Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(324,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.324");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 324.5 | ||
Root | \(0.403032 + 0.403032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.324 |
Dual form | 475.2.b.d.324.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.48119i | 1.04736i | 0.851914 | + | 0.523681i | \(0.175442\pi\) | ||||
−0.851914 | + | 0.523681i | \(0.824558\pi\) | |||||||
\(3\) | 0.806063i | 0.465381i | 0.972551 | + | 0.232690i | \(0.0747529\pi\) | ||||
−0.972551 | + | 0.232690i | \(0.925247\pi\) | |||||||
\(4\) | −0.193937 | −0.0969683 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.19394 | −0.487423 | ||||||||
\(7\) | − 3.35026i | − 1.26628i | −0.774037 | − | 0.633140i | \(-0.781766\pi\) | ||||
0.774037 | − | 0.633140i | \(-0.218234\pi\) | |||||||
\(8\) | 2.67513i | 0.945802i | ||||||||
\(9\) | 2.35026 | 0.783421 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.962389 | 0.290171 | 0.145086 | − | 0.989419i | \(-0.453654\pi\) | ||||
0.145086 | + | 0.989419i | \(0.453654\pi\) | |||||||
\(12\) | − 0.156325i | − 0.0451272i | ||||||||
\(13\) | 6.15633i | 1.70746i | 0.520718 | + | 0.853729i | \(0.325664\pi\) | ||||
−0.520718 | + | 0.853729i | \(0.674336\pi\) | |||||||
\(14\) | 4.96239 | 1.32625 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.35026 | −1.08757 | ||||||||
\(17\) | 6.31265i | 1.53104i | 0.643411 | + | 0.765521i | \(0.277519\pi\) | ||||
−0.643411 | + | 0.765521i | \(0.722481\pi\) | |||||||
\(18\) | 3.48119i | 0.820525i | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.70052 | 0.589303 | ||||||||
\(22\) | 1.42548i | 0.303914i | ||||||||
\(23\) | − 4.96239i | − 1.03473i | −0.855765 | − | 0.517365i | \(-0.826913\pi\) | ||||
0.855765 | − | 0.517365i | \(-0.173087\pi\) | |||||||
\(24\) | −2.15633 | −0.440158 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.11871 | −1.78833 | ||||||||
\(27\) | 4.31265i | 0.829970i | ||||||||
\(28\) | 0.649738i | 0.122789i | ||||||||
\(29\) | 3.61213 | 0.670755 | 0.335378 | − | 0.942084i | \(-0.391136\pi\) | ||||
0.335378 | + | 0.942084i | \(0.391136\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.92478 | −1.06412 | −0.532061 | − | 0.846706i | \(-0.678582\pi\) | ||||
−0.532061 | + | 0.846706i | \(0.678582\pi\) | |||||||
\(32\) | − 1.09332i | − 0.193274i | ||||||||
\(33\) | 0.775746i | 0.135040i | ||||||||
\(34\) | −9.35026 | −1.60356 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.455802 | −0.0759669 | ||||||||
\(37\) | − 10.1563i | − 1.66969i | −0.550485 | − | 0.834845i | \(-0.685557\pi\) | ||||
0.550485 | − | 0.834845i | \(-0.314443\pi\) | |||||||
\(38\) | 1.48119i | 0.240281i | ||||||||
\(39\) | −4.96239 | −0.794618 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.31265 | 0.985870 | 0.492935 | − | 0.870066i | \(-0.335924\pi\) | ||||
0.492935 | + | 0.870066i | \(0.335924\pi\) | |||||||
\(42\) | 4.00000i | 0.617213i | ||||||||
\(43\) | − 4.12601i | − 0.629210i | −0.949223 | − | 0.314605i | \(-0.898128\pi\) | ||||
0.949223 | − | 0.314605i | \(-0.101872\pi\) | |||||||
\(44\) | −0.186642 | −0.0281374 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.35026 | 1.08374 | ||||||||
\(47\) | − 3.35026i | − 0.488686i | −0.969689 | − | 0.244343i | \(-0.921428\pi\) | ||||
0.969689 | − | 0.244343i | \(-0.0785723\pi\) | |||||||
\(48\) | − 3.50659i | − 0.506132i | ||||||||
\(49\) | −4.22425 | −0.603465 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.08840 | −0.712518 | ||||||||
\(52\) | − 1.19394i | − 0.165569i | ||||||||
\(53\) | 1.84367i | 0.253248i | 0.991951 | + | 0.126624i | \(0.0404142\pi\) | ||||
−0.991951 | + | 0.126624i | \(0.959586\pi\) | |||||||
\(54\) | −6.38787 | −0.869279 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.96239 | 1.19765 | ||||||||
\(57\) | 0.806063i | 0.106766i | ||||||||
\(58\) | 5.35026i | 0.702524i | ||||||||
\(59\) | 6.38787 | 0.831630 | 0.415815 | − | 0.909449i | \(-0.363496\pi\) | ||||
0.415815 | + | 0.909449i | \(0.363496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.2750 | −1.44362 | −0.721810 | − | 0.692091i | \(-0.756690\pi\) | ||||
−0.721810 | + | 0.692091i | \(0.756690\pi\) | |||||||
\(62\) | − 8.77575i | − 1.11452i | ||||||||
\(63\) | − 7.87399i | − 0.992030i | ||||||||
\(64\) | −7.08110 | −0.885138 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.14903 | −0.141436 | ||||||||
\(67\) | 6.73084i | 0.822303i | 0.911567 | + | 0.411152i | \(0.134873\pi\) | ||||
−0.911567 | + | 0.411152i | \(0.865127\pi\) | |||||||
\(68\) | − 1.22425i | − 0.148463i | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.775746 | −0.0920641 | −0.0460321 | − | 0.998940i | \(-0.514658\pi\) | ||||
−0.0460321 | + | 0.998940i | \(0.514658\pi\) | |||||||
\(72\) | 6.28726i | 0.740960i | ||||||||
\(73\) | 0.387873i | 0.0453971i | 0.999742 | + | 0.0226986i | \(0.00722580\pi\) | ||||
−0.999742 | + | 0.0226986i | \(0.992774\pi\) | |||||||
\(74\) | 15.0435 | 1.74877 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.193937 | −0.0222460 | ||||||||
\(77\) | − 3.22425i | − 0.367438i | ||||||||
\(78\) | − 7.35026i | − 0.832253i | ||||||||
\(79\) | 0.836381 | 0.0941002 | 0.0470501 | − | 0.998893i | \(-0.485018\pi\) | ||||
0.0470501 | + | 0.998893i | \(0.485018\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.57452 | 0.397168 | ||||||||
\(82\) | 9.35026i | 1.03256i | ||||||||
\(83\) | − 7.03761i | − 0.772478i | −0.922399 | − | 0.386239i | \(-0.873774\pi\) | ||||
0.922399 | − | 0.386239i | \(-0.126226\pi\) | |||||||
\(84\) | −0.523730 | −0.0571437 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.11142 | 0.659011 | ||||||||
\(87\) | 2.91160i | 0.312157i | ||||||||
\(88\) | 2.57452i | 0.274444i | ||||||||
\(89\) | −7.08840 | −0.751369 | −0.375684 | − | 0.926748i | \(-0.622592\pi\) | ||||
−0.375684 | + | 0.926748i | \(0.622592\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.6253 | 2.16212 | ||||||||
\(92\) | 0.962389i | 0.100336i | ||||||||
\(93\) | − 4.77575i | − 0.495222i | ||||||||
\(94\) | 4.96239 | 0.511831 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.881286 | 0.0899459 | ||||||||
\(97\) | − 10.9927i | − 1.11614i | −0.829794 | − | 0.558070i | \(-0.811542\pi\) | ||||
0.829794 | − | 0.558070i | \(-0.188458\pi\) | |||||||
\(98\) | − 6.25694i | − 0.632046i | ||||||||
\(99\) | 2.26187 | 0.227326 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.64974 | −0.263659 | −0.131829 | − | 0.991272i | \(-0.542085\pi\) | ||||
−0.131829 | + | 0.991272i | \(0.542085\pi\) | |||||||
\(102\) | − 7.53690i | − 0.746265i | ||||||||
\(103\) | − 10.7308i | − 1.05734i | −0.848827 | − | 0.528671i | \(-0.822691\pi\) | ||||
0.848827 | − | 0.528671i | \(-0.177309\pi\) | |||||||
\(104\) | −16.4690 | −1.61492 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.73084 | −0.265243 | ||||||||
\(107\) | − 4.80606i | − 0.464620i | −0.972642 | − | 0.232310i | \(-0.925372\pi\) | ||||
0.972642 | − | 0.232310i | \(-0.0746283\pi\) | |||||||
\(108\) | − 0.836381i | − 0.0804808i | ||||||||
\(109\) | 2.77575 | 0.265868 | 0.132934 | − | 0.991125i | \(-0.457560\pi\) | ||||
0.132934 | + | 0.991125i | \(0.457560\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.18664 | 0.777042 | ||||||||
\(112\) | 14.5745i | 1.37716i | ||||||||
\(113\) | 6.99271i | 0.657818i | 0.944362 | + | 0.328909i | \(0.106681\pi\) | ||||
−0.944362 | + | 0.328909i | \(0.893319\pi\) | |||||||
\(114\) | −1.19394 | −0.111822 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.700523 | −0.0650420 | ||||||||
\(117\) | 14.4690i | 1.33766i | ||||||||
\(118\) | 9.46168i | 0.871018i | ||||||||
\(119\) | 21.1490 | 1.93873 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0738 | −0.915801 | ||||||||
\(122\) | − 16.7005i | − 1.51199i | ||||||||
\(123\) | 5.08840i | 0.458805i | ||||||||
\(124\) | 1.14903 | 0.103186 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 11.6629 | 1.03901 | ||||||||
\(127\) | − 13.4314i | − 1.19184i | −0.803043 | − | 0.595920i | \(-0.796787\pi\) | ||||
0.803043 | − | 0.595920i | \(-0.203213\pi\) | |||||||
\(128\) | − 12.6751i | − 1.12033i | ||||||||
\(129\) | 3.32582 | 0.292822 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.6253 | 1.80204 | 0.901020 | − | 0.433777i | \(-0.142819\pi\) | ||||
0.901020 | + | 0.433777i | \(0.142819\pi\) | |||||||
\(132\) | − 0.150446i | − 0.0130946i | ||||||||
\(133\) | − 3.35026i | − 0.290505i | ||||||||
\(134\) | −9.96968 | −0.861249 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −16.8872 | −1.44806 | ||||||||
\(137\) | − 20.2374i | − 1.72900i | −0.502633 | − | 0.864500i | \(-0.667635\pi\) | ||||
0.502633 | − | 0.864500i | \(-0.332365\pi\) | |||||||
\(138\) | 5.92478i | 0.504351i | ||||||||
\(139\) | 17.5877 | 1.49177 | 0.745884 | − | 0.666076i | \(-0.232027\pi\) | ||||
0.745884 | + | 0.666076i | \(0.232027\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.70052 | 0.227425 | ||||||||
\(142\) | − 1.14903i | − 0.0964245i | ||||||||
\(143\) | 5.92478i | 0.495455i | ||||||||
\(144\) | −10.2243 | −0.852021 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.574515 | −0.0475472 | ||||||||
\(147\) | − 3.40502i | − 0.280841i | ||||||||
\(148\) | 1.96968i | 0.161907i | ||||||||
\(149\) | 7.42548 | 0.608319 | 0.304160 | − | 0.952621i | \(-0.401624\pi\) | ||||
0.304160 | + | 0.952621i | \(0.401624\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.61213 | −0.131193 | −0.0655965 | − | 0.997846i | \(-0.520895\pi\) | ||||
−0.0655965 | + | 0.997846i | \(0.520895\pi\) | |||||||
\(152\) | 2.67513i | 0.216982i | ||||||||
\(153\) | 14.8364i | 1.19945i | ||||||||
\(154\) | 4.77575 | 0.384841 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.962389 | 0.0770528 | ||||||||
\(157\) | − 4.38787i | − 0.350190i | −0.984552 | − | 0.175095i | \(-0.943977\pi\) | ||||
0.984552 | − | 0.175095i | \(-0.0560233\pi\) | |||||||
\(158\) | 1.23884i | 0.0985570i | ||||||||
\(159\) | −1.48612 | −0.117857 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.6253 | −1.31026 | ||||||||
\(162\) | 5.29455i | 0.415979i | ||||||||
\(163\) | − 0.649738i | − 0.0508914i | −0.999676 | − | 0.0254457i | \(-0.991900\pi\) | ||||
0.999676 | − | 0.0254457i | \(-0.00810050\pi\) | |||||||
\(164\) | −1.22425 | −0.0955982 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.4241 | 0.809065 | ||||||||
\(167\) | 15.3561i | 1.18829i | 0.804357 | + | 0.594147i | \(0.202510\pi\) | ||||
−0.804357 | + | 0.594147i | \(0.797490\pi\) | |||||||
\(168\) | 7.22425i | 0.557363i | ||||||||
\(169\) | −24.9003 | −1.91541 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.35026 | 0.179729 | ||||||||
\(172\) | 0.800184i | 0.0610134i | ||||||||
\(173\) | 3.24472i | 0.246692i | 0.992364 | + | 0.123346i | \(0.0393624\pi\) | ||||
−0.992364 | + | 0.123346i | \(0.960638\pi\) | |||||||
\(174\) | −4.31265 | −0.326941 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.18664 | −0.315580 | ||||||||
\(177\) | 5.14903i | 0.387025i | ||||||||
\(178\) | − 10.4993i | − 0.786955i | ||||||||
\(179\) | −15.0132 | −1.12214 | −0.561069 | − | 0.827769i | \(-0.689610\pi\) | ||||
−0.561069 | + | 0.827769i | \(0.689610\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.22425 | 0.685633 | 0.342817 | − | 0.939402i | \(-0.388619\pi\) | ||||
0.342817 | + | 0.939402i | \(0.388619\pi\) | |||||||
\(182\) | 30.5501i | 2.26452i | ||||||||
\(183\) | − 9.08840i | − 0.671834i | ||||||||
\(184\) | 13.2750 | 0.978649 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.07381 | 0.518677 | ||||||||
\(187\) | 6.07522i | 0.444264i | ||||||||
\(188\) | 0.649738i | 0.0473870i | ||||||||
\(189\) | 14.4485 | 1.05097 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.7743 | −1.57554 | −0.787768 | − | 0.615972i | \(-0.788763\pi\) | ||||
−0.787768 | + | 0.615972i | \(0.788763\pi\) | |||||||
\(192\) | − 5.70782i | − 0.411926i | ||||||||
\(193\) | 12.5442i | 0.902951i | 0.892283 | + | 0.451476i | \(0.149102\pi\) | ||||
−0.892283 | + | 0.451476i | \(0.850898\pi\) | |||||||
\(194\) | 16.2823 | 1.16900 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.819237 | 0.0585169 | ||||||||
\(197\) | − 24.5501i | − 1.74912i | −0.484917 | − | 0.874560i | \(-0.661150\pi\) | ||||
0.484917 | − | 0.874560i | \(-0.338850\pi\) | |||||||
\(198\) | 3.35026i | 0.238093i | ||||||||
\(199\) | −23.0738 | −1.63566 | −0.817829 | − | 0.575461i | \(-0.804823\pi\) | ||||
−0.817829 | + | 0.575461i | \(0.804823\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.42548 | −0.382684 | ||||||||
\(202\) | − 3.92478i | − 0.276146i | ||||||||
\(203\) | − 12.1016i | − 0.849364i | ||||||||
\(204\) | 0.986826 | 0.0690917 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.8945 | 1.10742 | ||||||||
\(207\) | − 11.6629i | − 0.810628i | ||||||||
\(208\) | − 26.7816i | − 1.85697i | ||||||||
\(209\) | 0.962389 | 0.0665698 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.9380 | −1.44143 | −0.720714 | − | 0.693233i | \(-0.756186\pi\) | ||||
−0.720714 | + | 0.693233i | \(0.756186\pi\) | |||||||
\(212\) | − 0.357556i | − 0.0245570i | ||||||||
\(213\) | − 0.625301i | − 0.0428449i | ||||||||
\(214\) | 7.11871 | 0.486625 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −11.5369 | −0.784987 | ||||||||
\(217\) | 19.8496i | 1.34748i | ||||||||
\(218\) | 4.11142i | 0.278460i | ||||||||
\(219\) | −0.312650 | −0.0211270 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −38.8627 | −2.61419 | ||||||||
\(222\) | 12.1260i | 0.813844i | ||||||||
\(223\) | − 0.0303172i | − 0.00203019i | −0.999999 | − | 0.00101509i | \(-0.999677\pi\) | ||||
0.999999 | − | 0.00101509i | \(-0.000323114\pi\) | |||||||
\(224\) | −3.66291 | −0.244739 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.3576 | −0.688974 | ||||||||
\(227\) | − 4.80606i | − 0.318990i | −0.987199 | − | 0.159495i | \(-0.949013\pi\) | ||||
0.987199 | − | 0.159495i | \(-0.0509865\pi\) | |||||||
\(228\) | − 0.156325i | − 0.0103529i | ||||||||
\(229\) | −1.87399 | −0.123837 | −0.0619184 | − | 0.998081i | \(-0.519722\pi\) | ||||
−0.0619184 | + | 0.998081i | \(0.519722\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.59895 | 0.170999 | ||||||||
\(232\) | 9.66291i | 0.634401i | ||||||||
\(233\) | − 11.1490i | − 0.730397i | −0.930930 | − | 0.365199i | \(-0.881001\pi\) | ||||
0.930930 | − | 0.365199i | \(-0.118999\pi\) | |||||||
\(234\) | −21.4314 | −1.40101 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.23884 | −0.0806418 | ||||||||
\(237\) | 0.674176i | 0.0437924i | ||||||||
\(238\) | 31.3258i | 2.03055i | ||||||||
\(239\) | −9.29948 | −0.601533 | −0.300767 | − | 0.953698i | \(-0.597243\pi\) | ||||
−0.300767 | + | 0.953698i | \(0.597243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.31265 | −0.148971 | −0.0744855 | − | 0.997222i | \(-0.523731\pi\) | ||||
−0.0744855 | + | 0.997222i | \(0.523731\pi\) | |||||||
\(242\) | − 14.9213i | − 0.959175i | ||||||||
\(243\) | 15.8192i | 1.01480i | ||||||||
\(244\) | 2.18664 | 0.139985 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.53690 | −0.480535 | ||||||||
\(247\) | 6.15633i | 0.391718i | ||||||||
\(248\) | − 15.8496i | − 1.00645i | ||||||||
\(249\) | 5.67276 | 0.359497 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.1016 | 1.52128 | 0.760639 | − | 0.649175i | \(-0.224886\pi\) | ||||
0.760639 | + | 0.649175i | \(0.224886\pi\) | |||||||
\(252\) | 1.52705i | 0.0961954i | ||||||||
\(253\) | − 4.77575i | − 0.300249i | ||||||||
\(254\) | 19.8945 | 1.24829 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.61213 | 0.288258 | ||||||||
\(257\) | 13.3199i | 0.830875i | 0.909622 | + | 0.415438i | \(0.136372\pi\) | ||||
−0.909622 | + | 0.415438i | \(0.863628\pi\) | |||||||
\(258\) | 4.92619i | 0.306691i | ||||||||
\(259\) | −34.0263 | −2.11429 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.48944 | 0.525483 | ||||||||
\(262\) | 30.5501i | 1.88739i | ||||||||
\(263\) | 12.9624i | 0.799295i | 0.916669 | + | 0.399648i | \(0.130867\pi\) | ||||
−0.916669 | + | 0.399648i | \(0.869133\pi\) | |||||||
\(264\) | −2.07522 | −0.127721 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.96239 | 0.304264 | ||||||||
\(267\) | − 5.71370i | − 0.349673i | ||||||||
\(268\) | − 1.30536i | − 0.0797373i | ||||||||
\(269\) | 11.4010 | 0.695134 | 0.347567 | − | 0.937655i | \(-0.387008\pi\) | ||||
0.347567 | + | 0.937655i | \(0.387008\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.8119 | 1.02125 | 0.510626 | − | 0.859803i | \(-0.329414\pi\) | ||||
0.510626 | + | 0.859803i | \(0.329414\pi\) | |||||||
\(272\) | − 27.4617i | − 1.66511i | ||||||||
\(273\) | 16.6253i | 1.00621i | ||||||||
\(274\) | 29.9756 | 1.81089 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.775746 | −0.0466944 | ||||||||
\(277\) | 29.7889i | 1.78984i | 0.446224 | + | 0.894921i | \(0.352769\pi\) | ||||
−0.446224 | + | 0.894921i | \(0.647231\pi\) | |||||||
\(278\) | 26.0508i | 1.56242i | ||||||||
\(279\) | −13.9248 | −0.833655 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.6121 | −0.692721 | −0.346361 | − | 0.938101i | \(-0.612583\pi\) | ||||
−0.346361 | + | 0.938101i | \(0.612583\pi\) | |||||||
\(282\) | 4.00000i | 0.238197i | ||||||||
\(283\) | 2.26187i | 0.134454i | 0.997738 | + | 0.0672270i | \(0.0214152\pi\) | ||||
−0.997738 | + | 0.0672270i | \(0.978585\pi\) | |||||||
\(284\) | 0.150446 | 0.00892730 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.77575 | −0.518921 | ||||||||
\(287\) | − 21.1490i | − 1.24839i | ||||||||
\(288\) | − 2.56959i | − 0.151415i | ||||||||
\(289\) | −22.8496 | −1.34409 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.86082 | 0.519430 | ||||||||
\(292\) | − 0.0752228i | − 0.00440208i | ||||||||
\(293\) | 1.84367i | 0.107709i | 0.998549 | + | 0.0538543i | \(0.0171507\pi\) | ||||
−0.998549 | + | 0.0538543i | \(0.982849\pi\) | |||||||
\(294\) | 5.04349 | 0.294142 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 27.1695 | 1.57920 | ||||||||
\(297\) | 4.15045i | 0.240833i | ||||||||
\(298\) | 10.9986i | 0.637131i | ||||||||
\(299\) | 30.5501 | 1.76676 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.8232 | −0.796756 | ||||||||
\(302\) | − 2.38787i | − 0.137407i | ||||||||
\(303\) | − 2.13586i | − 0.122702i | ||||||||
\(304\) | −4.35026 | −0.249505 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −21.9756 | −1.25626 | ||||||||
\(307\) | − 26.2071i | − 1.49572i | −0.663857 | − | 0.747859i | \(-0.731082\pi\) | ||||
0.663857 | − | 0.747859i | \(-0.268918\pi\) | |||||||
\(308\) | 0.625301i | 0.0356298i | ||||||||
\(309\) | 8.64974 | 0.492066 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.51388 | 0.369368 | 0.184684 | − | 0.982798i | \(-0.440874\pi\) | ||||
0.184684 | + | 0.982798i | \(0.440874\pi\) | |||||||
\(312\) | − 13.2750i | − 0.751551i | ||||||||
\(313\) | 16.0752i | 0.908625i | 0.890842 | + | 0.454313i | \(0.150115\pi\) | ||||
−0.890842 | + | 0.454313i | \(0.849885\pi\) | |||||||
\(314\) | 6.49929 | 0.366776 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.162205 | −0.00912473 | ||||||||
\(317\) | 5.69323i | 0.319764i | 0.987136 | + | 0.159882i | \(0.0511113\pi\) | ||||
−0.987136 | + | 0.159882i | \(0.948889\pi\) | |||||||
\(318\) | − 2.20123i | − 0.123439i | ||||||||
\(319\) | 3.47627 | 0.194634 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.87399 | 0.216225 | ||||||||
\(322\) | − 24.6253i | − 1.37231i | ||||||||
\(323\) | 6.31265i | 0.351245i | ||||||||
\(324\) | −0.693229 | −0.0385127 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.962389 | 0.0533018 | ||||||||
\(327\) | 2.23743i | 0.123730i | ||||||||
\(328\) | 16.8872i | 0.932438i | ||||||||
\(329\) | −11.2243 | −0.618813 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.3127 | −0.676764 | −0.338382 | − | 0.941009i | \(-0.609880\pi\) | ||||
−0.338382 | + | 0.941009i | \(0.609880\pi\) | |||||||
\(332\) | 1.36485i | 0.0749059i | ||||||||
\(333\) | − 23.8700i | − 1.30807i | ||||||||
\(334\) | −22.7454 | −1.24457 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −11.7480 | −0.640905 | ||||||||
\(337\) | − 3.76845i | − 0.205281i | −0.994719 | − | 0.102640i | \(-0.967271\pi\) | ||||
0.994719 | − | 0.102640i | \(-0.0327291\pi\) | |||||||
\(338\) | − 36.8822i | − 2.00613i | ||||||||
\(339\) | −5.63656 | −0.306136 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.70194 | −0.308777 | ||||||||
\(342\) | 3.48119i | 0.188241i | ||||||||
\(343\) | − 9.29948i | − 0.502125i | ||||||||
\(344\) | 11.0376 | 0.595108 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.80606 | −0.258376 | ||||||||
\(347\) | 22.3634i | 1.20053i | 0.799800 | + | 0.600266i | \(0.204939\pi\) | ||||
−0.799800 | + | 0.600266i | \(0.795061\pi\) | |||||||
\(348\) | − 0.564666i | − 0.0302693i | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.5501 | −1.41714 | ||||||||
\(352\) | − 1.05220i | − 0.0560824i | ||||||||
\(353\) | 5.53690i | 0.294700i | 0.989084 | + | 0.147350i | \(0.0470743\pi\) | ||||
−0.989084 | + | 0.147350i | \(0.952926\pi\) | |||||||
\(354\) | −7.62672 | −0.405355 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.37470 | 0.0728589 | ||||||||
\(357\) | 17.0475i | 0.902247i | ||||||||
\(358\) | − 22.2374i | − 1.17528i | ||||||||
\(359\) | 10.3634 | 0.546961 | 0.273481 | − | 0.961878i | \(-0.411825\pi\) | ||||
0.273481 | + | 0.961878i | \(0.411825\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 13.6629i | 0.718107i | ||||||||
\(363\) | − 8.12013i | − 0.426196i | ||||||||
\(364\) | −4.00000 | −0.209657 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 13.4617 | 0.703653 | ||||||||
\(367\) | − 3.35026i | − 0.174882i | −0.996170 | − | 0.0874411i | \(-0.972131\pi\) | ||||
0.996170 | − | 0.0874411i | \(-0.0278690\pi\) | |||||||
\(368\) | 21.5877i | 1.12534i | ||||||||
\(369\) | 14.8364 | 0.772351 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.17679 | 0.320683 | ||||||||
\(372\) | 0.926192i | 0.0480208i | ||||||||
\(373\) | − 12.6048i | − 0.652653i | −0.945257 | − | 0.326327i | \(-0.894189\pi\) | ||||
0.945257 | − | 0.326327i | \(-0.105811\pi\) | |||||||
\(374\) | −8.99859 | −0.465306 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.96239 | 0.462200 | ||||||||
\(377\) | 22.2374i | 1.14529i | ||||||||
\(378\) | 21.4010i | 1.10075i | ||||||||
\(379\) | 37.2506 | 1.91343 | 0.956717 | − | 0.291018i | \(-0.0939941\pi\) | ||||
0.956717 | + | 0.291018i | \(0.0939941\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.8265 | 0.554660 | ||||||||
\(382\) | − 32.2520i | − 1.65016i | ||||||||
\(383\) | 30.8324i | 1.57546i | 0.616019 | + | 0.787731i | \(0.288744\pi\) | ||||
−0.616019 | + | 0.787731i | \(0.711256\pi\) | |||||||
\(384\) | 10.2170 | 0.521382 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.5804 | −0.945717 | ||||||||
\(387\) | − 9.69720i | − 0.492936i | ||||||||
\(388\) | 2.13189i | 0.108230i | ||||||||
\(389\) | 1.37470 | 0.0697000 | 0.0348500 | − | 0.999393i | \(-0.488905\pi\) | ||||
0.0348500 | + | 0.999393i | \(0.488905\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.3258 | 1.58422 | ||||||||
\(392\) | − 11.3004i | − 0.570758i | ||||||||
\(393\) | 16.6253i | 0.838635i | ||||||||
\(394\) | 36.3634 | 1.83196 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.438658 | −0.0220434 | ||||||||
\(397\) | 9.38646i | 0.471093i | 0.971863 | + | 0.235546i | \(0.0756880\pi\) | ||||
−0.971863 | + | 0.235546i | \(0.924312\pi\) | |||||||
\(398\) | − 34.1768i | − 1.71313i | ||||||||
\(399\) | 2.70052 | 0.135195 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.1016 | 0.704199 | 0.352099 | − | 0.935963i | \(-0.385468\pi\) | ||||
0.352099 | + | 0.935963i | \(0.385468\pi\) | |||||||
\(402\) | − 8.03620i | − 0.400809i | ||||||||
\(403\) | − 36.4749i | − 1.81694i | ||||||||
\(404\) | 0.513881 | 0.0255665 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.9248 | 0.889592 | ||||||||
\(407\) | − 9.77433i | − 0.484496i | ||||||||
\(408\) | − 13.6121i | − 0.673901i | ||||||||
\(409\) | −35.1490 | −1.73801 | −0.869004 | − | 0.494805i | \(-0.835239\pi\) | ||||
−0.869004 | + | 0.494805i | \(0.835239\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.3127 | 0.804644 | ||||||||
\(412\) | 2.08110i | 0.102529i | ||||||||
\(413\) | − 21.4010i | − 1.05308i | ||||||||
\(414\) | 17.2750 | 0.849022 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.73084 | 0.330007 | ||||||||
\(417\) | 14.1768i | 0.694241i | ||||||||
\(418\) | 1.42548i | 0.0697227i | ||||||||
\(419\) | −9.02776 | −0.441035 | −0.220518 | − | 0.975383i | \(-0.570775\pi\) | ||||
−0.220518 | + | 0.975383i | \(0.570775\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.2097 | 0.741274 | 0.370637 | − | 0.928778i | \(-0.379139\pi\) | ||||
0.370637 | + | 0.928778i | \(0.379139\pi\) | |||||||
\(422\) | − 31.0132i | − 1.50970i | ||||||||
\(423\) | − 7.87399i | − 0.382847i | ||||||||
\(424\) | −4.93207 | −0.239523 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.926192 | 0.0448741 | ||||||||
\(427\) | 37.7743i | 1.82803i | ||||||||
\(428\) | 0.932071i | 0.0450534i | ||||||||
\(429\) | −4.77575 | −0.230575 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.3127 | 0.785753 | 0.392876 | − | 0.919591i | \(-0.371480\pi\) | ||||
0.392876 | + | 0.919591i | \(0.371480\pi\) | |||||||
\(432\) | − 18.7612i | − 0.902647i | ||||||||
\(433\) | 11.1432i | 0.535506i | 0.963488 | + | 0.267753i | \(0.0862811\pi\) | ||||
−0.963488 | + | 0.267753i | \(0.913719\pi\) | |||||||
\(434\) | −29.4010 | −1.41130 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.538319 | −0.0257808 | ||||||||
\(437\) | − 4.96239i | − 0.237383i | ||||||||
\(438\) | − 0.463096i | − 0.0221276i | ||||||||
\(439\) | −27.3865 | −1.30708 | −0.653542 | − | 0.756890i | \(-0.726718\pi\) | ||||
−0.653542 | + | 0.756890i | \(0.726718\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.92810 | −0.472767 | ||||||||
\(442\) | − 57.5633i | − 2.73800i | ||||||||
\(443\) | 19.5125i | 0.927065i | 0.886080 | + | 0.463533i | \(0.153418\pi\) | ||||
−0.886080 | + | 0.463533i | \(0.846582\pi\) | |||||||
\(444\) | −1.58769 | −0.0753484 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.0449056 | 0.00212634 | ||||||||
\(447\) | 5.98541i | 0.283100i | ||||||||
\(448\) | 23.7235i | 1.12083i | ||||||||
\(449\) | 22.1016 | 1.04304 | 0.521519 | − | 0.853240i | \(-0.325366\pi\) | ||||
0.521519 | + | 0.853240i | \(0.325366\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.07522 | 0.286071 | ||||||||
\(452\) | − 1.35614i | − 0.0637875i | ||||||||
\(453\) | − 1.29948i | − 0.0610547i | ||||||||
\(454\) | 7.11871 | 0.334098 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.15633 | −0.100979 | ||||||||
\(457\) | 17.8496i | 0.834967i | 0.908685 | + | 0.417483i | \(0.137088\pi\) | ||||
−0.908685 | + | 0.417483i | \(0.862912\pi\) | |||||||
\(458\) | − 2.77575i | − 0.129702i | ||||||||
\(459\) | −27.2243 | −1.27072 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.2506 | −1.64178 | −0.820892 | − | 0.571083i | \(-0.806523\pi\) | ||||
−0.820892 | + | 0.571083i | \(0.806523\pi\) | |||||||
\(462\) | 3.84955i | 0.179097i | ||||||||
\(463\) | − 26.3634i | − 1.22521i | −0.790388 | − | 0.612606i | \(-0.790121\pi\) | ||||
0.790388 | − | 0.612606i | \(-0.209879\pi\) | |||||||
\(464\) | −15.7137 | −0.729490 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.5139 | 0.764991 | ||||||||
\(467\) | 6.78560i | 0.314000i | 0.987599 | + | 0.157000i | \(0.0501823\pi\) | ||||
−0.987599 | + | 0.157000i | \(0.949818\pi\) | |||||||
\(468\) | − 2.80606i | − 0.129710i | ||||||||
\(469\) | 22.5501 | 1.04127 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.53690 | 0.162972 | ||||||||
\(472\) | 17.0884i | 0.786557i | ||||||||
\(473\) | − 3.97082i | − 0.182579i | ||||||||
\(474\) | −0.998585 | −0.0458665 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.10157 | −0.187995 | ||||||||
\(477\) | 4.33312i | 0.198400i | ||||||||
\(478\) | − 13.7743i | − 0.630023i | ||||||||
\(479\) | −12.7104 | −0.580752 | −0.290376 | − | 0.956913i | \(-0.593780\pi\) | ||||
−0.290376 | + | 0.956913i | \(0.593780\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 62.5256 | 2.85092 | ||||||||
\(482\) | − 3.42548i | − 0.156027i | ||||||||
\(483\) | − 13.4010i | − 0.609769i | ||||||||
\(484\) | 1.95368 | 0.0888036 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −23.4314 | −1.06287 | ||||||||
\(487\) | 15.7586i | 0.714090i | 0.934087 | + | 0.357045i | \(0.116216\pi\) | ||||
−0.934087 | + | 0.357045i | \(0.883784\pi\) | |||||||
\(488\) | − 30.1622i | − 1.36538i | ||||||||
\(489\) | 0.523730 | 0.0236839 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.5501 | −0.656636 | −0.328318 | − | 0.944567i | \(-0.606482\pi\) | ||||
−0.328318 | + | 0.944567i | \(0.606482\pi\) | |||||||
\(492\) | − 0.986826i | − 0.0444896i | ||||||||
\(493\) | 22.8021i | 1.02695i | ||||||||
\(494\) | −9.11871 | −0.410270 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 25.7743 | 1.15730 | ||||||||
\(497\) | 2.59895i | 0.116579i | ||||||||
\(498\) | 8.40246i | 0.376523i | ||||||||
\(499\) | 5.48612 | 0.245592 | 0.122796 | − | 0.992432i | \(-0.460814\pi\) | ||||
0.122796 | + | 0.992432i | \(0.460814\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.3780 | −0.553009 | ||||||||
\(502\) | 35.6991i | 1.59333i | ||||||||
\(503\) | − 36.6615i | − 1.63466i | −0.576173 | − | 0.817328i | \(-0.695455\pi\) | ||||
0.576173 | − | 0.817328i | \(-0.304545\pi\) | |||||||
\(504\) | 21.0640 | 0.938263 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.07381 | 0.314469 | ||||||||
\(507\) | − 20.0713i | − 0.891396i | ||||||||
\(508\) | 2.60483i | 0.115571i | ||||||||
\(509\) | −39.1900 | −1.73706 | −0.868532 | − | 0.495632i | \(-0.834936\pi\) | ||||
−0.868532 | + | 0.495632i | \(0.834936\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.29948 | 0.0574855 | ||||||||
\(512\) | − 18.5188i | − 0.818423i | ||||||||
\(513\) | 4.31265i | 0.190408i | ||||||||
\(514\) | −19.7294 | −0.870228 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.644999 | −0.0283945 | ||||||||
\(517\) | − 3.22425i | − 0.141803i | ||||||||
\(518\) | − 50.3996i | − 2.21443i | ||||||||
\(519\) | −2.61545 | −0.114806 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.7283 | −0.776690 | −0.388345 | − | 0.921514i | \(-0.626953\pi\) | ||||
−0.388345 | + | 0.921514i | \(0.626953\pi\) | |||||||
\(522\) | 12.5745i | 0.550372i | ||||||||
\(523\) | − 40.7572i | − 1.78219i | −0.453819 | − | 0.891094i | \(-0.649939\pi\) | ||||
0.453819 | − | 0.891094i | \(-0.350061\pi\) | |||||||
\(524\) | −4.00000 | −0.174741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.1998 | −0.837152 | ||||||||
\(527\) | − 37.4010i | − 1.62922i | ||||||||
\(528\) | − 3.37470i | − 0.146865i | ||||||||
\(529\) | −1.62530 | −0.0706652 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.0132 | 0.651516 | ||||||||
\(532\) | 0.649738i | 0.0281697i | ||||||||
\(533\) | 38.8627i | 1.68333i | ||||||||
\(534\) | 8.46310 | 0.366234 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −18.0059 | −0.777736 | ||||||||
\(537\) | − 12.1016i | − 0.522221i | ||||||||
\(538\) | 16.8872i | 0.728057i | ||||||||
\(539\) | −4.06537 | −0.175108 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.9003 | 1.02756 | 0.513778 | − | 0.857923i | \(-0.328246\pi\) | ||||
0.513778 | + | 0.857923i | \(0.328246\pi\) | |||||||
\(542\) | 24.9018i | 1.06962i | ||||||||
\(543\) | 7.43533i | 0.319081i | ||||||||
\(544\) | 6.90175 | 0.295910 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −24.6253 | −1.05387 | ||||||||
\(547\) | − 8.55405i | − 0.365745i | −0.983137 | − | 0.182872i | \(-0.941461\pi\) | ||||
0.983137 | − | 0.182872i | \(-0.0585395\pi\) | |||||||
\(548\) | 3.92478i | 0.167658i | ||||||||
\(549\) | −26.4993 | −1.13096 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.61213 | 0.153882 | ||||||||
\(552\) | 10.7005i | 0.455445i | ||||||||
\(553\) | − 2.80209i | − 0.119157i | ||||||||
\(554\) | −44.1232 | −1.87461 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.41090 | −0.144654 | ||||||||
\(557\) | 4.23743i | 0.179546i | 0.995962 | + | 0.0897728i | \(0.0286141\pi\) | ||||
−0.995962 | + | 0.0897728i | \(0.971386\pi\) | |||||||
\(558\) | − 20.6253i | − 0.873139i | ||||||||
\(559\) | 25.4010 | 1.07435 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.89701 | −0.206752 | ||||||||
\(562\) | − 17.1998i | − 0.725530i | ||||||||
\(563\) | 16.4934i | 0.695114i | 0.937659 | + | 0.347557i | \(0.112989\pi\) | ||||
−0.937659 | + | 0.347557i | \(0.887011\pi\) | |||||||
\(564\) | −0.523730 | −0.0220530 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.35026 | −0.140822 | ||||||||
\(567\) | − 11.9756i | − 0.502926i | ||||||||
\(568\) | − 2.07522i | − 0.0870744i | ||||||||
\(569\) | 10.0000 | 0.419222 | 0.209611 | − | 0.977785i | \(-0.432780\pi\) | ||||
0.209611 | + | 0.977785i | \(0.432780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.2619 | −1.09902 | −0.549512 | − | 0.835486i | \(-0.685186\pi\) | ||||
−0.549512 | + | 0.835486i | \(0.685186\pi\) | |||||||
\(572\) | − 1.14903i | − 0.0480434i | ||||||||
\(573\) | − 17.5515i | − 0.733224i | ||||||||
\(574\) | 31.3258 | 1.30751 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −16.6424 | −0.693435 | ||||||||
\(577\) | − 30.1016i | − 1.25314i | −0.779363 | − | 0.626572i | \(-0.784457\pi\) | ||||
0.779363 | − | 0.626572i | \(-0.215543\pi\) | |||||||
\(578\) | − 33.8446i | − 1.40775i | ||||||||
\(579\) | −10.1114 | −0.420216 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.5778 | −0.978174 | ||||||||
\(582\) | 13.1246i | 0.544032i | ||||||||
\(583\) | 1.77433i | 0.0734853i | ||||||||
\(584\) | −1.03761 | −0.0429367 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.73084 | −0.112810 | ||||||||
\(587\) | 35.1392i | 1.45035i | 0.688565 | + | 0.725175i | \(0.258241\pi\) | ||||
−0.688565 | + | 0.725175i | \(0.741759\pi\) | |||||||
\(588\) | 0.660357i | 0.0272327i | ||||||||
\(589\) | −5.92478 | −0.244126 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.7889 | 0.814007 | ||||||||
\(592\) | 44.1827i | 1.81590i | ||||||||
\(593\) | 34.3244i | 1.40953i | 0.709439 | + | 0.704767i | \(0.248949\pi\) | ||||
−0.709439 | + | 0.704767i | \(0.751051\pi\) | |||||||
\(594\) | −6.14762 | −0.252240 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.44007 | −0.0589877 | ||||||||
\(597\) | − 18.5990i | − 0.761204i | ||||||||
\(598\) | 45.2506i | 1.85043i | ||||||||
\(599\) | −14.6107 | −0.596978 | −0.298489 | − | 0.954413i | \(-0.596483\pi\) | ||||
−0.298489 | + | 0.954413i | \(0.596483\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.5633 | 0.961165 | 0.480583 | − | 0.876949i | \(-0.340425\pi\) | ||||
0.480583 | + | 0.876949i | \(0.340425\pi\) | |||||||
\(602\) | − 20.4749i | − 0.834493i | ||||||||
\(603\) | 15.8192i | 0.644209i | ||||||||
\(604\) | 0.312650 | 0.0127216 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.16362 | 0.128513 | ||||||||
\(607\) | 8.80606i | 0.357427i | 0.983901 | + | 0.178714i | \(0.0571935\pi\) | ||||
−0.983901 | + | 0.178714i | \(0.942806\pi\) | |||||||
\(608\) | − 1.09332i | − 0.0443400i | ||||||||
\(609\) | 9.75463 | 0.395278 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.6253 | 0.834410 | ||||||||
\(612\) | − 2.87732i | − 0.116309i | ||||||||
\(613\) | 10.4142i | 0.420626i | 0.977634 | + | 0.210313i | \(0.0674484\pi\) | ||||
−0.977634 | + | 0.210313i | \(0.932552\pi\) | |||||||
\(614\) | 38.8178 | 1.56656 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.62530 | 0.347523 | ||||||||
\(617\) | 17.2849i | 0.695863i | 0.937520 | + | 0.347932i | \(0.113116\pi\) | ||||
−0.937520 | + | 0.347932i | \(0.886884\pi\) | |||||||
\(618\) | 12.8119i | 0.515372i | ||||||||
\(619\) | 10.6351 | 0.427463 | 0.213731 | − | 0.976892i | \(-0.431438\pi\) | ||||
0.213731 | + | 0.976892i | \(0.431438\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21.4010 | 0.858794 | ||||||||
\(622\) | 9.64832i | 0.386863i | ||||||||
\(623\) | 23.7480i | 0.951443i | ||||||||
\(624\) | 21.5877 | 0.864199 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −23.8105 | −0.951660 | ||||||||
\(627\) | 0.775746i | 0.0309803i | ||||||||
\(628\) | 0.850969i | 0.0339574i | ||||||||
\(629\) | 64.1133 | 2.55637 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.5599 | −0.659240 | −0.329620 | − | 0.944114i | \(-0.606921\pi\) | ||||
−0.329620 | + | 0.944114i | \(0.606921\pi\) | |||||||
\(632\) | 2.23743i | 0.0890001i | ||||||||
\(633\) | − 16.8773i | − 0.670813i | ||||||||
\(634\) | −8.43278 | −0.334908 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.288213 | 0.0114284 | ||||||||
\(637\) | − 26.0059i | − 1.03039i | ||||||||
\(638\) | 5.14903i | 0.203852i | ||||||||
\(639\) | −1.82321 | −0.0721249 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.7612 | −0.662026 | −0.331013 | − | 0.943626i | \(-0.607390\pi\) | ||||
−0.331013 | + | 0.943626i | \(0.607390\pi\) | |||||||
\(642\) | 5.73813i | 0.226466i | ||||||||
\(643\) | 5.73813i | 0.226290i | 0.993578 | + | 0.113145i | \(0.0360925\pi\) | ||||
−0.993578 | + | 0.113145i | \(0.963908\pi\) | |||||||
\(644\) | 3.22425 | 0.127053 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.35026 | −0.367881 | ||||||||
\(647\) | 37.2144i | 1.46305i | 0.681815 | + | 0.731525i | \(0.261191\pi\) | ||||
−0.681815 | + | 0.731525i | \(0.738809\pi\) | |||||||
\(648\) | 9.56230i | 0.375642i | ||||||||
\(649\) | 6.14762 | 0.241315 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.0000 | −0.627089 | ||||||||
\(652\) | 0.126008i | 0.00493485i | ||||||||
\(653\) | 11.7626i | 0.460305i | 0.973155 | + | 0.230153i | \(0.0739225\pi\) | ||||
−0.973155 | + | 0.230153i | \(0.926077\pi\) | |||||||
\(654\) | −3.31406 | −0.129590 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −27.4617 | −1.07220 | ||||||||
\(657\) | 0.911603i | 0.0355650i | ||||||||
\(658\) | − 16.6253i | − 0.648122i | ||||||||
\(659\) | −1.23884 | −0.0482584 | −0.0241292 | − | 0.999709i | \(-0.507681\pi\) | ||||
−0.0241292 | + | 0.999709i | \(0.507681\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.53690 | −0.370943 | −0.185471 | − | 0.982650i | \(-0.559381\pi\) | ||||
−0.185471 | + | 0.982650i | \(0.559381\pi\) | |||||||
\(662\) | − 18.2374i | − 0.708818i | ||||||||
\(663\) | − 31.3258i | − 1.21659i | ||||||||
\(664\) | 18.8265 | 0.730611 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 35.3561 | 1.37002 | ||||||||
\(667\) | − 17.9248i | − 0.694050i | ||||||||
\(668\) | − 2.97812i | − 0.115227i | ||||||||
\(669\) | 0.0244376 | 0.000944811 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.8510 | −0.418897 | ||||||||
\(672\) | − 2.95254i | − 0.113897i | ||||||||
\(673\) | 39.9307i | 1.53921i | 0.638518 | + | 0.769607i | \(0.279548\pi\) | ||||
−0.638518 | + | 0.769607i | \(0.720452\pi\) | |||||||
\(674\) | 5.58181 | 0.215003 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.82909 | 0.185734 | ||||||||
\(677\) | 3.05334i | 0.117349i | 0.998277 | + | 0.0586747i | \(0.0186875\pi\) | ||||
−0.998277 | + | 0.0586747i | \(0.981313\pi\) | |||||||
\(678\) | − 8.34885i | − 0.320636i | ||||||||
\(679\) | −36.8284 | −1.41335 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.87399 | 0.148452 | ||||||||
\(682\) | − 8.44568i | − 0.323402i | ||||||||
\(683\) | 29.2692i | 1.11995i | 0.828508 | + | 0.559977i | \(0.189190\pi\) | ||||
−0.828508 | + | 0.559977i | \(0.810810\pi\) | |||||||
\(684\) | −0.455802 | −0.0174280 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 13.7743 | 0.525906 | ||||||||
\(687\) | − 1.51056i | − 0.0576313i | ||||||||
\(688\) | 17.9492i | 0.684307i | ||||||||
\(689\) | −11.3503 | −0.432411 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.63515 | 0.100246 | 0.0501229 | − | 0.998743i | \(-0.484039\pi\) | ||||
0.0501229 | + | 0.998743i | \(0.484039\pi\) | |||||||
\(692\) | − 0.629270i | − 0.0239213i | ||||||||
\(693\) | − 7.57784i | − 0.287858i | ||||||||
\(694\) | −33.1246 | −1.25739 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.78892 | −0.295238 | ||||||||
\(697\) | 39.8496i | 1.50941i | ||||||||
\(698\) | 14.8119i | 0.560640i | ||||||||
\(699\) | 8.98683 | 0.339913 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.0494 | −0.946102 | −0.473051 | − | 0.881035i | \(-0.656847\pi\) | ||||
−0.473051 | + | 0.881035i | \(0.656847\pi\) | |||||||
\(702\) | − 39.3258i | − 1.48426i | ||||||||
\(703\) | − 10.1563i | − 0.383053i | ||||||||
\(704\) | −6.81477 | −0.256841 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.20123 | −0.308657 | ||||||||
\(707\) | 8.87732i | 0.333866i | ||||||||
\(708\) | − 0.998585i | − 0.0375291i | ||||||||
\(709\) | 41.6991 | 1.56604 | 0.783021 | − | 0.621995i | \(-0.213677\pi\) | ||||
0.783021 | + | 0.621995i | \(0.213677\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.96571 | 0.0737200 | ||||||||
\(712\) | − 18.9624i | − 0.710646i | ||||||||
\(713\) | 29.4010i | 1.10108i | ||||||||
\(714\) | −25.2506 | −0.944980 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.91160 | 0.108812 | ||||||||
\(717\) | − 7.49597i | − 0.279942i | ||||||||
\(718\) | 15.3503i | 0.572867i | ||||||||
\(719\) | −30.6351 | −1.14250 | −0.571249 | − | 0.820777i | \(-0.693541\pi\) | ||||
−0.571249 | + | 0.820777i | \(0.693541\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.9511 | −1.33889 | ||||||||
\(722\) | 1.48119i | 0.0551243i | ||||||||
\(723\) | − 1.86414i | − 0.0693282i | ||||||||
\(724\) | −1.78892 | −0.0664847 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 12.0275 | 0.446382 | ||||||||
\(727\) | − 7.50071i | − 0.278186i | −0.990279 | − | 0.139093i | \(-0.955581\pi\) | ||||
0.990279 | − | 0.139093i | \(-0.0444187\pi\) | |||||||
\(728\) | 55.1754i | 2.04494i | ||||||||
\(729\) | −2.02776 | −0.0751023 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.0460 | 0.963348 | ||||||||
\(732\) | 1.76257i | 0.0651466i | ||||||||
\(733\) | 9.84955i | 0.363802i | 0.983317 | + | 0.181901i | \(0.0582250\pi\) | ||||
−0.983317 | + | 0.181901i | \(0.941775\pi\) | |||||||
\(734\) | 4.96239 | 0.183165 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.42548 | −0.199986 | ||||||||
\(737\) | 6.47768i | 0.238609i | ||||||||
\(738\) | 21.9756i | 0.808932i | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.96239 | −0.182298 | ||||||||
\(742\) | 9.14903i | 0.335871i | ||||||||
\(743\) | − 15.7177i | − 0.576625i | −0.957536 | − | 0.288313i | \(-0.906906\pi\) | ||||
0.957536 | − | 0.288313i | \(-0.0930942\pi\) | |||||||
\(744\) | 12.7757 | 0.468382 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 18.6702 | 0.683565 | ||||||||
\(747\) | − 16.5402i | − 0.605175i | ||||||||
\(748\) | − 1.17821i | − 0.0430795i | ||||||||
\(749\) | −16.1016 | −0.588339 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.7400 | −1.59610 | −0.798048 | − | 0.602593i | \(-0.794134\pi\) | ||||
−0.798048 | + | 0.602593i | \(0.794134\pi\) | |||||||
\(752\) | 14.5745i | 0.531478i | ||||||||
\(753\) | 19.4274i | 0.707974i | ||||||||
\(754\) | −32.9380 | −1.19953 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.80209 | −0.101911 | ||||||||
\(757\) | 15.7743i | 0.573328i | 0.958031 | + | 0.286664i | \(0.0925463\pi\) | ||||
−0.958031 | + | 0.286664i | \(0.907454\pi\) | |||||||
\(758\) | 55.1754i | 2.00406i | ||||||||
\(759\) | 3.84955 | 0.139730 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.2262 | 1.56695 | 0.783474 | − | 0.621425i | \(-0.213446\pi\) | ||||
0.783474 | + | 0.621425i | \(0.213446\pi\) | |||||||
\(762\) | 16.0362i | 0.580930i | ||||||||
\(763\) | − 9.29948i | − 0.336664i | ||||||||
\(764\) | 4.22284 | 0.152777 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −45.6688 | −1.65008 | ||||||||
\(767\) | 39.3258i | 1.41997i | ||||||||
\(768\) | 3.71767i | 0.134150i | ||||||||
\(769\) | 19.1246 | 0.689650 | 0.344825 | − | 0.938667i | \(-0.387938\pi\) | ||||
0.344825 | + | 0.938667i | \(0.387938\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.7367 | −0.386674 | ||||||||
\(772\) | − 2.43278i | − 0.0875576i | ||||||||
\(773\) | 25.8846i | 0.931005i | 0.885047 | + | 0.465502i | \(0.154126\pi\) | ||||
−0.885047 | + | 0.465502i | \(0.845874\pi\) | |||||||
\(774\) | 14.3634 | 0.516283 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 29.4069 | 1.05565 | ||||||||
\(777\) | − 27.4274i | − 0.983952i | ||||||||
\(778\) | 2.03620i | 0.0730012i | ||||||||
\(779\) | 6.31265 | 0.226174 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.746569 | −0.0267144 | ||||||||
\(782\) | 46.3996i | 1.65925i | ||||||||
\(783\) | 15.5778i | 0.556707i | ||||||||
\(784\) | 18.3766 | 0.656307 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −24.6253 | −0.878355 | ||||||||
\(787\) | − 19.9814i | − 0.712261i | −0.934436 | − | 0.356131i | \(-0.884096\pi\) | ||||
0.934436 | − | 0.356131i | \(-0.115904\pi\) | |||||||
\(788\) | 4.76116i | 0.169609i | ||||||||
\(789\) | −10.4485 | −0.371977 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.4274 | 0.832982 | ||||||||
\(792\) | 6.05079i | 0.215005i | ||||||||
\(793\) | − 69.4128i | − 2.46492i | ||||||||
\(794\) | −13.9032 | −0.493405 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.47486 | 0.158607 | ||||||||
\(797\) | − 28.6458i | − 1.01469i | −0.861744 | − | 0.507343i | \(-0.830628\pi\) | ||||
0.861744 | − | 0.507343i | \(-0.169372\pi\) | |||||||
\(798\) | 4.00000i | 0.141598i | ||||||||
\(799\) | 21.1490 | 0.748199 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.6596 | −0.588638 | ||||||||
\(802\) | 20.8872i | 0.737551i | ||||||||
\(803\) | 0.373285i | 0.0131729i | ||||||||
\(804\) | 1.05220 | 0.0371082 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 54.0263 | 1.90300 | ||||||||
\(807\) | 9.18997i | 0.323502i | ||||||||
\(808\) | − 7.08840i | − 0.249369i | ||||||||
\(809\) | 17.2243 | 0.605573 | 0.302786 | − | 0.953058i | \(-0.402083\pi\) | ||||
0.302786 | + | 0.953058i | \(0.402083\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.6267 | −0.548728 | −0.274364 | − | 0.961626i | \(-0.588467\pi\) | ||||
−0.274364 | + | 0.961626i | \(0.588467\pi\) | |||||||
\(812\) | 2.34694i | 0.0823613i | ||||||||
\(813\) | 13.5515i | 0.475272i | ||||||||
\(814\) | 14.4777 | 0.507443 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 22.1359 | 0.774910 | ||||||||
\(817\) | − 4.12601i | − 0.144351i | ||||||||
\(818\) | − 52.0625i | − 1.82032i | ||||||||
\(819\) | 48.4749 | 1.69385 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.2506 | 1.36986 | 0.684928 | − | 0.728611i | \(-0.259834\pi\) | ||||
0.684928 | + | 0.728611i | \(0.259834\pi\) | |||||||
\(822\) | 24.1622i | 0.842754i | ||||||||
\(823\) | − 45.5271i | − 1.58697i | −0.608588 | − | 0.793487i | \(-0.708264\pi\) | ||||
0.608588 | − | 0.793487i | \(-0.291736\pi\) | |||||||
\(824\) | 28.7064 | 1.00003 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 31.6991 | 1.10295 | ||||||||
\(827\) | − 17.0698i | − 0.593576i | −0.954943 | − | 0.296788i | \(-0.904084\pi\) | ||||
0.954943 | − | 0.296788i | \(-0.0959155\pi\) | |||||||
\(828\) | 2.26187i | 0.0786052i | ||||||||
\(829\) | −1.69911 | −0.0590125 | −0.0295062 | − | 0.999565i | \(-0.509393\pi\) | ||||
−0.0295062 | + | 0.999565i | \(0.509393\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.0118 | −0.832959 | ||||||||
\(832\) | − 43.5936i | − 1.51134i | ||||||||
\(833\) | − 26.6662i | − 0.923930i | ||||||||
\(834\) | −20.9986 | −0.727122 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.186642 | −0.00645516 | ||||||||
\(837\) | − 25.5515i | − 0.883189i | ||||||||
\(838\) | − 13.3719i | − 0.461924i | ||||||||
\(839\) | 50.5910 | 1.74660 | 0.873298 | − | 0.487187i | \(-0.161977\pi\) | ||||
0.873298 | + | 0.487187i | \(0.161977\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9525 | −0.550088 | ||||||||
\(842\) | 22.5285i | 0.776382i | ||||||||
\(843\) | − 9.36011i | − 0.322379i | ||||||||
\(844\) | 4.06063 | 0.139773 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11.6629 | 0.400979 | ||||||||
\(847\) | 33.7499i | 1.15966i | ||||||||
\(848\) | − 8.02047i | − 0.275424i | ||||||||
\(849\) | −1.82321 | −0.0625723 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −50.3996 | −1.72768 | ||||||||
\(852\) | 0.121269i | 0.00415460i | ||||||||
\(853\) | − 22.5237i | − 0.771198i | −0.922667 | − | 0.385599i | \(-0.873995\pi\) | ||||
0.922667 | − | 0.385599i | \(-0.126005\pi\) | |||||||
\(854\) | −55.9511 | −1.91461 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.8568 | 0.439438 | ||||||||
\(857\) | 23.6180i | 0.806776i | 0.915029 | + | 0.403388i | \(0.132167\pi\) | ||||
−0.915029 | + | 0.403388i | \(0.867833\pi\) | |||||||
\(858\) | − 7.07381i | − 0.241496i | ||||||||
\(859\) | −15.1754 | −0.517777 | −0.258889 | − | 0.965907i | \(-0.583356\pi\) | ||||
−0.258889 | + | 0.965907i | \(0.583356\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.0475 | 0.580976 | ||||||||
\(862\) | 24.1622i | 0.822968i | ||||||||
\(863\) | 30.1055i | 1.02480i | 0.858746 | + | 0.512402i | \(0.171244\pi\) | ||||
−0.858746 | + | 0.512402i | \(0.828756\pi\) | |||||||
\(864\) | 4.71511 | 0.160411 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.5052 | −0.560869 | ||||||||
\(867\) | − 18.4182i | − 0.625515i | ||||||||
\(868\) | − 3.84955i | − 0.130662i | ||||||||
\(869\) | 0.804923 | 0.0273051 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.4372 | −1.40405 | ||||||||
\(872\) | 7.42548i | 0.251459i | ||||||||
\(873\) | − 25.8357i | − 0.874407i | ||||||||
\(874\) | 7.35026 | 0.248626 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.0606343 | 0.00204864 | ||||||||
\(877\) | 5.53102i | 0.186769i | 0.995630 | + | 0.0933847i | \(0.0297687\pi\) | ||||
−0.995630 | + | 0.0933847i | \(0.970231\pi\) | |||||||
\(878\) | − 40.5647i | − 1.36899i | ||||||||
\(879\) | −1.48612 | −0.0501255 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.8265 | 0.701664 | 0.350832 | − | 0.936438i | \(-0.385899\pi\) | ||||
0.350832 | + | 0.936438i | \(0.385899\pi\) | |||||||
\(882\) | − 14.7054i | − 0.495158i | ||||||||
\(883\) | 43.1509i | 1.45214i | 0.687618 | + | 0.726072i | \(0.258656\pi\) | ||||
−0.687618 | + | 0.726072i | \(0.741344\pi\) | |||||||
\(884\) | 7.53690 | 0.253494 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.9018 | −0.970973 | ||||||||
\(887\) | 44.5461i | 1.49571i | 0.663861 | + | 0.747856i | \(0.268917\pi\) | ||||
−0.663861 | + | 0.747856i | \(0.731083\pi\) | |||||||
\(888\) | 21.9003i | 0.734927i | ||||||||
\(889\) | −44.9986 | −1.50920 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.44007 | 0.115247 | ||||||||
\(892\) | 0.00587961i | 0 0.000196864i | ||||||||
\(893\) | − 3.35026i | − 0.112112i | ||||||||
\(894\) | −8.86556 | −0.296509 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −42.4650 | −1.41866 | ||||||||
\(897\) | 24.6253i | 0.822215i | ||||||||
\(898\) | 32.7367i | 1.09244i | ||||||||
\(899\) | −21.4010 | −0.713765 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.6385 | −0.387734 | ||||||||
\(902\) | 8.99859i | 0.299620i | ||||||||
\(903\) | − 11.1424i | − 0.370795i | ||||||||
\(904\) | −18.7064 | −0.622166 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.92478 | 0.0639464 | ||||||||
\(907\) | − 53.7558i | − 1.78493i | −0.451115 | − | 0.892466i | \(-0.648974\pi\) | ||||
0.451115 | − | 0.892466i | \(-0.351026\pi\) | |||||||
\(908\) | 0.932071i | 0.0309319i | ||||||||
\(909\) | −6.22758 | −0.206556 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.28630 | −0.0757486 | −0.0378743 | − | 0.999283i | \(-0.512059\pi\) | ||||
−0.0378743 | + | 0.999283i | \(0.512059\pi\) | |||||||
\(912\) | − 3.50659i | − 0.116115i | ||||||||
\(913\) | − 6.77292i | − 0.224151i | ||||||||
\(914\) | −26.4387 | −0.874513 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.363436 | 0.0120082 | ||||||||
\(917\) | − 69.1002i | − 2.28189i | ||||||||
\(918\) | − 40.3244i | − 1.33090i | ||||||||
\(919\) | 34.8510 | 1.14963 | 0.574814 | − | 0.818284i | \(-0.305075\pi\) | ||||
0.574814 | + | 0.818284i | \(0.305075\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.1246 | 0.696079 | ||||||||
\(922\) | − 52.2130i | − 1.71954i | ||||||||
\(923\) | − 4.77575i | − 0.157196i | ||||||||
\(924\) | −0.504032 | −0.0165814 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 39.0494 | 1.28324 | ||||||||
\(927\) | − 25.2203i | − 0.828343i | ||||||||
\(928\) | − 3.94921i | − 0.129639i | ||||||||
\(929\) | −41.6991 | −1.36810 | −0.684052 | − | 0.729434i | \(-0.739784\pi\) | ||||
−0.684052 | + | 0.729434i | \(0.739784\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.22425 | −0.138444 | ||||||||
\(932\) | 2.16220i | 0.0708254i | ||||||||
\(933\) | 5.25060i | 0.171897i | ||||||||
\(934\) | −10.0508 | −0.328872 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −38.7064 | −1.26516 | ||||||||
\(937\) | − 21.9102i | − 0.715775i | −0.933765 | − | 0.357887i | \(-0.883497\pi\) | ||||
0.933765 | − | 0.357887i | \(-0.116503\pi\) | |||||||
\(938\) | 33.4010i | 1.09058i | ||||||||
\(939\) | −12.9576 | −0.422857 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.55149 | −0.115775 | −0.0578877 | − | 0.998323i | \(-0.518437\pi\) | ||||
−0.0578877 | + | 0.998323i | \(0.518437\pi\) | |||||||
\(942\) | 5.23884i | 0.170691i | ||||||||
\(943\) | − 31.3258i | − 1.02011i | ||||||||
\(944\) | −27.7889 | −0.904452 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.88156 | 0.191226 | ||||||||
\(947\) | − 38.3634i | − 1.24664i | −0.781965 | − | 0.623322i | \(-0.785783\pi\) | ||||
0.781965 | − | 0.623322i | \(-0.214217\pi\) | |||||||
\(948\) | − 0.130747i | − 0.00424648i | ||||||||
\(949\) | −2.38787 | −0.0775136 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.58910 | −0.148812 | ||||||||
\(952\) | 56.5764i | 1.83365i | ||||||||
\(953\) | − 22.8714i | − 0.740879i | −0.928857 | − | 0.370439i | \(-0.879207\pi\) | ||||
0.928857 | − | 0.370439i | \(-0.120793\pi\) | |||||||
\(954\) | −6.41819 | −0.207797 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.80351 | 0.0583296 | ||||||||
\(957\) | 2.80209i | 0.0905788i | ||||||||
\(958\) | − 18.8265i | − 0.608258i | ||||||||
\(959\) | −67.8007 | −2.18940 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.10299 | 0.132354 | ||||||||
\(962\) | 92.6126i | 2.98595i | ||||||||
\(963\) | − 11.2955i | − 0.363993i | ||||||||
\(964\) | 0.448507 | 0.0144455 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 19.8496 | 0.638649 | ||||||||
\(967\) | − 27.6629i | − 0.889579i | −0.895635 | − | 0.444790i | \(-0.853278\pi\) | ||||
0.895635 | − | 0.444790i | \(-0.146722\pi\) | |||||||
\(968\) | − 26.9488i | − 0.866166i | ||||||||
\(969\) | −5.08840 | −0.163463 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.1768 | −1.35352 | −0.676759 | − | 0.736205i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736205i | \(0.736616\pi\) | |||||||
\(972\) | − 3.06793i | − 0.0984039i | ||||||||
\(973\) | − 58.9234i | − 1.88900i | ||||||||
\(974\) | −23.3416 | −0.747912 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 49.0494 | 1.57003 | ||||||||
\(977\) | − 0.856849i | − 0.0274130i | −0.999906 | − | 0.0137065i | \(-0.995637\pi\) | ||||
0.999906 | − | 0.0137065i | \(-0.00436305\pi\) | |||||||
\(978\) | 0.775746i | 0.0248056i | ||||||||
\(979\) | −6.82179 | −0.218025 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.52373 | 0.208287 | ||||||||
\(982\) | − 21.5515i | − 0.687736i | ||||||||
\(983\) | 45.2809i | 1.44424i | 0.691769 | + | 0.722119i | \(0.256831\pi\) | ||||
−0.691769 | + | 0.722119i | \(0.743169\pi\) | |||||||
\(984\) | −13.6121 | −0.433939 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −33.7743 | −1.07559 | ||||||||
\(987\) | − 9.04746i | − 0.287984i | ||||||||
\(988\) | − 1.19394i | − 0.0379842i | ||||||||
\(989\) | −20.4749 | −0.651063 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.0132 | 1.49342 | 0.746711 | − | 0.665148i | \(-0.231632\pi\) | ||||
0.746711 | + | 0.665148i | \(0.231632\pi\) | |||||||
\(992\) | 6.47768i | 0.205667i | ||||||||
\(993\) | − 9.92478i | − 0.314953i | ||||||||
\(994\) | −3.84955 | −0.122100 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.10016 | −0.0348598 | ||||||||
\(997\) | − 13.6873i | − 0.433483i | −0.976229 | − | 0.216741i | \(-0.930457\pi\) | ||||
0.976229 | − | 0.216741i | \(-0.0695428\pi\) | |||||||
\(998\) | 8.12601i | 0.257224i | ||||||||
\(999\) | 43.8007 | 1.38579 |
(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 | 475.2.b.d.324.5 | 6 | ||
5.2 | odd | 4 | 95.2.a.a.1.1 | ✓ | 3 | ||
5.3 | odd | 4 | 475.2.a.f.1.3 | 3 | |||
5.4 | even | 2 | inner | 475.2.b.d.324.2 | 6 | ||
15.2 | even | 4 | 855.2.a.i.1.3 | 3 | |||
15.8 | even | 4 | 4275.2.a.bk.1.1 | 3 | |||
20.3 | even | 4 | 7600.2.a.bx.1.2 | 3 | |||
20.7 | even | 4 | 1520.2.a.p.1.2 | 3 | |||
35.27 | even | 4 | 4655.2.a.u.1.1 | 3 | |||
40.27 | even | 4 | 6080.2.a.by.1.2 | 3 | |||
40.37 | odd | 4 | 6080.2.a.bo.1.2 | 3 | |||
95.18 | even | 4 | 9025.2.a.bb.1.1 | 3 | |||
95.37 | even | 4 | 1805.2.a.f.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.a.a.1.1 | ✓ | 3 | 5.2 | odd | 4 | ||
475.2.a.f.1.3 | 3 | 5.3 | odd | 4 | |||
475.2.b.d.324.2 | 6 | 5.4 | even | 2 | inner | ||
475.2.b.d.324.5 | 6 | 1.1 | even | 1 | trivial | ||
855.2.a.i.1.3 | 3 | 15.2 | even | 4 | |||
1520.2.a.p.1.2 | 3 | 20.7 | even | 4 | |||
1805.2.a.f.1.3 | 3 | 95.37 | even | 4 | |||
4275.2.a.bk.1.1 | 3 | 15.8 | even | 4 | |||
4655.2.a.u.1.1 | 3 | 35.27 | even | 4 | |||
6080.2.a.bo.1.2 | 3 | 40.37 | odd | 4 | |||
6080.2.a.by.1.2 | 3 | 40.27 | even | 4 | |||
7600.2.a.bx.1.2 | 3 | 20.3 | even | 4 | |||
9025.2.a.bb.1.1 | 3 | 95.18 | even | 4 |