Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(1,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1183.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.7674048.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.38595\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.38595 | −0.980016 | −0.490008 | − | 0.871718i | \(-0.663006\pi\) | ||||
−0.490008 | + | 0.871718i | \(0.663006\pi\) | |||||||
\(3\) | −2.82577 | −1.63146 | −0.815731 | − | 0.578432i | \(-0.803665\pi\) | ||||
−0.815731 | + | 0.578432i | \(0.803665\pi\) | |||||||
\(4\) | −0.0791355 | −0.0395678 | ||||||||
\(5\) | −0.518957 | −0.232085 | −0.116042 | − | 0.993244i | \(-0.537021\pi\) | ||||
−0.116042 | + | 0.993244i | \(0.537021\pi\) | |||||||
\(6\) | 3.91639 | 1.59886 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.88158 | 1.01879 | ||||||||
\(9\) | 4.98500 | 1.66167 | ||||||||
\(10\) | 0.719250 | 0.227447 | ||||||||
\(11\) | −1.62416 | −0.489702 | −0.244851 | − | 0.969561i | \(-0.578739\pi\) | ||||
−0.244851 | + | 0.969561i | \(0.578739\pi\) | |||||||
\(12\) | 0.223619 | 0.0645533 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.38595 | 0.370411 | ||||||||
\(15\) | 1.46646 | 0.378637 | ||||||||
\(16\) | −3.83547 | −0.958867 | ||||||||
\(17\) | 1.94825 | 0.472521 | 0.236260 | − | 0.971690i | \(-0.424078\pi\) | ||||
0.236260 | + | 0.971690i | \(0.424078\pi\) | |||||||
\(18\) | −6.90897 | −1.62846 | ||||||||
\(19\) | −2.49115 | −0.571510 | −0.285755 | − | 0.958303i | \(-0.592244\pi\) | ||||
−0.285755 | + | 0.958303i | \(0.592244\pi\) | |||||||
\(20\) | 0.0410679 | 0.00918307 | ||||||||
\(21\) | 2.82577 | 0.616634 | ||||||||
\(22\) | 2.25101 | 0.479916 | ||||||||
\(23\) | −9.14058 | −1.90594 | −0.952971 | − | 0.303060i | \(-0.901992\pi\) | ||||
−0.952971 | + | 0.303060i | \(0.901992\pi\) | |||||||
\(24\) | −8.14270 | −1.66212 | ||||||||
\(25\) | −4.73068 | −0.946137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.60916 | −1.07948 | ||||||||
\(28\) | 0.0791355 | 0.0149552 | ||||||||
\(29\) | −5.22996 | −0.971179 | −0.485589 | − | 0.874187i | \(-0.661395\pi\) | ||||
−0.485589 | + | 0.874187i | \(0.661395\pi\) | |||||||
\(30\) | −2.03244 | −0.371071 | ||||||||
\(31\) | −5.79391 | −1.04062 | −0.520308 | − | 0.853978i | \(-0.674183\pi\) | ||||
−0.520308 | + | 0.853978i | \(0.674183\pi\) | |||||||
\(32\) | −0.447392 | −0.0790885 | ||||||||
\(33\) | 4.58951 | 0.798931 | ||||||||
\(34\) | −2.70019 | −0.463078 | ||||||||
\(35\) | 0.518957 | 0.0877197 | ||||||||
\(36\) | −0.394491 | −0.0657484 | ||||||||
\(37\) | 10.2293 | 1.68168 | 0.840840 | − | 0.541284i | \(-0.182062\pi\) | ||||
0.840840 | + | 0.541284i | \(0.182062\pi\) | |||||||
\(38\) | 3.45262 | 0.560089 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.49542 | −0.236446 | ||||||||
\(41\) | 4.20903 | 0.657340 | 0.328670 | − | 0.944445i | \(-0.393400\pi\) | ||||
0.328670 | + | 0.944445i | \(0.393400\pi\) | |||||||
\(42\) | −3.91639 | −0.604312 | ||||||||
\(43\) | −0.997311 | −0.152088 | −0.0760442 | − | 0.997104i | \(-0.524229\pi\) | ||||
−0.0760442 | + | 0.997104i | \(0.524229\pi\) | |||||||
\(44\) | 0.128529 | 0.0193764 | ||||||||
\(45\) | −2.58700 | −0.385647 | ||||||||
\(46\) | 12.6684 | 1.86786 | ||||||||
\(47\) | 4.51725 | 0.658909 | 0.329455 | − | 0.944171i | \(-0.393135\pi\) | ||||
0.329455 | + | 0.944171i | \(0.393135\pi\) | |||||||
\(48\) | 10.8382 | 1.56435 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 6.55650 | 0.927230 | ||||||||
\(51\) | −5.50532 | −0.770899 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.89651 | −1.22203 | −0.611015 | − | 0.791619i | \(-0.709238\pi\) | ||||
−0.611015 | + | 0.791619i | \(0.709238\pi\) | |||||||
\(54\) | 7.77403 | 1.05791 | ||||||||
\(55\) | 0.842869 | 0.113652 | ||||||||
\(56\) | −2.88158 | −0.385068 | ||||||||
\(57\) | 7.03944 | 0.932397 | ||||||||
\(58\) | 7.24847 | 0.951771 | ||||||||
\(59\) | −6.20526 | −0.807856 | −0.403928 | − | 0.914791i | \(-0.632355\pi\) | ||||
−0.403928 | + | 0.914791i | \(0.632355\pi\) | |||||||
\(60\) | −0.116049 | −0.0149818 | ||||||||
\(61\) | −13.4707 | −1.72475 | −0.862375 | − | 0.506270i | \(-0.831024\pi\) | ||||
−0.862375 | + | 0.506270i | \(0.831024\pi\) | |||||||
\(62\) | 8.03008 | 1.01982 | ||||||||
\(63\) | −4.98500 | −0.628051 | ||||||||
\(64\) | 8.29100 | 1.03637 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.36084 | −0.782965 | ||||||||
\(67\) | −8.37266 | −1.02288 | −0.511442 | − | 0.859318i | \(-0.670888\pi\) | ||||
−0.511442 | + | 0.859318i | \(0.670888\pi\) | |||||||
\(68\) | −0.154176 | −0.0186966 | ||||||||
\(69\) | 25.8292 | 3.10947 | ||||||||
\(70\) | −0.719250 | −0.0859668 | ||||||||
\(71\) | 5.19809 | 0.616900 | 0.308450 | − | 0.951241i | \(-0.400190\pi\) | ||||
0.308450 | + | 0.951241i | \(0.400190\pi\) | |||||||
\(72\) | 14.3647 | 1.69289 | ||||||||
\(73\) | 11.8395 | 1.38571 | 0.692856 | − | 0.721076i | \(-0.256352\pi\) | ||||
0.692856 | + | 0.721076i | \(0.256352\pi\) | |||||||
\(74\) | −14.1773 | −1.64807 | ||||||||
\(75\) | 13.3678 | 1.54359 | ||||||||
\(76\) | 0.197139 | 0.0226134 | ||||||||
\(77\) | 1.62416 | 0.185090 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.982310 | 0.110518 | 0.0552592 | − | 0.998472i | \(-0.482401\pi\) | ||||
0.0552592 | + | 0.998472i | \(0.482401\pi\) | |||||||
\(80\) | 1.99044 | 0.222538 | ||||||||
\(81\) | 0.895217 | 0.0994686 | ||||||||
\(82\) | −5.83352 | −0.644204 | ||||||||
\(83\) | 8.91851 | 0.978934 | 0.489467 | − | 0.872022i | \(-0.337191\pi\) | ||||
0.489467 | + | 0.872022i | \(0.337191\pi\) | |||||||
\(84\) | −0.223619 | −0.0243989 | ||||||||
\(85\) | −1.01106 | −0.109665 | ||||||||
\(86\) | 1.38223 | 0.149049 | ||||||||
\(87\) | 14.7787 | 1.58444 | ||||||||
\(88\) | −4.68015 | −0.498906 | ||||||||
\(89\) | 12.0190 | 1.27401 | 0.637005 | − | 0.770860i | \(-0.280173\pi\) | ||||
0.637005 | + | 0.770860i | \(0.280173\pi\) | |||||||
\(90\) | 3.58546 | 0.377941 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.723345 | 0.0754139 | ||||||||
\(93\) | 16.3723 | 1.69773 | ||||||||
\(94\) | −6.26070 | −0.645742 | ||||||||
\(95\) | 1.29280 | 0.132639 | ||||||||
\(96\) | 1.26423 | 0.129030 | ||||||||
\(97\) | −4.42228 | −0.449015 | −0.224507 | − | 0.974472i | \(-0.572077\pi\) | ||||
−0.224507 | + | 0.974472i | \(0.572077\pi\) | |||||||
\(98\) | −1.38595 | −0.140002 | ||||||||
\(99\) | −8.09643 | −0.813722 | ||||||||
\(100\) | 0.374365 | 0.0374365 | ||||||||
\(101\) | 18.3026 | 1.82118 | 0.910591 | − | 0.413309i | \(-0.135627\pi\) | ||||
0.910591 | + | 0.413309i | \(0.135627\pi\) | |||||||
\(102\) | 7.63012 | 0.755494 | ||||||||
\(103\) | 5.02046 | 0.494680 | 0.247340 | − | 0.968929i | \(-0.420444\pi\) | ||||
0.247340 | + | 0.968929i | \(0.420444\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.46646 | −0.143111 | ||||||||
\(106\) | 12.3301 | 1.19761 | ||||||||
\(107\) | 6.14456 | 0.594017 | 0.297008 | − | 0.954875i | \(-0.404011\pi\) | ||||
0.297008 | + | 0.954875i | \(0.404011\pi\) | |||||||
\(108\) | 0.443884 | 0.0427127 | ||||||||
\(109\) | −11.8962 | −1.13945 | −0.569727 | − | 0.821834i | \(-0.692951\pi\) | ||||
−0.569727 | + | 0.821834i | \(0.692951\pi\) | |||||||
\(110\) | −1.16818 | −0.111381 | ||||||||
\(111\) | −28.9056 | −2.74359 | ||||||||
\(112\) | 3.83547 | 0.362418 | ||||||||
\(113\) | 3.55612 | 0.334532 | 0.167266 | − | 0.985912i | \(-0.446506\pi\) | ||||
0.167266 | + | 0.985912i | \(0.446506\pi\) | |||||||
\(114\) | −9.75633 | −0.913764 | ||||||||
\(115\) | 4.74357 | 0.442340 | ||||||||
\(116\) | 0.413875 | 0.0384274 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.60020 | 0.791713 | ||||||||
\(119\) | −1.94825 | −0.178596 | ||||||||
\(120\) | 4.22571 | 0.385753 | ||||||||
\(121\) | −8.36211 | −0.760191 | ||||||||
\(122\) | 18.6698 | 1.69028 | ||||||||
\(123\) | −11.8938 | −1.07243 | ||||||||
\(124\) | 0.458504 | 0.0411749 | ||||||||
\(125\) | 5.04981 | 0.451668 | ||||||||
\(126\) | 6.90897 | 0.615500 | ||||||||
\(127\) | −1.42350 | −0.126315 | −0.0631575 | − | 0.998004i | \(-0.520117\pi\) | ||||
−0.0631575 | + | 0.998004i | \(0.520117\pi\) | |||||||
\(128\) | −10.5961 | −0.936576 | ||||||||
\(129\) | 2.81818 | 0.248127 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.67374 | 0.757828 | 0.378914 | − | 0.925432i | \(-0.376298\pi\) | ||||
0.378914 | + | 0.925432i | \(0.376298\pi\) | |||||||
\(132\) | −0.363193 | −0.0316119 | ||||||||
\(133\) | 2.49115 | 0.216011 | ||||||||
\(134\) | 11.6041 | 1.00244 | ||||||||
\(135\) | 2.91091 | 0.250531 | ||||||||
\(136\) | 5.61405 | 0.481401 | ||||||||
\(137\) | 8.51784 | 0.727728 | 0.363864 | − | 0.931452i | \(-0.381457\pi\) | ||||
0.363864 | + | 0.931452i | \(0.381457\pi\) | |||||||
\(138\) | −35.7981 | −3.04733 | ||||||||
\(139\) | −5.03844 | −0.427355 | −0.213677 | − | 0.976904i | \(-0.568544\pi\) | ||||
−0.213677 | + | 0.976904i | \(0.568544\pi\) | |||||||
\(140\) | −0.0410679 | −0.00347087 | ||||||||
\(141\) | −12.7647 | −1.07499 | ||||||||
\(142\) | −7.20431 | −0.604572 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −19.1198 | −1.59332 | ||||||||
\(145\) | 2.71412 | 0.225396 | ||||||||
\(146\) | −16.4090 | −1.35802 | ||||||||
\(147\) | −2.82577 | −0.233066 | ||||||||
\(148\) | −0.809498 | −0.0665403 | ||||||||
\(149\) | −3.36490 | −0.275663 | −0.137832 | − | 0.990456i | \(-0.544013\pi\) | ||||
−0.137832 | + | 0.990456i | \(0.544013\pi\) | |||||||
\(150\) | −18.5272 | −1.51274 | ||||||||
\(151\) | −12.6566 | −1.02998 | −0.514991 | − | 0.857196i | \(-0.672205\pi\) | ||||
−0.514991 | + | 0.857196i | \(0.672205\pi\) | |||||||
\(152\) | −7.17847 | −0.582251 | ||||||||
\(153\) | 9.71204 | 0.785172 | ||||||||
\(154\) | −2.25101 | −0.181391 | ||||||||
\(155\) | 3.00679 | 0.241511 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3691 | 0.827547 | 0.413773 | − | 0.910380i | \(-0.364211\pi\) | ||||
0.413773 | + | 0.910380i | \(0.364211\pi\) | |||||||
\(158\) | −1.36143 | −0.108310 | ||||||||
\(159\) | 25.1395 | 1.99369 | ||||||||
\(160\) | 0.232177 | 0.0183552 | ||||||||
\(161\) | 9.14058 | 0.720379 | ||||||||
\(162\) | −1.24073 | −0.0974808 | ||||||||
\(163\) | 15.7534 | 1.23390 | 0.616950 | − | 0.787002i | \(-0.288368\pi\) | ||||
0.616950 | + | 0.787002i | \(0.288368\pi\) | |||||||
\(164\) | −0.333084 | −0.0260095 | ||||||||
\(165\) | −2.38176 | −0.185420 | ||||||||
\(166\) | −12.3606 | −0.959371 | ||||||||
\(167\) | 16.3986 | 1.26896 | 0.634481 | − | 0.772939i | \(-0.281214\pi\) | ||||
0.634481 | + | 0.772939i | \(0.281214\pi\) | |||||||
\(168\) | 8.14270 | 0.628223 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.40128 | 0.107473 | ||||||||
\(171\) | −12.4184 | −0.949659 | ||||||||
\(172\) | 0.0789227 | 0.00601780 | ||||||||
\(173\) | −0.301355 | −0.0229116 | −0.0114558 | − | 0.999934i | \(-0.503647\pi\) | ||||
−0.0114558 | + | 0.999934i | \(0.503647\pi\) | |||||||
\(174\) | −20.4825 | −1.55278 | ||||||||
\(175\) | 4.73068 | 0.357606 | ||||||||
\(176\) | 6.22941 | 0.469559 | ||||||||
\(177\) | 17.5347 | 1.31799 | ||||||||
\(178\) | −16.6577 | −1.24855 | ||||||||
\(179\) | −9.81582 | −0.733669 | −0.366834 | − | 0.930286i | \(-0.619558\pi\) | ||||
−0.366834 | + | 0.930286i | \(0.619558\pi\) | |||||||
\(180\) | 0.204724 | 0.0152592 | ||||||||
\(181\) | −12.4320 | −0.924062 | −0.462031 | − | 0.886864i | \(-0.652879\pi\) | ||||
−0.462031 | + | 0.886864i | \(0.652879\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 38.0652 | 2.81386 | ||||||||
\(184\) | −26.3393 | −1.94176 | ||||||||
\(185\) | −5.30854 | −0.390292 | ||||||||
\(186\) | −22.6912 | −1.66380 | ||||||||
\(187\) | −3.16427 | −0.231395 | ||||||||
\(188\) | −0.357475 | −0.0260716 | ||||||||
\(189\) | 5.60916 | 0.408006 | ||||||||
\(190\) | −1.79176 | −0.129988 | ||||||||
\(191\) | −12.2469 | −0.886156 | −0.443078 | − | 0.896483i | \(-0.646114\pi\) | ||||
−0.443078 | + | 0.896483i | \(0.646114\pi\) | |||||||
\(192\) | −23.4285 | −1.69081 | ||||||||
\(193\) | 11.6338 | 0.837422 | 0.418711 | − | 0.908119i | \(-0.362482\pi\) | ||||
0.418711 | + | 0.908119i | \(0.362482\pi\) | |||||||
\(194\) | 6.12908 | 0.440042 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0791355 | −0.00565254 | ||||||||
\(197\) | −1.80114 | −0.128326 | −0.0641631 | − | 0.997939i | \(-0.520438\pi\) | ||||
−0.0641631 | + | 0.997939i | \(0.520438\pi\) | |||||||
\(198\) | 11.2213 | 0.797461 | ||||||||
\(199\) | 6.59313 | 0.467375 | 0.233687 | − | 0.972312i | \(-0.424921\pi\) | ||||
0.233687 | + | 0.972312i | \(0.424921\pi\) | |||||||
\(200\) | −13.6319 | −0.963918 | ||||||||
\(201\) | 23.6592 | 1.66879 | ||||||||
\(202\) | −25.3666 | −1.78479 | ||||||||
\(203\) | 5.22996 | 0.367071 | ||||||||
\(204\) | 0.435667 | 0.0305028 | ||||||||
\(205\) | −2.18431 | −0.152559 | ||||||||
\(206\) | −6.95811 | −0.484795 | ||||||||
\(207\) | −45.5658 | −3.16704 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.04603 | 0.279870 | ||||||||
\(210\) | 2.03244 | 0.140252 | ||||||||
\(211\) | 10.7199 | 0.737990 | 0.368995 | − | 0.929431i | \(-0.379702\pi\) | ||||
0.368995 | + | 0.929431i | \(0.379702\pi\) | |||||||
\(212\) | 0.704030 | 0.0483530 | ||||||||
\(213\) | −14.6886 | −1.00645 | ||||||||
\(214\) | −8.51607 | −0.582146 | ||||||||
\(215\) | 0.517562 | 0.0352974 | ||||||||
\(216\) | −16.1633 | −1.09977 | ||||||||
\(217\) | 5.79391 | 0.393316 | ||||||||
\(218\) | 16.4876 | 1.11668 | ||||||||
\(219\) | −33.4558 | −2.26074 | ||||||||
\(220\) | −0.0667009 | −0.00449697 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 40.0617 | 2.68877 | ||||||||
\(223\) | −12.8878 | −0.863034 | −0.431517 | − | 0.902105i | \(-0.642021\pi\) | ||||
−0.431517 | + | 0.902105i | \(0.642021\pi\) | |||||||
\(224\) | 0.447392 | 0.0298926 | ||||||||
\(225\) | −23.5825 | −1.57216 | ||||||||
\(226\) | −4.92862 | −0.327847 | ||||||||
\(227\) | 0.699155 | 0.0464045 | 0.0232023 | − | 0.999731i | \(-0.492614\pi\) | ||||
0.0232023 | + | 0.999731i | \(0.492614\pi\) | |||||||
\(228\) | −0.557070 | −0.0368929 | ||||||||
\(229\) | −18.2868 | −1.20843 | −0.604214 | − | 0.796822i | \(-0.706513\pi\) | ||||
−0.604214 | + | 0.796822i | \(0.706513\pi\) | |||||||
\(230\) | −6.57436 | −0.433501 | ||||||||
\(231\) | −4.58951 | −0.301967 | ||||||||
\(232\) | −15.0706 | −0.989431 | ||||||||
\(233\) | 26.7796 | 1.75439 | 0.877194 | − | 0.480137i | \(-0.159413\pi\) | ||||
0.877194 | + | 0.480137i | \(0.159413\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.34426 | −0.152923 | ||||||||
\(236\) | 0.491057 | 0.0319651 | ||||||||
\(237\) | −2.77579 | −0.180307 | ||||||||
\(238\) | 2.70019 | 0.175027 | ||||||||
\(239\) | 16.6177 | 1.07491 | 0.537454 | − | 0.843293i | \(-0.319386\pi\) | ||||
0.537454 | + | 0.843293i | \(0.319386\pi\) | |||||||
\(240\) | −5.62454 | −0.363063 | ||||||||
\(241\) | 17.4129 | 1.12166 | 0.560830 | − | 0.827931i | \(-0.310482\pi\) | ||||
0.560830 | + | 0.827931i | \(0.310482\pi\) | |||||||
\(242\) | 11.5895 | 0.745000 | ||||||||
\(243\) | 14.2978 | 0.917204 | ||||||||
\(244\) | 1.06601 | 0.0682445 | ||||||||
\(245\) | −0.518957 | −0.0331549 | ||||||||
\(246\) | 16.4842 | 1.05099 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −16.6956 | −1.06017 | ||||||||
\(249\) | −25.2017 | −1.59709 | ||||||||
\(250\) | −6.99879 | −0.442642 | ||||||||
\(251\) | −6.44982 | −0.407109 | −0.203554 | − | 0.979064i | \(-0.565249\pi\) | ||||
−0.203554 | + | 0.979064i | \(0.565249\pi\) | |||||||
\(252\) | 0.394491 | 0.0248506 | ||||||||
\(253\) | 14.8458 | 0.933345 | ||||||||
\(254\) | 1.97290 | 0.123791 | ||||||||
\(255\) | 2.85703 | 0.178914 | ||||||||
\(256\) | −1.89624 | −0.118515 | ||||||||
\(257\) | −3.67156 | −0.229025 | −0.114513 | − | 0.993422i | \(-0.536531\pi\) | ||||
−0.114513 | + | 0.993422i | \(0.536531\pi\) | |||||||
\(258\) | −3.90586 | −0.243168 | ||||||||
\(259\) | −10.2293 | −0.635615 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −26.0713 | −1.61377 | ||||||||
\(262\) | −12.0214 | −0.742684 | ||||||||
\(263\) | 18.3193 | 1.12961 | 0.564807 | − | 0.825223i | \(-0.308950\pi\) | ||||
0.564807 | + | 0.825223i | \(0.308950\pi\) | |||||||
\(264\) | 13.2250 | 0.813945 | ||||||||
\(265\) | 4.61690 | 0.283614 | ||||||||
\(266\) | −3.45262 | −0.211694 | ||||||||
\(267\) | −33.9629 | −2.07850 | ||||||||
\(268\) | 0.662575 | 0.0404732 | ||||||||
\(269\) | 27.5429 | 1.67932 | 0.839661 | − | 0.543111i | \(-0.182754\pi\) | ||||
0.839661 | + | 0.543111i | \(0.182754\pi\) | |||||||
\(270\) | −4.03439 | −0.245525 | ||||||||
\(271\) | −6.51923 | −0.396015 | −0.198007 | − | 0.980201i | \(-0.563447\pi\) | ||||
−0.198007 | + | 0.980201i | \(0.563447\pi\) | |||||||
\(272\) | −7.47246 | −0.453084 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.8053 | −0.713186 | ||||||||
\(275\) | 7.68338 | 0.463325 | ||||||||
\(276\) | −2.04401 | −0.123035 | ||||||||
\(277\) | 5.44186 | 0.326970 | 0.163485 | − | 0.986546i | \(-0.447727\pi\) | ||||
0.163485 | + | 0.986546i | \(0.447727\pi\) | |||||||
\(278\) | 6.98304 | 0.418815 | ||||||||
\(279\) | −28.8826 | −1.72916 | ||||||||
\(280\) | 1.49542 | 0.0893683 | ||||||||
\(281\) | −3.54237 | −0.211320 | −0.105660 | − | 0.994402i | \(-0.533696\pi\) | ||||
−0.105660 | + | 0.994402i | \(0.533696\pi\) | |||||||
\(282\) | 17.6913 | 1.05350 | ||||||||
\(283\) | −14.1391 | −0.840484 | −0.420242 | − | 0.907412i | \(-0.638055\pi\) | ||||
−0.420242 | + | 0.907412i | \(0.638055\pi\) | |||||||
\(284\) | −0.411354 | −0.0244094 | ||||||||
\(285\) | −3.65317 | −0.216395 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.20903 | −0.248451 | ||||||||
\(288\) | −2.23025 | −0.131419 | ||||||||
\(289\) | −13.2043 | −0.776724 | ||||||||
\(290\) | −3.76165 | −0.220891 | ||||||||
\(291\) | 12.4964 | 0.732551 | ||||||||
\(292\) | −0.936928 | −0.0548295 | ||||||||
\(293\) | −8.34931 | −0.487772 | −0.243886 | − | 0.969804i | \(-0.578422\pi\) | ||||
−0.243886 | + | 0.969804i | \(0.578422\pi\) | |||||||
\(294\) | 3.91639 | 0.228408 | ||||||||
\(295\) | 3.22027 | 0.187491 | ||||||||
\(296\) | 29.4765 | 1.71328 | ||||||||
\(297\) | 9.11017 | 0.528626 | ||||||||
\(298\) | 4.66359 | 0.270155 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.05787 | −0.0610762 | ||||||||
\(301\) | 0.997311 | 0.0574840 | ||||||||
\(302\) | 17.5415 | 1.00940 | ||||||||
\(303\) | −51.7192 | −2.97119 | ||||||||
\(304\) | 9.55474 | 0.548002 | ||||||||
\(305\) | 6.99073 | 0.400288 | ||||||||
\(306\) | −13.4604 | −0.769481 | ||||||||
\(307\) | 8.33362 | 0.475625 | 0.237813 | − | 0.971311i | \(-0.423570\pi\) | ||||
0.237813 | + | 0.971311i | \(0.423570\pi\) | |||||||
\(308\) | −0.128529 | −0.00732360 | ||||||||
\(309\) | −14.1867 | −0.807052 | ||||||||
\(310\) | −4.16727 | −0.236685 | ||||||||
\(311\) | −14.6227 | −0.829176 | −0.414588 | − | 0.910009i | \(-0.636074\pi\) | ||||
−0.414588 | + | 0.910009i | \(0.636074\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.1328 | 0.968404 | 0.484202 | − | 0.874956i | \(-0.339110\pi\) | ||||
0.484202 | + | 0.874956i | \(0.339110\pi\) | |||||||
\(314\) | −14.3711 | −0.811009 | ||||||||
\(315\) | 2.58700 | 0.145761 | ||||||||
\(316\) | −0.0777356 | −0.00437297 | ||||||||
\(317\) | 14.0000 | 0.786320 | 0.393160 | − | 0.919470i | \(-0.371382\pi\) | ||||
0.393160 | + | 0.919470i | \(0.371382\pi\) | |||||||
\(318\) | −34.8422 | −1.95385 | ||||||||
\(319\) | 8.49428 | 0.475589 | ||||||||
\(320\) | −4.30267 | −0.240527 | ||||||||
\(321\) | −17.3631 | −0.969116 | ||||||||
\(322\) | −12.6684 | −0.705983 | ||||||||
\(323\) | −4.85340 | −0.270050 | ||||||||
\(324\) | −0.0708435 | −0.00393575 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −21.8334 | −1.20924 | ||||||||
\(327\) | 33.6161 | 1.85897 | ||||||||
\(328\) | 12.1287 | 0.669694 | ||||||||
\(329\) | −4.51725 | −0.249044 | ||||||||
\(330\) | 3.30100 | 0.181714 | ||||||||
\(331\) | −6.91996 | −0.380355 | −0.190178 | − | 0.981750i | \(-0.560906\pi\) | ||||
−0.190178 | + | 0.981750i | \(0.560906\pi\) | |||||||
\(332\) | −0.705771 | −0.0387342 | ||||||||
\(333\) | 50.9928 | 2.79439 | ||||||||
\(334\) | −22.7277 | −1.24360 | ||||||||
\(335\) | 4.34505 | 0.237395 | ||||||||
\(336\) | −10.8382 | −0.591270 | ||||||||
\(337\) | −11.1559 | −0.607703 | −0.303852 | − | 0.952719i | \(-0.598273\pi\) | ||||
−0.303852 | + | 0.952719i | \(0.598273\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.0488 | −0.545776 | ||||||||
\(340\) | 0.0800108 | 0.00433919 | ||||||||
\(341\) | 9.41023 | 0.509593 | ||||||||
\(342\) | 17.2113 | 0.930682 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −2.87383 | −0.154947 | ||||||||
\(345\) | −13.4043 | −0.721661 | ||||||||
\(346\) | 0.417663 | 0.0224537 | ||||||||
\(347\) | −4.92511 | −0.264393 | −0.132197 | − | 0.991223i | \(-0.542203\pi\) | ||||
−0.132197 | + | 0.991223i | \(0.542203\pi\) | |||||||
\(348\) | −1.16952 | −0.0626928 | ||||||||
\(349\) | −1.52335 | −0.0815430 | −0.0407715 | − | 0.999168i | \(-0.512982\pi\) | ||||
−0.0407715 | + | 0.999168i | \(0.512982\pi\) | |||||||
\(350\) | −6.55650 | −0.350460 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.726636 | 0.0387298 | ||||||||
\(353\) | 17.9280 | 0.954212 | 0.477106 | − | 0.878846i | \(-0.341686\pi\) | ||||
0.477106 | + | 0.878846i | \(0.341686\pi\) | |||||||
\(354\) | −24.3022 | −1.29165 | ||||||||
\(355\) | −2.69759 | −0.143173 | ||||||||
\(356\) | −0.951129 | −0.0504097 | ||||||||
\(357\) | 5.50532 | 0.291373 | ||||||||
\(358\) | 13.6043 | 0.719007 | ||||||||
\(359\) | 20.0014 | 1.05563 | 0.527816 | − | 0.849359i | \(-0.323011\pi\) | ||||
0.527816 | + | 0.849359i | \(0.323011\pi\) | |||||||
\(360\) | −7.45466 | −0.392895 | ||||||||
\(361\) | −12.7941 | −0.673376 | ||||||||
\(362\) | 17.2301 | 0.905596 | ||||||||
\(363\) | 23.6294 | 1.24022 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.14421 | −0.321602 | ||||||||
\(366\) | −52.7566 | −2.75763 | ||||||||
\(367\) | 27.4157 | 1.43109 | 0.715544 | − | 0.698568i | \(-0.246179\pi\) | ||||
0.715544 | + | 0.698568i | \(0.246179\pi\) | |||||||
\(368\) | 35.0584 | 1.82754 | ||||||||
\(369\) | 20.9820 | 1.09228 | ||||||||
\(370\) | 7.35739 | 0.382492 | ||||||||
\(371\) | 8.89651 | 0.461884 | ||||||||
\(372\) | −1.29563 | −0.0671752 | ||||||||
\(373\) | −15.8929 | −0.822901 | −0.411451 | − | 0.911432i | \(-0.634978\pi\) | ||||
−0.411451 | + | 0.911432i | \(0.634978\pi\) | |||||||
\(374\) | 4.38553 | 0.226771 | ||||||||
\(375\) | −14.2696 | −0.736880 | ||||||||
\(376\) | 13.0168 | 0.671292 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −7.77403 | −0.399853 | ||||||||
\(379\) | 8.77900 | 0.450947 | 0.225474 | − | 0.974249i | \(-0.427607\pi\) | ||||
0.225474 | + | 0.974249i | \(0.427607\pi\) | |||||||
\(380\) | −0.102307 | −0.00524822 | ||||||||
\(381\) | 4.02249 | 0.206078 | ||||||||
\(382\) | 16.9736 | 0.868447 | ||||||||
\(383\) | −7.96237 | −0.406858 | −0.203429 | − | 0.979090i | \(-0.565209\pi\) | ||||
−0.203429 | + | 0.979090i | \(0.565209\pi\) | |||||||
\(384\) | 29.9423 | 1.52799 | ||||||||
\(385\) | −0.842869 | −0.0429566 | ||||||||
\(386\) | −16.1240 | −0.820688 | ||||||||
\(387\) | −4.97159 | −0.252720 | ||||||||
\(388\) | 0.349960 | 0.0177665 | ||||||||
\(389\) | 32.0434 | 1.62467 | 0.812333 | − | 0.583194i | \(-0.198197\pi\) | ||||
0.812333 | + | 0.583194i | \(0.198197\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.8082 | −0.900598 | ||||||||
\(392\) | 2.88158 | 0.145542 | ||||||||
\(393\) | −24.5100 | −1.23637 | ||||||||
\(394\) | 2.49630 | 0.125762 | ||||||||
\(395\) | −0.509777 | −0.0256496 | ||||||||
\(396\) | 0.640716 | 0.0321972 | ||||||||
\(397\) | 6.43457 | 0.322942 | 0.161471 | − | 0.986877i | \(-0.448376\pi\) | ||||
0.161471 | + | 0.986877i | \(0.448376\pi\) | |||||||
\(398\) | −9.13777 | −0.458035 | ||||||||
\(399\) | −7.03944 | −0.352413 | ||||||||
\(400\) | 18.1444 | 0.907219 | ||||||||
\(401\) | 0.533577 | 0.0266456 | 0.0133228 | − | 0.999911i | \(-0.495759\pi\) | ||||
0.0133228 | + | 0.999911i | \(0.495759\pi\) | |||||||
\(402\) | −32.7906 | −1.63545 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1.44839 | −0.0720601 | ||||||||
\(405\) | −0.464579 | −0.0230851 | ||||||||
\(406\) | −7.24847 | −0.359736 | ||||||||
\(407\) | −16.6139 | −0.823522 | ||||||||
\(408\) | −15.8640 | −0.785387 | ||||||||
\(409\) | 39.7528 | 1.96565 | 0.982824 | − | 0.184547i | \(-0.0590817\pi\) | ||||
0.982824 | + | 0.184547i | \(0.0590817\pi\) | |||||||
\(410\) | 3.02735 | 0.149510 | ||||||||
\(411\) | −24.0695 | −1.18726 | ||||||||
\(412\) | −0.397296 | −0.0195734 | ||||||||
\(413\) | 6.20526 | 0.305341 | ||||||||
\(414\) | 63.1520 | 3.10375 | ||||||||
\(415\) | −4.62832 | −0.227195 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.2375 | 0.697213 | ||||||||
\(418\) | −5.60761 | −0.274277 | ||||||||
\(419\) | 23.8176 | 1.16357 | 0.581783 | − | 0.813344i | \(-0.302355\pi\) | ||||
0.581783 | + | 0.813344i | \(0.302355\pi\) | |||||||
\(420\) | 0.116049 | 0.00566260 | ||||||||
\(421\) | −23.2419 | −1.13274 | −0.566370 | − | 0.824151i | \(-0.691653\pi\) | ||||
−0.566370 | + | 0.824151i | \(0.691653\pi\) | |||||||
\(422\) | −14.8573 | −0.723243 | ||||||||
\(423\) | 22.5185 | 1.09489 | ||||||||
\(424\) | −25.6360 | −1.24500 | ||||||||
\(425\) | −9.21657 | −0.447069 | ||||||||
\(426\) | 20.3578 | 0.986336 | ||||||||
\(427\) | 13.4707 | 0.651894 | ||||||||
\(428\) | −0.486253 | −0.0235039 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.717316 | −0.0345920 | ||||||||
\(431\) | −2.70689 | −0.130386 | −0.0651932 | − | 0.997873i | \(-0.520766\pi\) | ||||
−0.0651932 | + | 0.997873i | \(0.520766\pi\) | |||||||
\(432\) | 21.5137 | 1.03508 | ||||||||
\(433\) | −5.81890 | −0.279638 | −0.139819 | − | 0.990177i | \(-0.544652\pi\) | ||||
−0.139819 | + | 0.990177i | \(0.544652\pi\) | |||||||
\(434\) | −8.03008 | −0.385456 | ||||||||
\(435\) | −7.66950 | −0.367724 | ||||||||
\(436\) | 0.941416 | 0.0450856 | ||||||||
\(437\) | 22.7706 | 1.08927 | ||||||||
\(438\) | 46.3682 | 2.21556 | ||||||||
\(439\) | 38.1702 | 1.82176 | 0.910882 | − | 0.412668i | \(-0.135403\pi\) | ||||
0.910882 | + | 0.412668i | \(0.135403\pi\) | |||||||
\(440\) | 2.42880 | 0.115788 | ||||||||
\(441\) | 4.98500 | 0.237381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.6740 | −1.50488 | −0.752440 | − | 0.658661i | \(-0.771123\pi\) | ||||
−0.752440 | + | 0.658661i | \(0.771123\pi\) | |||||||
\(444\) | 2.28746 | 0.108558 | ||||||||
\(445\) | −6.23734 | −0.295678 | ||||||||
\(446\) | 17.8619 | 0.845787 | ||||||||
\(447\) | 9.50845 | 0.449734 | ||||||||
\(448\) | −8.29100 | −0.391713 | ||||||||
\(449\) | 31.4049 | 1.48209 | 0.741045 | − | 0.671455i | \(-0.234331\pi\) | ||||
0.741045 | + | 0.671455i | \(0.234331\pi\) | |||||||
\(450\) | 32.6842 | 1.54075 | ||||||||
\(451\) | −6.83614 | −0.321901 | ||||||||
\(452\) | −0.281416 | −0.0132367 | ||||||||
\(453\) | 35.7648 | 1.68037 | ||||||||
\(454\) | −0.968995 | −0.0454772 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 20.2847 | 0.949920 | ||||||||
\(457\) | 31.8281 | 1.48886 | 0.744429 | − | 0.667702i | \(-0.232722\pi\) | ||||
0.744429 | + | 0.667702i | \(0.232722\pi\) | |||||||
\(458\) | 25.3447 | 1.18428 | ||||||||
\(459\) | −10.9281 | −0.510078 | ||||||||
\(460\) | −0.375385 | −0.0175024 | ||||||||
\(461\) | −1.16631 | −0.0543203 | −0.0271601 | − | 0.999631i | \(-0.508646\pi\) | ||||
−0.0271601 | + | 0.999631i | \(0.508646\pi\) | |||||||
\(462\) | 6.36084 | 0.295933 | ||||||||
\(463\) | −20.3441 | −0.945469 | −0.472734 | − | 0.881205i | \(-0.656733\pi\) | ||||
−0.472734 | + | 0.881205i | \(0.656733\pi\) | |||||||
\(464\) | 20.0593 | 0.931231 | ||||||||
\(465\) | −8.49651 | −0.394016 | ||||||||
\(466\) | −37.1152 | −1.71933 | ||||||||
\(467\) | −1.56939 | −0.0726229 | −0.0363114 | − | 0.999341i | \(-0.511561\pi\) | ||||
−0.0363114 | + | 0.999341i | \(0.511561\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.37266 | 0.386614 | ||||||||
\(470\) | 3.24903 | 0.149867 | ||||||||
\(471\) | −29.3008 | −1.35011 | ||||||||
\(472\) | −17.8810 | −0.823039 | ||||||||
\(473\) | 1.61979 | 0.0744781 | ||||||||
\(474\) | 3.84711 | 0.176703 | ||||||||
\(475\) | 11.7849 | 0.540727 | ||||||||
\(476\) | 0.154176 | 0.00706665 | ||||||||
\(477\) | −44.3491 | −2.03060 | ||||||||
\(478\) | −23.0313 | −1.05343 | ||||||||
\(479\) | −7.71918 | −0.352699 | −0.176349 | − | 0.984328i | \(-0.556429\pi\) | ||||
−0.176349 | + | 0.984328i | \(0.556429\pi\) | |||||||
\(480\) | −0.656080 | −0.0299458 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −24.1334 | −1.09925 | ||||||||
\(483\) | −25.8292 | −1.17527 | ||||||||
\(484\) | 0.661740 | 0.0300791 | ||||||||
\(485\) | 2.29498 | 0.104209 | ||||||||
\(486\) | −19.8161 | −0.898875 | ||||||||
\(487\) | 0.0761801 | 0.00345205 | 0.00172602 | − | 0.999999i | \(-0.499451\pi\) | ||||
0.00172602 | + | 0.999999i | \(0.499451\pi\) | |||||||
\(488\) | −38.8170 | −1.75716 | ||||||||
\(489\) | −44.5155 | −2.01306 | ||||||||
\(490\) | 0.719250 | 0.0324924 | ||||||||
\(491\) | 1.78715 | 0.0806529 | 0.0403264 | − | 0.999187i | \(-0.487160\pi\) | ||||
0.0403264 | + | 0.999187i | \(0.487160\pi\) | |||||||
\(492\) | 0.941220 | 0.0424335 | ||||||||
\(493\) | −10.1893 | −0.458902 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.20170 | 0.188852 | ||||||||
\(496\) | 22.2223 | 0.997813 | ||||||||
\(497\) | −5.19809 | −0.233166 | ||||||||
\(498\) | 34.9284 | 1.56518 | ||||||||
\(499\) | −8.33493 | −0.373123 | −0.186561 | − | 0.982443i | \(-0.559734\pi\) | ||||
−0.186561 | + | 0.982443i | \(0.559734\pi\) | |||||||
\(500\) | −0.399619 | −0.0178715 | ||||||||
\(501\) | −46.3387 | −2.07026 | ||||||||
\(502\) | 8.93914 | 0.398973 | ||||||||
\(503\) | 1.44048 | 0.0642277 | 0.0321138 | − | 0.999484i | \(-0.489776\pi\) | ||||
0.0321138 | + | 0.999484i | \(0.489776\pi\) | |||||||
\(504\) | −14.3647 | −0.639854 | ||||||||
\(505\) | −9.49829 | −0.422668 | ||||||||
\(506\) | −20.5755 | −0.914693 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.112649 | 0.00499801 | ||||||||
\(509\) | 14.8256 | 0.657135 | 0.328568 | − | 0.944480i | \(-0.393434\pi\) | ||||
0.328568 | + | 0.944480i | \(0.393434\pi\) | |||||||
\(510\) | −3.95970 | −0.175339 | ||||||||
\(511\) | −11.8395 | −0.523750 | ||||||||
\(512\) | 23.8204 | 1.05272 | ||||||||
\(513\) | 13.9733 | 0.616935 | ||||||||
\(514\) | 5.08860 | 0.224449 | ||||||||
\(515\) | −2.60540 | −0.114808 | ||||||||
\(516\) | −0.223018 | −0.00981781 | ||||||||
\(517\) | −7.33674 | −0.322670 | ||||||||
\(518\) | 14.1773 | 0.622913 | ||||||||
\(519\) | 0.851561 | 0.0373794 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.334388 | −0.0146498 | −0.00732489 | − | 0.999973i | \(-0.502332\pi\) | ||||
−0.00732489 | + | 0.999973i | \(0.502332\pi\) | |||||||
\(522\) | 36.1336 | 1.58153 | ||||||||
\(523\) | −32.5065 | −1.42141 | −0.710705 | − | 0.703490i | \(-0.751624\pi\) | ||||
−0.710705 | + | 0.703490i | \(0.751624\pi\) | |||||||
\(524\) | −0.686401 | −0.0299856 | ||||||||
\(525\) | −13.3678 | −0.583420 | ||||||||
\(526\) | −25.3896 | −1.10704 | ||||||||
\(527\) | −11.2880 | −0.491713 | ||||||||
\(528\) | −17.6029 | −0.766068 | ||||||||
\(529\) | 60.5502 | 2.63262 | ||||||||
\(530\) | −6.39881 | −0.277947 | ||||||||
\(531\) | −30.9332 | −1.34239 | ||||||||
\(532\) | −0.197139 | −0.00854706 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 47.0710 | 2.03696 | ||||||||
\(535\) | −3.18876 | −0.137862 | ||||||||
\(536\) | −24.1265 | −1.04211 | ||||||||
\(537\) | 27.7373 | 1.19695 | ||||||||
\(538\) | −38.1732 | −1.64576 | ||||||||
\(539\) | −1.62416 | −0.0699575 | ||||||||
\(540\) | −0.230357 | −0.00991297 | ||||||||
\(541\) | −10.6015 | −0.455796 | −0.227898 | − | 0.973685i | \(-0.573185\pi\) | ||||
−0.227898 | + | 0.973685i | \(0.573185\pi\) | |||||||
\(542\) | 9.03534 | 0.388101 | ||||||||
\(543\) | 35.1300 | 1.50757 | ||||||||
\(544\) | −0.871633 | −0.0373709 | ||||||||
\(545\) | 6.17364 | 0.264450 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.2327 | 0.437519 | 0.218760 | − | 0.975779i | \(-0.429799\pi\) | ||||
0.218760 | + | 0.975779i | \(0.429799\pi\) | |||||||
\(548\) | −0.674064 | −0.0287946 | ||||||||
\(549\) | −67.1515 | −2.86596 | ||||||||
\(550\) | −10.6488 | −0.454067 | ||||||||
\(551\) | 13.0286 | 0.555038 | ||||||||
\(552\) | 74.4290 | 3.16791 | ||||||||
\(553\) | −0.982310 | −0.0417721 | ||||||||
\(554\) | −7.54216 | −0.320436 | ||||||||
\(555\) | 15.0007 | 0.636746 | ||||||||
\(556\) | 0.398720 | 0.0169095 | ||||||||
\(557\) | −31.9930 | −1.35559 | −0.677793 | − | 0.735253i | \(-0.737063\pi\) | ||||
−0.677793 | + | 0.735253i | \(0.737063\pi\) | |||||||
\(558\) | 40.0300 | 1.69460 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.99044 | −0.0841115 | ||||||||
\(561\) | 8.94152 | 0.377511 | ||||||||
\(562\) | 4.90956 | 0.207097 | ||||||||
\(563\) | 10.7913 | 0.454800 | 0.227400 | − | 0.973801i | \(-0.426978\pi\) | ||||
0.227400 | + | 0.973801i | \(0.426978\pi\) | |||||||
\(564\) | 1.01014 | 0.0425348 | ||||||||
\(565\) | −1.84547 | −0.0776397 | ||||||||
\(566\) | 19.5962 | 0.823688 | ||||||||
\(567\) | −0.895217 | −0.0375956 | ||||||||
\(568\) | 14.9787 | 0.628494 | ||||||||
\(569\) | −24.6014 | −1.03134 | −0.515672 | − | 0.856786i | \(-0.672458\pi\) | ||||
−0.515672 | + | 0.856786i | \(0.672458\pi\) | |||||||
\(570\) | 5.06312 | 0.212071 | ||||||||
\(571\) | 16.5724 | 0.693534 | 0.346767 | − | 0.937951i | \(-0.387279\pi\) | ||||
0.346767 | + | 0.937951i | \(0.387279\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 34.6070 | 1.44573 | ||||||||
\(574\) | 5.83352 | 0.243486 | ||||||||
\(575\) | 43.2412 | 1.80328 | ||||||||
\(576\) | 41.3306 | 1.72211 | ||||||||
\(577\) | −14.6611 | −0.610348 | −0.305174 | − | 0.952297i | \(-0.598715\pi\) | ||||
−0.305174 | + | 0.952297i | \(0.598715\pi\) | |||||||
\(578\) | 18.3005 | 0.761202 | ||||||||
\(579\) | −32.8746 | −1.36622 | ||||||||
\(580\) | −0.214784 | −0.00891840 | ||||||||
\(581\) | −8.91851 | −0.370002 | ||||||||
\(582\) | −17.3194 | −0.717912 | ||||||||
\(583\) | 14.4493 | 0.598431 | ||||||||
\(584\) | 34.1166 | 1.41175 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.5717 | 0.478024 | ||||||||
\(587\) | 35.3336 | 1.45837 | 0.729186 | − | 0.684315i | \(-0.239899\pi\) | ||||
0.729186 | + | 0.684315i | \(0.239899\pi\) | |||||||
\(588\) | 0.223619 | 0.00922190 | ||||||||
\(589\) | 14.4335 | 0.594723 | ||||||||
\(590\) | −4.46313 | −0.183744 | ||||||||
\(591\) | 5.08963 | 0.209359 | ||||||||
\(592\) | −39.2340 | −1.61251 | ||||||||
\(593\) | −16.4294 | −0.674675 | −0.337338 | − | 0.941384i | \(-0.609526\pi\) | ||||
−0.337338 | + | 0.941384i | \(0.609526\pi\) | |||||||
\(594\) | −12.6263 | −0.518062 | ||||||||
\(595\) | 1.01106 | 0.0414494 | ||||||||
\(596\) | 0.266283 | 0.0109074 | ||||||||
\(597\) | −18.6307 | −0.762504 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0819 | 0.493653 | 0.246826 | − | 0.969060i | \(-0.420612\pi\) | ||||
0.246826 | + | 0.969060i | \(0.420612\pi\) | |||||||
\(600\) | 38.5206 | 1.57259 | ||||||||
\(601\) | 7.81486 | 0.318775 | 0.159387 | − | 0.987216i | \(-0.449048\pi\) | ||||
0.159387 | + | 0.987216i | \(0.449048\pi\) | |||||||
\(602\) | −1.38223 | −0.0563353 | ||||||||
\(603\) | −41.7377 | −1.69969 | ||||||||
\(604\) | 1.00159 | 0.0407541 | ||||||||
\(605\) | 4.33957 | 0.176429 | ||||||||
\(606\) | 71.6803 | 2.91181 | ||||||||
\(607\) | 35.5649 | 1.44354 | 0.721768 | − | 0.692135i | \(-0.243330\pi\) | ||||
0.721768 | + | 0.692135i | \(0.243330\pi\) | |||||||
\(608\) | 1.11452 | 0.0451999 | ||||||||
\(609\) | −14.7787 | −0.598862 | ||||||||
\(610\) | −9.68882 | −0.392289 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.768568 | −0.0310675 | ||||||||
\(613\) | −11.9368 | −0.482122 | −0.241061 | − | 0.970510i | \(-0.577495\pi\) | ||||
−0.241061 | + | 0.970510i | \(0.577495\pi\) | |||||||
\(614\) | −11.5500 | −0.466120 | ||||||||
\(615\) | 6.17236 | 0.248893 | ||||||||
\(616\) | 4.68015 | 0.188569 | ||||||||
\(617\) | 23.5702 | 0.948901 | 0.474450 | − | 0.880282i | \(-0.342647\pi\) | ||||
0.474450 | + | 0.880282i | \(0.342647\pi\) | |||||||
\(618\) | 19.6621 | 0.790924 | ||||||||
\(619\) | −28.5571 | −1.14781 | −0.573904 | − | 0.818923i | \(-0.694572\pi\) | ||||
−0.573904 | + | 0.818923i | \(0.694572\pi\) | |||||||
\(620\) | −0.237944 | −0.00955606 | ||||||||
\(621\) | 51.2710 | 2.05743 | ||||||||
\(622\) | 20.2663 | 0.812607 | ||||||||
\(623\) | −12.0190 | −0.481530 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.0328 | 0.841311 | ||||||||
\(626\) | −23.7453 | −0.949052 | ||||||||
\(627\) | −11.4332 | −0.456597 | ||||||||
\(628\) | −0.820567 | −0.0327442 | ||||||||
\(629\) | 19.9292 | 0.794628 | ||||||||
\(630\) | −3.58546 | −0.142848 | ||||||||
\(631\) | −44.9925 | −1.79112 | −0.895561 | − | 0.444938i | \(-0.853226\pi\) | ||||
−0.895561 | + | 0.444938i | \(0.853226\pi\) | |||||||
\(632\) | 2.83061 | 0.112596 | ||||||||
\(633\) | −30.2921 | −1.20400 | ||||||||
\(634\) | −19.4034 | −0.770607 | ||||||||
\(635\) | 0.738735 | 0.0293158 | ||||||||
\(636\) | −1.98943 | −0.0788860 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.7727 | −0.466085 | ||||||||
\(639\) | 25.9125 | 1.02508 | ||||||||
\(640\) | 5.49894 | 0.217365 | ||||||||
\(641\) | −2.53300 | −0.100048 | −0.0500238 | − | 0.998748i | \(-0.515930\pi\) | ||||
−0.0500238 | + | 0.998748i | \(0.515930\pi\) | |||||||
\(642\) | 24.0645 | 0.949749 | ||||||||
\(643\) | −18.3771 | −0.724721 | −0.362360 | − | 0.932038i | \(-0.618029\pi\) | ||||
−0.362360 | + | 0.932038i | \(0.618029\pi\) | |||||||
\(644\) | −0.723345 | −0.0285038 | ||||||||
\(645\) | −1.46251 | −0.0575863 | ||||||||
\(646\) | 6.72658 | 0.264654 | ||||||||
\(647\) | 20.9287 | 0.822791 | 0.411396 | − | 0.911457i | \(-0.365041\pi\) | ||||
0.411396 | + | 0.911457i | \(0.365041\pi\) | |||||||
\(648\) | 2.57964 | 0.101338 | ||||||||
\(649\) | 10.0783 | 0.395609 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.3723 | −0.641680 | ||||||||
\(652\) | −1.24665 | −0.0488227 | ||||||||
\(653\) | −48.1160 | −1.88292 | −0.941461 | − | 0.337121i | \(-0.890547\pi\) | ||||
−0.941461 | + | 0.337121i | \(0.890547\pi\) | |||||||
\(654\) | −46.5903 | −1.82183 | ||||||||
\(655\) | −4.50130 | −0.175880 | ||||||||
\(656\) | −16.1436 | −0.630302 | ||||||||
\(657\) | 59.0200 | 2.30259 | ||||||||
\(658\) | 6.26070 | 0.244068 | ||||||||
\(659\) | −2.21638 | −0.0863379 | −0.0431690 | − | 0.999068i | \(-0.513745\pi\) | ||||
−0.0431690 | + | 0.999068i | \(0.513745\pi\) | |||||||
\(660\) | 0.188482 | 0.00733664 | ||||||||
\(661\) | 0.637434 | 0.0247933 | 0.0123966 | − | 0.999923i | \(-0.496054\pi\) | ||||
0.0123966 | + | 0.999923i | \(0.496054\pi\) | |||||||
\(662\) | 9.59073 | 0.372754 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 25.6994 | 0.997331 | ||||||||
\(665\) | −1.29280 | −0.0501327 | ||||||||
\(666\) | −70.6736 | −2.73855 | ||||||||
\(667\) | 47.8048 | 1.85101 | ||||||||
\(668\) | −1.29771 | −0.0502100 | ||||||||
\(669\) | 36.4181 | 1.40801 | ||||||||
\(670\) | −6.02203 | −0.232651 | ||||||||
\(671\) | 21.8786 | 0.844614 | ||||||||
\(672\) | −1.26423 | −0.0487687 | ||||||||
\(673\) | 15.4069 | 0.593891 | 0.296945 | − | 0.954895i | \(-0.404032\pi\) | ||||
0.296945 | + | 0.954895i | \(0.404032\pi\) | |||||||
\(674\) | 15.4616 | 0.595559 | ||||||||
\(675\) | 26.5352 | 1.02134 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.6812 | −0.448945 | −0.224473 | − | 0.974480i | \(-0.572066\pi\) | ||||
−0.224473 | + | 0.974480i | \(0.572066\pi\) | |||||||
\(678\) | 13.9272 | 0.534869 | ||||||||
\(679\) | 4.42228 | 0.169712 | ||||||||
\(680\) | −2.91345 | −0.111726 | ||||||||
\(681\) | −1.97565 | −0.0757072 | ||||||||
\(682\) | −13.0421 | −0.499409 | ||||||||
\(683\) | 22.9114 | 0.876680 | 0.438340 | − | 0.898809i | \(-0.355567\pi\) | ||||
0.438340 | + | 0.898809i | \(0.355567\pi\) | |||||||
\(684\) | 0.982737 | 0.0375759 | ||||||||
\(685\) | −4.42039 | −0.168895 | ||||||||
\(686\) | 1.38595 | 0.0529159 | ||||||||
\(687\) | 51.6745 | 1.97150 | ||||||||
\(688\) | 3.82515 | 0.145833 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 18.5777 | 0.707239 | ||||||||
\(691\) | −47.2325 | −1.79681 | −0.898405 | − | 0.439167i | \(-0.855274\pi\) | ||||
−0.898405 | + | 0.439167i | \(0.855274\pi\) | |||||||
\(692\) | 0.0238479 | 0.000906560 0 | ||||||||
\(693\) | 8.09643 | 0.307558 | ||||||||
\(694\) | 6.82596 | 0.259110 | ||||||||
\(695\) | 2.61473 | 0.0991825 | ||||||||
\(696\) | 42.5860 | 1.61422 | ||||||||
\(697\) | 8.20026 | 0.310607 | ||||||||
\(698\) | 2.11129 | 0.0799135 | ||||||||
\(699\) | −75.6730 | −2.86222 | ||||||||
\(700\) | −0.374365 | −0.0141497 | ||||||||
\(701\) | −12.2098 | −0.461158 | −0.230579 | − | 0.973054i | \(-0.574062\pi\) | ||||
−0.230579 | + | 0.973054i | \(0.574062\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.4827 | −0.961097 | ||||||||
\(704\) | −13.4659 | −0.507515 | ||||||||
\(705\) | 6.62435 | 0.249488 | ||||||||
\(706\) | −24.8474 | −0.935144 | ||||||||
\(707\) | −18.3026 | −0.688342 | ||||||||
\(708\) | −1.38762 | −0.0521498 | ||||||||
\(709\) | −17.8875 | −0.671778 | −0.335889 | − | 0.941902i | \(-0.609037\pi\) | ||||
−0.335889 | + | 0.941902i | \(0.609037\pi\) | |||||||
\(710\) | 3.73873 | 0.140312 | ||||||||
\(711\) | 4.89681 | 0.183645 | ||||||||
\(712\) | 34.6337 | 1.29795 | ||||||||
\(713\) | 52.9597 | 1.98336 | ||||||||
\(714\) | −7.63012 | −0.285550 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.776780 | 0.0290296 | ||||||||
\(717\) | −46.9578 | −1.75367 | ||||||||
\(718\) | −27.7210 | −1.03454 | ||||||||
\(719\) | 9.12634 | 0.340355 | 0.170178 | − | 0.985413i | \(-0.445566\pi\) | ||||
0.170178 | + | 0.985413i | \(0.445566\pi\) | |||||||
\(720\) | 9.92235 | 0.369784 | ||||||||
\(721\) | −5.02046 | −0.186972 | ||||||||
\(722\) | 17.7321 | 0.659920 | ||||||||
\(723\) | −49.2048 | −1.82995 | ||||||||
\(724\) | 0.983812 | 0.0365631 | ||||||||
\(725\) | 24.7413 | 0.918868 | ||||||||
\(726\) | −32.7493 | −1.21544 | ||||||||
\(727\) | −33.6859 | −1.24934 | −0.624670 | − | 0.780889i | \(-0.714767\pi\) | ||||
−0.624670 | + | 0.780889i | \(0.714767\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.0880 | −1.59585 | ||||||||
\(730\) | 8.51558 | 0.315176 | ||||||||
\(731\) | −1.94301 | −0.0718650 | ||||||||
\(732\) | −3.01231 | −0.111338 | ||||||||
\(733\) | −46.4344 | −1.71509 | −0.857547 | − | 0.514406i | \(-0.828013\pi\) | ||||
−0.857547 | + | 0.514406i | \(0.828013\pi\) | |||||||
\(734\) | −37.9968 | −1.40249 | ||||||||
\(735\) | 1.46646 | 0.0540910 | ||||||||
\(736\) | 4.08942 | 0.150738 | ||||||||
\(737\) | 13.5985 | 0.500908 | ||||||||
\(738\) | −29.0801 | −1.07045 | ||||||||
\(739\) | 1.85025 | 0.0680627 | 0.0340314 | − | 0.999421i | \(-0.489165\pi\) | ||||
0.0340314 | + | 0.999421i | \(0.489165\pi\) | |||||||
\(740\) | 0.420095 | 0.0154430 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.3301 | −0.452654 | ||||||||
\(743\) | 33.1509 | 1.21619 | 0.608094 | − | 0.793865i | \(-0.291934\pi\) | ||||
0.608094 | + | 0.793865i | \(0.291934\pi\) | |||||||
\(744\) | 47.1781 | 1.72963 | ||||||||
\(745\) | 1.74624 | 0.0639773 | ||||||||
\(746\) | 22.0268 | 0.806457 | ||||||||
\(747\) | 44.4588 | 1.62666 | ||||||||
\(748\) | 0.250407 | 0.00915577 | ||||||||
\(749\) | −6.14456 | −0.224517 | ||||||||
\(750\) | 19.7770 | 0.722154 | ||||||||
\(751\) | −20.7743 | −0.758064 | −0.379032 | − | 0.925384i | \(-0.623743\pi\) | ||||
−0.379032 | + | 0.925384i | \(0.623743\pi\) | |||||||
\(752\) | −17.3258 | −0.631806 | ||||||||
\(753\) | 18.2257 | 0.664182 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.56824 | 0.239043 | ||||||||
\(756\) | −0.443884 | −0.0161439 | ||||||||
\(757\) | 43.6150 | 1.58521 | 0.792607 | − | 0.609733i | \(-0.208723\pi\) | ||||
0.792607 | + | 0.609733i | \(0.208723\pi\) | |||||||
\(758\) | −12.1673 | −0.441936 | ||||||||
\(759\) | −41.9508 | −1.52272 | ||||||||
\(760\) | 3.72532 | 0.135131 | ||||||||
\(761\) | 12.3902 | 0.449145 | 0.224573 | − | 0.974457i | \(-0.427901\pi\) | ||||
0.224573 | + | 0.974457i | \(0.427901\pi\) | |||||||
\(762\) | −5.57497 | −0.201960 | ||||||||
\(763\) | 11.8962 | 0.430673 | ||||||||
\(764\) | 0.969167 | 0.0350632 | ||||||||
\(765\) | −5.04013 | −0.182226 | ||||||||
\(766\) | 11.0355 | 0.398728 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 5.35835 | 0.193353 | ||||||||
\(769\) | −5.55359 | −0.200268 | −0.100134 | − | 0.994974i | \(-0.531927\pi\) | ||||
−0.100134 | + | 0.994974i | \(0.531927\pi\) | |||||||
\(770\) | 1.16818 | 0.0420982 | ||||||||
\(771\) | 10.3750 | 0.373646 | ||||||||
\(772\) | −0.920651 | −0.0331349 | ||||||||
\(773\) | −43.8042 | −1.57553 | −0.787764 | − | 0.615977i | \(-0.788761\pi\) | ||||
−0.787764 | + | 0.615977i | \(0.788761\pi\) | |||||||
\(774\) | 6.89039 | 0.247670 | ||||||||
\(775\) | 27.4092 | 0.984566 | ||||||||
\(776\) | −12.7432 | −0.457454 | ||||||||
\(777\) | 28.9056 | 1.03698 | ||||||||
\(778\) | −44.4107 | −1.59220 | ||||||||
\(779\) | −10.4853 | −0.375677 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.44253 | −0.302098 | ||||||||
\(782\) | 24.6813 | 0.882600 | ||||||||
\(783\) | 29.3357 | 1.04837 | ||||||||
\(784\) | −3.83547 | −0.136981 | ||||||||
\(785\) | −5.38113 | −0.192061 | ||||||||
\(786\) | 33.9697 | 1.21166 | ||||||||
\(787\) | 24.8009 | 0.884057 | 0.442029 | − | 0.897001i | \(-0.354259\pi\) | ||||
0.442029 | + | 0.897001i | \(0.354259\pi\) | |||||||
\(788\) | 0.142535 | 0.00507758 | ||||||||
\(789\) | −51.7661 | −1.84292 | ||||||||
\(790\) | 0.706526 | 0.0251371 | ||||||||
\(791\) | −3.55612 | −0.126441 | ||||||||
\(792\) | −23.3305 | −0.829015 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −8.91801 | −0.316489 | ||||||||
\(795\) | −13.0463 | −0.462706 | ||||||||
\(796\) | −0.521751 | −0.0184930 | ||||||||
\(797\) | −16.4715 | −0.583451 | −0.291725 | − | 0.956502i | \(-0.594229\pi\) | ||||
−0.291725 | + | 0.956502i | \(0.594229\pi\) | |||||||
\(798\) | 9.75633 | 0.345370 | ||||||||
\(799\) | 8.80076 | 0.311348 | ||||||||
\(800\) | 2.11647 | 0.0748285 | ||||||||
\(801\) | 59.9146 | 2.11698 | ||||||||
\(802\) | −0.739513 | −0.0261131 | ||||||||
\(803\) | −19.2293 | −0.678587 | ||||||||
\(804\) | −1.87229 | −0.0660305 | ||||||||
\(805\) | −4.74357 | −0.167189 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −77.8301 | −2.73975 | ||||||||
\(808\) | 52.7406 | 1.85541 | ||||||||
\(809\) | 1.38194 | 0.0485863 | 0.0242932 | − | 0.999705i | \(-0.492266\pi\) | ||||
0.0242932 | + | 0.999705i | \(0.492266\pi\) | |||||||
\(810\) | 0.643885 | 0.0226238 | ||||||||
\(811\) | 6.83571 | 0.240034 | 0.120017 | − | 0.992772i | \(-0.461705\pi\) | ||||
0.120017 | + | 0.992772i | \(0.461705\pi\) | |||||||
\(812\) | −0.413875 | −0.0145242 | ||||||||
\(813\) | 18.4219 | 0.646083 | ||||||||
\(814\) | 23.0261 | 0.807066 | ||||||||
\(815\) | −8.17533 | −0.286369 | ||||||||
\(816\) | 21.1155 | 0.739190 | ||||||||
\(817\) | 2.48446 | 0.0869201 | ||||||||
\(818\) | −55.0954 | −1.92637 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.172856 | 0.00603640 | ||||||||
\(821\) | −10.5425 | −0.367936 | −0.183968 | − | 0.982932i | \(-0.558894\pi\) | ||||
−0.183968 | + | 0.982932i | \(0.558894\pi\) | |||||||
\(822\) | 33.3592 | 1.16353 | ||||||||
\(823\) | 14.8330 | 0.517047 | 0.258524 | − | 0.966005i | \(-0.416764\pi\) | ||||
0.258524 | + | 0.966005i | \(0.416764\pi\) | |||||||
\(824\) | 14.4669 | 0.503977 | ||||||||
\(825\) | −21.7115 | −0.755898 | ||||||||
\(826\) | −8.60020 | −0.299239 | ||||||||
\(827\) | −55.6758 | −1.93604 | −0.968018 | − | 0.250879i | \(-0.919280\pi\) | ||||
−0.968018 | + | 0.250879i | \(0.919280\pi\) | |||||||
\(828\) | 3.60587 | 0.125313 | ||||||||
\(829\) | −0.0464848 | −0.00161448 | −0.000807242 | − | 1.00000i | \(-0.500257\pi\) | ||||
−0.000807242 | 1.00000i | \(0.500257\pi\) | ||||||||
\(830\) | 6.41464 | 0.222655 | ||||||||
\(831\) | −15.3775 | −0.533438 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.94825 | 0.0675030 | ||||||||
\(834\) | −19.7325 | −0.683280 | ||||||||
\(835\) | −8.51016 | −0.294506 | ||||||||
\(836\) | −0.320185 | −0.0110738 | ||||||||
\(837\) | 32.4990 | 1.12333 | ||||||||
\(838\) | −33.0100 | −1.14031 | ||||||||
\(839\) | 25.5475 | 0.881999 | 0.440999 | − | 0.897507i | \(-0.354624\pi\) | ||||
0.440999 | + | 0.897507i | \(0.354624\pi\) | |||||||
\(840\) | −4.22571 | −0.145801 | ||||||||
\(841\) | −1.64755 | −0.0568120 | ||||||||
\(842\) | 32.2121 | 1.11010 | ||||||||
\(843\) | 10.0099 | 0.344761 | ||||||||
\(844\) | −0.848327 | −0.0292006 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −31.2096 | −1.07301 | ||||||||
\(847\) | 8.36211 | 0.287325 | ||||||||
\(848\) | 34.1223 | 1.17176 | ||||||||
\(849\) | 39.9540 | 1.37122 | ||||||||
\(850\) | 12.7737 | 0.438135 | ||||||||
\(851\) | −93.5013 | −3.20518 | ||||||||
\(852\) | 1.16239 | 0.0398229 | ||||||||
\(853\) | 22.6671 | 0.776105 | 0.388053 | − | 0.921637i | \(-0.373148\pi\) | ||||
0.388053 | + | 0.921637i | \(0.373148\pi\) | |||||||
\(854\) | −18.6698 | −0.638867 | ||||||||
\(855\) | 6.44462 | 0.220401 | ||||||||
\(856\) | 17.7061 | 0.605181 | ||||||||
\(857\) | −37.0535 | −1.26572 | −0.632862 | − | 0.774264i | \(-0.718120\pi\) | ||||
−0.632862 | + | 0.774264i | \(0.718120\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.24339 | −0.144782 | −0.0723912 | − | 0.997376i | \(-0.523063\pi\) | ||||
−0.0723912 | + | 0.997376i | \(0.523063\pi\) | |||||||
\(860\) | −0.0409575 | −0.00139664 | ||||||||
\(861\) | 11.8938 | 0.405339 | ||||||||
\(862\) | 3.75162 | 0.127781 | ||||||||
\(863\) | 7.50051 | 0.255320 | 0.127660 | − | 0.991818i | \(-0.459253\pi\) | ||||
0.127660 | + | 0.991818i | \(0.459253\pi\) | |||||||
\(864\) | 2.50949 | 0.0853746 | ||||||||
\(865\) | 0.156390 | 0.00531743 | ||||||||
\(866\) | 8.06472 | 0.274050 | ||||||||
\(867\) | 37.3124 | 1.26720 | ||||||||
\(868\) | −0.458504 | −0.0155626 | ||||||||
\(869\) | −1.59543 | −0.0541212 | ||||||||
\(870\) | 10.6296 | 0.360376 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −34.2800 | −1.16087 | ||||||||
\(873\) | −22.0451 | −0.746113 | ||||||||
\(874\) | −31.5590 | −1.06750 | ||||||||
\(875\) | −5.04981 | −0.170715 | ||||||||
\(876\) | 2.64755 | 0.0894523 | ||||||||
\(877\) | 28.2897 | 0.955274 | 0.477637 | − | 0.878557i | \(-0.341493\pi\) | ||||
0.477637 | + | 0.878557i | \(0.341493\pi\) | |||||||
\(878\) | −52.9021 | −1.78536 | ||||||||
\(879\) | 23.5933 | 0.795781 | ||||||||
\(880\) | −3.23280 | −0.108978 | ||||||||
\(881\) | −39.5721 | −1.33322 | −0.666609 | − | 0.745408i | \(-0.732255\pi\) | ||||
−0.666609 | + | 0.745408i | \(0.732255\pi\) | |||||||
\(882\) | −6.90897 | −0.232637 | ||||||||
\(883\) | 28.3609 | 0.954419 | 0.477209 | − | 0.878790i | \(-0.341648\pi\) | ||||
0.477209 | + | 0.878790i | \(0.341648\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.09974 | −0.305884 | ||||||||
\(886\) | 43.8987 | 1.47481 | ||||||||
\(887\) | −43.7186 | −1.46793 | −0.733963 | − | 0.679189i | \(-0.762331\pi\) | ||||
−0.733963 | + | 0.679189i | \(0.762331\pi\) | |||||||
\(888\) | −83.2938 | −2.79516 | ||||||||
\(889\) | 1.42350 | 0.0477426 | ||||||||
\(890\) | 8.64465 | 0.289769 | ||||||||
\(891\) | −1.45398 | −0.0487100 | ||||||||
\(892\) | 1.01989 | 0.0341483 | ||||||||
\(893\) | −11.2532 | −0.376573 | ||||||||
\(894\) | −13.1783 | −0.440747 | ||||||||
\(895\) | 5.09399 | 0.170273 | ||||||||
\(896\) | 10.5961 | 0.353992 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −43.5257 | −1.45247 | ||||||||
\(899\) | 30.3019 | 1.01062 | ||||||||
\(900\) | 1.86621 | 0.0622070 | ||||||||
\(901\) | −17.3326 | −0.577434 | ||||||||
\(902\) | 9.47456 | 0.315468 | ||||||||
\(903\) | −2.81818 | −0.0937830 | ||||||||
\(904\) | 10.2473 | 0.340819 | ||||||||
\(905\) | 6.45167 | 0.214461 | ||||||||
\(906\) | −49.5683 | −1.64679 | ||||||||
\(907\) | −36.6985 | −1.21855 | −0.609277 | − | 0.792957i | \(-0.708540\pi\) | ||||
−0.609277 | + | 0.792957i | \(0.708540\pi\) | |||||||
\(908\) | −0.0553280 | −0.00183612 | ||||||||
\(909\) | 91.2387 | 3.02620 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.5211 | −1.17686 | −0.588432 | − | 0.808546i | \(-0.700255\pi\) | ||||
−0.588432 | + | 0.808546i | \(0.700255\pi\) | |||||||
\(912\) | −26.9995 | −0.894044 | ||||||||
\(913\) | −14.4851 | −0.479386 | ||||||||
\(914\) | −44.1123 | −1.45911 | ||||||||
\(915\) | −19.7542 | −0.653054 | ||||||||
\(916\) | 1.44714 | 0.0478148 | ||||||||
\(917\) | −8.67374 | −0.286432 | ||||||||
\(918\) | 15.1458 | 0.499885 | ||||||||
\(919\) | 21.9334 | 0.723516 | 0.361758 | − | 0.932272i | \(-0.382177\pi\) | ||||
0.361758 | + | 0.932272i | \(0.382177\pi\) | |||||||
\(920\) | 13.6690 | 0.450653 | ||||||||
\(921\) | −23.5489 | −0.775964 | ||||||||
\(922\) | 1.61644 | 0.0532348 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.363193 | 0.0119482 | ||||||||
\(925\) | −48.3914 | −1.59110 | ||||||||
\(926\) | 28.1959 | 0.926575 | ||||||||
\(927\) | 25.0270 | 0.821993 | ||||||||
\(928\) | 2.33984 | 0.0768090 | ||||||||
\(929\) | 15.5172 | 0.509102 | 0.254551 | − | 0.967059i | \(-0.418072\pi\) | ||||
0.254551 | + | 0.967059i | \(0.418072\pi\) | |||||||
\(930\) | 11.7758 | 0.386142 | ||||||||
\(931\) | −2.49115 | −0.0816443 | ||||||||
\(932\) | −2.11922 | −0.0694172 | ||||||||
\(933\) | 41.3204 | 1.35277 | ||||||||
\(934\) | 2.17510 | 0.0711716 | ||||||||
\(935\) | 1.64212 | 0.0537031 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.8110 | 1.33324 | 0.666618 | − | 0.745399i | \(-0.267741\pi\) | ||||
0.666618 | + | 0.745399i | \(0.267741\pi\) | |||||||
\(938\) | −11.6041 | −0.378888 | ||||||||
\(939\) | −48.4135 | −1.57991 | ||||||||
\(940\) | 0.185514 | 0.00605081 | ||||||||
\(941\) | 51.5936 | 1.68190 | 0.840952 | − | 0.541109i | \(-0.181996\pi\) | ||||
0.840952 | + | 0.541109i | \(0.181996\pi\) | |||||||
\(942\) | 40.6096 | 1.32313 | ||||||||
\(943\) | −38.4730 | −1.25285 | ||||||||
\(944\) | 23.8001 | 0.774627 | ||||||||
\(945\) | −2.91091 | −0.0946920 | ||||||||
\(946\) | −2.24495 | −0.0729898 | ||||||||
\(947\) | 4.98209 | 0.161896 | 0.0809482 | − | 0.996718i | \(-0.474205\pi\) | ||||
0.0809482 | + | 0.996718i | \(0.474205\pi\) | |||||||
\(948\) | 0.219663 | 0.00713433 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −16.3333 | −0.529921 | ||||||||
\(951\) | −39.5609 | −1.28285 | ||||||||
\(952\) | −5.61405 | −0.181953 | ||||||||
\(953\) | 30.2325 | 0.979328 | 0.489664 | − | 0.871911i | \(-0.337119\pi\) | ||||
0.489664 | + | 0.871911i | \(0.337119\pi\) | |||||||
\(954\) | 61.4657 | 1.99003 | ||||||||
\(955\) | 6.35562 | 0.205663 | ||||||||
\(956\) | −1.31505 | −0.0425317 | ||||||||
\(957\) | −24.0029 | −0.775904 | ||||||||
\(958\) | 10.6984 | 0.345650 | ||||||||
\(959\) | −8.51784 | −0.275055 | ||||||||
\(960\) | 12.1584 | 0.392410 | ||||||||
\(961\) | 2.56939 | 0.0828835 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.6306 | 0.987058 | ||||||||
\(964\) | −1.37798 | −0.0443816 | ||||||||
\(965\) | −6.03746 | −0.194353 | ||||||||
\(966\) | 35.7981 | 1.15178 | ||||||||
\(967\) | 29.9990 | 0.964703 | 0.482352 | − | 0.875978i | \(-0.339783\pi\) | ||||
0.482352 | + | 0.875978i | \(0.339783\pi\) | |||||||
\(968\) | −24.0961 | −0.774478 | ||||||||
\(969\) | 13.7146 | 0.440577 | ||||||||
\(970\) | −3.18073 | −0.102127 | ||||||||
\(971\) | 44.1240 | 1.41601 | 0.708003 | − | 0.706209i | \(-0.249596\pi\) | ||||
0.708003 | + | 0.706209i | \(0.249596\pi\) | |||||||
\(972\) | −1.13146 | −0.0362917 | ||||||||
\(973\) | 5.03844 | 0.161525 | ||||||||
\(974\) | −0.105582 | −0.00338306 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 51.6665 | 1.65380 | ||||||||
\(977\) | −15.0024 | −0.479970 | −0.239985 | − | 0.970777i | \(-0.577142\pi\) | ||||
−0.239985 | + | 0.970777i | \(0.577142\pi\) | |||||||
\(978\) | 61.6964 | 1.97283 | ||||||||
\(979\) | −19.5207 | −0.623886 | ||||||||
\(980\) | 0.0410679 | 0.00131187 | ||||||||
\(981\) | −59.3028 | −1.89339 | ||||||||
\(982\) | −2.47690 | −0.0790411 | ||||||||
\(983\) | 6.01856 | 0.191962 | 0.0959812 | − | 0.995383i | \(-0.469401\pi\) | ||||
0.0959812 | + | 0.995383i | \(0.469401\pi\) | |||||||
\(984\) | −34.2729 | −1.09258 | ||||||||
\(985\) | 0.934717 | 0.0297825 | ||||||||
\(986\) | 14.1219 | 0.449732 | ||||||||
\(987\) | 12.7647 | 0.406306 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.11600 | 0.289872 | ||||||||
\(990\) | −5.82336 | −0.185078 | ||||||||
\(991\) | 33.8400 | 1.07496 | 0.537482 | − | 0.843275i | \(-0.319376\pi\) | ||||
0.537482 | + | 0.843275i | \(0.319376\pi\) | |||||||
\(992\) | 2.59215 | 0.0823008 | ||||||||
\(993\) | 19.5542 | 0.620535 | ||||||||
\(994\) | 7.20431 | 0.228507 | ||||||||
\(995\) | −3.42155 | −0.108471 | ||||||||
\(996\) | 1.99435 | 0.0631934 | ||||||||
\(997\) | 26.3215 | 0.833610 | 0.416805 | − | 0.908996i | \(-0.363150\pi\) | ||||
0.416805 | + | 0.908996i | \(0.363150\pi\) | |||||||
\(998\) | 11.5518 | 0.365666 | ||||||||
\(999\) | −57.3775 | −1.81534 |
(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 | 1183.2.a.p.1.1 | 6 | ||
7.6 | odd | 2 | 8281.2.a.ch.1.1 | 6 | |||
13.2 | odd | 12 | 91.2.q.a.43.2 | yes | 12 | ||
13.5 | odd | 4 | 1183.2.c.i.337.10 | 12 | |||
13.7 | odd | 12 | 91.2.q.a.36.2 | ✓ | 12 | ||
13.8 | odd | 4 | 1183.2.c.i.337.3 | 12 | |||
13.12 | even | 2 | 1183.2.a.m.1.6 | 6 | |||
39.2 | even | 12 | 819.2.ct.a.316.5 | 12 | |||
39.20 | even | 12 | 819.2.ct.a.127.5 | 12 | |||
52.7 | even | 12 | 1456.2.cc.c.673.1 | 12 | |||
52.15 | even | 12 | 1456.2.cc.c.225.1 | 12 | |||
91.2 | odd | 12 | 637.2.k.h.459.5 | 12 | |||
91.20 | even | 12 | 637.2.q.h.491.2 | 12 | |||
91.33 | even | 12 | 637.2.u.i.361.5 | 12 | |||
91.41 | even | 12 | 637.2.q.h.589.2 | 12 | |||
91.46 | odd | 12 | 637.2.k.h.569.2 | 12 | |||
91.54 | even | 12 | 637.2.k.g.459.5 | 12 | |||
91.59 | even | 12 | 637.2.k.g.569.2 | 12 | |||
91.67 | odd | 12 | 637.2.u.h.30.5 | 12 | |||
91.72 | odd | 12 | 637.2.u.h.361.5 | 12 | |||
91.80 | even | 12 | 637.2.u.i.30.5 | 12 | |||
91.90 | odd | 2 | 8281.2.a.by.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.2 | ✓ | 12 | 13.7 | odd | 12 | ||
91.2.q.a.43.2 | yes | 12 | 13.2 | odd | 12 | ||
637.2.k.g.459.5 | 12 | 91.54 | even | 12 | |||
637.2.k.g.569.2 | 12 | 91.59 | even | 12 | |||
637.2.k.h.459.5 | 12 | 91.2 | odd | 12 | |||
637.2.k.h.569.2 | 12 | 91.46 | odd | 12 | |||
637.2.q.h.491.2 | 12 | 91.20 | even | 12 | |||
637.2.q.h.589.2 | 12 | 91.41 | even | 12 | |||
637.2.u.h.30.5 | 12 | 91.67 | odd | 12 | |||
637.2.u.h.361.5 | 12 | 91.72 | odd | 12 | |||
637.2.u.i.30.5 | 12 | 91.80 | even | 12 | |||
637.2.u.i.361.5 | 12 | 91.33 | even | 12 | |||
819.2.ct.a.127.5 | 12 | 39.20 | even | 12 | |||
819.2.ct.a.316.5 | 12 | 39.2 | even | 12 | |||
1183.2.a.m.1.6 | 6 | 13.12 | even | 2 | |||
1183.2.a.p.1.1 | 6 | 1.1 | even | 1 | trivial | ||
1183.2.c.i.337.3 | 12 | 13.8 | odd | 4 | |||
1183.2.c.i.337.10 | 12 | 13.5 | odd | 4 | |||
1456.2.cc.c.225.1 | 12 | 52.15 | even | 12 | |||
1456.2.cc.c.673.1 | 12 | 52.7 | even | 12 | |||
8281.2.a.by.1.6 | 6 | 91.90 | odd | 2 | |||
8281.2.a.ch.1.1 | 6 | 7.6 | odd | 2 |