Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,3,Mod(26,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.26");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.04360198270\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-11}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 26.1 | ||
Root | \(0.500000 + 1.65831i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.26 |
Dual form | 75.3.c.c.26.2 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.31662i | − | 1.65831i | −0.559017 | − | 0.829156i | \(-0.688821\pi\) | ||
0.559017 | − | 0.829156i | \(-0.311179\pi\) | |||||||
\(3\) | −2.50000 | − | 1.65831i | −0.833333 | − | 0.552771i | ||||
\(4\) | −7.00000 | −1.75000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.50000 | + | 8.29156i | −0.916667 | + | 1.38193i | ||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 9.94987i | 1.24373i | ||||||||
\(9\) | 3.50000 | + | 8.29156i | 0.388889 | + | 0.921285i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 16.5831i | − | 1.50756i | −0.657129 | − | 0.753778i | \(-0.728229\pi\) | ||
0.657129 | − | 0.753778i | \(-0.271771\pi\) | |||||||
\(12\) | 17.5000 | + | 11.6082i | 1.45833 | + | 0.967349i | ||||
\(13\) | −10.0000 | −0.769231 | −0.384615 | − | 0.923077i | \(-0.625666\pi\) | ||||
−0.384615 | + | 0.923077i | \(0.625666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.00000 | 0.312500 | ||||||||
\(17\) | − | 3.31662i | − | 0.195096i | −0.995231 | − | 0.0975478i | \(-0.968900\pi\) | ||
0.995231 | − | 0.0975478i | \(-0.0310999\pi\) | |||||||
\(18\) | 27.5000 | − | 11.6082i | 1.52778 | − | 0.644899i | ||||
\(19\) | 7.00000 | 0.368421 | 0.184211 | − | 0.982887i | \(-0.441027\pi\) | ||||
0.184211 | + | 0.982887i | \(0.441027\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −55.0000 | −2.50000 | ||||||||
\(23\) | − | 19.8997i | − | 0.865206i | −0.901584 | − | 0.432603i | \(-0.857595\pi\) | ||
0.901584 | − | 0.432603i | \(-0.142405\pi\) | |||||||
\(24\) | 16.5000 | − | 24.8747i | 0.687500 | − | 1.03645i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 33.1662i | 1.27562i | ||||||||
\(27\) | 5.00000 | − | 26.5330i | 0.185185 | − | 0.982704i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 33.1662i | − | 1.14366i | −0.820371 | − | 0.571832i | \(-0.806233\pi\) | ||
0.820371 | − | 0.571832i | \(-0.193767\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 42.0000 | 1.35484 | 0.677419 | − | 0.735597i | \(-0.263098\pi\) | ||||
0.677419 | + | 0.735597i | \(0.263098\pi\) | |||||||
\(32\) | 23.2164i | 0.725512i | ||||||||
\(33\) | −27.5000 | + | 41.4578i | −0.833333 | + | 1.25630i | ||||
\(34\) | −11.0000 | −0.323529 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −24.5000 | − | 58.0409i | −0.680556 | − | 1.61225i | ||||
\(37\) | 40.0000 | 1.08108 | 0.540541 | − | 0.841318i | \(-0.318220\pi\) | ||||
0.540541 | + | 0.841318i | \(0.318220\pi\) | |||||||
\(38\) | − | 23.2164i | − | 0.610957i | ||||||
\(39\) | 25.0000 | + | 16.5831i | 0.641026 | + | 0.425208i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16.5831i | 0.404466i | 0.979337 | + | 0.202233i | \(0.0648199\pi\) | ||||
−0.979337 | + | 0.202233i | \(0.935180\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 50.0000 | 1.16279 | 0.581395 | − | 0.813621i | \(-0.302507\pi\) | ||||
0.581395 | + | 0.813621i | \(0.302507\pi\) | |||||||
\(44\) | 116.082i | 2.63822i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −66.0000 | −1.43478 | ||||||||
\(47\) | 46.4327i | 0.987931i | 0.869482 | + | 0.493965i | \(0.164453\pi\) | ||||
−0.869482 | + | 0.493965i | \(0.835547\pi\) | |||||||
\(48\) | −12.5000 | − | 8.29156i | −0.260417 | − | 0.172741i | ||||
\(49\) | −49.0000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.50000 | + | 8.29156i | −0.107843 | + | 0.162580i | ||||
\(52\) | 70.0000 | 1.34615 | ||||||||
\(53\) | 46.4327i | 0.876090i | 0.898953 | + | 0.438045i | \(0.144329\pi\) | ||||
−0.898953 | + | 0.438045i | \(0.855671\pi\) | |||||||
\(54\) | −88.0000 | − | 16.5831i | −1.62963 | − | 0.307095i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17.5000 | − | 11.6082i | −0.307018 | − | 0.203652i | ||||
\(58\) | −110.000 | −1.89655 | ||||||||
\(59\) | − | 66.3325i | − | 1.12428i | −0.827042 | − | 0.562140i | \(-0.809978\pi\) | ||
0.827042 | − | 0.562140i | \(-0.190022\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.00000 | −0.131148 | −0.0655738 | − | 0.997848i | \(-0.520888\pi\) | ||||
−0.0655738 | + | 0.997848i | \(0.520888\pi\) | |||||||
\(62\) | − | 139.298i | − | 2.24675i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 97.0000 | 1.51562 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 137.500 | + | 91.2072i | 2.08333 | + | 1.38193i | ||||
\(67\) | −45.0000 | −0.671642 | −0.335821 | − | 0.941926i | \(-0.609014\pi\) | ||||
−0.335821 | + | 0.941926i | \(0.609014\pi\) | |||||||
\(68\) | 23.2164i | 0.341417i | ||||||||
\(69\) | −33.0000 | + | 49.7494i | −0.478261 | + | 0.721005i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 33.1662i | − | 0.467130i | −0.972341 | − | 0.233565i | \(-0.924961\pi\) | ||
0.972341 | − | 0.233565i | \(-0.0750392\pi\) | |||||||
\(72\) | −82.5000 | + | 34.8246i | −1.14583 | + | 0.483674i | ||||
\(73\) | 35.0000 | 0.479452 | 0.239726 | − | 0.970841i | \(-0.422942\pi\) | ||||
0.239726 | + | 0.970841i | \(0.422942\pi\) | |||||||
\(74\) | − | 132.665i | − | 1.79277i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −49.0000 | −0.644737 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 55.0000 | − | 82.9156i | 0.705128 | − | 1.06302i | ||||
\(79\) | 12.0000 | 0.151899 | 0.0759494 | − | 0.997112i | \(-0.475801\pi\) | ||||
0.0759494 | + | 0.997112i | \(0.475801\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −56.5000 | + | 58.0409i | −0.697531 | + | 0.716555i | ||||
\(82\) | 55.0000 | 0.670732 | ||||||||
\(83\) | − | 69.6491i | − | 0.839146i | −0.907722 | − | 0.419573i | \(-0.862180\pi\) | ||
0.907722 | − | 0.419573i | \(-0.137820\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 165.831i | − | 1.92827i | ||||||
\(87\) | −55.0000 | + | 82.9156i | −0.632184 | + | 0.953053i | ||||
\(88\) | 165.000 | 1.87500 | ||||||||
\(89\) | 149.248i | 1.67695i | 0.544944 | + | 0.838473i | \(0.316551\pi\) | ||||
−0.544944 | + | 0.838473i | \(0.683449\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 139.298i | 1.51411i | ||||||||
\(93\) | −105.000 | − | 69.6491i | −1.12903 | − | 0.748915i | ||||
\(94\) | 154.000 | 1.63830 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 38.5000 | − | 58.0409i | 0.401042 | − | 0.604593i | ||||
\(97\) | 70.0000 | 0.721649 | 0.360825 | − | 0.932634i | \(-0.382495\pi\) | ||||
0.360825 | + | 0.932634i | \(0.382495\pi\) | |||||||
\(98\) | 162.515i | 1.65831i | ||||||||
\(99\) | 137.500 | − | 58.0409i | 1.38889 | − | 0.586272i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 27.5000 | + | 18.2414i | 0.269608 | + | 0.178838i | ||||
\(103\) | 70.0000 | 0.679612 | 0.339806 | − | 0.940496i | \(-0.389639\pi\) | ||||
0.339806 | + | 0.940496i | \(0.389639\pi\) | |||||||
\(104\) | − | 99.4987i | − | 0.956719i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 154.000 | 1.45283 | ||||||||
\(107\) | − | 69.6491i | − | 0.650926i | −0.945555 | − | 0.325463i | \(-0.894480\pi\) | ||
0.945555 | − | 0.325463i | \(-0.105520\pi\) | |||||||
\(108\) | −35.0000 | + | 185.731i | −0.324074 | + | 1.71973i | ||||
\(109\) | −88.0000 | −0.807339 | −0.403670 | − | 0.914905i | \(-0.632266\pi\) | ||||
−0.403670 | + | 0.914905i | \(0.632266\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −100.000 | − | 66.3325i | −0.900901 | − | 0.597590i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 102.815i | − | 0.909871i | −0.890525 | − | 0.454935i | \(-0.849662\pi\) | ||
0.890525 | − | 0.454935i | \(-0.150338\pi\) | |||||||
\(114\) | −38.5000 | + | 58.0409i | −0.337719 | + | 0.509131i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 232.164i | 2.00141i | ||||||||
\(117\) | −35.0000 | − | 82.9156i | −0.299145 | − | 0.708681i | ||||
\(118\) | −220.000 | −1.86441 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −154.000 | −1.27273 | ||||||||
\(122\) | 26.5330i | 0.217484i | ||||||||
\(123\) | 27.5000 | − | 41.4578i | 0.223577 | − | 0.337055i | ||||
\(124\) | −294.000 | −2.37097 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −190.000 | −1.49606 | −0.748031 | − | 0.663663i | \(-0.769001\pi\) | ||||
−0.748031 | + | 0.663663i | \(0.769001\pi\) | |||||||
\(128\) | − | 228.847i | − | 1.78787i | ||||||
\(129\) | −125.000 | − | 82.9156i | −0.968992 | − | 0.642757i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 198.997i | 1.51906i | 0.650469 | + | 0.759532i | \(0.274572\pi\) | ||||
−0.650469 | + | 0.759532i | \(0.725428\pi\) | |||||||
\(132\) | 192.500 | − | 290.205i | 1.45833 | − | 2.19852i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 149.248i | 1.11379i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 33.0000 | 0.242647 | ||||||||
\(137\) | − | 69.6491i | − | 0.508388i | −0.967153 | − | 0.254194i | \(-0.918190\pi\) | ||
0.967153 | − | 0.254194i | \(-0.0818101\pi\) | |||||||
\(138\) | 165.000 | + | 109.449i | 1.19565 | + | 0.793106i | ||||
\(139\) | 77.0000 | 0.553957 | 0.276978 | − | 0.960876i | \(-0.410667\pi\) | ||||
0.276978 | + | 0.960876i | \(0.410667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 77.0000 | − | 116.082i | 0.546099 | − | 0.823276i | ||||
\(142\) | −110.000 | −0.774648 | ||||||||
\(143\) | 165.831i | 1.15966i | ||||||||
\(144\) | 17.5000 | + | 41.4578i | 0.121528 | + | 0.287901i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 116.082i | − | 0.795081i | ||||||
\(147\) | 122.500 | + | 81.2573i | 0.833333 | + | 0.552771i | ||||
\(148\) | −280.000 | −1.89189 | ||||||||
\(149\) | 165.831i | 1.11296i | 0.830861 | + | 0.556481i | \(0.187849\pi\) | ||||
−0.830861 | + | 0.556481i | \(0.812151\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 172.000 | 1.13907 | 0.569536 | − | 0.821966i | \(-0.307123\pi\) | ||||
0.569536 | + | 0.821966i | \(0.307123\pi\) | |||||||
\(152\) | 69.6491i | 0.458218i | ||||||||
\(153\) | 27.5000 | − | 11.6082i | 0.179739 | − | 0.0758705i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −175.000 | − | 116.082i | −1.12179 | − | 0.744115i | ||||
\(157\) | 250.000 | 1.59236 | 0.796178 | − | 0.605062i | \(-0.206852\pi\) | ||||
0.796178 | + | 0.605062i | \(0.206852\pi\) | |||||||
\(158\) | − | 39.7995i | − | 0.251896i | ||||||
\(159\) | 77.0000 | − | 116.082i | 0.484277 | − | 0.730075i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 192.500 | + | 187.389i | 1.18827 | + | 1.15672i | ||||
\(163\) | −35.0000 | −0.214724 | −0.107362 | − | 0.994220i | \(-0.534240\pi\) | ||||
−0.107362 | + | 0.994220i | \(0.534240\pi\) | |||||||
\(164\) | − | 116.082i | − | 0.707816i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −231.000 | −1.39157 | ||||||||
\(167\) | 179.098i | 1.07244i | 0.844078 | + | 0.536221i | \(0.180149\pi\) | ||||
−0.844078 | + | 0.536221i | \(0.819851\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −69.0000 | −0.408284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.5000 | + | 58.0409i | 0.143275 | + | 0.339421i | ||||
\(172\) | −350.000 | −2.03488 | ||||||||
\(173\) | 278.596i | 1.61038i | 0.593014 | + | 0.805192i | \(0.297938\pi\) | ||||
−0.593014 | + | 0.805192i | \(0.702062\pi\) | |||||||
\(174\) | 275.000 | + | 182.414i | 1.58046 | + | 1.04836i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 82.9156i | − | 0.471111i | ||||||
\(177\) | −110.000 | + | 165.831i | −0.621469 | + | 0.936900i | ||||
\(178\) | 495.000 | 2.78090 | ||||||||
\(179\) | − | 116.082i | − | 0.648502i | −0.945971 | − | 0.324251i | \(-0.894888\pi\) | ||
0.945971 | − | 0.324251i | \(-0.105112\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 182.000 | 1.00552 | 0.502762 | − | 0.864425i | \(-0.332317\pi\) | ||||
0.502762 | + | 0.864425i | \(0.332317\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 20.0000 | + | 13.2665i | 0.109290 | + | 0.0724945i | ||||
\(184\) | 198.000 | 1.07609 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −231.000 | + | 348.246i | −1.24194 | + | 1.87229i | ||||
\(187\) | −55.0000 | −0.294118 | ||||||||
\(188\) | − | 325.029i | − | 1.72888i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 232.164i | − | 1.21552i | −0.794122 | − | 0.607758i | \(-0.792069\pi\) | ||
0.794122 | − | 0.607758i | \(-0.207931\pi\) | |||||||
\(192\) | −242.500 | − | 160.856i | −1.26302 | − | 0.837793i | ||||
\(193\) | 25.0000 | 0.129534 | 0.0647668 | − | 0.997900i | \(-0.479370\pi\) | ||||
0.0647668 | + | 0.997900i | \(0.479370\pi\) | |||||||
\(194\) | − | 232.164i | − | 1.19672i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 343.000 | 1.75000 | ||||||||
\(197\) | − | 218.897i | − | 1.11115i | −0.831465 | − | 0.555577i | \(-0.812498\pi\) | ||
0.831465 | − | 0.555577i | \(-0.187502\pi\) | |||||||
\(198\) | −192.500 | − | 456.036i | −0.972222 | − | 2.30321i | ||||
\(199\) | −68.0000 | −0.341709 | −0.170854 | − | 0.985296i | \(-0.554653\pi\) | ||||
−0.170854 | + | 0.985296i | \(0.554653\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 112.500 | + | 74.6241i | 0.559701 | + | 0.371264i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 38.5000 | − | 58.0409i | 0.188725 | − | 0.284514i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 232.164i | − | 1.12701i | ||||||
\(207\) | 165.000 | − | 69.6491i | 0.797101 | − | 0.336469i | ||||
\(208\) | −50.0000 | −0.240385 | ||||||||
\(209\) | − | 116.082i | − | 0.555416i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 77.0000 | 0.364929 | 0.182464 | − | 0.983212i | \(-0.441593\pi\) | ||||
0.182464 | + | 0.983212i | \(0.441593\pi\) | |||||||
\(212\) | − | 325.029i | − | 1.53316i | ||||||
\(213\) | −55.0000 | + | 82.9156i | −0.258216 | + | 0.389275i | ||||
\(214\) | −231.000 | −1.07944 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 264.000 | + | 49.7494i | 1.22222 | + | 0.230321i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 291.863i | 1.33882i | ||||||||
\(219\) | −87.5000 | − | 58.0409i | −0.399543 | − | 0.265027i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.1662i | 0.150074i | ||||||||
\(222\) | −220.000 | + | 331.662i | −0.990991 | + | 1.49398i | ||||
\(223\) | −140.000 | −0.627803 | −0.313901 | − | 0.949456i | \(-0.601636\pi\) | ||||
−0.313901 | + | 0.949456i | \(0.601636\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −341.000 | −1.50885 | ||||||||
\(227\) | − | 185.731i | − | 0.818198i | −0.912490 | − | 0.409099i | \(-0.865843\pi\) | ||
0.912490 | − | 0.409099i | \(-0.134157\pi\) | |||||||
\(228\) | 122.500 | + | 81.2573i | 0.537281 | + | 0.356392i | ||||
\(229\) | 372.000 | 1.62445 | 0.812227 | − | 0.583341i | \(-0.198255\pi\) | ||||
0.812227 | + | 0.583341i | \(0.198255\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 330.000 | 1.42241 | ||||||||
\(233\) | − | 119.398i | − | 0.512440i | −0.966619 | − | 0.256220i | \(-0.917523\pi\) | ||
0.966619 | − | 0.256220i | \(-0.0824771\pi\) | |||||||
\(234\) | −275.000 | + | 116.082i | −1.17521 | + | 0.496076i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 464.327i | 1.96749i | ||||||||
\(237\) | −30.0000 | − | 19.8997i | −0.126582 | − | 0.0839652i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 232.164i | 0.971396i | 0.874127 | + | 0.485698i | \(0.161435\pi\) | ||||
−0.874127 | + | 0.485698i | \(0.838565\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −413.000 | −1.71369 | −0.856846 | − | 0.515572i | \(-0.827580\pi\) | ||||
−0.856846 | + | 0.515572i | \(0.827580\pi\) | |||||||
\(242\) | 510.760i | 2.11058i | ||||||||
\(243\) | 237.500 | − | 51.4077i | 0.977366 | − | 0.211554i | ||||
\(244\) | 56.0000 | 0.229508 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −137.500 | − | 91.2072i | −0.558943 | − | 0.370761i | ||||
\(247\) | −70.0000 | −0.283401 | ||||||||
\(248\) | 417.895i | 1.68506i | ||||||||
\(249\) | −115.500 | + | 174.123i | −0.463855 | + | 0.699288i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 248.747i | − | 0.991023i | −0.868601 | − | 0.495512i | \(-0.834981\pi\) | ||
0.868601 | − | 0.495512i | \(-0.165019\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −330.000 | −1.30435 | ||||||||
\(254\) | 630.159i | 2.48094i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −371.000 | −1.44922 | ||||||||
\(257\) | 278.596i | 1.08403i | 0.840368 | + | 0.542017i | \(0.182339\pi\) | ||||
−0.840368 | + | 0.542017i | \(0.817661\pi\) | |||||||
\(258\) | −275.000 | + | 414.578i | −1.06589 | + | 1.60689i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 275.000 | − | 116.082i | 1.05364 | − | 0.444758i | ||||
\(262\) | 660.000 | 2.51908 | ||||||||
\(263\) | − | 285.230i | − | 1.08452i | −0.840210 | − | 0.542262i | \(-0.817568\pi\) | ||
0.840210 | − | 0.542262i | \(-0.182432\pi\) | |||||||
\(264\) | −412.500 | − | 273.622i | −1.56250 | − | 1.03645i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 247.500 | − | 373.120i | 0.926966 | − | 1.39745i | ||||
\(268\) | 315.000 | 1.17537 | ||||||||
\(269\) | − | 464.327i | − | 1.72612i | −0.505098 | − | 0.863062i | \(-0.668544\pi\) | ||
0.505098 | − | 0.863062i | \(-0.331456\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.0000 | 0.0811808 | 0.0405904 | − | 0.999176i | \(-0.487076\pi\) | ||||
0.0405904 | + | 0.999176i | \(0.487076\pi\) | |||||||
\(272\) | − | 16.5831i | − | 0.0609674i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −231.000 | −0.843066 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 231.000 | − | 348.246i | 0.836957 | − | 1.26176i | ||||
\(277\) | 210.000 | 0.758123 | 0.379061 | − | 0.925372i | \(-0.376247\pi\) | ||||
0.379061 | + | 0.925372i | \(0.376247\pi\) | |||||||
\(278\) | − | 255.380i | − | 0.918633i | ||||||
\(279\) | 147.000 | + | 348.246i | 0.526882 | + | 1.24819i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 198.997i | 0.708176i | 0.935212 | + | 0.354088i | \(0.115209\pi\) | ||||
−0.935212 | + | 0.354088i | \(0.884791\pi\) | |||||||
\(282\) | −385.000 | − | 255.380i | −1.36525 | − | 0.905603i | ||||
\(283\) | −345.000 | −1.21908 | −0.609541 | − | 0.792755i | \(-0.708646\pi\) | ||||
−0.609541 | + | 0.792755i | \(0.708646\pi\) | |||||||
\(284\) | 232.164i | 0.817478i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 550.000 | 1.92308 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −192.500 | + | 81.2573i | −0.668403 | + | 0.282143i | ||||
\(289\) | 278.000 | 0.961938 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −175.000 | − | 116.082i | −0.601375 | − | 0.398907i | ||||
\(292\) | −245.000 | −0.839041 | ||||||||
\(293\) | − | 318.396i | − | 1.08668i | −0.839514 | − | 0.543338i | \(-0.817160\pi\) | ||
0.839514 | − | 0.543338i | \(-0.182840\pi\) | |||||||
\(294\) | 269.500 | − | 406.287i | 0.916667 | − | 1.38193i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 397.995i | 1.34458i | ||||||||
\(297\) | −440.000 | − | 82.9156i | −1.48148 | − | 0.279177i | ||||
\(298\) | 550.000 | 1.84564 | ||||||||
\(299\) | 198.997i | 0.665543i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 570.459i | − | 1.88894i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 35.0000 | 0.115132 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −38.5000 | − | 91.2072i | −0.125817 | − | 0.298063i | ||||
\(307\) | −325.000 | −1.05863 | −0.529316 | − | 0.848425i | \(-0.677551\pi\) | ||||
−0.529316 | + | 0.848425i | \(0.677551\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −175.000 | − | 116.082i | −0.566343 | − | 0.375669i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 397.995i | 1.27973i | 0.768489 | + | 0.639863i | \(0.221009\pi\) | ||||
−0.768489 | + | 0.639863i | \(0.778991\pi\) | |||||||
\(312\) | −165.000 | + | 248.747i | −0.528846 | + | 0.797266i | ||||
\(313\) | 490.000 | 1.56550 | 0.782748 | − | 0.622339i | \(-0.213818\pi\) | ||||
0.782748 | + | 0.622339i | \(0.213818\pi\) | |||||||
\(314\) | − | 829.156i | − | 2.64062i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −84.0000 | −0.265823 | ||||||||
\(317\) | 212.264i | 0.669602i | 0.942289 | + | 0.334801i | \(0.108669\pi\) | ||||
−0.942289 | + | 0.334801i | \(0.891331\pi\) | |||||||
\(318\) | −385.000 | − | 255.380i | −1.21069 | − | 0.803082i | ||||
\(319\) | −550.000 | −1.72414 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −115.500 | + | 174.123i | −0.359813 | + | 0.542439i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 23.2164i | − | 0.0718773i | ||||||
\(324\) | 395.500 | − | 406.287i | 1.22068 | − | 1.25397i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 116.082i | 0.356079i | ||||||||
\(327\) | 220.000 | + | 145.931i | 0.672783 | + | 0.446274i | ||||
\(328\) | −165.000 | −0.503049 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −243.000 | −0.734139 | −0.367069 | − | 0.930194i | \(-0.619639\pi\) | ||||
−0.367069 | + | 0.930194i | \(0.619639\pi\) | |||||||
\(332\) | 487.544i | 1.46851i | ||||||||
\(333\) | 140.000 | + | 331.662i | 0.420420 | + | 0.995983i | ||||
\(334\) | 594.000 | 1.77844 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −385.000 | −1.14243 | −0.571217 | − | 0.820799i | \(-0.693528\pi\) | ||||
−0.571217 | + | 0.820799i | \(0.693528\pi\) | |||||||
\(338\) | 228.847i | 0.677062i | ||||||||
\(339\) | −170.500 | + | 257.038i | −0.502950 | + | 0.758225i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 696.491i | − | 2.04250i | ||||||
\(342\) | 192.500 | − | 81.2573i | 0.562865 | − | 0.237594i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 497.494i | 1.44620i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 924.000 | 2.67052 | ||||||||
\(347\) | 295.180i | 0.850662i | 0.905038 | + | 0.425331i | \(0.139842\pi\) | ||||
−0.905038 | + | 0.425331i | \(0.860158\pi\) | |||||||
\(348\) | 385.000 | − | 580.409i | 1.10632 | − | 1.66784i | ||||
\(349\) | 532.000 | 1.52436 | 0.762178 | − | 0.647368i | \(-0.224130\pi\) | ||||
0.762178 | + | 0.647368i | \(0.224130\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −50.0000 | + | 265.330i | −0.142450 | + | 0.755926i | ||||
\(352\) | 385.000 | 1.09375 | ||||||||
\(353\) | 278.596i | 0.789225i | 0.918848 | + | 0.394613i | \(0.129121\pi\) | ||||
−0.918848 | + | 0.394613i | \(0.870879\pi\) | |||||||
\(354\) | 550.000 | + | 364.829i | 1.55367 | + | 1.03059i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 1044.74i | − | 2.93465i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −385.000 | −1.07542 | ||||||||
\(359\) | − | 397.995i | − | 1.10862i | −0.832310 | − | 0.554311i | \(-0.812982\pi\) | ||
0.832310 | − | 0.554311i | \(-0.187018\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −312.000 | −0.864266 | ||||||||
\(362\) | − | 603.626i | − | 1.66747i | ||||||
\(363\) | 385.000 | + | 255.380i | 1.06061 | + | 0.703526i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 44.0000 | − | 66.3325i | 0.120219 | − | 0.181236i | ||||
\(367\) | 180.000 | 0.490463 | 0.245232 | − | 0.969465i | \(-0.421136\pi\) | ||||
0.245232 | + | 0.969465i | \(0.421136\pi\) | |||||||
\(368\) | − | 99.4987i | − | 0.270377i | ||||||
\(369\) | −137.500 | + | 58.0409i | −0.372629 | + | 0.157293i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 735.000 | + | 487.544i | 1.97581 | + | 1.31060i | ||||
\(373\) | 110.000 | 0.294906 | 0.147453 | − | 0.989069i | \(-0.452892\pi\) | ||||
0.147453 | + | 0.989069i | \(0.452892\pi\) | |||||||
\(374\) | 182.414i | 0.487739i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −462.000 | −1.22872 | ||||||||
\(377\) | 331.662i | 0.879741i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −533.000 | −1.40633 | −0.703166 | − | 0.711025i | \(-0.748231\pi\) | ||||
−0.703166 | + | 0.711025i | \(0.748231\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 475.000 | + | 315.079i | 1.24672 | + | 0.826980i | ||||
\(382\) | −770.000 | −2.01571 | ||||||||
\(383\) | 79.5990i | 0.207830i | 0.994586 | + | 0.103915i | \(0.0331370\pi\) | ||||
−0.994586 | + | 0.103915i | \(0.966863\pi\) | |||||||
\(384\) | −379.500 | + | 572.118i | −0.988281 | + | 1.48989i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 82.9156i | − | 0.214807i | ||||||
\(387\) | 175.000 | + | 414.578i | 0.452196 | + | 1.07126i | ||||
\(388\) | −490.000 | −1.26289 | ||||||||
\(389\) | − | 99.4987i | − | 0.255781i | −0.991788 | − | 0.127890i | \(-0.959179\pi\) | ||
0.991788 | − | 0.127890i | \(-0.0408206\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −66.0000 | −0.168798 | ||||||||
\(392\) | − | 487.544i | − | 1.24373i | ||||||
\(393\) | 330.000 | − | 497.494i | 0.839695 | − | 1.26589i | ||||
\(394\) | −726.000 | −1.84264 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −962.500 | + | 406.287i | −2.43056 | + | 1.02598i | ||||
\(397\) | 20.0000 | 0.0503778 | 0.0251889 | − | 0.999683i | \(-0.491981\pi\) | ||||
0.0251889 | + | 0.999683i | \(0.491981\pi\) | |||||||
\(398\) | 225.530i | 0.566660i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 746.241i | 1.86095i | 0.366357 | + | 0.930475i | \(0.380605\pi\) | ||||
−0.366357 | + | 0.930475i | \(0.619395\pi\) | |||||||
\(402\) | 247.500 | − | 373.120i | 0.615672 | − | 0.928160i | ||||
\(403\) | −420.000 | −1.04218 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 663.325i | − | 1.62979i | ||||||
\(408\) | −82.5000 | − | 54.7243i | −0.202206 | − | 0.134128i | ||||
\(409\) | 77.0000 | 0.188264 | 0.0941320 | − | 0.995560i | \(-0.469992\pi\) | ||||
0.0941320 | + | 0.995560i | \(0.469992\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −115.500 | + | 174.123i | −0.281022 | + | 0.423656i | ||||
\(412\) | −490.000 | −1.18932 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −231.000 | − | 547.243i | −0.557971 | − | 1.32184i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 232.164i | − | 0.558086i | ||||||
\(417\) | −192.500 | − | 127.690i | −0.461631 | − | 0.306211i | ||||
\(418\) | −385.000 | −0.921053 | ||||||||
\(419\) | 116.082i | 0.277045i | 0.990359 | + | 0.138523i | \(0.0442353\pi\) | ||||
−0.990359 | + | 0.138523i | \(0.955765\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 412.000 | 0.978622 | 0.489311 | − | 0.872109i | \(-0.337248\pi\) | ||||
0.489311 | + | 0.872109i | \(0.337248\pi\) | |||||||
\(422\) | − | 255.380i | − | 0.605166i | ||||||
\(423\) | −385.000 | + | 162.515i | −0.910165 | + | 0.384195i | ||||
\(424\) | −462.000 | −1.08962 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 275.000 | + | 182.414i | 0.645540 | + | 0.428203i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 487.544i | 1.13912i | ||||||||
\(429\) | 275.000 | − | 414.578i | 0.641026 | − | 0.966383i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 198.997i | 0.461711i | 0.972988 | + | 0.230856i | \(0.0741525\pi\) | ||||
−0.972988 | + | 0.230856i | \(0.925848\pi\) | |||||||
\(432\) | 25.0000 | − | 132.665i | 0.0578704 | − | 0.307095i | ||||
\(433\) | 455.000 | 1.05081 | 0.525404 | − | 0.850853i | \(-0.323914\pi\) | ||||
0.525404 | + | 0.850853i | \(0.323914\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 616.000 | 1.41284 | ||||||||
\(437\) | − | 139.298i | − | 0.318760i | ||||||
\(438\) | −192.500 | + | 290.205i | −0.439498 | + | 0.662568i | ||||
\(439\) | 22.0000 | 0.0501139 | 0.0250569 | − | 0.999686i | \(-0.492023\pi\) | ||||
0.0250569 | + | 0.999686i | \(0.492023\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −171.500 | − | 406.287i | −0.388889 | − | 0.921285i | ||||
\(442\) | 110.000 | 0.248869 | ||||||||
\(443\) | 527.343i | 1.19039i | 0.803581 | + | 0.595196i | \(0.202925\pi\) | ||||
−0.803581 | + | 0.595196i | \(0.797075\pi\) | |||||||
\(444\) | 700.000 | + | 464.327i | 1.57658 | + | 1.04578i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 464.327i | 1.04109i | ||||||||
\(447\) | 275.000 | − | 414.578i | 0.615213 | − | 0.927468i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 82.9156i | 0.184667i | 0.995728 | + | 0.0923337i | \(0.0294326\pi\) | ||||
−0.995728 | + | 0.0923337i | \(0.970567\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 275.000 | 0.609756 | ||||||||
\(452\) | 719.708i | 1.59227i | ||||||||
\(453\) | −430.000 | − | 285.230i | −0.949227 | − | 0.629646i | ||||
\(454\) | −616.000 | −1.35683 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 115.500 | − | 174.123i | 0.253289 | − | 0.381848i | ||||
\(457\) | 275.000 | 0.601751 | 0.300875 | − | 0.953663i | \(-0.402721\pi\) | ||||
0.300875 | + | 0.953663i | \(0.402721\pi\) | |||||||
\(458\) | − | 1233.78i | − | 2.69385i | ||||||
\(459\) | −88.0000 | − | 16.5831i | −0.191721 | − | 0.0361288i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 596.992i | − | 1.29499i | −0.762068 | − | 0.647497i | \(-0.775816\pi\) | ||
0.762068 | − | 0.647497i | \(-0.224184\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 240.000 | 0.518359 | 0.259179 | − | 0.965829i | \(-0.416548\pi\) | ||||
0.259179 | + | 0.965829i | \(0.416548\pi\) | |||||||
\(464\) | − | 165.831i | − | 0.357395i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −396.000 | −0.849785 | ||||||||
\(467\) | 13.2665i | 0.0284079i | 0.999899 | + | 0.0142040i | \(0.00452141\pi\) | ||||
−0.999899 | + | 0.0142040i | \(0.995479\pi\) | |||||||
\(468\) | 245.000 | + | 580.409i | 0.523504 | + | 1.24019i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −625.000 | − | 414.578i | −1.32696 | − | 0.880208i | ||||
\(472\) | 660.000 | 1.39831 | ||||||||
\(473\) | − | 829.156i | − | 1.75297i | ||||||
\(474\) | −66.0000 | + | 99.4987i | −0.139241 | + | 0.209913i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −385.000 | + | 162.515i | −0.807128 | + | 0.340701i | ||||
\(478\) | 770.000 | 1.61088 | ||||||||
\(479\) | 298.496i | 0.623165i | 0.950219 | + | 0.311583i | \(0.100859\pi\) | ||||
−0.950219 | + | 0.311583i | \(0.899141\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −400.000 | −0.831601 | ||||||||
\(482\) | 1369.77i | 2.84184i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1078.00 | 2.22727 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −170.500 | − | 787.698i | −0.350823 | − | 1.62078i | ||||
\(487\) | −410.000 | −0.841889 | −0.420945 | − | 0.907086i | \(-0.638301\pi\) | ||||
−0.420945 | + | 0.907086i | \(0.638301\pi\) | |||||||
\(488\) | − | 79.5990i | − | 0.163113i | ||||||
\(489\) | 87.5000 | + | 58.0409i | 0.178937 | + | 0.118693i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 265.330i | 0.540387i | 0.962806 | + | 0.270193i | \(0.0870877\pi\) | ||||
−0.962806 | + | 0.270193i | \(0.912912\pi\) | |||||||
\(492\) | −192.500 | + | 290.205i | −0.391260 | + | 0.589847i | ||||
\(493\) | −110.000 | −0.223124 | ||||||||
\(494\) | 232.164i | 0.469967i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 210.000 | 0.423387 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 577.500 | + | 383.070i | 1.15964 | + | 0.769217i | ||||
\(499\) | 322.000 | 0.645291 | 0.322645 | − | 0.946520i | \(-0.395428\pi\) | ||||
0.322645 | + | 0.946520i | \(0.395428\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 297.000 | − | 447.744i | 0.592814 | − | 0.893701i | ||||
\(502\) | −825.000 | −1.64343 | ||||||||
\(503\) | 411.261i | 0.817617i | 0.912620 | + | 0.408809i | \(0.134056\pi\) | ||||
−0.912620 | + | 0.408809i | \(0.865944\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1094.49i | 2.16302i | ||||||||
\(507\) | 172.500 | + | 114.424i | 0.340237 | + | 0.225687i | ||||
\(508\) | 1330.00 | 2.61811 | ||||||||
\(509\) | 431.161i | 0.847075i | 0.905879 | + | 0.423538i | \(0.139212\pi\) | ||||
−0.905879 | + | 0.423538i | \(0.860788\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 315.079i | 0.615389i | ||||||||
\(513\) | 35.0000 | − | 185.731i | 0.0682261 | − | 0.362049i | ||||
\(514\) | 924.000 | 1.79767 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 875.000 | + | 580.409i | 1.69574 | + | 1.12482i | ||||
\(517\) | 770.000 | 1.48936 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 462.000 | − | 696.491i | 0.890173 | − | 1.34199i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 281.913i | − | 0.541100i | −0.962706 | − | 0.270550i | \(-0.912794\pi\) | ||
0.962706 | − | 0.270550i | \(-0.0872055\pi\) | |||||||
\(522\) | −385.000 | − | 912.072i | −0.737548 | − | 1.74726i | ||||
\(523\) | −1015.00 | −1.94073 | −0.970363 | − | 0.241651i | \(-0.922311\pi\) | ||||
−0.970363 | + | 0.241651i | \(0.922311\pi\) | |||||||
\(524\) | − | 1392.98i | − | 2.65836i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −946.000 | −1.79848 | ||||||||
\(527\) | − | 139.298i | − | 0.264323i | ||||||
\(528\) | −137.500 | + | 207.289i | −0.260417 | + | 0.392593i | ||||
\(529\) | 133.000 | 0.251418 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 550.000 | − | 232.164i | 1.03578 | − | 0.437220i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 165.831i | − | 0.311128i | ||||||
\(534\) | −1237.50 | − | 820.865i | −2.31742 | − | 1.53720i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 447.744i | − | 0.835344i | ||||||
\(537\) | −192.500 | + | 290.205i | −0.358473 | + | 0.540418i | ||||
\(538\) | −1540.00 | −2.86245 | ||||||||
\(539\) | 812.573i | 1.50756i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 912.000 | 1.68577 | 0.842884 | − | 0.538096i | \(-0.180856\pi\) | ||||
0.842884 | + | 0.538096i | \(0.180856\pi\) | |||||||
\(542\) | − | 72.9657i | − | 0.134623i | ||||||
\(543\) | −455.000 | − | 301.813i | −0.837937 | − | 0.555825i | ||||
\(544\) | 77.0000 | 0.141544 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −55.0000 | −0.100548 | −0.0502742 | − | 0.998735i | \(-0.516010\pi\) | ||||
−0.0502742 | + | 0.998735i | \(0.516010\pi\) | |||||||
\(548\) | 487.544i | 0.889679i | ||||||||
\(549\) | −28.0000 | − | 66.3325i | −0.0510018 | − | 0.120824i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 232.164i | − | 0.421350i | ||||||
\(552\) | −495.000 | − | 328.346i | −0.896739 | − | 0.594829i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 696.491i | − | 1.25720i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −539.000 | −0.969424 | ||||||||
\(557\) | − | 1014.89i | − | 1.82206i | −0.412341 | − | 0.911030i | \(-0.635289\pi\) | ||
0.412341 | − | 0.911030i | \(-0.364711\pi\) | |||||||
\(558\) | 1155.00 | − | 487.544i | 2.06989 | − | 0.873734i | ||||
\(559\) | −500.000 | −0.894454 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 137.500 | + | 91.2072i | 0.245098 | + | 0.162580i | ||||
\(562\) | 660.000 | 1.17438 | ||||||||
\(563\) | − | 119.398i | − | 0.212075i | −0.994362 | − | 0.106038i | \(-0.966184\pi\) | ||
0.994362 | − | 0.106038i | \(-0.0338164\pi\) | |||||||
\(564\) | −539.000 | + | 812.573i | −0.955674 | + | 1.44073i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1144.24i | 2.02162i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 330.000 | 0.580986 | ||||||||
\(569\) | − | 49.7494i | − | 0.0874330i | −0.999044 | − | 0.0437165i | \(-0.986080\pi\) | ||
0.999044 | − | 0.0437165i | \(-0.0139198\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 242.000 | 0.423818 | 0.211909 | − | 0.977289i | \(-0.432032\pi\) | ||||
0.211909 | + | 0.977289i | \(0.432032\pi\) | |||||||
\(572\) | − | 1160.82i | − | 2.02940i | ||||||
\(573\) | −385.000 | + | 580.409i | −0.671902 | + | 1.01293i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 339.500 | + | 804.282i | 0.589410 | + | 1.39632i | ||||
\(577\) | −665.000 | −1.15251 | −0.576256 | − | 0.817269i | \(-0.695487\pi\) | ||||
−0.576256 | + | 0.817269i | \(0.695487\pi\) | |||||||
\(578\) | − | 922.022i | − | 1.59519i | ||||||
\(579\) | −62.5000 | − | 41.4578i | −0.107945 | − | 0.0716024i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −385.000 | + | 580.409i | −0.661512 | + | 0.997267i | ||||
\(583\) | 770.000 | 1.32075 | ||||||||
\(584\) | 348.246i | 0.596311i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1056.00 | −1.80205 | ||||||||
\(587\) | 626.842i | 1.06787i | 0.845524 | + | 0.533937i | \(0.179288\pi\) | ||||
−0.845524 | + | 0.533937i | \(0.820712\pi\) | |||||||
\(588\) | −857.500 | − | 568.801i | −1.45833 | − | 0.967349i | ||||
\(589\) | 294.000 | 0.499151 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −363.000 | + | 547.243i | −0.614213 | + | 0.925961i | ||||
\(592\) | 200.000 | 0.337838 | ||||||||
\(593\) | 859.006i | 1.44858i | 0.689497 | + | 0.724288i | \(0.257831\pi\) | ||||
−0.689497 | + | 0.724288i | \(0.742169\pi\) | |||||||
\(594\) | −275.000 | + | 1459.31i | −0.462963 | + | 2.45676i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 1160.82i | − | 1.94768i | ||||||
\(597\) | 170.000 | + | 112.765i | 0.284757 | + | 0.188887i | ||||
\(598\) | 660.000 | 1.10368 | ||||||||
\(599\) | − | 331.662i | − | 0.553694i | −0.960914 | − | 0.276847i | \(-0.910711\pi\) | ||
0.960914 | − | 0.276847i | \(-0.0892895\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −343.000 | −0.570715 | −0.285358 | − | 0.958421i | \(-0.592112\pi\) | ||||
−0.285358 | + | 0.958421i | \(0.592112\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −157.500 | − | 373.120i | −0.261194 | − | 0.618773i | ||||
\(604\) | −1204.00 | −1.99338 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1100.00 | 1.81219 | 0.906096 | − | 0.423073i | \(-0.139049\pi\) | ||||
0.906096 | + | 0.423073i | \(0.139049\pi\) | |||||||
\(608\) | 162.515i | 0.267294i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 464.327i | − | 0.759947i | ||||||
\(612\) | −192.500 | + | 81.2573i | −0.314542 | + | 0.132773i | ||||
\(613\) | 290.000 | 0.473083 | 0.236542 | − | 0.971621i | \(-0.423986\pi\) | ||||
0.236542 | + | 0.971621i | \(0.423986\pi\) | |||||||
\(614\) | 1077.90i | 1.75554i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 79.5990i | 0.129010i | 0.997917 | + | 0.0645049i | \(0.0205468\pi\) | ||||
−0.997917 | + | 0.0645049i | \(0.979453\pi\) | |||||||
\(618\) | −385.000 | + | 580.409i | −0.622977 | + | 0.939174i | ||||
\(619\) | −58.0000 | −0.0936995 | −0.0468498 | − | 0.998902i | \(-0.514918\pi\) | ||||
−0.0468498 | + | 0.998902i | \(0.514918\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −528.000 | − | 99.4987i | −0.850242 | − | 0.160223i | ||||
\(622\) | 1320.00 | 2.12219 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 125.000 | + | 82.9156i | 0.200321 | + | 0.132878i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 1625.15i | − | 2.59608i | ||||||
\(627\) | −192.500 | + | 290.205i | −0.307018 | + | 0.462846i | ||||
\(628\) | −1750.00 | −2.78662 | ||||||||
\(629\) | − | 132.665i | − | 0.210914i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 862.000 | 1.36609 | 0.683043 | − | 0.730378i | \(-0.260656\pi\) | ||||
0.683043 | + | 0.730378i | \(0.260656\pi\) | |||||||
\(632\) | 119.398i | 0.188922i | ||||||||
\(633\) | −192.500 | − | 127.690i | −0.304107 | − | 0.201722i | ||||
\(634\) | 704.000 | 1.11041 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −539.000 | + | 812.573i | −0.847484 | + | 1.27763i | ||||
\(637\) | 490.000 | 0.769231 | ||||||||
\(638\) | 1824.14i | 2.85916i | ||||||||
\(639\) | 275.000 | − | 116.082i | 0.430360 | − | 0.181662i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 596.992i | 0.931345i | 0.884957 | + | 0.465673i | \(0.154188\pi\) | ||||
−0.884957 | + | 0.465673i | \(0.845812\pi\) | |||||||
\(642\) | 577.500 | + | 383.070i | 0.899533 | + | 0.596682i | ||||
\(643\) | 1050.00 | 1.63297 | 0.816485 | − | 0.577366i | \(-0.195920\pi\) | ||||
0.816485 | + | 0.577366i | \(0.195920\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −77.0000 | −0.119195 | ||||||||
\(647\) | − | 252.063i | − | 0.389588i | −0.980844 | − | 0.194794i | \(-0.937596\pi\) | ||
0.980844 | − | 0.194794i | \(-0.0624038\pi\) | |||||||
\(648\) | −577.500 | − | 562.168i | −0.891204 | − | 0.867543i | ||||
\(649\) | −1100.00 | −1.69492 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 245.000 | 0.375767 | ||||||||
\(653\) | 1207.25i | 1.84878i | 0.381452 | + | 0.924389i | \(0.375424\pi\) | ||||
−0.381452 | + | 0.924389i | \(0.624576\pi\) | |||||||
\(654\) | 484.000 | − | 729.657i | 0.740061 | − | 1.11568i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 82.9156i | 0.126396i | ||||||||
\(657\) | 122.500 | + | 290.205i | 0.186454 | + | 0.441712i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 812.573i | − | 1.23304i | −0.787339 | − | 0.616520i | \(-0.788542\pi\) | ||
0.787339 | − | 0.616520i | \(-0.211458\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −98.0000 | −0.148260 | −0.0741301 | − | 0.997249i | \(-0.523618\pi\) | ||||
−0.0741301 | + | 0.997249i | \(0.523618\pi\) | |||||||
\(662\) | 805.940i | 1.21743i | ||||||||
\(663\) | 55.0000 | − | 82.9156i | 0.0829563 | − | 0.125061i | ||||
\(664\) | 693.000 | 1.04367 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1100.00 | − | 464.327i | 1.65165 | − | 0.697188i | ||||
\(667\) | −660.000 | −0.989505 | ||||||||
\(668\) | − | 1253.68i | − | 1.87677i | ||||||
\(669\) | 350.000 | + | 232.164i | 0.523169 | + | 0.347031i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 132.665i | 0.197712i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 210.000 | 0.312036 | 0.156018 | − | 0.987754i | \(-0.450134\pi\) | ||||
0.156018 | + | 0.987754i | \(0.450134\pi\) | |||||||
\(674\) | 1276.90i | 1.89451i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 483.000 | 0.714497 | ||||||||
\(677\) | 79.5990i | 0.117576i | 0.998270 | + | 0.0587880i | \(0.0187236\pi\) | ||||
−0.998270 | + | 0.0587880i | \(0.981276\pi\) | |||||||
\(678\) | 852.500 | + | 565.485i | 1.25737 | + | 0.834048i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −308.000 | + | 464.327i | −0.452276 | + | 0.681832i | ||||
\(682\) | −2310.00 | −3.38710 | ||||||||
\(683\) | − | 169.148i | − | 0.247654i | −0.992304 | − | 0.123827i | \(-0.960483\pi\) | ||
0.992304 | − | 0.123827i | \(-0.0395168\pi\) | |||||||
\(684\) | −171.500 | − | 406.287i | −0.250731 | − | 0.593986i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −930.000 | − | 616.892i | −1.35371 | − | 0.897951i | ||||
\(688\) | 250.000 | 0.363372 | ||||||||
\(689\) | − | 464.327i | − | 0.673915i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −713.000 | −1.03184 | −0.515919 | − | 0.856637i | \(-0.672549\pi\) | ||||
−0.515919 | + | 0.856637i | \(0.672549\pi\) | |||||||
\(692\) | − | 1950.18i | − | 2.81817i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 979.000 | 1.41066 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −825.000 | − | 547.243i | −1.18534 | − | 0.786269i | ||||
\(697\) | 55.0000 | 0.0789096 | ||||||||
\(698\) | − | 1764.44i | − | 2.52786i | ||||||
\(699\) | −198.000 | + | 298.496i | −0.283262 | + | 0.427033i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1160.82i | 1.65595i | 0.560767 | + | 0.827973i | \(0.310506\pi\) | ||||
−0.560767 | + | 0.827973i | \(0.689494\pi\) | |||||||
\(702\) | 880.000 | + | 165.831i | 1.25356 | + | 0.236227i | ||||
\(703\) | 280.000 | 0.398293 | ||||||||
\(704\) | − | 1608.56i | − | 2.28489i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 924.000 | 1.30878 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 770.000 | − | 1160.82i | 1.08757 | − | 1.63957i | ||||
\(709\) | −248.000 | −0.349788 | −0.174894 | − | 0.984587i | \(-0.555958\pi\) | ||||
−0.174894 | + | 0.984587i | \(0.555958\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 42.0000 | + | 99.4987i | 0.0590717 | + | 0.139942i | ||||
\(712\) | −1485.00 | −2.08567 | ||||||||
\(713\) | − | 835.789i | − | 1.17222i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 812.573i | 1.13488i | ||||||||
\(717\) | 385.000 | − | 580.409i | 0.536960 | − | 0.809497i | ||||
\(718\) | −1320.00 | −1.83844 | ||||||||
\(719\) | 198.997i | 0.276770i | 0.990379 | + | 0.138385i | \(0.0441911\pi\) | ||||
−0.990379 | + | 0.138385i | \(0.955809\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1034.79i | 1.43322i | ||||||||
\(723\) | 1032.50 | + | 684.883i | 1.42808 | + | 0.947279i | ||||
\(724\) | −1274.00 | −1.75967 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 847.000 | − | 1276.90i | 1.16667 | − | 1.75882i | ||||
\(727\) | 10.0000 | 0.0137552 | 0.00687758 | − | 0.999976i | \(-0.497811\pi\) | ||||
0.00687758 | + | 0.999976i | \(0.497811\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −679.000 | − | 265.330i | −0.931413 | − | 0.363964i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 165.831i | − | 0.226855i | ||||||
\(732\) | −140.000 | − | 92.8655i | −0.191257 | − | 0.126865i | ||||
\(733\) | −770.000 | −1.05048 | −0.525239 | − | 0.850955i | \(-0.676024\pi\) | ||||
−0.525239 | + | 0.850955i | \(0.676024\pi\) | |||||||
\(734\) | − | 596.992i | − | 0.813341i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 462.000 | 0.627717 | ||||||||
\(737\) | 746.241i | 1.01254i | ||||||||
\(738\) | 192.500 | + | 456.036i | 0.260840 | + | 0.617935i | ||||
\(739\) | 802.000 | 1.08525 | 0.542625 | − | 0.839975i | \(-0.317430\pi\) | ||||
0.542625 | + | 0.839975i | \(0.317430\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 175.000 | + | 116.082i | 0.236167 | + | 0.156656i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1346.55i | − | 1.81231i | −0.422941 | − | 0.906157i | \(-0.639002\pi\) | ||
0.422941 | − | 0.906157i | \(-0.360998\pi\) | |||||||
\(744\) | 693.000 | − | 1044.74i | 0.931452 | − | 1.40422i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 364.829i | − | 0.489047i | ||||||
\(747\) | 577.500 | − | 243.772i | 0.773092 | − | 0.326335i | ||||
\(748\) | 385.000 | 0.514706 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 322.000 | 0.428762 | 0.214381 | − | 0.976750i | \(-0.431227\pi\) | ||||
0.214381 | + | 0.976750i | \(0.431227\pi\) | |||||||
\(752\) | 232.164i | 0.308728i | ||||||||
\(753\) | −412.500 | + | 621.867i | −0.547809 | + | 0.825853i | ||||
\(754\) | 1100.00 | 1.45889 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −400.000 | −0.528402 | −0.264201 | − | 0.964468i | \(-0.585108\pi\) | ||||
−0.264201 | + | 0.964468i | \(0.585108\pi\) | |||||||
\(758\) | 1767.76i | 2.33214i | ||||||||
\(759\) | 825.000 | + | 547.243i | 1.08696 | + | 0.721005i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 348.246i | − | 0.457616i | −0.973472 | − | 0.228808i | \(-0.926517\pi\) | ||
0.973472 | − | 0.228808i | \(-0.0734828\pi\) | |||||||
\(762\) | 1045.00 | − | 1575.40i | 1.37139 | − | 2.06745i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1625.15i | 2.12715i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 264.000 | 0.344648 | ||||||||
\(767\) | 663.325i | 0.864830i | ||||||||
\(768\) | 927.500 | + | 615.234i | 1.20768 | + | 0.801086i | ||||
\(769\) | −193.000 | −0.250975 | −0.125488 | − | 0.992095i | \(-0.540050\pi\) | ||||
−0.125488 | + | 0.992095i | \(0.540050\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 462.000 | − | 696.491i | 0.599222 | − | 0.903361i | ||||
\(772\) | −175.000 | −0.226684 | ||||||||
\(773\) | − | 417.895i | − | 0.540614i | −0.962774 | − | 0.270307i | \(-0.912875\pi\) | ||
0.962774 | − | 0.270307i | \(-0.0871252\pi\) | |||||||
\(774\) | 1375.00 | − | 580.409i | 1.77649 | − | 0.749883i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 696.491i | 0.897540i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −330.000 | −0.424165 | ||||||||
\(779\) | 116.082i | 0.149014i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −550.000 | −0.704225 | ||||||||
\(782\) | 218.897i | 0.279920i | ||||||||
\(783\) | −880.000 | − | 165.831i | −1.12388 | − | 0.211790i | ||||
\(784\) | −245.000 | −0.312500 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1650.00 | − | 1094.49i | −2.09924 | − | 1.39248i | ||||
\(787\) | −910.000 | −1.15629 | −0.578145 | − | 0.815934i | \(-0.696223\pi\) | ||||
−0.578145 | + | 0.815934i | \(0.696223\pi\) | |||||||
\(788\) | 1532.28i | 1.94452i | ||||||||
\(789\) | −473.000 | + | 713.074i | −0.599493 | + | 0.903770i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 577.500 | + | 1368.11i | 0.729167 | + | 1.72741i | ||||
\(793\) | 80.0000 | 0.100883 | ||||||||
\(794\) | − | 66.3325i | − | 0.0835422i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 476.000 | 0.597990 | ||||||||
\(797\) | 1107.75i | 1.38990i | 0.719057 | + | 0.694951i | \(0.244574\pi\) | ||||
−0.719057 | + | 0.694951i | \(0.755426\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 154.000 | 0.192741 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1237.50 | + | 522.368i | −1.54494 | + | 0.652145i | ||||
\(802\) | 2475.00 | 3.08603 | ||||||||
\(803\) | − | 580.409i | − | 0.722801i | ||||||
\(804\) | −787.500 | − | 522.368i | −0.979478 | − | 0.649712i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1392.98i | 1.72827i | ||||||||
\(807\) | −770.000 | + | 1160.82i | −0.954151 | + | 1.43844i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1260.32i | 1.55787i | 0.627104 | + | 0.778935i | \(0.284240\pi\) | ||||
−0.627104 | + | 0.778935i | \(0.715760\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −858.000 | −1.05795 | −0.528977 | − | 0.848636i | \(-0.677424\pi\) | ||||
−0.528977 | + | 0.848636i | \(0.677424\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −55.0000 | − | 36.4829i | −0.0676507 | − | 0.0448744i | ||||
\(814\) | −2200.00 | −2.70270 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −27.5000 | + | 41.4578i | −0.0337010 | + | 0.0508061i | ||||
\(817\) | 350.000 | 0.428397 | ||||||||
\(818\) | − | 255.380i | − | 0.312201i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 696.491i | − | 0.848345i | −0.905581 | − | 0.424172i | \(-0.860565\pi\) | ||
0.905581 | − | 0.424172i | \(-0.139435\pi\) | |||||||
\(822\) | 577.500 | + | 383.070i | 0.702555 | + | 0.466022i | ||||
\(823\) | 1060.00 | 1.28797 | 0.643985 | − | 0.765038i | \(-0.277280\pi\) | ||||
0.643985 | + | 0.765038i | \(0.277280\pi\) | |||||||
\(824\) | 696.491i | 0.845256i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 500.810i | − | 0.605575i | −0.953058 | − | 0.302787i | \(-0.902083\pi\) | ||
0.953058 | − | 0.302787i | \(-0.0979172\pi\) | |||||||
\(828\) | −1155.00 | + | 487.544i | −1.39493 | + | 0.588821i | ||||
\(829\) | −1038.00 | −1.25211 | −0.626055 | − | 0.779779i | \(-0.715332\pi\) | ||||
−0.626055 | + | 0.779779i | \(0.715332\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −525.000 | − | 348.246i | −0.631769 | − | 0.419068i | ||||
\(832\) | −970.000 | −1.16587 | ||||||||
\(833\) | 162.515i | 0.195096i | ||||||||
\(834\) | −423.500 | + | 638.450i | −0.507794 | + | 0.765528i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 812.573i | 0.971977i | ||||||||
\(837\) | 210.000 | − | 1114.39i | 0.250896 | − | 1.33140i | ||||
\(838\) | 385.000 | 0.459427 | ||||||||
\(839\) | − | 928.655i | − | 1.10686i | −0.832896 | − | 0.553430i | \(-0.813319\pi\) | ||
0.832896 | − | 0.553430i | \(-0.186681\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −259.000 | −0.307967 | ||||||||
\(842\) | − | 1366.45i | − | 1.62286i | ||||||
\(843\) | 330.000 | − | 497.494i | 0.391459 | − | 0.590147i | ||||
\(844\) | −539.000 | −0.638626 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 539.000 | + | 1276.90i | 0.637116 | + | 1.50934i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 232.164i | 0.273778i | ||||||||
\(849\) | 862.500 | + | 572.118i | 1.01590 | + | 0.673873i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 795.990i | − | 0.935358i | ||||||
\(852\) | 385.000 | − | 580.409i | 0.451878 | − | 0.681232i | ||||
\(853\) | −630.000 | −0.738570 | −0.369285 | − | 0.929316i | \(-0.620397\pi\) | ||||
−0.369285 | + | 0.929316i | \(0.620397\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 693.000 | 0.809579 | ||||||||
\(857\) | − | 1296.80i | − | 1.51319i | −0.653886 | − | 0.756593i | \(-0.726862\pi\) | ||
0.653886 | − | 0.756593i | \(-0.273138\pi\) | |||||||
\(858\) | −1375.00 | − | 912.072i | −1.60256 | − | 1.06302i | ||||
\(859\) | 307.000 | 0.357392 | 0.178696 | − | 0.983904i | \(-0.442812\pi\) | ||||
0.178696 | + | 0.983904i | \(0.442812\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 660.000 | 0.765661 | ||||||||
\(863\) | − | 484.227i | − | 0.561098i | −0.959840 | − | 0.280549i | \(-0.909484\pi\) | ||
0.959840 | − | 0.280549i | \(-0.0905165\pi\) | |||||||
\(864\) | 616.000 | + | 116.082i | 0.712963 | + | 0.134354i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 1509.06i | − | 1.74257i | ||||||
\(867\) | −695.000 | − | 461.011i | −0.801615 | − | 0.531731i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 198.997i | − | 0.228996i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 450.000 | 0.516648 | ||||||||
\(872\) | − | 875.589i | − | 1.00412i | ||||||
\(873\) | 245.000 | + | 580.409i | 0.280641 | + | 0.664845i | ||||
\(874\) | −462.000 | −0.528604 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 612.500 | + | 406.287i | 0.699201 | + | 0.463797i | ||||
\(877\) | −840.000 | −0.957811 | −0.478905 | − | 0.877867i | \(-0.658966\pi\) | ||||
−0.478905 | + | 0.877867i | \(0.658966\pi\) | |||||||
\(878\) | − | 72.9657i | − | 0.0831045i | ||||||
\(879\) | −528.000 | + | 795.990i | −0.600683 | + | 0.905563i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 464.327i | − | 0.527046i | −0.964653 | − | 0.263523i | \(-0.915116\pi\) | ||
0.964653 | − | 0.263523i | \(-0.0848845\pi\) | |||||||
\(882\) | −1347.50 | + | 568.801i | −1.52778 | + | 0.644899i | ||||
\(883\) | −995.000 | −1.12684 | −0.563420 | − | 0.826171i | \(-0.690515\pi\) | ||||
−0.563420 | + | 0.826171i | \(0.690515\pi\) | |||||||
\(884\) | − | 232.164i | − | 0.262629i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1749.00 | 1.97404 | ||||||||
\(887\) | 477.594i | 0.538437i | 0.963079 | + | 0.269219i | \(0.0867654\pi\) | ||||
−0.963079 | + | 0.269219i | \(0.913235\pi\) | |||||||
\(888\) | 660.000 | − | 994.987i | 0.743243 | − | 1.12048i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 962.500 | + | 936.947i | 1.08025 | + | 1.05157i | ||||
\(892\) | 980.000 | 1.09865 | ||||||||
\(893\) | 325.029i | 0.363975i | ||||||||
\(894\) | −1375.00 | − | 912.072i | −1.53803 | − | 1.02021i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 330.000 | − | 497.494i | 0.367893 | − | 0.554620i | ||||
\(898\) | 275.000 | 0.306236 | ||||||||
\(899\) | − | 1392.98i | − | 1.54948i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 154.000 | 0.170921 | ||||||||
\(902\) | − | 912.072i | − | 1.01117i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1023.00 | 1.13164 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −946.000 | + | 1426.15i | −1.04415 | + | 1.57412i | ||||
\(907\) | 1050.00 | 1.15766 | 0.578831 | − | 0.815447i | \(-0.303509\pi\) | ||||
0.578831 | + | 0.815447i | \(0.303509\pi\) | |||||||
\(908\) | 1300.12i | 1.43185i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 729.657i | 0.800941i | 0.916310 | + | 0.400471i | \(0.131153\pi\) | ||||
−0.916310 | + | 0.400471i | \(0.868847\pi\) | |||||||
\(912\) | −87.5000 | − | 58.0409i | −0.0959430 | − | 0.0636414i | ||||
\(913\) | −1155.00 | −1.26506 | ||||||||
\(914\) | − | 912.072i | − | 0.997890i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2604.00 | −2.84279 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −55.0000 | + | 291.863i | −0.0599129 | + | 0.317934i | ||||
\(919\) | 1342.00 | 1.46028 | 0.730141 | − | 0.683296i | \(-0.239454\pi\) | ||||
0.730141 | + | 0.683296i | \(0.239454\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 812.500 | + | 538.952i | 0.882193 | + | 0.585181i | ||||
\(922\) | −1980.00 | −2.14751 | ||||||||
\(923\) | 331.662i | 0.359331i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 795.990i | − | 0.859600i | ||||||
\(927\) | 245.000 | + | 580.409i | 0.264293 | + | 0.626116i | ||||
\(928\) | 770.000 | 0.829741 | ||||||||
\(929\) | 464.327i | 0.499814i | 0.968270 | + | 0.249907i | \(0.0804001\pi\) | ||||
−0.968270 | + | 0.249907i | \(0.919600\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −343.000 | −0.368421 | ||||||||
\(932\) | 835.789i | 0.896770i | ||||||||
\(933\) | 660.000 | − | 994.987i | 0.707395 | − | 1.06644i | ||||
\(934\) | 44.0000 | 0.0471092 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 825.000 | − | 348.246i | 0.881410 | − | 0.372057i | ||||
\(937\) | 165.000 | 0.176094 | 0.0880470 | − | 0.996116i | \(-0.471937\pi\) | ||||
0.0880470 | + | 0.996116i | \(0.471937\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1225.00 | − | 812.573i | −1.30458 | − | 0.865360i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 232.164i | − | 0.246720i | −0.992362 | − | 0.123360i | \(-0.960633\pi\) | ||
0.992362 | − | 0.123360i | \(-0.0393670\pi\) | |||||||
\(942\) | −1375.00 | + | 2072.89i | −1.45966 | + | 2.20052i | ||||
\(943\) | 330.000 | 0.349947 | ||||||||
\(944\) | − | 331.662i | − | 0.351337i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2750.00 | −2.90698 | ||||||||
\(947\) | 278.596i | 0.294188i | 0.989122 | + | 0.147094i | \(0.0469921\pi\) | ||||
−0.989122 | + | 0.147094i | \(0.953008\pi\) | |||||||
\(948\) | 210.000 | + | 139.298i | 0.221519 | + | 0.146939i | ||||
\(949\) | −350.000 | −0.368809 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 352.000 | − | 530.660i | 0.370137 | − | 0.558002i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 195.681i | 0.205331i | 0.994716 | + | 0.102666i | \(0.0327372\pi\) | ||||
−0.994716 | + | 0.102666i | \(0.967263\pi\) | |||||||
\(954\) | 539.000 | + | 1276.90i | 0.564990 | + | 1.33847i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 1625.15i | − | 1.69994i | ||||||
\(957\) | 1375.00 | + | 912.072i | 1.43678 | + | 0.953053i | ||||
\(958\) | 990.000 | 1.03340 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 803.000 | 0.835588 | ||||||||
\(962\) | 1326.65i | 1.37905i | ||||||||
\(963\) | 577.500 | − | 243.772i | 0.599688 | − | 0.253138i | ||||
\(964\) | 2891.00 | 2.99896 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 280.000 | 0.289555 | 0.144778 | − | 0.989464i | \(-0.453753\pi\) | ||||
0.144778 | + | 0.989464i | \(0.453753\pi\) | |||||||
\(968\) | − | 1532.28i | − | 1.58293i | ||||||
\(969\) | −38.5000 | + | 58.0409i | −0.0397317 | + | 0.0598978i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1044.74i | 1.07594i | 0.842964 | + | 0.537970i | \(0.180808\pi\) | ||||
−0.842964 | + | 0.537970i | \(0.819192\pi\) | |||||||
\(972\) | −1662.50 | + | 359.854i | −1.71039 | + | 0.370220i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1359.82i | 1.39612i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −40.0000 | −0.0409836 | ||||||||
\(977\) | − | 1097.80i | − | 1.12365i | −0.827257 | − | 0.561823i | \(-0.810100\pi\) | ||
0.827257 | − | 0.561823i | \(-0.189900\pi\) | |||||||
\(978\) | 192.500 | − | 290.205i | 0.196830 | − | 0.296733i | ||||
\(979\) | 2475.00 | 2.52809 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −308.000 | − | 729.657i | −0.313965 | − | 0.743789i | ||||
\(982\) | 880.000 | 0.896130 | ||||||||
\(983\) | 1671.58i | 1.70049i | 0.526389 | + | 0.850244i | \(0.323545\pi\) | ||||
−0.526389 | + | 0.850244i | \(0.676455\pi\) | |||||||
\(984\) | 412.500 | + | 273.622i | 0.419207 | + | 0.278071i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 364.829i | 0.370009i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 490.000 | 0.495951 | ||||||||
\(989\) | − | 994.987i | − | 1.00605i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 452.000 | 0.456105 | 0.228052 | − | 0.973649i | \(-0.426764\pi\) | ||||
0.228052 | + | 0.973649i | \(0.426764\pi\) | |||||||
\(992\) | 975.088i | 0.982951i | ||||||||
\(993\) | 607.500 | + | 402.970i | 0.611782 | + | 0.405811i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 808.500 | − | 1218.86i | 0.811747 | − | 1.22375i | ||||
\(997\) | 420.000 | 0.421264 | 0.210632 | − | 0.977565i | \(-0.432448\pi\) | ||||
0.210632 | + | 0.977565i | \(0.432448\pi\) | |||||||
\(998\) | − | 1067.95i | − | 1.07009i | ||||||
\(999\) | 200.000 | − | 1061.32i | 0.200200 | − | 1.06238i |
(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 | 75.3.c.c.26.1 | ✓ | 2 | |
3.2 | odd | 2 | inner | 75.3.c.c.26.2 | yes | 2 | |
4.3 | odd | 2 | 1200.3.l.s.401.2 | 2 | |||
5.2 | odd | 4 | 75.3.d.c.74.4 | 4 | |||
5.3 | odd | 4 | 75.3.d.c.74.1 | 4 | |||
5.4 | even | 2 | 75.3.c.f.26.2 | yes | 2 | ||
12.11 | even | 2 | 1200.3.l.s.401.1 | 2 | |||
15.2 | even | 4 | 75.3.d.c.74.2 | 4 | |||
15.8 | even | 4 | 75.3.d.c.74.3 | 4 | |||
15.14 | odd | 2 | 75.3.c.f.26.1 | yes | 2 | ||
20.3 | even | 4 | 1200.3.c.d.449.2 | 4 | |||
20.7 | even | 4 | 1200.3.c.d.449.3 | 4 | |||
20.19 | odd | 2 | 1200.3.l.f.401.1 | 2 | |||
60.23 | odd | 4 | 1200.3.c.d.449.4 | 4 | |||
60.47 | odd | 4 | 1200.3.c.d.449.1 | 4 | |||
60.59 | even | 2 | 1200.3.l.f.401.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.3.c.c.26.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
75.3.c.c.26.2 | yes | 2 | 3.2 | odd | 2 | inner | |
75.3.c.f.26.1 | yes | 2 | 15.14 | odd | 2 | ||
75.3.c.f.26.2 | yes | 2 | 5.4 | even | 2 | ||
75.3.d.c.74.1 | 4 | 5.3 | odd | 4 | |||
75.3.d.c.74.2 | 4 | 15.2 | even | 4 | |||
75.3.d.c.74.3 | 4 | 15.8 | even | 4 | |||
75.3.d.c.74.4 | 4 | 5.2 | odd | 4 | |||
1200.3.c.d.449.1 | 4 | 60.47 | odd | 4 | |||
1200.3.c.d.449.2 | 4 | 20.3 | even | 4 | |||
1200.3.c.d.449.3 | 4 | 20.7 | even | 4 | |||
1200.3.c.d.449.4 | 4 | 60.23 | odd | 4 | |||
1200.3.l.f.401.1 | 2 | 20.19 | odd | 2 | |||
1200.3.l.f.401.2 | 2 | 60.59 | even | 2 | |||
1200.3.l.s.401.1 | 2 | 12.11 | even | 2 | |||
1200.3.l.s.401.2 | 2 | 4.3 | odd | 2 |