Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6045,2,Mod(1,6045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6045.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6045.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: | \(48.2695680219\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 25 x^{15} + 47 x^{14} + 252 x^{13} - 437 x^{12} - 1319 x^{11} + 2056 x^{10} + \cdots + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(2.54626\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6045.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.54626 | 1.80048 | 0.900240 | − | 0.435393i | \(-0.143391\pi\) | ||||
0.900240 | + | 0.435393i | \(0.143391\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.48346 | 2.24173 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.54626 | −1.03951 | ||||||||
\(7\) | −1.02990 | −0.389265 | −0.194633 | − | 0.980876i | \(-0.562351\pi\) | ||||
−0.194633 | + | 0.980876i | \(0.562351\pi\) | |||||||
\(8\) | 6.32355 | 2.23571 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.54626 | 0.805199 | ||||||||
\(11\) | 2.98909 | 0.901246 | 0.450623 | − | 0.892714i | \(-0.351202\pi\) | ||||
0.450623 | + | 0.892714i | \(0.351202\pi\) | |||||||
\(12\) | −4.48346 | −1.29426 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −2.62239 | −0.700864 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 7.13450 | 1.78363 | ||||||||
\(17\) | 5.98536 | 1.45166 | 0.725832 | − | 0.687872i | \(-0.241455\pi\) | ||||
0.725832 | + | 0.687872i | \(0.241455\pi\) | |||||||
\(18\) | 2.54626 | 0.600160 | ||||||||
\(19\) | −2.06421 | −0.473561 | −0.236781 | − | 0.971563i | \(-0.576092\pi\) | ||||
−0.236781 | + | 0.971563i | \(0.576092\pi\) | |||||||
\(20\) | 4.48346 | 1.00253 | ||||||||
\(21\) | 1.02990 | 0.224742 | ||||||||
\(22\) | 7.61102 | 1.62268 | ||||||||
\(23\) | 4.10895 | 0.856775 | 0.428387 | − | 0.903595i | \(-0.359082\pi\) | ||||
0.428387 | + | 0.903595i | \(0.359082\pi\) | |||||||
\(24\) | −6.32355 | −1.29079 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.54626 | 0.499363 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.61751 | −0.872628 | ||||||||
\(29\) | 2.98050 | 0.553464 | 0.276732 | − | 0.960947i | \(-0.410749\pi\) | ||||
0.276732 | + | 0.960947i | \(0.410749\pi\) | |||||||
\(30\) | −2.54626 | −0.464882 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 5.51923 | 0.975671 | ||||||||
\(33\) | −2.98909 | −0.520334 | ||||||||
\(34\) | 15.2403 | 2.61369 | ||||||||
\(35\) | −1.02990 | −0.174085 | ||||||||
\(36\) | 4.48346 | 0.747244 | ||||||||
\(37\) | −4.03351 | −0.663105 | −0.331552 | − | 0.943437i | \(-0.607572\pi\) | ||||
−0.331552 | + | 0.943437i | \(0.607572\pi\) | |||||||
\(38\) | −5.25601 | −0.852638 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 6.32355 | 0.999841 | ||||||||
\(41\) | 0.184510 | 0.0288157 | 0.0144078 | − | 0.999896i | \(-0.495414\pi\) | ||||
0.0144078 | + | 0.999896i | \(0.495414\pi\) | |||||||
\(42\) | 2.62239 | 0.404644 | ||||||||
\(43\) | −0.571830 | −0.0872032 | −0.0436016 | − | 0.999049i | \(-0.513883\pi\) | ||||
−0.0436016 | + | 0.999049i | \(0.513883\pi\) | |||||||
\(44\) | 13.4015 | 2.02035 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 10.4625 | 1.54261 | ||||||||
\(47\) | −9.24553 | −1.34860 | −0.674299 | − | 0.738458i | \(-0.735554\pi\) | ||||
−0.674299 | + | 0.738458i | \(0.735554\pi\) | |||||||
\(48\) | −7.13450 | −1.02978 | ||||||||
\(49\) | −5.93931 | −0.848473 | ||||||||
\(50\) | 2.54626 | 0.360096 | ||||||||
\(51\) | −5.98536 | −0.838119 | ||||||||
\(52\) | 4.48346 | 0.621744 | ||||||||
\(53\) | −6.11650 | −0.840165 | −0.420083 | − | 0.907486i | \(-0.637999\pi\) | ||||
−0.420083 | + | 0.907486i | \(0.637999\pi\) | |||||||
\(54\) | −2.54626 | −0.346503 | ||||||||
\(55\) | 2.98909 | 0.403049 | ||||||||
\(56\) | −6.51262 | −0.870285 | ||||||||
\(57\) | 2.06421 | 0.273411 | ||||||||
\(58\) | 7.58913 | 0.996502 | ||||||||
\(59\) | 13.2766 | 1.72847 | 0.864236 | − | 0.503087i | \(-0.167802\pi\) | ||||
0.864236 | + | 0.503087i | \(0.167802\pi\) | |||||||
\(60\) | −4.48346 | −0.578812 | ||||||||
\(61\) | −10.5214 | −1.34712 | −0.673561 | − | 0.739132i | \(-0.735236\pi\) | ||||
−0.673561 | + | 0.739132i | \(0.735236\pi\) | |||||||
\(62\) | 2.54626 | 0.323376 | ||||||||
\(63\) | −1.02990 | −0.129755 | ||||||||
\(64\) | −0.215586 | −0.0269483 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | −7.61102 | −0.936852 | ||||||||
\(67\) | 3.87908 | 0.473905 | 0.236953 | − | 0.971521i | \(-0.423851\pi\) | ||||
0.236953 | + | 0.971521i | \(0.423851\pi\) | |||||||
\(68\) | 26.8351 | 3.25424 | ||||||||
\(69\) | −4.10895 | −0.494659 | ||||||||
\(70\) | −2.62239 | −0.313436 | ||||||||
\(71\) | −2.68065 | −0.318135 | −0.159067 | − | 0.987268i | \(-0.550849\pi\) | ||||
−0.159067 | + | 0.987268i | \(0.550849\pi\) | |||||||
\(72\) | 6.32355 | 0.745237 | ||||||||
\(73\) | 1.90612 | 0.223095 | 0.111547 | − | 0.993759i | \(-0.464419\pi\) | ||||
0.111547 | + | 0.993759i | \(0.464419\pi\) | |||||||
\(74\) | −10.2704 | −1.19391 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −9.25478 | −1.06160 | ||||||||
\(77\) | −3.07846 | −0.350824 | ||||||||
\(78\) | −2.54626 | −0.288308 | ||||||||
\(79\) | 4.03783 | 0.454291 | 0.227145 | − | 0.973861i | \(-0.427061\pi\) | ||||
0.227145 | + | 0.973861i | \(0.427061\pi\) | |||||||
\(80\) | 7.13450 | 0.797662 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.469812 | 0.0518821 | ||||||||
\(83\) | 10.2125 | 1.12096 | 0.560481 | − | 0.828167i | \(-0.310616\pi\) | ||||
0.560481 | + | 0.828167i | \(0.310616\pi\) | |||||||
\(84\) | 4.61751 | 0.503812 | ||||||||
\(85\) | 5.98536 | 0.649204 | ||||||||
\(86\) | −1.45603 | −0.157008 | ||||||||
\(87\) | −2.98050 | −0.319543 | ||||||||
\(88\) | 18.9017 | 2.01493 | ||||||||
\(89\) | 5.50706 | 0.583748 | 0.291874 | − | 0.956457i | \(-0.405721\pi\) | ||||
0.291874 | + | 0.956457i | \(0.405721\pi\) | |||||||
\(90\) | 2.54626 | 0.268400 | ||||||||
\(91\) | −1.02990 | −0.107963 | ||||||||
\(92\) | 18.4223 | 1.92066 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | −23.5416 | −2.42813 | ||||||||
\(95\) | −2.06421 | −0.211783 | ||||||||
\(96\) | −5.51923 | −0.563304 | ||||||||
\(97\) | 14.5645 | 1.47880 | 0.739402 | − | 0.673264i | \(-0.235108\pi\) | ||||
0.739402 | + | 0.673264i | \(0.235108\pi\) | |||||||
\(98\) | −15.1230 | −1.52766 | ||||||||
\(99\) | 2.98909 | 0.300415 | ||||||||
\(100\) | 4.48346 | 0.448346 | ||||||||
\(101\) | 13.1527 | 1.30874 | 0.654371 | − | 0.756174i | \(-0.272934\pi\) | ||||
0.654371 | + | 0.756174i | \(0.272934\pi\) | |||||||
\(102\) | −15.2403 | −1.50902 | ||||||||
\(103\) | 15.5954 | 1.53666 | 0.768328 | − | 0.640056i | \(-0.221089\pi\) | ||||
0.768328 | + | 0.640056i | \(0.221089\pi\) | |||||||
\(104\) | 6.32355 | 0.620075 | ||||||||
\(105\) | 1.02990 | 0.100508 | ||||||||
\(106\) | −15.5742 | −1.51270 | ||||||||
\(107\) | 17.4613 | 1.68805 | 0.844023 | − | 0.536307i | \(-0.180181\pi\) | ||||
0.844023 | + | 0.536307i | \(0.180181\pi\) | |||||||
\(108\) | −4.48346 | −0.431421 | ||||||||
\(109\) | −11.7879 | −1.12908 | −0.564540 | − | 0.825406i | \(-0.690946\pi\) | ||||
−0.564540 | + | 0.825406i | \(0.690946\pi\) | |||||||
\(110\) | 7.61102 | 0.725682 | ||||||||
\(111\) | 4.03351 | 0.382844 | ||||||||
\(112\) | −7.34782 | −0.694303 | ||||||||
\(113\) | 9.33207 | 0.877888 | 0.438944 | − | 0.898514i | \(-0.355353\pi\) | ||||
0.438944 | + | 0.898514i | \(0.355353\pi\) | |||||||
\(114\) | 5.25601 | 0.492271 | ||||||||
\(115\) | 4.10895 | 0.383161 | ||||||||
\(116\) | 13.3629 | 1.24072 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 33.8058 | 3.11208 | ||||||||
\(119\) | −6.16432 | −0.565082 | ||||||||
\(120\) | −6.32355 | −0.577258 | ||||||||
\(121\) | −2.06532 | −0.187757 | ||||||||
\(122\) | −26.7902 | −2.42547 | ||||||||
\(123\) | −0.184510 | −0.0166367 | ||||||||
\(124\) | 4.48346 | 0.402627 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −2.62239 | −0.233621 | ||||||||
\(127\) | −19.2252 | −1.70596 | −0.852980 | − | 0.521944i | \(-0.825207\pi\) | ||||
−0.852980 | + | 0.521944i | \(0.825207\pi\) | |||||||
\(128\) | −11.5874 | −1.02419 | ||||||||
\(129\) | 0.571830 | 0.0503468 | ||||||||
\(130\) | 2.54626 | 0.223322 | ||||||||
\(131\) | 17.5732 | 1.53538 | 0.767690 | − | 0.640821i | \(-0.221406\pi\) | ||||
0.767690 | + | 0.640821i | \(0.221406\pi\) | |||||||
\(132\) | −13.4015 | −1.16645 | ||||||||
\(133\) | 2.12592 | 0.184341 | ||||||||
\(134\) | 9.87717 | 0.853258 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 37.8487 | 3.24550 | ||||||||
\(137\) | 16.0467 | 1.37096 | 0.685480 | − | 0.728092i | \(-0.259592\pi\) | ||||
0.685480 | + | 0.728092i | \(0.259592\pi\) | |||||||
\(138\) | −10.4625 | −0.890624 | ||||||||
\(139\) | −3.71894 | −0.315436 | −0.157718 | − | 0.987484i | \(-0.550414\pi\) | ||||
−0.157718 | + | 0.987484i | \(0.550414\pi\) | |||||||
\(140\) | −4.61751 | −0.390251 | ||||||||
\(141\) | 9.24553 | 0.778614 | ||||||||
\(142\) | −6.82565 | −0.572796 | ||||||||
\(143\) | 2.98909 | 0.249961 | ||||||||
\(144\) | 7.13450 | 0.594542 | ||||||||
\(145\) | 2.98050 | 0.247517 | ||||||||
\(146\) | 4.85349 | 0.401678 | ||||||||
\(147\) | 5.93931 | 0.489866 | ||||||||
\(148\) | −18.0841 | −1.48650 | ||||||||
\(149\) | −7.10280 | −0.581884 | −0.290942 | − | 0.956741i | \(-0.593969\pi\) | ||||
−0.290942 | + | 0.956741i | \(0.593969\pi\) | |||||||
\(150\) | −2.54626 | −0.207902 | ||||||||
\(151\) | 3.51700 | 0.286209 | 0.143105 | − | 0.989708i | \(-0.454291\pi\) | ||||
0.143105 | + | 0.989708i | \(0.454291\pi\) | |||||||
\(152\) | −13.0531 | −1.05875 | ||||||||
\(153\) | 5.98536 | 0.483888 | ||||||||
\(154\) | −7.83858 | −0.631651 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | −4.48346 | −0.358964 | ||||||||
\(157\) | 9.43952 | 0.753356 | 0.376678 | − | 0.926344i | \(-0.377066\pi\) | ||||
0.376678 | + | 0.926344i | \(0.377066\pi\) | |||||||
\(158\) | 10.2814 | 0.817942 | ||||||||
\(159\) | 6.11650 | 0.485070 | ||||||||
\(160\) | 5.51923 | 0.436333 | ||||||||
\(161\) | −4.23180 | −0.333513 | ||||||||
\(162\) | 2.54626 | 0.200053 | ||||||||
\(163\) | −23.4792 | −1.83903 | −0.919517 | − | 0.393050i | \(-0.871420\pi\) | ||||
−0.919517 | + | 0.393050i | \(0.871420\pi\) | |||||||
\(164\) | 0.827245 | 0.0645970 | ||||||||
\(165\) | −2.98909 | −0.232701 | ||||||||
\(166\) | 26.0036 | 2.01827 | ||||||||
\(167\) | −16.5512 | −1.28077 | −0.640384 | − | 0.768055i | \(-0.721225\pi\) | ||||
−0.640384 | + | 0.768055i | \(0.721225\pi\) | |||||||
\(168\) | 6.51262 | 0.502459 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 15.2403 | 1.16888 | ||||||||
\(171\) | −2.06421 | −0.157854 | ||||||||
\(172\) | −2.56378 | −0.195486 | ||||||||
\(173\) | −10.4571 | −0.795037 | −0.397519 | − | 0.917594i | \(-0.630129\pi\) | ||||
−0.397519 | + | 0.917594i | \(0.630129\pi\) | |||||||
\(174\) | −7.58913 | −0.575331 | ||||||||
\(175\) | −1.02990 | −0.0778530 | ||||||||
\(176\) | 21.3257 | 1.60748 | ||||||||
\(177\) | −13.2766 | −0.997934 | ||||||||
\(178\) | 14.0224 | 1.05103 | ||||||||
\(179\) | 17.3282 | 1.29517 | 0.647585 | − | 0.761994i | \(-0.275779\pi\) | ||||
0.647585 | + | 0.761994i | \(0.275779\pi\) | |||||||
\(180\) | 4.48346 | 0.334177 | ||||||||
\(181\) | −19.9080 | −1.47975 | −0.739877 | − | 0.672743i | \(-0.765116\pi\) | ||||
−0.739877 | + | 0.672743i | \(0.765116\pi\) | |||||||
\(182\) | −2.62239 | −0.194385 | ||||||||
\(183\) | 10.5214 | 0.777761 | ||||||||
\(184\) | 25.9831 | 1.91550 | ||||||||
\(185\) | −4.03351 | −0.296550 | ||||||||
\(186\) | −2.54626 | −0.186701 | ||||||||
\(187\) | 17.8908 | 1.30831 | ||||||||
\(188\) | −41.4520 | −3.02319 | ||||||||
\(189\) | 1.02990 | 0.0749141 | ||||||||
\(190\) | −5.25601 | −0.381311 | ||||||||
\(191\) | 0.704657 | 0.0509872 | 0.0254936 | − | 0.999675i | \(-0.491884\pi\) | ||||
0.0254936 | + | 0.999675i | \(0.491884\pi\) | |||||||
\(192\) | 0.215586 | 0.0155586 | ||||||||
\(193\) | −9.84575 | −0.708713 | −0.354356 | − | 0.935110i | \(-0.615300\pi\) | ||||
−0.354356 | + | 0.935110i | \(0.615300\pi\) | |||||||
\(194\) | 37.0852 | 2.66256 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | −26.6287 | −1.90205 | ||||||||
\(197\) | −21.8244 | −1.55493 | −0.777463 | − | 0.628928i | \(-0.783494\pi\) | ||||
−0.777463 | + | 0.628928i | \(0.783494\pi\) | |||||||
\(198\) | 7.61102 | 0.540892 | ||||||||
\(199\) | 6.36012 | 0.450857 | 0.225429 | − | 0.974260i | \(-0.427622\pi\) | ||||
0.225429 | + | 0.974260i | \(0.427622\pi\) | |||||||
\(200\) | 6.32355 | 0.447142 | ||||||||
\(201\) | −3.87908 | −0.273609 | ||||||||
\(202\) | 33.4902 | 2.35636 | ||||||||
\(203\) | −3.06961 | −0.215444 | ||||||||
\(204\) | −26.8351 | −1.87884 | ||||||||
\(205\) | 0.184510 | 0.0128868 | ||||||||
\(206\) | 39.7099 | 2.76672 | ||||||||
\(207\) | 4.10895 | 0.285592 | ||||||||
\(208\) | 7.13450 | 0.494689 | ||||||||
\(209\) | −6.17010 | −0.426795 | ||||||||
\(210\) | 2.62239 | 0.180962 | ||||||||
\(211\) | −6.35199 | −0.437289 | −0.218645 | − | 0.975805i | \(-0.570164\pi\) | ||||
−0.218645 | + | 0.975805i | \(0.570164\pi\) | |||||||
\(212\) | −27.4231 | −1.88342 | ||||||||
\(213\) | 2.68065 | 0.183675 | ||||||||
\(214\) | 44.4610 | 3.03929 | ||||||||
\(215\) | −0.571830 | −0.0389985 | ||||||||
\(216\) | −6.32355 | −0.430263 | ||||||||
\(217\) | −1.02990 | −0.0699141 | ||||||||
\(218\) | −30.0152 | −2.03288 | ||||||||
\(219\) | −1.90612 | −0.128804 | ||||||||
\(220\) | 13.4015 | 0.903528 | ||||||||
\(221\) | 5.98536 | 0.402619 | ||||||||
\(222\) | 10.2704 | 0.689303 | ||||||||
\(223\) | −4.60136 | −0.308130 | −0.154065 | − | 0.988061i | \(-0.549236\pi\) | ||||
−0.154065 | + | 0.988061i | \(0.549236\pi\) | |||||||
\(224\) | −5.68425 | −0.379795 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 23.7619 | 1.58062 | ||||||||
\(227\) | 25.2676 | 1.67707 | 0.838533 | − | 0.544851i | \(-0.183414\pi\) | ||||
0.838533 | + | 0.544851i | \(0.183414\pi\) | |||||||
\(228\) | 9.25478 | 0.612913 | ||||||||
\(229\) | −28.8995 | −1.90973 | −0.954867 | − | 0.297033i | \(-0.904003\pi\) | ||||
−0.954867 | + | 0.297033i | \(0.904003\pi\) | |||||||
\(230\) | 10.4625 | 0.689875 | ||||||||
\(231\) | 3.07846 | 0.202548 | ||||||||
\(232\) | 18.8473 | 1.23739 | ||||||||
\(233\) | −18.4093 | −1.20603 | −0.603017 | − | 0.797729i | \(-0.706035\pi\) | ||||
−0.603017 | + | 0.797729i | \(0.706035\pi\) | |||||||
\(234\) | 2.54626 | 0.166454 | ||||||||
\(235\) | −9.24553 | −0.603112 | ||||||||
\(236\) | 59.5253 | 3.87477 | ||||||||
\(237\) | −4.03783 | −0.262285 | ||||||||
\(238\) | −15.6960 | −1.01742 | ||||||||
\(239\) | −3.95948 | −0.256117 | −0.128059 | − | 0.991767i | \(-0.540875\pi\) | ||||
−0.128059 | + | 0.991767i | \(0.540875\pi\) | |||||||
\(240\) | −7.13450 | −0.460530 | ||||||||
\(241\) | 22.2978 | 1.43633 | 0.718164 | − | 0.695874i | \(-0.244983\pi\) | ||||
0.718164 | + | 0.695874i | \(0.244983\pi\) | |||||||
\(242\) | −5.25885 | −0.338052 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −47.1721 | −3.01988 | ||||||||
\(245\) | −5.93931 | −0.379448 | ||||||||
\(246\) | −0.469812 | −0.0299541 | ||||||||
\(247\) | −2.06421 | −0.131342 | ||||||||
\(248\) | 6.32355 | 0.401546 | ||||||||
\(249\) | −10.2125 | −0.647188 | ||||||||
\(250\) | 2.54626 | 0.161040 | ||||||||
\(251\) | 9.88327 | 0.623826 | 0.311913 | − | 0.950111i | \(-0.399030\pi\) | ||||
0.311913 | + | 0.950111i | \(0.399030\pi\) | |||||||
\(252\) | −4.61751 | −0.290876 | ||||||||
\(253\) | 12.2820 | 0.772164 | ||||||||
\(254\) | −48.9524 | −3.07155 | ||||||||
\(255\) | −5.98536 | −0.374818 | ||||||||
\(256\) | −29.0734 | −1.81709 | ||||||||
\(257\) | 16.4824 | 1.02815 | 0.514073 | − | 0.857747i | \(-0.328136\pi\) | ||||
0.514073 | + | 0.857747i | \(0.328136\pi\) | |||||||
\(258\) | 1.45603 | 0.0906484 | ||||||||
\(259\) | 4.15411 | 0.258124 | ||||||||
\(260\) | 4.48346 | 0.278052 | ||||||||
\(261\) | 2.98050 | 0.184488 | ||||||||
\(262\) | 44.7461 | 2.76442 | ||||||||
\(263\) | −26.5559 | −1.63750 | −0.818752 | − | 0.574147i | \(-0.805334\pi\) | ||||
−0.818752 | + | 0.574147i | \(0.805334\pi\) | |||||||
\(264\) | −18.9017 | −1.16332 | ||||||||
\(265\) | −6.11650 | −0.375733 | ||||||||
\(266\) | 5.41316 | 0.331902 | ||||||||
\(267\) | −5.50706 | −0.337027 | ||||||||
\(268\) | 17.3917 | 1.06237 | ||||||||
\(269\) | −17.0294 | −1.03830 | −0.519151 | − | 0.854683i | \(-0.673752\pi\) | ||||
−0.519151 | + | 0.854683i | \(0.673752\pi\) | |||||||
\(270\) | −2.54626 | −0.154961 | ||||||||
\(271\) | −16.0825 | −0.976945 | −0.488473 | − | 0.872579i | \(-0.662446\pi\) | ||||
−0.488473 | + | 0.872579i | \(0.662446\pi\) | |||||||
\(272\) | 42.7026 | 2.58922 | ||||||||
\(273\) | 1.02990 | 0.0623323 | ||||||||
\(274\) | 40.8591 | 2.46839 | ||||||||
\(275\) | 2.98909 | 0.180249 | ||||||||
\(276\) | −18.4223 | −1.10889 | ||||||||
\(277\) | −14.3164 | −0.860191 | −0.430095 | − | 0.902783i | \(-0.641520\pi\) | ||||
−0.430095 | + | 0.902783i | \(0.641520\pi\) | |||||||
\(278\) | −9.46940 | −0.567937 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | −6.51262 | −0.389203 | ||||||||
\(281\) | −1.36079 | −0.0811779 | −0.0405889 | − | 0.999176i | \(-0.512923\pi\) | ||||
−0.0405889 | + | 0.999176i | \(0.512923\pi\) | |||||||
\(282\) | 23.5416 | 1.40188 | ||||||||
\(283\) | −17.6046 | −1.04648 | −0.523241 | − | 0.852185i | \(-0.675277\pi\) | ||||
−0.523241 | + | 0.852185i | \(0.675277\pi\) | |||||||
\(284\) | −12.0186 | −0.713173 | ||||||||
\(285\) | 2.06421 | 0.122273 | ||||||||
\(286\) | 7.61102 | 0.450049 | ||||||||
\(287\) | −0.190027 | −0.0112169 | ||||||||
\(288\) | 5.51923 | 0.325224 | ||||||||
\(289\) | 18.8246 | 1.10733 | ||||||||
\(290\) | 7.58913 | 0.445649 | ||||||||
\(291\) | −14.5645 | −0.853788 | ||||||||
\(292\) | 8.54602 | 0.500118 | ||||||||
\(293\) | 24.1496 | 1.41084 | 0.705419 | − | 0.708791i | \(-0.250759\pi\) | ||||
0.705419 | + | 0.708791i | \(0.250759\pi\) | |||||||
\(294\) | 15.1230 | 0.881994 | ||||||||
\(295\) | 13.2766 | 0.772996 | ||||||||
\(296\) | −25.5061 | −1.48251 | ||||||||
\(297\) | −2.98909 | −0.173445 | ||||||||
\(298\) | −18.0856 | −1.04767 | ||||||||
\(299\) | 4.10895 | 0.237627 | ||||||||
\(300\) | −4.48346 | −0.258853 | ||||||||
\(301\) | 0.588927 | 0.0339452 | ||||||||
\(302\) | 8.95520 | 0.515314 | ||||||||
\(303\) | −13.1527 | −0.755602 | ||||||||
\(304\) | −14.7271 | −0.844656 | ||||||||
\(305\) | −10.5214 | −0.602451 | ||||||||
\(306\) | 15.2403 | 0.871231 | ||||||||
\(307\) | 14.1858 | 0.809627 | 0.404814 | − | 0.914399i | \(-0.367336\pi\) | ||||
0.404814 | + | 0.914399i | \(0.367336\pi\) | |||||||
\(308\) | −13.8022 | −0.786452 | ||||||||
\(309\) | −15.5954 | −0.887189 | ||||||||
\(310\) | 2.54626 | 0.144618 | ||||||||
\(311\) | −22.0702 | −1.25149 | −0.625744 | − | 0.780029i | \(-0.715204\pi\) | ||||
−0.625744 | + | 0.780029i | \(0.715204\pi\) | |||||||
\(312\) | −6.32355 | −0.358000 | ||||||||
\(313\) | −30.5339 | −1.72588 | −0.862940 | − | 0.505307i | \(-0.831379\pi\) | ||||
−0.862940 | + | 0.505307i | \(0.831379\pi\) | |||||||
\(314\) | 24.0355 | 1.35640 | ||||||||
\(315\) | −1.02990 | −0.0580282 | ||||||||
\(316\) | 18.1034 | 1.01840 | ||||||||
\(317\) | 10.7132 | 0.601712 | 0.300856 | − | 0.953670i | \(-0.402728\pi\) | ||||
0.300856 | + | 0.953670i | \(0.402728\pi\) | |||||||
\(318\) | 15.5742 | 0.873359 | ||||||||
\(319\) | 8.90898 | 0.498807 | ||||||||
\(320\) | −0.215586 | −0.0120516 | ||||||||
\(321\) | −17.4613 | −0.974594 | ||||||||
\(322\) | −10.7753 | −0.600483 | ||||||||
\(323\) | −12.3550 | −0.687452 | ||||||||
\(324\) | 4.48346 | 0.249081 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | −59.7843 | −3.31115 | ||||||||
\(327\) | 11.7879 | 0.651874 | ||||||||
\(328\) | 1.16676 | 0.0644236 | ||||||||
\(329\) | 9.52196 | 0.524963 | ||||||||
\(330\) | −7.61102 | −0.418973 | ||||||||
\(331\) | −17.4529 | −0.959299 | −0.479650 | − | 0.877460i | \(-0.659236\pi\) | ||||
−0.479650 | + | 0.877460i | \(0.659236\pi\) | |||||||
\(332\) | 45.7871 | 2.51290 | ||||||||
\(333\) | −4.03351 | −0.221035 | ||||||||
\(334\) | −42.1437 | −2.30600 | ||||||||
\(335\) | 3.87908 | 0.211937 | ||||||||
\(336\) | 7.34782 | 0.400856 | ||||||||
\(337\) | −18.0176 | −0.981480 | −0.490740 | − | 0.871306i | \(-0.663273\pi\) | ||||
−0.490740 | + | 0.871306i | \(0.663273\pi\) | |||||||
\(338\) | 2.54626 | 0.138499 | ||||||||
\(339\) | −9.33207 | −0.506849 | ||||||||
\(340\) | 26.8351 | 1.45534 | ||||||||
\(341\) | 2.98909 | 0.161868 | ||||||||
\(342\) | −5.25601 | −0.284213 | ||||||||
\(343\) | 13.3262 | 0.719546 | ||||||||
\(344\) | −3.61599 | −0.194961 | ||||||||
\(345\) | −4.10895 | −0.221218 | ||||||||
\(346\) | −26.6265 | −1.43145 | ||||||||
\(347\) | 23.0409 | 1.23690 | 0.618449 | − | 0.785825i | \(-0.287761\pi\) | ||||
0.618449 | + | 0.785825i | \(0.287761\pi\) | |||||||
\(348\) | −13.3629 | −0.716329 | ||||||||
\(349\) | −20.3725 | −1.09052 | −0.545258 | − | 0.838268i | \(-0.683568\pi\) | ||||
−0.545258 | + | 0.838268i | \(0.683568\pi\) | |||||||
\(350\) | −2.62239 | −0.140173 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 16.4975 | 0.879319 | ||||||||
\(353\) | 15.1058 | 0.803998 | 0.401999 | − | 0.915640i | \(-0.368315\pi\) | ||||
0.401999 | + | 0.915640i | \(0.368315\pi\) | |||||||
\(354\) | −33.8058 | −1.79676 | ||||||||
\(355\) | −2.68065 | −0.142274 | ||||||||
\(356\) | 24.6907 | 1.30860 | ||||||||
\(357\) | 6.16432 | 0.326250 | ||||||||
\(358\) | 44.1221 | 2.33193 | ||||||||
\(359\) | −23.3231 | −1.23094 | −0.615472 | − | 0.788159i | \(-0.711035\pi\) | ||||
−0.615472 | + | 0.788159i | \(0.711035\pi\) | |||||||
\(360\) | 6.32355 | 0.333280 | ||||||||
\(361\) | −14.7391 | −0.775740 | ||||||||
\(362\) | −50.6911 | −2.66427 | ||||||||
\(363\) | 2.06532 | 0.108401 | ||||||||
\(364\) | −4.61751 | −0.242023 | ||||||||
\(365\) | 1.90612 | 0.0997709 | ||||||||
\(366\) | 26.7902 | 1.40034 | ||||||||
\(367\) | 30.5957 | 1.59708 | 0.798541 | − | 0.601940i | \(-0.205605\pi\) | ||||
0.798541 | + | 0.601940i | \(0.205605\pi\) | |||||||
\(368\) | 29.3153 | 1.52817 | ||||||||
\(369\) | 0.184510 | 0.00960523 | ||||||||
\(370\) | −10.2704 | −0.533932 | ||||||||
\(371\) | 6.29937 | 0.327047 | ||||||||
\(372\) | −4.48346 | −0.232457 | ||||||||
\(373\) | −25.9370 | −1.34297 | −0.671483 | − | 0.741020i | \(-0.734342\pi\) | ||||
−0.671483 | + | 0.741020i | \(0.734342\pi\) | |||||||
\(374\) | 45.5547 | 2.35558 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −58.4645 | −3.01508 | ||||||||
\(377\) | 2.98050 | 0.153503 | ||||||||
\(378\) | 2.62239 | 0.134881 | ||||||||
\(379\) | 36.8095 | 1.89078 | 0.945388 | − | 0.325946i | \(-0.105683\pi\) | ||||
0.945388 | + | 0.325946i | \(0.105683\pi\) | |||||||
\(380\) | −9.25478 | −0.474760 | ||||||||
\(381\) | 19.2252 | 0.984936 | ||||||||
\(382\) | 1.79424 | 0.0918014 | ||||||||
\(383\) | −13.7763 | −0.703938 | −0.351969 | − | 0.936012i | \(-0.614488\pi\) | ||||
−0.351969 | + | 0.936012i | \(0.614488\pi\) | |||||||
\(384\) | 11.5874 | 0.591317 | ||||||||
\(385\) | −3.07846 | −0.156893 | ||||||||
\(386\) | −25.0699 | −1.27602 | ||||||||
\(387\) | −0.571830 | −0.0290677 | ||||||||
\(388\) | 65.2995 | 3.31508 | ||||||||
\(389\) | −11.3914 | −0.577565 | −0.288783 | − | 0.957395i | \(-0.593250\pi\) | ||||
−0.288783 | + | 0.957395i | \(0.593250\pi\) | |||||||
\(390\) | −2.54626 | −0.128935 | ||||||||
\(391\) | 24.5935 | 1.24375 | ||||||||
\(392\) | −37.5575 | −1.89694 | ||||||||
\(393\) | −17.5732 | −0.886452 | ||||||||
\(394\) | −55.5708 | −2.79962 | ||||||||
\(395\) | 4.03783 | 0.203165 | ||||||||
\(396\) | 13.4015 | 0.673450 | ||||||||
\(397\) | 12.8893 | 0.646897 | 0.323449 | − | 0.946246i | \(-0.395158\pi\) | ||||
0.323449 | + | 0.946246i | \(0.395158\pi\) | |||||||
\(398\) | 16.1946 | 0.811760 | ||||||||
\(399\) | −2.12592 | −0.106429 | ||||||||
\(400\) | 7.13450 | 0.356725 | ||||||||
\(401\) | −20.9202 | −1.04470 | −0.522352 | − | 0.852730i | \(-0.674945\pi\) | ||||
−0.522352 | + | 0.852730i | \(0.674945\pi\) | |||||||
\(402\) | −9.87717 | −0.492629 | ||||||||
\(403\) | 1.00000 | 0.0498135 | ||||||||
\(404\) | 58.9696 | 2.93385 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −7.81604 | −0.387903 | ||||||||
\(407\) | −12.0565 | −0.597620 | ||||||||
\(408\) | −37.8487 | −1.87379 | ||||||||
\(409\) | −28.3919 | −1.40389 | −0.701945 | − | 0.712231i | \(-0.747685\pi\) | ||||
−0.701945 | + | 0.712231i | \(0.747685\pi\) | |||||||
\(410\) | 0.469812 | 0.0232024 | ||||||||
\(411\) | −16.0467 | −0.791524 | ||||||||
\(412\) | 69.9212 | 3.44477 | ||||||||
\(413\) | −13.6736 | −0.672834 | ||||||||
\(414\) | 10.4625 | 0.514202 | ||||||||
\(415\) | 10.2125 | 0.501310 | ||||||||
\(416\) | 5.51923 | 0.270603 | ||||||||
\(417\) | 3.71894 | 0.182117 | ||||||||
\(418\) | −15.7107 | −0.768436 | ||||||||
\(419\) | 2.40036 | 0.117265 | 0.0586326 | − | 0.998280i | \(-0.481326\pi\) | ||||
0.0586326 | + | 0.998280i | \(0.481326\pi\) | |||||||
\(420\) | 4.61751 | 0.225312 | ||||||||
\(421\) | −3.44590 | −0.167943 | −0.0839714 | − | 0.996468i | \(-0.526760\pi\) | ||||
−0.0839714 | + | 0.996468i | \(0.526760\pi\) | |||||||
\(422\) | −16.1738 | −0.787331 | ||||||||
\(423\) | −9.24553 | −0.449533 | ||||||||
\(424\) | −38.6780 | −1.87837 | ||||||||
\(425\) | 5.98536 | 0.290333 | ||||||||
\(426\) | 6.82565 | 0.330704 | ||||||||
\(427\) | 10.8359 | 0.524388 | ||||||||
\(428\) | 78.2870 | 3.78414 | ||||||||
\(429\) | −2.98909 | −0.144315 | ||||||||
\(430\) | −1.45603 | −0.0702160 | ||||||||
\(431\) | 7.92699 | 0.381830 | 0.190915 | − | 0.981607i | \(-0.438855\pi\) | ||||
0.190915 | + | 0.981607i | \(0.438855\pi\) | |||||||
\(432\) | −7.13450 | −0.343259 | ||||||||
\(433\) | −18.2173 | −0.875467 | −0.437734 | − | 0.899105i | \(-0.644219\pi\) | ||||
−0.437734 | + | 0.899105i | \(0.644219\pi\) | |||||||
\(434\) | −2.62239 | −0.125879 | ||||||||
\(435\) | −2.98050 | −0.142904 | ||||||||
\(436\) | −52.8507 | −2.53109 | ||||||||
\(437\) | −8.48171 | −0.405735 | ||||||||
\(438\) | −4.85349 | −0.231909 | ||||||||
\(439\) | −14.8335 | −0.707964 | −0.353982 | − | 0.935252i | \(-0.615173\pi\) | ||||
−0.353982 | + | 0.935252i | \(0.615173\pi\) | |||||||
\(440\) | 18.9017 | 0.901102 | ||||||||
\(441\) | −5.93931 | −0.282824 | ||||||||
\(442\) | 15.2403 | 0.724908 | ||||||||
\(443\) | 3.05615 | 0.145202 | 0.0726010 | − | 0.997361i | \(-0.476870\pi\) | ||||
0.0726010 | + | 0.997361i | \(0.476870\pi\) | |||||||
\(444\) | 18.0841 | 0.858233 | ||||||||
\(445\) | 5.50706 | 0.261060 | ||||||||
\(446\) | −11.7163 | −0.554781 | ||||||||
\(447\) | 7.10280 | 0.335951 | ||||||||
\(448\) | 0.222032 | 0.0104900 | ||||||||
\(449\) | −15.2214 | −0.718345 | −0.359172 | − | 0.933271i | \(-0.616941\pi\) | ||||
−0.359172 | + | 0.933271i | \(0.616941\pi\) | |||||||
\(450\) | 2.54626 | 0.120032 | ||||||||
\(451\) | 0.551519 | 0.0259700 | ||||||||
\(452\) | 41.8400 | 1.96799 | ||||||||
\(453\) | −3.51700 | −0.165243 | ||||||||
\(454\) | 64.3379 | 3.01953 | ||||||||
\(455\) | −1.02990 | −0.0482824 | ||||||||
\(456\) | 13.0531 | 0.611268 | ||||||||
\(457\) | 27.0921 | 1.26732 | 0.633659 | − | 0.773613i | \(-0.281552\pi\) | ||||
0.633659 | + | 0.773613i | \(0.281552\pi\) | |||||||
\(458\) | −73.5858 | −3.43844 | ||||||||
\(459\) | −5.98536 | −0.279373 | ||||||||
\(460\) | 18.4223 | 0.858944 | ||||||||
\(461\) | 2.23692 | 0.104184 | 0.0520919 | − | 0.998642i | \(-0.483411\pi\) | ||||
0.0520919 | + | 0.998642i | \(0.483411\pi\) | |||||||
\(462\) | 7.83858 | 0.364684 | ||||||||
\(463\) | 29.5767 | 1.37454 | 0.687272 | − | 0.726400i | \(-0.258808\pi\) | ||||
0.687272 | + | 0.726400i | \(0.258808\pi\) | |||||||
\(464\) | 21.2644 | 0.987173 | ||||||||
\(465\) | −1.00000 | −0.0463739 | ||||||||
\(466\) | −46.8749 | −2.17144 | ||||||||
\(467\) | 8.76483 | 0.405588 | 0.202794 | − | 0.979221i | \(-0.434998\pi\) | ||||
0.202794 | + | 0.979221i | \(0.434998\pi\) | |||||||
\(468\) | 4.48346 | 0.207248 | ||||||||
\(469\) | −3.99506 | −0.184475 | ||||||||
\(470\) | −23.5416 | −1.08589 | ||||||||
\(471\) | −9.43952 | −0.434950 | ||||||||
\(472\) | 83.9555 | 3.86436 | ||||||||
\(473\) | −1.70925 | −0.0785915 | ||||||||
\(474\) | −10.2814 | −0.472239 | ||||||||
\(475\) | −2.06421 | −0.0947122 | ||||||||
\(476\) | −27.6375 | −1.26676 | ||||||||
\(477\) | −6.11650 | −0.280055 | ||||||||
\(478\) | −10.0819 | −0.461134 | ||||||||
\(479\) | 18.6669 | 0.852913 | 0.426457 | − | 0.904508i | \(-0.359762\pi\) | ||||
0.426457 | + | 0.904508i | \(0.359762\pi\) | |||||||
\(480\) | −5.51923 | −0.251917 | ||||||||
\(481\) | −4.03351 | −0.183912 | ||||||||
\(482\) | 56.7761 | 2.58608 | ||||||||
\(483\) | 4.23180 | 0.192554 | ||||||||
\(484\) | −9.25979 | −0.420900 | ||||||||
\(485\) | 14.5645 | 0.661342 | ||||||||
\(486\) | −2.54626 | −0.115501 | ||||||||
\(487\) | 36.4892 | 1.65348 | 0.826742 | − | 0.562581i | \(-0.190191\pi\) | ||||
0.826742 | + | 0.562581i | \(0.190191\pi\) | |||||||
\(488\) | −66.5323 | −3.01178 | ||||||||
\(489\) | 23.4792 | 1.06177 | ||||||||
\(490\) | −15.1230 | −0.683190 | ||||||||
\(491\) | 31.9476 | 1.44177 | 0.720887 | − | 0.693052i | \(-0.243735\pi\) | ||||
0.720887 | + | 0.693052i | \(0.243735\pi\) | |||||||
\(492\) | −0.827245 | −0.0372951 | ||||||||
\(493\) | 17.8394 | 0.803444 | ||||||||
\(494\) | −5.25601 | −0.236479 | ||||||||
\(495\) | 2.98909 | 0.134350 | ||||||||
\(496\) | 7.13450 | 0.320349 | ||||||||
\(497\) | 2.76080 | 0.123839 | ||||||||
\(498\) | −26.0036 | −1.16525 | ||||||||
\(499\) | 15.6012 | 0.698406 | 0.349203 | − | 0.937047i | \(-0.386452\pi\) | ||||
0.349203 | + | 0.937047i | \(0.386452\pi\) | |||||||
\(500\) | 4.48346 | 0.200506 | ||||||||
\(501\) | 16.5512 | 0.739452 | ||||||||
\(502\) | 25.1654 | 1.12319 | ||||||||
\(503\) | −30.8788 | −1.37682 | −0.688409 | − | 0.725323i | \(-0.741690\pi\) | ||||
−0.688409 | + | 0.725323i | \(0.741690\pi\) | |||||||
\(504\) | −6.51262 | −0.290095 | ||||||||
\(505\) | 13.1527 | 0.585287 | ||||||||
\(506\) | 31.2733 | 1.39027 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −86.1954 | −3.82430 | ||||||||
\(509\) | −26.7054 | −1.18370 | −0.591848 | − | 0.806049i | \(-0.701602\pi\) | ||||
−0.591848 | + | 0.806049i | \(0.701602\pi\) | |||||||
\(510\) | −15.2403 | −0.674853 | ||||||||
\(511\) | −1.96311 | −0.0868430 | ||||||||
\(512\) | −50.8538 | −2.24744 | ||||||||
\(513\) | 2.06421 | 0.0911369 | ||||||||
\(514\) | 41.9686 | 1.85116 | ||||||||
\(515\) | 15.5954 | 0.687214 | ||||||||
\(516\) | 2.56378 | 0.112864 | ||||||||
\(517\) | −27.6357 | −1.21542 | ||||||||
\(518\) | 10.5775 | 0.464747 | ||||||||
\(519\) | 10.4571 | 0.459015 | ||||||||
\(520\) | 6.32355 | 0.277306 | ||||||||
\(521\) | 8.72083 | 0.382066 | 0.191033 | − | 0.981584i | \(-0.438816\pi\) | ||||
0.191033 | + | 0.981584i | \(0.438816\pi\) | |||||||
\(522\) | 7.58913 | 0.332167 | ||||||||
\(523\) | −11.9681 | −0.523329 | −0.261665 | − | 0.965159i | \(-0.584271\pi\) | ||||
−0.261665 | + | 0.965159i | \(0.584271\pi\) | |||||||
\(524\) | 78.7889 | 3.44191 | ||||||||
\(525\) | 1.02990 | 0.0449485 | ||||||||
\(526\) | −67.6182 | −2.94830 | ||||||||
\(527\) | 5.98536 | 0.260727 | ||||||||
\(528\) | −21.3257 | −0.928082 | ||||||||
\(529\) | −6.11655 | −0.265937 | ||||||||
\(530\) | −15.5742 | −0.676501 | ||||||||
\(531\) | 13.2766 | 0.576157 | ||||||||
\(532\) | 9.53149 | 0.413243 | ||||||||
\(533\) | 0.184510 | 0.00799203 | ||||||||
\(534\) | −14.0224 | −0.606810 | ||||||||
\(535\) | 17.4613 | 0.754917 | ||||||||
\(536\) | 24.5296 | 1.05952 | ||||||||
\(537\) | −17.3282 | −0.747766 | ||||||||
\(538\) | −43.3614 | −1.86944 | ||||||||
\(539\) | −17.7531 | −0.764682 | ||||||||
\(540\) | −4.48346 | −0.192937 | ||||||||
\(541\) | 14.3912 | 0.618725 | 0.309363 | − | 0.950944i | \(-0.399884\pi\) | ||||
0.309363 | + | 0.950944i | \(0.399884\pi\) | |||||||
\(542\) | −40.9504 | −1.75897 | ||||||||
\(543\) | 19.9080 | 0.854336 | ||||||||
\(544\) | 33.0346 | 1.41635 | ||||||||
\(545\) | −11.7879 | −0.504939 | ||||||||
\(546\) | 2.62239 | 0.112228 | ||||||||
\(547\) | 4.62695 | 0.197834 | 0.0989171 | − | 0.995096i | \(-0.468462\pi\) | ||||
0.0989171 | + | 0.995096i | \(0.468462\pi\) | |||||||
\(548\) | 71.9446 | 3.07332 | ||||||||
\(549\) | −10.5214 | −0.449041 | ||||||||
\(550\) | 7.61102 | 0.324535 | ||||||||
\(551\) | −6.15236 | −0.262099 | ||||||||
\(552\) | −25.9831 | −1.10592 | ||||||||
\(553\) | −4.15855 | −0.176840 | ||||||||
\(554\) | −36.4534 | −1.54876 | ||||||||
\(555\) | 4.03351 | 0.171213 | ||||||||
\(556\) | −16.6737 | −0.707123 | ||||||||
\(557\) | −25.1268 | −1.06466 | −0.532329 | − | 0.846538i | \(-0.678683\pi\) | ||||
−0.532329 | + | 0.846538i | \(0.678683\pi\) | |||||||
\(558\) | 2.54626 | 0.107792 | ||||||||
\(559\) | −0.571830 | −0.0241858 | ||||||||
\(560\) | −7.34782 | −0.310502 | ||||||||
\(561\) | −17.8908 | −0.755351 | ||||||||
\(562\) | −3.46493 | −0.146159 | ||||||||
\(563\) | −33.3074 | −1.40374 | −0.701870 | − | 0.712305i | \(-0.747651\pi\) | ||||
−0.701870 | + | 0.712305i | \(0.747651\pi\) | |||||||
\(564\) | 41.4520 | 1.74544 | ||||||||
\(565\) | 9.33207 | 0.392603 | ||||||||
\(566\) | −44.8258 | −1.88417 | ||||||||
\(567\) | −1.02990 | −0.0432517 | ||||||||
\(568\) | −16.9512 | −0.711258 | ||||||||
\(569\) | −43.8888 | −1.83991 | −0.919957 | − | 0.392019i | \(-0.871777\pi\) | ||||
−0.919957 | + | 0.392019i | \(0.871777\pi\) | |||||||
\(570\) | 5.25601 | 0.220150 | ||||||||
\(571\) | −31.1265 | −1.30260 | −0.651301 | − | 0.758820i | \(-0.725776\pi\) | ||||
−0.651301 | + | 0.758820i | \(0.725776\pi\) | |||||||
\(572\) | 13.4015 | 0.560344 | ||||||||
\(573\) | −0.704657 | −0.0294375 | ||||||||
\(574\) | −0.483859 | −0.0201959 | ||||||||
\(575\) | 4.10895 | 0.171355 | ||||||||
\(576\) | −0.215586 | −0.00898277 | ||||||||
\(577\) | 26.1014 | 1.08661 | 0.543307 | − | 0.839534i | \(-0.317172\pi\) | ||||
0.543307 | + | 0.839534i | \(0.317172\pi\) | |||||||
\(578\) | 47.9323 | 1.99372 | ||||||||
\(579\) | 9.84575 | 0.409175 | ||||||||
\(580\) | 13.3629 | 0.554866 | ||||||||
\(581\) | −10.5178 | −0.436352 | ||||||||
\(582\) | −37.0852 | −1.53723 | ||||||||
\(583\) | −18.2828 | −0.757195 | ||||||||
\(584\) | 12.0534 | 0.498775 | ||||||||
\(585\) | 1.00000 | 0.0413449 | ||||||||
\(586\) | 61.4914 | 2.54019 | ||||||||
\(587\) | −26.8276 | −1.10729 | −0.553647 | − | 0.832752i | \(-0.686764\pi\) | ||||
−0.553647 | + | 0.832752i | \(0.686764\pi\) | |||||||
\(588\) | 26.6287 | 1.09815 | ||||||||
\(589\) | −2.06421 | −0.0850541 | ||||||||
\(590\) | 33.8058 | 1.39176 | ||||||||
\(591\) | 21.8244 | 0.897737 | ||||||||
\(592\) | −28.7771 | −1.18273 | ||||||||
\(593\) | −21.1052 | −0.866688 | −0.433344 | − | 0.901229i | \(-0.642667\pi\) | ||||
−0.433344 | + | 0.901229i | \(0.642667\pi\) | |||||||
\(594\) | −7.61102 | −0.312284 | ||||||||
\(595\) | −6.16432 | −0.252712 | ||||||||
\(596\) | −31.8451 | −1.30443 | ||||||||
\(597\) | −6.36012 | −0.260302 | ||||||||
\(598\) | 10.4625 | 0.427842 | ||||||||
\(599\) | 3.19247 | 0.130441 | 0.0652204 | − | 0.997871i | \(-0.479225\pi\) | ||||
0.0652204 | + | 0.997871i | \(0.479225\pi\) | |||||||
\(600\) | −6.32355 | −0.258158 | ||||||||
\(601\) | −11.8287 | −0.482501 | −0.241251 | − | 0.970463i | \(-0.577558\pi\) | ||||
−0.241251 | + | 0.970463i | \(0.577558\pi\) | |||||||
\(602\) | 1.49956 | 0.0611176 | ||||||||
\(603\) | 3.87908 | 0.157968 | ||||||||
\(604\) | 15.7683 | 0.641604 | ||||||||
\(605\) | −2.06532 | −0.0839673 | ||||||||
\(606\) | −33.4902 | −1.36045 | ||||||||
\(607\) | −27.1084 | −1.10030 | −0.550149 | − | 0.835067i | \(-0.685429\pi\) | ||||
−0.550149 | + | 0.835067i | \(0.685429\pi\) | |||||||
\(608\) | −11.3928 | −0.462040 | ||||||||
\(609\) | 3.06961 | 0.124387 | ||||||||
\(610\) | −26.7902 | −1.08470 | ||||||||
\(611\) | −9.24553 | −0.374034 | ||||||||
\(612\) | 26.8351 | 1.08475 | ||||||||
\(613\) | 12.8802 | 0.520225 | 0.260112 | − | 0.965578i | \(-0.416240\pi\) | ||||
0.260112 | + | 0.965578i | \(0.416240\pi\) | |||||||
\(614\) | 36.1208 | 1.45772 | ||||||||
\(615\) | −0.184510 | −0.00744018 | ||||||||
\(616\) | −19.4668 | −0.784340 | ||||||||
\(617\) | 21.0379 | 0.846956 | 0.423478 | − | 0.905906i | \(-0.360809\pi\) | ||||
0.423478 | + | 0.905906i | \(0.360809\pi\) | |||||||
\(618\) | −39.7099 | −1.59737 | ||||||||
\(619\) | 28.6853 | 1.15296 | 0.576480 | − | 0.817111i | \(-0.304426\pi\) | ||||
0.576480 | + | 0.817111i | \(0.304426\pi\) | |||||||
\(620\) | 4.48346 | 0.180060 | ||||||||
\(621\) | −4.10895 | −0.164886 | ||||||||
\(622\) | −56.1966 | −2.25328 | ||||||||
\(623\) | −5.67172 | −0.227233 | ||||||||
\(624\) | −7.13450 | −0.285609 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −77.7474 | −3.10741 | ||||||||
\(627\) | 6.17010 | 0.246410 | ||||||||
\(628\) | 42.3217 | 1.68882 | ||||||||
\(629\) | −24.1420 | −0.962605 | ||||||||
\(630\) | −2.62239 | −0.104479 | ||||||||
\(631\) | −26.2936 | −1.04673 | −0.523366 | − | 0.852108i | \(-0.675324\pi\) | ||||
−0.523366 | + | 0.852108i | \(0.675324\pi\) | |||||||
\(632\) | 25.5334 | 1.01566 | ||||||||
\(633\) | 6.35199 | 0.252469 | ||||||||
\(634\) | 27.2786 | 1.08337 | ||||||||
\(635\) | −19.2252 | −0.762928 | ||||||||
\(636\) | 27.4231 | 1.08740 | ||||||||
\(637\) | −5.93931 | −0.235324 | ||||||||
\(638\) | 22.6846 | 0.898093 | ||||||||
\(639\) | −2.68065 | −0.106045 | ||||||||
\(640\) | −11.5874 | −0.458032 | ||||||||
\(641\) | −30.4820 | −1.20397 | −0.601983 | − | 0.798509i | \(-0.705623\pi\) | ||||
−0.601983 | + | 0.798509i | \(0.705623\pi\) | |||||||
\(642\) | −44.4610 | −1.75474 | ||||||||
\(643\) | −11.7036 | −0.461544 | −0.230772 | − | 0.973008i | \(-0.574125\pi\) | ||||
−0.230772 | + | 0.973008i | \(0.574125\pi\) | |||||||
\(644\) | −18.9731 | −0.747645 | ||||||||
\(645\) | 0.571830 | 0.0225158 | ||||||||
\(646\) | −31.4591 | −1.23774 | ||||||||
\(647\) | −7.15157 | −0.281157 | −0.140579 | − | 0.990070i | \(-0.544896\pi\) | ||||
−0.140579 | + | 0.990070i | \(0.544896\pi\) | |||||||
\(648\) | 6.32355 | 0.248412 | ||||||||
\(649\) | 39.6851 | 1.55778 | ||||||||
\(650\) | 2.54626 | 0.0998727 | ||||||||
\(651\) | 1.02990 | 0.0403649 | ||||||||
\(652\) | −105.268 | −4.12262 | ||||||||
\(653\) | −18.7502 | −0.733752 | −0.366876 | − | 0.930270i | \(-0.619573\pi\) | ||||
−0.366876 | + | 0.930270i | \(0.619573\pi\) | |||||||
\(654\) | 30.0152 | 1.17369 | ||||||||
\(655\) | 17.5732 | 0.686643 | ||||||||
\(656\) | 1.31639 | 0.0513964 | ||||||||
\(657\) | 1.90612 | 0.0743649 | ||||||||
\(658\) | 24.2454 | 0.945185 | ||||||||
\(659\) | −35.2215 | −1.37203 | −0.686017 | − | 0.727585i | \(-0.740643\pi\) | ||||
−0.686017 | + | 0.727585i | \(0.740643\pi\) | |||||||
\(660\) | −13.4015 | −0.521652 | ||||||||
\(661\) | 9.17490 | 0.356862 | 0.178431 | − | 0.983952i | \(-0.442898\pi\) | ||||
0.178431 | + | 0.983952i | \(0.442898\pi\) | |||||||
\(662\) | −44.4397 | −1.72720 | ||||||||
\(663\) | −5.98536 | −0.232452 | ||||||||
\(664\) | 64.5789 | 2.50615 | ||||||||
\(665\) | 2.12592 | 0.0824398 | ||||||||
\(666\) | −10.2704 | −0.397969 | ||||||||
\(667\) | 12.2467 | 0.474194 | ||||||||
\(668\) | −74.2066 | −2.87114 | ||||||||
\(669\) | 4.60136 | 0.177899 | ||||||||
\(670\) | 9.87717 | 0.381588 | ||||||||
\(671\) | −31.4493 | −1.21409 | ||||||||
\(672\) | 5.68425 | 0.219275 | ||||||||
\(673\) | 10.7394 | 0.413973 | 0.206987 | − | 0.978344i | \(-0.433634\pi\) | ||||
0.206987 | + | 0.978344i | \(0.433634\pi\) | |||||||
\(674\) | −45.8775 | −1.76714 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 4.48346 | 0.172441 | ||||||||
\(677\) | 22.6753 | 0.871481 | 0.435741 | − | 0.900072i | \(-0.356486\pi\) | ||||
0.435741 | + | 0.900072i | \(0.356486\pi\) | |||||||
\(678\) | −23.7619 | −0.912571 | ||||||||
\(679\) | −15.0000 | −0.575647 | ||||||||
\(680\) | 37.8487 | 1.45143 | ||||||||
\(681\) | −25.2676 | −0.968255 | ||||||||
\(682\) | 7.61102 | 0.291441 | ||||||||
\(683\) | 19.4597 | 0.744603 | 0.372301 | − | 0.928112i | \(-0.378569\pi\) | ||||
0.372301 | + | 0.928112i | \(0.378569\pi\) | |||||||
\(684\) | −9.25478 | −0.353866 | ||||||||
\(685\) | 16.0467 | 0.613112 | ||||||||
\(686\) | 33.9320 | 1.29553 | ||||||||
\(687\) | 28.8995 | 1.10259 | ||||||||
\(688\) | −4.07972 | −0.155538 | ||||||||
\(689\) | −6.11650 | −0.233020 | ||||||||
\(690\) | −10.4625 | −0.398299 | ||||||||
\(691\) | −31.3908 | −1.19416 | −0.597082 | − | 0.802180i | \(-0.703673\pi\) | ||||
−0.597082 | + | 0.802180i | \(0.703673\pi\) | |||||||
\(692\) | −46.8839 | −1.78226 | ||||||||
\(693\) | −3.07846 | −0.116941 | ||||||||
\(694\) | 58.6681 | 2.22701 | ||||||||
\(695\) | −3.71894 | −0.141067 | ||||||||
\(696\) | −18.8473 | −0.714406 | ||||||||
\(697\) | 1.10436 | 0.0418307 | ||||||||
\(698\) | −51.8738 | −1.96345 | ||||||||
\(699\) | 18.4093 | 0.696304 | ||||||||
\(700\) | −4.61751 | −0.174526 | ||||||||
\(701\) | 25.7856 | 0.973910 | 0.486955 | − | 0.873427i | \(-0.338108\pi\) | ||||
0.486955 | + | 0.873427i | \(0.338108\pi\) | |||||||
\(702\) | −2.54626 | −0.0961025 | ||||||||
\(703\) | 8.32599 | 0.314021 | ||||||||
\(704\) | −0.644408 | −0.0242870 | ||||||||
\(705\) | 9.24553 | 0.348207 | ||||||||
\(706\) | 38.4632 | 1.44758 | ||||||||
\(707\) | −13.5459 | −0.509447 | ||||||||
\(708\) | −59.5253 | −2.23710 | ||||||||
\(709\) | 2.11047 | 0.0792603 | 0.0396301 | − | 0.999214i | \(-0.487382\pi\) | ||||
0.0396301 | + | 0.999214i | \(0.487382\pi\) | |||||||
\(710\) | −6.82565 | −0.256162 | ||||||||
\(711\) | 4.03783 | 0.151430 | ||||||||
\(712\) | 34.8242 | 1.30509 | ||||||||
\(713\) | 4.10895 | 0.153881 | ||||||||
\(714\) | 15.6960 | 0.587407 | ||||||||
\(715\) | 2.98909 | 0.111786 | ||||||||
\(716\) | 77.6902 | 2.90342 | ||||||||
\(717\) | 3.95948 | 0.147869 | ||||||||
\(718\) | −59.3867 | −2.21629 | ||||||||
\(719\) | 26.6750 | 0.994811 | 0.497405 | − | 0.867518i | \(-0.334286\pi\) | ||||
0.497405 | + | 0.867518i | \(0.334286\pi\) | |||||||
\(720\) | 7.13450 | 0.265887 | ||||||||
\(721\) | −16.0616 | −0.598167 | ||||||||
\(722\) | −37.5295 | −1.39670 | ||||||||
\(723\) | −22.2978 | −0.829265 | ||||||||
\(724\) | −89.2569 | −3.31721 | ||||||||
\(725\) | 2.98050 | 0.110693 | ||||||||
\(726\) | 5.25885 | 0.195174 | ||||||||
\(727\) | −10.1824 | −0.377643 | −0.188822 | − | 0.982011i | \(-0.560467\pi\) | ||||
−0.188822 | + | 0.982011i | \(0.560467\pi\) | |||||||
\(728\) | −6.51262 | −0.241374 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.85349 | 0.179636 | ||||||||
\(731\) | −3.42261 | −0.126590 | ||||||||
\(732\) | 47.1721 | 1.74353 | ||||||||
\(733\) | −1.33430 | −0.0492836 | −0.0246418 | − | 0.999696i | \(-0.507845\pi\) | ||||
−0.0246418 | + | 0.999696i | \(0.507845\pi\) | |||||||
\(734\) | 77.9047 | 2.87552 | ||||||||
\(735\) | 5.93931 | 0.219075 | ||||||||
\(736\) | 22.6782 | 0.835930 | ||||||||
\(737\) | 11.5949 | 0.427105 | ||||||||
\(738\) | 0.469812 | 0.0172940 | ||||||||
\(739\) | −37.2444 | −1.37006 | −0.685028 | − | 0.728517i | \(-0.740210\pi\) | ||||
−0.685028 | + | 0.728517i | \(0.740210\pi\) | |||||||
\(740\) | −18.0841 | −0.664784 | ||||||||
\(741\) | 2.06421 | 0.0758305 | ||||||||
\(742\) | 16.0399 | 0.588842 | ||||||||
\(743\) | 29.6029 | 1.08602 | 0.543012 | − | 0.839725i | \(-0.317284\pi\) | ||||
0.543012 | + | 0.839725i | \(0.317284\pi\) | |||||||
\(744\) | −6.32355 | −0.231833 | ||||||||
\(745\) | −7.10280 | −0.260227 | ||||||||
\(746\) | −66.0424 | −2.41798 | ||||||||
\(747\) | 10.2125 | 0.373654 | ||||||||
\(748\) | 80.2127 | 2.93287 | ||||||||
\(749\) | −17.9834 | −0.657098 | ||||||||
\(750\) | −2.54626 | −0.0929764 | ||||||||
\(751\) | −40.2013 | −1.46697 | −0.733483 | − | 0.679708i | \(-0.762106\pi\) | ||||
−0.733483 | + | 0.679708i | \(0.762106\pi\) | |||||||
\(752\) | −65.9622 | −2.40539 | ||||||||
\(753\) | −9.88327 | −0.360166 | ||||||||
\(754\) | 7.58913 | 0.276380 | ||||||||
\(755\) | 3.51700 | 0.127997 | ||||||||
\(756\) | 4.61751 | 0.167937 | ||||||||
\(757\) | 39.3618 | 1.43063 | 0.715314 | − | 0.698803i | \(-0.246284\pi\) | ||||
0.715314 | + | 0.698803i | \(0.246284\pi\) | |||||||
\(758\) | 93.7267 | 3.40431 | ||||||||
\(759\) | −12.2820 | −0.445809 | ||||||||
\(760\) | −13.0531 | −0.473486 | ||||||||
\(761\) | 1.38032 | 0.0500364 | 0.0250182 | − | 0.999687i | \(-0.492036\pi\) | ||||
0.0250182 | + | 0.999687i | \(0.492036\pi\) | |||||||
\(762\) | 48.9524 | 1.77336 | ||||||||
\(763\) | 12.1404 | 0.439511 | ||||||||
\(764\) | 3.15930 | 0.114300 | ||||||||
\(765\) | 5.98536 | 0.216401 | ||||||||
\(766\) | −35.0782 | −1.26743 | ||||||||
\(767\) | 13.2766 | 0.479392 | ||||||||
\(768\) | 29.0734 | 1.04910 | ||||||||
\(769\) | 40.8468 | 1.47297 | 0.736487 | − | 0.676451i | \(-0.236483\pi\) | ||||
0.736487 | + | 0.676451i | \(0.236483\pi\) | |||||||
\(770\) | −7.83858 | −0.282483 | ||||||||
\(771\) | −16.4824 | −0.593600 | ||||||||
\(772\) | −44.1430 | −1.58874 | ||||||||
\(773\) | −6.42680 | −0.231156 | −0.115578 | − | 0.993298i | \(-0.536872\pi\) | ||||
−0.115578 | + | 0.993298i | \(0.536872\pi\) | |||||||
\(774\) | −1.45603 | −0.0523359 | ||||||||
\(775\) | 1.00000 | 0.0359211 | ||||||||
\(776\) | 92.0996 | 3.30618 | ||||||||
\(777\) | −4.15411 | −0.149028 | ||||||||
\(778\) | −29.0054 | −1.03989 | ||||||||
\(779\) | −0.380867 | −0.0136460 | ||||||||
\(780\) | −4.48346 | −0.160534 | ||||||||
\(781\) | −8.01272 | −0.286718 | ||||||||
\(782\) | 62.6217 | 2.23935 | ||||||||
\(783\) | −2.98050 | −0.106514 | ||||||||
\(784\) | −42.3740 | −1.51336 | ||||||||
\(785\) | 9.43952 | 0.336911 | ||||||||
\(786\) | −44.7461 | −1.59604 | ||||||||
\(787\) | −13.3250 | −0.474985 | −0.237493 | − | 0.971389i | \(-0.576326\pi\) | ||||
−0.237493 | + | 0.971389i | \(0.576326\pi\) | |||||||
\(788\) | −97.8490 | −3.48573 | ||||||||
\(789\) | 26.5559 | 0.945414 | ||||||||
\(790\) | 10.2814 | 0.365795 | ||||||||
\(791\) | −9.61109 | −0.341731 | ||||||||
\(792\) | 18.9017 | 0.671642 | ||||||||
\(793\) | −10.5214 | −0.373624 | ||||||||
\(794\) | 32.8197 | 1.16473 | ||||||||
\(795\) | 6.11650 | 0.216930 | ||||||||
\(796\) | 28.5154 | 1.01070 | ||||||||
\(797\) | −34.6416 | −1.22707 | −0.613534 | − | 0.789668i | \(-0.710253\pi\) | ||||
−0.613534 | + | 0.789668i | \(0.710253\pi\) | |||||||
\(798\) | −5.41316 | −0.191624 | ||||||||
\(799\) | −55.3378 | −1.95771 | ||||||||
\(800\) | 5.51923 | 0.195134 | ||||||||
\(801\) | 5.50706 | 0.194583 | ||||||||
\(802\) | −53.2683 | −1.88097 | ||||||||
\(803\) | 5.69757 | 0.201063 | ||||||||
\(804\) | −17.3917 | −0.613359 | ||||||||
\(805\) | −4.23180 | −0.149151 | ||||||||
\(806\) | 2.54626 | 0.0896883 | ||||||||
\(807\) | 17.0294 | 0.599463 | ||||||||
\(808\) | 83.1716 | 2.92597 | ||||||||
\(809\) | 5.24719 | 0.184481 | 0.0922406 | − | 0.995737i | \(-0.470597\pi\) | ||||
0.0922406 | + | 0.995737i | \(0.470597\pi\) | |||||||
\(810\) | 2.54626 | 0.0894666 | ||||||||
\(811\) | −15.2806 | −0.536575 | −0.268288 | − | 0.963339i | \(-0.586458\pi\) | ||||
−0.268288 | + | 0.963339i | \(0.586458\pi\) | |||||||
\(812\) | −13.7625 | −0.482968 | ||||||||
\(813\) | 16.0825 | 0.564039 | ||||||||
\(814\) | −30.6991 | −1.07600 | ||||||||
\(815\) | −23.4792 | −0.822441 | ||||||||
\(816\) | −42.7026 | −1.49489 | ||||||||
\(817\) | 1.18037 | 0.0412961 | ||||||||
\(818\) | −72.2934 | −2.52768 | ||||||||
\(819\) | −1.02990 | −0.0359876 | ||||||||
\(820\) | 0.827245 | 0.0288886 | ||||||||
\(821\) | 32.3116 | 1.12768 | 0.563841 | − | 0.825883i | \(-0.309323\pi\) | ||||
0.563841 | + | 0.825883i | \(0.309323\pi\) | |||||||
\(822\) | −40.8591 | −1.42512 | ||||||||
\(823\) | −36.8710 | −1.28524 | −0.642621 | − | 0.766184i | \(-0.722153\pi\) | ||||
−0.642621 | + | 0.766184i | \(0.722153\pi\) | |||||||
\(824\) | 98.6180 | 3.43552 | ||||||||
\(825\) | −2.98909 | −0.104067 | ||||||||
\(826\) | −34.8166 | −1.21142 | ||||||||
\(827\) | 49.4955 | 1.72113 | 0.860564 | − | 0.509343i | \(-0.170111\pi\) | ||||
0.860564 | + | 0.509343i | \(0.170111\pi\) | |||||||
\(828\) | 18.4223 | 0.640219 | ||||||||
\(829\) | 29.1011 | 1.01072 | 0.505361 | − | 0.862908i | \(-0.331359\pi\) | ||||
0.505361 | + | 0.862908i | \(0.331359\pi\) | |||||||
\(830\) | 26.0036 | 0.902598 | ||||||||
\(831\) | 14.3164 | 0.496631 | ||||||||
\(832\) | −0.215586 | −0.00747412 | ||||||||
\(833\) | −35.5489 | −1.23170 | ||||||||
\(834\) | 9.46940 | 0.327899 | ||||||||
\(835\) | −16.5512 | −0.572777 | ||||||||
\(836\) | −27.6634 | −0.956759 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | 6.11195 | 0.211134 | ||||||||
\(839\) | 26.7611 | 0.923897 | 0.461948 | − | 0.886907i | \(-0.347151\pi\) | ||||
0.461948 | + | 0.886907i | \(0.347151\pi\) | |||||||
\(840\) | 6.51262 | 0.224707 | ||||||||
\(841\) | −20.1166 | −0.693677 | ||||||||
\(842\) | −8.77417 | −0.302378 | ||||||||
\(843\) | 1.36079 | 0.0468681 | ||||||||
\(844\) | −28.4789 | −0.980284 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | −23.5416 | −0.809375 | ||||||||
\(847\) | 2.12707 | 0.0730871 | ||||||||
\(848\) | −43.6382 | −1.49854 | ||||||||
\(849\) | 17.6046 | 0.604187 | ||||||||
\(850\) | 15.2403 | 0.522739 | ||||||||
\(851\) | −16.5735 | −0.568132 | ||||||||
\(852\) | 12.0186 | 0.411751 | ||||||||
\(853\) | 8.78342 | 0.300739 | 0.150369 | − | 0.988630i | \(-0.451954\pi\) | ||||
0.150369 | + | 0.988630i | \(0.451954\pi\) | |||||||
\(854\) | 27.5912 | 0.944150 | ||||||||
\(855\) | −2.06421 | −0.0705943 | ||||||||
\(856\) | 110.417 | 3.77398 | ||||||||
\(857\) | 6.53948 | 0.223384 | 0.111692 | − | 0.993743i | \(-0.464373\pi\) | ||||
0.111692 | + | 0.993743i | \(0.464373\pi\) | |||||||
\(858\) | −7.61102 | −0.259836 | ||||||||
\(859\) | 1.01343 | 0.0345780 | 0.0172890 | − | 0.999851i | \(-0.494496\pi\) | ||||
0.0172890 | + | 0.999851i | \(0.494496\pi\) | |||||||
\(860\) | −2.56378 | −0.0874240 | ||||||||
\(861\) | 0.190027 | 0.00647610 | ||||||||
\(862\) | 20.1842 | 0.687477 | ||||||||
\(863\) | 0.410115 | 0.0139605 | 0.00698024 | − | 0.999976i | \(-0.497778\pi\) | ||||
0.00698024 | + | 0.999976i | \(0.497778\pi\) | |||||||
\(864\) | −5.51923 | −0.187768 | ||||||||
\(865\) | −10.4571 | −0.355552 | ||||||||
\(866\) | −46.3860 | −1.57626 | ||||||||
\(867\) | −18.8246 | −0.639316 | ||||||||
\(868\) | −4.61751 | −0.156729 | ||||||||
\(869\) | 12.0694 | 0.409428 | ||||||||
\(870\) | −7.58913 | −0.257296 | ||||||||
\(871\) | 3.87908 | 0.131438 | ||||||||
\(872\) | −74.5416 | −2.52430 | ||||||||
\(873\) | 14.5645 | 0.492935 | ||||||||
\(874\) | −21.5967 | −0.730518 | ||||||||
\(875\) | −1.02990 | −0.0348169 | ||||||||
\(876\) | −8.54602 | −0.288743 | ||||||||
\(877\) | −53.8975 | −1.81999 | −0.909994 | − | 0.414622i | \(-0.863914\pi\) | ||||
−0.909994 | + | 0.414622i | \(0.863914\pi\) | |||||||
\(878\) | −37.7700 | −1.27467 | ||||||||
\(879\) | −24.1496 | −0.814547 | ||||||||
\(880\) | 21.3257 | 0.718889 | ||||||||
\(881\) | −42.5548 | −1.43371 | −0.716854 | − | 0.697223i | \(-0.754419\pi\) | ||||
−0.716854 | + | 0.697223i | \(0.754419\pi\) | |||||||
\(882\) | −15.1230 | −0.509219 | ||||||||
\(883\) | 40.9687 | 1.37871 | 0.689354 | − | 0.724425i | \(-0.257895\pi\) | ||||
0.689354 | + | 0.724425i | \(0.257895\pi\) | |||||||
\(884\) | 26.8351 | 0.902564 | ||||||||
\(885\) | −13.2766 | −0.446289 | ||||||||
\(886\) | 7.78177 | 0.261434 | ||||||||
\(887\) | 8.44077 | 0.283413 | 0.141707 | − | 0.989909i | \(-0.454741\pi\) | ||||
0.141707 | + | 0.989909i | \(0.454741\pi\) | |||||||
\(888\) | 25.5061 | 0.855928 | ||||||||
\(889\) | 19.8000 | 0.664071 | ||||||||
\(890\) | 14.0224 | 0.470033 | ||||||||
\(891\) | 2.98909 | 0.100138 | ||||||||
\(892\) | −20.6300 | −0.690744 | ||||||||
\(893\) | 19.0847 | 0.638644 | ||||||||
\(894\) | 18.0856 | 0.604873 | ||||||||
\(895\) | 17.3282 | 0.579217 | ||||||||
\(896\) | 11.9339 | 0.398682 | ||||||||
\(897\) | −4.10895 | −0.137194 | ||||||||
\(898\) | −38.7578 | −1.29337 | ||||||||
\(899\) | 2.98050 | 0.0994051 | ||||||||
\(900\) | 4.48346 | 0.149449 | ||||||||
\(901\) | −36.6095 | −1.21964 | ||||||||
\(902\) | 1.40431 | 0.0467585 | ||||||||
\(903\) | −0.588927 | −0.0195983 | ||||||||
\(904\) | 59.0118 | 1.96270 | ||||||||
\(905\) | −19.9080 | −0.661766 | ||||||||
\(906\) | −8.95520 | −0.297517 | ||||||||
\(907\) | −6.79221 | −0.225532 | −0.112766 | − | 0.993622i | \(-0.535971\pi\) | ||||
−0.112766 | + | 0.993622i | \(0.535971\pi\) | |||||||
\(908\) | 113.286 | 3.75953 | ||||||||
\(909\) | 13.1527 | 0.436247 | ||||||||
\(910\) | −2.62239 | −0.0869315 | ||||||||
\(911\) | 1.83902 | 0.0609295 | 0.0304647 | − | 0.999536i | \(-0.490301\pi\) | ||||
0.0304647 | + | 0.999536i | \(0.490301\pi\) | |||||||
\(912\) | 14.7271 | 0.487662 | ||||||||
\(913\) | 30.5260 | 1.01026 | ||||||||
\(914\) | 68.9838 | 2.28178 | ||||||||
\(915\) | 10.5214 | 0.347825 | ||||||||
\(916\) | −129.570 | −4.28111 | ||||||||
\(917\) | −18.0987 | −0.597670 | ||||||||
\(918\) | −15.2403 | −0.503005 | ||||||||
\(919\) | 12.7552 | 0.420757 | 0.210378 | − | 0.977620i | \(-0.432530\pi\) | ||||
0.210378 | + | 0.977620i | \(0.432530\pi\) | |||||||
\(920\) | 25.9831 | 0.856638 | ||||||||
\(921\) | −14.1858 | −0.467438 | ||||||||
\(922\) | 5.69579 | 0.187581 | ||||||||
\(923\) | −2.68065 | −0.0882348 | ||||||||
\(924\) | 13.8022 | 0.454058 | ||||||||
\(925\) | −4.03351 | −0.132621 | ||||||||
\(926\) | 75.3100 | 2.47484 | ||||||||
\(927\) | 15.5954 | 0.512219 | ||||||||
\(928\) | 16.4500 | 0.539999 | ||||||||
\(929\) | −30.9896 | −1.01674 | −0.508368 | − | 0.861140i | \(-0.669751\pi\) | ||||
−0.508368 | + | 0.861140i | \(0.669751\pi\) | |||||||
\(930\) | −2.54626 | −0.0834953 | ||||||||
\(931\) | 12.2600 | 0.401804 | ||||||||
\(932\) | −82.5374 | −2.70360 | ||||||||
\(933\) | 22.0702 | 0.722546 | ||||||||
\(934\) | 22.3176 | 0.730254 | ||||||||
\(935\) | 17.8908 | 0.585092 | ||||||||
\(936\) | 6.32355 | 0.206692 | ||||||||
\(937\) | −0.000644290 0 | −2.10480e−5 0 | −1.05240e−5 | − | 1.00000i | \(-0.500003\pi\) | ||||
−1.05240e−5 | 1.00000i | \(0.500003\pi\) | ||||||||
\(938\) | −10.1725 | −0.332144 | ||||||||
\(939\) | 30.5339 | 0.996437 | ||||||||
\(940\) | −41.4520 | −1.35201 | ||||||||
\(941\) | 25.3483 | 0.826332 | 0.413166 | − | 0.910656i | \(-0.364423\pi\) | ||||
0.413166 | + | 0.910656i | \(0.364423\pi\) | |||||||
\(942\) | −24.0355 | −0.783120 | ||||||||
\(943\) | 0.758143 | 0.0246885 | ||||||||
\(944\) | 94.7222 | 3.08295 | ||||||||
\(945\) | 1.02990 | 0.0335026 | ||||||||
\(946\) | −4.35221 | −0.141502 | ||||||||
\(947\) | −18.8142 | −0.611378 | −0.305689 | − | 0.952131i | \(-0.598887\pi\) | ||||
−0.305689 | + | 0.952131i | \(0.598887\pi\) | |||||||
\(948\) | −18.1034 | −0.587972 | ||||||||
\(949\) | 1.90612 | 0.0618753 | ||||||||
\(950\) | −5.25601 | −0.170528 | ||||||||
\(951\) | −10.7132 | −0.347398 | ||||||||
\(952\) | −38.9804 | −1.26336 | ||||||||
\(953\) | 43.2871 | 1.40221 | 0.701103 | − | 0.713060i | \(-0.252691\pi\) | ||||
0.701103 | + | 0.713060i | \(0.252691\pi\) | |||||||
\(954\) | −15.5742 | −0.504234 | ||||||||
\(955\) | 0.704657 | 0.0228022 | ||||||||
\(956\) | −17.7522 | −0.574146 | ||||||||
\(957\) | −8.90898 | −0.287986 | ||||||||
\(958\) | 47.5309 | 1.53565 | ||||||||
\(959\) | −16.5265 | −0.533667 | ||||||||
\(960\) | 0.215586 | 0.00695802 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −10.2704 | −0.331130 | ||||||||
\(963\) | 17.4613 | 0.562682 | ||||||||
\(964\) | 99.9714 | 3.21986 | ||||||||
\(965\) | −9.84575 | −0.316946 | ||||||||
\(966\) | 10.7753 | 0.346689 | ||||||||
\(967\) | −14.8781 | −0.478448 | −0.239224 | − | 0.970964i | \(-0.576893\pi\) | ||||
−0.239224 | + | 0.970964i | \(0.576893\pi\) | |||||||
\(968\) | −13.0602 | −0.419770 | ||||||||
\(969\) | 12.3550 | 0.396900 | ||||||||
\(970\) | 37.0852 | 1.19073 | ||||||||
\(971\) | 40.3860 | 1.29605 | 0.648025 | − | 0.761619i | \(-0.275595\pi\) | ||||
0.648025 | + | 0.761619i | \(0.275595\pi\) | |||||||
\(972\) | −4.48346 | −0.143807 | ||||||||
\(973\) | 3.83013 | 0.122788 | ||||||||
\(974\) | 92.9112 | 2.97707 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | −75.0647 | −2.40276 | ||||||||
\(977\) | 42.0759 | 1.34613 | 0.673063 | − | 0.739585i | \(-0.264978\pi\) | ||||
0.673063 | + | 0.739585i | \(0.264978\pi\) | |||||||
\(978\) | 59.7843 | 1.91169 | ||||||||
\(979\) | 16.4611 | 0.526100 | ||||||||
\(980\) | −26.6287 | −0.850621 | ||||||||
\(981\) | −11.7879 | −0.376360 | ||||||||
\(982\) | 81.3470 | 2.59589 | ||||||||
\(983\) | 28.8047 | 0.918727 | 0.459363 | − | 0.888248i | \(-0.348078\pi\) | ||||
0.459363 | + | 0.888248i | \(0.348078\pi\) | |||||||
\(984\) | −1.16676 | −0.0371950 | ||||||||
\(985\) | −21.8244 | −0.695384 | ||||||||
\(986\) | 45.4237 | 1.44659 | ||||||||
\(987\) | −9.52196 | −0.303087 | ||||||||
\(988\) | −9.25478 | −0.294434 | ||||||||
\(989\) | −2.34962 | −0.0747135 | ||||||||
\(990\) | 7.61102 | 0.241894 | ||||||||
\(991\) | −22.5487 | −0.716284 | −0.358142 | − | 0.933667i | \(-0.616590\pi\) | ||||
−0.358142 | + | 0.933667i | \(0.616590\pi\) | |||||||
\(992\) | 5.51923 | 0.175236 | ||||||||
\(993\) | 17.4529 | 0.553852 | ||||||||
\(994\) | 7.02973 | 0.222969 | ||||||||
\(995\) | 6.36012 | 0.201629 | ||||||||
\(996\) | −45.7871 | −1.45082 | ||||||||
\(997\) | 50.0207 | 1.58417 | 0.792086 | − | 0.610409i | \(-0.208995\pi\) | ||||
0.792086 | + | 0.610409i | \(0.208995\pi\) | |||||||
\(998\) | 39.7248 | 1.25747 | ||||||||
\(999\) | 4.03351 | 0.127615 |
(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 | 6045.2.a.bh.1.15 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6045.2.a.bh.1.15 | ✓ | 17 | 1.1 | even | 1 | trivial |