Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4851,2,Mod(1,4851)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4851, 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("4851.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4851 = 3^{2} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4851.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: | \(38.7354300205\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1617) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4851.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.61803 | 1.85123 | 0.925615 | − | 0.378467i | \(-0.123549\pi\) | ||||
0.925615 | + | 0.378467i | \(0.123549\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.85410 | 2.42705 | ||||||||
\(5\) | 2.23607 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 7.47214 | 2.64180 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.85410 | 1.85123 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.47214 | 0.962997 | 0.481499 | − | 0.876447i | \(-0.340093\pi\) | ||||
0.481499 | + | 0.876447i | \(0.340093\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9.85410 | 2.46353 | ||||||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.23607 | −0.971821 | −0.485910 | − | 0.874009i | \(-0.661512\pi\) | ||||
−0.485910 | + | 0.874009i | \(0.661512\pi\) | |||||||
\(20\) | 10.8541 | 2.42705 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.61803 | 0.558167 | ||||||||
\(23\) | 2.47214 | 0.515476 | 0.257738 | − | 0.966215i | \(-0.417023\pi\) | ||||
0.257738 | + | 0.966215i | \(0.417023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 9.09017 | 1.78273 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.2361 | 1.90079 | 0.950395 | − | 0.311045i | \(-0.100679\pi\) | ||||
0.950395 | + | 0.311045i | \(0.100679\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.47214 | 1.52164 | 0.760820 | − | 0.648963i | \(-0.224797\pi\) | ||||
0.760820 | + | 0.648963i | \(0.224797\pi\) | |||||||
\(32\) | 10.8541 | 1.91875 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −15.7082 | −2.69393 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.527864 | −0.0867803 | −0.0433902 | − | 0.999058i | \(-0.513816\pi\) | ||||
−0.0433902 | + | 0.999058i | \(0.513816\pi\) | |||||||
\(38\) | −11.0902 | −1.79906 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 16.7082 | 2.64180 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.472136 | −0.0720001 | −0.0360000 | − | 0.999352i | \(-0.511462\pi\) | ||||
−0.0360000 | + | 0.999352i | \(0.511462\pi\) | |||||||
\(44\) | 4.85410 | 0.731783 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.47214 | 0.954264 | ||||||||
\(47\) | −11.4721 | −1.67338 | −0.836692 | − | 0.547674i | \(-0.815513\pi\) | ||||
−0.836692 | + | 0.547674i | \(0.815513\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 16.8541 | 2.33724 | ||||||||
\(53\) | 12.9443 | 1.77803 | 0.889016 | − | 0.457876i | \(-0.151390\pi\) | ||||
0.889016 | + | 0.457876i | \(0.151390\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.23607 | 0.301511 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 26.7984 | 3.51880 | ||||||||
\(59\) | 11.9443 | 1.55501 | 0.777506 | − | 0.628876i | \(-0.216485\pi\) | ||||
0.777506 | + | 0.628876i | \(0.216485\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.94427 | −0.889123 | −0.444561 | − | 0.895748i | \(-0.646640\pi\) | ||||
−0.444561 | + | 0.895748i | \(0.646640\pi\) | |||||||
\(62\) | 22.1803 | 2.81691 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.70820 | 1.08853 | ||||||||
\(65\) | 7.76393 | 0.962997 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.708204 | 0.0865209 | 0.0432604 | − | 0.999064i | \(-0.486225\pi\) | ||||
0.0432604 | + | 0.999064i | \(0.486225\pi\) | |||||||
\(68\) | −29.1246 | −3.53188 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.47214 | −0.530745 | −0.265372 | − | 0.964146i | \(-0.585495\pi\) | ||||
−0.265372 | + | 0.964146i | \(0.585495\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | −0.117041 | −0.0585206 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585206 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(74\) | −1.38197 | −0.160650 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −20.5623 | −2.35866 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.47214 | −0.278137 | −0.139069 | − | 0.990283i | \(-0.544411\pi\) | ||||
−0.139069 | + | 0.990283i | \(0.544411\pi\) | |||||||
\(80\) | 22.0344 | 2.46353 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −15.7082 | −1.73468 | ||||||||
\(83\) | −12.4721 | −1.36899 | −0.684497 | − | 0.729015i | \(-0.739978\pi\) | ||||
−0.684497 | + | 0.729015i | \(0.739978\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.4164 | −1.45521 | ||||||||
\(86\) | −1.23607 | −0.133289 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.47214 | 0.796532 | ||||||||
\(89\) | 13.4164 | 1.42214 | 0.711068 | − | 0.703123i | \(-0.248212\pi\) | ||||
0.711068 | + | 0.703123i | \(0.248212\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 12.0000 | 1.25109 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −30.0344 | −3.09782 | ||||||||
\(95\) | −9.47214 | −0.971821 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.94427 | −0.705084 | −0.352542 | − | 0.935796i | \(-0.614683\pi\) | ||||
−0.352542 | + | 0.935796i | \(0.614683\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.52786 | −0.351036 | −0.175518 | − | 0.984476i | \(-0.556160\pi\) | ||||
−0.175518 | + | 0.984476i | \(0.556160\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.41641 | −0.730760 | −0.365380 | − | 0.930858i | \(-0.619061\pi\) | ||||
−0.365380 | + | 0.930858i | \(0.619061\pi\) | |||||||
\(104\) | 25.9443 | 2.54405 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 33.8885 | 3.29155 | ||||||||
\(107\) | −19.9443 | −1.92809 | −0.964043 | − | 0.265747i | \(-0.914381\pi\) | ||||
−0.964043 | + | 0.265747i | \(0.914381\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.00000 | 0.574696 | 0.287348 | − | 0.957826i | \(-0.407226\pi\) | ||||
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | 5.85410 | 0.558167 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.47214 | −0.608847 | −0.304424 | − | 0.952537i | \(-0.598464\pi\) | ||||
−0.304424 | + | 0.952537i | \(0.598464\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.52786 | 0.515476 | ||||||||
\(116\) | 49.6869 | 4.61331 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 31.2705 | 2.87868 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −18.1803 | −1.64597 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 41.1246 | 3.69310 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000 | 1.41977 | 0.709885 | − | 0.704317i | \(-0.248747\pi\) | ||||
0.709885 | + | 0.704317i | \(0.248747\pi\) | |||||||
\(128\) | 1.09017 | 0.0963583 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 20.3262 | 1.78273 | ||||||||
\(131\) | 4.47214 | 0.390732 | 0.195366 | − | 0.980730i | \(-0.437410\pi\) | ||||
0.195366 | + | 0.980730i | \(0.437410\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.85410 | 0.160170 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −44.8328 | −3.84438 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.7082 | −0.982531 | ||||||||
\(143\) | 3.47214 | 0.290355 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.8885 | 1.90079 | ||||||||
\(146\) | −2.61803 | −0.216670 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.56231 | −0.210620 | ||||||||
\(149\) | −15.6525 | −1.28230 | −0.641150 | − | 0.767415i | \(-0.721543\pi\) | ||||
−0.641150 | + | 0.767415i | \(0.721543\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.94427 | −0.565117 | −0.282558 | − | 0.959250i | \(-0.591183\pi\) | ||||
−0.282558 | + | 0.959250i | \(0.591183\pi\) | |||||||
\(152\) | −31.6525 | −2.56735 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.9443 | 1.52164 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.41641 | 0.272659 | 0.136330 | − | 0.990664i | \(-0.456469\pi\) | ||||
0.136330 | + | 0.990664i | \(0.456469\pi\) | |||||||
\(158\) | −6.47214 | −0.514895 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 24.2705 | 1.91875 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.1246 | −1.41963 | −0.709815 | − | 0.704389i | \(-0.751221\pi\) | ||||
−0.709815 | + | 0.704389i | \(0.751221\pi\) | |||||||
\(164\) | −29.1246 | −2.27425 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −32.6525 | −2.53432 | ||||||||
\(167\) | −18.4721 | −1.42942 | −0.714708 | − | 0.699423i | \(-0.753441\pi\) | ||||
−0.714708 | + | 0.699423i | \(0.753441\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.944272 | −0.0726363 | ||||||||
\(170\) | −35.1246 | −2.69393 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.29180 | −0.174748 | ||||||||
\(173\) | −5.52786 | −0.420276 | −0.210138 | − | 0.977672i | \(-0.567391\pi\) | ||||
−0.210138 | + | 0.977672i | \(0.567391\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.85410 | 0.742781 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 35.1246 | 2.63270 | ||||||||
\(179\) | 5.52786 | 0.413172 | 0.206586 | − | 0.978428i | \(-0.433765\pi\) | ||||
0.206586 | + | 0.978428i | \(0.433765\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.472136 | 0.0350936 | 0.0175468 | − | 0.999846i | \(-0.494414\pi\) | ||||
0.0175468 | + | 0.999846i | \(0.494414\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 18.4721 | 1.36178 | ||||||||
\(185\) | −1.18034 | −0.0867803 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00000 | −0.438763 | ||||||||
\(188\) | −55.6869 | −4.06139 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −24.7984 | −1.79906 | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.8885 | 1.86350 | 0.931749 | − | 0.363103i | \(-0.118283\pi\) | ||||
0.931749 | + | 0.363103i | \(0.118283\pi\) | |||||||
\(194\) | −18.1803 | −1.30527 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.47214 | 0.603615 | 0.301807 | − | 0.953369i | \(-0.402410\pi\) | ||||
0.301807 | + | 0.953369i | \(0.402410\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.4721 | 1.73478 | 0.867392 | − | 0.497626i | \(-0.165795\pi\) | ||||
0.867392 | + | 0.497626i | \(0.165795\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.23607 | −0.649847 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.4164 | −0.937043 | ||||||||
\(206\) | −19.4164 | −1.35281 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 34.2148 | 2.37237 | ||||||||
\(209\) | −4.23607 | −0.293015 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.9443 | 1.30418 | 0.652089 | − | 0.758143i | \(-0.273893\pi\) | ||||
0.652089 | + | 0.758143i | \(0.273893\pi\) | |||||||
\(212\) | 62.8328 | 4.31538 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −52.2148 | −3.56933 | ||||||||
\(215\) | −1.05573 | −0.0720001 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 15.7082 | 1.06389 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.8541 | 0.731783 | ||||||||
\(221\) | −20.8328 | −1.40137 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.0000 | 1.20537 | 0.602685 | − | 0.797980i | \(-0.294098\pi\) | ||||
0.602685 | + | 0.797980i | \(0.294098\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.9443 | −1.12712 | ||||||||
\(227\) | −26.8328 | −1.78096 | −0.890478 | − | 0.455026i | \(-0.849630\pi\) | ||||
−0.890478 | + | 0.455026i | \(0.849630\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.4164 | 1.01874 | 0.509372 | − | 0.860546i | \(-0.329878\pi\) | ||||
0.509372 | + | 0.860546i | \(0.329878\pi\) | |||||||
\(230\) | 14.4721 | 0.954264 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 76.4853 | 5.02151 | ||||||||
\(233\) | −13.4164 | −0.878938 | −0.439469 | − | 0.898258i | \(-0.644833\pi\) | ||||
−0.439469 | + | 0.898258i | \(0.644833\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.6525 | −1.67338 | ||||||||
\(236\) | 57.9787 | 3.77409 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.3607 | −1.12297 | −0.561485 | − | 0.827487i | \(-0.689770\pi\) | ||||
−0.561485 | + | 0.827487i | \(0.689770\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.0000 | −1.22390 | −0.611949 | − | 0.790897i | \(-0.709614\pi\) | ||||
−0.611949 | + | 0.790897i | \(0.709614\pi\) | |||||||
\(242\) | 2.61803 | 0.168294 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −33.7082 | −2.15795 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.7082 | −0.935861 | ||||||||
\(248\) | 63.3050 | 4.01987 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −29.2705 | −1.85123 | ||||||||
\(251\) | −3.94427 | −0.248960 | −0.124480 | − | 0.992222i | \(-0.539726\pi\) | ||||
−0.124480 | + | 0.992222i | \(0.539726\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.47214 | 0.155422 | ||||||||
\(254\) | 41.8885 | 2.62832 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.5623 | −0.910144 | ||||||||
\(257\) | 7.76393 | 0.484301 | 0.242150 | − | 0.970239i | \(-0.422147\pi\) | ||||
0.242150 | + | 0.970239i | \(0.422147\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 37.6869 | 2.33724 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.7082 | 0.723335 | ||||||||
\(263\) | 4.41641 | 0.272327 | 0.136164 | − | 0.990686i | \(-0.456523\pi\) | ||||
0.136164 | + | 0.990686i | \(0.456523\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.9443 | 1.77803 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.43769 | 0.209991 | ||||||||
\(269\) | 16.4721 | 1.00432 | 0.502162 | − | 0.864774i | \(-0.332538\pi\) | ||||
0.502162 | + | 0.864774i | \(0.332538\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.29180 | 0.321454 | 0.160727 | − | 0.986999i | \(-0.448616\pi\) | ||||
0.160727 | + | 0.986999i | \(0.448616\pi\) | |||||||
\(272\) | −59.1246 | −3.58496 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.7082 | −0.948967 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.9443 | −1.13825 | −0.569125 | − | 0.822251i | \(-0.692718\pi\) | ||||
−0.569125 | + | 0.822251i | \(0.692718\pi\) | |||||||
\(278\) | 20.9443 | 1.25615 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.18034 | −0.309033 | −0.154517 | − | 0.987990i | \(-0.549382\pi\) | ||||
−0.154517 | + | 0.987990i | \(0.549382\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.70820 | 0.279874 | 0.139937 | − | 0.990160i | \(-0.455310\pi\) | ||||
0.139937 | + | 0.990160i | \(0.455310\pi\) | |||||||
\(284\) | −21.7082 | −1.28814 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.09017 | 0.537513 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 59.9230 | 3.51880 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.85410 | −0.284065 | ||||||||
\(293\) | 9.88854 | 0.577695 | 0.288847 | − | 0.957375i | \(-0.406728\pi\) | ||||
0.288847 | + | 0.957375i | \(0.406728\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.7082 | 1.55501 | ||||||||
\(296\) | −3.94427 | −0.229256 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −40.9787 | −2.37383 | ||||||||
\(299\) | 8.58359 | 0.496402 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −18.1803 | −1.04616 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −41.7426 | −2.39410 | ||||||||
\(305\) | −15.5279 | −0.889123 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0000 | 0.913168 | 0.456584 | − | 0.889680i | \(-0.349073\pi\) | ||||
0.456584 | + | 0.889680i | \(0.349073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 49.5967 | 2.81691 | ||||||||
\(311\) | 12.9443 | 0.734002 | 0.367001 | − | 0.930220i | \(-0.380385\pi\) | ||||
0.367001 | + | 0.930220i | \(0.380385\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.3607 | 1.48999 | 0.744997 | − | 0.667068i | \(-0.232451\pi\) | ||||
0.744997 | + | 0.667068i | \(0.232451\pi\) | |||||||
\(314\) | 8.94427 | 0.504754 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.0000 | −0.675053 | ||||||||
\(317\) | −26.9443 | −1.51334 | −0.756671 | − | 0.653796i | \(-0.773175\pi\) | ||||
−0.756671 | + | 0.653796i | \(0.773175\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.2361 | 0.573110 | ||||||||
\(320\) | 19.4721 | 1.08853 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.4164 | 1.41421 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −47.4508 | −2.62806 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −44.8328 | −2.47548 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0000 | −0.879440 | −0.439720 | − | 0.898135i | \(-0.644922\pi\) | ||||
−0.439720 | + | 0.898135i | \(0.644922\pi\) | |||||||
\(332\) | −60.5410 | −3.32262 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −48.3607 | −2.64618 | ||||||||
\(335\) | 1.58359 | 0.0865209 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.4164 | 0.621891 | 0.310946 | − | 0.950428i | \(-0.399354\pi\) | ||||
0.310946 | + | 0.950428i | \(0.399354\pi\) | |||||||
\(338\) | −2.47214 | −0.134466 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −65.1246 | −3.53188 | ||||||||
\(341\) | 8.47214 | 0.458792 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.52786 | −0.190210 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.4721 | −0.778027 | ||||||||
\(347\) | −0.944272 | −0.0506912 | −0.0253456 | − | 0.999679i | \(-0.508069\pi\) | ||||
−0.0253456 | + | 0.999679i | \(0.508069\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.41641 | −0.129347 | −0.0646737 | − | 0.997906i | \(-0.520601\pi\) | ||||
−0.0646737 | + | 0.997906i | \(0.520601\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.8541 | 0.578526 | ||||||||
\(353\) | 4.23607 | 0.225463 | 0.112732 | − | 0.993625i | \(-0.464040\pi\) | ||||
0.112732 | + | 0.993625i | \(0.464040\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.0000 | −0.530745 | ||||||||
\(356\) | 65.1246 | 3.45160 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.4721 | 0.764876 | ||||||||
\(359\) | 20.9443 | 1.10540 | 0.552698 | − | 0.833381i | \(-0.313598\pi\) | ||||
0.552698 | + | 0.833381i | \(0.313598\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.05573 | −0.0555646 | ||||||||
\(362\) | 1.23607 | 0.0649663 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.23607 | −0.117041 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.4164 | −1.32673 | −0.663363 | − | 0.748298i | \(-0.730871\pi\) | ||||
−0.663363 | + | 0.748298i | \(0.730871\pi\) | |||||||
\(368\) | 24.3607 | 1.26989 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.09017 | −0.160650 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.9443 | −0.877341 | −0.438671 | − | 0.898648i | \(-0.644550\pi\) | ||||
−0.438671 | + | 0.898648i | \(0.644550\pi\) | |||||||
\(374\) | −15.7082 | −0.812252 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −85.7214 | −4.42074 | ||||||||
\(377\) | 35.5410 | 1.83046 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.6525 | −1.31768 | −0.658840 | − | 0.752283i | \(-0.728952\pi\) | ||||
−0.658840 | + | 0.752283i | \(0.728952\pi\) | |||||||
\(380\) | −45.9787 | −2.35866 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −31.4164 | −1.60740 | ||||||||
\(383\) | −8.94427 | −0.457031 | −0.228515 | − | 0.973540i | \(-0.573387\pi\) | ||||
−0.228515 | + | 0.973540i | \(0.573387\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 67.7771 | 3.44976 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −33.7082 | −1.71127 | ||||||||
\(389\) | −20.8328 | −1.05627 | −0.528133 | − | 0.849162i | \(-0.677108\pi\) | ||||
−0.528133 | + | 0.849162i | \(0.677108\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.8328 | −0.750128 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 22.1803 | 1.11743 | ||||||||
\(395\) | −5.52786 | −0.278137 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.41641 | 0.472596 | 0.236298 | − | 0.971681i | \(-0.424066\pi\) | ||||
0.236298 | + | 0.971681i | \(0.424066\pi\) | |||||||
\(398\) | 64.0689 | 3.21148 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.47214 | 0.423078 | 0.211539 | − | 0.977370i | \(-0.432152\pi\) | ||||
0.211539 | + | 0.977370i | \(0.432152\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.4164 | 1.46534 | ||||||||
\(404\) | −17.1246 | −0.851981 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.527864 | −0.0261652 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0000 | 0.692255 | 0.346128 | − | 0.938187i | \(-0.387496\pi\) | ||||
0.346128 | + | 0.938187i | \(0.387496\pi\) | |||||||
\(410\) | −35.1246 | −1.73468 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −36.0000 | −1.77359 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.8885 | −1.36899 | ||||||||
\(416\) | 37.6869 | 1.84775 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.0902 | −0.542438 | ||||||||
\(419\) | −3.00000 | −0.146560 | −0.0732798 | − | 0.997311i | \(-0.523347\pi\) | ||||
−0.0732798 | + | 0.997311i | \(0.523347\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.4721 | 1.43638 | 0.718192 | − | 0.695845i | \(-0.244970\pi\) | ||||
0.718192 | + | 0.695845i | \(0.244970\pi\) | |||||||
\(422\) | 49.5967 | 2.41433 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 96.7214 | 4.69720 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −96.8115 | −4.67956 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.76393 | −0.133289 | ||||||||
\(431\) | 17.3607 | 0.836235 | 0.418117 | − | 0.908393i | \(-0.362690\pi\) | ||||
0.418117 | + | 0.908393i | \(0.362690\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.5836 | −0.604729 | −0.302364 | − | 0.953192i | \(-0.597776\pi\) | ||||
−0.302364 | + | 0.953192i | \(0.597776\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 29.1246 | 1.39482 | ||||||||
\(437\) | −10.4721 | −0.500950 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.12461 | 0.387767 | 0.193883 | − | 0.981025i | \(-0.437892\pi\) | ||||
0.193883 | + | 0.981025i | \(0.437892\pi\) | |||||||
\(440\) | 16.7082 | 0.796532 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −54.5410 | −2.59425 | ||||||||
\(443\) | −9.05573 | −0.430251 | −0.215125 | − | 0.976586i | \(-0.569016\pi\) | ||||
−0.215125 | + | 0.976586i | \(0.569016\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.0000 | 1.42214 | ||||||||
\(446\) | 47.1246 | 2.23142 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.4164 | 1.19947 | 0.599737 | − | 0.800197i | \(-0.295272\pi\) | ||||
0.599737 | + | 0.800197i | \(0.295272\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | −0.282529 | ||||||||
\(452\) | −31.4164 | −1.47770 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −70.2492 | −3.29696 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.4164 | −0.534037 | −0.267019 | − | 0.963691i | \(-0.586038\pi\) | ||||
−0.267019 | + | 0.963691i | \(0.586038\pi\) | |||||||
\(458\) | 40.3607 | 1.88593 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 26.8328 | 1.25109 | ||||||||
\(461\) | −16.4721 | −0.767184 | −0.383592 | − | 0.923503i | \(-0.625313\pi\) | ||||
−0.383592 | + | 0.923503i | \(0.625313\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.70820 | −0.125861 | −0.0629305 | − | 0.998018i | \(-0.520045\pi\) | ||||
−0.0629305 | + | 0.998018i | \(0.520045\pi\) | |||||||
\(464\) | 100.867 | 4.68264 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −35.1246 | −1.62712 | ||||||||
\(467\) | −23.8328 | −1.10285 | −0.551426 | − | 0.834224i | \(-0.685916\pi\) | ||||
−0.551426 | + | 0.834224i | \(0.685916\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −67.1591 | −3.09782 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 89.2492 | 4.10803 | ||||||||
\(473\) | −0.472136 | −0.0217088 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −45.4508 | −2.07887 | ||||||||
\(479\) | −21.8885 | −1.00011 | −0.500057 | − | 0.865993i | \(-0.666687\pi\) | ||||
−0.500057 | + | 0.865993i | \(0.666687\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.83282 | −0.0835692 | ||||||||
\(482\) | −49.7426 | −2.26572 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.85410 | 0.220641 | ||||||||
\(485\) | −15.5279 | −0.705084 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.8885 | −0.991865 | −0.495932 | − | 0.868361i | \(-0.665174\pi\) | ||||
−0.495932 | + | 0.868361i | \(0.665174\pi\) | |||||||
\(488\) | −51.8885 | −2.34888 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.8885 | 0.491393 | 0.245697 | − | 0.969347i | \(-0.420983\pi\) | ||||
0.245697 | + | 0.969347i | \(0.420983\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −61.4164 | −2.76606 | ||||||||
\(494\) | −38.5066 | −1.73249 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 83.4853 | 3.74860 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.1246 | 0.990434 | 0.495217 | − | 0.868769i | \(-0.335089\pi\) | ||||
0.495217 | + | 0.868769i | \(0.335089\pi\) | |||||||
\(500\) | −54.2705 | −2.42705 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.3262 | −0.460883 | ||||||||
\(503\) | −10.5836 | −0.471899 | −0.235950 | − | 0.971765i | \(-0.575820\pi\) | ||||
−0.235950 | + | 0.971765i | \(0.575820\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.88854 | −0.351036 | ||||||||
\(506\) | 6.47214 | 0.287722 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 77.6656 | 3.44586 | ||||||||
\(509\) | −35.5279 | −1.57474 | −0.787372 | − | 0.616478i | \(-0.788559\pi\) | ||||
−0.787372 | + | 0.616478i | \(0.788559\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −40.3050 | −1.78124 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.3262 | 0.896552 | ||||||||
\(515\) | −16.5836 | −0.730760 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.4721 | −0.504544 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 58.0132 | 2.54405 | ||||||||
\(521\) | 23.7639 | 1.04112 | 0.520558 | − | 0.853826i | \(-0.325724\pi\) | ||||
0.520558 | + | 0.853826i | \(0.325724\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.29180 | 0.143940 | 0.0719701 | − | 0.997407i | \(-0.477071\pi\) | ||||
0.0719701 | + | 0.997407i | \(0.477071\pi\) | |||||||
\(524\) | 21.7082 | 0.948327 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.5623 | 0.504140 | ||||||||
\(527\) | −50.8328 | −2.21431 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8885 | −0.734285 | ||||||||
\(530\) | 75.7771 | 3.29155 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.8328 | −0.902369 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −44.5967 | −1.92809 | ||||||||
\(536\) | 5.29180 | 0.228571 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 43.1246 | 1.85923 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.4164 | 0.920763 | 0.460382 | − | 0.887721i | \(-0.347713\pi\) | ||||
0.460382 | + | 0.887721i | \(0.347713\pi\) | |||||||
\(542\) | 13.8541 | 0.595085 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −65.1246 | −2.79219 | ||||||||
\(545\) | 13.4164 | 0.574696 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.4164 | −0.573644 | −0.286822 | − | 0.957984i | \(-0.592599\pi\) | ||||
−0.286822 | + | 0.957984i | \(0.592599\pi\) | |||||||
\(548\) | −29.1246 | −1.24414 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −43.3607 | −1.84723 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −49.5967 | −2.10716 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 38.8328 | 1.64688 | ||||||||
\(557\) | 8.12461 | 0.344251 | 0.172125 | − | 0.985075i | \(-0.444937\pi\) | ||||
0.172125 | + | 0.985075i | \(0.444937\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.63932 | −0.0693359 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.5623 | −0.572091 | ||||||||
\(563\) | 4.47214 | 0.188478 | 0.0942390 | − | 0.995550i | \(-0.469958\pi\) | ||||
0.0942390 | + | 0.995550i | \(0.469958\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.4721 | −0.608847 | ||||||||
\(566\) | 12.3262 | 0.518110 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −33.4164 | −1.40212 | ||||||||
\(569\) | 12.4721 | 0.522859 | 0.261430 | − | 0.965223i | \(-0.415806\pi\) | ||||
0.261430 | + | 0.965223i | \(0.415806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.5836 | −0.442910 | −0.221455 | − | 0.975171i | \(-0.571081\pi\) | ||||
−0.221455 | + | 0.975171i | \(0.571081\pi\) | |||||||
\(572\) | 16.8541 | 0.704705 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.9443 | 1.45475 | 0.727375 | − | 0.686241i | \(-0.240740\pi\) | ||||
0.727375 | + | 0.686241i | \(0.240740\pi\) | |||||||
\(578\) | 49.7426 | 2.06902 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 111.103 | 4.61331 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.9443 | 0.536097 | ||||||||
\(584\) | −7.47214 | −0.309199 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.8885 | 1.06945 | ||||||||
\(587\) | −14.0557 | −0.580142 | −0.290071 | − | 0.957005i | \(-0.593679\pi\) | ||||
−0.290071 | + | 0.957005i | \(0.593679\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.8885 | −1.47876 | ||||||||
\(590\) | 69.9230 | 2.87868 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.20163 | −0.213786 | ||||||||
\(593\) | 37.4164 | 1.53651 | 0.768254 | − | 0.640145i | \(-0.221126\pi\) | ||||
0.768254 | + | 0.640145i | \(0.221126\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −75.9787 | −3.11221 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 22.4721 | 0.918954 | ||||||||
\(599\) | −25.3050 | −1.03393 | −0.516966 | − | 0.856006i | \(-0.672939\pi\) | ||||
−0.516966 | + | 0.856006i | \(0.672939\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.83282 | 0.237926 | 0.118963 | − | 0.992899i | \(-0.462043\pi\) | ||||
0.118963 | + | 0.992899i | \(0.462043\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −33.7082 | −1.37157 | ||||||||
\(605\) | 2.23607 | 0.0909091 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.7082 | −0.921698 | −0.460849 | − | 0.887479i | \(-0.652455\pi\) | ||||
−0.460849 | + | 0.887479i | \(0.652455\pi\) | |||||||
\(608\) | −45.9787 | −1.86468 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −40.6525 | −1.64597 | ||||||||
\(611\) | −39.8328 | −1.61146 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.4164 | 0.784221 | 0.392111 | − | 0.919918i | \(-0.371745\pi\) | ||||
0.392111 | + | 0.919918i | \(0.371745\pi\) | |||||||
\(614\) | 41.8885 | 1.69048 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.2492 | 1.62037 | 0.810186 | − | 0.586172i | \(-0.199366\pi\) | ||||
0.810186 | + | 0.586172i | \(0.199366\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.4164 | 1.10196 | 0.550979 | − | 0.834519i | \(-0.314254\pi\) | ||||
0.550979 | + | 0.834519i | \(0.314254\pi\) | |||||||
\(620\) | 91.9574 | 3.69310 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 33.8885 | 1.35881 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 69.0132 | 2.75832 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.5836 | 0.661757 | ||||||||
\(629\) | 3.16718 | 0.126284 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.00000 | −0.159237 | −0.0796187 | − | 0.996825i | \(-0.525370\pi\) | ||||
−0.0796187 | + | 0.996825i | \(0.525370\pi\) | |||||||
\(632\) | −18.4721 | −0.734782 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −70.5410 | −2.80154 | ||||||||
\(635\) | 35.7771 | 1.41977 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 26.7984 | 1.06096 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.43769 | 0.0963583 | ||||||||
\(641\) | −31.5279 | −1.24528 | −0.622638 | − | 0.782510i | \(-0.713939\pi\) | ||||
−0.622638 | + | 0.782510i | \(0.713939\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.41641 | 0.213602 | 0.106801 | − | 0.994280i | \(-0.465939\pi\) | ||||
0.106801 | + | 0.994280i | \(0.465939\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 66.5410 | 2.61802 | ||||||||
\(647\) | 4.41641 | 0.173627 | 0.0868135 | − | 0.996225i | \(-0.472332\pi\) | ||||
0.0868135 | + | 0.996225i | \(0.472332\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.9443 | 0.468854 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −87.9787 | −3.44551 | ||||||||
\(653\) | −5.88854 | −0.230437 | −0.115218 | − | 0.993340i | \(-0.536757\pi\) | ||||
−0.115218 | + | 0.993340i | \(0.536757\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.0000 | 0.390732 | ||||||||
\(656\) | −59.1246 | −2.30843 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.8885 | −1.28116 | −0.640578 | − | 0.767893i | \(-0.721305\pi\) | ||||
−0.640578 | + | 0.767893i | \(0.721305\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.00000 | −0.155582 | −0.0777910 | − | 0.996970i | \(-0.524787\pi\) | ||||
−0.0777910 | + | 0.996970i | \(0.524787\pi\) | |||||||
\(662\) | −41.8885 | −1.62804 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −93.1935 | −3.61661 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.3050 | 0.979812 | ||||||||
\(668\) | −89.6656 | −3.46927 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.14590 | 0.160170 | ||||||||
\(671\) | −6.94427 | −0.268081 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.5836 | −0.716345 | −0.358172 | − | 0.933655i | \(-0.616600\pi\) | ||||
−0.358172 | + | 0.933655i | \(0.616600\pi\) | |||||||
\(674\) | 29.8885 | 1.15126 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.58359 | −0.176292 | ||||||||
\(677\) | −43.4164 | −1.66863 | −0.834314 | − | 0.551289i | \(-0.814136\pi\) | ||||
−0.834314 | + | 0.551289i | \(0.814136\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −100.249 | −3.84438 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 22.1803 | 0.849329 | ||||||||
\(683\) | −9.52786 | −0.364574 | −0.182287 | − | 0.983245i | \(-0.558350\pi\) | ||||
−0.182287 | + | 0.983245i | \(0.558350\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.4164 | −0.512615 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.65248 | −0.177374 | ||||||||
\(689\) | 44.9443 | 1.71224 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.58359 | 0.250452 | 0.125226 | − | 0.992128i | \(-0.460034\pi\) | ||||
0.125226 | + | 0.992128i | \(0.460034\pi\) | |||||||
\(692\) | −26.8328 | −1.02003 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.47214 | −0.0938410 | ||||||||
\(695\) | 17.8885 | 0.678551 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.0000 | 1.36360 | ||||||||
\(698\) | −6.32624 | −0.239452 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.4164 | 0.506731 | 0.253365 | − | 0.967371i | \(-0.418463\pi\) | ||||
0.253365 | + | 0.967371i | \(0.418463\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.23607 | 0.0843349 | ||||||||
\(704\) | 8.70820 | 0.328203 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.0902 | 0.417384 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.4164 | 0.841866 | 0.420933 | − | 0.907092i | \(-0.361703\pi\) | ||||
0.420933 | + | 0.907092i | \(0.361703\pi\) | |||||||
\(710\) | −26.1803 | −0.982531 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 100.249 | 3.75700 | ||||||||
\(713\) | 20.9443 | 0.784369 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.76393 | 0.290355 | ||||||||
\(716\) | 26.8328 | 1.00279 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 54.8328 | 2.04634 | ||||||||
\(719\) | 4.63932 | 0.173017 | 0.0865087 | − | 0.996251i | \(-0.472429\pi\) | ||||
0.0865087 | + | 0.996251i | \(0.472429\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.76393 | −0.102863 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.29180 | 0.0851739 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.58359 | 0.169996 | 0.0849980 | − | 0.996381i | \(-0.472912\pi\) | ||||
0.0849980 | + | 0.996381i | \(0.472912\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.85410 | −0.216670 | ||||||||
\(731\) | 2.83282 | 0.104775 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.0557 | 1.07320 | 0.536599 | − | 0.843837i | \(-0.319709\pi\) | ||||
0.536599 | + | 0.843837i | \(0.319709\pi\) | |||||||
\(734\) | −66.5410 | −2.45607 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.8328 | 0.989071 | ||||||||
\(737\) | 0.708204 | 0.0260870 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.4164 | 1.59710 | 0.798549 | − | 0.601930i | \(-0.205601\pi\) | ||||
0.798549 | + | 0.601930i | \(0.205601\pi\) | |||||||
\(740\) | −5.72949 | −0.210620 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.3050 | −0.451425 | −0.225712 | − | 0.974194i | \(-0.572471\pi\) | ||||
−0.225712 | + | 0.974194i | \(0.572471\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −35.0000 | −1.28230 | ||||||||
\(746\) | −44.3607 | −1.62416 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −29.1246 | −1.06490 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.1246 | 0.442433 | 0.221217 | − | 0.975225i | \(-0.428997\pi\) | ||||
0.221217 | + | 0.975225i | \(0.428997\pi\) | |||||||
\(752\) | −113.048 | −4.12242 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 93.0476 | 3.38859 | ||||||||
\(755\) | −15.5279 | −0.565117 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.5836 | −0.421013 | −0.210506 | − | 0.977592i | \(-0.567511\pi\) | ||||
−0.210506 | + | 0.977592i | \(0.567511\pi\) | |||||||
\(758\) | −67.1591 | −2.43933 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −70.7771 | −2.56735 | ||||||||
\(761\) | −13.5279 | −0.490385 | −0.245192 | − | 0.969474i | \(-0.578851\pi\) | ||||
−0.245192 | + | 0.969474i | \(0.578851\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −58.2492 | −2.10738 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.4164 | −0.846069 | ||||||||
\(767\) | 41.4721 | 1.49747 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.00000 | 0.0360609 | 0.0180305 | − | 0.999837i | \(-0.494260\pi\) | ||||
0.0180305 | + | 0.999837i | \(0.494260\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 125.666 | 4.52281 | ||||||||
\(773\) | 20.3475 | 0.731850 | 0.365925 | − | 0.930644i | \(-0.380753\pi\) | ||||
0.365925 | + | 0.930644i | \(0.380753\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −51.8885 | −1.86269 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −54.5410 | −1.95539 | ||||||||
\(779\) | 25.4164 | 0.910637 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.47214 | −0.160026 | ||||||||
\(782\) | −38.8328 | −1.38866 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.63932 | 0.272659 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.1246 | 1.35900 | 0.679498 | − | 0.733678i | \(-0.262198\pi\) | ||||
0.679498 | + | 0.733678i | \(0.262198\pi\) | |||||||
\(788\) | 41.1246 | 1.46500 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.4721 | −0.514895 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.1115 | −0.856223 | ||||||||
\(794\) | 24.6525 | 0.874884 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 118.790 | 4.21041 | ||||||||
\(797\) | 45.7639 | 1.62104 | 0.810521 | − | 0.585710i | \(-0.199184\pi\) | ||||
0.810521 | + | 0.585710i | \(0.199184\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 68.8328 | 2.43513 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.1803 | 0.783215 | ||||||||
\(803\) | −1.00000 | −0.0352892 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 77.0132 | 2.71267 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −26.3607 | −0.927365 | ||||||||
\(809\) | 14.8197 | 0.521032 | 0.260516 | − | 0.965470i | \(-0.416107\pi\) | ||||
0.260516 | + | 0.965470i | \(0.416107\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.5410 | −0.967096 | −0.483548 | − | 0.875318i | \(-0.660652\pi\) | ||||
−0.483548 | + | 0.875318i | \(0.660652\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.38197 | −0.0484379 | ||||||||
\(815\) | −40.5279 | −1.41963 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.00000 | 0.0699711 | ||||||||
\(818\) | 36.6525 | 1.28152 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −65.1246 | −2.27425 | ||||||||
\(821\) | 33.5410 | 1.17059 | 0.585295 | − | 0.810821i | \(-0.300979\pi\) | ||||
0.585295 | + | 0.810821i | \(0.300979\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −45.5410 | −1.58746 | −0.793730 | − | 0.608270i | \(-0.791864\pi\) | ||||
−0.793730 | + | 0.608270i | \(0.791864\pi\) | |||||||
\(824\) | −55.4164 | −1.93052 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.167184 | −0.00581357 | −0.00290678 | − | 0.999996i | \(-0.500925\pi\) | ||||
−0.00290678 | + | 0.999996i | \(0.500925\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.8328 | −1.20979 | −0.604897 | − | 0.796304i | \(-0.706786\pi\) | ||||
−0.604897 | + | 0.796304i | \(0.706786\pi\) | |||||||
\(830\) | −73.0132 | −2.53432 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 30.2361 | 1.04825 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41.3050 | −1.42942 | ||||||||
\(836\) | −20.5623 | −0.711162 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.85410 | −0.271315 | ||||||||
\(839\) | 20.5279 | 0.708701 | 0.354350 | − | 0.935113i | \(-0.384702\pi\) | ||||
0.354350 | + | 0.935113i | \(0.384702\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 75.7771 | 2.61300 | ||||||||
\(842\) | 77.1591 | 2.65908 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 91.9574 | 3.16531 | ||||||||
\(845\) | −2.11146 | −0.0726363 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 127.554 | 4.38023 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.30495 | −0.0447332 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −54.7214 | −1.87362 | −0.936812 | − | 0.349834i | \(-0.886238\pi\) | ||||
−0.936812 | + | 0.349834i | \(0.886238\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −149.026 | −5.09361 | ||||||||
\(857\) | 50.7214 | 1.73261 | 0.866304 | − | 0.499517i | \(-0.166489\pi\) | ||||
0.866304 | + | 0.499517i | \(0.166489\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.4164 | 0.526001 | 0.263001 | − | 0.964796i | \(-0.415288\pi\) | ||||
0.263001 | + | 0.964796i | \(0.415288\pi\) | |||||||
\(860\) | −5.12461 | −0.174748 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 45.4508 | 1.54806 | ||||||||
\(863\) | −35.3050 | −1.20179 | −0.600897 | − | 0.799326i | \(-0.705190\pi\) | ||||
−0.600897 | + | 0.799326i | \(0.705190\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.3607 | −0.420276 | ||||||||
\(866\) | −32.9443 | −1.11949 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.47214 | −0.0838615 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.45898 | 0.0833194 | ||||||||
\(872\) | 44.8328 | 1.51823 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −27.4164 | −0.927374 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.8885 | −0.739124 | −0.369562 | − | 0.929206i | \(-0.620492\pi\) | ||||
−0.369562 | + | 0.929206i | \(0.620492\pi\) | |||||||
\(878\) | 21.2705 | 0.717845 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 22.0344 | 0.742781 | ||||||||
\(881\) | 22.5967 | 0.761304 | 0.380652 | − | 0.924718i | \(-0.375700\pi\) | ||||
0.380652 | + | 0.924718i | \(0.375700\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.23607 | 0.142555 | 0.0712775 | − | 0.997457i | \(-0.477292\pi\) | ||||
0.0712775 | + | 0.997457i | \(0.477292\pi\) | |||||||
\(884\) | −101.125 | −3.40119 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23.7082 | −0.796493 | ||||||||
\(887\) | 28.3607 | 0.952258 | 0.476129 | − | 0.879375i | \(-0.342039\pi\) | ||||
0.476129 | + | 0.879375i | \(0.342039\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 78.5410 | 2.63270 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 87.3738 | 2.92549 | ||||||||
\(893\) | 48.5967 | 1.62623 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.3607 | 0.413172 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 66.5410 | 2.22050 | ||||||||
\(899\) | 86.7214 | 2.89232 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −77.6656 | −2.58742 | ||||||||
\(902\) | −15.7082 | −0.523026 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −48.3607 | −1.60845 | ||||||||
\(905\) | 1.05573 | 0.0350936 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.1115 | −0.468563 | −0.234282 | − | 0.972169i | \(-0.575274\pi\) | ||||
−0.234282 | + | 0.972169i | \(0.575274\pi\) | |||||||
\(908\) | −130.249 | −4.32247 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.4164 | 1.04087 | 0.520436 | − | 0.853901i | \(-0.325769\pi\) | ||||
0.520436 | + | 0.853901i | \(0.325769\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.4721 | −0.412767 | ||||||||
\(914\) | −29.8885 | −0.988625 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 74.8328 | 2.47255 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.88854 | 0.0622973 | 0.0311487 | − | 0.999515i | \(-0.490083\pi\) | ||||
0.0311487 | + | 0.999515i | \(0.490083\pi\) | |||||||
\(920\) | 41.3050 | 1.36178 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −43.1246 | −1.42023 | ||||||||
\(923\) | −15.5279 | −0.511106 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7.09017 | −0.232997 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 111.103 | 3.64715 | ||||||||
\(929\) | −52.4853 | −1.72199 | −0.860993 | − | 0.508616i | \(-0.830157\pi\) | ||||
−0.860993 | + | 0.508616i | \(0.830157\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −65.1246 | −2.13323 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −62.3951 | −2.04163 | ||||||||
\(935\) | −13.4164 | −0.438763 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.7214 | 1.39565 | 0.697823 | − | 0.716270i | \(-0.254152\pi\) | ||||
0.697823 | + | 0.716270i | \(0.254152\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −124.520 | −4.06139 | ||||||||
\(941\) | −51.1935 | −1.66886 | −0.834430 | − | 0.551114i | \(-0.814203\pi\) | ||||
−0.834430 | + | 0.551114i | \(0.814203\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.8328 | −0.483023 | ||||||||
\(944\) | 117.700 | 3.83081 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.23607 | −0.0401880 | ||||||||
\(947\) | −0.111456 | −0.00362184 | −0.00181092 | − | 0.999998i | \(-0.500576\pi\) | ||||
−0.00181092 | + | 0.999998i | \(0.500576\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.47214 | −0.112710 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.4853 | 0.922729 | 0.461365 | − | 0.887211i | \(-0.347360\pi\) | ||||
0.461365 | + | 0.887211i | \(0.347360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26.8328 | −0.868290 | ||||||||
\(956\) | −84.2705 | −2.72550 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −57.3050 | −1.85144 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.7771 | 1.31539 | ||||||||
\(962\) | −4.79837 | −0.154706 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −92.2279 | −2.97046 | ||||||||
\(965\) | 57.8885 | 1.86350 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.2492 | 1.48727 | 0.743637 | − | 0.668583i | \(-0.233099\pi\) | ||||
0.743637 | + | 0.668583i | \(0.233099\pi\) | |||||||
\(968\) | 7.47214 | 0.240164 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −40.6525 | −1.30527 | ||||||||
\(971\) | −24.8885 | −0.798711 | −0.399356 | − | 0.916796i | \(-0.630766\pi\) | ||||
−0.399356 | + | 0.916796i | \(0.630766\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −57.3050 | −1.83617 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −68.4296 | −2.19038 | ||||||||
\(977\) | 13.5279 | 0.432795 | 0.216397 | − | 0.976305i | \(-0.430569\pi\) | ||||
0.216397 | + | 0.976305i | \(0.430569\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.4164 | 0.428790 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 28.5066 | 0.909681 | ||||||||
\(983\) | −38.8328 | −1.23857 | −0.619287 | − | 0.785165i | \(-0.712578\pi\) | ||||
−0.619287 | + | 0.785165i | \(0.712578\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.9443 | 0.603615 | ||||||||
\(986\) | −160.790 | −5.12060 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −71.3951 | −2.27138 | ||||||||
\(989\) | −1.16718 | −0.0371143 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.2918 | 0.422228 | 0.211114 | − | 0.977461i | \(-0.432291\pi\) | ||||
0.211114 | + | 0.977461i | \(0.432291\pi\) | |||||||
\(992\) | 91.9574 | 2.91965 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 54.7214 | 1.73478 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.0000 | 1.33015 | 0.665077 | − | 0.746775i | \(-0.268399\pi\) | ||||
0.665077 | + | 0.746775i | \(0.268399\pi\) | |||||||
\(998\) | 57.9230 | 1.83352 | ||||||||
\(999\) | 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 | 4851.2.a.bh.1.2 | 2 | ||
3.2 | odd | 2 | 1617.2.a.k.1.1 | ✓ | 2 | ||
7.6 | odd | 2 | 4851.2.a.bg.1.2 | 2 | |||
21.20 | even | 2 | 1617.2.a.l.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1617.2.a.k.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
1617.2.a.l.1.1 | yes | 2 | 21.20 | even | 2 | ||
4851.2.a.bg.1.2 | 2 | 7.6 | odd | 2 | |||
4851.2.a.bh.1.2 | 2 | 1.1 | even | 1 | trivial |