Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(1,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.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: | \(21.1284163748\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.41421 | −0.632456 | −0.316228 | − | 0.948683i | \(-0.602416\pi\) | ||||
−0.316228 | + | 0.948683i | \(0.602416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.41421 | −0.447214 | ||||||||
\(11\) | 2.24264 | 0.676182 | 0.338091 | − | 0.941113i | \(-0.390219\pi\) | ||||
0.338091 | + | 0.941113i | \(0.390219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | −0.832050 | −0.416025 | − | 0.909353i | \(-0.636577\pi\) | ||||
−0.416025 | + | 0.909353i | \(0.636577\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.41421 | −1.07060 | −0.535302 | − | 0.844661i | \(-0.679802\pi\) | ||||
−0.535302 | + | 0.844661i | \(0.679802\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.58579 | −1.05205 | −0.526026 | − | 0.850469i | \(-0.676318\pi\) | ||||
−0.526026 | + | 0.850469i | \(0.676318\pi\) | |||||||
\(20\) | −1.41421 | −0.316228 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.24264 | 0.478133 | ||||||||
\(23\) | −1.00000 | −0.208514 | −0.104257 | − | 0.994550i | \(-0.533247\pi\) | ||||
−0.104257 | + | 0.994550i | \(0.533247\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | −3.00000 | −0.588348 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.24264 | −0.973534 | −0.486767 | − | 0.873532i | \(-0.661824\pi\) | ||||
−0.486767 | + | 0.873532i | \(0.661824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.24264 | 0.223185 | 0.111592 | − | 0.993754i | \(-0.464405\pi\) | ||||
0.111592 | + | 0.993754i | \(0.464405\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.41421 | −0.757031 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.4853 | −1.72377 | −0.861885 | − | 0.507104i | \(-0.830716\pi\) | ||||
−0.861885 | + | 0.507104i | \(0.830716\pi\) | |||||||
\(38\) | −4.58579 | −0.743913 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.41421 | −0.223607 | ||||||||
\(41\) | 2.82843 | 0.441726 | 0.220863 | − | 0.975305i | \(-0.429113\pi\) | ||||
0.220863 | + | 0.975305i | \(0.429113\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.24264 | 0.494498 | 0.247249 | − | 0.968952i | \(-0.420473\pi\) | ||||
0.247249 | + | 0.968952i | \(0.420473\pi\) | |||||||
\(44\) | 2.24264 | 0.338091 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 7.07107 | 1.03142 | 0.515711 | − | 0.856763i | \(-0.327528\pi\) | ||||
0.515711 | + | 0.856763i | \(0.327528\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.00000 | −0.424264 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.00000 | −0.416025 | ||||||||
\(53\) | 11.2426 | 1.54430 | 0.772148 | − | 0.635443i | \(-0.219183\pi\) | ||||
0.772148 | + | 0.635443i | \(0.219183\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.17157 | −0.427655 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.24264 | −0.688392 | ||||||||
\(59\) | −0.171573 | −0.0223369 | −0.0111684 | − | 0.999938i | \(-0.503555\pi\) | ||||
−0.0111684 | + | 0.999938i | \(0.503555\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.6569 | −1.49251 | −0.746254 | − | 0.665662i | \(-0.768149\pi\) | ||||
−0.746254 | + | 0.665662i | \(0.768149\pi\) | |||||||
\(62\) | 1.24264 | 0.157816 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.24264 | 0.526235 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.2426 | 1.61785 | 0.808923 | − | 0.587915i | \(-0.200051\pi\) | ||||
0.808923 | + | 0.587915i | \(0.200051\pi\) | |||||||
\(68\) | −4.41421 | −0.535302 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.48528 | −0.650983 | −0.325492 | − | 0.945545i | \(-0.605530\pi\) | ||||
−0.325492 | + | 0.945545i | \(0.605530\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.89949 | −1.15865 | −0.579324 | − | 0.815097i | \(-0.696683\pi\) | ||||
−0.579324 | + | 0.815097i | \(0.696683\pi\) | |||||||
\(74\) | −10.4853 | −1.21889 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.58579 | −0.526026 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.7279 | −1.20699 | −0.603493 | − | 0.797368i | \(-0.706225\pi\) | ||||
−0.603493 | + | 0.797368i | \(0.706225\pi\) | |||||||
\(80\) | −1.41421 | −0.158114 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.82843 | 0.312348 | ||||||||
\(83\) | −17.3137 | −1.90043 | −0.950213 | − | 0.311601i | \(-0.899135\pi\) | ||||
−0.950213 | + | 0.311601i | \(0.899135\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.24264 | 0.677109 | ||||||||
\(86\) | 3.24264 | 0.349663 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.24264 | 0.239066 | ||||||||
\(89\) | 1.92893 | 0.204466 | 0.102233 | − | 0.994760i | \(-0.467401\pi\) | ||||
0.102233 | + | 0.994760i | \(0.467401\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.07107 | 0.729325 | ||||||||
\(95\) | 6.48528 | 0.665376 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.8284 | −1.50560 | −0.752799 | − | 0.658250i | \(-0.771297\pi\) | ||||
−0.752799 | + | 0.658250i | \(0.771297\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | −0.300000 | ||||||||
\(101\) | 10.2426 | 1.01918 | 0.509590 | − | 0.860417i | \(-0.329797\pi\) | ||||
0.509590 | + | 0.860417i | \(0.329797\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.92893 | −0.190063 | −0.0950317 | − | 0.995474i | \(-0.530295\pi\) | ||||
−0.0950317 | + | 0.995474i | \(0.530295\pi\) | |||||||
\(104\) | −3.00000 | −0.294174 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.2426 | 1.09198 | ||||||||
\(107\) | −0.485281 | −0.0469139 | −0.0234570 | − | 0.999725i | \(-0.507467\pi\) | ||||
−0.0234570 | + | 0.999725i | \(0.507467\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.485281 | 0.0464815 | 0.0232408 | − | 0.999730i | \(-0.492602\pi\) | ||||
0.0232408 | + | 0.999730i | \(0.492602\pi\) | |||||||
\(110\) | −3.17157 | −0.302398 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.7279 | −1.19734 | −0.598671 | − | 0.800995i | \(-0.704304\pi\) | ||||
−0.598671 | + | 0.800995i | \(0.704304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.41421 | 0.131876 | ||||||||
\(116\) | −5.24264 | −0.486767 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.171573 | −0.0157946 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.97056 | −0.542778 | ||||||||
\(122\) | −11.6569 | −1.05536 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.24264 | 0.111592 | ||||||||
\(125\) | 11.3137 | 1.01193 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.72792 | 0.419535 | 0.209768 | − | 0.977751i | \(-0.432729\pi\) | ||||
0.209768 | + | 0.977751i | \(0.432729\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.24264 | 0.372104 | ||||||||
\(131\) | 0.514719 | 0.0449712 | 0.0224856 | − | 0.999747i | \(-0.492842\pi\) | ||||
0.0224856 | + | 0.999747i | \(0.492842\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.2426 | 1.14399 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.41421 | −0.378516 | ||||||||
\(137\) | −13.7574 | −1.17537 | −0.587685 | − | 0.809090i | \(-0.699961\pi\) | ||||
−0.587685 | + | 0.809090i | \(0.699961\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.3137 | −1.46853 | −0.734265 | − | 0.678863i | \(-0.762473\pi\) | ||||
−0.734265 | + | 0.678863i | \(0.762473\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.48528 | −0.460315 | ||||||||
\(143\) | −6.72792 | −0.562617 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.41421 | 0.615717 | ||||||||
\(146\) | −9.89949 | −0.819288 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.4853 | −0.861885 | ||||||||
\(149\) | −9.24264 | −0.757187 | −0.378593 | − | 0.925563i | \(-0.623592\pi\) | ||||
−0.378593 | + | 0.925563i | \(0.623592\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.7279 | 1.19854 | 0.599271 | − | 0.800546i | \(-0.295457\pi\) | ||||
0.599271 | + | 0.800546i | \(0.295457\pi\) | |||||||
\(152\) | −4.58579 | −0.371956 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.75736 | −0.141154 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.6569 | 1.16974 | 0.584872 | − | 0.811125i | \(-0.301145\pi\) | ||||
0.584872 | + | 0.811125i | \(0.301145\pi\) | |||||||
\(158\) | −10.7279 | −0.853468 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.41421 | −0.111803 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.2426 | −1.66385 | −0.831926 | − | 0.554887i | \(-0.812762\pi\) | ||||
−0.831926 | + | 0.554887i | \(0.812762\pi\) | |||||||
\(164\) | 2.82843 | 0.220863 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.3137 | −1.34380 | ||||||||
\(167\) | 3.89949 | 0.301752 | 0.150876 | − | 0.988553i | \(-0.451791\pi\) | ||||
0.150876 | + | 0.988553i | \(0.451791\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | 6.24264 | 0.478789 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.24264 | 0.247249 | ||||||||
\(173\) | 20.4853 | 1.55747 | 0.778734 | − | 0.627355i | \(-0.215862\pi\) | ||||
0.778734 | + | 0.627355i | \(0.215862\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.24264 | 0.169045 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.92893 | 0.144580 | ||||||||
\(179\) | 22.2426 | 1.66249 | 0.831247 | − | 0.555904i | \(-0.187628\pi\) | ||||
0.831247 | + | 0.555904i | \(0.187628\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.51472 | −0.484235 | −0.242118 | − | 0.970247i | \(-0.577842\pi\) | ||||
−0.242118 | + | 0.970247i | \(0.577842\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 14.8284 | 1.09021 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.89949 | −0.723923 | ||||||||
\(188\) | 7.07107 | 0.515711 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.48528 | 0.470492 | ||||||||
\(191\) | −26.9706 | −1.95152 | −0.975761 | − | 0.218840i | \(-0.929773\pi\) | ||||
−0.975761 | + | 0.218840i | \(0.929773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.00000 | 0.359908 | 0.179954 | − | 0.983675i | \(-0.442405\pi\) | ||||
0.179954 | + | 0.983675i | \(0.442405\pi\) | |||||||
\(194\) | −14.8284 | −1.06462 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.4853 | 0.747045 | 0.373523 | − | 0.927621i | \(-0.378150\pi\) | ||||
0.373523 | + | 0.927621i | \(0.378150\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.2426 | −0.938746 | −0.469373 | − | 0.883000i | \(-0.655520\pi\) | ||||
−0.469373 | + | 0.883000i | \(0.655520\pi\) | |||||||
\(200\) | −3.00000 | −0.212132 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.2426 | 0.720670 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00000 | −0.279372 | ||||||||
\(206\) | −1.92893 | −0.134395 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.00000 | −0.208013 | ||||||||
\(209\) | −10.2843 | −0.711378 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.2426 | 1.32472 | 0.662359 | − | 0.749187i | \(-0.269555\pi\) | ||||
0.662359 | + | 0.749187i | \(0.269555\pi\) | |||||||
\(212\) | 11.2426 | 0.772148 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.485281 | −0.0331732 | ||||||||
\(215\) | −4.58579 | −0.312748 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.485281 | 0.0328674 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.17157 | −0.213827 | ||||||||
\(221\) | 13.2426 | 0.890796 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.9706 | 1.13643 | 0.568216 | − | 0.822879i | \(-0.307634\pi\) | ||||
0.568216 | + | 0.822879i | \(0.307634\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.7279 | −0.846649 | ||||||||
\(227\) | 19.9706 | 1.32549 | 0.662746 | − | 0.748844i | \(-0.269391\pi\) | ||||
0.662746 | + | 0.748844i | \(0.269391\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(230\) | 1.41421 | 0.0932505 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.24264 | −0.344196 | ||||||||
\(233\) | 8.48528 | 0.555889 | 0.277945 | − | 0.960597i | \(-0.410347\pi\) | ||||
0.277945 | + | 0.960597i | \(0.410347\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.0000 | −0.652328 | ||||||||
\(236\) | −0.171573 | −0.0111684 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.9706 | 1.48584 | 0.742921 | − | 0.669379i | \(-0.233440\pi\) | ||||
0.742921 | + | 0.669379i | \(0.233440\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.727922 | 0.0468896 | 0.0234448 | − | 0.999725i | \(-0.492537\pi\) | ||||
0.0234448 | + | 0.999725i | \(0.492537\pi\) | |||||||
\(242\) | −5.97056 | −0.383802 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.6569 | −0.746254 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.7574 | 0.875360 | ||||||||
\(248\) | 1.24264 | 0.0789078 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.3137 | 0.715542 | ||||||||
\(251\) | 28.6274 | 1.80695 | 0.903473 | − | 0.428644i | \(-0.141009\pi\) | ||||
0.903473 | + | 0.428644i | \(0.141009\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.24264 | −0.140994 | ||||||||
\(254\) | 4.72792 | 0.296656 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.9706 | 1.43286 | 0.716432 | − | 0.697657i | \(-0.245774\pi\) | ||||
0.716432 | + | 0.697657i | \(0.245774\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.24264 | 0.263117 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.514719 | 0.0317994 | ||||||||
\(263\) | −6.51472 | −0.401715 | −0.200857 | − | 0.979620i | \(-0.564373\pi\) | ||||
−0.200857 | + | 0.979620i | \(0.564373\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.8995 | −0.976698 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.2426 | 0.808923 | ||||||||
\(269\) | −3.55635 | −0.216834 | −0.108417 | − | 0.994105i | \(-0.534578\pi\) | ||||
−0.108417 | + | 0.994105i | \(0.534578\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.89949 | 0.419114 | 0.209557 | − | 0.977796i | \(-0.432798\pi\) | ||||
0.209557 | + | 0.977796i | \(0.432798\pi\) | |||||||
\(272\) | −4.41421 | −0.267651 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.7574 | −0.831112 | ||||||||
\(275\) | −6.72792 | −0.405709 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.48528 | −0.269494 | −0.134747 | − | 0.990880i | \(-0.543022\pi\) | ||||
−0.134747 | + | 0.990880i | \(0.543022\pi\) | |||||||
\(278\) | −17.3137 | −1.03841 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.4853 | −1.34136 | −0.670680 | − | 0.741747i | \(-0.733997\pi\) | ||||
−0.670680 | + | 0.741747i | \(0.733997\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.6569 | −1.04959 | −0.524796 | − | 0.851228i | \(-0.675858\pi\) | ||||
−0.524796 | + | 0.851228i | \(0.675858\pi\) | |||||||
\(284\) | −5.48528 | −0.325492 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.72792 | −0.397830 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.48528 | 0.146193 | ||||||||
\(290\) | 7.41421 | 0.435378 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.89949 | −0.579324 | ||||||||
\(293\) | 27.1716 | 1.58738 | 0.793690 | − | 0.608322i | \(-0.208157\pi\) | ||||
0.793690 | + | 0.608322i | \(0.208157\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.242641 | 0.0141271 | ||||||||
\(296\) | −10.4853 | −0.609445 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.24264 | −0.535412 | ||||||||
\(299\) | 3.00000 | 0.173494 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 14.7279 | 0.847497 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.58579 | −0.263013 | ||||||||
\(305\) | 16.4853 | 0.943944 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.3431 | 0.704461 | 0.352230 | − | 0.935913i | \(-0.385423\pi\) | ||||
0.352230 | + | 0.935913i | \(0.385423\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.75736 | −0.0998113 | ||||||||
\(311\) | 0.686292 | 0.0389160 | 0.0194580 | − | 0.999811i | \(-0.493806\pi\) | ||||
0.0194580 | + | 0.999811i | \(0.493806\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.24264 | 0.239808 | 0.119904 | − | 0.992785i | \(-0.461741\pi\) | ||||
0.119904 | + | 0.992785i | \(0.461741\pi\) | |||||||
\(314\) | 14.6569 | 0.827134 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.7279 | −0.603493 | ||||||||
\(317\) | 10.0000 | 0.561656 | 0.280828 | − | 0.959758i | \(-0.409391\pi\) | ||||
0.280828 | + | 0.959758i | \(0.409391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.7574 | −0.658286 | ||||||||
\(320\) | −1.41421 | −0.0790569 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.2426 | 1.12633 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.00000 | 0.499230 | ||||||||
\(326\) | −21.2426 | −1.17652 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.82843 | 0.156174 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.72792 | 0.0949752 | 0.0474876 | − | 0.998872i | \(-0.484879\pi\) | ||||
0.0474876 | + | 0.998872i | \(0.484879\pi\) | |||||||
\(332\) | −17.3137 | −0.950213 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.89949 | 0.213371 | ||||||||
\(335\) | −18.7279 | −1.02322 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.4853 | 1.38827 | 0.694136 | − | 0.719844i | \(-0.255787\pi\) | ||||
0.694136 | + | 0.719844i | \(0.255787\pi\) | |||||||
\(338\) | −4.00000 | −0.217571 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.24264 | 0.338555 | ||||||||
\(341\) | 2.78680 | 0.150913 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.24264 | 0.174831 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.4853 | 1.10130 | ||||||||
\(347\) | 2.48528 | 0.133417 | 0.0667084 | − | 0.997773i | \(-0.478750\pi\) | ||||
0.0667084 | + | 0.997773i | \(0.478750\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.00000 | 0.160586 | 0.0802932 | − | 0.996771i | \(-0.474414\pi\) | ||||
0.0802932 | + | 0.996771i | \(0.474414\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.24264 | 0.119533 | ||||||||
\(353\) | 12.5563 | 0.668307 | 0.334154 | − | 0.942519i | \(-0.391550\pi\) | ||||
0.334154 | + | 0.942519i | \(0.391550\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.75736 | 0.411718 | ||||||||
\(356\) | 1.92893 | 0.102233 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.2426 | 1.17556 | ||||||||
\(359\) | −21.9706 | −1.15956 | −0.579781 | − | 0.814772i | \(-0.696862\pi\) | ||||
−0.579781 | + | 0.814772i | \(0.696862\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.02944 | 0.106812 | ||||||||
\(362\) | −6.51472 | −0.342406 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0000 | 0.732793 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.5858 | 0.709172 | 0.354586 | − | 0.935023i | \(-0.384622\pi\) | ||||
0.354586 | + | 0.935023i | \(0.384622\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 14.8284 | 0.770893 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.6985 | 1.74484 | 0.872421 | − | 0.488756i | \(-0.162549\pi\) | ||||
0.872421 | + | 0.488756i | \(0.162549\pi\) | |||||||
\(374\) | −9.89949 | −0.511891 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.07107 | 0.364662 | ||||||||
\(377\) | 15.7279 | 0.810029 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.9706 | −0.974452 | −0.487226 | − | 0.873276i | \(-0.661991\pi\) | ||||
−0.487226 | + | 0.873276i | \(0.661991\pi\) | |||||||
\(380\) | 6.48528 | 0.332688 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −26.9706 | −1.37993 | ||||||||
\(383\) | −9.55635 | −0.488307 | −0.244153 | − | 0.969737i | \(-0.578510\pi\) | ||||
−0.244153 | + | 0.969737i | \(0.578510\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.00000 | 0.254493 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.8284 | −0.752799 | ||||||||
\(389\) | −38.9706 | −1.97589 | −0.987943 | − | 0.154818i | \(-0.950521\pi\) | ||||
−0.987943 | + | 0.154818i | \(0.950521\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.41421 | 0.223236 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.4853 | 0.528241 | ||||||||
\(395\) | 15.1716 | 0.763365 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.8284 | −0.744217 | −0.372109 | − | 0.928189i | \(-0.621365\pi\) | ||||
−0.372109 | + | 0.928189i | \(0.621365\pi\) | |||||||
\(398\) | −13.2426 | −0.663794 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | −0.150000 | ||||||||
\(401\) | 14.4853 | 0.723360 | 0.361680 | − | 0.932302i | \(-0.382203\pi\) | ||||
0.361680 | + | 0.932302i | \(0.382203\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.72792 | −0.185701 | ||||||||
\(404\) | 10.2426 | 0.509590 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.5147 | −1.16558 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.4853 | −0.716251 | −0.358126 | − | 0.933673i | \(-0.616584\pi\) | ||||
−0.358126 | + | 0.933673i | \(0.616584\pi\) | |||||||
\(410\) | −4.00000 | −0.197546 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.92893 | −0.0950317 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.4853 | 1.20194 | ||||||||
\(416\) | −3.00000 | −0.147087 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.2843 | −0.503020 | ||||||||
\(419\) | −26.6569 | −1.30227 | −0.651136 | − | 0.758961i | \(-0.725707\pi\) | ||||
−0.651136 | + | 0.758961i | \(0.725707\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −40.2426 | −1.96131 | −0.980653 | − | 0.195753i | \(-0.937285\pi\) | ||||
−0.980653 | + | 0.195753i | \(0.937285\pi\) | |||||||
\(422\) | 19.2426 | 0.936717 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.2426 | 0.545991 | ||||||||
\(425\) | 13.2426 | 0.642362 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.485281 | −0.0234570 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.58579 | −0.221146 | ||||||||
\(431\) | 34.9706 | 1.68447 | 0.842236 | − | 0.539108i | \(-0.181239\pi\) | ||||
0.842236 | + | 0.539108i | \(0.181239\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.4853 | 1.56114 | 0.780571 | − | 0.625067i | \(-0.214928\pi\) | ||||
0.780571 | + | 0.625067i | \(0.214928\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.485281 | 0.0232408 | ||||||||
\(437\) | 4.58579 | 0.219368 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.2132 | −0.582904 | −0.291452 | − | 0.956585i | \(-0.594138\pi\) | ||||
−0.291452 | + | 0.956585i | \(0.594138\pi\) | |||||||
\(440\) | −3.17157 | −0.151199 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.2426 | 0.629888 | ||||||||
\(443\) | −26.9706 | −1.28141 | −0.640705 | − | 0.767787i | \(-0.721358\pi\) | ||||
−0.640705 | + | 0.767787i | \(0.721358\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.72792 | −0.129316 | ||||||||
\(446\) | 16.9706 | 0.803579 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.727922 | −0.0343528 | −0.0171764 | − | 0.999852i | \(-0.505468\pi\) | ||||
−0.0171764 | + | 0.999852i | \(0.505468\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.34315 | 0.298687 | ||||||||
\(452\) | −12.7279 | −0.598671 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19.9706 | 0.937265 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.0000 | −0.701670 | −0.350835 | − | 0.936437i | \(-0.614102\pi\) | ||||
−0.350835 | + | 0.936437i | \(0.614102\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.41421 | 0.0659380 | ||||||||
\(461\) | −1.07107 | −0.0498846 | −0.0249423 | − | 0.999689i | \(-0.507940\pi\) | ||||
−0.0249423 | + | 0.999689i | \(0.507940\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.2132 | −1.07881 | −0.539405 | − | 0.842047i | \(-0.681351\pi\) | ||||
−0.539405 | + | 0.842047i | \(0.681351\pi\) | |||||||
\(464\) | −5.24264 | −0.243383 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.48528 | 0.393073 | ||||||||
\(467\) | −23.6569 | −1.09471 | −0.547354 | − | 0.836901i | \(-0.684365\pi\) | ||||
−0.547354 | + | 0.836901i | \(0.684365\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −10.0000 | −0.461266 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.171573 | −0.00789728 | ||||||||
\(473\) | 7.27208 | 0.334370 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.7574 | 0.631231 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 22.9706 | 1.05065 | ||||||||
\(479\) | 18.0416 | 0.824343 | 0.412172 | − | 0.911106i | \(-0.364770\pi\) | ||||
0.412172 | + | 0.911106i | \(0.364770\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.4558 | 1.43426 | ||||||||
\(482\) | 0.727922 | 0.0331559 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.97056 | −0.271389 | ||||||||
\(485\) | 20.9706 | 0.952224 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.2426 | −1.00791 | −0.503955 | − | 0.863730i | \(-0.668122\pi\) | ||||
−0.503955 | + | 0.863730i | \(0.668122\pi\) | |||||||
\(488\) | −11.6569 | −0.527681 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.2426 | −0.462244 | −0.231122 | − | 0.972925i | \(-0.574240\pi\) | ||||
−0.231122 | + | 0.972925i | \(0.574240\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.1421 | 1.04227 | ||||||||
\(494\) | 13.7574 | 0.618973 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.24264 | 0.0557962 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.9706 | 1.11784 | 0.558918 | − | 0.829223i | \(-0.311217\pi\) | ||||
0.558918 | + | 0.829223i | \(0.311217\pi\) | |||||||
\(500\) | 11.3137 | 0.505964 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.6274 | 1.27770 | ||||||||
\(503\) | −8.10051 | −0.361184 | −0.180592 | − | 0.983558i | \(-0.557801\pi\) | ||||
−0.180592 | + | 0.983558i | \(0.557801\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.4853 | −0.644587 | ||||||||
\(506\) | −2.24264 | −0.0996975 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.72792 | 0.209768 | ||||||||
\(509\) | 8.14214 | 0.360894 | 0.180447 | − | 0.983585i | \(-0.442246\pi\) | ||||
0.180447 | + | 0.983585i | \(0.442246\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.9706 | 1.01319 | ||||||||
\(515\) | 2.72792 | 0.120207 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.8579 | 0.697428 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.24264 | 0.186052 | ||||||||
\(521\) | −10.4142 | −0.456255 | −0.228127 | − | 0.973631i | \(-0.573260\pi\) | ||||
−0.228127 | + | 0.973631i | \(0.573260\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.2721 | 0.492894 | 0.246447 | − | 0.969156i | \(-0.420737\pi\) | ||||
0.246447 | + | 0.969156i | \(0.420737\pi\) | |||||||
\(524\) | 0.514719 | 0.0224856 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.51472 | −0.284055 | ||||||||
\(527\) | −5.48528 | −0.238943 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | −15.8995 | −0.690630 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.48528 | −0.367538 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.686292 | 0.0296710 | ||||||||
\(536\) | 13.2426 | 0.571995 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.55635 | −0.153325 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.7279 | 0.461229 | 0.230615 | − | 0.973045i | \(-0.425926\pi\) | ||||
0.230615 | + | 0.973045i | \(0.425926\pi\) | |||||||
\(542\) | 6.89949 | 0.296359 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.41421 | −0.189258 | ||||||||
\(545\) | −0.686292 | −0.0293975 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.48528 | −0.191777 | −0.0958884 | − | 0.995392i | \(-0.530569\pi\) | ||||
−0.0958884 | + | 0.995392i | \(0.530569\pi\) | |||||||
\(548\) | −13.7574 | −0.587685 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.72792 | −0.286880 | ||||||||
\(551\) | 24.0416 | 1.02421 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.48528 | −0.190561 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.3137 | −0.734265 | ||||||||
\(557\) | −14.6985 | −0.622795 | −0.311397 | − | 0.950280i | \(-0.600797\pi\) | ||||
−0.311397 | + | 0.950280i | \(0.600797\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.72792 | −0.411447 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −22.4853 | −0.948484 | ||||||||
\(563\) | −41.1421 | −1.73393 | −0.866967 | − | 0.498365i | \(-0.833934\pi\) | ||||
−0.866967 | + | 0.498365i | \(0.833934\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.0000 | 0.757266 | ||||||||
\(566\) | −17.6569 | −0.742173 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.48528 | −0.230157 | ||||||||
\(569\) | 1.21320 | 0.0508601 | 0.0254301 | − | 0.999677i | \(-0.491904\pi\) | ||||
0.0254301 | + | 0.999677i | \(0.491904\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.24264 | −0.135700 | −0.0678501 | − | 0.997696i | \(-0.521614\pi\) | ||||
−0.0678501 | + | 0.997696i | \(0.521614\pi\) | |||||||
\(572\) | −6.72792 | −0.281309 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.00000 | 0.125109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.48528 | 0.103464 | 0.0517318 | − | 0.998661i | \(-0.483526\pi\) | ||||
0.0517318 | + | 0.998661i | \(0.483526\pi\) | |||||||
\(578\) | 2.48528 | 0.103374 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.41421 | 0.307858 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.2132 | 1.04422 | ||||||||
\(584\) | −9.89949 | −0.409644 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.1716 | 1.12245 | ||||||||
\(587\) | −40.4558 | −1.66979 | −0.834896 | − | 0.550408i | \(-0.814472\pi\) | ||||
−0.834896 | + | 0.550408i | \(0.814472\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.69848 | −0.234802 | ||||||||
\(590\) | 0.242641 | 0.00998936 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.4853 | −0.430942 | ||||||||
\(593\) | 20.1421 | 0.827138 | 0.413569 | − | 0.910473i | \(-0.364282\pi\) | ||||
0.413569 | + | 0.910473i | \(0.364282\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.24264 | −0.378593 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.00000 | 0.122679 | ||||||||
\(599\) | −7.00000 | −0.286012 | −0.143006 | − | 0.989722i | \(-0.545677\pi\) | ||||
−0.143006 | + | 0.989722i | \(0.545677\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.2426 | 1.39679 | 0.698393 | − | 0.715714i | \(-0.253899\pi\) | ||||
0.698393 | + | 0.715714i | \(0.253899\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.7279 | 0.599271 | ||||||||
\(605\) | 8.44365 | 0.343283 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.6985 | 1.32719 | 0.663595 | − | 0.748092i | \(-0.269030\pi\) | ||||
0.663595 | + | 0.748092i | \(0.269030\pi\) | |||||||
\(608\) | −4.58579 | −0.185978 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.4853 | 0.667470 | ||||||||
\(611\) | −21.2132 | −0.858194 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.2426 | 1.14071 | 0.570355 | − | 0.821398i | \(-0.306806\pi\) | ||||
0.570355 | + | 0.821398i | \(0.306806\pi\) | |||||||
\(614\) | 12.3431 | 0.498129 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.9411 | −1.44694 | −0.723468 | − | 0.690358i | \(-0.757453\pi\) | ||||
−0.723468 | + | 0.690358i | \(0.757453\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.82843 | −0.354844 | −0.177422 | − | 0.984135i | \(-0.556776\pi\) | ||||
−0.177422 | + | 0.984135i | \(0.556776\pi\) | |||||||
\(620\) | −1.75736 | −0.0705772 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.686292 | 0.0275178 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 4.24264 | 0.169570 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.6569 | 0.584872 | ||||||||
\(629\) | 46.2843 | 1.84547 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.75736 | 0.149578 | 0.0747891 | − | 0.997199i | \(-0.476172\pi\) | ||||
0.0747891 | + | 0.997199i | \(0.476172\pi\) | |||||||
\(632\) | −10.7279 | −0.426734 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.0000 | 0.397151 | ||||||||
\(635\) | −6.68629 | −0.265337 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.7574 | −0.465478 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.41421 | −0.0559017 | ||||||||
\(641\) | 9.45584 | 0.373483 | 0.186742 | − | 0.982409i | \(-0.440207\pi\) | ||||
0.186742 | + | 0.982409i | \(0.440207\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.9289 | 0.667612 | 0.333806 | − | 0.942642i | \(-0.391667\pi\) | ||||
0.333806 | + | 0.942642i | \(0.391667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.2426 | 0.796436 | ||||||||
\(647\) | −42.0000 | −1.65119 | −0.825595 | − | 0.564263i | \(-0.809160\pi\) | ||||
−0.825595 | + | 0.564263i | \(0.809160\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.384776 | −0.0151038 | ||||||||
\(650\) | 9.00000 | 0.353009 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −21.2426 | −0.831926 | ||||||||
\(653\) | 32.6985 | 1.27959 | 0.639795 | − | 0.768545i | \(-0.279019\pi\) | ||||
0.639795 | + | 0.768545i | \(0.279019\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.727922 | −0.0284423 | ||||||||
\(656\) | 2.82843 | 0.110432 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.9411 | −0.853411 | −0.426705 | − | 0.904391i | \(-0.640326\pi\) | ||||
−0.426705 | + | 0.904391i | \(0.640326\pi\) | |||||||
\(662\) | 1.72792 | 0.0671576 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17.3137 | −0.671902 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.24264 | 0.202996 | ||||||||
\(668\) | 3.89949 | 0.150876 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18.7279 | −0.723523 | ||||||||
\(671\) | −26.1421 | −1.00921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.4558 | −1.09689 | −0.548446 | − | 0.836186i | \(-0.684780\pi\) | ||||
−0.548446 | + | 0.836186i | \(0.684780\pi\) | |||||||
\(674\) | 25.4853 | 0.981656 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.00000 | −0.153846 | ||||||||
\(677\) | −29.6985 | −1.14141 | −0.570703 | − | 0.821157i | \(-0.693329\pi\) | ||||
−0.570703 | + | 0.821157i | \(0.693329\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.24264 | 0.239394 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.78680 | 0.106712 | ||||||||
\(683\) | −13.7574 | −0.526411 | −0.263205 | − | 0.964740i | \(-0.584780\pi\) | ||||
−0.263205 | + | 0.964740i | \(0.584780\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.4558 | 0.743370 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.24264 | 0.123625 | ||||||||
\(689\) | −33.7279 | −1.28493 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.2132 | −1.26349 | −0.631745 | − | 0.775176i | \(-0.717661\pi\) | ||||
−0.631745 | + | 0.775176i | \(0.717661\pi\) | |||||||
\(692\) | 20.4853 | 0.778734 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.48528 | 0.0943400 | ||||||||
\(695\) | 24.4853 | 0.928780 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.4853 | −0.472914 | ||||||||
\(698\) | 3.00000 | 0.113552 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.02944 | 0.0388813 | 0.0194407 | − | 0.999811i | \(-0.493811\pi\) | ||||
0.0194407 | + | 0.999811i | \(0.493811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48.0833 | 1.81349 | ||||||||
\(704\) | 2.24264 | 0.0845227 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.5563 | 0.472564 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.2132 | 0.721567 | 0.360784 | − | 0.932650i | \(-0.382509\pi\) | ||||
0.360784 | + | 0.932650i | \(0.382509\pi\) | |||||||
\(710\) | 7.75736 | 0.291129 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.92893 | 0.0722898 | ||||||||
\(713\) | −1.24264 | −0.0465373 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.51472 | 0.355830 | ||||||||
\(716\) | 22.2426 | 0.831247 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −21.9706 | −0.819934 | ||||||||
\(719\) | −34.6274 | −1.29138 | −0.645692 | − | 0.763598i | \(-0.723431\pi\) | ||||
−0.645692 | + | 0.763598i | \(0.723431\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.02944 | 0.0755278 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.51472 | −0.242118 | ||||||||
\(725\) | 15.7279 | 0.584120 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.8406 | 1.73722 | 0.868611 | − | 0.495494i | \(-0.165013\pi\) | ||||
0.868611 | + | 0.495494i | \(0.165013\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.0000 | 0.518163 | ||||||||
\(731\) | −14.3137 | −0.529412 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.9411 | 1.36445 | 0.682226 | − | 0.731142i | \(-0.261012\pi\) | ||||
0.682226 | + | 0.731142i | \(0.261012\pi\) | |||||||
\(734\) | 13.5858 | 0.501461 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 29.6985 | 1.09396 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.9706 | 0.844986 | 0.422493 | − | 0.906366i | \(-0.361155\pi\) | ||||
0.422493 | + | 0.906366i | \(0.361155\pi\) | |||||||
\(740\) | 14.8284 | 0.545104 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.4853 | 0.788219 | 0.394109 | − | 0.919064i | \(-0.371053\pi\) | ||||
0.394109 | + | 0.919064i | \(0.371053\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.0711 | 0.478887 | ||||||||
\(746\) | 33.6985 | 1.23379 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.89949 | −0.361961 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.0000 | −0.802791 | −0.401396 | − | 0.915905i | \(-0.631475\pi\) | ||||
−0.401396 | + | 0.915905i | \(0.631475\pi\) | |||||||
\(752\) | 7.07107 | 0.257855 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 15.7279 | 0.572777 | ||||||||
\(755\) | −20.8284 | −0.758024 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.6985 | 1.15210 | 0.576051 | − | 0.817414i | \(-0.304593\pi\) | ||||
0.576051 | + | 0.817414i | \(0.304593\pi\) | |||||||
\(758\) | −18.9706 | −0.689042 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.48528 | 0.235246 | ||||||||
\(761\) | −11.5269 | −0.417850 | −0.208925 | − | 0.977932i | \(-0.566996\pi\) | ||||
−0.208925 | + | 0.977932i | \(0.566996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −26.9706 | −0.975761 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.55635 | −0.345285 | ||||||||
\(767\) | 0.514719 | 0.0185854 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.2132 | 0.981333 | 0.490667 | − | 0.871347i | \(-0.336753\pi\) | ||||
0.490667 | + | 0.871347i | \(0.336753\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.00000 | 0.179954 | ||||||||
\(773\) | 18.3848 | 0.661254 | 0.330627 | − | 0.943761i | \(-0.392740\pi\) | ||||
0.330627 | + | 0.943761i | \(0.392740\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.72792 | −0.133911 | ||||||||
\(776\) | −14.8284 | −0.532310 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −38.9706 | −1.39716 | ||||||||
\(779\) | −12.9706 | −0.464719 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.3015 | −0.440183 | ||||||||
\(782\) | 4.41421 | 0.157852 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.7279 | −0.739811 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.8284 | 1.17021 | 0.585104 | − | 0.810959i | \(-0.301054\pi\) | ||||
0.585104 | + | 0.810959i | \(0.301054\pi\) | |||||||
\(788\) | 10.4853 | 0.373523 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15.1716 | 0.539780 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.9706 | 1.24184 | ||||||||
\(794\) | −14.8284 | −0.526241 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.2426 | −0.469373 | ||||||||
\(797\) | 33.5147 | 1.18715 | 0.593576 | − | 0.804778i | \(-0.297716\pi\) | ||||
0.593576 | + | 0.804778i | \(0.297716\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.2132 | −1.10424 | ||||||||
\(800\) | −3.00000 | −0.106066 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.4853 | 0.511493 | ||||||||
\(803\) | −22.2010 | −0.783457 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.72792 | −0.131310 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.2426 | 0.360335 | ||||||||
\(809\) | −4.00000 | −0.140633 | −0.0703163 | − | 0.997525i | \(-0.522401\pi\) | ||||
−0.0703163 | + | 0.997525i | \(0.522401\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.9411 | −1.82390 | −0.911950 | − | 0.410302i | \(-0.865423\pi\) | ||||
−0.911950 | + | 0.410302i | \(0.865423\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −23.5147 | −0.824190 | ||||||||
\(815\) | 30.0416 | 1.05231 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.8701 | −0.520237 | ||||||||
\(818\) | −14.4853 | −0.506466 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.00000 | −0.139686 | ||||||||
\(821\) | 18.2132 | 0.635645 | 0.317823 | − | 0.948150i | \(-0.397048\pi\) | ||||
0.317823 | + | 0.948150i | \(0.397048\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.97056 | −0.242979 | −0.121489 | − | 0.992593i | \(-0.538767\pi\) | ||||
−0.121489 | + | 0.992593i | \(0.538767\pi\) | |||||||
\(824\) | −1.92893 | −0.0671975 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.6985 | 1.03272 | 0.516359 | − | 0.856372i | \(-0.327287\pi\) | ||||
0.516359 | + | 0.856372i | \(0.327287\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.1716 | −0.735319 | −0.367660 | − | 0.929960i | \(-0.619841\pi\) | ||||
−0.367660 | + | 0.929960i | \(0.619841\pi\) | |||||||
\(830\) | 24.4853 | 0.849897 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.00000 | −0.104006 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.51472 | −0.190845 | ||||||||
\(836\) | −10.2843 | −0.355689 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −26.6569 | −0.920846 | ||||||||
\(839\) | 1.79899 | 0.0621080 | 0.0310540 | − | 0.999518i | \(-0.490114\pi\) | ||||
0.0310540 | + | 0.999518i | \(0.490114\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.51472 | −0.0522317 | ||||||||
\(842\) | −40.2426 | −1.38685 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 19.2426 | 0.662359 | ||||||||
\(845\) | 5.65685 | 0.194602 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11.2426 | 0.386074 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.2426 | 0.454219 | ||||||||
\(851\) | 10.4853 | 0.359431 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.4264 | −1.55537 | −0.777685 | − | 0.628654i | \(-0.783606\pi\) | ||||
−0.777685 | + | 0.628654i | \(0.783606\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.485281 | −0.0165866 | ||||||||
\(857\) | −43.5858 | −1.48886 | −0.744431 | − | 0.667699i | \(-0.767279\pi\) | ||||
−0.744431 | + | 0.667699i | \(0.767279\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.7696 | 1.45928 | 0.729639 | − | 0.683832i | \(-0.239688\pi\) | ||||
0.729639 | + | 0.683832i | \(0.239688\pi\) | |||||||
\(860\) | −4.58579 | −0.156374 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 34.9706 | 1.19110 | ||||||||
\(863\) | 2.51472 | 0.0856020 | 0.0428010 | − | 0.999084i | \(-0.486372\pi\) | ||||
0.0428010 | + | 0.999084i | \(0.486372\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.9706 | −0.985029 | ||||||||
\(866\) | 32.4853 | 1.10389 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.0589 | −0.816141 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.7279 | −1.34613 | ||||||||
\(872\) | 0.485281 | 0.0164337 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.58579 | 0.155117 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.48528 | 0.151457 | 0.0757286 | − | 0.997128i | \(-0.475872\pi\) | ||||
0.0757286 | + | 0.997128i | \(0.475872\pi\) | |||||||
\(878\) | −12.2132 | −0.412176 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.17157 | −0.106914 | ||||||||
\(881\) | 8.27208 | 0.278693 | 0.139347 | − | 0.990244i | \(-0.455500\pi\) | ||||
0.139347 | + | 0.990244i | \(0.455500\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.7279 | −1.26965 | −0.634823 | − | 0.772658i | \(-0.718927\pi\) | ||||
−0.634823 | + | 0.772658i | \(0.718927\pi\) | |||||||
\(884\) | 13.2426 | 0.445398 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.9706 | −0.906094 | ||||||||
\(887\) | −38.8284 | −1.30373 | −0.651865 | − | 0.758335i | \(-0.726013\pi\) | ||||
−0.651865 | + | 0.758335i | \(0.726013\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.72792 | −0.0914402 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.9706 | 0.568216 | ||||||||
\(893\) | −32.4264 | −1.08511 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.4558 | −1.05145 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.727922 | −0.0242911 | ||||||||
\(899\) | −6.51472 | −0.217278 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49.6274 | −1.65333 | ||||||||
\(902\) | 6.34315 | 0.211204 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.7279 | −0.423324 | ||||||||
\(905\) | 9.21320 | 0.306257 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.9411 | −0.794952 | −0.397476 | − | 0.917613i | \(-0.630114\pi\) | ||||
−0.397476 | + | 0.917613i | \(0.630114\pi\) | |||||||
\(908\) | 19.9706 | 0.662746 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.4853 | 1.14255 | 0.571274 | − | 0.820759i | \(-0.306449\pi\) | ||||
0.571274 | + | 0.820759i | \(0.306449\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −38.8284 | −1.28503 | ||||||||
\(914\) | −15.0000 | −0.496156 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.2426 | 0.469821 | 0.234911 | − | 0.972017i | \(-0.424520\pi\) | ||||
0.234911 | + | 0.972017i | \(0.424520\pi\) | |||||||
\(920\) | 1.41421 | 0.0466252 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.07107 | −0.0352737 | ||||||||
\(923\) | 16.4558 | 0.541651 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 31.4558 | 1.03426 | ||||||||
\(926\) | −23.2132 | −0.762833 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.24264 | −0.172098 | ||||||||
\(929\) | −18.6863 | −0.613077 | −0.306539 | − | 0.951858i | \(-0.599171\pi\) | ||||
−0.306539 | + | 0.951858i | \(0.599171\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.48528 | 0.277945 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −23.6569 | −0.774076 | ||||||||
\(935\) | 14.0000 | 0.457849 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.9289 | 0.749056 | 0.374528 | − | 0.927216i | \(-0.377805\pi\) | ||||
0.374528 | + | 0.927216i | \(0.377805\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.0000 | −0.326164 | ||||||||
\(941\) | 34.2843 | 1.11764 | 0.558818 | − | 0.829291i | \(-0.311255\pi\) | ||||
0.558818 | + | 0.829291i | \(0.311255\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.82843 | −0.0921063 | ||||||||
\(944\) | −0.171573 | −0.00558422 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.27208 | 0.236436 | ||||||||
\(947\) | −11.2721 | −0.366293 | −0.183147 | − | 0.983086i | \(-0.558628\pi\) | ||||
−0.183147 | + | 0.983086i | \(0.558628\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.6985 | 0.964054 | ||||||||
\(950\) | 13.7574 | 0.446348 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −49.6985 | −1.60989 | −0.804946 | − | 0.593348i | \(-0.797806\pi\) | ||||
−0.804946 | + | 0.593348i | \(0.797806\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38.1421 | 1.23425 | ||||||||
\(956\) | 22.9706 | 0.742921 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.0416 | 0.582899 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4558 | −0.950189 | ||||||||
\(962\) | 31.4558 | 1.01418 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.727922 | 0.0234448 | ||||||||
\(965\) | −7.07107 | −0.227626 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55.1543 | 1.77364 | 0.886822 | − | 0.462112i | \(-0.152908\pi\) | ||||
0.886822 | + | 0.462112i | \(0.152908\pi\) | |||||||
\(968\) | −5.97056 | −0.191901 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 20.9706 | 0.673324 | ||||||||
\(971\) | 45.7696 | 1.46881 | 0.734407 | − | 0.678709i | \(-0.237460\pi\) | ||||
0.734407 | + | 0.678709i | \(0.237460\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.2426 | −0.712700 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.6569 | −0.373127 | ||||||||
\(977\) | −40.6690 | −1.30112 | −0.650559 | − | 0.759456i | \(-0.725465\pi\) | ||||
−0.650559 | + | 0.759456i | \(0.725465\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.32590 | 0.138256 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.2426 | −0.326856 | ||||||||
\(983\) | −21.5563 | −0.687541 | −0.343770 | − | 0.939054i | \(-0.611704\pi\) | ||||
−0.343770 | + | 0.939054i | \(0.611704\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.8284 | −0.472473 | ||||||||
\(986\) | 23.1421 | 0.736996 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.7574 | 0.437680 | ||||||||
\(989\) | −3.24264 | −0.103110 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.4558 | −0.363907 | −0.181953 | − | 0.983307i | \(-0.558242\pi\) | ||||
−0.181953 | + | 0.983307i | \(0.558242\pi\) | |||||||
\(992\) | 1.24264 | 0.0394539 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.7279 | 0.593715 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.8579 | 0.597235 | 0.298617 | − | 0.954373i | \(-0.403475\pi\) | ||||
0.298617 | + | 0.954373i | \(0.403475\pi\) | |||||||
\(998\) | 24.9706 | 0.790429 | ||||||||
\(999\) | 0 | 0 |
(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 | 2646.2.a.bm.1.1 | yes | 2 | |
3.2 | odd | 2 | 2646.2.a.bg.1.2 | ✓ | 2 | ||
7.6 | odd | 2 | 2646.2.a.bn.1.2 | yes | 2 | ||
21.20 | even | 2 | 2646.2.a.bh.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2646.2.a.bg.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
2646.2.a.bh.1.1 | yes | 2 | 21.20 | even | 2 | ||
2646.2.a.bm.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
2646.2.a.bn.1.2 | yes | 2 | 7.6 | odd | 2 |