Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(263,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.263");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.g (of order \(3\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 373.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.373 |
Dual form | 637.2.g.f.263.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.207107 | − | 0.358719i | −0.146447 | − | 0.253653i | 0.783465 | − | 0.621436i | \(-0.213450\pi\) |
−0.929912 | + | 0.367783i | \(0.880117\pi\) | |||||||
\(3\) | 1.41421 | 0.816497 | 0.408248 | − | 0.912871i | \(-0.366140\pi\) | ||||
0.408248 | + | 0.912871i | \(0.366140\pi\) | |||||||
\(4\) | 0.914214 | − | 1.58346i | 0.457107 | − | 0.791732i | ||||
\(5\) | 0.914214 | − | 1.58346i | 0.408849 | − | 0.708147i | −0.585912 | − | 0.810374i | \(-0.699264\pi\) |
0.994761 | + | 0.102228i | \(0.0325970\pi\) | |||||||
\(6\) | −0.292893 | − | 0.507306i | −0.119573 | − | 0.207107i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.58579 | −0.560660 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.757359 | −0.239498 | ||||||||
\(11\) | 0.585786 | 0.176621 | 0.0883106 | − | 0.996093i | \(-0.471853\pi\) | ||||
0.0883106 | + | 0.996093i | \(0.471853\pi\) | |||||||
\(12\) | 1.29289 | − | 2.23936i | 0.373226 | − | 0.646447i | ||||
\(13\) | −3.50000 | − | 0.866025i | −0.970725 | − | 0.240192i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.29289 | − | 2.23936i | 0.333824 | − | 0.578199i | ||||
\(16\) | −1.50000 | − | 2.59808i | −0.375000 | − | 0.649519i | ||||
\(17\) | 2.91421 | − | 5.04757i | 0.706801 | − | 1.22421i | −0.259237 | − | 0.965814i | \(-0.583471\pi\) |
0.966038 | − | 0.258401i | \(-0.0831955\pi\) | |||||||
\(18\) | 0.207107 | + | 0.358719i | 0.0488155 | + | 0.0845510i | ||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | −1.67157 | − | 2.89525i | −0.373775 | − | 0.647397i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.121320 | − | 0.210133i | −0.0258656 | − | 0.0448005i | ||||
\(23\) | 0.707107 | + | 1.22474i | 0.147442 | + | 0.255377i | 0.930281 | − | 0.366847i | \(-0.119563\pi\) |
−0.782839 | + | 0.622224i | \(0.786229\pi\) | |||||||
\(24\) | −2.24264 | −0.457777 | ||||||||
\(25\) | 0.828427 | + | 1.43488i | 0.165685 | + | 0.286976i | ||||
\(26\) | 0.414214 | + | 1.43488i | 0.0812340 | + | 0.281403i | ||||
\(27\) | −5.65685 | −1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.08579 | + | 3.61269i | −0.387321 | + | 0.670859i | −0.992088 | − | 0.125543i | \(-0.959933\pi\) |
0.604767 | + | 0.796402i | \(0.293266\pi\) | |||||||
\(30\) | −1.07107 | −0.195549 | ||||||||
\(31\) | −1.29289 | − | 2.23936i | −0.232210 | − | 0.402200i | 0.726248 | − | 0.687433i | \(-0.241262\pi\) |
−0.958458 | + | 0.285233i | \(0.907929\pi\) | |||||||
\(32\) | −2.20711 | + | 3.82282i | −0.390165 | + | 0.675786i | ||||
\(33\) | 0.828427 | 0.144211 | ||||||||
\(34\) | −2.41421 | −0.414034 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.914214 | + | 1.58346i | −0.152369 | + | 0.263911i | ||||
\(37\) | 4.74264 | + | 8.21449i | 0.779685 | + | 1.35045i | 0.932123 | + | 0.362142i | \(0.117954\pi\) |
−0.152438 | + | 0.988313i | \(0.548712\pi\) | |||||||
\(38\) | −1.24264 | − | 2.15232i | −0.201583 | − | 0.349152i | ||||
\(39\) | −4.94975 | − | 1.22474i | −0.792594 | − | 0.196116i | ||||
\(40\) | −1.44975 | + | 2.51104i | −0.229225 | + | 0.397030i | ||||
\(41\) | −0.0857864 | + | 0.148586i | −0.0133976 | + | 0.0232053i | −0.872646 | − | 0.488352i | \(-0.837598\pi\) |
0.859249 | + | 0.511558i | \(0.170931\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.70711 | − | 2.95680i | −0.260331 | − | 0.450907i | 0.705999 | − | 0.708213i | \(-0.250498\pi\) |
−0.966330 | + | 0.257306i | \(0.917165\pi\) | |||||||
\(44\) | 0.535534 | − | 0.927572i | 0.0807348 | − | 0.139837i | ||||
\(45\) | −0.914214 | + | 1.58346i | −0.136283 | + | 0.236049i | ||||
\(46\) | 0.292893 | − | 0.507306i | 0.0431847 | − | 0.0747982i | ||||
\(47\) | 1.82843 | − | 3.16693i | 0.266704 | − | 0.461944i | −0.701305 | − | 0.712861i | \(-0.747399\pi\) |
0.968009 | + | 0.250917i | \(0.0807322\pi\) | |||||||
\(48\) | −2.12132 | − | 3.67423i | −0.306186 | − | 0.530330i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.343146 | − | 0.594346i | 0.0485281 | − | 0.0840532i | ||||
\(51\) | 4.12132 | − | 7.13834i | 0.577100 | − | 0.999567i | ||||
\(52\) | −4.57107 | + | 4.75039i | −0.633893 | + | 0.658761i | ||||
\(53\) | 1.50000 | + | 2.59808i | 0.206041 | + | 0.356873i | 0.950464 | − | 0.310835i | \(-0.100609\pi\) |
−0.744423 | + | 0.667708i | \(0.767275\pi\) | |||||||
\(54\) | 1.17157 | + | 2.02922i | 0.159431 | + | 0.276142i | ||||
\(55\) | 0.535534 | − | 0.927572i | 0.0722114 | − | 0.125074i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.48528 | 1.12390 | ||||||||
\(58\) | 1.72792 | 0.226887 | ||||||||
\(59\) | 5.12132 | − | 8.87039i | 0.666739 | − | 1.15483i | −0.312072 | − | 0.950059i | \(-0.601023\pi\) |
0.978811 | − | 0.204767i | \(-0.0656438\pi\) | |||||||
\(60\) | −2.36396 | − | 4.09450i | −0.305186 | − | 0.528598i | ||||
\(61\) | 4.17157 | 0.534115 | 0.267058 | − | 0.963681i | \(-0.413949\pi\) | ||||
0.267058 | + | 0.963681i | \(0.413949\pi\) | |||||||
\(62\) | −0.535534 | + | 0.927572i | −0.0680129 | + | 0.117802i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | −4.57107 | + | 4.75039i | −0.566971 | + | 0.589214i | ||||
\(66\) | −0.171573 | − | 0.297173i | −0.0211192 | − | 0.0365795i | ||||
\(67\) | 4.24264 | 0.518321 | 0.259161 | − | 0.965834i | \(-0.416554\pi\) | ||||
0.259161 | + | 0.965834i | \(0.416554\pi\) | |||||||
\(68\) | −5.32843 | − | 9.22911i | −0.646167 | − | 1.11919i | ||||
\(69\) | 1.00000 | + | 1.73205i | 0.120386 | + | 0.208514i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.82843 | + | 10.0951i | 0.691707 | + | 1.19807i | 0.971278 | + | 0.237947i | \(0.0764744\pi\) |
−0.279571 | + | 0.960125i | \(0.590192\pi\) | |||||||
\(72\) | 1.58579 | 0.186887 | ||||||||
\(73\) | 5.32843 | + | 9.22911i | 0.623645 | + | 1.08019i | 0.988801 | + | 0.149239i | \(0.0476823\pi\) |
−0.365156 | + | 0.930946i | \(0.618984\pi\) | |||||||
\(74\) | 1.96447 | − | 3.40256i | 0.228365 | − | 0.395539i | ||||
\(75\) | 1.17157 | + | 2.02922i | 0.135282 | + | 0.234315i | ||||
\(76\) | 5.48528 | − | 9.50079i | 0.629205 | − | 1.08981i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.585786 | + | 2.02922i | 0.0663273 | + | 0.229764i | ||||
\(79\) | −0.878680 | + | 1.52192i | −0.0988592 | + | 0.171229i | −0.911213 | − | 0.411936i | \(-0.864853\pi\) |
0.812354 | + | 0.583165i | \(0.198186\pi\) | |||||||
\(80\) | −5.48528 | −0.613273 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 0.0710678 | 0.00784813 | ||||||||
\(83\) | 1.07107 | 0.117565 | 0.0587825 | − | 0.998271i | \(-0.481278\pi\) | ||||
0.0587825 | + | 0.998271i | \(0.481278\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.32843 | − | 9.22911i | −0.577949 | − | 1.00104i | ||||
\(86\) | −0.707107 | + | 1.22474i | −0.0762493 | + | 0.132068i | ||||
\(87\) | −2.94975 | + | 5.10911i | −0.316246 | + | 0.547754i | ||||
\(88\) | −0.928932 | −0.0990245 | ||||||||
\(89\) | −7.65685 | − | 13.2621i | −0.811625 | − | 1.40578i | −0.911726 | − | 0.410798i | \(-0.865250\pi\) |
0.100101 | − | 0.994977i | \(-0.468083\pi\) | |||||||
\(90\) | 0.757359 | 0.0798327 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.58579 | 0.269587 | ||||||||
\(93\) | −1.82843 | − | 3.16693i | −0.189599 | − | 0.328395i | ||||
\(94\) | −1.51472 | −0.156231 | ||||||||
\(95\) | 5.48528 | − | 9.50079i | 0.562778 | − | 0.974760i | ||||
\(96\) | −3.12132 | + | 5.40629i | −0.318568 | + | 0.551777i | ||||
\(97\) | 5.41421 | + | 9.37769i | 0.549730 | + | 0.952160i | 0.998293 | + | 0.0584091i | \(0.0186028\pi\) |
−0.448563 | + | 0.893751i | \(0.648064\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.585786 | −0.0588738 | ||||||||
\(100\) | 3.02944 | 0.302944 | ||||||||
\(101\) | 14.6569 | 1.45841 | 0.729206 | − | 0.684295i | \(-0.239890\pi\) | ||||
0.729206 | + | 0.684295i | \(0.239890\pi\) | |||||||
\(102\) | −3.41421 | −0.338058 | ||||||||
\(103\) | −7.00000 | + | 12.1244i | −0.689730 | + | 1.19465i | 0.282194 | + | 0.959357i | \(0.408938\pi\) |
−0.971925 | + | 0.235291i | \(0.924396\pi\) | |||||||
\(104\) | 5.55025 | + | 1.37333i | 0.544247 | + | 0.134666i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.621320 | − | 1.07616i | 0.0603480 | − | 0.104526i | ||||
\(107\) | −8.65685 | − | 14.9941i | −0.836890 | − | 1.44954i | −0.892483 | − | 0.451082i | \(-0.851038\pi\) |
0.0555929 | − | 0.998454i | \(-0.482295\pi\) | |||||||
\(108\) | −5.17157 | + | 8.95743i | −0.497635 | + | 0.861929i | ||||
\(109\) | 6.82843 | + | 11.8272i | 0.654045 | + | 1.13284i | 0.982132 | + | 0.188191i | \(0.0602625\pi\) |
−0.328088 | + | 0.944647i | \(0.606404\pi\) | |||||||
\(110\) | −0.443651 | −0.0423004 | ||||||||
\(111\) | 6.70711 | + | 11.6170i | 0.636610 | + | 1.10264i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.1569 | − | 17.5922i | −0.955476 | − | 1.65493i | −0.733274 | − | 0.679933i | \(-0.762009\pi\) |
−0.222202 | − | 0.975001i | \(-0.571325\pi\) | |||||||
\(114\) | −1.75736 | − | 3.04384i | −0.164592 | − | 0.285081i | ||||
\(115\) | 2.58579 | 0.241126 | ||||||||
\(116\) | 3.81371 | + | 6.60554i | 0.354094 | + | 0.613309i | ||||
\(117\) | 3.50000 | + | 0.866025i | 0.323575 | + | 0.0800641i | ||||
\(118\) | −4.24264 | −0.390567 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.05025 | + | 3.55114i | −0.187162 | + | 0.324173i | ||||
\(121\) | −10.6569 | −0.968805 | ||||||||
\(122\) | −0.863961 | − | 1.49642i | −0.0782194 | − | 0.135480i | ||||
\(123\) | −0.121320 | + | 0.210133i | −0.0109391 | + | 0.0189471i | ||||
\(124\) | −4.72792 | −0.424580 | ||||||||
\(125\) | 12.1716 | 1.08866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.65685 | + | 11.5300i | −0.590700 | + | 1.02312i | 0.403438 | + | 0.915007i | \(0.367815\pi\) |
−0.994138 | + | 0.108116i | \(0.965518\pi\) | |||||||
\(128\) | 5.27817 | + | 9.14207i | 0.466529 | + | 0.808052i | ||||
\(129\) | −2.41421 | − | 4.18154i | −0.212560 | − | 0.368164i | ||||
\(130\) | 2.65076 | + | 0.655892i | 0.232487 | + | 0.0575256i | ||||
\(131\) | −10.6569 | + | 18.4582i | −0.931094 | + | 1.61270i | −0.149638 | + | 0.988741i | \(0.547811\pi\) |
−0.781456 | + | 0.623961i | \(0.785523\pi\) | |||||||
\(132\) | 0.757359 | − | 1.31178i | 0.0659197 | − | 0.114176i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.878680 | − | 1.52192i | −0.0759064 | − | 0.131474i | ||||
\(135\) | −5.17157 | + | 8.95743i | −0.445098 | + | 0.770933i | ||||
\(136\) | −4.62132 | + | 8.00436i | −0.396275 | + | 0.686368i | ||||
\(137\) | 0.0857864 | − | 0.148586i | 0.00732923 | − | 0.0126946i | −0.862338 | − | 0.506334i | \(-0.831000\pi\) |
0.869667 | + | 0.493639i | \(0.164334\pi\) | |||||||
\(138\) | 0.414214 | − | 0.717439i | 0.0352602 | − | 0.0610725i | ||||
\(139\) | 5.94975 | + | 10.3053i | 0.504651 | + | 0.874081i | 0.999986 | + | 0.00537886i | \(0.00171215\pi\) |
−0.495335 | + | 0.868702i | \(0.664955\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.58579 | − | 4.47871i | 0.217763 | − | 0.377176i | ||||
\(142\) | 2.41421 | − | 4.18154i | 0.202596 | − | 0.350907i | ||||
\(143\) | −2.05025 | − | 0.507306i | −0.171451 | − | 0.0424231i | ||||
\(144\) | 1.50000 | + | 2.59808i | 0.125000 | + | 0.216506i | ||||
\(145\) | 3.81371 | + | 6.60554i | 0.316711 | + | 0.548560i | ||||
\(146\) | 2.20711 | − | 3.82282i | 0.182661 | − | 0.316379i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.3431 | 1.42560 | ||||||||
\(149\) | 3.00000 | 0.245770 | 0.122885 | − | 0.992421i | \(-0.460785\pi\) | ||||
0.122885 | + | 0.992421i | \(0.460785\pi\) | |||||||
\(150\) | 0.485281 | − | 0.840532i | 0.0396231 | − | 0.0686292i | ||||
\(151\) | −7.48528 | − | 12.9649i | −0.609144 | − | 1.05507i | −0.991382 | − | 0.131004i | \(-0.958180\pi\) |
0.382238 | − | 0.924064i | \(-0.375153\pi\) | |||||||
\(152\) | −9.51472 | −0.771746 | ||||||||
\(153\) | −2.91421 | + | 5.04757i | −0.235600 | + | 0.408072i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.72792 | −0.379756 | ||||||||
\(156\) | −6.46447 | + | 6.71807i | −0.517572 | + | 0.537876i | ||||
\(157\) | −2.74264 | − | 4.75039i | −0.218887 | − | 0.379123i | 0.735581 | − | 0.677436i | \(-0.236909\pi\) |
−0.954468 | + | 0.298314i | \(0.903576\pi\) | |||||||
\(158\) | 0.727922 | 0.0579104 | ||||||||
\(159\) | 2.12132 | + | 3.67423i | 0.168232 | + | 0.291386i | ||||
\(160\) | 4.03553 | + | 6.98975i | 0.319037 | + | 0.552588i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.03553 | + | 1.79360i | 0.0813592 | + | 0.140918i | ||||
\(163\) | 12.5858 | 0.985795 | 0.492897 | − | 0.870087i | \(-0.335938\pi\) | ||||
0.492897 | + | 0.870087i | \(0.335938\pi\) | |||||||
\(164\) | 0.156854 | + | 0.271680i | 0.0122483 | + | 0.0212146i | ||||
\(165\) | 0.757359 | − | 1.31178i | 0.0589603 | − | 0.102122i | ||||
\(166\) | −0.221825 | − | 0.384213i | −0.0172170 | − | 0.0298207i | ||||
\(167\) | −3.36396 | + | 5.82655i | −0.260311 | + | 0.450872i | −0.966325 | − | 0.257326i | \(-0.917158\pi\) |
0.706013 | + | 0.708198i | \(0.250492\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | + | 6.06218i | 0.884615 | + | 0.466321i | ||||
\(170\) | −2.20711 | + | 3.82282i | −0.169277 | + | 0.293197i | ||||
\(171\) | −6.00000 | −0.458831 | ||||||||
\(172\) | −6.24264 | −0.475997 | ||||||||
\(173\) | −10.1421 | −0.771092 | −0.385546 | − | 0.922689i | \(-0.625987\pi\) | ||||
−0.385546 | + | 0.922689i | \(0.625987\pi\) | |||||||
\(174\) | 2.44365 | 0.185253 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.878680 | − | 1.52192i | −0.0662330 | − | 0.114719i | ||||
\(177\) | 7.24264 | − | 12.5446i | 0.544390 | − | 0.942912i | ||||
\(178\) | −3.17157 | + | 5.49333i | −0.237719 | + | 0.411742i | ||||
\(179\) | −5.65685 | −0.422813 | −0.211407 | − | 0.977398i | \(-0.567804\pi\) | ||||
−0.211407 | + | 0.977398i | \(0.567804\pi\) | |||||||
\(180\) | 1.67157 | + | 2.89525i | 0.124592 | + | 0.215799i | ||||
\(181\) | 9.14214 | 0.679530 | 0.339765 | − | 0.940510i | \(-0.389653\pi\) | ||||
0.339765 | + | 0.940510i | \(0.389653\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.89949 | 0.436103 | ||||||||
\(184\) | −1.12132 | − | 1.94218i | −0.0826648 | − | 0.143180i | ||||
\(185\) | 17.3431 | 1.27509 | ||||||||
\(186\) | −0.757359 | + | 1.31178i | −0.0555323 | + | 0.0961847i | ||||
\(187\) | 1.70711 | − | 2.95680i | 0.124836 | − | 0.216222i | ||||
\(188\) | −3.34315 | − | 5.79050i | −0.243824 | − | 0.422315i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.54416 | −0.329668 | ||||||||
\(191\) | 16.2426 | 1.17528 | 0.587638 | − | 0.809124i | \(-0.300058\pi\) | ||||
0.587638 | + | 0.809124i | \(0.300058\pi\) | |||||||
\(192\) | −5.89949 | −0.425759 | ||||||||
\(193\) | 7.14214 | 0.514102 | 0.257051 | − | 0.966398i | \(-0.417249\pi\) | ||||
0.257051 | + | 0.966398i | \(0.417249\pi\) | |||||||
\(194\) | 2.24264 | − | 3.88437i | 0.161012 | − | 0.278881i | ||||
\(195\) | −6.46447 | + | 6.71807i | −0.462930 | + | 0.481091i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.41421 | + | 12.8418i | −0.528241 | + | 0.914940i | 0.471217 | + | 0.882017i | \(0.343815\pi\) |
−0.999458 | + | 0.0329227i | \(0.989518\pi\) | |||||||
\(198\) | 0.121320 | + | 0.210133i | 0.00862186 | + | 0.0149335i | ||||
\(199\) | 7.48528 | − | 12.9649i | 0.530618 | − | 0.919057i | −0.468744 | − | 0.883334i | \(-0.655293\pi\) |
0.999362 | − | 0.0357226i | \(-0.0113733\pi\) | |||||||
\(200\) | −1.31371 | − | 2.27541i | −0.0928932 | − | 0.160896i | ||||
\(201\) | 6.00000 | 0.423207 | ||||||||
\(202\) | −3.03553 | − | 5.25770i | −0.213579 | − | 0.369930i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.53553 | − | 13.0519i | −0.527593 | − | 0.913818i | ||||
\(205\) | 0.156854 | + | 0.271680i | 0.0109552 | + | 0.0189749i | ||||
\(206\) | 5.79899 | 0.404035 | ||||||||
\(207\) | −0.707107 | − | 1.22474i | −0.0491473 | − | 0.0851257i | ||||
\(208\) | 3.00000 | + | 10.3923i | 0.208013 | + | 0.720577i | ||||
\(209\) | 3.51472 | 0.243118 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.3640 | + | 21.4150i | −0.851170 | + | 1.47427i | 0.0289828 | + | 0.999580i | \(0.490773\pi\) |
−0.880153 | + | 0.474690i | \(0.842560\pi\) | |||||||
\(212\) | 5.48528 | 0.376731 | ||||||||
\(213\) | 8.24264 | + | 14.2767i | 0.564776 | + | 0.978221i | ||||
\(214\) | −3.58579 | + | 6.21076i | −0.245119 | + | 0.424559i | ||||
\(215\) | −6.24264 | −0.425745 | ||||||||
\(216\) | 8.97056 | 0.610369 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.82843 | − | 4.89898i | 0.191565 | − | 0.331801i | ||||
\(219\) | 7.53553 | + | 13.0519i | 0.509204 | + | 0.881968i | ||||
\(220\) | −0.979185 | − | 1.69600i | −0.0660166 | − | 0.114344i | ||||
\(221\) | −14.5711 | + | 15.1427i | −0.980156 | + | 1.01861i | ||||
\(222\) | 2.77817 | − | 4.81194i | 0.186459 | − | 0.322956i | ||||
\(223\) | −1.00000 | + | 1.73205i | −0.0669650 | + | 0.115987i | −0.897564 | − | 0.440884i | \(-0.854665\pi\) |
0.830599 | + | 0.556871i | \(0.187998\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.828427 | − | 1.43488i | −0.0552285 | − | 0.0956585i | ||||
\(226\) | −4.20711 | + | 7.28692i | −0.279853 | + | 0.484719i | ||||
\(227\) | −2.94975 | + | 5.10911i | −0.195782 | + | 0.339104i | −0.947156 | − | 0.320772i | \(-0.896058\pi\) |
0.751375 | + | 0.659876i | \(0.229391\pi\) | |||||||
\(228\) | 7.75736 | − | 13.4361i | 0.513744 | − | 0.889830i | ||||
\(229\) | 6.24264 | − | 10.8126i | 0.412525 | − | 0.714515i | −0.582640 | − | 0.812730i | \(-0.697980\pi\) |
0.995165 | + | 0.0982157i | \(0.0313135\pi\) | |||||||
\(230\) | −0.535534 | − | 0.927572i | −0.0353121 | − | 0.0611623i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.30761 | − | 5.72895i | 0.217155 | − | 0.376124i | ||||
\(233\) | −1.41421 | + | 2.44949i | −0.0926482 | + | 0.160471i | −0.908625 | − | 0.417614i | \(-0.862867\pi\) |
0.815976 | + | 0.578085i | \(0.196200\pi\) | |||||||
\(234\) | −0.414214 | − | 1.43488i | −0.0270780 | − | 0.0938009i | ||||
\(235\) | −3.34315 | − | 5.79050i | −0.218083 | − | 0.377730i | ||||
\(236\) | −9.36396 | − | 16.2189i | −0.609542 | − | 1.05576i | ||||
\(237\) | −1.24264 | + | 2.15232i | −0.0807182 | + | 0.139808i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.3848 | 1.57732 | 0.788660 | − | 0.614830i | \(-0.210775\pi\) | ||||
0.788660 | + | 0.614830i | \(0.210775\pi\) | |||||||
\(240\) | −7.75736 | −0.500735 | ||||||||
\(241\) | −7.74264 | + | 13.4106i | −0.498747 | + | 0.863856i | −0.999999 | − | 0.00144585i | \(-0.999540\pi\) |
0.501252 | + | 0.865302i | \(0.332873\pi\) | |||||||
\(242\) | 2.20711 | + | 3.82282i | 0.141878 | + | 0.245740i | ||||
\(243\) | 9.89949 | 0.635053 | ||||||||
\(244\) | 3.81371 | − | 6.60554i | 0.244148 | − | 0.422876i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.100505 | 0.00640797 | ||||||||
\(247\) | −21.0000 | − | 5.19615i | −1.33620 | − | 0.330623i | ||||
\(248\) | 2.05025 | + | 3.55114i | 0.130191 | + | 0.225498i | ||||
\(249\) | 1.51472 | 0.0959914 | ||||||||
\(250\) | −2.52082 | − | 4.36618i | −0.159430 | − | 0.276141i | ||||
\(251\) | −11.4853 | − | 19.8931i | −0.724945 | − | 1.25564i | −0.958997 | − | 0.283417i | \(-0.908532\pi\) |
0.234052 | − | 0.972224i | \(-0.424801\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.414214 | + | 0.717439i | 0.0260414 | + | 0.0451050i | ||||
\(254\) | 5.51472 | 0.346024 | ||||||||
\(255\) | −7.53553 | − | 13.0519i | −0.471893 | − | 0.817343i | ||||
\(256\) | −1.98528 | + | 3.43861i | −0.124080 | + | 0.214913i | ||||
\(257\) | −7.50000 | − | 12.9904i | −0.467837 | − | 0.810318i | 0.531487 | − | 0.847066i | \(-0.321633\pi\) |
−0.999325 | + | 0.0367485i | \(0.988300\pi\) | |||||||
\(258\) | −1.00000 | + | 1.73205i | −0.0622573 | + | 0.107833i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.34315 | + | 11.5810i | 0.207333 | + | 0.718223i | ||||
\(261\) | 2.08579 | − | 3.61269i | 0.129107 | − | 0.223620i | ||||
\(262\) | 8.82843 | 0.545422 | ||||||||
\(263\) | −6.72792 | −0.414861 | −0.207431 | − | 0.978250i | \(-0.566510\pi\) | ||||
−0.207431 | + | 0.978250i | \(0.566510\pi\) | |||||||
\(264\) | −1.31371 | −0.0808532 | ||||||||
\(265\) | 5.48528 | 0.336958 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.8284 | − | 18.7554i | −0.662689 | − | 1.14781i | ||||
\(268\) | 3.87868 | − | 6.71807i | 0.236928 | − | 0.410371i | ||||
\(269\) | 9.00000 | − | 15.5885i | 0.548740 | − | 0.950445i | −0.449622 | − | 0.893219i | \(-0.648441\pi\) |
0.998361 | − | 0.0572259i | \(-0.0182255\pi\) | |||||||
\(270\) | 4.28427 | 0.260732 | ||||||||
\(271\) | 10.5355 | + | 18.2481i | 0.639988 | + | 1.10849i | 0.985435 | + | 0.170054i | \(0.0543941\pi\) |
−0.345447 | + | 0.938438i | \(0.612273\pi\) | |||||||
\(272\) | −17.4853 | −1.06020 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.0710678 | −0.00429336 | ||||||||
\(275\) | 0.485281 | + | 0.840532i | 0.0292636 | + | 0.0506860i | ||||
\(276\) | 3.65685 | 0.220117 | ||||||||
\(277\) | −0.985281 | + | 1.70656i | −0.0591998 | + | 0.102537i | −0.894106 | − | 0.447855i | \(-0.852188\pi\) |
0.834907 | + | 0.550392i | \(0.185522\pi\) | |||||||
\(278\) | 2.46447 | − | 4.26858i | 0.147809 | − | 0.256012i | ||||
\(279\) | 1.29289 | + | 2.23936i | 0.0774035 | + | 0.134067i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.4853 | −1.04308 | −0.521542 | − | 0.853225i | \(-0.674643\pi\) | ||||
−0.521542 | + | 0.853225i | \(0.674643\pi\) | |||||||
\(282\) | −2.14214 | −0.127562 | ||||||||
\(283\) | −19.8995 | −1.18290 | −0.591451 | − | 0.806341i | \(-0.701445\pi\) | ||||
−0.591451 | + | 0.806341i | \(0.701445\pi\) | |||||||
\(284\) | 21.3137 | 1.26474 | ||||||||
\(285\) | 7.75736 | − | 13.4361i | 0.459506 | − | 0.795888i | ||||
\(286\) | 0.242641 | + | 0.840532i | 0.0143476 | + | 0.0497017i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.20711 | − | 3.82282i | 0.130055 | − | 0.225262i | ||||
\(289\) | −8.48528 | − | 14.6969i | −0.499134 | − | 0.864526i | ||||
\(290\) | 1.57969 | − | 2.73610i | 0.0927626 | − | 0.160669i | ||||
\(291\) | 7.65685 | + | 13.2621i | 0.448853 | + | 0.777436i | ||||
\(292\) | 19.4853 | 1.14029 | ||||||||
\(293\) | −14.2279 | − | 24.6435i | −0.831204 | − | 1.43969i | −0.897084 | − | 0.441860i | \(-0.854319\pi\) |
0.0658799 | − | 0.997828i | \(-0.479015\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.36396 | − | 16.2189i | −0.545191 | − | 0.944298i | ||||
\(296\) | −7.52082 | − | 13.0264i | −0.437139 | − | 0.757146i | ||||
\(297\) | −3.31371 | −0.192281 | ||||||||
\(298\) | −0.621320 | − | 1.07616i | −0.0359921 | − | 0.0623402i | ||||
\(299\) | −1.41421 | − | 4.89898i | −0.0817861 | − | 0.283315i | ||||
\(300\) | 4.28427 | 0.247353 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.10051 | + | 5.37023i | −0.178414 | + | 0.309022i | ||||
\(303\) | 20.7279 | 1.19079 | ||||||||
\(304\) | −9.00000 | − | 15.5885i | −0.516185 | − | 0.894059i | ||||
\(305\) | 3.81371 | − | 6.60554i | 0.218372 | − | 0.378232i | ||||
\(306\) | 2.41421 | 0.138011 | ||||||||
\(307\) | −32.7279 | −1.86788 | −0.933941 | − | 0.357428i | \(-0.883654\pi\) | ||||
−0.933941 | + | 0.357428i | \(0.883654\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.89949 | + | 17.1464i | −0.563163 | + | 0.975426i | ||||
\(310\) | 0.979185 | + | 1.69600i | 0.0556140 | + | 0.0963262i | ||||
\(311\) | 6.46447 | + | 11.1968i | 0.366566 | + | 0.634911i | 0.989026 | − | 0.147740i | \(-0.0472000\pi\) |
−0.622460 | + | 0.782652i | \(0.713867\pi\) | |||||||
\(312\) | 7.84924 | + | 1.94218i | 0.444376 | + | 0.109955i | ||||
\(313\) | 7.00000 | − | 12.1244i | 0.395663 | − | 0.685309i | −0.597522 | − | 0.801852i | \(-0.703848\pi\) |
0.993186 | + | 0.116543i | \(0.0371814\pi\) | |||||||
\(314\) | −1.13604 | + | 1.96768i | −0.0641104 | + | 0.111042i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.60660 | + | 2.78272i | 0.0903784 | + | 0.156540i | ||||
\(317\) | −16.3284 | + | 28.2817i | −0.917096 | + | 1.58846i | −0.113292 | + | 0.993562i | \(0.536140\pi\) |
−0.803804 | + | 0.594895i | \(0.797194\pi\) | |||||||
\(318\) | 0.878680 | − | 1.52192i | 0.0492739 | − | 0.0853449i | ||||
\(319\) | −1.22183 | + | 2.11626i | −0.0684091 | + | 0.118488i | ||||
\(320\) | −3.81371 | + | 6.60554i | −0.213193 | + | 0.369261i | ||||
\(321\) | −12.2426 | − | 21.2049i | −0.683318 | − | 1.18354i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.4853 | − | 30.2854i | 0.972907 | − | 1.68512i | ||||
\(324\) | −4.57107 | + | 7.91732i | −0.253948 | + | 0.439851i | ||||
\(325\) | −1.65685 | − | 5.73951i | −0.0919057 | − | 0.318371i | ||||
\(326\) | −2.60660 | − | 4.51477i | −0.144366 | − | 0.250050i | ||||
\(327\) | 9.65685 | + | 16.7262i | 0.534025 | + | 0.924959i | ||||
\(328\) | 0.136039 | − | 0.235626i | 0.00751150 | − | 0.0130103i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.627417 | −0.0345382 | ||||||||
\(331\) | −24.8701 | −1.36698 | −0.683491 | − | 0.729959i | \(-0.739539\pi\) | ||||
−0.683491 | + | 0.729959i | \(0.739539\pi\) | |||||||
\(332\) | 0.979185 | − | 1.69600i | 0.0537397 | − | 0.0930800i | ||||
\(333\) | −4.74264 | − | 8.21449i | −0.259895 | − | 0.450152i | ||||
\(334\) | 2.78680 | 0.152487 | ||||||||
\(335\) | 3.87868 | − | 6.71807i | 0.211915 | − | 0.367047i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.48528 | −0.189855 | −0.0949277 | − | 0.995484i | \(-0.530262\pi\) | ||||
−0.0949277 | + | 0.995484i | \(0.530262\pi\) | |||||||
\(338\) | −0.207107 | − | 5.38079i | −0.0112651 | − | 0.292677i | ||||
\(339\) | −14.3640 | − | 24.8791i | −0.780143 | − | 1.35125i | ||||
\(340\) | −19.4853 | −1.05674 | ||||||||
\(341\) | −0.757359 | − | 1.31178i | −0.0410133 | − | 0.0710371i | ||||
\(342\) | 1.24264 | + | 2.15232i | 0.0671943 | + | 0.116384i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.70711 | + | 4.68885i | 0.145957 | + | 0.252806i | ||||
\(345\) | 3.65685 | 0.196878 | ||||||||
\(346\) | 2.10051 | + | 3.63818i | 0.112924 | + | 0.195590i | ||||
\(347\) | 3.05025 | − | 5.28319i | 0.163746 | − | 0.283617i | −0.772463 | − | 0.635060i | \(-0.780976\pi\) |
0.936209 | + | 0.351443i | \(0.114309\pi\) | |||||||
\(348\) | 5.39340 | + | 9.34164i | 0.289116 | + | 0.500764i | ||||
\(349\) | −4.65685 | + | 8.06591i | −0.249276 | + | 0.431758i | −0.963325 | − | 0.268337i | \(-0.913526\pi\) |
0.714049 | + | 0.700095i | \(0.246859\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.7990 | + | 4.89898i | 1.05679 | + | 0.261488i | ||||
\(352\) | −1.29289 | + | 2.23936i | −0.0689114 | + | 0.119358i | ||||
\(353\) | 5.82843 | 0.310216 | 0.155108 | − | 0.987898i | \(-0.450427\pi\) | ||||
0.155108 | + | 0.987898i | \(0.450427\pi\) | |||||||
\(354\) | −6.00000 | −0.318896 | ||||||||
\(355\) | 21.3137 | 1.13121 | ||||||||
\(356\) | −28.0000 | −1.48400 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.17157 | + | 2.02922i | 0.0619196 | + | 0.107248i | ||||
\(359\) | 8.48528 | − | 14.6969i | 0.447836 | − | 0.775675i | −0.550409 | − | 0.834895i | \(-0.685528\pi\) |
0.998245 | + | 0.0592205i | \(0.0188615\pi\) | |||||||
\(360\) | 1.44975 | − | 2.51104i | 0.0764084 | − | 0.132343i | ||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | −1.89340 | − | 3.27946i | −0.0995148 | − | 0.172365i | ||||
\(363\) | −15.0711 | −0.791026 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.4853 | 1.01991 | ||||||||
\(366\) | −1.22183 | − | 2.11626i | −0.0638658 | − | 0.110619i | ||||
\(367\) | −28.7279 | −1.49959 | −0.749793 | − | 0.661673i | \(-0.769847\pi\) | ||||
−0.749793 | + | 0.661673i | \(0.769847\pi\) | |||||||
\(368\) | 2.12132 | − | 3.67423i | 0.110581 | − | 0.191533i | ||||
\(369\) | 0.0857864 | − | 0.148586i | 0.00446586 | − | 0.00773510i | ||||
\(370\) | −3.59188 | − | 6.22132i | −0.186733 | − | 0.323431i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.68629 | −0.346668 | ||||||||
\(373\) | 26.4558 | 1.36983 | 0.684916 | − | 0.728622i | \(-0.259839\pi\) | ||||
0.684916 | + | 0.728622i | \(0.259839\pi\) | |||||||
\(374\) | −1.41421 | −0.0731272 | ||||||||
\(375\) | 17.2132 | 0.888886 | ||||||||
\(376\) | −2.89949 | + | 5.02207i | −0.149530 | + | 0.258994i | ||||
\(377\) | 10.4289 | − | 10.8381i | 0.537117 | − | 0.558189i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.121320 | − | 0.210133i | 0.00623181 | − | 0.0107938i | −0.862893 | − | 0.505387i | \(-0.831350\pi\) |
0.869124 | + | 0.494593i | \(0.164683\pi\) | |||||||
\(380\) | −10.0294 | − | 17.3715i | −0.514499 | − | 0.891139i | ||||
\(381\) | −9.41421 | + | 16.3059i | −0.482305 | + | 0.835376i | ||||
\(382\) | −3.36396 | − | 5.82655i | −0.172115 | − | 0.298112i | ||||
\(383\) | −34.0416 | −1.73945 | −0.869723 | − | 0.493540i | \(-0.835703\pi\) | ||||
−0.869723 | + | 0.493540i | \(0.835703\pi\) | |||||||
\(384\) | 7.46447 | + | 12.9288i | 0.380919 | + | 0.659772i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.47918 | − | 2.56202i | −0.0752885 | − | 0.130404i | ||||
\(387\) | 1.70711 | + | 2.95680i | 0.0867771 | + | 0.150302i | ||||
\(388\) | 19.7990 | 1.00514 | ||||||||
\(389\) | −13.5711 | − | 23.5058i | −0.688080 | − | 1.19179i | −0.972458 | − | 0.233078i | \(-0.925120\pi\) |
0.284378 | − | 0.958712i | \(-0.408213\pi\) | |||||||
\(390\) | 3.74874 | + | 0.927572i | 0.189825 | + | 0.0469694i | ||||
\(391\) | 8.24264 | 0.416848 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.0711 | + | 26.1039i | −0.760235 | + | 1.31677i | ||||
\(394\) | 6.14214 | 0.309436 | ||||||||
\(395\) | 1.60660 | + | 2.78272i | 0.0808369 | + | 0.140014i | ||||
\(396\) | −0.535534 | + | 0.927572i | −0.0269116 | + | 0.0466122i | ||||
\(397\) | 6.62742 | 0.332621 | 0.166310 | − | 0.986073i | \(-0.446815\pi\) | ||||
0.166310 | + | 0.986073i | \(0.446815\pi\) | |||||||
\(398\) | −6.20101 | −0.310829 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.48528 | − | 4.30463i | 0.124264 | − | 0.215232i | ||||
\(401\) | −4.39949 | − | 7.62015i | −0.219700 | − | 0.380532i | 0.735016 | − | 0.678050i | \(-0.237175\pi\) |
−0.954716 | + | 0.297518i | \(0.903841\pi\) | |||||||
\(402\) | −1.24264 | − | 2.15232i | −0.0619773 | − | 0.107348i | ||||
\(403\) | 2.58579 | + | 8.95743i | 0.128807 | + | 0.446201i | ||||
\(404\) | 13.3995 | − | 23.2086i | 0.666650 | − | 1.15467i | ||||
\(405\) | −4.57107 | + | 7.91732i | −0.227138 | + | 0.393415i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.77817 | + | 4.81194i | 0.137709 | + | 0.238519i | ||||
\(408\) | −6.53553 | + | 11.3199i | −0.323557 | + | 0.560417i | ||||
\(409\) | 10.9853 | − | 19.0271i | 0.543187 | − | 0.940828i | −0.455531 | − | 0.890220i | \(-0.650551\pi\) |
0.998719 | − | 0.0506081i | \(-0.0161159\pi\) | |||||||
\(410\) | 0.0649712 | − | 0.112533i | 0.00320870 | − | 0.00555763i | ||||
\(411\) | 0.121320 | − | 0.210133i | 0.00598429 | − | 0.0103651i | ||||
\(412\) | 12.7990 | + | 22.1685i | 0.630561 | + | 1.09216i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.292893 | + | 0.507306i | −0.0143949 | + | 0.0249327i | ||||
\(415\) | 0.979185 | − | 1.69600i | 0.0480663 | − | 0.0832533i | ||||
\(416\) | 11.0355 | − | 11.4685i | 0.541062 | − | 0.562288i | ||||
\(417\) | 8.41421 | + | 14.5738i | 0.412046 | + | 0.713684i | ||||
\(418\) | −0.727922 | − | 1.26080i | −0.0356038 | − | 0.0616676i | ||||
\(419\) | 5.77817 | − | 10.0081i | 0.282282 | − | 0.488927i | −0.689664 | − | 0.724129i | \(-0.742242\pi\) |
0.971946 | + | 0.235202i | \(0.0755752\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.4853 | 1.04713 | 0.523564 | − | 0.851986i | \(-0.324602\pi\) | ||||
0.523564 | + | 0.851986i | \(0.324602\pi\) | |||||||
\(422\) | 10.2426 | 0.498604 | ||||||||
\(423\) | −1.82843 | + | 3.16693i | −0.0889012 | + | 0.153981i | ||||
\(424\) | −2.37868 | − | 4.11999i | −0.115519 | − | 0.200085i | ||||
\(425\) | 9.65685 | 0.468426 | ||||||||
\(426\) | 3.41421 | − | 5.91359i | 0.165419 | − | 0.286514i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −31.6569 | −1.53019 | ||||||||
\(429\) | −2.89949 | − | 0.717439i | −0.139989 | − | 0.0346383i | ||||
\(430\) | 1.29289 | + | 2.23936i | 0.0623488 | + | 0.107991i | ||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | 8.48528 | + | 14.6969i | 0.408248 | + | 0.707107i | ||||
\(433\) | −8.74264 | − | 15.1427i | −0.420144 | − | 0.727712i | 0.575809 | − | 0.817584i | \(-0.304687\pi\) |
−0.995953 | + | 0.0898728i | \(0.971354\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.39340 | + | 9.34164i | 0.258594 | + | 0.447897i | ||||
\(436\) | 24.9706 | 1.19587 | ||||||||
\(437\) | 4.24264 | + | 7.34847i | 0.202953 | + | 0.351525i | ||||
\(438\) | 3.12132 | − | 5.40629i | 0.149142 | − | 0.258322i | ||||
\(439\) | 0.636039 | + | 1.10165i | 0.0303565 | + | 0.0525790i | 0.880805 | − | 0.473480i | \(-0.157002\pi\) |
−0.850448 | + | 0.526059i | \(0.823669\pi\) | |||||||
\(440\) | −0.849242 | + | 1.47093i | −0.0404860 | + | 0.0701239i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.44975 | + | 2.09077i | 0.401914 | + | 0.0994478i | ||||
\(443\) | −12.8284 | + | 22.2195i | −0.609497 | + | 1.05568i | 0.381826 | + | 0.924234i | \(0.375295\pi\) |
−0.991323 | + | 0.131446i | \(0.958038\pi\) | |||||||
\(444\) | 24.5269 | 1.16400 | ||||||||
\(445\) | −28.0000 | −1.32733 | ||||||||
\(446\) | 0.828427 | 0.0392272 | ||||||||
\(447\) | 4.24264 | 0.200670 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.2426 | − | 28.1331i | −0.766538 | − | 1.32768i | −0.939430 | − | 0.342741i | \(-0.888645\pi\) |
0.172892 | − | 0.984941i | \(-0.444689\pi\) | |||||||
\(450\) | −0.343146 | + | 0.594346i | −0.0161760 | + | 0.0280177i | ||||
\(451\) | −0.0502525 | + | 0.0870399i | −0.00236630 | + | 0.00409855i | ||||
\(452\) | −37.1421 | −1.74702 | ||||||||
\(453\) | −10.5858 | − | 18.3351i | −0.497364 | − | 0.861459i | ||||
\(454\) | 2.44365 | 0.114686 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.4558 | −0.630128 | ||||||||
\(457\) | 12.5000 | + | 21.6506i | 0.584725 | + | 1.01277i | 0.994910 | + | 0.100771i | \(0.0321310\pi\) |
−0.410184 | + | 0.912003i | \(0.634536\pi\) | |||||||
\(458\) | −5.17157 | −0.241652 | ||||||||
\(459\) | −16.4853 | + | 28.5533i | −0.769467 | + | 1.33276i | ||||
\(460\) | 2.36396 | − | 4.09450i | 0.110220 | − | 0.190907i | ||||
\(461\) | −0.671573 | − | 1.16320i | −0.0312783 | − | 0.0541755i | 0.849963 | − | 0.526843i | \(-0.176624\pi\) |
−0.881241 | + | 0.472668i | \(0.843291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.72792 | 0.312673 | 0.156337 | − | 0.987704i | \(-0.450032\pi\) | ||||
0.156337 | + | 0.987704i | \(0.450032\pi\) | |||||||
\(464\) | 12.5147 | 0.580981 | ||||||||
\(465\) | −6.68629 | −0.310069 | ||||||||
\(466\) | 1.17157 | 0.0542721 | ||||||||
\(467\) | −5.70711 | + | 9.88500i | −0.264093 | + | 0.457423i | −0.967326 | − | 0.253537i | \(-0.918406\pi\) |
0.703232 | + | 0.710960i | \(0.251739\pi\) | |||||||
\(468\) | 4.57107 | − | 4.75039i | 0.211298 | − | 0.219587i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.38478 | + | 2.39850i | −0.0638750 | + | 0.110635i | ||||
\(471\) | −3.87868 | − | 6.71807i | −0.178720 | − | 0.309552i | ||||
\(472\) | −8.12132 | + | 14.0665i | −0.373814 | + | 0.647465i | ||||
\(473\) | −1.00000 | − | 1.73205i | −0.0459800 | − | 0.0796398i | ||||
\(474\) | 1.02944 | 0.0472836 | ||||||||
\(475\) | 4.97056 | + | 8.60927i | 0.228065 | + | 0.395020i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.50000 | − | 2.59808i | −0.0686803 | − | 0.118958i | ||||
\(478\) | −5.05025 | − | 8.74729i | −0.230993 | − | 0.400092i | ||||
\(479\) | −1.61522 | −0.0738015 | −0.0369007 | − | 0.999319i | \(-0.511749\pi\) | ||||
−0.0369007 | + | 0.999319i | \(0.511749\pi\) | |||||||
\(480\) | 5.70711 | + | 9.88500i | 0.260493 | + | 0.451186i | ||||
\(481\) | −9.48528 | − | 32.8580i | −0.432492 | − | 1.49819i | ||||
\(482\) | 6.41421 | 0.292159 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.74264 | + | 16.8747i | −0.442847 | + | 0.767034i | ||||
\(485\) | 19.7990 | 0.899026 | ||||||||
\(486\) | −2.05025 | − | 3.55114i | −0.0930013 | − | 0.161083i | ||||
\(487\) | 6.48528 | − | 11.2328i | 0.293876 | − | 0.509008i | −0.680847 | − | 0.732426i | \(-0.738388\pi\) |
0.974723 | + | 0.223418i | \(0.0717213\pi\) | |||||||
\(488\) | −6.61522 | −0.299457 | ||||||||
\(489\) | 17.7990 | 0.804898 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.34315 | + | 10.9867i | −0.286262 | + | 0.495821i | −0.972914 | − | 0.231165i | \(-0.925746\pi\) |
0.686652 | + | 0.726986i | \(0.259079\pi\) | |||||||
\(492\) | 0.221825 | + | 0.384213i | 0.0100007 | + | 0.0173217i | ||||
\(493\) | 12.1569 | + | 21.0563i | 0.547517 | + | 0.948328i | ||||
\(494\) | 2.48528 | + | 8.60927i | 0.111818 | + | 0.387349i | ||||
\(495\) | −0.535534 | + | 0.927572i | −0.0240705 | + | 0.0416913i | ||||
\(496\) | −3.87868 | + | 6.71807i | −0.174158 | + | 0.301650i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.313708 | − | 0.543359i | −0.0140576 | − | 0.0243485i | ||||
\(499\) | −10.0208 | + | 17.3566i | −0.448593 | + | 0.776986i | −0.998295 | − | 0.0583748i | \(-0.981408\pi\) |
0.549701 | + | 0.835361i | \(0.314741\pi\) | |||||||
\(500\) | 11.1274 | − | 19.2733i | 0.497633 | − | 0.861926i | ||||
\(501\) | −4.75736 | + | 8.23999i | −0.212543 | + | 0.368136i | ||||
\(502\) | −4.75736 | + | 8.23999i | −0.212331 | + | 0.367769i | ||||
\(503\) | 1.22183 | + | 2.11626i | 0.0544785 | + | 0.0943595i | 0.891979 | − | 0.452078i | \(-0.149317\pi\) |
−0.837500 | + | 0.546437i | \(0.815984\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.3995 | − | 23.2086i | 0.596270 | − | 1.03277i | ||||
\(506\) | 0.171573 | − | 0.297173i | 0.00762734 | − | 0.0132109i | ||||
\(507\) | 16.2635 | + | 8.57321i | 0.722285 | + | 0.380750i | ||||
\(508\) | 12.1716 | + | 21.0818i | 0.540026 | + | 0.935353i | ||||
\(509\) | −2.32843 | − | 4.03295i | −0.103206 | − | 0.178758i | 0.809798 | − | 0.586709i | \(-0.199577\pi\) |
−0.913004 | + | 0.407951i | \(0.866243\pi\) | |||||||
\(510\) | −3.12132 | + | 5.40629i | −0.138214 | + | 0.239394i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.7574 | 1.00574 | ||||||||
\(513\) | −33.9411 | −1.49854 | ||||||||
\(514\) | −3.10660 | + | 5.38079i | −0.137026 | + | 0.237337i | ||||
\(515\) | 12.7990 | + | 22.1685i | 0.563991 | + | 0.976861i | ||||
\(516\) | −8.82843 | −0.388650 | ||||||||
\(517\) | 1.07107 | − | 1.85514i | 0.0471055 | − | 0.0815891i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.3431 | −0.629594 | ||||||||
\(520\) | 7.24874 | − | 7.53311i | 0.317878 | − | 0.330349i | ||||
\(521\) | 12.3284 | + | 21.3535i | 0.540118 | + | 0.935512i | 0.998897 | + | 0.0469615i | \(0.0149538\pi\) |
−0.458779 | + | 0.888551i | \(0.651713\pi\) | |||||||
\(522\) | −1.72792 | −0.0756291 | ||||||||
\(523\) | 8.48528 | + | 14.6969i | 0.371035 | + | 0.642652i | 0.989725 | − | 0.142983i | \(-0.0456695\pi\) |
−0.618690 | + | 0.785635i | \(0.712336\pi\) | |||||||
\(524\) | 19.4853 | + | 33.7495i | 0.851218 | + | 1.47435i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.39340 | + | 2.41344i | 0.0607551 | + | 0.105231i | ||||
\(527\) | −15.0711 | −0.656506 | ||||||||
\(528\) | −1.24264 | − | 2.15232i | −0.0540790 | − | 0.0936676i | ||||
\(529\) | 10.5000 | − | 18.1865i | 0.456522 | − | 0.790719i | ||||
\(530\) | −1.13604 | − | 1.96768i | −0.0493464 | − | 0.0854704i | ||||
\(531\) | −5.12132 | + | 8.87039i | −0.222246 | + | 0.384942i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.428932 | − | 0.445759i | 0.0185791 | − | 0.0193080i | ||||
\(534\) | −4.48528 | + | 7.76874i | −0.194097 | + | 0.336186i | ||||
\(535\) | −31.6569 | −1.36865 | ||||||||
\(536\) | −6.72792 | −0.290602 | ||||||||
\(537\) | −8.00000 | −0.345225 | ||||||||
\(538\) | −7.45584 | −0.321444 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 9.45584 | + | 16.3780i | 0.406915 | + | 0.704797i | ||||
\(541\) | 5.74264 | − | 9.94655i | 0.246895 | − | 0.427635i | −0.715767 | − | 0.698339i | \(-0.753923\pi\) |
0.962663 | + | 0.270703i | \(0.0872563\pi\) | |||||||
\(542\) | 4.36396 | − | 7.55860i | 0.187448 | − | 0.324670i | ||||
\(543\) | 12.9289 | 0.554834 | ||||||||
\(544\) | 12.8640 | + | 22.2810i | 0.551538 | + | 0.955291i | ||||
\(545\) | 24.9706 | 1.06962 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.928932 | 0.0397183 | 0.0198591 | − | 0.999803i | \(-0.493678\pi\) | ||||
0.0198591 | + | 0.999803i | \(0.493678\pi\) | |||||||
\(548\) | −0.156854 | − | 0.271680i | −0.00670048 | − | 0.0116056i | ||||
\(549\) | −4.17157 | −0.178038 | ||||||||
\(550\) | 0.201010 | − | 0.348160i | 0.00857110 | − | 0.0148456i | ||||
\(551\) | −12.5147 | + | 21.6761i | −0.533145 | + | 0.923434i | ||||
\(552\) | −1.58579 | − | 2.74666i | −0.0674956 | − | 0.116906i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.816234 | 0.0346785 | ||||||||
\(555\) | 24.5269 | 1.04111 | ||||||||
\(556\) | 21.7574 | 0.922718 | ||||||||
\(557\) | 12.3137 | 0.521749 | 0.260874 | − | 0.965373i | \(-0.415989\pi\) | ||||
0.260874 | + | 0.965373i | \(0.415989\pi\) | |||||||
\(558\) | 0.535534 | − | 0.927572i | 0.0226710 | − | 0.0392673i | ||||
\(559\) | 3.41421 | + | 11.8272i | 0.144406 | + | 0.500237i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.41421 | − | 4.18154i | 0.101928 | − | 0.176545i | ||||
\(562\) | 3.62132 | + | 6.27231i | 0.152756 | + | 0.264581i | ||||
\(563\) | −0.0502525 | + | 0.0870399i | −0.00211789 | + | 0.00366830i | −0.867082 | − | 0.498165i | \(-0.834007\pi\) |
0.864965 | + | 0.501833i | \(0.167341\pi\) | |||||||
\(564\) | −4.72792 | − | 8.18900i | −0.199081 | − | 0.344819i | ||||
\(565\) | −37.1421 | −1.56258 | ||||||||
\(566\) | 4.12132 | + | 7.13834i | 0.173232 | + | 0.300047i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.24264 | − | 16.0087i | −0.387813 | − | 0.671711i | ||||
\(569\) | −9.41421 | − | 16.3059i | −0.394664 | − | 0.683579i | 0.598394 | − | 0.801202i | \(-0.295806\pi\) |
−0.993058 | + | 0.117623i | \(0.962472\pi\) | |||||||
\(570\) | −6.42641 | −0.269173 | ||||||||
\(571\) | −14.4853 | − | 25.0892i | −0.606190 | − | 1.04995i | −0.991862 | − | 0.127316i | \(-0.959364\pi\) |
0.385672 | − | 0.922636i | \(-0.373970\pi\) | |||||||
\(572\) | −2.67767 | + | 2.78272i | −0.111959 | + | 0.116351i | ||||
\(573\) | 22.9706 | 0.959609 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.17157 | + | 2.02922i | −0.0488580 | + | 0.0846245i | ||||
\(576\) | 4.17157 | 0.173816 | ||||||||
\(577\) | 6.84315 | + | 11.8527i | 0.284884 | + | 0.493433i | 0.972581 | − | 0.232564i | \(-0.0747116\pi\) |
−0.687697 | + | 0.725998i | \(0.741378\pi\) | |||||||
\(578\) | −3.51472 | + | 6.08767i | −0.146193 | + | 0.253214i | ||||
\(579\) | 10.1005 | 0.419763 | ||||||||
\(580\) | 13.9462 | 0.579083 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.17157 | − | 5.49333i | 0.131466 | − | 0.227706i | ||||
\(583\) | 0.878680 | + | 1.52192i | 0.0363912 | + | 0.0630314i | ||||
\(584\) | −8.44975 | − | 14.6354i | −0.349653 | − | 0.605617i | ||||
\(585\) | 4.57107 | − | 4.75039i | 0.188990 | − | 0.196405i | ||||
\(586\) | −5.89340 | + | 10.2077i | −0.243454 | + | 0.421675i | ||||
\(587\) | 14.8284 | − | 25.6836i | 0.612035 | − | 1.06008i | −0.378862 | − | 0.925453i | \(-0.623685\pi\) |
0.990897 | − | 0.134622i | \(-0.0429821\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.75736 | − | 13.4361i | −0.319636 | − | 0.553627i | ||||
\(590\) | −3.87868 | + | 6.71807i | −0.159683 | + | 0.276579i | ||||
\(591\) | −10.4853 | + | 18.1610i | −0.431307 | + | 0.747045i | ||||
\(592\) | 14.2279 | − | 24.6435i | 0.584764 | − | 1.01284i | ||||
\(593\) | −12.6421 | + | 21.8968i | −0.519150 | + | 0.899195i | 0.480602 | + | 0.876939i | \(0.340418\pi\) |
−0.999752 | + | 0.0222559i | \(0.992915\pi\) | |||||||
\(594\) | 0.686292 | + | 1.18869i | 0.0281589 | + | 0.0487726i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.74264 | − | 4.75039i | 0.112343 | − | 0.194584i | ||||
\(597\) | 10.5858 | − | 18.3351i | 0.433247 | − | 0.750407i | ||||
\(598\) | −1.46447 | + | 1.52192i | −0.0598865 | + | 0.0622358i | ||||
\(599\) | −14.1716 | − | 24.5459i | −0.579035 | − | 1.00292i | −0.995590 | − | 0.0938074i | \(-0.970096\pi\) |
0.416556 | − | 0.909110i | \(-0.363237\pi\) | |||||||
\(600\) | −1.85786 | − | 3.21792i | −0.0758470 | − | 0.131371i | ||||
\(601\) | −15.4706 | + | 26.7958i | −0.631057 | + | 1.09302i | 0.356278 | + | 0.934380i | \(0.384045\pi\) |
−0.987336 | + | 0.158644i | \(0.949288\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.24264 | −0.172774 | ||||||||
\(604\) | −27.3726 | −1.11377 | ||||||||
\(605\) | −9.74264 | + | 16.8747i | −0.396095 | + | 0.686056i | ||||
\(606\) | −4.29289 | − | 7.43551i | −0.174387 | − | 0.302047i | ||||
\(607\) | −32.3431 | −1.31277 | −0.656384 | − | 0.754427i | \(-0.727915\pi\) | ||||
−0.656384 | + | 0.754427i | \(0.727915\pi\) | |||||||
\(608\) | −13.2426 | + | 22.9369i | −0.537060 | + | 0.930215i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.15938 | −0.127920 | ||||||||
\(611\) | −9.14214 | + | 9.50079i | −0.369851 | + | 0.384361i | ||||
\(612\) | 5.32843 | + | 9.22911i | 0.215389 | + | 0.373065i | ||||
\(613\) | −14.7990 | −0.597726 | −0.298863 | − | 0.954296i | \(-0.596607\pi\) | ||||
−0.298863 | + | 0.954296i | \(0.596607\pi\) | |||||||
\(614\) | 6.77817 | + | 11.7401i | 0.273545 | + | 0.473794i | ||||
\(615\) | 0.221825 | + | 0.384213i | 0.00894486 | + | 0.0154930i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.5711 | + | 26.9699i | 0.626868 | + | 1.08577i | 0.988177 | + | 0.153320i | \(0.0489966\pi\) |
−0.361309 | + | 0.932446i | \(0.617670\pi\) | |||||||
\(618\) | 8.20101 | 0.329893 | ||||||||
\(619\) | −20.7782 | − | 35.9889i | −0.835145 | − | 1.44651i | −0.893912 | − | 0.448242i | \(-0.852050\pi\) |
0.0587667 | − | 0.998272i | \(-0.481283\pi\) | |||||||
\(620\) | −4.32233 | + | 7.48650i | −0.173589 | + | 0.300665i | ||||
\(621\) | −4.00000 | − | 6.92820i | −0.160514 | − | 0.278019i | ||||
\(622\) | 2.67767 | − | 4.63786i | 0.107365 | − | 0.185961i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.24264 | + | 14.6969i | 0.169842 | + | 0.588348i | ||||
\(625\) | 6.98528 | − | 12.0989i | 0.279411 | − | 0.483954i | ||||
\(626\) | −5.79899 | −0.231774 | ||||||||
\(627\) | 4.97056 | 0.198505 | ||||||||
\(628\) | −10.0294 | −0.400218 | ||||||||
\(629\) | 55.2843 | 2.20433 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.1421 | − | 21.0308i | −0.483371 | − | 0.837223i | 0.516447 | − | 0.856319i | \(-0.327254\pi\) |
−0.999818 | + | 0.0190965i | \(0.993921\pi\) | |||||||
\(632\) | 1.39340 | − | 2.41344i | 0.0554264 | − | 0.0960014i | ||||
\(633\) | −17.4853 | + | 30.2854i | −0.694978 | + | 1.20374i | ||||
\(634\) | 13.5269 | 0.537222 | ||||||||
\(635\) | 12.1716 | + | 21.0818i | 0.483014 | + | 0.836605i | ||||
\(636\) | 7.75736 | 0.307599 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.01219 | 0.0400731 | ||||||||
\(639\) | −5.82843 | − | 10.0951i | −0.230569 | − | 0.399357i | ||||
\(640\) | 19.3015 | 0.762959 | ||||||||
\(641\) | 7.39949 | − | 12.8163i | 0.292262 | − | 0.506213i | −0.682082 | − | 0.731276i | \(-0.738925\pi\) |
0.974344 | + | 0.225062i | \(0.0722586\pi\) | |||||||
\(642\) | −5.07107 | + | 8.78335i | −0.200139 | + | 0.346651i | ||||
\(643\) | −7.51472 | − | 13.0159i | −0.296352 | − | 0.513296i | 0.678947 | − | 0.734187i | \(-0.262437\pi\) |
−0.975298 | + | 0.220891i | \(0.929103\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.82843 | −0.347619 | ||||||||
\(646\) | −14.4853 | −0.569916 | ||||||||
\(647\) | −17.3137 | −0.680672 | −0.340336 | − | 0.940304i | \(-0.610541\pi\) | ||||
−0.340336 | + | 0.940304i | \(0.610541\pi\) | |||||||
\(648\) | 7.92893 | 0.311478 | ||||||||
\(649\) | 3.00000 | − | 5.19615i | 0.117760 | − | 0.203967i | ||||
\(650\) | −1.71573 | + | 1.78304i | −0.0672964 | + | 0.0699365i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.5061 | − | 19.9291i | 0.450614 | − | 0.780486i | ||||
\(653\) | −13.0711 | − | 22.6398i | −0.511510 | − | 0.885962i | −0.999911 | − | 0.0133425i | \(-0.995753\pi\) |
0.488401 | − | 0.872620i | \(-0.337580\pi\) | |||||||
\(654\) | 4.00000 | − | 6.92820i | 0.156412 | − | 0.270914i | ||||
\(655\) | 19.4853 | + | 33.7495i | 0.761353 | + | 1.31870i | ||||
\(656\) | 0.514719 | 0.0200964 | ||||||||
\(657\) | −5.32843 | − | 9.22911i | −0.207882 | − | 0.360062i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.65685 | + | 13.2621i | 0.298269 | + | 0.516617i | 0.975740 | − | 0.218933i | \(-0.0702575\pi\) |
−0.677471 | + | 0.735549i | \(0.736924\pi\) | |||||||
\(660\) | −1.38478 | − | 2.39850i | −0.0539023 | − | 0.0933616i | ||||
\(661\) | −33.1421 | −1.28908 | −0.644540 | − | 0.764571i | \(-0.722951\pi\) | ||||
−0.644540 | + | 0.764571i | \(0.722951\pi\) | |||||||
\(662\) | 5.15076 | + | 8.92137i | 0.200190 | + | 0.346739i | ||||
\(663\) | −20.6066 | + | 21.4150i | −0.800294 | + | 0.831690i | ||||
\(664\) | −1.69848 | −0.0659140 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.96447 | + | 3.40256i | −0.0761215 | + | 0.131846i | ||||
\(667\) | −5.89949 | −0.228429 | ||||||||
\(668\) | 6.15076 | + | 10.6534i | 0.237980 | + | 0.412193i | ||||
\(669\) | −1.41421 | + | 2.44949i | −0.0546767 | + | 0.0947027i | ||||
\(670\) | −3.21320 | −0.124137 | ||||||||
\(671\) | 2.44365 | 0.0943361 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.25736 | + | 12.5701i | −0.279751 | + | 0.484542i | −0.971323 | − | 0.237765i | \(-0.923585\pi\) |
0.691572 | + | 0.722308i | \(0.256918\pi\) | |||||||
\(674\) | 0.721825 | + | 1.25024i | 0.0278037 | + | 0.0481574i | ||||
\(675\) | −4.68629 | − | 8.11689i | −0.180375 | − | 0.312419i | ||||
\(676\) | 20.1127 | − | 12.6677i | 0.773565 | − | 0.487220i | ||||
\(677\) | 8.82843 | − | 15.2913i | 0.339304 | − | 0.587692i | −0.644998 | − | 0.764184i | \(-0.723142\pi\) |
0.984302 | + | 0.176492i | \(0.0564751\pi\) | |||||||
\(678\) | −5.94975 | + | 10.3053i | −0.228499 | + | 0.395771i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.44975 | + | 14.6354i | 0.324033 | + | 0.561242i | ||||
\(681\) | −4.17157 | + | 7.22538i | −0.159855 | + | 0.276877i | ||||
\(682\) | −0.313708 | + | 0.543359i | −0.0120125 | + | 0.0208063i | ||||
\(683\) | −2.65685 | + | 4.60181i | −0.101662 | + | 0.176083i | −0.912369 | − | 0.409368i | \(-0.865749\pi\) |
0.810708 | + | 0.585451i | \(0.199083\pi\) | |||||||
\(684\) | −5.48528 | + | 9.50079i | −0.209735 | + | 0.363272i | ||||
\(685\) | −0.156854 | − | 0.271680i | −0.00599309 | − | 0.0103803i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.82843 | − | 15.2913i | 0.336826 | − | 0.583399i | ||||
\(688\) | −5.12132 | + | 8.87039i | −0.195249 | + | 0.338180i | ||||
\(689\) | −3.00000 | − | 10.3923i | −0.114291 | − | 0.395915i | ||||
\(690\) | −0.757359 | − | 1.31178i | −0.0288322 | − | 0.0499388i | ||||
\(691\) | −14.9706 | − | 25.9298i | −0.569507 | − | 0.986415i | −0.996615 | − | 0.0822143i | \(-0.973801\pi\) |
0.427108 | − | 0.904201i | \(-0.359533\pi\) | |||||||
\(692\) | −9.27208 | + | 16.0597i | −0.352472 | + | 0.610499i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.52691 | −0.0959203 | ||||||||
\(695\) | 21.7574 | 0.825304 | ||||||||
\(696\) | 4.67767 | − | 8.10196i | 0.177307 | − | 0.307104i | ||||
\(697\) | 0.500000 | + | 0.866025i | 0.0189389 | + | 0.0328031i | ||||
\(698\) | 3.85786 | 0.146022 | ||||||||
\(699\) | −2.00000 | + | 3.46410i | −0.0756469 | + | 0.131024i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.8579 | 0.523404 | 0.261702 | − | 0.965149i | \(-0.415716\pi\) | ||||
0.261702 | + | 0.965149i | \(0.415716\pi\) | |||||||
\(702\) | −2.34315 | − | 8.11689i | −0.0884363 | − | 0.306352i | ||||
\(703\) | 28.4558 | + | 49.2870i | 1.07323 | + | 1.85889i | ||||
\(704\) | −2.44365 | −0.0920986 | ||||||||
\(705\) | −4.72792 | − | 8.18900i | −0.178064 | − | 0.308416i | ||||
\(706\) | −1.20711 | − | 2.09077i | −0.0454301 | − | 0.0786872i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −13.2426 | − | 22.9369i | −0.497689 | − | 0.862022i | ||||
\(709\) | 17.6274 | 0.662012 | 0.331006 | − | 0.943629i | \(-0.392612\pi\) | ||||
0.331006 | + | 0.943629i | \(0.392612\pi\) | |||||||
\(710\) | −4.41421 | − | 7.64564i | −0.165662 | − | 0.286936i | ||||
\(711\) | 0.878680 | − | 1.52192i | 0.0329531 | − | 0.0570764i | ||||
\(712\) | 12.1421 | + | 21.0308i | 0.455046 | + | 0.788162i | ||||
\(713\) | 1.82843 | − | 3.16693i | 0.0684751 | − | 0.118602i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.67767 | + | 2.78272i | −0.100139 | + | 0.104068i | ||||
\(716\) | −5.17157 | + | 8.95743i | −0.193271 | + | 0.334755i | ||||
\(717\) | 34.4853 | 1.28788 | ||||||||
\(718\) | −7.02944 | −0.262336 | ||||||||
\(719\) | 0.384776 | 0.0143497 | 0.00717487 | − | 0.999974i | \(-0.497716\pi\) | ||||
0.00717487 | + | 0.999974i | \(0.497716\pi\) | |||||||
\(720\) | 5.48528 | 0.204424 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.52082 | − | 6.09823i | −0.131031 | − | 0.226953i | ||||
\(723\) | −10.9497 | + | 18.9655i | −0.407225 | + | 0.705335i | ||||
\(724\) | 8.35786 | − | 14.4762i | 0.310618 | − | 0.538005i | ||||
\(725\) | −6.91169 | −0.256694 | ||||||||
\(726\) | 3.12132 | + | 5.40629i | 0.115843 | + | 0.200646i | ||||
\(727\) | 24.9706 | 0.926107 | 0.463053 | − | 0.886330i | \(-0.346754\pi\) | ||||
0.463053 | + | 0.886330i | \(0.346754\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | −4.03553 | − | 6.98975i | −0.149362 | − | 0.258702i | ||||
\(731\) | −19.8995 | −0.736009 | ||||||||
\(732\) | 5.39340 | − | 9.34164i | 0.199346 | − | 0.345277i | ||||
\(733\) | 10.5000 | − | 18.1865i | 0.387826 | − | 0.671735i | −0.604331 | − | 0.796734i | \(-0.706559\pi\) |
0.992157 | + | 0.124999i | \(0.0398927\pi\) | |||||||
\(734\) | 5.94975 | + | 10.3053i | 0.219609 | + | 0.380374i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.24264 | −0.230107 | ||||||||
\(737\) | 2.48528 | 0.0915465 | ||||||||
\(738\) | −0.0710678 | −0.00261604 | ||||||||
\(739\) | −20.2843 | −0.746169 | −0.373084 | − | 0.927797i | \(-0.621700\pi\) | ||||
−0.373084 | + | 0.927797i | \(0.621700\pi\) | |||||||
\(740\) | 15.8553 | − | 27.4623i | 0.582854 | − | 1.00953i | ||||
\(741\) | −29.6985 | − | 7.34847i | −1.09100 | − | 0.269953i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.7990 | + | 27.3647i | −0.579609 | + | 1.00391i | 0.415915 | + | 0.909403i | \(0.363461\pi\) |
−0.995524 | + | 0.0945084i | \(0.969872\pi\) | |||||||
\(744\) | 2.89949 | + | 5.02207i | 0.106301 | + | 0.184118i | ||||
\(745\) | 2.74264 | − | 4.75039i | 0.100483 | − | 0.174041i | ||||
\(746\) | −5.47918 | − | 9.49023i | −0.200607 | − | 0.347462i | ||||
\(747\) | −1.07107 | −0.0391883 | ||||||||
\(748\) | −3.12132 | − | 5.40629i | −0.114127 | − | 0.197673i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3.56497 | − | 6.17471i | −0.130174 | − | 0.225469i | ||||
\(751\) | 8.77817 | + | 15.2042i | 0.320320 | + | 0.554811i | 0.980554 | − | 0.196249i | \(-0.0628762\pi\) |
−0.660234 | + | 0.751060i | \(0.729543\pi\) | |||||||
\(752\) | −10.9706 | −0.400055 | ||||||||
\(753\) | −16.2426 | − | 28.1331i | −0.591915 | − | 1.02523i | ||||
\(754\) | −6.04773 | − | 1.49642i | −0.220245 | − | 0.0544966i | ||||
\(755\) | −27.3726 | −0.996190 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.7279 | + | 25.5095i | −0.535295 | + | 0.927159i | 0.463854 | + | 0.885912i | \(0.346466\pi\) |
−0.999149 | + | 0.0412470i | \(0.986867\pi\) | |||||||
\(758\) | −0.100505 | −0.00365051 | ||||||||
\(759\) | 0.585786 | + | 1.01461i | 0.0212627 | + | 0.0368281i | ||||
\(760\) | −8.69848 | + | 15.0662i | −0.315527 | + | 0.546509i | ||||
\(761\) | 17.8579 | 0.647347 | 0.323674 | − | 0.946169i | \(-0.395082\pi\) | ||||
0.323674 | + | 0.946169i | \(0.395082\pi\) | |||||||
\(762\) | 7.79899 | 0.282528 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 14.8492 | − | 25.7196i | 0.537227 | − | 0.930504i | ||||
\(765\) | 5.32843 | + | 9.22911i | 0.192650 | + | 0.333679i | ||||
\(766\) | 7.05025 | + | 12.2114i | 0.254736 | + | 0.441216i | ||||
\(767\) | −25.6066 | + | 26.6112i | −0.924601 | + | 0.960873i | ||||
\(768\) | −2.80761 | + | 4.86293i | −0.101311 | + | 0.175476i | ||||
\(769\) | 24.7279 | − | 42.8300i | 0.891712 | − | 1.54449i | 0.0538894 | − | 0.998547i | \(-0.482838\pi\) |
0.837822 | − | 0.545943i | \(-0.183828\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.6066 | − | 18.3712i | −0.381987 | − | 0.661622i | ||||
\(772\) | 6.52944 | − | 11.3093i | 0.235000 | − | 0.407031i | ||||
\(773\) | −3.17157 | + | 5.49333i | −0.114074 | + | 0.197581i | −0.917409 | − | 0.397946i | \(-0.869723\pi\) |
0.803335 | + | 0.595527i | \(0.203057\pi\) | |||||||
\(774\) | 0.707107 | − | 1.22474i | 0.0254164 | − | 0.0440225i | ||||
\(775\) | 2.14214 | − | 3.71029i | 0.0769478 | − | 0.133277i | ||||
\(776\) | −8.58579 | − | 14.8710i | −0.308212 | − | 0.533838i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.62132 | + | 9.73641i | −0.201534 | + | 0.349067i | ||||
\(779\) | −0.514719 | + | 0.891519i | −0.0184417 | + | 0.0319420i | ||||
\(780\) | 4.72792 | + | 16.3780i | 0.169287 | + | 0.586427i | ||||
\(781\) | 3.41421 | + | 5.91359i | 0.122170 | + | 0.211605i | ||||
\(782\) | −1.70711 | − | 2.95680i | −0.0610460 | − | 0.105735i | ||||
\(783\) | 11.7990 | − | 20.4364i | 0.421661 | − | 0.730339i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.0294 | −0.357966 | ||||||||
\(786\) | 12.4853 | 0.445335 | ||||||||
\(787\) | 6.94975 | − | 12.0373i | 0.247732 | − | 0.429084i | −0.715164 | − | 0.698956i | \(-0.753648\pi\) |
0.962896 | + | 0.269872i | \(0.0869815\pi\) | |||||||
\(788\) | 13.5563 | + | 23.4803i | 0.482925 | + | 0.836451i | ||||
\(789\) | −9.51472 | −0.338733 | ||||||||
\(790\) | 0.665476 | − | 1.15264i | 0.0236766 | − | 0.0410090i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.928932 | 0.0330082 | ||||||||
\(793\) | −14.6005 | − | 3.61269i | −0.518479 | − | 0.128290i | ||||
\(794\) | −1.37258 | − | 2.37738i | −0.0487111 | − | 0.0843702i | ||||
\(795\) | 7.75736 | 0.275125 | ||||||||
\(796\) | −13.6863 | − | 23.7054i | −0.485098 | − | 0.840214i | ||||
\(797\) | 9.07107 | + | 15.7116i | 0.321314 | + | 0.556532i | 0.980759 | − | 0.195221i | \(-0.0625423\pi\) |
−0.659446 | + | 0.751752i | \(0.729209\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.6569 | − | 18.4582i | −0.377012 | − | 0.653005i | ||||
\(800\) | −7.31371 | −0.258579 | ||||||||
\(801\) | 7.65685 | + | 13.2621i | 0.270542 | + | 0.468592i | ||||
\(802\) | −1.82233 | + | 3.15637i | −0.0643487 | + | 0.111455i | ||||
\(803\) | 3.12132 | + | 5.40629i | 0.110149 | + | 0.190784i | ||||
\(804\) | 5.48528 | − | 9.50079i | 0.193451 | − | 0.335067i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.67767 | − | 2.78272i | 0.0943169 | − | 0.0980170i | ||||
\(807\) | 12.7279 | − | 22.0454i | 0.448044 | − | 0.776035i | ||||
\(808\) | −23.2426 | −0.817673 | ||||||||
\(809\) | 35.1421 | 1.23553 | 0.617766 | − | 0.786362i | \(-0.288038\pi\) | ||||
0.617766 | + | 0.786362i | \(0.288038\pi\) | |||||||
\(810\) | 3.78680 | 0.133054 | ||||||||
\(811\) | −42.1838 | −1.48127 | −0.740636 | − | 0.671906i | \(-0.765476\pi\) | ||||
−0.740636 | + | 0.671906i | \(0.765476\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.8995 | + | 25.8067i | 0.522548 | + | 0.905080i | ||||
\(814\) | 1.15076 | − | 1.99317i | 0.0403340 | − | 0.0698606i | ||||
\(815\) | 11.5061 | − | 19.9291i | 0.403041 | − | 0.698087i | ||||
\(816\) | −24.7279 | −0.865650 | ||||||||
\(817\) | −10.2426 | − | 17.7408i | −0.358345 | − | 0.620671i | ||||
\(818\) | −9.10051 | −0.318192 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.573593 | 0.0200307 | ||||||||
\(821\) | 19.9706 | + | 34.5900i | 0.696977 | + | 1.20720i | 0.969510 | + | 0.245054i | \(0.0788056\pi\) |
−0.272532 | + | 0.962147i | \(0.587861\pi\) | |||||||
\(822\) | −0.100505 | −0.00350552 | ||||||||
\(823\) | −9.65685 | + | 16.7262i | −0.336617 | + | 0.583037i | −0.983794 | − | 0.179302i | \(-0.942616\pi\) |
0.647177 | + | 0.762340i | \(0.275949\pi\) | |||||||
\(824\) | 11.1005 | − | 19.2266i | 0.386704 | − | 0.669792i | ||||
\(825\) | 0.686292 | + | 1.18869i | 0.0238936 | + | 0.0413849i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −52.6690 | −1.83148 | −0.915741 | − | 0.401769i | \(-0.868396\pi\) | ||||
−0.915741 | + | 0.401769i | \(0.868396\pi\) | |||||||
\(828\) | −2.58579 | −0.0898623 | ||||||||
\(829\) | 46.3137 | 1.60854 | 0.804271 | − | 0.594263i | \(-0.202556\pi\) | ||||
0.804271 | + | 0.594263i | \(0.202556\pi\) | |||||||
\(830\) | −0.811183 | −0.0281566 | ||||||||
\(831\) | −1.39340 | + | 2.41344i | −0.0483365 | + | 0.0837212i | ||||
\(832\) | 14.6005 | + | 3.61269i | 0.506181 | + | 0.125247i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.48528 | − | 6.03668i | 0.120685 | − | 0.209033i | ||||
\(835\) | 6.15076 | + | 10.6534i | 0.212856 | + | 0.368677i | ||||
\(836\) | 3.21320 | − | 5.56543i | 0.111131 | − | 0.192484i | ||||
\(837\) | 7.31371 | + | 12.6677i | 0.252799 | + | 0.437860i | ||||
\(838\) | −4.78680 | −0.165357 | ||||||||
\(839\) | 20.7990 | + | 36.0249i | 0.718061 | + | 1.24372i | 0.961767 | + | 0.273869i | \(0.0883034\pi\) |
−0.243706 | + | 0.969849i | \(0.578363\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.79899 | + | 10.0441i | 0.199965 | + | 0.346350i | ||||
\(842\) | −4.44975 | − | 7.70719i | −0.153348 | − | 0.265607i | ||||
\(843\) | −24.7279 | −0.851675 | ||||||||
\(844\) | 22.6066 | + | 39.1558i | 0.778151 | + | 1.34780i | ||||
\(845\) | 20.1127 | − | 12.6677i | 0.691898 | − | 0.435783i | ||||
\(846\) | 1.51472 | 0.0520771 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.50000 | − | 7.79423i | 0.154531 | − | 0.267655i | ||||
\(849\) | −28.1421 | −0.965836 | ||||||||
\(850\) | −2.00000 | − | 3.46410i | −0.0685994 | − | 0.118818i | ||||
\(851\) | −6.70711 | + | 11.6170i | −0.229917 | + | 0.398227i | ||||
\(852\) | 30.1421 | 1.03265 | ||||||||
\(853\) | −35.0000 | −1.19838 | −0.599189 | − | 0.800608i | \(-0.704510\pi\) | ||||
−0.599189 | + | 0.800608i | \(0.704510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.48528 | + | 9.50079i | −0.187593 | + | 0.324920i | ||||
\(856\) | 13.7279 | + | 23.7775i | 0.469211 | + | 0.812697i | ||||
\(857\) | −0.600505 | − | 1.04011i | −0.0205129 | − | 0.0355293i | 0.855587 | − | 0.517659i | \(-0.173197\pi\) |
−0.876100 | + | 0.482130i | \(0.839863\pi\) | |||||||
\(858\) | 0.343146 | + | 1.18869i | 0.0117148 | + | 0.0405813i | ||||
\(859\) | 6.46447 | − | 11.1968i | 0.220565 | − | 0.382029i | −0.734415 | − | 0.678701i | \(-0.762543\pi\) |
0.954980 | + | 0.296672i | \(0.0958766\pi\) | |||||||
\(860\) | −5.70711 | + | 9.88500i | −0.194611 | + | 0.337076i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.48528 | − | 4.30463i | −0.0846490 | − | 0.146616i | ||||
\(863\) | 10.0919 | − | 17.4797i | 0.343532 | − | 0.595014i | −0.641554 | − | 0.767078i | \(-0.721710\pi\) |
0.985086 | + | 0.172063i | \(0.0550434\pi\) | |||||||
\(864\) | 12.4853 | − | 21.6251i | 0.424758 | − | 0.735702i | ||||
\(865\) | −9.27208 | + | 16.0597i | −0.315260 | + | 0.546047i | ||||
\(866\) | −3.62132 | + | 6.27231i | −0.123057 | + | 0.213142i | ||||
\(867\) | −12.0000 | − | 20.7846i | −0.407541 | − | 0.705882i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.514719 | + | 0.891519i | −0.0174606 | + | 0.0302427i | ||||
\(870\) | 2.23402 | − | 3.86943i | 0.0757403 | − | 0.131186i | ||||
\(871\) | −14.8492 | − | 3.67423i | −0.503147 | − | 0.124497i | ||||
\(872\) | −10.8284 | − | 18.7554i | −0.366697 | − | 0.635138i | ||||
\(873\) | −5.41421 | − | 9.37769i | −0.183243 | − | 0.317387i | ||||
\(874\) | 1.75736 | − | 3.04384i | 0.0594436 | − | 0.102959i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 27.5563 | 0.931043 | ||||||||
\(877\) | 17.0000 | 0.574049 | 0.287025 | − | 0.957923i | \(-0.407334\pi\) | ||||
0.287025 | + | 0.957923i | \(0.407334\pi\) | |||||||
\(878\) | 0.263456 | − | 0.456319i | 0.00889121 | − | 0.0154000i | ||||
\(879\) | −20.1213 | − | 34.8511i | −0.678675 | − | 1.17550i | ||||
\(880\) | −3.21320 | −0.108317 | ||||||||
\(881\) | −2.22792 | + | 3.85887i | −0.0750606 | + | 0.130009i | −0.901113 | − | 0.433585i | \(-0.857248\pi\) |
0.826052 | + | 0.563594i | \(0.190582\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 56.0416 | 1.88595 | 0.942976 | − | 0.332862i | \(-0.108014\pi\) | ||||
0.942976 | + | 0.332862i | \(0.108014\pi\) | |||||||
\(884\) | 10.6569 | + | 36.9164i | 0.358429 | + | 1.24163i | ||||
\(885\) | −13.2426 | − | 22.9369i | −0.445146 | − | 0.771016i | ||||
\(886\) | 10.6274 | 0.357035 | ||||||||
\(887\) | 17.3137 | + | 29.9882i | 0.581337 | + | 1.00691i | 0.995321 | + | 0.0966217i | \(0.0308037\pi\) |
−0.413984 | + | 0.910284i | \(0.635863\pi\) | |||||||
\(888\) | −10.6360 | − | 18.4222i | −0.356922 | − | 0.618207i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.79899 | + | 10.0441i | 0.194383 | + | 0.336681i | ||||
\(891\) | −2.92893 | −0.0981229 | ||||||||
\(892\) | 1.82843 | + | 3.16693i | 0.0612203 | + | 0.106037i | ||||
\(893\) | 10.9706 | − | 19.0016i | 0.367116 | − | 0.635863i | ||||
\(894\) | −0.878680 | − | 1.52192i | −0.0293874 | − | 0.0509005i | ||||
\(895\) | −5.17157 | + | 8.95743i | −0.172867 | + | 0.299414i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.00000 | − | 6.92820i | −0.0667781 | − | 0.231326i | ||||
\(898\) | −6.72792 | + | 11.6531i | −0.224514 | + | 0.388869i | ||||
\(899\) | 10.7868 | 0.359760 | ||||||||
\(900\) | −3.02944 | −0.100981 | ||||||||
\(901\) | 17.4853 | 0.582519 | ||||||||
\(902\) | 0.0416306 | 0.00138615 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.1066 | + | 27.8975i | 0.535698 | + | 0.927855i | ||||
\(905\) | 8.35786 | − | 14.4762i | 0.277825 | − | 0.481207i | ||||
\(906\) | −4.38478 | + | 7.59466i | −0.145674 | + | 0.252316i | ||||
\(907\) | −6.72792 | −0.223397 | −0.111698 | − | 0.993742i | \(-0.535629\pi\) | ||||
−0.111698 | + | 0.993742i | \(0.535629\pi\) | |||||||
\(908\) | 5.39340 | + | 9.34164i | 0.178986 | + | 0.310013i | ||||
\(909\) | −14.6569 | −0.486137 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.6569 | −0.982575 | −0.491288 | − | 0.870997i | \(-0.663474\pi\) | ||||
−0.491288 | + | 0.870997i | \(0.663474\pi\) | |||||||
\(912\) | −12.7279 | − | 22.0454i | −0.421464 | − | 0.729996i | ||||
\(913\) | 0.627417 | 0.0207645 | ||||||||
\(914\) | 5.17767 | − | 8.96799i | 0.171262 | − | 0.296635i | ||||
\(915\) | 5.39340 | − | 9.34164i | 0.178300 | − | 0.308825i | ||||
\(916\) | −11.4142 | − | 19.7700i | −0.377136 | − | 0.653219i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 13.6569 | 0.450743 | ||||||||
\(919\) | 2.68629 | 0.0886126 | 0.0443063 | − | 0.999018i | \(-0.485892\pi\) | ||||
0.0443063 | + | 0.999018i | \(0.485892\pi\) | |||||||
\(920\) | −4.10051 | −0.135190 | ||||||||
\(921\) | −46.2843 | −1.52512 | ||||||||
\(922\) | −0.278175 | + | 0.481813i | −0.00916119 | + | 0.0158677i | ||||
\(923\) | −11.6569 | − | 40.3805i | −0.383690 | − | 1.32914i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.85786 | + | 13.6102i | −0.258365 | + | 0.447501i | ||||
\(926\) | −1.39340 | − | 2.41344i | −0.0457899 | − | 0.0793104i | ||||
\(927\) | 7.00000 | − | 12.1244i | 0.229910 | − | 0.398216i | ||||
\(928\) | −9.20711 | − | 15.9472i | −0.302238 | − | 0.523492i | ||||
\(929\) | 48.9411 | 1.60571 | 0.802853 | − | 0.596177i | \(-0.203314\pi\) | ||||
0.802853 | + | 0.596177i | \(0.203314\pi\) | |||||||
\(930\) | 1.38478 | + | 2.39850i | 0.0454086 | + | 0.0786500i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.58579 | + | 4.47871i | 0.0847003 | + | 0.146705i | ||||
\(933\) | 9.14214 | + | 15.8346i | 0.299300 | + | 0.518403i | ||||
\(934\) | 4.72792 | 0.154702 | ||||||||
\(935\) | −3.12132 | − | 5.40629i | −0.102078 | − | 0.176804i | ||||
\(936\) | −5.55025 | − | 1.37333i | −0.181416 | − | 0.0448887i | ||||
\(937\) | −37.1421 | −1.21338 | −0.606690 | − | 0.794938i | \(-0.707503\pi\) | ||||
−0.606690 | + | 0.794938i | \(0.707503\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.89949 | − | 17.1464i | 0.323058 | − | 0.559553i | ||||
\(940\) | −12.2254 | −0.398748 | ||||||||
\(941\) | −26.4853 | − | 45.8739i | −0.863395 | − | 1.49544i | −0.868632 | − | 0.495459i | \(-0.835000\pi\) |
0.00523607 | − | 0.999986i | \(-0.498333\pi\) | |||||||
\(942\) | −1.60660 | + | 2.78272i | −0.0523459 | + | 0.0906658i | ||||
\(943\) | −0.242641 | −0.00790147 | ||||||||
\(944\) | −30.7279 | −1.00011 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.414214 | + | 0.717439i | −0.0134672 | + | 0.0233260i | ||||
\(947\) | −10.7071 | − | 18.5453i | −0.347934 | − | 0.602640i | 0.637948 | − | 0.770079i | \(-0.279783\pi\) |
−0.985882 | + | 0.167440i | \(0.946450\pi\) | |||||||
\(948\) | 2.27208 | + | 3.93535i | 0.0737937 | + | 0.127814i | ||||
\(949\) | −10.6569 | − | 36.9164i | −0.345936 | − | 1.19836i | ||||
\(950\) | 2.05887 | − | 3.56608i | 0.0667987 | − | 0.115699i | ||||
\(951\) | −23.0919 | + | 39.9963i | −0.748806 | + | 1.29697i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.31371 | − | 5.73951i | −0.107342 | − | 0.185921i | 0.807351 | − | 0.590072i | \(-0.200900\pi\) |
−0.914692 | + | 0.404151i | \(0.867567\pi\) | |||||||
\(954\) | −0.621320 | + | 1.07616i | −0.0201160 | + | 0.0348419i | ||||
\(955\) | 14.8492 | − | 25.7196i | 0.480510 | − | 0.832268i | ||||
\(956\) | 22.2929 | − | 38.6124i | 0.721004 | − | 1.24882i | ||||
\(957\) | −1.72792 | + | 2.99285i | −0.0558558 | + | 0.0967451i | ||||
\(958\) | 0.334524 | + | 0.579412i | 0.0108080 | + | 0.0187200i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −5.39340 | + | 9.34164i | −0.174071 | + | 0.301500i | ||||
\(961\) | 12.1569 | − | 21.0563i | 0.392157 | − | 0.679235i | ||||
\(962\) | −9.82233 | + | 10.2077i | −0.316685 | + | 0.329108i | ||||
\(963\) | 8.65685 | + | 14.9941i | 0.278963 | + | 0.483178i | ||||
\(964\) | 14.1569 | + | 24.5204i | 0.455962 | + | 0.789749i | ||||
\(965\) | 6.52944 | − | 11.3093i | 0.210190 | − | 0.364060i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.7574 | −0.635354 | −0.317677 | − | 0.948199i | \(-0.602903\pi\) | ||||
−0.317677 | + | 0.948199i | \(0.602903\pi\) | |||||||
\(968\) | 16.8995 | 0.543170 | ||||||||
\(969\) | 24.7279 | − | 42.8300i | 0.794375 | − | 1.37590i | ||||
\(970\) | −4.10051 | − | 7.10228i | −0.131659 | − | 0.228041i | ||||
\(971\) | 51.6569 | 1.65775 | 0.828874 | − | 0.559436i | \(-0.188982\pi\) | ||||
0.828874 | + | 0.559436i | \(0.188982\pi\) | |||||||
\(972\) | 9.05025 | − | 15.6755i | 0.290287 | − | 0.502792i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −5.37258 | −0.172149 | ||||||||
\(975\) | −2.34315 | − | 8.11689i | −0.0750407 | − | 0.259949i | ||||
\(976\) | −6.25736 | − | 10.8381i | −0.200293 | − | 0.346918i | ||||
\(977\) | 30.5980 | 0.978916 | 0.489458 | − | 0.872027i | \(-0.337195\pi\) | ||||
0.489458 | + | 0.872027i | \(0.337195\pi\) | |||||||
\(978\) | −3.68629 | − | 6.38484i | −0.117875 | − | 0.204165i | ||||
\(979\) | −4.48528 | − | 7.76874i | −0.143350 | − | 0.248290i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.82843 | − | 11.8272i | −0.218015 | − | 0.377613i | ||||
\(982\) | 5.25483 | 0.167688 | ||||||||
\(983\) | 21.0000 | + | 36.3731i | 0.669796 | + | 1.16012i | 0.977961 | + | 0.208788i | \(0.0669518\pi\) |
−0.308165 | + | 0.951333i | \(0.599715\pi\) | |||||||
\(984\) | 0.192388 | − | 0.333226i | 0.00613311 | − | 0.0106229i | ||||
\(985\) | 13.5563 | + | 23.4803i | 0.431941 | + | 0.748144i | ||||
\(986\) | 5.03553 | − | 8.72180i | 0.160364 | − | 0.277759i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −27.4264 | + | 28.5024i | −0.872550 | + | 0.906781i | ||||
\(989\) | 2.41421 | − | 4.18154i | 0.0767675 | − | 0.132965i | ||||
\(990\) | 0.443651 | 0.0141001 | ||||||||
\(991\) | 19.7574 | 0.627613 | 0.313807 | − | 0.949487i | \(-0.398396\pi\) | ||||
0.313807 | + | 0.949487i | \(0.398396\pi\) | |||||||
\(992\) | 11.4142 | 0.362402 | ||||||||
\(993\) | −35.1716 | −1.11614 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.6863 | − | 23.7054i | −0.433885 | − | 0.751510i | ||||
\(996\) | 1.38478 | − | 2.39850i | 0.0438783 | − | 0.0759995i | ||||
\(997\) | −6.98528 | + | 12.0989i | −0.221226 | + | 0.383175i | −0.955181 | − | 0.296024i | \(-0.904339\pi\) |
0.733954 | + | 0.679199i | \(0.237673\pi\) | |||||||
\(998\) | 8.30152 | 0.262780 | ||||||||
\(999\) | −26.8284 | − | 46.4682i | −0.848814 | − | 1.47019i |
(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 | 637.2.g.f.373.1 | 4 | ||
7.2 | even | 3 | 637.2.f.f.295.1 | yes | 4 | ||
7.3 | odd | 6 | 637.2.h.c.165.2 | 4 | |||
7.4 | even | 3 | 637.2.h.b.165.2 | 4 | |||
7.5 | odd | 6 | 637.2.f.e.295.1 | ✓ | 4 | ||
7.6 | odd | 2 | 637.2.g.g.373.1 | 4 | |||
13.3 | even | 3 | 637.2.h.b.471.2 | 4 | |||
91.3 | odd | 6 | 637.2.g.g.263.1 | 4 | |||
91.9 | even | 3 | 8281.2.a.p.1.2 | 2 | |||
91.16 | even | 3 | 637.2.f.f.393.1 | yes | 4 | ||
91.30 | even | 6 | 8281.2.a.x.1.1 | 2 | |||
91.55 | odd | 6 | 637.2.h.c.471.2 | 4 | |||
91.61 | odd | 6 | 8281.2.a.o.1.2 | 2 | |||
91.68 | odd | 6 | 637.2.f.e.393.1 | yes | 4 | ||
91.81 | even | 3 | inner | 637.2.g.f.263.1 | 4 | ||
91.82 | odd | 6 | 8281.2.a.y.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.f.e.295.1 | ✓ | 4 | 7.5 | odd | 6 | ||
637.2.f.e.393.1 | yes | 4 | 91.68 | odd | 6 | ||
637.2.f.f.295.1 | yes | 4 | 7.2 | even | 3 | ||
637.2.f.f.393.1 | yes | 4 | 91.16 | even | 3 | ||
637.2.g.f.263.1 | 4 | 91.81 | even | 3 | inner | ||
637.2.g.f.373.1 | 4 | 1.1 | even | 1 | trivial | ||
637.2.g.g.263.1 | 4 | 91.3 | odd | 6 | |||
637.2.g.g.373.1 | 4 | 7.6 | odd | 2 | |||
637.2.h.b.165.2 | 4 | 7.4 | even | 3 | |||
637.2.h.b.471.2 | 4 | 13.3 | even | 3 | |||
637.2.h.c.165.2 | 4 | 7.3 | odd | 6 | |||
637.2.h.c.471.2 | 4 | 91.55 | odd | 6 | |||
8281.2.a.o.1.2 | 2 | 91.61 | odd | 6 | |||
8281.2.a.p.1.2 | 2 | 91.9 | even | 3 | |||
8281.2.a.x.1.1 | 2 | 91.30 | even | 6 | |||
8281.2.a.y.1.1 | 2 | 91.82 | odd | 6 |