Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(211,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, 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("546.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.l (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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-43})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 10x^{2} - 11x + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 295.2 | ||
Root | \(3.08945 - 1.20635i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.295 |
Dual form | 546.2.l.k.211.2 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.00000 | − | 1.73205i | 0.316228 | − | 0.547723i | ||||
\(11\) | 2.58945 | − | 4.48507i | 0.780750 | − | 1.35230i | −0.150756 | − | 0.988571i | \(-0.548171\pi\) |
0.931505 | − | 0.363727i | \(-0.118496\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.50000 | + | 3.27872i | −0.416025 | + | 0.909353i | ||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −1.00000 | + | 1.73205i | −0.258199 | + | 0.447214i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.50000 | − | 4.33013i | −0.606339 | − | 1.05021i | −0.991838 | − | 0.127502i | \(-0.959304\pi\) |
0.385499 | − | 0.922708i | \(-0.374029\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.58945 | − | 2.75302i | −0.364646 | − | 0.631585i | 0.624073 | − | 0.781366i | \(-0.285477\pi\) |
−0.988719 | + | 0.149781i | \(0.952143\pi\) | |||||||
\(20\) | 1.00000 | + | 1.73205i | 0.223607 | + | 0.387298i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 2.58945 | + | 4.48507i | 0.552073 | + | 0.956219i | ||||
\(23\) | 4.08945 | − | 7.08314i | 0.852710 | − | 1.47694i | −0.0260431 | − | 0.999661i | \(-0.508291\pi\) |
0.878753 | − | 0.477276i | \(-0.158376\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −2.08945 | − | 2.93840i | −0.409776 | − | 0.576267i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.500000 | − | 0.866025i | 0.0944911 | − | 0.163663i | ||||
\(29\) | 1.58945 | − | 2.75302i | 0.295154 | − | 0.511222i | −0.679867 | − | 0.733336i | \(-0.737962\pi\) |
0.975021 | + | 0.222114i | \(0.0712956\pi\) | |||||||
\(30\) | −1.00000 | − | 1.73205i | −0.182574 | − | 0.316228i | ||||
\(31\) | 4.17891 | 0.750554 | 0.375277 | − | 0.926913i | \(-0.377548\pi\) | ||||
0.375277 | + | 0.926913i | \(0.377548\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −2.58945 | − | 4.48507i | −0.450766 | − | 0.780750i | ||||
\(34\) | 5.00000 | 0.857493 | ||||||||
\(35\) | −1.00000 | − | 1.73205i | −0.169031 | − | 0.292770i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −1.00000 | + | 1.73205i | −0.164399 | + | 0.284747i | −0.936442 | − | 0.350823i | \(-0.885902\pi\) |
0.772043 | + | 0.635571i | \(0.219235\pi\) | |||||||
\(38\) | 3.17891 | 0.515687 | ||||||||
\(39\) | 2.08945 | + | 2.93840i | 0.334580 | + | 0.470520i | ||||
\(40\) | −2.00000 | −0.316228 | ||||||||
\(41\) | 3.58945 | − | 6.21712i | 0.560579 | − | 0.970951i | −0.436867 | − | 0.899526i | \(-0.643912\pi\) |
0.997446 | − | 0.0714247i | \(-0.0227545\pi\) | |||||||
\(42\) | −0.500000 | + | 0.866025i | −0.0771517 | + | 0.133631i | ||||
\(43\) | −6.08945 | − | 10.5472i | −0.928633 | − | 1.60844i | −0.785612 | − | 0.618720i | \(-0.787652\pi\) |
−0.143022 | − | 0.989720i | \(-0.545682\pi\) | |||||||
\(44\) | −5.17891 | −0.780750 | ||||||||
\(45\) | 1.00000 | + | 1.73205i | 0.149071 | + | 0.258199i | ||||
\(46\) | 4.08945 | + | 7.08314i | 0.602957 | + | 1.04435i | ||||
\(47\) | −7.17891 | −1.04715 | −0.523576 | − | 0.851979i | \(-0.675402\pi\) | ||||
−0.523576 | + | 0.851979i | \(0.675402\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0.500000 | − | 0.866025i | 0.0707107 | − | 0.122474i | ||||
\(51\) | −5.00000 | −0.700140 | ||||||||
\(52\) | 3.58945 | − | 0.340322i | 0.497768 | − | 0.0471941i | ||||
\(53\) | −3.00000 | −0.412082 | −0.206041 | − | 0.978543i | \(-0.566058\pi\) | ||||
−0.206041 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | −5.17891 | + | 8.97013i | −0.698324 | + | 1.20953i | ||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | −3.17891 | −0.421057 | ||||||||
\(58\) | 1.58945 | + | 2.75302i | 0.208706 | + | 0.361489i | ||||
\(59\) | 6.08945 | + | 10.5472i | 0.792779 | + | 1.37313i | 0.924240 | + | 0.381813i | \(0.124700\pi\) |
−0.131460 | + | 0.991321i | \(0.541967\pi\) | |||||||
\(60\) | 2.00000 | 0.258199 | ||||||||
\(61\) | 1.50000 | + | 2.59808i | 0.192055 | + | 0.332650i | 0.945931 | − | 0.324367i | \(-0.105151\pi\) |
−0.753876 | + | 0.657017i | \(0.771818\pi\) | |||||||
\(62\) | −2.08945 | + | 3.61904i | −0.265361 | + | 0.459619i | ||||
\(63\) | 0.500000 | − | 0.866025i | 0.0629941 | − | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.00000 | − | 6.55744i | 0.372104 | − | 0.813350i | ||||
\(66\) | 5.17891 | 0.637480 | ||||||||
\(67\) | 1.91055 | − | 3.30916i | 0.233410 | − | 0.404279i | −0.725399 | − | 0.688328i | \(-0.758345\pi\) |
0.958809 | + | 0.284050i | \(0.0916781\pi\) | |||||||
\(68\) | −2.50000 | + | 4.33013i | −0.303170 | + | 0.525105i | ||||
\(69\) | −4.08945 | − | 7.08314i | −0.492312 | − | 0.852710i | ||||
\(70\) | 2.00000 | 0.239046 | ||||||||
\(71\) | 1.08945 | + | 1.88699i | 0.129294 | + | 0.223945i | 0.923403 | − | 0.383831i | \(-0.125395\pi\) |
−0.794109 | + | 0.607775i | \(0.792062\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | −1.00000 | − | 1.73205i | −0.116248 | − | 0.201347i | ||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | −1.58945 | + | 2.75302i | −0.182323 | + | 0.315793i | ||||
\(77\) | 5.17891 | 0.590191 | ||||||||
\(78\) | −3.58945 | + | 0.340322i | −0.406426 | + | 0.0385338i | ||||
\(79\) | 13.1789 | 1.48274 | 0.741372 | − | 0.671095i | \(-0.234176\pi\) | ||||
0.741372 | + | 0.671095i | \(0.234176\pi\) | |||||||
\(80\) | 1.00000 | − | 1.73205i | 0.111803 | − | 0.193649i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 3.58945 | + | 6.21712i | 0.396389 | + | 0.686566i | ||||
\(83\) | 6.17891 | 0.678223 | 0.339112 | − | 0.940746i | \(-0.389874\pi\) | ||||
0.339112 | + | 0.940746i | \(0.389874\pi\) | |||||||
\(84\) | −0.500000 | − | 0.866025i | −0.0545545 | − | 0.0944911i | ||||
\(85\) | 5.00000 | + | 8.66025i | 0.542326 | + | 0.939336i | ||||
\(86\) | 12.1789 | 1.31329 | ||||||||
\(87\) | −1.58945 | − | 2.75302i | −0.170407 | − | 0.295154i | ||||
\(88\) | 2.58945 | − | 4.48507i | 0.276037 | − | 0.478110i | ||||
\(89\) | −4.50000 | + | 7.79423i | −0.476999 | + | 0.826187i | −0.999653 | − | 0.0263586i | \(-0.991609\pi\) |
0.522654 | + | 0.852545i | \(0.324942\pi\) | |||||||
\(90\) | −2.00000 | −0.210819 | ||||||||
\(91\) | −3.58945 | + | 0.340322i | −0.376277 | + | 0.0356754i | ||||
\(92\) | −8.17891 | −0.852710 | ||||||||
\(93\) | 2.08945 | − | 3.61904i | 0.216666 | − | 0.375277i | ||||
\(94\) | 3.58945 | − | 6.21712i | 0.370224 | − | 0.641247i | ||||
\(95\) | 3.17891 | + | 5.50603i | 0.326149 | + | 0.564907i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 5.17891 | + | 8.97013i | 0.525838 | + | 0.910779i | 0.999547 | + | 0.0300973i | \(0.00958170\pi\) |
−0.473709 | + | 0.880682i | \(0.657085\pi\) | |||||||
\(98\) | −0.500000 | − | 0.866025i | −0.0505076 | − | 0.0874818i | ||||
\(99\) | −5.17891 | −0.520500 | ||||||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | −3.17891 | + | 5.50603i | −0.316313 | + | 0.547871i | −0.979716 | − | 0.200392i | \(-0.935778\pi\) |
0.663403 | + | 0.748263i | \(0.269112\pi\) | |||||||
\(102\) | 2.50000 | − | 4.33013i | 0.247537 | − | 0.428746i | ||||
\(103\) | −8.17891 | −0.805892 | −0.402946 | − | 0.915224i | \(-0.632014\pi\) | ||||
−0.402946 | + | 0.915224i | \(0.632014\pi\) | |||||||
\(104\) | −1.50000 | + | 3.27872i | −0.147087 | + | 0.321505i | ||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | 1.50000 | − | 2.59808i | 0.145693 | − | 0.252347i | ||||
\(107\) | −9.58945 | + | 16.6094i | −0.927048 | + | 1.60569i | −0.138813 | + | 0.990319i | \(0.544329\pi\) |
−0.788235 | + | 0.615375i | \(0.789005\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 4.00000 | 0.383131 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(110\) | −5.17891 | − | 8.97013i | −0.493790 | − | 0.855269i | ||||
\(111\) | 1.00000 | + | 1.73205i | 0.0949158 | + | 0.164399i | ||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −9.17891 | − | 15.8983i | −0.863479 | − | 1.49559i | −0.868549 | − | 0.495602i | \(-0.834947\pi\) |
0.00507042 | − | 0.999987i | \(-0.498386\pi\) | |||||||
\(114\) | 1.58945 | − | 2.75302i | 0.148866 | − | 0.257844i | ||||
\(115\) | −8.17891 | + | 14.1663i | −0.762687 | + | 1.32101i | ||||
\(116\) | −3.17891 | −0.295154 | ||||||||
\(117\) | 3.58945 | − | 0.340322i | 0.331845 | − | 0.0314627i | ||||
\(118\) | −12.1789 | −1.12116 | ||||||||
\(119\) | 2.50000 | − | 4.33013i | 0.229175 | − | 0.396942i | ||||
\(120\) | −1.00000 | + | 1.73205i | −0.0912871 | + | 0.158114i | ||||
\(121\) | −7.91055 | − | 13.7015i | −0.719141 | − | 1.24559i | ||||
\(122\) | −3.00000 | −0.271607 | ||||||||
\(123\) | −3.58945 | − | 6.21712i | −0.323650 | − | 0.560579i | ||||
\(124\) | −2.08945 | − | 3.61904i | −0.187639 | − | 0.324999i | ||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0.500000 | + | 0.866025i | 0.0445435 | + | 0.0771517i | ||||
\(127\) | −6.00000 | + | 10.3923i | −0.532414 | + | 0.922168i | 0.466870 | + | 0.884326i | \(0.345382\pi\) |
−0.999284 | + | 0.0378419i | \(0.987952\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −12.1789 | −1.07229 | ||||||||
\(130\) | 4.17891 | + | 5.87680i | 0.366515 | + | 0.515429i | ||||
\(131\) | −14.5367 | −1.27008 | −0.635040 | − | 0.772479i | \(-0.719016\pi\) | ||||
−0.635040 | + | 0.772479i | \(0.719016\pi\) | |||||||
\(132\) | −2.58945 | + | 4.48507i | −0.225383 | + | 0.390375i | ||||
\(133\) | 1.58945 | − | 2.75302i | 0.137823 | − | 0.238717i | ||||
\(134\) | 1.91055 | + | 3.30916i | 0.165046 | + | 0.285868i | ||||
\(135\) | 2.00000 | 0.172133 | ||||||||
\(136\) | −2.50000 | − | 4.33013i | −0.214373 | − | 0.371305i | ||||
\(137\) | −3.17891 | − | 5.50603i | −0.271592 | − | 0.470412i | 0.697677 | − | 0.716412i | \(-0.254217\pi\) |
−0.969270 | + | 0.246000i | \(0.920884\pi\) | |||||||
\(138\) | 8.17891 | 0.696235 | ||||||||
\(139\) | 3.41055 | + | 5.90724i | 0.289279 | + | 0.501045i | 0.973638 | − | 0.228100i | \(-0.0732512\pi\) |
−0.684359 | + | 0.729145i | \(0.739918\pi\) | |||||||
\(140\) | −1.00000 | + | 1.73205i | −0.0845154 | + | 0.146385i | ||||
\(141\) | −3.58945 | + | 6.21712i | −0.302287 | + | 0.523576i | ||||
\(142\) | −2.17891 | −0.182850 | ||||||||
\(143\) | 10.8211 | + | 15.2177i | 0.904905 | + | 1.27257i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −3.17891 | + | 5.50603i | −0.263994 | + | 0.457251i | ||||
\(146\) | −2.00000 | + | 3.46410i | −0.165521 | + | 0.286691i | ||||
\(147\) | 0.500000 | + | 0.866025i | 0.0412393 | + | 0.0714286i | ||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | −8.08945 | − | 14.0113i | −0.662714 | − | 1.14785i | −0.979900 | − | 0.199491i | \(-0.936071\pi\) |
0.317186 | − | 0.948363i | \(-0.397262\pi\) | |||||||
\(150\) | −0.500000 | − | 0.866025i | −0.0408248 | − | 0.0707107i | ||||
\(151\) | 19.5367 | 1.58988 | 0.794938 | − | 0.606691i | \(-0.207503\pi\) | ||||
0.794938 | + | 0.606691i | \(0.207503\pi\) | |||||||
\(152\) | −1.58945 | − | 2.75302i | −0.128922 | − | 0.223299i | ||||
\(153\) | −2.50000 | + | 4.33013i | −0.202113 | + | 0.350070i | ||||
\(154\) | −2.58945 | + | 4.48507i | −0.208664 | + | 0.361417i | ||||
\(155\) | −8.35782 | −0.671316 | ||||||||
\(156\) | 1.50000 | − | 3.27872i | 0.120096 | − | 0.262508i | ||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | −6.58945 | + | 11.4133i | −0.524229 | + | 0.907991i | ||||
\(159\) | −1.50000 | + | 2.59808i | −0.118958 | + | 0.206041i | ||||
\(160\) | 1.00000 | + | 1.73205i | 0.0790569 | + | 0.136931i | ||||
\(161\) | 8.17891 | 0.644588 | ||||||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | 10.0895 | + | 17.4754i | 0.790267 | + | 1.36878i | 0.925801 | + | 0.378010i | \(0.123392\pi\) |
−0.135534 | + | 0.990773i | \(0.543275\pi\) | |||||||
\(164\) | −7.17891 | −0.560579 | ||||||||
\(165\) | 5.17891 | + | 8.97013i | 0.403177 | + | 0.698324i | ||||
\(166\) | −3.08945 | + | 5.35109i | −0.239788 | + | 0.415325i | ||||
\(167\) | 4.00000 | − | 6.92820i | 0.309529 | − | 0.536120i | −0.668730 | − | 0.743505i | \(-0.733162\pi\) |
0.978259 | + | 0.207385i | \(0.0664952\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | −8.50000 | − | 9.83616i | −0.653846 | − | 0.756628i | ||||
\(170\) | −10.0000 | −0.766965 | ||||||||
\(171\) | −1.58945 | + | 2.75302i | −0.121549 | + | 0.210528i | ||||
\(172\) | −6.08945 | + | 10.5472i | −0.464317 | + | 0.804220i | ||||
\(173\) | −2.00000 | − | 3.46410i | −0.152057 | − | 0.263371i | 0.779926 | − | 0.625871i | \(-0.215256\pi\) |
−0.931984 | + | 0.362500i | \(0.881923\pi\) | |||||||
\(174\) | 3.17891 | 0.240992 | ||||||||
\(175\) | −0.500000 | − | 0.866025i | −0.0377964 | − | 0.0654654i | ||||
\(176\) | 2.58945 | + | 4.48507i | 0.195187 | + | 0.338075i | ||||
\(177\) | 12.1789 | 0.915423 | ||||||||
\(178\) | −4.50000 | − | 7.79423i | −0.337289 | − | 0.584202i | ||||
\(179\) | −4.17891 | + | 7.23808i | −0.312346 | + | 0.541000i | −0.978870 | − | 0.204484i | \(-0.934448\pi\) |
0.666524 | + | 0.745484i | \(0.267782\pi\) | |||||||
\(180\) | 1.00000 | − | 1.73205i | 0.0745356 | − | 0.129099i | ||||
\(181\) | 19.1789 | 1.42556 | 0.712779 | − | 0.701389i | \(-0.247436\pi\) | ||||
0.712779 | + | 0.701389i | \(0.247436\pi\) | |||||||
\(182\) | 1.50000 | − | 3.27872i | 0.111187 | − | 0.243035i | ||||
\(183\) | 3.00000 | 0.221766 | ||||||||
\(184\) | 4.08945 | − | 7.08314i | 0.301479 | − | 0.522176i | ||||
\(185\) | 2.00000 | − | 3.46410i | 0.147043 | − | 0.254686i | ||||
\(186\) | 2.08945 | + | 3.61904i | 0.153206 | + | 0.265361i | ||||
\(187\) | −25.8945 | −1.89360 | ||||||||
\(188\) | 3.58945 | + | 6.21712i | 0.261788 | + | 0.453430i | ||||
\(189\) | −0.500000 | − | 0.866025i | −0.0363696 | − | 0.0629941i | ||||
\(190\) | −6.35782 | −0.461245 | ||||||||
\(191\) | 3.26836 | + | 5.66097i | 0.236490 | + | 0.409613i | 0.959705 | − | 0.281010i | \(-0.0906695\pi\) |
−0.723214 | + | 0.690624i | \(0.757336\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 6.76836 | − | 11.7231i | 0.487197 | − | 0.843851i | −0.512694 | − | 0.858571i | \(-0.671353\pi\) |
0.999892 | + | 0.0147206i | \(0.00468589\pi\) | |||||||
\(194\) | −10.3578 | −0.743648 | ||||||||
\(195\) | −4.17891 | − | 5.87680i | −0.299258 | − | 0.420846i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −8.50000 | + | 14.7224i | −0.605600 | + | 1.04893i | 0.386356 | + | 0.922350i | \(0.373733\pi\) |
−0.991956 | + | 0.126580i | \(0.959600\pi\) | |||||||
\(198\) | 2.58945 | − | 4.48507i | 0.184024 | − | 0.318740i | ||||
\(199\) | −12.0895 | − | 20.9395i | −0.856999 | − | 1.48437i | −0.874778 | − | 0.484523i | \(-0.838993\pi\) |
0.0177797 | − | 0.999842i | \(-0.494340\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −1.91055 | − | 3.30916i | −0.134760 | − | 0.233410i | ||||
\(202\) | −3.17891 | − | 5.50603i | −0.223667 | − | 0.387403i | ||||
\(203\) | 3.17891 | 0.223116 | ||||||||
\(204\) | 2.50000 | + | 4.33013i | 0.175035 | + | 0.303170i | ||||
\(205\) | −7.17891 | + | 12.4342i | −0.501397 | + | 0.868445i | ||||
\(206\) | 4.08945 | − | 7.08314i | 0.284926 | − | 0.493506i | ||||
\(207\) | −8.17891 | −0.568473 | ||||||||
\(208\) | −2.08945 | − | 2.93840i | −0.144878 | − | 0.203741i | ||||
\(209\) | −16.4633 | −1.13879 | ||||||||
\(210\) | 1.00000 | − | 1.73205i | 0.0690066 | − | 0.119523i | ||||
\(211\) | 3.17891 | − | 5.50603i | 0.218845 | − | 0.379051i | −0.735610 | − | 0.677405i | \(-0.763104\pi\) |
0.954455 | + | 0.298354i | \(0.0964377\pi\) | |||||||
\(212\) | 1.50000 | + | 2.59808i | 0.103020 | + | 0.178437i | ||||
\(213\) | 2.17891 | 0.149296 | ||||||||
\(214\) | −9.58945 | − | 16.6094i | −0.655522 | − | 1.13540i | ||||
\(215\) | 12.1789 | + | 21.0945i | 0.830595 | + | 1.43863i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 2.08945 | + | 3.61904i | 0.141841 | + | 0.245676i | ||||
\(218\) | −2.00000 | + | 3.46410i | −0.135457 | + | 0.234619i | ||||
\(219\) | 2.00000 | − | 3.46410i | 0.135147 | − | 0.234082i | ||||
\(220\) | 10.3578 | 0.698324 | ||||||||
\(221\) | 17.9473 | − | 1.70161i | 1.20726 | − | 0.114463i | ||||
\(222\) | −2.00000 | −0.134231 | ||||||||
\(223\) | 1.08945 | − | 1.88699i | 0.0729552 | − | 0.126362i | −0.827240 | − | 0.561849i | \(-0.810090\pi\) |
0.900195 | + | 0.435487i | \(0.143424\pi\) | |||||||
\(224\) | 0.500000 | − | 0.866025i | 0.0334077 | − | 0.0578638i | ||||
\(225\) | 0.500000 | + | 0.866025i | 0.0333333 | + | 0.0577350i | ||||
\(226\) | 18.3578 | 1.22114 | ||||||||
\(227\) | 7.17891 | + | 12.4342i | 0.476481 | + | 0.825289i | 0.999637 | − | 0.0269479i | \(-0.00857881\pi\) |
−0.523156 | + | 0.852237i | \(0.675245\pi\) | |||||||
\(228\) | 1.58945 | + | 2.75302i | 0.105264 | + | 0.182323i | ||||
\(229\) | 1.00000 | 0.0660819 | 0.0330409 | − | 0.999454i | \(-0.489481\pi\) | ||||
0.0330409 | + | 0.999454i | \(0.489481\pi\) | |||||||
\(230\) | −8.17891 | − | 14.1663i | −0.539301 | − | 0.934097i | ||||
\(231\) | 2.58945 | − | 4.48507i | 0.170374 | − | 0.295096i | ||||
\(232\) | 1.58945 | − | 2.75302i | 0.104353 | − | 0.180744i | ||||
\(233\) | 22.3578 | 1.46471 | 0.732355 | − | 0.680923i | \(-0.238421\pi\) | ||||
0.732355 | + | 0.680923i | \(0.238421\pi\) | |||||||
\(234\) | −1.50000 | + | 3.27872i | −0.0980581 | + | 0.214337i | ||||
\(235\) | 14.3578 | 0.936601 | ||||||||
\(236\) | 6.08945 | − | 10.5472i | 0.396390 | − | 0.686567i | ||||
\(237\) | 6.58945 | − | 11.4133i | 0.428031 | − | 0.741372i | ||||
\(238\) | 2.50000 | + | 4.33013i | 0.162051 | + | 0.280680i | ||||
\(239\) | 10.1789 | 0.658419 | 0.329209 | − | 0.944257i | \(-0.393218\pi\) | ||||
0.329209 | + | 0.944257i | \(0.393218\pi\) | |||||||
\(240\) | −1.00000 | − | 1.73205i | −0.0645497 | − | 0.111803i | ||||
\(241\) | −2.17891 | − | 3.77398i | −0.140356 | − | 0.243103i | 0.787275 | − | 0.616602i | \(-0.211491\pi\) |
−0.927631 | + | 0.373499i | \(0.878158\pi\) | |||||||
\(242\) | 15.8211 | 1.01702 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 1.50000 | − | 2.59808i | 0.0960277 | − | 0.166325i | ||||
\(245\) | 1.00000 | − | 1.73205i | 0.0638877 | − | 0.110657i | ||||
\(246\) | 7.17891 | 0.457710 | ||||||||
\(247\) | 11.4105 | − | 1.08185i | 0.726036 | − | 0.0688365i | ||||
\(248\) | 4.17891 | 0.265361 | ||||||||
\(249\) | 3.08945 | − | 5.35109i | 0.195786 | − | 0.339112i | ||||
\(250\) | −6.00000 | + | 10.3923i | −0.379473 | + | 0.657267i | ||||
\(251\) | −11.0895 | − | 19.2075i | −0.699960 | − | 1.21237i | −0.968480 | − | 0.249092i | \(-0.919868\pi\) |
0.268520 | − | 0.963274i | \(-0.413466\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | −21.1789 | − | 36.6829i | −1.33151 | − | 2.30624i | ||||
\(254\) | −6.00000 | − | 10.3923i | −0.376473 | − | 0.652071i | ||||
\(255\) | 10.0000 | 0.626224 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 9.85782 | − | 17.0742i | 0.614914 | − | 1.06506i | −0.375486 | − | 0.926828i | \(-0.622524\pi\) |
0.990400 | − | 0.138234i | \(-0.0441425\pi\) | |||||||
\(258\) | 6.08945 | − | 10.5472i | 0.379113 | − | 0.656643i | ||||
\(259\) | −2.00000 | −0.124274 | ||||||||
\(260\) | −7.17891 | + | 0.680643i | −0.445217 | + | 0.0422117i | ||||
\(261\) | −3.17891 | −0.196769 | ||||||||
\(262\) | 7.26836 | − | 12.5892i | 0.449041 | − | 0.777762i | ||||
\(263\) | 6.00000 | − | 10.3923i | 0.369976 | − | 0.640817i | −0.619586 | − | 0.784929i | \(-0.712699\pi\) |
0.989561 | + | 0.144112i | \(0.0460326\pi\) | |||||||
\(264\) | −2.58945 | − | 4.48507i | −0.159370 | − | 0.276037i | ||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | 1.58945 | + | 2.75302i | 0.0974557 | + | 0.168798i | ||||
\(267\) | 4.50000 | + | 7.79423i | 0.275396 | + | 0.476999i | ||||
\(268\) | −3.82109 | −0.233410 | ||||||||
\(269\) | 2.17891 | + | 3.77398i | 0.132850 | + | 0.230104i | 0.924774 | − | 0.380516i | \(-0.124254\pi\) |
−0.791924 | + | 0.610620i | \(0.790920\pi\) | |||||||
\(270\) | −1.00000 | + | 1.73205i | −0.0608581 | + | 0.105409i | ||||
\(271\) | −9.91055 | + | 17.1656i | −0.602023 | + | 1.04273i | 0.390492 | + | 0.920606i | \(0.372305\pi\) |
−0.992514 | + | 0.122128i | \(0.961028\pi\) | |||||||
\(272\) | 5.00000 | 0.303170 | ||||||||
\(273\) | −1.50000 | + | 3.27872i | −0.0907841 | + | 0.198437i | ||||
\(274\) | 6.35782 | 0.384090 | ||||||||
\(275\) | −2.58945 | + | 4.48507i | −0.156150 | + | 0.270460i | ||||
\(276\) | −4.08945 | + | 7.08314i | −0.246156 | + | 0.426355i | ||||
\(277\) | −2.82109 | − | 4.88627i | −0.169503 | − | 0.293588i | 0.768742 | − | 0.639559i | \(-0.220883\pi\) |
−0.938245 | + | 0.345971i | \(0.887550\pi\) | |||||||
\(278\) | −6.82109 | −0.409102 | ||||||||
\(279\) | −2.08945 | − | 3.61904i | −0.125092 | − | 0.216666i | ||||
\(280\) | −1.00000 | − | 1.73205i | −0.0597614 | − | 0.103510i | ||||
\(281\) | 28.3578 | 1.69169 | 0.845843 | − | 0.533432i | \(-0.179098\pi\) | ||||
0.845843 | + | 0.533432i | \(0.179098\pi\) | |||||||
\(282\) | −3.58945 | − | 6.21712i | −0.213749 | − | 0.370224i | ||||
\(283\) | −3.82109 | + | 6.61832i | −0.227140 | + | 0.393419i | −0.956959 | − | 0.290222i | \(-0.906271\pi\) |
0.729819 | + | 0.683640i | \(0.239604\pi\) | |||||||
\(284\) | 1.08945 | − | 1.88699i | 0.0646472 | − | 0.111972i | ||||
\(285\) | 6.35782 | 0.376605 | ||||||||
\(286\) | −18.5895 | + | 1.76249i | −1.09922 | + | 0.104218i | ||||
\(287\) | 7.17891 | 0.423758 | ||||||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | −3.17891 | − | 5.50603i | −0.186672 | − | 0.323325i | ||||
\(291\) | 10.3578 | 0.607186 | ||||||||
\(292\) | −2.00000 | − | 3.46410i | −0.117041 | − | 0.202721i | ||||
\(293\) | −6.00000 | − | 10.3923i | −0.350524 | − | 0.607125i | 0.635818 | − | 0.771839i | \(-0.280663\pi\) |
−0.986341 | + | 0.164714i | \(0.947330\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −12.1789 | − | 21.0945i | −0.709083 | − | 1.22817i | ||||
\(296\) | −1.00000 | + | 1.73205i | −0.0581238 | + | 0.100673i | ||||
\(297\) | −2.58945 | + | 4.48507i | −0.150255 | + | 0.260250i | ||||
\(298\) | 16.1789 | 0.937219 | ||||||||
\(299\) | 17.0895 | + | 24.0329i | 0.988309 | + | 1.38986i | ||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 6.08945 | − | 10.5472i | 0.350990 | − | 0.607933i | ||||
\(302\) | −9.76836 | + | 16.9193i | −0.562106 | + | 0.973596i | ||||
\(303\) | 3.17891 | + | 5.50603i | 0.182624 | + | 0.316313i | ||||
\(304\) | 3.17891 | 0.182323 | ||||||||
\(305\) | −3.00000 | − | 5.19615i | −0.171780 | − | 0.297531i | ||||
\(306\) | −2.50000 | − | 4.33013i | −0.142915 | − | 0.247537i | ||||
\(307\) | −31.8945 | −1.82032 | −0.910159 | − | 0.414259i | \(-0.864041\pi\) | ||||
−0.910159 | + | 0.414259i | \(0.864041\pi\) | |||||||
\(308\) | −2.58945 | − | 4.48507i | −0.147548 | − | 0.255560i | ||||
\(309\) | −4.08945 | + | 7.08314i | −0.232641 | + | 0.402946i | ||||
\(310\) | 4.17891 | − | 7.23808i | 0.237346 | − | 0.411095i | ||||
\(311\) | 25.5367 | 1.44805 | 0.724027 | − | 0.689771i | \(-0.242289\pi\) | ||||
0.724027 | + | 0.689771i | \(0.242289\pi\) | |||||||
\(312\) | 2.08945 | + | 2.93840i | 0.118292 | + | 0.166354i | ||||
\(313\) | 4.00000 | 0.226093 | 0.113047 | − | 0.993590i | \(-0.463939\pi\) | ||||
0.113047 | + | 0.993590i | \(0.463939\pi\) | |||||||
\(314\) | −1.00000 | + | 1.73205i | −0.0564333 | + | 0.0977453i | ||||
\(315\) | −1.00000 | + | 1.73205i | −0.0563436 | + | 0.0975900i | ||||
\(316\) | −6.58945 | − | 11.4133i | −0.370686 | − | 0.642047i | ||||
\(317\) | −4.17891 | −0.234711 | −0.117355 | − | 0.993090i | \(-0.537442\pi\) | ||||
−0.117355 | + | 0.993090i | \(0.537442\pi\) | |||||||
\(318\) | −1.50000 | − | 2.59808i | −0.0841158 | − | 0.145693i | ||||
\(319\) | −8.23164 | − | 14.2576i | −0.460883 | − | 0.798273i | ||||
\(320\) | −2.00000 | −0.111803 | ||||||||
\(321\) | 9.58945 | + | 16.6094i | 0.535231 | + | 0.927048i | ||||
\(322\) | −4.08945 | + | 7.08314i | −0.227896 | + | 0.394728i | ||||
\(323\) | −7.94727 | + | 13.7651i | −0.442198 | + | 0.765909i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.50000 | − | 3.27872i | 0.0832050 | − | 0.181871i | ||||
\(326\) | −20.1789 | −1.11761 | ||||||||
\(327\) | 2.00000 | − | 3.46410i | 0.110600 | − | 0.191565i | ||||
\(328\) | 3.58945 | − | 6.21712i | 0.198194 | − | 0.343283i | ||||
\(329\) | −3.58945 | − | 6.21712i | −0.197893 | − | 0.342761i | ||||
\(330\) | −10.3578 | −0.570179 | ||||||||
\(331\) | 0.821092 | + | 1.42217i | 0.0451313 | + | 0.0781697i | 0.887709 | − | 0.460406i | \(-0.152296\pi\) |
−0.842577 | + | 0.538575i | \(0.818963\pi\) | |||||||
\(332\) | −3.08945 | − | 5.35109i | −0.169556 | − | 0.293679i | ||||
\(333\) | 2.00000 | 0.109599 | ||||||||
\(334\) | 4.00000 | + | 6.92820i | 0.218870 | + | 0.379094i | ||||
\(335\) | −3.82109 | + | 6.61832i | −0.208769 | + | 0.361598i | ||||
\(336\) | −0.500000 | + | 0.866025i | −0.0272772 | + | 0.0472456i | ||||
\(337\) | 33.5367 | 1.82686 | 0.913431 | − | 0.406994i | \(-0.133423\pi\) | ||||
0.913431 | + | 0.406994i | \(0.133423\pi\) | |||||||
\(338\) | 12.7684 | − | 2.44314i | 0.694507 | − | 0.132889i | ||||
\(339\) | −18.3578 | −0.997060 | ||||||||
\(340\) | 5.00000 | − | 8.66025i | 0.271163 | − | 0.469668i | ||||
\(341\) | 10.8211 | − | 18.7427i | 0.585995 | − | 1.01497i | ||||
\(342\) | −1.58945 | − | 2.75302i | −0.0859478 | − | 0.148866i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −6.08945 | − | 10.5472i | −0.328321 | − | 0.568669i | ||||
\(345\) | 8.17891 | + | 14.1663i | 0.440338 | + | 0.762687i | ||||
\(346\) | 4.00000 | 0.215041 | ||||||||
\(347\) | 9.58945 | + | 16.6094i | 0.514789 | + | 0.891640i | 0.999853 | + | 0.0171617i | \(0.00546302\pi\) |
−0.485064 | + | 0.874479i | \(0.661204\pi\) | |||||||
\(348\) | −1.58945 | + | 2.75302i | −0.0852037 | + | 0.147577i | ||||
\(349\) | −4.08945 | + | 7.08314i | −0.218903 | + | 0.379152i | −0.954473 | − | 0.298297i | \(-0.903581\pi\) |
0.735570 | + | 0.677449i | \(0.236915\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 1.50000 | − | 3.27872i | 0.0800641 | − | 0.175005i | ||||
\(352\) | −5.17891 | −0.276037 | ||||||||
\(353\) | −2.08945 | + | 3.61904i | −0.111210 | + | 0.192622i | −0.916259 | − | 0.400587i | \(-0.868806\pi\) |
0.805048 | + | 0.593209i | \(0.202139\pi\) | |||||||
\(354\) | −6.08945 | + | 10.5472i | −0.323651 | + | 0.560580i | ||||
\(355\) | −2.17891 | − | 3.77398i | −0.115644 | − | 0.200302i | ||||
\(356\) | 9.00000 | 0.476999 | ||||||||
\(357\) | −2.50000 | − | 4.33013i | −0.132314 | − | 0.229175i | ||||
\(358\) | −4.17891 | − | 7.23808i | −0.220862 | − | 0.382544i | ||||
\(359\) | −10.3578 | −0.546665 | −0.273332 | − | 0.961920i | \(-0.588126\pi\) | ||||
−0.273332 | + | 0.961920i | \(0.588126\pi\) | |||||||
\(360\) | 1.00000 | + | 1.73205i | 0.0527046 | + | 0.0912871i | ||||
\(361\) | 4.44727 | − | 7.70290i | 0.234067 | − | 0.405416i | ||||
\(362\) | −9.58945 | + | 16.6094i | −0.504011 | + | 0.872972i | ||||
\(363\) | −15.8211 | −0.830392 | ||||||||
\(364\) | 2.08945 | + | 2.93840i | 0.109517 | + | 0.154014i | ||||
\(365\) | −8.00000 | −0.418739 | ||||||||
\(366\) | −1.50000 | + | 2.59808i | −0.0784063 | + | 0.135804i | ||||
\(367\) | 4.08945 | − | 7.08314i | 0.213468 | − | 0.369737i | −0.739330 | − | 0.673344i | \(-0.764857\pi\) |
0.952797 | + | 0.303607i | \(0.0981908\pi\) | |||||||
\(368\) | 4.08945 | + | 7.08314i | 0.213178 | + | 0.369234i | ||||
\(369\) | −7.17891 | −0.373719 | ||||||||
\(370\) | 2.00000 | + | 3.46410i | 0.103975 | + | 0.180090i | ||||
\(371\) | −1.50000 | − | 2.59808i | −0.0778761 | − | 0.134885i | ||||
\(372\) | −4.17891 | −0.216666 | ||||||||
\(373\) | 10.0000 | + | 17.3205i | 0.517780 | + | 0.896822i | 0.999787 | + | 0.0206542i | \(0.00657489\pi\) |
−0.482006 | + | 0.876168i | \(0.660092\pi\) | |||||||
\(374\) | 12.9473 | − | 22.4253i | 0.669487 | − | 1.15959i | ||||
\(375\) | 6.00000 | − | 10.3923i | 0.309839 | − | 0.536656i | ||||
\(376\) | −7.17891 | −0.370224 | ||||||||
\(377\) | 6.64218 | + | 9.34090i | 0.342090 | + | 0.481081i | ||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | 12.3578 | − | 21.4044i | 0.634778 | − | 1.09947i | −0.351784 | − | 0.936081i | \(-0.614425\pi\) |
0.986562 | − | 0.163387i | \(-0.0522420\pi\) | |||||||
\(380\) | 3.17891 | − | 5.50603i | 0.163075 | − | 0.282453i | ||||
\(381\) | 6.00000 | + | 10.3923i | 0.307389 | + | 0.532414i | ||||
\(382\) | −6.53673 | −0.334448 | ||||||||
\(383\) | −10.5895 | − | 18.3415i | −0.541096 | − | 0.937205i | −0.998841 | − | 0.0481223i | \(-0.984676\pi\) |
0.457746 | − | 0.889083i | \(-0.348657\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | −10.3578 | −0.527883 | ||||||||
\(386\) | 6.76836 | + | 11.7231i | 0.344501 | + | 0.596693i | ||||
\(387\) | −6.08945 | + | 10.5472i | −0.309544 | + | 0.536147i | ||||
\(388\) | 5.17891 | − | 8.97013i | 0.262919 | − | 0.455389i | ||||
\(389\) | −12.1789 | −0.617495 | −0.308748 | − | 0.951144i | \(-0.599910\pi\) | ||||
−0.308748 | + | 0.951144i | \(0.599910\pi\) | |||||||
\(390\) | 7.17891 | − | 0.680643i | 0.363518 | − | 0.0344657i | ||||
\(391\) | −40.8945 | −2.06813 | ||||||||
\(392\) | −0.500000 | + | 0.866025i | −0.0252538 | + | 0.0437409i | ||||
\(393\) | −7.26836 | + | 12.5892i | −0.366640 | + | 0.635040i | ||||
\(394\) | −8.50000 | − | 14.7224i | −0.428224 | − | 0.741705i | ||||
\(395\) | −26.3578 | −1.32621 | ||||||||
\(396\) | 2.58945 | + | 4.48507i | 0.130125 | + | 0.225383i | ||||
\(397\) | −1.50000 | − | 2.59808i | −0.0752828 | − | 0.130394i | 0.825926 | − | 0.563778i | \(-0.190653\pi\) |
−0.901209 | + | 0.433384i | \(0.857319\pi\) | |||||||
\(398\) | 24.1789 | 1.21198 | ||||||||
\(399\) | −1.58945 | − | 2.75302i | −0.0795722 | − | 0.137823i | ||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | −4.82109 | + | 8.35038i | −0.240754 | + | 0.416998i | −0.960929 | − | 0.276794i | \(-0.910728\pi\) |
0.720175 | + | 0.693792i | \(0.244061\pi\) | |||||||
\(402\) | 3.82109 | 0.190579 | ||||||||
\(403\) | −6.26836 | + | 13.7015i | −0.312249 | + | 0.682519i | ||||
\(404\) | 6.35782 | 0.316313 | ||||||||
\(405\) | 1.00000 | − | 1.73205i | 0.0496904 | − | 0.0860663i | ||||
\(406\) | −1.58945 | + | 2.75302i | −0.0788833 | + | 0.136630i | ||||
\(407\) | 5.17891 | + | 8.97013i | 0.256709 | + | 0.444633i | ||||
\(408\) | −5.00000 | −0.247537 | ||||||||
\(409\) | 18.1789 | + | 31.4868i | 0.898889 | + | 1.55692i | 0.828916 | + | 0.559373i | \(0.188958\pi\) |
0.0699730 | + | 0.997549i | \(0.477709\pi\) | |||||||
\(410\) | −7.17891 | − | 12.4342i | −0.354541 | − | 0.614083i | ||||
\(411\) | −6.35782 | −0.313608 | ||||||||
\(412\) | 4.08945 | + | 7.08314i | 0.201473 | + | 0.348961i | ||||
\(413\) | −6.08945 | + | 10.5472i | −0.299642 | + | 0.518996i | ||||
\(414\) | 4.08945 | − | 7.08314i | 0.200986 | − | 0.348117i | ||||
\(415\) | −12.3578 | −0.606621 | ||||||||
\(416\) | 3.58945 | − | 0.340322i | 0.175987 | − | 0.0166856i | ||||
\(417\) | 6.82109 | 0.334030 | ||||||||
\(418\) | 8.23164 | − | 14.2576i | 0.402623 | − | 0.697363i | ||||
\(419\) | 13.4473 | − | 23.2914i | 0.656942 | − | 1.13786i | −0.324461 | − | 0.945899i | \(-0.605183\pi\) |
0.981403 | − | 0.191958i | \(-0.0614838\pi\) | |||||||
\(420\) | 1.00000 | + | 1.73205i | 0.0487950 | + | 0.0845154i | ||||
\(421\) | 10.7156 | 0.522248 | 0.261124 | − | 0.965305i | \(-0.415907\pi\) | ||||
0.261124 | + | 0.965305i | \(0.415907\pi\) | |||||||
\(422\) | 3.17891 | + | 5.50603i | 0.154747 | + | 0.268029i | ||||
\(423\) | 3.58945 | + | 6.21712i | 0.174525 | + | 0.302287i | ||||
\(424\) | −3.00000 | −0.145693 | ||||||||
\(425\) | 2.50000 | + | 4.33013i | 0.121268 | + | 0.210042i | ||||
\(426\) | −1.08945 | + | 1.88699i | −0.0527842 | + | 0.0914250i | ||||
\(427\) | −1.50000 | + | 2.59808i | −0.0725901 | + | 0.125730i | ||||
\(428\) | 19.1789 | 0.927048 | ||||||||
\(429\) | 18.5895 | − | 1.76249i | 0.897507 | − | 0.0850940i | ||||
\(430\) | −24.3578 | −1.17464 | ||||||||
\(431\) | −5.08945 | + | 8.81519i | −0.245150 | + | 0.424613i | −0.962174 | − | 0.272436i | \(-0.912171\pi\) |
0.717024 | + | 0.697049i | \(0.245504\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −17.1789 | − | 29.7547i | −0.825566 | − | 1.42992i | −0.901486 | − | 0.432808i | \(-0.857523\pi\) |
0.0759206 | − | 0.997114i | \(-0.475810\pi\) | |||||||
\(434\) | −4.17891 | −0.200594 | ||||||||
\(435\) | 3.17891 | + | 5.50603i | 0.152417 | + | 0.263994i | ||||
\(436\) | −2.00000 | − | 3.46410i | −0.0957826 | − | 0.165900i | ||||
\(437\) | −26.0000 | −1.24375 | ||||||||
\(438\) | 2.00000 | + | 3.46410i | 0.0955637 | + | 0.165521i | ||||
\(439\) | −20.3578 | + | 35.2608i | −0.971626 | + | 1.68290i | −0.280977 | + | 0.959715i | \(0.590658\pi\) |
−0.690649 | + | 0.723190i | \(0.742675\pi\) | |||||||
\(440\) | −5.17891 | + | 8.97013i | −0.246895 | + | 0.427634i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −7.50000 | + | 16.3936i | −0.356739 | + | 0.779764i | ||||
\(443\) | 3.17891 | 0.151034 | 0.0755172 | − | 0.997144i | \(-0.475939\pi\) | ||||
0.0755172 | + | 0.997144i | \(0.475939\pi\) | |||||||
\(444\) | 1.00000 | − | 1.73205i | 0.0474579 | − | 0.0821995i | ||||
\(445\) | 9.00000 | − | 15.5885i | 0.426641 | − | 0.738964i | ||||
\(446\) | 1.08945 | + | 1.88699i | 0.0515872 | + | 0.0893516i | ||||
\(447\) | −16.1789 | −0.765236 | ||||||||
\(448\) | 0.500000 | + | 0.866025i | 0.0236228 | + | 0.0409159i | ||||
\(449\) | 7.00000 | + | 12.1244i | 0.330350 | + | 0.572184i | 0.982581 | − | 0.185837i | \(-0.0594997\pi\) |
−0.652230 | + | 0.758021i | \(0.726166\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −18.5895 | − | 32.1979i | −0.875343 | − | 1.51614i | ||||
\(452\) | −9.17891 | + | 15.8983i | −0.431740 | + | 0.747795i | ||||
\(453\) | 9.76836 | − | 16.9193i | 0.458958 | − | 0.794938i | ||||
\(454\) | −14.3578 | −0.673846 | ||||||||
\(455\) | 7.17891 | − | 0.680643i | 0.336552 | − | 0.0319090i | ||||
\(456\) | −3.17891 | −0.148866 | ||||||||
\(457\) | −12.4473 | + | 21.5593i | −0.582259 | + | 1.00850i | 0.412952 | + | 0.910753i | \(0.364498\pi\) |
−0.995211 | + | 0.0977491i | \(0.968836\pi\) | |||||||
\(458\) | −0.500000 | + | 0.866025i | −0.0233635 | + | 0.0404667i | ||||
\(459\) | 2.50000 | + | 4.33013i | 0.116690 | + | 0.202113i | ||||
\(460\) | 16.3578 | 0.762687 | ||||||||
\(461\) | −10.3578 | − | 17.9403i | −0.482412 | − | 0.835561i | 0.517385 | − | 0.855753i | \(-0.326906\pi\) |
−0.999796 | + | 0.0201916i | \(0.993572\pi\) | |||||||
\(462\) | 2.58945 | + | 4.48507i | 0.120472 | + | 0.208664i | ||||
\(463\) | 27.8945 | 1.29637 | 0.648185 | − | 0.761483i | \(-0.275528\pi\) | ||||
0.648185 | + | 0.761483i | \(0.275528\pi\) | |||||||
\(464\) | 1.58945 | + | 2.75302i | 0.0737886 | + | 0.127806i | ||||
\(465\) | −4.17891 | + | 7.23808i | −0.193792 | + | 0.335658i | ||||
\(466\) | −11.1789 | + | 19.3624i | −0.517853 | + | 0.896948i | ||||
\(467\) | −22.8945 | −1.05943 | −0.529717 | − | 0.848175i | \(-0.677702\pi\) | ||||
−0.529717 | + | 0.848175i | \(0.677702\pi\) | |||||||
\(468\) | −2.08945 | − | 2.93840i | −0.0965851 | − | 0.135827i | ||||
\(469\) | 3.82109 | 0.176442 | ||||||||
\(470\) | −7.17891 | + | 12.4342i | −0.331138 | + | 0.573548i | ||||
\(471\) | 1.00000 | − | 1.73205i | 0.0460776 | − | 0.0798087i | ||||
\(472\) | 6.08945 | + | 10.5472i | 0.280290 | + | 0.485476i | ||||
\(473\) | −63.0735 | −2.90012 | ||||||||
\(474\) | 6.58945 | + | 11.4133i | 0.302664 | + | 0.524229i | ||||
\(475\) | 1.58945 | + | 2.75302i | 0.0729292 | + | 0.126317i | ||||
\(476\) | −5.00000 | −0.229175 | ||||||||
\(477\) | 1.50000 | + | 2.59808i | 0.0686803 | + | 0.118958i | ||||
\(478\) | −5.08945 | + | 8.81519i | −0.232786 | + | 0.403198i | ||||
\(479\) | 20.5895 | − | 35.6620i | 0.940756 | − | 1.62944i | 0.176723 | − | 0.984261i | \(-0.443450\pi\) |
0.764033 | − | 0.645177i | \(-0.223216\pi\) | |||||||
\(480\) | 2.00000 | 0.0912871 | ||||||||
\(481\) | −4.17891 | − | 5.87680i | −0.190542 | − | 0.267959i | ||||
\(482\) | 4.35782 | 0.198493 | ||||||||
\(483\) | 4.08945 | − | 7.08314i | 0.186077 | − | 0.322294i | ||||
\(484\) | −7.91055 | + | 13.7015i | −0.359570 | + | 0.622794i | ||||
\(485\) | −10.3578 | − | 17.9403i | −0.470324 | − | 0.814625i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 13.4105 | + | 23.2277i | 0.607690 | + | 1.05255i | 0.991620 | + | 0.129188i | \(0.0412369\pi\) |
−0.383930 | + | 0.923362i | \(0.625430\pi\) | |||||||
\(488\) | 1.50000 | + | 2.59808i | 0.0679018 | + | 0.117609i | ||||
\(489\) | 20.1789 | 0.912522 | ||||||||
\(490\) | 1.00000 | + | 1.73205i | 0.0451754 | + | 0.0782461i | ||||
\(491\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(492\) | −3.58945 | + | 6.21712i | −0.161825 | + | 0.280289i | ||||
\(493\) | −15.8945 | −0.715854 | ||||||||
\(494\) | −4.76836 | + | 10.4227i | −0.214539 | + | 0.468942i | ||||
\(495\) | 10.3578 | 0.465549 | ||||||||
\(496\) | −2.08945 | + | 3.61904i | −0.0938193 | + | 0.162500i | ||||
\(497\) | −1.08945 | + | 1.88699i | −0.0488687 | + | 0.0846431i | ||||
\(498\) | 3.08945 | + | 5.35109i | 0.138442 | + | 0.239788i | ||||
\(499\) | 8.17891 | 0.366138 | 0.183069 | − | 0.983100i | \(-0.441397\pi\) | ||||
0.183069 | + | 0.983100i | \(0.441397\pi\) | |||||||
\(500\) | −6.00000 | − | 10.3923i | −0.268328 | − | 0.464758i | ||||
\(501\) | −4.00000 | − | 6.92820i | −0.178707 | − | 0.309529i | ||||
\(502\) | 22.1789 | 0.989893 | ||||||||
\(503\) | 12.0000 | + | 20.7846i | 0.535054 | + | 0.926740i | 0.999161 | + | 0.0409609i | \(0.0130419\pi\) |
−0.464107 | + | 0.885779i | \(0.653625\pi\) | |||||||
\(504\) | 0.500000 | − | 0.866025i | 0.0222718 | − | 0.0385758i | ||||
\(505\) | 6.35782 | − | 11.0121i | 0.282919 | − | 0.490030i | ||||
\(506\) | 42.3578 | 1.88303 | ||||||||
\(507\) | −12.7684 | + | 2.44314i | −0.567063 | + | 0.108504i | ||||
\(508\) | 12.0000 | 0.532414 | ||||||||
\(509\) | 8.35782 | − | 14.4762i | 0.370454 | − | 0.641645i | −0.619182 | − | 0.785248i | \(-0.712536\pi\) |
0.989635 | + | 0.143603i | \(0.0458689\pi\) | |||||||
\(510\) | −5.00000 | + | 8.66025i | −0.221404 | + | 0.383482i | ||||
\(511\) | 2.00000 | + | 3.46410i | 0.0884748 | + | 0.153243i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.58945 | + | 2.75302i | 0.0701761 | + | 0.121549i | ||||
\(514\) | 9.85782 | + | 17.0742i | 0.434810 | + | 0.753112i | ||||
\(515\) | 16.3578 | 0.720812 | ||||||||
\(516\) | 6.08945 | + | 10.5472i | 0.268073 | + | 0.464317i | ||||
\(517\) | −18.5895 | + | 32.1979i | −0.817563 | + | 1.41606i | ||||
\(518\) | 1.00000 | − | 1.73205i | 0.0439375 | − | 0.0761019i | ||||
\(519\) | −4.00000 | −0.175581 | ||||||||
\(520\) | 3.00000 | − | 6.55744i | 0.131559 | − | 0.287563i | ||||
\(521\) | 7.17891 | 0.314514 | 0.157257 | − | 0.987558i | \(-0.449735\pi\) | ||||
0.157257 | + | 0.987558i | \(0.449735\pi\) | |||||||
\(522\) | 1.58945 | − | 2.75302i | 0.0695685 | − | 0.120496i | ||||
\(523\) | −5.76836 | + | 9.99110i | −0.252233 | + | 0.436880i | −0.964140 | − | 0.265393i | \(-0.914498\pi\) |
0.711907 | + | 0.702273i | \(0.247832\pi\) | |||||||
\(524\) | 7.26836 | + | 12.5892i | 0.317520 | + | 0.549961i | ||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 6.00000 | + | 10.3923i | 0.261612 | + | 0.453126i | ||||
\(527\) | −10.4473 | − | 18.0952i | −0.455090 | − | 0.788239i | ||||
\(528\) | 5.17891 | 0.225383 | ||||||||
\(529\) | −21.9473 | − | 38.0138i | −0.954229 | − | 1.65277i | ||||
\(530\) | −3.00000 | + | 5.19615i | −0.130312 | + | 0.225706i | ||||
\(531\) | 6.08945 | − | 10.5472i | 0.264260 | − | 0.457711i | ||||
\(532\) | −3.17891 | −0.137823 | ||||||||
\(533\) | 15.0000 | + | 21.0945i | 0.649722 | + | 0.913704i | ||||
\(534\) | −9.00000 | −0.389468 | ||||||||
\(535\) | 19.1789 | − | 33.2188i | 0.829177 | − | 1.43618i | ||||
\(536\) | 1.91055 | − | 3.30916i | 0.0825230 | − | 0.142934i | ||||
\(537\) | 4.17891 | + | 7.23808i | 0.180333 | + | 0.312346i | ||||
\(538\) | −4.35782 | −0.187879 | ||||||||
\(539\) | 2.58945 | + | 4.48507i | 0.111536 | + | 0.193185i | ||||
\(540\) | −1.00000 | − | 1.73205i | −0.0430331 | − | 0.0745356i | ||||
\(541\) | −20.3578 | −0.875251 | −0.437625 | − | 0.899157i | \(-0.644180\pi\) | ||||
−0.437625 | + | 0.899157i | \(0.644180\pi\) | |||||||
\(542\) | −9.91055 | − | 17.1656i | −0.425694 | − | 0.737324i | ||||
\(543\) | 9.58945 | − | 16.6094i | 0.411523 | − | 0.712779i | ||||
\(544\) | −2.50000 | + | 4.33013i | −0.107187 | + | 0.185653i | ||||
\(545\) | −8.00000 | −0.342682 | ||||||||
\(546\) | −2.08945 | − | 2.93840i | −0.0894204 | − | 0.125752i | ||||
\(547\) | 36.0000 | 1.53925 | 0.769624 | − | 0.638497i | \(-0.220443\pi\) | ||||
0.769624 | + | 0.638497i | \(0.220443\pi\) | |||||||
\(548\) | −3.17891 | + | 5.50603i | −0.135796 | + | 0.235206i | ||||
\(549\) | 1.50000 | − | 2.59808i | 0.0640184 | − | 0.110883i | ||||
\(550\) | −2.58945 | − | 4.48507i | −0.110415 | − | 0.191244i | ||||
\(551\) | −10.1055 | −0.430507 | ||||||||
\(552\) | −4.08945 | − | 7.08314i | −0.174059 | − | 0.301479i | ||||
\(553\) | 6.58945 | + | 11.4133i | 0.280212 | + | 0.485342i | ||||
\(554\) | 5.64218 | 0.239713 | ||||||||
\(555\) | −2.00000 | − | 3.46410i | −0.0848953 | − | 0.147043i | ||||
\(556\) | 3.41055 | − | 5.90724i | 0.144639 | − | 0.250523i | ||||
\(557\) | −11.8578 | + | 20.5383i | −0.502432 | + | 0.870237i | 0.497564 | + | 0.867427i | \(0.334228\pi\) |
−0.999996 | + | 0.00281030i | \(0.999105\pi\) | |||||||
\(558\) | 4.17891 | 0.176907 | ||||||||
\(559\) | 43.7156 | − | 4.14474i | 1.84897 | − | 0.175304i | ||||
\(560\) | 2.00000 | 0.0845154 | ||||||||
\(561\) | −12.9473 | + | 22.4253i | −0.546634 | + | 0.946798i | ||||
\(562\) | −14.1789 | + | 24.5586i | −0.598101 | + | 1.03594i | ||||
\(563\) | 9.17891 | + | 15.8983i | 0.386845 | + | 0.670035i | 0.992023 | − | 0.126055i | \(-0.0402316\pi\) |
−0.605178 | + | 0.796090i | \(0.706898\pi\) | |||||||
\(564\) | 7.17891 | 0.302287 | ||||||||
\(565\) | 18.3578 | + | 31.7967i | 0.772319 | + | 1.33770i | ||||
\(566\) | −3.82109 | − | 6.61832i | −0.160612 | − | 0.278189i | ||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 1.08945 | + | 1.88699i | 0.0457125 | + | 0.0791763i | ||||
\(569\) | 1.82109 | − | 3.15422i | 0.0763441 | − | 0.132232i | −0.825326 | − | 0.564657i | \(-0.809009\pi\) |
0.901670 | + | 0.432425i | \(0.142342\pi\) | |||||||
\(570\) | −3.17891 | + | 5.50603i | −0.133150 | + | 0.230622i | ||||
\(571\) | −34.1789 | −1.43034 | −0.715171 | − | 0.698949i | \(-0.753651\pi\) | ||||
−0.715171 | + | 0.698949i | \(0.753651\pi\) | |||||||
\(572\) | 7.76836 | − | 16.9802i | 0.324812 | − | 0.709977i | ||||
\(573\) | 6.53673 | 0.273076 | ||||||||
\(574\) | −3.58945 | + | 6.21712i | −0.149821 | + | 0.259497i | ||||
\(575\) | −4.08945 | + | 7.08314i | −0.170542 | + | 0.295387i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −28.3578 | −1.18055 | −0.590276 | − | 0.807202i | \(-0.700981\pi\) | ||||
−0.590276 | + | 0.807202i | \(0.700981\pi\) | |||||||
\(578\) | −4.00000 | − | 6.92820i | −0.166378 | − | 0.288175i | ||||
\(579\) | −6.76836 | − | 11.7231i | −0.281284 | − | 0.487197i | ||||
\(580\) | 6.35782 | 0.263994 | ||||||||
\(581\) | 3.08945 | + | 5.35109i | 0.128172 | + | 0.222001i | ||||
\(582\) | −5.17891 | + | 8.97013i | −0.214673 | + | 0.371824i | ||||
\(583\) | −7.76836 | + | 13.4552i | −0.321733 | + | 0.557257i | ||||
\(584\) | 4.00000 | 0.165521 | ||||||||
\(585\) | −7.17891 | + | 0.680643i | −0.296811 | + | 0.0281411i | ||||
\(586\) | 12.0000 | 0.495715 | ||||||||
\(587\) | −0.0894542 | + | 0.154939i | −0.00369217 | + | 0.00639502i | −0.867866 | − | 0.496799i | \(-0.834509\pi\) |
0.864173 | + | 0.503194i | \(0.167842\pi\) | |||||||
\(588\) | 0.500000 | − | 0.866025i | 0.0206197 | − | 0.0357143i | ||||
\(589\) | −6.64218 | − | 11.5046i | −0.273686 | − | 0.474039i | ||||
\(590\) | 24.3578 | 1.00280 | ||||||||
\(591\) | 8.50000 | + | 14.7224i | 0.349643 | + | 0.605600i | ||||
\(592\) | −1.00000 | − | 1.73205i | −0.0410997 | − | 0.0711868i | ||||
\(593\) | −33.0000 | −1.35515 | −0.677574 | − | 0.735455i | \(-0.736969\pi\) | ||||
−0.677574 | + | 0.735455i | \(0.736969\pi\) | |||||||
\(594\) | −2.58945 | − | 4.48507i | −0.106247 | − | 0.184024i | ||||
\(595\) | −5.00000 | + | 8.66025i | −0.204980 | + | 0.355036i | ||||
\(596\) | −8.08945 | + | 14.0113i | −0.331357 | + | 0.573927i | ||||
\(597\) | −24.1789 | −0.989577 | ||||||||
\(598\) | −29.3578 | + | 2.78346i | −1.20053 | + | 0.113824i | ||||
\(599\) | 40.1789 | 1.64167 | 0.820833 | − | 0.571168i | \(-0.193510\pi\) | ||||
0.820833 | + | 0.571168i | \(0.193510\pi\) | |||||||
\(600\) | −0.500000 | + | 0.866025i | −0.0204124 | + | 0.0353553i | ||||
\(601\) | 11.0000 | − | 19.0526i | 0.448699 | − | 0.777170i | −0.549602 | − | 0.835426i | \(-0.685221\pi\) |
0.998302 | + | 0.0582563i | \(0.0185541\pi\) | |||||||
\(602\) | 6.08945 | + | 10.5472i | 0.248188 | + | 0.429874i | ||||
\(603\) | −3.82109 | −0.155607 | ||||||||
\(604\) | −9.76836 | − | 16.9193i | −0.397469 | − | 0.688437i | ||||
\(605\) | 15.8211 | + | 27.4029i | 0.643219 | + | 1.11409i | ||||
\(606\) | −6.35782 | −0.258269 | ||||||||
\(607\) | 0.268363 | + | 0.464818i | 0.0108925 | + | 0.0188664i | 0.871420 | − | 0.490537i | \(-0.163199\pi\) |
−0.860528 | + | 0.509404i | \(0.829866\pi\) | |||||||
\(608\) | −1.58945 | + | 2.75302i | −0.0644609 | + | 0.111650i | ||||
\(609\) | 1.58945 | − | 2.75302i | 0.0644079 | − | 0.111558i | ||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | 10.7684 | − | 23.5376i | 0.435641 | − | 0.952230i | ||||
\(612\) | 5.00000 | 0.202113 | ||||||||
\(613\) | −7.82109 | + | 13.5465i | −0.315891 | + | 0.547139i | −0.979626 | − | 0.200828i | \(-0.935637\pi\) |
0.663736 | + | 0.747967i | \(0.268970\pi\) | |||||||
\(614\) | 15.9473 | − | 27.6215i | 0.643579 | − | 1.11471i | ||||
\(615\) | 7.17891 | + | 12.4342i | 0.289482 | + | 0.501397i | ||||
\(616\) | 5.17891 | 0.208664 | ||||||||
\(617\) | −16.0000 | − | 27.7128i | −0.644136 | − | 1.11568i | −0.984500 | − | 0.175382i | \(-0.943884\pi\) |
0.340365 | − | 0.940294i | \(-0.389449\pi\) | |||||||
\(618\) | −4.08945 | − | 7.08314i | −0.164502 | − | 0.284926i | ||||
\(619\) | 25.5367 | 1.02641 | 0.513204 | − | 0.858267i | \(-0.328458\pi\) | ||||
0.513204 | + | 0.858267i | \(0.328458\pi\) | |||||||
\(620\) | 4.17891 | + | 7.23808i | 0.167829 | + | 0.290688i | ||||
\(621\) | −4.08945 | + | 7.08314i | −0.164104 | + | 0.284237i | ||||
\(622\) | −12.7684 | + | 22.1155i | −0.511965 | + | 0.886749i | ||||
\(623\) | −9.00000 | −0.360577 | ||||||||
\(624\) | −3.58945 | + | 0.340322i | −0.143693 | + | 0.0136238i | ||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −2.00000 | + | 3.46410i | −0.0799361 | + | 0.138453i | ||||
\(627\) | −8.23164 | + | 14.2576i | −0.328740 | + | 0.569394i | ||||
\(628\) | −1.00000 | − | 1.73205i | −0.0399043 | − | 0.0691164i | ||||
\(629\) | 10.0000 | 0.398726 | ||||||||
\(630\) | −1.00000 | − | 1.73205i | −0.0398410 | − | 0.0690066i | ||||
\(631\) | −12.9473 | − | 22.4253i | −0.515423 | − | 0.892738i | −0.999840 | − | 0.0179011i | \(-0.994302\pi\) |
0.484417 | − | 0.874837i | \(-0.339032\pi\) | |||||||
\(632\) | 13.1789 | 0.524229 | ||||||||
\(633\) | −3.17891 | − | 5.50603i | −0.126350 | − | 0.218845i | ||||
\(634\) | 2.08945 | − | 3.61904i | 0.0829828 | − | 0.143730i | ||||
\(635\) | 12.0000 | − | 20.7846i | 0.476205 | − | 0.824812i | ||||
\(636\) | 3.00000 | 0.118958 | ||||||||
\(637\) | −2.08945 | − | 2.93840i | −0.0827872 | − | 0.116424i | ||||
\(638\) | 16.4633 | 0.651787 | ||||||||
\(639\) | 1.08945 | − | 1.88699i | 0.0430981 | − | 0.0746482i | ||||
\(640\) | 1.00000 | − | 1.73205i | 0.0395285 | − | 0.0684653i | ||||
\(641\) | −13.5367 | − | 23.4463i | −0.534668 | − | 0.926073i | −0.999179 | − | 0.0405056i | \(-0.987103\pi\) |
0.464511 | − | 0.885567i | \(-0.346230\pi\) | |||||||
\(642\) | −19.1789 | −0.756931 | ||||||||
\(643\) | 4.41055 | + | 7.63929i | 0.173935 | + | 0.301264i | 0.939792 | − | 0.341746i | \(-0.111018\pi\) |
−0.765857 | + | 0.643011i | \(0.777685\pi\) | |||||||
\(644\) | −4.08945 | − | 7.08314i | −0.161147 | − | 0.279115i | ||||
\(645\) | 24.3578 | 0.959088 | ||||||||
\(646\) | −7.94727 | − | 13.7651i | −0.312681 | − | 0.541580i | ||||
\(647\) | −23.9473 | + | 41.4779i | −0.941464 | + | 1.63066i | −0.178784 | + | 0.983888i | \(0.557216\pi\) |
−0.762680 | + | 0.646776i | \(0.776117\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 63.0735 | 2.47585 | ||||||||
\(650\) | 2.08945 | + | 2.93840i | 0.0819551 | + | 0.115253i | ||||
\(651\) | 4.17891 | 0.163784 | ||||||||
\(652\) | 10.0895 | − | 17.4754i | 0.395134 | − | 0.684391i | ||||
\(653\) | −10.5000 | + | 18.1865i | −0.410897 | + | 0.711694i | −0.994988 | − | 0.0999939i | \(-0.968118\pi\) |
0.584091 | + | 0.811688i | \(0.301451\pi\) | |||||||
\(654\) | 2.00000 | + | 3.46410i | 0.0782062 | + | 0.135457i | ||||
\(655\) | 29.0735 | 1.13599 | ||||||||
\(656\) | 3.58945 | + | 6.21712i | 0.140145 | + | 0.242738i | ||||
\(657\) | −2.00000 | − | 3.46410i | −0.0780274 | − | 0.135147i | ||||
\(658\) | 7.17891 | 0.279863 | ||||||||
\(659\) | −8.76836 | − | 15.1872i | −0.341567 | − | 0.591611i | 0.643157 | − | 0.765734i | \(-0.277624\pi\) |
−0.984724 | + | 0.174123i | \(0.944291\pi\) | |||||||
\(660\) | 5.17891 | − | 8.97013i | 0.201589 | − | 0.349162i | ||||
\(661\) | −8.26836 | + | 14.3212i | −0.321602 | + | 0.557031i | −0.980819 | − | 0.194922i | \(-0.937555\pi\) |
0.659217 | + | 0.751953i | \(0.270888\pi\) | |||||||
\(662\) | −1.64218 | −0.0638253 | ||||||||
\(663\) | 7.50000 | − | 16.3936i | 0.291276 | − | 0.636675i | ||||
\(664\) | 6.17891 | 0.239788 | ||||||||
\(665\) | −3.17891 | + | 5.50603i | −0.123273 | + | 0.213515i | ||||
\(666\) | −1.00000 | + | 1.73205i | −0.0387492 | + | 0.0671156i | ||||
\(667\) | −13.0000 | − | 22.5167i | −0.503362 | − | 0.871849i | ||||
\(668\) | −8.00000 | −0.309529 | ||||||||
\(669\) | −1.08945 | − | 1.88699i | −0.0421207 | − | 0.0729552i | ||||
\(670\) | −3.82109 | − | 6.61832i | −0.147622 | − | 0.255688i | ||||
\(671\) | 15.5367 | 0.599789 | ||||||||
\(672\) | −0.500000 | − | 0.866025i | −0.0192879 | − | 0.0334077i | ||||
\(673\) | 0.500000 | − | 0.866025i | 0.0192736 | − | 0.0333828i | −0.856228 | − | 0.516599i | \(-0.827198\pi\) |
0.875501 | + | 0.483216i | \(0.160531\pi\) | |||||||
\(674\) | −16.7684 | + | 29.0437i | −0.645893 | + | 1.11872i | ||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −4.26836 | + | 12.2793i | −0.164168 | + | 0.472281i | ||||
\(677\) | 12.0000 | 0.461197 | 0.230599 | − | 0.973049i | \(-0.425932\pi\) | ||||
0.230599 | + | 0.973049i | \(0.425932\pi\) | |||||||
\(678\) | 9.17891 | − | 15.8983i | 0.352514 | − | 0.610572i | ||||
\(679\) | −5.17891 | + | 8.97013i | −0.198748 | + | 0.344242i | ||||
\(680\) | 5.00000 | + | 8.66025i | 0.191741 | + | 0.332106i | ||||
\(681\) | 14.3578 | 0.550193 | ||||||||
\(682\) | 10.8211 | + | 18.7427i | 0.414361 | + | 0.717694i | ||||
\(683\) | −4.17891 | − | 7.23808i | −0.159901 | − | 0.276957i | 0.774931 | − | 0.632045i | \(-0.217784\pi\) |
−0.934833 | + | 0.355088i | \(0.884451\pi\) | |||||||
\(684\) | 3.17891 | 0.121549 | ||||||||
\(685\) | 6.35782 | + | 11.0121i | 0.242920 | + | 0.420749i | ||||
\(686\) | 0.500000 | − | 0.866025i | 0.0190901 | − | 0.0330650i | ||||
\(687\) | 0.500000 | − | 0.866025i | 0.0190762 | − | 0.0330409i | ||||
\(688\) | 12.1789 | 0.464317 | ||||||||
\(689\) | 4.50000 | − | 9.83616i | 0.171436 | − | 0.374728i | ||||
\(690\) | −16.3578 | −0.622731 | ||||||||
\(691\) | 20.0000 | − | 34.6410i | 0.760836 | − | 1.31781i | −0.181584 | − | 0.983375i | \(-0.558123\pi\) |
0.942420 | − | 0.334431i | \(-0.108544\pi\) | |||||||
\(692\) | −2.00000 | + | 3.46410i | −0.0760286 | + | 0.131685i | ||||
\(693\) | −2.58945 | − | 4.48507i | −0.0983652 | − | 0.170374i | ||||
\(694\) | −19.1789 | −0.728021 | ||||||||
\(695\) | −6.82109 | − | 11.8145i | −0.258739 | − | 0.448149i | ||||
\(696\) | −1.58945 | − | 2.75302i | −0.0602481 | − | 0.104353i | ||||
\(697\) | −35.8945 | −1.35960 | ||||||||
\(698\) | −4.08945 | − | 7.08314i | −0.154788 | − | 0.268101i | ||||
\(699\) | 11.1789 | − | 19.3624i | 0.422825 | − | 0.732355i | ||||
\(700\) | −0.500000 | + | 0.866025i | −0.0188982 | + | 0.0327327i | ||||
\(701\) | −21.7156 | −0.820188 | −0.410094 | − | 0.912043i | \(-0.634504\pi\) | ||||
−0.410094 | + | 0.912043i | \(0.634504\pi\) | |||||||
\(702\) | 2.08945 | + | 2.93840i | 0.0788614 | + | 0.110903i | ||||
\(703\) | 6.35782 | 0.239790 | ||||||||
\(704\) | 2.58945 | − | 4.48507i | 0.0975937 | − | 0.169037i | ||||
\(705\) | 7.17891 | − | 12.4342i | 0.270373 | − | 0.468300i | ||||
\(706\) | −2.08945 | − | 3.61904i | −0.0786376 | − | 0.136204i | ||||
\(707\) | −6.35782 | −0.239110 | ||||||||
\(708\) | −6.08945 | − | 10.5472i | −0.228856 | − | 0.396390i | ||||
\(709\) | 8.00000 | + | 13.8564i | 0.300446 | + | 0.520388i | 0.976237 | − | 0.216705i | \(-0.0695310\pi\) |
−0.675791 | + | 0.737093i | \(0.736198\pi\) | |||||||
\(710\) | 4.35782 | 0.163546 | ||||||||
\(711\) | −6.58945 | − | 11.4133i | −0.247124 | − | 0.428031i | ||||
\(712\) | −4.50000 | + | 7.79423i | −0.168645 | + | 0.292101i | ||||
\(713\) | 17.0895 | − | 29.5998i | 0.640005 | − | 1.10852i | ||||
\(714\) | 5.00000 | 0.187120 | ||||||||
\(715\) | −21.6422 | − | 30.4354i | −0.809372 | − | 1.13822i | ||||
\(716\) | 8.35782 | 0.312346 | ||||||||
\(717\) | 5.08945 | − | 8.81519i | 0.190069 | − | 0.329209i | ||||
\(718\) | 5.17891 | − | 8.97013i | 0.193275 | − | 0.334762i | ||||
\(719\) | 18.5895 | + | 32.1979i | 0.693270 | + | 1.20078i | 0.970761 | + | 0.240050i | \(0.0771638\pi\) |
−0.277491 | + | 0.960728i | \(0.589503\pi\) | |||||||
\(720\) | −2.00000 | −0.0745356 | ||||||||
\(721\) | −4.08945 | − | 7.08314i | −0.152299 | − | 0.263790i | ||||
\(722\) | 4.44727 | + | 7.70290i | 0.165510 | + | 0.286672i | ||||
\(723\) | −4.35782 | −0.162069 | ||||||||
\(724\) | −9.58945 | − | 16.6094i | −0.356389 | − | 0.617284i | ||||
\(725\) | −1.58945 | + | 2.75302i | −0.0590308 | + | 0.102244i | ||||
\(726\) | 7.91055 | − | 13.7015i | 0.293588 | − | 0.508509i | ||||
\(727\) | 34.5367 | 1.28090 | 0.640448 | − | 0.768001i | \(-0.278749\pi\) | ||||
0.640448 | + | 0.768001i | \(0.278749\pi\) | |||||||
\(728\) | −3.58945 | + | 0.340322i | −0.133034 | + | 0.0126132i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.00000 | − | 6.92820i | 0.148047 | − | 0.256424i | ||||
\(731\) | −30.4473 | + | 52.7362i | −1.12613 | + | 1.95052i | ||||
\(732\) | −1.50000 | − | 2.59808i | −0.0554416 | − | 0.0960277i | ||||
\(733\) | 19.7156 | 0.728214 | 0.364107 | − | 0.931357i | \(-0.381374\pi\) | ||||
0.364107 | + | 0.931357i | \(0.381374\pi\) | |||||||
\(734\) | 4.08945 | + | 7.08314i | 0.150945 | + | 0.261444i | ||||
\(735\) | −1.00000 | − | 1.73205i | −0.0368856 | − | 0.0638877i | ||||
\(736\) | −8.17891 | −0.301479 | ||||||||
\(737\) | −9.89454 | − | 17.1378i | −0.364470 | − | 0.631281i | ||||
\(738\) | 3.58945 | − | 6.21712i | 0.132130 | − | 0.228855i | ||||
\(739\) | 8.08945 | − | 14.0113i | 0.297575 | − | 0.515416i | −0.678005 | − | 0.735057i | \(-0.737155\pi\) |
0.975581 | + | 0.219641i | \(0.0704887\pi\) | |||||||
\(740\) | −4.00000 | −0.147043 | ||||||||
\(741\) | 4.76836 | − | 10.4227i | 0.175170 | − | 0.382889i | ||||
\(742\) | 3.00000 | 0.110133 | ||||||||
\(743\) | −15.9105 | + | 27.5579i | −0.583701 | + | 1.01100i | 0.411335 | + | 0.911484i | \(0.365063\pi\) |
−0.995036 | + | 0.0995159i | \(0.968271\pi\) | |||||||
\(744\) | 2.08945 | − | 3.61904i | 0.0766031 | − | 0.132680i | ||||
\(745\) | 16.1789 | + | 28.0227i | 0.592749 | + | 1.02667i | ||||
\(746\) | −20.0000 | −0.732252 | ||||||||
\(747\) | −3.08945 | − | 5.35109i | −0.113037 | − | 0.195786i | ||||
\(748\) | 12.9473 | + | 22.4253i | 0.473399 | + | 0.819951i | ||||
\(749\) | −19.1789 | −0.700782 | ||||||||
\(750\) | 6.00000 | + | 10.3923i | 0.219089 | + | 0.379473i | ||||
\(751\) | 17.9473 | − | 31.0856i | 0.654905 | − | 1.13433i | −0.327012 | − | 0.945020i | \(-0.606042\pi\) |
0.981918 | − | 0.189309i | \(-0.0606248\pi\) | |||||||
\(752\) | 3.58945 | − | 6.21712i | 0.130894 | − | 0.226715i | ||||
\(753\) | −22.1789 | −0.808244 | ||||||||
\(754\) | −11.4105 | + | 1.08185i | −0.415548 | + | 0.0393987i | ||||
\(755\) | −39.0735 | −1.42203 | ||||||||
\(756\) | −0.500000 | + | 0.866025i | −0.0181848 | + | 0.0314970i | ||||
\(757\) | 10.1789 | − | 17.6304i | 0.369959 | − | 0.640787i | −0.619600 | − | 0.784918i | \(-0.712705\pi\) |
0.989559 | + | 0.144130i | \(0.0460385\pi\) | |||||||
\(758\) | 12.3578 | + | 21.4044i | 0.448856 | + | 0.777442i | ||||
\(759\) | −42.3578 | −1.53749 | ||||||||
\(760\) | 3.17891 | + | 5.50603i | 0.115311 | + | 0.199725i | ||||
\(761\) | 21.7156 | + | 37.6126i | 0.787191 | + | 1.36345i | 0.927681 | + | 0.373373i | \(0.121799\pi\) |
−0.140490 | + | 0.990082i | \(0.544868\pi\) | |||||||
\(762\) | −12.0000 | −0.434714 | ||||||||
\(763\) | 2.00000 | + | 3.46410i | 0.0724049 | + | 0.125409i | ||||
\(764\) | 3.26836 | − | 5.66097i | 0.118245 | − | 0.204807i | ||||
\(765\) | 5.00000 | − | 8.66025i | 0.180775 | − | 0.313112i | ||||
\(766\) | 21.1789 | 0.765225 | ||||||||
\(767\) | −43.7156 | + | 4.14474i | −1.57848 | + | 0.149658i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −9.17891 | + | 15.8983i | −0.331000 | + | 0.573309i | −0.982708 | − | 0.185161i | \(-0.940719\pi\) |
0.651708 | + | 0.758470i | \(0.274053\pi\) | |||||||
\(770\) | 5.17891 | − | 8.97013i | 0.186635 | − | 0.323261i | ||||
\(771\) | −9.85782 | − | 17.0742i | −0.355021 | − | 0.614914i | ||||
\(772\) | −13.5367 | −0.487197 | ||||||||
\(773\) | −7.35782 | − | 12.7441i | −0.264642 | − | 0.458374i | 0.702828 | − | 0.711360i | \(-0.251921\pi\) |
−0.967470 | + | 0.252986i | \(0.918587\pi\) | |||||||
\(774\) | −6.08945 | − | 10.5472i | −0.218881 | − | 0.379113i | ||||
\(775\) | −4.17891 | −0.150111 | ||||||||
\(776\) | 5.17891 | + | 8.97013i | 0.185912 | + | 0.322009i | ||||
\(777\) | −1.00000 | + | 1.73205i | −0.0358748 | + | 0.0621370i | ||||
\(778\) | 6.08945 | − | 10.5472i | 0.218318 | − | 0.378137i | ||||
\(779\) | −22.8211 | −0.817650 | ||||||||
\(780\) | −3.00000 | + | 6.55744i | −0.107417 | + | 0.234794i | ||||
\(781\) | 11.2844 | 0.403786 | ||||||||
\(782\) | 20.4473 | − | 35.4157i | 0.731193 | − | 1.26646i | ||||
\(783\) | −1.58945 | + | 2.75302i | −0.0568025 | + | 0.0983847i | ||||
\(784\) | −0.500000 | − | 0.866025i | −0.0178571 | − | 0.0309295i | ||||
\(785\) | −4.00000 | −0.142766 | ||||||||
\(786\) | −7.26836 | − | 12.5892i | −0.259254 | − | 0.449041i | ||||
\(787\) | 5.41055 | + | 9.37134i | 0.192865 | + | 0.334052i | 0.946199 | − | 0.323587i | \(-0.104889\pi\) |
−0.753333 | + | 0.657639i | \(0.771555\pi\) | |||||||
\(788\) | 17.0000 | 0.605600 | ||||||||
\(789\) | −6.00000 | − | 10.3923i | −0.213606 | − | 0.369976i | ||||
\(790\) | 13.1789 | − | 22.8265i | 0.468885 | − | 0.812132i | ||||
\(791\) | 9.17891 | − | 15.8983i | 0.326364 | − | 0.565280i | ||||
\(792\) | −5.17891 | −0.184024 | ||||||||
\(793\) | −10.7684 | + | 1.02096i | −0.382396 | + | 0.0362555i | ||||
\(794\) | 3.00000 | 0.106466 | ||||||||
\(795\) | 3.00000 | − | 5.19615i | 0.106399 | − | 0.184289i | ||||
\(796\) | −12.0895 | + | 20.9395i | −0.428499 | + | 0.742183i | ||||
\(797\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(798\) | 3.17891 | 0.112532 | ||||||||
\(799\) | 17.9473 | + | 31.0856i | 0.634929 | + | 1.09973i | ||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | 9.00000 | 0.317999 | ||||||||
\(802\) | −4.82109 | − | 8.35038i | −0.170239 | − | 0.294862i | ||||
\(803\) | 10.3578 | − | 17.9403i | 0.365519 | − | 0.633098i | ||||
\(804\) | −1.91055 | + | 3.30916i | −0.0673798 | + | 0.116705i | ||||
\(805\) | −16.3578 | −0.576537 | ||||||||
\(806\) | −8.73164 | − | 12.2793i | −0.307559 | − | 0.432520i | ||||
\(807\) | 4.35782 | 0.153402 | ||||||||
\(808\) | −3.17891 | + | 5.50603i | −0.111834 | + | 0.193701i | ||||
\(809\) | 10.0000 | − | 17.3205i | 0.351581 | − | 0.608957i | −0.634945 | − | 0.772557i | \(-0.718977\pi\) |
0.986527 | + | 0.163600i | \(0.0523108\pi\) | |||||||
\(810\) | 1.00000 | + | 1.73205i | 0.0351364 | + | 0.0608581i | ||||
\(811\) | −12.7156 | −0.446506 | −0.223253 | − | 0.974761i | \(-0.571668\pi\) | ||||
−0.223253 | + | 0.974761i | \(0.571668\pi\) | |||||||
\(812\) | −1.58945 | − | 2.75302i | −0.0557789 | − | 0.0966119i | ||||
\(813\) | 9.91055 | + | 17.1656i | 0.347578 | + | 0.602023i | ||||
\(814\) | −10.3578 | −0.363041 | ||||||||
\(815\) | −20.1789 | − | 34.9509i | −0.706836 | − | 1.22428i | ||||
\(816\) | 2.50000 | − | 4.33013i | 0.0875175 | − | 0.151585i | ||||
\(817\) | −19.3578 | + | 33.5287i | −0.677244 | + | 1.17302i | ||||
\(818\) | −36.3578 | −1.27122 | ||||||||
\(819\) | 2.08945 | + | 2.93840i | 0.0730114 | + | 0.102676i | ||||
\(820\) | 14.3578 | 0.501397 | ||||||||
\(821\) | −0.142183 | + | 0.246269i | −0.00496223 | + | 0.00859484i | −0.868496 | − | 0.495696i | \(-0.834913\pi\) |
0.863534 | + | 0.504291i | \(0.168246\pi\) | |||||||
\(822\) | 3.17891 | − | 5.50603i | 0.110877 | − | 0.192045i | ||||
\(823\) | −16.3578 | − | 28.3326i | −0.570198 | − | 0.987611i | −0.996545 | − | 0.0830519i | \(-0.973533\pi\) |
0.426348 | − | 0.904559i | \(-0.359800\pi\) | |||||||
\(824\) | −8.17891 | −0.284926 | ||||||||
\(825\) | 2.58945 | + | 4.48507i | 0.0901532 | + | 0.156150i | ||||
\(826\) | −6.08945 | − | 10.5472i | −0.211879 | − | 0.366986i | ||||
\(827\) | −40.7156 | −1.41582 | −0.707911 | − | 0.706302i | \(-0.750362\pi\) | ||||
−0.707911 | + | 0.706302i | \(0.750362\pi\) | |||||||
\(828\) | 4.08945 | + | 7.08314i | 0.142118 | + | 0.246156i | ||||
\(829\) | 1.58945 | − | 2.75302i | 0.0552040 | − | 0.0956162i | −0.837103 | − | 0.547046i | \(-0.815752\pi\) |
0.892307 | + | 0.451429i | \(0.149086\pi\) | |||||||
\(830\) | 6.17891 | − | 10.7022i | 0.214473 | − | 0.371478i | ||||
\(831\) | −5.64218 | −0.195725 | ||||||||
\(832\) | −1.50000 | + | 3.27872i | −0.0520031 | + | 0.113669i | ||||
\(833\) | 5.00000 | 0.173240 | ||||||||
\(834\) | −3.41055 | + | 5.90724i | −0.118098 | + | 0.204551i | ||||
\(835\) | −8.00000 | + | 13.8564i | −0.276851 | + | 0.479521i | ||||
\(836\) | 8.23164 | + | 14.2576i | 0.284697 | + | 0.493110i | ||||
\(837\) | −4.17891 | −0.144444 | ||||||||
\(838\) | 13.4473 | + | 23.2914i | 0.464528 | + | 0.804587i | ||||
\(839\) | −5.82109 | − | 10.0824i | −0.200966 | − | 0.348084i | 0.747874 | − | 0.663841i | \(-0.231075\pi\) |
−0.948840 | + | 0.315757i | \(0.897742\pi\) | |||||||
\(840\) | −2.00000 | −0.0690066 | ||||||||
\(841\) | 9.44727 | + | 16.3632i | 0.325768 | + | 0.564247i | ||||
\(842\) | −5.35782 | + | 9.28001i | −0.184643 | + | 0.319810i | ||||
\(843\) | 14.1789 | − | 24.5586i | 0.488348 | − | 0.845843i | ||||
\(844\) | −6.35782 | −0.218845 | ||||||||
\(845\) | 17.0000 | + | 19.6723i | 0.584818 | + | 0.676748i | ||||
\(846\) | −7.17891 | −0.246816 | ||||||||
\(847\) | 7.91055 | − | 13.7015i | 0.271810 | − | 0.470788i | ||||
\(848\) | 1.50000 | − | 2.59808i | 0.0515102 | − | 0.0892183i | ||||
\(849\) | 3.82109 | + | 6.61832i | 0.131140 | + | 0.227140i | ||||
\(850\) | −5.00000 | −0.171499 | ||||||||
\(851\) | 8.17891 | + | 14.1663i | 0.280369 | + | 0.485614i | ||||
\(852\) | −1.08945 | − | 1.88699i | −0.0373241 | − | 0.0646472i | ||||
\(853\) | 27.7156 | 0.948965 | 0.474483 | − | 0.880265i | \(-0.342635\pi\) | ||||
0.474483 | + | 0.880265i | \(0.342635\pi\) | |||||||
\(854\) | −1.50000 | − | 2.59808i | −0.0513289 | − | 0.0889043i | ||||
\(855\) | 3.17891 | − | 5.50603i | 0.108716 | − | 0.188302i | ||||
\(856\) | −9.58945 | + | 16.6094i | −0.327761 | + | 0.567698i | ||||
\(857\) | −10.7156 | −0.366039 | −0.183020 | − | 0.983109i | \(-0.558587\pi\) | ||||
−0.183020 | + | 0.983109i | \(0.558587\pi\) | |||||||
\(858\) | −7.76836 | + | 16.9802i | −0.265208 | + | 0.579694i | ||||
\(859\) | 19.8945 | 0.678793 | 0.339397 | − | 0.940643i | \(-0.389777\pi\) | ||||
0.339397 | + | 0.940643i | \(0.389777\pi\) | |||||||
\(860\) | 12.1789 | − | 21.0945i | 0.415297 | − | 0.719316i | ||||
\(861\) | 3.58945 | − | 6.21712i | 0.122328 | − | 0.211879i | ||||
\(862\) | −5.08945 | − | 8.81519i | −0.173347 | − | 0.300247i | ||||
\(863\) | 13.6422 | 0.464385 | 0.232193 | − | 0.972670i | \(-0.425410\pi\) | ||||
0.232193 | + | 0.972670i | \(0.425410\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 4.00000 | + | 6.92820i | 0.136004 | + | 0.235566i | ||||
\(866\) | 34.3578 | 1.16753 | ||||||||
\(867\) | 4.00000 | + | 6.92820i | 0.135847 | + | 0.235294i | ||||
\(868\) | 2.08945 | − | 3.61904i | 0.0709207 | − | 0.122838i | ||||
\(869\) | 34.1262 | − | 59.1083i | 1.15765 | − | 2.00511i | ||||
\(870\) | −6.35782 | −0.215550 | ||||||||
\(871\) | 7.98400 | + | 11.2279i | 0.270527 | + | 0.380442i | ||||
\(872\) | 4.00000 | 0.135457 | ||||||||
\(873\) | 5.17891 | − | 8.97013i | 0.175279 | − | 0.303593i | ||||
\(874\) | 13.0000 | − | 22.5167i | 0.439732 | − | 0.761637i | ||||
\(875\) | 6.00000 | + | 10.3923i | 0.202837 | + | 0.351324i | ||||
\(876\) | −4.00000 | −0.135147 | ||||||||
\(877\) | 20.1789 | + | 34.9509i | 0.681393 | + | 1.18021i | 0.974556 | + | 0.224145i | \(0.0719590\pi\) |
−0.293162 | + | 0.956063i | \(0.594708\pi\) | |||||||
\(878\) | −20.3578 | − | 35.2608i | −0.687043 | − | 1.18999i | ||||
\(879\) | −12.0000 | −0.404750 | ||||||||
\(880\) | −5.17891 | − | 8.97013i | −0.174581 | − | 0.302383i | ||||
\(881\) | −5.73164 | + | 9.92749i | −0.193104 | + | 0.334466i | −0.946277 | − | 0.323356i | \(-0.895189\pi\) |
0.753173 | + | 0.657822i | \(0.228522\pi\) | |||||||
\(882\) | −0.500000 | + | 0.866025i | −0.0168359 | + | 0.0291606i | ||||
\(883\) | −3.46327 | −0.116548 | −0.0582742 | − | 0.998301i | \(-0.518560\pi\) | ||||
−0.0582742 | + | 0.998301i | \(0.518560\pi\) | |||||||
\(884\) | −10.4473 | − | 14.6920i | −0.351380 | − | 0.494145i | ||||
\(885\) | −24.3578 | −0.818779 | ||||||||
\(886\) | −1.58945 | + | 2.75302i | −0.0533988 | + | 0.0924894i | ||||
\(887\) | 22.7684 | − | 39.4360i | 0.764487 | − | 1.32413i | −0.176031 | − | 0.984385i | \(-0.556326\pi\) |
0.940517 | − | 0.339745i | \(-0.110341\pi\) | |||||||
\(888\) | 1.00000 | + | 1.73205i | 0.0335578 | + | 0.0581238i | ||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | 9.00000 | + | 15.5885i | 0.301681 | + | 0.522526i | ||||
\(891\) | 2.58945 | + | 4.48507i | 0.0867500 | + | 0.150255i | ||||
\(892\) | −2.17891 | −0.0729552 | ||||||||
\(893\) | 11.4105 | + | 19.7636i | 0.381839 | + | 0.661365i | ||||
\(894\) | 8.08945 | − | 14.0113i | 0.270552 | − | 0.468609i | ||||
\(895\) | 8.35782 | − | 14.4762i | 0.279371 | − | 0.483885i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 29.3578 | − | 2.78346i | 0.980229 | − | 0.0929370i | ||||
\(898\) | −14.0000 | −0.467186 | ||||||||
\(899\) | 6.64218 | − | 11.5046i | 0.221529 | − | 0.383700i | ||||
\(900\) | 0.500000 | − | 0.866025i | 0.0166667 | − | 0.0288675i | ||||
\(901\) | 7.50000 | + | 12.9904i | 0.249861 | + | 0.432772i | ||||
\(902\) | 37.1789 | 1.23792 | ||||||||
\(903\) | −6.08945 | − | 10.5472i | −0.202644 | − | 0.350990i | ||||
\(904\) | −9.17891 | − | 15.8983i | −0.305286 | − | 0.528771i | ||||
\(905\) | −38.3578 | −1.27506 | ||||||||
\(906\) | 9.76836 | + | 16.9193i | 0.324532 | + | 0.562106i | ||||
\(907\) | −24.8051 | + | 42.9637i | −0.823639 | + | 1.42659i | 0.0793153 | + | 0.996850i | \(0.474727\pi\) |
−0.902955 | + | 0.429736i | \(0.858607\pi\) | |||||||
\(908\) | 7.17891 | − | 12.4342i | 0.238240 | − | 0.412645i | ||||
\(909\) | 6.35782 | 0.210875 | ||||||||
\(910\) | −3.00000 | + | 6.55744i | −0.0994490 | + | 0.217377i | ||||
\(911\) | 28.7156 | 0.951391 | 0.475696 | − | 0.879610i | \(-0.342196\pi\) | ||||
0.475696 | + | 0.879610i | \(0.342196\pi\) | |||||||
\(912\) | 1.58945 | − | 2.75302i | 0.0526321 | − | 0.0911614i | ||||
\(913\) | 16.0000 | − | 27.7128i | 0.529523 | − | 0.917160i | ||||
\(914\) | −12.4473 | − | 21.5593i | −0.411719 | − | 0.713118i | ||||
\(915\) | −6.00000 | −0.198354 | ||||||||
\(916\) | −0.500000 | − | 0.866025i | −0.0165205 | − | 0.0286143i | ||||
\(917\) | −7.26836 | − | 12.5892i | −0.240022 | − | 0.415731i | ||||
\(918\) | −5.00000 | −0.165025 | ||||||||
\(919\) | 29.1262 | + | 50.4480i | 0.960784 | + | 1.66413i | 0.720539 | + | 0.693414i | \(0.243894\pi\) |
0.240245 | + | 0.970712i | \(0.422772\pi\) | |||||||
\(920\) | −8.17891 | + | 14.1663i | −0.269651 | + | 0.467049i | ||||
\(921\) | −15.9473 | + | 27.6215i | −0.525480 | + | 0.910159i | ||||
\(922\) | 20.7156 | 0.682233 | ||||||||
\(923\) | −7.82109 | + | 0.741529i | −0.257434 | + | 0.0244077i | ||||
\(924\) | −5.17891 | −0.170374 | ||||||||
\(925\) | 1.00000 | − | 1.73205i | 0.0328798 | − | 0.0569495i | ||||
\(926\) | −13.9473 | + | 24.1574i | −0.458336 | + | 0.793861i | ||||
\(927\) | 4.08945 | + | 7.08314i | 0.134315 | + | 0.232641i | ||||
\(928\) | −3.17891 | −0.104353 | ||||||||
\(929\) | −19.5000 | − | 33.7750i | −0.639774 | − | 1.10812i | −0.985482 | − | 0.169779i | \(-0.945695\pi\) |
0.345708 | − | 0.938342i | \(-0.387639\pi\) | |||||||
\(930\) | −4.17891 | − | 7.23808i | −0.137032 | − | 0.237346i | ||||
\(931\) | 3.17891 | 0.104185 | ||||||||
\(932\) | −11.1789 | − | 19.3624i | −0.366177 | − | 0.634238i | ||||
\(933\) | 12.7684 | − | 22.1155i | 0.418017 | − | 0.724027i | ||||
\(934\) | 11.4473 | − | 19.8273i | 0.374566 | − | 0.648768i | ||||
\(935\) | 51.7891 | 1.69368 | ||||||||
\(936\) | 3.58945 | − | 0.340322i | 0.117325 | − | 0.0111238i | ||||
\(937\) | 21.0735 | 0.688440 | 0.344220 | − | 0.938889i | \(-0.388143\pi\) | ||||
0.344220 | + | 0.938889i | \(0.388143\pi\) | |||||||
\(938\) | −1.91055 | + | 3.30916i | −0.0623815 | + | 0.108048i | ||||
\(939\) | 2.00000 | − | 3.46410i | 0.0652675 | − | 0.113047i | ||||
\(940\) | −7.17891 | − | 12.4342i | −0.234150 | − | 0.405560i | ||||
\(941\) | −20.0000 | −0.651981 | −0.325991 | − | 0.945373i | \(-0.605698\pi\) | ||||
−0.325991 | + | 0.945373i | \(0.605698\pi\) | |||||||
\(942\) | 1.00000 | + | 1.73205i | 0.0325818 | + | 0.0564333i | ||||
\(943\) | −29.3578 | − | 50.8492i | −0.956022 | − | 1.65588i | ||||
\(944\) | −12.1789 | −0.396390 | ||||||||
\(945\) | 1.00000 | + | 1.73205i | 0.0325300 | + | 0.0563436i | ||||
\(946\) | 31.5367 | − | 54.6232i | 1.02535 | − | 1.77595i | ||||
\(947\) | 20.1262 | − | 34.8596i | 0.654013 | − | 1.13278i | −0.328127 | − | 0.944634i | \(-0.606418\pi\) |
0.982140 | − | 0.188150i | \(-0.0602492\pi\) | |||||||
\(948\) | −13.1789 | −0.428031 | ||||||||
\(949\) | −6.00000 | + | 13.1149i | −0.194768 | + | 0.425727i | ||||
\(950\) | −3.17891 | −0.103137 | ||||||||
\(951\) | −2.08945 | + | 3.61904i | −0.0677552 | + | 0.117355i | ||||
\(952\) | 2.50000 | − | 4.33013i | 0.0810255 | − | 0.140340i | ||||
\(953\) | 1.35782 | + | 2.35181i | 0.0439840 | + | 0.0761825i | 0.887179 | − | 0.461425i | \(-0.152662\pi\) |
−0.843195 | + | 0.537607i | \(0.819328\pi\) | |||||||
\(954\) | −3.00000 | −0.0971286 | ||||||||
\(955\) | −6.53673 | − | 11.3219i | −0.211523 | − | 0.366369i | ||||
\(956\) | −5.08945 | − | 8.81519i | −0.164605 | − | 0.285104i | ||||
\(957\) | −16.4633 | −0.532182 | ||||||||
\(958\) | 20.5895 | + | 35.6620i | 0.665215 | + | 1.15219i | ||||
\(959\) | 3.17891 | − | 5.50603i | 0.102652 | − | 0.177799i | ||||
\(960\) | −1.00000 | + | 1.73205i | −0.0322749 | + | 0.0559017i | ||||
\(961\) | −13.5367 | −0.436669 | ||||||||
\(962\) | 7.17891 | − | 0.680643i | 0.231457 | − | 0.0219448i | ||||
\(963\) | 19.1789 | 0.618032 | ||||||||
\(964\) | −2.17891 | + | 3.77398i | −0.0701779 | + | 0.121552i | ||||
\(965\) | −13.5367 | + | 23.4463i | −0.435763 | + | 0.754763i | ||||
\(966\) | 4.08945 | + | 7.08314i | 0.131576 | + | 0.227896i | ||||
\(967\) | 11.6422 | 0.374387 | 0.187194 | − | 0.982323i | \(-0.440061\pi\) | ||||
0.187194 | + | 0.982323i | \(0.440061\pi\) | |||||||
\(968\) | −7.91055 | − | 13.7015i | −0.254255 | − | 0.440382i | ||||
\(969\) | 7.94727 | + | 13.7651i | 0.255303 | + | 0.442198i | ||||
\(970\) | 20.7156 | 0.665139 | ||||||||
\(971\) | 14.0895 | + | 24.4037i | 0.452152 | + | 0.783150i | 0.998519 | − | 0.0543952i | \(-0.0173231\pi\) |
−0.546367 | + | 0.837546i | \(0.683990\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | −3.41055 | + | 5.90724i | −0.109337 | + | 0.189377i | ||||
\(974\) | −26.8211 | −0.859403 | ||||||||
\(975\) | −2.08945 | − | 2.93840i | −0.0669161 | − | 0.0941040i | ||||
\(976\) | −3.00000 | −0.0960277 | ||||||||
\(977\) | −6.00000 | + | 10.3923i | −0.191957 | + | 0.332479i | −0.945899 | − | 0.324462i | \(-0.894817\pi\) |
0.753942 | + | 0.656941i | \(0.228150\pi\) | |||||||
\(978\) | −10.0895 | + | 17.4754i | −0.322625 | + | 0.558803i | ||||
\(979\) | 23.3051 | + | 40.3656i | 0.744834 | + | 1.29009i | ||||
\(980\) | −2.00000 | −0.0638877 | ||||||||
\(981\) | −2.00000 | − | 3.46410i | −0.0638551 | − | 0.110600i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.0735 | −0.416978 | −0.208489 | − | 0.978025i | \(-0.566855\pi\) | ||||
−0.208489 | + | 0.978025i | \(0.566855\pi\) | |||||||
\(984\) | −3.58945 | − | 6.21712i | −0.114428 | − | 0.198194i | ||||
\(985\) | 17.0000 | − | 29.4449i | 0.541665 | − | 0.938191i | ||||
\(986\) | 7.94727 | − | 13.7651i | 0.253093 | − | 0.438369i | ||||
\(987\) | −7.17891 | −0.228507 | ||||||||
\(988\) | −6.64218 | − | 9.34090i | −0.211316 | − | 0.297174i | ||||
\(989\) | −99.6102 | −3.16742 | ||||||||
\(990\) | −5.17891 | + | 8.97013i | −0.164597 | + | 0.285090i | ||||
\(991\) | 24.7684 | − | 42.9001i | 0.786793 | − | 1.36277i | −0.141129 | − | 0.989991i | \(-0.545073\pi\) |
0.927922 | − | 0.372774i | \(-0.121593\pi\) | |||||||
\(992\) | −2.08945 | − | 3.61904i | −0.0663402 | − | 0.114905i | ||||
\(993\) | 1.64218 | 0.0521131 | ||||||||
\(994\) | −1.08945 | − | 1.88699i | −0.0345554 | − | 0.0598517i | ||||
\(995\) | 24.1789 | + | 41.8791i | 0.766523 | + | 1.32766i | ||||
\(996\) | −6.17891 | −0.195786 | ||||||||
\(997\) | −6.14218 | − | 10.6386i | −0.194525 | − | 0.336927i | 0.752220 | − | 0.658912i | \(-0.228983\pi\) |
−0.946745 | + | 0.321985i | \(0.895650\pi\) | |||||||
\(998\) | −4.08945 | + | 7.08314i | −0.129449 | + | 0.224213i | ||||
\(999\) | 1.00000 | − | 1.73205i | 0.0316386 | − | 0.0547997i |
(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 | 546.2.l.k.295.2 | yes | 4 | |
3.2 | odd | 2 | 1638.2.r.ba.1387.1 | 4 | |||
13.3 | even | 3 | inner | 546.2.l.k.211.2 | ✓ | 4 | |
13.4 | even | 6 | 7098.2.a.bk.1.2 | 2 | |||
13.9 | even | 3 | 7098.2.a.br.1.1 | 2 | |||
39.29 | odd | 6 | 1638.2.r.ba.757.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.k.211.2 | ✓ | 4 | 13.3 | even | 3 | inner | |
546.2.l.k.295.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1638.2.r.ba.757.1 | 4 | 39.29 | odd | 6 | |||
1638.2.r.ba.1387.1 | 4 | 3.2 | odd | 2 | |||
7098.2.a.bk.1.2 | 2 | 13.4 | even | 6 | |||
7098.2.a.br.1.1 | 2 | 13.9 | even | 3 |