Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(1,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("418.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.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: | \(3.33774680449\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.469.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.16425\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.16425 | −1.24953 | −0.624765 | − | 0.780813i | \(-0.714805\pi\) | ||||
−0.624765 | + | 0.780813i | \(0.714805\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.16425 | 1.86231 | 0.931154 | − | 0.364626i | \(-0.118803\pi\) | ||||
0.931154 | + | 0.364626i | \(0.118803\pi\) | |||||||
\(6\) | −2.16425 | −0.883551 | ||||||||
\(7\) | −0.683969 | −0.258516 | −0.129258 | − | 0.991611i | \(-0.541260\pi\) | ||||
−0.129258 | + | 0.991611i | \(0.541260\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.68397 | 0.561323 | ||||||||
\(10\) | 4.16425 | 1.31685 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −2.16425 | −0.624765 | ||||||||
\(13\) | 2.68397 | 0.744399 | 0.372200 | − | 0.928153i | \(-0.378604\pi\) | ||||
0.372200 | + | 0.928153i | \(0.378604\pi\) | |||||||
\(14\) | −0.683969 | −0.182798 | ||||||||
\(15\) | −9.01247 | −2.32701 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.36794 | 0.816845 | 0.408423 | − | 0.912793i | \(-0.366079\pi\) | ||||
0.408423 | + | 0.912793i | \(0.366079\pi\) | |||||||
\(18\) | 1.68397 | 0.396915 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 4.16425 | 0.931154 | ||||||||
\(21\) | 1.48028 | 0.323023 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −1.36794 | −0.285235 | −0.142617 | − | 0.989778i | \(-0.545552\pi\) | ||||
−0.142617 | + | 0.989778i | \(0.545552\pi\) | |||||||
\(24\) | −2.16425 | −0.441775 | ||||||||
\(25\) | 12.3410 | 2.46819 | ||||||||
\(26\) | 2.68397 | 0.526370 | ||||||||
\(27\) | 2.84822 | 0.548140 | ||||||||
\(28\) | −0.683969 | −0.129258 | ||||||||
\(29\) | 2.79631 | 0.519262 | 0.259631 | − | 0.965708i | \(-0.416399\pi\) | ||||
0.259631 | + | 0.965708i | \(0.416399\pi\) | |||||||
\(30\) | −9.01247 | −1.64544 | ||||||||
\(31\) | 5.01247 | 0.900265 | 0.450133 | − | 0.892962i | \(-0.351377\pi\) | ||||
0.450133 | + | 0.892962i | \(0.351377\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.16425 | 0.376747 | ||||||||
\(34\) | 3.36794 | 0.577597 | ||||||||
\(35\) | −2.84822 | −0.481437 | ||||||||
\(36\) | 1.68397 | 0.280662 | ||||||||
\(37\) | −11.6964 | −1.92288 | −0.961441 | − | 0.275011i | \(-0.911318\pi\) | ||||
−0.961441 | + | 0.275011i | \(0.911318\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −5.80877 | −0.930148 | ||||||||
\(40\) | 4.16425 | 0.658425 | ||||||||
\(41\) | −7.01247 | −1.09516 | −0.547582 | − | 0.836752i | \(-0.684451\pi\) | ||||
−0.547582 | + | 0.836752i | \(0.684451\pi\) | |||||||
\(42\) | 1.48028 | 0.228412 | ||||||||
\(43\) | 7.86068 | 1.19874 | 0.599371 | − | 0.800471i | \(-0.295417\pi\) | ||||
0.599371 | + | 0.800471i | \(0.295417\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 7.01247 | 1.04536 | ||||||||
\(46\) | −1.36794 | −0.201691 | ||||||||
\(47\) | 2.96056 | 0.431842 | 0.215921 | − | 0.976411i | \(-0.430725\pi\) | ||||
0.215921 | + | 0.976411i | \(0.430725\pi\) | |||||||
\(48\) | −2.16425 | −0.312382 | ||||||||
\(49\) | −6.53219 | −0.933169 | ||||||||
\(50\) | 12.3410 | 1.74528 | ||||||||
\(51\) | −7.28905 | −1.02067 | ||||||||
\(52\) | 2.68397 | 0.372200 | ||||||||
\(53\) | −10.3285 | −1.41873 | −0.709364 | − | 0.704842i | \(-0.751018\pi\) | ||||
−0.709364 | + | 0.704842i | \(0.751018\pi\) | |||||||
\(54\) | 2.84822 | 0.387593 | ||||||||
\(55\) | −4.16425 | −0.561507 | ||||||||
\(56\) | −0.683969 | −0.0913992 | ||||||||
\(57\) | 2.16425 | 0.286662 | ||||||||
\(58\) | 2.79631 | 0.367173 | ||||||||
\(59\) | −9.92112 | −1.29162 | −0.645810 | − | 0.763499i | \(-0.723480\pi\) | ||||
−0.645810 | + | 0.763499i | \(0.723480\pi\) | |||||||
\(60\) | −9.01247 | −1.16350 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 5.01247 | 0.636584 | ||||||||
\(63\) | −1.15178 | −0.145111 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 11.1767 | 1.38630 | ||||||||
\(66\) | 2.16425 | 0.266401 | ||||||||
\(67\) | −0.683969 | −0.0835601 | −0.0417801 | − | 0.999127i | \(-0.513303\pi\) | ||||
−0.0417801 | + | 0.999127i | \(0.513303\pi\) | |||||||
\(68\) | 3.36794 | 0.408423 | ||||||||
\(69\) | 2.96056 | 0.356409 | ||||||||
\(70\) | −2.84822 | −0.340427 | ||||||||
\(71\) | 3.53219 | 0.419193 | 0.209597 | − | 0.977788i | \(-0.432785\pi\) | ||||
0.209597 | + | 0.977788i | \(0.432785\pi\) | |||||||
\(72\) | 1.68397 | 0.198458 | ||||||||
\(73\) | 0.407381 | 0.0476803 | 0.0238402 | − | 0.999716i | \(-0.492411\pi\) | ||||
0.0238402 | + | 0.999716i | \(0.492411\pi\) | |||||||
\(74\) | −11.6964 | −1.35968 | ||||||||
\(75\) | −26.7089 | −3.08408 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0.683969 | 0.0779455 | ||||||||
\(78\) | −5.80877 | −0.657714 | ||||||||
\(79\) | −7.28905 | −0.820083 | −0.410041 | − | 0.912067i | \(-0.634486\pi\) | ||||
−0.410041 | + | 0.912067i | \(0.634486\pi\) | |||||||
\(80\) | 4.16425 | 0.465577 | ||||||||
\(81\) | −11.2162 | −1.24624 | ||||||||
\(82\) | −7.01247 | −0.774397 | ||||||||
\(83\) | −12.1892 | −1.33794 | −0.668968 | − | 0.743291i | \(-0.733264\pi\) | ||||
−0.668968 | + | 0.743291i | \(0.733264\pi\) | |||||||
\(84\) | 1.48028 | 0.161512 | ||||||||
\(85\) | 14.0249 | 1.52122 | ||||||||
\(86\) | 7.86068 | 0.847639 | ||||||||
\(87\) | −6.05191 | −0.648833 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −16.6819 | −1.76828 | −0.884140 | − | 0.467222i | \(-0.845255\pi\) | ||||
−0.884140 | + | 0.467222i | \(0.845255\pi\) | |||||||
\(90\) | 7.01247 | 0.739179 | ||||||||
\(91\) | −1.83575 | −0.192439 | ||||||||
\(92\) | −1.36794 | −0.142617 | ||||||||
\(93\) | −10.8482 | −1.12491 | ||||||||
\(94\) | 2.96056 | 0.305358 | ||||||||
\(95\) | −4.16425 | −0.427243 | ||||||||
\(96\) | −2.16425 | −0.220888 | ||||||||
\(97\) | −11.6964 | −1.18759 | −0.593796 | − | 0.804615i | \(-0.702372\pi\) | ||||
−0.593796 | + | 0.804615i | \(0.702372\pi\) | |||||||
\(98\) | −6.53219 | −0.659850 | ||||||||
\(99\) | −1.68397 | −0.169245 | ||||||||
\(100\) | 12.3410 | 1.23410 | ||||||||
\(101\) | 3.59262 | 0.357479 | 0.178739 | − | 0.983896i | \(-0.442798\pi\) | ||||
0.178739 | + | 0.983896i | \(0.442798\pi\) | |||||||
\(102\) | −7.28905 | −0.721724 | ||||||||
\(103\) | −4.46781 | −0.440227 | −0.220113 | − | 0.975474i | \(-0.570643\pi\) | ||||
−0.220113 | + | 0.975474i | \(0.570643\pi\) | |||||||
\(104\) | 2.68397 | 0.263185 | ||||||||
\(105\) | 6.16425 | 0.601569 | ||||||||
\(106\) | −10.3285 | −1.00319 | ||||||||
\(107\) | 9.69643 | 0.937390 | 0.468695 | − | 0.883360i | \(-0.344724\pi\) | ||||
0.468695 | + | 0.883360i | \(0.344724\pi\) | |||||||
\(108\) | 2.84822 | 0.274070 | ||||||||
\(109\) | 6.00000 | 0.574696 | 0.287348 | − | 0.957826i | \(-0.407226\pi\) | ||||
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | −4.16425 | −0.397045 | ||||||||
\(111\) | 25.3140 | 2.40270 | ||||||||
\(112\) | −0.683969 | −0.0646290 | ||||||||
\(113\) | 10.4323 | 0.981389 | 0.490695 | − | 0.871332i | \(-0.336743\pi\) | ||||
0.490695 | + | 0.871332i | \(0.336743\pi\) | |||||||
\(114\) | 2.16425 | 0.202700 | ||||||||
\(115\) | −5.69643 | −0.531195 | ||||||||
\(116\) | 2.79631 | 0.259631 | ||||||||
\(117\) | 4.51972 | 0.417848 | ||||||||
\(118\) | −9.92112 | −0.913313 | ||||||||
\(119\) | −2.30357 | −0.211168 | ||||||||
\(120\) | −9.01247 | −0.822722 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.00000 | 0.181071 | ||||||||
\(123\) | 15.1767 | 1.36844 | ||||||||
\(124\) | 5.01247 | 0.450133 | ||||||||
\(125\) | 30.5696 | 2.73423 | ||||||||
\(126\) | −1.15178 | −0.102609 | ||||||||
\(127\) | 15.2891 | 1.35668 | 0.678342 | − | 0.734746i | \(-0.262699\pi\) | ||||
0.678342 | + | 0.734746i | \(0.262699\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −17.0125 | −1.49786 | ||||||||
\(130\) | 11.1767 | 0.980263 | ||||||||
\(131\) | 3.64453 | 0.318424 | 0.159212 | − | 0.987244i | \(-0.449105\pi\) | ||||
0.159212 | + | 0.987244i | \(0.449105\pi\) | |||||||
\(132\) | 2.16425 | 0.188374 | ||||||||
\(133\) | 0.683969 | 0.0593076 | ||||||||
\(134\) | −0.683969 | −0.0590859 | ||||||||
\(135\) | 11.8607 | 1.02080 | ||||||||
\(136\) | 3.36794 | 0.288798 | ||||||||
\(137\) | 14.6840 | 1.25454 | 0.627268 | − | 0.778803i | \(-0.284173\pi\) | ||||
0.627268 | + | 0.778803i | \(0.284173\pi\) | |||||||
\(138\) | 2.96056 | 0.252019 | ||||||||
\(139\) | −18.5966 | −1.57734 | −0.788670 | − | 0.614817i | \(-0.789230\pi\) | ||||
−0.788670 | + | 0.614817i | \(0.789230\pi\) | |||||||
\(140\) | −2.84822 | −0.240718 | ||||||||
\(141\) | −6.40738 | −0.539599 | ||||||||
\(142\) | 3.53219 | 0.296414 | ||||||||
\(143\) | −2.68397 | −0.224445 | ||||||||
\(144\) | 1.68397 | 0.140331 | ||||||||
\(145\) | 11.6445 | 0.967025 | ||||||||
\(146\) | 0.407381 | 0.0337151 | ||||||||
\(147\) | 14.1373 | 1.16602 | ||||||||
\(148\) | −11.6964 | −0.961441 | ||||||||
\(149\) | 4.30357 | 0.352562 | 0.176281 | − | 0.984340i | \(-0.443593\pi\) | ||||
0.176281 | + | 0.984340i | \(0.443593\pi\) | |||||||
\(150\) | −26.7089 | −2.18077 | ||||||||
\(151\) | −21.6964 | −1.76563 | −0.882815 | − | 0.469720i | \(-0.844355\pi\) | ||||
−0.882815 | + | 0.469720i | \(0.844355\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 5.67150 | 0.458514 | ||||||||
\(154\) | 0.683969 | 0.0551158 | ||||||||
\(155\) | 20.8731 | 1.67657 | ||||||||
\(156\) | −5.80877 | −0.465074 | ||||||||
\(157\) | −10.9001 | −0.869925 | −0.434962 | − | 0.900449i | \(-0.643238\pi\) | ||||
−0.434962 | + | 0.900449i | \(0.643238\pi\) | |||||||
\(158\) | −7.28905 | −0.579886 | ||||||||
\(159\) | 22.3534 | 1.77274 | ||||||||
\(160\) | 4.16425 | 0.329213 | ||||||||
\(161\) | 0.935628 | 0.0737378 | ||||||||
\(162\) | −11.2162 | −0.881224 | ||||||||
\(163\) | 19.7214 | 1.54470 | 0.772348 | − | 0.635199i | \(-0.219082\pi\) | ||||
0.772348 | + | 0.635199i | \(0.219082\pi\) | |||||||
\(164\) | −7.01247 | −0.547582 | ||||||||
\(165\) | 9.01247 | 0.701619 | ||||||||
\(166\) | −12.1892 | −0.946064 | ||||||||
\(167\) | 7.77532 | 0.601672 | 0.300836 | − | 0.953676i | \(-0.402734\pi\) | ||||
0.300836 | + | 0.953676i | \(0.402734\pi\) | |||||||
\(168\) | 1.48028 | 0.114206 | ||||||||
\(169\) | −5.79631 | −0.445870 | ||||||||
\(170\) | 14.0249 | 1.07566 | ||||||||
\(171\) | −1.68397 | −0.128776 | ||||||||
\(172\) | 7.86068 | 0.599371 | ||||||||
\(173\) | 15.7818 | 1.19987 | 0.599934 | − | 0.800050i | \(-0.295194\pi\) | ||||
0.599934 | + | 0.800050i | \(0.295194\pi\) | |||||||
\(174\) | −6.05191 | −0.458794 | ||||||||
\(175\) | −8.44084 | −0.638067 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 21.4718 | 1.61392 | ||||||||
\(178\) | −16.6819 | −1.25036 | ||||||||
\(179\) | −7.97302 | −0.595932 | −0.297966 | − | 0.954577i | \(-0.596308\pi\) | ||||
−0.297966 | + | 0.954577i | \(0.596308\pi\) | |||||||
\(180\) | 7.01247 | 0.522678 | ||||||||
\(181\) | −2.55318 | −0.189776 | −0.0948881 | − | 0.995488i | \(-0.530249\pi\) | ||||
−0.0948881 | + | 0.995488i | \(0.530249\pi\) | |||||||
\(182\) | −1.83575 | −0.136075 | ||||||||
\(183\) | −4.32850 | −0.319972 | ||||||||
\(184\) | −1.36794 | −0.100846 | ||||||||
\(185\) | −48.7069 | −3.58100 | ||||||||
\(186\) | −10.8482 | −0.795430 | ||||||||
\(187\) | −3.36794 | −0.246288 | ||||||||
\(188\) | 2.96056 | 0.215921 | ||||||||
\(189\) | −1.94809 | −0.141703 | ||||||||
\(190\) | −4.16425 | −0.302106 | ||||||||
\(191\) | 8.22468 | 0.595117 | 0.297559 | − | 0.954704i | \(-0.403828\pi\) | ||||
0.297559 | + | 0.954704i | \(0.403828\pi\) | |||||||
\(192\) | −2.16425 | −0.156191 | ||||||||
\(193\) | −24.2141 | −1.74297 | −0.871485 | − | 0.490422i | \(-0.836842\pi\) | ||||
−0.871485 | + | 0.490422i | \(0.836842\pi\) | |||||||
\(194\) | −11.6964 | −0.839755 | ||||||||
\(195\) | −24.1892 | −1.73222 | ||||||||
\(196\) | −6.53219 | −0.466585 | ||||||||
\(197\) | 26.6570 | 1.89923 | 0.949616 | − | 0.313416i | \(-0.101473\pi\) | ||||
0.949616 | + | 0.313416i | \(0.101473\pi\) | |||||||
\(198\) | −1.68397 | −0.119674 | ||||||||
\(199\) | −7.06437 | −0.500780 | −0.250390 | − | 0.968145i | \(-0.580559\pi\) | ||||
−0.250390 | + | 0.968145i | \(0.580559\pi\) | |||||||
\(200\) | 12.3410 | 0.872638 | ||||||||
\(201\) | 1.48028 | 0.104411 | ||||||||
\(202\) | 3.59262 | 0.252776 | ||||||||
\(203\) | −1.91259 | −0.134237 | ||||||||
\(204\) | −7.28905 | −0.510336 | ||||||||
\(205\) | −29.2016 | −2.03953 | ||||||||
\(206\) | −4.46781 | −0.311287 | ||||||||
\(207\) | −2.30357 | −0.160109 | ||||||||
\(208\) | 2.68397 | 0.186100 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 6.16425 | 0.425374 | ||||||||
\(211\) | −11.0644 | −0.761703 | −0.380851 | − | 0.924636i | \(-0.624369\pi\) | ||||
−0.380851 | + | 0.924636i | \(0.624369\pi\) | |||||||
\(212\) | −10.3285 | −0.709364 | ||||||||
\(213\) | −7.64453 | −0.523794 | ||||||||
\(214\) | 9.69643 | 0.662835 | ||||||||
\(215\) | 32.7338 | 2.23243 | ||||||||
\(216\) | 2.84822 | 0.193797 | ||||||||
\(217\) | −3.42837 | −0.232733 | ||||||||
\(218\) | 6.00000 | 0.406371 | ||||||||
\(219\) | −0.881673 | −0.0595779 | ||||||||
\(220\) | −4.16425 | −0.280754 | ||||||||
\(221\) | 9.03944 | 0.608059 | ||||||||
\(222\) | 25.3140 | 1.69896 | ||||||||
\(223\) | −14.7359 | −0.986787 | −0.493394 | − | 0.869806i | \(-0.664244\pi\) | ||||
−0.493394 | + | 0.869806i | \(0.664244\pi\) | |||||||
\(224\) | −0.683969 | −0.0456996 | ||||||||
\(225\) | 20.7818 | 1.38545 | ||||||||
\(226\) | 10.4323 | 0.693947 | ||||||||
\(227\) | 21.8002 | 1.44693 | 0.723467 | − | 0.690359i | \(-0.242548\pi\) | ||||
0.723467 | + | 0.690359i | \(0.242548\pi\) | |||||||
\(228\) | 2.16425 | 0.143331 | ||||||||
\(229\) | 17.7483 | 1.17284 | 0.586422 | − | 0.810006i | \(-0.300536\pi\) | ||||
0.586422 | + | 0.810006i | \(0.300536\pi\) | |||||||
\(230\) | −5.69643 | −0.375612 | ||||||||
\(231\) | −1.48028 | −0.0973952 | ||||||||
\(232\) | 2.79631 | 0.183587 | ||||||||
\(233\) | −20.3534 | −1.33340 | −0.666699 | − | 0.745327i | \(-0.732293\pi\) | ||||
−0.666699 | + | 0.745327i | \(0.732293\pi\) | |||||||
\(234\) | 4.51972 | 0.295463 | ||||||||
\(235\) | 12.3285 | 0.804222 | ||||||||
\(236\) | −9.92112 | −0.645810 | ||||||||
\(237\) | 15.7753 | 1.02472 | ||||||||
\(238\) | −2.30357 | −0.149318 | ||||||||
\(239\) | 3.75687 | 0.243012 | 0.121506 | − | 0.992591i | \(-0.461228\pi\) | ||||
0.121506 | + | 0.992591i | \(0.461228\pi\) | |||||||
\(240\) | −9.01247 | −0.581752 | ||||||||
\(241\) | −9.14974 | −0.589386 | −0.294693 | − | 0.955592i | \(-0.595217\pi\) | ||||
−0.294693 | + | 0.955592i | \(0.595217\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 15.7299 | 1.00907 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | −27.2016 | −1.73785 | ||||||||
\(246\) | 15.1767 | 0.967632 | ||||||||
\(247\) | −2.68397 | −0.170777 | ||||||||
\(248\) | 5.01247 | 0.318292 | ||||||||
\(249\) | 26.3804 | 1.67179 | ||||||||
\(250\) | 30.5696 | 1.93339 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | −1.15178 | −0.0725555 | ||||||||
\(253\) | 1.36794 | 0.0860015 | ||||||||
\(254\) | 15.2891 | 0.959321 | ||||||||
\(255\) | −30.3534 | −1.90081 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.2102 | 1.44781 | 0.723905 | − | 0.689899i | \(-0.242345\pi\) | ||||
0.723905 | + | 0.689899i | \(0.242345\pi\) | |||||||
\(258\) | −17.0125 | −1.05915 | ||||||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 11.1767 | 0.693150 | ||||||||
\(261\) | 4.70890 | 0.291474 | ||||||||
\(262\) | 3.64453 | 0.225160 | ||||||||
\(263\) | −22.2141 | −1.36978 | −0.684890 | − | 0.728646i | \(-0.740150\pi\) | ||||
−0.684890 | + | 0.728646i | \(0.740150\pi\) | |||||||
\(264\) | 2.16425 | 0.133200 | ||||||||
\(265\) | −43.0104 | −2.64211 | ||||||||
\(266\) | 0.683969 | 0.0419368 | ||||||||
\(267\) | 36.1038 | 2.20952 | ||||||||
\(268\) | −0.683969 | −0.0417801 | ||||||||
\(269\) | −18.9855 | −1.15757 | −0.578783 | − | 0.815482i | \(-0.696472\pi\) | ||||
−0.578783 | + | 0.815482i | \(0.696472\pi\) | |||||||
\(270\) | 11.8607 | 0.721818 | ||||||||
\(271\) | 20.7338 | 1.25949 | 0.629745 | − | 0.776802i | \(-0.283159\pi\) | ||||
0.629745 | + | 0.776802i | \(0.283159\pi\) | |||||||
\(272\) | 3.36794 | 0.204211 | ||||||||
\(273\) | 3.97302 | 0.240458 | ||||||||
\(274\) | 14.6840 | 0.887091 | ||||||||
\(275\) | −12.3410 | −0.744188 | ||||||||
\(276\) | 2.96056 | 0.178205 | ||||||||
\(277\) | 21.8422 | 1.31237 | 0.656186 | − | 0.754599i | \(-0.272169\pi\) | ||||
0.656186 | + | 0.754599i | \(0.272169\pi\) | |||||||
\(278\) | −18.5966 | −1.11535 | ||||||||
\(279\) | 8.44084 | 0.505340 | ||||||||
\(280\) | −2.84822 | −0.170214 | ||||||||
\(281\) | 0.164248 | 0.00979821 | 0.00489911 | − | 0.999988i | \(-0.498441\pi\) | ||||
0.00489911 | + | 0.999988i | \(0.498441\pi\) | |||||||
\(282\) | −6.40738 | −0.381554 | ||||||||
\(283\) | 4.30152 | 0.255699 | 0.127849 | − | 0.991794i | \(-0.459193\pi\) | ||||
0.127849 | + | 0.991794i | \(0.459193\pi\) | |||||||
\(284\) | 3.53219 | 0.209597 | ||||||||
\(285\) | 9.01247 | 0.533852 | ||||||||
\(286\) | −2.68397 | −0.158706 | ||||||||
\(287\) | 4.79631 | 0.283117 | ||||||||
\(288\) | 1.68397 | 0.0992288 | ||||||||
\(289\) | −5.65699 | −0.332764 | ||||||||
\(290\) | 11.6445 | 0.683790 | ||||||||
\(291\) | 25.3140 | 1.48393 | ||||||||
\(292\) | 0.407381 | 0.0238402 | ||||||||
\(293\) | 32.5511 | 1.90166 | 0.950829 | − | 0.309717i | \(-0.100234\pi\) | ||||
0.950829 | + | 0.309717i | \(0.100234\pi\) | |||||||
\(294\) | 14.1373 | 0.824502 | ||||||||
\(295\) | −41.3140 | −2.40539 | ||||||||
\(296\) | −11.6964 | −0.679841 | ||||||||
\(297\) | −2.84822 | −0.165270 | ||||||||
\(298\) | 4.30357 | 0.249299 | ||||||||
\(299\) | −3.67150 | −0.212329 | ||||||||
\(300\) | −26.7089 | −1.54204 | ||||||||
\(301\) | −5.37646 | −0.309894 | ||||||||
\(302\) | −21.6964 | −1.24849 | ||||||||
\(303\) | −7.77532 | −0.446680 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 8.32850 | 0.476888 | ||||||||
\(306\) | 5.67150 | 0.324218 | ||||||||
\(307\) | 22.2496 | 1.26985 | 0.634926 | − | 0.772573i | \(-0.281030\pi\) | ||||
0.634926 | + | 0.772573i | \(0.281030\pi\) | |||||||
\(308\) | 0.683969 | 0.0389728 | ||||||||
\(309\) | 9.66946 | 0.550076 | ||||||||
\(310\) | 20.8731 | 1.18552 | ||||||||
\(311\) | −20.9855 | −1.18998 | −0.594989 | − | 0.803734i | \(-0.702844\pi\) | ||||
−0.594989 | + | 0.803734i | \(0.702844\pi\) | |||||||
\(312\) | −5.80877 | −0.328857 | ||||||||
\(313\) | −11.4533 | −0.647379 | −0.323689 | − | 0.946163i | \(-0.604923\pi\) | ||||
−0.323689 | + | 0.946163i | \(0.604923\pi\) | |||||||
\(314\) | −10.9001 | −0.615130 | ||||||||
\(315\) | −4.79631 | −0.270241 | ||||||||
\(316\) | −7.28905 | −0.410041 | ||||||||
\(317\) | 10.7109 | 0.601587 | 0.300793 | − | 0.953689i | \(-0.402749\pi\) | ||||
0.300793 | + | 0.953689i | \(0.402749\pi\) | |||||||
\(318\) | 22.3534 | 1.25352 | ||||||||
\(319\) | −2.79631 | −0.156563 | ||||||||
\(320\) | 4.16425 | 0.232789 | ||||||||
\(321\) | −20.9855 | −1.17130 | ||||||||
\(322\) | 0.935628 | 0.0521405 | ||||||||
\(323\) | −3.36794 | −0.187397 | ||||||||
\(324\) | −11.2162 | −0.623120 | ||||||||
\(325\) | 33.1228 | 1.83732 | ||||||||
\(326\) | 19.7214 | 1.09227 | ||||||||
\(327\) | −12.9855 | −0.718099 | ||||||||
\(328\) | −7.01247 | −0.387199 | ||||||||
\(329\) | −2.02493 | −0.111638 | ||||||||
\(330\) | 9.01247 | 0.496120 | ||||||||
\(331\) | −6.77138 | −0.372189 | −0.186094 | − | 0.982532i | \(-0.559583\pi\) | ||||
−0.186094 | + | 0.982532i | \(0.559583\pi\) | |||||||
\(332\) | −12.1892 | −0.668968 | ||||||||
\(333\) | −19.6964 | −1.07936 | ||||||||
\(334\) | 7.77532 | 0.425447 | ||||||||
\(335\) | −2.84822 | −0.155615 | ||||||||
\(336\) | 1.48028 | 0.0807558 | ||||||||
\(337\) | 21.0374 | 1.14598 | 0.572990 | − | 0.819562i | \(-0.305783\pi\) | ||||
0.572990 | + | 0.819562i | \(0.305783\pi\) | |||||||
\(338\) | −5.79631 | −0.315278 | ||||||||
\(339\) | −22.5781 | −1.22627 | ||||||||
\(340\) | 14.0249 | 0.760609 | ||||||||
\(341\) | −5.01247 | −0.271440 | ||||||||
\(342\) | −1.68397 | −0.0910586 | ||||||||
\(343\) | 9.25560 | 0.499755 | ||||||||
\(344\) | 7.86068 | 0.423820 | ||||||||
\(345\) | 12.3285 | 0.663744 | ||||||||
\(346\) | 15.7818 | 0.848435 | ||||||||
\(347\) | −29.9710 | −1.60893 | −0.804463 | − | 0.594003i | \(-0.797547\pi\) | ||||
−0.804463 | + | 0.594003i | \(0.797547\pi\) | |||||||
\(348\) | −6.05191 | −0.324416 | ||||||||
\(349\) | −22.6570 | −1.21280 | −0.606400 | − | 0.795159i | \(-0.707387\pi\) | ||||
−0.606400 | + | 0.795159i | \(0.707387\pi\) | |||||||
\(350\) | −8.44084 | −0.451182 | ||||||||
\(351\) | 7.64453 | 0.408035 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −1.18524 | −0.0630839 | −0.0315419 | − | 0.999502i | \(-0.510042\pi\) | ||||
−0.0315419 | + | 0.999502i | \(0.510042\pi\) | |||||||
\(354\) | 21.4718 | 1.14121 | ||||||||
\(355\) | 14.7089 | 0.780667 | ||||||||
\(356\) | −16.6819 | −0.884140 | ||||||||
\(357\) | 4.98549 | 0.263860 | ||||||||
\(358\) | −7.97302 | −0.421387 | ||||||||
\(359\) | 19.3659 | 1.02209 | 0.511046 | − | 0.859553i | \(-0.329258\pi\) | ||||
0.511046 | + | 0.859553i | \(0.329258\pi\) | |||||||
\(360\) | 7.01247 | 0.369589 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −2.55318 | −0.134192 | ||||||||
\(363\) | −2.16425 | −0.113594 | ||||||||
\(364\) | −1.83575 | −0.0962196 | ||||||||
\(365\) | 1.69643 | 0.0887954 | ||||||||
\(366\) | −4.32850 | −0.226254 | ||||||||
\(367\) | −18.3036 | −0.955438 | −0.477719 | − | 0.878513i | \(-0.658536\pi\) | ||||
−0.477719 | + | 0.878513i | \(0.658536\pi\) | |||||||
\(368\) | −1.36794 | −0.0713087 | ||||||||
\(369\) | −11.8088 | −0.614740 | ||||||||
\(370\) | −48.7069 | −2.53215 | ||||||||
\(371\) | 7.06437 | 0.366764 | ||||||||
\(372\) | −10.8482 | −0.562454 | ||||||||
\(373\) | 6.46781 | 0.334891 | 0.167445 | − | 0.985881i | \(-0.446448\pi\) | ||||
0.167445 | + | 0.985881i | \(0.446448\pi\) | |||||||
\(374\) | −3.36794 | −0.174152 | ||||||||
\(375\) | −66.1602 | −3.41650 | ||||||||
\(376\) | 2.96056 | 0.152679 | ||||||||
\(377\) | 7.50521 | 0.386538 | ||||||||
\(378\) | −1.94809 | −0.100199 | ||||||||
\(379\) | 31.9191 | 1.63957 | 0.819786 | − | 0.572670i | \(-0.194092\pi\) | ||||
0.819786 | + | 0.572670i | \(0.194092\pi\) | |||||||
\(380\) | −4.16425 | −0.213621 | ||||||||
\(381\) | −33.0893 | −1.69522 | ||||||||
\(382\) | 8.22468 | 0.420811 | ||||||||
\(383\) | 5.66946 | 0.289696 | 0.144848 | − | 0.989454i | \(-0.453731\pi\) | ||||
0.144848 | + | 0.989454i | \(0.453731\pi\) | |||||||
\(384\) | −2.16425 | −0.110444 | ||||||||
\(385\) | 2.84822 | 0.145159 | ||||||||
\(386\) | −24.2141 | −1.23247 | ||||||||
\(387\) | 13.2371 | 0.672882 | ||||||||
\(388\) | −11.6964 | −0.593796 | ||||||||
\(389\) | 20.1642 | 1.02237 | 0.511184 | − | 0.859471i | \(-0.329207\pi\) | ||||
0.511184 | + | 0.859471i | \(0.329207\pi\) | |||||||
\(390\) | −24.1892 | −1.22487 | ||||||||
\(391\) | −4.60713 | −0.232993 | ||||||||
\(392\) | −6.53219 | −0.329925 | ||||||||
\(393\) | −7.88766 | −0.397880 | ||||||||
\(394\) | 26.6570 | 1.34296 | ||||||||
\(395\) | −30.3534 | −1.52725 | ||||||||
\(396\) | −1.68397 | −0.0846226 | ||||||||
\(397\) | −15.8272 | −0.794346 | −0.397173 | − | 0.917744i | \(-0.630009\pi\) | ||||
−0.397173 | + | 0.917744i | \(0.630009\pi\) | |||||||
\(398\) | −7.06437 | −0.354105 | ||||||||
\(399\) | −1.48028 | −0.0741066 | ||||||||
\(400\) | 12.3410 | 0.617048 | ||||||||
\(401\) | 9.06437 | 0.452653 | 0.226327 | − | 0.974051i | \(-0.427328\pi\) | ||||
0.226327 | + | 0.974051i | \(0.427328\pi\) | |||||||
\(402\) | 1.48028 | 0.0738296 | ||||||||
\(403\) | 13.4533 | 0.670157 | ||||||||
\(404\) | 3.59262 | 0.178739 | ||||||||
\(405\) | −46.7069 | −2.32088 | ||||||||
\(406\) | −1.91259 | −0.0949202 | ||||||||
\(407\) | 11.6964 | 0.579771 | ||||||||
\(408\) | −7.28905 | −0.360862 | ||||||||
\(409\) | 2.90012 | 0.143402 | 0.0717010 | − | 0.997426i | \(-0.477157\pi\) | ||||
0.0717010 | + | 0.997426i | \(0.477157\pi\) | |||||||
\(410\) | −29.2016 | −1.44217 | ||||||||
\(411\) | −31.7797 | −1.56758 | ||||||||
\(412\) | −4.46781 | −0.220113 | ||||||||
\(413\) | 6.78574 | 0.333904 | ||||||||
\(414\) | −2.30357 | −0.113214 | ||||||||
\(415\) | −50.7588 | −2.49165 | ||||||||
\(416\) | 2.68397 | 0.131592 | ||||||||
\(417\) | 40.2476 | 1.97093 | ||||||||
\(418\) | 1.00000 | 0.0489116 | ||||||||
\(419\) | 19.7753 | 0.966088 | 0.483044 | − | 0.875596i | \(-0.339531\pi\) | ||||
0.483044 | + | 0.875596i | \(0.339531\pi\) | |||||||
\(420\) | 6.16425 | 0.300785 | ||||||||
\(421\) | 14.9855 | 0.730348 | 0.365174 | − | 0.930939i | \(-0.381009\pi\) | ||||
0.365174 | + | 0.930939i | \(0.381009\pi\) | |||||||
\(422\) | −11.0644 | −0.538605 | ||||||||
\(423\) | 4.98549 | 0.242403 | ||||||||
\(424\) | −10.3285 | −0.501596 | ||||||||
\(425\) | 41.5636 | 2.01613 | ||||||||
\(426\) | −7.64453 | −0.370379 | ||||||||
\(427\) | −1.36794 | −0.0661992 | ||||||||
\(428\) | 9.69643 | 0.468695 | ||||||||
\(429\) | 5.80877 | 0.280450 | ||||||||
\(430\) | 32.7338 | 1.57857 | ||||||||
\(431\) | 39.4427 | 1.89989 | 0.949945 | − | 0.312418i | \(-0.101139\pi\) | ||||
0.949945 | + | 0.312418i | \(0.101139\pi\) | |||||||
\(432\) | 2.84822 | 0.137035 | ||||||||
\(433\) | −1.23919 | −0.0595518 | −0.0297759 | − | 0.999557i | \(-0.509479\pi\) | ||||
−0.0297759 | + | 0.999557i | \(0.509479\pi\) | |||||||
\(434\) | −3.42837 | −0.164567 | ||||||||
\(435\) | −25.2016 | −1.20833 | ||||||||
\(436\) | 6.00000 | 0.287348 | ||||||||
\(437\) | 1.36794 | 0.0654374 | ||||||||
\(438\) | −0.881673 | −0.0421280 | ||||||||
\(439\) | −11.1852 | −0.533842 | −0.266921 | − | 0.963718i | \(-0.586006\pi\) | ||||
−0.266921 | + | 0.963718i | \(0.586006\pi\) | |||||||
\(440\) | −4.16425 | −0.198523 | ||||||||
\(441\) | −11.0000 | −0.523810 | ||||||||
\(442\) | 9.03944 | 0.429962 | ||||||||
\(443\) | 23.8422 | 1.13278 | 0.566389 | − | 0.824138i | \(-0.308340\pi\) | ||||
0.566389 | + | 0.824138i | \(0.308340\pi\) | |||||||
\(444\) | 25.3140 | 1.20135 | ||||||||
\(445\) | −69.4677 | −3.29308 | ||||||||
\(446\) | −14.7359 | −0.697764 | ||||||||
\(447\) | −9.31398 | −0.440536 | ||||||||
\(448\) | −0.683969 | −0.0323145 | ||||||||
\(449\) | 20.9066 | 0.986644 | 0.493322 | − | 0.869847i | \(-0.335783\pi\) | ||||
0.493322 | + | 0.869847i | \(0.335783\pi\) | |||||||
\(450\) | 20.7818 | 0.979663 | ||||||||
\(451\) | 7.01247 | 0.330204 | ||||||||
\(452\) | 10.4323 | 0.490695 | ||||||||
\(453\) | 46.9565 | 2.20621 | ||||||||
\(454\) | 21.8002 | 1.02314 | ||||||||
\(455\) | −7.64453 | −0.358381 | ||||||||
\(456\) | 2.16425 | 0.101350 | ||||||||
\(457\) | −4.18270 | −0.195658 | −0.0978292 | − | 0.995203i | \(-0.531190\pi\) | ||||
−0.0978292 | + | 0.995203i | \(0.531190\pi\) | |||||||
\(458\) | 17.7483 | 0.829326 | ||||||||
\(459\) | 9.59262 | 0.447745 | ||||||||
\(460\) | −5.69643 | −0.265598 | ||||||||
\(461\) | −31.5387 | −1.46890 | −0.734451 | − | 0.678662i | \(-0.762560\pi\) | ||||
−0.734451 | + | 0.678662i | \(0.762560\pi\) | |||||||
\(462\) | −1.48028 | −0.0688688 | ||||||||
\(463\) | −4.60713 | −0.214112 | −0.107056 | − | 0.994253i | \(-0.534142\pi\) | ||||
−0.107056 | + | 0.994253i | \(0.534142\pi\) | |||||||
\(464\) | 2.79631 | 0.129815 | ||||||||
\(465\) | −45.1747 | −2.09492 | ||||||||
\(466\) | −20.3534 | −0.942854 | ||||||||
\(467\) | −3.94605 | −0.182601 | −0.0913006 | − | 0.995823i | \(-0.529102\pi\) | ||||
−0.0913006 | + | 0.995823i | \(0.529102\pi\) | |||||||
\(468\) | 4.51972 | 0.208924 | ||||||||
\(469\) | 0.467814 | 0.0216016 | ||||||||
\(470\) | 12.3285 | 0.568671 | ||||||||
\(471\) | 23.5906 | 1.08700 | ||||||||
\(472\) | −9.92112 | −0.456656 | ||||||||
\(473\) | −7.86068 | −0.361435 | ||||||||
\(474\) | 15.7753 | 0.724584 | ||||||||
\(475\) | −12.3410 | −0.566242 | ||||||||
\(476\) | −2.30357 | −0.105584 | ||||||||
\(477\) | −17.3929 | −0.796365 | ||||||||
\(478\) | 3.75687 | 0.171835 | ||||||||
\(479\) | −16.6840 | −0.762310 | −0.381155 | − | 0.924511i | \(-0.624474\pi\) | ||||
−0.381155 | + | 0.924511i | \(0.624474\pi\) | |||||||
\(480\) | −9.01247 | −0.411361 | ||||||||
\(481\) | −31.3929 | −1.43139 | ||||||||
\(482\) | −9.14974 | −0.416759 | ||||||||
\(483\) | −2.02493 | −0.0921375 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −48.7069 | −2.21166 | ||||||||
\(486\) | 15.7299 | 0.713522 | ||||||||
\(487\) | −14.4388 | −0.654284 | −0.327142 | − | 0.944975i | \(-0.606086\pi\) | ||||
−0.327142 | + | 0.944975i | \(0.606086\pi\) | |||||||
\(488\) | 2.00000 | 0.0905357 | ||||||||
\(489\) | −42.6819 | −1.93014 | ||||||||
\(490\) | −27.2016 | −1.22884 | ||||||||
\(491\) | 6.38040 | 0.287944 | 0.143972 | − | 0.989582i | \(-0.454013\pi\) | ||||
0.143972 | + | 0.989582i | \(0.454013\pi\) | |||||||
\(492\) | 15.1767 | 0.684219 | ||||||||
\(493\) | 9.41780 | 0.424156 | ||||||||
\(494\) | −2.68397 | −0.120757 | ||||||||
\(495\) | −7.01247 | −0.315187 | ||||||||
\(496\) | 5.01247 | 0.225066 | ||||||||
\(497\) | −2.41591 | −0.108368 | ||||||||
\(498\) | 26.3804 | 1.18213 | ||||||||
\(499\) | −31.8252 | −1.42469 | −0.712345 | − | 0.701829i | \(-0.752367\pi\) | ||||
−0.712345 | + | 0.701829i | \(0.752367\pi\) | |||||||
\(500\) | 30.5696 | 1.36711 | ||||||||
\(501\) | −16.8277 | −0.751807 | ||||||||
\(502\) | −12.0000 | −0.535586 | ||||||||
\(503\) | 24.5716 | 1.09559 | 0.547797 | − | 0.836611i | \(-0.315466\pi\) | ||||
0.547797 | + | 0.836611i | \(0.315466\pi\) | |||||||
\(504\) | −1.15178 | −0.0513045 | ||||||||
\(505\) | 14.9606 | 0.665736 | ||||||||
\(506\) | 1.36794 | 0.0608123 | ||||||||
\(507\) | 12.5447 | 0.557128 | ||||||||
\(508\) | 15.2891 | 0.678342 | ||||||||
\(509\) | −5.56769 | −0.246783 | −0.123392 | − | 0.992358i | \(-0.539377\pi\) | ||||
−0.123392 | + | 0.992358i | \(0.539377\pi\) | |||||||
\(510\) | −30.3534 | −1.34407 | ||||||||
\(511\) | −0.278636 | −0.0123261 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.84822 | −0.125752 | ||||||||
\(514\) | 23.2102 | 1.02376 | ||||||||
\(515\) | −18.6051 | −0.819838 | ||||||||
\(516\) | −17.0125 | −0.748932 | ||||||||
\(517\) | −2.96056 | −0.130205 | ||||||||
\(518\) | 8.00000 | 0.351500 | ||||||||
\(519\) | −34.1557 | −1.49927 | ||||||||
\(520\) | 11.1767 | 0.490131 | ||||||||
\(521\) | −10.8148 | −0.473803 | −0.236902 | − | 0.971534i | \(-0.576132\pi\) | ||||
−0.236902 | + | 0.971534i | \(0.576132\pi\) | |||||||
\(522\) | 4.70890 | 0.206103 | ||||||||
\(523\) | −18.4074 | −0.804899 | −0.402449 | − | 0.915442i | \(-0.631841\pi\) | ||||
−0.402449 | + | 0.915442i | \(0.631841\pi\) | |||||||
\(524\) | 3.64453 | 0.159212 | ||||||||
\(525\) | 18.2681 | 0.797284 | ||||||||
\(526\) | −22.2141 | −0.968581 | ||||||||
\(527\) | 16.8817 | 0.735377 | ||||||||
\(528\) | 2.16425 | 0.0941868 | ||||||||
\(529\) | −21.1287 | −0.918641 | ||||||||
\(530\) | −43.0104 | −1.86825 | ||||||||
\(531\) | −16.7069 | −0.725016 | ||||||||
\(532\) | 0.683969 | 0.0296538 | ||||||||
\(533\) | −18.8212 | −0.815238 | ||||||||
\(534\) | 36.1038 | 1.56236 | ||||||||
\(535\) | 40.3784 | 1.74571 | ||||||||
\(536\) | −0.683969 | −0.0295430 | ||||||||
\(537\) | 17.2556 | 0.744634 | ||||||||
\(538\) | −18.9855 | −0.818522 | ||||||||
\(539\) | 6.53219 | 0.281361 | ||||||||
\(540\) | 11.8607 | 0.510402 | ||||||||
\(541\) | 33.0644 | 1.42155 | 0.710774 | − | 0.703420i | \(-0.248345\pi\) | ||||
0.710774 | + | 0.703420i | \(0.248345\pi\) | |||||||
\(542\) | 20.7338 | 0.890594 | ||||||||
\(543\) | 5.52571 | 0.237131 | ||||||||
\(544\) | 3.36794 | 0.144399 | ||||||||
\(545\) | 24.9855 | 1.07026 | ||||||||
\(546\) | 3.97302 | 0.170030 | ||||||||
\(547\) | 34.1287 | 1.45924 | 0.729620 | − | 0.683853i | \(-0.239697\pi\) | ||||
0.729620 | + | 0.683853i | \(0.239697\pi\) | |||||||
\(548\) | 14.6840 | 0.627268 | ||||||||
\(549\) | 3.36794 | 0.143740 | ||||||||
\(550\) | −12.3410 | −0.526220 | ||||||||
\(551\) | −2.79631 | −0.119127 | ||||||||
\(552\) | 2.96056 | 0.126010 | ||||||||
\(553\) | 4.98549 | 0.212004 | ||||||||
\(554\) | 21.8422 | 0.927987 | ||||||||
\(555\) | 105.414 | 4.47456 | ||||||||
\(556\) | −18.5966 | −0.788670 | ||||||||
\(557\) | 20.5112 | 0.869087 | 0.434544 | − | 0.900651i | \(-0.356910\pi\) | ||||
0.434544 | + | 0.900651i | \(0.356910\pi\) | |||||||
\(558\) | 8.44084 | 0.357329 | ||||||||
\(559\) | 21.0978 | 0.892343 | ||||||||
\(560\) | −2.84822 | −0.120359 | ||||||||
\(561\) | 7.28905 | 0.307744 | ||||||||
\(562\) | 0.164248 | 0.00692838 | ||||||||
\(563\) | −27.0104 | −1.13835 | −0.569177 | − | 0.822215i | \(-0.692738\pi\) | ||||
−0.569177 | + | 0.822215i | \(0.692738\pi\) | |||||||
\(564\) | −6.40738 | −0.269799 | ||||||||
\(565\) | 43.4427 | 1.82765 | ||||||||
\(566\) | 4.30152 | 0.180806 | ||||||||
\(567\) | 7.67150 | 0.322173 | ||||||||
\(568\) | 3.53219 | 0.148207 | ||||||||
\(569\) | 7.56564 | 0.317168 | 0.158584 | − | 0.987345i | \(-0.449307\pi\) | ||||
0.158584 | + | 0.987345i | \(0.449307\pi\) | |||||||
\(570\) | 9.01247 | 0.377491 | ||||||||
\(571\) | 42.2226 | 1.76696 | 0.883481 | − | 0.468467i | \(-0.155193\pi\) | ||||
0.883481 | + | 0.468467i | \(0.155193\pi\) | |||||||
\(572\) | −2.68397 | −0.112222 | ||||||||
\(573\) | −17.8002 | −0.743616 | ||||||||
\(574\) | 4.79631 | 0.200194 | ||||||||
\(575\) | −16.8817 | −0.704014 | ||||||||
\(576\) | 1.68397 | 0.0701654 | ||||||||
\(577\) | −25.9191 | −1.07902 | −0.539512 | − | 0.841978i | \(-0.681391\pi\) | ||||
−0.539512 | + | 0.841978i | \(0.681391\pi\) | |||||||
\(578\) | −5.65699 | −0.235300 | ||||||||
\(579\) | 52.4053 | 2.17789 | ||||||||
\(580\) | 11.6445 | 0.483513 | ||||||||
\(581\) | 8.33702 | 0.345878 | ||||||||
\(582\) | 25.3140 | 1.04930 | ||||||||
\(583\) | 10.3285 | 0.427763 | ||||||||
\(584\) | 0.407381 | 0.0168575 | ||||||||
\(585\) | 18.8212 | 0.778162 | ||||||||
\(586\) | 32.5511 | 1.34467 | ||||||||
\(587\) | 20.6570 | 0.852605 | 0.426303 | − | 0.904581i | \(-0.359816\pi\) | ||||
0.426303 | + | 0.904581i | \(0.359816\pi\) | |||||||
\(588\) | 14.1373 | 0.583011 | ||||||||
\(589\) | −5.01247 | −0.206535 | ||||||||
\(590\) | −41.3140 | −1.70087 | ||||||||
\(591\) | −57.6923 | −2.37315 | ||||||||
\(592\) | −11.6964 | −0.480720 | ||||||||
\(593\) | −28.1287 | −1.15511 | −0.577555 | − | 0.816352i | \(-0.695993\pi\) | ||||
−0.577555 | + | 0.816352i | \(0.695993\pi\) | |||||||
\(594\) | −2.84822 | −0.116864 | ||||||||
\(595\) | −9.59262 | −0.393259 | ||||||||
\(596\) | 4.30357 | 0.176281 | ||||||||
\(597\) | 15.2891 | 0.625739 | ||||||||
\(598\) | −3.67150 | −0.150139 | ||||||||
\(599\) | −26.3179 | −1.07532 | −0.537661 | − | 0.843161i | \(-0.680692\pi\) | ||||
−0.537661 | + | 0.843161i | \(0.680692\pi\) | |||||||
\(600\) | −26.7089 | −1.09039 | ||||||||
\(601\) | 38.4053 | 1.56659 | 0.783293 | − | 0.621653i | \(-0.213538\pi\) | ||||
0.783293 | + | 0.621653i | \(0.213538\pi\) | |||||||
\(602\) | −5.37646 | −0.219128 | ||||||||
\(603\) | −1.15178 | −0.0469042 | ||||||||
\(604\) | −21.6964 | −0.882815 | ||||||||
\(605\) | 4.16425 | 0.169301 | ||||||||
\(606\) | −7.77532 | −0.315851 | ||||||||
\(607\) | −33.2600 | −1.34998 | −0.674991 | − | 0.737826i | \(-0.735853\pi\) | ||||
−0.674991 | + | 0.737826i | \(0.735853\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 4.13932 | 0.167734 | ||||||||
\(610\) | 8.32850 | 0.337211 | ||||||||
\(611\) | 7.94605 | 0.321463 | ||||||||
\(612\) | 5.67150 | 0.229257 | ||||||||
\(613\) | 17.5506 | 0.708864 | 0.354432 | − | 0.935082i | \(-0.384674\pi\) | ||||
0.354432 | + | 0.935082i | \(0.384674\pi\) | |||||||
\(614\) | 22.2496 | 0.897921 | ||||||||
\(615\) | 63.1996 | 2.54845 | ||||||||
\(616\) | 0.683969 | 0.0275579 | ||||||||
\(617\) | 14.6840 | 0.591154 | 0.295577 | − | 0.955319i | \(-0.404488\pi\) | ||||
0.295577 | + | 0.955319i | \(0.404488\pi\) | |||||||
\(618\) | 9.66946 | 0.388963 | ||||||||
\(619\) | 11.1183 | 0.446883 | 0.223442 | − | 0.974717i | \(-0.428271\pi\) | ||||
0.223442 | + | 0.974717i | \(0.428271\pi\) | |||||||
\(620\) | 20.8731 | 0.838286 | ||||||||
\(621\) | −3.89619 | −0.156349 | ||||||||
\(622\) | −20.9855 | −0.841441 | ||||||||
\(623\) | 11.4099 | 0.457129 | ||||||||
\(624\) | −5.80877 | −0.232537 | ||||||||
\(625\) | 65.5945 | 2.62378 | ||||||||
\(626\) | −11.4533 | −0.457766 | ||||||||
\(627\) | −2.16425 | −0.0864317 | ||||||||
\(628\) | −10.9001 | −0.434962 | ||||||||
\(629\) | −39.3929 | −1.57070 | ||||||||
\(630\) | −4.79631 | −0.191090 | ||||||||
\(631\) | −46.0748 | −1.83421 | −0.917104 | − | 0.398648i | \(-0.869480\pi\) | ||||
−0.917104 | + | 0.398648i | \(0.869480\pi\) | |||||||
\(632\) | −7.28905 | −0.289943 | ||||||||
\(633\) | 23.9460 | 0.951770 | ||||||||
\(634\) | 10.7109 | 0.425386 | ||||||||
\(635\) | 63.6674 | 2.52656 | ||||||||
\(636\) | 22.3534 | 0.886371 | ||||||||
\(637\) | −17.5322 | −0.694651 | ||||||||
\(638\) | −2.79631 | −0.110707 | ||||||||
\(639\) | 5.94809 | 0.235303 | ||||||||
\(640\) | 4.16425 | 0.164606 | ||||||||
\(641\) | −11.3181 | −0.447037 | −0.223519 | − | 0.974700i | \(-0.571754\pi\) | ||||
−0.223519 | + | 0.974700i | \(0.571754\pi\) | |||||||
\(642\) | −20.9855 | −0.828231 | ||||||||
\(643\) | −30.6280 | −1.20785 | −0.603925 | − | 0.797041i | \(-0.706397\pi\) | ||||
−0.603925 | + | 0.797041i | \(0.706397\pi\) | |||||||
\(644\) | 0.935628 | 0.0368689 | ||||||||
\(645\) | −70.8441 | −2.78948 | ||||||||
\(646\) | −3.36794 | −0.132510 | ||||||||
\(647\) | −31.2720 | −1.22943 | −0.614715 | − | 0.788750i | \(-0.710729\pi\) | ||||
−0.614715 | + | 0.788750i | \(0.710729\pi\) | |||||||
\(648\) | −11.2162 | −0.440612 | ||||||||
\(649\) | 9.92112 | 0.389438 | ||||||||
\(650\) | 33.1228 | 1.29918 | ||||||||
\(651\) | 7.41985 | 0.290807 | ||||||||
\(652\) | 19.7214 | 0.772348 | ||||||||
\(653\) | −2.09389 | −0.0819402 | −0.0409701 | − | 0.999160i | \(-0.513045\pi\) | ||||
−0.0409701 | + | 0.999160i | \(0.513045\pi\) | |||||||
\(654\) | −12.9855 | −0.507773 | ||||||||
\(655\) | 15.1767 | 0.593003 | ||||||||
\(656\) | −7.01247 | −0.273791 | ||||||||
\(657\) | 0.686016 | 0.0267641 | ||||||||
\(658\) | −2.02493 | −0.0789400 | ||||||||
\(659\) | 24.7608 | 0.964544 | 0.482272 | − | 0.876022i | \(-0.339812\pi\) | ||||
0.482272 | + | 0.876022i | \(0.339812\pi\) | |||||||
\(660\) | 9.01247 | 0.350810 | ||||||||
\(661\) | 36.4033 | 1.41592 | 0.707962 | − | 0.706251i | \(-0.249615\pi\) | ||||
0.707962 | + | 0.706251i | \(0.249615\pi\) | |||||||
\(662\) | −6.77138 | −0.263177 | ||||||||
\(663\) | −19.5636 | −0.759787 | ||||||||
\(664\) | −12.1892 | −0.473032 | ||||||||
\(665\) | 2.84822 | 0.110449 | ||||||||
\(666\) | −19.6964 | −0.763221 | ||||||||
\(667\) | −3.82518 | −0.148112 | ||||||||
\(668\) | 7.77532 | 0.300836 | ||||||||
\(669\) | 31.8921 | 1.23302 | ||||||||
\(670\) | −2.84822 | −0.110036 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | 1.48028 | 0.0571030 | ||||||||
\(673\) | −16.1728 | −0.623415 | −0.311707 | − | 0.950178i | \(-0.600901\pi\) | ||||
−0.311707 | + | 0.950178i | \(0.600901\pi\) | |||||||
\(674\) | 21.0374 | 0.810330 | ||||||||
\(675\) | 35.1497 | 1.35291 | ||||||||
\(676\) | −5.79631 | −0.222935 | ||||||||
\(677\) | 5.32456 | 0.204639 | 0.102320 | − | 0.994752i | \(-0.467374\pi\) | ||||
0.102320 | + | 0.994752i | \(0.467374\pi\) | |||||||
\(678\) | −22.5781 | −0.867107 | ||||||||
\(679\) | 8.00000 | 0.307012 | ||||||||
\(680\) | 14.0249 | 0.537832 | ||||||||
\(681\) | −47.1811 | −1.80799 | ||||||||
\(682\) | −5.01247 | −0.191937 | ||||||||
\(683\) | 49.1562 | 1.88091 | 0.940455 | − | 0.339918i | \(-0.110399\pi\) | ||||
0.940455 | + | 0.339918i | \(0.110399\pi\) | |||||||
\(684\) | −1.68397 | −0.0643882 | ||||||||
\(685\) | 61.1477 | 2.33633 | ||||||||
\(686\) | 9.25560 | 0.353380 | ||||||||
\(687\) | −38.4118 | −1.46550 | ||||||||
\(688\) | 7.86068 | 0.299686 | ||||||||
\(689\) | −27.7214 | −1.05610 | ||||||||
\(690\) | 12.3285 | 0.469338 | ||||||||
\(691\) | −6.51120 | −0.247698 | −0.123849 | − | 0.992301i | \(-0.539524\pi\) | ||||
−0.123849 | + | 0.992301i | \(0.539524\pi\) | |||||||
\(692\) | 15.7818 | 0.599934 | ||||||||
\(693\) | 1.15178 | 0.0437526 | ||||||||
\(694\) | −29.9710 | −1.13768 | ||||||||
\(695\) | −77.4407 | −2.93749 | ||||||||
\(696\) | −6.05191 | −0.229397 | ||||||||
\(697\) | −23.6175 | −0.894578 | ||||||||
\(698\) | −22.6570 | −0.857580 | ||||||||
\(699\) | 44.0499 | 1.66612 | ||||||||
\(700\) | −8.44084 | −0.319034 | ||||||||
\(701\) | −5.77532 | −0.218131 | −0.109065 | − | 0.994035i | \(-0.534786\pi\) | ||||
−0.109065 | + | 0.994035i | \(0.534786\pi\) | |||||||
\(702\) | 7.64453 | 0.288524 | ||||||||
\(703\) | 11.6964 | 0.441139 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −26.6819 | −1.00490 | ||||||||
\(706\) | −1.18524 | −0.0446070 | ||||||||
\(707\) | −2.45724 | −0.0924140 | ||||||||
\(708\) | 21.4718 | 0.806958 | ||||||||
\(709\) | −35.6155 | −1.33757 | −0.668784 | − | 0.743457i | \(-0.733185\pi\) | ||||
−0.668784 | + | 0.743457i | \(0.733185\pi\) | |||||||
\(710\) | 14.7089 | 0.552015 | ||||||||
\(711\) | −12.2745 | −0.460331 | ||||||||
\(712\) | −16.6819 | −0.625181 | ||||||||
\(713\) | −6.85674 | −0.256787 | ||||||||
\(714\) | 4.98549 | 0.186577 | ||||||||
\(715\) | −11.1767 | −0.417985 | ||||||||
\(716\) | −7.97302 | −0.297966 | ||||||||
\(717\) | −8.13079 | −0.303650 | ||||||||
\(718\) | 19.3659 | 0.722729 | ||||||||
\(719\) | −8.93563 | −0.333243 | −0.166621 | − | 0.986021i | \(-0.553286\pi\) | ||||
−0.166621 | + | 0.986021i | \(0.553286\pi\) | |||||||
\(720\) | 7.01247 | 0.261339 | ||||||||
\(721\) | 3.05585 | 0.113806 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 19.8023 | 0.736455 | ||||||||
\(724\) | −2.55318 | −0.0948881 | ||||||||
\(725\) | 34.5091 | 1.28164 | ||||||||
\(726\) | −2.16425 | −0.0803228 | ||||||||
\(727\) | −1.42189 | −0.0527351 | −0.0263675 | − | 0.999652i | \(-0.508394\pi\) | ||||
−0.0263675 | + | 0.999652i | \(0.508394\pi\) | |||||||
\(728\) | −1.83575 | −0.0680375 | ||||||||
\(729\) | −0.394916 | −0.0146265 | ||||||||
\(730\) | 1.69643 | 0.0627878 | ||||||||
\(731\) | 26.4743 | 0.979187 | ||||||||
\(732\) | −4.32850 | −0.159986 | ||||||||
\(733\) | −46.7567 | −1.72700 | −0.863499 | − | 0.504350i | \(-0.831732\pi\) | ||||
−0.863499 | + | 0.504350i | \(0.831732\pi\) | |||||||
\(734\) | −18.3036 | −0.675597 | ||||||||
\(735\) | 58.8711 | 2.17149 | ||||||||
\(736\) | −1.36794 | −0.0504229 | ||||||||
\(737\) | 0.683969 | 0.0251943 | ||||||||
\(738\) | −11.8088 | −0.434687 | ||||||||
\(739\) | −34.4886 | −1.26869 | −0.634343 | − | 0.773052i | \(-0.718729\pi\) | ||||
−0.634343 | + | 0.773052i | \(0.718729\pi\) | |||||||
\(740\) | −48.7069 | −1.79050 | ||||||||
\(741\) | 5.80877 | 0.213391 | ||||||||
\(742\) | 7.06437 | 0.259341 | ||||||||
\(743\) | −10.9606 | −0.402104 | −0.201052 | − | 0.979581i | \(-0.564436\pi\) | ||||
−0.201052 | + | 0.979581i | \(0.564436\pi\) | |||||||
\(744\) | −10.8482 | −0.397715 | ||||||||
\(745\) | 17.9211 | 0.656579 | ||||||||
\(746\) | 6.46781 | 0.236803 | ||||||||
\(747\) | −20.5262 | −0.751014 | ||||||||
\(748\) | −3.36794 | −0.123144 | ||||||||
\(749\) | −6.63206 | −0.242330 | ||||||||
\(750\) | −66.1602 | −2.41583 | ||||||||
\(751\) | 13.3140 | 0.485834 | 0.242917 | − | 0.970047i | \(-0.421896\pi\) | ||||
0.242917 | + | 0.970047i | \(0.421896\pi\) | |||||||
\(752\) | 2.96056 | 0.107960 | ||||||||
\(753\) | 25.9710 | 0.946435 | ||||||||
\(754\) | 7.50521 | 0.273324 | ||||||||
\(755\) | −90.3493 | −3.28815 | ||||||||
\(756\) | −1.94809 | −0.0708514 | ||||||||
\(757\) | −8.54260 | −0.310486 | −0.155243 | − | 0.987876i | \(-0.549616\pi\) | ||||
−0.155243 | + | 0.987876i | \(0.549616\pi\) | |||||||
\(758\) | 31.9191 | 1.15935 | ||||||||
\(759\) | −2.96056 | −0.107461 | ||||||||
\(760\) | −4.16425 | −0.151053 | ||||||||
\(761\) | 32.7318 | 1.18653 | 0.593263 | − | 0.805009i | \(-0.297839\pi\) | ||||
0.593263 | + | 0.805009i | \(0.297839\pi\) | |||||||
\(762\) | −33.0893 | −1.19870 | ||||||||
\(763\) | −4.10381 | −0.148568 | ||||||||
\(764\) | 8.22468 | 0.297559 | ||||||||
\(765\) | 23.6175 | 0.853894 | ||||||||
\(766\) | 5.66946 | 0.204846 | ||||||||
\(767\) | −26.6280 | −0.961480 | ||||||||
\(768\) | −2.16425 | −0.0780956 | ||||||||
\(769\) | 50.5491 | 1.82285 | 0.911423 | − | 0.411470i | \(-0.134985\pi\) | ||||
0.911423 | + | 0.411470i | \(0.134985\pi\) | |||||||
\(770\) | 2.84822 | 0.102643 | ||||||||
\(771\) | −50.2326 | −1.80908 | ||||||||
\(772\) | −24.2141 | −0.871485 | ||||||||
\(773\) | −40.7359 | −1.46517 | −0.732584 | − | 0.680677i | \(-0.761686\pi\) | ||||
−0.732584 | + | 0.680677i | \(0.761686\pi\) | |||||||
\(774\) | 13.2371 | 0.475799 | ||||||||
\(775\) | 61.8586 | 2.22203 | ||||||||
\(776\) | −11.6964 | −0.419878 | ||||||||
\(777\) | −17.3140 | −0.621136 | ||||||||
\(778\) | 20.1642 | 0.722923 | ||||||||
\(779\) | 7.01247 | 0.251248 | ||||||||
\(780\) | −24.1892 | −0.866112 | ||||||||
\(781\) | −3.53219 | −0.126392 | ||||||||
\(782\) | −4.60713 | −0.164751 | ||||||||
\(783\) | 7.96450 | 0.284628 | ||||||||
\(784\) | −6.53219 | −0.233292 | ||||||||
\(785\) | −45.3908 | −1.62007 | ||||||||
\(786\) | −7.88766 | −0.281343 | ||||||||
\(787\) | 8.53613 | 0.304280 | 0.152140 | − | 0.988359i | \(-0.451384\pi\) | ||||
0.152140 | + | 0.988359i | \(0.451384\pi\) | |||||||
\(788\) | 26.6570 | 0.949616 | ||||||||
\(789\) | 48.0768 | 1.71158 | ||||||||
\(790\) | −30.3534 | −1.07993 | ||||||||
\(791\) | −7.13538 | −0.253705 | ||||||||
\(792\) | −1.68397 | −0.0598372 | ||||||||
\(793\) | 5.36794 | 0.190621 | ||||||||
\(794\) | −15.8272 | −0.561687 | ||||||||
\(795\) | 93.0852 | 3.30139 | ||||||||
\(796\) | −7.06437 | −0.250390 | ||||||||
\(797\) | −16.0249 | −0.567632 | −0.283816 | − | 0.958879i | \(-0.591601\pi\) | ||||
−0.283816 | + | 0.958879i | \(0.591601\pi\) | |||||||
\(798\) | −1.48028 | −0.0524013 | ||||||||
\(799\) | 9.97098 | 0.352748 | ||||||||
\(800\) | 12.3410 | 0.436319 | ||||||||
\(801\) | −28.0918 | −0.992576 | ||||||||
\(802\) | 9.06437 | 0.320074 | ||||||||
\(803\) | −0.407381 | −0.0143762 | ||||||||
\(804\) | 1.48028 | 0.0522054 | ||||||||
\(805\) | 3.89619 | 0.137322 | ||||||||
\(806\) | 13.4533 | 0.473872 | ||||||||
\(807\) | 41.0893 | 1.44641 | ||||||||
\(808\) | 3.59262 | 0.126388 | ||||||||
\(809\) | −20.1458 | −0.708288 | −0.354144 | − | 0.935191i | \(-0.615228\pi\) | ||||
−0.354144 | + | 0.935191i | \(0.615228\pi\) | |||||||
\(810\) | −46.7069 | −1.64111 | ||||||||
\(811\) | 8.27454 | 0.290558 | 0.145279 | − | 0.989391i | \(-0.453592\pi\) | ||||
0.145279 | + | 0.989391i | \(0.453592\pi\) | |||||||
\(812\) | −1.91259 | −0.0671187 | ||||||||
\(813\) | −44.8731 | −1.57377 | ||||||||
\(814\) | 11.6964 | 0.409960 | ||||||||
\(815\) | 82.1247 | 2.87670 | ||||||||
\(816\) | −7.28905 | −0.255168 | ||||||||
\(817\) | −7.86068 | −0.275010 | ||||||||
\(818\) | 2.90012 | 0.101400 | ||||||||
\(819\) | −3.09135 | −0.108021 | ||||||||
\(820\) | −29.2016 | −1.01977 | ||||||||
\(821\) | −21.5137 | −0.750835 | −0.375417 | − | 0.926856i | \(-0.622501\pi\) | ||||
−0.375417 | + | 0.926856i | \(0.622501\pi\) | |||||||
\(822\) | −31.7797 | −1.10845 | ||||||||
\(823\) | −5.26412 | −0.183496 | −0.0917479 | − | 0.995782i | \(-0.529245\pi\) | ||||
−0.0917479 | + | 0.995782i | \(0.529245\pi\) | |||||||
\(824\) | −4.46781 | −0.155644 | ||||||||
\(825\) | 26.7089 | 0.929885 | ||||||||
\(826\) | 6.78574 | 0.236106 | ||||||||
\(827\) | 16.7069 | 0.580954 | 0.290477 | − | 0.956882i | \(-0.406186\pi\) | ||||
0.290477 | + | 0.956882i | \(0.406186\pi\) | |||||||
\(828\) | −2.30357 | −0.0800544 | ||||||||
\(829\) | −5.55064 | −0.192782 | −0.0963908 | − | 0.995344i | \(-0.530730\pi\) | ||||
−0.0963908 | + | 0.995344i | \(0.530730\pi\) | |||||||
\(830\) | −50.7588 | −1.76186 | ||||||||
\(831\) | −47.2720 | −1.63985 | ||||||||
\(832\) | 2.68397 | 0.0930499 | ||||||||
\(833\) | −22.0000 | −0.762255 | ||||||||
\(834\) | 40.2476 | 1.39366 | ||||||||
\(835\) | 32.3784 | 1.12050 | ||||||||
\(836\) | 1.00000 | 0.0345857 | ||||||||
\(837\) | 14.2766 | 0.493471 | ||||||||
\(838\) | 19.7753 | 0.683127 | ||||||||
\(839\) | 15.3744 | 0.530784 | 0.265392 | − | 0.964141i | \(-0.414499\pi\) | ||||
0.265392 | + | 0.964141i | \(0.414499\pi\) | |||||||
\(840\) | 6.16425 | 0.212687 | ||||||||
\(841\) | −21.1807 | −0.730367 | ||||||||
\(842\) | 14.9855 | 0.516434 | ||||||||
\(843\) | −0.355473 | −0.0122431 | ||||||||
\(844\) | −11.0644 | −0.380851 | ||||||||
\(845\) | −24.1373 | −0.830347 | ||||||||
\(846\) | 4.98549 | 0.171405 | ||||||||
\(847\) | −0.683969 | −0.0235015 | ||||||||
\(848\) | −10.3285 | −0.354682 | ||||||||
\(849\) | −9.30955 | −0.319503 | ||||||||
\(850\) | 41.5636 | 1.42562 | ||||||||
\(851\) | 16.0000 | 0.548473 | ||||||||
\(852\) | −7.64453 | −0.261897 | ||||||||
\(853\) | 24.8028 | 0.849231 | 0.424616 | − | 0.905374i | \(-0.360409\pi\) | ||||
0.424616 | + | 0.905374i | \(0.360409\pi\) | |||||||
\(854\) | −1.36794 | −0.0468099 | ||||||||
\(855\) | −7.01247 | −0.239821 | ||||||||
\(856\) | 9.69643 | 0.331417 | ||||||||
\(857\) | −45.6445 | −1.55919 | −0.779594 | − | 0.626286i | \(-0.784574\pi\) | ||||
−0.779594 | + | 0.626286i | \(0.784574\pi\) | |||||||
\(858\) | 5.80877 | 0.198308 | ||||||||
\(859\) | 54.8356 | 1.87097 | 0.935483 | − | 0.353371i | \(-0.114965\pi\) | ||||
0.935483 | + | 0.353371i | \(0.114965\pi\) | |||||||
\(860\) | 32.7338 | 1.11621 | ||||||||
\(861\) | −10.3804 | −0.353763 | ||||||||
\(862\) | 39.4427 | 1.34342 | ||||||||
\(863\) | 45.8771 | 1.56167 | 0.780837 | − | 0.624735i | \(-0.214793\pi\) | ||||
0.780837 | + | 0.624735i | \(0.214793\pi\) | |||||||
\(864\) | 2.84822 | 0.0968983 | ||||||||
\(865\) | 65.7193 | 2.23452 | ||||||||
\(866\) | −1.23919 | −0.0421095 | ||||||||
\(867\) | 12.2431 | 0.415799 | ||||||||
\(868\) | −3.42837 | −0.116367 | ||||||||
\(869\) | 7.28905 | 0.247264 | ||||||||
\(870\) | −25.2016 | −0.854416 | ||||||||
\(871\) | −1.83575 | −0.0622021 | ||||||||
\(872\) | 6.00000 | 0.203186 | ||||||||
\(873\) | −19.6964 | −0.666623 | ||||||||
\(874\) | 1.36794 | 0.0462712 | ||||||||
\(875\) | −20.9087 | −0.706841 | ||||||||
\(876\) | −0.881673 | −0.0297890 | ||||||||
\(877\) | −15.6609 | −0.528832 | −0.264416 | − | 0.964409i | \(-0.585179\pi\) | ||||
−0.264416 | + | 0.964409i | \(0.585179\pi\) | |||||||
\(878\) | −11.1852 | −0.377484 | ||||||||
\(879\) | −70.4487 | −2.37618 | ||||||||
\(880\) | −4.16425 | −0.140377 | ||||||||
\(881\) | −3.39492 | −0.114378 | −0.0571888 | − | 0.998363i | \(-0.518214\pi\) | ||||
−0.0571888 | + | 0.998363i | \(0.518214\pi\) | |||||||
\(882\) | −11.0000 | −0.370389 | ||||||||
\(883\) | −33.6425 | −1.13216 | −0.566080 | − | 0.824350i | \(-0.691541\pi\) | ||||
−0.566080 | + | 0.824350i | \(0.691541\pi\) | |||||||
\(884\) | 9.03944 | 0.304029 | ||||||||
\(885\) | 89.4137 | 3.00561 | ||||||||
\(886\) | 23.8422 | 0.800995 | ||||||||
\(887\) | −22.1287 | −0.743011 | −0.371505 | − | 0.928431i | \(-0.621158\pi\) | ||||
−0.371505 | + | 0.928431i | \(0.621158\pi\) | |||||||
\(888\) | 25.3140 | 0.849482 | ||||||||
\(889\) | −10.4572 | −0.350725 | ||||||||
\(890\) | −69.4677 | −2.32856 | ||||||||
\(891\) | 11.2162 | 0.375755 | ||||||||
\(892\) | −14.7359 | −0.493394 | ||||||||
\(893\) | −2.96056 | −0.0990713 | ||||||||
\(894\) | −9.31398 | −0.311506 | ||||||||
\(895\) | −33.2016 | −1.10981 | ||||||||
\(896\) | −0.683969 | −0.0228498 | ||||||||
\(897\) | 7.94605 | 0.265311 | ||||||||
\(898\) | 20.9066 | 0.697662 | ||||||||
\(899\) | 14.0164 | 0.467473 | ||||||||
\(900\) | 20.7818 | 0.692727 | ||||||||
\(901\) | −34.7857 | −1.15888 | ||||||||
\(902\) | 7.01247 | 0.233490 | ||||||||
\(903\) | 11.6360 | 0.387222 | ||||||||
\(904\) | 10.4323 | 0.346973 | ||||||||
\(905\) | −10.6321 | −0.353422 | ||||||||
\(906\) | 46.9565 | 1.56002 | ||||||||
\(907\) | −21.7633 | −0.722640 | −0.361320 | − | 0.932442i | \(-0.617674\pi\) | ||||
−0.361320 | + | 0.932442i | \(0.617674\pi\) | |||||||
\(908\) | 21.8002 | 0.723467 | ||||||||
\(909\) | 6.04986 | 0.200661 | ||||||||
\(910\) | −7.64453 | −0.253414 | ||||||||
\(911\) | 46.8356 | 1.55173 | 0.775866 | − | 0.630897i | \(-0.217313\pi\) | ||||
0.775866 | + | 0.630897i | \(0.217313\pi\) | |||||||
\(912\) | 2.16425 | 0.0716654 | ||||||||
\(913\) | 12.1892 | 0.403403 | ||||||||
\(914\) | −4.18270 | −0.138351 | ||||||||
\(915\) | −18.0249 | −0.595886 | ||||||||
\(916\) | 17.7483 | 0.586422 | ||||||||
\(917\) | −2.49274 | −0.0823177 | ||||||||
\(918\) | 9.59262 | 0.316604 | ||||||||
\(919\) | −42.0563 | −1.38731 | −0.693655 | − | 0.720307i | \(-0.744001\pi\) | ||||
−0.693655 | + | 0.720307i | \(0.744001\pi\) | |||||||
\(920\) | −5.69643 | −0.187806 | ||||||||
\(921\) | −48.1537 | −1.58672 | ||||||||
\(922\) | −31.5387 | −1.03867 | ||||||||
\(923\) | 9.48028 | 0.312047 | ||||||||
\(924\) | −1.48028 | −0.0486976 | ||||||||
\(925\) | −144.345 | −4.74604 | ||||||||
\(926\) | −4.60713 | −0.151400 | ||||||||
\(927\) | −7.52366 | −0.247109 | ||||||||
\(928\) | 2.79631 | 0.0917934 | ||||||||
\(929\) | 36.1018 | 1.18446 | 0.592230 | − | 0.805769i | \(-0.298248\pi\) | ||||
0.592230 | + | 0.805769i | \(0.298248\pi\) | |||||||
\(930\) | −45.1747 | −1.48134 | ||||||||
\(931\) | 6.53219 | 0.214084 | ||||||||
\(932\) | −20.3534 | −0.666699 | ||||||||
\(933\) | 45.4178 | 1.48691 | ||||||||
\(934\) | −3.94605 | −0.129119 | ||||||||
\(935\) | −14.0249 | −0.458664 | ||||||||
\(936\) | 4.51972 | 0.147732 | ||||||||
\(937\) | 47.3638 | 1.54731 | 0.773655 | − | 0.633607i | \(-0.218427\pi\) | ||||
0.773655 | + | 0.633607i | \(0.218427\pi\) | |||||||
\(938\) | 0.467814 | 0.0152747 | ||||||||
\(939\) | 24.7878 | 0.808919 | ||||||||
\(940\) | 12.3285 | 0.402111 | ||||||||
\(941\) | −9.34301 | −0.304573 | −0.152287 | − | 0.988336i | \(-0.548664\pi\) | ||||
−0.152287 | + | 0.988336i | \(0.548664\pi\) | |||||||
\(942\) | 23.5906 | 0.768622 | ||||||||
\(943\) | 9.59262 | 0.312379 | ||||||||
\(944\) | −9.92112 | −0.322905 | ||||||||
\(945\) | −8.11234 | −0.263894 | ||||||||
\(946\) | −7.86068 | −0.255573 | ||||||||
\(947\) | 22.2496 | 0.723015 | 0.361508 | − | 0.932369i | \(-0.382262\pi\) | ||||
0.361508 | + | 0.932369i | \(0.382262\pi\) | |||||||
\(948\) | 15.7753 | 0.512359 | ||||||||
\(949\) | 1.09340 | 0.0354932 | ||||||||
\(950\) | −12.3410 | −0.400394 | ||||||||
\(951\) | −23.1811 | −0.751700 | ||||||||
\(952\) | −2.30357 | −0.0746590 | ||||||||
\(953\) | −31.9710 | −1.03564 | −0.517821 | − | 0.855489i | \(-0.673257\pi\) | ||||
−0.517821 | + | 0.855489i | \(0.673257\pi\) | |||||||
\(954\) | −17.3929 | −0.563115 | ||||||||
\(955\) | 34.2496 | 1.10829 | ||||||||
\(956\) | 3.75687 | 0.121506 | ||||||||
\(957\) | 6.05191 | 0.195630 | ||||||||
\(958\) | −16.6840 | −0.539035 | ||||||||
\(959\) | −10.0434 | −0.324318 | ||||||||
\(960\) | −9.01247 | −0.290876 | ||||||||
\(961\) | −5.87519 | −0.189522 | ||||||||
\(962\) | −31.3929 | −1.01215 | ||||||||
\(963\) | 16.3285 | 0.526178 | ||||||||
\(964\) | −9.14974 | −0.294693 | ||||||||
\(965\) | −100.834 | −3.24595 | ||||||||
\(966\) | −2.02493 | −0.0651511 | ||||||||
\(967\) | 5.97098 | 0.192014 | 0.0960068 | − | 0.995381i | \(-0.469393\pi\) | ||||
0.0960068 | + | 0.995381i | \(0.469393\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 7.28905 | 0.234158 | ||||||||
\(970\) | −48.7069 | −1.56388 | ||||||||
\(971\) | −19.0999 | −0.612944 | −0.306472 | − | 0.951880i | \(-0.599149\pi\) | ||||
−0.306472 | + | 0.951880i | \(0.599149\pi\) | |||||||
\(972\) | 15.7299 | 0.504536 | ||||||||
\(973\) | 12.7195 | 0.407768 | ||||||||
\(974\) | −14.4388 | −0.462649 | ||||||||
\(975\) | −71.6859 | −2.29578 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | −10.2745 | −0.328712 | −0.164356 | − | 0.986401i | \(-0.552555\pi\) | ||||
−0.164356 | + | 0.986401i | \(0.552555\pi\) | |||||||
\(978\) | −42.6819 | −1.36482 | ||||||||
\(979\) | 16.6819 | 0.533157 | ||||||||
\(980\) | −27.2016 | −0.868925 | ||||||||
\(981\) | 10.1038 | 0.322590 | ||||||||
\(982\) | 6.38040 | 0.203607 | ||||||||
\(983\) | 33.0084 | 1.05280 | 0.526402 | − | 0.850236i | \(-0.323541\pi\) | ||||
0.526402 | + | 0.850236i | \(0.323541\pi\) | |||||||
\(984\) | 15.1767 | 0.483816 | ||||||||
\(985\) | 111.006 | 3.53696 | ||||||||
\(986\) | 9.41780 | 0.299924 | ||||||||
\(987\) | 4.38245 | 0.139495 | ||||||||
\(988\) | −2.68397 | −0.0853884 | ||||||||
\(989\) | −10.7529 | −0.341923 | ||||||||
\(990\) | −7.01247 | −0.222871 | ||||||||
\(991\) | 1.56564 | 0.0497343 | 0.0248671 | − | 0.999691i | \(-0.492084\pi\) | ||||
0.0248671 | + | 0.999691i | \(0.492084\pi\) | |||||||
\(992\) | 5.01247 | 0.159146 | ||||||||
\(993\) | 14.6549 | 0.465061 | ||||||||
\(994\) | −2.41591 | −0.0766279 | ||||||||
\(995\) | −29.4178 | −0.932607 | ||||||||
\(996\) | 26.3804 | 0.835895 | ||||||||
\(997\) | 46.5361 | 1.47381 | 0.736907 | − | 0.675994i | \(-0.236286\pi\) | ||||
0.736907 | + | 0.675994i | \(0.236286\pi\) | |||||||
\(998\) | −31.8252 | −1.00741 | ||||||||
\(999\) | −33.3140 | −1.05401 |
(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 | 418.2.a.h.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 3762.2.a.bd.1.1 | 3 | |||
4.3 | odd | 2 | 3344.2.a.p.1.3 | 3 | |||
11.10 | odd | 2 | 4598.2.a.bm.1.1 | 3 | |||
19.18 | odd | 2 | 7942.2.a.bc.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.a.h.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3344.2.a.p.1.3 | 3 | 4.3 | odd | 2 | |||
3762.2.a.bd.1.1 | 3 | 3.2 | odd | 2 | |||
4598.2.a.bm.1.1 | 3 | 11.10 | odd | 2 | |||
7942.2.a.bc.1.3 | 3 | 19.18 | odd | 2 |