Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(211,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.i (of order \(3\), 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: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.211 |
Dual form | 930.2.i.i.811.1 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | 1.50000 | + | 2.59808i | 0.566947 | + | 0.981981i | 0.996866 | + | 0.0791130i | \(0.0252088\pi\) |
−0.429919 | + | 0.902867i | \(0.641458\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | 1.50000 | − | 2.59808i | 0.452267 | − | 0.783349i | −0.546259 | − | 0.837616i | \(-0.683949\pi\) |
0.998526 | + | 0.0542666i | \(0.0172821\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 1.00000 | − | 1.73205i | 0.277350 | − | 0.480384i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
0.970725 | + | 0.240192i | \(0.0772105\pi\) | |||||||
\(14\) | 1.50000 | + | 2.59808i | 0.400892 | + | 0.694365i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.00000 | + | 3.46410i | 0.485071 | + | 0.840168i | 0.999853 | − | 0.0171533i | \(-0.00546033\pi\) |
−0.514782 | + | 0.857321i | \(0.672127\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | −1.50000 | + | 2.59808i | −0.327327 | + | 0.566947i | ||||
\(22\) | 1.50000 | − | 2.59808i | 0.319801 | − | 0.553912i | ||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 1.00000 | − | 1.73205i | 0.196116 | − | 0.339683i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.50000 | + | 2.59808i | 0.283473 | + | 0.490990i | ||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 5.50000 | − | 0.866025i | 0.987829 | − | 0.155543i | ||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.00000 | 0.522233 | ||||||||
\(34\) | 2.00000 | + | 3.46410i | 0.342997 | + | 0.594089i | ||||
\(35\) | 3.00000 | 0.507093 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 3.00000 | + | 5.19615i | 0.493197 | + | 0.854242i | 0.999969 | − | 0.00783774i | \(-0.00249486\pi\) |
−0.506772 | + | 0.862080i | \(0.669162\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | 1.00000 | − | 1.73205i | 0.156174 | − | 0.270501i | −0.777312 | − | 0.629115i | \(-0.783417\pi\) |
0.933486 | + | 0.358614i | \(0.116751\pi\) | |||||||
\(42\) | −1.50000 | + | 2.59808i | −0.231455 | + | 0.400892i | ||||
\(43\) | 4.00000 | + | 6.92820i | 0.609994 | + | 1.05654i | 0.991241 | + | 0.132068i | \(0.0421616\pi\) |
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 1.50000 | − | 2.59808i | 0.226134 | − | 0.391675i | ||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | −1.00000 | + | 1.73205i | −0.142857 | + | 0.247436i | ||||
\(50\) | −0.500000 | − | 0.866025i | −0.0707107 | − | 0.122474i | ||||
\(51\) | −2.00000 | + | 3.46410i | −0.280056 | + | 0.485071i | ||||
\(52\) | 1.00000 | − | 1.73205i | 0.138675 | − | 0.240192i | ||||
\(53\) | 1.50000 | − | 2.59808i | 0.206041 | − | 0.356873i | −0.744423 | − | 0.667708i | \(-0.767275\pi\) |
0.950464 | + | 0.310835i | \(0.100609\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −1.50000 | − | 2.59808i | −0.202260 | − | 0.350325i | ||||
\(56\) | 1.50000 | + | 2.59808i | 0.200446 | + | 0.347183i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.00000 | −0.656532 | ||||||||
\(59\) | −1.50000 | − | 2.59808i | −0.195283 | − | 0.338241i | 0.751710 | − | 0.659494i | \(-0.229229\pi\) |
−0.946993 | + | 0.321253i | \(0.895896\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | −8.00000 | −1.02430 | −0.512148 | − | 0.858898i | \(-0.671150\pi\) | ||||
−0.512148 | + | 0.858898i | \(0.671150\pi\) | |||||||
\(62\) | 5.50000 | − | 0.866025i | 0.698501 | − | 0.109985i | ||||
\(63\) | −3.00000 | −0.377964 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.00000 | − | 1.73205i | −0.124035 | − | 0.214834i | ||||
\(66\) | 3.00000 | 0.369274 | ||||||||
\(67\) | 5.00000 | − | 8.66025i | 0.610847 | − | 1.05802i | −0.380251 | − | 0.924883i | \(-0.624162\pi\) |
0.991098 | − | 0.133135i | \(-0.0425044\pi\) | |||||||
\(68\) | 2.00000 | + | 3.46410i | 0.242536 | + | 0.420084i | ||||
\(69\) | −2.00000 | − | 3.46410i | −0.240772 | − | 0.417029i | ||||
\(70\) | 3.00000 | 0.358569 | ||||||||
\(71\) | 4.00000 | − | 6.92820i | 0.474713 | − | 0.822226i | −0.524868 | − | 0.851184i | \(-0.675885\pi\) |
0.999581 | + | 0.0289572i | \(0.00921865\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −7.00000 | + | 12.1244i | −0.819288 | + | 1.41905i | 0.0869195 | + | 0.996215i | \(0.472298\pi\) |
−0.906208 | + | 0.422833i | \(0.861036\pi\) | |||||||
\(74\) | 3.00000 | + | 5.19615i | 0.348743 | + | 0.604040i | ||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.00000 | 1.02565 | ||||||||
\(78\) | 2.00000 | 0.226455 | ||||||||
\(79\) | −4.00000 | − | 6.92820i | −0.450035 | − | 0.779484i | 0.548352 | − | 0.836247i | \(-0.315255\pi\) |
−0.998388 | + | 0.0567635i | \(0.981922\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.00000 | − | 1.73205i | 0.110432 | − | 0.191273i | ||||
\(83\) | 4.50000 | − | 7.79423i | 0.493939 | − | 0.855528i | −0.506036 | − | 0.862512i | \(-0.668890\pi\) |
0.999976 | + | 0.00698436i | \(0.00222321\pi\) | |||||||
\(84\) | −1.50000 | + | 2.59808i | −0.163663 | + | 0.283473i | ||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 4.00000 | + | 6.92820i | 0.431331 | + | 0.747087i | ||||
\(87\) | −2.50000 | − | 4.33013i | −0.268028 | − | 0.464238i | ||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | −8.00000 | −0.847998 | −0.423999 | − | 0.905663i | \(-0.639374\pi\) | ||||
−0.423999 | + | 0.905663i | \(0.639374\pi\) | |||||||
\(90\) | 0.500000 | + | 0.866025i | 0.0527046 | + | 0.0912871i | ||||
\(91\) | 6.00000 | 0.628971 | ||||||||
\(92\) | −4.00000 | −0.417029 | ||||||||
\(93\) | 3.50000 | + | 4.33013i | 0.362933 | + | 0.449013i | ||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | −7.00000 | −0.710742 | −0.355371 | − | 0.934725i | \(-0.615646\pi\) | ||||
−0.355371 | + | 0.934725i | \(0.615646\pi\) | |||||||
\(98\) | −1.00000 | + | 1.73205i | −0.101015 | + | 0.174964i | ||||
\(99\) | 1.50000 | + | 2.59808i | 0.150756 | + | 0.261116i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 11.0000 | 1.09454 | 0.547270 | − | 0.836956i | \(-0.315667\pi\) | ||||
0.547270 | + | 0.836956i | \(0.315667\pi\) | |||||||
\(102\) | −2.00000 | + | 3.46410i | −0.198030 | + | 0.342997i | ||||
\(103\) | −0.500000 | + | 0.866025i | −0.0492665 | + | 0.0853320i | −0.889607 | − | 0.456727i | \(-0.849022\pi\) |
0.840341 | + | 0.542059i | \(0.182355\pi\) | |||||||
\(104\) | 1.00000 | − | 1.73205i | 0.0980581 | − | 0.169842i | ||||
\(105\) | 1.50000 | + | 2.59808i | 0.146385 | + | 0.253546i | ||||
\(106\) | 1.50000 | − | 2.59808i | 0.145693 | − | 0.252347i | ||||
\(107\) | −7.50000 | − | 12.9904i | −0.725052 | − | 1.25583i | −0.958952 | − | 0.283567i | \(-0.908482\pi\) |
0.233900 | − | 0.972261i | \(-0.424851\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −16.0000 | −1.53252 | −0.766261 | − | 0.642529i | \(-0.777885\pi\) | ||||
−0.766261 | + | 0.642529i | \(0.777885\pi\) | |||||||
\(110\) | −1.50000 | − | 2.59808i | −0.143019 | − | 0.247717i | ||||
\(111\) | −3.00000 | + | 5.19615i | −0.284747 | + | 0.493197i | ||||
\(112\) | 1.50000 | + | 2.59808i | 0.141737 | + | 0.245495i | ||||
\(113\) | −3.00000 | + | 5.19615i | −0.282216 | + | 0.488813i | −0.971930 | − | 0.235269i | \(-0.924403\pi\) |
0.689714 | + | 0.724082i | \(0.257736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.00000 | + | 3.46410i | −0.186501 | + | 0.323029i | ||||
\(116\) | −5.00000 | −0.464238 | ||||||||
\(117\) | 1.00000 | + | 1.73205i | 0.0924500 | + | 0.160128i | ||||
\(118\) | −1.50000 | − | 2.59808i | −0.138086 | − | 0.239172i | ||||
\(119\) | −6.00000 | + | 10.3923i | −0.550019 | + | 0.952661i | ||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | −8.00000 | −0.724286 | ||||||||
\(123\) | 2.00000 | 0.180334 | ||||||||
\(124\) | 5.50000 | − | 0.866025i | 0.493915 | − | 0.0777714i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.00000 | −0.267261 | ||||||||
\(127\) | 0.500000 | + | 0.866025i | 0.0443678 | + | 0.0768473i | 0.887357 | − | 0.461084i | \(-0.152539\pi\) |
−0.842989 | + | 0.537931i | \(0.819206\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −4.00000 | + | 6.92820i | −0.352180 | + | 0.609994i | ||||
\(130\) | −1.00000 | − | 1.73205i | −0.0877058 | − | 0.151911i | ||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 3.00000 | 0.261116 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.00000 | − | 8.66025i | 0.431934 | − | 0.748132i | ||||
\(135\) | −0.500000 | + | 0.866025i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | 2.00000 | + | 3.46410i | 0.171499 | + | 0.297044i | ||||
\(137\) | 5.00000 | − | 8.66025i | 0.427179 | − | 0.739895i | −0.569442 | − | 0.822031i | \(-0.692841\pi\) |
0.996621 | + | 0.0821359i | \(0.0261741\pi\) | |||||||
\(138\) | −2.00000 | − | 3.46410i | −0.170251 | − | 0.294884i | ||||
\(139\) | −14.0000 | −1.18746 | −0.593732 | − | 0.804663i | \(-0.702346\pi\) | ||||
−0.593732 | + | 0.804663i | \(0.702346\pi\) | |||||||
\(140\) | 3.00000 | 0.253546 | ||||||||
\(141\) | −4.00000 | − | 6.92820i | −0.336861 | − | 0.583460i | ||||
\(142\) | 4.00000 | − | 6.92820i | 0.335673 | − | 0.581402i | ||||
\(143\) | −3.00000 | − | 5.19615i | −0.250873 | − | 0.434524i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −2.50000 | + | 4.33013i | −0.207614 | + | 0.359597i | ||||
\(146\) | −7.00000 | + | 12.1244i | −0.579324 | + | 1.00342i | ||||
\(147\) | −2.00000 | −0.164957 | ||||||||
\(148\) | 3.00000 | + | 5.19615i | 0.246598 | + | 0.427121i | ||||
\(149\) | −0.500000 | − | 0.866025i | −0.0409616 | − | 0.0709476i | 0.844818 | − | 0.535054i | \(-0.179709\pi\) |
−0.885779 | + | 0.464107i | \(0.846375\pi\) | |||||||
\(150\) | 0.500000 | − | 0.866025i | 0.0408248 | − | 0.0707107i | ||||
\(151\) | −9.00000 | −0.732410 | −0.366205 | − | 0.930534i | \(-0.619343\pi\) | ||||
−0.366205 | + | 0.930534i | \(0.619343\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 9.00000 | 0.725241 | ||||||||
\(155\) | 2.00000 | − | 5.19615i | 0.160644 | − | 0.417365i | ||||
\(156\) | 2.00000 | 0.160128 | ||||||||
\(157\) | 4.00000 | 0.319235 | 0.159617 | − | 0.987179i | \(-0.448974\pi\) | ||||
0.159617 | + | 0.987179i | \(0.448974\pi\) | |||||||
\(158\) | −4.00000 | − | 6.92820i | −0.318223 | − | 0.551178i | ||||
\(159\) | 3.00000 | 0.237915 | ||||||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | −6.00000 | − | 10.3923i | −0.472866 | − | 0.819028i | ||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | 1.00000 | − | 1.73205i | 0.0780869 | − | 0.135250i | ||||
\(165\) | 1.50000 | − | 2.59808i | 0.116775 | − | 0.202260i | ||||
\(166\) | 4.50000 | − | 7.79423i | 0.349268 | − | 0.604949i | ||||
\(167\) | −1.00000 | − | 1.73205i | −0.0773823 | − | 0.134030i | 0.824737 | − | 0.565516i | \(-0.191323\pi\) |
−0.902120 | + | 0.431486i | \(0.857990\pi\) | |||||||
\(168\) | −1.50000 | + | 2.59808i | −0.115728 | + | 0.200446i | ||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.00000 | + | 6.92820i | 0.304997 | + | 0.528271i | ||||
\(173\) | 6.50000 | − | 11.2583i | 0.494186 | − | 0.855955i | −0.505792 | − | 0.862656i | \(-0.668800\pi\) |
0.999978 | + | 0.00670064i | \(0.00213290\pi\) | |||||||
\(174\) | −2.50000 | − | 4.33013i | −0.189525 | − | 0.328266i | ||||
\(175\) | 1.50000 | − | 2.59808i | 0.113389 | − | 0.196396i | ||||
\(176\) | 1.50000 | − | 2.59808i | 0.113067 | − | 0.195837i | ||||
\(177\) | 1.50000 | − | 2.59808i | 0.112747 | − | 0.195283i | ||||
\(178\) | −8.00000 | −0.599625 | ||||||||
\(179\) | −9.50000 | − | 16.4545i | −0.710063 | − | 1.22987i | −0.964833 | − | 0.262864i | \(-0.915333\pi\) |
0.254770 | − | 0.967002i | \(-0.418000\pi\) | |||||||
\(180\) | 0.500000 | + | 0.866025i | 0.0372678 | + | 0.0645497i | ||||
\(181\) | 8.00000 | − | 13.8564i | 0.594635 | − | 1.02994i | −0.398963 | − | 0.916967i | \(-0.630630\pi\) |
0.993598 | − | 0.112972i | \(-0.0360369\pi\) | |||||||
\(182\) | 6.00000 | 0.444750 | ||||||||
\(183\) | −4.00000 | − | 6.92820i | −0.295689 | − | 0.512148i | ||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | 6.00000 | 0.441129 | ||||||||
\(186\) | 3.50000 | + | 4.33013i | 0.256632 | + | 0.317500i | ||||
\(187\) | 12.0000 | 0.877527 | ||||||||
\(188\) | −8.00000 | −0.583460 | ||||||||
\(189\) | −1.50000 | − | 2.59808i | −0.109109 | − | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.00000 | + | 8.66025i | −0.361787 | + | 0.626634i | −0.988255 | − | 0.152813i | \(-0.951167\pi\) |
0.626468 | + | 0.779447i | \(0.284500\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 4.50000 | + | 7.79423i | 0.323917 | + | 0.561041i | 0.981293 | − | 0.192522i | \(-0.0616668\pi\) |
−0.657376 | + | 0.753563i | \(0.728333\pi\) | |||||||
\(194\) | −7.00000 | −0.502571 | ||||||||
\(195\) | 1.00000 | − | 1.73205i | 0.0716115 | − | 0.124035i | ||||
\(196\) | −1.00000 | + | 1.73205i | −0.0714286 | + | 0.123718i | ||||
\(197\) | −3.00000 | + | 5.19615i | −0.213741 | + | 0.370211i | −0.952882 | − | 0.303340i | \(-0.901898\pi\) |
0.739141 | + | 0.673550i | \(0.235232\pi\) | |||||||
\(198\) | 1.50000 | + | 2.59808i | 0.106600 | + | 0.184637i | ||||
\(199\) | −3.50000 | + | 6.06218i | −0.248108 | + | 0.429736i | −0.963001 | − | 0.269498i | \(-0.913142\pi\) |
0.714893 | + | 0.699234i | \(0.246476\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | 10.0000 | 0.705346 | ||||||||
\(202\) | 11.0000 | 0.773957 | ||||||||
\(203\) | −7.50000 | − | 12.9904i | −0.526397 | − | 0.911746i | ||||
\(204\) | −2.00000 | + | 3.46410i | −0.140028 | + | 0.242536i | ||||
\(205\) | −1.00000 | − | 1.73205i | −0.0698430 | − | 0.120972i | ||||
\(206\) | −0.500000 | + | 0.866025i | −0.0348367 | + | 0.0603388i | ||||
\(207\) | 2.00000 | − | 3.46410i | 0.139010 | − | 0.240772i | ||||
\(208\) | 1.00000 | − | 1.73205i | 0.0693375 | − | 0.120096i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.50000 | + | 2.59808i | 0.103510 | + | 0.179284i | ||||
\(211\) | −10.0000 | − | 17.3205i | −0.688428 | − | 1.19239i | −0.972346 | − | 0.233544i | \(-0.924968\pi\) |
0.283918 | − | 0.958849i | \(-0.408366\pi\) | |||||||
\(212\) | 1.50000 | − | 2.59808i | 0.103020 | − | 0.178437i | ||||
\(213\) | 8.00000 | 0.548151 | ||||||||
\(214\) | −7.50000 | − | 12.9904i | −0.512689 | − | 0.888004i | ||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 10.5000 | + | 12.9904i | 0.712786 | + | 0.881845i | ||||
\(218\) | −16.0000 | −1.08366 | ||||||||
\(219\) | −14.0000 | −0.946032 | ||||||||
\(220\) | −1.50000 | − | 2.59808i | −0.101130 | − | 0.175162i | ||||
\(221\) | 8.00000 | 0.538138 | ||||||||
\(222\) | −3.00000 | + | 5.19615i | −0.201347 | + | 0.348743i | ||||
\(223\) | −4.50000 | − | 7.79423i | −0.301342 | − | 0.521940i | 0.675098 | − | 0.737728i | \(-0.264101\pi\) |
−0.976440 | + | 0.215788i | \(0.930768\pi\) | |||||||
\(224\) | 1.50000 | + | 2.59808i | 0.100223 | + | 0.173591i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −3.00000 | + | 5.19615i | −0.199557 | + | 0.345643i | ||||
\(227\) | 10.5000 | − | 18.1865i | 0.696909 | − | 1.20708i | −0.272623 | − | 0.962121i | \(-0.587891\pi\) |
0.969533 | − | 0.244962i | \(-0.0787754\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.00000 | + | 12.1244i | 0.462573 | + | 0.801200i | 0.999088 | − | 0.0426906i | \(-0.0135930\pi\) |
−0.536515 | + | 0.843891i | \(0.680260\pi\) | |||||||
\(230\) | −2.00000 | + | 3.46410i | −0.131876 | + | 0.228416i | ||||
\(231\) | 4.50000 | + | 7.79423i | 0.296078 | + | 0.512823i | ||||
\(232\) | −5.00000 | −0.328266 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 1.00000 | + | 1.73205i | 0.0653720 | + | 0.113228i | ||||
\(235\) | −4.00000 | + | 6.92820i | −0.260931 | + | 0.451946i | ||||
\(236\) | −1.50000 | − | 2.59808i | −0.0976417 | − | 0.169120i | ||||
\(237\) | 4.00000 | − | 6.92820i | 0.259828 | − | 0.450035i | ||||
\(238\) | −6.00000 | + | 10.3923i | −0.388922 | + | 0.673633i | ||||
\(239\) | −3.00000 | + | 5.19615i | −0.194054 | + | 0.336111i | −0.946590 | − | 0.322440i | \(-0.895497\pi\) |
0.752536 | + | 0.658551i | \(0.228830\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −1.50000 | − | 2.59808i | −0.0966235 | − | 0.167357i | 0.813662 | − | 0.581339i | \(-0.197471\pi\) |
−0.910285 | + | 0.413982i | \(0.864138\pi\) | |||||||
\(242\) | 1.00000 | + | 1.73205i | 0.0642824 | + | 0.111340i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −8.00000 | −0.512148 | ||||||||
\(245\) | 1.00000 | + | 1.73205i | 0.0638877 | + | 0.110657i | ||||
\(246\) | 2.00000 | 0.127515 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5.50000 | − | 0.866025i | 0.349250 | − | 0.0549927i | ||||
\(249\) | 9.00000 | 0.570352 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 6.00000 | + | 10.3923i | 0.378717 | + | 0.655956i | 0.990876 | − | 0.134778i | \(-0.0430322\pi\) |
−0.612159 | + | 0.790735i | \(0.709699\pi\) | |||||||
\(252\) | −3.00000 | −0.188982 | ||||||||
\(253\) | −6.00000 | + | 10.3923i | −0.377217 | + | 0.653359i | ||||
\(254\) | 0.500000 | + | 0.866025i | 0.0313728 | + | 0.0543393i | ||||
\(255\) | 2.00000 | + | 3.46410i | 0.125245 | + | 0.216930i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.0000 | − | 17.3205i | 0.623783 | − | 1.08042i | −0.364992 | − | 0.931011i | \(-0.618928\pi\) |
0.988775 | − | 0.149413i | \(-0.0477384\pi\) | |||||||
\(258\) | −4.00000 | + | 6.92820i | −0.249029 | + | 0.431331i | ||||
\(259\) | −9.00000 | + | 15.5885i | −0.559233 | + | 0.968620i | ||||
\(260\) | −1.00000 | − | 1.73205i | −0.0620174 | − | 0.107417i | ||||
\(261\) | 2.50000 | − | 4.33013i | 0.154746 | − | 0.268028i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −30.0000 | −1.84988 | −0.924940 | − | 0.380114i | \(-0.875885\pi\) | ||||
−0.924940 | + | 0.380114i | \(0.875885\pi\) | |||||||
\(264\) | 3.00000 | 0.184637 | ||||||||
\(265\) | −1.50000 | − | 2.59808i | −0.0921443 | − | 0.159599i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.00000 | − | 6.92820i | −0.244796 | − | 0.423999i | ||||
\(268\) | 5.00000 | − | 8.66025i | 0.305424 | − | 0.529009i | ||||
\(269\) | −7.00000 | + | 12.1244i | −0.426798 | + | 0.739235i | −0.996586 | − | 0.0825561i | \(-0.973692\pi\) |
0.569789 | + | 0.821791i | \(0.307025\pi\) | |||||||
\(270\) | −0.500000 | + | 0.866025i | −0.0304290 | + | 0.0527046i | ||||
\(271\) | −29.0000 | −1.76162 | −0.880812 | − | 0.473466i | \(-0.843003\pi\) | ||||
−0.880812 | + | 0.473466i | \(0.843003\pi\) | |||||||
\(272\) | 2.00000 | + | 3.46410i | 0.121268 | + | 0.210042i | ||||
\(273\) | 3.00000 | + | 5.19615i | 0.181568 | + | 0.314485i | ||||
\(274\) | 5.00000 | − | 8.66025i | 0.302061 | − | 0.523185i | ||||
\(275\) | −3.00000 | −0.180907 | ||||||||
\(276\) | −2.00000 | − | 3.46410i | −0.120386 | − | 0.208514i | ||||
\(277\) | 12.0000 | 0.721010 | 0.360505 | − | 0.932757i | \(-0.382604\pi\) | ||||
0.360505 | + | 0.932757i | \(0.382604\pi\) | |||||||
\(278\) | −14.0000 | −0.839664 | ||||||||
\(279\) | −2.00000 | + | 5.19615i | −0.119737 | + | 0.311086i | ||||
\(280\) | 3.00000 | 0.179284 | ||||||||
\(281\) | 16.0000 | 0.954480 | 0.477240 | − | 0.878773i | \(-0.341637\pi\) | ||||
0.477240 | + | 0.878773i | \(0.341637\pi\) | |||||||
\(282\) | −4.00000 | − | 6.92820i | −0.238197 | − | 0.412568i | ||||
\(283\) | 18.0000 | 1.06999 | 0.534994 | − | 0.844856i | \(-0.320314\pi\) | ||||
0.534994 | + | 0.844856i | \(0.320314\pi\) | |||||||
\(284\) | 4.00000 | − | 6.92820i | 0.237356 | − | 0.411113i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.00000 | − | 5.19615i | −0.177394 | − | 0.307255i | ||||
\(287\) | 6.00000 | 0.354169 | ||||||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | −2.50000 | + | 4.33013i | −0.146805 | + | 0.254274i | ||||
\(291\) | −3.50000 | − | 6.06218i | −0.205174 | − | 0.355371i | ||||
\(292\) | −7.00000 | + | 12.1244i | −0.409644 | + | 0.709524i | ||||
\(293\) | −4.50000 | − | 7.79423i | −0.262893 | − | 0.455344i | 0.704117 | − | 0.710084i | \(-0.251343\pi\) |
−0.967009 | + | 0.254741i | \(0.918010\pi\) | |||||||
\(294\) | −2.00000 | −0.116642 | ||||||||
\(295\) | −3.00000 | −0.174667 | ||||||||
\(296\) | 3.00000 | + | 5.19615i | 0.174371 | + | 0.302020i | ||||
\(297\) | −1.50000 | + | 2.59808i | −0.0870388 | + | 0.150756i | ||||
\(298\) | −0.500000 | − | 0.866025i | −0.0289642 | − | 0.0501675i | ||||
\(299\) | −4.00000 | + | 6.92820i | −0.231326 | + | 0.400668i | ||||
\(300\) | 0.500000 | − | 0.866025i | 0.0288675 | − | 0.0500000i | ||||
\(301\) | −12.0000 | + | 20.7846i | −0.691669 | + | 1.19800i | ||||
\(302\) | −9.00000 | −0.517892 | ||||||||
\(303\) | 5.50000 | + | 9.52628i | 0.315967 | + | 0.547270i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.00000 | + | 6.92820i | −0.229039 | + | 0.396708i | ||||
\(306\) | −4.00000 | −0.228665 | ||||||||
\(307\) | 13.0000 | + | 22.5167i | 0.741949 | + | 1.28509i | 0.951607 | + | 0.307319i | \(0.0994318\pi\) |
−0.209657 | + | 0.977775i | \(0.567235\pi\) | |||||||
\(308\) | 9.00000 | 0.512823 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 2.00000 | − | 5.19615i | 0.113592 | − | 0.295122i | ||||
\(311\) | 18.0000 | 1.02069 | 0.510343 | − | 0.859971i | \(-0.329518\pi\) | ||||
0.510343 | + | 0.859971i | \(0.329518\pi\) | |||||||
\(312\) | 2.00000 | 0.113228 | ||||||||
\(313\) | 10.5000 | + | 18.1865i | 0.593495 | + | 1.02796i | 0.993757 | + | 0.111563i | \(0.0355857\pi\) |
−0.400262 | + | 0.916401i | \(0.631081\pi\) | |||||||
\(314\) | 4.00000 | 0.225733 | ||||||||
\(315\) | −1.50000 | + | 2.59808i | −0.0845154 | + | 0.146385i | ||||
\(316\) | −4.00000 | − | 6.92820i | −0.225018 | − | 0.389742i | ||||
\(317\) | −0.500000 | − | 0.866025i | −0.0280828 | − | 0.0486408i | 0.851642 | − | 0.524123i | \(-0.175607\pi\) |
−0.879725 | + | 0.475482i | \(0.842274\pi\) | |||||||
\(318\) | 3.00000 | 0.168232 | ||||||||
\(319\) | −7.50000 | + | 12.9904i | −0.419919 | + | 0.727322i | ||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | 7.50000 | − | 12.9904i | 0.418609 | − | 0.725052i | ||||
\(322\) | −6.00000 | − | 10.3923i | −0.334367 | − | 0.579141i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −2.00000 | −0.110940 | ||||||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | −8.00000 | − | 13.8564i | −0.442401 | − | 0.766261i | ||||
\(328\) | 1.00000 | − | 1.73205i | 0.0552158 | − | 0.0956365i | ||||
\(329\) | −12.0000 | − | 20.7846i | −0.661581 | − | 1.14589i | ||||
\(330\) | 1.50000 | − | 2.59808i | 0.0825723 | − | 0.143019i | ||||
\(331\) | −12.0000 | + | 20.7846i | −0.659580 | + | 1.14243i | 0.321145 | + | 0.947030i | \(0.395932\pi\) |
−0.980725 | + | 0.195395i | \(0.937401\pi\) | |||||||
\(332\) | 4.50000 | − | 7.79423i | 0.246970 | − | 0.427764i | ||||
\(333\) | −6.00000 | −0.328798 | ||||||||
\(334\) | −1.00000 | − | 1.73205i | −0.0547176 | − | 0.0947736i | ||||
\(335\) | −5.00000 | − | 8.66025i | −0.273179 | − | 0.473160i | ||||
\(336\) | −1.50000 | + | 2.59808i | −0.0818317 | + | 0.141737i | ||||
\(337\) | −5.00000 | −0.272367 | −0.136184 | − | 0.990684i | \(-0.543484\pi\) | ||||
−0.136184 | + | 0.990684i | \(0.543484\pi\) | |||||||
\(338\) | 4.50000 | + | 7.79423i | 0.244768 | + | 0.423950i | ||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | 4.00000 | 0.216930 | ||||||||
\(341\) | 6.00000 | − | 15.5885i | 0.324918 | − | 0.844162i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | 4.00000 | + | 6.92820i | 0.215666 | + | 0.373544i | ||||
\(345\) | −4.00000 | −0.215353 | ||||||||
\(346\) | 6.50000 | − | 11.2583i | 0.349442 | − | 0.605252i | ||||
\(347\) | 11.5000 | + | 19.9186i | 0.617352 | + | 1.06929i | 0.989967 | + | 0.141299i | \(0.0451280\pi\) |
−0.372615 | + | 0.927986i | \(0.621539\pi\) | |||||||
\(348\) | −2.50000 | − | 4.33013i | −0.134014 | − | 0.232119i | ||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 1.50000 | − | 2.59808i | 0.0801784 | − | 0.138873i | ||||
\(351\) | −1.00000 | + | 1.73205i | −0.0533761 | + | 0.0924500i | ||||
\(352\) | 1.50000 | − | 2.59808i | 0.0799503 | − | 0.138478i | ||||
\(353\) | 9.00000 | + | 15.5885i | 0.479022 | + | 0.829690i | 0.999711 | − | 0.0240566i | \(-0.00765819\pi\) |
−0.520689 | + | 0.853746i | \(0.674325\pi\) | |||||||
\(354\) | 1.50000 | − | 2.59808i | 0.0797241 | − | 0.138086i | ||||
\(355\) | −4.00000 | − | 6.92820i | −0.212298 | − | 0.367711i | ||||
\(356\) | −8.00000 | −0.423999 | ||||||||
\(357\) | −12.0000 | −0.635107 | ||||||||
\(358\) | −9.50000 | − | 16.4545i | −0.502091 | − | 0.869646i | ||||
\(359\) | −12.0000 | + | 20.7846i | −0.633336 | + | 1.09697i | 0.353529 | + | 0.935423i | \(0.384981\pi\) |
−0.986865 | + | 0.161546i | \(0.948352\pi\) | |||||||
\(360\) | 0.500000 | + | 0.866025i | 0.0263523 | + | 0.0456435i | ||||
\(361\) | 9.50000 | − | 16.4545i | 0.500000 | − | 0.866025i | ||||
\(362\) | 8.00000 | − | 13.8564i | 0.420471 | − | 0.728277i | ||||
\(363\) | −1.00000 | + | 1.73205i | −0.0524864 | + | 0.0909091i | ||||
\(364\) | 6.00000 | 0.314485 | ||||||||
\(365\) | 7.00000 | + | 12.1244i | 0.366397 | + | 0.634618i | ||||
\(366\) | −4.00000 | − | 6.92820i | −0.209083 | − | 0.362143i | ||||
\(367\) | 14.0000 | − | 24.2487i | 0.730794 | − | 1.26577i | −0.225750 | − | 0.974185i | \(-0.572483\pi\) |
0.956544 | − | 0.291587i | \(-0.0941834\pi\) | |||||||
\(368\) | −4.00000 | −0.208514 | ||||||||
\(369\) | 1.00000 | + | 1.73205i | 0.0520579 | + | 0.0901670i | ||||
\(370\) | 6.00000 | 0.311925 | ||||||||
\(371\) | 9.00000 | 0.467257 | ||||||||
\(372\) | 3.50000 | + | 4.33013i | 0.181467 | + | 0.224507i | ||||
\(373\) | 24.0000 | 1.24267 | 0.621336 | − | 0.783544i | \(-0.286590\pi\) | ||||
0.621336 | + | 0.783544i | \(0.286590\pi\) | |||||||
\(374\) | 12.0000 | 0.620505 | ||||||||
\(375\) | −0.500000 | − | 0.866025i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | −8.00000 | −0.412568 | ||||||||
\(377\) | −5.00000 | + | 8.66025i | −0.257513 | + | 0.446026i | ||||
\(378\) | −1.50000 | − | 2.59808i | −0.0771517 | − | 0.133631i | ||||
\(379\) | 18.0000 | + | 31.1769i | 0.924598 | + | 1.60145i | 0.792207 | + | 0.610253i | \(0.208932\pi\) |
0.132391 | + | 0.991198i | \(0.457734\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.500000 | + | 0.866025i | −0.0256158 | + | 0.0443678i | ||||
\(382\) | −5.00000 | + | 8.66025i | −0.255822 | + | 0.443097i | ||||
\(383\) | 3.00000 | − | 5.19615i | 0.153293 | − | 0.265511i | −0.779143 | − | 0.626846i | \(-0.784346\pi\) |
0.932436 | + | 0.361335i | \(0.117679\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | 4.50000 | − | 7.79423i | 0.229341 | − | 0.397231i | ||||
\(386\) | 4.50000 | + | 7.79423i | 0.229044 | + | 0.396716i | ||||
\(387\) | −8.00000 | −0.406663 | ||||||||
\(388\) | −7.00000 | −0.355371 | ||||||||
\(389\) | 1.00000 | + | 1.73205i | 0.0507020 | + | 0.0878185i | 0.890263 | − | 0.455448i | \(-0.150521\pi\) |
−0.839561 | + | 0.543266i | \(0.817187\pi\) | |||||||
\(390\) | 1.00000 | − | 1.73205i | 0.0506370 | − | 0.0877058i | ||||
\(391\) | −8.00000 | − | 13.8564i | −0.404577 | − | 0.700749i | ||||
\(392\) | −1.00000 | + | 1.73205i | −0.0505076 | + | 0.0874818i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.00000 | + | 5.19615i | −0.151138 | + | 0.261778i | ||||
\(395\) | −8.00000 | −0.402524 | ||||||||
\(396\) | 1.50000 | + | 2.59808i | 0.0753778 | + | 0.130558i | ||||
\(397\) | 14.0000 | + | 24.2487i | 0.702640 | + | 1.21701i | 0.967537 | + | 0.252731i | \(0.0813288\pi\) |
−0.264897 | + | 0.964277i | \(0.585338\pi\) | |||||||
\(398\) | −3.50000 | + | 6.06218i | −0.175439 | + | 0.303870i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | 10.0000 | 0.499376 | 0.249688 | − | 0.968326i | \(-0.419672\pi\) | ||||
0.249688 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(402\) | 10.0000 | 0.498755 | ||||||||
\(403\) | 4.00000 | − | 10.3923i | 0.199254 | − | 0.517678i | ||||
\(404\) | 11.0000 | 0.547270 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −7.50000 | − | 12.9904i | −0.372219 | − | 0.644702i | ||||
\(407\) | 18.0000 | 0.892227 | ||||||||
\(408\) | −2.00000 | + | 3.46410i | −0.0990148 | + | 0.171499i | ||||
\(409\) | 12.5000 | + | 21.6506i | 0.618085 | + | 1.07056i | 0.989835 | + | 0.142222i | \(0.0454247\pi\) |
−0.371750 | + | 0.928333i | \(0.621242\pi\) | |||||||
\(410\) | −1.00000 | − | 1.73205i | −0.0493865 | − | 0.0855399i | ||||
\(411\) | 10.0000 | 0.493264 | ||||||||
\(412\) | −0.500000 | + | 0.866025i | −0.0246332 | + | 0.0426660i | ||||
\(413\) | 4.50000 | − | 7.79423i | 0.221431 | − | 0.383529i | ||||
\(414\) | 2.00000 | − | 3.46410i | 0.0982946 | − | 0.170251i | ||||
\(415\) | −4.50000 | − | 7.79423i | −0.220896 | − | 0.382604i | ||||
\(416\) | 1.00000 | − | 1.73205i | 0.0490290 | − | 0.0849208i | ||||
\(417\) | −7.00000 | − | 12.1244i | −0.342791 | − | 0.593732i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.0000 | 1.02592 | 0.512959 | − | 0.858413i | \(-0.328549\pi\) | ||||
0.512959 | + | 0.858413i | \(0.328549\pi\) | |||||||
\(420\) | 1.50000 | + | 2.59808i | 0.0731925 | + | 0.126773i | ||||
\(421\) | −10.0000 | + | 17.3205i | −0.487370 | + | 0.844150i | −0.999895 | − | 0.0145228i | \(-0.995377\pi\) |
0.512524 | + | 0.858673i | \(0.328710\pi\) | |||||||
\(422\) | −10.0000 | − | 17.3205i | −0.486792 | − | 0.843149i | ||||
\(423\) | 4.00000 | − | 6.92820i | 0.194487 | − | 0.336861i | ||||
\(424\) | 1.50000 | − | 2.59808i | 0.0728464 | − | 0.126174i | ||||
\(425\) | 2.00000 | − | 3.46410i | 0.0970143 | − | 0.168034i | ||||
\(426\) | 8.00000 | 0.387601 | ||||||||
\(427\) | −12.0000 | − | 20.7846i | −0.580721 | − | 1.00584i | ||||
\(428\) | −7.50000 | − | 12.9904i | −0.362526 | − | 0.627914i | ||||
\(429\) | 3.00000 | − | 5.19615i | 0.144841 | − | 0.250873i | ||||
\(430\) | 8.00000 | 0.385794 | ||||||||
\(431\) | 1.00000 | + | 1.73205i | 0.0481683 | + | 0.0834300i | 0.889104 | − | 0.457705i | \(-0.151328\pi\) |
−0.840936 | + | 0.541135i | \(0.817995\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 10.5000 | + | 12.9904i | 0.504016 | + | 0.623558i | ||||
\(435\) | −5.00000 | −0.239732 | ||||||||
\(436\) | −16.0000 | −0.766261 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −14.0000 | −0.668946 | ||||||||
\(439\) | −7.50000 | + | 12.9904i | −0.357955 | + | 0.619997i | −0.987619 | − | 0.156871i | \(-0.949859\pi\) |
0.629664 | + | 0.776868i | \(0.283193\pi\) | |||||||
\(440\) | −1.50000 | − | 2.59808i | −0.0715097 | − | 0.123858i | ||||
\(441\) | −1.00000 | − | 1.73205i | −0.0476190 | − | 0.0824786i | ||||
\(442\) | 8.00000 | 0.380521 | ||||||||
\(443\) | −12.0000 | + | 20.7846i | −0.570137 | + | 0.987507i | 0.426414 | + | 0.904528i | \(0.359777\pi\) |
−0.996551 | + | 0.0829786i | \(0.973557\pi\) | |||||||
\(444\) | −3.00000 | + | 5.19615i | −0.142374 | + | 0.246598i | ||||
\(445\) | −4.00000 | + | 6.92820i | −0.189618 | + | 0.328428i | ||||
\(446\) | −4.50000 | − | 7.79423i | −0.213081 | − | 0.369067i | ||||
\(447\) | 0.500000 | − | 0.866025i | 0.0236492 | − | 0.0409616i | ||||
\(448\) | 1.50000 | + | 2.59808i | 0.0708683 | + | 0.122748i | ||||
\(449\) | −40.0000 | −1.88772 | −0.943858 | − | 0.330350i | \(-0.892833\pi\) | ||||
−0.943858 | + | 0.330350i | \(0.892833\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −3.00000 | − | 5.19615i | −0.141264 | − | 0.244677i | ||||
\(452\) | −3.00000 | + | 5.19615i | −0.141108 | + | 0.244406i | ||||
\(453\) | −4.50000 | − | 7.79423i | −0.211428 | − | 0.366205i | ||||
\(454\) | 10.5000 | − | 18.1865i | 0.492789 | − | 0.853536i | ||||
\(455\) | 3.00000 | − | 5.19615i | 0.140642 | − | 0.243599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.0000 | 0.467780 | 0.233890 | − | 0.972263i | \(-0.424854\pi\) | ||||
0.233890 | + | 0.972263i | \(0.424854\pi\) | |||||||
\(458\) | 7.00000 | + | 12.1244i | 0.327089 | + | 0.566534i | ||||
\(459\) | −2.00000 | − | 3.46410i | −0.0933520 | − | 0.161690i | ||||
\(460\) | −2.00000 | + | 3.46410i | −0.0932505 | + | 0.161515i | ||||
\(461\) | 21.0000 | 0.978068 | 0.489034 | − | 0.872265i | \(-0.337349\pi\) | ||||
0.489034 | + | 0.872265i | \(0.337349\pi\) | |||||||
\(462\) | 4.50000 | + | 7.79423i | 0.209359 | + | 0.362620i | ||||
\(463\) | −5.00000 | −0.232370 | −0.116185 | − | 0.993228i | \(-0.537067\pi\) | ||||
−0.116185 | + | 0.993228i | \(0.537067\pi\) | |||||||
\(464\) | −5.00000 | −0.232119 | ||||||||
\(465\) | 5.50000 | − | 0.866025i | 0.255056 | − | 0.0401610i | ||||
\(466\) | −18.0000 | −0.833834 | ||||||||
\(467\) | 27.0000 | 1.24941 | 0.624705 | − | 0.780860i | \(-0.285219\pi\) | ||||
0.624705 | + | 0.780860i | \(0.285219\pi\) | |||||||
\(468\) | 1.00000 | + | 1.73205i | 0.0462250 | + | 0.0800641i | ||||
\(469\) | 30.0000 | 1.38527 | ||||||||
\(470\) | −4.00000 | + | 6.92820i | −0.184506 | + | 0.319574i | ||||
\(471\) | 2.00000 | + | 3.46410i | 0.0921551 | + | 0.159617i | ||||
\(472\) | −1.50000 | − | 2.59808i | −0.0690431 | − | 0.119586i | ||||
\(473\) | 24.0000 | 1.10352 | ||||||||
\(474\) | 4.00000 | − | 6.92820i | 0.183726 | − | 0.318223i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.00000 | + | 10.3923i | −0.275010 | + | 0.476331i | ||||
\(477\) | 1.50000 | + | 2.59808i | 0.0686803 | + | 0.118958i | ||||
\(478\) | −3.00000 | + | 5.19615i | −0.137217 | + | 0.237666i | ||||
\(479\) | −12.0000 | − | 20.7846i | −0.548294 | − | 0.949673i | −0.998392 | − | 0.0566937i | \(-0.981944\pi\) |
0.450098 | − | 0.892979i | \(-0.351389\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 12.0000 | 0.547153 | ||||||||
\(482\) | −1.50000 | − | 2.59808i | −0.0683231 | − | 0.118339i | ||||
\(483\) | 6.00000 | − | 10.3923i | 0.273009 | − | 0.472866i | ||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | −3.50000 | + | 6.06218i | −0.158927 | + | 0.275269i | ||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 15.5000 | − | 26.8468i | 0.702372 | − | 1.21654i | −0.265260 | − | 0.964177i | \(-0.585458\pi\) |
0.967632 | − | 0.252367i | \(-0.0812090\pi\) | |||||||
\(488\) | −8.00000 | −0.362143 | ||||||||
\(489\) | −2.00000 | − | 3.46410i | −0.0904431 | − | 0.156652i | ||||
\(490\) | 1.00000 | + | 1.73205i | 0.0451754 | + | 0.0782461i | ||||
\(491\) | −20.5000 | + | 35.5070i | −0.925152 | + | 1.60241i | −0.133836 | + | 0.991004i | \(0.542729\pi\) |
−0.791316 | + | 0.611407i | \(0.790604\pi\) | |||||||
\(492\) | 2.00000 | 0.0901670 | ||||||||
\(493\) | −10.0000 | − | 17.3205i | −0.450377 | − | 0.780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.00000 | 0.134840 | ||||||||
\(496\) | 5.50000 | − | 0.866025i | 0.246957 | − | 0.0388857i | ||||
\(497\) | 24.0000 | 1.07655 | ||||||||
\(498\) | 9.00000 | 0.403300 | ||||||||
\(499\) | −11.0000 | − | 19.0526i | −0.492428 | − | 0.852910i | 0.507534 | − | 0.861632i | \(-0.330557\pi\) |
−0.999962 | + | 0.00872186i | \(0.997224\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 1.00000 | − | 1.73205i | 0.0446767 | − | 0.0773823i | ||||
\(502\) | 6.00000 | + | 10.3923i | 0.267793 | + | 0.463831i | ||||
\(503\) | −1.00000 | − | 1.73205i | −0.0445878 | − | 0.0772283i | 0.842870 | − | 0.538117i | \(-0.180864\pi\) |
−0.887458 | + | 0.460889i | \(0.847531\pi\) | |||||||
\(504\) | −3.00000 | −0.133631 | ||||||||
\(505\) | 5.50000 | − | 9.52628i | 0.244747 | − | 0.423914i | ||||
\(506\) | −6.00000 | + | 10.3923i | −0.266733 | + | 0.461994i | ||||
\(507\) | −4.50000 | + | 7.79423i | −0.199852 | + | 0.346154i | ||||
\(508\) | 0.500000 | + | 0.866025i | 0.0221839 | + | 0.0384237i | ||||
\(509\) | −7.50000 | + | 12.9904i | −0.332432 | + | 0.575789i | −0.982988 | − | 0.183669i | \(-0.941202\pi\) |
0.650556 | + | 0.759458i | \(0.274536\pi\) | |||||||
\(510\) | 2.00000 | + | 3.46410i | 0.0885615 | + | 0.153393i | ||||
\(511\) | −42.0000 | −1.85797 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.0000 | − | 17.3205i | 0.441081 | − | 0.763975i | ||||
\(515\) | 0.500000 | + | 0.866025i | 0.0220326 | + | 0.0381616i | ||||
\(516\) | −4.00000 | + | 6.92820i | −0.176090 | + | 0.304997i | ||||
\(517\) | −12.0000 | + | 20.7846i | −0.527759 | + | 0.914106i | ||||
\(518\) | −9.00000 | + | 15.5885i | −0.395437 | + | 0.684917i | ||||
\(519\) | 13.0000 | 0.570637 | ||||||||
\(520\) | −1.00000 | − | 1.73205i | −0.0438529 | − | 0.0759555i | ||||
\(521\) | 9.00000 | + | 15.5885i | 0.394297 | + | 0.682943i | 0.993011 | − | 0.118020i | \(-0.0376547\pi\) |
−0.598714 | + | 0.800963i | \(0.704321\pi\) | |||||||
\(522\) | 2.50000 | − | 4.33013i | 0.109422 | − | 0.189525i | ||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.00000 | 0.130931 | ||||||||
\(526\) | −30.0000 | −1.30806 | ||||||||
\(527\) | 14.0000 | + | 17.3205i | 0.609850 | + | 0.754493i | ||||
\(528\) | 3.00000 | 0.130558 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −1.50000 | − | 2.59808i | −0.0651558 | − | 0.112853i | ||||
\(531\) | 3.00000 | 0.130189 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.00000 | − | 3.46410i | −0.0866296 | − | 0.150047i | ||||
\(534\) | −4.00000 | − | 6.92820i | −0.173097 | − | 0.299813i | ||||
\(535\) | −15.0000 | −0.648507 | ||||||||
\(536\) | 5.00000 | − | 8.66025i | 0.215967 | − | 0.374066i | ||||
\(537\) | 9.50000 | − | 16.4545i | 0.409955 | − | 0.710063i | ||||
\(538\) | −7.00000 | + | 12.1244i | −0.301791 | + | 0.522718i | ||||
\(539\) | 3.00000 | + | 5.19615i | 0.129219 | + | 0.223814i | ||||
\(540\) | −0.500000 | + | 0.866025i | −0.0215166 | + | 0.0372678i | ||||
\(541\) | 10.0000 | + | 17.3205i | 0.429934 | + | 0.744667i | 0.996867 | − | 0.0790969i | \(-0.0252036\pi\) |
−0.566933 | + | 0.823764i | \(0.691870\pi\) | |||||||
\(542\) | −29.0000 | −1.24566 | ||||||||
\(543\) | 16.0000 | 0.686626 | ||||||||
\(544\) | 2.00000 | + | 3.46410i | 0.0857493 | + | 0.148522i | ||||
\(545\) | −8.00000 | + | 13.8564i | −0.342682 | + | 0.593543i | ||||
\(546\) | 3.00000 | + | 5.19615i | 0.128388 | + | 0.222375i | ||||
\(547\) | 4.00000 | − | 6.92820i | 0.171028 | − | 0.296229i | −0.767752 | − | 0.640747i | \(-0.778625\pi\) |
0.938779 | + | 0.344519i | \(0.111958\pi\) | |||||||
\(548\) | 5.00000 | − | 8.66025i | 0.213589 | − | 0.369948i | ||||
\(549\) | 4.00000 | − | 6.92820i | 0.170716 | − | 0.295689i | ||||
\(550\) | −3.00000 | −0.127920 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −2.00000 | − | 3.46410i | −0.0851257 | − | 0.147442i | ||||
\(553\) | 12.0000 | − | 20.7846i | 0.510292 | − | 0.883852i | ||||
\(554\) | 12.0000 | 0.509831 | ||||||||
\(555\) | 3.00000 | + | 5.19615i | 0.127343 | + | 0.220564i | ||||
\(556\) | −14.0000 | −0.593732 | ||||||||
\(557\) | −37.0000 | −1.56774 | −0.783870 | − | 0.620925i | \(-0.786757\pi\) | ||||
−0.783870 | + | 0.620925i | \(0.786757\pi\) | |||||||
\(558\) | −2.00000 | + | 5.19615i | −0.0846668 | + | 0.219971i | ||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 3.00000 | 0.126773 | ||||||||
\(561\) | 6.00000 | + | 10.3923i | 0.253320 | + | 0.438763i | ||||
\(562\) | 16.0000 | 0.674919 | ||||||||
\(563\) | 3.50000 | − | 6.06218i | 0.147507 | − | 0.255490i | −0.782798 | − | 0.622276i | \(-0.786208\pi\) |
0.930306 | + | 0.366785i | \(0.119542\pi\) | |||||||
\(564\) | −4.00000 | − | 6.92820i | −0.168430 | − | 0.291730i | ||||
\(565\) | 3.00000 | + | 5.19615i | 0.126211 | + | 0.218604i | ||||
\(566\) | 18.0000 | 0.756596 | ||||||||
\(567\) | 1.50000 | − | 2.59808i | 0.0629941 | − | 0.109109i | ||||
\(568\) | 4.00000 | − | 6.92820i | 0.167836 | − | 0.290701i | ||||
\(569\) | −5.00000 | + | 8.66025i | −0.209611 | + | 0.363057i | −0.951592 | − | 0.307364i | \(-0.900553\pi\) |
0.741981 | + | 0.670421i | \(0.233886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.00000 | + | 3.46410i | −0.0836974 | + | 0.144968i | −0.904835 | − | 0.425762i | \(-0.860006\pi\) |
0.821138 | + | 0.570730i | \(0.193340\pi\) | |||||||
\(572\) | −3.00000 | − | 5.19615i | −0.125436 | − | 0.217262i | ||||
\(573\) | −10.0000 | −0.417756 | ||||||||
\(574\) | 6.00000 | 0.250435 | ||||||||
\(575\) | 2.00000 | + | 3.46410i | 0.0834058 | + | 0.144463i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −5.00000 | − | 8.66025i | −0.208153 | − | 0.360531i | 0.742980 | − | 0.669314i | \(-0.233412\pi\) |
−0.951133 | + | 0.308783i | \(0.900078\pi\) | |||||||
\(578\) | 0.500000 | − | 0.866025i | 0.0207973 | − | 0.0360219i | ||||
\(579\) | −4.50000 | + | 7.79423i | −0.187014 | + | 0.323917i | ||||
\(580\) | −2.50000 | + | 4.33013i | −0.103807 | + | 0.179799i | ||||
\(581\) | 27.0000 | 1.12015 | ||||||||
\(582\) | −3.50000 | − | 6.06218i | −0.145080 | − | 0.251285i | ||||
\(583\) | −4.50000 | − | 7.79423i | −0.186371 | − | 0.322804i | ||||
\(584\) | −7.00000 | + | 12.1244i | −0.289662 | + | 0.501709i | ||||
\(585\) | 2.00000 | 0.0826898 | ||||||||
\(586\) | −4.50000 | − | 7.79423i | −0.185893 | − | 0.321977i | ||||
\(587\) | −7.00000 | −0.288921 | −0.144460 | − | 0.989511i | \(-0.546145\pi\) | ||||
−0.144460 | + | 0.989511i | \(0.546145\pi\) | |||||||
\(588\) | −2.00000 | −0.0824786 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −3.00000 | −0.123508 | ||||||||
\(591\) | −6.00000 | −0.246807 | ||||||||
\(592\) | 3.00000 | + | 5.19615i | 0.123299 | + | 0.213561i | ||||
\(593\) | 34.0000 | 1.39621 | 0.698106 | − | 0.715994i | \(-0.254026\pi\) | ||||
0.698106 | + | 0.715994i | \(0.254026\pi\) | |||||||
\(594\) | −1.50000 | + | 2.59808i | −0.0615457 | + | 0.106600i | ||||
\(595\) | 6.00000 | + | 10.3923i | 0.245976 | + | 0.426043i | ||||
\(596\) | −0.500000 | − | 0.866025i | −0.0204808 | − | 0.0354738i | ||||
\(597\) | −7.00000 | −0.286491 | ||||||||
\(598\) | −4.00000 | + | 6.92820i | −0.163572 | + | 0.283315i | ||||
\(599\) | 12.0000 | − | 20.7846i | 0.490307 | − | 0.849236i | −0.509631 | − | 0.860393i | \(-0.670218\pi\) |
0.999938 | + | 0.0111569i | \(0.00355143\pi\) | |||||||
\(600\) | 0.500000 | − | 0.866025i | 0.0204124 | − | 0.0353553i | ||||
\(601\) | −15.0000 | − | 25.9808i | −0.611863 | − | 1.05978i | −0.990926 | − | 0.134407i | \(-0.957087\pi\) |
0.379063 | − | 0.925371i | \(-0.376246\pi\) | |||||||
\(602\) | −12.0000 | + | 20.7846i | −0.489083 | + | 0.847117i | ||||
\(603\) | 5.00000 | + | 8.66025i | 0.203616 | + | 0.352673i | ||||
\(604\) | −9.00000 | −0.366205 | ||||||||
\(605\) | 2.00000 | 0.0813116 | ||||||||
\(606\) | 5.50000 | + | 9.52628i | 0.223422 | + | 0.386979i | ||||
\(607\) | −4.00000 | + | 6.92820i | −0.162355 | + | 0.281207i | −0.935713 | − | 0.352763i | \(-0.885242\pi\) |
0.773358 | + | 0.633970i | \(0.218576\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.50000 | − | 12.9904i | 0.303915 | − | 0.526397i | ||||
\(610\) | −4.00000 | + | 6.92820i | −0.161955 | + | 0.280515i | ||||
\(611\) | −8.00000 | + | 13.8564i | −0.323645 | + | 0.560570i | ||||
\(612\) | −4.00000 | −0.161690 | ||||||||
\(613\) | 8.00000 | + | 13.8564i | 0.323117 | + | 0.559655i | 0.981129 | − | 0.193352i | \(-0.0619359\pi\) |
−0.658012 | + | 0.753007i | \(0.728603\pi\) | |||||||
\(614\) | 13.0000 | + | 22.5167i | 0.524637 | + | 0.908698i | ||||
\(615\) | 1.00000 | − | 1.73205i | 0.0403239 | − | 0.0698430i | ||||
\(616\) | 9.00000 | 0.362620 | ||||||||
\(617\) | 18.0000 | + | 31.1769i | 0.724653 | + | 1.25514i | 0.959117 | + | 0.283011i | \(0.0913331\pi\) |
−0.234464 | + | 0.972125i | \(0.575334\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 4.00000 | 0.160774 | 0.0803868 | − | 0.996764i | \(-0.474384\pi\) | ||||
0.0803868 | + | 0.996764i | \(0.474384\pi\) | |||||||
\(620\) | 2.00000 | − | 5.19615i | 0.0803219 | − | 0.208683i | ||||
\(621\) | 4.00000 | 0.160514 | ||||||||
\(622\) | 18.0000 | 0.721734 | ||||||||
\(623\) | −12.0000 | − | 20.7846i | −0.480770 | − | 0.832718i | ||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 10.5000 | + | 18.1865i | 0.419664 | + | 0.726880i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.00000 | 0.159617 | ||||||||
\(629\) | −12.0000 | + | 20.7846i | −0.478471 | + | 0.828737i | ||||
\(630\) | −1.50000 | + | 2.59808i | −0.0597614 | + | 0.103510i | ||||
\(631\) | 0.500000 | − | 0.866025i | 0.0199047 | − | 0.0344759i | −0.855901 | − | 0.517139i | \(-0.826997\pi\) |
0.875806 | + | 0.482663i | \(0.160330\pi\) | |||||||
\(632\) | −4.00000 | − | 6.92820i | −0.159111 | − | 0.275589i | ||||
\(633\) | 10.0000 | − | 17.3205i | 0.397464 | − | 0.688428i | ||||
\(634\) | −0.500000 | − | 0.866025i | −0.0198575 | − | 0.0343943i | ||||
\(635\) | 1.00000 | 0.0396838 | ||||||||
\(636\) | 3.00000 | 0.118958 | ||||||||
\(637\) | 2.00000 | + | 3.46410i | 0.0792429 | + | 0.137253i | ||||
\(638\) | −7.50000 | + | 12.9904i | −0.296928 | + | 0.514294i | ||||
\(639\) | 4.00000 | + | 6.92820i | 0.158238 | + | 0.274075i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −16.0000 | + | 27.7128i | −0.631962 | + | 1.09459i | 0.355188 | + | 0.934795i | \(0.384417\pi\) |
−0.987150 | + | 0.159795i | \(0.948917\pi\) | |||||||
\(642\) | 7.50000 | − | 12.9904i | 0.296001 | − | 0.512689i | ||||
\(643\) | 28.0000 | 1.10421 | 0.552106 | − | 0.833774i | \(-0.313824\pi\) | ||||
0.552106 | + | 0.833774i | \(0.313824\pi\) | |||||||
\(644\) | −6.00000 | − | 10.3923i | −0.236433 | − | 0.409514i | ||||
\(645\) | 4.00000 | + | 6.92820i | 0.157500 | + | 0.272798i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.0000 | −0.943537 | −0.471769 | − | 0.881722i | \(-0.656384\pi\) | ||||
−0.471769 | + | 0.881722i | \(0.656384\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −9.00000 | −0.353281 | ||||||||
\(650\) | −2.00000 | −0.0784465 | ||||||||
\(651\) | −6.00000 | + | 15.5885i | −0.235159 | + | 0.610960i | ||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | 31.0000 | 1.21312 | 0.606562 | − | 0.795036i | \(-0.292548\pi\) | ||||
0.606562 | + | 0.795036i | \(0.292548\pi\) | |||||||
\(654\) | −8.00000 | − | 13.8564i | −0.312825 | − | 0.541828i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.00000 | − | 1.73205i | 0.0390434 | − | 0.0676252i | ||||
\(657\) | −7.00000 | − | 12.1244i | −0.273096 | − | 0.473016i | ||||
\(658\) | −12.0000 | − | 20.7846i | −0.467809 | − | 0.810268i | ||||
\(659\) | 23.0000 | 0.895953 | 0.447976 | − | 0.894045i | \(-0.352145\pi\) | ||||
0.447976 | + | 0.894045i | \(0.352145\pi\) | |||||||
\(660\) | 1.50000 | − | 2.59808i | 0.0583874 | − | 0.101130i | ||||
\(661\) | −14.0000 | + | 24.2487i | −0.544537 | + | 0.943166i | 0.454099 | + | 0.890951i | \(0.349961\pi\) |
−0.998636 | + | 0.0522143i | \(0.983372\pi\) | |||||||
\(662\) | −12.0000 | + | 20.7846i | −0.466393 | + | 0.807817i | ||||
\(663\) | 4.00000 | + | 6.92820i | 0.155347 | + | 0.269069i | ||||
\(664\) | 4.50000 | − | 7.79423i | 0.174634 | − | 0.302475i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.00000 | −0.232495 | ||||||||
\(667\) | 20.0000 | 0.774403 | ||||||||
\(668\) | −1.00000 | − | 1.73205i | −0.0386912 | − | 0.0670151i | ||||
\(669\) | 4.50000 | − | 7.79423i | 0.173980 | − | 0.301342i | ||||
\(670\) | −5.00000 | − | 8.66025i | −0.193167 | − | 0.334575i | ||||
\(671\) | −12.0000 | + | 20.7846i | −0.463255 | + | 0.802381i | ||||
\(672\) | −1.50000 | + | 2.59808i | −0.0578638 | + | 0.100223i | ||||
\(673\) | 0.500000 | − | 0.866025i | 0.0192736 | − | 0.0333828i | −0.856228 | − | 0.516599i | \(-0.827198\pi\) |
0.875501 | + | 0.483216i | \(0.160531\pi\) | |||||||
\(674\) | −5.00000 | −0.192593 | ||||||||
\(675\) | 0.500000 | + | 0.866025i | 0.0192450 | + | 0.0333333i | ||||
\(676\) | 4.50000 | + | 7.79423i | 0.173077 | + | 0.299778i | ||||
\(677\) | −7.50000 | + | 12.9904i | −0.288248 | + | 0.499261i | −0.973392 | − | 0.229147i | \(-0.926406\pi\) |
0.685143 | + | 0.728408i | \(0.259740\pi\) | |||||||
\(678\) | −6.00000 | −0.230429 | ||||||||
\(679\) | −10.5000 | − | 18.1865i | −0.402953 | − | 0.697935i | ||||
\(680\) | 4.00000 | 0.153393 | ||||||||
\(681\) | 21.0000 | 0.804722 | ||||||||
\(682\) | 6.00000 | − | 15.5885i | 0.229752 | − | 0.596913i | ||||
\(683\) | 5.00000 | 0.191320 | 0.0956598 | − | 0.995414i | \(-0.469504\pi\) | ||||
0.0956598 | + | 0.995414i | \(0.469504\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.00000 | − | 8.66025i | −0.191040 | − | 0.330891i | ||||
\(686\) | 15.0000 | 0.572703 | ||||||||
\(687\) | −7.00000 | + | 12.1244i | −0.267067 | + | 0.462573i | ||||
\(688\) | 4.00000 | + | 6.92820i | 0.152499 | + | 0.264135i | ||||
\(689\) | −3.00000 | − | 5.19615i | −0.114291 | − | 0.197958i | ||||
\(690\) | −4.00000 | −0.152277 | ||||||||
\(691\) | 17.0000 | − | 29.4449i | 0.646710 | − | 1.12014i | −0.337193 | − | 0.941435i | \(-0.609478\pi\) |
0.983904 | − | 0.178700i | \(-0.0571891\pi\) | |||||||
\(692\) | 6.50000 | − | 11.2583i | 0.247093 | − | 0.427977i | ||||
\(693\) | −4.50000 | + | 7.79423i | −0.170941 | + | 0.296078i | ||||
\(694\) | 11.5000 | + | 19.9186i | 0.436534 | + | 0.756099i | ||||
\(695\) | −7.00000 | + | 12.1244i | −0.265525 | + | 0.459903i | ||||
\(696\) | −2.50000 | − | 4.33013i | −0.0947623 | − | 0.164133i | ||||
\(697\) | 8.00000 | 0.303022 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.00000 | − | 15.5885i | −0.340411 | − | 0.589610i | ||||
\(700\) | 1.50000 | − | 2.59808i | 0.0566947 | − | 0.0981981i | ||||
\(701\) | −13.5000 | − | 23.3827i | −0.509888 | − | 0.883152i | −0.999934 | − | 0.0114555i | \(-0.996354\pi\) |
0.490046 | − | 0.871696i | \(-0.336980\pi\) | |||||||
\(702\) | −1.00000 | + | 1.73205i | −0.0377426 | + | 0.0653720i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.50000 | − | 2.59808i | 0.0565334 | − | 0.0979187i | ||||
\(705\) | −8.00000 | −0.301297 | ||||||||
\(706\) | 9.00000 | + | 15.5885i | 0.338719 | + | 0.586679i | ||||
\(707\) | 16.5000 | + | 28.5788i | 0.620546 | + | 1.07482i | ||||
\(708\) | 1.50000 | − | 2.59808i | 0.0563735 | − | 0.0976417i | ||||
\(709\) | 38.0000 | 1.42712 | 0.713560 | − | 0.700594i | \(-0.247082\pi\) | ||||
0.713560 | + | 0.700594i | \(0.247082\pi\) | |||||||
\(710\) | −4.00000 | − | 6.92820i | −0.150117 | − | 0.260011i | ||||
\(711\) | 8.00000 | 0.300023 | ||||||||
\(712\) | −8.00000 | −0.299813 | ||||||||
\(713\) | −22.0000 | + | 3.46410i | −0.823906 | + | 0.129732i | ||||
\(714\) | −12.0000 | −0.449089 | ||||||||
\(715\) | −6.00000 | −0.224387 | ||||||||
\(716\) | −9.50000 | − | 16.4545i | −0.355032 | − | 0.614933i | ||||
\(717\) | −6.00000 | −0.224074 | ||||||||
\(718\) | −12.0000 | + | 20.7846i | −0.447836 | + | 0.775675i | ||||
\(719\) | −7.00000 | − | 12.1244i | −0.261056 | − | 0.452162i | 0.705467 | − | 0.708743i | \(-0.250737\pi\) |
−0.966523 | + | 0.256581i | \(0.917404\pi\) | |||||||
\(720\) | 0.500000 | + | 0.866025i | 0.0186339 | + | 0.0322749i | ||||
\(721\) | −3.00000 | −0.111726 | ||||||||
\(722\) | 9.50000 | − | 16.4545i | 0.353553 | − | 0.612372i | ||||
\(723\) | 1.50000 | − | 2.59808i | 0.0557856 | − | 0.0966235i | ||||
\(724\) | 8.00000 | − | 13.8564i | 0.297318 | − | 0.514969i | ||||
\(725\) | 2.50000 | + | 4.33013i | 0.0928477 | + | 0.160817i | ||||
\(726\) | −1.00000 | + | 1.73205i | −0.0371135 | + | 0.0642824i | ||||
\(727\) | −25.5000 | − | 44.1673i | −0.945743 | − | 1.63807i | −0.754257 | − | 0.656579i | \(-0.772003\pi\) |
−0.191485 | − | 0.981495i | \(-0.561330\pi\) | |||||||
\(728\) | 6.00000 | 0.222375 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.00000 | + | 12.1244i | 0.259082 | + | 0.448743i | ||||
\(731\) | −16.0000 | + | 27.7128i | −0.591781 | + | 1.02500i | ||||
\(732\) | −4.00000 | − | 6.92820i | −0.147844 | − | 0.256074i | ||||
\(733\) | 3.00000 | − | 5.19615i | 0.110808 | − | 0.191924i | −0.805289 | − | 0.592883i | \(-0.797990\pi\) |
0.916096 | + | 0.400959i | \(0.131323\pi\) | |||||||
\(734\) | 14.0000 | − | 24.2487i | 0.516749 | − | 0.895036i | ||||
\(735\) | −1.00000 | + | 1.73205i | −0.0368856 | + | 0.0638877i | ||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | −15.0000 | − | 25.9808i | −0.552532 | − | 0.957014i | ||||
\(738\) | 1.00000 | + | 1.73205i | 0.0368105 | + | 0.0637577i | ||||
\(739\) | 19.0000 | − | 32.9090i | 0.698926 | − | 1.21058i | −0.269913 | − | 0.962885i | \(-0.586995\pi\) |
0.968839 | − | 0.247691i | \(-0.0796718\pi\) | |||||||
\(740\) | 6.00000 | 0.220564 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.00000 | 0.330400 | ||||||||
\(743\) | −40.0000 | −1.46746 | −0.733729 | − | 0.679442i | \(-0.762222\pi\) | ||||
−0.733729 | + | 0.679442i | \(0.762222\pi\) | |||||||
\(744\) | 3.50000 | + | 4.33013i | 0.128316 | + | 0.158750i | ||||
\(745\) | −1.00000 | −0.0366372 | ||||||||
\(746\) | 24.0000 | 0.878702 | ||||||||
\(747\) | 4.50000 | + | 7.79423i | 0.164646 | + | 0.285176i | ||||
\(748\) | 12.0000 | 0.438763 | ||||||||
\(749\) | 22.5000 | − | 38.9711i | 0.822132 | − | 1.42397i | ||||
\(750\) | −0.500000 | − | 0.866025i | −0.0182574 | − | 0.0316228i | ||||
\(751\) | −21.5000 | − | 37.2391i | −0.784546 | − | 1.35887i | −0.929270 | − | 0.369402i | \(-0.879563\pi\) |
0.144724 | − | 0.989472i | \(-0.453771\pi\) | |||||||
\(752\) | −8.00000 | −0.291730 | ||||||||
\(753\) | −6.00000 | + | 10.3923i | −0.218652 | + | 0.378717i | ||||
\(754\) | −5.00000 | + | 8.66025i | −0.182089 | + | 0.315388i | ||||
\(755\) | −4.50000 | + | 7.79423i | −0.163772 | + | 0.283661i | ||||
\(756\) | −1.50000 | − | 2.59808i | −0.0545545 | − | 0.0944911i | ||||
\(757\) | −10.0000 | + | 17.3205i | −0.363456 | + | 0.629525i | −0.988527 | − | 0.151043i | \(-0.951737\pi\) |
0.625071 | + | 0.780568i | \(0.285070\pi\) | |||||||
\(758\) | 18.0000 | + | 31.1769i | 0.653789 | + | 1.13240i | ||||
\(759\) | −12.0000 | −0.435572 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0000 | + | 36.3731i | 0.761249 | + | 1.31852i | 0.942207 | + | 0.335032i | \(0.108747\pi\) |
−0.180957 | + | 0.983491i | \(0.557920\pi\) | |||||||
\(762\) | −0.500000 | + | 0.866025i | −0.0181131 | + | 0.0313728i | ||||
\(763\) | −24.0000 | − | 41.5692i | −0.868858 | − | 1.50491i | ||||
\(764\) | −5.00000 | + | 8.66025i | −0.180894 | + | 0.313317i | ||||
\(765\) | −2.00000 | + | 3.46410i | −0.0723102 | + | 0.125245i | ||||
\(766\) | 3.00000 | − | 5.19615i | 0.108394 | − | 0.187745i | ||||
\(767\) | −6.00000 | −0.216647 | ||||||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −4.50000 | − | 7.79423i | −0.162274 | − | 0.281067i | 0.773410 | − | 0.633906i | \(-0.218550\pi\) |
−0.935684 | + | 0.352839i | \(0.885216\pi\) | |||||||
\(770\) | 4.50000 | − | 7.79423i | 0.162169 | − | 0.280885i | ||||
\(771\) | 20.0000 | 0.720282 | ||||||||
\(772\) | 4.50000 | + | 7.79423i | 0.161959 | + | 0.280520i | ||||
\(773\) | −10.0000 | −0.359675 | −0.179838 | − | 0.983696i | \(-0.557557\pi\) | ||||
−0.179838 | + | 0.983696i | \(0.557557\pi\) | |||||||
\(774\) | −8.00000 | −0.287554 | ||||||||
\(775\) | −3.50000 | − | 4.33013i | −0.125724 | − | 0.155543i | ||||
\(776\) | −7.00000 | −0.251285 | ||||||||
\(777\) | −18.0000 | −0.645746 | ||||||||
\(778\) | 1.00000 | + | 1.73205i | 0.0358517 | + | 0.0620970i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 1.00000 | − | 1.73205i | 0.0358057 | − | 0.0620174i | ||||
\(781\) | −12.0000 | − | 20.7846i | −0.429394 | − | 0.743732i | ||||
\(782\) | −8.00000 | − | 13.8564i | −0.286079 | − | 0.495504i | ||||
\(783\) | 5.00000 | 0.178685 | ||||||||
\(784\) | −1.00000 | + | 1.73205i | −0.0357143 | + | 0.0618590i | ||||
\(785\) | 2.00000 | − | 3.46410i | 0.0713831 | − | 0.123639i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.0000 | + | 27.7128i | 0.570338 | + | 0.987855i | 0.996531 | + | 0.0832226i | \(0.0265213\pi\) |
−0.426193 | + | 0.904632i | \(0.640145\pi\) | |||||||
\(788\) | −3.00000 | + | 5.19615i | −0.106871 | + | 0.185105i | ||||
\(789\) | −15.0000 | − | 25.9808i | −0.534014 | − | 0.924940i | ||||
\(790\) | −8.00000 | −0.284627 | ||||||||
\(791\) | −18.0000 | −0.640006 | ||||||||
\(792\) | 1.50000 | + | 2.59808i | 0.0533002 | + | 0.0923186i | ||||
\(793\) | −8.00000 | + | 13.8564i | −0.284088 | + | 0.492055i | ||||
\(794\) | 14.0000 | + | 24.2487i | 0.496841 | + | 0.860555i | ||||
\(795\) | 1.50000 | − | 2.59808i | 0.0531995 | − | 0.0921443i | ||||
\(796\) | −3.50000 | + | 6.06218i | −0.124054 | + | 0.214868i | ||||
\(797\) | −23.5000 | + | 40.7032i | −0.832413 | + | 1.44178i | 0.0637070 | + | 0.997969i | \(0.479708\pi\) |
−0.896120 | + | 0.443812i | \(0.853626\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.0000 | − | 27.7128i | −0.566039 | − | 0.980409i | ||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 4.00000 | − | 6.92820i | 0.141333 | − | 0.244796i | ||||
\(802\) | 10.0000 | 0.353112 | ||||||||
\(803\) | 21.0000 | + | 36.3731i | 0.741074 | + | 1.28358i | ||||
\(804\) | 10.0000 | 0.352673 | ||||||||
\(805\) | −12.0000 | −0.422944 | ||||||||
\(806\) | 4.00000 | − | 10.3923i | 0.140894 | − | 0.366053i | ||||
\(807\) | −14.0000 | −0.492823 | ||||||||
\(808\) | 11.0000 | 0.386979 | ||||||||
\(809\) | 8.00000 | + | 13.8564i | 0.281265 | + | 0.487165i | 0.971697 | − | 0.236232i | \(-0.0759127\pi\) |
−0.690432 | + | 0.723398i | \(0.742579\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 15.0000 | − | 25.9808i | 0.526721 | − | 0.912308i | −0.472794 | − | 0.881173i | \(-0.656755\pi\) |
0.999515 | − | 0.0311349i | \(-0.00991216\pi\) | |||||||
\(812\) | −7.50000 | − | 12.9904i | −0.263198 | − | 0.455873i | ||||
\(813\) | −14.5000 | − | 25.1147i | −0.508537 | − | 0.880812i | ||||
\(814\) | 18.0000 | 0.630900 | ||||||||
\(815\) | −2.00000 | + | 3.46410i | −0.0700569 | + | 0.121342i | ||||
\(816\) | −2.00000 | + | 3.46410i | −0.0700140 | + | 0.121268i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 12.5000 | + | 21.6506i | 0.437052 | + | 0.756997i | ||||
\(819\) | −3.00000 | + | 5.19615i | −0.104828 | + | 0.181568i | ||||
\(820\) | −1.00000 | − | 1.73205i | −0.0349215 | − | 0.0604858i | ||||
\(821\) | −53.0000 | −1.84971 | −0.924856 | − | 0.380317i | \(-0.875815\pi\) | ||||
−0.924856 | + | 0.380317i | \(0.875815\pi\) | |||||||
\(822\) | 10.0000 | 0.348790 | ||||||||
\(823\) | 4.50000 | + | 7.79423i | 0.156860 | + | 0.271690i | 0.933735 | − | 0.357966i | \(-0.116529\pi\) |
−0.776875 | + | 0.629655i | \(0.783196\pi\) | |||||||
\(824\) | −0.500000 | + | 0.866025i | −0.0174183 | + | 0.0301694i | ||||
\(825\) | −1.50000 | − | 2.59808i | −0.0522233 | − | 0.0904534i | ||||
\(826\) | 4.50000 | − | 7.79423i | 0.156575 | − | 0.271196i | ||||
\(827\) | −10.0000 | + | 17.3205i | −0.347734 | + | 0.602293i | −0.985847 | − | 0.167650i | \(-0.946382\pi\) |
0.638112 | + | 0.769943i | \(0.279715\pi\) | |||||||
\(828\) | 2.00000 | − | 3.46410i | 0.0695048 | − | 0.120386i | ||||
\(829\) | 4.00000 | 0.138926 | 0.0694629 | − | 0.997585i | \(-0.477871\pi\) | ||||
0.0694629 | + | 0.997585i | \(0.477871\pi\) | |||||||
\(830\) | −4.50000 | − | 7.79423i | −0.156197 | − | 0.270542i | ||||
\(831\) | 6.00000 | + | 10.3923i | 0.208138 | + | 0.360505i | ||||
\(832\) | 1.00000 | − | 1.73205i | 0.0346688 | − | 0.0600481i | ||||
\(833\) | −8.00000 | −0.277184 | ||||||||
\(834\) | −7.00000 | − | 12.1244i | −0.242390 | − | 0.419832i | ||||
\(835\) | −2.00000 | −0.0692129 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.50000 | + | 0.866025i | −0.190108 | + | 0.0299342i | ||||
\(838\) | 21.0000 | 0.725433 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 1.50000 | + | 2.59808i | 0.0517549 | + | 0.0896421i | ||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | −10.0000 | + | 17.3205i | −0.344623 | + | 0.596904i | ||||
\(843\) | 8.00000 | + | 13.8564i | 0.275535 | + | 0.477240i | ||||
\(844\) | −10.0000 | − | 17.3205i | −0.344214 | − | 0.596196i | ||||
\(845\) | 9.00000 | 0.309609 | ||||||||
\(846\) | 4.00000 | − | 6.92820i | 0.137523 | − | 0.238197i | ||||
\(847\) | −3.00000 | + | 5.19615i | −0.103081 | + | 0.178542i | ||||
\(848\) | 1.50000 | − | 2.59808i | 0.0515102 | − | 0.0892183i | ||||
\(849\) | 9.00000 | + | 15.5885i | 0.308879 | + | 0.534994i | ||||
\(850\) | 2.00000 | − | 3.46410i | 0.0685994 | − | 0.118818i | ||||
\(851\) | −12.0000 | − | 20.7846i | −0.411355 | − | 0.712487i | ||||
\(852\) | 8.00000 | 0.274075 | ||||||||
\(853\) | −56.0000 | −1.91740 | −0.958702 | − | 0.284413i | \(-0.908201\pi\) | ||||
−0.958702 | + | 0.284413i | \(0.908201\pi\) | |||||||
\(854\) | −12.0000 | − | 20.7846i | −0.410632 | − | 0.711235i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.50000 | − | 12.9904i | −0.256345 | − | 0.444002i | ||||
\(857\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(858\) | 3.00000 | − | 5.19615i | 0.102418 | − | 0.177394i | ||||
\(859\) | 17.0000 | − | 29.4449i | 0.580033 | − | 1.00465i | −0.415442 | − | 0.909620i | \(-0.636373\pi\) |
0.995475 | − | 0.0950262i | \(-0.0302935\pi\) | |||||||
\(860\) | 8.00000 | 0.272798 | ||||||||
\(861\) | 3.00000 | + | 5.19615i | 0.102240 | + | 0.177084i | ||||
\(862\) | 1.00000 | + | 1.73205i | 0.0340601 | + | 0.0589939i | ||||
\(863\) | 16.0000 | − | 27.7128i | 0.544646 | − | 0.943355i | −0.453983 | − | 0.891010i | \(-0.649997\pi\) |
0.998629 | − | 0.0523446i | \(-0.0166694\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −6.50000 | − | 11.2583i | −0.221007 | − | 0.382795i | ||||
\(866\) | 14.0000 | 0.475739 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 10.5000 | + | 12.9904i | 0.356393 | + | 0.440922i | ||||
\(869\) | −24.0000 | −0.814144 | ||||||||
\(870\) | −5.00000 | −0.169516 | ||||||||
\(871\) | −10.0000 | − | 17.3205i | −0.338837 | − | 0.586883i | ||||
\(872\) | −16.0000 | −0.541828 | ||||||||
\(873\) | 3.50000 | − | 6.06218i | 0.118457 | − | 0.205174i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.50000 | − | 2.59808i | −0.0507093 | − | 0.0878310i | ||||
\(876\) | −14.0000 | −0.473016 | ||||||||
\(877\) | −26.0000 | + | 45.0333i | −0.877958 | + | 1.52067i | −0.0243792 | + | 0.999703i | \(0.507761\pi\) |
−0.853578 | + | 0.520964i | \(0.825572\pi\) | |||||||
\(878\) | −7.50000 | + | 12.9904i | −0.253113 | + | 0.438404i | ||||
\(879\) | 4.50000 | − | 7.79423i | 0.151781 | − | 0.262893i | ||||
\(880\) | −1.50000 | − | 2.59808i | −0.0505650 | − | 0.0875811i | ||||
\(881\) | 29.0000 | − | 50.2295i | 0.977035 | − | 1.69227i | 0.303985 | − | 0.952677i | \(-0.401683\pi\) |
0.673050 | − | 0.739597i | \(-0.264984\pi\) | |||||||
\(882\) | −1.00000 | − | 1.73205i | −0.0336718 | − | 0.0583212i | ||||
\(883\) | 2.00000 | 0.0673054 | 0.0336527 | − | 0.999434i | \(-0.489286\pi\) | ||||
0.0336527 | + | 0.999434i | \(0.489286\pi\) | |||||||
\(884\) | 8.00000 | 0.269069 | ||||||||
\(885\) | −1.50000 | − | 2.59808i | −0.0504219 | − | 0.0873334i | ||||
\(886\) | −12.0000 | + | 20.7846i | −0.403148 | + | 0.698273i | ||||
\(887\) | 14.0000 | + | 24.2487i | 0.470074 | + | 0.814192i | 0.999414 | − | 0.0342175i | \(-0.0108939\pi\) |
−0.529340 | + | 0.848410i | \(0.677561\pi\) | |||||||
\(888\) | −3.00000 | + | 5.19615i | −0.100673 | + | 0.174371i | ||||
\(889\) | −1.50000 | + | 2.59808i | −0.0503084 | + | 0.0871367i | ||||
\(890\) | −4.00000 | + | 6.92820i | −0.134080 | + | 0.232234i | ||||
\(891\) | −3.00000 | −0.100504 | ||||||||
\(892\) | −4.50000 | − | 7.79423i | −0.150671 | − | 0.260970i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0.500000 | − | 0.866025i | 0.0167225 | − | 0.0289642i | ||||
\(895\) | −19.0000 | −0.635100 | ||||||||
\(896\) | 1.50000 | + | 2.59808i | 0.0501115 | + | 0.0867956i | ||||
\(897\) | −8.00000 | −0.267112 | ||||||||
\(898\) | −40.0000 | −1.33482 | ||||||||
\(899\) | −27.5000 | + | 4.33013i | −0.917176 | + | 0.144418i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | −3.00000 | − | 5.19615i | −0.0998891 | − | 0.173013i | ||||
\(903\) | −24.0000 | −0.798670 | ||||||||
\(904\) | −3.00000 | + | 5.19615i | −0.0997785 | + | 0.172821i | ||||
\(905\) | −8.00000 | − | 13.8564i | −0.265929 | − | 0.460603i | ||||
\(906\) | −4.50000 | − | 7.79423i | −0.149502 | − | 0.258946i | ||||
\(907\) | −58.0000 | −1.92586 | −0.962929 | − | 0.269754i | \(-0.913058\pi\) | ||||
−0.962929 | + | 0.269754i | \(0.913058\pi\) | |||||||
\(908\) | 10.5000 | − | 18.1865i | 0.348455 | − | 0.603541i | ||||
\(909\) | −5.50000 | + | 9.52628i | −0.182423 | + | 0.315967i | ||||
\(910\) | 3.00000 | − | 5.19615i | 0.0994490 | − | 0.172251i | ||||
\(911\) | 11.0000 | + | 19.0526i | 0.364446 | + | 0.631239i | 0.988687 | − | 0.149992i | \(-0.0479250\pi\) |
−0.624241 | + | 0.781232i | \(0.714592\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.5000 | − | 23.3827i | −0.446785 | − | 0.773854i | ||||
\(914\) | 10.0000 | 0.330771 | ||||||||
\(915\) | −8.00000 | −0.264472 | ||||||||
\(916\) | 7.00000 | + | 12.1244i | 0.231287 | + | 0.400600i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.00000 | − | 3.46410i | −0.0660098 | − | 0.114332i | ||||
\(919\) | 5.50000 | − | 9.52628i | 0.181428 | − | 0.314243i | −0.760939 | − | 0.648824i | \(-0.775261\pi\) |
0.942367 | + | 0.334581i | \(0.108595\pi\) | |||||||
\(920\) | −2.00000 | + | 3.46410i | −0.0659380 | + | 0.114208i | ||||
\(921\) | −13.0000 | + | 22.5167i | −0.428365 | + | 0.741949i | ||||
\(922\) | 21.0000 | 0.691598 | ||||||||
\(923\) | −8.00000 | − | 13.8564i | −0.263323 | − | 0.456089i | ||||
\(924\) | 4.50000 | + | 7.79423i | 0.148039 | + | 0.256411i | ||||
\(925\) | 3.00000 | − | 5.19615i | 0.0986394 | − | 0.170848i | ||||
\(926\) | −5.00000 | −0.164310 | ||||||||
\(927\) | −0.500000 | − | 0.866025i | −0.0164222 | − | 0.0284440i | ||||
\(928\) | −5.00000 | −0.164133 | ||||||||
\(929\) | −8.00000 | −0.262471 | −0.131236 | − | 0.991351i | \(-0.541894\pi\) | ||||
−0.131236 | + | 0.991351i | \(0.541894\pi\) | |||||||
\(930\) | 5.50000 | − | 0.866025i | 0.180352 | − | 0.0283981i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −18.0000 | −0.589610 | ||||||||
\(933\) | 9.00000 | + | 15.5885i | 0.294647 | + | 0.510343i | ||||
\(934\) | 27.0000 | 0.883467 | ||||||||
\(935\) | 6.00000 | − | 10.3923i | 0.196221 | − | 0.339865i | ||||
\(936\) | 1.00000 | + | 1.73205i | 0.0326860 | + | 0.0566139i | ||||
\(937\) | −1.00000 | − | 1.73205i | −0.0326686 | − | 0.0565836i | 0.849229 | − | 0.528025i | \(-0.177067\pi\) |
−0.881897 | + | 0.471441i | \(0.843734\pi\) | |||||||
\(938\) | 30.0000 | 0.979535 | ||||||||
\(939\) | −10.5000 | + | 18.1865i | −0.342655 | + | 0.593495i | ||||
\(940\) | −4.00000 | + | 6.92820i | −0.130466 | + | 0.225973i | ||||
\(941\) | 17.5000 | − | 30.3109i | 0.570484 | − | 0.988107i | −0.426033 | − | 0.904708i | \(-0.640089\pi\) |
0.996516 | − | 0.0833989i | \(-0.0265776\pi\) | |||||||
\(942\) | 2.00000 | + | 3.46410i | 0.0651635 | + | 0.112867i | ||||
\(943\) | −4.00000 | + | 6.92820i | −0.130258 | + | 0.225613i | ||||
\(944\) | −1.50000 | − | 2.59808i | −0.0488208 | − | 0.0845602i | ||||
\(945\) | −3.00000 | −0.0975900 | ||||||||
\(946\) | 24.0000 | 0.780307 | ||||||||
\(947\) | −18.0000 | − | 31.1769i | −0.584921 | − | 1.01311i | −0.994885 | − | 0.101012i | \(-0.967792\pi\) |
0.409964 | − | 0.912102i | \(-0.365541\pi\) | |||||||
\(948\) | 4.00000 | − | 6.92820i | 0.129914 | − | 0.225018i | ||||
\(949\) | 14.0000 | + | 24.2487i | 0.454459 | + | 0.787146i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.500000 | − | 0.866025i | 0.0162136 | − | 0.0280828i | ||||
\(952\) | −6.00000 | + | 10.3923i | −0.194461 | + | 0.336817i | ||||
\(953\) | 44.0000 | 1.42530 | 0.712650 | − | 0.701520i | \(-0.247495\pi\) | ||||
0.712650 | + | 0.701520i | \(0.247495\pi\) | |||||||
\(954\) | 1.50000 | + | 2.59808i | 0.0485643 | + | 0.0841158i | ||||
\(955\) | 5.00000 | + | 8.66025i | 0.161796 | + | 0.280239i | ||||
\(956\) | −3.00000 | + | 5.19615i | −0.0970269 | + | 0.168056i | ||||
\(957\) | −15.0000 | −0.484881 | ||||||||
\(958\) | −12.0000 | − | 20.7846i | −0.387702 | − | 0.671520i | ||||
\(959\) | 30.0000 | 0.968751 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | 29.5000 | − | 9.52628i | 0.951613 | − | 0.307299i | ||||
\(962\) | 12.0000 | 0.386896 | ||||||||
\(963\) | 15.0000 | 0.483368 | ||||||||
\(964\) | −1.50000 | − | 2.59808i | −0.0483117 | − | 0.0836784i | ||||
\(965\) | 9.00000 | 0.289720 | ||||||||
\(966\) | 6.00000 | − | 10.3923i | 0.193047 | − | 0.334367i | ||||
\(967\) | −24.0000 | − | 41.5692i | −0.771788 | − | 1.33678i | −0.936582 | − | 0.350448i | \(-0.886029\pi\) |
0.164794 | − | 0.986328i | \(-0.447304\pi\) | |||||||
\(968\) | 1.00000 | + | 1.73205i | 0.0321412 | + | 0.0556702i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.50000 | + | 6.06218i | −0.112378 | + | 0.194645i | ||||
\(971\) | −7.50000 | + | 12.9904i | −0.240686 | + | 0.416881i | −0.960910 | − | 0.276861i | \(-0.910706\pi\) |
0.720224 | + | 0.693742i | \(0.244039\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | −21.0000 | − | 36.3731i | −0.673229 | − | 1.16607i | ||||
\(974\) | 15.5000 | − | 26.8468i | 0.496652 | − | 0.860227i | ||||
\(975\) | −1.00000 | − | 1.73205i | −0.0320256 | − | 0.0554700i | ||||
\(976\) | −8.00000 | −0.256074 | ||||||||
\(977\) | −16.0000 | −0.511885 | −0.255943 | − | 0.966692i | \(-0.582386\pi\) | ||||
−0.255943 | + | 0.966692i | \(0.582386\pi\) | |||||||
\(978\) | −2.00000 | − | 3.46410i | −0.0639529 | − | 0.110770i | ||||
\(979\) | −12.0000 | + | 20.7846i | −0.383522 | + | 0.664279i | ||||
\(980\) | 1.00000 | + | 1.73205i | 0.0319438 | + | 0.0553283i | ||||
\(981\) | 8.00000 | − | 13.8564i | 0.255420 | − | 0.442401i | ||||
\(982\) | −20.5000 | + | 35.5070i | −0.654181 | + | 1.13308i | ||||
\(983\) | −14.0000 | + | 24.2487i | −0.446531 | + | 0.773414i | −0.998157 | − | 0.0606773i | \(-0.980674\pi\) |
0.551627 | + | 0.834091i | \(0.314007\pi\) | |||||||
\(984\) | 2.00000 | 0.0637577 | ||||||||
\(985\) | 3.00000 | + | 5.19615i | 0.0955879 | + | 0.165563i | ||||
\(986\) | −10.0000 | − | 17.3205i | −0.318465 | − | 0.551597i | ||||
\(987\) | 12.0000 | − | 20.7846i | 0.381964 | − | 0.661581i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.0000 | − | 27.7128i | −0.508770 | − | 0.881216i | ||||
\(990\) | 3.00000 | 0.0953463 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | 5.50000 | − | 0.866025i | 0.174625 | − | 0.0274963i | ||||
\(993\) | −24.0000 | −0.761617 | ||||||||
\(994\) | 24.0000 | 0.761234 | ||||||||
\(995\) | 3.50000 | + | 6.06218i | 0.110957 | + | 0.192184i | ||||
\(996\) | 9.00000 | 0.285176 | ||||||||
\(997\) | −21.0000 | + | 36.3731i | −0.665077 | + | 1.15195i | 0.314188 | + | 0.949361i | \(0.398268\pi\) |
−0.979265 | + | 0.202586i | \(0.935066\pi\) | |||||||
\(998\) | −11.0000 | − | 19.0526i | −0.348199 | − | 0.603098i | ||||
\(999\) | −3.00000 | − | 5.19615i | −0.0949158 | − | 0.164399i |
(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.i.i.211.1 | ✓ | 2 | |
31.5 | even | 3 | inner | 930.2.i.i.811.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.i.i.211.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
930.2.i.i.811.1 | yes | 2 | 31.5 | even | 3 | inner |