Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4830,2,Mod(1,4830)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4830, 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("4830.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4830.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: | \(38.5677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.34292\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4830.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 2.68585 | 0.809813 | 0.404907 | − | 0.914358i | \(-0.367304\pi\) | ||||
0.404907 | + | 0.914358i | \(0.367304\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0.292731 | 0.0811890 | 0.0405945 | − | 0.999176i | \(-0.487075\pi\) | ||||
0.0405945 | + | 0.999176i | \(0.487075\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.97858 | −1.69255 | −0.846277 | − | 0.532743i | \(-0.821161\pi\) | ||||
−0.846277 | + | 0.532743i | \(0.821161\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.39312 | 1.00785 | 0.503925 | − | 0.863747i | \(-0.331889\pi\) | ||||
0.503925 | + | 0.863747i | \(0.331889\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −2.68585 | −0.572624 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.292731 | −0.0574093 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 0.685846 | 0.127358 | 0.0636792 | − | 0.997970i | \(-0.479717\pi\) | ||||
0.0636792 | + | 0.997970i | \(0.479717\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 8.97858 | 1.61260 | 0.806300 | − | 0.591507i | \(-0.201467\pi\) | ||||
0.806300 | + | 0.591507i | \(0.201467\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.68585 | −0.467546 | ||||||||
\(34\) | 6.97858 | 1.19682 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | −4.39312 | −0.712657 | ||||||||
\(39\) | −0.292731 | −0.0468745 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −7.37169 | −1.15126 | −0.575632 | − | 0.817709i | \(-0.695244\pi\) | ||||
−0.575632 | + | 0.817709i | \(0.695244\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | −6.68585 | −1.01958 | −0.509791 | − | 0.860298i | \(-0.670277\pi\) | ||||
−0.509791 | + | 0.860298i | \(0.670277\pi\) | |||||||
\(44\) | 2.68585 | 0.404907 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 10.3503 | 1.50974 | 0.754871 | − | 0.655873i | \(-0.227699\pi\) | ||||
0.754871 | + | 0.655873i | \(0.227699\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 6.97858 | 0.977196 | ||||||||
\(52\) | 0.292731 | 0.0405945 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −2.68585 | −0.362159 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −4.39312 | −0.581882 | ||||||||
\(58\) | −0.685846 | −0.0900560 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 7.37169 | 0.943848 | 0.471924 | − | 0.881639i | \(-0.343560\pi\) | ||||
0.471924 | + | 0.881639i | \(0.343560\pi\) | |||||||
\(62\) | −8.97858 | −1.14028 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.292731 | −0.0363088 | ||||||||
\(66\) | 2.68585 | 0.330605 | ||||||||
\(67\) | 1.31415 | 0.160549 | 0.0802747 | − | 0.996773i | \(-0.474420\pi\) | ||||
0.0802747 | + | 0.996773i | \(0.474420\pi\) | |||||||
\(68\) | −6.97858 | −0.846277 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | 7.27131 | 0.862946 | 0.431473 | − | 0.902126i | \(-0.357994\pi\) | ||||
0.431473 | + | 0.902126i | \(0.357994\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 11.9572 | 1.39948 | 0.699740 | − | 0.714398i | \(-0.253299\pi\) | ||||
0.699740 | + | 0.714398i | \(0.253299\pi\) | |||||||
\(74\) | 6.00000 | 0.697486 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 4.39312 | 0.503925 | ||||||||
\(77\) | −2.68585 | −0.306081 | ||||||||
\(78\) | 0.292731 | 0.0331453 | ||||||||
\(79\) | −15.3288 | −1.72463 | −0.862315 | − | 0.506372i | \(-0.830986\pi\) | ||||
−0.862315 | + | 0.506372i | \(0.830986\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.37169 | 0.814067 | ||||||||
\(83\) | 0.393115 | 0.0431500 | 0.0215750 | − | 0.999767i | \(-0.493132\pi\) | ||||
0.0215750 | + | 0.999767i | \(0.493132\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 6.97858 | 0.756933 | ||||||||
\(86\) | 6.68585 | 0.720953 | ||||||||
\(87\) | −0.685846 | −0.0735304 | ||||||||
\(88\) | −2.68585 | −0.286312 | ||||||||
\(89\) | −9.66442 | −1.02443 | −0.512213 | − | 0.858858i | \(-0.671174\pi\) | ||||
−0.512213 | + | 0.858858i | \(0.671174\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | −0.292731 | −0.0306865 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −8.97858 | −0.931035 | ||||||||
\(94\) | −10.3503 | −1.06755 | ||||||||
\(95\) | −4.39312 | −0.450724 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −10.2499 | −1.04072 | −0.520359 | − | 0.853948i | \(-0.674202\pi\) | ||||
−0.520359 | + | 0.853948i | \(0.674202\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 2.68585 | 0.269938 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 4.29273 | 0.427143 | 0.213571 | − | 0.976927i | \(-0.431490\pi\) | ||||
0.213571 | + | 0.976927i | \(0.431490\pi\) | |||||||
\(102\) | −6.97858 | −0.690982 | ||||||||
\(103\) | −4.58546 | −0.451819 | −0.225909 | − | 0.974148i | \(-0.572535\pi\) | ||||
−0.225909 | + | 0.974148i | \(0.572535\pi\) | |||||||
\(104\) | −0.292731 | −0.0287046 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 1.37169 | 0.132607 | 0.0663033 | − | 0.997800i | \(-0.478880\pi\) | ||||
0.0663033 | + | 0.997800i | \(0.478880\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 6.00000 | 0.574696 | 0.287348 | − | 0.957826i | \(-0.407226\pi\) | ||||
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | 2.68585 | 0.256085 | ||||||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 15.9572 | 1.50112 | 0.750561 | − | 0.660801i | \(-0.229783\pi\) | ||||
0.750561 | + | 0.660801i | \(0.229783\pi\) | |||||||
\(114\) | 4.39312 | 0.411453 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0.685846 | 0.0636792 | ||||||||
\(117\) | 0.292731 | 0.0270630 | ||||||||
\(118\) | 4.00000 | 0.368230 | ||||||||
\(119\) | 6.97858 | 0.639725 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −3.78623 | −0.344203 | ||||||||
\(122\) | −7.37169 | −0.667402 | ||||||||
\(123\) | 7.37169 | 0.664683 | ||||||||
\(124\) | 8.97858 | 0.806300 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 12.0575 | 1.06993 | 0.534967 | − | 0.844873i | \(-0.320324\pi\) | ||||
0.534967 | + | 0.844873i | \(0.320324\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 6.68585 | 0.588656 | ||||||||
\(130\) | 0.292731 | 0.0256742 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | −2.68585 | −0.233773 | ||||||||
\(133\) | −4.39312 | −0.380931 | ||||||||
\(134\) | −1.31415 | −0.113526 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 6.97858 | 0.598408 | ||||||||
\(137\) | −21.9143 | −1.87227 | −0.936133 | − | 0.351646i | \(-0.885622\pi\) | ||||
−0.936133 | + | 0.351646i | \(0.885622\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | 18.7434 | 1.58979 | 0.794897 | − | 0.606745i | \(-0.207525\pi\) | ||||
0.794897 | + | 0.606745i | \(0.207525\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | −10.3503 | −0.871650 | ||||||||
\(142\) | −7.27131 | −0.610195 | ||||||||
\(143\) | 0.786230 | 0.0657479 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.685846 | −0.0569564 | ||||||||
\(146\) | −11.9572 | −0.989581 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −6.00000 | −0.493197 | ||||||||
\(149\) | −16.7434 | −1.37167 | −0.685836 | − | 0.727756i | \(-0.740563\pi\) | ||||
−0.685836 | + | 0.727756i | \(0.740563\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −15.3288 | −1.24744 | −0.623722 | − | 0.781646i | \(-0.714380\pi\) | ||||
−0.623722 | + | 0.781646i | \(0.714380\pi\) | |||||||
\(152\) | −4.39312 | −0.356329 | ||||||||
\(153\) | −6.97858 | −0.564185 | ||||||||
\(154\) | 2.68585 | 0.216432 | ||||||||
\(155\) | −8.97858 | −0.721177 | ||||||||
\(156\) | −0.292731 | −0.0234372 | ||||||||
\(157\) | 10.5855 | 0.844812 | 0.422406 | − | 0.906407i | \(-0.361186\pi\) | ||||
0.422406 | + | 0.906407i | \(0.361186\pi\) | |||||||
\(158\) | 15.3288 | 1.21950 | ||||||||
\(159\) | 6.00000 | 0.475831 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −8.00000 | −0.626608 | −0.313304 | − | 0.949653i | \(-0.601436\pi\) | ||||
−0.313304 | + | 0.949653i | \(0.601436\pi\) | |||||||
\(164\) | −7.37169 | −0.575632 | ||||||||
\(165\) | 2.68585 | 0.209093 | ||||||||
\(166\) | −0.393115 | −0.0305117 | ||||||||
\(167\) | 4.19235 | 0.324414 | 0.162207 | − | 0.986757i | \(-0.448139\pi\) | ||||
0.162207 | + | 0.986757i | \(0.448139\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | −12.9143 | −0.993408 | ||||||||
\(170\) | −6.97858 | −0.535232 | ||||||||
\(171\) | 4.39312 | 0.335950 | ||||||||
\(172\) | −6.68585 | −0.509791 | ||||||||
\(173\) | 11.7648 | 0.894462 | 0.447231 | − | 0.894419i | \(-0.352410\pi\) | ||||
0.447231 | + | 0.894419i | \(0.352410\pi\) | |||||||
\(174\) | 0.685846 | 0.0519939 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 2.68585 | 0.202453 | ||||||||
\(177\) | 4.00000 | 0.300658 | ||||||||
\(178\) | 9.66442 | 0.724379 | ||||||||
\(179\) | 5.95715 | 0.445259 | 0.222629 | − | 0.974903i | \(-0.428536\pi\) | ||||
0.222629 | + | 0.974903i | \(0.428536\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 24.5426 | 1.82424 | 0.912119 | − | 0.409925i | \(-0.134445\pi\) | ||||
0.912119 | + | 0.409925i | \(0.134445\pi\) | |||||||
\(182\) | 0.292731 | 0.0216987 | ||||||||
\(183\) | −7.37169 | −0.544931 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 6.00000 | 0.441129 | ||||||||
\(186\) | 8.97858 | 0.658341 | ||||||||
\(187\) | −18.7434 | −1.37065 | ||||||||
\(188\) | 10.3503 | 0.754871 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 4.39312 | 0.318710 | ||||||||
\(191\) | −13.9572 | −1.00990 | −0.504952 | − | 0.863147i | \(-0.668490\pi\) | ||||
−0.504952 | + | 0.863147i | \(0.668490\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 25.3288 | 1.82321 | 0.911605 | − | 0.411067i | \(-0.134844\pi\) | ||||
0.911605 | + | 0.411067i | \(0.134844\pi\) | |||||||
\(194\) | 10.2499 | 0.735899 | ||||||||
\(195\) | 0.292731 | 0.0209629 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 11.9572 | 0.851912 | 0.425956 | − | 0.904744i | \(-0.359938\pi\) | ||||
0.425956 | + | 0.904744i | \(0.359938\pi\) | |||||||
\(198\) | −2.68585 | −0.190875 | ||||||||
\(199\) | 15.3288 | 1.08663 | 0.543317 | − | 0.839528i | \(-0.317168\pi\) | ||||
0.543317 | + | 0.839528i | \(0.317168\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −1.31415 | −0.0926933 | ||||||||
\(202\) | −4.29273 | −0.302035 | ||||||||
\(203\) | −0.685846 | −0.0481370 | ||||||||
\(204\) | 6.97858 | 0.488598 | ||||||||
\(205\) | 7.37169 | 0.514861 | ||||||||
\(206\) | 4.58546 | 0.319484 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0.292731 | 0.0202972 | ||||||||
\(209\) | 11.7992 | 0.816170 | ||||||||
\(210\) | 1.00000 | 0.0690066 | ||||||||
\(211\) | 7.41454 | 0.510438 | 0.255219 | − | 0.966883i | \(-0.417852\pi\) | ||||
0.255219 | + | 0.966883i | \(0.417852\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | −7.27131 | −0.498222 | ||||||||
\(214\) | −1.37169 | −0.0937670 | ||||||||
\(215\) | 6.68585 | 0.455971 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −8.97858 | −0.609506 | ||||||||
\(218\) | −6.00000 | −0.406371 | ||||||||
\(219\) | −11.9572 | −0.807990 | ||||||||
\(220\) | −2.68585 | −0.181080 | ||||||||
\(221\) | −2.04285 | −0.137417 | ||||||||
\(222\) | −6.00000 | −0.402694 | ||||||||
\(223\) | 19.0790 | 1.27762 | 0.638811 | − | 0.769364i | \(-0.279427\pi\) | ||||
0.638811 | + | 0.769364i | \(0.279427\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −15.9572 | −1.06145 | ||||||||
\(227\) | 12.9786 | 0.861418 | 0.430709 | − | 0.902491i | \(-0.358263\pi\) | ||||
0.430709 | + | 0.902491i | \(0.358263\pi\) | |||||||
\(228\) | −4.39312 | −0.290941 | ||||||||
\(229\) | 18.7862 | 1.24143 | 0.620715 | − | 0.784037i | \(-0.286843\pi\) | ||||
0.620715 | + | 0.784037i | \(0.286843\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | 2.68585 | 0.176716 | ||||||||
\(232\) | −0.685846 | −0.0450280 | ||||||||
\(233\) | 15.9572 | 1.04539 | 0.522694 | − | 0.852520i | \(-0.324927\pi\) | ||||
0.522694 | + | 0.852520i | \(0.324927\pi\) | |||||||
\(234\) | −0.292731 | −0.0191364 | ||||||||
\(235\) | −10.3503 | −0.675177 | ||||||||
\(236\) | −4.00000 | −0.260378 | ||||||||
\(237\) | 15.3288 | 0.995716 | ||||||||
\(238\) | −6.97858 | −0.452354 | ||||||||
\(239\) | 7.27131 | 0.470342 | 0.235171 | − | 0.971954i | \(-0.424435\pi\) | ||||
0.235171 | + | 0.971954i | \(0.424435\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 3.64973 | 0.235100 | 0.117550 | − | 0.993067i | \(-0.462496\pi\) | ||||
0.117550 | + | 0.993067i | \(0.462496\pi\) | |||||||
\(242\) | 3.78623 | 0.243388 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 7.37169 | 0.471924 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −7.37169 | −0.470002 | ||||||||
\(247\) | 1.28600 | 0.0818263 | ||||||||
\(248\) | −8.97858 | −0.570140 | ||||||||
\(249\) | −0.393115 | −0.0249127 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −13.6216 | −0.859786 | −0.429893 | − | 0.902880i | \(-0.641449\pi\) | ||||
−0.429893 | + | 0.902880i | \(0.641449\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | 2.68585 | 0.168858 | ||||||||
\(254\) | −12.0575 | −0.756557 | ||||||||
\(255\) | −6.97858 | −0.437015 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.5855 | 0.909816 | 0.454908 | − | 0.890538i | \(-0.349672\pi\) | ||||
0.454908 | + | 0.890538i | \(0.349672\pi\) | |||||||
\(258\) | −6.68585 | −0.416243 | ||||||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | −0.292731 | −0.0181544 | ||||||||
\(261\) | 0.685846 | 0.0424528 | ||||||||
\(262\) | 4.00000 | 0.247121 | ||||||||
\(263\) | −31.3288 | −1.93182 | −0.965910 | − | 0.258879i | \(-0.916647\pi\) | ||||
−0.965910 | + | 0.258879i | \(0.916647\pi\) | |||||||
\(264\) | 2.68585 | 0.165302 | ||||||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | 4.39312 | 0.269359 | ||||||||
\(267\) | 9.66442 | 0.591453 | ||||||||
\(268\) | 1.31415 | 0.0802747 | ||||||||
\(269\) | −10.2499 | −0.624947 | −0.312473 | − | 0.949927i | \(-0.601157\pi\) | ||||
−0.312473 | + | 0.949927i | \(0.601157\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −1.76481 | −0.107204 | −0.0536022 | − | 0.998562i | \(-0.517070\pi\) | ||||
−0.0536022 | + | 0.998562i | \(0.517070\pi\) | |||||||
\(272\) | −6.97858 | −0.423138 | ||||||||
\(273\) | 0.292731 | 0.0177169 | ||||||||
\(274\) | 21.9143 | 1.32389 | ||||||||
\(275\) | 2.68585 | 0.161963 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 9.47208 | 0.569122 | 0.284561 | − | 0.958658i | \(-0.408152\pi\) | ||||
0.284561 | + | 0.958658i | \(0.408152\pi\) | |||||||
\(278\) | −18.7434 | −1.12415 | ||||||||
\(279\) | 8.97858 | 0.537533 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 32.8009 | 1.95674 | 0.978370 | − | 0.206865i | \(-0.0663261\pi\) | ||||
0.978370 | + | 0.206865i | \(0.0663261\pi\) | |||||||
\(282\) | 10.3503 | 0.616350 | ||||||||
\(283\) | −9.03612 | −0.537141 | −0.268571 | − | 0.963260i | \(-0.586551\pi\) | ||||
−0.268571 | + | 0.963260i | \(0.586551\pi\) | |||||||
\(284\) | 7.27131 | 0.431473 | ||||||||
\(285\) | 4.39312 | 0.260226 | ||||||||
\(286\) | −0.786230 | −0.0464908 | ||||||||
\(287\) | 7.37169 | 0.435137 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 31.7005 | 1.86474 | ||||||||
\(290\) | 0.685846 | 0.0402743 | ||||||||
\(291\) | 10.2499 | 0.600859 | ||||||||
\(292\) | 11.9572 | 0.699740 | ||||||||
\(293\) | −13.3288 | −0.778680 | −0.389340 | − | 0.921094i | \(-0.627297\pi\) | ||||
−0.389340 | + | 0.921094i | \(0.627297\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | 6.00000 | 0.348743 | ||||||||
\(297\) | −2.68585 | −0.155849 | ||||||||
\(298\) | 16.7434 | 0.969918 | ||||||||
\(299\) | 0.292731 | 0.0169291 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 6.68585 | 0.385366 | ||||||||
\(302\) | 15.3288 | 0.882076 | ||||||||
\(303\) | −4.29273 | −0.246611 | ||||||||
\(304\) | 4.39312 | 0.251962 | ||||||||
\(305\) | −7.37169 | −0.422102 | ||||||||
\(306\) | 6.97858 | 0.398939 | ||||||||
\(307\) | 10.1579 | 0.579743 | 0.289872 | − | 0.957066i | \(-0.406387\pi\) | ||||
0.289872 | + | 0.957066i | \(0.406387\pi\) | |||||||
\(308\) | −2.68585 | −0.153040 | ||||||||
\(309\) | 4.58546 | 0.260858 | ||||||||
\(310\) | 8.97858 | 0.509949 | ||||||||
\(311\) | −5.03612 | −0.285572 | −0.142786 | − | 0.989754i | \(-0.545606\pi\) | ||||
−0.142786 | + | 0.989754i | \(0.545606\pi\) | |||||||
\(312\) | 0.292731 | 0.0165726 | ||||||||
\(313\) | 29.0790 | 1.64364 | 0.821820 | − | 0.569747i | \(-0.192959\pi\) | ||||
0.821820 | + | 0.569747i | \(0.192959\pi\) | |||||||
\(314\) | −10.5855 | −0.597372 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | −15.3288 | −0.862315 | ||||||||
\(317\) | −18.5855 | −1.04386 | −0.521932 | − | 0.852987i | \(-0.674788\pi\) | ||||
−0.521932 | + | 0.852987i | \(0.674788\pi\) | |||||||
\(318\) | −6.00000 | −0.336463 | ||||||||
\(319\) | 1.84208 | 0.103137 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −1.37169 | −0.0765604 | ||||||||
\(322\) | 1.00000 | 0.0557278 | ||||||||
\(323\) | −30.6577 | −1.70584 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.292731 | 0.0162378 | ||||||||
\(326\) | 8.00000 | 0.443079 | ||||||||
\(327\) | −6.00000 | −0.331801 | ||||||||
\(328\) | 7.37169 | 0.407034 | ||||||||
\(329\) | −10.3503 | −0.570629 | ||||||||
\(330\) | −2.68585 | −0.147851 | ||||||||
\(331\) | −0.585462 | −0.0321799 | −0.0160899 | − | 0.999871i | \(-0.505122\pi\) | ||||
−0.0160899 | + | 0.999871i | \(0.505122\pi\) | |||||||
\(332\) | 0.393115 | 0.0215750 | ||||||||
\(333\) | −6.00000 | −0.328798 | ||||||||
\(334\) | −4.19235 | −0.229395 | ||||||||
\(335\) | −1.31415 | −0.0717999 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | −5.85677 | −0.319039 | −0.159519 | − | 0.987195i | \(-0.550994\pi\) | ||||
−0.159519 | + | 0.987195i | \(0.550994\pi\) | |||||||
\(338\) | 12.9143 | 0.702446 | ||||||||
\(339\) | −15.9572 | −0.866674 | ||||||||
\(340\) | 6.97858 | 0.378466 | ||||||||
\(341\) | 24.1151 | 1.30590 | ||||||||
\(342\) | −4.39312 | −0.237552 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 6.68585 | 0.360477 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | −11.7648 | −0.632480 | ||||||||
\(347\) | −22.7434 | −1.22093 | −0.610464 | − | 0.792044i | \(-0.709017\pi\) | ||||
−0.610464 | + | 0.792044i | \(0.709017\pi\) | |||||||
\(348\) | −0.685846 | −0.0367652 | ||||||||
\(349\) | 22.3931 | 1.19868 | 0.599338 | − | 0.800496i | \(-0.295431\pi\) | ||||
0.599338 | + | 0.800496i | \(0.295431\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −0.292731 | −0.0156248 | ||||||||
\(352\) | −2.68585 | −0.143156 | ||||||||
\(353\) | 18.7862 | 0.999890 | 0.499945 | − | 0.866057i | \(-0.333354\pi\) | ||||
0.499945 | + | 0.866057i | \(0.333354\pi\) | |||||||
\(354\) | −4.00000 | −0.212598 | ||||||||
\(355\) | −7.27131 | −0.385921 | ||||||||
\(356\) | −9.66442 | −0.512213 | ||||||||
\(357\) | −6.97858 | −0.369345 | ||||||||
\(358\) | −5.95715 | −0.314845 | ||||||||
\(359\) | −31.5296 | −1.66407 | −0.832035 | − | 0.554724i | \(-0.812824\pi\) | ||||
−0.832035 | + | 0.554724i | \(0.812824\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 0.299461 | 0.0157611 | ||||||||
\(362\) | −24.5426 | −1.28993 | ||||||||
\(363\) | 3.78623 | 0.198726 | ||||||||
\(364\) | −0.292731 | −0.0153433 | ||||||||
\(365\) | −11.9572 | −0.625866 | ||||||||
\(366\) | 7.37169 | 0.385325 | ||||||||
\(367\) | 26.0722 | 1.36096 | 0.680480 | − | 0.732767i | \(-0.261771\pi\) | ||||
0.680480 | + | 0.732767i | \(0.261771\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −7.37169 | −0.383755 | ||||||||
\(370\) | −6.00000 | −0.311925 | ||||||||
\(371\) | 6.00000 | 0.311504 | ||||||||
\(372\) | −8.97858 | −0.465518 | ||||||||
\(373\) | 19.1709 | 0.992633 | 0.496316 | − | 0.868142i | \(-0.334686\pi\) | ||||
0.496316 | + | 0.868142i | \(0.334686\pi\) | |||||||
\(374\) | 18.7434 | 0.969197 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −10.3503 | −0.533774 | ||||||||
\(377\) | 0.200768 | 0.0103401 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 6.62831 | 0.340473 | 0.170237 | − | 0.985403i | \(-0.445547\pi\) | ||||
0.170237 | + | 0.985403i | \(0.445547\pi\) | |||||||
\(380\) | −4.39312 | −0.225362 | ||||||||
\(381\) | −12.0575 | −0.617726 | ||||||||
\(382\) | 13.9572 | 0.714110 | ||||||||
\(383\) | −1.37169 | −0.0700902 | −0.0350451 | − | 0.999386i | \(-0.511157\pi\) | ||||
−0.0350451 | + | 0.999386i | \(0.511157\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 2.68585 | 0.136883 | ||||||||
\(386\) | −25.3288 | −1.28920 | ||||||||
\(387\) | −6.68585 | −0.339861 | ||||||||
\(388\) | −10.2499 | −0.520359 | ||||||||
\(389\) | 18.7862 | 0.952500 | 0.476250 | − | 0.879310i | \(-0.341996\pi\) | ||||
0.476250 | + | 0.879310i | \(0.341996\pi\) | |||||||
\(390\) | −0.292731 | −0.0148230 | ||||||||
\(391\) | −6.97858 | −0.352922 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 4.00000 | 0.201773 | ||||||||
\(394\) | −11.9572 | −0.602393 | ||||||||
\(395\) | 15.3288 | 0.771278 | ||||||||
\(396\) | 2.68585 | 0.134969 | ||||||||
\(397\) | −17.2797 | −0.867245 | −0.433622 | − | 0.901095i | \(-0.642765\pi\) | ||||
−0.433622 | + | 0.901095i | \(0.642765\pi\) | |||||||
\(398\) | −15.3288 | −0.768366 | ||||||||
\(399\) | 4.39312 | 0.219931 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −15.3142 | −0.764752 | −0.382376 | − | 0.924007i | \(-0.624894\pi\) | ||||
−0.382376 | + | 0.924007i | \(0.624894\pi\) | |||||||
\(402\) | 1.31415 | 0.0655440 | ||||||||
\(403\) | 2.62831 | 0.130925 | ||||||||
\(404\) | 4.29273 | 0.213571 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0.685846 | 0.0340380 | ||||||||
\(407\) | −16.1151 | −0.798795 | ||||||||
\(408\) | −6.97858 | −0.345491 | ||||||||
\(409\) | −12.1579 | −0.601171 | −0.300585 | − | 0.953755i | \(-0.597182\pi\) | ||||
−0.300585 | + | 0.953755i | \(0.597182\pi\) | |||||||
\(410\) | −7.37169 | −0.364062 | ||||||||
\(411\) | 21.9143 | 1.08095 | ||||||||
\(412\) | −4.58546 | −0.225909 | ||||||||
\(413\) | 4.00000 | 0.196827 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | −0.393115 | −0.0192973 | ||||||||
\(416\) | −0.292731 | −0.0143523 | ||||||||
\(417\) | −18.7434 | −0.917867 | ||||||||
\(418\) | −11.7992 | −0.577119 | ||||||||
\(419\) | 28.8353 | 1.40870 | 0.704349 | − | 0.709853i | \(-0.251239\pi\) | ||||
0.704349 | + | 0.709853i | \(0.251239\pi\) | |||||||
\(420\) | −1.00000 | −0.0487950 | ||||||||
\(421\) | 12.0428 | 0.586932 | 0.293466 | − | 0.955969i | \(-0.405191\pi\) | ||||
0.293466 | + | 0.955969i | \(0.405191\pi\) | |||||||
\(422\) | −7.41454 | −0.360934 | ||||||||
\(423\) | 10.3503 | 0.503247 | ||||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | −6.97858 | −0.338511 | ||||||||
\(426\) | 7.27131 | 0.352296 | ||||||||
\(427\) | −7.37169 | −0.356741 | ||||||||
\(428\) | 1.37169 | 0.0663033 | ||||||||
\(429\) | −0.786230 | −0.0379596 | ||||||||
\(430\) | −6.68585 | −0.322420 | ||||||||
\(431\) | 19.3288 | 0.931038 | 0.465519 | − | 0.885038i | \(-0.345868\pi\) | ||||
0.465519 | + | 0.885038i | \(0.345868\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −4.99327 | −0.239961 | −0.119981 | − | 0.992776i | \(-0.538283\pi\) | ||||
−0.119981 | + | 0.992776i | \(0.538283\pi\) | |||||||
\(434\) | 8.97858 | 0.430985 | ||||||||
\(435\) | 0.685846 | 0.0328838 | ||||||||
\(436\) | 6.00000 | 0.287348 | ||||||||
\(437\) | 4.39312 | 0.210151 | ||||||||
\(438\) | 11.9572 | 0.571335 | ||||||||
\(439\) | 21.5640 | 1.02920 | 0.514598 | − | 0.857432i | \(-0.327941\pi\) | ||||
0.514598 | + | 0.857432i | \(0.327941\pi\) | |||||||
\(440\) | 2.68585 | 0.128043 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 2.04285 | 0.0971683 | ||||||||
\(443\) | 34.6577 | 1.64664 | 0.823318 | − | 0.567580i | \(-0.192120\pi\) | ||||
0.823318 | + | 0.567580i | \(0.192120\pi\) | |||||||
\(444\) | 6.00000 | 0.284747 | ||||||||
\(445\) | 9.66442 | 0.458138 | ||||||||
\(446\) | −19.0790 | −0.903415 | ||||||||
\(447\) | 16.7434 | 0.791935 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 18.7862 | 0.886577 | 0.443289 | − | 0.896379i | \(-0.353812\pi\) | ||||
0.443289 | + | 0.896379i | \(0.353812\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −19.7992 | −0.932309 | ||||||||
\(452\) | 15.9572 | 0.750561 | ||||||||
\(453\) | 15.3288 | 0.720212 | ||||||||
\(454\) | −12.9786 | −0.609115 | ||||||||
\(455\) | 0.292731 | 0.0137234 | ||||||||
\(456\) | 4.39312 | 0.205726 | ||||||||
\(457\) | 11.8139 | 0.552632 | 0.276316 | − | 0.961067i | \(-0.410886\pi\) | ||||
0.276316 | + | 0.961067i | \(0.410886\pi\) | |||||||
\(458\) | −18.7862 | −0.877823 | ||||||||
\(459\) | 6.97858 | 0.325732 | ||||||||
\(460\) | −1.00000 | −0.0466252 | ||||||||
\(461\) | 21.4637 | 0.999662 | 0.499831 | − | 0.866123i | \(-0.333395\pi\) | ||||
0.499831 | + | 0.866123i | \(0.333395\pi\) | |||||||
\(462\) | −2.68585 | −0.124957 | ||||||||
\(463\) | 40.6430 | 1.88884 | 0.944420 | − | 0.328741i | \(-0.106624\pi\) | ||||
0.944420 | + | 0.328741i | \(0.106624\pi\) | |||||||
\(464\) | 0.685846 | 0.0318396 | ||||||||
\(465\) | 8.97858 | 0.416372 | ||||||||
\(466\) | −15.9572 | −0.739201 | ||||||||
\(467\) | −28.3074 | −1.30991 | −0.654956 | − | 0.755667i | \(-0.727313\pi\) | ||||
−0.654956 | + | 0.755667i | \(0.727313\pi\) | |||||||
\(468\) | 0.292731 | 0.0135315 | ||||||||
\(469\) | −1.31415 | −0.0606820 | ||||||||
\(470\) | 10.3503 | 0.477422 | ||||||||
\(471\) | −10.5855 | −0.487752 | ||||||||
\(472\) | 4.00000 | 0.184115 | ||||||||
\(473\) | −17.9572 | −0.825671 | ||||||||
\(474\) | −15.3288 | −0.704077 | ||||||||
\(475\) | 4.39312 | 0.201570 | ||||||||
\(476\) | 6.97858 | 0.319863 | ||||||||
\(477\) | −6.00000 | −0.274721 | ||||||||
\(478\) | −7.27131 | −0.332582 | ||||||||
\(479\) | 14.1579 | 0.646892 | 0.323446 | − | 0.946247i | \(-0.395159\pi\) | ||||
0.323446 | + | 0.946247i | \(0.395159\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −1.75639 | −0.0800843 | ||||||||
\(482\) | −3.64973 | −0.166241 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | −3.78623 | −0.172101 | ||||||||
\(485\) | 10.2499 | 0.465423 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 15.4721 | 0.701107 | 0.350553 | − | 0.936543i | \(-0.385994\pi\) | ||||
0.350553 | + | 0.936543i | \(0.385994\pi\) | |||||||
\(488\) | −7.37169 | −0.333701 | ||||||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 23.1281 | 1.04376 | 0.521878 | − | 0.853020i | \(-0.325232\pi\) | ||||
0.521878 | + | 0.853020i | \(0.325232\pi\) | |||||||
\(492\) | 7.37169 | 0.332342 | ||||||||
\(493\) | −4.78623 | −0.215561 | ||||||||
\(494\) | −1.28600 | −0.0578599 | ||||||||
\(495\) | −2.68585 | −0.120720 | ||||||||
\(496\) | 8.97858 | 0.403150 | ||||||||
\(497\) | −7.27131 | −0.326163 | ||||||||
\(498\) | 0.393115 | 0.0176159 | ||||||||
\(499\) | −24.5855 | −1.10060 | −0.550298 | − | 0.834968i | \(-0.685486\pi\) | ||||
−0.550298 | + | 0.834968i | \(0.685486\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −4.19235 | −0.187300 | ||||||||
\(502\) | 13.6216 | 0.607961 | ||||||||
\(503\) | 23.4145 | 1.04400 | 0.522001 | − | 0.852945i | \(-0.325186\pi\) | ||||
0.522001 | + | 0.852945i | \(0.325186\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −4.29273 | −0.191024 | ||||||||
\(506\) | −2.68585 | −0.119400 | ||||||||
\(507\) | 12.9143 | 0.573545 | ||||||||
\(508\) | 12.0575 | 0.534967 | ||||||||
\(509\) | −14.4507 | −0.640514 | −0.320257 | − | 0.947331i | \(-0.603769\pi\) | ||||
−0.320257 | + | 0.947331i | \(0.603769\pi\) | |||||||
\(510\) | 6.97858 | 0.309017 | ||||||||
\(511\) | −11.9572 | −0.528953 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.39312 | −0.193961 | ||||||||
\(514\) | −14.5855 | −0.643337 | ||||||||
\(515\) | 4.58546 | 0.202060 | ||||||||
\(516\) | 6.68585 | 0.294328 | ||||||||
\(517\) | 27.7992 | 1.22261 | ||||||||
\(518\) | −6.00000 | −0.263625 | ||||||||
\(519\) | −11.7648 | −0.516418 | ||||||||
\(520\) | 0.292731 | 0.0128371 | ||||||||
\(521\) | −8.09196 | −0.354515 | −0.177258 | − | 0.984164i | \(-0.556723\pi\) | ||||
−0.177258 | + | 0.984164i | \(0.556723\pi\) | |||||||
\(522\) | −0.685846 | −0.0300187 | ||||||||
\(523\) | 24.3650 | 1.06541 | 0.532703 | − | 0.846302i | \(-0.321176\pi\) | ||||
0.532703 | + | 0.846302i | \(0.321176\pi\) | |||||||
\(524\) | −4.00000 | −0.174741 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 31.3288 | 1.36600 | ||||||||
\(527\) | −62.6577 | −2.72941 | ||||||||
\(528\) | −2.68585 | −0.116886 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −6.00000 | −0.260623 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | −4.39312 | −0.190466 | ||||||||
\(533\) | −2.15792 | −0.0934700 | ||||||||
\(534\) | −9.66442 | −0.418220 | ||||||||
\(535\) | −1.37169 | −0.0593034 | ||||||||
\(536\) | −1.31415 | −0.0567628 | ||||||||
\(537\) | −5.95715 | −0.257070 | ||||||||
\(538\) | 10.2499 | 0.441904 | ||||||||
\(539\) | 2.68585 | 0.115688 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | 32.4569 | 1.39543 | 0.697716 | − | 0.716374i | \(-0.254200\pi\) | ||||
0.697716 | + | 0.716374i | \(0.254200\pi\) | |||||||
\(542\) | 1.76481 | 0.0758050 | ||||||||
\(543\) | −24.5426 | −1.05322 | ||||||||
\(544\) | 6.97858 | 0.299204 | ||||||||
\(545\) | −6.00000 | −0.257012 | ||||||||
\(546\) | −0.292731 | −0.0125277 | ||||||||
\(547\) | −14.8291 | −0.634046 | −0.317023 | − | 0.948418i | \(-0.602683\pi\) | ||||
−0.317023 | + | 0.948418i | \(0.602683\pi\) | |||||||
\(548\) | −21.9143 | −0.936133 | ||||||||
\(549\) | 7.37169 | 0.314616 | ||||||||
\(550\) | −2.68585 | −0.114525 | ||||||||
\(551\) | 3.01300 | 0.128358 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 15.3288 | 0.651849 | ||||||||
\(554\) | −9.47208 | −0.402430 | ||||||||
\(555\) | −6.00000 | −0.254686 | ||||||||
\(556\) | 18.7434 | 0.794897 | ||||||||
\(557\) | 44.7434 | 1.89584 | 0.947919 | − | 0.318511i | \(-0.103183\pi\) | ||||
0.947919 | + | 0.318511i | \(0.103183\pi\) | |||||||
\(558\) | −8.97858 | −0.380093 | ||||||||
\(559\) | −1.95715 | −0.0827788 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 18.7434 | 0.791346 | ||||||||
\(562\) | −32.8009 | −1.38362 | ||||||||
\(563\) | 35.1365 | 1.48083 | 0.740413 | − | 0.672152i | \(-0.234630\pi\) | ||||
0.740413 | + | 0.672152i | \(0.234630\pi\) | |||||||
\(564\) | −10.3503 | −0.435825 | ||||||||
\(565\) | −15.9572 | −0.671323 | ||||||||
\(566\) | 9.03612 | 0.379816 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −7.27131 | −0.305097 | ||||||||
\(569\) | 39.3435 | 1.64937 | 0.824683 | − | 0.565595i | \(-0.191353\pi\) | ||||
0.824683 | + | 0.565595i | \(0.191353\pi\) | |||||||
\(570\) | −4.39312 | −0.184007 | ||||||||
\(571\) | 36.4998 | 1.52747 | 0.763734 | − | 0.645531i | \(-0.223364\pi\) | ||||
0.763734 | + | 0.645531i | \(0.223364\pi\) | |||||||
\(572\) | 0.786230 | 0.0328739 | ||||||||
\(573\) | 13.9572 | 0.583068 | ||||||||
\(574\) | −7.37169 | −0.307688 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −18.5855 | −0.773723 | −0.386861 | − | 0.922138i | \(-0.626441\pi\) | ||||
−0.386861 | + | 0.922138i | \(0.626441\pi\) | |||||||
\(578\) | −31.7005 | −1.31857 | ||||||||
\(579\) | −25.3288 | −1.05263 | ||||||||
\(580\) | −0.685846 | −0.0284782 | ||||||||
\(581\) | −0.393115 | −0.0163092 | ||||||||
\(582\) | −10.2499 | −0.424871 | ||||||||
\(583\) | −16.1151 | −0.667418 | ||||||||
\(584\) | −11.9572 | −0.494791 | ||||||||
\(585\) | −0.292731 | −0.0121029 | ||||||||
\(586\) | 13.3288 | 0.550610 | ||||||||
\(587\) | −7.91431 | −0.326658 | −0.163329 | − | 0.986572i | \(-0.552223\pi\) | ||||
−0.163329 | + | 0.986572i | \(0.552223\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | 39.4439 | 1.62526 | ||||||||
\(590\) | −4.00000 | −0.164677 | ||||||||
\(591\) | −11.9572 | −0.491852 | ||||||||
\(592\) | −6.00000 | −0.246598 | ||||||||
\(593\) | 2.67115 | 0.109691 | 0.0548456 | − | 0.998495i | \(-0.482533\pi\) | ||||
0.0548456 | + | 0.998495i | \(0.482533\pi\) | |||||||
\(594\) | 2.68585 | 0.110202 | ||||||||
\(595\) | −6.97858 | −0.286094 | ||||||||
\(596\) | −16.7434 | −0.685836 | ||||||||
\(597\) | −15.3288 | −0.627368 | ||||||||
\(598\) | −0.292731 | −0.0119707 | ||||||||
\(599\) | −4.14323 | −0.169288 | −0.0846439 | − | 0.996411i | \(-0.526975\pi\) | ||||
−0.0846439 | + | 0.996411i | \(0.526975\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 23.3717 | 0.953351 | 0.476676 | − | 0.879079i | \(-0.341842\pi\) | ||||
0.476676 | + | 0.879079i | \(0.341842\pi\) | |||||||
\(602\) | −6.68585 | −0.272495 | ||||||||
\(603\) | 1.31415 | 0.0535165 | ||||||||
\(604\) | −15.3288 | −0.623722 | ||||||||
\(605\) | 3.78623 | 0.153932 | ||||||||
\(606\) | 4.29273 | 0.174380 | ||||||||
\(607\) | −0.450654 | −0.0182915 | −0.00914573 | − | 0.999958i | \(-0.502911\pi\) | ||||
−0.00914573 | + | 0.999958i | \(0.502911\pi\) | |||||||
\(608\) | −4.39312 | −0.178164 | ||||||||
\(609\) | 0.685846 | 0.0277919 | ||||||||
\(610\) | 7.37169 | 0.298471 | ||||||||
\(611\) | 3.02984 | 0.122574 | ||||||||
\(612\) | −6.97858 | −0.282092 | ||||||||
\(613\) | −29.4439 | −1.18923 | −0.594614 | − | 0.804011i | \(-0.702695\pi\) | ||||
−0.594614 | + | 0.804011i | \(0.702695\pi\) | |||||||
\(614\) | −10.1579 | −0.409940 | ||||||||
\(615\) | −7.37169 | −0.297255 | ||||||||
\(616\) | 2.68585 | 0.108216 | ||||||||
\(617\) | −27.2860 | −1.09849 | −0.549247 | − | 0.835660i | \(-0.685085\pi\) | ||||
−0.549247 | + | 0.835660i | \(0.685085\pi\) | |||||||
\(618\) | −4.58546 | −0.184454 | ||||||||
\(619\) | −23.1365 | −0.929934 | −0.464967 | − | 0.885328i | \(-0.653934\pi\) | ||||
−0.464967 | + | 0.885328i | \(0.653934\pi\) | |||||||
\(620\) | −8.97858 | −0.360588 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 5.03612 | 0.201930 | ||||||||
\(623\) | 9.66442 | 0.387197 | ||||||||
\(624\) | −0.292731 | −0.0117186 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −29.0790 | −1.16223 | ||||||||
\(627\) | −11.7992 | −0.471216 | ||||||||
\(628\) | 10.5855 | 0.422406 | ||||||||
\(629\) | 41.8715 | 1.66952 | ||||||||
\(630\) | −1.00000 | −0.0398410 | ||||||||
\(631\) | 15.3288 | 0.610232 | 0.305116 | − | 0.952315i | \(-0.401305\pi\) | ||||
0.305116 | + | 0.952315i | \(0.401305\pi\) | |||||||
\(632\) | 15.3288 | 0.609749 | ||||||||
\(633\) | −7.41454 | −0.294701 | ||||||||
\(634\) | 18.5855 | 0.738123 | ||||||||
\(635\) | −12.0575 | −0.478489 | ||||||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | 0.292731 | 0.0115984 | ||||||||
\(638\) | −1.84208 | −0.0729285 | ||||||||
\(639\) | 7.27131 | 0.287649 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 39.6300 | 1.56529 | 0.782645 | − | 0.622468i | \(-0.213870\pi\) | ||||
0.782645 | + | 0.622468i | \(0.213870\pi\) | |||||||
\(642\) | 1.37169 | 0.0541364 | ||||||||
\(643\) | −7.07896 | −0.279167 | −0.139583 | − | 0.990210i | \(-0.544576\pi\) | ||||
−0.139583 | + | 0.990210i | \(0.544576\pi\) | |||||||
\(644\) | −1.00000 | −0.0394055 | ||||||||
\(645\) | −6.68585 | −0.263255 | ||||||||
\(646\) | 30.6577 | 1.20621 | ||||||||
\(647\) | 2.73496 | 0.107522 | 0.0537612 | − | 0.998554i | \(-0.482879\pi\) | ||||
0.0537612 | + | 0.998554i | \(0.482879\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −10.7434 | −0.421715 | ||||||||
\(650\) | −0.292731 | −0.0114819 | ||||||||
\(651\) | 8.97858 | 0.351898 | ||||||||
\(652\) | −8.00000 | −0.313304 | ||||||||
\(653\) | 8.54262 | 0.334298 | 0.167149 | − | 0.985932i | \(-0.446544\pi\) | ||||
0.167149 | + | 0.985932i | \(0.446544\pi\) | |||||||
\(654\) | 6.00000 | 0.234619 | ||||||||
\(655\) | 4.00000 | 0.156293 | ||||||||
\(656\) | −7.37169 | −0.287816 | ||||||||
\(657\) | 11.9572 | 0.466493 | ||||||||
\(658\) | 10.3503 | 0.403496 | ||||||||
\(659\) | 30.2155 | 1.17703 | 0.588514 | − | 0.808487i | \(-0.299713\pi\) | ||||
0.588514 | + | 0.808487i | \(0.299713\pi\) | |||||||
\(660\) | 2.68585 | 0.104546 | ||||||||
\(661\) | −41.1281 | −1.59970 | −0.799848 | − | 0.600202i | \(-0.795087\pi\) | ||||
−0.799848 | + | 0.600202i | \(0.795087\pi\) | |||||||
\(662\) | 0.585462 | 0.0227546 | ||||||||
\(663\) | 2.04285 | 0.0793376 | ||||||||
\(664\) | −0.393115 | −0.0152558 | ||||||||
\(665\) | 4.39312 | 0.170358 | ||||||||
\(666\) | 6.00000 | 0.232495 | ||||||||
\(667\) | 0.685846 | 0.0265561 | ||||||||
\(668\) | 4.19235 | 0.162207 | ||||||||
\(669\) | −19.0790 | −0.737635 | ||||||||
\(670\) | 1.31415 | 0.0507702 | ||||||||
\(671\) | 19.7992 | 0.764341 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 34.7862 | 1.34091 | 0.670455 | − | 0.741950i | \(-0.266099\pi\) | ||||
0.670455 | + | 0.741950i | \(0.266099\pi\) | |||||||
\(674\) | 5.85677 | 0.225594 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −12.9143 | −0.496704 | ||||||||
\(677\) | −16.7434 | −0.643501 | −0.321750 | − | 0.946825i | \(-0.604271\pi\) | ||||
−0.321750 | + | 0.946825i | \(0.604271\pi\) | |||||||
\(678\) | 15.9572 | 0.612831 | ||||||||
\(679\) | 10.2499 | 0.393354 | ||||||||
\(680\) | −6.97858 | −0.267616 | ||||||||
\(681\) | −12.9786 | −0.497340 | ||||||||
\(682\) | −24.1151 | −0.923414 | ||||||||
\(683\) | 15.9143 | 0.608944 | 0.304472 | − | 0.952521i | \(-0.401520\pi\) | ||||
0.304472 | + | 0.952521i | \(0.401520\pi\) | |||||||
\(684\) | 4.39312 | 0.167975 | ||||||||
\(685\) | 21.9143 | 0.837303 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −18.7862 | −0.716739 | ||||||||
\(688\) | −6.68585 | −0.254895 | ||||||||
\(689\) | −1.75639 | −0.0669130 | ||||||||
\(690\) | −1.00000 | −0.0380693 | ||||||||
\(691\) | −31.4439 | −1.19618 | −0.598092 | − | 0.801428i | \(-0.704074\pi\) | ||||
−0.598092 | + | 0.801428i | \(0.704074\pi\) | |||||||
\(692\) | 11.7648 | 0.447231 | ||||||||
\(693\) | −2.68585 | −0.102027 | ||||||||
\(694\) | 22.7434 | 0.863327 | ||||||||
\(695\) | −18.7434 | −0.710977 | ||||||||
\(696\) | 0.685846 | 0.0259969 | ||||||||
\(697\) | 51.4439 | 1.94858 | ||||||||
\(698\) | −22.3931 | −0.847592 | ||||||||
\(699\) | −15.9572 | −0.603555 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | −8.62831 | −0.325887 | −0.162943 | − | 0.986635i | \(-0.552099\pi\) | ||||
−0.162943 | + | 0.986635i | \(0.552099\pi\) | |||||||
\(702\) | 0.292731 | 0.0110484 | ||||||||
\(703\) | −26.3587 | −0.994137 | ||||||||
\(704\) | 2.68585 | 0.101227 | ||||||||
\(705\) | 10.3503 | 0.389814 | ||||||||
\(706\) | −18.7862 | −0.707029 | ||||||||
\(707\) | −4.29273 | −0.161445 | ||||||||
\(708\) | 4.00000 | 0.150329 | ||||||||
\(709\) | −5.12808 | −0.192589 | −0.0962945 | − | 0.995353i | \(-0.530699\pi\) | ||||
−0.0962945 | + | 0.995353i | \(0.530699\pi\) | |||||||
\(710\) | 7.27131 | 0.272887 | ||||||||
\(711\) | −15.3288 | −0.574877 | ||||||||
\(712\) | 9.66442 | 0.362190 | ||||||||
\(713\) | 8.97858 | 0.336250 | ||||||||
\(714\) | 6.97858 | 0.261167 | ||||||||
\(715\) | −0.786230 | −0.0294033 | ||||||||
\(716\) | 5.95715 | 0.222629 | ||||||||
\(717\) | −7.27131 | −0.271552 | ||||||||
\(718\) | 31.5296 | 1.17667 | ||||||||
\(719\) | −37.5359 | −1.39985 | −0.699926 | − | 0.714215i | \(-0.746784\pi\) | ||||
−0.699926 | + | 0.714215i | \(0.746784\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 4.58546 | 0.170772 | ||||||||
\(722\) | −0.299461 | −0.0111448 | ||||||||
\(723\) | −3.64973 | −0.135735 | ||||||||
\(724\) | 24.5426 | 0.912119 | ||||||||
\(725\) | 0.685846 | 0.0254717 | ||||||||
\(726\) | −3.78623 | −0.140520 | ||||||||
\(727\) | −31.3288 | −1.16192 | −0.580961 | − | 0.813931i | \(-0.697323\pi\) | ||||
−0.580961 | + | 0.813931i | \(0.697323\pi\) | |||||||
\(728\) | 0.292731 | 0.0108493 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.9572 | 0.442554 | ||||||||
\(731\) | 46.6577 | 1.72570 | ||||||||
\(732\) | −7.37169 | −0.272466 | ||||||||
\(733\) | 6.78623 | 0.250655 | 0.125328 | − | 0.992115i | \(-0.460002\pi\) | ||||
0.125328 | + | 0.992115i | \(0.460002\pi\) | |||||||
\(734\) | −26.0722 | −0.962344 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 3.52962 | 0.130015 | ||||||||
\(738\) | 7.37169 | 0.271356 | ||||||||
\(739\) | 22.7434 | 0.836629 | 0.418314 | − | 0.908302i | \(-0.362621\pi\) | ||||
0.418314 | + | 0.908302i | \(0.362621\pi\) | |||||||
\(740\) | 6.00000 | 0.220564 | ||||||||
\(741\) | −1.28600 | −0.0472424 | ||||||||
\(742\) | −6.00000 | −0.220267 | ||||||||
\(743\) | 24.9013 | 0.913540 | 0.456770 | − | 0.889585i | \(-0.349006\pi\) | ||||
0.456770 | + | 0.889585i | \(0.349006\pi\) | |||||||
\(744\) | 8.97858 | 0.329171 | ||||||||
\(745\) | 16.7434 | 0.613430 | ||||||||
\(746\) | −19.1709 | −0.701897 | ||||||||
\(747\) | 0.393115 | 0.0143833 | ||||||||
\(748\) | −18.7434 | −0.685326 | ||||||||
\(749\) | −1.37169 | −0.0501205 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −37.0852 | −1.35326 | −0.676630 | − | 0.736323i | \(-0.736560\pi\) | ||||
−0.676630 | + | 0.736323i | \(0.736560\pi\) | |||||||
\(752\) | 10.3503 | 0.377435 | ||||||||
\(753\) | 13.6216 | 0.496398 | ||||||||
\(754\) | −0.200768 | −0.00731155 | ||||||||
\(755\) | 15.3288 | 0.557874 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | −7.95715 | −0.289208 | −0.144604 | − | 0.989490i | \(-0.546191\pi\) | ||||
−0.144604 | + | 0.989490i | \(0.546191\pi\) | |||||||
\(758\) | −6.62831 | −0.240751 | ||||||||
\(759\) | −2.68585 | −0.0974900 | ||||||||
\(760\) | 4.39312 | 0.159355 | ||||||||
\(761\) | 0.243614 | 0.00883101 | 0.00441550 | − | 0.999990i | \(-0.498594\pi\) | ||||
0.00441550 | + | 0.999990i | \(0.498594\pi\) | |||||||
\(762\) | 12.0575 | 0.436799 | ||||||||
\(763\) | −6.00000 | −0.217215 | ||||||||
\(764\) | −13.9572 | −0.504952 | ||||||||
\(765\) | 6.97858 | 0.252311 | ||||||||
\(766\) | 1.37169 | 0.0495613 | ||||||||
\(767\) | −1.17092 | −0.0422796 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 39.6791 | 1.43087 | 0.715433 | − | 0.698682i | \(-0.246230\pi\) | ||||
0.715433 | + | 0.698682i | \(0.246230\pi\) | |||||||
\(770\) | −2.68585 | −0.0967912 | ||||||||
\(771\) | −14.5855 | −0.525283 | ||||||||
\(772\) | 25.3288 | 0.911605 | ||||||||
\(773\) | −22.1151 | −0.795424 | −0.397712 | − | 0.917510i | \(-0.630196\pi\) | ||||
−0.397712 | + | 0.917510i | \(0.630196\pi\) | |||||||
\(774\) | 6.68585 | 0.240318 | ||||||||
\(775\) | 8.97858 | 0.322520 | ||||||||
\(776\) | 10.2499 | 0.367949 | ||||||||
\(777\) | −6.00000 | −0.215249 | ||||||||
\(778\) | −18.7862 | −0.673519 | ||||||||
\(779\) | −32.3847 | −1.16030 | ||||||||
\(780\) | 0.292731 | 0.0104815 | ||||||||
\(781\) | 19.5296 | 0.698825 | ||||||||
\(782\) | 6.97858 | 0.249553 | ||||||||
\(783\) | −0.685846 | −0.0245101 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −10.5855 | −0.377811 | ||||||||
\(786\) | −4.00000 | −0.142675 | ||||||||
\(787\) | −6.67742 | −0.238024 | −0.119012 | − | 0.992893i | \(-0.537973\pi\) | ||||
−0.119012 | + | 0.992893i | \(0.537973\pi\) | |||||||
\(788\) | 11.9572 | 0.425956 | ||||||||
\(789\) | 31.3288 | 1.11534 | ||||||||
\(790\) | −15.3288 | −0.545376 | ||||||||
\(791\) | −15.9572 | −0.567371 | ||||||||
\(792\) | −2.68585 | −0.0954374 | ||||||||
\(793\) | 2.15792 | 0.0766301 | ||||||||
\(794\) | 17.2797 | 0.613235 | ||||||||
\(795\) | −6.00000 | −0.212798 | ||||||||
\(796\) | 15.3288 | 0.543317 | ||||||||
\(797\) | −21.2138 | −0.751430 | −0.375715 | − | 0.926735i | \(-0.622603\pi\) | ||||
−0.375715 | + | 0.926735i | \(0.622603\pi\) | |||||||
\(798\) | −4.39312 | −0.155515 | ||||||||
\(799\) | −72.2302 | −2.55532 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −9.66442 | −0.341476 | ||||||||
\(802\) | 15.3142 | 0.540762 | ||||||||
\(803\) | 32.1151 | 1.13332 | ||||||||
\(804\) | −1.31415 | −0.0463466 | ||||||||
\(805\) | 1.00000 | 0.0352454 | ||||||||
\(806\) | −2.62831 | −0.0925782 | ||||||||
\(807\) | 10.2499 | 0.360813 | ||||||||
\(808\) | −4.29273 | −0.151018 | ||||||||
\(809\) | −25.2432 | −0.887502 | −0.443751 | − | 0.896150i | \(-0.646353\pi\) | ||||
−0.443751 | + | 0.896150i | \(0.646353\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 33.1709 | 1.16479 | 0.582394 | − | 0.812906i | \(-0.302116\pi\) | ||||
0.582394 | + | 0.812906i | \(0.302116\pi\) | |||||||
\(812\) | −0.685846 | −0.0240685 | ||||||||
\(813\) | 1.76481 | 0.0618945 | ||||||||
\(814\) | 16.1151 | 0.564833 | ||||||||
\(815\) | 8.00000 | 0.280228 | ||||||||
\(816\) | 6.97858 | 0.244299 | ||||||||
\(817\) | −29.3717 | −1.02759 | ||||||||
\(818\) | 12.1579 | 0.425092 | ||||||||
\(819\) | −0.292731 | −0.0102288 | ||||||||
\(820\) | 7.37169 | 0.257431 | ||||||||
\(821\) | −51.7282 | −1.80533 | −0.902664 | − | 0.430346i | \(-0.858391\pi\) | ||||
−0.902664 | + | 0.430346i | \(0.858391\pi\) | |||||||
\(822\) | −21.9143 | −0.764349 | ||||||||
\(823\) | 6.80092 | 0.237065 | 0.118533 | − | 0.992950i | \(-0.462181\pi\) | ||||
0.118533 | + | 0.992950i | \(0.462181\pi\) | |||||||
\(824\) | 4.58546 | 0.159742 | ||||||||
\(825\) | −2.68585 | −0.0935092 | ||||||||
\(826\) | −4.00000 | −0.139178 | ||||||||
\(827\) | 29.2860 | 1.01837 | 0.509187 | − | 0.860656i | \(-0.329946\pi\) | ||||
0.509187 | + | 0.860656i | \(0.329946\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −39.8799 | −1.38509 | −0.692543 | − | 0.721377i | \(-0.743510\pi\) | ||||
−0.692543 | + | 0.721377i | \(0.743510\pi\) | |||||||
\(830\) | 0.393115 | 0.0136452 | ||||||||
\(831\) | −9.47208 | −0.328583 | ||||||||
\(832\) | 0.292731 | 0.0101486 | ||||||||
\(833\) | −6.97858 | −0.241793 | ||||||||
\(834\) | 18.7434 | 0.649030 | ||||||||
\(835\) | −4.19235 | −0.145082 | ||||||||
\(836\) | 11.7992 | 0.408085 | ||||||||
\(837\) | −8.97858 | −0.310345 | ||||||||
\(838\) | −28.8353 | −0.996101 | ||||||||
\(839\) | 16.4015 | 0.566244 | 0.283122 | − | 0.959084i | \(-0.408630\pi\) | ||||
0.283122 | + | 0.959084i | \(0.408630\pi\) | |||||||
\(840\) | 1.00000 | 0.0345033 | ||||||||
\(841\) | −28.5296 | −0.983780 | ||||||||
\(842\) | −12.0428 | −0.415024 | ||||||||
\(843\) | −32.8009 | −1.12972 | ||||||||
\(844\) | 7.41454 | 0.255219 | ||||||||
\(845\) | 12.9143 | 0.444266 | ||||||||
\(846\) | −10.3503 | −0.355850 | ||||||||
\(847\) | 3.78623 | 0.130096 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | 9.03612 | 0.310119 | ||||||||
\(850\) | 6.97858 | 0.239363 | ||||||||
\(851\) | −6.00000 | −0.205677 | ||||||||
\(852\) | −7.27131 | −0.249111 | ||||||||
\(853\) | −18.4507 | −0.631738 | −0.315869 | − | 0.948803i | \(-0.602296\pi\) | ||||
−0.315869 | + | 0.948803i | \(0.602296\pi\) | |||||||
\(854\) | 7.37169 | 0.252254 | ||||||||
\(855\) | −4.39312 | −0.150241 | ||||||||
\(856\) | −1.37169 | −0.0468835 | ||||||||
\(857\) | 19.9572 | 0.681723 | 0.340862 | − | 0.940113i | \(-0.389281\pi\) | ||||
0.340862 | + | 0.940113i | \(0.389281\pi\) | |||||||
\(858\) | 0.786230 | 0.0268415 | ||||||||
\(859\) | −7.21377 | −0.246131 | −0.123065 | − | 0.992399i | \(-0.539272\pi\) | ||||
−0.123065 | + | 0.992399i | \(0.539272\pi\) | |||||||
\(860\) | 6.68585 | 0.227985 | ||||||||
\(861\) | −7.37169 | −0.251227 | ||||||||
\(862\) | −19.3288 | −0.658343 | ||||||||
\(863\) | −44.8156 | −1.52554 | −0.762771 | − | 0.646669i | \(-0.776161\pi\) | ||||
−0.762771 | + | 0.646669i | \(0.776161\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −11.7648 | −0.400015 | ||||||||
\(866\) | 4.99327 | 0.169678 | ||||||||
\(867\) | −31.7005 | −1.07661 | ||||||||
\(868\) | −8.97858 | −0.304753 | ||||||||
\(869\) | −41.1709 | −1.39663 | ||||||||
\(870\) | −0.685846 | −0.0232524 | ||||||||
\(871\) | 0.384694 | 0.0130348 | ||||||||
\(872\) | −6.00000 | −0.203186 | ||||||||
\(873\) | −10.2499 | −0.346906 | ||||||||
\(874\) | −4.39312 | −0.148599 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −11.9572 | −0.403995 | ||||||||
\(877\) | −47.1428 | −1.59190 | −0.795949 | − | 0.605364i | \(-0.793028\pi\) | ||||
−0.795949 | + | 0.605364i | \(0.793028\pi\) | |||||||
\(878\) | −21.5640 | −0.727751 | ||||||||
\(879\) | 13.3288 | 0.449571 | ||||||||
\(880\) | −2.68585 | −0.0905399 | ||||||||
\(881\) | 1.46365 | 0.0493118 | 0.0246559 | − | 0.999696i | \(-0.492151\pi\) | ||||
0.0246559 | + | 0.999696i | \(0.492151\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | −49.4011 | −1.66248 | −0.831239 | − | 0.555915i | \(-0.812368\pi\) | ||||
−0.831239 | + | 0.555915i | \(0.812368\pi\) | |||||||
\(884\) | −2.04285 | −0.0687083 | ||||||||
\(885\) | −4.00000 | −0.134459 | ||||||||
\(886\) | −34.6577 | −1.16435 | ||||||||
\(887\) | 23.0508 | 0.773970 | 0.386985 | − | 0.922086i | \(-0.373516\pi\) | ||||
0.386985 | + | 0.922086i | \(0.373516\pi\) | |||||||
\(888\) | −6.00000 | −0.201347 | ||||||||
\(889\) | −12.0575 | −0.404397 | ||||||||
\(890\) | −9.66442 | −0.323952 | ||||||||
\(891\) | 2.68585 | 0.0899792 | ||||||||
\(892\) | 19.0790 | 0.638811 | ||||||||
\(893\) | 45.4699 | 1.52159 | ||||||||
\(894\) | −16.7434 | −0.559983 | ||||||||
\(895\) | −5.95715 | −0.199126 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −0.292731 | −0.00977400 | ||||||||
\(898\) | −18.7862 | −0.626905 | ||||||||
\(899\) | 6.15792 | 0.205378 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 41.8715 | 1.39494 | ||||||||
\(902\) | 19.7992 | 0.659242 | ||||||||
\(903\) | −6.68585 | −0.222491 | ||||||||
\(904\) | −15.9572 | −0.530727 | ||||||||
\(905\) | −24.5426 | −0.815824 | ||||||||
\(906\) | −15.3288 | −0.509267 | ||||||||
\(907\) | −42.2155 | −1.40174 | −0.700871 | − | 0.713288i | \(-0.747205\pi\) | ||||
−0.700871 | + | 0.713288i | \(0.747205\pi\) | |||||||
\(908\) | 12.9786 | 0.430709 | ||||||||
\(909\) | 4.29273 | 0.142381 | ||||||||
\(910\) | −0.292731 | −0.00970394 | ||||||||
\(911\) | −44.9013 | −1.48765 | −0.743823 | − | 0.668376i | \(-0.766990\pi\) | ||||
−0.743823 | + | 0.668376i | \(0.766990\pi\) | |||||||
\(912\) | −4.39312 | −0.145471 | ||||||||
\(913\) | 1.05585 | 0.0349434 | ||||||||
\(914\) | −11.8139 | −0.390770 | ||||||||
\(915\) | 7.37169 | 0.243701 | ||||||||
\(916\) | 18.7862 | 0.620715 | ||||||||
\(917\) | 4.00000 | 0.132092 | ||||||||
\(918\) | −6.97858 | −0.230327 | ||||||||
\(919\) | −46.6577 | −1.53910 | −0.769548 | − | 0.638589i | \(-0.779518\pi\) | ||||
−0.769548 | + | 0.638589i | \(0.779518\pi\) | |||||||
\(920\) | 1.00000 | 0.0329690 | ||||||||
\(921\) | −10.1579 | −0.334715 | ||||||||
\(922\) | −21.4637 | −0.706868 | ||||||||
\(923\) | 2.12854 | 0.0700617 | ||||||||
\(924\) | 2.68585 | 0.0883579 | ||||||||
\(925\) | −6.00000 | −0.197279 | ||||||||
\(926\) | −40.6430 | −1.33561 | ||||||||
\(927\) | −4.58546 | −0.150606 | ||||||||
\(928\) | −0.685846 | −0.0225140 | ||||||||
\(929\) | 6.00000 | 0.196854 | 0.0984268 | − | 0.995144i | \(-0.468619\pi\) | ||||
0.0984268 | + | 0.995144i | \(0.468619\pi\) | |||||||
\(930\) | −8.97858 | −0.294419 | ||||||||
\(931\) | 4.39312 | 0.143979 | ||||||||
\(932\) | 15.9572 | 0.522694 | ||||||||
\(933\) | 5.03612 | 0.164875 | ||||||||
\(934\) | 28.3074 | 0.926247 | ||||||||
\(935\) | 18.7434 | 0.612974 | ||||||||
\(936\) | −0.292731 | −0.00956821 | ||||||||
\(937\) | −41.4637 | −1.35456 | −0.677279 | − | 0.735726i | \(-0.736841\pi\) | ||||
−0.677279 | + | 0.735726i | \(0.736841\pi\) | |||||||
\(938\) | 1.31415 | 0.0429086 | ||||||||
\(939\) | −29.0790 | −0.948956 | ||||||||
\(940\) | −10.3503 | −0.337589 | ||||||||
\(941\) | −4.82908 | −0.157423 | −0.0787117 | − | 0.996897i | \(-0.525081\pi\) | ||||
−0.0787117 | + | 0.996897i | \(0.525081\pi\) | |||||||
\(942\) | 10.5855 | 0.344893 | ||||||||
\(943\) | −7.37169 | −0.240055 | ||||||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | −1.00000 | −0.0325300 | ||||||||
\(946\) | 17.9572 | 0.583837 | ||||||||
\(947\) | 1.75639 | 0.0570749 | 0.0285374 | − | 0.999593i | \(-0.490915\pi\) | ||||
0.0285374 | + | 0.999593i | \(0.490915\pi\) | |||||||
\(948\) | 15.3288 | 0.497858 | ||||||||
\(949\) | 3.50023 | 0.113622 | ||||||||
\(950\) | −4.39312 | −0.142531 | ||||||||
\(951\) | 18.5855 | 0.602675 | ||||||||
\(952\) | −6.97858 | −0.226177 | ||||||||
\(953\) | 1.12808 | 0.0365420 | 0.0182710 | − | 0.999833i | \(-0.494184\pi\) | ||||
0.0182710 | + | 0.999833i | \(0.494184\pi\) | |||||||
\(954\) | 6.00000 | 0.194257 | ||||||||
\(955\) | 13.9572 | 0.451643 | ||||||||
\(956\) | 7.27131 | 0.235171 | ||||||||
\(957\) | −1.84208 | −0.0595459 | ||||||||
\(958\) | −14.1579 | −0.457422 | ||||||||
\(959\) | 21.9143 | 0.707650 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | 49.6148 | 1.60048 | ||||||||
\(962\) | 1.75639 | 0.0566282 | ||||||||
\(963\) | 1.37169 | 0.0442022 | ||||||||
\(964\) | 3.64973 | 0.117550 | ||||||||
\(965\) | −25.3288 | −0.815364 | ||||||||
\(966\) | −1.00000 | −0.0321745 | ||||||||
\(967\) | −56.3565 | −1.81230 | −0.906152 | − | 0.422952i | \(-0.860994\pi\) | ||||
−0.906152 | + | 0.422952i | \(0.860994\pi\) | |||||||
\(968\) | 3.78623 | 0.121694 | ||||||||
\(969\) | 30.6577 | 0.984867 | ||||||||
\(970\) | −10.2499 | −0.329104 | ||||||||
\(971\) | 26.2070 | 0.841024 | 0.420512 | − | 0.907287i | \(-0.361850\pi\) | ||||
0.420512 | + | 0.907287i | \(0.361850\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −18.7434 | −0.600885 | ||||||||
\(974\) | −15.4721 | −0.495757 | ||||||||
\(975\) | −0.292731 | −0.00937489 | ||||||||
\(976\) | 7.37169 | 0.235962 | ||||||||
\(977\) | 23.4574 | 0.750468 | 0.375234 | − | 0.926930i | \(-0.377562\pi\) | ||||
0.375234 | + | 0.926930i | \(0.377562\pi\) | |||||||
\(978\) | −8.00000 | −0.255812 | ||||||||
\(979\) | −25.9572 | −0.829594 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 6.00000 | 0.191565 | ||||||||
\(982\) | −23.1281 | −0.738047 | ||||||||
\(983\) | −0.200768 | −0.00640352 | −0.00320176 | − | 0.999995i | \(-0.501019\pi\) | ||||
−0.00320176 | + | 0.999995i | \(0.501019\pi\) | |||||||
\(984\) | −7.37169 | −0.235001 | ||||||||
\(985\) | −11.9572 | −0.380987 | ||||||||
\(986\) | 4.78623 | 0.152425 | ||||||||
\(987\) | 10.3503 | 0.329453 | ||||||||
\(988\) | 1.28600 | 0.0409131 | ||||||||
\(989\) | −6.68585 | −0.212598 | ||||||||
\(990\) | 2.68585 | 0.0853618 | ||||||||
\(991\) | −9.84208 | −0.312644 | −0.156322 | − | 0.987706i | \(-0.549964\pi\) | ||||
−0.156322 | + | 0.987706i | \(0.549964\pi\) | |||||||
\(992\) | −8.97858 | −0.285070 | ||||||||
\(993\) | 0.585462 | 0.0185791 | ||||||||
\(994\) | 7.27131 | 0.230632 | ||||||||
\(995\) | −15.3288 | −0.485957 | ||||||||
\(996\) | −0.393115 | −0.0124563 | ||||||||
\(997\) | −23.7073 | −0.750817 | −0.375408 | − | 0.926860i | \(-0.622498\pi\) | ||||
−0.375408 | + | 0.926860i | \(0.622498\pi\) | |||||||
\(998\) | 24.5855 | 0.778239 | ||||||||
\(999\) | 6.00000 | 0.189832 |
(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 | 4830.2.a.bw.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4830.2.a.bw.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial |