Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,2,Mod(107,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.h (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.58715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.2 | ||
Root | \(1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.107 |
Dual form | 324.2.h.b.215.2 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | − | 0.707107i | 0.866025 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(5\) | 2.44949 | − | 1.41421i | 1.09545 | − | 0.632456i | 0.160424 | − | 0.987048i | \(-0.448714\pi\) |
0.935021 | + | 0.354593i | \(0.115380\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.50000 | − | 0.866025i | −0.566947 | − | 0.327327i | 0.188982 | − | 0.981981i | \(-0.439481\pi\) |
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | − | 2.82843i | − | 1.00000i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | − | 3.46410i | 0.632456 | − | 1.09545i | ||||
\(11\) | −2.44949 | + | 4.24264i | −0.738549 | + | 1.27920i | 0.214600 | + | 0.976702i | \(0.431155\pi\) |
−0.953149 | + | 0.302502i | \(0.902178\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | + | 0.866025i | 0.138675 | + | 0.240192i | 0.926995 | − | 0.375073i | \(-0.122382\pi\) |
−0.788320 | + | 0.615265i | \(0.789049\pi\) | |||||||
\(14\) | −2.44949 | −0.654654 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | 2.82843i | 0.685994i | 0.939336 | + | 0.342997i | \(0.111442\pi\) | ||||
−0.939336 | + | 0.342997i | \(0.888558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.19615i | − | 1.19208i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) | ||
0.802955 | − | 0.596040i | \(-0.203260\pi\) | |||||||
\(20\) | − | 5.65685i | − | 1.26491i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.92820i | 1.47710i | ||||||||
\(23\) | 2.44949 | + | 4.24264i | 0.510754 | + | 0.884652i | 0.999922 | + | 0.0124624i | \(0.00396701\pi\) |
−0.489168 | + | 0.872189i | \(0.662700\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.50000 | − | 2.59808i | 0.300000 | − | 0.519615i | ||||
\(26\) | 1.22474 | + | 0.707107i | 0.240192 | + | 0.138675i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.00000 | + | 1.73205i | −0.566947 | + | 0.327327i | ||||
\(29\) | 4.89898 | + | 2.82843i | 0.909718 | + | 0.525226i | 0.880340 | − | 0.474343i | \(-0.157314\pi\) |
0.0293774 | + | 0.999568i | \(0.490648\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | − | 1.73205i | 0.538816 | − | 0.311086i | −0.205783 | − | 0.978598i | \(-0.565974\pi\) |
0.744599 | + | 0.667512i | \(0.232641\pi\) | |||||||
\(32\) | −4.89898 | − | 2.82843i | −0.866025 | − | 0.500000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | + | 3.46410i | 0.342997 | + | 0.594089i | ||||
\(35\) | −4.89898 | −0.828079 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | −3.67423 | − | 6.36396i | −0.596040 | − | 1.03237i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.00000 | − | 6.92820i | −0.632456 | − | 1.09545i | ||||
\(41\) | −4.89898 | + | 2.82843i | −0.765092 | + | 0.441726i | −0.831121 | − | 0.556092i | \(-0.812300\pi\) |
0.0660290 | + | 0.997818i | \(0.478967\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.00000 | + | 1.73205i | 0.457496 | + | 0.264135i | 0.710991 | − | 0.703201i | \(-0.248247\pi\) |
−0.253495 | + | 0.967337i | \(0.581580\pi\) | |||||||
\(44\) | 4.89898 | + | 8.48528i | 0.738549 | + | 1.27920i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | + | 3.46410i | 0.884652 | + | 0.510754i | ||||
\(47\) | −2.44949 | + | 4.24264i | −0.357295 | + | 0.618853i | −0.987508 | − | 0.157569i | \(-0.949634\pi\) |
0.630213 | + | 0.776422i | \(0.282968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.00000 | − | 3.46410i | −0.285714 | − | 0.494872i | ||||
\(50\) | − | 4.24264i | − | 0.600000i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | − | 5.65685i | − | 0.777029i | −0.921443 | − | 0.388514i | \(-0.872988\pi\) | ||
0.921443 | − | 0.388514i | \(-0.127012\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.8564i | 1.86840i | ||||||||
\(56\) | −2.44949 | + | 4.24264i | −0.327327 | + | 0.566947i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.00000 | 1.05045 | ||||||||
\(59\) | 2.44949 | + | 4.24264i | 0.318896 | + | 0.552345i | 0.980258 | − | 0.197722i | \(-0.0633545\pi\) |
−0.661362 | + | 0.750067i | \(0.730021\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.50000 | + | 9.52628i | −0.704203 | + | 1.21972i | 0.262776 | + | 0.964857i | \(0.415362\pi\) |
−0.966978 | + | 0.254858i | \(0.917971\pi\) | |||||||
\(62\) | 2.44949 | − | 4.24264i | 0.311086 | − | 0.538816i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 2.44949 | + | 1.41421i | 0.303822 | + | 0.175412i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.5000 | + | 6.06218i | −1.28278 | + | 0.740613i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) |
−0.305424 | + | 0.952217i | \(0.598798\pi\) | |||||||
\(68\) | 4.89898 | + | 2.82843i | 0.594089 | + | 0.342997i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.00000 | + | 3.46410i | −0.717137 | + | 0.414039i | ||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | −0.117041 | −0.0585206 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585206 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(74\) | −1.22474 | + | 0.707107i | −0.142374 | + | 0.0821995i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.00000 | − | 5.19615i | −1.03237 | − | 0.596040i | ||||
\(77\) | 7.34847 | − | 4.24264i | 0.837436 | − | 0.483494i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.50000 | − | 0.866025i | −0.168763 | − | 0.0974355i | 0.413239 | − | 0.910622i | \(-0.364397\pi\) |
−0.582003 | + | 0.813187i | \(0.697731\pi\) | |||||||
\(80\) | −9.79796 | − | 5.65685i | −1.09545 | − | 0.632456i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.00000 | + | 6.92820i | −0.441726 | + | 0.765092i | ||||
\(83\) | 4.89898 | − | 8.48528i | 0.537733 | − | 0.931381i | −0.461293 | − | 0.887248i | \(-0.652614\pi\) |
0.999026 | − | 0.0441327i | \(-0.0140524\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | + | 6.92820i | 0.433861 | + | 0.751469i | ||||
\(86\) | 4.89898 | 0.528271 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.0000 | + | 6.92820i | 1.27920 | + | 0.738549i | ||||
\(89\) | 2.82843i | 0.299813i | 0.988700 | + | 0.149906i | \(0.0478972\pi\) | ||||
−0.988700 | + | 0.149906i | \(0.952103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.73205i | − | 0.181568i | ||||||
\(92\) | 9.79796 | 1.02151 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.92820i | 0.714590i | ||||||||
\(95\) | −7.34847 | − | 12.7279i | −0.753937 | − | 1.30586i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.50000 | − | 11.2583i | 0.659975 | − | 1.14311i | −0.320647 | − | 0.947199i | \(-0.603900\pi\) |
0.980622 | − | 0.195911i | \(-0.0627665\pi\) | |||||||
\(98\) | −4.89898 | − | 2.82843i | −0.494872 | − | 0.285714i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | − | 5.19615i | −0.300000 | − | 0.519615i | ||||
\(101\) | −9.79796 | − | 5.65685i | −0.974933 | − | 0.562878i | −0.0741967 | − | 0.997244i | \(-0.523639\pi\) |
−0.900737 | + | 0.434366i | \(0.856973\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.50000 | − | 4.33013i | 0.738997 | − | 0.426660i | −0.0827075 | − | 0.996574i | \(-0.526357\pi\) |
0.821705 | + | 0.569914i | \(0.193023\pi\) | |||||||
\(104\) | 2.44949 | − | 1.41421i | 0.240192 | − | 0.138675i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | − | 6.92820i | −0.388514 | − | 0.672927i | ||||
\(107\) | 14.6969 | 1.42081 | 0.710403 | − | 0.703795i | \(-0.248513\pi\) | ||||
0.710403 | + | 0.703795i | \(0.248513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 9.79796 | + | 16.9706i | 0.934199 | + | 1.61808i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.92820i | 0.654654i | ||||||||
\(113\) | 2.44949 | − | 1.41421i | 0.230429 | − | 0.133038i | −0.380341 | − | 0.924846i | \(-0.624193\pi\) |
0.610770 | + | 0.791808i | \(0.290860\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.0000 | + | 6.92820i | 1.11901 | + | 0.646058i | ||||
\(116\) | 9.79796 | − | 5.65685i | 0.909718 | − | 0.525226i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000 | + | 3.46410i | 0.552345 | + | 0.318896i | ||||
\(119\) | 2.44949 | − | 4.24264i | 0.224544 | − | 0.388922i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.50000 | − | 11.2583i | −0.590909 | − | 1.02348i | ||||
\(122\) | 15.5563i | 1.40841i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 6.92820i | − | 0.622171i | ||||||
\(125\) | 5.65685i | 0.505964i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.3923i | − | 0.922168i | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||
0.887357 | − | 0.461084i | \(-0.152539\pi\) | |||||||
\(128\) | −9.79796 | + | 5.65685i | −0.866025 | + | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.00000 | 0.350823 | ||||||||
\(131\) | −4.89898 | − | 8.48528i | −0.428026 | − | 0.741362i | 0.568672 | − | 0.822564i | \(-0.307457\pi\) |
−0.996698 | + | 0.0812020i | \(0.974124\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.50000 | + | 7.79423i | −0.390199 | + | 0.675845i | ||||
\(134\) | −8.57321 | + | 14.8492i | −0.740613 | + | 1.28278i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.00000 | 0.685994 | ||||||||
\(137\) | −17.1464 | − | 9.89949i | −1.46492 | − | 0.845771i | −0.465686 | − | 0.884950i | \(-0.654192\pi\) |
−0.999232 | + | 0.0391791i | \(0.987526\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.50000 | − | 4.33013i | 0.636142 | − | 0.367277i | −0.146985 | − | 0.989139i | \(-0.546957\pi\) |
0.783127 | + | 0.621862i | \(0.213624\pi\) | |||||||
\(140\) | −4.89898 | + | 8.48528i | −0.414039 | + | 0.717137i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.89898 | −0.409673 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.0000 | 1.32873 | ||||||||
\(146\) | −1.22474 | + | 0.707107i | −0.101361 | + | 0.0585206i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00000 | + | 1.73205i | −0.0821995 | + | 0.142374i | ||||
\(149\) | −19.5959 | + | 11.3137i | −1.60536 | + | 0.926855i | −0.614970 | + | 0.788550i | \(0.710832\pi\) |
−0.990390 | + | 0.138305i | \(0.955835\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5000 | − | 11.2583i | −1.58689 | − | 0.916190i | −0.993816 | − | 0.111040i | \(-0.964582\pi\) |
−0.593072 | − | 0.805150i | \(-0.702085\pi\) | |||||||
\(152\) | −14.6969 | −1.19208 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.00000 | − | 10.3923i | 0.483494 | − | 0.837436i | ||||
\(155\) | 4.89898 | − | 8.48528i | 0.393496 | − | 0.681554i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.00000 | + | 8.66025i | 0.399043 | + | 0.691164i | 0.993608 | − | 0.112884i | \(-0.0360089\pi\) |
−0.594565 | + | 0.804048i | \(0.702676\pi\) | |||||||
\(158\) | −2.44949 | −0.194871 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −16.0000 | −1.26491 | ||||||||
\(161\) | − | 8.48528i | − | 0.668734i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5.19615i | − | 0.406994i | −0.979076 | − | 0.203497i | \(-0.934769\pi\) | ||
0.979076 | − | 0.203497i | \(-0.0652307\pi\) | |||||||
\(164\) | 11.3137i | 0.883452i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 13.8564i | − | 1.07547i | ||||||
\(167\) | 2.44949 | + | 4.24264i | 0.189547 | + | 0.328305i | 0.945099 | − | 0.326783i | \(-0.105965\pi\) |
−0.755552 | + | 0.655089i | \(0.772631\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 9.79796 | + | 5.65685i | 0.751469 | + | 0.433861i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.00000 | − | 3.46410i | 0.457496 | − | 0.264135i | ||||
\(173\) | 4.89898 | + | 2.82843i | 0.372463 | + | 0.215041i | 0.674534 | − | 0.738244i | \(-0.264345\pi\) |
−0.302071 | + | 0.953285i | \(0.597678\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.50000 | + | 2.59808i | −0.340168 | + | 0.196396i | ||||
\(176\) | 19.5959 | 1.47710 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.00000 | + | 3.46410i | 0.149906 | + | 0.259645i | ||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0000 | 0.817624 | 0.408812 | − | 0.912619i | \(-0.365943\pi\) | ||||
0.408812 | + | 0.912619i | \(0.365943\pi\) | |||||||
\(182\) | −1.22474 | − | 2.12132i | −0.0907841 | − | 0.157243i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.0000 | − | 6.92820i | 0.884652 | − | 0.510754i | ||||
\(185\) | −2.44949 | + | 1.41421i | −0.180090 | + | 0.103975i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | − | 6.92820i | −0.877527 | − | 0.506640i | ||||
\(188\) | 4.89898 | + | 8.48528i | 0.357295 | + | 0.618853i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −18.0000 | − | 10.3923i | −1.30586 | − | 0.753937i | ||||
\(191\) | 12.2474 | − | 21.2132i | 0.886194 | − | 1.53493i | 0.0418556 | − | 0.999124i | \(-0.486673\pi\) |
0.844339 | − | 0.535810i | \(-0.179994\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.500000 | + | 0.866025i | 0.0359908 | + | 0.0623379i | 0.883460 | − | 0.468507i | \(-0.155208\pi\) |
−0.847469 | + | 0.530845i | \(0.821875\pi\) | |||||||
\(194\) | − | 18.3848i | − | 1.31995i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.00000 | −0.571429 | ||||||||
\(197\) | 2.82843i | 0.201517i | 0.994911 | + | 0.100759i | \(0.0321270\pi\) | ||||
−0.994911 | + | 0.100759i | \(0.967873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.19615i | − | 0.368345i | −0.982894 | − | 0.184173i | \(-0.941039\pi\) | ||
0.982894 | − | 0.184173i | \(-0.0589606\pi\) | |||||||
\(200\) | −7.34847 | − | 4.24264i | −0.519615 | − | 0.300000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −16.0000 | −1.12576 | ||||||||
\(203\) | −4.89898 | − | 8.48528i | −0.343841 | − | 0.595550i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.00000 | + | 13.8564i | −0.558744 | + | 0.967773i | ||||
\(206\) | 6.12372 | − | 10.6066i | 0.426660 | − | 0.738997i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000 | − | 3.46410i | 0.138675 | − | 0.240192i | ||||
\(209\) | 22.0454 | + | 12.7279i | 1.52491 | + | 0.880409i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.5000 | + | 6.06218i | −0.722850 | + | 0.417338i | −0.815801 | − | 0.578333i | \(-0.803703\pi\) |
0.0929509 | + | 0.995671i | \(0.470370\pi\) | |||||||
\(212\) | −9.79796 | − | 5.65685i | −0.672927 | − | 0.388514i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.0000 | − | 10.3923i | 1.23045 | − | 0.710403i | ||||
\(215\) | 9.79796 | 0.668215 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | −0.407307 | ||||||||
\(218\) | −12.2474 | + | 7.07107i | −0.829502 | + | 0.478913i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 24.0000 | + | 13.8564i | 1.61808 | + | 0.934199i | ||||
\(221\) | −2.44949 | + | 1.41421i | −0.164771 | + | 0.0951303i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.0000 | + | 12.1244i | 1.40626 | + | 0.811907i | 0.995025 | − | 0.0996209i | \(-0.0317630\pi\) |
0.411239 | + | 0.911528i | \(0.365096\pi\) | |||||||
\(224\) | 4.89898 | + | 8.48528i | 0.327327 | + | 0.566947i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.00000 | − | 3.46410i | 0.133038 | − | 0.230429i | ||||
\(227\) | −9.79796 | + | 16.9706i | −0.650313 | + | 1.12638i | 0.332733 | + | 0.943021i | \(0.392029\pi\) |
−0.983047 | + | 0.183355i | \(0.941304\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000 | + | 8.66025i | 0.330409 | + | 0.572286i | 0.982592 | − | 0.185776i | \(-0.0594799\pi\) |
−0.652183 | + | 0.758062i | \(0.726147\pi\) | |||||||
\(230\) | 19.5959 | 1.29212 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.00000 | − | 13.8564i | 0.525226 | − | 0.909718i | ||||
\(233\) | − | 22.6274i | − | 1.48237i | −0.671300 | − | 0.741186i | \(-0.734264\pi\) | ||
0.671300 | − | 0.741186i | \(-0.265736\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.8564i | 0.903892i | ||||||||
\(236\) | 9.79796 | 0.637793 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 6.92820i | − | 0.449089i | ||||||
\(239\) | 9.79796 | + | 16.9706i | 0.633777 | + | 1.09773i | 0.986773 | + | 0.162109i | \(0.0518298\pi\) |
−0.352996 | + | 0.935625i | \(0.614837\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.5000 | − | 21.6506i | 0.805196 | − | 1.39464i | −0.110963 | − | 0.993825i | \(-0.535394\pi\) |
0.916159 | − | 0.400815i | \(-0.131273\pi\) | |||||||
\(242\) | −15.9217 | − | 9.19239i | −1.02348 | − | 0.590909i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.0000 | + | 19.0526i | 0.704203 | + | 1.21972i | ||||
\(245\) | −9.79796 | − | 5.65685i | −0.625969 | − | 0.361403i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.50000 | − | 2.59808i | 0.286328 | − | 0.165312i | ||||
\(248\) | −4.89898 | − | 8.48528i | −0.311086 | − | 0.538816i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.00000 | + | 6.92820i | 0.252982 | + | 0.438178i | ||||
\(251\) | −29.3939 | −1.85533 | −0.927663 | − | 0.373420i | \(-0.878185\pi\) | ||||
−0.927663 | + | 0.373420i | \(0.878185\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.0000 | −1.50887 | ||||||||
\(254\) | −7.34847 | − | 12.7279i | −0.461084 | − | 0.798621i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 24.4949 | − | 14.1421i | 1.52795 | − | 0.882162i | 0.528502 | − | 0.848932i | \(-0.322754\pi\) |
0.999448 | − | 0.0332301i | \(-0.0105794\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.50000 | + | 0.866025i | 0.0932055 | + | 0.0538122i | ||||
\(260\) | 4.89898 | − | 2.82843i | 0.303822 | − | 0.175412i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.0000 | − | 6.92820i | −0.741362 | − | 0.428026i | ||||
\(263\) | −9.79796 | + | 16.9706i | −0.604168 | + | 1.04645i | 0.388014 | + | 0.921653i | \(0.373161\pi\) |
−0.992182 | + | 0.124796i | \(0.960172\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.00000 | − | 13.8564i | −0.491436 | − | 0.851192i | ||||
\(266\) | 12.7279i | 0.780399i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 24.2487i | 1.48123i | ||||||||
\(269\) | 2.82843i | 0.172452i | 0.996276 | + | 0.0862261i | \(0.0274808\pi\) | ||||
−0.996276 | + | 0.0862261i | \(0.972519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5.19615i | − | 0.315644i | −0.987468 | − | 0.157822i | \(-0.949553\pi\) | ||
0.987468 | − | 0.157822i | \(-0.0504472\pi\) | |||||||
\(272\) | 9.79796 | − | 5.65685i | 0.594089 | − | 0.342997i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −28.0000 | −1.69154 | ||||||||
\(275\) | 7.34847 | + | 12.7279i | 0.443129 | + | 0.767523i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.00000 | + | 12.1244i | −0.420589 | + | 0.728482i | −0.995997 | − | 0.0893846i | \(-0.971510\pi\) |
0.575408 | + | 0.817867i | \(0.304843\pi\) | |||||||
\(278\) | 6.12372 | − | 10.6066i | 0.367277 | − | 0.636142i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 13.8564i | 0.828079i | ||||||||
\(281\) | 4.89898 | + | 2.82843i | 0.292249 | + | 0.168730i | 0.638955 | − | 0.769244i | \(-0.279367\pi\) |
−0.346707 | + | 0.937974i | \(0.612700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.0000 | − | 12.1244i | 1.24832 | − | 0.720718i | 0.277546 | − | 0.960712i | \(-0.410479\pi\) |
0.970774 | + | 0.239994i | \(0.0771455\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | + | 3.46410i | −0.354787 | + | 0.204837i | ||||
\(287\) | 9.79796 | 0.578355 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.00000 | 0.529412 | ||||||||
\(290\) | 19.5959 | − | 11.3137i | 1.15071 | − | 0.664364i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.00000 | + | 1.73205i | −0.0585206 | + | 0.101361i | ||||
\(293\) | 2.44949 | − | 1.41421i | 0.143101 | − | 0.0826192i | −0.426740 | − | 0.904374i | \(-0.640338\pi\) |
0.569841 | + | 0.821755i | \(0.307005\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0000 | + | 6.92820i | 0.698667 | + | 0.403376i | ||||
\(296\) | 2.82843i | 0.164399i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.0000 | + | 27.7128i | −0.926855 | + | 1.60536i | ||||
\(299\) | −2.44949 | + | 4.24264i | −0.141658 | + | 0.245358i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | − | 5.19615i | −0.172917 | − | 0.299501i | ||||
\(302\) | −31.8434 | −1.83238 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −18.0000 | + | 10.3923i | −1.03237 | + | 0.596040i | ||||
\(305\) | 31.1127i | 1.78151i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.3923i | 0.593120i | 0.955014 | + | 0.296560i | \(0.0958395\pi\) | ||||
−0.955014 | + | 0.296560i | \(0.904160\pi\) | |||||||
\(308\) | − | 16.9706i | − | 0.966988i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 13.8564i | − | 0.786991i | ||||||
\(311\) | −12.2474 | − | 21.2132i | −0.694489 | − | 1.20289i | −0.970353 | − | 0.241694i | \(-0.922297\pi\) |
0.275864 | − | 0.961197i | \(-0.411036\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.50000 | + | 9.52628i | −0.310878 | + | 0.538457i | −0.978553 | − | 0.205996i | \(-0.933957\pi\) |
0.667674 | + | 0.744453i | \(0.267290\pi\) | |||||||
\(314\) | 12.2474 | + | 7.07107i | 0.691164 | + | 0.399043i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.00000 | + | 1.73205i | −0.168763 | + | 0.0974355i | ||||
\(317\) | 4.89898 | + | 2.82843i | 0.275154 | + | 0.158860i | 0.631228 | − | 0.775598i | \(-0.282551\pi\) |
−0.356073 | + | 0.934458i | \(0.615885\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.0000 | + | 13.8564i | −1.34374 | + | 0.775810i | ||||
\(320\) | −19.5959 | + | 11.3137i | −1.09545 | + | 0.632456i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.00000 | − | 10.3923i | −0.334367 | − | 0.579141i | ||||
\(323\) | 14.6969 | 0.817760 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | 0.166410 | ||||||||
\(326\) | −3.67423 | − | 6.36396i | −0.203497 | − | 0.352467i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.00000 | + | 13.8564i | 0.441726 | + | 0.765092i | ||||
\(329\) | 7.34847 | − | 4.24264i | 0.405134 | − | 0.233904i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.5000 | − | 11.2583i | −1.07182 | − | 0.618814i | −0.143140 | − | 0.989703i | \(-0.545720\pi\) |
−0.928677 | + | 0.370889i | \(0.879053\pi\) | |||||||
\(332\) | −9.79796 | − | 16.9706i | −0.537733 | − | 0.931381i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.00000 | + | 3.46410i | 0.328305 | + | 0.189547i | ||||
\(335\) | −17.1464 | + | 29.6985i | −0.936809 | + | 1.62260i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.50000 | − | 9.52628i | −0.299604 | − | 0.518930i | 0.676441 | − | 0.736497i | \(-0.263521\pi\) |
−0.976045 | + | 0.217567i | \(0.930188\pi\) | |||||||
\(338\) | − | 16.9706i | − | 0.923077i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 16.0000 | 0.867722 | ||||||||
\(341\) | 16.9706i | 0.919007i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0526i | 1.02874i | ||||||||
\(344\) | 4.89898 | − | 8.48528i | 0.264135 | − | 0.457496i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.00000 | 0.430083 | ||||||||
\(347\) | 9.79796 | + | 16.9706i | 0.525982 | + | 0.911028i | 0.999542 | + | 0.0302659i | \(0.00963541\pi\) |
−0.473560 | + | 0.880762i | \(0.657031\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.5000 | + | 19.9186i | −0.615581 | + | 1.06622i | 0.374701 | + | 0.927146i | \(0.377745\pi\) |
−0.990282 | + | 0.139072i | \(0.955588\pi\) | |||||||
\(350\) | −3.67423 | + | 6.36396i | −0.196396 | + | 0.340168i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 24.0000 | − | 13.8564i | 1.27920 | − | 0.738549i | ||||
\(353\) | −9.79796 | − | 5.65685i | −0.521493 | − | 0.301084i | 0.216052 | − | 0.976382i | \(-0.430682\pi\) |
−0.737545 | + | 0.675298i | \(0.764015\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.89898 | + | 2.82843i | 0.259645 | + | 0.149906i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.6969 | −0.775675 | −0.387837 | − | 0.921728i | \(-0.626778\pi\) | ||||
−0.387837 | + | 0.921728i | \(0.626778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | −0.421053 | ||||||||
\(362\) | 13.4722 | − | 7.77817i | 0.708083 | − | 0.408812i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.00000 | − | 1.73205i | −0.157243 | − | 0.0907841i | ||||
\(365\) | −2.44949 | + | 1.41421i | −0.128212 | + | 0.0740233i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.5000 | + | 9.52628i | 0.861293 | + | 0.497268i | 0.864445 | − | 0.502727i | \(-0.167670\pi\) |
−0.00315207 | + | 0.999995i | \(0.501003\pi\) | |||||||
\(368\) | 9.79796 | − | 16.9706i | 0.510754 | − | 0.884652i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.00000 | + | 3.46410i | −0.103975 | + | 0.180090i | ||||
\(371\) | −4.89898 | + | 8.48528i | −0.254342 | + | 0.440534i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5000 | + | 21.6506i | 0.647225 | + | 1.12103i | 0.983783 | + | 0.179364i | \(0.0574041\pi\) |
−0.336557 | + | 0.941663i | \(0.609263\pi\) | |||||||
\(374\) | −19.5959 | −1.01328 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.0000 | + | 6.92820i | 0.618853 | + | 0.357295i | ||||
\(377\) | 5.65685i | 0.291343i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.5885i | 0.800725i | 0.916357 | + | 0.400363i | \(0.131116\pi\) | ||||
−0.916357 | + | 0.400363i | \(0.868884\pi\) | |||||||
\(380\) | −29.3939 | −1.50787 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 34.6410i | − | 1.77239i | ||||||
\(383\) | 9.79796 | + | 16.9706i | 0.500652 | + | 0.867155i | 1.00000 | 0.000753393i | \(0.000239813\pi\) | |
−0.499347 | + | 0.866402i | \(0.666427\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.0000 | − | 20.7846i | 0.611577 | − | 1.05928i | ||||
\(386\) | 1.22474 | + | 0.707107i | 0.0623379 | + | 0.0359908i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.0000 | − | 22.5167i | −0.659975 | − | 1.14311i | ||||
\(389\) | 12.2474 | + | 7.07107i | 0.620970 | + | 0.358517i | 0.777247 | − | 0.629196i | \(-0.216616\pi\) |
−0.156276 | + | 0.987713i | \(0.549949\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0000 | + | 6.92820i | −0.606866 | + | 0.350374i | ||||
\(392\) | −9.79796 | + | 5.65685i | −0.494872 | + | 0.285714i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.00000 | + | 3.46410i | 0.100759 | + | 0.174519i | ||||
\(395\) | −4.89898 | −0.246494 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.0000 | −0.501886 | −0.250943 | − | 0.968002i | \(-0.580741\pi\) | ||||
−0.250943 | + | 0.968002i | \(0.580741\pi\) | |||||||
\(398\) | −3.67423 | − | 6.36396i | −0.184173 | − | 0.318997i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.0000 | −0.600000 | ||||||||
\(401\) | −19.5959 | + | 11.3137i | −0.978573 | + | 0.564980i | −0.901839 | − | 0.432072i | \(-0.857783\pi\) |
−0.0767343 | + | 0.997052i | \(0.524449\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.00000 | + | 1.73205i | 0.149441 | + | 0.0862796i | ||||
\(404\) | −19.5959 | + | 11.3137i | −0.974933 | + | 0.562878i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.0000 | − | 6.92820i | −0.595550 | − | 0.343841i | ||||
\(407\) | 2.44949 | − | 4.24264i | 0.121417 | − | 0.210300i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.500000 | + | 0.866025i | 0.0247234 | + | 0.0428222i | 0.878122 | − | 0.478436i | \(-0.158796\pi\) |
−0.853399 | + | 0.521258i | \(0.825463\pi\) | |||||||
\(410\) | 22.6274i | 1.11749i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 17.3205i | − | 0.853320i | ||||||
\(413\) | − | 8.48528i | − | 0.417533i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 27.7128i | − | 1.36037i | ||||||
\(416\) | − | 5.65685i | − | 0.277350i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 36.0000 | 1.76082 | ||||||||
\(419\) | 2.44949 | + | 4.24264i | 0.119665 | + | 0.207267i | 0.919635 | − | 0.392774i | \(-0.128484\pi\) |
−0.799970 | + | 0.600040i | \(0.795151\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.5000 | − | 21.6506i | 0.609213 | − | 1.05519i | −0.382158 | − | 0.924097i | \(-0.624819\pi\) |
0.991370 | − | 0.131090i | \(-0.0418478\pi\) | |||||||
\(422\) | −8.57321 | + | 14.8492i | −0.417338 | + | 0.722850i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −16.0000 | −0.777029 | ||||||||
\(425\) | 7.34847 | + | 4.24264i | 0.356453 | + | 0.205798i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.5000 | − | 9.52628i | 0.798491 | − | 0.461009i | ||||
\(428\) | 14.6969 | − | 25.4558i | 0.710403 | − | 1.23045i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.0000 | − | 6.92820i | 0.578691 | − | 0.334108i | ||||
\(431\) | −14.6969 | −0.707927 | −0.353963 | − | 0.935259i | \(-0.615166\pi\) | ||||
−0.353963 | + | 0.935259i | \(0.615166\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.0000 | 1.24948 | 0.624740 | − | 0.780833i | \(-0.285205\pi\) | ||||
0.624740 | + | 0.780833i | \(0.285205\pi\) | |||||||
\(434\) | −7.34847 | + | 4.24264i | −0.352738 | + | 0.203653i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.0000 | + | 17.3205i | −0.478913 | + | 0.829502i | ||||
\(437\) | 22.0454 | − | 12.7279i | 1.05457 | − | 0.608859i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.0000 | − | 8.66025i | −0.715911 | − | 0.413331i | 0.0973349 | − | 0.995252i | \(-0.468968\pi\) |
−0.813246 | + | 0.581920i | \(0.802302\pi\) | |||||||
\(440\) | 39.1918 | 1.86840 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.00000 | + | 3.46410i | −0.0951303 | + | 0.164771i | ||||
\(443\) | 4.89898 | − | 8.48528i | 0.232758 | − | 0.403148i | −0.725861 | − | 0.687841i | \(-0.758558\pi\) |
0.958619 | + | 0.284693i | \(0.0918918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.00000 | + | 6.92820i | 0.189618 | + | 0.328428i | ||||
\(446\) | 34.2929 | 1.62381 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12.0000 | + | 6.92820i | 0.566947 | + | 0.327327i | ||||
\(449\) | − | 31.1127i | − | 1.46830i | −0.678988 | − | 0.734150i | \(-0.737581\pi\) | ||
0.678988 | − | 0.734150i | \(-0.262419\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 27.7128i | − | 1.30495i | ||||||
\(452\) | − | 5.65685i | − | 0.266076i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 27.7128i | 1.30063i | ||||||||
\(455\) | −2.44949 | − | 4.24264i | −0.114834 | − | 0.198898i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | + | 1.73205i | −0.0467780 | + | 0.0810219i | −0.888466 | − | 0.458942i | \(-0.848229\pi\) |
0.841688 | + | 0.539964i | \(0.181562\pi\) | |||||||
\(458\) | 12.2474 | + | 7.07107i | 0.572286 | + | 0.330409i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 24.0000 | − | 13.8564i | 1.11901 | − | 0.646058i | ||||
\(461\) | 12.2474 | + | 7.07107i | 0.570421 | + | 0.329332i | 0.757317 | − | 0.653047i | \(-0.226510\pi\) |
−0.186897 | + | 0.982380i | \(0.559843\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.5000 | + | 6.06218i | −0.487976 | + | 0.281733i | −0.723735 | − | 0.690078i | \(-0.757576\pi\) |
0.235758 | + | 0.971812i | \(0.424243\pi\) | |||||||
\(464\) | − | 22.6274i | − | 1.05045i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.0000 | − | 27.7128i | −0.741186 | − | 1.28377i | ||||
\(467\) | 14.6969 | 0.680093 | 0.340047 | − | 0.940409i | \(-0.389557\pi\) | ||||
0.340047 | + | 0.940409i | \(0.389557\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.0000 | 0.969690 | ||||||||
\(470\) | 9.79796 | + | 16.9706i | 0.451946 | + | 0.782794i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.0000 | − | 6.92820i | 0.552345 | − | 0.318896i | ||||
\(473\) | −14.6969 | + | 8.48528i | −0.675766 | + | 0.390154i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.5000 | − | 7.79423i | −0.619422 | − | 0.357624i | ||||
\(476\) | −4.89898 | − | 8.48528i | −0.224544 | − | 0.388922i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.0000 | + | 13.8564i | 1.09773 | + | 0.633777i | ||||
\(479\) | 4.89898 | − | 8.48528i | 0.223840 | − | 0.387702i | −0.732131 | − | 0.681164i | \(-0.761474\pi\) |
0.955971 | + | 0.293462i | \(0.0948073\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.500000 | − | 0.866025i | −0.0227980 | − | 0.0394874i | ||||
\(482\) | − | 35.3553i | − | 1.61039i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −26.0000 | −1.18182 | ||||||||
\(485\) | − | 36.7696i | − | 1.66962i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 25.9808i | − | 1.17730i | −0.808388 | − | 0.588650i | \(-0.799659\pi\) | ||
0.808388 | − | 0.588650i | \(-0.200341\pi\) | |||||||
\(488\) | 26.9444 | + | 15.5563i | 1.21972 | + | 0.704203i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.0000 | −0.722806 | ||||||||
\(491\) | −12.2474 | − | 21.2132i | −0.552720 | − | 0.957338i | −0.998077 | − | 0.0619856i | \(-0.980257\pi\) |
0.445357 | − | 0.895353i | \(-0.353077\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.00000 | + | 13.8564i | −0.360302 | + | 0.624061i | ||||
\(494\) | 3.67423 | − | 6.36396i | 0.165312 | − | 0.286328i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.0000 | − | 6.92820i | −0.538816 | − | 0.311086i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.0000 | − | 12.1244i | 0.940089 | − | 0.542761i | 0.0501009 | − | 0.998744i | \(-0.484046\pi\) |
0.889988 | + | 0.455983i | \(0.150712\pi\) | |||||||
\(500\) | 9.79796 | + | 5.65685i | 0.438178 | + | 0.252982i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −36.0000 | + | 20.7846i | −1.60676 | + | 0.927663i | ||||
\(503\) | −14.6969 | −0.655304 | −0.327652 | − | 0.944798i | \(-0.606257\pi\) | ||||
−0.327652 | + | 0.944798i | \(0.606257\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.0000 | −1.42398 | ||||||||
\(506\) | −29.3939 | + | 16.9706i | −1.30672 | + | 0.754434i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.0000 | − | 10.3923i | −0.798621 | − | 0.461084i | ||||
\(509\) | 17.1464 | − | 9.89949i | 0.760002 | − | 0.438787i | −0.0692944 | − | 0.997596i | \(-0.522075\pi\) |
0.829296 | + | 0.558809i | \(0.188741\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.50000 | + | 0.866025i | 0.0663561 | + | 0.0383107i | ||||
\(512\) | 22.6274i | 1.00000i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.0000 | − | 34.6410i | 0.882162 | − | 1.52795i | ||||
\(515\) | 12.2474 | − | 21.2132i | 0.539687 | − | 0.934765i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | − | 20.7846i | −0.527759 | − | 0.914106i | ||||
\(518\) | 2.44949 | 0.107624 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.00000 | − | 6.92820i | 0.175412 | − | 0.303822i | ||||
\(521\) | 19.7990i | 0.867409i | 0.901055 | + | 0.433705i | \(0.142794\pi\) | ||||
−0.901055 | + | 0.433705i | \(0.857206\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.5885i | 0.681636i | 0.940129 | + | 0.340818i | \(0.110704\pi\) | ||||
−0.940129 | + | 0.340818i | \(0.889296\pi\) | |||||||
\(524\) | −19.5959 | −0.856052 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.7128i | 1.20834i | ||||||||
\(527\) | 4.89898 | + | 8.48528i | 0.213403 | + | 0.369625i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | −19.5959 | − | 11.3137i | −0.851192 | − | 0.491436i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9.00000 | + | 15.5885i | 0.390199 | + | 0.675845i | ||||
\(533\) | −4.89898 | − | 2.82843i | −0.212198 | − | 0.122513i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 36.0000 | − | 20.7846i | 1.55642 | − | 0.898597i | ||||
\(536\) | 17.1464 | + | 29.6985i | 0.740613 | + | 1.28278i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.00000 | + | 3.46410i | 0.0862261 | + | 0.149348i | ||||
\(539\) | 19.5959 | 0.844056 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.00000 | −0.0429934 | −0.0214967 | − | 0.999769i | \(-0.506843\pi\) | ||||
−0.0214967 | + | 0.999769i | \(0.506843\pi\) | |||||||
\(542\) | −3.67423 | − | 6.36396i | −0.157822 | − | 0.273356i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.00000 | − | 13.8564i | 0.342997 | − | 0.594089i | ||||
\(545\) | −24.4949 | + | 14.1421i | −1.04925 | + | 0.605783i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.5000 | − | 11.2583i | −0.833760 | − | 0.481371i | 0.0213785 | − | 0.999771i | \(-0.493195\pi\) |
−0.855138 | + | 0.518400i | \(0.826528\pi\) | |||||||
\(548\) | −34.2929 | + | 19.7990i | −1.46492 | + | 0.845771i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18.0000 | + | 10.3923i | 0.767523 | + | 0.443129i | ||||
\(551\) | 14.6969 | − | 25.4558i | 0.626111 | − | 1.08446i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.50000 | + | 2.59808i | 0.0637865 | + | 0.110481i | ||||
\(554\) | 19.7990i | 0.841178i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 17.3205i | − | 0.734553i | ||||||
\(557\) | 2.82843i | 0.119844i | 0.998203 | + | 0.0599222i | \(0.0190852\pi\) | ||||
−0.998203 | + | 0.0599222i | \(0.980915\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.46410i | 0.146516i | ||||||||
\(560\) | 9.79796 | + | 16.9706i | 0.414039 | + | 0.717137i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.00000 | 0.337460 | ||||||||
\(563\) | −4.89898 | − | 8.48528i | −0.206467 | − | 0.357612i | 0.744132 | − | 0.668033i | \(-0.232863\pi\) |
−0.950599 | + | 0.310421i | \(0.899530\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00000 | − | 6.92820i | 0.168281 | − | 0.291472i | ||||
\(566\) | 17.1464 | − | 29.6985i | 0.720718 | − | 1.24832i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.1464 | − | 9.89949i | −0.718816 | − | 0.415008i | 0.0955010 | − | 0.995429i | \(-0.469555\pi\) |
−0.814317 | + | 0.580421i | \(0.802888\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.5000 | + | 16.4545i | −1.19269 | + | 0.688599i | −0.958915 | − | 0.283693i | \(-0.908440\pi\) |
−0.233773 | + | 0.972291i | \(0.575107\pi\) | |||||||
\(572\) | −4.89898 | + | 8.48528i | −0.204837 | + | 0.354787i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.0000 | − | 6.92820i | 0.500870 | − | 0.289178i | ||||
\(575\) | 14.6969 | 0.612905 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.0000 | 1.45707 | 0.728535 | − | 0.685009i | \(-0.240202\pi\) | ||||
0.728535 | + | 0.685009i | \(0.240202\pi\) | |||||||
\(578\) | 11.0227 | − | 6.36396i | 0.458484 | − | 0.264706i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 16.0000 | − | 27.7128i | 0.664364 | − | 1.15071i | ||||
\(581\) | −14.6969 | + | 8.48528i | −0.609732 | + | 0.352029i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.0000 | + | 13.8564i | 0.993978 | + | 0.573874i | ||||
\(584\) | 2.82843i | 0.117041i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.00000 | − | 3.46410i | 0.0826192 | − | 0.143101i | ||||
\(587\) | −2.44949 | + | 4.24264i | −0.101101 | + | 0.175113i | −0.912139 | − | 0.409882i | \(-0.865570\pi\) |
0.811037 | + | 0.584994i | \(0.198903\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.00000 | − | 15.5885i | −0.370839 | − | 0.642311i | ||||
\(590\) | 19.5959 | 0.806751 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.00000 | + | 3.46410i | 0.0821995 | + | 0.142374i | ||||
\(593\) | 28.2843i | 1.16150i | 0.814083 | + | 0.580748i | \(0.197240\pi\) | ||||
−0.814083 | + | 0.580748i | \(0.802760\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 13.8564i | − | 0.568057i | ||||||
\(596\) | 45.2548i | 1.85371i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.92820i | 0.283315i | ||||||||
\(599\) | −4.89898 | − | 8.48528i | −0.200167 | − | 0.346699i | 0.748415 | − | 0.663231i | \(-0.230815\pi\) |
−0.948582 | + | 0.316531i | \(0.897482\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00000 | + | 1.73205i | −0.0407909 | + | 0.0706518i | −0.885700 | − | 0.464258i | \(-0.846321\pi\) |
0.844909 | + | 0.534910i | \(0.179654\pi\) | |||||||
\(602\) | −7.34847 | − | 4.24264i | −0.299501 | − | 0.172917i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −39.0000 | + | 22.5167i | −1.58689 | + | 0.916190i | ||||
\(605\) | −31.8434 | − | 18.3848i | −1.29462 | − | 0.747447i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.5000 | + | 6.06218i | −0.426182 | + | 0.246056i | −0.697719 | − | 0.716372i | \(-0.745801\pi\) |
0.271537 | + | 0.962428i | \(0.412468\pi\) | |||||||
\(608\) | −14.6969 | + | 25.4558i | −0.596040 | + | 1.03237i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.0000 | + | 38.1051i | 0.890754 | + | 1.54283i | ||||
\(611\) | −4.89898 | −0.198191 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.0000 | 0.444286 | 0.222143 | − | 0.975014i | \(-0.428695\pi\) | ||||
0.222143 | + | 0.975014i | \(0.428695\pi\) | |||||||
\(614\) | 7.34847 | + | 12.7279i | 0.296560 | + | 0.513657i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.0000 | − | 20.7846i | −0.483494 | − | 0.837436i | ||||
\(617\) | 2.44949 | − | 1.41421i | 0.0986127 | − | 0.0569341i | −0.449883 | − | 0.893088i | \(-0.648534\pi\) |
0.548495 | + | 0.836154i | \(0.315201\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.5000 | + | 9.52628i | 0.663191 | + | 0.382893i | 0.793492 | − | 0.608581i | \(-0.208261\pi\) |
−0.130301 | + | 0.991475i | \(0.541594\pi\) | |||||||
\(620\) | −9.79796 | − | 16.9706i | −0.393496 | − | 0.681554i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −30.0000 | − | 17.3205i | −1.20289 | − | 0.694489i | ||||
\(623\) | 2.44949 | − | 4.24264i | 0.0981367 | − | 0.169978i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5000 | + | 26.8468i | 0.620000 | + | 1.07387i | ||||
\(626\) | 15.5563i | 0.621757i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.0000 | 0.798087 | ||||||||
\(629\) | − | 2.82843i | − | 0.112777i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.3731i | 1.44799i | 0.689806 | + | 0.723994i | \(0.257696\pi\) | ||||
−0.689806 | + | 0.723994i | \(0.742304\pi\) | |||||||
\(632\) | −2.44949 | + | 4.24264i | −0.0974355 | + | 0.168763i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.00000 | 0.317721 | ||||||||
\(635\) | −14.6969 | − | 25.4558i | −0.583230 | − | 1.01018i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | − | 3.46410i | 0.0792429 | − | 0.137253i | ||||
\(638\) | −19.5959 | + | 33.9411i | −0.775810 | + | 1.34374i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.0000 | + | 27.7128i | −0.632456 | + | 1.09545i | ||||
\(641\) | −39.1918 | − | 22.6274i | −1.54798 | − | 0.893729i | −0.998296 | − | 0.0583597i | \(-0.981413\pi\) |
−0.549689 | − | 0.835369i | \(-0.685254\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.0000 | + | 8.66025i | −0.591542 | + | 0.341527i | −0.765707 | − | 0.643189i | \(-0.777611\pi\) |
0.174165 | + | 0.984717i | \(0.444277\pi\) | |||||||
\(644\) | −14.6969 | − | 8.48528i | −0.579141 | − | 0.334367i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18.0000 | − | 10.3923i | 0.708201 | − | 0.408880i | ||||
\(647\) | 29.3939 | 1.15559 | 0.577796 | − | 0.816181i | \(-0.303913\pi\) | ||||
0.577796 | + | 0.816181i | \(0.303913\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | 3.67423 | − | 2.12132i | 0.144115 | − | 0.0832050i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.00000 | − | 5.19615i | −0.352467 | − | 0.203497i | ||||
\(653\) | −4.89898 | + | 2.82843i | −0.191712 | + | 0.110685i | −0.592784 | − | 0.805362i | \(-0.701971\pi\) |
0.401072 | + | 0.916047i | \(0.368638\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.0000 | − | 13.8564i | −0.937758 | − | 0.541415i | ||||
\(656\) | 19.5959 | + | 11.3137i | 0.765092 | + | 0.441726i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.00000 | − | 10.3923i | 0.233904 | − | 0.405134i | ||||
\(659\) | 4.89898 | − | 8.48528i | 0.190837 | − | 0.330540i | −0.754691 | − | 0.656081i | \(-0.772213\pi\) |
0.945528 | + | 0.325541i | \(0.105546\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.5000 | + | 32.0429i | 0.719567 | + | 1.24633i | 0.961172 | + | 0.275951i | \(0.0889928\pi\) |
−0.241605 | + | 0.970375i | \(0.577674\pi\) | |||||||
\(662\) | −31.8434 | −1.23763 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −24.0000 | − | 13.8564i | −0.931381 | − | 0.537733i | ||||
\(665\) | 25.4558i | 0.987135i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.7128i | 1.07304i | ||||||||
\(668\) | 9.79796 | 0.379094 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 48.4974i | 1.87362i | ||||||||
\(671\) | −26.9444 | − | 46.6690i | −1.04018 | − | 1.80164i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.50000 | + | 9.52628i | −0.212009 | + | 0.367211i | −0.952343 | − | 0.305028i | \(-0.901334\pi\) |
0.740334 | + | 0.672239i | \(0.234667\pi\) | |||||||
\(674\) | −13.4722 | − | 7.77817i | −0.518930 | − | 0.299604i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | − | 20.7846i | −0.461538 | − | 0.799408i | ||||
\(677\) | 12.2474 | + | 7.07107i | 0.470708 | + | 0.271763i | 0.716536 | − | 0.697550i | \(-0.245727\pi\) |
−0.245828 | + | 0.969313i | \(0.579060\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.5000 | + | 11.2583i | −0.748341 | + | 0.432055i | ||||
\(680\) | 19.5959 | − | 11.3137i | 0.751469 | − | 0.433861i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.0000 | + | 20.7846i | 0.459504 | + | 0.795884i | ||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −56.0000 | −2.13965 | ||||||||
\(686\) | 13.4722 | + | 23.3345i | 0.514371 | + | 0.890916i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 13.8564i | − | 0.528271i | ||||||
\(689\) | 4.89898 | − | 2.82843i | 0.186636 | − | 0.107754i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.0000 | + | 22.5167i | 1.48363 | + | 0.856574i | 0.999827 | − | 0.0186028i | \(-0.00592180\pi\) |
0.483803 | + | 0.875177i | \(0.339255\pi\) | |||||||
\(692\) | 9.79796 | − | 5.65685i | 0.372463 | − | 0.215041i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.0000 | + | 13.8564i | 0.911028 | + | 0.525982i | ||||
\(695\) | 12.2474 | − | 21.2132i | 0.464572 | − | 0.804663i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.00000 | − | 13.8564i | −0.303022 | − | 0.524849i | ||||
\(698\) | 32.5269i | 1.23116i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.3923i | 0.392792i | ||||||||
\(701\) | 2.82843i | 0.106828i | 0.998572 | + | 0.0534141i | \(0.0170103\pi\) | ||||
−0.998572 | + | 0.0534141i | \(0.982990\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.19615i | 0.195977i | ||||||||
\(704\) | 19.5959 | − | 33.9411i | 0.738549 | − | 1.27920i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.0000 | −0.602168 | ||||||||
\(707\) | 9.79796 | + | 16.9706i | 0.368490 | + | 0.638244i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.5000 | − | 21.6506i | 0.469447 | − | 0.813107i | −0.529943 | − | 0.848034i | \(-0.677787\pi\) |
0.999390 | + | 0.0349269i | \(0.0111198\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.00000 | 0.299813 | ||||||||
\(713\) | 14.6969 | + | 8.48528i | 0.550405 | + | 0.317776i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | + | 6.92820i | −0.448775 | + | 0.259100i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.0000 | + | 10.3923i | −0.671754 | + | 0.387837i | ||||
\(719\) | 29.3939 | 1.09621 | 0.548103 | − | 0.836411i | \(-0.315350\pi\) | ||||
0.548103 | + | 0.836411i | \(0.315350\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.0000 | −0.558629 | ||||||||
\(722\) | −9.79796 | + | 5.65685i | −0.364642 | + | 0.210526i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.0000 | − | 19.0526i | 0.408812 | − | 0.708083i | ||||
\(725\) | 14.6969 | − | 8.48528i | 0.545831 | − | 0.315135i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.0000 | − | 8.66025i | −0.556319 | − | 0.321191i | 0.195348 | − | 0.980734i | \(-0.437416\pi\) |
−0.751667 | + | 0.659543i | \(0.770750\pi\) | |||||||
\(728\) | −4.89898 | −0.181568 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.00000 | + | 3.46410i | −0.0740233 | + | 0.128212i | ||||
\(731\) | −4.89898 | + | 8.48528i | −0.181195 | + | 0.313839i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.0000 | − | 32.9090i | −0.701781 | − | 1.21552i | −0.967841 | − | 0.251564i | \(-0.919055\pi\) |
0.266060 | − | 0.963957i | \(-0.414278\pi\) | |||||||
\(734\) | 26.9444 | 0.994535 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 27.7128i | − | 1.02151i | ||||||
\(737\) | − | 59.3970i | − | 2.18792i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.3923i | 0.382287i | 0.981562 | + | 0.191144i | \(0.0612196\pi\) | ||||
−0.981562 | + | 0.191144i | \(0.938780\pi\) | |||||||
\(740\) | 5.65685i | 0.207950i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.8564i | 0.508685i | ||||||||
\(743\) | 17.1464 | + | 29.6985i | 0.629041 | + | 1.08953i | 0.987744 | + | 0.156080i | \(0.0498858\pi\) |
−0.358703 | + | 0.933452i | \(0.616781\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.0000 | + | 55.4256i | −1.17239 | + | 2.03064i | ||||
\(746\) | 30.6186 | + | 17.6777i | 1.12103 | + | 0.647225i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −24.0000 | + | 13.8564i | −0.877527 | + | 0.506640i | ||||
\(749\) | −22.0454 | − | 12.7279i | −0.805522 | − | 0.465068i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.5000 | − | 14.7224i | 0.930508 | − | 0.537229i | 0.0435359 | − | 0.999052i | \(-0.486138\pi\) |
0.886972 | + | 0.461823i | \(0.152804\pi\) | |||||||
\(752\) | 19.5959 | 0.714590 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.00000 | + | 6.92820i | 0.145671 | + | 0.252310i | ||||
\(755\) | −63.6867 | −2.31780 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.0000 | 1.70824 | 0.854122 | − | 0.520073i | \(-0.174095\pi\) | ||||
0.854122 | + | 0.520073i | \(0.174095\pi\) | |||||||
\(758\) | 11.0227 | + | 19.0919i | 0.400363 | + | 0.693448i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −36.0000 | + | 20.7846i | −1.30586 | + | 0.753937i | ||||
\(761\) | 2.44949 | − | 1.41421i | 0.0887939 | − | 0.0512652i | −0.454946 | − | 0.890519i | \(-0.650341\pi\) |
0.543740 | + | 0.839254i | \(0.317008\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.0000 | + | 8.66025i | 0.543036 | + | 0.313522i | ||||
\(764\) | −24.4949 | − | 42.4264i | −0.886194 | − | 1.53493i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | + | 13.8564i | 0.867155 | + | 0.500652i | ||||
\(767\) | −2.44949 | + | 4.24264i | −0.0884459 | + | 0.153193i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.500000 | + | 0.866025i | 0.0180305 | + | 0.0312297i | 0.874900 | − | 0.484304i | \(-0.160927\pi\) |
−0.856869 | + | 0.515534i | \(0.827594\pi\) | |||||||
\(770\) | − | 33.9411i | − | 1.22315i | ||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.00000 | 0.0719816 | ||||||||
\(773\) | 28.2843i | 1.01731i | 0.860969 | + | 0.508657i | \(0.169858\pi\) | ||||
−0.860969 | + | 0.508657i | \(0.830142\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10.3923i | − | 0.373303i | ||||||
\(776\) | −31.8434 | − | 18.3848i | −1.14311 | − | 0.659975i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.0000 | 0.717035 | ||||||||
\(779\) | 14.6969 | + | 25.4558i | 0.526572 | + | 0.912050i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −9.79796 | + | 16.9706i | −0.350374 | + | 0.606866i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.00000 | + | 13.8564i | −0.285714 | + | 0.494872i | ||||
\(785\) | 24.4949 | + | 14.1421i | 0.874260 | + | 0.504754i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.50000 | − | 4.33013i | 0.267346 | − | 0.154352i | −0.360335 | − | 0.932823i | \(-0.617338\pi\) |
0.627681 | + | 0.778471i | \(0.284004\pi\) | |||||||
\(788\) | 4.89898 | + | 2.82843i | 0.174519 | + | 0.100759i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.00000 | + | 3.46410i | −0.213470 | + | 0.123247i | ||||
\(791\) | −4.89898 | −0.174188 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.0000 | −0.390621 | ||||||||
\(794\) | −12.2474 | + | 7.07107i | −0.434646 | + | 0.250943i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.00000 | − | 5.19615i | −0.318997 | − | 0.184173i | ||||
\(797\) | −19.5959 | + | 11.3137i | −0.694123 | + | 0.400752i | −0.805155 | − | 0.593065i | \(-0.797918\pi\) |
0.111032 | + | 0.993817i | \(0.464584\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.0000 | − | 6.92820i | −0.424529 | − | 0.245102i | ||||
\(800\) | −14.6969 | + | 8.48528i | −0.519615 | + | 0.300000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16.0000 | + | 27.7128i | −0.564980 | + | 0.978573i | ||||
\(803\) | 2.44949 | − | 4.24264i | 0.0864406 | − | 0.149720i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.0000 | − | 20.7846i | −0.422944 | − | 0.732561i | ||||
\(806\) | 4.89898 | 0.172559 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16.0000 | + | 27.7128i | −0.562878 | + | 0.974933i | ||||
\(809\) | − | 22.6274i | − | 0.795538i | −0.917486 | − | 0.397769i | \(-0.869785\pi\) | ||
0.917486 | − | 0.397769i | \(-0.130215\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.1769i | − | 1.09477i | −0.836881 | − | 0.547385i | \(-0.815623\pi\) | ||
0.836881 | − | 0.547385i | \(-0.184377\pi\) | |||||||
\(812\) | −19.5959 | −0.687682 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 6.92820i | − | 0.242833i | ||||||
\(815\) | −7.34847 | − | 12.7279i | −0.257406 | − | 0.445840i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.00000 | − | 15.5885i | 0.314870 | − | 0.545371i | ||||
\(818\) | 1.22474 | + | 0.707107i | 0.0428222 | + | 0.0247234i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.0000 | + | 27.7128i | 0.558744 | + | 0.967773i | ||||
\(821\) | 26.9444 | + | 15.5563i | 0.940366 | + | 0.542920i | 0.890075 | − | 0.455814i | \(-0.150652\pi\) |
0.0502907 | + | 0.998735i | \(0.483985\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.5000 | − | 25.1147i | 1.51631 | − | 0.875445i | 0.516498 | − | 0.856288i | \(-0.327235\pi\) |
0.999816 | − | 0.0191564i | \(-0.00609804\pi\) | |||||||
\(824\) | −12.2474 | − | 21.2132i | −0.426660 | − | 0.738997i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.00000 | − | 10.3923i | −0.208767 | − | 0.361595i | ||||
\(827\) | 14.6969 | 0.511063 | 0.255531 | − | 0.966801i | \(-0.417750\pi\) | ||||
0.255531 | + | 0.966801i | \(0.417750\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.0000 | 0.382046 | 0.191023 | − | 0.981586i | \(-0.438820\pi\) | ||||
0.191023 | + | 0.981586i | \(0.438820\pi\) | |||||||
\(830\) | −19.5959 | − | 33.9411i | −0.680184 | − | 1.17811i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.00000 | − | 6.92820i | −0.138675 | − | 0.240192i | ||||
\(833\) | 9.79796 | − | 5.65685i | 0.339479 | − | 0.195998i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0000 | + | 6.92820i | 0.415277 | + | 0.239760i | ||||
\(836\) | 44.0908 | − | 25.4558i | 1.52491 | − | 0.880409i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.00000 | + | 3.46410i | 0.207267 | + | 0.119665i | ||||
\(839\) | −24.4949 | + | 42.4264i | −0.845658 | + | 1.46472i | 0.0393910 | + | 0.999224i | \(0.487458\pi\) |
−0.885049 | + | 0.465498i | \(0.845875\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.50000 | + | 2.59808i | 0.0517241 | + | 0.0895888i | ||||
\(842\) | − | 35.3553i | − | 1.21843i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 24.2487i | 0.834675i | ||||||||
\(845\) | − | 33.9411i | − | 1.16761i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.5167i | 0.773682i | ||||||||
\(848\) | −19.5959 | + | 11.3137i | −0.672927 | + | 0.388514i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.0000 | 0.411597 | ||||||||
\(851\) | −2.44949 | − | 4.24264i | −0.0839674 | − | 0.145436i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.5000 | − | 42.4352i | 0.838864 | − | 1.45296i | −0.0519811 | − | 0.998648i | \(-0.516554\pi\) |
0.890845 | − | 0.454307i | \(-0.150113\pi\) | |||||||
\(854\) | 13.4722 | − | 23.3345i | 0.461009 | − | 0.798491i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 41.5692i | − | 1.42081i | ||||||
\(857\) | 48.9898 | + | 28.2843i | 1.67346 | + | 0.966172i | 0.965678 | + | 0.259740i | \(0.0836370\pi\) |
0.707781 | + | 0.706432i | \(0.249696\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.5000 | + | 6.06218i | −0.358255 | + | 0.206839i | −0.668315 | − | 0.743878i | \(-0.732984\pi\) |
0.310060 | + | 0.950717i | \(0.399651\pi\) | |||||||
\(860\) | 9.79796 | − | 16.9706i | 0.334108 | − | 0.578691i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18.0000 | + | 10.3923i | −0.613082 | + | 0.353963i | ||||
\(863\) | −14.6969 | −0.500290 | −0.250145 | − | 0.968208i | \(-0.580478\pi\) | ||||
−0.250145 | + | 0.968208i | \(0.580478\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.0000 | 0.544016 | ||||||||
\(866\) | 31.8434 | − | 18.3848i | 1.08208 | − | 0.624740i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.00000 | + | 10.3923i | −0.203653 | + | 0.352738i | ||||
\(869\) | 7.34847 | − | 4.24264i | 0.249280 | − | 0.143922i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.5000 | − | 6.06218i | −0.355779 | − | 0.205409i | ||||
\(872\) | 28.2843i | 0.957826i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.0000 | − | 31.1769i | 0.608859 | − | 1.05457i | ||||
\(875\) | 4.89898 | − | 8.48528i | 0.165616 | − | 0.286855i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.500000 | + | 0.866025i | 0.0168838 | + | 0.0292436i | 0.874344 | − | 0.485307i | \(-0.161292\pi\) |
−0.857460 | + | 0.514551i | \(0.827959\pi\) | |||||||
\(878\) | −24.4949 | −0.826663 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 48.0000 | − | 27.7128i | 1.61808 | − | 0.934199i | ||||
\(881\) | 19.7990i | 0.667045i | 0.942742 | + | 0.333522i | \(0.108237\pi\) | ||||
−0.942742 | + | 0.333522i | \(0.891763\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 5.19615i | − | 0.174864i | −0.996170 | − | 0.0874322i | \(-0.972134\pi\) | ||
0.996170 | − | 0.0874322i | \(-0.0278661\pi\) | |||||||
\(884\) | 5.65685i | 0.190261i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 13.8564i | − | 0.465515i | ||||||
\(887\) | 24.4949 | + | 42.4264i | 0.822458 | + | 1.42454i | 0.903847 | + | 0.427857i | \(0.140731\pi\) |
−0.0813883 | + | 0.996682i | \(0.525935\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.00000 | + | 15.5885i | −0.301850 | + | 0.522820i | ||||
\(890\) | 9.79796 | + | 5.65685i | 0.328428 | + | 0.189618i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 42.0000 | − | 24.2487i | 1.40626 | − | 0.811907i | ||||
\(893\) | 22.0454 | + | 12.7279i | 0.737721 | + | 0.425924i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 19.5959 | 0.654654 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.0000 | − | 38.1051i | −0.734150 | − | 1.27158i | ||||
\(899\) | 19.5959 | 0.653560 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.0000 | 0.533037 | ||||||||
\(902\) | −19.5959 | − | 33.9411i | −0.652473 | − | 1.13012i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.00000 | − | 6.92820i | −0.133038 | − | 0.230429i | ||||
\(905\) | 26.9444 | − | 15.5563i | 0.895662 | − | 0.517111i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.50000 | − | 0.866025i | −0.0498067 | − | 0.0287559i | 0.474890 | − | 0.880045i | \(-0.342488\pi\) |
−0.524697 | + | 0.851289i | \(0.675821\pi\) | |||||||
\(908\) | 19.5959 | + | 33.9411i | 0.650313 | + | 1.12638i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.00000 | − | 3.46410i | −0.198898 | − | 0.114834i | ||||
\(911\) | 4.89898 | − | 8.48528i | 0.162310 | − | 0.281130i | −0.773386 | − | 0.633935i | \(-0.781439\pi\) |
0.935697 | + | 0.352805i | \(0.114772\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.0000 | + | 41.5692i | 0.794284 | + | 1.37574i | ||||
\(914\) | 2.82843i | 0.0935561i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.0000 | 0.660819 | ||||||||
\(917\) | 16.9706i | 0.560417i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 10.3923i | − | 0.342811i | −0.985201 | − | 0.171405i | \(-0.945169\pi\) | ||
0.985201 | − | 0.171405i | \(-0.0548307\pi\) | |||||||
\(920\) | 19.5959 | − | 33.9411i | 0.646058 | − | 1.11901i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.0000 | 0.658665 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.50000 | + | 2.59808i | −0.0493197 | + | 0.0854242i | ||||
\(926\) | −8.57321 | + | 14.8492i | −0.281733 | + | 0.487976i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −16.0000 | − | 27.7128i | −0.525226 | − | 0.909718i | ||||
\(929\) | −39.1918 | − | 22.6274i | −1.28584 | − | 0.742381i | −0.307932 | − | 0.951408i | \(-0.599637\pi\) |
−0.977910 | + | 0.209027i | \(0.932970\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0000 | + | 10.3923i | −0.589926 | + | 0.340594i | ||||
\(932\) | −39.1918 | − | 22.6274i | −1.28377 | − | 0.741186i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.0000 | − | 10.3923i | 0.588978 | − | 0.340047i | ||||
\(935\) | −39.1918 | −1.28171 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.0000 | −1.20874 | −0.604369 | − | 0.796705i | \(-0.706575\pi\) | ||||
−0.604369 | + | 0.796705i | \(0.706575\pi\) | |||||||
\(938\) | 25.7196 | − | 14.8492i | 0.839776 | − | 0.484845i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 24.0000 | + | 13.8564i | 0.782794 | + | 0.451946i | ||||
\(941\) | −41.6413 | + | 24.0416i | −1.35747 | + | 0.783735i | −0.989282 | − | 0.146017i | \(-0.953354\pi\) |
−0.368186 | + | 0.929752i | \(0.620021\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.0000 | − | 13.8564i | −0.781548 | − | 0.451227i | ||||
\(944\) | 9.79796 | − | 16.9706i | 0.318896 | − | 0.552345i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.0000 | + | 20.7846i | −0.390154 | + | 0.675766i | ||||
\(947\) | −17.1464 | + | 29.6985i | −0.557184 | + | 0.965071i | 0.440546 | + | 0.897730i | \(0.354785\pi\) |
−0.997730 | + | 0.0673410i | \(0.978548\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.500000 | − | 0.866025i | −0.0162307 | − | 0.0281124i | ||||
\(950\) | −22.0454 | −0.715247 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.0000 | − | 6.92820i | −0.388922 | − | 0.224544i | ||||
\(953\) | 2.82843i | 0.0916217i | 0.998950 | + | 0.0458109i | \(0.0145872\pi\) | ||||
−0.998950 | + | 0.0458109i | \(0.985413\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 69.2820i | − | 2.24191i | ||||||
\(956\) | 39.1918 | 1.26755 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 13.8564i | − | 0.447680i | ||||||
\(959\) | 17.1464 | + | 29.6985i | 0.553687 | + | 0.959014i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.50000 | + | 16.4545i | −0.306452 | + | 0.530790i | ||||
\(962\) | −1.22474 | − | 0.707107i | −0.0394874 | − | 0.0227980i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −25.0000 | − | 43.3013i | −0.805196 | − | 1.39464i | ||||
\(965\) | 2.44949 | + | 1.41421i | 0.0788519 | + | 0.0455251i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.5000 | + | 26.8468i | −1.49534 | + | 0.863334i | −0.999986 | − | 0.00535699i | \(-0.998295\pi\) |
−0.495354 | + | 0.868691i | \(0.664961\pi\) | |||||||
\(968\) | −31.8434 | + | 18.3848i | −1.02348 | + | 0.590909i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −26.0000 | − | 45.0333i | −0.834810 | − | 1.44593i | ||||
\(971\) | −14.6969 | −0.471647 | −0.235824 | − | 0.971796i | \(-0.575779\pi\) | ||||
−0.235824 | + | 0.971796i | \(0.575779\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.0000 | −0.480878 | ||||||||
\(974\) | −18.3712 | − | 31.8198i | −0.588650 | − | 1.01957i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 44.0000 | 1.40841 | ||||||||
\(977\) | −4.89898 | + | 2.82843i | −0.156732 | + | 0.0904894i | −0.576315 | − | 0.817228i | \(-0.695510\pi\) |
0.419583 | + | 0.907717i | \(0.362176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.0000 | − | 6.92820i | −0.383522 | − | 0.221426i | ||||
\(980\) | −19.5959 | + | 11.3137i | −0.625969 | + | 0.361403i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −30.0000 | − | 17.3205i | −0.957338 | − | 0.552720i | ||||
\(983\) | −17.1464 | + | 29.6985i | −0.546886 | + | 0.947235i | 0.451599 | + | 0.892221i | \(0.350854\pi\) |
−0.998486 | + | 0.0550138i | \(0.982480\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.00000 | + | 6.92820i | 0.127451 | + | 0.220751i | ||||
\(986\) | 22.6274i | 0.720604i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 10.3923i | − | 0.330623i | ||||||
\(989\) | 16.9706i | 0.539633i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.3731i | 1.15543i | 0.816239 | + | 0.577714i | \(0.196055\pi\) | ||||
−0.816239 | + | 0.577714i | \(0.803945\pi\) | |||||||
\(992\) | −19.5959 | −0.622171 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.34847 | − | 12.7279i | −0.232962 | − | 0.403502i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.0000 | − | 29.4449i | 0.538395 | − | 0.932528i | −0.460595 | − | 0.887610i | \(-0.652364\pi\) |
0.998991 | − | 0.0449179i | \(-0.0143026\pi\) | |||||||
\(998\) | 17.1464 | − | 29.6985i | 0.542761 | − | 0.940089i | ||||
\(999\) | 0 | 0 |
(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 | 324.2.h.b.107.2 | 4 | ||
3.2 | odd | 2 | inner | 324.2.h.b.107.1 | 4 | ||
4.3 | odd | 2 | 324.2.h.a.107.2 | 4 | |||
9.2 | odd | 6 | 108.2.b.b.107.4 | yes | 4 | ||
9.4 | even | 3 | 324.2.h.a.215.2 | 4 | |||
9.5 | odd | 6 | 324.2.h.a.215.1 | 4 | |||
9.7 | even | 3 | 108.2.b.b.107.1 | ✓ | 4 | ||
12.11 | even | 2 | 324.2.h.a.107.1 | 4 | |||
36.7 | odd | 6 | 108.2.b.b.107.3 | yes | 4 | ||
36.11 | even | 6 | 108.2.b.b.107.2 | yes | 4 | ||
36.23 | even | 6 | inner | 324.2.h.b.215.2 | 4 | ||
36.31 | odd | 6 | inner | 324.2.h.b.215.1 | 4 | ||
72.11 | even | 6 | 1728.2.c.d.1727.3 | 4 | |||
72.29 | odd | 6 | 1728.2.c.d.1727.4 | 4 | |||
72.43 | odd | 6 | 1728.2.c.d.1727.1 | 4 | |||
72.61 | even | 6 | 1728.2.c.d.1727.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.b.b.107.1 | ✓ | 4 | 9.7 | even | 3 | ||
108.2.b.b.107.2 | yes | 4 | 36.11 | even | 6 | ||
108.2.b.b.107.3 | yes | 4 | 36.7 | odd | 6 | ||
108.2.b.b.107.4 | yes | 4 | 9.2 | odd | 6 | ||
324.2.h.a.107.1 | 4 | 12.11 | even | 2 | |||
324.2.h.a.107.2 | 4 | 4.3 | odd | 2 | |||
324.2.h.a.215.1 | 4 | 9.5 | odd | 6 | |||
324.2.h.a.215.2 | 4 | 9.4 | even | 3 | |||
324.2.h.b.107.1 | 4 | 3.2 | odd | 2 | inner | ||
324.2.h.b.107.2 | 4 | 1.1 | even | 1 | trivial | ||
324.2.h.b.215.1 | 4 | 36.31 | odd | 6 | inner | ||
324.2.h.b.215.2 | 4 | 36.23 | even | 6 | inner | ||
1728.2.c.d.1727.1 | 4 | 72.43 | odd | 6 | |||
1728.2.c.d.1727.2 | 4 | 72.61 | even | 6 | |||
1728.2.c.d.1727.3 | 4 | 72.11 | even | 6 | |||
1728.2.c.d.1727.4 | 4 | 72.29 | odd | 6 |