Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1274,2,Mod(79,1274)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1274, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1274.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1274 = 2 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1274.f (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.1729412175\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 182) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1145.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1274.1145 |
Dual form | 1274.2.f.i.79.1 |
$q$-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 \(\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(885\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | −0.684819 | − | 0.728714i | \(-0.740119\pi\) |
0.973494 | + | 0.228714i | \(0.0734519\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | − | 2.59808i | 0.452267 | − | 0.783349i | −0.546259 | − | 0.837616i | \(-0.683949\pi\) |
0.998526 | + | 0.0542666i | \(0.0172821\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 1.00000 | − | 1.73205i | 0.235702 | − | 0.408248i | ||||
\(19\) | 1.00000 | + | 1.73205i | 0.229416 | + | 0.397360i | 0.957635 | − | 0.287984i | \(-0.0929851\pi\) |
−0.728219 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.00000 | −0.639602 | ||||||||
\(23\) | 1.50000 | + | 2.59808i | 0.312772 | + | 0.541736i | 0.978961 | − | 0.204046i | \(-0.0654092\pi\) |
−0.666190 | + | 0.745782i | \(0.732076\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | 0.500000 | + | 0.866025i | 0.0980581 | + | 0.169842i | ||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.50000 | − | 4.33013i | 0.449013 | − | 0.777714i | −0.549309 | − | 0.835619i | \(-0.685109\pi\) |
0.998322 | + | 0.0579057i | \(0.0184423\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −1.50000 | − | 2.59808i | −0.261116 | − | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | 3.50000 | + | 6.06218i | 0.575396 | + | 0.996616i | 0.995998 | + | 0.0893706i | \(0.0284856\pi\) |
−0.420602 | + | 0.907245i | \(0.638181\pi\) | |||||||
\(38\) | 1.00000 | − | 1.73205i | 0.162221 | − | 0.280976i | ||||
\(39\) | −0.500000 | + | 0.866025i | −0.0800641 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 1.50000 | + | 2.59808i | 0.226134 | + | 0.391675i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.50000 | − | 2.59808i | 0.221163 | − | 0.383065i | ||||
\(47\) | −1.50000 | − | 2.59808i | −0.218797 | − | 0.378968i | 0.735643 | − | 0.677369i | \(-0.236880\pi\) |
−0.954441 | + | 0.298401i | \(0.903547\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.00000 | −0.707107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.500000 | − | 0.866025i | 0.0693375 | − | 0.120096i | ||||
\(53\) | 6.00000 | − | 10.3923i | 0.824163 | − | 1.42749i | −0.0783936 | − | 0.996922i | \(-0.524979\pi\) |
0.902557 | − | 0.430570i | \(-0.141688\pi\) | |||||||
\(54\) | −2.50000 | − | 4.33013i | −0.340207 | − | 0.589256i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00000 | − | 5.19615i | 0.390567 | − | 0.676481i | −0.601958 | − | 0.798528i | \(-0.705612\pi\) |
0.992524 | + | 0.122047i | \(0.0389457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.500000 | − | 0.866025i | −0.0640184 | − | 0.110883i | 0.832240 | − | 0.554416i | \(-0.187058\pi\) |
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | −5.00000 | −0.635001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.50000 | + | 2.59808i | −0.184637 | + | 0.319801i | ||||
\(67\) | −2.50000 | + | 4.33013i | −0.305424 | + | 0.529009i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) |
0.671932 | + | 0.740613i | \(0.265465\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.00000 | 0.361158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 1.00000 | + | 1.73205i | 0.117851 | + | 0.204124i | ||||
\(73\) | 5.50000 | − | 9.52628i | 0.643726 | − | 1.11497i | −0.340868 | − | 0.940111i | \(-0.610721\pi\) |
0.984594 | − | 0.174855i | \(-0.0559458\pi\) | |||||||
\(74\) | 3.50000 | − | 6.06218i | 0.406867 | − | 0.704714i | ||||
\(75\) | −2.50000 | − | 4.33013i | −0.288675 | − | 0.500000i | ||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.50000 | + | 2.59808i | 0.165647 | + | 0.286910i | ||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.00000 | − | 6.92820i | −0.431331 | − | 0.747087i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | −9.00000 | − | 15.5885i | −0.953998 | − | 1.65237i | −0.736644 | − | 0.676280i | \(-0.763591\pi\) |
−0.217354 | − | 0.976093i | \(-0.569742\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.00000 | −0.312772 | ||||||||
\(93\) | −2.50000 | − | 4.33013i | −0.259238 | − | 0.449013i | ||||
\(94\) | −1.50000 | + | 2.59808i | −0.154713 | + | 0.267971i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | −17.0000 | −1.72609 | −0.863044 | − | 0.505128i | \(-0.831445\pi\) | ||||
−0.863044 | + | 0.505128i | \(0.831445\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | 2.50000 | + | 4.33013i | 0.250000 | + | 0.433013i | ||||
\(101\) | −1.50000 | + | 2.59808i | −0.149256 | + | 0.258518i | −0.930953 | − | 0.365140i | \(-0.881021\pi\) |
0.781697 | + | 0.623658i | \(0.214354\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.00000 | + | 12.1244i | 0.689730 | + | 1.19465i | 0.971925 | + | 0.235291i | \(0.0756043\pi\) |
−0.282194 | + | 0.959357i | \(0.591062\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(108\) | −2.50000 | + | 4.33013i | −0.240563 | + | 0.416667i | ||||
\(109\) | −1.00000 | + | 1.73205i | −0.0957826 | + | 0.165900i | −0.909935 | − | 0.414751i | \(-0.863869\pi\) |
0.814152 | + | 0.580651i | \(0.197202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.00000 | 0.664411 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.00000 | 0.846649 | 0.423324 | − | 0.905978i | \(-0.360863\pi\) | ||||
0.423324 | + | 0.905978i | \(0.360863\pi\) | |||||||
\(114\) | −1.00000 | − | 1.73205i | −0.0936586 | − | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | − | 1.73205i | −0.0924500 | − | 0.160128i | ||||
\(118\) | −6.00000 | −0.552345 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | −0.500000 | + | 0.866025i | −0.0452679 | + | 0.0784063i | ||||
\(123\) | −1.50000 | + | 2.59808i | −0.135250 | + | 0.234261i | ||||
\(124\) | 2.50000 | + | 4.33013i | 0.224507 | + | 0.388857i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.00000 | −0.621150 | −0.310575 | − | 0.950549i | \(-0.600522\pi\) | ||||
−0.310575 | + | 0.950549i | \(0.600522\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 4.00000 | − | 6.92820i | 0.352180 | − | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 3.00000 | 0.261116 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.00000 | 0.431934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.00000 | − | 5.19615i | 0.256307 | − | 0.443937i | −0.708942 | − | 0.705266i | \(-0.750827\pi\) |
0.965250 | + | 0.261329i | \(0.0841608\pi\) | |||||||
\(138\) | −1.50000 | − | 2.59808i | −0.127688 | − | 0.221163i | ||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.00000 | −0.252646 | ||||||||
\(142\) | −6.00000 | − | 10.3923i | −0.503509 | − | 0.872103i | ||||
\(143\) | −1.50000 | + | 2.59808i | −0.125436 | + | 0.217262i | ||||
\(144\) | 1.00000 | − | 1.73205i | 0.0833333 | − | 0.144338i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.0000 | −0.910366 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.00000 | −0.575396 | ||||||||
\(149\) | 7.50000 | + | 12.9904i | 0.614424 | + | 1.06421i | 0.990485 | + | 0.137619i | \(0.0439449\pi\) |
−0.376061 | + | 0.926595i | \(0.622722\pi\) | |||||||
\(150\) | −2.50000 | + | 4.33013i | −0.204124 | + | 0.353553i | ||||
\(151\) | −4.00000 | + | 6.92820i | −0.325515 | + | 0.563809i | −0.981617 | − | 0.190864i | \(-0.938871\pi\) |
0.656101 | + | 0.754673i | \(0.272204\pi\) | |||||||
\(152\) | 1.00000 | + | 1.73205i | 0.0811107 | + | 0.140488i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.500000 | − | 0.866025i | −0.0400320 | − | 0.0693375i | ||||
\(157\) | −6.50000 | + | 11.2583i | −0.518756 | + | 0.898513i | 0.481006 | + | 0.876717i | \(0.340272\pi\) |
−0.999762 | + | 0.0217953i | \(0.993062\pi\) | |||||||
\(158\) | 0.500000 | − | 0.866025i | 0.0397779 | − | 0.0688973i | ||||
\(159\) | −6.00000 | − | 10.3923i | −0.475831 | − | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −10.0000 | − | 17.3205i | −0.783260 | − | 1.35665i | −0.930033 | − | 0.367477i | \(-0.880222\pi\) |
0.146772 | − | 0.989170i | \(-0.453112\pi\) | |||||||
\(164\) | 1.50000 | − | 2.59808i | 0.117130 | − | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | + | 10.3923i | 0.465690 | + | 0.806599i | ||||
\(167\) | 24.0000 | 1.85718 | 0.928588 | − | 0.371113i | \(-0.121024\pi\) | ||||
0.928588 | + | 0.371113i | \(0.121024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | + | 3.46410i | −0.152944 | + | 0.264906i | ||||
\(172\) | −4.00000 | + | 6.92820i | −0.304997 | + | 0.528271i | ||||
\(173\) | −9.00000 | − | 15.5885i | −0.684257 | − | 1.18517i | −0.973670 | − | 0.227964i | \(-0.926793\pi\) |
0.289412 | − | 0.957205i | \(-0.406540\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | −3.00000 | − | 5.19615i | −0.225494 | − | 0.390567i | ||||
\(178\) | −9.00000 | + | 15.5885i | −0.674579 | + | 1.16840i | ||||
\(179\) | 3.00000 | − | 5.19615i | 0.224231 | − | 0.388379i | −0.731858 | − | 0.681457i | \(-0.761346\pi\) |
0.956088 | + | 0.293079i | \(0.0946798\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.00000 | 0.520306 | 0.260153 | − | 0.965567i | \(-0.416227\pi\) | ||||
0.260153 | + | 0.965567i | \(0.416227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | 1.50000 | + | 2.59808i | 0.110581 | + | 0.191533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.50000 | + | 4.33013i | −0.183309 | + | 0.317500i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.00000 | 0.218797 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 2.00000 | − | 3.46410i | 0.143963 | − | 0.249351i | −0.785022 | − | 0.619467i | \(-0.787349\pi\) |
0.928986 | + | 0.370116i | \(0.120682\pi\) | |||||||
\(194\) | 8.50000 | + | 14.7224i | 0.610264 | + | 1.05701i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.00000 | −0.213741 | −0.106871 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106871 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(198\) | −3.00000 | − | 5.19615i | −0.213201 | − | 0.369274i | ||||
\(199\) | −8.00000 | + | 13.8564i | −0.567105 | + | 0.982255i | 0.429745 | + | 0.902950i | \(0.358603\pi\) |
−0.996850 | + | 0.0793045i | \(0.974730\pi\) | |||||||
\(200\) | 2.50000 | − | 4.33013i | 0.176777 | − | 0.306186i | ||||
\(201\) | 2.50000 | + | 4.33013i | 0.176336 | + | 0.305424i | ||||
\(202\) | 3.00000 | 0.211079 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.00000 | − | 12.1244i | 0.487713 | − | 0.844744i | ||||
\(207\) | −3.00000 | + | 5.19615i | −0.208514 | + | 0.361158i | ||||
\(208\) | 0.500000 | + | 0.866025i | 0.0346688 | + | 0.0600481i | ||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.0000 | −1.51454 | −0.757271 | − | 0.653101i | \(-0.773468\pi\) | ||||
−0.757271 | + | 0.653101i | \(0.773468\pi\) | |||||||
\(212\) | 6.00000 | + | 10.3923i | 0.412082 | + | 0.713746i | ||||
\(213\) | 6.00000 | − | 10.3923i | 0.411113 | − | 0.712069i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.00000 | 0.135457 | ||||||||
\(219\) | −5.50000 | − | 9.52628i | −0.371656 | − | 0.643726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.50000 | − | 6.06218i | −0.234905 | − | 0.406867i | ||||
\(223\) | 1.00000 | 0.0669650 | 0.0334825 | − | 0.999439i | \(-0.489340\pi\) | ||||
0.0334825 | + | 0.999439i | \(0.489340\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.0000 | 0.666667 | ||||||||
\(226\) | −4.50000 | − | 7.79423i | −0.299336 | − | 0.518464i | ||||
\(227\) | −12.0000 | + | 20.7846i | −0.796468 | + | 1.37952i | 0.125435 | + | 0.992102i | \(0.459967\pi\) |
−0.921903 | + | 0.387421i | \(0.873366\pi\) | |||||||
\(228\) | −1.00000 | + | 1.73205i | −0.0662266 | + | 0.114708i | ||||
\(229\) | −2.00000 | − | 3.46410i | −0.132164 | − | 0.228914i | 0.792347 | − | 0.610071i | \(-0.208859\pi\) |
−0.924510 | + | 0.381157i | \(0.875526\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.50000 | − | 2.59808i | −0.0982683 | − | 0.170206i | 0.812700 | − | 0.582683i | \(-0.197997\pi\) |
−0.910968 | + | 0.412477i | \(0.864664\pi\) | |||||||
\(234\) | −1.00000 | + | 1.73205i | −0.0653720 | + | 0.113228i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.00000 | + | 5.19615i | 0.195283 | + | 0.338241i | ||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0000 | − | 22.5167i | 0.837404 | − | 1.45043i | −0.0546547 | − | 0.998505i | \(-0.517406\pi\) |
0.892058 | − | 0.451920i | \(-0.149261\pi\) | |||||||
\(242\) | 1.00000 | − | 1.73205i | 0.0642824 | − | 0.111340i | ||||
\(243\) | 8.00000 | + | 13.8564i | 0.513200 | + | 0.888889i | ||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.00000 | 0.191273 | ||||||||
\(247\) | −1.00000 | − | 1.73205i | −0.0636285 | − | 0.110208i | ||||
\(248\) | 2.50000 | − | 4.33013i | 0.158750 | − | 0.274963i | ||||
\(249\) | −6.00000 | + | 10.3923i | −0.380235 | + | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.0000 | 0.946792 | 0.473396 | − | 0.880850i | \(-0.343028\pi\) | ||||
0.473396 | + | 0.880850i | \(0.343028\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.00000 | 0.565825 | ||||||||
\(254\) | 3.50000 | + | 6.06218i | 0.219610 | + | 0.380375i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 12.0000 | + | 20.7846i | 0.748539 | + | 1.29651i | 0.948523 | + | 0.316709i | \(0.102578\pi\) |
−0.199983 | + | 0.979799i | \(0.564089\pi\) | |||||||
\(258\) | −8.00000 | −0.498058 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0000 | + | 20.7846i | −0.739952 | + | 1.28163i | 0.212565 | + | 0.977147i | \(0.431818\pi\) |
−0.952517 | + | 0.304487i | \(0.901515\pi\) | |||||||
\(264\) | −1.50000 | − | 2.59808i | −0.0923186 | − | 0.159901i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.0000 | −1.10158 | ||||||||
\(268\) | −2.50000 | − | 4.33013i | −0.152712 | − | 0.264505i | ||||
\(269\) | −4.50000 | + | 7.79423i | −0.274370 | + | 0.475223i | −0.969976 | − | 0.243201i | \(-0.921803\pi\) |
0.695606 | + | 0.718423i | \(0.255136\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.50000 | + | 9.52628i | 0.334101 | + | 0.578680i | 0.983312 | − | 0.181928i | \(-0.0582339\pi\) |
−0.649211 | + | 0.760609i | \(0.724901\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | −7.50000 | − | 12.9904i | −0.452267 | − | 0.783349i | ||||
\(276\) | −1.50000 | + | 2.59808i | −0.0902894 | + | 0.156386i | ||||
\(277\) | −13.0000 | + | 22.5167i | −0.781094 | + | 1.35290i | 0.150210 | + | 0.988654i | \(0.452005\pi\) |
−0.931305 | + | 0.364241i | \(0.881328\pi\) | |||||||
\(278\) | −2.00000 | − | 3.46410i | −0.119952 | − | 0.207763i | ||||
\(279\) | 10.0000 | 0.598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0000 | 0.715860 | 0.357930 | − | 0.933748i | \(-0.383483\pi\) | ||||
0.357930 | + | 0.933748i | \(0.383483\pi\) | |||||||
\(282\) | 1.50000 | + | 2.59808i | 0.0893237 | + | 0.154713i | ||||
\(283\) | −15.5000 | + | 26.8468i | −0.921379 | + | 1.59588i | −0.124096 | + | 0.992270i | \(0.539603\pi\) |
−0.797283 | + | 0.603606i | \(0.793730\pi\) | |||||||
\(284\) | −6.00000 | + | 10.3923i | −0.356034 | + | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.00000 | 0.177394 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.00000 | −0.117851 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.50000 | + | 14.7224i | −0.498279 | + | 0.863044i | ||||
\(292\) | 5.50000 | + | 9.52628i | 0.321863 | + | 0.557483i | ||||
\(293\) | −18.0000 | −1.05157 | −0.525786 | − | 0.850617i | \(-0.676229\pi\) | ||||
−0.525786 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.50000 | + | 6.06218i | 0.203433 | + | 0.352357i | ||||
\(297\) | 7.50000 | − | 12.9904i | 0.435194 | − | 0.753778i | ||||
\(298\) | 7.50000 | − | 12.9904i | 0.434463 | − | 0.752513i | ||||
\(299\) | −1.50000 | − | 2.59808i | −0.0867472 | − | 0.150251i | ||||
\(300\) | 5.00000 | 0.288675 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.00000 | 0.460348 | ||||||||
\(303\) | 1.50000 | + | 2.59808i | 0.0861727 | + | 0.149256i | ||||
\(304\) | 1.00000 | − | 1.73205i | 0.0573539 | − | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0000 | 0.913168 | 0.456584 | − | 0.889680i | \(-0.349073\pi\) | ||||
0.456584 | + | 0.889680i | \(0.349073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.0000 | 0.796432 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.0000 | − | 25.9808i | 0.850572 | − | 1.47323i | −0.0301210 | − | 0.999546i | \(-0.509589\pi\) |
0.880693 | − | 0.473688i | \(-0.157077\pi\) | |||||||
\(312\) | −0.500000 | + | 0.866025i | −0.0283069 | + | 0.0490290i | ||||
\(313\) | 13.0000 | + | 22.5167i | 0.734803 | + | 1.27272i | 0.954810 | + | 0.297218i | \(0.0960589\pi\) |
−0.220006 | + | 0.975499i | \(0.570608\pi\) | |||||||
\(314\) | 13.0000 | 0.733632 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.00000 | −0.0562544 | ||||||||
\(317\) | 1.50000 | + | 2.59808i | 0.0842484 | + | 0.145922i | 0.905071 | − | 0.425261i | \(-0.139818\pi\) |
−0.820822 | + | 0.571184i | \(0.806484\pi\) | |||||||
\(318\) | −6.00000 | + | 10.3923i | −0.336463 | + | 0.582772i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −2.50000 | + | 4.33013i | −0.138675 | + | 0.240192i | ||||
\(326\) | −10.0000 | + | 17.3205i | −0.553849 | + | 0.959294i | ||||
\(327\) | 1.00000 | + | 1.73205i | 0.0553001 | + | 0.0957826i | ||||
\(328\) | −3.00000 | −0.165647 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.50000 | + | 16.4545i | 0.522167 | + | 0.904420i | 0.999667 | + | 0.0257885i | \(0.00820965\pi\) |
−0.477500 | + | 0.878632i | \(0.658457\pi\) | |||||||
\(332\) | 6.00000 | − | 10.3923i | 0.329293 | − | 0.570352i | ||||
\(333\) | −7.00000 | + | 12.1244i | −0.383598 | + | 0.664411i | ||||
\(334\) | −12.0000 | − | 20.7846i | −0.656611 | − | 1.13728i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.0000 | −1.68868 | −0.844339 | − | 0.535810i | \(-0.820006\pi\) | ||||
−0.844339 | + | 0.535810i | \(0.820006\pi\) | |||||||
\(338\) | −0.500000 | − | 0.866025i | −0.0271964 | − | 0.0471056i | ||||
\(339\) | 4.50000 | − | 7.79423i | 0.244406 | − | 0.423324i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.50000 | − | 12.9904i | −0.406148 | − | 0.703469i | ||||
\(342\) | 4.00000 | 0.216295 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.00000 | 0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.00000 | + | 15.5885i | −0.483843 | + | 0.838041i | ||||
\(347\) | −12.0000 | + | 20.7846i | −0.644194 | + | 1.11578i | 0.340293 | + | 0.940319i | \(0.389474\pi\) |
−0.984487 | + | 0.175457i | \(0.943860\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | −0.266880 | ||||||||
\(352\) | 1.50000 | + | 2.59808i | 0.0799503 | + | 0.138478i | ||||
\(353\) | 7.50000 | − | 12.9904i | 0.399185 | − | 0.691408i | −0.594441 | − | 0.804139i | \(-0.702627\pi\) |
0.993626 | + | 0.112731i | \(0.0359599\pi\) | |||||||
\(354\) | −3.00000 | + | 5.19615i | −0.159448 | + | 0.276172i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 18.0000 | 0.953998 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.00000 | −0.317110 | ||||||||
\(359\) | 12.0000 | + | 20.7846i | 0.633336 | + | 1.09697i | 0.986865 | + | 0.161546i | \(0.0516481\pi\) |
−0.353529 | + | 0.935423i | \(0.615019\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | −3.50000 | − | 6.06218i | −0.183956 | − | 0.318621i | ||||
\(363\) | 2.00000 | 0.104973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.500000 | + | 0.866025i | 0.0261354 | + | 0.0452679i | ||||
\(367\) | −14.0000 | + | 24.2487i | −0.730794 | + | 1.26577i | 0.225750 | + | 0.974185i | \(0.427517\pi\) |
−0.956544 | + | 0.291587i | \(0.905817\pi\) | |||||||
\(368\) | 1.50000 | − | 2.59808i | 0.0781929 | − | 0.135434i | ||||
\(369\) | −3.00000 | − | 5.19615i | −0.156174 | − | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.00000 | 0.259238 | ||||||||
\(373\) | 2.00000 | + | 3.46410i | 0.103556 | + | 0.179364i | 0.913147 | − | 0.407630i | \(-0.133645\pi\) |
−0.809591 | + | 0.586994i | \(0.800311\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.50000 | − | 2.59808i | −0.0773566 | − | 0.133986i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.50000 | + | 6.06218i | −0.179310 | + | 0.310575i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.50000 | + | 2.59808i | 0.0766464 | + | 0.132755i | 0.901801 | − | 0.432151i | \(-0.142245\pi\) |
−0.825155 | + | 0.564907i | \(0.808912\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.00000 | −0.203595 | ||||||||
\(387\) | 8.00000 | + | 13.8564i | 0.406663 | + | 0.704361i | ||||
\(388\) | 8.50000 | − | 14.7224i | 0.431522 | − | 0.747418i | ||||
\(389\) | 18.0000 | − | 31.1769i | 0.912636 | − | 1.58073i | 0.102311 | − | 0.994753i | \(-0.467376\pi\) |
0.810326 | − | 0.585980i | \(-0.199290\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.50000 | + | 2.59808i | 0.0755689 | + | 0.130889i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.00000 | + | 5.19615i | −0.150756 | + | 0.261116i | ||||
\(397\) | 10.0000 | + | 17.3205i | 0.501886 | + | 0.869291i | 0.999998 | + | 0.00217869i | \(0.000693499\pi\) |
−0.498112 | + | 0.867113i | \(0.665973\pi\) | |||||||
\(398\) | 16.0000 | 0.802008 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | −12.0000 | − | 20.7846i | −0.599251 | − | 1.03793i | −0.992932 | − | 0.118686i | \(-0.962132\pi\) |
0.393680 | − | 0.919247i | \(-0.371202\pi\) | |||||||
\(402\) | 2.50000 | − | 4.33013i | 0.124689 | − | 0.215967i | ||||
\(403\) | −2.50000 | + | 4.33013i | −0.124534 | + | 0.215699i | ||||
\(404\) | −1.50000 | − | 2.59808i | −0.0746278 | − | 0.129259i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.0000 | 1.04093 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.0000 | + | 19.0526i | −0.543915 | + | 0.942088i | 0.454759 | + | 0.890614i | \(0.349725\pi\) |
−0.998674 | + | 0.0514740i | \(0.983608\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.00000 | − | 5.19615i | −0.147979 | − | 0.256307i | ||||
\(412\) | −14.0000 | −0.689730 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.00000 | 0.294884 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.500000 | − | 0.866025i | 0.0245145 | − | 0.0424604i | ||||
\(417\) | 2.00000 | − | 3.46410i | 0.0979404 | − | 0.169638i | ||||
\(418\) | −3.00000 | − | 5.19615i | −0.146735 | − | 0.254152i | ||||
\(419\) | −21.0000 | −1.02592 | −0.512959 | − | 0.858413i | \(-0.671451\pi\) | ||||
−0.512959 | + | 0.858413i | \(0.671451\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.0000 | −1.80327 | −0.901635 | − | 0.432498i | \(-0.857632\pi\) | ||||
−0.901635 | + | 0.432498i | \(0.857632\pi\) | |||||||
\(422\) | 11.0000 | + | 19.0526i | 0.535472 | + | 0.927464i | ||||
\(423\) | 3.00000 | − | 5.19615i | 0.145865 | − | 0.252646i | ||||
\(424\) | 6.00000 | − | 10.3923i | 0.291386 | − | 0.504695i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.0000 | −0.581402 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.50000 | + | 2.59808i | 0.0724207 | + | 0.125436i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.00000 | − | 5.19615i | 0.144505 | − | 0.250290i | −0.784683 | − | 0.619897i | \(-0.787174\pi\) |
0.929188 | + | 0.369607i | \(0.120508\pi\) | |||||||
\(432\) | −2.50000 | − | 4.33013i | −0.120281 | − | 0.208333i | ||||
\(433\) | −38.0000 | −1.82616 | −0.913082 | − | 0.407777i | \(-0.866304\pi\) | ||||
−0.913082 | + | 0.407777i | \(0.866304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | − | 1.73205i | −0.0478913 | − | 0.0829502i | ||||
\(437\) | −3.00000 | + | 5.19615i | −0.143509 | + | 0.248566i | ||||
\(438\) | −5.50000 | + | 9.52628i | −0.262800 | + | 0.455183i | ||||
\(439\) | 13.0000 | + | 22.5167i | 0.620456 | + | 1.07466i | 0.989401 | + | 0.145210i | \(0.0463858\pi\) |
−0.368945 | + | 0.929451i | \(0.620281\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.0000 | − | 20.7846i | −0.570137 | − | 0.987507i | −0.996551 | − | 0.0829786i | \(-0.973557\pi\) |
0.426414 | − | 0.904528i | \(-0.359777\pi\) | |||||||
\(444\) | −3.50000 | + | 6.06218i | −0.166103 | + | 0.287698i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.500000 | − | 0.866025i | −0.0236757 | − | 0.0410075i | ||||
\(447\) | 15.0000 | 0.709476 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | −5.00000 | − | 8.66025i | −0.235702 | − | 0.408248i | ||||
\(451\) | −4.50000 | + | 7.79423i | −0.211897 | + | 0.367016i | ||||
\(452\) | −4.50000 | + | 7.79423i | −0.211662 | + | 0.366610i | ||||
\(453\) | 4.00000 | + | 6.92820i | 0.187936 | + | 0.325515i | ||||
\(454\) | 24.0000 | 1.12638 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | −13.0000 | − | 22.5167i | −0.608114 | − | 1.05328i | −0.991551 | − | 0.129718i | \(-0.958593\pi\) |
0.383437 | − | 0.923567i | \(-0.374740\pi\) | |||||||
\(458\) | −2.00000 | + | 3.46410i | −0.0934539 | + | 0.161867i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.0000 | −1.11779 | −0.558896 | − | 0.829238i | \(-0.688775\pi\) | ||||
−0.558896 | + | 0.829238i | \(0.688775\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.0000 | −1.85896 | −0.929479 | − | 0.368875i | \(-0.879743\pi\) | ||||
−0.929479 | + | 0.368875i | \(0.879743\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.50000 | + | 2.59808i | −0.0694862 | + | 0.120354i | ||||
\(467\) | 6.00000 | + | 10.3923i | 0.277647 | + | 0.480899i | 0.970799 | − | 0.239892i | \(-0.0771121\pi\) |
−0.693153 | + | 0.720791i | \(0.743779\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.50000 | + | 11.2583i | 0.299504 | + | 0.518756i | ||||
\(472\) | 3.00000 | − | 5.19615i | 0.138086 | − | 0.239172i | ||||
\(473\) | 12.0000 | − | 20.7846i | 0.551761 | − | 0.955677i | ||||
\(474\) | −0.500000 | − | 0.866025i | −0.0229658 | − | 0.0397779i | ||||
\(475\) | 10.0000 | 0.458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.0000 | 1.09888 | ||||||||
\(478\) | −3.00000 | − | 5.19615i | −0.137217 | − | 0.237666i | ||||
\(479\) | 12.0000 | − | 20.7846i | 0.548294 | − | 0.949673i | −0.450098 | − | 0.892979i | \(-0.648611\pi\) |
0.998392 | − | 0.0566937i | \(-0.0180558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.50000 | − | 6.06218i | −0.159586 | − | 0.276412i | ||||
\(482\) | −26.0000 | −1.18427 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.00000 | − | 13.8564i | 0.362887 | − | 0.628539i | ||||
\(487\) | −1.00000 | + | 1.73205i | −0.0453143 | + | 0.0784867i | −0.887793 | − | 0.460243i | \(-0.847762\pi\) |
0.842479 | + | 0.538730i | \(0.181096\pi\) | |||||||
\(488\) | −0.500000 | − | 0.866025i | −0.0226339 | − | 0.0392031i | ||||
\(489\) | −20.0000 | −0.904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | −1.50000 | − | 2.59808i | −0.0676252 | − | 0.117130i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −1.00000 | + | 1.73205i | −0.0449921 | + | 0.0779287i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.00000 | −0.224507 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 12.0000 | 0.537733 | ||||||||
\(499\) | −11.5000 | − | 19.9186i | −0.514811 | − | 0.891678i | −0.999852 | − | 0.0171872i | \(-0.994529\pi\) |
0.485042 | − | 0.874491i | \(-0.338804\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.0000 | − | 20.7846i | 0.536120 | − | 0.928588i | ||||
\(502\) | −7.50000 | − | 12.9904i | −0.334741 | − | 0.579789i | ||||
\(503\) | −12.0000 | −0.535054 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.50000 | − | 7.79423i | −0.200049 | − | 0.346496i | ||||
\(507\) | 0.500000 | − | 0.866025i | 0.0222058 | − | 0.0384615i | ||||
\(508\) | 3.50000 | − | 6.06218i | 0.155287 | − | 0.268966i | ||||
\(509\) | −15.0000 | − | 25.9808i | −0.664863 | − | 1.15158i | −0.979322 | − | 0.202306i | \(-0.935156\pi\) |
0.314459 | − | 0.949271i | \(-0.398177\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.00000 | + | 8.66025i | 0.220755 | + | 0.382360i | ||||
\(514\) | 12.0000 | − | 20.7846i | 0.529297 | − | 0.916770i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.00000 | + | 6.92820i | 0.176090 | + | 0.304997i | ||||
\(517\) | −9.00000 | −0.395820 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.0000 | −0.790112 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.00000 | − | 5.19615i | 0.131432 | − | 0.227648i | −0.792797 | − | 0.609486i | \(-0.791376\pi\) |
0.924229 | + | 0.381839i | \(0.124709\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.50000 | − | 6.06218i | −0.153044 | − | 0.265081i | 0.779301 | − | 0.626650i | \(-0.215574\pi\) |
−0.932345 | + | 0.361569i | \(0.882241\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.50000 | + | 2.59808i | −0.0652791 | + | 0.113067i | ||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.00000 | 0.129944 | ||||||||
\(534\) | 9.00000 | + | 15.5885i | 0.389468 | + | 0.674579i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.50000 | + | 4.33013i | −0.107984 | + | 0.187033i | ||||
\(537\) | −3.00000 | − | 5.19615i | −0.129460 | − | 0.224231i | ||||
\(538\) | 9.00000 | 0.388018 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0000 | + | 29.4449i | 0.730887 | + | 1.26593i | 0.956504 | + | 0.291718i | \(0.0942267\pi\) |
−0.225617 | + | 0.974216i | \(0.572440\pi\) | |||||||
\(542\) | 5.50000 | − | 9.52628i | 0.236245 | − | 0.409189i | ||||
\(543\) | 3.50000 | − | 6.06218i | 0.150199 | − | 0.260153i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | 3.00000 | + | 5.19615i | 0.128154 | + | 0.221969i | ||||
\(549\) | 1.00000 | − | 1.73205i | 0.0426790 | − | 0.0739221i | ||||
\(550\) | −7.50000 | + | 12.9904i | −0.319801 | + | 0.553912i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 3.00000 | 0.127688 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 26.0000 | 1.10463 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.00000 | + | 3.46410i | −0.0848189 | + | 0.146911i | ||||
\(557\) | 7.50000 | − | 12.9904i | 0.317785 | − | 0.550420i | −0.662240 | − | 0.749291i | \(-0.730394\pi\) |
0.980026 | + | 0.198871i | \(0.0637276\pi\) | |||||||
\(558\) | −5.00000 | − | 8.66025i | −0.211667 | − | 0.366618i | ||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.00000 | − | 10.3923i | −0.253095 | − | 0.438373i | ||||
\(563\) | −19.5000 | + | 33.7750i | −0.821827 | + | 1.42345i | 0.0824933 | + | 0.996592i | \(0.473712\pi\) |
−0.904320 | + | 0.426855i | \(0.859622\pi\) | |||||||
\(564\) | 1.50000 | − | 2.59808i | 0.0631614 | − | 0.109399i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 31.0000 | 1.30303 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.0000 | 0.503509 | ||||||||
\(569\) | −10.5000 | − | 18.1865i | −0.440183 | − | 0.762419i | 0.557520 | − | 0.830164i | \(-0.311753\pi\) |
−0.997703 | + | 0.0677445i | \(0.978420\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.0000 | − | 19.0526i | 0.460336 | − | 0.797325i | −0.538642 | − | 0.842535i | \(-0.681062\pi\) |
0.998978 | + | 0.0452101i | \(0.0143957\pi\) | |||||||
\(572\) | −1.50000 | − | 2.59808i | −0.0627182 | − | 0.108631i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.0000 | 0.625543 | ||||||||
\(576\) | 1.00000 | + | 1.73205i | 0.0416667 | + | 0.0721688i | ||||
\(577\) | 1.00000 | − | 1.73205i | 0.0416305 | − | 0.0721062i | −0.844459 | − | 0.535620i | \(-0.820078\pi\) |
0.886090 | + | 0.463513i | \(0.153411\pi\) | |||||||
\(578\) | 8.50000 | − | 14.7224i | 0.353553 | − | 0.612372i | ||||
\(579\) | −2.00000 | − | 3.46410i | −0.0831172 | − | 0.143963i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 17.0000 | 0.704673 | ||||||||
\(583\) | −18.0000 | − | 31.1769i | −0.745484 | − | 1.29122i | ||||
\(584\) | 5.50000 | − | 9.52628i | 0.227592 | − | 0.394200i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.00000 | + | 15.5885i | 0.371787 | + | 0.643953i | ||||
\(587\) | −18.0000 | −0.742940 | −0.371470 | − | 0.928445i | \(-0.621146\pi\) | ||||
−0.371470 | + | 0.928445i | \(0.621146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0000 | 0.412043 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.50000 | + | 2.59808i | −0.0617018 | + | 0.106871i | ||||
\(592\) | 3.50000 | − | 6.06218i | 0.143849 | − | 0.249154i | ||||
\(593\) | −3.00000 | − | 5.19615i | −0.123195 | − | 0.213380i | 0.797831 | − | 0.602881i | \(-0.205981\pi\) |
−0.921026 | + | 0.389501i | \(0.872647\pi\) | |||||||
\(594\) | −15.0000 | −0.615457 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.0000 | −0.614424 | ||||||||
\(597\) | 8.00000 | + | 13.8564i | 0.327418 | + | 0.567105i | ||||
\(598\) | −1.50000 | + | 2.59808i | −0.0613396 | + | 0.106243i | ||||
\(599\) | −19.5000 | + | 33.7750i | −0.796748 | + | 1.38001i | 0.124975 | + | 0.992160i | \(0.460115\pi\) |
−0.921723 | + | 0.387849i | \(0.873218\pi\) | |||||||
\(600\) | −2.50000 | − | 4.33013i | −0.102062 | − | 0.176777i | ||||
\(601\) | 10.0000 | 0.407909 | 0.203954 | − | 0.978980i | \(-0.434621\pi\) | ||||
0.203954 | + | 0.978980i | \(0.434621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.0000 | −0.407231 | ||||||||
\(604\) | −4.00000 | − | 6.92820i | −0.162758 | − | 0.281905i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.50000 | − | 2.59808i | 0.0609333 | − | 0.105540i | ||||
\(607\) | 7.00000 | + | 12.1244i | 0.284121 | + | 0.492112i | 0.972396 | − | 0.233338i | \(-0.0749648\pi\) |
−0.688274 | + | 0.725450i | \(0.741632\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.50000 | + | 2.59808i | 0.0606835 | + | 0.105107i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.5000 | − | 21.6506i | 0.504870 | − | 0.874461i | −0.495114 | − | 0.868828i | \(-0.664874\pi\) |
0.999984 | − | 0.00563283i | \(-0.00179300\pi\) | |||||||
\(614\) | −8.00000 | − | 13.8564i | −0.322854 | − | 0.559199i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000 | 0.724653 | 0.362326 | − | 0.932051i | \(-0.381983\pi\) | ||||
0.362326 | + | 0.932051i | \(0.381983\pi\) | |||||||
\(618\) | −7.00000 | − | 12.1244i | −0.281581 | − | 0.487713i | ||||
\(619\) | −5.00000 | + | 8.66025i | −0.200967 | + | 0.348085i | −0.948840 | − | 0.315757i | \(-0.897742\pi\) |
0.747873 | + | 0.663842i | \(0.231075\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.50000 | + | 12.9904i | 0.300965 | + | 0.521286i | ||||
\(622\) | −30.0000 | −1.20289 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | 13.0000 | − | 22.5167i | 0.519584 | − | 0.899947i | ||||
\(627\) | 3.00000 | − | 5.19615i | 0.119808 | − | 0.207514i | ||||
\(628\) | −6.50000 | − | 11.2583i | −0.259378 | − | 0.449256i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0000 | −1.35352 | −0.676759 | − | 0.736204i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(632\) | 0.500000 | + | 0.866025i | 0.0198889 | + | 0.0344486i | ||||
\(633\) | −11.0000 | + | 19.0526i | −0.437211 | + | 0.757271i | ||||
\(634\) | 1.50000 | − | 2.59808i | 0.0595726 | − | 0.103183i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 12.0000 | 0.475831 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | + | 20.7846i | 0.474713 | + | 0.822226i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5000 | − | 28.5788i | 0.651711 | − | 1.12880i | −0.330997 | − | 0.943632i | \(-0.607385\pi\) |
0.982708 | − | 0.185164i | \(-0.0592817\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.0000 | −1.26196 | −0.630978 | − | 0.775800i | \(-0.717346\pi\) | ||||
−0.630978 | + | 0.775800i | \(0.717346\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.00000 | − | 10.3923i | 0.235884 | − | 0.408564i | −0.723645 | − | 0.690172i | \(-0.757535\pi\) |
0.959529 | + | 0.281609i | \(0.0908680\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −9.00000 | − | 15.5885i | −0.353281 | − | 0.611900i | ||||
\(650\) | 5.00000 | 0.196116 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.0000 | 0.783260 | ||||||||
\(653\) | −12.0000 | − | 20.7846i | −0.469596 | − | 0.813365i | 0.529799 | − | 0.848123i | \(-0.322267\pi\) |
−0.999396 | + | 0.0347583i | \(0.988934\pi\) | |||||||
\(654\) | 1.00000 | − | 1.73205i | 0.0391031 | − | 0.0677285i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.50000 | + | 2.59808i | 0.0585652 | + | 0.101438i | ||||
\(657\) | 22.0000 | 0.858302 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.0000 | 1.63609 | 0.818044 | − | 0.575156i | \(-0.195059\pi\) | ||||
0.818044 | + | 0.575156i | \(0.195059\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.0000 | − | 27.7128i | 0.622328 | − | 1.07790i | −0.366723 | − | 0.930330i | \(-0.619520\pi\) |
0.989051 | − | 0.147573i | \(-0.0471463\pi\) | |||||||
\(662\) | 9.50000 | − | 16.4545i | 0.369228 | − | 0.639522i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 14.0000 | 0.542489 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −12.0000 | + | 20.7846i | −0.464294 | + | 0.804181i | ||||
\(669\) | 0.500000 | − | 0.866025i | 0.0193311 | − | 0.0334825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.00000 | −0.115814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.00000 | −0.0385472 | −0.0192736 | − | 0.999814i | \(-0.506135\pi\) | ||||
−0.0192736 | + | 0.999814i | \(0.506135\pi\) | |||||||
\(674\) | 15.5000 | + | 26.8468i | 0.597038 | + | 1.03410i | ||||
\(675\) | 12.5000 | − | 21.6506i | 0.481125 | − | 0.833333i | ||||
\(676\) | −0.500000 | + | 0.866025i | −0.0192308 | + | 0.0333087i | ||||
\(677\) | −19.5000 | − | 33.7750i | −0.749446 | − | 1.29808i | −0.948089 | − | 0.318006i | \(-0.896987\pi\) |
0.198643 | − | 0.980072i | \(-0.436347\pi\) | |||||||
\(678\) | −9.00000 | −0.345643 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0000 | + | 20.7846i | 0.459841 | + | 0.796468i | ||||
\(682\) | −7.50000 | + | 12.9904i | −0.287190 | + | 0.497427i | ||||
\(683\) | 13.5000 | − | 23.3827i | 0.516563 | − | 0.894714i | −0.483252 | − | 0.875481i | \(-0.660544\pi\) |
0.999815 | − | 0.0192323i | \(-0.00612219\pi\) | |||||||
\(684\) | −2.00000 | − | 3.46410i | −0.0764719 | − | 0.132453i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.00000 | −0.152610 | ||||||||
\(688\) | −4.00000 | − | 6.92820i | −0.152499 | − | 0.264135i | ||||
\(689\) | −6.00000 | + | 10.3923i | −0.228582 | + | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.00000 | + | 6.92820i | 0.152167 | + | 0.263561i | 0.932024 | − | 0.362397i | \(-0.118041\pi\) |
−0.779857 | + | 0.625958i | \(0.784708\pi\) | |||||||
\(692\) | 18.0000 | 0.684257 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.0000 | 0.911028 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −5.00000 | − | 8.66025i | −0.189253 | − | 0.327795i | ||||
\(699\) | −3.00000 | −0.113470 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.0000 | −1.35970 | −0.679851 | − | 0.733351i | \(-0.737955\pi\) | ||||
−0.679851 | + | 0.733351i | \(0.737955\pi\) | |||||||
\(702\) | 2.50000 | + | 4.33013i | 0.0943564 | + | 0.163430i | ||||
\(703\) | −7.00000 | + | 12.1244i | −0.264010 | + | 0.457279i | ||||
\(704\) | 1.50000 | − | 2.59808i | 0.0565334 | − | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.0000 | −0.564532 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6.00000 | 0.225494 | ||||||||
\(709\) | −17.5000 | − | 30.3109i | −0.657226 | − | 1.13835i | −0.981331 | − | 0.192328i | \(-0.938396\pi\) |
0.324104 | − | 0.946021i | \(-0.394937\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.00000 | + | 1.73205i | −0.0375029 | + | 0.0649570i | ||||
\(712\) | −9.00000 | − | 15.5885i | −0.337289 | − | 0.584202i | ||||
\(713\) | 15.0000 | 0.561754 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.00000 | + | 5.19615i | 0.112115 | + | 0.194189i | ||||
\(717\) | 3.00000 | − | 5.19615i | 0.112037 | − | 0.194054i | ||||
\(718\) | 12.0000 | − | 20.7846i | 0.447836 | − | 0.775675i | ||||
\(719\) | 3.00000 | + | 5.19615i | 0.111881 | + | 0.193784i | 0.916529 | − | 0.399969i | \(-0.130979\pi\) |
−0.804648 | + | 0.593753i | \(0.797646\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | −13.0000 | − | 22.5167i | −0.483475 | − | 0.837404i | ||||
\(724\) | −3.50000 | + | 6.06218i | −0.130076 | + | 0.225299i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.00000 | − | 1.73205i | −0.0371135 | − | 0.0642824i | ||||
\(727\) | −26.0000 | −0.964287 | −0.482143 | − | 0.876092i | \(-0.660142\pi\) | ||||
−0.482143 | + | 0.876092i | \(0.660142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.500000 | − | 0.866025i | 0.0184805 | − | 0.0320092i | ||||
\(733\) | −2.00000 | − | 3.46410i | −0.0738717 | − | 0.127950i | 0.826723 | − | 0.562609i | \(-0.190202\pi\) |
−0.900595 | + | 0.434659i | \(0.856869\pi\) | |||||||
\(734\) | 28.0000 | 1.03350 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.00000 | −0.110581 | ||||||||
\(737\) | 7.50000 | + | 12.9904i | 0.276266 | + | 0.478507i | ||||
\(738\) | −3.00000 | + | 5.19615i | −0.110432 | + | 0.191273i | ||||
\(739\) | 8.00000 | − | 13.8564i | 0.294285 | − | 0.509716i | −0.680534 | − | 0.732717i | \(-0.738252\pi\) |
0.974818 | + | 0.223001i | \(0.0715853\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.0000 | −0.880475 | −0.440237 | − | 0.897881i | \(-0.645106\pi\) | ||||
−0.440237 | + | 0.897881i | \(0.645106\pi\) | |||||||
\(744\) | −2.50000 | − | 4.33013i | −0.0916544 | − | 0.158750i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.00000 | − | 3.46410i | 0.0732252 | − | 0.126830i | ||||
\(747\) | −12.0000 | − | 20.7846i | −0.439057 | − | 0.760469i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.5000 | + | 26.8468i | 0.565603 | + | 0.979653i | 0.996993 | + | 0.0774878i | \(0.0246899\pi\) |
−0.431390 | + | 0.902165i | \(0.641977\pi\) | |||||||
\(752\) | −1.50000 | + | 2.59808i | −0.0546994 | + | 0.0947421i | ||||
\(753\) | 7.50000 | − | 12.9904i | 0.273315 | − | 0.473396i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | 8.00000 | + | 13.8564i | 0.290573 | + | 0.503287i | ||||
\(759\) | 4.50000 | − | 7.79423i | 0.163340 | − | 0.282913i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.50000 | + | 2.59808i | 0.0543750 | + | 0.0941802i | 0.891932 | − | 0.452170i | \(-0.149350\pi\) |
−0.837557 | + | 0.546350i | \(0.816017\pi\) | |||||||
\(762\) | 7.00000 | 0.253583 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.50000 | − | 2.59808i | 0.0541972 | − | 0.0938723i | ||||
\(767\) | −3.00000 | + | 5.19615i | −0.108324 | + | 0.187622i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 13.0000 | 0.468792 | 0.234396 | − | 0.972141i | \(-0.424689\pi\) | ||||
0.234396 | + | 0.972141i | \(0.424689\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.0000 | 0.864339 | ||||||||
\(772\) | 2.00000 | + | 3.46410i | 0.0719816 | + | 0.124676i | ||||
\(773\) | −27.0000 | + | 46.7654i | −0.971123 | + | 1.68203i | −0.278944 | + | 0.960307i | \(0.589984\pi\) |
−0.692179 | + | 0.721726i | \(0.743349\pi\) | |||||||
\(774\) | 8.00000 | − | 13.8564i | 0.287554 | − | 0.498058i | ||||
\(775\) | −12.5000 | − | 21.6506i | −0.449013 | − | 0.777714i | ||||
\(776\) | −17.0000 | −0.610264 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −36.0000 | −1.29066 | ||||||||
\(779\) | −3.00000 | − | 5.19615i | −0.107486 | − | 0.186171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | − | 31.1769i | 0.644091 | − | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.0000 | − | 27.7128i | 0.570338 | − | 0.987855i | −0.426193 | − | 0.904632i | \(-0.640145\pi\) |
0.996531 | − | 0.0832226i | \(-0.0265213\pi\) | |||||||
\(788\) | 1.50000 | − | 2.59808i | 0.0534353 | − | 0.0925526i | ||||
\(789\) | 12.0000 | + | 20.7846i | 0.427211 | + | 0.739952i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.00000 | 0.213201 | ||||||||
\(793\) | 0.500000 | + | 0.866025i | 0.0177555 | + | 0.0307535i | ||||
\(794\) | 10.0000 | − | 17.3205i | 0.354887 | − | 0.614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.00000 | − | 13.8564i | −0.283552 | − | 0.491127i | ||||
\(797\) | −9.00000 | −0.318796 | −0.159398 | − | 0.987214i | \(-0.550955\pi\) | ||||
−0.159398 | + | 0.987214i | \(0.550955\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 2.50000 | + | 4.33013i | 0.0883883 | + | 0.153093i | ||||
\(801\) | 18.0000 | − | 31.1769i | 0.635999 | − | 1.10158i | ||||
\(802\) | −12.0000 | + | 20.7846i | −0.423735 | + | 0.733930i | ||||
\(803\) | −16.5000 | − | 28.5788i | −0.582272 | − | 1.00853i | ||||
\(804\) | −5.00000 | −0.176336 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.00000 | 0.176117 | ||||||||
\(807\) | 4.50000 | + | 7.79423i | 0.158408 | + | 0.274370i | ||||
\(808\) | −1.50000 | + | 2.59808i | −0.0527698 | + | 0.0914000i | ||||
\(809\) | −15.0000 | + | 25.9808i | −0.527372 | + | 0.913435i | 0.472119 | + | 0.881535i | \(0.343489\pi\) |
−0.999491 | + | 0.0319002i | \(0.989844\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.0000 | −0.702295 | −0.351147 | − | 0.936320i | \(-0.614208\pi\) | ||||
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.0000 | 0.385787 | ||||||||
\(814\) | −10.5000 | − | 18.1865i | −0.368025 | − | 0.637438i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.00000 | + | 13.8564i | 0.279885 | + | 0.484774i | ||||
\(818\) | 22.0000 | 0.769212 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.00000 | + | 5.19615i | 0.104701 | + | 0.181347i | 0.913616 | − | 0.406578i | \(-0.133278\pi\) |
−0.808915 | + | 0.587925i | \(0.799945\pi\) | |||||||
\(822\) | −3.00000 | + | 5.19615i | −0.104637 | + | 0.181237i | ||||
\(823\) | −20.5000 | + | 35.5070i | −0.714585 | + | 1.23770i | 0.248534 | + | 0.968623i | \(0.420051\pi\) |
−0.963119 | + | 0.269075i | \(0.913282\pi\) | |||||||
\(824\) | 7.00000 | + | 12.1244i | 0.243857 | + | 0.422372i | ||||
\(825\) | −15.0000 | −0.522233 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.0000 | −1.25184 | −0.625921 | − | 0.779886i | \(-0.715277\pi\) | ||||
−0.625921 | + | 0.779886i | \(0.715277\pi\) | |||||||
\(828\) | −3.00000 | − | 5.19615i | −0.104257 | − | 0.180579i | ||||
\(829\) | 19.0000 | − | 32.9090i | 0.659897 | − | 1.14298i | −0.320745 | − | 0.947166i | \(-0.603933\pi\) |
0.980642 | − | 0.195810i | \(-0.0627335\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.0000 | + | 22.5167i | 0.450965 | + | 0.781094i | ||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.00000 | −0.138509 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.00000 | + | 5.19615i | −0.103757 | + | 0.179713i | ||||
\(837\) | 12.5000 | − | 21.6506i | 0.432063 | − | 0.748355i | ||||
\(838\) | 10.5000 | + | 18.1865i | 0.362716 | + | 0.628243i | ||||
\(839\) | 21.0000 | 0.725001 | 0.362500 | − | 0.931984i | \(-0.381923\pi\) | ||||
0.362500 | + | 0.931984i | \(0.381923\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 18.5000 | + | 32.0429i | 0.637552 | + | 1.10427i | ||||
\(843\) | 6.00000 | − | 10.3923i | 0.206651 | − | 0.357930i | ||||
\(844\) | 11.0000 | − | 19.0526i | 0.378636 | − | 0.655816i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.00000 | −0.206284 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −12.0000 | −0.412082 | ||||||||
\(849\) | 15.5000 | + | 26.8468i | 0.531959 | + | 0.921379i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.5000 | + | 18.1865i | −0.359935 | + | 0.623426i | ||||
\(852\) | 6.00000 | + | 10.3923i | 0.205557 | + | 0.356034i | ||||
\(853\) | −44.0000 | −1.50653 | −0.753266 | − | 0.657716i | \(-0.771523\pi\) | ||||
−0.753266 | + | 0.657716i | \(0.771523\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.0000 | − | 46.7654i | 0.922302 | − | 1.59747i | 0.126459 | − | 0.991972i | \(-0.459639\pi\) |
0.795843 | − | 0.605503i | \(-0.207028\pi\) | |||||||
\(858\) | 1.50000 | − | 2.59808i | 0.0512092 | − | 0.0886969i | ||||
\(859\) | 11.5000 | + | 19.9186i | 0.392375 | + | 0.679613i | 0.992762 | − | 0.120096i | \(-0.0383202\pi\) |
−0.600387 | + | 0.799709i | \(0.704987\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.00000 | −0.204361 | ||||||||
\(863\) | −6.00000 | − | 10.3923i | −0.204242 | − | 0.353758i | 0.745649 | − | 0.666339i | \(-0.232140\pi\) |
−0.949891 | + | 0.312581i | \(0.898806\pi\) | |||||||
\(864\) | −2.50000 | + | 4.33013i | −0.0850517 | + | 0.147314i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19.0000 | + | 32.9090i | 0.645646 | + | 1.11829i | ||||
\(867\) | 17.0000 | 0.577350 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.00000 | 0.101768 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.50000 | − | 4.33013i | 0.0847093 | − | 0.146721i | ||||
\(872\) | −1.00000 | + | 1.73205i | −0.0338643 | + | 0.0586546i | ||||
\(873\) | −17.0000 | − | 29.4449i | −0.575363 | − | 0.996558i | ||||
\(874\) | 6.00000 | 0.202953 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.0000 | 0.371656 | ||||||||
\(877\) | 6.50000 | + | 11.2583i | 0.219489 | + | 0.380167i | 0.954652 | − | 0.297724i | \(-0.0962275\pi\) |
−0.735163 | + | 0.677891i | \(0.762894\pi\) | |||||||
\(878\) | 13.0000 | − | 22.5167i | 0.438729 | − | 0.759900i | ||||
\(879\) | −9.00000 | + | 15.5885i | −0.303562 | + | 0.525786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.00000 | −0.202145 | −0.101073 | − | 0.994879i | \(-0.532227\pi\) | ||||
−0.101073 | + | 0.994879i | \(0.532227\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.00000 | 0.0673054 | 0.0336527 | − | 0.999434i | \(-0.489286\pi\) | ||||
0.0336527 | + | 0.999434i | \(0.489286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.0000 | + | 20.7846i | −0.403148 | + | 0.698273i | ||||
\(887\) | 21.0000 | + | 36.3731i | 0.705111 | + | 1.22129i | 0.966651 | + | 0.256096i | \(0.0824362\pi\) |
−0.261540 | + | 0.965193i | \(0.584230\pi\) | |||||||
\(888\) | 7.00000 | 0.234905 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.50000 | + | 2.59808i | 0.0502519 | + | 0.0870388i | ||||
\(892\) | −0.500000 | + | 0.866025i | −0.0167412 | + | 0.0289967i | ||||
\(893\) | 3.00000 | − | 5.19615i | 0.100391 | − | 0.173883i | ||||
\(894\) | −7.50000 | − | 12.9904i | −0.250838 | − | 0.434463i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.00000 | −0.100167 | ||||||||
\(898\) | 3.00000 | + | 5.19615i | 0.100111 | + | 0.173398i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −5.00000 | + | 8.66025i | −0.166667 | + | 0.288675i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 9.00000 | 0.299667 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.00000 | 0.299336 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.00000 | − | 6.92820i | 0.132891 | − | 0.230174i | ||||
\(907\) | −13.0000 | + | 22.5167i | −0.431658 | + | 0.747653i | −0.997016 | − | 0.0771920i | \(-0.975405\pi\) |
0.565358 | + | 0.824845i | \(0.308738\pi\) | |||||||
\(908\) | −12.0000 | − | 20.7846i | −0.398234 | − | 0.689761i | ||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | −1.00000 | − | 1.73205i | −0.0331133 | − | 0.0573539i | ||||
\(913\) | −18.0000 | + | 31.1769i | −0.595713 | + | 1.03181i | ||||
\(914\) | −13.0000 | + | 22.5167i | −0.430002 | + | 0.744785i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.00000 | 0.132164 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.5000 | + | 21.6506i | 0.412337 | + | 0.714189i | 0.995145 | − | 0.0984214i | \(-0.0313793\pi\) |
−0.582808 | + | 0.812610i | \(0.698046\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.00000 | − | 13.8564i | 0.263609 | − | 0.456584i | ||||
\(922\) | 12.0000 | + | 20.7846i | 0.395199 | + | 0.684505i | ||||
\(923\) | −12.0000 | −0.394985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.0000 | 1.15079 | ||||||||
\(926\) | 20.0000 | + | 34.6410i | 0.657241 | + | 1.13837i | ||||
\(927\) | −14.0000 | + | 24.2487i | −0.459820 | + | 0.796432i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.50000 | − | 7.79423i | −0.147640 | − | 0.255720i | 0.782715 | − | 0.622381i | \(-0.213834\pi\) |
−0.930355 | + | 0.366660i | \(0.880501\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.00000 | 0.0982683 | ||||||||
\(933\) | −15.0000 | − | 25.9808i | −0.491078 | − | 0.850572i | ||||
\(934\) | 6.00000 | − | 10.3923i | 0.196326 | − | 0.340047i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.00000 | − | 1.73205i | −0.0326860 | − | 0.0566139i | ||||
\(937\) | 52.0000 | 1.69877 | 0.849383 | − | 0.527777i | \(-0.176974\pi\) | ||||
0.849383 | + | 0.527777i | \(0.176974\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.0000 | 0.848478 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.0000 | − | 25.9808i | 0.488986 | − | 0.846949i | −0.510934 | − | 0.859620i | \(-0.670700\pi\) |
0.999920 | + | 0.0126715i | \(0.00403357\pi\) | |||||||
\(942\) | 6.50000 | − | 11.2583i | 0.211781 | − | 0.366816i | ||||
\(943\) | −4.50000 | − | 7.79423i | −0.146540 | − | 0.253815i | ||||
\(944\) | −6.00000 | −0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.0000 | −0.780307 | ||||||||
\(947\) | −24.0000 | − | 41.5692i | −0.779895 | − | 1.35082i | −0.932002 | − | 0.362454i | \(-0.881939\pi\) |
0.152106 | − | 0.988364i | \(-0.451394\pi\) | |||||||
\(948\) | −0.500000 | + | 0.866025i | −0.0162392 | + | 0.0281272i | ||||
\(949\) | −5.50000 | + | 9.52628i | −0.178538 | + | 0.309236i | ||||
\(950\) | −5.00000 | − | 8.66025i | −0.162221 | − | 0.280976i | ||||
\(951\) | 3.00000 | 0.0972817 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.0000 | −1.36051 | −0.680257 | − | 0.732974i | \(-0.738132\pi\) | ||||
−0.680257 | + | 0.732974i | \(0.738132\pi\) | |||||||
\(954\) | −12.0000 | − | 20.7846i | −0.388514 | − | 0.672927i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.00000 | + | 5.19615i | −0.0970269 | + | 0.168056i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.0000 | −0.775405 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | + | 5.19615i | 0.0967742 | + | 0.167618i | ||||
\(962\) | −3.50000 | + | 6.06218i | −0.112845 | + | 0.195452i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.0000 | + | 22.5167i | 0.418702 | + | 0.725213i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.0000 | −0.707472 | −0.353736 | − | 0.935345i | \(-0.615089\pi\) | ||||
−0.353736 | + | 0.935345i | \(0.615089\pi\) | |||||||
\(968\) | 1.00000 | + | 1.73205i | 0.0321412 | + | 0.0556702i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.5000 | − | 18.1865i | −0.336961 | − | 0.583634i | 0.646899 | − | 0.762576i | \(-0.276066\pi\) |
−0.983860 | + | 0.178942i | \(0.942732\pi\) | |||||||
\(972\) | −16.0000 | −0.513200 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.00000 | 0.0640841 | ||||||||
\(975\) | 2.50000 | + | 4.33013i | 0.0800641 | + | 0.138675i | ||||
\(976\) | −0.500000 | + | 0.866025i | −0.0160046 | + | 0.0277208i | ||||
\(977\) | −9.00000 | + | 15.5885i | −0.287936 | + | 0.498719i | −0.973317 | − | 0.229465i | \(-0.926302\pi\) |
0.685381 | + | 0.728184i | \(0.259636\pi\) | |||||||
\(978\) | 10.0000 | + | 17.3205i | 0.319765 | + | 0.553849i | ||||
\(979\) | −54.0000 | −1.72585 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.00000 | −0.127710 | ||||||||
\(982\) | −6.00000 | − | 10.3923i | −0.191468 | − | 0.331632i | ||||
\(983\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(984\) | −1.50000 | + | 2.59808i | −0.0478183 | + | 0.0828236i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.00000 | 0.0636285 | ||||||||
\(989\) | 12.0000 | + | 20.7846i | 0.381578 | + | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.50000 | + | 9.52628i | −0.174713 | + | 0.302612i | −0.940062 | − | 0.341004i | \(-0.889233\pi\) |
0.765349 | + | 0.643616i | \(0.222567\pi\) | |||||||
\(992\) | 2.50000 | + | 4.33013i | 0.0793751 | + | 0.137482i | ||||
\(993\) | 19.0000 | 0.602947 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.00000 | − | 10.3923i | −0.190117 | − | 0.329293i | ||||
\(997\) | −18.5000 | + | 32.0429i | −0.585901 | + | 1.01481i | 0.408862 | + | 0.912596i | \(0.365926\pi\) |
−0.994762 | + | 0.102214i | \(0.967407\pi\) | |||||||
\(998\) | −11.5000 | + | 19.9186i | −0.364026 | + | 0.630512i | ||||
\(999\) | 17.5000 | + | 30.3109i | 0.553675 | + | 0.958994i |
(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 | 1274.2.f.i.1145.1 | 2 | ||
7.2 | even | 3 | inner | 1274.2.f.i.79.1 | 2 | ||
7.3 | odd | 6 | 182.2.a.d.1.1 | ✓ | 1 | ||
7.4 | even | 3 | 1274.2.a.j.1.1 | 1 | |||
7.5 | odd | 6 | 1274.2.f.d.79.1 | 2 | |||
7.6 | odd | 2 | 1274.2.f.d.1145.1 | 2 | |||
21.17 | even | 6 | 1638.2.a.f.1.1 | 1 | |||
28.3 | even | 6 | 1456.2.a.d.1.1 | 1 | |||
35.24 | odd | 6 | 4550.2.a.c.1.1 | 1 | |||
56.3 | even | 6 | 5824.2.a.x.1.1 | 1 | |||
56.45 | odd | 6 | 5824.2.a.k.1.1 | 1 | |||
91.31 | even | 12 | 2366.2.d.e.337.1 | 2 | |||
91.38 | odd | 6 | 2366.2.a.e.1.1 | 1 | |||
91.73 | even | 12 | 2366.2.d.e.337.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
182.2.a.d.1.1 | ✓ | 1 | 7.3 | odd | 6 | ||
1274.2.a.j.1.1 | 1 | 7.4 | even | 3 | |||
1274.2.f.d.79.1 | 2 | 7.5 | odd | 6 | |||
1274.2.f.d.1145.1 | 2 | 7.6 | odd | 2 | |||
1274.2.f.i.79.1 | 2 | 7.2 | even | 3 | inner | ||
1274.2.f.i.1145.1 | 2 | 1.1 | even | 1 | trivial | ||
1456.2.a.d.1.1 | 1 | 28.3 | even | 6 | |||
1638.2.a.f.1.1 | 1 | 21.17 | even | 6 | |||
2366.2.a.e.1.1 | 1 | 91.38 | odd | 6 | |||
2366.2.d.e.337.1 | 2 | 91.31 | even | 12 | |||
2366.2.d.e.337.2 | 2 | 91.73 | even | 12 | |||
4550.2.a.c.1.1 | 1 | 35.24 | odd | 6 | |||
5824.2.a.k.1.1 | 1 | 56.45 | odd | 6 | |||
5824.2.a.x.1.1 | 1 | 56.3 | even | 6 |