Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [920,2,Mod(1,920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(920, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("920.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 920 = 2^{3} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 920.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: | \(7.34623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2597.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 9x + 8 \) |
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 | 1.3 | ||
Root | \(3.07912\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 920.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.07912 | 1.77773 | 0.888865 | − | 0.458169i | \(-0.151495\pi\) | ||||
0.888865 | + | 0.458169i | \(0.151495\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.07912 | −0.785833 | −0.392917 | − | 0.919574i | \(-0.628534\pi\) | ||||
−0.392917 | + | 0.919574i | \(0.628534\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.48097 | 2.16032 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.07912 | 1.53141 | 0.765706 | − | 0.643191i | \(-0.222390\pi\) | ||||
0.765706 | + | 0.643191i | \(0.222390\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.48097 | −0.965448 | −0.482724 | − | 0.875772i | \(-0.660353\pi\) | ||||
−0.482724 | + | 0.875772i | \(0.660353\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.07912 | 0.795025 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.48097 | 1.57187 | 0.785933 | − | 0.618311i | \(-0.212183\pi\) | ||||
0.785933 | + | 0.618311i | \(0.212183\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.48097 | −1.71625 | −0.858126 | − | 0.513438i | \(-0.828371\pi\) | ||||
−0.858126 | + | 0.513438i | \(0.828371\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.40185 | −1.39700 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.7183 | 2.06274 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.56009 | −0.289702 | −0.144851 | − | 0.989453i | \(-0.546270\pi\) | ||||
−0.144851 | + | 0.989453i | \(0.546270\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0791189 | 0.0142102 | 0.00710508 | − | 0.999975i | \(-0.497738\pi\) | ||||
0.00710508 | + | 0.999975i | \(0.497738\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 15.6392 | 2.72244 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.07912 | −0.351435 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.71833 | −1.59768 | −0.798842 | − | 0.601541i | \(-0.794554\pi\) | ||||
−0.798842 | + | 0.601541i | \(0.794554\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.7183 | −1.71631 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.480973 | −0.0751154 | −0.0375577 | − | 0.999294i | \(-0.511958\pi\) | ||||
−0.0375577 | + | 0.999294i | \(0.511958\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.48097 | 0.966126 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.96195 | 1.01550 | 0.507752 | − | 0.861503i | \(-0.330477\pi\) | ||||
0.507752 | + | 0.861503i | \(0.330477\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.67726 | −0.382466 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 19.9557 | 2.79435 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.7183 | 1.60964 | 0.804818 | − | 0.593521i | \(-0.202263\pi\) | ||||
0.804818 | + | 0.593521i | \(0.202263\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.07912 | 0.684868 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −23.0348 | −3.05103 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.5601 | −1.50500 | −0.752498 | − | 0.658595i | \(-0.771151\pi\) | ||||
−0.752498 | + | 0.658595i | \(0.771151\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.88283 | 1.00929 | 0.504646 | − | 0.863326i | \(-0.331623\pi\) | ||||
0.504646 | + | 0.863326i | \(0.331623\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −13.4747 | −1.69765 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.48097 | −0.431762 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.71833 | −1.18728 | −0.593641 | − | 0.804730i | \(-0.702310\pi\) | ||||
−0.593641 | + | 0.804730i | \(0.702310\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.07912 | 0.370682 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.67726 | −1.14848 | −0.574240 | − | 0.818687i | \(-0.694702\pi\) | ||||
−0.574240 | + | 0.818687i | \(0.694702\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.2784 | −1.55412 | −0.777061 | − | 0.629425i | \(-0.783290\pi\) | ||||
−0.777061 | + | 0.629425i | \(0.783290\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.07912 | 0.355546 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.5601 | −1.20343 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.3165 | −1.38571 | −0.692856 | − | 0.721076i | \(-0.743648\pi\) | ||||
−0.692856 | + | 0.721076i | \(0.743648\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 13.5601 | 1.50668 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.59815 | −0.504712 | −0.252356 | − | 0.967634i | \(-0.581205\pi\) | ||||
−0.252356 | + | 0.967634i | \(0.581205\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.48097 | 0.702960 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.80371 | −0.515012 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.31648 | 0.881545 | 0.440772 | − | 0.897619i | \(-0.354705\pi\) | ||||
0.440772 | + | 0.897619i | \(0.354705\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.23736 | 0.758681 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.243616 | 0.0252618 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.48097 | −0.767532 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.23736 | 0.734842 | 0.367421 | − | 0.930055i | \(-0.380241\pi\) | ||||
0.367421 | + | 0.930055i | \(0.380241\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 32.9176 | 3.30835 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.43991 | 0.242780 | 0.121390 | − | 0.992605i | \(-0.461265\pi\) | ||||
0.121390 | + | 0.992605i | \(0.461265\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.88283 | 0.776718 | 0.388359 | − | 0.921508i | \(-0.373042\pi\) | ||||
0.388359 | + | 0.921508i | \(0.373042\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.40185 | −0.624757 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.6803 | −1.61254 | −0.806272 | − | 0.591546i | \(-0.798518\pi\) | ||||
−0.806272 | + | 0.591546i | \(0.798518\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.32274 | 0.509826 | 0.254913 | − | 0.966964i | \(-0.417953\pi\) | ||||
0.254913 | + | 0.966964i | \(0.417953\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −29.9239 | −2.84025 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.20556 | −0.207482 | −0.103741 | − | 0.994604i | \(-0.533081\pi\) | ||||
−0.103741 | + | 0.994604i | \(0.533081\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −22.5601 | −2.08568 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.4747 | −1.23522 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.7974 | 1.34522 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.48097 | −0.133535 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.15824 | 0.546455 | 0.273228 | − | 0.961949i | \(-0.411909\pi\) | ||||
0.273228 | + | 0.961949i | \(0.411909\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24.6330 | 2.16881 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.19629 | −0.628743 | −0.314371 | − | 0.949300i | \(-0.601794\pi\) | ||||
−0.314371 | + | 0.949300i | \(0.601794\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.5538 | 1.34869 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.7183 | 0.922487 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.6012 | 1.07659 | 0.538295 | − | 0.842757i | \(-0.319069\pi\) | ||||
0.538295 | + | 0.842757i | \(0.319069\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.75638 | −0.742707 | −0.371353 | − | 0.928492i | \(-0.621106\pi\) | ||||
−0.371353 | + | 0.928492i | \(0.621106\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.4367 | 1.80529 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.6803 | −1.47850 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.56009 | −0.129559 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.24362 | −0.679922 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.79745 | 0.147253 | 0.0736264 | − | 0.997286i | \(-0.476543\pi\) | ||||
0.0736264 | + | 0.997286i | \(0.476543\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.3956 | −1.57839 | −0.789196 | − | 0.614142i | \(-0.789502\pi\) | ||||
−0.789196 | + | 0.614142i | \(0.789502\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 42.0030 | 3.39574 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0791189 | 0.00635498 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.36380 | 0.348269 | 0.174135 | − | 0.984722i | \(-0.444287\pi\) | ||||
0.174135 | + | 0.984722i | \(0.444287\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 36.0821 | 2.86150 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.07912 | −0.163858 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.32274 | 0.416909 | 0.208454 | − | 0.978032i | \(-0.433157\pi\) | ||||
0.208454 | + | 0.978032i | \(0.433157\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.6392 | 1.21751 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.882827 | −0.0679098 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −48.4840 | −3.70766 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.23736 | −0.702303 | −0.351152 | − | 0.936319i | \(-0.614210\pi\) | ||||
−0.351152 | + | 0.936319i | \(0.614210\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.07912 | −0.157167 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −35.5949 | −2.67548 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.96195 | 0.221386 | 0.110693 | − | 0.993855i | \(-0.464693\pi\) | ||||
0.110693 | + | 0.993855i | \(0.464693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.8355 | 0.805397 | 0.402698 | − | 0.915333i | \(-0.368072\pi\) | ||||
0.402698 | + | 0.915333i | \(0.368072\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24.2722 | 1.79425 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.71833 | −0.714506 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 32.9176 | 2.40718 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −22.2847 | −1.62097 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.76565 | 0.561903 | 0.280952 | − | 0.959722i | \(-0.409350\pi\) | ||||
0.280952 | + | 0.959722i | \(0.409350\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.15824 | −0.155353 | −0.0776767 | − | 0.996979i | \(-0.524750\pi\) | ||||
−0.0776767 | + | 0.996979i | \(0.524750\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.7183 | −0.767556 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0411 | 0.857890 | 0.428945 | − | 0.903331i | \(-0.358885\pi\) | ||||
0.428945 | + | 0.903331i | \(0.358885\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.0000 | −0.992434 | −0.496217 | − | 0.868199i | \(-0.665278\pi\) | ||||
−0.496217 | + | 0.868199i | \(0.665278\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −29.9239 | −2.11067 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.24362 | 0.227657 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.480973 | −0.0335926 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.48097 | 0.450459 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −37.9968 | −2.62829 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.40185 | 0.234193 | 0.117097 | − | 0.993121i | \(-0.462641\pi\) | ||||
0.117097 | + | 0.993121i | \(0.462641\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −29.7974 | −2.04169 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.164498 | −0.0111668 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −40.8858 | −2.76281 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.5601 | −1.51756 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.19629 | 0.347969 | 0.173985 | − | 0.984748i | \(-0.444336\pi\) | ||||
0.173985 | + | 0.984748i | \(0.444336\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.48097 | 0.432065 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.35453 | 0.355393 | 0.177696 | − | 0.984085i | \(-0.443136\pi\) | ||||
0.177696 | + | 0.984085i | \(0.443136\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.803708 | −0.0531105 | −0.0265553 | − | 0.999647i | \(-0.508454\pi\) | ||||
−0.0265553 | + | 0.999647i | \(0.508454\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −32.5158 | −2.13938 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.1582 | 0.927537 | 0.463768 | − | 0.885956i | \(-0.346497\pi\) | ||||
0.463768 | + | 0.885956i | \(0.346497\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.96195 | 0.454147 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −37.9239 | −2.46342 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.9146 | 0.706008 | 0.353004 | − | 0.935622i | \(-0.385160\pi\) | ||||
0.353004 | + | 0.935622i | \(0.385160\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.4367 | −1.76735 | −0.883675 | − | 0.468100i | \(-0.844939\pi\) | ||||
−0.883675 | + | 0.468100i | \(0.844939\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.59815 | 0.615721 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.67726 | −0.171044 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.0411 | 1.65695 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.1582 | −0.897242 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.5190 | −1.04267 | −0.521336 | − | 0.853352i | \(-0.674566\pi\) | ||||
−0.521336 | + | 0.853352i | \(0.674566\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.07912 | 0.319321 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 19.9557 | 1.24967 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.7657 | 1.23295 | 0.616474 | − | 0.787375i | \(-0.288561\pi\) | ||||
0.616474 | + | 0.787375i | \(0.288561\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.2056 | 1.25551 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.1109 | −0.625850 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.44292 | 0.458950 | 0.229475 | − | 0.973315i | \(-0.426299\pi\) | ||||
0.229475 | + | 0.973315i | \(0.426299\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.7183 | 0.719851 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 25.6074 | 1.56715 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.7564 | −1.38748 | −0.693741 | − | 0.720225i | \(-0.744039\pi\) | ||||
−0.693741 | + | 0.720225i | \(0.744039\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.0411 | −1.15666 | −0.578331 | − | 0.815802i | \(-0.696296\pi\) | ||||
−0.578331 | + | 0.815802i | \(0.696296\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 22.2847 | 1.34873 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.07912 | 0.306282 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.3165 | −1.10053 | −0.550265 | − | 0.834990i | \(-0.685473\pi\) | ||||
−0.550265 | + | 0.834990i | \(0.685473\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.512767 | 0.0306986 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.0821 | 1.55593 | 0.777965 | − | 0.628308i | \(-0.216252\pi\) | ||||
0.777965 | + | 0.628308i | \(0.216252\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.6422 | −1.52427 | −0.762136 | − | 0.647417i | \(-0.775849\pi\) | ||||
−0.762136 | + | 0.647417i | \(0.775849\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −23.0348 | −1.36446 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.00000 | 0.0590281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.0030 | 1.47077 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.2847 | 1.30635 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.8385 | 1.80161 | 0.900803 | − | 0.434229i | \(-0.142979\pi\) | ||||
0.900803 | + | 0.434229i | \(0.142979\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.5601 | −0.673055 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 54.4397 | 3.15891 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.48097 | −0.201310 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.6330 | −0.958707 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.51277 | 0.431597 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.88283 | 0.451369 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.88283 | −0.107459 | −0.0537293 | − | 0.998556i | \(-0.517111\pi\) | ||||
−0.0537293 | + | 0.998556i | \(0.517111\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.2722 | 1.38080 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.60742 | 0.0911482 | 0.0455741 | − | 0.998961i | \(-0.485488\pi\) | ||||
0.0455741 | + | 0.998961i | \(0.485488\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.68654 | −0.0953286 | −0.0476643 | − | 0.998863i | \(-0.515178\pi\) | ||||
−0.0476643 | + | 0.998863i | \(0.515178\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −13.4747 | −0.759214 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.6773 | −0.712026 | −0.356013 | − | 0.934481i | \(-0.615864\pi\) | ||||
−0.356013 | + | 0.934481i | \(0.615864\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.92389 | −0.443653 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −51.3606 | −2.86667 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −48.4840 | −2.69772 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.48097 | −0.193090 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.3893 | 0.906332 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.4747 | −0.798017 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.3893 | 1.83524 | 0.917622 | − | 0.397454i | \(-0.130106\pi\) | ||||
0.917622 | + | 0.397454i | \(0.130106\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −62.9842 | −3.45151 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.71833 | −0.530969 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.6392 | −0.960869 | −0.480435 | − | 0.877031i | \(-0.659521\pi\) | ||||
−0.480435 | + | 0.877031i | \(0.659521\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.79119 | −0.368847 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.401854 | 0.0217616 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1202 | 1.08639 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.07912 | 0.165774 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.7121 | 1.05820 | 0.529100 | − | 0.848560i | \(-0.322530\pi\) | ||||
0.529100 | + | 0.848560i | \(0.322530\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.0348 | −0.858323 | −0.429162 | − | 0.903228i | \(-0.641191\pi\) | ||||
−0.429162 | + | 0.903228i | \(0.641191\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −37.3102 | −1.99147 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.00000 | −0.425797 | −0.212899 | − | 0.977074i | \(-0.568290\pi\) | ||||
−0.212899 | + | 0.977074i | \(0.568290\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.67726 | −0.513616 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −41.4902 | −2.19590 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.1202 | −0.692457 | −0.346228 | − | 0.938150i | \(-0.612538\pi\) | ||||
−0.346228 | + | 0.938150i | \(0.612538\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.9650 | 1.94552 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 45.5631 | 2.39144 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.2784 | −0.695024 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.47796 | 0.181548 | 0.0907741 | − | 0.995872i | \(-0.471066\pi\) | ||||
0.0907741 | + | 0.995872i | \(0.471066\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.11717 | −0.162274 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.3638 | −1.26491 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.5949 | 1.11814 | 0.559071 | − | 0.829120i | \(-0.311158\pi\) | ||||
0.559071 | + | 0.829120i | \(0.311158\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.07912 | 0.159005 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.43064 | 0.279692 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.80070 | 0.400695 | 0.200347 | − | 0.979725i | \(-0.435793\pi\) | ||||
0.200347 | + | 0.979725i | \(0.435793\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.9619 | 0.971450 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.4274 | 1.65696 | 0.828481 | − | 0.560017i | \(-0.189205\pi\) | ||||
0.828481 | + | 0.560017i | \(0.189205\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.5601 | −0.538192 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 51.8478 | 2.63557 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.5538 | 1.19423 | 0.597113 | − | 0.802157i | \(-0.296314\pi\) | ||||
0.597113 | + | 0.802157i | \(0.296314\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.48097 | 0.327757 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.1582 | −1.11774 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.3165 | −0.619709 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.370060 | −0.0185728 | −0.00928639 | − | 0.999957i | \(-0.502956\pi\) | ||||
−0.00928639 | + | 0.999957i | \(0.502956\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 47.8921 | 2.39760 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.3545 | 0.567018 | 0.283509 | − | 0.958970i | \(-0.408501\pi\) | ||||
0.283509 | + | 0.958970i | \(0.408501\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.275411 | −0.0137192 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.5601 | 0.673806 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −49.3606 | −2.44671 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.88283 | 0.241440 | 0.120720 | − | 0.992687i | \(-0.461480\pi\) | ||||
0.120720 | + | 0.992687i | \(0.461480\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 38.8005 | 1.91389 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.0348 | 1.18268 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.59815 | −0.225714 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.9619 | −1.32033 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.51277 | 0.0739035 | 0.0369518 | − | 0.999317i | \(-0.488235\pi\) | ||||
0.0369518 | + | 0.999317i | \(0.488235\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.2722 | 1.08548 | 0.542739 | − | 0.839901i | \(-0.317387\pi\) | ||||
0.542739 | + | 0.839901i | \(0.317387\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 45.1202 | 2.19382 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.48097 | 0.314373 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.3893 | −0.793135 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −54.4397 | −2.62837 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.8858 | −0.813362 | −0.406681 | − | 0.913570i | \(-0.633314\pi\) | ||||
−0.406681 | + | 0.913570i | \(0.633314\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.3956 | 1.17238 | 0.586189 | − | 0.810175i | \(-0.300628\pi\) | ||||
0.586189 | + | 0.810175i | \(0.300628\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.80371 | −0.230320 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.48097 | −0.357863 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.0378 | 1.91090 | 0.955450 | − | 0.295152i | \(-0.0953703\pi\) | ||||
0.955450 | + | 0.295152i | \(0.0953703\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.3513 | −0.826251 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.22809 | −0.248394 | −0.124197 | − | 0.992258i | \(-0.539635\pi\) | ||||
−0.124197 | + | 0.992258i | \(0.539635\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.31648 | 0.394239 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.53456 | 0.261776 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.72459 | 0.222967 | 0.111484 | − | 0.993766i | \(-0.464440\pi\) | ||||
0.111484 | + | 0.993766i | \(0.464440\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.44292 | −0.115033 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −59.7213 | −2.80595 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.23736 | 0.339293 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.2311 | 1.55449 | 0.777243 | − | 0.629201i | \(-0.216618\pi\) | ||||
0.777243 | + | 0.629201i | \(0.216618\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 69.4652 | 3.24236 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.9619 | −1.34889 | −0.674446 | − | 0.738324i | \(-0.735618\pi\) | ||||
−0.674446 | + | 0.738324i | \(0.735618\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.39258 | 0.204141 | 0.102070 | − | 0.994777i | \(-0.467453\pi\) | ||||
0.102070 | + | 0.994777i | \(0.467453\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.243616 | 0.0112974 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.0729 | 0.790038 | 0.395019 | − | 0.918673i | \(-0.370738\pi\) | ||||
0.395019 | + | 0.918673i | \(0.370738\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.2056 | 0.933006 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.4367 | 0.619129 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 40.6330 | 1.86831 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.48097 | −0.343251 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 75.9462 | 3.47734 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.0441 | 1.23568 | 0.617838 | − | 0.786306i | \(-0.288009\pi\) | ||||
0.617838 | + | 0.786306i | \(0.288009\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.8292 | 1.54248 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.40185 | −0.291294 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.23736 | 0.328631 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.0821 | −1.27252 | −0.636261 | − | 0.771474i | \(-0.719520\pi\) | ||||
−0.636261 | + | 0.771474i | \(0.719520\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.3893 | 0.741151 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.48398 | −0.337747 | −0.168874 | − | 0.985638i | \(-0.554013\pi\) | ||||
−0.168874 | + | 0.985638i | \(0.554013\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.1109 | −0.455373 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 32.9176 | 1.47954 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.1202 | 0.902514 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.7183 | 0.972246 | 0.486123 | − | 0.873890i | \(-0.338411\pi\) | ||||
0.486123 | + | 0.873890i | \(0.338411\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.6330 | −1.10052 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.27541 | −0.324395 | −0.162197 | − | 0.986758i | \(-0.551858\pi\) | ||||
−0.162197 | + | 0.986758i | \(0.551858\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.43991 | 0.108574 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.71833 | −0.120725 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.7151 | 1.00683 | 0.503414 | − | 0.864045i | \(-0.332077\pi\) | ||||
0.503414 | + | 0.864045i | \(0.332077\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.6074 | 1.22128 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −80.1835 | −3.54019 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.88283 | 0.347359 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.3606 | 1.55516 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.4429 | −1.24851 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.5568 | −0.725368 | −0.362684 | − | 0.931912i | \(-0.618140\pi\) | ||||
−0.362684 | + | 0.931912i | \(0.618140\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.8037 | 1.08459 | 0.542295 | − | 0.840188i | \(-0.317555\pi\) | ||||
0.542295 | + | 0.840188i | \(0.317555\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.40185 | −0.279400 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.512767 | 0.0223365 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −74.9206 | −3.25128 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.67425 | 0.0725200 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.6803 | −0.721151 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.12018 | 0.393565 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.5981 | −0.585714 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.8292 | −0.938512 | −0.469256 | − | 0.883062i | \(-0.655478\pi\) | ||||
−0.469256 | + | 0.883062i | \(0.655478\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 33.3638 | 1.43178 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.32274 | 0.228001 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.0759 | −1.24319 | −0.621597 | − | 0.783337i | \(-0.713516\pi\) | ||||
−0.621597 | + | 0.783337i | \(0.713516\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 51.0884 | 2.18040 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.6710 | 0.497202 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.6074 | 1.08894 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −29.9239 | −1.27020 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.0348 | −0.933645 | −0.466822 | − | 0.884351i | \(-0.654601\pi\) | ||||
−0.466822 | + | 0.884351i | \(0.654601\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.8478 | −1.17784 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 101.357 | 4.27931 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.40185 | 0.0590811 | 0.0295406 | − | 0.999564i | \(-0.490596\pi\) | ||||
0.0295406 | + | 0.999564i | \(0.490596\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.20556 | −0.0927887 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −28.1930 | −1.18400 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.00000 | 0.251533 | 0.125767 | − | 0.992060i | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.3575 | −0.768239 | −0.384120 | − | 0.923283i | \(-0.625495\pi\) | ||||
−0.384120 | + | 0.923283i | \(0.625495\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.9114 | 0.998912 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.5128 | −0.479283 | −0.239641 | − | 0.970861i | \(-0.577030\pi\) | ||||
−0.239641 | + | 0.970861i | \(0.577030\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.64547 | −0.276176 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.56009 | 0.396619 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 59.5188 | 2.46502 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22.5601 | −0.932745 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 40.1232 | 1.65606 | 0.828031 | − | 0.560683i | \(-0.189461\pi\) | ||||
0.828031 | + | 0.560683i | \(0.189461\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.591886 | −0.0243882 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 37.0759 | 1.52510 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.7912 | 0.771662 | 0.385831 | − | 0.922570i | \(-0.373915\pi\) | ||||
0.385831 | + | 0.922570i | \(0.373915\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.4747 | −0.552409 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −43.1077 | −1.76428 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.4777 | −1.12271 | −0.561355 | − | 0.827575i | \(-0.689720\pi\) | ||||
−0.561355 | + | 0.827575i | \(0.689720\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.5283 | −0.796576 | −0.398288 | − | 0.917260i | \(-0.630396\pi\) | ||||
−0.398288 | + | 0.917260i | \(0.630396\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −62.9842 | −2.56492 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.7974 | 0.601602 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 45.9239 | 1.86399 | 0.931997 | − | 0.362467i | \(-0.118065\pi\) | ||||
0.931997 | + | 0.362467i | \(0.118065\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.98748 | 0.404713 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.2343 | −0.980417 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.7091 | 0.513314 | 0.256657 | − | 0.966503i | \(-0.417379\pi\) | ||||
0.256657 | + | 0.966503i | \(0.417379\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.48097 | −0.0597186 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 48.3102 | 1.94490 | 0.972448 | − | 0.233120i | \(-0.0748934\pi\) | ||||
0.972448 | + | 0.233120i | \(0.0748934\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.677265 | 0.0272216 | 0.0136108 | − | 0.999907i | \(-0.495667\pi\) | ||||
0.0136108 | + | 0.999907i | \(0.495667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.7183 | 0.430112 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.2909 | −0.692747 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −116.997 | −4.67239 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −62.9842 | −2.51135 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.3986 | 1.76748 | 0.883740 | − | 0.467978i | \(-0.155017\pi\) | ||||
0.883740 | + | 0.467978i | \(0.155017\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.4747 | 0.416332 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.15824 | 0.244382 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.31949 | 0.369251 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −62.7181 | −2.48109 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.8798 | 0.666713 | 0.333356 | − | 0.942801i | \(-0.391819\pi\) | ||||
0.333356 | + | 0.942801i | \(0.391819\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.7564 | −1.05517 | −0.527584 | − | 0.849503i | \(-0.676902\pi\) | ||||
−0.527584 | + | 0.849503i | \(0.676902\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.6330 | 0.969921 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.5568 | 1.27994 | 0.639971 | − | 0.768399i | \(-0.278946\pi\) | ||||
0.639971 | + | 0.768399i | \(0.278946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −58.7151 | −2.30477 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.506507 | −0.0198516 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.87356 | −0.386382 | −0.193191 | − | 0.981161i | \(-0.561884\pi\) | ||||
−0.193191 | + | 0.981161i | \(0.561884\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.19629 | −0.281182 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −86.0571 | −3.35741 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.5128 | −0.526383 | −0.263191 | − | 0.964744i | \(-0.584775\pi\) | ||||
−0.263191 | + | 0.964744i | \(0.584775\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.7687 | −1.04118 | −0.520590 | − | 0.853807i | \(-0.674288\pi\) | ||||
−0.520590 | + | 0.853807i | \(0.674288\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −69.4652 | −2.69780 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.5538 | 0.603152 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.56009 | −0.0604070 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.0000 | 0.618596 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 40.0378 | 1.54564 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.803708 | −0.0309807 | −0.0154903 | − | 0.999880i | \(-0.504931\pi\) | ||||
−0.0154903 | + | 0.999880i | \(0.504931\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.7183 | 0.412549 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.6422 | −1.29298 | −0.646488 | − | 0.762924i | \(-0.723763\pi\) | ||||
−0.646488 | + | 0.762924i | \(0.723763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.0473 | −0.577463 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.4872 | 0.631792 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.8736 | −0.454329 | −0.227165 | − | 0.973856i | \(-0.572946\pi\) | ||||
−0.227165 | + | 0.973856i | \(0.572946\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.6012 | 0.481465 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.47471 | −0.0944162 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −40.7912 | −1.55402 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.9114 | 1.06180 | 0.530899 | − | 0.847435i | \(-0.321854\pi\) | ||||
0.530899 | + | 0.847435i | \(0.321854\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −68.4397 | −2.59981 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.75638 | −0.332149 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.11717 | −0.118071 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 43.5949 | 1.64891 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.3668 | −0.995861 | −0.497930 | − | 0.867217i | \(-0.665906\pi\) | ||||
−0.497930 | + | 0.867217i | \(0.665906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 72.7026 | 2.74203 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 21.4367 | 0.807351 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.07286 | −0.190785 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.8007 | 0.443184 | 0.221592 | − | 0.975139i | \(-0.428875\pi\) | ||||
0.221592 | + | 0.975139i | \(0.428875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −79.8227 | −2.99359 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.0791189 | 0.00296302 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.6803 | −0.661205 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 33.6074 | 1.25509 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.9589 | −0.483287 | −0.241643 | − | 0.970365i | \(-0.577686\pi\) | ||||
−0.241643 | + | 0.970365i | \(0.577686\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.3893 | −0.610371 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −84.4807 | −3.14187 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.56009 | −0.0579404 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.0318 | −0.705850 | −0.352925 | − | 0.935652i | \(-0.614813\pi\) | ||||
−0.352925 | + | 0.935652i | \(0.614813\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.1264 | −0.412090 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 51.8478 | 1.91766 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.5220 | −1.12736 | −0.563679 | − | 0.825994i | \(-0.690614\pi\) | ||||
−0.563679 | + | 0.825994i | \(0.690614\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.24362 | −0.304070 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −49.3606 | −1.81822 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.18702 | −0.227593 | −0.113797 | − | 0.993504i | \(-0.536301\pi\) | ||||
−0.113797 | + | 0.993504i | \(0.536301\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 80.1835 | 2.94562 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.2722 | 0.596968 | 0.298484 | − | 0.954415i | \(-0.403519\pi\) | ||||
0.298484 | + | 0.954415i | \(0.403519\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.79745 | 0.0658534 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −29.8005 | −1.09034 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 34.6803 | 1.26719 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.5949 | −0.642047 | −0.321023 | − | 0.947071i | \(-0.604027\pi\) | ||||
−0.321023 | + | 0.947071i | \(0.604027\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −50.8640 | −1.85359 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.3956 | −0.705878 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.2496 | 1.49924 | 0.749622 | − | 0.661866i | \(-0.230235\pi\) | ||||
0.749622 | + | 0.661866i | \(0.230235\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.6392 | 0.567667 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.8067 | 0.971743 | 0.485871 | − | 0.874030i | \(-0.338502\pi\) | ||||
0.485871 | + | 0.874030i | \(0.338502\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.0666 | −0.400638 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 42.0030 | 1.51862 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40.2404 | 1.45300 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.8798 | −0.969311 | −0.484655 | − | 0.874705i | \(-0.661055\pi\) | ||||
−0.484655 | + | 0.874705i | \(0.661055\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60.8608 | 2.19185 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.0441 | 1.47625 | 0.738126 | − | 0.674662i | \(-0.235711\pi\) | ||||
0.738126 | + | 0.674662i | \(0.235711\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0791189 | 0.00284203 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 62.2153 | 2.23196 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.59815 | 0.128917 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −49.1520 | −1.75880 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.7216 | −0.597580 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.36380 | 0.155751 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.4840 | −0.765821 | −0.382911 | − | 0.923785i | \(-0.625078\pi\) | ||||
−0.382911 | + | 0.923785i | \(0.625078\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.9176 | 0.815889 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.58563 | 0.163046 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.4399 | −0.974420 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 36.0821 | 1.27970 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.2692 | 1.35556 | 0.677781 | − | 0.735263i | \(-0.262942\pi\) | ||||
0.677781 | + | 0.735263i | \(0.262942\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.1202 | 1.59624 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 53.8989 | 1.90442 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −67.4427 | −2.38000 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.07912 | −0.0732793 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −70.0696 | −2.46657 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.2026 | −0.956391 | −0.478195 | − | 0.878253i | \(-0.658709\pi\) | ||||
−0.478195 | + | 0.878253i | \(0.658709\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.5095 | 1.35225 | 0.676126 | − | 0.736786i | \(-0.263657\pi\) | ||||
0.676126 | + | 0.736786i | \(0.263657\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −58.6297 | −2.05623 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.32274 | 0.186447 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −59.8478 | −2.09381 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 46.9051 | 1.63900 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.0000 | 0.349002 | 0.174501 | − | 0.984657i | \(-0.444169\pi\) | ||||
0.174501 | + | 0.984657i | \(0.444169\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.1457 | 1.39939 | 0.699696 | − | 0.714441i | \(-0.253319\pi\) | ||||
0.699696 | + | 0.714441i | \(0.253319\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.6392 | 0.544487 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.851033 | 0.0295933 | 0.0147967 | − | 0.999891i | \(-0.495290\pi\) | ||||
0.0147967 | + | 0.999891i | \(0.495290\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.83851 | −0.0985856 | −0.0492928 | − | 0.998784i | \(-0.515697\pi\) | ||||
−0.0492928 | + | 0.998784i | \(0.515697\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −56.3986 | −1.95645 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.3513 | −0.601186 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.00000 | −0.276851 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.848022 | 0.0293119 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.2343 | −0.353329 | −0.176664 | − | 0.984271i | \(-0.556531\pi\) | ||||
−0.176664 | + | 0.984271i | \(0.556531\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.5661 | −0.916073 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 80.3100 | 2.76602 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.882827 | −0.0303702 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.7657 | −1.05712 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −78.9554 | −2.70974 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.71833 | −0.333140 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.7213 | 0.606767 | 0.303384 | − | 0.952869i | \(-0.401884\pi\) | ||||
0.303384 | + | 0.952869i | \(0.401884\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −48.4840 | −1.65812 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.6835 | 0.604058 | 0.302029 | − | 0.953299i | \(-0.402336\pi\) | ||||
0.302029 | + | 0.953299i | \(0.402336\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.6042 | −0.907722 | −0.453861 | − | 0.891072i | \(-0.649954\pi\) | ||||
−0.453861 | + | 0.891072i | \(0.649954\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.07912 | 0.104936 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −53.5949 | −1.82439 | −0.912196 | − | 0.409755i | \(-0.865614\pi\) | ||||
−0.912196 | + | 0.409755i | \(0.865614\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.23736 | −0.314080 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 76.9872 | 2.61462 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −62.5568 | −2.12210 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.8292 | 1.14626 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.9051 | 1.58750 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.07912 | −0.0702870 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.9650 | 0.876774 | 0.438387 | − | 0.898786i | \(-0.355550\pi\) | ||||
0.438387 | + | 0.898786i | \(0.355550\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 94.9554 | 3.20277 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.9239 | 1.00816 | 0.504081 | − | 0.863657i | \(-0.331831\pi\) | ||||
0.504081 | + | 0.863657i | \(0.331831\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.75939 | −0.160166 | −0.0800832 | − | 0.996788i | \(-0.525519\pi\) | ||||
−0.0800832 | + | 0.996788i | \(0.525519\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −35.5949 | −1.19651 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38.8037 | 1.30290 | 0.651451 | − | 0.758691i | \(-0.274161\pi\) | ||||
0.651451 | + | 0.758691i | \(0.274161\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.8037 | −0.429423 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 68.8733 | 2.30734 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −52.0821 | −1.74286 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.96195 | 0.0990069 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.7183 | −0.357875 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.123433 | −0.00411671 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 75.9462 | 2.53013 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −51.2148 | −1.70432 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.8355 | 0.360184 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −51.0729 | −1.69585 | −0.847923 | − | 0.530119i | \(-0.822147\pi\) | ||||
−0.847923 | + | 0.530119i | \(0.822147\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.8130 | 0.524483 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.4933 | −1.01029 | −0.505143 | − | 0.863035i | \(-0.668560\pi\) | ||||
−0.505143 | + | 0.863035i | \(0.668560\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.3545 | −0.772922 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.2722 | 0.802413 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.9619 | 0.494087 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.00000 | 0.263896 | 0.131948 | − | 0.991257i | \(-0.457877\pi\) | ||||
0.131948 | + | 0.991257i | \(0.457877\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.79745 | −0.191032 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 33.6863 | 1.10880 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.71833 | −0.319537 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 51.0884 | 1.67796 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.3257 | −0.568439 | −0.284220 | − | 0.958759i | \(-0.591734\pi\) | ||||
−0.284220 | + | 0.958759i | \(0.591734\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.0285 | 0.656409 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.94943 | 0.162037 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 32.9176 | 1.07652 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.5631 | −1.55382 | −0.776909 | − | 0.629612i | \(-0.783214\pi\) | ||||
−0.776909 | + | 0.629612i | \(0.783214\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.19304 | −0.169469 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.2754 | 0.465365 | 0.232683 | − | 0.972553i | \(-0.425250\pi\) | ||||
0.232683 | + | 0.972553i | \(0.425250\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.480973 | −0.0156626 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −22.2847 | −0.724921 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.1900 | 1.17602 | 0.588009 | − | 0.808854i | \(-0.299912\pi\) | ||||
0.588009 | + | 0.808854i | \(0.299912\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 46.2218 | 1.50042 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −39.0348 | −1.26579 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.7942 | 1.22427 | 0.612137 | − | 0.790752i | \(-0.290310\pi\) | ||||
0.612137 | + | 0.790752i | \(0.290310\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.76565 | 0.251291 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −24.3986 | −0.788695 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.1993 | −0.846020 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9937 | −0.999798 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −108.104 | −3.48362 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.15824 | −0.0694761 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.6390 | 1.62844 | 0.814220 | − | 0.580557i | \(-0.197165\pi\) | ||||
0.814220 | + | 0.580557i | \(0.197165\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −149.288 | −4.79582 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.82623 | 0.0906981 | 0.0453490 | − | 0.998971i | \(-0.485560\pi\) | ||||
0.0453490 | + | 0.998971i | \(0.485560\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.2056 | 0.583644 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.7183 | −0.343261 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.8448 | 0.826848 | 0.413424 | − | 0.910539i | \(-0.364333\pi\) | ||||
0.413424 | + | 0.910539i | \(0.364333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 42.2404 | 1.35001 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 34.4965 | 1.10139 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.3668 | −1.31940 | −0.659698 | − | 0.751531i | \(-0.729316\pi\) | ||||
−0.659698 | + | 0.751531i | \(0.729316\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0411 | 0.383660 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −44.5694 | −1.41866 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.00000 | 0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.4745 | 1.73044 | 0.865219 | − | 0.501394i | \(-0.167179\pi\) | ||||
0.865219 | + | 0.501394i | \(0.167179\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 102.810 | 3.26257 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.0000 | −0.443830 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.5128 | −0.491294 | −0.245647 | − | 0.969359i | \(-0.579000\pi\) | ||||
−0.245647 | + | 0.969359i | \(0.579000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −104.164 | −3.29561 |
(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 | 920.2.a.h.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 8280.2.a.bj.1.1 | 3 | |||
4.3 | odd | 2 | 1840.2.a.s.1.1 | 3 | |||
5.2 | odd | 4 | 4600.2.e.p.4049.1 | 6 | |||
5.3 | odd | 4 | 4600.2.e.p.4049.6 | 6 | |||
5.4 | even | 2 | 4600.2.a.x.1.1 | 3 | |||
8.3 | odd | 2 | 7360.2.a.cc.1.3 | 3 | |||
8.5 | even | 2 | 7360.2.a.by.1.1 | 3 | |||
20.19 | odd | 2 | 9200.2.a.ce.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.h.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1840.2.a.s.1.1 | 3 | 4.3 | odd | 2 | |||
4600.2.a.x.1.1 | 3 | 5.4 | even | 2 | |||
4600.2.e.p.4049.1 | 6 | 5.2 | odd | 4 | |||
4600.2.e.p.4049.6 | 6 | 5.3 | odd | 4 | |||
7360.2.a.by.1.1 | 3 | 8.5 | even | 2 | |||
7360.2.a.cc.1.3 | 3 | 8.3 | odd | 2 | |||
8280.2.a.bj.1.1 | 3 | 3.2 | odd | 2 | |||
9200.2.a.ce.1.3 | 3 | 20.19 | odd | 2 |