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: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.48119\) 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 | ||||||||
\(11\) | −1.61213 | −0.486075 | −0.243037 | − | 0.970017i | \(-0.578144\pi\) | ||||
−0.243037 | + | 0.970017i | \(0.578144\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.31265 | 1.53104 | 0.765521 | − | 0.643411i | \(-0.222481\pi\) | ||||
0.765521 | + | 0.643411i | \(0.222481\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.61213 | 0.369847 | 0.184924 | − | 0.982753i | \(-0.440796\pi\) | ||||
0.184924 | + | 0.982753i | \(0.440796\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 1.61213 | 0.343707 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 0.387873 | 0.0720262 | 0.0360131 | − | 0.999351i | \(-0.488534\pi\) | ||||
0.0360131 | + | 0.999351i | \(0.488534\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 4.31265 | 0.774575 | 0.387287 | − | 0.921959i | \(-0.373412\pi\) | ||||
0.387287 | + | 0.921959i | \(0.373412\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.61213 | 0.280635 | ||||||||
\(34\) | −6.31265 | −1.08261 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.92478 | −0.645229 | −0.322615 | − | 0.946530i | \(-0.604562\pi\) | ||||
−0.322615 | + | 0.946530i | \(0.604562\pi\) | |||||||
\(38\) | −1.61213 | −0.261522 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 7.92478 | 1.23764 | 0.618821 | − | 0.785532i | \(-0.287611\pi\) | ||||
0.618821 | + | 0.785532i | \(0.287611\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | −4.31265 | −0.657673 | −0.328837 | − | 0.944387i | \(-0.606657\pi\) | ||||
−0.328837 | + | 0.944387i | \(0.606657\pi\) | |||||||
\(44\) | −1.61213 | −0.243037 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −1.61213 | −0.235153 | −0.117576 | − | 0.993064i | \(-0.537513\pi\) | ||||
−0.117576 | + | 0.993064i | \(0.537513\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −6.31265 | −0.883948 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 2.77575 | 0.381278 | 0.190639 | − | 0.981660i | \(-0.438944\pi\) | ||||
0.190639 | + | 0.981660i | \(0.438944\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −1.61213 | −0.217379 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −1.61213 | −0.213531 | ||||||||
\(58\) | −0.387873 | −0.0509302 | ||||||||
\(59\) | −10.7005 | −1.39309 | −0.696545 | − | 0.717513i | \(-0.745280\pi\) | ||||
−0.696545 | + | 0.717513i | \(0.745280\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | −4.31265 | −0.547707 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | −1.61213 | −0.198439 | ||||||||
\(67\) | 9.08840 | 1.11032 | 0.555162 | − | 0.831742i | \(-0.312656\pi\) | ||||
0.555162 | + | 0.831742i | \(0.312656\pi\) | |||||||
\(68\) | 6.31265 | 0.765521 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −9.08840 | −1.07859 | −0.539297 | − | 0.842116i | \(-0.681310\pi\) | ||||
−0.539297 | + | 0.842116i | \(0.681310\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 5.22425 | 0.611453 | 0.305726 | − | 0.952119i | \(-0.401101\pi\) | ||||
0.305726 | + | 0.952119i | \(0.401101\pi\) | |||||||
\(74\) | 3.92478 | 0.456246 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 1.61213 | 0.184924 | ||||||||
\(77\) | −1.61213 | −0.183719 | ||||||||
\(78\) | 2.00000 | 0.226455 | ||||||||
\(79\) | 9.92478 | 1.11662 | 0.558312 | − | 0.829631i | \(-0.311449\pi\) | ||||
0.558312 | + | 0.829631i | \(0.311449\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.92478 | −0.875145 | ||||||||
\(83\) | −11.0132 | −1.20885 | −0.604426 | − | 0.796661i | \(-0.706598\pi\) | ||||
−0.604426 | + | 0.796661i | \(0.706598\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | 6.31265 | 0.684703 | ||||||||
\(86\) | 4.31265 | 0.465045 | ||||||||
\(87\) | −0.387873 | −0.0415844 | ||||||||
\(88\) | 1.61213 | 0.171853 | ||||||||
\(89\) | −4.70052 | −0.498254 | −0.249127 | − | 0.968471i | \(-0.580144\pi\) | ||||
−0.249127 | + | 0.968471i | \(0.580144\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −4.31265 | −0.447201 | ||||||||
\(94\) | 1.61213 | 0.166278 | ||||||||
\(95\) | 1.61213 | 0.165401 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 15.9248 | 1.61692 | 0.808458 | − | 0.588554i | \(-0.200302\pi\) | ||||
0.808458 | + | 0.588554i | \(0.200302\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −1.61213 | −0.162025 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −3.29948 | −0.328310 | −0.164155 | − | 0.986435i | \(-0.552490\pi\) | ||||
−0.164155 | + | 0.986435i | \(0.552490\pi\) | |||||||
\(102\) | 6.31265 | 0.625046 | ||||||||
\(103\) | 16.6253 | 1.63814 | 0.819070 | − | 0.573694i | \(-0.194490\pi\) | ||||
0.819070 | + | 0.573694i | \(0.194490\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | −2.77575 | −0.269604 | ||||||||
\(107\) | −18.5501 | −1.79330 | −0.896652 | − | 0.442736i | \(-0.854008\pi\) | ||||
−0.896652 | + | 0.442736i | \(0.854008\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −11.1490 | −1.06788 | −0.533942 | − | 0.845521i | \(-0.679290\pi\) | ||||
−0.533942 | + | 0.845521i | \(0.679290\pi\) | |||||||
\(110\) | 1.61213 | 0.153710 | ||||||||
\(111\) | 3.92478 | 0.372523 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 11.1490 | 1.04881 | 0.524406 | − | 0.851468i | \(-0.324287\pi\) | ||||
0.524406 | + | 0.851468i | \(0.324287\pi\) | |||||||
\(114\) | 1.61213 | 0.150990 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0.387873 | 0.0360131 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 10.7005 | 0.985063 | ||||||||
\(119\) | 6.31265 | 0.578680 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −8.40105 | −0.763732 | ||||||||
\(122\) | −6.00000 | −0.543214 | ||||||||
\(123\) | −7.92478 | −0.714553 | ||||||||
\(124\) | 4.31265 | 0.387287 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | 5.08840 | 0.451522 | 0.225761 | − | 0.974183i | \(-0.427513\pi\) | ||||
0.225761 | + | 0.974183i | \(0.427513\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.31265 | 0.379708 | ||||||||
\(130\) | −2.00000 | −0.175412 | ||||||||
\(131\) | 19.3258 | 1.68851 | 0.844253 | − | 0.535946i | \(-0.180045\pi\) | ||||
0.844253 | + | 0.535946i | \(0.180045\pi\) | |||||||
\(132\) | 1.61213 | 0.140318 | ||||||||
\(133\) | 1.61213 | 0.139789 | ||||||||
\(134\) | −9.08840 | −0.785118 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −6.31265 | −0.541305 | ||||||||
\(137\) | −5.47627 | −0.467869 | −0.233935 | − | 0.972252i | \(-0.575160\pi\) | ||||
−0.233935 | + | 0.972252i | \(0.575160\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | −6.70052 | −0.568331 | −0.284165 | − | 0.958775i | \(-0.591717\pi\) | ||||
−0.284165 | + | 0.958775i | \(0.591717\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 1.61213 | 0.135766 | ||||||||
\(142\) | 9.08840 | 0.762681 | ||||||||
\(143\) | −3.22425 | −0.269626 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.387873 | 0.0322111 | ||||||||
\(146\) | −5.22425 | −0.432362 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −3.92478 | −0.322615 | ||||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −19.8496 | −1.61533 | −0.807667 | − | 0.589639i | \(-0.799270\pi\) | ||||
−0.807667 | + | 0.589639i | \(0.799270\pi\) | |||||||
\(152\) | −1.61213 | −0.130761 | ||||||||
\(153\) | 6.31265 | 0.510348 | ||||||||
\(154\) | 1.61213 | 0.129909 | ||||||||
\(155\) | 4.31265 | 0.346400 | ||||||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | −6.62530 | −0.528757 | −0.264378 | − | 0.964419i | \(-0.585167\pi\) | ||||
−0.264378 | + | 0.964419i | \(0.585167\pi\) | |||||||
\(158\) | −9.92478 | −0.789573 | ||||||||
\(159\) | −2.77575 | −0.220131 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 23.3258 | 1.82702 | 0.913510 | − | 0.406817i | \(-0.133361\pi\) | ||||
0.913510 | + | 0.406817i | \(0.133361\pi\) | |||||||
\(164\) | 7.92478 | 0.618821 | ||||||||
\(165\) | 1.61213 | 0.125504 | ||||||||
\(166\) | 11.0132 | 0.854788 | ||||||||
\(167\) | 6.38787 | 0.494308 | 0.247154 | − | 0.968976i | \(-0.420505\pi\) | ||||
0.247154 | + | 0.968976i | \(0.420505\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −6.31265 | −0.484158 | ||||||||
\(171\) | 1.61213 | 0.123282 | ||||||||
\(172\) | −4.31265 | −0.328837 | ||||||||
\(173\) | −11.8641 | −0.902014 | −0.451007 | − | 0.892520i | \(-0.648935\pi\) | ||||
−0.451007 | + | 0.892520i | \(0.648935\pi\) | |||||||
\(174\) | 0.387873 | 0.0294046 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −1.61213 | −0.121519 | ||||||||
\(177\) | 10.7005 | 0.804301 | ||||||||
\(178\) | 4.70052 | 0.352319 | ||||||||
\(179\) | 1.14903 | 0.0858826 | 0.0429413 | − | 0.999078i | \(-0.486327\pi\) | ||||
0.0429413 | + | 0.999078i | \(0.486327\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −5.84955 | −0.434794 | −0.217397 | − | 0.976083i | \(-0.569757\pi\) | ||||
−0.217397 | + | 0.976083i | \(0.569757\pi\) | |||||||
\(182\) | −2.00000 | −0.148250 | ||||||||
\(183\) | −6.00000 | −0.443533 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −3.92478 | −0.288555 | ||||||||
\(186\) | 4.31265 | 0.316219 | ||||||||
\(187\) | −10.1768 | −0.744201 | ||||||||
\(188\) | −1.61213 | −0.117576 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −1.61213 | −0.116956 | ||||||||
\(191\) | 10.7005 | 0.774263 | 0.387131 | − | 0.922025i | \(-0.373466\pi\) | ||||
0.387131 | + | 0.922025i | \(0.373466\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −6.00000 | −0.431889 | −0.215945 | − | 0.976406i | \(-0.569283\pi\) | ||||
−0.215945 | + | 0.976406i | \(0.569283\pi\) | |||||||
\(194\) | −15.9248 | −1.14333 | ||||||||
\(195\) | −2.00000 | −0.143223 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 18.6253 | 1.32700 | 0.663499 | − | 0.748177i | \(-0.269071\pi\) | ||||
0.663499 | + | 0.748177i | \(0.269071\pi\) | |||||||
\(198\) | 1.61213 | 0.114569 | ||||||||
\(199\) | 3.47627 | 0.246426 | 0.123213 | − | 0.992380i | \(-0.460680\pi\) | ||||
0.123213 | + | 0.992380i | \(0.460680\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −9.08840 | −0.641046 | ||||||||
\(202\) | 3.29948 | 0.232150 | ||||||||
\(203\) | 0.387873 | 0.0272234 | ||||||||
\(204\) | −6.31265 | −0.441974 | ||||||||
\(205\) | 7.92478 | 0.553490 | ||||||||
\(206\) | −16.6253 | −1.15834 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | −2.59895 | −0.179773 | ||||||||
\(210\) | 1.00000 | 0.0690066 | ||||||||
\(211\) | −15.8496 | −1.09113 | −0.545564 | − | 0.838069i | \(-0.683685\pi\) | ||||
−0.545564 | + | 0.838069i | \(0.683685\pi\) | |||||||
\(212\) | 2.77575 | 0.190639 | ||||||||
\(213\) | 9.08840 | 0.622727 | ||||||||
\(214\) | 18.5501 | 1.26806 | ||||||||
\(215\) | −4.31265 | −0.294120 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 4.31265 | 0.292762 | ||||||||
\(218\) | 11.1490 | 0.755108 | ||||||||
\(219\) | −5.22425 | −0.353022 | ||||||||
\(220\) | −1.61213 | −0.108690 | ||||||||
\(221\) | 12.6253 | 0.849270 | ||||||||
\(222\) | −3.92478 | −0.263414 | ||||||||
\(223\) | 10.4485 | 0.699684 | 0.349842 | − | 0.936809i | \(-0.386235\pi\) | ||||
0.349842 | + | 0.936809i | \(0.386235\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −11.1490 | −0.741623 | ||||||||
\(227\) | 10.3879 | 0.689467 | 0.344734 | − | 0.938701i | \(-0.387969\pi\) | ||||
0.344734 | + | 0.938701i | \(0.387969\pi\) | |||||||
\(228\) | −1.61213 | −0.106766 | ||||||||
\(229\) | −13.8496 | −0.915204 | −0.457602 | − | 0.889157i | \(-0.651292\pi\) | ||||
−0.457602 | + | 0.889157i | \(0.651292\pi\) | |||||||
\(230\) | −1.00000 | −0.0659380 | ||||||||
\(231\) | 1.61213 | 0.106070 | ||||||||
\(232\) | −0.387873 | −0.0254651 | ||||||||
\(233\) | 14.0000 | 0.917170 | 0.458585 | − | 0.888650i | \(-0.348356\pi\) | ||||
0.458585 | + | 0.888650i | \(0.348356\pi\) | |||||||
\(234\) | −2.00000 | −0.130744 | ||||||||
\(235\) | −1.61213 | −0.105164 | ||||||||
\(236\) | −10.7005 | −0.696545 | ||||||||
\(237\) | −9.92478 | −0.644684 | ||||||||
\(238\) | −6.31265 | −0.409188 | ||||||||
\(239\) | −23.5369 | −1.52248 | −0.761238 | − | 0.648473i | \(-0.775408\pi\) | ||||
−0.761238 | + | 0.648473i | \(0.775408\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 27.7137 | 1.78520 | 0.892598 | − | 0.450853i | \(-0.148880\pi\) | ||||
0.892598 | + | 0.450853i | \(0.148880\pi\) | |||||||
\(242\) | 8.40105 | 0.540040 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 7.92478 | 0.505265 | ||||||||
\(247\) | 3.22425 | 0.205154 | ||||||||
\(248\) | −4.31265 | −0.273854 | ||||||||
\(249\) | 11.0132 | 0.697932 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −30.5501 | −1.92830 | −0.964152 | − | 0.265351i | \(-0.914512\pi\) | ||||
−0.964152 | + | 0.265351i | \(0.914512\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −1.61213 | −0.101354 | ||||||||
\(254\) | −5.08840 | −0.319274 | ||||||||
\(255\) | −6.31265 | −0.395313 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.29948 | 0.205816 | 0.102908 | − | 0.994691i | \(-0.467185\pi\) | ||||
0.102908 | + | 0.994691i | \(0.467185\pi\) | |||||||
\(258\) | −4.31265 | −0.268494 | ||||||||
\(259\) | −3.92478 | −0.243874 | ||||||||
\(260\) | 2.00000 | 0.124035 | ||||||||
\(261\) | 0.387873 | 0.0240087 | ||||||||
\(262\) | −19.3258 | −1.19395 | ||||||||
\(263\) | −16.6253 | −1.02516 | −0.512580 | − | 0.858639i | \(-0.671310\pi\) | ||||
−0.512580 | + | 0.858639i | \(0.671310\pi\) | |||||||
\(264\) | −1.61213 | −0.0992195 | ||||||||
\(265\) | 2.77575 | 0.170513 | ||||||||
\(266\) | −1.61213 | −0.0988458 | ||||||||
\(267\) | 4.70052 | 0.287667 | ||||||||
\(268\) | 9.08840 | 0.555162 | ||||||||
\(269\) | −17.3258 | −1.05637 | −0.528187 | − | 0.849128i | \(-0.677128\pi\) | ||||
−0.528187 | + | 0.849128i | \(0.677128\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 5.86414 | 0.356221 | 0.178111 | − | 0.984010i | \(-0.443001\pi\) | ||||
0.178111 | + | 0.984010i | \(0.443001\pi\) | |||||||
\(272\) | 6.31265 | 0.382761 | ||||||||
\(273\) | −2.00000 | −0.121046 | ||||||||
\(274\) | 5.47627 | 0.330834 | ||||||||
\(275\) | −1.61213 | −0.0972149 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 31.4617 | 1.89035 | 0.945175 | − | 0.326565i | \(-0.105891\pi\) | ||||
0.945175 | + | 0.326565i | \(0.105891\pi\) | |||||||
\(278\) | 6.70052 | 0.401871 | ||||||||
\(279\) | 4.31265 | 0.258192 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 0.135857 | 0.00810456 | 0.00405228 | − | 0.999992i | \(-0.498710\pi\) | ||||
0.00405228 | + | 0.999992i | \(0.498710\pi\) | |||||||
\(282\) | −1.61213 | −0.0960008 | ||||||||
\(283\) | 0.523730 | 0.0311325 | 0.0155663 | − | 0.999879i | \(-0.495045\pi\) | ||||
0.0155663 | + | 0.999879i | \(0.495045\pi\) | |||||||
\(284\) | −9.08840 | −0.539297 | ||||||||
\(285\) | −1.61213 | −0.0954942 | ||||||||
\(286\) | 3.22425 | 0.190654 | ||||||||
\(287\) | 7.92478 | 0.467785 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 22.8496 | 1.34409 | ||||||||
\(290\) | −0.387873 | −0.0227767 | ||||||||
\(291\) | −15.9248 | −0.933527 | ||||||||
\(292\) | 5.22425 | 0.305726 | ||||||||
\(293\) | −2.00000 | −0.116841 | −0.0584206 | − | 0.998292i | \(-0.518606\pi\) | ||||
−0.0584206 | + | 0.998292i | \(0.518606\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | −10.7005 | −0.623009 | ||||||||
\(296\) | 3.92478 | 0.228123 | ||||||||
\(297\) | 1.61213 | 0.0935451 | ||||||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | 2.00000 | 0.115663 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | −4.31265 | −0.248577 | ||||||||
\(302\) | 19.8496 | 1.14221 | ||||||||
\(303\) | 3.29948 | 0.189550 | ||||||||
\(304\) | 1.61213 | 0.0924618 | ||||||||
\(305\) | 6.00000 | 0.343559 | ||||||||
\(306\) | −6.31265 | −0.360870 | ||||||||
\(307\) | 32.4749 | 1.85344 | 0.926719 | − | 0.375755i | \(-0.122617\pi\) | ||||
0.926719 | + | 0.375755i | \(0.122617\pi\) | |||||||
\(308\) | −1.61213 | −0.0918595 | ||||||||
\(309\) | −16.6253 | −0.945780 | ||||||||
\(310\) | −4.31265 | −0.244942 | ||||||||
\(311\) | 0.523730 | 0.0296980 | 0.0148490 | − | 0.999890i | \(-0.495273\pi\) | ||||
0.0148490 | + | 0.999890i | \(0.495273\pi\) | |||||||
\(312\) | 2.00000 | 0.113228 | ||||||||
\(313\) | −10.3733 | −0.586333 | −0.293166 | − | 0.956061i | \(-0.594709\pi\) | ||||
−0.293166 | + | 0.956061i | \(0.594709\pi\) | |||||||
\(314\) | 6.62530 | 0.373887 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 9.92478 | 0.558312 | ||||||||
\(317\) | 16.9525 | 0.952149 | 0.476075 | − | 0.879405i | \(-0.342059\pi\) | ||||
0.476075 | + | 0.879405i | \(0.342059\pi\) | |||||||
\(318\) | 2.77575 | 0.155656 | ||||||||
\(319\) | −0.625301 | −0.0350101 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 18.5501 | 1.03536 | ||||||||
\(322\) | −1.00000 | −0.0557278 | ||||||||
\(323\) | 10.1768 | 0.566252 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | −23.3258 | −1.29190 | ||||||||
\(327\) | 11.1490 | 0.616543 | ||||||||
\(328\) | −7.92478 | −0.437573 | ||||||||
\(329\) | −1.61213 | −0.0888794 | ||||||||
\(330\) | −1.61213 | −0.0887447 | ||||||||
\(331\) | 7.22425 | 0.397081 | 0.198540 | − | 0.980093i | \(-0.436380\pi\) | ||||
0.198540 | + | 0.980093i | \(0.436380\pi\) | |||||||
\(332\) | −11.0132 | −0.604426 | ||||||||
\(333\) | −3.92478 | −0.215076 | ||||||||
\(334\) | −6.38787 | −0.349529 | ||||||||
\(335\) | 9.08840 | 0.496552 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 19.6121 | 1.06834 | 0.534170 | − | 0.845377i | \(-0.320624\pi\) | ||||
0.534170 | + | 0.845377i | \(0.320624\pi\) | |||||||
\(338\) | 9.00000 | 0.489535 | ||||||||
\(339\) | −11.1490 | −0.605532 | ||||||||
\(340\) | 6.31265 | 0.342352 | ||||||||
\(341\) | −6.95254 | −0.376501 | ||||||||
\(342\) | −1.61213 | −0.0871738 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.31265 | 0.232523 | ||||||||
\(345\) | −1.00000 | −0.0538382 | ||||||||
\(346\) | 11.8641 | 0.637820 | ||||||||
\(347\) | −2.32724 | −0.124933 | −0.0624664 | − | 0.998047i | \(-0.519897\pi\) | ||||
−0.0624664 | + | 0.998047i | \(0.519897\pi\) | |||||||
\(348\) | −0.387873 | −0.0207922 | ||||||||
\(349\) | 7.61213 | 0.407468 | 0.203734 | − | 0.979026i | \(-0.434692\pi\) | ||||
0.203734 | + | 0.979026i | \(0.434692\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 1.61213 | 0.0859267 | ||||||||
\(353\) | 11.9248 | 0.634692 | 0.317346 | − | 0.948310i | \(-0.397208\pi\) | ||||
0.317346 | + | 0.948310i | \(0.397208\pi\) | |||||||
\(354\) | −10.7005 | −0.568726 | ||||||||
\(355\) | −9.08840 | −0.482362 | ||||||||
\(356\) | −4.70052 | −0.249127 | ||||||||
\(357\) | −6.31265 | −0.334101 | ||||||||
\(358\) | −1.14903 | −0.0607282 | ||||||||
\(359\) | 10.7005 | 0.564752 | 0.282376 | − | 0.959304i | \(-0.408877\pi\) | ||||
0.282376 | + | 0.959304i | \(0.408877\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −16.4010 | −0.863213 | ||||||||
\(362\) | 5.84955 | 0.307446 | ||||||||
\(363\) | 8.40105 | 0.440941 | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | 5.22425 | 0.273450 | ||||||||
\(366\) | 6.00000 | 0.313625 | ||||||||
\(367\) | 31.0738 | 1.62204 | 0.811020 | − | 0.585019i | \(-0.198913\pi\) | ||||
0.811020 | + | 0.585019i | \(0.198913\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 7.92478 | 0.412547 | ||||||||
\(370\) | 3.92478 | 0.204039 | ||||||||
\(371\) | 2.77575 | 0.144110 | ||||||||
\(372\) | −4.31265 | −0.223601 | ||||||||
\(373\) | 31.9248 | 1.65300 | 0.826501 | − | 0.562935i | \(-0.190328\pi\) | ||||
0.826501 | + | 0.562935i | \(0.190328\pi\) | |||||||
\(374\) | 10.1768 | 0.526229 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 1.61213 | 0.0831391 | ||||||||
\(377\) | 0.775746 | 0.0399530 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | 15.0738 | 0.774290 | 0.387145 | − | 0.922019i | \(-0.373461\pi\) | ||||
0.387145 | + | 0.922019i | \(0.373461\pi\) | |||||||
\(380\) | 1.61213 | 0.0827004 | ||||||||
\(381\) | −5.08840 | −0.260686 | ||||||||
\(382\) | −10.7005 | −0.547486 | ||||||||
\(383\) | −13.9248 | −0.711523 | −0.355761 | − | 0.934577i | \(-0.615778\pi\) | ||||
−0.355761 | + | 0.934577i | \(0.615778\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −1.61213 | −0.0821616 | ||||||||
\(386\) | 6.00000 | 0.305392 | ||||||||
\(387\) | −4.31265 | −0.219224 | ||||||||
\(388\) | 15.9248 | 0.808458 | ||||||||
\(389\) | −16.0263 | −0.812568 | −0.406284 | − | 0.913747i | \(-0.633176\pi\) | ||||
−0.406284 | + | 0.913747i | \(0.633176\pi\) | |||||||
\(390\) | 2.00000 | 0.101274 | ||||||||
\(391\) | 6.31265 | 0.319244 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −19.3258 | −0.974859 | ||||||||
\(394\) | −18.6253 | −0.938329 | ||||||||
\(395\) | 9.92478 | 0.499370 | ||||||||
\(396\) | −1.61213 | −0.0810124 | ||||||||
\(397\) | 37.8496 | 1.89961 | 0.949807 | − | 0.312835i | \(-0.101279\pi\) | ||||
0.949807 | + | 0.312835i | \(0.101279\pi\) | |||||||
\(398\) | −3.47627 | −0.174250 | ||||||||
\(399\) | −1.61213 | −0.0807073 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 36.6107 | 1.82825 | 0.914126 | − | 0.405431i | \(-0.132878\pi\) | ||||
0.914126 | + | 0.405431i | \(0.132878\pi\) | |||||||
\(402\) | 9.08840 | 0.453288 | ||||||||
\(403\) | 8.62530 | 0.429657 | ||||||||
\(404\) | −3.29948 | −0.164155 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −0.387873 | −0.0192498 | ||||||||
\(407\) | 6.32724 | 0.313630 | ||||||||
\(408\) | 6.31265 | 0.312523 | ||||||||
\(409\) | 19.5515 | 0.966759 | 0.483380 | − | 0.875411i | \(-0.339409\pi\) | ||||
0.483380 | + | 0.875411i | \(0.339409\pi\) | |||||||
\(410\) | −7.92478 | −0.391377 | ||||||||
\(411\) | 5.47627 | 0.270124 | ||||||||
\(412\) | 16.6253 | 0.819070 | ||||||||
\(413\) | −10.7005 | −0.526538 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | −11.0132 | −0.540615 | ||||||||
\(416\) | −2.00000 | −0.0980581 | ||||||||
\(417\) | 6.70052 | 0.328126 | ||||||||
\(418\) | 2.59895 | 0.127119 | ||||||||
\(419\) | −27.3258 | −1.33495 | −0.667477 | − | 0.744630i | \(-0.732626\pi\) | ||||
−0.667477 | + | 0.744630i | \(0.732626\pi\) | |||||||
\(420\) | −1.00000 | −0.0487950 | ||||||||
\(421\) | 24.7005 | 1.20383 | 0.601915 | − | 0.798560i | \(-0.294405\pi\) | ||||
0.601915 | + | 0.798560i | \(0.294405\pi\) | |||||||
\(422\) | 15.8496 | 0.771544 | ||||||||
\(423\) | −1.61213 | −0.0783843 | ||||||||
\(424\) | −2.77575 | −0.134802 | ||||||||
\(425\) | 6.31265 | 0.306209 | ||||||||
\(426\) | −9.08840 | −0.440334 | ||||||||
\(427\) | 6.00000 | 0.290360 | ||||||||
\(428\) | −18.5501 | −0.896652 | ||||||||
\(429\) | 3.22425 | 0.155668 | ||||||||
\(430\) | 4.31265 | 0.207974 | ||||||||
\(431\) | −20.3733 | −0.981347 | −0.490673 | − | 0.871344i | \(-0.663249\pi\) | ||||
−0.490673 | + | 0.871344i | \(0.663249\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 9.47627 | 0.455400 | 0.227700 | − | 0.973731i | \(-0.426879\pi\) | ||||
0.227700 | + | 0.973731i | \(0.426879\pi\) | |||||||
\(434\) | −4.31265 | −0.207014 | ||||||||
\(435\) | −0.387873 | −0.0185971 | ||||||||
\(436\) | −11.1490 | −0.533942 | ||||||||
\(437\) | 1.61213 | 0.0771185 | ||||||||
\(438\) | 5.22425 | 0.249624 | ||||||||
\(439\) | −20.9380 | −0.999314 | −0.499657 | − | 0.866223i | \(-0.666541\pi\) | ||||
−0.499657 | + | 0.866223i | \(0.666541\pi\) | |||||||
\(440\) | 1.61213 | 0.0768551 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −12.6253 | −0.600524 | ||||||||
\(443\) | 36.6253 | 1.74012 | 0.870060 | − | 0.492945i | \(-0.164080\pi\) | ||||
0.870060 | + | 0.492945i | \(0.164080\pi\) | |||||||
\(444\) | 3.92478 | 0.186262 | ||||||||
\(445\) | −4.70052 | −0.222826 | ||||||||
\(446\) | −10.4485 | −0.494751 | ||||||||
\(447\) | −6.00000 | −0.283790 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −2.77575 | −0.130996 | −0.0654978 | − | 0.997853i | \(-0.520864\pi\) | ||||
−0.0654978 | + | 0.997853i | \(0.520864\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −12.7757 | −0.601586 | ||||||||
\(452\) | 11.1490 | 0.524406 | ||||||||
\(453\) | 19.8496 | 0.932613 | ||||||||
\(454\) | −10.3879 | −0.487527 | ||||||||
\(455\) | 2.00000 | 0.0937614 | ||||||||
\(456\) | 1.61213 | 0.0754948 | ||||||||
\(457\) | 19.6121 | 0.917417 | 0.458708 | − | 0.888587i | \(-0.348312\pi\) | ||||
0.458708 | + | 0.888587i | \(0.348312\pi\) | |||||||
\(458\) | 13.8496 | 0.647147 | ||||||||
\(459\) | −6.31265 | −0.294649 | ||||||||
\(460\) | 1.00000 | 0.0466252 | ||||||||
\(461\) | −0.700523 | −0.0326266 | −0.0163133 | − | 0.999867i | \(-0.505193\pi\) | ||||
−0.0163133 | + | 0.999867i | \(0.505193\pi\) | |||||||
\(462\) | −1.61213 | −0.0750029 | ||||||||
\(463\) | −12.1622 | −0.565226 | −0.282613 | − | 0.959234i | \(-0.591201\pi\) | ||||
−0.282613 | + | 0.959234i | \(0.591201\pi\) | |||||||
\(464\) | 0.387873 | 0.0180066 | ||||||||
\(465\) | −4.31265 | −0.199994 | ||||||||
\(466\) | −14.0000 | −0.648537 | ||||||||
\(467\) | 4.56467 | 0.211228 | 0.105614 | − | 0.994407i | \(-0.466319\pi\) | ||||
0.105614 | + | 0.994407i | \(0.466319\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | 9.08840 | 0.419663 | ||||||||
\(470\) | 1.61213 | 0.0743619 | ||||||||
\(471\) | 6.62530 | 0.305278 | ||||||||
\(472\) | 10.7005 | 0.492532 | ||||||||
\(473\) | 6.95254 | 0.319678 | ||||||||
\(474\) | 9.92478 | 0.455860 | ||||||||
\(475\) | 1.61213 | 0.0739695 | ||||||||
\(476\) | 6.31265 | 0.289340 | ||||||||
\(477\) | 2.77575 | 0.127093 | ||||||||
\(478\) | 23.5369 | 1.07655 | ||||||||
\(479\) | 30.0263 | 1.37194 | 0.685969 | − | 0.727630i | \(-0.259378\pi\) | ||||
0.685969 | + | 0.727630i | \(0.259378\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −7.84955 | −0.357909 | ||||||||
\(482\) | −27.7137 | −1.26232 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | −8.40105 | −0.381866 | ||||||||
\(485\) | 15.9248 | 0.723107 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 1.23884 | 0.0561373 | 0.0280686 | − | 0.999606i | \(-0.491064\pi\) | ||||
0.0280686 | + | 0.999606i | \(0.491064\pi\) | |||||||
\(488\) | −6.00000 | −0.271607 | ||||||||
\(489\) | −23.3258 | −1.05483 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 4.25202 | 0.191891 | 0.0959454 | − | 0.995387i | \(-0.469413\pi\) | ||||
0.0959454 | + | 0.995387i | \(0.469413\pi\) | |||||||
\(492\) | −7.92478 | −0.357277 | ||||||||
\(493\) | 2.44851 | 0.110275 | ||||||||
\(494\) | −3.22425 | −0.145066 | ||||||||
\(495\) | −1.61213 | −0.0724597 | ||||||||
\(496\) | 4.31265 | 0.193644 | ||||||||
\(497\) | −9.08840 | −0.407670 | ||||||||
\(498\) | −11.0132 | −0.493512 | ||||||||
\(499\) | 22.2981 | 0.998198 | 0.499099 | − | 0.866545i | \(-0.333664\pi\) | ||||
0.499099 | + | 0.866545i | \(0.333664\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −6.38787 | −0.285389 | ||||||||
\(502\) | 30.5501 | 1.36352 | ||||||||
\(503\) | −21.2995 | −0.949697 | −0.474848 | − | 0.880068i | \(-0.657497\pi\) | ||||
−0.474848 | + | 0.880068i | \(0.657497\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | −3.29948 | −0.146825 | ||||||||
\(506\) | 1.61213 | 0.0716678 | ||||||||
\(507\) | 9.00000 | 0.399704 | ||||||||
\(508\) | 5.08840 | 0.225761 | ||||||||
\(509\) | 39.5026 | 1.75092 | 0.875461 | − | 0.483288i | \(-0.160558\pi\) | ||||
0.875461 | + | 0.483288i | \(0.160558\pi\) | |||||||
\(510\) | 6.31265 | 0.279529 | ||||||||
\(511\) | 5.22425 | 0.231107 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.61213 | −0.0711771 | ||||||||
\(514\) | −3.29948 | −0.145534 | ||||||||
\(515\) | 16.6253 | 0.732598 | ||||||||
\(516\) | 4.31265 | 0.189854 | ||||||||
\(517\) | 2.59895 | 0.114302 | ||||||||
\(518\) | 3.92478 | 0.172445 | ||||||||
\(519\) | 11.8641 | 0.520778 | ||||||||
\(520\) | −2.00000 | −0.0877058 | ||||||||
\(521\) | 0.700523 | 0.0306905 | 0.0153452 | − | 0.999882i | \(-0.495115\pi\) | ||||
0.0153452 | + | 0.999882i | \(0.495115\pi\) | |||||||
\(522\) | −0.387873 | −0.0169767 | ||||||||
\(523\) | −12.3733 | −0.541046 | −0.270523 | − | 0.962714i | \(-0.587197\pi\) | ||||
−0.270523 | + | 0.962714i | \(0.587197\pi\) | |||||||
\(524\) | 19.3258 | 0.844253 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 16.6253 | 0.724898 | ||||||||
\(527\) | 27.2243 | 1.18591 | ||||||||
\(528\) | 1.61213 | 0.0701588 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −2.77575 | −0.120571 | ||||||||
\(531\) | −10.7005 | −0.464363 | ||||||||
\(532\) | 1.61213 | 0.0698946 | ||||||||
\(533\) | 15.8496 | 0.686520 | ||||||||
\(534\) | −4.70052 | −0.203412 | ||||||||
\(535\) | −18.5501 | −0.801990 | ||||||||
\(536\) | −9.08840 | −0.392559 | ||||||||
\(537\) | −1.14903 | −0.0495843 | ||||||||
\(538\) | 17.3258 | 0.746969 | ||||||||
\(539\) | −1.61213 | −0.0694392 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −42.3244 | −1.81967 | −0.909834 | − | 0.414972i | \(-0.863791\pi\) | ||||
−0.909834 | + | 0.414972i | \(0.863791\pi\) | |||||||
\(542\) | −5.86414 | −0.251887 | ||||||||
\(543\) | 5.84955 | 0.251028 | ||||||||
\(544\) | −6.31265 | −0.270653 | ||||||||
\(545\) | −11.1490 | −0.477572 | ||||||||
\(546\) | 2.00000 | 0.0855921 | ||||||||
\(547\) | −7.32582 | −0.313230 | −0.156615 | − | 0.987660i | \(-0.550058\pi\) | ||||
−0.156615 | + | 0.987660i | \(0.550058\pi\) | |||||||
\(548\) | −5.47627 | −0.233935 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 1.61213 | 0.0687413 | ||||||||
\(551\) | 0.625301 | 0.0266387 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 9.92478 | 0.422044 | ||||||||
\(554\) | −31.4617 | −1.33668 | ||||||||
\(555\) | 3.92478 | 0.166598 | ||||||||
\(556\) | −6.70052 | −0.284165 | ||||||||
\(557\) | 16.1768 | 0.685433 | 0.342716 | − | 0.939439i | \(-0.388653\pi\) | ||||
0.342716 | + | 0.939439i | \(0.388653\pi\) | |||||||
\(558\) | −4.31265 | −0.182569 | ||||||||
\(559\) | −8.62530 | −0.364811 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 10.1768 | 0.429665 | ||||||||
\(562\) | −0.135857 | −0.00573079 | ||||||||
\(563\) | −4.56467 | −0.192378 | −0.0961889 | − | 0.995363i | \(-0.530665\pi\) | ||||
−0.0961889 | + | 0.995363i | \(0.530665\pi\) | |||||||
\(564\) | 1.61213 | 0.0678828 | ||||||||
\(565\) | 11.1490 | 0.469043 | ||||||||
\(566\) | −0.523730 | −0.0220140 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 9.08840 | 0.381341 | ||||||||
\(569\) | 31.7137 | 1.32951 | 0.664754 | − | 0.747063i | \(-0.268536\pi\) | ||||
0.664754 | + | 0.747063i | \(0.268536\pi\) | |||||||
\(570\) | 1.61213 | 0.0675246 | ||||||||
\(571\) | 45.1002 | 1.88738 | 0.943691 | − | 0.330827i | \(-0.107328\pi\) | ||||
0.943691 | + | 0.330827i | \(0.107328\pi\) | |||||||
\(572\) | −3.22425 | −0.134813 | ||||||||
\(573\) | −10.7005 | −0.447021 | ||||||||
\(574\) | −7.92478 | −0.330774 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −43.7255 | −1.82031 | −0.910157 | − | 0.414263i | \(-0.864039\pi\) | ||||
−0.910157 | + | 0.414263i | \(0.864039\pi\) | |||||||
\(578\) | −22.8496 | −0.950416 | ||||||||
\(579\) | 6.00000 | 0.249351 | ||||||||
\(580\) | 0.387873 | 0.0161056 | ||||||||
\(581\) | −11.0132 | −0.456903 | ||||||||
\(582\) | 15.9248 | 0.660103 | ||||||||
\(583\) | −4.47486 | −0.185330 | ||||||||
\(584\) | −5.22425 | −0.216181 | ||||||||
\(585\) | 2.00000 | 0.0826898 | ||||||||
\(586\) | 2.00000 | 0.0826192 | ||||||||
\(587\) | −46.8021 | −1.93173 | −0.965865 | − | 0.259048i | \(-0.916591\pi\) | ||||
−0.965865 | + | 0.259048i | \(0.916591\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | 6.95254 | 0.286474 | ||||||||
\(590\) | 10.7005 | 0.440534 | ||||||||
\(591\) | −18.6253 | −0.766142 | ||||||||
\(592\) | −3.92478 | −0.161307 | ||||||||
\(593\) | −30.9986 | −1.27296 | −0.636480 | − | 0.771293i | \(-0.719610\pi\) | ||||
−0.636480 | + | 0.771293i | \(0.719610\pi\) | |||||||
\(594\) | −1.61213 | −0.0661464 | ||||||||
\(595\) | 6.31265 | 0.258793 | ||||||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | −3.47627 | −0.142274 | ||||||||
\(598\) | −2.00000 | −0.0817861 | ||||||||
\(599\) | 17.2097 | 0.703168 | 0.351584 | − | 0.936156i | \(-0.385643\pi\) | ||||
0.351584 | + | 0.936156i | \(0.385643\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −5.07381 | −0.206965 | −0.103482 | − | 0.994631i | \(-0.532999\pi\) | ||||
−0.103482 | + | 0.994631i | \(0.532999\pi\) | |||||||
\(602\) | 4.31265 | 0.175771 | ||||||||
\(603\) | 9.08840 | 0.370108 | ||||||||
\(604\) | −19.8496 | −0.807667 | ||||||||
\(605\) | −8.40105 | −0.341551 | ||||||||
\(606\) | −3.29948 | −0.134032 | ||||||||
\(607\) | −8.47486 | −0.343984 | −0.171992 | − | 0.985098i | \(-0.555020\pi\) | ||||
−0.171992 | + | 0.985098i | \(0.555020\pi\) | |||||||
\(608\) | −1.61213 | −0.0653804 | ||||||||
\(609\) | −0.387873 | −0.0157174 | ||||||||
\(610\) | −6.00000 | −0.242933 | ||||||||
\(611\) | −3.22425 | −0.130439 | ||||||||
\(612\) | 6.31265 | 0.255174 | ||||||||
\(613\) | −44.5501 | −1.79936 | −0.899680 | − | 0.436549i | \(-0.856200\pi\) | ||||
−0.899680 | + | 0.436549i | \(0.856200\pi\) | |||||||
\(614\) | −32.4749 | −1.31058 | ||||||||
\(615\) | −7.92478 | −0.319558 | ||||||||
\(616\) | 1.61213 | 0.0649544 | ||||||||
\(617\) | −6.10157 | −0.245640 | −0.122820 | − | 0.992429i | \(-0.539194\pi\) | ||||
−0.122820 | + | 0.992429i | \(0.539194\pi\) | |||||||
\(618\) | 16.6253 | 0.668768 | ||||||||
\(619\) | 23.6385 | 0.950111 | 0.475055 | − | 0.879956i | \(-0.342428\pi\) | ||||
0.475055 | + | 0.879956i | \(0.342428\pi\) | |||||||
\(620\) | 4.31265 | 0.173200 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −0.523730 | −0.0209997 | ||||||||
\(623\) | −4.70052 | −0.188322 | ||||||||
\(624\) | −2.00000 | −0.0800641 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 10.3733 | 0.414600 | ||||||||
\(627\) | 2.59895 | 0.103792 | ||||||||
\(628\) | −6.62530 | −0.264378 | ||||||||
\(629\) | −24.7757 | −0.987874 | ||||||||
\(630\) | −1.00000 | −0.0398410 | ||||||||
\(631\) | 35.1754 | 1.40031 | 0.700155 | − | 0.713991i | \(-0.253114\pi\) | ||||
0.700155 | + | 0.713991i | \(0.253114\pi\) | |||||||
\(632\) | −9.92478 | −0.394786 | ||||||||
\(633\) | 15.8496 | 0.629963 | ||||||||
\(634\) | −16.9525 | −0.673271 | ||||||||
\(635\) | 5.08840 | 0.201927 | ||||||||
\(636\) | −2.77575 | −0.110065 | ||||||||
\(637\) | 2.00000 | 0.0792429 | ||||||||
\(638\) | 0.625301 | 0.0247559 | ||||||||
\(639\) | −9.08840 | −0.359531 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −7.86414 | −0.310615 | −0.155307 | − | 0.987866i | \(-0.549637\pi\) | ||||
−0.155307 | + | 0.987866i | \(0.549637\pi\) | |||||||
\(642\) | −18.5501 | −0.732113 | ||||||||
\(643\) | −13.2995 | −0.524480 | −0.262240 | − | 0.965003i | \(-0.584461\pi\) | ||||
−0.262240 | + | 0.965003i | \(0.584461\pi\) | |||||||
\(644\) | 1.00000 | 0.0394055 | ||||||||
\(645\) | 4.31265 | 0.169810 | ||||||||
\(646\) | −10.1768 | −0.400401 | ||||||||
\(647\) | 16.0606 | 0.631409 | 0.315704 | − | 0.948858i | \(-0.397759\pi\) | ||||
0.315704 | + | 0.948858i | \(0.397759\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 17.2506 | 0.677145 | ||||||||
\(650\) | −2.00000 | −0.0784465 | ||||||||
\(651\) | −4.31265 | −0.169026 | ||||||||
\(652\) | 23.3258 | 0.913510 | ||||||||
\(653\) | 6.77575 | 0.265155 | 0.132578 | − | 0.991173i | \(-0.457675\pi\) | ||||
0.132578 | + | 0.991173i | \(0.457675\pi\) | |||||||
\(654\) | −11.1490 | −0.435962 | ||||||||
\(655\) | 19.3258 | 0.755122 | ||||||||
\(656\) | 7.92478 | 0.309411 | ||||||||
\(657\) | 5.22425 | 0.203818 | ||||||||
\(658\) | 1.61213 | 0.0628472 | ||||||||
\(659\) | −22.3879 | −0.872108 | −0.436054 | − | 0.899921i | \(-0.643624\pi\) | ||||
−0.436054 | + | 0.899921i | \(0.643624\pi\) | |||||||
\(660\) | 1.61213 | 0.0627520 | ||||||||
\(661\) | −19.2506 | −0.748762 | −0.374381 | − | 0.927275i | \(-0.622145\pi\) | ||||
−0.374381 | + | 0.927275i | \(0.622145\pi\) | |||||||
\(662\) | −7.22425 | −0.280779 | ||||||||
\(663\) | −12.6253 | −0.490326 | ||||||||
\(664\) | 11.0132 | 0.427394 | ||||||||
\(665\) | 1.61213 | 0.0625156 | ||||||||
\(666\) | 3.92478 | 0.152082 | ||||||||
\(667\) | 0.387873 | 0.0150185 | ||||||||
\(668\) | 6.38787 | 0.247154 | ||||||||
\(669\) | −10.4485 | −0.403963 | ||||||||
\(670\) | −9.08840 | −0.351115 | ||||||||
\(671\) | −9.67276 | −0.373413 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | 3.67276 | 0.141575 | 0.0707873 | − | 0.997491i | \(-0.477449\pi\) | ||||
0.0707873 | + | 0.997491i | \(0.477449\pi\) | |||||||
\(674\) | −19.6121 | −0.755431 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −40.1476 | −1.54300 | −0.771499 | − | 0.636230i | \(-0.780493\pi\) | ||||
−0.771499 | + | 0.636230i | \(0.780493\pi\) | |||||||
\(678\) | 11.1490 | 0.428176 | ||||||||
\(679\) | 15.9248 | 0.611137 | ||||||||
\(680\) | −6.31265 | −0.242079 | ||||||||
\(681\) | −10.3879 | −0.398064 | ||||||||
\(682\) | 6.95254 | 0.266226 | ||||||||
\(683\) | 0.775746 | 0.0296831 | 0.0148416 | − | 0.999890i | \(-0.495276\pi\) | ||||
0.0148416 | + | 0.999890i | \(0.495276\pi\) | |||||||
\(684\) | 1.61213 | 0.0616412 | ||||||||
\(685\) | −5.47627 | −0.209238 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 13.8496 | 0.528393 | ||||||||
\(688\) | −4.31265 | −0.164418 | ||||||||
\(689\) | 5.55149 | 0.211495 | ||||||||
\(690\) | 1.00000 | 0.0380693 | ||||||||
\(691\) | 3.47627 | 0.132244 | 0.0661218 | − | 0.997812i | \(-0.478937\pi\) | ||||
0.0661218 | + | 0.997812i | \(0.478937\pi\) | |||||||
\(692\) | −11.8641 | −0.451007 | ||||||||
\(693\) | −1.61213 | −0.0612396 | ||||||||
\(694\) | 2.32724 | 0.0883408 | ||||||||
\(695\) | −6.70052 | −0.254165 | ||||||||
\(696\) | 0.387873 | 0.0147023 | ||||||||
\(697\) | 50.0263 | 1.89488 | ||||||||
\(698\) | −7.61213 | −0.288123 | ||||||||
\(699\) | −14.0000 | −0.529529 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −2.62530 | −0.0991562 | −0.0495781 | − | 0.998770i | \(-0.515788\pi\) | ||||
−0.0495781 | + | 0.998770i | \(0.515788\pi\) | |||||||
\(702\) | 2.00000 | 0.0754851 | ||||||||
\(703\) | −6.32724 | −0.238636 | ||||||||
\(704\) | −1.61213 | −0.0607593 | ||||||||
\(705\) | 1.61213 | 0.0607162 | ||||||||
\(706\) | −11.9248 | −0.448795 | ||||||||
\(707\) | −3.29948 | −0.124090 | ||||||||
\(708\) | 10.7005 | 0.402150 | ||||||||
\(709\) | 12.8510 | 0.482628 | 0.241314 | − | 0.970447i | \(-0.422422\pi\) | ||||
0.241314 | + | 0.970447i | \(0.422422\pi\) | |||||||
\(710\) | 9.08840 | 0.341081 | ||||||||
\(711\) | 9.92478 | 0.372208 | ||||||||
\(712\) | 4.70052 | 0.176160 | ||||||||
\(713\) | 4.31265 | 0.161510 | ||||||||
\(714\) | 6.31265 | 0.236245 | ||||||||
\(715\) | −3.22425 | −0.120580 | ||||||||
\(716\) | 1.14903 | 0.0429413 | ||||||||
\(717\) | 23.5369 | 0.879002 | ||||||||
\(718\) | −10.7005 | −0.399340 | ||||||||
\(719\) | 40.2228 | 1.50006 | 0.750029 | − | 0.661405i | \(-0.230039\pi\) | ||||
0.750029 | + | 0.661405i | \(0.230039\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 16.6253 | 0.619159 | ||||||||
\(722\) | 16.4010 | 0.610384 | ||||||||
\(723\) | −27.7137 | −1.03068 | ||||||||
\(724\) | −5.84955 | −0.217397 | ||||||||
\(725\) | 0.387873 | 0.0144052 | ||||||||
\(726\) | −8.40105 | −0.311792 | ||||||||
\(727\) | −10.5990 | −0.393093 | −0.196547 | − | 0.980494i | \(-0.562973\pi\) | ||||
−0.196547 | + | 0.980494i | \(0.562973\pi\) | |||||||
\(728\) | −2.00000 | −0.0741249 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.22425 | −0.193358 | ||||||||
\(731\) | −27.2243 | −1.00693 | ||||||||
\(732\) | −6.00000 | −0.221766 | ||||||||
\(733\) | −13.3747 | −0.494006 | −0.247003 | − | 0.969015i | \(-0.579446\pi\) | ||||
−0.247003 | + | 0.969015i | \(0.579446\pi\) | |||||||
\(734\) | −31.0738 | −1.14696 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −14.6516 | −0.539700 | ||||||||
\(738\) | −7.92478 | −0.291715 | ||||||||
\(739\) | −23.7283 | −0.872859 | −0.436430 | − | 0.899738i | \(-0.643757\pi\) | ||||
−0.436430 | + | 0.899738i | \(0.643757\pi\) | |||||||
\(740\) | −3.92478 | −0.144278 | ||||||||
\(741\) | −3.22425 | −0.118446 | ||||||||
\(742\) | −2.77575 | −0.101901 | ||||||||
\(743\) | −16.5040 | −0.605474 | −0.302737 | − | 0.953074i | \(-0.597900\pi\) | ||||
−0.302737 | + | 0.953074i | \(0.597900\pi\) | |||||||
\(744\) | 4.31265 | 0.158109 | ||||||||
\(745\) | 6.00000 | 0.219823 | ||||||||
\(746\) | −31.9248 | −1.16885 | ||||||||
\(747\) | −11.0132 | −0.402951 | ||||||||
\(748\) | −10.1768 | −0.372100 | ||||||||
\(749\) | −18.5501 | −0.677805 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 41.6239 | 1.51888 | 0.759439 | − | 0.650579i | \(-0.225474\pi\) | ||||
0.759439 | + | 0.650579i | \(0.225474\pi\) | |||||||
\(752\) | −1.61213 | −0.0587882 | ||||||||
\(753\) | 30.5501 | 1.11331 | ||||||||
\(754\) | −0.775746 | −0.0282510 | ||||||||
\(755\) | −19.8496 | −0.722399 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 7.29948 | 0.265304 | 0.132652 | − | 0.991163i | \(-0.457651\pi\) | ||||
0.132652 | + | 0.991163i | \(0.457651\pi\) | |||||||
\(758\) | −15.0738 | −0.547505 | ||||||||
\(759\) | 1.61213 | 0.0585165 | ||||||||
\(760\) | −1.61213 | −0.0584780 | ||||||||
\(761\) | −5.47627 | −0.198515 | −0.0992573 | − | 0.995062i | \(-0.531647\pi\) | ||||
−0.0992573 | + | 0.995062i | \(0.531647\pi\) | |||||||
\(762\) | 5.08840 | 0.184333 | ||||||||
\(763\) | −11.1490 | −0.403622 | ||||||||
\(764\) | 10.7005 | 0.387131 | ||||||||
\(765\) | 6.31265 | 0.228234 | ||||||||
\(766\) | 13.9248 | 0.503123 | ||||||||
\(767\) | −21.4010 | −0.772747 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −10.3127 | −0.371884 | −0.185942 | − | 0.982561i | \(-0.559534\pi\) | ||||
−0.185942 | + | 0.982561i | \(0.559534\pi\) | |||||||
\(770\) | 1.61213 | 0.0580970 | ||||||||
\(771\) | −3.29948 | −0.118828 | ||||||||
\(772\) | −6.00000 | −0.215945 | ||||||||
\(773\) | −1.37470 | −0.0494445 | −0.0247222 | − | 0.999694i | \(-0.507870\pi\) | ||||
−0.0247222 | + | 0.999694i | \(0.507870\pi\) | |||||||
\(774\) | 4.31265 | 0.155015 | ||||||||
\(775\) | 4.31265 | 0.154915 | ||||||||
\(776\) | −15.9248 | −0.571666 | ||||||||
\(777\) | 3.92478 | 0.140801 | ||||||||
\(778\) | 16.0263 | 0.574572 | ||||||||
\(779\) | 12.7757 | 0.457739 | ||||||||
\(780\) | −2.00000 | −0.0716115 | ||||||||
\(781\) | 14.6516 | 0.524277 | ||||||||
\(782\) | −6.31265 | −0.225740 | ||||||||
\(783\) | −0.387873 | −0.0138615 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −6.62530 | −0.236467 | ||||||||
\(786\) | 19.3258 | 0.689329 | ||||||||
\(787\) | 40.1016 | 1.42947 | 0.714733 | − | 0.699397i | \(-0.246548\pi\) | ||||
0.714733 | + | 0.699397i | \(0.246548\pi\) | |||||||
\(788\) | 18.6253 | 0.663499 | ||||||||
\(789\) | 16.6253 | 0.591876 | ||||||||
\(790\) | −9.92478 | −0.353108 | ||||||||
\(791\) | 11.1490 | 0.396414 | ||||||||
\(792\) | 1.61213 | 0.0572844 | ||||||||
\(793\) | 12.0000 | 0.426132 | ||||||||
\(794\) | −37.8496 | −1.34323 | ||||||||
\(795\) | −2.77575 | −0.0984456 | ||||||||
\(796\) | 3.47627 | 0.123213 | ||||||||
\(797\) | 15.8759 | 0.562353 | 0.281177 | − | 0.959656i | \(-0.409275\pi\) | ||||
0.281177 | + | 0.959656i | \(0.409275\pi\) | |||||||
\(798\) | 1.61213 | 0.0570687 | ||||||||
\(799\) | −10.1768 | −0.360029 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −4.70052 | −0.166085 | ||||||||
\(802\) | −36.6107 | −1.29277 | ||||||||
\(803\) | −8.42216 | −0.297212 | ||||||||
\(804\) | −9.08840 | −0.320523 | ||||||||
\(805\) | 1.00000 | 0.0352454 | ||||||||
\(806\) | −8.62530 | −0.303813 | ||||||||
\(807\) | 17.3258 | 0.609898 | ||||||||
\(808\) | 3.29948 | 0.116075 | ||||||||
\(809\) | −16.2981 | −0.573009 | −0.286505 | − | 0.958079i | \(-0.592493\pi\) | ||||
−0.286505 | + | 0.958079i | \(0.592493\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 45.3522 | 1.59253 | 0.796265 | − | 0.604948i | \(-0.206806\pi\) | ||||
0.796265 | + | 0.604948i | \(0.206806\pi\) | |||||||
\(812\) | 0.387873 | 0.0136117 | ||||||||
\(813\) | −5.86414 | −0.205664 | ||||||||
\(814\) | −6.32724 | −0.221770 | ||||||||
\(815\) | 23.3258 | 0.817068 | ||||||||
\(816\) | −6.31265 | −0.220987 | ||||||||
\(817\) | −6.95254 | −0.243239 | ||||||||
\(818\) | −19.5515 | −0.683602 | ||||||||
\(819\) | 2.00000 | 0.0698857 | ||||||||
\(820\) | 7.92478 | 0.276745 | ||||||||
\(821\) | −5.01317 | −0.174961 | −0.0874805 | − | 0.996166i | \(-0.527882\pi\) | ||||
−0.0874805 | + | 0.996166i | \(0.527882\pi\) | |||||||
\(822\) | −5.47627 | −0.191007 | ||||||||
\(823\) | −41.8641 | −1.45929 | −0.729646 | − | 0.683825i | \(-0.760315\pi\) | ||||
−0.729646 | + | 0.683825i | \(0.760315\pi\) | |||||||
\(824\) | −16.6253 | −0.579170 | ||||||||
\(825\) | 1.61213 | 0.0561271 | ||||||||
\(826\) | 10.7005 | 0.372319 | ||||||||
\(827\) | −6.70052 | −0.233000 | −0.116500 | − | 0.993191i | \(-0.537168\pi\) | ||||
−0.116500 | + | 0.993191i | \(0.537168\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −9.31406 | −0.323491 | −0.161745 | − | 0.986833i | \(-0.551712\pi\) | ||||
−0.161745 | + | 0.986833i | \(0.551712\pi\) | |||||||
\(830\) | 11.0132 | 0.382273 | ||||||||
\(831\) | −31.4617 | −1.09139 | ||||||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | 6.31265 | 0.218720 | ||||||||
\(834\) | −6.70052 | −0.232020 | ||||||||
\(835\) | 6.38787 | 0.221061 | ||||||||
\(836\) | −2.59895 | −0.0898867 | ||||||||
\(837\) | −4.31265 | −0.149067 | ||||||||
\(838\) | 27.3258 | 0.943955 | ||||||||
\(839\) | −1.67276 | −0.0577501 | −0.0288751 | − | 0.999583i | \(-0.509192\pi\) | ||||
−0.0288751 | + | 0.999583i | \(0.509192\pi\) | |||||||
\(840\) | 1.00000 | 0.0345033 | ||||||||
\(841\) | −28.8496 | −0.994812 | ||||||||
\(842\) | −24.7005 | −0.851236 | ||||||||
\(843\) | −0.135857 | −0.00467917 | ||||||||
\(844\) | −15.8496 | −0.545564 | ||||||||
\(845\) | −9.00000 | −0.309609 | ||||||||
\(846\) | 1.61213 | 0.0554261 | ||||||||
\(847\) | −8.40105 | −0.288663 | ||||||||
\(848\) | 2.77575 | 0.0953195 | ||||||||
\(849\) | −0.523730 | −0.0179744 | ||||||||
\(850\) | −6.31265 | −0.216522 | ||||||||
\(851\) | −3.92478 | −0.134540 | ||||||||
\(852\) | 9.08840 | 0.311363 | ||||||||
\(853\) | −44.9525 | −1.53915 | −0.769573 | − | 0.638559i | \(-0.779531\pi\) | ||||
−0.769573 | + | 0.638559i | \(0.779531\pi\) | |||||||
\(854\) | −6.00000 | −0.205316 | ||||||||
\(855\) | 1.61213 | 0.0551336 | ||||||||
\(856\) | 18.5501 | 0.634029 | ||||||||
\(857\) | −17.1754 | −0.586700 | −0.293350 | − | 0.956005i | \(-0.594770\pi\) | ||||
−0.293350 | + | 0.956005i | \(0.594770\pi\) | |||||||
\(858\) | −3.22425 | −0.110074 | ||||||||
\(859\) | −25.9248 | −0.884542 | −0.442271 | − | 0.896881i | \(-0.645827\pi\) | ||||
−0.442271 | + | 0.896881i | \(0.645827\pi\) | |||||||
\(860\) | −4.31265 | −0.147060 | ||||||||
\(861\) | −7.92478 | −0.270076 | ||||||||
\(862\) | 20.3733 | 0.693917 | ||||||||
\(863\) | 35.8496 | 1.22033 | 0.610167 | − | 0.792273i | \(-0.291103\pi\) | ||||
0.610167 | + | 0.792273i | \(0.291103\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −11.8641 | −0.403393 | ||||||||
\(866\) | −9.47627 | −0.322017 | ||||||||
\(867\) | −22.8496 | −0.776012 | ||||||||
\(868\) | 4.31265 | 0.146381 | ||||||||
\(869\) | −16.0000 | −0.542763 | ||||||||
\(870\) | 0.387873 | 0.0131501 | ||||||||
\(871\) | 18.1768 | 0.615897 | ||||||||
\(872\) | 11.1490 | 0.377554 | ||||||||
\(873\) | 15.9248 | 0.538972 | ||||||||
\(874\) | −1.61213 | −0.0545310 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −5.22425 | −0.176511 | ||||||||
\(877\) | 48.5910 | 1.64080 | 0.820401 | − | 0.571789i | \(-0.193750\pi\) | ||||
0.820401 | + | 0.571789i | \(0.193750\pi\) | |||||||
\(878\) | 20.9380 | 0.706622 | ||||||||
\(879\) | 2.00000 | 0.0674583 | ||||||||
\(880\) | −1.61213 | −0.0543448 | ||||||||
\(881\) | 34.5764 | 1.16491 | 0.582455 | − | 0.812863i | \(-0.302092\pi\) | ||||
0.582455 | + | 0.812863i | \(0.302092\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | −23.6267 | −0.795102 | −0.397551 | − | 0.917580i | \(-0.630140\pi\) | ||||
−0.397551 | + | 0.917580i | \(0.630140\pi\) | |||||||
\(884\) | 12.6253 | 0.424635 | ||||||||
\(885\) | 10.7005 | 0.359694 | ||||||||
\(886\) | −36.6253 | −1.23045 | ||||||||
\(887\) | 7.01317 | 0.235479 | 0.117740 | − | 0.993044i | \(-0.462435\pi\) | ||||
0.117740 | + | 0.993044i | \(0.462435\pi\) | |||||||
\(888\) | −3.92478 | −0.131707 | ||||||||
\(889\) | 5.08840 | 0.170659 | ||||||||
\(890\) | 4.70052 | 0.157562 | ||||||||
\(891\) | −1.61213 | −0.0540083 | ||||||||
\(892\) | 10.4485 | 0.349842 | ||||||||
\(893\) | −2.59895 | −0.0869706 | ||||||||
\(894\) | 6.00000 | 0.200670 | ||||||||
\(895\) | 1.14903 | 0.0384079 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −2.00000 | −0.0667781 | ||||||||
\(898\) | 2.77575 | 0.0926279 | ||||||||
\(899\) | 1.67276 | 0.0557897 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 17.5223 | 0.583753 | ||||||||
\(902\) | 12.7757 | 0.425386 | ||||||||
\(903\) | 4.31265 | 0.143516 | ||||||||
\(904\) | −11.1490 | −0.370811 | ||||||||
\(905\) | −5.84955 | −0.194446 | ||||||||
\(906\) | −19.8496 | −0.659457 | ||||||||
\(907\) | −9.08840 | −0.301775 | −0.150888 | − | 0.988551i | \(-0.548213\pi\) | ||||
−0.150888 | + | 0.988551i | \(0.548213\pi\) | |||||||
\(908\) | 10.3879 | 0.344734 | ||||||||
\(909\) | −3.29948 | −0.109437 | ||||||||
\(910\) | −2.00000 | −0.0662994 | ||||||||
\(911\) | −28.8773 | −0.956748 | −0.478374 | − | 0.878156i | \(-0.658774\pi\) | ||||
−0.478374 | + | 0.878156i | \(0.658774\pi\) | |||||||
\(912\) | −1.61213 | −0.0533829 | ||||||||
\(913\) | 17.7546 | 0.587593 | ||||||||
\(914\) | −19.6121 | −0.648711 | ||||||||
\(915\) | −6.00000 | −0.198354 | ||||||||
\(916\) | −13.8496 | −0.457602 | ||||||||
\(917\) | 19.3258 | 0.638195 | ||||||||
\(918\) | 6.31265 | 0.208349 | ||||||||
\(919\) | −50.2492 | −1.65757 | −0.828784 | − | 0.559569i | \(-0.810967\pi\) | ||||
−0.828784 | + | 0.559569i | \(0.810967\pi\) | |||||||
\(920\) | −1.00000 | −0.0329690 | ||||||||
\(921\) | −32.4749 | −1.07008 | ||||||||
\(922\) | 0.700523 | 0.0230705 | ||||||||
\(923\) | −18.1768 | −0.598296 | ||||||||
\(924\) | 1.61213 | 0.0530351 | ||||||||
\(925\) | −3.92478 | −0.129046 | ||||||||
\(926\) | 12.1622 | 0.399675 | ||||||||
\(927\) | 16.6253 | 0.546047 | ||||||||
\(928\) | −0.387873 | −0.0127326 | ||||||||
\(929\) | 10.5237 | 0.345272 | 0.172636 | − | 0.984986i | \(-0.444772\pi\) | ||||
0.172636 | + | 0.984986i | \(0.444772\pi\) | |||||||
\(930\) | 4.31265 | 0.141417 | ||||||||
\(931\) | 1.61213 | 0.0528353 | ||||||||
\(932\) | 14.0000 | 0.458585 | ||||||||
\(933\) | −0.523730 | −0.0171462 | ||||||||
\(934\) | −4.56467 | −0.149360 | ||||||||
\(935\) | −10.1768 | −0.332817 | ||||||||
\(936\) | −2.00000 | −0.0653720 | ||||||||
\(937\) | −5.59754 | −0.182864 | −0.0914318 | − | 0.995811i | \(-0.529144\pi\) | ||||
−0.0914318 | + | 0.995811i | \(0.529144\pi\) | |||||||
\(938\) | −9.08840 | −0.296747 | ||||||||
\(939\) | 10.3733 | 0.338519 | ||||||||
\(940\) | −1.61213 | −0.0525818 | ||||||||
\(941\) | 1.10299 | 0.0359563 | 0.0179781 | − | 0.999838i | \(-0.494277\pi\) | ||||
0.0179781 | + | 0.999838i | \(0.494277\pi\) | |||||||
\(942\) | −6.62530 | −0.215864 | ||||||||
\(943\) | 7.92478 | 0.258066 | ||||||||
\(944\) | −10.7005 | −0.348272 | ||||||||
\(945\) | −1.00000 | −0.0325300 | ||||||||
\(946\) | −6.95254 | −0.226047 | ||||||||
\(947\) | −13.2506 | −0.430587 | −0.215293 | − | 0.976549i | \(-0.569071\pi\) | ||||
−0.215293 | + | 0.976549i | \(0.569071\pi\) | |||||||
\(948\) | −9.92478 | −0.322342 | ||||||||
\(949\) | 10.4485 | 0.339173 | ||||||||
\(950\) | −1.61213 | −0.0523043 | ||||||||
\(951\) | −16.9525 | −0.549724 | ||||||||
\(952\) | −6.31265 | −0.204594 | ||||||||
\(953\) | −4.85097 | −0.157138 | −0.0785692 | − | 0.996909i | \(-0.525035\pi\) | ||||
−0.0785692 | + | 0.996909i | \(0.525035\pi\) | |||||||
\(954\) | −2.77575 | −0.0898681 | ||||||||
\(955\) | 10.7005 | 0.346261 | ||||||||
\(956\) | −23.5369 | −0.761238 | ||||||||
\(957\) | 0.625301 | 0.0202131 | ||||||||
\(958\) | −30.0263 | −0.970107 | ||||||||
\(959\) | −5.47627 | −0.176838 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −12.4010 | −0.400034 | ||||||||
\(962\) | 7.84955 | 0.253080 | ||||||||
\(963\) | −18.5501 | −0.597768 | ||||||||
\(964\) | 27.7137 | 0.892598 | ||||||||
\(965\) | −6.00000 | −0.193147 | ||||||||
\(966\) | 1.00000 | 0.0321745 | ||||||||
\(967\) | 2.28630 | 0.0735225 | 0.0367613 | − | 0.999324i | \(-0.488296\pi\) | ||||
0.0367613 | + | 0.999324i | \(0.488296\pi\) | |||||||
\(968\) | 8.40105 | 0.270020 | ||||||||
\(969\) | −10.1768 | −0.326926 | ||||||||
\(970\) | −15.9248 | −0.511314 | ||||||||
\(971\) | −42.3996 | −1.36067 | −0.680334 | − | 0.732902i | \(-0.738165\pi\) | ||||
−0.680334 | + | 0.732902i | \(0.738165\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −6.70052 | −0.214809 | ||||||||
\(974\) | −1.23884 | −0.0396951 | ||||||||
\(975\) | −2.00000 | −0.0640513 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | 16.8510 | 0.539110 | 0.269555 | − | 0.962985i | \(-0.413123\pi\) | ||||
0.269555 | + | 0.962985i | \(0.413123\pi\) | |||||||
\(978\) | 23.3258 | 0.745878 | ||||||||
\(979\) | 7.57784 | 0.242189 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −11.1490 | −0.355961 | ||||||||
\(982\) | −4.25202 | −0.135687 | ||||||||
\(983\) | −33.0278 | −1.05342 | −0.526711 | − | 0.850044i | \(-0.676575\pi\) | ||||
−0.526711 | + | 0.850044i | \(0.676575\pi\) | |||||||
\(984\) | 7.92478 | 0.252633 | ||||||||
\(985\) | 18.6253 | 0.593451 | ||||||||
\(986\) | −2.44851 | −0.0779764 | ||||||||
\(987\) | 1.61213 | 0.0513146 | ||||||||
\(988\) | 3.22425 | 0.102577 | ||||||||
\(989\) | −4.31265 | −0.137134 | ||||||||
\(990\) | 1.61213 | 0.0512368 | ||||||||
\(991\) | 14.6516 | 0.465425 | 0.232712 | − | 0.972546i | \(-0.425240\pi\) | ||||
0.232712 | + | 0.972546i | \(0.425240\pi\) | |||||||
\(992\) | −4.31265 | −0.136927 | ||||||||
\(993\) | −7.22425 | −0.229255 | ||||||||
\(994\) | 9.08840 | 0.288266 | ||||||||
\(995\) | 3.47627 | 0.110205 | ||||||||
\(996\) | 11.0132 | 0.348966 | ||||||||
\(997\) | 28.2981 | 0.896209 | 0.448104 | − | 0.893981i | \(-0.352099\pi\) | ||||
0.448104 | + | 0.893981i | \(0.352099\pi\) | |||||||
\(998\) | −22.2981 | −0.705833 | ||||||||
\(999\) | 3.92478 | 0.124174 |
(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.by.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4830.2.a.by.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial |