | 0.938963i | \(-0.388211\pi\) | ||||
0.344019 | + | 0.938963i | \(0.388211\pi\) | |||||||
\(992\) | 40.9122 | − | 40.9122i | 1.29896 | − | 1.29896i | ||||
\(993\) | −11.2879 | − | 48.2300i | −0.358210 | − | 1.53053i | ||||
\(994\) | 5.70150i | 0.180840i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −28.1342 | − | 17.4626i | −0.891466 | − | 0.553324i | ||||
\(997\) | 22.8411 | + | 22.8411i | 0.723386 | + | 0.723386i | 0.969293 | − | 0.245907i | \(-0.0790858\pi\) |
−0.245907 | + | 0.969293i | \(0.579086\pi\) | |||||||
\(998\) | 44.1536 | + | 44.1536i | 1.39766 | + | 1.39766i | ||||
\(999\) | −3.50057 | + | 36.4726i | −0.110753 | + | 1.15394i |
(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 | 525.2.j.c.407.1 | yes | 32 | |
3.2 | odd | 2 | inner | 525.2.j.c.407.15 | yes | 32 | |
5.2 | odd | 4 | inner | 525.2.j.c.218.2 | yes | 32 | |
5.3 | odd | 4 | inner | 525.2.j.c.218.15 | yes | 32 | |
5.4 | even | 2 | inner | 525.2.j.c.407.16 | yes | 32 | |
15.2 | even | 4 | inner | 525.2.j.c.218.16 | yes | 32 | |
15.8 | even | 4 | inner | 525.2.j.c.218.1 | ✓ | 32 | |
15.14 | odd | 2 | inner | 525.2.j.c.407.2 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.j.c.218.1 | ✓ | 32 | 15.8 | even | 4 | inner | |
525.2.j.c.218.2 | yes | 32 | 5.2 | odd | 4 | inner | |
525.2.j.c.218.15 | yes | 32 | 5.3 | odd | 4 | inner | |
525.2.j.c.218.16 | yes | 32 | 15.2 | even | 4 | inner | |
525.2.j.c.407.1 | yes | 32 | 1.1 | even | 1 | trivial | |
525.2.j.c.407.2 | yes | 32 | 15.14 | odd | 2 | inner | |
525.2.j.c.407.15 | yes | 32 | 3.2 | odd | 2 | inner | |
525.2.j.c.407.16 | yes | 32 | 5.4 | even | 2 | inner |