Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4018,2,Mod(1,4018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4018, 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("4018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4018 = 2 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4018.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: | \(32.0838915322\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 17x^{8} + 36x^{7} + 75x^{6} - 174x^{5} - 69x^{4} + 260x^{3} - 104x^{2} - 24x + 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(0.553933\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4018.1 |
$q$-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 | ||||||||
\(3\) | 2.84461 | 1.64233 | 0.821167 | − | 0.570687i | \(-0.193323\pi\) | ||||
0.821167 | + | 0.570687i | \(0.193323\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.100034 | 0.0447367 | 0.0223684 | − | 0.999750i | \(-0.492879\pi\) | ||||
0.0223684 | + | 0.999750i | \(0.492879\pi\) | |||||||
\(6\) | −2.84461 | −1.16131 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 5.09179 | 1.69726 | ||||||||
\(10\) | −0.100034 | −0.0316336 | ||||||||
\(11\) | 5.49180 | 1.65584 | 0.827921 | − | 0.560845i | \(-0.189524\pi\) | ||||
0.827921 | + | 0.560845i | \(0.189524\pi\) | |||||||
\(12\) | 2.84461 | 0.821167 | ||||||||
\(13\) | 2.00425 | 0.555878 | 0.277939 | − | 0.960599i | \(-0.410349\pi\) | ||||
0.277939 | + | 0.960599i | \(0.410349\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.284559 | 0.0734727 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.02518 | −0.491179 | −0.245590 | − | 0.969374i | \(-0.578982\pi\) | ||||
−0.245590 | + | 0.969374i | \(0.578982\pi\) | |||||||
\(18\) | −5.09179 | −1.20015 | ||||||||
\(19\) | 5.25933 | 1.20657 | 0.603287 | − | 0.797524i | \(-0.293857\pi\) | ||||
0.603287 | + | 0.797524i | \(0.293857\pi\) | |||||||
\(20\) | 0.100034 | 0.0223684 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.49180 | −1.17086 | ||||||||
\(23\) | −0.177764 | −0.0370663 | −0.0185332 | − | 0.999828i | \(-0.505900\pi\) | ||||
−0.0185332 | + | 0.999828i | \(0.505900\pi\) | |||||||
\(24\) | −2.84461 | −0.580653 | ||||||||
\(25\) | −4.98999 | −0.997999 | ||||||||
\(26\) | −2.00425 | −0.393065 | ||||||||
\(27\) | 5.95032 | 1.14514 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.92418 | 0.357311 | 0.178655 | − | 0.983912i | \(-0.442825\pi\) | ||||
0.178655 | + | 0.983912i | \(0.442825\pi\) | |||||||
\(30\) | −0.284559 | −0.0519530 | ||||||||
\(31\) | −1.74323 | −0.313093 | −0.156546 | − | 0.987671i | \(-0.550036\pi\) | ||||
−0.156546 | + | 0.987671i | \(0.550036\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 15.6220 | 2.71945 | ||||||||
\(34\) | 2.02518 | 0.347316 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.09179 | 0.848632 | ||||||||
\(37\) | 0.296315 | 0.0487138 | 0.0243569 | − | 0.999703i | \(-0.492246\pi\) | ||||
0.0243569 | + | 0.999703i | \(0.492246\pi\) | |||||||
\(38\) | −5.25933 | −0.853176 | ||||||||
\(39\) | 5.70130 | 0.912938 | ||||||||
\(40\) | −0.100034 | −0.0158168 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.48995 | −0.532213 | −0.266106 | − | 0.963944i | \(-0.585737\pi\) | ||||
−0.266106 | + | 0.963944i | \(0.585737\pi\) | |||||||
\(44\) | 5.49180 | 0.827921 | ||||||||
\(45\) | 0.509354 | 0.0759300 | ||||||||
\(46\) | 0.177764 | 0.0262099 | ||||||||
\(47\) | 12.7178 | 1.85509 | 0.927543 | − | 0.373718i | \(-0.121917\pi\) | ||||
0.927543 | + | 0.373718i | \(0.121917\pi\) | |||||||
\(48\) | 2.84461 | 0.410584 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.98999 | 0.705692 | ||||||||
\(51\) | −5.76085 | −0.806681 | ||||||||
\(52\) | 2.00425 | 0.277939 | ||||||||
\(53\) | −0.522296 | −0.0717429 | −0.0358714 | − | 0.999356i | \(-0.511421\pi\) | ||||
−0.0358714 | + | 0.999356i | \(0.511421\pi\) | |||||||
\(54\) | −5.95032 | −0.809736 | ||||||||
\(55\) | 0.549369 | 0.0740769 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.9607 | 1.98160 | ||||||||
\(58\) | −1.92418 | −0.252657 | ||||||||
\(59\) | −10.3189 | −1.34341 | −0.671703 | − | 0.740820i | \(-0.734437\pi\) | ||||
−0.671703 | + | 0.740820i | \(0.734437\pi\) | |||||||
\(60\) | 0.284559 | 0.0367363 | ||||||||
\(61\) | 10.2472 | 1.31202 | 0.656012 | − | 0.754751i | \(-0.272242\pi\) | ||||
0.656012 | + | 0.754751i | \(0.272242\pi\) | |||||||
\(62\) | 1.74323 | 0.221390 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.200494 | 0.0248682 | ||||||||
\(66\) | −15.6220 | −1.92294 | ||||||||
\(67\) | 7.52851 | 0.919754 | 0.459877 | − | 0.887983i | \(-0.347894\pi\) | ||||
0.459877 | + | 0.887983i | \(0.347894\pi\) | |||||||
\(68\) | −2.02518 | −0.245590 | ||||||||
\(69\) | −0.505669 | −0.0608753 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0873211 | 0.0103631 | 0.00518155 | − | 0.999987i | \(-0.498351\pi\) | ||||
0.00518155 | + | 0.999987i | \(0.498351\pi\) | |||||||
\(72\) | −5.09179 | −0.600073 | ||||||||
\(73\) | −7.69792 | −0.900974 | −0.450487 | − | 0.892783i | \(-0.648750\pi\) | ||||
−0.450487 | + | 0.892783i | \(0.648750\pi\) | |||||||
\(74\) | −0.296315 | −0.0344459 | ||||||||
\(75\) | −14.1946 | −1.63905 | ||||||||
\(76\) | 5.25933 | 0.603287 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.70130 | −0.645545 | ||||||||
\(79\) | −2.15620 | −0.242591 | −0.121295 | − | 0.992616i | \(-0.538705\pi\) | ||||
−0.121295 | + | 0.992616i | \(0.538705\pi\) | |||||||
\(80\) | 0.100034 | 0.0111842 | ||||||||
\(81\) | 1.65095 | 0.183439 | ||||||||
\(82\) | −1.00000 | −0.110432 | ||||||||
\(83\) | −1.63342 | −0.179291 | −0.0896455 | − | 0.995974i | \(-0.528573\pi\) | ||||
−0.0896455 | + | 0.995974i | \(0.528573\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.202588 | −0.0219738 | ||||||||
\(86\) | 3.48995 | 0.376331 | ||||||||
\(87\) | 5.47353 | 0.586824 | ||||||||
\(88\) | −5.49180 | −0.585428 | ||||||||
\(89\) | −6.70260 | −0.710475 | −0.355237 | − | 0.934776i | \(-0.615600\pi\) | ||||
−0.355237 | + | 0.934776i | \(0.615600\pi\) | |||||||
\(90\) | −0.509354 | −0.0536906 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.177764 | −0.0185332 | ||||||||
\(93\) | −4.95879 | −0.514203 | ||||||||
\(94\) | −12.7178 | −1.31174 | ||||||||
\(95\) | 0.526114 | 0.0539782 | ||||||||
\(96\) | −2.84461 | −0.290326 | ||||||||
\(97\) | −0.783908 | −0.0795938 | −0.0397969 | − | 0.999208i | \(-0.512671\pi\) | ||||
−0.0397969 | + | 0.999208i | \(0.512671\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 27.9631 | 2.81040 | ||||||||
\(100\) | −4.98999 | −0.498999 | ||||||||
\(101\) | −9.35530 | −0.930888 | −0.465444 | − | 0.885077i | \(-0.654105\pi\) | ||||
−0.465444 | + | 0.885077i | \(0.654105\pi\) | |||||||
\(102\) | 5.76085 | 0.570410 | ||||||||
\(103\) | −3.51803 | −0.346642 | −0.173321 | − | 0.984865i | \(-0.555450\pi\) | ||||
−0.173321 | + | 0.984865i | \(0.555450\pi\) | |||||||
\(104\) | −2.00425 | −0.196533 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.522296 | 0.0507299 | ||||||||
\(107\) | −20.6228 | −1.99368 | −0.996840 | − | 0.0794300i | \(-0.974690\pi\) | ||||
−0.996840 | + | 0.0794300i | \(0.974690\pi\) | |||||||
\(108\) | 5.95032 | 0.572570 | ||||||||
\(109\) | 9.45841 | 0.905951 | 0.452976 | − | 0.891523i | \(-0.350362\pi\) | ||||
0.452976 | + | 0.891523i | \(0.350362\pi\) | |||||||
\(110\) | −0.549369 | −0.0523803 | ||||||||
\(111\) | 0.842898 | 0.0800044 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.7178 | 1.85490 | 0.927449 | − | 0.373951i | \(-0.121997\pi\) | ||||
0.927449 | + | 0.373951i | \(0.121997\pi\) | |||||||
\(114\) | −14.9607 | −1.40120 | ||||||||
\(115\) | −0.0177825 | −0.00165823 | ||||||||
\(116\) | 1.92418 | 0.178655 | ||||||||
\(117\) | 10.2052 | 0.943472 | ||||||||
\(118\) | 10.3189 | 0.949932 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.284559 | −0.0259765 | ||||||||
\(121\) | 19.1599 | 1.74181 | ||||||||
\(122\) | −10.2472 | −0.927740 | ||||||||
\(123\) | 2.84461 | 0.256490 | ||||||||
\(124\) | −1.74323 | −0.156546 | ||||||||
\(125\) | −0.999343 | −0.0893839 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.1085 | −1.60687 | −0.803436 | − | 0.595391i | \(-0.796997\pi\) | ||||
−0.803436 | + | 0.595391i | \(0.796997\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −9.92754 | −0.874071 | ||||||||
\(130\) | −0.200494 | −0.0175845 | ||||||||
\(131\) | 5.55912 | 0.485703 | 0.242851 | − | 0.970063i | \(-0.421917\pi\) | ||||
0.242851 | + | 0.970063i | \(0.421917\pi\) | |||||||
\(132\) | 15.6220 | 1.35972 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.52851 | −0.650364 | ||||||||
\(135\) | 0.595237 | 0.0512298 | ||||||||
\(136\) | 2.02518 | 0.173658 | ||||||||
\(137\) | −1.42351 | −0.121619 | −0.0608093 | − | 0.998149i | \(-0.519368\pi\) | ||||
−0.0608093 | + | 0.998149i | \(0.519368\pi\) | |||||||
\(138\) | 0.505669 | 0.0430454 | ||||||||
\(139\) | −9.46170 | −0.802531 | −0.401265 | − | 0.915962i | \(-0.631429\pi\) | ||||
−0.401265 | + | 0.915962i | \(0.631429\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 36.1772 | 3.04667 | ||||||||
\(142\) | −0.0873211 | −0.00732783 | ||||||||
\(143\) | 11.0069 | 0.920446 | ||||||||
\(144\) | 5.09179 | 0.424316 | ||||||||
\(145\) | 0.192484 | 0.0159849 | ||||||||
\(146\) | 7.69792 | 0.637085 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.296315 | 0.0243569 | ||||||||
\(149\) | 1.81036 | 0.148310 | 0.0741551 | − | 0.997247i | \(-0.476374\pi\) | ||||
0.0741551 | + | 0.997247i | \(0.476374\pi\) | |||||||
\(150\) | 14.1946 | 1.15898 | ||||||||
\(151\) | −3.08499 | −0.251053 | −0.125526 | − | 0.992090i | \(-0.540062\pi\) | ||||
−0.125526 | + | 0.992090i | \(0.540062\pi\) | |||||||
\(152\) | −5.25933 | −0.426588 | ||||||||
\(153\) | −10.3118 | −0.833661 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.174383 | −0.0140067 | ||||||||
\(156\) | 5.70130 | 0.456469 | ||||||||
\(157\) | 7.34951 | 0.586555 | 0.293278 | − | 0.956027i | \(-0.405254\pi\) | ||||
0.293278 | + | 0.956027i | \(0.405254\pi\) | |||||||
\(158\) | 2.15620 | 0.171538 | ||||||||
\(159\) | −1.48573 | −0.117826 | ||||||||
\(160\) | −0.100034 | −0.00790841 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.65095 | −0.129711 | ||||||||
\(163\) | 3.24890 | 0.254473 | 0.127237 | − | 0.991872i | \(-0.459389\pi\) | ||||
0.127237 | + | 0.991872i | \(0.459389\pi\) | |||||||
\(164\) | 1.00000 | 0.0780869 | ||||||||
\(165\) | 1.56274 | 0.121659 | ||||||||
\(166\) | 1.63342 | 0.126778 | ||||||||
\(167\) | 22.7027 | 1.75679 | 0.878393 | − | 0.477939i | \(-0.158616\pi\) | ||||
0.878393 | + | 0.477939i | \(0.158616\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.98299 | −0.690999 | ||||||||
\(170\) | 0.202588 | 0.0155378 | ||||||||
\(171\) | 26.7794 | 2.04787 | ||||||||
\(172\) | −3.48995 | −0.266106 | ||||||||
\(173\) | 18.8660 | 1.43436 | 0.717179 | − | 0.696889i | \(-0.245433\pi\) | ||||
0.717179 | + | 0.696889i | \(0.245433\pi\) | |||||||
\(174\) | −5.47353 | −0.414947 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.49180 | 0.413960 | ||||||||
\(177\) | −29.3532 | −2.20632 | ||||||||
\(178\) | 6.70260 | 0.502381 | ||||||||
\(179\) | −13.1779 | −0.984965 | −0.492482 | − | 0.870322i | \(-0.663910\pi\) | ||||
−0.492482 | + | 0.870322i | \(0.663910\pi\) | |||||||
\(180\) | 0.509354 | 0.0379650 | ||||||||
\(181\) | −11.4642 | −0.852127 | −0.426064 | − | 0.904693i | \(-0.640100\pi\) | ||||
−0.426064 | + | 0.904693i | \(0.640100\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 29.1493 | 2.15478 | ||||||||
\(184\) | 0.177764 | 0.0131049 | ||||||||
\(185\) | 0.0296416 | 0.00217930 | ||||||||
\(186\) | 4.95879 | 0.363596 | ||||||||
\(187\) | −11.1219 | −0.813315 | ||||||||
\(188\) | 12.7178 | 0.927543 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.526114 | −0.0381683 | ||||||||
\(191\) | 11.5032 | 0.832340 | 0.416170 | − | 0.909287i | \(-0.363372\pi\) | ||||
0.416170 | + | 0.909287i | \(0.363372\pi\) | |||||||
\(192\) | 2.84461 | 0.205292 | ||||||||
\(193\) | −10.8671 | −0.782232 | −0.391116 | − | 0.920341i | \(-0.627911\pi\) | ||||
−0.391116 | + | 0.920341i | \(0.627911\pi\) | |||||||
\(194\) | 0.783908 | 0.0562813 | ||||||||
\(195\) | 0.570326 | 0.0408419 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.6123 | 1.75355 | 0.876777 | − | 0.480897i | \(-0.159689\pi\) | ||||
0.876777 | + | 0.480897i | \(0.159689\pi\) | |||||||
\(198\) | −27.9631 | −1.98725 | ||||||||
\(199\) | 14.6903 | 1.04137 | 0.520685 | − | 0.853749i | \(-0.325677\pi\) | ||||
0.520685 | + | 0.853749i | \(0.325677\pi\) | |||||||
\(200\) | 4.98999 | 0.352846 | ||||||||
\(201\) | 21.4156 | 1.51054 | ||||||||
\(202\) | 9.35530 | 0.658237 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.76085 | −0.403340 | ||||||||
\(205\) | 0.100034 | 0.00698670 | ||||||||
\(206\) | 3.51803 | 0.245113 | ||||||||
\(207\) | −0.905137 | −0.0629113 | ||||||||
\(208\) | 2.00425 | 0.138970 | ||||||||
\(209\) | 28.8832 | 1.99789 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.10608 | −0.282675 | −0.141337 | − | 0.989962i | \(-0.545140\pi\) | ||||
−0.141337 | + | 0.989962i | \(0.545140\pi\) | |||||||
\(212\) | −0.522296 | −0.0358714 | ||||||||
\(213\) | 0.248394 | 0.0170197 | ||||||||
\(214\) | 20.6228 | 1.40975 | ||||||||
\(215\) | −0.349115 | −0.0238095 | ||||||||
\(216\) | −5.95032 | −0.404868 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.45841 | −0.640604 | ||||||||
\(219\) | −21.8976 | −1.47970 | ||||||||
\(220\) | 0.549369 | 0.0370385 | ||||||||
\(221\) | −4.05897 | −0.273036 | ||||||||
\(222\) | −0.842898 | −0.0565716 | ||||||||
\(223\) | 3.97766 | 0.266364 | 0.133182 | − | 0.991092i | \(-0.457481\pi\) | ||||
0.133182 | + | 0.991092i | \(0.457481\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25.4080 | −1.69387 | ||||||||
\(226\) | −19.7178 | −1.31161 | ||||||||
\(227\) | 22.8040 | 1.51355 | 0.756777 | − | 0.653674i | \(-0.226773\pi\) | ||||
0.756777 | + | 0.653674i | \(0.226773\pi\) | |||||||
\(228\) | 14.9607 | 0.990799 | ||||||||
\(229\) | −20.3461 | −1.34451 | −0.672255 | − | 0.740320i | \(-0.734674\pi\) | ||||
−0.672255 | + | 0.740320i | \(0.734674\pi\) | |||||||
\(230\) | 0.0177825 | 0.00117254 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.92418 | −0.126328 | ||||||||
\(233\) | 29.0821 | 1.90523 | 0.952614 | − | 0.304181i | \(-0.0983827\pi\) | ||||
0.952614 | + | 0.304181i | \(0.0983827\pi\) | |||||||
\(234\) | −10.2052 | −0.667135 | ||||||||
\(235\) | 1.27222 | 0.0829905 | ||||||||
\(236\) | −10.3189 | −0.671703 | ||||||||
\(237\) | −6.13353 | −0.398415 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.3310 | −1.12105 | −0.560523 | − | 0.828139i | \(-0.689400\pi\) | ||||
−0.560523 | + | 0.828139i | \(0.689400\pi\) | |||||||
\(240\) | 0.284559 | 0.0183682 | ||||||||
\(241\) | −11.3155 | −0.728897 | −0.364448 | − | 0.931224i | \(-0.618742\pi\) | ||||
−0.364448 | + | 0.931224i | \(0.618742\pi\) | |||||||
\(242\) | −19.1599 | −1.23165 | ||||||||
\(243\) | −13.1546 | −0.843871 | ||||||||
\(244\) | 10.2472 | 0.656012 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.84461 | −0.181366 | ||||||||
\(247\) | 10.5410 | 0.670708 | ||||||||
\(248\) | 1.74323 | 0.110695 | ||||||||
\(249\) | −4.64643 | −0.294456 | ||||||||
\(250\) | 0.999343 | 0.0632040 | ||||||||
\(251\) | −21.4095 | −1.35135 | −0.675676 | − | 0.737198i | \(-0.736148\pi\) | ||||
−0.675676 | + | 0.737198i | \(0.736148\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.976245 | −0.0613760 | ||||||||
\(254\) | 18.1085 | 1.13623 | ||||||||
\(255\) | −0.576283 | −0.0360883 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.68866 | 0.354849 | 0.177424 | − | 0.984134i | \(-0.443223\pi\) | ||||
0.177424 | + | 0.984134i | \(0.443223\pi\) | |||||||
\(258\) | 9.92754 | 0.618062 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.200494 | 0.0124341 | ||||||||
\(261\) | 9.79751 | 0.606451 | ||||||||
\(262\) | −5.55912 | −0.343444 | ||||||||
\(263\) | −13.9215 | −0.858436 | −0.429218 | − | 0.903201i | \(-0.641211\pi\) | ||||
−0.429218 | + | 0.903201i | \(0.641211\pi\) | |||||||
\(264\) | −15.6220 | −0.961469 | ||||||||
\(265\) | −0.0522476 | −0.00320954 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19.0663 | −1.16684 | ||||||||
\(268\) | 7.52851 | 0.459877 | ||||||||
\(269\) | 12.4410 | 0.758539 | 0.379270 | − | 0.925286i | \(-0.376175\pi\) | ||||
0.379270 | + | 0.925286i | \(0.376175\pi\) | |||||||
\(270\) | −0.595237 | −0.0362249 | ||||||||
\(271\) | 10.3626 | 0.629481 | 0.314741 | − | 0.949178i | \(-0.398082\pi\) | ||||
0.314741 | + | 0.949178i | \(0.398082\pi\) | |||||||
\(272\) | −2.02518 | −0.122795 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.42351 | 0.0859973 | ||||||||
\(275\) | −27.4041 | −1.65253 | ||||||||
\(276\) | −0.505669 | −0.0304377 | ||||||||
\(277\) | 4.84034 | 0.290828 | 0.145414 | − | 0.989371i | \(-0.453549\pi\) | ||||
0.145414 | + | 0.989371i | \(0.453549\pi\) | |||||||
\(278\) | 9.46170 | 0.567475 | ||||||||
\(279\) | −8.87614 | −0.531401 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.0716 | −1.73426 | −0.867132 | − | 0.498079i | \(-0.834039\pi\) | ||||
−0.867132 | + | 0.498079i | \(0.834039\pi\) | |||||||
\(282\) | −36.1772 | −2.15432 | ||||||||
\(283\) | 3.80733 | 0.226322 | 0.113161 | − | 0.993577i | \(-0.463902\pi\) | ||||
0.113161 | + | 0.993577i | \(0.463902\pi\) | |||||||
\(284\) | 0.0873211 | 0.00518155 | ||||||||
\(285\) | 1.49659 | 0.0886502 | ||||||||
\(286\) | −11.0069 | −0.650854 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.09179 | −0.300037 | ||||||||
\(289\) | −12.8986 | −0.758743 | ||||||||
\(290\) | −0.192484 | −0.0113030 | ||||||||
\(291\) | −2.22991 | −0.130720 | ||||||||
\(292\) | −7.69792 | −0.450487 | ||||||||
\(293\) | 21.2048 | 1.23880 | 0.619398 | − | 0.785077i | \(-0.287377\pi\) | ||||
0.619398 | + | 0.785077i | \(0.287377\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.03224 | −0.0600996 | ||||||||
\(296\) | −0.296315 | −0.0172229 | ||||||||
\(297\) | 32.6780 | 1.89617 | ||||||||
\(298\) | −1.81036 | −0.104871 | ||||||||
\(299\) | −0.356283 | −0.0206044 | ||||||||
\(300\) | −14.1946 | −0.819524 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.08499 | 0.177521 | ||||||||
\(303\) | −26.6122 | −1.52883 | ||||||||
\(304\) | 5.25933 | 0.301643 | ||||||||
\(305\) | 1.02508 | 0.0586956 | ||||||||
\(306\) | 10.3118 | 0.589487 | ||||||||
\(307\) | 23.6483 | 1.34968 | 0.674840 | − | 0.737964i | \(-0.264213\pi\) | ||||
0.674840 | + | 0.737964i | \(0.264213\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.0074 | −0.569302 | ||||||||
\(310\) | 0.174383 | 0.00990426 | ||||||||
\(311\) | −4.53369 | −0.257082 | −0.128541 | − | 0.991704i | \(-0.541029\pi\) | ||||
−0.128541 | + | 0.991704i | \(0.541029\pi\) | |||||||
\(312\) | −5.70130 | −0.322772 | ||||||||
\(313\) | −13.9532 | −0.788681 | −0.394340 | − | 0.918964i | \(-0.629027\pi\) | ||||
−0.394340 | + | 0.918964i | \(0.629027\pi\) | |||||||
\(314\) | −7.34951 | −0.414757 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.15620 | −0.121295 | ||||||||
\(317\) | −18.2179 | −1.02322 | −0.511610 | − | 0.859218i | \(-0.670951\pi\) | ||||
−0.511610 | + | 0.859218i | \(0.670951\pi\) | |||||||
\(318\) | 1.48573 | 0.0833154 | ||||||||
\(319\) | 10.5672 | 0.591650 | ||||||||
\(320\) | 0.100034 | 0.00559209 | ||||||||
\(321\) | −58.6638 | −3.27429 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.6511 | −0.592644 | ||||||||
\(324\) | 1.65095 | 0.0917196 | ||||||||
\(325\) | −10.0012 | −0.554766 | ||||||||
\(326\) | −3.24890 | −0.179940 | ||||||||
\(327\) | 26.9055 | 1.48788 | ||||||||
\(328\) | −1.00000 | −0.0552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.56274 | −0.0860260 | ||||||||
\(331\) | −9.32265 | −0.512419 | −0.256210 | − | 0.966621i | \(-0.582474\pi\) | ||||
−0.256210 | + | 0.966621i | \(0.582474\pi\) | |||||||
\(332\) | −1.63342 | −0.0896455 | ||||||||
\(333\) | 1.50877 | 0.0826802 | ||||||||
\(334\) | −22.7027 | −1.24224 | ||||||||
\(335\) | 0.753110 | 0.0411468 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.3634 | −1.54505 | −0.772525 | − | 0.634984i | \(-0.781007\pi\) | ||||
−0.772525 | + | 0.634984i | \(0.781007\pi\) | |||||||
\(338\) | 8.98299 | 0.488610 | ||||||||
\(339\) | 56.0895 | 3.04636 | ||||||||
\(340\) | −0.202588 | −0.0109869 | ||||||||
\(341\) | −9.57346 | −0.518432 | ||||||||
\(342\) | −26.7794 | −1.44806 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.48995 | 0.188166 | ||||||||
\(345\) | −0.0505842 | −0.00272336 | ||||||||
\(346\) | −18.8660 | −1.01424 | ||||||||
\(347\) | 25.9901 | 1.39522 | 0.697612 | − | 0.716476i | \(-0.254246\pi\) | ||||
0.697612 | + | 0.716476i | \(0.254246\pi\) | |||||||
\(348\) | 5.47353 | 0.293412 | ||||||||
\(349\) | 6.07191 | 0.325022 | 0.162511 | − | 0.986707i | \(-0.448041\pi\) | ||||
0.162511 | + | 0.986707i | \(0.448041\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.9259 | 0.636558 | ||||||||
\(352\) | −5.49180 | −0.292714 | ||||||||
\(353\) | 8.90538 | 0.473986 | 0.236993 | − | 0.971511i | \(-0.423838\pi\) | ||||
0.236993 | + | 0.971511i | \(0.423838\pi\) | |||||||
\(354\) | 29.3532 | 1.56011 | ||||||||
\(355\) | 0.00873511 | 0.000463612 0 | ||||||||
\(356\) | −6.70260 | −0.355237 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.1779 | 0.696475 | ||||||||
\(359\) | −22.2052 | −1.17195 | −0.585973 | − | 0.810331i | \(-0.699288\pi\) | ||||
−0.585973 | + | 0.810331i | \(0.699288\pi\) | |||||||
\(360\) | −0.509354 | −0.0268453 | ||||||||
\(361\) | 8.66057 | 0.455819 | ||||||||
\(362\) | 11.4642 | 0.602545 | ||||||||
\(363\) | 54.5024 | 2.86063 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.770057 | −0.0403066 | ||||||||
\(366\) | −29.1493 | −1.52366 | ||||||||
\(367\) | −22.7662 | −1.18839 | −0.594193 | − | 0.804323i | \(-0.702528\pi\) | ||||
−0.594193 | + | 0.804323i | \(0.702528\pi\) | |||||||
\(368\) | −0.177764 | −0.00926659 | ||||||||
\(369\) | 5.09179 | 0.265068 | ||||||||
\(370\) | −0.0296416 | −0.00154100 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.95879 | −0.257101 | ||||||||
\(373\) | 25.1403 | 1.30172 | 0.650859 | − | 0.759199i | \(-0.274409\pi\) | ||||
0.650859 | + | 0.759199i | \(0.274409\pi\) | |||||||
\(374\) | 11.1219 | 0.575101 | ||||||||
\(375\) | −2.84274 | −0.146798 | ||||||||
\(376\) | −12.7178 | −0.655872 | ||||||||
\(377\) | 3.85653 | 0.198621 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.7756 | 0.604874 | 0.302437 | − | 0.953169i | \(-0.402200\pi\) | ||||
0.302437 | + | 0.953169i | \(0.402200\pi\) | |||||||
\(380\) | 0.526114 | 0.0269891 | ||||||||
\(381\) | −51.5117 | −2.63902 | ||||||||
\(382\) | −11.5032 | −0.588553 | ||||||||
\(383\) | 32.1184 | 1.64117 | 0.820586 | − | 0.571522i | \(-0.193647\pi\) | ||||
0.820586 | + | 0.571522i | \(0.193647\pi\) | |||||||
\(384\) | −2.84461 | −0.145163 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.8671 | 0.553122 | ||||||||
\(387\) | −17.7701 | −0.903305 | ||||||||
\(388\) | −0.783908 | −0.0397969 | ||||||||
\(389\) | −20.4285 | −1.03576 | −0.517882 | − | 0.855452i | \(-0.673279\pi\) | ||||
−0.517882 | + | 0.855452i | \(0.673279\pi\) | |||||||
\(390\) | −0.570326 | −0.0288796 | ||||||||
\(391\) | 0.360005 | 0.0182062 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.8135 | 0.797687 | ||||||||
\(394\) | −24.6123 | −1.23995 | ||||||||
\(395\) | −0.215694 | −0.0108527 | ||||||||
\(396\) | 27.9631 | 1.40520 | ||||||||
\(397\) | 13.2034 | 0.662660 | 0.331330 | − | 0.943515i | \(-0.392503\pi\) | ||||
0.331330 | + | 0.943515i | \(0.392503\pi\) | |||||||
\(398\) | −14.6903 | −0.736360 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.98999 | −0.249500 | ||||||||
\(401\) | −6.19120 | −0.309174 | −0.154587 | − | 0.987979i | \(-0.549405\pi\) | ||||
−0.154587 | + | 0.987979i | \(0.549405\pi\) | |||||||
\(402\) | −21.4156 | −1.06812 | ||||||||
\(403\) | −3.49386 | −0.174041 | ||||||||
\(404\) | −9.35530 | −0.465444 | ||||||||
\(405\) | 0.165152 | 0.00820647 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.62730 | 0.0806623 | ||||||||
\(408\) | 5.76085 | 0.285205 | ||||||||
\(409\) | −7.68619 | −0.380058 | −0.190029 | − | 0.981779i | \(-0.560858\pi\) | ||||
−0.190029 | + | 0.981779i | \(0.560858\pi\) | |||||||
\(410\) | −0.100034 | −0.00494035 | ||||||||
\(411\) | −4.04932 | −0.199738 | ||||||||
\(412\) | −3.51803 | −0.173321 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.905137 | 0.0444850 | ||||||||
\(415\) | −0.163398 | −0.00802089 | ||||||||
\(416\) | −2.00425 | −0.0982663 | ||||||||
\(417\) | −26.9148 | −1.31802 | ||||||||
\(418\) | −28.8832 | −1.41272 | ||||||||
\(419\) | 5.34493 | 0.261117 | 0.130559 | − | 0.991441i | \(-0.458323\pi\) | ||||
0.130559 | + | 0.991441i | \(0.458323\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.0458 | 1.51308 | 0.756539 | − | 0.653949i | \(-0.226889\pi\) | ||||
0.756539 | + | 0.653949i | \(0.226889\pi\) | |||||||
\(422\) | 4.10608 | 0.199881 | ||||||||
\(423\) | 64.7565 | 3.14857 | ||||||||
\(424\) | 0.522296 | 0.0253649 | ||||||||
\(425\) | 10.1057 | 0.490196 | ||||||||
\(426\) | −0.248394 | −0.0120347 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −20.6228 | −0.996840 | ||||||||
\(429\) | 31.3104 | 1.51168 | ||||||||
\(430\) | 0.349115 | 0.0168358 | ||||||||
\(431\) | −28.4490 | −1.37034 | −0.685170 | − | 0.728383i | \(-0.740272\pi\) | ||||
−0.685170 | + | 0.728383i | \(0.740272\pi\) | |||||||
\(432\) | 5.95032 | 0.286285 | ||||||||
\(433\) | 2.21499 | 0.106446 | 0.0532229 | − | 0.998583i | \(-0.483051\pi\) | ||||
0.0532229 | + | 0.998583i | \(0.483051\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.547541 | 0.0262526 | ||||||||
\(436\) | 9.45841 | 0.452976 | ||||||||
\(437\) | −0.934919 | −0.0447233 | ||||||||
\(438\) | 21.8976 | 1.04631 | ||||||||
\(439\) | −33.6220 | −1.60469 | −0.802346 | − | 0.596859i | \(-0.796415\pi\) | ||||
−0.802346 | + | 0.596859i | \(0.796415\pi\) | |||||||
\(440\) | −0.549369 | −0.0261901 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.05897 | 0.193066 | ||||||||
\(443\) | 4.73115 | 0.224784 | 0.112392 | − | 0.993664i | \(-0.464149\pi\) | ||||
0.112392 | + | 0.993664i | \(0.464149\pi\) | |||||||
\(444\) | 0.842898 | 0.0400022 | ||||||||
\(445\) | −0.670491 | −0.0317843 | ||||||||
\(446\) | −3.97766 | −0.188348 | ||||||||
\(447\) | 5.14976 | 0.243575 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.0673 | −0.899844 | −0.449922 | − | 0.893068i | \(-0.648548\pi\) | ||||
−0.449922 | + | 0.893068i | \(0.648548\pi\) | |||||||
\(450\) | 25.4080 | 1.19774 | ||||||||
\(451\) | 5.49180 | 0.258599 | ||||||||
\(452\) | 19.7178 | 0.927449 | ||||||||
\(453\) | −8.77557 | −0.412312 | ||||||||
\(454\) | −22.8040 | −1.07024 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −14.9607 | −0.700600 | ||||||||
\(457\) | −21.8939 | −1.02415 | −0.512076 | − | 0.858940i | \(-0.671123\pi\) | ||||
−0.512076 | + | 0.858940i | \(0.671123\pi\) | |||||||
\(458\) | 20.3461 | 0.950712 | ||||||||
\(459\) | −12.0505 | −0.562469 | ||||||||
\(460\) | −0.0177825 | −0.000829114 0 | ||||||||
\(461\) | 35.8923 | 1.67167 | 0.835836 | − | 0.548979i | \(-0.184983\pi\) | ||||
0.835836 | + | 0.548979i | \(0.184983\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.2360 | −0.801027 | −0.400513 | − | 0.916291i | \(-0.631168\pi\) | ||||
−0.400513 | + | 0.916291i | \(0.631168\pi\) | |||||||
\(464\) | 1.92418 | 0.0893277 | ||||||||
\(465\) | −0.496050 | −0.0230038 | ||||||||
\(466\) | −29.0821 | −1.34720 | ||||||||
\(467\) | 32.8802 | 1.52152 | 0.760758 | − | 0.649036i | \(-0.224828\pi\) | ||||
0.760758 | + | 0.649036i | \(0.224828\pi\) | |||||||
\(468\) | 10.2052 | 0.471736 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.27222 | −0.0586831 | ||||||||
\(471\) | 20.9065 | 0.963320 | ||||||||
\(472\) | 10.3189 | 0.474966 | ||||||||
\(473\) | −19.1661 | −0.881259 | ||||||||
\(474\) | 6.13353 | 0.281722 | ||||||||
\(475\) | −26.2440 | −1.20416 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.65942 | −0.121767 | ||||||||
\(478\) | 17.3310 | 0.792700 | ||||||||
\(479\) | −25.1914 | −1.15103 | −0.575513 | − | 0.817793i | \(-0.695198\pi\) | ||||
−0.575513 | + | 0.817793i | \(0.695198\pi\) | |||||||
\(480\) | −0.284559 | −0.0129883 | ||||||||
\(481\) | 0.593888 | 0.0270789 | ||||||||
\(482\) | 11.3155 | 0.515408 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.1599 | 0.870905 | ||||||||
\(485\) | −0.0784177 | −0.00356077 | ||||||||
\(486\) | 13.1546 | 0.596707 | ||||||||
\(487\) | −31.1451 | −1.41132 | −0.705659 | − | 0.708552i | \(-0.749349\pi\) | ||||
−0.705659 | + | 0.708552i | \(0.749349\pi\) | |||||||
\(488\) | −10.2472 | −0.463870 | ||||||||
\(489\) | 9.24184 | 0.417930 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.81906 | −0.0820930 | −0.0410465 | − | 0.999157i | \(-0.513069\pi\) | ||||
−0.0410465 | + | 0.999157i | \(0.513069\pi\) | |||||||
\(492\) | 2.84461 | 0.128245 | ||||||||
\(493\) | −3.89682 | −0.175504 | ||||||||
\(494\) | −10.5410 | −0.474262 | ||||||||
\(495\) | 2.79727 | 0.125728 | ||||||||
\(496\) | −1.74323 | −0.0782732 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.64643 | 0.208212 | ||||||||
\(499\) | −1.22056 | −0.0546398 | −0.0273199 | − | 0.999627i | \(-0.508697\pi\) | ||||
−0.0273199 | + | 0.999627i | \(0.508697\pi\) | |||||||
\(500\) | −0.999343 | −0.0446920 | ||||||||
\(501\) | 64.5802 | 2.88523 | ||||||||
\(502\) | 21.4095 | 0.955551 | ||||||||
\(503\) | −0.303892 | −0.0135499 | −0.00677493 | − | 0.999977i | \(-0.502157\pi\) | ||||
−0.00677493 | + | 0.999977i | \(0.502157\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.935852 | −0.0416449 | ||||||||
\(506\) | 0.976245 | 0.0433994 | ||||||||
\(507\) | −25.5531 | −1.13485 | ||||||||
\(508\) | −18.1085 | −0.803436 | ||||||||
\(509\) | 23.7535 | 1.05286 | 0.526429 | − | 0.850219i | \(-0.323531\pi\) | ||||
0.526429 | + | 0.850219i | \(0.323531\pi\) | |||||||
\(510\) | 0.576283 | 0.0255183 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 31.2947 | 1.38169 | ||||||||
\(514\) | −5.68866 | −0.250916 | ||||||||
\(515\) | −0.351924 | −0.0155076 | ||||||||
\(516\) | −9.92754 | −0.437036 | ||||||||
\(517\) | 69.8438 | 3.07173 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 53.6664 | 2.35570 | ||||||||
\(520\) | −0.200494 | −0.00879223 | ||||||||
\(521\) | −12.1542 | −0.532486 | −0.266243 | − | 0.963906i | \(-0.585782\pi\) | ||||
−0.266243 | + | 0.963906i | \(0.585782\pi\) | |||||||
\(522\) | −9.79751 | −0.428825 | ||||||||
\(523\) | 28.3221 | 1.23844 | 0.619218 | − | 0.785219i | \(-0.287450\pi\) | ||||
0.619218 | + | 0.785219i | \(0.287450\pi\) | |||||||
\(524\) | 5.55912 | 0.242851 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.9215 | 0.607006 | ||||||||
\(527\) | 3.53035 | 0.153785 | ||||||||
\(528\) | 15.6220 | 0.679861 | ||||||||
\(529\) | −22.9684 | −0.998626 | ||||||||
\(530\) | 0.0522476 | 0.00226949 | ||||||||
\(531\) | −52.5417 | −2.28011 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.00425 | 0.0868136 | ||||||||
\(534\) | 19.0663 | 0.825078 | ||||||||
\(535\) | −2.06299 | −0.0891908 | ||||||||
\(536\) | −7.52851 | −0.325182 | ||||||||
\(537\) | −37.4860 | −1.61764 | ||||||||
\(538\) | −12.4410 | −0.536368 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.595237 | 0.0256149 | ||||||||
\(541\) | 30.8867 | 1.32792 | 0.663961 | − | 0.747768i | \(-0.268874\pi\) | ||||
0.663961 | + | 0.747768i | \(0.268874\pi\) | |||||||
\(542\) | −10.3626 | −0.445110 | ||||||||
\(543\) | −32.6111 | −1.39948 | ||||||||
\(544\) | 2.02518 | 0.0868291 | ||||||||
\(545\) | 0.946166 | 0.0405293 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.6662 | −0.669839 | −0.334920 | − | 0.942247i | \(-0.608709\pi\) | ||||
−0.334920 | + | 0.942247i | \(0.608709\pi\) | |||||||
\(548\) | −1.42351 | −0.0608093 | ||||||||
\(549\) | 52.1767 | 2.22685 | ||||||||
\(550\) | 27.4041 | 1.16851 | ||||||||
\(551\) | 10.1199 | 0.431122 | ||||||||
\(552\) | 0.505669 | 0.0215227 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.84034 | −0.205646 | ||||||||
\(555\) | 0.0843188 | 0.00357913 | ||||||||
\(556\) | −9.46170 | −0.401265 | ||||||||
\(557\) | −23.0865 | −0.978207 | −0.489104 | − | 0.872226i | \(-0.662676\pi\) | ||||
−0.489104 | + | 0.872226i | \(0.662676\pi\) | |||||||
\(558\) | 8.87614 | 0.375757 | ||||||||
\(559\) | −6.99472 | −0.295845 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31.6375 | −1.33574 | ||||||||
\(562\) | 29.0716 | 1.22631 | ||||||||
\(563\) | −5.20512 | −0.219369 | −0.109685 | − | 0.993966i | \(-0.534984\pi\) | ||||
−0.109685 | + | 0.993966i | \(0.534984\pi\) | |||||||
\(564\) | 36.1772 | 1.52334 | ||||||||
\(565\) | 1.97246 | 0.0829820 | ||||||||
\(566\) | −3.80733 | −0.160034 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.0873211 | −0.00366391 | ||||||||
\(569\) | −6.61422 | −0.277283 | −0.138641 | − | 0.990343i | \(-0.544274\pi\) | ||||
−0.138641 | + | 0.990343i | \(0.544274\pi\) | |||||||
\(570\) | −1.49659 | −0.0626852 | ||||||||
\(571\) | −10.4373 | −0.436788 | −0.218394 | − | 0.975861i | \(-0.570082\pi\) | ||||
−0.218394 | + | 0.975861i | \(0.570082\pi\) | |||||||
\(572\) | 11.0069 | 0.460223 | ||||||||
\(573\) | 32.7220 | 1.36698 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.887041 | 0.0369922 | ||||||||
\(576\) | 5.09179 | 0.212158 | ||||||||
\(577\) | −44.8936 | −1.86894 | −0.934472 | − | 0.356037i | \(-0.884128\pi\) | ||||
−0.934472 | + | 0.356037i | \(0.884128\pi\) | |||||||
\(578\) | 12.8986 | 0.536512 | ||||||||
\(579\) | −30.9127 | −1.28469 | ||||||||
\(580\) | 0.192484 | 0.00799246 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.22991 | 0.0924327 | ||||||||
\(583\) | −2.86835 | −0.118795 | ||||||||
\(584\) | 7.69792 | 0.318542 | ||||||||
\(585\) | 1.02087 | 0.0422078 | ||||||||
\(586\) | −21.2048 | −0.875961 | ||||||||
\(587\) | −4.58306 | −0.189163 | −0.0945816 | − | 0.995517i | \(-0.530151\pi\) | ||||
−0.0945816 | + | 0.995517i | \(0.530151\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.16820 | −0.377769 | ||||||||
\(590\) | 1.03224 | 0.0424968 | ||||||||
\(591\) | 70.0124 | 2.87992 | ||||||||
\(592\) | 0.296315 | 0.0121785 | ||||||||
\(593\) | 40.8080 | 1.67578 | 0.837891 | − | 0.545837i | \(-0.183788\pi\) | ||||
0.837891 | + | 0.545837i | \(0.183788\pi\) | |||||||
\(594\) | −32.6780 | −1.34079 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.81036 | 0.0741551 | ||||||||
\(597\) | 41.7882 | 1.71028 | ||||||||
\(598\) | 0.356283 | 0.0145695 | ||||||||
\(599\) | −35.9219 | −1.46773 | −0.733865 | − | 0.679295i | \(-0.762286\pi\) | ||||
−0.733865 | + | 0.679295i | \(0.762286\pi\) | |||||||
\(600\) | 14.1946 | 0.579491 | ||||||||
\(601\) | 3.31498 | 0.135221 | 0.0676105 | − | 0.997712i | \(-0.478462\pi\) | ||||
0.0676105 | + | 0.997712i | \(0.478462\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 38.3336 | 1.56106 | ||||||||
\(604\) | −3.08499 | −0.125526 | ||||||||
\(605\) | 1.91665 | 0.0779229 | ||||||||
\(606\) | 26.6122 | 1.08105 | ||||||||
\(607\) | 46.0105 | 1.86751 | 0.933754 | − | 0.357916i | \(-0.116513\pi\) | ||||
0.933754 | + | 0.357916i | \(0.116513\pi\) | |||||||
\(608\) | −5.25933 | −0.213294 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.02508 | −0.0415041 | ||||||||
\(611\) | 25.4897 | 1.03120 | ||||||||
\(612\) | −10.3118 | −0.416830 | ||||||||
\(613\) | 27.3935 | 1.10641 | 0.553206 | − | 0.833044i | \(-0.313404\pi\) | ||||
0.553206 | + | 0.833044i | \(0.313404\pi\) | |||||||
\(614\) | −23.6483 | −0.954368 | ||||||||
\(615\) | 0.284559 | 0.0114745 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.8256 | −0.476082 | −0.238041 | − | 0.971255i | \(-0.576505\pi\) | ||||
−0.238041 | + | 0.971255i | \(0.576505\pi\) | |||||||
\(618\) | 10.0074 | 0.402557 | ||||||||
\(619\) | −30.5284 | −1.22704 | −0.613519 | − | 0.789680i | \(-0.710247\pi\) | ||||
−0.613519 | + | 0.789680i | \(0.710247\pi\) | |||||||
\(620\) | −0.174383 | −0.00700337 | ||||||||
\(621\) | −1.05775 | −0.0424461 | ||||||||
\(622\) | 4.53369 | 0.181784 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.70130 | 0.228234 | ||||||||
\(625\) | 24.8500 | 0.994000 | ||||||||
\(626\) | 13.9532 | 0.557682 | ||||||||
\(627\) | 82.1614 | 3.28121 | ||||||||
\(628\) | 7.34951 | 0.293278 | ||||||||
\(629\) | −0.600092 | −0.0239272 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.4403 | −0.415621 | −0.207811 | − | 0.978169i | \(-0.566634\pi\) | ||||
−0.207811 | + | 0.978169i | \(0.566634\pi\) | |||||||
\(632\) | 2.15620 | 0.0857688 | ||||||||
\(633\) | −11.6802 | −0.464246 | ||||||||
\(634\) | 18.2179 | 0.723525 | ||||||||
\(635\) | −1.81148 | −0.0718862 | ||||||||
\(636\) | −1.48573 | −0.0589129 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10.5672 | −0.418360 | ||||||||
\(639\) | 0.444621 | 0.0175889 | ||||||||
\(640\) | −0.100034 | −0.00395421 | ||||||||
\(641\) | 16.2483 | 0.641771 | 0.320886 | − | 0.947118i | \(-0.396019\pi\) | ||||
0.320886 | + | 0.947118i | \(0.396019\pi\) | |||||||
\(642\) | 58.6638 | 2.31527 | ||||||||
\(643\) | −48.1432 | −1.89858 | −0.949292 | − | 0.314396i | \(-0.898198\pi\) | ||||
−0.949292 | + | 0.314396i | \(0.898198\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.993095 | −0.0391031 | ||||||||
\(646\) | 10.6511 | 0.419063 | ||||||||
\(647\) | 6.61217 | 0.259951 | 0.129976 | − | 0.991517i | \(-0.458510\pi\) | ||||
0.129976 | + | 0.991517i | \(0.458510\pi\) | |||||||
\(648\) | −1.65095 | −0.0648555 | ||||||||
\(649\) | −56.6694 | −2.22447 | ||||||||
\(650\) | 10.0012 | 0.392279 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.24890 | 0.127237 | ||||||||
\(653\) | 33.6484 | 1.31676 | 0.658381 | − | 0.752685i | \(-0.271242\pi\) | ||||
0.658381 | + | 0.752685i | \(0.271242\pi\) | |||||||
\(654\) | −26.9055 | −1.05209 | ||||||||
\(655\) | 0.556104 | 0.0217288 | ||||||||
\(656\) | 1.00000 | 0.0390434 | ||||||||
\(657\) | −39.1962 | −1.52919 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.5436 | 1.03399 | 0.516996 | − | 0.855988i | \(-0.327050\pi\) | ||||
0.516996 | + | 0.855988i | \(0.327050\pi\) | |||||||
\(660\) | 1.56274 | 0.0608296 | ||||||||
\(661\) | 22.9496 | 0.892635 | 0.446317 | − | 0.894875i | \(-0.352735\pi\) | ||||
0.446317 | + | 0.894875i | \(0.352735\pi\) | |||||||
\(662\) | 9.32265 | 0.362335 | ||||||||
\(663\) | −11.5462 | −0.448416 | ||||||||
\(664\) | 1.63342 | 0.0633889 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.50877 | −0.0584637 | ||||||||
\(667\) | −0.342049 | −0.0132442 | ||||||||
\(668\) | 22.7027 | 0.878393 | ||||||||
\(669\) | 11.3149 | 0.437458 | ||||||||
\(670\) | −0.753110 | −0.0290952 | ||||||||
\(671\) | 56.2758 | 2.17250 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.7757 | 0.800844 | 0.400422 | − | 0.916331i | \(-0.368864\pi\) | ||||
0.400422 | + | 0.916331i | \(0.368864\pi\) | |||||||
\(674\) | 28.3634 | 1.09252 | ||||||||
\(675\) | −29.6921 | −1.14285 | ||||||||
\(676\) | −8.98299 | −0.345500 | ||||||||
\(677\) | −35.0420 | −1.34677 | −0.673386 | − | 0.739291i | \(-0.735161\pi\) | ||||
−0.673386 | + | 0.739291i | \(0.735161\pi\) | |||||||
\(678\) | −56.0895 | −2.15410 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.202588 | 0.00776890 | ||||||||
\(681\) | 64.8684 | 2.48576 | ||||||||
\(682\) | 9.57346 | 0.366587 | ||||||||
\(683\) | −25.1924 | −0.963959 | −0.481979 | − | 0.876183i | \(-0.660082\pi\) | ||||
−0.481979 | + | 0.876183i | \(0.660082\pi\) | |||||||
\(684\) | 26.7794 | 1.02394 | ||||||||
\(685\) | −0.142400 | −0.00544082 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −57.8767 | −2.20814 | ||||||||
\(688\) | −3.48995 | −0.133053 | ||||||||
\(689\) | −1.04681 | −0.0398803 | ||||||||
\(690\) | 0.0505842 | 0.00192571 | ||||||||
\(691\) | −11.8598 | −0.451170 | −0.225585 | − | 0.974224i | \(-0.572429\pi\) | ||||
−0.225585 | + | 0.974224i | \(0.572429\pi\) | |||||||
\(692\) | 18.8660 | 0.717179 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.9901 | −0.986572 | ||||||||
\(695\) | −0.946495 | −0.0359026 | ||||||||
\(696\) | −5.47353 | −0.207474 | ||||||||
\(697\) | −2.02518 | −0.0767093 | ||||||||
\(698\) | −6.07191 | −0.229825 | ||||||||
\(699\) | 82.7270 | 3.12902 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.7864 | −1.01171 | −0.505853 | − | 0.862620i | \(-0.668822\pi\) | ||||
−0.505853 | + | 0.862620i | \(0.668822\pi\) | |||||||
\(702\) | −11.9259 | −0.450115 | ||||||||
\(703\) | 1.55842 | 0.0587768 | ||||||||
\(704\) | 5.49180 | 0.206980 | ||||||||
\(705\) | 3.61896 | 0.136298 | ||||||||
\(706\) | −8.90538 | −0.335159 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −29.3532 | −1.10316 | ||||||||
\(709\) | 2.12837 | 0.0799325 | 0.0399663 | − | 0.999201i | \(-0.487275\pi\) | ||||
0.0399663 | + | 0.999201i | \(0.487275\pi\) | |||||||
\(710\) | −0.00873511 | −0.000327823 0 | ||||||||
\(711\) | −10.9789 | −0.411741 | ||||||||
\(712\) | 6.70260 | 0.251191 | ||||||||
\(713\) | 0.309883 | 0.0116052 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.10107 | 0.0411777 | ||||||||
\(716\) | −13.1779 | −0.492482 | ||||||||
\(717\) | −49.2998 | −1.84113 | ||||||||
\(718\) | 22.2052 | 0.828691 | ||||||||
\(719\) | −27.0515 | −1.00885 | −0.504426 | − | 0.863455i | \(-0.668296\pi\) | ||||
−0.504426 | + | 0.863455i | \(0.668296\pi\) | |||||||
\(720\) | 0.509354 | 0.0189825 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8.66057 | −0.322313 | ||||||||
\(723\) | −32.1882 | −1.19709 | ||||||||
\(724\) | −11.4642 | −0.426064 | ||||||||
\(725\) | −9.60163 | −0.356596 | ||||||||
\(726\) | −54.5024 | −2.02277 | ||||||||
\(727\) | −7.85211 | −0.291219 | −0.145609 | − | 0.989342i | \(-0.546514\pi\) | ||||
−0.145609 | + | 0.989342i | \(0.546514\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.3727 | −1.56936 | ||||||||
\(730\) | 0.770057 | 0.0285011 | ||||||||
\(731\) | 7.06779 | 0.261412 | ||||||||
\(732\) | 29.1493 | 1.07739 | ||||||||
\(733\) | −19.5270 | −0.721247 | −0.360624 | − | 0.932711i | \(-0.617436\pi\) | ||||
−0.360624 | + | 0.932711i | \(0.617436\pi\) | |||||||
\(734\) | 22.7662 | 0.840316 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.177764 | 0.00655247 | ||||||||
\(737\) | 41.3451 | 1.52297 | ||||||||
\(738\) | −5.09179 | −0.187431 | ||||||||
\(739\) | 3.91797 | 0.144125 | 0.0720625 | − | 0.997400i | \(-0.477042\pi\) | ||||
0.0720625 | + | 0.997400i | \(0.477042\pi\) | |||||||
\(740\) | 0.0296416 | 0.00108965 | ||||||||
\(741\) | 29.9850 | 1.10153 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.6030 | 1.52627 | 0.763133 | − | 0.646241i | \(-0.223660\pi\) | ||||
0.763133 | + | 0.646241i | \(0.223660\pi\) | |||||||
\(744\) | 4.95879 | 0.181798 | ||||||||
\(745\) | 0.181098 | 0.00663492 | ||||||||
\(746\) | −25.1403 | −0.920453 | ||||||||
\(747\) | −8.31702 | −0.304304 | ||||||||
\(748\) | −11.1219 | −0.406657 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.84274 | 0.103802 | ||||||||
\(751\) | −39.0167 | −1.42374 | −0.711869 | − | 0.702312i | \(-0.752151\pi\) | ||||
−0.711869 | + | 0.702312i | \(0.752151\pi\) | |||||||
\(752\) | 12.7178 | 0.463771 | ||||||||
\(753\) | −60.9015 | −2.21937 | ||||||||
\(754\) | −3.85653 | −0.140446 | ||||||||
\(755\) | −0.308605 | −0.0112313 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.8068 | −1.37411 | −0.687055 | − | 0.726605i | \(-0.741097\pi\) | ||||
−0.687055 | + | 0.726605i | \(0.741097\pi\) | |||||||
\(758\) | −11.7756 | −0.427710 | ||||||||
\(759\) | −2.77703 | −0.100800 | ||||||||
\(760\) | −0.526114 | −0.0190842 | ||||||||
\(761\) | 1.71848 | 0.0622949 | 0.0311475 | − | 0.999515i | \(-0.490084\pi\) | ||||
0.0311475 | + | 0.999515i | \(0.490084\pi\) | |||||||
\(762\) | 51.5117 | 1.86607 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 11.5032 | 0.416170 | ||||||||
\(765\) | −1.03154 | −0.0372953 | ||||||||
\(766\) | −32.1184 | −1.16048 | ||||||||
\(767\) | −20.6816 | −0.746770 | ||||||||
\(768\) | 2.84461 | 0.102646 | ||||||||
\(769\) | −12.0903 | −0.435988 | −0.217994 | − | 0.975950i | \(-0.569951\pi\) | ||||
−0.217994 | + | 0.975950i | \(0.569951\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.1820 | 0.582780 | ||||||||
\(772\) | −10.8671 | −0.391116 | ||||||||
\(773\) | −43.1222 | −1.55100 | −0.775499 | − | 0.631349i | \(-0.782502\pi\) | ||||
−0.775499 | + | 0.631349i | \(0.782502\pi\) | |||||||
\(774\) | 17.7701 | 0.638733 | ||||||||
\(775\) | 8.69869 | 0.312466 | ||||||||
\(776\) | 0.783908 | 0.0281406 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.4285 | 0.732396 | ||||||||
\(779\) | 5.25933 | 0.188435 | ||||||||
\(780\) | 0.570326 | 0.0204209 | ||||||||
\(781\) | 0.479550 | 0.0171597 | ||||||||
\(782\) | −0.360005 | −0.0128737 | ||||||||
\(783\) | 11.4495 | 0.409171 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.735204 | 0.0262406 | ||||||||
\(786\) | −15.8135 | −0.564050 | ||||||||
\(787\) | −46.6990 | −1.66464 | −0.832321 | − | 0.554295i | \(-0.812988\pi\) | ||||
−0.832321 | + | 0.554295i | \(0.812988\pi\) | |||||||
\(788\) | 24.6123 | 0.876777 | ||||||||
\(789\) | −39.6012 | −1.40984 | ||||||||
\(790\) | 0.215694 | 0.00767404 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −27.9631 | −0.993626 | ||||||||
\(793\) | 20.5380 | 0.729325 | ||||||||
\(794\) | −13.2034 | −0.468571 | ||||||||
\(795\) | −0.148624 | −0.00527114 | ||||||||
\(796\) | 14.6903 | 0.520685 | ||||||||
\(797\) | 13.3684 | 0.473535 | 0.236767 | − | 0.971566i | \(-0.423912\pi\) | ||||
0.236767 | + | 0.971566i | \(0.423912\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.7559 | −0.911180 | ||||||||
\(800\) | 4.98999 | 0.176423 | ||||||||
\(801\) | −34.1282 | −1.20586 | ||||||||
\(802\) | 6.19120 | 0.218619 | ||||||||
\(803\) | −42.2755 | −1.49187 | ||||||||
\(804\) | 21.4156 | 0.755272 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.49386 | 0.123066 | ||||||||
\(807\) | 35.3897 | 1.24577 | ||||||||
\(808\) | 9.35530 | 0.329118 | ||||||||
\(809\) | 9.16465 | 0.322212 | 0.161106 | − | 0.986937i | \(-0.448494\pi\) | ||||
0.161106 | + | 0.986937i | \(0.448494\pi\) | |||||||
\(810\) | −0.165152 | −0.00580285 | ||||||||
\(811\) | 13.7703 | 0.483542 | 0.241771 | − | 0.970333i | \(-0.422272\pi\) | ||||
0.241771 | + | 0.970333i | \(0.422272\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.4774 | 1.03382 | ||||||||
\(814\) | −1.62730 | −0.0570369 | ||||||||
\(815\) | 0.325001 | 0.0113843 | ||||||||
\(816\) | −5.76085 | −0.201670 | ||||||||
\(817\) | −18.3548 | −0.642153 | ||||||||
\(818\) | 7.68619 | 0.268741 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.100034 | 0.00349335 | ||||||||
\(821\) | 18.0395 | 0.629581 | 0.314791 | − | 0.949161i | \(-0.398066\pi\) | ||||
0.314791 | + | 0.949161i | \(0.398066\pi\) | |||||||
\(822\) | 4.04932 | 0.141236 | ||||||||
\(823\) | −50.5380 | −1.76164 | −0.880821 | − | 0.473449i | \(-0.843009\pi\) | ||||
−0.880821 | + | 0.473449i | \(0.843009\pi\) | |||||||
\(824\) | 3.51803 | 0.122556 | ||||||||
\(825\) | −77.9538 | −2.71400 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.6901 | −1.13675 | −0.568373 | − | 0.822771i | \(-0.692427\pi\) | ||||
−0.568373 | + | 0.822771i | \(0.692427\pi\) | |||||||
\(828\) | −0.905137 | −0.0314557 | ||||||||
\(829\) | −5.77411 | −0.200543 | −0.100272 | − | 0.994960i | \(-0.531971\pi\) | ||||
−0.100272 | + | 0.994960i | \(0.531971\pi\) | |||||||
\(830\) | 0.163398 | 0.00567163 | ||||||||
\(831\) | 13.7689 | 0.477637 | ||||||||
\(832\) | 2.00425 | 0.0694848 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 26.9148 | 0.931984 | ||||||||
\(835\) | 2.27105 | 0.0785929 | ||||||||
\(836\) | 28.8832 | 0.998947 | ||||||||
\(837\) | −10.3728 | −0.358535 | ||||||||
\(838\) | −5.34493 | −0.184638 | ||||||||
\(839\) | −16.1542 | −0.557705 | −0.278853 | − | 0.960334i | \(-0.589954\pi\) | ||||
−0.278853 | + | 0.960334i | \(0.589954\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.2975 | −0.872329 | ||||||||
\(842\) | −31.0458 | −1.06991 | ||||||||
\(843\) | −82.6971 | −2.84824 | ||||||||
\(844\) | −4.10608 | −0.141337 | ||||||||
\(845\) | −0.898608 | −0.0309131 | ||||||||
\(846\) | −64.7565 | −2.22637 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.522296 | −0.0179357 | ||||||||
\(849\) | 10.8304 | 0.371697 | ||||||||
\(850\) | −10.1057 | −0.346621 | ||||||||
\(851\) | −0.0526740 | −0.00180564 | ||||||||
\(852\) | 0.248394 | 0.00850985 | ||||||||
\(853\) | −51.3396 | −1.75784 | −0.878918 | − | 0.476974i | \(-0.841734\pi\) | ||||
−0.878918 | + | 0.476974i | \(0.841734\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.67886 | 0.0916151 | ||||||||
\(856\) | 20.6228 | 0.704873 | ||||||||
\(857\) | −2.40688 | −0.0822175 | −0.0411088 | − | 0.999155i | \(-0.513089\pi\) | ||||
−0.0411088 | + | 0.999155i | \(0.513089\pi\) | |||||||
\(858\) | −31.3104 | −1.06892 | ||||||||
\(859\) | 19.6567 | 0.670678 | 0.335339 | − | 0.942098i | \(-0.391149\pi\) | ||||
0.335339 | + | 0.942098i | \(0.391149\pi\) | |||||||
\(860\) | −0.349115 | −0.0119047 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.4490 | 0.968977 | ||||||||
\(863\) | 11.4517 | 0.389820 | 0.194910 | − | 0.980821i | \(-0.437559\pi\) | ||||
0.194910 | + | 0.980821i | \(0.437559\pi\) | |||||||
\(864\) | −5.95032 | −0.202434 | ||||||||
\(865\) | 1.88725 | 0.0641685 | ||||||||
\(866\) | −2.21499 | −0.0752686 | ||||||||
\(867\) | −36.6915 | −1.24611 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.8414 | −0.401692 | ||||||||
\(870\) | −0.547541 | −0.0185634 | ||||||||
\(871\) | 15.0890 | 0.511271 | ||||||||
\(872\) | −9.45841 | −0.320302 | ||||||||
\(873\) | −3.99149 | −0.135092 | ||||||||
\(874\) | 0.934919 | 0.0316241 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −21.8976 | −0.739850 | ||||||||
\(877\) | 0.985999 | 0.0332948 | 0.0166474 | − | 0.999861i | \(-0.494701\pi\) | ||||
0.0166474 | + | 0.999861i | \(0.494701\pi\) | |||||||
\(878\) | 33.6220 | 1.13469 | ||||||||
\(879\) | 60.3193 | 2.03452 | ||||||||
\(880\) | 0.549369 | 0.0185192 | ||||||||
\(881\) | −34.6171 | −1.16628 | −0.583139 | − | 0.812372i | \(-0.698176\pi\) | ||||
−0.583139 | + | 0.812372i | \(0.698176\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.2742 | 1.11977 | 0.559884 | − | 0.828571i | \(-0.310846\pi\) | ||||
0.559884 | + | 0.828571i | \(0.310846\pi\) | |||||||
\(884\) | −4.05897 | −0.136518 | ||||||||
\(885\) | −2.93633 | −0.0987037 | ||||||||
\(886\) | −4.73115 | −0.158946 | ||||||||
\(887\) | 11.5309 | 0.387168 | 0.193584 | − | 0.981084i | \(-0.437989\pi\) | ||||
0.193584 | + | 0.981084i | \(0.437989\pi\) | |||||||
\(888\) | −0.842898 | −0.0282858 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.670491 | 0.0224749 | ||||||||
\(891\) | 9.06671 | 0.303746 | ||||||||
\(892\) | 3.97766 | 0.133182 | ||||||||
\(893\) | 66.8872 | 2.23830 | ||||||||
\(894\) | −5.14976 | −0.172234 | ||||||||
\(895\) | −1.31825 | −0.0440641 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.01348 | −0.0338393 | ||||||||
\(898\) | 19.0673 | 0.636286 | ||||||||
\(899\) | −3.35428 | −0.111871 | ||||||||
\(900\) | −25.4080 | −0.846933 | ||||||||
\(901\) | 1.05775 | 0.0352386 | ||||||||
\(902\) | −5.49180 | −0.182857 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.7178 | −0.655805 | ||||||||
\(905\) | −1.14681 | −0.0381214 | ||||||||
\(906\) | 8.77557 | 0.291549 | ||||||||
\(907\) | −17.3966 | −0.577644 | −0.288822 | − | 0.957383i | \(-0.593264\pi\) | ||||
−0.288822 | + | 0.957383i | \(0.593264\pi\) | |||||||
\(908\) | 22.8040 | 0.756777 | ||||||||
\(909\) | −47.6352 | −1.57996 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.3873 | 1.80193 | 0.900966 | − | 0.433889i | \(-0.142859\pi\) | ||||
0.900966 | + | 0.433889i | \(0.142859\pi\) | |||||||
\(912\) | 14.9607 | 0.495399 | ||||||||
\(913\) | −8.97041 | −0.296877 | ||||||||
\(914\) | 21.8939 | 0.724184 | ||||||||
\(915\) | 2.91594 | 0.0963979 | ||||||||
\(916\) | −20.3461 | −0.672255 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 12.0505 | 0.397726 | ||||||||
\(919\) | 17.4287 | 0.574919 | 0.287459 | − | 0.957793i | \(-0.407189\pi\) | ||||
0.287459 | + | 0.957793i | \(0.407189\pi\) | |||||||
\(920\) | 0.0177825 | 0.000586272 0 | ||||||||
\(921\) | 67.2701 | 2.21663 | ||||||||
\(922\) | −35.8923 | −1.18205 | ||||||||
\(923\) | 0.175013 | 0.00576063 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.47861 | −0.0486163 | ||||||||
\(926\) | 17.2360 | 0.566411 | ||||||||
\(927\) | −17.9131 | −0.588343 | ||||||||
\(928\) | −1.92418 | −0.0631642 | ||||||||
\(929\) | 37.0389 | 1.21521 | 0.607604 | − | 0.794240i | \(-0.292131\pi\) | ||||
0.607604 | + | 0.794240i | \(0.292131\pi\) | |||||||
\(930\) | 0.496050 | 0.0162661 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 29.0821 | 0.952614 | ||||||||
\(933\) | −12.8966 | −0.422215 | ||||||||
\(934\) | −32.8802 | −1.07587 | ||||||||
\(935\) | −1.11257 | −0.0363851 | ||||||||
\(936\) | −10.2052 | −0.333568 | ||||||||
\(937\) | −7.43914 | −0.243026 | −0.121513 | − | 0.992590i | \(-0.538775\pi\) | ||||
−0.121513 | + | 0.992590i | \(0.538775\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −39.6913 | −1.29528 | ||||||||
\(940\) | 1.27222 | 0.0414952 | ||||||||
\(941\) | 48.7109 | 1.58793 | 0.793966 | − | 0.607962i | \(-0.208013\pi\) | ||||
0.793966 | + | 0.607962i | \(0.208013\pi\) | |||||||
\(942\) | −20.9065 | −0.681170 | ||||||||
\(943\) | −0.177764 | −0.00578879 | ||||||||
\(944\) | −10.3189 | −0.335852 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.1661 | 0.623144 | ||||||||
\(947\) | −25.7136 | −0.835580 | −0.417790 | − | 0.908544i | \(-0.637195\pi\) | ||||
−0.417790 | + | 0.908544i | \(0.637195\pi\) | |||||||
\(948\) | −6.13353 | −0.199208 | ||||||||
\(949\) | −15.4285 | −0.500832 | ||||||||
\(950\) | 26.2440 | 0.851469 | ||||||||
\(951\) | −51.8228 | −1.68047 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.4560 | 0.727422 | 0.363711 | − | 0.931512i | \(-0.381510\pi\) | ||||
0.363711 | + | 0.931512i | \(0.381510\pi\) | |||||||
\(954\) | 2.65942 | 0.0861019 | ||||||||
\(955\) | 1.15071 | 0.0372362 | ||||||||
\(956\) | −17.3310 | −0.560523 | ||||||||
\(957\) | 30.0596 | 0.971687 | ||||||||
\(958\) | 25.1914 | 0.813898 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.284559 | 0.00918409 | ||||||||
\(961\) | −27.9612 | −0.901973 | ||||||||
\(962\) | −0.593888 | −0.0191477 | ||||||||
\(963\) | −105.007 | −3.38380 | ||||||||
\(964\) | −11.3155 | −0.364448 | ||||||||
\(965\) | −1.08709 | −0.0349945 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.3511 | −1.36192 | −0.680960 | − | 0.732320i | \(-0.738437\pi\) | ||||
−0.680960 | + | 0.732320i | \(0.738437\pi\) | |||||||
\(968\) | −19.1599 | −0.615823 | ||||||||
\(969\) | −30.2982 | −0.973320 | ||||||||
\(970\) | 0.0784177 | 0.00251784 | ||||||||
\(971\) | −33.3395 | −1.06991 | −0.534957 | − | 0.844879i | \(-0.679672\pi\) | ||||
−0.534957 | + | 0.844879i | \(0.679672\pi\) | |||||||
\(972\) | −13.1546 | −0.421936 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 31.1451 | 0.997953 | ||||||||
\(975\) | −28.4494 | −0.911111 | ||||||||
\(976\) | 10.2472 | 0.328006 | ||||||||
\(977\) | 50.5717 | 1.61793 | 0.808966 | − | 0.587855i | \(-0.200028\pi\) | ||||
0.808966 | + | 0.587855i | \(0.200028\pi\) | |||||||
\(978\) | −9.24184 | −0.295521 | ||||||||
\(979\) | −36.8094 | −1.17643 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 48.1602 | 1.53764 | ||||||||
\(982\) | 1.81906 | 0.0580485 | ||||||||
\(983\) | 16.7283 | 0.533551 | 0.266775 | − | 0.963759i | \(-0.414042\pi\) | ||||
0.266775 | + | 0.963759i | \(0.414042\pi\) | |||||||
\(984\) | −2.84461 | −0.0906828 | ||||||||
\(985\) | 2.46208 | 0.0784483 | ||||||||
\(986\) | 3.89682 | 0.124100 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.5410 | 0.335354 | ||||||||
\(989\) | 0.620387 | 0.0197272 | ||||||||
\(990\) | −2.79727 | −0.0889032 | ||||||||
\(991\) | −18.9987 | −0.603513 | −0.301756 | − | 0.953385i | \(-0.597573\pi\) | ||||
−0.301756 | + | 0.953385i | \(0.597573\pi\) | |||||||
\(992\) | 1.74323 | 0.0553475 | ||||||||
\(993\) | −26.5193 | −0.841564 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.46954 | 0.0465875 | ||||||||
\(996\) | −4.64643 | −0.147228 | ||||||||
\(997\) | −5.34619 | −0.169316 | −0.0846578 | − | 0.996410i | \(-0.526980\pi\) | ||||
−0.0846578 | + | 0.996410i | \(0.526980\pi\) | |||||||
\(998\) | 1.22056 | 0.0386362 | ||||||||
\(999\) | 1.76317 | 0.0557841 |
(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 | 4018.2.a.bs.1.9 | yes | 10 | |
7.6 | odd | 2 | 4018.2.a.br.1.2 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4018.2.a.br.1.2 | ✓ | 10 | 7.6 | odd | 2 | ||
4018.2.a.bs.1.9 | yes | 10 | 1.1 | even | 1 | trivial |