Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,4,Mod(49,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.c (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: | \(8.85028650086\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 30) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 150.49 |
Dual form | 150.4.c.c.49.2 |
$q$-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 \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.00000i | − 0.707107i | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 4.00000i | 0.215980i | 0.994152 | + | 0.107990i | \(0.0344414\pi\) | ||||
−0.994152 | + | 0.107990i | \(0.965559\pi\) | |||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −48.0000 | −1.31569 | −0.657843 | − | 0.753155i | \(-0.728531\pi\) | ||||
−0.657843 | + | 0.753155i | \(0.728531\pi\) | |||||||
\(12\) | − 12.0000i | − 0.288675i | ||||||||
\(13\) | 2.00000i | 0.0426692i | 0.999772 | + | 0.0213346i | \(0.00679154\pi\) | ||||
−0.999772 | + | 0.0213346i | \(0.993208\pi\) | |||||||
\(14\) | 8.00000 | 0.152721 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 114.000i | 1.62642i | 0.581974 | + | 0.813208i | \(0.302281\pi\) | ||||
−0.581974 | + | 0.813208i | \(0.697719\pi\) | |||||||
\(18\) | 18.0000i | 0.235702i | ||||||||
\(19\) | −140.000 | −1.69043 | −0.845216 | − | 0.534425i | \(-0.820528\pi\) | ||||
−0.845216 | + | 0.534425i | \(0.820528\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.0000 | −0.124696 | ||||||||
\(22\) | 96.0000i | 0.930330i | ||||||||
\(23\) | 72.0000i | 0.652741i | 0.945242 | + | 0.326370i | \(0.105826\pi\) | ||||
−0.945242 | + | 0.326370i | \(0.894174\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.00000 | 0.0301717 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | − 16.0000i | − 0.107990i | ||||||||
\(29\) | −210.000 | −1.34469 | −0.672345 | − | 0.740238i | \(-0.734713\pi\) | ||||
−0.672345 | + | 0.740238i | \(0.734713\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 272.000 | 1.57589 | 0.787946 | − | 0.615745i | \(-0.211145\pi\) | ||||
0.787946 | + | 0.615745i | \(0.211145\pi\) | |||||||
\(32\) | − 32.0000i | − 0.176777i | ||||||||
\(33\) | − 144.000i | − 0.759612i | ||||||||
\(34\) | 228.000 | 1.15005 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 334.000i | 1.48403i | 0.670381 | + | 0.742017i | \(0.266131\pi\) | ||||
−0.670381 | + | 0.742017i | \(0.733869\pi\) | |||||||
\(38\) | 280.000i | 1.19532i | ||||||||
\(39\) | −6.00000 | −0.0246351 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −198.000 | −0.754205 | −0.377102 | − | 0.926172i | \(-0.623080\pi\) | ||||
−0.377102 | + | 0.926172i | \(0.623080\pi\) | |||||||
\(42\) | 24.0000i | 0.0881733i | ||||||||
\(43\) | − 268.000i | − 0.950456i | −0.879863 | − | 0.475228i | \(-0.842366\pi\) | ||||
0.879863 | − | 0.475228i | \(-0.157634\pi\) | |||||||
\(44\) | 192.000 | 0.657843 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 144.000 | 0.461557 | ||||||||
\(47\) | − 216.000i | − 0.670358i | −0.942154 | − | 0.335179i | \(-0.891203\pi\) | ||||
0.942154 | − | 0.335179i | \(-0.108797\pi\) | |||||||
\(48\) | 48.0000i | 0.144338i | ||||||||
\(49\) | 327.000 | 0.953353 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −342.000 | −0.939011 | ||||||||
\(52\) | − 8.00000i | − 0.0213346i | ||||||||
\(53\) | − 78.0000i | − 0.202153i | −0.994879 | − | 0.101077i | \(-0.967771\pi\) | ||||
0.994879 | − | 0.101077i | \(-0.0322287\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −32.0000 | −0.0763604 | ||||||||
\(57\) | − 420.000i | − 0.975971i | ||||||||
\(58\) | 420.000i | 0.950840i | ||||||||
\(59\) | −240.000 | −0.529582 | −0.264791 | − | 0.964306i | \(-0.585303\pi\) | ||||
−0.264791 | + | 0.964306i | \(0.585303\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 302.000 | 0.633888 | 0.316944 | − | 0.948444i | \(-0.397343\pi\) | ||||
0.316944 | + | 0.948444i | \(0.397343\pi\) | |||||||
\(62\) | − 544.000i | − 1.11432i | ||||||||
\(63\) | − 36.0000i | − 0.0719932i | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −288.000 | −0.537127 | ||||||||
\(67\) | − 596.000i | − 1.08676i | −0.839487 | − | 0.543381i | \(-0.817144\pi\) | ||||
0.839487 | − | 0.543381i | \(-0.182856\pi\) | |||||||
\(68\) | − 456.000i | − 0.813208i | ||||||||
\(69\) | −216.000 | −0.376860 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −768.000 | −1.28373 | −0.641865 | − | 0.766818i | \(-0.721839\pi\) | ||||
−0.641865 | + | 0.766818i | \(0.721839\pi\) | |||||||
\(72\) | − 72.0000i | − 0.117851i | ||||||||
\(73\) | − 478.000i | − 0.766379i | −0.923670 | − | 0.383190i | \(-0.874826\pi\) | ||||
0.923670 | − | 0.383190i | \(-0.125174\pi\) | |||||||
\(74\) | 668.000 | 1.04937 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 560.000 | 0.845216 | ||||||||
\(77\) | − 192.000i | − 0.284161i | ||||||||
\(78\) | 12.0000i | 0.0174196i | ||||||||
\(79\) | 640.000 | 0.911464 | 0.455732 | − | 0.890117i | \(-0.349378\pi\) | ||||
0.455732 | + | 0.890117i | \(0.349378\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 396.000i | 0.533303i | ||||||||
\(83\) | − 348.000i | − 0.460216i | −0.973165 | − | 0.230108i | \(-0.926092\pi\) | ||||
0.973165 | − | 0.230108i | \(-0.0739080\pi\) | |||||||
\(84\) | 48.0000 | 0.0623480 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −536.000 | −0.672074 | ||||||||
\(87\) | − 630.000i | − 0.776357i | ||||||||
\(88\) | − 384.000i | − 0.465165i | ||||||||
\(89\) | −210.000 | −0.250112 | −0.125056 | − | 0.992150i | \(-0.539911\pi\) | ||||
−0.125056 | + | 0.992150i | \(0.539911\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.00000 | −0.00921569 | ||||||||
\(92\) | − 288.000i | − 0.326370i | ||||||||
\(93\) | 816.000i | 0.909841i | ||||||||
\(94\) | −432.000 | −0.474015 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | 1534.00i | 1.60571i | 0.596173 | + | 0.802856i | \(0.296687\pi\) | ||||
−0.596173 | + | 0.802856i | \(0.703313\pi\) | |||||||
\(98\) | − 654.000i | − 0.674122i | ||||||||
\(99\) | 432.000 | 0.438562 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1722.00 | 1.69649 | 0.848245 | − | 0.529605i | \(-0.177660\pi\) | ||||
0.848245 | + | 0.529605i | \(0.177660\pi\) | |||||||
\(102\) | 684.000i | 0.663981i | ||||||||
\(103\) | 1052.00i | 1.00638i | 0.864177 | + | 0.503188i | \(0.167840\pi\) | ||||
−0.864177 | + | 0.503188i | \(0.832160\pi\) | |||||||
\(104\) | −16.0000 | −0.0150859 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −156.000 | −0.142944 | ||||||||
\(107\) | 564.000i | 0.509570i | 0.966998 | + | 0.254785i | \(0.0820046\pi\) | ||||
−0.966998 | + | 0.254785i | \(0.917995\pi\) | |||||||
\(108\) | 108.000i | 0.0962250i | ||||||||
\(109\) | 610.000 | 0.536031 | 0.268016 | − | 0.963415i | \(-0.413632\pi\) | ||||
0.268016 | + | 0.963415i | \(0.413632\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1002.00 | −0.856807 | ||||||||
\(112\) | 64.0000i | 0.0539949i | ||||||||
\(113\) | 1302.00i | 1.08391i | 0.840407 | + | 0.541955i | \(0.182316\pi\) | ||||
−0.840407 | + | 0.541955i | \(0.817684\pi\) | |||||||
\(114\) | −840.000 | −0.690116 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 840.000 | 0.672345 | ||||||||
\(117\) | − 18.0000i | − 0.0142231i | ||||||||
\(118\) | 480.000i | 0.374471i | ||||||||
\(119\) | −456.000 | −0.351273 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 973.000 | 0.731029 | ||||||||
\(122\) | − 604.000i | − 0.448226i | ||||||||
\(123\) | − 594.000i | − 0.435440i | ||||||||
\(124\) | −1088.00 | −0.787946 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −72.0000 | −0.0509069 | ||||||||
\(127\) | 124.000i | 0.0866395i | 0.999061 | + | 0.0433198i | \(0.0137934\pi\) | ||||
−0.999061 | + | 0.0433198i | \(0.986207\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | 804.000 | 0.548746 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 192.000 | 0.128054 | 0.0640272 | − | 0.997948i | \(-0.479606\pi\) | ||||
0.0640272 | + | 0.997948i | \(0.479606\pi\) | |||||||
\(132\) | 576.000i | 0.379806i | ||||||||
\(133\) | − 560.000i | − 0.365099i | ||||||||
\(134\) | −1192.00 | −0.768456 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −912.000 | −0.575025 | ||||||||
\(137\) | 2514.00i | 1.56778i | 0.620901 | + | 0.783889i | \(0.286767\pi\) | ||||
−0.620901 | + | 0.783889i | \(0.713233\pi\) | |||||||
\(138\) | 432.000i | 0.266480i | ||||||||
\(139\) | −1340.00 | −0.817679 | −0.408839 | − | 0.912606i | \(-0.634066\pi\) | ||||
−0.408839 | + | 0.912606i | \(0.634066\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 648.000 | 0.387032 | ||||||||
\(142\) | 1536.00i | 0.907734i | ||||||||
\(143\) | − 96.0000i | − 0.0561393i | ||||||||
\(144\) | −144.000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −956.000 | −0.541912 | ||||||||
\(147\) | 981.000i | 0.550418i | ||||||||
\(148\) | − 1336.00i | − 0.742017i | ||||||||
\(149\) | −1410.00 | −0.775246 | −0.387623 | − | 0.921818i | \(-0.626704\pi\) | ||||
−0.387623 | + | 0.921818i | \(0.626704\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2128.00 | −1.14685 | −0.573424 | − | 0.819258i | \(-0.694385\pi\) | ||||
−0.573424 | + | 0.819258i | \(0.694385\pi\) | |||||||
\(152\) | − 1120.00i | − 0.597658i | ||||||||
\(153\) | − 1026.00i | − 0.542138i | ||||||||
\(154\) | −384.000 | −0.200932 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 24.0000 | 0.0123176 | ||||||||
\(157\) | − 3026.00i | − 1.53822i | −0.639114 | − | 0.769112i | \(-0.720699\pi\) | ||||
0.639114 | − | 0.769112i | \(-0.279301\pi\) | |||||||
\(158\) | − 1280.00i | − 0.644502i | ||||||||
\(159\) | 234.000 | 0.116713 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −288.000 | −0.140979 | ||||||||
\(162\) | − 162.000i | − 0.0785674i | ||||||||
\(163\) | 2612.00i | 1.25514i | 0.778561 | + | 0.627569i | \(0.215950\pi\) | ||||
−0.778561 | + | 0.627569i | \(0.784050\pi\) | |||||||
\(164\) | 792.000 | 0.377102 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −696.000 | −0.325422 | ||||||||
\(167\) | 24.0000i | 0.0111208i | 0.999985 | + | 0.00556041i | \(0.00176994\pi\) | ||||
−0.999985 | + | 0.00556041i | \(0.998230\pi\) | |||||||
\(168\) | − 96.0000i | − 0.0440867i | ||||||||
\(169\) | 2193.00 | 0.998179 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1260.00 | 0.563477 | ||||||||
\(172\) | 1072.00i | 0.475228i | ||||||||
\(173\) | 1962.00i | 0.862243i | 0.902294 | + | 0.431122i | \(0.141882\pi\) | ||||
−0.902294 | + | 0.431122i | \(0.858118\pi\) | |||||||
\(174\) | −1260.00 | −0.548968 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −768.000 | −0.328921 | ||||||||
\(177\) | − 720.000i | − 0.305754i | ||||||||
\(178\) | 420.000i | 0.176856i | ||||||||
\(179\) | 120.000 | 0.0501074 | 0.0250537 | − | 0.999686i | \(-0.492024\pi\) | ||||
0.0250537 | + | 0.999686i | \(0.492024\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 902.000 | 0.370415 | 0.185208 | − | 0.982699i | \(-0.440704\pi\) | ||||
0.185208 | + | 0.982699i | \(0.440704\pi\) | |||||||
\(182\) | 16.0000i | 0.00651648i | ||||||||
\(183\) | 906.000i | 0.365975i | ||||||||
\(184\) | −576.000 | −0.230779 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1632.00 | 0.643355 | ||||||||
\(187\) | − 5472.00i | − 2.13985i | ||||||||
\(188\) | 864.000i | 0.335179i | ||||||||
\(189\) | 108.000 | 0.0415653 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −168.000 | −0.0636443 | −0.0318221 | − | 0.999494i | \(-0.510131\pi\) | ||||
−0.0318221 | + | 0.999494i | \(0.510131\pi\) | |||||||
\(192\) | − 192.000i | − 0.0721688i | ||||||||
\(193\) | − 1318.00i | − 0.491563i | −0.969325 | − | 0.245782i | \(-0.920955\pi\) | ||||
0.969325 | − | 0.245782i | \(-0.0790446\pi\) | |||||||
\(194\) | 3068.00 | 1.13541 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1308.00 | −0.476676 | ||||||||
\(197\) | 4014.00i | 1.45170i | 0.687851 | + | 0.725852i | \(0.258554\pi\) | ||||
−0.687851 | + | 0.725852i | \(0.741446\pi\) | |||||||
\(198\) | − 864.000i | − 0.310110i | ||||||||
\(199\) | −2000.00 | −0.712443 | −0.356222 | − | 0.934401i | \(-0.615935\pi\) | ||||
−0.356222 | + | 0.934401i | \(0.615935\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1788.00 | 0.627442 | ||||||||
\(202\) | − 3444.00i | − 1.19960i | ||||||||
\(203\) | − 840.000i | − 0.290426i | ||||||||
\(204\) | 1368.00 | 0.469506 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2104.00 | 0.711615 | ||||||||
\(207\) | − 648.000i | − 0.217580i | ||||||||
\(208\) | 32.0000i | 0.0106673i | ||||||||
\(209\) | 6720.00 | 2.22408 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3868.00 | −1.26201 | −0.631005 | − | 0.775779i | \(-0.717357\pi\) | ||||
−0.631005 | + | 0.775779i | \(0.717357\pi\) | |||||||
\(212\) | 312.000i | 0.101077i | ||||||||
\(213\) | − 2304.00i | − 0.741162i | ||||||||
\(214\) | 1128.00 | 0.360320 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | 1088.00i | 0.340361i | ||||||||
\(218\) | − 1220.00i | − 0.379031i | ||||||||
\(219\) | 1434.00 | 0.442469 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −228.000 | −0.0693979 | ||||||||
\(222\) | 2004.00i | 0.605854i | ||||||||
\(223\) | − 3148.00i | − 0.945317i | −0.881246 | − | 0.472658i | \(-0.843294\pi\) | ||||
0.881246 | − | 0.472658i | \(-0.156706\pi\) | |||||||
\(224\) | 128.000 | 0.0381802 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2604.00 | 0.766440 | ||||||||
\(227\) | − 2556.00i | − 0.747347i | −0.927560 | − | 0.373673i | \(-0.878098\pi\) | ||||
0.927560 | − | 0.373673i | \(-0.121902\pi\) | |||||||
\(228\) | 1680.00i | 0.487986i | ||||||||
\(229\) | 610.000 | 0.176026 | 0.0880130 | − | 0.996119i | \(-0.471948\pi\) | ||||
0.0880130 | + | 0.996119i | \(0.471948\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 576.000 | 0.164061 | ||||||||
\(232\) | − 1680.00i | − 0.475420i | ||||||||
\(233\) | − 2058.00i | − 0.578644i | −0.957232 | − | 0.289322i | \(-0.906570\pi\) | ||||
0.957232 | − | 0.289322i | \(-0.0934298\pi\) | |||||||
\(234\) | −36.0000 | −0.0100572 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 960.000 | 0.264791 | ||||||||
\(237\) | 1920.00i | 0.526234i | ||||||||
\(238\) | 912.000i | 0.248387i | ||||||||
\(239\) | −4920.00 | −1.33158 | −0.665792 | − | 0.746138i | \(-0.731906\pi\) | ||||
−0.665792 | + | 0.746138i | \(0.731906\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1438.00 | −0.384356 | −0.192178 | − | 0.981360i | \(-0.561555\pi\) | ||||
−0.192178 | + | 0.981360i | \(0.561555\pi\) | |||||||
\(242\) | − 1946.00i | − 0.516916i | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | −1208.00 | −0.316944 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1188.00 | −0.307903 | ||||||||
\(247\) | − 280.000i | − 0.0721294i | ||||||||
\(248\) | 2176.00i | 0.557162i | ||||||||
\(249\) | 1044.00 | 0.265706 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 792.000 | 0.199166 | 0.0995829 | − | 0.995029i | \(-0.468249\pi\) | ||||
0.0995829 | + | 0.995029i | \(0.468249\pi\) | |||||||
\(252\) | 144.000i | 0.0359966i | ||||||||
\(253\) | − 3456.00i | − 0.858802i | ||||||||
\(254\) | 248.000 | 0.0612634 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − 2166.00i | − 0.525725i | −0.964833 | − | 0.262863i | \(-0.915333\pi\) | ||||
0.964833 | − | 0.262863i | \(-0.0846666\pi\) | |||||||
\(258\) | − 1608.00i | − 0.388022i | ||||||||
\(259\) | −1336.00 | −0.320521 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1890.00 | 0.448230 | ||||||||
\(262\) | − 384.000i | − 0.0905481i | ||||||||
\(263\) | 3192.00i | 0.748392i | 0.927350 | + | 0.374196i | \(0.122081\pi\) | ||||
−0.927350 | + | 0.374196i | \(0.877919\pi\) | |||||||
\(264\) | 1152.00 | 0.268563 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1120.00 | −0.258164 | ||||||||
\(267\) | − 630.000i | − 0.144402i | ||||||||
\(268\) | 2384.00i | 0.543381i | ||||||||
\(269\) | −5490.00 | −1.24435 | −0.622177 | − | 0.782877i | \(-0.713752\pi\) | ||||
−0.622177 | + | 0.782877i | \(0.713752\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6328.00 | −1.41845 | −0.709223 | − | 0.704985i | \(-0.750954\pi\) | ||||
−0.709223 | + | 0.704985i | \(0.750954\pi\) | |||||||
\(272\) | 1824.00i | 0.406604i | ||||||||
\(273\) | − 24.0000i | − 0.00532068i | ||||||||
\(274\) | 5028.00 | 1.10859 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 864.000 | 0.188430 | ||||||||
\(277\) | 574.000i | 0.124507i | 0.998060 | + | 0.0622533i | \(0.0198287\pi\) | ||||
−0.998060 | + | 0.0622533i | \(0.980171\pi\) | |||||||
\(278\) | 2680.00i | 0.578186i | ||||||||
\(279\) | −2448.00 | −0.525297 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4242.00 | 0.900557 | 0.450278 | − | 0.892888i | \(-0.351325\pi\) | ||||
0.450278 | + | 0.892888i | \(0.351325\pi\) | |||||||
\(282\) | − 1296.00i | − 0.273673i | ||||||||
\(283\) | − 628.000i | − 0.131911i | −0.997823 | − | 0.0659553i | \(-0.978991\pi\) | ||||
0.997823 | − | 0.0659553i | \(-0.0210095\pi\) | |||||||
\(284\) | 3072.00 | 0.641865 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −192.000 | −0.0396965 | ||||||||
\(287\) | − 792.000i | − 0.162893i | ||||||||
\(288\) | 288.000i | 0.0589256i | ||||||||
\(289\) | −8083.00 | −1.64523 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4602.00 | −0.927058 | ||||||||
\(292\) | 1912.00i | 0.383190i | ||||||||
\(293\) | − 558.000i | − 0.111258i | −0.998451 | − | 0.0556292i | \(-0.982284\pi\) | ||||
0.998451 | − | 0.0556292i | \(-0.0177165\pi\) | |||||||
\(294\) | 1962.00 | 0.389205 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2672.00 | −0.524685 | ||||||||
\(297\) | 1296.00i | 0.253204i | ||||||||
\(298\) | 2820.00i | 0.548182i | ||||||||
\(299\) | −144.000 | −0.0278520 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1072.00 | 0.205279 | ||||||||
\(302\) | 4256.00i | 0.810945i | ||||||||
\(303\) | 5166.00i | 0.979468i | ||||||||
\(304\) | −2240.00 | −0.422608 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2052.00 | −0.383350 | ||||||||
\(307\) | 6964.00i | 1.29465i | 0.762216 | + | 0.647323i | \(0.224112\pi\) | ||||
−0.762216 | + | 0.647323i | \(0.775888\pi\) | |||||||
\(308\) | 768.000i | 0.142081i | ||||||||
\(309\) | −3156.00 | −0.581031 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2832.00 | 0.516360 | 0.258180 | − | 0.966097i | \(-0.416877\pi\) | ||||
0.258180 | + | 0.966097i | \(0.416877\pi\) | |||||||
\(312\) | − 48.0000i | − 0.00870982i | ||||||||
\(313\) | 8642.00i | 1.56062i | 0.625392 | + | 0.780311i | \(0.284939\pi\) | ||||
−0.625392 | + | 0.780311i | \(0.715061\pi\) | |||||||
\(314\) | −6052.00 | −1.08769 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2560.00 | −0.455732 | ||||||||
\(317\) | 2214.00i | 0.392273i | 0.980577 | + | 0.196137i | \(0.0628396\pi\) | ||||
−0.980577 | + | 0.196137i | \(0.937160\pi\) | |||||||
\(318\) | − 468.000i | − 0.0825287i | ||||||||
\(319\) | 10080.0 | 1.76919 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1692.00 | −0.294200 | ||||||||
\(322\) | 576.000i | 0.0996870i | ||||||||
\(323\) | − 15960.0i | − 2.74934i | ||||||||
\(324\) | −324.000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5224.00 | 0.887517 | ||||||||
\(327\) | 1830.00i | 0.309478i | ||||||||
\(328\) | − 1584.00i | − 0.266652i | ||||||||
\(329\) | 864.000 | 0.144784 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10772.0 | 1.78877 | 0.894385 | − | 0.447299i | \(-0.147614\pi\) | ||||
0.894385 | + | 0.447299i | \(0.147614\pi\) | |||||||
\(332\) | 1392.00i | 0.230108i | ||||||||
\(333\) | − 3006.00i | − 0.494678i | ||||||||
\(334\) | 48.0000 | 0.00786360 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −192.000 | −0.0311740 | ||||||||
\(337\) | 1654.00i | 0.267356i | 0.991025 | + | 0.133678i | \(0.0426789\pi\) | ||||
−0.991025 | + | 0.133678i | \(0.957321\pi\) | |||||||
\(338\) | − 4386.00i | − 0.705819i | ||||||||
\(339\) | −3906.00 | −0.625796 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13056.0 | −2.07338 | ||||||||
\(342\) | − 2520.00i | − 0.398439i | ||||||||
\(343\) | 2680.00i | 0.421885i | ||||||||
\(344\) | 2144.00 | 0.336037 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3924.00 | 0.609698 | ||||||||
\(347\) | − 2196.00i | − 0.339733i | −0.985467 | − | 0.169867i | \(-0.945666\pi\) | ||||
0.985467 | − | 0.169867i | \(-0.0543337\pi\) | |||||||
\(348\) | 2520.00i | 0.388179i | ||||||||
\(349\) | −8270.00 | −1.26843 | −0.634216 | − | 0.773156i | \(-0.718677\pi\) | ||||
−0.634216 | + | 0.773156i | \(0.718677\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 54.0000 | 0.00821170 | ||||||||
\(352\) | 1536.00i | 0.232583i | ||||||||
\(353\) | 10302.0i | 1.55331i | 0.629923 | + | 0.776657i | \(0.283086\pi\) | ||||
−0.629923 | + | 0.776657i | \(0.716914\pi\) | |||||||
\(354\) | −1440.00 | −0.216201 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 840.000 | 0.125056 | ||||||||
\(357\) | − 1368.00i | − 0.202807i | ||||||||
\(358\) | − 240.000i | − 0.0354313i | ||||||||
\(359\) | 2280.00 | 0.335192 | 0.167596 | − | 0.985856i | \(-0.446400\pi\) | ||||
0.167596 | + | 0.985856i | \(0.446400\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12741.0 | 1.85756 | ||||||||
\(362\) | − 1804.00i | − 0.261923i | ||||||||
\(363\) | 2919.00i | 0.422060i | ||||||||
\(364\) | 32.0000 | 0.00460785 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1812.00 | 0.258783 | ||||||||
\(367\) | 8764.00i | 1.24653i | 0.782010 | + | 0.623266i | \(0.214195\pi\) | ||||
−0.782010 | + | 0.623266i | \(0.785805\pi\) | |||||||
\(368\) | 1152.00i | 0.163185i | ||||||||
\(369\) | 1782.00 | 0.251402 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 312.000 | 0.0436610 | ||||||||
\(372\) | − 3264.00i | − 0.454921i | ||||||||
\(373\) | − 1318.00i | − 0.182958i | −0.995807 | − | 0.0914792i | \(-0.970841\pi\) | ||||
0.995807 | − | 0.0914792i | \(-0.0291595\pi\) | |||||||
\(374\) | −10944.0 | −1.51310 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1728.00 | 0.237007 | ||||||||
\(377\) | − 420.000i | − 0.0573769i | ||||||||
\(378\) | − 216.000i | − 0.0293911i | ||||||||
\(379\) | −1100.00 | −0.149085 | −0.0745425 | − | 0.997218i | \(-0.523750\pi\) | ||||
−0.0745425 | + | 0.997218i | \(0.523750\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −372.000 | −0.0500214 | ||||||||
\(382\) | 336.000i | 0.0450033i | ||||||||
\(383\) | − 3528.00i | − 0.470685i | −0.971912 | − | 0.235343i | \(-0.924379\pi\) | ||||
0.971912 | − | 0.235343i | \(-0.0756212\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2636.00 | −0.347588 | ||||||||
\(387\) | 2412.00i | 0.316819i | ||||||||
\(388\) | − 6136.00i | − 0.802856i | ||||||||
\(389\) | 9630.00 | 1.25517 | 0.627584 | − | 0.778549i | \(-0.284044\pi\) | ||||
0.627584 | + | 0.778549i | \(0.284044\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8208.00 | −1.06163 | ||||||||
\(392\) | 2616.00i | 0.337061i | ||||||||
\(393\) | 576.000i | 0.0739322i | ||||||||
\(394\) | 8028.00 | 1.02651 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1728.00 | −0.219281 | ||||||||
\(397\) | 3094.00i | 0.391142i | 0.980690 | + | 0.195571i | \(0.0626560\pi\) | ||||
−0.980690 | + | 0.195571i | \(0.937344\pi\) | |||||||
\(398\) | 4000.00i | 0.503774i | ||||||||
\(399\) | 1680.00 | 0.210790 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1638.00 | −0.203985 | −0.101992 | − | 0.994785i | \(-0.532522\pi\) | ||||
−0.101992 | + | 0.994785i | \(0.532522\pi\) | |||||||
\(402\) | − 3576.00i | − 0.443668i | ||||||||
\(403\) | 544.000i | 0.0672421i | ||||||||
\(404\) | −6888.00 | −0.848245 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1680.00 | −0.205362 | ||||||||
\(407\) | − 16032.0i | − 1.95252i | ||||||||
\(408\) | − 2736.00i | − 0.331991i | ||||||||
\(409\) | 13750.0 | 1.66233 | 0.831166 | − | 0.556024i | \(-0.187674\pi\) | ||||
0.831166 | + | 0.556024i | \(0.187674\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7542.00 | −0.905157 | ||||||||
\(412\) | − 4208.00i | − 0.503188i | ||||||||
\(413\) | − 960.000i | − 0.114379i | ||||||||
\(414\) | −1296.00 | −0.153852 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 64.0000 | 0.00754293 | ||||||||
\(417\) | − 4020.00i | − 0.472087i | ||||||||
\(418\) | − 13440.0i | − 1.57266i | ||||||||
\(419\) | 12480.0 | 1.45510 | 0.727551 | − | 0.686053i | \(-0.240658\pi\) | ||||
0.727551 | + | 0.686053i | \(0.240658\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7262.00 | 0.840685 | 0.420342 | − | 0.907366i | \(-0.361910\pi\) | ||||
0.420342 | + | 0.907366i | \(0.361910\pi\) | |||||||
\(422\) | 7736.00i | 0.892376i | ||||||||
\(423\) | 1944.00i | 0.223453i | ||||||||
\(424\) | 624.000 | 0.0714720 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4608.00 | −0.524081 | ||||||||
\(427\) | 1208.00i | 0.136907i | ||||||||
\(428\) | − 2256.00i | − 0.254785i | ||||||||
\(429\) | 288.000 | 0.0324121 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9792.00 | 1.09435 | 0.547174 | − | 0.837019i | \(-0.315704\pi\) | ||||
0.547174 | + | 0.837019i | \(0.315704\pi\) | |||||||
\(432\) | − 432.000i | − 0.0481125i | ||||||||
\(433\) | 1802.00i | 0.199997i | 0.994988 | + | 0.0999984i | \(0.0318838\pi\) | ||||
−0.994988 | + | 0.0999984i | \(0.968116\pi\) | |||||||
\(434\) | 2176.00 | 0.240671 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2440.00 | −0.268016 | ||||||||
\(437\) | − 10080.0i | − 1.10341i | ||||||||
\(438\) | − 2868.00i | − 0.312873i | ||||||||
\(439\) | 2320.00 | 0.252227 | 0.126113 | − | 0.992016i | \(-0.459750\pi\) | ||||
0.126113 | + | 0.992016i | \(0.459750\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2943.00 | −0.317784 | ||||||||
\(442\) | 456.000i | 0.0490717i | ||||||||
\(443\) | 11172.0i | 1.19819i | 0.800678 | + | 0.599095i | \(0.204473\pi\) | ||||
−0.800678 | + | 0.599095i | \(0.795527\pi\) | |||||||
\(444\) | 4008.00 | 0.428404 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6296.00 | −0.668440 | ||||||||
\(447\) | − 4230.00i | − 0.447589i | ||||||||
\(448\) | − 256.000i | − 0.0269975i | ||||||||
\(449\) | −6810.00 | −0.715777 | −0.357888 | − | 0.933764i | \(-0.616503\pi\) | ||||
−0.357888 | + | 0.933764i | \(0.616503\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9504.00 | 0.992297 | ||||||||
\(452\) | − 5208.00i | − 0.541955i | ||||||||
\(453\) | − 6384.00i | − 0.662134i | ||||||||
\(454\) | −5112.00 | −0.528454 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3360.00 | 0.345058 | ||||||||
\(457\) | − 17066.0i | − 1.74686i | −0.486952 | − | 0.873429i | \(-0.661891\pi\) | ||||
0.486952 | − | 0.873429i | \(-0.338109\pi\) | |||||||
\(458\) | − 1220.00i | − 0.124469i | ||||||||
\(459\) | 3078.00 | 0.313004 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18918.0 | −1.91128 | −0.955639 | − | 0.294541i | \(-0.904833\pi\) | ||||
−0.955639 | + | 0.294541i | \(0.904833\pi\) | |||||||
\(462\) | − 1152.00i | − 0.116008i | ||||||||
\(463\) | 1052.00i | 0.105595i | 0.998605 | + | 0.0527976i | \(0.0168138\pi\) | ||||
−0.998605 | + | 0.0527976i | \(0.983186\pi\) | |||||||
\(464\) | −3360.00 | −0.336173 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4116.00 | −0.409163 | ||||||||
\(467\) | − 11076.0i | − 1.09751i | −0.835984 | − | 0.548754i | \(-0.815102\pi\) | ||||
0.835984 | − | 0.548754i | \(-0.184898\pi\) | |||||||
\(468\) | 72.0000i | 0.00711154i | ||||||||
\(469\) | 2384.00 | 0.234718 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9078.00 | 0.888094 | ||||||||
\(472\) | − 1920.00i | − 0.187236i | ||||||||
\(473\) | 12864.0i | 1.25050i | ||||||||
\(474\) | 3840.00 | 0.372103 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1824.00 | 0.175636 | ||||||||
\(477\) | 702.000i | 0.0673844i | ||||||||
\(478\) | 9840.00i | 0.941571i | ||||||||
\(479\) | 9000.00 | 0.858498 | 0.429249 | − | 0.903186i | \(-0.358778\pi\) | ||||
0.429249 | + | 0.903186i | \(0.358778\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −668.000 | −0.0633226 | ||||||||
\(482\) | 2876.00i | 0.271781i | ||||||||
\(483\) | − 864.000i | − 0.0813941i | ||||||||
\(484\) | −3892.00 | −0.365515 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | 8764.00i | 0.815472i | 0.913100 | + | 0.407736i | \(0.133682\pi\) | ||||
−0.913100 | + | 0.407736i | \(0.866318\pi\) | |||||||
\(488\) | 2416.00i | 0.224113i | ||||||||
\(489\) | −7836.00 | −0.724655 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5592.00 | 0.513978 | 0.256989 | − | 0.966414i | \(-0.417270\pi\) | ||||
0.256989 | + | 0.966414i | \(0.417270\pi\) | |||||||
\(492\) | 2376.00i | 0.217720i | ||||||||
\(493\) | − 23940.0i | − 2.18703i | ||||||||
\(494\) | −560.000 | −0.0510032 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4352.00 | 0.393973 | ||||||||
\(497\) | − 3072.00i | − 0.277260i | ||||||||
\(498\) | − 2088.00i | − 0.187883i | ||||||||
\(499\) | −4700.00 | −0.421645 | −0.210823 | − | 0.977524i | \(-0.567614\pi\) | ||||
−0.210823 | + | 0.977524i | \(0.567614\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −72.0000 | −0.00642060 | ||||||||
\(502\) | − 1584.00i | − 0.140831i | ||||||||
\(503\) | − 11808.0i | − 1.04671i | −0.852116 | − | 0.523353i | \(-0.824681\pi\) | ||||
0.852116 | − | 0.523353i | \(-0.175319\pi\) | |||||||
\(504\) | 288.000 | 0.0254535 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6912.00 | −0.607265 | ||||||||
\(507\) | 6579.00i | 0.576299i | ||||||||
\(508\) | − 496.000i | − 0.0433198i | ||||||||
\(509\) | −1170.00 | −0.101885 | −0.0509424 | − | 0.998702i | \(-0.516222\pi\) | ||||
−0.0509424 | + | 0.998702i | \(0.516222\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1912.00 | 0.165522 | ||||||||
\(512\) | − 512.000i | − 0.0441942i | ||||||||
\(513\) | 3780.00i | 0.325324i | ||||||||
\(514\) | −4332.00 | −0.371744 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3216.00 | −0.274373 | ||||||||
\(517\) | 10368.0i | 0.881981i | ||||||||
\(518\) | 2672.00i | 0.226643i | ||||||||
\(519\) | −5886.00 | −0.497816 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16638.0 | −1.39909 | −0.699543 | − | 0.714590i | \(-0.746613\pi\) | ||||
−0.699543 | + | 0.714590i | \(0.746613\pi\) | |||||||
\(522\) | − 3780.00i | − 0.316947i | ||||||||
\(523\) | 15692.0i | 1.31198i | 0.754771 | + | 0.655988i | \(0.227748\pi\) | ||||
−0.754771 | + | 0.655988i | \(0.772252\pi\) | |||||||
\(524\) | −768.000 | −0.0640272 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6384.00 | 0.529193 | ||||||||
\(527\) | 31008.0i | 2.56305i | ||||||||
\(528\) | − 2304.00i | − 0.189903i | ||||||||
\(529\) | 6983.00 | 0.573929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2160.00 | 0.176527 | ||||||||
\(532\) | 2240.00i | 0.182549i | ||||||||
\(533\) | − 396.000i | − 0.0321814i | ||||||||
\(534\) | −1260.00 | −0.102108 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4768.00 | 0.384228 | ||||||||
\(537\) | 360.000i | 0.0289295i | ||||||||
\(538\) | 10980.0i | 0.879891i | ||||||||
\(539\) | −15696.0 | −1.25431 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22018.0 | −1.74977 | −0.874887 | − | 0.484327i | \(-0.839064\pi\) | ||||
−0.874887 | + | 0.484327i | \(0.839064\pi\) | |||||||
\(542\) | 12656.0i | 1.00299i | ||||||||
\(543\) | 2706.00i | 0.213859i | ||||||||
\(544\) | 3648.00 | 0.287512 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −48.0000 | −0.00376229 | ||||||||
\(547\) | 4564.00i | 0.356751i | 0.983963 | + | 0.178375i | \(0.0570841\pi\) | ||||
−0.983963 | + | 0.178375i | \(0.942916\pi\) | |||||||
\(548\) | − 10056.0i | − 0.783889i | ||||||||
\(549\) | −2718.00 | −0.211296 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29400.0 | 2.27311 | ||||||||
\(552\) | − 1728.00i | − 0.133240i | ||||||||
\(553\) | 2560.00i | 0.196858i | ||||||||
\(554\) | 1148.00 | 0.0880394 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5360.00 | 0.408839 | ||||||||
\(557\) | 7734.00i | 0.588331i | 0.955755 | + | 0.294165i | \(0.0950416\pi\) | ||||
−0.955755 | + | 0.294165i | \(0.904958\pi\) | |||||||
\(558\) | 4896.00i | 0.371441i | ||||||||
\(559\) | 536.000 | 0.0405552 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16416.0 | 1.23544 | ||||||||
\(562\) | − 8484.00i | − 0.636790i | ||||||||
\(563\) | − 20148.0i | − 1.50824i | −0.656739 | − | 0.754118i | \(-0.728065\pi\) | ||||
0.656739 | − | 0.754118i | \(-0.271935\pi\) | |||||||
\(564\) | −2592.00 | −0.193516 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1256.00 | −0.0932749 | ||||||||
\(567\) | 324.000i | 0.0239977i | ||||||||
\(568\) | − 6144.00i | − 0.453867i | ||||||||
\(569\) | 24030.0 | 1.77046 | 0.885228 | − | 0.465156i | \(-0.154002\pi\) | ||||
0.885228 | + | 0.465156i | \(0.154002\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2372.00 | 0.173844 | 0.0869222 | − | 0.996215i | \(-0.472297\pi\) | ||||
0.0869222 | + | 0.996215i | \(0.472297\pi\) | |||||||
\(572\) | 384.000i | 0.0280697i | ||||||||
\(573\) | − 504.000i | − 0.0367450i | ||||||||
\(574\) | −1584.00 | −0.115183 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | − 8546.00i | − 0.616594i | −0.951290 | − | 0.308297i | \(-0.900241\pi\) | ||||
0.951290 | − | 0.308297i | \(-0.0997590\pi\) | |||||||
\(578\) | 16166.0i | 1.16335i | ||||||||
\(579\) | 3954.00 | 0.283804 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1392.00 | 0.0993974 | ||||||||
\(582\) | 9204.00i | 0.655529i | ||||||||
\(583\) | 3744.00i | 0.265970i | ||||||||
\(584\) | 3824.00 | 0.270956 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1116.00 | −0.0786716 | ||||||||
\(587\) | 15444.0i | 1.08593i | 0.839755 | + | 0.542966i | \(0.182699\pi\) | ||||
−0.839755 | + | 0.542966i | \(0.817301\pi\) | |||||||
\(588\) | − 3924.00i | − 0.275209i | ||||||||
\(589\) | −38080.0 | −2.66394 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12042.0 | −0.838142 | ||||||||
\(592\) | 5344.00i | 0.371009i | ||||||||
\(593\) | 18342.0i | 1.27018i | 0.772439 | + | 0.635089i | \(0.219037\pi\) | ||||
−0.772439 | + | 0.635089i | \(0.780963\pi\) | |||||||
\(594\) | 2592.00 | 0.179042 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5640.00 | 0.387623 | ||||||||
\(597\) | − 6000.00i | − 0.411329i | ||||||||
\(598\) | 288.000i | 0.0196943i | ||||||||
\(599\) | −24600.0 | −1.67801 | −0.839006 | − | 0.544123i | \(-0.816863\pi\) | ||||
−0.839006 | + | 0.544123i | \(0.816863\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8998.00 | −0.610709 | −0.305354 | − | 0.952239i | \(-0.598775\pi\) | ||||
−0.305354 | + | 0.952239i | \(0.598775\pi\) | |||||||
\(602\) | − 2144.00i | − 0.145154i | ||||||||
\(603\) | 5364.00i | 0.362254i | ||||||||
\(604\) | 8512.00 | 0.573424 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10332.0 | 0.692589 | ||||||||
\(607\) | − 4076.00i | − 0.272553i | −0.990671 | − | 0.136277i | \(-0.956486\pi\) | ||||
0.990671 | − | 0.136277i | \(-0.0435136\pi\) | |||||||
\(608\) | 4480.00i | 0.298829i | ||||||||
\(609\) | 2520.00 | 0.167677 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 432.000 | 0.0286037 | ||||||||
\(612\) | 4104.00i | 0.271069i | ||||||||
\(613\) | − 4078.00i | − 0.268693i | −0.990934 | − | 0.134347i | \(-0.957106\pi\) | ||||
0.990934 | − | 0.134347i | \(-0.0428935\pi\) | |||||||
\(614\) | 13928.0 | 0.915453 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1536.00 | 0.100466 | ||||||||
\(617\) | − 10086.0i | − 0.658099i | −0.944313 | − | 0.329049i | \(-0.893272\pi\) | ||||
0.944313 | − | 0.329049i | \(-0.106728\pi\) | |||||||
\(618\) | 6312.00i | 0.410851i | ||||||||
\(619\) | −8780.00 | −0.570110 | −0.285055 | − | 0.958511i | \(-0.592012\pi\) | ||||
−0.285055 | + | 0.958511i | \(0.592012\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1944.00 | 0.125620 | ||||||||
\(622\) | − 5664.00i | − 0.365122i | ||||||||
\(623\) | − 840.000i | − 0.0540191i | ||||||||
\(624\) | −96.0000 | −0.00615878 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17284.0 | 1.10353 | ||||||||
\(627\) | 20160.0i | 1.28407i | ||||||||
\(628\) | 12104.0i | 0.769112i | ||||||||
\(629\) | −38076.0 | −2.41366 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2792.00 | 0.176145 | 0.0880727 | − | 0.996114i | \(-0.471929\pi\) | ||||
0.0880727 | + | 0.996114i | \(0.471929\pi\) | |||||||
\(632\) | 5120.00i | 0.322251i | ||||||||
\(633\) | − 11604.0i | − 0.728622i | ||||||||
\(634\) | 4428.00 | 0.277379 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −936.000 | −0.0583566 | ||||||||
\(637\) | 654.000i | 0.0406788i | ||||||||
\(638\) | − 20160.0i | − 1.25101i | ||||||||
\(639\) | 6912.00 | 0.427910 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7602.00 | 0.468426 | 0.234213 | − | 0.972185i | \(-0.424749\pi\) | ||||
0.234213 | + | 0.972185i | \(0.424749\pi\) | |||||||
\(642\) | 3384.00i | 0.208031i | ||||||||
\(643\) | 24212.0i | 1.48496i | 0.669869 | + | 0.742479i | \(0.266350\pi\) | ||||
−0.669869 | + | 0.742479i | \(0.733650\pi\) | |||||||
\(644\) | 1152.00 | 0.0704894 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31920.0 | −1.94408 | ||||||||
\(647\) | − 9456.00i | − 0.574581i | −0.957844 | − | 0.287290i | \(-0.907246\pi\) | ||||
0.957844 | − | 0.287290i | \(-0.0927545\pi\) | |||||||
\(648\) | 648.000i | 0.0392837i | ||||||||
\(649\) | 11520.0 | 0.696764 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3264.00 | −0.196507 | ||||||||
\(652\) | − 10448.0i | − 0.627569i | ||||||||
\(653\) | − 9558.00i | − 0.572792i | −0.958111 | − | 0.286396i | \(-0.907543\pi\) | ||||
0.958111 | − | 0.286396i | \(-0.0924574\pi\) | |||||||
\(654\) | 3660.00 | 0.218834 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3168.00 | −0.188551 | ||||||||
\(657\) | 4302.00i | 0.255460i | ||||||||
\(658\) | − 1728.00i | − 0.102378i | ||||||||
\(659\) | 29280.0 | 1.73078 | 0.865392 | − | 0.501095i | \(-0.167069\pi\) | ||||
0.865392 | + | 0.501095i | \(0.167069\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29098.0 | −1.71223 | −0.856113 | − | 0.516789i | \(-0.827127\pi\) | ||||
−0.856113 | + | 0.516789i | \(0.827127\pi\) | |||||||
\(662\) | − 21544.0i | − 1.26485i | ||||||||
\(663\) | − 684.000i | − 0.0400669i | ||||||||
\(664\) | 2784.00 | 0.162711 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6012.00 | −0.349790 | ||||||||
\(667\) | − 15120.0i | − 0.877734i | ||||||||
\(668\) | − 96.0000i | − 0.00556041i | ||||||||
\(669\) | 9444.00 | 0.545779 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14496.0 | −0.833997 | ||||||||
\(672\) | 384.000i | 0.0220433i | ||||||||
\(673\) | − 11638.0i | − 0.666585i | −0.942823 | − | 0.333293i | \(-0.891840\pi\) | ||||
0.942823 | − | 0.333293i | \(-0.108160\pi\) | |||||||
\(674\) | 3308.00 | 0.189050 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8772.00 | −0.499090 | ||||||||
\(677\) | − 3426.00i | − 0.194493i | −0.995260 | − | 0.0972466i | \(-0.968996\pi\) | ||||
0.995260 | − | 0.0972466i | \(-0.0310035\pi\) | |||||||
\(678\) | 7812.00i | 0.442505i | ||||||||
\(679\) | −6136.00 | −0.346801 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7668.00 | 0.431481 | ||||||||
\(682\) | 26112.0i | 1.46610i | ||||||||
\(683\) | − 20148.0i | − 1.12876i | −0.825516 | − | 0.564379i | \(-0.809116\pi\) | ||||
0.825516 | − | 0.564379i | \(-0.190884\pi\) | |||||||
\(684\) | −5040.00 | −0.281739 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5360.00 | 0.298317 | ||||||||
\(687\) | 1830.00i | 0.101629i | ||||||||
\(688\) | − 4288.00i | − 0.237614i | ||||||||
\(689\) | 156.000 | 0.00862573 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29428.0 | −1.62011 | −0.810053 | − | 0.586356i | \(-0.800562\pi\) | ||||
−0.810053 | + | 0.586356i | \(0.800562\pi\) | |||||||
\(692\) | − 7848.00i | − 0.431122i | ||||||||
\(693\) | 1728.00i | 0.0947205i | ||||||||
\(694\) | −4392.00 | −0.240228 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5040.00 | 0.274484 | ||||||||
\(697\) | − 22572.0i | − 1.22665i | ||||||||
\(698\) | 16540.0i | 0.896917i | ||||||||
\(699\) | 6174.00 | 0.334080 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16242.0 | 0.875110 | 0.437555 | − | 0.899192i | \(-0.355845\pi\) | ||||
0.437555 | + | 0.899192i | \(0.355845\pi\) | |||||||
\(702\) | − 108.000i | − 0.00580655i | ||||||||
\(703\) | − 46760.0i | − 2.50866i | ||||||||
\(704\) | 3072.00 | 0.164461 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20604.0 | 1.09836 | ||||||||
\(707\) | 6888.00i | 0.366407i | ||||||||
\(708\) | 2880.00i | 0.152877i | ||||||||
\(709\) | −2030.00 | −0.107529 | −0.0537646 | − | 0.998554i | \(-0.517122\pi\) | ||||
−0.0537646 | + | 0.998554i | \(0.517122\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5760.00 | −0.303821 | ||||||||
\(712\) | − 1680.00i | − 0.0884279i | ||||||||
\(713\) | 19584.0i | 1.02865i | ||||||||
\(714\) | −2736.00 | −0.143406 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −480.000 | −0.0250537 | ||||||||
\(717\) | − 14760.0i | − 0.768790i | ||||||||
\(718\) | − 4560.00i | − 0.237016i | ||||||||
\(719\) | −6960.00 | −0.361007 | −0.180504 | − | 0.983574i | \(-0.557773\pi\) | ||||
−0.180504 | + | 0.983574i | \(0.557773\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4208.00 | −0.217357 | ||||||||
\(722\) | − 25482.0i | − 1.31349i | ||||||||
\(723\) | − 4314.00i | − 0.221908i | ||||||||
\(724\) | −3608.00 | −0.185208 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5838.00 | 0.298441 | ||||||||
\(727\) | − 18596.0i | − 0.948676i | −0.880343 | − | 0.474338i | \(-0.842687\pi\) | ||||
0.880343 | − | 0.474338i | \(-0.157313\pi\) | |||||||
\(728\) | − 64.0000i | − 0.00325824i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30552.0 | 1.54584 | ||||||||
\(732\) | − 3624.00i | − 0.182988i | ||||||||
\(733\) | 21242.0i | 1.07038i | 0.844731 | + | 0.535192i | \(0.179761\pi\) | ||||
−0.844731 | + | 0.535192i | \(0.820239\pi\) | |||||||
\(734\) | 17528.0 | 0.881431 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2304.00 | 0.115389 | ||||||||
\(737\) | 28608.0i | 1.42984i | ||||||||
\(738\) | − 3564.00i | − 0.177768i | ||||||||
\(739\) | 340.000 | 0.0169244 | 0.00846218 | − | 0.999964i | \(-0.497306\pi\) | ||||
0.00846218 | + | 0.999964i | \(0.497306\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 840.000 | 0.0416440 | ||||||||
\(742\) | − 624.000i | − 0.0308730i | ||||||||
\(743\) | − 21888.0i | − 1.08074i | −0.841426 | − | 0.540372i | \(-0.818284\pi\) | ||||
0.841426 | − | 0.540372i | \(-0.181716\pi\) | |||||||
\(744\) | −6528.00 | −0.321678 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2636.00 | −0.129371 | ||||||||
\(747\) | 3132.00i | 0.153405i | ||||||||
\(748\) | 21888.0i | 1.06993i | ||||||||
\(749\) | −2256.00 | −0.110057 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17792.0 | 0.864500 | 0.432250 | − | 0.901754i | \(-0.357720\pi\) | ||||
0.432250 | + | 0.901754i | \(0.357720\pi\) | |||||||
\(752\) | − 3456.00i | − 0.167590i | ||||||||
\(753\) | 2376.00i | 0.114988i | ||||||||
\(754\) | −840.000 | −0.0405716 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −432.000 | −0.0207827 | ||||||||
\(757\) | − 37346.0i | − 1.79308i | −0.442960 | − | 0.896541i | \(-0.646072\pi\) | ||||
0.442960 | − | 0.896541i | \(-0.353928\pi\) | |||||||
\(758\) | 2200.00i | 0.105419i | ||||||||
\(759\) | 10368.0 | 0.495829 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11358.0 | −0.541034 | −0.270517 | − | 0.962715i | \(-0.587195\pi\) | ||||
−0.270517 | + | 0.962715i | \(0.587195\pi\) | |||||||
\(762\) | 744.000i | 0.0353704i | ||||||||
\(763\) | 2440.00i | 0.115772i | ||||||||
\(764\) | 672.000 | 0.0318221 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7056.00 | −0.332825 | ||||||||
\(767\) | − 480.000i | − 0.0225969i | ||||||||
\(768\) | 768.000i | 0.0360844i | ||||||||
\(769\) | 34270.0 | 1.60703 | 0.803516 | − | 0.595283i | \(-0.202960\pi\) | ||||
0.803516 | + | 0.595283i | \(0.202960\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6498.00 | 0.303528 | ||||||||
\(772\) | 5272.00i | 0.245782i | ||||||||
\(773\) | − 13278.0i | − 0.617822i | −0.951091 | − | 0.308911i | \(-0.900035\pi\) | ||||
0.951091 | − | 0.308911i | \(-0.0999645\pi\) | |||||||
\(774\) | 4824.00 | 0.224025 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12272.0 | −0.567705 | ||||||||
\(777\) | − 4008.00i | − 0.185053i | ||||||||
\(778\) | − 19260.0i | − 0.887538i | ||||||||
\(779\) | 27720.0 | 1.27493 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36864.0 | 1.68899 | ||||||||
\(782\) | 16416.0i | 0.750684i | ||||||||
\(783\) | 5670.00i | 0.258786i | ||||||||
\(784\) | 5232.00 | 0.238338 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1152.00 | 0.0522780 | ||||||||
\(787\) | 11164.0i | 0.505659i | 0.967511 | + | 0.252829i | \(0.0813612\pi\) | ||||
−0.967511 | + | 0.252829i | \(0.918639\pi\) | |||||||
\(788\) | − 16056.0i | − 0.725852i | ||||||||
\(789\) | −9576.00 | −0.432084 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5208.00 | −0.234103 | ||||||||
\(792\) | 3456.00i | 0.155055i | ||||||||
\(793\) | 604.000i | 0.0270475i | ||||||||
\(794\) | 6188.00 | 0.276579 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8000.00 | 0.356222 | ||||||||
\(797\) | 5094.00i | 0.226397i | 0.993572 | + | 0.113199i | \(0.0361097\pi\) | ||||
−0.993572 | + | 0.113199i | \(0.963890\pi\) | |||||||
\(798\) | − 3360.00i | − 0.149051i | ||||||||
\(799\) | 24624.0 | 1.09028 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1890.00 | 0.0833706 | ||||||||
\(802\) | 3276.00i | 0.144239i | ||||||||
\(803\) | 22944.0i | 1.00831i | ||||||||
\(804\) | −7152.00 | −0.313721 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1088.00 | 0.0475474 | ||||||||
\(807\) | − 16470.0i | − 0.718428i | ||||||||
\(808\) | 13776.0i | 0.599799i | ||||||||
\(809\) | 8790.00 | 0.382002 | 0.191001 | − | 0.981590i | \(-0.438827\pi\) | ||||
0.191001 | + | 0.981590i | \(0.438827\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5852.00 | 0.253380 | 0.126690 | − | 0.991942i | \(-0.459565\pi\) | ||||
0.126690 | + | 0.991942i | \(0.459565\pi\) | |||||||
\(812\) | 3360.00i | 0.145213i | ||||||||
\(813\) | − 18984.0i | − 0.818940i | ||||||||
\(814\) | −32064.0 | −1.38064 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5472.00 | −0.234753 | ||||||||
\(817\) | 37520.0i | 1.60668i | ||||||||
\(818\) | − 27500.0i | − 1.17545i | ||||||||
\(819\) | 72.0000 | 0.00307190 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29478.0 | −1.25309 | −0.626546 | − | 0.779384i | \(-0.715532\pi\) | ||||
−0.626546 | + | 0.779384i | \(0.715532\pi\) | |||||||
\(822\) | 15084.0i | 0.640042i | ||||||||
\(823\) | 39332.0i | 1.66589i | 0.553356 | + | 0.832945i | \(0.313347\pi\) | ||||
−0.553356 | + | 0.832945i | \(0.686653\pi\) | |||||||
\(824\) | −8416.00 | −0.355807 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1920.00 | −0.0808781 | ||||||||
\(827\) | − 6756.00i | − 0.284074i | −0.989861 | − | 0.142037i | \(-0.954635\pi\) | ||||
0.989861 | − | 0.142037i | \(-0.0453652\pi\) | |||||||
\(828\) | 2592.00i | 0.108790i | ||||||||
\(829\) | −3950.00 | −0.165488 | −0.0827438 | − | 0.996571i | \(-0.526368\pi\) | ||||
−0.0827438 | + | 0.996571i | \(0.526368\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1722.00 | −0.0718839 | ||||||||
\(832\) | − 128.000i | − 0.00533366i | ||||||||
\(833\) | 37278.0i | 1.55055i | ||||||||
\(834\) | −8040.00 | −0.333816 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −26880.0 | −1.11204 | ||||||||
\(837\) | − 7344.00i | − 0.303280i | ||||||||
\(838\) | − 24960.0i | − 1.02891i | ||||||||
\(839\) | −12360.0 | −0.508599 | −0.254300 | − | 0.967126i | \(-0.581845\pi\) | ||||
−0.254300 | + | 0.967126i | \(0.581845\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19711.0 | 0.808192 | ||||||||
\(842\) | − 14524.0i | − 0.594454i | ||||||||
\(843\) | 12726.0i | 0.519937i | ||||||||
\(844\) | 15472.0 | 0.631005 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3888.00 | 0.158005 | ||||||||
\(847\) | 3892.00i | 0.157887i | ||||||||
\(848\) | − 1248.00i | − 0.0505383i | ||||||||
\(849\) | 1884.00 | 0.0761587 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24048.0 | −0.968690 | ||||||||
\(852\) | 9216.00i | 0.370581i | ||||||||
\(853\) | − 35998.0i | − 1.44496i | −0.691394 | − | 0.722478i | \(-0.743003\pi\) | ||||
0.691394 | − | 0.722478i | \(-0.256997\pi\) | |||||||
\(854\) | 2416.00 | 0.0968077 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4512.00 | −0.180160 | ||||||||
\(857\) | 21594.0i | 0.860720i | 0.902657 | + | 0.430360i | \(0.141613\pi\) | ||||
−0.902657 | + | 0.430360i | \(0.858387\pi\) | |||||||
\(858\) | − 576.000i | − 0.0229188i | ||||||||
\(859\) | −9260.00 | −0.367808 | −0.183904 | − | 0.982944i | \(-0.558874\pi\) | ||||
−0.183904 | + | 0.982944i | \(0.558874\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2376.00 | 0.0940463 | ||||||||
\(862\) | − 19584.0i | − 0.773821i | ||||||||
\(863\) | 31632.0i | 1.24770i | 0.781544 | + | 0.623850i | \(0.214433\pi\) | ||||
−0.781544 | + | 0.623850i | \(0.785567\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3604.00 | 0.141419 | ||||||||
\(867\) | − 24249.0i | − 0.949872i | ||||||||
\(868\) | − 4352.00i | − 0.170180i | ||||||||
\(869\) | −30720.0 | −1.19920 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1192.00 | 0.0463713 | ||||||||
\(872\) | 4880.00i | 0.189516i | ||||||||
\(873\) | − 13806.0i | − 0.535237i | ||||||||
\(874\) | −20160.0 | −0.780231 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5736.00 | −0.221235 | ||||||||
\(877\) | 39694.0i | 1.52836i | 0.645003 | + | 0.764180i | \(0.276856\pi\) | ||||
−0.645003 | + | 0.764180i | \(0.723144\pi\) | |||||||
\(878\) | − 4640.00i | − 0.178351i | ||||||||
\(879\) | 1674.00 | 0.0642351 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1242.00 | 0.0474961 | 0.0237480 | − | 0.999718i | \(-0.492440\pi\) | ||||
0.0237480 | + | 0.999718i | \(0.492440\pi\) | |||||||
\(882\) | 5886.00i | 0.224707i | ||||||||
\(883\) | − 2668.00i | − 0.101682i | −0.998707 | − | 0.0508411i | \(-0.983810\pi\) | ||||
0.998707 | − | 0.0508411i | \(-0.0161902\pi\) | |||||||
\(884\) | 912.000 | 0.0346990 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22344.0 | 0.847248 | ||||||||
\(887\) | 4344.00i | 0.164439i | 0.996614 | + | 0.0822194i | \(0.0262008\pi\) | ||||
−0.996614 | + | 0.0822194i | \(0.973799\pi\) | |||||||
\(888\) | − 8016.00i | − 0.302927i | ||||||||
\(889\) | −496.000 | −0.0187124 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3888.00 | −0.146187 | ||||||||
\(892\) | 12592.0i | 0.472658i | ||||||||
\(893\) | 30240.0i | 1.13319i | ||||||||
\(894\) | −8460.00 | −0.316493 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −512.000 | −0.0190901 | ||||||||
\(897\) | − 432.000i | − 0.0160803i | ||||||||
\(898\) | 13620.0i | 0.506131i | ||||||||
\(899\) | −57120.0 | −2.11909 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8892.00 | 0.328785 | ||||||||
\(902\) | − 19008.0i | − 0.701660i | ||||||||
\(903\) | 3216.00i | 0.118518i | ||||||||
\(904\) | −10416.0 | −0.383220 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −12768.0 | −0.468199 | ||||||||
\(907\) | − 4436.00i | − 0.162398i | −0.996698 | − | 0.0811990i | \(-0.974125\pi\) | ||||
0.996698 | − | 0.0811990i | \(-0.0258749\pi\) | |||||||
\(908\) | 10224.0i | 0.373673i | ||||||||
\(909\) | −15498.0 | −0.565496 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22752.0 | 0.827450 | 0.413725 | − | 0.910402i | \(-0.364227\pi\) | ||||
0.413725 | + | 0.910402i | \(0.364227\pi\) | |||||||
\(912\) | − 6720.00i | − 0.243993i | ||||||||
\(913\) | 16704.0i | 0.605500i | ||||||||
\(914\) | −34132.0 | −1.23521 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2440.00 | −0.0880130 | ||||||||
\(917\) | 768.000i | 0.0276571i | ||||||||
\(918\) | − 6156.00i | − 0.221327i | ||||||||
\(919\) | 27160.0 | 0.974892 | 0.487446 | − | 0.873153i | \(-0.337929\pi\) | ||||
0.487446 | + | 0.873153i | \(0.337929\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20892.0 | −0.747465 | ||||||||
\(922\) | 37836.0i | 1.35148i | ||||||||
\(923\) | − 1536.00i | − 0.0547758i | ||||||||
\(924\) | −2304.00 | −0.0820303 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2104.00 | 0.0746671 | ||||||||
\(927\) | − 9468.00i | − 0.335458i | ||||||||
\(928\) | 6720.00i | 0.237710i | ||||||||
\(929\) | 33030.0 | 1.16650 | 0.583250 | − | 0.812292i | \(-0.301781\pi\) | ||||
0.583250 | + | 0.812292i | \(0.301781\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45780.0 | −1.61158 | ||||||||
\(932\) | 8232.00i | 0.289322i | ||||||||
\(933\) | 8496.00i | 0.298121i | ||||||||
\(934\) | −22152.0 | −0.776055 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 144.000 | 0.00502862 | ||||||||
\(937\) | 29974.0i | 1.04505i | 0.852625 | + | 0.522523i | \(0.175009\pi\) | ||||
−0.852625 | + | 0.522523i | \(0.824991\pi\) | |||||||
\(938\) | − 4768.00i | − 0.165971i | ||||||||
\(939\) | −25926.0 | −0.901026 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13962.0 | 0.483686 | 0.241843 | − | 0.970315i | \(-0.422248\pi\) | ||||
0.241843 | + | 0.970315i | \(0.422248\pi\) | |||||||
\(942\) | − 18156.0i | − 0.627977i | ||||||||
\(943\) | − 14256.0i | − 0.492300i | ||||||||
\(944\) | −3840.00 | −0.132396 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25728.0 | 0.884238 | ||||||||
\(947\) | − 35196.0i | − 1.20773i | −0.797088 | − | 0.603863i | \(-0.793627\pi\) | ||||
0.797088 | − | 0.603863i | \(-0.206373\pi\) | |||||||
\(948\) | − 7680.00i | − 0.263117i | ||||||||
\(949\) | 956.000 | 0.0327008 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6642.00 | −0.226479 | ||||||||
\(952\) | − 3648.00i | − 0.124194i | ||||||||
\(953\) | − 28338.0i | − 0.963230i | −0.876383 | − | 0.481615i | \(-0.840050\pi\) | ||||
0.876383 | − | 0.481615i | \(-0.159950\pi\) | |||||||
\(954\) | 1404.00 | 0.0476480 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 19680.0 | 0.665792 | ||||||||
\(957\) | 30240.0i | 1.02144i | ||||||||
\(958\) | − 18000.0i | − 0.607050i | ||||||||
\(959\) | −10056.0 | −0.338608 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44193.0 | 1.48343 | ||||||||
\(962\) | 1336.00i | 0.0447759i | ||||||||
\(963\) | − 5076.00i | − 0.169857i | ||||||||
\(964\) | 5752.00 | 0.192178 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1728.00 | −0.0575543 | ||||||||
\(967\) | 17524.0i | 0.582765i | 0.956607 | + | 0.291383i | \(0.0941153\pi\) | ||||
−0.956607 | + | 0.291383i | \(0.905885\pi\) | |||||||
\(968\) | 7784.00i | 0.258458i | ||||||||
\(969\) | 47880.0 | 1.58733 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26808.0 | −0.886004 | −0.443002 | − | 0.896521i | \(-0.646087\pi\) | ||||
−0.443002 | + | 0.896521i | \(0.646087\pi\) | |||||||
\(972\) | − 972.000i | − 0.0320750i | ||||||||
\(973\) | − 5360.00i | − 0.176602i | ||||||||
\(974\) | 17528.0 | 0.576626 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4832.00 | 0.158472 | ||||||||
\(977\) | 10914.0i | 0.357390i | 0.983905 | + | 0.178695i | \(0.0571875\pi\) | ||||
−0.983905 | + | 0.178695i | \(0.942813\pi\) | |||||||
\(978\) | 15672.0i | 0.512408i | ||||||||
\(979\) | 10080.0 | 0.329069 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5490.00 | −0.178677 | ||||||||
\(982\) | − 11184.0i | − 0.363438i | ||||||||
\(983\) | 22272.0i | 0.722652i | 0.932440 | + | 0.361326i | \(0.117676\pi\) | ||||
−0.932440 | + | 0.361326i | \(0.882324\pi\) | |||||||
\(984\) | 4752.00 | 0.153951 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −47880.0 | −1.54646 | ||||||||
\(987\) | 2592.00i | 0.0835910i | ||||||||
\(988\) | 1120.00i | 0.0360647i | ||||||||
\(989\) | 19296.0 | 0.620402 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14072.0 | 0.451071 | 0.225536 | − | 0.974235i | \(-0.427587\pi\) | ||||
0.225536 | + | 0.974235i | \(0.427587\pi\) | |||||||
\(992\) | − 8704.00i | − 0.278581i | ||||||||
\(993\) | 32316.0i | 1.03275i | ||||||||
\(994\) | −6144.00 | −0.196052 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4176.00 | −0.132853 | ||||||||
\(997\) | − 4826.00i | − 0.153301i | −0.997058 | − | 0.0766504i | \(-0.975577\pi\) | ||||
0.997058 | − | 0.0766504i | \(-0.0244225\pi\) | |||||||
\(998\) | 9400.00i | 0.298148i | ||||||||
\(999\) | 9018.00 | 0.285602 |
(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 | 150.4.c.c.49.1 | 2 | ||
3.2 | odd | 2 | 450.4.c.j.199.2 | 2 | |||
4.3 | odd | 2 | 1200.4.f.r.49.1 | 2 | |||
5.2 | odd | 4 | 30.4.a.b.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 150.4.a.b.1.1 | 1 | |||
5.4 | even | 2 | inner | 150.4.c.c.49.2 | 2 | ||
15.2 | even | 4 | 90.4.a.c.1.1 | 1 | |||
15.8 | even | 4 | 450.4.a.r.1.1 | 1 | |||
15.14 | odd | 2 | 450.4.c.j.199.1 | 2 | |||
20.3 | even | 4 | 1200.4.a.ba.1.1 | 1 | |||
20.7 | even | 4 | 240.4.a.b.1.1 | 1 | |||
20.19 | odd | 2 | 1200.4.f.r.49.2 | 2 | |||
35.27 | even | 4 | 1470.4.a.r.1.1 | 1 | |||
40.27 | even | 4 | 960.4.a.bg.1.1 | 1 | |||
40.37 | odd | 4 | 960.4.a.n.1.1 | 1 | |||
45.2 | even | 12 | 810.4.e.p.271.1 | 2 | |||
45.7 | odd | 12 | 810.4.e.i.271.1 | 2 | |||
45.22 | odd | 12 | 810.4.e.i.541.1 | 2 | |||
45.32 | even | 12 | 810.4.e.p.541.1 | 2 | |||
60.47 | odd | 4 | 720.4.a.y.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.4.a.b.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
90.4.a.c.1.1 | 1 | 15.2 | even | 4 | |||
150.4.a.b.1.1 | 1 | 5.3 | odd | 4 | |||
150.4.c.c.49.1 | 2 | 1.1 | even | 1 | trivial | ||
150.4.c.c.49.2 | 2 | 5.4 | even | 2 | inner | ||
240.4.a.b.1.1 | 1 | 20.7 | even | 4 | |||
450.4.a.r.1.1 | 1 | 15.8 | even | 4 | |||
450.4.c.j.199.1 | 2 | 15.14 | odd | 2 | |||
450.4.c.j.199.2 | 2 | 3.2 | odd | 2 | |||
720.4.a.y.1.1 | 1 | 60.47 | odd | 4 | |||
810.4.e.i.271.1 | 2 | 45.7 | odd | 12 | |||
810.4.e.i.541.1 | 2 | 45.22 | odd | 12 | |||
810.4.e.p.271.1 | 2 | 45.2 | even | 12 | |||
810.4.e.p.541.1 | 2 | 45.32 | even | 12 | |||
960.4.a.n.1.1 | 1 | 40.37 | odd | 4 | |||
960.4.a.bg.1.1 | 1 | 40.27 | even | 4 | |||
1200.4.a.ba.1.1 | 1 | 20.3 | even | 4 | |||
1200.4.f.r.49.1 | 2 | 4.3 | odd | 2 | |||
1200.4.f.r.49.2 | 2 | 20.19 | odd | 2 | |||
1470.4.a.r.1.1 | 1 | 35.27 | even | 4 |