Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2695,2,Mod(1,2695)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2695, 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("2695.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2695 = 5 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2695.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: | \(21.5196833447\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2695.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.41421 | 1.70711 | 0.853553 | − | 0.521005i | \(-0.174443\pi\) | ||||
0.853553 | + | 0.521005i | \(0.174443\pi\) | |||||||
\(3\) | 2.82843 | 1.63299 | 0.816497 | − | 0.577350i | \(-0.195913\pi\) | ||||
0.816497 | + | 0.577350i | \(0.195913\pi\) | |||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 6.82843 | 2.78769 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 4.41421 | 1.56066 | ||||||||
\(9\) | 5.00000 | 1.66667 | ||||||||
\(10\) | 2.41421 | 0.763441 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 10.8284 | 3.12590 | ||||||||
\(13\) | 1.17157 | 0.324936 | 0.162468 | − | 0.986714i | \(-0.448055\pi\) | ||||
0.162468 | + | 0.986714i | \(0.448055\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.82843 | 0.730297 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | −6.82843 | −1.65614 | −0.828068 | − | 0.560627i | \(-0.810560\pi\) | ||||
−0.828068 | + | 0.560627i | \(0.810560\pi\) | |||||||
\(18\) | 12.0711 | 2.84518 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 3.82843 | 0.856062 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.41421 | 0.514712 | ||||||||
\(23\) | −2.82843 | −0.589768 | −0.294884 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(24\) | 12.4853 | 2.54855 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.82843 | 0.554700 | ||||||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.65685 | −0.679061 | −0.339530 | − | 0.940595i | \(-0.610268\pi\) | ||||
−0.339530 | + | 0.940595i | \(0.610268\pi\) | |||||||
\(30\) | 6.82843 | 1.24669 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | −1.58579 | −0.280330 | ||||||||
\(33\) | 2.82843 | 0.492366 | ||||||||
\(34\) | −16.4853 | −2.82720 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 19.1421 | 3.19036 | ||||||||
\(37\) | −7.65685 | −1.25878 | −0.629390 | − | 0.777090i | \(-0.716695\pi\) | ||||
−0.629390 | + | 0.777090i | \(0.716695\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.31371 | 0.530618 | ||||||||
\(40\) | 4.41421 | 0.697948 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | 3.82843 | 0.577157 | ||||||||
\(45\) | 5.00000 | 0.745356 | ||||||||
\(46\) | −6.82843 | −1.00680 | ||||||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | 8.48528 | 1.22474 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.41421 | 0.341421 | ||||||||
\(51\) | −19.3137 | −2.70446 | ||||||||
\(52\) | 4.48528 | 0.621997 | ||||||||
\(53\) | 11.6569 | 1.60119 | 0.800596 | − | 0.599204i | \(-0.204516\pi\) | ||||
0.800596 | + | 0.599204i | \(0.204516\pi\) | |||||||
\(54\) | 13.6569 | 1.85846 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.82843 | −1.15923 | ||||||||
\(59\) | −1.65685 | −0.215704 | −0.107852 | − | 0.994167i | \(-0.534397\pi\) | ||||
−0.107852 | + | 0.994167i | \(0.534397\pi\) | |||||||
\(60\) | 10.8284 | 1.39794 | ||||||||
\(61\) | 9.31371 | 1.19250 | 0.596249 | − | 0.802799i | \(-0.296657\pi\) | ||||
0.596249 | + | 0.802799i | \(0.296657\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | 1.17157 | 0.145316 | ||||||||
\(66\) | 6.82843 | 0.840521 | ||||||||
\(67\) | 12.4853 | 1.52532 | 0.762660 | − | 0.646800i | \(-0.223893\pi\) | ||||
0.762660 | + | 0.646800i | \(0.223893\pi\) | |||||||
\(68\) | −26.1421 | −3.17020 | ||||||||
\(69\) | −8.00000 | −0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3137 | 1.34269 | 0.671345 | − | 0.741145i | \(-0.265717\pi\) | ||||
0.671345 | + | 0.741145i | \(0.265717\pi\) | |||||||
\(72\) | 22.0711 | 2.60110 | ||||||||
\(73\) | 1.17157 | 0.137122 | 0.0685611 | − | 0.997647i | \(-0.478159\pi\) | ||||
0.0685611 | + | 0.997647i | \(0.478159\pi\) | |||||||
\(74\) | −18.4853 | −2.14887 | ||||||||
\(75\) | 2.82843 | 0.326599 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 8.00000 | 0.905822 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −14.4853 | −1.59963 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.82843 | −0.740647 | ||||||||
\(86\) | −14.4853 | −1.56199 | ||||||||
\(87\) | −10.3431 | −1.10890 | ||||||||
\(88\) | 4.41421 | 0.470557 | ||||||||
\(89\) | 13.3137 | 1.41125 | 0.705625 | − | 0.708585i | \(-0.250666\pi\) | ||||
0.705625 | + | 0.708585i | \(0.250666\pi\) | |||||||
\(90\) | 12.0711 | 1.27240 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −10.8284 | −1.12894 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.82843 | −0.704298 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.48528 | −0.457777 | ||||||||
\(97\) | −3.65685 | −0.371297 | −0.185649 | − | 0.982616i | \(-0.559439\pi\) | ||||
−0.185649 | + | 0.982616i | \(0.559439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.00000 | 0.502519 | ||||||||
\(100\) | 3.82843 | 0.382843 | ||||||||
\(101\) | −9.31371 | −0.926749 | −0.463374 | − | 0.886163i | \(-0.653361\pi\) | ||||
−0.463374 | + | 0.886163i | \(0.653361\pi\) | |||||||
\(102\) | −46.6274 | −4.61680 | ||||||||
\(103\) | −6.82843 | −0.672825 | −0.336412 | − | 0.941715i | \(-0.609214\pi\) | ||||
−0.336412 | + | 0.941715i | \(0.609214\pi\) | |||||||
\(104\) | 5.17157 | 0.507114 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 28.1421 | 2.73341 | ||||||||
\(107\) | 7.65685 | 0.740216 | 0.370108 | − | 0.928989i | \(-0.379321\pi\) | ||||
0.370108 | + | 0.928989i | \(0.379321\pi\) | |||||||
\(108\) | 21.6569 | 2.08393 | ||||||||
\(109\) | −7.65685 | −0.733394 | −0.366697 | − | 0.930341i | \(-0.619511\pi\) | ||||
−0.366697 | + | 0.930341i | \(0.619511\pi\) | |||||||
\(110\) | 2.41421 | 0.230186 | ||||||||
\(111\) | −21.6569 | −2.05558 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.6569 | 1.84916 | 0.924581 | − | 0.380986i | \(-0.124416\pi\) | ||||
0.924581 | + | 0.380986i | \(0.124416\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.82843 | −0.263752 | ||||||||
\(116\) | −14.0000 | −1.29987 | ||||||||
\(117\) | 5.85786 | 0.541560 | ||||||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 12.4853 | 1.13975 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 22.4853 | 2.03572 | ||||||||
\(123\) | −16.9706 | −1.53018 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.34315 | 0.385392 | 0.192696 | − | 0.981259i | \(-0.438277\pi\) | ||||
0.192696 | + | 0.981259i | \(0.438277\pi\) | |||||||
\(128\) | −20.5563 | −1.81694 | ||||||||
\(129\) | −16.9706 | −1.49417 | ||||||||
\(130\) | 2.82843 | 0.248069 | ||||||||
\(131\) | 11.3137 | 0.988483 | 0.494242 | − | 0.869325i | \(-0.335446\pi\) | ||||
0.494242 | + | 0.869325i | \(0.335446\pi\) | |||||||
\(132\) | 10.8284 | 0.942494 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 30.1421 | 2.60388 | ||||||||
\(135\) | 5.65685 | 0.486864 | ||||||||
\(136\) | −30.1421 | −2.58467 | ||||||||
\(137\) | −10.9706 | −0.937278 | −0.468639 | − | 0.883390i | \(-0.655256\pi\) | ||||
−0.468639 | + | 0.883390i | \(0.655256\pi\) | |||||||
\(138\) | −19.3137 | −1.64409 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | 27.3137 | 2.29212 | ||||||||
\(143\) | 1.17157 | 0.0979718 | ||||||||
\(144\) | 15.0000 | 1.25000 | ||||||||
\(145\) | −3.65685 | −0.303685 | ||||||||
\(146\) | 2.82843 | 0.234082 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −29.3137 | −2.40957 | ||||||||
\(149\) | 0.343146 | 0.0281116 | 0.0140558 | − | 0.999901i | \(-0.495526\pi\) | ||||
0.0140558 | + | 0.999901i | \(0.495526\pi\) | |||||||
\(150\) | 6.82843 | 0.557539 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −34.1421 | −2.76023 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 12.6863 | 1.01572 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 9.65685 | 0.768258 | ||||||||
\(159\) | 32.9706 | 2.61474 | ||||||||
\(160\) | −1.58579 | −0.125367 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.41421 | 0.189679 | ||||||||
\(163\) | 16.4853 | 1.29123 | 0.645613 | − | 0.763664i | \(-0.276602\pi\) | ||||
0.645613 | + | 0.763664i | \(0.276602\pi\) | |||||||
\(164\) | −22.9706 | −1.79370 | ||||||||
\(165\) | 2.82843 | 0.220193 | ||||||||
\(166\) | 14.4853 | 1.12428 | ||||||||
\(167\) | 22.9706 | 1.77752 | 0.888758 | − | 0.458377i | \(-0.151569\pi\) | ||||
0.888758 | + | 0.458377i | \(0.151569\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6274 | −0.894417 | ||||||||
\(170\) | −16.4853 | −1.26436 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −22.9706 | −1.75149 | ||||||||
\(173\) | 22.1421 | 1.68344 | 0.841718 | − | 0.539918i | \(-0.181545\pi\) | ||||
0.841718 | + | 0.539918i | \(0.181545\pi\) | |||||||
\(174\) | −24.9706 | −1.89301 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000 | 0.226134 | ||||||||
\(177\) | −4.68629 | −0.352243 | ||||||||
\(178\) | 32.1421 | 2.40915 | ||||||||
\(179\) | 9.65685 | 0.721787 | 0.360894 | − | 0.932607i | \(-0.382472\pi\) | ||||
0.360894 | + | 0.932607i | \(0.382472\pi\) | |||||||
\(180\) | 19.1421 | 1.42677 | ||||||||
\(181\) | −21.3137 | −1.58424 | −0.792118 | − | 0.610368i | \(-0.791021\pi\) | ||||
−0.792118 | + | 0.610368i | \(0.791021\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 26.3431 | 1.94734 | ||||||||
\(184\) | −12.4853 | −0.920427 | ||||||||
\(185\) | −7.65685 | −0.562943 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.82843 | −0.499344 | ||||||||
\(188\) | −10.8284 | −0.789744 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.31371 | 0.239772 | 0.119886 | − | 0.992788i | \(-0.461747\pi\) | ||||
0.119886 | + | 0.992788i | \(0.461747\pi\) | |||||||
\(192\) | −27.7990 | −2.00622 | ||||||||
\(193\) | −1.17157 | −0.0843317 | −0.0421658 | − | 0.999111i | \(-0.513426\pi\) | ||||
−0.0421658 | + | 0.999111i | \(0.513426\pi\) | |||||||
\(194\) | −8.82843 | −0.633844 | ||||||||
\(195\) | 3.31371 | 0.237300 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.8284 | −0.771493 | −0.385747 | − | 0.922605i | \(-0.626056\pi\) | ||||
−0.385747 | + | 0.922605i | \(0.626056\pi\) | |||||||
\(198\) | 12.0711 | 0.857853 | ||||||||
\(199\) | −10.3431 | −0.733206 | −0.366603 | − | 0.930377i | \(-0.619479\pi\) | ||||
−0.366603 | + | 0.930377i | \(0.619479\pi\) | |||||||
\(200\) | 4.41421 | 0.312132 | ||||||||
\(201\) | 35.3137 | 2.49084 | ||||||||
\(202\) | −22.4853 | −1.58206 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −73.9411 | −5.17691 | ||||||||
\(205\) | −6.00000 | −0.419058 | ||||||||
\(206\) | −16.4853 | −1.14858 | ||||||||
\(207\) | −14.1421 | −0.982946 | ||||||||
\(208\) | 3.51472 | 0.243702 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 44.6274 | 3.06502 | ||||||||
\(213\) | 32.0000 | 2.19260 | ||||||||
\(214\) | 18.4853 | 1.26363 | ||||||||
\(215\) | −6.00000 | −0.409197 | ||||||||
\(216\) | 24.9706 | 1.69903 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −18.4853 | −1.25198 | ||||||||
\(219\) | 3.31371 | 0.223920 | ||||||||
\(220\) | 3.82843 | 0.258113 | ||||||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | −52.2843 | −3.50909 | ||||||||
\(223\) | 10.8284 | 0.725125 | 0.362563 | − | 0.931959i | \(-0.381902\pi\) | ||||
0.362563 | + | 0.931959i | \(0.381902\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.00000 | 0.333333 | ||||||||
\(226\) | 47.4558 | 3.15672 | ||||||||
\(227\) | −25.3137 | −1.68013 | −0.840065 | − | 0.542486i | \(-0.817483\pi\) | ||||
−0.840065 | + | 0.542486i | \(0.817483\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.31371 | −0.0868123 | −0.0434062 | − | 0.999058i | \(-0.513821\pi\) | ||||
−0.0434062 | + | 0.999058i | \(0.513821\pi\) | |||||||
\(230\) | −6.82843 | −0.450253 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.1421 | −1.05978 | ||||||||
\(233\) | −6.14214 | −0.402385 | −0.201192 | − | 0.979552i | \(-0.564482\pi\) | ||||
−0.201192 | + | 0.979552i | \(0.564482\pi\) | |||||||
\(234\) | 14.1421 | 0.924500 | ||||||||
\(235\) | −2.82843 | −0.184506 | ||||||||
\(236\) | −6.34315 | −0.412904 | ||||||||
\(237\) | 11.3137 | 0.734904 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.3137 | −1.50804 | −0.754019 | − | 0.656852i | \(-0.771887\pi\) | ||||
−0.754019 | + | 0.656852i | \(0.771887\pi\) | |||||||
\(240\) | 8.48528 | 0.547723 | ||||||||
\(241\) | −6.00000 | −0.386494 | −0.193247 | − | 0.981150i | \(-0.561902\pi\) | ||||
−0.193247 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(242\) | 2.41421 | 0.155192 | ||||||||
\(243\) | −14.1421 | −0.907218 | ||||||||
\(244\) | 35.6569 | 2.28270 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −40.9706 | −2.61219 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.9706 | 1.07547 | ||||||||
\(250\) | 2.41421 | 0.152688 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.82843 | −0.177822 | ||||||||
\(254\) | 10.4853 | 0.657905 | ||||||||
\(255\) | −19.3137 | −1.20947 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 9.31371 | 0.580973 | 0.290487 | − | 0.956879i | \(-0.406183\pi\) | ||||
0.290487 | + | 0.956879i | \(0.406183\pi\) | |||||||
\(258\) | −40.9706 | −2.55072 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.48528 | 0.278165 | ||||||||
\(261\) | −18.2843 | −1.13177 | ||||||||
\(262\) | 27.3137 | 1.68745 | ||||||||
\(263\) | −10.9706 | −0.676474 | −0.338237 | − | 0.941061i | \(-0.609831\pi\) | ||||
−0.338237 | + | 0.941061i | \(0.609831\pi\) | |||||||
\(264\) | 12.4853 | 0.768416 | ||||||||
\(265\) | 11.6569 | 0.716075 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 37.6569 | 2.30456 | ||||||||
\(268\) | 47.7990 | 2.91979 | ||||||||
\(269\) | −17.3137 | −1.05564 | −0.527818 | − | 0.849358i | \(-0.676990\pi\) | ||||
−0.527818 | + | 0.849358i | \(0.676990\pi\) | |||||||
\(270\) | 13.6569 | 0.831130 | ||||||||
\(271\) | −7.31371 | −0.444276 | −0.222138 | − | 0.975015i | \(-0.571304\pi\) | ||||
−0.222138 | + | 0.975015i | \(0.571304\pi\) | |||||||
\(272\) | −20.4853 | −1.24210 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −26.4853 | −1.60003 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −30.6274 | −1.84355 | ||||||||
\(277\) | 6.82843 | 0.410280 | 0.205140 | − | 0.978733i | \(-0.434235\pi\) | ||||
0.205140 | + | 0.978733i | \(0.434235\pi\) | |||||||
\(278\) | 9.65685 | 0.579180 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.3137 | 1.03285 | 0.516425 | − | 0.856333i | \(-0.327263\pi\) | ||||
0.516425 | + | 0.856333i | \(0.327263\pi\) | |||||||
\(282\) | −19.3137 | −1.15011 | ||||||||
\(283\) | −32.6274 | −1.93950 | −0.969749 | − | 0.244103i | \(-0.921507\pi\) | ||||
−0.969749 | + | 0.244103i | \(0.921507\pi\) | |||||||
\(284\) | 43.3137 | 2.57020 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.82843 | 0.167248 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.92893 | −0.467217 | ||||||||
\(289\) | 29.6274 | 1.74279 | ||||||||
\(290\) | −8.82843 | −0.518423 | ||||||||
\(291\) | −10.3431 | −0.606326 | ||||||||
\(292\) | 4.48528 | 0.262481 | ||||||||
\(293\) | 9.17157 | 0.535809 | 0.267905 | − | 0.963445i | \(-0.413669\pi\) | ||||
0.267905 | + | 0.963445i | \(0.413669\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.65685 | −0.0964658 | ||||||||
\(296\) | −33.7990 | −1.96453 | ||||||||
\(297\) | 5.65685 | 0.328244 | ||||||||
\(298\) | 0.828427 | 0.0479895 | ||||||||
\(299\) | −3.31371 | −0.191637 | ||||||||
\(300\) | 10.8284 | 0.625180 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −28.9706 | −1.66707 | ||||||||
\(303\) | −26.3431 | −1.51337 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.31371 | 0.533301 | ||||||||
\(306\) | −82.4264 | −4.71200 | ||||||||
\(307\) | 16.3431 | 0.932753 | 0.466376 | − | 0.884586i | \(-0.345559\pi\) | ||||
0.466376 | + | 0.884586i | \(0.345559\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.3137 | −1.09872 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.68629 | −0.265735 | −0.132868 | − | 0.991134i | \(-0.542419\pi\) | ||||
−0.132868 | + | 0.991134i | \(0.542419\pi\) | |||||||
\(312\) | 14.6274 | 0.828114 | ||||||||
\(313\) | 1.31371 | 0.0742552 | 0.0371276 | − | 0.999311i | \(-0.488179\pi\) | ||||
0.0371276 | + | 0.999311i | \(0.488179\pi\) | |||||||
\(314\) | 33.7990 | 1.90739 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.3137 | 0.861463 | ||||||||
\(317\) | −1.31371 | −0.0737852 | −0.0368926 | − | 0.999319i | \(-0.511746\pi\) | ||||
−0.0368926 | + | 0.999319i | \(0.511746\pi\) | |||||||
\(318\) | 79.5980 | 4.46363 | ||||||||
\(319\) | −3.65685 | −0.204745 | ||||||||
\(320\) | −9.82843 | −0.549426 | ||||||||
\(321\) | 21.6569 | 1.20877 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 3.82843 | 0.212690 | ||||||||
\(325\) | 1.17157 | 0.0649872 | ||||||||
\(326\) | 39.7990 | 2.20426 | ||||||||
\(327\) | −21.6569 | −1.19763 | ||||||||
\(328\) | −26.4853 | −1.46241 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.82843 | 0.375893 | ||||||||
\(331\) | −7.31371 | −0.401998 | −0.200999 | − | 0.979591i | \(-0.564419\pi\) | ||||
−0.200999 | + | 0.979591i | \(0.564419\pi\) | |||||||
\(332\) | 22.9706 | 1.26067 | ||||||||
\(333\) | −38.2843 | −2.09797 | ||||||||
\(334\) | 55.4558 | 3.03441 | ||||||||
\(335\) | 12.4853 | 0.682144 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.4853 | −1.11590 | −0.557952 | − | 0.829873i | \(-0.688413\pi\) | ||||
−0.557952 | + | 0.829873i | \(0.688413\pi\) | |||||||
\(338\) | −28.0711 | −1.52686 | ||||||||
\(339\) | 55.5980 | 3.01967 | ||||||||
\(340\) | −26.1421 | −1.41776 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −26.4853 | −1.42799 | ||||||||
\(345\) | −8.00000 | −0.430706 | ||||||||
\(346\) | 53.4558 | 2.87380 | ||||||||
\(347\) | 10.9706 | 0.588931 | 0.294465 | − | 0.955662i | \(-0.404858\pi\) | ||||
0.294465 | + | 0.955662i | \(0.404858\pi\) | |||||||
\(348\) | −39.5980 | −2.12267 | ||||||||
\(349\) | −26.9706 | −1.44370 | −0.721851 | − | 0.692049i | \(-0.756708\pi\) | ||||
−0.721851 | + | 0.692049i | \(0.756708\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.62742 | 0.353745 | ||||||||
\(352\) | −1.58579 | −0.0845227 | ||||||||
\(353\) | −21.3137 | −1.13441 | −0.567207 | − | 0.823575i | \(-0.691976\pi\) | ||||
−0.567207 | + | 0.823575i | \(0.691976\pi\) | |||||||
\(354\) | −11.3137 | −0.601317 | ||||||||
\(355\) | 11.3137 | 0.600469 | ||||||||
\(356\) | 50.9706 | 2.70143 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 23.3137 | 1.23217 | ||||||||
\(359\) | 0.686292 | 0.0362211 | 0.0181105 | − | 0.999836i | \(-0.494235\pi\) | ||||
0.0181105 | + | 0.999836i | \(0.494235\pi\) | |||||||
\(360\) | 22.0711 | 1.16325 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | −51.4558 | −2.70446 | ||||||||
\(363\) | 2.82843 | 0.148454 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.17157 | 0.0613229 | ||||||||
\(366\) | 63.5980 | 3.32432 | ||||||||
\(367\) | 8.48528 | 0.442928 | 0.221464 | − | 0.975169i | \(-0.428916\pi\) | ||||
0.221464 | + | 0.975169i | \(0.428916\pi\) | |||||||
\(368\) | −8.48528 | −0.442326 | ||||||||
\(369\) | −30.0000 | −1.56174 | ||||||||
\(370\) | −18.4853 | −0.961004 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.7990 | 1.85360 | 0.926801 | − | 0.375554i | \(-0.122547\pi\) | ||||
0.926801 | + | 0.375554i | \(0.122547\pi\) | |||||||
\(374\) | −16.4853 | −0.852434 | ||||||||
\(375\) | 2.82843 | 0.146059 | ||||||||
\(376\) | −12.4853 | −0.643879 | ||||||||
\(377\) | −4.28427 | −0.220651 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.6569 | 1.72884 | 0.864418 | − | 0.502773i | \(-0.167687\pi\) | ||||
0.864418 | + | 0.502773i | \(0.167687\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.2843 | 0.629342 | ||||||||
\(382\) | 8.00000 | 0.409316 | ||||||||
\(383\) | 5.85786 | 0.299323 | 0.149661 | − | 0.988737i | \(-0.452182\pi\) | ||||
0.149661 | + | 0.988737i | \(0.452182\pi\) | |||||||
\(384\) | −58.1421 | −2.96705 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.82843 | −0.143963 | ||||||||
\(387\) | −30.0000 | −1.52499 | ||||||||
\(388\) | −14.0000 | −0.710742 | ||||||||
\(389\) | 20.6274 | 1.04585 | 0.522926 | − | 0.852378i | \(-0.324840\pi\) | ||||
0.522926 | + | 0.852378i | \(0.324840\pi\) | |||||||
\(390\) | 8.00000 | 0.405096 | ||||||||
\(391\) | 19.3137 | 0.976736 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 32.0000 | 1.61419 | ||||||||
\(394\) | −26.1421 | −1.31702 | ||||||||
\(395\) | 4.00000 | 0.201262 | ||||||||
\(396\) | 19.1421 | 0.961929 | ||||||||
\(397\) | 9.31371 | 0.467442 | 0.233721 | − | 0.972304i | \(-0.424910\pi\) | ||||
0.233721 | + | 0.972304i | \(0.424910\pi\) | |||||||
\(398\) | −24.9706 | −1.25166 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | −5.31371 | −0.265354 | −0.132677 | − | 0.991159i | \(-0.542357\pi\) | ||||
−0.132677 | + | 0.991159i | \(0.542357\pi\) | |||||||
\(402\) | 85.2548 | 4.25212 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −35.6569 | −1.77399 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.65685 | −0.379536 | ||||||||
\(408\) | −85.2548 | −4.22074 | ||||||||
\(409\) | −1.02944 | −0.0509024 | −0.0254512 | − | 0.999676i | \(-0.508102\pi\) | ||||
−0.0254512 | + | 0.999676i | \(0.508102\pi\) | |||||||
\(410\) | −14.4853 | −0.715377 | ||||||||
\(411\) | −31.0294 | −1.53057 | ||||||||
\(412\) | −26.1421 | −1.28793 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −34.1421 | −1.67799 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | −1.85786 | −0.0910893 | ||||||||
\(417\) | 11.3137 | 0.554035 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.6569 | 1.25342 | 0.626710 | − | 0.779253i | \(-0.284401\pi\) | ||||
0.626710 | + | 0.779253i | \(0.284401\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | −38.6274 | −1.88035 | ||||||||
\(423\) | −14.1421 | −0.687614 | ||||||||
\(424\) | 51.4558 | 2.49892 | ||||||||
\(425\) | −6.82843 | −0.331227 | ||||||||
\(426\) | 77.2548 | 3.74301 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 29.3137 | 1.41693 | ||||||||
\(429\) | 3.31371 | 0.159987 | ||||||||
\(430\) | −14.4853 | −0.698542 | ||||||||
\(431\) | −11.3137 | −0.544962 | −0.272481 | − | 0.962161i | \(-0.587844\pi\) | ||||
−0.272481 | + | 0.962161i | \(0.587844\pi\) | |||||||
\(432\) | 16.9706 | 0.816497 | ||||||||
\(433\) | 7.65685 | 0.367965 | 0.183982 | − | 0.982930i | \(-0.441101\pi\) | ||||
0.183982 | + | 0.982930i | \(0.441101\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.3431 | −0.495916 | ||||||||
\(436\) | −29.3137 | −1.40387 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 8.00000 | 0.382255 | ||||||||
\(439\) | 16.0000 | 0.763638 | 0.381819 | − | 0.924237i | \(-0.375298\pi\) | ||||
0.381819 | + | 0.924237i | \(0.375298\pi\) | |||||||
\(440\) | 4.41421 | 0.210439 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −19.3137 | −0.918659 | ||||||||
\(443\) | −26.8284 | −1.27466 | −0.637329 | − | 0.770592i | \(-0.719961\pi\) | ||||
−0.637329 | + | 0.770592i | \(0.719961\pi\) | |||||||
\(444\) | −82.9117 | −3.93481 | ||||||||
\(445\) | 13.3137 | 0.631130 | ||||||||
\(446\) | 26.1421 | 1.23787 | ||||||||
\(447\) | 0.970563 | 0.0459060 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.6274 | 1.35101 | 0.675506 | − | 0.737355i | \(-0.263925\pi\) | ||||
0.675506 | + | 0.737355i | \(0.263925\pi\) | |||||||
\(450\) | 12.0711 | 0.569036 | ||||||||
\(451\) | −6.00000 | −0.282529 | ||||||||
\(452\) | 75.2548 | 3.53969 | ||||||||
\(453\) | −33.9411 | −1.59469 | ||||||||
\(454\) | −61.1127 | −2.86816 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.485281 | 0.0227005 | 0.0113503 | − | 0.999936i | \(-0.496387\pi\) | ||||
0.0113503 | + | 0.999936i | \(0.496387\pi\) | |||||||
\(458\) | −3.17157 | −0.148198 | ||||||||
\(459\) | −38.6274 | −1.80297 | ||||||||
\(460\) | −10.8284 | −0.504878 | ||||||||
\(461\) | −12.6274 | −0.588117 | −0.294059 | − | 0.955787i | \(-0.595006\pi\) | ||||
−0.294059 | + | 0.955787i | \(0.595006\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.14214 | −0.285449 | −0.142725 | − | 0.989762i | \(-0.545586\pi\) | ||||
−0.142725 | + | 0.989762i | \(0.545586\pi\) | |||||||
\(464\) | −10.9706 | −0.509296 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.8284 | −0.686914 | ||||||||
\(467\) | 14.8284 | 0.686178 | 0.343089 | − | 0.939303i | \(-0.388527\pi\) | ||||
0.343089 | + | 0.939303i | \(0.388527\pi\) | |||||||
\(468\) | 22.4264 | 1.03666 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.82843 | −0.314972 | ||||||||
\(471\) | 39.5980 | 1.82458 | ||||||||
\(472\) | −7.31371 | −0.336641 | ||||||||
\(473\) | −6.00000 | −0.275880 | ||||||||
\(474\) | 27.3137 | 1.25456 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 58.2843 | 2.66865 | ||||||||
\(478\) | −56.2843 | −2.57438 | ||||||||
\(479\) | 36.0000 | 1.64488 | 0.822441 | − | 0.568850i | \(-0.192612\pi\) | ||||
0.822441 | + | 0.568850i | \(0.192612\pi\) | |||||||
\(480\) | −4.48528 | −0.204724 | ||||||||
\(481\) | −8.97056 | −0.409022 | ||||||||
\(482\) | −14.4853 | −0.659786 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.82843 | 0.174019 | ||||||||
\(485\) | −3.65685 | −0.166049 | ||||||||
\(486\) | −34.1421 | −1.54872 | ||||||||
\(487\) | −24.4853 | −1.10953 | −0.554767 | − | 0.832006i | \(-0.687193\pi\) | ||||
−0.554767 | + | 0.832006i | \(0.687193\pi\) | |||||||
\(488\) | 41.1127 | 1.86108 | ||||||||
\(489\) | 46.6274 | 2.10856 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.686292 | −0.0309719 | −0.0154860 | − | 0.999880i | \(-0.504930\pi\) | ||||
−0.0154860 | + | 0.999880i | \(0.504930\pi\) | |||||||
\(492\) | −64.9706 | −2.92910 | ||||||||
\(493\) | 24.9706 | 1.12462 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.00000 | 0.224733 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 40.9706 | 1.83593 | ||||||||
\(499\) | 9.65685 | 0.432300 | 0.216150 | − | 0.976360i | \(-0.430650\pi\) | ||||
0.216150 | + | 0.976360i | \(0.430650\pi\) | |||||||
\(500\) | 3.82843 | 0.171212 | ||||||||
\(501\) | 64.9706 | 2.90267 | ||||||||
\(502\) | −28.9706 | −1.29302 | ||||||||
\(503\) | −16.6274 | −0.741380 | −0.370690 | − | 0.928757i | \(-0.620879\pi\) | ||||
−0.370690 | + | 0.928757i | \(0.620879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.31371 | −0.414455 | ||||||||
\(506\) | −6.82843 | −0.303561 | ||||||||
\(507\) | −32.8873 | −1.46058 | ||||||||
\(508\) | 16.6274 | 0.737722 | ||||||||
\(509\) | 13.3137 | 0.590120 | 0.295060 | − | 0.955479i | \(-0.404660\pi\) | ||||
0.295060 | + | 0.955479i | \(0.404660\pi\) | |||||||
\(510\) | −46.6274 | −2.06470 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −31.2426 | −1.38074 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.4853 | 0.991783 | ||||||||
\(515\) | −6.82843 | −0.300896 | ||||||||
\(516\) | −64.9706 | −2.86017 | ||||||||
\(517\) | −2.82843 | −0.124394 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 62.6274 | 2.74904 | ||||||||
\(520\) | 5.17157 | 0.226788 | ||||||||
\(521\) | −25.3137 | −1.10901 | −0.554507 | − | 0.832179i | \(-0.687093\pi\) | ||||
−0.554507 | + | 0.832179i | \(0.687093\pi\) | |||||||
\(522\) | −44.1421 | −1.93205 | ||||||||
\(523\) | 41.5980 | 1.81895 | 0.909476 | − | 0.415756i | \(-0.136483\pi\) | ||||
0.909476 | + | 0.415756i | \(0.136483\pi\) | |||||||
\(524\) | 43.3137 | 1.89217 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −26.4853 | −1.15481 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 8.48528 | 0.369274 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 28.1421 | 1.22242 | ||||||||
\(531\) | −8.28427 | −0.359507 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.02944 | −0.304479 | ||||||||
\(534\) | 90.9117 | 3.93413 | ||||||||
\(535\) | 7.65685 | 0.331035 | ||||||||
\(536\) | 55.1127 | 2.38051 | ||||||||
\(537\) | 27.3137 | 1.17867 | ||||||||
\(538\) | −41.7990 | −1.80208 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 21.6569 | 0.931963 | ||||||||
\(541\) | 6.00000 | 0.257960 | 0.128980 | − | 0.991647i | \(-0.458830\pi\) | ||||
0.128980 | + | 0.991647i | \(0.458830\pi\) | |||||||
\(542\) | −17.6569 | −0.758427 | ||||||||
\(543\) | −60.2843 | −2.58705 | ||||||||
\(544\) | 10.8284 | 0.464265 | ||||||||
\(545\) | −7.65685 | −0.327984 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.0000 | −1.45374 | −0.726868 | − | 0.686778i | \(-0.759025\pi\) | ||||
−0.726868 | + | 0.686778i | \(0.759025\pi\) | |||||||
\(548\) | −42.0000 | −1.79415 | ||||||||
\(549\) | 46.5685 | 1.98750 | ||||||||
\(550\) | 2.41421 | 0.102942 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −35.3137 | −1.50305 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 16.4853 | 0.700392 | ||||||||
\(555\) | −21.6569 | −0.919282 | ||||||||
\(556\) | 15.3137 | 0.649446 | ||||||||
\(557\) | 9.85786 | 0.417691 | 0.208846 | − | 0.977949i | \(-0.433029\pi\) | ||||
0.208846 | + | 0.977949i | \(0.433029\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.02944 | −0.297314 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.3137 | −0.815425 | ||||||||
\(562\) | 41.7990 | 1.76318 | ||||||||
\(563\) | −0.343146 | −0.0144619 | −0.00723093 | − | 0.999974i | \(-0.502302\pi\) | ||||
−0.00723093 | + | 0.999974i | \(0.502302\pi\) | |||||||
\(564\) | −30.6274 | −1.28965 | ||||||||
\(565\) | 19.6569 | 0.826970 | ||||||||
\(566\) | −78.7696 | −3.31093 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 49.9411 | 2.09548 | ||||||||
\(569\) | 31.6569 | 1.32712 | 0.663562 | − | 0.748121i | \(-0.269044\pi\) | ||||
0.663562 | + | 0.748121i | \(0.269044\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.9411 | −0.918208 | −0.459104 | − | 0.888383i | \(-0.651829\pi\) | ||||
−0.459104 | + | 0.888383i | \(0.651829\pi\) | |||||||
\(572\) | 4.48528 | 0.187539 | ||||||||
\(573\) | 9.37258 | 0.391545 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.82843 | −0.117954 | ||||||||
\(576\) | −49.1421 | −2.04759 | ||||||||
\(577\) | 26.9706 | 1.12280 | 0.561400 | − | 0.827545i | \(-0.310263\pi\) | ||||
0.561400 | + | 0.827545i | \(0.310263\pi\) | |||||||
\(578\) | 71.5269 | 2.97513 | ||||||||
\(579\) | −3.31371 | −0.137713 | ||||||||
\(580\) | −14.0000 | −0.581318 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −24.9706 | −1.03506 | ||||||||
\(583\) | 11.6569 | 0.482778 | ||||||||
\(584\) | 5.17157 | 0.214001 | ||||||||
\(585\) | 5.85786 | 0.242193 | ||||||||
\(586\) | 22.1421 | 0.914683 | ||||||||
\(587\) | 2.14214 | 0.0884154 | 0.0442077 | − | 0.999022i | \(-0.485924\pi\) | ||||
0.0442077 | + | 0.999022i | \(0.485924\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −4.00000 | −0.164677 | ||||||||
\(591\) | −30.6274 | −1.25984 | ||||||||
\(592\) | −22.9706 | −0.944084 | ||||||||
\(593\) | −3.51472 | −0.144332 | −0.0721661 | − | 0.997393i | \(-0.522991\pi\) | ||||
−0.0721661 | + | 0.997393i | \(0.522991\pi\) | |||||||
\(594\) | 13.6569 | 0.560348 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.31371 | 0.0538116 | ||||||||
\(597\) | −29.2548 | −1.19732 | ||||||||
\(598\) | −8.00000 | −0.327144 | ||||||||
\(599\) | −5.65685 | −0.231133 | −0.115566 | − | 0.993300i | \(-0.536868\pi\) | ||||
−0.115566 | + | 0.993300i | \(0.536868\pi\) | |||||||
\(600\) | 12.4853 | 0.509709 | ||||||||
\(601\) | −23.9411 | −0.976579 | −0.488289 | − | 0.872682i | \(-0.662379\pi\) | ||||
−0.488289 | + | 0.872682i | \(0.662379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 62.4264 | 2.54220 | ||||||||
\(604\) | −45.9411 | −1.86932 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −63.5980 | −2.58349 | ||||||||
\(607\) | −38.2843 | −1.55391 | −0.776955 | − | 0.629556i | \(-0.783237\pi\) | ||||
−0.776955 | + | 0.629556i | \(0.783237\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.4853 | 0.910402 | ||||||||
\(611\) | −3.31371 | −0.134058 | ||||||||
\(612\) | −130.711 | −5.28367 | ||||||||
\(613\) | −25.4558 | −1.02815 | −0.514076 | − | 0.857745i | \(-0.671865\pi\) | ||||
−0.514076 | + | 0.857745i | \(0.671865\pi\) | |||||||
\(614\) | 39.4558 | 1.59231 | ||||||||
\(615\) | −16.9706 | −0.684319 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.343146 | 0.0138145 | 0.00690726 | − | 0.999976i | \(-0.497801\pi\) | ||||
0.00690726 | + | 0.999976i | \(0.497801\pi\) | |||||||
\(618\) | −46.6274 | −1.87563 | ||||||||
\(619\) | 14.3431 | 0.576500 | 0.288250 | − | 0.957555i | \(-0.406927\pi\) | ||||
0.288250 | + | 0.957555i | \(0.406927\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.0000 | −0.642058 | ||||||||
\(622\) | −11.3137 | −0.453638 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 9.94113 | 0.397964 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.17157 | 0.126762 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 53.5980 | 2.13879 | ||||||||
\(629\) | 52.2843 | 2.08471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 17.6569 | 0.702352 | ||||||||
\(633\) | −45.2548 | −1.79872 | ||||||||
\(634\) | −3.17157 | −0.125959 | ||||||||
\(635\) | 4.34315 | 0.172352 | ||||||||
\(636\) | 126.225 | 5.00516 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.82843 | −0.349521 | ||||||||
\(639\) | 56.5685 | 2.23782 | ||||||||
\(640\) | −20.5563 | −0.812561 | ||||||||
\(641\) | 30.0000 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(642\) | 52.2843 | 2.06350 | ||||||||
\(643\) | 1.45584 | 0.0574129 | 0.0287064 | − | 0.999588i | \(-0.490861\pi\) | ||||
0.0287064 | + | 0.999588i | \(0.490861\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.9706 | −0.668215 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.1127 | −1.06591 | −0.532955 | − | 0.846144i | \(-0.678919\pi\) | ||||
−0.532955 | + | 0.846144i | \(0.678919\pi\) | |||||||
\(648\) | 4.41421 | 0.173407 | ||||||||
\(649\) | −1.65685 | −0.0650372 | ||||||||
\(650\) | 2.82843 | 0.110940 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 63.1127 | 2.47168 | ||||||||
\(653\) | 11.6569 | 0.456168 | 0.228084 | − | 0.973641i | \(-0.426754\pi\) | ||||
0.228084 | + | 0.973641i | \(0.426754\pi\) | |||||||
\(654\) | −52.2843 | −2.04448 | ||||||||
\(655\) | 11.3137 | 0.442063 | ||||||||
\(656\) | −18.0000 | −0.702782 | ||||||||
\(657\) | 5.85786 | 0.228537 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.9411 | 1.78961 | 0.894806 | − | 0.446455i | \(-0.147314\pi\) | ||||
0.894806 | + | 0.446455i | \(0.147314\pi\) | |||||||
\(660\) | 10.8284 | 0.421496 | ||||||||
\(661\) | −44.6274 | −1.73581 | −0.867903 | − | 0.496734i | \(-0.834532\pi\) | ||||
−0.867903 | + | 0.496734i | \(0.834532\pi\) | |||||||
\(662\) | −17.6569 | −0.686253 | ||||||||
\(663\) | −22.6274 | −0.878776 | ||||||||
\(664\) | 26.4853 | 1.02783 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −92.4264 | −3.58145 | ||||||||
\(667\) | 10.3431 | 0.400488 | ||||||||
\(668\) | 87.9411 | 3.40254 | ||||||||
\(669\) | 30.6274 | 1.18412 | ||||||||
\(670\) | 30.1421 | 1.16449 | ||||||||
\(671\) | 9.31371 | 0.359552 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.4853 | −0.481272 | −0.240636 | − | 0.970615i | \(-0.577356\pi\) | ||||
−0.240636 | + | 0.970615i | \(0.577356\pi\) | |||||||
\(674\) | −49.4558 | −1.90497 | ||||||||
\(675\) | 5.65685 | 0.217732 | ||||||||
\(676\) | −44.5147 | −1.71210 | ||||||||
\(677\) | −22.8284 | −0.877368 | −0.438684 | − | 0.898641i | \(-0.644555\pi\) | ||||
−0.438684 | + | 0.898641i | \(0.644555\pi\) | |||||||
\(678\) | 134.225 | 5.15490 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −30.1421 | −1.15590 | ||||||||
\(681\) | −71.5980 | −2.74364 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.79899 | −0.298420 | −0.149210 | − | 0.988806i | \(-0.547673\pi\) | ||||
−0.149210 | + | 0.988806i | \(0.547673\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.9706 | −0.419164 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.71573 | −0.141764 | ||||||||
\(688\) | −18.0000 | −0.686244 | ||||||||
\(689\) | 13.6569 | 0.520285 | ||||||||
\(690\) | −19.3137 | −0.735260 | ||||||||
\(691\) | 39.3137 | 1.49556 | 0.747782 | − | 0.663944i | \(-0.231119\pi\) | ||||
0.747782 | + | 0.663944i | \(0.231119\pi\) | |||||||
\(692\) | 84.7696 | 3.22245 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.4853 | 1.00537 | ||||||||
\(695\) | 4.00000 | 0.151729 | ||||||||
\(696\) | −45.6569 | −1.73062 | ||||||||
\(697\) | 40.9706 | 1.55187 | ||||||||
\(698\) | −65.1127 | −2.46455 | ||||||||
\(699\) | −17.3726 | −0.657091 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.6274 | −0.476931 | −0.238465 | − | 0.971151i | \(-0.576644\pi\) | ||||
−0.238465 | + | 0.971151i | \(0.576644\pi\) | |||||||
\(702\) | 16.0000 | 0.603881 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −9.82843 | −0.370423 | ||||||||
\(705\) | −8.00000 | −0.301297 | ||||||||
\(706\) | −51.4558 | −1.93657 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −17.9411 | −0.674269 | ||||||||
\(709\) | 24.6274 | 0.924902 | 0.462451 | − | 0.886645i | \(-0.346970\pi\) | ||||
0.462451 | + | 0.886645i | \(0.346970\pi\) | |||||||
\(710\) | 27.3137 | 1.02507 | ||||||||
\(711\) | 20.0000 | 0.750059 | ||||||||
\(712\) | 58.7696 | 2.20248 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.17157 | 0.0438143 | ||||||||
\(716\) | 36.9706 | 1.38165 | ||||||||
\(717\) | −65.9411 | −2.46262 | ||||||||
\(718\) | 1.65685 | 0.0618333 | ||||||||
\(719\) | −18.3431 | −0.684084 | −0.342042 | − | 0.939685i | \(-0.611118\pi\) | ||||
−0.342042 | + | 0.939685i | \(0.611118\pi\) | |||||||
\(720\) | 15.0000 | 0.559017 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −45.8701 | −1.70711 | ||||||||
\(723\) | −16.9706 | −0.631142 | ||||||||
\(724\) | −81.5980 | −3.03257 | ||||||||
\(725\) | −3.65685 | −0.135812 | ||||||||
\(726\) | 6.82843 | 0.253427 | ||||||||
\(727\) | 19.5147 | 0.723761 | 0.361880 | − | 0.932225i | \(-0.382135\pi\) | ||||
0.361880 | + | 0.932225i | \(0.382135\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.0000 | −1.59259 | ||||||||
\(730\) | 2.82843 | 0.104685 | ||||||||
\(731\) | 40.9706 | 1.51535 | ||||||||
\(732\) | 100.853 | 3.72763 | ||||||||
\(733\) | 17.4558 | 0.644746 | 0.322373 | − | 0.946613i | \(-0.395519\pi\) | ||||
0.322373 | + | 0.946613i | \(0.395519\pi\) | |||||||
\(734\) | 20.4853 | 0.756126 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.48528 | 0.165330 | ||||||||
\(737\) | 12.4853 | 0.459901 | ||||||||
\(738\) | −72.4264 | −2.66605 | ||||||||
\(739\) | 29.9411 | 1.10140 | 0.550701 | − | 0.834703i | \(-0.314360\pi\) | ||||
0.550701 | + | 0.834703i | \(0.314360\pi\) | |||||||
\(740\) | −29.3137 | −1.07759 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −49.5980 | −1.81957 | −0.909787 | − | 0.415076i | \(-0.863755\pi\) | ||||
−0.909787 | + | 0.415076i | \(0.863755\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.343146 | 0.0125719 | ||||||||
\(746\) | 86.4264 | 3.16430 | ||||||||
\(747\) | 30.0000 | 1.09764 | ||||||||
\(748\) | −26.1421 | −0.955851 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 6.82843 | 0.249339 | ||||||||
\(751\) | −16.0000 | −0.583848 | −0.291924 | − | 0.956441i | \(-0.594295\pi\) | ||||
−0.291924 | + | 0.956441i | \(0.594295\pi\) | |||||||
\(752\) | −8.48528 | −0.309426 | ||||||||
\(753\) | −33.9411 | −1.23688 | ||||||||
\(754\) | −10.3431 | −0.376675 | ||||||||
\(755\) | −12.0000 | −0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.3137 | 0.483895 | 0.241947 | − | 0.970289i | \(-0.422214\pi\) | ||||
0.241947 | + | 0.970289i | \(0.422214\pi\) | |||||||
\(758\) | 81.2548 | 2.95131 | ||||||||
\(759\) | −8.00000 | −0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.0000 | 1.08750 | 0.543750 | − | 0.839248i | \(-0.317004\pi\) | ||||
0.543750 | + | 0.839248i | \(0.317004\pi\) | |||||||
\(762\) | 29.6569 | 1.07435 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 12.6863 | 0.458974 | ||||||||
\(765\) | −34.1421 | −1.23441 | ||||||||
\(766\) | 14.1421 | 0.510976 | ||||||||
\(767\) | −1.94113 | −0.0700900 | ||||||||
\(768\) | −84.7696 | −3.05886 | ||||||||
\(769\) | 18.9706 | 0.684096 | 0.342048 | − | 0.939682i | \(-0.388879\pi\) | ||||
0.342048 | + | 0.939682i | \(0.388879\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.3431 | 0.948725 | ||||||||
\(772\) | −4.48528 | −0.161429 | ||||||||
\(773\) | −26.2843 | −0.945380 | −0.472690 | − | 0.881229i | \(-0.656717\pi\) | ||||
−0.472690 | + | 0.881229i | \(0.656717\pi\) | |||||||
\(774\) | −72.4264 | −2.60331 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16.1421 | −0.579469 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 49.7990 | 1.78538 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 12.6863 | 0.454242 | ||||||||
\(781\) | 11.3137 | 0.404836 | ||||||||
\(782\) | 46.6274 | 1.66739 | ||||||||
\(783\) | −20.6863 | −0.739268 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.0000 | 0.499681 | ||||||||
\(786\) | 77.2548 | 2.75559 | ||||||||
\(787\) | 14.9706 | 0.533643 | 0.266821 | − | 0.963746i | \(-0.414027\pi\) | ||||
0.266821 | + | 0.963746i | \(0.414027\pi\) | |||||||
\(788\) | −41.4558 | −1.47680 | ||||||||
\(789\) | −31.0294 | −1.10468 | ||||||||
\(790\) | 9.65685 | 0.343575 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 22.0711 | 0.784261 | ||||||||
\(793\) | 10.9117 | 0.387485 | ||||||||
\(794\) | 22.4853 | 0.797973 | ||||||||
\(795\) | 32.9706 | 1.16935 | ||||||||
\(796\) | −39.5980 | −1.40351 | ||||||||
\(797\) | −32.6274 | −1.15572 | −0.577861 | − | 0.816135i | \(-0.696113\pi\) | ||||
−0.577861 | + | 0.816135i | \(0.696113\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.3137 | 0.683270 | ||||||||
\(800\) | −1.58579 | −0.0560660 | ||||||||
\(801\) | 66.5685 | 2.35208 | ||||||||
\(802\) | −12.8284 | −0.452988 | ||||||||
\(803\) | 1.17157 | 0.0413439 | ||||||||
\(804\) | 135.196 | 4.76799 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −48.9706 | −1.72385 | ||||||||
\(808\) | −41.1127 | −1.44634 | ||||||||
\(809\) | −10.9706 | −0.385704 | −0.192852 | − | 0.981228i | \(-0.561774\pi\) | ||||
−0.192852 | + | 0.981228i | \(0.561774\pi\) | |||||||
\(810\) | 2.41421 | 0.0848268 | ||||||||
\(811\) | −53.9411 | −1.89413 | −0.947065 | − | 0.321043i | \(-0.895967\pi\) | ||||
−0.947065 | + | 0.321043i | \(0.895967\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.6863 | −0.725500 | ||||||||
\(814\) | −18.4853 | −0.647909 | ||||||||
\(815\) | 16.4853 | 0.577454 | ||||||||
\(816\) | −57.9411 | −2.02835 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −2.48528 | −0.0868958 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.9706 | −0.802167 | ||||||||
\(821\) | −41.3137 | −1.44186 | −0.720929 | − | 0.693009i | \(-0.756285\pi\) | ||||
−0.720929 | + | 0.693009i | \(0.756285\pi\) | |||||||
\(822\) | −74.9117 | −2.61285 | ||||||||
\(823\) | 19.5147 | 0.680240 | 0.340120 | − | 0.940382i | \(-0.389532\pi\) | ||||
0.340120 | + | 0.940382i | \(0.389532\pi\) | |||||||
\(824\) | −30.1421 | −1.05005 | ||||||||
\(825\) | 2.82843 | 0.0984732 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.2843 | 0.774900 | 0.387450 | − | 0.921891i | \(-0.373356\pi\) | ||||
0.387450 | + | 0.921891i | \(0.373356\pi\) | |||||||
\(828\) | −54.1421 | −1.88157 | ||||||||
\(829\) | −18.0000 | −0.625166 | −0.312583 | − | 0.949890i | \(-0.601194\pi\) | ||||
−0.312583 | + | 0.949890i | \(0.601194\pi\) | |||||||
\(830\) | 14.4853 | 0.502791 | ||||||||
\(831\) | 19.3137 | 0.669985 | ||||||||
\(832\) | −11.5147 | −0.399201 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 27.3137 | 0.945796 | ||||||||
\(835\) | 22.9706 | 0.794929 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 61.9411 | 2.13972 | ||||||||
\(839\) | −26.3431 | −0.909466 | −0.454733 | − | 0.890628i | \(-0.650265\pi\) | ||||
−0.454733 | + | 0.890628i | \(0.650265\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6274 | −0.538876 | ||||||||
\(842\) | −14.4853 | −0.499196 | ||||||||
\(843\) | 48.9706 | 1.68664 | ||||||||
\(844\) | −61.2548 | −2.10848 | ||||||||
\(845\) | −11.6274 | −0.399995 | ||||||||
\(846\) | −34.1421 | −1.17383 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 34.9706 | 1.20089 | ||||||||
\(849\) | −92.2843 | −3.16719 | ||||||||
\(850\) | −16.4853 | −0.565440 | ||||||||
\(851\) | 21.6569 | 0.742387 | ||||||||
\(852\) | 122.510 | 4.19711 | ||||||||
\(853\) | 15.5147 | 0.531214 | 0.265607 | − | 0.964081i | \(-0.414428\pi\) | ||||
0.265607 | + | 0.964081i | \(0.414428\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 33.7990 | 1.15523 | ||||||||
\(857\) | −24.7696 | −0.846112 | −0.423056 | − | 0.906104i | \(-0.639043\pi\) | ||||
−0.423056 | + | 0.906104i | \(0.639043\pi\) | |||||||
\(858\) | 8.00000 | 0.273115 | ||||||||
\(859\) | −24.2843 | −0.828569 | −0.414284 | − | 0.910148i | \(-0.635968\pi\) | ||||
−0.414284 | + | 0.910148i | \(0.635968\pi\) | |||||||
\(860\) | −22.9706 | −0.783290 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27.3137 | −0.930309 | ||||||||
\(863\) | −9.17157 | −0.312204 | −0.156102 | − | 0.987741i | \(-0.549893\pi\) | ||||
−0.156102 | + | 0.987741i | \(0.549893\pi\) | |||||||
\(864\) | −8.97056 | −0.305185 | ||||||||
\(865\) | 22.1421 | 0.752855 | ||||||||
\(866\) | 18.4853 | 0.628155 | ||||||||
\(867\) | 83.7990 | 2.84596 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.00000 | 0.135691 | ||||||||
\(870\) | −24.9706 | −0.846581 | ||||||||
\(871\) | 14.6274 | 0.495631 | ||||||||
\(872\) | −33.7990 | −1.14458 | ||||||||
\(873\) | −18.2843 | −0.618829 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.6863 | 0.428630 | ||||||||
\(877\) | −49.4558 | −1.67001 | −0.835003 | − | 0.550246i | \(-0.814534\pi\) | ||||
−0.835003 | + | 0.550246i | \(0.814534\pi\) | |||||||
\(878\) | 38.6274 | 1.30361 | ||||||||
\(879\) | 25.9411 | 0.874972 | ||||||||
\(880\) | 3.00000 | 0.101130 | ||||||||
\(881\) | 7.37258 | 0.248389 | 0.124194 | − | 0.992258i | \(-0.460365\pi\) | ||||
0.124194 | + | 0.992258i | \(0.460365\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.1716 | 1.25092 | 0.625462 | − | 0.780255i | \(-0.284911\pi\) | ||||
0.625462 | + | 0.780255i | \(0.284911\pi\) | |||||||
\(884\) | −30.6274 | −1.03011 | ||||||||
\(885\) | −4.68629 | −0.157528 | ||||||||
\(886\) | −64.7696 | −2.17598 | ||||||||
\(887\) | −38.2843 | −1.28546 | −0.642730 | − | 0.766093i | \(-0.722198\pi\) | ||||
−0.642730 | + | 0.766093i | \(0.722198\pi\) | |||||||
\(888\) | −95.5980 | −3.20806 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 32.1421 | 1.07741 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 41.4558 | 1.38804 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 2.34315 | 0.0783665 | ||||||||
\(895\) | 9.65685 | 0.322793 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.37258 | −0.312941 | ||||||||
\(898\) | 69.1127 | 2.30632 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 19.1421 | 0.638071 | ||||||||
\(901\) | −79.5980 | −2.65179 | ||||||||
\(902\) | −14.4853 | −0.482307 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 86.7696 | 2.88591 | ||||||||
\(905\) | −21.3137 | −0.708492 | ||||||||
\(906\) | −81.9411 | −2.72231 | ||||||||
\(907\) | −27.5147 | −0.913611 | −0.456806 | − | 0.889567i | \(-0.651007\pi\) | ||||
−0.456806 | + | 0.889567i | \(0.651007\pi\) | |||||||
\(908\) | −96.9117 | −3.21613 | ||||||||
\(909\) | −46.5685 | −1.54458 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.94113 | −0.329364 | −0.164682 | − | 0.986347i | \(-0.552660\pi\) | ||||
−0.164682 | + | 0.986347i | \(0.552660\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.00000 | 0.198571 | ||||||||
\(914\) | 1.17157 | 0.0387522 | ||||||||
\(915\) | 26.3431 | 0.870878 | ||||||||
\(916\) | −5.02944 | −0.166177 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −93.2548 | −3.07787 | ||||||||
\(919\) | −32.0000 | −1.05558 | −0.527791 | − | 0.849374i | \(-0.676980\pi\) | ||||
−0.527791 | + | 0.849374i | \(0.676980\pi\) | |||||||
\(920\) | −12.4853 | −0.411628 | ||||||||
\(921\) | 46.2254 | 1.52318 | ||||||||
\(922\) | −30.4853 | −1.00398 | ||||||||
\(923\) | 13.2548 | 0.436288 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.65685 | −0.251756 | ||||||||
\(926\) | −14.8284 | −0.487292 | ||||||||
\(927\) | −34.1421 | −1.12137 | ||||||||
\(928\) | 5.79899 | 0.190361 | ||||||||
\(929\) | −5.31371 | −0.174337 | −0.0871686 | − | 0.996194i | \(-0.527782\pi\) | ||||
−0.0871686 | + | 0.996194i | \(0.527782\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −23.5147 | −0.770250 | ||||||||
\(933\) | −13.2548 | −0.433944 | ||||||||
\(934\) | 35.7990 | 1.17138 | ||||||||
\(935\) | −6.82843 | −0.223313 | ||||||||
\(936\) | 25.8579 | 0.845191 | ||||||||
\(937\) | 1.45584 | 0.0475604 | 0.0237802 | − | 0.999717i | \(-0.492430\pi\) | ||||
0.0237802 | + | 0.999717i | \(0.492430\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.71573 | 0.121258 | ||||||||
\(940\) | −10.8284 | −0.353184 | ||||||||
\(941\) | 6.68629 | 0.217967 | 0.108983 | − | 0.994044i | \(-0.465240\pi\) | ||||
0.108983 | + | 0.994044i | \(0.465240\pi\) | |||||||
\(942\) | 95.5980 | 3.11475 | ||||||||
\(943\) | 16.9706 | 0.552638 | ||||||||
\(944\) | −4.97056 | −0.161778 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.4853 | −0.470957 | ||||||||
\(947\) | 41.1716 | 1.33790 | 0.668948 | − | 0.743309i | \(-0.266745\pi\) | ||||
0.668948 | + | 0.743309i | \(0.266745\pi\) | |||||||
\(948\) | 43.3137 | 1.40676 | ||||||||
\(949\) | 1.37258 | 0.0445559 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.71573 | −0.120491 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.1716 | 1.72240 | 0.861198 | − | 0.508269i | \(-0.169715\pi\) | ||||
0.861198 | + | 0.508269i | \(0.169715\pi\) | |||||||
\(954\) | 140.711 | 4.55568 | ||||||||
\(955\) | 3.31371 | 0.107229 | ||||||||
\(956\) | −89.2548 | −2.88671 | ||||||||
\(957\) | −10.3431 | −0.334346 | ||||||||
\(958\) | 86.9117 | 2.80799 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −27.7990 | −0.897209 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −21.6569 | −0.698245 | ||||||||
\(963\) | 38.2843 | 1.23369 | ||||||||
\(964\) | −22.9706 | −0.739832 | ||||||||
\(965\) | −1.17157 | −0.0377143 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.9706 | −0.481421 | −0.240710 | − | 0.970597i | \(-0.577380\pi\) | ||||
−0.240710 | + | 0.970597i | \(0.577380\pi\) | |||||||
\(968\) | 4.41421 | 0.141878 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.82843 | −0.283464 | ||||||||
\(971\) | 8.68629 | 0.278756 | 0.139378 | − | 0.990239i | \(-0.455490\pi\) | ||||
0.139378 | + | 0.990239i | \(0.455490\pi\) | |||||||
\(972\) | −54.1421 | −1.73661 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −59.1127 | −1.89409 | ||||||||
\(975\) | 3.31371 | 0.106124 | ||||||||
\(976\) | 27.9411 | 0.894374 | ||||||||
\(977\) | 32.3431 | 1.03475 | 0.517374 | − | 0.855759i | \(-0.326909\pi\) | ||||
0.517374 | + | 0.855759i | \(0.326909\pi\) | |||||||
\(978\) | 112.569 | 3.59955 | ||||||||
\(979\) | 13.3137 | 0.425508 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −38.2843 | −1.22232 | ||||||||
\(982\) | −1.65685 | −0.0528723 | ||||||||
\(983\) | 21.8579 | 0.697158 | 0.348579 | − | 0.937279i | \(-0.386664\pi\) | ||||
0.348579 | + | 0.937279i | \(0.386664\pi\) | |||||||
\(984\) | −74.9117 | −2.38810 | ||||||||
\(985\) | −10.8284 | −0.345022 | ||||||||
\(986\) | 60.2843 | 1.91984 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.9706 | 0.539633 | ||||||||
\(990\) | 12.0711 | 0.383644 | ||||||||
\(991\) | −57.9411 | −1.84056 | −0.920280 | − | 0.391260i | \(-0.872039\pi\) | ||||
−0.920280 | + | 0.391260i | \(0.872039\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.6863 | −0.656460 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.3431 | −0.327900 | ||||||||
\(996\) | 64.9706 | 2.05867 | ||||||||
\(997\) | 41.4558 | 1.31292 | 0.656460 | − | 0.754361i | \(-0.272053\pi\) | ||||
0.656460 | + | 0.754361i | \(0.272053\pi\) | |||||||
\(998\) | 23.3137 | 0.737983 | ||||||||
\(999\) | −43.3137 | −1.37039 |
(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 | 2695.2.a.f.1.2 | 2 | ||
7.6 | odd | 2 | 55.2.a.b.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 495.2.a.b.1.1 | 2 | |||
28.27 | even | 2 | 880.2.a.m.1.2 | 2 | |||
35.13 | even | 4 | 275.2.b.d.199.1 | 4 | |||
35.27 | even | 4 | 275.2.b.d.199.4 | 4 | |||
35.34 | odd | 2 | 275.2.a.c.1.1 | 2 | |||
56.13 | odd | 2 | 3520.2.a.bn.1.2 | 2 | |||
56.27 | even | 2 | 3520.2.a.bo.1.1 | 2 | |||
77.6 | even | 10 | 605.2.g.l.366.2 | 8 | |||
77.13 | even | 10 | 605.2.g.l.81.2 | 8 | |||
77.20 | odd | 10 | 605.2.g.f.81.1 | 8 | |||
77.27 | odd | 10 | 605.2.g.f.366.1 | 8 | |||
77.41 | even | 10 | 605.2.g.l.251.1 | 8 | |||
77.48 | odd | 10 | 605.2.g.f.511.2 | 8 | |||
77.62 | even | 10 | 605.2.g.l.511.1 | 8 | |||
77.69 | odd | 10 | 605.2.g.f.251.2 | 8 | |||
77.76 | even | 2 | 605.2.a.d.1.1 | 2 | |||
84.83 | odd | 2 | 7920.2.a.ch.1.2 | 2 | |||
91.90 | odd | 2 | 9295.2.a.g.1.1 | 2 | |||
105.62 | odd | 4 | 2475.2.c.l.199.1 | 4 | |||
105.83 | odd | 4 | 2475.2.c.l.199.4 | 4 | |||
105.104 | even | 2 | 2475.2.a.x.1.2 | 2 | |||
140.27 | odd | 4 | 4400.2.b.q.4049.2 | 4 | |||
140.83 | odd | 4 | 4400.2.b.q.4049.3 | 4 | |||
140.139 | even | 2 | 4400.2.a.bn.1.1 | 2 | |||
231.230 | odd | 2 | 5445.2.a.y.1.2 | 2 | |||
308.307 | odd | 2 | 9680.2.a.bn.1.2 | 2 | |||
385.384 | even | 2 | 3025.2.a.o.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.a.b.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
275.2.a.c.1.1 | 2 | 35.34 | odd | 2 | |||
275.2.b.d.199.1 | 4 | 35.13 | even | 4 | |||
275.2.b.d.199.4 | 4 | 35.27 | even | 4 | |||
495.2.a.b.1.1 | 2 | 21.20 | even | 2 | |||
605.2.a.d.1.1 | 2 | 77.76 | even | 2 | |||
605.2.g.f.81.1 | 8 | 77.20 | odd | 10 | |||
605.2.g.f.251.2 | 8 | 77.69 | odd | 10 | |||
605.2.g.f.366.1 | 8 | 77.27 | odd | 10 | |||
605.2.g.f.511.2 | 8 | 77.48 | odd | 10 | |||
605.2.g.l.81.2 | 8 | 77.13 | even | 10 | |||
605.2.g.l.251.1 | 8 | 77.41 | even | 10 | |||
605.2.g.l.366.2 | 8 | 77.6 | even | 10 | |||
605.2.g.l.511.1 | 8 | 77.62 | even | 10 | |||
880.2.a.m.1.2 | 2 | 28.27 | even | 2 | |||
2475.2.a.x.1.2 | 2 | 105.104 | even | 2 | |||
2475.2.c.l.199.1 | 4 | 105.62 | odd | 4 | |||
2475.2.c.l.199.4 | 4 | 105.83 | odd | 4 | |||
2695.2.a.f.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3025.2.a.o.1.2 | 2 | 385.384 | even | 2 | |||
3520.2.a.bn.1.2 | 2 | 56.13 | odd | 2 | |||
3520.2.a.bo.1.1 | 2 | 56.27 | even | 2 | |||
4400.2.a.bn.1.1 | 2 | 140.139 | even | 2 | |||
4400.2.b.q.4049.2 | 4 | 140.27 | odd | 4 | |||
4400.2.b.q.4049.3 | 4 | 140.83 | odd | 4 | |||
5445.2.a.y.1.2 | 2 | 231.230 | odd | 2 | |||
7920.2.a.ch.1.2 | 2 | 84.83 | odd | 2 | |||
9295.2.a.g.1.1 | 2 | 91.90 | odd | 2 | |||
9680.2.a.bn.1.2 | 2 | 308.307 | odd | 2 |