Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(497,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.497");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 683.2 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.683 |
Dual form | 930.2.j.b.497.2 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 1.70711 | + | 0.292893i | 0.985599 | + | 0.169102i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −2.12132 | + | 0.707107i | −0.948683 | + | 0.316228i | ||||
\(6\) | 1.00000 | + | 1.41421i | 0.408248 | + | 0.577350i | ||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 2.82843 | + | 1.00000i | 0.942809 | + | 0.333333i | ||||
\(10\) | −2.00000 | − | 1.00000i | −0.632456 | − | 0.316228i | ||||
\(11\) | 1.41421i | 0.426401i | 0.977008 | + | 0.213201i | \(0.0683888\pi\) | ||||
−0.977008 | + | 0.213201i | \(0.931611\pi\) | |||||||
\(12\) | −0.292893 | + | 1.70711i | −0.0845510 | + | 0.492799i | ||||
\(13\) | 3.00000 | + | 3.00000i | 0.832050 | + | 0.832050i | 0.987797 | − | 0.155747i | \(-0.0497784\pi\) |
−0.155747 | + | 0.987797i | \(0.549778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.82843 | + | 0.585786i | −0.988496 | + | 0.151249i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.41421 | − | 1.41421i | −0.342997 | − | 0.342997i | 0.514496 | − | 0.857493i | \(-0.327979\pi\) |
−0.857493 | + | 0.514496i | \(0.827979\pi\) | |||||||
\(18\) | 1.29289 | + | 2.70711i | 0.304738 | + | 0.638071i | ||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | −0.707107 | − | 2.12132i | −0.158114 | − | 0.474342i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | + | 1.00000i | −0.213201 | + | 0.213201i | ||||
\(23\) | −2.82843 | + | 2.82843i | −0.589768 | + | 0.589768i | −0.937568 | − | 0.347801i | \(-0.886929\pi\) |
0.347801 | + | 0.937568i | \(0.386929\pi\) | |||||||
\(24\) | −1.41421 | + | 1.00000i | −0.288675 | + | 0.204124i | ||||
\(25\) | 4.00000 | − | 3.00000i | 0.800000 | − | 0.600000i | ||||
\(26\) | 4.24264i | 0.832050i | ||||||||
\(27\) | 4.53553 | + | 2.53553i | 0.872864 | + | 0.487964i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.82843 | −0.525226 | −0.262613 | − | 0.964901i | \(-0.584584\pi\) | ||||
−0.262613 | + | 0.964901i | \(0.584584\pi\) | |||||||
\(30\) | −3.12132 | − | 2.29289i | −0.569873 | − | 0.418623i | ||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −0.414214 | + | 2.41421i | −0.0721053 | + | 0.420261i | ||||
\(34\) | − | 2.00000i | − | 0.342997i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | + | 2.82843i | −0.166667 | + | 0.471405i | ||||
\(37\) | −3.00000 | + | 3.00000i | −0.493197 | + | 0.493197i | −0.909312 | − | 0.416115i | \(-0.863391\pi\) |
0.416115 | + | 0.909312i | \(0.363391\pi\) | |||||||
\(38\) | −2.82843 | + | 2.82843i | −0.458831 | + | 0.458831i | ||||
\(39\) | 4.24264 | + | 6.00000i | 0.679366 | + | 0.960769i | ||||
\(40\) | 1.00000 | − | 2.00000i | 0.158114 | − | 0.316228i | ||||
\(41\) | − | 5.65685i | − | 0.883452i | −0.897150 | − | 0.441726i | \(-0.854366\pi\) | ||
0.897150 | − | 0.441726i | \(-0.145634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(44\) | −1.41421 | −0.213201 | ||||||||
\(45\) | −6.70711 | − | 0.121320i | −0.999836 | − | 0.0180854i | ||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | 1.41421 | + | 1.41421i | 0.206284 | + | 0.206284i | 0.802686 | − | 0.596402i | \(-0.203403\pi\) |
−0.596402 | + | 0.802686i | \(0.703403\pi\) | |||||||
\(48\) | −1.70711 | − | 0.292893i | −0.246400 | − | 0.0422755i | ||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | 4.94975 | + | 0.707107i | 0.700000 | + | 0.100000i | ||||
\(51\) | −2.00000 | − | 2.82843i | −0.280056 | − | 0.396059i | ||||
\(52\) | −3.00000 | + | 3.00000i | −0.416025 | + | 0.416025i | ||||
\(53\) | 1.41421 | − | 1.41421i | 0.194257 | − | 0.194257i | −0.603276 | − | 0.797533i | \(-0.706138\pi\) |
0.797533 | + | 0.603276i | \(0.206138\pi\) | |||||||
\(54\) | 1.41421 | + | 5.00000i | 0.192450 | + | 0.680414i | ||||
\(55\) | −1.00000 | − | 3.00000i | −0.134840 | − | 0.404520i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.17157 | + | 6.82843i | −0.155179 | + | 0.904447i | ||||
\(58\) | −2.00000 | − | 2.00000i | −0.262613 | − | 0.262613i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | −0.585786 | − | 3.82843i | −0.0756247 | − | 0.494248i | ||||
\(61\) | 8.00000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | 0.707107 | + | 0.707107i | 0.0898027 | + | 0.0898027i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −8.48528 | − | 4.24264i | −1.05247 | − | 0.526235i | ||||
\(66\) | −2.00000 | + | 1.41421i | −0.246183 | + | 0.174078i | ||||
\(67\) | 7.00000 | − | 7.00000i | 0.855186 | − | 0.855186i | −0.135580 | − | 0.990766i | \(-0.543290\pi\) |
0.990766 | + | 0.135580i | \(0.0432899\pi\) | |||||||
\(68\) | 1.41421 | − | 1.41421i | 0.171499 | − | 0.171499i | ||||
\(69\) | −5.65685 | + | 4.00000i | −0.681005 | + | 0.481543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.7279i | − | 1.51053i | −0.655422 | − | 0.755263i | \(-0.727509\pi\) | ||
0.655422 | − | 0.755263i | \(-0.272491\pi\) | |||||||
\(72\) | −2.70711 | + | 1.29289i | −0.319036 | + | 0.152369i | ||||
\(73\) | −2.00000 | − | 2.00000i | −0.234082 | − | 0.234082i | 0.580312 | − | 0.814394i | \(-0.302931\pi\) |
−0.814394 | + | 0.580312i | \(0.802931\pi\) | |||||||
\(74\) | −4.24264 | −0.493197 | ||||||||
\(75\) | 7.70711 | − | 3.94975i | 0.889940 | − | 0.456078i | ||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.24264 | + | 7.24264i | −0.140701 | + | 0.820068i | ||||
\(79\) | − | 2.00000i | − | 0.225018i | −0.993651 | − | 0.112509i | \(-0.964111\pi\) | ||
0.993651 | − | 0.112509i | \(-0.0358886\pi\) | |||||||
\(80\) | 2.12132 | − | 0.707107i | 0.237171 | − | 0.0790569i | ||||
\(81\) | 7.00000 | + | 5.65685i | 0.777778 | + | 0.628539i | ||||
\(82\) | 4.00000 | − | 4.00000i | 0.441726 | − | 0.441726i | ||||
\(83\) | 4.24264 | − | 4.24264i | 0.465690 | − | 0.465690i | −0.434825 | − | 0.900515i | \(-0.643190\pi\) |
0.900515 | + | 0.434825i | \(0.143190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | + | 2.00000i | 0.433861 | + | 0.216930i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.82843 | − | 0.828427i | −0.517662 | − | 0.0888167i | ||||
\(88\) | −1.00000 | − | 1.00000i | −0.106600 | − | 0.106600i | ||||
\(89\) | 7.07107 | 0.749532 | 0.374766 | − | 0.927119i | \(-0.377723\pi\) | ||||
0.374766 | + | 0.927119i | \(0.377723\pi\) | |||||||
\(90\) | −4.65685 | − | 4.82843i | −0.490876 | − | 0.508961i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.82843 | − | 2.82843i | −0.294884 | − | 0.294884i | ||||
\(93\) | 1.70711 | + | 0.292893i | 0.177019 | + | 0.0303716i | ||||
\(94\) | 2.00000i | 0.206284i | ||||||||
\(95\) | −2.82843 | − | 8.48528i | −0.290191 | − | 0.870572i | ||||
\(96\) | −1.00000 | − | 1.41421i | −0.102062 | − | 0.144338i | ||||
\(97\) | 11.0000 | − | 11.0000i | 1.11688 | − | 1.11688i | 0.124684 | − | 0.992196i | \(-0.460208\pi\) |
0.992196 | − | 0.124684i | \(-0.0397918\pi\) | |||||||
\(98\) | −4.94975 | + | 4.94975i | −0.500000 | + | 0.500000i | ||||
\(99\) | −1.41421 | + | 4.00000i | −0.142134 | + | 0.402015i | ||||
\(100\) | 3.00000 | + | 4.00000i | 0.300000 | + | 0.400000i | ||||
\(101\) | − | 15.5563i | − | 1.54791i | −0.633238 | − | 0.773957i | \(-0.718274\pi\) | ||
0.633238 | − | 0.773957i | \(-0.281726\pi\) | |||||||
\(102\) | 0.585786 | − | 3.41421i | 0.0580015 | − | 0.338058i | ||||
\(103\) | −6.00000 | − | 6.00000i | −0.591198 | − | 0.591198i | 0.346757 | − | 0.937955i | \(-0.387283\pi\) |
−0.937955 | + | 0.346757i | \(0.887283\pi\) | |||||||
\(104\) | −4.24264 | −0.416025 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | 8.48528 | + | 8.48528i | 0.820303 | + | 0.820303i | 0.986151 | − | 0.165848i | \(-0.0530362\pi\) |
−0.165848 | + | 0.986151i | \(0.553036\pi\) | |||||||
\(108\) | −2.53553 | + | 4.53553i | −0.243982 | + | 0.436432i | ||||
\(109\) | 10.0000i | 0.957826i | 0.877862 | + | 0.478913i | \(0.158969\pi\) | ||||
−0.877862 | + | 0.478913i | \(0.841031\pi\) | |||||||
\(110\) | 1.41421 | − | 2.82843i | 0.134840 | − | 0.269680i | ||||
\(111\) | −6.00000 | + | 4.24264i | −0.569495 | + | 0.402694i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.24264 | − | 4.24264i | 0.399114 | − | 0.399114i | −0.478806 | − | 0.877920i | \(-0.658930\pi\) |
0.877920 | + | 0.478806i | \(0.158930\pi\) | |||||||
\(114\) | −5.65685 | + | 4.00000i | −0.529813 | + | 0.374634i | ||||
\(115\) | 4.00000 | − | 8.00000i | 0.373002 | − | 0.746004i | ||||
\(116\) | − | 2.82843i | − | 0.262613i | ||||||
\(117\) | 5.48528 | + | 11.4853i | 0.507114 | + | 1.06181i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.29289 | − | 3.12132i | 0.209312 | − | 0.284936i | ||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 5.65685 | + | 5.65685i | 0.512148 | + | 0.512148i | ||||
\(123\) | 1.65685 | − | 9.65685i | 0.149394 | − | 0.870729i | ||||
\(124\) | 1.00000i | 0.0898027i | ||||||||
\(125\) | −6.36396 | + | 9.19239i | −0.569210 | + | 0.822192i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.00000 | − | 5.00000i | 0.443678 | − | 0.443678i | −0.449568 | − | 0.893246i | \(-0.648422\pi\) |
0.893246 | + | 0.449568i | \(0.148422\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.00000 | − | 9.00000i | −0.263117 | − | 0.789352i | ||||
\(131\) | 14.1421i | 1.23560i | 0.786334 | + | 0.617802i | \(0.211977\pi\) | ||||
−0.786334 | + | 0.617802i | \(0.788023\pi\) | |||||||
\(132\) | −2.41421 | − | 0.414214i | −0.210130 | − | 0.0360527i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.89949 | 0.855186 | ||||||||
\(135\) | −11.4142 | − | 2.17157i | −0.982379 | − | 0.186899i | ||||
\(136\) | 2.00000 | 0.171499 | ||||||||
\(137\) | −7.07107 | − | 7.07107i | −0.604122 | − | 0.604122i | 0.337282 | − | 0.941404i | \(-0.390493\pi\) |
−0.941404 | + | 0.337282i | \(0.890493\pi\) | |||||||
\(138\) | −6.82843 | − | 1.17157i | −0.581274 | − | 0.0997309i | ||||
\(139\) | − | 12.0000i | − | 1.01783i | −0.860818 | − | 0.508913i | \(-0.830047\pi\) | ||
0.860818 | − | 0.508913i | \(-0.169953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.00000 | + | 2.82843i | 0.168430 | + | 0.238197i | ||||
\(142\) | 9.00000 | − | 9.00000i | 0.755263 | − | 0.755263i | ||||
\(143\) | −4.24264 | + | 4.24264i | −0.354787 | + | 0.354787i | ||||
\(144\) | −2.82843 | − | 1.00000i | −0.235702 | − | 0.0833333i | ||||
\(145\) | 6.00000 | − | 2.00000i | 0.498273 | − | 0.166091i | ||||
\(146\) | − | 2.82843i | − | 0.234082i | ||||||
\(147\) | −2.05025 | + | 11.9497i | −0.169102 | + | 0.985599i | ||||
\(148\) | −3.00000 | − | 3.00000i | −0.246598 | − | 0.246598i | ||||
\(149\) | −1.41421 | −0.115857 | −0.0579284 | − | 0.998321i | \(-0.518450\pi\) | ||||
−0.0579284 | + | 0.998321i | \(0.518450\pi\) | |||||||
\(150\) | 8.24264 | + | 2.65685i | 0.673009 | + | 0.216931i | ||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | −2.82843 | − | 2.82843i | −0.229416 | − | 0.229416i | ||||
\(153\) | −2.58579 | − | 5.41421i | −0.209048 | − | 0.437713i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.12132 | + | 0.707107i | −0.170389 | + | 0.0567962i | ||||
\(156\) | −6.00000 | + | 4.24264i | −0.480384 | + | 0.339683i | ||||
\(157\) | −4.00000 | + | 4.00000i | −0.319235 | + | 0.319235i | −0.848473 | − | 0.529238i | \(-0.822478\pi\) |
0.529238 | + | 0.848473i | \(0.322478\pi\) | |||||||
\(158\) | 1.41421 | − | 1.41421i | 0.112509 | − | 0.112509i | ||||
\(159\) | 2.82843 | − | 2.00000i | 0.224309 | − | 0.158610i | ||||
\(160\) | 2.00000 | + | 1.00000i | 0.158114 | + | 0.0790569i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.949747 | + | 8.94975i | 0.0746192 | + | 0.703159i | ||||
\(163\) | −11.0000 | − | 11.0000i | −0.861586 | − | 0.861586i | 0.129936 | − | 0.991522i | \(-0.458523\pi\) |
−0.991522 | + | 0.129936i | \(0.958523\pi\) | |||||||
\(164\) | 5.65685 | 0.441726 | ||||||||
\(165\) | −0.828427 | − | 5.41421i | −0.0644930 | − | 0.421496i | ||||
\(166\) | 6.00000 | 0.465690 | ||||||||
\(167\) | −5.65685 | − | 5.65685i | −0.437741 | − | 0.437741i | 0.453510 | − | 0.891251i | \(-0.350171\pi\) |
−0.891251 | + | 0.453510i | \(0.850171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000i | 0.384615i | ||||||||
\(170\) | 1.41421 | + | 4.24264i | 0.108465 | + | 0.325396i | ||||
\(171\) | −4.00000 | + | 11.3137i | −0.305888 | + | 0.865181i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.1421 | + | 14.1421i | −1.07521 | + | 1.07521i | −0.0782748 | + | 0.996932i | \(0.524941\pi\) |
−0.996932 | + | 0.0782748i | \(0.975059\pi\) | |||||||
\(174\) | −2.82843 | − | 4.00000i | −0.214423 | − | 0.303239i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.41421i | − | 0.106600i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.00000 | + | 5.00000i | 0.374766 | + | 0.374766i | ||||
\(179\) | 12.7279 | 0.951330 | 0.475665 | − | 0.879627i | \(-0.342208\pi\) | ||||
0.475665 | + | 0.879627i | \(0.342208\pi\) | |||||||
\(180\) | 0.121320 | − | 6.70711i | 0.00904268 | − | 0.499918i | ||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.6569 | + | 2.34315i | 1.00954 | + | 0.173210i | ||||
\(184\) | − | 4.00000i | − | 0.294884i | ||||||
\(185\) | 4.24264 | − | 8.48528i | 0.311925 | − | 0.623850i | ||||
\(186\) | 1.00000 | + | 1.41421i | 0.0733236 | + | 0.103695i | ||||
\(187\) | 2.00000 | − | 2.00000i | 0.146254 | − | 0.146254i | ||||
\(188\) | −1.41421 | + | 1.41421i | −0.103142 | + | 0.103142i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.00000 | − | 8.00000i | 0.290191 | − | 0.580381i | ||||
\(191\) | 21.2132i | 1.53493i | 0.641089 | + | 0.767467i | \(0.278483\pi\) | ||||
−0.641089 | + | 0.767467i | \(0.721517\pi\) | |||||||
\(192\) | 0.292893 | − | 1.70711i | 0.0211377 | − | 0.123200i | ||||
\(193\) | −9.00000 | − | 9.00000i | −0.647834 | − | 0.647834i | 0.304635 | − | 0.952469i | \(-0.401466\pi\) |
−0.952469 | + | 0.304635i | \(0.901466\pi\) | |||||||
\(194\) | 15.5563 | 1.11688 | ||||||||
\(195\) | −13.2426 | − | 9.72792i | −0.948325 | − | 0.696631i | ||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | 7.07107 | + | 7.07107i | 0.503793 | + | 0.503793i | 0.912614 | − | 0.408822i | \(-0.134060\pi\) |
−0.408822 | + | 0.912614i | \(0.634060\pi\) | |||||||
\(198\) | −3.82843 | + | 1.82843i | −0.272074 | + | 0.129941i | ||||
\(199\) | 24.0000i | 1.70131i | 0.525720 | + | 0.850657i | \(0.323796\pi\) | ||||
−0.525720 | + | 0.850657i | \(0.676204\pi\) | |||||||
\(200\) | −0.707107 | + | 4.94975i | −0.0500000 | + | 0.350000i | ||||
\(201\) | 14.0000 | − | 9.89949i | 0.987484 | − | 0.698257i | ||||
\(202\) | 11.0000 | − | 11.0000i | 0.773957 | − | 0.773957i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.82843 | − | 2.00000i | 0.198030 | − | 0.140028i | ||||
\(205\) | 4.00000 | + | 12.0000i | 0.279372 | + | 0.838116i | ||||
\(206\) | − | 8.48528i | − | 0.591198i | ||||||
\(207\) | −10.8284 | + | 5.17157i | −0.752628 | + | 0.359449i | ||||
\(208\) | −3.00000 | − | 3.00000i | −0.208013 | − | 0.208013i | ||||
\(209\) | −5.65685 | −0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000 | 0.688428 | 0.344214 | − | 0.938891i | \(-0.388145\pi\) | ||||
0.344214 | + | 0.938891i | \(0.388145\pi\) | |||||||
\(212\) | 1.41421 | + | 1.41421i | 0.0971286 | + | 0.0971286i | ||||
\(213\) | 3.72792 | − | 21.7279i | 0.255433 | − | 1.48877i | ||||
\(214\) | 12.0000i | 0.820303i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | + | 1.41421i | −0.340207 | + | 0.0962250i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.07107 | + | 7.07107i | −0.478913 | + | 0.478913i | ||||
\(219\) | −2.82843 | − | 4.00000i | −0.191127 | − | 0.270295i | ||||
\(220\) | 3.00000 | − | 1.00000i | 0.202260 | − | 0.0674200i | ||||
\(221\) | − | 8.48528i | − | 0.570782i | ||||||
\(222\) | −7.24264 | − | 1.24264i | −0.486094 | − | 0.0834006i | ||||
\(223\) | −11.0000 | − | 11.0000i | −0.736614 | − | 0.736614i | 0.235307 | − | 0.971921i | \(-0.424391\pi\) |
−0.971921 | + | 0.235307i | \(0.924391\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.3137 | − | 4.48528i | 0.954247 | − | 0.299019i | ||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | 11.3137 | + | 11.3137i | 0.750917 | + | 0.750917i | 0.974650 | − | 0.223733i | \(-0.0718244\pi\) |
−0.223733 | + | 0.974650i | \(0.571824\pi\) | |||||||
\(228\) | −6.82843 | − | 1.17157i | −0.452224 | − | 0.0775893i | ||||
\(229\) | − | 26.0000i | − | 1.71813i | −0.511868 | − | 0.859064i | \(-0.671046\pi\) | ||
0.511868 | − | 0.859064i | \(-0.328954\pi\) | |||||||
\(230\) | 8.48528 | − | 2.82843i | 0.559503 | − | 0.186501i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.00000 | − | 2.00000i | 0.131306 | − | 0.131306i | ||||
\(233\) | −9.89949 | + | 9.89949i | −0.648537 | + | 0.648537i | −0.952639 | − | 0.304102i | \(-0.901644\pi\) |
0.304102 | + | 0.952639i | \(0.401644\pi\) | |||||||
\(234\) | −4.24264 | + | 12.0000i | −0.277350 | + | 0.784465i | ||||
\(235\) | −4.00000 | − | 2.00000i | −0.260931 | − | 0.130466i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.585786 | − | 3.41421i | 0.0380509 | − | 0.221777i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.6274 | 1.46365 | 0.731823 | − | 0.681495i | \(-0.238670\pi\) | ||||
0.731823 | + | 0.681495i | \(0.238670\pi\) | |||||||
\(240\) | 3.82843 | − | 0.585786i | 0.247124 | − | 0.0378124i | ||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | 6.36396 | + | 6.36396i | 0.409091 | + | 0.409091i | ||||
\(243\) | 10.2929 | + | 11.7071i | 0.660289 | + | 0.751011i | ||||
\(244\) | 8.00000i | 0.512148i | ||||||||
\(245\) | −4.94975 | − | 14.8492i | −0.316228 | − | 0.948683i | ||||
\(246\) | 8.00000 | − | 5.65685i | 0.510061 | − | 0.360668i | ||||
\(247\) | −12.0000 | + | 12.0000i | −0.763542 | + | 0.763542i | ||||
\(248\) | −0.707107 | + | 0.707107i | −0.0449013 | + | 0.0449013i | ||||
\(249\) | 8.48528 | − | 6.00000i | 0.537733 | − | 0.380235i | ||||
\(250\) | −11.0000 | + | 2.00000i | −0.695701 | + | 0.126491i | ||||
\(251\) | 4.24264i | 0.267793i | 0.990995 | + | 0.133897i | \(0.0427490\pi\) | ||||
−0.990995 | + | 0.133897i | \(0.957251\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | − | 4.00000i | −0.251478 | − | 0.251478i | ||||
\(254\) | 7.07107 | 0.443678 | ||||||||
\(255\) | 6.24264 | + | 4.58579i | 0.390929 | + | 0.287173i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.24264 | − | 4.24264i | −0.264649 | − | 0.264649i | 0.562291 | − | 0.826940i | \(-0.309920\pi\) |
−0.826940 | + | 0.562291i | \(0.809920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.24264 | − | 8.48528i | 0.263117 | − | 0.526235i | ||||
\(261\) | −8.00000 | − | 2.82843i | −0.495188 | − | 0.175075i | ||||
\(262\) | −10.0000 | + | 10.0000i | −0.617802 | + | 0.617802i | ||||
\(263\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(264\) | −1.41421 | − | 2.00000i | −0.0870388 | − | 0.123091i | ||||
\(265\) | −2.00000 | + | 4.00000i | −0.122859 | + | 0.245718i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.0711 | + | 2.07107i | 0.738737 | + | 0.126747i | ||||
\(268\) | 7.00000 | + | 7.00000i | 0.427593 | + | 0.427593i | ||||
\(269\) | 25.4558 | 1.55207 | 0.776035 | − | 0.630690i | \(-0.217228\pi\) | ||||
0.776035 | + | 0.630690i | \(0.217228\pi\) | |||||||
\(270\) | −6.53553 | − | 9.60660i | −0.397740 | − | 0.584639i | ||||
\(271\) | 10.0000 | 0.607457 | 0.303728 | − | 0.952759i | \(-0.401768\pi\) | ||||
0.303728 | + | 0.952759i | \(0.401768\pi\) | |||||||
\(272\) | 1.41421 | + | 1.41421i | 0.0857493 | + | 0.0857493i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 10.0000i | − | 0.604122i | ||||||
\(275\) | 4.24264 | + | 5.65685i | 0.255841 | + | 0.341121i | ||||
\(276\) | −4.00000 | − | 5.65685i | −0.240772 | − | 0.340503i | ||||
\(277\) | 5.00000 | − | 5.00000i | 0.300421 | − | 0.300421i | −0.540758 | − | 0.841178i | \(-0.681862\pi\) |
0.841178 | + | 0.540758i | \(0.181862\pi\) | |||||||
\(278\) | 8.48528 | − | 8.48528i | 0.508913 | − | 0.508913i | ||||
\(279\) | 2.82843 | + | 1.00000i | 0.169334 | + | 0.0598684i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.6274i | − | 1.34984i | −0.737892 | − | 0.674919i | \(-0.764178\pi\) | ||
0.737892 | − | 0.674919i | \(-0.235822\pi\) | |||||||
\(282\) | −0.585786 | + | 3.41421i | −0.0348831 | + | 0.203313i | ||||
\(283\) | −19.0000 | − | 19.0000i | −1.12943 | − | 1.12943i | −0.990269 | − | 0.139163i | \(-0.955559\pi\) |
−0.139163 | − | 0.990269i | \(-0.544441\pi\) | |||||||
\(284\) | 12.7279 | 0.755263 | ||||||||
\(285\) | −2.34315 | − | 15.3137i | −0.138796 | − | 0.907106i | ||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.29289 | − | 2.70711i | −0.0761845 | − | 0.159518i | ||||
\(289\) | − | 13.0000i | − | 0.764706i | ||||||
\(290\) | 5.65685 | + | 2.82843i | 0.332182 | + | 0.166091i | ||||
\(291\) | 22.0000 | − | 15.5563i | 1.28966 | − | 0.911929i | ||||
\(292\) | 2.00000 | − | 2.00000i | 0.117041 | − | 0.117041i | ||||
\(293\) | −16.9706 | + | 16.9706i | −0.991431 | + | 0.991431i | −0.999964 | − | 0.00853273i | \(-0.997284\pi\) |
0.00853273 | + | 0.999964i | \(0.497284\pi\) | |||||||
\(294\) | −9.89949 | + | 7.00000i | −0.577350 | + | 0.408248i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 4.24264i | − | 0.246598i | ||||||
\(297\) | −3.58579 | + | 6.41421i | −0.208068 | + | 0.372190i | ||||
\(298\) | −1.00000 | − | 1.00000i | −0.0579284 | − | 0.0579284i | ||||
\(299\) | −16.9706 | −0.981433 | ||||||||
\(300\) | 3.94975 | + | 7.70711i | 0.228039 | + | 0.444970i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.65685 | − | 5.65685i | −0.325515 | − | 0.325515i | ||||
\(303\) | 4.55635 | − | 26.5563i | 0.261755 | − | 1.52562i | ||||
\(304\) | − | 4.00000i | − | 0.229416i | ||||||
\(305\) | −16.9706 | + | 5.65685i | −0.971732 | + | 0.323911i | ||||
\(306\) | 2.00000 | − | 5.65685i | 0.114332 | − | 0.323381i | ||||
\(307\) | 5.00000 | − | 5.00000i | 0.285365 | − | 0.285365i | −0.549879 | − | 0.835244i | \(-0.685326\pi\) |
0.835244 | + | 0.549879i | \(0.185326\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.48528 | − | 12.0000i | −0.482711 | − | 0.682656i | ||||
\(310\) | −2.00000 | − | 1.00000i | −0.113592 | − | 0.0567962i | ||||
\(311\) | − | 1.41421i | − | 0.0801927i | −0.999196 | − | 0.0400963i | \(-0.987234\pi\) | ||
0.999196 | − | 0.0400963i | \(-0.0127665\pi\) | |||||||
\(312\) | −7.24264 | − | 1.24264i | −0.410034 | − | 0.0703507i | ||||
\(313\) | −10.0000 | − | 10.0000i | −0.565233 | − | 0.565233i | 0.365556 | − | 0.930789i | \(-0.380879\pi\) |
−0.930789 | + | 0.365556i | \(0.880879\pi\) | |||||||
\(314\) | −5.65685 | −0.319235 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | 4.24264 | + | 4.24264i | 0.238290 | + | 0.238290i | 0.816142 | − | 0.577851i | \(-0.196109\pi\) |
−0.577851 | + | 0.816142i | \(0.696109\pi\) | |||||||
\(318\) | 3.41421 | + | 0.585786i | 0.191460 | + | 0.0328493i | ||||
\(319\) | − | 4.00000i | − | 0.223957i | ||||||
\(320\) | 0.707107 | + | 2.12132i | 0.0395285 | + | 0.118585i | ||||
\(321\) | 12.0000 | + | 16.9706i | 0.669775 | + | 0.947204i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.65685 | − | 5.65685i | 0.314756 | − | 0.314756i | ||||
\(324\) | −5.65685 | + | 7.00000i | −0.314270 | + | 0.388889i | ||||
\(325\) | 21.0000 | + | 3.00000i | 1.16487 | + | 0.166410i | ||||
\(326\) | − | 15.5563i | − | 0.861586i | ||||||
\(327\) | −2.92893 | + | 17.0711i | −0.161970 | + | 0.944032i | ||||
\(328\) | 4.00000 | + | 4.00000i | 0.220863 | + | 0.220863i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.24264 | − | 4.41421i | 0.178501 | − | 0.242994i | ||||
\(331\) | 32.0000 | 1.75888 | 0.879440 | − | 0.476011i | \(-0.157918\pi\) | ||||
0.879440 | + | 0.476011i | \(0.157918\pi\) | |||||||
\(332\) | 4.24264 | + | 4.24264i | 0.232845 | + | 0.232845i | ||||
\(333\) | −11.4853 | + | 5.48528i | −0.629390 | + | 0.300592i | ||||
\(334\) | − | 8.00000i | − | 0.437741i | ||||||
\(335\) | −9.89949 | + | 19.7990i | −0.540867 | + | 1.08173i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.00000 | + | 8.00000i | −0.435788 | + | 0.435788i | −0.890592 | − | 0.454804i | \(-0.849709\pi\) |
0.454804 | + | 0.890592i | \(0.349709\pi\) | |||||||
\(338\) | −3.53553 | + | 3.53553i | −0.192308 | + | 0.192308i | ||||
\(339\) | 8.48528 | − | 6.00000i | 0.460857 | − | 0.325875i | ||||
\(340\) | −2.00000 | + | 4.00000i | −0.108465 | + | 0.216930i | ||||
\(341\) | 1.41421i | 0.0765840i | ||||||||
\(342\) | −10.8284 | + | 5.17157i | −0.585534 | + | 0.279647i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.17157 | − | 12.4853i | 0.493781 | − | 0.672185i | ||||
\(346\) | −20.0000 | −1.07521 | ||||||||
\(347\) | 4.24264 | + | 4.24264i | 0.227757 | + | 0.227757i | 0.811755 | − | 0.583998i | \(-0.198512\pi\) |
−0.583998 | + | 0.811755i | \(0.698512\pi\) | |||||||
\(348\) | 0.828427 | − | 4.82843i | 0.0444084 | − | 0.258831i | ||||
\(349\) | − | 30.0000i | − | 1.60586i | −0.596071 | − | 0.802932i | \(-0.703272\pi\) | ||
0.596071 | − | 0.802932i | \(-0.296728\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.00000 | + | 21.2132i | 0.320256 | + | 1.13228i | ||||
\(352\) | 1.00000 | − | 1.00000i | 0.0533002 | − | 0.0533002i | ||||
\(353\) | −25.4558 | + | 25.4558i | −1.35488 | + | 1.35488i | −0.474766 | + | 0.880112i | \(0.657467\pi\) |
−0.880112 | + | 0.474766i | \(0.842533\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.00000 | + | 27.0000i | 0.477670 | + | 1.43301i | ||||
\(356\) | 7.07107i | 0.374766i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.00000 | + | 9.00000i | 0.475665 | + | 0.475665i | ||||
\(359\) | 7.07107 | 0.373197 | 0.186598 | − | 0.982436i | \(-0.440254\pi\) | ||||
0.186598 | + | 0.982436i | \(0.440254\pi\) | |||||||
\(360\) | 4.82843 | − | 4.65685i | 0.254480 | − | 0.245438i | ||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | −7.07107 | − | 7.07107i | −0.371647 | − | 0.371647i | ||||
\(363\) | 15.3640 | + | 2.63604i | 0.806399 | + | 0.138356i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.65685 | + | 2.82843i | 0.296093 | + | 0.148047i | ||||
\(366\) | 8.00000 | + | 11.3137i | 0.418167 | + | 0.591377i | ||||
\(367\) | −15.0000 | + | 15.0000i | −0.782994 | + | 0.782994i | −0.980335 | − | 0.197341i | \(-0.936769\pi\) |
0.197341 | + | 0.980335i | \(0.436769\pi\) | |||||||
\(368\) | 2.82843 | − | 2.82843i | 0.147442 | − | 0.147442i | ||||
\(369\) | 5.65685 | − | 16.0000i | 0.294484 | − | 0.832927i | ||||
\(370\) | 9.00000 | − | 3.00000i | 0.467888 | − | 0.155963i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.292893 | + | 1.70711i | −0.0151858 | + | 0.0885094i | ||||
\(373\) | −12.0000 | − | 12.0000i | −0.621336 | − | 0.621336i | 0.324537 | − | 0.945873i | \(-0.394792\pi\) |
−0.945873 | + | 0.324537i | \(0.894792\pi\) | |||||||
\(374\) | 2.82843 | 0.146254 | ||||||||
\(375\) | −13.5563 | + | 13.8284i | −0.700047 | + | 0.714097i | ||||
\(376\) | −2.00000 | −0.103142 | ||||||||
\(377\) | −8.48528 | − | 8.48528i | −0.437014 | − | 0.437014i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.0000i | 1.74646i | 0.487306 | + | 0.873231i | \(0.337980\pi\) | ||||
−0.487306 | + | 0.873231i | \(0.662020\pi\) | |||||||
\(380\) | 8.48528 | − | 2.82843i | 0.435286 | − | 0.145095i | ||||
\(381\) | 10.0000 | − | 7.07107i | 0.512316 | − | 0.362262i | ||||
\(382\) | −15.0000 | + | 15.0000i | −0.767467 | + | 0.767467i | ||||
\(383\) | −25.4558 | + | 25.4558i | −1.30073 | + | 1.30073i | −0.372835 | + | 0.927898i | \(0.621614\pi\) |
−0.927898 | + | 0.372835i | \(0.878386\pi\) | |||||||
\(384\) | 1.41421 | − | 1.00000i | 0.0721688 | − | 0.0510310i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 12.7279i | − | 0.647834i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.0000 | + | 11.0000i | 0.558440 | + | 0.558440i | ||||
\(389\) | −5.65685 | −0.286814 | −0.143407 | − | 0.989664i | \(-0.545806\pi\) | ||||
−0.143407 | + | 0.989664i | \(0.545806\pi\) | |||||||
\(390\) | −2.48528 | − | 16.2426i | −0.125847 | − | 0.822478i | ||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | −4.94975 | − | 4.94975i | −0.250000 | − | 0.250000i | ||||
\(393\) | −4.14214 | + | 24.1421i | −0.208943 | + | 1.21781i | ||||
\(394\) | 10.0000i | 0.503793i | ||||||||
\(395\) | 1.41421 | + | 4.24264i | 0.0711568 | + | 0.213470i | ||||
\(396\) | −4.00000 | − | 1.41421i | −0.201008 | − | 0.0710669i | ||||
\(397\) | −8.00000 | + | 8.00000i | −0.401508 | + | 0.401508i | −0.878764 | − | 0.477256i | \(-0.841631\pi\) |
0.477256 | + | 0.878764i | \(0.341631\pi\) | |||||||
\(398\) | −16.9706 | + | 16.9706i | −0.850657 | + | 0.850657i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | + | 3.00000i | −0.200000 | + | 0.150000i | ||||
\(401\) | − | 26.8701i | − | 1.34183i | −0.741536 | − | 0.670913i | \(-0.765902\pi\) | ||
0.741536 | − | 0.670913i | \(-0.234098\pi\) | |||||||
\(402\) | 16.8995 | + | 2.89949i | 0.842870 | + | 0.144614i | ||||
\(403\) | 3.00000 | + | 3.00000i | 0.149441 | + | 0.149441i | ||||
\(404\) | 15.5563 | 0.773957 | ||||||||
\(405\) | −18.8492 | − | 7.05025i | −0.936626 | − | 0.350330i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.24264 | − | 4.24264i | −0.210300 | − | 0.210300i | ||||
\(408\) | 3.41421 | + | 0.585786i | 0.169029 | + | 0.0290008i | ||||
\(409\) | − | 6.00000i | − | 0.296681i | −0.988936 | − | 0.148340i | \(-0.952607\pi\) | ||
0.988936 | − | 0.148340i | \(-0.0473931\pi\) | |||||||
\(410\) | −5.65685 | + | 11.3137i | −0.279372 | + | 0.558744i | ||||
\(411\) | −10.0000 | − | 14.1421i | −0.493264 | − | 0.697580i | ||||
\(412\) | 6.00000 | − | 6.00000i | 0.295599 | − | 0.295599i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −11.3137 | − | 4.00000i | −0.556038 | − | 0.196589i | ||||
\(415\) | −6.00000 | + | 12.0000i | −0.294528 | + | 0.589057i | ||||
\(416\) | − | 4.24264i | − | 0.208013i | ||||||
\(417\) | 3.51472 | − | 20.4853i | 0.172117 | − | 1.00317i | ||||
\(418\) | −4.00000 | − | 4.00000i | −0.195646 | − | 0.195646i | ||||
\(419\) | −5.65685 | −0.276355 | −0.138178 | − | 0.990407i | \(-0.544125\pi\) | ||||
−0.138178 | + | 0.990407i | \(0.544125\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | 7.07107 | + | 7.07107i | 0.344214 | + | 0.344214i | ||||
\(423\) | 2.58579 | + | 5.41421i | 0.125725 | + | 0.263248i | ||||
\(424\) | 2.00000i | 0.0971286i | ||||||||
\(425\) | −9.89949 | − | 1.41421i | −0.480196 | − | 0.0685994i | ||||
\(426\) | 18.0000 | − | 12.7279i | 0.872103 | − | 0.616670i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −8.48528 | + | 8.48528i | −0.410152 | + | 0.410152i | ||||
\(429\) | −8.48528 | + | 6.00000i | −0.409673 | + | 0.289683i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.5269i | 1.56677i | 0.621539 | + | 0.783383i | \(0.286508\pi\) | ||||
−0.621539 | + | 0.783383i | \(0.713492\pi\) | |||||||
\(432\) | −4.53553 | − | 2.53553i | −0.218216 | − | 0.121991i | ||||
\(433\) | 2.00000 | + | 2.00000i | 0.0961139 | + | 0.0961139i | 0.753529 | − | 0.657415i | \(-0.228350\pi\) |
−0.657415 | + | 0.753529i | \(0.728350\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.8284 | − | 1.65685i | 0.519183 | − | 0.0794401i | ||||
\(436\) | −10.0000 | −0.478913 | ||||||||
\(437\) | −11.3137 | − | 11.3137i | −0.541208 | − | 0.541208i | ||||
\(438\) | 0.828427 | − | 4.82843i | 0.0395838 | − | 0.230711i | ||||
\(439\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(440\) | 2.82843 | + | 1.41421i | 0.134840 | + | 0.0674200i | ||||
\(441\) | −7.00000 | + | 19.7990i | −0.333333 | + | 0.942809i | ||||
\(442\) | 6.00000 | − | 6.00000i | 0.285391 | − | 0.285391i | ||||
\(443\) | 16.9706 | − | 16.9706i | 0.806296 | − | 0.806296i | −0.177775 | − | 0.984071i | \(-0.556890\pi\) |
0.984071 | + | 0.177775i | \(0.0568900\pi\) | |||||||
\(444\) | −4.24264 | − | 6.00000i | −0.201347 | − | 0.284747i | ||||
\(445\) | −15.0000 | + | 5.00000i | −0.711068 | + | 0.237023i | ||||
\(446\) | − | 15.5563i | − | 0.736614i | ||||||
\(447\) | −2.41421 | − | 0.414214i | −0.114188 | − | 0.0195916i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.89949 | 0.467186 | 0.233593 | − | 0.972334i | \(-0.424952\pi\) | ||||
0.233593 | + | 0.972334i | \(0.424952\pi\) | |||||||
\(450\) | 13.2929 | + | 6.94975i | 0.626633 | + | 0.327614i | ||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | 4.24264 | + | 4.24264i | 0.199557 | + | 0.199557i | ||||
\(453\) | −13.6569 | − | 2.34315i | −0.641655 | − | 0.110091i | ||||
\(454\) | 16.0000i | 0.750917i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.00000 | − | 5.65685i | −0.187317 | − | 0.264906i | ||||
\(457\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(458\) | 18.3848 | − | 18.3848i | 0.859064 | − | 0.859064i | ||||
\(459\) | −2.82843 | − | 10.0000i | −0.132020 | − | 0.466760i | ||||
\(460\) | 8.00000 | + | 4.00000i | 0.373002 | + | 0.186501i | ||||
\(461\) | − | 2.82843i | − | 0.131733i | −0.997828 | − | 0.0658665i | \(-0.979019\pi\) | ||
0.997828 | − | 0.0658665i | \(-0.0209811\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.00000 | − | 7.00000i | −0.325318 | − | 0.325318i | 0.525485 | − | 0.850803i | \(-0.323884\pi\) |
−0.850803 | + | 0.525485i | \(0.823884\pi\) | |||||||
\(464\) | 2.82843 | 0.131306 | ||||||||
\(465\) | −3.82843 | + | 0.585786i | −0.177539 | + | 0.0271652i | ||||
\(466\) | −14.0000 | −0.648537 | ||||||||
\(467\) | −2.82843 | − | 2.82843i | −0.130884 | − | 0.130884i | 0.638630 | − | 0.769514i | \(-0.279501\pi\) |
−0.769514 | + | 0.638630i | \(0.779501\pi\) | |||||||
\(468\) | −11.4853 | + | 5.48528i | −0.530907 | + | 0.253557i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.41421 | − | 4.24264i | −0.0652328 | − | 0.195698i | ||||
\(471\) | −8.00000 | + | 5.65685i | −0.368621 | + | 0.260654i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 2.82843 | − | 2.00000i | 0.129914 | − | 0.0918630i | ||||
\(475\) | 12.0000 | + | 16.0000i | 0.550598 | + | 0.734130i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.41421 | − | 2.58579i | 0.247900 | − | 0.118395i | ||||
\(478\) | 16.0000 | + | 16.0000i | 0.731823 | + | 0.731823i | ||||
\(479\) | −38.1838 | −1.74466 | −0.872330 | − | 0.488917i | \(-0.837392\pi\) | ||||
−0.872330 | + | 0.488917i | \(0.837392\pi\) | |||||||
\(480\) | 3.12132 | + | 2.29289i | 0.142468 | + | 0.104656i | ||||
\(481\) | −18.0000 | −0.820729 | ||||||||
\(482\) | −1.41421 | − | 1.41421i | −0.0644157 | − | 0.0644157i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.00000i | 0.409091i | ||||||||
\(485\) | −15.5563 | + | 31.1127i | −0.706377 | + | 1.41275i | ||||
\(486\) | −1.00000 | + | 15.5563i | −0.0453609 | + | 0.705650i | ||||
\(487\) | −11.0000 | + | 11.0000i | −0.498458 | + | 0.498458i | −0.910958 | − | 0.412500i | \(-0.864656\pi\) |
0.412500 | + | 0.910958i | \(0.364656\pi\) | |||||||
\(488\) | −5.65685 | + | 5.65685i | −0.256074 | + | 0.256074i | ||||
\(489\) | −15.5563 | − | 22.0000i | −0.703482 | − | 0.994874i | ||||
\(490\) | 7.00000 | − | 14.0000i | 0.316228 | − | 0.632456i | ||||
\(491\) | 12.7279i | 0.574403i | 0.957870 | + | 0.287202i | \(0.0927249\pi\) | ||||
−0.957870 | + | 0.287202i | \(0.907275\pi\) | |||||||
\(492\) | 9.65685 | + | 1.65685i | 0.435365 | + | 0.0746968i | ||||
\(493\) | 4.00000 | + | 4.00000i | 0.180151 | + | 0.180151i | ||||
\(494\) | −16.9706 | −0.763542 | ||||||||
\(495\) | 0.171573 | − | 9.48528i | 0.00771163 | − | 0.426332i | ||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 10.2426 | + | 1.75736i | 0.458984 | + | 0.0787492i | ||||
\(499\) | 36.0000i | 1.61158i | 0.592200 | + | 0.805791i | \(0.298259\pi\) | ||||
−0.592200 | + | 0.805791i | \(0.701741\pi\) | |||||||
\(500\) | −9.19239 | − | 6.36396i | −0.411096 | − | 0.284605i | ||||
\(501\) | −8.00000 | − | 11.3137i | −0.357414 | − | 0.505459i | ||||
\(502\) | −3.00000 | + | 3.00000i | −0.133897 | + | 0.133897i | ||||
\(503\) | −18.3848 | + | 18.3848i | −0.819737 | + | 0.819737i | −0.986070 | − | 0.166333i | \(-0.946807\pi\) |
0.166333 | + | 0.986070i | \(0.446807\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.0000 | + | 33.0000i | 0.489494 | + | 1.46848i | ||||
\(506\) | − | 5.65685i | − | 0.251478i | ||||||
\(507\) | −1.46447 | + | 8.53553i | −0.0650392 | + | 0.379076i | ||||
\(508\) | 5.00000 | + | 5.00000i | 0.221839 | + | 0.221839i | ||||
\(509\) | 11.3137 | 0.501471 | 0.250736 | − | 0.968056i | \(-0.419328\pi\) | ||||
0.250736 | + | 0.968056i | \(0.419328\pi\) | |||||||
\(510\) | 1.17157 | + | 7.65685i | 0.0518781 | + | 0.339051i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −10.1421 | + | 18.1421i | −0.447786 | + | 0.800995i | ||||
\(514\) | − | 6.00000i | − | 0.264649i | ||||||
\(515\) | 16.9706 | + | 8.48528i | 0.747812 | + | 0.373906i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.00000 | + | 2.00000i | −0.0879599 | + | 0.0879599i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.2843 | + | 20.0000i | −1.24154 | + | 0.877903i | ||||
\(520\) | 9.00000 | − | 3.00000i | 0.394676 | − | 0.131559i | ||||
\(521\) | 14.1421i | 0.619578i | 0.950805 | + | 0.309789i | \(0.100258\pi\) | ||||
−0.950805 | + | 0.309789i | \(0.899742\pi\) | |||||||
\(522\) | −3.65685 | − | 7.65685i | −0.160056 | − | 0.335131i | ||||
\(523\) | 18.0000 | + | 18.0000i | 0.787085 | + | 0.787085i | 0.981015 | − | 0.193930i | \(-0.0621236\pi\) |
−0.193930 | + | 0.981015i | \(0.562124\pi\) | |||||||
\(524\) | −14.1421 | −0.617802 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.41421 | − | 1.41421i | −0.0616041 | − | 0.0616041i | ||||
\(528\) | 0.414214 | − | 2.41421i | 0.0180263 | − | 0.105065i | ||||
\(529\) | 7.00000i | 0.304348i | ||||||||
\(530\) | −4.24264 | + | 1.41421i | −0.184289 | + | 0.0614295i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.9706 | − | 16.9706i | 0.735077 | − | 0.735077i | ||||
\(534\) | 7.07107 | + | 10.0000i | 0.305995 | + | 0.432742i | ||||
\(535\) | −24.0000 | − | 12.0000i | −1.03761 | − | 0.518805i | ||||
\(536\) | 9.89949i | 0.427593i | ||||||||
\(537\) | 21.7279 | + | 3.72792i | 0.937629 | + | 0.160872i | ||||
\(538\) | 18.0000 | + | 18.0000i | 0.776035 | + | 0.776035i | ||||
\(539\) | −9.89949 | −0.426401 | ||||||||
\(540\) | 2.17157 | − | 11.4142i | 0.0934496 | − | 0.491190i | ||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | 7.07107 | + | 7.07107i | 0.303728 | + | 0.303728i | ||||
\(543\) | −17.0711 | − | 2.92893i | −0.732590 | − | 0.125693i | ||||
\(544\) | 2.00000i | 0.0857493i | ||||||||
\(545\) | −7.07107 | − | 21.2132i | −0.302891 | − | 0.908674i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.00000 | + | 5.00000i | −0.213785 | + | 0.213785i | −0.805873 | − | 0.592088i | \(-0.798304\pi\) |
0.592088 | + | 0.805873i | \(0.298304\pi\) | |||||||
\(548\) | 7.07107 | − | 7.07107i | 0.302061 | − | 0.302061i | ||||
\(549\) | 22.6274 | + | 8.00000i | 0.965715 | + | 0.341432i | ||||
\(550\) | −1.00000 | + | 7.00000i | −0.0426401 | + | 0.298481i | ||||
\(551\) | − | 11.3137i | − | 0.481980i | ||||||
\(552\) | 1.17157 | − | 6.82843i | 0.0498655 | − | 0.290637i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.07107 | 0.300421 | ||||||||
\(555\) | 9.72792 | − | 13.2426i | 0.412927 | − | 0.562119i | ||||
\(556\) | 12.0000 | 0.508913 | ||||||||
\(557\) | −26.8701 | − | 26.8701i | −1.13852 | − | 1.13852i | −0.988716 | − | 0.149805i | \(-0.952135\pi\) |
−0.149805 | − | 0.988716i | \(-0.547865\pi\) | |||||||
\(558\) | 1.29289 | + | 2.70711i | 0.0547325 | + | 0.114601i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.00000 | − | 2.82843i | 0.168880 | − | 0.119416i | ||||
\(562\) | 16.0000 | − | 16.0000i | 0.674919 | − | 0.674919i | ||||
\(563\) | 11.3137 | − | 11.3137i | 0.476816 | − | 0.476816i | −0.427296 | − | 0.904112i | \(-0.640534\pi\) |
0.904112 | + | 0.427296i | \(0.140534\pi\) | |||||||
\(564\) | −2.82843 | + | 2.00000i | −0.119098 | + | 0.0842152i | ||||
\(565\) | −6.00000 | + | 12.0000i | −0.252422 | + | 0.504844i | ||||
\(566\) | − | 26.8701i | − | 1.12943i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.00000 | + | 9.00000i | 0.377632 | + | 0.377632i | ||||
\(569\) | 26.8701 | 1.12645 | 0.563226 | − | 0.826303i | \(-0.309560\pi\) | ||||
0.563226 | + | 0.826303i | \(0.309560\pi\) | |||||||
\(570\) | 9.17157 | − | 12.4853i | 0.384155 | − | 0.522951i | ||||
\(571\) | −40.0000 | −1.67395 | −0.836974 | − | 0.547243i | \(-0.815677\pi\) | ||||
−0.836974 | + | 0.547243i | \(0.815677\pi\) | |||||||
\(572\) | −4.24264 | − | 4.24264i | −0.177394 | − | 0.177394i | ||||
\(573\) | −6.21320 | + | 36.2132i | −0.259560 | + | 1.51283i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.82843 | + | 19.7990i | −0.117954 | + | 0.825675i | ||||
\(576\) | 1.00000 | − | 2.82843i | 0.0416667 | − | 0.117851i | ||||
\(577\) | 21.0000 | − | 21.0000i | 0.874241 | − | 0.874241i | −0.118690 | − | 0.992931i | \(-0.537869\pi\) |
0.992931 | + | 0.118690i | \(0.0378694\pi\) | |||||||
\(578\) | 9.19239 | − | 9.19239i | 0.382353 | − | 0.382353i | ||||
\(579\) | −12.7279 | − | 18.0000i | −0.528954 | − | 0.748054i | ||||
\(580\) | 2.00000 | + | 6.00000i | 0.0830455 | + | 0.249136i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 26.5563 | + | 4.55635i | 1.10080 | + | 0.188867i | ||||
\(583\) | 2.00000 | + | 2.00000i | 0.0828315 | + | 0.0828315i | ||||
\(584\) | 2.82843 | 0.117041 | ||||||||
\(585\) | −19.7574 | − | 20.4853i | −0.816866 | − | 0.846962i | ||||
\(586\) | −24.0000 | −0.991431 | ||||||||
\(587\) | −25.4558 | − | 25.4558i | −1.05068 | − | 1.05068i | −0.998646 | − | 0.0520296i | \(-0.983431\pi\) |
−0.0520296 | − | 0.998646i | \(-0.516569\pi\) | |||||||
\(588\) | −11.9497 | − | 2.05025i | −0.492799 | − | 0.0845510i | ||||
\(589\) | 4.00000i | 0.164817i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0000 | + | 14.1421i | 0.411345 | + | 0.581730i | ||||
\(592\) | 3.00000 | − | 3.00000i | 0.123299 | − | 0.123299i | ||||
\(593\) | 4.24264 | − | 4.24264i | 0.174224 | − | 0.174224i | −0.614608 | − | 0.788833i | \(-0.710686\pi\) |
0.788833 | + | 0.614608i | \(0.210686\pi\) | |||||||
\(594\) | −7.07107 | + | 2.00000i | −0.290129 | + | 0.0820610i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 1.41421i | − | 0.0579284i | ||||||
\(597\) | −7.02944 | + | 40.9706i | −0.287696 | + | 1.67681i | ||||
\(598\) | −12.0000 | − | 12.0000i | −0.490716 | − | 0.490716i | ||||
\(599\) | 43.8406 | 1.79128 | 0.895640 | − | 0.444781i | \(-0.146718\pi\) | ||||
0.895640 | + | 0.444781i | \(0.146718\pi\) | |||||||
\(600\) | −2.65685 | + | 8.24264i | −0.108466 | + | 0.336504i | ||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26.7990 | − | 12.7990i | 1.09134 | − | 0.521215i | ||||
\(604\) | − | 8.00000i | − | 0.325515i | ||||||
\(605\) | −19.0919 | + | 6.36396i | −0.776195 | + | 0.258732i | ||||
\(606\) | 22.0000 | − | 15.5563i | 0.893689 | − | 0.631933i | ||||
\(607\) | −20.0000 | + | 20.0000i | −0.811775 | + | 0.811775i | −0.984900 | − | 0.173125i | \(-0.944614\pi\) |
0.173125 | + | 0.984900i | \(0.444614\pi\) | |||||||
\(608\) | 2.82843 | − | 2.82843i | 0.114708 | − | 0.114708i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.0000 | − | 8.00000i | −0.647821 | − | 0.323911i | ||||
\(611\) | 8.48528i | 0.343278i | ||||||||
\(612\) | 5.41421 | − | 2.58579i | 0.218857 | − | 0.104524i | ||||
\(613\) | −13.0000 | − | 13.0000i | −0.525065 | − | 0.525065i | 0.394032 | − | 0.919097i | \(-0.371080\pi\) |
−0.919097 | + | 0.394032i | \(0.871080\pi\) | |||||||
\(614\) | 7.07107 | 0.285365 | ||||||||
\(615\) | 3.31371 | + | 21.6569i | 0.133622 | + | 0.873289i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.6985 | − | 29.6985i | −1.19562 | − | 1.19562i | −0.975466 | − | 0.220150i | \(-0.929345\pi\) |
−0.220150 | − | 0.975466i | \(-0.570655\pi\) | |||||||
\(618\) | 2.48528 | − | 14.4853i | 0.0999727 | − | 0.582683i | ||||
\(619\) | 4.00000i | 0.160774i | 0.996764 | + | 0.0803868i | \(0.0256155\pi\) | ||||
−0.996764 | + | 0.0803868i | \(0.974384\pi\) | |||||||
\(620\) | −0.707107 | − | 2.12132i | −0.0283981 | − | 0.0851943i | ||||
\(621\) | −20.0000 | + | 5.65685i | −0.802572 | + | 0.227002i | ||||
\(622\) | 1.00000 | − | 1.00000i | 0.0400963 | − | 0.0400963i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.24264 | − | 6.00000i | −0.169842 | − | 0.240192i | ||||
\(625\) | 7.00000 | − | 24.0000i | 0.280000 | − | 0.960000i | ||||
\(626\) | − | 14.1421i | − | 0.565233i | ||||||
\(627\) | −9.65685 | − | 1.65685i | −0.385658 | − | 0.0661684i | ||||
\(628\) | −4.00000 | − | 4.00000i | −0.159617 | − | 0.159617i | ||||
\(629\) | 8.48528 | 0.338330 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0000 | 1.27390 | 0.636950 | − | 0.770905i | \(-0.280196\pi\) | ||||
0.636950 | + | 0.770905i | \(0.280196\pi\) | |||||||
\(632\) | 1.41421 | + | 1.41421i | 0.0562544 | + | 0.0562544i | ||||
\(633\) | 17.0711 | + | 2.92893i | 0.678514 | + | 0.116415i | ||||
\(634\) | 6.00000i | 0.238290i | ||||||||
\(635\) | −7.07107 | + | 14.1421i | −0.280607 | + | 0.561214i | ||||
\(636\) | 2.00000 | + | 2.82843i | 0.0793052 | + | 0.112154i | ||||
\(637\) | −21.0000 | + | 21.0000i | −0.832050 | + | 0.832050i | ||||
\(638\) | 2.82843 | − | 2.82843i | 0.111979 | − | 0.111979i | ||||
\(639\) | 12.7279 | − | 36.0000i | 0.503509 | − | 1.42414i | ||||
\(640\) | −1.00000 | + | 2.00000i | −0.0395285 | + | 0.0790569i | ||||
\(641\) | − | 26.8701i | − | 1.06130i | −0.847590 | − | 0.530652i | \(-0.821947\pi\) | ||
0.847590 | − | 0.530652i | \(-0.178053\pi\) | |||||||
\(642\) | −3.51472 | + | 20.4853i | −0.138715 | + | 0.808490i | ||||
\(643\) | 6.00000 | + | 6.00000i | 0.236617 | + | 0.236617i | 0.815448 | − | 0.578831i | \(-0.196491\pi\) |
−0.578831 | + | 0.815448i | \(0.696491\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.00000 | 0.314756 | ||||||||
\(647\) | 8.48528 | + | 8.48528i | 0.333591 | + | 0.333591i | 0.853948 | − | 0.520358i | \(-0.174201\pi\) |
−0.520358 | + | 0.853948i | \(0.674201\pi\) | |||||||
\(648\) | −8.94975 | + | 0.949747i | −0.351579 | + | 0.0373096i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 12.7279 | + | 16.9706i | 0.499230 | + | 0.665640i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.0000 | − | 11.0000i | 0.430793 | − | 0.430793i | ||||
\(653\) | 12.7279 | − | 12.7279i | 0.498082 | − | 0.498082i | −0.412758 | − | 0.910841i | \(-0.635435\pi\) |
0.910841 | + | 0.412758i | \(0.135435\pi\) | |||||||
\(654\) | −14.1421 | + | 10.0000i | −0.553001 | + | 0.391031i | ||||
\(655\) | −10.0000 | − | 30.0000i | −0.390732 | − | 1.17220i | ||||
\(656\) | 5.65685i | 0.220863i | ||||||||
\(657\) | −3.65685 | − | 7.65685i | −0.142667 | − | 0.298722i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.9706 | 0.661079 | 0.330540 | − | 0.943792i | \(-0.392769\pi\) | ||||
0.330540 | + | 0.943792i | \(0.392769\pi\) | |||||||
\(660\) | 5.41421 | − | 0.828427i | 0.210748 | − | 0.0322465i | ||||
\(661\) | −34.0000 | −1.32245 | −0.661223 | − | 0.750189i | \(-0.729962\pi\) | ||||
−0.661223 | + | 0.750189i | \(0.729962\pi\) | |||||||
\(662\) | 22.6274 | + | 22.6274i | 0.879440 | + | 0.879440i | ||||
\(663\) | 2.48528 | − | 14.4853i | 0.0965203 | − | 0.562562i | ||||
\(664\) | 6.00000i | 0.232845i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −12.0000 | − | 4.24264i | −0.464991 | − | 0.164399i | ||||
\(667\) | 8.00000 | − | 8.00000i | 0.309761 | − | 0.309761i | ||||
\(668\) | 5.65685 | − | 5.65685i | 0.218870 | − | 0.218870i | ||||
\(669\) | −15.5563 | − | 22.0000i | −0.601443 | − | 0.850569i | ||||
\(670\) | −21.0000 | + | 7.00000i | −0.811301 | + | 0.270434i | ||||
\(671\) | 11.3137i | 0.436761i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.0000 | + | 24.0000i | 0.925132 | + | 0.925132i | 0.997386 | − | 0.0722542i | \(-0.0230193\pi\) |
−0.0722542 | + | 0.997386i | \(0.523019\pi\) | |||||||
\(674\) | −11.3137 | −0.435788 | ||||||||
\(675\) | 25.7487 | − | 3.46447i | 0.991069 | − | 0.133347i | ||||
\(676\) | −5.00000 | −0.192308 | ||||||||
\(677\) | −15.5563 | − | 15.5563i | −0.597879 | − | 0.597879i | 0.341869 | − | 0.939748i | \(-0.388940\pi\) |
−0.939748 | + | 0.341869i | \(0.888940\pi\) | |||||||
\(678\) | 10.2426 | + | 1.75736i | 0.393366 | + | 0.0674910i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.24264 | + | 1.41421i | −0.162698 | + | 0.0542326i | ||||
\(681\) | 16.0000 | + | 22.6274i | 0.613121 | + | 0.867085i | ||||
\(682\) | −1.00000 | + | 1.00000i | −0.0382920 | + | 0.0382920i | ||||
\(683\) | 16.9706 | − | 16.9706i | 0.649361 | − | 0.649361i | −0.303478 | − | 0.952838i | \(-0.598148\pi\) |
0.952838 | + | 0.303478i | \(0.0981479\pi\) | |||||||
\(684\) | −11.3137 | − | 4.00000i | −0.432590 | − | 0.152944i | ||||
\(685\) | 20.0000 | + | 10.0000i | 0.764161 | + | 0.382080i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.61522 | − | 44.3848i | 0.290539 | − | 1.69338i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.48528 | 0.323263 | ||||||||
\(690\) | 15.3137 | − | 2.34315i | 0.582983 | − | 0.0892020i | ||||
\(691\) | −14.0000 | −0.532585 | −0.266293 | − | 0.963892i | \(-0.585799\pi\) | ||||
−0.266293 | + | 0.963892i | \(0.585799\pi\) | |||||||
\(692\) | −14.1421 | − | 14.1421i | −0.537603 | − | 0.537603i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.00000i | 0.227757i | ||||||||
\(695\) | 8.48528 | + | 25.4558i | 0.321865 | + | 0.965595i | ||||
\(696\) | 4.00000 | − | 2.82843i | 0.151620 | − | 0.107211i | ||||
\(697\) | −8.00000 | + | 8.00000i | −0.303022 | + | 0.303022i | ||||
\(698\) | 21.2132 | − | 21.2132i | 0.802932 | − | 0.802932i | ||||
\(699\) | −19.7990 | + | 14.0000i | −0.748867 | + | 0.529529i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4.24264i | − | 0.160242i | −0.996785 | − | 0.0801212i | \(-0.974469\pi\) | ||
0.996785 | − | 0.0801212i | \(-0.0255307\pi\) | |||||||
\(702\) | −10.7574 | + | 19.2426i | −0.406010 | + | 0.726267i | ||||
\(703\) | −12.0000 | − | 12.0000i | −0.452589 | − | 0.452589i | ||||
\(704\) | 1.41421 | 0.0533002 | ||||||||
\(705\) | −6.24264 | − | 4.58579i | −0.235111 | − | 0.172711i | ||||
\(706\) | −36.0000 | −1.35488 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 48.0000i | − | 1.80268i | −0.433114 | − | 0.901339i | \(-0.642585\pi\) | ||
0.433114 | − | 0.901339i | \(-0.357415\pi\) | |||||||
\(710\) | −12.7279 | + | 25.4558i | −0.477670 | + | 0.955341i | ||||
\(711\) | 2.00000 | − | 5.65685i | 0.0750059 | − | 0.212149i | ||||
\(712\) | −5.00000 | + | 5.00000i | −0.187383 | + | 0.187383i | ||||
\(713\) | −2.82843 | + | 2.82843i | −0.105925 | + | 0.105925i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | − | 12.0000i | 0.224387 | − | 0.448775i | ||||
\(716\) | 12.7279i | 0.475665i | ||||||||
\(717\) | 38.6274 | + | 6.62742i | 1.44257 | + | 0.247505i | ||||
\(718\) | 5.00000 | + | 5.00000i | 0.186598 | + | 0.186598i | ||||
\(719\) | 39.5980 | 1.47676 | 0.738378 | − | 0.674387i | \(-0.235592\pi\) | ||||
0.738378 | + | 0.674387i | \(0.235592\pi\) | |||||||
\(720\) | 6.70711 | + | 0.121320i | 0.249959 | + | 0.00452134i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.12132 | + | 2.12132i | 0.0789474 | + | 0.0789474i | ||||
\(723\) | −3.41421 | − | 0.585786i | −0.126976 | − | 0.0217856i | ||||
\(724\) | − | 10.0000i | − | 0.371647i | ||||||
\(725\) | −11.3137 | + | 8.48528i | −0.420181 | + | 0.315135i | ||||
\(726\) | 9.00000 | + | 12.7279i | 0.334021 | + | 0.472377i | ||||
\(727\) | −18.0000 | + | 18.0000i | −0.667583 | + | 0.667583i | −0.957156 | − | 0.289573i | \(-0.906487\pi\) |
0.289573 | + | 0.957156i | \(0.406487\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.1421 | + | 23.0000i | 0.523783 | + | 0.851852i | ||||
\(730\) | 2.00000 | + | 6.00000i | 0.0740233 | + | 0.222070i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −2.34315 | + | 13.6569i | −0.0866052 | + | 0.504772i | ||||
\(733\) | 24.0000 | + | 24.0000i | 0.886460 | + | 0.886460i | 0.994181 | − | 0.107721i | \(-0.0343553\pi\) |
−0.107721 | + | 0.994181i | \(0.534355\pi\) | |||||||
\(734\) | −21.2132 | −0.782994 | ||||||||
\(735\) | −4.10051 | − | 26.7990i | −0.151249 | − | 0.988496i | ||||
\(736\) | 4.00000 | 0.147442 | ||||||||
\(737\) | 9.89949 | + | 9.89949i | 0.364653 | + | 0.364653i | ||||
\(738\) | 15.3137 | − | 7.31371i | 0.563705 | − | 0.269221i | ||||
\(739\) | 40.0000i | 1.47142i | 0.677295 | + | 0.735712i | \(0.263152\pi\) | ||||
−0.677295 | + | 0.735712i | \(0.736848\pi\) | |||||||
\(740\) | 8.48528 | + | 4.24264i | 0.311925 | + | 0.155963i | ||||
\(741\) | −24.0000 | + | 16.9706i | −0.881662 | + | 0.623429i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.1421 | − | 14.1421i | 0.518825 | − | 0.518825i | −0.398391 | − | 0.917216i | \(-0.630431\pi\) |
0.917216 | + | 0.398391i | \(0.130431\pi\) | |||||||
\(744\) | −1.41421 | + | 1.00000i | −0.0518476 | + | 0.0366618i | ||||
\(745\) | 3.00000 | − | 1.00000i | 0.109911 | − | 0.0366372i | ||||
\(746\) | − | 16.9706i | − | 0.621336i | ||||||
\(747\) | 16.2426 | − | 7.75736i | 0.594287 | − | 0.283827i | ||||
\(748\) | 2.00000 | + | 2.00000i | 0.0731272 | + | 0.0731272i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −19.3640 | + | 0.192388i | −0.707072 | + | 0.00702502i | ||||
\(751\) | 4.00000 | 0.145962 | 0.0729810 | − | 0.997333i | \(-0.476749\pi\) | ||||
0.0729810 | + | 0.997333i | \(0.476749\pi\) | |||||||
\(752\) | −1.41421 | − | 1.41421i | −0.0515711 | − | 0.0515711i | ||||
\(753\) | −1.24264 | + | 7.24264i | −0.0452843 | + | 0.263936i | ||||
\(754\) | − | 12.0000i | − | 0.437014i | ||||||
\(755\) | 16.9706 | − | 5.65685i | 0.617622 | − | 0.205874i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.0000 | + | 35.0000i | −1.27210 | + | 1.27210i | −0.327111 | + | 0.944986i | \(0.606075\pi\) |
−0.944986 | + | 0.327111i | \(0.893925\pi\) | |||||||
\(758\) | −24.0416 | + | 24.0416i | −0.873231 | + | 0.873231i | ||||
\(759\) | −5.65685 | − | 8.00000i | −0.205331 | − | 0.290382i | ||||
\(760\) | 8.00000 | + | 4.00000i | 0.290191 | + | 0.145095i | ||||
\(761\) | 52.3259i | 1.89681i | 0.317058 | + | 0.948406i | \(0.397305\pi\) | ||||
−0.317058 | + | 0.948406i | \(0.602695\pi\) | |||||||
\(762\) | 12.0711 | + | 2.07107i | 0.437289 | + | 0.0750269i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −21.2132 | −0.767467 | ||||||||
\(765\) | 9.31371 | + | 9.65685i | 0.336738 | + | 0.349144i | ||||
\(766\) | −36.0000 | −1.30073 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.70711 | + | 0.292893i | 0.0615999 | + | 0.0105689i | ||||
\(769\) | − | 48.0000i | − | 1.73092i | −0.500974 | − | 0.865462i | \(-0.667025\pi\) | ||
0.500974 | − | 0.865462i | \(-0.332975\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.00000 | − | 8.48528i | −0.216085 | − | 0.305590i | ||||
\(772\) | 9.00000 | − | 9.00000i | 0.323917 | − | 0.323917i | ||||
\(773\) | 12.7279 | − | 12.7279i | 0.457792 | − | 0.457792i | −0.440138 | − | 0.897930i | \(-0.645071\pi\) |
0.897930 | + | 0.440138i | \(0.145071\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.00000 | − | 3.00000i | 0.143684 | − | 0.107763i | ||||
\(776\) | 15.5563i | 0.558440i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.00000 | − | 4.00000i | −0.143407 | − | 0.143407i | ||||
\(779\) | 22.6274 | 0.810711 | ||||||||
\(780\) | 9.72792 | − | 13.2426i | 0.348315 | − | 0.474163i | ||||
\(781\) | 18.0000 | 0.644091 | ||||||||
\(782\) | 5.65685 | + | 5.65685i | 0.202289 | + | 0.202289i | ||||
\(783\) | −12.8284 | − | 7.17157i | −0.458451 | − | 0.256291i | ||||
\(784\) | − | 7.00000i | − | 0.250000i | ||||||
\(785\) | 5.65685 | − | 11.3137i | 0.201902 | − | 0.403804i | ||||
\(786\) | −20.0000 | + | 14.1421i | −0.713376 | + | 0.504433i | ||||
\(787\) | −24.0000 | + | 24.0000i | −0.855508 | + | 0.855508i | −0.990805 | − | 0.135297i | \(-0.956801\pi\) |
0.135297 | + | 0.990805i | \(0.456801\pi\) | |||||||
\(788\) | −7.07107 | + | 7.07107i | −0.251896 | + | 0.251896i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.00000 | + | 4.00000i | −0.0711568 | + | 0.142314i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.82843 | − | 3.82843i | −0.0649703 | − | 0.136037i | ||||
\(793\) | 24.0000 | + | 24.0000i | 0.852265 | + | 0.852265i | ||||
\(794\) | −11.3137 | −0.401508 | ||||||||
\(795\) | −4.58579 | + | 6.24264i | −0.162641 | + | 0.221404i | ||||
\(796\) | −24.0000 | −0.850657 | ||||||||
\(797\) | 4.24264 | + | 4.24264i | 0.150282 | + | 0.150282i | 0.778244 | − | 0.627962i | \(-0.216111\pi\) |
−0.627962 | + | 0.778244i | \(0.716111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4.00000i | − | 0.141510i | ||||||
\(800\) | −4.94975 | − | 0.707107i | −0.175000 | − | 0.0250000i | ||||
\(801\) | 20.0000 | + | 7.07107i | 0.706665 | + | 0.249844i | ||||
\(802\) | 19.0000 | − | 19.0000i | 0.670913 | − | 0.670913i | ||||
\(803\) | 2.82843 | − | 2.82843i | 0.0998130 | − | 0.0998130i | ||||
\(804\) | 9.89949 | + | 14.0000i | 0.349128 | + | 0.493742i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.24264i | 0.149441i | ||||||||
\(807\) | 43.4558 | + | 7.45584i | 1.52972 | + | 0.262458i | ||||
\(808\) | 11.0000 | + | 11.0000i | 0.386979 | + | 0.386979i | ||||
\(809\) | −7.07107 | −0.248606 | −0.124303 | − | 0.992244i | \(-0.539669\pi\) | ||||
−0.124303 | + | 0.992244i | \(0.539669\pi\) | |||||||
\(810\) | −8.34315 | − | 18.3137i | −0.293148 | − | 0.643478i | ||||
\(811\) | 6.00000 | 0.210688 | 0.105344 | − | 0.994436i | \(-0.466406\pi\) | ||||
0.105344 | + | 0.994436i | \(0.466406\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.0711 | + | 2.92893i | 0.598708 | + | 0.102722i | ||||
\(814\) | − | 6.00000i | − | 0.210300i | ||||||
\(815\) | 31.1127 | + | 15.5563i | 1.08983 | + | 0.544915i | ||||
\(816\) | 2.00000 | + | 2.82843i | 0.0700140 | + | 0.0990148i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 4.24264 | − | 4.24264i | 0.148340 | − | 0.148340i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.0000 | + | 4.00000i | −0.419058 | + | 0.139686i | ||||
\(821\) | − | 14.1421i | − | 0.493564i | −0.969071 | − | 0.246782i | \(-0.920627\pi\) | ||
0.969071 | − | 0.246782i | \(-0.0793731\pi\) | |||||||
\(822\) | 2.92893 | − | 17.0711i | 0.102158 | − | 0.595422i | ||||
\(823\) | −25.0000 | − | 25.0000i | −0.871445 | − | 0.871445i | 0.121185 | − | 0.992630i | \(-0.461331\pi\) |
−0.992630 | + | 0.121185i | \(0.961331\pi\) | |||||||
\(824\) | 8.48528 | 0.295599 | ||||||||
\(825\) | 5.58579 | + | 10.8995i | 0.194472 | + | 0.379472i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.4558 | − | 25.4558i | −0.885186 | − | 0.885186i | 0.108870 | − | 0.994056i | \(-0.465277\pi\) |
−0.994056 | + | 0.108870i | \(0.965277\pi\) | |||||||
\(828\) | −5.17157 | − | 10.8284i | −0.179725 | − | 0.376314i | ||||
\(829\) | 28.0000i | 0.972480i | 0.873825 | + | 0.486240i | \(0.161632\pi\) | ||||
−0.873825 | + | 0.486240i | \(0.838368\pi\) | |||||||
\(830\) | −12.7279 | + | 4.24264i | −0.441793 | + | 0.147264i | ||||
\(831\) | 10.0000 | − | 7.07107i | 0.346896 | − | 0.245293i | ||||
\(832\) | 3.00000 | − | 3.00000i | 0.104006 | − | 0.104006i | ||||
\(833\) | 9.89949 | − | 9.89949i | 0.342997 | − | 0.342997i | ||||
\(834\) | 16.9706 | − | 12.0000i | 0.587643 | − | 0.415526i | ||||
\(835\) | 16.0000 | + | 8.00000i | 0.553703 | + | 0.276851i | ||||
\(836\) | − | 5.65685i | − | 0.195646i | ||||||
\(837\) | 4.53553 | + | 2.53553i | 0.156771 | + | 0.0876409i | ||||
\(838\) | −4.00000 | − | 4.00000i | −0.138178 | − | 0.138178i | ||||
\(839\) | −35.3553 | −1.22060 | −0.610301 | − | 0.792170i | \(-0.708951\pi\) | ||||
−0.610301 | + | 0.792170i | \(0.708951\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | −15.5563 | − | 15.5563i | −0.536107 | − | 0.536107i | ||||
\(843\) | 6.62742 | − | 38.6274i | 0.228260 | − | 1.33040i | ||||
\(844\) | 10.0000i | 0.344214i | ||||||||
\(845\) | −3.53553 | − | 10.6066i | −0.121626 | − | 0.364878i | ||||
\(846\) | −2.00000 | + | 5.65685i | −0.0687614 | + | 0.194487i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.41421 | + | 1.41421i | −0.0485643 | + | 0.0485643i | ||||
\(849\) | −26.8701 | − | 38.0000i | −0.922178 | − | 1.30416i | ||||
\(850\) | −6.00000 | − | 8.00000i | −0.205798 | − | 0.274398i | ||||
\(851\) | − | 16.9706i | − | 0.581743i | ||||||
\(852\) | 21.7279 | + | 3.72792i | 0.744386 | + | 0.127717i | ||||
\(853\) | 8.00000 | + | 8.00000i | 0.273915 | + | 0.273915i | 0.830674 | − | 0.556759i | \(-0.187955\pi\) |
−0.556759 | + | 0.830674i | \(0.687955\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.485281 | − | 26.8284i | 0.0165963 | − | 0.917513i | ||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | −21.2132 | − | 21.2132i | −0.724629 | − | 0.724629i | 0.244915 | − | 0.969544i | \(-0.421240\pi\) |
−0.969544 | + | 0.244915i | \(0.921240\pi\) | |||||||
\(858\) | −10.2426 | − | 1.75736i | −0.349678 | − | 0.0599953i | ||||
\(859\) | 12.0000i | 0.409435i | 0.978821 | + | 0.204717i | \(0.0656275\pi\) | ||||
−0.978821 | + | 0.204717i | \(0.934372\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.0000 | + | 23.0000i | −0.783383 | + | 0.783383i | ||||
\(863\) | 16.9706 | − | 16.9706i | 0.577685 | − | 0.577685i | −0.356580 | − | 0.934265i | \(-0.616057\pi\) |
0.934265 | + | 0.356580i | \(0.116057\pi\) | |||||||
\(864\) | −1.41421 | − | 5.00000i | −0.0481125 | − | 0.170103i | ||||
\(865\) | 20.0000 | − | 40.0000i | 0.680020 | − | 1.36004i | ||||
\(866\) | 2.82843i | 0.0961139i | ||||||||
\(867\) | 3.80761 | − | 22.1924i | 0.129313 | − | 0.753693i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.82843 | 0.0959478 | ||||||||
\(870\) | 8.82843 | + | 6.48528i | 0.299312 | + | 0.219872i | ||||
\(871\) | 42.0000 | 1.42312 | ||||||||
\(872\) | −7.07107 | − | 7.07107i | −0.239457 | − | 0.239457i | ||||
\(873\) | 42.1127 | − | 20.1127i | 1.42530 | − | 0.680712i | ||||
\(874\) | − | 16.0000i | − | 0.541208i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.00000 | − | 2.82843i | 0.135147 | − | 0.0955637i | ||||
\(877\) | 30.0000 | − | 30.0000i | 1.01303 | − | 1.01303i | 0.0131140 | − | 0.999914i | \(-0.495826\pi\) |
0.999914 | − | 0.0131140i | \(-0.00417444\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −33.9411 | + | 24.0000i | −1.14481 | + | 0.809500i | ||||
\(880\) | 1.00000 | + | 3.00000i | 0.0337100 | + | 0.101130i | ||||
\(881\) | 24.0416i | 0.809983i | 0.914320 | + | 0.404992i | \(0.132726\pi\) | ||||
−0.914320 | + | 0.404992i | \(0.867274\pi\) | |||||||
\(882\) | −18.9497 | + | 9.05025i | −0.638071 | + | 0.304738i | ||||
\(883\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(884\) | 8.48528 | 0.285391 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.0000 | 0.806296 | ||||||||
\(887\) | 1.41421 | + | 1.41421i | 0.0474846 | + | 0.0474846i | 0.730450 | − | 0.682966i | \(-0.239310\pi\) |
−0.682966 | + | 0.730450i | \(0.739310\pi\) | |||||||
\(888\) | 1.24264 | − | 7.24264i | 0.0417003 | − | 0.243047i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −14.1421 | − | 7.07107i | −0.474045 | − | 0.237023i | ||||
\(891\) | −8.00000 | + | 9.89949i | −0.268010 | + | 0.331646i | ||||
\(892\) | 11.0000 | − | 11.0000i | 0.368307 | − | 0.368307i | ||||
\(893\) | −5.65685 | + | 5.65685i | −0.189299 | + | 0.189299i | ||||
\(894\) | −1.41421 | − | 2.00000i | −0.0472984 | − | 0.0668900i | ||||
\(895\) | −27.0000 | + | 9.00000i | −0.902510 | + | 0.300837i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.9706 | − | 4.97056i | −0.967299 | − | 0.165962i | ||||
\(898\) | 7.00000 | + | 7.00000i | 0.233593 | + | 0.233593i | ||||
\(899\) | −2.82843 | −0.0943333 | ||||||||
\(900\) | 4.48528 | + | 14.3137i | 0.149509 | + | 0.477124i | ||||
\(901\) | −4.00000 | −0.133259 | ||||||||
\(902\) | 5.65685 | + | 5.65685i | 0.188353 | + | 0.188353i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.00000i | 0.199557i | ||||||||
\(905\) | 21.2132 | − | 7.07107i | 0.705151 | − | 0.235050i | ||||
\(906\) | −8.00000 | − | 11.3137i | −0.265782 | − | 0.375873i | ||||
\(907\) | 25.0000 | − | 25.0000i | 0.830111 | − | 0.830111i | −0.157420 | − | 0.987532i | \(-0.550318\pi\) |
0.987532 | + | 0.157420i | \(0.0503177\pi\) | |||||||
\(908\) | −11.3137 | + | 11.3137i | −0.375459 | + | 0.375459i | ||||
\(909\) | 15.5563 | − | 44.0000i | 0.515972 | − | 1.45939i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.3137i | 0.374840i | 0.982280 | + | 0.187420i | \(0.0600125\pi\) | ||||
−0.982280 | + | 0.187420i | \(0.939987\pi\) | |||||||
\(912\) | 1.17157 | − | 6.82843i | 0.0387947 | − | 0.226112i | ||||
\(913\) | 6.00000 | + | 6.00000i | 0.198571 | + | 0.198571i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −30.6274 | + | 4.68629i | −1.01251 | + | 0.154924i | ||||
\(916\) | 26.0000 | 0.859064 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.07107 | − | 9.07107i | 0.167370 | − | 0.299390i | ||||
\(919\) | − | 4.00000i | − | 0.131948i | −0.997821 | − | 0.0659739i | \(-0.978985\pi\) | ||
0.997821 | − | 0.0659739i | \(-0.0210154\pi\) | |||||||
\(920\) | 2.82843 | + | 8.48528i | 0.0932505 | + | 0.279751i | ||||
\(921\) | 10.0000 | − | 7.07107i | 0.329511 | − | 0.233000i | ||||
\(922\) | 2.00000 | − | 2.00000i | 0.0658665 | − | 0.0658665i | ||||
\(923\) | 38.1838 | − | 38.1838i | 1.25683 | − | 1.25683i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.00000 | + | 21.0000i | −0.0986394 | + | 0.690476i | ||||
\(926\) | − | 9.89949i | − | 0.325318i | ||||||
\(927\) | −10.9706 | − | 22.9706i | −0.360321 | − | 0.754452i | ||||
\(928\) | 2.00000 | + | 2.00000i | 0.0656532 | + | 0.0656532i | ||||
\(929\) | 1.41421 | 0.0463988 | 0.0231994 | − | 0.999731i | \(-0.492615\pi\) | ||||
0.0231994 | + | 0.999731i | \(0.492615\pi\) | |||||||
\(930\) | −3.12132 | − | 2.29289i | −0.102352 | − | 0.0751869i | ||||
\(931\) | −28.0000 | −0.917663 | ||||||||
\(932\) | −9.89949 | − | 9.89949i | −0.324269 | − | 0.324269i | ||||
\(933\) | 0.414214 | − | 2.41421i | 0.0135607 | − | 0.0790378i | ||||
\(934\) | − | 4.00000i | − | 0.130884i | ||||||
\(935\) | −2.82843 | + | 5.65685i | −0.0924995 | + | 0.184999i | ||||
\(936\) | −12.0000 | − | 4.24264i | −0.392232 | − | 0.138675i | ||||
\(937\) | 13.0000 | − | 13.0000i | 0.424691 | − | 0.424691i | −0.462124 | − | 0.886815i | \(-0.652912\pi\) |
0.886815 | + | 0.462124i | \(0.152912\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.1421 | − | 20.0000i | −0.461511 | − | 0.652675i | ||||
\(940\) | 2.00000 | − | 4.00000i | 0.0652328 | − | 0.130466i | ||||
\(941\) | − | 16.9706i | − | 0.553225i | −0.960982 | − | 0.276612i | \(-0.910788\pi\) | ||
0.960982 | − | 0.276612i | \(-0.0892118\pi\) | |||||||
\(942\) | −9.65685 | − | 1.65685i | −0.314637 | − | 0.0539832i | ||||
\(943\) | 16.0000 | + | 16.0000i | 0.521032 | + | 0.521032i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.4558 | + | 25.4558i | 0.827204 | + | 0.827204i | 0.987129 | − | 0.159925i | \(-0.0511253\pi\) |
−0.159925 | + | 0.987129i | \(0.551125\pi\) | |||||||
\(948\) | 3.41421 | + | 0.585786i | 0.110889 | + | 0.0190255i | ||||
\(949\) | − | 12.0000i | − | 0.389536i | ||||||
\(950\) | −2.82843 | + | 19.7990i | −0.0917663 | + | 0.642364i | ||||
\(951\) | 6.00000 | + | 8.48528i | 0.194563 | + | 0.275154i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.4558 | + | 25.4558i | −0.824596 | + | 0.824596i | −0.986763 | − | 0.162168i | \(-0.948151\pi\) |
0.162168 | + | 0.986763i | \(0.448151\pi\) | |||||||
\(954\) | 5.65685 | + | 2.00000i | 0.183147 | + | 0.0647524i | ||||
\(955\) | −15.0000 | − | 45.0000i | −0.485389 | − | 1.45617i | ||||
\(956\) | 22.6274i | 0.731823i | ||||||||
\(957\) | 1.17157 | − | 6.82843i | 0.0378716 | − | 0.220732i | ||||
\(958\) | −27.0000 | − | 27.0000i | −0.872330 | − | 0.872330i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.585786 | + | 3.82843i | 0.0189062 | + | 0.123562i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −12.7279 | − | 12.7279i | −0.410365 | − | 0.410365i | ||||
\(963\) | 15.5147 | + | 32.4853i | 0.499955 | + | 1.04682i | ||||
\(964\) | − | 2.00000i | − | 0.0644157i | ||||||
\(965\) | 25.4558 | + | 12.7279i | 0.819453 | + | 0.409726i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.0000 | − | 31.0000i | 0.996893 | − | 0.996893i | −0.00310239 | − | 0.999995i | \(-0.500988\pi\) |
0.999995 | + | 0.00310239i | \(0.000987524\pi\) | |||||||
\(968\) | −6.36396 | + | 6.36396i | −0.204545 | + | 0.204545i | ||||
\(969\) | 11.3137 | − | 8.00000i | 0.363449 | − | 0.256997i | ||||
\(970\) | −33.0000 | + | 11.0000i | −1.05957 | + | 0.353189i | ||||
\(971\) | − | 39.5980i | − | 1.27076i | −0.772200 | − | 0.635380i | \(-0.780844\pi\) | ||
0.772200 | − | 0.635380i | \(-0.219156\pi\) | |||||||
\(972\) | −11.7071 | + | 10.2929i | −0.375506 | + | 0.330145i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −15.5563 | −0.498458 | ||||||||
\(975\) | 34.9706 | + | 11.2721i | 1.11995 | + | 0.360995i | ||||
\(976\) | −8.00000 | −0.256074 | ||||||||
\(977\) | −21.2132 | − | 21.2132i | −0.678671 | − | 0.678671i | 0.281029 | − | 0.959699i | \(-0.409324\pi\) |
−0.959699 | + | 0.281029i | \(0.909324\pi\) | |||||||
\(978\) | 4.55635 | − | 26.5563i | 0.145696 | − | 0.849178i | ||||
\(979\) | 10.0000i | 0.319601i | ||||||||
\(980\) | 14.8492 | − | 4.94975i | 0.474342 | − | 0.158114i | ||||
\(981\) | −10.0000 | + | 28.2843i | −0.319275 | + | 0.903047i | ||||
\(982\) | −9.00000 | + | 9.00000i | −0.287202 | + | 0.287202i | ||||
\(983\) | −16.9706 | + | 16.9706i | −0.541277 | + | 0.541277i | −0.923903 | − | 0.382626i | \(-0.875020\pi\) |
0.382626 | + | 0.923903i | \(0.375020\pi\) | |||||||
\(984\) | 5.65685 | + | 8.00000i | 0.180334 | + | 0.255031i | ||||
\(985\) | −20.0000 | − | 10.0000i | −0.637253 | − | 0.318626i | ||||
\(986\) | 5.65685i | 0.180151i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.0000 | − | 12.0000i | −0.381771 | − | 0.381771i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 6.82843 | − | 6.58579i | 0.217022 | − | 0.209310i | ||||
\(991\) | −22.0000 | −0.698853 | −0.349427 | − | 0.936964i | \(-0.613624\pi\) | ||||
−0.349427 | + | 0.936964i | \(0.613624\pi\) | |||||||
\(992\) | −0.707107 | − | 0.707107i | −0.0224507 | − | 0.0224507i | ||||
\(993\) | 54.6274 | + | 9.37258i | 1.73355 | + | 0.297430i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.9706 | − | 50.9117i | −0.538003 | − | 1.61401i | ||||
\(996\) | 6.00000 | + | 8.48528i | 0.190117 | + | 0.268866i | ||||
\(997\) | 24.0000 | − | 24.0000i | 0.760088 | − | 0.760088i | −0.216250 | − | 0.976338i | \(-0.569383\pi\) |
0.976338 | + | 0.216250i | \(0.0693827\pi\) | |||||||
\(998\) | −25.4558 | + | 25.4558i | −0.805791 | + | 0.805791i | ||||
\(999\) | −21.2132 | + | 6.00000i | −0.671156 | + | 0.189832i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 930.2.j.b.683.2 | yes | 4 | |
3.2 | odd | 2 | inner | 930.2.j.b.683.1 | yes | 4 | |
5.2 | odd | 4 | inner | 930.2.j.b.497.1 | ✓ | 4 | |
15.2 | even | 4 | inner | 930.2.j.b.497.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.j.b.497.1 | ✓ | 4 | 5.2 | odd | 4 | inner | |
930.2.j.b.497.2 | yes | 4 | 15.2 | even | 4 | inner | |
930.2.j.b.683.1 | yes | 4 | 3.2 | odd | 2 | inner | |
930.2.j.b.683.2 | yes | 4 | 1.1 | even | 1 | trivial |