Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1791,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1791");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.k (of order \(2\), degree \(1\), not 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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1791.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1791 |
Dual form | 2240.2.k.b.1791.1 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.73205 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | + | 2.00000i | 0.654654 | + | 0.755929i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.267949i | − | 0.0807897i | −0.999184 | − | 0.0403949i | \(-0.987138\pi\) | ||
0.999184 | − | 0.0403949i | \(-0.0128616\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.464102i | 0.128719i | 0.997927 | + | 0.0643593i | \(0.0205004\pi\) | ||||
−0.997927 | + | 0.0643593i | \(0.979500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.73205i | − | 0.447214i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.46410i | − | 1.56777i | −0.620903 | − | 0.783887i | \(-0.713234\pi\) | ||
0.620903 | − | 0.783887i | \(-0.286766\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | − | 3.46410i | −0.654654 | − | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.46410i | 0.305286i | 0.988281 | + | 0.152643i | \(0.0487785\pi\) | ||||
−0.988281 | + | 0.152643i | \(0.951221\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.92820 | −1.47223 | −0.736115 | − | 0.676856i | \(-0.763342\pi\) | ||||
−0.736115 | + | 0.676856i | \(0.763342\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.464102i | 0.0807897i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | + | 1.73205i | −0.338062 | + | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.46410 | 1.55589 | 0.777944 | − | 0.628333i | \(-0.216263\pi\) | ||||
0.777944 | + | 0.628333i | \(0.216263\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 0.803848i | − | 0.128719i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.46410i | − | 0.541002i | −0.962720 | − | 0.270501i | \(-0.912811\pi\) | ||
0.962720 | − | 0.270501i | \(-0.0871893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.00000i | − | 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.73205 | −0.252646 | −0.126323 | − | 0.991989i | \(-0.540318\pi\) | ||||
−0.126323 | + | 0.991989i | \(0.540318\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | + | 6.92820i | −0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.1962i | 1.56777i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.267949 | 0.0361303 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.3923 | −1.37649 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.46410 | −0.450988 | −0.225494 | − | 0.974245i | \(-0.572400\pi\) | ||||
−0.225494 | + | 0.974245i | \(0.572400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.46410i | − | 1.21175i | −0.795558 | − | 0.605877i | \(-0.792822\pi\) | ||
0.795558 | − | 0.605877i | \(-0.207178\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.464102 | −0.0575647 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.46410i | 0.423207i | 0.977356 | + | 0.211604i | \(0.0678686\pi\) | ||||
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 2.53590i | − | 0.305286i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.46410i | 0.885826i | 0.896565 | + | 0.442913i | \(0.146055\pi\) | ||||
−0.896565 | + | 0.442913i | \(0.853945\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.9282i | 1.51313i | 0.653917 | + | 0.756566i | \(0.273124\pi\) | ||||
−0.653917 | + | 0.756566i | \(0.726876\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.73205 | 0.200000 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.535898 | − | 0.464102i | 0.0610713 | − | 0.0528893i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.6603i | 1.64941i | 0.565565 | + | 0.824704i | \(0.308658\pi\) | ||||
−0.565565 | + | 0.824704i | \(0.691342\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.4641 | 1.69741 | 0.848703 | − | 0.528870i | \(-0.177384\pi\) | ||||
0.848703 | + | 0.528870i | \(0.177384\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.46410 | 0.701130 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.7321 | 1.47223 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.53590i | 0.268805i | 0.990927 | + | 0.134402i | \(0.0429115\pi\) | ||||
−0.990927 | + | 0.134402i | \(0.957089\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.928203 | + | 0.803848i | −0.0973021 | + | 0.0842661i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.3923 | −1.07763 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.00000i | 0.615587i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.3923i | − | 1.35978i | −0.733313 | − | 0.679891i | \(-0.762027\pi\) | ||
0.733313 | − | 0.679891i | \(-0.237973\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.4641i | 1.53874i | 0.638806 | + | 0.769368i | \(0.279429\pi\) | ||||
−0.638806 | + | 0.769368i | \(0.720571\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.80385 | 0.670403 | 0.335202 | − | 0.942146i | \(-0.391196\pi\) | ||||
0.335202 | + | 0.942146i | \(0.391196\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.46410 | − | 3.00000i | 0.338062 | − | 0.292770i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.39230i | 0.231273i | 0.993292 | + | 0.115636i | \(0.0368907\pi\) | ||||
−0.993292 | + | 0.115636i | \(0.963109\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.07180 | −0.198442 | −0.0992211 | − | 0.995065i | \(-0.531635\pi\) | ||||
−0.0992211 | + | 0.995065i | \(0.531635\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.3923 | −1.55589 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.46410 | 0.514019 | 0.257010 | − | 0.966409i | \(-0.417263\pi\) | ||||
0.257010 | + | 0.966409i | \(0.417263\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.46410 | −0.136528 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.9282 | − | 11.1962i | 1.18513 | − | 1.02635i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9282 | 0.993473 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.00000i | 0.541002i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.4641i | − | 1.37222i | −0.727499 | − | 0.686109i | \(-0.759317\pi\) | ||
0.727499 | − | 0.686109i | \(-0.240683\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.46410i | 0.304997i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.53590 | 0.221562 | 0.110781 | − | 0.993845i | \(-0.464665\pi\) | ||||
0.110781 | + | 0.993845i | \(0.464665\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.3923 | + | 12.0000i | 0.901127 | + | 1.04053i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.19615i | 0.447214i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.3923 | 1.74223 | 0.871116 | − | 0.491077i | \(-0.163397\pi\) | ||||
0.871116 | + | 0.491077i | \(0.163397\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.92820 | 0.587643 | 0.293821 | − | 0.955860i | \(-0.405073\pi\) | ||||
0.293821 | + | 0.955860i | \(0.405073\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.124356 | 0.0103991 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 7.92820i | − | 0.658401i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.73205 | − | 12.0000i | 0.142857 | − | 0.989743i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.07180 | −0.251651 | −0.125826 | − | 0.992052i | \(-0.540158\pi\) | ||||
−0.125826 | + | 0.992052i | \(0.540158\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.1962i | 1.23665i | 0.785924 | + | 0.618323i | \(0.212188\pi\) | ||||
−0.785924 | + | 0.618323i | \(0.787812\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000i | 0.481932i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.85641i | − | 0.627009i | −0.949587 | − | 0.313505i | \(-0.898497\pi\) | ||
0.949587 | − | 0.313505i | \(-0.101503\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.46410 | 0.274721 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.92820 | + | 2.53590i | −0.230775 | + | 0.199857i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.7846i | 1.62798i | 0.580881 | + | 0.813988i | \(0.302708\pi\) | ||||
−0.580881 | + | 0.813988i | \(0.697292\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.464102 | −0.0361303 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.19615 | 0.402090 | 0.201045 | − | 0.979582i | \(-0.435566\pi\) | ||||
0.201045 | + | 0.979582i | \(0.435566\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.7846 | 0.983432 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.3205i | 1.08877i | 0.838836 | + | 0.544384i | \(0.183237\pi\) | ||||
−0.838836 | + | 0.544384i | \(0.816763\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.73205 | − | 2.00000i | −0.130931 | − | 0.151186i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00000 | 0.450988 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.39230i | 0.477783i | 0.971046 | + | 0.238892i | \(0.0767841\pi\) | ||||
−0.971046 | + | 0.238892i | \(0.923216\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.928203i | 0.0689928i | 0.999405 | + | 0.0344964i | \(0.0109827\pi\) | ||||
−0.999405 | + | 0.0344964i | \(0.989017\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.3923i | 1.21175i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.46410i | 0.695815i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.73205 | −0.126660 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.00000 | + | 10.3923i | 0.654654 | + | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.19615i | 0.520695i | 0.965515 | + | 0.260348i | \(0.0838372\pi\) | ||||
−0.965515 | + | 0.260348i | \(0.916163\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.46410 | −0.681241 | −0.340620 | − | 0.940201i | \(-0.610637\pi\) | ||||
−0.340620 | + | 0.940201i | \(0.610637\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.803848 | 0.0575647 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.3205 | 0.949047 | 0.474523 | − | 0.880243i | \(-0.342620\pi\) | ||||
0.474523 | + | 0.880243i | \(0.342620\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.46410 | −0.245564 | −0.122782 | − | 0.992434i | \(-0.539182\pi\) | ||||
−0.122782 | + | 0.992434i | \(0.539182\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 6.00000i | − | 0.423207i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.7321 | − | 15.8564i | −0.963801 | − | 1.11290i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.46410 | 0.241943 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.60770i | − | 0.111207i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.19615i | − | 0.220032i | −0.993930 | − | 0.110016i | \(-0.964910\pi\) | ||
0.993930 | − | 0.110016i | \(-0.0350902\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 12.9282i | − | 0.885826i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.00000 | 0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.3923 | + | 12.0000i | 0.705476 | + | 0.814613i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 22.3923i | − | 1.51313i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | 0.201802 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.7321 | 0.919566 | 0.459783 | − | 0.888031i | \(-0.347927\pi\) | ||||
0.459783 | + | 0.888031i | \(0.347927\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.6603 | 1.37127 | 0.685635 | − | 0.727946i | \(-0.259525\pi\) | ||||
0.685635 | + | 0.727946i | \(0.259525\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.53590i | 0.564068i | 0.959404 | + | 0.282034i | \(0.0910091\pi\) | ||||
−0.959404 | + | 0.282034i | \(0.908991\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.928203 | + | 0.803848i | −0.0610713 | + | 0.0528893i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.07180 | −0.594313 | −0.297157 | − | 0.954829i | \(-0.596038\pi\) | ||||
−0.297157 | + | 0.954829i | \(0.596038\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1.73205i | − | 0.112987i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 25.3923i | − | 1.64941i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 23.9808i | − | 1.55119i | −0.631233 | − | 0.775593i | \(-0.717451\pi\) | ||
0.631233 | − | 0.775593i | \(-0.282549\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.3923i | 1.05592i | 0.849269 | + | 0.527961i | \(0.177043\pi\) | ||||
−0.849269 | + | 0.527961i | \(0.822957\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.92820 | − | 1.00000i | −0.442627 | − | 0.0638877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.78461i | 0.177180i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −26.7846 | −1.69741 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.8564 | −1.63204 | −0.816021 | − | 0.578022i | \(-0.803825\pi\) | ||||
−0.816021 | + | 0.578022i | \(0.803825\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.392305 | 0.0246640 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.1962 | −0.701130 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000i | 0.374270i | 0.982334 | + | 0.187135i | \(0.0599201\pi\) | ||||
−0.982334 | + | 0.187135i | \(0.940080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.3923 | + | 18.9282i | 1.01857 | + | 1.17614i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 11.4641i | − | 0.706907i | −0.935452 | − | 0.353453i | \(-0.885007\pi\) | ||
0.935452 | − | 0.353453i | \(-0.114993\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.00000i | − | 0.122859i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 4.39230i | − | 0.268805i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.0000i | 0.731653i | 0.930683 | + | 0.365826i | \(0.119214\pi\) | ||||
−0.930683 | + | 0.365826i | \(0.880786\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.46410 | −0.574903 | −0.287452 | − | 0.957795i | \(-0.592808\pi\) | ||||
−0.287452 | + | 0.957795i | \(0.592808\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.60770 | − | 1.39230i | 0.0973021 | − | 0.0842661i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.267949i | 0.0161579i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.7846 | −1.00849 | −0.504245 | − | 0.863561i | \(-0.668229\pi\) | ||||
−0.504245 | + | 0.863561i | \(0.668229\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.92820 | −0.472957 | −0.236478 | − | 0.971637i | \(-0.575993\pi\) | ||||
−0.236478 | + | 0.971637i | \(0.575993\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1244 | 0.720718 | 0.360359 | − | 0.932814i | \(-0.382654\pi\) | ||||
0.360359 | + | 0.932814i | \(0.382654\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 10.3923i | − | 0.615587i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.92820 | − | 6.00000i | 0.408959 | − | 0.354169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −24.7846 | −1.45792 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.1962i | 1.35978i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 20.3205i | − | 1.18714i | −0.804784 | − | 0.593568i | \(-0.797719\pi\) | ||
0.804784 | − | 0.593568i | \(-0.202281\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3.46410i | − | 0.201688i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.39230i | − | 0.0807897i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.679492 | −0.0392960 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | − | 3.46410i | 0.230556 | − | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 26.7846i | − | 1.53874i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.46410 | 0.541913 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.73205 | 0.0988534 | 0.0494267 | − | 0.998778i | \(-0.484261\pi\) | ||||
0.0494267 | + | 0.998778i | \(0.484261\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.7846 | −0.670403 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.85641 | −0.445496 | −0.222748 | − | 0.974876i | \(-0.571503\pi\) | ||||
−0.222748 | + | 0.974876i | \(0.571503\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 17.5359i | − | 0.991188i | −0.868554 | − | 0.495594i | \(-0.834950\pi\) | ||
0.868554 | − | 0.495594i | \(-0.165050\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.07180 | 0.172529 | 0.0862646 | − | 0.996272i | \(-0.472507\pi\) | ||||
0.0862646 | + | 0.996272i | \(0.472507\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.12436i | 0.118941i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 4.14359i | − | 0.231273i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 38.7846i | − | 2.15803i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 0.464102i | − | 0.0257437i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.58846 | 0.198442 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.00000 | − | 3.46410i | −0.165395 | − | 0.190982i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.3923i | 1.45065i | 0.688405 | + | 0.725326i | \(0.258311\pi\) | ||||
−0.688405 | + | 0.725326i | \(0.741689\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.46410 | −0.189264 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.46410 | −0.514019 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.60770i | − | 0.0870616i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5885 | + | 10.0000i | −0.841698 | + | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.53590 | 0.136528 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 34.2487i | − | 1.83857i | −0.393596 | − | 0.919284i | \(-0.628769\pi\) | ||
0.393596 | − | 0.919284i | \(-0.371231\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.32051i | 0.284800i | 0.989809 | + | 0.142400i | \(0.0454820\pi\) | ||||
−0.989809 | + | 0.142400i | \(0.954518\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.41154i | 0.128719i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 7.39230i | − | 0.393453i | −0.980458 | − | 0.196726i | \(-0.936969\pi\) | ||
0.980458 | − | 0.196726i | \(-0.0630311\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.46410 | −0.396153 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22.3923 | + | 19.3923i | −1.18513 | + | 1.02635i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.3205i | 1.33637i | 0.743997 | + | 0.668183i | \(0.232928\pi\) | ||||
−0.743997 | + | 0.668183i | \(0.767072\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.9282 | −0.993473 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.9282 | −0.676693 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.8756 | −0.619904 | −0.309952 | − | 0.950752i | \(-0.600313\pi\) | ||||
−0.309952 | + | 0.950752i | \(0.600313\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.46410 | − | 4.00000i | −0.179847 | − | 0.207670i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.60770 | 0.186799 | 0.0933997 | − | 0.995629i | \(-0.470227\pi\) | ||||
0.0933997 | + | 0.995629i | \(0.470227\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.73205i | 0.0894427i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.67949i | − | 0.189503i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 5.60770i | − | 0.288048i | −0.989574 | − | 0.144024i | \(-0.953996\pi\) | ||
0.989574 | − | 0.144024i | \(-0.0460042\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 26.7846i | 1.37222i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.4641 | −1.40335 | −0.701675 | − | 0.712497i | \(-0.747564\pi\) | ||||
−0.701675 | + | 0.712497i | \(0.747564\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.464102 | + | 0.535898i | 0.0236528 | + | 0.0273119i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.8564 | 1.05746 | 0.528731 | − | 0.848790i | \(-0.322668\pi\) | ||||
0.528731 | + | 0.848790i | \(0.322668\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.46410 | 0.478620 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.39230 | −0.221562 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.6603 | −0.737637 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 12.4641i | − | 0.625555i | −0.949826 | − | 0.312778i | \(-0.898741\pi\) | ||
0.949826 | − | 0.312778i | \(-0.101259\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.0000 | − | 20.7846i | −0.901127 | − | 1.04053i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.0718 | −0.502962 | −0.251481 | − | 0.967862i | \(-0.580918\pi\) | ||||
−0.251481 | + | 0.967862i | \(0.580918\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.78461i | 0.138711i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 9.00000i | − | 0.447214i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.53590i | − | 0.125700i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.14359i | 0.204888i | 0.994739 | + | 0.102444i | \(0.0326662\pi\) | ||||
−0.994739 | + | 0.102444i | \(0.967334\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −35.3205 | −1.74223 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.00000 | − | 6.92820i | −0.295241 | − | 0.340915i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.4641i | 0.759103i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.0000 | −0.587643 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.2487 | −1.18463 | −0.592314 | − | 0.805708i | \(-0.701785\pi\) | ||||
−0.592314 | + | 0.805708i | \(0.701785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0000 | −0.926003 | −0.463002 | − | 0.886357i | \(-0.653228\pi\) | ||||
−0.463002 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.46410i | 0.313555i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.9282 | − | 16.3923i | 0.916000 | − | 0.793279i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.215390 | −0.0103991 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 13.5885i | − | 0.654533i | −0.944932 | − | 0.327266i | \(-0.893873\pi\) | ||
0.944932 | − | 0.327266i | \(-0.106127\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 31.8564i | − | 1.53092i | −0.643483 | − | 0.765461i | \(-0.722511\pi\) | ||
0.643483 | − | 0.765461i | \(-0.277489\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.7321i | 0.658401i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.78461i | 0.420225i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.7128 | 1.89539 | 0.947695 | − | 0.319179i | \(-0.103407\pi\) | ||||
0.947695 | + | 0.319179i | \(0.103407\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.0000i | 1.23530i | 0.786454 | + | 0.617649i | \(0.211915\pi\) | ||||
−0.786454 | + | 0.617649i | \(0.788085\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.53590 | −0.120213 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.32051 | 0.251651 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.9282 | 0.562927 | 0.281463 | − | 0.959572i | \(-0.409180\pi\) | ||||
0.281463 | + | 0.959572i | \(0.409180\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.928203 | −0.0437074 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 26.3205i | − | 1.23665i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.803848 | − | 0.928203i | −0.0376850 | − | 0.0435148i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.5359 | 0.960629 | 0.480314 | − | 0.877096i | \(-0.340523\pi\) | ||||
0.480314 | + | 0.877096i | \(0.340523\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 33.5885i | − | 1.56777i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 27.7128i | − | 1.29071i | −0.763881 | − | 0.645357i | \(-0.776709\pi\) | ||
0.763881 | − | 0.645357i | \(-0.223291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.3923i | − | 0.761815i | −0.924613 | − | 0.380908i | \(-0.875612\pi\) | ||
0.924613 | − | 0.380908i | \(-0.124388\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 10.3923i | − | 0.481932i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.5167 | 1.04195 | 0.520973 | − | 0.853573i | \(-0.325569\pi\) | ||||
0.520973 | + | 0.853573i | \(0.325569\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.92820 | + | 6.00000i | −0.319915 | + | 0.277054i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.6077i | 0.627009i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.535898 | −0.0246406 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | −0.275299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.1769 | −1.15036 | −0.575181 | − | 0.818026i | \(-0.695068\pi\) | ||||
−0.575181 | + | 0.818026i | \(0.695068\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.39230i | 0.200272i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.07180 | − | 4.39230i | 0.230775 | − | 0.199857i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.3923 | 0.608113 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.7846i | − | 0.579326i | −0.957129 | − | 0.289663i | \(-0.906457\pi\) | ||
0.957129 | − | 0.289663i | \(-0.0935432\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 36.0000i | − | 1.62798i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.87564i | 0.445682i | 0.974855 | + | 0.222841i | \(0.0715330\pi\) | ||||
−0.974855 | + | 0.222841i | \(0.928467\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 51.2487i | 2.30813i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.9282 | + | 12.9282i | −0.669621 | + | 0.579909i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 25.5885i | − | 1.14550i | −0.819731 | − | 0.572748i | \(-0.805877\pi\) | ||
0.819731 | − | 0.572748i | \(-0.194123\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.00000 | −0.402090 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.5885 | 0.695055 | 0.347527 | − | 0.937670i | \(-0.387021\pi\) | ||||
0.347527 | + | 0.937670i | \(0.387021\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.4641 | −0.688143 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.1436 | −0.983432 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 25.8564i | − | 1.14607i | −0.819533 | − | 0.573033i | \(-0.805767\pi\) | ||
0.819533 | − | 0.573033i | \(-0.194233\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.8564 | + | 22.3923i | −1.14382 | + | 0.990577i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 31.1769 | 1.37649 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.80385i | 0.299813i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.464102i | 0.0204112i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 24.8038i | − | 1.08877i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.6077i | 0.596164i | 0.954540 | + | 0.298082i | \(0.0963469\pi\) | ||||
−0.954540 | + | 0.298082i | \(0.903653\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.2487 | −1.06032 | −0.530161 | − | 0.847897i | \(-0.677869\pi\) | ||||
−0.530161 | + | 0.847897i | \(0.677869\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.00000 | + | 3.46410i | 0.130931 | + | 0.151186i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 38.7846i | − | 1.68948i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.8564 | 0.906800 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.60770 | 0.0696370 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.39230 | −0.103428 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 11.0718i | − | 0.477783i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.85641 | + | 0.267949i | 0.0799611 | + | 0.0115414i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.78461 | −0.334687 | −0.167343 | − | 0.985899i | \(-0.553519\pi\) | ||||
−0.167343 | + | 0.985899i | \(0.553519\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1.60770i | − | 0.0689928i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 2.07180i | − | 0.0887460i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 21.4641i | − | 0.917739i | −0.888504 | − | 0.458869i | \(-0.848255\pi\) | ||
0.888504 | − | 0.458869i | \(-0.151745\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −47.5692 | −2.02652 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −29.3205 | + | 25.3923i | −1.24683 | + | 1.07979i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 16.3923i | − | 0.695815i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.8564 | 0.926086 | 0.463043 | − | 0.886336i | \(-0.346758\pi\) | ||||
0.463043 | + | 0.886336i | \(0.346758\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.928203 | 0.0392588 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.00000 | 0.126660 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.1769 | 0.808211 | 0.404105 | − | 0.914712i | \(-0.367583\pi\) | ||||
0.404105 | + | 0.914712i | \(0.367583\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.46410i | 0.229876i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15.5885 | − | 18.0000i | −0.654654 | − | 0.755929i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.07180 | 0.296465 | 0.148233 | − | 0.988953i | \(-0.452642\pi\) | ||||
0.148233 | + | 0.988953i | \(0.452642\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.67949i | 0.279528i | 0.990185 | + | 0.139764i | \(0.0446344\pi\) | ||||
−0.990185 | + | 0.139764i | \(0.955366\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 12.4641i | − | 0.520695i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.46410i | − | 0.0610573i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.3923i | 0.807312i | 0.914911 | + | 0.403656i | \(0.132261\pi\) | ||||
−0.914911 | + | 0.403656i | \(0.867739\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.3923 | 0.681241 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.7846 | + | 30.9282i | 1.11121 | + | 1.28312i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.535898i | 0.0221946i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.5359 | −0.847607 | −0.423804 | − | 0.905754i | \(-0.639305\pi\) | ||||
−0.423804 | + | 0.905754i | \(0.639305\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.0000 | 1.48335 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.0718 | −0.949047 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.4641i | 1.25101i | 0.780220 | + | 0.625505i | \(0.215107\pi\) | ||||
−0.780220 | + | 0.625505i | \(0.784893\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.1962 | + | 12.9282i | 0.458997 | + | 0.530005i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.00000 | 0.245564 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 10.1244i | − | 0.413670i | −0.978376 | − | 0.206835i | \(-0.933684\pi\) | ||
0.978376 | − | 0.206835i | \(-0.0663163\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 14.7846i | − | 0.603077i | −0.953454 | − | 0.301538i | \(-0.902500\pi\) | ||
0.953454 | − | 0.301538i | \(-0.0975001\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.9282i | 0.444295i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.1962 | 1.18504 | 0.592518 | − | 0.805557i | \(-0.298134\pi\) | ||||
0.592518 | + | 0.805557i | \(0.298134\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 23.7846 | + | 27.4641i | 0.963801 | + | 1.11290i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 0.803848i | − | 0.0325202i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.0000 | 0.403896 | 0.201948 | − | 0.979396i | \(-0.435273\pi\) | ||||
0.201948 | + | 0.979396i | \(0.435273\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.00000 | −0.241943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.9282 | −0.923055 | −0.461527 | − | 0.887126i | \(-0.652698\pi\) | ||||
−0.461527 | + | 0.887126i | \(0.652698\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.679492 | 0.0273111 | 0.0136555 | − | 0.999907i | \(-0.495653\pi\) | ||||
0.0136555 | + | 0.999907i | \(0.495653\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.60770i | 0.305286i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.07180 | + | 4.39230i | −0.203197 | + | 0.175974i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.78461i | 0.111207i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 61.1769i | − | 2.43928i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.9090i | 1.54894i | 0.632610 | + | 0.774471i | \(0.281984\pi\) | ||||
−0.632610 | + | 0.774471i | \(0.718016\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.53590i | 0.220032i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.4641 | 0.613674 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.21539 | − | 0.464102i | −0.127398 | − | 0.0183884i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.92820 | 0.352643 | 0.176321 | − | 0.984333i | \(-0.443580\pi\) | ||||
0.176321 | + | 0.984333i | \(0.443580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.05256 | 0.278126 | 0.139063 | − | 0.990284i | \(-0.455591\pi\) | ||||
0.139063 | + | 0.990284i | \(0.455591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.46410 | −0.136399 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.3923 | 0.408564 | 0.204282 | − | 0.978912i | \(-0.434514\pi\) | ||||
0.204282 | + | 0.978912i | \(0.434514\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.928203i | 0.0364352i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.0000 | − | 20.7846i | −0.705476 | − | 0.814613i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.6077 | −0.689042 | −0.344521 | − | 0.938779i | \(-0.611959\pi\) | ||||
−0.344521 | + | 0.938779i | \(0.611959\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.53590i | 0.0990857i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.1962i | 1.21523i | 0.794232 | + | 0.607615i | \(0.207874\pi\) | ||||
−0.794232 | + | 0.607615i | \(0.792126\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 39.7128i | − | 1.54465i | −0.635228 | − | 0.772325i | \(-0.719094\pi\) | ||
0.635228 | − | 0.772325i | \(-0.280906\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.19615 | −0.201802 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.0000 | + | 10.3923i | −0.465340 | + | 0.402996i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 11.6077i | − | 0.449452i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.7846 | −0.919566 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.53590 | −0.0978973 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.1769 | −0.507933 | −0.253966 | − | 0.967213i | \(-0.581735\pi\) | ||||
−0.253966 | + | 0.967213i | \(0.581735\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.19615 | −0.200000 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.3923i | 0.975906i | 0.872870 | + | 0.487953i | \(0.162256\pi\) | ||||
−0.872870 | + | 0.487953i | \(0.837744\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.7846 | − | 23.1962i | 1.02790 | − | 0.890187i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −35.7846 | −1.37127 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 7.32051i | − | 0.280111i | −0.990144 | − | 0.140056i | \(-0.955272\pi\) | ||
0.990144 | − | 0.140056i | \(-0.0447282\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.3923i | 0.779150i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 14.7846i | − | 0.564068i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 0.928203i | − | 0.0353617i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.6410 | −0.861305 | −0.430652 | − | 0.902518i | \(-0.641717\pi\) | ||||
−0.430652 | + | 0.902518i | \(0.641717\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.92820i | 0.262802i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.3923 | −0.848169 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.7128 | 0.594313 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.7846 | 1.42711 | 0.713553 | − | 0.700602i | \(-0.247085\pi\) | ||||
0.713553 | + | 0.700602i | \(0.247085\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 56.7846 | 2.14167 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.00000i | 0.112987i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −30.9282 | + | 26.7846i | −1.16317 | + | 1.00734i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.0000 | −0.788672 | −0.394336 | − | 0.918966i | \(-0.629025\pi\) | ||||
−0.394336 | + | 0.918966i | \(0.629025\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.78461i | 0.328986i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.124356i | 0.00465064i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 41.5359i | 1.55119i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.5359 | −1.43715 | −0.718573 | − | 0.695451i | \(-0.755205\pi\) | ||||
−0.718573 | + | 0.695451i | \(0.755205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.7846 | + | 13.6077i | 0.438882 | + | 0.506777i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 28.3923i | − | 1.05592i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.92820 | 0.294446 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.6077 | 0.504681 | 0.252341 | − | 0.967638i | \(-0.418800\pi\) | ||||
0.252341 | + | 0.967638i | \(0.418800\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.9282 | −0.478167 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 11.5359i | − | 0.426088i | −0.977043 | − | 0.213044i | \(-0.931662\pi\) | ||
0.977043 | − | 0.213044i | \(-0.0683378\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.0000 | + | 1.73205i | 0.442627 | + | 0.0638877i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.928203 | 0.0341908 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.26795i | 0.156999i | 0.996914 | + | 0.0784995i | \(0.0250129\pi\) | ||||
−0.996914 | + | 0.0784995i | \(0.974987\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 4.82309i | − | 0.177180i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.3923i | 1.11499i | 0.830182 | + | 0.557493i | \(0.188237\pi\) | ||||
−0.830182 | + | 0.557493i | \(0.811763\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 3.07180i | − | 0.112542i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.78461 | + | 4.14359i | −0.174826 | + | 0.151404i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 25.5885i | − | 0.933736i | −0.884327 | − | 0.466868i | \(-0.845382\pi\) | ||
0.884327 | − | 0.466868i | \(-0.154618\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 44.7846 | 1.63204 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.1962 | −0.553045 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.8564 | −1.37591 | −0.687957 | − | 0.725751i | \(-0.741492\pi\) | ||||
−0.687957 | + | 0.725751i | \(0.741492\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.679492 | −0.0246640 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 42.2487i | − | 1.53151i | −0.643130 | − | 0.765757i | \(-0.722364\pi\) | ||
0.643130 | − | 0.765757i | \(-0.277636\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.58846 | − | 4.14359i | −0.129911 | − | 0.150008i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1.60770i | − | 0.0580505i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.0000i | 0.649097i | 0.945869 | + | 0.324548i | \(0.105212\pi\) | ||||
−0.945869 | + | 0.324548i | \(0.894788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 10.3923i | − | 0.374270i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.53590i | 0.199112i | 0.995032 | + | 0.0995562i | \(0.0317423\pi\) | ||||
−0.995032 | + | 0.0995562i | \(0.968258\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.00000 | −0.215526 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −28.3923 | − | 32.7846i | −1.01857 | − | 1.17614i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 20.7846i | − | 0.744686i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | 0.0715656 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −41.1962 | −1.47223 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.85641 | 0.280407 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.6603 | 1.16421 | 0.582106 | − | 0.813113i | \(-0.302229\pi\) | ||||
0.582106 | + | 0.813113i | \(0.302229\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.8564i | 0.706907i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.46410 | + | 10.9282i | 0.336505 | + | 0.388562i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.39230 | 0.155975 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.46410i | 0.122859i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.1769i | 0.785547i | 0.919635 | + | 0.392773i | \(0.128484\pi\) | ||||
−0.919635 | + | 0.392773i | \(0.871516\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.1962i | 0.396091i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.46410 | 0.122245 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.53590 | − | 2.92820i | −0.0893787 | − | 0.103206i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 20.7846i | − | 0.731653i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.92820 | 0.278741 | 0.139370 | − | 0.990240i | \(-0.455492\pi\) | ||||
0.139370 | + | 0.990240i | \(0.455492\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.0718 | 1.02085 | 0.510424 | − | 0.859923i | \(-0.329488\pi\) | ||||
0.510424 | + | 0.859923i | \(0.329488\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.3923 | 0.574903 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.7846 | −0.728053 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 12.0000i | − | 0.419827i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.7846 | −0.969690 | −0.484845 | − | 0.874600i | \(-0.661124\pi\) | ||||
−0.484845 | + | 0.874600i | \(0.661124\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.0718i | 0.385939i | 0.981205 | + | 0.192969i | \(0.0618118\pi\) | ||||
−0.981205 | + | 0.192969i | \(0.938188\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 0.464102i | − | 0.0161579i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 14.1436i | − | 0.491821i | −0.969293 | − | 0.245910i | \(-0.920913\pi\) | ||
0.969293 | − | 0.245910i | \(-0.0790869\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 0.248711i | − | 0.00863810i | −0.999991 | − | 0.00431905i | \(-0.998625\pi\) | ||
0.999991 | − | 0.00431905i | \(-0.00137480\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.0718 | 1.00849 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 44.7846 | + | 6.46410i | 1.55169 | + | 0.223968i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.19615i | 0.179820i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31.1769 | 1.07763 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.39230 | −0.151639 | −0.0758196 | − | 0.997122i | \(-0.524157\pi\) | ||||
−0.0758196 | + | 0.997122i | \(0.524157\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.8564 | 1.16746 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.7321 | 0.472957 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.7846i | 0.439804i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.9282 | + | 21.8564i | 0.650381 | + | 0.750995i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.0000 | −0.720718 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.8564i | 0.474991i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.78461i | 0.0953432i | 0.998863 | + | 0.0476716i | \(0.0151801\pi\) | ||||
−0.998863 | + | 0.0476716i | \(0.984820\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 57.7128i | 1.97143i | 0.168416 | + | 0.985716i | \(0.446135\pi\) | ||||
−0.168416 | + | 0.985716i | \(0.553865\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.7128 | 1.35498 | 0.677492 | − | 0.735530i | \(-0.263067\pi\) | ||||
0.677492 | + | 0.735530i | \(0.263067\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0000 | + | 10.3923i | −0.408959 | + | 0.354169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 39.8564i | − | 1.35673i | −0.734726 | − | 0.678364i | \(-0.762689\pi\) | ||
0.734726 | − | 0.678364i | \(-0.237311\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.3205 | −0.486912 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 42.9282 | 1.45792 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.92820 | 0.133255 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.60770 | −0.0544747 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.00000 | − | 1.73205i | 0.0676123 | − | 0.0585540i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.3923 | 0.621064 | 0.310532 | − | 0.950563i | \(-0.399493\pi\) | ||||
0.310532 | + | 0.950563i | \(0.399493\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 35.1962i | 1.18714i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 29.0718i | − | 0.979454i | −0.871876 | − | 0.489727i | \(-0.837096\pi\) | ||
0.871876 | − | 0.489727i | \(-0.162904\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.6077i | 0.794462i | 0.917719 | + | 0.397231i | \(0.130029\pi\) | ||||
−0.917719 | + | 0.397231i | \(0.869971\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.00000i | 0.201688i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.53590 | 0.286607 | 0.143304 | − | 0.989679i | \(-0.454227\pi\) | ||||
0.143304 | + | 0.989679i | \(0.454227\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.9282 | − | 26.7846i | 1.03730 | − | 0.898327i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.41154i | 0.0807897i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.3923 | −0.347765 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.39230 | −0.213671 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.17691 | 0.0392960 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −47.5692 | −1.58652 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.9282i | 0.430701i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.92820 | + | 6.00000i | −0.230556 | + | 0.199667i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.928203 | −0.0308545 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.3923i | 1.07557i | 0.843082 | + | 0.537784i | \(0.180739\pi\) | ||||
−0.843082 | + | 0.537784i | \(0.819261\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 20.2487i | − | 0.670870i | −0.942063 | − | 0.335435i | \(-0.891117\pi\) | ||
0.942063 | − | 0.335435i | \(-0.108883\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 4.14359i | − | 0.137133i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16.3923 | −0.541913 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.39230 | + | 5.07180i | 0.145047 | + | 0.167485i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 6.41154i | − | 0.211497i | −0.994393 | − | 0.105749i | \(-0.966276\pi\) | ||
0.994393 | − | 0.105749i | \(-0.0337239\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.00000 | −0.0988534 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.46410 | −0.114022 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.46410 | −0.311178 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 54.4974i | − | 1.78800i | −0.448065 | − | 0.894001i | \(-0.647887\pi\) | ||
0.448065 | − | 0.894001i | \(-0.352113\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.00000 | + | 41.5692i | −0.196642 | + | 1.36238i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.6077 | 0.445496 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1.73205i | − | 0.0566441i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 25.3923i | − | 0.829530i | −0.909928 | − | 0.414765i | \(-0.863864\pi\) | ||
0.909928 | − | 0.414765i | \(-0.136136\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.3731i | 0.991188i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 39.0333i | − | 1.27245i | −0.771504 | − | 0.636225i | \(-0.780495\pi\) | ||
0.771504 | − | 0.636225i | \(-0.219505\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.07180 | 0.165160 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.3923 | + | 9.00000i | −0.338062 | + | 0.292770i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 22.7846i | − | 0.740400i | −0.928952 | − | 0.370200i | \(-0.879289\pi\) | ||
0.928952 | − | 0.370200i | \(-0.120711\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.00000 | −0.194768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.32051 | −0.172529 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.3205 | 0.690639 | 0.345320 | − | 0.938485i | \(-0.387771\pi\) | ||||
0.345320 | + | 0.938485i | \(0.387771\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.19615 | −0.232862 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3.67949i | − | 0.118941i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.3205 | + | 40.7846i | 1.14056 | + | 1.31700i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 9.46410i | − | 0.304660i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.1769i | 1.00258i | 0.865279 | + | 0.501291i | \(0.167141\pi\) | ||||
−0.865279 | + | 0.501291i | \(0.832859\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 67.1769i | 2.15803i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.7846 | 0.474461 | 0.237230 | − | 0.971453i | \(-0.423760\pi\) | ||||
0.237230 | + | 0.971453i | \(0.423760\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0000 | + | 13.8564i | 0.384702 | + | 0.444216i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.803848i | 0.0257437i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.24871 | −0.135928 | −0.0679642 | − | 0.997688i | \(-0.521650\pi\) | ||||
−0.0679642 | + | 0.997688i | \(0.521650\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.679492 | 0.0217167 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.5885 | 0.879935 | 0.439968 | − | 0.898014i | \(-0.354990\pi\) | ||||
0.439968 | + | 0.898014i | \(0.354990\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.3205i | 0.424427i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.19615 | + | 6.00000i | 0.165395 | + | 0.190982i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.92820 | 0.0931114 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.1769i | 1.49862i | 0.662217 | + | 0.749312i | \(0.269616\pi\) | ||||
−0.662217 | + | 0.749312i | \(0.730384\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 45.7128i | − | 1.45065i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 3.46410i | − | 0.109819i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 5.53590i | − | 0.175324i | −0.996150 | − | 0.0876618i | \(-0.972061\pi\) | ||
0.996150 | − | 0.0876618i | \(-0.0279395\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 49.1769 | 1.55589 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))