Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,4,Mod(541,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.541");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.i (of order \(3\), degree \(2\), 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: | \(95.5830942093\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 541.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.541 |
Dual form | 1620.4.i.i.1081.1 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.50000 | + | 4.33013i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 1.73205i | −0.0539949 | + | 0.0935220i | −0.891760 | − | 0.452510i | \(-0.850529\pi\) |
0.837765 | + | 0.546032i | \(0.183862\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.0000 | − | 25.9808i | 0.411152 | − | 0.712136i | −0.583864 | − | 0.811851i | \(-0.698460\pi\) |
0.995016 | + | 0.0997155i | \(0.0317933\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | + | 3.46410i | 0.0426692 | + | 0.0739053i | 0.886571 | − | 0.462592i | \(-0.153080\pi\) |
−0.843902 | + | 0.536497i | \(0.819747\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −90.0000 | −1.28401 | −0.642006 | − | 0.766700i | \(-0.721898\pi\) | ||||
−0.642006 | + | 0.766700i | \(0.721898\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −28.0000 | −0.338086 | −0.169043 | − | 0.985609i | \(-0.554068\pi\) | ||||
−0.169043 | + | 0.985609i | \(0.554068\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 60.0000 | + | 103.923i | 0.543951 | + | 0.942150i | 0.998672 | + | 0.0515165i | \(0.0164055\pi\) |
−0.454721 | + | 0.890634i | \(0.650261\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 105.000 | − | 181.865i | 0.672345 | − | 1.16454i | −0.304892 | − | 0.952387i | \(-0.598620\pi\) |
0.977237 | − | 0.212149i | \(-0.0680463\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | + | 3.46410i | 0.0115874 | + | 0.0200700i | 0.871761 | − | 0.489931i | \(-0.162978\pi\) |
−0.860174 | + | 0.510001i | \(0.829645\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.0000 | −0.0482945 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 200.000 | 0.888643 | 0.444322 | − | 0.895867i | \(-0.353445\pi\) | ||||
0.444322 | + | 0.895867i | \(0.353445\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 120.000 | + | 207.846i | 0.457094 | + | 0.791710i | 0.998806 | − | 0.0488543i | \(-0.0155570\pi\) |
−0.541712 | + | 0.840564i | \(0.682224\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 68.0000 | − | 117.779i | 0.241161 | − | 0.417702i | −0.719885 | − | 0.694094i | \(-0.755805\pi\) |
0.961045 | + | 0.276391i | \(0.0891386\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −60.0000 | + | 103.923i | −0.186211 | + | 0.322526i | −0.943984 | − | 0.329992i | \(-0.892954\pi\) |
0.757773 | + | 0.652518i | \(0.226287\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 169.500 | + | 293.583i | 0.494169 | + | 0.855926i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 30.0000 | 0.0777513 | 0.0388756 | − | 0.999244i | \(-0.487622\pi\) | ||||
0.0388756 | + | 0.999244i | \(0.487622\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 150.000 | 0.367745 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −225.000 | − | 389.711i | −0.496483 | − | 0.859934i | 0.503509 | − | 0.863990i | \(-0.332042\pi\) |
−0.999992 | + | 0.00405618i | \(0.998709\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 83.0000 | − | 143.760i | 0.174214 | − | 0.301748i | −0.765675 | − | 0.643228i | \(-0.777595\pi\) |
0.939889 | + | 0.341480i | \(0.110928\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.0000 | + | 17.3205i | −0.0190823 | + | 0.0330515i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −454.000 | − | 786.351i | −0.827835 | − | 1.43385i | −0.899733 | − | 0.436440i | \(-0.856239\pi\) |
0.0718987 | − | 0.997412i | \(-0.477094\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1020.00 | 1.70495 | 0.852477 | − | 0.522765i | \(-0.175099\pi\) | ||||
0.852477 | + | 0.522765i | \(0.175099\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −250.000 | −0.400826 | −0.200413 | − | 0.979712i | \(-0.564228\pi\) | ||||
−0.200413 | + | 0.979712i | \(0.564228\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 30.0000 | + | 51.9615i | 0.0444002 | + | 0.0769034i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 458.000 | − | 793.279i | 0.652266 | − | 1.12976i | −0.330306 | − | 0.943874i | \(-0.607152\pi\) |
0.982572 | − | 0.185884i | \(-0.0595149\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −570.000 | + | 987.269i | −0.753803 | + | 1.30562i | 0.192165 | + | 0.981363i | \(0.438449\pi\) |
−0.945967 | + | 0.324262i | \(0.894884\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −225.000 | − | 389.711i | −0.287114 | − | 0.497296i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 420.000 | 0.500224 | 0.250112 | − | 0.968217i | \(-0.419533\pi\) | ||||
0.250112 | + | 0.968217i | \(0.419533\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.00000 | −0.00921569 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −70.0000 | − | 121.244i | −0.0755984 | − | 0.130940i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −769.000 | + | 1331.95i | −0.804950 | + | 1.39421i | 0.111375 | + | 0.993778i | \(0.464474\pi\) |
−0.916325 | + | 0.400435i | \(0.868859\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 225.000 | − | 389.711i | 0.221667 | − | 0.383938i | −0.733647 | − | 0.679530i | \(-0.762184\pi\) |
0.955314 | + | 0.295592i | \(0.0955170\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 575.000 | + | 995.929i | 0.550062 | + | 0.952736i | 0.998269 | + | 0.0588063i | \(0.0187294\pi\) |
−0.448207 | + | 0.893930i | \(0.647937\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1620.00 | 1.46366 | 0.731829 | − | 0.681489i | \(-0.238667\pi\) | ||||
0.731829 | + | 0.681489i | \(0.238667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1702.00 | −1.49561 | −0.747807 | − | 0.663916i | \(-0.768893\pi\) | ||||
−0.747807 | + | 0.663916i | \(0.768893\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 675.000 | + | 1169.13i | 0.561935 | + | 0.973300i | 0.997328 | + | 0.0730593i | \(0.0232762\pi\) |
−0.435393 | + | 0.900241i | \(0.643390\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −300.000 | + | 519.615i | −0.243262 | + | 0.421342i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 90.0000 | − | 155.885i | 0.0693301 | − | 0.120083i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 215.500 | + | 373.257i | 0.161908 | + | 0.280433i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2450.00 | 1.71183 | 0.855915 | − | 0.517117i | \(-0.172995\pi\) | ||||
0.855915 | + | 0.517117i | \(0.172995\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 345.000 | + | 597.558i | 0.230098 | + | 0.398541i | 0.957837 | − | 0.287313i | \(-0.0927621\pi\) |
−0.727739 | + | 0.685854i | \(0.759429\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 28.0000 | − | 48.4974i | 0.0182549 | − | 0.0316185i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1035.00 | − | 1792.67i | 0.645445 | − | 1.11794i | −0.338753 | − | 0.940875i | \(-0.610005\pi\) |
0.984198 | − | 0.177069i | \(-0.0566615\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 962.000 | + | 1666.23i | 0.587020 | + | 1.01675i | 0.994620 | + | 0.103588i | \(0.0330323\pi\) |
−0.407600 | + | 0.913160i | \(0.633634\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 120.000 | 0.0701742 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1050.00 | 0.601364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1455.00 | + | 2520.13i | 0.799988 | + | 1.38562i | 0.919623 | + | 0.392802i | \(0.128494\pi\) |
−0.119635 | + | 0.992818i | \(0.538172\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −88.0000 | + | 152.420i | −0.0474261 | + | 0.0821444i | −0.888764 | − | 0.458365i | \(-0.848435\pi\) |
0.841338 | + | 0.540510i | \(0.181769\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.0000 | + | 17.3205i | −0.00518206 | + | 0.00897559i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1174.00 | − | 2033.43i | −0.596786 | − | 1.03366i | −0.993292 | − | 0.115632i | \(-0.963111\pi\) |
0.396506 | − | 0.918032i | \(-0.370223\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −240.000 | −0.117482 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1996.00 | −0.959134 | −0.479567 | − | 0.877505i | \(-0.659206\pi\) | ||||
−0.479567 | + | 0.877505i | \(0.659206\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1560.00 | + | 2702.00i | 0.722853 | + | 1.25202i | 0.959852 | + | 0.280508i | \(0.0905029\pi\) |
−0.236999 | + | 0.971510i | \(0.576164\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1090.50 | − | 1888.80i | 0.496359 | − | 0.859718i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 885.000 | − | 1532.86i | 0.388932 | − | 0.673651i | −0.603374 | − | 0.797458i | \(-0.706177\pi\) |
0.992306 | + | 0.123808i | \(0.0395106\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −25.0000 | − | 43.3013i | −0.0107990 | − | 0.0187044i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2130.00 | 0.889406 | 0.444703 | − | 0.895678i | \(-0.353309\pi\) | ||||
0.444703 | + | 0.895678i | \(0.353309\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1654.00 | −0.679231 | −0.339616 | − | 0.940564i | \(-0.610297\pi\) | ||||
−0.339616 | + | 0.940564i | \(0.610297\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 500.000 | + | 866.025i | 0.198707 | + | 0.344170i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1350.00 | + | 2338.27i | −0.527924 | + | 0.914391i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 870.000 | − | 1506.88i | 0.329586 | − | 0.570860i | −0.652843 | − | 0.757493i | \(-0.726424\pi\) |
0.982430 | + | 0.186633i | \(0.0597574\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −43.0000 | − | 74.4782i | −0.0160373 | − | 0.0277775i | 0.857895 | − | 0.513824i | \(-0.171772\pi\) |
−0.873933 | + | 0.486047i | \(0.838438\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2490.00 | 0.900534 | 0.450267 | − | 0.892894i | \(-0.351329\pi\) | ||||
0.450267 | + | 0.892894i | \(0.351329\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −832.000 | −0.296376 | −0.148188 | − | 0.988959i | \(-0.547344\pi\) | ||||
−0.148188 | + | 0.988959i | \(0.547344\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 210.000 | + | 363.731i | 0.0726065 | + | 0.125758i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −600.000 | + | 1039.23i | −0.204419 | + | 0.354063i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −420.000 | + | 727.461i | −0.139005 | + | 0.240763i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1042.00 | − | 1804.80i | −0.339973 | − | 0.588850i | 0.644455 | − | 0.764643i | \(-0.277085\pi\) |
−0.984427 | + | 0.175793i | \(0.943751\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 680.000 | 0.215701 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.00000 | −0.00250265 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −180.000 | − | 311.769i | −0.0547878 | − | 0.0948953i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 587.000 | − | 1016.71i | 0.176271 | − | 0.305310i | −0.764329 | − | 0.644826i | \(-0.776930\pi\) |
0.940600 | + | 0.339516i | \(0.110263\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1560.00 | + | 2702.00i | −0.456127 | + | 0.790035i | −0.998752 | − | 0.0499397i | \(-0.984097\pi\) |
0.542625 | + | 0.839975i | \(0.317430\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.0000 | + | 50.2295i | 0.00836845 | + | 0.0144946i | 0.870179 | − | 0.492735i | \(-0.164003\pi\) |
−0.861811 | + | 0.507230i | \(0.830670\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5910.00 | 1.66170 | 0.830852 | − | 0.556494i | \(-0.187854\pi\) | ||||
0.830852 | + | 0.556494i | \(0.187854\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −600.000 | −0.166552 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1650.00 | + | 2857.88i | 0.446567 | + | 0.773478i | 0.998160 | − | 0.0606362i | \(-0.0193129\pi\) |
−0.551592 | + | 0.834114i | \(0.685980\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1493.00 | − | 2585.95i | 0.399056 | − | 0.691186i | −0.594553 | − | 0.804056i | \(-0.702671\pi\) |
0.993610 | + | 0.112870i | \(0.0360044\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −847.500 | + | 1467.91i | −0.220999 | + | 0.382782i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −56.0000 | − | 96.9948i | −0.0144259 | − | 0.0249864i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6630.00 | 1.66726 | 0.833629 | − | 0.552324i | \(-0.186259\pi\) | ||||
0.833629 | + | 0.552324i | \(0.186259\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3600.00 | 0.894585 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −765.000 | − | 1325.02i | −0.185679 | − | 0.321605i | 0.758126 | − | 0.652108i | \(-0.226115\pi\) |
−0.943805 | + | 0.330503i | \(0.892782\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −200.000 | + | 346.410i | −0.0479822 | + | 0.0831076i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1320.00 | − | 2286.31i | 0.309486 | − | 0.536045i | −0.668764 | − | 0.743474i | \(-0.733177\pi\) |
0.978250 | + | 0.207430i | \(0.0665098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 75.0000 | + | 129.904i | 0.0173857 | + | 0.0301129i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7350.00 | 1.66594 | 0.832969 | − | 0.553319i | \(-0.186639\pi\) | ||||
0.832969 | + | 0.553319i | \(0.186639\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3512.00 | 0.787228 | 0.393614 | − | 0.919276i | \(-0.371225\pi\) | ||||
0.393614 | + | 0.919276i | \(0.371225\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 375.000 | + | 649.519i | 0.0822304 | + | 0.142427i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2684.00 | − | 4648.82i | 0.582187 | − | 1.00838i | −0.413032 | − | 0.910716i | \(-0.635530\pi\) |
0.995220 | − | 0.0976619i | \(-0.0311364\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1530.00 | + | 2650.04i | −0.324812 | + | 0.562591i | −0.981474 | − | 0.191594i | \(-0.938634\pi\) |
0.656662 | + | 0.754185i | \(0.271968\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2522.00 | + | 4368.23i | 0.529743 | + | 0.917542i | 0.999398 | + | 0.0346921i | \(0.0110450\pi\) |
−0.469655 | + | 0.882850i | \(0.655622\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −480.000 | −0.0987230 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3187.00 | 0.648687 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1005.00 | − | 1740.71i | −0.200385 | − | 0.347077i | 0.748268 | − | 0.663397i | \(-0.230886\pi\) |
−0.948652 | + | 0.316320i | \(0.897553\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1125.00 | − | 1948.56i | 0.222034 | − | 0.384574i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −240.000 | + | 415.692i | −0.0464199 | + | 0.0804017i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 136.000 | + | 235.559i | 0.0260429 | + | 0.0451076i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 830.000 | 0.155822 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2752.00 | −0.511612 | −0.255806 | − | 0.966728i | \(-0.582341\pi\) | ||||
−0.255806 | + | 0.966728i | \(0.582341\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4770.00 | + | 8261.88i | 0.869717 | + | 1.50639i | 0.862286 | + | 0.506421i | \(0.169032\pi\) |
0.00743035 | + | 0.999972i | \(0.497635\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4627.00 | + | 8014.20i | −0.835570 | + | 1.44725i | 0.0579950 | + | 0.998317i | \(0.481529\pi\) |
−0.893565 | + | 0.448933i | \(0.851804\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 75.0000 | − | 129.904i | 0.0132884 | − | 0.0230162i | −0.859305 | − | 0.511464i | \(-0.829103\pi\) |
0.872593 | + | 0.488448i | \(0.162437\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3150.00 | − | 5455.96i | −0.552872 | − | 0.957602i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2520.00 | 0.434107 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −100.000 | −0.0170677 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −120.000 | − | 207.846i | −0.0201089 | − | 0.0348296i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −946.000 | + | 1638.52i | −0.157090 | + | 0.272088i | −0.933818 | − | 0.357748i | \(-0.883545\pi\) |
0.776728 | + | 0.629836i | \(0.216878\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2270.00 | − | 3931.76i | 0.370219 | − | 0.641238i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3689.00 | + | 6389.54i | 0.596299 | + | 1.03282i | 0.993362 | + | 0.115028i | \(0.0366959\pi\) |
−0.397064 | + | 0.917791i | \(0.629971\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 120.000 | 0.0190568 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1364.00 | −0.214720 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3360.00 | + | 5819.69i | 0.519811 | + | 0.900338i | 0.999735 | + | 0.0230283i | \(0.00733079\pi\) |
−0.479924 | + | 0.877310i | \(0.659336\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2593.00 | + | 4491.21i | −0.397708 | + | 0.688851i | −0.993443 | − | 0.114331i | \(-0.963528\pi\) |
0.595735 | + | 0.803181i | \(0.296861\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1665.00 | − | 2883.86i | 0.251045 | − | 0.434823i | −0.712769 | − | 0.701399i | \(-0.752559\pi\) |
0.963814 | + | 0.266576i | \(0.0858923\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2550.00 | + | 4416.73i | 0.381239 | + | 0.660326i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9000.00 | −1.32312 | −0.661562 | − | 0.749890i | \(-0.730106\pi\) | ||||
−0.661562 | + | 0.749890i | \(0.730106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6075.00 | −0.885698 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −625.000 | − | 1082.53i | −0.0896274 | − | 0.155239i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4379.00 | − | 7584.65i | 0.622839 | − | 1.07879i | −0.366115 | − | 0.930569i | \(-0.619312\pi\) |
0.988954 | − | 0.148219i | \(-0.0473542\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −30.0000 | + | 51.9615i | −0.00419817 | + | 0.00727145i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2362.00 | − | 4091.10i | −0.327881 | − | 0.567907i | 0.654210 | − | 0.756313i | \(-0.273001\pi\) |
−0.982091 | + | 0.188406i | \(0.939668\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 840.000 | 0.114754 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7292.00 | 0.988298 | 0.494149 | − | 0.869377i | \(-0.335480\pi\) | ||||
0.494149 | + | 0.869377i | \(0.335480\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7260.00 | + | 12574.7i | 0.968587 | + | 1.67764i | 0.699653 | + | 0.714482i | \(0.253338\pi\) |
0.268933 | + | 0.963159i | \(0.413329\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −150.000 | + | 259.808i | −0.0198564 | + | 0.0343923i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3555.00 | − | 6157.44i | 0.463356 | − | 0.802557i | −0.535769 | − | 0.844364i | \(-0.679978\pi\) |
0.999126 | + | 0.0418076i | \(0.0133116\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5400.00 | − | 9353.07i | −0.698439 | − | 1.20973i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4580.00 | 0.583405 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11488.0 | −1.45231 | −0.726154 | − | 0.687532i | \(-0.758694\pi\) | ||||
−0.726154 | + | 0.687532i | \(0.758694\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 390.000 | + | 675.500i | 0.0485678 | + | 0.0841218i | 0.889287 | − | 0.457349i | \(-0.151201\pi\) |
−0.840720 | + | 0.541471i | \(0.817868\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00000 | + | 13.8564i | −0.000988855 | + | 0.00171275i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3000.00 | − | 5196.15i | 0.365367 | − | 0.632835i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2701.00 | − | 4678.27i | −0.326542 | − | 0.565588i | 0.655281 | − | 0.755385i | \(-0.272550\pi\) |
−0.981823 | + | 0.189797i | \(0.939217\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 900.000 | 0.107230 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5700.00 | −0.674222 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1095.00 | − | 1896.60i | −0.127671 | − | 0.221133i | 0.795103 | − | 0.606475i | \(-0.207417\pi\) |
−0.922774 | + | 0.385342i | \(0.874084\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3581.00 | − | 6202.47i | 0.414554 | − | 0.718029i | −0.580827 | − | 0.814027i | \(-0.697271\pi\) |
0.995382 | + | 0.0959980i | \(0.0306042\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1125.00 | − | 1948.56i | 0.128401 | − | 0.222397i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 166.000 | + | 287.520i | 0.0188134 | + | 0.0325857i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9360.00 | −1.04607 | −0.523034 | − | 0.852312i | \(-0.675200\pi\) | ||||
−0.523034 | + | 0.852312i | \(0.675200\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12806.0 | 1.42129 | 0.710643 | − | 0.703552i | \(-0.248404\pi\) | ||||
0.710643 | + | 0.703552i | \(0.248404\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1680.00 | − | 2909.85i | −0.183902 | − | 0.318528i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5644.00 | + | 9775.69i | −0.613607 | + | 1.06280i | 0.377020 | + | 0.926205i | \(0.376949\pi\) |
−0.990627 | + | 0.136593i | \(0.956385\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4260.00 | + | 7378.54i | −0.456882 | + | 0.791343i | −0.998794 | − | 0.0490923i | \(-0.984367\pi\) |
0.541912 | + | 0.840435i | \(0.317700\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1050.00 | + | 1818.65i | 0.111853 | + | 0.193736i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1260.00 | 0.132434 | 0.0662172 | − | 0.997805i | \(-0.478907\pi\) | ||||
0.0662172 | + | 0.997805i | \(0.478907\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7200.00 | 0.751740 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.0000 | − | 34.6410i | −0.00206069 | − | 0.00356922i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6875.00 | − | 11907.8i | 0.703718 | − | 1.21887i | −0.263435 | − | 0.964677i | \(-0.584855\pi\) |
0.967152 | − | 0.254197i | \(-0.0818113\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1605.00 | + | 2779.94i | −0.162152 | + | 0.280856i | −0.935640 | − | 0.352955i | \(-0.885177\pi\) |
0.773488 | + | 0.633811i | \(0.218510\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6425.00 | + | 11128.4i | 0.644914 | + | 1.11702i | 0.984321 | + | 0.176384i | \(0.0564401\pi\) |
−0.339408 | + | 0.940639i | \(0.610227\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8220.00 | 0.814510 | 0.407255 | − | 0.913314i | \(-0.366486\pi\) | ||||
0.407255 | + | 0.913314i | \(0.366486\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1816.00 | 0.178795 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2040.00 | − | 3533.38i | −0.198307 | − | 0.343478i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 350.000 | − | 606.218i | 0.0338086 | − | 0.0585583i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3510.00 | + | 6079.50i | −0.334814 | + | 0.579915i | −0.983449 | − | 0.181184i | \(-0.942007\pi\) |
0.648635 | + | 0.761100i | \(0.275340\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 400.000 | + | 692.820i | 0.0379177 | + | 0.0656754i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7690.00 | −0.719969 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8122.00 | −0.755735 | −0.377868 | − | 0.925860i | \(-0.623343\pi\) | ||||
−0.377868 | + | 0.925860i | \(0.623343\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6735.00 | − | 11665.4i | −0.619035 | − | 1.07220i | −0.989662 | − | 0.143419i | \(-0.954190\pi\) |
0.370627 | − | 0.928782i | \(-0.379143\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9450.00 | + | 16367.9i | −0.863299 | + | 1.49528i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1020.00 | + | 1766.69i | −0.0920589 | + | 0.159451i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1234.00 | − | 2137.35i | −0.110704 | − | 0.191745i | 0.805350 | − | 0.592799i | \(-0.201977\pi\) |
−0.916054 | + | 0.401054i | \(0.868644\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4440.00 | 0.393578 | 0.196789 | − | 0.980446i | \(-0.436949\pi\) | ||||
0.196789 | + | 0.980446i | \(0.436949\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2250.00 | 0.198265 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5595.00 | − | 9690.82i | −0.487218 | − | 0.843887i | 0.512674 | − | 0.858583i | \(-0.328655\pi\) |
−0.999892 | + | 0.0146969i | \(0.995322\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 250.000 | − | 433.013i | 0.0216426 | − | 0.0374860i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2875.00 | + | 4979.65i | −0.245995 | + | 0.426077i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1800.00 | + | 3117.69i | 0.153122 | + | 0.265215i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4020.00 | 0.338041 | 0.169021 | − | 0.985613i | \(-0.445940\pi\) | ||||
0.169021 | + | 0.985613i | \(0.445940\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9076.00 | −0.758826 | −0.379413 | − | 0.925228i | \(-0.623874\pi\) | ||||
−0.379413 | + | 0.925228i | \(0.623874\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −180.000 | − | 311.769i | −0.0148784 | − | 0.0257702i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1116.50 | + | 1933.83i | −0.0917646 | + | 0.158941i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −480.000 | + | 831.384i | −0.0390077 | + | 0.0675633i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4050.00 | + | 7014.81i | 0.327284 | + | 0.566872i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10170.0 | 0.812714 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7486.00 | −0.594914 | −0.297457 | − | 0.954735i | \(-0.596138\pi\) | ||||
−0.297457 | + | 0.954735i | \(0.596138\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4255.00 | − | 7369.88i | −0.334430 | − | 0.579249i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3700.00 | + | 6408.59i | −0.289215 | + | 0.500935i | −0.973623 | − | 0.228165i | \(-0.926728\pi\) |
0.684408 | + | 0.729100i | \(0.260061\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2940.00 | + | 5092.23i | −0.227311 | + | 0.393714i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 916.000 | + | 1586.56i | 0.0704381 | + | 0.122002i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11490.0 | −0.874052 | −0.437026 | − | 0.899449i | \(-0.643968\pi\) | ||||
−0.437026 | + | 0.899449i | \(0.643968\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 544.000 | 0.0411606 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9660.00 | − | 16731.6i | −0.723127 | − | 1.25249i | −0.959740 | − | 0.280889i | \(-0.909371\pi\) |
0.236613 | − | 0.971604i | \(-0.423963\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3375.00 | + | 5845.67i | −0.251305 | + | 0.435273i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4170.00 | − | 7222.65i | 0.307233 | − | 0.532143i | −0.670523 | − | 0.741889i | \(-0.733930\pi\) |
0.977756 | + | 0.209746i | \(0.0672636\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10522.0 | − | 18224.6i | −0.771159 | − | 1.33569i | −0.936928 | − | 0.349523i | \(-0.886344\pi\) |
0.165769 | − | 0.986165i | \(-0.446990\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3000.00 | −0.217580 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1418.00 | 0.102309 | 0.0511543 | − | 0.998691i | \(-0.483710\pi\) | ||||
0.0511543 | + | 0.998691i | \(0.483710\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1140.00 | − | 1974.54i | −0.0814030 | − | 0.140994i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 450.000 | − | 779.423i | 0.0319676 | − | 0.0553695i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11010.0 | + | 19069.9i | −0.774159 | + | 1.34088i | 0.161107 | + | 0.986937i | \(0.448494\pi\) |
−0.935266 | + | 0.353946i | \(0.884840\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −56.0000 | − | 96.9948i | −0.00391755 | − | 0.00678540i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25230.0 | −1.74717 | −0.873585 | − | 0.486671i | \(-0.838211\pi\) | ||||
−0.873585 | + | 0.486671i | \(0.838211\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 900.000 | 0.0620108 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4140.00 | + | 7170.69i | 0.282397 | + | 0.489126i | 0.971975 | − | 0.235086i | \(-0.0755371\pi\) |
−0.689578 | + | 0.724212i | \(0.742204\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9437.00 | − | 16345.4i | 0.640505 | − | 1.10939i | −0.344816 | − | 0.938670i | \(-0.612059\pi\) |
0.985320 | − | 0.170716i | \(-0.0546081\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1077.50 | + | 1866.28i | −0.0724076 | + | 0.125414i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5275.00 | − | 9136.57i | −0.352728 | − | 0.610942i | 0.633999 | − | 0.773334i | \(-0.281412\pi\) |
−0.986726 | + | 0.162392i | \(0.948079\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −480.000 | −0.0317819 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11000.0 | 0.724773 | 0.362386 | − | 0.932028i | \(-0.381962\pi\) | ||||
0.362386 | + | 0.932028i | \(0.381962\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5655.00 | − | 9794.75i | −0.368982 | − | 0.639095i | 0.620425 | − | 0.784266i | \(-0.286960\pi\) |
−0.989407 | + | 0.145171i | \(0.953627\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8786.00 | − | 15217.8i | 0.570499 | − | 0.988134i | −0.426015 | − | 0.904716i | \(-0.640083\pi\) |
0.996515 | − | 0.0834180i | \(-0.0265837\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −420.000 | + | 727.461i | −0.0270095 | + | 0.0467819i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18000.0 | −1.14103 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1604.00 | 0.101195 | 0.0505976 | − | 0.998719i | \(-0.483887\pi\) | ||||
0.0505976 | + | 0.998719i | \(0.483887\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6125.00 | + | 10608.8i | 0.382777 | + | 0.662989i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −678.000 | + | 1174.33i | −0.0421716 | + | 0.0730434i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15660.0 | − | 27123.9i | 0.964950 | − | 1.67134i | 0.255200 | − | 0.966888i | \(-0.417859\pi\) |
0.709750 | − | 0.704454i | \(-0.248808\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15650.0 | + | 27106.6i | 0.959838 | + | 1.66249i | 0.722887 | + | 0.690966i | \(0.242815\pi\) |
0.236951 | + | 0.971522i | \(0.423852\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10920.0 | −0.663539 | −0.331769 | − | 0.943361i | \(-0.607646\pi\) | ||||
−0.331769 | + | 0.943361i | \(0.607646\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13500.0 | −0.816520 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1605.00 | − | 2779.94i | −0.0961845 | − | 0.166597i | 0.813918 | − | 0.580980i | \(-0.197331\pi\) |
−0.910102 | + | 0.414384i | \(0.863997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1725.00 | + | 2987.79i | −0.102903 | + | 0.178233i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5955.00 | + | 10314.4i | −0.352009 | + | 0.609697i | −0.986601 | − | 0.163150i | \(-0.947835\pi\) |
0.634592 | + | 0.772847i | \(0.281168\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1691.00 | + | 2928.90i | 0.0995042 | + | 0.172346i | 0.911480 | − | 0.411345i | \(-0.134941\pi\) |
−0.811975 | + | 0.583692i | \(0.801608\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 280.000 | 0.0163277 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25200.0 | 1.46289 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2490.00 | − | 4312.81i | −0.143257 | − | 0.248128i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7975.00 | + | 13813.1i | −0.456781 | + | 0.791168i | −0.998789 | − | 0.0492056i | \(-0.984331\pi\) |
0.542008 | + | 0.840374i | \(0.317664\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16095.0 | − | 27877.4i | 0.913709 | − | 1.58259i | 0.104929 | − | 0.994480i | \(-0.466538\pi\) |
0.808780 | − | 0.588111i | \(-0.200128\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1538.00 | − | 2663.89i | −0.0869264 | − | 0.150561i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22140.0 | −1.24036 | −0.620178 | − | 0.784461i | \(-0.712940\pi\) | ||||
−0.620178 | + | 0.784461i | \(0.712940\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10350.0 | 0.577304 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 60.0000 | + | 103.923i | 0.00331759 | + | 0.00574623i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3086.00 | − | 5345.11i | 0.169894 | − | 0.294266i | −0.768488 | − | 0.639864i | \(-0.778991\pi\) |
0.938383 | + | 0.345598i | \(0.112324\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4810.00 | + | 8331.16i | −0.262523 | + | 0.454704i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10800.0 | − | 18706.1i | −0.586914 | − | 1.01657i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19170.0 | −1.03287 | −0.516434 | − | 0.856327i | \(-0.672741\pi\) | ||||
−0.516434 | + | 0.856327i | \(0.672741\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5600.00 | −0.300438 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 450.000 | + | 779.423i | 0.0239378 | + | 0.0414614i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10949.0 | − | 18964.2i | 0.579969 | − | 1.00454i | −0.415513 | − | 0.909587i | \(-0.636398\pi\) |
0.995482 | − | 0.0949491i | \(-0.0302688\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −240.000 | + | 415.692i | −0.0126060 | + | 0.0218342i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 300.000 | + | 519.615i | 0.0156914 | + | 0.0271783i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16680.0 | −0.865173 | −0.432586 | − | 0.901593i | \(-0.642399\pi\) | ||||
−0.432586 | + | 0.901593i | \(0.642399\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2300.00 | −0.118802 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2625.00 | + | 4546.63i | 0.134469 | + | 0.232907i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3259.00 | + | 5644.75i | −0.166258 | + | 0.287967i | −0.937101 | − | 0.349057i | \(-0.886502\pi\) |
0.770843 | + | 0.637025i | \(0.219835\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6120.00 | + | 10600.2i | −0.309653 | + | 0.536335i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11600.0 | + | 20091.8i | 0.584524 | + | 1.01242i | 0.994935 | + | 0.100524i | \(0.0320519\pi\) |
−0.410411 | + | 0.911901i | \(0.634615\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27240.0 | −1.36146 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16324.0 | −0.812568 | −0.406284 | − | 0.913747i | \(-0.633176\pi\) | ||||
−0.406284 | + | 0.913747i | \(0.633176\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −60.0000 | − | 103.923i | −0.00296257 | − | 0.00513131i | 0.864540 | − | 0.502563i | \(-0.167610\pi\) |
−0.867503 | + | 0.497432i | \(0.834276\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7275.00 | + | 12600.7i | −0.357766 | + | 0.619668i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1620.00 | + | 2805.92i | −0.0790301 | + | 0.136884i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15274.0 | − | 26455.3i | −0.742152 | − | 1.28545i | −0.951514 | − | 0.307607i | \(-0.900472\pi\) |
0.209362 | − | 0.977838i | \(-0.432861\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −880.000 | −0.0424192 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16952.0 | 0.813911 | 0.406956 | − | 0.913448i | \(-0.366590\pi\) | ||||
0.406956 | + | 0.913448i | \(0.366590\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10110.0 | − | 17511.0i | −0.481586 | − | 0.834132i | 0.518190 | − | 0.855265i | \(-0.326606\pi\) |
−0.999777 | + | 0.0211333i | \(0.993273\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1702.00 | − | 2947.95i | 0.0807556 | − | 0.139873i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 900.000 | − | 1558.85i | 0.0423691 | − | 0.0733855i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10361.0 | + | 17945.8i | 0.485861 | + | 0.841536i | 0.999868 | − | 0.0162499i | \(-0.00517274\pi\) |
−0.514007 | + | 0.857786i | \(0.671839\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4350.00 | −0.202404 | −0.101202 | − | 0.994866i | \(-0.532269\pi\) | ||||
−0.101202 | + | 0.994866i | \(0.532269\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −100.000 | −0.00463498 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3360.00 | − | 5819.69i | −0.154537 | − | 0.267666i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15300.0 | − | 26500.4i | 0.700995 | − | 1.21416i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5870.00 | − | 10167.1i | 0.266891 | − | 0.462268i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20986.0 | − | 36348.8i | −0.950534 | − | 1.64637i | −0.744273 | − | 0.667876i | \(-0.767204\pi\) |
−0.206261 | − | 0.978497i | \(-0.566130\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2700.00 | −0.121367 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 664.000 | 0.0297343 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19755.0 | − | 34216.7i | −0.877990 | − | 1.52072i | −0.853543 | − | 0.521022i | \(-0.825551\pi\) |
−0.0244468 | − | 0.999701i | \(-0.507782\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5400.00 | − | 9353.07i | 0.239097 | − | 0.414128i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3750.00 | + | 6495.19i | −0.164800 | + | 0.285442i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −600.000 | − | 1039.23i | −0.0262698 | − | 0.0455007i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16680.0 | −0.724892 | −0.362446 | − | 0.932005i | \(-0.618058\pi\) | ||||
−0.362446 | + | 0.932005i | \(0.618058\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15484.0 | −0.670428 | −0.335214 | − | 0.942142i | \(-0.608809\pi\) | ||||
−0.335214 | + | 0.942142i | \(0.608809\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4990.00 | − | 8642.93i | −0.214469 | − | 0.371471i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1904.00 | + | 3297.82i | −0.0815331 | + | 0.141219i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2085.00 | − | 3611.33i | 0.0886322 | − | 0.153515i | −0.818301 | − | 0.574790i | \(-0.805084\pi\) |
0.906933 | + | 0.421275i | \(0.138417\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15113.0 | + | 26176.5i | 0.640105 | + | 1.10869i | 0.985409 | + | 0.170203i | \(0.0544423\pi\) |
−0.345304 | + | 0.938491i | \(0.612224\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14760.0 | 0.620623 | 0.310312 | − | 0.950635i | \(-0.399567\pi\) | ||||
0.310312 | + | 0.950635i | \(0.399567\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9934.00 | −0.416191 | −0.208095 | − | 0.978109i | \(-0.566726\pi\) | ||||
−0.208095 | + | 0.978109i | \(0.566726\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15255.0 | − | 26422.4i | −0.634519 | − | 1.09902i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7800.00 | + | 13510.0i | −0.323270 | + | 0.559919i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11760.0 | + | 20368.9i | −0.483910 | + | 0.838156i | −0.999829 | − | 0.0184808i | \(-0.994117\pi\) |
0.515919 | + | 0.856637i | \(0.327450\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9855.50 | − | 17070.2i | −0.404096 | − | 0.699915i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10905.0 | 0.443957 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −862.000 | −0.0349689 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12000.0 | + | 20784.6i | 0.483378 | + | 0.837235i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14908.0 | + | 25821.4i | −0.598406 | + | 1.03647i | 0.394651 | + | 0.918831i | \(0.370866\pi\) |
−0.993057 | + | 0.117638i | \(0.962468\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17715.0 | + | 30683.3i | −0.706106 | + | 1.22301i | 0.260185 | + | 0.965559i | \(0.416216\pi\) |
−0.966291 | + | 0.257453i | \(0.917117\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18098.0 | + | 31346.7i | 0.718854 | + | 1.24509i | 0.961454 | + | 0.274966i | \(0.0886665\pi\) |
−0.242600 | + | 0.970126i | \(0.578000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −480.000 | −0.0189332 | −0.00946662 | − | 0.999955i | \(-0.503013\pi\) | ||||
−0.00946662 | + | 0.999955i | \(0.503013\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8850.00 | 0.347872 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13740.0 | − | 23798.4i | −0.536361 | − | 0.929004i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1816.00 | − | 3145.40i | 0.0706462 | − | 0.122363i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 125.000 | − | 216.506i | 0.00482945 | − | 0.00836486i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14266.0 | − | 24709.4i | −0.549291 | − | 0.951401i | −0.998323 | − | 0.0578849i | \(-0.981564\pi\) |
0.449032 | − | 0.893516i | \(-0.351769\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20340.0 | 0.777834 | 0.388917 | − | 0.921273i | \(-0.372849\pi\) | ||||
0.388917 | + | 0.921273i | \(0.372849\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10756.0 | −0.409930 | −0.204965 | − | 0.978769i | \(-0.565708\pi\) | ||||
−0.204965 | + | 0.978769i | \(0.565708\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 300.000 | + | 519.615i | 0.0113563 | + | 0.0196696i | 0.871648 | − | 0.490133i | \(-0.163052\pi\) |
−0.860291 | + | 0.509803i | \(0.829718\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2450.00 | + | 4243.52i | −0.0924301 | + | 0.160094i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1680.00 | − | 2909.85i | 0.0629553 | − | 0.109042i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5325.00 | + | 9223.17i | 0.198877 | + | 0.344465i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 840.000 | 0.0311630 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2700.00 | −0.0998336 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4135.00 | − | 7162.03i | −0.151881 | − | 0.263065i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12700.0 | + | 21997.0i | −0.464936 | + | 0.805292i | −0.999199 | − | 0.0400262i | \(-0.987256\pi\) |
0.534263 | + | 0.845318i | \(0.320589\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18120.0 | + | 31384.8i | −0.658993 | + | 1.14141i | 0.321884 | + | 0.946779i | \(0.395684\pi\) |
−0.980877 | + | 0.194630i | \(0.937649\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17100.0 | + | 29618.1i | 0.619855 | + | 1.07362i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1380.00 | −0.0496964 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6572.00 | 0.235898 | 0.117949 | − | 0.993020i | \(-0.462368\pi\) | ||||
0.117949 | + | 0.993020i | \(0.462368\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2040.00 | + | 3533.38i | 0.0727491 | + | 0.126005i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2500.00 | + | 4330.13i | −0.0888643 | + | 0.153918i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1170.00 | − | 2026.50i | 0.0413202 | − | 0.0715687i | −0.844626 | − | 0.535357i | \(-0.820177\pi\) |
0.885946 | + | 0.463789i | \(0.153510\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4746.00 | − | 8220.31i | −0.167072 | − | 0.289377i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13500.0 | −0.472190 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2522.00 | 0.0879297 | 0.0439649 | − | 0.999033i | \(-0.486001\pi\) | ||||
0.0439649 | + | 0.999033i | \(0.486001\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26385.0 | − | 45700.2i | −0.914056 | − | 1.58319i | −0.808278 | − | 0.588801i | \(-0.799600\pi\) |
−0.105778 | − | 0.994390i | \(-0.533733\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14400.0 | + | 24941.5i | −0.497273 | + | 0.861302i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14100.0 | − | 24421.9i | 0.483832 | − | 0.838021i | −0.515996 | − | 0.856591i | \(-0.672578\pi\) |
0.999828 | + | 0.0185702i | \(0.00591142\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −500.000 | − | 866.025i | −0.0171029 | − | 0.0296232i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15570.0 | 0.529236 | 0.264618 | − | 0.964353i | \(-0.414754\pi\) | ||||
0.264618 | + | 0.964353i | \(0.414754\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8700.00 | 0.294791 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2070.00 | + | 3585.35i | 0.0697015 | + | 0.120727i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14887.5 | − | 25785.9i | 0.499731 | − | 0.865560i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 215.000 | − | 372.391i | 0.00717212 | − | 0.0124225i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4175.00 | + | 7231.31i | 0.138841 | + | 0.240479i | 0.927058 | − | 0.374918i | \(-0.122329\pi\) |
−0.788217 | + | 0.615397i | \(0.788996\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43650.0 | −1.44263 | −0.721316 | − | 0.692606i | \(-0.756462\pi\) | ||||
−0.721316 | + | 0.692606i | \(0.756462\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3848.00 | −0.126784 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9405.00 | + | 16289.9i | 0.307976 | + | 0.533430i | 0.977919 | − | 0.208982i | \(-0.0670150\pi\) |
−0.669943 | + | 0.742412i | \(0.733682\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6300.00 | − | 10911.9i | 0.205668 | − | 0.356227i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12660.0 | + | 21927.8i | −0.410774 | + | 0.711482i | −0.994975 | − | 0.100127i | \(-0.968075\pi\) |
0.584200 | + | 0.811610i | \(0.301408\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6225.00 | + | 10782.0i | 0.201365 | + | 0.348775i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16320.0 | 0.524718 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6736.00 | −0.215919 | −0.107960 | − | 0.994155i | \(-0.534432\pi\) | ||||
−0.107960 | + | 0.994155i | \(0.534432\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2080.00 | − | 3602.67i | −0.0662718 | − | 0.114786i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10250.0 | − | 17753.5i | 0.325598 | − | 0.563951i | −0.656036 | − | 0.754730i | \(-0.727768\pi\) |
0.981633 | + | 0.190778i | \(0.0611012\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1620.4.i.i.541.1 | 2 | ||
3.2 | odd | 2 | 1620.4.i.c.541.1 | 2 | |||
9.2 | odd | 6 | 180.4.a.e.1.1 | yes | 1 | ||
9.4 | even | 3 | inner | 1620.4.i.i.1081.1 | 2 | ||
9.5 | odd | 6 | 1620.4.i.c.1081.1 | 2 | |||
9.7 | even | 3 | 180.4.a.b.1.1 | ✓ | 1 | ||
36.7 | odd | 6 | 720.4.a.h.1.1 | 1 | |||
36.11 | even | 6 | 720.4.a.w.1.1 | 1 | |||
45.2 | even | 12 | 900.4.d.i.649.2 | 2 | |||
45.7 | odd | 12 | 900.4.d.d.649.2 | 2 | |||
45.29 | odd | 6 | 900.4.a.j.1.1 | 1 | |||
45.34 | even | 6 | 900.4.a.i.1.1 | 1 | |||
45.38 | even | 12 | 900.4.d.i.649.1 | 2 | |||
45.43 | odd | 12 | 900.4.d.d.649.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.4.a.b.1.1 | ✓ | 1 | 9.7 | even | 3 | ||
180.4.a.e.1.1 | yes | 1 | 9.2 | odd | 6 | ||
720.4.a.h.1.1 | 1 | 36.7 | odd | 6 | |||
720.4.a.w.1.1 | 1 | 36.11 | even | 6 | |||
900.4.a.i.1.1 | 1 | 45.34 | even | 6 | |||
900.4.a.j.1.1 | 1 | 45.29 | odd | 6 | |||
900.4.d.d.649.1 | 2 | 45.43 | odd | 12 | |||
900.4.d.d.649.2 | 2 | 45.7 | odd | 12 | |||
900.4.d.i.649.1 | 2 | 45.38 | even | 12 | |||
900.4.d.i.649.2 | 2 | 45.2 | even | 12 | |||
1620.4.i.c.541.1 | 2 | 3.2 | odd | 2 | |||
1620.4.i.c.1081.1 | 2 | 9.5 | odd | 6 | |||
1620.4.i.i.541.1 | 2 | 1.1 | even | 1 | trivial | ||
1620.4.i.i.1081.1 | 2 | 9.4 | even | 3 | inner |