Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(95,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.95");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.r (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 191.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.191 |
Dual form | 224.3.r.b.95.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.866025 | − | 0.500000i | 0.288675 | − | 0.166667i | −0.348669 | − | 0.937246i | \(-0.613366\pi\) |
0.637344 | + | 0.770579i | \(0.280033\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | −0.911684 | − | 0.410891i | \(-0.865218\pi\) |
0.811684 | + | 0.584096i | \(0.198551\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000i | 1.00000i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.00000 | + | 6.92820i | −0.444444 | + | 0.769800i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.7224 | + | 8.50000i | −1.33840 | + | 0.772727i | −0.986571 | − | 0.163336i | \(-0.947775\pi\) |
−0.351832 | + | 0.936063i | \(0.614441\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 24.0000 | 1.84615 | 0.923077 | − | 0.384615i | \(-0.125666\pi\) | ||||
0.923077 | + | 0.384615i | \(0.125666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000i | 0.0666667i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.500000 | − | 0.866025i | −0.0294118 | − | 0.0509427i | 0.850945 | − | 0.525255i | \(-0.176030\pi\) |
−0.880357 | + | 0.474312i | \(0.842697\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.06218 | + | 3.50000i | 0.319062 | + | 0.184211i | 0.650974 | − | 0.759100i | \(-0.274361\pi\) |
−0.331912 | + | 0.943310i | \(0.607694\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.50000 | + | 6.06218i | 0.166667 | + | 0.288675i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.06218 | − | 3.50000i | −0.263573 | − | 0.152174i | 0.362390 | − | 0.932026i | \(-0.381961\pi\) |
−0.625963 | + | 0.779852i | \(0.715294\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.0000 | + | 20.7846i | 0.480000 | + | 0.831384i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 17.0000i | 0.629630i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 24.0000 | 0.827586 | 0.413793 | − | 0.910371i | \(-0.364204\pi\) | ||||
0.413793 | + | 0.910371i | \(0.364204\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −35.5070 | + | 20.5000i | −1.14539 | + | 0.661290i | −0.947759 | − | 0.318987i | \(-0.896658\pi\) |
−0.197629 | + | 0.980277i | \(0.563324\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.50000 | + | 14.7224i | −0.257576 | + | 0.446134i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.06218 | − | 3.50000i | −0.173205 | − | 0.100000i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 24.5000 | − | 42.4352i | 0.662162 | − | 1.14690i | −0.317884 | − | 0.948130i | \(-0.602972\pi\) |
0.980046 | − | 0.198769i | \(-0.0636943\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 20.7846 | − | 12.0000i | 0.532939 | − | 0.307692i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −48.0000 | −1.17073 | −0.585366 | − | 0.810769i | \(-0.699049\pi\) | ||||
−0.585366 | + | 0.810769i | \(0.699049\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 24.0000i | − | 0.558140i | −0.960271 | − | 0.279070i | \(-0.909974\pi\) | ||
0.960271 | − | 0.279070i | \(-0.0900261\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.00000 | − | 6.92820i | −0.0888889 | − | 0.153960i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 47.6314 | + | 27.5000i | 1.01343 | + | 0.585106i | 0.912195 | − | 0.409756i | \(-0.134386\pi\) |
0.101239 | + | 0.994862i | \(0.467719\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.866025 | − | 0.500000i | −0.0169809 | − | 0.00980392i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.5000 | + | 21.6506i | 0.235849 | + | 0.408503i | 0.959519 | − | 0.281644i | \(-0.0908796\pi\) |
−0.723670 | + | 0.690146i | \(0.757546\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 17.0000i | − | 0.309091i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.00000 | 0.122807 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.7224 | − | 8.50000i | 0.249533 | − | 0.144068i | −0.370018 | − | 0.929025i | \(-0.620648\pi\) |
0.619550 | + | 0.784957i | \(0.287315\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | − | 0.866025i | 0.00819672 | − | 0.0141971i | −0.861898 | − | 0.507082i | \(-0.830724\pi\) |
0.870095 | + | 0.492885i | \(0.164058\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −48.4974 | − | 28.0000i | −0.769800 | − | 0.444444i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.0000 | + | 20.7846i | −0.184615 | + | 0.319763i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 56.2917 | − | 32.5000i | 0.840174 | − | 0.485075i | −0.0171494 | − | 0.999853i | \(-0.505459\pi\) |
0.857323 | + | 0.514778i | \(0.172126\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.00000 | −0.101449 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 96.0000i | − | 1.35211i | −0.736850 | − | 0.676056i | \(-0.763688\pi\) | ||
0.736850 | − | 0.676056i | \(-0.236312\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −47.5000 | − | 82.2724i | −0.650685 | − | 1.12702i | −0.982957 | − | 0.183836i | \(-0.941149\pi\) |
0.332272 | − | 0.943184i | \(-0.392185\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 20.7846 | + | 12.0000i | 0.277128 | + | 0.160000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −59.5000 | − | 103.057i | −0.772727 | − | 1.33840i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 35.5070 | + | 20.5000i | 0.449456 | + | 0.259494i | 0.707601 | − | 0.706613i | \(-0.249778\pi\) |
−0.258144 | + | 0.966106i | \(0.583111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −27.5000 | − | 47.6314i | −0.339506 | − | 0.588042i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 72.0000i | − | 0.867470i | −0.901041 | − | 0.433735i | \(-0.857195\pi\) | ||
0.901041 | − | 0.433735i | \(-0.142805\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00000 | 0.0117647 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 20.7846 | − | 12.0000i | 0.238904 | − | 0.137931i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −47.5000 | + | 82.2724i | −0.533708 | + | 0.924409i | 0.465517 | + | 0.885039i | \(0.345868\pi\) |
−0.999225 | + | 0.0393701i | \(0.987465\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 168.000i | 1.84615i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20.5000 | + | 35.5070i | −0.220430 | + | 0.381796i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.06218 | + | 3.50000i | −0.0638124 | + | 0.0368421i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 144.000 | 1.48454 | 0.742268 | − | 0.670103i | \(-0.233750\pi\) | ||||
0.742268 | + | 0.670103i | \(0.233750\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 136.000i | − | 1.37374i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −36.5000 | − | 63.2199i | −0.361386 | − | 0.625939i | 0.626803 | − | 0.779178i | \(-0.284363\pi\) |
−0.988189 | + | 0.153239i | \(0.951030\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 77.0763 | + | 44.5000i | 0.748313 | + | 0.432039i | 0.825084 | − | 0.565010i | \(-0.191128\pi\) |
−0.0767709 | + | 0.997049i | \(0.524461\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.00000 | −0.0666667 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −160.215 | − | 92.5000i | −1.49733 | − | 0.864486i | −0.497338 | − | 0.867557i | \(-0.665689\pi\) |
−0.999995 | + | 0.00307068i | \(0.999023\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 35.5000 | + | 61.4878i | 0.325688 | + | 0.564108i | 0.981651 | − | 0.190684i | \(-0.0610707\pi\) |
−0.655963 | + | 0.754793i | \(0.727737\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 49.0000i | − | 0.441441i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 96.0000 | 0.849558 | 0.424779 | − | 0.905297i | \(-0.360352\pi\) | ||||
0.424779 | + | 0.905297i | \(0.360352\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.06218 | − | 3.50000i | 0.0527146 | − | 0.0304348i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −96.0000 | + | 166.277i | −0.820513 | + | 1.42117i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.06218 | − | 3.50000i | 0.0509427 | − | 0.0294118i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 84.0000 | − | 145.492i | 0.694215 | − | 1.20242i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −41.5692 | + | 24.0000i | −0.337961 | + | 0.195122i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −49.0000 | −0.392000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 144.000i | 1.13386i | 0.823767 | + | 0.566929i | \(0.191869\pi\) | ||||
−0.823767 | + | 0.566929i | \(0.808131\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.0000 | − | 20.7846i | −0.0930233 | − | 0.161121i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 160.215 | + | 92.5000i | 1.22301 | + | 0.706107i | 0.965559 | − | 0.260184i | \(-0.0837831\pi\) |
0.257454 | + | 0.966291i | \(0.417116\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.5000 | + | 42.4352i | −0.184211 | + | 0.319062i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −14.7224 | − | 8.50000i | −0.109055 | − | 0.0629630i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 71.5000 | + | 123.842i | 0.521898 | + | 0.903954i | 0.999676 | + | 0.0254728i | \(0.00810911\pi\) |
−0.477778 | + | 0.878481i | \(0.658558\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 216.000i | 1.55396i | 0.629527 | + | 0.776978i | \(0.283249\pi\) | ||||
−0.629527 | + | 0.776978i | \(0.716751\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 55.0000 | 0.390071 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −353.338 | + | 204.000i | −2.47090 | + | 1.42657i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0000 | + | 20.7846i | −0.0827586 | + | 0.143342i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −42.4352 | + | 24.5000i | −0.288675 | + | 0.166667i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.5000 | − | 40.7032i | 0.157718 | − | 0.273176i | −0.776327 | − | 0.630330i | \(-0.782920\pi\) |
0.934045 | + | 0.357154i | \(0.116253\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 172.339 | − | 99.5000i | 1.14132 | − | 0.658940i | 0.194562 | − | 0.980890i | \(-0.437672\pi\) |
0.946757 | + | 0.321950i | \(0.104338\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.00000 | 0.0522876 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 41.0000i | − | 0.264516i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 36.5000 | + | 63.2199i | 0.232484 | + | 0.402674i | 0.958539 | − | 0.284963i | \(-0.0919813\pi\) |
−0.726054 | + | 0.687637i | \(0.758648\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 21.6506 | + | 12.5000i | 0.136168 | + | 0.0786164i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.5000 | − | 42.4352i | 0.152174 | − | 0.263573i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −47.6314 | − | 27.5000i | −0.292217 | − | 0.168712i | 0.346724 | − | 0.937967i | \(-0.387294\pi\) |
−0.638941 | + | 0.769255i | \(0.720627\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.50000 | − | 14.7224i | −0.0515152 | − | 0.0892269i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 206.000i | − | 1.23353i | −0.787146 | − | 0.616766i | \(-0.788442\pi\) | ||
0.787146 | − | 0.616766i | \(-0.211558\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 407.000 | 2.40828 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −48.4974 | + | 28.0000i | −0.283611 | + | 0.163743i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −119.500 | + | 206.980i | −0.690751 | + | 1.19642i | 0.280841 | + | 0.959754i | \(0.409387\pi\) |
−0.971592 | + | 0.236662i | \(0.923947\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −145.492 | + | 84.0000i | −0.831384 | + | 0.480000i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.50000 | − | 14.7224i | 0.0480226 | − | 0.0831776i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.7224 | + | 8.50000i | −0.0822482 | + | 0.0474860i | −0.540560 | − | 0.841305i | \(-0.681788\pi\) |
0.458312 | + | 0.888791i | \(0.348454\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 70.0000 | 0.386740 | 0.193370 | − | 0.981126i | \(-0.438058\pi\) | ||||
0.193370 | + | 0.981126i | \(0.438058\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.00000i | − | 0.00546448i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.5000 | + | 42.4352i | 0.132432 | + | 0.229380i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.7224 | + | 8.50000i | 0.0787296 | + | 0.0454545i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −119.000 | −0.629630 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 172.339 | + | 99.5000i | 0.902299 | + | 0.520942i | 0.877945 | − | 0.478761i | \(-0.158914\pi\) |
0.0243534 | + | 0.999703i | \(0.492247\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.5000 | + | 40.7032i | 0.121762 | + | 0.210897i | 0.920462 | − | 0.390831i | \(-0.127812\pi\) |
−0.798701 | + | 0.601728i | \(0.794479\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 24.0000i | 0.123077i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.0000 | 0.121827 | 0.0609137 | − | 0.998143i | \(-0.480599\pi\) | ||||
0.0609137 | + | 0.998143i | \(0.480599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −118.645 | + | 68.5000i | −0.596208 | + | 0.344221i | −0.767549 | − | 0.640991i | \(-0.778524\pi\) |
0.171340 | + | 0.985212i | \(0.445190\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 32.5000 | − | 56.2917i | 0.161692 | − | 0.280058i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 168.000i | 0.827586i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.0000 | − | 41.5692i | 0.117073 | − | 0.202777i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 48.4974 | − | 28.0000i | 0.234287 | − | 0.135266i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −119.000 | −0.569378 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 264.000i | − | 1.25118i | −0.780150 | − | 0.625592i | \(-0.784857\pi\) | ||
0.780150 | − | 0.625592i | \(-0.215143\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −48.0000 | − | 83.1384i | −0.225352 | − | 0.390321i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.7846 | + | 12.0000i | 0.0966726 | + | 0.0558140i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −143.500 | − | 248.549i | −0.661290 | − | 1.14539i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −82.2724 | − | 47.5000i | −0.375673 | − | 0.216895i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0000 | − | 20.7846i | −0.0542986 | − | 0.0940480i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −192.000 | −0.853333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 359.401 | − | 207.500i | 1.58326 | − | 0.914097i | 0.588883 | − | 0.808218i | \(-0.299568\pi\) |
0.994379 | − | 0.105879i | \(-0.0337656\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 71.5000 | − | 123.842i | 0.312227 | − | 0.540793i | −0.666617 | − | 0.745400i | \(-0.732258\pi\) |
0.978844 | + | 0.204607i | \(0.0655917\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −103.057 | − | 59.5000i | −0.446134 | − | 0.257576i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −144.500 | + | 250.281i | −0.620172 | + | 1.07417i | 0.369282 | + | 0.929317i | \(0.379604\pi\) |
−0.989453 | + | 0.144851i | \(0.953730\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −47.6314 | + | 27.5000i | −0.202687 | + | 0.117021i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 41.0000 | 0.172996 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 226.000i | − | 0.945607i | −0.881168 | − | 0.472803i | \(-0.843242\pi\) | ||
0.881168 | − | 0.472803i | \(-0.156758\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −47.5000 | − | 82.2724i | −0.197095 | − | 0.341379i | 0.750490 | − | 0.660882i | \(-0.229818\pi\) |
−0.947585 | + | 0.319502i | \(0.896484\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −180.133 | − | 104.000i | −0.741289 | − | 0.427984i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 24.5000 | − | 42.4352i | 0.100000 | − | 0.173205i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 145.492 | + | 84.0000i | 0.589038 | + | 0.340081i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −36.0000 | − | 62.3538i | −0.144578 | − | 0.250417i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 38.0000i | 0.151394i | 0.997131 | + | 0.0756972i | \(0.0241182\pi\) | ||||
−0.997131 | + | 0.0756972i | \(0.975882\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 119.000 | 0.470356 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.866025 | − | 0.500000i | 0.00339618 | − | 0.00196078i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −96.5000 | + | 167.143i | −0.375486 | + | 0.650361i | −0.990400 | − | 0.138233i | \(-0.955858\pi\) |
0.614913 | + | 0.788595i | \(0.289191\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 297.047 | + | 171.500i | 1.14690 | + | 0.662162i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −96.0000 | + | 166.277i | −0.367816 | + | 0.637076i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 201.784 | − | 116.500i | 0.767239 | − | 0.442966i | −0.0646496 | − | 0.997908i | \(-0.520593\pi\) |
0.831889 | + | 0.554942i | \(0.187260\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.0000 | −0.0943396 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 95.0000i | 0.355805i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −227.500 | − | 394.042i | −0.845725 | − | 1.46484i | −0.884990 | − | 0.465610i | \(-0.845835\pi\) |
0.0392653 | − | 0.999229i | \(-0.487498\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 368.061 | + | 212.500i | 1.35816 | + | 0.784133i | 0.989375 | − | 0.145383i | \(-0.0464414\pi\) |
0.368782 | + | 0.929516i | \(0.379775\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 84.0000 | + | 145.492i | 0.307692 | + | 0.532939i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −353.338 | − | 204.000i | −1.28487 | − | 0.741818i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −83.5000 | − | 144.626i | −0.301444 | − | 0.522116i | 0.675019 | − | 0.737800i | \(-0.264135\pi\) |
−0.976463 | + | 0.215684i | \(0.930802\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 328.000i | − | 1.17563i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −432.000 | −1.53737 | −0.768683 | − | 0.639630i | \(-0.779088\pi\) | ||||
−0.768683 | + | 0.639630i | \(0.779088\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 193.124 | − | 111.500i | 0.682416 | − | 0.393993i | −0.118349 | − | 0.992972i | \(-0.537760\pi\) |
0.800765 | + | 0.598979i | \(0.204427\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.50000 | + | 6.06218i | −0.0122807 | + | 0.0212708i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 336.000i | − | 1.17073i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 144.000 | − | 249.415i | 0.498270 | − | 0.863029i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 124.708 | − | 72.0000i | 0.428549 | − | 0.247423i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.0000 | 0.0887372 | 0.0443686 | − | 0.999015i | \(-0.485872\pi\) | ||||
0.0443686 | + | 0.999015i | \(0.485872\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.0000i | 0.0576271i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −144.500 | − | 250.281i | −0.486532 | − | 0.842698i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −145.492 | − | 84.0000i | −0.486596 | − | 0.280936i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 168.000 | 0.558140 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −63.2199 | − | 36.5000i | −0.208646 | − | 0.120462i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.500000 | + | 0.866025i | 0.00163934 | + | 0.00283943i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 264.000i | 0.859935i | 0.902844 | + | 0.429967i | \(0.141475\pi\) | ||||
−0.902844 | + | 0.429967i | \(0.858525\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 89.0000 | 0.288026 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −297.047 | + | 171.500i | −0.955134 | + | 0.551447i | −0.894672 | − | 0.446724i | \(-0.852591\pi\) |
−0.0604621 | + | 0.998170i | \(0.519257\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −167.500 | + | 290.119i | −0.535144 | + | 0.926896i | 0.464013 | + | 0.885829i | \(0.346409\pi\) |
−0.999156 | + | 0.0410676i | \(0.986924\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 48.4974 | − | 28.0000i | 0.153960 | − | 0.0888889i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 264.500 | − | 458.127i | 0.834385 | − | 1.44520i | −0.0601454 | − | 0.998190i | \(-0.519156\pi\) |
0.894530 | − | 0.447007i | \(-0.147510\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −353.338 | + | 204.000i | −1.10764 | + | 0.639498i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −185.000 | −0.576324 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 7.00000i | − | 0.0216718i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 288.000 | + | 498.831i | 0.886154 | + | 1.53486i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 61.4878 | + | 35.5000i | 0.188036 | + | 0.108563i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −192.500 | + | 333.420i | −0.585106 | + | 1.01343i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −47.6314 | − | 27.5000i | −0.143902 | − | 0.0830816i | 0.426321 | − | 0.904572i | \(-0.359810\pi\) |
−0.570222 | + | 0.821491i | \(0.693143\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 196.000 | + | 339.482i | 0.588589 | + | 1.01947i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 65.0000i | 0.194030i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −240.000 | −0.712166 | −0.356083 | − | 0.934454i | \(-0.615888\pi\) | ||||
−0.356083 | + | 0.934454i | \(0.615888\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 83.1384 | − | 48.0000i | 0.245246 | − | 0.141593i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 348.500 | − | 603.620i | 1.02199 | − | 1.77015i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 343.000i | − | 1.00000i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.50000 | − | 6.06218i | 0.0101449 | − | 0.0175715i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.8468 | + | 15.5000i | −0.0773683 | + | 0.0446686i | −0.538185 | − | 0.842827i | \(-0.680890\pi\) |
0.460817 | + | 0.887495i | \(0.347557\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −120.000 | −0.343840 | −0.171920 | − | 0.985111i | \(-0.554997\pi\) | ||||
−0.171920 | + | 0.985111i | \(0.554997\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 408.000i | 1.16239i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 263.500 | + | 456.395i | 0.746459 | + | 1.29290i | 0.949510 | + | 0.313737i | \(0.101581\pi\) |
−0.203051 | + | 0.979168i | \(0.565086\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 83.1384 | + | 48.0000i | 0.234193 | + | 0.135211i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.50000 | − | 6.06218i | 0.00980392 | − | 0.0169809i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 463.324 | + | 267.500i | 1.29059 | + | 0.745125i | 0.978760 | − | 0.205011i | \(-0.0657230\pi\) |
0.311835 | + | 0.950136i | \(0.399056\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −156.000 | − | 270.200i | −0.432133 | − | 0.748476i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 168.000i | − | 0.462810i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 95.0000 | 0.260274 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 77.0763 | − | 44.5000i | 0.210017 | − | 0.121253i | −0.391302 | − | 0.920262i | \(-0.627975\pi\) |
0.601319 | + | 0.799009i | \(0.294642\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 192.000 | − | 332.554i | 0.520325 | − | 0.901230i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −151.554 | + | 87.5000i | −0.408503 | + | 0.235849i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −167.500 | + | 290.119i | −0.449062 | + | 0.777798i | −0.998325 | − | 0.0578516i | \(-0.981575\pi\) |
0.549264 | + | 0.835649i | \(0.314908\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −42.4352 | + | 24.5000i | −0.113161 | + | 0.0653333i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 576.000 | 1.52785 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 38.0000i | − | 0.100264i | −0.998743 | − | 0.0501319i | \(-0.984036\pi\) | ||
0.998743 | − | 0.0501319i | \(-0.0159642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 72.0000 | + | 124.708i | 0.188976 | + | 0.327317i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −575.907 | − | 332.500i | −1.50367 | − | 0.868146i | −0.999991 | − | 0.00425732i | \(-0.998645\pi\) |
−0.503682 | − | 0.863889i | \(-0.668022\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 119.000 | 0.309091 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 166.277 | + | 96.0000i | 0.429656 | + | 0.248062i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −36.5000 | − | 63.2199i | −0.0938303 | − | 0.162519i | 0.815290 | − | 0.579054i | \(-0.196578\pi\) |
−0.909120 | + | 0.416535i | \(0.863244\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.00000i | 0.0179028i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 185.000 | 0.470738 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −35.5070 | + | 20.5000i | −0.0898912 | + | 0.0518987i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.500000 | + | 0.866025i | −0.00125945 | + | 0.00218142i | −0.866654 | − | 0.498909i | \(-0.833734\pi\) |
0.865395 | + | 0.501090i | \(0.167068\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 49.0000i | 0.122807i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −168.500 | + | 291.851i | −0.420200 | + | 0.727807i | −0.995959 | − | 0.0898124i | \(-0.971373\pi\) |
0.575759 | + | 0.817619i | \(0.304707\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −852.169 | + | 492.000i | −2.11456 | + | 1.22084i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 55.0000 | 0.135802 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 833.000i | 2.04668i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 239.500 | + | 414.826i | 0.585575 | + | 1.01424i | 0.994804 | + | 0.101813i | \(0.0324644\pi\) |
−0.409229 | + | 0.912432i | \(0.634202\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 123.842 | + | 71.5000i | 0.301318 | + | 0.173966i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 59.5000 | + | 103.057i | 0.144068 | + | 0.249533i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 62.3538 | + | 36.0000i | 0.150250 | + | 0.0867470i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 108.000 | + | 187.061i | 0.258993 | + | 0.448589i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 552.000i | 1.31742i | 0.752396 | + | 0.658711i | \(0.228898\pi\) | ||||
−0.752396 | + | 0.658711i | \(0.771102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −216.000 | −0.513064 | −0.256532 | − | 0.966536i | \(-0.582580\pi\) | ||||
−0.256532 | + | 0.966536i | \(0.582580\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −381.051 | + | 220.000i | −0.900830 | + | 0.520095i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0000 | − | 20.7846i | 0.0282353 | − | 0.0489050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.06218 | + | 3.50000i | 0.0141971 | + | 0.00819672i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −204.000 | + | 353.338i | −0.475524 | + | 0.823633i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 380.185 | − | 219.500i | 0.882100 | − | 0.509281i | 0.0107498 | − | 0.999942i | \(-0.496578\pi\) |
0.871350 | + | 0.490661i | \(0.163245\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −288.000 | −0.665127 | −0.332564 | − | 0.943081i | \(-0.607914\pi\) | ||||
−0.332564 | + | 0.943081i | \(0.607914\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 24.0000i | 0.0551724i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.5000 | − | 42.4352i | −0.0560641 | − | 0.0971058i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −534.338 | − | 308.500i | −1.21717 | − | 0.702733i | −0.252858 | − | 0.967503i | \(-0.581371\pi\) |
−0.964312 | + | 0.264770i | \(0.914704\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 196.000 | − | 339.482i | 0.444444 | − | 0.769800i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 213.908 | + | 123.500i | 0.482863 | + | 0.278781i | 0.721609 | − | 0.692301i | \(-0.243403\pi\) |
−0.238746 | + | 0.971082i | \(0.576736\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −47.5000 | − | 82.2724i | −0.106742 | − | 0.184882i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 47.0000i | − | 0.105145i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −288.000 | −0.641425 | −0.320713 | − | 0.947177i | \(-0.603922\pi\) | ||||
−0.320713 | + | 0.947177i | \(0.603922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 706.677 | − | 408.000i | 1.56691 | − | 0.904656i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 99.5000 | − | 172.339i | 0.219647 | − | 0.380439i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −145.492 | − | 84.0000i | −0.319763 | − | 0.184615i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 48.5000 | − | 84.0045i | 0.106127 | − | 0.183817i | −0.808071 | − | 0.589085i | \(-0.799488\pi\) |
0.914198 | + | 0.405268i | \(0.132822\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.7224 | − | 8.50000i | 0.0320750 | − | 0.0185185i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 312.000 | 0.676790 | 0.338395 | − | 0.941004i | \(-0.390116\pi\) | ||||
0.338395 | + | 0.941004i | \(0.390116\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 192.000i | − | 0.414687i | −0.978268 | − | 0.207343i | \(-0.933518\pi\) | ||
0.978268 | − | 0.207343i | \(-0.0664817\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.5000 | − | 35.5070i | −0.0440860 | − | 0.0763592i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −255.477 | − | 147.500i | −0.547061 | − | 0.315846i | 0.200875 | − | 0.979617i | \(-0.435622\pi\) |
−0.747936 | + | 0.663771i | \(0.768955\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 227.500 | + | 394.042i | 0.485075 | + | 0.840174i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 63.2199 | + | 36.5000i | 0.134225 | + | 0.0774947i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 204.000 | + | 353.338i | 0.431290 | + | 0.747016i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 168.000i | 0.353684i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −200.000 | −0.419287 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 534.338 | − | 308.500i | 1.11553 | − | 0.644050i | 0.175272 | − | 0.984520i | \(-0.443919\pi\) |
0.940255 | + | 0.340470i | \(0.110586\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 588.000 | − | 1018.45i | 1.22245 | − | 2.11735i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 49.0000i | − | 0.101449i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −72.0000 | + | 124.708i | −0.148454 | + | 0.257129i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −213.908 | + | 123.500i | −0.439237 | + | 0.253593i | −0.703274 | − | 0.710919i | \(-0.748279\pi\) |
0.264037 | + | 0.964513i | \(0.414946\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −55.0000 | −0.112474 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 134.000i | − | 0.272912i | −0.990646 | − | 0.136456i | \(-0.956429\pi\) | ||
0.990646 | − | 0.136456i | \(-0.0435713\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.0000 | − | 20.7846i | −0.0243408 | − | 0.0421595i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 117.779 | + | 68.0000i | 0.237938 | + | 0.137374i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 672.000 | 1.35211 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −629.600 | − | 363.500i | −1.26172 | − | 0.728457i | −0.288316 | − | 0.957535i | \(-0.593095\pi\) |
−0.973408 | + | 0.229078i | \(0.926429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −103.000 | − | 178.401i | −0.205589 | − | 0.356090i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 432.000i | 0.858847i | 0.903103 | + | 0.429423i | \(0.141283\pi\) | ||||
−0.903103 | + | 0.429423i | \(0.858717\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 73.0000 | 0.144554 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 352.472 | − | 203.500i | 0.695212 | − | 0.401381i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −216.500 | + | 374.989i | −0.425344 | + | 0.736717i | −0.996452 | − | 0.0841574i | \(-0.973180\pi\) |
0.571109 | + | 0.820874i | \(0.306513\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 575.907 | − | 332.500i | 1.12702 | − | 0.650685i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −59.5000 | + | 103.057i | −0.115984 | + | 0.200891i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −77.0763 | + | 44.5000i | −0.149663 | + | 0.0864078i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −935.000 | −1.80851 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 239.000i | 0.460501i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −239.500 | − | 414.826i | −0.459693 | − | 0.796211i | 0.539252 | − | 0.842145i | \(-0.318707\pi\) |
−0.998945 | + | 0.0459332i | \(0.985374\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −783.753 | − | 452.500i | −1.49857 | − | 0.865201i | −0.498573 | − | 0.866848i | \(-0.666142\pi\) |
−0.999999 | + | 0.00164693i | \(0.999476\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −84.0000 | + | 145.492i | −0.160000 | + | 0.277128i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 35.5070 | + | 20.5000i | 0.0673758 | + | 0.0388994i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −240.000 | − | 415.692i | −0.453686 | − | 0.785808i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 136.000i | 0.256121i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1152.00 | −2.16135 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 160.215 | − | 92.5000i | 0.299467 | − | 0.172897i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.50000 | + | 14.7224i | −0.0158287 | + | 0.0274161i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 721.399 | − | 416.500i | 1.33840 | − | 0.772727i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 95.5000 | − | 165.411i | 0.176525 | − | 0.305750i | −0.764163 | − | 0.645023i | \(-0.776848\pi\) |
0.940688 | + | 0.339273i | \(0.110181\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 60.6218 | − | 35.0000i | 0.111642 | − | 0.0644567i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −71.0000 | −0.130275 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 374.000i | 0.683729i | 0.939749 | + | 0.341865i | \(0.111058\pi\) | ||||
−0.939749 | + | 0.341865i | \(0.888942\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.00000 | + | 6.92820i | 0.00728597 | + | 0.0126197i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 145.492 | + | 84.0000i | 0.264051 | + | 0.152450i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −143.500 | + | 248.549i | −0.259494 | + | 0.449456i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 42.4352 | + | 24.5000i | 0.0764599 | + | 0.0441441i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −468.500 | − | 811.466i | −0.841113 | − | 1.45685i | −0.888954 | − | 0.457996i | \(-0.848568\pi\) |
0.0478413 | − | 0.998855i | \(-0.484766\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 576.000i | − | 1.03041i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.0000 | 0.0303030 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −691.954 | + | 399.500i | −1.22905 | + | 0.709591i | −0.966831 | − | 0.255417i | \(-0.917787\pi\) |
−0.262218 | + | 0.965009i | \(0.584454\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −48.0000 | + | 83.1384i | −0.0849558 | + | 0.147148i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 333.420 | − | 192.500i | 0.588042 | − | 0.339506i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 264.500 | − | 458.127i | 0.464851 | − | 0.805145i | −0.534344 | − | 0.845267i | \(-0.679441\pi\) |
0.999195 | + | 0.0401221i | \(0.0127747\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 899.800 | − | 519.500i | 1.57583 | − | 0.909807i | 0.580401 | − | 0.814331i | \(-0.302896\pi\) |
0.995432 | − | 0.0954765i | \(-0.0304375\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 199.000 | 0.347295 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 168.000i | − | 0.292174i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 264.500 | + | 458.127i | 0.458406 | + | 0.793982i | 0.998877 | − | 0.0473807i | \(-0.0150874\pi\) |
−0.540471 | + | 0.841362i | \(0.681754\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 40.7032 | + | 23.5000i | 0.0702991 | + | 0.0405872i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 504.000 | 0.867470 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −368.061 | − | 212.500i | −0.631322 | − | 0.364494i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −96.0000 | − | 166.277i | −0.164103 | − | 0.284234i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 840.000i | − | 1.43101i | −0.698610 | − | 0.715503i | \(-0.746198\pi\) | ||
0.698610 | − | 0.715503i | \(-0.253802\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −287.000 | −0.487267 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.7846 | − | 12.0000i | 0.0351685 | − | 0.0203046i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 191.500 | − | 331.688i | 0.322934 | − | 0.559338i | −0.658158 | − | 0.752880i | \(-0.728664\pi\) |
0.981092 | + | 0.193541i | \(0.0619974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.00000i | 0.0117647i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −68.5000 | + | 118.645i | −0.114740 | + | 0.198736i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −297.047 | + | 171.500i | −0.495904 | + | 0.286311i | −0.727021 | − | 0.686616i | \(-0.759096\pi\) |
0.231116 | + | 0.972926i | \(0.425762\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −624.000 | −1.03827 | −0.519135 | − | 0.854692i | \(-0.673746\pi\) | ||||
−0.519135 | + | 0.854692i | \(0.673746\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 520.000i | 0.862355i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 84.0000 | + | 145.492i | 0.138843 | + | 0.240483i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −118.645 | − | 68.5000i | −0.195462 | − | 0.112850i | 0.399075 | − | 0.916918i | \(-0.369331\pi\) |
−0.594537 | + | 0.804068i | \(0.702665\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 84.0000 | + | 145.492i | 0.137931 | + | 0.238904i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1143.15 | + | 660.000i | 1.87096 | + | 1.08020i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.5000 | + | 61.4878i | 0.0579119 | + | 0.100306i | 0.893528 | − | 0.449008i | \(-0.148222\pi\) |
−0.835616 | + | 0.549314i | \(0.814889\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 48.0000i | − | 0.0780488i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 384.000 | 0.622366 | 0.311183 | − | 0.950350i | \(-0.399275\pi\) | ||||
0.311183 | + | 0.950350i | \(0.399275\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 513.553 | − | 296.500i | 0.829650 | − | 0.478998i | −0.0240831 | − | 0.999710i | \(-0.507667\pi\) |
0.853733 | + | 0.520712i | \(0.174333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 59.5000 | − | 103.057i | 0.0958132 | − | 0.165953i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −575.907 | − | 332.500i | −0.924409 | − | 0.533708i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −275.500 | + | 477.180i | −0.440800 | + | 0.763488i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −103.057 | + | 59.5000i | −0.164365 | + | 0.0948963i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −49.0000 | −0.0779014 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 384.000i | − | 0.608558i | −0.952583 | − | 0.304279i | \(-0.901585\pi\) | ||
0.952583 | − | 0.304279i | \(-0.0984155\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −132.000 | − | 228.631i | −0.208531 | − | 0.361186i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −124.708 | − | 72.0000i | −0.196390 | − | 0.113386i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1176.00 | −1.84615 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 665.108 | + | 384.000i | 1.04086 | + | 0.600939i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −383.500 | − | 664.241i | −0.598284 | − | 1.03626i | −0.993074 | − | 0.117487i | \(-0.962516\pi\) |
0.394790 | − | 0.918771i | \(-0.370817\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 456.000i | − | 0.709176i | −0.935023 | − | 0.354588i | \(-0.884621\pi\) | ||
0.935023 | − | 0.354588i | \(-0.115379\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.0000 | 0.0372093 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 77.0763 | − | 44.5000i | 0.119129 | − | 0.0687790i | −0.439252 | − | 0.898364i | \(-0.644756\pi\) |
0.558380 | + | 0.829585i | \(0.311423\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −144.500 | + | 250.281i | −0.222650 | + | 0.385642i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −248.549 | − | 143.500i | −0.381796 | − | 0.220430i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −263.500 | + | 456.395i | −0.403522 | + | 0.698921i | −0.994148 | − | 0.108024i | \(-0.965548\pi\) |
0.590626 | + | 0.806945i | \(0.298881\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −160.215 | + | 92.5000i | −0.244603 | + | 0.141221i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 760.000 | 1.15677 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 936.000i | 1.42033i | 0.704033 | + | 0.710167i | \(0.251381\pi\) | ||||
−0.704033 | + | 0.710167i | \(0.748619\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 372.500 | + | 645.189i | 0.563540 | + | 0.976080i | 0.997184 | + | 0.0749957i | \(0.0238943\pi\) |
−0.433644 | + | 0.901084i | \(0.642772\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −20.7846 | − | 12.0000i | −0.0313493 | − | 0.0180995i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −24.5000 | − | 42.4352i | −0.0368421 | − | 0.0638124i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −145.492 | − | 84.0000i | −0.218129 | − | 0.125937i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.0000i | 0.0253353i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −720.000 | −1.06984 | −0.534918 | − | 0.844904i | \(-0.679658\pi\) | ||||
−0.534918 | + | 0.844904i | \(0.679658\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −353.338 | + | 204.000i | −0.523464 | + | 0.302222i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 575.500 | − | 996.795i | 0.850074 | − | 1.47237i | −0.0310670 | − | 0.999517i | \(-0.509891\pi\) |
0.881141 | − | 0.472854i | \(-0.156776\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1008.00i | 1.48454i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 207.500 | − | 359.401i | 0.304699 | − | 0.527754i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −638.261 | + | 368.500i | −0.934496 | + | 0.539531i | −0.888231 | − | 0.459398i | \(-0.848065\pi\) |
−0.0462653 | + | 0.998929i | \(0.514732\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −143.000 | −0.208759 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 143.000i | − | 0.208151i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 300.000 | + | 519.615i | 0.435414 | + | 0.754159i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −879.016 | − | 507.500i | −1.27209 | − | 0.734443i | −0.296711 | − | 0.954967i | \(-0.595890\pi\) |
−0.975381 | + | 0.220525i | \(0.929223\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 952.000 | 1.37374 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −187.061 | − | 108.000i | −0.269153 | − | 0.155396i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0000 | + | 41.5692i | 0.0344333 | + | 0.0596402i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 289.000i | 0.413448i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1226.00 | 1.74893 | 0.874465 | − | 0.485089i | \(-0.161213\pi\) | ||||
0.874465 | + | 0.485089i | \(0.161213\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 297.047 | − | 171.500i | 0.422542 | − | 0.243954i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −27.5000 | + | 47.6314i | −0.0390071 | + | 0.0675623i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 442.539 | − | 255.500i | 0.625939 | − | 0.361386i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 312.500 | − | 541.266i | 0.440762 | − | 0.763422i | −0.556985 | − | 0.830523i | \(-0.688042\pi\) |
0.997746 | + | 0.0671013i | \(0.0213751\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −284.056 | + | 164.000i | −0.399517 | + | 0.230661i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 287.000 | 0.402525 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 408.000i | − | 0.570629i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −113.000 | − | 195.722i | −0.157601 | − | 0.272973i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 118.645 | + | 68.5000i | 0.165015 | + | 0.0952712i | 0.580233 | − | 0.814451i | \(-0.302962\pi\) |
−0.415218 | + | 0.909722i | \(0.636295\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −311.500 | + | 539.534i | −0.432039 | + | 0.748313i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −82.2724 | − | 47.5000i | −0.113793 | − | 0.0656985i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 288.000 | + | 498.831i | 0.397241 | + | 0.688042i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 960.000i | 1.32050i | 0.751048 | + | 0.660248i | \(0.229549\pi\) | ||||
−0.751048 | + | 0.660248i | \(0.770451\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 287.000 | 0.393690 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.7846 | + | 12.0000i | −0.0284331 | + | 0.0164159i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −239.500 | + | 414.826i | −0.326739 | + | 0.565929i | −0.981863 | − | 0.189593i | \(-0.939283\pi\) |
0.655123 | + | 0.755522i | \(0.272617\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 49.0000i | − | 0.0666667i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −552.500 | + | 956.958i | −0.749661 | + | 1.29845i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 442.539 | − | 255.500i | 0.598835 | − | 0.345737i | −0.169748 | − | 0.985487i | \(-0.554295\pi\) |
0.768583 | + | 0.639750i | \(0.220962\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 168.000 | 0.226721 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 528.000i | 0.710633i | 0.934746 | + | 0.355316i | \(0.115627\pi\) | ||||
−0.934746 | + | 0.355316i | \(0.884373\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.5000 | + | 40.7032i | 0.0315436 | + | 0.0546352i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 498.831 | + | 288.000i | 0.667779 | + | 0.385542i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 647.500 | − | 1121.50i | 0.864486 | − | 1.49733i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −700.615 | − | 404.500i | −0.932909 | − | 0.538615i | −0.0451785 | − | 0.998979i | \(-0.514386\pi\) |
−0.887730 | + | 0.460364i | \(0.847719\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.0000 | + | 32.9090i | 0.0252324 | + | 0.0437038i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 199.000i | 0.263576i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −120.000 | −0.158520 | −0.0792602 | − | 0.996854i | \(-0.525256\pi\) | ||||
−0.0792602 | + | 0.996854i | \(0.525256\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 103.057 | − | 59.5000i | 0.135780 | − | 0.0783926i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −384.500 | + | 665.974i | −0.505256 | + | 0.875129i | 0.494725 | + | 0.869049i | \(0.335269\pi\) |
−0.999982 | + | 0.00608006i | \(0.998065\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −430.415 | + | 248.500i | −0.564108 | + | 0.325688i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.00000 | + | 6.92820i | −0.00522876 | + | 0.00905647i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 353.338 | − | 204.000i | 0.460676 | − | 0.265971i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −144.000 | −0.187256 | −0.0936281 | − | 0.995607i | \(-0.529846\pi\) | ||||
−0.0936281 | + | 0.995607i | \(0.529846\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 193.000i | 0.250324i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 203.500 | + | 352.472i | 0.263260 | + | 0.455980i | 0.967106 | − | 0.254373i | \(-0.0818690\pi\) |
−0.703846 | + | 0.710352i | \(0.748536\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −852.169 | − | 492.000i | −1.09957 | − | 0.634839i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 343.000 | 0.441441 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −290.985 | − | 168.000i | −0.373536 | − | 0.215661i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 816.000 | + | 1413.35i | 1.04481 | + | 1.80967i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 408.000i | 0.521073i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −73.0000 | −0.0929936 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −982.939 | + | 567.500i | −1.24897 | + | 0.721093i | −0.970904 | − | 0.239469i | \(-0.923027\pi\) |
−0.278065 | + | 0.960562i | \(0.589693\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 116.500 | − | 201.784i | 0.147655 | − | 0.255746i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 672.000i | 0.849558i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.0000 | − | 20.7846i | 0.0151324 | − | 0.0262101i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −21.6506 | + | 12.5000i | −0.0272335 | + | 0.0157233i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 312.000 | 0.391468 | 0.195734 | − | 0.980657i | \(-0.437291\pi\) | ||||
0.195734 | + | 0.980657i | \(0.437291\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 55.0000i | − | 0.0688360i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −380.000 | − | 658.179i | −0.474407 | − | 0.821697i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1398.63 | + | 807.500i | 1.74176 | + | 1.00560i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.5000 | + | 42.4352i | 0.0304348 | + | 0.0527146i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −394.042 | − | 227.500i | −0.488280 | − | 0.281908i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 648.500 | + | 1123.23i | 0.801607 | + | 1.38842i | 0.918558 | + | 0.395286i | \(0.129355\pi\) |
−0.116951 | + | 0.993138i | \(0.537312\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1128.00i | 1.39088i | 0.718586 | + | 0.695438i | \(0.244789\pi\) | ||||
−0.718586 | + | 0.695438i | \(0.755211\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 425.000 | 0.522755 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 47.6314 | − | 27.5000i | 0.0584434 | − | 0.0337423i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 84.0000 | − | 145.492i | 0.102815 | − | 0.178081i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1163.94 | − | 672.000i | −1.42117 | − | 0.820513i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 191.500 | − | 331.688i | 0.233252 | − | 0.404005i | −0.725511 | − | 0.688210i | \(-0.758397\pi\) |
0.958763 | + | 0.284206i | \(0.0917299\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.6314 | + | 27.5000i | −0.0578753 | + | 0.0334143i | −0.528658 | − | 0.848835i | \(-0.677305\pi\) |
0.470783 | + | 0.882249i | \(0.343971\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −408.000 | −0.494545 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 696.000i | − | 0.841596i | −0.907154 | − | 0.420798i | \(-0.861750\pi\) | ||
0.907154 | − | 0.420798i | \(-0.138250\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −252.500 | − | 437.343i | −0.304584 | − | 0.527555i | 0.672585 | − | 0.740020i | \(-0.265184\pi\) |
−0.977169 | + | 0.212465i | \(0.931851\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −144.626 | − | 83.5000i | −0.174039 | − | 0.100481i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.5000 | + | 42.4352i | 0.0294118 | + | 0.0509427i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 178.401 | + | 103.000i | 0.213654 | + | 0.123353i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −348.500 | − | 603.620i | −0.416368 | − | 0.721170i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.0000i | 0.0572110i | 0.999591 | + | 0.0286055i | \(0.00910665\pi\) | ||||
−0.999591 | + | 0.0286055i | \(0.990893\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −265.000 | −0.315101 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −374.123 | + | 216.000i | −0.443799 | + | 0.256228i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −203.500 | + | 352.472i | −0.240828 | + | 0.417127i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1018.45 | + | 588.000i | 1.20242 | + | 0.694215i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 111.500 | − | 193.124i | 0.131331 | − | 0.227472i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −297.047 | + | 171.500i | −0.349056 | + | 0.201528i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 696.000 | 0.815944 | 0.407972 | − | 0.912995i | \(-0.366236\pi\) | ||||
0.407972 | + | 0.912995i | \(0.366236\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 56.0000i | − | 0.0654971i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −599.500 | − | 1038.36i | −0.699533 | − | 1.21163i | −0.968628 | − | 0.248514i | \(-0.920058\pi\) |
0.269095 | − | 0.963114i | \(-0.413275\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 671.170 | + | 387.500i | 0.781338 | + | 0.451106i | 0.836904 | − | 0.547349i | \(-0.184363\pi\) |
−0.0555660 | + | 0.998455i | \(0.517696\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −168.000 | − | 290.985i | −0.195122 | − | 0.337961i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −297.047 | − | 171.500i | −0.344202 | − | 0.198725i | 0.317926 | − | 0.948115i | \(-0.397014\pi\) |
−0.662129 | + | 0.749390i | \(0.730347\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −119.500 | − | 206.980i | −0.138150 | − | 0.239283i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 288.000i | − | 0.332180i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −697.000 | −0.802071 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1351.00 | − | 780.000i | 1.55109 | − | 0.895522i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −576.000 | + | 997.661i | −0.659794 | + | 1.14280i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 343.000i | − | 0.392000i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 575.500 | − | 996.795i | 0.656214 | − | 1.13660i | −0.325374 | − | 0.945586i | \(-0.605490\pi\) |
0.981588 | − | 0.191011i | \(-0.0611766\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.5167 | − | 13.0000i | 0.0256162 | − | 0.0147895i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −866.000 | −0.982974 | −0.491487 | − | 0.870885i | \(-0.663546\pi\) | ||||
−0.491487 | + | 0.870885i | \(0.663546\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 648.000i | − | 0.733862i | −0.930248 | − | 0.366931i | \(-0.880409\pi\) | ||
0.930248 | − | 0.366931i | \(-0.119591\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.50000 | + | 14.7224i | 0.00960452 | + | 0.0166355i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 588.031 | + | 339.500i | 0.662944 | + | 0.382751i | 0.793398 | − | 0.608704i | \(-0.208310\pi\) |
−0.130454 | + | 0.991454i | \(0.541643\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1008.00 | −1.13386 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 809.734 | + | 467.500i | 0.908792 | + | 0.524691i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 192.500 | + | 333.420i | 0.215566 | + | 0.373370i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 17.0000i | − | 0.0189944i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −168.000 | −0.187291 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −852.169 | + | 492.000i | −0.947908 | + | 0.547275i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.5000 | − | 21.6506i | 0.0138735 | − | 0.0240296i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 145.492 | − | 84.0000i | 0.161121 | − | 0.0930233i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −35.0000 | + | 60.6218i | −0.0386740 | + | 0.0669854i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 305.707 | − | 176.500i | 0.337053 | − | 0.194598i | −0.321915 | − | 0.946769i | \(-0.604327\pi\) |
0.658968 | + | 0.752171i | \(0.270993\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 584.000 | 0.642464 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 144.000i | − | 0.158068i | −0.996872 | − | 0.0790340i | \(-0.974816\pi\) | ||
0.996872 | − | 0.0790340i | \(-0.0251836\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 612.000 | + | 1060.02i | 0.670318 | + | 1.16102i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.866025 | + | 0.500000i | 0.000946476 | + | 0.000546448i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −647.500 | + | 1121.50i | −0.706107 | + | 1.22301i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −950.030 | − | 548.500i | −1.03376 | − | 0.596844i | −0.115704 | − | 0.993284i | \(-0.536912\pi\) |
−0.918061 | + | 0.396439i | \(0.870246\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 132.000 | + | 228.631i | 0.143322 | + | 0.248242i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 2304.00i | − | 2.49621i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1176.00 | 1.27135 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −616.610 | + | 356.000i | −0.665167 | + | 0.384035i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 264.500 | − | 458.127i | 0.284715 | − | 0.493140i | −0.687825 | − | 0.725876i | \(-0.741434\pi\) |
0.972540 | + | 0.232736i | \(0.0747678\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −297.047 | − | 171.500i | −0.319062 | − | 0.184211i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −171.500 | + | 297.047i | −0.183816 | + | 0.318378i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.7224 | + | 8.50000i | −0.0157459 | + | 0.00909091i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 146.000 | 0.155816 | 0.0779082 | − | 0.996961i | \(-0.475176\pi\) | ||||
0.0779082 | + | 0.996961i | \(0.475176\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 335.000i | 0.356763i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −371.500 | − | 643.457i | −0.394793 | − | 0.683801i | 0.598282 | − | 0.801286i | \(-0.295850\pi\) |
−0.993075 | + | 0.117485i | \(0.962517\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 290.985 | + | 168.000i | 0.308573 | + | 0.178155i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 59.5000 | − | 103.057i | 0.0629630 | − | 0.109055i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 451.199 | + | 260.500i | 0.476451 | + | 0.275079i | 0.718936 | − | 0.695076i | \(-0.244629\pi\) |
−0.242485 | + | 0.970155i | \(0.577963\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1140.00 | − | 1974.54i | −1.20126 | − | 2.08065i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 529.000i | − | 0.556257i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1440.00 | 1.51102 | 0.755509 | − | 0.655138i | \(-0.227390\pi\) | ||||
0.755509 | + | 0.655138i | \(0.227390\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −172.339 | + | 99.5000i | −0.180460 | + | 0.104188i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −204.000 | + | 353.338i | −0.213166 | + | 0.369215i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −866.891 | + | 500.500i | −0.903954 | + | 0.521898i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 360.000 | − | 623.538i | 0.374610 | − | 0.648843i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1281.72 | − | 740.000i | 1.33096 | − | 0.768432i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −47.0000 | −0.0487047 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1920.00i | − | 1.98552i | −0.120106 | − | 0.992761i | \(-0.538323\pi\) | ||
0.120106 | − | 0.992761i | \(-0.461677\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.50000 | − | 6.06218i | −0.00361197 | − | 0.00625612i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 284.922 | + | 164.500i | 0.293432 | + | 0.169413i | 0.639489 | − | 0.768801i | \(-0.279146\pi\) |
−0.346057 | + | 0.938214i | \(0.612479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1512.00 | −1.55396 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 498.831 | + | 288.000i | 0.511621 | + | 0.295385i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −360.500 | − | 624.404i | −0.368987 | − | 0.639104i | 0.620421 | − | 0.784269i | \(-0.286962\pi\) |
−0.989407 | + | 0.145165i | \(0.953629\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1615.00i | − | 1.64964i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −568.000 | −0.579001 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 546.462 | − | 315.500i | 0.555913 | − | 0.320956i | −0.195591 | − | 0.980686i | \(-0.562662\pi\) |
0.751503 | + | 0.659729i | \(0.229329\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.0000 | + | 20.7846i | −0.0121827 | + | 0.0211011i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 385.000i | 0.390071i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −84.0000 | + | 145.492i | −0.0849343 | + | 0.147110i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −629.600 | + | 363.500i | −0.635318 | + | 0.366801i | −0.782809 | − | 0.622262i | \(-0.786214\pi\) |
0.147491 | + | 0.989063i | \(0.452880\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −55.0000 | −0.0553877 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 137.000i | − | 0.137688i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.5000 | + | 21.6506i | 0.0125376 | + | 0.0217158i | 0.872226 | − | 0.489103i | \(-0.162676\pi\) |
−0.859689 | + | 0.510819i | \(0.829342\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 721.399 | + | 416.500i | 0.722121 | + | 0.416917i |
(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 | 224.3.r.b.191.2 | yes | 4 | |
4.3 | odd | 2 | inner | 224.3.r.b.191.1 | yes | 4 | |
7.2 | even | 3 | 1568.3.d.d.1471.2 | 2 | |||
7.4 | even | 3 | inner | 224.3.r.b.95.1 | ✓ | 4 | |
7.5 | odd | 6 | 1568.3.d.c.1471.1 | 2 | |||
8.3 | odd | 2 | 448.3.r.b.191.2 | 4 | |||
8.5 | even | 2 | 448.3.r.b.191.1 | 4 | |||
28.11 | odd | 6 | inner | 224.3.r.b.95.2 | yes | 4 | |
28.19 | even | 6 | 1568.3.d.c.1471.2 | 2 | |||
28.23 | odd | 6 | 1568.3.d.d.1471.1 | 2 | |||
56.11 | odd | 6 | 448.3.r.b.319.1 | 4 | |||
56.53 | even | 6 | 448.3.r.b.319.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.r.b.95.1 | ✓ | 4 | 7.4 | even | 3 | inner | |
224.3.r.b.95.2 | yes | 4 | 28.11 | odd | 6 | inner | |
224.3.r.b.191.1 | yes | 4 | 4.3 | odd | 2 | inner | |
224.3.r.b.191.2 | yes | 4 | 1.1 | even | 1 | trivial | |
448.3.r.b.191.1 | 4 | 8.5 | even | 2 | |||
448.3.r.b.191.2 | 4 | 8.3 | odd | 2 | |||
448.3.r.b.319.1 | 4 | 56.11 | odd | 6 | |||
448.3.r.b.319.2 | 4 | 56.53 | even | 6 | |||
1568.3.d.c.1471.1 | 2 | 7.5 | odd | 6 | |||
1568.3.d.c.1471.2 | 2 | 28.19 | even | 6 | |||
1568.3.d.d.1471.1 | 2 | 28.23 | odd | 6 | |||
1568.3.d.d.1471.2 | 2 | 7.2 | even | 3 |