Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,4,Mod(641,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.641");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(75.5224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 641.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.641 |
Dual form | 1280.4.d.b.641.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 10.0000i | − 1.92450i | −0.272166 | − | 0.962250i | \(-0.587740\pi\) | ||||
0.272166 | − | 0.962250i | \(-0.412260\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.0000 | −0.971909 | −0.485954 | − | 0.873984i | \(-0.661528\pi\) | ||||
−0.485954 | + | 0.873984i | \(0.661528\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −73.0000 | −2.70370 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 16.0000i | − 0.438562i | −0.975662 | − | 0.219281i | \(-0.929629\pi\) | ||||
0.975662 | − | 0.219281i | \(-0.0703711\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 6.00000i | − 0.128008i | −0.997950 | − | 0.0640039i | \(-0.979613\pi\) | ||||
0.997950 | − | 0.0640039i | \(-0.0203870\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 50.0000 | 0.860663 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.00000 | −0.0856008 | −0.0428004 | − | 0.999084i | \(-0.513628\pi\) | ||||
−0.0428004 | + | 0.999084i | \(0.513628\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 124.000i | 1.49724i | 0.663000 | + | 0.748620i | \(0.269283\pi\) | ||||
−0.663000 | + | 0.748620i | \(0.730717\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 180.000i | 1.87044i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 42.0000 | 0.380765 | 0.190383 | − | 0.981710i | \(-0.439027\pi\) | ||||
0.190383 | + | 0.981710i | \(0.439027\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −25.0000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 460.000i | 3.27878i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 142.000i | 0.909267i | 0.890679 | + | 0.454633i | \(0.150230\pi\) | ||||
−0.890679 | + | 0.454633i | \(0.849770\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 188.000 | 1.08922 | 0.544610 | − | 0.838690i | \(-0.316678\pi\) | ||||
0.544610 | + | 0.838690i | \(0.316678\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −160.000 | −0.844013 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 90.0000i | − 0.434651i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 202.000i | − 0.897530i | −0.893650 | − | 0.448765i | \(-0.851864\pi\) | ||||
0.893650 | − | 0.448765i | \(-0.148136\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −60.0000 | −0.246351 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −54.0000 | −0.205692 | −0.102846 | − | 0.994697i | \(-0.532795\pi\) | ||||
−0.102846 | + | 0.994697i | \(0.532795\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 66.0000i | 0.234068i | 0.993128 | + | 0.117034i | \(0.0373386\pi\) | ||||
−0.993128 | + | 0.117034i | \(0.962661\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 365.000i | − 1.20913i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −38.0000 | −0.117933 | −0.0589667 | − | 0.998260i | \(-0.518781\pi\) | ||||
−0.0589667 | + | 0.998260i | \(0.518781\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −19.0000 | −0.0553936 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 60.0000i | 0.164739i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 738.000i | − 1.91268i | −0.292255 | − | 0.956341i | \(-0.594405\pi\) | ||||
0.292255 | − | 0.956341i | \(-0.405595\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 80.0000 | 0.196131 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1240.00 | 2.88144 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 564.000i | 1.24452i | 0.782812 | + | 0.622259i | \(0.213785\pi\) | ||||
−0.782812 | + | 0.622259i | \(0.786215\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 262.000i | − 0.549929i | −0.961454 | − | 0.274964i | \(-0.911334\pi\) | ||||
0.961454 | − | 0.274964i | \(-0.0886661\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1314.00 | 2.62775 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 30.0000 | 0.0572468 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 554.000i | 1.01018i | 0.863067 | + | 0.505089i | \(0.168540\pi\) | ||||
−0.863067 | + | 0.505089i | \(0.831460\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 420.000i | − 0.732783i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 140.000 | 0.234013 | 0.117007 | − | 0.993131i | \(-0.462670\pi\) | ||||
0.117007 | + | 0.993131i | \(0.462670\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −882.000 | −1.41411 | −0.707057 | − | 0.707157i | \(-0.749977\pi\) | ||||
−0.707057 | + | 0.707157i | \(0.749977\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 250.000i | 0.384900i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 288.000i | 0.426242i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1160.00 | 1.65203 | 0.826014 | − | 0.563650i | \(-0.190603\pi\) | ||||
0.826014 | + | 0.563650i | \(0.190603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2629.00 | 3.60631 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 642.000i | − 0.849020i | −0.905423 | − | 0.424510i | \(-0.860446\pi\) | ||||
0.905423 | − | 0.424510i | \(-0.139554\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 30.0000i | − 0.0382818i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1420.00 | 1.74988 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 854.000 | 1.01712 | 0.508561 | − | 0.861026i | \(-0.330178\pi\) | ||||
0.508561 | + | 0.861026i | \(0.330178\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 108.000i | 0.124412i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 1880.00i | − 2.09620i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −620.000 | −0.669586 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −478.000 | −0.500346 | −0.250173 | − | 0.968201i | \(-0.580487\pi\) | ||||
−0.250173 | + | 0.968201i | \(0.580487\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1168.00i | 1.18574i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1794.00i | 1.76742i | 0.468033 | + | 0.883711i | \(0.344963\pi\) | ||||
−0.468033 | + | 0.883711i | \(0.655037\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 642.000 | 0.614157 | 0.307078 | − | 0.951684i | \(-0.400649\pi\) | ||||
0.307078 | + | 0.951684i | \(0.400649\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −900.000 | −0.836486 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 850.000i | − 0.767968i | −0.923340 | − | 0.383984i | \(-0.874552\pi\) | ||||
0.923340 | − | 0.383984i | \(-0.125448\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 666.000i | 0.585241i | 0.956229 | + | 0.292620i | \(0.0945272\pi\) | ||||
−0.956229 | + | 0.292620i | \(0.905473\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2020.00 | −1.72730 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1446.00 | −1.20379 | −0.601895 | − | 0.798575i | \(-0.705587\pi\) | ||||
−0.601895 | + | 0.798575i | \(0.705587\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 210.000i | 0.170283i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 438.000i | 0.346095i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 108.000 | 0.0831962 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1075.00 | 0.807663 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 540.000i | 0.395855i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 125.000i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1154.00 | 0.806307 | 0.403153 | − | 0.915132i | \(-0.367914\pi\) | ||||
0.403153 | + | 0.915132i | \(0.367914\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 660.000 | 0.450463 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 368.000i | 0.245437i | 0.992441 | + | 0.122719i | \(0.0391613\pi\) | ||||
−0.992441 | + | 0.122719i | \(0.960839\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2232.00i | − 1.45518i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2300.00 | −1.46631 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 670.000 | 0.417825 | 0.208912 | − | 0.977934i | \(-0.433008\pi\) | ||||
0.208912 | + | 0.977934i | \(0.433008\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 572.000i | − 0.349039i | −0.984654 | − | 0.174519i | \(-0.944163\pi\) | ||||
0.984654 | − | 0.174519i | \(-0.0558372\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 380.000i | 0.226963i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −96.0000 | −0.0561393 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −710.000 | −0.406636 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 190.000i | 0.106605i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 1730.00i | − 0.951189i | −0.879665 | − | 0.475594i | \(-0.842233\pi\) | ||||
0.879665 | − | 0.475594i | \(-0.157767\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1324.00 | 0.713547 | 0.356773 | − | 0.934191i | \(-0.383877\pi\) | ||||
0.356773 | + | 0.934191i | \(0.383877\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 438.000 | 0.231439 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 940.000i | 0.487114i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2946.00i | 1.49756i | 0.662820 | + | 0.748778i | \(0.269359\pi\) | ||||
−0.662820 | + | 0.748778i | \(0.730641\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7380.00 | −3.68096 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −756.000 | −0.370069 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2098.00i | − 1.00815i | −0.863661 | − | 0.504074i | \(-0.831834\pi\) | ||||
0.863661 | − | 0.504074i | \(-0.168166\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 800.000i | − 0.377454i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −866.000 | −0.401276 | −0.200638 | − | 0.979665i | \(-0.564301\pi\) | ||||
−0.200638 | + | 0.979665i | \(0.564301\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2161.00 | 0.983614 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 9052.00i | − 4.04809i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1678.00i | − 0.737433i | −0.929542 | − | 0.368717i | \(-0.879797\pi\) | ||||
0.929542 | − | 0.368717i | \(-0.120203\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 450.000 | 0.194382 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5640.00 | 2.39508 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1620.00i | 0.676450i | 0.941065 | + | 0.338225i | \(0.109826\pi\) | ||||
−0.941065 | + | 0.338225i | \(0.890174\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 2510.00i | − 1.03076i | −0.856963 | − | 0.515378i | \(-0.827652\pi\) | ||||
0.856963 | − | 0.515378i | \(-0.172348\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2620.00 | −1.05834 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1010.00 | 0.401387 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 96.0000i | 0.0375413i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 8280.00i | − 3.18667i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 372.000 | 0.140927 | 0.0704633 | − | 0.997514i | \(-0.477552\pi\) | ||||
0.0704633 | + | 0.997514i | \(0.477552\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2938.00 | 1.09576 | 0.547880 | − | 0.836557i | \(-0.315435\pi\) | ||||
0.547880 | + | 0.836557i | \(0.315435\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 300.000i | − 0.110172i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2234.00i | − 0.807949i | −0.914770 | − | 0.403974i | \(-0.867628\pi\) | ||||
0.914770 | − | 0.403974i | \(-0.132372\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3048.00 | −1.08576 | −0.542882 | − | 0.839809i | \(-0.682667\pi\) | ||||
−0.542882 | + | 0.839809i | \(0.682667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5540.00 | 1.94409 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2556.00i | − 0.883724i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 270.000i | − 0.0919884i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3066.00 | −1.02948 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1984.00 | 0.656632 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 4896.00i | − 1.59741i | −0.601720 | − | 0.798707i | \(-0.705518\pi\) | ||||
0.601720 | − | 0.798707i | \(-0.294482\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1400.00i | − 0.450359i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −330.000 | −0.104678 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3384.00 | −1.05862 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8820.00i | 2.72146i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 36.0000i | 0.0109576i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5302.00 | 1.59214 | 0.796072 | − | 0.605202i | \(-0.206908\pi\) | ||||
0.796072 | + | 0.605202i | \(0.206908\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1825.00 | 0.540741 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3778.00i | 1.10465i | 0.833630 | + | 0.552323i | \(0.186259\pi\) | ||||
−0.833630 | + | 0.552323i | \(0.813741\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3034.00i | 0.875513i | 0.899094 | + | 0.437756i | \(0.144227\pi\) | ||||
−0.899094 | + | 0.437756i | \(0.855773\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2880.00 | 0.820303 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3478.00 | 0.977903 | 0.488951 | − | 0.872311i | \(-0.337380\pi\) | ||||
0.488951 | + | 0.872311i | \(0.337380\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 190.000i | − 0.0527414i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 11600.0i | − 3.17933i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1560.00 | −0.422209 | −0.211105 | − | 0.977463i | \(-0.567706\pi\) | ||||
−0.211105 | + | 0.977463i | \(0.567706\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3218.00 | −0.860123 | −0.430061 | − | 0.902800i | \(-0.641508\pi\) | ||||
−0.430061 | + | 0.902800i | \(0.641508\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 13870.0i | − 3.66157i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 95.0000i | − 0.0247728i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 744.000 | 0.191658 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6420.00 | −1.63394 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 688.000i | 0.173013i | 0.996251 | + | 0.0865063i | \(0.0275703\pi\) | ||||
−0.996251 | + | 0.0865063i | \(0.972430\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 672.000i | − 0.166989i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −300.000 | −0.0736734 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2170.00 | 0.526696 | 0.263348 | − | 0.964701i | \(-0.415173\pi\) | ||||
0.263348 | + | 0.964701i | \(0.415173\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3636.00i | 0.872317i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 10366.0i | − 2.45839i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2274.00 | 0.533159 | 0.266580 | − | 0.963813i | \(-0.414106\pi\) | ||||
0.266580 | + | 0.963813i | \(0.414106\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3690.00 | 0.855377 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 8540.00i | − 1.95745i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7146.00i | 1.61970i | 0.586637 | + | 0.809850i | \(0.300452\pi\) | ||||
−0.586637 | + | 0.809850i | \(0.699548\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2604.00 | −0.583696 | −0.291848 | − | 0.956465i | \(-0.594270\pi\) | ||||
−0.291848 | + | 0.956465i | \(0.594270\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1080.00 | 0.239431 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 400.000i | 0.0877124i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5150.00i | 1.11709i | 0.829475 | + | 0.558544i | \(0.188640\pi\) | ||||
−0.829475 | + | 0.558544i | \(0.811360\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13724.0 | −2.94493 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5270.00 | −1.11880 | −0.559398 | − | 0.828899i | \(-0.688968\pi\) | ||||
−0.559398 | + | 0.828899i | \(0.688968\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3434.00i | 0.721308i | 0.932700 | + | 0.360654i | \(0.117446\pi\) | ||||
−0.932700 | + | 0.360654i | \(0.882554\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6200.00i | 1.28862i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 972.000 | 0.199914 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4877.00 | −0.992673 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4780.00i | 0.962916i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9878.00i | 1.96955i | 0.173826 | + | 0.984776i | \(0.444387\pi\) | ||||
−0.173826 | + | 0.984776i | \(0.555613\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2820.00 | −0.556565 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7360.00 | 1.43795 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 252.000i | − 0.0487409i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1188.00i | − 0.227492i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17940.0 | 3.40141 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1310.00 | 0.245936 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 8054.00i | − 1.49728i | −0.662975 | − | 0.748642i | \(-0.730706\pi\) | ||||
0.662975 | − | 0.748642i | \(-0.269294\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 6420.00i | − 1.18195i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5492.00 | 1.00136 | 0.500680 | − | 0.865633i | \(-0.333083\pi\) | ||||
0.500680 | + | 0.865633i | \(0.333083\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 422.000 | 0.0762072 | 0.0381036 | − | 0.999274i | \(-0.487868\pi\) | ||||
0.0381036 | + | 0.999274i | \(0.487868\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6570.00i | 1.17517i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6194.00i | 1.09744i | 0.836005 | + | 0.548722i | \(0.184885\pi\) | ||||
−0.836005 | + | 0.548722i | \(0.815115\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2272.00 | 0.398770 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8500.00 | −1.47796 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 744.000i | − 0.128165i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 150.000i | 0.0256015i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6660.00 | 1.12630 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 684.000 | 0.114620 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7688.00i | 1.27665i | 0.769768 | + | 0.638324i | \(0.220372\pi\) | ||||
−0.769768 | + | 0.638324i | \(0.779628\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14746.0i | 2.42665i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2770.00 | −0.451765 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1438.00 | −0.232442 | −0.116221 | − | 0.993223i | \(-0.537078\pi\) | ||||
−0.116221 | + | 0.993223i | \(0.537078\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14460.0i | 2.31669i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 3008.00i | − 0.477690i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6516.00 | 1.02575 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2100.00 | 0.327711 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8838.00i | 1.36729i | 0.729816 | + | 0.683644i | \(0.239606\pi\) | ||||
−0.729816 | + | 0.683644i | \(0.760394\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 7810.00i | − 1.19788i | −0.800794 | − | 0.598939i | \(-0.795589\pi\) | ||||
0.800794 | − | 0.598939i | \(-0.204411\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2760.00 | 0.419709 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5906.00 | 0.890495 | 0.445247 | − | 0.895408i | \(-0.353116\pi\) | ||||
0.445247 | + | 0.895408i | \(0.353116\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 700.000i | 0.104654i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 1080.00i | − 0.160111i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8904.00 | 1.30901 | 0.654506 | − | 0.756057i | \(-0.272877\pi\) | ||||
0.654506 | + | 0.756057i | \(0.272877\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8517.00 | −1.24173 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 10750.0i | − 1.55435i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 4410.00i | − 0.632411i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7370.00 | 1.04826 | 0.524129 | − | 0.851639i | \(-0.324391\pi\) | ||||
0.524129 | + | 0.851639i | \(0.324391\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3942.00 | 0.556131 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13284.0i | 1.85895i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 734.000i | 0.101890i | 0.998701 | + | 0.0509451i | \(0.0162234\pi\) | ||||
−0.998701 | + | 0.0509451i | \(0.983777\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1250.00 | −0.172133 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 852.000 | 0.116393 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10300.0i | 1.39598i | 0.716109 | + | 0.697989i | \(0.245921\pi\) | ||||
−0.716109 | + | 0.697989i | \(0.754079\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 11540.0i | − 1.55174i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2682.00 | −0.357817 | −0.178908 | − | 0.983866i | \(-0.557257\pi\) | ||||
−0.178908 | + | 0.983866i | \(0.557257\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1440.00 | −0.190621 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 4818.00i | − 0.632849i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 6114.00i | − 0.796895i | −0.917191 | − | 0.398447i | \(-0.869549\pi\) | ||||
0.917191 | − | 0.398447i | \(-0.130451\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −252.000 | −0.0325938 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3680.00 | 0.472345 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5800.00i | 0.738809i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 7174.00i | − 0.906934i | −0.891273 | − | 0.453467i | \(-0.850187\pi\) | ||||
0.891273 | − | 0.453467i | \(-0.149813\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −22320.0 | −2.80050 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10498.0 | 1.30734 | 0.653672 | − | 0.756778i | \(-0.273228\pi\) | ||||
0.653672 | + | 0.756778i | \(0.273228\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1128.00i | − 0.139428i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13145.0i | 1.61279i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3232.00 | −0.393622 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1810.00 | 0.218823 | 0.109412 | − | 0.993997i | \(-0.465103\pi\) | ||||
0.109412 | + | 0.993997i | \(0.465103\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 6700.00i | − 0.804104i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 10152.0i | − 1.20956i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3210.00 | 0.379693 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5720.00 | −0.671726 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3396.00i | 0.395956i | 0.980206 | + | 0.197978i | \(0.0634374\pi\) | ||||
−0.980206 | + | 0.197978i | \(0.936563\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14974.0i | 1.73346i | 0.498775 | + | 0.866732i | \(0.333784\pi\) | ||||
−0.498775 | + | 0.866732i | \(0.666216\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2774.00 | 0.318857 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 150.000 | 0.0171202 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4716.00i | 0.534481i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 960.000i | 0.108040i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13540.0 | 1.51322 | 0.756611 | − | 0.653865i | \(-0.226854\pi\) | ||||
0.756611 | + | 0.653865i | \(0.226854\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15426.0 | 1.71207 | 0.856035 | − | 0.516918i | \(-0.172921\pi\) | ||||
0.856035 | + | 0.516918i | \(0.172921\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7100.00i | 0.782572i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5208.00i | 0.570097i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10472.0 | −1.13850 | −0.569250 | − | 0.822165i | \(-0.692766\pi\) | ||||
−0.569250 | + | 0.822165i | \(0.692766\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1387.00 | 0.149768 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 722.000i | 0.0774340i | 0.999250 | + | 0.0387170i | \(0.0123271\pi\) | ||||
−0.999250 | + | 0.0387170i | \(0.987673\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4270.00i | 0.454871i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17300.0 | −1.83056 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11898.0 | −1.25056 | −0.625280 | − | 0.780401i | \(-0.715015\pi\) | ||||
−0.625280 | + | 0.780401i | \(0.715015\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 864.000i | 0.0902088i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 13240.0i | − 1.37322i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −540.000 | −0.0556387 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 790.000 | 0.0808635 | 0.0404318 | − | 0.999182i | \(-0.487127\pi\) | ||||
0.0404318 | + | 0.999182i | \(0.487127\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 2760.00i | − 0.280666i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 3418.00i | − 0.345319i | −0.984982 | − | 0.172660i | \(-0.944764\pi\) | ||||
0.984982 | − | 0.172660i | \(-0.0552360\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7534.00 | 0.756230 | 0.378115 | − | 0.925759i | \(-0.376572\pi\) | ||||
0.378115 | + | 0.925759i | \(0.376572\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9400.00 | 0.937451 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14314.0i | 1.41836i | 0.705029 | + | 0.709179i | \(0.250934\pi\) | ||||
−0.705029 | + | 0.709179i | \(0.749066\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 9972.00i | − 0.981800i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29460.0 | 2.88205 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1056.00 | 0.102653 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 3100.00i | − 0.299448i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 53874.0i | 5.17132i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7016.00 | 0.669247 | 0.334623 | − | 0.942352i | \(-0.391391\pi\) | ||||
0.334623 | + | 0.942352i | \(0.391391\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1212.00 | −0.114891 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7560.00i | 0.712199i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 2390.00i | − 0.223761i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15190.0 | 1.41340 | 0.706699 | − | 0.707515i | \(-0.250184\pi\) | ||||
0.706699 | + | 0.707515i | \(0.250184\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20980.0 | −1.94018 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 12624.0i | − 1.16031i | −0.814505 | − | 0.580156i | \(-0.802992\pi\) | ||||
0.814505 | − | 0.580156i | \(-0.197008\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 852.000i | − 0.0778340i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5840.00 | −0.530280 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2520.00 | −0.227440 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2492.00i | 0.223562i | 0.993733 | + | 0.111781i | \(0.0356555\pi\) | ||||
−0.993733 | + | 0.111781i | \(0.964345\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8660.00i | 0.772256i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11714.0 | 1.03837 | 0.519186 | − | 0.854661i | \(-0.326235\pi\) | ||||
0.519186 | + | 0.854661i | \(0.326235\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8970.00 | −0.790415 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 21610.0i | − 1.89297i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 5618.00i | − 0.489221i | −0.969621 | − | 0.244610i | \(-0.921340\pi\) | ||||
0.969621 | − | 0.244610i | \(-0.0786601\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15876.0 | 1.37439 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −57040.0 | −4.90912 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3210.00i | 0.274659i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 608.000i | 0.0517211i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16780.0 | −1.41919 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13770.0 | −1.15792 | −0.578958 | − | 0.815357i | \(-0.696541\pi\) | ||||
−0.578958 | + | 0.815357i | \(0.696541\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6986.00i | 0.584085i | 0.956405 | + | 0.292042i | \(0.0943349\pi\) | ||||
−0.956405 | + | 0.292042i | \(0.905665\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 4500.00i | − 0.374088i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1128.00 | −0.0932380 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10403.0 | −0.855018 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 41172.0i | − 3.36481i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 324.000i | 0.0263302i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4250.00 | 0.343446 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16200.0 | 1.30183 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 304.000i | 0.0242935i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11958.0i | 0.950304i | 0.879904 | + | 0.475152i | \(0.157607\pi\) | ||||
−0.879904 | + | 0.475152i | \(0.842393\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25100.0 | −1.98369 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3330.00 | −0.261728 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4194.00i | 0.327829i | 0.986475 | + | 0.163915i | \(0.0524121\pi\) | ||||
−0.986475 | + | 0.163915i | \(0.947588\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 19126.0i | 1.48684i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17608.0 | −1.36139 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20880.0 | −1.60562 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 10100.0i | − 0.772470i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 5382.00i | − 0.409412i | −0.978823 | − | 0.204706i | \(-0.934376\pi\) | ||||
0.978823 | − | 0.204706i | \(-0.0656239\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 396.000 | 0.0299625 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 960.000 | 0.0722482 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 15418.0i | − 1.15416i | −0.816688 | − | 0.577079i | \(-0.804192\pi\) | ||||
0.816688 | − | 0.577079i | \(-0.195808\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 7230.00i | − 0.538351i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −47322.0 | −3.50500 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5778.00 | 0.425705 | 0.212853 | − | 0.977084i | \(-0.431725\pi\) | ||||
0.212853 | + | 0.977084i | \(0.431725\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6024.00i | 0.441500i | 0.975330 | + | 0.220750i | \(0.0708505\pi\) | ||||
−0.975330 | + | 0.220750i | \(0.929149\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 3720.00i | − 0.271213i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1050.00 | −0.0761531 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 554.000 | 0.0399711 | 0.0199855 | − | 0.999800i | \(-0.493638\pi\) | ||||
0.0199855 | + | 0.999800i | \(0.493638\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 29380.0i | − 2.10879i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11556.0i | 0.825170i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11808.0 | −0.838829 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2190.00 | −0.154778 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 2386.00i | − 0.167770i | −0.996475 | − | 0.0838848i | \(-0.973267\pi\) | ||||
0.996475 | − | 0.0838848i | \(-0.0267328\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23312.0i | 1.63082i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22340.0 | −1.55490 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −846.000 | −0.0585853 | −0.0292926 | − | 0.999571i | \(-0.509325\pi\) | ||||
−0.0292926 | + | 0.999571i | \(0.509325\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 540.000i | 0.0372065i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 30480.0i | 2.08955i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22304.0 | 1.52140 | 0.760698 | − | 0.649105i | \(-0.224857\pi\) | ||||
0.760698 | + | 0.649105i | \(0.224857\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5510.00 | −0.373973 | −0.186986 | − | 0.982363i | \(-0.559872\pi\) | ||||
−0.186986 | + | 0.982363i | \(0.559872\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 40442.0i | − 2.73122i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5375.00i | 0.361198i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8234.00 | 0.550589 | 0.275295 | − | 0.961360i | \(-0.411225\pi\) | ||||
0.275295 | + | 0.961360i | \(0.411225\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −25560.0 | −1.70073 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 228.000i | 0.0150964i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1046.00i | 0.0689193i | 0.999406 | + | 0.0344597i | \(0.0109710\pi\) | ||||
−0.999406 | + | 0.0344597i | \(0.989029\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2700.00 | −0.177032 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3862.00 | 0.251991 | 0.125995 | − | 0.992031i | \(-0.459788\pi\) | ||||
0.125995 | + | 0.992031i | \(0.459788\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13964.0i | 0.906721i | 0.891327 | + | 0.453361i | \(0.149775\pi\) | ||||
−0.891327 | + | 0.453361i | \(0.850225\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 19320.0i | 1.24845i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15372.0 | −0.988549 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 19840.0i | − 1.26369i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1212.00i | 0.0768293i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14884.0 | −0.939022 | −0.469511 | − | 0.882927i | \(-0.655570\pi\) | ||||
−0.469511 | + | 0.882927i | \(0.655570\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −48960.0 | −3.07423 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5770.00i | 0.360591i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 114.000i | 0.00709081i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10220.0 | −0.632703 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17838.0 | 1.09916 | 0.549578 | − | 0.835443i | \(-0.314789\pi\) | ||||
0.549578 | + | 0.835443i | \(0.314789\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7814.00i | 0.479244i | 0.970866 | + | 0.239622i | \(0.0770236\pi\) | ||||
−0.970866 | + | 0.239622i | \(0.922976\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3300.00i | 0.201453i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 774.000 | 0.0470310 | 0.0235155 | − | 0.999723i | \(-0.492514\pi\) | ||||
0.0235155 | + | 0.999723i | \(0.492514\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9024.00 | 0.545798 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 33840.0i | 2.03732i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 23422.0i | − 1.40364i | −0.712357 | − | 0.701818i | \(-0.752372\pi\) | ||||
0.712357 | − | 0.701818i | \(-0.247628\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1840.00 | −0.109763 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 64386.0 | 3.82334 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13508.0i | 0.798478i | 0.916847 | + | 0.399239i | \(0.130726\pi\) | ||||
−0.916847 | + | 0.399239i | \(0.869274\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6222.00i | 0.366124i | 0.983101 | + | 0.183062i | \(0.0586009\pi\) | ||||
−0.983101 | + | 0.183062i | \(0.941399\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 360.000 | 0.0210878 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11160.0 | 0.650776 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5964.00i | 0.346217i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 53020.0i | − 3.06408i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4192.00 | −0.241178 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15566.0 | −0.891568 | −0.445784 | − | 0.895141i | \(-0.647075\pi\) | ||||
−0.445784 | + | 0.895141i | \(0.647075\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 11500.0i | − 0.655756i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 2234.00i | − 0.126824i | −0.997987 | − | 0.0634118i | \(-0.979802\pi\) | ||||
0.997987 | − | 0.0634118i | \(-0.0201982\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8604.00 | 0.486290 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37780.0 | 2.12589 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13282.0i | 0.744102i | 0.928212 | + | 0.372051i | \(0.121345\pi\) | ||||
−0.928212 | + | 0.372051i | \(0.878655\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3350.00i | 0.186857i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30340.0 | 1.68492 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4428.00 | −0.244838 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27416.0i | 1.50934i | 0.656105 | + | 0.754670i | \(0.272203\pi\) | ||||
−0.656105 | + | 0.754670i | \(0.727797\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 21024.0i | − 1.15243i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2860.00 | 0.156095 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 324.000 | 0.0176074 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 34780.0i | − 1.88197i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25626.0i | 1.38071i | 0.723469 | + | 0.690357i | \(0.242547\pi\) | ||||
−0.723469 | + | 0.690357i | \(0.757453\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25048.0 | 1.34382 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1900.00 | −0.101501 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 32292.0i | − 1.71777i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 11702.0i | − 0.619856i | −0.950760 | − | 0.309928i | \(-0.899695\pi\) | ||||
0.950760 | − | 0.309928i | \(-0.100305\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −84680.0 | −4.46659 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7896.00 | 0.414737 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 480.000i | − 0.0251063i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15600.0i | 0.812542i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28008.0 | 1.45274 | 0.726371 | − | 0.687302i | \(-0.241205\pi\) | ||||
0.726371 | + | 0.687302i | \(0.241205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11556.0 | −0.596904 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32180.0i | 1.65531i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 3550.00i | − 0.181853i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7682.00 | −0.391898 | −0.195949 | − | 0.980614i | \(-0.562779\pi\) | ||||
−0.195949 | + | 0.980614i | \(0.562779\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −67717.0 | −3.44038 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 396.000i | − 0.0200364i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 14270.0i | − 0.719065i | −0.933133 | − | 0.359532i | \(-0.882936\pi\) | ||||
0.933133 | − | 0.359532i | \(-0.117064\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −950.000 | −0.0476752 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8864.00 | 0.443025 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 29324.0i | − 1.45968i | −0.683620 | − | 0.729838i | \(-0.739595\pi\) | ||||
0.683620 | − | 0.729838i | \(-0.260405\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 7440.00i | − 0.368846i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29258.0 | 1.44465 | 0.722323 | − | 0.691556i | \(-0.243074\pi\) | ||||
0.722323 | + | 0.691556i | \(0.243074\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8650.00 | 0.425385 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 46866.0i | 2.29550i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15300.0i | 0.746395i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19076.0 | −0.926888 | −0.463444 | − | 0.886126i | \(-0.653387\pi\) | ||||
−0.463444 | + | 0.886126i | \(0.653387\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6880.00 | 0.332963 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6620.00i | 0.319108i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22670.0i | 1.08845i | 0.838940 | + | 0.544224i | \(0.183176\pi\) | ||||
−0.838940 | + | 0.544224i | \(0.816824\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6720.00 | −0.321371 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23206.0 | 1.10541 | 0.552705 | − | 0.833377i | \(-0.313596\pi\) | ||||
0.552705 | + | 0.833377i | \(0.313596\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 11988.0i | − 0.568800i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2190.00i | 0.103503i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3384.00 | 0.159308 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1854.00 | −0.0869401 | −0.0434701 | − | 0.999055i | \(-0.513841\pi\) | ||||
−0.0434701 | + | 0.999055i | \(0.513841\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 21700.0i | − 1.01363i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 6474.00i | − 0.301234i | −0.988592 | − | 0.150617i | \(-0.951874\pi\) | ||||
0.988592 | − | 0.150617i | \(-0.0481260\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4700.00 | −0.217844 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 36360.0 | 1.67877 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 6696.00i | − 0.307971i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 2240.00i | − 0.102629i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −65320.0 | −2.98129 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14730.0 | −0.669728 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20354.0i | 0.921908i | 0.887424 | + | 0.460954i | \(0.152493\pi\) | ||||
−0.887424 | + | 0.460954i | \(0.847507\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 22740.0i | − 1.02607i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26028.0 | 1.16997 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1572.00 | −0.0703952 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 36900.0i | − 1.64617i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1886.00i | − 0.0838213i | −0.999121 | − | 0.0419106i | \(-0.986656\pi\) | ||||
0.999121 | − | 0.0419106i | \(-0.0133445\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 228.000 | 0.0100952 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −62342.0 | −2.75000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14112.0i | 0.620176i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 3780.00i | − 0.165500i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 71460.0 | 3.11711 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9462.00 | 0.411207 | 0.205603 | − | 0.978635i | \(-0.434084\pi\) | ||||
0.205603 | + | 0.978635i | \(0.434084\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24512.0i | 1.06132i | 0.847584 | + | 0.530661i | \(0.178056\pi\) | ||||
−0.847584 | + | 0.530661i | \(0.821944\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26040.0i | 1.12332i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10490.0 | 0.450857 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8184.00 | −0.350455 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 7884.00i | − 0.336373i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 36242.0i | − 1.54063i | −0.637666 | − | 0.770313i | \(-0.720100\pi\) | ||||
0.637666 | − | 0.770313i | \(-0.279900\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17718.0 | −0.750438 | −0.375219 | − | 0.926936i | \(-0.622433\pi\) | ||||
−0.375219 | + | 0.926936i | \(0.622433\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4000.00 | 0.168803 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6726.00i | 0.282812i | 0.989952 | + | 0.141406i | \(0.0451624\pi\) | ||||
−0.989952 | + | 0.141406i | \(0.954838\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41722.0i | 1.74797i | 0.485955 | + | 0.873984i | \(0.338472\pi\) | ||||
−0.485955 | + | 0.873984i | \(0.661528\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 51500.0 | 2.14984 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 114.000 | 0.00474174 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 4330.00i | − 0.179456i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 86480.0i | 3.57131i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16720.0 | 0.688008 | 0.344004 | − | 0.938968i | \(-0.388217\pi\) | ||||
0.344004 | + | 0.938968i | \(0.388217\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4225.00 | 0.173234 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 52700.0i | 2.15313i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10805.0i | 0.439886i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19350.0 | −0.784975 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 34340.0 | 1.38816 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 8484.00i | − 0.341748i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33286.0i | 1.33610i | 0.744118 | + | 0.668049i | \(0.232870\pi\) | ||||
−0.744118 | + | 0.668049i | \(0.767130\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 45260.0 | 1.81036 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −38978.0 | −1.55363 | −0.776816 | − | 0.629727i | \(-0.783167\pi\) | ||||
−0.776816 | + | 0.629727i | \(0.783167\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1916.00i | − 0.0761037i | −0.999276 | − | 0.0380518i | \(-0.987885\pi\) | ||||
0.999276 | − | 0.0380518i | \(-0.0121152\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 9720.00i | − 0.384735i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2374.00 | 0.0936407 | 0.0468203 | − | 0.998903i | \(-0.485091\pi\) | ||||
0.0468203 | + | 0.998903i | \(0.485091\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8390.00 | 0.329790 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 48770.0i | 1.91040i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 18560.0i | − 0.724517i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3324.00 | 0.129310 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 34894.0 | 1.35279 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2250.00i | 0.0869302i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32722.0i | 1.25991i | 0.776631 | + | 0.629956i | \(0.216927\pi\) | ||||
−0.776631 | + | 0.629956i | \(0.783073\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 98780.0 | 3.79041 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5390.00 | 0.206122 | 0.103061 | − | 0.994675i | \(-0.467136\pi\) | ||||
0.103061 | + | 0.994675i | \(0.467136\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43238.0i | 1.64788i | 0.566680 | + | 0.823938i | \(0.308228\pi\) | ||||
−0.566680 | + | 0.823938i | \(0.691772\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28200.0i | 1.07111i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11010.0 | −0.416775 | −0.208388 | − | 0.978046i | \(-0.566822\pi\) | ||||
−0.208388 | + | 0.978046i | \(0.566822\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20772.0 | −0.783656 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 42064.0i | − 1.58159i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 4712.00i | − 0.176575i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8100.00 | −0.302517 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2520.00 | −0.0938020 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26696.0i | 0.990391i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4428.00i | 0.163727i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11880.0 | −0.437809 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12550.0 | 0.460968 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 74.0000i | − 0.00270907i | −0.999999 | − | 0.00135454i | \(-0.999569\pi\) | ||||
0.999999 | − | 0.00135454i | \(-0.000431163\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 130962.i | − 4.77859i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17460.0 | −0.634990 | −0.317495 | − | 0.948260i | \(-0.602842\pi\) | ||||
−0.317495 | + | 0.948260i | \(0.602842\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10272.0 | −0.372348 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 13100.0i | − 0.473303i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 6624.00i | − 0.238543i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17072.0 | 0.612789 | 0.306395 | − | 0.951905i | \(-0.400877\pi\) | ||||
0.306395 | + | 0.951905i | \(0.400877\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −80540.0 | −2.88152 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 840.000i | − 0.0299555i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5050.00i | 0.179506i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −46866.0 | −1.66050 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14826.0 | −0.523601 | −0.261800 | − | 0.965122i | \(-0.584316\pi\) | ||||
−0.261800 | + | 0.965122i | \(0.584316\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 2356.00i | − 0.0829375i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 54920.0i | − 1.92712i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −480.000 | −0.0167890 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3354.00 | −0.116937 | −0.0584687 | − | 0.998289i | \(-0.518622\pi\) | ||||
−0.0584687 | + | 0.998289i | \(0.518622\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 4220.00i | − 0.146661i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 15434.0i | − 0.534680i | −0.963602 | − | 0.267340i | \(-0.913855\pi\) | ||||
0.963602 | − | 0.267340i | \(-0.0861447\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2268.00 | −0.0783205 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 41400.0 | 1.42512 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9306.00i | 0.319329i | 0.987171 | + | 0.159664i | \(0.0510412\pi\) | ||||
−0.987171 | + | 0.159664i | \(0.948959\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5292.00i | 0.181017i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 61940.0 | 2.11203 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12202.0 | −0.414755 | −0.207378 | − | 0.978261i | \(-0.566493\pi\) | ||||
−0.207378 | + | 0.978261i | \(0.566493\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1860.00i | 0.0630243i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 22720.0i | − 0.767433i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12060.0 | −0.406087 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5553.00 | 0.186399 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 62050.0i | 2.07636i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14690.0i | 0.490039i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17478.0 | 0.581235 | 0.290618 | − | 0.956839i | \(-0.406139\pi\) | ||||
0.290618 | + | 0.956839i | \(0.406139\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7440.00 | −0.246653 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10920.0i | 0.360906i | 0.983584 | + | 0.180453i | \(0.0577563\pi\) | ||||
−0.983584 | + | 0.180453i | \(0.942244\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10296.0i | 0.339234i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1500.00 | 0.0492702 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10834.0 | 0.354770 | 0.177385 | − | 0.984142i | \(-0.443236\pi\) | ||||
0.177385 | + | 0.984142i | \(0.443236\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 13664.0i | − 0.446071i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 48618.0i | − 1.58232i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36862.0 | −1.19605 | −0.598024 | − | 0.801478i | \(-0.704047\pi\) | ||||
−0.598024 | + | 0.801478i | \(0.704047\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11170.0 | 0.361326 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 6840.00i | − 0.220587i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2772.00i | 0.0891248i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5380.00 | −0.172453 | −0.0862267 | − | 0.996276i | \(-0.527481\pi\) | ||||
−0.0862267 | + | 0.996276i | \(0.527481\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 76880.0 | 2.45691 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 15240.0i | − 0.485568i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 31266.0i | − 0.993184i | −0.867984 | − | 0.496592i | \(-0.834585\pi\) | ||||
0.867984 | − | 0.496592i | \(-0.165415\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 92920.0 | 2.94280 |
(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 | 1280.4.d.b.641.1 | 2 | ||
4.3 | odd | 2 | 1280.4.d.o.641.2 | 2 | |||
8.3 | odd | 2 | 1280.4.d.o.641.1 | 2 | |||
8.5 | even | 2 | inner | 1280.4.d.b.641.2 | 2 | ||
16.3 | odd | 4 | 320.4.a.a.1.1 | 1 | |||
16.5 | even | 4 | 80.4.a.a.1.1 | 1 | |||
16.11 | odd | 4 | 40.4.a.c.1.1 | ✓ | 1 | ||
16.13 | even | 4 | 320.4.a.n.1.1 | 1 | |||
48.5 | odd | 4 | 720.4.a.ba.1.1 | 1 | |||
48.11 | even | 4 | 360.4.a.i.1.1 | 1 | |||
80.19 | odd | 4 | 1600.4.a.ca.1.1 | 1 | |||
80.27 | even | 4 | 200.4.c.a.49.1 | 2 | |||
80.29 | even | 4 | 1600.4.a.a.1.1 | 1 | |||
80.37 | odd | 4 | 400.4.c.a.49.2 | 2 | |||
80.43 | even | 4 | 200.4.c.a.49.2 | 2 | |||
80.53 | odd | 4 | 400.4.c.a.49.1 | 2 | |||
80.59 | odd | 4 | 200.4.a.a.1.1 | 1 | |||
80.69 | even | 4 | 400.4.a.u.1.1 | 1 | |||
112.27 | even | 4 | 1960.4.a.a.1.1 | 1 | |||
240.59 | even | 4 | 1800.4.a.bd.1.1 | 1 | |||
240.107 | odd | 4 | 1800.4.f.n.649.1 | 2 | |||
240.203 | odd | 4 | 1800.4.f.n.649.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.4.a.c.1.1 | ✓ | 1 | 16.11 | odd | 4 | ||
80.4.a.a.1.1 | 1 | 16.5 | even | 4 | |||
200.4.a.a.1.1 | 1 | 80.59 | odd | 4 | |||
200.4.c.a.49.1 | 2 | 80.27 | even | 4 | |||
200.4.c.a.49.2 | 2 | 80.43 | even | 4 | |||
320.4.a.a.1.1 | 1 | 16.3 | odd | 4 | |||
320.4.a.n.1.1 | 1 | 16.13 | even | 4 | |||
360.4.a.i.1.1 | 1 | 48.11 | even | 4 | |||
400.4.a.u.1.1 | 1 | 80.69 | even | 4 | |||
400.4.c.a.49.1 | 2 | 80.53 | odd | 4 | |||
400.4.c.a.49.2 | 2 | 80.37 | odd | 4 | |||
720.4.a.ba.1.1 | 1 | 48.5 | odd | 4 | |||
1280.4.d.b.641.1 | 2 | 1.1 | even | 1 | trivial | ||
1280.4.d.b.641.2 | 2 | 8.5 | even | 2 | inner | ||
1280.4.d.o.641.1 | 2 | 8.3 | odd | 2 | |||
1280.4.d.o.641.2 | 2 | 4.3 | odd | 2 | |||
1600.4.a.a.1.1 | 1 | 80.29 | even | 4 | |||
1600.4.a.ca.1.1 | 1 | 80.19 | odd | 4 | |||
1800.4.a.bd.1.1 | 1 | 240.59 | even | 4 | |||
1800.4.f.n.649.1 | 2 | 240.107 | odd | 4 | |||
1800.4.f.n.649.2 | 2 | 240.203 | odd | 4 | |||
1960.4.a.a.1.1 | 1 | 112.27 | even | 4 |