Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,3,Mod(641,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("768.641");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.h (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: | \(20.9264843029\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.157351936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 641.6 | ||
Root | \(1.28897 - 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.641 |
Dual form | 768.3.h.e.641.8 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.41421 | − | 2.64575i | 0.471405 | − | 0.881917i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.48331 | 1.49666 | 0.748331 | − | 0.663325i | \(-0.230855\pi\) | ||||
0.748331 | + | 0.663325i | \(0.230855\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.29150 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.00000 | − | 7.48331i | −0.555556 | − | 0.831479i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.1421 | 1.28565 | 0.642824 | − | 0.766014i | \(-0.277763\pi\) | ||||
0.642824 | + | 0.766014i | \(0.277763\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.0000i | 0.769231i | 0.923077 | + | 0.384615i | \(0.125666\pi\) | ||||
−0.923077 | + | 0.384615i | \(0.874334\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.5830 | − | 19.7990i | 0.705534 | − | 1.31993i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 26.4575i | − | 1.39250i | −0.717799 | − | 0.696250i | \(-0.754850\pi\) | ||
0.717799 | − | 0.696250i | \(-0.245150\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.48331 | + | 14.0000i | −0.356348 | + | 0.666667i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 16.9706i | − | 0.737851i | −0.929459 | − | 0.368925i | \(-0.879726\pi\) | ||
0.929459 | − | 0.368925i | \(-0.120274\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 31.0000 | 1.24000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −26.8701 | + | 2.64575i | −0.995187 | + | 0.0979908i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 37.4166 | 1.29023 | 0.645113 | − | 0.764087i | \(-0.276810\pi\) | ||||
0.645113 | + | 0.764087i | \(0.276810\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26.4575 | 0.853468 | 0.426734 | − | 0.904377i | \(-0.359664\pi\) | ||||
0.426734 | + | 0.904377i | \(0.359664\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 20.0000 | − | 37.4166i | 0.606061 | − | 1.13384i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −39.5980 | −1.13137 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.0000i | − | 0.270270i | −0.990827 | − | 0.135135i | \(-0.956853\pi\) | ||
0.990827 | − | 0.135135i | \(-0.0431469\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 26.4575 | + | 14.1421i | 0.678398 | + | 0.362619i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14.9666i | 0.365040i | 0.983202 | + | 0.182520i | \(0.0584254\pi\) | ||||
−0.983202 | + | 0.182520i | \(0.941575\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 58.2065i | − | 1.35364i | −0.736148 | − | 0.676820i | \(-0.763357\pi\) | ||
0.736148 | − | 0.676820i | \(-0.236643\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −37.4166 | − | 56.0000i | −0.831479 | − | 1.24444i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.3137i | 0.240717i | 0.992730 | + | 0.120359i | \(0.0384044\pi\) | ||||
−0.992730 | + | 0.120359i | \(0.961596\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −21.0000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 37.4166 | 0.705973 | 0.352987 | − | 0.935628i | \(-0.385166\pi\) | ||||
0.352987 | + | 0.935628i | \(0.385166\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 105.830 | 1.92418 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −70.0000 | − | 37.4166i | −1.22807 | − | 0.656431i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −98.9949 | −1.67788 | −0.838940 | − | 0.544224i | \(-0.816824\pi\) | ||||
−0.838940 | + | 0.544224i | \(0.816824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 90.0000i | 1.47541i | 0.675123 | + | 0.737705i | \(0.264090\pi\) | ||||
−0.675123 | + | 0.737705i | \(0.735910\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 26.4575 | + | 39.5980i | 0.419961 | + | 0.628539i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 74.8331i | 1.15128i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.29150i | − | 0.0789777i | −0.999220 | − | 0.0394888i | \(-0.987427\pi\) | ||
0.999220 | − | 0.0394888i | \(-0.0125730\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −44.8999 | − | 24.0000i | −0.650723 | − | 0.347826i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 28.2843i | − | 0.398370i | −0.979962 | − | 0.199185i | \(-0.936171\pi\) | ||
0.979962 | − | 0.199185i | \(-0.0638295\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 30.0000 | 0.410959 | 0.205479 | − | 0.978661i | \(-0.434125\pi\) | ||||
0.205479 | + | 0.978661i | \(0.434125\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 43.8406 | − | 82.0183i | 0.584542 | − | 1.09358i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −74.8331 | −0.971859 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 26.4575 | 0.334905 | 0.167453 | − | 0.985880i | \(-0.446446\pi\) | ||||
0.167453 | + | 0.985880i | \(0.446446\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −31.0000 | + | 74.8331i | −0.382716 | + | 0.923866i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 25.4558 | 0.306697 | 0.153348 | − | 0.988172i | \(-0.450994\pi\) | ||||
0.153348 | + | 0.988172i | \(0.450994\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 52.9150 | − | 98.9949i | 0.608219 | − | 1.13787i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 74.8331i | 0.840822i | 0.907334 | + | 0.420411i | \(0.138114\pi\) | ||||
−0.907334 | + | 0.420411i | \(0.861886\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 52.9150i | − | 0.581484i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 37.4166 | − | 70.0000i | 0.402329 | − | 0.752688i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 197.990i | − | 2.08410i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000 | 0.103093 | 0.0515464 | − | 0.998671i | \(-0.483585\pi\) | ||||
0.0515464 | + | 0.998671i | \(0.483585\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −70.7107 | − | 105.830i | −0.714249 | − | 1.06899i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −112.250 | −1.11138 | −0.555692 | − | 0.831388i | \(-0.687546\pi\) | ||||
−0.555692 | + | 0.831388i | \(0.687546\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −47.6235 | −0.462364 | −0.231182 | − | 0.972910i | \(-0.574259\pi\) | ||||
−0.231182 | + | 0.972910i | \(0.574259\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −56.0000 | + | 104.766i | −0.533333 | + | 0.997775i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.82843 | 0.0264339 | 0.0132169 | − | 0.999913i | \(-0.495793\pi\) | ||||
0.0132169 | + | 0.999913i | \(0.495793\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 70.0000i | − | 0.642202i | −0.947045 | − | 0.321101i | \(-0.895947\pi\) | ||
0.947045 | − | 0.321101i | \(-0.104053\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26.4575 | − | 14.1421i | −0.238356 | − | 0.127407i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 149.666i | − | 1.32448i | −0.749292 | − | 0.662240i | \(-0.769606\pi\) | ||
0.749292 | − | 0.662240i | \(-0.230394\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 126.996i | − | 1.10431i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 74.8331 | − | 50.0000i | 0.639600 | − | 0.427350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 79.0000 | 0.652893 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 39.5980 | + | 21.1660i | 0.321935 | + | 0.172081i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 44.8999 | 0.359199 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 153.454 | 1.20830 | 0.604148 | − | 0.796872i | \(-0.293514\pi\) | ||||
0.604148 | + | 0.796872i | \(0.293514\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −154.000 | − | 82.3165i | −1.19380 | − | 0.638112i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 70.7107 | 0.539776 | 0.269888 | − | 0.962892i | \(-0.413013\pi\) | ||||
0.269888 | + | 0.962892i | \(0.413013\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 140.000i | 1.05263i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −201.077 | + | 19.7990i | −1.48946 | + | 0.146659i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 224.499i | − | 1.63868i | −0.573306 | − | 0.819341i | \(-0.694340\pi\) | ||
0.573306 | − | 0.819341i | \(-0.305660\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 132.288i | 0.951709i | 0.879524 | + | 0.475855i | \(0.157861\pi\) | ||||
−0.879524 | + | 0.475855i | \(0.842139\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 29.9333 | + | 16.0000i | 0.212293 | + | 0.113475i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 141.421i | 0.988961i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 280.000 | 1.93103 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −29.6985 | + | 55.5608i | −0.202031 | + | 0.377964i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.4499 | −0.150671 | −0.0753354 | − | 0.997158i | \(-0.524003\pi\) | ||||
−0.0753354 | + | 0.997158i | \(0.524003\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 79.3725 | 0.525646 | 0.262823 | − | 0.964844i | \(-0.415346\pi\) | ||||
0.262823 | + | 0.964844i | \(0.415346\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 197.990 | 1.27735 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 170.000i | 1.08280i | 0.840764 | + | 0.541401i | \(0.182106\pi\) | ||||
−0.840764 | + | 0.541401i | \(0.817894\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 52.9150 | − | 98.9949i | 0.332799 | − | 0.622610i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 89.7998i | 0.557763i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 100.539i | 0.616801i | 0.951257 | + | 0.308400i | \(0.0997937\pi\) | ||||
−0.951257 | + | 0.308400i | \(0.900206\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 149.666 | − | 280.000i | 0.907068 | − | 1.69697i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 243.245i | 1.45656i | 0.685282 | + | 0.728278i | \(0.259679\pi\) | ||||
−0.685282 | + | 0.728278i | \(0.740321\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 69.0000 | 0.408284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −197.990 | + | 132.288i | −1.15784 | + | 0.773611i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −112.250 | −0.648842 | −0.324421 | − | 0.945913i | \(-0.605169\pi\) | ||||
−0.324421 | + | 0.945913i | \(0.605169\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −164.037 | −0.937352 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −140.000 | + | 261.916i | −0.790960 | + | 1.47975i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −212.132 | −1.18510 | −0.592548 | − | 0.805535i | \(-0.701878\pi\) | ||||
−0.592548 | + | 0.805535i | \(0.701878\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 262.000i | 1.44751i | 0.690055 | + | 0.723757i | \(0.257586\pi\) | ||||
−0.690055 | + | 0.723757i | \(0.742414\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 238.118 | + | 127.279i | 1.30119 | + | 0.695515i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 74.8331i | − | 0.404504i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 142.183 | − | 14.0000i | 0.752291 | − | 0.0740741i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 339.411i | 1.77702i | 0.458855 | + | 0.888511i | \(0.348260\pi\) | ||||
−0.458855 | + | 0.888511i | \(0.651740\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 210.000 | 1.08808 | 0.544041 | − | 0.839058i | \(-0.316893\pi\) | ||||
0.544041 | + | 0.839058i | \(0.316893\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 197.990 | + | 105.830i | 1.01533 | + | 0.542718i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 187.083 | 0.949659 | 0.474830 | − | 0.880078i | \(-0.342510\pi\) | ||||
0.474830 | + | 0.880078i | \(0.342510\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −343.948 | −1.72838 | −0.864190 | − | 0.503165i | \(-0.832169\pi\) | ||||
−0.864190 | + | 0.503165i | \(0.832169\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.0000 | − | 7.48331i | −0.0696517 | − | 0.0372304i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −197.990 | −0.975320 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 112.000i | 0.546341i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −126.996 | + | 84.8528i | −0.613508 | + | 0.409917i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 374.166i | − | 1.79027i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 291.033i | 1.37930i | 0.724142 | + | 0.689651i | \(0.242236\pi\) | ||||
−0.724142 | + | 0.689651i | \(0.757764\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −74.8331 | − | 40.0000i | −0.351329 | − | 0.187793i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 435.578i | − | 2.02594i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −140.000 | −0.645161 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 42.4264 | − | 79.3725i | 0.193728 | − | 0.362432i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −312.199 | −1.39999 | −0.699997 | − | 0.714146i | \(-0.746815\pi\) | ||||
−0.699997 | + | 0.714146i | \(0.746815\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −155.000 | − | 231.983i | −0.688889 | − | 1.03103i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 59.3970 | 0.261661 | 0.130830 | − | 0.991405i | \(-0.458236\pi\) | ||||
0.130830 | + | 0.991405i | \(0.458236\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 358.000i | 1.56332i | 0.623706 | + | 0.781659i | \(0.285626\pi\) | ||||
−0.623706 | + | 0.781659i | \(0.714374\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −105.830 | + | 197.990i | −0.458139 | + | 0.857099i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 224.499i | 0.963517i | 0.876304 | + | 0.481758i | \(0.160002\pi\) | ||||
−0.876304 | + | 0.481758i | \(0.839998\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 84.6640i | 0.360273i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 37.4166 | − | 70.0000i | 0.157876 | − | 0.295359i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 169.706i | − | 0.710065i | −0.934854 | − | 0.355033i | \(-0.884470\pi\) | ||
0.934854 | − | 0.355033i | \(-0.115530\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −110.000 | −0.456432 | −0.228216 | − | 0.973611i | \(-0.573289\pi\) | ||||
−0.228216 | + | 0.973611i | \(0.573289\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 154.149 | + | 187.848i | 0.634359 | + | 0.773038i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −157.150 | −0.641427 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 264.575 | 1.07115 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 36.0000 | − | 67.3498i | 0.144578 | − | 0.270481i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 296.985 | 1.18321 | 0.591603 | − | 0.806229i | \(-0.298495\pi\) | ||||
0.591603 | + | 0.806229i | \(0.298495\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 240.000i | − | 0.948617i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 299.333i | 1.16472i | 0.812932 | + | 0.582359i | \(0.197870\pi\) | ||||
−0.812932 | + | 0.582359i | \(0.802130\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 52.9150i | 0.204305i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −187.083 | − | 280.000i | −0.716793 | − | 1.07280i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 152.735i | 0.580742i | 0.956914 | + | 0.290371i | \(0.0937787\pi\) | ||||
−0.956914 | + | 0.290371i | \(0.906221\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 280.000 | 1.05660 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 197.990 | + | 105.830i | 0.741535 | + | 0.396367i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 426.549 | 1.58568 | 0.792842 | − | 0.609427i | \(-0.208601\pi\) | ||||
0.792842 | + | 0.609427i | \(0.208601\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −396.863 | −1.46444 | −0.732219 | − | 0.681069i | \(-0.761515\pi\) | ||||
−0.732219 | + | 0.681069i | \(0.761515\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −140.000 | − | 74.8331i | −0.512821 | − | 0.274114i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 438.406 | 1.59420 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 490.000i | − | 1.76895i | −0.466585 | − | 0.884477i | \(-0.654516\pi\) | ||
0.466585 | − | 0.884477i | \(-0.345484\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −132.288 | − | 197.990i | −0.474149 | − | 0.709641i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 134.700i | 0.479358i | 0.970852 | + | 0.239679i | \(0.0770422\pi\) | ||||
−0.970852 | + | 0.239679i | \(0.922958\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.29150i | 0.0186979i | 0.999956 | + | 0.00934894i | \(0.00297590\pi\) | ||||
−0.999956 | + | 0.00934894i | \(0.997024\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −523.832 | − | 280.000i | −1.83801 | − | 0.982456i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 79.1960i | − | 0.275944i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 289.000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.1421 | − | 26.4575i | 0.0485984 | − | 0.0909193i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −112.250 | −0.383105 | −0.191552 | − | 0.981482i | \(-0.561352\pi\) | ||||
−0.191552 | + | 0.981482i | \(0.561352\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −740.810 | −2.51122 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −380.000 | + | 37.4166i | −1.27946 | + | 0.125982i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 169.706 | 0.567577 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 308.000i | 1.02326i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −158.745 | + | 296.985i | −0.523911 | + | 0.980148i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 673.498i | 2.20819i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 47.6235i | − | 0.155125i | −0.996987 | − | 0.0775627i | \(-0.975286\pi\) | ||
0.996987 | − | 0.0775627i | \(-0.0247138\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −67.3498 | + | 126.000i | −0.217961 | + | 0.407767i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 254.558i | 0.818516i | 0.912419 | + | 0.409258i | \(0.134212\pi\) | ||||
−0.912419 | + | 0.409258i | \(0.865788\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 230.000 | 0.734824 | 0.367412 | − | 0.930058i | \(-0.380244\pi\) | ||||
0.367412 | + | 0.930058i | \(0.380244\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 197.990 | + | 296.324i | 0.628539 | + | 0.940712i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −561.249 | −1.77050 | −0.885250 | − | 0.465115i | \(-0.846013\pi\) | ||||
−0.885250 | + | 0.465115i | \(0.846013\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 529.150 | 1.65878 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.00000 | − | 7.48331i | 0.0124611 | − | 0.0233125i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 310.000i | 0.953846i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −185.203 | − | 98.9949i | −0.566369 | − | 0.302737i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 59.8665i | − | 0.181965i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 132.288i | 0.399660i | 0.979831 | + | 0.199830i | \(0.0640390\pi\) | ||||
−0.979831 | + | 0.199830i | \(0.935961\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −74.8331 | + | 50.0000i | −0.224724 | + | 0.150150i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 39.5980i | − | 0.118203i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −70.0000 | −0.207715 | −0.103858 | − | 0.994592i | \(-0.533119\pi\) | ||||
−0.103858 | + | 0.994592i | \(0.533119\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −395.980 | − | 211.660i | −1.16808 | − | 0.624366i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 374.166 | 1.09726 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 370.405 | 1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −336.000 | − | 179.600i | −0.973913 | − | 0.520578i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −540.230 | −1.55686 | −0.778429 | − | 0.627733i | \(-0.783983\pi\) | ||||
−0.778429 | + | 0.627733i | \(0.783983\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 298.000i | 0.853868i | 0.904283 | + | 0.426934i | \(0.140406\pi\) | ||||
−0.904283 | + | 0.426934i | \(0.859594\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.4575 | − | 268.701i | −0.0753775 | − | 0.765529i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 299.333i | − | 0.847968i | −0.905670 | − | 0.423984i | \(-0.860631\pi\) | ||
0.905670 | − | 0.423984i | \(-0.139369\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 211.660i | − | 0.596226i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 537.401i | 1.49694i | 0.663169 | + | 0.748470i | \(0.269211\pi\) | ||||
−0.663169 | + | 0.748470i | \(0.730789\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −339.000 | −0.939058 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 111.723 | − | 209.014i | 0.307777 | − | 0.575797i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 224.499 | 0.615067 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 111.122 | 0.302784 | 0.151392 | − | 0.988474i | \(-0.451625\pi\) | ||||
0.151392 | + | 0.988474i | \(0.451625\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 112.000 | − | 74.8331i | 0.303523 | − | 0.202800i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −197.990 | −0.533665 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 410.000i | − | 1.09920i | −0.835429 | − | 0.549598i | \(-0.814781\pi\) | ||
0.835429 | − | 0.549598i | \(-0.185219\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 63.4980 | − | 118.794i | 0.169328 | − | 0.316784i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 374.166i | 0.992482i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 661.438i | 1.74522i | 0.488419 | + | 0.872609i | \(0.337574\pi\) | ||||
−0.488419 | + | 0.872609i | \(0.662426\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 217.016 | − | 406.000i | 0.569596 | − | 1.06562i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 158.392i | − | 0.413556i | −0.978388 | − | 0.206778i | \(-0.933702\pi\) | ||
0.978388 | − | 0.206778i | \(-0.0662978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −560.000 | −1.45455 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −435.578 | + | 291.033i | −1.12552 | + | 0.752022i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 246.949 | 0.634831 | 0.317416 | − | 0.948287i | \(-0.397185\pi\) | ||||
0.317416 | + | 0.948287i | \(0.397185\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 100.000 | − | 187.083i | 0.254453 | − | 0.476038i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 197.990 | 0.501240 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 230.000i | − | 0.579345i | −0.957126 | − | 0.289673i | \(-0.906454\pi\) | ||
0.957126 | − | 0.289673i | \(-0.0935464\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 370.405 | + | 197.990i | 0.928334 | + | 0.496215i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 299.333i | − | 0.746465i | −0.927738 | − | 0.373233i | \(-0.878249\pi\) | ||
0.927738 | − | 0.373233i | \(-0.121751\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 264.575i | 0.656514i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −231.983 | + | 560.000i | −0.572797 | + | 1.38272i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 141.421i | − | 0.347473i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 590.000 | 1.44254 | 0.721271 | − | 0.692653i | \(-0.243558\pi\) | ||||
0.721271 | + | 0.692653i | \(0.243558\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −593.970 | − | 317.490i | −1.44518 | − | 0.772482i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 523.832 | 1.26836 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 190.494 | 0.459022 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 350.000 | + | 187.083i | 0.839329 | + | 0.448640i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −98.9949 | −0.236265 | −0.118132 | − | 0.992998i | \(-0.537691\pi\) | ||||
−0.118132 | + | 0.992998i | \(0.537691\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 70.0000i | 0.166271i | 0.996538 | + | 0.0831354i | \(0.0264934\pi\) | ||||
−0.996538 | + | 0.0831354i | \(0.973507\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 84.6640 | − | 56.5685i | 0.200151 | − | 0.133732i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 476.235i | − | 1.11531i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 374.166 | + | 200.000i | 0.872181 | + | 0.466200i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 509.117i | 1.18125i | 0.806948 | + | 0.590623i | \(0.201118\pi\) | ||||
−0.806948 | + | 0.590623i | \(0.798882\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.0000 | 0.0230947 | 0.0115473 | − | 0.999933i | \(-0.496324\pi\) | ||||
0.0115473 | + | 0.999933i | \(0.496324\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 395.980 | − | 740.810i | 0.910298 | − | 1.70301i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −448.999 | −1.02746 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 502.693 | 1.14509 | 0.572543 | − | 0.819875i | \(-0.305957\pi\) | ||||
0.572543 | + | 0.819875i | \(0.305957\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 105.000 | + | 157.150i | 0.238095 | + | 0.356348i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −313.955 | −0.708703 | −0.354351 | − | 0.935112i | \(-0.615298\pi\) | ||||
−0.354351 | + | 0.935112i | \(0.615298\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 560.000i | 1.25843i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −31.7490 | + | 59.3970i | −0.0710269 | + | 0.132879i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 209.533i | − | 0.466666i | −0.972397 | − | 0.233333i | \(-0.925037\pi\) | ||
0.972397 | − | 0.233333i | \(-0.0749631\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 211.660i | 0.469313i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 112.250 | − | 210.000i | 0.247792 | − | 0.463576i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 395.980i | − | 0.870285i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 430.000 | 0.940919 | 0.470460 | − | 0.882422i | \(-0.344088\pi\) | ||||
0.470460 | + | 0.882422i | \(0.344088\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −112.250 | −0.243492 | −0.121746 | − | 0.992561i | \(-0.538849\pi\) | ||||
−0.121746 | + | 0.992561i | \(0.538849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −100.539 | −0.217146 | −0.108573 | − | 0.994088i | \(-0.534628\pi\) | ||||
−0.108573 | + | 0.994088i | \(0.534628\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 280.000 | − | 523.832i | 0.602151 | − | 1.12652i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 138.593 | 0.296773 | 0.148386 | − | 0.988929i | \(-0.452592\pi\) | ||||
0.148386 | + | 0.988929i | \(0.452592\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.0000i | 0.0597015i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 449.778 | + | 240.416i | 0.954942 | + | 0.510438i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 823.165i | − | 1.74031i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 820.183i | − | 1.72670i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −187.083 | − | 280.000i | −0.392207 | − | 0.587002i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 339.411i | − | 0.708583i | −0.935135 | − | 0.354291i | \(-0.884722\pi\) | ||
0.935135 | − | 0.354291i | \(-0.115278\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 100.000 | 0.207900 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 237.588 | + | 126.996i | 0.491900 | + | 0.262932i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 74.8331 | 0.154295 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 375.697 | 0.771451 | 0.385726 | − | 0.922614i | \(-0.373951\pi\) | ||||
0.385726 | + | 0.922614i | \(0.373951\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 266.000 | + | 142.183i | 0.543967 | + | 0.290763i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 523.259 | 1.06570 | 0.532850 | − | 0.846210i | \(-0.321121\pi\) | ||||
0.532850 | + | 0.846210i | \(0.321121\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −529.150 | − | 791.960i | −1.06899 | − | 1.59992i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 149.666i | 0.301139i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 555.608i | − | 1.11344i | −0.830699 | − | 0.556721i | \(-0.812059\pi\) | ||
0.830699 | − | 0.556721i | \(-0.187941\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 643.565 | + | 344.000i | 1.28456 | + | 0.686627i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 831.558i | − | 1.65320i | −0.562793 | − | 0.826598i | \(-0.690273\pi\) | ||
0.562793 | − | 0.826598i | \(-0.309727\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −840.000 | −1.66337 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 97.5807 | − | 182.557i | 0.192467 | − | 0.360073i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −561.249 | −1.10265 | −0.551325 | − | 0.834291i | \(-0.685877\pi\) | ||||
−0.551325 | + | 0.834291i | \(0.685877\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −158.745 | −0.310656 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 70.0000 | + | 710.915i | 0.136452 | + | 1.38580i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −356.382 | −0.692004 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 160.000i | 0.309478i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −158.745 | + | 296.985i | −0.305867 | + | 0.572225i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 224.499i | − | 0.430901i | −0.976515 | − | 0.215451i | \(-0.930878\pi\) | ||
0.976515 | − | 0.215451i | \(-0.0691220\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 904.847i | − | 1.73011i | −0.501678 | − | 0.865054i | \(-0.667284\pi\) | ||
0.501678 | − | 0.865054i | \(-0.332716\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −231.983 | + | 434.000i | −0.441872 | + | 0.826667i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 241.000 | 0.455577 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 494.975 | + | 740.810i | 0.932156 | + | 1.39512i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −149.666 | −0.280800 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.1660 | 0.0395626 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −300.000 | + | 561.249i | −0.558659 | + | 1.04516i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −296.985 | −0.550992 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 518.000i | − | 0.957486i | −0.877955 | − | 0.478743i | \(-0.841093\pi\) | ||
0.877955 | − | 0.478743i | \(-0.158907\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 693.187 | + | 370.524i | 1.27659 | + | 0.682365i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 523.832i | − | 0.961160i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1000.09i | − | 1.82833i | −0.405347 | − | 0.914163i | \(-0.632849\pi\) | ||
0.405347 | − | 0.914163i | \(-0.367151\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 673.498 | − | 450.000i | 1.22677 | − | 0.819672i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 989.949i | − | 1.79664i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −140.000 | −0.253165 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −197.990 | − | 105.830i | −0.356739 | − | 0.190685i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −411.582 | −0.738927 | −0.369463 | − | 0.929245i | \(-0.620459\pi\) | ||||
−0.369463 | + | 0.929245i | \(0.620459\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 582.065 | 1.04126 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −653.367 | −1.16051 | −0.580255 | − | 0.814435i | \(-0.697047\pi\) | ||||
−0.580255 | + | 0.814435i | \(0.697047\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1120.00i | − | 1.98230i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 164.037 | − | 395.980i | 0.289306 | − | 0.698377i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 613.632i | − | 1.07844i | −0.842165 | − | 0.539220i | \(-0.818719\pi\) | ||
0.842165 | − | 0.539220i | \(-0.181281\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 343.948i | 0.602360i | 0.953567 | + | 0.301180i | \(0.0973805\pi\) | ||||
−0.953567 | + | 0.301180i | \(0.902619\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 897.998 | + | 480.000i | 1.56719 | + | 0.837696i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 526.087i | − | 0.914935i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −390.000 | −0.675910 | −0.337955 | − | 0.941162i | \(-0.609735\pi\) | ||||
−0.337955 | + | 0.941162i | \(0.609735\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 296.985 | − | 555.608i | 0.512927 | − | 0.959599i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −134.700 | −0.231841 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 529.150 | 0.907633 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 560.000 | − | 374.166i | 0.957265 | − | 0.639600i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −653.367 | −1.11306 | −0.556530 | − | 0.830827i | \(-0.687868\pi\) | ||||
−0.556530 | + | 0.830827i | \(0.687868\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 700.000i | − | 1.18846i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 264.575 | − | 494.975i | 0.447674 | − | 0.837521i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 448.999i | 0.757165i | 0.925568 | + | 0.378583i | \(0.123588\pi\) | ||||
−0.925568 | + | 0.378583i | \(0.876412\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −486.415 | + | 910.000i | −0.814766 | + | 1.52429i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 480.833i | 0.802726i | 0.915919 | + | 0.401363i | \(0.131463\pi\) | ||||
−0.915919 | + | 0.401363i | \(0.868537\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −130.000 | −0.216306 | −0.108153 | − | 0.994134i | \(-0.534494\pi\) | ||||
−0.108153 | + | 0.994134i | \(0.534494\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −39.5980 | + | 26.4575i | −0.0656683 | + | 0.0438765i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 591.182 | 0.977160 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 153.454 | 0.252807 | 0.126403 | − | 0.991979i | \(-0.459657\pi\) | ||||
0.126403 | + | 0.991979i | \(0.459657\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −280.000 | + | 523.832i | −0.459770 | + | 0.860151i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −113.137 | −0.185167 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 630.000i | 1.02773i | 0.857870 | + | 0.513866i | \(0.171787\pi\) | ||||
−0.857870 | + | 0.513866i | \(0.828213\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 296.324 | + | 158.392i | 0.481828 | + | 0.257548i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1122.50i | 1.81928i | 0.415395 | + | 0.909641i | \(0.363643\pi\) | ||||
−0.415395 | + | 0.909641i | \(0.636357\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 555.608i | 0.897589i | 0.893635 | + | 0.448795i | \(0.148147\pi\) | ||||
−0.893635 | + | 0.448795i | \(0.851853\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 44.8999 | + | 456.000i | 0.0723026 | + | 0.734300i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 395.980i | − | 0.635602i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −439.000 | −0.702400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −989.949 | − | 529.150i | −1.57887 | − | 0.843940i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −978.928 | −1.55139 | −0.775696 | − | 0.631107i | \(-0.782601\pi\) | ||||
−0.775696 | + | 0.631107i | \(0.782601\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 770.000 | + | 411.582i | 1.21643 | + | 0.650209i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1148.34 | 1.80841 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 210.000i | − | 0.329670i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −211.660 | + | 141.421i | −0.331236 | + | 0.221317i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 389.132i | − | 0.607071i | −0.952820 | − | 0.303535i | \(-0.901833\pi\) | ||
0.952820 | − | 0.303535i | \(-0.0981671\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 269.867i | 0.419699i | 0.977734 | + | 0.209850i | \(0.0672974\pi\) | ||||
−0.977734 | + | 0.209850i | \(0.932703\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1152.43 | − | 616.000i | −1.78671 | − | 0.955039i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1170.97i | 1.80984i | 0.425578 | + | 0.904922i | \(0.360071\pi\) | ||||
−0.425578 | + | 0.904922i | \(0.639929\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1400.00 | −2.15716 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −197.990 | + | 370.405i | −0.304132 | + | 0.568979i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −710.915 | −1.08869 | −0.544345 | − | 0.838861i | \(-0.683222\pi\) | ||||
−0.544345 | + | 0.838861i | \(0.683222\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 529.150 | 0.807863 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −150.000 | − | 224.499i | −0.228311 | − | 0.341704i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 127.279 | 0.193140 | 0.0965700 | − | 0.995326i | \(-0.469213\pi\) | ||||
0.0965700 | + | 0.995326i | \(0.469213\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 170.000i | − | 0.257186i | −0.991697 | − | 0.128593i | \(-0.958954\pi\) | ||
0.991697 | − | 0.128593i | \(-0.0410461\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1047.66i | 1.57543i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 634.980i | − | 0.951994i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −441.516 | + | 826.000i | −0.659963 | + | 1.23468i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1272.79i | 1.89686i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −310.000 | −0.460624 | −0.230312 | − | 0.973117i | \(-0.573975\pi\) | ||||
−0.230312 | + | 0.973117i | \(0.573975\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −832.972 | + | 82.0183i | −1.23403 | + | 0.121509i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1309.58 | −1.93439 | −0.967194 | − | 0.254041i | \(-0.918240\pi\) | ||||
−0.967194 | + | 0.254041i | \(0.918240\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −52.9150 | −0.0779308 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 84.0000 | − | 157.150i | 0.123348 | − | 0.230763i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1162.48 | −1.70203 | −0.851013 | − | 0.525145i | \(-0.824011\pi\) | ||||
−0.851013 | + | 0.525145i | \(0.824011\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1680.00i | − | 2.45255i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 947.179 | + | 506.288i | 1.37872 | + | 0.736956i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 374.166i | 0.543056i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 26.4575i | − | 0.0382887i | −0.999817 | − | 0.0191444i | \(-0.993906\pi\) | ||
0.999817 | − | 0.0191444i | \(-0.00609421\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 374.166 | + | 560.000i | 0.539922 | + | 0.808081i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 989.949i | 1.42439i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 593.970 | + | 317.490i | 0.849742 | + | 0.454206i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.4499 | −0.0320256 | −0.0160128 | − | 0.999872i | \(-0.505097\pi\) | ||||
−0.0160128 | + | 0.999872i | \(0.505097\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −264.575 | −0.376352 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 224.000 | + | 119.733i | 0.317730 | + | 0.169834i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 593.970 | 0.840127 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 182.000i | 0.256700i | 0.991729 | + | 0.128350i | \(0.0409680\pi\) | ||||
−0.991729 | + | 0.128350i | \(0.959032\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −132.288 | − | 197.990i | −0.186058 | − | 0.278467i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 448.999i | − | 0.629732i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1058.30i | 1.48014i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −448.999 | − | 240.000i | −0.626219 | − | 0.334728i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 395.980i | − | 0.550737i | −0.961339 | − | 0.275368i | \(-0.911200\pi\) | ||
0.961339 | − | 0.275368i | \(-0.0887998\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 252.000 | 0.349515 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −155.563 | + | 291.033i | −0.215164 | + | 0.402535i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1159.91 | 1.59988 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −47.6235 | −0.0655069 | −0.0327535 | − | 0.999463i | \(-0.510428\pi\) | ||||
−0.0327535 | + | 0.999463i | \(0.510428\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 715.000 | − | 142.183i | 0.980796 | − | 0.195038i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 650.000i | 0.886767i | 0.896332 | + | 0.443383i | \(0.146222\pi\) | ||||
−0.896332 | + | 0.443383i | \(0.853778\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −222.243 | + | 415.779i | −0.302372 | + | 0.565685i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 74.8331i | − | 0.101538i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 343.948i | − | 0.465423i | −0.972546 | − | 0.232712i | \(-0.925240\pi\) | ||
0.972546 | − | 0.232712i | \(-0.0747598\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 374.166 | − | 700.000i | 0.504947 | − | 0.944669i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 661.852i | − | 0.890783i | −0.895336 | − | 0.445392i | \(-0.853064\pi\) | ||
0.895336 | − | 0.445392i | \(-0.146936\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −168.000 | −0.225503 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −127.279 | − | 190.494i | −0.170387 | − | 0.255012i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.9666 | −0.0199821 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −608.523 | −0.810283 | −0.405142 | − | 0.914254i | \(-0.632778\pi\) | ||||
−0.405142 | + | 0.914254i | \(0.632778\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 420.000 | − | 785.748i | 0.557769 | − | 1.04349i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 593.970 | 0.786715 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1050.00i | − | 1.38705i | −0.720431 | − | 0.693527i | \(-0.756056\pi\) | ||
0.720431 | − | 0.693527i | \(-0.243944\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −634.980 | − | 339.411i | −0.836601 | − | 0.447182i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 673.498i | − | 0.885018i | −0.896764 | − | 0.442509i | \(-0.854089\pi\) | ||
0.896764 | − | 0.442509i | \(-0.145911\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 370.405i | 0.485459i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 989.949i | − | 1.29068i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1138.00 | 1.47984 | 0.739922 | − | 0.672693i | \(-0.234862\pi\) | ||||
0.739922 | + | 0.672693i | \(0.234862\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 791.960 | + | 423.320i | 1.02718 | + | 0.549053i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 785.748 | 1.01649 | 0.508246 | − | 0.861212i | \(-0.330294\pi\) | ||||
0.508246 | + | 0.861212i | \(0.330294\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 820.183 | 1.05830 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 140.000 | + | 74.8331i | 0.180180 | + | 0.0963104i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 395.980 | 0.508318 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 400.000i | − | 0.512164i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1005.39 | + | 98.9949i | −1.28402 | + | 0.126430i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1272.16i | 1.62059i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 904.847i | 1.14974i | 0.818244 | + | 0.574871i | \(0.194948\pi\) | ||||
−0.818244 | + | 0.574871i | \(0.805052\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 404.099 | + | 216.000i | 0.512166 | + | 0.273764i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 791.960i | 1.00121i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −900.000 | −1.13493 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 395.980 | − | 740.810i | 0.498088 | − | 0.931837i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1234.75 | 1.54924 | 0.774622 | − | 0.632425i | \(-0.217940\pi\) | ||||
0.774622 | + | 0.632425i | \(0.217940\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 560.000 | − | 374.166i | 0.699126 | − | 0.467123i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 424.264 | 0.528349 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 672.000i | 0.834783i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 603.231 | − | 1128.54i | 0.747499 | − | 1.39844i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 823.165i | − | 1.01751i | −0.860912 | − | 0.508754i | \(-0.830106\pi\) | ||
0.860912 | − | 0.508754i | \(-0.169894\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.4575i | 0.0326233i | 0.999867 | + | 0.0163117i | \(0.00519239\pi\) | ||||
−0.999867 | + | 0.0163117i | \(0.994808\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −561.249 | + | 1050.00i | −0.690343 | + | 1.29151i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 752.362i | 0.923143i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1540.00 | −1.88494 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −395.980 | + | 264.575i | −0.483492 | + | 0.323047i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 97.2831 | 0.118493 | 0.0592467 | − | 0.998243i | \(-0.481130\pi\) | ||||
0.0592467 | + | 0.998243i | \(0.481130\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −894.264 | −1.08659 | −0.543295 | − | 0.839542i | \(-0.682824\pi\) | ||||
−0.543295 | + | 0.839542i | \(0.682824\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 620.000 | − | 1159.91i | 0.751515 | − | 1.40596i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 285.671 | 0.345431 | 0.172715 | − | 0.984972i | \(-0.444746\pi\) | ||||
0.172715 | + | 0.984972i | \(0.444746\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 170.000i | 0.205066i | 0.994730 | + | 0.102533i | \(0.0326948\pi\) | ||||
−0.994730 | + | 0.102533i | \(0.967305\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1296.42 | − | 692.965i | −1.56007 | − | 0.833892i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1820.28i | 2.17997i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −710.915 | + | 70.0000i | −0.849361 | + | 0.0836320i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 707.107i | − | 0.842797i | −0.906876 | − | 0.421399i | \(-0.861539\pi\) | ||
0.906876 | − | 0.421399i | \(-0.138461\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 559.000 | 0.664685 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 356.382 | + | 190.494i | 0.422754 | + | 0.225972i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 516.349 | 0.611064 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −418.029 | −0.493540 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.0000 | + | 7.48331i | 0.0164900 | + | 0.00881427i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −169.706 | −0.199419 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 570.000i | − | 0.668230i | −0.942532 | − | 0.334115i | \(-0.891563\pi\) | ||
0.942532 | − | 0.334115i | \(-0.108437\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1481.62 | + | 989.949i | −1.73289 | + | 1.15784i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 523.832i | 0.611239i | 0.952154 | + | 0.305620i | \(0.0988636\pi\) | ||||
−0.952154 | + | 0.305620i | \(0.901136\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1455.16i | − | 1.69402i | −0.531577 | − | 0.847010i | \(-0.678400\pi\) | ||
0.531577 | − | 0.847010i | \(-0.321600\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −209.533 | − | 112.000i | −0.243360 | − | 0.130081i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 181.019i | 0.209756i | 0.994485 | + | 0.104878i | \(0.0334452\pi\) | ||||
−0.994485 | + | 0.104878i | \(0.966555\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −840.000 | −0.971098 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 408.708 | − | 764.622i | 0.471405 | − | 0.881917i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 374.166 | 0.430570 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.9150 | 0.0607520 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −50.0000 | − | 74.8331i | −0.0572738 | − | 0.0857195i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −237.588 | −0.271529 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 490.000i | 0.558723i | 0.960186 | + | 0.279361i | \(0.0901228\pi\) | ||||
−0.960186 | + | 0.279361i | \(0.909877\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −158.745 | + | 296.985i | −0.180597 | + | 0.337867i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 987.798i | − | 1.12122i | −0.828079 | − | 0.560612i | \(-0.810566\pi\) | ||
0.828079 | − | 0.560612i | \(-0.189434\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 957.762i | − | 1.08467i | −0.840163 | − | 0.542334i | \(-0.817541\pi\) | ||
0.840163 | − | 0.542334i | \(-0.182459\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1047.66 | + | 1960.00i | −1.18380 | + | 2.21469i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1374.62i | − | 1.54974i | −0.632123 | − | 0.774868i | \(-0.717816\pi\) | ||
0.632123 | − | 0.774868i | \(-0.282184\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −812.000 | −0.913386 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −438.406 | + | 1058.30i | −0.492038 | + | 1.18777i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 299.333 | 0.335199 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1587.45 | −1.77369 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 240.000 | − | 448.999i | 0.267559 | − | 0.500556i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 989.949 | 1.10117 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 814.891 | + | 435.578i | 0.902427 | + | 0.482367i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1960.63i | 2.16644i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 534.442i | 0.589241i | 0.955614 | + | 0.294621i | \(0.0951933\pi\) | ||||
−0.955614 | + | 0.294621i | \(0.904807\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 561.249 | + | 840.000i | 0.617435 | + | 0.924092i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 169.706i | 0.186285i | 0.995653 | + | 0.0931425i | \(0.0296912\pi\) | ||||
−0.995653 | + | 0.0931425i | \(0.970309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 360.000 | 0.394304 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1781.91 | + | 952.470i | 1.94744 | + | 1.04095i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −374.166 | −0.408032 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −555.608 | −0.604579 | −0.302289 | − | 0.953216i | \(-0.597751\pi\) | ||||
−0.302289 | + | 0.953216i | \(0.597751\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −126.000 | − | 67.3498i | −0.136808 | − | 0.0731269i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 282.843 | 0.306438 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 310.000i | − | 0.335135i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 238.118 | + | 356.382i | 0.256869 | + | 0.384446i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 89.7998i | − | 0.0966628i | −0.998831 | − | 0.0483314i | \(-0.984610\pi\) | ||
0.998831 | − | 0.0483314i | \(-0.0153904\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 555.608i | 0.596786i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 673.498 | + | 360.000i | 0.721863 | + | 0.385852i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1270.00 | 1.35539 | 0.677695 | − | 0.735343i | \(-0.262979\pi\) | ||||
0.677695 | + | 0.735343i | \(0.262979\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 325.269 | − | 608.523i | 0.346399 | − | 0.648054i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 187.083 | 0.198813 | 0.0994064 | − | 0.995047i | \(-0.468306\pi\) | ||||
0.0994064 | + | 0.995047i | \(0.468306\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 253.992 | 0.269345 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1064.00 | − | 104.766i | 1.12593 | − | 0.110864i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −280.014 | −0.295686 | −0.147843 | − | 0.989011i | \(-0.547233\pi\) | ||||
−0.147843 | + | 0.989011i | \(0.547233\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 300.000i | 0.316122i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −793.725 | + | 1484.92i | −0.834622 | + | 1.56143i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 224.499i | 0.235571i | 0.993039 | + | 0.117786i | \(0.0375796\pi\) | ||||
−0.993039 | + | 0.117786i | \(0.962420\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2539.92i | 2.65960i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 748.331 | − | 1400.00i | 0.781956 | − | 1.46290i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1187.94i | 1.23873i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −261.000 | −0.271592 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.1421 | − | 21.1660i | −0.0146855 | − | 0.0219792i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1571.50 | 1.62849 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 206.369 | 0.213411 | 0.106706 | − | 0.994291i | \(-0.465970\pi\) | ||||
0.106706 | + | 0.994291i | \(0.465970\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1711.20 | 1.76231 | 0.881153 | − | 0.472832i | \(-0.156768\pi\) | ||||
0.881153 | + | 0.472832i | \(0.156768\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 700.000i | − | 0.719424i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 820.183 | + | 438.406i | 0.841213 | + | 0.449647i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 598.665i | − | 0.612759i | −0.951910 | − | 0.306379i | \(-0.900882\pi\) | ||
0.951910 | − | 0.306379i | \(-0.0991176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1058.30i | 1.08100i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −523.832 | + | 350.000i | −0.533978 | + | 0.356779i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1544.32i | 1.57103i | 0.618843 | + | 0.785514i | \(0.287602\pi\) | ||||
−0.618843 | + | 0.785514i | \(0.712398\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1400.00 | 1.42132 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −158.392 | − | 84.6640i | −0.160478 | − | 0.0857792i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −987.798 | −0.998784 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −608.523 | −0.614049 | −0.307025 | − | 0.951702i | \(-0.599333\pi\) | ||||
−0.307025 | + | 0.951702i | \(0.599333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 350.000 | + | 187.083i | 0.352467 | + | 0.188402i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2573.87 | −2.58680 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 810.000i | − | 0.812437i | −0.913776 | − | 0.406219i | \(-0.866847\pi\) | ||
0.913776 | − | 0.406219i | \(-0.133153\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26.4575 | + | 268.701i | 0.0264840 | + | 0.268970i |
(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 | 768.3.h.e.641.6 | 8 | ||
3.2 | odd | 2 | inner | 768.3.h.e.641.1 | 8 | ||
4.3 | odd | 2 | inner | 768.3.h.e.641.4 | 8 | ||
8.3 | odd | 2 | inner | 768.3.h.e.641.5 | 8 | ||
8.5 | even | 2 | inner | 768.3.h.e.641.3 | 8 | ||
12.11 | even | 2 | inner | 768.3.h.e.641.7 | 8 | ||
16.3 | odd | 4 | 192.3.e.f.65.1 | 4 | |||
16.5 | even | 4 | 96.3.e.b.65.1 | ✓ | 4 | ||
16.11 | odd | 4 | 96.3.e.b.65.4 | yes | 4 | ||
16.13 | even | 4 | 192.3.e.f.65.4 | 4 | |||
24.5 | odd | 2 | inner | 768.3.h.e.641.8 | 8 | ||
24.11 | even | 2 | inner | 768.3.h.e.641.2 | 8 | ||
48.5 | odd | 4 | 96.3.e.b.65.2 | yes | 4 | ||
48.11 | even | 4 | 96.3.e.b.65.3 | yes | 4 | ||
48.29 | odd | 4 | 192.3.e.f.65.3 | 4 | |||
48.35 | even | 4 | 192.3.e.f.65.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.3.e.b.65.1 | ✓ | 4 | 16.5 | even | 4 | ||
96.3.e.b.65.2 | yes | 4 | 48.5 | odd | 4 | ||
96.3.e.b.65.3 | yes | 4 | 48.11 | even | 4 | ||
96.3.e.b.65.4 | yes | 4 | 16.11 | odd | 4 | ||
192.3.e.f.65.1 | 4 | 16.3 | odd | 4 | |||
192.3.e.f.65.2 | 4 | 48.35 | even | 4 | |||
192.3.e.f.65.3 | 4 | 48.29 | odd | 4 | |||
192.3.e.f.65.4 | 4 | 16.13 | even | 4 | |||
768.3.h.e.641.1 | 8 | 3.2 | odd | 2 | inner | ||
768.3.h.e.641.2 | 8 | 24.11 | even | 2 | inner | ||
768.3.h.e.641.3 | 8 | 8.5 | even | 2 | inner | ||
768.3.h.e.641.4 | 8 | 4.3 | odd | 2 | inner | ||
768.3.h.e.641.5 | 8 | 8.3 | odd | 2 | inner | ||
768.3.h.e.641.6 | 8 | 1.1 | even | 1 | trivial | ||
768.3.h.e.641.7 | 8 | 12.11 | even | 2 | inner | ||
768.3.h.e.641.8 | 8 | 24.5 | odd | 2 | inner |