Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4730,2,Mod(1,4730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4730, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4730.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4730.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: | \(37.7692401561\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 32 x^{11} - 5 x^{10} + 376 x^{9} + 100 x^{8} - 1985 x^{7} - 576 x^{6} + 4708 x^{5} + 889 x^{4} - 4774 x^{3} - 296 x^{2} + 1648 x - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.30046\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4730.1 |
$q$-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 | ||||||||
\(3\) | −1.30046 | −0.750823 | −0.375411 | − | 0.926858i | \(-0.622499\pi\) | ||||
−0.375411 | + | 0.926858i | \(0.622499\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.30046 | −0.530912 | ||||||||
\(7\) | 3.42310 | 1.29381 | 0.646905 | − | 0.762570i | \(-0.276063\pi\) | ||||
0.646905 | + | 0.762570i | \(0.276063\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.30880 | −0.436265 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.30046 | −0.375411 | ||||||||
\(13\) | 2.16503 | 0.600471 | 0.300236 | − | 0.953865i | \(-0.402935\pi\) | ||||
0.300236 | + | 0.953865i | \(0.402935\pi\) | |||||||
\(14\) | 3.42310 | 0.914863 | ||||||||
\(15\) | 1.30046 | 0.335778 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.19311 | 1.50205 | 0.751024 | − | 0.660275i | \(-0.229560\pi\) | ||||
0.751024 | + | 0.660275i | \(0.229560\pi\) | |||||||
\(18\) | −1.30880 | −0.308486 | ||||||||
\(19\) | 4.97577 | 1.14152 | 0.570760 | − | 0.821117i | \(-0.306649\pi\) | ||||
0.570760 | + | 0.821117i | \(0.306649\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −4.45162 | −0.971422 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −4.95191 | −1.03254 | −0.516272 | − | 0.856424i | \(-0.672681\pi\) | ||||
−0.516272 | + | 0.856424i | \(0.672681\pi\) | |||||||
\(24\) | −1.30046 | −0.265456 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.16503 | 0.424597 | ||||||||
\(27\) | 5.60343 | 1.07838 | ||||||||
\(28\) | 3.42310 | 0.646905 | ||||||||
\(29\) | −8.41999 | −1.56355 | −0.781777 | − | 0.623559i | \(-0.785686\pi\) | ||||
−0.781777 | + | 0.623559i | \(0.785686\pi\) | |||||||
\(30\) | 1.30046 | 0.237431 | ||||||||
\(31\) | 7.34665 | 1.31950 | 0.659749 | − | 0.751486i | \(-0.270663\pi\) | ||||
0.659749 | + | 0.751486i | \(0.270663\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.30046 | −0.226382 | ||||||||
\(34\) | 6.19311 | 1.06211 | ||||||||
\(35\) | −3.42310 | −0.578610 | ||||||||
\(36\) | −1.30880 | −0.218133 | ||||||||
\(37\) | −4.92683 | −0.809967 | −0.404983 | − | 0.914324i | \(-0.632723\pi\) | ||||
−0.404983 | + | 0.914324i | \(0.632723\pi\) | |||||||
\(38\) | 4.97577 | 0.807177 | ||||||||
\(39\) | −2.81554 | −0.450847 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −6.22563 | −0.972280 | −0.486140 | − | 0.873881i | \(-0.661595\pi\) | ||||
−0.486140 | + | 0.873881i | \(0.661595\pi\) | |||||||
\(42\) | −4.45162 | −0.686899 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 1.30880 | 0.195104 | ||||||||
\(46\) | −4.95191 | −0.730120 | ||||||||
\(47\) | 4.34083 | 0.633176 | 0.316588 | − | 0.948563i | \(-0.397463\pi\) | ||||
0.316588 | + | 0.948563i | \(0.397463\pi\) | |||||||
\(48\) | −1.30046 | −0.187706 | ||||||||
\(49\) | 4.71763 | 0.673947 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −8.05390 | −1.12777 | ||||||||
\(52\) | 2.16503 | 0.300236 | ||||||||
\(53\) | 0.623093 | 0.0855884 | 0.0427942 | − | 0.999084i | \(-0.486374\pi\) | ||||
0.0427942 | + | 0.999084i | \(0.486374\pi\) | |||||||
\(54\) | 5.60343 | 0.762530 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 3.42310 | 0.457431 | ||||||||
\(57\) | −6.47081 | −0.857079 | ||||||||
\(58\) | −8.41999 | −1.10560 | ||||||||
\(59\) | 2.83303 | 0.368829 | 0.184415 | − | 0.982849i | \(-0.440961\pi\) | ||||
0.184415 | + | 0.982849i | \(0.440961\pi\) | |||||||
\(60\) | 1.30046 | 0.167889 | ||||||||
\(61\) | −4.29500 | −0.549919 | −0.274959 | − | 0.961456i | \(-0.588664\pi\) | ||||
−0.274959 | + | 0.961456i | \(0.588664\pi\) | |||||||
\(62\) | 7.34665 | 0.933026 | ||||||||
\(63\) | −4.48014 | −0.564445 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.16503 | −0.268539 | ||||||||
\(66\) | −1.30046 | −0.160076 | ||||||||
\(67\) | 11.2990 | 1.38039 | 0.690194 | − | 0.723624i | \(-0.257525\pi\) | ||||
0.690194 | + | 0.723624i | \(0.257525\pi\) | |||||||
\(68\) | 6.19311 | 0.751024 | ||||||||
\(69\) | 6.43978 | 0.775258 | ||||||||
\(70\) | −3.42310 | −0.409139 | ||||||||
\(71\) | −5.78909 | −0.687039 | −0.343520 | − | 0.939146i | \(-0.611619\pi\) | ||||
−0.343520 | + | 0.939146i | \(0.611619\pi\) | |||||||
\(72\) | −1.30880 | −0.154243 | ||||||||
\(73\) | 10.7001 | 1.25235 | 0.626174 | − | 0.779684i | \(-0.284620\pi\) | ||||
0.626174 | + | 0.779684i | \(0.284620\pi\) | |||||||
\(74\) | −4.92683 | −0.572733 | ||||||||
\(75\) | −1.30046 | −0.150165 | ||||||||
\(76\) | 4.97577 | 0.570760 | ||||||||
\(77\) | 3.42310 | 0.390099 | ||||||||
\(78\) | −2.81554 | −0.318797 | ||||||||
\(79\) | −9.34359 | −1.05124 | −0.525618 | − | 0.850721i | \(-0.676166\pi\) | ||||
−0.525618 | + | 0.850721i | \(0.676166\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −3.36066 | −0.373407 | ||||||||
\(82\) | −6.22563 | −0.687506 | ||||||||
\(83\) | −7.05958 | −0.774890 | −0.387445 | − | 0.921893i | \(-0.626642\pi\) | ||||
−0.387445 | + | 0.921893i | \(0.626642\pi\) | |||||||
\(84\) | −4.45162 | −0.485711 | ||||||||
\(85\) | −6.19311 | −0.671737 | ||||||||
\(86\) | 1.00000 | 0.107833 | ||||||||
\(87\) | 10.9499 | 1.17395 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 8.33954 | 0.883990 | 0.441995 | − | 0.897018i | \(-0.354271\pi\) | ||||
0.441995 | + | 0.897018i | \(0.354271\pi\) | |||||||
\(90\) | 1.30880 | 0.137959 | ||||||||
\(91\) | 7.41112 | 0.776896 | ||||||||
\(92\) | −4.95191 | −0.516272 | ||||||||
\(93\) | −9.55405 | −0.990708 | ||||||||
\(94\) | 4.34083 | 0.447723 | ||||||||
\(95\) | −4.97577 | −0.510503 | ||||||||
\(96\) | −1.30046 | −0.132728 | ||||||||
\(97\) | 2.72798 | 0.276984 | 0.138492 | − | 0.990364i | \(-0.455774\pi\) | ||||
0.138492 | + | 0.990364i | \(0.455774\pi\) | |||||||
\(98\) | 4.71763 | 0.476552 | ||||||||
\(99\) | −1.30880 | −0.131539 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 12.4002 | 1.23386 | 0.616932 | − | 0.787016i | \(-0.288375\pi\) | ||||
0.616932 | + | 0.787016i | \(0.288375\pi\) | |||||||
\(102\) | −8.05390 | −0.797455 | ||||||||
\(103\) | 6.32565 | 0.623285 | 0.311643 | − | 0.950199i | \(-0.399121\pi\) | ||||
0.311643 | + | 0.950199i | \(0.399121\pi\) | |||||||
\(104\) | 2.16503 | 0.212299 | ||||||||
\(105\) | 4.45162 | 0.434433 | ||||||||
\(106\) | 0.623093 | 0.0605201 | ||||||||
\(107\) | 3.29446 | 0.318488 | 0.159244 | − | 0.987239i | \(-0.449094\pi\) | ||||
0.159244 | + | 0.987239i | \(0.449094\pi\) | |||||||
\(108\) | 5.60343 | 0.539190 | ||||||||
\(109\) | 3.61019 | 0.345794 | 0.172897 | − | 0.984940i | \(-0.444687\pi\) | ||||
0.172897 | + | 0.984940i | \(0.444687\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 6.40716 | 0.608141 | ||||||||
\(112\) | 3.42310 | 0.323453 | ||||||||
\(113\) | −12.0417 | −1.13279 | −0.566394 | − | 0.824135i | \(-0.691662\pi\) | ||||
−0.566394 | + | 0.824135i | \(0.691662\pi\) | |||||||
\(114\) | −6.47081 | −0.606047 | ||||||||
\(115\) | 4.95191 | 0.461768 | ||||||||
\(116\) | −8.41999 | −0.781777 | ||||||||
\(117\) | −2.83358 | −0.261965 | ||||||||
\(118\) | 2.83303 | 0.260802 | ||||||||
\(119\) | 21.1996 | 1.94337 | ||||||||
\(120\) | 1.30046 | 0.118715 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −4.29500 | −0.388851 | ||||||||
\(123\) | 8.09620 | 0.730010 | ||||||||
\(124\) | 7.34665 | 0.659749 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −4.48014 | −0.399123 | ||||||||
\(127\) | 15.6355 | 1.38743 | 0.693715 | − | 0.720249i | \(-0.255973\pi\) | ||||
0.693715 | + | 0.720249i | \(0.255973\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.30046 | −0.114499 | ||||||||
\(130\) | −2.16503 | −0.189886 | ||||||||
\(131\) | −8.49576 | −0.742278 | −0.371139 | − | 0.928577i | \(-0.621033\pi\) | ||||
−0.371139 | + | 0.928577i | \(0.621033\pi\) | |||||||
\(132\) | −1.30046 | −0.113191 | ||||||||
\(133\) | 17.0326 | 1.47691 | ||||||||
\(134\) | 11.2990 | 0.976082 | ||||||||
\(135\) | −5.60343 | −0.482266 | ||||||||
\(136\) | 6.19311 | 0.531054 | ||||||||
\(137\) | −12.2600 | −1.04744 | −0.523720 | − | 0.851891i | \(-0.675456\pi\) | ||||
−0.523720 | + | 0.851891i | \(0.675456\pi\) | |||||||
\(138\) | 6.43978 | 0.548190 | ||||||||
\(139\) | 4.33409 | 0.367613 | 0.183806 | − | 0.982962i | \(-0.441158\pi\) | ||||
0.183806 | + | 0.982962i | \(0.441158\pi\) | |||||||
\(140\) | −3.42310 | −0.289305 | ||||||||
\(141\) | −5.64509 | −0.475403 | ||||||||
\(142\) | −5.78909 | −0.485810 | ||||||||
\(143\) | 2.16503 | 0.181049 | ||||||||
\(144\) | −1.30880 | −0.109066 | ||||||||
\(145\) | 8.41999 | 0.699242 | ||||||||
\(146\) | 10.7001 | 0.885543 | ||||||||
\(147\) | −6.13510 | −0.506014 | ||||||||
\(148\) | −4.92683 | −0.404983 | ||||||||
\(149\) | 2.58758 | 0.211983 | 0.105991 | − | 0.994367i | \(-0.466198\pi\) | ||||
0.105991 | + | 0.994367i | \(0.466198\pi\) | |||||||
\(150\) | −1.30046 | −0.106182 | ||||||||
\(151\) | 6.91199 | 0.562490 | 0.281245 | − | 0.959636i | \(-0.409253\pi\) | ||||
0.281245 | + | 0.959636i | \(0.409253\pi\) | |||||||
\(152\) | 4.97577 | 0.403588 | ||||||||
\(153\) | −8.10551 | −0.655292 | ||||||||
\(154\) | 3.42310 | 0.275841 | ||||||||
\(155\) | −7.34665 | −0.590097 | ||||||||
\(156\) | −2.81554 | −0.225424 | ||||||||
\(157\) | 14.8219 | 1.18292 | 0.591459 | − | 0.806335i | \(-0.298552\pi\) | ||||
0.591459 | + | 0.806335i | \(0.298552\pi\) | |||||||
\(158\) | −9.34359 | −0.743336 | ||||||||
\(159\) | −0.810309 | −0.0642617 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −16.9509 | −1.33592 | ||||||||
\(162\) | −3.36066 | −0.264039 | ||||||||
\(163\) | −2.87721 | −0.225360 | −0.112680 | − | 0.993631i | \(-0.535944\pi\) | ||||
−0.112680 | + | 0.993631i | \(0.535944\pi\) | |||||||
\(164\) | −6.22563 | −0.486140 | ||||||||
\(165\) | 1.30046 | 0.101241 | ||||||||
\(166\) | −7.05958 | −0.547930 | ||||||||
\(167\) | 25.2030 | 1.95027 | 0.975134 | − | 0.221616i | \(-0.0711332\pi\) | ||||
0.975134 | + | 0.221616i | \(0.0711332\pi\) | |||||||
\(168\) | −4.45162 | −0.343450 | ||||||||
\(169\) | −8.31264 | −0.639434 | ||||||||
\(170\) | −6.19311 | −0.474989 | ||||||||
\(171\) | −6.51227 | −0.498006 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | 8.32115 | 0.632645 | 0.316323 | − | 0.948652i | \(-0.397552\pi\) | ||||
0.316323 | + | 0.948652i | \(0.397552\pi\) | |||||||
\(174\) | 10.9499 | 0.830109 | ||||||||
\(175\) | 3.42310 | 0.258762 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −3.68425 | −0.276925 | ||||||||
\(178\) | 8.33954 | 0.625075 | ||||||||
\(179\) | 16.8744 | 1.26125 | 0.630627 | − | 0.776086i | \(-0.282798\pi\) | ||||
0.630627 | + | 0.776086i | \(0.282798\pi\) | |||||||
\(180\) | 1.30880 | 0.0975519 | ||||||||
\(181\) | 3.36414 | 0.250055 | 0.125027 | − | 0.992153i | \(-0.460098\pi\) | ||||
0.125027 | + | 0.992153i | \(0.460098\pi\) | |||||||
\(182\) | 7.41112 | 0.549349 | ||||||||
\(183\) | 5.58549 | 0.412891 | ||||||||
\(184\) | −4.95191 | −0.365060 | ||||||||
\(185\) | 4.92683 | 0.362228 | ||||||||
\(186\) | −9.55405 | −0.700537 | ||||||||
\(187\) | 6.19311 | 0.452885 | ||||||||
\(188\) | 4.34083 | 0.316588 | ||||||||
\(189\) | 19.1811 | 1.39522 | ||||||||
\(190\) | −4.97577 | −0.360980 | ||||||||
\(191\) | 13.3995 | 0.969556 | 0.484778 | − | 0.874637i | \(-0.338900\pi\) | ||||
0.484778 | + | 0.874637i | \(0.338900\pi\) | |||||||
\(192\) | −1.30046 | −0.0938528 | ||||||||
\(193\) | 8.68042 | 0.624830 | 0.312415 | − | 0.949946i | \(-0.398862\pi\) | ||||
0.312415 | + | 0.949946i | \(0.398862\pi\) | |||||||
\(194\) | 2.72798 | 0.195857 | ||||||||
\(195\) | 2.81554 | 0.201625 | ||||||||
\(196\) | 4.71763 | 0.336973 | ||||||||
\(197\) | −2.92760 | −0.208583 | −0.104291 | − | 0.994547i | \(-0.533257\pi\) | ||||
−0.104291 | + | 0.994547i | \(0.533257\pi\) | |||||||
\(198\) | −1.30880 | −0.0930121 | ||||||||
\(199\) | −7.46077 | −0.528880 | −0.264440 | − | 0.964402i | \(-0.585187\pi\) | ||||
−0.264440 | + | 0.964402i | \(0.585187\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −14.6939 | −1.03643 | ||||||||
\(202\) | 12.4002 | 0.872474 | ||||||||
\(203\) | −28.8225 | −2.02294 | ||||||||
\(204\) | −8.05390 | −0.563886 | ||||||||
\(205\) | 6.22563 | 0.434817 | ||||||||
\(206\) | 6.32565 | 0.440729 | ||||||||
\(207\) | 6.48104 | 0.450464 | ||||||||
\(208\) | 2.16503 | 0.150118 | ||||||||
\(209\) | 4.97577 | 0.344181 | ||||||||
\(210\) | 4.45162 | 0.307191 | ||||||||
\(211\) | 9.23358 | 0.635666 | 0.317833 | − | 0.948147i | \(-0.397045\pi\) | ||||
0.317833 | + | 0.948147i | \(0.397045\pi\) | |||||||
\(212\) | 0.623093 | 0.0427942 | ||||||||
\(213\) | 7.52850 | 0.515845 | ||||||||
\(214\) | 3.29446 | 0.225205 | ||||||||
\(215\) | −1.00000 | −0.0681994 | ||||||||
\(216\) | 5.60343 | 0.381265 | ||||||||
\(217\) | 25.1483 | 1.70718 | ||||||||
\(218\) | 3.61019 | 0.244513 | ||||||||
\(219\) | −13.9150 | −0.940291 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | 13.4083 | 0.901937 | ||||||||
\(222\) | 6.40716 | 0.430021 | ||||||||
\(223\) | −15.0062 | −1.00489 | −0.502444 | − | 0.864610i | \(-0.667566\pi\) | ||||
−0.502444 | + | 0.864610i | \(0.667566\pi\) | |||||||
\(224\) | 3.42310 | 0.228716 | ||||||||
\(225\) | −1.30880 | −0.0872531 | ||||||||
\(226\) | −12.0417 | −0.801002 | ||||||||
\(227\) | −9.38383 | −0.622827 | −0.311413 | − | 0.950275i | \(-0.600802\pi\) | ||||
−0.311413 | + | 0.950275i | \(0.600802\pi\) | |||||||
\(228\) | −6.47081 | −0.428540 | ||||||||
\(229\) | 0.644040 | 0.0425593 | 0.0212797 | − | 0.999774i | \(-0.493226\pi\) | ||||
0.0212797 | + | 0.999774i | \(0.493226\pi\) | |||||||
\(230\) | 4.95191 | 0.326519 | ||||||||
\(231\) | −4.45162 | −0.292895 | ||||||||
\(232\) | −8.41999 | −0.552800 | ||||||||
\(233\) | −6.49014 | −0.425183 | −0.212592 | − | 0.977141i | \(-0.568190\pi\) | ||||
−0.212592 | + | 0.977141i | \(0.568190\pi\) | |||||||
\(234\) | −2.83358 | −0.185237 | ||||||||
\(235\) | −4.34083 | −0.283165 | ||||||||
\(236\) | 2.83303 | 0.184415 | ||||||||
\(237\) | 12.1510 | 0.789292 | ||||||||
\(238\) | 21.1996 | 1.37417 | ||||||||
\(239\) | 14.7664 | 0.955157 | 0.477578 | − | 0.878589i | \(-0.341515\pi\) | ||||
0.477578 | + | 0.878589i | \(0.341515\pi\) | |||||||
\(240\) | 1.30046 | 0.0839445 | ||||||||
\(241\) | 18.0201 | 1.16078 | 0.580388 | − | 0.814340i | \(-0.302901\pi\) | ||||
0.580388 | + | 0.814340i | \(0.302901\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −12.4399 | −0.798018 | ||||||||
\(244\) | −4.29500 | −0.274959 | ||||||||
\(245\) | −4.71763 | −0.301398 | ||||||||
\(246\) | 8.09620 | 0.516195 | ||||||||
\(247\) | 10.7727 | 0.685450 | ||||||||
\(248\) | 7.34665 | 0.466513 | ||||||||
\(249\) | 9.18072 | 0.581805 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −31.1292 | −1.96486 | −0.982429 | − | 0.186636i | \(-0.940241\pi\) | ||||
−0.982429 | + | 0.186636i | \(0.940241\pi\) | |||||||
\(252\) | −4.48014 | −0.282223 | ||||||||
\(253\) | −4.95191 | −0.311324 | ||||||||
\(254\) | 15.6355 | 0.981062 | ||||||||
\(255\) | 8.05390 | 0.504355 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.37282 | −0.0856344 | −0.0428172 | − | 0.999083i | \(-0.513633\pi\) | ||||
−0.0428172 | + | 0.999083i | \(0.513633\pi\) | |||||||
\(258\) | −1.30046 | −0.0809633 | ||||||||
\(259\) | −16.8651 | −1.04794 | ||||||||
\(260\) | −2.16503 | −0.134269 | ||||||||
\(261\) | 11.0201 | 0.682124 | ||||||||
\(262\) | −8.49576 | −0.524870 | ||||||||
\(263\) | 21.9517 | 1.35360 | 0.676801 | − | 0.736166i | \(-0.263366\pi\) | ||||
0.676801 | + | 0.736166i | \(0.263366\pi\) | |||||||
\(264\) | −1.30046 | −0.0800380 | ||||||||
\(265\) | −0.623093 | −0.0382763 | ||||||||
\(266\) | 17.0326 | 1.04433 | ||||||||
\(267\) | −10.8453 | −0.663719 | ||||||||
\(268\) | 11.2990 | 0.690194 | ||||||||
\(269\) | −12.2234 | −0.745276 | −0.372638 | − | 0.927977i | \(-0.621547\pi\) | ||||
−0.372638 | + | 0.927977i | \(0.621547\pi\) | |||||||
\(270\) | −5.60343 | −0.341014 | ||||||||
\(271\) | 9.73963 | 0.591640 | 0.295820 | − | 0.955244i | \(-0.404407\pi\) | ||||
0.295820 | + | 0.955244i | \(0.404407\pi\) | |||||||
\(272\) | 6.19311 | 0.375512 | ||||||||
\(273\) | −9.63789 | −0.583311 | ||||||||
\(274\) | −12.2600 | −0.740651 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 6.43978 | 0.387629 | ||||||||
\(277\) | −16.9494 | −1.01839 | −0.509195 | − | 0.860651i | \(-0.670057\pi\) | ||||
−0.509195 | + | 0.860651i | \(0.670057\pi\) | |||||||
\(278\) | 4.33409 | 0.259942 | ||||||||
\(279\) | −9.61527 | −0.575651 | ||||||||
\(280\) | −3.42310 | −0.204569 | ||||||||
\(281\) | 6.37151 | 0.380092 | 0.190046 | − | 0.981775i | \(-0.439136\pi\) | ||||
0.190046 | + | 0.981775i | \(0.439136\pi\) | |||||||
\(282\) | −5.64509 | −0.336160 | ||||||||
\(283\) | −19.9176 | −1.18398 | −0.591990 | − | 0.805945i | \(-0.701658\pi\) | ||||
−0.591990 | + | 0.805945i | \(0.701658\pi\) | |||||||
\(284\) | −5.78909 | −0.343520 | ||||||||
\(285\) | 6.47081 | 0.383298 | ||||||||
\(286\) | 2.16503 | 0.128021 | ||||||||
\(287\) | −21.3110 | −1.25795 | ||||||||
\(288\) | −1.30880 | −0.0771216 | ||||||||
\(289\) | 21.3546 | 1.25615 | ||||||||
\(290\) | 8.41999 | 0.494439 | ||||||||
\(291\) | −3.54763 | −0.207966 | ||||||||
\(292\) | 10.7001 | 0.626174 | ||||||||
\(293\) | 13.4631 | 0.786525 | 0.393263 | − | 0.919426i | \(-0.371346\pi\) | ||||
0.393263 | + | 0.919426i | \(0.371346\pi\) | |||||||
\(294\) | −6.13510 | −0.357806 | ||||||||
\(295\) | −2.83303 | −0.164945 | ||||||||
\(296\) | −4.92683 | −0.286366 | ||||||||
\(297\) | 5.60343 | 0.325144 | ||||||||
\(298\) | 2.58758 | 0.149895 | ||||||||
\(299\) | −10.7210 | −0.620014 | ||||||||
\(300\) | −1.30046 | −0.0750823 | ||||||||
\(301\) | 3.42310 | 0.197304 | ||||||||
\(302\) | 6.91199 | 0.397740 | ||||||||
\(303\) | −16.1260 | −0.926413 | ||||||||
\(304\) | 4.97577 | 0.285380 | ||||||||
\(305\) | 4.29500 | 0.245931 | ||||||||
\(306\) | −8.10551 | −0.463361 | ||||||||
\(307\) | 7.49575 | 0.427805 | 0.213902 | − | 0.976855i | \(-0.431383\pi\) | ||||
0.213902 | + | 0.976855i | \(0.431383\pi\) | |||||||
\(308\) | 3.42310 | 0.195049 | ||||||||
\(309\) | −8.22628 | −0.467977 | ||||||||
\(310\) | −7.34665 | −0.417262 | ||||||||
\(311\) | 3.71197 | 0.210486 | 0.105243 | − | 0.994447i | \(-0.466438\pi\) | ||||
0.105243 | + | 0.994447i | \(0.466438\pi\) | |||||||
\(312\) | −2.81554 | −0.159399 | ||||||||
\(313\) | −24.8649 | −1.40545 | −0.702724 | − | 0.711462i | \(-0.748033\pi\) | ||||
−0.702724 | + | 0.711462i | \(0.748033\pi\) | |||||||
\(314\) | 14.8219 | 0.836449 | ||||||||
\(315\) | 4.48014 | 0.252427 | ||||||||
\(316\) | −9.34359 | −0.525618 | ||||||||
\(317\) | −30.2711 | −1.70020 | −0.850098 | − | 0.526624i | \(-0.823457\pi\) | ||||
−0.850098 | + | 0.526624i | \(0.823457\pi\) | |||||||
\(318\) | −0.810309 | −0.0454399 | ||||||||
\(319\) | −8.41999 | −0.471429 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −4.28433 | −0.239128 | ||||||||
\(322\) | −16.9509 | −0.944637 | ||||||||
\(323\) | 30.8155 | 1.71462 | ||||||||
\(324\) | −3.36066 | −0.186703 | ||||||||
\(325\) | 2.16503 | 0.120094 | ||||||||
\(326\) | −2.87721 | −0.159354 | ||||||||
\(327\) | −4.69492 | −0.259630 | ||||||||
\(328\) | −6.22563 | −0.343753 | ||||||||
\(329\) | 14.8591 | 0.819210 | ||||||||
\(330\) | 1.30046 | 0.0715881 | ||||||||
\(331\) | −28.0973 | −1.54437 | −0.772183 | − | 0.635400i | \(-0.780835\pi\) | ||||
−0.772183 | + | 0.635400i | \(0.780835\pi\) | |||||||
\(332\) | −7.05958 | −0.387445 | ||||||||
\(333\) | 6.44822 | 0.353360 | ||||||||
\(334\) | 25.2030 | 1.37905 | ||||||||
\(335\) | −11.2990 | −0.617329 | ||||||||
\(336\) | −4.45162 | −0.242856 | ||||||||
\(337\) | 21.0302 | 1.14559 | 0.572795 | − | 0.819699i | \(-0.305859\pi\) | ||||
0.572795 | + | 0.819699i | \(0.305859\pi\) | |||||||
\(338\) | −8.31264 | −0.452148 | ||||||||
\(339\) | 15.6598 | 0.850523 | ||||||||
\(340\) | −6.19311 | −0.335868 | ||||||||
\(341\) | 7.34665 | 0.397843 | ||||||||
\(342\) | −6.51227 | −0.352143 | ||||||||
\(343\) | −7.81279 | −0.421851 | ||||||||
\(344\) | 1.00000 | 0.0539164 | ||||||||
\(345\) | −6.43978 | −0.346706 | ||||||||
\(346\) | 8.32115 | 0.447348 | ||||||||
\(347\) | 22.0487 | 1.18364 | 0.591818 | − | 0.806071i | \(-0.298410\pi\) | ||||
0.591818 | + | 0.806071i | \(0.298410\pi\) | |||||||
\(348\) | 10.9499 | 0.586976 | ||||||||
\(349\) | −2.14153 | −0.114634 | −0.0573168 | − | 0.998356i | \(-0.518255\pi\) | ||||
−0.0573168 | + | 0.998356i | \(0.518255\pi\) | |||||||
\(350\) | 3.42310 | 0.182973 | ||||||||
\(351\) | 12.1316 | 0.647537 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −4.04206 | −0.215137 | −0.107569 | − | 0.994198i | \(-0.534306\pi\) | ||||
−0.107569 | + | 0.994198i | \(0.534306\pi\) | |||||||
\(354\) | −3.68425 | −0.195816 | ||||||||
\(355\) | 5.78909 | 0.307253 | ||||||||
\(356\) | 8.33954 | 0.441995 | ||||||||
\(357\) | −27.5693 | −1.45912 | ||||||||
\(358\) | 16.8744 | 0.891842 | ||||||||
\(359\) | 22.3355 | 1.17882 | 0.589411 | − | 0.807833i | \(-0.299360\pi\) | ||||
0.589411 | + | 0.807833i | \(0.299360\pi\) | |||||||
\(360\) | 1.30880 | 0.0689796 | ||||||||
\(361\) | 5.75831 | 0.303069 | ||||||||
\(362\) | 3.36414 | 0.176815 | ||||||||
\(363\) | −1.30046 | −0.0682566 | ||||||||
\(364\) | 7.41112 | 0.388448 | ||||||||
\(365\) | −10.7001 | −0.560067 | ||||||||
\(366\) | 5.58549 | 0.291958 | ||||||||
\(367\) | −1.19297 | −0.0622726 | −0.0311363 | − | 0.999515i | \(-0.509913\pi\) | ||||
−0.0311363 | + | 0.999515i | \(0.509913\pi\) | |||||||
\(368\) | −4.95191 | −0.258136 | ||||||||
\(369\) | 8.14808 | 0.424172 | ||||||||
\(370\) | 4.92683 | 0.256134 | ||||||||
\(371\) | 2.13291 | 0.110735 | ||||||||
\(372\) | −9.55405 | −0.495354 | ||||||||
\(373\) | −10.6679 | −0.552362 | −0.276181 | − | 0.961106i | \(-0.589069\pi\) | ||||
−0.276181 | + | 0.961106i | \(0.589069\pi\) | |||||||
\(374\) | 6.19311 | 0.320238 | ||||||||
\(375\) | 1.30046 | 0.0671556 | ||||||||
\(376\) | 4.34083 | 0.223861 | ||||||||
\(377\) | −18.2295 | −0.938869 | ||||||||
\(378\) | 19.1811 | 0.986570 | ||||||||
\(379\) | −12.0989 | −0.621479 | −0.310740 | − | 0.950495i | \(-0.600577\pi\) | ||||
−0.310740 | + | 0.950495i | \(0.600577\pi\) | |||||||
\(380\) | −4.97577 | −0.255252 | ||||||||
\(381\) | −20.3335 | −1.04171 | ||||||||
\(382\) | 13.3995 | 0.685580 | ||||||||
\(383\) | 9.76694 | 0.499067 | 0.249534 | − | 0.968366i | \(-0.419723\pi\) | ||||
0.249534 | + | 0.968366i | \(0.419723\pi\) | |||||||
\(384\) | −1.30046 | −0.0663640 | ||||||||
\(385\) | −3.42310 | −0.174457 | ||||||||
\(386\) | 8.68042 | 0.441822 | ||||||||
\(387\) | −1.30880 | −0.0665299 | ||||||||
\(388\) | 2.72798 | 0.138492 | ||||||||
\(389\) | 27.6691 | 1.40288 | 0.701439 | − | 0.712729i | \(-0.252541\pi\) | ||||
0.701439 | + | 0.712729i | \(0.252541\pi\) | |||||||
\(390\) | 2.81554 | 0.142570 | ||||||||
\(391\) | −30.6677 | −1.55093 | ||||||||
\(392\) | 4.71763 | 0.238276 | ||||||||
\(393\) | 11.0484 | 0.557319 | ||||||||
\(394\) | −2.92760 | −0.147490 | ||||||||
\(395\) | 9.34359 | 0.470127 | ||||||||
\(396\) | −1.30880 | −0.0657695 | ||||||||
\(397\) | −5.32288 | −0.267148 | −0.133574 | − | 0.991039i | \(-0.542645\pi\) | ||||
−0.133574 | + | 0.991039i | \(0.542645\pi\) | |||||||
\(398\) | −7.46077 | −0.373974 | ||||||||
\(399\) | −22.1502 | −1.10890 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −24.3895 | −1.21795 | −0.608976 | − | 0.793189i | \(-0.708419\pi\) | ||||
−0.608976 | + | 0.793189i | \(0.708419\pi\) | |||||||
\(402\) | −14.6939 | −0.732865 | ||||||||
\(403\) | 15.9057 | 0.792320 | ||||||||
\(404\) | 12.4002 | 0.616932 | ||||||||
\(405\) | 3.36066 | 0.166993 | ||||||||
\(406\) | −28.8225 | −1.43044 | ||||||||
\(407\) | −4.92683 | −0.244214 | ||||||||
\(408\) | −8.05390 | −0.398728 | ||||||||
\(409\) | 15.8080 | 0.781655 | 0.390828 | − | 0.920464i | \(-0.372189\pi\) | ||||
0.390828 | + | 0.920464i | \(0.372189\pi\) | |||||||
\(410\) | 6.22563 | 0.307462 | ||||||||
\(411\) | 15.9436 | 0.786441 | ||||||||
\(412\) | 6.32565 | 0.311643 | ||||||||
\(413\) | 9.69775 | 0.477195 | ||||||||
\(414\) | 6.48104 | 0.318526 | ||||||||
\(415\) | 7.05958 | 0.346541 | ||||||||
\(416\) | 2.16503 | 0.106149 | ||||||||
\(417\) | −5.63633 | −0.276012 | ||||||||
\(418\) | 4.97577 | 0.243373 | ||||||||
\(419\) | −22.0577 | −1.07759 | −0.538795 | − | 0.842437i | \(-0.681120\pi\) | ||||
−0.538795 | + | 0.842437i | \(0.681120\pi\) | |||||||
\(420\) | 4.45162 | 0.217217 | ||||||||
\(421\) | −1.98468 | −0.0967272 | −0.0483636 | − | 0.998830i | \(-0.515401\pi\) | ||||
−0.0483636 | + | 0.998830i | \(0.515401\pi\) | |||||||
\(422\) | 9.23358 | 0.449484 | ||||||||
\(423\) | −5.68127 | −0.276233 | ||||||||
\(424\) | 0.623093 | 0.0302601 | ||||||||
\(425\) | 6.19311 | 0.300410 | ||||||||
\(426\) | 7.52850 | 0.364757 | ||||||||
\(427\) | −14.7022 | −0.711491 | ||||||||
\(428\) | 3.29446 | 0.159244 | ||||||||
\(429\) | −2.81554 | −0.135936 | ||||||||
\(430\) | −1.00000 | −0.0482243 | ||||||||
\(431\) | 8.17853 | 0.393946 | 0.196973 | − | 0.980409i | \(-0.436889\pi\) | ||||
0.196973 | + | 0.980409i | \(0.436889\pi\) | |||||||
\(432\) | 5.60343 | 0.269595 | ||||||||
\(433\) | 36.1824 | 1.73882 | 0.869409 | − | 0.494094i | \(-0.164500\pi\) | ||||
0.869409 | + | 0.494094i | \(0.164500\pi\) | |||||||
\(434\) | 25.1483 | 1.20716 | ||||||||
\(435\) | −10.9499 | −0.525007 | ||||||||
\(436\) | 3.61019 | 0.172897 | ||||||||
\(437\) | −24.6396 | −1.17867 | ||||||||
\(438\) | −13.9150 | −0.664886 | ||||||||
\(439\) | −16.7014 | −0.797113 | −0.398557 | − | 0.917144i | \(-0.630489\pi\) | ||||
−0.398557 | + | 0.917144i | \(0.630489\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | −6.17441 | −0.294020 | ||||||||
\(442\) | 13.4083 | 0.637766 | ||||||||
\(443\) | 5.77900 | 0.274569 | 0.137284 | − | 0.990532i | \(-0.456163\pi\) | ||||
0.137284 | + | 0.990532i | \(0.456163\pi\) | |||||||
\(444\) | 6.40716 | 0.304071 | ||||||||
\(445\) | −8.33954 | −0.395332 | ||||||||
\(446\) | −15.0062 | −0.710563 | ||||||||
\(447\) | −3.36505 | −0.159162 | ||||||||
\(448\) | 3.42310 | 0.161726 | ||||||||
\(449\) | 20.4579 | 0.965469 | 0.482735 | − | 0.875767i | \(-0.339644\pi\) | ||||
0.482735 | + | 0.875767i | \(0.339644\pi\) | |||||||
\(450\) | −1.30880 | −0.0616973 | ||||||||
\(451\) | −6.22563 | −0.293153 | ||||||||
\(452\) | −12.0417 | −0.566394 | ||||||||
\(453\) | −8.98878 | −0.422330 | ||||||||
\(454\) | −9.38383 | −0.440405 | ||||||||
\(455\) | −7.41112 | −0.347439 | ||||||||
\(456\) | −6.47081 | −0.303023 | ||||||||
\(457\) | 31.2053 | 1.45972 | 0.729862 | − | 0.683595i | \(-0.239584\pi\) | ||||
0.729862 | + | 0.683595i | \(0.239584\pi\) | |||||||
\(458\) | 0.644040 | 0.0300940 | ||||||||
\(459\) | 34.7026 | 1.61978 | ||||||||
\(460\) | 4.95191 | 0.230884 | ||||||||
\(461\) | 28.2199 | 1.31433 | 0.657165 | − | 0.753747i | \(-0.271756\pi\) | ||||
0.657165 | + | 0.753747i | \(0.271756\pi\) | |||||||
\(462\) | −4.45162 | −0.207108 | ||||||||
\(463\) | 39.3122 | 1.82699 | 0.913497 | − | 0.406845i | \(-0.133371\pi\) | ||||
0.913497 | + | 0.406845i | \(0.133371\pi\) | |||||||
\(464\) | −8.41999 | −0.390888 | ||||||||
\(465\) | 9.55405 | 0.443058 | ||||||||
\(466\) | −6.49014 | −0.300650 | ||||||||
\(467\) | −11.9611 | −0.553493 | −0.276746 | − | 0.960943i | \(-0.589256\pi\) | ||||
−0.276746 | + | 0.960943i | \(0.589256\pi\) | |||||||
\(468\) | −2.83358 | −0.130982 | ||||||||
\(469\) | 38.6775 | 1.78596 | ||||||||
\(470\) | −4.34083 | −0.200228 | ||||||||
\(471\) | −19.2753 | −0.888161 | ||||||||
\(472\) | 2.83303 | 0.130401 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 12.1510 | 0.558114 | ||||||||
\(475\) | 4.97577 | 0.228304 | ||||||||
\(476\) | 21.1996 | 0.971684 | ||||||||
\(477\) | −0.815502 | −0.0373393 | ||||||||
\(478\) | 14.7664 | 0.675398 | ||||||||
\(479\) | 25.2739 | 1.15479 | 0.577397 | − | 0.816464i | \(-0.304069\pi\) | ||||
0.577397 | + | 0.816464i | \(0.304069\pi\) | |||||||
\(480\) | 1.30046 | 0.0593577 | ||||||||
\(481\) | −10.6667 | −0.486362 | ||||||||
\(482\) | 18.0201 | 0.820793 | ||||||||
\(483\) | 22.0440 | 1.00304 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −2.72798 | −0.123871 | ||||||||
\(486\) | −12.4399 | −0.564284 | ||||||||
\(487\) | 5.91495 | 0.268032 | 0.134016 | − | 0.990979i | \(-0.457213\pi\) | ||||
0.134016 | + | 0.990979i | \(0.457213\pi\) | |||||||
\(488\) | −4.29500 | −0.194426 | ||||||||
\(489\) | 3.74170 | 0.169206 | ||||||||
\(490\) | −4.71763 | −0.213121 | ||||||||
\(491\) | −28.8499 | −1.30198 | −0.650989 | − | 0.759087i | \(-0.725646\pi\) | ||||
−0.650989 | + | 0.759087i | \(0.725646\pi\) | |||||||
\(492\) | 8.09620 | 0.365005 | ||||||||
\(493\) | −52.1459 | −2.34853 | ||||||||
\(494\) | 10.7727 | 0.484687 | ||||||||
\(495\) | 1.30880 | 0.0588260 | ||||||||
\(496\) | 7.34665 | 0.329874 | ||||||||
\(497\) | −19.8167 | −0.888899 | ||||||||
\(498\) | 9.18072 | 0.411398 | ||||||||
\(499\) | 11.3045 | 0.506059 | 0.253030 | − | 0.967459i | \(-0.418573\pi\) | ||||
0.253030 | + | 0.967459i | \(0.418573\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −32.7756 | −1.46431 | ||||||||
\(502\) | −31.1292 | −1.38936 | ||||||||
\(503\) | −38.4606 | −1.71487 | −0.857437 | − | 0.514589i | \(-0.827945\pi\) | ||||
−0.857437 | + | 0.514589i | \(0.827945\pi\) | |||||||
\(504\) | −4.48014 | −0.199561 | ||||||||
\(505\) | −12.4002 | −0.551801 | ||||||||
\(506\) | −4.95191 | −0.220139 | ||||||||
\(507\) | 10.8103 | 0.480102 | ||||||||
\(508\) | 15.6355 | 0.693715 | ||||||||
\(509\) | 14.8900 | 0.659986 | 0.329993 | − | 0.943983i | \(-0.392954\pi\) | ||||
0.329993 | + | 0.943983i | \(0.392954\pi\) | |||||||
\(510\) | 8.05390 | 0.356633 | ||||||||
\(511\) | 36.6274 | 1.62030 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 27.8814 | 1.23099 | ||||||||
\(514\) | −1.37282 | −0.0605526 | ||||||||
\(515\) | −6.32565 | −0.278742 | ||||||||
\(516\) | −1.30046 | −0.0572497 | ||||||||
\(517\) | 4.34083 | 0.190910 | ||||||||
\(518\) | −16.8651 | −0.741008 | ||||||||
\(519\) | −10.8213 | −0.475004 | ||||||||
\(520\) | −2.16503 | −0.0949429 | ||||||||
\(521\) | 24.1955 | 1.06002 | 0.530012 | − | 0.847990i | \(-0.322187\pi\) | ||||
0.530012 | + | 0.847990i | \(0.322187\pi\) | |||||||
\(522\) | 11.0201 | 0.482335 | ||||||||
\(523\) | 20.6699 | 0.903834 | 0.451917 | − | 0.892060i | \(-0.350740\pi\) | ||||
0.451917 | + | 0.892060i | \(0.350740\pi\) | |||||||
\(524\) | −8.49576 | −0.371139 | ||||||||
\(525\) | −4.45162 | −0.194284 | ||||||||
\(526\) | 21.9517 | 0.957141 | ||||||||
\(527\) | 45.4986 | 1.98195 | ||||||||
\(528\) | −1.30046 | −0.0565954 | ||||||||
\(529\) | 1.52143 | 0.0661491 | ||||||||
\(530\) | −0.623093 | −0.0270654 | ||||||||
\(531\) | −3.70786 | −0.160907 | ||||||||
\(532\) | 17.0326 | 0.738456 | ||||||||
\(533\) | −13.4787 | −0.583826 | ||||||||
\(534\) | −10.8453 | −0.469320 | ||||||||
\(535\) | −3.29446 | −0.142432 | ||||||||
\(536\) | 11.2990 | 0.488041 | ||||||||
\(537\) | −21.9446 | −0.946979 | ||||||||
\(538\) | −12.2234 | −0.526990 | ||||||||
\(539\) | 4.71763 | 0.203203 | ||||||||
\(540\) | −5.60343 | −0.241133 | ||||||||
\(541\) | 3.27057 | 0.140613 | 0.0703063 | − | 0.997525i | \(-0.477602\pi\) | ||||
0.0703063 | + | 0.997525i | \(0.477602\pi\) | |||||||
\(542\) | 9.73963 | 0.418353 | ||||||||
\(543\) | −4.37494 | −0.187747 | ||||||||
\(544\) | 6.19311 | 0.265527 | ||||||||
\(545\) | −3.61019 | −0.154644 | ||||||||
\(546\) | −9.63789 | −0.412463 | ||||||||
\(547\) | −3.76828 | −0.161120 | −0.0805600 | − | 0.996750i | \(-0.525671\pi\) | ||||
−0.0805600 | + | 0.996750i | \(0.525671\pi\) | |||||||
\(548\) | −12.2600 | −0.523720 | ||||||||
\(549\) | 5.62128 | 0.239910 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | −41.8960 | −1.78483 | ||||||||
\(552\) | 6.43978 | 0.274095 | ||||||||
\(553\) | −31.9841 | −1.36010 | ||||||||
\(554\) | −16.9494 | −0.720110 | ||||||||
\(555\) | −6.40716 | −0.271969 | ||||||||
\(556\) | 4.33409 | 0.183806 | ||||||||
\(557\) | −35.9041 | −1.52131 | −0.760653 | − | 0.649158i | \(-0.775121\pi\) | ||||
−0.760653 | + | 0.649158i | \(0.775121\pi\) | |||||||
\(558\) | −9.61527 | −0.407047 | ||||||||
\(559\) | 2.16503 | 0.0915710 | ||||||||
\(560\) | −3.42310 | −0.144652 | ||||||||
\(561\) | −8.05390 | −0.340036 | ||||||||
\(562\) | 6.37151 | 0.268766 | ||||||||
\(563\) | −30.6715 | −1.29265 | −0.646325 | − | 0.763062i | \(-0.723695\pi\) | ||||
−0.646325 | + | 0.763062i | \(0.723695\pi\) | |||||||
\(564\) | −5.64509 | −0.237701 | ||||||||
\(565\) | 12.0417 | 0.506598 | ||||||||
\(566\) | −19.9176 | −0.837200 | ||||||||
\(567\) | −11.5039 | −0.483118 | ||||||||
\(568\) | −5.78909 | −0.242905 | ||||||||
\(569\) | −19.9792 | −0.837570 | −0.418785 | − | 0.908085i | \(-0.637544\pi\) | ||||
−0.418785 | + | 0.908085i | \(0.637544\pi\) | |||||||
\(570\) | 6.47081 | 0.271032 | ||||||||
\(571\) | −12.3359 | −0.516241 | −0.258121 | − | 0.966113i | \(-0.583103\pi\) | ||||
−0.258121 | + | 0.966113i | \(0.583103\pi\) | |||||||
\(572\) | 2.16503 | 0.0905245 | ||||||||
\(573\) | −17.4256 | −0.727965 | ||||||||
\(574\) | −21.3110 | −0.889502 | ||||||||
\(575\) | −4.95191 | −0.206509 | ||||||||
\(576\) | −1.30880 | −0.0545332 | ||||||||
\(577\) | −23.3094 | −0.970385 | −0.485192 | − | 0.874407i | \(-0.661250\pi\) | ||||
−0.485192 | + | 0.874407i | \(0.661250\pi\) | |||||||
\(578\) | 21.3546 | 0.888232 | ||||||||
\(579\) | −11.2886 | −0.469137 | ||||||||
\(580\) | 8.41999 | 0.349621 | ||||||||
\(581\) | −24.1657 | −1.00256 | ||||||||
\(582\) | −3.54763 | −0.147054 | ||||||||
\(583\) | 0.623093 | 0.0258059 | ||||||||
\(584\) | 10.7001 | 0.442772 | ||||||||
\(585\) | 2.83358 | 0.117154 | ||||||||
\(586\) | 13.4631 | 0.556157 | ||||||||
\(587\) | 8.90757 | 0.367655 | 0.183827 | − | 0.982959i | \(-0.441151\pi\) | ||||
0.183827 | + | 0.982959i | \(0.441151\pi\) | |||||||
\(588\) | −6.13510 | −0.253007 | ||||||||
\(589\) | 36.5553 | 1.50623 | ||||||||
\(590\) | −2.83303 | −0.116634 | ||||||||
\(591\) | 3.80723 | 0.156609 | ||||||||
\(592\) | −4.92683 | −0.202492 | ||||||||
\(593\) | −43.9580 | −1.80514 | −0.902570 | − | 0.430544i | \(-0.858322\pi\) | ||||
−0.902570 | + | 0.430544i | \(0.858322\pi\) | |||||||
\(594\) | 5.60343 | 0.229912 | ||||||||
\(595\) | −21.1996 | −0.869100 | ||||||||
\(596\) | 2.58758 | 0.105991 | ||||||||
\(597\) | 9.70245 | 0.397095 | ||||||||
\(598\) | −10.7210 | −0.438416 | ||||||||
\(599\) | 9.49400 | 0.387915 | 0.193957 | − | 0.981010i | \(-0.437868\pi\) | ||||
0.193957 | + | 0.981010i | \(0.437868\pi\) | |||||||
\(600\) | −1.30046 | −0.0530912 | ||||||||
\(601\) | −5.61247 | −0.228938 | −0.114469 | − | 0.993427i | \(-0.536517\pi\) | ||||
−0.114469 | + | 0.993427i | \(0.536517\pi\) | |||||||
\(602\) | 3.42310 | 0.139515 | ||||||||
\(603\) | −14.7881 | −0.602216 | ||||||||
\(604\) | 6.91199 | 0.281245 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −16.1260 | −0.655073 | ||||||||
\(607\) | −36.3459 | −1.47524 | −0.737618 | − | 0.675219i | \(-0.764049\pi\) | ||||
−0.737618 | + | 0.675219i | \(0.764049\pi\) | |||||||
\(608\) | 4.97577 | 0.201794 | ||||||||
\(609\) | 37.4826 | 1.51887 | ||||||||
\(610\) | 4.29500 | 0.173900 | ||||||||
\(611\) | 9.39803 | 0.380204 | ||||||||
\(612\) | −8.10551 | −0.327646 | ||||||||
\(613\) | −16.1489 | −0.652247 | −0.326124 | − | 0.945327i | \(-0.605743\pi\) | ||||
−0.326124 | + | 0.945327i | \(0.605743\pi\) | |||||||
\(614\) | 7.49575 | 0.302504 | ||||||||
\(615\) | −8.09620 | −0.326470 | ||||||||
\(616\) | 3.42310 | 0.137921 | ||||||||
\(617\) | 3.11745 | 0.125504 | 0.0627518 | − | 0.998029i | \(-0.480012\pi\) | ||||
0.0627518 | + | 0.998029i | \(0.480012\pi\) | |||||||
\(618\) | −8.22628 | −0.330909 | ||||||||
\(619\) | −11.3967 | −0.458072 | −0.229036 | − | 0.973418i | \(-0.573557\pi\) | ||||
−0.229036 | + | 0.973418i | \(0.573557\pi\) | |||||||
\(620\) | −7.34665 | −0.295049 | ||||||||
\(621\) | −27.7477 | −1.11348 | ||||||||
\(622\) | 3.71197 | 0.148836 | ||||||||
\(623\) | 28.5471 | 1.14372 | ||||||||
\(624\) | −2.81554 | −0.112712 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −24.8649 | −0.993802 | ||||||||
\(627\) | −6.47081 | −0.258419 | ||||||||
\(628\) | 14.8219 | 0.591459 | ||||||||
\(629\) | −30.5124 | −1.21661 | ||||||||
\(630\) | 4.48014 | 0.178493 | ||||||||
\(631\) | −30.4536 | −1.21234 | −0.606169 | − | 0.795336i | \(-0.707294\pi\) | ||||
−0.606169 | + | 0.795336i | \(0.707294\pi\) | |||||||
\(632\) | −9.34359 | −0.371668 | ||||||||
\(633\) | −12.0079 | −0.477272 | ||||||||
\(634\) | −30.2711 | −1.20222 | ||||||||
\(635\) | −15.6355 | −0.620478 | ||||||||
\(636\) | −0.810309 | −0.0321309 | ||||||||
\(637\) | 10.2138 | 0.404686 | ||||||||
\(638\) | −8.41999 | −0.333351 | ||||||||
\(639\) | 7.57675 | 0.299731 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −0.916790 | −0.0362110 | −0.0181055 | − | 0.999836i | \(-0.505763\pi\) | ||||
−0.0181055 | + | 0.999836i | \(0.505763\pi\) | |||||||
\(642\) | −4.28433 | −0.169089 | ||||||||
\(643\) | −40.7833 | −1.60833 | −0.804167 | − | 0.594403i | \(-0.797388\pi\) | ||||
−0.804167 | + | 0.594403i | \(0.797388\pi\) | |||||||
\(644\) | −16.9509 | −0.667959 | ||||||||
\(645\) | 1.30046 | 0.0512057 | ||||||||
\(646\) | 30.8155 | 1.21242 | ||||||||
\(647\) | −44.1766 | −1.73676 | −0.868380 | − | 0.495900i | \(-0.834838\pi\) | ||||
−0.868380 | + | 0.495900i | \(0.834838\pi\) | |||||||
\(648\) | −3.36066 | −0.132019 | ||||||||
\(649\) | 2.83303 | 0.111206 | ||||||||
\(650\) | 2.16503 | 0.0849195 | ||||||||
\(651\) | −32.7045 | −1.28179 | ||||||||
\(652\) | −2.87721 | −0.112680 | ||||||||
\(653\) | −8.78419 | −0.343752 | −0.171876 | − | 0.985119i | \(-0.554983\pi\) | ||||
−0.171876 | + | 0.985119i | \(0.554983\pi\) | |||||||
\(654\) | −4.69492 | −0.183586 | ||||||||
\(655\) | 8.49576 | 0.331957 | ||||||||
\(656\) | −6.22563 | −0.243070 | ||||||||
\(657\) | −14.0042 | −0.546356 | ||||||||
\(658\) | 14.8591 | 0.579269 | ||||||||
\(659\) | −38.3196 | −1.49272 | −0.746361 | − | 0.665542i | \(-0.768201\pi\) | ||||
−0.746361 | + | 0.665542i | \(0.768201\pi\) | |||||||
\(660\) | 1.30046 | 0.0506204 | ||||||||
\(661\) | 39.8144 | 1.54860 | 0.774301 | − | 0.632818i | \(-0.218102\pi\) | ||||
0.774301 | + | 0.632818i | \(0.218102\pi\) | |||||||
\(662\) | −28.0973 | −1.09203 | ||||||||
\(663\) | −17.4369 | −0.677195 | ||||||||
\(664\) | −7.05958 | −0.273965 | ||||||||
\(665\) | −17.0326 | −0.660495 | ||||||||
\(666\) | 6.44822 | 0.249864 | ||||||||
\(667\) | 41.6951 | 1.61444 | ||||||||
\(668\) | 25.2030 | 0.975134 | ||||||||
\(669\) | 19.5150 | 0.754493 | ||||||||
\(670\) | −11.2990 | −0.436517 | ||||||||
\(671\) | −4.29500 | −0.165807 | ||||||||
\(672\) | −4.45162 | −0.171725 | ||||||||
\(673\) | −32.1996 | −1.24120 | −0.620602 | − | 0.784126i | \(-0.713112\pi\) | ||||
−0.620602 | + | 0.784126i | \(0.713112\pi\) | |||||||
\(674\) | 21.0302 | 0.810055 | ||||||||
\(675\) | 5.60343 | 0.215676 | ||||||||
\(676\) | −8.31264 | −0.319717 | ||||||||
\(677\) | 29.3103 | 1.12649 | 0.563244 | − | 0.826291i | \(-0.309553\pi\) | ||||
0.563244 | + | 0.826291i | \(0.309553\pi\) | |||||||
\(678\) | 15.6598 | 0.601410 | ||||||||
\(679\) | 9.33814 | 0.358365 | ||||||||
\(680\) | −6.19311 | −0.237495 | ||||||||
\(681\) | 12.2033 | 0.467632 | ||||||||
\(682\) | 7.34665 | 0.281318 | ||||||||
\(683\) | −49.4801 | −1.89330 | −0.946652 | − | 0.322259i | \(-0.895558\pi\) | ||||
−0.946652 | + | 0.322259i | \(0.895558\pi\) | |||||||
\(684\) | −6.51227 | −0.249003 | ||||||||
\(685\) | 12.2600 | 0.468429 | ||||||||
\(686\) | −7.81279 | −0.298294 | ||||||||
\(687\) | −0.837550 | −0.0319545 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | 1.34902 | 0.0513934 | ||||||||
\(690\) | −6.43978 | −0.245158 | ||||||||
\(691\) | 41.1902 | 1.56695 | 0.783474 | − | 0.621424i | \(-0.213446\pi\) | ||||
0.783474 | + | 0.621424i | \(0.213446\pi\) | |||||||
\(692\) | 8.32115 | 0.316323 | ||||||||
\(693\) | −4.48014 | −0.170187 | ||||||||
\(694\) | 22.0487 | 0.836958 | ||||||||
\(695\) | −4.33409 | −0.164401 | ||||||||
\(696\) | 10.9499 | 0.415054 | ||||||||
\(697\) | −38.5560 | −1.46041 | ||||||||
\(698\) | −2.14153 | −0.0810582 | ||||||||
\(699\) | 8.44018 | 0.319237 | ||||||||
\(700\) | 3.42310 | 0.129381 | ||||||||
\(701\) | 9.87256 | 0.372882 | 0.186441 | − | 0.982466i | \(-0.440305\pi\) | ||||
0.186441 | + | 0.982466i | \(0.440305\pi\) | |||||||
\(702\) | 12.1316 | 0.457878 | ||||||||
\(703\) | −24.5148 | −0.924593 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 5.64509 | 0.212606 | ||||||||
\(706\) | −4.04206 | −0.152125 | ||||||||
\(707\) | 42.4471 | 1.59639 | ||||||||
\(708\) | −3.68425 | −0.138463 | ||||||||
\(709\) | −4.94667 | −0.185776 | −0.0928880 | − | 0.995677i | \(-0.529610\pi\) | ||||
−0.0928880 | + | 0.995677i | \(0.529610\pi\) | |||||||
\(710\) | 5.78909 | 0.217261 | ||||||||
\(711\) | 12.2289 | 0.458618 | ||||||||
\(712\) | 8.33954 | 0.312537 | ||||||||
\(713\) | −36.3800 | −1.36244 | ||||||||
\(714\) | −27.5693 | −1.03176 | ||||||||
\(715\) | −2.16503 | −0.0809675 | ||||||||
\(716\) | 16.8744 | 0.630627 | ||||||||
\(717\) | −19.2031 | −0.717153 | ||||||||
\(718\) | 22.3355 | 0.833553 | ||||||||
\(719\) | 35.1117 | 1.30944 | 0.654722 | − | 0.755870i | \(-0.272786\pi\) | ||||
0.654722 | + | 0.755870i | \(0.272786\pi\) | |||||||
\(720\) | 1.30880 | 0.0487760 | ||||||||
\(721\) | 21.6534 | 0.806413 | ||||||||
\(722\) | 5.75831 | 0.214302 | ||||||||
\(723\) | −23.4345 | −0.871537 | ||||||||
\(724\) | 3.36414 | 0.125027 | ||||||||
\(725\) | −8.41999 | −0.312711 | ||||||||
\(726\) | −1.30046 | −0.0482647 | ||||||||
\(727\) | −39.3046 | −1.45773 | −0.728864 | − | 0.684659i | \(-0.759951\pi\) | ||||
−0.728864 | + | 0.684659i | \(0.759951\pi\) | |||||||
\(728\) | 7.41112 | 0.274674 | ||||||||
\(729\) | 26.2596 | 0.972577 | ||||||||
\(730\) | −10.7001 | −0.396027 | ||||||||
\(731\) | 6.19311 | 0.229060 | ||||||||
\(732\) | 5.58549 | 0.206446 | ||||||||
\(733\) | −24.9663 | −0.922151 | −0.461075 | − | 0.887361i | \(-0.652536\pi\) | ||||
−0.461075 | + | 0.887361i | \(0.652536\pi\) | |||||||
\(734\) | −1.19297 | −0.0440334 | ||||||||
\(735\) | 6.13510 | 0.226297 | ||||||||
\(736\) | −4.95191 | −0.182530 | ||||||||
\(737\) | 11.2990 | 0.416203 | ||||||||
\(738\) | 8.14808 | 0.299935 | ||||||||
\(739\) | 20.2667 | 0.745522 | 0.372761 | − | 0.927927i | \(-0.378411\pi\) | ||||
0.372761 | + | 0.927927i | \(0.378411\pi\) | |||||||
\(740\) | 4.92683 | 0.181114 | ||||||||
\(741\) | −14.0095 | −0.514652 | ||||||||
\(742\) | 2.13291 | 0.0783016 | ||||||||
\(743\) | −7.96430 | −0.292182 | −0.146091 | − | 0.989271i | \(-0.546669\pi\) | ||||
−0.146091 | + | 0.989271i | \(0.546669\pi\) | |||||||
\(744\) | −9.55405 | −0.350268 | ||||||||
\(745\) | −2.58758 | −0.0948016 | ||||||||
\(746\) | −10.6679 | −0.390579 | ||||||||
\(747\) | 9.23956 | 0.338058 | ||||||||
\(748\) | 6.19311 | 0.226442 | ||||||||
\(749\) | 11.2773 | 0.412063 | ||||||||
\(750\) | 1.30046 | 0.0474862 | ||||||||
\(751\) | −21.5523 | −0.786456 | −0.393228 | − | 0.919441i | \(-0.628642\pi\) | ||||
−0.393228 | + | 0.919441i | \(0.628642\pi\) | |||||||
\(752\) | 4.34083 | 0.158294 | ||||||||
\(753\) | 40.4824 | 1.47526 | ||||||||
\(754\) | −18.2295 | −0.663881 | ||||||||
\(755\) | −6.91199 | −0.251553 | ||||||||
\(756\) | 19.1811 | 0.697610 | ||||||||
\(757\) | −10.2568 | −0.372788 | −0.186394 | − | 0.982475i | \(-0.559680\pi\) | ||||
−0.186394 | + | 0.982475i | \(0.559680\pi\) | |||||||
\(758\) | −12.0989 | −0.439452 | ||||||||
\(759\) | 6.43978 | 0.233749 | ||||||||
\(760\) | −4.97577 | −0.180490 | ||||||||
\(761\) | −21.6999 | −0.786621 | −0.393310 | − | 0.919406i | \(-0.628670\pi\) | ||||
−0.393310 | + | 0.919406i | \(0.628670\pi\) | |||||||
\(762\) | −20.3335 | −0.736603 | ||||||||
\(763\) | 12.3581 | 0.447392 | ||||||||
\(764\) | 13.3995 | 0.484778 | ||||||||
\(765\) | 8.10551 | 0.293055 | ||||||||
\(766\) | 9.76694 | 0.352894 | ||||||||
\(767\) | 6.13360 | 0.221471 | ||||||||
\(768\) | −1.30046 | −0.0469264 | ||||||||
\(769\) | 39.5504 | 1.42622 | 0.713112 | − | 0.701050i | \(-0.247285\pi\) | ||||
0.713112 | + | 0.701050i | \(0.247285\pi\) | |||||||
\(770\) | −3.42310 | −0.123360 | ||||||||
\(771\) | 1.78531 | 0.0642962 | ||||||||
\(772\) | 8.68042 | 0.312415 | ||||||||
\(773\) | 5.35245 | 0.192514 | 0.0962572 | − | 0.995356i | \(-0.469313\pi\) | ||||
0.0962572 | + | 0.995356i | \(0.469313\pi\) | |||||||
\(774\) | −1.30880 | −0.0470437 | ||||||||
\(775\) | 7.34665 | 0.263899 | ||||||||
\(776\) | 2.72798 | 0.0979286 | ||||||||
\(777\) | 21.9324 | 0.786820 | ||||||||
\(778\) | 27.6691 | 0.991985 | ||||||||
\(779\) | −30.9773 | −1.10988 | ||||||||
\(780\) | 2.81554 | 0.100813 | ||||||||
\(781\) | −5.78909 | −0.207150 | ||||||||
\(782\) | −30.6677 | −1.09668 | ||||||||
\(783\) | −47.1808 | −1.68611 | ||||||||
\(784\) | 4.71763 | 0.168487 | ||||||||
\(785\) | −14.8219 | −0.529017 | ||||||||
\(786\) | 11.0484 | 0.394084 | ||||||||
\(787\) | −48.9484 | −1.74482 | −0.872411 | − | 0.488773i | \(-0.837444\pi\) | ||||
−0.872411 | + | 0.488773i | \(0.837444\pi\) | |||||||
\(788\) | −2.92760 | −0.104291 | ||||||||
\(789\) | −28.5474 | −1.01631 | ||||||||
\(790\) | 9.34359 | 0.332430 | ||||||||
\(791\) | −41.2200 | −1.46561 | ||||||||
\(792\) | −1.30880 | −0.0465061 | ||||||||
\(793\) | −9.29881 | −0.330210 | ||||||||
\(794\) | −5.32288 | −0.188902 | ||||||||
\(795\) | 0.810309 | 0.0287387 | ||||||||
\(796\) | −7.46077 | −0.264440 | ||||||||
\(797\) | −21.4499 | −0.759795 | −0.379897 | − | 0.925029i | \(-0.624041\pi\) | ||||
−0.379897 | + | 0.925029i | \(0.624041\pi\) | |||||||
\(798\) | −22.1502 | −0.784110 | ||||||||
\(799\) | 26.8832 | 0.951061 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −10.9148 | −0.385654 | ||||||||
\(802\) | −24.3895 | −0.861222 | ||||||||
\(803\) | 10.7001 | 0.377597 | ||||||||
\(804\) | −14.6939 | −0.518214 | ||||||||
\(805\) | 16.9509 | 0.597441 | ||||||||
\(806\) | 15.9057 | 0.560255 | ||||||||
\(807\) | 15.8961 | 0.559570 | ||||||||
\(808\) | 12.4002 | 0.436237 | ||||||||
\(809\) | 24.9438 | 0.876976 | 0.438488 | − | 0.898737i | \(-0.355514\pi\) | ||||
0.438488 | + | 0.898737i | \(0.355514\pi\) | |||||||
\(810\) | 3.36066 | 0.118082 | ||||||||
\(811\) | 12.0392 | 0.422754 | 0.211377 | − | 0.977405i | \(-0.432205\pi\) | ||||
0.211377 | + | 0.977405i | \(0.432205\pi\) | |||||||
\(812\) | −28.8225 | −1.01147 | ||||||||
\(813\) | −12.6660 | −0.444217 | ||||||||
\(814\) | −4.92683 | −0.172685 | ||||||||
\(815\) | 2.87721 | 0.100784 | ||||||||
\(816\) | −8.05390 | −0.281943 | ||||||||
\(817\) | 4.97577 | 0.174080 | ||||||||
\(818\) | 15.8080 | 0.552714 | ||||||||
\(819\) | −9.69965 | −0.338933 | ||||||||
\(820\) | 6.22563 | 0.217408 | ||||||||
\(821\) | −32.9154 | −1.14875 | −0.574377 | − | 0.818591i | \(-0.694756\pi\) | ||||
−0.574377 | + | 0.818591i | \(0.694756\pi\) | |||||||
\(822\) | 15.9436 | 0.556098 | ||||||||
\(823\) | 32.5040 | 1.13302 | 0.566508 | − | 0.824056i | \(-0.308294\pi\) | ||||
0.566508 | + | 0.824056i | \(0.308294\pi\) | |||||||
\(824\) | 6.32565 | 0.220365 | ||||||||
\(825\) | −1.30046 | −0.0452763 | ||||||||
\(826\) | 9.69775 | 0.337428 | ||||||||
\(827\) | −47.7989 | −1.66213 | −0.831065 | − | 0.556176i | \(-0.812268\pi\) | ||||
−0.831065 | + | 0.556176i | \(0.812268\pi\) | |||||||
\(828\) | 6.48104 | 0.225232 | ||||||||
\(829\) | −19.9280 | −0.692128 | −0.346064 | − | 0.938211i | \(-0.612482\pi\) | ||||
−0.346064 | + | 0.938211i | \(0.612482\pi\) | |||||||
\(830\) | 7.05958 | 0.245042 | ||||||||
\(831\) | 22.0420 | 0.764629 | ||||||||
\(832\) | 2.16503 | 0.0750589 | ||||||||
\(833\) | 29.2168 | 1.01230 | ||||||||
\(834\) | −5.63633 | −0.195170 | ||||||||
\(835\) | −25.2030 | −0.872186 | ||||||||
\(836\) | 4.97577 | 0.172091 | ||||||||
\(837\) | 41.1664 | 1.42292 | ||||||||
\(838\) | −22.0577 | −0.761971 | ||||||||
\(839\) | −40.7524 | −1.40693 | −0.703465 | − | 0.710730i | \(-0.748365\pi\) | ||||
−0.703465 | + | 0.710730i | \(0.748365\pi\) | |||||||
\(840\) | 4.45162 | 0.153595 | ||||||||
\(841\) | 41.8963 | 1.44470 | ||||||||
\(842\) | −1.98468 | −0.0683965 | ||||||||
\(843\) | −8.28591 | −0.285382 | ||||||||
\(844\) | 9.23358 | 0.317833 | ||||||||
\(845\) | 8.31264 | 0.285964 | ||||||||
\(846\) | −5.68127 | −0.195326 | ||||||||
\(847\) | 3.42310 | 0.117619 | ||||||||
\(848\) | 0.623093 | 0.0213971 | ||||||||
\(849\) | 25.9021 | 0.888959 | ||||||||
\(850\) | 6.19311 | 0.212422 | ||||||||
\(851\) | 24.3972 | 0.836327 | ||||||||
\(852\) | 7.52850 | 0.257922 | ||||||||
\(853\) | 16.6264 | 0.569278 | 0.284639 | − | 0.958635i | \(-0.408126\pi\) | ||||
0.284639 | + | 0.958635i | \(0.408126\pi\) | |||||||
\(854\) | −14.7022 | −0.503100 | ||||||||
\(855\) | 6.51227 | 0.222715 | ||||||||
\(856\) | 3.29446 | 0.112602 | ||||||||
\(857\) | 11.6808 | 0.399007 | 0.199504 | − | 0.979897i | \(-0.436067\pi\) | ||||
0.199504 | + | 0.979897i | \(0.436067\pi\) | |||||||
\(858\) | −2.81554 | −0.0961210 | ||||||||
\(859\) | 9.63507 | 0.328744 | 0.164372 | − | 0.986398i | \(-0.447440\pi\) | ||||
0.164372 | + | 0.986398i | \(0.447440\pi\) | |||||||
\(860\) | −1.00000 | −0.0340997 | ||||||||
\(861\) | 27.7141 | 0.944495 | ||||||||
\(862\) | 8.17853 | 0.278562 | ||||||||
\(863\) | 13.0559 | 0.444427 | 0.222213 | − | 0.974998i | \(-0.428672\pi\) | ||||
0.222213 | + | 0.974998i | \(0.428672\pi\) | |||||||
\(864\) | 5.60343 | 0.190633 | ||||||||
\(865\) | −8.32115 | −0.282928 | ||||||||
\(866\) | 36.1824 | 1.22953 | ||||||||
\(867\) | −27.7708 | −0.943146 | ||||||||
\(868\) | 25.1483 | 0.853590 | ||||||||
\(869\) | −9.34359 | −0.316960 | ||||||||
\(870\) | −10.9499 | −0.371236 | ||||||||
\(871\) | 24.4626 | 0.828884 | ||||||||
\(872\) | 3.61019 | 0.122256 | ||||||||
\(873\) | −3.57037 | −0.120839 | ||||||||
\(874\) | −24.6396 | −0.833446 | ||||||||
\(875\) | −3.42310 | −0.115722 | ||||||||
\(876\) | −13.9150 | −0.470145 | ||||||||
\(877\) | −49.9901 | −1.68805 | −0.844023 | − | 0.536307i | \(-0.819819\pi\) | ||||
−0.844023 | + | 0.536307i | \(0.819819\pi\) | |||||||
\(878\) | −16.7014 | −0.563644 | ||||||||
\(879\) | −17.5083 | −0.590541 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | −6.46920 | −0.217953 | −0.108976 | − | 0.994044i | \(-0.534757\pi\) | ||||
−0.108976 | + | 0.994044i | \(0.534757\pi\) | |||||||
\(882\) | −6.17441 | −0.207903 | ||||||||
\(883\) | −4.04902 | −0.136260 | −0.0681302 | − | 0.997676i | \(-0.521703\pi\) | ||||
−0.0681302 | + | 0.997676i | \(0.521703\pi\) | |||||||
\(884\) | 13.4083 | 0.450969 | ||||||||
\(885\) | 3.68425 | 0.123845 | ||||||||
\(886\) | 5.77900 | 0.194149 | ||||||||
\(887\) | 21.8544 | 0.733798 | 0.366899 | − | 0.930261i | \(-0.380419\pi\) | ||||
0.366899 | + | 0.930261i | \(0.380419\pi\) | |||||||
\(888\) | 6.40716 | 0.215010 | ||||||||
\(889\) | 53.5221 | 1.79507 | ||||||||
\(890\) | −8.33954 | −0.279542 | ||||||||
\(891\) | −3.36066 | −0.112586 | ||||||||
\(892\) | −15.0062 | −0.502444 | ||||||||
\(893\) | 21.5990 | 0.722783 | ||||||||
\(894\) | −3.36505 | −0.112544 | ||||||||
\(895\) | −16.8744 | −0.564050 | ||||||||
\(896\) | 3.42310 | 0.114358 | ||||||||
\(897\) | 13.9423 | 0.465520 | ||||||||
\(898\) | 20.4579 | 0.682690 | ||||||||
\(899\) | −61.8587 | −2.06310 | ||||||||
\(900\) | −1.30880 | −0.0436265 | ||||||||
\(901\) | 3.85888 | 0.128558 | ||||||||
\(902\) | −6.22563 | −0.207291 | ||||||||
\(903\) | −4.45162 | −0.148141 | ||||||||
\(904\) | −12.0417 | −0.400501 | ||||||||
\(905\) | −3.36414 | −0.111828 | ||||||||
\(906\) | −8.98878 | −0.298632 | ||||||||
\(907\) | −51.6022 | −1.71342 | −0.856711 | − | 0.515797i | \(-0.827496\pi\) | ||||
−0.856711 | + | 0.515797i | \(0.827496\pi\) | |||||||
\(908\) | −9.38383 | −0.311413 | ||||||||
\(909\) | −16.2293 | −0.538292 | ||||||||
\(910\) | −7.41112 | −0.245676 | ||||||||
\(911\) | −28.2551 | −0.936132 | −0.468066 | − | 0.883693i | \(-0.655049\pi\) | ||||
−0.468066 | + | 0.883693i | \(0.655049\pi\) | |||||||
\(912\) | −6.47081 | −0.214270 | ||||||||
\(913\) | −7.05958 | −0.233638 | ||||||||
\(914\) | 31.2053 | 1.03218 | ||||||||
\(915\) | −5.58549 | −0.184651 | ||||||||
\(916\) | 0.644040 | 0.0212797 | ||||||||
\(917\) | −29.0818 | −0.960367 | ||||||||
\(918\) | 34.7026 | 1.14536 | ||||||||
\(919\) | −7.76545 | −0.256158 | −0.128079 | − | 0.991764i | \(-0.540881\pi\) | ||||
−0.128079 | + | 0.991764i | \(0.540881\pi\) | |||||||
\(920\) | 4.95191 | 0.163260 | ||||||||
\(921\) | −9.74794 | −0.321206 | ||||||||
\(922\) | 28.2199 | 0.929371 | ||||||||
\(923\) | −12.5336 | −0.412547 | ||||||||
\(924\) | −4.45162 | −0.146447 | ||||||||
\(925\) | −4.92683 | −0.161993 | ||||||||
\(926\) | 39.3122 | 1.29188 | ||||||||
\(927\) | −8.27899 | −0.271918 | ||||||||
\(928\) | −8.41999 | −0.276400 | ||||||||
\(929\) | −5.13456 | −0.168459 | −0.0842297 | − | 0.996446i | \(-0.526843\pi\) | ||||
−0.0842297 | + | 0.996446i | \(0.526843\pi\) | |||||||
\(930\) | 9.55405 | 0.313290 | ||||||||
\(931\) | 23.4738 | 0.769324 | ||||||||
\(932\) | −6.49014 | −0.212592 | ||||||||
\(933\) | −4.82727 | −0.158038 | ||||||||
\(934\) | −11.9611 | −0.391378 | ||||||||
\(935\) | −6.19311 | −0.202536 | ||||||||
\(936\) | −2.83358 | −0.0926186 | ||||||||
\(937\) | 51.9015 | 1.69555 | 0.847773 | − | 0.530359i | \(-0.177943\pi\) | ||||
0.847773 | + | 0.530359i | \(0.177943\pi\) | |||||||
\(938\) | 38.6775 | 1.26287 | ||||||||
\(939\) | 32.3359 | 1.05524 | ||||||||
\(940\) | −4.34083 | −0.141582 | ||||||||
\(941\) | −0.710465 | −0.0231605 | −0.0115802 | − | 0.999933i | \(-0.503686\pi\) | ||||
−0.0115802 | + | 0.999933i | \(0.503686\pi\) | |||||||
\(942\) | −19.2753 | −0.628025 | ||||||||
\(943\) | 30.8288 | 1.00392 | ||||||||
\(944\) | 2.83303 | 0.0922073 | ||||||||
\(945\) | −19.1811 | −0.623962 | ||||||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | −39.9473 | −1.29811 | −0.649057 | − | 0.760740i | \(-0.724836\pi\) | ||||
−0.649057 | + | 0.760740i | \(0.724836\pi\) | |||||||
\(948\) | 12.1510 | 0.394646 | ||||||||
\(949\) | 23.1660 | 0.751999 | ||||||||
\(950\) | 4.97577 | 0.161435 | ||||||||
\(951\) | 39.3665 | 1.27655 | ||||||||
\(952\) | 21.1996 | 0.687084 | ||||||||
\(953\) | −31.0993 | −1.00740 | −0.503702 | − | 0.863878i | \(-0.668029\pi\) | ||||
−0.503702 | + | 0.863878i | \(0.668029\pi\) | |||||||
\(954\) | −0.815502 | −0.0264028 | ||||||||
\(955\) | −13.3995 | −0.433599 | ||||||||
\(956\) | 14.7664 | 0.477578 | ||||||||
\(957\) | 10.9499 | 0.353960 | ||||||||
\(958\) | 25.2739 | 0.816563 | ||||||||
\(959\) | −41.9671 | −1.35519 | ||||||||
\(960\) | 1.30046 | 0.0419723 | ||||||||
\(961\) | 22.9733 | 0.741074 | ||||||||
\(962\) | −10.6667 | −0.343910 | ||||||||
\(963\) | −4.31178 | −0.138945 | ||||||||
\(964\) | 18.0201 | 0.580388 | ||||||||
\(965\) | −8.68042 | −0.279433 | ||||||||
\(966\) | 22.0440 | 0.709255 | ||||||||
\(967\) | 5.99406 | 0.192756 | 0.0963780 | − | 0.995345i | \(-0.469274\pi\) | ||||
0.0963780 | + | 0.995345i | \(0.469274\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −40.0744 | −1.28737 | ||||||||
\(970\) | −2.72798 | −0.0875900 | ||||||||
\(971\) | 1.26628 | 0.0406370 | 0.0203185 | − | 0.999794i | \(-0.493532\pi\) | ||||
0.0203185 | + | 0.999794i | \(0.493532\pi\) | |||||||
\(972\) | −12.4399 | −0.399009 | ||||||||
\(973\) | 14.8360 | 0.475622 | ||||||||
\(974\) | 5.91495 | 0.189527 | ||||||||
\(975\) | −2.81554 | −0.0901695 | ||||||||
\(976\) | −4.29500 | −0.137480 | ||||||||
\(977\) | −21.1001 | −0.675052 | −0.337526 | − | 0.941316i | \(-0.609590\pi\) | ||||
−0.337526 | + | 0.941316i | \(0.609590\pi\) | |||||||
\(978\) | 3.74170 | 0.119646 | ||||||||
\(979\) | 8.33954 | 0.266533 | ||||||||
\(980\) | −4.71763 | −0.150699 | ||||||||
\(981\) | −4.72500 | −0.150858 | ||||||||
\(982\) | −28.8499 | −0.920638 | ||||||||
\(983\) | 16.1900 | 0.516382 | 0.258191 | − | 0.966094i | \(-0.416874\pi\) | ||||
0.258191 | + | 0.966094i | \(0.416874\pi\) | |||||||
\(984\) | 8.09620 | 0.258097 | ||||||||
\(985\) | 2.92760 | 0.0932810 | ||||||||
\(986\) | −52.1459 | −1.66066 | ||||||||
\(987\) | −19.3237 | −0.615081 | ||||||||
\(988\) | 10.7727 | 0.342725 | ||||||||
\(989\) | −4.95191 | −0.157462 | ||||||||
\(990\) | 1.30880 | 0.0415963 | ||||||||
\(991\) | 21.8380 | 0.693707 | 0.346853 | − | 0.937919i | \(-0.387250\pi\) | ||||
0.346853 | + | 0.937919i | \(0.387250\pi\) | |||||||
\(992\) | 7.34665 | 0.233256 | ||||||||
\(993\) | 36.5395 | 1.15955 | ||||||||
\(994\) | −19.8167 | −0.628546 | ||||||||
\(995\) | 7.46077 | 0.236522 | ||||||||
\(996\) | 9.18072 | 0.290902 | ||||||||
\(997\) | 50.9650 | 1.61408 | 0.807039 | − | 0.590498i | \(-0.201069\pi\) | ||||
0.807039 | + | 0.590498i | \(0.201069\pi\) | |||||||
\(998\) | 11.3045 | 0.357838 | ||||||||
\(999\) | −27.6072 | −0.873452 |
(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 | 4730.2.a.bf.1.4 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4730.2.a.bf.1.4 | ✓ | 13 | 1.1 | even | 1 | trivial |