Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,3,Mod(74,75)]
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, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.74");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.04360198270\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 74.3 | ||
Root | \(1.65831 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.74 |
Dual form | 75.3.d.c.74.4 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.31662 | 1.65831 | 0.829156 | − | 0.559017i | \(-0.188821\pi\) | ||||
0.829156 | + | 0.559017i | \(0.188821\pi\) | |||||||
\(3\) | −1.65831 | − | 2.50000i | −0.552771 | − | 0.833333i | ||||
\(4\) | 7.00000 | 1.75000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.50000 | − | 8.29156i | −0.916667 | − | 1.38193i | ||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 9.94987 | 1.24373 | ||||||||
\(9\) | −3.50000 | + | 8.29156i | −0.388889 | + | 0.921285i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.5831i | 1.50756i | 0.657129 | + | 0.753778i | \(0.271771\pi\) | ||||
−0.657129 | + | 0.753778i | \(0.728229\pi\) | |||||||
\(12\) | −11.6082 | − | 17.5000i | −0.967349 | − | 1.45833i | ||||
\(13\) | − | 10.0000i | − | 0.769231i | −0.923077 | − | 0.384615i | \(-0.874334\pi\) | ||
0.923077 | − | 0.384615i | \(-0.125666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.00000 | 0.312500 | ||||||||
\(17\) | 3.31662 | 0.195096 | 0.0975478 | − | 0.995231i | \(-0.468900\pi\) | ||||
0.0975478 | + | 0.995231i | \(0.468900\pi\) | |||||||
\(18\) | −11.6082 | + | 27.5000i | −0.644899 | + | 1.52778i | ||||
\(19\) | −7.00000 | −0.368421 | −0.184211 | − | 0.982887i | \(-0.558973\pi\) | ||||
−0.184211 | + | 0.982887i | \(0.558973\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 55.0000i | 2.50000i | ||||||||
\(23\) | −19.8997 | −0.865206 | −0.432603 | − | 0.901584i | \(-0.642405\pi\) | ||||
−0.432603 | + | 0.901584i | \(0.642405\pi\) | |||||||
\(24\) | −16.5000 | − | 24.8747i | −0.687500 | − | 1.03645i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 33.1662i | − | 1.27562i | ||||||
\(27\) | 26.5330 | − | 5.00000i | 0.982704 | − | 0.185185i | ||||
\(28\) | 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 | \(0.263098\pi\) | |||||||
\(32\) | −23.2164 | −0.725512 | ||||||||
\(33\) | 41.4578 | − | 27.5000i | 1.25630 | − | 0.833333i | ||||
\(34\) | 11.0000 | 0.323529 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −24.5000 | + | 58.0409i | −0.680556 | + | 1.61225i | ||||
\(37\) | − | 40.0000i | − | 1.08108i | −0.841318 | − | 0.540541i | \(-0.818220\pi\) | ||
0.841318 | − | 0.540541i | \(-0.181780\pi\) | |||||||
\(38\) | −23.2164 | −0.610957 | ||||||||
\(39\) | −25.0000 | + | 16.5831i | −0.641026 | + | 0.425208i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 16.5831i | − | 0.404466i | −0.979337 | − | 0.202233i | \(-0.935180\pi\) | ||
0.979337 | − | 0.202233i | \(-0.0648199\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 50.0000i | 1.16279i | 0.813621 | + | 0.581395i | \(0.197493\pi\) | ||||
−0.813621 | + | 0.581395i | \(0.802507\pi\) | |||||||
\(44\) | 116.082i | 2.63822i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −66.0000 | −1.43478 | ||||||||
\(47\) | −46.4327 | −0.987931 | −0.493965 | − | 0.869482i | \(-0.664453\pi\) | ||||
−0.493965 | + | 0.869482i | \(0.664453\pi\) | |||||||
\(48\) | −8.29156 | − | 12.5000i | −0.172741 | − | 0.260417i | ||||
\(49\) | 49.0000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.50000 | − | 8.29156i | −0.107843 | − | 0.162580i | ||||
\(52\) | − | 70.0000i | − | 1.34615i | ||||||
\(53\) | 46.4327 | 0.876090 | 0.438045 | − | 0.898953i | \(-0.355671\pi\) | ||||
0.438045 | + | 0.898953i | \(0.355671\pi\) | |||||||
\(54\) | 88.0000 | − | 16.5831i | 1.62963 | − | 0.307095i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.6082 | + | 17.5000i | 0.203652 | + | 0.307018i | ||||
\(58\) | − | 110.000i | − | 1.89655i | ||||||
\(59\) | − | 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 | \(0.520888\pi\) | |||||||
\(62\) | 139.298 | 2.24675 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −97.0000 | −1.51562 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 137.500 | − | 91.2072i | 2.08333 | − | 1.38193i | ||||
\(67\) | 45.0000i | 0.671642i | 0.941926 | + | 0.335821i | \(0.109014\pi\) | ||||
−0.941926 | + | 0.335821i | \(0.890986\pi\) | |||||||
\(68\) | 23.2164 | 0.341417 | ||||||||
\(69\) | 33.0000 | + | 49.7494i | 0.478261 | + | 0.721005i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 33.1662i | 0.467130i | 0.972341 | + | 0.233565i | \(0.0750392\pi\) | ||||
−0.972341 | + | 0.233565i | \(0.924961\pi\) | |||||||
\(72\) | −34.8246 | + | 82.5000i | −0.483674 | + | 1.14583i | ||||
\(73\) | 35.0000i | 0.479452i | 0.970841 | + | 0.239726i | \(0.0770576\pi\) | ||||
−0.970841 | + | 0.239726i | \(0.922942\pi\) | |||||||
\(74\) | − | 132.665i | − | 1.79277i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −49.0000 | −0.644737 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −82.9156 | + | 55.0000i | −1.06302 | + | 0.705128i | ||||
\(79\) | −12.0000 | −0.151899 | −0.0759494 | − | 0.997112i | \(-0.524199\pi\) | ||||
−0.0759494 | + | 0.997112i | \(0.524199\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −56.5000 | − | 58.0409i | −0.697531 | − | 0.716555i | ||||
\(82\) | − | 55.0000i | − | 0.670732i | ||||||
\(83\) | −69.6491 | −0.839146 | −0.419573 | − | 0.907722i | \(-0.637820\pi\) | ||||
−0.419573 | + | 0.907722i | \(0.637820\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 165.831i | 1.92827i | ||||||||
\(87\) | −82.9156 | + | 55.0000i | −0.953053 | + | 0.632184i | ||||
\(88\) | 165.000i | 1.87500i | ||||||||
\(89\) | 149.248i | 1.67695i | 0.544944 | + | 0.838473i | \(0.316551\pi\) | ||||
−0.544944 | + | 0.838473i | \(0.683449\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −139.298 | −1.51411 | ||||||||
\(93\) | −69.6491 | − | 105.000i | −0.748915 | − | 1.12903i | ||||
\(94\) | −154.000 | −1.63830 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 38.5000 | + | 58.0409i | 0.401042 | + | 0.604593i | ||||
\(97\) | − | 70.0000i | − | 0.721649i | −0.932634 | − | 0.360825i | \(-0.882495\pi\) | ||
0.932634 | − | 0.360825i | \(-0.117505\pi\) | |||||||
\(98\) | 162.515 | 1.65831 | ||||||||
\(99\) | −137.500 | − | 58.0409i | −1.38889 | − | 0.586272i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | −18.2414 | − | 27.5000i | −0.178838 | − | 0.269608i | ||||
\(103\) | 70.0000i | 0.679612i | 0.940496 | + | 0.339806i | \(0.110361\pi\) | ||||
−0.940496 | + | 0.339806i | \(0.889639\pi\) | |||||||
\(104\) | − | 99.4987i | − | 0.956719i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 154.000 | 1.45283 | ||||||||
\(107\) | 69.6491 | 0.650926 | 0.325463 | − | 0.945555i | \(-0.394480\pi\) | ||||
0.325463 | + | 0.945555i | \(0.394480\pi\) | |||||||
\(108\) | 185.731 | − | 35.0000i | 1.71973 | − | 0.324074i | ||||
\(109\) | 88.0000 | 0.807339 | 0.403670 | − | 0.914905i | \(-0.367734\pi\) | ||||
0.403670 | + | 0.914905i | \(0.367734\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −100.000 | + | 66.3325i | −0.900901 | + | 0.597590i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −102.815 | −0.909871 | −0.454935 | − | 0.890525i | \(-0.650338\pi\) | ||||
−0.454935 | + | 0.890525i | \(0.650338\pi\) | |||||||
\(114\) | 38.5000 | + | 58.0409i | 0.337719 | + | 0.509131i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 232.164i | − | 2.00141i | ||||||
\(117\) | 82.9156 | + | 35.0000i | 0.708681 | + | 0.299145i | ||||
\(118\) | − | 220.000i | − | 1.86441i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −154.000 | −1.27273 | ||||||||
\(122\) | −26.5330 | −0.217484 | ||||||||
\(123\) | −41.4578 | + | 27.5000i | −0.337055 | + | 0.223577i | ||||
\(124\) | 294.000 | 2.37097 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 190.000i | 1.49606i | 0.663663 | + | 0.748031i | \(0.269001\pi\) | ||||
−0.663663 | + | 0.748031i | \(0.730999\pi\) | |||||||
\(128\) | −228.847 | −1.78787 | ||||||||
\(129\) | 125.000 | − | 82.9156i | 0.968992 | − | 0.642757i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 198.997i | − | 1.51906i | −0.650469 | − | 0.759532i | \(-0.725428\pi\) | ||
0.650469 | − | 0.759532i | \(-0.274572\pi\) | |||||||
\(132\) | 290.205 | − | 192.500i | 2.19852 | − | 1.45833i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 149.248i | 1.11379i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 33.0000 | 0.242647 | ||||||||
\(137\) | 69.6491 | 0.508388 | 0.254194 | − | 0.967153i | \(-0.418190\pi\) | ||||
0.254194 | + | 0.967153i | \(0.418190\pi\) | |||||||
\(138\) | 109.449 | + | 165.000i | 0.793106 | + | 1.19565i | ||||
\(139\) | −77.0000 | −0.553957 | −0.276978 | − | 0.960876i | \(-0.589333\pi\) | ||||
−0.276978 | + | 0.960876i | \(0.589333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 77.0000 | + | 116.082i | 0.546099 | + | 0.823276i | ||||
\(142\) | 110.000i | 0.774648i | ||||||||
\(143\) | 165.831 | 1.15966 | ||||||||
\(144\) | −17.5000 | + | 41.4578i | −0.121528 | + | 0.287901i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 116.082i | 0.795081i | ||||||||
\(147\) | −81.2573 | − | 122.500i | −0.552771 | − | 0.833333i | ||||
\(148\) | − | 280.000i | − | 1.89189i | ||||||
\(149\) | 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 | \(0.307123\pi\) | |||||||
\(152\) | −69.6491 | −0.458218 | ||||||||
\(153\) | −11.6082 | + | 27.5000i | −0.0758705 | + | 0.179739i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −175.000 | + | 116.082i | −1.12179 | + | 0.744115i | ||||
\(157\) | − | 250.000i | − | 1.59236i | −0.605062 | − | 0.796178i | \(-0.706852\pi\) | ||
0.605062 | − | 0.796178i | \(-0.293148\pi\) | |||||||
\(158\) | −39.7995 | −0.251896 | ||||||||
\(159\) | −77.0000 | − | 116.082i | −0.484277 | − | 0.730075i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −187.389 | − | 192.500i | −1.15672 | − | 1.18827i | ||||
\(163\) | − | 35.0000i | − | 0.214724i | −0.994220 | − | 0.107362i | \(-0.965760\pi\) | ||
0.994220 | − | 0.107362i | \(-0.0342404\pi\) | |||||||
\(164\) | − | 116.082i | − | 0.707816i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −231.000 | −1.39157 | ||||||||
\(167\) | −179.098 | −1.07244 | −0.536221 | − | 0.844078i | \(-0.680149\pi\) | ||||
−0.536221 | + | 0.844078i | \(0.680149\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 69.0000 | 0.408284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.5000 | − | 58.0409i | 0.143275 | − | 0.339421i | ||||
\(172\) | 350.000i | 2.03488i | ||||||||
\(173\) | 278.596 | 1.61038 | 0.805192 | − | 0.593014i | \(-0.202062\pi\) | ||||
0.805192 | + | 0.593014i | \(0.202062\pi\) | |||||||
\(174\) | −275.000 | + | 182.414i | −1.58046 | + | 1.04836i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 82.9156i | 0.471111i | ||||||||
\(177\) | −165.831 | + | 110.000i | −0.936900 | + | 0.621469i | ||||
\(178\) | 495.000i | 2.78090i | ||||||||
\(179\) | − | 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 | ||||||||
\(183\) | 13.2665 | + | 20.0000i | 0.0724945 | + | 0.109290i | ||||
\(184\) | −198.000 | −1.07609 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −231.000 | − | 348.246i | −1.24194 | − | 1.87229i | ||||
\(187\) | 55.0000i | 0.294118i | ||||||||
\(188\) | −325.029 | −1.72888 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 232.164i | 1.21552i | 0.794122 | + | 0.607758i | \(0.207931\pi\) | ||||
−0.794122 | + | 0.607758i | \(0.792069\pi\) | |||||||
\(192\) | 160.856 | + | 242.500i | 0.837793 | + | 1.26302i | ||||
\(193\) | 25.0000i | 0.129534i | 0.997900 | + | 0.0647668i | \(0.0206304\pi\) | ||||
−0.997900 | + | 0.0647668i | \(0.979370\pi\) | |||||||
\(194\) | − | 232.164i | − | 1.19672i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 343.000 | 1.75000 | ||||||||
\(197\) | 218.897 | 1.11115 | 0.555577 | − | 0.831465i | \(-0.312498\pi\) | ||||
0.555577 | + | 0.831465i | \(0.312498\pi\) | |||||||
\(198\) | −456.036 | − | 192.500i | −2.30321 | − | 0.972222i | ||||
\(199\) | 68.0000 | 0.341709 | 0.170854 | − | 0.985296i | \(-0.445347\pi\) | ||||
0.170854 | + | 0.985296i | \(0.445347\pi\) | |||||||
\(200\) | 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 | ||||||||
\(207\) | 69.6491 | − | 165.000i | 0.336469 | − | 0.797101i | ||||
\(208\) | − | 50.0000i | − | 0.240385i | ||||||
\(209\) | − | 116.082i | − | 0.555416i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 77.0000 | 0.364929 | 0.182464 | − | 0.983212i | \(-0.441593\pi\) | ||||
0.182464 | + | 0.983212i | \(0.441593\pi\) | |||||||
\(212\) | 325.029 | 1.53316 | ||||||||
\(213\) | 82.9156 | − | 55.0000i | 0.389275 | − | 0.258216i | ||||
\(214\) | 231.000 | 1.07944 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 264.000 | − | 49.7494i | 1.22222 | − | 0.230321i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 291.863 | 1.33882 | ||||||||
\(219\) | 87.5000 | − | 58.0409i | 0.399543 | − | 0.265027i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 33.1662i | − | 0.150074i | ||||||
\(222\) | −331.662 | + | 220.000i | −1.49398 | + | 0.990991i | ||||
\(223\) | − | 140.000i | − | 0.627803i | −0.949456 | − | 0.313901i | \(-0.898364\pi\) | ||
0.949456 | − | 0.313901i | \(-0.101636\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −341.000 | −1.50885 | ||||||||
\(227\) | 185.731 | 0.818198 | 0.409099 | − | 0.912490i | \(-0.365843\pi\) | ||||
0.409099 | + | 0.912490i | \(0.365843\pi\) | |||||||
\(228\) | 81.2573 | + | 122.500i | 0.356392 | + | 0.537281i | ||||
\(229\) | −372.000 | −1.62445 | −0.812227 | − | 0.583341i | \(-0.801745\pi\) | ||||
−0.812227 | + | 0.583341i | \(0.801745\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 330.000i | − | 1.42241i | ||||||
\(233\) | −119.398 | −0.512440 | −0.256220 | − | 0.966619i | \(-0.582477\pi\) | ||||
−0.256220 | + | 0.966619i | \(0.582477\pi\) | |||||||
\(234\) | 275.000 | + | 116.082i | 1.17521 | + | 0.496076i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 464.327i | − | 1.96749i | ||||||
\(237\) | 19.8997 | + | 30.0000i | 0.0839652 | + | 0.126582i | ||||
\(238\) | 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 | \(0.827580\pi\) | |||||||
\(242\) | −510.760 | −2.11058 | ||||||||
\(243\) | −51.4077 | + | 237.500i | −0.211554 | + | 0.977366i | ||||
\(244\) | −56.0000 | −0.229508 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −137.500 | + | 91.2072i | −0.558943 | + | 0.370761i | ||||
\(247\) | 70.0000i | 0.283401i | ||||||||
\(248\) | 417.895 | 1.68506 | ||||||||
\(249\) | 115.500 | + | 174.123i | 0.463855 | + | 0.699288i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 248.747i | 0.991023i | 0.868601 | + | 0.495512i | \(0.165019\pi\) | ||||
−0.868601 | + | 0.495512i | \(0.834981\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 330.000i | − | 1.30435i | ||||||
\(254\) | 630.159i | 2.48094i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −371.000 | −1.44922 | ||||||||
\(257\) | −278.596 | −1.08403 | −0.542017 | − | 0.840368i | \(-0.682339\pi\) | ||||
−0.542017 | + | 0.840368i | \(0.682339\pi\) | |||||||
\(258\) | 414.578 | − | 275.000i | 1.60689 | − | 1.06589i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 275.000 | + | 116.082i | 1.05364 | + | 0.444758i | ||||
\(262\) | − | 660.000i | − | 2.51908i | ||||||
\(263\) | −285.230 | −1.08452 | −0.542262 | − | 0.840210i | \(-0.682432\pi\) | ||||
−0.542262 | + | 0.840210i | \(0.682432\pi\) | |||||||
\(264\) | 412.500 | − | 273.622i | 1.56250 | − | 1.03645i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 373.120 | − | 247.500i | 1.39745 | − | 0.926966i | ||||
\(268\) | 315.000i | 1.17537i | ||||||||
\(269\) | − | 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 | \(0.487076\pi\) | |||||||
\(272\) | 16.5831 | 0.0609674 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 231.000 | 0.843066 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 231.000 | + | 348.246i | 0.836957 | + | 1.26176i | ||||
\(277\) | − | 210.000i | − | 0.758123i | −0.925372 | − | 0.379061i | \(-0.876247\pi\) | ||
0.925372 | − | 0.379061i | \(-0.123753\pi\) | |||||||
\(278\) | −255.380 | −0.918633 | ||||||||
\(279\) | −147.000 | + | 348.246i | −0.526882 | + | 1.24819i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 198.997i | − | 0.708176i | −0.935212 | − | 0.354088i | \(-0.884791\pi\) | ||
0.935212 | − | 0.354088i | \(-0.115209\pi\) | |||||||
\(282\) | 255.380 | + | 385.000i | 0.905603 | + | 1.36525i | ||||
\(283\) | − | 345.000i | − | 1.21908i | −0.792755 | − | 0.609541i | \(-0.791354\pi\) | ||
0.792755 | − | 0.609541i | \(-0.208646\pi\) | |||||||
\(284\) | 232.164i | 0.817478i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 550.000 | 1.92308 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 81.2573 | − | 192.500i | 0.282143 | − | 0.668403i | ||||
\(289\) | −278.000 | −0.961938 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −175.000 | + | 116.082i | −0.601375 | + | 0.398907i | ||||
\(292\) | 245.000i | 0.839041i | ||||||||
\(293\) | −318.396 | −1.08668 | −0.543338 | − | 0.839514i | \(-0.682840\pi\) | ||||
−0.543338 | + | 0.839514i | \(0.682840\pi\) | |||||||
\(294\) | −269.500 | − | 406.287i | −0.916667 | − | 1.38193i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 397.995i | − | 1.34458i | ||||||
\(297\) | 82.9156 | + | 440.000i | 0.279177 | + | 1.48148i | ||||
\(298\) | 550.000i | 1.84564i | ||||||||
\(299\) | 198.997i | 0.665543i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 570.459 | 1.88894 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −35.0000 | −0.115132 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −38.5000 | + | 91.2072i | −0.125817 | + | 0.298063i | ||||
\(307\) | 325.000i | 1.05863i | 0.848425 | + | 0.529316i | \(0.177551\pi\) | ||||
−0.848425 | + | 0.529316i | \(0.822449\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 175.000 | − | 116.082i | 0.566343 | − | 0.375669i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 397.995i | − | 1.27973i | −0.768489 | − | 0.639863i | \(-0.778991\pi\) | ||
0.768489 | − | 0.639863i | \(-0.221009\pi\) | |||||||
\(312\) | −248.747 | + | 165.000i | −0.797266 | + | 0.528846i | ||||
\(313\) | 490.000i | 1.56550i | 0.622339 | + | 0.782748i | \(0.286182\pi\) | ||||
−0.622339 | + | 0.782748i | \(0.713818\pi\) | |||||||
\(314\) | − | 829.156i | − | 2.64062i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −84.0000 | −0.265823 | ||||||||
\(317\) | −212.264 | −0.669602 | −0.334801 | − | 0.942289i | \(-0.608669\pi\) | ||||
−0.334801 | + | 0.942289i | \(0.608669\pi\) | |||||||
\(318\) | −255.380 | − | 385.000i | −0.803082 | − | 1.21069i | ||||
\(319\) | 550.000 | 1.72414 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −115.500 | − | 174.123i | −0.359813 | − | 0.542439i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.2164 | −0.0718773 | ||||||||
\(324\) | −395.500 | − | 406.287i | −1.22068 | − | 1.25397i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 116.082i | − | 0.356079i | ||||||
\(327\) | −145.931 | − | 220.000i | −0.446274 | − | 0.672783i | ||||
\(328\) | − | 165.000i | − | 0.503049i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −243.000 | −0.734139 | −0.367069 | − | 0.930194i | \(-0.619639\pi\) | ||||
−0.367069 | + | 0.930194i | \(0.619639\pi\) | |||||||
\(332\) | −487.544 | −1.46851 | ||||||||
\(333\) | 331.662 | + | 140.000i | 0.995983 | + | 0.420420i | ||||
\(334\) | −594.000 | −1.77844 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 385.000i | 1.14243i | 0.820799 | + | 0.571217i | \(0.193528\pi\) | ||||
−0.820799 | + | 0.571217i | \(0.806472\pi\) | |||||||
\(338\) | 228.847 | 0.677062 | ||||||||
\(339\) | 170.500 | + | 257.038i | 0.502950 | + | 0.758225i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 696.491i | 2.04250i | ||||||||
\(342\) | 81.2573 | − | 192.500i | 0.237594 | − | 0.562865i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 497.494i | 1.44620i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 924.000 | 2.67052 | ||||||||
\(347\) | −295.180 | −0.850662 | −0.425331 | − | 0.905038i | \(-0.639842\pi\) | ||||
−0.425331 | + | 0.905038i | \(0.639842\pi\) | |||||||
\(348\) | −580.409 | + | 385.000i | −1.66784 | + | 1.10632i | ||||
\(349\) | −532.000 | −1.52436 | −0.762178 | − | 0.647368i | \(-0.775870\pi\) | ||||
−0.762178 | + | 0.647368i | \(0.775870\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −50.0000 | − | 265.330i | −0.142450 | − | 0.755926i | ||||
\(352\) | − | 385.000i | − | 1.09375i | ||||||
\(353\) | 278.596 | 0.789225 | 0.394613 | − | 0.918848i | \(-0.370879\pi\) | ||||
0.394613 | + | 0.918848i | \(0.370879\pi\) | |||||||
\(354\) | −550.000 | + | 364.829i | −1.55367 | + | 1.03059i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1044.74i | 2.93465i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 385.000i | − | 1.07542i | ||||||
\(359\) | − | 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 | ||||||||
\(362\) | 603.626 | 1.66747 | ||||||||
\(363\) | 255.380 | + | 385.000i | 0.703526 | + | 1.06061i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 44.0000 | + | 66.3325i | 0.120219 | + | 0.181236i | ||||
\(367\) | − | 180.000i | − | 0.490463i | −0.969465 | − | 0.245232i | \(-0.921136\pi\) | ||
0.969465 | − | 0.245232i | \(-0.0788640\pi\) | |||||||
\(368\) | −99.4987 | −0.270377 | ||||||||
\(369\) | 137.500 | + | 58.0409i | 0.372629 | + | 0.157293i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −487.544 | − | 735.000i | −1.31060 | − | 1.97581i | ||||
\(373\) | 110.000i | 0.294906i | 0.989069 | + | 0.147453i | \(0.0471075\pi\) | ||||
−0.989069 | + | 0.147453i | \(0.952892\pi\) | |||||||
\(374\) | 182.414i | 0.487739i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −462.000 | −1.22872 | ||||||||
\(377\) | −331.662 | −0.879741 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 533.000 | 1.40633 | 0.703166 | − | 0.711025i | \(-0.251769\pi\) | ||||
0.703166 | + | 0.711025i | \(0.251769\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 475.000 | − | 315.079i | 1.24672 | − | 0.826980i | ||||
\(382\) | 770.000i | 2.01571i | ||||||||
\(383\) | 79.5990 | 0.207830 | 0.103915 | − | 0.994586i | \(-0.466863\pi\) | ||||
0.103915 | + | 0.994586i | \(0.466863\pi\) | |||||||
\(384\) | 379.500 | + | 572.118i | 0.988281 | + | 1.48989i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 82.9156i | 0.214807i | ||||||||
\(387\) | −414.578 | − | 175.000i | −1.07126 | − | 0.452196i | ||||
\(388\) | − | 490.000i | − | 1.26289i | ||||||
\(389\) | − | 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 | ||||||||
\(392\) | 487.544 | 1.24373 | ||||||||
\(393\) | −497.494 | + | 330.000i | −1.26589 | + | 0.839695i | ||||
\(394\) | 726.000 | 1.84264 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −962.500 | − | 406.287i | −2.43056 | − | 1.02598i | ||||
\(397\) | − | 20.0000i | − | 0.0503778i | −0.999683 | − | 0.0251889i | \(-0.991981\pi\) | ||
0.999683 | − | 0.0251889i | \(-0.00801873\pi\) | |||||||
\(398\) | 225.530 | 0.566660 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 746.241i | − | 1.86095i | −0.366357 | − | 0.930475i | \(-0.619395\pi\) | ||
0.366357 | − | 0.930475i | \(-0.380605\pi\) | |||||||
\(402\) | 373.120 | − | 247.500i | 0.928160 | − | 0.615672i | ||||
\(403\) | − | 420.000i | − | 1.04218i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 663.325 | 1.62979 | ||||||||
\(408\) | −54.7243 | − | 82.5000i | −0.134128 | − | 0.202206i | ||||
\(409\) | −77.0000 | −0.188264 | −0.0941320 | − | 0.995560i | \(-0.530008\pi\) | ||||
−0.0941320 | + | 0.995560i | \(0.530008\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −115.500 | − | 174.123i | −0.281022 | − | 0.423656i | ||||
\(412\) | 490.000i | 1.18932i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 231.000 | − | 547.243i | 0.557971 | − | 1.32184i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 232.164i | 0.558086i | ||||||||
\(417\) | 127.690 | + | 192.500i | 0.306211 | + | 0.461631i | ||||
\(418\) | − | 385.000i | − | 0.921053i | ||||||
\(419\) | 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 | \(0.337248\pi\) | |||||||
\(422\) | 255.380 | 0.605166 | ||||||||
\(423\) | 162.515 | − | 385.000i | 0.384195 | − | 0.910165i | ||||
\(424\) | 462.000 | 1.08962 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 275.000 | − | 182.414i | 0.645540 | − | 0.428203i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 487.544 | 1.13912 | ||||||||
\(429\) | −275.000 | − | 414.578i | −0.641026 | − | 0.966383i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 198.997i | − | 0.461711i | −0.972988 | − | 0.230856i | \(-0.925848\pi\) | ||
0.972988 | − | 0.230856i | \(-0.0741525\pi\) | |||||||
\(432\) | 132.665 | − | 25.0000i | 0.307095 | − | 0.0578704i | ||||
\(433\) | 455.000i | 1.05081i | 0.850853 | + | 0.525404i | \(0.176086\pi\) | ||||
−0.850853 | + | 0.525404i | \(0.823914\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 616.000 | 1.41284 | ||||||||
\(437\) | 139.298 | 0.318760 | ||||||||
\(438\) | 290.205 | − | 192.500i | 0.662568 | − | 0.439498i | ||||
\(439\) | −22.0000 | −0.0501139 | −0.0250569 | − | 0.999686i | \(-0.507977\pi\) | ||||
−0.0250569 | + | 0.999686i | \(0.507977\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −171.500 | + | 406.287i | −0.388889 | + | 0.921285i | ||||
\(442\) | − | 110.000i | − | 0.248869i | ||||||
\(443\) | 527.343 | 1.19039 | 0.595196 | − | 0.803581i | \(-0.297075\pi\) | ||||
0.595196 | + | 0.803581i | \(0.297075\pi\) | |||||||
\(444\) | −700.000 | + | 464.327i | −1.57658 | + | 1.04578i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 464.327i | − | 1.04109i | ||||||
\(447\) | 414.578 | − | 275.000i | 0.927468 | − | 0.615213i | ||||
\(448\) | 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 | ||||||||
\(452\) | −719.708 | −1.59227 | ||||||||
\(453\) | −285.230 | − | 430.000i | −0.629646 | − | 0.949227i | ||||
\(454\) | 616.000 | 1.35683 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 115.500 | + | 174.123i | 0.253289 | + | 0.381848i | ||||
\(457\) | − | 275.000i | − | 0.601751i | −0.953663 | − | 0.300875i | \(-0.902721\pi\) | ||
0.953663 | − | 0.300875i | \(-0.0972788\pi\) | |||||||
\(458\) | −1233.78 | −2.69385 | ||||||||
\(459\) | 88.0000 | − | 16.5831i | 0.191721 | − | 0.0361288i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 596.992i | 1.29499i | 0.762068 | + | 0.647497i | \(0.224184\pi\) | ||||
−0.762068 | + | 0.647497i | \(0.775816\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 240.000i | 0.518359i | 0.965829 | + | 0.259179i | \(0.0834520\pi\) | ||||
−0.965829 | + | 0.259179i | \(0.916548\pi\) | |||||||
\(464\) | − | 165.831i | − | 0.357395i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −396.000 | −0.849785 | ||||||||
\(467\) | −13.2665 | −0.0284079 | −0.0142040 | − | 0.999899i | \(-0.504521\pi\) | ||||
−0.0142040 | + | 0.999899i | \(0.504521\pi\) | |||||||
\(468\) | 580.409 | + | 245.000i | 1.24019 | + | 0.523504i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −625.000 | + | 414.578i | −1.32696 | + | 0.880208i | ||||
\(472\) | − | 660.000i | − | 1.39831i | ||||||
\(473\) | −829.156 | −1.75297 | ||||||||
\(474\) | 66.0000 | + | 99.4987i | 0.139241 | + | 0.209913i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −162.515 | + | 385.000i | −0.340701 | + | 0.807128i | ||||
\(478\) | 770.000i | 1.61088i | ||||||||
\(479\) | 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 | ||||||||
\(482\) | −1369.77 | −2.84184 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1078.00 | −2.22727 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −170.500 | + | 787.698i | −0.350823 | + | 1.62078i | ||||
\(487\) | 410.000i | 0.841889i | 0.907086 | + | 0.420945i | \(0.138301\pi\) | ||||
−0.907086 | + | 0.420945i | \(0.861699\pi\) | |||||||
\(488\) | −79.5990 | −0.163113 | ||||||||
\(489\) | −87.5000 | + | 58.0409i | −0.178937 | + | 0.118693i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 265.330i | − | 0.540387i | −0.962806 | − | 0.270193i | \(-0.912912\pi\) | ||
0.962806 | − | 0.270193i | \(-0.0870877\pi\) | |||||||
\(492\) | −290.205 | + | 192.500i | −0.589847 | + | 0.391260i | ||||
\(493\) | − | 110.000i | − | 0.223124i | ||||||
\(494\) | 232.164i | 0.469967i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 210.000 | 0.423387 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 383.070 | + | 577.500i | 0.769217 | + | 1.15964i | ||||
\(499\) | −322.000 | −0.645291 | −0.322645 | − | 0.946520i | \(-0.604572\pi\) | ||||
−0.322645 | + | 0.946520i | \(0.604572\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 297.000 | + | 447.744i | 0.592814 | + | 0.893701i | ||||
\(502\) | 825.000i | 1.64343i | ||||||||
\(503\) | 411.261 | 0.817617 | 0.408809 | − | 0.912620i | \(-0.365944\pi\) | ||||
0.408809 | + | 0.912620i | \(0.365944\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 1094.49i | − | 2.16302i | ||||||
\(507\) | −114.424 | − | 172.500i | −0.225687 | − | 0.340237i | ||||
\(508\) | 1330.00i | 2.61811i | ||||||||
\(509\) | 431.161i | 0.847075i | 0.905879 | + | 0.423538i | \(0.139212\pi\) | ||||
−0.905879 | + | 0.423538i | \(0.860788\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −315.079 | −0.615389 | ||||||||
\(513\) | −185.731 | + | 35.0000i | −0.362049 | + | 0.0682261i | ||||
\(514\) | −924.000 | −1.79767 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 875.000 | − | 580.409i | 1.69574 | − | 1.12482i | ||||
\(517\) | − | 770.000i | − | 1.48936i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −462.000 | − | 696.491i | −0.890173 | − | 1.34199i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 281.913i | 0.541100i | 0.962706 | + | 0.270550i | \(0.0872055\pi\) | ||||
−0.962706 | + | 0.270550i | \(0.912794\pi\) | |||||||
\(522\) | 912.072 | + | 385.000i | 1.74726 | + | 0.737548i | ||||
\(523\) | − | 1015.00i | − | 1.94073i | −0.241651 | − | 0.970363i | \(-0.577689\pi\) | ||
0.241651 | − | 0.970363i | \(-0.422311\pi\) | |||||||
\(524\) | − | 1392.98i | − | 2.65836i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −946.000 | −1.79848 | ||||||||
\(527\) | 139.298 | 0.264323 | ||||||||
\(528\) | 207.289 | − | 137.500i | 0.392593 | − | 0.260417i | ||||
\(529\) | −133.000 | −0.251418 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 550.000 | + | 232.164i | 1.03578 | + | 0.437220i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −165.831 | −0.311128 | ||||||||
\(534\) | 1237.50 | − | 820.865i | 2.31742 | − | 1.53720i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 447.744i | 0.835344i | ||||||||
\(537\) | −290.205 | + | 192.500i | −0.540418 | + | 0.358473i | ||||
\(538\) | − | 1540.00i | − | 2.86245i | ||||||
\(539\) | 812.573i | 1.50756i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 912.000 | 1.68577 | 0.842884 | − | 0.538096i | \(-0.180856\pi\) | ||||
0.842884 | + | 0.538096i | \(0.180856\pi\) | |||||||
\(542\) | 72.9657 | 0.134623 | ||||||||
\(543\) | −301.813 | − | 455.000i | −0.555825 | − | 0.837937i | ||||
\(544\) | −77.0000 | −0.141544 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 55.0000i | 0.100548i | 0.998735 | + | 0.0502742i | \(0.0160095\pi\) | ||||
−0.998735 | + | 0.0502742i | \(0.983990\pi\) | |||||||
\(548\) | 487.544 | 0.889679 | ||||||||
\(549\) | 28.0000 | − | 66.3325i | 0.0510018 | − | 0.120824i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 232.164i | 0.421350i | ||||||||
\(552\) | 328.346 | + | 495.000i | 0.594829 | + | 0.896739i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 696.491i | − | 1.25720i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −539.000 | −0.969424 | ||||||||
\(557\) | 1014.89 | 1.82206 | 0.911030 | − | 0.412341i | \(-0.135289\pi\) | ||||
0.911030 | + | 0.412341i | \(0.135289\pi\) | |||||||
\(558\) | −487.544 | + | 1155.00i | −0.873734 | + | 2.06989i | ||||
\(559\) | 500.000 | 0.894454 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 137.500 | − | 91.2072i | 0.245098 | − | 0.162580i | ||||
\(562\) | − | 660.000i | − | 1.17438i | ||||||
\(563\) | −119.398 | −0.212075 | −0.106038 | − | 0.994362i | \(-0.533816\pi\) | ||||
−0.106038 | + | 0.994362i | \(0.533816\pi\) | |||||||
\(564\) | 539.000 | + | 812.573i | 0.955674 | + | 1.44073i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 1144.24i | − | 2.02162i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 330.000i | 0.580986i | ||||||||
\(569\) | − | 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 | \(0.432032\pi\) | |||||||
\(572\) | 1160.82 | 2.02940 | ||||||||
\(573\) | 580.409 | − | 385.000i | 1.01293 | − | 0.671902i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 339.500 | − | 804.282i | 0.589410 | − | 1.39632i | ||||
\(577\) | 665.000i | 1.15251i | 0.817269 | + | 0.576256i | \(0.195487\pi\) | ||||
−0.817269 | + | 0.576256i | \(0.804513\pi\) | |||||||
\(578\) | −922.022 | −1.59519 | ||||||||
\(579\) | 62.5000 | − | 41.4578i | 0.107945 | − | 0.0716024i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −580.409 | + | 385.000i | −0.997267 | + | 0.661512i | ||||
\(583\) | 770.000i | 1.32075i | ||||||||
\(584\) | 348.246i | 0.596311i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1056.00 | −1.80205 | ||||||||
\(587\) | −626.842 | −1.06787 | −0.533937 | − | 0.845524i | \(-0.679288\pi\) | ||||
−0.533937 | + | 0.845524i | \(0.679288\pi\) | |||||||
\(588\) | −568.801 | − | 857.500i | −0.967349 | − | 1.45833i | ||||
\(589\) | −294.000 | −0.499151 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −363.000 | − | 547.243i | −0.614213 | − | 0.925961i | ||||
\(592\) | − | 200.000i | − | 0.337838i | ||||||
\(593\) | 859.006 | 1.44858 | 0.724288 | − | 0.689497i | \(-0.242169\pi\) | ||||
0.724288 | + | 0.689497i | \(0.242169\pi\) | |||||||
\(594\) | 275.000 | + | 1459.31i | 0.462963 | + | 2.45676i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1160.82i | 1.94768i | ||||||||
\(597\) | −112.765 | − | 170.000i | −0.188887 | − | 0.284757i | ||||
\(598\) | 660.000i | 1.10368i | ||||||||
\(599\) | − | 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 | ||||||||
\(603\) | −373.120 | − | 157.500i | −0.618773 | − | 0.261194i | ||||
\(604\) | 1204.00 | 1.99338 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1100.00i | − | 1.81219i | −0.423073 | − | 0.906096i | \(-0.639049\pi\) | ||
0.423073 | − | 0.906096i | \(-0.360951\pi\) | |||||||
\(608\) | 162.515 | 0.267294 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 464.327i | 0.759947i | ||||||||
\(612\) | −81.2573 | + | 192.500i | −0.132773 | + | 0.314542i | ||||
\(613\) | 290.000i | 0.473083i | 0.971621 | + | 0.236542i | \(0.0760140\pi\) | ||||
−0.971621 | + | 0.236542i | \(0.923986\pi\) | |||||||
\(614\) | 1077.90i | 1.75554i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −79.5990 | −0.129010 | −0.0645049 | − | 0.997917i | \(-0.520547\pi\) | ||||
−0.0645049 | + | 0.997917i | \(0.520547\pi\) | |||||||
\(618\) | 580.409 | − | 385.000i | 0.939174 | − | 0.622977i | ||||
\(619\) | 58.0000 | 0.0936995 | 0.0468498 | − | 0.998902i | \(-0.485082\pi\) | ||||
0.0468498 | + | 0.998902i | \(0.485082\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −528.000 | + | 99.4987i | −0.850242 | + | 0.160223i | ||||
\(622\) | − | 1320.00i | − | 2.12219i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −125.000 | + | 82.9156i | −0.200321 | + | 0.132878i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1625.15i | 2.59608i | ||||||||
\(627\) | −290.205 | + | 192.500i | −0.462846 | + | 0.307018i | ||||
\(628\) | − | 1750.00i | − | 2.78662i | ||||||
\(629\) | − | 132.665i | − | 0.210914i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 862.000 | 1.36609 | 0.683043 | − | 0.730378i | \(-0.260656\pi\) | ||||
0.683043 | + | 0.730378i | \(0.260656\pi\) | |||||||
\(632\) | −119.398 | −0.188922 | ||||||||
\(633\) | −127.690 | − | 192.500i | −0.201722 | − | 0.304107i | ||||
\(634\) | −704.000 | −1.11041 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −539.000 | − | 812.573i | −0.847484 | − | 1.27763i | ||||
\(637\) | − | 490.000i | − | 0.769231i | ||||||
\(638\) | 1824.14 | 2.85916 | ||||||||
\(639\) | −275.000 | − | 116.082i | −0.430360 | − | 0.181662i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 596.992i | − | 0.931345i | −0.884957 | − | 0.465673i | \(-0.845812\pi\) | ||
0.884957 | − | 0.465673i | \(-0.154188\pi\) | |||||||
\(642\) | −383.070 | − | 577.500i | −0.596682 | − | 0.899533i | ||||
\(643\) | 1050.00i | 1.63297i | 0.577366 | + | 0.816485i | \(0.304080\pi\) | ||||
−0.577366 | + | 0.816485i | \(0.695920\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −77.0000 | −0.119195 | ||||||||
\(647\) | 252.063 | 0.389588 | 0.194794 | − | 0.980844i | \(-0.437596\pi\) | ||||
0.194794 | + | 0.980844i | \(0.437596\pi\) | |||||||
\(648\) | −562.168 | − | 577.500i | −0.867543 | − | 0.891204i | ||||
\(649\) | 1100.00 | 1.69492 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 245.000i | − | 0.375767i | ||||||
\(653\) | 1207.25 | 1.84878 | 0.924389 | − | 0.381452i | \(-0.124576\pi\) | ||||
0.924389 | + | 0.381452i | \(0.124576\pi\) | |||||||
\(654\) | −484.000 | − | 729.657i | −0.740061 | − | 1.11568i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 82.9156i | − | 0.126396i | ||||||
\(657\) | −290.205 | − | 122.500i | −0.441712 | − | 0.186454i | ||||
\(658\) | 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 | \(0.523618\pi\) | |||||||
\(662\) | −805.940 | −1.21743 | ||||||||
\(663\) | −82.9156 | + | 55.0000i | −0.125061 | + | 0.0829563i | ||||
\(664\) | −693.000 | −1.04367 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1100.00 | + | 464.327i | 1.65165 | + | 0.697188i | ||||
\(667\) | 660.000i | 0.989505i | ||||||||
\(668\) | −1253.68 | −1.87677 | ||||||||
\(669\) | −350.000 | + | 232.164i | −0.523169 | + | 0.347031i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 132.665i | − | 0.197712i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 210.000i | 0.312036i | 0.987754 | + | 0.156018i | \(0.0498657\pi\) | ||||
−0.987754 | + | 0.156018i | \(0.950134\pi\) | |||||||
\(674\) | 1276.90i | 1.89451i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 483.000 | 0.714497 | ||||||||
\(677\) | −79.5990 | −0.117576 | −0.0587880 | − | 0.998270i | \(-0.518724\pi\) | ||||
−0.0587880 | + | 0.998270i | \(0.518724\pi\) | |||||||
\(678\) | 565.485 | + | 852.500i | 0.834048 | + | 1.25737i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −308.000 | − | 464.327i | −0.452276 | − | 0.681832i | ||||
\(682\) | 2310.00i | 3.38710i | ||||||||
\(683\) | −169.148 | −0.247654 | −0.123827 | − | 0.992304i | \(-0.539517\pi\) | ||||
−0.123827 | + | 0.992304i | \(0.539517\pi\) | |||||||
\(684\) | 171.500 | − | 406.287i | 0.250731 | − | 0.593986i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 616.892 | + | 930.000i | 0.897951 | + | 1.35371i | ||||
\(688\) | 250.000i | 0.363372i | ||||||||
\(689\) | − | 464.327i | − | 0.673915i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −713.000 | −1.03184 | −0.515919 | − | 0.856637i | \(-0.672549\pi\) | ||||
−0.515919 | + | 0.856637i | \(0.672549\pi\) | |||||||
\(692\) | 1950.18 | 2.81817 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −979.000 | −1.41066 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −825.000 | + | 547.243i | −1.18534 | + | 0.786269i | ||||
\(697\) | − | 55.0000i | − | 0.0789096i | ||||||
\(698\) | −1764.44 | −2.52786 | ||||||||
\(699\) | 198.000 | + | 298.496i | 0.283262 | + | 0.427033i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1160.82i | − | 1.65595i | −0.560767 | − | 0.827973i | \(-0.689494\pi\) | ||
0.560767 | − | 0.827973i | \(-0.310506\pi\) | |||||||
\(702\) | −165.831 | − | 880.000i | −0.236227 | − | 1.25356i | ||||
\(703\) | 280.000i | 0.398293i | ||||||||
\(704\) | − | 1608.56i | − | 2.28489i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 924.000 | 1.30878 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1160.82 | + | 770.000i | −1.63957 | + | 1.08757i | ||||
\(709\) | 248.000 | 0.349788 | 0.174894 | − | 0.984587i | \(-0.444042\pi\) | ||||
0.174894 | + | 0.984587i | \(0.444042\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 42.0000 | − | 99.4987i | 0.0590717 | − | 0.139942i | ||||
\(712\) | 1485.00i | 2.08567i | ||||||||
\(713\) | −835.789 | −1.17222 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 812.573i | − | 1.13488i | ||||||
\(717\) | 580.409 | − | 385.000i | 0.809497 | − | 0.536960i | ||||
\(718\) | − | 1320.00i | − | 1.83844i | ||||||
\(719\) | 198.997i | 0.276770i | 0.990379 | + | 0.138385i | \(0.0441911\pi\) | ||||
−0.990379 | + | 0.138385i | \(0.955809\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1034.79 | −1.43322 | ||||||||
\(723\) | 684.883 | + | 1032.50i | 0.947279 | + | 1.42808i | ||||
\(724\) | 1274.00 | 1.75967 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 847.000 | + | 1276.90i | 1.16667 | + | 1.75882i | ||||
\(727\) | − | 10.0000i | − | 0.0137552i | −0.999976 | − | 0.00687758i | \(-0.997811\pi\) | ||
0.999976 | − | 0.00687758i | \(-0.00218922\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 679.000 | − | 265.330i | 0.931413 | − | 0.363964i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 165.831i | 0.226855i | ||||||||
\(732\) | 92.8655 | + | 140.000i | 0.126865 | + | 0.191257i | ||||
\(733\) | − | 770.000i | − | 1.05048i | −0.850955 | − | 0.525239i | \(-0.823976\pi\) | ||
0.850955 | − | 0.525239i | \(-0.176024\pi\) | |||||||
\(734\) | − | 596.992i | − | 0.813341i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 462.000 | 0.627717 | ||||||||
\(737\) | −746.241 | −1.01254 | ||||||||
\(738\) | 456.036 | + | 192.500i | 0.617935 | + | 0.260840i | ||||
\(739\) | −802.000 | −1.08525 | −0.542625 | − | 0.839975i | \(-0.682570\pi\) | ||||
−0.542625 | + | 0.839975i | \(0.682570\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 175.000 | − | 116.082i | 0.236167 | − | 0.156656i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1346.55 | −1.81231 | −0.906157 | − | 0.422941i | \(-0.860998\pi\) | ||||
−0.906157 | + | 0.422941i | \(0.860998\pi\) | |||||||
\(744\) | −693.000 | − | 1044.74i | −0.931452 | − | 1.40422i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 364.829i | 0.489047i | ||||||||
\(747\) | 243.772 | − | 577.500i | 0.326335 | − | 0.773092i | ||||
\(748\) | 385.000i | 0.514706i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 322.000 | 0.428762 | 0.214381 | − | 0.976750i | \(-0.431227\pi\) | ||||
0.214381 | + | 0.976750i | \(0.431227\pi\) | |||||||
\(752\) | −232.164 | −0.308728 | ||||||||
\(753\) | 621.867 | − | 412.500i | 0.825853 | − | 0.547809i | ||||
\(754\) | −1100.00 | −1.45889 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 400.000i | 0.528402i | 0.964468 | + | 0.264201i | \(0.0851082\pi\) | ||||
−0.964468 | + | 0.264201i | \(0.914892\pi\) | |||||||
\(758\) | 1767.76 | 2.33214 | ||||||||
\(759\) | −825.000 | + | 547.243i | −1.08696 | + | 0.721005i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 348.246i | 0.457616i | 0.973472 | + | 0.228808i | \(0.0734828\pi\) | ||||
−0.973472 | + | 0.228808i | \(0.926517\pi\) | |||||||
\(762\) | 1575.40 | − | 1045.00i | 2.06745 | − | 1.37139i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1625.15i | 2.12715i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 264.000 | 0.344648 | ||||||||
\(767\) | −663.325 | −0.864830 | ||||||||
\(768\) | 615.234 | + | 927.500i | 0.801086 | + | 1.20768i | ||||
\(769\) | 193.000 | 0.250975 | 0.125488 | − | 0.992095i | \(-0.459950\pi\) | ||||
0.125488 | + | 0.992095i | \(0.459950\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 462.000 | + | 696.491i | 0.599222 | + | 0.903361i | ||||
\(772\) | 175.000i | 0.226684i | ||||||||
\(773\) | −417.895 | −0.540614 | −0.270307 | − | 0.962774i | \(-0.587125\pi\) | ||||
−0.270307 | + | 0.962774i | \(0.587125\pi\) | |||||||
\(774\) | −1375.00 | − | 580.409i | −1.77649 | − | 0.749883i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 696.491i | − | 0.897540i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 330.000i | − | 0.424165i | ||||||
\(779\) | 116.082i | 0.149014i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −550.000 | −0.704225 | ||||||||
\(782\) | −218.897 | −0.279920 | ||||||||
\(783\) | −165.831 | − | 880.000i | −0.211790 | − | 1.12388i | ||||
\(784\) | 245.000 | 0.312500 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1650.00 | + | 1094.49i | −2.09924 | + | 1.39248i | ||||
\(787\) | 910.000i | 1.15629i | 0.815934 | + | 0.578145i | \(0.196223\pi\) | ||||
−0.815934 | + | 0.578145i | \(0.803777\pi\) | |||||||
\(788\) | 1532.28 | 1.94452 | ||||||||
\(789\) | 473.000 | + | 713.074i | 0.599493 | + | 0.903770i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1368.11 | − | 577.500i | −1.72741 | − | 0.729167i | ||||
\(793\) | 80.0000i | 0.100883i | ||||||||
\(794\) | − | 66.3325i | − | 0.0835422i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 476.000 | 0.597990 | ||||||||
\(797\) | −1107.75 | −1.38990 | −0.694951 | − | 0.719057i | \(-0.744574\pi\) | ||||
−0.694951 | + | 0.719057i | \(0.744574\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −154.000 | −0.192741 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1237.50 | − | 522.368i | −1.54494 | − | 0.652145i | ||||
\(802\) | − | 2475.00i | − | 3.08603i | ||||||
\(803\) | −580.409 | −0.722801 | ||||||||
\(804\) | 787.500 | − | 522.368i | 0.979478 | − | 0.649712i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 1392.98i | − | 1.72827i | ||||||
\(807\) | −1160.82 | + | 770.000i | −1.43844 | + | 0.954151i | ||||
\(808\) | 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 | ||||||||
\(813\) | −36.4829 | − | 55.0000i | −0.0448744 | − | 0.0676507i | ||||
\(814\) | 2200.00 | 2.70270 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −27.5000 | − | 41.4578i | −0.0337010 | − | 0.0508061i | ||||
\(817\) | − | 350.000i | − | 0.428397i | ||||||
\(818\) | −255.380 | −0.312201 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 696.491i | 0.848345i | 0.905581 | + | 0.424172i | \(0.139435\pi\) | ||||
−0.905581 | + | 0.424172i | \(0.860565\pi\) | |||||||
\(822\) | −383.070 | − | 577.500i | −0.466022 | − | 0.702555i | ||||
\(823\) | 1060.00i | 1.28797i | 0.765038 | + | 0.643985i | \(0.222720\pi\) | ||||
−0.765038 | + | 0.643985i | \(0.777280\pi\) | |||||||
\(824\) | 696.491i | 0.845256i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 500.810 | 0.605575 | 0.302787 | − | 0.953058i | \(-0.402083\pi\) | ||||
0.302787 | + | 0.953058i | \(0.402083\pi\) | |||||||
\(828\) | 487.544 | − | 1155.00i | 0.588821 | − | 1.39493i | ||||
\(829\) | 1038.00 | 1.25211 | 0.626055 | − | 0.779779i | \(-0.284668\pi\) | ||||
0.626055 | + | 0.779779i | \(0.284668\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −525.000 | + | 348.246i | −0.631769 | + | 0.419068i | ||||
\(832\) | 970.000i | 1.16587i | ||||||||
\(833\) | 162.515 | 0.195096 | ||||||||
\(834\) | 423.500 | + | 638.450i | 0.507794 | + | 0.765528i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 812.573i | − | 0.971977i | ||||||
\(837\) | 1114.39 | − | 210.000i | 1.33140 | − | 0.250896i | ||||
\(838\) | 385.000i | 0.459427i | ||||||||
\(839\) | − | 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 | ||||||||
\(842\) | 1366.45 | 1.62286 | ||||||||
\(843\) | −497.494 | + | 330.000i | −0.590147 | + | 0.391459i | ||||
\(844\) | 539.000 | 0.638626 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 539.000 | − | 1276.90i | 0.637116 | − | 1.50934i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 232.164 | 0.273778 | ||||||||
\(849\) | −862.500 | + | 572.118i | −1.01590 | + | 0.673873i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 795.990i | 0.935358i | ||||||||
\(852\) | 580.409 | − | 385.000i | 0.681232 | − | 0.451878i | ||||
\(853\) | − | 630.000i | − | 0.738570i | −0.929316 | − | 0.369285i | \(-0.879603\pi\) | ||
0.929316 | − | 0.369285i | \(-0.120397\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 693.000 | 0.809579 | ||||||||
\(857\) | 1296.80 | 1.51319 | 0.756593 | − | 0.653886i | \(-0.226862\pi\) | ||||
0.756593 | + | 0.653886i | \(0.226862\pi\) | |||||||
\(858\) | −912.072 | − | 1375.00i | −1.06302 | − | 1.60256i | ||||
\(859\) | −307.000 | −0.357392 | −0.178696 | − | 0.983904i | \(-0.557188\pi\) | ||||
−0.178696 | + | 0.983904i | \(0.557188\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 660.000i | − | 0.765661i | ||||||
\(863\) | −484.227 | −0.561098 | −0.280549 | − | 0.959840i | \(-0.590516\pi\) | ||||
−0.280549 | + | 0.959840i | \(0.590516\pi\) | |||||||
\(864\) | −616.000 | + | 116.082i | −0.712963 | + | 0.134354i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1509.06i | 1.74257i | ||||||||
\(867\) | 461.011 | + | 695.000i | 0.531731 | + | 0.801615i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 198.997i | − | 0.228996i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 450.000 | 0.516648 | ||||||||
\(872\) | 875.589 | 1.00412 | ||||||||
\(873\) | 580.409 | + | 245.000i | 0.664845 | + | 0.280641i | ||||
\(874\) | 462.000 | 0.528604 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 612.500 | − | 406.287i | 0.699201 | − | 0.463797i | ||||
\(877\) | 840.000i | 0.957811i | 0.877867 | + | 0.478905i | \(0.158966\pi\) | ||||
−0.877867 | + | 0.478905i | \(0.841034\pi\) | |||||||
\(878\) | −72.9657 | −0.0831045 | ||||||||
\(879\) | 528.000 | + | 795.990i | 0.600683 | + | 0.905563i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 464.327i | 0.527046i | 0.964653 | + | 0.263523i | \(0.0848845\pi\) | ||||
−0.964653 | + | 0.263523i | \(0.915116\pi\) | |||||||
\(882\) | −568.801 | + | 1347.50i | −0.644899 | + | 1.52778i | ||||
\(883\) | − | 995.000i | − | 1.12684i | −0.826171 | − | 0.563420i | \(-0.809485\pi\) | ||
0.826171 | − | 0.563420i | \(-0.190515\pi\) | |||||||
\(884\) | − | 232.164i | − | 0.262629i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1749.00 | 1.97404 | ||||||||
\(887\) | −477.594 | −0.538437 | −0.269219 | − | 0.963079i | \(-0.586765\pi\) | ||||
−0.269219 | + | 0.963079i | \(0.586765\pi\) | |||||||
\(888\) | −994.987 | + | 660.000i | −1.12048 | + | 0.743243i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 962.500 | − | 936.947i | 1.08025 | − | 1.05157i | ||||
\(892\) | − | 980.000i | − | 1.09865i | ||||||
\(893\) | 325.029 | 0.363975 | ||||||||
\(894\) | 1375.00 | − | 912.072i | 1.53803 | − | 1.02021i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 497.494 | − | 330.000i | 0.554620 | − | 0.367893i | ||||
\(898\) | 275.000i | 0.306236i | ||||||||
\(899\) | − | 1392.98i | − | 1.54948i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 154.000 | 0.170921 | ||||||||
\(902\) | 912.072 | 1.01117 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1023.00 | −1.13164 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −946.000 | − | 1426.15i | −1.04415 | − | 1.57412i | ||||
\(907\) | − | 1050.00i | − | 1.15766i | −0.815447 | − | 0.578831i | \(-0.803509\pi\) | ||
0.815447 | − | 0.578831i | \(-0.196491\pi\) | |||||||
\(908\) | 1300.12 | 1.43185 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 729.657i | − | 0.800941i | −0.916310 | − | 0.400471i | \(-0.868847\pi\) | ||
0.916310 | − | 0.400471i | \(-0.131153\pi\) | |||||||
\(912\) | 58.0409 | + | 87.5000i | 0.0636414 | + | 0.0959430i | ||||
\(913\) | − | 1155.00i | − | 1.26506i | ||||||
\(914\) | − | 912.072i | − | 0.997890i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2604.00 | −2.84279 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 291.863 | − | 55.0000i | 0.317934 | − | 0.0599129i | ||||
\(919\) | −1342.00 | −1.46028 | −0.730141 | − | 0.683296i | \(-0.760546\pi\) | ||||
−0.730141 | + | 0.683296i | \(0.760546\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 812.500 | − | 538.952i | 0.882193 | − | 0.585181i | ||||
\(922\) | 1980.00i | 2.14751i | ||||||||
\(923\) | 331.662 | 0.359331 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 795.990i | 0.859600i | ||||||||
\(927\) | −580.409 | − | 245.000i | −0.626116 | − | 0.264293i | ||||
\(928\) | 770.000i | 0.829741i | ||||||||
\(929\) | 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 | ||||||||
\(932\) | −835.789 | −0.896770 | ||||||||
\(933\) | −994.987 | + | 660.000i | −1.06644 | + | 0.707395i | ||||
\(934\) | −44.0000 | −0.0471092 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 825.000 | + | 348.246i | 0.881410 | + | 0.372057i | ||||
\(937\) | − | 165.000i | − | 0.176094i | −0.996116 | − | 0.0880470i | \(-0.971937\pi\) | ||
0.996116 | − | 0.0880470i | \(-0.0280626\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1225.00 | − | 812.573i | 1.30458 | − | 0.865360i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 232.164i | 0.246720i | 0.992362 | + | 0.123360i | \(0.0393670\pi\) | ||||
−0.992362 | + | 0.123360i | \(0.960633\pi\) | |||||||
\(942\) | −2072.89 | + | 1375.00i | −2.20052 | + | 1.45966i | ||||
\(943\) | 330.000i | 0.349947i | ||||||||
\(944\) | − | 331.662i | − | 0.351337i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2750.00 | −2.90698 | ||||||||
\(947\) | −278.596 | −0.294188 | −0.147094 | − | 0.989122i | \(-0.546992\pi\) | ||||
−0.147094 | + | 0.989122i | \(0.546992\pi\) | |||||||
\(948\) | 139.298 | + | 210.000i | 0.146939 | + | 0.221519i | ||||
\(949\) | 350.000 | 0.368809 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 352.000 | + | 530.660i | 0.370137 | + | 0.558002i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 195.681 | 0.205331 | 0.102666 | − | 0.994716i | \(-0.467263\pi\) | ||||
0.102666 | + | 0.994716i | \(0.467263\pi\) | |||||||
\(954\) | −539.000 | + | 1276.90i | −0.564990 | + | 1.33847i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1625.15i | 1.69994i | ||||||||
\(957\) | −912.072 | − | 1375.00i | −0.953053 | − | 1.43678i | ||||
\(958\) | 990.000i | 1.03340i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 803.000 | 0.835588 | ||||||||
\(962\) | −1326.65 | −1.37905 | ||||||||
\(963\) | −243.772 | + | 577.500i | −0.253138 | + | 0.599688i | ||||
\(964\) | −2891.00 | −2.99896 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 280.000i | − | 0.289555i | −0.989464 | − | 0.144778i | \(-0.953753\pi\) | ||
0.989464 | − | 0.144778i | \(-0.0462467\pi\) | |||||||
\(968\) | −1532.28 | −1.58293 | ||||||||
\(969\) | 38.5000 | + | 58.0409i | 0.0397317 | + | 0.0598978i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1044.74i | − | 1.07594i | −0.842964 | − | 0.537970i | \(-0.819192\pi\) | ||
0.842964 | − | 0.537970i | \(-0.180808\pi\) | |||||||
\(972\) | −359.854 | + | 1662.50i | −0.370220 | + | 1.71039i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1359.82i | 1.39612i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −40.0000 | −0.0409836 | ||||||||
\(977\) | 1097.80 | 1.12365 | 0.561823 | − | 0.827257i | \(-0.310100\pi\) | ||||
0.561823 | + | 0.827257i | \(0.310100\pi\) | |||||||
\(978\) | −290.205 | + | 192.500i | −0.296733 | + | 0.196830i | ||||
\(979\) | −2475.00 | −2.52809 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −308.000 | + | 729.657i | −0.313965 | + | 0.743789i | ||||
\(982\) | − | 880.000i | − | 0.896130i | ||||||
\(983\) | 1671.58 | 1.70049 | 0.850244 | − | 0.526389i | \(-0.176455\pi\) | ||||
0.850244 | + | 0.526389i | \(0.176455\pi\) | |||||||
\(984\) | −412.500 | + | 273.622i | −0.419207 | + | 0.278071i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 364.829i | − | 0.370009i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 490.000i | 0.495951i | ||||||||
\(989\) | − | 994.987i | − | 1.00605i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 452.000 | 0.456105 | 0.228052 | − | 0.973649i | \(-0.426764\pi\) | ||||
0.228052 | + | 0.973649i | \(0.426764\pi\) | |||||||
\(992\) | −975.088 | −0.982951 | ||||||||
\(993\) | 402.970 | + | 607.500i | 0.405811 | + | 0.611782i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 808.500 | + | 1218.86i | 0.811747 | + | 1.22375i | ||||
\(997\) | − | 420.000i | − | 0.421264i | −0.977565 | − | 0.210632i | \(-0.932448\pi\) | ||
0.977565 | − | 0.210632i | \(-0.0675521\pi\) | |||||||
\(998\) | −1067.95 | −1.07009 | ||||||||
\(999\) | −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.d.c.74.3 | 4 | ||
3.2 | odd | 2 | inner | 75.3.d.c.74.1 | 4 | ||
4.3 | odd | 2 | 1200.3.c.d.449.4 | 4 | |||
5.2 | odd | 4 | 75.3.c.c.26.2 | yes | 2 | ||
5.3 | odd | 4 | 75.3.c.f.26.1 | yes | 2 | ||
5.4 | even | 2 | inner | 75.3.d.c.74.2 | 4 | ||
12.11 | even | 2 | 1200.3.c.d.449.2 | 4 | |||
15.2 | even | 4 | 75.3.c.c.26.1 | ✓ | 2 | ||
15.8 | even | 4 | 75.3.c.f.26.2 | yes | 2 | ||
15.14 | odd | 2 | inner | 75.3.d.c.74.4 | 4 | ||
20.3 | even | 4 | 1200.3.l.f.401.2 | 2 | |||
20.7 | even | 4 | 1200.3.l.s.401.1 | 2 | |||
20.19 | odd | 2 | 1200.3.c.d.449.1 | 4 | |||
60.23 | odd | 4 | 1200.3.l.f.401.1 | 2 | |||
60.47 | odd | 4 | 1200.3.l.s.401.2 | 2 | |||
60.59 | even | 2 | 1200.3.c.d.449.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.3.c.c.26.1 | ✓ | 2 | 15.2 | even | 4 | ||
75.3.c.c.26.2 | yes | 2 | 5.2 | odd | 4 | ||
75.3.c.f.26.1 | yes | 2 | 5.3 | odd | 4 | ||
75.3.c.f.26.2 | yes | 2 | 15.8 | even | 4 | ||
75.3.d.c.74.1 | 4 | 3.2 | odd | 2 | inner | ||
75.3.d.c.74.2 | 4 | 5.4 | even | 2 | inner | ||
75.3.d.c.74.3 | 4 | 1.1 | even | 1 | trivial | ||
75.3.d.c.74.4 | 4 | 15.14 | odd | 2 | inner | ||
1200.3.c.d.449.1 | 4 | 20.19 | odd | 2 | |||
1200.3.c.d.449.2 | 4 | 12.11 | even | 2 | |||
1200.3.c.d.449.3 | 4 | 60.59 | even | 2 | |||
1200.3.c.d.449.4 | 4 | 4.3 | odd | 2 | |||
1200.3.l.f.401.1 | 2 | 60.23 | odd | 4 | |||
1200.3.l.f.401.2 | 2 | 20.3 | even | 4 | |||
1200.3.l.s.401.1 | 2 | 20.7 | even | 4 | |||
1200.3.l.s.401.2 | 2 | 60.47 | odd | 4 |