Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(1,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, 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("2394.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.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: | \(19.1161862439\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2394.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.622216 | 0.278263 | 0.139132 | − | 0.990274i | \(-0.455569\pi\) | ||||
0.139132 | + | 0.990274i | \(0.455569\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.622216 | 0.196762 | ||||||||
\(11\) | −2.42864 | −0.732262 | −0.366131 | − | 0.930563i | \(-0.619318\pi\) | ||||
−0.366131 | + | 0.930563i | \(0.619318\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.62222 | 0.727272 | 0.363636 | − | 0.931541i | \(-0.381535\pi\) | ||||
0.363636 | + | 0.931541i | \(0.381535\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.42864 | 1.07410 | 0.537051 | − | 0.843550i | \(-0.319538\pi\) | ||||
0.537051 | + | 0.843550i | \(0.319538\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.622216 | 0.139132 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.42864 | −0.517788 | ||||||||
\(23\) | 1.37778 | 0.287288 | 0.143644 | − | 0.989629i | \(-0.454118\pi\) | ||||
0.143644 | + | 0.989629i | \(0.454118\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.61285 | −0.922570 | ||||||||
\(26\) | 2.62222 | 0.514259 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 9.61285 | 1.78506 | 0.892531 | − | 0.450987i | \(-0.148928\pi\) | ||||
0.892531 | + | 0.450987i | \(0.148928\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.80642 | 0.683654 | 0.341827 | − | 0.939763i | \(-0.388954\pi\) | ||||
0.341827 | + | 0.939763i | \(0.388954\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.42864 | 0.759505 | ||||||||
\(35\) | −0.622216 | −0.105174 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.80642 | 0.954570 | 0.477285 | − | 0.878749i | \(-0.341621\pi\) | ||||
0.477285 | + | 0.878749i | \(0.341621\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.622216 | 0.0983809 | ||||||||
\(41\) | 0.755569 | 0.118000 | 0.0590000 | − | 0.998258i | \(-0.481209\pi\) | ||||
0.0590000 | + | 0.998258i | \(0.481209\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.61285 | 1.16095 | 0.580474 | − | 0.814279i | \(-0.302867\pi\) | ||||
0.580474 | + | 0.814279i | \(0.302867\pi\) | |||||||
\(44\) | −2.42864 | −0.366131 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.37778 | 0.203143 | ||||||||
\(47\) | 0.949145 | 0.138447 | 0.0692235 | − | 0.997601i | \(-0.477948\pi\) | ||||
0.0692235 | + | 0.997601i | \(0.477948\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.61285 | −0.652355 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.62222 | 0.363636 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.51114 | −0.203762 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.61285 | 1.26223 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.61285 | −0.718652 | −0.359326 | − | 0.933212i | \(-0.616993\pi\) | ||||
−0.359326 | + | 0.933212i | \(0.616993\pi\) | |||||||
\(62\) | 3.80642 | 0.483416 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.63158 | 0.202373 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.42864 | −0.541044 | −0.270522 | − | 0.962714i | \(-0.587196\pi\) | ||||
−0.270522 | + | 0.962714i | \(0.587196\pi\) | |||||||
\(68\) | 4.42864 | 0.537051 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.622216 | −0.0743690 | ||||||||
\(71\) | −0.857279 | −0.101740 | −0.0508701 | − | 0.998705i | \(-0.516199\pi\) | ||||
−0.0508701 | + | 0.998705i | \(0.516199\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.85728 | 0.802584 | 0.401292 | − | 0.915950i | \(-0.368561\pi\) | ||||
0.401292 | + | 0.915950i | \(0.368561\pi\) | |||||||
\(74\) | 5.80642 | 0.674983 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 2.42864 | 0.276769 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.7239 | −1.65657 | −0.828286 | − | 0.560306i | \(-0.810683\pi\) | ||||
−0.828286 | + | 0.560306i | \(0.810683\pi\) | |||||||
\(80\) | 0.622216 | 0.0695658 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.755569 | 0.0834386 | ||||||||
\(83\) | 4.75557 | 0.521991 | 0.260996 | − | 0.965340i | \(-0.415949\pi\) | ||||
0.260996 | + | 0.965340i | \(0.415949\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.75557 | 0.298883 | ||||||||
\(86\) | 7.61285 | 0.820914 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.42864 | −0.258894 | ||||||||
\(89\) | 14.8573 | 1.57487 | 0.787434 | − | 0.616399i | \(-0.211409\pi\) | ||||
0.787434 | + | 0.616399i | \(0.211409\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.62222 | −0.274883 | ||||||||
\(92\) | 1.37778 | 0.143644 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.949145 | 0.0978968 | ||||||||
\(95\) | −0.622216 | −0.0638380 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.67307 | 0.372944 | 0.186472 | − | 0.982460i | \(-0.440295\pi\) | ||||
0.186472 | + | 0.982460i | \(0.440295\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.61285 | −0.461285 | ||||||||
\(101\) | −3.37778 | −0.336102 | −0.168051 | − | 0.985778i | \(-0.553747\pi\) | ||||
−0.168051 | + | 0.985778i | \(0.553747\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.2953 | −1.01442 | −0.507212 | − | 0.861821i | \(-0.669324\pi\) | ||||
−0.507212 | + | 0.861821i | \(0.669324\pi\) | |||||||
\(104\) | 2.62222 | 0.257129 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | 16.8573 | 1.62965 | 0.814827 | − | 0.579704i | \(-0.196832\pi\) | ||||
0.814827 | + | 0.579704i | \(0.196832\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.41927 | 0.902203 | 0.451101 | − | 0.892473i | \(-0.351031\pi\) | ||||
0.451101 | + | 0.892473i | \(0.351031\pi\) | |||||||
\(110\) | −1.51114 | −0.144081 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 4.10171 | 0.385856 | 0.192928 | − | 0.981213i | \(-0.438202\pi\) | ||||
0.192928 | + | 0.981213i | \(0.438202\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.857279 | 0.0799417 | ||||||||
\(116\) | 9.61285 | 0.892531 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.42864 | −0.405973 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.10171 | −0.463792 | ||||||||
\(122\) | −5.61285 | −0.508163 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.80642 | 0.341827 | ||||||||
\(125\) | −5.98126 | −0.534981 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.47949 | −0.131284 | −0.0656420 | − | 0.997843i | \(-0.520910\pi\) | ||||
−0.0656420 | + | 0.997843i | \(0.520910\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.63158 | 0.143099 | ||||||||
\(131\) | −8.10171 | −0.707850 | −0.353925 | − | 0.935274i | \(-0.615153\pi\) | ||||
−0.353925 | + | 0.935274i | \(0.615153\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | 0.0867110 | ||||||||
\(134\) | −4.42864 | −0.382576 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.42864 | 0.379753 | ||||||||
\(137\) | 2.75557 | 0.235424 | 0.117712 | − | 0.993048i | \(-0.462444\pi\) | ||||
0.117712 | + | 0.993048i | \(0.462444\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.1017 | −0.856816 | −0.428408 | − | 0.903585i | \(-0.640925\pi\) | ||||
−0.428408 | + | 0.903585i | \(0.640925\pi\) | |||||||
\(140\) | −0.622216 | −0.0525868 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.857279 | −0.0719413 | ||||||||
\(143\) | −6.36842 | −0.532554 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.98126 | 0.496717 | ||||||||
\(146\) | 6.85728 | 0.567512 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.80642 | 0.477285 | ||||||||
\(149\) | 1.43801 | 0.117806 | 0.0589031 | − | 0.998264i | \(-0.481240\pi\) | ||||
0.0589031 | + | 0.998264i | \(0.481240\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.74620 | −0.793135 | −0.396567 | − | 0.918006i | \(-0.629799\pi\) | ||||
−0.396567 | + | 0.918006i | \(0.629799\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.42864 | 0.195705 | ||||||||
\(155\) | 2.36842 | 0.190236 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.71456 | −0.615689 | −0.307844 | − | 0.951437i | \(-0.599608\pi\) | ||||
−0.307844 | + | 0.951437i | \(0.599608\pi\) | |||||||
\(158\) | −14.7239 | −1.17137 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.622216 | 0.0491905 | ||||||||
\(161\) | −1.37778 | −0.108585 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.51114 | −0.744970 | −0.372485 | − | 0.928038i | \(-0.621494\pi\) | ||||
−0.372485 | + | 0.928038i | \(0.621494\pi\) | |||||||
\(164\) | 0.755569 | 0.0590000 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.75557 | 0.369104 | ||||||||
\(167\) | −5.24443 | −0.405826 | −0.202913 | − | 0.979197i | \(-0.565041\pi\) | ||||
−0.202913 | + | 0.979197i | \(0.565041\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.12399 | −0.471076 | ||||||||
\(170\) | 2.75557 | 0.211342 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.61285 | 0.580474 | ||||||||
\(173\) | −23.7146 | −1.80298 | −0.901492 | − | 0.432795i | \(-0.857527\pi\) | ||||
−0.901492 | + | 0.432795i | \(0.857527\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.61285 | 0.348699 | ||||||||
\(176\) | −2.42864 | −0.183066 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.8573 | 1.11360 | ||||||||
\(179\) | 24.2034 | 1.80905 | 0.904524 | − | 0.426422i | \(-0.140226\pi\) | ||||
0.904524 | + | 0.426422i | \(0.140226\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.13335 | −0.307230 | −0.153615 | − | 0.988131i | \(-0.549092\pi\) | ||||
−0.153615 | + | 0.988131i | \(0.549092\pi\) | |||||||
\(182\) | −2.62222 | −0.194372 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.37778 | 0.101572 | ||||||||
\(185\) | 3.61285 | 0.265622 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.7556 | −0.786525 | ||||||||
\(188\) | 0.949145 | 0.0692235 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.622216 | −0.0451403 | ||||||||
\(191\) | 20.6035 | 1.49082 | 0.745408 | − | 0.666609i | \(-0.232255\pi\) | ||||
0.745408 | + | 0.666609i | \(0.232255\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.61285 | 0.116095 | 0.0580477 | − | 0.998314i | \(-0.481512\pi\) | ||||
0.0580477 | + | 0.998314i | \(0.481512\pi\) | |||||||
\(194\) | 3.67307 | 0.263711 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 5.43801 | 0.387442 | 0.193721 | − | 0.981057i | \(-0.437944\pi\) | ||||
0.193721 | + | 0.981057i | \(0.437944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −27.2257 | −1.92998 | −0.964989 | − | 0.262290i | \(-0.915522\pi\) | ||||
−0.964989 | + | 0.262290i | \(0.915522\pi\) | |||||||
\(200\) | −4.61285 | −0.326178 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.37778 | −0.237660 | ||||||||
\(203\) | −9.61285 | −0.674690 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.470127 | 0.0328351 | ||||||||
\(206\) | −10.2953 | −0.717307 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.62222 | 0.181818 | ||||||||
\(209\) | 2.42864 | 0.167993 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.8988 | 1.43873 | 0.719365 | − | 0.694632i | \(-0.244433\pi\) | ||||
0.719365 | + | 0.694632i | \(0.244433\pi\) | |||||||
\(212\) | 2.00000 | 0.137361 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.8573 | 1.15234 | ||||||||
\(215\) | 4.73683 | 0.323049 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.80642 | −0.258397 | ||||||||
\(218\) | 9.41927 | 0.637954 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.51114 | −0.101881 | ||||||||
\(221\) | 11.6128 | 0.781165 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.1526 | 0.746831 | 0.373416 | − | 0.927664i | \(-0.378187\pi\) | ||||
0.373416 | + | 0.927664i | \(0.378187\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.10171 | 0.272842 | ||||||||
\(227\) | −17.1240 | −1.13656 | −0.568279 | − | 0.822836i | \(-0.692391\pi\) | ||||
−0.568279 | + | 0.822836i | \(0.692391\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.2444 | −1.00738 | −0.503690 | − | 0.863884i | \(-0.668025\pi\) | ||||
−0.503690 | + | 0.863884i | \(0.668025\pi\) | |||||||
\(230\) | 0.857279 | 0.0565273 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.61285 | 0.631114 | ||||||||
\(233\) | 16.8573 | 1.10436 | 0.552179 | − | 0.833726i | \(-0.313797\pi\) | ||||
0.552179 | + | 0.833726i | \(0.313797\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.590573 | 0.0385247 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.42864 | −0.287066 | ||||||||
\(239\) | 4.99063 | 0.322817 | 0.161409 | − | 0.986888i | \(-0.448396\pi\) | ||||
0.161409 | + | 0.986888i | \(0.448396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.326929 | 0.0210594 | 0.0105297 | − | 0.999945i | \(-0.496648\pi\) | ||||
0.0105297 | + | 0.999945i | \(0.496648\pi\) | |||||||
\(242\) | −5.10171 | −0.327950 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.61285 | −0.359326 | ||||||||
\(245\) | 0.622216 | 0.0397519 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.62222 | −0.166848 | ||||||||
\(248\) | 3.80642 | 0.241708 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.98126 | −0.378288 | ||||||||
\(251\) | 6.38715 | 0.403153 | 0.201577 | − | 0.979473i | \(-0.435393\pi\) | ||||
0.201577 | + | 0.979473i | \(0.435393\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.34614 | −0.210370 | ||||||||
\(254\) | −1.47949 | −0.0928317 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.00000 | 0.124757 | 0.0623783 | − | 0.998053i | \(-0.480131\pi\) | ||||
0.0623783 | + | 0.998053i | \(0.480131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.80642 | −0.360794 | ||||||||
\(260\) | 1.63158 | 0.101187 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −8.10171 | −0.500525 | ||||||||
\(263\) | −6.88892 | −0.424789 | −0.212395 | − | 0.977184i | \(-0.568126\pi\) | ||||
−0.212395 | + | 0.977184i | \(0.568126\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.24443 | 0.0764448 | ||||||||
\(266\) | 1.00000 | 0.0613139 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.42864 | −0.270522 | ||||||||
\(269\) | −15.7146 | −0.958134 | −0.479067 | − | 0.877778i | \(-0.659025\pi\) | ||||
−0.479067 | + | 0.877778i | \(0.659025\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.1017 | −1.09960 | −0.549800 | − | 0.835296i | \(-0.685296\pi\) | ||||
−0.549800 | + | 0.835296i | \(0.685296\pi\) | |||||||
\(272\) | 4.42864 | 0.268526 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.75557 | 0.166470 | ||||||||
\(275\) | 11.2029 | 0.675563 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.59057 | 0.395989 | 0.197995 | − | 0.980203i | \(-0.436557\pi\) | ||||
0.197995 | + | 0.980203i | \(0.436557\pi\) | |||||||
\(278\) | −10.1017 | −0.605860 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.622216 | −0.0371845 | ||||||||
\(281\) | −17.6128 | −1.05069 | −0.525347 | − | 0.850888i | \(-0.676065\pi\) | ||||
−0.525347 | + | 0.850888i | \(0.676065\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.61285 | 0.452537 | 0.226268 | − | 0.974065i | \(-0.427347\pi\) | ||||
0.226268 | + | 0.974065i | \(0.427347\pi\) | |||||||
\(284\) | −0.857279 | −0.0508701 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.36842 | −0.376572 | ||||||||
\(287\) | −0.755569 | −0.0445998 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.61285 | 0.153697 | ||||||||
\(290\) | 5.98126 | 0.351232 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.85728 | 0.401292 | ||||||||
\(293\) | 17.2257 | 1.00634 | 0.503168 | − | 0.864189i | \(-0.332168\pi\) | ||||
0.503168 | + | 0.864189i | \(0.332168\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.80642 | 0.337492 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.43801 | 0.0833015 | ||||||||
\(299\) | 3.61285 | 0.208936 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.61285 | −0.438797 | ||||||||
\(302\) | −9.74620 | −0.560831 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −3.49240 | −0.199974 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.24443 | −0.527608 | −0.263804 | − | 0.964576i | \(-0.584977\pi\) | ||||
−0.263804 | + | 0.964576i | \(0.584977\pi\) | |||||||
\(308\) | 2.42864 | 0.138385 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.36842 | 0.134517 | ||||||||
\(311\) | 17.0321 | 0.965803 | 0.482901 | − | 0.875675i | \(-0.339583\pi\) | ||||
0.482901 | + | 0.875675i | \(0.339583\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.0000 | −0.791327 | −0.395663 | − | 0.918396i | \(-0.629485\pi\) | ||||
−0.395663 | + | 0.918396i | \(0.629485\pi\) | |||||||
\(314\) | −7.71456 | −0.435358 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.7239 | −0.828286 | ||||||||
\(317\) | −5.22570 | −0.293504 | −0.146752 | − | 0.989173i | \(-0.546882\pi\) | ||||
−0.146752 | + | 0.989173i | \(0.546882\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.3461 | −1.30713 | ||||||||
\(320\) | 0.622216 | 0.0347829 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.37778 | −0.0767809 | ||||||||
\(323\) | −4.42864 | −0.246416 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.0959 | −0.670959 | ||||||||
\(326\) | −9.51114 | −0.526773 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.755569 | 0.0417193 | ||||||||
\(329\) | −0.949145 | −0.0523281 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.7748 | −1.08692 | −0.543460 | − | 0.839435i | \(-0.682886\pi\) | ||||
−0.543460 | + | 0.839435i | \(0.682886\pi\) | |||||||
\(332\) | 4.75557 | 0.260996 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.24443 | −0.286963 | ||||||||
\(335\) | −2.75557 | −0.150553 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.1427 | 0.715930 | 0.357965 | − | 0.933735i | \(-0.383471\pi\) | ||||
0.357965 | + | 0.933735i | \(0.383471\pi\) | |||||||
\(338\) | −6.12399 | −0.333101 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.75557 | 0.149442 | ||||||||
\(341\) | −9.24443 | −0.500614 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 7.61285 | 0.410457 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −23.7146 | −1.27490 | ||||||||
\(347\) | −22.3082 | −1.19757 | −0.598783 | − | 0.800911i | \(-0.704349\pi\) | ||||
−0.598783 | + | 0.800911i | \(0.704349\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.24443 | −0.173670 | −0.0868352 | − | 0.996223i | \(-0.527675\pi\) | ||||
−0.0868352 | + | 0.996223i | \(0.527675\pi\) | |||||||
\(350\) | 4.61285 | 0.246567 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.42864 | −0.129447 | ||||||||
\(353\) | −11.9585 | −0.636487 | −0.318244 | − | 0.948009i | \(-0.603093\pi\) | ||||
−0.318244 | + | 0.948009i | \(0.603093\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.533412 | −0.0283106 | ||||||||
\(356\) | 14.8573 | 0.787434 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.2034 | 1.27919 | ||||||||
\(359\) | 27.7462 | 1.46439 | 0.732194 | − | 0.681096i | \(-0.238496\pi\) | ||||
0.732194 | + | 0.681096i | \(0.238496\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −4.13335 | −0.217244 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.62222 | −0.137441 | ||||||||
\(365\) | 4.26671 | 0.223330 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.1240 | 1.10266 | 0.551332 | − | 0.834286i | \(-0.314120\pi\) | ||||
0.551332 | + | 0.834286i | \(0.314120\pi\) | |||||||
\(368\) | 1.37778 | 0.0718220 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.61285 | 0.187823 | ||||||||
\(371\) | −2.00000 | −0.103835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.1748 | 0.630389 | 0.315195 | − | 0.949027i | \(-0.397930\pi\) | ||||
0.315195 | + | 0.949027i | \(0.397930\pi\) | |||||||
\(374\) | −10.7556 | −0.556157 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.949145 | 0.0489484 | ||||||||
\(377\) | 25.2070 | 1.29822 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.5116 | −1.25908 | −0.629539 | − | 0.776969i | \(-0.716756\pi\) | ||||
−0.629539 | + | 0.776969i | \(0.716756\pi\) | |||||||
\(380\) | −0.622216 | −0.0319190 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.6035 | 1.05417 | ||||||||
\(383\) | −30.1017 | −1.53813 | −0.769063 | − | 0.639173i | \(-0.779277\pi\) | ||||
−0.769063 | + | 0.639173i | \(0.779277\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.51114 | 0.0770147 | ||||||||
\(386\) | 1.61285 | 0.0820918 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.67307 | 0.186472 | ||||||||
\(389\) | 9.70471 | 0.492049 | 0.246024 | − | 0.969264i | \(-0.420876\pi\) | ||||
0.246024 | + | 0.969264i | \(0.420876\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.10171 | 0.308577 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.43801 | 0.273963 | ||||||||
\(395\) | −9.16146 | −0.460963 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.61285 | 0.281701 | 0.140850 | − | 0.990031i | \(-0.455016\pi\) | ||||
0.140850 | + | 0.990031i | \(0.455016\pi\) | |||||||
\(398\) | −27.2257 | −1.36470 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.61285 | −0.230642 | ||||||||
\(401\) | −18.0830 | −0.903021 | −0.451510 | − | 0.892266i | \(-0.649115\pi\) | ||||
−0.451510 | + | 0.892266i | \(0.649115\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.98126 | 0.497202 | ||||||||
\(404\) | −3.37778 | −0.168051 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.61285 | −0.477078 | ||||||||
\(407\) | −14.1017 | −0.698996 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.4099 | 1.60257 | 0.801283 | − | 0.598285i | \(-0.204151\pi\) | ||||
0.801283 | + | 0.598285i | \(0.204151\pi\) | |||||||
\(410\) | 0.470127 | 0.0232179 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.2953 | −0.507212 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.95899 | 0.145251 | ||||||||
\(416\) | 2.62222 | 0.128565 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.42864 | 0.118789 | ||||||||
\(419\) | −22.9403 | −1.12070 | −0.560352 | − | 0.828254i | \(-0.689334\pi\) | ||||
−0.560352 | + | 0.828254i | \(0.689334\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.6637 | 0.909613 | 0.454807 | − | 0.890590i | \(-0.349708\pi\) | ||||
0.454807 | + | 0.890590i | \(0.349708\pi\) | |||||||
\(422\) | 20.8988 | 1.01734 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.00000 | 0.0971286 | ||||||||
\(425\) | −20.4286 | −0.990935 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.61285 | 0.271625 | ||||||||
\(428\) | 16.8573 | 0.814827 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.73683 | 0.228430 | ||||||||
\(431\) | −10.4889 | −0.505231 | −0.252615 | − | 0.967567i | \(-0.581291\pi\) | ||||
−0.252615 | + | 0.967567i | \(0.581291\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.2449 | −1.83793 | −0.918966 | − | 0.394336i | \(-0.870975\pi\) | ||||
−0.918966 | + | 0.394336i | \(0.870975\pi\) | |||||||
\(434\) | −3.80642 | −0.182714 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.41927 | 0.451101 | ||||||||
\(437\) | −1.37778 | −0.0659084 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.5210 | 0.836231 | 0.418115 | − | 0.908394i | \(-0.362691\pi\) | ||||
0.418115 | + | 0.908394i | \(0.362691\pi\) | |||||||
\(440\) | −1.51114 | −0.0720407 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.6128 | 0.552367 | ||||||||
\(443\) | −12.9175 | −0.613729 | −0.306865 | − | 0.951753i | \(-0.599280\pi\) | ||||
−0.306865 | + | 0.951753i | \(0.599280\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.24443 | 0.438228 | ||||||||
\(446\) | 11.1526 | 0.528089 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 6.97773 | 0.329299 | 0.164650 | − | 0.986352i | \(-0.447351\pi\) | ||||
0.164650 | + | 0.986352i | \(0.447351\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.83500 | −0.0864070 | ||||||||
\(452\) | 4.10171 | 0.192928 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.1240 | −0.803668 | ||||||||
\(455\) | −1.63158 | −0.0764898 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.8385 | −1.53612 | −0.768061 | − | 0.640377i | \(-0.778778\pi\) | ||||
−0.768061 | + | 0.640377i | \(0.778778\pi\) | |||||||
\(458\) | −15.2444 | −0.712325 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.857279 | 0.0399708 | ||||||||
\(461\) | −34.2163 | −1.59361 | −0.796807 | − | 0.604234i | \(-0.793479\pi\) | ||||
−0.796807 | + | 0.604234i | \(0.793479\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.2444 | 0.801417 | 0.400708 | − | 0.916206i | \(-0.368764\pi\) | ||||
0.400708 | + | 0.916206i | \(0.368764\pi\) | |||||||
\(464\) | 9.61285 | 0.446265 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.8573 | 0.780898 | ||||||||
\(467\) | −1.52987 | −0.0707941 | −0.0353970 | − | 0.999373i | \(-0.511270\pi\) | ||||
−0.0353970 | + | 0.999373i | \(0.511270\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.42864 | 0.204496 | ||||||||
\(470\) | 0.590573 | 0.0272411 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.4889 | −0.850119 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.61285 | 0.211652 | ||||||||
\(476\) | −4.42864 | −0.202986 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.99063 | 0.228266 | ||||||||
\(479\) | −19.5210 | −0.891936 | −0.445968 | − | 0.895049i | \(-0.647141\pi\) | ||||
−0.445968 | + | 0.895049i | \(0.647141\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.2257 | 0.694232 | ||||||||
\(482\) | 0.326929 | 0.0148912 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.10171 | −0.231896 | ||||||||
\(485\) | 2.28544 | 0.103777 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.0701 | −1.36260 | −0.681302 | − | 0.732002i | \(-0.738586\pi\) | ||||
−0.681302 | + | 0.732002i | \(0.738586\pi\) | |||||||
\(488\) | −5.61285 | −0.254082 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.622216 | 0.0281088 | ||||||||
\(491\) | −8.40990 | −0.379534 | −0.189767 | − | 0.981829i | \(-0.560773\pi\) | ||||
−0.189767 | + | 0.981829i | \(0.560773\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 42.5718 | 1.91734 | ||||||||
\(494\) | −2.62222 | −0.117979 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.80642 | 0.170913 | ||||||||
\(497\) | 0.857279 | 0.0384542 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.26671 | −0.191004 | −0.0955020 | − | 0.995429i | \(-0.530446\pi\) | ||||
−0.0955020 | + | 0.995429i | \(0.530446\pi\) | |||||||
\(500\) | −5.98126 | −0.267490 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.38715 | 0.285073 | ||||||||
\(503\) | 34.0098 | 1.51642 | 0.758212 | − | 0.652008i | \(-0.226073\pi\) | ||||
0.758212 | + | 0.652008i | \(0.226073\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.10171 | −0.0935249 | ||||||||
\(506\) | −3.34614 | −0.148754 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.47949 | −0.0656420 | ||||||||
\(509\) | −32.9590 | −1.46088 | −0.730441 | − | 0.682976i | \(-0.760685\pi\) | ||||
−0.730441 | + | 0.682976i | \(0.760685\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.85728 | −0.303348 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.00000 | 0.0882162 | ||||||||
\(515\) | −6.40589 | −0.282277 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.30513 | −0.101380 | ||||||||
\(518\) | −5.80642 | −0.255120 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.63158 | 0.0715497 | ||||||||
\(521\) | −39.9180 | −1.74884 | −0.874419 | − | 0.485171i | \(-0.838757\pi\) | ||||
−0.874419 | + | 0.485171i | \(0.838757\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.9813 | −1.48590 | −0.742948 | − | 0.669349i | \(-0.766573\pi\) | ||||
−0.742948 | + | 0.669349i | \(0.766573\pi\) | |||||||
\(524\) | −8.10171 | −0.353925 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.88892 | −0.300371 | ||||||||
\(527\) | 16.8573 | 0.734315 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.1017 | −0.917466 | ||||||||
\(530\) | 1.24443 | 0.0540546 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.00000 | 0.0433555 | ||||||||
\(533\) | 1.98126 | 0.0858181 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.4889 | 0.453473 | ||||||||
\(536\) | −4.42864 | −0.191288 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15.7146 | −0.677503 | ||||||||
\(539\) | −2.42864 | −0.104609 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.3684 | −0.531760 | −0.265880 | − | 0.964006i | \(-0.585662\pi\) | ||||
−0.265880 | + | 0.964006i | \(0.585662\pi\) | |||||||
\(542\) | −18.1017 | −0.777535 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.42864 | 0.189876 | ||||||||
\(545\) | 5.86082 | 0.251050 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.71408 | −0.287073 | −0.143537 | − | 0.989645i | \(-0.545848\pi\) | ||||
−0.143537 | + | 0.989645i | \(0.545848\pi\) | |||||||
\(548\) | 2.75557 | 0.117712 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.2029 | 0.477695 | ||||||||
\(551\) | −9.61285 | −0.409521 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.7239 | 0.626125 | ||||||||
\(554\) | 6.59057 | 0.280007 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.1017 | −0.428408 | ||||||||
\(557\) | −30.5620 | −1.29495 | −0.647477 | − | 0.762085i | \(-0.724176\pi\) | ||||
−0.647477 | + | 0.762085i | \(0.724176\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.9625 | 0.844325 | ||||||||
\(560\) | −0.622216 | −0.0262934 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.6128 | −0.742953 | ||||||||
\(563\) | −7.02227 | −0.295954 | −0.147977 | − | 0.988991i | \(-0.547276\pi\) | ||||
−0.147977 | + | 0.988991i | \(0.547276\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.55215 | 0.107370 | ||||||||
\(566\) | 7.61285 | 0.319992 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.857279 | −0.0359706 | ||||||||
\(569\) | 24.1847 | 1.01387 | 0.506937 | − | 0.861983i | \(-0.330778\pi\) | ||||
0.506937 | + | 0.861983i | \(0.330778\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.22216 | −0.260389 | −0.130195 | − | 0.991488i | \(-0.541560\pi\) | ||||
−0.130195 | + | 0.991488i | \(0.541560\pi\) | |||||||
\(572\) | −6.36842 | −0.266277 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.755569 | −0.0315368 | ||||||||
\(575\) | −6.35551 | −0.265043 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.7975 | 1.65679 | 0.828396 | − | 0.560142i | \(-0.189254\pi\) | ||||
0.828396 | + | 0.560142i | \(0.189254\pi\) | |||||||
\(578\) | 2.61285 | 0.108680 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.98126 | 0.248358 | ||||||||
\(581\) | −4.75557 | −0.197294 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.85728 | −0.201168 | ||||||||
\(584\) | 6.85728 | 0.283756 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.2257 | 0.711587 | ||||||||
\(587\) | 24.5718 | 1.01419 | 0.507094 | − | 0.861891i | \(-0.330720\pi\) | ||||
0.507094 | + | 0.861891i | \(0.330720\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.80642 | −0.156841 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.80642 | 0.238643 | ||||||||
\(593\) | −8.81579 | −0.362021 | −0.181011 | − | 0.983481i | \(-0.557937\pi\) | ||||
−0.181011 | + | 0.983481i | \(0.557937\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.75557 | −0.112967 | ||||||||
\(596\) | 1.43801 | 0.0589031 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.61285 | 0.147740 | ||||||||
\(599\) | 4.47013 | 0.182644 | 0.0913222 | − | 0.995821i | \(-0.470891\pi\) | ||||
0.0913222 | + | 0.995821i | \(0.470891\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.1432 | −0.495331 | −0.247666 | − | 0.968846i | \(-0.579663\pi\) | ||||
−0.247666 | + | 0.968846i | \(0.579663\pi\) | |||||||
\(602\) | −7.61285 | −0.310277 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.74620 | −0.396567 | ||||||||
\(605\) | −3.17436 | −0.129056 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.7431 | 1.45077 | 0.725385 | − | 0.688344i | \(-0.241662\pi\) | ||||
0.725385 | + | 0.688344i | \(0.241662\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.49240 | −0.141403 | ||||||||
\(611\) | 2.48886 | 0.100689 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.5111 | 0.626489 | 0.313244 | − | 0.949673i | \(-0.398584\pi\) | ||||
0.313244 | + | 0.949673i | \(0.398584\pi\) | |||||||
\(614\) | −9.24443 | −0.373075 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.42864 | 0.0978527 | ||||||||
\(617\) | 16.6539 | 0.670459 | 0.335230 | − | 0.942136i | \(-0.391186\pi\) | ||||
0.335230 | + | 0.942136i | \(0.391186\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.9813 | −1.20505 | −0.602524 | − | 0.798100i | \(-0.705838\pi\) | ||||
−0.602524 | + | 0.798100i | \(0.705838\pi\) | |||||||
\(620\) | 2.36842 | 0.0951179 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.0321 | 0.682926 | ||||||||
\(623\) | −14.8573 | −0.595244 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.3426 | 0.773704 | ||||||||
\(626\) | −14.0000 | −0.559553 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.71456 | −0.307844 | ||||||||
\(629\) | 25.7146 | 1.02531 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.4701 | 1.29262 | 0.646308 | − | 0.763077i | \(-0.276312\pi\) | ||||
0.646308 | + | 0.763077i | \(0.276312\pi\) | |||||||
\(632\) | −14.7239 | −0.585686 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.22570 | −0.207539 | ||||||||
\(635\) | −0.920565 | −0.0365315 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.62222 | 0.103896 | ||||||||
\(638\) | −23.3461 | −0.924283 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.622216 | 0.0245952 | ||||||||
\(641\) | −17.2257 | −0.680374 | −0.340187 | − | 0.940358i | \(-0.610490\pi\) | ||||
−0.340187 | + | 0.940358i | \(0.610490\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.7975 | −1.17510 | −0.587550 | − | 0.809188i | \(-0.699907\pi\) | ||||
−0.587550 | + | 0.809188i | \(0.699907\pi\) | |||||||
\(644\) | −1.37778 | −0.0542923 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.42864 | −0.174242 | ||||||||
\(647\) | −42.0098 | −1.65158 | −0.825789 | − | 0.563980i | \(-0.809270\pi\) | ||||
−0.825789 | + | 0.563980i | \(0.809270\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −12.0959 | −0.474440 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.51114 | −0.372485 | ||||||||
\(653\) | 25.5210 | 0.998713 | 0.499357 | − | 0.866397i | \(-0.333570\pi\) | ||||
0.499357 | + | 0.866397i | \(0.333570\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.04101 | −0.196969 | ||||||||
\(656\) | 0.755569 | 0.0295000 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.949145 | −0.0370015 | ||||||||
\(659\) | −29.0607 | −1.13204 | −0.566022 | − | 0.824390i | \(-0.691518\pi\) | ||||
−0.566022 | + | 0.824390i | \(0.691518\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.9906 | 1.12760 | 0.563802 | − | 0.825910i | \(-0.309338\pi\) | ||||
0.563802 | + | 0.825910i | \(0.309338\pi\) | |||||||
\(662\) | −19.7748 | −0.768569 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.75557 | 0.184552 | ||||||||
\(665\) | 0.622216 | 0.0241285 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.2444 | 0.512826 | ||||||||
\(668\) | −5.24443 | −0.202913 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.75557 | −0.106457 | ||||||||
\(671\) | 13.6316 | 0.526241 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.9813 | 1.23279 | 0.616394 | − | 0.787438i | \(-0.288593\pi\) | ||||
0.616394 | + | 0.787438i | \(0.288593\pi\) | |||||||
\(674\) | 13.1427 | 0.506239 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.12399 | −0.235538 | ||||||||
\(677\) | −4.01874 | −0.154453 | −0.0772263 | − | 0.997014i | \(-0.524606\pi\) | ||||
−0.0772263 | + | 0.997014i | \(0.524606\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.67307 | −0.140960 | ||||||||
\(680\) | 2.75557 | 0.105671 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.24443 | −0.353988 | ||||||||
\(683\) | −4.53341 | −0.173466 | −0.0867331 | − | 0.996232i | \(-0.527643\pi\) | ||||
−0.0867331 | + | 0.996232i | \(0.527643\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.71456 | 0.0655099 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.61285 | 0.290237 | ||||||||
\(689\) | 5.24443 | 0.199797 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.6548 | −1.47050 | −0.735249 | − | 0.677797i | \(-0.762935\pi\) | ||||
−0.735249 | + | 0.677797i | \(0.762935\pi\) | |||||||
\(692\) | −23.7146 | −0.901492 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.3082 | −0.846807 | ||||||||
\(695\) | −6.28544 | −0.238420 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.34614 | 0.126744 | ||||||||
\(698\) | −3.24443 | −0.122804 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.61285 | 0.174349 | ||||||||
\(701\) | 26.6824 | 1.00778 | 0.503891 | − | 0.863767i | \(-0.331901\pi\) | ||||
0.503891 | + | 0.863767i | \(0.331901\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.80642 | −0.218993 | ||||||||
\(704\) | −2.42864 | −0.0915328 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.9585 | −0.450065 | ||||||||
\(707\) | 3.37778 | 0.127035 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.6735 | 1.15197 | 0.575985 | − | 0.817461i | \(-0.304619\pi\) | ||||
0.575985 | + | 0.817461i | \(0.304619\pi\) | |||||||
\(710\) | −0.533412 | −0.0200186 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.8573 | 0.556800 | ||||||||
\(713\) | 5.24443 | 0.196405 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.96253 | −0.148190 | ||||||||
\(716\) | 24.2034 | 0.904524 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 27.7462 | 1.03548 | ||||||||
\(719\) | 2.58073 | 0.0962449 | 0.0481225 | − | 0.998841i | \(-0.484676\pi\) | ||||
0.0481225 | + | 0.998841i | \(0.484676\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.2953 | 0.383417 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.13335 | −0.153615 | ||||||||
\(725\) | −44.3426 | −1.64684 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.20342 | −0.155896 | −0.0779481 | − | 0.996957i | \(-0.524837\pi\) | ||||
−0.0779481 | + | 0.996957i | \(0.524837\pi\) | |||||||
\(728\) | −2.62222 | −0.0971858 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.26671 | 0.157918 | ||||||||
\(731\) | 33.7146 | 1.24698 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.0187359 | 0.000692025 0 | 0.000346012 | − | 1.00000i | \(-0.499890\pi\) | ||||
0.000346012 | 1.00000i | \(0.499890\pi\) | ||||||||
\(734\) | 21.1240 | 0.779701 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.37778 | 0.0507858 | ||||||||
\(737\) | 10.7556 | 0.396186 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.0830 | −1.32733 | −0.663667 | − | 0.748028i | \(-0.731001\pi\) | ||||
−0.663667 | + | 0.748028i | \(0.731001\pi\) | |||||||
\(740\) | 3.61285 | 0.132811 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.00000 | −0.0734223 | ||||||||
\(743\) | 16.8573 | 0.618434 | 0.309217 | − | 0.950992i | \(-0.399933\pi\) | ||||
0.309217 | + | 0.950992i | \(0.399933\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.894751 | 0.0327811 | ||||||||
\(746\) | 12.1748 | 0.445753 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.7556 | −0.393263 | ||||||||
\(749\) | −16.8573 | −0.615952 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.8702 | 1.12647 | 0.563235 | − | 0.826297i | \(-0.309557\pi\) | ||||
0.563235 | + | 0.826297i | \(0.309557\pi\) | |||||||
\(752\) | 0.949145 | 0.0346118 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 25.2070 | 0.917983 | ||||||||
\(755\) | −6.06424 | −0.220700 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.9180 | 1.16008 | 0.580039 | − | 0.814588i | \(-0.303037\pi\) | ||||
0.580039 | + | 0.814588i | \(0.303037\pi\) | |||||||
\(758\) | −24.5116 | −0.890302 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.622216 | −0.0225701 | ||||||||
\(761\) | 28.5116 | 1.03355 | 0.516773 | − | 0.856123i | \(-0.327133\pi\) | ||||
0.516773 | + | 0.856123i | \(0.327133\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.41927 | −0.341001 | ||||||||
\(764\) | 20.6035 | 0.745408 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.1017 | −1.08762 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.4514 | 0.881740 | 0.440870 | − | 0.897571i | \(-0.354670\pi\) | ||||
0.440870 | + | 0.897571i | \(0.354670\pi\) | |||||||
\(770\) | 1.51114 | 0.0544576 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.61285 | 0.0580477 | ||||||||
\(773\) | −0.0187359 | −0.000673882 0 | −0.000336941 | − | 1.00000i | \(-0.500107\pi\) | ||||
−0.000336941 | 1.00000i | \(0.500107\pi\) | ||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.5585 | −0.630718 | ||||||||
\(776\) | 3.67307 | 0.131856 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.70471 | 0.347931 | ||||||||
\(779\) | −0.755569 | −0.0270711 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.08202 | 0.0745006 | ||||||||
\(782\) | 6.10171 | 0.218197 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −4.80012 | −0.171324 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.83500 | 0.350580 | 0.175290 | − | 0.984517i | \(-0.443914\pi\) | ||||
0.175290 | + | 0.984517i | \(0.443914\pi\) | |||||||
\(788\) | 5.43801 | 0.193721 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.16146 | −0.325950 | ||||||||
\(791\) | −4.10171 | −0.145840 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.7181 | −0.522655 | ||||||||
\(794\) | 5.61285 | 0.199193 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −27.2257 | −0.964989 | ||||||||
\(797\) | −21.9367 | −0.777038 | −0.388519 | − | 0.921441i | \(-0.627013\pi\) | ||||
−0.388519 | + | 0.921441i | \(0.627013\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.20342 | 0.148706 | ||||||||
\(800\) | −4.61285 | −0.163089 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.0830 | −0.638532 | ||||||||
\(803\) | −16.6539 | −0.587702 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.857279 | −0.0302151 | ||||||||
\(806\) | 9.98126 | 0.351575 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.37778 | −0.118830 | ||||||||
\(809\) | −43.0420 | −1.51327 | −0.756637 | − | 0.653835i | \(-0.773159\pi\) | ||||
−0.756637 | + | 0.653835i | \(0.773159\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.4104 | 1.45412 | 0.727058 | − | 0.686577i | \(-0.240887\pi\) | ||||
0.727058 | + | 0.686577i | \(0.240887\pi\) | |||||||
\(812\) | −9.61285 | −0.337345 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −14.1017 | −0.494265 | ||||||||
\(815\) | −5.91798 | −0.207298 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.61285 | −0.266340 | ||||||||
\(818\) | 32.4099 | 1.13319 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.470127 | 0.0164175 | ||||||||
\(821\) | 50.7654 | 1.77173 | 0.885863 | − | 0.463948i | \(-0.153567\pi\) | ||||
0.885863 | + | 0.463948i | \(0.153567\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.9813 | −0.487356 | −0.243678 | − | 0.969856i | \(-0.578354\pi\) | ||||
−0.243678 | + | 0.969856i | \(0.578354\pi\) | |||||||
\(824\) | −10.2953 | −0.358653 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.6923 | 1.20637 | 0.603184 | − | 0.797602i | \(-0.293898\pi\) | ||||
0.603184 | + | 0.797602i | \(0.293898\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.96836 | −0.0683639 | −0.0341819 | − | 0.999416i | \(-0.510883\pi\) | ||||
−0.0341819 | + | 0.999416i | \(0.510883\pi\) | |||||||
\(830\) | 2.95899 | 0.102708 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.62222 | 0.0909090 | ||||||||
\(833\) | 4.42864 | 0.153443 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.26317 | −0.112927 | ||||||||
\(836\) | 2.42864 | 0.0839963 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22.9403 | −0.792458 | ||||||||
\(839\) | −2.16500 | −0.0747440 | −0.0373720 | − | 0.999301i | \(-0.511899\pi\) | ||||
−0.0373720 | + | 0.999301i | \(0.511899\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 63.4068 | 2.18644 | ||||||||
\(842\) | 18.6637 | 0.643194 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.8988 | 0.719365 | ||||||||
\(845\) | −3.81044 | −0.131083 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.10171 | 0.175297 | ||||||||
\(848\) | 2.00000 | 0.0686803 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −20.4286 | −0.700697 | ||||||||
\(851\) | 8.00000 | 0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 55.7975 | 1.91047 | 0.955236 | − | 0.295846i | \(-0.0956016\pi\) | ||||
0.955236 | + | 0.295846i | \(0.0956016\pi\) | |||||||
\(854\) | 5.61285 | 0.192068 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.8573 | 0.576170 | ||||||||
\(857\) | −52.5718 | −1.79582 | −0.897910 | − | 0.440179i | \(-0.854915\pi\) | ||||
−0.897910 | + | 0.440179i | \(0.854915\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.95899 | 0.100959 | 0.0504797 | − | 0.998725i | \(-0.483925\pi\) | ||||
0.0504797 | + | 0.998725i | \(0.483925\pi\) | |||||||
\(860\) | 4.73683 | 0.161525 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.4889 | −0.357252 | ||||||||
\(863\) | −13.0607 | −0.444591 | −0.222296 | − | 0.974979i | \(-0.571355\pi\) | ||||
−0.222296 | + | 0.974979i | \(0.571355\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.7556 | −0.501704 | ||||||||
\(866\) | −38.2449 | −1.29961 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.80642 | −0.129198 | ||||||||
\(869\) | 35.7591 | 1.21304 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.6128 | −0.393486 | ||||||||
\(872\) | 9.41927 | 0.318977 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.37778 | −0.0466043 | ||||||||
\(875\) | 5.98126 | 0.202204 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.1116 | −0.814189 | −0.407095 | − | 0.913386i | \(-0.633458\pi\) | ||||
−0.407095 | + | 0.913386i | \(0.633458\pi\) | |||||||
\(878\) | 17.5210 | 0.591304 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.51114 | −0.0509404 | ||||||||
\(881\) | 44.0415 | 1.48380 | 0.741898 | − | 0.670513i | \(-0.233926\pi\) | ||||
0.741898 | + | 0.670513i | \(0.233926\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.24443 | −0.311100 | −0.155550 | − | 0.987828i | \(-0.549715\pi\) | ||||
−0.155550 | + | 0.987828i | \(0.549715\pi\) | |||||||
\(884\) | 11.6128 | 0.390582 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.9175 | −0.433972 | ||||||||
\(887\) | −8.77430 | −0.294612 | −0.147306 | − | 0.989091i | \(-0.547060\pi\) | ||||
−0.147306 | + | 0.989091i | \(0.547060\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.47949 | 0.0496207 | ||||||||
\(890\) | 9.24443 | 0.309874 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.1526 | 0.373416 | ||||||||
\(893\) | −0.949145 | −0.0317619 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.0597 | 0.503392 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.97773 | 0.232850 | ||||||||
\(899\) | 36.5906 | 1.22036 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.85728 | 0.295079 | ||||||||
\(902\) | −1.83500 | −0.0610990 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.10171 | 0.136421 | ||||||||
\(905\) | −2.57184 | −0.0854908 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.0602 | −0.466862 | −0.233431 | − | 0.972373i | \(-0.574995\pi\) | ||||
−0.233431 | + | 0.972373i | \(0.574995\pi\) | |||||||
\(908\) | −17.1240 | −0.568279 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.63158 | −0.0540865 | ||||||||
\(911\) | −30.9590 | −1.02572 | −0.512859 | − | 0.858473i | \(-0.671413\pi\) | ||||
−0.512859 | + | 0.858473i | \(0.671413\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.5496 | −0.382235 | ||||||||
\(914\) | −32.8385 | −1.08620 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.2444 | −0.503690 | ||||||||
\(917\) | 8.10171 | 0.267542 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.9813 | 0.988991 | 0.494495 | − | 0.869180i | \(-0.335353\pi\) | ||||
0.494495 | + | 0.869180i | \(0.335353\pi\) | |||||||
\(920\) | 0.857279 | 0.0282637 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −34.2163 | −1.12685 | ||||||||
\(923\) | −2.24797 | −0.0739928 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26.7841 | −0.880657 | ||||||||
\(926\) | 17.2444 | 0.566687 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.61285 | 0.315557 | ||||||||
\(929\) | 26.1432 | 0.857730 | 0.428865 | − | 0.903368i | \(-0.358914\pi\) | ||||
0.428865 | + | 0.903368i | \(0.358914\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | 16.8573 | 0.552179 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.52987 | −0.0500590 | ||||||||
\(935\) | −6.69228 | −0.218861 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.02227 | 0.294745 | 0.147372 | − | 0.989081i | \(-0.452918\pi\) | ||||
0.147372 | + | 0.989081i | \(0.452918\pi\) | |||||||
\(938\) | 4.42864 | 0.144600 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.590573 | 0.0192624 | ||||||||
\(941\) | 49.1624 | 1.60265 | 0.801324 | − | 0.598230i | \(-0.204129\pi\) | ||||
0.801324 | + | 0.598230i | \(0.204129\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.04101 | 0.0339000 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18.4889 | −0.601125 | ||||||||
\(947\) | 7.59010 | 0.246645 | 0.123322 | − | 0.992367i | \(-0.460645\pi\) | ||||
0.123322 | + | 0.992367i | \(0.460645\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.9813 | 0.583697 | ||||||||
\(950\) | 4.61285 | 0.149661 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.42864 | −0.143533 | ||||||||
\(953\) | −10.3872 | −0.336473 | −0.168236 | − | 0.985747i | \(-0.553807\pi\) | ||||
−0.168236 | + | 0.985747i | \(0.553807\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.8198 | 0.414839 | ||||||||
\(956\) | 4.99063 | 0.161409 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −19.5210 | −0.630694 | ||||||||
\(959\) | −2.75557 | −0.0889820 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5111 | −0.532617 | ||||||||
\(962\) | 15.2257 | 0.490896 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.326929 | 0.0105297 | ||||||||
\(965\) | 1.00354 | 0.0323051 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.0000 | −0.514525 | −0.257263 | − | 0.966342i | \(-0.582821\pi\) | ||||
−0.257263 | + | 0.966342i | \(0.582821\pi\) | |||||||
\(968\) | −5.10171 | −0.163975 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.28544 | 0.0733811 | ||||||||
\(971\) | 28.7940 | 0.924043 | 0.462022 | − | 0.886869i | \(-0.347124\pi\) | ||||
0.462022 | + | 0.886869i | \(0.347124\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.1017 | 0.323846 | ||||||||
\(974\) | −30.0701 | −0.963507 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.61285 | −0.179663 | ||||||||
\(977\) | 5.14272 | 0.164530 | 0.0822651 | − | 0.996610i | \(-0.473785\pi\) | ||||
0.0822651 | + | 0.996610i | \(0.473785\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.0830 | −1.15322 | ||||||||
\(980\) | 0.622216 | 0.0198759 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.40990 | −0.268371 | ||||||||
\(983\) | −10.7556 | −0.343049 | −0.171525 | − | 0.985180i | \(-0.554869\pi\) | ||||
−0.171525 | + | 0.985180i | \(0.554869\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.38361 | 0.107811 | ||||||||
\(986\) | 42.5718 | 1.35576 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.62222 | −0.0834238 | ||||||||
\(989\) | 10.4889 | 0.333526 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.15563 | −0.0367097 | −0.0183549 | − | 0.999832i | \(-0.505843\pi\) | ||||
−0.0183549 | + | 0.999832i | \(0.505843\pi\) | |||||||
\(992\) | 3.80642 | 0.120854 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.857279 | 0.0271912 | ||||||||
\(995\) | −16.9403 | −0.537042 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.2034 | −0.829871 | −0.414935 | − | 0.909851i | \(-0.636196\pi\) | ||||
−0.414935 | + | 0.909851i | \(0.636196\pi\) | |||||||
\(998\) | −4.26671 | −0.135060 | ||||||||
\(999\) | 0 | 0 |
(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 | 2394.2.a.bc.1.2 | yes | 3 | |
3.2 | odd | 2 | 2394.2.a.bb.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2394.2.a.bb.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
2394.2.a.bc.1.2 | yes | 3 | 1.1 | even | 1 | trivial |