Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4830,2,Mod(1,4830)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4830, 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("4830.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4830.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: | \(38.5677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.6809.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.582772\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4830.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.16554 | −0.351425 | −0.175712 | − | 0.984442i | \(-0.556223\pi\) | ||||
−0.175712 | + | 0.984442i | \(0.556223\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.26633 | −0.628567 | −0.314283 | − | 0.949329i | \(-0.601764\pi\) | ||||
−0.314283 | + | 0.949329i | \(0.601764\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.43187 | 0.832352 | 0.416176 | − | 0.909284i | \(-0.363370\pi\) | ||||
0.416176 | + | 0.909284i | \(0.363370\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 5.43187 | 1.24616 | 0.623079 | − | 0.782159i | \(-0.285882\pi\) | ||||
0.623079 | + | 0.782159i | \(0.285882\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −1.16554 | −0.248495 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.26633 | −0.444464 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −4.75263 | −0.882541 | −0.441270 | − | 0.897374i | \(-0.645472\pi\) | ||||
−0.441270 | + | 0.897374i | \(0.645472\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | −4.15521 | −0.746298 | −0.373149 | − | 0.927771i | \(-0.621722\pi\) | ||||
−0.373149 | + | 0.927771i | \(0.621722\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.16554 | −0.202895 | ||||||||
\(34\) | 3.43187 | 0.588562 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.723336 | 0.118916 | 0.0594578 | − | 0.998231i | \(-0.481063\pi\) | ||||
0.0594578 | + | 0.998231i | \(0.481063\pi\) | |||||||
\(38\) | 5.43187 | 0.881166 | ||||||||
\(39\) | −2.26633 | −0.362903 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 8.64151 | 1.34958 | 0.674788 | − | 0.738011i | \(-0.264235\pi\) | ||||
0.674788 | + | 0.738011i | \(0.264235\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | 8.42154 | 1.28427 | 0.642136 | − | 0.766590i | \(-0.278048\pi\) | ||||
0.642136 | + | 0.766590i | \(0.278048\pi\) | |||||||
\(44\) | −1.16554 | −0.175712 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 0.899214 | 0.131164 | 0.0655819 | − | 0.997847i | \(-0.479110\pi\) | ||||
0.0655819 | + | 0.997847i | \(0.479110\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 3.43187 | 0.480558 | ||||||||
\(52\) | −2.26633 | −0.314283 | ||||||||
\(53\) | 3.27666 | 0.450084 | 0.225042 | − | 0.974349i | \(-0.427748\pi\) | ||||
0.225042 | + | 0.974349i | \(0.427748\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −1.16554 | −0.157162 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 5.43187 | 0.719469 | ||||||||
\(58\) | −4.75263 | −0.624051 | ||||||||
\(59\) | 5.05442 | 0.658030 | 0.329015 | − | 0.944325i | \(-0.393283\pi\) | ||||
0.329015 | + | 0.944325i | \(0.393283\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 6.53266 | 0.836421 | 0.418211 | − | 0.908350i | \(-0.362657\pi\) | ||||
0.418211 | + | 0.908350i | \(0.362657\pi\) | |||||||
\(62\) | −4.15521 | −0.527712 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.26633 | −0.281104 | ||||||||
\(66\) | −1.16554 | −0.143469 | ||||||||
\(67\) | −10.7526 | −1.31364 | −0.656821 | − | 0.754046i | \(-0.728099\pi\) | ||||
−0.656821 | + | 0.754046i | \(0.728099\pi\) | |||||||
\(68\) | 3.43187 | 0.416176 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 3.88888 | 0.461525 | 0.230763 | − | 0.973010i | \(-0.425878\pi\) | ||||
0.230763 | + | 0.973010i | \(0.425878\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −3.05442 | −0.357493 | −0.178747 | − | 0.983895i | \(-0.557204\pi\) | ||||
−0.178747 | + | 0.983895i | \(0.557204\pi\) | |||||||
\(74\) | 0.723336 | 0.0840861 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 5.43187 | 0.623079 | ||||||||
\(77\) | −1.16554 | −0.132826 | ||||||||
\(78\) | −2.26633 | −0.256611 | ||||||||
\(79\) | −1.27666 | −0.143636 | −0.0718180 | − | 0.997418i | \(-0.522880\pi\) | ||||
−0.0718180 | + | 0.997418i | \(0.522880\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.64151 | 0.954295 | ||||||||
\(83\) | 7.76296 | 0.852096 | 0.426048 | − | 0.904701i | \(-0.359906\pi\) | ||||
0.426048 | + | 0.904701i | \(0.359906\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 3.43187 | 0.372239 | ||||||||
\(86\) | 8.42154 | 0.908118 | ||||||||
\(87\) | −4.75263 | −0.509535 | ||||||||
\(88\) | −1.16554 | −0.124247 | ||||||||
\(89\) | −9.52233 | −1.00936 | −0.504682 | − | 0.863305i | \(-0.668390\pi\) | ||||
−0.504682 | + | 0.863305i | \(0.668390\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | −2.26633 | −0.237576 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −4.15521 | −0.430875 | ||||||||
\(94\) | 0.899214 | 0.0927468 | ||||||||
\(95\) | 5.43187 | 0.557299 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −10.1845 | −1.03408 | −0.517040 | − | 0.855961i | \(-0.672966\pi\) | ||||
−0.517040 | + | 0.855961i | \(0.672966\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −1.16554 | −0.117142 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −2.78809 | −0.277426 | −0.138713 | − | 0.990333i | \(-0.544297\pi\) | ||||
−0.138713 | + | 0.990333i | \(0.544297\pi\) | |||||||
\(102\) | 3.43187 | 0.339806 | ||||||||
\(103\) | 4.53266 | 0.446616 | 0.223308 | − | 0.974748i | \(-0.428314\pi\) | ||||
0.223308 | + | 0.974748i | \(0.428314\pi\) | |||||||
\(104\) | −2.26633 | −0.222232 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 3.27666 | 0.318258 | ||||||||
\(107\) | −20.3690 | −1.96915 | −0.984573 | − | 0.174975i | \(-0.944016\pi\) | ||||
−0.984573 | + | 0.174975i | \(0.944016\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 18.3690 | 1.75943 | 0.879716 | − | 0.475500i | \(-0.157733\pi\) | ||||
0.879716 | + | 0.475500i | \(0.157733\pi\) | |||||||
\(110\) | −1.16554 | −0.111130 | ||||||||
\(111\) | 0.723336 | 0.0686560 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 7.80932 | 0.734639 | 0.367320 | − | 0.930095i | \(-0.380275\pi\) | ||||
0.367320 | + | 0.930095i | \(0.380275\pi\) | |||||||
\(114\) | 5.43187 | 0.508742 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | −4.75263 | −0.441270 | ||||||||
\(117\) | −2.26633 | −0.209522 | ||||||||
\(118\) | 5.05442 | 0.465297 | ||||||||
\(119\) | 3.43187 | 0.314599 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −9.64151 | −0.876501 | ||||||||
\(122\) | 6.53266 | 0.591439 | ||||||||
\(123\) | 8.64151 | 0.779178 | ||||||||
\(124\) | −4.15521 | −0.373149 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 2.44221 | 0.216711 | 0.108355 | − | 0.994112i | \(-0.465442\pi\) | ||||
0.108355 | + | 0.994112i | \(0.465442\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 8.42154 | 0.741475 | ||||||||
\(130\) | −2.26633 | −0.198770 | ||||||||
\(131\) | −10.1197 | −0.884166 | −0.442083 | − | 0.896974i | \(-0.645760\pi\) | ||||
−0.442083 | + | 0.896974i | \(0.645760\pi\) | |||||||
\(132\) | −1.16554 | −0.101448 | ||||||||
\(133\) | 5.43187 | 0.471003 | ||||||||
\(134\) | −10.7526 | −0.928886 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 3.43187 | 0.294281 | ||||||||
\(137\) | 16.1197 | 1.37720 | 0.688601 | − | 0.725140i | \(-0.258225\pi\) | ||||
0.688601 | + | 0.725140i | \(0.258225\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | −4.92491 | −0.417725 | −0.208863 | − | 0.977945i | \(-0.566976\pi\) | ||||
−0.208863 | + | 0.977945i | \(0.566976\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 0.899214 | 0.0757275 | ||||||||
\(142\) | 3.88888 | 0.326348 | ||||||||
\(143\) | 2.64151 | 0.220894 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −4.75263 | −0.394684 | ||||||||
\(146\) | −3.05442 | −0.252786 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0.723336 | 0.0594578 | ||||||||
\(149\) | 0.331088 | 0.0271238 | 0.0135619 | − | 0.999908i | \(-0.495683\pi\) | ||||
0.0135619 | + | 0.999908i | \(0.495683\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 8.53266 | 0.694378 | 0.347189 | − | 0.937795i | \(-0.387136\pi\) | ||||
0.347189 | + | 0.937795i | \(0.387136\pi\) | |||||||
\(152\) | 5.43187 | 0.440583 | ||||||||
\(153\) | 3.43187 | 0.277451 | ||||||||
\(154\) | −1.16554 | −0.0939222 | ||||||||
\(155\) | −4.15521 | −0.333754 | ||||||||
\(156\) | −2.26633 | −0.181452 | ||||||||
\(157\) | 13.7068 | 1.09392 | 0.546962 | − | 0.837157i | \(-0.315784\pi\) | ||||
0.546962 | + | 0.837157i | \(0.315784\pi\) | |||||||
\(158\) | −1.27666 | −0.101566 | ||||||||
\(159\) | 3.27666 | 0.259856 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −1.35849 | −0.106405 | −0.0532027 | − | 0.998584i | \(-0.516943\pi\) | ||||
−0.0532027 | + | 0.998584i | \(0.516943\pi\) | |||||||
\(164\) | 8.64151 | 0.674788 | ||||||||
\(165\) | −1.16554 | −0.0907375 | ||||||||
\(166\) | 7.76296 | 0.602523 | ||||||||
\(167\) | 20.6060 | 1.59454 | 0.797272 | − | 0.603621i | \(-0.206276\pi\) | ||||
0.797272 | + | 0.603621i | \(0.206276\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | −7.86375 | −0.604904 | ||||||||
\(170\) | 3.43187 | 0.263213 | ||||||||
\(171\) | 5.43187 | 0.415386 | ||||||||
\(172\) | 8.42154 | 0.642136 | ||||||||
\(173\) | 1.62255 | 0.123360 | 0.0616801 | − | 0.998096i | \(-0.480354\pi\) | ||||
0.0616801 | + | 0.998096i | \(0.480354\pi\) | |||||||
\(174\) | −4.75263 | −0.360296 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −1.16554 | −0.0878562 | ||||||||
\(177\) | 5.05442 | 0.379914 | ||||||||
\(178\) | −9.52233 | −0.713728 | ||||||||
\(179\) | −12.8431 | −0.959937 | −0.479968 | − | 0.877286i | \(-0.659352\pi\) | ||||
−0.479968 | + | 0.877286i | \(0.659352\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −13.0860 | −0.972674 | −0.486337 | − | 0.873771i | \(-0.661667\pi\) | ||||
−0.486337 | + | 0.873771i | \(0.661667\pi\) | |||||||
\(182\) | −2.26633 | −0.167992 | ||||||||
\(183\) | 6.53266 | 0.482908 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 0.723336 | 0.0531807 | ||||||||
\(186\) | −4.15521 | −0.304675 | ||||||||
\(187\) | −4.00000 | −0.292509 | ||||||||
\(188\) | 0.899214 | 0.0655819 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 5.43187 | 0.394070 | ||||||||
\(191\) | 19.0923 | 1.38147 | 0.690737 | − | 0.723106i | \(-0.257286\pi\) | ||||
0.690737 | + | 0.723106i | \(0.257286\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −20.3897 | −1.46768 | −0.733840 | − | 0.679322i | \(-0.762274\pi\) | ||||
−0.733840 | + | 0.679322i | \(0.762274\pi\) | |||||||
\(194\) | −10.1845 | −0.731205 | ||||||||
\(195\) | −2.26633 | −0.162295 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 6.31042 | 0.449599 | 0.224799 | − | 0.974405i | \(-0.427827\pi\) | ||||
0.224799 | + | 0.974405i | \(0.427827\pi\) | |||||||
\(198\) | −1.16554 | −0.0828316 | ||||||||
\(199\) | −2.33109 | −0.165246 | −0.0826232 | − | 0.996581i | \(-0.526330\pi\) | ||||
−0.0826232 | + | 0.996581i | \(0.526330\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −10.7526 | −0.758432 | ||||||||
\(202\) | −2.78809 | −0.196170 | ||||||||
\(203\) | −4.75263 | −0.333569 | ||||||||
\(204\) | 3.43187 | 0.240279 | ||||||||
\(205\) | 8.64151 | 0.603549 | ||||||||
\(206\) | 4.53266 | 0.315805 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −2.26633 | −0.157142 | ||||||||
\(209\) | −6.33109 | −0.437931 | ||||||||
\(210\) | 1.00000 | 0.0690066 | ||||||||
\(211\) | 26.1674 | 1.80144 | 0.900720 | − | 0.434400i | \(-0.143040\pi\) | ||||
0.900720 | + | 0.434400i | \(0.143040\pi\) | |||||||
\(212\) | 3.27666 | 0.225042 | ||||||||
\(213\) | 3.88888 | 0.266462 | ||||||||
\(214\) | −20.3690 | −1.39240 | ||||||||
\(215\) | 8.42154 | 0.574344 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −4.15521 | −0.282074 | ||||||||
\(218\) | 18.3690 | 1.24411 | ||||||||
\(219\) | −3.05442 | −0.206399 | ||||||||
\(220\) | −1.16554 | −0.0785810 | ||||||||
\(221\) | −7.77776 | −0.523189 | ||||||||
\(222\) | 0.723336 | 0.0485471 | ||||||||
\(223\) | −22.6038 | −1.51366 | −0.756830 | − | 0.653612i | \(-0.773253\pi\) | ||||
−0.756830 | + | 0.653612i | \(0.773253\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 7.80932 | 0.519469 | ||||||||
\(227\) | −29.2682 | −1.94260 | −0.971300 | − | 0.237858i | \(-0.923555\pi\) | ||||
−0.971300 | + | 0.237858i | \(0.923555\pi\) | |||||||
\(228\) | 5.43187 | 0.359735 | ||||||||
\(229\) | −7.66891 | −0.506776 | −0.253388 | − | 0.967365i | \(-0.581545\pi\) | ||||
−0.253388 | + | 0.967365i | \(0.581545\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | −1.16554 | −0.0766872 | ||||||||
\(232\) | −4.75263 | −0.312025 | ||||||||
\(233\) | −26.3690 | −1.72749 | −0.863745 | − | 0.503928i | \(-0.831888\pi\) | ||||
−0.863745 | + | 0.503928i | \(0.831888\pi\) | |||||||
\(234\) | −2.26633 | −0.148155 | ||||||||
\(235\) | 0.899214 | 0.0586582 | ||||||||
\(236\) | 5.05442 | 0.329015 | ||||||||
\(237\) | −1.27666 | −0.0829283 | ||||||||
\(238\) | 3.43187 | 0.222455 | ||||||||
\(239\) | −4.11112 | −0.265926 | −0.132963 | − | 0.991121i | \(-0.542449\pi\) | ||||
−0.132963 | + | 0.991121i | \(0.542449\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −21.4698 | −1.38299 | −0.691495 | − | 0.722381i | \(-0.743048\pi\) | ||||
−0.691495 | + | 0.722381i | \(0.743048\pi\) | |||||||
\(242\) | −9.64151 | −0.619780 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 6.53266 | 0.418211 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 8.64151 | 0.550962 | ||||||||
\(247\) | −12.3104 | −0.783293 | ||||||||
\(248\) | −4.15521 | −0.263856 | ||||||||
\(249\) | 7.76296 | 0.491958 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −16.4949 | −1.04115 | −0.520575 | − | 0.853816i | \(-0.674282\pi\) | ||||
−0.520575 | + | 0.853816i | \(0.674282\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −1.16554 | −0.0732771 | ||||||||
\(254\) | 2.44221 | 0.153238 | ||||||||
\(255\) | 3.43187 | 0.214912 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.7887 | 1.35914 | 0.679570 | − | 0.733611i | \(-0.262167\pi\) | ||||
0.679570 | + | 0.733611i | \(0.262167\pi\) | |||||||
\(258\) | 8.42154 | 0.524302 | ||||||||
\(259\) | 0.723336 | 0.0449459 | ||||||||
\(260\) | −2.26633 | −0.140552 | ||||||||
\(261\) | −4.75263 | −0.294180 | ||||||||
\(262\) | −10.1197 | −0.625200 | ||||||||
\(263\) | −14.8637 | −0.916538 | −0.458269 | − | 0.888814i | \(-0.651530\pi\) | ||||
−0.458269 | + | 0.888814i | \(0.651530\pi\) | |||||||
\(264\) | −1.16554 | −0.0717343 | ||||||||
\(265\) | 3.27666 | 0.201284 | ||||||||
\(266\) | 5.43187 | 0.333050 | ||||||||
\(267\) | −9.52233 | −0.582757 | ||||||||
\(268\) | −10.7526 | −0.656821 | ||||||||
\(269\) | 6.05499 | 0.369179 | 0.184590 | − | 0.982816i | \(-0.440904\pi\) | ||||
0.184590 | + | 0.982816i | \(0.440904\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −5.22053 | −0.317125 | −0.158562 | − | 0.987349i | \(-0.550686\pi\) | ||||
−0.158562 | + | 0.987349i | \(0.550686\pi\) | |||||||
\(272\) | 3.43187 | 0.208088 | ||||||||
\(273\) | −2.26633 | −0.137165 | ||||||||
\(274\) | 16.1197 | 0.973829 | ||||||||
\(275\) | −1.16554 | −0.0702849 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | 1.35622 | 0.0814873 | 0.0407437 | − | 0.999170i | \(-0.487027\pi\) | ||||
0.0407437 | + | 0.999170i | \(0.487027\pi\) | |||||||
\(278\) | −4.92491 | −0.295376 | ||||||||
\(279\) | −4.15521 | −0.248766 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −15.9268 | −0.950113 | −0.475056 | − | 0.879955i | \(-0.657572\pi\) | ||||
−0.475056 | + | 0.879955i | \(0.657572\pi\) | |||||||
\(282\) | 0.899214 | 0.0535474 | ||||||||
\(283\) | −7.21191 | −0.428703 | −0.214352 | − | 0.976757i | \(-0.568764\pi\) | ||||
−0.214352 | + | 0.976757i | \(0.568764\pi\) | |||||||
\(284\) | 3.88888 | 0.230763 | ||||||||
\(285\) | 5.43187 | 0.321756 | ||||||||
\(286\) | 2.64151 | 0.156196 | ||||||||
\(287\) | 8.64151 | 0.510092 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −5.22224 | −0.307191 | ||||||||
\(290\) | −4.75263 | −0.279084 | ||||||||
\(291\) | −10.1845 | −0.597026 | ||||||||
\(292\) | −3.05442 | −0.178747 | ||||||||
\(293\) | 0.863748 | 0.0504607 | 0.0252303 | − | 0.999682i | \(-0.491968\pi\) | ||||
0.0252303 | + | 0.999682i | \(0.491968\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | 5.05442 | 0.294280 | ||||||||
\(296\) | 0.723336 | 0.0420430 | ||||||||
\(297\) | −1.16554 | −0.0676317 | ||||||||
\(298\) | 0.331088 | 0.0191794 | ||||||||
\(299\) | −2.26633 | −0.131065 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 8.42154 | 0.485409 | ||||||||
\(302\) | 8.53266 | 0.490999 | ||||||||
\(303\) | −2.78809 | −0.160172 | ||||||||
\(304\) | 5.43187 | 0.311539 | ||||||||
\(305\) | 6.53266 | 0.374059 | ||||||||
\(306\) | 3.43187 | 0.196187 | ||||||||
\(307\) | −2.80516 | −0.160099 | −0.0800496 | − | 0.996791i | \(-0.525508\pi\) | ||||
−0.0800496 | + | 0.996791i | \(0.525508\pi\) | |||||||
\(308\) | −1.16554 | −0.0664130 | ||||||||
\(309\) | 4.53266 | 0.257854 | ||||||||
\(310\) | −4.15521 | −0.236000 | ||||||||
\(311\) | 16.0441 | 0.909777 | 0.454888 | − | 0.890548i | \(-0.349679\pi\) | ||||
0.454888 | + | 0.890548i | \(0.349679\pi\) | |||||||
\(312\) | −2.26633 | −0.128306 | ||||||||
\(313\) | −4.36883 | −0.246941 | −0.123470 | − | 0.992348i | \(-0.539402\pi\) | ||||
−0.123470 | + | 0.992348i | \(0.539402\pi\) | |||||||
\(314\) | 13.7068 | 0.773521 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | −1.27666 | −0.0718180 | ||||||||
\(317\) | 28.2602 | 1.58725 | 0.793624 | − | 0.608408i | \(-0.208192\pi\) | ||||
0.793624 | + | 0.608408i | \(0.208192\pi\) | |||||||
\(318\) | 3.27666 | 0.183746 | ||||||||
\(319\) | 5.53940 | 0.310147 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −20.3690 | −1.13689 | ||||||||
\(322\) | 1.00000 | 0.0557278 | ||||||||
\(323\) | 18.6415 | 1.03724 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.26633 | −0.125713 | ||||||||
\(326\) | −1.35849 | −0.0752400 | ||||||||
\(327\) | 18.3690 | 1.01581 | ||||||||
\(328\) | 8.64151 | 0.477147 | ||||||||
\(329\) | 0.899214 | 0.0495753 | ||||||||
\(330\) | −1.16554 | −0.0641611 | ||||||||
\(331\) | 8.31042 | 0.456782 | 0.228391 | − | 0.973569i | \(-0.426654\pi\) | ||||
0.228391 | + | 0.973569i | \(0.426654\pi\) | |||||||
\(332\) | 7.76296 | 0.426048 | ||||||||
\(333\) | 0.723336 | 0.0396386 | ||||||||
\(334\) | 20.6060 | 1.12751 | ||||||||
\(335\) | −10.7526 | −0.587479 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | −0.834456 | −0.0454557 | −0.0227279 | − | 0.999742i | \(-0.507235\pi\) | ||||
−0.0227279 | + | 0.999742i | \(0.507235\pi\) | |||||||
\(338\) | −7.86375 | −0.427732 | ||||||||
\(339\) | 7.80932 | 0.424144 | ||||||||
\(340\) | 3.43187 | 0.186120 | ||||||||
\(341\) | 4.84308 | 0.262267 | ||||||||
\(342\) | 5.43187 | 0.293722 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 8.42154 | 0.454059 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | 1.62255 | 0.0872288 | ||||||||
\(347\) | −14.6415 | −0.785997 | −0.392999 | − | 0.919539i | \(-0.628562\pi\) | ||||
−0.392999 | + | 0.919539i | \(0.628562\pi\) | |||||||
\(348\) | −4.75263 | −0.254768 | ||||||||
\(349\) | −18.2029 | −0.974379 | −0.487189 | − | 0.873296i | \(-0.661978\pi\) | ||||
−0.487189 | + | 0.873296i | \(0.661978\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −2.26633 | −0.120968 | ||||||||
\(352\) | −1.16554 | −0.0621237 | ||||||||
\(353\) | −13.3855 | −0.712439 | −0.356219 | − | 0.934402i | \(-0.615934\pi\) | ||||
−0.356219 | + | 0.934402i | \(0.615934\pi\) | |||||||
\(354\) | 5.05442 | 0.268640 | ||||||||
\(355\) | 3.88888 | 0.206400 | ||||||||
\(356\) | −9.52233 | −0.504682 | ||||||||
\(357\) | 3.43187 | 0.181634 | ||||||||
\(358\) | −12.8431 | −0.678778 | ||||||||
\(359\) | −18.0270 | −0.951430 | −0.475715 | − | 0.879600i | \(-0.657811\pi\) | ||||
−0.475715 | + | 0.879600i | \(0.657811\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 10.5053 | 0.552908 | ||||||||
\(362\) | −13.0860 | −0.687784 | ||||||||
\(363\) | −9.64151 | −0.506048 | ||||||||
\(364\) | −2.26633 | −0.118788 | ||||||||
\(365\) | −3.05442 | −0.159876 | ||||||||
\(366\) | 6.53266 | 0.341468 | ||||||||
\(367\) | 25.8157 | 1.34757 | 0.673784 | − | 0.738929i | \(-0.264668\pi\) | ||||
0.673784 | + | 0.738929i | \(0.264668\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 8.64151 | 0.449859 | ||||||||
\(370\) | 0.723336 | 0.0376044 | ||||||||
\(371\) | 3.27666 | 0.170116 | ||||||||
\(372\) | −4.15521 | −0.215438 | ||||||||
\(373\) | −19.2353 | −0.995967 | −0.497984 | − | 0.867186i | \(-0.665926\pi\) | ||||
−0.497984 | + | 0.867186i | \(0.665926\pi\) | |||||||
\(374\) | −4.00000 | −0.206835 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0.899214 | 0.0463734 | ||||||||
\(377\) | 10.7710 | 0.554736 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | −7.03376 | −0.361300 | −0.180650 | − | 0.983547i | \(-0.557820\pi\) | ||||
−0.180650 | + | 0.983547i | \(0.557820\pi\) | |||||||
\(380\) | 5.43187 | 0.278649 | ||||||||
\(381\) | 2.44221 | 0.125118 | ||||||||
\(382\) | 19.0923 | 0.976849 | ||||||||
\(383\) | 25.9084 | 1.32386 | 0.661929 | − | 0.749567i | \(-0.269738\pi\) | ||||
0.661929 | + | 0.749567i | \(0.269738\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −1.16554 | −0.0594016 | ||||||||
\(386\) | −20.3897 | −1.03781 | ||||||||
\(387\) | 8.42154 | 0.428091 | ||||||||
\(388\) | −10.1845 | −0.517040 | ||||||||
\(389\) | 11.3244 | 0.574167 | 0.287084 | − | 0.957905i | \(-0.407314\pi\) | ||||
0.287084 | + | 0.957905i | \(0.407314\pi\) | |||||||
\(390\) | −2.26633 | −0.114760 | ||||||||
\(391\) | 3.43187 | 0.173557 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −10.1197 | −0.510474 | ||||||||
\(394\) | 6.31042 | 0.317914 | ||||||||
\(395\) | −1.27666 | −0.0642360 | ||||||||
\(396\) | −1.16554 | −0.0585708 | ||||||||
\(397\) | −34.7235 | −1.74272 | −0.871362 | − | 0.490641i | \(-0.836762\pi\) | ||||
−0.871362 | + | 0.490641i | \(0.836762\pi\) | |||||||
\(398\) | −2.33109 | −0.116847 | ||||||||
\(399\) | 5.43187 | 0.271934 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 35.1423 | 1.75492 | 0.877461 | − | 0.479647i | \(-0.159235\pi\) | ||||
0.877461 | + | 0.479647i | \(0.159235\pi\) | |||||||
\(402\) | −10.7526 | −0.536292 | ||||||||
\(403\) | 9.41708 | 0.469098 | ||||||||
\(404\) | −2.78809 | −0.138713 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −4.75263 | −0.235869 | ||||||||
\(407\) | −0.843080 | −0.0417899 | ||||||||
\(408\) | 3.43187 | 0.169903 | ||||||||
\(409\) | −6.47408 | −0.320122 | −0.160061 | − | 0.987107i | \(-0.551169\pi\) | ||||
−0.160061 | + | 0.987107i | \(0.551169\pi\) | |||||||
\(410\) | 8.64151 | 0.426774 | ||||||||
\(411\) | 16.1197 | 0.795128 | ||||||||
\(412\) | 4.53266 | 0.223308 | ||||||||
\(413\) | 5.05442 | 0.248712 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 7.76296 | 0.381069 | ||||||||
\(416\) | −2.26633 | −0.111116 | ||||||||
\(417\) | −4.92491 | −0.241174 | ||||||||
\(418\) | −6.33109 | −0.309664 | ||||||||
\(419\) | 12.5876 | 0.614947 | 0.307473 | − | 0.951557i | \(-0.400516\pi\) | ||||
0.307473 | + | 0.951557i | \(0.400516\pi\) | |||||||
\(420\) | 1.00000 | 0.0487950 | ||||||||
\(421\) | 24.1306 | 1.17606 | 0.588028 | − | 0.808841i | \(-0.299905\pi\) | ||||
0.588028 | + | 0.808841i | \(0.299905\pi\) | |||||||
\(422\) | 26.1674 | 1.27381 | ||||||||
\(423\) | 0.899214 | 0.0437213 | ||||||||
\(424\) | 3.27666 | 0.159129 | ||||||||
\(425\) | 3.43187 | 0.166470 | ||||||||
\(426\) | 3.88888 | 0.188417 | ||||||||
\(427\) | 6.53266 | 0.316138 | ||||||||
\(428\) | −20.3690 | −0.984573 | ||||||||
\(429\) | 2.64151 | 0.127533 | ||||||||
\(430\) | 8.42154 | 0.406123 | ||||||||
\(431\) | 15.5664 | 0.749808 | 0.374904 | − | 0.927064i | \(-0.377676\pi\) | ||||
0.374904 | + | 0.927064i | \(0.377676\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −4.90149 | −0.235550 | −0.117775 | − | 0.993040i | \(-0.537576\pi\) | ||||
−0.117775 | + | 0.993040i | \(0.537576\pi\) | |||||||
\(434\) | −4.15521 | −0.199456 | ||||||||
\(435\) | −4.75263 | −0.227871 | ||||||||
\(436\) | 18.3690 | 0.879716 | ||||||||
\(437\) | 5.43187 | 0.259842 | ||||||||
\(438\) | −3.05442 | −0.145946 | ||||||||
\(439\) | −3.62255 | −0.172895 | −0.0864474 | − | 0.996256i | \(-0.527551\pi\) | ||||
−0.0864474 | + | 0.996256i | \(0.527551\pi\) | |||||||
\(440\) | −1.16554 | −0.0555651 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −7.77776 | −0.369950 | ||||||||
\(443\) | 14.6415 | 0.695639 | 0.347820 | − | 0.937562i | \(-0.386922\pi\) | ||||
0.347820 | + | 0.937562i | \(0.386922\pi\) | |||||||
\(444\) | 0.723336 | 0.0343280 | ||||||||
\(445\) | −9.52233 | −0.451402 | ||||||||
\(446\) | −22.6038 | −1.07032 | ||||||||
\(447\) | 0.331088 | 0.0156599 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −23.9497 | −1.13026 | −0.565129 | − | 0.825003i | \(-0.691174\pi\) | ||||
−0.565129 | + | 0.825003i | \(0.691174\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −10.0721 | −0.474275 | ||||||||
\(452\) | 7.80932 | 0.367320 | ||||||||
\(453\) | 8.53266 | 0.400899 | ||||||||
\(454\) | −29.2682 | −1.37363 | ||||||||
\(455\) | −2.26633 | −0.106247 | ||||||||
\(456\) | 5.43187 | 0.254371 | ||||||||
\(457\) | −22.6501 | −1.05953 | −0.529764 | − | 0.848145i | \(-0.677720\pi\) | ||||
−0.529764 | + | 0.848145i | \(0.677720\pi\) | |||||||
\(458\) | −7.66891 | −0.358345 | ||||||||
\(459\) | 3.43187 | 0.160186 | ||||||||
\(460\) | 1.00000 | 0.0466252 | ||||||||
\(461\) | −24.5156 | −1.14180 | −0.570902 | − | 0.821018i | \(-0.693407\pi\) | ||||
−0.570902 | + | 0.821018i | \(0.693407\pi\) | |||||||
\(462\) | −1.16554 | −0.0542260 | ||||||||
\(463\) | 26.8112 | 1.24602 | 0.623011 | − | 0.782213i | \(-0.285909\pi\) | ||||
0.623011 | + | 0.782213i | \(0.285909\pi\) | |||||||
\(464\) | −4.75263 | −0.220635 | ||||||||
\(465\) | −4.15521 | −0.192693 | ||||||||
\(466\) | −26.3690 | −1.22152 | ||||||||
\(467\) | 3.83389 | 0.177411 | 0.0887057 | − | 0.996058i | \(-0.471727\pi\) | ||||
0.0887057 | + | 0.996058i | \(0.471727\pi\) | |||||||
\(468\) | −2.26633 | −0.104761 | ||||||||
\(469\) | −10.7526 | −0.496510 | ||||||||
\(470\) | 0.899214 | 0.0414776 | ||||||||
\(471\) | 13.7068 | 0.631577 | ||||||||
\(472\) | 5.05442 | 0.232649 | ||||||||
\(473\) | −9.81567 | −0.451325 | ||||||||
\(474\) | −1.27666 | −0.0586391 | ||||||||
\(475\) | 5.43187 | 0.249231 | ||||||||
\(476\) | 3.43187 | 0.157300 | ||||||||
\(477\) | 3.27666 | 0.150028 | ||||||||
\(478\) | −4.11112 | −0.188038 | ||||||||
\(479\) | −14.6415 | −0.668988 | −0.334494 | − | 0.942398i | \(-0.608565\pi\) | ||||
−0.334494 | + | 0.942398i | \(0.608565\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −1.63932 | −0.0747464 | ||||||||
\(482\) | −21.4698 | −0.977922 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | −9.64151 | −0.438250 | ||||||||
\(485\) | −10.1845 | −0.462454 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −0.199299 | −0.00903110 | −0.00451555 | − | 0.999990i | \(-0.501437\pi\) | ||||
−0.00451555 | + | 0.999990i | \(0.501437\pi\) | |||||||
\(488\) | 6.53266 | 0.295720 | ||||||||
\(489\) | −1.35849 | −0.0614332 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 22.0379 | 0.994557 | 0.497279 | − | 0.867591i | \(-0.334333\pi\) | ||||
0.497279 | + | 0.867591i | \(0.334333\pi\) | |||||||
\(492\) | 8.64151 | 0.389589 | ||||||||
\(493\) | −16.3104 | −0.734584 | ||||||||
\(494\) | −12.3104 | −0.553872 | ||||||||
\(495\) | −1.16554 | −0.0523873 | ||||||||
\(496\) | −4.15521 | −0.186574 | ||||||||
\(497\) | 3.88888 | 0.174440 | ||||||||
\(498\) | 7.76296 | 0.347867 | ||||||||
\(499\) | −2.49474 | −0.111680 | −0.0558401 | − | 0.998440i | \(-0.517784\pi\) | ||||
−0.0558401 | + | 0.998440i | \(0.517784\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 20.6060 | 0.920610 | ||||||||
\(502\) | −16.4949 | −0.736204 | ||||||||
\(503\) | −36.9944 | −1.64950 | −0.824749 | − | 0.565499i | \(-0.808684\pi\) | ||||
−0.824749 | + | 0.565499i | \(0.808684\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −2.78809 | −0.124069 | ||||||||
\(506\) | −1.16554 | −0.0518147 | ||||||||
\(507\) | −7.86375 | −0.349241 | ||||||||
\(508\) | 2.44221 | 0.108355 | ||||||||
\(509\) | 25.7104 | 1.13959 | 0.569797 | − | 0.821785i | \(-0.307022\pi\) | ||||
0.569797 | + | 0.821785i | \(0.307022\pi\) | |||||||
\(510\) | 3.43187 | 0.151966 | ||||||||
\(511\) | −3.05442 | −0.135120 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.43187 | 0.239823 | ||||||||
\(514\) | 21.7887 | 0.961056 | ||||||||
\(515\) | 4.53266 | 0.199733 | ||||||||
\(516\) | 8.42154 | 0.370738 | ||||||||
\(517\) | −1.04807 | −0.0460942 | ||||||||
\(518\) | 0.723336 | 0.0317815 | ||||||||
\(519\) | 1.62255 | 0.0712220 | ||||||||
\(520\) | −2.26633 | −0.0993851 | ||||||||
\(521\) | −38.8053 | −1.70009 | −0.850046 | − | 0.526708i | \(-0.823426\pi\) | ||||
−0.850046 | + | 0.526708i | \(0.823426\pi\) | |||||||
\(522\) | −4.75263 | −0.208017 | ||||||||
\(523\) | 10.9187 | 0.477443 | 0.238721 | − | 0.971088i | \(-0.423272\pi\) | ||||
0.238721 | + | 0.971088i | \(0.423272\pi\) | |||||||
\(524\) | −10.1197 | −0.442083 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | −14.8637 | −0.648090 | ||||||||
\(527\) | −14.2602 | −0.621182 | ||||||||
\(528\) | −1.16554 | −0.0507238 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 3.27666 | 0.142329 | ||||||||
\(531\) | 5.05442 | 0.219343 | ||||||||
\(532\) | 5.43187 | 0.235502 | ||||||||
\(533\) | −19.5845 | −0.848299 | ||||||||
\(534\) | −9.52233 | −0.412071 | ||||||||
\(535\) | −20.3690 | −0.880629 | ||||||||
\(536\) | −10.7526 | −0.464443 | ||||||||
\(537\) | −12.8431 | −0.554220 | ||||||||
\(538\) | 6.05499 | 0.261049 | ||||||||
\(539\) | −1.16554 | −0.0502035 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −3.88661 | −0.167098 | −0.0835491 | − | 0.996504i | \(-0.526626\pi\) | ||||
−0.0835491 | + | 0.996504i | \(0.526626\pi\) | |||||||
\(542\) | −5.22053 | −0.224241 | ||||||||
\(543\) | −13.0860 | −0.561574 | ||||||||
\(544\) | 3.43187 | 0.147140 | ||||||||
\(545\) | 18.3690 | 0.786842 | ||||||||
\(546\) | −2.26633 | −0.0969900 | ||||||||
\(547\) | 10.7297 | 0.458768 | 0.229384 | − | 0.973336i | \(-0.426329\pi\) | ||||
0.229384 | + | 0.973336i | \(0.426329\pi\) | |||||||
\(548\) | 16.1197 | 0.688601 | ||||||||
\(549\) | 6.53266 | 0.278807 | ||||||||
\(550\) | −1.16554 | −0.0496990 | ||||||||
\(551\) | −25.8157 | −1.09978 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | −1.27666 | −0.0542893 | ||||||||
\(554\) | 1.35622 | 0.0576202 | ||||||||
\(555\) | 0.723336 | 0.0307039 | ||||||||
\(556\) | −4.92491 | −0.208863 | ||||||||
\(557\) | 28.8701 | 1.22327 | 0.611633 | − | 0.791142i | \(-0.290513\pi\) | ||||
0.611633 | + | 0.791142i | \(0.290513\pi\) | |||||||
\(558\) | −4.15521 | −0.175904 | ||||||||
\(559\) | −19.0860 | −0.807251 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | −15.9268 | −0.671831 | ||||||||
\(563\) | −38.5854 | −1.62618 | −0.813090 | − | 0.582138i | \(-0.802216\pi\) | ||||
−0.813090 | + | 0.582138i | \(0.802216\pi\) | |||||||
\(564\) | 0.899214 | 0.0378637 | ||||||||
\(565\) | 7.80932 | 0.328541 | ||||||||
\(566\) | −7.21191 | −0.303139 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 3.88888 | 0.163174 | ||||||||
\(569\) | −26.7024 | −1.11942 | −0.559711 | − | 0.828688i | \(-0.689088\pi\) | ||||
−0.559711 | + | 0.828688i | \(0.689088\pi\) | |||||||
\(570\) | 5.43187 | 0.227516 | ||||||||
\(571\) | 6.72334 | 0.281363 | 0.140681 | − | 0.990055i | \(-0.455071\pi\) | ||||
0.140681 | + | 0.990055i | \(0.455071\pi\) | |||||||
\(572\) | 2.64151 | 0.110447 | ||||||||
\(573\) | 19.0923 | 0.797594 | ||||||||
\(574\) | 8.64151 | 0.360690 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −21.7887 | −0.907074 | −0.453537 | − | 0.891238i | \(-0.649838\pi\) | ||||
−0.453537 | + | 0.891238i | \(0.649838\pi\) | |||||||
\(578\) | −5.22224 | −0.217217 | ||||||||
\(579\) | −20.3897 | −0.847366 | ||||||||
\(580\) | −4.75263 | −0.197342 | ||||||||
\(581\) | 7.76296 | 0.322062 | ||||||||
\(582\) | −10.1845 | −0.422161 | ||||||||
\(583\) | −3.81910 | −0.158171 | ||||||||
\(584\) | −3.05442 | −0.126393 | ||||||||
\(585\) | −2.26633 | −0.0937012 | ||||||||
\(586\) | 0.863748 | 0.0356811 | ||||||||
\(587\) | 48.2981 | 1.99347 | 0.996737 | − | 0.0807131i | \(-0.0257197\pi\) | ||||
0.996737 | + | 0.0807131i | \(0.0257197\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | −22.5706 | −0.930004 | ||||||||
\(590\) | 5.05442 | 0.208087 | ||||||||
\(591\) | 6.31042 | 0.259576 | ||||||||
\(592\) | 0.723336 | 0.0297289 | ||||||||
\(593\) | 15.2767 | 0.627337 | 0.313669 | − | 0.949532i | \(-0.398442\pi\) | ||||
0.313669 | + | 0.949532i | \(0.398442\pi\) | |||||||
\(594\) | −1.16554 | −0.0478228 | ||||||||
\(595\) | 3.43187 | 0.140693 | ||||||||
\(596\) | 0.331088 | 0.0135619 | ||||||||
\(597\) | −2.33109 | −0.0954051 | ||||||||
\(598\) | −2.26633 | −0.0926771 | ||||||||
\(599\) | 22.3667 | 0.913880 | 0.456940 | − | 0.889498i | \(-0.348945\pi\) | ||||
0.456940 | + | 0.889498i | \(0.348945\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 23.5638 | 0.961189 | 0.480595 | − | 0.876943i | \(-0.340421\pi\) | ||||
0.480595 | + | 0.876943i | \(0.340421\pi\) | |||||||
\(602\) | 8.42154 | 0.343236 | ||||||||
\(603\) | −10.7526 | −0.437881 | ||||||||
\(604\) | 8.53266 | 0.347189 | ||||||||
\(605\) | −9.64151 | −0.391983 | ||||||||
\(606\) | −2.78809 | −0.113259 | ||||||||
\(607\) | −2.33469 | −0.0947620 | −0.0473810 | − | 0.998877i | \(-0.515087\pi\) | ||||
−0.0473810 | + | 0.998877i | \(0.515087\pi\) | |||||||
\(608\) | 5.43187 | 0.220292 | ||||||||
\(609\) | −4.75263 | −0.192586 | ||||||||
\(610\) | 6.53266 | 0.264500 | ||||||||
\(611\) | −2.03792 | −0.0824452 | ||||||||
\(612\) | 3.43187 | 0.138725 | ||||||||
\(613\) | 9.16327 | 0.370101 | 0.185051 | − | 0.982729i | \(-0.440755\pi\) | ||||
0.185051 | + | 0.982729i | \(0.440755\pi\) | |||||||
\(614\) | −2.80516 | −0.113207 | ||||||||
\(615\) | 8.64151 | 0.348459 | ||||||||
\(616\) | −1.16554 | −0.0469611 | ||||||||
\(617\) | −3.89750 | −0.156908 | −0.0784538 | − | 0.996918i | \(-0.524998\pi\) | ||||
−0.0784538 | + | 0.996918i | \(0.524998\pi\) | |||||||
\(618\) | 4.53266 | 0.182330 | ||||||||
\(619\) | −28.4837 | −1.14486 | −0.572429 | − | 0.819954i | \(-0.693999\pi\) | ||||
−0.572429 | + | 0.819954i | \(0.693999\pi\) | |||||||
\(620\) | −4.15521 | −0.166877 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 16.0441 | 0.643309 | ||||||||
\(623\) | −9.52233 | −0.381504 | ||||||||
\(624\) | −2.26633 | −0.0907258 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −4.36883 | −0.174613 | ||||||||
\(627\) | −6.33109 | −0.252839 | ||||||||
\(628\) | 13.7068 | 0.546962 | ||||||||
\(629\) | 2.48240 | 0.0989796 | ||||||||
\(630\) | 1.00000 | 0.0398410 | ||||||||
\(631\) | −40.6903 | −1.61986 | −0.809928 | − | 0.586529i | \(-0.800494\pi\) | ||||
−0.809928 | + | 0.586529i | \(0.800494\pi\) | |||||||
\(632\) | −1.27666 | −0.0507830 | ||||||||
\(633\) | 26.1674 | 1.04006 | ||||||||
\(634\) | 28.2602 | 1.12235 | ||||||||
\(635\) | 2.44221 | 0.0969161 | ||||||||
\(636\) | 3.27666 | 0.129928 | ||||||||
\(637\) | −2.26633 | −0.0897953 | ||||||||
\(638\) | 5.53940 | 0.219307 | ||||||||
\(639\) | 3.88888 | 0.153842 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −39.3060 | −1.55249 | −0.776246 | − | 0.630430i | \(-0.782879\pi\) | ||||
−0.776246 | + | 0.630430i | \(0.782879\pi\) | |||||||
\(642\) | −20.3690 | −0.803900 | ||||||||
\(643\) | 1.37934 | 0.0543958 | 0.0271979 | − | 0.999630i | \(-0.491342\pi\) | ||||
0.0271979 | + | 0.999630i | \(0.491342\pi\) | |||||||
\(644\) | 1.00000 | 0.0394055 | ||||||||
\(645\) | 8.42154 | 0.331598 | ||||||||
\(646\) | 18.6415 | 0.733440 | ||||||||
\(647\) | −16.7356 | −0.657943 | −0.328971 | − | 0.944340i | \(-0.606702\pi\) | ||||
−0.328971 | + | 0.944340i | \(0.606702\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −5.89115 | −0.231248 | ||||||||
\(650\) | −2.26633 | −0.0888928 | ||||||||
\(651\) | −4.15521 | −0.162856 | ||||||||
\(652\) | −1.35849 | −0.0532027 | ||||||||
\(653\) | 27.3416 | 1.06996 | 0.534980 | − | 0.844865i | \(-0.320319\pi\) | ||||
0.534980 | + | 0.844865i | \(0.320319\pi\) | |||||||
\(654\) | 18.3690 | 0.718285 | ||||||||
\(655\) | −10.1197 | −0.395411 | ||||||||
\(656\) | 8.64151 | 0.337394 | ||||||||
\(657\) | −3.05442 | −0.119164 | ||||||||
\(658\) | 0.899214 | 0.0350550 | ||||||||
\(659\) | 6.70039 | 0.261010 | 0.130505 | − | 0.991448i | \(-0.458340\pi\) | ||||
0.130505 | + | 0.991448i | \(0.458340\pi\) | |||||||
\(660\) | −1.16554 | −0.0453687 | ||||||||
\(661\) | 10.1809 | 0.395991 | 0.197996 | − | 0.980203i | \(-0.436557\pi\) | ||||
0.197996 | + | 0.980203i | \(0.436557\pi\) | |||||||
\(662\) | 8.31042 | 0.322994 | ||||||||
\(663\) | −7.77776 | −0.302063 | ||||||||
\(664\) | 7.76296 | 0.301261 | ||||||||
\(665\) | 5.43187 | 0.210639 | ||||||||
\(666\) | 0.723336 | 0.0280287 | ||||||||
\(667\) | −4.75263 | −0.184022 | ||||||||
\(668\) | 20.6060 | 0.797272 | ||||||||
\(669\) | −22.6038 | −0.873912 | ||||||||
\(670\) | −10.7526 | −0.415410 | ||||||||
\(671\) | −7.61410 | −0.293939 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | −28.6119 | −1.10291 | −0.551454 | − | 0.834205i | \(-0.685927\pi\) | ||||
−0.551454 | + | 0.834205i | \(0.685927\pi\) | |||||||
\(674\) | −0.834456 | −0.0321420 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −7.86375 | −0.302452 | ||||||||
\(677\) | −4.10885 | −0.157916 | −0.0789579 | − | 0.996878i | \(-0.525159\pi\) | ||||
−0.0789579 | + | 0.996878i | \(0.525159\pi\) | |||||||
\(678\) | 7.80932 | 0.299915 | ||||||||
\(679\) | −10.1845 | −0.390845 | ||||||||
\(680\) | 3.43187 | 0.131606 | ||||||||
\(681\) | −29.2682 | −1.12156 | ||||||||
\(682\) | 4.84308 | 0.185451 | ||||||||
\(683\) | 20.3690 | 0.779398 | 0.389699 | − | 0.920942i | \(-0.372579\pi\) | ||||
0.389699 | + | 0.920942i | \(0.372579\pi\) | |||||||
\(684\) | 5.43187 | 0.207693 | ||||||||
\(685\) | 16.1197 | 0.615904 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −7.66891 | −0.292587 | ||||||||
\(688\) | 8.42154 | 0.321068 | ||||||||
\(689\) | −7.42600 | −0.282908 | ||||||||
\(690\) | 1.00000 | 0.0380693 | ||||||||
\(691\) | −8.89077 | −0.338221 | −0.169110 | − | 0.985597i | \(-0.554089\pi\) | ||||
−0.169110 | + | 0.985597i | \(0.554089\pi\) | |||||||
\(692\) | 1.62255 | 0.0616801 | ||||||||
\(693\) | −1.16554 | −0.0442754 | ||||||||
\(694\) | −14.6415 | −0.555784 | ||||||||
\(695\) | −4.92491 | −0.186812 | ||||||||
\(696\) | −4.75263 | −0.180148 | ||||||||
\(697\) | 29.6566 | 1.12332 | ||||||||
\(698\) | −18.2029 | −0.688990 | ||||||||
\(699\) | −26.3690 | −0.997367 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 15.3244 | 0.578793 | 0.289396 | − | 0.957209i | \(-0.406545\pi\) | ||||
0.289396 | + | 0.957209i | \(0.406545\pi\) | |||||||
\(702\) | −2.26633 | −0.0855371 | ||||||||
\(703\) | 3.92907 | 0.148188 | ||||||||
\(704\) | −1.16554 | −0.0439281 | ||||||||
\(705\) | 0.899214 | 0.0338664 | ||||||||
\(706\) | −13.3855 | −0.503770 | ||||||||
\(707\) | −2.78809 | −0.104857 | ||||||||
\(708\) | 5.05442 | 0.189957 | ||||||||
\(709\) | −43.5934 | −1.63719 | −0.818593 | − | 0.574374i | \(-0.805245\pi\) | ||||
−0.818593 | + | 0.574374i | \(0.805245\pi\) | |||||||
\(710\) | 3.88888 | 0.145947 | ||||||||
\(711\) | −1.27666 | −0.0478787 | ||||||||
\(712\) | −9.52233 | −0.356864 | ||||||||
\(713\) | −4.15521 | −0.155614 | ||||||||
\(714\) | 3.43187 | 0.128435 | ||||||||
\(715\) | 2.64151 | 0.0987868 | ||||||||
\(716\) | −12.8431 | −0.479968 | ||||||||
\(717\) | −4.11112 | −0.153533 | ||||||||
\(718\) | −18.0270 | −0.672762 | ||||||||
\(719\) | −4.70627 | −0.175514 | −0.0877570 | − | 0.996142i | \(-0.527970\pi\) | ||||
−0.0877570 | + | 0.996142i | \(0.527970\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 4.53266 | 0.168805 | ||||||||
\(722\) | 10.5053 | 0.390965 | ||||||||
\(723\) | −21.4698 | −0.798470 | ||||||||
\(724\) | −13.0860 | −0.486337 | ||||||||
\(725\) | −4.75263 | −0.176508 | ||||||||
\(726\) | −9.64151 | −0.357830 | ||||||||
\(727\) | −9.57619 | −0.355161 | −0.177581 | − | 0.984106i | \(-0.556827\pi\) | ||||
−0.177581 | + | 0.984106i | \(0.556827\pi\) | |||||||
\(728\) | −2.26633 | −0.0839958 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −3.05442 | −0.113049 | ||||||||
\(731\) | 28.9017 | 1.06897 | ||||||||
\(732\) | 6.53266 | 0.241454 | ||||||||
\(733\) | −32.8224 | −1.21232 | −0.606162 | − | 0.795341i | \(-0.707292\pi\) | ||||
−0.606162 | + | 0.795341i | \(0.707292\pi\) | |||||||
\(734\) | 25.8157 | 0.952874 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 12.5327 | 0.461646 | ||||||||
\(738\) | 8.64151 | 0.318098 | ||||||||
\(739\) | −17.8157 | −0.655360 | −0.327680 | − | 0.944789i | \(-0.606267\pi\) | ||||
−0.327680 | + | 0.944789i | \(0.606267\pi\) | |||||||
\(740\) | 0.723336 | 0.0265903 | ||||||||
\(741\) | −12.3104 | −0.452235 | ||||||||
\(742\) | 3.27666 | 0.120290 | ||||||||
\(743\) | 1.04807 | 0.0384501 | 0.0192250 | − | 0.999815i | \(-0.493880\pi\) | ||||
0.0192250 | + | 0.999815i | \(0.493880\pi\) | |||||||
\(744\) | −4.15521 | −0.152337 | ||||||||
\(745\) | 0.331088 | 0.0121301 | ||||||||
\(746\) | −19.2353 | −0.704255 | ||||||||
\(747\) | 7.76296 | 0.284032 | ||||||||
\(748\) | −4.00000 | −0.146254 | ||||||||
\(749\) | −20.3690 | −0.744267 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 31.4441 | 1.14741 | 0.573706 | − | 0.819062i | \(-0.305505\pi\) | ||||
0.573706 | + | 0.819062i | \(0.305505\pi\) | |||||||
\(752\) | 0.899214 | 0.0327910 | ||||||||
\(753\) | −16.4949 | −0.601108 | ||||||||
\(754\) | 10.7710 | 0.392258 | ||||||||
\(755\) | 8.53266 | 0.310535 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | 42.2286 | 1.53482 | 0.767412 | − | 0.641154i | \(-0.221544\pi\) | ||||
0.767412 | + | 0.641154i | \(0.221544\pi\) | |||||||
\(758\) | −7.03376 | −0.255477 | ||||||||
\(759\) | −1.16554 | −0.0423066 | ||||||||
\(760\) | 5.43187 | 0.197035 | ||||||||
\(761\) | 37.8536 | 1.37219 | 0.686096 | − | 0.727511i | \(-0.259323\pi\) | ||||
0.686096 | + | 0.727511i | \(0.259323\pi\) | |||||||
\(762\) | 2.44221 | 0.0884719 | ||||||||
\(763\) | 18.3690 | 0.665003 | ||||||||
\(764\) | 19.0923 | 0.690737 | ||||||||
\(765\) | 3.43187 | 0.124080 | ||||||||
\(766\) | 25.9084 | 0.936109 | ||||||||
\(767\) | −11.4550 | −0.413616 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −39.9645 | −1.44116 | −0.720579 | − | 0.693373i | \(-0.756124\pi\) | ||||
−0.720579 | + | 0.693373i | \(0.756124\pi\) | |||||||
\(770\) | −1.16554 | −0.0420033 | ||||||||
\(771\) | 21.7887 | 0.784699 | ||||||||
\(772\) | −20.3897 | −0.733840 | ||||||||
\(773\) | −12.9978 | −0.467499 | −0.233749 | − | 0.972297i | \(-0.575100\pi\) | ||||
−0.233749 | + | 0.972297i | \(0.575100\pi\) | |||||||
\(774\) | 8.42154 | 0.302706 | ||||||||
\(775\) | −4.15521 | −0.149260 | ||||||||
\(776\) | −10.1845 | −0.365602 | ||||||||
\(777\) | 0.723336 | 0.0259495 | ||||||||
\(778\) | 11.3244 | 0.405998 | ||||||||
\(779\) | 46.9396 | 1.68178 | ||||||||
\(780\) | −2.26633 | −0.0811476 | ||||||||
\(781\) | −4.53266 | −0.162191 | ||||||||
\(782\) | 3.43187 | 0.122724 | ||||||||
\(783\) | −4.75263 | −0.169845 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 13.7068 | 0.489218 | ||||||||
\(786\) | −10.1197 | −0.360959 | ||||||||
\(787\) | −31.8032 | −1.13366 | −0.566830 | − | 0.823835i | \(-0.691830\pi\) | ||||
−0.566830 | + | 0.823835i | \(0.691830\pi\) | |||||||
\(788\) | 6.31042 | 0.224799 | ||||||||
\(789\) | −14.8637 | −0.529163 | ||||||||
\(790\) | −1.27666 | −0.0454217 | ||||||||
\(791\) | 7.80932 | 0.277668 | ||||||||
\(792\) | −1.16554 | −0.0414158 | ||||||||
\(793\) | −14.8052 | −0.525747 | ||||||||
\(794\) | −34.7235 | −1.23229 | ||||||||
\(795\) | 3.27666 | 0.116211 | ||||||||
\(796\) | −2.33109 | −0.0826232 | ||||||||
\(797\) | −42.7676 | −1.51491 | −0.757453 | − | 0.652890i | \(-0.773557\pi\) | ||||
−0.757453 | + | 0.652890i | \(0.773557\pi\) | |||||||
\(798\) | 5.43187 | 0.192286 | ||||||||
\(799\) | 3.08599 | 0.109174 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −9.52233 | −0.336455 | ||||||||
\(802\) | 35.1423 | 1.24092 | ||||||||
\(803\) | 3.56006 | 0.125632 | ||||||||
\(804\) | −10.7526 | −0.379216 | ||||||||
\(805\) | 1.00000 | 0.0352454 | ||||||||
\(806\) | 9.41708 | 0.331702 | ||||||||
\(807\) | 6.05499 | 0.213146 | ||||||||
\(808\) | −2.78809 | −0.0980848 | ||||||||
\(809\) | 8.72969 | 0.306919 | 0.153460 | − | 0.988155i | \(-0.450958\pi\) | ||||
0.153460 | + | 0.988155i | \(0.450958\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 22.0488 | 0.774239 | 0.387119 | − | 0.922030i | \(-0.373470\pi\) | ||||
0.387119 | + | 0.922030i | \(0.373470\pi\) | |||||||
\(812\) | −4.75263 | −0.166785 | ||||||||
\(813\) | −5.22053 | −0.183092 | ||||||||
\(814\) | −0.843080 | −0.0295499 | ||||||||
\(815\) | −1.35849 | −0.0475859 | ||||||||
\(816\) | 3.43187 | 0.120140 | ||||||||
\(817\) | 45.7447 | 1.60041 | ||||||||
\(818\) | −6.47408 | −0.226361 | ||||||||
\(819\) | −2.26633 | −0.0791920 | ||||||||
\(820\) | 8.64151 | 0.301775 | ||||||||
\(821\) | −31.6750 | −1.10546 | −0.552732 | − | 0.833359i | \(-0.686415\pi\) | ||||
−0.552732 | + | 0.833359i | \(0.686415\pi\) | |||||||
\(822\) | 16.1197 | 0.562241 | ||||||||
\(823\) | −29.6750 | −1.03440 | −0.517202 | − | 0.855863i | \(-0.673026\pi\) | ||||
−0.517202 | + | 0.855863i | \(0.673026\pi\) | |||||||
\(824\) | 4.53266 | 0.157903 | ||||||||
\(825\) | −1.16554 | −0.0405790 | ||||||||
\(826\) | 5.05442 | 0.175866 | ||||||||
\(827\) | 2.42381 | 0.0842842 | 0.0421421 | − | 0.999112i | \(-0.486582\pi\) | ||||
0.0421421 | + | 0.999112i | \(0.486582\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | 0.497194 | 0.0172683 | 0.00863414 | − | 0.999963i | \(-0.497252\pi\) | ||||
0.00863414 | + | 0.999963i | \(0.497252\pi\) | |||||||
\(830\) | 7.76296 | 0.269456 | ||||||||
\(831\) | 1.35622 | 0.0470467 | ||||||||
\(832\) | −2.26633 | −0.0785709 | ||||||||
\(833\) | 3.43187 | 0.118907 | ||||||||
\(834\) | −4.92491 | −0.170536 | ||||||||
\(835\) | 20.6060 | 0.713101 | ||||||||
\(836\) | −6.33109 | −0.218965 | ||||||||
\(837\) | −4.15521 | −0.143625 | ||||||||
\(838\) | 12.5876 | 0.434833 | ||||||||
\(839\) | −43.0518 | −1.48631 | −0.743157 | − | 0.669117i | \(-0.766673\pi\) | ||||
−0.743157 | + | 0.669117i | \(0.766673\pi\) | |||||||
\(840\) | 1.00000 | 0.0345033 | ||||||||
\(841\) | −6.41253 | −0.221122 | ||||||||
\(842\) | 24.1306 | 0.831597 | ||||||||
\(843\) | −15.9268 | −0.548548 | ||||||||
\(844\) | 26.1674 | 0.900720 | ||||||||
\(845\) | −7.86375 | −0.270521 | ||||||||
\(846\) | 0.899214 | 0.0309156 | ||||||||
\(847\) | −9.64151 | −0.331286 | ||||||||
\(848\) | 3.27666 | 0.112521 | ||||||||
\(849\) | −7.21191 | −0.247512 | ||||||||
\(850\) | 3.43187 | 0.117712 | ||||||||
\(851\) | 0.723336 | 0.0247956 | ||||||||
\(852\) | 3.88888 | 0.133231 | ||||||||
\(853\) | −20.3752 | −0.697633 | −0.348816 | − | 0.937191i | \(-0.613416\pi\) | ||||
−0.348816 | + | 0.937191i | \(0.613416\pi\) | |||||||
\(854\) | 6.53266 | 0.223543 | ||||||||
\(855\) | 5.43187 | 0.185766 | ||||||||
\(856\) | −20.3690 | −0.696198 | ||||||||
\(857\) | 30.9494 | 1.05721 | 0.528605 | − | 0.848868i | \(-0.322715\pi\) | ||||
0.528605 | + | 0.848868i | \(0.322715\pi\) | |||||||
\(858\) | 2.64151 | 0.0901796 | ||||||||
\(859\) | −37.7384 | −1.28762 | −0.643809 | − | 0.765187i | \(-0.722647\pi\) | ||||
−0.643809 | + | 0.765187i | \(0.722647\pi\) | |||||||
\(860\) | 8.42154 | 0.287172 | ||||||||
\(861\) | 8.64151 | 0.294502 | ||||||||
\(862\) | 15.5664 | 0.530194 | ||||||||
\(863\) | 24.3690 | 0.829531 | 0.414765 | − | 0.909928i | \(-0.363864\pi\) | ||||
0.414765 | + | 0.909928i | \(0.363864\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 1.62255 | 0.0551683 | ||||||||
\(866\) | −4.90149 | −0.166559 | ||||||||
\(867\) | −5.22224 | −0.177357 | ||||||||
\(868\) | −4.15521 | −0.141037 | ||||||||
\(869\) | 1.48801 | 0.0504772 | ||||||||
\(870\) | −4.75263 | −0.161129 | ||||||||
\(871\) | 24.3690 | 0.825712 | ||||||||
\(872\) | 18.3690 | 0.622053 | ||||||||
\(873\) | −10.1845 | −0.344693 | ||||||||
\(874\) | 5.43187 | 0.183736 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −3.05442 | −0.103199 | ||||||||
\(877\) | 22.3288 | 0.753990 | 0.376995 | − | 0.926215i | \(-0.376957\pi\) | ||||
0.376995 | + | 0.926215i | \(0.376957\pi\) | |||||||
\(878\) | −3.62255 | −0.122255 | ||||||||
\(879\) | 0.863748 | 0.0291335 | ||||||||
\(880\) | −1.16554 | −0.0392905 | ||||||||
\(881\) | 48.7333 | 1.64187 | 0.820933 | − | 0.571024i | \(-0.193454\pi\) | ||||
0.820933 | + | 0.571024i | \(0.193454\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | −27.9245 | −0.939735 | −0.469867 | − | 0.882737i | \(-0.655698\pi\) | ||||
−0.469867 | + | 0.882737i | \(0.655698\pi\) | |||||||
\(884\) | −7.77776 | −0.261594 | ||||||||
\(885\) | 5.05442 | 0.169903 | ||||||||
\(886\) | 14.6415 | 0.491891 | ||||||||
\(887\) | 33.2096 | 1.11507 | 0.557535 | − | 0.830153i | \(-0.311747\pi\) | ||||
0.557535 | + | 0.830153i | \(0.311747\pi\) | |||||||
\(888\) | 0.723336 | 0.0242736 | ||||||||
\(889\) | 2.44221 | 0.0819090 | ||||||||
\(890\) | −9.52233 | −0.319189 | ||||||||
\(891\) | −1.16554 | −0.0390472 | ||||||||
\(892\) | −22.6038 | −0.756830 | ||||||||
\(893\) | 4.88442 | 0.163451 | ||||||||
\(894\) | 0.331088 | 0.0110732 | ||||||||
\(895\) | −12.8431 | −0.429297 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −2.26633 | −0.0756706 | ||||||||
\(898\) | −23.9497 | −0.799213 | ||||||||
\(899\) | 19.7482 | 0.658638 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 11.2451 | 0.374629 | ||||||||
\(902\) | −10.0721 | −0.335363 | ||||||||
\(903\) | 8.42154 | 0.280251 | ||||||||
\(904\) | 7.80932 | 0.259734 | ||||||||
\(905\) | −13.0860 | −0.434993 | ||||||||
\(906\) | 8.53266 | 0.283479 | ||||||||
\(907\) | −20.5728 | −0.683110 | −0.341555 | − | 0.939862i | \(-0.610954\pi\) | ||||
−0.341555 | + | 0.939862i | \(0.610954\pi\) | |||||||
\(908\) | −29.2682 | −0.971300 | ||||||||
\(909\) | −2.78809 | −0.0924752 | ||||||||
\(910\) | −2.26633 | −0.0751281 | ||||||||
\(911\) | 38.4887 | 1.27519 | 0.637595 | − | 0.770372i | \(-0.279930\pi\) | ||||
0.637595 | + | 0.770372i | \(0.279930\pi\) | |||||||
\(912\) | 5.43187 | 0.179867 | ||||||||
\(913\) | −9.04807 | −0.299448 | ||||||||
\(914\) | −22.6501 | −0.749200 | ||||||||
\(915\) | 6.53266 | 0.215963 | ||||||||
\(916\) | −7.66891 | −0.253388 | ||||||||
\(917\) | −10.1197 | −0.334183 | ||||||||
\(918\) | 3.43187 | 0.113269 | ||||||||
\(919\) | −54.4887 | −1.79742 | −0.898709 | − | 0.438546i | \(-0.855494\pi\) | ||||
−0.898709 | + | 0.438546i | \(0.855494\pi\) | |||||||
\(920\) | 1.00000 | 0.0329690 | ||||||||
\(921\) | −2.80516 | −0.0924333 | ||||||||
\(922\) | −24.5156 | −0.807378 | ||||||||
\(923\) | −8.81348 | −0.290099 | ||||||||
\(924\) | −1.16554 | −0.0383436 | ||||||||
\(925\) | 0.723336 | 0.0237831 | ||||||||
\(926\) | 26.8112 | 0.881071 | ||||||||
\(927\) | 4.53266 | 0.148872 | ||||||||
\(928\) | −4.75263 | −0.156013 | ||||||||
\(929\) | −4.90509 | −0.160931 | −0.0804653 | − | 0.996757i | \(-0.525641\pi\) | ||||
−0.0804653 | + | 0.996757i | \(0.525641\pi\) | |||||||
\(930\) | −4.15521 | −0.136255 | ||||||||
\(931\) | 5.43187 | 0.178022 | ||||||||
\(932\) | −26.3690 | −0.863745 | ||||||||
\(933\) | 16.0441 | 0.525260 | ||||||||
\(934\) | 3.83389 | 0.125449 | ||||||||
\(935\) | −4.00000 | −0.130814 | ||||||||
\(936\) | −2.26633 | −0.0740773 | ||||||||
\(937\) | −54.7344 | −1.78810 | −0.894048 | − | 0.447972i | \(-0.852146\pi\) | ||||
−0.894048 | + | 0.447972i | \(0.852146\pi\) | |||||||
\(938\) | −10.7526 | −0.351086 | ||||||||
\(939\) | −4.36883 | −0.142571 | ||||||||
\(940\) | 0.899214 | 0.0293291 | ||||||||
\(941\) | 8.72969 | 0.284580 | 0.142290 | − | 0.989825i | \(-0.454554\pi\) | ||||
0.142290 | + | 0.989825i | \(0.454554\pi\) | |||||||
\(942\) | 13.7068 | 0.446593 | ||||||||
\(943\) | 8.64151 | 0.281406 | ||||||||
\(944\) | 5.05442 | 0.164507 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | −9.81567 | −0.319135 | ||||||||
\(947\) | 6.11339 | 0.198659 | 0.0993293 | − | 0.995055i | \(-0.468330\pi\) | ||||
0.0993293 | + | 0.995055i | \(0.468330\pi\) | |||||||
\(948\) | −1.27666 | −0.0414641 | ||||||||
\(949\) | 6.92233 | 0.224708 | ||||||||
\(950\) | 5.43187 | 0.176233 | ||||||||
\(951\) | 28.2602 | 0.916398 | ||||||||
\(952\) | 3.43187 | 0.111228 | ||||||||
\(953\) | 53.1141 | 1.72054 | 0.860268 | − | 0.509843i | \(-0.170296\pi\) | ||||
0.860268 | + | 0.509843i | \(0.170296\pi\) | |||||||
\(954\) | 3.27666 | 0.106086 | ||||||||
\(955\) | 19.0923 | 0.617814 | ||||||||
\(956\) | −4.11112 | −0.132963 | ||||||||
\(957\) | 5.53940 | 0.179063 | ||||||||
\(958\) | −14.6415 | −0.473046 | ||||||||
\(959\) | 16.1197 | 0.520534 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −13.7342 | −0.443040 | ||||||||
\(962\) | −1.63932 | −0.0528537 | ||||||||
\(963\) | −20.3690 | −0.656382 | ||||||||
\(964\) | −21.4698 | −0.691495 | ||||||||
\(965\) | −20.3897 | −0.656367 | ||||||||
\(966\) | 1.00000 | 0.0321745 | ||||||||
\(967\) | 25.7459 | 0.827932 | 0.413966 | − | 0.910292i | \(-0.364143\pi\) | ||||
0.413966 | + | 0.910292i | \(0.364143\pi\) | |||||||
\(968\) | −9.64151 | −0.309890 | ||||||||
\(969\) | 18.6415 | 0.598851 | ||||||||
\(970\) | −10.1845 | −0.327005 | ||||||||
\(971\) | −6.10525 | −0.195927 | −0.0979634 | − | 0.995190i | \(-0.531233\pi\) | ||||
−0.0979634 | + | 0.995190i | \(0.531233\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −4.92491 | −0.157885 | ||||||||
\(974\) | −0.199299 | −0.00638595 | ||||||||
\(975\) | −2.26633 | −0.0725806 | ||||||||
\(976\) | 6.53266 | 0.209105 | ||||||||
\(977\) | −55.3525 | −1.77088 | −0.885442 | − | 0.464751i | \(-0.846144\pi\) | ||||
−0.885442 | + | 0.464751i | \(0.846144\pi\) | |||||||
\(978\) | −1.35849 | −0.0434398 | ||||||||
\(979\) | 11.0987 | 0.354716 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 18.3690 | 0.586477 | ||||||||
\(982\) | 22.0379 | 0.703258 | ||||||||
\(983\) | −6.45341 | −0.205832 | −0.102916 | − | 0.994690i | \(-0.532817\pi\) | ||||
−0.102916 | + | 0.994690i | \(0.532817\pi\) | |||||||
\(984\) | 8.64151 | 0.275481 | ||||||||
\(985\) | 6.31042 | 0.201067 | ||||||||
\(986\) | −16.3104 | −0.519430 | ||||||||
\(987\) | 0.899214 | 0.0286223 | ||||||||
\(988\) | −12.3104 | −0.391647 | ||||||||
\(989\) | 8.42154 | 0.267789 | ||||||||
\(990\) | −1.16554 | −0.0370434 | ||||||||
\(991\) | −29.8157 | −0.947126 | −0.473563 | − | 0.880760i | \(-0.657032\pi\) | ||||
−0.473563 | + | 0.880760i | \(0.657032\pi\) | |||||||
\(992\) | −4.15521 | −0.131928 | ||||||||
\(993\) | 8.31042 | 0.263723 | ||||||||
\(994\) | 3.88888 | 0.123348 | ||||||||
\(995\) | −2.33109 | −0.0739005 | ||||||||
\(996\) | 7.76296 | 0.245979 | ||||||||
\(997\) | −21.6042 | −0.684210 | −0.342105 | − | 0.939662i | \(-0.611140\pi\) | ||||
−0.342105 | + | 0.939662i | \(0.611140\pi\) | |||||||
\(998\) | −2.49474 | −0.0789698 | ||||||||
\(999\) | 0.723336 | 0.0228853 |
(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 | 4830.2.a.ce.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4830.2.a.ce.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial |