Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(1,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, 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("3234.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.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: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2700.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 15x - 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 462) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.61323\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.61323 | 0.721458 | 0.360729 | − | 0.932671i | \(-0.382528\pi\) | ||||
0.360729 | + | 0.932671i | \(0.382528\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.61323 | 0.510148 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.61323 | 0.416534 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.34206 | 1.78071 | 0.890356 | − | 0.455266i | \(-0.150456\pi\) | ||||
0.890356 | + | 0.455266i | \(0.150456\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.17103 | −0.268653 | −0.134326 | − | 0.990937i | \(-0.542887\pi\) | ||||
−0.134326 | + | 0.990937i | \(0.542887\pi\) | |||||||
\(20\) | 1.61323 | 0.360729 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 3.55780 | 0.741853 | 0.370926 | − | 0.928662i | \(-0.379040\pi\) | ||||
0.370926 | + | 0.928662i | \(0.379040\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −2.39749 | −0.479498 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.3975 | 1.93077 | 0.965383 | − | 0.260838i | \(-0.0839988\pi\) | ||||
0.965383 | + | 0.260838i | \(0.0839988\pi\) | |||||||
\(30\) | 1.61323 | 0.294534 | ||||||||
\(31\) | −6.34206 | −1.13907 | −0.569534 | − | 0.821968i | \(-0.692876\pi\) | ||||
−0.569534 | + | 0.821968i | \(0.692876\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 7.34206 | 1.25915 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.82897 | 0.465080 | 0.232540 | − | 0.972587i | \(-0.425296\pi\) | ||||
0.232540 | + | 0.972587i | \(0.425296\pi\) | |||||||
\(38\) | −1.17103 | −0.189966 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.61323 | 0.255074 | ||||||||
\(41\) | −4.94457 | −0.772212 | −0.386106 | − | 0.922454i | \(-0.626180\pi\) | ||||
−0.386106 | + | 0.922454i | \(0.626180\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.5131 | −1.75573 | −0.877865 | − | 0.478908i | \(-0.841033\pi\) | ||||
−0.877865 | + | 0.478908i | \(0.841033\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 1.61323 | 0.240486 | ||||||||
\(46\) | 3.55780 | 0.524569 | ||||||||
\(47\) | −6.78426 | −0.989586 | −0.494793 | − | 0.869011i | \(-0.664756\pi\) | ||||
−0.494793 | + | 0.869011i | \(0.664756\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.39749 | −0.339056 | ||||||||
\(51\) | 7.34206 | 1.02809 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.00000 | 1.09888 | 0.549442 | − | 0.835532i | \(-0.314840\pi\) | ||||
0.549442 | + | 0.835532i | \(0.314840\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −1.61323 | −0.217528 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.17103 | −0.155107 | ||||||||
\(58\) | 10.3975 | 1.36526 | ||||||||
\(59\) | −4.39749 | −0.572504 | −0.286252 | − | 0.958154i | \(-0.592410\pi\) | ||||
−0.286252 | + | 0.958154i | \(0.592410\pi\) | |||||||
\(60\) | 1.61323 | 0.208267 | ||||||||
\(61\) | 11.9553 | 1.53072 | 0.765359 | − | 0.643604i | \(-0.222561\pi\) | ||||
0.765359 | + | 0.643604i | \(0.222561\pi\) | |||||||
\(62\) | −6.34206 | −0.805442 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | 2.94457 | 0.359736 | 0.179868 | − | 0.983691i | \(-0.442433\pi\) | ||||
0.179868 | + | 0.983691i | \(0.442433\pi\) | |||||||
\(68\) | 7.34206 | 0.890356 | ||||||||
\(69\) | 3.55780 | 0.428309 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.5131 | 1.84106 | 0.920532 | − | 0.390666i | \(-0.127755\pi\) | ||||
0.920532 | + | 0.390666i | \(0.127755\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 5.11560 | 0.598736 | 0.299368 | − | 0.954138i | \(-0.403224\pi\) | ||||
0.299368 | + | 0.954138i | \(0.403224\pi\) | |||||||
\(74\) | 2.82897 | 0.328861 | ||||||||
\(75\) | −2.39749 | −0.276838 | ||||||||
\(76\) | −1.17103 | −0.134326 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.61323 | 0.631538 | 0.315769 | − | 0.948836i | \(-0.397738\pi\) | ||||
0.315769 | + | 0.948836i | \(0.397738\pi\) | |||||||
\(80\) | 1.61323 | 0.180365 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.94457 | −0.546036 | ||||||||
\(83\) | −5.05543 | −0.554906 | −0.277453 | − | 0.960739i | \(-0.589490\pi\) | ||||
−0.277453 | + | 0.960739i | \(0.589490\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.8444 | 1.28471 | ||||||||
\(86\) | −11.5131 | −1.24149 | ||||||||
\(87\) | 10.3975 | 1.11473 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 0.773540 | 0.0819951 | 0.0409976 | − | 0.999159i | \(-0.486946\pi\) | ||||
0.0409976 | + | 0.999159i | \(0.486946\pi\) | |||||||
\(90\) | 1.61323 | 0.170049 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.55780 | 0.370926 | ||||||||
\(93\) | −6.34206 | −0.657641 | ||||||||
\(94\) | −6.78426 | −0.699743 | ||||||||
\(95\) | −1.88914 | −0.193822 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −7.00000 | −0.710742 | −0.355371 | − | 0.934725i | \(-0.615646\pi\) | ||||
−0.355371 | + | 0.934725i | \(0.615646\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −2.39749 | −0.239749 | ||||||||
\(101\) | −13.6239 | −1.35563 | −0.677817 | − | 0.735231i | \(-0.737074\pi\) | ||||
−0.677817 | + | 0.735231i | \(0.737074\pi\) | |||||||
\(102\) | 7.34206 | 0.726972 | ||||||||
\(103\) | 12.3421 | 1.21610 | 0.608050 | − | 0.793899i | \(-0.291952\pi\) | ||||
0.608050 | + | 0.793899i | \(0.291952\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.00000 | 0.777029 | ||||||||
\(107\) | −15.7395 | −1.52160 | −0.760800 | − | 0.648987i | \(-0.775193\pi\) | ||||
−0.760800 | + | 0.648987i | \(0.775193\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 3.95529 | 0.378848 | 0.189424 | − | 0.981895i | \(-0.439338\pi\) | ||||
0.189424 | + | 0.981895i | \(0.439338\pi\) | |||||||
\(110\) | −1.61323 | −0.153815 | ||||||||
\(111\) | 2.82897 | 0.268514 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.34206 | −0.408467 | −0.204233 | − | 0.978922i | \(-0.565470\pi\) | ||||
−0.204233 | + | 0.978922i | \(0.565470\pi\) | |||||||
\(114\) | −1.17103 | −0.109677 | ||||||||
\(115\) | 5.73955 | 0.535216 | ||||||||
\(116\) | 10.3975 | 0.965383 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.39749 | −0.404822 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.61323 | 0.147267 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 11.9553 | 1.08238 | ||||||||
\(123\) | −4.94457 | −0.445837 | ||||||||
\(124\) | −6.34206 | −0.569534 | ||||||||
\(125\) | −11.9339 | −1.06740 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.442200 | −0.0392389 | −0.0196195 | − | 0.999808i | \(-0.506245\pi\) | ||||
−0.0196195 | + | 0.999808i | \(0.506245\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −11.5131 | −1.01367 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.34206 | 0.204627 | 0.102313 | − | 0.994752i | \(-0.467376\pi\) | ||||
0.102313 | + | 0.994752i | \(0.467376\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.94457 | 0.254372 | ||||||||
\(135\) | 1.61323 | 0.138845 | ||||||||
\(136\) | 7.34206 | 0.629576 | ||||||||
\(137\) | 3.22646 | 0.275655 | 0.137828 | − | 0.990456i | \(-0.455988\pi\) | ||||
0.137828 | + | 0.990456i | \(0.455988\pi\) | |||||||
\(138\) | 3.55780 | 0.302860 | ||||||||
\(139\) | −18.3975 | −1.56045 | −0.780227 | − | 0.625496i | \(-0.784897\pi\) | ||||
−0.780227 | + | 0.625496i | \(0.784897\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.78426 | −0.571338 | ||||||||
\(142\) | 15.5131 | 1.30183 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 16.7735 | 1.39297 | ||||||||
\(146\) | 5.11560 | 0.423370 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.82897 | 0.232540 | ||||||||
\(149\) | 19.6239 | 1.60766 | 0.803828 | − | 0.594861i | \(-0.202793\pi\) | ||||
0.803828 | + | 0.594861i | \(0.202793\pi\) | |||||||
\(150\) | −2.39749 | −0.195754 | ||||||||
\(151\) | −0.331340 | −0.0269641 | −0.0134820 | − | 0.999909i | \(-0.504292\pi\) | ||||
−0.0134820 | + | 0.999909i | \(0.504292\pi\) | |||||||
\(152\) | −1.17103 | −0.0949831 | ||||||||
\(153\) | 7.34206 | 0.593570 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.2312 | −0.821790 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.9660 | −1.59346 | −0.796730 | − | 0.604335i | \(-0.793439\pi\) | ||||
−0.796730 | + | 0.604335i | \(0.793439\pi\) | |||||||
\(158\) | 5.61323 | 0.446565 | ||||||||
\(159\) | 8.00000 | 0.634441 | ||||||||
\(160\) | 1.61323 | 0.127537 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 21.2866 | 1.66730 | 0.833649 | − | 0.552295i | \(-0.186248\pi\) | ||||
0.833649 | + | 0.552295i | \(0.186248\pi\) | |||||||
\(164\) | −4.94457 | −0.386106 | ||||||||
\(165\) | −1.61323 | −0.125590 | ||||||||
\(166\) | −5.05543 | −0.392377 | ||||||||
\(167\) | −22.0214 | −1.70407 | −0.852035 | − | 0.523485i | \(-0.824632\pi\) | ||||
−0.852035 | + | 0.523485i | \(0.824632\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 11.8444 | 0.908426 | ||||||||
\(171\) | −1.17103 | −0.0895509 | ||||||||
\(172\) | −11.5131 | −0.877865 | ||||||||
\(173\) | −1.65794 | −0.126051 | −0.0630254 | − | 0.998012i | \(-0.520075\pi\) | ||||
−0.0630254 | + | 0.998012i | \(0.520075\pi\) | |||||||
\(174\) | 10.3975 | 0.788232 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −4.39749 | −0.330536 | ||||||||
\(178\) | 0.773540 | 0.0579793 | ||||||||
\(179\) | 15.0602 | 1.12565 | 0.562825 | − | 0.826576i | \(-0.309715\pi\) | ||||
0.562825 | + | 0.826576i | \(0.309715\pi\) | |||||||
\(180\) | 1.61323 | 0.120243 | ||||||||
\(181\) | −15.1156 | −1.12353 | −0.561767 | − | 0.827296i | \(-0.689878\pi\) | ||||
−0.561767 | + | 0.827296i | \(0.689878\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.9553 | 0.883760 | ||||||||
\(184\) | 3.55780 | 0.262284 | ||||||||
\(185\) | 4.56378 | 0.335536 | ||||||||
\(186\) | −6.34206 | −0.465022 | ||||||||
\(187\) | −7.34206 | −0.536905 | ||||||||
\(188\) | −6.78426 | −0.494793 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.88914 | −0.137053 | ||||||||
\(191\) | −4.77354 | −0.345401 | −0.172701 | − | 0.984974i | \(-0.555249\pi\) | ||||
−0.172701 | + | 0.984974i | \(0.555249\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 3.11560 | 0.224266 | 0.112133 | − | 0.993693i | \(-0.464232\pi\) | ||||
0.112133 | + | 0.993693i | \(0.464232\pi\) | |||||||
\(194\) | −7.00000 | −0.502571 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.82897 | −0.344050 | −0.172025 | − | 0.985093i | \(-0.555031\pi\) | ||||
−0.172025 | + | 0.985093i | \(0.555031\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | −5.88914 | −0.417470 | −0.208735 | − | 0.977972i | \(-0.566935\pi\) | ||||
−0.208735 | + | 0.977972i | \(0.566935\pi\) | |||||||
\(200\) | −2.39749 | −0.169528 | ||||||||
\(201\) | 2.94457 | 0.207694 | ||||||||
\(202\) | −13.6239 | −0.958578 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.34206 | 0.514047 | ||||||||
\(205\) | −7.97673 | −0.557119 | ||||||||
\(206\) | 12.3421 | 0.859912 | ||||||||
\(207\) | 3.55780 | 0.247284 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.17103 | 0.0810018 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.6794 | −0.941727 | −0.470864 | − | 0.882206i | \(-0.656058\pi\) | ||||
−0.470864 | + | 0.882206i | \(0.656058\pi\) | |||||||
\(212\) | 8.00000 | 0.549442 | ||||||||
\(213\) | 15.5131 | 1.06294 | ||||||||
\(214\) | −15.7395 | −1.07593 | ||||||||
\(215\) | −18.5733 | −1.26669 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.95529 | 0.267886 | ||||||||
\(219\) | 5.11560 | 0.345680 | ||||||||
\(220\) | −1.61323 | −0.108764 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.82897 | 0.189868 | ||||||||
\(223\) | 5.11560 | 0.342566 | 0.171283 | − | 0.985222i | \(-0.445209\pi\) | ||||
0.171283 | + | 0.985222i | \(0.445209\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.39749 | −0.159833 | ||||||||
\(226\) | −4.34206 | −0.288830 | ||||||||
\(227\) | 5.28663 | 0.350886 | 0.175443 | − | 0.984490i | \(-0.443864\pi\) | ||||
0.175443 | + | 0.984490i | \(0.443864\pi\) | |||||||
\(228\) | −1.17103 | −0.0775533 | ||||||||
\(229\) | 4.88440 | 0.322770 | 0.161385 | − | 0.986892i | \(-0.448404\pi\) | ||||
0.161385 | + | 0.986892i | \(0.448404\pi\) | |||||||
\(230\) | 5.73955 | 0.378455 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.3975 | 0.682629 | ||||||||
\(233\) | 9.79498 | 0.641690 | 0.320845 | − | 0.947132i | \(-0.396033\pi\) | ||||
0.320845 | + | 0.947132i | \(0.396033\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.9446 | −0.713945 | ||||||||
\(236\) | −4.39749 | −0.286252 | ||||||||
\(237\) | 5.61323 | 0.364618 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.9106 | −1.54665 | −0.773323 | − | 0.634012i | \(-0.781407\pi\) | ||||
−0.773323 | + | 0.634012i | \(0.781407\pi\) | |||||||
\(240\) | 1.61323 | 0.104134 | ||||||||
\(241\) | −1.88914 | −0.121690 | −0.0608451 | − | 0.998147i | \(-0.519380\pi\) | ||||
−0.0608451 | + | 0.998147i | \(0.519380\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 11.9553 | 0.765359 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.94457 | −0.315254 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.34206 | −0.402721 | ||||||||
\(249\) | −5.05543 | −0.320375 | ||||||||
\(250\) | −11.9339 | −0.754763 | ||||||||
\(251\) | −0.939830 | −0.0593215 | −0.0296608 | − | 0.999560i | \(-0.509443\pi\) | ||||
−0.0296608 | + | 0.999560i | \(0.509443\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.55780 | −0.223677 | ||||||||
\(254\) | −0.442200 | −0.0277461 | ||||||||
\(255\) | 11.8444 | 0.741727 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.2265 | 0.700287 | 0.350144 | − | 0.936696i | \(-0.386133\pi\) | ||||
0.350144 | + | 0.936696i | \(0.386133\pi\) | |||||||
\(258\) | −11.5131 | −0.716774 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.3975 | 0.643588 | ||||||||
\(262\) | 2.34206 | 0.144693 | ||||||||
\(263\) | −1.22646 | −0.0756267 | −0.0378134 | − | 0.999285i | \(-0.512039\pi\) | ||||
−0.0378134 | + | 0.999285i | \(0.512039\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | 12.9058 | 0.792799 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.773540 | 0.0473399 | ||||||||
\(268\) | 2.94457 | 0.179868 | ||||||||
\(269\) | −9.50237 | −0.579370 | −0.289685 | − | 0.957122i | \(-0.593551\pi\) | ||||
−0.289685 | + | 0.957122i | \(0.593551\pi\) | |||||||
\(270\) | 1.61323 | 0.0981780 | ||||||||
\(271\) | −3.22646 | −0.195993 | −0.0979967 | − | 0.995187i | \(-0.531243\pi\) | ||||
−0.0979967 | + | 0.995187i | \(0.531243\pi\) | |||||||
\(272\) | 7.34206 | 0.445178 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.22646 | 0.194918 | ||||||||
\(275\) | 2.39749 | 0.144574 | ||||||||
\(276\) | 3.55780 | 0.214154 | ||||||||
\(277\) | −16.0000 | −0.961347 | −0.480673 | − | 0.876900i | \(-0.659608\pi\) | ||||
−0.480673 | + | 0.876900i | \(0.659608\pi\) | |||||||
\(278\) | −18.3975 | −1.10341 | ||||||||
\(279\) | −6.34206 | −0.379689 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.2312 | −0.669997 | −0.334999 | − | 0.942219i | \(-0.608736\pi\) | ||||
−0.334999 | + | 0.942219i | \(0.608736\pi\) | |||||||
\(282\) | −6.78426 | −0.403997 | ||||||||
\(283\) | 25.4577 | 1.51330 | 0.756650 | − | 0.653820i | \(-0.226835\pi\) | ||||
0.756650 | + | 0.653820i | \(0.226835\pi\) | |||||||
\(284\) | 15.5131 | 0.920532 | ||||||||
\(285\) | −1.88914 | −0.111903 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 36.9058 | 2.17093 | ||||||||
\(290\) | 16.7735 | 0.984976 | ||||||||
\(291\) | −7.00000 | −0.410347 | ||||||||
\(292\) | 5.11560 | 0.299368 | ||||||||
\(293\) | −17.9446 | −1.04833 | −0.524166 | − | 0.851616i | \(-0.675623\pi\) | ||||
−0.524166 | + | 0.851616i | \(0.675623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.09416 | −0.413038 | ||||||||
\(296\) | 2.82897 | 0.164431 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 19.6239 | 1.13678 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2.39749 | −0.138419 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.331340 | −0.0190665 | ||||||||
\(303\) | −13.6239 | −0.782675 | ||||||||
\(304\) | −1.17103 | −0.0671632 | ||||||||
\(305\) | 19.2866 | 1.10435 | ||||||||
\(306\) | 7.34206 | 0.419718 | ||||||||
\(307\) | 33.0262 | 1.88490 | 0.942452 | − | 0.334342i | \(-0.108514\pi\) | ||||
0.942452 | + | 0.334342i | \(0.108514\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.3421 | 0.702115 | ||||||||
\(310\) | −10.2312 | −0.581093 | ||||||||
\(311\) | 0.331340 | 0.0187886 | 0.00939429 | − | 0.999956i | \(-0.497010\pi\) | ||||
0.00939429 | + | 0.999956i | \(0.497010\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.3975 | 0.813794 | 0.406897 | − | 0.913474i | \(-0.366611\pi\) | ||||
0.406897 | + | 0.913474i | \(0.366611\pi\) | |||||||
\(314\) | −19.9660 | −1.12675 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.61323 | 0.315769 | ||||||||
\(317\) | 17.5238 | 0.984235 | 0.492118 | − | 0.870529i | \(-0.336223\pi\) | ||||
0.492118 | + | 0.870529i | \(0.336223\pi\) | |||||||
\(318\) | 8.00000 | 0.448618 | ||||||||
\(319\) | −10.3975 | −0.582148 | ||||||||
\(320\) | 1.61323 | 0.0901823 | ||||||||
\(321\) | −15.7395 | −0.878496 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.59777 | −0.478393 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 21.2866 | 1.17896 | ||||||||
\(327\) | 3.95529 | 0.218728 | ||||||||
\(328\) | −4.94457 | −0.273018 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.61323 | −0.0888054 | ||||||||
\(331\) | −8.94457 | −0.491638 | −0.245819 | − | 0.969316i | \(-0.579057\pi\) | ||||
−0.245819 | + | 0.969316i | \(0.579057\pi\) | |||||||
\(332\) | −5.05543 | −0.277453 | ||||||||
\(333\) | 2.82897 | 0.155027 | ||||||||
\(334\) | −22.0214 | −1.20496 | ||||||||
\(335\) | 4.75027 | 0.259535 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.33732 | −0.181795 | −0.0908977 | − | 0.995860i | \(-0.528974\pi\) | ||||
−0.0908977 | + | 0.995860i | \(0.528974\pi\) | |||||||
\(338\) | −13.0000 | −0.707107 | ||||||||
\(339\) | −4.34206 | −0.235828 | ||||||||
\(340\) | 11.8444 | 0.642354 | ||||||||
\(341\) | 6.34206 | 0.343442 | ||||||||
\(342\) | −1.17103 | −0.0633220 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −11.5131 | −0.620744 | ||||||||
\(345\) | 5.73955 | 0.309007 | ||||||||
\(346\) | −1.65794 | −0.0891314 | ||||||||
\(347\) | −30.4237 | −1.63323 | −0.816614 | − | 0.577184i | \(-0.804151\pi\) | ||||
−0.816614 | + | 0.577184i | \(0.804151\pi\) | |||||||
\(348\) | 10.3975 | 0.557364 | ||||||||
\(349\) | −17.5238 | −0.938028 | −0.469014 | − | 0.883191i | \(-0.655391\pi\) | ||||
−0.469014 | + | 0.883191i | \(0.655391\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −5.11560 | −0.272276 | −0.136138 | − | 0.990690i | \(-0.543469\pi\) | ||||
−0.136138 | + | 0.990690i | \(0.543469\pi\) | |||||||
\(354\) | −4.39749 | −0.233724 | ||||||||
\(355\) | 25.0262 | 1.32825 | ||||||||
\(356\) | 0.773540 | 0.0409976 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.0602 | 0.795955 | ||||||||
\(359\) | −30.6841 | −1.61945 | −0.809723 | − | 0.586812i | \(-0.800383\pi\) | ||||
−0.809723 | + | 0.586812i | \(0.800383\pi\) | |||||||
\(360\) | 1.61323 | 0.0850247 | ||||||||
\(361\) | −17.6287 | −0.927826 | ||||||||
\(362\) | −15.1156 | −0.794458 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.25264 | 0.431963 | ||||||||
\(366\) | 11.9553 | 0.624913 | ||||||||
\(367\) | −1.45766 | −0.0760892 | −0.0380446 | − | 0.999276i | \(-0.512113\pi\) | ||||
−0.0380446 | + | 0.999276i | \(0.512113\pi\) | |||||||
\(368\) | 3.55780 | 0.185463 | ||||||||
\(369\) | −4.94457 | −0.257404 | ||||||||
\(370\) | 4.56378 | 0.237260 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.34206 | −0.328820 | ||||||||
\(373\) | −34.1865 | −1.77011 | −0.885055 | − | 0.465487i | \(-0.845879\pi\) | ||||
−0.885055 | + | 0.465487i | \(0.845879\pi\) | |||||||
\(374\) | −7.34206 | −0.379649 | ||||||||
\(375\) | −11.9339 | −0.616261 | ||||||||
\(376\) | −6.78426 | −0.349871 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.28663 | −0.477022 | −0.238511 | − | 0.971140i | \(-0.576659\pi\) | ||||
−0.238511 | + | 0.971140i | \(0.576659\pi\) | |||||||
\(380\) | −1.88914 | −0.0969108 | ||||||||
\(381\) | −0.442200 | −0.0226546 | ||||||||
\(382\) | −4.77354 | −0.244236 | ||||||||
\(383\) | 3.62395 | 0.185175 | 0.0925876 | − | 0.995705i | \(-0.470486\pi\) | ||||
0.0925876 | + | 0.995705i | \(0.470486\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.11560 | 0.158580 | ||||||||
\(387\) | −11.5131 | −0.585243 | ||||||||
\(388\) | −7.00000 | −0.355371 | ||||||||
\(389\) | 7.16031 | 0.363042 | 0.181521 | − | 0.983387i | \(-0.441898\pi\) | ||||
0.181521 | + | 0.983387i | \(0.441898\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.1216 | 1.32103 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.34206 | 0.118141 | ||||||||
\(394\) | −4.82897 | −0.243280 | ||||||||
\(395\) | 9.05543 | 0.455628 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 30.3975 | 1.52561 | 0.762803 | − | 0.646631i | \(-0.223823\pi\) | ||||
0.762803 | + | 0.646631i | \(0.223823\pi\) | |||||||
\(398\) | −5.88914 | −0.295196 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.39749 | −0.119874 | ||||||||
\(401\) | −12.0214 | −0.600322 | −0.300161 | − | 0.953889i | \(-0.597040\pi\) | ||||
−0.300161 | + | 0.953889i | \(0.597040\pi\) | |||||||
\(402\) | 2.94457 | 0.146862 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −13.6239 | −0.677817 | ||||||||
\(405\) | 1.61323 | 0.0801620 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.82897 | −0.140227 | ||||||||
\(408\) | 7.34206 | 0.363486 | ||||||||
\(409\) | −17.5685 | −0.868707 | −0.434354 | − | 0.900742i | \(-0.643023\pi\) | ||||
−0.434354 | + | 0.900742i | \(0.643023\pi\) | |||||||
\(410\) | −7.97673 | −0.393943 | ||||||||
\(411\) | 3.22646 | 0.159150 | ||||||||
\(412\) | 12.3421 | 0.608050 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.55780 | 0.174856 | ||||||||
\(415\) | −8.15557 | −0.400341 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.3975 | −0.900929 | ||||||||
\(418\) | 1.17103 | 0.0572769 | ||||||||
\(419\) | 27.1710 | 1.32739 | 0.663696 | − | 0.748003i | \(-0.268987\pi\) | ||||
0.663696 | + | 0.748003i | \(0.268987\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.1710 | 1.12929 | 0.564643 | − | 0.825335i | \(-0.309014\pi\) | ||||
0.564643 | + | 0.825335i | \(0.309014\pi\) | |||||||
\(422\) | −13.6794 | −0.665902 | ||||||||
\(423\) | −6.78426 | −0.329862 | ||||||||
\(424\) | 8.00000 | 0.388514 | ||||||||
\(425\) | −17.6025 | −0.853847 | ||||||||
\(426\) | 15.5131 | 0.751612 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −15.7395 | −0.760800 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.5733 | −0.895682 | ||||||||
\(431\) | −16.7735 | −0.807953 | −0.403977 | − | 0.914769i | \(-0.632372\pi\) | ||||
−0.403977 | + | 0.914769i | \(0.632372\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −17.3421 | −0.833406 | −0.416703 | − | 0.909043i | \(-0.636815\pi\) | ||||
−0.416703 | + | 0.909043i | \(0.636815\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.7735 | 0.804230 | ||||||||
\(436\) | 3.95529 | 0.189424 | ||||||||
\(437\) | −4.16629 | −0.199301 | ||||||||
\(438\) | 5.11560 | 0.244433 | ||||||||
\(439\) | −33.1478 | −1.58206 | −0.791028 | − | 0.611780i | \(-0.790454\pi\) | ||||
−0.791028 | + | 0.611780i | \(0.790454\pi\) | |||||||
\(440\) | −1.61323 | −0.0769077 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.0554 | −0.572771 | −0.286385 | − | 0.958115i | \(-0.592454\pi\) | ||||
−0.286385 | + | 0.958115i | \(0.592454\pi\) | |||||||
\(444\) | 2.82897 | 0.134257 | ||||||||
\(445\) | 1.24790 | 0.0591561 | ||||||||
\(446\) | 5.11560 | 0.242231 | ||||||||
\(447\) | 19.6239 | 0.928181 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.5947 | −1.72701 | −0.863505 | − | 0.504340i | \(-0.831736\pi\) | ||||
−0.863505 | + | 0.504340i | \(0.831736\pi\) | |||||||
\(450\) | −2.39749 | −0.113019 | ||||||||
\(451\) | 4.94457 | 0.232831 | ||||||||
\(452\) | −4.34206 | −0.204233 | ||||||||
\(453\) | −0.331340 | −0.0155677 | ||||||||
\(454\) | 5.28663 | 0.248114 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.17103 | −0.0548385 | ||||||||
\(457\) | 37.8212 | 1.76920 | 0.884600 | − | 0.466351i | \(-0.154432\pi\) | ||||
0.884600 | + | 0.466351i | \(0.154432\pi\) | |||||||
\(458\) | 4.88440 | 0.228233 | ||||||||
\(459\) | 7.34206 | 0.342698 | ||||||||
\(460\) | 5.73955 | 0.267608 | ||||||||
\(461\) | −34.9707 | −1.62875 | −0.814375 | − | 0.580339i | \(-0.802920\pi\) | ||||
−0.814375 | + | 0.580339i | \(0.802920\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.56852 | 0.351739 | 0.175869 | − | 0.984413i | \(-0.443726\pi\) | ||||
0.175869 | + | 0.984413i | \(0.443726\pi\) | |||||||
\(464\) | 10.3975 | 0.482691 | ||||||||
\(465\) | −10.2312 | −0.474461 | ||||||||
\(466\) | 9.79498 | 0.453744 | ||||||||
\(467\) | 14.6287 | 0.676935 | 0.338468 | − | 0.940978i | \(-0.390091\pi\) | ||||
0.338468 | + | 0.940978i | \(0.390091\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −10.9446 | −0.504835 | ||||||||
\(471\) | −19.9660 | −0.919985 | ||||||||
\(472\) | −4.39749 | −0.202411 | ||||||||
\(473\) | 11.5131 | 0.529372 | ||||||||
\(474\) | 5.61323 | 0.257824 | ||||||||
\(475\) | 2.80753 | 0.128818 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.00000 | 0.366295 | ||||||||
\(478\) | −23.9106 | −1.09364 | ||||||||
\(479\) | 1.22646 | 0.0560384 | 0.0280192 | − | 0.999607i | \(-0.491080\pi\) | ||||
0.0280192 | + | 0.999607i | \(0.491080\pi\) | |||||||
\(480\) | 1.61323 | 0.0736335 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1.88914 | −0.0860480 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −11.2926 | −0.512771 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 30.7056 | 1.39140 | 0.695701 | − | 0.718332i | \(-0.255094\pi\) | ||||
0.695701 | + | 0.718332i | \(0.255094\pi\) | |||||||
\(488\) | 11.9553 | 0.541191 | ||||||||
\(489\) | 21.2866 | 0.962615 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.9446 | 1.39651 | 0.698254 | − | 0.715850i | \(-0.253960\pi\) | ||||
0.698254 | + | 0.715850i | \(0.253960\pi\) | |||||||
\(492\) | −4.94457 | −0.222918 | ||||||||
\(493\) | 76.3390 | 3.43814 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.61323 | −0.0725093 | ||||||||
\(496\) | −6.34206 | −0.284767 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −5.05543 | −0.226539 | ||||||||
\(499\) | −10.3421 | −0.462974 | −0.231487 | − | 0.972838i | \(-0.574359\pi\) | ||||
−0.231487 | + | 0.972838i | \(0.574359\pi\) | |||||||
\(500\) | −11.9339 | −0.533698 | ||||||||
\(501\) | −22.0214 | −0.983845 | ||||||||
\(502\) | −0.939830 | −0.0419467 | ||||||||
\(503\) | −4.66268 | −0.207899 | −0.103949 | − | 0.994583i | \(-0.533148\pi\) | ||||
−0.103949 | + | 0.994583i | \(0.533148\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.9786 | −0.978033 | ||||||||
\(506\) | −3.55780 | −0.158163 | ||||||||
\(507\) | −13.0000 | −0.577350 | ||||||||
\(508\) | −0.442200 | −0.0196195 | ||||||||
\(509\) | −25.5900 | −1.13425 | −0.567127 | − | 0.823630i | \(-0.691945\pi\) | ||||
−0.567127 | + | 0.823630i | \(0.691945\pi\) | |||||||
\(510\) | 11.8444 | 0.524480 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.17103 | −0.0517022 | ||||||||
\(514\) | 11.2265 | 0.495178 | ||||||||
\(515\) | 19.9106 | 0.877365 | ||||||||
\(516\) | −11.5131 | −0.506835 | ||||||||
\(517\) | 6.78426 | 0.298371 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.65794 | −0.0727755 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 10.3975 | 0.455086 | ||||||||
\(523\) | −30.3635 | −1.32770 | −0.663852 | − | 0.747864i | \(-0.731079\pi\) | ||||
−0.663852 | + | 0.747864i | \(0.731079\pi\) | |||||||
\(524\) | 2.34206 | 0.102313 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.22646 | −0.0534762 | ||||||||
\(527\) | −46.5638 | −2.02835 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −10.3421 | −0.449655 | ||||||||
\(530\) | 12.9058 | 0.560594 | ||||||||
\(531\) | −4.39749 | −0.190835 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.773540 | 0.0334744 | ||||||||
\(535\) | −25.3915 | −1.09777 | ||||||||
\(536\) | 2.94457 | 0.127186 | ||||||||
\(537\) | 15.0602 | 0.649894 | ||||||||
\(538\) | −9.50237 | −0.409676 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.61323 | 0.0694224 | ||||||||
\(541\) | 1.61323 | 0.0693582 | 0.0346791 | − | 0.999398i | \(-0.488959\pi\) | ||||
0.0346791 | + | 0.999398i | \(0.488959\pi\) | |||||||
\(542\) | −3.22646 | −0.138588 | ||||||||
\(543\) | −15.1156 | −0.648672 | ||||||||
\(544\) | 7.34206 | 0.314788 | ||||||||
\(545\) | 6.38079 | 0.273323 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.7348 | 0.672772 | 0.336386 | − | 0.941724i | \(-0.390795\pi\) | ||||
0.336386 | + | 0.941724i | \(0.390795\pi\) | |||||||
\(548\) | 3.22646 | 0.137828 | ||||||||
\(549\) | 11.9553 | 0.510239 | ||||||||
\(550\) | 2.39749 | 0.102229 | ||||||||
\(551\) | −12.1758 | −0.518705 | ||||||||
\(552\) | 3.55780 | 0.151430 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −16.0000 | −0.679775 | ||||||||
\(555\) | 4.56378 | 0.193722 | ||||||||
\(556\) | −18.3975 | −0.780227 | ||||||||
\(557\) | 11.2819 | 0.478029 | 0.239015 | − | 0.971016i | \(-0.423176\pi\) | ||||
0.239015 | + | 0.971016i | \(0.423176\pi\) | |||||||
\(558\) | −6.34206 | −0.268481 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.34206 | −0.309982 | ||||||||
\(562\) | −11.2312 | −0.473760 | ||||||||
\(563\) | −20.9058 | −0.881076 | −0.440538 | − | 0.897734i | \(-0.645212\pi\) | ||||
−0.440538 | + | 0.897734i | \(0.645212\pi\) | |||||||
\(564\) | −6.78426 | −0.285669 | ||||||||
\(565\) | −7.00474 | −0.294692 | ||||||||
\(566\) | 25.4577 | 1.07007 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.5131 | 0.650915 | ||||||||
\(569\) | −7.83371 | −0.328406 | −0.164203 | − | 0.986427i | \(-0.552505\pi\) | ||||
−0.164203 | + | 0.986427i | \(0.552505\pi\) | |||||||
\(570\) | −1.88914 | −0.0791274 | ||||||||
\(571\) | 2.39749 | 0.100332 | 0.0501659 | − | 0.998741i | \(-0.484025\pi\) | ||||
0.0501659 | + | 0.998741i | \(0.484025\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.77354 | −0.199418 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.52979 | −0.355717 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −25.6287 | −1.06694 | −0.533468 | − | 0.845820i | \(-0.679112\pi\) | ||||
−0.533468 | + | 0.845820i | \(0.679112\pi\) | |||||||
\(578\) | 36.9058 | 1.53508 | ||||||||
\(579\) | 3.11560 | 0.129480 | ||||||||
\(580\) | 16.7735 | 0.696483 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −7.00000 | −0.290159 | ||||||||
\(583\) | −8.00000 | −0.331326 | ||||||||
\(584\) | 5.11560 | 0.211685 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.9446 | −0.741283 | ||||||||
\(587\) | −5.79972 | −0.239380 | −0.119690 | − | 0.992811i | \(-0.538190\pi\) | ||||
−0.119690 | + | 0.992811i | \(0.538190\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.42674 | 0.306014 | ||||||||
\(590\) | −7.09416 | −0.292062 | ||||||||
\(591\) | −4.82897 | −0.198637 | ||||||||
\(592\) | 2.82897 | 0.116270 | ||||||||
\(593\) | −31.1925 | −1.28092 | −0.640461 | − | 0.767991i | \(-0.721257\pi\) | ||||
−0.640461 | + | 0.767991i | \(0.721257\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.6239 | 0.803828 | ||||||||
\(597\) | −5.88914 | −0.241026 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.2926 | −1.27858 | −0.639291 | − | 0.768965i | \(-0.720772\pi\) | ||||
−0.639291 | + | 0.768965i | \(0.720772\pi\) | |||||||
\(600\) | −2.39749 | −0.0978771 | ||||||||
\(601\) | 22.1203 | 0.902307 | 0.451154 | − | 0.892446i | \(-0.351013\pi\) | ||||
0.451154 | + | 0.892446i | \(0.351013\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.94457 | 0.119912 | ||||||||
\(604\) | −0.331340 | −0.0134820 | ||||||||
\(605\) | 1.61323 | 0.0655871 | ||||||||
\(606\) | −13.6239 | −0.553435 | ||||||||
\(607\) | 20.6180 | 0.836858 | 0.418429 | − | 0.908250i | \(-0.362581\pi\) | ||||
0.418429 | + | 0.908250i | \(0.362581\pi\) | |||||||
\(608\) | −1.17103 | −0.0474915 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 19.2866 | 0.780893 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 7.34206 | 0.296785 | ||||||||
\(613\) | −15.7550 | −0.636339 | −0.318169 | − | 0.948034i | \(-0.603068\pi\) | ||||
−0.318169 | + | 0.948034i | \(0.603068\pi\) | |||||||
\(614\) | 33.0262 | 1.33283 | ||||||||
\(615\) | −7.97673 | −0.321653 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.2526 | 1.37896 | 0.689480 | − | 0.724305i | \(-0.257839\pi\) | ||||
0.689480 | + | 0.724305i | \(0.257839\pi\) | |||||||
\(618\) | 12.3421 | 0.496470 | ||||||||
\(619\) | 21.9707 | 0.883079 | 0.441539 | − | 0.897242i | \(-0.354433\pi\) | ||||
0.441539 | + | 0.897242i | \(0.354433\pi\) | |||||||
\(620\) | −10.2312 | −0.410895 | ||||||||
\(621\) | 3.55780 | 0.142770 | ||||||||
\(622\) | 0.331340 | 0.0132855 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.26460 | −0.290584 | ||||||||
\(626\) | 14.3975 | 0.575439 | ||||||||
\(627\) | 1.17103 | 0.0467664 | ||||||||
\(628\) | −19.9660 | −0.796730 | ||||||||
\(629\) | 20.7705 | 0.828173 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.5685 | −1.09749 | −0.548743 | − | 0.835991i | \(-0.684893\pi\) | ||||
−0.548743 | + | 0.835991i | \(0.684893\pi\) | |||||||
\(632\) | 5.61323 | 0.223282 | ||||||||
\(633\) | −13.6794 | −0.543707 | ||||||||
\(634\) | 17.5238 | 0.695959 | ||||||||
\(635\) | −0.713370 | −0.0283092 | ||||||||
\(636\) | 8.00000 | 0.317221 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10.3975 | −0.411641 | ||||||||
\(639\) | 15.5131 | 0.613688 | ||||||||
\(640\) | 1.61323 | 0.0637685 | ||||||||
\(641\) | 5.65794 | 0.223475 | 0.111738 | − | 0.993738i | \(-0.464358\pi\) | ||||
0.111738 | + | 0.993738i | \(0.464358\pi\) | |||||||
\(642\) | −15.7395 | −0.621190 | ||||||||
\(643\) | −17.4791 | −0.689308 | −0.344654 | − | 0.938730i | \(-0.612004\pi\) | ||||
−0.344654 | + | 0.938730i | \(0.612004\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.5733 | −0.731321 | ||||||||
\(646\) | −8.59777 | −0.338275 | ||||||||
\(647\) | 8.83969 | 0.347524 | 0.173762 | − | 0.984788i | \(-0.444408\pi\) | ||||
0.173762 | + | 0.984788i | \(0.444408\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 4.39749 | 0.172617 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21.2866 | 0.833649 | ||||||||
\(653\) | −24.7503 | −0.968553 | −0.484276 | − | 0.874915i | \(-0.660917\pi\) | ||||
−0.484276 | + | 0.874915i | \(0.660917\pi\) | |||||||
\(654\) | 3.95529 | 0.154664 | ||||||||
\(655\) | 3.77828 | 0.147630 | ||||||||
\(656\) | −4.94457 | −0.193053 | ||||||||
\(657\) | 5.11560 | 0.199579 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.62869 | 0.219263 | 0.109631 | − | 0.993972i | \(-0.465033\pi\) | ||||
0.109631 | + | 0.993972i | \(0.465033\pi\) | |||||||
\(660\) | −1.61323 | −0.0627949 | ||||||||
\(661\) | 13.4022 | 0.521286 | 0.260643 | − | 0.965435i | \(-0.416065\pi\) | ||||
0.260643 | + | 0.965435i | \(0.416065\pi\) | |||||||
\(662\) | −8.94457 | −0.347641 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.05543 | −0.196189 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.82897 | 0.109620 | ||||||||
\(667\) | 36.9922 | 1.43234 | ||||||||
\(668\) | −22.0214 | −0.852035 | ||||||||
\(669\) | 5.11560 | 0.197781 | ||||||||
\(670\) | 4.75027 | 0.183519 | ||||||||
\(671\) | −11.9553 | −0.461529 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.0262 | −1.11888 | −0.559438 | − | 0.828872i | \(-0.688983\pi\) | ||||
−0.559438 | + | 0.828872i | \(0.688983\pi\) | |||||||
\(674\) | −3.33732 | −0.128549 | ||||||||
\(675\) | −2.39749 | −0.0922794 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | 20.3081 | 0.780502 | 0.390251 | − | 0.920708i | \(-0.372388\pi\) | ||||
0.390251 | + | 0.920708i | \(0.372388\pi\) | |||||||
\(678\) | −4.34206 | −0.166756 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 11.8444 | 0.454213 | ||||||||
\(681\) | 5.28663 | 0.202584 | ||||||||
\(682\) | 6.34206 | 0.242850 | ||||||||
\(683\) | −10.7395 | −0.410937 | −0.205469 | − | 0.978664i | \(-0.565872\pi\) | ||||
−0.205469 | + | 0.978664i | \(0.565872\pi\) | |||||||
\(684\) | −1.17103 | −0.0447754 | ||||||||
\(685\) | 5.20502 | 0.198874 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.88440 | 0.186351 | ||||||||
\(688\) | −11.5131 | −0.438932 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 5.73955 | 0.218501 | ||||||||
\(691\) | −5.97075 | −0.227138 | −0.113569 | − | 0.993530i | \(-0.536228\pi\) | ||||
−0.113569 | + | 0.993530i | \(0.536228\pi\) | |||||||
\(692\) | −1.65794 | −0.0630254 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30.4237 | −1.15487 | ||||||||
\(695\) | −29.6794 | −1.12580 | ||||||||
\(696\) | 10.3975 | 0.394116 | ||||||||
\(697\) | −36.3033 | −1.37509 | ||||||||
\(698\) | −17.5238 | −0.663286 | ||||||||
\(699\) | 9.79498 | 0.370480 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.28189 | −0.199494 | −0.0997471 | − | 0.995013i | \(-0.531803\pi\) | ||||
−0.0997471 | + | 0.995013i | \(0.531803\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.31281 | −0.124945 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −10.9446 | −0.412196 | ||||||||
\(706\) | −5.11560 | −0.192528 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.39749 | −0.165268 | ||||||||
\(709\) | 39.3128 | 1.47642 | 0.738212 | − | 0.674569i | \(-0.235671\pi\) | ||||
0.738212 | + | 0.674569i | \(0.235671\pi\) | |||||||
\(710\) | 25.0262 | 0.939216 | ||||||||
\(711\) | 5.61323 | 0.210513 | ||||||||
\(712\) | 0.773540 | 0.0289896 | ||||||||
\(713\) | −22.5638 | −0.845020 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.0602 | 0.562825 | ||||||||
\(717\) | −23.9106 | −0.892957 | ||||||||
\(718\) | −30.6841 | −1.14512 | ||||||||
\(719\) | 35.3575 | 1.31861 | 0.659306 | − | 0.751874i | \(-0.270850\pi\) | ||||
0.659306 | + | 0.751874i | \(0.270850\pi\) | |||||||
\(720\) | 1.61323 | 0.0601215 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.6287 | −0.656072 | ||||||||
\(723\) | −1.88914 | −0.0702579 | ||||||||
\(724\) | −15.1156 | −0.561767 | ||||||||
\(725\) | −24.9279 | −0.925798 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | 40.2312 | 1.49209 | 0.746046 | − | 0.665894i | \(-0.231950\pi\) | ||||
0.746046 | + | 0.665894i | \(0.231950\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 8.25264 | 0.305444 | ||||||||
\(731\) | −84.5298 | −3.12645 | ||||||||
\(732\) | 11.9553 | 0.441880 | ||||||||
\(733\) | −28.7288 | −1.06112 | −0.530562 | − | 0.847646i | \(-0.678019\pi\) | ||||
−0.530562 | + | 0.847646i | \(0.678019\pi\) | |||||||
\(734\) | −1.45766 | −0.0538032 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.55780 | 0.131142 | ||||||||
\(737\) | −2.94457 | −0.108465 | ||||||||
\(738\) | −4.94457 | −0.182012 | ||||||||
\(739\) | −16.3421 | −0.601152 | −0.300576 | − | 0.953758i | \(-0.597179\pi\) | ||||
−0.300576 | + | 0.953758i | \(0.597179\pi\) | |||||||
\(740\) | 4.56378 | 0.167768 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.3897 | 1.66519 | 0.832593 | − | 0.553885i | \(-0.186855\pi\) | ||||
0.832593 | + | 0.553885i | \(0.186855\pi\) | |||||||
\(744\) | −6.34206 | −0.232511 | ||||||||
\(745\) | 31.6579 | 1.15986 | ||||||||
\(746\) | −34.1865 | −1.25166 | ||||||||
\(747\) | −5.05543 | −0.184969 | ||||||||
\(748\) | −7.34206 | −0.268452 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −11.9339 | −0.435763 | ||||||||
\(751\) | −27.7997 | −1.01443 | −0.507213 | − | 0.861821i | \(-0.669324\pi\) | ||||
−0.507213 | + | 0.861821i | \(0.669324\pi\) | |||||||
\(752\) | −6.78426 | −0.247396 | ||||||||
\(753\) | −0.939830 | −0.0342493 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.534528 | −0.0194535 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.0816 | 0.693533 | 0.346766 | − | 0.937952i | \(-0.387280\pi\) | ||||
0.346766 | + | 0.937952i | \(0.387280\pi\) | |||||||
\(758\) | −9.28663 | −0.337306 | ||||||||
\(759\) | −3.55780 | −0.129140 | ||||||||
\(760\) | −1.88914 | −0.0685263 | ||||||||
\(761\) | −47.2186 | −1.71167 | −0.855837 | − | 0.517245i | \(-0.826958\pi\) | ||||
−0.855837 | + | 0.517245i | \(0.826958\pi\) | |||||||
\(762\) | −0.442200 | −0.0160192 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.77354 | −0.172701 | ||||||||
\(765\) | 11.8444 | 0.428236 | ||||||||
\(766\) | 3.62395 | 0.130939 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 9.56852 | 0.345050 | 0.172525 | − | 0.985005i | \(-0.444808\pi\) | ||||
0.172525 | + | 0.985005i | \(0.444808\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.2265 | 0.404311 | ||||||||
\(772\) | 3.11560 | 0.112133 | ||||||||
\(773\) | −15.9553 | −0.573872 | −0.286936 | − | 0.957950i | \(-0.592637\pi\) | ||||
−0.286936 | + | 0.957950i | \(0.592637\pi\) | |||||||
\(774\) | −11.5131 | −0.413829 | ||||||||
\(775\) | 15.2050 | 0.546180 | ||||||||
\(776\) | −7.00000 | −0.251285 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.16031 | 0.256710 | ||||||||
\(779\) | 5.79024 | 0.207457 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.5131 | −0.555102 | ||||||||
\(782\) | 26.1216 | 0.934106 | ||||||||
\(783\) | 10.3975 | 0.371576 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −32.2098 | −1.14962 | ||||||||
\(786\) | 2.34206 | 0.0835385 | ||||||||
\(787\) | −49.8551 | −1.77714 | −0.888572 | − | 0.458737i | \(-0.848302\pi\) | ||||
−0.888572 | + | 0.458737i | \(0.848302\pi\) | |||||||
\(788\) | −4.82897 | −0.172025 | ||||||||
\(789\) | −1.22646 | −0.0436631 | ||||||||
\(790\) | 9.05543 | 0.322178 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 30.3975 | 1.07877 | ||||||||
\(795\) | 12.9058 | 0.457723 | ||||||||
\(796\) | −5.88914 | −0.208735 | ||||||||
\(797\) | −36.4177 | −1.28998 | −0.644990 | − | 0.764191i | \(-0.723139\pi\) | ||||
−0.644990 | + | 0.764191i | \(0.723139\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −49.8104 | −1.76217 | ||||||||
\(800\) | −2.39749 | −0.0847641 | ||||||||
\(801\) | 0.773540 | 0.0273317 | ||||||||
\(802\) | −12.0214 | −0.424492 | ||||||||
\(803\) | −5.11560 | −0.180526 | ||||||||
\(804\) | 2.94457 | 0.103847 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.50237 | −0.334499 | ||||||||
\(808\) | −13.6239 | −0.479289 | ||||||||
\(809\) | 48.4237 | 1.70249 | 0.851243 | − | 0.524772i | \(-0.175849\pi\) | ||||
0.851243 | + | 0.524772i | \(0.175849\pi\) | |||||||
\(810\) | 1.61323 | 0.0566831 | ||||||||
\(811\) | 41.0262 | 1.44062 | 0.720312 | − | 0.693650i | \(-0.243999\pi\) | ||||
0.720312 | + | 0.693650i | \(0.243999\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.22646 | −0.113157 | ||||||||
\(814\) | −2.82897 | −0.0991554 | ||||||||
\(815\) | 34.3402 | 1.20289 | ||||||||
\(816\) | 7.34206 | 0.257023 | ||||||||
\(817\) | 13.4822 | 0.471681 | ||||||||
\(818\) | −17.5685 | −0.614269 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.97673 | −0.278559 | ||||||||
\(821\) | 39.9320 | 1.39364 | 0.696819 | − | 0.717247i | \(-0.254598\pi\) | ||||
0.696819 | + | 0.717247i | \(0.254598\pi\) | |||||||
\(822\) | 3.22646 | 0.112536 | ||||||||
\(823\) | −15.7997 | −0.550744 | −0.275372 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275372 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(824\) | 12.3421 | 0.429956 | ||||||||
\(825\) | 2.39749 | 0.0834699 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.8766 | −0.934591 | −0.467295 | − | 0.884101i | \(-0.654771\pi\) | ||||
−0.467295 | + | 0.884101i | \(0.654771\pi\) | |||||||
\(828\) | 3.55780 | 0.123642 | ||||||||
\(829\) | 8.30807 | 0.288551 | 0.144276 | − | 0.989538i | \(-0.453915\pi\) | ||||
0.144276 | + | 0.989538i | \(0.453915\pi\) | |||||||
\(830\) | −8.15557 | −0.283084 | ||||||||
\(831\) | −16.0000 | −0.555034 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −18.3975 | −0.637053 | ||||||||
\(835\) | −35.5256 | −1.22942 | ||||||||
\(836\) | 1.17103 | 0.0405009 | ||||||||
\(837\) | −6.34206 | −0.219214 | ||||||||
\(838\) | 27.1710 | 0.938608 | ||||||||
\(839\) | 4.28787 | 0.148034 | 0.0740168 | − | 0.997257i | \(-0.476418\pi\) | ||||
0.0740168 | + | 0.997257i | \(0.476418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 79.1078 | 2.72785 | ||||||||
\(842\) | 23.1710 | 0.798526 | ||||||||
\(843\) | −11.2312 | −0.386823 | ||||||||
\(844\) | −13.6794 | −0.470864 | ||||||||
\(845\) | −20.9720 | −0.721458 | ||||||||
\(846\) | −6.78426 | −0.233248 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.00000 | 0.274721 | ||||||||
\(849\) | 25.4577 | 0.873705 | ||||||||
\(850\) | −17.6025 | −0.603761 | ||||||||
\(851\) | 10.0649 | 0.345021 | ||||||||
\(852\) | 15.5131 | 0.531470 | ||||||||
\(853\) | 46.2973 | 1.58519 | 0.792596 | − | 0.609748i | \(-0.208729\pi\) | ||||
0.792596 | + | 0.609748i | \(0.208729\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.88914 | −0.0646072 | ||||||||
\(856\) | −15.7395 | −0.537967 | ||||||||
\(857\) | 27.4624 | 0.938098 | 0.469049 | − | 0.883172i | \(-0.344597\pi\) | ||||
0.469049 | + | 0.883172i | \(0.344597\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.1925 | 0.416002 | 0.208001 | − | 0.978129i | \(-0.433304\pi\) | ||||
0.208001 | + | 0.978129i | \(0.433304\pi\) | |||||||
\(860\) | −18.5733 | −0.633343 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.7735 | −0.571309 | ||||||||
\(863\) | 0.839690 | 0.0285834 | 0.0142917 | − | 0.999898i | \(-0.495451\pi\) | ||||
0.0142917 | + | 0.999898i | \(0.495451\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −2.67464 | −0.0909405 | ||||||||
\(866\) | −17.3421 | −0.589307 | ||||||||
\(867\) | 36.9058 | 1.25339 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.61323 | −0.190416 | ||||||||
\(870\) | 16.7735 | 0.568676 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 3.95529 | 0.133943 | ||||||||
\(873\) | −7.00000 | −0.236914 | ||||||||
\(874\) | −4.16629 | −0.140927 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.11560 | 0.172840 | ||||||||
\(877\) | −20.5285 | −0.693200 | −0.346600 | − | 0.938013i | \(-0.612664\pi\) | ||||
−0.346600 | + | 0.938013i | \(0.612664\pi\) | |||||||
\(878\) | −33.1478 | −1.11868 | ||||||||
\(879\) | −17.9446 | −0.605255 | ||||||||
\(880\) | −1.61323 | −0.0543820 | ||||||||
\(881\) | −1.88914 | −0.0636468 | −0.0318234 | − | 0.999494i | \(-0.510131\pi\) | ||||
−0.0318234 | + | 0.999494i | \(0.510131\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.5345 | 0.892958 | 0.446479 | − | 0.894794i | \(-0.352678\pi\) | ||||
0.446479 | + | 0.894794i | \(0.352678\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.09416 | −0.238468 | ||||||||
\(886\) | −12.0554 | −0.405010 | ||||||||
\(887\) | −17.1156 | −0.574686 | −0.287343 | − | 0.957828i | \(-0.592772\pi\) | ||||
−0.287343 | + | 0.957828i | \(0.592772\pi\) | |||||||
\(888\) | 2.82897 | 0.0949340 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.24790 | 0.0418296 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 5.11560 | 0.171283 | ||||||||
\(893\) | 7.94457 | 0.265855 | ||||||||
\(894\) | 19.6239 | 0.656323 | ||||||||
\(895\) | 24.2955 | 0.812110 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −36.5947 | −1.22118 | ||||||||
\(899\) | −65.9415 | −2.19927 | ||||||||
\(900\) | −2.39749 | −0.0799163 | ||||||||
\(901\) | 58.7365 | 1.95680 | ||||||||
\(902\) | 4.94457 | 0.164636 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.34206 | −0.144415 | ||||||||
\(905\) | −24.3849 | −0.810583 | ||||||||
\(906\) | −0.331340 | −0.0110080 | ||||||||
\(907\) | 3.28663 | 0.109131 | 0.0545654 | − | 0.998510i | \(-0.482623\pi\) | ||||
0.0545654 | + | 0.998510i | \(0.482623\pi\) | |||||||
\(908\) | 5.28663 | 0.175443 | ||||||||
\(909\) | −13.6239 | −0.451878 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.0107 | 0.464196 | 0.232098 | − | 0.972692i | \(-0.425441\pi\) | ||||
0.232098 | + | 0.972692i | \(0.425441\pi\) | |||||||
\(912\) | −1.17103 | −0.0387767 | ||||||||
\(913\) | 5.05543 | 0.167310 | ||||||||
\(914\) | 37.8212 | 1.25101 | ||||||||
\(915\) | 19.2866 | 0.637596 | ||||||||
\(916\) | 4.88440 | 0.161385 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 7.34206 | 0.242324 | ||||||||
\(919\) | −46.5160 | −1.53442 | −0.767211 | − | 0.641395i | \(-0.778356\pi\) | ||||
−0.767211 | + | 0.641395i | \(0.778356\pi\) | |||||||
\(920\) | 5.73955 | 0.189227 | ||||||||
\(921\) | 33.0262 | 1.08825 | ||||||||
\(922\) | −34.9707 | −1.15170 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.78243 | −0.223005 | ||||||||
\(926\) | 7.56852 | 0.248717 | ||||||||
\(927\) | 12.3421 | 0.405366 | ||||||||
\(928\) | 10.3975 | 0.341314 | ||||||||
\(929\) | 24.8844 | 0.816431 | 0.408215 | − | 0.912886i | \(-0.366151\pi\) | ||||
0.408215 | + | 0.912886i | \(0.366151\pi\) | |||||||
\(930\) | −10.2312 | −0.335494 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.79498 | 0.320845 | ||||||||
\(933\) | 0.331340 | 0.0108476 | ||||||||
\(934\) | 14.6287 | 0.478665 | ||||||||
\(935\) | −11.8444 | −0.387354 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.7950 | 1.52873 | 0.764363 | − | 0.644787i | \(-0.223054\pi\) | ||||
0.764363 | + | 0.644787i | \(0.223054\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.3975 | 0.469844 | ||||||||
\(940\) | −10.9446 | −0.356973 | ||||||||
\(941\) | −17.4917 | −0.570212 | −0.285106 | − | 0.958496i | \(-0.592029\pi\) | ||||
−0.285106 | + | 0.958496i | \(0.592029\pi\) | |||||||
\(942\) | −19.9660 | −0.650528 | ||||||||
\(943\) | −17.5918 | −0.572868 | ||||||||
\(944\) | −4.39749 | −0.143126 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.5131 | 0.374323 | ||||||||
\(947\) | 14.6192 | 0.475060 | 0.237530 | − | 0.971380i | \(-0.423662\pi\) | ||||
0.237530 | + | 0.971380i | \(0.423662\pi\) | |||||||
\(948\) | 5.61323 | 0.182309 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.80753 | 0.0910884 | ||||||||
\(951\) | 17.5238 | 0.568248 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.0816 | −0.650507 | −0.325254 | − | 0.945627i | \(-0.605450\pi\) | ||||
−0.325254 | + | 0.945627i | \(0.605450\pi\) | |||||||
\(954\) | 8.00000 | 0.259010 | ||||||||
\(955\) | −7.70082 | −0.249193 | ||||||||
\(956\) | −23.9106 | −0.773323 | ||||||||
\(957\) | −10.3975 | −0.336103 | ||||||||
\(958\) | 1.22646 | 0.0396251 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.61323 | 0.0520668 | ||||||||
\(961\) | 9.22172 | 0.297475 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.7395 | −0.507200 | ||||||||
\(964\) | −1.88914 | −0.0608451 | ||||||||
\(965\) | 5.02618 | 0.161798 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −60.2634 | −1.93794 | −0.968969 | − | 0.247180i | \(-0.920496\pi\) | ||||
−0.968969 | + | 0.247180i | \(0.920496\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −8.59777 | −0.276200 | ||||||||
\(970\) | −11.2926 | −0.362584 | ||||||||
\(971\) | 52.8473 | 1.69595 | 0.847976 | − | 0.530035i | \(-0.177821\pi\) | ||||
0.847976 | + | 0.530035i | \(0.177821\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 30.7056 | 0.983870 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.9553 | 0.382679 | ||||||||
\(977\) | 24.9058 | 0.796808 | 0.398404 | − | 0.917210i | \(-0.369564\pi\) | ||||
0.398404 | + | 0.917210i | \(0.369564\pi\) | |||||||
\(978\) | 21.2866 | 0.680671 | ||||||||
\(979\) | −0.773540 | −0.0247225 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.95529 | 0.126283 | ||||||||
\(982\) | 30.9446 | 0.987481 | ||||||||
\(983\) | 25.1263 | 0.801405 | 0.400703 | − | 0.916208i | \(-0.368766\pi\) | ||||
0.400703 | + | 0.916208i | \(0.368766\pi\) | |||||||
\(984\) | −4.94457 | −0.157627 | ||||||||
\(985\) | −7.79024 | −0.248218 | ||||||||
\(986\) | 76.3390 | 2.43113 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −40.9613 | −1.30249 | ||||||||
\(990\) | −1.61323 | −0.0512718 | ||||||||
\(991\) | 57.9201 | 1.83989 | 0.919946 | − | 0.392046i | \(-0.128233\pi\) | ||||
0.919946 | + | 0.392046i | \(0.128233\pi\) | |||||||
\(992\) | −6.34206 | −0.201361 | ||||||||
\(993\) | −8.94457 | −0.283847 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.50054 | −0.301187 | ||||||||
\(996\) | −5.05543 | −0.160187 | ||||||||
\(997\) | −17.3682 | −0.550058 | −0.275029 | − | 0.961436i | \(-0.588687\pi\) | ||||
−0.275029 | + | 0.961436i | \(0.588687\pi\) | |||||||
\(998\) | −10.3421 | −0.327372 | ||||||||
\(999\) | 2.82897 | 0.0895047 |
(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 | 3234.2.a.bh.1.2 | 3 | ||
3.2 | odd | 2 | 9702.2.a.dw.1.2 | 3 | |||
7.3 | odd | 6 | 462.2.i.g.331.2 | yes | 6 | ||
7.5 | odd | 6 | 462.2.i.g.67.2 | ✓ | 6 | ||
7.6 | odd | 2 | 3234.2.a.bf.1.2 | 3 | |||
21.5 | even | 6 | 1386.2.k.v.991.2 | 6 | |||
21.17 | even | 6 | 1386.2.k.v.793.2 | 6 | |||
21.20 | even | 2 | 9702.2.a.dv.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.g.67.2 | ✓ | 6 | 7.5 | odd | 6 | ||
462.2.i.g.331.2 | yes | 6 | 7.3 | odd | 6 | ||
1386.2.k.v.793.2 | 6 | 21.17 | even | 6 | |||
1386.2.k.v.991.2 | 6 | 21.5 | even | 6 | |||
3234.2.a.bf.1.2 | 3 | 7.6 | odd | 2 | |||
3234.2.a.bh.1.2 | 3 | 1.1 | even | 1 | trivial | ||
9702.2.a.dv.1.2 | 3 | 21.20 | even | 2 | |||
9702.2.a.dw.1.2 | 3 | 3.2 | odd | 2 |