Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1932,2,Mod(1,1932)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1932, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("1932.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1932.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: | \(15.4270976705\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
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 | 1.1 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1932.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.30278 | −1.92426 | −0.962130 | − | 0.272591i | \(-0.912119\pi\) | ||||
−0.962130 | + | 0.272591i | \(0.912119\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.60555 | −0.484092 | −0.242046 | − | 0.970265i | \(-0.577818\pi\) | ||||
−0.242046 | + | 0.970265i | \(0.577818\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.30278 | −0.361325 | −0.180662 | − | 0.983545i | \(-0.557824\pi\) | ||||
−0.180662 | + | 0.983545i | \(0.557824\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.30278 | 1.11097 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.60555 | −1.84462 | −0.922309 | − | 0.386454i | \(-0.873700\pi\) | ||||
−0.922309 | + | 0.386454i | \(0.873700\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.60555 | −1.74483 | −0.872417 | − | 0.488763i | \(-0.837448\pi\) | ||||
−0.872417 | + | 0.488763i | \(0.837448\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.5139 | 2.70278 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.60555 | 0.298143 | 0.149072 | − | 0.988826i | \(-0.452371\pi\) | ||||
0.149072 | + | 0.988826i | \(0.452371\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.60555 | 0.647576 | 0.323788 | − | 0.946130i | \(-0.395044\pi\) | ||||
0.323788 | + | 0.946130i | \(0.395044\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.60555 | 0.279491 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.30278 | 0.727302 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.60555 | −0.263951 | −0.131976 | − | 0.991253i | \(-0.542132\pi\) | ||||
−0.131976 | + | 0.991253i | \(0.542132\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.30278 | 0.208611 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.60555 | −0.563093 | −0.281546 | − | 0.959548i | \(-0.590847\pi\) | ||||
−0.281546 | + | 0.959548i | \(0.590847\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.697224 | 0.106326 | 0.0531629 | − | 0.998586i | \(-0.483070\pi\) | ||||
0.0531629 | + | 0.998586i | \(0.483070\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.30278 | −0.641420 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.60555 | 0.380059 | 0.190029 | − | 0.981778i | \(-0.439142\pi\) | ||||
0.190029 | + | 0.981778i | \(0.439142\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.60555 | 1.06499 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.90833 | −0.674211 | −0.337105 | − | 0.941467i | \(-0.609448\pi\) | ||||
−0.337105 | + | 0.941467i | \(0.609448\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.90833 | 0.931519 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.60555 | 1.00738 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.90833 | −0.899388 | −0.449694 | − | 0.893183i | \(-0.648467\pi\) | ||||
−0.449694 | + | 0.893183i | \(0.648467\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.90833 | −0.756484 | −0.378242 | − | 0.925707i | \(-0.623471\pi\) | ||||
−0.378242 | + | 0.925707i | \(0.623471\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.60555 | 0.695283 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.69722 | 1.18470 | 0.592352 | − | 0.805679i | \(-0.298199\pi\) | ||||
0.592352 | + | 0.805679i | \(0.298199\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.09167 | 0.248236 | 0.124118 | − | 0.992267i | \(-0.460390\pi\) | ||||
0.124118 | + | 0.992267i | \(0.460390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.0000 | 1.28745 | 0.643726 | − | 0.765256i | \(-0.277388\pi\) | ||||
0.643726 | + | 0.765256i | \(0.277388\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.5139 | −1.56045 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.60555 | 0.182970 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.4222 | −1.73513 | −0.867567 | − | 0.497321i | \(-0.834317\pi\) | ||||
−0.867567 | + | 0.497321i | \(0.834317\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.78890 | 0.196357 | 0.0981785 | − | 0.995169i | \(-0.468698\pi\) | ||||
0.0981785 | + | 0.995169i | \(0.468698\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 32.7250 | 3.54952 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.60555 | −0.172133 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.51388 | 0.266471 | 0.133235 | − | 0.991084i | \(-0.457463\pi\) | ||||
0.133235 | + | 0.991084i | \(0.457463\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.30278 | 0.136568 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.60555 | −0.373878 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 32.7250 | 3.35751 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.2111 | 1.84906 | 0.924529 | − | 0.381113i | \(-0.124459\pi\) | ||||
0.924529 | + | 0.381113i | \(0.124459\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.60555 | −0.161364 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.51388 | 0.548651 | 0.274326 | − | 0.961637i | \(-0.411545\pi\) | ||||
0.274326 | + | 0.961637i | \(0.411545\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.2111 | 1.69586 | 0.847930 | − | 0.530108i | \(-0.177849\pi\) | ||||
0.847930 | + | 0.530108i | \(0.177849\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.30278 | −0.419908 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.30278 | −0.319291 | −0.159646 | − | 0.987174i | \(-0.551035\pi\) | ||||
−0.159646 | + | 0.987174i | \(0.551035\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.5139 | 1.29439 | 0.647197 | − | 0.762322i | \(-0.275941\pi\) | ||||
0.647197 | + | 0.762322i | \(0.275941\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.60555 | 0.152392 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.69722 | 0.159661 | 0.0798307 | − | 0.996808i | \(-0.474562\pi\) | ||||
0.0798307 | + | 0.996808i | \(0.474562\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.30278 | 0.401236 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.30278 | −0.120442 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.60555 | 0.697200 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.42221 | −0.765655 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.60555 | 0.325102 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −36.6333 | −3.27658 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.11943 | −0.631747 | −0.315874 | − | 0.948801i | \(-0.602298\pi\) | ||||
−0.315874 | + | 0.948801i | \(0.602298\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.697224 | −0.0613872 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.8167 | 1.29454 | 0.647269 | − | 0.762262i | \(-0.275911\pi\) | ||||
0.647269 | + | 0.762262i | \(0.275911\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.60555 | 0.659485 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.30278 | 0.370324 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.60555 | 0.137172 | 0.0685858 | − | 0.997645i | \(-0.478151\pi\) | ||||
0.0685858 | + | 0.997645i | \(0.478151\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.1194 | 0.858319 | 0.429159 | − | 0.903229i | \(-0.358810\pi\) | ||||
0.429159 | + | 0.903229i | \(0.358810\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.60555 | −0.219427 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.09167 | 0.174914 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.90833 | −0.573705 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.6056 | −1.85192 | −0.925959 | − | 0.377623i | \(-0.876742\pi\) | ||||
−0.925959 | + | 0.377623i | \(0.876742\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.39445 | 0.113479 | 0.0567393 | − | 0.998389i | \(-0.481930\pi\) | ||||
0.0567393 | + | 0.998389i | \(0.481930\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.60555 | −0.614872 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.5139 | −1.24610 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.81665 | −0.783454 | −0.391727 | − | 0.920081i | \(-0.628122\pi\) | ||||
−0.391727 | + | 0.920081i | \(0.628122\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.90833 | 0.389256 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.1194 | 1.26257 | 0.631286 | − | 0.775550i | \(-0.282528\pi\) | ||||
0.631286 | + | 0.775550i | \(0.282528\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.90833 | −0.537813 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.0278 | 1.70456 | 0.852279 | − | 0.523087i | \(-0.175220\pi\) | ||||
0.852279 | + | 0.523087i | \(0.175220\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3028 | −0.869444 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.60555 | −0.581611 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.6056 | −1.03441 | −0.517205 | − | 0.855861i | \(-0.673028\pi\) | ||||
−0.517205 | + | 0.855861i | \(0.673028\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.5139 | −1.02155 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.90833 | 0.519262 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.9361 | −1.63958 | −0.819790 | − | 0.572664i | \(-0.805910\pi\) | ||||
−0.819790 | + | 0.572664i | \(0.805910\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.0000 | −1.41226 | −0.706129 | − | 0.708083i | \(-0.749560\pi\) | ||||
−0.706129 | + | 0.708083i | \(0.749560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.90833 | 0.436756 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.90833 | 0.507910 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.2111 | 0.892964 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.39445 | −0.100899 | −0.0504494 | − | 0.998727i | \(-0.516065\pi\) | ||||
−0.0504494 | + | 0.998727i | \(0.516065\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.0278 | −1.08172 | −0.540861 | − | 0.841112i | \(-0.681901\pi\) | ||||
−0.540861 | + | 0.841112i | \(0.681901\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.60555 | −0.401422 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.9361 | 1.49163 | 0.745817 | − | 0.666151i | \(-0.232059\pi\) | ||||
0.745817 | + | 0.666151i | \(0.232059\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.90833 | 0.631495 | 0.315747 | − | 0.948843i | \(-0.397745\pi\) | ||||
0.315747 | + | 0.948843i | \(0.397745\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.69722 | −0.683989 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.60555 | −0.112688 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.5139 | 1.08354 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.2111 | 0.844660 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.3944 | 1.26633 | 0.633163 | − | 0.774018i | \(-0.281756\pi\) | ||||
0.633163 | + | 0.774018i | \(0.281756\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.09167 | −0.143319 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.00000 | −0.204598 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.60555 | −0.244761 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.0000 | −0.743311 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.90833 | 0.666506 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.7250 | −0.986058 | −0.493029 | − | 0.870013i | \(-0.664110\pi\) | ||||
−0.493029 | + | 0.870013i | \(0.664110\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.5139 | 0.900925 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.09167 | 0.0724569 | 0.0362284 | − | 0.999344i | \(-0.488466\pi\) | ||||
0.0362284 | + | 0.999344i | \(0.488466\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.1194 | −1.46169 | −0.730847 | − | 0.682542i | \(-0.760874\pi\) | ||||
−0.730847 | + | 0.682542i | \(0.760874\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.60555 | −0.105638 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.1194 | −1.18704 | −0.593522 | − | 0.804818i | \(-0.702263\pi\) | ||||
−0.593522 | + | 0.804818i | \(0.702263\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.2111 | −0.731332 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.4222 | 1.00178 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.90833 | −0.317493 | −0.158747 | − | 0.987319i | \(-0.550745\pi\) | ||||
−0.158747 | + | 0.987319i | \(0.550745\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.21110 | −0.400092 | −0.200046 | − | 0.979786i | \(-0.564109\pi\) | ||||
−0.200046 | + | 0.979786i | \(0.564109\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.30278 | −0.274894 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.90833 | 0.630452 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.78890 | −0.113367 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.8167 | 1.62953 | 0.814766 | − | 0.579789i | \(-0.196865\pi\) | ||||
0.814766 | + | 0.579789i | \(0.196865\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.60555 | 0.100940 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −32.7250 | −2.04932 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.18335 | 0.260950 | 0.130475 | − | 0.991452i | \(-0.458350\pi\) | ||||
0.130475 | + | 0.991452i | \(0.458350\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.60555 | 0.0997641 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.60555 | 0.0993811 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.4222 | 1.19762 | 0.598812 | − | 0.800889i | \(-0.295640\pi\) | ||||
0.598812 | + | 0.800889i | \(0.295640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.1194 | 1.29736 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.51388 | −0.153847 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.1194 | −0.799906 | −0.399953 | − | 0.916536i | \(-0.630974\pi\) | ||||
−0.399953 | + | 0.916536i | \(0.630974\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.4222 | −1.78727 | −0.893636 | − | 0.448793i | \(-0.851854\pi\) | ||||
−0.893636 | + | 0.448793i | \(0.851854\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.30278 | −0.0788476 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.6972 | −1.30839 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.5416 | −1.77498 | −0.887492 | − | 0.460822i | \(-0.847555\pi\) | ||||
−0.887492 | + | 0.460822i | \(0.847555\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.60555 | 0.215859 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.605551 | −0.0361242 | −0.0180621 | − | 0.999837i | \(-0.505750\pi\) | ||||
−0.0180621 | + | 0.999837i | \(0.505750\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.6972 | 1.28977 | 0.644883 | − | 0.764281i | \(-0.276906\pi\) | ||||
0.644883 | + | 0.764281i | \(0.276906\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −32.7250 | −1.93846 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.60555 | 0.212829 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.8444 | 2.40261 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.2111 | −1.06755 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −33.2111 | −1.94021 | −0.970107 | − | 0.242679i | \(-0.921974\pi\) | ||||
−0.970107 | + | 0.242679i | \(0.921974\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29.7250 | 1.73066 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.60555 | 0.0931635 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.30278 | 0.0753415 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.697224 | −0.0401873 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.51388 | −0.316764 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 25.4222 | 1.45567 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.3944 | −1.04983 | −0.524913 | − | 0.851156i | \(-0.675902\pi\) | ||||
−0.524913 | + | 0.851156i | \(0.675902\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.2111 | −0.979105 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.1194 | −0.857344 | −0.428672 | − | 0.903460i | \(-0.641018\pi\) | ||||
−0.428672 | + | 0.903460i | \(0.641018\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.57779 | −0.0891822 | −0.0445911 | − | 0.999005i | \(-0.514199\pi\) | ||||
−0.0445911 | + | 0.999005i | \(0.514199\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.30278 | 0.242434 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.3028 | −0.915655 | −0.457828 | − | 0.889041i | \(-0.651372\pi\) | ||||
−0.457828 | + | 0.889041i | \(0.651372\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.57779 | −0.144329 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.30278 | 0.184343 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 57.8444 | 3.21855 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.6056 | −0.976580 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.5139 | −0.747319 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.60555 | −0.143649 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.00000 | −0.109930 | −0.0549650 | − | 0.998488i | \(-0.517505\pi\) | ||||
−0.0549650 | + | 0.998488i | \(0.517505\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.60555 | −0.0879837 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −41.7250 | −2.27968 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.7250 | −0.856594 | −0.428297 | − | 0.903638i | \(-0.640886\pi\) | ||||
−0.428297 | + | 0.903638i | \(0.640886\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.69722 | −0.0921806 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.78890 | −0.313486 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.30278 | −0.231654 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.2111 | −0.762892 | −0.381446 | − | 0.924391i | \(-0.624574\pi\) | ||||
−0.381446 | + | 0.924391i | \(0.624574\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.30278 | 0.230322 | 0.115161 | − | 0.993347i | \(-0.463262\pi\) | ||||
0.115161 | + | 0.993347i | \(0.463262\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.30278 | 0.0695370 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.39445 | 0.446791 | 0.223396 | − | 0.974728i | \(-0.428286\pi\) | ||||
0.223396 | + | 0.974728i | \(0.428286\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.00000 | −0.477670 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.60555 | −0.402528 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.908327 | −0.0479397 | −0.0239698 | − | 0.999713i | \(-0.507631\pi\) | ||||
−0.0239698 | + | 0.999713i | \(0.507631\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.8444 | 2.04444 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.42221 | 0.442051 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −47.3305 | −2.47739 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.48612 | 0.390772 | 0.195386 | − | 0.980726i | \(-0.437404\pi\) | ||||
0.195386 | + | 0.980726i | \(0.437404\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.60555 | −0.187698 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.90833 | 0.254828 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.8167 | 1.69918 | 0.849591 | − | 0.527442i | \(-0.176849\pi\) | ||||
0.849591 | + | 0.527442i | \(0.176849\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 36.6333 | 1.89174 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.09167 | −0.107727 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.4222 | 0.946285 | 0.473143 | − | 0.880986i | \(-0.343120\pi\) | ||||
0.473143 | + | 0.880986i | \(0.343120\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.11943 | 0.364739 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.6333 | 0.849922 | 0.424961 | − | 0.905212i | \(-0.360288\pi\) | ||||
0.424961 | + | 0.905212i | \(0.360288\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.90833 | −0.352081 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.697224 | 0.0354419 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.6333 | 1.55317 | 0.776585 | − | 0.630012i | \(-0.216950\pi\) | ||||
0.776585 | + | 0.630012i | \(0.216950\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.60555 | 0.384629 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.8167 | −0.747401 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 66.3583 | 3.33885 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.39445 | −0.0699854 | −0.0349927 | − | 0.999388i | \(-0.511141\pi\) | ||||
−0.0349927 | + | 0.999388i | \(0.511141\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.60555 | −0.380754 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.6333 | 0.830628 | 0.415314 | − | 0.909678i | \(-0.363672\pi\) | ||||
0.415314 | + | 0.909678i | \(0.363672\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.69722 | −0.233985 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.30278 | −0.213807 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.57779 | 0.127777 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.6056 | 0.771645 | 0.385822 | − | 0.922573i | \(-0.373918\pi\) | ||||
0.385822 | + | 0.922573i | \(0.373918\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.60555 | −0.0791960 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.90833 | 0.339937 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.69722 | −0.377842 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.1194 | −0.495551 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.09167 | −0.0533317 | −0.0266659 | − | 0.999644i | \(-0.508489\pi\) | ||||
−0.0266659 | + | 0.999644i | \(0.508489\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.9083 | −0.872798 | −0.436399 | − | 0.899753i | \(-0.643746\pi\) | ||||
−0.436399 | + | 0.899753i | \(0.643746\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.60555 | 0.126686 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −102.780 | −4.98559 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.90833 | 0.285924 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.09167 | −0.100987 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.697224 | −0.0335841 | −0.0167921 | − | 0.999859i | \(-0.505345\pi\) | ||||
−0.0167921 | + | 0.999859i | \(0.505345\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.18335 | 0.104925 | 0.0524625 | − | 0.998623i | \(-0.483293\pi\) | ||||
0.0524625 | + | 0.998623i | \(0.483293\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.90833 | 0.331229 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.60555 | 0.363823 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.3944 | −0.973374 | −0.486687 | − | 0.873576i | \(-0.661795\pi\) | ||||
−0.486687 | + | 0.873576i | \(0.661795\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.2111 | −1.00777 | −0.503885 | − | 0.863771i | \(-0.668096\pi\) | ||||
−0.503885 | + | 0.863771i | \(0.668096\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.8167 | −0.512759 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.6056 | 1.06921 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.1194 | 0.855109 | 0.427554 | − | 0.903990i | \(-0.359375\pi\) | ||||
0.427554 | + | 0.903990i | \(0.359375\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.78890 | 0.272589 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.39445 | −0.0655169 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.60555 | −0.262792 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.3028 | −1.13684 | −0.568418 | − | 0.822740i | \(-0.692444\pi\) | ||||
−0.568418 | + | 0.822740i | \(0.692444\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.60555 | 0.354997 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.9083 | −1.71899 | −0.859496 | − | 0.511142i | \(-0.829222\pi\) | ||||
−0.859496 | + | 0.511142i | \(0.829222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.0000 | 0.790057 | 0.395029 | − | 0.918669i | \(-0.370735\pi\) | ||||
0.395029 | + | 0.918669i | \(0.370735\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.5139 | 0.719439 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.8444 | 1.56613 | 0.783066 | − | 0.621938i | \(-0.213655\pi\) | ||||
0.783066 | + | 0.621938i | \(0.213655\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.69722 | −0.447776 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.81665 | 0.452328 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.11943 | −0.0514714 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −102.780 | −4.71589 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.90833 | −0.224737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.2389 | 1.06181 | 0.530905 | − | 0.847431i | \(-0.321852\pi\) | ||||
0.530905 | + | 0.847431i | \(0.321852\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.09167 | 0.0953721 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −78.3583 | −3.55807 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.2111 | −0.462709 | −0.231355 | − | 0.972869i | \(-0.574316\pi\) | ||||
−0.231355 | + | 0.972869i | \(0.574316\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.1194 | −0.728946 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.0917 | 1.08724 | 0.543621 | − | 0.839331i | \(-0.317053\pi\) | ||||
0.543621 | + | 0.839331i | \(0.317053\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.2111 | −0.549960 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.90833 | 0.310506 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.09167 | −0.0938244 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.1194 | 1.70646 | 0.853230 | − | 0.521535i | \(-0.174640\pi\) | ||||
0.853230 | + | 0.521535i | \(0.174640\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.0278 | −0.984128 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.11943 | −0.183676 | −0.0918381 | − | 0.995774i | \(-0.529274\pi\) | ||||
−0.0918381 | + | 0.995774i | \(0.529274\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.7250 | −1.05575 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.3028 | 0.501974 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.6056 | −1.17927 | −0.589635 | − | 0.807670i | \(-0.700728\pi\) | ||||
−0.589635 | + | 0.807670i | \(0.700728\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.0000 | −0.486611 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.60555 | 0.335793 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −74.0555 | −3.26328 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.18335 | −0.183983 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.6056 | 0.597217 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.2111 | 0.841654 | 0.420827 | − | 0.907141i | \(-0.361740\pi\) | ||||
0.420827 | + | 0.907141i | \(0.361740\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.7889 | 0.734127 | 0.367064 | − | 0.930196i | \(-0.380363\pi\) | ||||
0.367064 | + | 0.930196i | \(0.380363\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.5139 | 0.589794 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −27.4222 | −1.19453 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.90833 | −0.299796 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.69722 | 0.203459 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.2111 | 0.614400 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.9361 | 0.946612 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.60555 | −0.0691560 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.02776 | −0.388134 | −0.194067 | − | 0.980988i | \(-0.562168\pi\) | ||||
−0.194067 | + | 0.980988i | \(0.562168\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.0000 | 0.815368 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −58.1472 | −2.49075 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.3305 | 0.484459 | 0.242229 | − | 0.970219i | \(-0.422121\pi\) | ||||
0.242229 | + | 0.970219i | \(0.422121\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.90833 | −0.252161 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.2111 | −0.520210 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.4222 | 0.655819 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.90833 | −0.293242 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 37.8167 | 1.60234 | 0.801172 | − | 0.598435i | \(-0.204210\pi\) | ||||
0.801172 | + | 0.598435i | \(0.204210\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.908327 | −0.0384181 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.2111 | −0.515553 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.5416 | 0.655002 | 0.327501 | − | 0.944851i | \(-0.393794\pi\) | ||||
0.327501 | + | 0.944851i | \(0.393794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.30278 | −0.307230 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.2111 | −1.22459 | −0.612297 | − | 0.790628i | \(-0.709754\pi\) | ||||
−0.612297 | + | 0.790628i | \(0.709754\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.2111 | −1.85018 | −0.925089 | − | 0.379752i | \(-0.876009\pi\) | ||||
−0.925089 | + | 0.379752i | \(0.876009\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.39445 | 0.0582539 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.5139 | −0.563568 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0000 | 0.582828 | 0.291414 | − | 0.956597i | \(-0.405874\pi\) | ||||
0.291414 | + | 0.956597i | \(0.405874\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.0278 | 0.624532 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.78890 | −0.0742160 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.88057 | 0.326380 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.60555 | 0.231761 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.4861 | −0.721729 | −0.360865 | − | 0.932618i | \(-0.617518\pi\) | ||||
−0.360865 | + | 0.932618i | \(0.617518\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.4222 | −1.12991 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.9361 | −0.861195 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.6056 | 1.17469 | 0.587345 | − | 0.809337i | \(-0.300173\pi\) | ||||
0.587345 | + | 0.809337i | \(0.300173\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.7250 | −1.34159 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.90833 | −0.364594 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.5416 | −1.12532 | −0.562660 | − | 0.826688i | \(-0.690222\pi\) | ||||
−0.562660 | + | 0.826688i | \(0.690222\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.5416 | 1.08266 | 0.541328 | − | 0.840812i | \(-0.317922\pi\) | ||||
0.541328 | + | 0.840812i | \(0.317922\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.69722 | 0.394902 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 36.2389 | 1.47332 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.5416 | 1.36141 | 0.680706 | − | 0.732556i | \(-0.261673\pi\) | ||||
0.680706 | + | 0.732556i | \(0.261673\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.60555 | 0.0650602 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.39445 | −0.137325 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.6333 | 0.591034 | 0.295517 | − | 0.955338i | \(-0.404508\pi\) | ||||
0.295517 | + | 0.955338i | \(0.404508\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.5139 | −0.625580 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.6972 | 0.672205 | 0.336102 | − | 0.941825i | \(-0.390891\pi\) | ||||
0.336102 | + | 0.941825i | \(0.390891\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.6972 | 1.47499 | 0.737493 | − | 0.675355i | \(-0.236009\pi\) | ||||
0.737493 | + | 0.675355i | \(0.236009\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.51388 | −0.100716 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 90.0555 | 3.60222 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.2111 | −0.487664 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.2111 | 0.486889 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.6056 | 0.939722 | 0.469861 | − | 0.882740i | \(-0.344304\pi\) | ||||
0.469861 | + | 0.882740i | \(0.344304\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.3944 | −0.731114 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 30.6333 | 1.21565 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.30278 | −0.0516179 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.09167 | 0.0827453 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.5416 | 0.929839 | 0.464919 | − | 0.885353i | \(-0.346083\pi\) | ||||
0.464919 | + | 0.885353i | \(0.346083\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.9083 | 1.17947 | 0.589735 | − | 0.807597i | \(-0.299232\pi\) | ||||
0.589735 | + | 0.807597i | \(0.299232\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.00000 | 0.118125 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.51388 | 0.0595167 | 0.0297583 | − | 0.999557i | \(-0.490526\pi\) | ||||
0.0297583 | + | 0.999557i | \(0.490526\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.0917 | 0.435386 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.60555 | 0.141313 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.09167 | 0.277519 | 0.138759 | − | 0.990326i | \(-0.455689\pi\) | ||||
0.138759 | + | 0.990326i | \(0.455689\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −63.7527 | −2.49103 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.0000 | 0.429151 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.8167 | −1.35626 | −0.678132 | − | 0.734940i | \(-0.737210\pi\) | ||||
−0.678132 | + | 0.734940i | \(0.737210\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.4222 | 0.911018 | 0.455509 | − | 0.890231i | \(-0.349457\pi\) | ||||
0.455509 | + | 0.890231i | \(0.349457\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.90833 | −0.384808 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −32.7250 | −1.26902 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.60555 | −0.0621672 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.7250 | 0.569301 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.48612 | 0.366208 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.00000 | 0.192736 | 0.0963679 | − | 0.995346i | \(-0.469277\pi\) | ||||
0.0963679 | + | 0.995346i | \(0.469277\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −13.5139 | −0.520149 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.88057 | −0.187576 | −0.0937878 | − | 0.995592i | \(-0.529898\pi\) | ||||
−0.0937878 | + | 0.995592i | \(0.529898\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.2111 | −0.698878 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.09167 | −0.0418330 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.6333 | 0.483400 | 0.241700 | − | 0.970351i | \(-0.422295\pi\) | ||||
0.241700 | + | 0.970351i | \(0.422295\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.90833 | −0.263954 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.1194 | 0.843909 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.39445 | 0.243609 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.9083 | −0.529098 | −0.264549 | − | 0.964372i | \(-0.585223\pi\) | ||||
−0.264549 | + | 0.964372i | \(0.585223\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.60555 | 0.0609898 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −43.5416 | −1.65163 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.4222 | 1.03869 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.1194 | 0.685340 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.9361 | −1.05513 | −0.527566 | − | 0.849514i | \(-0.676895\pi\) | ||||
−0.527566 | + | 0.849514i | \(0.676895\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.2111 | 0.460550 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.2111 | 0.422235 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.51388 | −0.207371 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.11943 | 0.192264 | 0.0961321 | − | 0.995369i | \(-0.469353\pi\) | ||||
0.0961321 | + | 0.995369i | \(0.469353\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.4222 | −0.578378 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.60555 | −0.135029 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.00000 | −0.336581 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.90833 | 0.183305 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.8444 | −0.590897 | −0.295448 | − | 0.955359i | \(-0.595469\pi\) | ||||
−0.295448 | + | 0.955359i | \(0.595469\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.2111 | −0.640975 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.21110 | 0.230993 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.6972 | 0.805815 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.6056 | −0.504602 | −0.252301 | − | 0.967649i | \(-0.581187\pi\) | ||||
−0.252301 | + | 0.967649i | \(0.581187\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.30278 | −0.196130 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.972244 | −0.0359106 | −0.0179553 | − | 0.999839i | \(-0.505716\pi\) | ||||
−0.0179553 | + | 0.999839i | \(0.505716\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.30278 | 0.158710 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.5694 | −0.573506 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.1833 | −0.558528 | −0.279264 | − | 0.960214i | \(-0.590091\pi\) | ||||
−0.279264 | + | 0.960214i | \(0.590091\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.90833 | −0.363991 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.5139 | 1.66974 | 0.834871 | − | 0.550445i | \(-0.185542\pi\) | ||||
0.834871 | + | 0.550445i | \(0.185542\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 97.2666 | 3.56357 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.78890 | 0.0654523 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.30278 | 0.120681 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.93608 | 0.143630 | 0.0718149 | − | 0.997418i | \(-0.477121\pi\) | ||||
0.0718149 | + | 0.997418i | \(0.477121\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −25.8167 | −0.940811 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.00000 | −0.218362 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.816654 | −0.0296818 | −0.0148409 | − | 0.999890i | \(-0.504724\pi\) | ||||
−0.0148409 | + | 0.999890i | \(0.504724\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.60555 | −0.0582778 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.6333 | 1.00171 | 0.500853 | − | 0.865532i | \(-0.333020\pi\) | ||||
0.500853 | + | 0.865532i | \(0.333020\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.5139 | −0.489235 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 32.7250 | 1.18317 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.00000 | 0.324971 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.81665 | −0.353998 | −0.176999 | − | 0.984211i | \(-0.556639\pi\) | ||||
−0.176999 | + | 0.984211i | \(0.556639\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.18335 | −0.150660 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.2111 | 0.439203 | 0.219601 | − | 0.975590i | \(-0.429524\pi\) | ||||
0.219601 | + | 0.975590i | \(0.429524\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 48.7250 | 1.75025 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.60555 | −0.0575988 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.4222 | 0.982502 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.35829 | −0.120169 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.60555 | −0.0573777 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42.2389 | 1.50757 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.88057 | −0.209620 | −0.104810 | − | 0.994492i | \(-0.533423\pi\) | ||||
−0.104810 | + | 0.994492i | \(0.533423\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.4222 | −0.691449 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.69722 | −0.0603464 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.69722 | 0.273336 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −21.1194 | −0.749029 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.1833 | −0.998305 | −0.499153 | − | 0.866514i | \(-0.666355\pi\) | ||||
−0.499153 | + | 0.866514i | \(0.666355\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.8167 | −0.701063 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.51388 | 0.0888235 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.6611 | −0.623245 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.30278 | −0.151653 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.1194 | 0.461826 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.48612 | 0.263198 | 0.131599 | − | 0.991303i | \(-0.457989\pi\) | ||||
0.131599 | + | 0.991303i | \(0.457989\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.6333 | −1.14591 | −0.572955 | − | 0.819587i | \(-0.694203\pi\) | ||||
−0.572955 | + | 0.819587i | \(0.694203\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.4222 | 1.03188 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −69.3583 | −2.42951 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.30278 | −0.185521 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.30278 | 0.0455227 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.4500 | 1.65602 | 0.828008 | − | 0.560717i | \(-0.189474\pi\) | ||||
0.828008 | + | 0.560717i | \(0.189474\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.4861 | −1.06268 | −0.531340 | − | 0.847159i | \(-0.678311\pi\) | ||||
−0.531340 | + | 0.847159i | \(0.678311\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21.6972 | 0.755400 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.3028 | 0.914637 | 0.457319 | − | 0.889303i | \(-0.348810\pi\) | ||||
0.457319 | + | 0.889303i | \(0.348810\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.8167 | 0.792455 | 0.396228 | − | 0.918152i | \(-0.370319\pi\) | ||||
0.396228 | + | 0.918152i | \(0.370319\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.5416 | 1.02479 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.60555 | −0.263517 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −94.7805 | −3.28001 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.60555 | −0.124626 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.5416 | 0.881795 | 0.440898 | − | 0.897557i | \(-0.354660\pi\) | ||||
0.440898 | + | 0.897557i | \(0.354660\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.4222 | −0.911111 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.605551 | 0.0208563 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 48.6333 | 1.67304 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.42221 | 0.289390 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.6972 | −0.744647 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.60555 | 0.0550376 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.60555 | 0.157691 | 0.0788455 | − | 0.996887i | \(-0.474877\pi\) | ||||
0.0788455 | + | 0.996887i | \(0.474877\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 32.7250 | 1.11917 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.0278 | −0.923251 | −0.461625 | − | 0.887075i | \(-0.652734\pi\) | ||||
−0.461625 | + | 0.887075i | \(0.652734\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.0555 | −1.50315 | −0.751577 | − | 0.659645i | \(-0.770707\pi\) | ||||
−0.751577 | + | 0.659645i | \(0.770707\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.60555 | −0.122877 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.81665 | 0.334163 | 0.167081 | − | 0.985943i | \(-0.446566\pi\) | ||||
0.167081 | + | 0.985943i | \(0.446566\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 58.5416 | 1.99048 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −40.8444 | −1.38715 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.7611 | 0.839964 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.6333 | −0.428063 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.2111 | 0.616352 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.6333 | 1.23843 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.0000 | −1.08056 | −0.540282 | − | 0.841484i | \(-0.681682\pi\) | ||||
−0.540282 | + | 0.841484i | \(0.681682\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 33.2111 | 1.12018 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.2389 | 1.62521 | 0.812604 | − | 0.582816i | \(-0.198049\pi\) | ||||
0.812604 | + | 0.582816i | \(0.198049\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.90833 | 0.131526 | 0.0657628 | − | 0.997835i | \(-0.479052\pi\) | ||||
0.0657628 | + | 0.997835i | \(0.479052\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −29.7250 | −0.999194 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.5139 | 0.554482 | 0.277241 | − | 0.960800i | \(-0.410580\pi\) | ||||
0.277241 | + | 0.960800i | \(0.410580\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.11943 | 0.238778 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.60555 | −0.0537880 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −19.8167 | −0.663139 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 94.3860 | 3.15498 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.30278 | −0.0434984 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.78890 | 0.193071 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.3305 | 1.24366 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.697224 | 0.0232022 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 81.7527 | 2.71755 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.2750 | −0.573608 | −0.286804 | − | 0.957989i | \(-0.592593\pi\) | ||||
−0.286804 | + | 0.957989i | \(0.592593\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.51388 | 0.182884 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.3944 | 0.576304 | 0.288152 | − | 0.957585i | \(-0.406959\pi\) | ||||
0.288152 | + | 0.957585i | \(0.406959\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.87217 | −0.0950548 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −25.4222 | −0.840432 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.8167 | −0.489289 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.0278 | −0.924550 | −0.462275 | − | 0.886737i | \(-0.652967\pi\) | ||||
−0.462275 | + | 0.886737i | \(0.652967\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.3944 | 0.606118 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.72498 | −0.0896938 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.6972 | −0.713400 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.2111 | 0.565287 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.3028 | −1.25667 | −0.628337 | − | 0.777942i | \(-0.716264\pi\) | ||||
−0.628337 | + | 0.777942i | \(0.716264\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.60555 | −0.249262 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.1194 | 0.494988 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −52.5416 | −1.71830 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.0278 | −1.37299 | −0.686493 | − | 0.727136i | \(-0.740851\pi\) | ||||
−0.686493 | + | 0.727136i | \(0.740851\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.57779 | 0.0514894 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.21110 | 0.300273 | 0.150137 | − | 0.988665i | \(-0.452029\pi\) | ||||
0.150137 | + | 0.988665i | \(0.452029\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.60555 | 0.117413 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.30278 | −0.139969 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.8444 | 1.26227 | 0.631137 | − | 0.775671i | \(-0.282589\pi\) | ||||
0.631137 | + | 0.775671i | \(0.282589\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.3305 | −0.465189 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.3028 | 0.528654 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.72498 | −0.185450 | −0.0927252 | − | 0.995692i | \(-0.529558\pi\) | ||||
−0.0927252 | + | 0.995692i | \(0.529558\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.00000 | 0.194155 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.57779 | 0.0833283 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.60555 | −0.0518460 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.0000 | −0.580645 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.30278 | −0.106430 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 64.6611 | 2.08151 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.0555 | 1.80262 | 0.901312 | − | 0.433171i | \(-0.142605\pi\) | ||||
0.901312 | + | 0.433171i | \(0.142605\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −57.8444 | −1.85823 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.9361 | 1.69880 | 0.849400 | − | 0.527750i | \(-0.176964\pi\) | ||||
0.849400 | + | 0.527750i | \(0.176964\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.1194 | −0.324414 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.6056 | 0.563829 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.3028 | −0.553565 | −0.276782 | − | 0.960933i | \(-0.589268\pi\) | ||||
−0.276782 | + | 0.960933i | \(0.589268\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.03616 | −0.128996 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.5139 | 0.431465 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.4222 | 1.00221 | 0.501106 | − | 0.865386i | \(-0.332927\pi\) | ||||
0.501106 | + | 0.865386i | \(0.332927\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −90.0833 | −2.87029 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.60555 | 0.0829356 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.697224 | −0.0221704 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.9638 | 1.65069 | 0.825343 | − | 0.564632i | \(-0.190982\pi\) | ||||
0.825343 | + | 0.564632i | \(0.190982\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.00000 | 0.0634681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −38.3305 | −1.21516 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.8167 | −0.785951 | −0.392976 | − | 0.919549i | \(-0.628554\pi\) | ||||
−0.392976 | + | 0.919549i | \(0.628554\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.60555 | 0.0507974 |
(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 | 1932.2.a.c.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 5796.2.a.m.1.2 | 2 | |||
4.3 | odd | 2 | 7728.2.a.bf.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1932.2.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
5796.2.a.m.1.2 | 2 | 3.2 | odd | 2 | |||
7728.2.a.bf.1.1 | 2 | 4.3 | odd | 2 |