Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(415,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.415");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.m (of order \(4\), 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: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6x^{14} + 10x^{12} + 88x^{10} - 752x^{8} + 1408x^{6} + 2560x^{4} - 24576x^{2} + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 415.2 | ||
Root | \(1.66730 + 1.10459i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.415 |
Dual form | 1152.3.m.d.991.2 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(5\) | −4.23991 | − | 4.23991i | −0.847982 | − | 0.847982i | 0.141900 | − | 0.989881i | \(-0.454679\pi\) |
−0.989881 | + | 0.141900i | \(0.954679\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.262225 | 0.0374608 | 0.0187304 | − | 0.999825i | \(-0.494038\pi\) | ||||
0.0187304 | + | 0.999825i | \(0.494038\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.60531 | − | 8.60531i | 0.782301 | − | 0.782301i | −0.197917 | − | 0.980219i | \(-0.563418\pi\) |
0.980219 | + | 0.197917i | \(0.0634178\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.9957 | − | 15.9957i | 1.23044 | − | 1.23044i | 0.266640 | − | 0.963796i | \(-0.414087\pi\) |
0.963796 | − | 0.266640i | \(-0.0859134\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.51534 | 0.206785 | 0.103392 | − | 0.994641i | \(-0.467030\pi\) | ||||
0.103392 | + | 0.994641i | \(0.467030\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.7566 | + | 10.7566i | 0.566138 | + | 0.566138i | 0.931044 | − | 0.364906i | \(-0.118899\pi\) |
−0.364906 | + | 0.931044i | \(0.618899\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −16.4968 | −0.717253 | −0.358626 | − | 0.933481i | \(-0.616755\pi\) | ||||
−0.358626 | + | 0.933481i | \(0.616755\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.9536i | 0.438145i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −25.9522 | + | 25.9522i | −0.894903 | + | 0.894903i | −0.994980 | − | 0.100077i | \(-0.968091\pi\) |
0.100077 | + | 0.994980i | \(0.468091\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 46.2072i | 1.49055i | 0.666755 | + | 0.745277i | \(0.267683\pi\) | ||||
−0.666755 | + | 0.745277i | \(0.732317\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.11181 | − | 1.11181i | −0.0317660 | − | 0.0317660i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.99313 | + | 2.99313i | 0.0808955 | + | 0.0808955i | 0.746397 | − | 0.665501i | \(-0.231782\pi\) |
−0.665501 | + | 0.746397i | \(0.731782\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 21.9026i | − | 0.534210i | −0.963667 | − | 0.267105i | \(-0.913933\pi\) | ||
0.963667 | − | 0.267105i | \(-0.0860670\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 48.7016 | − | 48.7016i | 1.13260 | − | 1.13260i | 0.142851 | − | 0.989744i | \(-0.454373\pi\) |
0.989744 | − | 0.142851i | \(-0.0456270\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 70.7760i | − | 1.50587i | −0.658094 | − | 0.752936i | \(-0.728637\pi\) | ||
0.658094 | − | 0.752936i | \(-0.271363\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.9312 | −0.998597 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −52.8193 | − | 52.8193i | −0.996590 | − | 0.996590i | 0.00340427 | − | 0.999994i | \(-0.498916\pi\) |
−0.999994 | + | 0.00340427i | \(0.998916\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −72.9715 | −1.32675 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 61.7726 | − | 61.7726i | 1.04699 | − | 1.04699i | 0.0481541 | − | 0.998840i | \(-0.484666\pi\) |
0.998840 | − | 0.0481541i | \(-0.0153339\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 22.9004 | − | 22.9004i | 0.375416 | − | 0.375416i | −0.494029 | − | 0.869445i | \(-0.664476\pi\) |
0.869445 | + | 0.494029i | \(0.164476\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −135.640 | −2.08677 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −54.9939 | − | 54.9939i | −0.820804 | − | 0.820804i | 0.165419 | − | 0.986223i | \(-0.447102\pi\) |
−0.986223 | + | 0.165419i | \(0.947102\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 84.2532 | 1.18666 | 0.593332 | − | 0.804958i | \(-0.297812\pi\) | ||||
0.593332 | + | 0.804958i | \(0.297812\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 78.0341i | 1.06896i | 0.845181 | + | 0.534480i | \(0.179493\pi\) | ||||
−0.845181 | + | 0.534480i | \(0.820507\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.25653 | − | 2.25653i | 0.0293056 | − | 0.0293056i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 59.2887i | − | 0.750490i | −0.926926 | − | 0.375245i | \(-0.877559\pi\) | ||
0.926926 | − | 0.375245i | \(-0.122441\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −111.661 | − | 111.661i | −1.34531 | − | 1.34531i | −0.890676 | − | 0.454638i | \(-0.849769\pi\) |
−0.454638 | − | 0.890676i | \(-0.650231\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.9047 | − | 14.9047i | −0.175350 | − | 0.175350i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 34.5426i | 0.388119i | 0.980990 | + | 0.194060i | \(0.0621655\pi\) | ||||
−0.980990 | + | 0.194060i | \(0.937834\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.19447 | − | 4.19447i | 0.0460931 | − | 0.0460931i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 91.2142i | − | 0.960150i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −66.0805 | −0.681242 | −0.340621 | − | 0.940201i | \(-0.610637\pi\) | ||||
−0.340621 | + | 0.940201i | \(0.610637\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −25.5254 | − | 25.5254i | −0.252727 | − | 0.252727i | 0.569361 | − | 0.822088i | \(-0.307191\pi\) |
−0.822088 | + | 0.569361i | \(0.807191\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.2072 | 0.137934 | 0.0689670 | − | 0.997619i | \(-0.478030\pi\) | ||||
0.0689670 | + | 0.997619i | \(0.478030\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −21.8489 | + | 21.8489i | −0.204195 | + | 0.204195i | −0.801795 | − | 0.597600i | \(-0.796121\pi\) |
0.597600 | + | 0.801795i | \(0.296121\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.8979 | + | 17.8979i | −0.164201 | + | 0.164201i | −0.784425 | − | 0.620224i | \(-0.787042\pi\) |
0.620224 | + | 0.784425i | \(0.287042\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −174.546 | −1.54465 | −0.772325 | − | 0.635227i | \(-0.780907\pi\) | ||||
−0.772325 | + | 0.635227i | \(0.780907\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 69.9450 | + | 69.9450i | 0.608217 | + | 0.608217i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.921813 | 0.00774632 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 27.1029i | − | 0.223991i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −59.5553 | + | 59.5553i | −0.476442 | + | 0.476442i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 45.3438i | 0.357037i | 0.983937 | + | 0.178519i | \(0.0571305\pi\) | ||||
−0.983937 | + | 0.178519i | \(0.942869\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 32.6213 | + | 32.6213i | 0.249017 | + | 0.249017i | 0.820567 | − | 0.571550i | \(-0.193658\pi\) |
−0.571550 | + | 0.820567i | \(0.693658\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.82066 | + | 2.82066i | 0.0212080 | + | 0.0212080i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 115.159i | − | 0.840577i | −0.907390 | − | 0.420289i | \(-0.861929\pi\) | ||
0.907390 | − | 0.420289i | \(-0.138071\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −122.841 | + | 122.841i | −0.883748 | + | 0.883748i | −0.993913 | − | 0.110165i | \(-0.964862\pi\) |
0.110165 | + | 0.993913i | \(0.464862\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 275.296i | − | 1.92514i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 220.070 | 1.51772 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −99.9710 | − | 99.9710i | −0.670946 | − | 0.670946i | 0.286988 | − | 0.957934i | \(-0.407346\pi\) |
−0.957934 | + | 0.286988i | \(0.907346\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 222.762 | 1.47525 | 0.737623 | − | 0.675212i | \(-0.235948\pi\) | ||||
0.737623 | + | 0.675212i | \(0.235948\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 195.914 | − | 195.914i | 1.26396 | − | 1.26396i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −45.9080 | + | 45.9080i | −0.292408 | + | 0.292408i | −0.838031 | − | 0.545623i | \(-0.816293\pi\) |
0.545623 | + | 0.838031i | \(0.316293\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.32588 | −0.0268689 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 37.3289 | + | 37.3289i | 0.229012 | + | 0.229012i | 0.812280 | − | 0.583268i | \(-0.198226\pi\) |
−0.583268 | + | 0.812280i | \(0.698226\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 71.6232 | 0.428882 | 0.214441 | − | 0.976737i | \(-0.431207\pi\) | ||||
0.214441 | + | 0.976737i | \(0.431207\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 342.723i | − | 2.02795i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −100.398 | + | 100.398i | −0.580334 | + | 0.580334i | −0.934995 | − | 0.354661i | \(-0.884596\pi\) |
0.354661 | + | 0.934995i | \(0.384596\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.87232i | 0.0164133i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −64.4199 | − | 64.4199i | −0.359888 | − | 0.359888i | 0.503884 | − | 0.863771i | \(-0.331904\pi\) |
−0.863771 | + | 0.503884i | \(0.831904\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 79.0033 | + | 79.0033i | 0.436482 | + | 0.436482i | 0.890826 | − | 0.454344i | \(-0.150126\pi\) |
−0.454344 | + | 0.890826i | \(0.650126\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 25.3812i | − | 0.137196i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30.2506 | − | 30.2506i | 0.161768 | − | 0.161768i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 304.422i | 1.59383i | 0.604089 | + | 0.796917i | \(0.293537\pi\) | ||||
−0.604089 | + | 0.796917i | \(0.706463\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 253.689 | 1.31445 | 0.657225 | − | 0.753695i | \(-0.271730\pi\) | ||||
0.657225 | + | 0.753695i | \(0.271730\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −89.4218 | − | 89.4218i | −0.453918 | − | 0.453918i | 0.442735 | − | 0.896653i | \(-0.354008\pi\) |
−0.896653 | + | 0.442735i | \(0.854008\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −117.278 | −0.589339 | −0.294670 | − | 0.955599i | \(-0.595210\pi\) | ||||
−0.294670 | + | 0.955599i | \(0.595210\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.80533 | + | 6.80533i | −0.0335238 | + | 0.0335238i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −92.8650 | + | 92.8650i | −0.453000 | + | 0.453000i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 185.128 | 0.885781 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −80.8941 | − | 80.8941i | −0.383384 | − | 0.383384i | 0.488936 | − | 0.872320i | \(-0.337385\pi\) |
−0.872320 | + | 0.488936i | \(0.837385\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −412.981 | −1.92084 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.1167i | 0.0558373i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 56.2303 | − | 56.2303i | 0.254436 | − | 0.254436i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 263.109i | − | 1.17986i | −0.807453 | − | 0.589931i | \(-0.799155\pi\) | ||
0.807453 | − | 0.589931i | \(-0.200845\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 112.085 | + | 112.085i | 0.493765 | + | 0.493765i | 0.909490 | − | 0.415725i | \(-0.136472\pi\) |
−0.415725 | + | 0.909490i | \(0.636472\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −100.869 | − | 100.869i | −0.440477 | − | 0.440477i | 0.451695 | − | 0.892172i | \(-0.350820\pi\) |
−0.892172 | + | 0.451695i | \(0.850820\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 325.669i | 1.39772i | 0.715259 | + | 0.698860i | \(0.246309\pi\) | ||||
−0.715259 | + | 0.698860i | \(0.753691\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −300.084 | + | 300.084i | −1.27695 | + | 1.27695i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.2269i | 0.105552i | 0.998606 | + | 0.0527760i | \(0.0168069\pi\) | ||||
−0.998606 | + | 0.0527760i | \(0.983193\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −305.987 | −1.26966 | −0.634828 | − | 0.772653i | \(-0.718929\pi\) | ||||
−0.634828 | + | 0.772653i | \(0.718929\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 207.464 | + | 207.464i | 0.846792 | + | 0.846792i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 344.119 | 1.39319 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −99.5293 | + | 99.5293i | −0.396531 | + | 0.396531i | −0.877008 | − | 0.480476i | \(-0.840464\pi\) |
0.480476 | + | 0.877008i | \(0.340464\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −141.960 | + | 141.960i | −0.561108 | + | 0.561108i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 265.635 | 1.03360 | 0.516799 | − | 0.856107i | \(-0.327124\pi\) | ||||
0.516799 | + | 0.856107i | \(0.327124\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.784876 | + | 0.784876i | 0.00303041 | + | 0.00303041i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 206.692 | 0.785901 | 0.392950 | − | 0.919560i | \(-0.371454\pi\) | ||||
0.392950 | + | 0.919560i | \(0.371454\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 447.898i | 1.69018i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.03470 | − | 8.03470i | 0.0298688 | − | 0.0298688i | −0.692015 | − | 0.721883i | \(-0.743277\pi\) |
0.721883 | + | 0.692015i | \(0.243277\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 216.666i | − | 0.799507i | −0.916623 | − | 0.399754i | \(-0.869096\pi\) | ||
0.916623 | − | 0.399754i | \(-0.130904\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 94.2595 | + | 94.2595i | 0.342762 | + | 0.342762i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −65.0909 | − | 65.0909i | −0.234985 | − | 0.234985i | 0.579785 | − | 0.814770i | \(-0.303137\pi\) |
−0.814770 | + | 0.579785i | \(0.803137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 403.952i | − | 1.43755i | −0.695242 | − | 0.718776i | \(-0.744703\pi\) | ||
0.695242 | − | 0.718776i | \(-0.255297\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 245.705 | − | 245.705i | 0.868214 | − | 0.868214i | −0.124061 | − | 0.992275i | \(-0.539592\pi\) |
0.992275 | + | 0.124061i | \(0.0395917\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 5.74342i | − | 0.0200119i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −276.642 | −0.957240 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 67.6849 | + | 67.6849i | 0.231007 | + | 0.231007i | 0.813113 | − | 0.582106i | \(-0.197771\pi\) |
−0.582106 | + | 0.813113i | \(0.697771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −523.821 | −1.77566 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −263.878 | + | 263.878i | −0.882534 | + | 0.882534i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.7708 | − | 12.7708i | 0.0424279 | − | 0.0424279i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −194.191 | −0.636692 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.98162 | − | 4.98162i | −0.0162268 | − | 0.0162268i | 0.698947 | − | 0.715174i | \(-0.253652\pi\) |
−0.715174 | + | 0.698947i | \(0.753652\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 380.390 | 1.22312 | 0.611560 | − | 0.791198i | \(-0.290542\pi\) | ||||
0.611560 | + | 0.791198i | \(0.290542\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 145.761i | − | 0.465691i | −0.972514 | − | 0.232845i | \(-0.925196\pi\) | ||
0.972514 | − | 0.232845i | \(-0.0748036\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 283.175 | − | 283.175i | 0.893295 | − | 0.893295i | −0.101537 | − | 0.994832i | \(-0.532376\pi\) |
0.994832 | + | 0.101537i | \(0.0323759\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 446.654i | 1.40017i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 37.8132 | + | 37.8132i | 0.117069 | + | 0.117069i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 175.211 | + | 175.211i | 0.539110 | + | 0.539110i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 18.5593i | − | 0.0564111i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 105.963 | − | 105.963i | 0.320131 | − | 0.320131i | −0.528687 | − | 0.848817i | \(-0.677315\pi\) |
0.848817 | + | 0.528687i | \(0.177315\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 466.338i | 1.39205i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 249.581 | 0.740595 | 0.370298 | − | 0.928913i | \(-0.379256\pi\) | ||||
0.370298 | + | 0.928913i | \(0.379256\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 397.627 | + | 397.627i | 1.16606 | + | 1.16606i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −25.6801 | −0.0748690 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −297.586 | + | 297.586i | −0.857597 | + | 0.857597i | −0.991054 | − | 0.133458i | \(-0.957392\pi\) |
0.133458 | + | 0.991054i | \(0.457392\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 288.797 | − | 288.797i | 0.827498 | − | 0.827498i | −0.159672 | − | 0.987170i | \(-0.551044\pi\) |
0.987170 | + | 0.159672i | \(0.0510436\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 255.362 | 0.723404 | 0.361702 | − | 0.932294i | \(-0.382196\pi\) | ||||
0.361702 | + | 0.932294i | \(0.382196\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −357.226 | − | 357.226i | −1.00627 | − | 1.00627i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −381.798 | −1.06350 | −0.531752 | − | 0.846900i | \(-0.678466\pi\) | ||||
−0.531752 | + | 0.846900i | \(0.678466\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 129.590i | − | 0.358975i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 330.857 | − | 330.857i | 0.906459 | − | 0.906459i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 18.6026i | − | 0.0506884i | −0.999679 | − | 0.0253442i | \(-0.991932\pi\) | ||
0.999679 | − | 0.0253442i | \(-0.00806817\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.8506 | − | 13.8506i | −0.0373330 | − | 0.0373330i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −150.079 | − | 150.079i | −0.402357 | − | 0.402357i | 0.476706 | − | 0.879063i | \(-0.341831\pi\) |
−0.879063 | + | 0.476706i | \(0.841831\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 830.245i | 2.20224i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 379.359 | − | 379.359i | 1.00095 | − | 1.00095i | 0.000948851 | − | 1.00000i | \(-0.499698\pi\) |
1.00000 | 0.000948851i | \(-0.000302029\pi\) | ||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 427.421i | 1.11598i | 0.829847 | + | 0.557991i | \(0.188428\pi\) | ||||
−0.829847 | + | 0.557991i | \(0.811572\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.1350 | −0.0497012 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 236.247 | + | 236.247i | 0.607318 | + | 0.607318i | 0.942244 | − | 0.334926i | \(-0.108711\pi\) |
−0.334926 | + | 0.942244i | \(0.608711\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −57.9920 | −0.148317 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −251.379 | + | 251.379i | −0.636402 | + | 0.636402i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 427.593 | − | 427.593i | 1.07706 | − | 1.07706i | 0.0802895 | − | 0.996772i | \(-0.474416\pi\) |
0.996772 | − | 0.0802895i | \(-0.0255845\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 638.396 | 1.59201 | 0.796005 | − | 0.605290i | \(-0.206943\pi\) | ||||
0.796005 | + | 0.605290i | \(0.206943\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 739.115 | + | 739.115i | 1.83403 | + | 1.83403i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 51.5137 | 0.126569 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 273.582i | 0.668905i | 0.942413 | + | 0.334453i | \(0.108551\pi\) | ||||
−0.942413 | + | 0.334453i | \(0.891449\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.1984 | − | 16.1984i | 0.0392212 | − | 0.0392212i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 946.865i | 2.28160i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 150.314 | + | 150.314i | 0.358745 | + | 0.358745i | 0.863350 | − | 0.504606i | \(-0.168362\pi\) |
−0.504606 | + | 0.863350i | \(0.668362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 220.826 | + | 220.826i | 0.524527 | + | 0.524527i | 0.918935 | − | 0.394408i | \(-0.129050\pi\) |
−0.394408 | + | 0.918935i | \(0.629050\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 38.5058i | 0.0906018i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00507 | − | 6.00507i | 0.0140634 | − | 0.0140634i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 463.722i | 1.07592i | 0.842970 | + | 0.537960i | \(0.180805\pi\) | ||||
−0.842970 | + | 0.537960i | \(0.819195\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −310.114 | −0.716199 | −0.358099 | − | 0.933683i | \(-0.616575\pi\) | ||||
−0.358099 | + | 0.933683i | \(0.616575\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −177.450 | − | 177.450i | −0.406064 | − | 0.406064i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −89.9103 | −0.204807 | −0.102404 | − | 0.994743i | \(-0.532653\pi\) | ||||
−0.102404 | + | 0.994743i | \(0.532653\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −78.9267 | + | 78.9267i | −0.178164 | + | 0.178164i | −0.790555 | − | 0.612391i | \(-0.790208\pi\) |
0.612391 | + | 0.790555i | \(0.290208\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 146.458 | − | 146.458i | 0.329118 | − | 0.329118i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 187.048 | 0.416587 | 0.208294 | − | 0.978066i | \(-0.433209\pi\) | ||||
0.208294 | + | 0.978066i | \(0.433209\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −188.479 | − | 188.479i | −0.417913 | − | 0.417913i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −35.5683 | −0.0781722 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 153.318i | 0.335489i | 0.985831 | + | 0.167744i | \(0.0536483\pi\) | ||||
−0.985831 | + | 0.167744i | \(0.946352\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −99.6025 | + | 99.6025i | −0.216057 | + | 0.216057i | −0.806835 | − | 0.590777i | \(-0.798821\pi\) |
0.590777 | + | 0.806835i | \(0.298821\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 255.682i | − | 0.552229i | −0.961125 | − | 0.276114i | \(-0.910953\pi\) | ||
0.961125 | − | 0.276114i | \(-0.0890469\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 285.533 | + | 285.533i | 0.611420 | + | 0.611420i | 0.943316 | − | 0.331896i | \(-0.107688\pi\) |
−0.331896 | + | 0.943316i | \(0.607688\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.4208 | − | 14.4208i | −0.0307480 | − | 0.0307480i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 838.185i | − | 1.77206i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −117.824 | + | 117.824i | −0.248051 | + | 0.248051i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 418.575i | − | 0.873852i | −0.899498 | − | 0.436926i | \(-0.856067\pi\) | ||
0.899498 | − | 0.436926i | \(-0.143933\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 95.7543 | 0.199073 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 280.175 | + | 280.175i | 0.577681 | + | 0.577681i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 162.560 | 0.333800 | 0.166900 | − | 0.985974i | \(-0.446624\pi\) | ||||
0.166900 | + | 0.985974i | \(0.446624\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 559.393 | − | 559.393i | 1.13929 | − | 1.13929i | 0.150715 | − | 0.988577i | \(-0.451842\pi\) |
0.988577 | − | 0.150715i | \(-0.0481577\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −91.2309 | + | 91.2309i | −0.185052 | + | 0.185052i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.0933 | 0.0444534 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 247.957 | + | 247.957i | 0.496908 | + | 0.496908i | 0.910474 | − | 0.413566i | \(-0.135717\pi\) |
−0.413566 | + | 0.910474i | \(0.635717\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −260.971 | −0.518829 | −0.259415 | − | 0.965766i | \(-0.583530\pi\) | ||||
−0.259415 | + | 0.965766i | \(0.583530\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 216.451i | 0.428616i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −149.941 | + | 149.941i | −0.294580 | + | 0.294580i | −0.838886 | − | 0.544306i | \(-0.816793\pi\) |
0.544306 | + | 0.838886i | \(0.316793\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.4625i | 0.0400441i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −60.2372 | − | 60.2372i | −0.116965 | − | 0.116965i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −609.049 | − | 609.049i | −1.17805 | − | 1.17805i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 391.686i | − | 0.751797i | −0.926661 | − | 0.375899i | \(-0.877334\pi\) | ||
0.926661 | − | 0.375899i | \(-0.122666\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −128.962 | + | 128.962i | −0.246582 | + | 0.246582i | −0.819566 | − | 0.572985i | \(-0.805786\pi\) |
0.572985 | + | 0.819566i | \(0.305786\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 162.434i | 0.308224i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −256.855 | −0.485548 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −350.347 | − | 350.347i | −0.657311 | − | 0.657311i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 185.274 | 0.346307 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −421.069 | + | 421.069i | −0.781204 | + | 0.781204i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −71.0166 | + | 71.0166i | −0.131269 | + | 0.131269i | −0.769689 | − | 0.638420i | \(-0.779589\pi\) |
0.638420 | + | 0.769689i | \(0.279589\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 151.771 | 0.278478 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −672.846 | − | 672.846i | −1.23007 | − | 1.23007i | −0.963938 | − | 0.266128i | \(-0.914255\pi\) |
−0.266128 | − | 0.963938i | \(-0.585745\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −558.316 | −1.01328 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 15.5470i | − | 0.0281140i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −294.546 | + | 294.546i | −0.528809 | + | 0.528809i | −0.920217 | − | 0.391408i | \(-0.871988\pi\) |
0.391408 | + | 0.920217i | \(0.371988\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1558.03i | − | 2.78717i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 613.943 | + | 613.943i | 1.09048 | + | 1.09048i | 0.995477 | + | 0.0950080i | \(0.0302877\pi\) |
0.0950080 | + | 0.995477i | \(0.469712\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 740.057 | + | 740.057i | 1.30984 | + | 1.30984i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1044.74i | 1.83610i | 0.396460 | + | 0.918052i | \(0.370239\pi\) | ||||
−0.396460 | + | 0.918052i | \(0.629761\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 131.781 | − | 131.781i | 0.230789 | − | 0.230789i | −0.582233 | − | 0.813022i | \(-0.697821\pi\) |
0.813022 | + | 0.582233i | \(0.197821\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 180.700i | − | 0.314261i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −114.453 | −0.198359 | −0.0991794 | − | 0.995070i | \(-0.531622\pi\) | ||||
−0.0991794 | + | 0.995070i | \(0.531622\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.2804 | − | 29.2804i | −0.0503965 | − | 0.0503965i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −909.053 | −1.55927 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 308.249 | − | 308.249i | 0.525125 | − | 0.525125i | −0.393990 | − | 0.919115i | \(-0.628905\pi\) |
0.919115 | + | 0.393990i | \(0.128905\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −497.034 | + | 497.034i | −0.843860 | + | 0.843860i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 646.173 | 1.08967 | 0.544834 | − | 0.838544i | \(-0.316593\pi\) | ||||
0.544834 | + | 0.838544i | \(0.316593\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.90840 | − | 3.90840i | −0.00656874 | − | 0.00656874i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 528.055 | 0.881561 | 0.440780 | − | 0.897615i | \(-0.354702\pi\) | ||||
0.440780 | + | 0.897615i | \(0.354702\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 280.764i | − | 0.467161i | −0.972338 | − | 0.233580i | \(-0.924956\pi\) | ||
0.972338 | − | 0.233580i | \(-0.0750442\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −114.914 | + | 114.914i | −0.189940 | + | 0.189940i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 662.871i | 1.09204i | 0.837771 | + | 0.546022i | \(0.183859\pi\) | ||||
−0.837771 | + | 0.546022i | \(0.816141\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1132.11 | − | 1132.11i | −1.85288 | − | 1.85288i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −128.389 | − | 128.389i | −0.209443 | − | 0.209443i | 0.594588 | − | 0.804031i | \(-0.297315\pi\) |
−0.804031 | + | 0.594588i | \(0.797315\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.8646i | 0.0338162i | 0.999857 | + | 0.0169081i | \(0.00538228\pi\) | ||||
−0.999857 | + | 0.0169081i | \(0.994618\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −472.367 | + | 472.367i | −0.763113 | + | 0.763113i | −0.976884 | − | 0.213771i | \(-0.931425\pi\) |
0.213771 | + | 0.976884i | \(0.431425\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.05795i | 0.0145393i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 778.859 | 1.24617 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.5219 | + | 10.5219i | 0.0167280 | + | 0.0167280i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 906.653 | 1.43685 | 0.718426 | − | 0.695604i | \(-0.244863\pi\) | ||||
0.718426 | + | 0.695604i | \(0.244863\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 192.253 | − | 192.253i | 0.302761 | − | 0.302761i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −782.688 | + | 782.688i | −1.22871 | + | 1.22871i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1125.11 | −1.75524 | −0.877622 | − | 0.479353i | \(-0.840871\pi\) | ||||
−0.877622 | + | 0.479353i | \(0.840871\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −607.794 | − | 607.794i | −0.945247 | − | 0.945247i | 0.0533302 | − | 0.998577i | \(-0.483016\pi\) |
−0.998577 | + | 0.0533302i | \(0.983016\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −383.377 | −0.592545 | −0.296273 | − | 0.955103i | \(-0.595744\pi\) | ||||
−0.296273 | + | 0.955103i | \(0.595744\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1063.15i | − | 1.63813i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 755.121 | − | 755.121i | 1.15639 | − | 1.15639i | 0.171141 | − | 0.985246i | \(-0.445254\pi\) |
0.985246 | − | 0.171141i | \(-0.0547455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 276.622i | − | 0.422324i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.8233 | − | 31.8233i | −0.0482902 | − | 0.0482902i | 0.682549 | − | 0.730840i | \(-0.260871\pi\) |
−0.730840 | + | 0.682549i | \(0.760871\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −579.890 | − | 579.890i | −0.877292 | − | 0.877292i | 0.115961 | − | 0.993254i | \(-0.463005\pi\) |
−0.993254 | + | 0.115961i | \(0.963005\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 23.9187i | − | 0.0359680i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 428.129 | − | 428.129i | 0.641872 | − | 0.641872i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 394.130i | − | 0.587377i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 262.375 | 0.389859 | 0.194930 | − | 0.980817i | \(-0.437552\pi\) | ||||
0.194930 | + | 0.980817i | \(0.437552\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −574.436 | − | 574.436i | −0.848502 | − | 0.848502i | 0.141444 | − | 0.989946i | \(-0.454825\pi\) |
−0.989946 | + | 0.141444i | \(0.954825\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.3280 | −0.0255199 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 253.790 | − | 253.790i | 0.371582 | − | 0.371582i | −0.496471 | − | 0.868053i | \(-0.665371\pi\) |
0.868053 | + | 0.496471i | \(0.165371\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −488.264 | + | 488.264i | −0.712794 | + | 0.712794i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1689.76 | −2.45248 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 734.512 | + | 734.512i | 1.06297 | + | 1.06297i | 0.997879 | + | 0.0650902i | \(0.0207335\pi\) |
0.0650902 | + | 0.997879i | \(0.479266\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1041.67 | 1.49880 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 76.9952i | − | 0.110467i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −745.410 | + | 745.410i | −1.06335 | + | 1.06335i | −0.0655005 | + | 0.997853i | \(0.520864\pi\) |
−0.997853 | + | 0.0655005i | \(0.979136\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 64.3920i | 0.0915961i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.69342 | − | 6.69342i | −0.00946735 | − | 0.00946735i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 809.881 | + | 809.881i | 1.14229 | + | 1.14229i | 0.988031 | + | 0.154255i | \(0.0492978\pi\) |
0.154255 | + | 0.988031i | \(0.450702\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 762.272i | − | 1.06910i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1167.23 | + | 1167.23i | −1.63249 | + | 1.63249i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 662.400i | − | 0.921280i | −0.887587 | − | 0.460640i | \(-0.847620\pi\) | ||
0.887587 | − | 0.460640i | \(-0.152380\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.72549 | 0.00516711 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −284.271 | − | 284.271i | −0.392098 | − | 0.392098i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1253.93 | 1.72481 | 0.862403 | − | 0.506222i | \(-0.168958\pi\) | ||||
0.862403 | + | 0.506222i | \(0.168958\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 171.203 | − | 171.203i | 0.234204 | − | 0.234204i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 509.300 | − | 509.300i | 0.694816 | − | 0.694816i | −0.268472 | − | 0.963288i | \(-0.586519\pi\) |
0.963288 | + | 0.268472i | \(0.0865186\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −946.479 | −1.28423 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 818.847 | + | 818.847i | 1.10805 | + | 1.10805i | 0.993407 | + | 0.114640i | \(0.0365716\pi\) |
0.114640 | + | 0.993407i | \(0.463428\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1110.03 | 1.49398 | 0.746991 | − | 0.664834i | \(-0.231498\pi\) | ||||
0.746991 | + | 0.664834i | \(0.231498\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 847.736i | 1.13790i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.72933 | + | 5.72933i | −0.00764931 | + | 0.00764931i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 34.0597i | − | 0.0453525i | −0.999743 | − | 0.0226762i | \(-0.992781\pi\) | ||
0.999743 | − | 0.0226762i | \(-0.00721869\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −944.491 | − | 944.491i | −1.25098 | − | 1.25098i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −398.543 | − | 398.543i | −0.526477 | − | 0.526477i | 0.393043 | − | 0.919520i | \(-0.371422\pi\) |
−0.919520 | + | 0.393043i | \(0.871422\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 903.338i | − | 1.18704i | −0.804819 | − | 0.593520i | \(-0.797738\pi\) | ||
0.804819 | − | 0.593520i | \(-0.202262\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.69328 | + | 4.69328i | −0.00615108 | + | 0.00615108i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1976.19i | − | 2.57652i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −98.9621 | −0.128689 | −0.0643447 | − | 0.997928i | \(-0.520496\pi\) | ||||
−0.0643447 | + | 0.997928i | \(0.520496\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 111.945 | + | 111.945i | 0.144818 | + | 0.144818i | 0.775799 | − | 0.630980i | \(-0.217347\pi\) |
−0.630980 | + | 0.775799i | \(0.717347\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −506.137 | −0.653080 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 235.598 | − | 235.598i | 0.302437 | − | 0.302437i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 725.025 | − | 725.025i | 0.928329 | − | 0.928329i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 389.291 | 0.495913 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −163.931 | − | 163.931i | −0.208299 | − | 0.208299i | 0.595245 | − | 0.803544i | \(-0.297055\pi\) |
−0.803544 | + | 0.595245i | \(0.797055\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −45.7703 | −0.0578638 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 732.614i | − | 0.923852i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 271.277 | − | 271.277i | 0.340373 | − | 0.340373i | −0.516135 | − | 0.856507i | \(-0.672630\pi\) |
0.856507 | + | 0.516135i | \(0.172630\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 248.802i | − | 0.311392i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 671.508 | + | 671.508i | 0.836249 | + | 0.836249i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.3414 | + | 18.3414i | 0.0227843 | + | 0.0227843i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1505.90i | 1.86144i | 0.365736 | + | 0.930718i | \(0.380817\pi\) | ||||
−0.365736 | + | 0.930718i | \(0.619183\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −492.677 | + | 492.677i | −0.607493 | + | 0.607493i | −0.942290 | − | 0.334797i | \(-0.891332\pi\) |
0.334797 | + | 0.942290i | \(0.391332\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 316.542i | − | 0.388396i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1047.73 | 1.28241 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −139.500 | − | 139.500i | −0.169914 | − | 0.169914i | 0.617027 | − | 0.786942i | \(-0.288337\pi\) |
−0.786942 | + | 0.617027i | \(0.788337\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1262.09 | 1.53353 | 0.766763 | − | 0.641931i | \(-0.221866\pi\) | ||||
0.766763 | + | 0.641931i | \(0.221866\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −179.936 | + | 179.936i | −0.217577 | + | 0.217577i | −0.807477 | − | 0.589900i | \(-0.799167\pi\) |
0.589900 | + | 0.807477i | \(0.299167\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 144.901 | − | 144.901i | 0.174790 | − | 0.174790i | −0.614290 | − | 0.789080i | \(-0.710557\pi\) |
0.789080 | + | 0.614290i | \(0.210557\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −172.010 | −0.206495 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −303.676 | − | 303.676i | −0.363684 | − | 0.363684i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1006.03 | −1.19908 | −0.599540 | − | 0.800345i | \(-0.704650\pi\) | ||||
−0.599540 | + | 0.800345i | \(0.704650\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 506.033i | − | 0.601703i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1453.11 | + | 1453.11i | −1.71966 | + | 1.71966i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.10706i | − | 0.00839087i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −49.3772 | − | 49.3772i | −0.0580225 | − | 0.0580225i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −77.4150 | − | 77.4150i | −0.0907561 | − | 0.0907561i | 0.660271 | − | 0.751027i | \(-0.270441\pi\) |
−0.751027 | + | 0.660271i | \(0.770441\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 175.567i | − | 0.204863i | −0.994740 | − | 0.102431i | \(-0.967338\pi\) | ||
0.994740 | − | 0.102431i | \(-0.0326622\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1058.18 | − | 1058.18i | 1.23188 | − | 1.23188i | 0.268634 | − | 0.963242i | \(-0.413428\pi\) |
0.963242 | − | 0.268634i | \(-0.0865722\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 569.219i | 0.659581i | 0.944054 | + | 0.329791i | \(0.106978\pi\) | ||||
−0.944054 | + | 0.329791i | \(0.893022\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 851.355 | 0.984225 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −510.198 | − | 510.198i | −0.587110 | − | 0.587110i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1759.33 | −2.01989 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.6169 | + | 15.6169i | −0.0178479 | + | 0.0178479i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 166.695 | − | 166.695i | 0.190074 | − | 0.190074i | −0.605654 | − | 0.795728i | \(-0.707088\pi\) |
0.795728 | + | 0.605654i | \(0.207088\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1495.53 | −1.69754 | −0.848771 | − | 0.528761i | \(-0.822657\pi\) | ||||
−0.848771 | + | 0.528761i | \(0.822657\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 134.367 | + | 134.367i | 0.152171 | + | 0.152171i | 0.779087 | − | 0.626916i | \(-0.215683\pi\) |
−0.626916 | + | 0.779087i | \(0.715683\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −414.255 | −0.467030 | −0.233515 | − | 0.972353i | \(-0.575023\pi\) | ||||
−0.233515 | + | 0.972353i | \(0.575023\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.8903i | 0.0133749i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 761.311 | − | 761.311i | 0.852531 | − | 0.852531i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 546.269i | 0.610356i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1199.18 | − | 1199.18i | −1.33390 | − | 1.33390i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −185.678 | − | 185.678i | −0.206080 | − | 0.206080i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 669.933i | − | 0.740258i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −312.683 | + | 312.683i | −0.344744 | + | 0.344744i | −0.858148 | − | 0.513403i | \(-0.828385\pi\) |
0.513403 | + | 0.858148i | \(0.328385\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 391.366i | 0.429601i | 0.976658 | + | 0.214800i | \(0.0689101\pi\) | ||||
−0.976658 | + | 0.214800i | \(0.931090\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1921.76 | −2.10488 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.55413 | + | 8.55413i | 0.00932838 | + | 0.00932838i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −294.161 | −0.320088 | −0.160044 | − | 0.987110i | \(-0.551164\pi\) | ||||
−0.160044 | + | 0.987110i | \(0.551164\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1347.69 | − | 1347.69i | 1.46011 | − | 1.46011i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.7857 | + | 32.7857i | −0.0354440 | + | 0.0354440i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1015.40 | 1.09300 | 0.546501 | − | 0.837458i | \(-0.315959\pi\) | ||||
0.546501 | + | 0.837458i | \(0.315959\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −526.335 | − | 526.335i | −0.565344 | − | 0.565344i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −256.520 | −0.274353 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1582.09i | 1.68846i | 0.535977 | + | 0.844232i | \(0.319943\pi\) | ||||
−0.535977 | + | 0.844232i | \(0.680057\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −113.842 | + | 113.842i | −0.120980 | + | 0.120980i | −0.765005 | − | 0.644025i | \(-0.777263\pi\) |
0.644025 | + | 0.765005i | \(0.277263\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 361.323i | 0.383163i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 388.664 | + | 388.664i | 0.410416 | + | 0.410416i | 0.881884 | − | 0.471467i | \(-0.156275\pi\) |
−0.471467 | + | 0.881884i | \(0.656275\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1248.21 | + | 1248.21i | 1.31529 | + | 1.31529i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 211.977i | 0.222431i | 0.993796 | + | 0.111215i | \(0.0354744\pi\) | ||||
−0.993796 | + | 0.111215i | \(0.964526\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1290.72 | − | 1290.72i | 1.35154 | − | 1.35154i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 30.1976i | − | 0.0314887i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1174.11 | −1.22175 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1075.62 | − | 1075.62i | −1.11463 | − | 1.11463i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −516.501 | −0.534127 | −0.267063 | − | 0.963679i | \(-0.586053\pi\) | ||||
−0.267063 | + | 0.963679i | \(0.586053\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 795.556 | − | 795.556i | 0.819316 | − | 0.819316i | −0.166693 | − | 0.986009i | \(-0.553309\pi\) |
0.986009 | + | 0.166693i | \(0.0533089\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.2120 | + | 32.2120i | −0.0331059 | + | 0.0331059i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 512.430 | 0.524493 | 0.262246 | − | 0.965001i | \(-0.415537\pi\) | ||||
0.262246 | + | 0.965001i | \(0.415537\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 297.250 | + | 297.250i | 0.303626 | + | 0.303626i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 722.200 | 0.734690 | 0.367345 | − | 0.930085i | \(-0.380267\pi\) | ||||
0.367345 | + | 0.930085i | \(0.380267\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 758.281i | 0.769828i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −803.421 | + | 803.421i | −0.812357 | + | 0.812357i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 794.715i | 0.801932i | 0.916093 | + | 0.400966i | \(0.131325\pi\) | ||||
−0.916093 | + | 0.400966i | \(0.868675\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 497.250 | + | 497.250i | 0.499749 | + | 0.499749i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1080.18 | − | 1080.18i | −1.08343 | − | 1.08343i | −0.996187 | − | 0.0872401i | \(-0.972195\pi\) |
−0.0872401 | − | 0.996187i | \(-0.527805\pi\) | |||||||
\(998\) | 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 | 1152.3.m.d.415.2 | 16 | ||
3.2 | odd | 2 | inner | 1152.3.m.d.415.7 | 16 | ||
4.3 | odd | 2 | 1152.3.m.e.415.2 | 16 | |||
8.3 | odd | 2 | 144.3.m.b.91.6 | yes | 16 | ||
8.5 | even | 2 | 576.3.m.b.271.7 | 16 | |||
12.11 | even | 2 | 1152.3.m.e.415.7 | 16 | |||
16.3 | odd | 4 | inner | 1152.3.m.d.991.2 | 16 | ||
16.5 | even | 4 | 144.3.m.b.19.6 | yes | 16 | ||
16.11 | odd | 4 | 576.3.m.b.559.7 | 16 | |||
16.13 | even | 4 | 1152.3.m.e.991.2 | 16 | |||
24.5 | odd | 2 | 576.3.m.b.271.2 | 16 | |||
24.11 | even | 2 | 144.3.m.b.91.3 | yes | 16 | ||
48.5 | odd | 4 | 144.3.m.b.19.3 | ✓ | 16 | ||
48.11 | even | 4 | 576.3.m.b.559.2 | 16 | |||
48.29 | odd | 4 | 1152.3.m.e.991.7 | 16 | |||
48.35 | even | 4 | inner | 1152.3.m.d.991.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.3.m.b.19.3 | ✓ | 16 | 48.5 | odd | 4 | ||
144.3.m.b.19.6 | yes | 16 | 16.5 | even | 4 | ||
144.3.m.b.91.3 | yes | 16 | 24.11 | even | 2 | ||
144.3.m.b.91.6 | yes | 16 | 8.3 | odd | 2 | ||
576.3.m.b.271.2 | 16 | 24.5 | odd | 2 | |||
576.3.m.b.271.7 | 16 | 8.5 | even | 2 | |||
576.3.m.b.559.2 | 16 | 48.11 | even | 4 | |||
576.3.m.b.559.7 | 16 | 16.11 | odd | 4 | |||
1152.3.m.d.415.2 | 16 | 1.1 | even | 1 | trivial | ||
1152.3.m.d.415.7 | 16 | 3.2 | odd | 2 | inner | ||
1152.3.m.d.991.2 | 16 | 16.3 | odd | 4 | inner | ||
1152.3.m.d.991.7 | 16 | 48.35 | even | 4 | inner | ||
1152.3.m.e.415.2 | 16 | 4.3 | odd | 2 | |||
1152.3.m.e.415.7 | 16 | 12.11 | even | 2 | |||
1152.3.m.e.991.2 | 16 | 16.13 | even | 4 | |||
1152.3.m.e.991.7 | 16 | 48.29 | odd | 4 |