Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(127,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.bj (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: | \(13.0794958511\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1135.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.1135 |
Dual form | 1638.2.bj.b.127.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | − | 2.73205i | − | 1.22181i | −0.791704 | − | 0.610905i | \(-0.790806\pi\) | ||
0.791704 | − | 0.610905i | \(-0.209194\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.866025 | + | 0.500000i | −0.327327 | + | 0.188982i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.36603 | + | 2.36603i | −0.431975 | + | 0.748203i | ||||
\(11\) | −1.50000 | − | 0.866025i | −0.452267 | − | 0.261116i | 0.256520 | − | 0.966539i | \(-0.417424\pi\) |
−0.708787 | + | 0.705422i | \(0.750757\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.59808 | − | 0.232051i | −0.997927 | − | 0.0643593i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.133975 | − | 0.232051i | −0.0324936 | − | 0.0562806i | 0.849321 | − | 0.527876i | \(-0.177012\pi\) |
−0.881815 | + | 0.471596i | \(0.843678\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.866025 | + | 0.500000i | −0.198680 | + | 0.114708i | −0.596040 | − | 0.802955i | \(-0.703260\pi\) |
0.397360 | + | 0.917663i | \(0.369927\pi\) | |||||||
\(20\) | 2.36603 | − | 1.36603i | 0.529059 | − | 0.305453i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.866025 | + | 1.50000i | 0.184637 | + | 0.319801i | ||||
\(23\) | −1.73205 | + | 3.00000i | −0.361158 | + | 0.625543i | −0.988152 | − | 0.153481i | \(-0.950952\pi\) |
0.626994 | + | 0.779024i | \(0.284285\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.46410 | −0.492820 | ||||||||
\(26\) | 3.00000 | + | 2.00000i | 0.588348 | + | 0.392232i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.866025 | − | 0.500000i | −0.163663 | − | 0.0944911i | ||||
\(29\) | −0.232051 | + | 0.401924i | −0.0430908 | + | 0.0746354i | −0.886766 | − | 0.462218i | \(-0.847054\pi\) |
0.843676 | + | 0.536853i | \(0.180387\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.19615i | 1.47207i | 0.676942 | + | 0.736036i | \(0.263305\pi\) | ||||
−0.676942 | + | 0.736036i | \(0.736695\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.267949i | 0.0459529i | ||||||||
\(35\) | 1.36603 | + | 2.36603i | 0.230900 | + | 0.399931i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.83013 | − | 1.63397i | −0.465270 | − | 0.268624i | 0.248988 | − | 0.968507i | \(-0.419902\pi\) |
−0.714258 | + | 0.699883i | \(0.753235\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.73205 | −0.431975 | ||||||||
\(41\) | 2.59808 | + | 1.50000i | 0.405751 | + | 0.234261i | 0.688963 | − | 0.724797i | \(-0.258066\pi\) |
−0.283211 | + | 0.959058i | \(0.591400\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.36603 | + | 5.83013i | 0.513314 | + | 0.889086i | 0.999881 | + | 0.0154426i | \(0.00491573\pi\) |
−0.486567 | + | 0.873643i | \(0.661751\pi\) | |||||||
\(44\) | − | 1.73205i | − | 0.261116i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | − | 1.73205i | 0.442326 | − | 0.255377i | ||||
\(47\) | − | 4.46410i | − | 0.651156i | −0.945515 | − | 0.325578i | \(-0.894441\pi\) | ||
0.945515 | − | 0.325578i | \(-0.105559\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.500000 | − | 0.866025i | 0.0714286 | − | 0.123718i | ||||
\(50\) | 2.13397 | + | 1.23205i | 0.301790 | + | 0.174238i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.59808 | − | 3.23205i | −0.221613 | − | 0.448205i | ||||
\(53\) | −7.00000 | −0.961524 | −0.480762 | − | 0.876851i | \(-0.659640\pi\) | ||||
−0.480762 | + | 0.876851i | \(0.659640\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.36603 | + | 4.09808i | −0.319035 | + | 0.552584i | ||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.401924 | − | 0.232051i | 0.0527752 | − | 0.0304698i | ||||
\(59\) | −11.1962 | + | 6.46410i | −1.45761 | + | 0.841554i | −0.998894 | − | 0.0470259i | \(-0.985026\pi\) |
−0.458721 | + | 0.888580i | \(0.651692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.59808 | + | 4.50000i | 0.332650 | + | 0.576166i | 0.983030 | − | 0.183442i | \(-0.0587240\pi\) |
−0.650381 | + | 0.759608i | \(0.725391\pi\) | |||||||
\(62\) | 4.09808 | − | 7.09808i | 0.520456 | − | 0.901457i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.633975 | + | 9.83013i | −0.0786349 | + | 1.21928i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.26795 | + | 2.46410i | 0.521413 | + | 0.301038i | 0.737513 | − | 0.675333i | \(-0.236000\pi\) |
−0.216100 | + | 0.976371i | \(0.569334\pi\) | |||||||
\(68\) | 0.133975 | − | 0.232051i | 0.0162468 | − | 0.0281403i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 2.73205i | − | 0.326543i | ||||||
\(71\) | 7.09808 | − | 4.09808i | 0.842387 | − | 0.486352i | −0.0156881 | − | 0.999877i | \(-0.504994\pi\) |
0.858075 | + | 0.513525i | \(0.171661\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.46410i | − | 0.171360i | −0.996323 | − | 0.0856801i | \(-0.972694\pi\) | ||
0.996323 | − | 0.0856801i | \(-0.0273063\pi\) | |||||||
\(74\) | 1.63397 | + | 2.83013i | 0.189946 | + | 0.328996i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.866025 | − | 0.500000i | −0.0993399 | − | 0.0573539i | ||||
\(77\) | 1.73205 | 0.197386 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.9282 | 1.79206 | 0.896031 | − | 0.443991i | \(-0.146438\pi\) | ||||
0.896031 | + | 0.443991i | \(0.146438\pi\) | |||||||
\(80\) | 2.36603 | + | 1.36603i | 0.264530 | + | 0.152726i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.50000 | − | 2.59808i | −0.165647 | − | 0.286910i | ||||
\(83\) | − | 10.1962i | − | 1.11917i | −0.828772 | − | 0.559587i | \(-0.810960\pi\) | ||
0.828772 | − | 0.559587i | \(-0.189040\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.633975 | + | 0.366025i | −0.0687642 | + | 0.0397010i | ||||
\(86\) | − | 6.73205i | − | 0.725936i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.866025 | + | 1.50000i | −0.0923186 | + | 0.159901i | ||||
\(89\) | −3.06218 | − | 1.76795i | −0.324590 | − | 0.187402i | 0.328847 | − | 0.944383i | \(-0.393340\pi\) |
−0.653437 | + | 0.756981i | \(0.726673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.23205 | − | 1.59808i | 0.338811 | − | 0.167524i | ||||
\(92\) | −3.46410 | −0.361158 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.23205 | + | 3.86603i | −0.230218 | + | 0.398750i | ||||
\(95\) | 1.36603 | + | 2.36603i | 0.140151 | + | 0.242749i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.43782 | − | 0.830127i | 0.145989 | − | 0.0842866i | −0.425226 | − | 0.905087i | \(-0.639806\pi\) |
0.571215 | + | 0.820800i | \(0.306472\pi\) | |||||||
\(98\) | −0.866025 | + | 0.500000i | −0.0874818 | + | 0.0505076i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.23205 | − | 2.13397i | −0.123205 | − | 0.213397i | ||||
\(101\) | −8.46410 | + | 14.6603i | −0.842210 | + | 1.45875i | 0.0458130 | + | 0.998950i | \(0.485412\pi\) |
−0.888023 | + | 0.459800i | \(0.847921\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.2679 | −1.11026 | −0.555132 | − | 0.831762i | \(-0.687332\pi\) | ||||
−0.555132 | + | 0.831762i | \(0.687332\pi\) | |||||||
\(104\) | −0.232051 | + | 3.59808i | −0.0227545 | + | 0.352820i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.06218 | + | 3.50000i | 0.588811 | + | 0.339950i | ||||
\(107\) | −8.42820 | + | 14.5981i | −0.814785 | + | 1.41125i | 0.0946969 | + | 0.995506i | \(0.469812\pi\) |
−0.909482 | + | 0.415743i | \(0.863522\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.26795i | − | 0.121448i | −0.998155 | − | 0.0607238i | \(-0.980659\pi\) | ||
0.998155 | − | 0.0607238i | \(-0.0193409\pi\) | |||||||
\(110\) | 4.09808 | − | 2.36603i | 0.390736 | − | 0.225592i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1.00000i | − | 0.0944911i | ||||||
\(113\) | 9.36603 | + | 16.2224i | 0.881082 | + | 1.52608i | 0.850140 | + | 0.526557i | \(0.176517\pi\) |
0.0309416 | + | 0.999521i | \(0.490149\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.19615 | + | 4.73205i | 0.764295 | + | 0.441266i | ||||
\(116\) | −0.464102 | −0.0430908 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.9282 | 1.19014 | ||||||||
\(119\) | 0.232051 | + | 0.133975i | 0.0212721 | + | 0.0122814i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00000 | − | 6.92820i | −0.363636 | − | 0.629837i | ||||
\(122\) | − | 5.19615i | − | 0.470438i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.09808 | + | 4.09808i | −0.637426 | + | 0.368018i | ||||
\(125\) | − | 6.92820i | − | 0.619677i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.26795 | + | 7.39230i | −0.378719 | + | 0.655961i | −0.990876 | − | 0.134775i | \(-0.956969\pi\) |
0.612157 | + | 0.790736i | \(0.290302\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.46410 | − | 8.19615i | 0.479233 | − | 0.718850i | ||||
\(131\) | −13.8564 | −1.21064 | −0.605320 | − | 0.795982i | \(-0.706955\pi\) | ||||
−0.605320 | + | 0.795982i | \(0.706955\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.500000 | − | 0.866025i | 0.0433555 | − | 0.0750939i | ||||
\(134\) | −2.46410 | − | 4.26795i | −0.212866 | − | 0.368695i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.232051 | + | 0.133975i | −0.0198982 | + | 0.0114882i | ||||
\(137\) | −5.53590 | + | 3.19615i | −0.472964 | + | 0.273066i | −0.717480 | − | 0.696580i | \(-0.754704\pi\) |
0.244516 | + | 0.969645i | \(0.421371\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.79423 | + | 16.9641i | 0.830736 | + | 1.43888i | 0.897456 | + | 0.441105i | \(0.145413\pi\) |
−0.0667201 | + | 0.997772i | \(0.521253\pi\) | |||||||
\(140\) | −1.36603 | + | 2.36603i | −0.115450 | + | 0.199966i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.19615 | −0.687806 | ||||||||
\(143\) | 5.19615 | + | 3.46410i | 0.434524 | + | 0.289683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.09808 | + | 0.633975i | 0.0911903 | + | 0.0526487i | ||||
\(146\) | −0.732051 | + | 1.26795i | −0.0605850 | + | 0.104936i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 3.26795i | − | 0.268624i | ||||||
\(149\) | −12.0000 | + | 6.92820i | −0.983078 | + | 0.567581i | −0.903198 | − | 0.429224i | \(-0.858787\pi\) |
−0.0798802 | + | 0.996804i | \(0.525454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.19615i | 0.422857i | 0.977393 | + | 0.211428i | \(0.0678115\pi\) | ||||
−0.977393 | + | 0.211428i | \(0.932188\pi\) | |||||||
\(152\) | 0.500000 | + | 0.866025i | 0.0405554 | + | 0.0702439i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.50000 | − | 0.866025i | −0.120873 | − | 0.0697863i | ||||
\(155\) | 22.3923 | 1.79859 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.46410 | −0.595700 | −0.297850 | − | 0.954613i | \(-0.596270\pi\) | ||||
−0.297850 | + | 0.954613i | \(0.596270\pi\) | |||||||
\(158\) | −13.7942 | − | 7.96410i | −1.09741 | − | 0.633590i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.36603 | − | 2.36603i | −0.107994 | − | 0.187051i | ||||
\(161\) | − | 3.46410i | − | 0.273009i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.633975 | − | 0.366025i | 0.0496567 | − | 0.0286693i | −0.474966 | − | 0.880004i | \(-0.657540\pi\) |
0.524623 | + | 0.851335i | \(0.324206\pi\) | |||||||
\(164\) | 3.00000i | 0.234261i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.09808 | + | 8.83013i | −0.395687 | + | 0.685351i | ||||
\(167\) | 12.0000 | + | 6.92820i | 0.928588 | + | 0.536120i | 0.886365 | − | 0.462988i | \(-0.153223\pi\) |
0.0422232 | + | 0.999108i | \(0.486556\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8923 | + | 1.66987i | 0.991716 | + | 0.128452i | ||||
\(170\) | 0.732051 | 0.0561457 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.36603 | + | 5.83013i | −0.256657 | + | 0.444543i | ||||
\(173\) | −7.56218 | − | 13.0981i | −0.574942 | − | 0.995828i | −0.996048 | − | 0.0888170i | \(-0.971691\pi\) |
0.421106 | − | 0.907011i | \(-0.361642\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.13397 | − | 1.23205i | 0.161313 | − | 0.0931343i | ||||
\(176\) | 1.50000 | − | 0.866025i | 0.113067 | − | 0.0652791i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.76795 | + | 3.06218i | 0.132513 | + | 0.229520i | ||||
\(179\) | −2.26795 | + | 3.92820i | −0.169514 | + | 0.293608i | −0.938249 | − | 0.345960i | \(-0.887553\pi\) |
0.768735 | + | 0.639568i | \(0.220887\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.6603 | −1.08969 | −0.544844 | − | 0.838537i | \(-0.683411\pi\) | ||||
−0.544844 | + | 0.838537i | \(0.683411\pi\) | |||||||
\(182\) | −3.59808 | − | 0.232051i | −0.266707 | − | 0.0172008i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.00000 | + | 1.73205i | 0.221163 | + | 0.127688i | ||||
\(185\) | −4.46410 | + | 7.73205i | −0.328207 | + | 0.568472i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.464102i | 0.0339385i | ||||||||
\(188\) | 3.86603 | − | 2.23205i | 0.281959 | − | 0.162789i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 2.73205i | − | 0.198204i | ||||||
\(191\) | −0.562178 | − | 0.973721i | −0.0406778 | − | 0.0704559i | 0.844970 | − | 0.534814i | \(-0.179618\pi\) |
−0.885647 | + | 0.464358i | \(0.846285\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.96410 | − | 4.59808i | −0.573269 | − | 0.330977i | 0.185185 | − | 0.982704i | \(-0.440712\pi\) |
−0.758454 | + | 0.651727i | \(0.774045\pi\) | |||||||
\(194\) | −1.66025 | −0.119199 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 8.08846 | + | 4.66987i | 0.576279 | + | 0.332715i | 0.759653 | − | 0.650328i | \(-0.225369\pi\) |
−0.183374 | + | 0.983043i | \(0.558702\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.90192 | − | 5.02628i | −0.205712 | − | 0.356304i | 0.744647 | − | 0.667458i | \(-0.232618\pi\) |
−0.950359 | + | 0.311155i | \(0.899284\pi\) | |||||||
\(200\) | 2.46410i | 0.174238i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.6603 | − | 8.46410i | 1.03149 | − | 0.595532i | ||||
\(203\) | − | 0.464102i | − | 0.0325735i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.09808 | − | 7.09808i | 0.286222 | − | 0.495751i | ||||
\(206\) | 9.75833 | + | 5.63397i | 0.679895 | + | 0.392538i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000 | − | 3.00000i | 0.138675 | − | 0.208013i | ||||
\(209\) | 1.73205 | 0.119808 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.0000 | + | 22.5167i | −0.894957 | + | 1.55011i | −0.0610990 | + | 0.998132i | \(0.519461\pi\) |
−0.833858 | + | 0.551979i | \(0.813873\pi\) | |||||||
\(212\) | −3.50000 | − | 6.06218i | −0.240381 | − | 0.416352i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.5981 | − | 8.42820i | 0.997904 | − | 0.576140i | ||||
\(215\) | 15.9282 | − | 9.19615i | 1.08629 | − | 0.627172i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.09808 | − | 7.09808i | −0.278196 | − | 0.481849i | ||||
\(218\) | −0.633975 | + | 1.09808i | −0.0429382 | + | 0.0743711i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.73205 | −0.319035 | ||||||||
\(221\) | 0.428203 | + | 0.866025i | 0.0288041 | + | 0.0582552i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.12436 | − | 1.80385i | −0.209222 | − | 0.120795i | 0.391728 | − | 0.920081i | \(-0.371878\pi\) |
−0.600950 | + | 0.799287i | \(0.705211\pi\) | |||||||
\(224\) | −0.500000 | + | 0.866025i | −0.0334077 | + | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 18.7321i | − | 1.24604i | ||||||
\(227\) | −2.07180 | + | 1.19615i | −0.137510 | + | 0.0793914i | −0.567177 | − | 0.823596i | \(-0.691964\pi\) |
0.429667 | + | 0.902988i | \(0.358631\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.07180i | 0.401236i | 0.979670 | + | 0.200618i | \(0.0642949\pi\) | ||||
−0.979670 | + | 0.200618i | \(0.935705\pi\) | |||||||
\(230\) | −4.73205 | − | 8.19615i | −0.312022 | − | 0.540438i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.401924 | + | 0.232051i | 0.0263876 | + | 0.0152349i | ||||
\(233\) | 15.1244 | 0.990829 | 0.495415 | − | 0.868657i | \(-0.335016\pi\) | ||||
0.495415 | + | 0.868657i | \(0.335016\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.1962 | −0.795589 | ||||||||
\(236\) | −11.1962 | − | 6.46410i | −0.728807 | − | 0.420777i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.133975 | − | 0.232051i | −0.00868428 | − | 0.0150416i | ||||
\(239\) | − | 2.73205i | − | 0.176722i | −0.996089 | − | 0.0883608i | \(-0.971837\pi\) | ||
0.996089 | − | 0.0883608i | \(-0.0281629\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.92820 | − | 4.00000i | 0.446285 | − | 0.257663i | −0.259975 | − | 0.965615i | \(-0.583714\pi\) |
0.706260 | + | 0.707953i | \(0.250381\pi\) | |||||||
\(242\) | 8.00000i | 0.514259i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.59808 | + | 4.50000i | −0.166325 | + | 0.288083i | ||||
\(245\) | −2.36603 | − | 1.36603i | −0.151160 | − | 0.0872722i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.23205 | − | 1.59808i | 0.205650 | − | 0.101683i | ||||
\(248\) | 8.19615 | 0.520456 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.46410 | + | 6.00000i | −0.219089 | + | 0.379473i | ||||
\(251\) | 5.56218 | + | 9.63397i | 0.351082 | + | 0.608091i | 0.986439 | − | 0.164127i | \(-0.0524807\pi\) |
−0.635358 | + | 0.772218i | \(0.719147\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.19615 | − | 3.00000i | 0.326679 | − | 0.188608i | ||||
\(254\) | 7.39230 | − | 4.26795i | 0.463834 | − | 0.267795i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1.66987 | + | 2.89230i | −0.104164 | + | 0.180417i | −0.913396 | − | 0.407072i | \(-0.866550\pi\) |
0.809232 | + | 0.587489i | \(0.199883\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.26795 | 0.203060 | ||||||||
\(260\) | −8.83013 | + | 4.36603i | −0.547621 | + | 0.270769i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.0000 | + | 6.92820i | 0.741362 | + | 0.428026i | ||||
\(263\) | 4.56218 | − | 7.90192i | 0.281316 | − | 0.487253i | −0.690393 | − | 0.723434i | \(-0.742562\pi\) |
0.971709 | + | 0.236181i | \(0.0758958\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.1244i | 1.17480i | ||||||||
\(266\) | −0.866025 | + | 0.500000i | −0.0530994 | + | 0.0306570i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.92820i | 0.301038i | ||||||||
\(269\) | 8.92820 | + | 15.4641i | 0.544362 | + | 0.942863i | 0.998647 | + | 0.0520063i | \(0.0165616\pi\) |
−0.454285 | + | 0.890857i | \(0.650105\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.70577 | − | 5.02628i | −0.528838 | − | 0.305325i | 0.211705 | − | 0.977334i | \(-0.432098\pi\) |
−0.740543 | + | 0.672009i | \(0.765432\pi\) | |||||||
\(272\) | 0.267949 | 0.0162468 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.39230 | 0.386173 | ||||||||
\(275\) | 3.69615 | + | 2.13397i | 0.222886 | + | 0.128684i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.6603 | − | 21.9282i | −0.760681 | − | 1.31754i | −0.942500 | − | 0.334206i | \(-0.891532\pi\) |
0.181819 | − | 0.983332i | \(-0.441801\pi\) | |||||||
\(278\) | − | 19.5885i | − | 1.17484i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.36603 | − | 1.36603i | 0.141397 | − | 0.0816356i | ||||
\(281\) | − | 17.6603i | − | 1.05352i | −0.850013 | − | 0.526761i | \(-0.823406\pi\) | ||
0.850013 | − | 0.526761i | \(-0.176594\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.92820 | − | 15.4641i | 0.530727 | − | 0.919245i | −0.468631 | − | 0.883394i | \(-0.655252\pi\) |
0.999357 | − | 0.0358512i | \(-0.0114142\pi\) | |||||||
\(284\) | 7.09808 | + | 4.09808i | 0.421193 | + | 0.243176i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.76795 | − | 5.59808i | −0.163672 | − | 0.331021i | ||||
\(287\) | −3.00000 | −0.177084 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.46410 | − | 14.6603i | 0.497888 | − | 0.862368i | ||||
\(290\) | −0.633975 | − | 1.09808i | −0.0372283 | − | 0.0644813i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.26795 | − | 0.732051i | 0.0742011 | − | 0.0428400i | ||||
\(293\) | −26.7846 | + | 15.4641i | −1.56477 | + | 0.903422i | −0.568011 | + | 0.823021i | \(0.692287\pi\) |
−0.996763 | + | 0.0804015i | \(0.974380\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.6603 | + | 30.5885i | 1.02822 | + | 1.78093i | ||||
\(296\) | −1.63397 | + | 2.83013i | −0.0949728 | + | 0.164498i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.8564 | 0.802680 | ||||||||
\(299\) | 6.92820 | − | 10.3923i | 0.400668 | − | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.83013 | − | 3.36603i | −0.336043 | − | 0.194014i | ||||
\(302\) | 2.59808 | − | 4.50000i | 0.149502 | − | 0.258946i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 1.00000i | − | 0.0573539i | ||||||
\(305\) | 12.2942 | − | 7.09808i | 0.703965 | − | 0.406435i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 29.3923i | − | 1.67751i | −0.544511 | − | 0.838754i | \(-0.683285\pi\) | ||
0.544511 | − | 0.838754i | \(-0.316715\pi\) | |||||||
\(308\) | 0.866025 | + | 1.50000i | 0.0493464 | + | 0.0854704i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −19.3923 | − | 11.1962i | −1.10141 | − | 0.635899i | ||||
\(311\) | 7.73205 | 0.438444 | 0.219222 | − | 0.975675i | \(-0.429648\pi\) | ||||
0.219222 | + | 0.975675i | \(0.429648\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.5167 | −1.78143 | −0.890713 | − | 0.454565i | \(-0.849795\pi\) | ||||
−0.890713 | + | 0.454565i | \(0.849795\pi\) | |||||||
\(314\) | 6.46410 | + | 3.73205i | 0.364790 | + | 0.210612i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.96410 | + | 13.7942i | 0.448016 | + | 0.775986i | ||||
\(317\) | − | 15.8564i | − | 0.890585i | −0.895385 | − | 0.445292i | \(-0.853100\pi\) | ||
0.895385 | − | 0.445292i | \(-0.146900\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.696152 | − | 0.401924i | 0.0389771 | − | 0.0225034i | ||||
\(320\) | 2.73205i | 0.152726i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.73205 | + | 3.00000i | −0.0965234 | + | 0.167183i | ||||
\(323\) | 0.232051 | + | 0.133975i | 0.0129117 | + | 0.00745455i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.86603 | + | 0.571797i | 0.491799 | + | 0.0317176i | ||||
\(326\) | −0.732051 | −0.0405445 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.50000 | − | 2.59808i | 0.0828236 | − | 0.143455i | ||||
\(329\) | 2.23205 | + | 3.86603i | 0.123057 | + | 0.213141i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.124356 | + | 0.0717968i | −0.00683520 | + | 0.00394631i | −0.503414 | − | 0.864046i | \(-0.667923\pi\) |
0.496579 | + | 0.867992i | \(0.334589\pi\) | |||||||
\(332\) | 8.83013 | − | 5.09808i | 0.484616 | − | 0.279793i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.92820 | − | 12.0000i | −0.379094 | − | 0.656611i | ||||
\(335\) | 6.73205 | − | 11.6603i | 0.367811 | − | 0.637068i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.0000 | −1.03500 | −0.517498 | − | 0.855684i | \(-0.673136\pi\) | ||||
−0.517498 | + | 0.855684i | \(0.673136\pi\) | |||||||
\(338\) | −10.3301 | − | 7.89230i | −0.561885 | − | 0.429285i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.633975 | − | 0.366025i | −0.0343821 | − | 0.0198505i | ||||
\(341\) | 7.09808 | − | 12.2942i | 0.384382 | − | 0.665770i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 5.83013 | − | 3.36603i | 0.314339 | − | 0.181484i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.1244i | 0.813090i | ||||||||
\(347\) | −7.69615 | − | 13.3301i | −0.413151 | − | 0.715599i | 0.582081 | − | 0.813131i | \(-0.302239\pi\) |
−0.995232 | + | 0.0975319i | \(0.968905\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.4641 | − | 15.8564i | −1.47012 | − | 0.848774i | −0.470682 | − | 0.882303i | \(-0.655992\pi\) |
−0.999438 | + | 0.0335290i | \(0.989325\pi\) | |||||||
\(350\) | −2.46410 | −0.131712 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.73205 | −0.0923186 | ||||||||
\(353\) | −2.19615 | − | 1.26795i | −0.116889 | − | 0.0674861i | 0.440415 | − | 0.897794i | \(-0.354831\pi\) |
−0.557305 | + | 0.830308i | \(0.688165\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.1962 | − | 19.3923i | −0.594230 | − | 1.02924i | ||||
\(356\) | − | 3.53590i | − | 0.187402i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.92820 | − | 2.26795i | 0.207612 | − | 0.119865i | ||||
\(359\) | − | 14.1962i | − | 0.749244i | −0.927178 | − | 0.374622i | \(-0.877772\pi\) | ||
0.927178 | − | 0.374622i | \(-0.122228\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.00000 | + | 15.5885i | −0.473684 | + | 0.820445i | ||||
\(362\) | 12.6962 | + | 7.33013i | 0.667295 | + | 0.385263i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.00000 | + | 2.00000i | 0.157243 | + | 0.104828i | ||||
\(365\) | −4.00000 | −0.209370 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.66025 | − | 8.07180i | 0.243263 | − | 0.421344i | −0.718379 | − | 0.695652i | \(-0.755115\pi\) |
0.961642 | + | 0.274308i | \(0.0884488\pi\) | |||||||
\(368\) | −1.73205 | − | 3.00000i | −0.0902894 | − | 0.156386i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.73205 | − | 4.46410i | 0.401970 | − | 0.232078i | ||||
\(371\) | 6.06218 | − | 3.50000i | 0.314733 | − | 0.181711i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.83013 | + | 6.63397i | 0.198316 | + | 0.343494i | 0.947983 | − | 0.318322i | \(-0.103119\pi\) |
−0.749666 | + | 0.661816i | \(0.769786\pi\) | |||||||
\(374\) | 0.232051 | − | 0.401924i | 0.0119991 | − | 0.0207830i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.46410 | −0.230218 | ||||||||
\(377\) | 0.928203 | − | 1.39230i | 0.0478049 | − | 0.0717073i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.3660 | + | 15.2224i | 1.35433 | + | 0.781924i | 0.988853 | − | 0.148896i | \(-0.0475719\pi\) |
0.365479 | + | 0.930820i | \(0.380905\pi\) | |||||||
\(380\) | −1.36603 | + | 2.36603i | −0.0700756 | + | 0.121375i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.12436i | 0.0575270i | ||||||||
\(383\) | −10.7942 | + | 6.23205i | −0.551559 | + | 0.318443i | −0.749751 | − | 0.661720i | \(-0.769827\pi\) |
0.198191 | + | 0.980163i | \(0.436493\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 4.73205i | − | 0.241168i | ||||||
\(386\) | 4.59808 | + | 7.96410i | 0.234036 | + | 0.405362i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.43782 | + | 0.830127i | 0.0729944 | + | 0.0421433i | ||||
\(389\) | −12.3923 | −0.628315 | −0.314157 | − | 0.949371i | \(-0.601722\pi\) | ||||
−0.314157 | + | 0.949371i | \(0.601722\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.928203 | 0.0469413 | ||||||||
\(392\) | −0.866025 | − | 0.500000i | −0.0437409 | − | 0.0252538i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.66987 | − | 8.08846i | −0.235265 | − | 0.407491i | ||||
\(395\) | − | 43.5167i | − | 2.18956i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.9904 | + | 10.9641i | −0.953100 | + | 0.550272i | −0.894043 | − | 0.447982i | \(-0.852143\pi\) |
−0.0590574 | + | 0.998255i | \(0.518809\pi\) | |||||||
\(398\) | 5.80385i | 0.290921i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.23205 | − | 2.13397i | 0.0616025 | − | 0.106699i | ||||
\(401\) | 2.41154 | + | 1.39230i | 0.120427 | + | 0.0695284i | 0.559003 | − | 0.829165i | \(-0.311184\pi\) |
−0.438577 | + | 0.898694i | \(0.644517\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.90192 | − | 29.4904i | 0.0947416 | − | 1.46902i | ||||
\(404\) | −16.9282 | −0.842210 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.232051 | + | 0.401924i | −0.0115165 | + | 0.0199471i | ||||
\(407\) | 2.83013 | + | 4.90192i | 0.140284 | + | 0.242979i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.5429 | − | 17.6340i | 1.51025 | − | 0.871944i | 0.510323 | − | 0.859983i | \(-0.329526\pi\) |
0.999928 | − | 0.0119609i | \(-0.00380738\pi\) | |||||||
\(410\) | −7.09808 | + | 4.09808i | −0.350549 | + | 0.202390i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.63397 | − | 9.75833i | −0.277566 | − | 0.480758i | ||||
\(413\) | 6.46410 | − | 11.1962i | 0.318078 | − | 0.550927i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.8564 | −1.36742 | ||||||||
\(416\) | −3.23205 | + | 1.59808i | −0.158464 | + | 0.0783521i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.50000 | − | 0.866025i | −0.0733674 | − | 0.0423587i | ||||
\(419\) | −1.36603 | + | 2.36603i | −0.0667347 | + | 0.115588i | −0.897462 | − | 0.441091i | \(-0.854591\pi\) |
0.830727 | + | 0.556679i | \(0.187925\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.60770i | − | 0.0783543i | −0.999232 | − | 0.0391771i | \(-0.987526\pi\) | ||
0.999232 | − | 0.0391771i | \(-0.0124737\pi\) | |||||||
\(422\) | 22.5167 | − | 13.0000i | 1.09609 | − | 0.632830i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.00000i | 0.339950i | ||||||||
\(425\) | 0.330127 | + | 0.571797i | 0.0160135 | + | 0.0277362i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.50000 | − | 2.59808i | −0.217770 | − | 0.125730i | ||||
\(428\) | −16.8564 | −0.814785 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.3923 | −0.886956 | ||||||||
\(431\) | −3.29423 | − | 1.90192i | −0.158677 | − | 0.0916124i | 0.418559 | − | 0.908190i | \(-0.362535\pi\) |
−0.577236 | + | 0.816577i | \(0.695869\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.4641 | − | 35.4449i | −0.983442 | − | 1.70337i | −0.648665 | − | 0.761074i | \(-0.724672\pi\) |
−0.334777 | − | 0.942297i | \(-0.608661\pi\) | |||||||
\(434\) | 8.19615i | 0.393428i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.09808 | − | 0.633975i | 0.0525883 | − | 0.0303619i | ||||
\(437\) | − | 3.46410i | − | 0.165710i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.5885 | − | 32.1962i | 0.887179 | − | 1.53664i | 0.0439826 | − | 0.999032i | \(-0.485995\pi\) |
0.843196 | − | 0.537606i | \(-0.180671\pi\) | |||||||
\(440\) | 4.09808 | + | 2.36603i | 0.195368 | + | 0.112796i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.0621778 | − | 0.964102i | 0.00295750 | − | 0.0458576i | ||||
\(443\) | −35.6410 | −1.69336 | −0.846678 | − | 0.532106i | \(-0.821401\pi\) | ||||
−0.846678 | + | 0.532106i | \(0.821401\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.83013 | + | 8.36603i | −0.228970 | + | 0.396588i | ||||
\(446\) | 1.80385 | + | 3.12436i | 0.0854147 | + | 0.147943i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.866025 | − | 0.500000i | 0.0409159 | − | 0.0236228i | ||||
\(449\) | −9.16987 | + | 5.29423i | −0.432753 | + | 0.249850i | −0.700519 | − | 0.713634i | \(-0.747048\pi\) |
0.267766 | + | 0.963484i | \(0.413715\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.59808 | − | 4.50000i | −0.122339 | − | 0.211897i | ||||
\(452\) | −9.36603 | + | 16.2224i | −0.440541 | + | 0.763039i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.39230 | 0.112276 | ||||||||
\(455\) | −4.36603 | − | 8.83013i | −0.204682 | − | 0.413963i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.7321 | + | 7.92820i | 0.642358 | + | 0.370866i | 0.785522 | − | 0.618833i | \(-0.212394\pi\) |
−0.143164 | + | 0.989699i | \(0.545728\pi\) | |||||||
\(458\) | 3.03590 | − | 5.25833i | 0.141858 | − | 0.245706i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.46410i | 0.441266i | ||||||||
\(461\) | −11.3205 | + | 6.53590i | −0.527249 | + | 0.304407i | −0.739895 | − | 0.672722i | \(-0.765125\pi\) |
0.212647 | + | 0.977129i | \(0.431792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.73205i | 0.452287i | 0.974094 | + | 0.226143i | \(0.0726118\pi\) | ||||
−0.974094 | + | 0.226143i | \(0.927388\pi\) | |||||||
\(464\) | −0.232051 | − | 0.401924i | −0.0107727 | − | 0.0186588i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.0981 | − | 7.56218i | −0.606757 | − | 0.350311i | ||||
\(467\) | 13.8564 | 0.641198 | 0.320599 | − | 0.947215i | \(-0.396116\pi\) | ||||
0.320599 | + | 0.947215i | \(0.396116\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.92820 | −0.227563 | ||||||||
\(470\) | 10.5622 | + | 6.09808i | 0.487197 | + | 0.281283i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.46410 | + | 11.1962i | 0.297534 | + | 0.515345i | ||||
\(473\) | − | 11.6603i | − | 0.536139i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.13397 | − | 1.23205i | 0.0979135 | − | 0.0565304i | ||||
\(476\) | 0.267949i | 0.0122814i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.36603 | + | 2.36603i | −0.0624805 | + | 0.108219i | ||||
\(479\) | −22.1147 | − | 12.7679i | −1.01045 | − | 0.583382i | −0.0991253 | − | 0.995075i | \(-0.531604\pi\) |
−0.911323 | + | 0.411692i | \(0.864938\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.80385 | + | 6.53590i | 0.447017 | + | 0.298011i | ||||
\(482\) | −8.00000 | −0.364390 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.00000 | − | 6.92820i | 0.181818 | − | 0.314918i | ||||
\(485\) | −2.26795 | − | 3.92820i | −0.102982 | − | 0.178371i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.571797 | + | 0.330127i | −0.0259106 | + | 0.0149595i | −0.512899 | − | 0.858449i | \(-0.671429\pi\) |
0.486989 | + | 0.873408i | \(0.338095\pi\) | |||||||
\(488\) | 4.50000 | − | 2.59808i | 0.203705 | − | 0.117609i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.36603 | + | 2.36603i | 0.0617107 | + | 0.106886i | ||||
\(491\) | −14.2679 | + | 24.7128i | −0.643904 | + | 1.11527i | 0.340650 | + | 0.940190i | \(0.389353\pi\) |
−0.984554 | + | 0.175083i | \(0.943980\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.124356 | 0.00560070 | ||||||||
\(494\) | −3.59808 | − | 0.232051i | −0.161885 | − | 0.0104405i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.09808 | − | 4.09808i | −0.318713 | − | 0.184009i | ||||
\(497\) | −4.09808 | + | 7.09808i | −0.183824 | + | 0.318392i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 33.5167i | − | 1.50041i | −0.661204 | − | 0.750206i | \(-0.729954\pi\) | ||
0.661204 | − | 0.750206i | \(-0.270046\pi\) | |||||||
\(500\) | 6.00000 | − | 3.46410i | 0.268328 | − | 0.154919i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 11.1244i | − | 0.496504i | ||||||
\(503\) | −3.46410 | − | 6.00000i | −0.154457 | − | 0.267527i | 0.778404 | − | 0.627763i | \(-0.216029\pi\) |
−0.932861 | + | 0.360236i | \(0.882696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 40.0526 | + | 23.1244i | 1.78232 | + | 1.02902i | ||||
\(506\) | −6.00000 | −0.266733 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.53590 | −0.378719 | ||||||||
\(509\) | −34.3468 | − | 19.8301i | −1.52239 | − | 0.878955i | −0.999650 | − | 0.0264657i | \(-0.991575\pi\) |
−0.522745 | − | 0.852489i | \(-0.675092\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.732051 | + | 1.26795i | 0.0323840 | + | 0.0560908i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.89230 | − | 1.66987i | 0.127574 | − | 0.0736549i | ||||
\(515\) | 30.7846i | 1.35653i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.86603 | + | 6.69615i | −0.170028 | + | 0.294496i | ||||
\(518\) | −2.83013 | − | 1.63397i | −0.124349 | − | 0.0717927i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.83013 | + | 0.633975i | 0.431080 | + | 0.0278016i | ||||
\(521\) | 31.0526 | 1.36044 | 0.680219 | − | 0.733009i | \(-0.261885\pi\) | ||||
0.680219 | + | 0.733009i | \(0.261885\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.0622 | − | 33.0167i | 0.833531 | − | 1.44372i | −0.0616902 | − | 0.998095i | \(-0.519649\pi\) |
0.895221 | − | 0.445622i | \(-0.147018\pi\) | |||||||
\(524\) | −6.92820 | − | 12.0000i | −0.302660 | − | 0.524222i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.90192 | + | 4.56218i | −0.344540 | + | 0.198920i | ||||
\(527\) | 1.90192 | − | 1.09808i | 0.0828491 | − | 0.0478330i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.50000 | + | 9.52628i | 0.239130 | + | 0.414186i | ||||
\(530\) | 9.56218 | − | 16.5622i | 0.415354 | − | 0.719415i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.00000 | 0.0433555 | ||||||||
\(533\) | −9.00000 | − | 6.00000i | −0.389833 | − | 0.259889i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39.8827 | + | 23.0263i | 1.72428 | + | 0.995513i | ||||
\(536\) | 2.46410 | − | 4.26795i | 0.106433 | − | 0.184347i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 17.8564i | − | 0.769844i | ||||||
\(539\) | −1.50000 | + | 0.866025i | −0.0646096 | + | 0.0373024i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.6603i | 1.79111i | 0.444947 | + | 0.895557i | \(0.353223\pi\) | ||||
−0.444947 | + | 0.895557i | \(0.646777\pi\) | |||||||
\(542\) | 5.02628 | + | 8.70577i | 0.215897 | + | 0.373945i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.232051 | − | 0.133975i | −0.00994910 | − | 0.00574411i | ||||
\(545\) | −3.46410 | −0.148386 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.73205 | −0.202328 | −0.101164 | − | 0.994870i | \(-0.532257\pi\) | ||||
−0.101164 | + | 0.994870i | \(0.532257\pi\) | |||||||
\(548\) | −5.53590 | − | 3.19615i | −0.236482 | − | 0.136533i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.13397 | − | 3.69615i | −0.0909930 | − | 0.157604i | ||||
\(551\) | − | 0.464102i | − | 0.0197714i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.7942 | + | 7.96410i | −0.586590 | + | 0.338668i | ||||
\(554\) | 25.3205i | 1.07577i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.79423 | + | 16.9641i | −0.415368 | + | 0.719438i | ||||
\(557\) | −21.6962 | − | 12.5263i | −0.919295 | − | 0.530755i | −0.0358852 | − | 0.999356i | \(-0.511425\pi\) |
−0.883410 | + | 0.468600i | \(0.844758\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.7583 | − | 21.7583i | −0.455029 | − | 0.920279i | ||||
\(560\) | −2.73205 | −0.115450 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.83013 | + | 15.2942i | −0.372476 | + | 0.645148i | ||||
\(563\) | 12.9019 | + | 22.3468i | 0.543751 | + | 0.941805i | 0.998684 | + | 0.0512792i | \(0.0163298\pi\) |
−0.454933 | + | 0.890526i | \(0.650337\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 44.3205 | − | 25.5885i | 1.86458 | − | 1.07651i | ||||
\(566\) | −15.4641 | + | 8.92820i | −0.650005 | + | 0.375280i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.09808 | − | 7.09808i | −0.171951 | − | 0.297829i | ||||
\(569\) | −10.2224 | + | 17.7058i | −0.428547 | + | 0.742265i | −0.996744 | − | 0.0806276i | \(-0.974308\pi\) |
0.568198 | + | 0.822892i | \(0.307641\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.9808 | 1.46390 | 0.731950 | − | 0.681359i | \(-0.238611\pi\) | ||||
0.731950 | + | 0.681359i | \(0.238611\pi\) | |||||||
\(572\) | −0.401924 | + | 6.23205i | −0.0168053 | + | 0.260575i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.59808 | + | 1.50000i | 0.108442 | + | 0.0626088i | ||||
\(575\) | 4.26795 | − | 7.39230i | 0.177986 | − | 0.308280i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.6603i | 1.15151i | 0.817622 | + | 0.575756i | \(0.195292\pi\) | ||||
−0.817622 | + | 0.575756i | \(0.804708\pi\) | |||||||
\(578\) | −14.6603 | + | 8.46410i | −0.609786 | + | 0.352060i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.26795i | 0.0526487i | ||||||||
\(581\) | 5.09808 | + | 8.83013i | 0.211504 | + | 0.366335i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.5000 | + | 6.06218i | 0.434866 | + | 0.251070i | ||||
\(584\) | −1.46410 | −0.0605850 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.9282 | 1.27763 | ||||||||
\(587\) | 25.6865 | + | 14.8301i | 1.06020 | + | 0.612105i | 0.925487 | − | 0.378780i | \(-0.123656\pi\) |
0.134710 | + | 0.990885i | \(0.456990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.09808 | − | 7.09808i | −0.168858 | − | 0.292471i | ||||
\(590\) | − | 35.3205i | − | 1.45412i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.83013 | − | 1.63397i | 0.116318 | − | 0.0671559i | ||||
\(593\) | − | 6.46410i | − | 0.265449i | −0.991153 | − | 0.132724i | \(-0.957627\pi\) | ||
0.991153 | − | 0.132724i | \(-0.0423725\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.366025 | − | 0.633975i | 0.0150056 | − | 0.0259904i | ||||
\(596\) | −12.0000 | − | 6.92820i | −0.491539 | − | 0.283790i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.1962 | + | 5.53590i | −0.457845 | + | 0.226380i | ||||
\(599\) | −40.6410 | −1.66055 | −0.830273 | − | 0.557356i | \(-0.811816\pi\) | ||||
−0.830273 | + | 0.557356i | \(0.811816\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.63397 | − | 16.6865i | 0.392978 | − | 0.680658i | −0.599863 | − | 0.800103i | \(-0.704778\pi\) |
0.992841 | + | 0.119445i | \(0.0381115\pi\) | |||||||
\(602\) | 3.36603 | + | 5.83013i | 0.137189 | + | 0.237618i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.50000 | + | 2.59808i | −0.183102 | + | 0.105714i | ||||
\(605\) | −18.9282 | + | 10.9282i | −0.769541 | + | 0.444295i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.75833 | − | 11.7058i | −0.274312 | − | 0.475123i | 0.695649 | − | 0.718382i | \(-0.255117\pi\) |
−0.969961 | + | 0.243259i | \(0.921783\pi\) | |||||||
\(608\) | −0.500000 | + | 0.866025i | −0.0202777 | + | 0.0351220i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.1962 | −0.574785 | ||||||||
\(611\) | −1.03590 | + | 16.0622i | −0.0419080 | + | 0.649806i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.46410 | − | 2.00000i | −0.139914 | − | 0.0807792i | 0.428409 | − | 0.903585i | \(-0.359074\pi\) |
−0.568323 | + | 0.822806i | \(0.692408\pi\) | |||||||
\(614\) | −14.6962 | + | 25.4545i | −0.593088 | + | 1.02726i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 1.73205i | − | 0.0697863i | ||||||
\(617\) | −7.09808 | + | 4.09808i | −0.285758 | + | 0.164982i | −0.636027 | − | 0.771667i | \(-0.719423\pi\) |
0.350269 | + | 0.936649i | \(0.386090\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 35.9282i | − | 1.44408i | −0.691853 | − | 0.722038i | \(-0.743205\pi\) | ||
0.691853 | − | 0.722038i | \(-0.256795\pi\) | |||||||
\(620\) | 11.1962 | + | 19.3923i | 0.449648 | + | 0.778814i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.69615 | − | 3.86603i | −0.268491 | − | 0.155013i | ||||
\(623\) | 3.53590 | 0.141663 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2487 | −1.24995 | ||||||||
\(626\) | 27.2942 | + | 15.7583i | 1.09090 | + | 0.629830i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.73205 | − | 6.46410i | −0.148925 | − | 0.257946i | ||||
\(629\) | 0.875644i | 0.0349142i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.5526 | + | 13.5981i | −0.937613 | + | 0.541331i | −0.889211 | − | 0.457497i | \(-0.848746\pi\) |
−0.0484014 | + | 0.998828i | \(0.515413\pi\) | |||||||
\(632\) | − | 15.9282i | − | 0.633590i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.92820 | + | 13.7321i | −0.314869 | + | 0.545369i | ||||
\(635\) | 20.1962 | + | 11.6603i | 0.801460 | + | 0.462723i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.00000 | + | 3.00000i | −0.0792429 | + | 0.118864i | ||||
\(638\) | −0.803848 | −0.0318246 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.36603 | − | 2.36603i | 0.0539969 | − | 0.0935254i | ||||
\(641\) | 15.5885 | + | 27.0000i | 0.615707 | + | 1.06644i | 0.990260 | + | 0.139230i | \(0.0444629\pi\) |
−0.374553 | + | 0.927206i | \(0.622204\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.45448 | + | 2.57180i | −0.175668 | + | 0.101422i | −0.585256 | − | 0.810849i | \(-0.699006\pi\) |
0.409588 | + | 0.912271i | \(0.365672\pi\) | |||||||
\(644\) | 3.00000 | − | 1.73205i | 0.118217 | − | 0.0682524i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.133975 | − | 0.232051i | −0.00527116 | − | 0.00912992i | ||||
\(647\) | 21.9186 | − | 37.9641i | 0.861708 | − | 1.49252i | −0.00857027 | − | 0.999963i | \(-0.502728\pi\) |
0.870279 | − | 0.492560i | \(-0.163939\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.3923 | 0.878975 | ||||||||
\(650\) | −7.39230 | − | 4.92820i | −0.289950 | − | 0.193300i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.633975 | + | 0.366025i | 0.0248284 | + | 0.0143347i | ||||
\(653\) | −4.35641 | + | 7.54552i | −0.170479 | + | 0.295279i | −0.938588 | − | 0.345041i | \(-0.887865\pi\) |
0.768108 | + | 0.640320i | \(0.221198\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37.8564i | 1.47917i | ||||||||
\(656\) | −2.59808 | + | 1.50000i | −0.101438 | + | 0.0585652i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 4.46410i | − | 0.174029i | ||||||
\(659\) | 19.6962 | + | 34.1147i | 0.767253 | + | 1.32892i | 0.939047 | + | 0.343789i | \(0.111710\pi\) |
−0.171794 | + | 0.985133i | \(0.554956\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.26795 | + | 4.19615i | 0.282690 | + | 0.163211i | 0.634641 | − | 0.772807i | \(-0.281148\pi\) |
−0.351950 | + | 0.936019i | \(0.614481\pi\) | |||||||
\(662\) | 0.143594 | 0.00558092 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.1962 | −0.395687 | ||||||||
\(665\) | −2.36603 | − | 1.36603i | −0.0917505 | − | 0.0529722i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.803848 | − | 1.39230i | −0.0311251 | − | 0.0539103i | ||||
\(668\) | 13.8564i | 0.536120i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.6603 | + | 6.73205i | −0.450475 | + | 0.260082i | ||||
\(671\) | − | 9.00000i | − | 0.347441i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.3564 | − | 19.6699i | 0.437757 | − | 0.758218i | −0.559759 | − | 0.828656i | \(-0.689106\pi\) |
0.997516 | + | 0.0704376i | \(0.0224396\pi\) | |||||||
\(674\) | 16.4545 | + | 9.50000i | 0.633803 | + | 0.365926i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.00000 | + | 12.0000i | 0.192308 | + | 0.461538i | ||||
\(677\) | −33.2679 | −1.27859 | −0.639296 | − | 0.768961i | \(-0.720774\pi\) | ||||
−0.639296 | + | 0.768961i | \(0.720774\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.830127 | + | 1.43782i | −0.0318574 | + | 0.0551786i | ||||
\(680\) | 0.366025 | + | 0.633975i | 0.0140364 | + | 0.0243118i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.2942 | + | 7.09808i | −0.470770 | + | 0.271799i | ||||
\(683\) | 43.6410 | − | 25.1962i | 1.66988 | − | 0.964104i | 0.702176 | − | 0.712003i | \(-0.252212\pi\) |
0.967701 | − | 0.252101i | \(-0.0811214\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.73205 | + | 15.1244i | 0.333635 | + | 0.577872i | ||||
\(686\) | 0.500000 | − | 0.866025i | 0.0190901 | − | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.73205 | −0.256657 | ||||||||
\(689\) | 25.1865 | + | 1.62436i | 0.959531 | + | 0.0618830i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.1436 | + | 5.85641i | 0.385880 | + | 0.222788i | 0.680374 | − | 0.732865i | \(-0.261817\pi\) |
−0.294493 | + | 0.955654i | \(0.595151\pi\) | |||||||
\(692\) | 7.56218 | − | 13.0981i | 0.287471 | − | 0.497914i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.3923i | 0.584284i | ||||||||
\(695\) | 46.3468 | − | 26.7583i | 1.75803 | − | 1.01500i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 0.803848i | − | 0.0304479i | ||||||
\(698\) | 15.8564 | + | 27.4641i | 0.600174 | + | 1.03953i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.13397 | + | 1.23205i | 0.0806567 | + | 0.0465671i | ||||
\(701\) | 28.8564 | 1.08989 | 0.544946 | − | 0.838471i | \(-0.316550\pi\) | ||||
0.544946 | + | 0.838471i | \(0.316550\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.26795 | 0.123253 | ||||||||
\(704\) | 1.50000 | + | 0.866025i | 0.0565334 | + | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.26795 | + | 2.19615i | 0.0477199 | + | 0.0826533i | ||||
\(707\) | − | 16.9282i | − | 0.636651i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.24167 | + | 3.02628i | −0.196855 | + | 0.113654i | −0.595188 | − | 0.803587i | \(-0.702922\pi\) |
0.398333 | + | 0.917241i | \(0.369589\pi\) | |||||||
\(710\) | 22.3923i | 0.840368i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.76795 | + | 3.06218i | −0.0662567 | + | 0.114760i | ||||
\(713\) | −24.5885 | − | 14.1962i | −0.920845 | − | 0.531650i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.46410 | − | 14.1962i | 0.353937 | − | 0.530906i | ||||
\(716\) | −4.53590 | −0.169514 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.09808 | + | 12.2942i | −0.264898 | + | 0.458817i | ||||
\(719\) | 9.25833 | + | 16.0359i | 0.345277 | + | 0.598038i | 0.985404 | − | 0.170231i | \(-0.0544515\pi\) |
−0.640127 | + | 0.768269i | \(0.721118\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.75833 | − | 5.63397i | 0.363419 | − | 0.209820i | ||||
\(722\) | 15.5885 | − | 9.00000i | 0.580142 | − | 0.334945i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.33013 | − | 12.6962i | −0.272422 | − | 0.471849i | ||||
\(725\) | 0.571797 | − | 0.990381i | 0.0212360 | − | 0.0367818i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.3205 | −0.568206 | −0.284103 | − | 0.958794i | \(-0.591696\pi\) | ||||
−0.284103 | + | 0.958794i | \(0.591696\pi\) | |||||||
\(728\) | −1.59808 | − | 3.23205i | −0.0592286 | − | 0.119788i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.46410 | + | 2.00000i | 0.128212 | + | 0.0740233i | ||||
\(731\) | 0.901924 | − | 1.56218i | 0.0333589 | − | 0.0577792i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 14.1769i | − | 0.523636i | −0.965117 | − | 0.261818i | \(-0.915678\pi\) | ||
0.965117 | − | 0.261818i | \(-0.0843221\pi\) | |||||||
\(734\) | −8.07180 | + | 4.66025i | −0.297935 | + | 0.172013i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.46410i | 0.127688i | ||||||||
\(737\) | −4.26795 | − | 7.39230i | −0.157212 | − | 0.272299i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.8564 | + | 23.5885i | 1.50293 | + | 0.867715i | 0.999994 | + | 0.00339000i | \(0.00107907\pi\) |
0.502933 | + | 0.864325i | \(0.332254\pi\) | |||||||
\(740\) | −8.92820 | −0.328207 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.00000 | −0.256978 | ||||||||
\(743\) | 20.8301 | + | 12.0263i | 0.764183 | + | 0.441201i | 0.830796 | − | 0.556578i | \(-0.187886\pi\) |
−0.0666124 | + | 0.997779i | \(0.521219\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.9282 | + | 32.7846i | 0.693476 | + | 1.20114i | ||||
\(746\) | − | 7.66025i | − | 0.280462i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.401924 | + | 0.232051i | −0.0146958 | + | 0.00848462i | ||||
\(749\) | − | 16.8564i | − | 0.615920i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.4282 | + | 40.5788i | −0.854907 | + | 1.48074i | 0.0218237 | + | 0.999762i | \(0.493053\pi\) |
−0.876731 | + | 0.480981i | \(0.840281\pi\) | |||||||
\(752\) | 3.86603 | + | 2.23205i | 0.140979 | + | 0.0813945i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.50000 | + | 0.741670i | −0.0546268 | + | 0.0270100i | ||||
\(755\) | 14.1962 | 0.516651 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.2942 | + | 26.4904i | −0.555878 | + | 0.962809i | 0.441956 | + | 0.897037i | \(0.354285\pi\) |
−0.997835 | + | 0.0657728i | \(0.979049\pi\) | |||||||
\(758\) | −15.2224 | − | 26.3660i | −0.552904 | − | 0.957657i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.36603 | − | 1.36603i | 0.0858248 | − | 0.0495509i | ||||
\(761\) | −16.7321 | + | 9.66025i | −0.606536 | + | 0.350184i | −0.771609 | − | 0.636098i | \(-0.780548\pi\) |
0.165072 | + | 0.986281i | \(0.447214\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.633975 | + | 1.09808i | 0.0229514 | + | 0.0397530i | ||||
\(764\) | 0.562178 | − | 0.973721i | 0.0203389 | − | 0.0352280i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.4641 | 0.450346 | ||||||||
\(767\) | 41.7846 | − | 20.6603i | 1.50875 | − | 0.745999i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.3660 | + | 22.1506i | 1.38351 | + | 0.798772i | 0.992574 | − | 0.121644i | \(-0.0388165\pi\) |
0.390940 | + | 0.920416i | \(0.372150\pi\) | |||||||
\(770\) | −2.36603 | + | 4.09808i | −0.0852656 | + | 0.147684i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 9.19615i | − | 0.330977i | ||||||
\(773\) | 13.1436 | − | 7.58846i | 0.472742 | − | 0.272938i | −0.244645 | − | 0.969613i | \(-0.578671\pi\) |
0.717387 | + | 0.696675i | \(0.245338\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 20.1962i | − | 0.725467i | ||||||
\(776\) | −0.830127 | − | 1.43782i | −0.0297998 | − | 0.0516148i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.7321 | + | 6.19615i | 0.384763 | + | 0.222143i | ||||
\(779\) | −3.00000 | −0.107486 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.1962 | −0.507978 | ||||||||
\(782\) | −0.803848 | − | 0.464102i | −0.0287455 | − | 0.0165962i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.500000 | + | 0.866025i | 0.0178571 | + | 0.0309295i | ||||
\(785\) | 20.3923i | 0.727833i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.1865 | + | 19.1603i | −1.18297 | + | 0.682989i | −0.956700 | − | 0.291075i | \(-0.905987\pi\) |
−0.226272 | + | 0.974064i | \(0.572654\pi\) | |||||||
\(788\) | 9.33975i | 0.332715i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −21.7583 | + | 37.6865i | −0.774127 | + | 1.34083i | ||||
\(791\) | −16.2224 | − | 9.36603i | −0.576803 | − | 0.333018i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.30385 | − | 16.7942i | −0.294878 | − | 0.596381i | ||||
\(794\) | 21.9282 | 0.778203 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.90192 | − | 5.02628i | 0.102856 | − | 0.178152i | ||||
\(797\) | 13.5622 | + | 23.4904i | 0.480397 | + | 0.832072i | 0.999747 | − | 0.0224896i | \(-0.00715926\pi\) |
−0.519350 | + | 0.854562i | \(0.673826\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.03590 | + | 0.598076i | −0.0366475 | + | 0.0211584i | ||||
\(800\) | −2.13397 | + | 1.23205i | −0.0754474 | + | 0.0435596i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.39230 | − | 2.41154i | −0.0491640 | − | 0.0851545i | ||||
\(803\) | −1.26795 | + | 2.19615i | −0.0447450 | + | 0.0775005i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.46410 | −0.333566 | ||||||||
\(806\) | −16.3923 | + | 24.5885i | −0.577394 | + | 0.866091i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14.6603 | + | 8.46410i | 0.515746 | + | 0.297766i | ||||
\(809\) | 26.2224 | − | 45.4186i | 0.921932 | − | 1.59683i | 0.125509 | − | 0.992093i | \(-0.459944\pi\) |
0.796423 | − | 0.604740i | \(-0.206723\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.4641i | 1.10485i | 0.833561 | + | 0.552427i | \(0.186298\pi\) | ||||
−0.833561 | + | 0.552427i | \(0.813702\pi\) | |||||||
\(812\) | 0.401924 | − | 0.232051i | 0.0141048 | − | 0.00814339i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 5.66025i | − | 0.198392i | ||||||
\(815\) | −1.00000 | − | 1.73205i | −0.0350285 | − | 0.0606711i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.83013 | − | 3.36603i | −0.203970 | − | 0.117762i | ||||
\(818\) | −35.2679 | −1.23311 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.19615 | 0.286222 | ||||||||
\(821\) | 24.1077 | + | 13.9186i | 0.841364 | + | 0.485762i | 0.857728 | − | 0.514104i | \(-0.171876\pi\) |
−0.0163634 | + | 0.999866i | \(0.505209\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.3923 | + | 30.1244i | 0.606258 | + | 1.05007i | 0.991851 | + | 0.127400i | \(0.0406633\pi\) |
−0.385594 | + | 0.922669i | \(0.626003\pi\) | |||||||
\(824\) | 11.2679i | 0.392538i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.1962 | + | 6.46410i | −0.389564 | + | 0.224915i | ||||
\(827\) | 27.3205i | 0.950027i | 0.879978 | + | 0.475014i | \(0.157557\pi\) | ||||
−0.879978 | + | 0.475014i | \(0.842443\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.3301 | + | 30.0167i | −0.601900 | + | 1.04252i | 0.390633 | + | 0.920547i | \(0.372256\pi\) |
−0.992533 | + | 0.121975i | \(0.961077\pi\) | |||||||
\(830\) | 24.1244 | + | 13.9282i | 0.837369 | + | 0.483455i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.59808 | + | 0.232051i | 0.124741 | + | 0.00804491i | ||||
\(833\) | −0.267949 | −0.00928389 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.9282 | − | 32.7846i | 0.655037 | − | 1.13456i | ||||
\(836\) | 0.866025 | + | 1.50000i | 0.0299521 | + | 0.0518786i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.36603 | − | 1.36603i | 0.0817330 | − | 0.0471886i | ||||
\(839\) | 36.4641 | − | 21.0526i | 1.25888 | − | 0.726815i | 0.286024 | − | 0.958223i | \(-0.407666\pi\) |
0.972857 | + | 0.231408i | \(0.0743331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.3923 | + | 24.9282i | 0.496286 | + | 0.859593i | ||||
\(842\) | −0.803848 | + | 1.39230i | −0.0277024 | + | 0.0479820i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −26.0000 | −0.894957 | ||||||||
\(845\) | 4.56218 | − | 35.2224i | 0.156944 | − | 1.21169i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.92820 | + | 4.00000i | 0.238056 | + | 0.137442i | ||||
\(848\) | 3.50000 | − | 6.06218i | 0.120190 | − | 0.208176i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 0.660254i | − | 0.0226465i | ||||||
\(851\) | 9.80385 | − | 5.66025i | 0.336072 | − | 0.194031i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 5.92820i | − | 0.202978i | −0.994837 | − | 0.101489i | \(-0.967639\pi\) | ||
0.994837 | − | 0.101489i | \(-0.0323606\pi\) | |||||||
\(854\) | 2.59808 | + | 4.50000i | 0.0889043 | + | 0.153987i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.5981 | + | 8.42820i | 0.498952 | + | 0.288070i | ||||
\(857\) | −39.4641 | −1.34807 | −0.674034 | − | 0.738700i | \(-0.735440\pi\) | ||||
−0.674034 | + | 0.738700i | \(0.735440\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −50.7654 | −1.73209 | −0.866046 | − | 0.499964i | \(-0.833346\pi\) | ||||
−0.866046 | + | 0.499964i | \(0.833346\pi\) | |||||||
\(860\) | 15.9282 | + | 9.19615i | 0.543147 | + | 0.313586i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.90192 | + | 3.29423i | 0.0647798 | + | 0.112202i | ||||
\(863\) | 16.9282i | 0.576243i | 0.957594 | + | 0.288121i | \(0.0930307\pi\) | ||||
−0.957594 | + | 0.288121i | \(0.906969\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.7846 | + | 20.6603i | −1.21671 | + | 0.702470i | ||||
\(866\) | 40.9282i | 1.39080i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.09808 | − | 7.09808i | 0.139098 | − | 0.240924i | ||||
\(869\) | −23.8923 | − | 13.7942i | −0.810491 | − | 0.467937i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.7846 | − | 9.85641i | −0.500957 | − | 0.333972i | ||||
\(872\) | −1.26795 | −0.0429382 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.73205 | + | 3.00000i | −0.0585875 | + | 0.101477i | ||||
\(875\) | 3.46410 | + | 6.00000i | 0.117108 | + | 0.202837i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.1506 | + | 13.3660i | −0.781741 | + | 0.451339i | −0.837047 | − | 0.547131i | \(-0.815720\pi\) |
0.0553057 | + | 0.998469i | \(0.482387\pi\) | |||||||
\(878\) | −32.1962 | + | 18.5885i | −1.08657 | + | 0.627330i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.36603 | − | 4.09808i | −0.0797587 | − | 0.138146i | ||||
\(881\) | −4.53590 | + | 7.85641i | −0.152818 | + | 0.264689i | −0.932262 | − | 0.361783i | \(-0.882168\pi\) |
0.779444 | + | 0.626472i | \(0.215502\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.0526 | −1.01135 | −0.505675 | − | 0.862724i | \(-0.668756\pi\) | ||||
−0.505675 | + | 0.862724i | \(0.668756\pi\) | |||||||
\(884\) | −0.535898 | + | 0.803848i | −0.0180242 | + | 0.0270363i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.8660 | + | 17.8205i | 1.03696 | + | 0.598692i | ||||
\(887\) | 21.7224 | − | 37.6244i | 0.729368 | − | 1.26330i | −0.227783 | − | 0.973712i | \(-0.573148\pi\) |
0.957151 | − | 0.289590i | \(-0.0935190\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 8.53590i | − | 0.286285i | ||||||
\(890\) | 8.36603 | − | 4.83013i | 0.280430 | − | 0.161906i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 3.60770i | − | 0.120795i | ||||||
\(893\) | 2.23205 | + | 3.86603i | 0.0746927 | + | 0.129372i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.7321 | + | 6.19615i | 0.358733 | + | 0.207115i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.5885 | 0.353341 | ||||||||
\(899\) | −3.29423 | − | 1.90192i | −0.109869 | − | 0.0634327i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.937822 | + | 1.62436i | 0.0312434 | + | 0.0541151i | ||||
\(902\) | 5.19615i | 0.173013i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.2224 | − | 9.36603i | 0.539550 | − | 0.311509i | ||||
\(905\) | 40.0526i | 1.33139i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.1962 | + | 19.3923i | −0.371762 | + | 0.643911i | −0.989837 | − | 0.142209i | \(-0.954580\pi\) |
0.618075 | + | 0.786119i | \(0.287913\pi\) | |||||||
\(908\) | −2.07180 | − | 1.19615i | −0.0687550 | − | 0.0396957i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.633975 | + | 9.83013i | −0.0210161 | + | 0.325866i | ||||
\(911\) | −28.8372 | −0.955418 | −0.477709 | − | 0.878518i | \(-0.658533\pi\) | ||||
−0.477709 | + | 0.878518i | \(0.658533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.83013 | + | 15.2942i | −0.292235 | + | 0.506165i | ||||
\(914\) | −7.92820 | − | 13.7321i | −0.262242 | − | 0.454216i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.25833 | + | 3.03590i | −0.173740 | + | 0.100309i | ||||
\(917\) | 12.0000 | − | 6.92820i | 0.396275 | − | 0.228789i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.57180 | − | 4.45448i | −0.0848357 | − | 0.146940i | 0.820485 | − | 0.571667i | \(-0.193703\pi\) |
−0.905321 | + | 0.424728i | \(0.860370\pi\) | |||||||
\(920\) | 4.73205 | − | 8.19615i | 0.156011 | − | 0.270219i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.0718 | 0.430497 | ||||||||
\(923\) | −26.4904 | + | 13.0981i | −0.871942 | + | 0.431128i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.97372 | + | 4.02628i | 0.229295 | + | 0.132383i | ||||
\(926\) | 4.86603 | − | 8.42820i | 0.159908 | − | 0.276968i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.464102i | 0.0152349i | ||||||||
\(929\) | −27.9904 | + | 16.1603i | −0.918335 | + | 0.530201i | −0.883103 | − | 0.469178i | \(-0.844550\pi\) |
−0.0352312 | + | 0.999379i | \(0.511217\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000i | 0.0327737i | ||||||||
\(932\) | 7.56218 | + | 13.0981i | 0.247707 | + | 0.429042i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.0000 | − | 6.92820i | −0.392652 | − | 0.226698i | ||||
\(935\) | 1.26795 | 0.0414664 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.9282 | 0.487683 | 0.243842 | − | 0.969815i | \(-0.421592\pi\) | ||||
0.243842 | + | 0.969815i | \(0.421592\pi\) | |||||||
\(938\) | 4.26795 | + | 2.46410i | 0.139353 | + | 0.0804558i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.09808 | − | 10.5622i | −0.198897 | − | 0.344500i | ||||
\(941\) | − | 32.3923i | − | 1.05596i | −0.849257 | − | 0.527979i | \(-0.822950\pi\) | ||
0.849257 | − | 0.527979i | \(-0.177050\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.00000 | + | 5.19615i | −0.293080 | + | 0.169210i | ||||
\(944\) | − | 12.9282i | − | 0.420777i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.83013 | + | 10.0981i | −0.189554 | + | 0.328317i | ||||
\(947\) | 10.8397 | + | 6.25833i | 0.352244 | + | 0.203368i | 0.665673 | − | 0.746243i | \(-0.268144\pi\) |
−0.313429 | + | 0.949612i | \(0.601478\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.339746 | + | 5.26795i | −0.0110286 | + | 0.171005i | ||||
\(950\) | −2.46410 | −0.0799460 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.133975 | − | 0.232051i | 0.00434214 | − | 0.00752081i | ||||
\(953\) | −11.9019 | − | 20.6147i | −0.385541 | − | 0.667777i | 0.606303 | − | 0.795234i | \(-0.292652\pi\) |
−0.991844 | + | 0.127457i | \(0.959319\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.66025 | + | 1.53590i | −0.0860838 | + | 0.0497005i | ||||
\(956\) | 2.36603 | − | 1.36603i | 0.0765227 | − | 0.0441804i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.7679 | + | 22.1147i | 0.412514 | + | 0.714495i | ||||
\(959\) | 3.19615 | − | 5.53590i | 0.103209 | − | 0.178763i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −36.1769 | −1.16700 | ||||||||
\(962\) | −5.22243 | − | 10.5622i | −0.168378 | − | 0.340538i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.92820 | + | 4.00000i | 0.223142 | + | 0.128831i | ||||
\(965\) | −12.5622 | + | 21.7583i | −0.404391 | + | 0.700425i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 55.7128i | − | 1.79160i | −0.444454 | − | 0.895802i | \(-0.646602\pi\) | ||
0.444454 | − | 0.895802i | \(-0.353398\pi\) | |||||||
\(968\) | −6.92820 | + | 4.00000i | −0.222681 | + | 0.128565i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.53590i | 0.145639i | ||||||||
\(971\) | 11.0526 | + | 19.1436i | 0.354693 | + | 0.614347i | 0.987065 | − | 0.160318i | \(-0.0512519\pi\) |
−0.632372 | + | 0.774665i | \(0.717919\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.9641 | − | 9.79423i | −0.543844 | − | 0.313989i | ||||
\(974\) | 0.660254 | 0.0211559 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.19615 | −0.166325 | ||||||||
\(977\) | 3.80385 | + | 2.19615i | 0.121696 | + | 0.0702611i | 0.559612 | − | 0.828755i | \(-0.310950\pi\) |
−0.437916 | + | 0.899016i | \(0.644283\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.06218 | + | 5.30385i | 0.0978676 | + | 0.169512i | ||||
\(980\) | − | 2.73205i | − | 0.0872722i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 24.7128 | − | 14.2679i | 0.788618 | − | 0.455309i | ||||
\(983\) | − | 8.14359i | − | 0.259740i | −0.991531 | − | 0.129870i | \(-0.958544\pi\) | ||
0.991531 | − | 0.129870i | \(-0.0414560\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.7583 | − | 22.0981i | 0.406514 | − | 0.704103i | ||||
\(986\) | −0.107695 | − | 0.0621778i | −0.00342971 | − | 0.00198015i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.00000 | + | 2.00000i | 0.0954427 | + | 0.0636285i | ||||
\(989\) | −23.3205 | −0.741549 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.37564 | − | 9.31089i | 0.170763 | − | 0.295770i | −0.767924 | − | 0.640541i | \(-0.778710\pi\) |
0.938687 | + | 0.344771i | \(0.112043\pi\) | |||||||
\(992\) | 4.09808 | + | 7.09808i | 0.130114 | + | 0.225364i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.09808 | − | 4.09808i | 0.225137 | − | 0.129983i | ||||
\(995\) | −13.7321 | + | 7.92820i | −0.435335 | + | 0.251341i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.52628 | − | 14.7679i | −0.270030 | − | 0.467706i | 0.698839 | − | 0.715279i | \(-0.253700\pi\) |
−0.968869 | + | 0.247573i | \(0.920367\pi\) | |||||||
\(998\) | −16.7583 | + | 29.0263i | −0.530476 | + | 0.918811i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1638.2.bj.b.1135.1 | 4 | ||
3.2 | odd | 2 | 546.2.s.a.43.2 | ✓ | 4 | ||
13.10 | even | 6 | inner | 1638.2.bj.b.127.1 | 4 | ||
39.20 | even | 12 | 7098.2.a.bx.1.1 | 2 | |||
39.23 | odd | 6 | 546.2.s.a.127.2 | yes | 4 | ||
39.32 | even | 12 | 7098.2.a.bp.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.s.a.43.2 | ✓ | 4 | 3.2 | odd | 2 | ||
546.2.s.a.127.2 | yes | 4 | 39.23 | odd | 6 | ||
1638.2.bj.b.127.1 | 4 | 13.10 | even | 6 | inner | ||
1638.2.bj.b.1135.1 | 4 | 1.1 | even | 1 | trivial | ||
7098.2.a.bp.1.2 | 2 | 39.32 | even | 12 | |||
7098.2.a.bx.1.1 | 2 | 39.20 | even | 12 |