Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(1049,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.1049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.d (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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1049.2 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.1049 |
Dual form | 1050.2.d.b.1049.1 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.22474 | + | 1.22474i | −0.707107 | + | 0.707107i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.22474 | − | 1.22474i | 0.500000 | − | 0.500000i | ||||
\(7\) | −2.44949 | + | 1.00000i | −0.925820 | + | 0.377964i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | − | 3.00000i | − | 1.00000i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | −1.22474 | + | 1.22474i | −0.353553 | + | 0.353553i | ||||
\(13\) | −2.44949 | −0.679366 | −0.339683 | − | 0.940540i | \(-0.610320\pi\) | ||||
−0.339683 | + | 0.940540i | \(0.610320\pi\) | |||||||
\(14\) | 2.44949 | − | 1.00000i | 0.654654 | − | 0.267261i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 4.89898i | − | 1.18818i | −0.804400 | − | 0.594089i | \(-0.797513\pi\) | ||
0.804400 | − | 0.594089i | \(-0.202487\pi\) | |||||||
\(18\) | 3.00000i | 0.707107i | ||||||||
\(19\) | 2.44949i | 0.561951i | 0.959715 | + | 0.280976i | \(0.0906580\pi\) | ||||
−0.959715 | + | 0.280976i | \(0.909342\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.77526 | − | 4.22474i | 0.387392 | − | 0.921915i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.00000 | 1.25109 | 0.625543 | − | 0.780189i | \(-0.284877\pi\) | ||||
0.625543 | + | 0.780189i | \(0.284877\pi\) | |||||||
\(24\) | 1.22474 | − | 1.22474i | 0.250000 | − | 0.250000i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.44949 | 0.480384 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.707107 | + | 0.707107i | ||||
\(28\) | −2.44949 | + | 1.00000i | −0.462910 | + | 0.188982i | ||||
\(29\) | − | 6.00000i | − | 1.11417i | −0.830455 | − | 0.557086i | \(-0.811919\pi\) | ||
0.830455 | − | 0.557086i | \(-0.188081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.89898i | 0.840168i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | − | 3.00000i | − | 0.500000i | ||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | − | 2.44949i | − | 0.397360i | ||||||
\(39\) | 3.00000 | − | 3.00000i | 0.480384 | − | 0.480384i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.89898 | −0.765092 | −0.382546 | − | 0.923936i | \(-0.624953\pi\) | ||||
−0.382546 | + | 0.923936i | \(0.624953\pi\) | |||||||
\(42\) | −1.77526 | + | 4.22474i | −0.273928 | + | 0.651892i | ||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | − | 4.89898i | − | 0.714590i | −0.933992 | − | 0.357295i | \(-0.883699\pi\) | ||
0.933992 | − | 0.357295i | \(-0.116301\pi\) | |||||||
\(48\) | −1.22474 | + | 1.22474i | −0.176777 | + | 0.176777i | ||||
\(49\) | 5.00000 | − | 4.89898i | 0.714286 | − | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.00000 | + | 6.00000i | 0.840168 | + | 0.840168i | ||||
\(52\) | −2.44949 | −0.339683 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | −3.67423 | − | 3.67423i | −0.500000 | − | 0.500000i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.44949 | − | 1.00000i | 0.327327 | − | 0.133631i | ||||
\(57\) | −3.00000 | − | 3.00000i | −0.397360 | − | 0.397360i | ||||
\(58\) | 6.00000i | 0.787839i | ||||||||
\(59\) | 12.2474 | 1.59448 | 0.797241 | − | 0.603661i | \(-0.206292\pi\) | ||||
0.797241 | + | 0.603661i | \(0.206292\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.2474i | 1.56813i | 0.620682 | + | 0.784063i | \(0.286856\pi\) | ||||
−0.620682 | + | 0.784063i | \(0.713144\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.00000 | + | 7.34847i | 0.377964 | + | 0.925820i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.00000i | − | 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | − | 4.89898i | − | 0.594089i | ||||||
\(69\) | −7.34847 | + | 7.34847i | −0.884652 | + | 0.884652i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 3.00000i | 0.353553i | ||||||||
\(73\) | 9.79796 | 1.14676 | 0.573382 | − | 0.819288i | \(-0.305631\pi\) | ||||
0.573382 | + | 0.819288i | \(0.305631\pi\) | |||||||
\(74\) | − | 2.00000i | − | 0.232495i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.44949i | 0.280976i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.00000 | + | 3.00000i | −0.339683 | + | 0.339683i | ||||
\(79\) | 10.0000 | 1.12509 | 0.562544 | − | 0.826767i | \(-0.309823\pi\) | ||||
0.562544 | + | 0.826767i | \(0.309823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 4.89898 | 0.541002 | ||||||||
\(83\) | 2.44949i | 0.268866i | 0.990923 | + | 0.134433i | \(0.0429214\pi\) | ||||
−0.990923 | + | 0.134433i | \(0.957079\pi\) | |||||||
\(84\) | 1.77526 | − | 4.22474i | 0.193696 | − | 0.460957i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 4.00000i | − | 0.431331i | ||||||
\(87\) | 7.34847 | + | 7.34847i | 0.787839 | + | 0.787839i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | − | 2.44949i | 0.628971 | − | 0.256776i | ||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.89898i | 0.505291i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.22474 | − | 1.22474i | 0.125000 | − | 0.125000i | ||||
\(97\) | −4.89898 | −0.497416 | −0.248708 | − | 0.968579i | \(-0.580006\pi\) | ||||
−0.248708 | + | 0.968579i | \(0.580006\pi\) | |||||||
\(98\) | −5.00000 | + | 4.89898i | −0.505076 | + | 0.494872i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.34847 | 0.731200 | 0.365600 | − | 0.930772i | \(-0.380864\pi\) | ||||
0.365600 | + | 0.930772i | \(0.380864\pi\) | |||||||
\(102\) | −6.00000 | − | 6.00000i | −0.594089 | − | 0.594089i | ||||
\(103\) | 9.79796 | 0.965422 | 0.482711 | − | 0.875780i | \(-0.339652\pi\) | ||||
0.482711 | + | 0.875780i | \(0.339652\pi\) | |||||||
\(104\) | 2.44949 | 0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 3.67423 | + | 3.67423i | 0.353553 | + | 0.353553i | ||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.44949 | − | 2.44949i | −0.232495 | − | 0.232495i | ||||
\(112\) | −2.44949 | + | 1.00000i | −0.231455 | + | 0.0944911i | ||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 3.00000 | + | 3.00000i | 0.280976 | + | 0.280976i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 6.00000i | − | 0.557086i | ||||||
\(117\) | 7.34847i | 0.679366i | ||||||||
\(118\) | −12.2474 | −1.12747 | ||||||||
\(119\) | 4.89898 | + | 12.0000i | 0.449089 | + | 1.10004i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | − | 12.2474i | − | 1.10883i | ||||||
\(123\) | 6.00000 | − | 6.00000i | 0.541002 | − | 0.541002i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.00000 | − | 7.34847i | −0.267261 | − | 0.654654i | ||||
\(127\) | − | 8.00000i | − | 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.89898 | − | 4.89898i | −0.431331 | − | 0.431331i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.34847 | 0.642039 | 0.321019 | − | 0.947073i | \(-0.395975\pi\) | ||||
0.321019 | + | 0.947073i | \(0.395975\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.44949 | − | 6.00000i | −0.212398 | − | 0.520266i | ||||
\(134\) | 8.00000i | 0.691095i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.89898i | 0.420084i | ||||||||
\(137\) | 12.0000 | 1.02523 | 0.512615 | − | 0.858619i | \(-0.328677\pi\) | ||||
0.512615 | + | 0.858619i | \(0.328677\pi\) | |||||||
\(138\) | 7.34847 | − | 7.34847i | 0.625543 | − | 0.625543i | ||||
\(139\) | 2.44949i | 0.207763i | 0.994590 | + | 0.103882i | \(0.0331263\pi\) | ||||
−0.994590 | + | 0.103882i | \(0.966874\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | + | 6.00000i | 0.505291 | + | 0.505291i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | − | 3.00000i | − | 0.250000i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.79796 | −0.810885 | ||||||||
\(147\) | −0.123724 | + | 12.1237i | −0.0102046 | + | 0.999948i | ||||
\(148\) | 2.00000i | 0.164399i | ||||||||
\(149\) | − | 6.00000i | − | 0.491539i | −0.969328 | − | 0.245770i | \(-0.920959\pi\) | ||
0.969328 | − | 0.245770i | \(-0.0790407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | − | 2.44949i | − | 0.198680i | ||||||
\(153\) | −14.6969 | −1.18818 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.00000 | − | 3.00000i | 0.240192 | − | 0.240192i | ||||
\(157\) | 7.34847 | 0.586472 | 0.293236 | − | 0.956040i | \(-0.405268\pi\) | ||||
0.293236 | + | 0.956040i | \(0.405268\pi\) | |||||||
\(158\) | −10.0000 | −0.795557 | ||||||||
\(159\) | −7.34847 | + | 7.34847i | −0.582772 | + | 0.582772i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.6969 | + | 6.00000i | −1.15828 | + | 0.472866i | ||||
\(162\) | 9.00000 | 0.707107 | ||||||||
\(163\) | − | 16.0000i | − | 1.25322i | −0.779334 | − | 0.626608i | \(-0.784443\pi\) | ||
0.779334 | − | 0.626608i | \(-0.215557\pi\) | |||||||
\(164\) | −4.89898 | −0.382546 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 2.44949i | − | 0.190117i | ||||||
\(167\) | − | 4.89898i | − | 0.379094i | −0.981872 | − | 0.189547i | \(-0.939298\pi\) | ||
0.981872 | − | 0.189547i | \(-0.0607020\pi\) | |||||||
\(168\) | −1.77526 | + | 4.22474i | −0.136964 | + | 0.325946i | ||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.34847 | 0.561951 | ||||||||
\(172\) | 4.00000i | 0.304997i | ||||||||
\(173\) | − | 22.0454i | − | 1.67608i | −0.545608 | − | 0.838041i | \(-0.683701\pi\) | ||
0.545608 | − | 0.838041i | \(-0.316299\pi\) | |||||||
\(174\) | −7.34847 | − | 7.34847i | −0.557086 | − | 0.557086i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.0000 | + | 15.0000i | −1.12747 | + | 1.12747i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.0000i | 1.79384i | 0.442189 | + | 0.896922i | \(0.354202\pi\) | ||||
−0.442189 | + | 0.896922i | \(0.645798\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 12.2474i | − | 0.910346i | −0.890403 | − | 0.455173i | \(-0.849577\pi\) | ||
0.890403 | − | 0.455173i | \(-0.150423\pi\) | |||||||
\(182\) | −6.00000 | + | 2.44949i | −0.444750 | + | 0.181568i | ||||
\(183\) | −15.0000 | − | 15.0000i | −1.10883 | − | 1.10883i | ||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 4.89898i | − | 0.357295i | ||||||
\(189\) | −12.6742 | − | 5.32577i | −0.921915 | − | 0.387392i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | −1.22474 | + | 1.22474i | −0.0883883 | + | 0.0883883i | ||||
\(193\) | 4.00000i | 0.287926i | 0.989583 | + | 0.143963i | \(0.0459847\pi\) | ||||
−0.989583 | + | 0.143963i | \(0.954015\pi\) | |||||||
\(194\) | 4.89898 | 0.351726 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.00000 | − | 4.89898i | 0.357143 | − | 0.349927i | ||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.79796i | − | 0.694559i | −0.937762 | − | 0.347279i | \(-0.887106\pi\) | ||
0.937762 | − | 0.347279i | \(-0.112894\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.79796 | + | 9.79796i | 0.691095 | + | 0.691095i | ||||
\(202\) | −7.34847 | −0.517036 | ||||||||
\(203\) | 6.00000 | + | 14.6969i | 0.421117 | + | 1.03152i | ||||
\(204\) | 6.00000 | + | 6.00000i | 0.420084 | + | 0.420084i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.79796 | −0.682656 | ||||||||
\(207\) | − | 18.0000i | − | 1.25109i | ||||||
\(208\) | −2.44949 | −0.169842 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 6.00000 | 0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.0000 | −0.820303 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.67423 | − | 3.67423i | −0.250000 | − | 0.250000i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.0000 | 0.677285 | ||||||||
\(219\) | −12.0000 | + | 12.0000i | −0.810885 | + | 0.810885i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000i | 0.807207i | ||||||||
\(222\) | 2.44949 | + | 2.44949i | 0.164399 | + | 0.164399i | ||||
\(223\) | −14.6969 | −0.984180 | −0.492090 | − | 0.870544i | \(-0.663767\pi\) | ||||
−0.492090 | + | 0.870544i | \(0.663767\pi\) | |||||||
\(224\) | 2.44949 | − | 1.00000i | 0.163663 | − | 0.0668153i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 7.34847i | 0.487735i | 0.969809 | + | 0.243868i | \(0.0784162\pi\) | ||||
−0.969809 | + | 0.243868i | \(0.921584\pi\) | |||||||
\(228\) | −3.00000 | − | 3.00000i | −0.198680 | − | 0.198680i | ||||
\(229\) | − | 22.0454i | − | 1.45680i | −0.685151 | − | 0.728401i | \(-0.740264\pi\) | ||
0.685151 | − | 0.728401i | \(-0.259736\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.00000i | 0.393919i | ||||||||
\(233\) | −24.0000 | −1.57229 | −0.786146 | − | 0.618041i | \(-0.787927\pi\) | ||||
−0.786146 | + | 0.618041i | \(0.787927\pi\) | |||||||
\(234\) | − | 7.34847i | − | 0.480384i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.2474 | 0.797241 | ||||||||
\(237\) | −12.2474 | + | 12.2474i | −0.795557 | + | 0.795557i | ||||
\(238\) | −4.89898 | − | 12.0000i | −0.317554 | − | 0.777844i | ||||
\(239\) | − | 6.00000i | − | 0.388108i | −0.980991 | − | 0.194054i | \(-0.937836\pi\) | ||
0.980991 | − | 0.194054i | \(-0.0621637\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 24.4949i | − | 1.57786i | −0.614486 | − | 0.788928i | \(-0.710637\pi\) | ||
0.614486 | − | 0.788928i | \(-0.289363\pi\) | |||||||
\(242\) | −11.0000 | −0.707107 | ||||||||
\(243\) | 11.0227 | − | 11.0227i | 0.707107 | − | 0.707107i | ||||
\(244\) | 12.2474i | 0.784063i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | + | 6.00000i | −0.382546 | + | 0.382546i | ||||
\(247\) | − | 6.00000i | − | 0.381771i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.00000 | − | 3.00000i | −0.190117 | − | 0.190117i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.1464 | −1.08227 | −0.541136 | − | 0.840935i | \(-0.682006\pi\) | ||||
−0.541136 | + | 0.840935i | \(0.682006\pi\) | |||||||
\(252\) | 3.00000 | + | 7.34847i | 0.188982 | + | 0.462910i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 8.00000i | 0.501965i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 29.3939i | − | 1.83354i | −0.399416 | − | 0.916770i | \(-0.630787\pi\) | ||
0.399416 | − | 0.916770i | \(-0.369213\pi\) | |||||||
\(258\) | 4.89898 | + | 4.89898i | 0.304997 | + | 0.304997i | ||||
\(259\) | −2.00000 | − | 4.89898i | −0.124274 | − | 0.304408i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.0000 | −1.11417 | ||||||||
\(262\) | −7.34847 | −0.453990 | ||||||||
\(263\) | −24.0000 | −1.47990 | −0.739952 | − | 0.672660i | \(-0.765152\pi\) | ||||
−0.739952 | + | 0.672660i | \(0.765152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.44949 | + | 6.00000i | 0.150188 | + | 0.367884i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 8.00000i | − | 0.488678i | ||||||
\(269\) | 12.2474 | 0.746740 | 0.373370 | − | 0.927682i | \(-0.378202\pi\) | ||||
0.373370 | + | 0.927682i | \(0.378202\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.4949i | 1.48796i | 0.668202 | + | 0.743980i | \(0.267064\pi\) | ||||
−0.668202 | + | 0.743980i | \(0.732936\pi\) | |||||||
\(272\) | − | 4.89898i | − | 0.297044i | ||||||
\(273\) | −4.34847 | + | 10.3485i | −0.263181 | + | 0.626318i | ||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.34847 | + | 7.34847i | −0.442326 | + | 0.442326i | ||||
\(277\) | 22.0000i | 1.32185i | 0.750451 | + | 0.660926i | \(0.229836\pi\) | ||||
−0.750451 | + | 0.660926i | \(0.770164\pi\) | |||||||
\(278\) | − | 2.44949i | − | 0.146911i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | −6.00000 | − | 6.00000i | −0.357295 | − | 0.357295i | ||||
\(283\) | 22.0454 | 1.31046 | 0.655232 | − | 0.755428i | \(-0.272571\pi\) | ||||
0.655232 | + | 0.755428i | \(0.272571\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0000 | − | 4.89898i | 0.708338 | − | 0.289178i | ||||
\(288\) | 3.00000i | 0.176777i | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000 | − | 6.00000i | 0.351726 | − | 0.351726i | ||||
\(292\) | 9.79796 | 0.573382 | ||||||||
\(293\) | 2.44949i | 0.143101i | 0.997437 | + | 0.0715504i | \(0.0227947\pi\) | ||||
−0.997437 | + | 0.0715504i | \(0.977205\pi\) | |||||||
\(294\) | 0.123724 | − | 12.1237i | 0.00721575 | − | 0.707070i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 2.00000i | − | 0.116248i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000i | 0.347571i | ||||||||
\(299\) | −14.6969 | −0.849946 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00000 | − | 9.79796i | −0.230556 | − | 0.564745i | ||||
\(302\) | 8.00000 | 0.460348 | ||||||||
\(303\) | −9.00000 | + | 9.00000i | −0.517036 | + | 0.517036i | ||||
\(304\) | 2.44949i | 0.140488i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 14.6969 | 0.840168 | ||||||||
\(307\) | 7.34847 | 0.419399 | 0.209700 | − | 0.977766i | \(-0.432751\pi\) | ||||
0.209700 | + | 0.977766i | \(0.432751\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.0000 | + | 12.0000i | −0.682656 | + | 0.682656i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.5959 | 1.11118 | 0.555591 | − | 0.831456i | \(-0.312492\pi\) | ||||
0.555591 | + | 0.831456i | \(0.312492\pi\) | |||||||
\(312\) | −3.00000 | + | 3.00000i | −0.169842 | + | 0.169842i | ||||
\(313\) | 34.2929 | 1.93835 | 0.969173 | − | 0.246380i | \(-0.0792410\pi\) | ||||
0.969173 | + | 0.246380i | \(0.0792410\pi\) | |||||||
\(314\) | −7.34847 | −0.414698 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | −18.0000 | −1.01098 | −0.505490 | − | 0.862832i | \(-0.668688\pi\) | ||||
−0.505490 | + | 0.862832i | \(0.668688\pi\) | |||||||
\(318\) | 7.34847 | − | 7.34847i | 0.412082 | − | 0.412082i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.6969 | + | 14.6969i | −0.820303 | + | 0.820303i | ||||
\(322\) | 14.6969 | − | 6.00000i | 0.819028 | − | 0.334367i | ||||
\(323\) | 12.0000 | 0.667698 | ||||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.0000i | 0.886158i | ||||||||
\(327\) | 12.2474 | − | 12.2474i | 0.677285 | − | 0.677285i | ||||
\(328\) | 4.89898 | 0.270501 | ||||||||
\(329\) | 4.89898 | + | 12.0000i | 0.270089 | + | 0.661581i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 2.44949i | 0.134433i | ||||||||
\(333\) | 6.00000 | 0.328798 | ||||||||
\(334\) | 4.89898i | 0.268060i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.77526 | − | 4.22474i | 0.0968481 | − | 0.230479i | ||||
\(337\) | 32.0000i | 1.74315i | 0.490261 | + | 0.871576i | \(0.336901\pi\) | ||||
−0.490261 | + | 0.871576i | \(0.663099\pi\) | |||||||
\(338\) | 7.00000 | 0.380750 | ||||||||
\(339\) | −7.34847 | + | 7.34847i | −0.399114 | + | 0.399114i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −7.34847 | −0.397360 | ||||||||
\(343\) | −7.34847 | + | 17.0000i | −0.396780 | + | 0.917914i | ||||
\(344\) | − | 4.00000i | − | 0.215666i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.0454i | 1.18517i | ||||||||
\(347\) | 12.0000 | 0.644194 | 0.322097 | − | 0.946707i | \(-0.395612\pi\) | ||||
0.322097 | + | 0.946707i | \(0.395612\pi\) | |||||||
\(348\) | 7.34847 | + | 7.34847i | 0.393919 | + | 0.393919i | ||||
\(349\) | 2.44949i | 0.131118i | 0.997849 | + | 0.0655591i | \(0.0208831\pi\) | ||||
−0.997849 | + | 0.0655591i | \(0.979117\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.00000 | − | 9.00000i | −0.480384 | − | 0.480384i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 9.79796i | − | 0.521493i | −0.965407 | − | 0.260746i | \(-0.916031\pi\) | ||
0.965407 | − | 0.260746i | \(-0.0839686\pi\) | |||||||
\(354\) | 15.0000 | − | 15.0000i | 0.797241 | − | 0.797241i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −20.6969 | − | 8.69694i | −1.09540 | − | 0.460291i | ||||
\(358\) | − | 24.0000i | − | 1.26844i | ||||||
\(359\) | − | 6.00000i | − | 0.316668i | −0.987386 | − | 0.158334i | \(-0.949388\pi\) | ||
0.987386 | − | 0.158334i | \(-0.0506123\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 12.2474i | 0.643712i | ||||||||
\(363\) | −13.4722 | + | 13.4722i | −0.707107 | + | 0.707107i | ||||
\(364\) | 6.00000 | − | 2.44949i | 0.314485 | − | 0.128388i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 15.0000 | + | 15.0000i | 0.784063 | + | 0.784063i | ||||
\(367\) | −4.89898 | −0.255725 | −0.127862 | − | 0.991792i | \(-0.540812\pi\) | ||||
−0.127862 | + | 0.991792i | \(0.540812\pi\) | |||||||
\(368\) | 6.00000 | 0.312772 | ||||||||
\(369\) | 14.6969i | 0.765092i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.6969 | + | 6.00000i | −0.763027 | + | 0.311504i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.0000i | 0.724893i | 0.932005 | + | 0.362446i | \(0.118058\pi\) | ||||
−0.932005 | + | 0.362446i | \(0.881942\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.89898i | 0.252646i | ||||||||
\(377\) | 14.6969i | 0.756931i | ||||||||
\(378\) | 12.6742 | + | 5.32577i | 0.651892 | + | 0.273928i | ||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.79796 | + | 9.79796i | 0.501965 | + | 0.501965i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 34.2929i | − | 1.75228i | −0.482054 | − | 0.876142i | \(-0.660109\pi\) | ||
0.482054 | − | 0.876142i | \(-0.339891\pi\) | |||||||
\(384\) | 1.22474 | − | 1.22474i | 0.0625000 | − | 0.0625000i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 4.00000i | − | 0.203595i | ||||||
\(387\) | 12.0000 | 0.609994 | ||||||||
\(388\) | −4.89898 | −0.248708 | ||||||||
\(389\) | − | 6.00000i | − | 0.304212i | −0.988364 | − | 0.152106i | \(-0.951394\pi\) | ||
0.988364 | − | 0.152106i | \(-0.0486055\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 29.3939i | − | 1.48651i | ||||||
\(392\) | −5.00000 | + | 4.89898i | −0.252538 | + | 0.247436i | ||||
\(393\) | −9.00000 | + | 9.00000i | −0.453990 | + | 0.453990i | ||||
\(394\) | 18.0000 | 0.906827 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.34847 | 0.368809 | 0.184405 | − | 0.982850i | \(-0.440964\pi\) | ||||
0.184405 | + | 0.982850i | \(0.440964\pi\) | |||||||
\(398\) | 9.79796i | 0.491127i | ||||||||
\(399\) | 10.3485 | + | 4.34847i | 0.518071 | + | 0.217696i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 30.0000i | − | 1.49813i | −0.662497 | − | 0.749064i | \(-0.730503\pi\) | ||
0.662497 | − | 0.749064i | \(-0.269497\pi\) | |||||||
\(402\) | −9.79796 | − | 9.79796i | −0.488678 | − | 0.488678i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 7.34847 | 0.365600 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.00000 | − | 14.6969i | −0.297775 | − | 0.729397i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −6.00000 | − | 6.00000i | −0.297044 | − | 0.297044i | ||||
\(409\) | − | 34.2929i | − | 1.69567i | −0.530258 | − | 0.847836i | \(-0.677905\pi\) | ||
0.530258 | − | 0.847836i | \(-0.322095\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.6969 | + | 14.6969i | −0.724947 | + | 0.724947i | ||||
\(412\) | 9.79796 | 0.482711 | ||||||||
\(413\) | −30.0000 | + | 12.2474i | −1.47620 | + | 0.602658i | ||||
\(414\) | 18.0000i | 0.884652i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.44949 | 0.120096 | ||||||||
\(417\) | −3.00000 | − | 3.00000i | −0.146911 | − | 0.146911i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.2474 | −0.598327 | −0.299164 | − | 0.954202i | \(-0.596708\pi\) | ||||
−0.299164 | + | 0.954202i | \(0.596708\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000 | 0.0974740 | 0.0487370 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487370 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(422\) | 8.00000 | 0.389434 | ||||||||
\(423\) | −14.6969 | −0.714590 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.2474 | − | 30.0000i | −0.592696 | − | 1.45180i | ||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 30.0000i | − | 1.44505i | −0.691345 | − | 0.722525i | \(-0.742982\pi\) | ||
0.691345 | − | 0.722525i | \(-0.257018\pi\) | |||||||
\(432\) | 3.67423 | + | 3.67423i | 0.176777 | + | 0.176777i | ||||
\(433\) | −14.6969 | −0.706290 | −0.353145 | − | 0.935569i | \(-0.614888\pi\) | ||||
−0.353145 | + | 0.935569i | \(0.614888\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.0000 | −0.478913 | ||||||||
\(437\) | 14.6969i | 0.703050i | ||||||||
\(438\) | 12.0000 | − | 12.0000i | 0.573382 | − | 0.573382i | ||||
\(439\) | 14.6969i | 0.701447i | 0.936479 | + | 0.350723i | \(0.114064\pi\) | ||||
−0.936479 | + | 0.350723i | \(0.885936\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.6969 | − | 15.0000i | −0.699854 | − | 0.714286i | ||||
\(442\) | − | 12.0000i | − | 0.570782i | ||||||
\(443\) | 36.0000 | 1.71041 | 0.855206 | − | 0.518289i | \(-0.173431\pi\) | ||||
0.855206 | + | 0.518289i | \(0.173431\pi\) | |||||||
\(444\) | −2.44949 | − | 2.44949i | −0.116248 | − | 0.116248i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.6969 | 0.695920 | ||||||||
\(447\) | 7.34847 | + | 7.34847i | 0.347571 | + | 0.347571i | ||||
\(448\) | −2.44949 | + | 1.00000i | −0.115728 | + | 0.0472456i | ||||
\(449\) | − | 36.0000i | − | 1.69895i | −0.527633 | − | 0.849473i | \(-0.676920\pi\) | ||
0.527633 | − | 0.849473i | \(-0.323080\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | 9.79796 | − | 9.79796i | 0.460348 | − | 0.460348i | ||||
\(454\) | − | 7.34847i | − | 0.344881i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.00000 | + | 3.00000i | 0.140488 | + | 0.140488i | ||||
\(457\) | − | 28.0000i | − | 1.30978i | −0.755722 | − | 0.654892i | \(-0.772714\pi\) | ||
0.755722 | − | 0.654892i | \(-0.227286\pi\) | |||||||
\(458\) | 22.0454i | 1.03011i | ||||||||
\(459\) | 18.0000 | − | 18.0000i | 0.840168 | − | 0.840168i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.8434 | 1.48309 | 0.741547 | − | 0.670901i | \(-0.234093\pi\) | ||||
0.741547 | + | 0.670901i | \(0.234093\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0000i | 0.650635i | 0.945605 | + | 0.325318i | \(0.105471\pi\) | ||||
−0.945605 | + | 0.325318i | \(0.894529\pi\) | |||||||
\(464\) | − | 6.00000i | − | 0.278543i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.0000 | 1.11178 | ||||||||
\(467\) | 7.34847i | 0.340047i | 0.985440 | + | 0.170023i | \(0.0543843\pi\) | ||||
−0.985440 | + | 0.170023i | \(0.945616\pi\) | |||||||
\(468\) | 7.34847i | 0.339683i | ||||||||
\(469\) | 8.00000 | + | 19.5959i | 0.369406 | + | 0.904855i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.00000 | + | 9.00000i | −0.414698 | + | 0.414698i | ||||
\(472\) | −12.2474 | −0.563735 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 12.2474 | − | 12.2474i | 0.562544 | − | 0.562544i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.89898 | + | 12.0000i | 0.224544 | + | 0.550019i | ||||
\(477\) | − | 18.0000i | − | 0.824163i | ||||||
\(478\) | 6.00000i | 0.274434i | ||||||||
\(479\) | −24.4949 | −1.11920 | −0.559600 | − | 0.828763i | \(-0.689045\pi\) | ||||
−0.559600 | + | 0.828763i | \(0.689045\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 4.89898i | − | 0.223374i | ||||||
\(482\) | 24.4949i | 1.11571i | ||||||||
\(483\) | 10.6515 | − | 25.3485i | 0.484661 | − | 1.15340i | ||||
\(484\) | 11.0000 | 0.500000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −11.0227 | + | 11.0227i | −0.500000 | + | 0.500000i | ||||
\(487\) | 32.0000i | 1.45006i | 0.688718 | + | 0.725029i | \(0.258174\pi\) | ||||
−0.688718 | + | 0.725029i | \(0.741826\pi\) | |||||||
\(488\) | − | 12.2474i | − | 0.554416i | ||||||
\(489\) | 19.5959 | + | 19.5959i | 0.886158 | + | 0.886158i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 6.00000 | − | 6.00000i | 0.270501 | − | 0.270501i | ||||
\(493\) | −29.3939 | −1.32383 | ||||||||
\(494\) | 6.00000i | 0.269953i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.00000 | + | 3.00000i | 0.134433 | + | 0.134433i | ||||
\(499\) | 20.0000 | 0.895323 | 0.447661 | − | 0.894203i | \(-0.352257\pi\) | ||||
0.447661 | + | 0.894203i | \(0.352257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000 | + | 6.00000i | 0.268060 | + | 0.268060i | ||||
\(502\) | 17.1464 | 0.765283 | ||||||||
\(503\) | 39.1918i | 1.74748i | 0.486395 | + | 0.873739i | \(0.338311\pi\) | ||||
−0.486395 | + | 0.873739i | \(0.661689\pi\) | |||||||
\(504\) | −3.00000 | − | 7.34847i | −0.133631 | − | 0.327327i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.57321 | − | 8.57321i | 0.380750 | − | 0.380750i | ||||
\(508\) | − | 8.00000i | − | 0.354943i | ||||||
\(509\) | 12.2474 | 0.542859 | 0.271429 | − | 0.962458i | \(-0.412504\pi\) | ||||
0.271429 | + | 0.962458i | \(0.412504\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.0000 | + | 9.79796i | −1.06170 | + | 0.433436i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −9.00000 | + | 9.00000i | −0.397360 | + | 0.397360i | ||||
\(514\) | 29.3939i | 1.29651i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.89898 | − | 4.89898i | −0.215666 | − | 0.215666i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.00000 | + | 4.89898i | 0.0878750 | + | 0.215249i | ||||
\(519\) | 27.0000 | + | 27.0000i | 1.18517 | + | 1.18517i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.89898 | −0.214628 | −0.107314 | − | 0.994225i | \(-0.534225\pi\) | ||||
−0.107314 | + | 0.994225i | \(0.534225\pi\) | |||||||
\(522\) | 18.0000 | 0.787839 | ||||||||
\(523\) | −2.44949 | −0.107109 | −0.0535544 | − | 0.998565i | \(-0.517055\pi\) | ||||
−0.0535544 | + | 0.998565i | \(0.517055\pi\) | |||||||
\(524\) | 7.34847 | 0.321019 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 36.7423i | − | 1.59448i | ||||||
\(532\) | −2.44949 | − | 6.00000i | −0.106199 | − | 0.260133i | ||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.00000i | 0.345547i | ||||||||
\(537\) | −29.3939 | − | 29.3939i | −1.26844 | − | 1.26844i | ||||
\(538\) | −12.2474 | −0.528025 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | − | 24.4949i | − | 1.05215i | ||||||
\(543\) | 15.0000 | + | 15.0000i | 0.643712 | + | 0.643712i | ||||
\(544\) | 4.89898i | 0.210042i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.34847 | − | 10.3485i | 0.186097 | − | 0.442874i | ||||
\(547\) | − | 8.00000i | − | 0.342055i | −0.985266 | − | 0.171028i | \(-0.945291\pi\) | ||
0.985266 | − | 0.171028i | \(-0.0547087\pi\) | |||||||
\(548\) | 12.0000 | 0.512615 | ||||||||
\(549\) | 36.7423 | 1.56813 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.6969 | 0.626111 | ||||||||
\(552\) | 7.34847 | − | 7.34847i | 0.312772 | − | 0.312772i | ||||
\(553\) | −24.4949 | + | 10.0000i | −1.04163 | + | 0.425243i | ||||
\(554\) | − | 22.0000i | − | 0.934690i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.44949i | 0.103882i | ||||||||
\(557\) | −18.0000 | −0.762684 | −0.381342 | − | 0.924434i | \(-0.624538\pi\) | ||||
−0.381342 | + | 0.924434i | \(0.624538\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.79796i | − | 0.414410i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 22.0454i | − | 0.929103i | −0.885546 | − | 0.464552i | \(-0.846216\pi\) | ||
0.885546 | − | 0.464552i | \(-0.153784\pi\) | |||||||
\(564\) | 6.00000 | + | 6.00000i | 0.252646 | + | 0.252646i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −22.0454 | −0.926638 | ||||||||
\(567\) | 22.0454 | − | 9.00000i | 0.925820 | − | 0.377964i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 6.00000i | − | 0.251533i | −0.992060 | − | 0.125767i | \(-0.959861\pi\) | ||
0.992060 | − | 0.125767i | \(-0.0401390\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.0000 | + | 4.89898i | −0.500870 | + | 0.204479i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | − | 3.00000i | − | 0.125000i | ||||||
\(577\) | 19.5959 | 0.815789 | 0.407894 | − | 0.913029i | \(-0.366263\pi\) | ||||
0.407894 | + | 0.913029i | \(0.366263\pi\) | |||||||
\(578\) | 7.00000 | 0.291162 | ||||||||
\(579\) | −4.89898 | − | 4.89898i | −0.203595 | − | 0.203595i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.44949 | − | 6.00000i | −0.101622 | − | 0.248922i | ||||
\(582\) | −6.00000 | + | 6.00000i | −0.248708 | + | 0.248708i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −9.79796 | −0.405442 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 2.44949i | − | 0.101187i | ||||||
\(587\) | 7.34847i | 0.303304i | 0.988434 | + | 0.151652i | \(0.0484593\pi\) | ||||
−0.988434 | + | 0.151652i | \(0.951541\pi\) | |||||||
\(588\) | −0.123724 | + | 12.1237i | −0.00510231 | + | 0.499974i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.0454 | − | 22.0454i | 0.906827 | − | 0.906827i | ||||
\(592\) | 2.00000i | 0.0821995i | ||||||||
\(593\) | 39.1918i | 1.60942i | 0.593671 | + | 0.804708i | \(0.297678\pi\) | ||||
−0.593671 | + | 0.804708i | \(0.702322\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 6.00000i | − | 0.245770i | ||||||
\(597\) | 12.0000 | + | 12.0000i | 0.491127 | + | 0.491127i | ||||
\(598\) | 14.6969 | 0.601003 | ||||||||
\(599\) | 24.0000i | 0.980613i | 0.871550 | + | 0.490307i | \(0.163115\pi\) | ||||
−0.871550 | + | 0.490307i | \(0.836885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 4.00000 | + | 9.79796i | 0.163028 | + | 0.399335i | ||||
\(603\) | −24.0000 | −0.977356 | ||||||||
\(604\) | −8.00000 | −0.325515 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.00000 | − | 9.00000i | 0.365600 | − | 0.365600i | ||||
\(607\) | −4.89898 | −0.198843 | −0.0994217 | − | 0.995045i | \(-0.531699\pi\) | ||||
−0.0994217 | + | 0.995045i | \(0.531699\pi\) | |||||||
\(608\) | − | 2.44949i | − | 0.0993399i | ||||||
\(609\) | −25.3485 | − | 10.6515i | −1.02717 | − | 0.431622i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0000i | 0.485468i | ||||||||
\(612\) | −14.6969 | −0.594089 | ||||||||
\(613\) | 14.0000i | 0.565455i | 0.959200 | + | 0.282727i | \(0.0912392\pi\) | ||||
−0.959200 | + | 0.282727i | \(0.908761\pi\) | |||||||
\(614\) | −7.34847 | −0.296560 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.0000 | −0.724653 | −0.362326 | − | 0.932051i | \(-0.618017\pi\) | ||||
−0.362326 | + | 0.932051i | \(0.618017\pi\) | |||||||
\(618\) | 12.0000 | − | 12.0000i | 0.482711 | − | 0.482711i | ||||
\(619\) | 26.9444i | 1.08299i | 0.840705 | + | 0.541493i | \(0.182141\pi\) | ||||
−0.840705 | + | 0.541493i | \(0.817859\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.0454 | + | 22.0454i | 0.884652 | + | 0.884652i | ||||
\(622\) | −19.5959 | −0.785725 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.00000 | − | 3.00000i | 0.120096 | − | 0.120096i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −34.2929 | −1.37062 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.34847 | 0.293236 | ||||||||
\(629\) | 9.79796 | 0.390670 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000 | 0.0796187 | 0.0398094 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398094 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(632\) | −10.0000 | −0.397779 | ||||||||
\(633\) | 9.79796 | − | 9.79796i | 0.389434 | − | 0.389434i | ||||
\(634\) | 18.0000 | 0.714871 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.34847 | + | 7.34847i | −0.291386 | + | 0.291386i | ||||
\(637\) | −12.2474 | + | 12.0000i | −0.485262 | + | 0.475457i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.0000i | 1.18493i | 0.805597 | + | 0.592464i | \(0.201845\pi\) | ||||
−0.805597 | + | 0.592464i | \(0.798155\pi\) | |||||||
\(642\) | 14.6969 | − | 14.6969i | 0.580042 | − | 0.580042i | ||||
\(643\) | 22.0454 | 0.869386 | 0.434693 | − | 0.900579i | \(-0.356857\pi\) | ||||
0.434693 | + | 0.900579i | \(0.356857\pi\) | |||||||
\(644\) | −14.6969 | + | 6.00000i | −0.579141 | + | 0.236433i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0000 | −0.472134 | ||||||||
\(647\) | 44.0908i | 1.73339i | 0.498839 | + | 0.866694i | \(0.333760\pi\) | ||||
−0.498839 | + | 0.866694i | \(0.666240\pi\) | |||||||
\(648\) | 9.00000 | 0.353553 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 16.0000i | − | 0.626608i | ||||||
\(653\) | 6.00000 | 0.234798 | 0.117399 | − | 0.993085i | \(-0.462544\pi\) | ||||
0.117399 | + | 0.993085i | \(0.462544\pi\) | |||||||
\(654\) | −12.2474 | + | 12.2474i | −0.478913 | + | 0.478913i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.89898 | −0.191273 | ||||||||
\(657\) | − | 29.3939i | − | 1.14676i | ||||||
\(658\) | −4.89898 | − | 12.0000i | −0.190982 | − | 0.467809i | ||||
\(659\) | − | 36.0000i | − | 1.40236i | −0.712984 | − | 0.701180i | \(-0.752657\pi\) | ||
0.712984 | − | 0.701180i | \(-0.247343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 12.2474i | − | 0.476371i | −0.971220 | − | 0.238185i | \(-0.923447\pi\) | ||
0.971220 | − | 0.238185i | \(-0.0765525\pi\) | |||||||
\(662\) | 8.00000 | 0.310929 | ||||||||
\(663\) | −14.6969 | − | 14.6969i | −0.570782 | − | 0.570782i | ||||
\(664\) | − | 2.44949i | − | 0.0950586i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.00000 | −0.232495 | ||||||||
\(667\) | − | 36.0000i | − | 1.39393i | ||||||
\(668\) | − | 4.89898i | − | 0.189547i | ||||||
\(669\) | 18.0000 | − | 18.0000i | 0.695920 | − | 0.695920i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.77526 | + | 4.22474i | −0.0684820 | + | 0.162973i | ||||
\(673\) | 34.0000i | 1.31060i | 0.755367 | + | 0.655302i | \(0.227459\pi\) | ||||
−0.755367 | + | 0.655302i | \(0.772541\pi\) | |||||||
\(674\) | − | 32.0000i | − | 1.23259i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.00000 | −0.269231 | ||||||||
\(677\) | 7.34847i | 0.282425i | 0.989979 | + | 0.141212i | \(0.0451000\pi\) | ||||
−0.989979 | + | 0.141212i | \(0.954900\pi\) | |||||||
\(678\) | 7.34847 | − | 7.34847i | 0.282216 | − | 0.282216i | ||||
\(679\) | 12.0000 | − | 4.89898i | 0.460518 | − | 0.188006i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.00000 | − | 9.00000i | −0.344881 | − | 0.344881i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.0000 | −0.918334 | −0.459167 | − | 0.888350i | \(-0.651852\pi\) | ||||
−0.459167 | + | 0.888350i | \(0.651852\pi\) | |||||||
\(684\) | 7.34847 | 0.280976 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.34847 | − | 17.0000i | 0.280566 | − | 0.649063i | ||||
\(687\) | 27.0000 | + | 27.0000i | 1.03011 | + | 1.03011i | ||||
\(688\) | 4.00000i | 0.152499i | ||||||||
\(689\) | −14.6969 | −0.559909 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.7423i | 1.39774i | 0.715246 | + | 0.698872i | \(0.246314\pi\) | ||||
−0.715246 | + | 0.698872i | \(0.753686\pi\) | |||||||
\(692\) | − | 22.0454i | − | 0.838041i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.34847 | − | 7.34847i | −0.278543 | − | 0.278543i | ||||
\(697\) | 24.0000i | 0.909065i | ||||||||
\(698\) | − | 2.44949i | − | 0.0927146i | ||||||
\(699\) | 29.3939 | − | 29.3939i | 1.11178 | − | 1.11178i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 30.0000i | − | 1.13308i | −0.824033 | − | 0.566542i | \(-0.808281\pi\) | ||
0.824033 | − | 0.566542i | \(-0.191719\pi\) | |||||||
\(702\) | 9.00000 | + | 9.00000i | 0.339683 | + | 0.339683i | ||||
\(703\) | −4.89898 | −0.184769 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.79796i | 0.368751i | ||||||||
\(707\) | −18.0000 | + | 7.34847i | −0.676960 | + | 0.276368i | ||||
\(708\) | −15.0000 | + | 15.0000i | −0.563735 | + | 0.563735i | ||||
\(709\) | −10.0000 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 30.0000i | − | 1.12509i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 20.6969 | + | 8.69694i | 0.774563 | + | 0.325475i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.0000i | 0.896922i | ||||||||
\(717\) | 7.34847 | + | 7.34847i | 0.274434 | + | 0.274434i | ||||
\(718\) | 6.00000i | 0.223918i | ||||||||
\(719\) | −24.4949 | −0.913506 | −0.456753 | − | 0.889594i | \(-0.650988\pi\) | ||||
−0.456753 | + | 0.889594i | \(0.650988\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | + | 9.79796i | −0.893807 | + | 0.364895i | ||||
\(722\) | −13.0000 | −0.483810 | ||||||||
\(723\) | 30.0000 | + | 30.0000i | 1.11571 | + | 1.11571i | ||||
\(724\) | − | 12.2474i | − | 0.455173i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13.4722 | − | 13.4722i | 0.500000 | − | 0.500000i | ||||
\(727\) | −29.3939 | −1.09016 | −0.545079 | − | 0.838385i | \(-0.683500\pi\) | ||||
−0.545079 | + | 0.838385i | \(0.683500\pi\) | |||||||
\(728\) | −6.00000 | + | 2.44949i | −0.222375 | + | 0.0907841i | ||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.5959 | 0.724781 | ||||||||
\(732\) | −15.0000 | − | 15.0000i | −0.554416 | − | 0.554416i | ||||
\(733\) | 22.0454 | 0.814266 | 0.407133 | − | 0.913369i | \(-0.366529\pi\) | ||||
0.407133 | + | 0.913369i | \(0.366529\pi\) | |||||||
\(734\) | 4.89898 | 0.180825 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 14.6969i | − | 0.541002i | ||||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.34847 | + | 7.34847i | 0.269953 | + | 0.269953i | ||||
\(742\) | 14.6969 | − | 6.00000i | 0.539542 | − | 0.220267i | ||||
\(743\) | 6.00000 | 0.220119 | 0.110059 | − | 0.993925i | \(-0.464896\pi\) | ||||
0.110059 | + | 0.993925i | \(0.464896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 14.0000i | − | 0.512576i | ||||||
\(747\) | 7.34847 | 0.268866 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.3939 | + | 12.0000i | −1.07403 | + | 0.438470i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.00000 | −0.291924 | −0.145962 | − | 0.989290i | \(-0.546628\pi\) | ||||
−0.145962 | + | 0.989290i | \(0.546628\pi\) | |||||||
\(752\) | − | 4.89898i | − | 0.178647i | ||||||
\(753\) | 21.0000 | − | 21.0000i | 0.765283 | − | 0.765283i | ||||
\(754\) | − | 14.6969i | − | 0.535231i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −12.6742 | − | 5.32577i | −0.460957 | − | 0.193696i | ||||
\(757\) | 2.00000i | 0.0726912i | 0.999339 | + | 0.0363456i | \(0.0115717\pi\) | ||||
−0.999339 | + | 0.0363456i | \(0.988428\pi\) | |||||||
\(758\) | −20.0000 | −0.726433 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.89898 | −0.177588 | −0.0887939 | − | 0.996050i | \(-0.528301\pi\) | ||||
−0.0887939 | + | 0.996050i | \(0.528301\pi\) | |||||||
\(762\) | −9.79796 | − | 9.79796i | −0.354943 | − | 0.354943i | ||||
\(763\) | 24.4949 | − | 10.0000i | 0.886775 | − | 0.362024i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.2929i | 1.23905i | ||||||||
\(767\) | −30.0000 | −1.08324 | ||||||||
\(768\) | −1.22474 | + | 1.22474i | −0.0441942 | + | 0.0441942i | ||||
\(769\) | − | 34.2929i | − | 1.23663i | −0.785930 | − | 0.618316i | \(-0.787815\pi\) | ||
0.785930 | − | 0.618316i | \(-0.212185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.0000 | + | 36.0000i | 1.29651 | + | 1.29651i | ||||
\(772\) | 4.00000i | 0.143963i | ||||||||
\(773\) | 26.9444i | 0.969122i | 0.874757 | + | 0.484561i | \(0.161021\pi\) | ||||
−0.874757 | + | 0.484561i | \(0.838979\pi\) | |||||||
\(774\) | −12.0000 | −0.431331 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.89898 | 0.175863 | ||||||||
\(777\) | 8.44949 | + | 3.55051i | 0.303124 | + | 0.127374i | ||||
\(778\) | 6.00000i | 0.215110i | ||||||||
\(779\) | − | 12.0000i | − | 0.429945i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 29.3939i | 1.05112i | ||||||||
\(783\) | 22.0454 | − | 22.0454i | 0.787839 | − | 0.787839i | ||||
\(784\) | 5.00000 | − | 4.89898i | 0.178571 | − | 0.174964i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.00000 | − | 9.00000i | 0.321019 | − | 0.321019i | ||||
\(787\) | 31.8434 | 1.13509 | 0.567547 | − | 0.823341i | \(-0.307893\pi\) | ||||
0.567547 | + | 0.823341i | \(0.307893\pi\) | |||||||
\(788\) | −18.0000 | −0.641223 | ||||||||
\(789\) | 29.3939 | − | 29.3939i | 1.04645 | − | 1.04645i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.6969 | + | 6.00000i | −0.522563 | + | 0.213335i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 30.0000i | − | 1.06533i | ||||||
\(794\) | −7.34847 | −0.260787 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 9.79796i | − | 0.347279i | ||||||
\(797\) | 7.34847i | 0.260296i | 0.991495 | + | 0.130148i | \(0.0415453\pi\) | ||||
−0.991495 | + | 0.130148i | \(0.958455\pi\) | |||||||
\(798\) | −10.3485 | − | 4.34847i | −0.366332 | − | 0.153934i | ||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 30.0000i | 1.05934i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 9.79796 | + | 9.79796i | 0.345547 | + | 0.345547i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.0000 | + | 15.0000i | −0.528025 | + | 0.528025i | ||||
\(808\) | −7.34847 | −0.258518 | ||||||||
\(809\) | − | 6.00000i | − | 0.210949i | −0.994422 | − | 0.105474i | \(-0.966364\pi\) | ||
0.994422 | − | 0.105474i | \(-0.0336361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.7423i | 1.29020i | 0.764099 | + | 0.645099i | \(0.223184\pi\) | ||||
−0.764099 | + | 0.645099i | \(0.776816\pi\) | |||||||
\(812\) | 6.00000 | + | 14.6969i | 0.210559 | + | 0.515761i | ||||
\(813\) | −30.0000 | − | 30.0000i | −1.05215 | − | 1.05215i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.00000 | + | 6.00000i | 0.210042 | + | 0.210042i | ||||
\(817\) | −9.79796 | −0.342787 | ||||||||
\(818\) | 34.2929i | 1.19902i | ||||||||
\(819\) | −7.34847 | − | 18.0000i | −0.256776 | − | 0.628971i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.0000i | 1.04701i | 0.852023 | + | 0.523504i | \(0.175375\pi\) | ||||
−0.852023 | + | 0.523504i | \(0.824625\pi\) | |||||||
\(822\) | 14.6969 | − | 14.6969i | 0.512615 | − | 0.512615i | ||||
\(823\) | 14.0000i | 0.488009i | 0.969774 | + | 0.244005i | \(0.0784612\pi\) | ||||
−0.969774 | + | 0.244005i | \(0.921539\pi\) | |||||||
\(824\) | −9.79796 | −0.341328 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 30.0000 | − | 12.2474i | 1.04383 | − | 0.426143i | ||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | − | 18.0000i | − | 0.625543i | ||||||
\(829\) | 26.9444i | 0.935817i | 0.883777 | + | 0.467909i | \(0.154992\pi\) | ||||
−0.883777 | + | 0.467909i | \(0.845008\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.9444 | − | 26.9444i | −0.934690 | − | 0.934690i | ||||
\(832\) | −2.44949 | −0.0849208 | ||||||||
\(833\) | −24.0000 | − | 24.4949i | −0.831551 | − | 0.848698i | ||||
\(834\) | 3.00000 | + | 3.00000i | 0.103882 | + | 0.103882i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.2474 | 0.423081 | ||||||||
\(839\) | 24.4949 | 0.845658 | 0.422829 | − | 0.906210i | \(-0.361037\pi\) | ||||
0.422829 | + | 0.906210i | \(0.361037\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | −2.00000 | −0.0689246 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.00000 | −0.275371 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 14.6969 | 0.505291 | ||||||||
\(847\) | −26.9444 | + | 11.0000i | −0.925820 | + | 0.377964i | ||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | −27.0000 | + | 27.0000i | −0.926638 | + | 0.926638i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0000i | 0.411355i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.44949 | −0.0838689 | −0.0419345 | − | 0.999120i | \(-0.513352\pi\) | ||||
−0.0419345 | + | 0.999120i | \(0.513352\pi\) | |||||||
\(854\) | 12.2474 | + | 30.0000i | 0.419099 | + | 1.02658i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | − | 4.89898i | − | 0.167346i | −0.996493 | − | 0.0836730i | \(-0.973335\pi\) | ||
0.996493 | − | 0.0836730i | \(-0.0266651\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.9444i | 0.919331i | 0.888092 | + | 0.459665i | \(0.152031\pi\) | ||||
−0.888092 | + | 0.459665i | \(0.847969\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.69694 | + | 20.6969i | −0.296391 | + | 0.705350i | ||||
\(862\) | 30.0000i | 1.02180i | ||||||||
\(863\) | −24.0000 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(864\) | −3.67423 | − | 3.67423i | −0.125000 | − | 0.125000i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.6969 | 0.499422 | ||||||||
\(867\) | 8.57321 | − | 8.57321i | 0.291162 | − | 0.291162i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.5959i | 0.663982i | ||||||||
\(872\) | 10.0000 | 0.338643 | ||||||||
\(873\) | 14.6969i | 0.497416i | ||||||||
\(874\) | − | 14.6969i | − | 0.497131i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.0000 | + | 12.0000i | −0.405442 | + | 0.405442i | ||||
\(877\) | 22.0000i | 0.742887i | 0.928456 | + | 0.371444i | \(0.121137\pi\) | ||||
−0.928456 | + | 0.371444i | \(0.878863\pi\) | |||||||
\(878\) | − | 14.6969i | − | 0.495998i | ||||||
\(879\) | −3.00000 | − | 3.00000i | −0.101187 | − | 0.101187i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.3939 | −0.990305 | −0.495152 | − | 0.868806i | \(-0.664888\pi\) | ||||
−0.495152 | + | 0.868806i | \(0.664888\pi\) | |||||||
\(882\) | 14.6969 | + | 15.0000i | 0.494872 | + | 0.505076i | ||||
\(883\) | − | 56.0000i | − | 1.88455i | −0.334840 | − | 0.942275i | \(-0.608682\pi\) | ||
0.334840 | − | 0.942275i | \(-0.391318\pi\) | |||||||
\(884\) | 12.0000i | 0.403604i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.0000 | −1.20944 | ||||||||
\(887\) | − | 4.89898i | − | 0.164492i | −0.996612 | − | 0.0822458i | \(-0.973791\pi\) | ||
0.996612 | − | 0.0822458i | \(-0.0262093\pi\) | |||||||
\(888\) | 2.44949 | + | 2.44949i | 0.0821995 | + | 0.0821995i | ||||
\(889\) | 8.00000 | + | 19.5959i | 0.268311 | + | 0.657226i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.6969 | −0.492090 | ||||||||
\(893\) | 12.0000 | 0.401565 | ||||||||
\(894\) | −7.34847 | − | 7.34847i | −0.245770 | − | 0.245770i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.44949 | − | 1.00000i | 0.0818317 | − | 0.0334077i | ||||
\(897\) | 18.0000 | − | 18.0000i | 0.601003 | − | 0.601003i | ||||
\(898\) | 36.0000i | 1.20134i | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 29.3939i | − | 0.979252i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.8990 | + | 7.10102i | 0.562363 | + | 0.236307i | ||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.79796 | + | 9.79796i | −0.325515 | + | 0.325515i | ||||
\(907\) | − | 28.0000i | − | 0.929725i | −0.885383 | − | 0.464862i | \(-0.846104\pi\) | ||
0.885383 | − | 0.464862i | \(-0.153896\pi\) | |||||||
\(908\) | 7.34847i | 0.243868i | ||||||||
\(909\) | − | 22.0454i | − | 0.731200i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 30.0000i | − | 0.993944i | −0.867766 | − | 0.496972i | \(-0.834445\pi\) | ||
0.867766 | − | 0.496972i | \(-0.165555\pi\) | |||||||
\(912\) | −3.00000 | − | 3.00000i | −0.0993399 | − | 0.0993399i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 28.0000i | 0.926158i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 22.0454i | − | 0.728401i | ||||||
\(917\) | −18.0000 | + | 7.34847i | −0.594412 | + | 0.242668i | ||||
\(918\) | −18.0000 | + | 18.0000i | −0.594089 | + | 0.594089i | ||||
\(919\) | −10.0000 | −0.329870 | −0.164935 | − | 0.986304i | \(-0.552741\pi\) | ||||
−0.164935 | + | 0.986304i | \(0.552741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.00000 | + | 9.00000i | −0.296560 | + | 0.296560i | ||||
\(922\) | −31.8434 | −1.04871 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 14.0000i | − | 0.460069i | ||||||
\(927\) | − | 29.3939i | − | 0.965422i | ||||||
\(928\) | 6.00000i | 0.196960i | ||||||||
\(929\) | 24.4949 | 0.803652 | 0.401826 | − | 0.915716i | \(-0.368376\pi\) | ||||
0.401826 | + | 0.915716i | \(0.368376\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.0000 | + | 12.2474i | 0.393284 | + | 0.401394i | ||||
\(932\) | −24.0000 | −0.786146 | ||||||||
\(933\) | −24.0000 | + | 24.0000i | −0.785725 | + | 0.785725i | ||||
\(934\) | − | 7.34847i | − | 0.240449i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 7.34847i | − | 0.240192i | ||||||
\(937\) | 19.5959 | 0.640171 | 0.320085 | − | 0.947389i | \(-0.396288\pi\) | ||||
0.320085 | + | 0.947389i | \(0.396288\pi\) | |||||||
\(938\) | −8.00000 | − | 19.5959i | −0.261209 | − | 0.639829i | ||||
\(939\) | −42.0000 | + | 42.0000i | −1.37062 | + | 1.37062i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.8434 | 1.03806 | 0.519032 | − | 0.854755i | \(-0.326293\pi\) | ||||
0.519032 | + | 0.854755i | \(0.326293\pi\) | |||||||
\(942\) | 9.00000 | − | 9.00000i | 0.293236 | − | 0.293236i | ||||
\(943\) | −29.3939 | −0.957196 | ||||||||
\(944\) | 12.2474 | 0.398621 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.0000 | 0.389948 | 0.194974 | − | 0.980808i | \(-0.437538\pi\) | ||||
0.194974 | + | 0.980808i | \(0.437538\pi\) | |||||||
\(948\) | −12.2474 | + | 12.2474i | −0.397779 | + | 0.397779i | ||||
\(949\) | −24.0000 | −0.779073 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.0454 | − | 22.0454i | 0.714871 | − | 0.714871i | ||||
\(952\) | −4.89898 | − | 12.0000i | −0.158777 | − | 0.388922i | ||||
\(953\) | 36.0000 | 1.16615 | 0.583077 | − | 0.812417i | \(-0.301849\pi\) | ||||
0.583077 | + | 0.812417i | \(0.301849\pi\) | |||||||
\(954\) | 18.0000i | 0.582772i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 6.00000i | − | 0.194054i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 24.4949 | 0.791394 | ||||||||
\(959\) | −29.3939 | + | 12.0000i | −0.949178 | + | 0.387500i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 4.89898i | 0.157949i | ||||||||
\(963\) | − | 36.0000i | − | 1.16008i | ||||||
\(964\) | − | 24.4949i | − | 0.788928i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −10.6515 | + | 25.3485i | −0.342707 | + | 0.815574i | ||||
\(967\) | − | 8.00000i | − | 0.257263i | −0.991692 | − | 0.128631i | \(-0.958942\pi\) | ||
0.991692 | − | 0.128631i | \(-0.0410584\pi\) | |||||||
\(968\) | −11.0000 | −0.353553 | ||||||||
\(969\) | −14.6969 | + | 14.6969i | −0.472134 | + | 0.472134i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.6413 | −1.33633 | −0.668167 | − | 0.744011i | \(-0.732921\pi\) | ||||
−0.668167 | + | 0.744011i | \(0.732921\pi\) | |||||||
\(972\) | 11.0227 | − | 11.0227i | 0.353553 | − | 0.353553i | ||||
\(973\) | −2.44949 | − | 6.00000i | −0.0785270 | − | 0.192351i | ||||
\(974\) | − | 32.0000i | − | 1.02535i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.2474i | 0.392031i | ||||||||
\(977\) | 12.0000 | 0.383914 | 0.191957 | − | 0.981403i | \(-0.438517\pi\) | ||||
0.191957 | + | 0.981403i | \(0.438517\pi\) | |||||||
\(978\) | −19.5959 | − | 19.5959i | −0.626608 | − | 0.626608i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.0000i | 0.957826i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 34.2929i | − | 1.09377i | −0.837207 | − | 0.546886i | \(-0.815813\pi\) | ||
0.837207 | − | 0.546886i | \(-0.184187\pi\) | |||||||
\(984\) | −6.00000 | + | 6.00000i | −0.191273 | + | 0.191273i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 29.3939 | 0.936092 | ||||||||
\(987\) | −20.6969 | − | 8.69694i | −0.658791 | − | 0.276827i | ||||
\(988\) | − | 6.00000i | − | 0.190885i | ||||||
\(989\) | 24.0000i | 0.763156i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.0000 | −1.20711 | −0.603555 | − | 0.797321i | \(-0.706250\pi\) | ||||
−0.603555 | + | 0.797321i | \(0.706250\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.79796 | − | 9.79796i | 0.310929 | − | 0.310929i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.00000 | − | 3.00000i | −0.0950586 | − | 0.0950586i | ||||
\(997\) | 7.34847 | 0.232728 | 0.116364 | − | 0.993207i | \(-0.462876\pi\) | ||||
0.116364 | + | 0.993207i | \(0.462876\pi\) | |||||||
\(998\) | −20.0000 | −0.633089 | ||||||||
\(999\) | −7.34847 | + | 7.34847i | −0.232495 | + | 0.232495i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))