Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,4,Mod(449,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, 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("700.449");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.e (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: | \(41.3013370040\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 700.449 |
Dual form | 700.4.e.f.449.1 |
$q$-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 \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 4.00000i | 0.769800i | 0.922958 | + | 0.384900i | \(0.125764\pi\) | ||||
−0.922958 | + | 0.384900i | \(0.874236\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 7.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 11.0000 | 0.407407 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −12.0000 | −0.328921 | −0.164461 | − | 0.986384i | \(-0.552588\pi\) | ||||
−0.164461 | + | 0.986384i | \(0.552588\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 82.0000i | − 1.74944i | −0.484629 | − | 0.874720i | \(-0.661046\pi\) | ||||
0.484629 | − | 0.874720i | \(-0.338954\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 30.0000i | 0.428004i | 0.976833 | + | 0.214002i | \(0.0686499\pi\) | ||||
−0.976833 | + | 0.214002i | \(0.931350\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −68.0000 | −0.821067 | −0.410533 | − | 0.911846i | \(-0.634657\pi\) | ||||
−0.410533 | + | 0.911846i | \(0.634657\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 28.0000 | 0.290957 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 216.000i | 1.95822i | 0.203326 | + | 0.979111i | \(0.434825\pi\) | ||||
−0.203326 | + | 0.979111i | \(0.565175\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 152.000i | 1.08342i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −246.000 | −1.57521 | −0.787604 | − | 0.616181i | \(-0.788679\pi\) | ||||
−0.787604 | + | 0.616181i | \(0.788679\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −112.000 | −0.648897 | −0.324448 | − | 0.945903i | \(-0.605179\pi\) | ||||
−0.324448 | + | 0.945903i | \(0.605179\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 48.0000i | − 0.253204i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 110.000i | − 0.488754i | −0.969680 | − | 0.244377i | \(-0.921417\pi\) | ||||
0.969680 | − | 0.244377i | \(-0.0785834\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 328.000 | 1.34672 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −246.000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 172.000i | − 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 192.000i | − 0.595874i | −0.954586 | − | 0.297937i | \(-0.903701\pi\) | ||||
0.954586 | − | 0.297937i | \(-0.0962985\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −120.000 | −0.329478 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 558.000i | 1.44617i | 0.690757 | + | 0.723087i | \(0.257277\pi\) | ||||
−0.690757 | + | 0.723087i | \(0.742723\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 272.000i | − 0.632058i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −540.000 | −1.19156 | −0.595780 | − | 0.803148i | \(-0.703157\pi\) | ||||
−0.595780 | + | 0.803148i | \(0.703157\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 110.000 | 0.230886 | 0.115443 | − | 0.993314i | \(-0.463171\pi\) | ||||
0.115443 | + | 0.993314i | \(0.463171\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 77.0000i | − 0.153986i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 140.000i | − 0.255279i | −0.991821 | − | 0.127640i | \(-0.959260\pi\) | ||||
0.991821 | − | 0.127640i | \(-0.0407401\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −864.000 | −1.50744 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −840.000 | −1.40408 | −0.702040 | − | 0.712138i | \(-0.747727\pi\) | ||||
−0.702040 | + | 0.712138i | \(0.747727\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 550.000i | − 0.881817i | −0.897552 | − | 0.440908i | \(-0.854656\pi\) | ||||
0.897552 | − | 0.440908i | \(-0.145344\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 84.0000i | 0.124321i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 208.000 | 0.296226 | 0.148113 | − | 0.988970i | \(-0.452680\pi\) | ||||
0.148113 | + | 0.988970i | \(0.452680\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −311.000 | −0.426612 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 516.000i | 0.682390i | 0.939993 | + | 0.341195i | \(0.110832\pi\) | ||||
−0.939993 | + | 0.341195i | \(0.889168\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 984.000i | − 1.21260i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1398.00 | 1.66503 | 0.832515 | − | 0.554002i | \(-0.186900\pi\) | ||||
0.832515 | + | 0.554002i | \(0.186900\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −574.000 | −0.661226 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 448.000i | − 0.499521i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1586.00i | − 1.66014i | −0.557657 | − | 0.830072i | \(-0.688299\pi\) | ||||
0.557657 | − | 0.830072i | \(-0.311701\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −132.000 | −0.134005 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1242.00 | −1.22360 | −0.611800 | − | 0.791012i | \(-0.709554\pi\) | ||||
−0.611800 | + | 0.791012i | \(0.709554\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 680.000i | 0.650509i | 0.945627 | + | 0.325254i | \(0.105450\pi\) | ||||
−0.945627 | + | 0.325254i | \(0.894550\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 996.000i | − 0.899878i | −0.893059 | − | 0.449939i | \(-0.851446\pi\) | ||||
0.893059 | − | 0.449939i | \(-0.148554\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1382.00 | −1.21442 | −0.607209 | − | 0.794542i | \(-0.707711\pi\) | ||||
−0.607209 | + | 0.794542i | \(0.707711\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 440.000 | 0.376243 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 750.000i | − 0.624372i | −0.950021 | − | 0.312186i | \(-0.898939\pi\) | ||||
0.950021 | − | 0.312186i | \(-0.101061\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 902.000i | − 0.712734i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 210.000 | 0.161770 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 984.000i | − 0.721336i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 176.000i | − 0.122972i | −0.998108 | − | 0.0614861i | \(-0.980416\pi\) | ||||
0.998108 | − | 0.0614861i | \(-0.0195840\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 688.000 | 0.469574 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1548.00 | −1.03244 | −0.516219 | − | 0.856457i | \(-0.672661\pi\) | ||||
−0.516219 | + | 0.856457i | \(0.672661\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 476.000i | 0.310334i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 378.000i | − 0.235728i | −0.993030 | − | 0.117864i | \(-0.962395\pi\) | ||||
0.993030 | − | 0.117864i | \(-0.0376047\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2500.00 | 1.52552 | 0.762760 | − | 0.646682i | \(-0.223844\pi\) | ||||
0.762760 | + | 0.646682i | \(0.223844\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 768.000 | 0.458704 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 984.000i | 0.575428i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 196.000i | − 0.109971i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −846.000 | −0.465148 | −0.232574 | − | 0.972579i | \(-0.574715\pi\) | ||||
−0.232574 | + | 0.972579i | \(0.574715\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2536.00 | −1.36673 | −0.683367 | − | 0.730075i | \(-0.739485\pi\) | ||||
−0.683367 | + | 0.730075i | \(0.739485\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 330.000i | 0.174372i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1186.00i | 0.602886i | 0.953484 | + | 0.301443i | \(0.0974683\pi\) | ||||
−0.953484 | + | 0.301443i | \(0.902532\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2232.00 | −1.11326 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1512.00 | 0.740138 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2108.00i | 1.01295i | 0.862254 | + | 0.506476i | \(0.169052\pi\) | ||||
−0.862254 | + | 0.506476i | \(0.830948\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1944.00i | 0.900786i | 0.892830 | + | 0.450393i | \(0.148716\pi\) | ||||
−0.892830 | + | 0.450393i | \(0.851284\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4527.00 | −2.06054 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −748.000 | −0.334509 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1362.00i | − 0.598560i | −0.954165 | − | 0.299280i | \(-0.903253\pi\) | ||||
0.954165 | − | 0.299280i | \(-0.0967465\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 2160.00i | − 0.917263i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1596.00 | −0.666428 | −0.333214 | − | 0.942851i | \(-0.608133\pi\) | ||||
−0.333214 | + | 0.942851i | \(0.608133\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1690.00 | −0.694015 | −0.347007 | − | 0.937862i | \(-0.612802\pi\) | ||||
−0.347007 | + | 0.937862i | \(0.612802\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 440.000i | 0.177736i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 360.000i | − 0.140780i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1064.00 | 0.409495 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3552.00 | 1.34562 | 0.672811 | − | 0.739815i | \(-0.265087\pi\) | ||||
0.672811 | + | 0.739815i | \(0.265087\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 2686.00i | − 1.00177i | −0.865512 | − | 0.500887i | \(-0.833007\pi\) | ||||
0.865512 | − | 0.500887i | \(-0.166993\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1410.00i | 0.509941i | 0.966949 | + | 0.254970i | \(0.0820657\pi\) | ||||
−0.966949 | + | 0.254970i | \(0.917934\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2968.00 | 1.05727 | 0.528633 | − | 0.848850i | \(-0.322705\pi\) | ||||
0.528633 | + | 0.848850i | \(0.322705\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 560.000 | 0.196514 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1722.00i | 0.595373i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2376.00i | 0.797794i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 816.000 | 0.270067 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1348.00 | −0.439811 | −0.219906 | − | 0.975521i | \(-0.570575\pi\) | ||||
−0.219906 | + | 0.975521i | \(0.570575\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 3360.00i | − 1.08086i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 784.000i | 0.245260i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2200.00 | 0.678823 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2460.00 | 0.748767 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3872.00i | 1.16273i | 0.813644 | + | 0.581364i | \(0.197481\pi\) | ||||
−0.813644 | + | 0.581364i | \(0.802519\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 5364.00i | − 1.56838i | −0.620524 | − | 0.784188i | \(-0.713080\pi\) | ||||
0.620524 | − | 0.784188i | \(-0.286920\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 874.000 | 0.252208 | 0.126104 | − | 0.992017i | \(-0.459753\pi\) | ||||
0.126104 | + | 0.992017i | \(0.459753\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −336.000 | −0.0957021 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 378.000i | 0.106282i | 0.998587 | + | 0.0531408i | \(0.0169232\pi\) | ||||
−0.998587 | + | 0.0531408i | \(0.983077\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 832.000i | 0.228035i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1920.00 | −0.519642 | −0.259821 | − | 0.965657i | \(-0.583664\pi\) | ||||
−0.259821 | + | 0.965657i | \(0.583664\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4322.00 | 1.15521 | 0.577603 | − | 0.816318i | \(-0.303988\pi\) | ||||
0.577603 | + | 0.816318i | \(0.303988\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2860.00i | 0.755017i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5576.00i | 1.43641i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2064.00 | −0.525304 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5292.00 | 1.33079 | 0.665395 | − | 0.746492i | \(-0.268263\pi\) | ||||
0.665395 | + | 0.746492i | \(0.268263\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2592.00i | − 0.644101i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5118.00i | 1.24223i | 0.783721 | + | 0.621113i | \(0.213319\pi\) | ||||
−0.783721 | + | 0.621113i | \(0.786681\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −770.000 | −0.184732 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2706.00 | −0.641752 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3768.00i | 0.883440i | 0.897153 | + | 0.441720i | \(0.145632\pi\) | ||||
−0.897153 | + | 0.441720i | \(0.854368\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5592.00i | 1.28174i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3918.00 | −0.888047 | −0.444024 | − | 0.896015i | \(-0.646449\pi\) | ||||
−0.444024 | + | 0.896015i | \(0.646449\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4880.00 | 1.09387 | 0.546935 | − | 0.837175i | \(-0.315794\pi\) | ||||
0.546935 | + | 0.837175i | \(0.315794\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 2296.00i | − 0.509012i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3538.00i | 0.767429i | 0.923452 | + | 0.383714i | \(0.125355\pi\) | ||||
−0.923452 | + | 0.383714i | \(0.874645\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1232.00 | −0.264365 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5430.00 | −1.15276 | −0.576382 | − | 0.817180i | \(-0.695536\pi\) | ||||
−0.576382 | + | 0.817180i | \(0.695536\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 6436.00i | − 1.35187i | −0.736959 | − | 0.675937i | \(-0.763739\pi\) | ||||
0.736959 | − | 0.675937i | \(-0.236261\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1722.00i | 0.354169i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4013.00 | 0.816813 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6344.00 | 1.27798 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1350.00i | 0.269174i | 0.990902 | + | 0.134587i | \(0.0429707\pi\) | ||||
−0.990902 | + | 0.134587i | \(0.957029\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 1824.00i | − 0.356361i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17712.0 | 3.42579 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1204.00 | −0.230556 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 4968.00i | − 0.941928i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 3332.00i | − 0.619437i | −0.950828 | − | 0.309719i | \(-0.899765\pi\) | ||||
0.950828 | − | 0.309719i | \(-0.100235\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2720.00 | −0.500762 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4728.00 | −0.862059 | −0.431029 | − | 0.902338i | \(-0.641849\pi\) | ||||
−0.431029 | + | 0.902338i | \(0.641849\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5114.00i | 0.923516i | 0.887006 | + | 0.461758i | \(0.152781\pi\) | ||||
−0.887006 | + | 0.461758i | \(0.847219\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 7206.00i | − 1.27675i | −0.769726 | − | 0.638374i | \(-0.779607\pi\) | ||||
0.769726 | − | 0.638374i | \(-0.220393\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2952.00 | 0.518120 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3984.00 | 0.692726 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2040.00i | − 0.351420i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 5528.00i | − 0.934860i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1344.00 | −0.225219 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6260.00 | 1.03952 | 0.519759 | − | 0.854313i | \(-0.326022\pi\) | ||||
0.519759 | + | 0.854313i | \(0.326022\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 1210.00i | − 0.199122i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5326.00i | 0.860907i | 0.902613 | + | 0.430454i | \(0.141646\pi\) | ||||
−0.902613 | + | 0.430454i | \(0.858354\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3000.00 | 0.480642 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1344.00 | 0.213436 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 36.0000i | − 0.00556940i | −0.999996 | − | 0.00278470i | \(-0.999114\pi\) | ||||
0.999996 | − | 0.00278470i | \(-0.000886398\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3134.00 | −0.480685 | −0.240343 | − | 0.970688i | \(-0.577260\pi\) | ||||
−0.240343 | + | 0.970688i | \(0.577260\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12464.0 | 1.89538 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1218.00i | 0.183648i | 0.995775 | + | 0.0918238i | \(0.0292697\pi\) | ||||
−0.995775 | + | 0.0918238i | \(0.970730\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 840.000i | 0.124531i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10008.0 | 1.47131 | 0.735657 | − | 0.677354i | \(-0.236873\pi\) | ||||
0.735657 | + | 0.677354i | \(0.236873\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2235.00 | −0.325849 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 4748.00i | − 0.686516i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1072.00i | 0.152474i | 0.997090 | + | 0.0762370i | \(0.0242906\pi\) | ||||
−0.997090 | + | 0.0762370i | \(0.975709\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2706.00 | −0.381758 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3906.00 | 0.546602 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 274.000i | − 0.0380353i | −0.999819 | − | 0.0190177i | \(-0.993946\pi\) | ||||
0.999819 | − | 0.0190177i | \(-0.00605388\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20172.0i | 2.75573i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7652.00 | −1.03709 | −0.518545 | − | 0.855051i | \(-0.673526\pi\) | ||||
−0.518545 | + | 0.855051i | \(0.673526\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 704.000 | 0.0946641 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2160.00i | 0.288175i | 0.989565 | + | 0.144087i | \(0.0460246\pi\) | ||||
−0.989565 | + | 0.144087i | \(0.953975\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1892.00i | − 0.248516i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1074.00 | 0.139984 | 0.0699922 | − | 0.997548i | \(-0.477703\pi\) | ||||
0.0699922 | + | 0.997548i | \(0.477703\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6480.00 | −0.838127 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 6192.00i | − 0.794771i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 6926.00i | − 0.875582i | −0.899077 | − | 0.437791i | \(-0.855761\pi\) | ||||
0.899077 | − | 0.437791i | \(-0.144239\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1904.00 | −0.238895 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1938.00 | 0.241344 | 0.120672 | − | 0.992692i | \(-0.461495\pi\) | ||||
0.120672 | + | 0.992692i | \(0.461495\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9184.00i | 1.13521i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1320.00i | 0.160762i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9574.00 | 1.15747 | 0.578733 | − | 0.815517i | \(-0.303547\pi\) | ||||
0.578733 | + | 0.815517i | \(0.303547\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1512.00 | 0.181463 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3780.00i | 0.450367i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10000.0i | 1.17435i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5052.00 | 0.589037 | 0.294518 | − | 0.955646i | \(-0.404841\pi\) | ||||
0.294518 | + | 0.955646i | \(0.404841\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3422.00 | 0.396147 | 0.198074 | − | 0.980187i | \(-0.436531\pi\) | ||||
0.198074 | + | 0.980187i | \(0.436531\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 2112.00i | − 0.242763i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 770.000i | − 0.0872668i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3936.00 | −0.442965 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2208.00 | 0.246765 | 0.123382 | − | 0.992359i | \(-0.460626\pi\) | ||||
0.123382 | + | 0.992359i | \(0.460626\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 6814.00i | − 0.756259i | −0.925753 | − | 0.378129i | \(-0.876567\pi\) | ||||
0.925753 | − | 0.378129i | \(-0.123433\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 14688.0i | − 1.60783i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12584.0 | −1.36811 | −0.684056 | − | 0.729429i | \(-0.739786\pi\) | ||||
−0.684056 | + | 0.729429i | \(0.739786\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −539.000 | −0.0582011 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6996.00i | 0.750316i | 0.926961 | + | 0.375158i | \(0.122412\pi\) | ||||
−0.926961 | + | 0.375158i | \(0.877588\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 3384.00i | − 0.358071i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9474.00 | −0.995781 | −0.497891 | − | 0.867240i | \(-0.665892\pi\) | ||||
−0.497891 | + | 0.867240i | \(0.665892\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2952.00 | 0.308213 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 10144.0i | − 1.05211i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 5786.00i | − 0.592249i | −0.955149 | − | 0.296124i | \(-0.904306\pi\) | ||||
0.955149 | − | 0.296124i | \(-0.0956943\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4560.00 | −0.463709 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3438.00 | 0.347340 | 0.173670 | − | 0.984804i | \(-0.444437\pi\) | ||||
0.173670 | + | 0.984804i | \(0.444437\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9392.00i | 0.942728i | 0.881939 | + | 0.471364i | \(0.156238\pi\) | ||||
−0.881939 | + | 0.471364i | \(0.843762\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4956.00i | 0.491084i | 0.969386 | + | 0.245542i | \(0.0789660\pi\) | ||||
−0.969386 | + | 0.245542i | \(0.921034\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −980.000 | −0.0964866 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4744.00 | −0.464102 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2064.00i | 0.200640i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6138.00i | 0.589182i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20592.0 | 1.96424 | 0.982122 | − | 0.188248i | \(-0.0602807\pi\) | ||||
0.982122 | + | 0.188248i | \(0.0602807\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9020.00 | −0.855045 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6048.00i | 0.569759i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13432.0i | 1.24982i | 0.780697 | + | 0.624910i | \(0.214864\pi\) | ||||
−0.780697 | + | 0.624910i | \(0.785136\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8432.00 | −0.779771 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14172.0 | −1.30259 | −0.651297 | − | 0.758823i | \(-0.725775\pi\) | ||||
−0.651297 | + | 0.758823i | \(0.725775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 7380.00i | − 0.674196i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5880.00i | 0.530692i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5956.00 | 0.534323 | 0.267162 | − | 0.963652i | \(-0.413914\pi\) | ||||
0.267162 | + | 0.963652i | \(0.413914\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7776.00 | −0.693425 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16968.0i | 1.50411i | 0.659102 | + | 0.752053i | \(0.270936\pi\) | ||||
−0.659102 | + | 0.752053i | \(0.729064\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 18108.0i | − 1.58620i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5214.00 | −0.454040 | −0.227020 | − | 0.973890i | \(-0.572898\pi\) | ||||
−0.227020 | + | 0.973890i | \(0.572898\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3850.00 | −0.333295 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 10336.0i | − 0.889562i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2304.00i | 0.195996i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5448.00 | 0.460772 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1398.00 | −0.117558 | −0.0587788 | − | 0.998271i | \(-0.518721\pi\) | ||||
−0.0587788 | + | 0.998271i | \(0.518721\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 18580.0i | − 1.55344i | −0.629849 | − | 0.776718i | \(-0.716883\pi\) | ||||
0.629849 | − | 0.776718i | \(-0.283117\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 3360.00i | − 0.277730i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −34489.0 | −2.83463 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5940.00 | −0.485450 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20172.0i | 1.63930i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 6384.00i | − 0.513017i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 588.000 | 0.0469888 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18970.0 | −1.50755 | −0.753774 | − | 0.657133i | \(-0.771769\pi\) | ||||
−0.753774 | + | 0.657133i | \(0.771769\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 6760.00i | − 0.534253i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16036.0i | 1.25347i | 0.779231 | + | 0.626737i | \(0.215610\pi\) | ||||
−0.779231 | + | 0.626737i | \(0.784390\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1210.00 | 0.0940647 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16728.0 | 1.29335 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1456.00i | − 0.111963i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 8310.00i | − 0.632147i | −0.948735 | − | 0.316074i | \(-0.897635\pi\) | ||||
0.948735 | − | 0.316074i | \(-0.102365\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14104.0 | −1.06715 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1440.00 | 0.108372 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7092.00i | 0.530892i | 0.964126 | + | 0.265446i | \(0.0855192\pi\) | ||||
−0.964126 | + | 0.265446i | \(0.914481\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2177.00i | 0.161244i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7158.00 | 0.527380 | 0.263690 | − | 0.964608i | \(-0.415060\pi\) | ||||
0.263690 | + | 0.964608i | \(0.415060\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6500.00 | 0.476386 | 0.238193 | − | 0.971218i | \(-0.423445\pi\) | ||||
0.238193 | + | 0.971218i | \(0.423445\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14208.0i | 1.03586i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 21794.0i | − 1.57244i | −0.617949 | − | 0.786218i | \(-0.712036\pi\) | ||||
0.617949 | − | 0.786218i | \(-0.287964\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10744.0 | 0.771166 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3612.00 | 0.257919 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 6696.00i | − 0.475678i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 9756.00i | − 0.685985i | −0.939338 | − | 0.342993i | \(-0.888559\pi\) | ||||
0.939338 | − | 0.342993i | \(-0.111441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7616.00 | 0.532787 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5640.00 | −0.392553 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5586.00i | 0.386829i | 0.981117 | + | 0.193414i | \(0.0619562\pi\) | ||||
−0.981117 | + | 0.193414i | \(0.938044\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11872.0i | 0.813884i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0000 | 0.00163708 | 0.000818542 | − | 1.00000i | \(-0.499739\pi\) | ||||
0.000818542 | 1.00000i | \(0.499739\pi\) | ||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4298.00 | 0.291712 | 0.145856 | − | 0.989306i | \(-0.453406\pi\) | ||||
0.145856 | + | 0.989306i | \(0.453406\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1540.00i | − 0.104003i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 8480.00i | − 0.567039i | −0.958966 | − | 0.283519i | \(-0.908498\pi\) | ||||
0.958966 | − | 0.283519i | \(-0.0915020\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6888.00 | −0.458318 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15744.0 | −1.04245 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1906.00i | − 0.125583i | −0.998027 | − | 0.0627917i | \(-0.980000\pi\) | ||||
0.998027 | − | 0.0627917i | \(-0.0200004\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 7482.00i | − 0.488191i | −0.969751 | − | 0.244096i | \(-0.921509\pi\) | ||||
0.969751 | − | 0.244096i | \(-0.0784911\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7348.00 | 0.477126 | 0.238563 | − | 0.971127i | \(-0.423324\pi\) | ||||
0.238563 | + | 0.971127i | \(0.423324\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −32832.0 | −2.12158 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 9786.00i | − 0.629322i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3264.00i | 0.207897i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3300.00 | 0.209189 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4520.00 | 0.285164 | 0.142582 | − | 0.989783i | \(-0.454460\pi\) | ||||
0.142582 | + | 0.989783i | \(0.454460\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 5392.00i | − 0.338567i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4018.00i | 0.249920i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9240.00 | −0.572032 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19806.0 | −1.22042 | −0.610211 | − | 0.792239i | \(-0.708915\pi\) | ||||
−0.610211 | + | 0.792239i | \(0.708915\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 5020.00i | − 0.307884i | −0.988080 | − | 0.153942i | \(-0.950803\pi\) | ||||
0.988080 | − | 0.153942i | \(-0.0491969\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 28392.0i | − 1.72520i | −0.505886 | − | 0.862600i | \(-0.668834\pi\) | ||||
0.505886 | − | 0.862600i | \(-0.331166\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6480.00 | 0.391930 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3136.00 | −0.188801 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 17562.0i | − 1.05246i | −0.850343 | − | 0.526228i | \(-0.823606\pi\) | ||||
0.850343 | − | 0.526228i | \(-0.176394\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 6050.00i | − 0.359259i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4716.00 | −0.278770 | −0.139385 | − | 0.990238i | \(-0.544513\pi\) | ||||
−0.139385 | + | 0.990238i | \(0.544513\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22762.0 | −1.33939 | −0.669697 | − | 0.742635i | \(-0.733576\pi\) | ||||
−0.669697 | + | 0.742635i | \(0.733576\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9840.00i | 0.576401i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 53136.0i | − 3.08461i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15488.0 | −0.895068 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1320.00 | −0.0759434 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4802.00i | 0.275042i | 0.990499 | + | 0.137521i | \(0.0439135\pi\) | ||||
−0.990499 | + | 0.137521i | \(0.956086\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 21558.0i | − 1.22384i | −0.790919 | − | 0.611921i | \(-0.790397\pi\) | ||||
0.790919 | − | 0.611921i | \(-0.209603\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11102.0 | −0.627475 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21456.0 | 1.20734 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3780.00i | 0.211768i | 0.994378 | + | 0.105884i | \(0.0337673\pi\) | ||||
−0.994378 | + | 0.105884i | \(0.966233\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3496.00i | 0.194150i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 45756.0 | 2.52999 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5500.00 | −0.302793 | −0.151396 | − | 0.988473i | \(-0.548377\pi\) | ||||
−0.151396 | + | 0.988473i | \(0.548377\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 924.000i | 0.0506491i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 7380.00i | − 0.401058i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1512.00 | −0.0818156 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10230.0 | 0.551187 | 0.275593 | − | 0.961274i | \(-0.411126\pi\) | ||||
0.275593 | + | 0.961274i | \(0.411126\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7480.00i | 0.401299i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8694.00i | 0.462477i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10190.0 | −0.539765 | −0.269883 | − | 0.962893i | \(-0.586985\pi\) | ||||
−0.269883 | + | 0.962893i | \(0.586985\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2288.00 | 0.120685 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 24192.0i | − 1.27068i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 7680.00i | − 0.400021i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9408.00 | −0.487982 | −0.243991 | − | 0.969777i | \(-0.578457\pi\) | ||||
−0.243991 | + | 0.969777i | \(0.578457\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4760.00 | 0.245869 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17288.0i | 0.889278i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33064.0i | 1.68676i | 0.537316 | + | 0.843381i | \(0.319438\pi\) | ||||
−0.537316 | + | 0.843381i | \(0.680562\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19837.0 | −1.00782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5160.00 | 0.261080 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 6322.00i | − 0.318565i | −0.987233 | − | 0.159283i | \(-0.949082\pi\) | ||||
0.987233 | − | 0.159283i | \(-0.0509181\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1680.00i | 0.0839669i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20740.0 | 1.03239 | 0.516193 | − | 0.856472i | \(-0.327349\pi\) | ||||
0.516193 | + | 0.856472i | \(0.327349\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22304.0 | −1.10575 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32040.0i | 1.58201i | 0.611810 | + | 0.791005i | \(0.290442\pi\) | ||||
−0.611810 | + | 0.791005i | \(0.709558\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5676.00i | 0.278011i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6972.00 | −0.340122 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12832.0 | −0.623497 | −0.311749 | − | 0.950165i | \(-0.600915\pi\) | ||||
−0.311749 | + | 0.950165i | \(0.600915\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21168.0i | 1.02444i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19906.0i | 0.955741i | 0.878430 | + | 0.477870i | \(0.158591\pi\) | ||||
−0.878430 | + | 0.477870i | \(0.841409\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10368.0 | 0.495829 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10842.0 | 0.516455 | 0.258227 | − | 0.966084i | \(-0.416862\pi\) | ||||
0.258227 | + | 0.966084i | \(0.416862\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9674.00i | 0.459007i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 44280.0i | 2.08456i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28274.0 | −1.32586 | −0.662930 | − | 0.748681i | \(-0.730687\pi\) | ||||
−0.662930 | + | 0.748681i | \(0.730687\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20472.0 | −0.956266 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 32346.0i | − 1.50505i | −0.658563 | − | 0.752526i | \(-0.728835\pi\) | ||||
0.658563 | − | 0.752526i | \(-0.271165\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 3080.00i | − 0.142206i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16728.0 | 0.769375 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10080.0 | 0.461832 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 37392.0i | − 1.70662i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 30116.0i | − 1.36407i | −0.731322 | − | 0.682033i | \(-0.761096\pi\) | ||||
0.731322 | − | 0.682033i | \(-0.238904\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15072.0 | −0.680073 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5250.00 | −0.235991 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 9020.00i | − 0.403921i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6594.00i | 0.293063i | 0.989206 | + | 0.146532i | \(0.0468110\pi\) | ||||
−0.989206 | + | 0.146532i | \(0.953189\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5760.00 | 0.255036 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15378.0 | 0.678346 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6600.00i | 0.290048i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 15672.0i | − 0.683619i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43014.0 | 1.86933 | 0.934667 | − | 0.355524i | \(-0.115697\pi\) | ||||
0.934667 | + | 0.355524i | \(0.115697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14164.0 | −0.613274 | −0.306637 | − | 0.951827i | \(-0.599204\pi\) | ||||
−0.306637 | + | 0.951827i | \(0.599204\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19520.0i | 0.842062i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11696.0i | 0.500846i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6314.00 | −0.269388 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34830.0 | 1.48060 | 0.740302 | − | 0.672275i | \(-0.234683\pi\) | ||||
0.740302 | + | 0.672275i | \(0.234683\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31016.0i | 1.31367i | 0.754035 | + | 0.656835i | \(0.228105\pi\) | ||||
−0.754035 | + | 0.656835i | \(0.771895\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 9876.00i | − 0.415263i | −0.978207 | − | 0.207631i | \(-0.933425\pi\) | ||||
0.978207 | − | 0.207631i | \(-0.0665754\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3154.00 | 0.132139 | 0.0660693 | − | 0.997815i | \(-0.478954\pi\) | ||||
0.0660693 | + | 0.997815i | \(0.478954\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14152.0 | −0.590767 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1470.00i | − 0.0611434i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 17024.0i | − 0.703029i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36936.0 | −1.51987 | −0.759936 | − | 0.649998i | \(-0.774770\pi\) | ||||
−0.759936 | + | 0.649998i | \(0.774770\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36127.0 | 1.48128 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 21720.0i | − 0.887398i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8309.00i | 0.337073i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25744.0 | 1.04067 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23760.0 | 0.957088 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9638.00i | 0.386869i | 0.981113 | + | 0.193434i | \(0.0619626\pi\) | ||||
−0.981113 | + | 0.193434i | \(0.938037\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 10266.0i | − 0.409195i | −0.978846 | − | 0.204597i | \(-0.934411\pi\) | ||||
0.978846 | − | 0.204597i | \(-0.0655885\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4084.00 | 0.162217 | 0.0811084 | − | 0.996705i | \(-0.474154\pi\) | ||||
0.0811084 | + | 0.996705i | \(0.474154\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6888.00 | −0.272639 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 192.000i | − 0.00757330i | −0.999993 | − | 0.00378665i | \(-0.998795\pi\) | ||||
0.999993 | − | 0.00378665i | \(-0.00120533\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16052.0i | 0.628783i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2496.00 | −0.0974350 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11480.0 | −0.446596 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 17446.0i | − 0.676355i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 19910.0i | − 0.766605i | −0.923623 | − | 0.383303i | \(-0.874787\pi\) | ||||
0.923623 | − | 0.383303i | \(-0.125213\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5400.00 | −0.207210 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14802.0 | 0.566052 | 0.283026 | − | 0.959112i | \(-0.408662\pi\) | ||||
0.283026 | + | 0.959112i | \(0.408662\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 32548.0i | − 1.24046i | −0.784419 | − | 0.620231i | \(-0.787039\pi\) | ||||
0.784419 | − | 0.620231i | \(-0.212961\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1464.00i | − 0.0554186i | −0.999616 | − | 0.0277093i | \(-0.991179\pi\) | ||||
0.999616 | − | 0.0277093i | \(-0.00882128\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1232.00 | −0.0464791 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3732.00 | 0.140322 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13056.0i | 0.489252i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 70848.0i | 2.63717i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27552.0 | 1.02215 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16740.0 | −0.618968 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 4816.00i | − 0.177482i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49564.0i | 1.81449i | 0.420599 | + | 0.907247i | \(0.361820\pi\) | ||||
−0.420599 | + | 0.907247i | \(0.638180\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13662.0 | −0.498504 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8448.00 | 0.307239 | 0.153619 | − | 0.988130i | \(-0.450907\pi\) | ||||
0.153619 | + | 0.988130i | \(0.450907\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 6192.00i | − 0.224453i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10836.0i | 0.390225i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14600.0 | −0.524058 | −0.262029 | − | 0.965060i | \(-0.584392\pi\) | ||||
−0.262029 | + | 0.965060i | \(0.584392\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13328.0 | 0.476843 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 68880.0i | 2.45635i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7480.00i | 0.265022i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21102.0 | 0.745247 | 0.372623 | − | 0.927983i | \(-0.378458\pi\) | ||||
0.372623 | + | 0.927983i | \(0.378458\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3332.00 | 0.117295 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 18912.0i | − 0.663613i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20806.0i | 0.725403i | 0.931905 | + | 0.362701i | \(0.118146\pi\) | ||||
−0.931905 | + | 0.362701i | \(0.881854\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20456.0 | −0.710923 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24510.0 | 0.849100 | 0.424550 | − | 0.905404i | \(-0.360432\pi\) | ||||
0.424550 | + | 0.905404i | \(0.360432\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 53136.0i | − 1.83494i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44148.0i | 1.51491i | 0.652889 | + | 0.757454i | \(0.273557\pi\) | ||||
−0.652889 | + | 0.757454i | \(0.726443\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45100.0 | −1.54268 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28824.0 | 0.982841 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27114.0i | 0.921625i | 0.887498 | + | 0.460812i | \(0.152442\pi\) | ||||
−0.887498 | + | 0.460812i | \(0.847558\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11808.0i | 0.398849i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2646.00 | −0.0890968 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17247.0 | −0.578933 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 10956.0i | − 0.366617i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10264.0i | 0.341332i | 0.985329 | + | 0.170666i | \(0.0545919\pi\) | ||||
−0.985329 | + | 0.170666i | \(0.945408\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8160.00 | 0.270523 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51468.0 | 1.70102 | 0.850508 | − | 0.525962i | \(-0.176295\pi\) | ||||
0.850508 | + | 0.525962i | \(0.176295\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 17500.0i | − 0.576592i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23790.0i | 0.779027i | 0.921021 | + | 0.389514i | \(0.127357\pi\) | ||||
−0.921021 | + | 0.389514i | \(0.872643\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16776.0 | −0.547664 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15202.0 | −0.494763 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26424.0i | 0.857370i | 0.903454 | + | 0.428685i | \(0.141023\pi\) | ||||
−0.903454 | + | 0.428685i | \(0.858977\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 5376.00i | − 0.173374i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37152.0 | 1.19450 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39488.0 | 1.26577 | 0.632885 | − | 0.774246i | \(-0.281871\pi\) | ||||
0.632885 | + | 0.774246i | \(0.281871\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25040.0i | 0.800222i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 30854.0i | − 0.980096i | −0.871695 | − | 0.490048i | \(-0.836979\pi\) | ||||
0.871695 | − | 0.490048i | \(-0.163021\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16720.0 | 0.529527 |
(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 | 700.4.e.f.449.2 | 2 | ||
5.2 | odd | 4 | 28.4.a.b.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 700.4.a.e.1.1 | 1 | |||
5.4 | even | 2 | inner | 700.4.e.f.449.1 | 2 | ||
15.2 | even | 4 | 252.4.a.c.1.1 | 1 | |||
20.7 | even | 4 | 112.4.a.c.1.1 | 1 | |||
35.2 | odd | 12 | 196.4.e.c.165.1 | 2 | |||
35.12 | even | 12 | 196.4.e.d.165.1 | 2 | |||
35.17 | even | 12 | 196.4.e.d.177.1 | 2 | |||
35.27 | even | 4 | 196.4.a.b.1.1 | 1 | |||
35.32 | odd | 12 | 196.4.e.c.177.1 | 2 | |||
40.27 | even | 4 | 448.4.a.m.1.1 | 1 | |||
40.37 | odd | 4 | 448.4.a.d.1.1 | 1 | |||
60.47 | odd | 4 | 1008.4.a.f.1.1 | 1 | |||
105.2 | even | 12 | 1764.4.k.k.361.1 | 2 | |||
105.17 | odd | 12 | 1764.4.k.e.1549.1 | 2 | |||
105.32 | even | 12 | 1764.4.k.k.1549.1 | 2 | |||
105.47 | odd | 12 | 1764.4.k.e.361.1 | 2 | |||
105.62 | odd | 4 | 1764.4.a.k.1.1 | 1 | |||
140.27 | odd | 4 | 784.4.a.n.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.4.a.b.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
112.4.a.c.1.1 | 1 | 20.7 | even | 4 | |||
196.4.a.b.1.1 | 1 | 35.27 | even | 4 | |||
196.4.e.c.165.1 | 2 | 35.2 | odd | 12 | |||
196.4.e.c.177.1 | 2 | 35.32 | odd | 12 | |||
196.4.e.d.165.1 | 2 | 35.12 | even | 12 | |||
196.4.e.d.177.1 | 2 | 35.17 | even | 12 | |||
252.4.a.c.1.1 | 1 | 15.2 | even | 4 | |||
448.4.a.d.1.1 | 1 | 40.37 | odd | 4 | |||
448.4.a.m.1.1 | 1 | 40.27 | even | 4 | |||
700.4.a.e.1.1 | 1 | 5.3 | odd | 4 | |||
700.4.e.f.449.1 | 2 | 5.4 | even | 2 | inner | ||
700.4.e.f.449.2 | 2 | 1.1 | even | 1 | trivial | ||
784.4.a.n.1.1 | 1 | 140.27 | odd | 4 | |||
1008.4.a.f.1.1 | 1 | 60.47 | odd | 4 | |||
1764.4.a.k.1.1 | 1 | 105.62 | odd | 4 | |||
1764.4.k.e.361.1 | 2 | 105.47 | odd | 12 | |||
1764.4.k.e.1549.1 | 2 | 105.17 | odd | 12 | |||
1764.4.k.k.361.1 | 2 | 105.2 | even | 12 | |||
1764.4.k.k.1549.1 | 2 | 105.32 | even | 12 |