Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(703,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.703");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.bk (of order \(6\), 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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.3 | ||
Character | \(\chi\) | \(=\) | 1386.901 |
Dual form | 1386.2.bk.d.703.3 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.23351 | − | 0.712169i | −0.551643 | − | 0.318491i | 0.198141 | − | 0.980173i | \(-0.436510\pi\) |
−0.749785 | + | 0.661682i | \(0.769843\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.484566 | + | 2.60100i | −0.183149 | + | 0.983085i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.712169 | + | 1.23351i | 0.225207 | + | 0.390071i | ||||
\(11\) | 2.51113 | − | 2.16661i | 0.757135 | − | 0.653258i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.39347 | −0.663829 | −0.331915 | − | 0.943309i | \(-0.607695\pi\) | ||||
−0.331915 | + | 0.943309i | \(0.607695\pi\) | |||||||
\(14\) | 1.72015 | − | 2.01025i | 0.459728 | − | 0.537261i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.529896 | + | 0.917806i | 0.128519 | + | 0.222601i | 0.923103 | − | 0.384553i | \(-0.125644\pi\) |
−0.794584 | + | 0.607154i | \(0.792311\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.37329 | + | 4.11067i | −0.544471 | + | 0.943052i | 0.454169 | + | 0.890916i | \(0.349936\pi\) |
−0.998640 | + | 0.0521360i | \(0.983397\pi\) | |||||||
\(20\) | − | 1.42434i | − | 0.318491i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.25801 | + | 0.620776i | −0.694610 | + | 0.132350i | ||||
\(23\) | 1.72015 | − | 2.97938i | 0.358675 | − | 0.621244i | −0.629064 | − | 0.777353i | \(-0.716562\pi\) |
0.987740 | + | 0.156109i | \(0.0498952\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.48563 | − | 2.57319i | −0.297126 | − | 0.514638i | ||||
\(26\) | 2.07281 | + | 1.19674i | 0.406511 | + | 0.234699i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.49481 | + | 0.880853i | −0.471476 | + | 0.166466i | ||||
\(29\) | 4.13565i | 0.767971i | 0.923339 | + | 0.383986i | \(0.125449\pi\) | ||||
−0.923339 | + | 0.383986i | \(0.874551\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.122361 | − | 0.0706450i | 0.0219766 | − | 0.0126882i | −0.488971 | − | 0.872300i | \(-0.662628\pi\) |
0.510948 | + | 0.859612i | \(0.329294\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.05979i | − | 0.181753i | ||||||
\(35\) | 2.45007 | − | 2.86327i | 0.414137 | − | 0.483981i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.19019 | − | 2.06146i | 0.195665 | − | 0.338902i | −0.751453 | − | 0.659787i | \(-0.770647\pi\) |
0.947118 | + | 0.320884i | \(0.103980\pi\) | |||||||
\(38\) | 4.11067 | − | 2.37329i | 0.666838 | − | 0.384999i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.712169 | + | 1.23351i | −0.112604 | + | 0.195035i | ||||
\(41\) | −9.17779 | −1.43333 | −0.716665 | − | 0.697418i | \(-0.754332\pi\) | ||||
−0.716665 | + | 0.697418i | \(0.754332\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.73823i | 0.875072i | 0.899201 | + | 0.437536i | \(0.144149\pi\) | ||||
−0.899201 | + | 0.437536i | \(0.855851\pi\) | |||||||
\(44\) | 3.13191 | + | 1.09140i | 0.472153 | + | 0.164534i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.97938 | + | 1.72015i | −0.439286 | + | 0.253622i | ||||
\(47\) | −3.08763 | − | 1.78265i | −0.450378 | − | 0.260026i | 0.257612 | − | 0.966248i | \(-0.417064\pi\) |
−0.707990 | + | 0.706223i | \(0.750398\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.53039 | − | 2.52071i | −0.932913 | − | 0.360102i | ||||
\(50\) | 2.97126i | 0.420200i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.19674 | − | 2.07281i | −0.165957 | − | 0.287446i | ||||
\(53\) | −1.98826 | − | 3.44377i | −0.273109 | − | 0.473038i | 0.696547 | − | 0.717511i | \(-0.254719\pi\) |
−0.969656 | + | 0.244472i | \(0.921385\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.64051 | + | 0.884194i | −0.625726 | + | 0.119225i | ||||
\(56\) | 2.60100 | + | 0.484566i | 0.347573 | + | 0.0647529i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.06783 | − | 3.58158i | 0.271519 | − | 0.470284i | ||||
\(59\) | −4.71536 | + | 2.72242i | −0.613888 | + | 0.354428i | −0.774486 | − | 0.632592i | \(-0.781991\pi\) |
0.160598 | + | 0.987020i | \(0.448658\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.58028 | + | 9.66532i | −0.714481 | + | 1.23752i | 0.248678 | + | 0.968586i | \(0.420004\pi\) |
−0.963159 | + | 0.268932i | \(0.913329\pi\) | |||||||
\(62\) | −0.141290 | −0.0179438 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.95237 | + | 1.70455i | 0.366197 | + | 0.211424i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.567825 | − | 0.983502i | −0.0693709 | − | 0.120154i | 0.829254 | − | 0.558872i | \(-0.188766\pi\) |
−0.898625 | + | 0.438719i | \(0.855433\pi\) | |||||||
\(68\) | −0.529896 | + | 0.917806i | −0.0642593 | + | 0.111300i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.55346 | + | 1.25463i | −0.424719 | + | 0.149957i | ||||
\(71\) | −10.9563 | −1.30027 | −0.650137 | − | 0.759817i | \(-0.725289\pi\) | ||||
−0.650137 | + | 0.759817i | \(0.725289\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.969133 | − | 1.67859i | −0.113428 | − | 0.196464i | 0.803722 | − | 0.595005i | \(-0.202850\pi\) |
−0.917150 | + | 0.398541i | \(0.869517\pi\) | |||||||
\(74\) | −2.06146 | + | 1.19019i | −0.239640 | + | 0.138356i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.74659 | −0.544471 | ||||||||
\(77\) | 4.41855 | + | 7.58132i | 0.503540 | + | 0.863972i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.82226 | − | 2.20678i | −0.430037 | − | 0.248282i | 0.269325 | − | 0.963049i | \(-0.413199\pi\) |
−0.699363 | + | 0.714767i | \(0.746533\pi\) | |||||||
\(80\) | 1.23351 | − | 0.712169i | 0.137911 | − | 0.0796229i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.94820 | + | 4.58889i | 0.877732 | + | 0.506759i | ||||
\(83\) | −3.73539 | −0.410013 | −0.205006 | − | 0.978761i | \(-0.565721\pi\) | ||||
−0.205006 | + | 0.978761i | \(0.565721\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.50950i | − | 0.163728i | ||||||
\(86\) | 2.86912 | − | 4.96945i | 0.309385 | − | 0.535870i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.16661 | − | 2.51113i | −0.230962 | − | 0.267688i | ||||
\(89\) | −1.67859 | − | 0.969133i | −0.177930 | − | 0.102728i | 0.408390 | − | 0.912808i | \(-0.366090\pi\) |
−0.586320 | + | 0.810080i | \(0.699424\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.15980 | − | 6.22541i | 0.121580 | − | 0.652601i | ||||
\(92\) | 3.44029 | 0.358675 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.78265 | + | 3.08763i | 0.183866 | + | 0.318465i | ||||
\(95\) | 5.85498 | − | 3.38037i | 0.600708 | − | 0.346819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.9915i | 1.92829i | 0.265368 | + | 0.964147i | \(0.414507\pi\) | ||||
−0.265368 | + | 0.964147i | \(0.585493\pi\) | |||||||
\(98\) | 4.39513 | + | 5.44820i | 0.443975 | + | 0.550351i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.48563 | − | 2.57319i | 0.148563 | − | 0.257319i | ||||
\(101\) | −2.97996 | − | 5.16145i | −0.296518 | − | 0.513583i | 0.678819 | − | 0.734305i | \(-0.262492\pi\) |
−0.975337 | + | 0.220722i | \(0.929159\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.65167 | + | 5.57240i | 0.951008 | + | 0.549064i | 0.893394 | − | 0.449274i | \(-0.148317\pi\) |
0.0576138 | + | 0.998339i | \(0.481651\pi\) | |||||||
\(104\) | 2.39347i | 0.234699i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.97653i | 0.386234i | ||||||||
\(107\) | −3.72394 | − | 2.15002i | −0.360007 | − | 0.207850i | 0.309077 | − | 0.951037i | \(-0.399980\pi\) |
−0.669084 | + | 0.743187i | \(0.733313\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.85329 | + | 5.68880i | −0.943774 | + | 0.544888i | −0.891141 | − | 0.453726i | \(-0.850095\pi\) |
−0.0526326 | + | 0.998614i | \(0.516761\pi\) | |||||||
\(110\) | 4.46089 | + | 1.55452i | 0.425330 | + | 0.148218i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.01025 | − | 1.72015i | −0.189951 | − | 0.162539i | ||||
\(113\) | −8.29122 | −0.779973 | −0.389986 | − | 0.920821i | \(-0.627520\pi\) | ||||
−0.389986 | + | 0.920821i | \(0.627520\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.24364 | + | 2.45007i | −0.395722 | + | 0.228470i | ||||
\(116\) | −3.58158 | + | 2.06783i | −0.332541 | + | 0.191993i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.44483 | 0.501238 | ||||||||
\(119\) | −2.64398 | + | 0.933520i | −0.242374 | + | 0.0855757i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.61157 | − | 10.8813i | 0.146507 | − | 0.989210i | ||||
\(122\) | 9.66532 | − | 5.58028i | 0.875057 | − | 0.505215i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.122361 | + | 0.0706450i | 0.0109883 | + | 0.00634411i | ||||
\(125\) | 11.3538i | 1.01551i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.86776i | 0.875622i | 0.899067 | + | 0.437811i | \(0.144246\pi\) | ||||
−0.899067 | + | 0.437811i | \(0.855754\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.70455 | − | 2.95237i | −0.149499 | − | 0.258940i | ||||
\(131\) | 4.97078 | − | 8.60965i | 0.434299 | − | 0.752228i | −0.562939 | − | 0.826498i | \(-0.690329\pi\) |
0.997238 | + | 0.0742702i | \(0.0236627\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.54182 | − | 8.16483i | −0.827381 | − | 0.707980i | ||||
\(134\) | 1.13565i | 0.0981053i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.917806 | − | 0.529896i | 0.0787013 | − | 0.0454382i | ||||
\(137\) | 7.68510 | + | 13.3110i | 0.656583 | + | 1.13723i | 0.981495 | + | 0.191490i | \(0.0613320\pi\) |
−0.324912 | + | 0.945744i | \(0.605335\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.38399 | 0.202208 | 0.101104 | − | 0.994876i | \(-0.467763\pi\) | ||||
0.101104 | + | 0.994876i | \(0.467763\pi\) | |||||||
\(140\) | 3.70470 | + | 0.690186i | 0.313104 | + | 0.0583314i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.48844 | + | 5.47815i | 0.796252 | + | 0.459716i | ||||
\(143\) | −6.01032 | + | 5.18572i | −0.502608 | + | 0.433652i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.94528 | − | 5.10138i | 0.244592 | − | 0.423646i | ||||
\(146\) | 1.93827i | 0.160412i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.38037 | 0.195665 | ||||||||
\(149\) | −10.6719 | − | 6.16145i | −0.874280 | − | 0.504766i | −0.00551161 | − | 0.999985i | \(-0.501754\pi\) |
−0.868768 | + | 0.495219i | \(0.835088\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.22136 | + | 0.705152i | −0.0993928 | + | 0.0573844i | −0.548872 | − | 0.835906i | \(-0.684943\pi\) |
0.449480 | + | 0.893291i | \(0.351609\pi\) | |||||||
\(152\) | 4.11067 | + | 2.37329i | 0.333419 | + | 0.192500i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.0359145 | − | 8.77489i | −0.00289408 | − | 0.707101i | ||||
\(155\) | −0.201245 | −0.0161644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.57056 | + | 3.79351i | −0.524388 | + | 0.302755i | −0.738728 | − | 0.674004i | \(-0.764573\pi\) |
0.214340 | + | 0.976759i | \(0.431240\pi\) | |||||||
\(158\) | 2.20678 | + | 3.82226i | 0.175562 | + | 0.304082i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.42434 | −0.112604 | ||||||||
\(161\) | 6.91584 | + | 5.91781i | 0.545045 | + | 0.466388i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.65275 | − | 6.32675i | 0.286106 | − | 0.495549i | −0.686771 | − | 0.726874i | \(-0.740973\pi\) |
0.972877 | + | 0.231324i | \(0.0743059\pi\) | |||||||
\(164\) | −4.58889 | − | 7.94820i | −0.358332 | − | 0.620650i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.23495 | + | 1.86770i | 0.251080 | + | 0.144961i | ||||
\(167\) | −11.1448 | −0.862410 | −0.431205 | − | 0.902254i | \(-0.641911\pi\) | ||||
−0.431205 | + | 0.902254i | \(0.641911\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.27130 | −0.559331 | ||||||||
\(170\) | −0.754750 | + | 1.30727i | −0.0578867 | + | 0.100263i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.96945 | + | 2.86912i | −0.378917 | + | 0.218768i | ||||
\(173\) | 0.813549 | − | 1.40911i | 0.0618530 | − | 0.107133i | −0.833441 | − | 0.552609i | \(-0.813632\pi\) |
0.895294 | + | 0.445476i | \(0.146966\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.41275 | − | 2.61725i | 0.560351 | − | 0.197845i | ||||
\(176\) | 0.620776 | + | 3.25801i | 0.0467927 | + | 0.245582i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.969133 | + | 1.67859i | 0.0726396 | + | 0.125815i | ||||
\(179\) | −8.77643 | − | 15.2012i | −0.655981 | − | 1.13619i | −0.981647 | − | 0.190708i | \(-0.938922\pi\) |
0.325665 | − | 0.945485i | \(-0.394412\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.92820i | − | 0.514969i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||
0.966282 | − | 0.257485i | \(-0.0828937\pi\) | |||||||
\(182\) | −4.11712 | + | 4.81147i | −0.305181 | + | 0.356650i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.97938 | − | 1.72015i | −0.219643 | − | 0.126811i | ||||
\(185\) | −2.93622 | + | 1.69523i | −0.215875 | + | 0.124636i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.31917 | + | 1.15665i | 0.242722 | + | 0.0845829i | ||||
\(188\) | − | 3.56529i | − | 0.260026i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.76074 | −0.490476 | ||||||||
\(191\) | −11.5035 | + | 19.9247i | −0.832366 | + | 1.44170i | 0.0637902 | + | 0.997963i | \(0.479681\pi\) |
−0.896157 | + | 0.443738i | \(0.853652\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.2144 | − | 8.20668i | 1.02317 | − | 0.590730i | 0.108152 | − | 0.994134i | \(-0.465507\pi\) |
0.915022 | + | 0.403405i | \(0.132173\pi\) | |||||||
\(194\) | 9.49575 | − | 16.4471i | 0.681755 | − | 1.18083i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.08219 | − | 6.91584i | −0.0772995 | − | 0.493989i | ||||
\(197\) | 8.65167i | 0.616406i | 0.951321 | + | 0.308203i | \(0.0997276\pi\) | ||||
−0.951321 | + | 0.308203i | \(0.900272\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0608 | + | 6.38595i | −0.784078 | + | 0.452688i | −0.837874 | − | 0.545864i | \(-0.816201\pi\) |
0.0537956 | + | 0.998552i | \(0.482868\pi\) | |||||||
\(200\) | −2.57319 | + | 1.48563i | −0.181952 | + | 0.105050i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.95993i | 0.419339i | ||||||||
\(203\) | −10.7568 | − | 2.00400i | −0.754981 | − | 0.140653i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.3209 | + | 6.53613i | 0.790687 | + | 0.456503i | ||||
\(206\) | −5.57240 | − | 9.65167i | −0.388247 | − | 0.672464i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.19674 | − | 2.07281i | 0.0829786 | − | 0.143723i | ||||
\(209\) | 2.94657 | + | 15.4644i | 0.203818 | + | 1.06970i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 22.2186i | − | 1.52959i | −0.644272 | − | 0.764797i | \(-0.722839\pi\) | ||
0.644272 | − | 0.764797i | \(-0.277161\pi\) | |||||||
\(212\) | 1.98826 | − | 3.44377i | 0.136554 | − | 0.236519i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.15002 | + | 3.72394i | 0.146972 | + | 0.254563i | ||||
\(215\) | 4.08659 | − | 7.07818i | 0.278703 | − | 0.482728i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.124456 | + | 0.352492i | 0.00844860 | + | 0.0239287i | ||||
\(218\) | 11.3776 | 0.770588 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.08599 | − | 3.57670i | −0.208057 | − | 0.241141i | ||||
\(221\) | −1.26829 | − | 2.19674i | −0.0853144 | − | 0.147769i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.98498i | 0.400784i | 0.979716 | + | 0.200392i | \(0.0642215\pi\) | ||||
−0.979716 | + | 0.200392i | \(0.935778\pi\) | |||||||
\(224\) | 0.880853 | + | 2.49481i | 0.0588544 | + | 0.166692i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.18041 | + | 4.14561i | 0.477634 | + | 0.275762i | ||||
\(227\) | 2.52071 | + | 4.36600i | 0.167306 | + | 0.289782i | 0.937472 | − | 0.348062i | \(-0.113160\pi\) |
−0.770166 | + | 0.637843i | \(0.779827\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.3837 | + | 10.6138i | 1.21483 | + | 0.701381i | 0.963807 | − | 0.266601i | \(-0.0859004\pi\) |
0.251021 | + | 0.967982i | \(0.419234\pi\) | |||||||
\(230\) | 4.90014 | 0.323105 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.13565 | 0.271519 | ||||||||
\(233\) | 12.7287 | + | 7.34890i | 0.833883 | + | 0.481443i | 0.855180 | − | 0.518331i | \(-0.173446\pi\) |
−0.0212973 | + | 0.999773i | \(0.506780\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.53909 | + | 4.39783i | 0.165632 | + | 0.286883i | ||||
\(236\) | −4.71536 | − | 2.72242i | −0.306944 | − | 0.177214i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.75652 | + | 0.513539i | 0.178678 | + | 0.0332878i | ||||
\(239\) | 21.0320i | 1.36045i | 0.733003 | + | 0.680225i | \(0.238118\pi\) | ||||
−0.733003 | + | 0.680225i | \(0.761882\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.15656 | + | 15.8596i | 0.589826 | + | 1.02161i | 0.994255 | + | 0.107039i | \(0.0341369\pi\) |
−0.404429 | + | 0.914569i | \(0.632530\pi\) | |||||||
\(242\) | −6.83632 | + | 8.61770i | −0.439455 | + | 0.553967i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.1606 | −0.714481 | ||||||||
\(245\) | 6.26014 | + | 7.76007i | 0.399946 | + | 0.495773i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.68041 | − | 9.83876i | 0.361436 | − | 0.626025i | ||||
\(248\) | −0.0706450 | − | 0.122361i | −0.00448596 | − | 0.00776991i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.67688 | − | 9.83265i | 0.359038 | − | 0.621871i | ||||
\(251\) | − | 30.7321i | − | 1.93979i | −0.243522 | − | 0.969895i | \(-0.578303\pi\) | ||
0.243522 | − | 0.969895i | \(-0.421697\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.13565 | − | 11.2085i | −0.134267 | − | 0.704673i | ||||
\(254\) | 4.93388 | − | 8.54573i | 0.309579 | − | 0.536207i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 10.7582 | + | 6.21128i | 0.671081 | + | 0.387449i | 0.796486 | − | 0.604657i | \(-0.206690\pi\) |
−0.125405 | + | 0.992106i | \(0.540023\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.78514 | + | 4.09459i | 0.297334 | + | 0.254425i | ||||
\(260\) | 3.40911i | 0.211424i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −8.60965 | + | 4.97078i | −0.531906 | + | 0.307096i | ||||
\(263\) | −1.49710 | + | 0.864349i | −0.0923150 | + | 0.0532981i | −0.545447 | − | 0.838145i | \(-0.683640\pi\) |
0.453132 | + | 0.891444i | \(0.350307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.66391i | 0.347931i | ||||||||
\(266\) | 4.18105 | + | 11.8419i | 0.256356 | + | 0.726071i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.567825 | − | 0.983502i | 0.0346854 | − | 0.0600770i | ||||
\(269\) | 0.418337 | − | 0.241527i | 0.0255065 | − | 0.0147262i | −0.487193 | − | 0.873295i | \(-0.661979\pi\) |
0.512699 | + | 0.858568i | \(0.328646\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.53549 | − | 11.3198i | 0.397002 | − | 0.687628i | −0.596352 | − | 0.802723i | \(-0.703384\pi\) |
0.993355 | + | 0.115095i | \(0.0367171\pi\) | |||||||
\(272\) | −1.05979 | −0.0642593 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 15.3702i | − | 0.928548i | ||||||
\(275\) | −9.30572 | − | 3.24283i | −0.561156 | − | 0.195550i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.7031 | − | 10.7982i | 1.12376 | − | 0.648802i | 0.181400 | − | 0.983409i | \(-0.441937\pi\) |
0.942358 | + | 0.334608i | \(0.108604\pi\) | |||||||
\(278\) | −2.06460 | − | 1.19200i | −0.123826 | − | 0.0714912i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.86327 | − | 2.45007i | −0.171113 | − | 0.146420i | ||||
\(281\) | − | 1.07487i | − | 0.0641213i | −0.999486 | − | 0.0320607i | \(-0.989793\pi\) | ||
0.999486 | − | 0.0320607i | \(-0.0102070\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.4644 | − | 25.0531i | −0.859821 | − | 1.48925i | −0.872099 | − | 0.489330i | \(-0.837241\pi\) |
0.0122775 | − | 0.999925i | \(-0.496092\pi\) | |||||||
\(284\) | −5.47815 | − | 9.48844i | −0.325069 | − | 0.563035i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.79795 | − | 1.48581i | 0.461103 | − | 0.0878577i | ||||
\(287\) | 4.44725 | − | 23.8714i | 0.262513 | − | 1.40909i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.93842 | − | 13.7497i | 0.466966 | − | 0.808809i | ||||
\(290\) | −5.10138 | + | 2.94528i | −0.299563 | + | 0.172953i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.969133 | − | 1.67859i | 0.0567142 | − | 0.0982319i | ||||
\(293\) | −23.8916 | −1.39576 | −0.697882 | − | 0.716213i | \(-0.745874\pi\) | ||||
−0.697882 | + | 0.716213i | \(0.745874\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.75528 | 0.451530 | ||||||||
\(296\) | −2.06146 | − | 1.19019i | −0.119820 | − | 0.0691782i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.16145 | + | 10.6719i | 0.356923 | + | 0.618209i | ||||
\(299\) | −4.11712 | + | 7.13106i | −0.238099 | + | 0.412400i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.9251 | − | 2.78055i | −0.860270 | − | 0.160268i | ||||
\(302\) | 1.41030 | 0.0811539 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.37329 | − | 4.11067i | −0.136118 | − | 0.235763i | ||||
\(305\) | 13.7667 | − | 7.94820i | 0.788278 | − | 0.455112i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.5620 | 1.05939 | 0.529695 | − | 0.848188i | \(-0.322306\pi\) | ||||
0.529695 | + | 0.848188i | \(0.322306\pi\) | |||||||
\(308\) | −4.35634 | + | 7.61724i | −0.248226 | + | 0.434032i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.174283 | + | 0.100622i | 0.00989860 | + | 0.00571496i | ||||
\(311\) | −5.13370 | + | 2.96394i | −0.291105 | + | 0.168070i | −0.638440 | − | 0.769671i | \(-0.720420\pi\) |
0.347335 | + | 0.937741i | \(0.387087\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.5264 | + | 11.2736i | 1.10370 | + | 0.637219i | 0.937189 | − | 0.348821i | \(-0.113418\pi\) |
0.166507 | + | 0.986040i | \(0.446751\pi\) | |||||||
\(314\) | 7.58703 | 0.428161 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 4.41356i | − | 0.248282i | ||||||
\(317\) | 9.12767 | − | 15.8096i | 0.512661 | − | 0.887955i | −0.487231 | − | 0.873273i | \(-0.661993\pi\) |
0.999892 | − | 0.0146817i | \(-0.00467350\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.96036 | + | 10.3852i | 0.501684 | + | 0.581458i | ||||
\(320\) | 1.23351 | + | 0.712169i | 0.0689554 | + | 0.0398114i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.03039 | − | 8.58289i | −0.168877 | − | 0.478306i | ||||
\(323\) | −5.03040 | −0.279899 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.55581 | + | 6.15885i | 0.197241 | + | 0.341632i | ||||
\(326\) | −6.32675 | + | 3.65275i | −0.350406 | + | 0.202307i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.17779i | 0.506759i | ||||||||
\(329\) | 6.13282 | − | 7.16712i | 0.338113 | − | 0.395136i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.6240 | − | 23.5975i | 0.748844 | − | 1.29704i | −0.199534 | − | 0.979891i | \(-0.563943\pi\) |
0.948377 | − | 0.317144i | \(-0.102724\pi\) | |||||||
\(332\) | −1.86770 | − | 3.23495i | −0.102503 | − | 0.177541i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.65167 | + | 5.57240i | 0.528116 | + | 0.304908i | ||||
\(335\) | 1.61755i | 0.0883762i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 20.1352i | − | 1.09683i | −0.836206 | − | 0.548416i | \(-0.815231\pi\) | ||
0.836206 | − | 0.548416i | \(-0.184769\pi\) | |||||||
\(338\) | 6.29713 | + | 3.63565i | 0.342519 | + | 0.197753i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.30727 | − | 0.754750i | 0.0708964 | − | 0.0409321i | ||||
\(341\) | 0.154204 | − | 0.442507i | 0.00835059 | − | 0.0239631i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.72078 | − | 15.7641i | 0.524873 | − | 0.851181i | ||||
\(344\) | 5.73823 | 0.309385 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.40911 | + | 0.813549i | −0.0757541 | + | 0.0437367i | ||||
\(347\) | 21.1648 | − | 12.2195i | 1.13619 | − | 0.655977i | 0.190702 | − | 0.981648i | \(-0.438923\pi\) |
0.945483 | + | 0.325671i | \(0.105590\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.06974 | −0.164319 | −0.0821596 | − | 0.996619i | \(-0.526182\pi\) | ||||
−0.0821596 | + | 0.996619i | \(0.526182\pi\) | |||||||
\(350\) | −7.72825 | − | 1.43977i | −0.413092 | − | 0.0769592i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.09140 | − | 3.13191i | 0.0581717 | − | 0.166931i | ||||
\(353\) | 29.1124 | − | 16.8081i | 1.54950 | − | 0.894604i | 0.551319 | − | 0.834294i | \(-0.314125\pi\) |
0.998180 | − | 0.0603093i | \(-0.0192087\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.5147 | + | 7.80274i | 0.717288 | + | 0.414126i | ||||
\(356\) | − | 1.93827i | − | 0.102728i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.5529i | 0.927698i | ||||||||
\(359\) | −19.7114 | − | 11.3804i | −1.04033 | − | 0.600633i | −0.120401 | − | 0.992725i | \(-0.538418\pi\) |
−0.919926 | + | 0.392092i | \(0.871751\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.76505 | − | 3.05716i | −0.0928976 | − | 0.160903i | ||||
\(362\) | −3.46410 | + | 6.00000i | −0.182069 | + | 0.315353i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.97126 | − | 2.10829i | 0.312979 | − | 0.110505i | ||||
\(365\) | 2.76074i | 0.144504i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.0969 | + | 6.40682i | −0.579255 | + | 0.334433i | −0.760837 | − | 0.648943i | \(-0.775212\pi\) |
0.181582 | + | 0.983376i | \(0.441878\pi\) | |||||||
\(368\) | 1.72015 | + | 2.97938i | 0.0896688 | + | 0.155311i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.39045 | 0.176261 | ||||||||
\(371\) | 9.92069 | − | 3.50273i | 0.515057 | − | 0.181853i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.3658 | − | 7.13940i | −0.640277 | − | 0.369664i | 0.144444 | − | 0.989513i | \(-0.453861\pi\) |
−0.784721 | + | 0.619849i | \(0.787194\pi\) | |||||||
\(374\) | −2.29616 | − | 2.66128i | −0.118732 | − | 0.137611i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.78265 | + | 3.08763i | −0.0919329 | + | 0.159233i | ||||
\(377\) | − | 9.89856i | − | 0.509802i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.2480 | −1.39964 | −0.699819 | − | 0.714321i | \(-0.746736\pi\) | ||||
−0.699819 | + | 0.714321i | \(0.746736\pi\) | |||||||
\(380\) | 5.85498 | + | 3.38037i | 0.300354 | + | 0.173409i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 19.9247 | − | 11.5035i | 1.01944 | − | 0.588572i | ||||
\(383\) | −10.7500 | − | 6.20654i | −0.549301 | − | 0.317139i | 0.199539 | − | 0.979890i | \(-0.436056\pi\) |
−0.748840 | + | 0.662751i | \(0.769389\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0511544 | − | 12.4984i | −0.00260707 | − | 0.636978i | ||||
\(386\) | −16.4134 | −0.835418 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.4471 | + | 9.49575i | −0.834976 | + | 0.482074i | ||||
\(389\) | 15.7575 | + | 27.2927i | 0.798936 | + | 1.38380i | 0.920310 | + | 0.391190i | \(0.127937\pi\) |
−0.121374 | + | 0.992607i | \(0.538730\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.64599 | 0.184386 | ||||||||
\(392\) | −2.52071 | + | 6.53039i | −0.127315 | + | 0.329835i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.32584 | − | 7.49257i | 0.217932 | − | 0.377470i | ||||
\(395\) | 3.14320 | + | 5.44418i | 0.158152 | + | 0.273926i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.1419 | + | 8.16483i | 0.709761 | + | 0.409781i | 0.810973 | − | 0.585084i | \(-0.198938\pi\) |
−0.101211 | + | 0.994865i | \(0.532272\pi\) | |||||||
\(398\) | 12.7719 | 0.640197 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.97126 | 0.148563 | ||||||||
\(401\) | −9.17852 | + | 15.8977i | −0.458354 | + | 0.793892i | −0.998874 | − | 0.0474391i | \(-0.984894\pi\) |
0.540521 | + | 0.841331i | \(0.318227\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.292867 | + | 0.169087i | −0.0145887 | + | 0.00842281i | ||||
\(404\) | 2.97996 | − | 5.16145i | 0.148259 | − | 0.256792i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.31368 | + | 7.11392i | 0.412601 | + | 0.353058i | ||||
\(407\) | −1.47768 | − | 7.75528i | −0.0732458 | − | 0.384415i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.7702 | − | 29.0468i | −0.829233 | − | 1.43627i | −0.898641 | − | 0.438685i | \(-0.855444\pi\) |
0.0694082 | − | 0.997588i | \(-0.477889\pi\) | |||||||
\(410\) | −6.53613 | − | 11.3209i | −0.322797 | − | 0.559100i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.1448i | 0.549064i | ||||||||
\(413\) | −4.79610 | − | 13.5838i | −0.236000 | − | 0.668417i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.60765 | + | 2.66023i | 0.226181 | + | 0.130586i | ||||
\(416\) | −2.07281 | + | 1.19674i | −0.101628 | + | 0.0586748i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.18042 | − | 14.8659i | 0.253383 | − | 0.727114i | ||||
\(419\) | − | 35.5948i | − | 1.73892i | −0.494005 | − | 0.869459i | \(-0.664467\pi\) | ||
0.494005 | − | 0.869459i | \(-0.335533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.56215 | −0.0761348 | −0.0380674 | − | 0.999275i | \(-0.512120\pi\) | ||||
−0.0380674 | + | 0.999275i | \(0.512120\pi\) | |||||||
\(422\) | −11.1093 | + | 19.2419i | −0.540793 | + | 0.936681i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.44377 | + | 1.98826i | −0.167244 | + | 0.0965586i | ||||
\(425\) | 1.57446 | − | 2.72704i | 0.0763725 | − | 0.132281i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.4355 | − | 19.1978i | −1.08573 | − | 0.929046i | ||||
\(428\) | − | 4.30004i | − | 0.207850i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.07818 | + | 4.08659i | −0.341340 | + | 0.197073i | ||||
\(431\) | 9.26930 | − | 5.35164i | 0.446487 | − | 0.257779i | −0.259859 | − | 0.965647i | \(-0.583676\pi\) |
0.706345 | + | 0.707867i | \(0.250343\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.1461i | 0.487589i | 0.969827 | + | 0.243794i | \(0.0783922\pi\) | ||||
−0.969827 | + | 0.243794i | \(0.921608\pi\) | |||||||
\(434\) | 0.0684644 | − | 0.367495i | 0.00328639 | − | 0.0176403i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.85329 | − | 5.68880i | −0.471887 | − | 0.272444i | ||||
\(437\) | 8.16483 | + | 14.1419i | 0.390577 | + | 0.676499i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.4282 | + | 18.0622i | −0.497711 | + | 0.862061i | −0.999997 | − | 0.00264068i | \(-0.999159\pi\) |
0.502285 | + | 0.864702i | \(0.332493\pi\) | |||||||
\(440\) | 0.884194 | + | 4.64051i | 0.0421523 | + | 0.221227i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.53658i | 0.120653i | ||||||||
\(443\) | 11.0758 | − | 19.1838i | 0.526227 | − | 0.911452i | −0.473306 | − | 0.880898i | \(-0.656940\pi\) |
0.999533 | − | 0.0305538i | \(-0.00972709\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.38037 | + | 2.39087i | 0.0654359 | + | 0.113338i | ||||
\(446\) | 2.99249 | − | 5.18314i | 0.141698 | − | 0.245429i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.484566 | − | 2.60100i | 0.0228936 | − | 0.122886i | ||||
\(449\) | 36.1782 | 1.70735 | 0.853677 | − | 0.520802i | \(-0.174367\pi\) | ||||
0.853677 | + | 0.520802i | \(0.174367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.0466 | + | 19.8847i | −1.08522 | + | 0.936335i | ||||
\(452\) | −4.14561 | − | 7.18041i | −0.194993 | − | 0.337738i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 5.04143i | − | 0.236606i | ||||||
\(455\) | −5.86417 | + | 6.85315i | −0.274916 | + | 0.321281i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.5981 | + | 16.5111i | 1.33776 | + | 0.772358i | 0.986475 | − | 0.163909i | \(-0.0524104\pi\) |
0.351288 | + | 0.936267i | \(0.385744\pi\) | |||||||
\(458\) | −10.6138 | − | 18.3837i | −0.495951 | − | 0.859013i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.24364 | − | 2.45007i | −0.197861 | − | 0.114235i | ||||
\(461\) | −36.8048 | −1.71417 | −0.857086 | − | 0.515174i | \(-0.827727\pi\) | ||||
−0.857086 | + | 0.515174i | \(0.827727\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.0895 | −0.980113 | −0.490057 | − | 0.871691i | \(-0.663024\pi\) | ||||
−0.490057 | + | 0.871691i | \(0.663024\pi\) | |||||||
\(464\) | −3.58158 | − | 2.06783i | −0.166271 | − | 0.0959964i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.34890 | − | 12.7287i | −0.340431 | − | 0.589644i | ||||
\(467\) | −4.00895 | − | 2.31457i | −0.185512 | − | 0.107106i | 0.404368 | − | 0.914597i | \(-0.367492\pi\) |
−0.589880 | + | 0.807491i | \(0.700825\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.83324 | − | 1.00034i | 0.130827 | − | 0.0461914i | ||||
\(470\) | − | 5.07818i | − | 0.234239i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.72242 | + | 4.71536i | 0.125309 | + | 0.217042i | ||||
\(473\) | 12.4325 | + | 14.4095i | 0.571648 | + | 0.662548i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.1034 | 0.647107 | ||||||||
\(476\) | −2.13044 | − | 1.82300i | −0.0976487 | − | 0.0835569i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.5160 | − | 18.2143i | 0.480992 | − | 0.833102i | ||||
\(479\) | 15.2924 | + | 26.4873i | 0.698729 | + | 1.21023i | 0.968907 | + | 0.247425i | \(0.0795842\pi\) |
−0.270178 | + | 0.962810i | \(0.587082\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.84867 | + | 4.93405i | −0.129888 | + | 0.224973i | ||||
\(482\) | − | 18.3131i | − | 0.834140i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.2293 | − | 4.04499i | 0.464967 | − | 0.183863i | ||||
\(485\) | 13.5251 | − | 23.4262i | 0.614145 | − | 1.06373i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.5293 | + | 26.8976i | 0.703700 | + | 1.21884i | 0.967159 | + | 0.254174i | \(0.0818036\pi\) |
−0.263458 | + | 0.964671i | \(0.584863\pi\) | |||||||
\(488\) | 9.66532 | + | 5.58028i | 0.437529 | + | 0.252607i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.54141 | − | 9.85049i | −0.0696337 | − | 0.445000i | ||||
\(491\) | 32.7320i | 1.47717i | 0.674158 | + | 0.738587i | \(0.264507\pi\) | ||||
−0.674158 | + | 0.738587i | \(0.735493\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.79573 | + | 2.19146i | −0.170951 | + | 0.0986986i | ||||
\(494\) | −9.83876 | + | 5.68041i | −0.442667 | + | 0.255574i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.141290i | 0.00634411i | ||||||||
\(497\) | 5.30906 | − | 28.4973i | 0.238144 | − | 1.27828i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.0033 | − | 32.9147i | 0.850705 | − | 1.47346i | −0.0298682 | − | 0.999554i | \(-0.509509\pi\) |
0.880573 | − | 0.473910i | \(-0.157158\pi\) | |||||||
\(500\) | −9.83265 | + | 5.67688i | −0.439730 | + | 0.253878i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.3660 | + | 26.6147i | −0.685820 | + | 1.18787i | ||||
\(503\) | −11.9467 | −0.532678 | −0.266339 | − | 0.963879i | \(-0.585814\pi\) | ||||
−0.266339 | + | 0.963879i | \(0.585814\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.48895i | 0.377753i | ||||||||
\(506\) | −3.75473 | + | 10.7747i | −0.166918 | + | 0.478993i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.54573 | + | 4.93388i | −0.379156 | + | 0.218906i | ||||
\(509\) | 26.5048 | + | 15.3026i | 1.17481 | + | 0.678275i | 0.954807 | − | 0.297226i | \(-0.0960614\pi\) |
0.219999 | + | 0.975500i | \(0.429395\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.83561 | − | 1.70733i | 0.213915 | − | 0.0755277i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.21128 | − | 10.7582i | −0.273968 | − | 0.474526i | ||||
\(515\) | −7.93697 | − | 13.7472i | −0.349745 | − | 0.605776i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.6158 | + | 2.21325i | −0.510861 | + | 0.0973385i | ||||
\(518\) | −2.09676 | − | 5.93859i | −0.0921262 | − | 0.260926i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.70455 | − | 2.95237i | 0.0747496 | − | 0.129470i | ||||
\(521\) | −18.8615 | + | 10.8897i | −0.826335 | + | 0.477085i | −0.852596 | − | 0.522570i | \(-0.824973\pi\) |
0.0262609 | + | 0.999655i | \(0.491640\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.66648 | + | 11.5467i | −0.291505 | + | 0.504901i | −0.974166 | − | 0.225834i | \(-0.927489\pi\) |
0.682661 | + | 0.730735i | \(0.260823\pi\) | |||||||
\(524\) | 9.94156 | 0.434299 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.72870 | 0.0753749 | ||||||||
\(527\) | 0.129677 | + | 0.0748690i | 0.00564881 | + | 0.00326134i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.58219 | + | 9.66864i | 0.242704 | + | 0.420376i | ||||
\(530\) | 2.83196 | − | 4.90509i | 0.123012 | − | 0.213064i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.30004 | − | 12.3459i | 0.0997193 | − | 0.535262i | ||||
\(533\) | 21.9668 | 0.951486 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.06235 | + | 5.30415i | 0.132397 | + | 0.229318i | ||||
\(536\) | −0.983502 | + | 0.567825i | −0.0424808 | + | 0.0245263i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.483054 | −0.0208259 | ||||||||
\(539\) | −21.8601 | + | 7.81899i | −0.941581 | + | 0.336788i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.35710 | − | 1.36087i | −0.101340 | − | 0.0585085i | 0.448474 | − | 0.893796i | \(-0.351968\pi\) |
−0.549813 | + | 0.835288i | \(0.685301\pi\) | |||||||
\(542\) | −11.3198 | + | 6.53549i | −0.486227 | + | 0.280723i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.917806 | + | 0.529896i | 0.0393506 | + | 0.0227191i | ||||
\(545\) | 16.2055 | 0.694169 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.1418i | 1.71634i | 0.513365 | + | 0.858170i | \(0.328399\pi\) | ||||
−0.513365 | + | 0.858170i | \(0.671601\pi\) | |||||||
\(548\) | −7.68510 | + | 13.3110i | −0.328291 | + | 0.568617i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.43758 | + | 7.46124i | 0.274499 | + | 0.318148i | ||||
\(551\) | −17.0003 | − | 9.81512i | −0.724236 | − | 0.418138i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.59197 | − | 8.87235i | 0.322843 | − | 0.377291i | ||||
\(554\) | −21.5964 | −0.917544 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.19200 | + | 2.06460i | 0.0505519 | + | 0.0875585i | ||||
\(557\) | 9.06246 | − | 5.23221i | 0.383989 | − | 0.221696i | −0.295564 | − | 0.955323i | \(-0.595507\pi\) |
0.679552 | + | 0.733627i | \(0.262174\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 13.7343i | − | 0.580898i | ||||||
\(560\) | 1.25463 | + | 3.55346i | 0.0530178 | + | 0.150161i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.537434 | + | 0.930864i | −0.0226703 | + | 0.0392661i | ||||
\(563\) | 5.24207 | + | 9.07954i | 0.220927 | + | 0.382657i | 0.955090 | − | 0.296317i | \(-0.0957584\pi\) |
−0.734163 | + | 0.678974i | \(0.762425\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.2273 | + | 5.90475i | 0.430267 | + | 0.248415i | ||||
\(566\) | 28.9289i | 1.21597i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.9563i | 0.459716i | ||||||||
\(569\) | 7.77730 | + | 4.49022i | 0.326041 | + | 0.188240i | 0.654082 | − | 0.756424i | \(-0.273055\pi\) |
−0.328041 | + | 0.944664i | \(0.606388\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.8399 | + | 12.0319i | −0.872121 | + | 0.503519i | −0.868052 | − | 0.496473i | \(-0.834628\pi\) |
−0.00406827 | + | 0.999992i | \(0.501295\pi\) | |||||||
\(572\) | −7.49613 | − | 2.61223i | −0.313429 | − | 0.109223i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −15.7871 | + | 18.4496i | −0.658942 | + | 0.770073i | ||||
\(575\) | −10.2220 | −0.426288 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.6693 | + | 6.73730i | −0.485801 | + | 0.280478i | −0.722831 | − | 0.691025i | \(-0.757159\pi\) |
0.237030 | + | 0.971502i | \(0.423826\pi\) | |||||||
\(578\) | −13.7497 | + | 7.93842i | −0.571914 | + | 0.330195i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.89056 | 0.244592 | ||||||||
\(581\) | 1.81005 | − | 9.71575i | 0.0750934 | − | 0.403077i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.4541 | − | 4.33997i | −0.515797 | − | 0.179743i | ||||
\(584\) | −1.67859 | + | 0.969133i | −0.0694604 | + | 0.0401030i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.6908 | + | 11.9458i | 0.854727 | + | 0.493477i | ||||
\(587\) | 5.46623i | 0.225616i | 0.993617 | + | 0.112808i | \(0.0359844\pi\) | ||||
−0.993617 | + | 0.112808i | \(0.964016\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.670645i | 0.0276335i | ||||||||
\(590\) | −6.71627 | − | 3.87764i | −0.276504 | − | 0.159640i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.19019 | + | 2.06146i | 0.0489163 | + | 0.0847256i | ||||
\(593\) | −17.1992 | + | 29.7899i | −0.706286 | + | 1.22332i | 0.259940 | + | 0.965625i | \(0.416297\pi\) |
−0.966226 | + | 0.257698i | \(0.917036\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.92621 | + | 0.731453i | 0.160959 | + | 0.0299867i | ||||
\(596\) | − | 12.3229i | − | 0.504766i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.13106 | − | 4.11712i | 0.291611 | − | 0.168361i | ||||
\(599\) | 13.6689 | + | 23.6753i | 0.558497 | + | 0.967345i | 0.997622 | + | 0.0689193i | \(0.0219551\pi\) |
−0.439125 | + | 0.898426i | \(0.644712\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.3071 | −0.828343 | −0.414172 | − | 0.910199i | \(-0.635929\pi\) | ||||
−0.414172 | + | 0.910199i | \(0.635929\pi\) | |||||||
\(602\) | 11.5353 | + | 9.87060i | 0.470142 | + | 0.402295i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.22136 | − | 0.705152i | −0.0496964 | − | 0.0286922i | ||||
\(605\) | −9.73722 | + | 12.2745i | −0.395874 | + | 0.499030i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.37513 | − | 11.0420i | 0.258758 | − | 0.448183i | −0.707151 | − | 0.707062i | \(-0.750020\pi\) |
0.965910 | + | 0.258880i | \(0.0833533\pi\) | |||||||
\(608\) | 4.74659i | 0.192500i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.8964 | −0.643626 | ||||||||
\(611\) | 7.39016 | + | 4.26671i | 0.298974 | + | 0.172613i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.6426 | + | 7.87655i | −0.551019 | + | 0.318131i | −0.749533 | − | 0.661967i | \(-0.769722\pi\) |
0.198514 | + | 0.980098i | \(0.436388\pi\) | |||||||
\(614\) | −16.0752 | − | 9.28101i | −0.648742 | − | 0.374551i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.58132 | − | 4.41855i | 0.305460 | − | 0.178028i | ||||
\(617\) | 21.5108 | 0.865992 | 0.432996 | − | 0.901396i | \(-0.357456\pi\) | ||||
0.432996 | + | 0.901396i | \(0.357456\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.3551 | + | 16.9482i | −1.17988 | + | 0.681206i | −0.955988 | − | 0.293407i | \(-0.905211\pi\) |
−0.223896 | + | 0.974613i | \(0.571877\pi\) | |||||||
\(620\) | −0.100622 | − | 0.174283i | −0.00404109 | − | 0.00699937i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.92789 | 0.237687 | ||||||||
\(623\) | 3.33410 | − | 3.89639i | 0.133578 | − | 0.156106i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.657638 | − | 1.13906i | 0.0263055 | − | 0.0455625i | ||||
\(626\) | −11.2736 | − | 19.5264i | −0.450582 | − | 0.780431i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.57056 | − | 3.79351i | −0.262194 | − | 0.151378i | ||||
\(629\) | 2.52270 | 0.100587 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.994535 | 0.0395918 | 0.0197959 | − | 0.999804i | \(-0.493698\pi\) | ||||
0.0197959 | + | 0.999804i | \(0.493698\pi\) | |||||||
\(632\) | −2.20678 | + | 3.82226i | −0.0877810 | + | 0.152041i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.8096 | + | 9.12767i | −0.627879 | + | 0.362506i | ||||
\(635\) | 7.02751 | − | 12.1720i | 0.278878 | − | 0.483031i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.6303 | + | 6.03325i | 0.619295 | + | 0.239046i | ||||
\(638\) | −2.56731 | − | 13.4740i | −0.101641 | − | 0.533441i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.712169 | − | 1.23351i | −0.0281509 | − | 0.0487589i | ||||
\(641\) | 7.95305 | + | 13.7751i | 0.314127 | + | 0.544083i | 0.979251 | − | 0.202649i | \(-0.0649550\pi\) |
−0.665125 | + | 0.746732i | \(0.731622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.3990i | 0.567841i | 0.958848 | + | 0.283920i | \(0.0916351\pi\) | ||||
−0.958848 | + | 0.283920i | \(0.908365\pi\) | |||||||
\(644\) | −1.66705 | + | 8.94820i | −0.0656910 | + | 0.352608i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.35645 | + | 2.51520i | 0.171402 | + | 0.0989591i | ||||
\(647\) | 21.9409 | − | 12.6676i | 0.862585 | − | 0.498014i | −0.00229205 | − | 0.999997i | \(-0.500730\pi\) |
0.864877 | + | 0.501984i | \(0.167396\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.94248 | + | 17.0527i | −0.233263 | + | 0.669378i | ||||
\(650\) | − | 7.11163i | − | 0.278941i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.30550 | 0.286106 | ||||||||
\(653\) | −23.0579 | + | 39.9375i | −0.902326 | + | 1.56287i | −0.0778597 | + | 0.996964i | \(0.524809\pi\) |
−0.824467 | + | 0.565911i | \(0.808525\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.2630 | + | 7.08007i | −0.479157 | + | 0.276641i | ||||
\(656\) | 4.58889 | − | 7.94820i | 0.179166 | − | 0.310325i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.89474 | + | 3.14050i | −0.346753 | + | 0.122429i | ||||
\(659\) | − | 5.72654i | − | 0.223074i | −0.993760 | − | 0.111537i | \(-0.964423\pi\) | ||
0.993760 | − | 0.111537i | \(-0.0355774\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.83855 | + | 3.94824i | −0.265989 | + | 0.153569i | −0.627063 | − | 0.778968i | \(-0.715743\pi\) |
0.361075 | + | 0.932537i | \(0.382410\pi\) | |||||||
\(662\) | −23.5975 | + | 13.6240i | −0.917142 | + | 0.529512i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.73539i | 0.144961i | ||||||||
\(665\) | 5.95522 | + | 16.8668i | 0.230933 | + | 0.654066i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.3217 | + | 7.11392i | 0.477097 | + | 0.275452i | ||||
\(668\) | −5.57240 | − | 9.65167i | −0.215602 | − | 0.373434i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.808775 | − | 1.40084i | 0.0312457 | − | 0.0541191i | ||||
\(671\) | 6.92820 | + | 36.3612i | 0.267460 | + | 1.40371i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.3080i | 0.435893i | 0.975961 | + | 0.217947i | \(0.0699358\pi\) | ||||
−0.975961 | + | 0.217947i | \(0.930064\pi\) | |||||||
\(674\) | −10.0676 | + | 17.4376i | −0.387789 | + | 0.671670i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.63565 | − | 6.29713i | −0.139833 | − | 0.242197i | ||||
\(677\) | −22.4183 | + | 38.8297i | −0.861607 | + | 1.49235i | 0.00876985 | + | 0.999962i | \(0.497208\pi\) |
−0.870377 | + | 0.492386i | \(0.836125\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −49.3969 | − | 9.20264i | −1.89568 | − | 0.353165i | ||||
\(680\) | −1.50950 | −0.0578867 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.354798 | + | 0.306121i | −0.0135859 | + | 0.0117220i | ||||
\(683\) | −21.9999 | − | 38.1050i | −0.841804 | − | 1.45805i | −0.888368 | − | 0.459133i | \(-0.848160\pi\) |
0.0465632 | − | 0.998915i | \(-0.485173\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 21.8924i | − | 0.836464i | ||||||
\(686\) | −16.3005 | + | 8.79171i | −0.622355 | + | 0.335669i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.96945 | − | 2.86912i | −0.189459 | − | 0.109384i | ||||
\(689\) | 4.75885 | + | 8.24256i | 0.181298 | + | 0.314017i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.380577 | + | 0.219726i | 0.0144778 | + | 0.00835878i | 0.507221 | − | 0.861816i | \(-0.330673\pi\) |
−0.492744 | + | 0.870175i | \(0.664006\pi\) | |||||||
\(692\) | 1.62710 | 0.0618530 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −24.4390 | −0.927692 | ||||||||
\(695\) | −2.94069 | − | 1.69781i | −0.111547 | − | 0.0644014i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.86327 | − | 8.42343i | −0.184210 | − | 0.319060i | ||||
\(698\) | 2.65847 | + | 1.53487i | 0.100625 | + | 0.0580956i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.97298 | + | 5.11101i | 0.225757 | + | 0.193178i | ||||
\(701\) | − | 5.98591i | − | 0.226085i | −0.993590 | − | 0.113042i | \(-0.963940\pi\) | ||
0.993590 | − | 0.113042i | \(-0.0360596\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.64932 | + | 9.78492i | 0.213068 | + | 0.369045i | ||||
\(704\) | −2.51113 | + | 2.16661i | −0.0946419 | + | 0.0816573i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33.6162 | −1.26516 | ||||||||
\(707\) | 14.8689 | − | 5.24982i | 0.559203 | − | 0.197440i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.51308 | − | 13.0130i | 0.282160 | − | 0.488715i | −0.689757 | − | 0.724041i | \(-0.742282\pi\) |
0.971916 | + | 0.235326i | \(0.0756158\pi\) | |||||||
\(710\) | −7.80274 | − | 13.5147i | −0.292832 | − | 0.507199i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.969133 | + | 1.67859i | −0.0363198 | + | 0.0629077i | ||||
\(713\) | − | 0.486079i | − | 0.0182038i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.1069 | − | 2.11629i | 0.415375 | − | 0.0791448i | ||||
\(716\) | 8.77643 | − | 15.2012i | 0.327991 | − | 0.568097i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11.3804 | + | 19.7114i | 0.424712 | + | 0.735622i | ||||
\(719\) | 19.6269 | + | 11.3316i | 0.731961 | + | 0.422598i | 0.819139 | − | 0.573595i | \(-0.194452\pi\) |
−0.0871782 | + | 0.996193i | \(0.527785\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.1707 | + | 22.4038i | −0.713953 | + | 0.834361i | ||||
\(722\) | 3.53011i | 0.131377i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.00000 | − | 3.46410i | 0.222988 | − | 0.128742i | ||||
\(725\) | 10.6418 | − | 6.14405i | 0.395227 | − | 0.228184i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.35788i | 0.161625i | 0.996729 | + | 0.0808124i | \(0.0257515\pi\) | ||||
−0.996729 | + | 0.0808124i | \(0.974249\pi\) | |||||||
\(728\) | −6.22541 | − | 1.15980i | −0.230729 | − | 0.0429849i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.38037 | − | 2.39087i | 0.0510899 | − | 0.0884902i | ||||
\(731\) | −5.26658 | + | 3.04066i | −0.194792 | + | 0.112463i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.95832 | − | 15.5163i | 0.330883 | − | 0.573106i | −0.651802 | − | 0.758389i | \(-0.725987\pi\) |
0.982685 | + | 0.185283i | \(0.0593201\pi\) | |||||||
\(734\) | 12.8136 | 0.472960 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 3.44029i | − | 0.126811i | ||||||
\(737\) | −3.55675 | − | 1.23945i | −0.131015 | − | 0.0456556i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.10706 | + | 1.79386i | −0.114295 | + | 0.0659883i | −0.556058 | − | 0.831144i | \(-0.687687\pi\) |
0.441763 | + | 0.897132i | \(0.354353\pi\) | |||||||
\(740\) | −2.93622 | − | 1.69523i | −0.107938 | − | 0.0623178i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.3429 | − | 1.92689i | −0.379701 | − | 0.0707384i | ||||
\(743\) | − | 39.1927i | − | 1.43784i | −0.695092 | − | 0.718921i | \(-0.744636\pi\) | ||
0.695092 | − | 0.718921i | \(-0.255364\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.77598 | + | 15.2004i | 0.321527 | + | 0.556901i | ||||
\(746\) | 7.13940 | + | 12.3658i | 0.261392 | + | 0.452744i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.657893 | + | 3.45281i | 0.0240550 | + | 0.126247i | ||||
\(749\) | 7.39669 | − | 8.64414i | 0.270269 | − | 0.315850i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.04203 | + | 5.26894i | −0.111005 | + | 0.192267i | −0.916176 | − | 0.400777i | \(-0.868740\pi\) |
0.805171 | + | 0.593043i | \(0.202074\pi\) | |||||||
\(752\) | 3.08763 | − | 1.78265i | 0.112594 | − | 0.0650064i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.94928 | + | 8.57240i | −0.180242 | + | 0.312188i | ||||
\(755\) | 2.00875 | 0.0731058 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.922974 | −0.0335461 | −0.0167730 | − | 0.999859i | \(-0.505339\pi\) | ||||
−0.0167730 | + | 0.999859i | \(0.505339\pi\) | |||||||
\(758\) | 23.5975 | + | 13.6240i | 0.857099 | + | 0.494847i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.38037 | − | 5.85498i | −0.122619 | − | 0.212382i | ||||
\(761\) | −17.7810 | + | 30.7976i | −0.644561 | + | 1.11641i | 0.339842 | + | 0.940482i | \(0.389626\pi\) |
−0.984403 | + | 0.175929i | \(0.943707\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0220 | − | 28.3850i | −0.362820 | − | 1.02761i | ||||
\(764\) | −23.0071 | −0.832366 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.20654 | + | 10.7500i | 0.224251 | + | 0.388415i | ||||
\(767\) | 11.2861 | − | 6.51602i | 0.407517 | − | 0.235280i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −50.1085 | −1.80696 | −0.903478 | − | 0.428633i | \(-0.858995\pi\) | ||||
−0.903478 | + | 0.428633i | \(0.858995\pi\) | |||||||
\(770\) | −6.20490 | + | 10.8495i | −0.223609 | + | 0.390989i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.2144 | + | 8.20668i | 0.511587 | + | 0.295365i | ||||
\(773\) | 30.2054 | − | 17.4391i | 1.08641 | − | 0.627240i | 0.153793 | − | 0.988103i | \(-0.450851\pi\) |
0.932619 | + | 0.360863i | \(0.117518\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.363566 | − | 0.209905i | −0.0130597 | − | 0.00754000i | ||||
\(776\) | 18.9915 | 0.681755 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 31.5149i | − | 1.12987i | ||||||
\(779\) | 21.7816 | − | 37.7268i | 0.780407 | − | 1.35170i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.5127 | + | 23.7381i | −0.984483 | + | 0.849415i | ||||
\(782\) | −3.15752 | − | 1.82300i | −0.112913 | − | 0.0651902i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.44820 | − | 4.39513i | 0.194578 | − | 0.156969i | ||||
\(785\) | 10.8065 | 0.385700 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.96056 | − | 10.3240i | −0.212471 | − | 0.368011i | 0.740016 | − | 0.672589i | \(-0.234818\pi\) |
−0.952487 | + | 0.304578i | \(0.901484\pi\) | |||||||
\(788\) | −7.49257 | + | 4.32584i | −0.266912 | + | 0.154102i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 6.28640i | − | 0.223660i | ||||||
\(791\) | 4.01765 | − | 21.5655i | 0.142851 | − | 0.766780i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.3562 | − | 23.1337i | 0.474294 | − | 0.821501i | ||||
\(794\) | −8.16483 | − | 14.1419i | −0.289759 | − | 0.501877i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.0608 | − | 6.38595i | −0.392039 | − | 0.226344i | ||||
\(797\) | 10.4434i | 0.369923i | 0.982746 | + | 0.184961i | \(0.0592160\pi\) | ||||
−0.982746 | + | 0.184961i | \(0.940784\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.77847i | − | 0.133673i | ||||||
\(800\) | −2.57319 | − | 1.48563i | −0.0909760 | − | 0.0525250i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15.8977 | − | 9.17852i | 0.561366 | − | 0.324105i | ||||
\(803\) | −6.07047 | − | 2.11542i | −0.214222 | − | 0.0746515i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.31630 | − | 12.2249i | −0.152130 | − | 0.430872i | ||||
\(806\) | 0.338173 | 0.0119116 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.16145 | + | 2.97996i | −0.181579 | + | 0.104835i | ||||
\(809\) | −26.8647 | + | 15.5104i | −0.944513 | + | 0.545315i | −0.891372 | − | 0.453272i | \(-0.850257\pi\) |
−0.0531410 | + | 0.998587i | \(0.516923\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.1419 | −0.917968 | −0.458984 | − | 0.888445i | \(-0.651786\pi\) | ||||
−0.458984 | + | 0.888445i | \(0.651786\pi\) | |||||||
\(812\) | −3.64290 | − | 10.3177i | −0.127841 | − | 0.362080i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.59793 | + | 7.45511i | −0.0910575 | + | 0.261301i | ||||
\(815\) | −9.01143 | + | 5.20275i | −0.315657 | + | 0.182244i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.5880 | − | 13.6185i | −0.825238 | − | 0.476451i | ||||
\(818\) | 33.5404i | 1.17271i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.0723i | 0.456503i | ||||||||
\(821\) | 8.69274 | + | 5.01876i | 0.303379 | + | 0.175156i | 0.643960 | − | 0.765059i | \(-0.277290\pi\) |
−0.340581 | + | 0.940215i | \(0.610624\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.0320 | − | 46.8209i | −0.942278 | − | 1.63207i | −0.761112 | − | 0.648621i | \(-0.775346\pi\) |
−0.181166 | − | 0.983453i | \(-0.557987\pi\) | |||||||
\(824\) | 5.57240 | − | 9.65167i | 0.194124 | − | 0.336232i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.63838 | + | 14.1620i | −0.0918011 | + | 0.492759i | ||||
\(827\) | − | 27.7091i | − | 0.963541i | −0.876297 | − | 0.481771i | \(-0.839994\pi\) | ||
0.876297 | − | 0.481771i | \(-0.160006\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.30844 | + | 0.755429i | −0.0454440 | + | 0.0262371i | −0.522550 | − | 0.852609i | \(-0.675019\pi\) |
0.477106 | + | 0.878846i | \(0.341686\pi\) | |||||||
\(830\) | −2.66023 | − | 4.60765i | −0.0923379 | − | 0.159934i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.39347 | 0.0829786 | ||||||||
\(833\) | −1.14690 | − | 7.32935i | −0.0397377 | − | 0.253947i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.7472 | + | 7.93697i | 0.475743 | + | 0.274670i | ||||
\(836\) | −11.9193 | + | 10.2840i | −0.412238 | + | 0.355680i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −17.7974 | + | 30.8260i | −0.614800 | + | 1.06487i | ||||
\(839\) | 9.67749i | 0.334104i | 0.985948 | + | 0.167052i | \(0.0534248\pi\) | ||||
−0.985948 | + | 0.167052i | \(0.946575\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.8964 | 0.410220 | ||||||||
\(842\) | 1.35287 | + | 0.781077i | 0.0466228 | + | 0.0269177i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 19.2419 | − | 11.1093i | 0.662333 | − | 0.382398i | ||||
\(845\) | 8.96924 | + | 5.17839i | 0.308551 | + | 0.178142i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.5214 | + | 9.46442i | 0.945645 | + | 0.325201i | ||||
\(848\) | 3.97653 | 0.136554 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.72704 | + | 1.57446i | −0.0935369 | + | 0.0540035i | ||||
\(851\) | −4.09459 | − | 7.09203i | −0.140361 | − | 0.243112i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.71419 | −0.0929320 | −0.0464660 | − | 0.998920i | \(-0.514796\pi\) | ||||
−0.0464660 | + | 0.998920i | \(0.514796\pi\) | |||||||
\(854\) | 9.83080 | + | 27.8435i | 0.336403 | + | 0.952785i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.15002 | + | 3.72394i | −0.0734861 | + | 0.127282i | ||||
\(857\) | −8.74704 | − | 15.1503i | −0.298793 | − | 0.517525i | 0.677067 | − | 0.735921i | \(-0.263251\pi\) |
−0.975860 | + | 0.218397i | \(0.929917\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.8720 | + | 23.5975i | 1.39454 | + | 0.805136i | 0.993813 | − | 0.111063i | \(-0.0354257\pi\) |
0.400723 | + | 0.916199i | \(0.368759\pi\) | |||||||
\(860\) | 8.17318 | 0.278703 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.7033 | −0.364555 | ||||||||
\(863\) | −3.72585 | + | 6.45336i | −0.126829 | + | 0.219675i | −0.922447 | − | 0.386125i | \(-0.873813\pi\) |
0.795617 | + | 0.605800i | \(0.207147\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.00705 | + | 1.15877i | −0.0682416 | + | 0.0393993i | ||||
\(866\) | 5.07303 | − | 8.78675i | 0.172389 | − | 0.298586i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.243039 | + | 0.284028i | −0.00824929 | + | 0.00964053i | ||||
\(869\) | −14.3794 | + | 2.73983i | −0.487789 | + | 0.0929424i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.35907 | + | 2.35398i | 0.0460504 | + | 0.0797617i | ||||
\(872\) | 5.68880 | + | 9.85329i | 0.192647 | + | 0.333674i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 16.3297i | − | 0.552359i | ||||||
\(875\) | −29.5311 | − | 5.50165i | −0.998335 | − | 0.185990i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.6239 | + | 11.9072i | 0.696420 | + | 0.402078i | 0.806013 | − | 0.591898i | \(-0.201621\pi\) |
−0.109593 | + | 0.993977i | \(0.534955\pi\) | |||||||
\(878\) | 18.0622 | − | 10.4282i | 0.609569 | − | 0.351935i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.55452 | − | 4.46089i | 0.0524028 | − | 0.150377i | ||||
\(881\) | − | 42.1622i | − | 1.42048i | −0.703960 | − | 0.710240i | \(-0.748586\pi\) | ||
0.703960 | − | 0.710240i | \(-0.251414\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.28264 | −0.0768170 | −0.0384085 | − | 0.999262i | \(-0.512229\pi\) | ||||
−0.0384085 | + | 0.999262i | \(0.512229\pi\) | |||||||
\(884\) | 1.26829 | − | 2.19674i | 0.0426572 | − | 0.0738844i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.1838 | + | 11.0758i | −0.644494 | + | 0.372099i | ||||
\(887\) | 23.7065 | − | 41.0608i | 0.795985 | − | 1.37869i | −0.126227 | − | 0.992001i | \(-0.540287\pi\) |
0.922212 | − | 0.386685i | \(-0.126380\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.6660 | − | 4.78159i | −0.860811 | − | 0.160369i | ||||
\(890\) | − | 2.76074i | − | 0.0925403i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.18314 | + | 2.99249i | −0.173544 | + | 0.100196i | ||||
\(893\) | 14.6557 | − | 8.46149i | 0.490435 | − | 0.283153i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.0012i | 0.835698i | ||||||||
\(896\) | −1.72015 | + | 2.01025i | −0.0574661 | + | 0.0671577i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −31.3312 | − | 18.0891i | −1.04554 | − | 0.603641i | ||||
\(899\) | 0.292163 | + | 0.506041i | 0.00974418 | + | 0.0168774i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.10714 | − | 3.64968i | 0.0701991 | − | 0.121588i | ||||
\(902\) | 29.9013 | − | 5.69735i | 0.995606 | − | 0.189701i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.29122i | 0.275762i | ||||||||
\(905\) | −4.93405 | + | 8.54602i | −0.164013 | + | 0.284079i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.05727 | − | 5.29534i | −0.101515 | − | 0.175829i | 0.810794 | − | 0.585332i | \(-0.199036\pi\) |
−0.912309 | + | 0.409503i | \(0.865702\pi\) | |||||||
\(908\) | −2.52071 | + | 4.36600i | −0.0836528 | + | 0.144891i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.50509 | − | 3.00292i | 0.281941 | − | 0.0995459i | ||||
\(911\) | −45.2069 | −1.49777 | −0.748886 | − | 0.662699i | \(-0.769411\pi\) | ||||
−0.748886 | + | 0.662699i | \(0.769411\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.38007 | + | 8.09315i | −0.310435 | + | 0.267844i | ||||
\(914\) | −16.5111 | − | 28.5981i | −0.546140 | − | 0.945942i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21.2276i | 0.701381i | ||||||||
\(917\) | 19.9850 | + | 17.1009i | 0.659963 | + | 0.564723i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.5385 | − | 12.4352i | −0.710489 | − | 0.410201i | 0.100753 | − | 0.994911i | \(-0.467875\pi\) |
−0.811242 | + | 0.584711i | \(0.801208\pi\) | |||||||
\(920\) | 2.45007 | + | 4.24364i | 0.0807764 | + | 0.139909i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 31.8739 | + | 18.4024i | 1.04971 | + | 0.606051i | ||||
\(923\) | 26.2236 | 0.863160 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.07271 | −0.232549 | ||||||||
\(926\) | 18.2641 | + | 10.5448i | 0.600194 | + | 0.346522i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.06783 | + | 3.58158i | 0.0678797 | + | 0.117571i | ||||
\(929\) | 16.0270 | + | 9.25316i | 0.525827 | + | 0.303586i | 0.739316 | − | 0.673359i | \(-0.235149\pi\) |
−0.213488 | + | 0.976946i | \(0.568483\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.8604 | − | 20.8619i | 0.847539 | − | 0.683720i | ||||
\(932\) | 14.6978i | 0.481443i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.31457 | + | 4.00895i | 0.0757351 | + | 0.131177i | ||||
\(935\) | −3.27050 | − | 3.79056i | −0.106957 | − | 0.123964i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.2698 | 1.57691 | 0.788453 | − | 0.615094i | \(-0.210882\pi\) | ||||
0.788453 | + | 0.615094i | \(0.210882\pi\) | |||||||
\(938\) | −2.95383 | − | 0.550298i | −0.0964458 | − | 0.0179679i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.53909 | + | 4.39783i | −0.0828159 | + | 0.143441i | ||||
\(941\) | 8.14181 | + | 14.1020i | 0.265415 | + | 0.459713i | 0.967672 | − | 0.252211i | \(-0.0811576\pi\) |
−0.702257 | + | 0.711924i | \(0.747824\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.7871 | + | 27.3441i | −0.514100 | + | 0.890447i | ||||
\(944\) | − | 5.44483i | − | 0.177214i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.56215 | − | 18.6952i | −0.115816 | − | 0.607834i | ||||
\(947\) | 25.9080 | − | 44.8740i | 0.841897 | − | 1.45821i | −0.0463918 | − | 0.998923i | \(-0.514772\pi\) |
0.888289 | − | 0.459285i | \(-0.151894\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.31959 | + | 4.01765i | 0.0752971 | + | 0.130418i | ||||
\(950\) | −12.2139 | − | 7.05168i | −0.396270 | − | 0.228787i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.933520 | + | 2.64398i | 0.0302556 | + | 0.0856920i | ||||
\(953\) | 9.07156i | 0.293857i | 0.989147 | + | 0.146928i | \(0.0469387\pi\) | ||||
−0.989147 | + | 0.146928i | \(0.953061\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.3795 | − | 16.3849i | 0.918339 | − | 0.530203i | ||||
\(956\) | −18.2143 | + | 10.5160i | −0.589092 | + | 0.340112i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 30.5849i | − | 0.988153i | ||||||
\(959\) | −38.3458 | + | 13.5389i | −1.23825 | + | 0.437193i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.4900 | + | 26.8295i | −0.499678 | + | 0.865468i | ||||
\(962\) | 4.93405 | − | 2.84867i | 0.159080 | − | 0.0918450i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.15656 | + | 15.8596i | −0.294913 | + | 0.510804i | ||||
\(965\) | −23.3782 | −0.752570 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.46214i | 0.207809i | 0.994587 | + | 0.103904i | \(0.0331336\pi\) | ||||
−0.994587 | + | 0.103904i | \(0.966866\pi\) | |||||||
\(968\) | −10.8813 | − | 1.61157i | −0.349738 | − | 0.0517979i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23.4262 | + | 13.5251i | −0.752171 | + | 0.434266i | ||||
\(971\) | −23.2226 | − | 13.4076i | −0.745250 | − | 0.430270i | 0.0787253 | − | 0.996896i | \(-0.474915\pi\) |
−0.823975 | + | 0.566626i | \(0.808248\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.15520 | + | 6.20076i | −0.0370341 | + | 0.198787i | ||||
\(974\) | − | 31.0586i | − | 0.995183i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.58028 | − | 9.66532i | −0.178620 | − | 0.309379i | ||||
\(977\) | −10.9940 | − | 19.0422i | −0.351730 | − | 0.609215i | 0.634822 | − | 0.772658i | \(-0.281073\pi\) |
−0.986553 | + | 0.163443i | \(0.947740\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.31489 | + | 1.20323i | −0.201825 | + | 0.0384553i | ||||
\(980\) | −3.59035 | + | 9.30148i | −0.114689 | + | 0.297125i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16.3660 | − | 28.3467i | 0.522260 | − | 0.904581i | ||||
\(983\) | −28.9179 | + | 16.6957i | −0.922337 | + | 0.532512i | −0.884380 | − | 0.466768i | \(-0.845418\pi\) |
−0.0379571 | + | 0.999279i | \(0.512085\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.16145 | − | 10.6719i | 0.196320 | − | 0.340036i | ||||
\(986\) | 4.38293 | 0.139581 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.3608 | 0.361436 | ||||||||
\(989\) | 17.0964 | + | 9.87060i | 0.543633 | + | 0.313867i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.9097 | + | 36.2166i | 0.664218 | + | 1.15046i | 0.979497 | + | 0.201460i | \(0.0645687\pi\) |
−0.315279 | + | 0.948999i | \(0.602098\pi\) | |||||||
\(992\) | 0.0706450 | − | 0.122361i | 0.00224298 | − | 0.00388496i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −18.8465 | + | 22.0249i | −0.597773 | + | 0.698587i | ||||
\(995\) | 18.1915 | 0.576709 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.8703 | + | 30.9523i | 0.565959 | + | 0.980269i | 0.996960 | + | 0.0779180i | \(0.0248272\pi\) |
−0.431001 | + | 0.902351i | \(0.641839\pi\) | |||||||
\(998\) | −32.9147 | + | 19.0033i | −1.04190 | + | 0.601539i | ||||
\(999\) | 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 | 1386.2.bk.d.901.3 | yes | 32 | |
3.2 | odd | 2 | inner | 1386.2.bk.d.901.14 | yes | 32 | |
7.3 | odd | 6 | inner | 1386.2.bk.d.703.13 | yes | 32 | |
11.10 | odd | 2 | inner | 1386.2.bk.d.901.13 | yes | 32 | |
21.17 | even | 6 | inner | 1386.2.bk.d.703.4 | yes | 32 | |
33.32 | even | 2 | inner | 1386.2.bk.d.901.4 | yes | 32 | |
77.10 | even | 6 | inner | 1386.2.bk.d.703.3 | ✓ | 32 | |
231.164 | odd | 6 | inner | 1386.2.bk.d.703.14 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.bk.d.703.3 | ✓ | 32 | 77.10 | even | 6 | inner | |
1386.2.bk.d.703.4 | yes | 32 | 21.17 | even | 6 | inner | |
1386.2.bk.d.703.13 | yes | 32 | 7.3 | odd | 6 | inner | |
1386.2.bk.d.703.14 | yes | 32 | 231.164 | odd | 6 | inner | |
1386.2.bk.d.901.3 | yes | 32 | 1.1 | even | 1 | trivial | |
1386.2.bk.d.901.4 | yes | 32 | 33.32 | even | 2 | inner | |
1386.2.bk.d.901.13 | yes | 32 | 11.10 | odd | 2 | inner | |
1386.2.bk.d.901.14 | yes | 32 | 3.2 | odd | 2 | inner |