Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(1,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.a (trivial) |
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: | yes |
Analytic conductor: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.41421 | 1.97410 | 0.987048 | − | 0.160424i | \(-0.0512862\pi\) | ||||
0.987048 | + | 0.160424i | \(0.0512862\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.41421 | 1.39590 | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.24264 | −1.17670 | −0.588348 | − | 0.808608i | \(-0.700222\pi\) | ||||
−0.588348 | + | 0.808608i | \(0.700222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.82843 | −0.685994 | −0.342997 | − | 0.939336i | \(-0.611442\pi\) | ||||
−0.342997 | + | 0.939336i | \(0.611442\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.82843 | 1.33713 | 0.668566 | − | 0.743652i | \(-0.266908\pi\) | ||||
0.668566 | + | 0.743652i | \(0.266908\pi\) | |||||||
\(20\) | 4.41421 | 0.987048 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −5.24264 | −1.09317 | −0.546583 | − | 0.837405i | \(-0.684072\pi\) | ||||
−0.546583 | + | 0.837405i | \(0.684072\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.4853 | 2.89706 | ||||||||
\(26\) | −4.24264 | −0.832050 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.242641 | 0.0450572 | 0.0225286 | − | 0.999746i | \(-0.492828\pi\) | ||||
0.0225286 | + | 0.999746i | \(0.492828\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.24264 | 1.30082 | 0.650408 | − | 0.759585i | \(-0.274598\pi\) | ||||
0.650408 | + | 0.759585i | \(0.274598\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.82843 | −0.485071 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.24264 | 0.861885 | 0.430942 | − | 0.902379i | \(-0.358181\pi\) | ||||
0.430942 | + | 0.902379i | \(0.358181\pi\) | |||||||
\(38\) | 5.82843 | 0.945496 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.41421 | 0.697948 | ||||||||
\(41\) | 6.17157 | 0.963838 | 0.481919 | − | 0.876216i | \(-0.339940\pi\) | ||||
0.481919 | + | 0.876216i | \(0.339940\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.48528 | −0.988996 | −0.494498 | − | 0.869179i | \(-0.664648\pi\) | ||||
−0.494498 | + | 0.869179i | \(0.664648\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.24264 | −0.772985 | ||||||||
\(47\) | 11.6569 | 1.70033 | 0.850163 | − | 0.526519i | \(-0.176503\pi\) | ||||
0.850163 | + | 0.526519i | \(0.176503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 14.4853 | 2.04853 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.24264 | −0.588348 | ||||||||
\(53\) | −8.00000 | −1.09888 | −0.549442 | − | 0.835532i | \(-0.685160\pi\) | ||||
−0.549442 | + | 0.835532i | \(0.685160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.41421 | 0.595212 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.242641 | 0.0318603 | ||||||||
\(59\) | 11.6569 | 1.51759 | 0.758797 | − | 0.651328i | \(-0.225788\pi\) | ||||
0.758797 | + | 0.651328i | \(0.225788\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.8284 | −1.89859 | −0.949293 | − | 0.314393i | \(-0.898199\pi\) | ||||
−0.949293 | + | 0.314393i | \(0.898199\pi\) | |||||||
\(62\) | 7.24264 | 0.919816 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −18.7279 | −2.32291 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.75736 | −0.214696 | −0.107348 | − | 0.994222i | \(-0.534236\pi\) | ||||
−0.107348 | + | 0.994222i | \(0.534236\pi\) | |||||||
\(68\) | −2.82843 | −0.342997 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.24264 | 0.147474 | 0.0737372 | − | 0.997278i | \(-0.476507\pi\) | ||||
0.0737372 | + | 0.997278i | \(0.476507\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.17157 | 0.371205 | 0.185602 | − | 0.982625i | \(-0.440576\pi\) | ||||
0.185602 | + | 0.982625i | \(0.440576\pi\) | |||||||
\(74\) | 5.24264 | 0.609445 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.82843 | 0.668566 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.48528 | −0.729651 | −0.364826 | − | 0.931076i | \(-0.618871\pi\) | ||||
−0.364826 | + | 0.931076i | \(0.618871\pi\) | |||||||
\(80\) | 4.41421 | 0.493524 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.17157 | 0.681536 | ||||||||
\(83\) | −3.89949 | −0.428025 | −0.214013 | − | 0.976831i | \(-0.568653\pi\) | ||||
−0.214013 | + | 0.976831i | \(0.568653\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.4853 | −1.35422 | ||||||||
\(86\) | −6.48528 | −0.699326 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 3.34315 | 0.354373 | 0.177186 | − | 0.984177i | \(-0.443300\pi\) | ||||
0.177186 | + | 0.984177i | \(0.443300\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.24264 | −0.546583 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.6569 | 1.20231 | ||||||||
\(95\) | 25.7279 | 2.63963 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.3137 | 1.14873 | 0.574367 | − | 0.818598i | \(-0.305248\pi\) | ||||
0.574367 | + | 0.818598i | \(0.305248\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 14.4853 | 1.44853 | ||||||||
\(101\) | −14.4853 | −1.44134 | −0.720670 | − | 0.693279i | \(-0.756166\pi\) | ||||
−0.720670 | + | 0.693279i | \(0.756166\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0711 | −0.992332 | −0.496166 | − | 0.868228i | \(-0.665259\pi\) | ||||
−0.496166 | + | 0.868228i | \(0.665259\pi\) | |||||||
\(104\) | −4.24264 | −0.416025 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.00000 | −0.777029 | ||||||||
\(107\) | −14.9706 | −1.44726 | −0.723629 | − | 0.690189i | \(-0.757528\pi\) | ||||
−0.723629 | + | 0.690189i | \(0.757528\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.2426 | −1.45998 | −0.729990 | − | 0.683458i | \(-0.760475\pi\) | ||||
−0.729990 | + | 0.683458i | \(0.760475\pi\) | |||||||
\(110\) | 4.41421 | 0.420879 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.24264 | −0.399114 | −0.199557 | − | 0.979886i | \(-0.563950\pi\) | ||||
−0.199557 | + | 0.979886i | \(0.563950\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23.1421 | −2.15802 | ||||||||
\(116\) | 0.242641 | 0.0225286 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.6569 | 1.07310 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | −14.8284 | −1.34250 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.24264 | 0.650408 | ||||||||
\(125\) | 41.8701 | 3.74497 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.2426 | −1.08636 | −0.543179 | − | 0.839617i | \(-0.682780\pi\) | ||||
−0.543179 | + | 0.839617i | \(0.682780\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −18.7279 | −1.64255 | ||||||||
\(131\) | 14.4853 | 1.26558 | 0.632792 | − | 0.774321i | \(-0.281909\pi\) | ||||
0.632792 | + | 0.774321i | \(0.281909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.75736 | −0.151813 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.82843 | −0.242536 | ||||||||
\(137\) | −1.75736 | −0.150141 | −0.0750707 | − | 0.997178i | \(-0.523918\pi\) | ||||
−0.0750707 | + | 0.997178i | \(0.523918\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.82843 | 0.748817 | 0.374409 | − | 0.927264i | \(-0.377846\pi\) | ||||
0.374409 | + | 0.927264i | \(0.377846\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.24264 | 0.104280 | ||||||||
\(143\) | −4.24264 | −0.354787 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.07107 | 0.0889473 | ||||||||
\(146\) | 3.17157 | 0.262481 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.24264 | 0.430942 | ||||||||
\(149\) | 5.75736 | 0.471661 | 0.235831 | − | 0.971794i | \(-0.424219\pi\) | ||||
0.235831 | + | 0.971794i | \(0.424219\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.7279 | 1.19854 | 0.599271 | − | 0.800546i | \(-0.295457\pi\) | ||||
0.599271 | + | 0.800546i | \(0.295457\pi\) | |||||||
\(152\) | 5.82843 | 0.472748 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 31.9706 | 2.56794 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.92893 | −0.393372 | −0.196686 | − | 0.980467i | \(-0.563018\pi\) | ||||
−0.196686 | + | 0.980467i | \(0.563018\pi\) | |||||||
\(158\) | −6.48528 | −0.515941 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.41421 | 0.348974 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.7279 | −1.15358 | −0.576790 | − | 0.816893i | \(-0.695695\pi\) | ||||
−0.576790 | + | 0.816893i | \(0.695695\pi\) | |||||||
\(164\) | 6.17157 | 0.481919 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.89949 | −0.302660 | ||||||||
\(167\) | −12.3848 | −0.958363 | −0.479181 | − | 0.877716i | \(-0.659066\pi\) | ||||
−0.479181 | + | 0.877716i | \(0.659066\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | −12.4853 | −0.957577 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.48528 | −0.494498 | ||||||||
\(173\) | −13.2426 | −1.00682 | −0.503410 | − | 0.864048i | \(-0.667921\pi\) | ||||
−0.503410 | + | 0.864048i | \(0.667921\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.34315 | 0.250579 | ||||||||
\(179\) | 10.9706 | 0.819978 | 0.409989 | − | 0.912090i | \(-0.365532\pi\) | ||||
0.409989 | + | 0.912090i | \(0.365532\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.2426 | −0.761329 | −0.380665 | − | 0.924713i | \(-0.624305\pi\) | ||||
−0.380665 | + | 0.924713i | \(0.624305\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.24264 | −0.386493 | ||||||||
\(185\) | 23.1421 | 1.70144 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.82843 | −0.206835 | ||||||||
\(188\) | 11.6569 | 0.850163 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 25.7279 | 1.86650 | ||||||||
\(191\) | 0.757359 | 0.0548006 | 0.0274003 | − | 0.999625i | \(-0.491277\pi\) | ||||
0.0274003 | + | 0.999625i | \(0.491277\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.48528 | 0.322858 | 0.161429 | − | 0.986884i | \(-0.448390\pi\) | ||||
0.161429 | + | 0.986884i | \(0.448390\pi\) | |||||||
\(194\) | 11.3137 | 0.812277 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.72792 | 0.194356 | 0.0971782 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971782 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.75736 | −0.337240 | −0.168620 | − | 0.985681i | \(-0.553931\pi\) | ||||
−0.168620 | + | 0.985681i | \(0.553931\pi\) | |||||||
\(200\) | 14.4853 | 1.02426 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.4853 | −1.01918 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 27.2426 | 1.90271 | ||||||||
\(206\) | −10.0711 | −0.701685 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.24264 | −0.294174 | ||||||||
\(209\) | 5.82843 | 0.403161 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.7279 | 0.876226 | 0.438113 | − | 0.898920i | \(-0.355647\pi\) | ||||
0.438113 | + | 0.898920i | \(0.355647\pi\) | |||||||
\(212\) | −8.00000 | −0.549442 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.9706 | −1.02337 | ||||||||
\(215\) | −28.6274 | −1.95237 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −15.2426 | −1.03236 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.41421 | 0.297606 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.24264 | −0.485003 | −0.242502 | − | 0.970151i | \(-0.577968\pi\) | ||||
−0.242502 | + | 0.970151i | \(0.577968\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.24264 | −0.282216 | ||||||||
\(227\) | 12.7279 | 0.844782 | 0.422391 | − | 0.906414i | \(-0.361191\pi\) | ||||
0.422391 | + | 0.906414i | \(0.361191\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.0000 | −0.792982 | −0.396491 | − | 0.918039i | \(-0.629772\pi\) | ||||
−0.396491 | + | 0.918039i | \(0.629772\pi\) | |||||||
\(230\) | −23.1421 | −1.52595 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.242641 | 0.0159301 | ||||||||
\(233\) | −16.2426 | −1.06409 | −0.532045 | − | 0.846716i | \(-0.678576\pi\) | ||||
−0.532045 | + | 0.846716i | \(0.678576\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 51.4558 | 3.35661 | ||||||||
\(236\) | 11.6569 | 0.758797 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.0000 | 1.16432 | 0.582162 | − | 0.813073i | \(-0.302207\pi\) | ||||
0.582162 | + | 0.813073i | \(0.302207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.48528 | 0.160091 | 0.0800455 | − | 0.996791i | \(-0.474493\pi\) | ||||
0.0800455 | + | 0.996791i | \(0.474493\pi\) | |||||||
\(242\) | −10.0000 | −0.642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.8284 | −0.949293 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.7279 | −1.57340 | ||||||||
\(248\) | 7.24264 | 0.459908 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 41.8701 | 2.64809 | ||||||||
\(251\) | 11.3137 | 0.714115 | 0.357057 | − | 0.934082i | \(-0.383780\pi\) | ||||
0.357057 | + | 0.934082i | \(0.383780\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.24264 | −0.329602 | ||||||||
\(254\) | −12.2426 | −0.768172 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.4853 | −0.716432 | −0.358216 | − | 0.933639i | \(-0.616615\pi\) | ||||
−0.358216 | + | 0.933639i | \(0.616615\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −18.7279 | −1.16146 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.4853 | 0.894904 | ||||||||
\(263\) | −3.72792 | −0.229874 | −0.114937 | − | 0.993373i | \(-0.536667\pi\) | ||||
−0.114937 | + | 0.993373i | \(0.536667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −35.3137 | −2.16930 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.75736 | −0.107348 | ||||||||
\(269\) | −15.3848 | −0.938026 | −0.469013 | − | 0.883191i | \(-0.655390\pi\) | ||||
−0.469013 | + | 0.883191i | \(0.655390\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.68629 | −0.406163 | −0.203082 | − | 0.979162i | \(-0.565096\pi\) | ||||
−0.203082 | + | 0.979162i | \(0.565096\pi\) | |||||||
\(272\) | −2.82843 | −0.171499 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.75736 | −0.106166 | ||||||||
\(275\) | 14.4853 | 0.873495 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.2132 | −0.853989 | −0.426994 | − | 0.904254i | \(-0.640428\pi\) | ||||
−0.426994 | + | 0.904254i | \(0.640428\pi\) | |||||||
\(278\) | 8.82843 | 0.529494 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.4853 | −0.625499 | −0.312750 | − | 0.949836i | \(-0.601250\pi\) | ||||
−0.312750 | + | 0.949836i | \(0.601250\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.14214 | 0.484000 | 0.242000 | − | 0.970276i | \(-0.422197\pi\) | ||||
0.242000 | + | 0.970276i | \(0.422197\pi\) | |||||||
\(284\) | 1.24264 | 0.0737372 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.24264 | −0.250873 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | 1.07107 | 0.0628953 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.17157 | 0.185602 | ||||||||
\(293\) | 0.343146 | 0.0200468 | 0.0100234 | − | 0.999950i | \(-0.496809\pi\) | ||||
0.0100234 | + | 0.999950i | \(0.496809\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 51.4558 | 2.99588 | ||||||||
\(296\) | 5.24264 | 0.304722 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.75736 | 0.333515 | ||||||||
\(299\) | 22.2426 | 1.28633 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 14.7279 | 0.847497 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.82843 | 0.334283 | ||||||||
\(305\) | −65.4558 | −3.74799 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.7990 | −1.30121 | −0.650604 | − | 0.759418i | \(-0.725484\pi\) | ||||
−0.650604 | + | 0.759418i | \(0.725484\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 31.9706 | 1.81581 | ||||||||
\(311\) | 15.5563 | 0.882120 | 0.441060 | − | 0.897478i | \(-0.354603\pi\) | ||||
0.441060 | + | 0.897478i | \(0.354603\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.75736 | 0.0993318 | 0.0496659 | − | 0.998766i | \(-0.484184\pi\) | ||||
0.0496659 | + | 0.998766i | \(0.484184\pi\) | |||||||
\(314\) | −4.92893 | −0.278156 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.48528 | −0.364826 | ||||||||
\(317\) | 10.0000 | 0.561656 | 0.280828 | − | 0.959758i | \(-0.409391\pi\) | ||||
0.280828 | + | 0.959758i | \(0.409391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.242641 | 0.0135853 | ||||||||
\(320\) | 4.41421 | 0.246762 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.4853 | −0.917266 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −61.4558 | −3.40896 | ||||||||
\(326\) | −14.7279 | −0.815704 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.17157 | 0.340768 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.51472 | 0.413046 | 0.206523 | − | 0.978442i | \(-0.433785\pi\) | ||||
0.206523 | + | 0.978442i | \(0.433785\pi\) | |||||||
\(332\) | −3.89949 | −0.214013 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.3848 | −0.677665 | ||||||||
\(335\) | −7.75736 | −0.423830 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.48528 | −0.189855 | −0.0949277 | − | 0.995484i | \(-0.530262\pi\) | ||||
−0.0949277 | + | 0.995484i | \(0.530262\pi\) | |||||||
\(338\) | 5.00000 | 0.271964 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.4853 | −0.677109 | ||||||||
\(341\) | 7.24264 | 0.392211 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.48528 | −0.349663 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.2426 | −0.711929 | ||||||||
\(347\) | 18.5147 | 0.993922 | 0.496961 | − | 0.867773i | \(-0.334449\pi\) | ||||
0.496961 | + | 0.867773i | \(0.334449\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.7574 | −0.736415 | −0.368207 | − | 0.929744i | \(-0.620028\pi\) | ||||
−0.368207 | + | 0.929744i | \(0.620028\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 2.65685 | 0.141410 | 0.0707050 | − | 0.997497i | \(-0.477475\pi\) | ||||
0.0707050 | + | 0.997497i | \(0.477475\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.48528 | 0.291129 | ||||||||
\(356\) | 3.34315 | 0.177186 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.9706 | 0.579812 | ||||||||
\(359\) | 17.4558 | 0.921284 | 0.460642 | − | 0.887586i | \(-0.347619\pi\) | ||||
0.460642 | + | 0.887586i | \(0.347619\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.9706 | 0.787924 | ||||||||
\(362\) | −10.2426 | −0.538341 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0000 | 0.732793 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.8995 | 1.61294 | 0.806470 | − | 0.591275i | \(-0.201375\pi\) | ||||
0.806470 | + | 0.591275i | \(0.201375\pi\) | |||||||
\(368\) | −5.24264 | −0.273292 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 23.1421 | 1.20310 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.2426 | −0.789234 | −0.394617 | − | 0.918846i | \(-0.629123\pi\) | ||||
−0.394617 | + | 0.918846i | \(0.629123\pi\) | |||||||
\(374\) | −2.82843 | −0.146254 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.6569 | 0.601156 | ||||||||
\(377\) | −1.02944 | −0.0530187 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.97056 | 0.152588 | 0.0762938 | − | 0.997085i | \(-0.475691\pi\) | ||||
0.0762938 | + | 0.997085i | \(0.475691\pi\) | |||||||
\(380\) | 25.7279 | 1.31981 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.757359 | 0.0387499 | ||||||||
\(383\) | 18.0416 | 0.921884 | 0.460942 | − | 0.887430i | \(-0.347512\pi\) | ||||
0.460942 | + | 0.887430i | \(0.347512\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.48528 | 0.228295 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.3137 | 0.574367 | ||||||||
\(389\) | 36.9706 | 1.87448 | 0.937241 | − | 0.348682i | \(-0.113371\pi\) | ||||
0.937241 | + | 0.348682i | \(0.113371\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.8284 | 0.749906 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.72792 | 0.137431 | ||||||||
\(395\) | −28.6274 | −1.44040 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.4142 | −0.974371 | −0.487186 | − | 0.873298i | \(-0.661977\pi\) | ||||
−0.487186 | + | 0.873298i | \(0.661977\pi\) | |||||||
\(398\) | −4.75736 | −0.238465 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.4853 | 0.724264 | ||||||||
\(401\) | −1.75736 | −0.0877583 | −0.0438792 | − | 0.999037i | \(-0.513972\pi\) | ||||
−0.0438792 | + | 0.999037i | \(0.513972\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −30.7279 | −1.53067 | ||||||||
\(404\) | −14.4853 | −0.720670 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.24264 | 0.259868 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.00000 | 0.296681 | 0.148340 | − | 0.988936i | \(-0.452607\pi\) | ||||
0.148340 | + | 0.988936i | \(0.452607\pi\) | |||||||
\(410\) | 27.2426 | 1.34542 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.0711 | −0.496166 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.2132 | −0.844963 | ||||||||
\(416\) | −4.24264 | −0.208013 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.82843 | 0.285078 | ||||||||
\(419\) | −36.0416 | −1.76075 | −0.880374 | − | 0.474279i | \(-0.842709\pi\) | ||||
−0.880374 | + | 0.474279i | \(0.842709\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.2132 | −1.18008 | −0.590040 | − | 0.807374i | \(-0.700888\pi\) | ||||
−0.590040 | + | 0.807374i | \(0.700888\pi\) | |||||||
\(422\) | 12.7279 | 0.619586 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.00000 | −0.388514 | ||||||||
\(425\) | −40.9706 | −1.98736 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −14.9706 | −0.723629 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −28.6274 | −1.38054 | ||||||||
\(431\) | −10.7574 | −0.518164 | −0.259082 | − | 0.965855i | \(-0.583420\pi\) | ||||
−0.259082 | + | 0.965855i | \(0.583420\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.27208 | −0.253360 | −0.126680 | − | 0.991944i | \(-0.540432\pi\) | ||||
−0.126680 | + | 0.991944i | \(0.540432\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.2426 | −0.729990 | ||||||||
\(437\) | −30.5563 | −1.46171 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.97056 | −0.237232 | −0.118616 | − | 0.992940i | \(-0.537846\pi\) | ||||
−0.118616 | + | 0.992940i | \(0.537846\pi\) | |||||||
\(440\) | 4.41421 | 0.210439 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.0000 | 0.570782 | ||||||||
\(443\) | 38.9411 | 1.85015 | 0.925074 | − | 0.379786i | \(-0.124002\pi\) | ||||
0.925074 | + | 0.379786i | \(0.124002\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.7574 | 0.699566 | ||||||||
\(446\) | −7.24264 | −0.342949 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.7279 | −1.73330 | −0.866649 | − | 0.498919i | \(-0.833731\pi\) | ||||
−0.866649 | + | 0.498919i | \(0.833731\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.17157 | 0.290608 | ||||||||
\(452\) | −4.24264 | −0.199557 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.7279 | 0.597351 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.9706 | 0.934184 | 0.467092 | − | 0.884209i | \(-0.345302\pi\) | ||||
0.467092 | + | 0.884209i | \(0.345302\pi\) | |||||||
\(458\) | −12.0000 | −0.560723 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −23.1421 | −1.07901 | ||||||||
\(461\) | −12.8995 | −0.600789 | −0.300395 | − | 0.953815i | \(-0.597118\pi\) | ||||
−0.300395 | + | 0.953815i | \(0.597118\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.7279 | −1.79984 | −0.899920 | − | 0.436056i | \(-0.856375\pi\) | ||||
−0.899920 | + | 0.436056i | \(0.856375\pi\) | |||||||
\(464\) | 0.242641 | 0.0112643 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.2426 | −0.752426 | ||||||||
\(467\) | −12.3431 | −0.571173 | −0.285586 | − | 0.958353i | \(-0.592188\pi\) | ||||
−0.285586 | + | 0.958353i | \(0.592188\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 51.4558 | 2.37348 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.6569 | 0.536550 | ||||||||
\(473\) | −6.48528 | −0.298194 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 84.4264 | 3.87375 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.0000 | 0.823301 | ||||||||
\(479\) | 29.6569 | 1.35506 | 0.677528 | − | 0.735497i | \(-0.263051\pi\) | ||||
0.677528 | + | 0.735497i | \(0.263051\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.2426 | −1.01418 | ||||||||
\(482\) | 2.48528 | 0.113201 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.0000 | −0.454545 | ||||||||
\(485\) | 49.9411 | 2.26771 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.4853 | −1.74393 | −0.871967 | − | 0.489564i | \(-0.837156\pi\) | ||||
−0.871967 | + | 0.489564i | \(0.837156\pi\) | |||||||
\(488\) | −14.8284 | −0.671251 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.4853 | −0.789100 | −0.394550 | − | 0.918875i | \(-0.629099\pi\) | ||||
−0.394550 | + | 0.918875i | \(0.629099\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.686292 | −0.0309090 | ||||||||
\(494\) | −24.7279 | −1.11256 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.24264 | 0.325204 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.9706 | −0.670174 | −0.335087 | − | 0.942187i | \(-0.608766\pi\) | ||||
−0.335087 | + | 0.942187i | \(0.608766\pi\) | |||||||
\(500\) | 41.8701 | 1.87249 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.3137 | 0.504956 | ||||||||
\(503\) | −8.44365 | −0.376484 | −0.188242 | − | 0.982123i | \(-0.560279\pi\) | ||||
−0.188242 | + | 0.982123i | \(0.560279\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −63.9411 | −2.84534 | ||||||||
\(506\) | −5.24264 | −0.233064 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.2426 | −0.543179 | ||||||||
\(509\) | 34.2843 | 1.51962 | 0.759812 | − | 0.650143i | \(-0.225291\pi\) | ||||
0.759812 | + | 0.650143i | \(0.225291\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.4853 | −0.506594 | ||||||||
\(515\) | −44.4558 | −1.95896 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.6569 | 0.512668 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −18.7279 | −0.821274 | ||||||||
\(521\) | 23.1421 | 1.01388 | 0.506938 | − | 0.861983i | \(-0.330777\pi\) | ||||
0.506938 | + | 0.861983i | \(0.330777\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.4853 | 0.764578 | 0.382289 | − | 0.924043i | \(-0.375136\pi\) | ||||
0.382289 | + | 0.924043i | \(0.375136\pi\) | |||||||
\(524\) | 14.4853 | 0.632792 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.72792 | −0.162545 | ||||||||
\(527\) | −20.4853 | −0.892353 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.48528 | 0.195012 | ||||||||
\(530\) | −35.3137 | −1.53393 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.1838 | −1.13414 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −66.0833 | −2.85703 | ||||||||
\(536\) | −1.75736 | −0.0759064 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15.3848 | −0.663285 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.7574 | −1.06440 | −0.532201 | − | 0.846618i | \(-0.678635\pi\) | ||||
−0.532201 | + | 0.846618i | \(0.678635\pi\) | |||||||
\(542\) | −6.68629 | −0.287201 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.82843 | −0.121268 | ||||||||
\(545\) | −67.2843 | −2.88214 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.4853 | 1.04692 | 0.523458 | − | 0.852052i | \(-0.324642\pi\) | ||||
0.523458 | + | 0.852052i | \(0.324642\pi\) | |||||||
\(548\) | −1.75736 | −0.0750707 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 14.4853 | 0.617654 | ||||||||
\(551\) | 1.41421 | 0.0602475 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14.2132 | −0.603861 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.82843 | 0.374409 | ||||||||
\(557\) | −18.7279 | −0.793528 | −0.396764 | − | 0.917921i | \(-0.629867\pi\) | ||||
−0.396764 | + | 0.917921i | \(0.629867\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.5147 | 1.16375 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.4853 | −0.442295 | ||||||||
\(563\) | −16.5858 | −0.699008 | −0.349504 | − | 0.936935i | \(-0.613650\pi\) | ||||
−0.349504 | + | 0.936935i | \(0.613650\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.7279 | −0.787890 | ||||||||
\(566\) | 8.14214 | 0.342239 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.24264 | 0.0521400 | ||||||||
\(569\) | −27.7574 | −1.16365 | −0.581825 | − | 0.813314i | \(-0.697661\pi\) | ||||
−0.581825 | + | 0.813314i | \(0.697661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.21320 | 0.0507710 | 0.0253855 | − | 0.999678i | \(-0.491919\pi\) | ||||
0.0253855 | + | 0.999678i | \(0.491919\pi\) | |||||||
\(572\) | −4.24264 | −0.177394 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −75.9411 | −3.16696 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.7574 | 0.822510 | 0.411255 | − | 0.911520i | \(-0.365091\pi\) | ||||
0.411255 | + | 0.911520i | \(0.365091\pi\) | |||||||
\(578\) | −9.00000 | −0.374351 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.07107 | 0.0444737 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.00000 | −0.331326 | ||||||||
\(584\) | 3.17157 | 0.131241 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.343146 | 0.0141752 | ||||||||
\(587\) | −7.75736 | −0.320180 | −0.160090 | − | 0.987102i | \(-0.551179\pi\) | ||||
−0.160090 | + | 0.987102i | \(0.551179\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 42.2132 | 1.73936 | ||||||||
\(590\) | 51.4558 | 2.11840 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.24264 | 0.215471 | ||||||||
\(593\) | −2.65685 | −0.109104 | −0.0545520 | − | 0.998511i | \(-0.517373\pi\) | ||||
−0.0545520 | + | 0.998511i | \(0.517373\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.75736 | 0.235831 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 22.2426 | 0.909569 | ||||||||
\(599\) | −19.7279 | −0.806061 | −0.403031 | − | 0.915187i | \(-0.632043\pi\) | ||||
−0.403031 | + | 0.915187i | \(0.632043\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.7279 | −1.25342 | −0.626709 | − | 0.779253i | \(-0.715599\pi\) | ||||
−0.626709 | + | 0.779253i | \(0.715599\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.7279 | 0.599271 | ||||||||
\(605\) | −44.1421 | −1.79463 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.0000 | 1.21766 | 0.608831 | − | 0.793300i | \(-0.291639\pi\) | ||||
0.608831 | + | 0.793300i | \(0.291639\pi\) | |||||||
\(608\) | 5.82843 | 0.236374 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −65.4558 | −2.65023 | ||||||||
\(611\) | −49.4558 | −2.00077 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.7279 | −0.877583 | −0.438791 | − | 0.898589i | \(-0.644593\pi\) | ||||
−0.438791 | + | 0.898589i | \(0.644593\pi\) | |||||||
\(614\) | −22.7990 | −0.920092 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.9706 | 1.08579 | 0.542897 | − | 0.839799i | \(-0.317327\pi\) | ||||
0.542897 | + | 0.839799i | \(0.317327\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.7990 | 0.675208 | 0.337604 | − | 0.941288i | \(-0.390383\pi\) | ||||
0.337604 | + | 0.941288i | \(0.390383\pi\) | |||||||
\(620\) | 31.9706 | 1.28397 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.5563 | 0.623753 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 112.397 | 4.49588 | ||||||||
\(626\) | 1.75736 | 0.0702382 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.92893 | −0.196686 | ||||||||
\(629\) | −14.8284 | −0.591248 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0000 | 0.557331 | 0.278666 | − | 0.960388i | \(-0.410108\pi\) | ||||
0.278666 | + | 0.960388i | \(0.410108\pi\) | |||||||
\(632\) | −6.48528 | −0.257971 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.0000 | 0.397151 | ||||||||
\(635\) | −54.0416 | −2.14458 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.242641 | 0.00960624 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.41421 | 0.174487 | ||||||||
\(641\) | 41.2132 | 1.62782 | 0.813912 | − | 0.580988i | \(-0.197334\pi\) | ||||
0.813912 | + | 0.580988i | \(0.197334\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.82843 | 0.229851 | 0.114925 | − | 0.993374i | \(-0.463337\pi\) | ||||
0.114925 | + | 0.993374i | \(0.463337\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.4853 | −0.648605 | ||||||||
\(647\) | −38.4853 | −1.51301 | −0.756506 | − | 0.653986i | \(-0.773095\pi\) | ||||
−0.756506 | + | 0.653986i | \(0.773095\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.6569 | 0.457572 | ||||||||
\(650\) | −61.4558 | −2.41050 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.7279 | −0.576790 | ||||||||
\(653\) | 39.9411 | 1.56302 | 0.781509 | − | 0.623895i | \(-0.214451\pi\) | ||||
0.781509 | + | 0.623895i | \(0.214451\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 63.9411 | 2.49839 | ||||||||
\(656\) | 6.17157 | 0.240959 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.9411 | −1.67275 | −0.836374 | − | 0.548159i | \(-0.815329\pi\) | ||||
−0.836374 | + | 0.548159i | \(0.815329\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.7279 | 0.961805 | 0.480902 | − | 0.876774i | \(-0.340309\pi\) | ||||
0.480902 | + | 0.876774i | \(0.340309\pi\) | |||||||
\(662\) | 7.51472 | 0.292068 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.89949 | −0.151330 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.27208 | −0.0492551 | ||||||||
\(668\) | −12.3848 | −0.479181 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.75736 | −0.299693 | ||||||||
\(671\) | −14.8284 | −0.572445 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.45584 | −0.0561187 | −0.0280593 | − | 0.999606i | \(-0.508933\pi\) | ||||
−0.0280593 | + | 0.999606i | \(0.508933\pi\) | |||||||
\(674\) | −3.48528 | −0.134248 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.00000 | 0.192308 | ||||||||
\(677\) | 20.6985 | 0.795507 | 0.397754 | − | 0.917492i | \(-0.369790\pi\) | ||||
0.397754 | + | 0.917492i | \(0.369790\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −12.4853 | −0.478789 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.24264 | 0.277335 | ||||||||
\(683\) | 19.9706 | 0.764152 | 0.382076 | − | 0.924131i | \(-0.375209\pi\) | ||||
0.382076 | + | 0.924131i | \(0.375209\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.75736 | −0.296393 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.48528 | −0.247249 | ||||||||
\(689\) | 33.9411 | 1.29305 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.9411 | −1.74768 | −0.873841 | − | 0.486211i | \(-0.838379\pi\) | ||||
−0.873841 | + | 0.486211i | \(0.838379\pi\) | |||||||
\(692\) | −13.2426 | −0.503410 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.5147 | 0.702809 | ||||||||
\(695\) | 38.9706 | 1.47824 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.4558 | −0.661187 | ||||||||
\(698\) | −13.7574 | −0.520724 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.2426 | 1.06671 | 0.533355 | − | 0.845892i | \(-0.320931\pi\) | ||||
0.533355 | + | 0.845892i | \(0.320931\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.5563 | 1.15245 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.65685 | 0.0999920 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.7574 | −0.704447 | −0.352224 | − | 0.935916i | \(-0.614574\pi\) | ||||
−0.352224 | + | 0.935916i | \(0.614574\pi\) | |||||||
\(710\) | 5.48528 | 0.205859 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.34315 | 0.125290 | ||||||||
\(713\) | −37.9706 | −1.42201 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.7279 | −0.700385 | ||||||||
\(716\) | 10.9706 | 0.409989 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.4558 | 0.651446 | ||||||||
\(719\) | −12.3431 | −0.460322 | −0.230161 | − | 0.973153i | \(-0.573925\pi\) | ||||
−0.230161 | + | 0.973153i | \(0.573925\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 14.9706 | 0.557147 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.2426 | −0.380665 | ||||||||
\(725\) | 3.51472 | 0.130533 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.1421 | −0.524503 | −0.262251 | − | 0.965000i | \(-0.584465\pi\) | ||||
−0.262251 | + | 0.965000i | \(0.584465\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.0000 | 0.518163 | ||||||||
\(731\) | 18.3431 | 0.678446 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.9411 | 1.47526 | 0.737630 | − | 0.675206i | \(-0.235945\pi\) | ||||
0.737630 | + | 0.675206i | \(0.235945\pi\) | |||||||
\(734\) | 30.8995 | 1.14052 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.24264 | −0.193246 | ||||||||
\(737\) | −1.75736 | −0.0647332 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.2721 | 0.856077 | 0.428039 | − | 0.903760i | \(-0.359205\pi\) | ||||
0.428039 | + | 0.903760i | \(0.359205\pi\) | |||||||
\(740\) | 23.1421 | 0.850722 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.2426 | 0.852690 | 0.426345 | − | 0.904561i | \(-0.359801\pi\) | ||||
0.426345 | + | 0.904561i | \(0.359801\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.4142 | 0.931105 | ||||||||
\(746\) | −15.2426 | −0.558073 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.82843 | −0.103418 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.4558 | −0.418030 | −0.209015 | − | 0.977912i | \(-0.567026\pi\) | ||||
−0.209015 | + | 0.977912i | \(0.567026\pi\) | |||||||
\(752\) | 11.6569 | 0.425082 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.02944 | −0.0374899 | ||||||||
\(755\) | 65.0122 | 2.36604 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.45584 | 0.125605 | 0.0628024 | − | 0.998026i | \(-0.479996\pi\) | ||||
0.0628024 | + | 0.998026i | \(0.479996\pi\) | |||||||
\(758\) | 2.97056 | 0.107896 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 25.7279 | 0.933250 | ||||||||
\(761\) | −6.68629 | −0.242378 | −0.121189 | − | 0.992629i | \(-0.538671\pi\) | ||||
−0.121189 | + | 0.992629i | \(0.538671\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.757359 | 0.0274003 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.0416 | 0.651871 | ||||||||
\(767\) | −49.4558 | −1.78575 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.1838 | −1.16058 | −0.580288 | − | 0.814411i | \(-0.697060\pi\) | ||||
−0.580288 | + | 0.814411i | \(0.697060\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.48528 | 0.161429 | ||||||||
\(773\) | 2.61522 | 0.0940631 | 0.0470315 | − | 0.998893i | \(-0.485024\pi\) | ||||
0.0470315 | + | 0.998893i | \(0.485024\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 104.912 | 3.76854 | ||||||||
\(776\) | 11.3137 | 0.406138 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 36.9706 | 1.32546 | ||||||||
\(779\) | 35.9706 | 1.28878 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.24264 | 0.0444652 | ||||||||
\(782\) | 14.8284 | 0.530263 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.7574 | −0.776553 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.6863 | 1.09385 | 0.546924 | − | 0.837182i | \(-0.315799\pi\) | ||||
0.546924 | + | 0.837182i | \(0.315799\pi\) | |||||||
\(788\) | 2.72792 | 0.0971782 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −28.6274 | −1.01852 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 62.9117 | 2.23406 | ||||||||
\(794\) | −19.4142 | −0.688985 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.75736 | −0.168620 | ||||||||
\(797\) | −16.7574 | −0.593576 | −0.296788 | − | 0.954943i | \(-0.595915\pi\) | ||||
−0.296788 | + | 0.954943i | \(0.595915\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.9706 | −1.16641 | ||||||||
\(800\) | 14.4853 | 0.512132 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.75736 | −0.0620545 | ||||||||
\(803\) | 3.17157 | 0.111922 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −30.7279 | −1.08234 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −14.4853 | −0.509590 | ||||||||
\(809\) | 9.75736 | 0.343050 | 0.171525 | − | 0.985180i | \(-0.445130\pi\) | ||||
0.171525 | + | 0.985180i | \(0.445130\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.4264 | −1.38445 | −0.692224 | − | 0.721683i | \(-0.743369\pi\) | ||||
−0.692224 | + | 0.721683i | \(0.743369\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.24264 | 0.183754 | ||||||||
\(815\) | −65.0122 | −2.27728 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.7990 | −1.32242 | ||||||||
\(818\) | 6.00000 | 0.209785 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 27.2426 | 0.951354 | ||||||||
\(821\) | 46.9706 | 1.63928 | 0.819642 | − | 0.572876i | \(-0.194172\pi\) | ||||
0.819642 | + | 0.572876i | \(0.194172\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.2426 | 1.33305 | 0.666527 | − | 0.745481i | \(-0.267780\pi\) | ||||
0.666527 | + | 0.745481i | \(0.267780\pi\) | |||||||
\(824\) | −10.0711 | −0.350842 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.9411 | 1.91049 | 0.955245 | − | 0.295816i | \(-0.0955914\pi\) | ||||
0.955245 | + | 0.295816i | \(0.0955914\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.1421 | 1.53312 | 0.766560 | − | 0.642173i | \(-0.221967\pi\) | ||||
0.766560 | + | 0.642173i | \(0.221967\pi\) | |||||||
\(830\) | −17.2132 | −0.597479 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.24264 | −0.147087 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −54.6690 | −1.89190 | ||||||||
\(836\) | 5.82843 | 0.201580 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −36.0416 | −1.24504 | ||||||||
\(839\) | 54.3848 | 1.87757 | 0.938785 | − | 0.344502i | \(-0.111952\pi\) | ||||
0.938785 | + | 0.344502i | \(0.111952\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9411 | −0.997970 | ||||||||
\(842\) | −24.2132 | −0.834442 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.7279 | 0.438113 | ||||||||
\(845\) | 22.0711 | 0.759268 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.00000 | −0.274721 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −40.9706 | −1.40528 | ||||||||
\(851\) | −27.4853 | −0.942183 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.0000 | −0.821744 | −0.410872 | − | 0.911693i | \(-0.634776\pi\) | ||||
−0.410872 | + | 0.911693i | \(0.634776\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.9706 | −0.511683 | ||||||||
\(857\) | 39.7696 | 1.35850 | 0.679251 | − | 0.733906i | \(-0.262305\pi\) | ||||
0.679251 | + | 0.733906i | \(0.262305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.1716 | 0.824723 | 0.412362 | − | 0.911020i | \(-0.364704\pi\) | ||||
0.412362 | + | 0.911020i | \(0.364704\pi\) | |||||||
\(860\) | −28.6274 | −0.976187 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.7574 | −0.366397 | ||||||||
\(863\) | 30.9706 | 1.05425 | 0.527125 | − | 0.849788i | \(-0.323270\pi\) | ||||
0.527125 | + | 0.849788i | \(0.323270\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −58.4558 | −1.98756 | ||||||||
\(866\) | −5.27208 | −0.179153 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.48528 | −0.219998 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.45584 | 0.252632 | ||||||||
\(872\) | −15.2426 | −0.516181 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −30.5563 | −1.03358 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.9706 | 0.640590 | 0.320295 | − | 0.947318i | \(-0.396218\pi\) | ||||
0.320295 | + | 0.947318i | \(0.396218\pi\) | |||||||
\(878\) | −4.97056 | −0.167748 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.41421 | 0.148803 | ||||||||
\(881\) | −12.9411 | −0.435998 | −0.217999 | − | 0.975949i | \(-0.569953\pi\) | ||||
−0.217999 | + | 0.975949i | \(0.569953\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.4853 | 0.958606 | 0.479303 | − | 0.877649i | \(-0.340889\pi\) | ||||
0.479303 | + | 0.877649i | \(0.340889\pi\) | |||||||
\(884\) | 12.0000 | 0.403604 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 38.9411 | 1.30825 | ||||||||
\(887\) | −23.3553 | −0.784196 | −0.392098 | − | 0.919924i | \(-0.628251\pi\) | ||||
−0.392098 | + | 0.919924i | \(0.628251\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 14.7574 | 0.494668 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.24264 | −0.242502 | ||||||||
\(893\) | 67.9411 | 2.27356 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 48.4264 | 1.61872 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −36.7279 | −1.22563 | ||||||||
\(899\) | 1.75736 | 0.0586112 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.6274 | 0.753829 | ||||||||
\(902\) | 6.17157 | 0.205491 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.24264 | −0.141108 | ||||||||
\(905\) | −45.2132 | −1.50294 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.7279 | 0.555442 | 0.277721 | − | 0.960662i | \(-0.410421\pi\) | ||||
0.277721 | + | 0.960662i | \(0.410421\pi\) | |||||||
\(908\) | 12.7279 | 0.422391 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.48528 | 0.148604 | 0.0743020 | − | 0.997236i | \(-0.476327\pi\) | ||||
0.0743020 | + | 0.997236i | \(0.476327\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.89949 | −0.129054 | ||||||||
\(914\) | 19.9706 | 0.660568 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.0000 | −0.396491 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.48528 | −0.147956 | −0.0739779 | − | 0.997260i | \(-0.523569\pi\) | ||||
−0.0739779 | + | 0.997260i | \(0.523569\pi\) | |||||||
\(920\) | −23.1421 | −0.762974 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.8995 | −0.424822 | ||||||||
\(923\) | −5.27208 | −0.173533 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 75.9411 | 2.49693 | ||||||||
\(926\) | −38.7279 | −1.27268 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.242641 | 0.00796507 | ||||||||
\(929\) | −40.2843 | −1.32168 | −0.660842 | − | 0.750525i | \(-0.729801\pi\) | ||||
−0.660842 | + | 0.750525i | \(0.729801\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −16.2426 | −0.532045 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.3431 | −0.403880 | ||||||||
\(935\) | −12.4853 | −0.408312 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.3137 | 0.761626 | 0.380813 | − | 0.924652i | \(-0.375644\pi\) | ||||
0.380813 | + | 0.924652i | \(0.375644\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 51.4558 | 1.67830 | ||||||||
\(941\) | −4.07107 | −0.132713 | −0.0663565 | − | 0.997796i | \(-0.521137\pi\) | ||||
−0.0663565 | + | 0.997796i | \(0.521137\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.3553 | −1.05363 | ||||||||
\(944\) | 11.6569 | 0.379398 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.48528 | −0.210855 | ||||||||
\(947\) | −49.9706 | −1.62383 | −0.811913 | − | 0.583779i | \(-0.801573\pi\) | ||||
−0.811913 | + | 0.583779i | \(0.801573\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.4558 | −0.436795 | ||||||||
\(950\) | 84.4264 | 2.73915 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.2426 | 0.850083 | 0.425041 | − | 0.905174i | \(-0.360260\pi\) | ||||
0.425041 | + | 0.905174i | \(0.360260\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.34315 | 0.108182 | ||||||||
\(956\) | 18.0000 | 0.582162 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 29.6569 | 0.958169 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.4558 | 0.692124 | ||||||||
\(962\) | −22.2426 | −0.717132 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.48528 | 0.0800455 | ||||||||
\(965\) | 19.7990 | 0.637352 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.6690 | 1.30783 | 0.653914 | − | 0.756569i | \(-0.273126\pi\) | ||||
0.653914 | + | 0.756569i | \(0.273126\pi\) | |||||||
\(968\) | −10.0000 | −0.321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 49.9411 | 1.60351 | ||||||||
\(971\) | −43.4975 | −1.39590 | −0.697950 | − | 0.716146i | \(-0.745904\pi\) | ||||
−0.697950 | + | 0.716146i | \(0.745904\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −38.4853 | −1.23315 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.8284 | −0.474646 | ||||||||
\(977\) | −16.9706 | −0.542936 | −0.271468 | − | 0.962447i | \(-0.587509\pi\) | ||||
−0.271468 | + | 0.962447i | \(0.587509\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.34315 | 0.106847 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.4853 | −0.557978 | ||||||||
\(983\) | 37.7990 | 1.20560 | 0.602800 | − | 0.797892i | \(-0.294052\pi\) | ||||
0.602800 | + | 0.797892i | \(0.294052\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0416 | 0.383678 | ||||||||
\(986\) | −0.686292 | −0.0218560 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.7279 | −0.786700 | ||||||||
\(989\) | 34.0000 | 1.08114 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.24264 | −0.261836 | −0.130918 | − | 0.991393i | \(-0.541792\pi\) | ||||
−0.130918 | + | 0.991393i | \(0.541792\pi\) | |||||||
\(992\) | 7.24264 | 0.229954 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.0000 | −0.665745 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.1005 | −0.636589 | −0.318295 | − | 0.947992i | \(-0.603110\pi\) | ||||
−0.318295 | + | 0.947992i | \(0.603110\pi\) | |||||||
\(998\) | −14.9706 | −0.473885 | ||||||||
\(999\) | 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 | 2646.2.a.bp.1.2 | yes | 2 | |
3.2 | odd | 2 | 2646.2.a.be.1.1 | ✓ | 2 | ||
7.6 | odd | 2 | 2646.2.a.bk.1.1 | yes | 2 | ||
21.20 | even | 2 | 2646.2.a.bj.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2646.2.a.be.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
2646.2.a.bj.1.2 | yes | 2 | 21.20 | even | 2 | ||
2646.2.a.bk.1.1 | yes | 2 | 7.6 | odd | 2 | ||
2646.2.a.bp.1.2 | yes | 2 | 1.1 | even | 1 | trivial |