Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,5,Mod(197,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.197");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(91.1723074400\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-53})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 52x^{2} + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.2 | ||
Root | \(5.14782 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.197 |
Dual form | 882.5.b.c.197.3 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.82843i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | 29.1204i | 1.16482i | 0.812896 | + | 0.582409i | \(0.197890\pi\) | ||||
−0.812896 | + | 0.582409i | \(0.802110\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 22.6274i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 82.3650 | 0.823650 | ||||||||
\(11\) | 1.41421i | 0.0116877i | 0.999983 | + | 0.00584386i | \(0.00186017\pi\) | ||||
−0.999983 | + | 0.00584386i | \(0.998140\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −82.3650 | −0.487367 | −0.243684 | − | 0.969855i | \(-0.578356\pi\) | ||||
−0.243684 | + | 0.969855i | \(0.578356\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 262.084i | 0.906865i | 0.891291 | + | 0.453432i | \(0.149801\pi\) | ||||
−0.891291 | + | 0.453432i | \(0.850199\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −453.008 | −1.25487 | −0.627435 | − | 0.778669i | \(-0.715895\pi\) | ||||
−0.627435 | + | 0.778669i | \(0.715895\pi\) | |||||||
\(20\) | − 232.964i | − 0.582409i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000 | 0.00826446 | ||||||||
\(23\) | − 63.6396i | − 0.120302i | −0.998189 | − | 0.0601509i | \(-0.980842\pi\) | ||||
0.998189 | − | 0.0601509i | \(-0.0191582\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −223.000 | −0.356800 | ||||||||
\(26\) | 232.964i | 0.344621i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 502.046i | 0.596963i | 0.954415 | + | 0.298481i | \(0.0964801\pi\) | ||||
−0.954415 | + | 0.298481i | \(0.903520\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1276.66 | −1.32847 | −0.664234 | − | 0.747525i | \(-0.731242\pi\) | ||||
−0.664234 | + | 0.747525i | \(0.731242\pi\) | |||||||
\(32\) | − 181.019i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 741.285 | 0.641250 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1560.00 | 1.13952 | 0.569759 | − | 0.821812i | \(-0.307037\pi\) | ||||
0.569759 | + | 0.821812i | \(0.307037\pi\) | |||||||
\(38\) | 1281.30i | 0.887326i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −658.920 | −0.411825 | ||||||||
\(41\) | − 1310.42i | − 0.779548i | −0.920911 | − | 0.389774i | \(-0.872553\pi\) | ||||
0.920911 | − | 0.389774i | \(-0.127447\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 328.000 | 0.177393 | 0.0886966 | − | 0.996059i | \(-0.471730\pi\) | ||||
0.0886966 | + | 0.996059i | \(0.471730\pi\) | |||||||
\(44\) | − 11.3137i | − 0.00584386i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −180.000 | −0.0850662 | ||||||||
\(47\) | 4135.10i | 1.87193i | 0.352088 | + | 0.935967i | \(0.385472\pi\) | ||||
−0.352088 | + | 0.935967i | \(0.614528\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 630.739i | 0.252296i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 658.920 | 0.243684 | ||||||||
\(53\) | − 4012.12i | − 1.42831i | −0.699987 | − | 0.714155i | \(-0.746811\pi\) | ||||
0.699987 | − | 0.714155i | \(-0.253189\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −41.1825 | −0.0136141 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1420.00 | 0.422117 | ||||||||
\(59\) | − 757.131i | − 0.217504i | −0.994069 | − | 0.108752i | \(-0.965315\pi\) | ||||
0.994069 | − | 0.108752i | \(-0.0346854\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1194.29 | 0.320960 | 0.160480 | − | 0.987039i | \(-0.448696\pi\) | ||||
0.160480 | + | 0.987039i | \(0.448696\pi\) | |||||||
\(62\) | 3610.93i | 0.939369i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | − 2398.51i | − 0.567694i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1130.00 | −0.251726 | −0.125863 | − | 0.992048i | \(-0.540170\pi\) | ||||
−0.125863 | + | 0.992048i | \(0.540170\pi\) | |||||||
\(68\) | − 2096.67i | − 0.453432i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 422.850i | − 0.0838821i | −0.999120 | − | 0.0419411i | \(-0.986646\pi\) | ||||
0.999120 | − | 0.0419411i | \(-0.0133542\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3006.32 | −0.564144 | −0.282072 | − | 0.959393i | \(-0.591022\pi\) | ||||
−0.282072 | + | 0.959393i | \(0.591022\pi\) | |||||||
\(74\) | − 4412.35i | − 0.805761i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3624.06 | 0.627435 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8650.00 | 1.38600 | 0.692998 | − | 0.720940i | \(-0.256289\pi\) | ||||
0.692998 | + | 0.720940i | \(0.256289\pi\) | |||||||
\(80\) | 1863.71i | 0.291204i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3706.43 | −0.551224 | ||||||||
\(83\) | − 2970.28i | − 0.431163i | −0.976486 | − | 0.215582i | \(-0.930835\pi\) | ||||
0.976486 | − | 0.215582i | \(-0.0691648\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7632.00 | −1.05633 | ||||||||
\(86\) | − 927.724i | − 0.125436i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −32.0000 | −0.00413223 | ||||||||
\(89\) | − 13308.0i | − 1.68010i | −0.542512 | − | 0.840048i | \(-0.682527\pi\) | ||||
0.542512 | − | 0.840048i | \(-0.317473\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 509.117i | 0.0601509i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11695.8 | 1.32366 | ||||||||
\(95\) | − 13191.8i | − 1.46169i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13137.2 | −1.39624 | −0.698120 | − | 0.715981i | \(-0.745980\pi\) | ||||
−0.698120 | + | 0.715981i | \(0.745980\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1784.00 | 0.178400 | ||||||||
\(101\) | − 12026.7i | − 1.17898i | −0.807777 | − | 0.589488i | \(-0.799329\pi\) | ||||
0.807777 | − | 0.589488i | \(-0.200671\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10913.4 | 1.02869 | 0.514345 | − | 0.857583i | \(-0.328035\pi\) | ||||
0.514345 | + | 0.857583i | \(0.328035\pi\) | |||||||
\(104\) | − 1863.71i | − 0.172310i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11348.0 | −1.00997 | ||||||||
\(107\) | − 12703.9i | − 1.10961i | −0.831982 | − | 0.554803i | \(-0.812794\pi\) | ||||
0.831982 | − | 0.554803i | \(-0.187206\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9752.00 | −0.820806 | −0.410403 | − | 0.911904i | \(-0.634612\pi\) | ||||
−0.410403 | + | 0.911904i | \(0.634612\pi\) | |||||||
\(110\) | 116.482i | 0.00962659i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 11303.8i | − 0.885254i | −0.896706 | − | 0.442627i | \(-0.854047\pi\) | ||||
0.896706 | − | 0.442627i | \(-0.145953\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1853.21 | 0.140130 | ||||||||
\(116\) | − 4016.37i | − 0.298481i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2141.49 | −0.153799 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14639.0 | 0.999863 | ||||||||
\(122\) | − 3377.97i | − 0.226953i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10213.3 | 0.664234 | ||||||||
\(125\) | 11706.4i | 0.749211i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −30922.0 | −1.91717 | −0.958584 | − | 0.284810i | \(-0.908069\pi\) | ||||
−0.958584 | + | 0.284810i | \(0.908069\pi\) | |||||||
\(128\) | 1448.15i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6784.00 | −0.401420 | ||||||||
\(131\) | 5940.57i | 0.346167i | 0.984907 | + | 0.173083i | \(0.0553730\pi\) | ||||
−0.984907 | + | 0.173083i | \(0.944627\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3196.12i | 0.177997i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5930.28 | −0.320625 | ||||||||
\(137\) | − 18929.2i | − 1.00854i | −0.863547 | − | 0.504269i | \(-0.831762\pi\) | ||||
0.863547 | − | 0.504269i | \(-0.168238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10872.2 | 0.562713 | 0.281357 | − | 0.959603i | \(-0.409216\pi\) | ||||
0.281357 | + | 0.959603i | \(0.409216\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1196.00 | −0.0593136 | ||||||||
\(143\) | − 116.482i | − 0.00569621i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14619.8 | −0.695353 | ||||||||
\(146\) | 8503.17i | 0.398910i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12480.0 | −0.569759 | ||||||||
\(149\) | − 7448.66i | − 0.335510i | −0.985829 | − | 0.167755i | \(-0.946348\pi\) | ||||
0.985829 | − | 0.167755i | \(-0.0536518\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −35792.0 | −1.56976 | −0.784878 | − | 0.619651i | \(-0.787274\pi\) | ||||
−0.784878 | + | 0.619651i | \(0.787274\pi\) | |||||||
\(152\) | − 10250.4i | − 0.443663i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 37176.8i | − 1.54742i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2676.86 | −0.108599 | −0.0542996 | − | 0.998525i | \(-0.517293\pi\) | ||||
−0.0542996 | + | 0.998525i | \(0.517293\pi\) | |||||||
\(158\) | − 24465.9i | − 0.980047i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5271.36 | 0.205913 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19254.0 | 0.724679 | 0.362340 | − | 0.932046i | \(-0.381978\pi\) | ||||
0.362340 | + | 0.932046i | \(0.381978\pi\) | |||||||
\(164\) | 10483.4i | 0.389774i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8401.23 | −0.304879 | ||||||||
\(167\) | − 12521.8i | − 0.448987i | −0.974476 | − | 0.224493i | \(-0.927927\pi\) | ||||
0.974476 | − | 0.224493i | \(-0.0720727\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −21777.0 | −0.762473 | ||||||||
\(170\) | 21586.6i | 0.746940i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2624.00 | −0.0886966 | ||||||||
\(173\) | 23558.4i | 0.787144i | 0.919294 | + | 0.393572i | \(0.128761\pi\) | ||||
−0.919294 | + | 0.393572i | \(0.871239\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 90.5097i | 0.00292193i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −37640.8 | −1.18801 | ||||||||
\(179\) | − 25511.0i | − 0.796199i | −0.917342 | − | 0.398099i | \(-0.869670\pi\) | ||||
0.917342 | − | 0.398099i | \(-0.130330\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 38876.3 | 1.18666 | 0.593332 | − | 0.804958i | \(-0.297812\pi\) | ||||
0.593332 | + | 0.804958i | \(0.297812\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1440.00 | 0.0425331 | ||||||||
\(185\) | 45427.9i | 1.32733i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −370.643 | −0.0105992 | ||||||||
\(188\) | − 33080.8i | − 0.935967i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −37312.0 | −1.03357 | ||||||||
\(191\) | 34352.7i | 0.941659i | 0.882224 | + | 0.470829i | \(0.156045\pi\) | ||||
−0.882224 | + | 0.470829i | \(0.843955\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −65824.0 | −1.76713 | −0.883567 | − | 0.468304i | \(-0.844865\pi\) | ||||
−0.883567 | + | 0.468304i | \(0.844865\pi\) | |||||||
\(194\) | 37157.7i | 0.987291i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 64831.8i | − 1.67053i | −0.549844 | − | 0.835267i | \(-0.685313\pi\) | ||||
0.549844 | − | 0.835267i | \(-0.314687\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 46536.2 | 1.17513 | 0.587564 | − | 0.809178i | \(-0.300087\pi\) | ||||
0.587564 | + | 0.809178i | \(0.300087\pi\) | |||||||
\(200\) | − 5045.91i | − 0.126148i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −34016.8 | −0.833662 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 38160.0 | 0.908031 | ||||||||
\(206\) | − 30867.7i | − 0.727393i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5271.36 | −0.121842 | ||||||||
\(209\) | − 640.650i | − 0.0146666i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8504.00 | 0.191011 | 0.0955055 | − | 0.995429i | \(-0.469553\pi\) | ||||
0.0955055 | + | 0.995429i | \(0.469553\pi\) | |||||||
\(212\) | 32097.0i | 0.714155i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −35932.0 | −0.784610 | ||||||||
\(215\) | 9551.50i | 0.206631i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 27582.8i | 0.580398i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 329.460 | 0.00680703 | ||||||||
\(221\) | − 21586.6i | − 0.441976i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −56749.5 | −1.14118 | −0.570588 | − | 0.821237i | \(-0.693285\pi\) | ||||
−0.570588 | + | 0.821237i | \(0.693285\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −31972.0 | −0.625969 | ||||||||
\(227\) | 55969.5i | 1.08617i | 0.839676 | + | 0.543087i | \(0.182745\pi\) | ||||
−0.839676 | + | 0.543087i | \(0.817255\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −84588.9 | −1.61303 | −0.806515 | − | 0.591214i | \(-0.798649\pi\) | ||||
−0.806515 | + | 0.591214i | \(0.798649\pi\) | |||||||
\(230\) | − 5241.68i | − 0.0990866i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11360.0 | −0.211058 | ||||||||
\(233\) | 35469.9i | 0.653353i | 0.945136 | + | 0.326677i | \(0.105929\pi\) | ||||
−0.945136 | + | 0.326677i | \(0.894071\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −120416. | −2.18046 | ||||||||
\(236\) | 6057.05i | 0.108752i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 57330.8i | − 1.00367i | −0.864963 | − | 0.501836i | \(-0.832658\pi\) | ||||
0.864963 | − | 0.501836i | \(-0.167342\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −85783.2 | −1.47696 | −0.738479 | − | 0.674277i | \(-0.764456\pi\) | ||||
−0.738479 | + | 0.674277i | \(0.764456\pi\) | |||||||
\(242\) | − 41405.3i | − 0.707010i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9554.34 | −0.160480 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 37312.0 | 0.611582 | ||||||||
\(248\) | − 28887.5i | − 0.469685i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 33110.7 | 0.529772 | ||||||||
\(251\) | 25276.5i | 0.401209i | 0.979672 | + | 0.200604i | \(0.0642905\pi\) | ||||
−0.979672 | + | 0.200604i | \(0.935709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 90.0000 | 0.00140605 | ||||||||
\(254\) | 87460.6i | 1.35564i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | − 87215.7i | − 1.32047i | −0.751059 | − | 0.660235i | \(-0.770457\pi\) | ||||
0.751059 | − | 0.660235i | \(-0.229543\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 19188.0i | 0.283847i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16802.5 | 0.244777 | ||||||||
\(263\) | 60747.5i | 0.878248i | 0.898426 | + | 0.439124i | \(0.144711\pi\) | ||||
−0.898426 | + | 0.439124i | \(0.855289\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 116835. | 1.66372 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9040.00 | 0.125863 | ||||||||
\(269\) | − 109871.i | − 1.51838i | −0.650870 | − | 0.759189i | \(-0.725596\pi\) | ||||
0.650870 | − | 0.759189i | \(-0.274404\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 115188. | 1.56844 | 0.784218 | − | 0.620485i | \(-0.213064\pi\) | ||||
0.784218 | + | 0.620485i | \(0.213064\pi\) | |||||||
\(272\) | 16773.4i | 0.226716i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −53540.0 | −0.713144 | ||||||||
\(275\) | − 315.370i | − 0.00417018i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −109310. | −1.42462 | −0.712312 | − | 0.701863i | \(-0.752352\pi\) | ||||
−0.712312 | + | 0.701863i | \(0.752352\pi\) | |||||||
\(278\) | − 30751.2i | − 0.397898i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 103576.i | − 1.31173i | −0.754878 | − | 0.655865i | \(-0.772304\pi\) | ||||
0.754878 | − | 0.655865i | \(-0.227696\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 144015. | 1.79819 | 0.899095 | − | 0.437753i | \(-0.144226\pi\) | ||||
0.899095 | + | 0.437753i | \(0.144226\pi\) | |||||||
\(284\) | 3382.80i | 0.0419411i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −329.460 | −0.00402783 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14833.0 | 0.177596 | ||||||||
\(290\) | 41351.0i | 0.491689i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 24050.6 | 0.282072 | ||||||||
\(293\) | 42370.2i | 0.493544i | 0.969074 | + | 0.246772i | \(0.0793698\pi\) | ||||
−0.969074 | + | 0.246772i | \(0.920630\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22048.0 | 0.253352 | ||||||||
\(296\) | 35298.8i | 0.402880i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −21068.0 | −0.237242 | ||||||||
\(299\) | 5241.68i | 0.0586311i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 101235.i | 1.10998i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −28992.5 | −0.313717 | ||||||||
\(305\) | 34778.3i | 0.373860i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −64533.0 | −0.684708 | −0.342354 | − | 0.939571i | \(-0.611224\pi\) | ||||
−0.342354 | + | 0.939571i | \(0.611224\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −105152. | −1.09419 | ||||||||
\(311\) | − 33838.0i | − 0.349851i | −0.984582 | − | 0.174926i | \(-0.944032\pi\) | ||||
0.984582 | − | 0.174926i | \(-0.0559685\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 53619.6 | 0.547312 | 0.273656 | − | 0.961828i | \(-0.411767\pi\) | ||||
0.273656 | + | 0.961828i | \(0.411767\pi\) | |||||||
\(314\) | 7571.31i | 0.0767913i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −69200.0 | −0.692998 | ||||||||
\(317\) | 25426.1i | 0.253024i | 0.991965 | + | 0.126512i | \(0.0403783\pi\) | ||||
−0.991965 | + | 0.126512i | \(0.959622\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −710.000 | −0.00697713 | ||||||||
\(320\) | − 14909.7i | − 0.145602i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 118726.i | − 1.13800i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18367.4 | 0.173893 | ||||||||
\(326\) | − 54458.5i | − 0.512426i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 29651.4 | 0.275612 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24392.0 | 0.222634 | 0.111317 | − | 0.993785i | \(-0.464493\pi\) | ||||
0.111317 | + | 0.993785i | \(0.464493\pi\) | |||||||
\(332\) | 23762.3i | 0.215582i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −35417.0 | −0.317482 | ||||||||
\(335\) | − 32906.1i | − 0.293215i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 105296. | 0.927154 | 0.463577 | − | 0.886057i | \(-0.346566\pi\) | ||||
0.463577 | + | 0.886057i | \(0.346566\pi\) | |||||||
\(338\) | 61594.7i | 0.539150i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 61056.0 | 0.528166 | ||||||||
\(341\) | − 1805.47i | − 0.0155268i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7421.79i | 0.0627180i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 66633.3 | 0.556595 | ||||||||
\(347\) | 39045.0i | 0.324270i | 0.986769 | + | 0.162135i | \(0.0518380\pi\) | ||||
−0.986769 | + | 0.162135i | \(0.948162\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −188410. | −1.54687 | −0.773434 | − | 0.633877i | \(-0.781463\pi\) | ||||
−0.773434 | + | 0.633877i | \(0.781463\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 256.000 | 0.00206612 | ||||||||
\(353\) | − 124140.i | − 0.996240i | −0.867108 | − | 0.498120i | \(-0.834024\pi\) | ||||
0.867108 | − | 0.498120i | \(-0.165976\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12313.6 | 0.0977074 | ||||||||
\(356\) | 106464.i | 0.840048i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −72156.0 | −0.562997 | ||||||||
\(359\) | − 202443.i | − 1.57078i | −0.619003 | − | 0.785388i | \(-0.712463\pi\) | ||||
0.619003 | − | 0.785388i | \(-0.287537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 74895.0 | 0.574696 | ||||||||
\(362\) | − 109959.i | − 0.839098i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 87545.5i | − 0.657125i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −228728. | −1.69819 | −0.849096 | − | 0.528239i | \(-0.822853\pi\) | ||||
−0.849096 | + | 0.528239i | \(0.822853\pi\) | |||||||
\(368\) | − 4072.94i | − 0.0300754i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 128489. | 0.938564 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −49874.0 | −0.358473 | −0.179237 | − | 0.983806i | \(-0.557363\pi\) | ||||
−0.179237 | + | 0.983806i | \(0.557363\pi\) | |||||||
\(374\) | 1048.34i | 0.00749475i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −93566.7 | −0.661829 | ||||||||
\(377\) | − 41351.0i | − 0.290940i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16632.0 | 0.115789 | 0.0578943 | − | 0.998323i | \(-0.481561\pi\) | ||||
0.0578943 | + | 0.998323i | \(0.481561\pi\) | |||||||
\(380\) | 105534.i | 0.730847i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 97164.0 | 0.665853 | ||||||||
\(383\) | 128596.i | 0.876656i | 0.898815 | + | 0.438328i | \(0.144429\pi\) | ||||
−0.898815 | + | 0.438328i | \(0.855571\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 186178.i | 1.24955i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 105098. | 0.698120 | ||||||||
\(389\) | 82370.9i | 0.544345i | 0.962248 | + | 0.272173i | \(0.0877422\pi\) | ||||
−0.962248 | + | 0.272173i | \(0.912258\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16678.9 | 0.109097 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −183372. | −1.18125 | ||||||||
\(395\) | 251892.i | 1.61443i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −208013. | −1.31980 | −0.659902 | − | 0.751352i | \(-0.729402\pi\) | ||||
−0.659902 | + | 0.751352i | \(0.729402\pi\) | |||||||
\(398\) | − 131624.i | − 0.830941i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14272.0 | −0.0892000 | ||||||||
\(401\) | − 274325.i | − 1.70599i | −0.521919 | − | 0.852995i | \(-0.674784\pi\) | ||||
0.521919 | − | 0.852995i | \(-0.325216\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 105152. | 0.647452 | ||||||||
\(404\) | 96213.9i | 0.589488i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2206.17i | 0.0133184i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −88830.7 | −0.531027 | −0.265513 | − | 0.964107i | \(-0.585541\pi\) | ||||
−0.265513 | + | 0.964107i | \(0.585541\pi\) | |||||||
\(410\) | − 107933.i | − 0.642075i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −87306.9 | −0.514345 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 86496.0 | 0.502227 | ||||||||
\(416\) | 14909.7i | 0.0861551i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1812.03 | −0.0103708 | ||||||||
\(419\) | − 228071.i | − 1.29910i | −0.760319 | − | 0.649550i | \(-0.774957\pi\) | ||||
0.760319 | − | 0.649550i | \(-0.225043\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 149694. | 0.844579 | 0.422289 | − | 0.906461i | \(-0.361227\pi\) | ||||
0.422289 | + | 0.906461i | \(0.361227\pi\) | |||||||
\(422\) | − 24052.9i | − 0.135065i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 90784.0 | 0.504984 | ||||||||
\(425\) | − 58444.7i | − 0.323569i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 101631.i | 0.554803i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 27015.7 | 0.146110 | ||||||||
\(431\) | 161643.i | 0.870168i | 0.900390 | + | 0.435084i | \(0.143281\pi\) | ||||
−0.900390 | + | 0.435084i | \(0.856719\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 112099. | 0.597895 | 0.298948 | − | 0.954269i | \(-0.403364\pi\) | ||||
0.298948 | + | 0.954269i | \(0.403364\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 78016.0 | 0.410403 | ||||||||
\(437\) | 28829.2i | 0.150963i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 185321. | 0.961604 | 0.480802 | − | 0.876829i | \(-0.340346\pi\) | ||||
0.480802 | + | 0.876829i | \(0.340346\pi\) | |||||||
\(440\) | − 931.854i | − 0.00481330i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −61056.0 | −0.312524 | ||||||||
\(443\) | − 129337.i | − 0.659045i | −0.944148 | − | 0.329522i | \(-0.893112\pi\) | ||||
0.944148 | − | 0.329522i | \(-0.106888\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 387536. | 1.95701 | ||||||||
\(446\) | 160512.i | 0.806933i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 4323.25i | − 0.0214446i | −0.999943 | − | 0.0107223i | \(-0.996587\pi\) | ||||
0.999943 | − | 0.0107223i | \(-0.00341308\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1853.21 | 0.00911113 | ||||||||
\(452\) | 90430.5i | 0.442627i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 158306. | 0.768041 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 133376. | 0.638624 | 0.319312 | − | 0.947650i | \(-0.396548\pi\) | ||||
0.319312 | + | 0.947650i | \(0.396548\pi\) | |||||||
\(458\) | 239254.i | 1.14058i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14825.7 | −0.0700648 | ||||||||
\(461\) | 111735.i | 0.525760i | 0.964828 | + | 0.262880i | \(0.0846724\pi\) | ||||
−0.964828 | + | 0.262880i | \(0.915328\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 324458. | 1.51355 | 0.756775 | − | 0.653676i | \(-0.226774\pi\) | ||||
0.756775 | + | 0.653676i | \(0.226774\pi\) | |||||||
\(464\) | 32130.9i | 0.149241i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 100324. | 0.461990 | ||||||||
\(467\) | 330109.i | 1.51364i | 0.653621 | + | 0.756822i | \(0.273249\pi\) | ||||
−0.653621 | + | 0.756822i | \(0.726751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 340588.i | 1.54182i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 17131.9 | 0.0768993 | ||||||||
\(473\) | 463.862i | 0.00207332i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 101021. | 0.447737 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −162156. | −0.709704 | ||||||||
\(479\) | − 142224.i | − 0.619873i | −0.950757 | − | 0.309936i | \(-0.899692\pi\) | ||||
0.950757 | − | 0.309936i | \(-0.100308\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −128489. | −0.555364 | ||||||||
\(482\) | 242632.i | 1.04437i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −117112. | −0.499932 | ||||||||
\(485\) | − 382562.i | − 1.62637i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35920.0 | 0.151453 | 0.0757266 | − | 0.997129i | \(-0.475872\pi\) | ||||
0.0757266 | + | 0.997129i | \(0.475872\pi\) | |||||||
\(488\) | 27023.8i | 0.113477i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 347986.i | 1.44344i | 0.692186 | + | 0.721719i | \(0.256648\pi\) | ||||
−0.692186 | + | 0.721719i | \(0.743352\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −131578. | −0.541365 | ||||||||
\(494\) | − 105534.i | − 0.432454i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −81706.1 | −0.332117 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12120.0 | 0.0486745 | 0.0243373 | − | 0.999704i | \(-0.492252\pi\) | ||||
0.0243373 | + | 0.999704i | \(0.492252\pi\) | |||||||
\(500\) | − 93651.3i | − 0.374605i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 71492.9 | 0.283697 | ||||||||
\(503\) | 222655.i | 0.880028i | 0.897991 | + | 0.440014i | \(0.145026\pi\) | ||||
−0.897991 | + | 0.440014i | \(0.854974\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 350224. | 1.37329 | ||||||||
\(506\) | − 254.558i | 0 0.000994229i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 247376. | 0.958584 | ||||||||
\(509\) | − 232760.i | − 0.898405i | −0.893430 | − | 0.449203i | \(-0.851708\pi\) | ||||
0.893430 | − | 0.449203i | \(-0.148292\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 11585.2i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −246683. | −0.933713 | ||||||||
\(515\) | 317802.i | 1.19824i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5847.92 | −0.0218786 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 54272.0 | 0.200710 | ||||||||
\(521\) | − 37245.0i | − 0.137212i | −0.997644 | − | 0.0686061i | \(-0.978145\pi\) | ||||
0.997644 | − | 0.0686061i | \(-0.0218552\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −112016. | −0.409523 | −0.204762 | − | 0.978812i | \(-0.565642\pi\) | ||||
−0.204762 | + | 0.978812i | \(0.565642\pi\) | |||||||
\(524\) | − 47524.6i | − 0.173083i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 171820. | 0.621015 | ||||||||
\(527\) | − 334592.i | − 1.20474i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 275791. | 0.985527 | ||||||||
\(530\) | − 330459.i | − 1.17643i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 107933.i | 0.379926i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 369943. | 1.29249 | ||||||||
\(536\) | − 25569.0i | − 0.0889987i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −310763. | −1.07366 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 128194. | 0.437999 | 0.219000 | − | 0.975725i | \(-0.429721\pi\) | ||||
0.219000 | + | 0.975725i | \(0.429721\pi\) | |||||||
\(542\) | − 325799.i | − 1.10905i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 47442.3 | 0.160313 | ||||||||
\(545\) | − 283983.i | − 0.956090i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 186442. | 0.623116 | 0.311558 | − | 0.950227i | \(-0.399149\pi\) | ||||
0.311558 | + | 0.950227i | \(0.399149\pi\) | |||||||
\(548\) | 151434.i | 0.504269i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −892.000 | −0.00294876 | ||||||||
\(551\) | − 227431.i | − 0.749110i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 309175.i | 1.00736i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −86977.5 | −0.281357 | ||||||||
\(557\) | 14318.9i | 0.0461530i | 0.999734 | + | 0.0230765i | \(0.00734613\pi\) | ||||
−0.999734 | + | 0.0230765i | \(0.992654\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27015.7 | −0.0864556 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −292956. | −0.927534 | ||||||||
\(563\) | − 66336.4i | − 0.209283i | −0.994510 | − | 0.104642i | \(-0.966630\pi\) | ||||
0.994510 | − | 0.104642i | \(-0.0333696\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 329172. | 1.03116 | ||||||||
\(566\) | − 407337.i | − 1.27151i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9568.00 | 0.0296568 | ||||||||
\(569\) | 208920.i | 0.645292i | 0.946520 | + | 0.322646i | \(0.104572\pi\) | ||||
−0.946520 | + | 0.322646i | \(0.895428\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 515862. | 1.58220 | 0.791100 | − | 0.611687i | \(-0.209509\pi\) | ||||
0.791100 | + | 0.611687i | \(0.209509\pi\) | |||||||
\(572\) | 931.854i | 0.00284810i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14191.6i | 0.0429237i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 352440. | 1.05860 | 0.529302 | − | 0.848433i | \(-0.322454\pi\) | ||||
0.529302 | + | 0.848433i | \(0.322454\pi\) | |||||||
\(578\) | − 41954.1i | − 0.125579i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 116958. | 0.347676 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5674.00 | 0.0166937 | ||||||||
\(584\) | − 68025.3i | − 0.199455i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 119841. | 0.348988 | ||||||||
\(587\) | 296621.i | 0.860846i | 0.902627 | + | 0.430423i | \(0.141636\pi\) | ||||
−0.902627 | + | 0.430423i | \(0.858364\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 578336. | 1.66705 | ||||||||
\(590\) | − 62361.2i | − 0.179147i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 99840.0 | 0.284879 | ||||||||
\(593\) | 22626.6i | 0.0643442i | 0.999482 | + | 0.0321721i | \(0.0102425\pi\) | ||||
−0.999482 | + | 0.0321721i | \(0.989758\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 59589.3i | 0.167755i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14825.7 | 0.0414584 | ||||||||
\(599\) | 146528.i | 0.408383i | 0.978931 | + | 0.204191i | \(0.0654565\pi\) | ||||
−0.978931 | + | 0.204191i | \(0.934544\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −136479. | −0.377847 | −0.188924 | − | 0.981992i | \(-0.560500\pi\) | ||||
−0.188924 | + | 0.981992i | \(0.560500\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 286336. | 0.784878 | ||||||||
\(605\) | 426294.i | 1.16466i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 79317.5 | 0.215274 | 0.107637 | − | 0.994190i | \(-0.465672\pi\) | ||||
0.107637 | + | 0.994190i | \(0.465672\pi\) | |||||||
\(608\) | 82003.2i | 0.221832i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 98368.0 | 0.264359 | ||||||||
\(611\) | − 340588.i | − 0.912319i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13742.0 | 0.0365703 | 0.0182852 | − | 0.999833i | \(-0.494179\pi\) | ||||
0.0182852 | + | 0.999833i | \(0.494179\pi\) | |||||||
\(614\) | 182527.i | 0.484161i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 125015.i | − 0.328392i | −0.986428 | − | 0.164196i | \(-0.947497\pi\) | ||||
0.986428 | − | 0.164196i | \(-0.0525029\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 318341. | 0.830828 | 0.415414 | − | 0.909632i | \(-0.363637\pi\) | ||||
0.415414 | + | 0.909632i | \(0.363637\pi\) | |||||||
\(620\) | 297415.i | 0.773712i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −95708.2 | −0.247382 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −480271. | −1.22949 | ||||||||
\(626\) | − 151659.i | − 0.387008i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21414.9 | 0.0542996 | ||||||||
\(629\) | 408851.i | 1.03339i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12618.0 | −0.0316907 | −0.0158453 | − | 0.999874i | \(-0.505044\pi\) | ||||
−0.0158453 | + | 0.999874i | \(0.505044\pi\) | |||||||
\(632\) | 195727.i | 0.490024i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 71916.0 | 0.178915 | ||||||||
\(635\) | − 900462.i | − 2.23315i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2008.18i | 0.00493358i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −42170.9 | −0.102956 | ||||||||
\(641\) | 88644.3i | 0.215742i | 0.994165 | + | 0.107871i | \(0.0344034\pi\) | ||||
−0.994165 | + | 0.107871i | \(0.965597\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −195329. | −0.472437 | −0.236219 | − | 0.971700i | \(-0.575908\pi\) | ||||
−0.236219 | + | 0.971700i | \(0.575908\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −335808. | −0.804685 | ||||||||
\(647\) | − 441524.i | − 1.05474i | −0.849635 | − | 0.527371i | \(-0.823178\pi\) | ||||
0.849635 | − | 0.527371i | \(-0.176822\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1070.75 | 0.00254212 | ||||||||
\(650\) | − 51950.9i | − 0.122961i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −154032. | −0.362340 | ||||||||
\(653\) | 346158.i | 0.811799i | 0.913918 | + | 0.405900i | \(0.133042\pi\) | ||||
−0.913918 | + | 0.405900i | \(0.866958\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −172992. | −0.403221 | ||||||||
\(656\) | − 83866.9i | − 0.194887i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 255677.i | 0.588737i | 0.955692 | + | 0.294368i | \(0.0951092\pi\) | ||||
−0.955692 | + | 0.294368i | \(0.904891\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −124742. | −0.285502 | −0.142751 | − | 0.989759i | \(-0.545595\pi\) | ||||
−0.142751 | + | 0.989759i | \(0.545595\pi\) | |||||||
\(662\) | − 68991.0i | − 0.157426i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 67209.9 | 0.152439 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31950.0 | 0.0718157 | ||||||||
\(668\) | 100174.i | 0.224493i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −93072.5 | −0.207335 | ||||||||
\(671\) | 1688.99i | 0.00375129i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −168784. | −0.372650 | −0.186325 | − | 0.982488i | \(-0.559658\pi\) | ||||
−0.186325 | + | 0.982488i | \(0.559658\pi\) | |||||||
\(674\) | − 297822.i | − 0.655597i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 174216. | 0.381237 | ||||||||
\(677\) | 709287.i | 1.54755i | 0.633461 | + | 0.773774i | \(0.281634\pi\) | ||||
−0.633461 | + | 0.773774i | \(0.718366\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 172692.i | − 0.373470i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5106.63 | −0.0109791 | ||||||||
\(683\) | 746025.i | 1.59923i | 0.600511 | + | 0.799616i | \(0.294964\pi\) | ||||
−0.600511 | + | 0.799616i | \(0.705036\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 551228. | 1.17476 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20992.0 | 0.0443483 | ||||||||
\(689\) | 330459.i | 0.696112i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −901815. | −1.88869 | −0.944346 | − | 0.328953i | \(-0.893304\pi\) | ||||
−0.944346 | + | 0.328953i | \(0.893304\pi\) | |||||||
\(692\) | − 188467.i | − 0.393572i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 110436. | 0.229293 | ||||||||
\(695\) | 316603.i | 0.655458i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 343440. | 0.706944 | ||||||||
\(698\) | 532904.i | 1.09380i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 571146.i | − 1.16228i | −0.813803 | − | 0.581140i | \(-0.802607\pi\) | ||||
0.813803 | − | 0.581140i | \(-0.197393\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −706692. | −1.42995 | ||||||||
\(704\) | − 724.077i | − 0.00146096i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −351122. | −0.704448 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −403688. | −0.803070 | −0.401535 | − | 0.915844i | \(-0.631523\pi\) | ||||
−0.401535 | + | 0.915844i | \(0.631523\pi\) | |||||||
\(710\) | − 34828.0i | − 0.0690896i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 301127. | 0.594004 | ||||||||
\(713\) | 81246.0i | 0.159817i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3392.00 | 0.00663504 | ||||||||
\(716\) | 204088.i | 0.398099i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −572596. | −1.11071 | ||||||||
\(719\) | 365170.i | 0.706379i | 0.935552 | + | 0.353189i | \(0.114903\pi\) | ||||
−0.935552 | + | 0.353189i | \(0.885097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 211835.i | − 0.406372i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −311010. | −0.593332 | ||||||||
\(725\) | − 111956.i | − 0.212996i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 941968. | 1.78224 | 0.891122 | − | 0.453764i | \(-0.149919\pi\) | ||||
0.891122 | + | 0.453764i | \(0.149919\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −247616. | −0.464658 | ||||||||
\(731\) | 85963.5i | 0.160872i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 418909. | 0.779671 | 0.389835 | − | 0.920885i | \(-0.372532\pi\) | ||||
0.389835 | + | 0.920885i | \(0.372532\pi\) | |||||||
\(734\) | 646940.i | 1.20080i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11520.0 | −0.0212665 | ||||||||
\(737\) | − 1598.06i | − 0.00294211i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.04476e6 | −1.91305 | −0.956526 | − | 0.291647i | \(-0.905797\pi\) | ||||
−0.956526 | + | 0.291647i | \(0.905797\pi\) | |||||||
\(740\) | − 363423.i | − 0.663665i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 232297.i | 0.420791i | 0.977616 | + | 0.210396i | \(0.0674752\pi\) | ||||
−0.977616 | + | 0.210396i | \(0.932525\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 216908. | 0.390808 | ||||||||
\(746\) | 141065.i | 0.253479i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2965.14 | 0.00529959 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −465408. | −0.825190 | −0.412595 | − | 0.910915i | \(-0.635378\pi\) | ||||
−0.412595 | + | 0.910915i | \(0.635378\pi\) | |||||||
\(752\) | 264647.i | 0.467984i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −116958. | −0.205726 | ||||||||
\(755\) | − 1.04228e6i | − 1.82848i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −496088. | −0.865699 | −0.432850 | − | 0.901466i | \(-0.642492\pi\) | ||||
−0.432850 | + | 0.901466i | \(0.642492\pi\) | |||||||
\(758\) | − 47042.4i | − 0.0818750i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 298496. | 0.516787 | ||||||||
\(761\) | 738407.i | 1.27505i | 0.770431 | + | 0.637524i | \(0.220041\pi\) | ||||
−0.770431 | + | 0.637524i | \(0.779959\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 274821.i | − 0.470829i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 363724. | 0.619890 | ||||||||
\(767\) | 62361.2i | 0.106004i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −527136. | −0.891395 | −0.445698 | − | 0.895184i | \(-0.647044\pi\) | ||||
−0.445698 | + | 0.895184i | \(0.647044\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 526592. | 0.883567 | ||||||||
\(773\) | − 100378.i | − 0.167989i | −0.996466 | − | 0.0839944i | \(-0.973232\pi\) | ||||
0.996466 | − | 0.0839944i | \(-0.0267678\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 284695. | 0.473998 | ||||||||
\(776\) | − 297261.i | − 0.493645i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 232980. | 0.384910 | ||||||||
\(779\) | 593630.i | 0.978230i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 598.000 | 0.000980391 0 | ||||||||
\(782\) | − 47175.1i | − 0.0771435i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 77951.5i | − 0.126498i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −715752. | −1.15562 | −0.577808 | − | 0.816173i | \(-0.696092\pi\) | ||||
−0.577808 | + | 0.816173i | \(0.696092\pi\) | |||||||
\(788\) | 518654.i | 0.835267i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 712458. | 1.14158 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −98368.0 | −0.156425 | ||||||||
\(794\) | 588349.i | 0.933242i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −372290. | −0.587564 | ||||||||
\(797\) | − 921924.i | − 1.45137i | −0.688027 | − | 0.725686i | \(-0.741523\pi\) | ||||
0.688027 | − | 0.725686i | \(-0.258477\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.08374e6 | −1.69759 | ||||||||
\(800\) | 40367.3i | 0.0630739i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −775908. | −1.20632 | ||||||||
\(803\) | − 4251.58i | − 0.00659356i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 297415.i | − 0.457818i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 272134. | 0.416831 | ||||||||
\(809\) | − 601594.i | − 0.919192i | −0.888128 | − | 0.459596i | \(-0.847994\pi\) | ||||
0.888128 | − | 0.459596i | \(-0.152006\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.22221e6 | −1.85826 | −0.929129 | − | 0.369757i | \(-0.879441\pi\) | ||||
−0.929129 | + | 0.369757i | \(0.879441\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6240.00 | 0.00941750 | ||||||||
\(815\) | 560685.i | 0.844119i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −148587. | −0.222605 | ||||||||
\(818\) | 251251.i | 0.375493i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −305280. | −0.454015 | ||||||||
\(821\) | 911304.i | 1.35200i | 0.736901 | + | 0.676000i | \(0.236288\pi\) | ||||
−0.736901 | + | 0.676000i | \(0.763712\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −207542. | −0.306412 | −0.153206 | − | 0.988194i | \(-0.548960\pi\) | ||||
−0.153206 | + | 0.988194i | \(0.548960\pi\) | |||||||
\(824\) | 246941.i | 0.363697i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 746785.i | − 1.09190i | −0.837816 | − | 0.545952i | \(-0.816168\pi\) | ||||
0.837816 | − | 0.545952i | \(-0.183832\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 233093. | 0.339172 | 0.169586 | − | 0.985515i | \(-0.445757\pi\) | ||||
0.169586 | + | 0.985515i | \(0.445757\pi\) | |||||||
\(830\) | − 244648.i | − 0.355128i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 42170.9 | 0.0609209 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 364640. | 0.522988 | ||||||||
\(836\) | 5125.20i | 0.00733328i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −645083. | −0.918602 | ||||||||
\(839\) | 798482.i | 1.13434i | 0.823602 | + | 0.567168i | \(0.191961\pi\) | ||||
−0.823602 | + | 0.567168i | \(0.808039\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 455231. | 0.643635 | ||||||||
\(842\) | − 423399.i | − 0.597207i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −68032.0 | −0.0955055 | ||||||||
\(845\) | − 634156.i | − 0.888142i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 256776.i | − 0.357078i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −165307. | −0.228798 | ||||||||
\(851\) | − 99277.8i | − 0.137086i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −432128. | −0.593902 | −0.296951 | − | 0.954893i | \(-0.595970\pi\) | ||||
−0.296951 | + | 0.954893i | \(0.595970\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 287456. | 0.392305 | ||||||||
\(857\) | − 466247.i | − 0.634826i | −0.948287 | − | 0.317413i | \(-0.897186\pi\) | ||||
0.948287 | − | 0.317413i | \(-0.102814\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −610449. | −0.827299 | −0.413650 | − | 0.910436i | \(-0.635746\pi\) | ||||
−0.413650 | + | 0.910436i | \(0.635746\pi\) | |||||||
\(860\) | − 76412.0i | − 0.103315i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 457196. | 0.615301 | ||||||||
\(863\) | 198424.i | 0.266424i | 0.991088 | + | 0.133212i | \(0.0425291\pi\) | ||||
−0.991088 | + | 0.133212i | \(0.957471\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −686032. | −0.916879 | ||||||||
\(866\) | − 317063.i | − 0.422776i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12232.9i | 0.0161991i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 93072.5 | 0.122683 | ||||||||
\(872\) | − 220663.i | − 0.290199i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 81541.4 | 0.106747 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33678.0 | −0.0437872 | −0.0218936 | − | 0.999760i | \(-0.506970\pi\) | ||||
−0.0218936 | + | 0.999760i | \(0.506970\pi\) | |||||||
\(878\) | − 524168.i | − 0.679957i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2635.68 | −0.00340351 | ||||||||
\(881\) | 1.11930e6i | 1.44210i | 0.692883 | + | 0.721050i | \(0.256340\pi\) | ||||
−0.692883 | + | 0.721050i | \(0.743660\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.28444e6 | −1.64737 | −0.823687 | − | 0.567044i | \(-0.808087\pi\) | ||||
−0.823687 | + | 0.567044i | \(0.808087\pi\) | |||||||
\(884\) | 172692.i | 0.220988i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −365820. | −0.466015 | ||||||||
\(887\) | − 111997.i | − 0.142351i | −0.997464 | − | 0.0711754i | \(-0.977325\pi\) | ||||
0.997464 | − | 0.0711754i | \(-0.0226750\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 1.09612e6i | − 1.38381i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 453996. | 0.570588 | ||||||||
\(893\) | − 1.87323e6i | − 2.34903i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 742891. | 0.927426 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12228.0 | −0.0151636 | ||||||||
\(899\) | − 640941.i | − 0.793046i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.05151e6 | 1.29528 | ||||||||
\(902\) | − 5241.68i | − 0.00644254i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 255776. | 0.312985 | ||||||||
\(905\) | 1.13209e6i | 1.38225i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.49953e6 | −1.82280 | −0.911402 | − | 0.411517i | \(-0.864999\pi\) | ||||
−0.911402 | + | 0.411517i | \(0.864999\pi\) | |||||||
\(908\) | − 447756.i | − 0.543087i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.62993e6i | 1.96396i | 0.188997 | + | 0.981978i | \(0.439476\pi\) | ||||
−0.188997 | + | 0.981978i | \(0.560524\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4200.62 | 0.00503932 | ||||||||
\(914\) | − 377244.i | − 0.451575i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 676711. | 0.806515 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 503520. | 0.596191 | 0.298096 | − | 0.954536i | \(-0.403649\pi\) | ||||
0.298096 | + | 0.954536i | \(0.403649\pi\) | |||||||
\(920\) | 41933.4i | 0.0495433i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 316035. | 0.371769 | ||||||||
\(923\) | 34828.0i | 0.0408814i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −347880. | −0.406580 | ||||||||
\(926\) | − 917706.i | − 1.07024i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 90880.0 | 0.105529 | ||||||||
\(929\) | 71898.4i | 0.0833082i | 0.999132 | + | 0.0416541i | \(0.0132627\pi\) | ||||
−0.999132 | + | 0.0416541i | \(0.986737\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 283759.i | − 0.326677i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 933690. | 1.07031 | ||||||||
\(935\) | − 10793.3i | − 0.0123461i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −679017. | −0.773396 | −0.386698 | − | 0.922206i | \(-0.626384\pi\) | ||||
−0.386698 | + | 0.922206i | \(0.626384\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 963328. | 1.09023 | ||||||||
\(941\) | − 364908.i | − 0.412102i | −0.978541 | − | 0.206051i | \(-0.933939\pi\) | ||||
0.978541 | − | 0.206051i | \(-0.0660612\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −83394.6 | −0.0937809 | ||||||||
\(944\) | − 48456.4i | − 0.0543760i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1312.00 | 0.00146606 | ||||||||
\(947\) | 186576.i | 0.208044i | 0.994575 | + | 0.104022i | \(0.0331712\pi\) | ||||
−0.994575 | + | 0.104022i | \(0.966829\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 247616. | 0.274945 | ||||||||
\(950\) | − 285730.i | − 0.316598i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 1.32111e6i | − 1.45463i | −0.686302 | − | 0.727317i | \(-0.740767\pi\) | ||||
0.686302 | − | 0.727317i | \(-0.259233\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.00036e6 | −1.09686 | ||||||||
\(956\) | 458646.i | 0.501836i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −402271. | −0.438316 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 706335. | 0.764828 | ||||||||
\(962\) | 363423.i | 0.392701i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 686266. | 0.738479 | ||||||||
\(965\) | − 1.91682e6i | − 2.05839i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −688022. | −0.735782 | −0.367891 | − | 0.929869i | \(-0.619920\pi\) | ||||
−0.367891 | + | 0.929869i | \(0.619920\pi\) | |||||||
\(968\) | 331243.i | 0.353505i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.08205e6 | −1.15001 | ||||||||
\(971\) | − 485088.i | − 0.514496i | −0.966345 | − | 0.257248i | \(-0.917184\pi\) | ||||
0.966345 | − | 0.257248i | \(-0.0828158\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 101597.i | − 0.107094i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 76434.8 | 0.0802401 | ||||||||
\(977\) | − 1.70595e6i | − 1.78721i | −0.448850 | − | 0.893607i | \(-0.648166\pi\) | ||||
0.448850 | − | 0.893607i | \(-0.351834\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18820.4 | 0.0196365 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 984252. | 1.02067 | ||||||||
\(983\) | − 964527.i | − 0.998177i | −0.866551 | − | 0.499088i | \(-0.833668\pi\) | ||||
0.866551 | − | 0.499088i | \(-0.166332\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.88793e6 | 1.94587 | ||||||||
\(986\) | 372159.i | 0.382803i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −298496. | −0.305791 | ||||||||
\(989\) | − 20873.8i | − 0.0213407i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −639856. | −0.651531 | −0.325765 | − | 0.945451i | \(-0.605622\pi\) | ||||
−0.325765 | + | 0.945451i | \(0.605622\pi\) | |||||||
\(992\) | 231100.i | 0.234842i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.35516e6i | 1.36881i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.60838e6 | 1.61808 | 0.809039 | − | 0.587755i | \(-0.199988\pi\) | ||||
0.809039 | + | 0.587755i | \(0.199988\pi\) | |||||||
\(998\) | − 34280.5i | − 0.0344181i | ||||||||
\(999\) | 0 | 0 |
(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 | 882.5.b.c.197.2 | yes | 4 | |
3.2 | odd | 2 | inner | 882.5.b.c.197.3 | yes | 4 | |
7.6 | odd | 2 | inner | 882.5.b.c.197.1 | ✓ | 4 | |
21.20 | even | 2 | inner | 882.5.b.c.197.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.5.b.c.197.1 | ✓ | 4 | 7.6 | odd | 2 | inner | |
882.5.b.c.197.2 | yes | 4 | 1.1 | even | 1 | trivial | |
882.5.b.c.197.3 | yes | 4 | 3.2 | odd | 2 | inner | |
882.5.b.c.197.4 | yes | 4 | 21.20 | even | 2 | inner |