Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(757,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, 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("1638.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.r (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: | \(13.0794958511\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 757.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.757 |
Dual form | 1638.2.r.l.1387.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | − | 1.73205i | −0.316228 | − | 0.547723i | ||||
\(11\) | 1.50000 | + | 2.59808i | 0.452267 | + | 0.783349i | 0.998526 | − | 0.0542666i | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.50000 | + | 0.866025i | 0.970725 | + | 0.240192i | ||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.50000 | + | 6.06218i | −0.848875 | + | 1.47029i | 0.0333386 | + | 0.999444i | \(0.489386\pi\) |
−0.882213 | + | 0.470850i | \(0.843947\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.50000 | − | 4.33013i | 0.573539 | − | 0.993399i | −0.422659 | − | 0.906289i | \(-0.638903\pi\) |
0.996199 | − | 0.0871106i | \(-0.0277634\pi\) | |||||||
\(20\) | −1.00000 | + | 1.73205i | −0.223607 | + | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.50000 | − | 2.59808i | 0.319801 | − | 0.553912i | ||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −1.00000 | − | 3.46410i | −0.196116 | − | 0.679366i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.500000 | + | 0.866025i | 0.0944911 | + | 0.163663i | ||||
\(29\) | 2.50000 | + | 4.33013i | 0.464238 | + | 0.804084i | 0.999167 | − | 0.0408130i | \(-0.0129948\pi\) |
−0.534928 | + | 0.844897i | \(0.679661\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.00000 | 1.20049 | ||||||||
\(35\) | 1.00000 | − | 1.73205i | 0.169031 | − | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | + | 1.73205i | 0.164399 | + | 0.284747i | 0.936442 | − | 0.350823i | \(-0.114098\pi\) |
−0.772043 | + | 0.635571i | \(0.780765\pi\) | |||||||
\(38\) | −5.00000 | −0.811107 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.00000 | 0.316228 | ||||||||
\(41\) | −2.50000 | − | 4.33013i | −0.390434 | − | 0.676252i | 0.602072 | − | 0.798441i | \(-0.294342\pi\) |
−0.992507 | + | 0.122189i | \(0.961009\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | + | 1.73205i | −0.152499 | + | 0.264135i | −0.932145 | − | 0.362084i | \(-0.882065\pi\) |
0.779647 | + | 0.626219i | \(0.215399\pi\) | |||||||
\(44\) | −3.00000 | −0.452267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | − | 5.19615i | 0.442326 | − | 0.766131i | ||||
\(47\) | 1.00000 | 0.145865 | 0.0729325 | − | 0.997337i | \(-0.476764\pi\) | ||||
0.0729325 | + | 0.997337i | \(0.476764\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0.500000 | + | 0.866025i | 0.0707107 | + | 0.122474i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.50000 | + | 2.59808i | −0.346688 | + | 0.360288i | ||||
\(53\) | −3.00000 | −0.412082 | −0.206041 | − | 0.978543i | \(-0.566058\pi\) | ||||
−0.206041 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000 | + | 5.19615i | 0.404520 | + | 0.700649i | ||||
\(56\) | 0.500000 | − | 0.866025i | 0.0668153 | − | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.50000 | − | 4.33013i | 0.328266 | − | 0.568574i | ||||
\(59\) | −3.00000 | + | 5.19615i | −0.390567 | + | 0.676481i | −0.992524 | − | 0.122047i | \(-0.961054\pi\) |
0.601958 | + | 0.798528i | \(0.294388\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.50000 | + | 6.06218i | −0.448129 | + | 0.776182i | −0.998264 | − | 0.0588933i | \(-0.981243\pi\) |
0.550135 | + | 0.835076i | \(0.314576\pi\) | |||||||
\(62\) | 1.00000 | + | 1.73205i | 0.127000 | + | 0.219971i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.00000 | + | 1.73205i | 0.868243 | + | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | −3.50000 | − | 6.06218i | −0.424437 | − | 0.735147i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00000 | −0.239046 | ||||||||
\(71\) | 4.00000 | − | 6.92820i | 0.474713 | − | 0.822226i | −0.524868 | − | 0.851184i | \(-0.675885\pi\) |
0.999581 | + | 0.0289572i | \(0.00921865\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0000 | 1.40449 | 0.702247 | − | 0.711934i | \(-0.252180\pi\) | ||||
0.702247 | + | 0.711934i | \(0.252180\pi\) | |||||||
\(74\) | 1.00000 | − | 1.73205i | 0.116248 | − | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.50000 | + | 4.33013i | 0.286770 | + | 0.496700i | ||||
\(77\) | 3.00000 | 0.341882 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.00000 | 0.337526 | 0.168763 | − | 0.985657i | \(-0.446023\pi\) | ||||
0.168763 | + | 0.985657i | \(0.446023\pi\) | |||||||
\(80\) | −1.00000 | − | 1.73205i | −0.111803 | − | 0.193649i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.50000 | + | 4.33013i | −0.276079 | + | 0.478183i | ||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.00000 | + | 12.1244i | −0.759257 | + | 1.31507i | ||||
\(86\) | 2.00000 | 0.215666 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.50000 | + | 2.59808i | 0.159901 | + | 0.276956i | ||||
\(89\) | −5.50000 | − | 9.52628i | −0.582999 | − | 1.00978i | −0.995122 | − | 0.0986553i | \(-0.968546\pi\) |
0.412123 | − | 0.911128i | \(-0.364787\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.50000 | − | 2.59808i | 0.262071 | − | 0.272352i | ||||
\(92\) | −6.00000 | −0.625543 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.500000 | − | 0.866025i | −0.0515711 | − | 0.0893237i | ||||
\(95\) | 5.00000 | − | 8.66025i | 0.512989 | − | 0.888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.00000 | − | 1.73205i | 0.101535 | − | 0.175863i | −0.810782 | − | 0.585348i | \(-0.800958\pi\) |
0.912317 | + | 0.409484i | \(0.134291\pi\) | |||||||
\(98\) | −0.500000 | + | 0.866025i | −0.0505076 | + | 0.0874818i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | 7.00000 | + | 12.1244i | 0.696526 | + | 1.20642i | 0.969664 | + | 0.244443i | \(0.0786053\pi\) |
−0.273138 | + | 0.961975i | \(0.588061\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0000 | 0.985329 | 0.492665 | − | 0.870219i | \(-0.336023\pi\) | ||||
0.492665 | + | 0.870219i | \(0.336023\pi\) | |||||||
\(104\) | 3.50000 | + | 0.866025i | 0.343203 | + | 0.0849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.50000 | + | 2.59808i | 0.145693 | + | 0.252347i | ||||
\(107\) | 7.50000 | + | 12.9904i | 0.725052 | + | 1.25583i | 0.958952 | + | 0.283567i | \(0.0915178\pi\) |
−0.233900 | + | 0.972261i | \(0.575149\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.0000 | −1.53252 | −0.766261 | − | 0.642529i | \(-0.777885\pi\) | ||||
−0.766261 | + | 0.642529i | \(0.777885\pi\) | |||||||
\(110\) | 3.00000 | − | 5.19615i | 0.286039 | − | 0.495434i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 3.00000 | − | 5.19615i | 0.282216 | − | 0.488813i | −0.689714 | − | 0.724082i | \(-0.742264\pi\) |
0.971930 | + | 0.235269i | \(0.0755971\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.00000 | + | 10.3923i | 0.559503 | + | 0.969087i | ||||
\(116\) | −5.00000 | −0.464238 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000 | 0.552345 | ||||||||
\(119\) | 3.50000 | + | 6.06218i | 0.320844 | + | 0.555719i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 7.00000 | 0.633750 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.00000 | − | 1.73205i | 0.0898027 | − | 0.155543i | ||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00000 | + | 10.3923i | 0.532414 | + | 0.922168i | 0.999284 | + | 0.0378419i | \(0.0120483\pi\) |
−0.466870 | + | 0.884326i | \(0.654618\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.00000 | − | 6.92820i | −0.175412 | − | 0.607644i | ||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.50000 | − | 4.33013i | −0.216777 | − | 0.375470i | ||||
\(134\) | −1.00000 | + | 1.73205i | −0.0863868 | + | 0.149626i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.50000 | + | 6.06218i | −0.300123 | + | 0.519827i | ||||
\(137\) | 9.00000 | − | 15.5885i | 0.768922 | − | 1.33181i | −0.169226 | − | 0.985577i | \(-0.554127\pi\) |
0.938148 | − | 0.346235i | \(-0.112540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.50000 | − | 16.4545i | 0.805779 | − | 1.39565i | −0.109984 | − | 0.993933i | \(-0.535080\pi\) |
0.915764 | − | 0.401718i | \(-0.131587\pi\) | |||||||
\(140\) | 1.00000 | + | 1.73205i | 0.0845154 | + | 0.146385i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.00000 | −0.671345 | ||||||||
\(143\) | 3.00000 | + | 10.3923i | 0.250873 | + | 0.869048i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.00000 | + | 8.66025i | 0.415227 | + | 0.719195i | ||||
\(146\) | −6.00000 | − | 10.3923i | −0.496564 | − | 0.860073i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | 7.00000 | − | 12.1244i | 0.573462 | − | 0.993266i | −0.422744 | − | 0.906249i | \(-0.638933\pi\) |
0.996207 | − | 0.0870170i | \(-0.0277334\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.0000 | 1.05792 | 0.528962 | − | 0.848645i | \(-0.322581\pi\) | ||||
0.528962 | + | 0.848645i | \(0.322581\pi\) | |||||||
\(152\) | 2.50000 | − | 4.33013i | 0.202777 | − | 0.351220i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.50000 | − | 2.59808i | −0.120873 | − | 0.209359i | ||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.0000 | −1.43656 | −0.718278 | − | 0.695756i | \(-0.755069\pi\) | ||||
−0.718278 | + | 0.695756i | \(0.755069\pi\) | |||||||
\(158\) | −1.50000 | − | 2.59808i | −0.119334 | − | 0.206692i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | + | 1.73205i | −0.0790569 | + | 0.136931i | ||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.00000 | − | 12.1244i | 0.548282 | − | 0.949653i | −0.450110 | − | 0.892973i | \(-0.648615\pi\) |
0.998392 | − | 0.0566798i | \(-0.0180514\pi\) | |||||||
\(164\) | 5.00000 | 0.390434 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.00000 | − | 6.92820i | −0.310460 | − | 0.537733i | ||||
\(167\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | + | 6.06218i | 0.884615 | + | 0.466321i | ||||
\(170\) | 14.0000 | 1.07375 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.00000 | − | 1.73205i | −0.0762493 | − | 0.132068i | ||||
\(173\) | 6.00000 | − | 10.3923i | 0.456172 | − | 0.790112i | −0.542583 | − | 0.840002i | \(-0.682554\pi\) |
0.998755 | + | 0.0498898i | \(0.0158870\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.500000 | + | 0.866025i | −0.0377964 | + | 0.0654654i | ||||
\(176\) | 1.50000 | − | 2.59808i | 0.113067 | − | 0.195837i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.50000 | + | 9.52628i | −0.412242 | + | 0.714025i | ||||
\(179\) | 10.0000 | + | 17.3205i | 0.747435 | + | 1.29460i | 0.949048 | + | 0.315130i | \(0.102048\pi\) |
−0.201613 | + | 0.979465i | \(0.564618\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.00000 | −0.668965 | −0.334482 | − | 0.942402i | \(-0.608561\pi\) | ||||
−0.334482 | + | 0.942402i | \(0.608561\pi\) | |||||||
\(182\) | −3.50000 | − | 0.866025i | −0.259437 | − | 0.0641941i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.00000 | + | 5.19615i | 0.221163 | + | 0.383065i | ||||
\(185\) | 2.00000 | + | 3.46410i | 0.147043 | + | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.0000 | −1.53567 | ||||||||
\(188\) | −0.500000 | + | 0.866025i | −0.0364662 | + | 0.0631614i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.0000 | −0.725476 | ||||||||
\(191\) | −2.00000 | + | 3.46410i | −0.144715 | + | 0.250654i | −0.929267 | − | 0.369410i | \(-0.879560\pi\) |
0.784552 | + | 0.620063i | \(0.212893\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.50000 | − | 11.2583i | −0.467880 | − | 0.810392i | 0.531446 | − | 0.847092i | \(-0.321649\pi\) |
−0.999326 | + | 0.0366998i | \(0.988315\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −4.50000 | − | 7.79423i | −0.320612 | − | 0.555316i | 0.660003 | − | 0.751263i | \(-0.270555\pi\) |
−0.980614 | + | 0.195947i | \(0.937222\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.0000 | − | 22.5167i | 0.921546 | − | 1.59616i | 0.124521 | − | 0.992217i | \(-0.460261\pi\) |
0.797025 | − | 0.603947i | \(-0.206406\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.00000 | − | 12.1244i | 0.492518 | − | 0.853067i | ||||
\(203\) | 5.00000 | 0.350931 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.00000 | − | 8.66025i | −0.349215 | − | 0.604858i | ||||
\(206\) | −5.00000 | − | 8.66025i | −0.348367 | − | 0.603388i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | − | 3.46410i | −0.0693375 | − | 0.240192i | ||||
\(209\) | 15.0000 | 1.03757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.00000 | + | 8.66025i | 0.344214 | + | 0.596196i | 0.985211 | − | 0.171347i | \(-0.0548120\pi\) |
−0.640996 | + | 0.767544i | \(0.721479\pi\) | |||||||
\(212\) | 1.50000 | − | 2.59808i | 0.103020 | − | 0.178437i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.50000 | − | 12.9904i | 0.512689 | − | 0.888004i | ||||
\(215\) | −2.00000 | + | 3.46410i | −0.136399 | + | 0.236250i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.00000 | + | 1.73205i | −0.0678844 | + | 0.117579i | ||||
\(218\) | 8.00000 | + | 13.8564i | 0.541828 | + | 0.938474i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.00000 | −0.404520 | ||||||||
\(221\) | −17.5000 | + | 18.1865i | −1.17718 | + | 1.22336i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.00000 | + | 3.46410i | 0.133930 | + | 0.231973i | 0.925188 | − | 0.379509i | \(-0.123907\pi\) |
−0.791258 | + | 0.611482i | \(0.790574\pi\) | |||||||
\(224\) | 0.500000 | + | 0.866025i | 0.0334077 | + | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 7.00000 | − | 12.1244i | 0.464606 | − | 0.804722i | −0.534577 | − | 0.845120i | \(-0.679529\pi\) |
0.999184 | + | 0.0403978i | \(0.0128625\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.0000 | 1.78421 | 0.892105 | − | 0.451828i | \(-0.149228\pi\) | ||||
0.892105 | + | 0.451828i | \(0.149228\pi\) | |||||||
\(230\) | 6.00000 | − | 10.3923i | 0.395628 | − | 0.685248i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.50000 | + | 4.33013i | 0.164133 | + | 0.284287i | ||||
\(233\) | −26.0000 | −1.70332 | −0.851658 | − | 0.524097i | \(-0.824403\pi\) | ||||
−0.851658 | + | 0.524097i | \(0.824403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.00000 | 0.130466 | ||||||||
\(236\) | −3.00000 | − | 5.19615i | −0.195283 | − | 0.338241i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.50000 | − | 6.06218i | 0.226871 | − | 0.392953i | ||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0000 | + | 24.2487i | −0.901819 | + | 1.56200i | −0.0766885 | + | 0.997055i | \(0.524435\pi\) |
−0.825131 | + | 0.564942i | \(0.808899\pi\) | |||||||
\(242\) | −2.00000 | −0.128565 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.50000 | − | 6.06218i | −0.224065 | − | 0.388091i | ||||
\(245\) | −1.00000 | − | 1.73205i | −0.0638877 | − | 0.110657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.5000 | − | 12.9904i | 0.795356 | − | 0.826558i | ||||
\(248\) | −2.00000 | −0.127000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.00000 | + | 10.3923i | 0.379473 | + | 0.657267i | ||||
\(251\) | −6.00000 | + | 10.3923i | −0.378717 | + | 0.655956i | −0.990876 | − | 0.134778i | \(-0.956968\pi\) |
0.612159 | + | 0.790735i | \(0.290301\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.00000 | + | 15.5885i | −0.565825 | + | 0.980038i | ||||
\(254\) | 6.00000 | − | 10.3923i | 0.376473 | − | 0.652071i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −7.50000 | − | 12.9904i | −0.467837 | − | 0.810318i | 0.531487 | − | 0.847066i | \(-0.321633\pi\) |
−0.999325 | + | 0.0367485i | \(0.988300\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00000 | 0.124274 | ||||||||
\(260\) | −5.00000 | + | 5.19615i | −0.310087 | + | 0.322252i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.00000 | + | 6.92820i | 0.247121 | + | 0.428026i | ||||
\(263\) | −12.0000 | − | 20.7846i | −0.739952 | − | 1.28163i | −0.952517 | − | 0.304487i | \(-0.901515\pi\) |
0.212565 | − | 0.977147i | \(-0.431818\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | −2.50000 | + | 4.33013i | −0.153285 | + | 0.265497i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.00000 | 0.122169 | ||||||||
\(269\) | −12.0000 | + | 20.7846i | −0.731653 | + | 1.26726i | 0.224523 | + | 0.974469i | \(0.427917\pi\) |
−0.956176 | + | 0.292791i | \(0.905416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.00000 | − | 1.73205i | −0.0607457 | − | 0.105215i | 0.834053 | − | 0.551684i | \(-0.186015\pi\) |
−0.894799 | + | 0.446469i | \(0.852681\pi\) | |||||||
\(272\) | 7.00000 | 0.424437 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.0000 | −1.08742 | ||||||||
\(275\) | −1.50000 | − | 2.59808i | −0.0904534 | − | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.00000 | + | 5.19615i | −0.180253 | + | 0.312207i | −0.941966 | − | 0.335707i | \(-0.891025\pi\) |
0.761714 | + | 0.647913i | \(0.224358\pi\) | |||||||
\(278\) | −19.0000 | −1.13954 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.00000 | − | 1.73205i | 0.0597614 | − | 0.103510i | ||||
\(281\) | −16.0000 | −0.954480 | −0.477240 | − | 0.878773i | \(-0.658363\pi\) | ||||
−0.477240 | + | 0.878773i | \(0.658363\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.0000 | − | 24.2487i | −0.832214 | − | 1.44144i | −0.896279 | − | 0.443491i | \(-0.853740\pi\) |
0.0640654 | − | 0.997946i | \(-0.479593\pi\) | |||||||
\(284\) | 4.00000 | + | 6.92820i | 0.237356 | + | 0.411113i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.50000 | − | 7.79423i | 0.443484 | − | 0.460882i | ||||
\(287\) | −5.00000 | −0.295141 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | − | 27.7128i | −0.941176 | − | 1.63017i | ||||
\(290\) | 5.00000 | − | 8.66025i | 0.293610 | − | 0.508548i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.00000 | + | 10.3923i | −0.351123 | + | 0.608164i | ||||
\(293\) | 6.00000 | − | 10.3923i | 0.350524 | − | 0.607125i | −0.635818 | − | 0.771839i | \(-0.719337\pi\) |
0.986341 | + | 0.164714i | \(0.0526703\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | + | 10.3923i | −0.349334 | + | 0.605063i | ||||
\(296\) | 1.00000 | + | 1.73205i | 0.0581238 | + | 0.100673i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.0000 | −0.810998 | ||||||||
\(299\) | 6.00000 | + | 20.7846i | 0.346989 | + | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.00000 | + | 1.73205i | 0.0576390 | + | 0.0998337i | ||||
\(302\) | −6.50000 | − | 11.2583i | −0.374033 | − | 0.647844i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.00000 | −0.286770 | ||||||||
\(305\) | −7.00000 | + | 12.1244i | −0.400819 | + | 0.694239i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.00000 | 0.513657 | 0.256829 | − | 0.966457i | \(-0.417322\pi\) | ||||
0.256829 | + | 0.966457i | \(0.417322\pi\) | |||||||
\(308\) | −1.50000 | + | 2.59808i | −0.0854704 | + | 0.148039i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.00000 | + | 3.46410i | 0.113592 | + | 0.196748i | ||||
\(311\) | −23.0000 | −1.30421 | −0.652105 | − | 0.758129i | \(-0.726114\pi\) | ||||
−0.652105 | + | 0.758129i | \(0.726114\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.0000 | 1.58265 | 0.791327 | − | 0.611393i | \(-0.209391\pi\) | ||||
0.791327 | + | 0.611393i | \(0.209391\pi\) | |||||||
\(314\) | 9.00000 | + | 15.5885i | 0.507899 | + | 0.879708i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.50000 | + | 2.59808i | −0.0843816 | + | 0.146153i | ||||
\(317\) | −30.0000 | −1.68497 | −0.842484 | − | 0.538721i | \(-0.818908\pi\) | ||||
−0.842484 | + | 0.538721i | \(0.818908\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.50000 | + | 12.9904i | −0.419919 | + | 0.727322i | ||||
\(320\) | 2.00000 | 0.111803 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.00000 | − | 5.19615i | −0.167183 | − | 0.289570i | ||||
\(323\) | 17.5000 | + | 30.3109i | 0.973726 | + | 1.68654i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.50000 | − | 0.866025i | −0.194145 | − | 0.0480384i | ||||
\(326\) | −14.0000 | −0.775388 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.50000 | − | 4.33013i | −0.138039 | − | 0.239091i | ||||
\(329\) | 0.500000 | − | 0.866025i | 0.0275659 | − | 0.0477455i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.0000 | + | 19.0526i | −0.604615 | + | 1.04722i | 0.387498 | + | 0.921871i | \(0.373340\pi\) |
−0.992112 | + | 0.125353i | \(0.959994\pi\) | |||||||
\(332\) | −4.00000 | + | 6.92820i | −0.219529 | + | 0.380235i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.00000 | − | 3.46410i | −0.109272 | − | 0.189264i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.0000 | −0.926049 | −0.463025 | − | 0.886345i | \(-0.653236\pi\) | ||||
−0.463025 | + | 0.886345i | \(0.653236\pi\) | |||||||
\(338\) | −0.500000 | − | 12.9904i | −0.0271964 | − | 0.706584i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.00000 | − | 12.1244i | −0.379628 | − | 0.657536i | ||||
\(341\) | −3.00000 | − | 5.19615i | −0.162459 | − | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −1.00000 | + | 1.73205i | −0.0539164 | + | 0.0933859i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.0000 | −0.645124 | ||||||||
\(347\) | 8.50000 | − | 14.7224i | 0.456304 | − | 0.790342i | −0.542458 | − | 0.840083i | \(-0.682506\pi\) |
0.998762 | + | 0.0497412i | \(0.0158397\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.00000 | + | 15.5885i | 0.481759 | + | 0.834431i | 0.999781 | − | 0.0209364i | \(-0.00666475\pi\) |
−0.518022 | + | 0.855367i | \(0.673331\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.00000 | −0.159901 | ||||||||
\(353\) | 7.00000 | + | 12.1244i | 0.372572 | + | 0.645314i | 0.989960 | − | 0.141344i | \(-0.0451425\pi\) |
−0.617388 | + | 0.786659i | \(0.711809\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | − | 13.8564i | 0.424596 | − | 0.735422i | ||||
\(356\) | 11.0000 | 0.582999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.0000 | − | 17.3205i | 0.528516 | − | 0.915417i | ||||
\(359\) | −18.0000 | −0.950004 | −0.475002 | − | 0.879985i | \(-0.657553\pi\) | ||||
−0.475002 | + | 0.879985i | \(0.657553\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 4.50000 | + | 7.79423i | 0.236515 | + | 0.409656i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.00000 | + | 3.46410i | 0.0524142 | + | 0.181568i | ||||
\(365\) | 24.0000 | 1.25622 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.00000 | + | 8.66025i | 0.260998 | + | 0.452062i | 0.966507 | − | 0.256639i | \(-0.0826151\pi\) |
−0.705509 | + | 0.708700i | \(0.749282\pi\) | |||||||
\(368\) | 3.00000 | − | 5.19615i | 0.156386 | − | 0.270868i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.00000 | − | 3.46410i | 0.103975 | − | 0.180090i | ||||
\(371\) | −1.50000 | + | 2.59808i | −0.0778761 | + | 0.134885i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.00000 | + | 3.46410i | −0.103556 | + | 0.179364i | −0.913147 | − | 0.407630i | \(-0.866355\pi\) |
0.809591 | + | 0.586994i | \(0.199689\pi\) | |||||||
\(374\) | 10.5000 | + | 18.1865i | 0.542942 | + | 0.940403i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.00000 | 0.0515711 | ||||||||
\(377\) | 5.00000 | + | 17.3205i | 0.257513 | + | 0.892052i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0000 | + | 17.3205i | 0.513665 | + | 0.889695i | 0.999874 | + | 0.0158521i | \(0.00504609\pi\) |
−0.486209 | + | 0.873843i | \(0.661621\pi\) | |||||||
\(380\) | 5.00000 | + | 8.66025i | 0.256495 | + | 0.444262i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.00000 | 0.204658 | ||||||||
\(383\) | 15.5000 | − | 26.8468i | 0.792013 | − | 1.37181i | −0.132706 | − | 0.991155i | \(-0.542367\pi\) |
0.924719 | − | 0.380651i | \(-0.124300\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | 0.305788 | ||||||||
\(386\) | −6.50000 | + | 11.2583i | −0.330841 | + | 0.573034i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.00000 | + | 1.73205i | 0.0507673 | + | 0.0879316i | ||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −42.0000 | −2.12403 | ||||||||
\(392\) | −0.500000 | − | 0.866025i | −0.0252538 | − | 0.0437409i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.50000 | + | 7.79423i | −0.226707 | + | 0.392668i | ||||
\(395\) | 6.00000 | 0.301893 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.50000 | − | 12.9904i | 0.376414 | − | 0.651969i | −0.614123 | − | 0.789210i | \(-0.710490\pi\) |
0.990538 | + | 0.137241i | \(0.0438236\pi\) | |||||||
\(398\) | −26.0000 | −1.30326 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | 9.00000 | + | 15.5885i | 0.449439 | + | 0.778450i | 0.998350 | − | 0.0574304i | \(-0.0182907\pi\) |
−0.548911 | + | 0.835881i | \(0.684957\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.00000 | − | 1.73205i | −0.348695 | − | 0.0862796i | ||||
\(404\) | −14.0000 | −0.696526 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.50000 | − | 4.33013i | −0.124073 | − | 0.214901i | ||||
\(407\) | −3.00000 | + | 5.19615i | −0.148704 | + | 0.257564i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(410\) | −5.00000 | + | 8.66025i | −0.246932 | + | 0.427699i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.00000 | + | 8.66025i | −0.246332 | + | 0.426660i | ||||
\(413\) | 3.00000 | + | 5.19615i | 0.147620 | + | 0.255686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.0000 | 0.785409 | ||||||||
\(416\) | −2.50000 | + | 2.59808i | −0.122573 | + | 0.127381i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.50000 | − | 12.9904i | −0.366837 | − | 0.635380i | ||||
\(419\) | 2.00000 | + | 3.46410i | 0.0977064 | + | 0.169232i | 0.910735 | − | 0.412991i | \(-0.135516\pi\) |
−0.813029 | + | 0.582224i | \(0.802183\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | 5.00000 | − | 8.66025i | 0.243396 | − | 0.421575i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.00000 | −0.145693 | ||||||||
\(425\) | 3.50000 | − | 6.06218i | 0.169775 | − | 0.294059i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.50000 | + | 6.06218i | 0.169377 | + | 0.293369i | ||||
\(428\) | −15.0000 | −0.725052 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.00000 | 0.192897 | ||||||||
\(431\) | −4.00000 | − | 6.92820i | −0.192673 | − | 0.333720i | 0.753462 | − | 0.657491i | \(-0.228382\pi\) |
−0.946135 | + | 0.323772i | \(0.895049\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.0000 | + | 22.5167i | −0.624740 | + | 1.08208i | 0.363851 | + | 0.931457i | \(0.381462\pi\) |
−0.988591 | + | 0.150624i | \(0.951872\pi\) | |||||||
\(434\) | 2.00000 | 0.0960031 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.00000 | − | 13.8564i | 0.383131 | − | 0.663602i | ||||
\(437\) | 30.0000 | 1.43509 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.00000 | − | 3.46410i | −0.0954548 | − | 0.165333i | 0.814344 | − | 0.580383i | \(-0.197097\pi\) |
−0.909798 | + | 0.415051i | \(0.863764\pi\) | |||||||
\(440\) | 3.00000 | + | 5.19615i | 0.143019 | + | 0.247717i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.5000 | + | 6.06218i | 1.16535 | + | 0.288348i | ||||
\(443\) | −15.0000 | −0.712672 | −0.356336 | − | 0.934358i | \(-0.615974\pi\) | ||||
−0.356336 | + | 0.934358i | \(0.615974\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.0000 | − | 19.0526i | −0.521450 | − | 0.903178i | ||||
\(446\) | 2.00000 | − | 3.46410i | 0.0947027 | − | 0.164030i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.500000 | − | 0.866025i | 0.0236228 | − | 0.0409159i | ||||
\(449\) | −19.0000 | + | 32.9090i | −0.896665 | + | 1.55307i | −0.0649356 | + | 0.997889i | \(0.520684\pi\) |
−0.831730 | + | 0.555181i | \(0.812649\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.50000 | − | 12.9904i | 0.353161 | − | 0.611693i | ||||
\(452\) | 3.00000 | + | 5.19615i | 0.141108 | + | 0.244406i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −14.0000 | −0.657053 | ||||||||
\(455\) | 5.00000 | − | 5.19615i | 0.234404 | − | 0.243599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.0000 | − | 22.5167i | −0.608114 | − | 1.05328i | −0.991551 | − | 0.129718i | \(-0.958593\pi\) |
0.383437 | − | 0.923567i | \(-0.374740\pi\) | |||||||
\(458\) | −13.5000 | − | 23.3827i | −0.630814 | − | 1.09260i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.0000 | −0.559503 | ||||||||
\(461\) | 4.00000 | − | 6.92820i | 0.186299 | − | 0.322679i | −0.757715 | − | 0.652586i | \(-0.773684\pi\) |
0.944013 | + | 0.329907i | \(0.107017\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.0000 | −1.44069 | −0.720346 | − | 0.693615i | \(-0.756017\pi\) | ||||
−0.720346 | + | 0.693615i | \(0.756017\pi\) | |||||||
\(464\) | 2.50000 | − | 4.33013i | 0.116060 | − | 0.201021i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.0000 | + | 22.5167i | 0.602213 | + | 1.04306i | ||||
\(467\) | 12.0000 | 0.555294 | 0.277647 | − | 0.960683i | \(-0.410445\pi\) | ||||
0.277647 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.00000 | −0.0923514 | ||||||||
\(470\) | −1.00000 | − | 1.73205i | −0.0461266 | − | 0.0798935i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.00000 | + | 5.19615i | −0.138086 | + | 0.239172i | ||||
\(473\) | −6.00000 | −0.275880 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.50000 | + | 4.33013i | −0.114708 | + | 0.198680i | ||||
\(476\) | −7.00000 | −0.320844 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.00000 | + | 10.3923i | 0.274434 | + | 0.475333i | ||||
\(479\) | 10.5000 | + | 18.1865i | 0.479757 | + | 0.830964i | 0.999730 | − | 0.0232187i | \(-0.00739140\pi\) |
−0.519973 | + | 0.854183i | \(0.674058\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | + | 6.92820i | 0.0911922 | + | 0.315899i | ||||
\(482\) | 28.0000 | 1.27537 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | 2.00000 | − | 3.46410i | 0.0908153 | − | 0.157297i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.5000 | + | 30.3109i | −0.793001 | + | 1.37352i | 0.131100 | + | 0.991369i | \(0.458149\pi\) |
−0.924101 | + | 0.382148i | \(0.875184\pi\) | |||||||
\(488\) | −3.50000 | + | 6.06218i | −0.158438 | + | 0.274422i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.00000 | + | 1.73205i | −0.0451754 | + | 0.0782461i | ||||
\(491\) | −4.00000 | − | 6.92820i | −0.180517 | − | 0.312665i | 0.761539 | − | 0.648119i | \(-0.224444\pi\) |
−0.942057 | + | 0.335453i | \(0.891111\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.0000 | −1.57632 | ||||||||
\(494\) | −17.5000 | − | 4.33013i | −0.787362 | − | 0.194822i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.00000 | + | 1.73205i | 0.0449013 | + | 0.0777714i | ||||
\(497\) | −4.00000 | − | 6.92820i | −0.179425 | − | 0.310772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0000 | 0.626726 | 0.313363 | − | 0.949633i | \(-0.398544\pi\) | ||||
0.313363 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(500\) | 6.00000 | − | 10.3923i | 0.268328 | − | 0.464758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0000 | 0.535586 | ||||||||
\(503\) | 12.0000 | − | 20.7846i | 0.535054 | − | 0.926740i | −0.464107 | − | 0.885779i | \(-0.653625\pi\) |
0.999161 | − | 0.0409609i | \(-0.0130419\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.0000 | + | 24.2487i | 0.622992 | + | 1.07905i | ||||
\(506\) | 18.0000 | 0.800198 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.0000 | −0.532414 | ||||||||
\(509\) | −20.0000 | − | 34.6410i | −0.886484 | − | 1.53544i | −0.844003 | − | 0.536339i | \(-0.819807\pi\) |
−0.0424816 | − | 0.999097i | \(-0.513526\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | − | 10.3923i | 0.265424 | − | 0.459728i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.50000 | + | 12.9904i | −0.330811 | + | 0.572981i | ||||
\(515\) | 20.0000 | 0.881305 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.50000 | + | 2.59808i | 0.0659699 | + | 0.114263i | ||||
\(518\) | −1.00000 | − | 1.73205i | −0.0439375 | − | 0.0761019i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.00000 | + | 1.73205i | 0.306970 | + | 0.0759555i | ||||
\(521\) | −21.0000 | −0.920027 | −0.460013 | − | 0.887912i | \(-0.652155\pi\) | ||||
−0.460013 | + | 0.887912i | \(0.652155\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.5000 | − | 33.7750i | −0.852675 | − | 1.47688i | −0.878785 | − | 0.477218i | \(-0.841645\pi\) |
0.0261094 | − | 0.999659i | \(-0.491688\pi\) | |||||||
\(524\) | 4.00000 | − | 6.92820i | 0.174741 | − | 0.302660i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.0000 | + | 20.7846i | −0.523225 | + | 0.906252i | ||||
\(527\) | 7.00000 | − | 12.1244i | 0.304925 | − | 0.528145i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 3.00000 | + | 5.19615i | 0.130312 | + | 0.225706i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.00000 | 0.216777 | ||||||||
\(533\) | −5.00000 | − | 17.3205i | −0.216574 | − | 0.750234i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.0000 | + | 25.9808i | 0.648507 | + | 1.12325i | ||||
\(536\) | −1.00000 | − | 1.73205i | −0.0431934 | − | 0.0748132i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24.0000 | 1.03471 | ||||||||
\(539\) | 1.50000 | − | 2.59808i | 0.0646096 | − | 0.111907i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0000 | 0.859867 | 0.429934 | − | 0.902861i | \(-0.358537\pi\) | ||||
0.429934 | + | 0.902861i | \(0.358537\pi\) | |||||||
\(542\) | −1.00000 | + | 1.73205i | −0.0429537 | + | 0.0743980i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.50000 | − | 6.06218i | −0.150061 | − | 0.259914i | ||||
\(545\) | −32.0000 | −1.37073 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.0000 | −1.36822 | −0.684111 | − | 0.729378i | \(-0.739809\pi\) | ||||
−0.684111 | + | 0.729378i | \(0.739809\pi\) | |||||||
\(548\) | 9.00000 | + | 15.5885i | 0.384461 | + | 0.665906i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.50000 | + | 2.59808i | −0.0639602 | + | 0.110782i | ||||
\(551\) | 25.0000 | 1.06504 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.50000 | − | 2.59808i | 0.0637865 | − | 0.110481i | ||||
\(554\) | 6.00000 | 0.254916 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.50000 | + | 16.4545i | 0.402890 | + | 0.697826i | ||||
\(557\) | −7.50000 | − | 12.9904i | −0.317785 | − | 0.550420i | 0.662240 | − | 0.749291i | \(-0.269606\pi\) |
−0.980026 | + | 0.198871i | \(0.936272\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.00000 | + | 5.19615i | −0.211477 | + | 0.219774i | ||||
\(560\) | −2.00000 | −0.0845154 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.00000 | + | 13.8564i | 0.337460 | + | 0.584497i | ||||
\(563\) | 15.0000 | − | 25.9808i | 0.632175 | − | 1.09496i | −0.354932 | − | 0.934892i | \(-0.615496\pi\) |
0.987106 | − | 0.160066i | \(-0.0511708\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.00000 | − | 10.3923i | 0.252422 | − | 0.437208i | ||||
\(566\) | −14.0000 | + | 24.2487i | −0.588464 | + | 1.01925i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.00000 | − | 6.92820i | 0.167836 | − | 0.290701i | ||||
\(569\) | −22.0000 | − | 38.1051i | −0.922288 | − | 1.59745i | −0.795866 | − | 0.605473i | \(-0.792984\pi\) |
−0.126422 | − | 0.991977i | \(-0.540349\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.0000 | −0.502184 | −0.251092 | − | 0.967963i | \(-0.580790\pi\) | ||||
−0.251092 | + | 0.967963i | \(0.580790\pi\) | |||||||
\(572\) | −10.5000 | − | 2.59808i | −0.439027 | − | 0.108631i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.50000 | + | 4.33013i | 0.104348 | + | 0.180736i | ||||
\(575\) | −3.00000 | − | 5.19615i | −0.125109 | − | 0.216695i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.0000 | 0.832611 | 0.416305 | − | 0.909225i | \(-0.363325\pi\) | ||||
0.416305 | + | 0.909225i | \(0.363325\pi\) | |||||||
\(578\) | −16.0000 | + | 27.7128i | −0.665512 | + | 1.15270i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10.0000 | −0.415227 | ||||||||
\(581\) | 4.00000 | − | 6.92820i | 0.165948 | − | 0.287430i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.50000 | − | 7.79423i | −0.186371 | − | 0.322804i | ||||
\(584\) | 12.0000 | 0.496564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.0000 | −0.495715 | ||||||||
\(587\) | 5.00000 | + | 8.66025i | 0.206372 | + | 0.357447i | 0.950569 | − | 0.310513i | \(-0.100501\pi\) |
−0.744197 | + | 0.667960i | \(0.767168\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.00000 | + | 8.66025i | −0.206021 | + | 0.356840i | ||||
\(590\) | 12.0000 | 0.494032 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000 | − | 1.73205i | 0.0410997 | − | 0.0711868i | ||||
\(593\) | 13.0000 | 0.533846 | 0.266923 | − | 0.963718i | \(-0.413993\pi\) | ||||
0.266923 | + | 0.963718i | \(0.413993\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.00000 | + | 12.1244i | 0.286972 | + | 0.497050i | ||||
\(596\) | 7.00000 | + | 12.1244i | 0.286731 | + | 0.496633i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15.0000 | − | 15.5885i | 0.613396 | − | 0.637459i | ||||
\(599\) | 26.0000 | 1.06233 | 0.531166 | − | 0.847268i | \(-0.321754\pi\) | ||||
0.531166 | + | 0.847268i | \(0.321754\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.0000 | − | 32.9090i | −0.775026 | − | 1.34238i | −0.934780 | − | 0.355228i | \(-0.884403\pi\) |
0.159754 | − | 0.987157i | \(-0.448930\pi\) | |||||||
\(602\) | 1.00000 | − | 1.73205i | 0.0407570 | − | 0.0705931i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.50000 | + | 11.2583i | −0.264481 | + | 0.458095i | ||||
\(605\) | 2.00000 | − | 3.46410i | 0.0813116 | − | 0.140836i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.0000 | − | 25.9808i | 0.608831 | − | 1.05453i | −0.382602 | − | 0.923913i | \(-0.624972\pi\) |
0.991433 | − | 0.130613i | \(-0.0416947\pi\) | |||||||
\(608\) | 2.50000 | + | 4.33013i | 0.101388 | + | 0.175610i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.0000 | 0.566843 | ||||||||
\(611\) | 3.50000 | + | 0.866025i | 0.141595 | + | 0.0350356i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0000 | + | 24.2487i | 0.565455 | + | 0.979396i | 0.997007 | + | 0.0773084i | \(0.0246326\pi\) |
−0.431553 | + | 0.902088i | \(0.642034\pi\) | |||||||
\(614\) | −4.50000 | − | 7.79423i | −0.181605 | − | 0.314549i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.00000 | 0.120873 | ||||||||
\(617\) | −10.0000 | + | 17.3205i | −0.402585 | + | 0.697297i | −0.994037 | − | 0.109043i | \(-0.965221\pi\) |
0.591452 | + | 0.806340i | \(0.298555\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.0000 | 1.64793 | 0.823965 | − | 0.566641i | \(-0.191757\pi\) | ||||
0.823965 | + | 0.566641i | \(0.191757\pi\) | |||||||
\(620\) | 2.00000 | − | 3.46410i | 0.0803219 | − | 0.139122i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.5000 | + | 19.9186i | 0.461108 | + | 0.798662i | ||||
\(623\) | −11.0000 | −0.440706 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −14.0000 | − | 24.2487i | −0.559553 | − | 0.969173i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.00000 | − | 15.5885i | 0.359139 | − | 0.622047i | ||||
\(629\) | −14.0000 | −0.558217 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.50000 | + | 12.9904i | −0.298570 | + | 0.517139i | −0.975809 | − | 0.218624i | \(-0.929843\pi\) |
0.677239 | + | 0.735763i | \(0.263176\pi\) | |||||||
\(632\) | 3.00000 | 0.119334 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 15.0000 | + | 25.9808i | 0.595726 | + | 1.03183i | ||||
\(635\) | 12.0000 | + | 20.7846i | 0.476205 | + | 0.824812i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | − | 3.46410i | −0.0396214 | − | 0.137253i | ||||
\(638\) | 15.0000 | 0.593856 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | − | 1.73205i | −0.0395285 | − | 0.0684653i | ||||
\(641\) | 9.00000 | − | 15.5885i | 0.355479 | − | 0.615707i | −0.631721 | − | 0.775196i | \(-0.717651\pi\) |
0.987200 | + | 0.159489i | \(0.0509845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.5000 | − | 42.4352i | 0.966186 | − | 1.67348i | 0.259791 | − | 0.965665i | \(-0.416346\pi\) |
0.706395 | − | 0.707818i | \(-0.250320\pi\) | |||||||
\(644\) | −3.00000 | + | 5.19615i | −0.118217 | + | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.5000 | − | 30.3109i | 0.688528 | − | 1.19257i | ||||
\(647\) | 0.500000 | + | 0.866025i | 0.0196570 | + | 0.0340470i | 0.875687 | − | 0.482880i | \(-0.160409\pi\) |
−0.856030 | + | 0.516927i | \(0.827076\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.0000 | −0.706562 | ||||||||
\(650\) | 1.00000 | + | 3.46410i | 0.0392232 | + | 0.135873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.00000 | + | 12.1244i | 0.274141 | + | 0.474826i | ||||
\(653\) | 13.5000 | + | 23.3827i | 0.528296 | + | 0.915035i | 0.999456 | + | 0.0329874i | \(0.0105021\pi\) |
−0.471160 | + | 0.882048i | \(0.656165\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.0000 | −0.625172 | ||||||||
\(656\) | −2.50000 | + | 4.33013i | −0.0976086 | + | 0.169063i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.00000 | −0.0389841 | ||||||||
\(659\) | −13.5000 | + | 23.3827i | −0.525885 | + | 0.910860i | 0.473660 | + | 0.880708i | \(0.342933\pi\) |
−0.999545 | + | 0.0301523i | \(0.990401\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.00000 | + | 12.1244i | 0.272268 | + | 0.471583i | 0.969442 | − | 0.245319i | \(-0.0788928\pi\) |
−0.697174 | + | 0.716902i | \(0.745559\pi\) | |||||||
\(662\) | 22.0000 | 0.855054 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.00000 | 0.310460 | ||||||||
\(665\) | −5.00000 | − | 8.66025i | −0.193892 | − | 0.335830i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.0000 | + | 25.9808i | −0.580802 | + | 1.00598i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.00000 | + | 3.46410i | −0.0772667 | + | 0.133830i | ||||
\(671\) | −21.0000 | −0.810696 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.5000 | − | 19.9186i | −0.443292 | − | 0.767805i | 0.554639 | − | 0.832091i | \(-0.312856\pi\) |
−0.997932 | + | 0.0642860i | \(0.979523\pi\) | |||||||
\(674\) | 8.50000 | + | 14.7224i | 0.327408 | + | 0.567087i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0000 | + | 6.92820i | −0.423077 | + | 0.266469i | ||||
\(677\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.00000 | − | 1.73205i | −0.0383765 | − | 0.0664700i | ||||
\(680\) | −7.00000 | + | 12.1244i | −0.268438 | + | 0.464948i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.00000 | + | 5.19615i | −0.114876 | + | 0.198971i | ||||
\(683\) | 18.0000 | − | 31.1769i | 0.688751 | − | 1.19295i | −0.283491 | − | 0.958975i | \(-0.591493\pi\) |
0.972242 | − | 0.233977i | \(-0.0751739\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.0000 | − | 31.1769i | 0.687745 | − | 1.19121i | ||||
\(686\) | 0.500000 | + | 0.866025i | 0.0190901 | + | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.00000 | 0.0762493 | ||||||||
\(689\) | −10.5000 | − | 2.59808i | −0.400018 | − | 0.0989788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.0000 | − | 34.6410i | −0.760836 | − | 1.31781i | −0.942420 | − | 0.334431i | \(-0.891456\pi\) |
0.181584 | − | 0.983375i | \(-0.441877\pi\) | |||||||
\(692\) | 6.00000 | + | 10.3923i | 0.228086 | + | 0.395056i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.0000 | −0.645311 | ||||||||
\(695\) | 19.0000 | − | 32.9090i | 0.720711 | − | 1.24831i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.0000 | 1.32572 | ||||||||
\(698\) | 9.00000 | − | 15.5885i | 0.340655 | − | 0.590032i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.500000 | − | 0.866025i | −0.0188982 | − | 0.0327327i | ||||
\(701\) | −13.0000 | −0.491003 | −0.245502 | − | 0.969396i | \(-0.578953\pi\) | ||||
−0.245502 | + | 0.969396i | \(0.578953\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.0000 | 0.377157 | ||||||||
\(704\) | 1.50000 | + | 2.59808i | 0.0565334 | + | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.00000 | − | 12.1244i | 0.263448 | − | 0.456306i | ||||
\(707\) | 14.0000 | 0.526524 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.0000 | − | 24.2487i | 0.525781 | − | 0.910679i | −0.473768 | − | 0.880650i | \(-0.657106\pi\) |
0.999549 | − | 0.0300298i | \(-0.00956021\pi\) | |||||||
\(710\) | −16.0000 | −0.600469 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.50000 | − | 9.52628i | −0.206121 | − | 0.357012i | ||||
\(713\) | −6.00000 | − | 10.3923i | −0.224702 | − | 0.389195i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | + | 20.7846i | 0.224387 | + | 0.777300i | ||||
\(716\) | −20.0000 | −0.747435 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.00000 | + | 15.5885i | 0.335877 | + | 0.581756i | ||||
\(719\) | −7.50000 | + | 12.9904i | −0.279703 | + | 0.484459i | −0.971311 | − | 0.237814i | \(-0.923569\pi\) |
0.691608 | + | 0.722273i | \(0.256903\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.00000 | − | 8.66025i | 0.186210 | − | 0.322525i | ||||
\(722\) | −3.00000 | + | 5.19615i | −0.111648 | + | 0.193381i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.50000 | − | 7.79423i | 0.167241 | − | 0.289670i | ||||
\(725\) | −2.50000 | − | 4.33013i | −0.0928477 | − | 0.160817i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 2.50000 | − | 2.59808i | 0.0926562 | − | 0.0962911i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12.0000 | − | 20.7846i | −0.444140 | − | 0.769273i | ||||
\(731\) | −7.00000 | − | 12.1244i | −0.258904 | − | 0.448435i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.00000 | −0.258551 | −0.129275 | − | 0.991609i | \(-0.541265\pi\) | ||||
−0.129275 | + | 0.991609i | \(0.541265\pi\) | |||||||
\(734\) | 5.00000 | − | 8.66025i | 0.184553 | − | 0.319656i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | 3.00000 | − | 5.19615i | 0.110506 | − | 0.191403i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.00000 | + | 12.1244i | 0.257499 | + | 0.446002i | 0.965571 | − | 0.260138i | \(-0.0837682\pi\) |
−0.708072 | + | 0.706140i | \(0.750435\pi\) | |||||||
\(740\) | −4.00000 | −0.147043 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.00000 | 0.110133 | ||||||||
\(743\) | −3.00000 | − | 5.19615i | −0.110059 | − | 0.190628i | 0.805735 | − | 0.592277i | \(-0.201771\pi\) |
−0.915794 | + | 0.401648i | \(0.868437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.0000 | − | 24.2487i | 0.512920 | − | 0.888404i | ||||
\(746\) | 4.00000 | 0.146450 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.5000 | − | 18.1865i | 0.383918 | − | 0.664966i | ||||
\(749\) | 15.0000 | 0.548088 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.5000 | + | 28.5788i | 0.602094 | + | 1.04286i | 0.992504 | + | 0.122216i | \(0.0389999\pi\) |
−0.390410 | + | 0.920641i | \(0.627667\pi\) | |||||||
\(752\) | −0.500000 | − | 0.866025i | −0.0182331 | − | 0.0315807i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.5000 | − | 12.9904i | 0.455223 | − | 0.473082i | ||||
\(755\) | 26.0000 | 0.946237 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.0000 | − | 27.7128i | −0.581530 | − | 1.00724i | −0.995298 | − | 0.0968571i | \(-0.969121\pi\) |
0.413768 | − | 0.910382i | \(-0.364212\pi\) | |||||||
\(758\) | 10.0000 | − | 17.3205i | 0.363216 | − | 0.629109i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.00000 | − | 8.66025i | 0.181369 | − | 0.314140i | ||||
\(761\) | −9.00000 | + | 15.5885i | −0.326250 | + | 0.565081i | −0.981764 | − | 0.190101i | \(-0.939118\pi\) |
0.655515 | + | 0.755182i | \(0.272452\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.00000 | + | 13.8564i | −0.289619 | + | 0.501636i | ||||
\(764\) | −2.00000 | − | 3.46410i | −0.0723575 | − | 0.125327i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −31.0000 | −1.12008 | ||||||||
\(767\) | −15.0000 | + | 15.5885i | −0.541619 | + | 0.562867i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.0000 | − | 39.8372i | −0.829401 | − | 1.43657i | −0.898509 | − | 0.438956i | \(-0.855348\pi\) |
0.0691074 | − | 0.997609i | \(-0.477985\pi\) | |||||||
\(770\) | −3.00000 | − | 5.19615i | −0.108112 | − | 0.187256i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.0000 | 0.467880 | ||||||||
\(773\) | −5.00000 | + | 8.66025i | −0.179838 | + | 0.311488i | −0.941825 | − | 0.336104i | \(-0.890891\pi\) |
0.761987 | + | 0.647592i | \(0.224224\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.00000 | 0.0718421 | ||||||||
\(776\) | 1.00000 | − | 1.73205i | 0.0358979 | − | 0.0621770i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.00000 | + | 5.19615i | 0.107555 | + | 0.186291i | ||||
\(779\) | −25.0000 | −0.895718 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | 21.0000 | + | 36.3731i | 0.750958 | + | 1.30070i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.500000 | + | 0.866025i | −0.0178571 | + | 0.0309295i | ||||
\(785\) | −36.0000 | −1.28490 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.5000 | + | 21.6506i | −0.445577 | + | 0.771762i | −0.998092 | − | 0.0617409i | \(-0.980335\pi\) |
0.552515 | + | 0.833503i | \(0.313668\pi\) | |||||||
\(788\) | 9.00000 | 0.320612 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.00000 | − | 5.19615i | −0.106735 | − | 0.184871i | ||||
\(791\) | −3.00000 | − | 5.19615i | −0.106668 | − | 0.184754i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.5000 | + | 18.1865i | −0.621443 | + | 0.645823i | ||||
\(794\) | −15.0000 | −0.532330 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.0000 | + | 22.5167i | 0.460773 | + | 0.798082i | ||||
\(797\) | 28.0000 | − | 48.4974i | 0.991811 | − | 1.71787i | 0.385301 | − | 0.922791i | \(-0.374098\pi\) |
0.606510 | − | 0.795076i | \(-0.292569\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.50000 | + | 6.06218i | −0.123821 | + | 0.214464i | ||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.00000 | − | 15.5885i | 0.317801 | − | 0.550448i | ||||
\(803\) | 18.0000 | + | 31.1769i | 0.635206 | + | 1.10021i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.0000 | 0.422944 | ||||||||
\(806\) | 2.00000 | + | 6.92820i | 0.0704470 | + | 0.244036i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.00000 | + | 12.1244i | 0.246259 | + | 0.426533i | ||||
\(809\) | 26.0000 | + | 45.0333i | 0.914111 | + | 1.58329i | 0.808197 | + | 0.588912i | \(0.200444\pi\) |
0.105914 | + | 0.994375i | \(0.466223\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.00000 | −0.140459 | −0.0702295 | − | 0.997531i | \(-0.522373\pi\) | ||||
−0.0702295 | + | 0.997531i | \(0.522373\pi\) | |||||||
\(812\) | −2.50000 | + | 4.33013i | −0.0877328 | + | 0.151958i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.00000 | 0.210300 | ||||||||
\(815\) | 14.0000 | − | 24.2487i | 0.490399 | − | 0.849395i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.00000 | + | 8.66025i | 0.174928 | + | 0.302984i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.0000 | 0.349215 | ||||||||
\(821\) | 7.50000 | + | 12.9904i | 0.261752 | + | 0.453367i | 0.966708 | − | 0.255884i | \(-0.0823665\pi\) |
−0.704956 | + | 0.709251i | \(0.749033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0000 | − | 41.5692i | 0.836587 | − | 1.44901i | −0.0561440 | − | 0.998423i | \(-0.517881\pi\) |
0.892731 | − | 0.450589i | \(-0.148786\pi\) | |||||||
\(824\) | 10.0000 | 0.348367 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.00000 | − | 5.19615i | 0.104383 | − | 0.180797i | ||||
\(827\) | 8.00000 | 0.278187 | 0.139094 | − | 0.990279i | \(-0.455581\pi\) | ||||
0.139094 | + | 0.990279i | \(0.455581\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.50000 | + | 6.06218i | 0.121560 | + | 0.210548i | 0.920383 | − | 0.391018i | \(-0.127877\pi\) |
−0.798823 | + | 0.601566i | \(0.794544\pi\) | |||||||
\(830\) | −8.00000 | − | 13.8564i | −0.277684 | − | 0.480963i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.50000 | + | 0.866025i | 0.121341 | + | 0.0300240i | ||||
\(833\) | 7.00000 | 0.242536 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.50000 | + | 12.9904i | −0.259393 | + | 0.449282i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.00000 | − | 3.46410i | 0.0690889 | − | 0.119665i | ||||
\(839\) | −12.0000 | + | 20.7846i | −0.414286 | + | 0.717564i | −0.995353 | − | 0.0962912i | \(-0.969302\pi\) |
0.581067 | + | 0.813856i | \(0.302635\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00000 | − | 3.46410i | 0.0689655 | − | 0.119452i | ||||
\(842\) | 11.0000 | + | 19.0526i | 0.379085 | + | 0.656595i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.0000 | −0.344214 | ||||||||
\(845\) | 23.0000 | + | 12.1244i | 0.791224 | + | 0.417091i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | − | 1.73205i | −0.0343604 | − | 0.0595140i | ||||
\(848\) | 1.50000 | + | 2.59808i | 0.0515102 | + | 0.0892183i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.00000 | −0.240098 | ||||||||
\(851\) | −6.00000 | + | 10.3923i | −0.205677 | + | 0.356244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.0000 | 1.40381 | 0.701907 | − | 0.712269i | \(-0.252332\pi\) | ||||
0.701907 | + | 0.712269i | \(0.252332\pi\) | |||||||
\(854\) | 3.50000 | − | 6.06218i | 0.119768 | − | 0.207443i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.50000 | + | 12.9904i | 0.256345 | + | 0.444002i | ||||
\(857\) | −6.00000 | −0.204956 | −0.102478 | − | 0.994735i | \(-0.532677\pi\) | ||||
−0.102478 | + | 0.994735i | \(0.532677\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.0000 | 1.19418 | 0.597092 | − | 0.802173i | \(-0.296323\pi\) | ||||
0.597092 | + | 0.802173i | \(0.296323\pi\) | |||||||
\(860\) | −2.00000 | − | 3.46410i | −0.0681994 | − | 0.118125i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.00000 | + | 6.92820i | −0.136241 | + | 0.235976i | ||||
\(863\) | −34.0000 | −1.15737 | −0.578687 | − | 0.815550i | \(-0.696435\pi\) | ||||
−0.578687 | + | 0.815550i | \(0.696435\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0000 | − | 20.7846i | 0.408012 | − | 0.706698i | ||||
\(866\) | 26.0000 | 0.883516 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.00000 | − | 1.73205i | −0.0339422 | − | 0.0587896i | ||||
\(869\) | 4.50000 | + | 7.79423i | 0.152652 | + | 0.264401i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.00000 | − | 6.92820i | −0.0677674 | − | 0.234753i | ||||
\(872\) | −16.0000 | −0.541828 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15.0000 | − | 25.9808i | −0.507383 | − | 0.878812i | ||||
\(875\) | −6.00000 | + | 10.3923i | −0.202837 | + | 0.351324i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.0000 | + | 34.6410i | −0.675352 | + | 1.16974i | 0.301014 | + | 0.953620i | \(0.402675\pi\) |
−0.976366 | + | 0.216124i | \(0.930658\pi\) | |||||||
\(878\) | −2.00000 | + | 3.46410i | −0.0674967 | + | 0.116908i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.00000 | − | 5.19615i | 0.101130 | − | 0.175162i | ||||
\(881\) | −13.0000 | − | 22.5167i | −0.437981 | − | 0.758606i | 0.559553 | − | 0.828795i | \(-0.310973\pi\) |
−0.997534 | + | 0.0701893i | \(0.977640\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.0000 | −0.471138 | −0.235569 | − | 0.971858i | \(-0.575695\pi\) | ||||
−0.235569 | + | 0.971858i | \(0.575695\pi\) | |||||||
\(884\) | −7.00000 | − | 24.2487i | −0.235435 | − | 0.815572i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.50000 | + | 12.9904i | 0.251967 | + | 0.436420i | ||||
\(887\) | 18.5000 | + | 32.0429i | 0.621169 | + | 1.07590i | 0.989268 | + | 0.146110i | \(0.0466754\pi\) |
−0.368099 | + | 0.929787i | \(0.619991\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.0000 | 0.402467 | ||||||||
\(890\) | −11.0000 | + | 19.0526i | −0.368721 | + | 0.638643i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.00000 | −0.133930 | ||||||||
\(893\) | 2.50000 | − | 4.33013i | 0.0836593 | − | 0.144902i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.0000 | + | 34.6410i | 0.668526 | + | 1.15792i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 38.0000 | 1.26808 | ||||||||
\(899\) | −5.00000 | − | 8.66025i | −0.166759 | − | 0.288836i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.5000 | − | 18.1865i | 0.349806 | − | 0.605881i | ||||
\(902\) | −15.0000 | −0.499445 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.00000 | − | 5.19615i | 0.0997785 | − | 0.172821i | ||||
\(905\) | −18.0000 | −0.598340 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.0000 | + | 32.9090i | 0.630885 | + | 1.09272i | 0.987371 | + | 0.158424i | \(0.0506412\pi\) |
−0.356487 | + | 0.934300i | \(0.616025\pi\) | |||||||
\(908\) | 7.00000 | + | 12.1244i | 0.232303 | + | 0.402361i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.00000 | − | 1.73205i | −0.232048 | − | 0.0574169i | ||||
\(911\) | 52.0000 | 1.72284 | 0.861418 | − | 0.507896i | \(-0.169577\pi\) | ||||
0.861418 | + | 0.507896i | \(0.169577\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000 | + | 20.7846i | 0.397142 | + | 0.687870i | ||||
\(914\) | −13.0000 | + | 22.5167i | −0.430002 | + | 0.744785i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.5000 | + | 23.3827i | −0.446053 | + | 0.772586i | ||||
\(917\) | −4.00000 | + | 6.92820i | −0.132092 | + | 0.228789i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.50000 | − | 9.52628i | 0.181428 | − | 0.314243i | −0.760939 | − | 0.648824i | \(-0.775261\pi\) |
0.942367 | + | 0.334581i | \(0.108595\pi\) | |||||||
\(920\) | 6.00000 | + | 10.3923i | 0.197814 | + | 0.342624i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.00000 | −0.263466 | ||||||||
\(923\) | 20.0000 | − | 20.7846i | 0.658308 | − | 0.684134i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00000 | − | 1.73205i | −0.0328798 | − | 0.0569495i | ||||
\(926\) | 15.5000 | + | 26.8468i | 0.509362 | + | 0.882240i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.00000 | −0.164133 | ||||||||
\(929\) | −6.50000 | + | 11.2583i | −0.213258 | + | 0.369374i | −0.952732 | − | 0.303811i | \(-0.901741\pi\) |
0.739474 | + | 0.673185i | \(0.235074\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.00000 | −0.163868 | ||||||||
\(932\) | 13.0000 | − | 22.5167i | 0.425829 | − | 0.737558i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.00000 | − | 10.3923i | −0.196326 | − | 0.340047i | ||||
\(935\) | −42.0000 | −1.37355 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.0000 | 1.69877 | 0.849383 | − | 0.527777i | \(-0.176974\pi\) | ||||
0.849383 | + | 0.527777i | \(0.176974\pi\) | |||||||
\(938\) | 1.00000 | + | 1.73205i | 0.0326512 | + | 0.0565535i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.00000 | + | 1.73205i | −0.0326164 | + | 0.0564933i | ||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.0000 | − | 25.9808i | 0.488467 | − | 0.846050i | ||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.00000 | + | 5.19615i | 0.0975384 | + | 0.168941i | ||||
\(947\) | −15.5000 | − | 26.8468i | −0.503682 | − | 0.872403i | −0.999991 | − | 0.00425721i | \(-0.998645\pi\) |
0.496309 | − | 0.868146i | \(-0.334688\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.0000 | + | 10.3923i | 1.36338 | + | 0.337348i | ||||
\(950\) | 5.00000 | 0.162221 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.50000 | + | 6.06218i | 0.113436 | + | 0.196476i | ||||
\(953\) | −7.00000 | + | 12.1244i | −0.226752 | + | 0.392746i | −0.956844 | − | 0.290603i | \(-0.906144\pi\) |
0.730091 | + | 0.683349i | \(0.239477\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.00000 | + | 6.92820i | −0.129437 | + | 0.224191i | ||||
\(956\) | 6.00000 | − | 10.3923i | 0.194054 | − | 0.336111i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.5000 | − | 18.1865i | 0.339240 | − | 0.587580i | ||||
\(959\) | −9.00000 | − | 15.5885i | −0.290625 | − | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 5.00000 | − | 5.19615i | 0.161206 | − | 0.167531i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.0000 | − | 24.2487i | −0.450910 | − | 0.780998i | ||||
\(965\) | −13.0000 | − | 22.5167i | −0.418485 | − | 0.724837i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.0000 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(968\) | 1.00000 | − | 1.73205i | 0.0321412 | − | 0.0556702i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.00000 | −0.128432 | ||||||||
\(971\) | 11.0000 | − | 19.0526i | 0.353007 | − | 0.611426i | −0.633768 | − | 0.773523i | \(-0.718493\pi\) |
0.986775 | + | 0.162098i | \(0.0518259\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.50000 | − | 16.4545i | −0.304556 | − | 0.527506i | ||||
\(974\) | 35.0000 | 1.12147 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.00000 | 0.224065 | ||||||||
\(977\) | 4.00000 | + | 6.92820i | 0.127971 | + | 0.221653i | 0.922890 | − | 0.385063i | \(-0.125820\pi\) |
−0.794919 | + | 0.606715i | \(0.792487\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.5000 | − | 28.5788i | 0.527342 | − | 0.913384i | ||||
\(980\) | 2.00000 | 0.0638877 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.00000 | + | 6.92820i | −0.127645 | + | 0.221088i | ||||
\(983\) | 32.0000 | 1.02064 | 0.510321 | − | 0.859984i | \(-0.329527\pi\) | ||||
0.510321 | + | 0.859984i | \(0.329527\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.00000 | − | 15.5885i | −0.286764 | − | 0.496690i | ||||
\(986\) | 17.5000 | + | 30.3109i | 0.557314 | + | 0.965295i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.00000 | + | 17.3205i | 0.159071 | + | 0.551039i | ||||
\(989\) | −12.0000 | −0.381578 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.50000 | + | 2.59808i | 0.0476491 | + | 0.0825306i | 0.888866 | − | 0.458167i | \(-0.151494\pi\) |
−0.841217 | + | 0.540697i | \(0.818160\pi\) | |||||||
\(992\) | 1.00000 | − | 1.73205i | 0.0317500 | − | 0.0549927i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.00000 | + | 6.92820i | −0.126872 | + | 0.219749i | ||||
\(995\) | 26.0000 | − | 45.0333i | 0.824255 | − | 1.42765i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.50000 | + | 6.06218i | −0.110846 | + | 0.191991i | −0.916112 | − | 0.400923i | \(-0.868689\pi\) |
0.805266 | + | 0.592914i | \(0.202023\pi\) | |||||||
\(998\) | −7.00000 | − | 12.1244i | −0.221581 | − | 0.383790i | ||||
\(999\) | 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 | 1638.2.r.l.757.1 | 2 | ||
3.2 | odd | 2 | 546.2.l.c.211.1 | ✓ | 2 | ||
13.9 | even | 3 | inner | 1638.2.r.l.1387.1 | 2 | ||
39.23 | odd | 6 | 7098.2.a.bd.1.1 | 1 | |||
39.29 | odd | 6 | 7098.2.a.i.1.1 | 1 | |||
39.35 | odd | 6 | 546.2.l.c.295.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.c.211.1 | ✓ | 2 | 3.2 | odd | 2 | ||
546.2.l.c.295.1 | yes | 2 | 39.35 | odd | 6 | ||
1638.2.r.l.757.1 | 2 | 1.1 | even | 1 | trivial | ||
1638.2.r.l.1387.1 | 2 | 13.9 | even | 3 | inner | ||
7098.2.a.i.1.1 | 1 | 39.29 | odd | 6 | |||
7098.2.a.bd.1.1 | 1 | 39.23 | odd | 6 |