Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3920,2,Mod(1,3920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3920, 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("3920.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3920.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: | \(31.3013575923\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 980) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3920.1 |
$q$-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 | ||||||||
\(3\) | 2.41421 | 1.39385 | 0.696923 | − | 0.717146i | \(-0.254552\pi\) | ||||
0.696923 | + | 0.717146i | \(0.254552\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.82843 | −0.551292 | −0.275646 | − | 0.961259i | \(-0.588892\pi\) | ||||
−0.275646 | + | 0.961259i | \(0.588892\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.41421 | −1.77898 | −0.889491 | − | 0.456952i | \(-0.848941\pi\) | ||||
−0.889491 | + | 0.456952i | \(0.848941\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.41421 | 0.623347 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.58579 | −0.869681 | −0.434840 | − | 0.900508i | \(-0.643195\pi\) | ||||
−0.434840 | + | 0.900508i | \(0.643195\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.65685 | −1.75660 | −0.878301 | − | 0.478107i | \(-0.841323\pi\) | ||||
−0.878301 | + | 0.478107i | \(0.841323\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.41421 | −0.711913 | −0.355956 | − | 0.934503i | \(-0.615845\pi\) | ||||
−0.355956 | + | 0.934503i | \(0.615845\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.414214 | −0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.65685 | −0.864756 | −0.432378 | − | 0.901692i | \(-0.642325\pi\) | ||||
−0.432378 | + | 0.901692i | \(0.642325\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.41421 | 1.33163 | 0.665816 | − | 0.746116i | \(-0.268084\pi\) | ||||
0.665816 | + | 0.746116i | \(0.268084\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.41421 | −0.768416 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.585786 | −0.0963027 | −0.0481513 | − | 0.998840i | \(-0.515333\pi\) | ||||
−0.0481513 | + | 0.998840i | \(0.515333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15.4853 | −2.47963 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.41421 | −0.533211 | −0.266605 | − | 0.963806i | \(-0.585902\pi\) | ||||
−0.266605 | + | 0.963806i | \(0.585902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.343146 | −0.0523292 | −0.0261646 | − | 0.999658i | \(-0.508329\pi\) | ||||
−0.0261646 | + | 0.999658i | \(0.508329\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.82843 | 0.421637 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.8995 | 1.58985 | 0.794927 | − | 0.606705i | \(-0.207509\pi\) | ||||
0.794927 | + | 0.606705i | \(0.207509\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.65685 | −1.21220 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.2426 | −1.68166 | −0.840828 | − | 0.541302i | \(-0.817931\pi\) | ||||
−0.840828 | + | 0.541302i | \(0.817931\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.82843 | −0.246545 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.4853 | −2.44844 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.585786 | 0.0762629 | 0.0381314 | − | 0.999273i | \(-0.487859\pi\) | ||||
0.0381314 | + | 0.999273i | \(0.487859\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8284 | −1.38644 | −0.693219 | − | 0.720727i | \(-0.743808\pi\) | ||||
−0.693219 | + | 0.720727i | \(0.743808\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.41421 | −0.795585 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.07107 | −0.375191 | −0.187595 | − | 0.982246i | \(-0.560069\pi\) | ||||
−0.187595 | + | 0.982246i | \(0.560069\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.24264 | −0.992297 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.4853 | 1.24437 | 0.622187 | − | 0.782869i | \(-0.286244\pi\) | ||||
0.622187 | + | 0.782869i | \(0.286244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.8284 | −1.26737 | −0.633686 | − | 0.773591i | \(-0.718459\pi\) | ||||
−0.633686 | + | 0.773591i | \(0.718459\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.41421 | 0.278769 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.1421 | 1.70362 | 0.851812 | − | 0.523848i | \(-0.175504\pi\) | ||||
0.851812 | + | 0.523848i | \(0.175504\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.58579 | −0.388933 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.2426 | −1.20534 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.9706 | 1.79888 | 0.899438 | − | 0.437048i | \(-0.143976\pi\) | ||||
0.899438 | + | 0.437048i | \(0.143976\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17.8995 | 1.85609 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.65685 | −0.785577 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.72792 | 0.987721 | 0.493860 | − | 0.869541i | \(-0.335585\pi\) | ||||
0.493860 | + | 0.869541i | \(0.335585\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.17157 | −0.519763 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.828427 | −0.0824316 | −0.0412158 | − | 0.999150i | \(-0.513123\pi\) | ||||
−0.0412158 | + | 0.999150i | \(0.513123\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.41421 | 0.434945 | 0.217473 | − | 0.976066i | \(-0.430219\pi\) | ||||
0.217473 | + | 0.976066i | \(0.430219\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.1716 | 1.08000 | 0.539998 | − | 0.841666i | \(-0.318425\pi\) | ||||
0.539998 | + | 0.841666i | \(0.318425\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.00000 | 0.862044 | 0.431022 | − | 0.902342i | \(-0.358153\pi\) | ||||
0.431022 | + | 0.902342i | \(0.358153\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.41421 | −0.134231 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.07107 | 0.853334 | 0.426667 | − | 0.904409i | \(-0.359688\pi\) | ||||
0.426667 | + | 0.904409i | \(0.359688\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.41421 | −0.318377 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −18.1421 | −1.67724 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.65685 | −0.696078 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.24264 | −0.743214 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.10051 | 0.186390 | 0.0931948 | − | 0.995648i | \(-0.470292\pi\) | ||||
0.0931948 | + | 0.995648i | \(0.470292\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.828427 | −0.0729389 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.2426 | −1.76861 | −0.884304 | − | 0.466912i | \(-0.845367\pi\) | ||||
−0.884304 | + | 0.466912i | \(0.845367\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.414214 | −0.0356498 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.9706 | −1.79164 | −0.895818 | − | 0.444421i | \(-0.853409\pi\) | ||||
−0.895818 | + | 0.444421i | \(0.853409\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.89949 | 0.500389 | 0.250194 | − | 0.968196i | \(-0.419505\pi\) | ||||
0.250194 | + | 0.968196i | \(0.419505\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26.3137 | 2.21601 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.7279 | 0.980738 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.65685 | −0.386731 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.4853 | 1.67822 | 0.839110 | − | 0.543962i | \(-0.183076\pi\) | ||||
0.839110 | + | 0.543962i | \(0.183076\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.17157 | 0.502235 | 0.251118 | − | 0.967957i | \(-0.419202\pi\) | ||||
0.251118 | + | 0.967957i | \(0.419202\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.1421 | −0.819943 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.41421 | 0.595524 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.48528 | 0.517582 | 0.258791 | − | 0.965933i | \(-0.416676\pi\) | ||||
0.258791 | + | 0.965933i | \(0.416676\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −29.5563 | −2.34397 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.55635 | 0.748511 | 0.374256 | − | 0.927326i | \(-0.377898\pi\) | ||||
0.374256 | + | 0.927326i | \(0.377898\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.41421 | −0.343646 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.414214 | −0.0320528 | −0.0160264 | − | 0.999872i | \(-0.505102\pi\) | ||||
−0.0160264 | + | 0.999872i | \(0.505102\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.1421 | 2.16478 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −21.6569 | −1.65614 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.5563 | 0.954642 | 0.477321 | − | 0.878729i | \(-0.341608\pi\) | ||||
0.477321 | + | 0.878729i | \(0.341608\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.41421 | 0.106299 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.4853 | 0.783707 | 0.391853 | − | 0.920028i | \(-0.371834\pi\) | ||||
0.391853 | + | 0.920028i | \(0.371834\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.2426 | −0.761329 | −0.380665 | − | 0.924713i | \(-0.624305\pi\) | ||||
−0.380665 | + | 0.924713i | \(0.624305\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −26.1421 | −1.93248 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.585786 | −0.0430679 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.55635 | 0.479448 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.34315 | −0.386616 | −0.193308 | − | 0.981138i | \(-0.561922\pi\) | ||||
−0.193308 | + | 0.981138i | \(0.561922\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.65685 | −0.407189 | −0.203595 | − | 0.979055i | \(-0.565262\pi\) | ||||
−0.203595 | + | 0.979055i | \(0.565262\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15.4853 | −1.10892 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.55635 | 0.253379 | 0.126690 | − | 0.991942i | \(-0.459565\pi\) | ||||
0.126690 | + | 0.991942i | \(0.459565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.27208 | −0.0901752 | −0.0450876 | − | 0.998983i | \(-0.514357\pi\) | ||||
−0.0450876 | + | 0.998983i | \(0.514357\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.41421 | −0.522958 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.41421 | −0.238459 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.65685 | −0.671198 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.0000 | 0.968400 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.68629 | 0.116089 | 0.0580445 | − | 0.998314i | \(-0.481513\pi\) | ||||
0.0580445 | + | 0.998314i | \(0.481513\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 25.3137 | 1.73447 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.343146 | −0.0234023 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −26.1421 | −1.76652 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.0000 | 1.54715 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.92893 | 0.664890 | 0.332445 | − | 0.943123i | \(-0.392126\pi\) | ||||
0.332445 | + | 0.943123i | \(0.392126\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.82843 | 0.188562 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.7279 | −1.17664 | −0.588322 | − | 0.808627i | \(-0.700211\pi\) | ||||
−0.588322 | + | 0.808627i | \(0.700211\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.10051 | −0.270969 | −0.135485 | − | 0.990779i | \(-0.543259\pi\) | ||||
−0.135485 | + | 0.990779i | \(0.543259\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.8284 | −0.971443 | −0.485721 | − | 0.874114i | \(-0.661443\pi\) | ||||
−0.485721 | + | 0.874114i | \(0.661443\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.8995 | 0.711005 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 36.5563 | 2.37459 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.8284 | −1.28259 | −0.641297 | − | 0.767293i | \(-0.721603\pi\) | ||||
−0.641297 | + | 0.767293i | \(0.721603\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.5563 | −1.77506 | −0.887530 | − | 0.460749i | \(-0.847581\pi\) | ||||
−0.887530 | + | 0.460749i | \(0.847581\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.6569 | −1.38929 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 49.1127 | 3.12497 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.3137 | −1.22396 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.9289 | −0.816067 | −0.408033 | − | 0.912967i | \(-0.633785\pi\) | ||||
−0.408033 | + | 0.912967i | \(0.633785\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.24264 | 0.392471 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.65685 | −0.542113 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.7990 | −0.860757 | −0.430379 | − | 0.902648i | \(-0.641620\pi\) | ||||
−0.430379 | + | 0.902648i | \(0.641620\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.1716 | −0.815300 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.0000 | −0.616626 | −0.308313 | − | 0.951285i | \(-0.599764\pi\) | ||||
−0.308313 | + | 0.951285i | \(0.599764\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.2426 | −0.752059 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 40.9706 | 2.50736 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.72792 | −0.532151 | −0.266075 | − | 0.963952i | \(-0.585727\pi\) | ||||
−0.266075 | + | 0.963952i | \(0.585727\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.97056 | −0.301940 | −0.150970 | − | 0.988538i | \(-0.548240\pi\) | ||||
−0.150970 | + | 0.988538i | \(0.548240\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.82843 | −0.110258 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.58579 | −0.275533 | −0.137767 | − | 0.990465i | \(-0.543992\pi\) | ||||
−0.137767 | + | 0.990465i | \(0.543992\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.9706 | 1.25547 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.00000 | −0.0596550 | −0.0298275 | − | 0.999555i | \(-0.509496\pi\) | ||||
−0.0298275 | + | 0.999555i | \(0.509496\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.2426 | −1.61941 | −0.809703 | − | 0.586839i | \(-0.800372\pi\) | ||||
−0.809703 | + | 0.586839i | \(0.800372\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.4853 | −1.09497 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.14214 | −0.243655 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.4853 | 1.37673 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.5858 | 0.676849 | 0.338424 | − | 0.940994i | \(-0.390106\pi\) | ||||
0.338424 | + | 0.940994i | \(0.390106\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.585786 | 0.0341058 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.757359 | 0.0439464 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.8995 | 1.26648 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.00000 | −0.114897 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.8284 | −0.620034 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.41421 | 0.366079 | 0.183039 | − | 0.983106i | \(-0.441406\pi\) | ||||
0.183039 | + | 0.983106i | \(0.441406\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.6569 | 0.606247 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.9706 | −1.52936 | −0.764680 | − | 0.644410i | \(-0.777103\pi\) | ||||
−0.764680 | + | 0.644410i | \(0.777103\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.5563 | 0.822774 | 0.411387 | − | 0.911461i | \(-0.365045\pi\) | ||||
0.411387 | + | 0.911461i | \(0.365045\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.9706 | 1.06549 | 0.532746 | − | 0.846275i | \(-0.321160\pi\) | ||||
0.532746 | + | 0.846275i | \(0.321160\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.51472 | 0.476733 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.9706 | 1.50535 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.4558 | 1.52768 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.41421 | −0.355797 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.7279 | 1.20156 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.828427 | 0.0455345 | 0.0227672 | − | 0.999741i | \(-0.492752\pi\) | ||||
0.0227672 | + | 0.999741i | \(0.492752\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.65685 | −0.0907951 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.07107 | −0.167790 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.72792 | 0.366493 | 0.183247 | − | 0.983067i | \(-0.441339\pi\) | ||||
0.183247 | + | 0.983067i | \(0.441339\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.8995 | 1.18942 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.5563 | −0.734117 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.24264 | −0.443769 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.58579 | 0.246178 | 0.123089 | − | 0.992396i | \(-0.460720\pi\) | ||||
0.123089 | + | 0.992396i | \(0.460720\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.0000 | −0.963518 | −0.481759 | − | 0.876304i | \(-0.660002\pi\) | ||||
−0.481759 | + | 0.876304i | \(0.660002\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.65685 | 0.141812 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.0711 | −0.642478 | −0.321239 | − | 0.946998i | \(-0.604099\pi\) | ||||
−0.321239 | + | 0.946998i | \(0.604099\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.4853 | 0.556501 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.3137 | 0.597115 | 0.298557 | − | 0.954392i | \(-0.403495\pi\) | ||||
0.298557 | + | 0.954392i | \(0.403495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.6274 | 2.08565 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.4853 | −0.970226 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.8284 | −0.566786 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.72792 | −0.298995 | −0.149498 | − | 0.988762i | \(-0.547766\pi\) | ||||
−0.149498 | + | 0.988762i | \(0.547766\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.65685 | −0.502716 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.485281 | −0.0251269 | −0.0125635 | − | 0.999921i | \(-0.503999\pi\) | ||||
−0.0125635 | + | 0.999921i | \(0.503999\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.41421 | 0.124669 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.8701 | 1.53839 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.0000 | −0.719132 | −0.359566 | − | 0.933120i | \(-0.617075\pi\) | ||||
−0.359566 | + | 0.933120i | \(0.617075\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.07107 | 0.259799 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.4853 | −1.04675 | −0.523374 | − | 0.852103i | \(-0.675327\pi\) | ||||
−0.523374 | + | 0.852103i | \(0.675327\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.970563 | −0.0493365 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.1421 | −0.767737 | −0.383868 | − | 0.923388i | \(-0.625408\pi\) | ||||
−0.383868 | + | 0.923388i | \(0.625408\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.2426 | 0.619137 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −48.8701 | −2.46517 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.1421 | 0.761884 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.5858 | −0.581474 | −0.290737 | − | 0.956803i | \(-0.593900\pi\) | ||||
−0.290737 | + | 0.956803i | \(0.593900\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.4853 | 0.873173 | 0.436587 | − | 0.899662i | \(-0.356187\pi\) | ||||
0.436587 | + | 0.899662i | \(0.356187\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −47.5563 | −2.36895 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.48528 | −0.471327 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.07107 | 0.0530909 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.1716 | −1.34355 | −0.671774 | − | 0.740756i | \(-0.734467\pi\) | ||||
−0.671774 | + | 0.740756i | \(0.734467\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −50.6274 | −2.49727 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.00000 | −0.392705 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.2426 | 0.697465 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.5563 | 1.05310 | 0.526548 | − | 0.850145i | \(-0.323486\pi\) | ||||
0.526548 | + | 0.850145i | \(0.323486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.31371 | −0.112763 | −0.0563816 | − | 0.998409i | \(-0.517956\pi\) | ||||
−0.0563816 | + | 0.998409i | \(0.517956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 30.8284 | 1.49893 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.58579 | −0.173936 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 28.3137 | 1.36700 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.17157 | 0.200938 | 0.100469 | − | 0.994940i | \(-0.467966\pi\) | ||||
0.100469 | + | 0.994940i | \(0.467966\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.2843 | −1.64760 | −0.823798 | − | 0.566883i | \(-0.808149\pi\) | ||||
−0.823798 | + | 0.566883i | \(0.808149\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.2426 | −0.539043 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.1421 | 1.25055 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.7574 | 0.752058 | 0.376029 | − | 0.926608i | \(-0.377289\pi\) | ||||
0.376029 | + | 0.926608i | \(0.377289\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.4558 | −0.734329 | −0.367165 | − | 0.930156i | \(-0.619671\pi\) | ||||
−0.367165 | + | 0.930156i | \(0.619671\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.9706 | 0.804482 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 49.4558 | 2.33918 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.1716 | 0.857570 | 0.428785 | − | 0.903407i | \(-0.358942\pi\) | ||||
0.428785 | + | 0.903407i | \(0.358942\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.24264 | 0.293954 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.8995 | 0.700039 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.928932 | −0.0434536 | −0.0217268 | − | 0.999764i | \(-0.506916\pi\) | ||||
−0.0217268 | + | 0.999764i | \(0.506916\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.48528 | 0.0693270 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.6569 | −1.56756 | −0.783778 | − | 0.621041i | \(-0.786710\pi\) | ||||
−0.783778 | + | 0.621041i | \(0.786710\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.4558 | −1.74072 | −0.870360 | − | 0.492415i | \(-0.836114\pi\) | ||||
−0.870360 | + | 0.492415i | \(0.836114\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17.8995 | 0.830069 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.8995 | −0.874564 | −0.437282 | − | 0.899324i | \(-0.644059\pi\) | ||||
−0.437282 | + | 0.899324i | \(0.644059\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.6569 | 0.721430 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.627417 | 0.0288487 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.65685 | −0.351321 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −34.6274 | −1.58548 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.58579 | 0.300912 | 0.150456 | − | 0.988617i | \(-0.451926\pi\) | ||||
0.150456 | + | 0.988617i | \(0.451926\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.75736 | 0.171321 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.72792 | 0.441722 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.58579 | 0.207802 | 0.103901 | − | 0.994588i | \(-0.466868\pi\) | ||||
0.103901 | + | 0.994588i | \(0.466868\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.0711 | 1.04331 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.2843 | 1.77287 | 0.886437 | − | 0.462849i | \(-0.153173\pi\) | ||||
0.886437 | + | 0.462849i | \(0.153173\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.6985 | 0.752062 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.17157 | −0.232445 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.6274 | −1.41584 | −0.707919 | − | 0.706294i | \(-0.750366\pi\) | ||||
−0.707919 | + | 0.706294i | \(0.750366\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.04163 | −0.403146 | −0.201573 | − | 0.979473i | \(-0.564605\pi\) | ||||
−0.201573 | + | 0.979473i | \(0.564605\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.828427 | −0.0368645 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 67.9411 | 3.01737 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.9289 | 0.927659 | 0.463829 | − | 0.885925i | \(-0.346475\pi\) | ||||
0.463829 | + | 0.885925i | \(0.346475\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.17157 | 0.140028 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.41421 | 0.194513 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.9289 | −0.876473 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.3137 | 1.33062 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.3137 | −1.28426 | −0.642128 | − | 0.766597i | \(-0.721948\pi\) | ||||
−0.642128 | + | 0.766597i | \(0.721948\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.1421 | 1.31802 | 0.659012 | − | 0.752133i | \(-0.270975\pi\) | ||||
0.659012 | + | 0.752133i | \(0.270975\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.5858 | −1.15810 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.3431 | −0.493180 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.65685 | 0.0719014 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.8995 | 0.948572 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.1716 | 0.482989 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.3137 | 1.09237 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.9706 | −0.772615 | −0.386307 | − | 0.922370i | \(-0.626250\pi\) | ||||
−0.386307 | + | 0.922370i | \(0.626250\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.7279 | −1.06118 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.00000 | 0.385518 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.4853 | −1.04692 | −0.523458 | − | 0.852052i | \(-0.675358\pi\) | ||||
−0.523458 | + | 0.852052i | \(0.675358\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −30.6274 | −1.30715 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.6569 | 1.51903 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.41421 | −0.0600300 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.7990 | 1.34737 | 0.673683 | − | 0.739020i | \(-0.264711\pi\) | ||||
0.673683 | + | 0.739020i | \(0.264711\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.20101 | 0.0930928 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.8284 | 0.668277 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.6274 | 1.03792 | 0.518961 | − | 0.854798i | \(-0.326319\pi\) | ||||
0.518961 | + | 0.854798i | \(0.326319\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.07107 | 0.381623 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.79899 | 0.326951 | 0.163475 | − | 0.986547i | \(-0.447730\pi\) | ||||
0.163475 | + | 0.986547i | \(0.447730\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.828427 | 0.0346686 | 0.0173343 | − | 0.999850i | \(-0.494482\pi\) | ||||
0.0173343 | + | 0.999850i | \(0.494482\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.8995 | −0.538884 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.41421 | −0.142383 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.0710678 | −0.00295859 | −0.00147930 | − | 0.999999i | \(-0.500471\pi\) | ||||
−0.00147930 | + | 0.999999i | \(0.500471\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.6569 | −0.567559 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.3848 | 0.927083 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −18.1421 | −0.750085 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.1716 | −1.03894 | −0.519471 | − | 0.854488i | \(-0.673871\pi\) | ||||
−0.519471 | + | 0.854488i | \(0.673871\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −56.7696 | −2.33915 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.58579 | 0.353172 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.72792 | 0.317348 | 0.158674 | − | 0.987331i | \(-0.449278\pi\) | ||||
0.158674 | + | 0.987331i | \(0.449278\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.07107 | −0.125690 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.7990 | −1.09498 | −0.547489 | − | 0.836813i | \(-0.684416\pi\) | ||||
−0.547489 | + | 0.836813i | \(0.684416\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.3431 | −1.15614 | −0.578071 | − | 0.815987i | \(-0.696194\pi\) | ||||
−0.578071 | + | 0.815987i | \(0.696194\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.68629 | −0.353733 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.65685 | −0.311295 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.0711 | 1.13937 | 0.569685 | − | 0.821863i | \(-0.307065\pi\) | ||||
0.569685 | + | 0.821863i | \(0.307065\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −69.9117 | −2.82832 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.6863 | −0.754732 | −0.377366 | − | 0.926064i | \(-0.623170\pi\) | ||||
−0.377366 | + | 0.926064i | \(0.623170\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.24264 | −0.332375 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.8701 | −0.518129 | −0.259065 | − | 0.965860i | \(-0.583414\pi\) | ||||
−0.259065 | + | 0.965860i | \(0.583414\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.8701 | −1.72309 | −0.861547 | − | 0.507679i | \(-0.830504\pi\) | ||||
−0.861547 | + | 0.507679i | \(0.830504\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.41421 | 0.0567504 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 33.7990 | 1.34980 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.10051 | 0.0837526 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.5147 | 0.896297 | 0.448148 | − | 0.893959i | \(-0.352084\pi\) | ||||
0.448148 | + | 0.893959i | \(0.352084\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.07107 | 0.161810 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.10051 | 0.0833560 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.6569 | 1.17321 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.6863 | 0.659069 | 0.329534 | − | 0.944144i | \(-0.393108\pi\) | ||||
0.329534 | + | 0.944144i | \(0.393108\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.2132 | −1.50698 | −0.753491 | − | 0.657458i | \(-0.771632\pi\) | ||||
−0.753491 | + | 0.657458i | \(0.771632\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.828427 | −0.0326193 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.1127 | −1.06591 | −0.532955 | − | 0.846144i | \(-0.678919\pi\) | ||||
−0.532955 | + | 0.846144i | \(0.678919\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.07107 | −0.0420431 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −49.3137 | −1.92979 | −0.964897 | − | 0.262628i | \(-0.915411\pi\) | ||||
−0.964897 | + | 0.262628i | \(0.915411\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.2426 | −0.790945 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −30.6274 | −1.19489 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.34315 | 0.363957 | 0.181979 | − | 0.983302i | \(-0.441750\pi\) | ||||
0.181979 | + | 0.983302i | \(0.441750\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.85786 | 0.227845 | 0.113922 | − | 0.993490i | \(-0.463659\pi\) | ||||
0.113922 | + | 0.993490i | \(0.463659\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 55.5269 | 2.15649 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.8995 | 0.615631 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.9706 | 0.926755 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.7990 | 0.764332 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.4853 | −1.71478 | −0.857391 | − | 0.514666i | \(-0.827916\pi\) | ||||
−0.857391 | + | 0.514666i | \(0.827916\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.414214 | −0.0159431 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.7279 | 1.37314 | 0.686568 | − | 0.727066i | \(-0.259116\pi\) | ||||
0.686568 | + | 0.727066i | \(0.259116\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.7990 | −1.64006 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.1127 | 1.03744 | 0.518719 | − | 0.854945i | \(-0.326409\pi\) | ||||
0.518719 | + | 0.854945i | \(0.326409\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.9706 | −0.801244 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.89949 | −0.377689 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 78.5269 | 2.99164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.4853 | 0.779297 | 0.389648 | − | 0.920964i | \(-0.372597\pi\) | ||||
0.389648 | + | 0.920964i | \(0.372597\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.89949 | 0.223781 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.2426 | 0.463723 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −35.7990 | −1.35404 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.4853 | 0.660410 | 0.330205 | − | 0.943909i | \(-0.392882\pi\) | ||||
0.330205 | + | 0.943909i | \(0.392882\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.48528 | 0.169166 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 26.3137 | 0.991032 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.6274 | −1.56335 | −0.781675 | − | 0.623686i | \(-0.785635\pi\) | ||||
−0.781675 | + | 0.623686i | \(0.785635\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 42.8284 | 1.60619 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.3137 | −0.948006 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.7279 | 0.438599 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −47.8701 | −1.78774 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.2426 | 0.904098 | 0.452049 | − | 0.891993i | \(-0.350693\pi\) | ||||
0.452049 | + | 0.891993i | \(0.350693\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −66.5269 | −2.47416 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.65685 | −0.172951 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.0000 | −0.667583 | −0.333792 | − | 0.942647i | \(-0.608328\pi\) | ||||
−0.333792 | + | 0.942647i | \(0.608328\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.23045 | 0.0455097 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.6985 | −1.06000 | −0.530001 | − | 0.847997i | \(-0.677809\pi\) | ||||
−0.530001 | + | 0.847997i | \(0.677809\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.61522 | 0.206839 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.34315 | −0.343693 | −0.171847 | − | 0.985124i | \(-0.554973\pi\) | ||||
−0.171847 | + | 0.985124i | \(0.554973\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 118.569 | 4.35572 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.0711 | 0.846395 | 0.423198 | − | 0.906037i | \(-0.360908\pi\) | ||||
0.423198 | + | 0.906037i | \(0.360908\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.4853 | 0.750523 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −22.6274 | −0.827894 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.1421 | 0.990431 | 0.495215 | − | 0.868770i | \(-0.335089\pi\) | ||||
0.495215 | + | 0.868770i | \(0.335089\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.2132 | −1.13747 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.17157 | 0.224607 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.8284 | 1.55663 | 0.778313 | − | 0.627877i | \(-0.216076\pi\) | ||||
0.778313 | + | 0.627877i | \(0.216076\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.0711 | 0.547045 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.8701 | −1.26404 | −0.632019 | − | 0.774953i | \(-0.717774\pi\) | ||||
−0.632019 | + | 0.774953i | \(0.717774\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.1421 | −0.366690 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.75736 | −0.135670 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.142136 | 0.00512554 | 0.00256277 | − | 0.999997i | \(-0.499184\pi\) | ||||
0.00256277 | + | 0.999997i | \(0.499184\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.3137 | −1.19976 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.2721 | 0.657201 | 0.328600 | − | 0.944469i | \(-0.393423\pi\) | ||||
0.328600 | + | 0.944469i | \(0.393423\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.41421 | 0.266326 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.1421 | 0.936639 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.1716 | −0.686013 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.92893 | 0.0689344 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.48528 | 0.231470 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.2721 | −0.651329 | −0.325665 | − | 0.945485i | \(-0.605588\pi\) | ||||
−0.325665 | + | 0.945485i | \(0.605588\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.1421 | −0.859483 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 69.4558 | 2.46645 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −29.5563 | −1.04826 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.38478 | −0.0490513 | −0.0245256 | − | 0.999699i | \(-0.507808\pi\) | ||||
−0.0245256 | + | 0.999699i | \(0.507808\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.0833 | −1.38267 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 48.0000 | 1.69600 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.7990 | 0.698691 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.0711 | −0.741737 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.9706 | 1.40529 | 0.702645 | − | 0.711541i | \(-0.252002\pi\) | ||||
0.702645 | + | 0.711541i | \(0.252002\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.5563 | 0.405798 | 0.202899 | − | 0.979200i | \(-0.434964\pi\) | ||||
0.202899 | + | 0.979200i | \(0.434964\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0000 | −0.420858 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.55635 | 0.334744 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.62742 | 0.0919217 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.1716 | 1.47180 | 0.735899 | − | 0.677091i | \(-0.236760\pi\) | ||||
0.735899 | + | 0.677091i | \(0.236760\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.5269 | 0.994386 | 0.497193 | − | 0.867640i | \(-0.334364\pi\) | ||||
0.497193 | + | 0.867640i | \(0.334364\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.41421 | −0.153683 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.0416 | −1.32284 | −0.661419 | − | 0.750017i | \(-0.730045\pi\) | ||||
−0.661419 | + | 0.750017i | \(0.730045\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.72792 | 0.0947446 | 0.0473723 | − | 0.998877i | \(-0.484915\pi\) | ||||
0.0473723 | + | 0.998877i | \(0.484915\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.0711 | −0.384051 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.414214 | −0.0143345 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.07107 | −0.106152 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.3848 | −0.496618 | −0.248309 | − | 0.968681i | \(-0.579875\pi\) | ||||
−0.248309 | + | 0.968681i | \(0.579875\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.31371 | −0.252197 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.41421 | −0.0831499 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.1421 | 0.968119 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −65.7696 | −2.25721 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.00000 | 0.0685591 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.2843 | −0.899956 | −0.449978 | − | 0.893040i | \(-0.648568\pi\) | ||||
−0.449978 | + | 0.893040i | \(0.648568\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21.6569 | −0.740649 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.1716 | 0.518251 | 0.259126 | − | 0.965844i | \(-0.416566\pi\) | ||||
0.259126 | + | 0.965844i | \(0.416566\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.45584 | 0.186151 | 0.0930755 | − | 0.995659i | \(-0.470330\pi\) | ||||
0.0930755 | + | 0.995659i | \(0.470330\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.2426 | 0.961391 | 0.480695 | − | 0.876888i | \(-0.340384\pi\) | ||||
0.480695 | + | 0.876888i | \(0.340384\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.5563 | 0.426929 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.0000 | −0.339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.6863 | −0.939193 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.6985 | 0.667458 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27.5147 | 0.931232 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.3137 | 1.12492 | 0.562462 | − | 0.826823i | \(-0.309854\pi\) | ||||
0.562462 | + | 0.826823i | \(0.309854\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27.9706 | 0.943424 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.284271 | −0.00957734 | −0.00478867 | − | 0.999989i | \(-0.501524\pi\) | ||||
−0.00478867 | + | 0.999989i | \(0.501524\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −55.1127 | −1.85469 | −0.927345 | − | 0.374208i | \(-0.877915\pi\) | ||||
−0.927345 | + | 0.374208i | \(0.877915\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.41421 | 0.0475383 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.5980 | −0.725189 | −0.362595 | − | 0.931947i | \(-0.618109\pi\) | ||||
−0.362595 | + | 0.931947i | \(0.618109\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17.3431 | 0.581017 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −83.4558 | −2.79274 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.4853 | 0.350484 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 52.8701 | 1.76528 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.5269 | −1.15154 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.8995 | 1.46250 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.2426 | −0.340477 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.5269 | 1.41208 | 0.706041 | − | 0.708170i | \(-0.250479\pi\) | ||||
0.706041 | + | 0.708170i | \(0.250479\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.34315 | −0.0777172 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.5980 | −0.781836 | −0.390918 | − | 0.920426i | \(-0.627842\pi\) | ||||
−0.390918 | + | 0.920426i | \(0.627842\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.6274 | 0.484097 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −26.1421 | −0.864232 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.4853 | 1.17055 | 0.585276 | − | 0.810834i | \(-0.300986\pi\) | ||||
0.585276 | + | 0.810834i | \(0.300986\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.4853 | 0.510257 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −67.2548 | −2.21372 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.585786 | −0.0192605 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.4853 | 0.410070 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.7279 | 1.53309 | 0.766547 | − | 0.642189i | \(-0.221973\pi\) | ||||
0.766547 | + | 0.642189i | \(0.221973\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −65.1127 | −2.13169 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.55635 | 0.214416 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.7279 | −0.579146 | −0.289573 | − | 0.957156i | \(-0.593513\pi\) | ||||
−0.289573 | + | 0.957156i | \(0.593513\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35.1421 | 1.14682 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.00000 | 0.130396 | 0.0651981 | − | 0.997872i | \(-0.479232\pi\) | ||||
0.0651981 | + | 0.997872i | \(0.479232\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.6569 | 0.379599 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.0416 | −0.521283 | −0.260641 | − | 0.965436i | \(-0.583934\pi\) | ||||
−0.260641 | + | 0.965436i | \(0.583934\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 69.4558 | 2.25463 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 45.7990 | 1.48513 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.8701 | 0.481688 | 0.240844 | − | 0.970564i | \(-0.422576\pi\) | ||||
0.240844 | + | 0.970564i | \(0.422576\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.34315 | −0.172900 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.5563 | 0.664492 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.9706 | 0.773244 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31.5980 | 1.01823 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.65685 | −0.182101 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.4558 | −1.39745 | −0.698723 | − | 0.715392i | \(-0.746248\pi\) | ||||
−0.698723 | + | 0.715392i | \(0.746248\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 66.2843 | 2.12936 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.5269 | 1.36475 | 0.682377 | − | 0.731001i | \(-0.260946\pi\) | ||||
0.682377 | + | 0.731001i | \(0.260946\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.4853 | −0.495926 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.1421 | 0.644404 | 0.322202 | − | 0.946671i | \(-0.395577\pi\) | ||||
0.322202 | + | 0.946671i | \(0.395577\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31.0294 | −0.991705 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.4558 | 0.812743 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.0122 | 1.27619 | 0.638095 | − | 0.769957i | \(-0.279723\pi\) | ||||
0.638095 | + | 0.769957i | \(0.279723\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.55635 | 0.113315 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.17157 | 0.0372539 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.68629 | −0.0853329 | −0.0426664 | − | 0.999089i | \(-0.513585\pi\) | ||||
−0.0426664 | + | 0.999089i | \(0.513585\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.00000 | 0.0634681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.27208 | −0.0403276 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.8406 | −1.16675 | −0.583377 | − | 0.812201i | \(-0.698269\pi\) | ||||
−0.583377 | + | 0.812201i | \(0.698269\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.242641 | 0.00767681 |
(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 | 3920.2.a.bx.1.2 | 2 | ||
4.3 | odd | 2 | 980.2.a.j.1.1 | ✓ | 2 | ||
7.6 | odd | 2 | 3920.2.a.bo.1.1 | 2 | |||
12.11 | even | 2 | 8820.2.a.bg.1.1 | 2 | |||
20.3 | even | 4 | 4900.2.e.q.2549.1 | 4 | |||
20.7 | even | 4 | 4900.2.e.q.2549.4 | 4 | |||
20.19 | odd | 2 | 4900.2.a.z.1.2 | 2 | |||
28.3 | even | 6 | 980.2.i.k.961.1 | 4 | |||
28.11 | odd | 6 | 980.2.i.l.961.2 | 4 | |||
28.19 | even | 6 | 980.2.i.k.361.1 | 4 | |||
28.23 | odd | 6 | 980.2.i.l.361.2 | 4 | |||
28.27 | even | 2 | 980.2.a.k.1.2 | yes | 2 | ||
84.83 | odd | 2 | 8820.2.a.bl.1.1 | 2 | |||
140.27 | odd | 4 | 4900.2.e.r.2549.1 | 4 | |||
140.83 | odd | 4 | 4900.2.e.r.2549.4 | 4 | |||
140.139 | even | 2 | 4900.2.a.x.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
980.2.a.j.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
980.2.a.k.1.2 | yes | 2 | 28.27 | even | 2 | ||
980.2.i.k.361.1 | 4 | 28.19 | even | 6 | |||
980.2.i.k.961.1 | 4 | 28.3 | even | 6 | |||
980.2.i.l.361.2 | 4 | 28.23 | odd | 6 | |||
980.2.i.l.961.2 | 4 | 28.11 | odd | 6 | |||
3920.2.a.bo.1.1 | 2 | 7.6 | odd | 2 | |||
3920.2.a.bx.1.2 | 2 | 1.1 | even | 1 | trivial | ||
4900.2.a.x.1.1 | 2 | 140.139 | even | 2 | |||
4900.2.a.z.1.2 | 2 | 20.19 | odd | 2 | |||
4900.2.e.q.2549.1 | 4 | 20.3 | even | 4 | |||
4900.2.e.q.2549.4 | 4 | 20.7 | even | 4 | |||
4900.2.e.r.2549.1 | 4 | 140.27 | odd | 4 | |||
4900.2.e.r.2549.4 | 4 | 140.83 | odd | 4 | |||
8820.2.a.bg.1.1 | 2 | 12.11 | even | 2 | |||
8820.2.a.bl.1.1 | 2 | 84.83 | odd | 2 |