Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + \cdots + 281 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(2.07185\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.07185 | 1.46502 | 0.732511 | − | 0.680755i | \(-0.238348\pi\) | ||||
0.732511 | + | 0.680755i | \(0.238348\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.29258 | 1.14629 | ||||||||
\(5\) | 3.98491 | 1.78211 | 0.891054 | − | 0.453898i | \(-0.149967\pi\) | ||||
0.891054 | + | 0.453898i | \(0.149967\pi\) | |||||||
\(6\) | 2.07185 | 0.845831 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.606176 | 0.214316 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 8.25616 | 2.61083 | ||||||||
\(11\) | 2.61487 | 0.788413 | 0.394207 | − | 0.919022i | \(-0.371019\pi\) | ||||
0.394207 | + | 0.919022i | \(0.371019\pi\) | |||||||
\(12\) | 2.29258 | 0.661810 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.07185 | −0.553726 | ||||||||
\(15\) | 3.98491 | 1.02890 | ||||||||
\(16\) | −3.32925 | −0.832311 | ||||||||
\(17\) | 2.46321 | 0.597416 | 0.298708 | − | 0.954345i | \(-0.403444\pi\) | ||||
0.298708 | + | 0.954345i | \(0.403444\pi\) | |||||||
\(18\) | 2.07185 | 0.488341 | ||||||||
\(19\) | 5.30899 | 1.21797 | 0.608983 | − | 0.793183i | \(-0.291578\pi\) | ||||
0.608983 | + | 0.793183i | \(0.291578\pi\) | |||||||
\(20\) | 9.13572 | 2.04281 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 5.41763 | 1.15504 | ||||||||
\(23\) | −8.91513 | −1.85893 | −0.929467 | − | 0.368905i | \(-0.879733\pi\) | ||||
−0.929467 | + | 0.368905i | \(0.879733\pi\) | |||||||
\(24\) | 0.606176 | 0.123735 | ||||||||
\(25\) | 10.8795 | 2.17591 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.29258 | −0.433256 | ||||||||
\(29\) | −3.55037 | −0.659287 | −0.329643 | − | 0.944105i | \(-0.606929\pi\) | ||||
−0.329643 | + | 0.944105i | \(0.606929\pi\) | |||||||
\(30\) | 8.25616 | 1.50736 | ||||||||
\(31\) | 6.25363 | 1.12319 | 0.561593 | − | 0.827414i | \(-0.310189\pi\) | ||||
0.561593 | + | 0.827414i | \(0.310189\pi\) | |||||||
\(32\) | −8.11006 | −1.43367 | ||||||||
\(33\) | 2.61487 | 0.455191 | ||||||||
\(34\) | 5.10341 | 0.875227 | ||||||||
\(35\) | −3.98491 | −0.673573 | ||||||||
\(36\) | 2.29258 | 0.382096 | ||||||||
\(37\) | −3.72795 | −0.612871 | −0.306435 | − | 0.951891i | \(-0.599136\pi\) | ||||
−0.306435 | + | 0.951891i | \(0.599136\pi\) | |||||||
\(38\) | 10.9995 | 1.78435 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.41556 | 0.381934 | ||||||||
\(41\) | −6.88324 | −1.07498 | −0.537490 | − | 0.843270i | \(-0.680628\pi\) | ||||
−0.537490 | + | 0.843270i | \(0.680628\pi\) | |||||||
\(42\) | −2.07185 | −0.319694 | ||||||||
\(43\) | 7.59739 | 1.15859 | 0.579296 | − | 0.815117i | \(-0.303328\pi\) | ||||
0.579296 | + | 0.815117i | \(0.303328\pi\) | |||||||
\(44\) | 5.99479 | 0.903749 | ||||||||
\(45\) | 3.98491 | 0.594036 | ||||||||
\(46\) | −18.4709 | −2.72338 | ||||||||
\(47\) | −2.43688 | −0.355455 | −0.177728 | − | 0.984080i | \(-0.556875\pi\) | ||||
−0.177728 | + | 0.984080i | \(0.556875\pi\) | |||||||
\(48\) | −3.32925 | −0.480535 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 22.5408 | 3.18775 | ||||||||
\(51\) | 2.46321 | 0.344918 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.8574 | −1.49138 | −0.745690 | − | 0.666293i | \(-0.767880\pi\) | ||||
−0.745690 | + | 0.666293i | \(0.767880\pi\) | |||||||
\(54\) | 2.07185 | 0.281944 | ||||||||
\(55\) | 10.4200 | 1.40504 | ||||||||
\(56\) | −0.606176 | −0.0810037 | ||||||||
\(57\) | 5.30899 | 0.703193 | ||||||||
\(58\) | −7.35584 | −0.965870 | ||||||||
\(59\) | −0.944885 | −0.123014 | −0.0615068 | − | 0.998107i | \(-0.519591\pi\) | ||||
−0.0615068 | + | 0.998107i | \(0.519591\pi\) | |||||||
\(60\) | 9.13572 | 1.17942 | ||||||||
\(61\) | 4.95925 | 0.634967 | 0.317483 | − | 0.948264i | \(-0.397162\pi\) | ||||
0.317483 | + | 0.948264i | \(0.397162\pi\) | |||||||
\(62\) | 12.9566 | 1.64549 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −10.1444 | −1.26805 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.41763 | 0.666864 | ||||||||
\(67\) | −16.0479 | −1.96056 | −0.980281 | − | 0.197609i | \(-0.936682\pi\) | ||||
−0.980281 | + | 0.197609i | \(0.936682\pi\) | |||||||
\(68\) | 5.64710 | 0.684811 | ||||||||
\(69\) | −8.91513 | −1.07326 | ||||||||
\(70\) | −8.25616 | −0.986799 | ||||||||
\(71\) | 15.8147 | 1.87686 | 0.938429 | − | 0.345471i | \(-0.112281\pi\) | ||||
0.938429 | + | 0.345471i | \(0.112281\pi\) | |||||||
\(72\) | 0.606176 | 0.0714386 | ||||||||
\(73\) | 3.16937 | 0.370947 | 0.185473 | − | 0.982649i | \(-0.440618\pi\) | ||||
0.185473 | + | 0.982649i | \(0.440618\pi\) | |||||||
\(74\) | −7.72376 | −0.897869 | ||||||||
\(75\) | 10.8795 | 1.25626 | ||||||||
\(76\) | 12.1713 | 1.39614 | ||||||||
\(77\) | −2.61487 | −0.297992 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.15670 | −0.580174 | −0.290087 | − | 0.957000i | \(-0.593684\pi\) | ||||
−0.290087 | + | 0.957000i | \(0.593684\pi\) | |||||||
\(80\) | −13.2668 | −1.48327 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −14.2611 | −1.57487 | ||||||||
\(83\) | 1.47510 | 0.161913 | 0.0809567 | − | 0.996718i | \(-0.474202\pi\) | ||||
0.0809567 | + | 0.996718i | \(0.474202\pi\) | |||||||
\(84\) | −2.29258 | −0.250141 | ||||||||
\(85\) | 9.81567 | 1.06466 | ||||||||
\(86\) | 15.7407 | 1.69736 | ||||||||
\(87\) | −3.55037 | −0.380639 | ||||||||
\(88\) | 1.58507 | 0.168969 | ||||||||
\(89\) | 13.7404 | 1.45648 | 0.728241 | − | 0.685321i | \(-0.240338\pi\) | ||||
0.728241 | + | 0.685321i | \(0.240338\pi\) | |||||||
\(90\) | 8.25616 | 0.870275 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −20.4386 | −2.13087 | ||||||||
\(93\) | 6.25363 | 0.648472 | ||||||||
\(94\) | −5.04886 | −0.520750 | ||||||||
\(95\) | 21.1559 | 2.17055 | ||||||||
\(96\) | −8.11006 | −0.827730 | ||||||||
\(97\) | −4.52869 | −0.459819 | −0.229910 | − | 0.973212i | \(-0.573843\pi\) | ||||
−0.229910 | + | 0.973212i | \(0.573843\pi\) | |||||||
\(98\) | 2.07185 | 0.209289 | ||||||||
\(99\) | 2.61487 | 0.262804 | ||||||||
\(100\) | 24.9422 | 2.49422 | ||||||||
\(101\) | −2.65442 | −0.264125 | −0.132062 | − | 0.991241i | \(-0.542160\pi\) | ||||
−0.132062 | + | 0.991241i | \(0.542160\pi\) | |||||||
\(102\) | 5.10341 | 0.505313 | ||||||||
\(103\) | −10.9414 | −1.07809 | −0.539044 | − | 0.842278i | \(-0.681214\pi\) | ||||
−0.539044 | + | 0.842278i | \(0.681214\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.98491 | −0.388888 | ||||||||
\(106\) | −22.4950 | −2.18490 | ||||||||
\(107\) | 5.83503 | 0.564094 | 0.282047 | − | 0.959401i | \(-0.408987\pi\) | ||||
0.282047 | + | 0.959401i | \(0.408987\pi\) | |||||||
\(108\) | 2.29258 | 0.220603 | ||||||||
\(109\) | 14.4487 | 1.38393 | 0.691965 | − | 0.721931i | \(-0.256745\pi\) | ||||
0.691965 | + | 0.721931i | \(0.256745\pi\) | |||||||
\(110\) | 21.5888 | 2.05841 | ||||||||
\(111\) | −3.72795 | −0.353841 | ||||||||
\(112\) | 3.32925 | 0.314584 | ||||||||
\(113\) | −9.37283 | −0.881721 | −0.440861 | − | 0.897576i | \(-0.645327\pi\) | ||||
−0.440861 | + | 0.897576i | \(0.645327\pi\) | |||||||
\(114\) | 10.9995 | 1.03019 | ||||||||
\(115\) | −35.5260 | −3.31282 | ||||||||
\(116\) | −8.13949 | −0.755733 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.95766 | −0.180218 | ||||||||
\(119\) | −2.46321 | −0.225802 | ||||||||
\(120\) | 2.41556 | 0.220509 | ||||||||
\(121\) | −4.16245 | −0.378405 | ||||||||
\(122\) | 10.2748 | 0.930240 | ||||||||
\(123\) | −6.88324 | −0.620640 | ||||||||
\(124\) | 14.3369 | 1.28749 | ||||||||
\(125\) | 23.4294 | 2.09559 | ||||||||
\(126\) | −2.07185 | −0.184575 | ||||||||
\(127\) | −3.25452 | −0.288792 | −0.144396 | − | 0.989520i | \(-0.546124\pi\) | ||||
−0.144396 | + | 0.989520i | \(0.546124\pi\) | |||||||
\(128\) | −4.79752 | −0.424045 | ||||||||
\(129\) | 7.59739 | 0.668913 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.26410 | 0.110445 | 0.0552224 | − | 0.998474i | \(-0.482413\pi\) | ||||
0.0552224 | + | 0.998474i | \(0.482413\pi\) | |||||||
\(132\) | 5.99479 | 0.521780 | ||||||||
\(133\) | −5.30899 | −0.460348 | ||||||||
\(134\) | −33.2489 | −2.87227 | ||||||||
\(135\) | 3.98491 | 0.342967 | ||||||||
\(136\) | 1.49314 | 0.128036 | ||||||||
\(137\) | −16.0982 | −1.37536 | −0.687682 | − | 0.726012i | \(-0.741371\pi\) | ||||
−0.687682 | + | 0.726012i | \(0.741371\pi\) | |||||||
\(138\) | −18.4709 | −1.57234 | ||||||||
\(139\) | 20.8156 | 1.76556 | 0.882778 | − | 0.469791i | \(-0.155671\pi\) | ||||
0.882778 | + | 0.469791i | \(0.155671\pi\) | |||||||
\(140\) | −9.13572 | −0.772109 | ||||||||
\(141\) | −2.43688 | −0.205222 | ||||||||
\(142\) | 32.7657 | 2.74964 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.32925 | −0.277437 | ||||||||
\(145\) | −14.1479 | −1.17492 | ||||||||
\(146\) | 6.56647 | 0.543445 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −8.54661 | −0.702527 | ||||||||
\(149\) | −14.5215 | −1.18965 | −0.594823 | − | 0.803856i | \(-0.702778\pi\) | ||||
−0.594823 | + | 0.803856i | \(0.702778\pi\) | |||||||
\(150\) | 22.5408 | 1.84045 | ||||||||
\(151\) | −10.2052 | −0.830489 | −0.415245 | − | 0.909710i | \(-0.636304\pi\) | ||||
−0.415245 | + | 0.909710i | \(0.636304\pi\) | |||||||
\(152\) | 3.21819 | 0.261029 | ||||||||
\(153\) | 2.46321 | 0.199139 | ||||||||
\(154\) | −5.41763 | −0.436565 | ||||||||
\(155\) | 24.9202 | 2.00164 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.86827 | 0.468339 | 0.234170 | − | 0.972196i | \(-0.424763\pi\) | ||||
0.234170 | + | 0.972196i | \(0.424763\pi\) | |||||||
\(158\) | −10.6839 | −0.849968 | ||||||||
\(159\) | −10.8574 | −0.861048 | ||||||||
\(160\) | −32.3179 | −2.55495 | ||||||||
\(161\) | 8.91513 | 0.702611 | ||||||||
\(162\) | 2.07185 | 0.162780 | ||||||||
\(163\) | −0.697676 | −0.0546462 | −0.0273231 | − | 0.999627i | \(-0.508698\pi\) | ||||
−0.0273231 | + | 0.999627i | \(0.508698\pi\) | |||||||
\(164\) | −15.7803 | −1.23224 | ||||||||
\(165\) | 10.4200 | 0.811199 | ||||||||
\(166\) | 3.05620 | 0.237207 | ||||||||
\(167\) | −25.1020 | −1.94245 | −0.971224 | − | 0.238169i | \(-0.923453\pi\) | ||||
−0.971224 | + | 0.238169i | \(0.923453\pi\) | |||||||
\(168\) | −0.606176 | −0.0467675 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 20.3366 | 1.55975 | ||||||||
\(171\) | 5.30899 | 0.405989 | ||||||||
\(172\) | 17.4176 | 1.32808 | ||||||||
\(173\) | 5.26644 | 0.400400 | 0.200200 | − | 0.979755i | \(-0.435841\pi\) | ||||
0.200200 | + | 0.979755i | \(0.435841\pi\) | |||||||
\(174\) | −7.35584 | −0.557645 | ||||||||
\(175\) | −10.8795 | −0.822415 | ||||||||
\(176\) | −8.70555 | −0.656205 | ||||||||
\(177\) | −0.944885 | −0.0710219 | ||||||||
\(178\) | 28.4681 | 2.13378 | ||||||||
\(179\) | 11.4454 | 0.855469 | 0.427734 | − | 0.903904i | \(-0.359312\pi\) | ||||
0.427734 | + | 0.903904i | \(0.359312\pi\) | |||||||
\(180\) | 9.13572 | 0.680936 | ||||||||
\(181\) | −13.2259 | −0.983072 | −0.491536 | − | 0.870857i | \(-0.663564\pi\) | ||||
−0.491536 | + | 0.870857i | \(0.663564\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.95925 | 0.366598 | ||||||||
\(184\) | −5.40414 | −0.398399 | ||||||||
\(185\) | −14.8556 | −1.09220 | ||||||||
\(186\) | 12.9566 | 0.950025 | ||||||||
\(187\) | 6.44097 | 0.471011 | ||||||||
\(188\) | −5.58673 | −0.407454 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 43.8319 | 3.17990 | ||||||||
\(191\) | 2.77448 | 0.200754 | 0.100377 | − | 0.994949i | \(-0.467995\pi\) | ||||
0.100377 | + | 0.994949i | \(0.467995\pi\) | |||||||
\(192\) | −10.1444 | −0.732107 | ||||||||
\(193\) | −16.6422 | −1.19793 | −0.598965 | − | 0.800776i | \(-0.704421\pi\) | ||||
−0.598965 | + | 0.800776i | \(0.704421\pi\) | |||||||
\(194\) | −9.38279 | −0.673645 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.29258 | 0.163755 | ||||||||
\(197\) | −0.164331 | −0.0117081 | −0.00585404 | − | 0.999983i | \(-0.501863\pi\) | ||||
−0.00585404 | + | 0.999983i | \(0.501863\pi\) | |||||||
\(198\) | 5.41763 | 0.385014 | ||||||||
\(199\) | 1.73169 | 0.122756 | 0.0613780 | − | 0.998115i | \(-0.480450\pi\) | ||||
0.0613780 | + | 0.998115i | \(0.480450\pi\) | |||||||
\(200\) | 6.59492 | 0.466331 | ||||||||
\(201\) | −16.0479 | −1.13193 | ||||||||
\(202\) | −5.49957 | −0.386948 | ||||||||
\(203\) | 3.55037 | 0.249187 | ||||||||
\(204\) | 5.64710 | 0.395376 | ||||||||
\(205\) | −27.4291 | −1.91573 | ||||||||
\(206\) | −22.6690 | −1.57942 | ||||||||
\(207\) | −8.91513 | −0.619645 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.8823 | 0.960261 | ||||||||
\(210\) | −8.25616 | −0.569729 | ||||||||
\(211\) | 14.7885 | 1.01808 | 0.509039 | − | 0.860743i | \(-0.330001\pi\) | ||||
0.509039 | + | 0.860743i | \(0.330001\pi\) | |||||||
\(212\) | −24.8914 | −1.70955 | ||||||||
\(213\) | 15.8147 | 1.08361 | ||||||||
\(214\) | 12.0893 | 0.826409 | ||||||||
\(215\) | 30.2749 | 2.06473 | ||||||||
\(216\) | 0.606176 | 0.0412451 | ||||||||
\(217\) | −6.25363 | −0.424524 | ||||||||
\(218\) | 29.9355 | 2.02749 | ||||||||
\(219\) | 3.16937 | 0.214166 | ||||||||
\(220\) | 23.8887 | 1.61058 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −7.72376 | −0.518385 | ||||||||
\(223\) | 16.6943 | 1.11793 | 0.558966 | − | 0.829191i | \(-0.311198\pi\) | ||||
0.558966 | + | 0.829191i | \(0.311198\pi\) | |||||||
\(224\) | 8.11006 | 0.541876 | ||||||||
\(225\) | 10.8795 | 0.725302 | ||||||||
\(226\) | −19.4191 | −1.29174 | ||||||||
\(227\) | −15.2365 | −1.01128 | −0.505640 | − | 0.862745i | \(-0.668743\pi\) | ||||
−0.505640 | + | 0.862745i | \(0.668743\pi\) | |||||||
\(228\) | 12.1713 | 0.806062 | ||||||||
\(229\) | −19.2701 | −1.27341 | −0.636703 | − | 0.771109i | \(-0.719702\pi\) | ||||
−0.636703 | + | 0.771109i | \(0.719702\pi\) | |||||||
\(230\) | −73.6047 | −4.85335 | ||||||||
\(231\) | −2.61487 | −0.172046 | ||||||||
\(232\) | −2.15215 | −0.141296 | ||||||||
\(233\) | 6.58317 | 0.431278 | 0.215639 | − | 0.976473i | \(-0.430817\pi\) | ||||
0.215639 | + | 0.976473i | \(0.430817\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.71075 | −0.633460 | ||||||||
\(236\) | −2.16622 | −0.141009 | ||||||||
\(237\) | −5.15670 | −0.334964 | ||||||||
\(238\) | −5.10341 | −0.330805 | ||||||||
\(239\) | −27.0508 | −1.74977 | −0.874885 | − | 0.484331i | \(-0.839063\pi\) | ||||
−0.874885 | + | 0.484331i | \(0.839063\pi\) | |||||||
\(240\) | −13.2668 | −0.856365 | ||||||||
\(241\) | 24.4670 | 1.57606 | 0.788029 | − | 0.615638i | \(-0.211102\pi\) | ||||
0.788029 | + | 0.615638i | \(0.211102\pi\) | |||||||
\(242\) | −8.62399 | −0.554371 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 11.3695 | 0.727855 | ||||||||
\(245\) | 3.98491 | 0.254587 | ||||||||
\(246\) | −14.2611 | −0.909252 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.79080 | 0.240716 | ||||||||
\(249\) | 1.47510 | 0.0934808 | ||||||||
\(250\) | 48.5424 | 3.07009 | ||||||||
\(251\) | 2.93895 | 0.185505 | 0.0927524 | − | 0.995689i | \(-0.470433\pi\) | ||||
0.0927524 | + | 0.995689i | \(0.470433\pi\) | |||||||
\(252\) | −2.29258 | −0.144419 | ||||||||
\(253\) | −23.3119 | −1.46561 | ||||||||
\(254\) | −6.74288 | −0.423086 | ||||||||
\(255\) | 9.81567 | 0.614681 | ||||||||
\(256\) | 10.3490 | 0.646811 | ||||||||
\(257\) | 5.57830 | 0.347965 | 0.173982 | − | 0.984749i | \(-0.444336\pi\) | ||||
0.173982 | + | 0.984749i | \(0.444336\pi\) | |||||||
\(258\) | 15.7407 | 0.979972 | ||||||||
\(259\) | 3.72795 | 0.231643 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.55037 | −0.219762 | ||||||||
\(262\) | 2.61903 | 0.161804 | ||||||||
\(263\) | 21.2240 | 1.30873 | 0.654365 | − | 0.756179i | \(-0.272936\pi\) | ||||
0.654365 | + | 0.756179i | \(0.272936\pi\) | |||||||
\(264\) | 1.58507 | 0.0975545 | ||||||||
\(265\) | −43.2658 | −2.65780 | ||||||||
\(266\) | −10.9995 | −0.674420 | ||||||||
\(267\) | 13.7404 | 0.840900 | ||||||||
\(268\) | −36.7910 | −2.24737 | ||||||||
\(269\) | −1.92240 | −0.117211 | −0.0586054 | − | 0.998281i | \(-0.518665\pi\) | ||||
−0.0586054 | + | 0.998281i | \(0.518665\pi\) | |||||||
\(270\) | 8.25616 | 0.502454 | ||||||||
\(271\) | 2.56202 | 0.155632 | 0.0778159 | − | 0.996968i | \(-0.475205\pi\) | ||||
0.0778159 | + | 0.996968i | \(0.475205\pi\) | |||||||
\(272\) | −8.20063 | −0.497236 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −33.3531 | −2.01494 | ||||||||
\(275\) | 28.4486 | 1.71551 | ||||||||
\(276\) | −20.4386 | −1.23026 | ||||||||
\(277\) | −9.31382 | −0.559613 | −0.279807 | − | 0.960056i | \(-0.590270\pi\) | ||||
−0.279807 | + | 0.960056i | \(0.590270\pi\) | |||||||
\(278\) | 43.1269 | 2.58658 | ||||||||
\(279\) | 6.25363 | 0.374395 | ||||||||
\(280\) | −2.41556 | −0.144357 | ||||||||
\(281\) | 14.0421 | 0.837682 | 0.418841 | − | 0.908060i | \(-0.362436\pi\) | ||||
0.418841 | + | 0.908060i | \(0.362436\pi\) | |||||||
\(282\) | −5.04886 | −0.300655 | ||||||||
\(283\) | 12.6395 | 0.751342 | 0.375671 | − | 0.926753i | \(-0.377412\pi\) | ||||
0.375671 | + | 0.926753i | \(0.377412\pi\) | |||||||
\(284\) | 36.2564 | 2.15142 | ||||||||
\(285\) | 21.1559 | 1.25317 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.88324 | 0.406305 | ||||||||
\(288\) | −8.11006 | −0.477890 | ||||||||
\(289\) | −10.9326 | −0.643094 | ||||||||
\(290\) | −29.3124 | −1.72128 | ||||||||
\(291\) | −4.52869 | −0.265477 | ||||||||
\(292\) | 7.26603 | 0.425212 | ||||||||
\(293\) | −22.0692 | −1.28930 | −0.644648 | − | 0.764480i | \(-0.722996\pi\) | ||||
−0.644648 | + | 0.764480i | \(0.722996\pi\) | |||||||
\(294\) | 2.07185 | 0.120833 | ||||||||
\(295\) | −3.76529 | −0.219223 | ||||||||
\(296\) | −2.25979 | −0.131348 | ||||||||
\(297\) | 2.61487 | 0.151730 | ||||||||
\(298\) | −30.0864 | −1.74286 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 24.9422 | 1.44004 | ||||||||
\(301\) | −7.59739 | −0.437906 | ||||||||
\(302\) | −21.1437 | −1.21668 | ||||||||
\(303\) | −2.65442 | −0.152492 | ||||||||
\(304\) | −17.6749 | −1.01373 | ||||||||
\(305\) | 19.7622 | 1.13158 | ||||||||
\(306\) | 5.10341 | 0.291742 | ||||||||
\(307\) | 3.30193 | 0.188451 | 0.0942255 | − | 0.995551i | \(-0.469963\pi\) | ||||
0.0942255 | + | 0.995551i | \(0.469963\pi\) | |||||||
\(308\) | −5.99479 | −0.341585 | ||||||||
\(309\) | −10.9414 | −0.622434 | ||||||||
\(310\) | 51.6310 | 2.93244 | ||||||||
\(311\) | 16.1831 | 0.917658 | 0.458829 | − | 0.888525i | \(-0.348269\pi\) | ||||
0.458829 | + | 0.888525i | \(0.348269\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.50394 | 0.141531 | 0.0707656 | − | 0.997493i | \(-0.477456\pi\) | ||||
0.0707656 | + | 0.997493i | \(0.477456\pi\) | |||||||
\(314\) | 12.1582 | 0.686127 | ||||||||
\(315\) | −3.98491 | −0.224524 | ||||||||
\(316\) | −11.8221 | −0.665047 | ||||||||
\(317\) | 24.1074 | 1.35401 | 0.677005 | − | 0.735979i | \(-0.263278\pi\) | ||||
0.677005 | + | 0.735979i | \(0.263278\pi\) | |||||||
\(318\) | −22.4950 | −1.26145 | ||||||||
\(319\) | −9.28376 | −0.519791 | ||||||||
\(320\) | −40.4244 | −2.25979 | ||||||||
\(321\) | 5.83503 | 0.325680 | ||||||||
\(322\) | 18.4709 | 1.02934 | ||||||||
\(323\) | 13.0772 | 0.727632 | ||||||||
\(324\) | 2.29258 | 0.127365 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.44548 | −0.0800579 | ||||||||
\(327\) | 14.4487 | 0.799012 | ||||||||
\(328\) | −4.17245 | −0.230385 | ||||||||
\(329\) | 2.43688 | 0.134350 | ||||||||
\(330\) | 21.5888 | 1.18842 | ||||||||
\(331\) | −5.36044 | −0.294637 | −0.147318 | − | 0.989089i | \(-0.547064\pi\) | ||||
−0.147318 | + | 0.989089i | \(0.547064\pi\) | |||||||
\(332\) | 3.38178 | 0.185600 | ||||||||
\(333\) | −3.72795 | −0.204290 | ||||||||
\(334\) | −52.0076 | −2.84573 | ||||||||
\(335\) | −63.9495 | −3.49393 | ||||||||
\(336\) | 3.32925 | 0.181625 | ||||||||
\(337\) | −16.4659 | −0.896952 | −0.448476 | − | 0.893795i | \(-0.648033\pi\) | ||||
−0.448476 | + | 0.893795i | \(0.648033\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.37283 | −0.509062 | ||||||||
\(340\) | 22.5032 | 1.22041 | ||||||||
\(341\) | 16.3524 | 0.885534 | ||||||||
\(342\) | 10.9995 | 0.594782 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 4.60536 | 0.248304 | ||||||||
\(345\) | −35.5260 | −1.91266 | ||||||||
\(346\) | 10.9113 | 0.586595 | ||||||||
\(347\) | −20.9577 | −1.12507 | −0.562534 | − | 0.826774i | \(-0.690173\pi\) | ||||
−0.562534 | + | 0.826774i | \(0.690173\pi\) | |||||||
\(348\) | −8.13949 | −0.436323 | ||||||||
\(349\) | −22.9993 | −1.23112 | −0.615562 | − | 0.788088i | \(-0.711071\pi\) | ||||
−0.615562 | + | 0.788088i | \(0.711071\pi\) | |||||||
\(350\) | −22.5408 | −1.20486 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −21.2068 | −1.13032 | ||||||||
\(353\) | −27.4204 | −1.45944 | −0.729722 | − | 0.683744i | \(-0.760350\pi\) | ||||
−0.729722 | + | 0.683744i | \(0.760350\pi\) | |||||||
\(354\) | −1.95766 | −0.104049 | ||||||||
\(355\) | 63.0202 | 3.34476 | ||||||||
\(356\) | 31.5010 | 1.66955 | ||||||||
\(357\) | −2.46321 | −0.130367 | ||||||||
\(358\) | 23.7132 | 1.25328 | ||||||||
\(359\) | −21.3329 | −1.12591 | −0.562953 | − | 0.826489i | \(-0.690335\pi\) | ||||
−0.562953 | + | 0.826489i | \(0.690335\pi\) | |||||||
\(360\) | 2.41556 | 0.127311 | ||||||||
\(361\) | 9.18541 | 0.483442 | ||||||||
\(362\) | −27.4021 | −1.44022 | ||||||||
\(363\) | −4.16245 | −0.218472 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.6297 | 0.661067 | ||||||||
\(366\) | 10.2748 | 0.537074 | ||||||||
\(367\) | −16.9232 | −0.883385 | −0.441692 | − | 0.897167i | \(-0.645622\pi\) | ||||
−0.441692 | + | 0.897167i | \(0.645622\pi\) | |||||||
\(368\) | 29.6807 | 1.54721 | ||||||||
\(369\) | −6.88324 | −0.358327 | ||||||||
\(370\) | −30.7785 | −1.60010 | ||||||||
\(371\) | 10.8574 | 0.563689 | ||||||||
\(372\) | 14.3369 | 0.743335 | ||||||||
\(373\) | 17.0966 | 0.885228 | 0.442614 | − | 0.896712i | \(-0.354051\pi\) | ||||
0.442614 | + | 0.896712i | \(0.354051\pi\) | |||||||
\(374\) | 13.3448 | 0.690041 | ||||||||
\(375\) | 23.4294 | 1.20989 | ||||||||
\(376\) | −1.47718 | −0.0761797 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.07185 | −0.106565 | ||||||||
\(379\) | 9.18462 | 0.471782 | 0.235891 | − | 0.971779i | \(-0.424199\pi\) | ||||
0.235891 | + | 0.971779i | \(0.424199\pi\) | |||||||
\(380\) | 48.5015 | 2.48807 | ||||||||
\(381\) | −3.25452 | −0.166734 | ||||||||
\(382\) | 5.74831 | 0.294109 | ||||||||
\(383\) | −38.9057 | −1.98799 | −0.993995 | − | 0.109427i | \(-0.965098\pi\) | ||||
−0.993995 | + | 0.109427i | \(0.965098\pi\) | |||||||
\(384\) | −4.79752 | −0.244822 | ||||||||
\(385\) | −10.4200 | −0.531054 | ||||||||
\(386\) | −34.4801 | −1.75499 | ||||||||
\(387\) | 7.59739 | 0.386197 | ||||||||
\(388\) | −10.3824 | −0.527086 | ||||||||
\(389\) | 24.3185 | 1.23299 | 0.616497 | − | 0.787357i | \(-0.288551\pi\) | ||||
0.616497 | + | 0.787357i | \(0.288551\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.9598 | −1.11056 | ||||||||
\(392\) | 0.606176 | 0.0306165 | ||||||||
\(393\) | 1.26410 | 0.0637654 | ||||||||
\(394\) | −0.340469 | −0.0171526 | ||||||||
\(395\) | −20.5490 | −1.03393 | ||||||||
\(396\) | 5.99479 | 0.301250 | ||||||||
\(397\) | −39.0819 | −1.96146 | −0.980732 | − | 0.195356i | \(-0.937414\pi\) | ||||
−0.980732 | + | 0.195356i | \(0.937414\pi\) | |||||||
\(398\) | 3.58780 | 0.179840 | ||||||||
\(399\) | −5.30899 | −0.265782 | ||||||||
\(400\) | −36.2206 | −1.81103 | ||||||||
\(401\) | 27.9732 | 1.39692 | 0.698458 | − | 0.715651i | \(-0.253870\pi\) | ||||
0.698458 | + | 0.715651i | \(0.253870\pi\) | |||||||
\(402\) | −33.2489 | −1.65830 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.08546 | −0.302763 | ||||||||
\(405\) | 3.98491 | 0.198012 | ||||||||
\(406\) | 7.35584 | 0.365064 | ||||||||
\(407\) | −9.74810 | −0.483196 | ||||||||
\(408\) | 1.49314 | 0.0739214 | ||||||||
\(409\) | 0.558520 | 0.0276171 | 0.0138085 | − | 0.999905i | \(-0.495604\pi\) | ||||
0.0138085 | + | 0.999905i | \(0.495604\pi\) | |||||||
\(410\) | −56.8291 | −2.80659 | ||||||||
\(411\) | −16.0982 | −0.794066 | ||||||||
\(412\) | −25.0840 | −1.23580 | ||||||||
\(413\) | 0.944885 | 0.0464948 | ||||||||
\(414\) | −18.4709 | −0.907793 | ||||||||
\(415\) | 5.87815 | 0.288547 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.8156 | 1.01934 | ||||||||
\(418\) | 28.7622 | 1.40680 | ||||||||
\(419\) | −8.74541 | −0.427241 | −0.213621 | − | 0.976917i | \(-0.568526\pi\) | ||||
−0.213621 | + | 0.976917i | \(0.568526\pi\) | |||||||
\(420\) | −9.13572 | −0.445777 | ||||||||
\(421\) | 25.1952 | 1.22794 | 0.613969 | − | 0.789330i | \(-0.289572\pi\) | ||||
0.613969 | + | 0.789330i | \(0.289572\pi\) | |||||||
\(422\) | 30.6395 | 1.49151 | ||||||||
\(423\) | −2.43688 | −0.118485 | ||||||||
\(424\) | −6.58150 | −0.319626 | ||||||||
\(425\) | 26.7986 | 1.29992 | ||||||||
\(426\) | 32.7657 | 1.58750 | ||||||||
\(427\) | −4.95925 | −0.239995 | ||||||||
\(428\) | 13.3773 | 0.646614 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 62.7253 | 3.02488 | ||||||||
\(431\) | 1.18445 | 0.0570532 | 0.0285266 | − | 0.999593i | \(-0.490918\pi\) | ||||
0.0285266 | + | 0.999593i | \(0.490918\pi\) | |||||||
\(432\) | −3.32925 | −0.160178 | ||||||||
\(433\) | −8.48096 | −0.407569 | −0.203785 | − | 0.979016i | \(-0.565324\pi\) | ||||
−0.203785 | + | 0.979016i | \(0.565324\pi\) | |||||||
\(434\) | −12.9566 | −0.621937 | ||||||||
\(435\) | −14.1479 | −0.678340 | ||||||||
\(436\) | 33.1246 | 1.58638 | ||||||||
\(437\) | −47.3304 | −2.26412 | ||||||||
\(438\) | 6.56647 | 0.313758 | ||||||||
\(439\) | 32.5677 | 1.55437 | 0.777186 | − | 0.629271i | \(-0.216647\pi\) | ||||
0.777186 | + | 0.629271i | \(0.216647\pi\) | |||||||
\(440\) | 6.31638 | 0.301121 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.3749 | 1.11057 | 0.555287 | − | 0.831659i | \(-0.312608\pi\) | ||||
0.555287 | + | 0.831659i | \(0.312608\pi\) | |||||||
\(444\) | −8.54661 | −0.405604 | ||||||||
\(445\) | 54.7544 | 2.59561 | ||||||||
\(446\) | 34.5881 | 1.63779 | ||||||||
\(447\) | −14.5215 | −0.686843 | ||||||||
\(448\) | 10.1444 | 0.479276 | ||||||||
\(449\) | −22.5296 | −1.06324 | −0.531618 | − | 0.846984i | \(-0.678416\pi\) | ||||
−0.531618 | + | 0.846984i | \(0.678416\pi\) | |||||||
\(450\) | 22.5408 | 1.06258 | ||||||||
\(451\) | −17.9988 | −0.847529 | ||||||||
\(452\) | −21.4879 | −1.01071 | ||||||||
\(453\) | −10.2052 | −0.479483 | ||||||||
\(454\) | −31.5677 | −1.48155 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.21819 | 0.150705 | ||||||||
\(457\) | 14.5781 | 0.681933 | 0.340966 | − | 0.940075i | \(-0.389246\pi\) | ||||
0.340966 | + | 0.940075i | \(0.389246\pi\) | |||||||
\(458\) | −39.9249 | −1.86557 | ||||||||
\(459\) | 2.46321 | 0.114973 | ||||||||
\(460\) | −81.4462 | −3.79745 | ||||||||
\(461\) | −26.0945 | −1.21534 | −0.607670 | − | 0.794189i | \(-0.707896\pi\) | ||||
−0.607670 | + | 0.794189i | \(0.707896\pi\) | |||||||
\(462\) | −5.41763 | −0.252051 | ||||||||
\(463\) | 25.6187 | 1.19060 | 0.595301 | − | 0.803502i | \(-0.297033\pi\) | ||||
0.595301 | + | 0.803502i | \(0.297033\pi\) | |||||||
\(464\) | 11.8200 | 0.548732 | ||||||||
\(465\) | 24.9202 | 1.15565 | ||||||||
\(466\) | 13.6394 | 0.631831 | ||||||||
\(467\) | 33.3200 | 1.54187 | 0.770933 | − | 0.636917i | \(-0.219790\pi\) | ||||
0.770933 | + | 0.636917i | \(0.219790\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.0479 | 0.741023 | ||||||||
\(470\) | −20.1193 | −0.928032 | ||||||||
\(471\) | 5.86827 | 0.270396 | ||||||||
\(472\) | −0.572767 | −0.0263637 | ||||||||
\(473\) | 19.8662 | 0.913449 | ||||||||
\(474\) | −10.6839 | −0.490729 | ||||||||
\(475\) | 57.7594 | 2.65018 | ||||||||
\(476\) | −5.64710 | −0.258834 | ||||||||
\(477\) | −10.8574 | −0.497127 | ||||||||
\(478\) | −56.0453 | −2.56345 | ||||||||
\(479\) | 6.09069 | 0.278291 | 0.139145 | − | 0.990272i | \(-0.455564\pi\) | ||||
0.139145 | + | 0.990272i | \(0.455564\pi\) | |||||||
\(480\) | −32.3179 | −1.47510 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 50.6920 | 2.30896 | ||||||||
\(483\) | 8.91513 | 0.405653 | ||||||||
\(484\) | −9.54274 | −0.433761 | ||||||||
\(485\) | −18.0465 | −0.819447 | ||||||||
\(486\) | 2.07185 | 0.0939812 | ||||||||
\(487\) | 29.1782 | 1.32219 | 0.661095 | − | 0.750302i | \(-0.270092\pi\) | ||||
0.661095 | + | 0.750302i | \(0.270092\pi\) | |||||||
\(488\) | 3.00618 | 0.136083 | ||||||||
\(489\) | −0.697676 | −0.0315500 | ||||||||
\(490\) | 8.25616 | 0.372975 | ||||||||
\(491\) | 31.2594 | 1.41072 | 0.705359 | − | 0.708850i | \(-0.250786\pi\) | ||||
0.705359 | + | 0.708850i | \(0.250786\pi\) | |||||||
\(492\) | −15.7803 | −0.711433 | ||||||||
\(493\) | −8.74530 | −0.393868 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.4200 | 0.468346 | ||||||||
\(496\) | −20.8199 | −0.934840 | ||||||||
\(497\) | −15.8147 | −0.709386 | ||||||||
\(498\) | 3.05620 | 0.136951 | ||||||||
\(499\) | 12.5804 | 0.563177 | 0.281588 | − | 0.959535i | \(-0.409139\pi\) | ||||
0.281588 | + | 0.959535i | \(0.409139\pi\) | |||||||
\(500\) | 53.7138 | 2.40215 | ||||||||
\(501\) | −25.1020 | −1.12147 | ||||||||
\(502\) | 6.08907 | 0.271769 | ||||||||
\(503\) | 39.2710 | 1.75101 | 0.875504 | − | 0.483211i | \(-0.160530\pi\) | ||||
0.875504 | + | 0.483211i | \(0.160530\pi\) | |||||||
\(504\) | −0.606176 | −0.0270012 | ||||||||
\(505\) | −10.5776 | −0.470698 | ||||||||
\(506\) | −48.2989 | −2.14715 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.46123 | −0.331039 | ||||||||
\(509\) | 32.2548 | 1.42967 | 0.714835 | − | 0.699293i | \(-0.246502\pi\) | ||||
0.714835 | + | 0.699293i | \(0.246502\pi\) | |||||||
\(510\) | 20.3366 | 0.900521 | ||||||||
\(511\) | −3.16937 | −0.140205 | ||||||||
\(512\) | 31.0366 | 1.37164 | ||||||||
\(513\) | 5.30899 | 0.234398 | ||||||||
\(514\) | 11.5574 | 0.509776 | ||||||||
\(515\) | −43.6005 | −1.92127 | ||||||||
\(516\) | 17.4176 | 0.766767 | ||||||||
\(517\) | −6.37213 | −0.280246 | ||||||||
\(518\) | 7.72376 | 0.339363 | ||||||||
\(519\) | 5.26644 | 0.231171 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.2921 | −0.626149 | −0.313075 | − | 0.949728i | \(-0.601359\pi\) | ||||
−0.313075 | + | 0.949728i | \(0.601359\pi\) | |||||||
\(522\) | −7.35584 | −0.321957 | ||||||||
\(523\) | 15.6499 | 0.684322 | 0.342161 | − | 0.939641i | \(-0.388841\pi\) | ||||
0.342161 | + | 0.939641i | \(0.388841\pi\) | |||||||
\(524\) | 2.89804 | 0.126602 | ||||||||
\(525\) | −10.8795 | −0.474822 | ||||||||
\(526\) | 43.9731 | 1.91732 | ||||||||
\(527\) | 15.4040 | 0.671009 | ||||||||
\(528\) | −8.70555 | −0.378860 | ||||||||
\(529\) | 56.4796 | 2.45564 | ||||||||
\(530\) | −89.6405 | −3.89373 | ||||||||
\(531\) | −0.944885 | −0.0410045 | ||||||||
\(532\) | −12.1713 | −0.527692 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 28.4681 | 1.23194 | ||||||||
\(535\) | 23.2521 | 1.00528 | ||||||||
\(536\) | −9.72785 | −0.420179 | ||||||||
\(537\) | 11.4454 | 0.493905 | ||||||||
\(538\) | −3.98293 | −0.171716 | ||||||||
\(539\) | 2.61487 | 0.112630 | ||||||||
\(540\) | 9.13572 | 0.393139 | ||||||||
\(541\) | −23.5020 | −1.01043 | −0.505216 | − | 0.862993i | \(-0.668587\pi\) | ||||
−0.505216 | + | 0.862993i | \(0.668587\pi\) | |||||||
\(542\) | 5.30814 | 0.228004 | ||||||||
\(543\) | −13.2259 | −0.567577 | ||||||||
\(544\) | −19.9768 | −0.856497 | ||||||||
\(545\) | 57.5766 | 2.46631 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.5884 | −0.538242 | −0.269121 | − | 0.963106i | \(-0.586733\pi\) | ||||
−0.269121 | + | 0.963106i | \(0.586733\pi\) | |||||||
\(548\) | −36.9064 | −1.57656 | ||||||||
\(549\) | 4.95925 | 0.211656 | ||||||||
\(550\) | 58.9413 | 2.51326 | ||||||||
\(551\) | −18.8489 | −0.802989 | ||||||||
\(552\) | −5.40414 | −0.230016 | ||||||||
\(553\) | 5.15670 | 0.219285 | ||||||||
\(554\) | −19.2969 | −0.819845 | ||||||||
\(555\) | −14.8556 | −0.630583 | ||||||||
\(556\) | 47.7213 | 2.02384 | ||||||||
\(557\) | 7.12504 | 0.301898 | 0.150949 | − | 0.988542i | \(-0.451767\pi\) | ||||
0.150949 | + | 0.988542i | \(0.451767\pi\) | |||||||
\(558\) | 12.9566 | 0.548497 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 13.2668 | 0.560623 | ||||||||
\(561\) | 6.44097 | 0.271938 | ||||||||
\(562\) | 29.0932 | 1.22722 | ||||||||
\(563\) | −37.5881 | −1.58415 | −0.792074 | − | 0.610425i | \(-0.790999\pi\) | ||||
−0.792074 | + | 0.610425i | \(0.790999\pi\) | |||||||
\(564\) | −5.58673 | −0.235244 | ||||||||
\(565\) | −37.3499 | −1.57132 | ||||||||
\(566\) | 26.1872 | 1.10073 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 9.58649 | 0.402240 | ||||||||
\(569\) | −15.9721 | −0.669584 | −0.334792 | − | 0.942292i | \(-0.608666\pi\) | ||||
−0.334792 | + | 0.942292i | \(0.608666\pi\) | |||||||
\(570\) | 43.8319 | 1.83592 | ||||||||
\(571\) | 1.19947 | 0.0501961 | 0.0250980 | − | 0.999685i | \(-0.492010\pi\) | ||||
0.0250980 | + | 0.999685i | \(0.492010\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.77448 | 0.115906 | ||||||||
\(574\) | 14.2611 | 0.595245 | ||||||||
\(575\) | −96.9925 | −4.04487 | ||||||||
\(576\) | −10.1444 | −0.422682 | ||||||||
\(577\) | 31.0326 | 1.29190 | 0.645952 | − | 0.763378i | \(-0.276461\pi\) | ||||
0.645952 | + | 0.763378i | \(0.276461\pi\) | |||||||
\(578\) | −22.6508 | −0.942147 | ||||||||
\(579\) | −16.6422 | −0.691625 | ||||||||
\(580\) | −32.4352 | −1.34680 | ||||||||
\(581\) | −1.47510 | −0.0611975 | ||||||||
\(582\) | −9.38279 | −0.388929 | ||||||||
\(583\) | −28.3907 | −1.17582 | ||||||||
\(584\) | 1.92120 | 0.0794997 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −45.7241 | −1.88885 | ||||||||
\(587\) | 9.60481 | 0.396433 | 0.198216 | − | 0.980158i | \(-0.436485\pi\) | ||||
0.198216 | + | 0.980158i | \(0.436485\pi\) | |||||||
\(588\) | 2.29258 | 0.0945443 | ||||||||
\(589\) | 33.2005 | 1.36800 | ||||||||
\(590\) | −7.80112 | −0.321167 | ||||||||
\(591\) | −0.164331 | −0.00675966 | ||||||||
\(592\) | 12.4113 | 0.510099 | ||||||||
\(593\) | −30.7042 | −1.26087 | −0.630435 | − | 0.776242i | \(-0.717123\pi\) | ||||
−0.630435 | + | 0.776242i | \(0.717123\pi\) | |||||||
\(594\) | 5.41763 | 0.222288 | ||||||||
\(595\) | −9.81567 | −0.402403 | ||||||||
\(596\) | −33.2916 | −1.36368 | ||||||||
\(597\) | 1.73169 | 0.0708732 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.9999 | −1.06233 | −0.531163 | − | 0.847269i | \(-0.678245\pi\) | ||||
−0.531163 | + | 0.847269i | \(0.678245\pi\) | |||||||
\(600\) | 6.59492 | 0.269236 | ||||||||
\(601\) | 9.31463 | 0.379952 | 0.189976 | − | 0.981789i | \(-0.439159\pi\) | ||||
0.189976 | + | 0.981789i | \(0.439159\pi\) | |||||||
\(602\) | −15.7407 | −0.641542 | ||||||||
\(603\) | −16.0479 | −0.653521 | ||||||||
\(604\) | −23.3963 | −0.951980 | ||||||||
\(605\) | −16.5870 | −0.674358 | ||||||||
\(606\) | −5.49957 | −0.223405 | ||||||||
\(607\) | −15.3649 | −0.623641 | −0.311821 | − | 0.950141i | \(-0.600939\pi\) | ||||
−0.311821 | + | 0.950141i | \(0.600939\pi\) | |||||||
\(608\) | −43.0563 | −1.74616 | ||||||||
\(609\) | 3.55037 | 0.143868 | ||||||||
\(610\) | 40.9443 | 1.65779 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 5.64710 | 0.228270 | ||||||||
\(613\) | −4.71856 | −0.190581 | −0.0952904 | − | 0.995450i | \(-0.530378\pi\) | ||||
−0.0952904 | + | 0.995450i | \(0.530378\pi\) | |||||||
\(614\) | 6.84111 | 0.276085 | ||||||||
\(615\) | −27.4291 | −1.10605 | ||||||||
\(616\) | −1.58507 | −0.0638644 | ||||||||
\(617\) | 16.7054 | 0.672533 | 0.336267 | − | 0.941767i | \(-0.390836\pi\) | ||||
0.336267 | + | 0.941767i | \(0.390836\pi\) | |||||||
\(618\) | −22.6690 | −0.911879 | ||||||||
\(619\) | 10.8625 | 0.436603 | 0.218301 | − | 0.975881i | \(-0.429948\pi\) | ||||
0.218301 | + | 0.975881i | \(0.429948\pi\) | |||||||
\(620\) | 57.1314 | 2.29445 | ||||||||
\(621\) | −8.91513 | −0.357752 | ||||||||
\(622\) | 33.5290 | 1.34439 | ||||||||
\(623\) | −13.7404 | −0.550498 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 38.9666 | 1.55866 | ||||||||
\(626\) | 5.18780 | 0.207346 | ||||||||
\(627\) | 13.8823 | 0.554407 | ||||||||
\(628\) | 13.4535 | 0.536852 | ||||||||
\(629\) | −9.18271 | −0.366139 | ||||||||
\(630\) | −8.25616 | −0.328933 | ||||||||
\(631\) | −19.8405 | −0.789837 | −0.394918 | − | 0.918716i | \(-0.629227\pi\) | ||||
−0.394918 | + | 0.918716i | \(0.629227\pi\) | |||||||
\(632\) | −3.12587 | −0.124340 | ||||||||
\(633\) | 14.7885 | 0.587788 | ||||||||
\(634\) | 49.9471 | 1.98365 | ||||||||
\(635\) | −12.9690 | −0.514658 | ||||||||
\(636\) | −24.8914 | −0.987010 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −19.2346 | −0.761504 | ||||||||
\(639\) | 15.8147 | 0.625620 | ||||||||
\(640\) | −19.1177 | −0.755694 | ||||||||
\(641\) | −25.7779 | −1.01817 | −0.509083 | − | 0.860717i | \(-0.670015\pi\) | ||||
−0.509083 | + | 0.860717i | \(0.670015\pi\) | |||||||
\(642\) | 12.0893 | 0.477128 | ||||||||
\(643\) | 25.4048 | 1.00187 | 0.500935 | − | 0.865485i | \(-0.332990\pi\) | ||||
0.500935 | + | 0.865485i | \(0.332990\pi\) | |||||||
\(644\) | 20.4386 | 0.805395 | ||||||||
\(645\) | 30.2749 | 1.19207 | ||||||||
\(646\) | 27.0940 | 1.06600 | ||||||||
\(647\) | −19.5858 | −0.769997 | −0.384999 | − | 0.922917i | \(-0.625798\pi\) | ||||
−0.384999 | + | 0.922917i | \(0.625798\pi\) | |||||||
\(648\) | 0.606176 | 0.0238129 | ||||||||
\(649\) | −2.47075 | −0.0969855 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.25363 | −0.245099 | ||||||||
\(652\) | −1.59948 | −0.0626403 | ||||||||
\(653\) | −13.7217 | −0.536971 | −0.268486 | − | 0.963284i | \(-0.586523\pi\) | ||||
−0.268486 | + | 0.963284i | \(0.586523\pi\) | |||||||
\(654\) | 29.9355 | 1.17057 | ||||||||
\(655\) | 5.03733 | 0.196825 | ||||||||
\(656\) | 22.9160 | 0.894719 | ||||||||
\(657\) | 3.16937 | 0.123649 | ||||||||
\(658\) | 5.04886 | 0.196825 | ||||||||
\(659\) | 26.6231 | 1.03709 | 0.518544 | − | 0.855051i | \(-0.326474\pi\) | ||||
0.518544 | + | 0.855051i | \(0.326474\pi\) | |||||||
\(660\) | 23.8887 | 0.929867 | ||||||||
\(661\) | −35.1844 | −1.36852 | −0.684258 | − | 0.729240i | \(-0.739874\pi\) | ||||
−0.684258 | + | 0.729240i | \(0.739874\pi\) | |||||||
\(662\) | −11.1061 | −0.431649 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.894172 | 0.0347006 | ||||||||
\(665\) | −21.1559 | −0.820390 | ||||||||
\(666\) | −7.72376 | −0.299290 | ||||||||
\(667\) | 31.6520 | 1.22557 | ||||||||
\(668\) | −57.5482 | −2.22661 | ||||||||
\(669\) | 16.6943 | 0.645438 | ||||||||
\(670\) | −132.494 | −5.11869 | ||||||||
\(671\) | 12.9678 | 0.500616 | ||||||||
\(672\) | 8.11006 | 0.312852 | ||||||||
\(673\) | −2.12183 | −0.0817905 | −0.0408953 | − | 0.999163i | \(-0.513021\pi\) | ||||
−0.0408953 | + | 0.999163i | \(0.513021\pi\) | |||||||
\(674\) | −34.1148 | −1.31405 | ||||||||
\(675\) | 10.8795 | 0.418753 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.8001 | −0.568813 | −0.284406 | − | 0.958704i | \(-0.591797\pi\) | ||||
−0.284406 | + | 0.958704i | \(0.591797\pi\) | |||||||
\(678\) | −19.4191 | −0.745787 | ||||||||
\(679\) | 4.52869 | 0.173795 | ||||||||
\(680\) | 5.95003 | 0.228173 | ||||||||
\(681\) | −15.2365 | −0.583862 | ||||||||
\(682\) | 33.8799 | 1.29733 | ||||||||
\(683\) | 17.8128 | 0.681590 | 0.340795 | − | 0.940138i | \(-0.389304\pi\) | ||||
0.340795 | + | 0.940138i | \(0.389304\pi\) | |||||||
\(684\) | 12.1713 | 0.465380 | ||||||||
\(685\) | −64.1500 | −2.45104 | ||||||||
\(686\) | −2.07185 | −0.0791037 | ||||||||
\(687\) | −19.2701 | −0.735202 | ||||||||
\(688\) | −25.2936 | −0.964309 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −73.6047 | −2.80208 | ||||||||
\(691\) | −11.7835 | −0.448264 | −0.224132 | − | 0.974559i | \(-0.571955\pi\) | ||||
−0.224132 | + | 0.974559i | \(0.571955\pi\) | |||||||
\(692\) | 12.0737 | 0.458974 | ||||||||
\(693\) | −2.61487 | −0.0993307 | ||||||||
\(694\) | −43.4212 | −1.64825 | ||||||||
\(695\) | 82.9483 | 3.14641 | ||||||||
\(696\) | −2.15215 | −0.0815770 | ||||||||
\(697\) | −16.9548 | −0.642211 | ||||||||
\(698\) | −47.6512 | −1.80362 | ||||||||
\(699\) | 6.58317 | 0.248998 | ||||||||
\(700\) | −24.9422 | −0.942725 | ||||||||
\(701\) | −10.5499 | −0.398465 | −0.199233 | − | 0.979952i | \(-0.563845\pi\) | ||||
−0.199233 | + | 0.979952i | \(0.563845\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.7917 | −0.746456 | ||||||||
\(704\) | −26.5262 | −0.999744 | ||||||||
\(705\) | −9.71075 | −0.365728 | ||||||||
\(706\) | −56.8112 | −2.13812 | ||||||||
\(707\) | 2.65442 | 0.0998297 | ||||||||
\(708\) | −2.16622 | −0.0814116 | ||||||||
\(709\) | −20.0085 | −0.751435 | −0.375717 | − | 0.926734i | \(-0.622604\pi\) | ||||
−0.375717 | + | 0.926734i | \(0.622604\pi\) | |||||||
\(710\) | 130.569 | 4.90015 | ||||||||
\(711\) | −5.15670 | −0.193391 | ||||||||
\(712\) | 8.32912 | 0.312147 | ||||||||
\(713\) | −55.7520 | −2.08793 | ||||||||
\(714\) | −5.10341 | −0.190990 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 26.2394 | 0.980614 | ||||||||
\(717\) | −27.0508 | −1.01023 | ||||||||
\(718\) | −44.1986 | −1.64948 | ||||||||
\(719\) | 2.64264 | 0.0985539 | 0.0492770 | − | 0.998785i | \(-0.484308\pi\) | ||||
0.0492770 | + | 0.998785i | \(0.484308\pi\) | |||||||
\(720\) | −13.2668 | −0.494423 | ||||||||
\(721\) | 10.9414 | 0.407479 | ||||||||
\(722\) | 19.0308 | 0.708254 | ||||||||
\(723\) | 24.4670 | 0.909937 | ||||||||
\(724\) | −30.3213 | −1.12688 | ||||||||
\(725\) | −38.6264 | −1.43455 | ||||||||
\(726\) | −8.62399 | −0.320066 | ||||||||
\(727\) | 23.9042 | 0.886557 | 0.443279 | − | 0.896384i | \(-0.353815\pi\) | ||||
0.443279 | + | 0.896384i | \(0.353815\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 26.1668 | 0.968478 | ||||||||
\(731\) | 18.7140 | 0.692161 | ||||||||
\(732\) | 11.3695 | 0.420227 | ||||||||
\(733\) | −33.1800 | −1.22553 | −0.612766 | − | 0.790265i | \(-0.709943\pi\) | ||||
−0.612766 | + | 0.790265i | \(0.709943\pi\) | |||||||
\(734\) | −35.0624 | −1.29418 | ||||||||
\(735\) | 3.98491 | 0.146986 | ||||||||
\(736\) | 72.3023 | 2.66510 | ||||||||
\(737\) | −41.9632 | −1.54573 | ||||||||
\(738\) | −14.2611 | −0.524957 | ||||||||
\(739\) | −1.27739 | −0.0469894 | −0.0234947 | − | 0.999724i | \(-0.507479\pi\) | ||||
−0.0234947 | + | 0.999724i | \(0.507479\pi\) | |||||||
\(740\) | −34.0575 | −1.25198 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 22.4950 | 0.825816 | ||||||||
\(743\) | 39.2019 | 1.43818 | 0.719088 | − | 0.694919i | \(-0.244560\pi\) | ||||
0.719088 | + | 0.694919i | \(0.244560\pi\) | |||||||
\(744\) | 3.79080 | 0.138978 | ||||||||
\(745\) | −57.8669 | −2.12008 | ||||||||
\(746\) | 35.4216 | 1.29688 | ||||||||
\(747\) | 1.47510 | 0.0539712 | ||||||||
\(748\) | 14.7664 | 0.539914 | ||||||||
\(749\) | −5.83503 | −0.213207 | ||||||||
\(750\) | 48.5424 | 1.77252 | ||||||||
\(751\) | −4.89411 | −0.178589 | −0.0892943 | − | 0.996005i | \(-0.528461\pi\) | ||||
−0.0892943 | + | 0.996005i | \(0.528461\pi\) | |||||||
\(752\) | 8.11297 | 0.295850 | ||||||||
\(753\) | 2.93895 | 0.107101 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −40.6669 | −1.48002 | ||||||||
\(756\) | −2.29258 | −0.0833802 | ||||||||
\(757\) | −38.0701 | −1.38368 | −0.691841 | − | 0.722050i | \(-0.743200\pi\) | ||||
−0.691841 | + | 0.722050i | \(0.743200\pi\) | |||||||
\(758\) | 19.0292 | 0.691171 | ||||||||
\(759\) | −23.3119 | −0.846169 | ||||||||
\(760\) | 12.8242 | 0.465182 | ||||||||
\(761\) | 31.9088 | 1.15669 | 0.578346 | − | 0.815792i | \(-0.303698\pi\) | ||||
0.578346 | + | 0.815792i | \(0.303698\pi\) | |||||||
\(762\) | −6.74288 | −0.244269 | ||||||||
\(763\) | −14.4487 | −0.523076 | ||||||||
\(764\) | 6.36071 | 0.230122 | ||||||||
\(765\) | 9.81567 | 0.354886 | ||||||||
\(766\) | −80.6070 | −2.91245 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 10.3490 | 0.373436 | ||||||||
\(769\) | −20.1643 | −0.727143 | −0.363571 | − | 0.931566i | \(-0.618443\pi\) | ||||
−0.363571 | + | 0.931566i | \(0.618443\pi\) | |||||||
\(770\) | −21.5888 | −0.778006 | ||||||||
\(771\) | 5.57830 | 0.200897 | ||||||||
\(772\) | −38.1534 | −1.37317 | ||||||||
\(773\) | −27.6159 | −0.993274 | −0.496637 | − | 0.867958i | \(-0.665432\pi\) | ||||
−0.496637 | + | 0.867958i | \(0.665432\pi\) | |||||||
\(774\) | 15.7407 | 0.565787 | ||||||||
\(775\) | 68.0366 | 2.44395 | ||||||||
\(776\) | −2.74519 | −0.0985465 | ||||||||
\(777\) | 3.72795 | 0.133739 | ||||||||
\(778\) | 50.3843 | 1.80636 | ||||||||
\(779\) | −36.5430 | −1.30929 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.3534 | 1.47974 | ||||||||
\(782\) | −45.4976 | −1.62699 | ||||||||
\(783\) | −3.55037 | −0.126880 | ||||||||
\(784\) | −3.32925 | −0.118902 | ||||||||
\(785\) | 23.3846 | 0.834631 | ||||||||
\(786\) | 2.61903 | 0.0934176 | ||||||||
\(787\) | −14.5494 | −0.518631 | −0.259315 | − | 0.965793i | \(-0.583497\pi\) | ||||
−0.259315 | + | 0.965793i | \(0.583497\pi\) | |||||||
\(788\) | −0.376741 | −0.0134208 | ||||||||
\(789\) | 21.2240 | 0.755596 | ||||||||
\(790\) | −42.5745 | −1.51473 | ||||||||
\(791\) | 9.37283 | 0.333259 | ||||||||
\(792\) | 1.58507 | 0.0563231 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −80.9720 | −2.87359 | ||||||||
\(795\) | −43.2658 | −1.53448 | ||||||||
\(796\) | 3.97003 | 0.140714 | ||||||||
\(797\) | −12.9466 | −0.458592 | −0.229296 | − | 0.973357i | \(-0.573642\pi\) | ||||
−0.229296 | + | 0.973357i | \(0.573642\pi\) | |||||||
\(798\) | −10.9995 | −0.389377 | ||||||||
\(799\) | −6.00254 | −0.212355 | ||||||||
\(800\) | −88.2337 | −3.11953 | ||||||||
\(801\) | 13.7404 | 0.485494 | ||||||||
\(802\) | 57.9564 | 2.04651 | ||||||||
\(803\) | 8.28750 | 0.292459 | ||||||||
\(804\) | −36.7910 | −1.29752 | ||||||||
\(805\) | 35.5260 | 1.25213 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.92240 | −0.0676717 | ||||||||
\(808\) | −1.60905 | −0.0566060 | ||||||||
\(809\) | −9.93693 | −0.349364 | −0.174682 | − | 0.984625i | \(-0.555890\pi\) | ||||
−0.174682 | + | 0.984625i | \(0.555890\pi\) | |||||||
\(810\) | 8.25616 | 0.290092 | ||||||||
\(811\) | −21.6049 | −0.758650 | −0.379325 | − | 0.925263i | \(-0.623844\pi\) | ||||
−0.379325 | + | 0.925263i | \(0.623844\pi\) | |||||||
\(812\) | 8.13949 | 0.285640 | ||||||||
\(813\) | 2.56202 | 0.0898541 | ||||||||
\(814\) | −20.1966 | −0.707892 | ||||||||
\(815\) | −2.78018 | −0.0973854 | ||||||||
\(816\) | −8.20063 | −0.287079 | ||||||||
\(817\) | 40.3345 | 1.41113 | ||||||||
\(818\) | 1.15717 | 0.0404596 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −62.8833 | −2.19598 | ||||||||
\(821\) | −7.37066 | −0.257238 | −0.128619 | − | 0.991694i | \(-0.541054\pi\) | ||||
−0.128619 | + | 0.991694i | \(0.541054\pi\) | |||||||
\(822\) | −33.3531 | −1.16332 | ||||||||
\(823\) | 39.7759 | 1.38650 | 0.693250 | − | 0.720697i | \(-0.256178\pi\) | ||||
0.693250 | + | 0.720697i | \(0.256178\pi\) | |||||||
\(824\) | −6.63241 | −0.231051 | ||||||||
\(825\) | 28.4486 | 0.990452 | ||||||||
\(826\) | 1.95766 | 0.0681158 | ||||||||
\(827\) | −2.35530 | −0.0819019 | −0.0409510 | − | 0.999161i | \(-0.513039\pi\) | ||||
−0.0409510 | + | 0.999161i | \(0.513039\pi\) | |||||||
\(828\) | −20.4386 | −0.710292 | ||||||||
\(829\) | −0.942767 | −0.0327436 | −0.0163718 | − | 0.999866i | \(-0.505212\pi\) | ||||
−0.0163718 | + | 0.999866i | \(0.505212\pi\) | |||||||
\(830\) | 12.1787 | 0.422728 | ||||||||
\(831\) | −9.31382 | −0.323093 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.46321 | 0.0853451 | ||||||||
\(834\) | 43.1269 | 1.49336 | ||||||||
\(835\) | −100.029 | −3.46165 | ||||||||
\(836\) | 31.8263 | 1.10074 | ||||||||
\(837\) | 6.25363 | 0.216157 | ||||||||
\(838\) | −18.1192 | −0.625918 | ||||||||
\(839\) | −22.0266 | −0.760442 | −0.380221 | − | 0.924896i | \(-0.624152\pi\) | ||||
−0.380221 | + | 0.924896i | \(0.624152\pi\) | |||||||
\(840\) | −2.41556 | −0.0833447 | ||||||||
\(841\) | −16.3949 | −0.565341 | ||||||||
\(842\) | 52.2007 | 1.79896 | ||||||||
\(843\) | 14.0421 | 0.483636 | ||||||||
\(844\) | 33.9037 | 1.16701 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.04886 | −0.173583 | ||||||||
\(847\) | 4.16245 | 0.143023 | ||||||||
\(848\) | 36.1470 | 1.24129 | ||||||||
\(849\) | 12.6395 | 0.433787 | ||||||||
\(850\) | 55.5227 | 1.90441 | ||||||||
\(851\) | 33.2352 | 1.13929 | ||||||||
\(852\) | 36.2564 | 1.24212 | ||||||||
\(853\) | 25.5160 | 0.873652 | 0.436826 | − | 0.899546i | \(-0.356103\pi\) | ||||
0.436826 | + | 0.899546i | \(0.356103\pi\) | |||||||
\(854\) | −10.2748 | −0.351598 | ||||||||
\(855\) | 21.1559 | 0.723516 | ||||||||
\(856\) | 3.53706 | 0.120894 | ||||||||
\(857\) | 11.1140 | 0.379646 | 0.189823 | − | 0.981818i | \(-0.439209\pi\) | ||||
0.189823 | + | 0.981818i | \(0.439209\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.03548 | 0.274167 | 0.137083 | − | 0.990560i | \(-0.456227\pi\) | ||||
0.137083 | + | 0.990560i | \(0.456227\pi\) | |||||||
\(860\) | 69.4076 | 2.36678 | ||||||||
\(861\) | 6.88324 | 0.234580 | ||||||||
\(862\) | 2.45402 | 0.0835841 | ||||||||
\(863\) | −3.40081 | −0.115765 | −0.0578825 | − | 0.998323i | \(-0.518435\pi\) | ||||
−0.0578825 | + | 0.998323i | \(0.518435\pi\) | |||||||
\(864\) | −8.11006 | −0.275910 | ||||||||
\(865\) | 20.9863 | 0.713556 | ||||||||
\(866\) | −17.5713 | −0.597098 | ||||||||
\(867\) | −10.9326 | −0.371291 | ||||||||
\(868\) | −14.3369 | −0.486627 | ||||||||
\(869\) | −13.4841 | −0.457417 | ||||||||
\(870\) | −29.3124 | −0.993783 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.75843 | 0.296598 | ||||||||
\(873\) | −4.52869 | −0.153273 | ||||||||
\(874\) | −98.0616 | −3.31698 | ||||||||
\(875\) | −23.4294 | −0.792059 | ||||||||
\(876\) | 7.26603 | 0.245496 | ||||||||
\(877\) | 22.1250 | 0.747110 | 0.373555 | − | 0.927608i | \(-0.378139\pi\) | ||||
0.373555 | + | 0.927608i | \(0.378139\pi\) | |||||||
\(878\) | 67.4755 | 2.27719 | ||||||||
\(879\) | −22.0692 | −0.744375 | ||||||||
\(880\) | −34.6908 | −1.16943 | ||||||||
\(881\) | 24.5254 | 0.826281 | 0.413141 | − | 0.910667i | \(-0.364432\pi\) | ||||
0.413141 | + | 0.910667i | \(0.364432\pi\) | |||||||
\(882\) | 2.07185 | 0.0697629 | ||||||||
\(883\) | −3.60395 | −0.121282 | −0.0606412 | − | 0.998160i | \(-0.519315\pi\) | ||||
−0.0606412 | + | 0.998160i | \(0.519315\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.76529 | −0.126569 | ||||||||
\(886\) | 48.4293 | 1.62701 | ||||||||
\(887\) | 28.8486 | 0.968642 | 0.484321 | − | 0.874890i | \(-0.339067\pi\) | ||||
0.484321 | + | 0.874890i | \(0.339067\pi\) | |||||||
\(888\) | −2.25979 | −0.0758337 | ||||||||
\(889\) | 3.25452 | 0.109153 | ||||||||
\(890\) | 113.443 | 3.80262 | ||||||||
\(891\) | 2.61487 | 0.0876015 | ||||||||
\(892\) | 38.2729 | 1.28147 | ||||||||
\(893\) | −12.9374 | −0.432933 | ||||||||
\(894\) | −30.0864 | −1.00624 | ||||||||
\(895\) | 45.6089 | 1.52454 | ||||||||
\(896\) | 4.79752 | 0.160274 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −46.6779 | −1.55766 | ||||||||
\(899\) | −22.2027 | −0.740502 | ||||||||
\(900\) | 24.9422 | 0.831406 | ||||||||
\(901\) | −26.7441 | −0.890974 | ||||||||
\(902\) | −37.2908 | −1.24165 | ||||||||
\(903\) | −7.59739 | −0.252825 | ||||||||
\(904\) | −5.68159 | −0.188967 | ||||||||
\(905\) | −52.7040 | −1.75194 | ||||||||
\(906\) | −21.1437 | −0.702453 | ||||||||
\(907\) | −5.15964 | −0.171323 | −0.0856615 | − | 0.996324i | \(-0.527300\pi\) | ||||
−0.0856615 | + | 0.996324i | \(0.527300\pi\) | |||||||
\(908\) | −34.9308 | −1.15922 | ||||||||
\(909\) | −2.65442 | −0.0880415 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.1096 | 1.26263 | 0.631313 | − | 0.775528i | \(-0.282516\pi\) | ||||
0.631313 | + | 0.775528i | \(0.282516\pi\) | |||||||
\(912\) | −17.6749 | −0.585276 | ||||||||
\(913\) | 3.85720 | 0.127655 | ||||||||
\(914\) | 30.2036 | 0.999046 | ||||||||
\(915\) | 19.7622 | 0.653317 | ||||||||
\(916\) | −44.1783 | −1.45969 | ||||||||
\(917\) | −1.26410 | −0.0417442 | ||||||||
\(918\) | 5.10341 | 0.168438 | ||||||||
\(919\) | 2.13480 | 0.0704205 | 0.0352103 | − | 0.999380i | \(-0.488790\pi\) | ||||
0.0352103 | + | 0.999380i | \(0.488790\pi\) | |||||||
\(920\) | −21.5350 | −0.709989 | ||||||||
\(921\) | 3.30193 | 0.108802 | ||||||||
\(922\) | −54.0639 | −1.78050 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −5.99479 | −0.197214 | ||||||||
\(925\) | −40.5583 | −1.33355 | ||||||||
\(926\) | 53.0782 | 1.74426 | ||||||||
\(927\) | −10.9414 | −0.359362 | ||||||||
\(928\) | 28.7937 | 0.945200 | ||||||||
\(929\) | 40.8343 | 1.33973 | 0.669865 | − | 0.742483i | \(-0.266352\pi\) | ||||
0.669865 | + | 0.742483i | \(0.266352\pi\) | |||||||
\(930\) | 51.6310 | 1.69305 | ||||||||
\(931\) | 5.30899 | 0.173995 | ||||||||
\(932\) | 15.0924 | 0.494369 | ||||||||
\(933\) | 16.1831 | 0.529810 | ||||||||
\(934\) | 69.0342 | 2.25887 | ||||||||
\(935\) | 25.6667 | 0.839391 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.9925 | 1.50251 | 0.751255 | − | 0.660012i | \(-0.229449\pi\) | ||||
0.751255 | + | 0.660012i | \(0.229449\pi\) | |||||||
\(938\) | 33.2489 | 1.08561 | ||||||||
\(939\) | 2.50394 | 0.0817130 | ||||||||
\(940\) | −22.2626 | −0.726128 | ||||||||
\(941\) | 9.55992 | 0.311645 | 0.155822 | − | 0.987785i | \(-0.450197\pi\) | ||||
0.155822 | + | 0.987785i | \(0.450197\pi\) | |||||||
\(942\) | 12.1582 | 0.396136 | ||||||||
\(943\) | 61.3650 | 1.99832 | ||||||||
\(944\) | 3.14575 | 0.102386 | ||||||||
\(945\) | −3.98491 | −0.129629 | ||||||||
\(946\) | 41.1599 | 1.33822 | ||||||||
\(947\) | −30.1550 | −0.979905 | −0.489952 | − | 0.871749i | \(-0.662986\pi\) | ||||
−0.489952 | + | 0.871749i | \(0.662986\pi\) | |||||||
\(948\) | −11.8221 | −0.383965 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 119.669 | 3.88257 | ||||||||
\(951\) | 24.1074 | 0.781738 | ||||||||
\(952\) | −1.49314 | −0.0483929 | ||||||||
\(953\) | 8.11627 | 0.262912 | 0.131456 | − | 0.991322i | \(-0.458035\pi\) | ||||
0.131456 | + | 0.991322i | \(0.458035\pi\) | |||||||
\(954\) | −22.4950 | −0.728301 | ||||||||
\(955\) | 11.0561 | 0.357766 | ||||||||
\(956\) | −62.0160 | −2.00574 | ||||||||
\(957\) | −9.28376 | −0.300101 | ||||||||
\(958\) | 12.6190 | 0.407702 | ||||||||
\(959\) | 16.0982 | 0.519838 | ||||||||
\(960\) | −40.4244 | −1.30469 | ||||||||
\(961\) | 8.10792 | 0.261546 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.83503 | 0.188031 | ||||||||
\(964\) | 56.0925 | 1.80662 | ||||||||
\(965\) | −66.3176 | −2.13484 | ||||||||
\(966\) | 18.4709 | 0.594290 | ||||||||
\(967\) | 32.9173 | 1.05855 | 0.529274 | − | 0.848451i | \(-0.322464\pi\) | ||||
0.529274 | + | 0.848451i | \(0.322464\pi\) | |||||||
\(968\) | −2.52318 | −0.0810980 | ||||||||
\(969\) | 13.0772 | 0.420099 | ||||||||
\(970\) | −37.3896 | −1.20051 | ||||||||
\(971\) | 21.6879 | 0.695997 | 0.347999 | − | 0.937495i | \(-0.386861\pi\) | ||||
0.347999 | + | 0.937495i | \(0.386861\pi\) | |||||||
\(972\) | 2.29258 | 0.0735344 | ||||||||
\(973\) | −20.8156 | −0.667317 | ||||||||
\(974\) | 60.4529 | 1.93704 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.5106 | −0.528490 | ||||||||
\(977\) | 13.2955 | 0.425360 | 0.212680 | − | 0.977122i | \(-0.431781\pi\) | ||||
0.212680 | + | 0.977122i | \(0.431781\pi\) | |||||||
\(978\) | −1.44548 | −0.0462214 | ||||||||
\(979\) | 35.9294 | 1.14831 | ||||||||
\(980\) | 9.13572 | 0.291830 | ||||||||
\(981\) | 14.4487 | 0.461310 | ||||||||
\(982\) | 64.7650 | 2.06673 | ||||||||
\(983\) | 53.4883 | 1.70601 | 0.853006 | − | 0.521902i | \(-0.174777\pi\) | ||||
0.853006 | + | 0.521902i | \(0.174777\pi\) | |||||||
\(984\) | −4.17245 | −0.133013 | ||||||||
\(985\) | −0.654844 | −0.0208651 | ||||||||
\(986\) | −18.1190 | −0.577026 | ||||||||
\(987\) | 2.43688 | 0.0775667 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −67.7318 | −2.15374 | ||||||||
\(990\) | 21.5888 | 0.686137 | ||||||||
\(991\) | −23.0550 | −0.732367 | −0.366183 | − | 0.930543i | \(-0.619336\pi\) | ||||
−0.366183 | + | 0.930543i | \(0.619336\pi\) | |||||||
\(992\) | −50.7173 | −1.61028 | ||||||||
\(993\) | −5.36044 | −0.170109 | ||||||||
\(994\) | −32.7657 | −1.03927 | ||||||||
\(995\) | 6.90062 | 0.218764 | ||||||||
\(996\) | 3.38178 | 0.107156 | ||||||||
\(997\) | −12.6450 | −0.400470 | −0.200235 | − | 0.979748i | \(-0.564171\pi\) | ||||
−0.200235 | + | 0.979748i | \(0.564171\pi\) | |||||||
\(998\) | 26.0648 | 0.825066 | ||||||||
\(999\) | −3.72795 | −0.117947 |
(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 | 3549.2.a.bh.1.12 | yes | 15 | |
13.12 | even | 2 | 3549.2.a.bg.1.4 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.bg.1.4 | ✓ | 15 | 13.12 | even | 2 | ||
3549.2.a.bh.1.12 | yes | 15 | 1.1 | even | 1 | trivial |