Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.a (trivial) |
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: | yes |
Analytic conductor: | \(138.772492334\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 294) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.58579 | 0.410165 | 0.205083 | − | 0.978745i | \(-0.434254\pi\) | ||||
0.205083 | + | 0.978745i | \(0.434254\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.48528 | 0.177762 | 0.0888812 | − | 0.996042i | \(-0.471671\pi\) | ||||
0.0888812 | + | 0.996042i | \(0.471671\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 45.2132 | 0.964607 | 0.482303 | − | 0.876004i | \(-0.339800\pi\) | ||||
0.482303 | + | 0.876004i | \(0.339800\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −13.7574 | −0.236809 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 81.5563 | 1.16355 | 0.581774 | − | 0.813350i | \(-0.302359\pi\) | ||||
0.581774 | + | 0.813350i | \(0.302359\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.05382 | 0.0610225 | 0.0305112 | − | 0.999534i | \(-0.490286\pi\) | ||||
0.0305112 | + | 0.999534i | \(0.490286\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −106.250 | −0.963244 | −0.481622 | − | 0.876379i | \(-0.659952\pi\) | ||||
−0.481622 | + | 0.876379i | \(0.659952\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −103.971 | −0.831765 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −268.132 | −1.71693 | −0.858463 | − | 0.512875i | \(-0.828580\pi\) | ||||
−0.858463 | + | 0.512875i | \(0.828580\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −292.368 | −1.69390 | −0.846948 | − | 0.531676i | \(-0.821562\pi\) | ||||
−0.846948 | + | 0.531676i | \(0.821562\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −19.4558 | −0.102631 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 114.558 | 0.509008 | 0.254504 | − | 0.967072i | \(-0.418088\pi\) | ||||
0.254504 | + | 0.967072i | \(0.418088\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −135.640 | −0.556916 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −161.605 | −0.615573 | −0.307786 | − | 0.951456i | \(-0.599588\pi\) | ||||
−0.307786 | + | 0.951456i | \(0.599588\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 471.294 | 1.67143 | 0.835716 | − | 0.549162i | \(-0.185053\pi\) | ||||
0.835716 | + | 0.549162i | \(0.185053\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 41.2721 | 0.136722 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −346.004 | −1.07383 | −0.536914 | − | 0.843637i | \(-0.680410\pi\) | ||||
−0.536914 | + | 0.843637i | \(0.680410\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −244.669 | −0.671775 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 405.529 | 1.05101 | 0.525507 | − | 0.850790i | \(-0.323876\pi\) | ||||
0.525507 | + | 0.850790i | \(0.323876\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 29.7401 | 0.0729119 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15.1615 | −0.0352313 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 253.436 | 0.559229 | 0.279614 | − | 0.960112i | \(-0.409793\pi\) | ||||
0.279614 | + | 0.960112i | \(0.409793\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −751.217 | −1.57678 | −0.788390 | − | 0.615176i | \(-0.789085\pi\) | ||||
−0.788390 | + | 0.615176i | \(0.789085\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 207.338 | 0.395648 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.6468 | −0.0212370 | −0.0106185 | − | 0.999944i | \(-0.503380\pi\) | ||||
−0.0106185 | + | 0.999944i | \(0.503380\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 318.749 | 0.556129 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 681.661 | 1.13941 | 0.569706 | − | 0.821848i | \(-0.307057\pi\) | ||||
0.569706 | + | 0.821848i | \(0.307057\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 685.457 | 1.09900 | 0.549498 | − | 0.835495i | \(-0.314819\pi\) | ||||
0.549498 | + | 0.835495i | \(0.314819\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 311.912 | 0.480219 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.264069 | −0.000376077 0 | −0.000188038 | − | 1.00000i | \(-0.500060\pi\) | ||||
−0.000188038 | 1.00000i | \(0.500060\pi\) | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 437.137 | 0.578097 | 0.289048 | − | 0.957314i | \(-0.406661\pi\) | ||||
0.289048 | + | 0.957314i | \(0.406661\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 374.000 | 0.477247 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 804.396 | 0.991268 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −58.5126 | −0.0696891 | −0.0348445 | − | 0.999393i | \(-0.511094\pi\) | ||||
−0.0348445 | + | 0.999393i | \(0.511094\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 877.103 | 0.977971 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 23.1758 | 0.0250293 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1280.09 | −1.33993 | −0.669966 | − | 0.742391i | \(-0.733692\pi\) | ||||
−0.669966 | + | 0.742391i | \(0.733692\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 58.3675 | 0.0592541 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1306.39 | −1.28704 | −0.643518 | − | 0.765431i | \(-0.722526\pi\) | ||||
−0.643518 | + | 0.765431i | \(0.722526\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 758.975 | 0.726058 | 0.363029 | − | 0.931778i | \(-0.381743\pi\) | ||||
0.363029 | + | 0.931778i | \(0.381743\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1262.51 | −1.14067 | −0.570336 | − | 0.821412i | \(-0.693187\pi\) | ||||
−0.570336 | + | 0.821412i | \(0.693187\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2105.53 | −1.85021 | −0.925105 | − | 0.379711i | \(-0.876023\pi\) | ||||
−0.925105 | + | 0.379711i | \(0.876023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −343.675 | −0.293876 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1535.76 | 1.27852 | 0.639258 | − | 0.768992i | \(-0.279241\pi\) | ||||
0.639258 | + | 0.768992i | \(0.279241\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −487.239 | −0.395089 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 406.919 | 0.321536 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1288.94 | −0.968401 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 484.815 | 0.355401 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1050.01 | −0.751326 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −24.1749 | −0.0168911 | −0.00844557 | − | 0.999964i | \(-0.502688\pi\) | ||||
−0.00844557 | + | 0.999964i | \(0.502688\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1413.88 | −0.965002 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1581.53 | −1.05480 | −0.527400 | − | 0.849617i | \(-0.676833\pi\) | ||||
−0.527400 | + | 0.849617i | \(0.676833\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −123.816 | −0.0789363 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −745.188 | −0.464713 | −0.232357 | − | 0.972631i | \(-0.574644\pi\) | ||||
−0.232357 | + | 0.972631i | \(0.574644\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1373.60 | 0.838179 | 0.419090 | − | 0.907945i | \(-0.362349\pi\) | ||||
0.419090 | + | 0.907945i | \(0.362349\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1038.01 | 0.619975 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 293.220 | 0.171471 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1229.60 | −0.704224 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 620.530 | 0.341180 | 0.170590 | − | 0.985342i | \(-0.445433\pi\) | ||||
0.170590 | + | 0.985342i | \(0.445433\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1939.26 | 1.04513 | 0.522567 | − | 0.852598i | \(-0.324975\pi\) | ||||
0.522567 | + | 0.852598i | \(0.324975\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 734.007 | 0.387849 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1340.74 | −0.694777 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −412.843 | −0.209863 | −0.104931 | − | 0.994479i | \(-0.533462\pi\) | ||||
−0.104931 | + | 0.994479i | \(0.533462\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1216.59 | −0.606803 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3907.44 | 1.87763 | 0.938817 | − | 0.344417i | \(-0.111923\pi\) | ||||
0.938817 | + | 0.344417i | \(0.111923\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −89.2203 | −0.0420957 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1286.41 | 0.596082 | 0.298041 | − | 0.954553i | \(-0.403667\pi\) | ||||
0.298041 | + | 0.954553i | \(0.403667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −152.766 | −0.0695340 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 45.4844 | 0.0203408 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1251.26 | −0.549892 | −0.274946 | − | 0.961460i | \(-0.588660\pi\) | ||||
−0.274946 | + | 0.961460i | \(0.588660\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −760.307 | −0.322871 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3623.51 | −1.51304 | −0.756520 | − | 0.653971i | \(-0.773102\pi\) | ||||
−0.756520 | + | 0.653971i | \(0.773102\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 181.727 | 0.0746280 | 0.0373140 | − | 0.999304i | \(-0.488120\pi\) | ||||
0.0373140 | + | 0.999304i | \(0.488120\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2253.65 | 0.910354 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 525.341 | 0.208777 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 528.916 | 0.206835 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1481.28 | −0.561160 | −0.280580 | − | 0.959831i | \(-0.590527\pi\) | ||||
−0.280580 | + | 0.959831i | \(0.590527\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −356.708 | −0.133038 | −0.0665192 | − | 0.997785i | \(-0.521189\pi\) | ||||
−0.0665192 | + | 0.997785i | \(0.521189\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −622.014 | −0.228428 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4890.53 | 1.76871 | 0.884355 | − | 0.466816i | \(-0.154599\pi\) | ||||
0.884355 | + | 0.466816i | \(0.154599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3542.85 | −1.26204 | −0.631020 | − | 0.775766i | \(-0.717364\pi\) | ||||
−0.631020 | + | 0.775766i | \(0.717364\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 34.9403 | 0.0122612 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −741.087 | −0.252486 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −956.248 | −0.321081 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 32.7755 | 0.0108475 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4289.50 | 1.39953 | 0.699765 | − | 0.714373i | \(-0.253288\pi\) | ||||
0.699765 | + | 0.714373i | \(0.253288\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2044.98 | −0.657840 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2161.25 | 0.685563 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2056.37 | −0.634505 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3687.42 | 1.12237 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5795.73 | −1.74041 | −0.870204 | − | 0.492692i | \(-0.836013\pi\) | ||||
−0.870204 | + | 0.492692i | \(0.836013\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −935.735 | −0.277255 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4104.04 | −1.19998 | −0.599989 | − | 0.800008i | \(-0.704828\pi\) | ||||
−0.599989 | + | 0.800008i | \(0.704828\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1296.83 | −0.374223 | −0.187111 | − | 0.982339i | \(-0.559913\pi\) | ||||
−0.187111 | + | 0.982339i | \(0.559913\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1478.33 | −0.415660 | −0.207830 | − | 0.978165i | \(-0.566640\pi\) | ||||
−0.207830 | + | 0.978165i | \(0.566640\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1586.70 | −0.440447 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.792206 | 0.000217128 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3776.92 | 1.02221 | 0.511106 | − | 0.859518i | \(-0.329236\pi\) | ||||
0.511106 | + | 0.859518i | \(0.329236\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3996.38 | −1.06817 | −0.534086 | − | 0.845430i | \(-0.679344\pi\) | ||||
−0.534086 | + | 0.845430i | \(0.679344\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 228.500 | 0.0588627 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1311.41 | −0.333764 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5423.58 | −1.36388 | −0.681939 | − | 0.731409i | \(-0.738863\pi\) | ||||
−0.681939 | + | 0.731409i | \(0.738863\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −689.060 | −0.171229 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1122.00 | −0.275539 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5964.22 | 1.44762 | 0.723809 | − | 0.690000i | \(-0.242389\pi\) | ||||
0.723809 | + | 0.690000i | \(0.242389\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2413.19 | −0.572309 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5166.01 | −1.21122 | −0.605608 | − | 0.795763i | \(-0.707070\pi\) | ||||
−0.605608 | + | 0.795763i | \(0.707070\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1859.67 | 0.431089 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 175.538 | 0.0402350 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3883.29 | 0.880180 | 0.440090 | − | 0.897954i | \(-0.354946\pi\) | ||||
0.440090 | + | 0.897954i | \(0.354946\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5527.65 | −1.23904 | −0.619522 | − | 0.784979i | \(-0.712674\pi\) | ||||
−0.619522 | + | 0.784979i | \(0.712674\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −674.278 | −0.147856 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2268.12 | 0.491979 | 0.245989 | − | 0.969273i | \(-0.420887\pi\) | ||||
0.245989 | + | 0.969273i | \(0.420887\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2631.31 | −0.564632 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 725.656 | 0.154053 | 0.0770267 | − | 0.997029i | \(-0.475457\pi\) | ||||
0.0770267 | + | 0.997029i | \(0.475457\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4237.00 | −0.889976 | −0.444988 | − | 0.895536i | \(-0.646792\pi\) | ||||
−0.444988 | + | 0.895536i | \(0.646792\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −69.5273 | −0.0144507 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1738.44 | 0.353845 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3840.27 | 0.773611 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4373.78 | −0.872079 | −0.436039 | − | 0.899928i | \(-0.643619\pi\) | ||||
−0.436039 | + | 0.899928i | \(0.643619\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1162.20 | 0.229376 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −175.103 | −0.0342104 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4803.89 | −0.929152 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3919.17 | 0.743070 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3444.92 | −0.646740 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4133.47 | −0.768435 | −0.384217 | − | 0.923243i | \(-0.625529\pi\) | ||||
−0.384217 | + | 0.923243i | \(0.625529\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2276.92 | −0.419190 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5063.23 | −0.923182 | −0.461591 | − | 0.887093i | \(-0.652721\pi\) | ||||
−0.461591 | + | 0.887093i | \(0.652721\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7411.56 | 1.33842 | 0.669211 | − | 0.743073i | \(-0.266632\pi\) | ||||
0.669211 | + | 0.743073i | \(0.266632\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6737.05 | −1.19366 | −0.596831 | − | 0.802367i | \(-0.703574\pi\) | ||||
−0.596831 | + | 0.802367i | \(0.703574\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1738.91 | −0.305205 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3787.54 | 0.658567 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 412.171 | 0.0710026 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4700.84 | −0.802326 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6316.58 | 1.06822 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11175.9 | −1.85585 | −0.927923 | − | 0.372771i | \(-0.878408\pi\) | ||||
−0.927923 | + | 0.372771i | \(0.878408\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1031.03 | 0.169669 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −53.4095 | −0.00871067 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9379.78 | 1.51617 | 0.758085 | − | 0.652156i | \(-0.226135\pi\) | ||||
0.758085 | + | 0.652156i | \(0.226135\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4607.29 | −0.738152 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1896.09 | −0.301111 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1461.72 | 0.228105 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5681.46 | −0.878953 | −0.439476 | − | 0.898254i | \(-0.644836\pi\) | ||||
−0.439476 | + | 0.898254i | \(0.644836\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −704.250 | −0.108016 | −0.0540080 | − | 0.998541i | \(-0.517200\pi\) | ||||
−0.0540080 | + | 0.998541i | \(0.517200\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1220.76 | −0.185639 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4284.96 | −0.646078 | −0.323039 | − | 0.946386i | \(-0.604705\pi\) | ||||
−0.323039 | + | 0.946386i | \(0.604705\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3125.95 | 0.467347 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4661.27 | −0.685272 | −0.342636 | − | 0.939468i | \(-0.611320\pi\) | ||||
−0.342636 | + | 0.939468i | \(0.611320\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6833.46 | −0.996276 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3866.82 | 0.559106 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3143.36 | 0.450770 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6935.30 | 0.986430 | 0.493215 | − | 0.869907i | \(-0.335822\pi\) | ||||
0.493215 | + | 0.869907i | \(0.335822\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1454.45 | −0.205191 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3081.10 | −0.427704 | −0.213852 | − | 0.976866i | \(-0.568601\pi\) | ||||
−0.213852 | + | 0.976866i | \(0.568601\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3150.03 | 0.433778 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12123.1 | −1.65616 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −941.827 | −0.127647 | −0.0638237 | − | 0.997961i | \(-0.520330\pi\) | ||||
−0.0638237 | + | 0.997961i | \(0.520330\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 72.5247 | 0.00975210 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 677.526 | 0.0903915 | 0.0451958 | − | 0.998978i | \(-0.485609\pi\) | ||||
0.0451958 | + | 0.998978i | \(0.485609\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4241.64 | 0.557144 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11865.4 | −1.54653 | −0.773266 | − | 0.634082i | \(-0.781378\pi\) | ||||
−0.773266 | + | 0.634082i | \(0.781378\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8665.34 | −1.12078 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4744.58 | 0.608989 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.21096 | −0.000154254 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5140.76 | −0.649893 | −0.324947 | − | 0.945732i | \(-0.605346\pi\) | ||||
−0.324947 | + | 0.945732i | \(0.605346\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12382.0 | −1.54196 | −0.770981 | − | 0.636858i | \(-0.780234\pi\) | ||||
−0.770981 | + | 0.636858i | \(0.780234\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13218.9 | −1.63394 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 371.449 | 0.0455739 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 742.944 | 0.0904824 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15875.6 | −1.91931 | −0.959657 | − | 0.281173i | \(-0.909277\pi\) | ||||
−0.959657 | + | 0.281173i | \(0.909277\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2235.56 | 0.268302 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2004.62 | 0.237115 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4120.79 | −0.483923 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16111.9 | 1.87857 | 0.939283 | − | 0.343145i | \(-0.111492\pi\) | ||||
0.939283 | + | 0.343145i | \(0.111492\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8691.58 | 1.00618 | 0.503090 | − | 0.864234i | \(-0.332197\pi\) | ||||
0.503090 | + | 0.864234i | \(0.332197\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3114.04 | −0.357943 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8479.46 | −0.967798 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −879.661 | −0.0989987 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4195.10 | 0.468842 | 0.234421 | − | 0.972135i | \(-0.424681\pi\) | ||||
0.234421 | + | 0.972135i | \(0.424681\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5426.54 | −0.602270 | −0.301135 | − | 0.953582i | \(-0.597365\pi\) | ||||
−0.301135 | + | 0.953582i | \(0.597365\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3688.79 | 0.406584 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −536.968 | −0.0587795 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3771.24 | 0.410003 | 0.205002 | − | 0.978762i | \(-0.434280\pi\) | ||||
0.205002 | + | 0.978762i | \(0.434280\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5930.30 | 0.636020 | 0.318010 | − | 0.948087i | \(-0.396985\pi\) | ||||
0.318010 | + | 0.948087i | \(0.396985\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −268.326 | −0.0285840 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1861.59 | −0.196980 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −529.065 | −0.0556083 | −0.0278041 | − | 0.999613i | \(-0.508851\pi\) | ||||
−0.0278041 | + | 0.999613i | \(0.508851\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1048.05 | −0.109426 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5817.79 | −0.603408 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10057.2 | 1.02944 | 0.514721 | − | 0.857358i | \(-0.327896\pi\) | ||||
0.514721 | + | 0.857358i | \(0.327896\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2202.02 | −0.223925 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5010.31 | −0.506190 | −0.253095 | − | 0.967441i | \(-0.581448\pi\) | ||||
−0.253095 | + | 0.967441i | \(0.581448\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7124.38 | 0.715114 | 0.357557 | − | 0.933891i | \(-0.383610\pi\) | ||||
0.357557 | + | 0.933891i | \(0.383610\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4022.21 | 0.401130 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7501.44 | −0.743309 | −0.371654 | − | 0.928371i | \(-0.621209\pi\) | ||||
−0.371654 | + | 0.928371i | \(0.621209\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1238.53 | 0.121164 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3056.47 | 0.297118 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −525.449 | −0.0507563 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3649.76 | 0.350338 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8173.80 | 0.779688 | 0.389844 | − | 0.920881i | \(-0.372529\pi\) | ||||
0.389844 | + | 0.920881i | \(0.372529\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5179.55 | 0.490992 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5870.22 | −0.549594 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11968.8 | 1.11367 | 0.556835 | − | 0.830623i | \(-0.312015\pi\) | ||||
0.556835 | + | 0.830623i | \(0.312015\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11722.3 | −1.08405 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2079.96 | −0.191176 | −0.0955878 | − | 0.995421i | \(-0.530473\pi\) | ||||
−0.0955878 | + | 0.995421i | \(0.530473\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21867.9 | −1.99773 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 267.661 | 0.0243040 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12834.4 | −1.15140 | −0.575699 | − | 0.817662i | \(-0.695270\pi\) | ||||
−0.575699 | + | 0.817662i | \(0.695270\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3859.24 | −0.344148 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16808.8 | −1.48999 | −0.744997 | − | 0.667068i | \(-0.767549\pi\) | ||||
−0.744997 | + | 0.667068i | \(0.767549\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5990.82 | −0.527897 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 458.299 | 0.0401455 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4270.26 | −0.371859 | −0.185929 | − | 0.982563i | \(-0.559530\pi\) | ||||
−0.185929 | + | 0.982563i | \(0.559530\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −136.453 | −0.0117438 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3480.50 | 0.297804 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2243.93 | −0.190886 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3753.77 | 0.317480 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15283.3 | 1.28517 | 0.642584 | − | 0.766215i | \(-0.277862\pi\) | ||||
0.642584 | + | 0.766215i | \(0.277862\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4499.33 | 0.376180 | 0.188090 | − | 0.982152i | \(-0.439770\pi\) | ||||
0.188090 | + | 0.982152i | \(0.439770\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23844.4 | −1.97093 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −877.984 | −0.0721611 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2280.92 | 0.186410 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7306.69 | −0.593785 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5789.62 | −0.467864 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10870.5 | 0.873554 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3970.82 | 0.315561 | 0.157781 | − | 0.987474i | \(-0.449566\pi\) | ||||
0.157781 | + | 0.987474i | \(0.449566\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −545.181 | −0.0430865 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9655.50 | −0.758892 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2703.90 | 0.211353 | 0.105677 | − | 0.994401i | \(-0.466299\pi\) | ||||
0.105677 | + | 0.994401i | \(0.466299\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6760.96 | −0.525593 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1355.09 | −0.104771 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1576.02 | −0.120538 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 790.824 | 0.0601585 | 0.0300793 | − | 0.999548i | \(-0.490424\pi\) | ||||
0.0300793 | + | 0.999548i | \(0.490424\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21308.7 | 1.61227 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1586.75 | −0.119416 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7517.15 | −0.562718 | −0.281359 | − | 0.959603i | \(-0.590785\pi\) | ||||
−0.281359 | + | 0.959603i | \(0.590785\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7042.68 | 0.524403 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13945.4 | 1.02746 | 0.513728 | − | 0.857953i | \(-0.328264\pi\) | ||||
0.513728 | + | 0.857953i | \(0.328264\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2118.49 | 0.155265 | 0.0776323 | − | 0.996982i | \(-0.475264\pi\) | ||||
0.0776323 | + | 0.996982i | \(0.475264\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4443.84 | 0.323986 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11046.8 | 0.801192 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22857.7 | 1.64918 | 0.824592 | − | 0.565728i | \(-0.191405\pi\) | ||||
0.824592 | + | 0.565728i | \(0.191405\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1070.12 | 0.0768098 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2629.97 | 0.186831 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1866.04 | 0.131883 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23955.3 | −1.68440 | −0.842199 | − | 0.539167i | \(-0.818739\pi\) | ||||
−0.842199 | + | 0.539167i | \(0.818739\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1477.57 | −0.103366 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14671.6 | −1.02116 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10778.0 | −0.746373 | −0.373186 | − | 0.927756i | \(-0.621735\pi\) | ||||
−0.373186 | + | 0.927756i | \(0.621735\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10628.6 | 0.728639 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7597.58 | −0.518245 | −0.259122 | − | 0.965845i | \(-0.583433\pi\) | ||||
−0.259122 | + | 0.965845i | \(0.583433\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19956.1 | 1.35445 | 0.677225 | − | 0.735776i | \(-0.263182\pi\) | ||||
0.677225 | + | 0.735776i | \(0.263182\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −104.821 | −0.00707899 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5910.81 | −0.397204 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 236.311 | 0.0158016 | 0.00790079 | − | 0.999969i | \(-0.497485\pi\) | ||||
0.00790079 | + | 0.999969i | \(0.497485\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15644.0 | −1.03582 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26414.9 | 1.74044 | 0.870219 | − | 0.492664i | \(-0.163977\pi\) | ||||
0.870219 | + | 0.492664i | \(0.163977\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2223.26 | 0.145773 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18473.6 | 1.20538 | 0.602689 | − | 0.797976i | \(-0.294096\pi\) | ||||
0.602689 | + | 0.797976i | \(0.294096\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16047.9 | −1.04204 | −0.521018 | − | 0.853546i | \(-0.674448\pi\) | ||||
−0.521018 | + | 0.853546i | \(0.674448\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2868.74 | 0.185376 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8181.20 | 0.523597 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −98.3264 | −0.00626280 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9342.97 | 0.592255 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15065.7 | 0.950487 | 0.475243 | − | 0.879854i | \(-0.342360\pi\) | ||||
0.475243 | + | 0.879854i | \(0.342360\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12868.5 | −0.808020 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −110.861 | −0.00692816 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6134.95 | 0.379804 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31198.4 | −1.92241 | −0.961203 | − | 0.275842i | \(-0.911043\pi\) | ||||
−0.961203 | + | 0.275842i | \(0.911043\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12497.9 | 0.766517 | 0.383259 | − | 0.923641i | \(-0.374802\pi\) | ||||
0.383259 | + | 0.923641i | \(0.374802\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6483.75 | −0.395810 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9929.72 | 0.603366 | 0.301683 | − | 0.953408i | \(-0.402452\pi\) | ||||
0.301683 | + | 0.953408i | \(0.402452\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1643.60 | 0.0994099 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8145.58 | −0.488149 | −0.244075 | − | 0.969756i | \(-0.578484\pi\) | ||||
−0.244075 | + | 0.969756i | \(0.578484\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7252.55 | −0.432642 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6169.11 | 0.366332 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16975.8 | 1.00347 | 0.501733 | − | 0.865022i | \(-0.332696\pi\) | ||||
0.501733 | + | 0.865022i | \(0.332696\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20637.8 | 1.21440 | 0.607199 | − | 0.794550i | \(-0.292293\pi\) | ||||
0.607199 | + | 0.794550i | \(0.292293\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11062.3 | −0.647999 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28489.0 | 1.65382 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17387.2 | 1.00482 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4871.86 | −0.280292 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2150.29 | −0.123161 | −0.0615807 | − | 0.998102i | \(-0.519614\pi\) | ||||
−0.0615807 | + | 0.998102i | \(0.519614\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2807.21 | 0.160073 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27783.4 | −1.57726 | −0.788628 | − | 0.614871i | \(-0.789208\pi\) | ||||
−0.788628 | + | 0.614871i | \(0.789208\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12312.1 | 0.692807 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18181.8 | −1.01860 | −0.509302 | − | 0.860588i | \(-0.670096\pi\) | ||||
−0.509302 | + | 0.860588i | \(0.670096\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3417.27 | −0.190609 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3890.49 | 0.216058 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18335.3 | 1.01381 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23935.1 | −1.31771 | −0.658853 | − | 0.752272i | \(-0.728958\pi\) | ||||
−0.658853 | + | 0.752272i | \(0.728958\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6299.02 | 0.343792 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13179.9 | −0.716249 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4435.00 | 0.239982 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20627.2 | −1.11138 | −0.555691 | − | 0.831389i | \(-0.687546\pi\) | ||||
−0.555691 | + | 0.831389i | \(0.687546\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 578.958 | 0.0310609 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4760.10 | 0.254292 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6584.64 | −0.348789 | −0.174394 | − | 0.984676i | \(-0.555797\pi\) | ||||
−0.174394 | + | 0.984676i | \(0.555797\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.37662 | −0.000125359 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31064.0 | 1.63163 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1344.65 | 0.0703313 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11330.8 | −0.590174 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −170.886 | −0.00886366 | −0.00443183 | − | 0.999990i | \(-0.501411\pi\) | ||||
−0.00443183 | + | 0.999990i | \(0.501411\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11989.1 | 0.616710 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 27877.8 | 1.42808 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11127.5 | 0.567671 | 0.283836 | − | 0.958873i | \(-0.408393\pi\) | ||||
0.283836 | + | 0.958873i | \(0.408393\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38437.0 | 1.94479 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22575.9 | −1.13760 | −0.568800 | − | 0.822476i | \(-0.692592\pi\) | ||||
−0.568800 | + | 0.822476i | \(0.692592\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −75.5325 | −0.00377513 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22936.4 | 1.14172 | 0.570860 | − | 0.821048i | \(-0.306610\pi\) | ||||
0.570860 | + | 0.821048i | \(0.306610\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −685.499 | −0.0339844 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16973.4 | −0.838081 | −0.419041 | − | 0.907967i | \(-0.637634\pi\) | ||||
−0.419041 | + | 0.907967i | \(0.637634\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2845.62 | 0.139940 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3934.23 | 0.192699 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21197.9 | 1.02999 | 0.514994 | − | 0.857194i | \(-0.327794\pi\) | ||||
0.514994 | + | 0.857194i | \(0.327794\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16270.8 | 0.787436 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8893.05 | 0.428677 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7962.24 | −0.382289 | −0.191144 | − | 0.981562i | \(-0.561220\pi\) | ||||
−0.191144 | + | 0.981562i | \(0.561220\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2067.18 | 0.0988588 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26856.2 | 1.27928 | 0.639642 | − | 0.768673i | \(-0.279083\pi\) | ||||
0.639642 | + | 0.768673i | \(0.279083\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3366.00 | 0.159082 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11458.6 | 0.539436 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12183.6 | −0.571331 | −0.285666 | − | 0.958329i | \(-0.592215\pi\) | ||||
−0.285666 | + | 0.958329i | \(0.592215\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17892.7 | −0.835783 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17455.2 | −0.812187 | −0.406093 | − | 0.913832i | \(-0.633109\pi\) | ||||
−0.406093 | + | 0.913832i | \(0.633109\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30397.6 | 1.40892 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −816.724 | −0.0375638 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4420.76 | 0.202545 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7239.56 | 0.330423 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1893.21 | −0.0860785 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30981.0 | −1.40324 | −0.701622 | − | 0.712549i | \(-0.747540\pi\) | ||||
−0.701622 | + | 0.712549i | \(0.747540\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15498.0 | 0.699296 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33964.9 | −1.52097 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5579.01 | −0.248889 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10517.6 | −0.467446 | −0.233723 | − | 0.972303i | \(-0.575091\pi\) | ||||
−0.233723 | + | 0.972303i | \(0.575091\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28218.8 | −1.24945 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −526.614 | −0.0232297 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4445.38 | 0.195360 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11649.9 | −0.508172 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41778.4 | −1.81564 | −0.907819 | − | 0.419361i | \(-0.862254\pi\) | ||||
−0.907819 | + | 0.419361i | \(0.862254\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12935.4 | 0.560079 | 0.280039 | − | 0.959988i | \(-0.409652\pi\) | ||||
0.280039 | + | 0.959988i | \(0.409652\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16583.0 | 0.715363 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17918.7 | 0.770140 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2381.83 | 0.101995 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14499.2 | −0.616354 | −0.308177 | − | 0.951329i | \(-0.599719\pi\) | ||||
−0.308177 | + | 0.951329i | \(0.599719\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11977.1 | 0.507287 | 0.253643 | − | 0.967298i | \(-0.418371\pi\) | ||||
0.253643 | + | 0.967298i | \(0.418371\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2022.84 | 0.0853649 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27613.5 | −1.16108 | −0.580541 | − | 0.814231i | \(-0.697159\pi\) | ||||
−0.580541 | + | 0.814231i | \(0.697159\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −677.836 | −0.0283983 | −0.0141992 | − | 0.999899i | \(-0.504520\pi\) | ||||
−0.0141992 | + | 0.999899i | \(0.504520\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6804.36 | −0.284044 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5899.22 | 0.244492 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7893.92 | 0.325990 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42209.6 | −1.73687 | −0.868436 | − | 0.495801i | \(-0.834874\pi\) | ||||
−0.868436 | + | 0.495801i | \(0.834874\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47505.8 | 1.94784 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2176.97 | −0.0889428 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −700.553 | −0.0285204 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12711.0 | 0.513828 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12171.8 | −0.490299 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2796.45 | −0.112249 | −0.0561247 | − | 0.998424i | \(-0.517874\pi\) | ||||
−0.0561247 | + | 0.998424i | \(0.517874\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 208.582 | 0.00834310 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23181.1 | 0.923979 | 0.461989 | − | 0.886886i | \(-0.347136\pi\) | ||||
0.461989 | + | 0.886886i | \(0.347136\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11897.5 | 0.472569 | 0.236285 | − | 0.971684i | \(-0.424070\pi\) | ||||
0.236285 | + | 0.971684i | \(0.424070\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29815.9 | 1.17607 | 0.588033 | − | 0.808837i | \(-0.299902\pi\) | ||||
0.588033 | + | 0.808837i | \(0.299902\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5737.99 | −0.225546 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5215.31 | −0.204292 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.71256 | −6.68523e−5 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −526.587 | −0.0204853 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11520.8 | −0.446644 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10338.8 | −0.398082 | −0.199041 | − | 0.979991i | \(-0.563783\pi\) | ||||
−0.199041 | + | 0.979991i | \(0.563783\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13121.3 | 0.503495 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24140.2 | 0.923160 | 0.461580 | − | 0.887099i | \(-0.347283\pi\) | ||||
0.461580 | + | 0.887099i | \(0.347283\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12997.6 | −0.495361 | −0.247681 | − | 0.968842i | \(-0.579668\pi\) | ||||
−0.247681 | + | 0.968842i | \(0.579668\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3486.61 | −0.132430 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45266.6 | −1.71353 | −0.856766 | − | 0.515705i | \(-0.827530\pi\) | ||||
−0.856766 | + | 0.515705i | \(0.827530\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 525.308 | 0.0197514 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1748.64 | −0.0655276 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16616.7 | −0.620596 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14411.7 | 0.536446 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 78393.1 | 2.90829 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33073.5 | 1.22290 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 833.361 | 0.0306098 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27766.5 | 1.01651 | 0.508253 | − | 0.861208i | \(-0.330292\pi\) | ||||
0.508253 | + | 0.861208i | \(0.330292\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11757.5 | −0.429012 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18531.2 | −0.673948 | −0.336974 | − | 0.941514i | \(-0.609403\pi\) | ||||
−0.336974 | + | 0.941514i | \(0.609403\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2834.96 | 0.102764 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10334.8 | 0.373395 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18093.4 | 0.649452 | 0.324726 | − | 0.945808i | \(-0.394728\pi\) | ||||
0.324726 | + | 0.945808i | \(0.394728\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12400.4 | 0.443656 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30820.1 | 1.09908 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11910.7 | −0.423375 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6830.77 | 0.242019 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10622.5 | 0.375149 | 0.187574 | − | 0.982250i | \(-0.439937\pi\) | ||||
0.187574 | + | 0.982250i | \(0.439937\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15189.7 | 0.532999 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2425.50 | 0.0848366 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16057.6 | 0.559851 | 0.279925 | − | 0.960022i | \(-0.409690\pi\) | ||||
0.279925 | + | 0.960022i | \(0.409690\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22234.7 | −0.772738 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 55153.3 | 1.91068 | 0.955338 | − | 0.295516i | \(-0.0954915\pi\) | ||||
0.955338 | + | 0.295516i | \(0.0954915\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17170.5 | 0.592947 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18785.7 | −0.644619 | −0.322309 | − | 0.946634i | \(-0.604459\pi\) | ||||
−0.322309 | + | 0.946634i | \(0.604459\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30991.7 | 1.06010 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20211.2 | 0.689161 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36499.4 | −1.24064 | −0.620321 | − | 0.784348i | \(-0.712998\pi\) | ||||
−0.620321 | + | 0.784348i | \(0.712998\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6792.83 | −0.230168 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5216.74 | 0.176210 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55687.8 | 1.86928 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11362.6 | −0.380224 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1635.79 | −0.0545677 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26059.9 | −0.866627 | −0.433314 | − | 0.901243i | \(-0.642656\pi\) | ||||
−0.433314 | + | 0.901243i | \(0.642656\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1236.51 | −0.0409934 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21689.0 | −0.716820 | −0.358410 | − | 0.933564i | \(-0.616681\pi\) | ||||
−0.358410 | + | 0.933564i | \(0.616681\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14102.5 | 0.463223 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2119.19 | 0.0693950 | 0.0346975 | − | 0.999398i | \(-0.488953\pi\) | ||||
0.0346975 | + | 0.999398i | \(0.488953\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −379.471 | −0.0123881 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18949.7 | −0.616737 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48504.1 | 1.57380 | 0.786898 | − | 0.617083i | \(-0.211686\pi\) | ||||
0.786898 | + | 0.617083i | \(0.211686\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22426.9 | 0.725463 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −50074.8 | −1.61000 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2043.84 | −0.0655144 | −0.0327572 | − | 0.999463i | \(-0.510429\pi\) | ||||
−0.0327572 | + | 0.999463i | \(0.510429\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33527.8 | 1.07147 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16246.8 | −0.517645 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26738.9 | −0.849378 | −0.424689 | − | 0.905339i | \(-0.639617\pi\) | ||||
−0.424689 | + | 0.905339i | \(0.639617\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3093.08 | −0.0979586 |
(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 | 2352.4.a.bu.1.1 | 2 | ||
4.3 | odd | 2 | 294.4.a.o.1.1 | yes | 2 | ||
7.6 | odd | 2 | 2352.4.a.bw.1.2 | 2 | |||
12.11 | even | 2 | 882.4.a.t.1.2 | 2 | |||
28.3 | even | 6 | 294.4.e.m.79.1 | 4 | |||
28.11 | odd | 6 | 294.4.e.k.79.2 | 4 | |||
28.19 | even | 6 | 294.4.e.m.67.1 | 4 | |||
28.23 | odd | 6 | 294.4.e.k.67.2 | 4 | |||
28.27 | even | 2 | 294.4.a.l.1.2 | ✓ | 2 | ||
84.11 | even | 6 | 882.4.g.bk.667.1 | 4 | |||
84.23 | even | 6 | 882.4.g.bk.361.1 | 4 | |||
84.47 | odd | 6 | 882.4.g.be.361.2 | 4 | |||
84.59 | odd | 6 | 882.4.g.be.667.2 | 4 | |||
84.83 | odd | 2 | 882.4.a.bb.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
294.4.a.l.1.2 | ✓ | 2 | 28.27 | even | 2 | ||
294.4.a.o.1.1 | yes | 2 | 4.3 | odd | 2 | ||
294.4.e.k.67.2 | 4 | 28.23 | odd | 6 | |||
294.4.e.k.79.2 | 4 | 28.11 | odd | 6 | |||
294.4.e.m.67.1 | 4 | 28.19 | even | 6 | |||
294.4.e.m.79.1 | 4 | 28.3 | even | 6 | |||
882.4.a.t.1.2 | 2 | 12.11 | even | 2 | |||
882.4.a.bb.1.1 | 2 | 84.83 | odd | 2 | |||
882.4.g.be.361.2 | 4 | 84.47 | odd | 6 | |||
882.4.g.be.667.2 | 4 | 84.59 | odd | 6 | |||
882.4.g.bk.361.1 | 4 | 84.23 | even | 6 | |||
882.4.g.bk.667.1 | 4 | 84.11 | even | 6 | |||
2352.4.a.bu.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2352.4.a.bw.1.2 | 2 | 7.6 | odd | 2 |