Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.4642000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 8x^{4} + 5x^{3} + 14x^{2} - 9x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.73934\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.73934 | −1.58156 | −0.790780 | − | 0.612100i | \(-0.790325\pi\) | ||||
−0.790780 | + | 0.612100i | \(0.790325\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.73934 | −1.11833 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.50401 | 1.50134 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.73934 | −0.790780 | ||||||||
\(13\) | 2.65196 | 0.735520 | 0.367760 | − | 0.929921i | \(-0.380125\pi\) | ||||
0.367760 | + | 0.929921i | \(0.380125\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −2.73934 | −0.707296 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.67727 | −1.61948 | −0.809738 | − | 0.586791i | \(-0.800391\pi\) | ||||
−0.809738 | + | 0.586791i | \(0.800391\pi\) | |||||||
\(18\) | 4.50401 | 1.06160 | ||||||||
\(19\) | 5.92140 | 1.35846 | 0.679231 | − | 0.733924i | \(-0.262313\pi\) | ||||
0.679231 | + | 0.733924i | \(0.262313\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 2.73934 | 0.597774 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.62208 | −1.38080 | −0.690400 | − | 0.723428i | \(-0.742565\pi\) | ||||
−0.690400 | + | 0.723428i | \(0.742565\pi\) | |||||||
\(24\) | −2.73934 | −0.559166 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.65196 | 0.520091 | ||||||||
\(27\) | −4.11999 | −0.792892 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 1.10448 | 0.205097 | 0.102549 | − | 0.994728i | \(-0.467300\pi\) | ||||
0.102549 | + | 0.994728i | \(0.467300\pi\) | |||||||
\(30\) | −2.73934 | −0.500133 | ||||||||
\(31\) | −5.57898 | −1.00201 | −0.501007 | − | 0.865443i | \(-0.667037\pi\) | ||||
−0.501007 | + | 0.865443i | \(0.667037\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.67727 | −1.14514 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 4.50401 | 0.750668 | ||||||||
\(37\) | 4.15191 | 0.682570 | 0.341285 | − | 0.939960i | \(-0.389138\pi\) | ||||
0.341285 | + | 0.939960i | \(0.389138\pi\) | |||||||
\(38\) | 5.92140 | 0.960578 | ||||||||
\(39\) | −7.26462 | −1.16327 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 9.08954 | 1.41955 | 0.709773 | − | 0.704430i | \(-0.248797\pi\) | ||||
0.709773 | + | 0.704430i | \(0.248797\pi\) | |||||||
\(42\) | 2.73934 | 0.422690 | ||||||||
\(43\) | −5.51500 | −0.841029 | −0.420515 | − | 0.907286i | \(-0.638150\pi\) | ||||
−0.420515 | + | 0.907286i | \(0.638150\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.50401 | 0.671417 | ||||||||
\(46\) | −6.62208 | −0.976373 | ||||||||
\(47\) | 0.907239 | 0.132334 | 0.0661672 | − | 0.997809i | \(-0.478923\pi\) | ||||
0.0661672 | + | 0.997809i | \(0.478923\pi\) | |||||||
\(48\) | −2.73934 | −0.395390 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 18.2913 | 2.56130 | ||||||||
\(52\) | 2.65196 | 0.367760 | ||||||||
\(53\) | −9.24121 | −1.26938 | −0.634689 | − | 0.772768i | \(-0.718872\pi\) | ||||
−0.634689 | + | 0.772768i | \(0.718872\pi\) | |||||||
\(54\) | −4.11999 | −0.560659 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −16.2208 | −2.14849 | ||||||||
\(58\) | 1.10448 | 0.145026 | ||||||||
\(59\) | 1.72702 | 0.224838 | 0.112419 | − | 0.993661i | \(-0.464140\pi\) | ||||
0.112419 | + | 0.993661i | \(0.464140\pi\) | |||||||
\(60\) | −2.73934 | −0.353648 | ||||||||
\(61\) | −8.93518 | −1.14403 | −0.572016 | − | 0.820242i | \(-0.693839\pi\) | ||||
−0.572016 | + | 0.820242i | \(0.693839\pi\) | |||||||
\(62\) | −5.57898 | −0.708531 | ||||||||
\(63\) | −4.50401 | −0.567451 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.65196 | 0.328935 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.10699 | −0.501748 | −0.250874 | − | 0.968020i | \(-0.580718\pi\) | ||||
−0.250874 | + | 0.968020i | \(0.580718\pi\) | |||||||
\(68\) | −6.67727 | −0.809738 | ||||||||
\(69\) | 18.1402 | 2.18382 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −7.02166 | −0.833318 | −0.416659 | − | 0.909063i | \(-0.636799\pi\) | ||||
−0.416659 | + | 0.909063i | \(0.636799\pi\) | |||||||
\(72\) | 4.50401 | 0.530802 | ||||||||
\(73\) | 0.967438 | 0.113230 | 0.0566150 | − | 0.998396i | \(-0.481969\pi\) | ||||
0.0566150 | + | 0.998396i | \(0.481969\pi\) | |||||||
\(74\) | 4.15191 | 0.482650 | ||||||||
\(75\) | −2.73934 | −0.316312 | ||||||||
\(76\) | 5.92140 | 0.679231 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.26462 | −0.822556 | ||||||||
\(79\) | 10.7456 | 1.20897 | 0.604487 | − | 0.796615i | \(-0.293378\pi\) | ||||
0.604487 | + | 0.796615i | \(0.293378\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −2.22595 | −0.247328 | ||||||||
\(82\) | 9.08954 | 1.00377 | ||||||||
\(83\) | −15.9031 | −1.74559 | −0.872794 | − | 0.488089i | \(-0.837694\pi\) | ||||
−0.872794 | + | 0.488089i | \(0.837694\pi\) | |||||||
\(84\) | 2.73934 | 0.298887 | ||||||||
\(85\) | −6.67727 | −0.724252 | ||||||||
\(86\) | −5.51500 | −0.594698 | ||||||||
\(87\) | −3.02556 | −0.324374 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.5040 | 1.32543 | 0.662713 | − | 0.748874i | \(-0.269405\pi\) | ||||
0.662713 | + | 0.748874i | \(0.269405\pi\) | |||||||
\(90\) | 4.50401 | 0.474764 | ||||||||
\(91\) | −2.65196 | −0.278000 | ||||||||
\(92\) | −6.62208 | −0.690400 | ||||||||
\(93\) | 15.2827 | 1.58475 | ||||||||
\(94\) | 0.907239 | 0.0935746 | ||||||||
\(95\) | 5.92140 | 0.607523 | ||||||||
\(96\) | −2.73934 | −0.279583 | ||||||||
\(97\) | 11.4362 | 1.16117 | 0.580584 | − | 0.814201i | \(-0.302824\pi\) | ||||
0.580584 | + | 0.814201i | \(0.302824\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 7.67893 | 0.764082 | 0.382041 | − | 0.924145i | \(-0.375221\pi\) | ||||
0.382041 | + | 0.924145i | \(0.375221\pi\) | |||||||
\(102\) | 18.2913 | 1.81111 | ||||||||
\(103\) | −1.29467 | −0.127567 | −0.0637836 | − | 0.997964i | \(-0.520317\pi\) | ||||
−0.0637836 | + | 0.997964i | \(0.520317\pi\) | |||||||
\(104\) | 2.65196 | 0.260046 | ||||||||
\(105\) | 2.73934 | 0.267333 | ||||||||
\(106\) | −9.24121 | −0.897586 | ||||||||
\(107\) | −14.0391 | −1.35721 | −0.678605 | − | 0.734503i | \(-0.737415\pi\) | ||||
−0.678605 | + | 0.734503i | \(0.737415\pi\) | |||||||
\(108\) | −4.11999 | −0.396446 | ||||||||
\(109\) | −13.6269 | −1.30522 | −0.652609 | − | 0.757695i | \(-0.726326\pi\) | ||||
−0.652609 | + | 0.757695i | \(0.726326\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.3735 | −1.07953 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 12.3826 | 1.16486 | 0.582430 | − | 0.812881i | \(-0.302102\pi\) | ||||
0.582430 | + | 0.812881i | \(0.302102\pi\) | |||||||
\(114\) | −16.2208 | −1.51921 | ||||||||
\(115\) | −6.62208 | −0.617512 | ||||||||
\(116\) | 1.10448 | 0.102549 | ||||||||
\(117\) | 11.9444 | 1.10426 | ||||||||
\(118\) | 1.72702 | 0.158985 | ||||||||
\(119\) | 6.67727 | 0.612105 | ||||||||
\(120\) | −2.73934 | −0.250067 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −8.93518 | −0.808953 | ||||||||
\(123\) | −24.8994 | −2.24510 | ||||||||
\(124\) | −5.57898 | −0.501007 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −4.50401 | −0.401249 | ||||||||
\(127\) | 8.64037 | 0.766709 | 0.383354 | − | 0.923601i | \(-0.374769\pi\) | ||||
0.383354 | + | 0.923601i | \(0.374769\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 15.1075 | 1.33014 | ||||||||
\(130\) | 2.65196 | 0.232592 | ||||||||
\(131\) | 6.27193 | 0.547981 | 0.273991 | − | 0.961732i | \(-0.411656\pi\) | ||||
0.273991 | + | 0.961732i | \(0.411656\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.92140 | −0.513451 | ||||||||
\(134\) | −4.10699 | −0.354790 | ||||||||
\(135\) | −4.11999 | −0.354592 | ||||||||
\(136\) | −6.67727 | −0.572571 | ||||||||
\(137\) | −10.9179 | −0.932783 | −0.466391 | − | 0.884579i | \(-0.654446\pi\) | ||||
−0.466391 | + | 0.884579i | \(0.654446\pi\) | |||||||
\(138\) | 18.1402 | 1.54419 | ||||||||
\(139\) | 12.5679 | 1.06600 | 0.532999 | − | 0.846116i | \(-0.321065\pi\) | ||||
0.532999 | + | 0.846116i | \(0.321065\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −2.48524 | −0.209295 | ||||||||
\(142\) | −7.02166 | −0.589245 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.50401 | 0.375334 | ||||||||
\(145\) | 1.10448 | 0.0917223 | ||||||||
\(146\) | 0.967438 | 0.0800657 | ||||||||
\(147\) | −2.73934 | −0.225937 | ||||||||
\(148\) | 4.15191 | 0.341285 | ||||||||
\(149\) | −18.9356 | −1.55126 | −0.775631 | − | 0.631187i | \(-0.782568\pi\) | ||||
−0.775631 | + | 0.631187i | \(0.782568\pi\) | |||||||
\(150\) | −2.73934 | −0.223666 | ||||||||
\(151\) | −9.07849 | −0.738797 | −0.369398 | − | 0.929271i | \(-0.620436\pi\) | ||||
−0.369398 | + | 0.929271i | \(0.620436\pi\) | |||||||
\(152\) | 5.92140 | 0.480289 | ||||||||
\(153\) | −30.0745 | −2.43138 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.57898 | −0.448114 | ||||||||
\(156\) | −7.26462 | −0.581635 | ||||||||
\(157\) | 13.0301 | 1.03991 | 0.519956 | − | 0.854193i | \(-0.325948\pi\) | ||||
0.519956 | + | 0.854193i | \(0.325948\pi\) | |||||||
\(158\) | 10.7456 | 0.854874 | ||||||||
\(159\) | 25.3148 | 2.00760 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 6.62208 | 0.521893 | ||||||||
\(162\) | −2.22595 | −0.174887 | ||||||||
\(163\) | 8.41437 | 0.659064 | 0.329532 | − | 0.944144i | \(-0.393109\pi\) | ||||
0.329532 | + | 0.944144i | \(0.393109\pi\) | |||||||
\(164\) | 9.08954 | 0.709773 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.9031 | −1.23432 | ||||||||
\(167\) | −11.2346 | −0.869363 | −0.434681 | − | 0.900584i | \(-0.643139\pi\) | ||||
−0.434681 | + | 0.900584i | \(0.643139\pi\) | |||||||
\(168\) | 2.73934 | 0.211345 | ||||||||
\(169\) | −5.96713 | −0.459010 | ||||||||
\(170\) | −6.67727 | −0.512123 | ||||||||
\(171\) | 26.6700 | 2.03951 | ||||||||
\(172\) | −5.51500 | −0.420515 | ||||||||
\(173\) | −0.0298132 | −0.00226666 | −0.00113333 | − | 0.999999i | \(-0.500361\pi\) | ||||
−0.00113333 | + | 0.999999i | \(0.500361\pi\) | |||||||
\(174\) | −3.02556 | −0.229367 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.73089 | −0.355596 | ||||||||
\(178\) | 12.5040 | 0.937218 | ||||||||
\(179\) | −23.6951 | −1.77106 | −0.885529 | − | 0.464584i | \(-0.846204\pi\) | ||||
−0.885529 | + | 0.464584i | \(0.846204\pi\) | |||||||
\(180\) | 4.50401 | 0.335709 | ||||||||
\(181\) | −5.38186 | −0.400031 | −0.200015 | − | 0.979793i | \(-0.564099\pi\) | ||||
−0.200015 | + | 0.979793i | \(0.564099\pi\) | |||||||
\(182\) | −2.65196 | −0.196576 | ||||||||
\(183\) | 24.4765 | 1.80936 | ||||||||
\(184\) | −6.62208 | −0.488186 | ||||||||
\(185\) | 4.15191 | 0.305255 | ||||||||
\(186\) | 15.2827 | 1.12058 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.907239 | 0.0661672 | ||||||||
\(189\) | 4.11999 | 0.299685 | ||||||||
\(190\) | 5.92140 | 0.429584 | ||||||||
\(191\) | −12.3548 | −0.893965 | −0.446982 | − | 0.894543i | \(-0.647501\pi\) | ||||
−0.446982 | + | 0.894543i | \(0.647501\pi\) | |||||||
\(192\) | −2.73934 | −0.197695 | ||||||||
\(193\) | 11.8011 | 0.849464 | 0.424732 | − | 0.905319i | \(-0.360368\pi\) | ||||
0.424732 | + | 0.905319i | \(0.360368\pi\) | |||||||
\(194\) | 11.4362 | 0.821069 | ||||||||
\(195\) | −7.26462 | −0.520230 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 19.4626 | 1.38665 | 0.693325 | − | 0.720625i | \(-0.256145\pi\) | ||||
0.693325 | + | 0.720625i | \(0.256145\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.5751 | 1.10409 | 0.552043 | − | 0.833815i | \(-0.313848\pi\) | ||||
0.552043 | + | 0.833815i | \(0.313848\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 11.2504 | 0.793545 | ||||||||
\(202\) | 7.67893 | 0.540288 | ||||||||
\(203\) | −1.10448 | −0.0775195 | ||||||||
\(204\) | 18.2913 | 1.28065 | ||||||||
\(205\) | 9.08954 | 0.634841 | ||||||||
\(206\) | −1.29467 | −0.0902036 | ||||||||
\(207\) | −29.8259 | −2.07304 | ||||||||
\(208\) | 2.65196 | 0.183880 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.73934 | 0.189033 | ||||||||
\(211\) | 13.8169 | 0.951191 | 0.475596 | − | 0.879664i | \(-0.342233\pi\) | ||||
0.475596 | + | 0.879664i | \(0.342233\pi\) | |||||||
\(212\) | −9.24121 | −0.634689 | ||||||||
\(213\) | 19.2347 | 1.31794 | ||||||||
\(214\) | −14.0391 | −0.959692 | ||||||||
\(215\) | −5.51500 | −0.376120 | ||||||||
\(216\) | −4.11999 | −0.280330 | ||||||||
\(217\) | 5.57898 | 0.378726 | ||||||||
\(218\) | −13.6269 | −0.922929 | ||||||||
\(219\) | −2.65015 | −0.179080 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.7078 | −1.19116 | ||||||||
\(222\) | −11.3735 | −0.763340 | ||||||||
\(223\) | −8.98060 | −0.601385 | −0.300693 | − | 0.953721i | \(-0.597218\pi\) | ||||
−0.300693 | + | 0.953721i | \(0.597218\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 4.50401 | 0.300267 | ||||||||
\(226\) | 12.3826 | 0.823681 | ||||||||
\(227\) | −18.5359 | −1.23027 | −0.615136 | − | 0.788421i | \(-0.710899\pi\) | ||||
−0.615136 | + | 0.788421i | \(0.710899\pi\) | |||||||
\(228\) | −16.2208 | −1.07425 | ||||||||
\(229\) | −26.3775 | −1.74307 | −0.871537 | − | 0.490329i | \(-0.836876\pi\) | ||||
−0.871537 | + | 0.490329i | \(0.836876\pi\) | |||||||
\(230\) | −6.62208 | −0.436647 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.10448 | 0.0725129 | ||||||||
\(233\) | 12.9030 | 0.845300 | 0.422650 | − | 0.906293i | \(-0.361100\pi\) | ||||
0.422650 | + | 0.906293i | \(0.361100\pi\) | |||||||
\(234\) | 11.9444 | 0.780831 | ||||||||
\(235\) | 0.907239 | 0.0591817 | ||||||||
\(236\) | 1.72702 | 0.112419 | ||||||||
\(237\) | −29.4359 | −1.91207 | ||||||||
\(238\) | 6.67727 | 0.432823 | ||||||||
\(239\) | 7.43785 | 0.481114 | 0.240557 | − | 0.970635i | \(-0.422670\pi\) | ||||
0.240557 | + | 0.970635i | \(0.422670\pi\) | |||||||
\(240\) | −2.73934 | −0.176824 | ||||||||
\(241\) | −29.9278 | −1.92782 | −0.963908 | − | 0.266234i | \(-0.914221\pi\) | ||||
−0.963908 | + | 0.266234i | \(0.914221\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.4576 | 1.18406 | ||||||||
\(244\) | −8.93518 | −0.572016 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −24.8994 | −1.58753 | ||||||||
\(247\) | 15.7033 | 0.999177 | ||||||||
\(248\) | −5.57898 | −0.354266 | ||||||||
\(249\) | 43.5640 | 2.76075 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 2.56811 | 0.162098 | 0.0810488 | − | 0.996710i | \(-0.474173\pi\) | ||||
0.0810488 | + | 0.996710i | \(0.474173\pi\) | |||||||
\(252\) | −4.50401 | −0.283726 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 8.64037 | 0.542145 | ||||||||
\(255\) | 18.2913 | 1.14545 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −27.7714 | −1.73233 | −0.866166 | − | 0.499756i | \(-0.833423\pi\) | ||||
−0.866166 | + | 0.499756i | \(0.833423\pi\) | |||||||
\(258\) | 15.1075 | 0.940550 | ||||||||
\(259\) | −4.15191 | −0.257987 | ||||||||
\(260\) | 2.65196 | 0.164467 | ||||||||
\(261\) | 4.97460 | 0.307920 | ||||||||
\(262\) | 6.27193 | 0.387481 | ||||||||
\(263\) | −14.1621 | −0.873273 | −0.436637 | − | 0.899638i | \(-0.643830\pi\) | ||||
−0.436637 | + | 0.899638i | \(0.643830\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.24121 | −0.567683 | ||||||||
\(266\) | −5.92140 | −0.363064 | ||||||||
\(267\) | −34.2529 | −2.09624 | ||||||||
\(268\) | −4.10699 | −0.250874 | ||||||||
\(269\) | 24.5685 | 1.49797 | 0.748983 | − | 0.662589i | \(-0.230543\pi\) | ||||
0.748983 | + | 0.662589i | \(0.230543\pi\) | |||||||
\(270\) | −4.11999 | −0.250734 | ||||||||
\(271\) | 10.4852 | 0.636933 | 0.318467 | − | 0.947934i | \(-0.396832\pi\) | ||||
0.318467 | + | 0.947934i | \(0.396832\pi\) | |||||||
\(272\) | −6.67727 | −0.404869 | ||||||||
\(273\) | 7.26462 | 0.439675 | ||||||||
\(274\) | −10.9179 | −0.659577 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 18.1402 | 1.09191 | ||||||||
\(277\) | −30.8423 | −1.85313 | −0.926566 | − | 0.376133i | \(-0.877254\pi\) | ||||
−0.926566 | + | 0.376133i | \(0.877254\pi\) | |||||||
\(278\) | 12.5679 | 0.753774 | ||||||||
\(279\) | −25.1277 | −1.50436 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −4.44483 | −0.265156 | −0.132578 | − | 0.991173i | \(-0.542326\pi\) | ||||
−0.132578 | + | 0.991173i | \(0.542326\pi\) | |||||||
\(282\) | −2.48524 | −0.147994 | ||||||||
\(283\) | −5.81252 | −0.345519 | −0.172759 | − | 0.984964i | \(-0.555268\pi\) | ||||
−0.172759 | + | 0.984964i | \(0.555268\pi\) | |||||||
\(284\) | −7.02166 | −0.416659 | ||||||||
\(285\) | −16.2208 | −0.960835 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.08954 | −0.536538 | ||||||||
\(288\) | 4.50401 | 0.265401 | ||||||||
\(289\) | 27.5860 | 1.62270 | ||||||||
\(290\) | 1.10448 | 0.0648575 | ||||||||
\(291\) | −31.3276 | −1.83646 | ||||||||
\(292\) | 0.967438 | 0.0566150 | ||||||||
\(293\) | 8.16127 | 0.476787 | 0.238393 | − | 0.971169i | \(-0.423379\pi\) | ||||
0.238393 | + | 0.971169i | \(0.423379\pi\) | |||||||
\(294\) | −2.73934 | −0.159762 | ||||||||
\(295\) | 1.72702 | 0.100551 | ||||||||
\(296\) | 4.15191 | 0.241325 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.9356 | −1.09691 | ||||||||
\(299\) | −17.5615 | −1.01561 | ||||||||
\(300\) | −2.73934 | −0.158156 | ||||||||
\(301\) | 5.51500 | 0.317879 | ||||||||
\(302\) | −9.07849 | −0.522408 | ||||||||
\(303\) | −21.0352 | −1.20844 | ||||||||
\(304\) | 5.92140 | 0.339616 | ||||||||
\(305\) | −8.93518 | −0.511627 | ||||||||
\(306\) | −30.0745 | −1.71924 | ||||||||
\(307\) | −15.7830 | −0.900782 | −0.450391 | − | 0.892832i | \(-0.648715\pi\) | ||||
−0.450391 | + | 0.892832i | \(0.648715\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.54653 | 0.201755 | ||||||||
\(310\) | −5.57898 | −0.316865 | ||||||||
\(311\) | −6.51788 | −0.369595 | −0.184798 | − | 0.982777i | \(-0.559163\pi\) | ||||
−0.184798 | + | 0.982777i | \(0.559163\pi\) | |||||||
\(312\) | −7.26462 | −0.411278 | ||||||||
\(313\) | −9.54938 | −0.539763 | −0.269881 | − | 0.962894i | \(-0.586985\pi\) | ||||
−0.269881 | + | 0.962894i | \(0.586985\pi\) | |||||||
\(314\) | 13.0301 | 0.735329 | ||||||||
\(315\) | −4.50401 | −0.253772 | ||||||||
\(316\) | 10.7456 | 0.604487 | ||||||||
\(317\) | −6.52267 | −0.366350 | −0.183175 | − | 0.983080i | \(-0.558637\pi\) | ||||
−0.183175 | + | 0.983080i | \(0.558637\pi\) | |||||||
\(318\) | 25.3148 | 1.41959 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 38.4579 | 2.14651 | ||||||||
\(322\) | 6.62208 | 0.369034 | ||||||||
\(323\) | −39.5388 | −2.20000 | ||||||||
\(324\) | −2.22595 | −0.123664 | ||||||||
\(325\) | 2.65196 | 0.147104 | ||||||||
\(326\) | 8.41437 | 0.466029 | ||||||||
\(327\) | 37.3287 | 2.06428 | ||||||||
\(328\) | 9.08954 | 0.501886 | ||||||||
\(329\) | −0.907239 | −0.0500177 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.3519 | −1.11864 | −0.559319 | − | 0.828952i | \(-0.688937\pi\) | ||||
−0.559319 | + | 0.828952i | \(0.688937\pi\) | |||||||
\(332\) | −15.9031 | −0.872794 | ||||||||
\(333\) | 18.7002 | 1.02477 | ||||||||
\(334\) | −11.2346 | −0.614732 | ||||||||
\(335\) | −4.10699 | −0.224389 | ||||||||
\(336\) | 2.73934 | 0.149443 | ||||||||
\(337\) | −20.3955 | −1.11101 | −0.555506 | − | 0.831513i | \(-0.687475\pi\) | ||||
−0.555506 | + | 0.831513i | \(0.687475\pi\) | |||||||
\(338\) | −5.96713 | −0.324569 | ||||||||
\(339\) | −33.9203 | −1.84230 | ||||||||
\(340\) | −6.67727 | −0.362126 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 26.6700 | 1.44215 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −5.51500 | −0.297349 | ||||||||
\(345\) | 18.1402 | 0.976634 | ||||||||
\(346\) | −0.0298132 | −0.00160277 | ||||||||
\(347\) | −25.1418 | −1.34968 | −0.674841 | − | 0.737963i | \(-0.735788\pi\) | ||||
−0.674841 | + | 0.737963i | \(0.735788\pi\) | |||||||
\(348\) | −3.02556 | −0.162187 | ||||||||
\(349\) | 6.48720 | 0.347252 | 0.173626 | − | 0.984812i | \(-0.444452\pi\) | ||||
0.173626 | + | 0.984812i | \(0.444452\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −10.9260 | −0.583188 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.671105 | −0.0357193 | −0.0178597 | − | 0.999841i | \(-0.505685\pi\) | ||||
−0.0178597 | + | 0.999841i | \(0.505685\pi\) | |||||||
\(354\) | −4.73089 | −0.251444 | ||||||||
\(355\) | −7.02166 | −0.372671 | ||||||||
\(356\) | 12.5040 | 0.662713 | ||||||||
\(357\) | −18.2913 | −0.968081 | ||||||||
\(358\) | −23.6951 | −1.25233 | ||||||||
\(359\) | −33.6491 | −1.77593 | −0.887965 | − | 0.459912i | \(-0.847881\pi\) | ||||
−0.887965 | + | 0.459912i | \(0.847881\pi\) | |||||||
\(360\) | 4.50401 | 0.237382 | ||||||||
\(361\) | 16.0630 | 0.845422 | ||||||||
\(362\) | −5.38186 | −0.282864 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.65196 | −0.139000 | ||||||||
\(365\) | 0.967438 | 0.0506380 | ||||||||
\(366\) | 24.4765 | 1.27941 | ||||||||
\(367\) | −5.36793 | −0.280204 | −0.140102 | − | 0.990137i | \(-0.544743\pi\) | ||||
−0.140102 | + | 0.990137i | \(0.544743\pi\) | |||||||
\(368\) | −6.62208 | −0.345200 | ||||||||
\(369\) | 40.9393 | 2.13122 | ||||||||
\(370\) | 4.15191 | 0.215848 | ||||||||
\(371\) | 9.24121 | 0.479780 | ||||||||
\(372\) | 15.2827 | 0.792373 | ||||||||
\(373\) | 16.1242 | 0.834878 | 0.417439 | − | 0.908705i | \(-0.362928\pi\) | ||||
0.417439 | + | 0.908705i | \(0.362928\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.73934 | −0.141459 | ||||||||
\(376\) | 0.907239 | 0.0467873 | ||||||||
\(377\) | 2.92904 | 0.150853 | ||||||||
\(378\) | 4.11999 | 0.211909 | ||||||||
\(379\) | −27.3566 | −1.40521 | −0.702607 | − | 0.711578i | \(-0.747981\pi\) | ||||
−0.702607 | + | 0.711578i | \(0.747981\pi\) | |||||||
\(380\) | 5.92140 | 0.303762 | ||||||||
\(381\) | −23.6689 | −1.21260 | ||||||||
\(382\) | −12.3548 | −0.632129 | ||||||||
\(383\) | 0.132352 | 0.00676285 | 0.00338142 | − | 0.999994i | \(-0.498924\pi\) | ||||
0.00338142 | + | 0.999994i | \(0.498924\pi\) | |||||||
\(384\) | −2.73934 | −0.139792 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.8011 | 0.600662 | ||||||||
\(387\) | −24.8396 | −1.26267 | ||||||||
\(388\) | 11.4362 | 0.580584 | ||||||||
\(389\) | 16.3662 | 0.829798 | 0.414899 | − | 0.909867i | \(-0.363817\pi\) | ||||
0.414899 | + | 0.909867i | \(0.363817\pi\) | |||||||
\(390\) | −7.26462 | −0.367858 | ||||||||
\(391\) | 44.2175 | 2.23617 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −17.1810 | −0.866666 | ||||||||
\(394\) | 19.4626 | 0.980509 | ||||||||
\(395\) | 10.7456 | 0.540670 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.8294 | 1.74804 | 0.874018 | − | 0.485893i | \(-0.161505\pi\) | ||||
0.874018 | + | 0.485893i | \(0.161505\pi\) | |||||||
\(398\) | 15.5751 | 0.780707 | ||||||||
\(399\) | 16.2208 | 0.812054 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −11.8605 | −0.592284 | −0.296142 | − | 0.955144i | \(-0.595700\pi\) | ||||
−0.296142 | + | 0.955144i | \(0.595700\pi\) | |||||||
\(402\) | 11.2504 | 0.561121 | ||||||||
\(403\) | −14.7952 | −0.737001 | ||||||||
\(404\) | 7.67893 | 0.382041 | ||||||||
\(405\) | −2.22595 | −0.110609 | ||||||||
\(406\) | −1.10448 | −0.0548146 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 18.2913 | 0.905557 | ||||||||
\(409\) | −7.78726 | −0.385055 | −0.192528 | − | 0.981292i | \(-0.561669\pi\) | ||||
−0.192528 | + | 0.981292i | \(0.561669\pi\) | |||||||
\(410\) | 9.08954 | 0.448900 | ||||||||
\(411\) | 29.9080 | 1.47525 | ||||||||
\(412\) | −1.29467 | −0.0637836 | ||||||||
\(413\) | −1.72702 | −0.0849810 | ||||||||
\(414\) | −29.8259 | −1.46586 | ||||||||
\(415\) | −15.9031 | −0.780651 | ||||||||
\(416\) | 2.65196 | 0.130023 | ||||||||
\(417\) | −34.4279 | −1.68594 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.59415 | −0.468705 | −0.234352 | − | 0.972152i | \(-0.575297\pi\) | ||||
−0.234352 | + | 0.972152i | \(0.575297\pi\) | |||||||
\(420\) | 2.73934 | 0.133666 | ||||||||
\(421\) | 19.7210 | 0.961144 | 0.480572 | − | 0.876955i | \(-0.340429\pi\) | ||||
0.480572 | + | 0.876955i | \(0.340429\pi\) | |||||||
\(422\) | 13.8169 | 0.672594 | ||||||||
\(423\) | 4.08621 | 0.198678 | ||||||||
\(424\) | −9.24121 | −0.448793 | ||||||||
\(425\) | −6.67727 | −0.323895 | ||||||||
\(426\) | 19.2347 | 0.931926 | ||||||||
\(427\) | 8.93518 | 0.432404 | ||||||||
\(428\) | −14.0391 | −0.678605 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.51500 | −0.265957 | ||||||||
\(431\) | −18.5608 | −0.894041 | −0.447021 | − | 0.894524i | \(-0.647515\pi\) | ||||
−0.447021 | + | 0.894524i | \(0.647515\pi\) | |||||||
\(432\) | −4.11999 | −0.198223 | ||||||||
\(433\) | −15.6876 | −0.753900 | −0.376950 | − | 0.926234i | \(-0.623027\pi\) | ||||
−0.376950 | + | 0.926234i | \(0.623027\pi\) | |||||||
\(434\) | 5.57898 | 0.267800 | ||||||||
\(435\) | −3.02556 | −0.145064 | ||||||||
\(436\) | −13.6269 | −0.652609 | ||||||||
\(437\) | −39.2120 | −1.87577 | ||||||||
\(438\) | −2.65015 | −0.126629 | ||||||||
\(439\) | −6.85571 | −0.327205 | −0.163602 | − | 0.986526i | \(-0.552311\pi\) | ||||
−0.163602 | + | 0.986526i | \(0.552311\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.50401 | 0.214476 | ||||||||
\(442\) | −17.7078 | −0.842275 | ||||||||
\(443\) | 13.6685 | 0.649411 | 0.324706 | − | 0.945815i | \(-0.394735\pi\) | ||||
0.324706 | + | 0.945815i | \(0.394735\pi\) | |||||||
\(444\) | −11.3735 | −0.539763 | ||||||||
\(445\) | 12.5040 | 0.592748 | ||||||||
\(446\) | −8.98060 | −0.425244 | ||||||||
\(447\) | 51.8710 | 2.45342 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −36.9601 | −1.74425 | −0.872127 | − | 0.489280i | \(-0.837259\pi\) | ||||
−0.872127 | + | 0.489280i | \(0.837259\pi\) | |||||||
\(450\) | 4.50401 | 0.212321 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 12.3826 | 0.582430 | ||||||||
\(453\) | 24.8691 | 1.16845 | ||||||||
\(454\) | −18.5359 | −0.869934 | ||||||||
\(455\) | −2.65196 | −0.124326 | ||||||||
\(456\) | −16.2208 | −0.759607 | ||||||||
\(457\) | 7.21944 | 0.337711 | 0.168856 | − | 0.985641i | \(-0.445993\pi\) | ||||
0.168856 | + | 0.985641i | \(0.445993\pi\) | |||||||
\(458\) | −26.3775 | −1.23254 | ||||||||
\(459\) | 27.5103 | 1.28407 | ||||||||
\(460\) | −6.62208 | −0.308756 | ||||||||
\(461\) | −35.7004 | −1.66273 | −0.831367 | − | 0.555724i | \(-0.812441\pi\) | ||||
−0.831367 | + | 0.555724i | \(0.812441\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.9145 | −0.925504 | −0.462752 | − | 0.886488i | \(-0.653138\pi\) | ||||
−0.462752 | + | 0.886488i | \(0.653138\pi\) | |||||||
\(464\) | 1.10448 | 0.0512743 | ||||||||
\(465\) | 15.2827 | 0.708720 | ||||||||
\(466\) | 12.9030 | 0.597718 | ||||||||
\(467\) | 12.8231 | 0.593383 | 0.296691 | − | 0.954973i | \(-0.404117\pi\) | ||||
0.296691 | + | 0.954973i | \(0.404117\pi\) | |||||||
\(468\) | 11.9444 | 0.552131 | ||||||||
\(469\) | 4.10699 | 0.189643 | ||||||||
\(470\) | 0.907239 | 0.0418478 | ||||||||
\(471\) | −35.6938 | −1.64468 | ||||||||
\(472\) | 1.72702 | 0.0794924 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −29.4359 | −1.35204 | ||||||||
\(475\) | 5.92140 | 0.271693 | ||||||||
\(476\) | 6.67727 | 0.306052 | ||||||||
\(477\) | −41.6224 | −1.90576 | ||||||||
\(478\) | 7.43785 | 0.340199 | ||||||||
\(479\) | −3.92060 | −0.179137 | −0.0895683 | − | 0.995981i | \(-0.528549\pi\) | ||||
−0.0895683 | + | 0.995981i | \(0.528549\pi\) | |||||||
\(480\) | −2.73934 | −0.125033 | ||||||||
\(481\) | 11.0107 | 0.502044 | ||||||||
\(482\) | −29.9278 | −1.36317 | ||||||||
\(483\) | −18.1402 | −0.825406 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.4362 | 0.519290 | ||||||||
\(486\) | 18.4576 | 0.837254 | ||||||||
\(487\) | −41.0411 | −1.85975 | −0.929874 | − | 0.367878i | \(-0.880084\pi\) | ||||
−0.929874 | + | 0.367878i | \(0.880084\pi\) | |||||||
\(488\) | −8.93518 | −0.404477 | ||||||||
\(489\) | −23.0499 | −1.04235 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 10.2674 | 0.463363 | 0.231681 | − | 0.972792i | \(-0.425577\pi\) | ||||
0.231681 | + | 0.972792i | \(0.425577\pi\) | |||||||
\(492\) | −24.8994 | −1.12255 | ||||||||
\(493\) | −7.37494 | −0.332150 | ||||||||
\(494\) | 15.7033 | 0.706525 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.57898 | −0.250504 | ||||||||
\(497\) | 7.02166 | 0.314964 | ||||||||
\(498\) | 43.5640 | 1.95215 | ||||||||
\(499\) | 33.4423 | 1.49708 | 0.748542 | − | 0.663087i | \(-0.230754\pi\) | ||||
0.748542 | + | 0.663087i | \(0.230754\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 30.7756 | 1.37495 | ||||||||
\(502\) | 2.56811 | 0.114620 | ||||||||
\(503\) | −20.8969 | −0.931745 | −0.465872 | − | 0.884852i | \(-0.654259\pi\) | ||||
−0.465872 | + | 0.884852i | \(0.654259\pi\) | |||||||
\(504\) | −4.50401 | −0.200624 | ||||||||
\(505\) | 7.67893 | 0.341708 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.3460 | 0.725953 | ||||||||
\(508\) | 8.64037 | 0.383354 | ||||||||
\(509\) | −44.2364 | −1.96074 | −0.980372 | − | 0.197159i | \(-0.936828\pi\) | ||||
−0.980372 | + | 0.197159i | \(0.936828\pi\) | |||||||
\(510\) | 18.2913 | 0.809954 | ||||||||
\(511\) | −0.967438 | −0.0427969 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −24.3961 | −1.07711 | ||||||||
\(514\) | −27.7714 | −1.22494 | ||||||||
\(515\) | −1.29467 | −0.0570498 | ||||||||
\(516\) | 15.1075 | 0.665070 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.15191 | −0.182424 | ||||||||
\(519\) | 0.0816686 | 0.00358485 | ||||||||
\(520\) | 2.65196 | 0.116296 | ||||||||
\(521\) | 29.2273 | 1.28047 | 0.640235 | − | 0.768179i | \(-0.278837\pi\) | ||||
0.640235 | + | 0.768179i | \(0.278837\pi\) | |||||||
\(522\) | 4.97460 | 0.217732 | ||||||||
\(523\) | −23.6402 | −1.03371 | −0.516857 | − | 0.856072i | \(-0.672898\pi\) | ||||
−0.516857 | + | 0.856072i | \(0.672898\pi\) | |||||||
\(524\) | 6.27193 | 0.273991 | ||||||||
\(525\) | 2.73934 | 0.119555 | ||||||||
\(526\) | −14.1621 | −0.617497 | ||||||||
\(527\) | 37.2524 | 1.62274 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.8520 | 0.906608 | ||||||||
\(530\) | −9.24121 | −0.401412 | ||||||||
\(531\) | 7.77849 | 0.337558 | ||||||||
\(532\) | −5.92140 | −0.256725 | ||||||||
\(533\) | 24.1050 | 1.04411 | ||||||||
\(534\) | −34.2529 | −1.48227 | ||||||||
\(535\) | −14.0391 | −0.606963 | ||||||||
\(536\) | −4.10699 | −0.177395 | ||||||||
\(537\) | 64.9092 | 2.80104 | ||||||||
\(538\) | 24.5685 | 1.05922 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.11999 | −0.177296 | ||||||||
\(541\) | −0.0638597 | −0.00274554 | −0.00137277 | − | 0.999999i | \(-0.500437\pi\) | ||||
−0.00137277 | + | 0.999999i | \(0.500437\pi\) | |||||||
\(542\) | 10.4852 | 0.450380 | ||||||||
\(543\) | 14.7428 | 0.632673 | ||||||||
\(544\) | −6.67727 | −0.286286 | ||||||||
\(545\) | −13.6269 | −0.583711 | ||||||||
\(546\) | 7.26462 | 0.310897 | ||||||||
\(547\) | 17.7223 | 0.757751 | 0.378876 | − | 0.925448i | \(-0.376311\pi\) | ||||
0.378876 | + | 0.925448i | \(0.376311\pi\) | |||||||
\(548\) | −10.9179 | −0.466391 | ||||||||
\(549\) | −40.2441 | −1.71758 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.54009 | 0.278617 | ||||||||
\(552\) | 18.1402 | 0.772097 | ||||||||
\(553\) | −10.7456 | −0.456950 | ||||||||
\(554\) | −30.8423 | −1.31036 | ||||||||
\(555\) | −11.3735 | −0.482779 | ||||||||
\(556\) | 12.5679 | 0.532999 | ||||||||
\(557\) | −37.7636 | −1.60009 | −0.800047 | − | 0.599937i | \(-0.795192\pi\) | ||||
−0.800047 | + | 0.599937i | \(0.795192\pi\) | |||||||
\(558\) | −25.1277 | −1.06374 | ||||||||
\(559\) | −14.6255 | −0.618594 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.44483 | −0.187494 | ||||||||
\(563\) | −40.4219 | −1.70358 | −0.851791 | − | 0.523882i | \(-0.824483\pi\) | ||||
−0.851791 | + | 0.523882i | \(0.824483\pi\) | |||||||
\(564\) | −2.48524 | −0.104647 | ||||||||
\(565\) | 12.3826 | 0.520941 | ||||||||
\(566\) | −5.81252 | −0.244319 | ||||||||
\(567\) | 2.22595 | 0.0934813 | ||||||||
\(568\) | −7.02166 | −0.294622 | ||||||||
\(569\) | −33.7555 | −1.41511 | −0.707553 | − | 0.706660i | \(-0.750201\pi\) | ||||
−0.707553 | + | 0.706660i | \(0.750201\pi\) | |||||||
\(570\) | −16.2208 | −0.679413 | ||||||||
\(571\) | −9.90555 | −0.414534 | −0.207267 | − | 0.978284i | \(-0.566457\pi\) | ||||
−0.207267 | + | 0.978284i | \(0.566457\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.8442 | 1.41386 | ||||||||
\(574\) | −9.08954 | −0.379390 | ||||||||
\(575\) | −6.62208 | −0.276160 | ||||||||
\(576\) | 4.50401 | 0.187667 | ||||||||
\(577\) | 25.7980 | 1.07398 | 0.536992 | − | 0.843587i | \(-0.319560\pi\) | ||||
0.536992 | + | 0.843587i | \(0.319560\pi\) | |||||||
\(578\) | 27.5860 | 1.14742 | ||||||||
\(579\) | −32.3274 | −1.34348 | ||||||||
\(580\) | 1.10448 | 0.0458612 | ||||||||
\(581\) | 15.9031 | 0.659770 | ||||||||
\(582\) | −31.3276 | −1.29857 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0.967438 | 0.0400329 | ||||||||
\(585\) | 11.9444 | 0.493841 | ||||||||
\(586\) | 8.16127 | 0.337139 | ||||||||
\(587\) | 0.761169 | 0.0314168 | 0.0157084 | − | 0.999877i | \(-0.495000\pi\) | ||||
0.0157084 | + | 0.999877i | \(0.495000\pi\) | |||||||
\(588\) | −2.73934 | −0.112969 | ||||||||
\(589\) | −33.0354 | −1.36120 | ||||||||
\(590\) | 1.72702 | 0.0711002 | ||||||||
\(591\) | −53.3146 | −2.19307 | ||||||||
\(592\) | 4.15191 | 0.170642 | ||||||||
\(593\) | −23.5344 | −0.966442 | −0.483221 | − | 0.875498i | \(-0.660533\pi\) | ||||
−0.483221 | + | 0.875498i | \(0.660533\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.67727 | 0.273741 | ||||||||
\(596\) | −18.9356 | −0.775631 | ||||||||
\(597\) | −42.6654 | −1.74618 | ||||||||
\(598\) | −17.5615 | −0.718142 | ||||||||
\(599\) | 12.2528 | 0.500637 | 0.250318 | − | 0.968164i | \(-0.419465\pi\) | ||||
0.250318 | + | 0.968164i | \(0.419465\pi\) | |||||||
\(600\) | −2.73934 | −0.111833 | ||||||||
\(601\) | 29.7034 | 1.21163 | 0.605813 | − | 0.795607i | \(-0.292848\pi\) | ||||
0.605813 | + | 0.795607i | \(0.292848\pi\) | |||||||
\(602\) | 5.51500 | 0.224775 | ||||||||
\(603\) | −18.4979 | −0.753292 | ||||||||
\(604\) | −9.07849 | −0.369398 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −21.0352 | −0.854498 | ||||||||
\(607\) | 38.5009 | 1.56270 | 0.781351 | − | 0.624092i | \(-0.214531\pi\) | ||||
0.781351 | + | 0.624092i | \(0.214531\pi\) | |||||||
\(608\) | 5.92140 | 0.240145 | ||||||||
\(609\) | 3.02556 | 0.122602 | ||||||||
\(610\) | −8.93518 | −0.361775 | ||||||||
\(611\) | 2.40596 | 0.0973346 | ||||||||
\(612\) | −30.0745 | −1.21569 | ||||||||
\(613\) | 11.0299 | 0.445493 | 0.222746 | − | 0.974876i | \(-0.428498\pi\) | ||||
0.222746 | + | 0.974876i | \(0.428498\pi\) | |||||||
\(614\) | −15.7830 | −0.636949 | ||||||||
\(615\) | −24.8994 | −1.00404 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.3964 | −0.861388 | −0.430694 | − | 0.902498i | \(-0.641731\pi\) | ||||
−0.430694 | + | 0.902498i | \(0.641731\pi\) | |||||||
\(618\) | 3.54653 | 0.142663 | ||||||||
\(619\) | −49.0198 | −1.97027 | −0.985136 | − | 0.171776i | \(-0.945049\pi\) | ||||
−0.985136 | + | 0.171776i | \(0.945049\pi\) | |||||||
\(620\) | −5.57898 | −0.224057 | ||||||||
\(621\) | 27.2829 | 1.09482 | ||||||||
\(622\) | −6.51788 | −0.261343 | ||||||||
\(623\) | −12.5040 | −0.500964 | ||||||||
\(624\) | −7.26462 | −0.290817 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −9.54938 | −0.381670 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.0301 | 0.519956 | ||||||||
\(629\) | −27.7234 | −1.10541 | ||||||||
\(630\) | −4.50401 | −0.179444 | ||||||||
\(631\) | 16.5923 | 0.660527 | 0.330264 | − | 0.943889i | \(-0.392862\pi\) | ||||
0.330264 | + | 0.943889i | \(0.392862\pi\) | |||||||
\(632\) | 10.7456 | 0.427437 | ||||||||
\(633\) | −37.8491 | −1.50437 | ||||||||
\(634\) | −6.52267 | −0.259048 | ||||||||
\(635\) | 8.64037 | 0.342883 | ||||||||
\(636\) | 25.3148 | 1.00380 | ||||||||
\(637\) | 2.65196 | 0.105074 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −31.6256 | −1.25109 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 10.8261 | 0.427606 | 0.213803 | − | 0.976877i | \(-0.431415\pi\) | ||||
0.213803 | + | 0.976877i | \(0.431415\pi\) | |||||||
\(642\) | 38.4579 | 1.51781 | ||||||||
\(643\) | −0.443804 | −0.0175019 | −0.00875095 | − | 0.999962i | \(-0.502786\pi\) | ||||
−0.00875095 | + | 0.999962i | \(0.502786\pi\) | |||||||
\(644\) | 6.62208 | 0.260947 | ||||||||
\(645\) | 15.1075 | 0.594856 | ||||||||
\(646\) | −39.5388 | −1.55563 | ||||||||
\(647\) | 31.8694 | 1.25292 | 0.626458 | − | 0.779455i | \(-0.284504\pi\) | ||||
0.626458 | + | 0.779455i | \(0.284504\pi\) | |||||||
\(648\) | −2.22595 | −0.0874437 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.65196 | 0.104018 | ||||||||
\(651\) | −15.2827 | −0.598978 | ||||||||
\(652\) | 8.41437 | 0.329532 | ||||||||
\(653\) | 23.5789 | 0.922715 | 0.461358 | − | 0.887214i | \(-0.347363\pi\) | ||||
0.461358 | + | 0.887214i | \(0.347363\pi\) | |||||||
\(654\) | 37.3287 | 1.45967 | ||||||||
\(655\) | 6.27193 | 0.245065 | ||||||||
\(656\) | 9.08954 | 0.354887 | ||||||||
\(657\) | 4.35735 | 0.169996 | ||||||||
\(658\) | −0.907239 | −0.0353679 | ||||||||
\(659\) | −18.1283 | −0.706178 | −0.353089 | − | 0.935590i | \(-0.614869\pi\) | ||||
−0.353089 | + | 0.935590i | \(0.614869\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.1392 | 1.36676 | 0.683378 | − | 0.730065i | \(-0.260510\pi\) | ||||
0.683378 | + | 0.730065i | \(0.260510\pi\) | |||||||
\(662\) | −20.3519 | −0.790997 | ||||||||
\(663\) | 48.5078 | 1.88389 | ||||||||
\(664\) | −15.9031 | −0.617159 | ||||||||
\(665\) | −5.92140 | −0.229622 | ||||||||
\(666\) | 18.7002 | 0.724619 | ||||||||
\(667\) | −7.31398 | −0.283198 | ||||||||
\(668\) | −11.2346 | −0.434681 | ||||||||
\(669\) | 24.6009 | 0.951127 | ||||||||
\(670\) | −4.10699 | −0.158667 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.73934 | 0.105672 | ||||||||
\(673\) | −11.5684 | −0.445929 | −0.222965 | − | 0.974827i | \(-0.571573\pi\) | ||||
−0.222965 | + | 0.974827i | \(0.571573\pi\) | |||||||
\(674\) | −20.3955 | −0.785603 | ||||||||
\(675\) | −4.11999 | −0.158578 | ||||||||
\(676\) | −5.96713 | −0.229505 | ||||||||
\(677\) | −4.02406 | −0.154657 | −0.0773286 | − | 0.997006i | \(-0.524639\pi\) | ||||
−0.0773286 | + | 0.997006i | \(0.524639\pi\) | |||||||
\(678\) | −33.9203 | −1.30270 | ||||||||
\(679\) | −11.4362 | −0.438880 | ||||||||
\(680\) | −6.67727 | −0.256062 | ||||||||
\(681\) | 50.7763 | 1.94575 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.85171 | −0.109118 | −0.0545588 | − | 0.998511i | \(-0.517375\pi\) | ||||
−0.0545588 | + | 0.998511i | \(0.517375\pi\) | |||||||
\(684\) | 26.6700 | 1.01975 | ||||||||
\(685\) | −10.9179 | −0.417153 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 72.2570 | 2.75678 | ||||||||
\(688\) | −5.51500 | −0.210257 | ||||||||
\(689\) | −24.5073 | −0.933653 | ||||||||
\(690\) | 18.1402 | 0.690584 | ||||||||
\(691\) | 9.12185 | 0.347011 | 0.173506 | − | 0.984833i | \(-0.444490\pi\) | ||||
0.173506 | + | 0.984833i | \(0.444490\pi\) | |||||||
\(692\) | −0.0298132 | −0.00113333 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.1418 | −0.954370 | ||||||||
\(695\) | 12.5679 | 0.476729 | ||||||||
\(696\) | −3.02556 | −0.114684 | ||||||||
\(697\) | −60.6933 | −2.29892 | ||||||||
\(698\) | 6.48720 | 0.245544 | ||||||||
\(699\) | −35.3456 | −1.33689 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | −51.5517 | −1.94708 | −0.973540 | − | 0.228516i | \(-0.926613\pi\) | ||||
−0.973540 | + | 0.228516i | \(0.926613\pi\) | |||||||
\(702\) | −10.9260 | −0.412376 | ||||||||
\(703\) | 24.5851 | 0.927246 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.48524 | −0.0935995 | ||||||||
\(706\) | −0.671105 | −0.0252574 | ||||||||
\(707\) | −7.67893 | −0.288796 | ||||||||
\(708\) | −4.73089 | −0.177798 | ||||||||
\(709\) | 30.4453 | 1.14340 | 0.571699 | − | 0.820463i | \(-0.306284\pi\) | ||||
0.571699 | + | 0.820463i | \(0.306284\pi\) | |||||||
\(710\) | −7.02166 | −0.263518 | ||||||||
\(711\) | 48.3982 | 1.81508 | ||||||||
\(712\) | 12.5040 | 0.468609 | ||||||||
\(713\) | 36.9445 | 1.38358 | ||||||||
\(714\) | −18.2913 | −0.684536 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23.6951 | −0.885529 | ||||||||
\(717\) | −20.3748 | −0.760912 | ||||||||
\(718\) | −33.6491 | −1.25577 | ||||||||
\(719\) | 41.3242 | 1.54113 | 0.770565 | − | 0.637361i | \(-0.219974\pi\) | ||||
0.770565 | + | 0.637361i | \(0.219974\pi\) | |||||||
\(720\) | 4.50401 | 0.167854 | ||||||||
\(721\) | 1.29467 | 0.0482159 | ||||||||
\(722\) | 16.0630 | 0.597803 | ||||||||
\(723\) | 81.9824 | 3.04896 | ||||||||
\(724\) | −5.38186 | −0.200015 | ||||||||
\(725\) | 1.10448 | 0.0410195 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.01006 | −0.0745492 | −0.0372746 | − | 0.999305i | \(-0.511868\pi\) | ||||
−0.0372746 | + | 0.999305i | \(0.511868\pi\) | |||||||
\(728\) | −2.65196 | −0.0982880 | ||||||||
\(729\) | −43.8839 | −1.62533 | ||||||||
\(730\) | 0.967438 | 0.0358065 | ||||||||
\(731\) | 36.8251 | 1.36203 | ||||||||
\(732\) | 24.4765 | 0.904679 | ||||||||
\(733\) | −23.9790 | −0.885686 | −0.442843 | − | 0.896599i | \(-0.646030\pi\) | ||||
−0.442843 | + | 0.896599i | \(0.646030\pi\) | |||||||
\(734\) | −5.36793 | −0.198134 | ||||||||
\(735\) | −2.73934 | −0.101042 | ||||||||
\(736\) | −6.62208 | −0.244093 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 40.9393 | 1.50700 | ||||||||
\(739\) | −12.9004 | −0.474551 | −0.237275 | − | 0.971442i | \(-0.576254\pi\) | ||||
−0.237275 | + | 0.971442i | \(0.576254\pi\) | |||||||
\(740\) | 4.15191 | 0.152627 | ||||||||
\(741\) | −43.0167 | −1.58026 | ||||||||
\(742\) | 9.24121 | 0.339255 | ||||||||
\(743\) | −12.6488 | −0.464039 | −0.232019 | − | 0.972711i | \(-0.574533\pi\) | ||||
−0.232019 | + | 0.972711i | \(0.574533\pi\) | |||||||
\(744\) | 15.2827 | 0.560292 | ||||||||
\(745\) | −18.9356 | −0.693745 | ||||||||
\(746\) | 16.1242 | 0.590348 | ||||||||
\(747\) | −71.6275 | −2.62071 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.0391 | 0.512977 | ||||||||
\(750\) | −2.73934 | −0.100027 | ||||||||
\(751\) | −7.57446 | −0.276396 | −0.138198 | − | 0.990405i | \(-0.544131\pi\) | ||||
−0.138198 | + | 0.990405i | \(0.544131\pi\) | |||||||
\(752\) | 0.907239 | 0.0330836 | ||||||||
\(753\) | −7.03494 | −0.256367 | ||||||||
\(754\) | 2.92904 | 0.106669 | ||||||||
\(755\) | −9.07849 | −0.330400 | ||||||||
\(756\) | 4.11999 | 0.149842 | ||||||||
\(757\) | 25.1439 | 0.913869 | 0.456934 | − | 0.889500i | \(-0.348947\pi\) | ||||
0.456934 | + | 0.889500i | \(0.348947\pi\) | |||||||
\(758\) | −27.3566 | −0.993636 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.92140 | 0.214792 | ||||||||
\(761\) | 33.9674 | 1.23132 | 0.615658 | − | 0.788013i | \(-0.288890\pi\) | ||||
0.615658 | + | 0.788013i | \(0.288890\pi\) | |||||||
\(762\) | −23.6689 | −0.857435 | ||||||||
\(763\) | 13.6269 | 0.493326 | ||||||||
\(764\) | −12.3548 | −0.446982 | ||||||||
\(765\) | −30.0745 | −1.08734 | ||||||||
\(766\) | 0.132352 | 0.00478205 | ||||||||
\(767\) | 4.57997 | 0.165373 | ||||||||
\(768\) | −2.73934 | −0.0988476 | ||||||||
\(769\) | 22.3766 | 0.806919 | 0.403460 | − | 0.914997i | \(-0.367808\pi\) | ||||
0.403460 | + | 0.914997i | \(0.367808\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 76.0754 | 2.73979 | ||||||||
\(772\) | 11.8011 | 0.424732 | ||||||||
\(773\) | 50.5235 | 1.81721 | 0.908603 | − | 0.417662i | \(-0.137150\pi\) | ||||
0.908603 | + | 0.417662i | \(0.137150\pi\) | |||||||
\(774\) | −24.8396 | −0.892840 | ||||||||
\(775\) | −5.57898 | −0.200403 | ||||||||
\(776\) | 11.4362 | 0.410535 | ||||||||
\(777\) | 11.3735 | 0.408022 | ||||||||
\(778\) | 16.3662 | 0.586756 | ||||||||
\(779\) | 53.8228 | 1.92840 | ||||||||
\(780\) | −7.26462 | −0.260115 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 44.2175 | 1.58121 | ||||||||
\(783\) | −4.55046 | −0.162620 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 13.0301 | 0.465063 | ||||||||
\(786\) | −17.1810 | −0.612825 | ||||||||
\(787\) | −25.9303 | −0.924315 | −0.462157 | − | 0.886798i | \(-0.652924\pi\) | ||||
−0.462157 | + | 0.886798i | \(0.652924\pi\) | |||||||
\(788\) | 19.4626 | 0.693325 | ||||||||
\(789\) | 38.7949 | 1.38113 | ||||||||
\(790\) | 10.7456 | 0.382311 | ||||||||
\(791\) | −12.3826 | −0.440276 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.6957 | −0.841459 | ||||||||
\(794\) | 34.8294 | 1.23605 | ||||||||
\(795\) | 25.3148 | 0.897825 | ||||||||
\(796\) | 15.5751 | 0.552043 | ||||||||
\(797\) | 11.5642 | 0.409624 | 0.204812 | − | 0.978801i | \(-0.434342\pi\) | ||||
0.204812 | + | 0.978801i | \(0.434342\pi\) | |||||||
\(798\) | 16.2208 | 0.574209 | ||||||||
\(799\) | −6.05788 | −0.214312 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 56.3183 | 1.98991 | ||||||||
\(802\) | −11.8605 | −0.418808 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 11.2504 | 0.396773 | ||||||||
\(805\) | 6.62208 | 0.233398 | ||||||||
\(806\) | −14.7952 | −0.521139 | ||||||||
\(807\) | −67.3015 | −2.36912 | ||||||||
\(808\) | 7.67893 | 0.270144 | ||||||||
\(809\) | 6.46814 | 0.227408 | 0.113704 | − | 0.993515i | \(-0.463728\pi\) | ||||
0.113704 | + | 0.993515i | \(0.463728\pi\) | |||||||
\(810\) | −2.22595 | −0.0782120 | ||||||||
\(811\) | −35.3469 | −1.24120 | −0.620598 | − | 0.784129i | \(-0.713110\pi\) | ||||
−0.620598 | + | 0.784129i | \(0.713110\pi\) | |||||||
\(812\) | −1.10448 | −0.0387598 | ||||||||
\(813\) | −28.7227 | −1.00735 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.41437 | 0.294743 | ||||||||
\(816\) | 18.2913 | 0.640325 | ||||||||
\(817\) | −32.6565 | −1.14251 | ||||||||
\(818\) | −7.78726 | −0.272275 | ||||||||
\(819\) | −11.9444 | −0.417372 | ||||||||
\(820\) | 9.08954 | 0.317420 | ||||||||
\(821\) | 30.6970 | 1.07133 | 0.535666 | − | 0.844430i | \(-0.320061\pi\) | ||||
0.535666 | + | 0.844430i | \(0.320061\pi\) | |||||||
\(822\) | 29.9080 | 1.04316 | ||||||||
\(823\) | 19.6396 | 0.684594 | 0.342297 | − | 0.939592i | \(-0.388795\pi\) | ||||
0.342297 | + | 0.939592i | \(0.388795\pi\) | |||||||
\(824\) | −1.29467 | −0.0451018 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.72702 | −0.0600906 | ||||||||
\(827\) | −28.3877 | −0.987138 | −0.493569 | − | 0.869707i | \(-0.664308\pi\) | ||||
−0.493569 | + | 0.869707i | \(0.664308\pi\) | |||||||
\(828\) | −29.8259 | −1.03652 | ||||||||
\(829\) | 32.4774 | 1.12799 | 0.563994 | − | 0.825779i | \(-0.309264\pi\) | ||||
0.563994 | + | 0.825779i | \(0.309264\pi\) | |||||||
\(830\) | −15.9031 | −0.552003 | ||||||||
\(831\) | 84.4876 | 2.93084 | ||||||||
\(832\) | 2.65196 | 0.0919400 | ||||||||
\(833\) | −6.67727 | −0.231354 | ||||||||
\(834\) | −34.4279 | −1.19214 | ||||||||
\(835\) | −11.2346 | −0.388791 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.9853 | 0.794489 | ||||||||
\(838\) | −9.59415 | −0.331424 | ||||||||
\(839\) | 26.4066 | 0.911659 | 0.455829 | − | 0.890067i | \(-0.349343\pi\) | ||||
0.455829 | + | 0.890067i | \(0.349343\pi\) | |||||||
\(840\) | 2.73934 | 0.0945163 | ||||||||
\(841\) | −27.7801 | −0.957935 | ||||||||
\(842\) | 19.7210 | 0.679631 | ||||||||
\(843\) | 12.1759 | 0.419361 | ||||||||
\(844\) | 13.8169 | 0.475596 | ||||||||
\(845\) | −5.96713 | −0.205276 | ||||||||
\(846\) | 4.08621 | 0.140487 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.24121 | −0.317344 | ||||||||
\(849\) | 15.9225 | 0.546459 | ||||||||
\(850\) | −6.67727 | −0.229029 | ||||||||
\(851\) | −27.4943 | −0.942492 | ||||||||
\(852\) | 19.2347 | 0.658971 | ||||||||
\(853\) | 28.0478 | 0.960338 | 0.480169 | − | 0.877176i | \(-0.340575\pi\) | ||||
0.480169 | + | 0.877176i | \(0.340575\pi\) | |||||||
\(854\) | 8.93518 | 0.305756 | ||||||||
\(855\) | 26.6700 | 0.912096 | ||||||||
\(856\) | −14.0391 | −0.479846 | ||||||||
\(857\) | 47.9742 | 1.63877 | 0.819383 | − | 0.573246i | \(-0.194316\pi\) | ||||
0.819383 | + | 0.573246i | \(0.194316\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.1815 | −0.961541 | −0.480770 | − | 0.876847i | \(-0.659643\pi\) | ||||
−0.480770 | + | 0.876847i | \(0.659643\pi\) | |||||||
\(860\) | −5.51500 | −0.188060 | ||||||||
\(861\) | 24.8994 | 0.848568 | ||||||||
\(862\) | −18.5608 | −0.632183 | ||||||||
\(863\) | 7.05526 | 0.240164 | 0.120082 | − | 0.992764i | \(-0.461684\pi\) | ||||
0.120082 | + | 0.992764i | \(0.461684\pi\) | |||||||
\(864\) | −4.11999 | −0.140165 | ||||||||
\(865\) | −0.0298132 | −0.00101368 | ||||||||
\(866\) | −15.6876 | −0.533088 | ||||||||
\(867\) | −75.5674 | −2.56641 | ||||||||
\(868\) | 5.57898 | 0.189363 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −3.02556 | −0.102576 | ||||||||
\(871\) | −10.8915 | −0.369046 | ||||||||
\(872\) | −13.6269 | −0.461464 | ||||||||
\(873\) | 51.5086 | 1.74330 | ||||||||
\(874\) | −39.2120 | −1.32637 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −2.65015 | −0.0895401 | ||||||||
\(877\) | −44.0677 | −1.48806 | −0.744030 | − | 0.668146i | \(-0.767088\pi\) | ||||
−0.744030 | + | 0.668146i | \(0.767088\pi\) | |||||||
\(878\) | −6.85571 | −0.231369 | ||||||||
\(879\) | −22.3565 | −0.754067 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.79232 | 0.0940757 | 0.0470379 | − | 0.998893i | \(-0.485022\pi\) | ||||
0.0470379 | + | 0.998893i | \(0.485022\pi\) | |||||||
\(882\) | 4.50401 | 0.151658 | ||||||||
\(883\) | −14.4756 | −0.487144 | −0.243572 | − | 0.969883i | \(-0.578319\pi\) | ||||
−0.243572 | + | 0.969883i | \(0.578319\pi\) | |||||||
\(884\) | −17.7078 | −0.595579 | ||||||||
\(885\) | −4.73089 | −0.159027 | ||||||||
\(886\) | 13.6685 | 0.459203 | ||||||||
\(887\) | −27.8169 | −0.933999 | −0.466999 | − | 0.884258i | \(-0.654665\pi\) | ||||
−0.466999 | + | 0.884258i | \(0.654665\pi\) | |||||||
\(888\) | −11.3735 | −0.381670 | ||||||||
\(889\) | −8.64037 | −0.289789 | ||||||||
\(890\) | 12.5040 | 0.419136 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.98060 | −0.300693 | ||||||||
\(893\) | 5.37213 | 0.179771 | ||||||||
\(894\) | 51.8710 | 1.73483 | ||||||||
\(895\) | −23.6951 | −0.792041 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 48.1069 | 1.60624 | ||||||||
\(898\) | −36.9601 | −1.23337 | ||||||||
\(899\) | −6.16189 | −0.205510 | ||||||||
\(900\) | 4.50401 | 0.150134 | ||||||||
\(901\) | 61.7061 | 2.05573 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.1075 | −0.502745 | ||||||||
\(904\) | 12.3826 | 0.411840 | ||||||||
\(905\) | −5.38186 | −0.178899 | ||||||||
\(906\) | 24.8691 | 0.826221 | ||||||||
\(907\) | −29.5574 | −0.981436 | −0.490718 | − | 0.871319i | \(-0.663265\pi\) | ||||
−0.490718 | + | 0.871319i | \(0.663265\pi\) | |||||||
\(908\) | −18.5359 | −0.615136 | ||||||||
\(909\) | 34.5859 | 1.14714 | ||||||||
\(910\) | −2.65196 | −0.0879115 | ||||||||
\(911\) | 48.6900 | 1.61317 | 0.806585 | − | 0.591118i | \(-0.201313\pi\) | ||||
0.806585 | + | 0.591118i | \(0.201313\pi\) | |||||||
\(912\) | −16.2208 | −0.537123 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 7.21944 | 0.238798 | ||||||||
\(915\) | 24.4765 | 0.809169 | ||||||||
\(916\) | −26.3775 | −0.871537 | ||||||||
\(917\) | −6.27193 | −0.207117 | ||||||||
\(918\) | 27.5103 | 0.907974 | ||||||||
\(919\) | −41.7897 | −1.37852 | −0.689258 | − | 0.724516i | \(-0.742063\pi\) | ||||
−0.689258 | + | 0.724516i | \(0.742063\pi\) | |||||||
\(920\) | −6.62208 | −0.218324 | ||||||||
\(921\) | 43.2350 | 1.42464 | ||||||||
\(922\) | −35.7004 | −1.17573 | ||||||||
\(923\) | −18.6211 | −0.612922 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.15191 | 0.136514 | ||||||||
\(926\) | −19.9145 | −0.654430 | ||||||||
\(927\) | −5.83118 | −0.191521 | ||||||||
\(928\) | 1.10448 | 0.0362564 | ||||||||
\(929\) | 10.2472 | 0.336200 | 0.168100 | − | 0.985770i | \(-0.446237\pi\) | ||||
0.168100 | + | 0.985770i | \(0.446237\pi\) | |||||||
\(930\) | 15.2827 | 0.501141 | ||||||||
\(931\) | 5.92140 | 0.194066 | ||||||||
\(932\) | 12.9030 | 0.422650 | ||||||||
\(933\) | 17.8547 | 0.584537 | ||||||||
\(934\) | 12.8231 | 0.419585 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 11.9444 | 0.390416 | ||||||||
\(937\) | −33.3518 | −1.08956 | −0.544779 | − | 0.838580i | \(-0.683386\pi\) | ||||
−0.544779 | + | 0.838580i | \(0.683386\pi\) | |||||||
\(938\) | 4.10699 | 0.134098 | ||||||||
\(939\) | 26.1590 | 0.853668 | ||||||||
\(940\) | 0.907239 | 0.0295909 | ||||||||
\(941\) | −4.77317 | −0.155601 | −0.0778005 | − | 0.996969i | \(-0.524790\pi\) | ||||
−0.0778005 | + | 0.996969i | \(0.524790\pi\) | |||||||
\(942\) | −35.6938 | −1.16297 | ||||||||
\(943\) | −60.1917 | −1.96011 | ||||||||
\(944\) | 1.72702 | 0.0562096 | ||||||||
\(945\) | 4.11999 | 0.134023 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.18216 | 0.298380 | 0.149190 | − | 0.988809i | \(-0.452333\pi\) | ||||
0.149190 | + | 0.988809i | \(0.452333\pi\) | |||||||
\(948\) | −29.4359 | −0.956034 | ||||||||
\(949\) | 2.56560 | 0.0832830 | ||||||||
\(950\) | 5.92140 | 0.192116 | ||||||||
\(951\) | 17.8678 | 0.579404 | ||||||||
\(952\) | 6.67727 | 0.216412 | ||||||||
\(953\) | 49.9893 | 1.61931 | 0.809656 | − | 0.586905i | \(-0.199654\pi\) | ||||
0.809656 | + | 0.586905i | \(0.199654\pi\) | |||||||
\(954\) | −41.6224 | −1.34758 | ||||||||
\(955\) | −12.3548 | −0.399793 | ||||||||
\(956\) | 7.43785 | 0.240557 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.92060 | −0.126669 | ||||||||
\(959\) | 10.9179 | 0.352559 | ||||||||
\(960\) | −2.73934 | −0.0884119 | ||||||||
\(961\) | 0.125003 | 0.00403237 | ||||||||
\(962\) | 11.0107 | 0.354999 | ||||||||
\(963\) | −63.2321 | −2.03763 | ||||||||
\(964\) | −29.9278 | −0.963908 | ||||||||
\(965\) | 11.8011 | 0.379892 | ||||||||
\(966\) | −18.1402 | −0.583650 | ||||||||
\(967\) | 4.16857 | 0.134052 | 0.0670261 | − | 0.997751i | \(-0.478649\pi\) | ||||
0.0670261 | + | 0.997751i | \(0.478649\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 108.310 | 3.47943 | ||||||||
\(970\) | 11.4362 | 0.367193 | ||||||||
\(971\) | 43.5285 | 1.39689 | 0.698447 | − | 0.715662i | \(-0.253875\pi\) | ||||
0.698447 | + | 0.715662i | \(0.253875\pi\) | |||||||
\(972\) | 18.4576 | 0.592028 | ||||||||
\(973\) | −12.5679 | −0.402909 | ||||||||
\(974\) | −41.0411 | −1.31504 | ||||||||
\(975\) | −7.26462 | −0.232654 | ||||||||
\(976\) | −8.93518 | −0.286008 | ||||||||
\(977\) | −24.6315 | −0.788033 | −0.394017 | − | 0.919103i | \(-0.628915\pi\) | ||||
−0.394017 | + | 0.919103i | \(0.628915\pi\) | |||||||
\(978\) | −23.0499 | −0.737053 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −61.3755 | −1.95957 | ||||||||
\(982\) | 10.2674 | 0.327647 | ||||||||
\(983\) | 37.8291 | 1.20656 | 0.603280 | − | 0.797530i | \(-0.293860\pi\) | ||||
0.603280 | + | 0.797530i | \(0.293860\pi\) | |||||||
\(984\) | −24.8994 | −0.793763 | ||||||||
\(985\) | 19.4626 | 0.620129 | ||||||||
\(986\) | −7.37494 | −0.234866 | ||||||||
\(987\) | 2.48524 | 0.0791061 | ||||||||
\(988\) | 15.7033 | 0.499588 | ||||||||
\(989\) | 36.5208 | 1.16129 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.2409 | −0.833570 | −0.416785 | − | 0.909005i | \(-0.636843\pi\) | ||||
−0.416785 | + | 0.909005i | \(0.636843\pi\) | |||||||
\(992\) | −5.57898 | −0.177133 | ||||||||
\(993\) | 55.7507 | 1.76920 | ||||||||
\(994\) | 7.02166 | 0.222714 | ||||||||
\(995\) | 15.5751 | 0.493763 | ||||||||
\(996\) | 43.5640 | 1.38038 | ||||||||
\(997\) | −6.27699 | −0.198794 | −0.0993971 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993971 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(998\) | 33.4423 | 1.05860 | ||||||||
\(999\) | −17.1058 | −0.541204 |
(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 | 8470.2.a.db.1.1 | 6 | ||
11.5 | even | 5 | 770.2.n.g.421.1 | ✓ | 12 | ||
11.9 | even | 5 | 770.2.n.g.631.1 | yes | 12 | ||
11.10 | odd | 2 | 8470.2.a.cv.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.g.421.1 | ✓ | 12 | 11.5 | even | 5 | ||
770.2.n.g.631.1 | yes | 12 | 11.9 | even | 5 | ||
8470.2.a.cv.1.1 | 6 | 11.10 | odd | 2 | |||
8470.2.a.db.1.1 | 6 | 1.1 | even | 1 | trivial |