Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.745749504.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 18x^{4} - 4x^{3} + 81x^{2} + 36x - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.23874\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 | ||||||||
\(3\) | 2.23874 | 1.29254 | 0.646268 | − | 0.763111i | \(-0.276329\pi\) | ||||
0.646268 | + | 0.763111i | \(0.276329\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.23874 | 0.913961 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.01195 | 0.670649 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.23874 | 0.646268 | ||||||||
\(13\) | 5.12829 | 1.42233 | 0.711167 | − | 0.703024i | \(-0.248167\pi\) | ||||
0.711167 | + | 0.703024i | \(0.248167\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −2.23874 | −0.578040 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.65568 | −1.61424 | −0.807119 | − | 0.590388i | \(-0.798975\pi\) | ||||
−0.807119 | + | 0.590388i | \(0.798975\pi\) | |||||||
\(18\) | 2.01195 | 0.474221 | ||||||||
\(19\) | −1.15751 | −0.265550 | −0.132775 | − | 0.991146i | \(-0.542389\pi\) | ||||
−0.132775 | + | 0.991146i | \(0.542389\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −2.23874 | −0.488533 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.87761 | 0.808537 | 0.404269 | − | 0.914640i | \(-0.367526\pi\) | ||||
0.404269 | + | 0.914640i | \(0.367526\pi\) | |||||||
\(24\) | 2.23874 | 0.456981 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.12829 | 1.00574 | ||||||||
\(27\) | −2.21199 | −0.425697 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 5.89442 | 1.09457 | 0.547283 | − | 0.836948i | \(-0.315662\pi\) | ||||
0.547283 | + | 0.836948i | \(0.315662\pi\) | |||||||
\(30\) | −2.23874 | −0.408736 | ||||||||
\(31\) | −6.64373 | −1.19325 | −0.596624 | − | 0.802521i | \(-0.703492\pi\) | ||||
−0.596624 | + | 0.802521i | \(0.703492\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.65568 | −1.14144 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 2.01195 | 0.335325 | ||||||||
\(37\) | 11.8944 | 1.95543 | 0.977715 | − | 0.209937i | \(-0.0673259\pi\) | ||||
0.977715 | + | 0.209937i | \(0.0673259\pi\) | |||||||
\(38\) | −1.15751 | −0.187772 | ||||||||
\(39\) | 11.4809 | 1.83842 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 10.4700 | 1.63514 | 0.817570 | − | 0.575829i | \(-0.195321\pi\) | ||||
0.817570 | + | 0.575829i | \(0.195321\pi\) | |||||||
\(42\) | −2.23874 | −0.345445 | ||||||||
\(43\) | 1.77464 | 0.270630 | 0.135315 | − | 0.990803i | \(-0.456795\pi\) | ||||
0.135315 | + | 0.990803i | \(0.456795\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.01195 | −0.299924 | ||||||||
\(46\) | 3.87761 | 0.571722 | ||||||||
\(47\) | 8.71479 | 1.27118 | 0.635591 | − | 0.772026i | \(-0.280756\pi\) | ||||
0.635591 | + | 0.772026i | \(0.280756\pi\) | |||||||
\(48\) | 2.23874 | 0.323134 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −14.9003 | −2.08646 | ||||||||
\(52\) | 5.12829 | 0.711167 | ||||||||
\(53\) | 8.28476 | 1.13800 | 0.568999 | − | 0.822338i | \(-0.307331\pi\) | ||||
0.568999 | + | 0.822338i | \(0.307331\pi\) | |||||||
\(54\) | −2.21199 | −0.301014 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −2.59135 | −0.343233 | ||||||||
\(58\) | 5.89442 | 0.773975 | ||||||||
\(59\) | −10.2614 | −1.33593 | −0.667963 | − | 0.744194i | \(-0.732834\pi\) | ||||
−0.667963 | + | 0.744194i | \(0.732834\pi\) | |||||||
\(60\) | −2.23874 | −0.289020 | ||||||||
\(61\) | −12.8132 | −1.64056 | −0.820280 | − | 0.571962i | \(-0.806182\pi\) | ||||
−0.820280 | + | 0.571962i | \(0.806182\pi\) | |||||||
\(62\) | −6.64373 | −0.843754 | ||||||||
\(63\) | −2.01195 | −0.253482 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.12829 | −0.636087 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.9682 | 1.82865 | 0.914327 | − | 0.404977i | \(-0.132720\pi\) | ||||
0.914327 | + | 0.404977i | \(0.132720\pi\) | |||||||
\(68\) | −6.65568 | −0.807119 | ||||||||
\(69\) | 8.68095 | 1.04506 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 7.76716 | 0.921793 | 0.460896 | − | 0.887454i | \(-0.347528\pi\) | ||||
0.460896 | + | 0.887454i | \(0.347528\pi\) | |||||||
\(72\) | 2.01195 | 0.237110 | ||||||||
\(73\) | −2.54037 | −0.297328 | −0.148664 | − | 0.988888i | \(-0.547497\pi\) | ||||
−0.148664 | + | 0.988888i | \(0.547497\pi\) | |||||||
\(74\) | 11.8944 | 1.38270 | ||||||||
\(75\) | 2.23874 | 0.258507 | ||||||||
\(76\) | −1.15751 | −0.132775 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 11.4809 | 1.29996 | ||||||||
\(79\) | 10.2605 | 1.15439 | 0.577197 | − | 0.816605i | \(-0.304146\pi\) | ||||
0.577197 | + | 0.816605i | \(0.304146\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −10.9879 | −1.22088 | ||||||||
\(82\) | 10.4700 | 1.15622 | ||||||||
\(83\) | −6.86423 | −0.753448 | −0.376724 | − | 0.926326i | \(-0.622949\pi\) | ||||
−0.376724 | + | 0.926326i | \(0.622949\pi\) | |||||||
\(84\) | −2.23874 | −0.244266 | ||||||||
\(85\) | 6.65568 | 0.721910 | ||||||||
\(86\) | 1.77464 | 0.191364 | ||||||||
\(87\) | 13.1961 | 1.41477 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.1923 | 1.61038 | 0.805188 | − | 0.593019i | \(-0.202064\pi\) | ||||
0.805188 | + | 0.593019i | \(0.202064\pi\) | |||||||
\(90\) | −2.01195 | −0.212078 | ||||||||
\(91\) | −5.12829 | −0.537591 | ||||||||
\(92\) | 3.87761 | 0.404269 | ||||||||
\(93\) | −14.8736 | −1.54232 | ||||||||
\(94\) | 8.71479 | 0.898862 | ||||||||
\(95\) | 1.15751 | 0.118758 | ||||||||
\(96\) | 2.23874 | 0.228490 | ||||||||
\(97\) | −0.406766 | −0.0413008 | −0.0206504 | − | 0.999787i | \(-0.506574\pi\) | ||||
−0.0206504 | + | 0.999787i | \(0.506574\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 0.964155 | 0.0959370 | 0.0479685 | − | 0.998849i | \(-0.484725\pi\) | ||||
0.0479685 | + | 0.998849i | \(0.484725\pi\) | |||||||
\(102\) | −14.9003 | −1.47535 | ||||||||
\(103\) | 12.4021 | 1.22202 | 0.611010 | − | 0.791623i | \(-0.290764\pi\) | ||||
0.611010 | + | 0.791623i | \(0.290764\pi\) | |||||||
\(104\) | 5.12829 | 0.502871 | ||||||||
\(105\) | 2.23874 | 0.218478 | ||||||||
\(106\) | 8.28476 | 0.804687 | ||||||||
\(107\) | 11.3466 | 1.09691 | 0.548457 | − | 0.836179i | \(-0.315215\pi\) | ||||
0.548457 | + | 0.836179i | \(0.315215\pi\) | |||||||
\(108\) | −2.21199 | −0.212849 | ||||||||
\(109\) | −9.81672 | −0.940271 | −0.470135 | − | 0.882594i | \(-0.655795\pi\) | ||||
−0.470135 | + | 0.882594i | \(0.655795\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 26.6285 | 2.52746 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −15.4263 | −1.45118 | −0.725591 | − | 0.688126i | \(-0.758433\pi\) | ||||
−0.725591 | + | 0.688126i | \(0.758433\pi\) | |||||||
\(114\) | −2.59135 | −0.242702 | ||||||||
\(115\) | −3.87761 | −0.361589 | ||||||||
\(116\) | 5.89442 | 0.547283 | ||||||||
\(117\) | 10.3179 | 0.953887 | ||||||||
\(118\) | −10.2614 | −0.944643 | ||||||||
\(119\) | 6.65568 | 0.610125 | ||||||||
\(120\) | −2.23874 | −0.204368 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −12.8132 | −1.16005 | ||||||||
\(123\) | 23.4396 | 2.11348 | ||||||||
\(124\) | −6.64373 | −0.596624 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.01195 | −0.179239 | ||||||||
\(127\) | 15.5058 | 1.37592 | 0.687961 | − | 0.725748i | \(-0.258506\pi\) | ||||
0.687961 | + | 0.725748i | \(0.258506\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.97295 | 0.349798 | ||||||||
\(130\) | −5.12829 | −0.449781 | ||||||||
\(131\) | −16.5157 | −1.44299 | −0.721493 | − | 0.692421i | \(-0.756544\pi\) | ||||
−0.721493 | + | 0.692421i | \(0.756544\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.15751 | 0.100368 | ||||||||
\(134\) | 14.9682 | 1.29305 | ||||||||
\(135\) | 2.21199 | 0.190378 | ||||||||
\(136\) | −6.65568 | −0.570720 | ||||||||
\(137\) | 13.8267 | 1.18129 | 0.590646 | − | 0.806931i | \(-0.298873\pi\) | ||||
0.590646 | + | 0.806931i | \(0.298873\pi\) | |||||||
\(138\) | 8.68095 | 0.738971 | ||||||||
\(139\) | 1.19890 | 0.101689 | 0.0508445 | − | 0.998707i | \(-0.483809\pi\) | ||||
0.0508445 | + | 0.998707i | \(0.483809\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 19.5101 | 1.64305 | ||||||||
\(142\) | 7.76716 | 0.651806 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.01195 | 0.167662 | ||||||||
\(145\) | −5.89442 | −0.489505 | ||||||||
\(146\) | −2.54037 | −0.210243 | ||||||||
\(147\) | 2.23874 | 0.184648 | ||||||||
\(148\) | 11.8944 | 0.977715 | ||||||||
\(149\) | −5.37555 | −0.440382 | −0.220191 | − | 0.975457i | \(-0.570668\pi\) | ||||
−0.220191 | + | 0.975457i | \(0.570668\pi\) | |||||||
\(150\) | 2.23874 | 0.182792 | ||||||||
\(151\) | 1.95930 | 0.159445 | 0.0797226 | − | 0.996817i | \(-0.474597\pi\) | ||||
0.0797226 | + | 0.996817i | \(0.474597\pi\) | |||||||
\(152\) | −1.15751 | −0.0938861 | ||||||||
\(153\) | −13.3909 | −1.08259 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.64373 | 0.533637 | ||||||||
\(156\) | 11.4809 | 0.919208 | ||||||||
\(157\) | 13.1054 | 1.04593 | 0.522964 | − | 0.852355i | \(-0.324826\pi\) | ||||
0.522964 | + | 0.852355i | \(0.324826\pi\) | |||||||
\(158\) | 10.2605 | 0.816280 | ||||||||
\(159\) | 18.5474 | 1.47090 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −3.87761 | −0.305598 | ||||||||
\(162\) | −10.9879 | −0.863292 | ||||||||
\(163\) | −21.5818 | −1.69041 | −0.845207 | − | 0.534438i | \(-0.820523\pi\) | ||||
−0.845207 | + | 0.534438i | \(0.820523\pi\) | |||||||
\(164\) | 10.4700 | 0.817570 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.86423 | −0.532768 | ||||||||
\(167\) | 0.900461 | 0.0696797 | 0.0348399 | − | 0.999393i | \(-0.488908\pi\) | ||||
0.0348399 | + | 0.999393i | \(0.488908\pi\) | |||||||
\(168\) | −2.23874 | −0.172722 | ||||||||
\(169\) | 13.2994 | 1.02303 | ||||||||
\(170\) | 6.65568 | 0.510467 | ||||||||
\(171\) | −2.32884 | −0.178091 | ||||||||
\(172\) | 1.77464 | 0.135315 | ||||||||
\(173\) | −14.9963 | −1.14015 | −0.570075 | − | 0.821592i | \(-0.693086\pi\) | ||||
−0.570075 | + | 0.821592i | \(0.693086\pi\) | |||||||
\(174\) | 13.1961 | 1.00039 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −22.9727 | −1.72673 | ||||||||
\(178\) | 15.1923 | 1.13871 | ||||||||
\(179\) | 10.7148 | 0.800861 | 0.400430 | − | 0.916327i | \(-0.368861\pi\) | ||||
0.400430 | + | 0.916327i | \(0.368861\pi\) | |||||||
\(180\) | −2.01195 | −0.149962 | ||||||||
\(181\) | −6.20078 | −0.460900 | −0.230450 | − | 0.973084i | \(-0.574020\pi\) | ||||
−0.230450 | + | 0.973084i | \(0.574020\pi\) | |||||||
\(182\) | −5.12829 | −0.380134 | ||||||||
\(183\) | −28.6854 | −2.12048 | ||||||||
\(184\) | 3.87761 | 0.285861 | ||||||||
\(185\) | −11.8944 | −0.874495 | ||||||||
\(186\) | −14.8736 | −1.09058 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.71479 | 0.635591 | ||||||||
\(189\) | 2.21199 | 0.160899 | ||||||||
\(190\) | 1.15751 | 0.0839743 | ||||||||
\(191\) | −0.133153 | −0.00963464 | −0.00481732 | − | 0.999988i | \(-0.501533\pi\) | ||||
−0.00481732 | + | 0.999988i | \(0.501533\pi\) | |||||||
\(192\) | 2.23874 | 0.161567 | ||||||||
\(193\) | −12.7468 | −0.917531 | −0.458766 | − | 0.888557i | \(-0.651708\pi\) | ||||
−0.458766 | + | 0.888557i | \(0.651708\pi\) | |||||||
\(194\) | −0.406766 | −0.0292041 | ||||||||
\(195\) | −11.4809 | −0.822165 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 4.39162 | 0.312890 | 0.156445 | − | 0.987687i | \(-0.449997\pi\) | ||||
0.156445 | + | 0.987687i | \(0.449997\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.430314 | −0.0305041 | −0.0152521 | − | 0.999884i | \(-0.504855\pi\) | ||||
−0.0152521 | + | 0.999884i | \(0.504855\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 33.5098 | 2.36360 | ||||||||
\(202\) | 0.964155 | 0.0678377 | ||||||||
\(203\) | −5.89442 | −0.413707 | ||||||||
\(204\) | −14.9003 | −1.04323 | ||||||||
\(205\) | −10.4700 | −0.731257 | ||||||||
\(206\) | 12.4021 | 0.864098 | ||||||||
\(207\) | 7.80155 | 0.542245 | ||||||||
\(208\) | 5.12829 | 0.355583 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.23874 | 0.154488 | ||||||||
\(211\) | −8.33737 | −0.573968 | −0.286984 | − | 0.957935i | \(-0.592653\pi\) | ||||
−0.286984 | + | 0.957935i | \(0.592653\pi\) | |||||||
\(212\) | 8.28476 | 0.568999 | ||||||||
\(213\) | 17.3886 | 1.19145 | ||||||||
\(214\) | 11.3466 | 0.775635 | ||||||||
\(215\) | −1.77464 | −0.121029 | ||||||||
\(216\) | −2.21199 | −0.150507 | ||||||||
\(217\) | 6.64373 | 0.451006 | ||||||||
\(218\) | −9.81672 | −0.664872 | ||||||||
\(219\) | −5.68723 | −0.384308 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −34.1323 | −2.29599 | ||||||||
\(222\) | 26.6285 | 1.78719 | ||||||||
\(223\) | 1.13218 | 0.0758166 | 0.0379083 | − | 0.999281i | \(-0.487931\pi\) | ||||
0.0379083 | + | 0.999281i | \(0.487931\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 2.01195 | 0.134130 | ||||||||
\(226\) | −15.4263 | −1.02614 | ||||||||
\(227\) | −10.2741 | −0.681915 | −0.340957 | − | 0.940079i | \(-0.610751\pi\) | ||||
−0.340957 | + | 0.940079i | \(0.610751\pi\) | |||||||
\(228\) | −2.59135 | −0.171616 | ||||||||
\(229\) | −9.23127 | −0.610019 | −0.305010 | − | 0.952349i | \(-0.598660\pi\) | ||||
−0.305010 | + | 0.952349i | \(0.598660\pi\) | |||||||
\(230\) | −3.87761 | −0.255682 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.89442 | 0.386987 | ||||||||
\(233\) | −6.68548 | −0.437980 | −0.218990 | − | 0.975727i | \(-0.570276\pi\) | ||||
−0.218990 | + | 0.975727i | \(0.570276\pi\) | |||||||
\(234\) | 10.3179 | 0.674500 | ||||||||
\(235\) | −8.71479 | −0.568490 | ||||||||
\(236\) | −10.2614 | −0.667963 | ||||||||
\(237\) | 22.9705 | 1.49210 | ||||||||
\(238\) | 6.65568 | 0.431423 | ||||||||
\(239\) | −22.4534 | −1.45239 | −0.726193 | − | 0.687490i | \(-0.758712\pi\) | ||||
−0.726193 | + | 0.687490i | \(0.758712\pi\) | |||||||
\(240\) | −2.23874 | −0.144510 | ||||||||
\(241\) | −28.6046 | −1.84258 | −0.921292 | − | 0.388872i | \(-0.872865\pi\) | ||||
−0.921292 | + | 0.388872i | \(0.872865\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −17.9631 | −1.15233 | ||||||||
\(244\) | −12.8132 | −0.820280 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 23.4396 | 1.49445 | ||||||||
\(247\) | −5.93603 | −0.377701 | ||||||||
\(248\) | −6.64373 | −0.421877 | ||||||||
\(249\) | −15.3672 | −0.973858 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 25.4351 | 1.60545 | 0.802725 | − | 0.596349i | \(-0.203383\pi\) | ||||
0.802725 | + | 0.596349i | \(0.203383\pi\) | |||||||
\(252\) | −2.01195 | −0.126741 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 15.5058 | 0.972924 | ||||||||
\(255\) | 14.9003 | 0.933094 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −24.9567 | −1.55676 | −0.778379 | − | 0.627795i | \(-0.783958\pi\) | ||||
−0.778379 | + | 0.627795i | \(0.783958\pi\) | |||||||
\(258\) | 3.97295 | 0.247345 | ||||||||
\(259\) | −11.8944 | −0.739083 | ||||||||
\(260\) | −5.12829 | −0.318043 | ||||||||
\(261\) | 11.8593 | 0.734070 | ||||||||
\(262\) | −16.5157 | −1.02035 | ||||||||
\(263\) | −0.333627 | −0.0205723 | −0.0102862 | − | 0.999947i | \(-0.503274\pi\) | ||||
−0.0102862 | + | 0.999947i | \(0.503274\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.28476 | −0.508929 | ||||||||
\(266\) | 1.15751 | 0.0709712 | ||||||||
\(267\) | 34.0115 | 2.08147 | ||||||||
\(268\) | 14.9682 | 0.914327 | ||||||||
\(269\) | 1.82597 | 0.111331 | 0.0556656 | − | 0.998449i | \(-0.482272\pi\) | ||||
0.0556656 | + | 0.998449i | \(0.482272\pi\) | |||||||
\(270\) | 2.21199 | 0.134617 | ||||||||
\(271\) | 13.3284 | 0.809642 | 0.404821 | − | 0.914396i | \(-0.367334\pi\) | ||||
0.404821 | + | 0.914396i | \(0.367334\pi\) | |||||||
\(272\) | −6.65568 | −0.403560 | ||||||||
\(273\) | −11.4809 | −0.694856 | ||||||||
\(274\) | 13.8267 | 0.835299 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.68095 | 0.522532 | ||||||||
\(277\) | −15.4834 | −0.930306 | −0.465153 | − | 0.885230i | \(-0.654001\pi\) | ||||
−0.465153 | + | 0.885230i | \(0.654001\pi\) | |||||||
\(278\) | 1.19890 | 0.0719050 | ||||||||
\(279\) | −13.3668 | −0.800252 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 28.3105 | 1.68886 | 0.844432 | − | 0.535663i | \(-0.179938\pi\) | ||||
0.844432 | + | 0.535663i | \(0.179938\pi\) | |||||||
\(282\) | 19.5101 | 1.16181 | ||||||||
\(283\) | 13.5891 | 0.807791 | 0.403895 | − | 0.914805i | \(-0.367656\pi\) | ||||
0.403895 | + | 0.914805i | \(0.367656\pi\) | |||||||
\(284\) | 7.76716 | 0.460896 | ||||||||
\(285\) | 2.59135 | 0.153498 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.4700 | −0.618025 | ||||||||
\(288\) | 2.01195 | 0.118555 | ||||||||
\(289\) | 27.2980 | 1.60577 | ||||||||
\(290\) | −5.89442 | −0.346132 | ||||||||
\(291\) | −0.910642 | −0.0533828 | ||||||||
\(292\) | −2.54037 | −0.148664 | ||||||||
\(293\) | 1.83423 | 0.107157 | 0.0535785 | − | 0.998564i | \(-0.482937\pi\) | ||||
0.0535785 | + | 0.998564i | \(0.482937\pi\) | |||||||
\(294\) | 2.23874 | 0.130566 | ||||||||
\(295\) | 10.2614 | 0.597445 | ||||||||
\(296\) | 11.8944 | 0.691349 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.37555 | −0.311397 | ||||||||
\(299\) | 19.8855 | 1.15001 | ||||||||
\(300\) | 2.23874 | 0.129254 | ||||||||
\(301\) | −1.77464 | −0.102288 | ||||||||
\(302\) | 1.95930 | 0.112745 | ||||||||
\(303\) | 2.15849 | 0.124002 | ||||||||
\(304\) | −1.15751 | −0.0663875 | ||||||||
\(305\) | 12.8132 | 0.733681 | ||||||||
\(306\) | −13.3909 | −0.765506 | ||||||||
\(307\) | 8.45358 | 0.482471 | 0.241236 | − | 0.970467i | \(-0.422447\pi\) | ||||
0.241236 | + | 0.970467i | \(0.422447\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.7652 | 1.57950 | ||||||||
\(310\) | 6.64373 | 0.377338 | ||||||||
\(311\) | 16.9898 | 0.963402 | 0.481701 | − | 0.876336i | \(-0.340019\pi\) | ||||
0.481701 | + | 0.876336i | \(0.340019\pi\) | |||||||
\(312\) | 11.4809 | 0.649978 | ||||||||
\(313\) | 18.0862 | 1.02230 | 0.511148 | − | 0.859493i | \(-0.329221\pi\) | ||||
0.511148 | + | 0.859493i | \(0.329221\pi\) | |||||||
\(314\) | 13.1054 | 0.739583 | ||||||||
\(315\) | 2.01195 | 0.113360 | ||||||||
\(316\) | 10.2605 | 0.577197 | ||||||||
\(317\) | −0.393194 | −0.0220840 | −0.0110420 | − | 0.999939i | \(-0.503515\pi\) | ||||
−0.0110420 | + | 0.999939i | \(0.503515\pi\) | |||||||
\(318\) | 18.5474 | 1.04009 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 25.4020 | 1.41780 | ||||||||
\(322\) | −3.87761 | −0.216091 | ||||||||
\(323\) | 7.70398 | 0.428661 | ||||||||
\(324\) | −10.9879 | −0.610439 | ||||||||
\(325\) | 5.12829 | 0.284467 | ||||||||
\(326\) | −21.5818 | −1.19530 | ||||||||
\(327\) | −21.9771 | −1.21533 | ||||||||
\(328\) | 10.4700 | 0.578109 | ||||||||
\(329\) | −8.71479 | −0.480462 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.5395 | −1.89846 | −0.949232 | − | 0.314577i | \(-0.898137\pi\) | ||||
−0.949232 | + | 0.314577i | \(0.898137\pi\) | |||||||
\(332\) | −6.86423 | −0.376724 | ||||||||
\(333\) | 23.9309 | 1.31141 | ||||||||
\(334\) | 0.900461 | 0.0492710 | ||||||||
\(335\) | −14.9682 | −0.817799 | ||||||||
\(336\) | −2.23874 | −0.122133 | ||||||||
\(337\) | 2.36075 | 0.128598 | 0.0642991 | − | 0.997931i | \(-0.479519\pi\) | ||||
0.0642991 | + | 0.997931i | \(0.479519\pi\) | |||||||
\(338\) | 13.2994 | 0.723392 | ||||||||
\(339\) | −34.5354 | −1.87570 | ||||||||
\(340\) | 6.65568 | 0.360955 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −2.32884 | −0.125929 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 1.77464 | 0.0956820 | ||||||||
\(345\) | −8.68095 | −0.467367 | ||||||||
\(346\) | −14.9963 | −0.806208 | ||||||||
\(347\) | −6.85646 | −0.368074 | −0.184037 | − | 0.982919i | \(-0.558917\pi\) | ||||
−0.184037 | + | 0.982919i | \(0.558917\pi\) | |||||||
\(348\) | 13.1961 | 0.707383 | ||||||||
\(349\) | −8.34033 | −0.446448 | −0.223224 | − | 0.974767i | \(-0.571658\pi\) | ||||
−0.223224 | + | 0.974767i | \(0.571658\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −11.3437 | −0.605484 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.7691 | 1.05220 | 0.526101 | − | 0.850422i | \(-0.323653\pi\) | ||||
0.526101 | + | 0.850422i | \(0.323653\pi\) | |||||||
\(354\) | −22.9727 | −1.22098 | ||||||||
\(355\) | −7.76716 | −0.412238 | ||||||||
\(356\) | 15.1923 | 0.805188 | ||||||||
\(357\) | 14.9003 | 0.788608 | ||||||||
\(358\) | 10.7148 | 0.566294 | ||||||||
\(359\) | 0.257703 | 0.0136010 | 0.00680051 | − | 0.999977i | \(-0.497835\pi\) | ||||
0.00680051 | + | 0.999977i | \(0.497835\pi\) | |||||||
\(360\) | −2.01195 | −0.106039 | ||||||||
\(361\) | −17.6602 | −0.929483 | ||||||||
\(362\) | −6.20078 | −0.325906 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.12829 | −0.268796 | ||||||||
\(365\) | 2.54037 | 0.132969 | ||||||||
\(366\) | −28.6854 | −1.49941 | ||||||||
\(367\) | 25.6755 | 1.34025 | 0.670125 | − | 0.742248i | \(-0.266241\pi\) | ||||
0.670125 | + | 0.742248i | \(0.266241\pi\) | |||||||
\(368\) | 3.87761 | 0.202134 | ||||||||
\(369\) | 21.0651 | 1.09661 | ||||||||
\(370\) | −11.8944 | −0.618361 | ||||||||
\(371\) | −8.28476 | −0.430123 | ||||||||
\(372\) | −14.8736 | −0.771159 | ||||||||
\(373\) | −5.70957 | −0.295631 | −0.147815 | − | 0.989015i | \(-0.547224\pi\) | ||||
−0.147815 | + | 0.989015i | \(0.547224\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.23874 | −0.115608 | ||||||||
\(376\) | 8.71479 | 0.449431 | ||||||||
\(377\) | 30.2283 | 1.55684 | ||||||||
\(378\) | 2.21199 | 0.113772 | ||||||||
\(379\) | 2.16686 | 0.111304 | 0.0556520 | − | 0.998450i | \(-0.482276\pi\) | ||||
0.0556520 | + | 0.998450i | \(0.482276\pi\) | |||||||
\(380\) | 1.15751 | 0.0593788 | ||||||||
\(381\) | 34.7135 | 1.77843 | ||||||||
\(382\) | −0.133153 | −0.00681272 | ||||||||
\(383\) | 10.3043 | 0.526523 | 0.263262 | − | 0.964725i | \(-0.415202\pi\) | ||||
0.263262 | + | 0.964725i | \(0.415202\pi\) | |||||||
\(384\) | 2.23874 | 0.114245 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.7468 | −0.648793 | ||||||||
\(387\) | 3.57048 | 0.181498 | ||||||||
\(388\) | −0.406766 | −0.0206504 | ||||||||
\(389\) | 5.86030 | 0.297129 | 0.148564 | − | 0.988903i | \(-0.452535\pi\) | ||||
0.148564 | + | 0.988903i | \(0.452535\pi\) | |||||||
\(390\) | −11.4809 | −0.581358 | ||||||||
\(391\) | −25.8081 | −1.30517 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −36.9744 | −1.86511 | ||||||||
\(394\) | 4.39162 | 0.221246 | ||||||||
\(395\) | −10.2605 | −0.516261 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.65824 | −0.484733 | −0.242367 | − | 0.970185i | \(-0.577924\pi\) | ||||
−0.242367 | + | 0.970185i | \(0.577924\pi\) | |||||||
\(398\) | −0.430314 | −0.0215697 | ||||||||
\(399\) | 2.59135 | 0.129730 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −3.76869 | −0.188199 | −0.0940996 | − | 0.995563i | \(-0.529997\pi\) | ||||
−0.0940996 | + | 0.995563i | \(0.529997\pi\) | |||||||
\(402\) | 33.5098 | 1.67132 | ||||||||
\(403\) | −34.0710 | −1.69720 | ||||||||
\(404\) | 0.964155 | 0.0479685 | ||||||||
\(405\) | 10.9879 | 0.545994 | ||||||||
\(406\) | −5.89442 | −0.292535 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −14.9003 | −0.737676 | ||||||||
\(409\) | 7.59552 | 0.375575 | 0.187787 | − | 0.982210i | \(-0.439868\pi\) | ||||
0.187787 | + | 0.982210i | \(0.439868\pi\) | |||||||
\(410\) | −10.4700 | −0.517077 | ||||||||
\(411\) | 30.9543 | 1.52686 | ||||||||
\(412\) | 12.4021 | 0.611010 | ||||||||
\(413\) | 10.2614 | 0.504933 | ||||||||
\(414\) | 7.80155 | 0.383425 | ||||||||
\(415\) | 6.86423 | 0.336952 | ||||||||
\(416\) | 5.12829 | 0.251435 | ||||||||
\(417\) | 2.68401 | 0.131437 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.0288 | −0.489937 | −0.244968 | − | 0.969531i | \(-0.578778\pi\) | ||||
−0.244968 | + | 0.969531i | \(0.578778\pi\) | |||||||
\(420\) | 2.23874 | 0.109239 | ||||||||
\(421\) | −4.21566 | −0.205459 | −0.102729 | − | 0.994709i | \(-0.532758\pi\) | ||||
−0.102729 | + | 0.994709i | \(0.532758\pi\) | |||||||
\(422\) | −8.33737 | −0.405857 | ||||||||
\(423\) | 17.5337 | 0.852518 | ||||||||
\(424\) | 8.28476 | 0.402343 | ||||||||
\(425\) | −6.65568 | −0.322848 | ||||||||
\(426\) | 17.3886 | 0.842483 | ||||||||
\(427\) | 12.8132 | 0.620073 | ||||||||
\(428\) | 11.3466 | 0.548457 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.77464 | −0.0855806 | ||||||||
\(431\) | −23.7780 | −1.14534 | −0.572672 | − | 0.819784i | \(-0.694093\pi\) | ||||
−0.572672 | + | 0.819784i | \(0.694093\pi\) | |||||||
\(432\) | −2.21199 | −0.106424 | ||||||||
\(433\) | −33.5935 | −1.61440 | −0.807199 | − | 0.590279i | \(-0.799018\pi\) | ||||
−0.807199 | + | 0.590279i | \(0.799018\pi\) | |||||||
\(434\) | 6.64373 | 0.318909 | ||||||||
\(435\) | −13.1961 | −0.632702 | ||||||||
\(436\) | −9.81672 | −0.470135 | ||||||||
\(437\) | −4.48835 | −0.214707 | ||||||||
\(438\) | −5.68723 | −0.271747 | ||||||||
\(439\) | −27.7198 | −1.32299 | −0.661496 | − | 0.749949i | \(-0.730078\pi\) | ||||
−0.661496 | + | 0.749949i | \(0.730078\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.01195 | 0.0958071 | ||||||||
\(442\) | −34.1323 | −1.62351 | ||||||||
\(443\) | 28.5238 | 1.35521 | 0.677603 | − | 0.735427i | \(-0.263019\pi\) | ||||
0.677603 | + | 0.735427i | \(0.263019\pi\) | |||||||
\(444\) | 26.6285 | 1.26373 | ||||||||
\(445\) | −15.1923 | −0.720182 | ||||||||
\(446\) | 1.13218 | 0.0536104 | ||||||||
\(447\) | −12.0344 | −0.569210 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −0.982968 | −0.0463891 | −0.0231946 | − | 0.999731i | \(-0.507384\pi\) | ||||
−0.0231946 | + | 0.999731i | \(0.507384\pi\) | |||||||
\(450\) | 2.01195 | 0.0948442 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −15.4263 | −0.725591 | ||||||||
\(453\) | 4.38635 | 0.206089 | ||||||||
\(454\) | −10.2741 | −0.482187 | ||||||||
\(455\) | 5.12829 | 0.240418 | ||||||||
\(456\) | −2.59135 | −0.121351 | ||||||||
\(457\) | 4.98742 | 0.233302 | 0.116651 | − | 0.993173i | \(-0.462784\pi\) | ||||
0.116651 | + | 0.993173i | \(0.462784\pi\) | |||||||
\(458\) | −9.23127 | −0.431349 | ||||||||
\(459\) | 14.7223 | 0.687177 | ||||||||
\(460\) | −3.87761 | −0.180794 | ||||||||
\(461\) | 1.28781 | 0.0599791 | 0.0299896 | − | 0.999550i | \(-0.490453\pi\) | ||||
0.0299896 | + | 0.999550i | \(0.490453\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.4015 | −0.808717 | −0.404358 | − | 0.914601i | \(-0.632505\pi\) | ||||
−0.404358 | + | 0.914601i | \(0.632505\pi\) | |||||||
\(464\) | 5.89442 | 0.273641 | ||||||||
\(465\) | 14.8736 | 0.689745 | ||||||||
\(466\) | −6.68548 | −0.309699 | ||||||||
\(467\) | 6.97072 | 0.322566 | 0.161283 | − | 0.986908i | \(-0.448437\pi\) | ||||
0.161283 | + | 0.986908i | \(0.448437\pi\) | |||||||
\(468\) | 10.3179 | 0.476943 | ||||||||
\(469\) | −14.9682 | −0.691166 | ||||||||
\(470\) | −8.71479 | −0.401983 | ||||||||
\(471\) | 29.3397 | 1.35190 | ||||||||
\(472\) | −10.2614 | −0.472321 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 22.9705 | 1.05507 | ||||||||
\(475\) | −1.15751 | −0.0531100 | ||||||||
\(476\) | 6.65568 | 0.305062 | ||||||||
\(477\) | 16.6685 | 0.763198 | ||||||||
\(478\) | −22.4534 | −1.02699 | ||||||||
\(479\) | −26.7035 | −1.22011 | −0.610056 | − | 0.792358i | \(-0.708853\pi\) | ||||
−0.610056 | + | 0.792358i | \(0.708853\pi\) | |||||||
\(480\) | −2.23874 | −0.102184 | ||||||||
\(481\) | 60.9981 | 2.78127 | ||||||||
\(482\) | −28.6046 | −1.30290 | ||||||||
\(483\) | −8.68095 | −0.394997 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.406766 | 0.0184703 | ||||||||
\(486\) | −17.9631 | −0.814822 | ||||||||
\(487\) | 4.32910 | 0.196170 | 0.0980851 | − | 0.995178i | \(-0.468728\pi\) | ||||
0.0980851 | + | 0.995178i | \(0.468728\pi\) | |||||||
\(488\) | −12.8132 | −0.580026 | ||||||||
\(489\) | −48.3159 | −2.18492 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 12.8945 | 0.581923 | 0.290961 | − | 0.956735i | \(-0.406025\pi\) | ||||
0.290961 | + | 0.956735i | \(0.406025\pi\) | |||||||
\(492\) | 23.4396 | 1.05674 | ||||||||
\(493\) | −39.2313 | −1.76689 | ||||||||
\(494\) | −5.93603 | −0.267075 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.64373 | −0.298312 | ||||||||
\(497\) | −7.76716 | −0.348405 | ||||||||
\(498\) | −15.3672 | −0.688622 | ||||||||
\(499\) | −3.01676 | −0.135049 | −0.0675243 | − | 0.997718i | \(-0.521510\pi\) | ||||
−0.0675243 | + | 0.997718i | \(0.521510\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 2.01590 | 0.0900636 | ||||||||
\(502\) | 25.4351 | 1.13523 | ||||||||
\(503\) | −6.17711 | −0.275424 | −0.137712 | − | 0.990472i | \(-0.543975\pi\) | ||||
−0.137712 | + | 0.990472i | \(0.543975\pi\) | |||||||
\(504\) | −2.01195 | −0.0896193 | ||||||||
\(505\) | −0.964155 | −0.0429043 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 29.7739 | 1.32230 | ||||||||
\(508\) | 15.5058 | 0.687961 | ||||||||
\(509\) | 33.6703 | 1.49241 | 0.746205 | − | 0.665717i | \(-0.231874\pi\) | ||||
0.746205 | + | 0.665717i | \(0.231874\pi\) | |||||||
\(510\) | 14.9003 | 0.659797 | ||||||||
\(511\) | 2.54037 | 0.112380 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.56039 | 0.113044 | ||||||||
\(514\) | −24.9567 | −1.10079 | ||||||||
\(515\) | −12.4021 | −0.546504 | ||||||||
\(516\) | 3.97295 | 0.174899 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −11.8944 | −0.522611 | ||||||||
\(519\) | −33.5729 | −1.47369 | ||||||||
\(520\) | −5.12829 | −0.224891 | ||||||||
\(521\) | 24.5687 | 1.07637 | 0.538187 | − | 0.842826i | \(-0.319110\pi\) | ||||
0.538187 | + | 0.842826i | \(0.319110\pi\) | |||||||
\(522\) | 11.8593 | 0.519066 | ||||||||
\(523\) | 44.4679 | 1.94444 | 0.972222 | − | 0.234059i | \(-0.0752010\pi\) | ||||
0.972222 | + | 0.234059i | \(0.0752010\pi\) | |||||||
\(524\) | −16.5157 | −0.721493 | ||||||||
\(525\) | −2.23874 | −0.0977065 | ||||||||
\(526\) | −0.333627 | −0.0145468 | ||||||||
\(527\) | 44.2185 | 1.92619 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.96415 | −0.346268 | ||||||||
\(530\) | −8.28476 | −0.359867 | ||||||||
\(531\) | −20.6455 | −0.895939 | ||||||||
\(532\) | 1.15751 | 0.0501842 | ||||||||
\(533\) | 53.6933 | 2.32571 | ||||||||
\(534\) | 34.0115 | 1.47182 | ||||||||
\(535\) | −11.3466 | −0.490555 | ||||||||
\(536\) | 14.9682 | 0.646527 | ||||||||
\(537\) | 23.9876 | 1.03514 | ||||||||
\(538\) | 1.82597 | 0.0787231 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.21199 | 0.0951888 | ||||||||
\(541\) | −1.30850 | −0.0562569 | −0.0281284 | − | 0.999604i | \(-0.508955\pi\) | ||||
−0.0281284 | + | 0.999604i | \(0.508955\pi\) | |||||||
\(542\) | 13.3284 | 0.572503 | ||||||||
\(543\) | −13.8819 | −0.595730 | ||||||||
\(544\) | −6.65568 | −0.285360 | ||||||||
\(545\) | 9.81672 | 0.420502 | ||||||||
\(546\) | −11.4809 | −0.491338 | ||||||||
\(547\) | −17.4553 | −0.746335 | −0.373168 | − | 0.927764i | \(-0.621728\pi\) | ||||
−0.373168 | + | 0.927764i | \(0.621728\pi\) | |||||||
\(548\) | 13.8267 | 0.590646 | ||||||||
\(549\) | −25.7795 | −1.10024 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.82282 | −0.290662 | ||||||||
\(552\) | 8.68095 | 0.369486 | ||||||||
\(553\) | −10.2605 | −0.436320 | ||||||||
\(554\) | −15.4834 | −0.657826 | ||||||||
\(555\) | −26.6285 | −1.13032 | ||||||||
\(556\) | 1.19890 | 0.0508445 | ||||||||
\(557\) | −0.219818 | −0.00931400 | −0.00465700 | − | 0.999989i | \(-0.501482\pi\) | ||||
−0.00465700 | + | 0.999989i | \(0.501482\pi\) | |||||||
\(558\) | −13.3668 | −0.565863 | ||||||||
\(559\) | 9.10086 | 0.384925 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.3105 | 1.19421 | ||||||||
\(563\) | 22.4246 | 0.945084 | 0.472542 | − | 0.881308i | \(-0.343336\pi\) | ||||
0.472542 | + | 0.881308i | \(0.343336\pi\) | |||||||
\(564\) | 19.5101 | 0.821525 | ||||||||
\(565\) | 15.4263 | 0.648988 | ||||||||
\(566\) | 13.5891 | 0.571194 | ||||||||
\(567\) | 10.9879 | 0.461449 | ||||||||
\(568\) | 7.76716 | 0.325903 | ||||||||
\(569\) | 3.86730 | 0.162126 | 0.0810629 | − | 0.996709i | \(-0.474169\pi\) | ||||
0.0810629 | + | 0.996709i | \(0.474169\pi\) | |||||||
\(570\) | 2.59135 | 0.108540 | ||||||||
\(571\) | 25.4899 | 1.06672 | 0.533360 | − | 0.845888i | \(-0.320929\pi\) | ||||
0.533360 | + | 0.845888i | \(0.320929\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.298095 | −0.0124531 | ||||||||
\(574\) | −10.4700 | −0.437010 | ||||||||
\(575\) | 3.87761 | 0.161707 | ||||||||
\(576\) | 2.01195 | 0.0838312 | ||||||||
\(577\) | −33.6011 | −1.39883 | −0.699415 | − | 0.714716i | \(-0.746556\pi\) | ||||
−0.699415 | + | 0.714716i | \(0.746556\pi\) | |||||||
\(578\) | 27.2980 | 1.13545 | ||||||||
\(579\) | −28.5366 | −1.18594 | ||||||||
\(580\) | −5.89442 | −0.244752 | ||||||||
\(581\) | 6.86423 | 0.284776 | ||||||||
\(582\) | −0.910642 | −0.0377473 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.54037 | −0.105121 | ||||||||
\(585\) | −10.3179 | −0.426591 | ||||||||
\(586\) | 1.83423 | 0.0757715 | ||||||||
\(587\) | 38.8396 | 1.60308 | 0.801542 | − | 0.597939i | \(-0.204013\pi\) | ||||
0.801542 | + | 0.597939i | \(0.204013\pi\) | |||||||
\(588\) | 2.23874 | 0.0923240 | ||||||||
\(589\) | 7.69015 | 0.316867 | ||||||||
\(590\) | 10.2614 | 0.422457 | ||||||||
\(591\) | 9.83168 | 0.404421 | ||||||||
\(592\) | 11.8944 | 0.488857 | ||||||||
\(593\) | −29.8393 | −1.22535 | −0.612677 | − | 0.790333i | \(-0.709907\pi\) | ||||
−0.612677 | + | 0.790333i | \(0.709907\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.65568 | −0.272856 | ||||||||
\(596\) | −5.37555 | −0.220191 | ||||||||
\(597\) | −0.963359 | −0.0394277 | ||||||||
\(598\) | 19.8855 | 0.813179 | ||||||||
\(599\) | 26.4186 | 1.07944 | 0.539718 | − | 0.841846i | \(-0.318531\pi\) | ||||
0.539718 | + | 0.841846i | \(0.318531\pi\) | |||||||
\(600\) | 2.23874 | 0.0913961 | ||||||||
\(601\) | −31.2101 | −1.27309 | −0.636543 | − | 0.771241i | \(-0.719636\pi\) | ||||
−0.636543 | + | 0.771241i | \(0.719636\pi\) | |||||||
\(602\) | −1.77464 | −0.0723288 | ||||||||
\(603\) | 30.1152 | 1.22639 | ||||||||
\(604\) | 1.95930 | 0.0797226 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.15849 | 0.0876827 | ||||||||
\(607\) | −29.3084 | −1.18959 | −0.594795 | − | 0.803878i | \(-0.702767\pi\) | ||||
−0.594795 | + | 0.803878i | \(0.702767\pi\) | |||||||
\(608\) | −1.15751 | −0.0469431 | ||||||||
\(609\) | −13.1961 | −0.534731 | ||||||||
\(610\) | 12.8132 | 0.518791 | ||||||||
\(611\) | 44.6920 | 1.80804 | ||||||||
\(612\) | −13.3909 | −0.541294 | ||||||||
\(613\) | −20.1964 | −0.815725 | −0.407863 | − | 0.913043i | \(-0.633726\pi\) | ||||
−0.407863 | + | 0.913043i | \(0.633726\pi\) | |||||||
\(614\) | 8.45358 | 0.341159 | ||||||||
\(615\) | −23.4396 | −0.945176 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.08426 | −0.0839091 | −0.0419546 | − | 0.999120i | \(-0.513358\pi\) | ||||
−0.0419546 | + | 0.999120i | \(0.513358\pi\) | |||||||
\(618\) | 27.7652 | 1.11688 | ||||||||
\(619\) | −3.03990 | −0.122184 | −0.0610919 | − | 0.998132i | \(-0.519458\pi\) | ||||
−0.0610919 | + | 0.998132i | \(0.519458\pi\) | |||||||
\(620\) | 6.64373 | 0.266819 | ||||||||
\(621\) | −8.57723 | −0.344192 | ||||||||
\(622\) | 16.9898 | 0.681228 | ||||||||
\(623\) | −15.1923 | −0.608665 | ||||||||
\(624\) | 11.4809 | 0.459604 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 18.0862 | 0.722872 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.1054 | 0.522964 | ||||||||
\(629\) | −79.1654 | −3.15653 | ||||||||
\(630\) | 2.01195 | 0.0801579 | ||||||||
\(631\) | −11.3562 | −0.452081 | −0.226041 | − | 0.974118i | \(-0.572578\pi\) | ||||
−0.226041 | + | 0.974118i | \(0.572578\pi\) | |||||||
\(632\) | 10.2605 | 0.408140 | ||||||||
\(633\) | −18.6652 | −0.741874 | ||||||||
\(634\) | −0.393194 | −0.0156157 | ||||||||
\(635\) | −15.5058 | −0.615331 | ||||||||
\(636\) | 18.5474 | 0.735452 | ||||||||
\(637\) | 5.12829 | 0.203190 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.6271 | 0.618200 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −34.4272 | −1.35979 | −0.679896 | − | 0.733308i | \(-0.737975\pi\) | ||||
−0.679896 | + | 0.733308i | \(0.737975\pi\) | |||||||
\(642\) | 25.4020 | 1.00254 | ||||||||
\(643\) | −31.4442 | −1.24004 | −0.620020 | − | 0.784586i | \(-0.712875\pi\) | ||||
−0.620020 | + | 0.784586i | \(0.712875\pi\) | |||||||
\(644\) | −3.87761 | −0.152799 | ||||||||
\(645\) | −3.97295 | −0.156435 | ||||||||
\(646\) | 7.70398 | 0.303109 | ||||||||
\(647\) | −48.9448 | −1.92422 | −0.962110 | − | 0.272662i | \(-0.912096\pi\) | ||||
−0.962110 | + | 0.272662i | \(0.912096\pi\) | |||||||
\(648\) | −10.9879 | −0.431646 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 5.12829 | 0.201148 | ||||||||
\(651\) | 14.8736 | 0.582941 | ||||||||
\(652\) | −21.5818 | −0.845207 | ||||||||
\(653\) | −17.0563 | −0.667463 | −0.333732 | − | 0.942668i | \(-0.608308\pi\) | ||||
−0.333732 | + | 0.942668i | \(0.608308\pi\) | |||||||
\(654\) | −21.9771 | −0.859371 | ||||||||
\(655\) | 16.5157 | 0.645323 | ||||||||
\(656\) | 10.4700 | 0.408785 | ||||||||
\(657\) | −5.11110 | −0.199403 | ||||||||
\(658\) | −8.71479 | −0.339738 | ||||||||
\(659\) | 39.3755 | 1.53385 | 0.766926 | − | 0.641736i | \(-0.221786\pi\) | ||||
0.766926 | + | 0.641736i | \(0.221786\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −47.5548 | −1.84967 | −0.924833 | − | 0.380374i | \(-0.875795\pi\) | ||||
−0.924833 | + | 0.380374i | \(0.875795\pi\) | |||||||
\(662\) | −34.5395 | −1.34242 | ||||||||
\(663\) | −76.4132 | −2.96764 | ||||||||
\(664\) | −6.86423 | −0.266384 | ||||||||
\(665\) | −1.15751 | −0.0448861 | ||||||||
\(666\) | 23.9309 | 0.927305 | ||||||||
\(667\) | 22.8562 | 0.884997 | ||||||||
\(668\) | 0.900461 | 0.0348399 | ||||||||
\(669\) | 2.53466 | 0.0979956 | ||||||||
\(670\) | −14.9682 | −0.578271 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.23874 | −0.0863612 | ||||||||
\(673\) | 30.7041 | 1.18356 | 0.591779 | − | 0.806100i | \(-0.298426\pi\) | ||||
0.591779 | + | 0.806100i | \(0.298426\pi\) | |||||||
\(674\) | 2.36075 | 0.0909326 | ||||||||
\(675\) | −2.21199 | −0.0851395 | ||||||||
\(676\) | 13.2994 | 0.511516 | ||||||||
\(677\) | −30.7722 | −1.18267 | −0.591335 | − | 0.806426i | \(-0.701399\pi\) | ||||
−0.591335 | + | 0.806426i | \(0.701399\pi\) | |||||||
\(678\) | −34.5354 | −1.32632 | ||||||||
\(679\) | 0.406766 | 0.0156102 | ||||||||
\(680\) | 6.65568 | 0.255234 | ||||||||
\(681\) | −23.0010 | −0.881400 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.3871 | −0.397451 | −0.198726 | − | 0.980055i | \(-0.563680\pi\) | ||||
−0.198726 | + | 0.980055i | \(0.563680\pi\) | |||||||
\(684\) | −2.32884 | −0.0890455 | ||||||||
\(685\) | −13.8267 | −0.528289 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −20.6664 | −0.788472 | ||||||||
\(688\) | 1.77464 | 0.0676574 | ||||||||
\(689\) | 42.4867 | 1.61861 | ||||||||
\(690\) | −8.68095 | −0.330478 | ||||||||
\(691\) | 20.9815 | 0.798175 | 0.399088 | − | 0.916913i | \(-0.369327\pi\) | ||||
0.399088 | + | 0.916913i | \(0.369327\pi\) | |||||||
\(692\) | −14.9963 | −0.570075 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.85646 | −0.260267 | ||||||||
\(695\) | −1.19890 | −0.0454767 | ||||||||
\(696\) | 13.1961 | 0.500195 | ||||||||
\(697\) | −69.6850 | −2.63951 | ||||||||
\(698\) | −8.34033 | −0.315686 | ||||||||
\(699\) | −14.9670 | −0.566105 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | 30.6295 | 1.15686 | 0.578431 | − | 0.815731i | \(-0.303665\pi\) | ||||
0.578431 | + | 0.815731i | \(0.303665\pi\) | |||||||
\(702\) | −11.3437 | −0.428142 | ||||||||
\(703\) | −13.7679 | −0.519264 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −19.5101 | −0.734794 | ||||||||
\(706\) | 19.7691 | 0.744019 | ||||||||
\(707\) | −0.964155 | −0.0362608 | ||||||||
\(708\) | −22.9727 | −0.863367 | ||||||||
\(709\) | 41.2618 | 1.54962 | 0.774810 | − | 0.632194i | \(-0.217845\pi\) | ||||
0.774810 | + | 0.632194i | \(0.217845\pi\) | |||||||
\(710\) | −7.76716 | −0.291496 | ||||||||
\(711\) | 20.6436 | 0.774194 | ||||||||
\(712\) | 15.1923 | 0.569354 | ||||||||
\(713\) | −25.7618 | −0.964786 | ||||||||
\(714\) | 14.9003 | 0.557630 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.7148 | 0.400430 | ||||||||
\(717\) | −50.2672 | −1.87726 | ||||||||
\(718\) | 0.257703 | 0.00961738 | ||||||||
\(719\) | 26.9646 | 1.00561 | 0.502804 | − | 0.864400i | \(-0.332302\pi\) | ||||
0.502804 | + | 0.864400i | \(0.332302\pi\) | |||||||
\(720\) | −2.01195 | −0.0749809 | ||||||||
\(721\) | −12.4021 | −0.461880 | ||||||||
\(722\) | −17.6602 | −0.657244 | ||||||||
\(723\) | −64.0382 | −2.38161 | ||||||||
\(724\) | −6.20078 | −0.230450 | ||||||||
\(725\) | 5.89442 | 0.218913 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.0208 | −1.07632 | −0.538161 | − | 0.842842i | \(-0.680881\pi\) | ||||
−0.538161 | + | 0.842842i | \(0.680881\pi\) | |||||||
\(728\) | −5.12829 | −0.190067 | ||||||||
\(729\) | −7.25091 | −0.268552 | ||||||||
\(730\) | 2.54037 | 0.0940235 | ||||||||
\(731\) | −11.8114 | −0.436861 | ||||||||
\(732\) | −28.6854 | −1.06024 | ||||||||
\(733\) | 28.4461 | 1.05068 | 0.525339 | − | 0.850893i | \(-0.323938\pi\) | ||||
0.525339 | + | 0.850893i | \(0.323938\pi\) | |||||||
\(734\) | 25.6755 | 0.947700 | ||||||||
\(735\) | −2.23874 | −0.0825771 | ||||||||
\(736\) | 3.87761 | 0.142931 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 21.0651 | 0.775417 | ||||||||
\(739\) | −24.4968 | −0.901128 | −0.450564 | − | 0.892744i | \(-0.648777\pi\) | ||||
−0.450564 | + | 0.892744i | \(0.648777\pi\) | |||||||
\(740\) | −11.8944 | −0.437247 | ||||||||
\(741\) | −13.2892 | −0.488192 | ||||||||
\(742\) | −8.28476 | −0.304143 | ||||||||
\(743\) | −6.04973 | −0.221943 | −0.110972 | − | 0.993824i | \(-0.535396\pi\) | ||||
−0.110972 | + | 0.993824i | \(0.535396\pi\) | |||||||
\(744\) | −14.8736 | −0.545291 | ||||||||
\(745\) | 5.37555 | 0.196945 | ||||||||
\(746\) | −5.70957 | −0.209042 | ||||||||
\(747\) | −13.8105 | −0.505299 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.3466 | −0.414595 | ||||||||
\(750\) | −2.23874 | −0.0817472 | ||||||||
\(751\) | 5.08525 | 0.185564 | 0.0927818 | − | 0.995686i | \(-0.470424\pi\) | ||||
0.0927818 | + | 0.995686i | \(0.470424\pi\) | |||||||
\(752\) | 8.71479 | 0.317796 | ||||||||
\(753\) | 56.9426 | 2.07510 | ||||||||
\(754\) | 30.2283 | 1.10085 | ||||||||
\(755\) | −1.95930 | −0.0713061 | ||||||||
\(756\) | 2.21199 | 0.0804493 | ||||||||
\(757\) | 25.4296 | 0.924254 | 0.462127 | − | 0.886814i | \(-0.347086\pi\) | ||||
0.462127 | + | 0.886814i | \(0.347086\pi\) | |||||||
\(758\) | 2.16686 | 0.0787039 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.15751 | 0.0419871 | ||||||||
\(761\) | 41.6911 | 1.51130 | 0.755650 | − | 0.654976i | \(-0.227321\pi\) | ||||
0.755650 | + | 0.654976i | \(0.227321\pi\) | |||||||
\(762\) | 34.7135 | 1.25754 | ||||||||
\(763\) | 9.81672 | 0.355389 | ||||||||
\(764\) | −0.133153 | −0.00481732 | ||||||||
\(765\) | 13.3909 | 0.484148 | ||||||||
\(766\) | 10.3043 | 0.372308 | ||||||||
\(767\) | −52.6237 | −1.90013 | ||||||||
\(768\) | 2.23874 | 0.0807835 | ||||||||
\(769\) | −14.8389 | −0.535106 | −0.267553 | − | 0.963543i | \(-0.586215\pi\) | ||||
−0.267553 | + | 0.963543i | \(0.586215\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −55.8716 | −2.01216 | ||||||||
\(772\) | −12.7468 | −0.458766 | ||||||||
\(773\) | 25.3422 | 0.911497 | 0.455749 | − | 0.890109i | \(-0.349372\pi\) | ||||
0.455749 | + | 0.890109i | \(0.349372\pi\) | |||||||
\(774\) | 3.57048 | 0.128338 | ||||||||
\(775\) | −6.64373 | −0.238650 | ||||||||
\(776\) | −0.406766 | −0.0146020 | ||||||||
\(777\) | −26.6285 | −0.955291 | ||||||||
\(778\) | 5.86030 | 0.210102 | ||||||||
\(779\) | −12.1191 | −0.434211 | ||||||||
\(780\) | −11.4809 | −0.411082 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −25.8081 | −0.922896 | ||||||||
\(783\) | −13.0384 | −0.465954 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −13.1054 | −0.467753 | ||||||||
\(786\) | −36.9744 | −1.31883 | ||||||||
\(787\) | 17.7718 | 0.633496 | 0.316748 | − | 0.948510i | \(-0.397409\pi\) | ||||
0.316748 | + | 0.948510i | \(0.397409\pi\) | |||||||
\(788\) | 4.39162 | 0.156445 | ||||||||
\(789\) | −0.746903 | −0.0265905 | ||||||||
\(790\) | −10.2605 | −0.365051 | ||||||||
\(791\) | 15.4263 | 0.548495 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −65.7098 | −2.33342 | ||||||||
\(794\) | −9.65824 | −0.342758 | ||||||||
\(795\) | −18.5474 | −0.657808 | ||||||||
\(796\) | −0.430314 | −0.0152521 | ||||||||
\(797\) | −3.36014 | −0.119022 | −0.0595112 | − | 0.998228i | \(-0.518954\pi\) | ||||
−0.0595112 | + | 0.998228i | \(0.518954\pi\) | |||||||
\(798\) | 2.59135 | 0.0917329 | ||||||||
\(799\) | −58.0028 | −2.05199 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 30.5661 | 1.08000 | ||||||||
\(802\) | −3.76869 | −0.133077 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 33.5098 | 1.18180 | ||||||||
\(805\) | 3.87761 | 0.136668 | ||||||||
\(806\) | −34.0710 | −1.20010 | ||||||||
\(807\) | 4.08787 | 0.143900 | ||||||||
\(808\) | 0.964155 | 0.0339189 | ||||||||
\(809\) | −17.3076 | −0.608502 | −0.304251 | − | 0.952592i | \(-0.598406\pi\) | ||||
−0.304251 | + | 0.952592i | \(0.598406\pi\) | |||||||
\(810\) | 10.9879 | 0.386076 | ||||||||
\(811\) | −12.3583 | −0.433960 | −0.216980 | − | 0.976176i | \(-0.569621\pi\) | ||||
−0.216980 | + | 0.976176i | \(0.569621\pi\) | |||||||
\(812\) | −5.89442 | −0.206853 | ||||||||
\(813\) | 29.8388 | 1.04649 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.5818 | 0.755977 | ||||||||
\(816\) | −14.9003 | −0.521615 | ||||||||
\(817\) | −2.05415 | −0.0718657 | ||||||||
\(818\) | 7.59552 | 0.265571 | ||||||||
\(819\) | −10.3179 | −0.360535 | ||||||||
\(820\) | −10.4700 | −0.365628 | ||||||||
\(821\) | −5.55685 | −0.193935 | −0.0969677 | − | 0.995288i | \(-0.530914\pi\) | ||||
−0.0969677 | + | 0.995288i | \(0.530914\pi\) | |||||||
\(822\) | 30.9543 | 1.07965 | ||||||||
\(823\) | −52.8246 | −1.84135 | −0.920676 | − | 0.390329i | \(-0.872361\pi\) | ||||
−0.920676 | + | 0.390329i | \(0.872361\pi\) | |||||||
\(824\) | 12.4021 | 0.432049 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.2614 | 0.357041 | ||||||||
\(827\) | −49.4908 | −1.72097 | −0.860483 | − | 0.509480i | \(-0.829838\pi\) | ||||
−0.860483 | + | 0.509480i | \(0.829838\pi\) | |||||||
\(828\) | 7.80155 | 0.271123 | ||||||||
\(829\) | −48.2163 | −1.67462 | −0.837311 | − | 0.546727i | \(-0.815873\pi\) | ||||
−0.837311 | + | 0.546727i | \(0.815873\pi\) | |||||||
\(830\) | 6.86423 | 0.238261 | ||||||||
\(831\) | −34.6632 | −1.20245 | ||||||||
\(832\) | 5.12829 | 0.177792 | ||||||||
\(833\) | −6.65568 | −0.230606 | ||||||||
\(834\) | 2.68401 | 0.0929398 | ||||||||
\(835\) | −0.900461 | −0.0311617 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.6959 | 0.507963 | ||||||||
\(838\) | −10.0288 | −0.346438 | ||||||||
\(839\) | 22.3658 | 0.772154 | 0.386077 | − | 0.922467i | \(-0.373830\pi\) | ||||
0.386077 | + | 0.922467i | \(0.373830\pi\) | |||||||
\(840\) | 2.23874 | 0.0772438 | ||||||||
\(841\) | 5.74413 | 0.198073 | ||||||||
\(842\) | −4.21566 | −0.145281 | ||||||||
\(843\) | 63.3798 | 2.18292 | ||||||||
\(844\) | −8.33737 | −0.286984 | ||||||||
\(845\) | −13.2994 | −0.457513 | ||||||||
\(846\) | 17.5337 | 0.602821 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.28476 | 0.284500 | ||||||||
\(849\) | 30.4225 | 1.04410 | ||||||||
\(850\) | −6.65568 | −0.228288 | ||||||||
\(851\) | 46.1219 | 1.58104 | ||||||||
\(852\) | 17.3886 | 0.595725 | ||||||||
\(853\) | 24.9471 | 0.854173 | 0.427087 | − | 0.904211i | \(-0.359540\pi\) | ||||
0.427087 | + | 0.904211i | \(0.359540\pi\) | |||||||
\(854\) | 12.8132 | 0.438458 | ||||||||
\(855\) | 2.32884 | 0.0796447 | ||||||||
\(856\) | 11.3466 | 0.387818 | ||||||||
\(857\) | −19.7163 | −0.673496 | −0.336748 | − | 0.941595i | \(-0.609327\pi\) | ||||
−0.336748 | + | 0.941595i | \(0.609327\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.4209 | 0.526156 | 0.263078 | − | 0.964775i | \(-0.415262\pi\) | ||||
0.263078 | + | 0.964775i | \(0.415262\pi\) | |||||||
\(860\) | −1.77464 | −0.0605146 | ||||||||
\(861\) | −23.4396 | −0.798819 | ||||||||
\(862\) | −23.7780 | −0.809881 | ||||||||
\(863\) | −14.2128 | −0.483810 | −0.241905 | − | 0.970300i | \(-0.577772\pi\) | ||||
−0.241905 | + | 0.970300i | \(0.577772\pi\) | |||||||
\(864\) | −2.21199 | −0.0752534 | ||||||||
\(865\) | 14.9963 | 0.509891 | ||||||||
\(866\) | −33.5935 | −1.14155 | ||||||||
\(867\) | 61.1132 | 2.07551 | ||||||||
\(868\) | 6.64373 | 0.225503 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −13.1961 | −0.447388 | ||||||||
\(871\) | 76.7612 | 2.60095 | ||||||||
\(872\) | −9.81672 | −0.332436 | ||||||||
\(873\) | −0.818392 | −0.0276984 | ||||||||
\(874\) | −4.48835 | −0.151821 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −5.68723 | −0.192154 | ||||||||
\(877\) | 6.27739 | 0.211972 | 0.105986 | − | 0.994368i | \(-0.466200\pi\) | ||||
0.105986 | + | 0.994368i | \(0.466200\pi\) | |||||||
\(878\) | −27.7198 | −0.935496 | ||||||||
\(879\) | 4.10637 | 0.138504 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.955481 | 0.0321910 | 0.0160955 | − | 0.999870i | \(-0.494876\pi\) | ||||
0.0160955 | + | 0.999870i | \(0.494876\pi\) | |||||||
\(882\) | 2.01195 | 0.0677458 | ||||||||
\(883\) | 8.50497 | 0.286215 | 0.143107 | − | 0.989707i | \(-0.454291\pi\) | ||||
0.143107 | + | 0.989707i | \(0.454291\pi\) | |||||||
\(884\) | −34.1323 | −1.14799 | ||||||||
\(885\) | 22.9727 | 0.772219 | ||||||||
\(886\) | 28.5238 | 0.958276 | ||||||||
\(887\) | −2.18620 | −0.0734056 | −0.0367028 | − | 0.999326i | \(-0.511685\pi\) | ||||
−0.0367028 | + | 0.999326i | \(0.511685\pi\) | |||||||
\(888\) | 26.6285 | 0.893593 | ||||||||
\(889\) | −15.5058 | −0.520049 | ||||||||
\(890\) | −15.1923 | −0.509246 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.13218 | 0.0379083 | ||||||||
\(893\) | −10.0874 | −0.337563 | ||||||||
\(894\) | −12.0344 | −0.402492 | ||||||||
\(895\) | −10.7148 | −0.358156 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 44.5185 | 1.48643 | ||||||||
\(898\) | −0.982968 | −0.0328021 | ||||||||
\(899\) | −39.1609 | −1.30609 | ||||||||
\(900\) | 2.01195 | 0.0670649 | ||||||||
\(901\) | −55.1407 | −1.83700 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.97295 | −0.132211 | ||||||||
\(904\) | −15.4263 | −0.513070 | ||||||||
\(905\) | 6.20078 | 0.206121 | ||||||||
\(906\) | 4.38635 | 0.145727 | ||||||||
\(907\) | 0.266857 | 0.00886082 | 0.00443041 | − | 0.999990i | \(-0.498590\pi\) | ||||
0.00443041 | + | 0.999990i | \(0.498590\pi\) | |||||||
\(908\) | −10.2741 | −0.340957 | ||||||||
\(909\) | 1.93983 | 0.0643401 | ||||||||
\(910\) | 5.12829 | 0.170001 | ||||||||
\(911\) | −20.3552 | −0.674397 | −0.337198 | − | 0.941434i | \(-0.609479\pi\) | ||||
−0.337198 | + | 0.941434i | \(0.609479\pi\) | |||||||
\(912\) | −2.59135 | −0.0858082 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 4.98742 | 0.164969 | ||||||||
\(915\) | 28.6854 | 0.948309 | ||||||||
\(916\) | −9.23127 | −0.305010 | ||||||||
\(917\) | 16.5157 | 0.545398 | ||||||||
\(918\) | 14.7223 | 0.485908 | ||||||||
\(919\) | 8.19185 | 0.270224 | 0.135112 | − | 0.990830i | \(-0.456861\pi\) | ||||
0.135112 | + | 0.990830i | \(0.456861\pi\) | |||||||
\(920\) | −3.87761 | −0.127841 | ||||||||
\(921\) | 18.9254 | 0.623612 | ||||||||
\(922\) | 1.28781 | 0.0424116 | ||||||||
\(923\) | 39.8323 | 1.31110 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.8944 | 0.391086 | ||||||||
\(926\) | −17.4015 | −0.571849 | ||||||||
\(927\) | 24.9525 | 0.819547 | ||||||||
\(928\) | 5.89442 | 0.193494 | ||||||||
\(929\) | −36.0873 | −1.18398 | −0.591992 | − | 0.805943i | \(-0.701658\pi\) | ||||
−0.591992 | + | 0.805943i | \(0.701658\pi\) | |||||||
\(930\) | 14.8736 | 0.487724 | ||||||||
\(931\) | −1.15751 | −0.0379357 | ||||||||
\(932\) | −6.68548 | −0.218990 | ||||||||
\(933\) | 38.0357 | 1.24523 | ||||||||
\(934\) | 6.97072 | 0.228089 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 10.3179 | 0.337250 | ||||||||
\(937\) | 42.0240 | 1.37286 | 0.686432 | − | 0.727194i | \(-0.259176\pi\) | ||||
0.686432 | + | 0.727194i | \(0.259176\pi\) | |||||||
\(938\) | −14.9682 | −0.488728 | ||||||||
\(939\) | 40.4904 | 1.32135 | ||||||||
\(940\) | −8.71479 | −0.284245 | ||||||||
\(941\) | −57.0071 | −1.85838 | −0.929189 | − | 0.369605i | \(-0.879493\pi\) | ||||
−0.929189 | + | 0.369605i | \(0.879493\pi\) | |||||||
\(942\) | 29.3397 | 0.955938 | ||||||||
\(943\) | 40.5986 | 1.32207 | ||||||||
\(944\) | −10.2614 | −0.333982 | ||||||||
\(945\) | −2.21199 | −0.0719560 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42.6517 | 1.38599 | 0.692997 | − | 0.720940i | \(-0.256290\pi\) | ||||
0.692997 | + | 0.720940i | \(0.256290\pi\) | |||||||
\(948\) | 22.9705 | 0.746048 | ||||||||
\(949\) | −13.0278 | −0.422900 | ||||||||
\(950\) | −1.15751 | −0.0375544 | ||||||||
\(951\) | −0.880257 | −0.0285443 | ||||||||
\(952\) | 6.65568 | 0.215712 | ||||||||
\(953\) | −11.5905 | −0.375453 | −0.187726 | − | 0.982221i | \(-0.560112\pi\) | ||||
−0.187726 | + | 0.982221i | \(0.560112\pi\) | |||||||
\(954\) | 16.6685 | 0.539663 | ||||||||
\(955\) | 0.133153 | 0.00430874 | ||||||||
\(956\) | −22.4534 | −0.726193 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26.7035 | −0.862750 | ||||||||
\(959\) | −13.8267 | −0.446486 | ||||||||
\(960\) | −2.23874 | −0.0722550 | ||||||||
\(961\) | 13.1391 | 0.423843 | ||||||||
\(962\) | 60.9981 | 1.96666 | ||||||||
\(963\) | 22.8287 | 0.735645 | ||||||||
\(964\) | −28.6046 | −0.921292 | ||||||||
\(965\) | 12.7468 | 0.410332 | ||||||||
\(966\) | −8.68095 | −0.279305 | ||||||||
\(967\) | −38.6220 | −1.24200 | −0.621000 | − | 0.783811i | \(-0.713273\pi\) | ||||
−0.621000 | + | 0.783811i | \(0.713273\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.2472 | 0.554060 | ||||||||
\(970\) | 0.406766 | 0.0130605 | ||||||||
\(971\) | −53.2173 | −1.70782 | −0.853912 | − | 0.520418i | \(-0.825776\pi\) | ||||
−0.853912 | + | 0.520418i | \(0.825776\pi\) | |||||||
\(972\) | −17.9631 | −0.576166 | ||||||||
\(973\) | −1.19890 | −0.0384348 | ||||||||
\(974\) | 4.32910 | 0.138713 | ||||||||
\(975\) | 11.4809 | 0.367683 | ||||||||
\(976\) | −12.8132 | −0.410140 | ||||||||
\(977\) | 3.80768 | 0.121819 | 0.0609093 | − | 0.998143i | \(-0.480600\pi\) | ||||
0.0609093 | + | 0.998143i | \(0.480600\pi\) | |||||||
\(978\) | −48.3159 | −1.54497 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −19.7507 | −0.630592 | ||||||||
\(982\) | 12.8945 | 0.411481 | ||||||||
\(983\) | 27.5427 | 0.878474 | 0.439237 | − | 0.898371i | \(-0.355249\pi\) | ||||
0.439237 | + | 0.898371i | \(0.355249\pi\) | |||||||
\(984\) | 23.4396 | 0.747227 | ||||||||
\(985\) | −4.39162 | −0.139929 | ||||||||
\(986\) | −39.2313 | −1.24938 | ||||||||
\(987\) | −19.5101 | −0.621014 | ||||||||
\(988\) | −5.93603 | −0.188850 | ||||||||
\(989\) | 6.88134 | 0.218814 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −59.3959 | −1.88677 | −0.943386 | − | 0.331697i | \(-0.892379\pi\) | ||||
−0.943386 | + | 0.331697i | \(0.892379\pi\) | |||||||
\(992\) | −6.64373 | −0.210939 | ||||||||
\(993\) | −77.3249 | −2.45383 | ||||||||
\(994\) | −7.76716 | −0.246360 | ||||||||
\(995\) | 0.430314 | 0.0136419 | ||||||||
\(996\) | −15.3672 | −0.486929 | ||||||||
\(997\) | 32.6231 | 1.03318 | 0.516592 | − | 0.856232i | \(-0.327201\pi\) | ||||
0.516592 | + | 0.856232i | \(0.327201\pi\) | |||||||
\(998\) | −3.01676 | −0.0954937 | ||||||||
\(999\) | −26.3103 | −0.832422 |
(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 | 8470.2.a.dd.1.5 | yes | 6 | |
11.10 | odd | 2 | 8470.2.a.cx.1.5 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.cx.1.5 | ✓ | 6 | 11.10 | odd | 2 | ||
8470.2.a.dd.1.5 | yes | 6 | 1.1 | even | 1 | trivial |