Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,2,Mod(1,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, 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("1568.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.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: | \(12.5205430369\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 224) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.41421 | 1.39385 | 0.696923 | − | 0.717146i | \(-0.254552\pi\) | ||||
0.696923 | + | 0.717146i | \(0.254552\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.82843 | 1.71212 | 0.856062 | − | 0.516873i | \(-0.172904\pi\) | ||||
0.856062 | + | 0.516873i | \(0.172904\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.414214 | 0.124890 | 0.0624450 | − | 0.998048i | \(-0.480110\pi\) | ||||
0.0624450 | + | 0.998048i | \(0.480110\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.82843 | −0.784465 | −0.392232 | − | 0.919866i | \(-0.628297\pi\) | ||||
−0.392232 | + | 0.919866i | \(0.628297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.24264 | 2.38644 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.82843 | −1.41360 | −0.706801 | − | 0.707413i | \(-0.749862\pi\) | ||||
−0.706801 | + | 0.707413i | \(0.749862\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.58579 | 0.822636 | 0.411318 | − | 0.911492i | \(-0.365069\pi\) | ||||
0.411318 | + | 0.911492i | \(0.365069\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.24264 | 0.676137 | 0.338069 | − | 0.941121i | \(-0.390226\pi\) | ||||
0.338069 | + | 0.941121i | \(0.390226\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.65685 | 1.93137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.414214 | −0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843 | 0.525226 | 0.262613 | − | 0.964901i | \(-0.415416\pi\) | ||||
0.262613 | + | 0.964901i | \(0.415416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.41421 | 1.51124 | 0.755619 | − | 0.655012i | \(-0.227336\pi\) | ||||
0.755619 | + | 0.655012i | \(0.227336\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.65685 | −0.436784 | −0.218392 | − | 0.975861i | \(-0.570081\pi\) | ||||
−0.218392 | + | 0.975861i | \(0.570081\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.82843 | −1.09342 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.17157 | −0.182969 | −0.0914845 | − | 0.995807i | \(-0.529161\pi\) | ||||
−0.0914845 | + | 0.995807i | \(0.529161\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.65685 | −0.252668 | −0.126334 | − | 0.991988i | \(-0.540321\pi\) | ||||
−0.126334 | + | 0.991988i | \(0.540321\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.8284 | 1.61421 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.58579 | 1.10650 | 0.553250 | − | 0.833015i | \(-0.313387\pi\) | ||||
0.553250 | + | 0.833015i | \(0.313387\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −14.0711 | −1.97034 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.00000 | −0.137361 | −0.0686803 | − | 0.997639i | \(-0.521879\pi\) | ||||
−0.0686803 | + | 0.997639i | \(0.521879\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.58579 | 0.213827 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.65685 | 1.14663 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.89949 | −1.15862 | −0.579308 | − | 0.815109i | \(-0.696677\pi\) | ||||
−0.579308 | + | 0.815109i | \(0.696677\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.65685 | −0.340175 | −0.170088 | − | 0.985429i | \(-0.554405\pi\) | ||||
−0.170088 | + | 0.985429i | \(0.554405\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.8284 | −1.34310 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.2426 | −1.37351 | −0.686754 | − | 0.726890i | \(-0.740965\pi\) | ||||
−0.686754 | + | 0.726890i | \(0.740965\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.82843 | 0.942432 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.34315 | 0.278080 | 0.139040 | − | 0.990287i | \(-0.455598\pi\) | ||||
0.139040 | + | 0.990287i | \(0.455598\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.34315 | −0.391286 | −0.195643 | − | 0.980675i | \(-0.562679\pi\) | ||||
−0.195643 | + | 0.980675i | \(0.562679\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 23.3137 | 2.69204 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.07107 | −0.908066 | −0.454033 | − | 0.890985i | \(-0.650015\pi\) | ||||
−0.454033 | + | 0.890985i | \(0.650015\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.3137 | 1.68090 | 0.840449 | − | 0.541891i | \(-0.182291\pi\) | ||||
0.840449 | + | 0.541891i | \(0.182291\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.3137 | −2.42026 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.82843 | 0.732084 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20.3137 | 2.10643 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 13.7279 | 1.40846 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.82843 | −0.693322 | −0.346661 | − | 0.937991i | \(-0.612685\pi\) | ||||
−0.346661 | + | 0.937991i | \(0.612685\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.17157 | 0.117748 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.48528 | −0.346798 | −0.173399 | − | 0.984852i | \(-0.555475\pi\) | ||||
−0.173399 | + | 0.984852i | \(0.555475\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.58579 | 0.550384 | 0.275192 | − | 0.961389i | \(-0.411259\pi\) | ||||
0.275192 | + | 0.961389i | \(0.411259\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.89949 | 0.666999 | 0.333500 | − | 0.942750i | \(-0.391770\pi\) | ||||
0.333500 | + | 0.942750i | \(0.391770\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.8284 | −1.32452 | −0.662262 | − | 0.749273i | \(-0.730403\pi\) | ||||
−0.662262 | + | 0.749273i | \(0.730403\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.41421 | −0.608810 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.1421 | −0.954092 | −0.477046 | − | 0.878878i | \(-0.658292\pi\) | ||||
−0.477046 | + | 0.878878i | \(0.658292\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.4142 | 1.15763 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.00000 | −0.739600 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8284 | −0.984402 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.82843 | −0.255031 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 17.8284 | 1.59462 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.65685 | 0.501965 | 0.250982 | − | 0.967992i | \(-0.419246\pi\) | ||||
0.250982 | + | 0.967992i | \(0.419246\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.00000 | −0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.7279 | −1.54890 | −0.774448 | − | 0.632638i | \(-0.781972\pi\) | ||||
−0.774448 | + | 0.632638i | \(0.781972\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.58579 | −0.136483 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.1421 | −1.46455 | −0.732276 | − | 0.681008i | \(-0.761542\pi\) | ||||
−0.732276 | + | 0.681008i | \(0.761542\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.31371 | −0.620341 | −0.310170 | − | 0.950681i | \(-0.600386\pi\) | ||||
−0.310170 | + | 0.950681i | \(0.600386\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.3137 | 1.54229 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.17157 | −0.0979718 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.8284 | 0.899252 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.8284 | 0.969023 | 0.484511 | − | 0.874785i | \(-0.338997\pi\) | ||||
0.484511 | + | 0.874785i | \(0.338997\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.8995 | −1.53802 | −0.769010 | − | 0.639237i | \(-0.779250\pi\) | ||||
−0.769010 | + | 0.639237i | \(0.779250\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.4853 | −1.33276 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 32.2132 | 2.58743 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.6569 | 1.64860 | 0.824298 | − | 0.566156i | \(-0.191570\pi\) | ||||
0.824298 | + | 0.566156i | \(0.191570\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.41421 | −0.191460 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.2426 | 1.19390 | 0.596948 | − | 0.802280i | \(-0.296380\pi\) | ||||
0.596948 | + | 0.802280i | \(0.296380\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.82843 | 0.298043 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.00000 | 0.154765 | 0.0773823 | − | 0.997001i | \(-0.475344\pi\) | ||||
0.0773823 | + | 0.997001i | \(0.475344\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.1421 | 0.775588 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.0000 | 0.836315 | 0.418157 | − | 0.908375i | \(-0.362676\pi\) | ||||
0.418157 | + | 0.908375i | \(0.362676\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.4853 | −1.61493 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.41421 | 0.628908 | 0.314454 | − | 0.949273i | \(-0.398179\pi\) | ||||
0.314454 | + | 0.949273i | \(0.398179\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3137 | 0.989600 | 0.494800 | − | 0.869007i | \(-0.335241\pi\) | ||||
0.494800 | + | 0.869007i | \(0.335241\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.41421 | −0.474152 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.1716 | −0.747829 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.41421 | −0.176545 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.8995 | 0.788660 | 0.394330 | − | 0.918969i | \(-0.370977\pi\) | ||||
0.394330 | + | 0.918969i | \(0.370977\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.1421 | 1.37788 | 0.688941 | − | 0.724818i | \(-0.258076\pi\) | ||||
0.688941 | + | 0.724818i | \(0.258076\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −26.1421 | −1.87208 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.1716 | −0.938436 | −0.469218 | − | 0.883082i | \(-0.655464\pi\) | ||||
−0.469218 | + | 0.883082i | \(0.655464\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.75736 | 0.195464 | 0.0977320 | − | 0.995213i | \(-0.468841\pi\) | ||||
0.0977320 | + | 0.995213i | \(0.468841\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −27.1421 | −1.91446 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.48528 | −0.313266 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.17157 | 0.637468 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.48528 | 0.102739 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.65685 | 0.387601 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.34315 | −0.432599 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.07107 | −0.545392 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.4853 | 1.10892 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.6569 | 0.914531 | 0.457265 | − | 0.889330i | \(-0.348829\pi\) | ||||
0.457265 | + | 0.889330i | \(0.348829\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 27.3137 | 1.82091 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.92893 | −0.128028 | −0.0640139 | − | 0.997949i | \(-0.520390\pi\) | ||||
−0.0640139 | + | 0.997949i | \(0.520390\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.82843 | −0.649481 | −0.324740 | − | 0.945803i | \(-0.605277\pi\) | ||||
−0.324740 | + | 0.945803i | \(0.605277\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.82843 | 0.512857 | 0.256429 | − | 0.966563i | \(-0.417454\pi\) | ||||
0.256429 | + | 0.966563i | \(0.417454\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.0416 | 1.89447 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.4853 | −1.26571 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.3137 | −1.37867 | −0.689335 | − | 0.724443i | \(-0.742097\pi\) | ||||
−0.689335 | + | 0.724443i | \(0.742097\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.3137 | −0.793196 | −0.396598 | − | 0.917992i | \(-0.629809\pi\) | ||||
−0.396598 | + | 0.917992i | \(0.629809\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.6569 | −1.38929 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.1421 | −0.645329 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 36.9706 | 2.34291 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.97056 | 0.187500 | 0.0937501 | − | 0.995596i | \(-0.470115\pi\) | ||||
0.0937501 | + | 0.995596i | \(0.470115\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.34315 | 0.0844428 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −53.8701 | −3.37347 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.4853 | 1.34022 | 0.670108 | − | 0.742264i | \(-0.266248\pi\) | ||||
0.670108 | + | 0.742264i | \(0.266248\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | 0.495188 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.89949 | −0.548766 | −0.274383 | − | 0.961620i | \(-0.588474\pi\) | ||||
−0.274383 | + | 0.961620i | \(0.588474\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.82843 | −0.235178 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.7279 | −1.32973 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.34315 | 0.0818930 | 0.0409465 | − | 0.999161i | \(-0.486963\pi\) | ||||
0.0409465 | + | 0.999161i | \(0.486963\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.2132 | 0.741899 | 0.370950 | − | 0.928653i | \(-0.379032\pi\) | ||||
0.370950 | + | 0.928653i | \(0.379032\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.00000 | 0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.3137 | −0.739859 | −0.369930 | − | 0.929060i | \(-0.620618\pi\) | ||||
−0.369930 | + | 0.929060i | \(0.620618\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.7990 | 1.42481 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.48528 | 0.267569 | 0.133785 | − | 0.991010i | \(-0.457287\pi\) | ||||
0.133785 | + | 0.991010i | \(0.457287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.41421 | 0.500173 | 0.250087 | − | 0.968223i | \(-0.419541\pi\) | ||||
0.250087 | + | 0.968223i | \(0.419541\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 33.1421 | 1.96317 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9706 | 0.998268 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.4853 | −0.966384 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.6274 | −0.971384 | −0.485692 | − | 0.874130i | \(-0.661432\pi\) | ||||
−0.485692 | + | 0.874130i | \(0.661432\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −34.0711 | −1.98369 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.171573 | −0.00995567 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.17157 | −0.530406 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.41421 | −0.483384 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.1716 | −0.582423 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.6569 | 1.46431 | 0.732157 | − | 0.681136i | \(-0.238514\pi\) | ||||
0.732157 | + | 0.681136i | \(0.238514\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.4853 | 0.767151 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.2426 | −1.54479 | −0.772394 | − | 0.635143i | \(-0.780941\pi\) | ||||
−0.772394 | + | 0.635143i | \(0.780941\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.2843 | 1.54220 | 0.771099 | − | 0.636715i | \(-0.219707\pi\) | ||||
0.771099 | + | 0.636715i | \(0.219707\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −32.3137 | −1.81492 | −0.907459 | − | 0.420140i | \(-0.861981\pi\) | ||||
−0.907459 | + | 0.420140i | \(0.861981\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.17157 | 0.0655955 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.6569 | 0.929695 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.8995 | −1.16288 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.3137 | −1.51509 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −33.3848 | −1.84618 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.5858 | 1.40632 | 0.703161 | − | 0.711031i | \(-0.251771\pi\) | ||||
0.703161 | + | 0.711031i | \(0.251771\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.51472 | −0.411804 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −43.0416 | −2.35162 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.8284 | 0.807756 | 0.403878 | − | 0.914813i | \(-0.367662\pi\) | ||||
0.403878 | + | 0.914813i | \(0.367662\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −24.4853 | −1.32986 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.48528 | 0.188739 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 29.9706 | 1.61356 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.1005 | 0.810638 | 0.405319 | − | 0.914175i | \(-0.367161\pi\) | ||||
0.405319 | + | 0.914175i | \(0.367161\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.8284 | 0.579632 | 0.289816 | − | 0.957082i | \(-0.406406\pi\) | ||||
0.289816 | + | 0.957082i | \(0.406406\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.17157 | 0.0625339 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.82843 | 0.416665 | 0.208333 | − | 0.978058i | \(-0.433196\pi\) | ||||
0.208333 | + | 0.978058i | \(0.433196\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.97056 | 0.476108 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.3848 | −1.33976 | −0.669879 | − | 0.742471i | \(-0.733654\pi\) | ||||
−0.669879 | + | 0.742471i | \(0.733654\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.14214 | −0.323270 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −26.1421 | −1.37211 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.7990 | −0.669930 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.7279 | 1.55178 | 0.775892 | − | 0.630865i | \(-0.217300\pi\) | ||||
0.775892 | + | 0.630865i | \(0.217300\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.31371 | −0.172505 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.3137 | 0.741136 | 0.370568 | − | 0.928805i | \(-0.379163\pi\) | ||||
0.370568 | + | 0.928805i | \(0.379163\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 43.0416 | 2.22266 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.00000 | −0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.02944 | −0.0528786 | −0.0264393 | − | 0.999650i | \(-0.508417\pi\) | ||||
−0.0264393 | + | 0.999650i | \(0.508417\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.6569 | 0.699662 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.75736 | −0.140894 | −0.0704472 | − | 0.997516i | \(-0.522443\pi\) | ||||
−0.0704472 | + | 0.997516i | \(0.522443\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.68629 | −0.238218 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.8284 | 1.20815 | 0.604075 | − | 0.796928i | \(-0.293543\pi\) | ||||
0.604075 | + | 0.796928i | \(0.293543\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.8995 | −0.955789 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −42.7990 | −2.15892 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −30.8995 | −1.55472 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.82843 | −0.493275 | −0.246637 | − | 0.969108i | \(-0.579326\pi\) | ||||
−0.246637 | + | 0.969108i | \(0.579326\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.17157 | 0.108443 | 0.0542216 | − | 0.998529i | \(-0.482732\pi\) | ||||
0.0542216 | + | 0.998529i | \(0.482732\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.7990 | −1.18551 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −36.3137 | −1.80444 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.10051 | −0.0545500 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.4558 | −1.80263 | −0.901313 | − | 0.433169i | \(-0.857395\pi\) | ||||
−0.901313 | + | 0.433169i | \(0.857395\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −41.3848 | −2.04136 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 58.6274 | 2.87791 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.6569 | −0.864660 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.65685 | −0.0809426 | −0.0404713 | − | 0.999181i | \(-0.512886\pi\) | ||||
−0.0404713 | + | 0.999181i | \(0.512886\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.485281 | 0.0236512 | 0.0118256 | − | 0.999930i | \(-0.496236\pi\) | ||||
0.0118256 | + | 0.999930i | \(0.496236\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.4558 | 1.04322 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −56.2843 | −2.73019 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.82843 | −0.136558 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.2426 | −1.02322 | −0.511611 | − | 0.859217i | \(-0.670951\pi\) | ||||
−0.511611 | + | 0.859217i | \(0.670951\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.4853 | 1.36892 | 0.684458 | − | 0.729053i | \(-0.260039\pi\) | ||||
0.684458 | + | 0.729053i | \(0.260039\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 26.1421 | 1.25342 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.6274 | 0.556215 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.6985 | −1.75152 | −0.875762 | − | 0.482744i | \(-0.839640\pi\) | ||||
−0.875762 | + | 0.482744i | \(0.839640\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.0711 | −1.23867 | −0.619337 | − | 0.785125i | \(-0.712598\pi\) | ||||
−0.619337 | + | 0.785125i | \(0.712598\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −34.4558 | −1.63336 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 28.5563 | 1.35067 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.82843 | 0.322253 | 0.161127 | − | 0.986934i | \(-0.448487\pi\) | ||||
0.161127 | + | 0.986934i | \(0.448487\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.485281 | −0.0228510 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −45.6274 | −2.14376 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.2843 | −1.74408 | −0.872042 | − | 0.489430i | \(-0.837205\pi\) | ||||
−0.872042 | + | 0.489430i | \(0.837205\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.41421 | 0.112686 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.4558 | 1.18560 | 0.592798 | − | 0.805351i | \(-0.298023\pi\) | ||||
0.592798 | + | 0.805351i | \(0.298023\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.3137 | 0.525793 | 0.262896 | − | 0.964824i | \(-0.415322\pi\) | ||||
0.262896 | + | 0.964824i | \(0.415322\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 77.7696 | 3.60648 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.5563 | 0.858685 | 0.429343 | − | 0.903142i | \(-0.358745\pi\) | ||||
0.429343 | + | 0.903142i | \(0.358745\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 49.8701 | 2.29789 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.686292 | −0.0315557 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 34.6274 | 1.58881 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.82843 | −0.129505 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.6985 | 1.40265 | 0.701325 | − | 0.712842i | \(-0.252592\pi\) | ||||
0.701325 | + | 0.712842i | \(0.252592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.51472 | 0.342642 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.1421 | −1.18705 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.7279 | 0.622072 | 0.311036 | − | 0.950398i | \(-0.399324\pi\) | ||||
0.311036 | + | 0.950398i | \(0.399324\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 36.7990 | 1.66411 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.65685 | −0.345549 | −0.172774 | − | 0.984961i | \(-0.555273\pi\) | ||||
−0.172774 | + | 0.984961i | \(0.555273\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.4853 | −0.742460 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.48528 | 0.201598 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.5563 | 1.18883 | 0.594413 | − | 0.804160i | \(-0.297385\pi\) | ||||
0.594413 | + | 0.804160i | \(0.297385\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.82843 | 0.215718 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.6569 | −0.965631 | −0.482816 | − | 0.875722i | \(-0.660386\pi\) | ||||
−0.482816 | + | 0.875722i | \(0.660386\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.3431 | −0.593762 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.0711 | −0.536095 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.5147 | 1.08660 | 0.543298 | − | 0.839540i | \(-0.317175\pi\) | ||||
0.543298 | + | 0.839540i | \(0.317175\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.48528 | −0.0655768 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21.3848 | 0.942326 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.14214 | 0.138191 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26.5563 | 1.16569 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.00000 | 0.306676 | 0.153338 | − | 0.988174i | \(-0.450998\pi\) | ||||
0.153338 | + | 0.988174i | \(0.450998\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.72792 | −0.337918 | −0.168959 | − | 0.985623i | \(-0.554041\pi\) | ||||
−0.168959 | + | 0.985623i | \(0.554041\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −49.0416 | −2.13629 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.4853 | −0.542838 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −25.1716 | −1.09235 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.31371 | 0.143533 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.4142 | 1.14199 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.3137 | 0.876601 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.1716 | −0.867244 | −0.433622 | − | 0.901095i | \(-0.642765\pi\) | ||||
−0.433622 | + | 0.901095i | \(0.642765\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 32.1421 | 1.37935 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −52.9411 | −2.26775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.9706 | −0.982150 | −0.491075 | − | 0.871117i | \(-0.663396\pi\) | ||||
−0.491075 | + | 0.871117i | \(0.663396\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.51472 | −0.320720 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.1421 | 0.432070 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.5563 | −1.04236 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.82843 | −0.246958 | −0.123479 | − | 0.992347i | \(-0.539405\pi\) | ||||
−0.123479 | + | 0.992347i | \(0.539405\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.68629 | 0.198209 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.82843 | −0.246076 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.0710678 | 0.00299515 | 0.00149758 | − | 0.999999i | \(-0.499523\pi\) | ||||
0.00149758 | + | 0.999999i | \(0.499523\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38.8284 | −1.63352 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.3431 | 1.06244 | 0.531220 | − | 0.847234i | \(-0.321734\pi\) | ||||
0.531220 | + | 0.847234i | \(0.321734\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.5858 | −0.652245 | −0.326122 | − | 0.945328i | \(-0.605742\pi\) | ||||
−0.326122 | + | 0.945328i | \(0.605742\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.3137 | 1.09927 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31.3137 | 1.30587 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.0000 | 1.62359 | 0.811796 | − | 0.583942i | \(-0.198490\pi\) | ||||
0.811796 | + | 0.583942i | \(0.198490\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 46.2132 | 1.92056 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.414214 | −0.0171550 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −30.6274 | −1.26629 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.97056 | −0.205157 | −0.102579 | − | 0.994725i | \(-0.532709\pi\) | ||||
−0.102579 | + | 0.994725i | \(0.532709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.1716 | 1.24320 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −31.7990 | −1.30804 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.4853 | −0.471644 | −0.235822 | − | 0.971796i | \(-0.575778\pi\) | ||||
−0.235822 | + | 0.971796i | \(0.575778\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.65685 | 0.272447 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.8701 | −0.730151 | −0.365075 | − | 0.930978i | \(-0.618957\pi\) | ||||
−0.365075 | + | 0.930978i | \(0.618957\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.14214 | −0.0873795 | −0.0436898 | − | 0.999045i | \(-0.513911\pi\) | ||||
−0.0436898 | + | 0.999045i | \(0.513911\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −31.7990 | −1.29495 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −41.4558 | −1.68542 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.38478 | −0.0562063 | −0.0281032 | − | 0.999605i | \(-0.508947\pi\) | ||||
−0.0281032 | + | 0.999605i | \(0.508947\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.4558 | −0.868011 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.4853 | 0.867782 | 0.433891 | − | 0.900965i | \(-0.357140\pi\) | ||||
0.433891 | + | 0.900965i | \(0.357140\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.8284 | −0.436644 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.1127 | −1.73565 | −0.867826 | − | 0.496868i | \(-0.834483\pi\) | ||||
−0.867826 | + | 0.496868i | \(0.834483\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.0711 | 1.28905 | 0.644523 | − | 0.764585i | \(-0.277056\pi\) | ||||
0.644523 | + | 0.764585i | \(0.277056\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.34315 | −0.0538986 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.58579 | 0.143203 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.4853 | 0.617439 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.3431 | 0.730229 | 0.365115 | − | 0.930963i | \(-0.381030\pi\) | ||||
0.365115 | + | 0.930963i | \(0.381030\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −28.9706 | −1.15148 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.6569 | 0.859426 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.62742 | 0.262177 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.0000 | −0.671460 | −0.335730 | − | 0.941958i | \(-0.608983\pi\) | ||||
−0.335730 | + | 0.941958i | \(0.608983\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.9706 | 1.77347 | 0.886733 | − | 0.462282i | \(-0.152969\pi\) | ||||
0.886733 | + | 0.462282i | \(0.152969\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.3137 | −0.602977 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.8701 | −1.01706 | −0.508528 | − | 0.861045i | \(-0.669810\pi\) | ||||
−0.508528 | + | 0.861045i | \(0.669810\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.68629 | −0.144700 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.9411 | 1.13255 | 0.566277 | − | 0.824215i | \(-0.308383\pi\) | ||||
0.566277 | + | 0.824215i | \(0.308383\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −67.8701 | −2.65190 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.45584 | −0.368908 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.6274 | −0.413985 | −0.206993 | − | 0.978342i | \(-0.566368\pi\) | ||||
−0.206993 | + | 0.978342i | \(0.566368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.3431 | −0.752361 | −0.376181 | − | 0.926546i | \(-0.622763\pi\) | ||||
−0.376181 | + | 0.926546i | \(0.622763\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 39.7990 | 1.54566 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.17157 | 0.355125 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 32.9706 | 1.27472 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.10051 | −0.0424845 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.1421 | 1.00771 | 0.503853 | − | 0.863790i | \(-0.331915\pi\) | ||||
0.503853 | + | 0.863790i | \(0.331915\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.7990 | 0.799370 | 0.399685 | − | 0.916653i | \(-0.369119\pi\) | ||||
0.399685 | + | 0.916653i | \(0.369119\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.65685 | −0.178451 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −48.5563 | −1.85796 | −0.928979 | − | 0.370134i | \(-0.879312\pi\) | ||||
−0.928979 | + | 0.370134i | \(0.879312\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −65.6274 | −2.50749 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.7279 | −0.905277 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.82843 | 0.107754 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.0416 | −0.800461 | −0.400231 | − | 0.916414i | \(-0.631070\pi\) | ||||
−0.400231 | + | 0.916414i | \(0.631070\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −28.0000 | −1.06210 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.82843 | 0.258645 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.8995 | 0.714845 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.0000 | 0.528773 | 0.264386 | − | 0.964417i | \(-0.414831\pi\) | ||||
0.264386 | + | 0.964417i | \(0.414831\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.52691 | −0.359314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 70.1127 | 2.64060 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.5980 | 1.59980 | 0.799900 | − | 0.600133i | \(-0.204886\pi\) | ||||
0.799900 | + | 0.600133i | \(0.204886\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.8284 | −0.856133 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.2843 | 1.02180 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.48528 | −0.167740 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −51.4558 | −1.92165 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.0416 | −0.635546 | −0.317773 | − | 0.948167i | \(-0.602935\pi\) | ||||
−0.317773 | + | 0.948167i | \(0.602935\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −29.7279 | −1.10559 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 27.3137 | 1.01441 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.6569 | 1.69332 | 0.846659 | − | 0.532135i | \(-0.178610\pi\) | ||||
0.846659 | + | 0.532135i | \(0.178610\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.65685 | 0.357172 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.3137 | 1.71064 | 0.855318 | − | 0.518104i | \(-0.173362\pi\) | ||||
0.855318 | + | 0.518104i | \(0.173362\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.65685 | −0.171537 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 52.6985 | 1.93855 | 0.969273 | − | 0.245989i | \(-0.0791128\pi\) | ||||
0.969273 | + | 0.245989i | \(0.0791128\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.4853 | −0.899489 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.6569 | 1.38150 | 0.690748 | − | 0.723096i | \(-0.257281\pi\) | ||||
0.690748 | + | 0.723096i | \(0.257281\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 45.2843 | 1.65909 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 43.3137 | 1.58477 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.72792 | −0.136034 | −0.0680169 | − | 0.997684i | \(-0.521667\pi\) | ||||
−0.0680169 | + | 0.997684i | \(0.521667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.17157 | 0.261347 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −72.3553 | −2.63328 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.1421 | 0.804770 | 0.402385 | − | 0.915471i | \(-0.368181\pi\) | ||||
0.402385 | + | 0.915471i | \(0.368181\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.24264 | 0.117700 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.1127 | 0.729085 | 0.364542 | − | 0.931187i | \(-0.381225\pi\) | ||||
0.364542 | + | 0.931187i | \(0.381225\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −63.1127 | −2.28184 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.1716 | 0.908893 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.1421 | 1.51968 | 0.759842 | − | 0.650108i | \(-0.225276\pi\) | ||||
0.759842 | + | 0.650108i | \(0.225276\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 51.8701 | 1.86805 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.1421 | 0.688495 | 0.344247 | − | 0.938879i | \(-0.388134\pi\) | ||||
0.344247 | + | 0.938879i | \(0.388134\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 81.2548 | 2.91876 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.20101 | −0.150517 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.970563 | 0.0347295 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.17157 | −0.0418686 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 79.0833 | 2.82260 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.78680 | 0.134985 | 0.0674924 | − | 0.997720i | \(-0.478500\pi\) | ||||
0.0674924 | + | 0.997720i | \(0.478500\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.4853 | −0.764896 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.51472 | 0.266855 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.24264 | −0.327803 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.1127 | −0.535319 | −0.267660 | − | 0.963514i | \(-0.586250\pi\) | ||||
−0.267660 | + | 0.963514i | \(0.586250\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.2132 | −1.56415 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25.4558 | −0.899438 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.38478 | −0.0488677 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.24264 | 0.114146 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.9706 | 0.561495 | 0.280748 | − | 0.959782i | \(-0.409418\pi\) | ||||
0.280748 | + | 0.959782i | \(0.409418\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.34315 | −0.222738 | −0.111369 | − | 0.993779i | \(-0.535524\pi\) | ||||
−0.111369 | + | 0.993779i | \(0.535524\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.4853 | 1.03409 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 58.3553 | 2.04410 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.94113 | −0.207854 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.1421 | −0.458664 | −0.229332 | − | 0.973348i | \(-0.573654\pi\) | ||||
−0.229332 | + | 0.973348i | \(0.573654\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.0122 | 1.18559 | 0.592795 | − | 0.805353i | \(-0.298024\pi\) | ||||
0.592795 | + | 0.805353i | \(0.298024\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.65685 | 0.336209 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.3431 | 1.05513 | 0.527567 | − | 0.849513i | \(-0.323104\pi\) | ||||
0.527567 | + | 0.849513i | \(0.323104\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.7990 | 1.41701 | 0.708504 | − | 0.705707i | \(-0.249371\pi\) | ||||
0.708504 | + | 0.705707i | \(0.249371\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.7279 | −1.03125 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.65685 | 0.264976 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.48528 | −0.120469 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.3137 | 0.666783 | 0.333392 | − | 0.942788i | \(-0.391807\pi\) | ||||
0.333392 | + | 0.942788i | \(0.391807\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.8284 | 0.372951 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.1421 | −0.658509 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.3137 | 0.697165 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.61522 | −0.295326 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.5147 | −0.805129 | −0.402564 | − | 0.915392i | \(-0.631881\pi\) | ||||
−0.402564 | + | 0.915392i | \(0.631881\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 38.8284 | 1.32790 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.6569 | 1.25217 | 0.626087 | − | 0.779753i | \(-0.284655\pi\) | ||||
0.626087 | + | 0.779753i | \(0.284655\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.5563 | 1.24729 | 0.623643 | − | 0.781709i | \(-0.285652\pi\) | ||||
0.623643 | + | 0.781709i | \(0.285652\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.38478 | −0.115219 | −0.0576096 | − | 0.998339i | \(-0.518348\pi\) | ||||
−0.0576096 | + | 0.998339i | \(0.518348\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 42.1127 | 1.43187 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 40.9706 | 1.39143 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.34315 | −0.113408 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.7990 | 1.07747 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.3137 | −0.653670 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.4264 | −1.12873 | −0.564365 | − | 0.825526i | \(-0.690879\pi\) | ||||
−0.564365 | + | 0.825526i | \(0.690879\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −40.1421 | −1.35396 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.0000 | −0.875962 | −0.437981 | − | 0.898984i | \(-0.644306\pi\) | ||||
−0.437981 | + | 0.898984i | \(0.644306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.2548 | 1.65756 | 0.828779 | − | 0.559577i | \(-0.189036\pi\) | ||||
0.828779 | + | 0.559577i | \(0.189036\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −82.2548 | −2.76497 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 50.8995 | 1.70904 | 0.854519 | − | 0.519420i | \(-0.173852\pi\) | ||||
0.854519 | + | 0.519420i | \(0.173852\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.92893 | −0.131624 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.2010 | 0.910247 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.2132 | 1.07677 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.1421 | −0.739304 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.7990 | 0.793741 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.82843 | 0.194173 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 50.9706 | 1.69432 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.5269 | −1.31247 | −0.656235 | − | 0.754557i | \(-0.727852\pi\) | ||||
−0.656235 | + | 0.754557i | \(0.727852\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.85786 | −0.326965 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.00000 | 0.265052 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.34315 | 0.209927 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −24.5563 | −0.811808 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.5563 | 0.810039 | 0.405020 | − | 0.914308i | \(-0.367265\pi\) | ||||
0.405020 | + | 0.914308i | \(0.367265\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 61.9411 | 2.04103 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.62742 | −0.218144 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.6569 | −0.843592 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.7990 | 0.518907 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.6569 | −1.00582 | −0.502909 | − | 0.864339i | \(-0.667737\pi\) | ||||
−0.502909 | + | 0.864339i | \(0.667737\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −65.7696 | −2.15320 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.24264 | −0.302267 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.6274 | −0.935217 | −0.467608 | − | 0.883936i | \(-0.654884\pi\) | ||||
−0.467608 | + | 0.883936i | \(0.654884\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 65.8701 | 2.14959 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.2548 | 1.70346 | 0.851729 | − | 0.523982i | \(-0.175554\pi\) | ||||
0.851729 | + | 0.523982i | \(0.175554\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.79899 | −0.123712 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.2132 | 0.786823 | 0.393412 | − | 0.919362i | \(-0.371295\pi\) | ||||
0.393412 | + | 0.919362i | \(0.371295\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.45584 | 0.306950 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −78.0122 | −2.52972 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.1127 | 1.13741 | 0.568706 | − | 0.822541i | \(-0.307444\pi\) | ||||
0.568706 | + | 0.822541i | \(0.307444\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41.7279 | 1.35028 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.82843 | 0.0914301 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 39.7990 | 1.28384 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19.5147 | 0.628853 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 73.2843 | 2.35910 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.6569 | −0.953700 | −0.476850 | − | 0.878985i | \(-0.658222\pi\) | ||||
−0.476850 | + | 0.878985i | \(0.658222\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −50.4558 | −1.62088 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.4142 | −1.23277 | −0.616385 | − | 0.787445i | \(-0.711404\pi\) | ||||
−0.616385 | + | 0.787445i | \(0.711404\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −65.9411 | −2.11181 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51.4853 | −1.64716 | −0.823580 | − | 0.567200i | \(-0.808027\pi\) | ||||
−0.823580 | + | 0.567200i | \(0.808027\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.72792 | −0.119145 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39.1127 | −1.24877 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −60.8406 | −1.94051 | −0.970257 | − | 0.242076i | \(-0.922172\pi\) | ||||
−0.970257 | + | 0.242076i | \(0.922172\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −50.4264 | −1.60672 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.37258 | −0.170838 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.6985 | 0.466913 | 0.233456 | − | 0.972367i | \(-0.424996\pi\) | ||||
0.233456 | + | 0.972367i | \(0.424996\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 61.7696 | 1.96020 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.5563 | 0.334659 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.2843 | 0.357376 | 0.178688 | − | 0.983906i | \(-0.442815\pi\) | ||||
0.178688 | + | 0.983906i | \(0.442815\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.10051 | 0.0348184 |
(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 | 1568.2.a.w.1.2 | 2 | ||
4.3 | odd | 2 | 1568.2.a.l.1.1 | 2 | |||
7.2 | even | 3 | 224.2.i.a.193.1 | yes | 4 | ||
7.3 | odd | 6 | 1568.2.i.x.961.2 | 4 | |||
7.4 | even | 3 | 224.2.i.a.65.1 | ✓ | 4 | ||
7.5 | odd | 6 | 1568.2.i.x.1537.2 | 4 | |||
7.6 | odd | 2 | 1568.2.a.j.1.1 | 2 | |||
8.3 | odd | 2 | 3136.2.a.bw.1.2 | 2 | |||
8.5 | even | 2 | 3136.2.a.bd.1.1 | 2 | |||
21.2 | odd | 6 | 2016.2.s.q.865.2 | 4 | |||
21.11 | odd | 6 | 2016.2.s.q.289.2 | 4 | |||
28.3 | even | 6 | 1568.2.i.o.961.1 | 4 | |||
28.11 | odd | 6 | 224.2.i.d.65.2 | yes | 4 | ||
28.19 | even | 6 | 1568.2.i.o.1537.1 | 4 | |||
28.23 | odd | 6 | 224.2.i.d.193.2 | yes | 4 | ||
28.27 | even | 2 | 1568.2.a.u.1.2 | 2 | |||
56.11 | odd | 6 | 448.2.i.g.65.1 | 4 | |||
56.13 | odd | 2 | 3136.2.a.bx.1.2 | 2 | |||
56.27 | even | 2 | 3136.2.a.be.1.1 | 2 | |||
56.37 | even | 6 | 448.2.i.j.193.2 | 4 | |||
56.51 | odd | 6 | 448.2.i.g.193.1 | 4 | |||
56.53 | even | 6 | 448.2.i.j.65.2 | 4 | |||
84.11 | even | 6 | 2016.2.s.s.289.2 | 4 | |||
84.23 | even | 6 | 2016.2.s.s.865.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.i.a.65.1 | ✓ | 4 | 7.4 | even | 3 | ||
224.2.i.a.193.1 | yes | 4 | 7.2 | even | 3 | ||
224.2.i.d.65.2 | yes | 4 | 28.11 | odd | 6 | ||
224.2.i.d.193.2 | yes | 4 | 28.23 | odd | 6 | ||
448.2.i.g.65.1 | 4 | 56.11 | odd | 6 | |||
448.2.i.g.193.1 | 4 | 56.51 | odd | 6 | |||
448.2.i.j.65.2 | 4 | 56.53 | even | 6 | |||
448.2.i.j.193.2 | 4 | 56.37 | even | 6 | |||
1568.2.a.j.1.1 | 2 | 7.6 | odd | 2 | |||
1568.2.a.l.1.1 | 2 | 4.3 | odd | 2 | |||
1568.2.a.u.1.2 | 2 | 28.27 | even | 2 | |||
1568.2.a.w.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1568.2.i.o.961.1 | 4 | 28.3 | even | 6 | |||
1568.2.i.o.1537.1 | 4 | 28.19 | even | 6 | |||
1568.2.i.x.961.2 | 4 | 7.3 | odd | 6 | |||
1568.2.i.x.1537.2 | 4 | 7.5 | odd | 6 | |||
2016.2.s.q.289.2 | 4 | 21.11 | odd | 6 | |||
2016.2.s.q.865.2 | 4 | 21.2 | odd | 6 | |||
2016.2.s.s.289.2 | 4 | 84.11 | even | 6 | |||
2016.2.s.s.865.2 | 4 | 84.23 | even | 6 | |||
3136.2.a.bd.1.1 | 2 | 8.5 | even | 2 | |||
3136.2.a.be.1.1 | 2 | 56.27 | even | 2 | |||
3136.2.a.bw.1.2 | 2 | 8.3 | odd | 2 | |||
3136.2.a.bx.1.2 | 2 | 56.13 | odd | 2 |