Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(1343,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.1343");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.n (of order \(4\), degree \(2\), 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1407.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1407 |
Dual form | 1600.2.n.a.1343.1 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.00000 | − | 2.00000i | −1.15470 | − | 1.15470i | −0.985599 | − | 0.169102i | \(-0.945913\pi\) |
−0.169102 | − | 0.985599i | \(-0.554087\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 2.00000i | 0.755929 | − | 0.755929i | −0.219650 | − | 0.975579i | \(-0.570491\pi\) |
0.975579 | + | 0.219650i | \(0.0704915\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.00000i | 1.66667i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | + | 1.00000i | −0.277350 | + | 0.277350i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) |
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.00000 | + | 5.00000i | 1.21268 | + | 1.21268i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) |
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.00000 | −1.74574 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | + | 2.00000i | 0.417029 | + | 0.417029i | 0.884178 | − | 0.467150i | \(-0.154719\pi\) |
−0.467150 | + | 0.884178i | \(0.654719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | − | 4.00000i | 0.769800 | − | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000i | 0.742781i | 0.928477 | + | 0.371391i | \(0.121119\pi\) | ||||
−0.928477 | + | 0.371391i | \(0.878881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000i | 0.718421i | 0.933257 | + | 0.359211i | \(0.116954\pi\) | ||||
−0.933257 | + | 0.359211i | \(0.883046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | + | 1.00000i | 0.164399 | + | 0.164399i | 0.784512 | − | 0.620113i | \(-0.212913\pi\) |
−0.620113 | + | 0.784512i | \(0.712913\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000 | + | 6.00000i | 0.914991 | + | 0.914991i | 0.996660 | − | 0.0816682i | \(-0.0260248\pi\) |
−0.0816682 | + | 0.996660i | \(0.526025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.00000 | + | 2.00000i | −0.291730 | + | 0.291730i | −0.837763 | − | 0.546033i | \(-0.816137\pi\) |
0.546033 | + | 0.837763i | \(0.316137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 20.0000i | − | 2.80056i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.00000 | + | 7.00000i | −0.961524 | + | 0.961524i | −0.999287 | − | 0.0377628i | \(-0.987977\pi\) |
0.0377628 | + | 0.999287i | \(0.487977\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.00000 | − | 8.00000i | −1.05963 | − | 1.05963i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | 0.512148 | 0.256074 | − | 0.966657i | \(-0.417571\pi\) | ||||
0.256074 | + | 0.966657i | \(0.417571\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.0000 | + | 10.0000i | 1.25988 | + | 1.25988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0000 | − | 10.0000i | 1.22169 | − | 1.22169i | 0.254665 | − | 0.967029i | \(-0.418035\pi\) |
0.967029 | − | 0.254665i | \(-0.0819652\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 8.00000i | − | 0.963087i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.0000i | − | 1.42414i | −0.702109 | − | 0.712069i | \(-0.747758\pi\) | ||
0.702109 | − | 0.712069i | \(-0.252242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.00000 | − | 3.00000i | 0.351123 | − | 0.351123i | −0.509404 | − | 0.860527i | \(-0.670134\pi\) |
0.860527 | + | 0.509404i | \(0.170134\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.0000 | −1.80014 | −0.900070 | − | 0.435745i | \(-0.856485\pi\) | ||||
−0.900070 | + | 0.435745i | \(0.856485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.00000 | + | 2.00000i | 0.219529 | + | 0.219529i | 0.808300 | − | 0.588771i | \(-0.200388\pi\) |
−0.588771 | + | 0.808300i | \(0.700388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.00000 | − | 8.00000i | 0.857690 | − | 0.857690i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000i | 0.419314i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.00000 | − | 8.00000i | 0.829561 | − | 0.829561i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.00000 | + | 3.00000i | 0.304604 | + | 0.304604i | 0.842812 | − | 0.538208i | \(-0.180899\pi\) |
−0.538208 | + | 0.842812i | \(0.680899\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.00000 | − | 6.00000i | −0.591198 | − | 0.591198i | 0.346757 | − | 0.937955i | \(-0.387283\pi\) |
−0.937955 | + | 0.346757i | \(0.887283\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.00000 | + | 6.00000i | −0.580042 | + | 0.580042i | −0.934915 | − | 0.354873i | \(-0.884524\pi\) |
0.354873 | + | 0.934915i | \(0.384524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.0000i | − | 0.957826i | −0.877862 | − | 0.478913i | \(-0.841031\pi\) | ||
0.877862 | − | 0.478913i | \(-0.158969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 4.00000i | − | 0.379663i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.00000 | − | 9.00000i | 0.846649 | − | 0.846649i | −0.143065 | − | 0.989713i | \(-0.545696\pi\) |
0.989713 | + | 0.143065i | \(0.0456957\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.00000 | − | 5.00000i | −0.462250 | − | 0.462250i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.0000 | 1.83340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.0000 | − | 10.0000i | 0.887357 | − | 0.887357i | −0.106912 | − | 0.994268i | \(-0.534096\pi\) |
0.994268 | + | 0.106912i | \(0.0340963\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 24.0000i | − | 2.11308i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.00000i | 0.698963i | 0.936943 | + | 0.349482i | \(0.113642\pi\) | ||||
−0.936943 | + | 0.349482i | \(0.886358\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000 | − | 8.00000i | 0.693688 | − | 0.693688i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.00000 | − | 1.00000i | −0.0854358 | − | 0.0854358i | 0.663097 | − | 0.748533i | \(-0.269242\pi\) |
−0.748533 | + | 0.663097i | \(0.769242\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0000 | −1.01783 | −0.508913 | − | 0.860818i | \(-0.669953\pi\) | ||||
−0.508913 | + | 0.860818i | \(0.669953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.00000 | + | 2.00000i | −0.164957 | + | 0.164957i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.0000i | 1.47462i | 0.675556 | + | 0.737309i | \(0.263904\pi\) | ||||
−0.675556 | + | 0.737309i | \(0.736096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.0000i | − | 0.976546i | −0.872691 | − | 0.488273i | \(-0.837627\pi\) | ||
0.872691 | − | 0.488273i | \(-0.162373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −25.0000 | + | 25.0000i | −2.02113 | + | 2.02113i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.00000 | − | 9.00000i | −0.718278 | − | 0.718278i | 0.249974 | − | 0.968252i | \(-0.419578\pi\) |
−0.968252 | + | 0.249974i | \(0.919578\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 28.0000 | 2.22054 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.00000 | 0.630488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00000 | − | 2.00000i | −0.156652 | − | 0.156652i | 0.624429 | − | 0.781081i | \(-0.285332\pi\) |
−0.781081 | + | 0.624429i | \(0.785332\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.00000 | + | 2.00000i | −0.154765 | + | 0.154765i | −0.780242 | − | 0.625478i | \(-0.784904\pi\) |
0.625478 | + | 0.780242i | \(0.284904\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000i | 0.846154i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 20.0000i | 1.52944i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.0000 | − | 13.0000i | 0.988372 | − | 0.988372i | −0.0115615 | − | 0.999933i | \(-0.503680\pi\) |
0.999933 | + | 0.0115615i | \(0.00368021\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.00000 | − | 8.00000i | −0.601317 | − | 0.601317i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.00000 | − | 8.00000i | −0.591377 | − | 0.591377i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 16.0000i | − | 1.16383i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.0000i | 1.44715i | 0.690246 | + | 0.723575i | \(0.257502\pi\) | ||||
−0.690246 | + | 0.723575i | \(0.742498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.00000 | − | 5.00000i | 0.359908 | − | 0.359908i | −0.503871 | − | 0.863779i | \(-0.668091\pi\) |
0.863779 | + | 0.503871i | \(0.168091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.00000 | + | 5.00000i | 0.356235 | + | 0.356235i | 0.862423 | − | 0.506188i | \(-0.168946\pi\) |
−0.506188 | + | 0.862423i | \(0.668946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.0000 | −1.70131 | −0.850657 | − | 0.525720i | \(-0.823796\pi\) | ||||
−0.850657 | + | 0.525720i | \(0.823796\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −40.0000 | −2.82138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.00000 | + | 8.00000i | 0.561490 | + | 0.561490i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.0000 | + | 10.0000i | −0.695048 | + | 0.695048i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000i | 1.10149i | 0.834675 | + | 0.550743i | \(0.185655\pi\) | ||||
−0.834675 | + | 0.550743i | \(0.814345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −24.0000 | + | 24.0000i | −1.64445 | + | 1.64445i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | + | 8.00000i | 0.543075 | + | 0.543075i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.0000 | −0.810885 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.0000 | −0.672673 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.0000 | − | 10.0000i | −0.669650 | − | 0.669650i | 0.287985 | − | 0.957635i | \(-0.407015\pi\) |
−0.957635 | + | 0.287985i | \(0.907015\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.0000 | + | 10.0000i | −0.663723 | + | 0.663723i | −0.956256 | − | 0.292532i | \(-0.905502\pi\) |
0.292532 | + | 0.956256i | \(0.405502\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.0000i | 1.32164i | 0.750546 | + | 0.660819i | \(0.229791\pi\) | ||||
−0.750546 | + | 0.660819i | \(0.770209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.00000 | − | 5.00000i | 0.327561 | − | 0.327561i | −0.524097 | − | 0.851658i | \(-0.675597\pi\) |
0.851658 | + | 0.524097i | \(0.175597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 32.0000 | + | 32.0000i | 2.07862 | + | 2.07862i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.0000 | −1.03065 | −0.515325 | − | 0.856995i | \(-0.672329\pi\) | ||||
−0.515325 | + | 0.856995i | \(0.672329\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.0000 | − | 10.0000i | −0.641500 | − | 0.641500i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.00000 | + | 4.00000i | −0.254514 | + | 0.254514i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 8.00000i | − | 0.506979i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 24.0000i | − | 1.51487i | −0.652913 | − | 0.757433i | \(-0.726453\pi\) | ||
0.652913 | − | 0.757433i | \(-0.273547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.00000 | − | 7.00000i | −0.436648 | − | 0.436648i | 0.454234 | − | 0.890882i | \(-0.349913\pi\) |
−0.890882 | + | 0.454234i | \(0.849913\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.0000 | −1.23797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000 | + | 6.00000i | 0.369976 | + | 0.369976i | 0.867468 | − | 0.497492i | \(-0.165746\pi\) |
−0.497492 | + | 0.867468i | \(0.665746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0000i | 0.609711i | 0.952399 | + | 0.304855i | \(0.0986081\pi\) | ||||
−0.952399 | + | 0.304855i | \(0.901392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 20.0000i | − | 1.21491i | −0.794353 | − | 0.607457i | \(-0.792190\pi\) | ||
0.794353 | − | 0.607457i | \(-0.207810\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.00000 | − | 8.00000i | 0.484182 | − | 0.484182i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.00000 | − | 9.00000i | −0.540758 | − | 0.540758i | 0.382993 | − | 0.923751i | \(-0.374893\pi\) |
−0.923751 | + | 0.382993i | \(0.874893\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −20.0000 | −1.19737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.00000 | 0.477240 | 0.238620 | − | 0.971113i | \(-0.423305\pi\) | ||||
0.238620 | + | 0.971113i | \(0.423305\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.00000 | − | 6.00000i | −0.356663 | − | 0.356663i | 0.505918 | − | 0.862581i | \(-0.331154\pi\) |
−0.862581 | + | 0.505918i | \(0.831154\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.0000i | 1.94118i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 12.0000i | − | 0.703452i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.00000 | + | 5.00000i | −0.292103 | + | 0.292103i | −0.837911 | − | 0.545807i | \(-0.816223\pi\) |
0.545807 | + | 0.837911i | \(0.316223\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.00000 | −0.231326 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.0000 | 1.38334 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.0000 | − | 12.0000i | −0.689382 | − | 0.689382i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0000 | − | 10.0000i | 0.570730 | − | 0.570730i | −0.361602 | − | 0.932332i | \(-0.617770\pi\) |
0.932332 | + | 0.361602i | \(0.117770\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.0000i | 1.36531i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.0000i | 1.58773i | 0.608091 | + | 0.793867i | \(0.291935\pi\) | ||||
−0.608091 | + | 0.793867i | \(0.708065\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.0000 | + | 15.0000i | −0.847850 | + | 0.847850i | −0.989865 | − | 0.142014i | \(-0.954642\pi\) |
0.142014 | + | 0.989865i | \(0.454642\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.0000 | + | 11.0000i | 0.617822 | + | 0.617822i | 0.944972 | − | 0.327151i | \(-0.106088\pi\) |
−0.327151 | + | 0.944972i | \(0.606088\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.0000 | 1.33955 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.0000 | + | 20.0000i | 1.11283 | + | 1.11283i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.0000 | + | 20.0000i | −1.10600 | + | 1.10600i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00000i | 0.441054i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.00000 | + | 5.00000i | −0.273998 | + | 0.273998i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0000 | + | 23.0000i | 1.25289 | + | 1.25289i | 0.954419 | + | 0.298471i | \(0.0964767\pi\) |
0.298471 | + | 0.954419i | \(0.403523\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −36.0000 | −1.95525 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | + | 12.0000i | 0.647939 | + | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.0000 | + | 18.0000i | −0.966291 | + | 0.966291i | −0.999450 | − | 0.0331594i | \(-0.989443\pi\) |
0.0331594 | + | 0.999450i | \(0.489443\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 20.0000i | − | 1.07058i | −0.844670 | − | 0.535288i | \(-0.820203\pi\) | ||
0.844670 | − | 0.535288i | \(-0.179797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.00000i | 0.427008i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.00000 | + | 9.00000i | −0.479022 | + | 0.479022i | −0.904819 | − | 0.425797i | \(-0.859994\pi\) |
0.425797 | + | 0.904819i | \(0.359994\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −40.0000 | − | 40.0000i | −2.11702 | − | 2.11702i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.0000 | 0.844448 | 0.422224 | − | 0.906492i | \(-0.361250\pi\) | ||||
0.422224 | + | 0.906492i | \(0.361250\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −22.0000 | − | 22.0000i | −1.15470 | − | 1.15470i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.0000 | + | 22.0000i | −1.14839 | + | 1.14839i | −0.161521 | + | 0.986869i | \(0.551640\pi\) |
−0.986869 | + | 0.161521i | \(0.948360\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.0000i | 1.45369i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.0000 | − | 21.0000i | 1.08734 | − | 1.08734i | 0.0915371 | − | 0.995802i | \(-0.470822\pi\) |
0.995802 | − | 0.0915371i | \(-0.0291780\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.00000 | − | 4.00000i | −0.206010 | − | 0.206010i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −40.0000 | −2.04926 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.0000 | + | 22.0000i | 1.12415 | + | 1.12415i | 0.991111 | + | 0.133036i | \(0.0424727\pi\) |
0.133036 | + | 0.991111i | \(0.457527\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −30.0000 | + | 30.0000i | −1.52499 | + | 1.52499i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 18.0000i | − | 0.912636i | −0.889817 | − | 0.456318i | \(-0.849168\pi\) | ||
0.889817 | − | 0.456318i | \(-0.150832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.0000i | 1.01144i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.0000 | − | 16.0000i | 0.807093 | − | 0.807093i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.0000 | + | 13.0000i | 0.652451 | + | 0.652451i | 0.953583 | − | 0.301131i | \(-0.0973643\pi\) |
−0.301131 | + | 0.953583i | \(0.597364\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −32.0000 | −1.60200 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.0000 | 1.69788 | 0.848939 | − | 0.528490i | \(-0.177242\pi\) | ||||
0.848939 | + | 0.528490i | \(0.177242\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | − | 4.00000i | −0.199254 | − | 0.199254i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.00000i | 0.0988936i | 0.998777 | + | 0.0494468i | \(0.0157458\pi\) | ||||
−0.998777 | + | 0.0494468i | \(0.984254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.00000i | 0.197305i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.00000 | − | 8.00000i | 0.393654 | − | 0.393654i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24.0000 | + | 24.0000i | 1.17529 | + | 1.17529i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0000 | −0.974740 | −0.487370 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.0000 | − | 10.0000i | −0.486217 | − | 0.486217i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.00000 | − | 8.00000i | 0.387147 | − | 0.387147i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4.00000i | − | 0.192673i | −0.995349 | − | 0.0963366i | \(-0.969287\pi\) | ||
0.995349 | − | 0.0963366i | \(-0.0307125\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.0000 | − | 19.0000i | 0.913082 | − | 0.913082i | −0.0834318 | − | 0.996513i | \(-0.526588\pi\) |
0.996513 | + | 0.0834318i | \(0.0265881\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.00000 | + | 8.00000i | 0.382692 | + | 0.382692i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000 | 0.763638 | 0.381819 | − | 0.924237i | \(-0.375298\pi\) | ||||
0.381819 | + | 0.924237i | \(0.375298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.00000 | 0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.0000 | − | 22.0000i | −1.04525 | − | 1.04525i | −0.998926 | − | 0.0463251i | \(-0.985249\pi\) |
−0.0463251 | − | 0.998926i | \(-0.514751\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 36.0000 | − | 36.0000i | 1.70274 | − | 1.70274i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 26.0000i | − | 1.22702i | −0.789689 | − | 0.613508i | \(-0.789758\pi\) | ||
0.789689 | − | 0.613508i | \(-0.210242\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.0000 | + | 24.0000i | −1.12762 | + | 1.12762i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.0000 | − | 15.0000i | −0.701670 | − | 0.701670i | 0.263099 | − | 0.964769i | \(-0.415256\pi\) |
−0.964769 | + | 0.263099i | \(0.915256\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 40.0000 | 1.86704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0000 | 0.652045 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.0000 | − | 22.0000i | −1.02243 | − | 1.02243i | −0.999743 | − | 0.0226840i | \(-0.992779\pi\) |
−0.0226840 | − | 0.999743i | \(-0.507221\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.00000 | + | 2.00000i | −0.0925490 | + | 0.0925490i | −0.751865 | − | 0.659317i | \(-0.770846\pi\) |
0.659317 | + | 0.751865i | \(0.270846\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 40.0000i | − | 1.84703i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 36.0000i | 1.65879i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −35.0000 | − | 35.0000i | −1.60254 | − | 1.60254i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.0000 | 1.09659 | 0.548294 | − | 0.836286i | \(-0.315277\pi\) | ||||
0.548294 | + | 0.836286i | \(0.315277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | −0.0911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.0000 | − | 16.0000i | −0.728025 | − | 0.728025i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.00000 | + | 6.00000i | −0.271886 | + | 0.271886i | −0.829859 | − | 0.557973i | \(-0.811579\pi\) |
0.557973 | + | 0.829859i | \(0.311579\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.00000i | 0.361773i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 16.0000i | − | 0.722070i | −0.932552 | − | 0.361035i | \(-0.882424\pi\) | ||
0.932552 | − | 0.361035i | \(-0.117576\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.0000 | + | 20.0000i | −0.900755 | + | 0.900755i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.0000 | − | 24.0000i | −1.07655 | − | 1.07655i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.00000 | 0.357414 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.0000 | + | 10.0000i | 0.445878 | + | 0.445878i | 0.893982 | − | 0.448104i | \(-0.147900\pi\) |
−0.448104 | + | 0.893982i | \(0.647900\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.0000 | − | 22.0000i | 0.977054 | − | 0.977054i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 36.0000i | − | 1.59567i | −0.602875 | − | 0.797836i | \(-0.705978\pi\) | ||
0.602875 | − | 0.797836i | \(-0.294022\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 12.0000i | − | 0.530849i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.0000 | − | 16.0000i | 0.706417 | − | 0.706417i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −52.0000 | −2.28255 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.0000 | − | 14.0000i | −0.612177 | − | 0.612177i | 0.331336 | − | 0.943513i | \(-0.392501\pi\) |
−0.943513 | + | 0.331336i | \(0.892501\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.0000 | + | 20.0000i | −0.871214 | + | 0.871214i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 15.0000i | − | 0.652174i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.0000i | 0.867926i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.0000 | − | 24.0000i | −1.03568 | − | 1.03568i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.0000 | − | 20.0000i | −0.858282 | − | 0.858282i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.00000 | − | 6.00000i | 0.256541 | − | 0.256541i | −0.567104 | − | 0.823646i | \(-0.691936\pi\) |
0.823646 | + | 0.567104i | \(0.191936\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.0000i | 0.853579i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.0000i | 0.681623i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.0000 | + | 32.0000i | −1.36078 | + | 1.36078i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.0000 | − | 15.0000i | −0.635570 | − | 0.635570i | 0.313889 | − | 0.949460i | \(-0.398368\pi\) |
−0.949460 | + | 0.313889i | \(0.898368\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.00000 | + | 6.00000i | 0.252870 | + | 0.252870i | 0.822146 | − | 0.569276i | \(-0.192777\pi\) |
−0.569276 | + | 0.822146i | \(0.692777\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.00000 | + | 2.00000i | −0.0839921 | + | 0.0839921i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 2.00000i | − | 0.0838444i | −0.999121 | − | 0.0419222i | \(-0.986652\pi\) | ||
0.999121 | − | 0.0419222i | \(-0.0133482\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 16.0000i | − | 0.669579i | −0.942293 | − | 0.334790i | \(-0.891335\pi\) | ||
0.942293 | − | 0.334790i | \(-0.108665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 40.0000 | − | 40.0000i | 1.67102 | − | 1.67102i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.0000 | − | 15.0000i | −0.624458 | − | 0.624458i | 0.322210 | − | 0.946668i | \(-0.395574\pi\) |
−0.946668 | + | 0.322210i | \(0.895574\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.0000 | −0.831172 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.00000 | 0.331896 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.0000 | − | 14.0000i | 0.577842 | − | 0.577842i | −0.356466 | − | 0.934308i | \(-0.616019\pi\) |
0.934308 | + | 0.356466i | \(0.116019\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000i | 0.659269i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 20.0000i | − | 0.822690i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.00000 | + | 1.00000i | −0.0410651 | + | 0.0410651i | −0.727341 | − | 0.686276i | \(-0.759244\pi\) |
0.686276 | + | 0.727341i | \(0.259244\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 48.0000 | + | 48.0000i | 1.96451 | + | 1.96451i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.00000 | 0.326871 | 0.163436 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163436 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.00000 | −0.326327 | −0.163163 | − | 0.986599i | \(-0.552170\pi\) | ||||
−0.163163 | + | 0.986599i | \(0.552170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 50.0000 | + | 50.0000i | 2.03616 | + | 2.03616i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.0000 | + | 18.0000i | −0.730597 | + | 0.730597i | −0.970738 | − | 0.240141i | \(-0.922806\pi\) |
0.240141 | + | 0.970738i | \(0.422806\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 32.0000i | − | 1.29671i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.00000i | − | 0.161823i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.00000 | + | 9.00000i | −0.363507 | + | 0.363507i | −0.865102 | − | 0.501596i | \(-0.832747\pi\) |
0.501596 | + | 0.865102i | \(0.332747\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.0000 | + | 29.0000i | 1.16750 | + | 1.16750i | 0.982795 | + | 0.184701i | \(0.0591318\pi\) |
0.184701 | + | 0.982795i | \(0.440868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.0000 | −1.12542 | −0.562708 | − | 0.826656i | \(-0.690240\pi\) | ||||
−0.562708 | + | 0.826656i | \(0.690240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.0000 | 0.642058 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.0000i | 0.398726i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4.00000i | − | 0.159237i | −0.996825 | − | 0.0796187i | \(-0.974630\pi\) | ||
0.996825 | − | 0.0796187i | \(-0.0253703\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32.0000 | − | 32.0000i | 1.27189 | − | 1.27189i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | + | 1.00000i | 0.0396214 | + | 0.0396214i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 60.0000 | 2.37356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −48.0000 | −1.89589 | −0.947943 | − | 0.318440i | \(-0.896841\pi\) | ||||
−0.947943 | + | 0.318440i | \(0.896841\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.0000 | + | 10.0000i | 0.394362 | + | 0.394362i | 0.876239 | − | 0.481877i | \(-0.160045\pi\) |
−0.481877 | + | 0.876239i | \(0.660045\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.0000 | − | 10.0000i | 0.393141 | − | 0.393141i | −0.482665 | − | 0.875805i | \(-0.660331\pi\) |
0.875805 | + | 0.482665i | \(0.160331\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 32.0000i | − | 1.25418i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.00000 | − | 1.00000i | 0.0391330 | − | 0.0391330i | −0.687270 | − | 0.726403i | \(-0.741191\pi\) |
0.726403 | + | 0.687270i | \(0.241191\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.0000 | + | 15.0000i | 0.585206 | + | 0.585206i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.0000 | 0.779089 | 0.389545 | − | 0.921008i | \(-0.372632\pi\) | ||||
0.389545 | + | 0.921008i | \(0.372632\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.0000 | −0.466746 | −0.233373 | − | 0.972387i | \(-0.574976\pi\) | ||||
−0.233373 | + | 0.972387i | \(0.574976\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.0000 | + | 20.0000i | 0.776736 | + | 0.776736i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.00000 | + | 8.00000i | −0.309761 | + | 0.309761i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 40.0000i | 1.54649i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.00000 | + | 5.00000i | −0.192736 | + | 0.192736i | −0.796877 | − | 0.604141i | \(-0.793516\pi\) |
0.604141 | + | 0.796877i | \(0.293516\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.00000 | − | 3.00000i | −0.115299 | − | 0.115299i | 0.647103 | − | 0.762402i | \(-0.275980\pi\) |
−0.762402 | + | 0.647103i | \(0.775980\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0000 | 0.460518 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 40.0000 | 1.53280 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.0000 | + | 22.0000i | 0.841807 | + | 0.841807i | 0.989094 | − | 0.147287i | \(-0.0470541\pi\) |
−0.147287 | + | 0.989094i | \(0.547054\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 40.0000 | − | 40.0000i | 1.52610 | − | 1.52610i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 14.0000i | − | 0.533358i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 32.0000i | − | 1.21734i | −0.793424 | − | 0.608669i | \(-0.791704\pi\) | ||
0.793424 | − | 0.608669i | \(-0.208296\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.0000 | −0.756469 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.0000 | −0.755390 | −0.377695 | − | 0.925930i | \(-0.623283\pi\) | ||||
−0.377695 | + | 0.925930i | \(0.623283\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.00000 | + | 4.00000i | 0.150863 | + | 0.150863i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.0000 | − | 12.0000i | 0.451306 | − | 0.451306i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.0000i | 0.450669i | 0.974281 | + | 0.225335i | \(0.0723476\pi\) | ||||
−0.974281 | + | 0.225335i | \(0.927652\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 80.0000i | − | 3.00023i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.00000 | + | 8.00000i | −0.299602 | + | 0.299602i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.0000 | + | 16.0000i | 0.597531 | + | 0.597531i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.00000 | −0.298350 | −0.149175 | − | 0.988811i | \(-0.547662\pi\) | ||||
−0.149175 | + | 0.988811i | \(0.547662\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | −0.893807 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.0000 | + | 32.0000i | 1.19009 | + | 1.19009i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.0000 | − | 18.0000i | 0.667583 | − | 0.667583i | −0.289573 | − | 0.957156i | \(-0.593513\pi\) |
0.957156 | + | 0.289573i | \(0.0935133\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 43.0000i | 1.59259i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 60.0000i | 2.21918i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.0000 | − | 21.0000i | 0.775653 | − | 0.775653i | −0.203436 | − | 0.979088i | \(-0.565211\pi\) |
0.979088 | + | 0.203436i | \(0.0652108\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.0000 | 1.61857 | 0.809283 | − | 0.587419i | \(-0.199856\pi\) | ||||
0.809283 | + | 0.587419i | \(0.199856\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.0000 | 0.587775 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.0000 | + | 30.0000i | 1.10059 | + | 1.10059i | 0.994339 | + | 0.106254i | \(0.0338857\pi\) |
0.106254 | + | 0.994339i | \(0.466114\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.0000 | + | 10.0000i | −0.365881 | + | 0.365881i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.0000i | 0.876941i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 44.0000i | − | 1.60558i | −0.596260 | − | 0.802791i | \(-0.703347\pi\) | ||
0.596260 | − | 0.802791i | \(-0.296653\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −48.0000 | + | 48.0000i | −1.74922 | + | 1.74922i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.00000 | − | 1.00000i | −0.0363456 | − | 0.0363456i | 0.688700 | − | 0.725046i | \(-0.258182\pi\) |
−0.725046 | + | 0.688700i | \(0.758182\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.0000 | −0.797499 | −0.398750 | − | 0.917060i | \(-0.630556\pi\) | ||||
−0.398750 | + | 0.917060i | \(0.630556\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.0000 | − | 20.0000i | −0.724049 | − | 0.724049i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.00000 | + | 4.00000i | −0.144432 | + | 0.144432i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.0000i | 1.44244i | 0.692708 | + | 0.721218i | \(0.256418\pi\) | ||||
−0.692708 | + | 0.721218i | \(0.743582\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.0000i | 1.00840i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.00000 | + | 1.00000i | −0.0359675 | + | 0.0359675i | −0.724862 | − | 0.688894i | \(-0.758096\pi\) |
0.688894 | + | 0.724862i | \(0.258096\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.00000 | − | 8.00000i | −0.286998 | − | 0.286998i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.0000 | + | 16.0000i | 0.571793 | + | 0.571793i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.0000 | + | 30.0000i | −1.06938 | + | 1.06938i | −0.0719783 | + | 0.997406i | \(0.522931\pi\) |
−0.997406 | + | 0.0719783i | \(0.977069\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 24.0000i | − | 0.854423i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 36.0000i | − | 1.28001i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.00000 | + | 4.00000i | −0.142044 | + | 0.142044i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) |