Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(449,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.q (of order \(6\), 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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 449.1 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.449 |
Dual form | 1728.3.q.f.1601.1 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(5\) | −3.39898 | − | 1.96240i | −0.679796 | − | 0.392480i | 0.119982 | − | 0.992776i | \(-0.461716\pi\) |
−0.799778 | + | 0.600296i | \(0.795050\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.39898 | + | 11.0834i | 0.914140 | + | 1.58334i | 0.808156 | + | 0.588969i | \(0.200466\pi\) |
0.105984 | + | 0.994368i | \(0.466201\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.2980 | − | 8.25493i | 1.29981 | − | 0.750448i | 0.319443 | − | 0.947606i | \(-0.396504\pi\) |
0.980372 | + | 0.197157i | \(0.0631710\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.39898 | + | 2.42310i | −0.107614 | + | 0.186393i | −0.914803 | − | 0.403900i | \(-0.867654\pi\) |
0.807189 | + | 0.590293i | \(0.200988\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.54270i | 0.149570i | 0.997200 | + | 0.0747852i | \(0.0238271\pi\) | ||||
−0.997200 | + | 0.0747852i | \(0.976173\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 21.5959 | 1.13663 | 0.568314 | − | 0.822812i | \(-0.307596\pi\) | ||||
0.568314 | + | 0.822812i | \(0.307596\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.60102 | + | 1.50170i | 0.113088 | + | 0.0652913i | 0.555477 | − | 0.831532i | \(-0.312536\pi\) |
−0.442389 | + | 0.896823i | \(0.645869\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.79796 | − | 8.31031i | −0.191918 | − | 0.332412i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −13.1969 | + | 7.61926i | −0.455067 | + | 0.262733i | −0.709968 | − | 0.704234i | \(-0.751290\pi\) |
0.254901 | + | 0.966967i | \(0.417957\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −13.6010 | + | 23.5577i | −0.438743 | + | 0.759924i | −0.997593 | − | 0.0693442i | \(-0.977909\pi\) |
0.558850 | + | 0.829269i | \(0.311243\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 50.2295i | − | 1.43513i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.4041 | 0.281191 | 0.140596 | − | 0.990067i | \(-0.455098\pi\) | ||||
0.140596 | + | 0.990067i | \(0.455098\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 34.5000 | + | 19.9186i | 0.841463 | + | 0.485819i | 0.857761 | − | 0.514048i | \(-0.171855\pi\) |
−0.0162980 | + | 0.999867i | \(0.505188\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −17.0959 | − | 29.6110i | −0.397579 | − | 0.688628i | 0.595847 | − | 0.803098i | \(-0.296816\pi\) |
−0.993427 | + | 0.114470i | \(0.963483\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 58.1969 | − | 33.6000i | 1.23823 | − | 0.714894i | 0.269500 | − | 0.963000i | \(-0.413142\pi\) |
0.968733 | + | 0.248106i | \(0.0798083\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −57.3939 | + | 99.4091i | −1.17130 | + | 2.02876i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 100.680i | − | 1.89963i | −0.312810 | − | 0.949816i | \(-0.601270\pi\) | ||
0.312810 | − | 0.949816i | \(-0.398730\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −64.7980 | −1.17814 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.29796 | − | 3.05878i | −0.0897959 | − | 0.0518437i | 0.454430 | − | 0.890783i | \(-0.349843\pi\) |
−0.544226 | + | 0.838939i | \(0.683176\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 20.3990 | + | 35.3321i | 0.334409 | + | 0.579214i | 0.983371 | − | 0.181607i | \(-0.0581298\pi\) |
−0.648962 | + | 0.760821i | \(0.724796\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.51021 | − | 5.49072i | 0.146311 | − | 0.0844726i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −54.4898 | + | 94.3791i | −0.813281 | + | 1.40864i | 0.0972755 | + | 0.995257i | \(0.468987\pi\) |
−0.910556 | + | 0.413386i | \(0.864346\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 52.8829i | 0.744830i | 0.928066 | + | 0.372415i | \(0.121470\pi\) | ||||
−0.928066 | + | 0.372415i | \(0.878530\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 68.7878 | 0.942298 | 0.471149 | − | 0.882054i | \(-0.343839\pi\) | ||||
0.471149 | + | 0.882054i | \(0.343839\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 182.985 | + | 105.646i | 2.37642 | + | 1.37203i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.7929 | − | 22.1579i | −0.161935 | − | 0.280479i | 0.773628 | − | 0.633640i | \(-0.218440\pi\) |
−0.935563 | + | 0.353161i | \(0.885107\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −52.0857 | + | 30.0717i | −0.627539 | + | 0.362310i | −0.779798 | − | 0.626031i | \(-0.784678\pi\) |
0.152260 | + | 0.988341i | \(0.451345\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.98979 | − | 8.64258i | 0.0587035 | − | 0.101677i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.62809i | 0.0857089i | 0.999081 | + | 0.0428545i | \(0.0136452\pi\) | ||||
−0.999081 | + | 0.0428545i | \(0.986355\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −35.8082 | −0.393496 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −73.4041 | − | 42.3799i | −0.772675 | − | 0.446104i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 50.7020 | + | 87.8185i | 0.522701 | + | 0.905345i | 0.999651 | + | 0.0264148i | \(0.00840908\pi\) |
−0.476950 | + | 0.878931i | \(0.658258\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.19694 | + | 0.691053i | −0.0118509 | + | 0.00684211i | −0.505914 | − | 0.862584i | \(-0.668845\pi\) |
0.494063 | + | 0.869426i | \(0.335511\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.792856 | + | 1.37327i | −0.00769763 | + | 0.0133327i | −0.869849 | − | 0.493319i | \(-0.835784\pi\) |
0.862151 | + | 0.506652i | \(0.169117\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 103.223i | 0.964702i | 0.875978 | + | 0.482351i | \(0.160217\pi\) | ||||
−0.875978 | + | 0.482351i | \(0.839783\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.4041 | −0.132148 | −0.0660738 | − | 0.997815i | \(-0.521047\pi\) | ||||
−0.0660738 | + | 0.997815i | \(0.521047\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 92.0755 | + | 53.1598i | 0.814828 | + | 0.470441i | 0.848630 | − | 0.528988i | \(-0.177428\pi\) |
−0.0338020 | + | 0.999429i | \(0.510762\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.89388 | − | 10.2085i | −0.0512511 | − | 0.0887695i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −28.1816 | + | 16.2707i | −0.236820 | + | 0.136728i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 75.7878 | − | 131.268i | 0.626345 | − | 1.08486i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 135.782i | 1.08626i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 183.980 | 1.44866 | 0.724329 | − | 0.689454i | \(-0.242150\pi\) | ||||
0.724329 | + | 0.689454i | \(0.242150\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 91.6918 | + | 52.9383i | 0.699938 | + | 0.404109i | 0.807324 | − | 0.590108i | \(-0.200915\pi\) |
−0.107387 | + | 0.994217i | \(0.534248\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 138.192 | + | 239.355i | 1.03904 | + | 1.79966i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 165.288 | − | 95.4289i | 1.20648 | − | 0.696562i | 0.244491 | − | 0.969651i | \(-0.421379\pi\) |
0.961989 | + | 0.273090i | \(0.0880457\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 47.4898 | − | 82.2547i | 0.341653 | − | 0.591761i | −0.643087 | − | 0.765793i | \(-0.722347\pi\) |
0.984740 | + | 0.174033i | \(0.0556798\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 46.1939i | 0.323034i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 59.8082 | 0.412470 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 79.6112 | + | 45.9636i | 0.534304 | + | 0.308480i | 0.742767 | − | 0.669550i | \(-0.233513\pi\) |
−0.208464 | + | 0.978030i | \(0.566846\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.20714 | − | 14.2152i | −0.0543519 | − | 0.0941403i | 0.837569 | − | 0.546331i | \(-0.183976\pi\) |
−0.891921 | + | 0.452191i | \(0.850643\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 92.4592 | − | 53.3813i | 0.596511 | − | 0.344396i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −105.985 | + | 183.571i | −0.675062 | + | 1.16924i | 0.301389 | + | 0.953501i | \(0.402550\pi\) |
−0.976451 | + | 0.215740i | \(0.930784\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 38.4374i | 0.238742i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 172.788 | 1.06005 | 0.530024 | − | 0.847983i | \(-0.322183\pi\) | ||||
0.530024 | + | 0.847983i | \(0.322183\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −163.197 | − | 94.2218i | −0.977227 | − | 0.564202i | −0.0757953 | − | 0.997123i | \(-0.524150\pi\) |
−0.901432 | + | 0.432921i | \(0.857483\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 80.5857 | + | 139.579i | 0.476839 | + | 0.825909i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 52.1969 | − | 30.1359i | 0.301716 | − | 0.174196i | −0.341497 | − | 0.939883i | \(-0.610934\pi\) |
0.643214 | + | 0.765687i | \(0.277601\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 61.4041 | − | 106.355i | 0.350880 | − | 0.607743i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 72.7108i | − | 0.406205i | −0.979157 | − | 0.203103i | \(-0.934897\pi\) | ||
0.979157 | − | 0.203103i | \(-0.0651025\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 97.5959 | 0.539204 | 0.269602 | − | 0.962972i | \(-0.413108\pi\) | ||||
0.269602 | + | 0.962972i | \(0.413108\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −35.3633 | − | 20.4170i | −0.191153 | − | 0.110362i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.9898 | + | 36.3554i | 0.112245 | + | 0.194414i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 282.560 | − | 163.136i | 1.47937 | − | 0.854116i | 0.479645 | − | 0.877462i | \(-0.340765\pi\) |
0.999727 | + | 0.0233462i | \(0.00743200\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5102 | + | 18.2042i | −0.0544570 | + | 0.0943223i | −0.891969 | − | 0.452097i | \(-0.850676\pi\) |
0.837512 | + | 0.546419i | \(0.184009\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 32.5413i | 0.165184i | 0.996583 | + | 0.0825922i | \(0.0263199\pi\) | ||||
−0.996583 | + | 0.0825922i | \(0.973680\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 62.0000 | 0.311558 | 0.155779 | − | 0.987792i | \(-0.450211\pi\) | ||||
0.155779 | + | 0.987792i | \(0.450211\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −168.894 | − | 97.5109i | −0.831990 | − | 0.480349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −78.1765 | − | 135.406i | −0.381349 | − | 0.660516i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 308.778 | − | 178.273i | 1.47740 | − | 0.852980i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 84.2980 | − | 146.008i | 0.399516 | − | 0.691983i | −0.594150 | − | 0.804354i | \(-0.702511\pi\) |
0.993666 | + | 0.112372i | \(0.0358447\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 134.196i | 0.624169i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −348.131 | −1.60429 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.16122 | − | 3.55718i | −0.0278788 | − | 0.0160958i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −78.1867 | − | 135.423i | −0.350613 | − | 0.607280i | 0.635744 | − | 0.771900i | \(-0.280693\pi\) |
−0.986357 | + | 0.164620i | \(0.947360\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −86.6510 | + | 50.0280i | −0.381723 | + | 0.220388i | −0.678567 | − | 0.734538i | \(-0.737399\pi\) |
0.296845 | + | 0.954926i | \(0.404066\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −104.995 | + | 181.856i | −0.458493 | + | 0.794133i | −0.998882 | − | 0.0472824i | \(-0.984944\pi\) |
0.540389 | + | 0.841416i | \(0.318277\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 307.127i | 1.31814i | 0.752081 | + | 0.659070i | \(0.229050\pi\) | ||||
−0.752081 | + | 0.659070i | \(0.770950\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −263.747 | −1.12233 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −70.3888 | − | 40.6390i | −0.294514 | − | 0.170038i | 0.345462 | − | 0.938433i | \(-0.387722\pi\) |
−0.639976 | + | 0.768395i | \(0.721056\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 180.096 | + | 311.935i | 0.747286 | + | 1.29434i | 0.949119 | + | 0.314917i | \(0.101977\pi\) |
−0.201833 | + | 0.979420i | \(0.564690\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 390.161 | − | 225.260i | 1.59249 | − | 0.919427i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.2122 | + | 52.3291i | −0.122317 | + | 0.211859i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 400.179i | 1.59434i | 0.603755 | + | 0.797170i | \(0.293670\pi\) | ||||
−0.603755 | + | 0.797170i | \(0.706330\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 49.5857 | 0.195991 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −315.035 | − | 181.885i | −1.22582 | − | 0.707725i | −0.259664 | − | 0.965699i | \(-0.583612\pi\) |
−0.966152 | + | 0.257974i | \(0.916945\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 66.5755 | + | 115.312i | 0.257048 | + | 0.445221i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −326.570 | + | 188.546i | −1.24171 | + | 0.716903i | −0.969443 | − | 0.245318i | \(-0.921108\pi\) |
−0.272270 | + | 0.962221i | \(0.587774\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −197.576 | + | 342.211i | −0.745568 | + | 1.29136i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 170.849i | − | 0.635125i | −0.948237 | − | 0.317562i | \(-0.897136\pi\) | ||
0.948237 | − | 0.317562i | \(-0.102864\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 50.4041 | 0.185993 | 0.0929965 | − | 0.995666i | \(-0.470355\pi\) | ||||
0.0929965 | + | 0.995666i | \(0.470355\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −137.202 | − | 79.2136i | −0.498917 | − | 0.288050i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.8031 | + | 22.1756i | 0.0462204 | + | 0.0800561i | 0.888210 | − | 0.459438i | \(-0.151949\pi\) |
−0.841990 | + | 0.539494i | \(0.818616\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −290.267 | + | 167.586i | −1.03298 | + | 0.596391i | −0.917837 | − | 0.396958i | \(-0.870066\pi\) |
−0.115143 | + | 0.993349i | \(0.536733\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.48979 | − | 12.9727i | 0.0264657 | − | 0.0458399i | −0.852489 | − | 0.522745i | \(-0.824908\pi\) |
0.878955 | + | 0.476905i | \(0.158241\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 509.834i | 1.77643i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 282.535 | 0.977629 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −261.015 | − | 150.697i | −0.890837 | − | 0.514325i | −0.0166210 | − | 0.999862i | \(-0.505291\pi\) |
−0.874216 | + | 0.485537i | \(0.838624\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0051 | + | 20.7934i | 0.0406953 | + | 0.0704863i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.27755 | + | 4.20169i | −0.0243396 | + | 0.0140525i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 218.793 | − | 378.960i | 0.726887 | − | 1.25900i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 160.124i | − | 0.524997i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −44.7469 | −0.145755 | −0.0728777 | − | 0.997341i | \(-0.523218\pi\) | ||||
−0.0728777 | + | 0.997341i | \(0.523218\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 281.348 | + | 162.436i | 0.904656 | + | 0.522303i | 0.878708 | − | 0.477360i | \(-0.158406\pi\) |
0.0259480 | + | 0.999663i | \(0.491740\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −156.894 | − | 271.748i | −0.501258 | − | 0.868205i | −0.999999 | − | 0.00145368i | \(-0.999537\pi\) |
0.498741 | − | 0.866751i | \(-0.333796\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −47.9847 | + | 27.7040i | −0.151371 | + | 0.0873942i | −0.573773 | − | 0.819015i | \(-0.694521\pi\) |
0.422401 | + | 0.906409i | \(0.361187\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −125.793 | + | 217.880i | −0.394335 | + | 0.683008i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 54.9119i | 0.170006i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.8490 | 0.0826123 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 744.802 | + | 430.012i | 2.26384 | + | 1.30703i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.70204 | − | 13.3403i | −0.0232690 | − | 0.0403031i | 0.854156 | − | 0.520016i | \(-0.174074\pi\) |
−0.877425 | + | 0.479713i | \(0.840741\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 370.419 | − | 213.862i | 1.10573 | − | 0.638393i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −37.8837 | + | 65.6164i | −0.112414 | + | 0.194708i | −0.916743 | − | 0.399477i | \(-0.869192\pi\) |
0.804329 | + | 0.594184i | \(0.202525\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 449.102i | 1.31701i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −841.949 | −2.45466 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −578.651 | − | 334.084i | −1.66758 | − | 0.962779i | −0.968936 | − | 0.247312i | \(-0.920453\pi\) |
−0.698646 | − | 0.715467i | \(-0.746214\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −123.015 | − | 213.069i | −0.352479 | − | 0.610512i | 0.634204 | − | 0.773166i | \(-0.281328\pi\) |
−0.986683 | + | 0.162654i | \(0.947995\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −156.510 | + | 90.3612i | −0.443372 | + | 0.255981i | −0.705027 | − | 0.709181i | \(-0.749065\pi\) |
0.261655 | + | 0.965161i | \(0.415732\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 103.778 | − | 179.748i | 0.292331 | − | 0.506332i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 256.273i | − | 0.713852i | −0.934133 | − | 0.356926i | \(-0.883825\pi\) | ||
0.934133 | − | 0.356926i | \(-0.116175\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 105.384 | 0.291922 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −233.808 | − | 134.989i | −0.640570 | − | 0.369833i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 270.358 | + | 468.274i | 0.736671 | + | 1.27595i | 0.953986 | + | 0.299850i | \(0.0969366\pi\) |
−0.217316 | + | 0.976101i | \(0.569730\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1115.88 | − | 644.252i | 3.00776 | − | 1.73653i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −85.9847 | + | 148.930i | −0.230522 | + | 0.399276i | −0.957962 | − | 0.286896i | \(-0.907377\pi\) |
0.727440 | + | 0.686171i | \(0.240710\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 42.6367i | − | 0.113095i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −170.849 | −0.450789 | −0.225394 | − | 0.974268i | \(-0.572367\pi\) | ||||
−0.225394 | + | 0.974268i | \(0.572367\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −505.681 | − | 291.955i | −1.32031 | − | 0.762284i | −0.336536 | − | 0.941671i | \(-0.609255\pi\) |
−0.983779 | + | 0.179386i | \(0.942589\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −414.641 | − | 718.179i | −1.07699 | − | 1.86540i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −384.752 | + | 222.137i | −0.989080 | + | 0.571045i | −0.904999 | − | 0.425413i | \(-0.860129\pi\) |
−0.0840807 | + | 0.996459i | \(0.526795\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.81837 | + | 6.61361i | −0.00976565 | + | 0.0169146i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 100.419i | 0.254225i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 575.090 | 1.44859 | 0.724294 | − | 0.689491i | \(-0.242166\pi\) | ||||
0.724294 | + | 0.689491i | \(0.242166\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −141.318 | − | 81.5902i | −0.352415 | − | 0.203467i | 0.313333 | − | 0.949643i | \(-0.398554\pi\) |
−0.665748 | + | 0.746176i | \(0.731888\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −38.0551 | − | 65.9134i | −0.0944295 | − | 0.163557i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 148.757 | − | 85.8850i | 0.365497 | − | 0.211020i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 300.641 | − | 520.725i | 0.735063 | − | 1.27317i | −0.219633 | − | 0.975583i | \(-0.570486\pi\) |
0.954696 | − | 0.297584i | \(-0.0961808\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 78.2922i | − | 0.189570i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 236.051 | 0.568798 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 158.620 | + | 91.5795i | 0.378569 | + | 0.218567i | 0.677195 | − | 0.735803i | \(-0.263195\pi\) |
−0.298626 | + | 0.954370i | \(0.596528\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 83.7724 | + | 145.098i | 0.198984 | + | 0.344651i | 0.948199 | − | 0.317676i | \(-0.102902\pi\) |
−0.749215 | + | 0.662327i | \(0.769569\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.1306 | − | 12.1998i | 0.0497191 | − | 0.0287053i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −261.065 | + | 452.178i | −0.611394 | + | 1.05897i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 644.766i | − | 1.49598i | −0.663712 | − | 0.747988i | \(-0.731020\pi\) | ||
0.663712 | − | 0.747988i | \(-0.268980\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 133.514 | 0.308347 | 0.154174 | − | 0.988044i | \(-0.450729\pi\) | ||||
0.154174 | + | 0.988044i | \(0.450729\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 56.1714 | + | 32.4306i | 0.128539 | + | 0.0742119i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −46.2276 | − | 80.0685i | −0.105302 | − | 0.182388i | 0.808560 | − | 0.588414i | \(-0.200248\pi\) |
−0.913862 | + | 0.406026i | \(0.866914\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 150.157 | − | 86.6933i | 0.338955 | − | 0.195696i | −0.320855 | − | 0.947128i | \(-0.603970\pi\) |
0.659810 | + | 0.751433i | \(0.270637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.9694 | − | 25.9277i | 0.0336391 | − | 0.0582646i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 430.692i | − | 0.959224i | −0.877481 | − | 0.479612i | \(-0.840777\pi\) | ||
0.877481 | − | 0.479612i | \(-0.159223\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 657.706 | 1.45833 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 121.711 | + | 70.2700i | 0.267497 | + | 0.154440i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 262.843 | + | 455.257i | 0.575148 | + | 0.996186i | 0.996025 | + | 0.0890687i | \(0.0283891\pi\) |
−0.420877 | + | 0.907118i | \(0.638278\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.54999 | − | 0.894890i | 0.00336224 | − | 0.00194119i | −0.498318 | − | 0.866994i | \(-0.666049\pi\) |
0.501680 | + | 0.865053i | \(0.332715\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 263.166 | − | 455.817i | 0.568394 | − | 0.984487i | −0.428331 | − | 0.903622i | \(-0.640898\pi\) |
0.996725 | − | 0.0808651i | \(-0.0257683\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 409.322i | − | 0.876494i | −0.898855 | − | 0.438247i | \(-0.855600\pi\) | ||
0.898855 | − | 0.438247i | \(-0.144400\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1394.72 | −2.97381 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −488.873 | − | 282.251i | −1.03356 | − | 0.596726i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −103.616 | − | 179.469i | −0.218140 | − | 0.377829i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 525.207 | − | 303.228i | 1.09647 | − | 0.633045i | 0.161175 | − | 0.986926i | \(-0.448472\pi\) |
0.935290 | + | 0.353881i | \(0.115138\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.5551 | + | 25.2102i | −0.0302601 | + | 0.0524120i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 397.991i | − | 0.820600i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 275.131 | 0.564950 | 0.282475 | − | 0.959275i | \(-0.408845\pi\) | ||||
0.282475 | + | 0.959275i | \(0.408845\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 127.469 | + | 73.5945i | 0.259612 | + | 0.149887i | 0.624157 | − | 0.781299i | \(-0.285442\pi\) |
−0.364546 | + | 0.931186i | \(0.618776\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.3735 | − | 33.5558i | −0.0392971 | − | 0.0680646i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −586.120 | + | 338.397i | −1.17932 | + | 0.680879i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −226.308 | + | 391.977i | −0.453523 | + | 0.785526i | −0.998602 | − | 0.0528594i | \(-0.983166\pi\) |
0.545079 | + | 0.838385i | \(0.316500\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 571.541i | 1.13627i | 0.822937 | + | 0.568133i | \(0.192334\pi\) | ||||
−0.822937 | + | 0.568133i | \(0.807666\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.42449 | 0.0107416 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 394.136 | + | 227.554i | 0.774333 | + | 0.447062i | 0.834418 | − | 0.551132i | \(-0.185804\pi\) |
−0.0600849 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 440.171 | + | 762.399i | 0.861392 | + | 1.49198i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.38981 | − | 3.11181i | 0.0104656 | − | 0.00604234i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 554.732 | − | 960.823i | 1.07298 | − | 1.85846i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 846.127i | − | 1.62404i | −0.583627 | − | 0.812022i | \(-0.698367\pi\) | ||
0.583627 | − | 0.812022i | \(-0.301633\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −487.616 | −0.932345 | −0.466172 | − | 0.884694i | \(-0.654367\pi\) | ||||
−0.466172 | + | 0.884694i | \(0.654367\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −59.9000 | − | 34.5833i | −0.113662 | − | 0.0656229i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −259.990 | − | 450.316i | −0.491474 | − | 0.851258i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −96.5296 | + | 55.7314i | −0.181106 | + | 0.104562i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 202.565 | − | 350.853i | 0.378627 | − | 0.655801i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1895.13i | 3.51601i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −608.302 | −1.12440 | −0.562202 | − | 0.827000i | \(-0.690045\pi\) | ||||
−0.562202 | + | 0.827000i | \(0.690045\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 48.9592 | + | 28.2666i | 0.0898334 | + | 0.0518653i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 431.671 | + | 747.677i | 0.789162 | + | 1.36687i | 0.926481 | + | 0.376341i | \(0.122818\pi\) |
−0.137319 | + | 0.990527i | \(0.543849\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −285.000 | + | 164.545i | −0.517241 | + | 0.298629i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 163.722 | − | 283.576i | 0.296062 | − | 0.512795i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 331.526i | 0.595200i | 0.954691 | + | 0.297600i | \(0.0961861\pi\) | ||||
−0.954691 | + | 0.297600i | \(0.903814\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 95.6674 | 0.171140 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −514.024 | − | 296.772i | −0.913010 | − | 0.527126i | −0.0316114 | − | 0.999500i | \(-0.510064\pi\) |
−0.881398 | + | 0.472374i | \(0.843397\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −208.642 | − | 361.378i | −0.369278 | − | 0.639608i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −889.155 | + | 513.354i | −1.56266 | + | 0.902204i | −0.565676 | + | 0.824627i | \(0.691385\pi\) |
−0.996986 | + | 0.0775764i | \(0.975282\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −191.843 | + | 332.282i | −0.335977 | + | 0.581929i | −0.983672 | − | 0.179971i | \(-0.942400\pi\) |
0.647695 | + | 0.761900i | \(0.275733\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 28.8204i | − | 0.0501224i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −777.433 | −1.34737 | −0.673685 | − | 0.739019i | \(-0.735290\pi\) | ||||
−0.673685 | + | 0.739019i | \(0.735290\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −666.591 | − | 384.856i | −1.14732 | − | 0.662403i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −831.110 | − | 1439.53i | −1.42557 | − | 2.46917i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −581.520 | + | 335.741i | −0.990665 | + | 0.571961i | −0.905473 | − | 0.424404i | \(-0.860484\pi\) |
−0.0851921 | + | 0.996365i | \(0.527150\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −293.727 | + | 508.749i | −0.498687 | + | 0.863751i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 536.457i | 0.904650i | 0.891853 | + | 0.452325i | \(0.149405\pi\) | ||||
−0.891853 | + | 0.452325i | \(0.850595\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 127.718 | 0.214653 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −735.438 | − | 424.605i | −1.22778 | − | 0.708857i | −0.261212 | − | 0.965282i | \(-0.584122\pi\) |
−0.966564 | + | 0.256425i | \(0.917455\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −330.692 | − | 572.775i | −0.550236 | − | 0.953037i | −0.998257 | − | 0.0590138i | \(-0.981204\pi\) |
0.448021 | − | 0.894023i | \(-0.352129\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −515.202 | + | 297.452i | −0.851574 | + | 0.491656i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.9541 | + | 18.9730i | −0.0180463 | + | 0.0312570i | −0.874908 | − | 0.484290i | \(-0.839078\pi\) |
0.856861 | + | 0.515547i | \(0.172411\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 188.023i | 0.307730i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1164.75 | 1.90008 | 0.950038 | − | 0.312133i | \(-0.101044\pi\) | ||||
0.950038 | + | 0.312133i | \(0.101044\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −558.227 | − | 322.292i | −0.904743 | − | 0.522354i | −0.0260071 | − | 0.999662i | \(-0.508279\pi\) |
−0.878736 | + | 0.477308i | \(0.841613\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −564.469 | − | 977.690i | −0.911905 | − | 1.57947i | −0.811370 | − | 0.584533i | \(-0.801278\pi\) |
−0.100535 | − | 0.994933i | \(-0.532056\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −84.5449 | + | 48.8120i | −0.135706 | + | 0.0783499i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 146.510 | − | 253.763i | 0.234416 | − | 0.406021i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.4544i | 0.0420579i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −143.212 | −0.226961 | −0.113480 | − | 0.993540i | \(-0.536200\pi\) | ||||
−0.113480 | + | 0.993540i | \(0.536200\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −625.343 | − | 361.042i | −0.984792 | − | 0.568570i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −160.586 | − | 278.143i | −0.252097 | − | 0.436645i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 198.418 | − | 114.557i | 0.309545 | − | 0.178716i | −0.337178 | − | 0.941441i | \(-0.609472\pi\) |
0.646723 | + | 0.762725i | \(0.276139\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 554.682 | − | 960.737i | 0.862646 | − | 1.49415i | −0.00671893 | − | 0.999977i | \(-0.502139\pi\) |
0.869365 | − | 0.494170i | \(-0.164528\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1052.57i | 1.62685i | 0.581669 | + | 0.813426i | \(0.302400\pi\) | ||||
−0.581669 | + | 0.813426i | \(0.697600\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −101.000 | −0.155624 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −795.499 | − | 459.282i | −1.21822 | − | 0.703341i | −0.253685 | − | 0.967287i | \(-0.581643\pi\) |
−0.964537 | + | 0.263946i | \(0.914976\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −207.772 | − | 359.872i | −0.317210 | − | 0.549424i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 207.288 | − | 119.678i | 0.314549 | − | 0.181605i | −0.334411 | − | 0.942427i | \(-0.608537\pi\) |
0.648960 | + | 0.760822i | \(0.275204\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 177.793 | − | 307.946i | 0.268976 | − | 0.465879i | −0.699622 | − | 0.714513i | \(-0.746648\pi\) |
0.968598 | + | 0.248634i | \(0.0799816\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1084.75i | − | 1.63121i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −45.7673 | −0.0686167 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 583.328 | + | 336.784i | 0.869341 | + | 0.501914i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 291.429 | + | 504.769i | 0.433029 | + | 0.750028i | 0.997132 | − | 0.0756758i | \(-0.0241114\pi\) |
−0.564103 | + | 0.825704i | \(0.690778\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −154.450 | + | 89.1718i | −0.228139 | + | 0.131716i | −0.609713 | − | 0.792622i | \(-0.708715\pi\) |
0.381574 | + | 0.924338i | \(0.375382\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −648.883 | + | 1123.90i | −0.955645 | + | 1.65522i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 660.510i | − | 0.967072i | −0.875325 | − | 0.483536i | \(-0.839352\pi\) | ||
0.875325 | − | 0.483536i | \(-0.160648\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −749.080 | −1.09355 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 243.959 | + | 140.850i | 0.354077 | + | 0.204427i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.2571 | − | 74.9236i | −0.0626008 | − | 0.108428i | 0.833026 | − | 0.553233i | \(-0.186606\pi\) |
−0.895627 | + | 0.444805i | \(0.853273\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −322.834 | + | 186.388i | −0.464509 | + | 0.268184i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −50.6469 | + | 87.7231i | −0.0726642 | + | 0.125858i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1204.11i | − | 1.71770i | −0.512227 | − | 0.858850i | \(-0.671179\pi\) | ||
0.512227 | − | 0.858850i | \(-0.328821\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 224.686 | 0.319610 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.3184 | − | 8.84406i | −0.0216667 | − | 0.0125093i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −401.944 | − | 696.187i | −0.566917 | − | 0.981928i | −0.996869 | − | 0.0790766i | \(-0.974803\pi\) |
0.429952 | − | 0.902852i | \(-0.358530\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −70.7531 | + | 40.8493i | −0.0992329 | + | 0.0572921i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 90.6510 | − | 157.012i | 0.126785 | − | 0.219597i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 66.1101i | − | 0.0919474i | −0.998943 | − | 0.0459737i | \(-0.985361\pi\) | ||
0.998943 | − | 0.0459737i | \(-0.0146390\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.2939 | −0.0281469 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 126.637 | + | 73.1138i | 0.174671 | + | 0.100847i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 259.834 | + | 450.045i | 0.357405 | + | 0.619044i | 0.987527 | − | 0.157453i | \(-0.0503281\pi\) |
−0.630121 | + | 0.776497i | \(0.716995\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 75.2918 | − | 43.4698i | 0.102998 | − | 0.0594662i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −80.1459 | + | 138.817i | −0.109340 | + | 0.189382i | −0.915503 | − | 0.402311i | \(-0.868207\pi\) |
0.806163 | + | 0.591693i | \(0.201540\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1799.24i | 2.44130i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −122.849 | −0.166237 | −0.0831184 | − | 0.996540i | \(-0.526488\pi\) | ||||
−0.0831184 | + | 0.996540i | \(0.526488\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −585.944 | − | 338.295i | −0.788619 | − | 0.455309i | 0.0508572 | − | 0.998706i | \(-0.483805\pi\) |
−0.839476 | + | 0.543397i | \(0.817138\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −180.398 | − | 312.458i | −0.242145 | − | 0.419407i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1144.06 | + | 660.523i | −1.52745 | + | 0.881873i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 171.430 | − | 296.925i | 0.228268 | − | 0.395373i | −0.729027 | − | 0.684485i | \(-0.760027\pi\) |
0.957295 | + | 0.289113i | \(0.0933603\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 64.4229i | 0.0853283i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 452.220 | 0.597385 | 0.298692 | − | 0.954349i | \(-0.403450\pi\) | ||||
0.298692 | + | 0.954349i | \(0.403450\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −203.520 | − | 117.503i | −0.267438 | − | 0.154405i | 0.360285 | − | 0.932842i | \(-0.382680\pi\) |
−0.627723 | + | 0.778437i | \(0.716013\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −92.1714 | − | 159.646i | −0.120801 | − | 0.209234i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.8235 | − | 8.55834i | 0.0193266 | − | 0.0111582i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 318.439 | − | 551.552i | 0.414095 | − | 0.717233i | −0.581238 | − | 0.813733i | \(-0.697432\pi\) |
0.995333 | + | 0.0965005i | \(0.0307649\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 592.885i | 0.766992i | 0.923543 | + | 0.383496i | \(0.125280\pi\) | ||||
−0.923543 | + | 0.383496i | \(0.874720\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 261.029 | 0.336811 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 745.059 | + | 430.160i | 0.956430 | + | 0.552195i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 436.545 | + | 756.118i | 0.558956 | + | 0.968141i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 720.480 | − | 415.969i | 0.917808 | − | 0.529897i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 666.904 | − | 1155.11i | 0.847400 | − | 1.46774i | −0.0361199 | − | 0.999347i | \(-0.511500\pi\) |
0.883520 | − | 0.468393i | \(-0.155167\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1360.67i | 1.72020i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −114.151 | −0.143948 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 638.540 | + | 368.661i | 0.801179 | + | 0.462561i | 0.843883 | − | 0.536527i | \(-0.180264\pi\) |
−0.0427041 | + | 0.999088i | \(0.513597\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 85.4347 | + | 147.977i | 0.106927 | + | 0.185203i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 983.524 | − | 567.838i | 1.22481 | − | 0.707146i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 75.4296 | − | 130.648i | 0.0937014 | − | 0.162296i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 71.6833i | 0.0886073i | 0.999018 | + | 0.0443037i | \(0.0141069\pi\) | ||||
−0.999018 | + | 0.0443037i | \(0.985893\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1086.24 | 1.33938 | 0.669692 | − | 0.742639i | \(-0.266426\pi\) | ||||
0.669692 | + | 0.742639i | \(0.266426\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −587.302 | − | 339.079i | −0.720616 | − | 0.416048i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −369.202 | − | 639.477i | −0.451900 | − | 0.782713i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1232.92 | − | 711.829i | 1.50173 | − | 0.867026i | 0.501736 | − | 0.865021i | \(-0.332695\pi\) |
0.999998 | − | 0.00200552i | \(-0.000638377\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −217.379 | + | 376.511i | −0.264129 | + | 0.457486i | −0.967335 | − | 0.253501i | \(-0.918418\pi\) |
0.703206 | + | 0.710986i | \(0.251751\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 677.821i | − | 0.819614i | −0.912172 | − | 0.409807i | \(-0.865596\pi\) | ||
0.912172 | − | 0.409807i | \(-0.134404\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 995.775 | 1.20118 | 0.600588 | − | 0.799558i | \(-0.294933\pi\) | ||||
0.600588 | + | 0.799558i | \(0.294933\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −252.767 | − | 145.935i | −0.303442 | − | 0.175192i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 369.802 | + | 640.516i | 0.442877 | + | 0.767085i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1149.53 | − | 663.681i | 1.37012 | − | 0.791038i | 0.379176 | − | 0.925325i | \(-0.376207\pi\) |
0.990943 | + | 0.134286i | \(0.0428741\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −304.394 | + | 527.226i | −0.361943 | + | 0.626903i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 632.566i | − | 0.748599i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1939.86 | 2.29027 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.0612 | + | 15.6238i | 0.0317993 | + | 0.0183594i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −685.317 | − | 1187.00i | −0.803420 | − | 1.39156i | −0.917352 | − | 0.398076i | \(-0.869678\pi\) |
0.113932 | − | 0.993489i | \(-0.463655\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1038.74 | − | 599.717i | 1.21207 | − | 0.699787i | 0.248857 | − | 0.968540i | \(-0.419945\pi\) |
0.963209 | + | 0.268753i | \(0.0866117\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.1163 | + | 53.8951i | −0.0362239 | + | 0.0627416i | −0.883569 | − | 0.468301i | \(-0.844866\pi\) |
0.847345 | + | 0.531043i | \(0.178200\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 154.565i | − | 0.179102i | −0.995982 | − | 0.0895509i | \(-0.971457\pi\) | ||
0.995982 | − | 0.0895509i | \(-0.0285432\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −236.555 | −0.273474 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −365.823 | − | 211.208i | −0.420971 | − | 0.243048i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −152.460 | − | 264.069i | −0.175040 | − | 0.303179i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1504.92 | + | 868.867i | −1.71991 | + | 0.992991i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −548.187 | + | 949.487i | −0.625070 | + | 1.08265i | 0.363457 | + | 0.931611i | \(0.381596\pi\) |
−0.988527 | + | 0.151043i | \(0.951737\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1241.22i | 1.40888i | 0.709765 | + | 0.704438i | \(0.248801\pi\) | ||||
−0.709765 | + | 0.704438i | \(0.751199\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 553.555 | 0.626903 | 0.313451 | − | 0.949604i | \(-0.398515\pi\) | ||||
0.313451 | + | 0.949604i | \(0.398515\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −351.905 | − | 203.173i | −0.396736 | − | 0.229056i | 0.288338 | − | 0.957529i | \(-0.406897\pi\) |
−0.685075 | + | 0.728473i | \(0.740231\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1177.28 | + | 2039.11i | 1.32428 | + | 2.29371i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1256.82 | − | 725.623i | 1.40741 | − | 0.812568i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −142.688 | + | 247.142i | −0.159428 | + | 0.276137i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 414.519i | − | 0.461089i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 256.000 | 0.284129 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −331.727 | − | 191.522i | −0.366549 | − | 0.211627i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 231.712 | + | 401.337i | 0.255471 | + | 0.442489i | 0.965023 | − | 0.262164i | \(-0.0844361\pi\) |
−0.709552 | + | 0.704653i | \(0.751103\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 997.489 | − | 575.900i | 1.09494 | − | 0.632163i | 0.160051 | − | 0.987109i | \(-0.448834\pi\) |
0.934887 | + | 0.354946i | \(0.115501\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −496.480 | + | 859.928i | −0.543789 | + | 0.941871i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1355.00i | 1.47765i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −944.665 | −1.02793 | −0.513964 | − | 0.857812i | \(-0.671823\pi\) | ||||
−0.513964 | + | 0.857812i | \(0.671823\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −128.141 | − | 73.9821i | −0.138831 | − | 0.0801540i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −49.9184 | − | 86.4611i | −0.0539658 | − | 0.0934715i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 912.702 | − | 526.949i | 0.982456 | − | 0.567221i | 0.0794456 | − | 0.996839i | \(-0.474685\pi\) |
0.903011 | + | 0.429618i | \(0.141352\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1239.47 | + | 2146.83i | −1.33134 | + | 2.30594i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 164.762i | − | 0.176216i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 561.392 | 0.599137 | 0.299569 | − | 0.954075i | \(-0.403157\pi\) | ||||
0.299569 | + | 0.954075i | \(0.403157\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −98.4092 | − | 56.8166i | −0.104579 | − | 0.0603789i | 0.446798 | − | 0.894635i | \(-0.352564\pi\) |
−0.551377 | + | 0.834256i | \(0.685898\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 59.8235 | + | 103.617i | 0.0634395 | + | 0.109880i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −62.6510 | + | 36.1716i | −0.0661574 | + | 0.0381960i | −0.532714 | − | 0.846295i | \(-0.678828\pi\) |
0.466556 | + | 0.884491i | \(0.345494\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −96.2327 | + | 166.680i | −0.101404 | + | 0.175637i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 776.447i | 0.814739i | 0.913263 | + | 0.407370i | \(0.133554\pi\) | ||||
−0.913263 | + | 0.407370i | \(0.866446\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1280.56 | −1.34090 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2115.35 | + | 1221.30i | 2.20578 | + | 1.27351i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 110.524 | + | 191.434i | 0.115010 | + | 0.199203i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 71.4479 | − | 41.2505i | 0.0740393 | − | 0.0427466i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.3888 | − | 19.7259i | 0.0117774 | − | 0.0203991i | −0.860077 | − | 0.510165i | \(-0.829584\pi\) |
0.871854 | + | 0.489766i | \(0.162918\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1016.98i | − | 1.04735i | −0.851919 | − | 0.523674i | \(-0.824561\pi\) | ||
0.851919 | − | 0.523674i | \(-0.175439\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1215.54 | 1.24928 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −975.802 | − | 563.380i | −0.998774 | − | 0.576642i | −0.0908886 | − | 0.995861i | \(-0.528971\pi\) |
−0.907885 | + | 0.419219i | \(0.862304\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 62.9694 | + | 109.066i | 0.0643201 | + | 0.111406i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −280.105 | + | 161.719i | −0.284949 | + | 0.164516i | −0.635662 | − | 0.771968i | \(-0.719273\pi\) |
0.350713 | + | 0.936483i | \(0.385939\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 63.8592 | − | 110.607i | 0.0648317 | − | 0.112292i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 102.692i | − | 0.103834i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1961.47 | −1.97929 | −0.989644 | − | 0.143547i | \(-0.954149\pi\) | ||||
−0.989644 | + | 0.143547i | \(0.954149\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −210.737 | − | 121.669i | −0.211796 | − | 0.122280i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 559.954 | + | 969.869i | 0.561639 | + | 0.972787i | 0.997354 | + | 0.0727024i | \(0.0231623\pi\) |
−0.435715 | + | 0.900085i | \(0.643504\pi\) | |||||||
\(998\) | 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 | 1728.3.q.f.449.1 | 4 | ||
3.2 | odd | 2 | 576.3.q.c.257.2 | 4 | |||
4.3 | odd | 2 | 1728.3.q.e.449.1 | 4 | |||
8.3 | odd | 2 | 216.3.m.a.17.2 | 4 | |||
8.5 | even | 2 | 432.3.q.c.17.2 | 4 | |||
9.2 | odd | 6 | inner | 1728.3.q.f.1601.1 | 4 | ||
9.7 | even | 3 | 576.3.q.c.65.2 | 4 | |||
12.11 | even | 2 | 576.3.q.h.257.2 | 4 | |||
24.5 | odd | 2 | 144.3.q.d.113.1 | 4 | |||
24.11 | even | 2 | 72.3.m.a.41.1 | ✓ | 4 | ||
36.7 | odd | 6 | 576.3.q.h.65.2 | 4 | |||
36.11 | even | 6 | 1728.3.q.e.1601.1 | 4 | |||
72.5 | odd | 6 | 1296.3.e.c.161.3 | 4 | |||
72.11 | even | 6 | 216.3.m.a.89.2 | 4 | |||
72.13 | even | 6 | 1296.3.e.c.161.2 | 4 | |||
72.29 | odd | 6 | 432.3.q.c.305.2 | 4 | |||
72.43 | odd | 6 | 72.3.m.a.65.1 | yes | 4 | ||
72.59 | even | 6 | 648.3.e.b.161.3 | 4 | |||
72.61 | even | 6 | 144.3.q.d.65.1 | 4 | |||
72.67 | odd | 6 | 648.3.e.b.161.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.m.a.41.1 | ✓ | 4 | 24.11 | even | 2 | ||
72.3.m.a.65.1 | yes | 4 | 72.43 | odd | 6 | ||
144.3.q.d.65.1 | 4 | 72.61 | even | 6 | |||
144.3.q.d.113.1 | 4 | 24.5 | odd | 2 | |||
216.3.m.a.17.2 | 4 | 8.3 | odd | 2 | |||
216.3.m.a.89.2 | 4 | 72.11 | even | 6 | |||
432.3.q.c.17.2 | 4 | 8.5 | even | 2 | |||
432.3.q.c.305.2 | 4 | 72.29 | odd | 6 | |||
576.3.q.c.65.2 | 4 | 9.7 | even | 3 | |||
576.3.q.c.257.2 | 4 | 3.2 | odd | 2 | |||
576.3.q.h.65.2 | 4 | 36.7 | odd | 6 | |||
576.3.q.h.257.2 | 4 | 12.11 | even | 2 | |||
648.3.e.b.161.2 | 4 | 72.67 | odd | 6 | |||
648.3.e.b.161.3 | 4 | 72.59 | even | 6 | |||
1296.3.e.c.161.2 | 4 | 72.13 | even | 6 | |||
1296.3.e.c.161.3 | 4 | 72.5 | odd | 6 | |||
1728.3.q.e.449.1 | 4 | 4.3 | odd | 2 | |||
1728.3.q.e.1601.1 | 4 | 36.11 | even | 6 | |||
1728.3.q.f.449.1 | 4 | 1.1 | even | 1 | trivial | ||
1728.3.q.f.1601.1 | 4 | 9.2 | odd | 6 | inner |