Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3856,2,Mod(1,3856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3856.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3856 = 2^{4} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3856.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: | \(30.7903150194\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} - 328 x^{3} - 45 x^{2} + 18 x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 241) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.342147\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3856.1 |
$q$-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 | ||||||||
\(3\) | −2.18519 | −1.26162 | −0.630811 | − | 0.775936i | \(-0.717278\pi\) | ||||
−0.630811 | + | 0.775936i | \(0.717278\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.548903 | −0.245477 | −0.122738 | − | 0.992439i | \(-0.539168\pi\) | ||||
−0.122738 | + | 0.992439i | \(0.539168\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.82459 | −0.689631 | −0.344815 | − | 0.938671i | \(-0.612058\pi\) | ||||
−0.344815 | + | 0.938671i | \(0.612058\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.77508 | 0.591692 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.99218 | −1.80671 | −0.903355 | − | 0.428894i | \(-0.858904\pi\) | ||||
−0.903355 | + | 0.428894i | \(0.858904\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.70515 | 1.02762 | 0.513812 | − | 0.857903i | \(-0.328233\pi\) | ||||
0.513812 | + | 0.857903i | \(0.328233\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.19946 | 0.309699 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.64451 | −0.398851 | −0.199426 | − | 0.979913i | \(-0.563908\pi\) | ||||
−0.199426 | + | 0.979913i | \(0.563908\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.15821 | 0.724543 | 0.362271 | − | 0.932073i | \(-0.382001\pi\) | ||||
0.362271 | + | 0.932073i | \(0.382001\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.98709 | 0.870054 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.46015 | 1.13852 | 0.569260 | − | 0.822158i | \(-0.307230\pi\) | ||||
0.569260 | + | 0.822158i | \(0.307230\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.69871 | −0.939741 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.67670 | 0.515130 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.24801 | 1.34592 | 0.672961 | − | 0.739678i | \(-0.265022\pi\) | ||||
0.672961 | + | 0.739678i | \(0.265022\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.41700 | 1.69134 | 0.845672 | − | 0.533703i | \(-0.179200\pi\) | ||||
0.845672 | + | 0.533703i | \(0.179200\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13.0941 | 2.27939 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00152 | 0.169288 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.27680 | 0.209904 | 0.104952 | − | 0.994477i | \(-0.466531\pi\) | ||||
0.104952 | + | 0.994477i | \(0.466531\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.09648 | −1.29647 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.81239 | −0.907743 | −0.453872 | − | 0.891067i | \(-0.649958\pi\) | ||||
−0.453872 | + | 0.891067i | \(0.649958\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.82887 | −1.19389 | −0.596946 | − | 0.802281i | \(-0.703619\pi\) | ||||
−0.596946 | + | 0.802281i | \(0.703619\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.974345 | −0.145247 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.61568 | −0.381537 | −0.190768 | − | 0.981635i | \(-0.561098\pi\) | ||||
−0.190768 | + | 0.981635i | \(0.561098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.67086 | −0.524409 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.59356 | 0.503200 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.81076 | 1.21025 | 0.605126 | − | 0.796130i | \(-0.293123\pi\) | ||||
0.605126 | + | 0.796130i | \(0.293123\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.28912 | 0.443505 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.90130 | −0.914100 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.78270 | 1.01322 | 0.506610 | − | 0.862175i | \(-0.330898\pi\) | ||||
0.506610 | + | 0.862175i | \(0.330898\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.03194 | 0.132127 | 0.0660635 | − | 0.997815i | \(-0.478956\pi\) | ||||
0.0660635 | + | 0.997815i | \(0.478956\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.23879 | −0.408049 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.03377 | −0.252258 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.39801 | 1.02598 | 0.512990 | − | 0.858395i | \(-0.328538\pi\) | ||||
0.512990 | + | 0.858395i | \(0.328538\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.9315 | −1.43638 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.1691 | −1.56288 | −0.781440 | − | 0.623981i | \(-0.785514\pi\) | ||||
−0.781440 | + | 0.623981i | \(0.785514\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.3963 | −1.56792 | −0.783959 | − | 0.620813i | \(-0.786803\pi\) | ||||
−0.783959 | + | 0.620813i | \(0.786803\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.2676 | 1.18560 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.9333 | 1.24596 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.6362 | 1.19666 | 0.598332 | − | 0.801248i | \(-0.295830\pi\) | ||||
0.598332 | + | 0.801248i | \(0.295830\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1743 | −1.24159 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.25636 | −0.686725 | −0.343362 | − | 0.939203i | \(-0.611566\pi\) | ||||
−0.343362 | + | 0.939203i | \(0.611566\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.902673 | 0.0979087 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −15.8383 | −1.69805 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.94129 | −0.417776 | −0.208888 | − | 0.977940i | \(-0.566984\pi\) | ||||
−0.208888 | + | 0.977940i | \(0.566984\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.76039 | −0.708681 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20.5780 | −2.13384 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.73355 | −0.177858 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.22451 | −0.225865 | −0.112933 | − | 0.993603i | \(-0.536024\pi\) | ||||
−0.112933 | + | 0.993603i | \(0.536024\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.6366 | −1.06902 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.24027 | −0.421923 | −0.210962 | − | 0.977494i | \(-0.567659\pi\) | ||||
−0.210962 | + | 0.977494i | \(0.567659\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.164858 | −0.0162439 | −0.00812196 | − | 0.999967i | \(-0.502585\pi\) | ||||
−0.00812196 | + | 0.999967i | \(0.502585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.18852 | −0.213578 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.28536 | −0.897650 | −0.448825 | − | 0.893620i | \(-0.648157\pi\) | ||||
−0.448825 | + | 0.893620i | \(0.648157\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.1952 | 1.16809 | 0.584044 | − | 0.811722i | \(-0.301470\pi\) | ||||
0.584044 | + | 0.811722i | \(0.301470\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.79005 | −0.264820 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.1834 | 1.24019 | 0.620093 | − | 0.784528i | \(-0.287095\pi\) | ||||
0.620093 | + | 0.784528i | \(0.287095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.99709 | −0.279480 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.57693 | 0.608037 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.00055 | 0.275060 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.9062 | 2.26420 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.7012 | 1.14523 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.32365 | 0.476161 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.7563 | 1.04321 | 0.521603 | − | 0.853188i | \(-0.325334\pi\) | ||||
0.521603 | + | 0.853188i | \(0.325334\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.1076 | 1.50624 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.0839 | −1.23051 | −0.615257 | − | 0.788326i | \(-0.710948\pi\) | ||||
−0.615257 | + | 0.788326i | \(0.710948\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.76244 | −0.499667 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.46925 | −0.126453 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.3993 | −1.05935 | −0.529673 | − | 0.848202i | \(-0.677685\pi\) | ||||
−0.529673 | + | 0.848202i | \(0.677685\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.5456 | 0.894464 | 0.447232 | − | 0.894418i | \(-0.352410\pi\) | ||||
0.447232 | + | 0.894418i | \(0.352410\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.71578 | 0.481356 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.2019 | −1.85662 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.97845 | −0.330393 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.02156 | 0.661607 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.30604 | −0.762380 | −0.381190 | − | 0.924497i | \(-0.624486\pi\) | ||||
−0.381190 | + | 0.924497i | \(0.624486\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.2870 | −0.837143 | −0.418572 | − | 0.908184i | \(-0.637469\pi\) | ||||
−0.418572 | + | 0.908184i | \(0.637469\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.91912 | −0.235997 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.16902 | −0.415186 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.23848 | −0.338268 | −0.169134 | − | 0.985593i | \(-0.554097\pi\) | ||||
−0.169134 | + | 0.985593i | \(0.554097\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.2532 | −1.52688 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.96254 | −0.785159 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.42582 | 0.503309 | 0.251655 | − | 0.967817i | \(-0.419025\pi\) | ||||
0.251655 | + | 0.967817i | \(0.419025\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.18738 | −0.559536 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.96260 | −0.306636 | −0.153318 | − | 0.988177i | \(-0.548996\pi\) | ||||
−0.153318 | + | 0.988177i | \(0.548996\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.728137 | 0.0560105 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.60606 | 0.428706 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.45221 | −0.642610 | −0.321305 | − | 0.946976i | \(-0.604121\pi\) | ||||
−0.321305 | + | 0.946976i | \(0.604121\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.57322 | 0.648075 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.0067 | −1.27830 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.5847 | 0.791138 | 0.395569 | − | 0.918436i | \(-0.370547\pi\) | ||||
0.395569 | + | 0.918436i | \(0.370547\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.4914 | −1.44879 | −0.724394 | − | 0.689387i | \(-0.757880\pi\) | ||||
−0.724394 | + | 0.689387i | \(0.757880\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.25500 | −0.166694 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.700837 | −0.0515265 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.85417 | 0.720608 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.88388 | −0.355250 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.21537 | 0.160298 | 0.0801491 | − | 0.996783i | \(-0.474460\pi\) | ||||
0.0801491 | + | 0.996783i | \(0.474460\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.84755 | −0.636861 | −0.318430 | − | 0.947946i | \(-0.603156\pi\) | ||||
−0.318430 | + | 0.947946i | \(0.603156\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.44418 | 0.318254 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.19744 | 0.441549 | 0.220775 | − | 0.975325i | \(-0.429141\pi\) | ||||
0.220775 | + | 0.975325i | \(0.429141\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.2303 | −1.43409 | −0.717043 | − | 0.697028i | \(-0.754505\pi\) | ||||
−0.717043 | + | 0.697028i | \(0.754505\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.3513 | −1.29440 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.2247 | −0.928190 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.19044 | 0.222830 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.69219 | 0.673653 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.9245 | −1.30904 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.96502 | −0.135278 | −0.0676388 | − | 0.997710i | \(-0.521547\pi\) | ||||
−0.0676388 | + | 0.997710i | \(0.521547\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 28.7769 | 1.97176 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.29729 | 0.293073 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.1822 | −1.16640 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 29.2735 | 1.97812 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.09314 | −0.409869 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.4906 | −1.43911 | −0.719557 | − | 0.694433i | \(-0.755655\pi\) | ||||
−0.719557 | + | 0.694433i | \(0.755655\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.34056 | −0.556038 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.7806 | −1.37925 | −0.689627 | − | 0.724165i | \(-0.742226\pi\) | ||||
−0.689627 | + | 0.724165i | \(0.742226\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.4761 | 1.88176 | 0.940878 | − | 0.338746i | \(-0.110003\pi\) | ||||
0.940878 | + | 0.338746i | \(0.110003\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −23.8914 | −1.57194 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.19220 | −0.143616 | −0.0718079 | − | 0.997418i | \(-0.522877\pi\) | ||||
−0.0718079 | + | 0.997418i | \(0.522877\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.43576 | 0.0936584 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −23.2421 | −1.50974 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.2449 | −1.63296 | −0.816478 | − | 0.577377i | \(-0.804076\pi\) | ||||
−0.816478 | + | 0.577377i | \(0.804076\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.3880 | 1.05129 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.01495 | 0.128730 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.7016 | 0.744557 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.6714 | 0.866388 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.2167 | −1.33919 | −0.669593 | − | 0.742728i | \(-0.733532\pi\) | ||||
−0.669593 | + | 0.742728i | \(0.733532\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.7182 | −2.05698 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.97252 | −0.123524 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.1130 | 1.19224 | 0.596119 | − | 0.802896i | \(-0.296708\pi\) | ||||
0.596119 | + | 0.802896i | \(0.296708\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.32963 | −0.144756 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.8658 | 0.796372 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.7792 | 0.787999 | 0.394000 | − | 0.919111i | \(-0.371091\pi\) | ||||
0.394000 | + | 0.919111i | \(0.371091\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.83625 | −0.297089 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.61249 | 0.527076 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.65545 | 0.100934 | 0.0504672 | − | 0.998726i | \(-0.483929\pi\) | ||||
0.0504672 | + | 0.998726i | \(0.483929\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.0226 | 1.03405 | 0.517023 | − | 0.855971i | \(-0.327040\pi\) | ||||
0.517023 | + | 0.855971i | \(0.327040\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.7728 | 0.894088 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 28.1555 | 1.69784 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.8245 | 1.01089 | 0.505443 | − | 0.862860i | \(-0.331329\pi\) | ||||
0.505443 | + | 0.862860i | \(0.331329\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.7159 | 1.00076 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.1664 | −0.964405 | −0.482203 | − | 0.876060i | \(-0.660163\pi\) | ||||
−0.482203 | + | 0.876060i | \(0.660163\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.53878 | −0.150915 | −0.0754573 | − | 0.997149i | \(-0.524042\pi\) | ||||
−0.0754573 | + | 0.997149i | \(0.524042\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.78814 | 0.224390 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.6052 | 0.626008 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.2956 | −0.840918 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.86100 | 0.284957 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.8971 | −1.33767 | −0.668833 | − | 0.743413i | \(-0.733206\pi\) | ||||
−0.668833 | + | 0.743413i | \(0.733206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.27194 | −0.248722 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −16.0392 | −0.930691 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.2307 | 1.16997 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.2845 | 0.823345 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.26583 | 0.532308 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.566437 | −0.0324341 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.71512 | 0.269106 | 0.134553 | − | 0.990906i | \(-0.457040\pi\) | ||||
0.134553 | + | 0.990906i | \(0.457040\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.360246 | 0.0204937 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.63908 | −0.263058 | −0.131529 | − | 0.991312i | \(-0.541989\pi\) | ||||
−0.131529 | + | 0.991312i | \(0.541989\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.04057 | −0.284910 | −0.142455 | − | 0.989801i | \(-0.545500\pi\) | ||||
−0.142455 | + | 0.989801i | \(0.545500\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.77778 | 0.100167 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.0992 | −1.57821 | −0.789105 | − | 0.614259i | \(-0.789455\pi\) | ||||
−0.789105 | + | 0.614259i | \(0.789455\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −43.4314 | −2.43169 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.2903 | 1.13250 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.19369 | −0.288985 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.4094 | −0.965700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −26.6489 | −1.47369 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.77256 | 0.263120 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.6777 | −1.63124 | −0.815618 | − | 0.578590i | \(-0.803603\pi\) | ||||
−0.815618 | + | 0.578590i | \(0.803603\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.26641 | 0.124199 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.60969 | −0.251854 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.2225 | −0.665799 | −0.332900 | − | 0.942962i | \(-0.608027\pi\) | ||||
−0.332900 | + | 0.942962i | \(0.608027\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −28.8082 | −1.56465 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −56.4284 | −3.05577 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.4700 | 1.05128 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.54923 | 0.352599 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.9815 | 0.965296 | 0.482648 | − | 0.875814i | \(-0.339675\pi\) | ||||
0.482648 | + | 0.875814i | \(0.339675\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.2848 | 1.40699 | 0.703496 | − | 0.710699i | \(-0.251621\pi\) | ||||
0.703496 | + | 0.710699i | \(0.251621\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.91756 | 0.529360 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.7610 | −0.732424 | −0.366212 | − | 0.930531i | \(-0.619346\pi\) | ||||
−0.366212 | + | 0.930531i | \(0.619346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.22853 | 0.383651 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.55679 | −0.347022 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.32555 | 0.0699598 | 0.0349799 | − | 0.999388i | \(-0.488863\pi\) | ||||
0.0349799 | + | 0.999388i | \(0.488863\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.02572 | −0.475038 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −54.4249 | −2.85657 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.35326 | 0.384887 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.05979 | −0.316319 | −0.158159 | − | 0.987414i | \(-0.550556\pi\) | ||||
−0.158159 | + | 0.987414i | \(0.550556\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.3174 | −0.537105 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.0760 | −0.834627 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.4445 | 1.05858 | 0.529288 | − | 0.848442i | \(-0.322459\pi\) | ||||
0.529288 | + | 0.848442i | \(0.322459\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.6332 | −0.600736 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.8550 | 1.38310 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.4042 | −1.81859 | −0.909296 | − | 0.416150i | \(-0.863379\pi\) | ||||
−0.909296 | + | 0.416150i | \(0.863379\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −25.6899 | −1.31613 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.79327 | −0.347120 | −0.173560 | − | 0.984823i | \(-0.555527\pi\) | ||||
−0.173560 | + | 0.984823i | \(0.555527\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00131 | −0.305855 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.8969 | −0.706417 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.6869 | 1.25168 | 0.625838 | − | 0.779953i | \(-0.284757\pi\) | ||||
0.625838 | + | 0.779953i | \(0.284757\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.97924 | −0.454100 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 30.7760 | 1.55245 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.83823 | −0.293753 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.3804 | 0.721730 | 0.360865 | − | 0.932618i | \(-0.382482\pi\) | ||||
0.360865 | + | 0.932618i | \(0.382482\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.5921 | 0.630391 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.62276 | 0.380663 | 0.190331 | − | 0.981720i | \(-0.439044\pi\) | ||||
0.190331 | + | 0.981720i | \(0.439044\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.8914 | 1.73806 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.13362 | 0.304782 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.65079 | −0.379236 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.12423 | 0.253377 | 0.126688 | − | 0.991943i | \(-0.459565\pi\) | ||||
0.126688 | + | 0.991943i | \(0.459565\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 27.0949 | 1.33649 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.2002 | −0.698748 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.43413 | 0.168575 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −23.0441 | −1.12848 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.3513 | −0.652254 | −0.326127 | − | 0.945326i | \(-0.605744\pi\) | ||||
−0.326127 | + | 0.945326i | \(0.605744\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.8059 | 1.35518 | 0.677588 | − | 0.735442i | \(-0.263025\pi\) | ||||
0.677588 | + | 0.735442i | \(0.263025\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.64304 | −0.225752 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.72705 | 0.374817 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.88288 | −0.0911188 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 48.5155 | 2.34235 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.5717 | −0.894567 | −0.447283 | − | 0.894392i | \(-0.647608\pi\) | ||||
−0.447283 | + | 0.894392i | \(0.647608\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.19376 | −0.345710 | −0.172855 | − | 0.984947i | \(-0.555299\pi\) | ||||
−0.172855 | + | 0.984947i | \(0.555299\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.69370 | 0.416831 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.2443 | 0.824906 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.2866 | 0.777315 | 0.388657 | − | 0.921382i | \(-0.372939\pi\) | ||||
0.388657 | + | 0.921382i | \(0.372939\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.51607 | −0.310289 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 37.0915 | 1.76227 | 0.881135 | − | 0.472864i | \(-0.156780\pi\) | ||||
0.881135 | + | 0.472864i | \(0.156780\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.16338 | 0.102554 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.3355 | 0.961837 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.1059 | −0.807275 | −0.403638 | − | 0.914919i | \(-0.632254\pi\) | ||||
−0.403638 | + | 0.914919i | \(0.632254\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.8289 | 1.64003 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.4791 | 1.05616 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.71079 | 0.173965 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.35857 | −0.437776 | −0.218888 | − | 0.975750i | \(-0.570243\pi\) | ||||
−0.218888 | + | 0.975750i | \(0.570243\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.40184 | −0.205460 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.8670 | −0.738999 | −0.369500 | − | 0.929231i | \(-0.620471\pi\) | ||||
−0.369500 | + | 0.929231i | \(0.620471\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.99749 | 0.325201 | 0.162601 | − | 0.986692i | \(-0.448012\pi\) | ||||
0.162601 | + | 0.986692i | \(0.448012\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.2953 | 0.523808 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.2782 | 1.12346 | 0.561729 | − | 0.827321i | \(-0.310136\pi\) | ||||
0.561729 | + | 0.827321i | \(0.310136\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.3229 | −0.707547 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.26191 | 0.426766 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 46.9120 | 2.15702 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.8395 | −0.680882 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.6398 | 0.716096 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.93171 | −0.408100 | −0.204050 | − | 0.978960i | \(-0.565411\pi\) | ||||
−0.204050 | + | 0.978960i | \(0.565411\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.73072 | 0.215702 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.7701 | 0.990574 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.22104 | 0.0554447 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.5963 | −1.56771 | −0.783855 | − | 0.620944i | \(-0.786750\pi\) | ||||
−0.783855 | + | 0.620944i | \(0.786750\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.0417 | −0.634987 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.3798 | −1.55154 | −0.775770 | − | 0.631016i | \(-0.782638\pi\) | ||||
−0.775770 | + | 0.631016i | \(0.782638\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.9194 | −0.536823 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.83845 | 0.262419 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.0281 | 1.07781 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.3126 | −1.71511 | −0.857554 | − | 0.514394i | \(-0.828017\pi\) | ||||
−0.857554 | + | 0.514394i | \(0.828017\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.65906 | 0.386858 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.6073 | 0.562132 | 0.281066 | − | 0.959688i | \(-0.409312\pi\) | ||||
0.281066 | + | 0.959688i | \(0.409312\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.32750 | 0.103572 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.59112 | −0.0706641 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.0748 | −0.845476 | −0.422738 | − | 0.906252i | \(-0.638931\pi\) | ||||
−0.422738 | + | 0.906252i | \(0.638931\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.4428 | 1.08128 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.45356 | 0.373234 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.0904909 | 0.00398750 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.6737 | 0.689326 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.4697 | 0.810731 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.5960 | 0.508028 | 0.254014 | − | 0.967201i | \(-0.418249\pi\) | ||||
0.254014 | + | 0.967201i | \(0.418249\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.2727 | 1.14883 | 0.574413 | − | 0.818566i | \(-0.305230\pi\) | ||||
0.574413 | + | 0.818566i | \(0.305230\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.7342 | −0.817626 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.4863 | −0.674594 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.81324 | 0.296228 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.8149 | 0.599515 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.5358 | −0.932819 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.09676 | 0.220352 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.1296 | −0.998118 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.9965 | 0.947455 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.1441 | −0.651097 | −0.325548 | − | 0.945525i | \(-0.605549\pi\) | ||||
−0.325548 | + | 0.945525i | \(0.605549\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 42.5926 | 1.82782 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.69397 | −0.286738 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.7331 | −1.48508 | −0.742540 | − | 0.669802i | \(-0.766379\pi\) | ||||
−0.742540 | + | 0.669802i | \(0.766379\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.83178 | 0.0781785 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.8907 | 0.975178 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.4067 | −0.825256 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.53146 | 0.0650071 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.1470 | 1.44685 | 0.723427 | − | 0.690401i | \(-0.242566\pi\) | ||||
0.723427 | + | 0.690401i | \(0.242566\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.0071 | −1.22687 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.5333 | −0.909136 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.2900 | 0.812975 | 0.406488 | − | 0.913656i | \(-0.366753\pi\) | ||||
0.406488 | + | 0.913656i | \(0.366753\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.23638 | −0.304437 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 20.3886 | 0.856241 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.4263 | −1.40130 | −0.700652 | − | 0.713503i | \(-0.747107\pi\) | ||||
−0.700652 | + | 0.713503i | \(0.747107\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.07936 | −0.128867 | −0.0644336 | − | 0.997922i | \(-0.520524\pi\) | ||||
−0.0644336 | + | 0.997922i | \(0.520524\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.84101 | −0.202236 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.6556 | −1.06991 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.95435 | −0.247883 | −0.123941 | − | 0.992290i | \(-0.539553\pi\) | ||||
−0.123941 | + | 0.992290i | \(0.539553\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.3336 | 0.803478 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.4153 | 0.473587 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −52.7957 | −2.18657 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.61009 | −0.149259 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −42.0432 | −1.73531 | −0.867655 | − | 0.497167i | \(-0.834374\pi\) | ||||
−0.867655 | + | 0.497167i | \(0.834374\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.7409 | 1.22545 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.5426 | −0.557068 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.9908 | 1.68329 | 0.841645 | − | 0.540031i | \(-0.181587\pi\) | ||||
0.841645 | + | 0.540031i | \(0.181587\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.64701 | −0.0675208 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 44.2071 | 1.80928 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.0862 | 1.10671 | 0.553356 | − | 0.832945i | \(-0.313347\pi\) | ||||
0.553356 | + | 0.832945i | \(0.313347\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.03033 | −0.123610 | −0.0618049 | − | 0.998088i | \(-0.519686\pi\) | ||||
−0.0618049 | + | 0.998088i | \(0.519686\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.9071 | 0.607064 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.6711 | −0.555809 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.560838 | −0.0227637 | −0.0113818 | − | 0.999935i | \(-0.503623\pi\) | ||||
−0.0113818 | + | 0.999935i | \(0.503623\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 28.8985 | 1.17103 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.69150 | −0.392076 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.7388 | 0.958801 | 0.479401 | − | 0.877596i | \(-0.340854\pi\) | ||||
0.479401 | + | 0.877596i | \(0.340854\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.97173 | −0.281127 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.2411 | −0.412290 | −0.206145 | − | 0.978521i | \(-0.566092\pi\) | ||||
−0.206145 | + | 0.978521i | \(0.566092\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.8348 | 1.11878 | 0.559388 | − | 0.828906i | \(-0.311036\pi\) | ||||
0.559388 | + | 0.828906i | \(0.311036\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.6152 | 0.586486 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.19125 | 0.288111 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.5714 | 0.822855 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 41.3538 | 1.65151 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.09970 | −0.0837204 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.0564 | −0.917861 | −0.458931 | − | 0.888472i | \(-0.651767\pi\) | ||||
−0.458931 | + | 0.888472i | \(0.651767\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.29396 | 0.170669 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.45309 | −0.256083 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.6011 | −0.538895 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.3761 | −0.924744 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.6143 | 1.40668 | 0.703340 | − | 0.710853i | \(-0.251691\pi\) | ||||
0.703340 | + | 0.710853i | \(0.251691\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.2806 | 1.11528 | 0.557639 | − | 0.830084i | \(-0.311707\pi\) | ||||
0.557639 | + | 0.830084i | \(0.311707\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.39042 | −0.369747 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.5953 | −0.573802 | −0.286901 | − | 0.957960i | \(-0.592625\pi\) | ||||
−0.286901 | + | 0.957960i | \(0.592625\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −46.6353 | −1.83060 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 37.5464 | 1.47156 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.0718 | −1.09853 | −0.549267 | − | 0.835647i | \(-0.685093\pi\) | ||||
−0.549267 | + | 0.835647i | \(0.685093\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.73068 | 0.302063 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −23.7794 | −0.927724 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.33181 | 0.0908343 | 0.0454172 | − | 0.998968i | \(-0.485538\pi\) | ||||
0.0454172 | + | 0.998968i | \(0.485538\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.3409 | −0.830063 | −0.415031 | − | 0.909807i | \(-0.636229\pi\) | ||||
−0.415031 | + | 0.909807i | \(0.636229\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.3147 | 0.517100 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.16302 | 0.122657 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 39.5752 | 1.53236 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 46.9611 | 1.81562 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.18360 | −0.238715 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.0948 | −0.967333 | −0.483667 | − | 0.875252i | \(-0.660695\pi\) | ||||
−0.483667 | + | 0.875252i | \(0.660695\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.5770 | −0.484089 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.78669 | −0.299267 | −0.149633 | − | 0.988742i | \(-0.547809\pi\) | ||||
−0.149633 | + | 0.988742i | \(0.547809\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.05883 | 0.155764 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 45.4096 | 1.74010 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.68470 | −0.102727 | −0.0513636 | − | 0.998680i | \(-0.516357\pi\) | ||||
−0.0513636 | + | 0.998680i | \(0.516357\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.80602 | 0.260045 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −62.2259 | −2.37407 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32.6452 | 1.24368 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.3260 | 1.76232 | 0.881162 | − | 0.472814i | \(-0.156762\pi\) | ||||
0.881162 | + | 0.472814i | \(0.156762\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 19.4074 | 0.737227 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.78849 | −0.219570 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.55851 | 0.362054 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.79039 | 0.181189 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.33233 | 0.163630 | 0.0818150 | − | 0.996648i | \(-0.473928\pi\) | ||||
0.0818150 | + | 0.996648i | \(0.473928\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.03239 | 0.152084 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.13741 | −0.118162 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.73677 | 0.290971 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −45.2491 | −1.69936 | −0.849682 | − | 0.527295i | \(-0.823206\pi\) | ||||
−0.849682 | + | 0.527295i | \(0.823206\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.8800 | 0.708057 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 51.4182 | 1.92563 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.1867 | 0.455757 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 55.1650 | 2.06017 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.3560 | −1.28126 | −0.640632 | − | 0.767848i | \(-0.721328\pi\) | ||||
−0.640632 | + | 0.767848i | \(0.721328\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.300798 | 0.0112023 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.18519 | −0.0812683 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −34.0563 | −1.26482 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.1579 | 1.08141 | 0.540703 | − | 0.841213i | \(-0.318158\pi\) | ||||
0.540703 | + | 0.841213i | \(0.318158\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.28799 | −0.0847405 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.8746 | 0.476185 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.8326 | 1.36044 | 0.680222 | − | 0.733007i | \(-0.261884\pi\) | ||||
0.680222 | + | 0.733007i | \(0.261884\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.40305 | −0.162409 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −50.3224 | −1.85365 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.4258 | −0.898517 | −0.449258 | − | 0.893402i | \(-0.648312\pi\) | ||||
−0.449258 | + | 0.893402i | \(0.648312\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.5704 | −0.939350 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.4245 | 0.896049 | 0.448024 | − | 0.894021i | \(-0.352128\pi\) | ||||
0.448024 | + | 0.894021i | \(0.352128\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.10811 | 0.187147 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.1055 | −0.406330 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.9420 | 0.619047 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.0598 | 1.09690 | 0.548449 | − | 0.836184i | \(-0.315219\pi\) | ||||
0.548449 | + | 0.836184i | \(0.315219\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 46.3627 | 1.68955 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.64656 | 0.205499 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.79087 | 0.210473 | 0.105236 | − | 0.994447i | \(-0.466440\pi\) | ||||
0.105236 | + | 0.994447i | \(0.466440\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 71.4956 | 2.59513 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.42691 | 0.0879754 | 0.0439877 | − | 0.999032i | \(-0.485994\pi\) | ||||
0.0439877 | + | 0.999032i | \(0.485994\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.2512 | −0.805549 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.60231 | 0.0579318 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.8361 | 1.04121 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.0750 | 0.796045 | 0.398022 | − | 0.917376i | \(-0.369697\pi\) | ||||
0.398022 | + | 0.917376i | \(0.369697\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −41.7657 | −1.50416 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.7802 | 1.03515 | 0.517576 | − | 0.855637i | \(-0.326834\pi\) | ||||
0.517576 | + | 0.855637i | \(0.326834\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −44.2477 | −1.58943 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.09070 | 0.182628 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.3567 | −0.657699 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 78.9113 | 2.82367 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.4007 | 0.693325 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.32651 | 0.0830369 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.4388 | 1.90489 | 0.952443 | − | 0.304715i | \(-0.0985613\pi\) | ||||
0.952443 | + | 0.304715i | \(0.0985613\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.9250 | −0.994158 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.0543 | −0.855271 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.82351 | 0.135777 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.5682 | 0.374814 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.4149 | 0.368914 | 0.184457 | − | 0.982841i | \(-0.440947\pi\) | ||||
0.184457 | + | 0.982841i | \(0.440947\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.30151 | 0.152176 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.99609 | −0.247195 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 80.2730 | 2.83277 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.46847 | 0.192738 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.61747 | −0.127341 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.9467 | −0.912237 | −0.456118 | − | 0.889919i | \(-0.650761\pi\) | ||||
−0.456118 | + | 0.889919i | \(0.650761\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.1712 | 0.392275 | 0.196137 | − | 0.980576i | \(-0.437160\pi\) | ||||
0.196137 | + | 0.980576i | \(0.437160\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −37.1976 | −1.30458 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.52715 | −0.123551 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.7252 | −0.865026 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.0002 | −0.419321 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.3232 | 0.639484 | 0.319742 | − | 0.947505i | \(-0.396404\pi\) | ||||
0.319742 | + | 0.947505i | \(0.396404\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.1230 | −0.736301 | −0.368150 | − | 0.929766i | \(-0.620009\pi\) | ||||
−0.368150 | + | 0.929766i | \(0.620009\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −61.5252 | −2.14203 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.5383 | −1.65307 | −0.826534 | − | 0.562887i | \(-0.809690\pi\) | ||||
−0.826534 | + | 0.562887i | \(0.809690\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.8701 | 0.551190 | 0.275595 | − | 0.961274i | \(-0.411125\pi\) | ||||
0.275595 | + | 0.961274i | \(0.411125\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.7648 | −1.27536 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.03676 | 0.209161 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.17508 | 0.0752719 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.2065 | 0.871262 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.3114 | −1.18456 | −0.592281 | − | 0.805732i | \(-0.701772\pi\) | ||||
−0.592281 | + | 0.805732i | \(0.701772\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.5337 | 0.811507 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 35.3267 | 1.21672 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.399676 | −0.0137493 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −45.4437 | −1.56146 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.54772 | 0.190397 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.97150 | 0.238980 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.8466 | −1.56976 | −0.784879 | − | 0.619649i | \(-0.787275\pi\) | ||||
−0.784879 | + | 0.619649i | \(0.787275\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.07718 | −0.105237 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.7254 | 0.742125 | 0.371063 | − | 0.928608i | \(-0.378993\pi\) | ||||
0.371063 | + | 0.928608i | \(0.378993\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.5363 | −1.79252 | −0.896258 | − | 0.443534i | \(-0.853725\pi\) | ||||
−0.896258 | + | 0.443534i | \(0.853725\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.1745 | −0.789786 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.9971 | −1.12323 | −0.561617 | − | 0.827397i | \(-0.689821\pi\) | ||||
−0.561617 | + | 0.827397i | \(0.689821\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.63944 | 0.157746 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 31.2387 | 1.06092 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −63.7339 | −2.16202 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.1159 | 1.05432 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.94868 | −0.133643 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.71348 | −0.328376 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.4221 | −0.723372 | −0.361686 | − | 0.932300i | \(-0.617799\pi\) | ||||
−0.361686 | + | 0.932300i | \(0.617799\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 50.0347 | 1.68763 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.1162 | −1.31786 | −0.658929 | − | 0.752205i | \(-0.728990\pi\) | ||||
−0.658929 | + | 0.752205i | \(0.728990\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.84717 | 0.0958150 | 0.0479075 | − | 0.998852i | \(-0.484745\pi\) | ||||
0.0479075 | + | 0.998852i | \(0.484745\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.33503 | 0.313794 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.9262 | 1.57563 | 0.787814 | − | 0.615913i | \(-0.211213\pi\) | ||||
0.787814 | + | 0.615913i | \(0.211213\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.4505 | −0.719428 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 66.9586 | 2.24320 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.26088 | −0.276440 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.80997 | −0.194206 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −44.2080 | −1.47606 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 68.2546 | 2.27642 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.4893 | −0.482710 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −31.2144 | −1.03875 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.6989 | 0.355644 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.7164 | −0.521856 | −0.260928 | − | 0.965358i | \(-0.584028\pi\) | ||||
−0.260928 | + | 0.965358i | \(0.584028\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.52681 | −0.249649 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.0451186 | −0.00149485 | −0.000747423 | − | 1.00000i | \(-0.500238\pi\) | ||||
−0.000747423 | 1.00000i | \(0.500238\pi\) | ||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.4892 | 1.24071 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.23778 | 0.0409196 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25.6973 | 0.848601 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.88987 | 0.260263 | 0.130131 | − | 0.991497i | \(-0.458460\pi\) | ||||
0.130131 | + | 0.991497i | \(0.458460\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.3035 | −0.339511 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −48.7933 | −1.60605 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.99929 | −0.197255 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.292635 | −0.00961140 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.6276 | 0.840815 | 0.420408 | − | 0.907335i | \(-0.361887\pi\) | ||||
0.420408 | + | 0.907335i | \(0.361887\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.5934 | −0.379957 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.1373 | 0.331880 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.40898 | −0.176893 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −57.8627 | −1.89029 | −0.945146 | − | 0.326649i | \(-0.894081\pi\) | ||||
−0.945146 | + | 0.326649i | \(0.894081\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.0146 | 0.359449 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.1272 | −0.460533 | −0.230266 | − | 0.973128i | \(-0.573960\pi\) | ||||
−0.230266 | + | 0.973128i | \(0.573960\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.7365 | −1.03348 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.68077 | 0.0872056 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.5318 | −0.732185 | −0.366092 | − | 0.930578i | \(-0.619305\pi\) | ||||
−0.366092 | + | 0.930578i | \(0.619305\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49.6353 | −1.61123 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 61.4023 | 1.99110 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.0142 | −1.10183 | −0.550914 | − | 0.834562i | \(-0.685721\pi\) | ||||
−0.550914 | + | 0.834562i | \(0.685721\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.21602 | −0.0393495 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 94.9061 | 3.06788 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.6237 | 0.730557 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57.6799 | 1.86064 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.4822 | −0.531133 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.85644 | 0.156334 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 62.1874 | 1.99981 | 0.999906 | − | 0.0137093i | \(-0.00436394\pi\) | ||||
0.999906 | + | 0.0137093i | \(0.00436394\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.3492 | 0.364590 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.4346 | −0.591594 | −0.295797 | − | 0.955251i | \(-0.595585\pi\) | ||||
−0.295797 | + | 0.955251i | \(0.595585\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.2414 | −0.616850 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 38.0430 | 1.21835 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.2228 | 0.806949 | 0.403474 | − | 0.914991i | \(-0.367802\pi\) | ||||
0.403474 | + | 0.914991i | \(0.367802\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.6169 | 0.754800 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.6474 | 0.691148 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.7405 | −0.406358 | −0.203179 | − | 0.979142i | \(-0.565127\pi\) | ||||
−0.203179 | + | 0.979142i | \(0.565127\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.40179 | −0.108390 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.4290 | −0.331958 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42.7468 | −1.35927 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.6775 | −0.498011 | −0.249005 | − | 0.968502i | \(-0.580104\pi\) | ||||
−0.249005 | + | 0.968502i | \(0.580104\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 64.8517 | 2.05801 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.1045 | 0.352035 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.1048 | 0.890088 | 0.445044 | − | 0.895509i | \(-0.353188\pi\) | ||||
0.445044 | + | 0.895509i | \(0.353188\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.41759 | 0.108128 |
(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 | 3856.2.a.n.1.3 | 12 | ||
4.3 | odd | 2 | 241.2.a.b.1.5 | ✓ | 12 | ||
12.11 | even | 2 | 2169.2.a.h.1.8 | 12 | |||
20.19 | odd | 2 | 6025.2.a.h.1.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
241.2.a.b.1.5 | ✓ | 12 | 4.3 | odd | 2 | ||
2169.2.a.h.1.8 | 12 | 12.11 | even | 2 | |||
3856.2.a.n.1.3 | 12 | 1.1 | even | 1 | trivial | ||
6025.2.a.h.1.8 | 12 | 20.19 | odd | 2 |