Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,2,Mod(299,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.299");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.h (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.39551206064\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.342102016.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 299.4 | ||
Root | \(-1.17915 - 0.780776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.299 |
Dual form | 300.2.h.b.299.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.780776 | + | 1.17915i | −0.552092 | + | 0.833783i | ||||
\(3\) | 0.848071 | + | 1.51022i | 0.489634 | + | 0.871928i | ||||
\(4\) | −0.780776 | − | 1.84130i | −0.390388 | − | 0.920650i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.44293 | − | 0.179147i | −0.997322 | − | 0.0731366i | ||||
\(7\) | 3.02045 | 1.14162 | 0.570811 | − | 0.821081i | \(-0.306629\pi\) | ||||
0.570811 | + | 0.821081i | \(0.306629\pi\) | |||||||
\(8\) | 2.78078 | + | 0.516994i | 0.983153 | + | 0.182785i | ||||
\(9\) | −1.56155 | + | 2.56155i | −0.520518 | + | 0.853851i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.32431 | 0.399294 | 0.199647 | − | 0.979868i | \(-0.436021\pi\) | ||||
0.199647 | + | 0.979868i | \(0.436021\pi\) | |||||||
\(12\) | 2.11862 | − | 2.74070i | 0.611594 | − | 0.791172i | ||||
\(13\) | 5.12311i | 1.42089i | 0.703751 | + | 0.710447i | \(0.251507\pi\) | ||||
−0.703751 | + | 0.710447i | \(0.748493\pi\) | |||||||
\(14\) | −2.35829 | + | 3.56155i | −0.630281 | + | 0.951865i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.78078 | + | 2.87529i | −0.695194 | + | 0.718822i | ||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | −1.80122 | − | 3.84130i | −0.424553 | − | 0.905403i | ||||
\(19\) | − | 1.32431i | − | 0.303817i | −0.988395 | − | 0.151908i | \(-0.951458\pi\) | ||
0.988395 | − | 0.151908i | \(-0.0485419\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.56155 | + | 4.56155i | 0.558977 | + | 0.995412i | ||||
\(22\) | −1.03399 | + | 1.56155i | −0.220447 | + | 0.332924i | ||||
\(23\) | − | 0.371834i | − | 0.0775328i | −0.999248 | − | 0.0387664i | \(-0.987657\pi\) | ||
0.999248 | − | 0.0387664i | \(-0.0123428\pi\) | |||||||
\(24\) | 1.57752 | + | 4.63804i | 0.322010 | + | 0.946736i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.04090 | − | 4.00000i | −1.18472 | − | 0.784465i | ||||
\(27\) | −5.19283 | − | 0.185917i | −0.999360 | − | 0.0357798i | ||||
\(28\) | −2.35829 | − | 5.56155i | −0.445676 | − | 1.05103i | ||||
\(29\) | − | 3.12311i | − | 0.579946i | −0.957035 | − | 0.289973i | \(-0.906354\pi\) | ||
0.957035 | − | 0.289973i | \(-0.0936464\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.71659i | − | 0.847124i | −0.905867 | − | 0.423562i | \(-0.860780\pi\) | ||
0.905867 | − | 0.423562i | \(-0.139220\pi\) | |||||||
\(32\) | −1.21922 | − | 5.52390i | −0.215530 | − | 0.976497i | ||||
\(33\) | 1.12311 | + | 2.00000i | 0.195508 | + | 0.348155i | ||||
\(34\) | 1.56155 | − | 2.35829i | 0.267804 | − | 0.404444i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.93581 | + | 0.875288i | 0.989302 | + | 0.145881i | ||||
\(37\) | 5.12311i | 0.842233i | 0.907006 | + | 0.421117i | \(0.138362\pi\) | ||||
−0.907006 | + | 0.421117i | \(0.861638\pi\) | |||||||
\(38\) | 1.56155 | + | 1.03399i | 0.253317 | + | 0.167735i | ||||
\(39\) | −7.73704 | + | 4.34475i | −1.23892 | + | 0.695718i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.12311i | − | 0.175400i | −0.996147 | − | 0.0876998i | \(-0.972048\pi\) | ||
0.996147 | − | 0.0876998i | \(-0.0279516\pi\) | |||||||
\(42\) | −7.37874 | − | 0.541105i | −1.13856 | − | 0.0834943i | ||||
\(43\) | 7.73704 | 1.17989 | 0.589944 | − | 0.807445i | \(-0.299150\pi\) | ||||
0.589944 | + | 0.807445i | \(0.299150\pi\) | |||||||
\(44\) | −1.03399 | − | 2.43845i | −0.155879 | − | 0.367610i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.438447 | + | 0.290319i | 0.0646455 | + | 0.0428052i | ||||
\(47\) | 3.02045i | 0.440578i | 0.975435 | + | 0.220289i | \(0.0707000\pi\) | ||||
−0.975435 | + | 0.220289i | \(0.929300\pi\) | |||||||
\(48\) | −6.70062 | − | 1.76115i | −0.967152 | − | 0.254200i | ||||
\(49\) | 2.12311 | 0.303301 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.69614 | − | 3.02045i | −0.237507 | − | 0.422947i | ||||
\(52\) | 9.43318 | − | 4.00000i | 1.30815 | − | 0.554700i | ||||
\(53\) | −12.2462 | −1.68215 | −0.841073 | − | 0.540921i | \(-0.818076\pi\) | ||||
−0.841073 | + | 0.540921i | \(0.818076\pi\) | |||||||
\(54\) | 4.27366 | − | 5.97795i | 0.581571 | − | 0.813495i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.39919 | + | 1.56155i | 1.12239 | + | 0.208671i | ||||
\(57\) | 2.00000 | − | 1.12311i | 0.264906 | − | 0.148759i | ||||
\(58\) | 3.68260 | + | 2.43845i | 0.483549 | + | 0.320184i | ||||
\(59\) | 14.1498 | 1.84214 | 0.921071 | − | 0.389394i | \(-0.127315\pi\) | ||||
0.921071 | + | 0.389394i | \(0.127315\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.12311 | 0.399873 | 0.199936 | − | 0.979809i | \(-0.435926\pi\) | ||||
0.199936 | + | 0.979809i | \(0.435926\pi\) | |||||||
\(62\) | 5.56155 | + | 3.68260i | 0.706318 | + | 0.467691i | ||||
\(63\) | −4.71659 | + | 7.73704i | −0.594234 | + | 0.974775i | ||||
\(64\) | 7.46543 | + | 2.87529i | 0.933179 | + | 0.359411i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.23519 | − | 0.237246i | −0.398224 | − | 0.0292030i | ||||
\(67\) | 4.34475 | 0.530796 | 0.265398 | − | 0.964139i | \(-0.414497\pi\) | ||||
0.265398 | + | 0.964139i | \(0.414497\pi\) | |||||||
\(68\) | 1.56155 | + | 3.68260i | 0.189366 | + | 0.446581i | ||||
\(69\) | 0.561553 | − | 0.315342i | 0.0676030 | − | 0.0379627i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.39228 | 0.402590 | 0.201295 | − | 0.979531i | \(-0.435485\pi\) | ||||
0.201295 | + | 0.979531i | \(0.435485\pi\) | |||||||
\(72\) | −5.66664 | + | 6.31579i | −0.667819 | + | 0.744323i | ||||
\(73\) | − | 8.24621i | − | 0.965146i | −0.875856 | − | 0.482573i | \(-0.839702\pi\) | ||
0.875856 | − | 0.482573i | \(-0.160298\pi\) | |||||||
\(74\) | −6.04090 | − | 4.00000i | −0.702240 | − | 0.464991i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.43845 | + | 1.03399i | −0.279709 | + | 0.118607i | ||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0.917790 | − | 12.5154i | 0.103919 | − | 1.41709i | ||||
\(79\) | − | 8.10887i | − | 0.912319i | −0.889898 | − | 0.456160i | \(-0.849225\pi\) | ||
0.889898 | − | 0.456160i | \(-0.150775\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.12311 | − | 8.00000i | −0.458123 | − | 0.888889i | ||||
\(82\) | 1.32431 | + | 0.876894i | 0.146245 | + | 0.0968368i | ||||
\(83\) | − | 15.1022i | − | 1.65769i | −0.559481 | − | 0.828843i | \(-0.689000\pi\) | ||
0.559481 | − | 0.828843i | \(-0.311000\pi\) | |||||||
\(84\) | 6.39919 | − | 8.27814i | 0.698209 | − | 0.903219i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.04090 | + | 9.12311i | −0.651407 | + | 0.983770i | ||||
\(87\) | 4.71659 | − | 2.64861i | 0.505671 | − | 0.283961i | ||||
\(88\) | 3.68260 | + | 0.684658i | 0.392567 | + | 0.0729848i | ||||
\(89\) | − | 10.2462i | − | 1.08610i | −0.839702 | − | 0.543048i | \(-0.817270\pi\) | ||
0.839702 | − | 0.543048i | \(-0.182730\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.4741i | 1.62212i | ||||||||
\(92\) | −0.684658 | + | 0.290319i | −0.0713806 | + | 0.0302679i | ||||
\(93\) | 7.12311 | − | 4.00000i | 0.738632 | − | 0.414781i | ||||
\(94\) | −3.56155 | − | 2.35829i | −0.367346 | − | 0.243240i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.30834 | − | 6.52596i | 0.745904 | − | 0.666053i | ||||
\(97\) | − | 6.00000i | − | 0.609208i | −0.952479 | − | 0.304604i | \(-0.901476\pi\) | ||
0.952479 | − | 0.304604i | \(-0.0985241\pi\) | |||||||
\(98\) | −1.65767 | + | 2.50345i | −0.167450 | + | 0.252887i | ||||
\(99\) | −2.06798 | + | 3.39228i | −0.207839 | + | 0.340937i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 0.876894i | − | 0.0872543i | −0.999048 | − | 0.0436271i | \(-0.986109\pi\) | ||
0.999048 | − | 0.0436271i | \(-0.0138914\pi\) | |||||||
\(102\) | 4.88586 | + | 0.358294i | 0.483772 | + | 0.0354764i | ||||
\(103\) | −9.80501 | −0.966117 | −0.483058 | − | 0.875588i | \(-0.660474\pi\) | ||||
−0.483058 | + | 0.875588i | \(0.660474\pi\) | |||||||
\(104\) | −2.64861 | + | 14.2462i | −0.259718 | + | 1.39696i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.56155 | − | 14.4401i | 0.928700 | − | 1.40255i | ||||
\(107\) | − | 3.02045i | − | 0.291998i | −0.989285 | − | 0.145999i | \(-0.953360\pi\) | ||
0.989285 | − | 0.145999i | \(-0.0466396\pi\) | |||||||
\(108\) | 3.71211 | + | 9.70671i | 0.357198 | + | 0.934029i | ||||
\(109\) | 0.876894 | 0.0839912 | 0.0419956 | − | 0.999118i | \(-0.486628\pi\) | ||||
0.0419956 | + | 0.999118i | \(0.486628\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.73704 | + | 4.34475i | −0.734367 | + | 0.412386i | ||||
\(112\) | −8.39919 | + | 8.68466i | −0.793649 | + | 0.820623i | ||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | −0.237246 | + | 3.23519i | −0.0222201 | + | 0.303003i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.75058 | + | 2.43845i | −0.533928 | + | 0.226404i | ||||
\(117\) | −13.1231 | − | 8.00000i | −1.21323 | − | 0.739600i | ||||
\(118\) | −11.0478 | + | 16.6847i | −1.01703 | + | 1.53595i | ||||
\(119\) | −6.04090 | −0.553768 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.24621 | −0.840565 | ||||||||
\(122\) | −2.43845 | + | 3.68260i | −0.220767 | + | 0.333407i | ||||
\(123\) | 1.69614 | − | 0.952473i | 0.152936 | − | 0.0858816i | ||||
\(124\) | −8.68466 | + | 3.68260i | −0.779905 | + | 0.330707i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.44050 | − | 11.6024i | −0.484679 | − | 1.03363i | ||||
\(127\) | −15.1022 | −1.34011 | −0.670054 | − | 0.742313i | \(-0.733729\pi\) | ||||
−0.670054 | + | 0.742313i | \(0.733729\pi\) | |||||||
\(128\) | −9.21922 | + | 6.55789i | −0.814872 | + | 0.579641i | ||||
\(129\) | 6.56155 | + | 11.6847i | 0.577713 | + | 1.02878i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.46026 | 0.477065 | 0.238532 | − | 0.971135i | \(-0.423334\pi\) | ||||
0.238532 | + | 0.971135i | \(0.423334\pi\) | |||||||
\(132\) | 2.80571 | − | 3.62953i | 0.244205 | − | 0.315910i | ||||
\(133\) | − | 4.00000i | − | 0.346844i | ||||||
\(134\) | −3.39228 | + | 5.12311i | −0.293049 | + | 0.442569i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.56155 | − | 1.03399i | −0.476899 | − | 0.0886637i | ||||
\(137\) | 8.24621 | 0.704521 | 0.352261 | − | 0.935902i | \(-0.385413\pi\) | ||||
0.352261 | + | 0.935902i | \(0.385413\pi\) | |||||||
\(138\) | −0.0666131 | + | 0.908365i | −0.00567048 | + | 0.0773251i | ||||
\(139\) | 17.5420i | 1.48790i | 0.668237 | + | 0.743949i | \(0.267049\pi\) | ||||
−0.668237 | + | 0.743949i | \(0.732951\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.56155 | + | 2.56155i | −0.384152 | + | 0.215722i | ||||
\(142\) | −2.64861 | + | 4.00000i | −0.222267 | + | 0.335673i | ||||
\(143\) | 6.78456i | 0.567354i | ||||||||
\(144\) | −3.02287 | − | 11.6130i | −0.251906 | − | 0.967752i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.72350 | + | 6.43845i | 0.804722 | + | 0.532850i | ||||
\(147\) | 1.80054 | + | 3.20636i | 0.148506 | + | 0.264457i | ||||
\(148\) | 9.43318 | − | 4.00000i | 0.775402 | − | 0.328798i | ||||
\(149\) | 14.0000i | 1.14692i | 0.819232 | + | 0.573462i | \(0.194400\pi\) | ||||
−0.819232 | + | 0.573462i | \(0.805600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 7.36520i | − | 0.599372i | −0.954038 | − | 0.299686i | \(-0.903118\pi\) | ||
0.954038 | − | 0.299686i | \(-0.0968819\pi\) | |||||||
\(152\) | 0.684658 | − | 3.68260i | 0.0555331 | − | 0.298698i | ||||
\(153\) | 3.12311 | − | 5.12311i | 0.252488 | − | 0.414179i | ||||
\(154\) | −3.12311 | + | 4.71659i | −0.251667 | + | 0.380074i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 14.0409 | + | 10.8539i | 1.12417 | + | 0.869010i | ||||
\(157\) | − | 3.36932i | − | 0.268901i | −0.990920 | − | 0.134450i | \(-0.957073\pi\) | ||
0.990920 | − | 0.134450i | \(-0.0429269\pi\) | |||||||
\(158\) | 9.56155 | + | 6.33122i | 0.760676 | + | 0.503684i | ||||
\(159\) | −10.3857 | − | 18.4945i | −0.823636 | − | 1.46671i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.12311i | − | 0.0885131i | ||||||
\(162\) | 12.6524 | + | 1.38446i | 0.994067 | + | 0.108774i | ||||
\(163\) | −15.6829 | −1.22838 | −0.614189 | − | 0.789159i | \(-0.710517\pi\) | ||||
−0.614189 | + | 0.789159i | \(0.710517\pi\) | |||||||
\(164\) | −2.06798 | + | 0.876894i | −0.161482 | + | 0.0684739i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.8078 | + | 11.7915i | 1.38215 | + | 0.915196i | ||||
\(167\) | − | 9.06134i | − | 0.701188i | −0.936528 | − | 0.350594i | \(-0.885980\pi\) | ||
0.936528 | − | 0.350594i | \(-0.114020\pi\) | |||||||
\(168\) | 4.76481 | + | 14.0090i | 0.367613 | + | 1.08082i | ||||
\(169\) | −13.2462 | −1.01894 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.39228 | + | 2.06798i | 0.259414 | + | 0.158142i | ||||
\(172\) | −6.04090 | − | 14.2462i | −0.460614 | − | 1.08626i | ||||
\(173\) | 2.00000 | 0.152057 | 0.0760286 | − | 0.997106i | \(-0.475776\pi\) | ||||
0.0760286 | + | 0.997106i | \(0.475776\pi\) | |||||||
\(174\) | −0.559496 | + | 7.62953i | −0.0424153 | + | 0.578393i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.68260 | + | 3.80776i | −0.277587 | + | 0.287021i | ||||
\(177\) | 12.0000 | + | 21.3693i | 0.901975 | + | 1.60622i | ||||
\(178\) | 12.0818 | + | 8.00000i | 0.905569 | + | 0.599625i | ||||
\(179\) | 10.0138 | 0.748468 | 0.374234 | − | 0.927334i | \(-0.377906\pi\) | ||||
0.374234 | + | 0.927334i | \(0.377906\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2462 | −0.910254 | −0.455127 | − | 0.890427i | \(-0.650406\pi\) | ||||
−0.455127 | + | 0.890427i | \(0.650406\pi\) | |||||||
\(182\) | −18.2462 | − | 12.0818i | −1.35250 | − | 0.895562i | ||||
\(183\) | 2.64861 | + | 4.71659i | 0.195791 | + | 0.348660i | ||||
\(184\) | 0.192236 | − | 1.03399i | 0.0141718 | − | 0.0762266i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.844964 | + | 11.5223i | −0.0619558 | + | 0.844856i | ||||
\(187\) | −2.64861 | −0.193686 | ||||||||
\(188\) | 5.56155 | − | 2.35829i | 0.405618 | − | 0.171996i | ||||
\(189\) | −15.6847 | − | 0.561553i | −1.14089 | − | 0.0408470i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.9073 | −1.80223 | −0.901113 | − | 0.433585i | \(-0.857248\pi\) | ||||
−0.901113 | + | 0.433585i | \(0.857248\pi\) | |||||||
\(192\) | 1.98889 | + | 13.7129i | 0.143535 | + | 0.989645i | ||||
\(193\) | 0.246211i | 0.0177227i | 0.999961 | + | 0.00886134i | \(0.00282069\pi\) | ||||
−0.999961 | + | 0.00886134i | \(0.997179\pi\) | |||||||
\(194\) | 7.07488 | + | 4.68466i | 0.507947 | + | 0.336339i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.65767 | − | 3.90928i | −0.118405 | − | 0.279234i | ||||
\(197\) | −4.24621 | −0.302530 | −0.151265 | − | 0.988493i | \(-0.548335\pi\) | ||||
−0.151265 | + | 0.988493i | \(0.548335\pi\) | |||||||
\(198\) | −2.38537 | − | 5.08706i | −0.169521 | − | 0.361522i | ||||
\(199\) | − | 5.46026i | − | 0.387067i | −0.981094 | − | 0.193534i | \(-0.938005\pi\) | ||
0.981094 | − | 0.193534i | \(-0.0619949\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.68466 | + | 6.56155i | 0.259896 | + | 0.462816i | ||||
\(202\) | 1.03399 | + | 0.684658i | 0.0727511 | + | 0.0481724i | ||||
\(203\) | − | 9.43318i | − | 0.662079i | ||||||
\(204\) | −4.23725 | + | 5.48140i | −0.296667 | + | 0.383775i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.65552 | − | 11.5616i | 0.533385 | − | 0.805532i | ||||
\(207\) | 0.952473 | + | 0.580639i | 0.0662014 | + | 0.0403572i | ||||
\(208\) | −14.7304 | − | 14.2462i | −1.02137 | − | 0.987797i | ||||
\(209\) | − | 1.75379i | − | 0.121312i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 16.7984i | − | 1.15645i | −0.815878 | − | 0.578224i | \(-0.803746\pi\) | ||
0.815878 | − | 0.578224i | \(-0.196254\pi\) | |||||||
\(212\) | 9.56155 | + | 22.5490i | 0.656690 | + | 1.54867i | ||||
\(213\) | 2.87689 | + | 5.12311i | 0.197122 | + | 0.351029i | ||||
\(214\) | 3.56155 | + | 2.35829i | 0.243463 | + | 0.161210i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −14.3440 | − | 3.20165i | −0.975983 | − | 0.217845i | ||||
\(217\) | − | 14.2462i | − | 0.967096i | ||||||
\(218\) | −0.684658 | + | 1.03399i | −0.0463709 | + | 0.0700305i | ||||
\(219\) | 12.4536 | − | 6.99337i | 0.841538 | − | 0.472568i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 10.2462i | − | 0.689235i | ||||||
\(222\) | 0.917790 | − | 12.5154i | 0.0615980 | − | 0.839978i | ||||
\(223\) | 8.31768 | 0.556993 | 0.278496 | − | 0.960437i | \(-0.410164\pi\) | ||||
0.278496 | + | 0.960437i | \(0.410164\pi\) | |||||||
\(224\) | −3.68260 | − | 16.6847i | −0.246054 | − | 1.11479i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.9309 | + | 16.5081i | −0.727111 | + | 1.09810i | ||||
\(227\) | 21.8868i | 1.45268i | 0.687337 | + | 0.726339i | \(0.258780\pi\) | ||||
−0.687337 | + | 0.726339i | \(0.741220\pi\) | |||||||
\(228\) | −3.62953 | − | 2.80571i | −0.240371 | − | 0.185812i | ||||
\(229\) | 16.2462 | 1.07358 | 0.536790 | − | 0.843716i | \(-0.319637\pi\) | ||||
0.536790 | + | 0.843716i | \(0.319637\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.39228 | + | 6.04090i | 0.223196 | + | 0.397462i | ||||
\(232\) | 1.61463 | − | 8.68466i | 0.106005 | − | 0.570176i | ||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | 19.6794 | − | 9.22786i | 1.28648 | − | 0.603244i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.0478 | − | 26.0540i | −0.719151 | − | 1.69597i | ||||
\(237\) | 12.2462 | − | 6.87689i | 0.795477 | − | 0.446702i | ||||
\(238\) | 4.71659 | − | 7.12311i | 0.305731 | − | 0.461722i | ||||
\(239\) | −17.3790 | −1.12416 | −0.562078 | − | 0.827084i | \(-0.689998\pi\) | ||||
−0.562078 | + | 0.827084i | \(0.689998\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.3693 | 0.861193 | 0.430597 | − | 0.902544i | \(-0.358303\pi\) | ||||
0.430597 | + | 0.902544i | \(0.358303\pi\) | |||||||
\(242\) | 7.21922 | − | 10.9026i | 0.464069 | − | 0.700849i | ||||
\(243\) | 8.58511 | − | 13.0114i | 0.550735 | − | 0.834680i | ||||
\(244\) | −2.43845 | − | 5.75058i | −0.156106 | − | 0.368143i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.201201 | + | 2.74367i | −0.0128281 | + | 0.174930i | ||||
\(247\) | 6.78456 | 0.431691 | ||||||||
\(248\) | 2.43845 | − | 13.1158i | 0.154842 | − | 0.832853i | ||||
\(249\) | 22.8078 | − | 12.8078i | 1.44538 | − | 0.811659i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7033 | 1.18054 | 0.590272 | − | 0.807205i | \(-0.299021\pi\) | ||||
0.590272 | + | 0.807205i | \(0.299021\pi\) | |||||||
\(252\) | 17.9288 | + | 2.64376i | 1.12941 | + | 0.166541i | ||||
\(253\) | − | 0.492423i | − | 0.0309583i | ||||||
\(254\) | 11.7915 | − | 17.8078i | 0.739863 | − | 1.11736i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.534565 | − | 15.9911i | −0.0334103 | − | 0.999442i | ||||
\(257\) | −30.4924 | −1.90207 | −0.951033 | − | 0.309091i | \(-0.899975\pi\) | ||||
−0.951033 | + | 0.309091i | \(0.899975\pi\) | |||||||
\(258\) | −18.9010 | − | 1.38607i | −1.17673 | − | 0.0862929i | ||||
\(259\) | 15.4741i | 0.961512i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | + | 4.87689i | 0.495188 | + | 0.301872i | ||||
\(262\) | −4.26324 | + | 6.43845i | −0.263384 | + | 0.397769i | ||||
\(263\) | 23.7917i | 1.46706i | 0.679656 | + | 0.733531i | \(0.262129\pi\) | ||||
−0.679656 | + | 0.733531i | \(0.737871\pi\) | |||||||
\(264\) | 2.08912 | + | 6.14219i | 0.128576 | + | 0.378026i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.71659 | + | 3.12311i | 0.289193 | + | 0.191490i | ||||
\(267\) | 15.4741 | − | 8.68951i | 0.946998 | − | 0.531789i | ||||
\(268\) | −3.39228 | − | 8.00000i | −0.207217 | − | 0.488678i | ||||
\(269\) | − | 14.0000i | − | 0.853595i | −0.904347 | − | 0.426798i | \(-0.859642\pi\) | ||
0.904347 | − | 0.426798i | \(-0.140358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.3110i | 0.930080i | 0.885290 | + | 0.465040i | \(0.153960\pi\) | ||||
−0.885290 | + | 0.465040i | \(0.846040\pi\) | |||||||
\(272\) | 5.56155 | − | 5.75058i | 0.337219 | − | 0.348680i | ||||
\(273\) | −23.3693 | + | 13.1231i | −1.41438 | + | 0.794246i | ||||
\(274\) | −6.43845 | + | 9.72350i | −0.388961 | + | 0.587418i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.01909 | − | 0.787776i | −0.0613418 | − | 0.0474186i | ||||
\(277\) | 23.3693i | 1.40413i | 0.712115 | + | 0.702063i | \(0.247738\pi\) | ||||
−0.712115 | + | 0.702063i | \(0.752262\pi\) | |||||||
\(278\) | −20.6847 | − | 13.6964i | −1.24058 | − | 0.821457i | ||||
\(279\) | 12.0818 | + | 7.36520i | 0.723318 | + | 0.440943i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.6155i | 0.812234i | 0.913821 | + | 0.406117i | \(0.133118\pi\) | ||||
−0.913821 | + | 0.406117i | \(0.866882\pi\) | |||||||
\(282\) | 0.541105 | − | 7.37874i | 0.0322223 | − | 0.439398i | ||||
\(283\) | 23.2111 | 1.37976 | 0.689879 | − | 0.723925i | \(-0.257664\pi\) | ||||
0.689879 | + | 0.723925i | \(0.257664\pi\) | |||||||
\(284\) | −2.64861 | − | 6.24621i | −0.157166 | − | 0.370644i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.00000 | − | 5.29723i | −0.473050 | − | 0.313232i | ||||
\(287\) | − | 3.39228i | − | 0.200240i | ||||||
\(288\) | 16.0536 | + | 5.50276i | 0.945970 | + | 0.324253i | ||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.06134 | − | 5.08842i | 0.531185 | − | 0.298289i | ||||
\(292\) | −15.1838 | + | 6.43845i | −0.888562 | + | 0.376782i | ||||
\(293\) | 2.49242 | 0.145609 | 0.0728044 | − | 0.997346i | \(-0.476805\pi\) | ||||
0.0728044 | + | 0.997346i | \(0.476805\pi\) | |||||||
\(294\) | −5.18660 | − | 0.380349i | −0.302489 | − | 0.0221824i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.64861 | + | 14.2462i | −0.153948 | + | 0.828044i | ||||
\(297\) | −6.87689 | − | 0.246211i | −0.399038 | − | 0.0142866i | ||||
\(298\) | −16.5081 | − | 10.9309i | −0.956286 | − | 0.633208i | ||||
\(299\) | 1.90495 | 0.110166 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.3693 | 1.34699 | ||||||||
\(302\) | 8.68466 | + | 5.75058i | 0.499746 | + | 0.330908i | ||||
\(303\) | 1.32431 | − | 0.743668i | 0.0760794 | − | 0.0427226i | ||||
\(304\) | 3.80776 | + | 3.68260i | 0.218390 | + | 0.211212i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.60245 | + | 7.68260i | 0.205938 | + | 0.439185i | ||||
\(307\) | −11.1293 | −0.635184 | −0.317592 | − | 0.948227i | \(-0.602874\pi\) | ||||
−0.317592 | + | 0.948227i | \(0.602874\pi\) | |||||||
\(308\) | −3.12311 | − | 7.36520i | −0.177955 | − | 0.419671i | ||||
\(309\) | −8.31534 | − | 14.8078i | −0.473043 | − | 0.842384i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.7713 | 1.17783 | 0.588916 | − | 0.808194i | \(-0.299555\pi\) | ||||
0.588916 | + | 0.808194i | \(0.299555\pi\) | |||||||
\(312\) | −23.7612 | + | 8.08179i | −1.34521 | + | 0.457541i | ||||
\(313\) | 22.4924i | 1.27135i | 0.771958 | + | 0.635673i | \(0.219278\pi\) | ||||
−0.771958 | + | 0.635673i | \(0.780722\pi\) | |||||||
\(314\) | 3.97292 | + | 2.63068i | 0.224205 | + | 0.148458i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.9309 | + | 6.33122i | −0.839927 | + | 0.356159i | ||||
\(317\) | 16.7386 | 0.940135 | 0.470068 | − | 0.882630i | \(-0.344230\pi\) | ||||
0.470068 | + | 0.882630i | \(0.344230\pi\) | |||||||
\(318\) | 29.9166 | + | 2.19387i | 1.67764 | + | 0.123026i | ||||
\(319\) | − | 4.13595i | − | 0.231569i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.56155 | − | 2.56155i | 0.254601 | − | 0.142972i | ||||
\(322\) | 1.32431 | + | 0.876894i | 0.0738007 | + | 0.0488674i | ||||
\(323\) | 2.64861i | 0.147373i | ||||||||
\(324\) | −11.5112 | + | 13.8381i | −0.639510 | + | 0.768783i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.2448 | − | 18.4924i | 0.678178 | − | 1.02420i | ||||
\(327\) | 0.743668 | + | 1.32431i | 0.0411249 | + | 0.0732343i | ||||
\(328\) | 0.580639 | − | 3.12311i | 0.0320604 | − | 0.172445i | ||||
\(329\) | 9.12311i | 0.502973i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 3.22925i | − | 0.177496i | −0.996054 | − | 0.0887479i | \(-0.971713\pi\) | ||
0.996054 | − | 0.0887479i | \(-0.0282865\pi\) | |||||||
\(332\) | −27.8078 | + | 11.7915i | −1.52615 | + | 0.647141i | ||||
\(333\) | −13.1231 | − | 8.00000i | −0.719142 | − | 0.438397i | ||||
\(334\) | 10.6847 | + | 7.07488i | 0.584638 | + | 0.387120i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −20.2389 | − | 5.31946i | −1.10412 | − | 0.290200i | ||||
\(337\) | − | 1.50758i | − | 0.0821230i | −0.999157 | − | 0.0410615i | \(-0.986926\pi\) | ||
0.999157 | − | 0.0410615i | \(-0.0130740\pi\) | |||||||
\(338\) | 10.3423 | − | 15.6192i | 0.562549 | − | 0.849574i | ||||
\(339\) | 11.8730 | + | 21.1431i | 0.644852 | + | 1.14834i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.24621i | − | 0.338251i | ||||||
\(342\) | −5.08706 | + | 2.38537i | −0.275077 | + | 0.128986i | ||||
\(343\) | −14.7304 | −0.795367 | ||||||||
\(344\) | 21.5150 | + | 4.00000i | 1.16001 | + | 0.215666i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.56155 | + | 2.35829i | −0.0839496 | + | 0.126783i | ||||
\(347\) | − | 22.6305i | − | 1.21487i | −0.794370 | − | 0.607434i | \(-0.792199\pi\) | ||
0.794370 | − | 0.607434i | \(-0.207801\pi\) | |||||||
\(348\) | −8.55950 | − | 6.61668i | −0.458837 | − | 0.354691i | ||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.952473 | − | 26.6034i | 0.0508392 | − | 1.41998i | ||||
\(352\) | −1.61463 | − | 7.31534i | −0.0860599 | − | 0.389909i | ||||
\(353\) | −20.2462 | −1.07760 | −0.538799 | − | 0.842435i | \(-0.681122\pi\) | ||||
−0.538799 | + | 0.842435i | \(0.681122\pi\) | |||||||
\(354\) | −34.5669 | − | 2.53489i | −1.83721 | − | 0.134728i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −18.8664 | + | 8.00000i | −0.999915 | + | 0.423999i | ||||
\(357\) | −5.12311 | − | 9.12311i | −0.271144 | − | 0.482846i | ||||
\(358\) | −7.81855 | + | 11.8078i | −0.413223 | + | 0.624060i | ||||
\(359\) | −21.5150 | −1.13552 | −0.567758 | − | 0.823195i | \(-0.692189\pi\) | ||||
−0.567758 | + | 0.823195i | \(0.692189\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.2462 | 0.907695 | ||||||||
\(362\) | 9.56155 | − | 14.4401i | 0.502544 | − | 0.758954i | ||||
\(363\) | −7.84144 | − | 13.9638i | −0.411569 | − | 0.732912i | ||||
\(364\) | 28.4924 | − | 12.0818i | 1.49341 | − | 0.633258i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.62953 | − | 0.559496i | −0.398802 | − | 0.0292453i | ||||
\(367\) | 10.9663 | 0.572436 | 0.286218 | − | 0.958165i | \(-0.407602\pi\) | ||||
0.286218 | + | 0.958165i | \(0.407602\pi\) | |||||||
\(368\) | 1.06913 | + | 1.03399i | 0.0557323 | + | 0.0539003i | ||||
\(369\) | 2.87689 | + | 1.75379i | 0.149765 | + | 0.0912986i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −36.9890 | −1.92038 | ||||||||
\(372\) | −12.9268 | − | 9.99267i | −0.670221 | − | 0.518096i | ||||
\(373\) | 9.12311i | 0.472377i | 0.971707 | + | 0.236188i | \(0.0758982\pi\) | ||||
−0.971707 | + | 0.236188i | \(0.924102\pi\) | |||||||
\(374\) | 2.06798 | − | 3.12311i | 0.106932 | − | 0.161492i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.56155 | + | 8.39919i | −0.0805309 | + | 0.433155i | ||||
\(377\) | 16.0000 | 0.824042 | ||||||||
\(378\) | 12.9084 | − | 18.0561i | 0.663935 | − | 0.928704i | ||||
\(379\) | − | 18.7033i | − | 0.960725i | −0.877070 | − | 0.480363i | \(-0.840505\pi\) | ||
0.877070 | − | 0.480363i | \(-0.159495\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.8078 | − | 22.8078i | −0.656162 | − | 1.16848i | ||||
\(382\) | 19.4470 | − | 29.3693i | 0.994995 | − | 1.50266i | ||||
\(383\) | 15.1022i | 0.771688i | 0.922564 | + | 0.385844i | \(0.126090\pi\) | ||||
−0.922564 | + | 0.385844i | \(0.873910\pi\) | |||||||
\(384\) | −17.7224 | − | 8.36154i | −0.904394 | − | 0.426698i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.290319 | − | 0.192236i | −0.0147769 | − | 0.00978455i | ||||
\(387\) | −12.0818 | + | 19.8188i | −0.614152 | + | 1.00745i | ||||
\(388\) | −11.0478 | + | 4.68466i | −0.560867 | + | 0.237827i | ||||
\(389\) | 20.7386i | 1.05149i | 0.850642 | + | 0.525745i | \(0.176213\pi\) | ||||
−0.850642 | + | 0.525745i | \(0.823787\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.743668i | 0.0376089i | ||||||||
\(392\) | 5.90388 | + | 1.09763i | 0.298191 | + | 0.0554388i | ||||
\(393\) | 4.63068 | + | 8.24621i | 0.233587 | + | 0.415966i | ||||
\(394\) | 3.31534 | − | 5.00691i | 0.167024 | − | 0.252244i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.86084 | + | 1.15915i | 0.395022 | + | 0.0582495i | ||||
\(397\) | 14.8769i | 0.746650i | 0.927701 | + | 0.373325i | \(0.121782\pi\) | ||||
−0.927701 | + | 0.373325i | \(0.878218\pi\) | |||||||
\(398\) | 6.43845 | + | 4.26324i | 0.322730 | + | 0.213697i | ||||
\(399\) | 6.04090 | − | 3.39228i | 0.302423 | − | 0.169827i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.0000i | 1.19850i | 0.800561 | + | 0.599251i | \(0.204535\pi\) | ||||
−0.800561 | + | 0.599251i | \(0.795465\pi\) | |||||||
\(402\) | −10.6139 | − | 0.778351i | −0.529375 | − | 0.0388206i | ||||
\(403\) | 24.1636 | 1.20367 | ||||||||
\(404\) | −1.61463 | + | 0.684658i | −0.0803307 | + | 0.0340630i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.1231 | + | 7.36520i | 0.552030 | + | 0.365529i | ||||
\(407\) | 6.78456i | 0.336298i | ||||||||
\(408\) | −3.15504 | − | 9.27608i | −0.156198 | − | 0.459235i | ||||
\(409\) | −25.3693 | −1.25443 | −0.627216 | − | 0.778845i | \(-0.715806\pi\) | ||||
−0.627216 | + | 0.778845i | \(0.715806\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.99337 | + | 12.4536i | 0.344957 | + | 0.614292i | ||||
\(412\) | 7.65552 | + | 18.0540i | 0.377161 | + | 0.889456i | ||||
\(413\) | 42.7386 | 2.10303 | ||||||||
\(414\) | −1.42833 | + | 0.669757i | −0.0701984 | + | 0.0329167i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 28.2995 | − | 6.24621i | 1.38750 | − | 0.306246i | ||||
\(417\) | −26.4924 | + | 14.8769i | −1.29734 | + | 0.728525i | ||||
\(418\) | 2.06798 | + | 1.36932i | 0.101148 | + | 0.0669755i | ||||
\(419\) | −7.36520 | −0.359814 | −0.179907 | − | 0.983684i | \(-0.557580\pi\) | ||||
−0.179907 | + | 0.983684i | \(0.557580\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.3693 | −1.23642 | −0.618212 | − | 0.786011i | \(-0.712143\pi\) | ||||
−0.618212 | + | 0.786011i | \(0.712143\pi\) | |||||||
\(422\) | 19.8078 | + | 13.1158i | 0.964227 | + | 0.638466i | ||||
\(423\) | −7.73704 | − | 4.71659i | −0.376188 | − | 0.229328i | ||||
\(424\) | −34.0540 | − | 6.33122i | −1.65381 | − | 0.307471i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.28711 | − | 0.607718i | −0.401512 | − | 0.0294440i | ||||
\(427\) | 9.43318 | 0.456503 | ||||||||
\(428\) | −5.56155 | + | 2.35829i | −0.268828 | + | 0.113992i | ||||
\(429\) | −10.2462 | + | 5.75379i | −0.494692 | + | 0.277796i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.6354 | −0.801297 | −0.400648 | − | 0.916232i | \(-0.631215\pi\) | ||||
−0.400648 | + | 0.916232i | \(0.631215\pi\) | |||||||
\(432\) | 14.9747 | − | 14.4139i | 0.720468 | − | 0.693488i | ||||
\(433\) | − | 18.0000i | − | 0.865025i | −0.901628 | − | 0.432512i | \(-0.857627\pi\) | ||
0.901628 | − | 0.432512i | \(-0.142373\pi\) | |||||||
\(434\) | 16.7984 | + | 11.1231i | 0.806348 | + | 0.533926i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.684658 | − | 1.61463i | −0.0327892 | − | 0.0773266i | ||||
\(437\) | −0.492423 | −0.0235558 | ||||||||
\(438\) | −1.47729 | + | 20.1449i | −0.0705875 | + | 0.962561i | ||||
\(439\) | − | 9.27015i | − | 0.442440i | −0.975224 | − | 0.221220i | \(-0.928996\pi\) | ||
0.975224 | − | 0.221220i | \(-0.0710039\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.31534 | + | 5.43845i | −0.157873 | + | 0.258974i | ||||
\(442\) | 12.0818 | + | 8.00000i | 0.574672 | + | 0.380521i | ||||
\(443\) | 16.5896i | 0.788195i | 0.919069 | + | 0.394097i | \(0.128943\pi\) | ||||
−0.919069 | + | 0.394097i | \(0.871057\pi\) | |||||||
\(444\) | 14.0409 | + | 10.8539i | 0.666351 | + | 0.515105i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.49424 | + | 9.80776i | −0.307511 | + | 0.464411i | ||||
\(447\) | −21.1431 | + | 11.8730i | −1.00004 | + | 0.561573i | ||||
\(448\) | 22.5490 | + | 8.68466i | 1.06534 | + | 0.410312i | ||||
\(449\) | 27.3693i | 1.29164i | 0.763491 | + | 0.645819i | \(0.223484\pi\) | ||||
−0.763491 | + | 0.645819i | \(0.776516\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.48734i | − | 0.0700359i | ||||||
\(452\) | −10.9309 | − | 25.7782i | −0.514145 | − | 1.21250i | ||||
\(453\) | 11.1231 | − | 6.24621i | 0.522609 | − | 0.293473i | ||||
\(454\) | −25.8078 | − | 17.0887i | −1.21122 | − | 0.802012i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.14219 | − | 2.08912i | 0.287634 | − | 0.0978319i | ||||
\(457\) | − | 10.0000i | − | 0.467780i | −0.972263 | − | 0.233890i | \(-0.924854\pi\) | ||
0.972263 | − | 0.233890i | \(-0.0751456\pi\) | |||||||
\(458\) | −12.6847 | + | 19.1567i | −0.592715 | + | 0.895133i | ||||
\(459\) | 10.3857 | + | 0.371834i | 0.484761 | + | 0.0173557i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.8617i | 1.94970i | 0.222872 | + | 0.974848i | \(0.428457\pi\) | ||||
−0.222872 | + | 0.974848i | \(0.571543\pi\) | |||||||
\(462\) | −9.77172 | − | 0.716589i | −0.454622 | − | 0.0333387i | ||||
\(463\) | 3.02045 | 0.140372 | 0.0701861 | − | 0.997534i | \(-0.477641\pi\) | ||||
0.0701861 | + | 0.997534i | \(0.477641\pi\) | |||||||
\(464\) | 8.97983 | + | 8.68466i | 0.416878 | + | 0.403175i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.80776 | − | 11.7915i | 0.361688 | − | 0.546229i | ||||
\(467\) | 2.27678i | 0.105357i | 0.998612 | + | 0.0526784i | \(0.0167758\pi\) | ||||
−0.998612 | + | 0.0526784i | \(0.983224\pi\) | |||||||
\(468\) | −4.48419 | + | 30.4098i | −0.207282 | + | 1.40569i | ||||
\(469\) | 13.1231 | 0.605969 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.08842 | − | 2.85742i | 0.234462 | − | 0.131663i | ||||
\(472\) | 39.3473 | + | 7.31534i | 1.81111 | + | 0.336716i | ||||
\(473\) | 10.2462 | 0.471121 | ||||||||
\(474\) | −1.45268 | + | 19.8094i | −0.0667239 | + | 0.909876i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.71659 | + | 11.1231i | 0.216184 | + | 0.509827i | ||||
\(477\) | 19.1231 | − | 31.3693i | 0.875587 | − | 1.43630i | ||||
\(478\) | 13.5691 | − | 20.4924i | 0.620637 | − | 0.937302i | ||||
\(479\) | −25.6509 | −1.17202 | −0.586010 | − | 0.810304i | \(-0.699302\pi\) | ||||
−0.586010 | + | 0.810304i | \(0.699302\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.2462 | −1.19672 | ||||||||
\(482\) | −10.4384 | + | 15.7644i | −0.475458 | + | 0.718048i | ||||
\(483\) | 1.69614 | − | 0.952473i | 0.0771771 | − | 0.0433390i | ||||
\(484\) | 7.21922 | + | 17.0251i | 0.328147 | + | 0.773866i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.63928 | + | 20.2821i | 0.391886 | + | 0.920014i | ||||
\(487\) | 25.2791 | 1.14550 | 0.572752 | − | 0.819728i | \(-0.305876\pi\) | ||||
0.572752 | + | 0.819728i | \(0.305876\pi\) | |||||||
\(488\) | 8.68466 | + | 1.61463i | 0.393136 | + | 0.0730907i | ||||
\(489\) | −13.3002 | − | 23.6847i | −0.601455 | − | 1.07106i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.9752 | 1.21737 | 0.608687 | − | 0.793410i | \(-0.291696\pi\) | ||||
0.608687 | + | 0.793410i | \(0.291696\pi\) | |||||||
\(492\) | −3.07810 | − | 2.37944i | −0.138771 | − | 0.107273i | ||||
\(493\) | 6.24621i | 0.281315i | ||||||||
\(494\) | −5.29723 | + | 8.00000i | −0.238334 | + | 0.359937i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.5616 | + | 13.1158i | 0.608932 | + | 0.588916i | ||||
\(497\) | 10.2462 | 0.459605 | ||||||||
\(498\) | −2.70552 | + | 36.8937i | −0.121237 | + | 1.65325i | ||||
\(499\) | − | 32.2725i | − | 1.44471i | −0.691521 | − | 0.722357i | \(-0.743059\pi\) | ||
0.691521 | − | 0.722357i | \(-0.256941\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.6847 | − | 7.68466i | 0.611385 | − | 0.343325i | ||||
\(502\) | −14.6031 | + | 22.0540i | −0.651769 | + | 0.984317i | ||||
\(503\) | − | 14.3586i | − | 0.640217i | −0.947381 | − | 0.320109i | \(-0.896281\pi\) | ||
0.947381 | − | 0.320109i | \(-0.103719\pi\) | |||||||
\(504\) | −17.1158 | + | 19.0765i | −0.762397 | + | 0.849736i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.580639 | + | 0.384472i | 0.0258125 | + | 0.0170919i | ||||
\(507\) | −11.2337 | − | 20.0047i | −0.498907 | − | 0.888442i | ||||
\(508\) | 11.7915 | + | 27.8078i | 0.523162 | + | 1.23377i | ||||
\(509\) | − | 11.1231i | − | 0.493023i | −0.969140 | − | 0.246511i | \(-0.920716\pi\) | ||
0.969140 | − | 0.246511i | \(-0.0792843\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 24.9073i | − | 1.10183i | ||||||
\(512\) | 19.2732 | + | 11.8551i | 0.851763 | + | 0.523927i | ||||
\(513\) | −0.246211 | + | 6.87689i | −0.0108705 | + | 0.303622i | ||||
\(514\) | 23.8078 | − | 35.9551i | 1.05012 | − | 1.58591i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 16.3919 | − | 21.2049i | 0.721612 | − | 0.933494i | ||||
\(517\) | 4.00000i | 0.175920i | ||||||||
\(518\) | −18.2462 | − | 12.0818i | −0.801692 | − | 0.530843i | ||||
\(519\) | 1.69614 | + | 3.02045i | 0.0744523 | + | 0.132583i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 38.2462i | − | 1.67560i | −0.545980 | − | 0.837798i | \(-0.683842\pi\) | ||
0.545980 | − | 0.837798i | \(-0.316158\pi\) | |||||||
\(522\) | −11.9968 | + | 5.62541i | −0.525085 | + | 0.246218i | ||||
\(523\) | −35.2929 | −1.54325 | −0.771625 | − | 0.636077i | \(-0.780556\pi\) | ||||
−0.771625 | + | 0.636077i | \(0.780556\pi\) | |||||||
\(524\) | −4.26324 | − | 10.0540i | −0.186241 | − | 0.439210i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.0540 | − | 18.5760i | −1.22321 | − | 0.809954i | ||||
\(527\) | 9.43318i | 0.410916i | ||||||||
\(528\) | −8.87368 | − | 2.33230i | −0.386177 | − | 0.101500i | ||||
\(529\) | 22.8617 | 0.993989 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.0956 | + | 36.2454i | −0.958868 | + | 1.57292i | ||||
\(532\) | −7.36520 | + | 3.12311i | −0.319322 | + | 0.135404i | ||||
\(533\) | 5.75379 | 0.249224 | ||||||||
\(534\) | −1.83558 | + | 25.0308i | −0.0794333 | + | 1.08319i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.0818 | + | 2.24621i | 0.521854 | + | 0.0970215i | ||||
\(537\) | 8.49242 | + | 15.1231i | 0.366475 | + | 0.652610i | ||||
\(538\) | 16.5081 | + | 10.9309i | 0.711713 | + | 0.471263i | ||||
\(539\) | 2.81164 | 0.121106 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.9848 | −1.16017 | −0.580085 | − | 0.814556i | \(-0.696980\pi\) | ||||
−0.580085 | + | 0.814556i | \(0.696980\pi\) | |||||||
\(542\) | −18.0540 | − | 11.9545i | −0.775485 | − | 0.513490i | ||||
\(543\) | −10.3857 | − | 18.4945i | −0.445691 | − | 0.793676i | ||||
\(544\) | 2.43845 | + | 11.0478i | 0.104548 | + | 0.473671i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.77214 | − | 37.8021i | 0.118637 | − | 1.61778i | ||||
\(547\) | −5.83209 | −0.249362 | −0.124681 | − | 0.992197i | \(-0.539791\pi\) | ||||
−0.124681 | + | 0.992197i | \(0.539791\pi\) | |||||||
\(548\) | −6.43845 | − | 15.1838i | −0.275037 | − | 0.648618i | ||||
\(549\) | −4.87689 | + | 8.00000i | −0.208141 | + | 0.341432i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.13595 | −0.176197 | ||||||||
\(552\) | 1.72458 | − | 0.586575i | 0.0734031 | − | 0.0249663i | ||||
\(553\) | − | 24.4924i | − | 1.04152i | ||||||
\(554\) | −27.5559 | − | 18.2462i | −1.17074 | − | 0.775207i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 32.3002 | − | 13.6964i | 1.36983 | − | 0.580858i | ||||
\(557\) | −36.2462 | −1.53580 | −0.767901 | − | 0.640569i | \(-0.778699\pi\) | ||||
−0.767901 | + | 0.640569i | \(0.778699\pi\) | |||||||
\(558\) | −18.1178 | + | 8.49563i | −0.766989 | + | 0.359649i | ||||
\(559\) | 39.6377i | 1.67649i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.24621 | − | 4.00000i | −0.0948351 | − | 0.168880i | ||||
\(562\) | −16.0547 | − | 10.6307i | −0.677227 | − | 0.448428i | ||||
\(563\) | 7.90007i | 0.332948i | 0.986046 | + | 0.166474i | \(0.0532382\pi\) | ||||
−0.986046 | + | 0.166474i | \(0.946762\pi\) | |||||||
\(564\) | 8.27814 | + | 6.39919i | 0.348573 | + | 0.269455i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −18.1227 | + | 27.3693i | −0.761753 | + | 1.15042i | ||||
\(567\) | −12.4536 | − | 24.1636i | −0.523003 | − | 1.01478i | ||||
\(568\) | 9.43318 | + | 1.75379i | 0.395807 | + | 0.0735873i | ||||
\(569\) | 13.1231i | 0.550149i | 0.961423 | + | 0.275075i | \(0.0887026\pi\) | ||||
−0.961423 | + | 0.275075i | \(0.911297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.0161i | 1.38168i | 0.723007 | + | 0.690841i | \(0.242759\pi\) | ||||
−0.723007 | + | 0.690841i | \(0.757241\pi\) | |||||||
\(572\) | 12.4924 | − | 5.29723i | 0.522334 | − | 0.221488i | ||||
\(573\) | −21.1231 | − | 37.6155i | −0.882430 | − | 1.57141i | ||||
\(574\) | 4.00000 | + | 2.64861i | 0.166957 | + | 0.110551i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −19.0229 | + | 14.6332i | −0.792620 | + | 0.609716i | ||||
\(577\) | − | 32.2462i | − | 1.34243i | −0.741264 | − | 0.671214i | \(-0.765773\pi\) | ||
0.741264 | − | 0.671214i | \(-0.234227\pi\) | |||||||
\(578\) | 10.1501 | − | 15.3289i | 0.422188 | − | 0.637599i | ||||
\(579\) | −0.371834 | + | 0.208805i | −0.0154529 | + | 0.00867762i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 45.6155i | − | 1.89245i | ||||||
\(582\) | −1.07488 | + | 14.6576i | −0.0445554 | + | 0.607576i | ||||
\(583\) | −16.2177 | −0.671670 | ||||||||
\(584\) | 4.26324 | − | 22.9309i | 0.176414 | − | 0.948886i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.94602 | + | 2.93893i | −0.0803895 | + | 0.121406i | ||||
\(587\) | 1.85917i | 0.0767362i | 0.999264 | + | 0.0383681i | \(0.0122159\pi\) | ||||
−0.999264 | + | 0.0383681i | \(0.987784\pi\) | |||||||
\(588\) | 4.49806 | − | 5.81880i | 0.185497 | − | 0.239963i | ||||
\(589\) | −6.24621 | −0.257371 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.60109 | − | 6.41273i | −0.148129 | − | 0.263784i | ||||
\(592\) | −14.7304 | − | 14.2462i | −0.605416 | − | 0.585516i | ||||
\(593\) | 8.24621 | 0.338631 | 0.169316 | − | 0.985562i | \(-0.445844\pi\) | ||||
0.169316 | + | 0.985562i | \(0.445844\pi\) | |||||||
\(594\) | 5.65964 | − | 7.91664i | 0.232218 | − | 0.324823i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 25.7782 | − | 10.9309i | 1.05592 | − | 0.447746i | ||||
\(597\) | 8.24621 | − | 4.63068i | 0.337495 | − | 0.189521i | ||||
\(598\) | −1.48734 | + | 2.24621i | −0.0608217 | + | 0.0918544i | ||||
\(599\) | 44.1912 | 1.80560 | 0.902802 | − | 0.430056i | \(-0.141506\pi\) | ||||
0.902802 | + | 0.430056i | \(0.141506\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.1231 | 0.943211 | 0.471606 | − | 0.881810i | \(-0.343675\pi\) | ||||
0.471606 | + | 0.881810i | \(0.343675\pi\) | |||||||
\(602\) | −18.2462 | + | 27.5559i | −0.743660 | + | 1.12309i | ||||
\(603\) | −6.78456 | + | 11.1293i | −0.276289 | + | 0.453221i | ||||
\(604\) | −13.5616 | + | 5.75058i | −0.551812 | + | 0.233988i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.157093 | + | 2.14219i | −0.00638148 | + | 0.0870206i | ||||
\(607\) | −4.50778 | −0.182965 | −0.0914827 | − | 0.995807i | \(-0.529161\pi\) | ||||
−0.0914827 | + | 0.995807i | \(0.529161\pi\) | |||||||
\(608\) | −7.31534 | + | 1.61463i | −0.296676 | + | 0.0654817i | ||||
\(609\) | 14.2462 | − | 8.00000i | 0.577286 | − | 0.324176i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.4741 | −0.626014 | ||||||||
\(612\) | −11.8716 | − | 1.75058i | −0.479882 | − | 0.0707629i | ||||
\(613\) | − | 9.12311i | − | 0.368479i | −0.982881 | − | 0.184239i | \(-0.941018\pi\) | ||
0.982881 | − | 0.184239i | \(-0.0589822\pi\) | |||||||
\(614\) | 8.68951 | − | 13.1231i | 0.350680 | − | 0.529605i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.1231 | + | 2.06798i | 0.448163 | + | 0.0833211i | ||||
\(617\) | 14.0000 | 0.563619 | 0.281809 | − | 0.959470i | \(-0.409065\pi\) | ||||
0.281809 | + | 0.959470i | \(0.409065\pi\) | |||||||
\(618\) | 23.9530 | + | 1.75654i | 0.963529 | + | 0.0706584i | ||||
\(619\) | 28.1365i | 1.13090i | 0.824782 | + | 0.565451i | \(0.191298\pi\) | ||||
−0.824782 | + | 0.565451i | \(0.808702\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.0691303 | + | 1.93087i | −0.00277410 | + | 0.0774831i | ||||
\(622\) | −16.2177 | + | 24.4924i | −0.650272 | + | 0.982057i | ||||
\(623\) | − | 30.9481i | − | 1.23991i | ||||||
\(624\) | 9.02255 | − | 34.3280i | 0.361191 | − | 1.37422i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −26.5219 | − | 17.5616i | −1.06003 | − | 0.701901i | ||||
\(627\) | 2.64861 | − | 1.48734i | 0.105775 | − | 0.0593985i | ||||
\(628\) | −6.20393 | + | 2.63068i | −0.247564 | + | 0.104976i | ||||
\(629\) | − | 10.2462i | − | 0.408543i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.8007i | 1.58444i | 0.610235 | + | 0.792220i | \(0.291075\pi\) | ||||
−0.610235 | + | 0.792220i | \(0.708925\pi\) | |||||||
\(632\) | 4.19224 | − | 22.5490i | 0.166758 | − | 0.896949i | ||||
\(633\) | 25.3693 | − | 14.2462i | 1.00834 | − | 0.566236i | ||||
\(634\) | −13.0691 | + | 19.7373i | −0.519041 | + | 0.783869i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −25.9451 | + | 33.5632i | −1.02879 | + | 1.33087i | ||||
\(637\) | 10.8769i | 0.430958i | ||||||||
\(638\) | 4.87689 | + | 3.22925i | 0.193078 | + | 0.127847i | ||||
\(639\) | −5.29723 | + | 8.68951i | −0.209555 | + | 0.343752i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 6.38447i | − | 0.252171i | −0.992019 | − | 0.126086i | \(-0.959759\pi\) | ||
0.992019 | − | 0.126086i | \(-0.0402414\pi\) | |||||||
\(642\) | −0.541105 | + | 7.37874i | −0.0213557 | + | 0.291216i | ||||
\(643\) | 3.60109 | 0.142013 | 0.0710065 | − | 0.997476i | \(-0.477379\pi\) | ||||
0.0710065 | + | 0.997476i | \(0.477379\pi\) | |||||||
\(644\) | −2.06798 | + | 0.876894i | −0.0814896 | + | 0.0345545i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.12311 | − | 2.06798i | −0.122877 | − | 0.0813634i | ||||
\(647\) | − | 36.6172i | − | 1.43957i | −0.694197 | − | 0.719786i | \(-0.744240\pi\) | ||
0.694197 | − | 0.719786i | \(-0.255760\pi\) | |||||||
\(648\) | −7.32948 | − | 24.3778i | −0.287929 | − | 0.957652i | ||||
\(649\) | 18.7386 | 0.735556 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.5150 | − | 12.0818i | 0.843238 | − | 0.473523i | ||||
\(652\) | 12.2448 | + | 28.8769i | 0.479544 | + | 1.13091i | ||||
\(653\) | −38.9848 | −1.52559 | −0.762797 | − | 0.646638i | \(-0.776175\pi\) | ||||
−0.762797 | + | 0.646638i | \(0.776175\pi\) | |||||||
\(654\) | −2.14219 | − | 0.157093i | −0.0837663 | − | 0.00614283i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.22925 | + | 3.12311i | 0.126081 | + | 0.121937i | ||||
\(657\) | 21.1231 | + | 12.8769i | 0.824091 | + | 0.502375i | ||||
\(658\) | −10.7575 | − | 7.12311i | −0.419370 | − | 0.277688i | ||||
\(659\) | −24.7442 | −0.963898 | −0.481949 | − | 0.876199i | \(-0.660071\pi\) | ||||
−0.481949 | + | 0.876199i | \(0.660071\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.1080 | 1.09327 | 0.546636 | − | 0.837370i | \(-0.315908\pi\) | ||||
0.546636 | + | 0.837370i | \(0.315908\pi\) | |||||||
\(662\) | 3.80776 | + | 2.52132i | 0.147993 | + | 0.0979940i | ||||
\(663\) | 15.4741 | − | 8.68951i | 0.600963 | − | 0.337473i | ||||
\(664\) | 7.80776 | − | 41.9960i | 0.303000 | − | 1.62976i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 19.6794 | − | 9.22786i | 0.762561 | − | 0.357572i | ||||
\(667\) | −1.16128 | −0.0449648 | ||||||||
\(668\) | −16.6847 | + | 7.07488i | −0.645549 | + | 0.273735i | ||||
\(669\) | 7.05398 | + | 12.5616i | 0.272722 | + | 0.485658i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.13595 | 0.159667 | ||||||||
\(672\) | 22.0745 | − | 19.7113i | 0.851541 | − | 0.760381i | ||||
\(673\) | − | 22.4924i | − | 0.867019i | −0.901149 | − | 0.433510i | \(-0.857275\pi\) | ||
0.901149 | − | 0.433510i | \(-0.142725\pi\) | |||||||
\(674\) | 1.77766 | + | 1.17708i | 0.0684727 | + | 0.0453395i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.3423 | + | 24.3903i | 0.397782 | + | 0.938087i | ||||
\(677\) | −1.50758 | −0.0579409 | −0.0289705 | − | 0.999580i | \(-0.509223\pi\) | ||||
−0.0289705 | + | 0.999580i | \(0.509223\pi\) | |||||||
\(678\) | −34.2010 | − | 2.50806i | −1.31348 | − | 0.0963215i | ||||
\(679\) | − | 18.1227i | − | 0.695485i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.0540 | + | 18.5616i | −1.26663 | + | 0.711280i | ||||
\(682\) | 7.36520 | + | 4.87689i | 0.282028 | + | 0.186746i | ||||
\(683\) | − | 7.90007i | − | 0.302288i | −0.988512 | − | 0.151144i | \(-0.951704\pi\) | ||
0.988512 | − | 0.151144i | \(-0.0482957\pi\) | |||||||
\(684\) | 1.15915 | − | 7.86084i | 0.0443212 | − | 0.300567i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 11.5012 | − | 17.3693i | 0.439116 | − | 0.663164i | ||||
\(687\) | 13.7779 | + | 24.5354i | 0.525661 | + | 0.936085i | ||||
\(688\) | −21.5150 | + | 22.2462i | −0.820251 | + | 0.848129i | ||||
\(689\) | − | 62.7386i | − | 2.39015i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 18.2857i | − | 0.695621i | −0.937565 | − | 0.347811i | \(-0.886925\pi\) | ||
0.937565 | − | 0.347811i | \(-0.113075\pi\) | |||||||
\(692\) | −1.56155 | − | 3.68260i | −0.0593613 | − | 0.139991i | ||||
\(693\) | −6.24621 | + | 10.2462i | −0.237274 | + | 0.389221i | ||||
\(694\) | 26.6847 | + | 17.6693i | 1.01294 | + | 0.670719i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 14.4851 | − | 4.92676i | 0.549056 | − | 0.186748i | ||||
\(697\) | 2.24621i | 0.0850813i | ||||||||
\(698\) | −10.9309 | + | 16.5081i | −0.413740 | + | 0.624839i | ||||
\(699\) | −8.48071 | − | 15.1022i | −0.320770 | − | 0.571219i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.5076i | 0.661252i | 0.943762 | + | 0.330626i | \(0.107260\pi\) | ||||
−0.943762 | + | 0.330626i | \(0.892740\pi\) | |||||||
\(702\) | 30.6256 | + | 21.8944i | 1.15589 | + | 0.826351i | ||||
\(703\) | 6.78456 | 0.255885 | ||||||||
\(704\) | 9.88653 | + | 3.80776i | 0.372612 | + | 0.143511i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.8078 | − | 23.8733i | 0.594933 | − | 0.898482i | ||||
\(707\) | − | 2.64861i | − | 0.0996114i | ||||||
\(708\) | 29.9780 | − | 38.7803i | 1.12664 | − | 1.45745i | ||||
\(709\) | −6.49242 | −0.243828 | −0.121914 | − | 0.992541i | \(-0.538903\pi\) | ||||
−0.121914 | + | 0.992541i | \(0.538903\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.7713 | + | 12.6624i | 0.778985 | + | 0.474878i | ||||
\(712\) | 5.29723 | − | 28.4924i | 0.198522 | − | 1.06780i | ||||
\(713\) | −1.75379 | −0.0656799 | ||||||||
\(714\) | 14.7575 | + | 1.08221i | 0.552285 | + | 0.0405007i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.81855 | − | 18.4384i | −0.292193 | − | 0.689077i | ||||
\(717\) | −14.7386 | − | 26.2462i | −0.550424 | − | 0.980183i | ||||
\(718\) | 16.7984 | − | 25.3693i | 0.626910 | − | 0.946774i | ||||
\(719\) | 30.9481 | 1.15417 | 0.577086 | − | 0.816684i | \(-0.304190\pi\) | ||||
0.577086 | + | 0.816684i | \(0.304190\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.6155 | −1.10294 | ||||||||
\(722\) | −13.4654 | + | 20.3358i | −0.501132 | + | 0.756821i | ||||
\(723\) | 11.3381 | + | 20.1907i | 0.421669 | + | 0.750899i | ||||
\(724\) | 9.56155 | + | 22.5490i | 0.355352 | + | 0.838025i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 22.5878 | + | 1.65643i | 0.838314 | + | 0.0614760i | ||||
\(727\) | −10.9663 | −0.406717 | −0.203359 | − | 0.979104i | \(-0.565186\pi\) | ||||
−0.203359 | + | 0.979104i | \(0.565186\pi\) | |||||||
\(728\) | −8.00000 | + | 43.0299i | −0.296500 | + | 1.59480i | ||||
\(729\) | 26.9309 | + | 1.93087i | 0.997440 | + | 0.0715137i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.4741 | −0.572329 | ||||||||
\(732\) | 6.61668 | − | 8.55950i | 0.244560 | − | 0.316368i | ||||
\(733\) | 26.8769i | 0.992721i | 0.868117 | + | 0.496360i | \(0.165331\pi\) | ||||
−0.868117 | + | 0.496360i | \(0.834669\pi\) | |||||||
\(734\) | −8.56222 | + | 12.9309i | −0.316037 | + | 0.477287i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.05398 | + | 0.453349i | −0.0757105 | + | 0.0167107i | ||||
\(737\) | 5.75379 | 0.211944 | ||||||||
\(738\) | −4.31419 | + | 2.02297i | −0.158807 | + | 0.0744664i | ||||
\(739\) | − | 26.9752i | − | 0.992300i | −0.868237 | − | 0.496150i | \(-0.834747\pi\) | ||
0.868237 | − | 0.496150i | \(-0.165253\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.75379 | + | 10.2462i | 0.211371 | + | 0.376404i | ||||
\(742\) | 28.8802 | − | 43.6155i | 1.06022 | − | 1.60118i | ||||
\(743\) | 9.80501i | 0.359711i | 0.983693 | + | 0.179856i | \(0.0575630\pi\) | ||||
−0.983693 | + | 0.179856i | \(0.942437\pi\) | |||||||
\(744\) | 21.8757 | − | 7.44050i | 0.802004 | − | 0.272782i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10.7575 | − | 7.12311i | −0.393860 | − | 0.260795i | ||||
\(747\) | 38.6852 | + | 23.5829i | 1.41542 | + | 0.862855i | ||||
\(748\) | 2.06798 | + | 4.87689i | 0.0756127 | + | 0.178317i | ||||
\(749\) | − | 9.12311i | − | 0.333351i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 11.5012i | − | 0.419683i | −0.977735 | − | 0.209842i | \(-0.932705\pi\) | ||
0.977735 | − | 0.209842i | \(-0.0672948\pi\) | |||||||
\(752\) | −8.68466 | − | 8.39919i | −0.316697 | − | 0.306287i | ||||
\(753\) | 15.8617 | + | 28.2462i | 0.578034 | + | 1.02935i | ||||
\(754\) | −12.4924 | + | 18.8664i | −0.454947 | + | 0.687072i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 11.2122 | + | 29.3186i | 0.407785 | + | 1.06631i | ||||
\(757\) | 10.8769i | 0.395327i | 0.980270 | + | 0.197664i | \(0.0633354\pi\) | ||||
−0.980270 | + | 0.197664i | \(0.936665\pi\) | |||||||
\(758\) | 22.0540 | + | 14.6031i | 0.801036 | + | 0.530409i | ||||
\(759\) | 0.743668 | − | 0.417609i | 0.0269934 | − | 0.0151582i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 31.2311i | − | 1.13212i | −0.824362 | − | 0.566062i | \(-0.808466\pi\) | ||
0.824362 | − | 0.566062i | \(-0.191534\pi\) | |||||||
\(762\) | 36.8937 | + | 2.70552i | 1.33652 | + | 0.0980108i | ||||
\(763\) | 2.64861 | 0.0958863 | ||||||||
\(764\) | 19.4470 | + | 45.8617i | 0.703568 | + | 1.65922i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.8078 | − | 11.7915i | −0.643421 | − | 0.426043i | ||||
\(767\) | 72.4908i | 2.61749i | ||||||||
\(768\) | 23.6967 | − | 14.3689i | 0.855083 | − | 0.518492i | ||||
\(769\) | −38.9848 | −1.40583 | −0.702915 | − | 0.711274i | \(-0.748118\pi\) | ||||
−0.702915 | + | 0.711274i | \(0.748118\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.8597 | − | 46.0504i | −0.931315 | − | 1.65846i | ||||
\(772\) | 0.453349 | − | 0.192236i | 0.0163164 | − | 0.00691872i | ||||
\(773\) | −0.246211 | −0.00885560 | −0.00442780 | − | 0.999990i | \(-0.501409\pi\) | ||||
−0.00442780 | + | 0.999990i | \(0.501409\pi\) | |||||||
\(774\) | −13.9361 | − | 29.7203i | −0.500924 | − | 1.06827i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.10196 | − | 16.6847i | 0.111354 | − | 0.598944i | ||||
\(777\) | −23.3693 | + | 13.1231i | −0.838370 | + | 0.470789i | ||||
\(778\) | −24.4539 | − | 16.1922i | −0.876715 | − | 0.580520i | ||||
\(779\) | −1.48734 | −0.0532894 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.49242 | 0.160752 | ||||||||
\(782\) | −0.876894 | − | 0.580639i | −0.0313577 | − | 0.0207636i | ||||
\(783\) | −0.580639 | + | 16.2177i | −0.0207503 | + | 0.579575i | ||||
\(784\) | −5.90388 | + | 6.10454i | −0.210853 | + | 0.218019i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −13.3390 | − | 0.978190i | −0.475787 | − | 0.0348909i | ||||
\(787\) | −42.0775 | −1.49990 | −0.749950 | − | 0.661495i | \(-0.769922\pi\) | ||||
−0.749950 | + | 0.661495i | \(0.769922\pi\) | |||||||
\(788\) | 3.31534 | + | 7.81855i | 0.118104 | + | 0.278524i | ||||
\(789\) | −35.9309 | + | 20.1771i | −1.27917 | + | 0.718323i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42.2863 | 1.50353 | ||||||||
\(792\) | −7.50437 | + | 8.36405i | −0.266656 | + | 0.297203i | ||||
\(793\) | 16.0000i | 0.568177i | ||||||||
\(794\) | −17.5420 | − | 11.6155i | −0.622544 | − | 0.412220i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.0540 | + | 4.26324i | −0.356354 | + | 0.151107i | ||||
\(797\) | −12.7386 | −0.451226 | −0.225613 | − | 0.974217i | \(-0.572438\pi\) | ||||
−0.225613 | + | 0.974217i | \(0.572438\pi\) | |||||||
\(798\) | −0.716589 | + | 9.77172i | −0.0253670 | + | 0.345915i | ||||
\(799\) | − | 6.04090i | − | 0.213712i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 26.2462 | + | 16.0000i | 0.927364 | + | 0.565332i | ||||
\(802\) | −28.2995 | − | 18.7386i | −0.999291 | − | 0.661684i | ||||
\(803\) | − | 10.9205i | − | 0.385377i | ||||||
\(804\) | 9.20490 | − | 11.9077i | 0.324632 | − | 0.419951i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −18.8664 | + | 28.4924i | −0.664539 | + | 1.00360i | ||||
\(807\) | 21.1431 | − | 11.8730i | 0.744274 | − | 0.417949i | ||||
\(808\) | 0.453349 | − | 2.43845i | 0.0159488 | − | 0.0857843i | ||||
\(809\) | 29.7538i | 1.04609i | 0.852306 | + | 0.523044i | \(0.175204\pi\) | ||||
−0.852306 | + | 0.523044i | \(0.824796\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 46.2592i | − | 1.62438i | −0.583393 | − | 0.812190i | \(-0.698275\pi\) | ||
0.583393 | − | 0.812190i | \(-0.301725\pi\) | |||||||
\(812\) | −17.3693 | + | 7.36520i | −0.609544 | + | 0.258468i | ||||
\(813\) | −23.1231 | + | 12.9848i | −0.810963 | + | 0.455398i | ||||
\(814\) | −8.00000 | − | 5.29723i | −0.280400 | − | 0.185668i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 13.4012 | + | 3.52230i | 0.469137 | + | 0.123305i | ||||
\(817\) | − | 10.2462i | − | 0.358470i | ||||||
\(818\) | 19.8078 | − | 29.9142i | 0.692562 | − | 1.04592i | ||||
\(819\) | −39.6377 | − | 24.1636i | −1.38505 | − | 0.844344i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 53.2311i | 1.85778i | 0.370360 | + | 0.928888i | \(0.379234\pi\) | ||||
−0.370360 | + | 0.928888i | \(0.620766\pi\) | |||||||
\(822\) | −20.1449 | − | 1.47729i | −0.702635 | − | 0.0515263i | ||||
\(823\) | 48.2814 | 1.68298 | 0.841492 | − | 0.540270i | \(-0.181678\pi\) | ||||
0.841492 | + | 0.540270i | \(0.181678\pi\) | |||||||
\(824\) | −27.2655 | − | 5.06913i | −0.949840 | − | 0.176592i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −33.3693 | + | 50.3951i | −1.16107 | + | 1.75347i | ||||
\(827\) | − | 17.7509i | − | 0.617258i | −0.951183 | − | 0.308629i | \(-0.900130\pi\) | ||
0.951183 | − | 0.308629i | \(-0.0998701\pi\) | |||||||
\(828\) | 0.325462 | − | 2.20714i | 0.0113106 | − | 0.0767033i | ||||
\(829\) | 8.87689 | 0.308307 | 0.154154 | − | 0.988047i | \(-0.450735\pi\) | ||||
0.154154 | + | 0.988047i | \(0.450735\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −35.2929 | + | 19.8188i | −1.22430 | + | 0.687508i | ||||
\(832\) | −14.7304 | + | 38.2462i | −0.510685 | + | 1.32595i | ||||
\(833\) | −4.24621 | −0.147122 | ||||||||
\(834\) | 3.14261 | − | 42.8540i | 0.108820 | − | 1.48391i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.22925 | + | 1.36932i | −0.111686 | + | 0.0473588i | ||||
\(837\) | −0.876894 | + | 24.4924i | −0.0303099 | + | 0.846582i | ||||
\(838\) | 5.75058 | − | 8.68466i | 0.198650 | − | 0.300007i | ||||
\(839\) | 17.7051 | 0.611247 | 0.305624 | − | 0.952152i | \(-0.401135\pi\) | ||||
0.305624 | + | 0.952152i | \(0.401135\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.2462 | 0.663662 | ||||||||
\(842\) | 19.8078 | − | 29.9142i | 0.682621 | − | 1.03091i | ||||
\(843\) | −20.5625 | + | 11.5469i | −0.708210 | + | 0.397697i | ||||
\(844\) | −30.9309 | + | 13.1158i | −1.06468 | + | 0.451464i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11.6024 | − | 5.44050i | 0.398900 | − | 0.187048i | ||||
\(847\) | −27.9277 | −0.959607 | ||||||||
\(848\) | 34.0540 | − | 35.2114i | 1.16942 | − | 1.20916i | ||||
\(849\) | 19.6847 | + | 35.0540i | 0.675576 | + | 1.20305i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.90495 | 0.0653007 | ||||||||
\(852\) | 7.18697 | − | 9.29723i | 0.246221 | − | 0.318518i | ||||
\(853\) | 7.86174i | 0.269181i | 0.990901 | + | 0.134590i | \(0.0429719\pi\) | ||||
−0.990901 | + | 0.134590i | \(0.957028\pi\) | |||||||
\(854\) | −7.36520 | + | 11.1231i | −0.252032 | + | 0.380625i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.56155 | − | 8.39919i | 0.0533728 | − | 0.287078i | ||||
\(857\) | 20.7386 | 0.708418 | 0.354209 | − | 0.935166i | \(-0.384750\pi\) | ||||
0.354209 | + | 0.935166i | \(0.384750\pi\) | |||||||
\(858\) | 1.21544 | − | 16.5742i | 0.0414943 | − | 0.565834i | ||||
\(859\) | 33.4337i | 1.14074i | 0.821386 | + | 0.570372i | \(0.193201\pi\) | ||||
−0.821386 | + | 0.570372i | \(0.806799\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.12311 | − | 2.87689i | 0.174595 | − | 0.0980443i | ||||
\(862\) | 12.9885 | − | 19.6155i | 0.442390 | − | 0.668108i | ||||
\(863\) | − | 10.5487i | − | 0.359081i | −0.983751 | − | 0.179541i | \(-0.942539\pi\) | ||
0.983751 | − | 0.179541i | \(-0.0574611\pi\) | |||||||
\(864\) | 5.30423 | + | 28.9113i | 0.180453 | + | 0.983584i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 21.2247 | + | 14.0540i | 0.721243 | + | 0.477574i | ||||
\(867\) | −11.0249 | − | 19.6329i | −0.374426 | − | 0.666769i | ||||
\(868\) | −26.2316 | + | 11.1231i | −0.890357 | + | 0.377543i | ||||
\(869\) | − | 10.7386i | − | 0.364283i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.2586i | 0.754205i | ||||||||
\(872\) | 2.43845 | + | 0.453349i | 0.0825762 | + | 0.0153523i | ||||
\(873\) | 15.3693 | + | 9.36932i | 0.520173 | + | 0.317103i | ||||
\(874\) | 0.384472 | − | 0.580639i | 0.0130050 | − | 0.0196404i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −22.6004 | − | 17.4706i | −0.763596 | − | 0.590277i | ||||
\(877\) | 37.6155i | 1.27019i | 0.772436 | + | 0.635093i | \(0.219038\pi\) | ||||
−0.772436 | + | 0.635093i | \(0.780962\pi\) | |||||||
\(878\) | 10.9309 | + | 7.23791i | 0.368899 | + | 0.244268i | ||||
\(879\) | 2.11375 | + | 3.76412i | 0.0712950 | + | 0.126960i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.630683i | 0.0212483i | 0.999944 | + | 0.0106241i | \(0.00338183\pi\) | ||||
−0.999944 | + | 0.0106241i | \(0.996618\pi\) | |||||||
\(882\) | −3.82419 | − | 8.15549i | −0.128767 | − | 0.274610i | ||||
\(883\) | −22.4674 | −0.756090 | −0.378045 | − | 0.925787i | \(-0.623403\pi\) | ||||
−0.378045 | + | 0.925787i | \(0.623403\pi\) | |||||||
\(884\) | −18.8664 | + | 8.00000i | −0.634544 | + | 0.269069i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.5616 | − | 12.9527i | −0.657183 | − | 0.435156i | ||||
\(887\) | − | 51.6737i | − | 1.73503i | −0.497409 | − | 0.867516i | \(-0.665715\pi\) | ||
0.497409 | − | 0.867516i | \(-0.334285\pi\) | |||||||
\(888\) | −23.7612 | + | 8.08179i | −0.797373 | + | 0.271207i | ||||
\(889\) | −45.6155 | −1.52990 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.46026 | − | 10.5945i | −0.182925 | − | 0.354928i | ||||
\(892\) | −6.49424 | − | 15.3153i | −0.217443 | − | 0.512796i | ||||
\(893\) | 4.00000 | 0.133855 | ||||||||
\(894\) | 2.50806 | − | 34.2010i | 0.0838821 | − | 1.14385i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −27.8462 | + | 19.8078i | −0.930276 | + | 0.661731i | ||||
\(897\) | 1.61553 | + | 2.87689i | 0.0539409 | + | 0.0960567i | ||||
\(898\) | −32.2725 | − | 21.3693i | −1.07695 | − | 0.713103i | ||||
\(899\) | −14.7304 | −0.491287 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.4924 | 0.815961 | ||||||||
\(902\) | 1.75379 | + | 1.16128i | 0.0583948 | + | 0.0386663i | ||||
\(903\) | 19.8188 | + | 35.2929i | 0.659529 | + | 1.17447i | ||||
\(904\) | 38.9309 | + | 7.23791i | 1.29482 | + | 0.240729i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.31946 | + | 17.9927i | −0.0438360 | + | 0.597767i | ||||
\(907\) | 46.2134 | 1.53449 | 0.767246 | − | 0.641353i | \(-0.221627\pi\) | ||||
0.767246 | + | 0.641353i | \(0.221627\pi\) | |||||||
\(908\) | 40.3002 | − | 17.0887i | 1.33741 | − | 0.567108i | ||||
\(909\) | 2.24621 | + | 1.36932i | 0.0745021 | + | 0.0454174i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.3128 | −0.474204 | −0.237102 | − | 0.971485i | \(-0.576198\pi\) | ||||
−0.237102 | + | 0.971485i | \(0.576198\pi\) | |||||||
\(912\) | −2.33230 | + | 8.87368i | −0.0772302 | + | 0.293837i | ||||
\(913\) | − | 20.0000i | − | 0.661903i | ||||||
\(914\) | 11.7915 | + | 7.80776i | 0.390027 | + | 0.258258i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.6847 | − | 29.9142i | −0.419113 | − | 0.988392i | ||||
\(917\) | 16.4924 | 0.544628 | ||||||||
\(918\) | −8.54732 | + | 11.9559i | −0.282104 | + | 0.394603i | ||||
\(919\) | 49.9775i | 1.64861i | 0.566148 | + | 0.824303i | \(0.308433\pi\) | ||||
−0.566148 | + | 0.824303i | \(0.691567\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.43845 | − | 16.8078i | −0.311007 | − | 0.553835i | ||||
\(922\) | −49.3612 | − | 32.6847i | −1.62562 | − | 1.07641i | ||||
\(923\) | 17.3790i | 0.572037i | ||||||||
\(924\) | 8.47449 | − | 10.9628i | 0.278790 | − | 0.360650i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.35829 | + | 3.56155i | −0.0774984 | + | 0.117040i | ||||
\(927\) | 15.3110 | − | 25.1161i | 0.502881 | − | 0.824920i | ||||
\(928\) | −17.2517 | + | 3.80776i | −0.566316 | + | 0.124996i | ||||
\(929\) | 33.1231i | 1.08673i | 0.839495 | + | 0.543367i | \(0.182851\pi\) | ||||
−0.839495 | + | 0.543367i | \(0.817149\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.81164i | − | 0.0921479i | ||||||
\(932\) | 7.80776 | + | 18.4130i | 0.255752 | + | 0.603138i | ||||
\(933\) | 17.6155 | + | 31.3693i | 0.576707 | + | 1.02699i | ||||
\(934\) | −2.68466 | − | 1.77766i | −0.0878447 | − | 0.0581667i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −32.3565 | − | 29.0308i | −1.05760 | − | 0.948901i | ||||
\(937\) | − | 22.4924i | − | 0.734795i | −0.930064 | − | 0.367398i | \(-0.880249\pi\) | ||
0.930064 | − | 0.367398i | \(-0.119751\pi\) | |||||||
\(938\) | −10.2462 | + | 15.4741i | −0.334551 | + | 0.505246i | ||||
\(939\) | −33.9686 | + | 19.0752i | −1.10852 | + | 0.622494i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.876894i | 0.0285859i | 0.999898 | + | 0.0142930i | \(0.00454975\pi\) | ||||
−0.999898 | + | 0.0142930i | \(0.995450\pi\) | |||||||
\(942\) | −0.603604 | + | 8.23100i | −0.0196665 | + | 0.268181i | ||||
\(943\) | −0.417609 | −0.0135992 | ||||||||
\(944\) | −39.3473 | + | 40.6847i | −1.28065 | + | 1.32417i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.00000 | + | 12.0818i | −0.260102 | + | 0.392813i | ||||
\(947\) | 32.4813i | 1.05550i | 0.849400 | + | 0.527750i | \(0.176964\pi\) | ||||
−0.849400 | + | 0.527750i | \(0.823036\pi\) | |||||||
\(948\) | −22.2240 | − | 17.1796i | −0.721801 | − | 0.557969i | ||||
\(949\) | 42.2462 | 1.37137 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.1955 | + | 25.2791i | 0.460322 | + | 0.819731i | ||||
\(952\) | −16.7984 | − | 3.12311i | −0.544439 | − | 0.101220i | ||||
\(953\) | −22.4924 | −0.728601 | −0.364301 | − | 0.931281i | \(-0.618692\pi\) | ||||
−0.364301 | + | 0.931281i | \(0.618692\pi\) | |||||||
\(954\) | 22.0582 | + | 47.0414i | 0.714160 | + | 1.52302i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.5691 | + | 32.0000i | 0.438857 | + | 1.03495i | ||||
\(957\) | 6.24621 | − | 3.50758i | 0.201911 | − | 0.113384i | ||||
\(958\) | 20.0276 | − | 30.2462i | 0.647063 | − | 0.977211i | ||||
\(959\) | 24.9073 | 0.804297 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.75379 | 0.282380 | ||||||||
\(962\) | 20.4924 | − | 30.9481i | 0.660702 | − | 0.997808i | ||||
\(963\) | 7.73704 | + | 4.71659i | 0.249323 | + | 0.151990i | ||||
\(964\) | −10.4384 | − | 24.6169i | −0.336200 | − | 0.792858i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.201201 | + | 2.74367i | −0.00647354 | + | 0.0882761i | ||||
\(967\) | −26.4404 | −0.850265 | −0.425132 | − | 0.905131i | \(-0.639772\pi\) | ||||
−0.425132 | + | 0.905131i | \(0.639772\pi\) | |||||||
\(968\) | −25.7116 | − | 4.78023i | −0.826404 | − | 0.153643i | ||||
\(969\) | −4.00000 | + | 2.24621i | −0.128499 | + | 0.0721587i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.6261 | 1.68885 | 0.844427 | − | 0.535671i | \(-0.179941\pi\) | ||||
0.844427 | + | 0.535671i | \(0.179941\pi\) | |||||||
\(972\) | −30.6609 | − | 5.64879i | −0.983449 | − | 0.181185i | ||||
\(973\) | 52.9848i | 1.69862i | ||||||||
\(974\) | −19.7373 | + | 29.8078i | −0.632424 | + | 0.955102i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.68466 | + | 8.97983i | −0.277989 | + | 0.287437i | ||||
\(977\) | −31.7538 | −1.01589 | −0.507947 | − | 0.861388i | \(-0.669595\pi\) | ||||
−0.507947 | + | 0.861388i | \(0.669595\pi\) | |||||||
\(978\) | 38.3122 | + | 2.80954i | 1.22509 | + | 0.0898393i | ||||
\(979\) | − | 13.5691i | − | 0.433671i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.36932 | + | 2.24621i | −0.0437189 | + | 0.0717160i | ||||
\(982\) | −21.0616 | + | 31.8078i | −0.672103 | + | 1.01503i | ||||
\(983\) | − | 40.0095i | − | 1.27610i | −0.769993 | − | 0.638052i | \(-0.779740\pi\) | ||
0.769993 | − | 0.638052i | \(-0.220260\pi\) | |||||||
\(984\) | 5.20901 | − | 1.77172i | 0.166057 | − | 0.0564804i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.36520 | − | 4.87689i | −0.234556 | − | 0.155312i | ||||
\(987\) | −13.7779 | + | 7.73704i | −0.438556 | + | 0.246273i | ||||
\(988\) | −5.29723 | − | 12.4924i | −0.168527 | − | 0.397437i | ||||
\(989\) | − | 2.87689i | − | 0.0914799i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 33.0161i | − | 1.04879i | −0.851475 | − | 0.524396i | \(-0.824291\pi\) | ||
0.851475 | − | 0.524396i | \(-0.175709\pi\) | |||||||
\(992\) | −26.0540 | + | 5.75058i | −0.827215 | + | 0.182581i | ||||
\(993\) | 4.87689 | − | 2.73863i | 0.154764 | − | 0.0869079i | ||||
\(994\) | −8.00000 | + | 12.0818i | −0.253745 | + | 0.383211i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −41.3907 | − | 31.9960i | −1.31151 | − | 1.01383i | ||||
\(997\) | − | 33.6155i | − | 1.06461i | −0.846551 | − | 0.532307i | \(-0.821325\pi\) | ||
0.846551 | − | 0.532307i | \(-0.178675\pi\) | |||||||
\(998\) | 38.0540 | + | 25.1976i | 1.20458 | + | 0.797615i | ||||
\(999\) | 0.952473 | − | 26.6034i | 0.0301349 | − | 0.841694i |
(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 | 300.2.h.b.299.4 | 8 | ||
3.2 | odd | 2 | 300.2.h.a.299.6 | 8 | |||
4.3 | odd | 2 | inner | 300.2.h.b.299.1 | 8 | ||
5.2 | odd | 4 | 300.2.e.c.251.1 | 8 | |||
5.3 | odd | 4 | 60.2.e.a.11.8 | yes | 8 | ||
5.4 | even | 2 | 300.2.h.a.299.5 | 8 | |||
12.11 | even | 2 | 300.2.h.a.299.7 | 8 | |||
15.2 | even | 4 | 300.2.e.c.251.8 | 8 | |||
15.8 | even | 4 | 60.2.e.a.11.1 | ✓ | 8 | ||
15.14 | odd | 2 | inner | 300.2.h.b.299.3 | 8 | ||
20.3 | even | 4 | 60.2.e.a.11.2 | yes | 8 | ||
20.7 | even | 4 | 300.2.e.c.251.7 | 8 | |||
20.19 | odd | 2 | 300.2.h.a.299.8 | 8 | |||
40.3 | even | 4 | 960.2.h.g.191.2 | 8 | |||
40.13 | odd | 4 | 960.2.h.g.191.7 | 8 | |||
60.23 | odd | 4 | 60.2.e.a.11.7 | yes | 8 | ||
60.47 | odd | 4 | 300.2.e.c.251.2 | 8 | |||
60.59 | even | 2 | inner | 300.2.h.b.299.2 | 8 | ||
120.53 | even | 4 | 960.2.h.g.191.1 | 8 | |||
120.83 | odd | 4 | 960.2.h.g.191.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.2.e.a.11.1 | ✓ | 8 | 15.8 | even | 4 | ||
60.2.e.a.11.2 | yes | 8 | 20.3 | even | 4 | ||
60.2.e.a.11.7 | yes | 8 | 60.23 | odd | 4 | ||
60.2.e.a.11.8 | yes | 8 | 5.3 | odd | 4 | ||
300.2.e.c.251.1 | 8 | 5.2 | odd | 4 | |||
300.2.e.c.251.2 | 8 | 60.47 | odd | 4 | |||
300.2.e.c.251.7 | 8 | 20.7 | even | 4 | |||
300.2.e.c.251.8 | 8 | 15.2 | even | 4 | |||
300.2.h.a.299.5 | 8 | 5.4 | even | 2 | |||
300.2.h.a.299.6 | 8 | 3.2 | odd | 2 | |||
300.2.h.a.299.7 | 8 | 12.11 | even | 2 | |||
300.2.h.a.299.8 | 8 | 20.19 | odd | 2 | |||
300.2.h.b.299.1 | 8 | 4.3 | odd | 2 | inner | ||
300.2.h.b.299.2 | 8 | 60.59 | even | 2 | inner | ||
300.2.h.b.299.3 | 8 | 15.14 | odd | 2 | inner | ||
300.2.h.b.299.4 | 8 | 1.1 | even | 1 | trivial | ||
960.2.h.g.191.1 | 8 | 120.53 | even | 4 | |||
960.2.h.g.191.2 | 8 | 40.3 | even | 4 | |||
960.2.h.g.191.7 | 8 | 40.13 | odd | 4 | |||
960.2.h.g.191.8 | 8 | 120.83 | odd | 4 |