Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,3,Mod(641,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.641");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.l (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: | \(26.1581053786\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-5}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 641.1 | ||
Root | \(-2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.641 |
Dual form | 960.3.l.b.641.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −2.00000 | − | 2.23607i | −0.666667 | − | 0.745356i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.00000 | 0.857143 | 0.428571 | − | 0.903508i | \(-0.359017\pi\) | ||||
0.428571 | + | 0.903508i | \(0.359017\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | + | 8.94427i | −0.111111 | + | 0.993808i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.47214i | − | 0.406558i | −0.979121 | − | 0.203279i | \(-0.934840\pi\) | ||
0.979121 | − | 0.203279i | \(-0.0651598\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16.0000 | −1.23077 | −0.615385 | − | 0.788227i | \(-0.710999\pi\) | ||||
−0.615385 | + | 0.788227i | \(0.710999\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.00000 | − | 4.47214i | 0.333333 | − | 0.298142i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.47214i | − | 0.263067i | −0.991312 | − | 0.131533i | \(-0.958010\pi\) | ||
0.991312 | − | 0.131533i | \(-0.0419901\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.105263 | −0.0526316 | − | 0.998614i | \(-0.516761\pi\) | ||||
−0.0526316 | + | 0.998614i | \(0.516761\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.0000 | − | 13.4164i | −0.571429 | − | 0.638877i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 13.4164i | 0.583322i | 0.956522 | + | 0.291661i | \(0.0942079\pi\) | ||||
−0.956522 | + | 0.291661i | \(0.905792\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 22.0000 | − | 15.6525i | 0.814815 | − | 0.579721i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 31.3050i | − | 1.07948i | −0.841831 | − | 0.539741i | \(-0.818522\pi\) | ||
0.841831 | − | 0.539741i | \(-0.181478\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.0000 | 0.580645 | 0.290323 | − | 0.956929i | \(-0.406237\pi\) | ||||
0.290323 | + | 0.956929i | \(0.406237\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.0000 | + | 8.94427i | −0.303030 | + | 0.271039i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.4164i | 0.383326i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 16.0000 | 0.432432 | 0.216216 | − | 0.976346i | \(-0.430628\pi\) | ||||
0.216216 | + | 0.976346i | \(0.430628\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 32.0000 | + | 35.7771i | 0.820513 | + | 0.917361i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 62.6099i | − | 1.52707i | −0.645766 | − | 0.763535i | \(-0.723462\pi\) | ||
0.645766 | − | 0.763535i | \(-0.276538\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16.0000 | 0.372093 | 0.186047 | − | 0.982541i | \(-0.440432\pi\) | ||||
0.186047 | + | 0.982541i | \(0.440432\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −20.0000 | − | 2.23607i | −0.444444 | − | 0.0496904i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 49.1935i | − | 1.04667i | −0.852127 | − | 0.523335i | \(-0.824688\pi\) | ||
0.852127 | − | 0.523335i | \(-0.175312\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.0000 | −0.265306 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.0000 | + | 8.94427i | −0.196078 | + | 0.175378i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.47214i | 0.0843799i | 0.999110 | + | 0.0421900i | \(0.0134335\pi\) | ||||
−0.999110 | + | 0.0421900i | \(0.986567\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.0000 | 0.181818 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | + | 4.47214i | 0.0701754 | + | 0.0784585i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 4.47214i | − | 0.0757989i | −0.999282 | − | 0.0378995i | \(-0.987933\pi\) | ||
0.999282 | − | 0.0378995i | \(-0.0120667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −82.0000 | −1.34426 | −0.672131 | − | 0.740432i | \(-0.734621\pi\) | ||||
−0.672131 | + | 0.740432i | \(0.734621\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.00000 | + | 53.6656i | −0.0952381 | + | 0.851835i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 35.7771i | − | 0.550417i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 24.0000 | 0.358209 | 0.179104 | − | 0.983830i | \(-0.442680\pi\) | ||||
0.179104 | + | 0.983830i | \(0.442680\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 30.0000 | − | 26.8328i | 0.434783 | − | 0.388881i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 125.220i | − | 1.76366i | −0.471568 | − | 0.881830i | \(-0.656312\pi\) | ||
0.471568 | − | 0.881830i | \(-0.343688\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −74.0000 | −1.01370 | −0.506849 | − | 0.862035i | \(-0.669190\pi\) | ||||
−0.506849 | + | 0.862035i | \(0.669190\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.0000 | + | 11.1803i | 0.133333 | + | 0.149071i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 26.8328i | − | 0.348478i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −138.000 | −1.74684 | −0.873418 | − | 0.486972i | \(-0.838101\pi\) | ||||
−0.873418 | + | 0.486972i | \(0.838101\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −79.0000 | − | 17.8885i | −0.975309 | − | 0.220846i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 93.9149i | 1.13150i | 0.824575 | + | 0.565752i | \(0.191414\pi\) | ||||
−0.824575 | + | 0.565752i | \(0.808586\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.0000 | 0.117647 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −70.0000 | + | 62.6099i | −0.804598 | + | 0.719654i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 107.331i | − | 1.20597i | −0.797753 | − | 0.602985i | \(-0.793978\pi\) | ||
0.797753 | − | 0.602985i | \(-0.206022\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −96.0000 | −1.05495 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −36.0000 | − | 40.2492i | −0.387097 | − | 0.432787i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 4.47214i | − | 0.0470751i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −166.000 | −1.71134 | −0.855670 | − | 0.517522i | \(-0.826855\pi\) | ||||
−0.855670 | + | 0.517522i | \(0.826855\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 40.0000 | + | 4.47214i | 0.404040 | + | 0.0451731i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 67.0820i | 0.664179i | 0.943248 | + | 0.332089i | \(0.107754\pi\) | ||||
−0.943248 | + | 0.332089i | \(0.892246\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −26.0000 | −0.252427 | −0.126214 | − | 0.992003i | \(-0.540282\pi\) | ||||
−0.126214 | + | 0.992003i | \(0.540282\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 30.0000 | − | 26.8328i | 0.285714 | − | 0.255551i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 201.246i | − | 1.88080i | −0.340064 | − | 0.940402i | \(-0.610449\pi\) | ||
0.340064 | − | 0.940402i | \(-0.389551\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −38.0000 | −0.348624 | −0.174312 | − | 0.984690i | \(-0.555770\pi\) | ||||
−0.174312 | + | 0.984690i | \(0.555770\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −32.0000 | − | 35.7771i | −0.288288 | − | 0.322316i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 31.3050i | − | 0.277035i | −0.990360 | − | 0.138517i | \(-0.955766\pi\) | ||
0.990360 | − | 0.138517i | \(-0.0442337\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −30.0000 | −0.260870 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.0000 | − | 143.108i | 0.136752 | − | 1.22315i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 26.8328i | − | 0.225486i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 101.000 | 0.834711 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −140.000 | + | 125.220i | −1.13821 | + | 1.01805i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 26.0000 | 0.204724 | 0.102362 | − | 0.994747i | \(-0.467360\pi\) | ||||
0.102362 | + | 0.994747i | \(0.467360\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −32.0000 | − | 35.7771i | −0.248062 | − | 0.277342i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 13.4164i | − | 0.102415i | −0.998688 | − | 0.0512077i | \(-0.983693\pi\) | ||
0.998688 | − | 0.0512077i | \(-0.0163070\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.0000 | −0.0902256 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 35.0000 | + | 49.1935i | 0.259259 | + | 0.364396i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 120.748i | 0.881370i | 0.897662 | + | 0.440685i | \(0.145264\pi\) | ||||
−0.897662 | + | 0.440685i | \(0.854736\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −82.0000 | −0.589928 | −0.294964 | − | 0.955508i | \(-0.595308\pi\) | ||||
−0.294964 | + | 0.955508i | \(0.595308\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −110.000 | + | 98.3870i | −0.780142 | + | 0.697780i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 71.5542i | 0.500379i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 70.0000 | 0.482759 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 26.0000 | + | 29.0689i | 0.176871 | + | 0.197748i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 111.803i | − | 0.750358i | −0.926952 | − | 0.375179i | \(-0.877581\pi\) | ||
0.926952 | − | 0.375179i | \(-0.122419\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 158.000 | 1.04636 | 0.523179 | − | 0.852223i | \(-0.324746\pi\) | ||||
0.523179 | + | 0.852223i | \(0.324746\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 40.0000 | + | 4.47214i | 0.261438 | + | 0.0292296i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 40.2492i | 0.259672i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −164.000 | −1.04459 | −0.522293 | − | 0.852766i | \(-0.674923\pi\) | ||||
−0.522293 | + | 0.852766i | \(0.674923\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.0000 | − | 8.94427i | 0.0628931 | − | 0.0562533i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 80.4984i | 0.499990i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 236.000 | 1.44785 | 0.723926 | − | 0.689877i | \(-0.242336\pi\) | ||||
0.723926 | + | 0.689877i | \(0.242336\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −20.0000 | − | 22.3607i | −0.121212 | − | 0.135519i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 93.9149i | 0.562364i | 0.959654 | + | 0.281182i | \(0.0907265\pi\) | ||||
−0.959654 | + | 0.281182i | \(0.909273\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 87.0000 | 0.514793 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | − | 17.8885i | 0.0116959 | − | 0.104611i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.4164i | 0.0775515i | 0.999248 | + | 0.0387757i | \(0.0123458\pi\) | ||||
−0.999248 | + | 0.0387757i | \(0.987654\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −30.0000 | −0.171429 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.0000 | + | 8.94427i | −0.0564972 | + | 0.0505326i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 192.302i | − | 1.07431i | −0.843483 | − | 0.537156i | \(-0.819499\pi\) | ||
0.843483 | − | 0.537156i | \(-0.180501\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.0110497 | −0.00552486 | − | 0.999985i | \(-0.501759\pi\) | ||||
−0.00552486 | + | 0.999985i | \(0.501759\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 164.000 | + | 183.358i | 0.896175 | + | 1.00195i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 35.7771i | 0.193390i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.0000 | −0.106952 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 132.000 | − | 93.9149i | 0.698413 | − | 0.496904i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 205.718i | − | 1.07706i | −0.842607 | − | 0.538529i | \(-0.818980\pi\) | ||
0.842607 | − | 0.538529i | \(-0.181020\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −214.000 | −1.10881 | −0.554404 | − | 0.832248i | \(-0.687054\pi\) | ||||
−0.554404 | + | 0.832248i | \(0.687054\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −80.0000 | + | 71.5542i | −0.410256 | + | 0.366944i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 93.9149i | − | 0.476725i | −0.971176 | − | 0.238363i | \(-0.923389\pi\) | ||
0.971176 | − | 0.238363i | \(-0.0766107\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 242.000 | 1.21608 | 0.608040 | − | 0.793906i | \(-0.291956\pi\) | ||||
0.608040 | + | 0.793906i | \(0.291956\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −48.0000 | − | 53.6656i | −0.238806 | − | 0.266993i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 187.830i | − | 0.925270i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 140.000 | 0.682927 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −120.000 | − | 13.4164i | −0.579710 | − | 0.0648136i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.94427i | 0.0427956i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | 0.00947867 | 0.00473934 | − | 0.999989i | \(-0.498491\pi\) | ||||
0.00473934 | + | 0.999989i | \(0.498491\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −280.000 | + | 250.440i | −1.31455 | + | 1.17577i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 35.7771i | 0.166405i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 108.000 | 0.497696 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 148.000 | + | 165.469i | 0.675799 | + | 0.755566i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 71.5542i | 0.323775i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −86.0000 | −0.385650 | −0.192825 | − | 0.981233i | \(-0.561765\pi\) | ||||
−0.192825 | + | 0.981233i | \(0.561765\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.00000 | − | 44.7214i | 0.0222222 | − | 0.198762i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 58.1378i | 0.256114i | 0.991767 | + | 0.128057i | \(0.0408740\pi\) | ||||
−0.991767 | + | 0.128057i | \(0.959126\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 282.000 | 1.23144 | 0.615721 | − | 0.787965i | \(-0.288865\pi\) | ||||
0.615721 | + | 0.787965i | \(0.288865\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −60.0000 | + | 53.6656i | −0.259740 | + | 0.232319i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 362.243i | 1.55469i | 0.629074 | + | 0.777346i | \(0.283434\pi\) | ||||
−0.629074 | + | 0.777346i | \(0.716566\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 110.000 | 0.468085 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 276.000 | + | 308.577i | 1.16456 | + | 1.30201i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 250.440i | − | 1.04786i | −0.851760 | − | 0.523932i | \(-0.824464\pi\) | ||
0.851760 | − | 0.523932i | \(-0.175536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 262.000 | 1.08714 | 0.543568 | − | 0.839365i | \(-0.317073\pi\) | ||||
0.543568 | + | 0.839365i | \(0.317073\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 118.000 | + | 212.426i | 0.485597 | + | 0.874183i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 29.0689i | − | 0.118649i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 32.0000 | 0.129555 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 210.000 | − | 187.830i | 0.843373 | − | 0.754336i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 469.574i | − | 1.87081i | −0.353573 | − | 0.935407i | \(-0.615033\pi\) | ||
0.353573 | − | 0.935407i | \(-0.384967\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 60.0000 | 0.237154 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −20.0000 | − | 22.3607i | −0.0784314 | − | 0.0876889i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 201.246i | − | 0.783059i | −0.920166 | − | 0.391529i | \(-0.871946\pi\) | ||
0.920166 | − | 0.391529i | \(-0.128054\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 96.0000 | 0.370656 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 280.000 | + | 31.3050i | 1.07280 | + | 0.119942i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 58.1378i | − | 0.221056i | −0.993873 | − | 0.110528i | \(-0.964746\pi\) | ||
0.993873 | − | 0.110528i | \(-0.0352542\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.0000 | −0.0377358 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −240.000 | + | 214.663i | −0.898876 | + | 0.803979i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 371.187i | − | 1.37988i | −0.723867 | − | 0.689939i | \(-0.757637\pi\) | ||
0.723867 | − | 0.689939i | \(-0.242363\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −82.0000 | −0.302583 | −0.151292 | − | 0.988489i | \(-0.548343\pi\) | ||||
−0.151292 | + | 0.988489i | \(0.548343\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 192.000 | + | 214.663i | 0.703297 | + | 0.786310i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.3607i | 0.0813116i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.0000 | −0.0866426 | −0.0433213 | − | 0.999061i | \(-0.513794\pi\) | ||||
−0.0433213 | + | 0.999061i | \(0.513794\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18.0000 | + | 160.997i | −0.0645161 | + | 0.577050i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 187.830i | 0.668433i | 0.942496 | + | 0.334217i | \(0.108472\pi\) | ||||
−0.942496 | + | 0.334217i | \(0.891528\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −144.000 | −0.508834 | −0.254417 | − | 0.967095i | \(-0.581884\pi\) | ||||
−0.254417 | + | 0.967095i | \(0.581884\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.0000 | + | 8.94427i | −0.0350877 | + | 0.0313834i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 375.659i | − | 1.30892i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 269.000 | 0.930796 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 332.000 | + | 371.187i | 1.14089 | + | 1.27556i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 469.574i | 1.60264i | 0.598234 | + | 0.801321i | \(0.295869\pi\) | ||||
−0.598234 | + | 0.801321i | \(0.704131\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.0000 | 0.0338983 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −70.0000 | − | 98.3870i | −0.235690 | − | 0.331269i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 214.663i | − | 0.717935i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 96.0000 | 0.318937 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 150.000 | − | 134.164i | 0.495050 | − | 0.442786i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 183.358i | − | 0.601172i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 184.000 | 0.599349 | 0.299674 | − | 0.954042i | \(-0.403122\pi\) | ||||
0.299674 | + | 0.954042i | \(0.403122\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 52.0000 | + | 58.1378i | 0.168285 | + | 0.188148i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 160.997i | 0.517675i | 0.965921 | + | 0.258837i | \(0.0833394\pi\) | ||||
−0.965921 | + | 0.258837i | \(0.916661\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −394.000 | −1.25879 | −0.629393 | − | 0.777087i | \(-0.716696\pi\) | ||||
−0.629393 | + | 0.777087i | \(0.716696\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −120.000 | − | 13.4164i | −0.380952 | − | 0.0425918i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 451.686i | 1.42488i | 0.701735 | + | 0.712438i | \(0.252409\pi\) | ||||
−0.701735 | + | 0.712438i | \(0.747591\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −140.000 | −0.438871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −450.000 | + | 402.492i | −1.40187 | + | 1.25387i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.94427i | 0.0276912i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 80.0000 | 0.246154 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 76.0000 | + | 84.9706i | 0.232416 | + | 0.259849i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 295.161i | − | 0.897146i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −198.000 | −0.598187 | −0.299094 | − | 0.954224i | \(-0.596684\pi\) | ||||
−0.299094 | + | 0.954224i | \(0.596684\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.0000 | + | 143.108i | −0.0480480 | + | 0.429755i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 53.6656i | 0.160196i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 394.000 | 1.16914 | 0.584570 | − | 0.811343i | \(-0.301263\pi\) | ||||
0.584570 | + | 0.811343i | \(0.301263\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −70.0000 | + | 62.6099i | −0.206490 | + | 0.184690i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 80.4984i | − | 0.236066i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −372.000 | −1.08455 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 60.0000 | + | 67.0820i | 0.173913 | + | 0.194441i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 183.358i | 0.528408i | 0.964467 | + | 0.264204i | \(0.0851092\pi\) | ||||
−0.964467 | + | 0.264204i | \(0.914891\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 362.000 | 1.03725 | 0.518625 | − | 0.855002i | \(-0.326444\pi\) | ||||
0.518625 | + | 0.855002i | \(0.326444\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −352.000 | + | 250.440i | −1.00285 | + | 0.713503i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 308.577i | 0.874157i | 0.899423 | + | 0.437078i | \(0.143987\pi\) | ||||
−0.899423 | + | 0.437078i | \(0.856013\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 280.000 | 0.788732 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −60.0000 | + | 53.6656i | −0.168067 | + | 0.150324i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 295.161i | 0.822175i | 0.911596 | + | 0.411088i | \(0.134851\pi\) | ||||
−0.911596 | + | 0.411088i | \(0.865149\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −357.000 | −0.988920 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −202.000 | − | 225.843i | −0.556474 | − | 0.622157i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 165.469i | − | 0.453340i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 186.000 | 0.506812 | 0.253406 | − | 0.967360i | \(-0.418449\pi\) | ||||
0.253406 | + | 0.967360i | \(0.418449\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 560.000 | + | 62.6099i | 1.51762 | + | 0.169675i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.8328i | 0.0723256i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 44.0000 | 0.117962 | 0.0589812 | − | 0.998259i | \(-0.481215\pi\) | ||||
0.0589812 | + | 0.998259i | \(0.481215\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −25.0000 | + | 22.3607i | −0.0666667 | + | 0.0596285i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 500.879i | 1.32859i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −362.000 | −0.955145 | −0.477573 | − | 0.878592i | \(-0.658483\pi\) | ||||
−0.477573 | + | 0.878592i | \(0.658483\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −52.0000 | − | 58.1378i | −0.136483 | − | 0.152593i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 362.243i | − | 0.945804i | −0.881115 | − | 0.472902i | \(-0.843206\pi\) | ||
0.881115 | − | 0.472902i | \(-0.156794\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 60.0000 | 0.155844 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −16.0000 | + | 143.108i | −0.0413437 | + | 0.369789i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 442.741i | 1.13815i | 0.822285 | + | 0.569076i | \(0.192699\pi\) | ||||
−0.822285 | + | 0.569076i | \(0.807301\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 60.0000 | 0.153453 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −30.0000 | + | 26.8328i | −0.0763359 | + | 0.0682769i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 308.577i | − | 0.781209i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −124.000 | −0.312343 | −0.156171 | − | 0.987730i | \(-0.549915\pi\) | ||||
−0.156171 | + | 0.987730i | \(0.549915\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 24.0000 | + | 26.8328i | 0.0601504 | + | 0.0672502i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 268.328i | 0.669148i | 0.942370 | + | 0.334574i | \(0.108592\pi\) | ||||
−0.942370 | + | 0.334574i | \(0.891408\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −288.000 | −0.714640 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 40.0000 | − | 176.649i | 0.0987654 | − | 0.436171i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 71.5542i | − | 0.175809i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 458.000 | 1.11980 | 0.559902 | − | 0.828559i | \(-0.310839\pi\) | ||||
0.559902 | + | 0.828559i | \(0.310839\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 270.000 | − | 241.495i | 0.656934 | − | 0.587580i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 26.8328i | − | 0.0649705i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −210.000 | −0.506024 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 164.000 | + | 183.358i | 0.393285 | + | 0.439706i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 594.794i | 1.41956i | 0.704425 | + | 0.709778i | \(0.251205\pi\) | ||||
−0.704425 | + | 0.709778i | \(0.748795\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −562.000 | −1.33492 | −0.667458 | − | 0.744647i | \(-0.732618\pi\) | ||||
−0.667458 | + | 0.744647i | \(0.732618\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 440.000 | + | 49.1935i | 1.04019 | + | 0.116297i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.3607i | 0.0526134i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −492.000 | −1.15222 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 160.000 | − | 143.108i | 0.372960 | − | 0.333586i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 348.827i | 0.809342i | 0.914462 | + | 0.404671i | \(0.132614\pi\) | ||||
−0.914462 | + | 0.404671i | \(0.867386\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 226.000 | 0.521940 | 0.260970 | − | 0.965347i | \(-0.415958\pi\) | ||||
0.260970 | + | 0.965347i | \(0.415958\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −140.000 | − | 156.525i | −0.321839 | − | 0.359827i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 26.8328i | − | 0.0614023i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.00000 | 0.00455581 | 0.00227790 | − | 0.999997i | \(-0.499275\pi\) | ||||
0.00227790 | + | 0.999997i | \(0.499275\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.0000 | − | 116.276i | 0.0294785 | − | 0.263663i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 201.246i | − | 0.454280i | −0.973862 | − | 0.227140i | \(-0.927062\pi\) | ||
0.973862 | − | 0.227140i | \(-0.0729375\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 240.000 | 0.539326 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −250.000 | + | 223.607i | −0.559284 | + | 0.500239i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 313.050i | − | 0.697215i | −0.937269 | − | 0.348607i | \(-0.886655\pi\) | ||
0.937269 | − | 0.348607i | \(-0.113345\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −280.000 | −0.620843 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −316.000 | − | 353.299i | −0.697572 | − | 0.779909i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 214.663i | − | 0.471786i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 334.000 | 0.730853 | 0.365427 | − | 0.930840i | \(-0.380923\pi\) | ||||
0.365427 | + | 0.930840i | \(0.380923\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −70.0000 | − | 98.3870i | −0.152505 | − | 0.214351i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 93.9149i | 0.203720i | 0.994799 | + | 0.101860i | \(0.0324794\pi\) | ||||
−0.994799 | + | 0.101860i | \(0.967521\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −366.000 | −0.790497 | −0.395248 | − | 0.918574i | \(-0.629341\pi\) | ||||
−0.395248 | + | 0.918574i | \(0.629341\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 90.0000 | − | 80.4984i | 0.193548 | − | 0.173115i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 451.686i | − | 0.967207i | −0.875287 | − | 0.483604i | \(-0.839328\pi\) | ||
0.875287 | − | 0.483604i | \(-0.160672\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 144.000 | 0.307036 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 328.000 | + | 366.715i | 0.696391 | + | 0.778588i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 71.5542i | − | 0.151277i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.0000 | 0.0210526 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −40.0000 | − | 4.47214i | −0.0838574 | − | 0.00937555i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 590.322i | − | 1.23240i | −0.787588 | − | 0.616202i | \(-0.788670\pi\) | ||
0.787588 | − | 0.616202i | \(-0.211330\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −256.000 | −0.532225 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 180.000 | − | 160.997i | 0.372671 | − | 0.333327i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 371.187i | − | 0.765335i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 886.000 | 1.81930 | 0.909651 | − | 0.415374i | \(-0.136349\pi\) | ||||
0.909651 | + | 0.415374i | \(0.136349\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −472.000 | − | 527.712i | −0.965235 | − | 1.07917i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 406.964i | 0.828848i | 0.910084 | + | 0.414424i | \(0.136017\pi\) | ||||
−0.910084 | + | 0.414424i | \(0.863983\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −140.000 | −0.283976 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.0000 | + | 89.4427i | −0.0202020 | + | 0.180692i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 751.319i | − | 1.51171i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.00000 | −0.00400802 | −0.00200401 | − | 0.999998i | \(-0.500638\pi\) | ||||
−0.00200401 | + | 0.999998i | \(0.500638\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 210.000 | − | 187.830i | 0.419162 | − | 0.374910i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 219.135i | − | 0.435655i | −0.975987 | − | 0.217828i | \(-0.930103\pi\) | ||
0.975987 | − | 0.217828i | \(-0.0698971\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −150.000 | −0.297030 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −174.000 | − | 194.538i | −0.343195 | − | 0.383704i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 800.512i | − | 1.57272i | −0.617771 | − | 0.786358i | \(-0.711964\pi\) | ||
0.617771 | − | 0.786358i | \(-0.288036\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −444.000 | −0.868885 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −44.0000 | + | 31.3050i | −0.0857700 | + | 0.0610233i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 58.1378i | − | 0.112889i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −220.000 | −0.425532 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.0000 | − | 26.8328i | 0.0578035 | − | 0.0517010i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 527.712i | 1.01288i | 0.862274 | + | 0.506441i | \(0.169039\pi\) | ||||
−0.862274 | + | 0.506441i | \(0.830961\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 376.000 | 0.718929 | 0.359465 | − | 0.933159i | \(-0.382959\pi\) | ||||
0.359465 | + | 0.933159i | \(0.382959\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 60.0000 | + | 67.0820i | 0.114286 | + | 0.127775i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 80.4984i | − | 0.152748i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 349.000 | 0.659735 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40.0000 | + | 4.47214i | 0.0753296 | + | 0.00842210i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1001.76i | 1.87947i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 450.000 | 0.841121 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −430.000 | + | 384.604i | −0.800745 | + | 0.716208i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 58.1378i | 0.107862i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 198.000 | 0.365989 | 0.182994 | − | 0.983114i | \(-0.441421\pi\) | ||||
0.182994 | + | 0.983114i | \(0.441421\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.00000 | + | 4.47214i | 0.00736648 | + | 0.00823598i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 84.9706i | − | 0.155909i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1024.00 | 1.87203 | 0.936015 | − | 0.351961i | \(-0.114485\pi\) | ||||
0.936015 | + | 0.351961i | \(0.114485\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 82.0000 | − | 733.430i | 0.149362 | − | 1.33594i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 62.6099i | 0.113630i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −828.000 | −1.49729 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 80.0000 | − | 71.5542i | 0.144144 | − | 0.128926i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 67.0820i | 0.120435i | 0.998185 | + | 0.0602173i | \(0.0191794\pi\) | ||||
−0.998185 | + | 0.0602173i | \(0.980821\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −256.000 | −0.457961 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.0000 | + | 44.7214i | 0.0713012 | + | 0.0797172i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 254.912i | − | 0.452774i | −0.974037 | − | 0.226387i | \(-0.927309\pi\) | ||
0.974037 | − | 0.226387i | \(-0.0726914\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 70.0000 | 0.123894 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −474.000 | − | 107.331i | −0.835979 | − | 0.189297i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 858.650i | − | 1.50905i | −0.656271 | − | 0.754526i | \(-0.727867\pi\) | ||
0.656271 | − | 0.754526i | \(-0.272133\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 962.000 | 1.68476 | 0.842382 | − | 0.538881i | \(-0.181153\pi\) | ||||
0.842382 | + | 0.538881i | \(0.181153\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −460.000 | + | 411.437i | −0.802792 | + | 0.718039i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 67.0820i | − | 0.116664i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −886.000 | −1.53553 | −0.767764 | − | 0.640732i | \(-0.778631\pi\) | ||||
−0.767764 | + | 0.640732i | \(0.778631\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 428.000 | + | 478.519i | 0.739206 | + | 0.826457i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 563.489i | 0.969861i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.0000 | 0.0343053 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 320.000 | + | 35.7771i | 0.547009 | + | 0.0611574i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 657.404i | 1.11994i | 0.828513 | + | 0.559969i | \(0.189187\pi\) | ||||
−0.828513 | + | 0.559969i | \(0.810813\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.0000 | −0.0611205 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −210.000 | + | 187.830i | −0.355330 | + | 0.317817i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 111.803i | 0.188539i | 0.995547 | + | 0.0942693i | \(0.0300515\pi\) | ||||
−0.995547 | + | 0.0942693i | \(0.969949\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 60.0000 | 0.100840 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −484.000 | − | 541.128i | −0.810720 | − | 0.906413i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 223.607i | 0.373300i | 0.982426 | + | 0.186650i | \(0.0597631\pi\) | ||||
−0.982426 | + | 0.186650i | \(0.940237\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.00000 | 0.00332779 | 0.00166389 | − | 0.999999i | \(-0.499470\pi\) | ||||
0.00166389 | + | 0.999999i | \(0.499470\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.0000 | + | 214.663i | −0.0398010 | + | 0.355991i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 225.843i | 0.373294i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 506.000 | 0.833608 | 0.416804 | − | 0.908996i | \(-0.363150\pi\) | ||||
0.416804 | + | 0.908996i | \(0.363150\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −420.000 | + | 375.659i | −0.689655 | + | 0.616846i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 787.096i | 1.28821i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −556.000 | −0.907015 | −0.453507 | − | 0.891253i | \(-0.649827\pi\) | ||||
−0.453507 | + | 0.891253i | \(0.649827\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −280.000 | − | 313.050i | −0.455285 | − | 0.509024i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 93.9149i | − | 0.152212i | −0.997100 | − | 0.0761060i | \(-0.975751\pi\) | ||
0.997100 | − | 0.0761060i | \(-0.0242488\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −802.000 | −1.29564 | −0.647819 | − | 0.761794i | \(-0.724319\pi\) | ||||
−0.647819 | + | 0.761794i | \(0.724319\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 210.000 | + | 295.161i | 0.338164 | + | 0.475299i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 643.988i | − | 1.03369i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.0000 | − | 17.8885i | 0.0318979 | − | 0.0285304i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 71.5542i | − | 0.113759i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 698.000 | 1.10618 | 0.553090 | − | 0.833121i | \(-0.313448\pi\) | ||||
0.553090 | + | 0.833121i | \(0.313448\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.00000 | − | 4.47214i | −0.00631912 | − | 0.00706499i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 58.1378i | 0.0915555i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 208.000 | 0.326531 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1120.00 | + | 125.220i | 1.75274 | + | 0.195962i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 912.316i | − | 1.42327i | −0.702550 | − | 0.711635i | \(-0.747955\pi\) | ||
0.702550 | − | 0.711635i | \(-0.252045\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 156.000 | 0.242613 | 0.121306 | − | 0.992615i | \(-0.461292\pi\) | ||||
0.121306 | + | 0.992615i | \(0.461292\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 80.0000 | − | 71.5542i | 0.124031 | − | 0.110937i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 755.791i | 1.16815i | 0.811701 | + | 0.584073i | \(0.198542\pi\) | ||||
−0.811701 | + | 0.584073i | \(0.801458\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.0000 | −0.0308166 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −216.000 | − | 241.495i | −0.331797 | − | 0.370961i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 487.463i | − | 0.746497i | −0.927731 | − | 0.373249i | \(-0.878244\pi\) | ||
0.927731 | − | 0.373249i | \(-0.121756\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30.0000 | 0.0458015 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 74.0000 | − | 661.876i | 0.112633 | − | 1.00742i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 406.964i | − | 0.617548i | −0.951135 | − | 0.308774i | \(-0.900081\pi\) | ||
0.951135 | − | 0.308774i | \(-0.0999187\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −682.000 | −1.03177 | −0.515885 | − | 0.856658i | \(-0.672537\pi\) | ||||
−0.515885 | + | 0.856658i | \(0.672537\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 160.000 | − | 143.108i | 0.241327 | − | 0.215850i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 26.8328i | − | 0.0403501i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 420.000 | 0.629685 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 172.000 | + | 192.302i | 0.257100 | + | 0.287447i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 366.715i | 0.546520i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −894.000 | −1.32838 | −0.664190 | − | 0.747564i | \(-0.731223\pi\) | ||||
−0.664190 | + | 0.747564i | \(0.731223\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −110.000 | + | 78.2624i | −0.162963 | + | 0.115944i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 550.073i | − | 0.812515i | −0.913759 | − | 0.406258i | \(-0.866834\pi\) | ||
0.913759 | − | 0.406258i | \(-0.133166\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −996.000 | −1.46686 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 130.000 | − | 116.276i | 0.190896 | − | 0.170742i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 442.741i | − | 0.648231i | −0.946018 | − | 0.324115i | \(-0.894933\pi\) | ||
0.946018 | − | 0.324115i | \(-0.105067\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −270.000 | −0.394161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −564.000 | − | 630.571i | −0.820961 | − | 0.917862i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 71.5542i | − | 0.103852i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −758.000 | −1.09696 | −0.548480 | − | 0.836163i | \(-0.684793\pi\) | ||||
−0.548480 | + | 0.836163i | \(0.684793\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 240.000 | + | 26.8328i | 0.346320 | + | 0.0387198i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 183.358i | − | 0.263824i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −280.000 | −0.401722 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 810.000 | − | 724.486i | 1.15880 | − | 1.03646i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 782.624i | − | 1.11644i | −0.829693 | − | 0.558220i | \(-0.811485\pi\) | ||
0.829693 | − | 0.558220i | \(-0.188515\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.0000 | −0.0455192 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −220.000 | − | 245.967i | −0.312057 | − | 0.348890i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 402.492i | 0.569296i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.00000 | 0.00282087 | 0.00141044 | − | 0.999999i | \(-0.499551\pi\) | ||||
0.00141044 | + | 0.999999i | \(0.499551\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 138.000 | − | 1234.31i | 0.194093 | − | 1.73602i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 241.495i | 0.338703i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −160.000 | −0.223776 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −560.000 | + | 500.879i | −0.781032 | + | 0.698576i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 858.650i | 1.19423i | 0.802156 | + | 0.597114i | \(0.203686\pi\) | ||||
−0.802156 | + | 0.597114i | \(0.796314\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −156.000 | −0.216366 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −524.000 | − | 585.850i | −0.724758 | − | 0.810304i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 156.525i | 0.215896i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −674.000 | −0.927098 | −0.463549 | − | 0.886071i | \(-0.653424\pi\) | ||||
−0.463549 | + | 0.886071i | \(0.653424\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 239.000 | − | 688.709i | 0.327846 | − | 0.944731i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 71.5542i | − | 0.0978853i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −656.000 | −0.894952 | −0.447476 | − | 0.894296i | \(-0.647677\pi\) | ||||
−0.447476 | + | 0.894296i | \(0.647677\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −65.0000 | + | 58.1378i | −0.0884354 | + | 0.0790990i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 107.331i | − | 0.145633i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 598.000 | 0.809202 | 0.404601 | − | 0.914493i | \(-0.367410\pi\) | ||||
0.404601 | + | 0.914493i | \(0.367410\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −64.0000 | − | 71.5542i | −0.0863698 | − | 0.0965643i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 782.624i | 1.05333i | 0.850073 | + | 0.526665i | \(0.176558\pi\) | ||||
−0.850073 | + | 0.526665i | \(0.823442\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 250.000 | 0.335570 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −840.000 | − | 93.9149i | −1.12450 | − | 0.125723i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1207.48i | − | 1.61212i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 338.000 | 0.450067 | 0.225033 | − | 0.974351i | \(-0.427751\pi\) | ||||
0.225033 | + | 0.974351i | \(0.427751\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1050.00 | + | 939.149i | −1.39442 | + | 1.24721i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 353.299i | 0.467945i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 656.000 | 0.866579 | 0.433289 | − | 0.901255i | \(-0.357353\pi\) | ||||
0.433289 | + | 0.901255i | \(0.357353\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −120.000 | − | 134.164i | −0.158103 | − | 0.176764i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 295.161i | − | 0.387859i | −0.981015 | − | 0.193930i | \(-0.937877\pi\) | ||
0.981015 | − | 0.193930i | \(-0.0621234\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −228.000 | −0.298820 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.0000 | + | 89.4427i | −0.0130719 | + | 0.116919i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 71.5542i | 0.0932910i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −82.0000 | −0.106632 | −0.0533160 | − | 0.998578i | \(-0.516979\pi\) | ||||
−0.0533160 | + | 0.998578i | \(0.516979\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −450.000 | + | 402.492i | −0.583658 | + | 0.522039i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1059.90i | − | 1.37115i | −0.728004 | − | 0.685573i | \(-0.759552\pi\) | ||
0.728004 | − | 0.685573i | \(-0.240448\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −90.0000 | −0.116129 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −192.000 | − | 214.663i | −0.247104 | − | 0.276271i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 125.220i | 0.160744i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −560.000 | −0.717029 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −490.000 | − | 688.709i | −0.625798 | − | 0.879577i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 366.715i | − | 0.467153i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −536.000 | −0.681067 | −0.340534 | − | 0.940232i | \(-0.610608\pi\) | ||||
−0.340534 | + | 0.940232i | \(0.610608\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −130.000 | + | 116.276i | −0.164766 | + | 0.147371i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 187.830i | − | 0.237459i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1312.00 | 1.65448 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.0000 | + | 22.3607i | 0.0251572 | + | 0.0281266i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 406.964i | − | 0.510620i | −0.966859 | − | 0.255310i | \(-0.917822\pi\) | ||
0.966859 | − | 0.255310i | \(-0.0821776\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −220.000 | −0.275344 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 960.000 | + | 107.331i | 1.19850 | + | 0.133997i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 330.938i | 0.412127i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −180.000 | −0.223602 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −830.000 | + | 742.375i | −1.02850 | + | 0.919919i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1091.20i | 1.34883i | 0.738354 | + | 0.674414i | \(0.235603\pi\) | ||||
−0.738354 | + | 0.674414i | \(0.764397\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −558.000 | −0.688039 | −0.344020 | − | 0.938962i | \(-0.611789\pi\) | ||||
−0.344020 | + | 0.938962i | \(0.611789\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 164.000 | + | 183.358i | 0.201722 | + | 0.225532i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 527.712i | 0.647499i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.0000 | −0.0391677 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 96.0000 | − | 858.650i | 0.117216 | − | 1.04841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 389.076i | 0.473905i | 0.971521 | + | 0.236952i | \(0.0761485\pi\) | ||||
−0.971521 | + | 0.236952i | \(0.923851\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 214.000 | 0.260024 | 0.130012 | − | 0.991512i | \(-0.458498\pi\) | ||||
0.130012 | + | 0.991512i | \(0.458498\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 50.0000 | − | 44.7214i | 0.0606061 | − | 0.0542077i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 31.3050i | − | 0.0378536i | −0.999821 | − | 0.0189268i | \(-0.993975\pi\) | ||
0.999821 | − | 0.0189268i | \(-0.00602495\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −318.000 | −0.383595 | −0.191797 | − | 0.981435i | \(-0.561432\pi\) | ||||
−0.191797 | + | 0.981435i | \(0.561432\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 48.0000 | + | 53.6656i | 0.0577617 | + | 0.0645796i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 58.1378i | 0.0697932i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −210.000 | −0.251497 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 396.000 | − | 281.745i | 0.473118 | − | 0.336612i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 62.6099i | 0.0746244i | 0.999304 | + | 0.0373122i | \(0.0118796\pi\) | ||||
−0.999304 | + | 0.0373122i | \(0.988120\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −139.000 | −0.165279 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 420.000 | − | 375.659i | 0.498221 | − | 0.445622i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 194.538i | 0.230222i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 606.000 | 0.715466 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 288.000 | + | 321.994i | 0.339223 | + | 0.379262i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 214.663i | 0.252247i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 684.000 | 0.801876 | 0.400938 | − | 0.916105i | \(-0.368684\pi\) | ||||
0.400938 | + | 0.916105i | \(0.368684\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 40.0000 | + | 4.47214i | 0.0467836 | + | 0.00523057i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1498.17i | 1.74815i | 0.485790 | + | 0.874076i | \(0.338532\pi\) | ||||
−0.485790 | + | 0.874076i | \(0.661468\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −842.000 | −0.980210 | −0.490105 | − | 0.871664i | \(-0.663041\pi\) | ||||
−0.490105 | + | 0.871664i | \(0.663041\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −840.000 | + | 751.319i | −0.975610 | + | 0.872612i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1015.17i | 1.17633i | 0.808740 | + | 0.588166i | \(0.200150\pi\) | ||||
−0.808740 | + | 0.588166i | \(0.799850\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.0000 | −0.0346821 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −538.000 | − | 601.502i | −0.620531 | − | 0.693774i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 617.155i | 0.710190i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −384.000 | −0.440873 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 166.000 | − | 1484.75i | 0.190149 | − | 1.70074i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 67.0820i | − | 0.0766652i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 156.000 | 0.177879 | 0.0889396 | − | 0.996037i | \(-0.471652\pi\) | ||||
0.0889396 | + | 0.996037i | \(0.471652\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1050.00 | − | 939.149i | 1.19454 | − | 1.06843i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 125.220i | − | 0.142134i | −0.997472 | − | 0.0710669i | \(-0.977360\pi\) | ||
0.997472 | − | 0.0710669i | \(-0.0226404\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −964.000 | −1.09173 | −0.545866 | − | 0.837872i | \(-0.683799\pi\) | ||||
−0.545866 | + | 0.837872i | \(0.683799\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.0000 | − | 22.3607i | −0.0225989 | − | 0.0252663i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 952.565i | 1.07392i | 0.843608 | + | 0.536959i | \(0.180427\pi\) | ||||
−0.843608 | + | 0.536959i | \(0.819573\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 156.000 | 0.175478 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −80.0000 | + | 353.299i | −0.0897868 | + | 0.396519i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 98.3870i | 0.110176i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 430.000 | 0.480447 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −480.000 | + | 429.325i | −0.535117 | + | 0.478623i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 563.489i | − | 0.626795i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.0000 | 0.0221976 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −192.000 | − | 214.663i | −0.212625 | − | 0.237722i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 4.47214i | − | 0.00494159i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1284.00 | 1.41566 | 0.707828 | − | 0.706385i | \(-0.249675\pi\) | ||||
0.707828 | + | 0.706385i | \(0.249675\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −600.000 | − | 67.0820i | −0.660066 | − | 0.0737976i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 62.6099i | − | 0.0687266i | −0.999409 | − | 0.0343633i | \(-0.989060\pi\) | ||
0.999409 | − | 0.0343633i | \(-0.0109403\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 420.000 | 0.460022 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −410.000 | + | 366.715i | −0.448087 | + | 0.400782i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 80.4984i | − | 0.0877846i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −418.000 | −0.454842 | −0.227421 | − | 0.973797i | \(-0.573029\pi\) | ||||
−0.227421 | + | 0.973797i | \(0.573029\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −368.000 | − | 411.437i | −0.399566 | − | 0.446728i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2003.52i | 2.17066i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −80.0000 | −0.0864865 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.0000 | − | 232.551i | 0.0280475 | − | 0.250864i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 169.941i | − | 0.182929i | −0.995808 | − | 0.0914646i | \(-0.970845\pi\) | ||
0.995808 | − | 0.0914646i | \(-0.0291548\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.0000 | 0.0279270 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 360.000 | − | 321.994i | 0.385852 | − | 0.345117i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 44.7214i | − | 0.0478303i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 534.000 | 0.569904 | 0.284952 | − | 0.958542i | \(-0.408022\pi\) | ||||
0.284952 | + | 0.958542i | \(0.408022\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 788.000 | + | 881.011i | 0.839191 | + | 0.938244i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 129.692i | 0.137824i | 0.997623 | + | 0.0689118i | \(0.0219527\pi\) | ||||
−0.997623 | + | 0.0689118i | \(0.978047\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 840.000 | 0.890774 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 210.000 | + | 295.161i | 0.222222 | + | 0.312340i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1516.05i | − | 1.60090i | −0.599398 | − | 0.800451i | \(-0.704593\pi\) | ||
0.599398 | − | 0.800451i | \(-0.295407\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1184.00 | 1.24763 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1010.00 | − | 903.371i | 1.06204 | − | 0.949917i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 406.964i | − | 0.427035i | −0.976939 | − | 0.213518i | \(-0.931508\pi\) | ||
0.976939 | − | 0.213518i | \(-0.0684920\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 460.000 | 0.481675 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 280.000 | + | 313.050i | 0.292581 | + | 0.327115i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 724.486i | 0.755460i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −637.000 | −0.662851 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1800.00 | + | 201.246i | 1.86916 | + | 0.208978i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 478.519i | − | 0.495874i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −674.000 | −0.697001 | −0.348501 | − | 0.937309i | \(-0.613309\pi\) | ||||
−0.348501 | + | 0.937309i | \(0.613309\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20.0000 | − | 17.8885i | 0.0206398 | − | 0.0184608i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1328.22i | − | 1.36789i | −0.729532 | − | 0.683947i | \(-0.760262\pi\) | ||
0.729532 | − | 0.683947i | \(-0.239738\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −492.000 | −0.505653 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −160.000 | − | 178.885i | −0.164103 | − | 0.183472i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 371.187i | 0.379926i | 0.981791 | + | 0.189963i | \(0.0608367\pi\) | ||||
−0.981791 | + | 0.189963i | \(0.939163\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −480.000 | −0.490296 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38.0000 | − | 339.882i | 0.0387360 | − | 0.346465i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 442.741i | 0.450398i | 0.974313 | + | 0.225199i | \(0.0723033\pi\) | ||||
−0.974313 | + | 0.225199i | \(0.927697\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 210.000 | 0.213198 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −660.000 | + | 590.322i | −0.668693 | + | 0.598097i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 214.663i | 0.217050i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −962.000 | −0.970737 | −0.485368 | − | 0.874310i | \(-0.661314\pi\) | ||||
−0.485368 | + | 0.874310i | \(0.661314\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 396.000 | + | 442.741i | 0.398792 | + | 0.445862i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 541.128i | 0.543848i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.0000 | −0.0240722 | −0.0120361 | − | 0.999928i | \(-0.503831\pi\) | ||||
−0.0120361 | + | 0.999928i | \(0.503831\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 352.000 | − | 250.440i | 0.352352 | − | 0.250690i |
(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 | 960.3.l.b.641.1 | 2 | ||
3.2 | odd | 2 | inner | 960.3.l.b.641.2 | 2 | ||
4.3 | odd | 2 | 960.3.l.c.641.2 | 2 | |||
8.3 | odd | 2 | 15.3.c.a.11.2 | yes | 2 | ||
8.5 | even | 2 | 240.3.l.b.161.2 | 2 | |||
12.11 | even | 2 | 960.3.l.c.641.1 | 2 | |||
24.5 | odd | 2 | 240.3.l.b.161.1 | 2 | |||
24.11 | even | 2 | 15.3.c.a.11.1 | ✓ | 2 | ||
40.3 | even | 4 | 75.3.d.b.74.3 | 4 | |||
40.13 | odd | 4 | 1200.3.c.f.449.2 | 4 | |||
40.19 | odd | 2 | 75.3.c.e.26.1 | 2 | |||
40.27 | even | 4 | 75.3.d.b.74.2 | 4 | |||
40.29 | even | 2 | 1200.3.l.g.401.1 | 2 | |||
40.37 | odd | 4 | 1200.3.c.f.449.3 | 4 | |||
72.11 | even | 6 | 405.3.i.b.296.1 | 4 | |||
72.43 | odd | 6 | 405.3.i.b.296.2 | 4 | |||
72.59 | even | 6 | 405.3.i.b.26.2 | 4 | |||
72.67 | odd | 6 | 405.3.i.b.26.1 | 4 | |||
120.29 | odd | 2 | 1200.3.l.g.401.2 | 2 | |||
120.53 | even | 4 | 1200.3.c.f.449.4 | 4 | |||
120.59 | even | 2 | 75.3.c.e.26.2 | 2 | |||
120.77 | even | 4 | 1200.3.c.f.449.1 | 4 | |||
120.83 | odd | 4 | 75.3.d.b.74.1 | 4 | |||
120.107 | odd | 4 | 75.3.d.b.74.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.3.c.a.11.1 | ✓ | 2 | 24.11 | even | 2 | ||
15.3.c.a.11.2 | yes | 2 | 8.3 | odd | 2 | ||
75.3.c.e.26.1 | 2 | 40.19 | odd | 2 | |||
75.3.c.e.26.2 | 2 | 120.59 | even | 2 | |||
75.3.d.b.74.1 | 4 | 120.83 | odd | 4 | |||
75.3.d.b.74.2 | 4 | 40.27 | even | 4 | |||
75.3.d.b.74.3 | 4 | 40.3 | even | 4 | |||
75.3.d.b.74.4 | 4 | 120.107 | odd | 4 | |||
240.3.l.b.161.1 | 2 | 24.5 | odd | 2 | |||
240.3.l.b.161.2 | 2 | 8.5 | even | 2 | |||
405.3.i.b.26.1 | 4 | 72.67 | odd | 6 | |||
405.3.i.b.26.2 | 4 | 72.59 | even | 6 | |||
405.3.i.b.296.1 | 4 | 72.11 | even | 6 | |||
405.3.i.b.296.2 | 4 | 72.43 | odd | 6 | |||
960.3.l.b.641.1 | 2 | 1.1 | even | 1 | trivial | ||
960.3.l.b.641.2 | 2 | 3.2 | odd | 2 | inner | ||
960.3.l.c.641.1 | 2 | 12.11 | even | 2 | |||
960.3.l.c.641.2 | 2 | 4.3 | odd | 2 | |||
1200.3.c.f.449.1 | 4 | 120.77 | even | 4 | |||
1200.3.c.f.449.2 | 4 | 40.13 | odd | 4 | |||
1200.3.c.f.449.3 | 4 | 40.37 | odd | 4 | |||
1200.3.c.f.449.4 | 4 | 120.53 | even | 4 | |||
1200.3.l.g.401.1 | 2 | 40.29 | even | 2 | |||
1200.3.l.g.401.2 | 2 | 120.29 | odd | 2 |