Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | −0.561553 | −0.251134 | −0.125567 | − | 0.992085i | \(-0.540075\pi\) | ||||
−0.125567 | + | 0.992085i | \(0.540075\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.12311 | 1.54467 | 0.772337 | − | 0.635213i | \(-0.219088\pi\) | ||||
0.772337 | + | 0.635213i | \(0.219088\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.561553 | 0.155747 | 0.0778734 | − | 0.996963i | \(-0.475187\pi\) | ||||
0.0778734 | + | 0.996963i | \(0.475187\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | −2.43845 | −0.591410 | −0.295705 | − | 0.955279i | \(-0.595555\pi\) | ||||
−0.295705 | + | 0.955279i | \(0.595555\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 1.12311 | 0.251134 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.68466 | −1.60236 | −0.801181 | − | 0.598422i | \(-0.795795\pi\) | ||||
−0.801181 | + | 0.598422i | \(0.795795\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.68466 | −0.936932 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.00000 | 0.377964 | ||||||||
\(29\) | 4.12311 | 0.765641 | 0.382821 | − | 0.923823i | \(-0.374953\pi\) | ||||
0.382821 | + | 0.923823i | \(0.374953\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.68466 | −1.38021 | −0.690103 | − | 0.723711i | \(-0.742435\pi\) | ||||
−0.690103 | + | 0.723711i | \(0.742435\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.561553 | 0.0949197 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.1231 | −1.66423 | −0.832114 | − | 0.554604i | \(-0.812870\pi\) | ||||
−0.832114 | + | 0.554604i | \(0.812870\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.80776 | −1.53172 | −0.765858 | − | 0.643010i | \(-0.777685\pi\) | ||||
−0.765858 | + | 0.643010i | \(0.777685\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.2462 | 1.86753 | 0.933765 | − | 0.357887i | \(-0.116503\pi\) | ||||
0.933765 | + | 0.357887i | \(0.116503\pi\) | |||||||
\(44\) | −10.2462 | −1.54467 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.1231 | 1.91420 | 0.957101 | − | 0.289755i | \(-0.0935738\pi\) | ||||
0.957101 | + | 0.289755i | \(0.0935738\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.12311 | −0.155747 | ||||||||
\(53\) | 11.0000 | 1.51097 | 0.755483 | − | 0.655168i | \(-0.227402\pi\) | ||||
0.755483 | + | 0.655168i | \(0.227402\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.87689 | −0.387920 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.56155 | 1.11462 | 0.557310 | − | 0.830305i | \(-0.311834\pi\) | ||||
0.557310 | + | 0.830305i | \(0.311834\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.43845 | −0.696322 | −0.348161 | − | 0.937435i | \(-0.613194\pi\) | ||||
−0.348161 | + | 0.937435i | \(0.613194\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −0.315342 | −0.0391133 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | −0.244339 | −0.122169 | − | 0.992509i | \(-0.538985\pi\) | ||||
−0.122169 | + | 0.992509i | \(0.538985\pi\) | |||||||
\(68\) | 4.87689 | 0.591410 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.87689 | 0.578781 | 0.289390 | − | 0.957211i | \(-0.406547\pi\) | ||||
0.289390 | + | 0.957211i | \(0.406547\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.56155 | −1.00205 | −0.501027 | − | 0.865432i | \(-0.667044\pi\) | ||||
−0.501027 | + | 0.865432i | \(0.667044\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.00000 | −0.917663 | ||||||||
\(77\) | −5.12311 | −0.583832 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.6847 | −1.42714 | −0.713568 | − | 0.700586i | \(-0.752922\pi\) | ||||
−0.713568 | + | 0.700586i | \(0.752922\pi\) | |||||||
\(80\) | −2.24621 | −0.251134 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.80776 | 0.308192 | 0.154096 | − | 0.988056i | \(-0.450753\pi\) | ||||
0.154096 | + | 0.988056i | \(0.450753\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.36932 | 0.148523 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.8078 | 1.35762 | 0.678810 | − | 0.734314i | \(-0.262496\pi\) | ||||
0.678810 | + | 0.734314i | \(0.262496\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.561553 | −0.0588667 | ||||||||
\(92\) | 15.3693 | 1.60236 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.24621 | −0.230456 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.8078 | 1.19890 | 0.599448 | − | 0.800413i | \(-0.295387\pi\) | ||||
0.599448 | + | 0.800413i | \(0.295387\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.36932 | 0.936932 | ||||||||
\(101\) | 0.807764 | 0.0803755 | 0.0401878 | − | 0.999192i | \(-0.487204\pi\) | ||||
0.0401878 | + | 0.999192i | \(0.487204\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.0000 | −1.18240 | −0.591198 | − | 0.806527i | \(-0.701345\pi\) | ||||
−0.591198 | + | 0.806527i | \(0.701345\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.00000 | −0.377964 | ||||||||
\(113\) | −11.1231 | −1.04637 | −0.523187 | − | 0.852218i | \(-0.675257\pi\) | ||||
−0.523187 | + | 0.852218i | \(0.675257\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.31534 | 0.402408 | ||||||||
\(116\) | −8.24621 | −0.765641 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.43845 | 0.223532 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.2462 | 1.38602 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 15.3693 | 1.38021 | ||||||||
\(125\) | 5.43845 | 0.486430 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.31534 | −0.114922 | −0.0574610 | − | 0.998348i | \(-0.518300\pi\) | ||||
−0.0574610 | + | 0.998348i | \(0.518300\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | −0.346844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.4384 | 1.31900 | 0.659498 | − | 0.751707i | \(-0.270769\pi\) | ||||
0.659498 | + | 0.751707i | \(0.270769\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.43845 | 0.715740 | 0.357870 | − | 0.933771i | \(-0.383503\pi\) | ||||
0.357870 | + | 0.933771i | \(0.383503\pi\) | |||||||
\(140\) | −1.12311 | −0.0949197 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.87689 | 0.240578 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.31534 | −0.192279 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 20.2462 | 1.66423 | ||||||||
\(149\) | −14.0000 | −1.14692 | −0.573462 | − | 0.819232i | \(-0.694400\pi\) | ||||
−0.573462 | + | 0.819232i | \(0.694400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.4924 | 0.853861 | 0.426931 | − | 0.904284i | \(-0.359595\pi\) | ||||
0.426931 | + | 0.904284i | \(0.359595\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.31534 | 0.346617 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.2462 | −1.29659 | −0.648294 | − | 0.761390i | \(-0.724517\pi\) | ||||
−0.648294 | + | 0.761390i | \(0.724517\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.68466 | 0.605636 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.6155 | 1.45808 | 0.729040 | − | 0.684471i | \(-0.239967\pi\) | ||||
0.729040 | + | 0.684471i | \(0.239967\pi\) | |||||||
\(164\) | 19.6155 | 1.53172 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.24621 | 0.483346 | 0.241673 | − | 0.970358i | \(-0.422304\pi\) | ||||
0.241673 | + | 0.970358i | \(0.422304\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6847 | −0.975743 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −24.4924 | −1.86753 | ||||||||
\(173\) | −23.3693 | −1.77674 | −0.888368 | − | 0.459132i | \(-0.848161\pi\) | ||||
−0.888368 | + | 0.459132i | \(0.848161\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.68466 | 0.354127 | ||||||||
\(176\) | 20.4924 | 1.54467 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.1231 | 0.831380 | 0.415690 | − | 0.909506i | \(-0.363540\pi\) | ||||
0.415690 | + | 0.909506i | \(0.363540\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.8078 | −1.76962 | −0.884809 | − | 0.465955i | \(-0.845711\pi\) | ||||
−0.884809 | + | 0.465955i | \(0.845711\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.68466 | 0.417944 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.4924 | −0.913536 | ||||||||
\(188\) | −26.2462 | −1.91420 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.36932 | 0.388510 | 0.194255 | − | 0.980951i | \(-0.437771\pi\) | ||||
0.194255 | + | 0.980951i | \(0.437771\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.12311 | −0.0808429 | −0.0404215 | − | 0.999183i | \(-0.512870\pi\) | ||||
−0.0404215 | + | 0.999183i | \(0.512870\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.00000 | −0.142857 | ||||||||
\(197\) | 2.63068 | 0.187428 | 0.0937142 | − | 0.995599i | \(-0.470126\pi\) | ||||
0.0937142 | + | 0.995599i | \(0.470126\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.43845 | −0.385521 | −0.192761 | − | 0.981246i | \(-0.561744\pi\) | ||||
−0.192761 | + | 0.981246i | \(0.561744\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.12311 | −0.289385 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.50758 | 0.384666 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.24621 | 0.155747 | ||||||||
\(209\) | 20.4924 | 1.41749 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.3153 | −1.12319 | −0.561597 | − | 0.827411i | \(-0.689813\pi\) | ||||
−0.561597 | + | 0.827411i | \(0.689813\pi\) | |||||||
\(212\) | −22.0000 | −1.51097 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.87689 | −0.469000 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.68466 | 0.521669 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.75379 | 0.387920 | ||||||||
\(221\) | −1.36932 | −0.0921102 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.80776 | 0.656776 | 0.328388 | − | 0.944543i | \(-0.393495\pi\) | ||||
0.328388 | + | 0.944543i | \(0.393495\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.3693 | −0.754608 | −0.377304 | − | 0.926089i | \(-0.623149\pi\) | ||||
−0.377304 | + | 0.926089i | \(0.623149\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.5616 | −0.896173 | −0.448086 | − | 0.893990i | \(-0.647894\pi\) | ||||
−0.448086 | + | 0.893990i | \(0.647894\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.369317 | 0.0241948 | 0.0120974 | − | 0.999927i | \(-0.496149\pi\) | ||||
0.0120974 | + | 0.999927i | \(0.496149\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.36932 | −0.480721 | ||||||||
\(236\) | −17.1231 | −1.11462 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −28.3693 | −1.83506 | −0.917529 | − | 0.397668i | \(-0.869820\pi\) | ||||
−0.917529 | + | 0.397668i | \(0.869820\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.56155 | −0.615914 | −0.307957 | − | 0.951400i | \(-0.599645\pi\) | ||||
−0.307957 | + | 0.951400i | \(0.599645\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.8769 | 0.696322 | ||||||||
\(245\) | −0.561553 | −0.0358763 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.24621 | 0.142923 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.19224 | 0.138373 | 0.0691864 | − | 0.997604i | \(-0.477960\pi\) | ||||
0.0691864 | + | 0.997604i | \(0.477960\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −39.3693 | −2.47513 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | −27.0540 | −1.68758 | −0.843790 | − | 0.536673i | \(-0.819681\pi\) | ||||
−0.843790 | + | 0.536673i | \(0.819681\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.1231 | 0.629019 | ||||||||
\(260\) | 0.630683 | 0.0391133 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.6155 | −1.70285 | −0.851423 | − | 0.524479i | \(-0.824260\pi\) | ||||
−0.851423 | + | 0.524479i | \(0.824260\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.17708 | −0.379455 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.00000 | 0.244339 | ||||||||
\(269\) | −15.8078 | −0.963816 | −0.481908 | − | 0.876222i | \(-0.660056\pi\) | ||||
−0.481908 | + | 0.876222i | \(0.660056\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.9309 | −0.967731 | −0.483866 | − | 0.875142i | \(-0.660768\pi\) | ||||
−0.483866 | + | 0.875142i | \(0.660768\pi\) | |||||||
\(272\) | −9.75379 | −0.591410 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −24.0000 | −1.44725 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.2462 | −1.09631 | −0.548154 | − | 0.836377i | \(-0.684669\pi\) | ||||
−0.548154 | + | 0.836377i | \(0.684669\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.43845 | −0.264776 | −0.132388 | − | 0.991198i | \(-0.542264\pi\) | ||||
−0.132388 | + | 0.991198i | \(0.542264\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.31534 | −0.197077 | −0.0985383 | − | 0.995133i | \(-0.531417\pi\) | ||||
−0.0985383 | + | 0.995133i | \(0.531417\pi\) | |||||||
\(284\) | −9.75379 | −0.578781 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.80776 | 0.578934 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.0540 | −0.650234 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 17.1231 | 1.00205 | ||||||||
\(293\) | 10.0000 | 0.584206 | 0.292103 | − | 0.956387i | \(-0.405645\pi\) | ||||
0.292103 | + | 0.956387i | \(0.405645\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.80776 | −0.279919 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.31534 | −0.249563 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.2462 | −0.705860 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.0000 | 0.917663 | ||||||||
\(305\) | 3.05398 | 0.174870 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.1922 | −0.809994 | −0.404997 | − | 0.914318i | \(-0.632727\pi\) | ||||
−0.404997 | + | 0.914318i | \(0.632727\pi\) | |||||||
\(308\) | 10.2462 | 0.583832 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.0540 | 0.967042 | 0.483521 | − | 0.875333i | \(-0.339358\pi\) | ||||
0.483521 | + | 0.875333i | \(0.339358\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.9309 | −0.956989 | −0.478495 | − | 0.878090i | \(-0.658817\pi\) | ||||
−0.478495 | + | 0.878090i | \(0.658817\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 25.3693 | 1.42714 | ||||||||
\(317\) | 24.2462 | 1.36180 | 0.680901 | − | 0.732375i | \(-0.261588\pi\) | ||||
0.680901 | + | 0.732375i | \(0.261588\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.1231 | 1.18267 | ||||||||
\(320\) | 4.49242 | 0.251134 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.75379 | −0.542715 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.63068 | −0.145924 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.1231 | −0.723500 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.2462 | 0.563183 | 0.281591 | − | 0.959534i | \(-0.409138\pi\) | ||||
0.281591 | + | 0.959534i | \(0.409138\pi\) | |||||||
\(332\) | −5.61553 | −0.308192 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.12311 | 0.0613618 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.2462 | 1.42972 | 0.714861 | − | 0.699266i | \(-0.246490\pi\) | ||||
0.714861 | + | 0.699266i | \(0.246490\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.73863 | −0.148523 | ||||||||
\(341\) | −39.3693 | −2.13197 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.49242 | −0.402214 | −0.201107 | − | 0.979569i | \(-0.564454\pi\) | ||||
−0.201107 | + | 0.979569i | \(0.564454\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.0540 | −0.859350 | −0.429675 | − | 0.902984i | \(-0.641372\pi\) | ||||
−0.429675 | + | 0.902984i | \(0.641372\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.1231 | 0.592023 | 0.296012 | − | 0.955184i | \(-0.404343\pi\) | ||||
0.296012 | + | 0.955184i | \(0.404343\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.73863 | −0.145352 | ||||||||
\(356\) | −25.6155 | −1.35762 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.93087 | 0.365797 | 0.182899 | − | 0.983132i | \(-0.441452\pi\) | ||||
0.182899 | + | 0.983132i | \(0.441452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.12311 | 0.0588667 | ||||||||
\(365\) | 4.80776 | 0.251650 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 38.1771 | 1.99283 | 0.996414 | − | 0.0846152i | \(-0.0269661\pi\) | ||||
0.996414 | + | 0.0846152i | \(0.0269661\pi\) | |||||||
\(368\) | −30.7386 | −1.60236 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.0000 | −0.571092 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.12311 | −0.265264 | −0.132632 | − | 0.991165i | \(-0.542343\pi\) | ||||
−0.132632 | + | 0.991165i | \(0.542343\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.31534 | 0.119246 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.8769 | −0.969641 | −0.484820 | − | 0.874614i | \(-0.661115\pi\) | ||||
−0.484820 | + | 0.874614i | \(0.661115\pi\) | |||||||
\(380\) | 4.49242 | 0.230456 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.06913 | 0.259020 | 0.129510 | − | 0.991578i | \(-0.458659\pi\) | ||||
0.129510 | + | 0.991578i | \(0.458659\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.87689 | 0.146620 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −23.6155 | −1.19890 | ||||||||
\(389\) | −16.4924 | −0.836199 | −0.418100 | − | 0.908401i | \(-0.637304\pi\) | ||||
−0.418100 | + | 0.908401i | \(0.637304\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.7386 | 0.947653 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.12311 | 0.358402 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.946025 | 0.0474796 | 0.0237398 | − | 0.999718i | \(-0.492443\pi\) | ||||
0.0237398 | + | 0.999718i | \(0.492443\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.7386 | −0.936932 | ||||||||
\(401\) | −10.3693 | −0.517819 | −0.258909 | − | 0.965902i | \(-0.583363\pi\) | ||||
−0.258909 | + | 0.965902i | \(0.583363\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.31534 | −0.214962 | ||||||||
\(404\) | −1.61553 | −0.0803755 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −51.8617 | −2.57069 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.0000 | −0.890043 | −0.445021 | − | 0.895520i | \(-0.646804\pi\) | ||||
−0.445021 | + | 0.895520i | \(0.646804\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 24.0000 | 1.18240 | ||||||||
\(413\) | −8.56155 | −0.421286 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.57671 | −0.0773975 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.12311 | −0.445693 | −0.222846 | − | 0.974854i | \(-0.571535\pi\) | ||||
−0.222846 | + | 0.974854i | \(0.571535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.7538 | −1.06021 | −0.530107 | − | 0.847931i | \(-0.677848\pi\) | ||||
−0.530107 | + | 0.847931i | \(0.677848\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.4233 | 0.554111 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.43845 | 0.263185 | ||||||||
\(428\) | 8.00000 | 0.386695 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.4924 | −0.698075 | −0.349038 | − | 0.937109i | \(-0.613491\pi\) | ||||
−0.349038 | + | 0.937109i | \(0.613491\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.49242 | 0.119778 | 0.0598891 | − | 0.998205i | \(-0.480925\pi\) | ||||
0.0598891 | + | 0.998205i | \(0.480925\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.00000 | −0.191565 | ||||||||
\(437\) | −30.7386 | −1.47043 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.8078 | −1.04083 | −0.520414 | − | 0.853914i | \(-0.674222\pi\) | ||||
−0.520414 | + | 0.853914i | \(0.674222\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.00000 | −0.190046 | −0.0950229 | − | 0.995475i | \(-0.530292\pi\) | ||||
−0.0950229 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.19224 | −0.340945 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.00000 | 0.377964 | ||||||||
\(449\) | 17.6155 | 0.831328 | 0.415664 | − | 0.909518i | \(-0.363549\pi\) | ||||
0.415664 | + | 0.909518i | \(0.363549\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −50.2462 | −2.36600 | ||||||||
\(452\) | 22.2462 | 1.04637 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.315342 | 0.0147834 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.00000 | 0.140334 | 0.0701670 | − | 0.997535i | \(-0.477647\pi\) | ||||
0.0701670 | + | 0.997535i | \(0.477647\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.63068 | −0.402408 | ||||||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.68466 | −0.171241 | −0.0856203 | − | 0.996328i | \(-0.527287\pi\) | ||||
−0.0856203 | + | 0.996328i | \(0.527287\pi\) | |||||||
\(464\) | 16.4924 | 0.765641 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.5616 | 0.488730 | 0.244365 | − | 0.969683i | \(-0.421420\pi\) | ||||
0.244365 | + | 0.969683i | \(0.421420\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.00000 | 0.0923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 62.7386 | 2.88473 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.7386 | −0.859787 | ||||||||
\(476\) | −4.87689 | −0.223532 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.5616 | −1.80761 | −0.903807 | − | 0.427941i | \(-0.859239\pi\) | ||||
−0.903807 | + | 0.427941i | \(0.859239\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.68466 | −0.259198 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −30.4924 | −1.38602 | ||||||||
\(485\) | −6.63068 | −0.301084 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.75379 | 0.441986 | 0.220993 | − | 0.975275i | \(-0.429070\pi\) | ||||
0.220993 | + | 0.975275i | \(0.429070\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.50758 | 0.338812 | 0.169406 | − | 0.985546i | \(-0.445815\pi\) | ||||
0.169406 | + | 0.985546i | \(0.445815\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.0540 | −0.452808 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −30.7386 | −1.38021 | ||||||||
\(497\) | −4.87689 | −0.218759 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.492423 | 0.0220439 | 0.0110219 | − | 0.999939i | \(-0.496492\pi\) | ||||
0.0110219 | + | 0.999939i | \(0.496492\pi\) | |||||||
\(500\) | −10.8769 | −0.486430 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.68466 | −0.387230 | −0.193615 | − | 0.981078i | \(-0.562021\pi\) | ||||
−0.193615 | + | 0.981078i | \(0.562021\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.453602 | −0.0201850 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.00000 | −0.0887357 | ||||||||
\(509\) | 3.31534 | 0.146950 | 0.0734750 | − | 0.997297i | \(-0.476591\pi\) | ||||
0.0734750 | + | 0.997297i | \(0.476591\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.56155 | 0.378741 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.73863 | 0.296940 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 67.2311 | 2.95682 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.12311 | −0.136826 | −0.0684129 | − | 0.997657i | \(-0.521794\pi\) | ||||
−0.0684129 | + | 0.997657i | \(0.521794\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.1771 | 1.31955 | 0.659776 | − | 0.751462i | \(-0.270651\pi\) | ||||
0.659776 | + | 0.751462i | \(0.270651\pi\) | |||||||
\(524\) | 2.63068 | 0.114922 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.7386 | 0.816268 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 36.0540 | 1.56756 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.00000 | 0.346844 | ||||||||
\(533\) | −5.50758 | −0.238560 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.24621 | 0.0971122 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.12311 | 0.220668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.2462 | 0.612492 | 0.306246 | − | 0.951952i | \(-0.400927\pi\) | ||||
0.306246 | + | 0.951952i | \(0.400927\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.12311 | −0.0481086 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.4924 | 1.21825 | 0.609124 | − | 0.793075i | \(-0.291521\pi\) | ||||
0.609124 | + | 0.793075i | \(0.291521\pi\) | |||||||
\(548\) | −30.8769 | −1.31900 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.4924 | 0.702601 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.6847 | 0.539407 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.8769 | −0.715740 | ||||||||
\(557\) | 17.1231 | 0.725529 | 0.362765 | − | 0.931881i | \(-0.381833\pi\) | ||||
0.362765 | + | 0.931881i | \(0.381833\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.87689 | 0.290862 | ||||||||
\(560\) | 2.24621 | 0.0949197 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.7386 | −1.63264 | −0.816319 | − | 0.577601i | \(-0.803989\pi\) | ||||
−0.816319 | + | 0.577601i | \(0.803989\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.24621 | 0.262780 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −37.3693 | −1.56660 | −0.783302 | − | 0.621642i | \(-0.786466\pi\) | ||||
−0.783302 | + | 0.621642i | \(0.786466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.1231 | −0.883974 | −0.441987 | − | 0.897021i | \(-0.645726\pi\) | ||||
−0.441987 | + | 0.897021i | \(0.645726\pi\) | |||||||
\(572\) | −5.75379 | −0.240578 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.0000 | 1.50130 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.8078 | 0.449933 | 0.224967 | − | 0.974366i | \(-0.427773\pi\) | ||||
0.224967 | + | 0.974366i | \(0.427773\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.63068 | 0.192279 | ||||||||
\(581\) | −2.80776 | −0.116486 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 56.3542 | 2.33395 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.3002 | −0.920427 | −0.460214 | − | 0.887808i | \(-0.652227\pi\) | ||||
−0.460214 | + | 0.887808i | \(0.652227\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.7386 | −1.26656 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −40.4924 | −1.66423 | ||||||||
\(593\) | −12.3153 | −0.505730 | −0.252865 | − | 0.967502i | \(-0.581373\pi\) | ||||
−0.252865 | + | 0.967502i | \(0.581373\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.36932 | −0.0561365 | ||||||||
\(596\) | 28.0000 | 1.14692 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.38447 | −0.220004 | −0.110002 | − | 0.993931i | \(-0.535086\pi\) | ||||
−0.110002 | + | 0.993931i | \(0.535086\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.93087 | −0.201134 | −0.100567 | − | 0.994930i | \(-0.532066\pi\) | ||||
−0.100567 | + | 0.994930i | \(0.532066\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20.9848 | −0.853861 | ||||||||
\(605\) | −8.56155 | −0.348077 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.8078 | 0.682206 | 0.341103 | − | 0.940026i | \(-0.389199\pi\) | ||||
0.341103 | + | 0.940026i | \(0.389199\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.36932 | 0.298131 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.63068 | 0.267811 | 0.133905 | − | 0.990994i | \(-0.457248\pi\) | ||||
0.133905 | + | 0.990994i | \(0.457248\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.1080 | 1.65494 | 0.827472 | − | 0.561507i | \(-0.189778\pi\) | ||||
0.827472 | + | 0.561507i | \(0.189778\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.6847 | 1.39409 | 0.697047 | − | 0.717025i | \(-0.254497\pi\) | ||||
0.697047 | + | 0.717025i | \(0.254497\pi\) | |||||||
\(620\) | −8.63068 | −0.346617 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.8078 | −0.513132 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.3693 | 0.814773 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 32.4924 | 1.29659 | ||||||||
\(629\) | 24.6847 | 0.984242 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.4924 | 0.895409 | 0.447705 | − | 0.894182i | \(-0.352242\pi\) | ||||
0.447705 | + | 0.894182i | \(0.352242\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.561553 | −0.0222845 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.561553 | 0.0222495 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.80776 | −0.229393 | −0.114696 | − | 0.993401i | \(-0.536590\pi\) | ||||
−0.114696 | + | 0.993401i | \(0.536590\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.7386 | −0.738980 | −0.369490 | − | 0.929235i | \(-0.620468\pi\) | ||||
−0.369490 | + | 0.929235i | \(0.620468\pi\) | |||||||
\(644\) | −15.3693 | −0.605636 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.0540 | 0.827717 | 0.413859 | − | 0.910341i | \(-0.364181\pi\) | ||||
0.413859 | + | 0.910341i | \(0.364181\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 43.8617 | 1.72172 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −37.2311 | −1.45808 | ||||||||
\(653\) | −35.8617 | −1.40338 | −0.701689 | − | 0.712483i | \(-0.747570\pi\) | ||||
−0.701689 | + | 0.712483i | \(0.747570\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.738634 | 0.0288608 | ||||||||
\(656\) | −39.2311 | −1.53172 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.5616 | −1.34633 | −0.673163 | − | 0.739494i | \(-0.735065\pi\) | ||||
−0.673163 | + | 0.739494i | \(0.735065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.4384 | 0.600486 | 0.300243 | − | 0.953863i | \(-0.402932\pi\) | ||||
0.300243 | + | 0.953863i | \(0.402932\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.24621 | 0.0871043 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.6847 | −1.22683 | ||||||||
\(668\) | −12.4924 | −0.483346 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27.8617 | −1.07559 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −49.1080 | −1.89297 | −0.946486 | − | 0.322744i | \(-0.895395\pi\) | ||||
−0.946486 | + | 0.322744i | \(0.895395\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25.3693 | 0.975743 | ||||||||
\(677\) | 6.93087 | 0.266375 | 0.133187 | − | 0.991091i | \(-0.457479\pi\) | ||||
0.133187 | + | 0.991091i | \(0.457479\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.8078 | −0.453140 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.7386 | 0.717014 | 0.358507 | − | 0.933527i | \(-0.383286\pi\) | ||||
0.358507 | + | 0.933527i | \(0.383286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.66950 | −0.331245 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 48.9848 | 1.86753 | ||||||||
\(689\) | 6.17708 | 0.235328 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.3002 | −1.38092 | −0.690462 | − | 0.723369i | \(-0.742593\pi\) | ||||
−0.690462 | + | 0.723369i | \(0.742593\pi\) | |||||||
\(692\) | 46.7386 | 1.77674 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.73863 | −0.179747 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.9157 | 0.905872 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.36932 | −0.354127 | ||||||||
\(701\) | 7.93087 | 0.299545 | 0.149772 | − | 0.988720i | \(-0.452146\pi\) | ||||
0.149772 | + | 0.988720i | \(0.452146\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −40.4924 | −1.52720 | ||||||||
\(704\) | −40.9848 | −1.54467 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.807764 | −0.0303791 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.9309 | −1.38697 | −0.693484 | − | 0.720472i | \(-0.743925\pi\) | ||||
−0.693484 | + | 0.720472i | \(0.743925\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 59.0540 | 2.21159 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.61553 | −0.0604173 | ||||||||
\(716\) | −22.2462 | −0.831380 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.1771 | −1.23730 | −0.618648 | − | 0.785668i | \(-0.712319\pi\) | ||||
−0.618648 | + | 0.785668i | \(0.712319\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 47.6155 | 1.76962 | ||||||||
\(725\) | −19.3153 | −0.717354 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.1771 | 1.15629 | 0.578147 | − | 0.815933i | \(-0.303776\pi\) | ||||
0.578147 | + | 0.815933i | \(0.303776\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29.8617 | −1.10448 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.68466 | 0.136096 | 0.0680480 | − | 0.997682i | \(-0.478323\pi\) | ||||
0.0680480 | + | 0.997682i | \(0.478323\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.2462 | −0.377424 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.1231 | 0.445956 | 0.222978 | − | 0.974824i | \(-0.428422\pi\) | ||||
0.222978 | + | 0.974824i | \(0.428422\pi\) | |||||||
\(740\) | −11.3693 | −0.417944 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.1080 | 1.72822 | 0.864112 | − | 0.503300i | \(-0.167881\pi\) | ||||
0.864112 | + | 0.503300i | \(0.167881\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.86174 | 0.288032 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 24.9848 | 0.913536 | ||||||||
\(749\) | 4.00000 | 0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.8769 | −1.05373 | −0.526866 | − | 0.849948i | \(-0.676633\pi\) | ||||
−0.526866 | + | 0.849948i | \(0.676633\pi\) | |||||||
\(752\) | 52.4924 | 1.91420 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.89205 | −0.214434 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.1080 | 1.49409 | 0.747047 | − | 0.664771i | \(-0.231471\pi\) | ||||
0.747047 | + | 0.664771i | \(0.231471\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.5464 | 0.926056 | 0.463028 | − | 0.886344i | \(-0.346763\pi\) | ||||
0.463028 | + | 0.886344i | \(0.346763\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00000 | −0.0724049 | ||||||||
\(764\) | −10.7386 | −0.388510 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.80776 | 0.173598 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.0540 | 1.15590 | 0.577948 | − | 0.816074i | \(-0.303854\pi\) | ||||
0.577948 | + | 0.816074i | \(0.303854\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.24621 | 0.0808429 | ||||||||
\(773\) | −30.3002 | −1.08982 | −0.544911 | − | 0.838494i | \(-0.683437\pi\) | ||||
−0.544911 | + | 0.838494i | \(0.683437\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.0000 | 1.29316 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −39.2311 | −1.40560 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.9848 | 0.894028 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.00000 | 0.142857 | ||||||||
\(785\) | 9.12311 | 0.325618 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −45.7926 | −1.63233 | −0.816165 | − | 0.577819i | \(-0.803904\pi\) | ||||
−0.816165 | + | 0.577819i | \(0.803904\pi\) | |||||||
\(788\) | −5.26137 | −0.187428 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.1231 | 0.395492 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.05398 | −0.108450 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.8769 | 0.385521 | ||||||||
\(797\) | 28.2462 | 1.00053 | 0.500266 | − | 0.865872i | \(-0.333236\pi\) | ||||
0.500266 | + | 0.865872i | \(0.333236\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.0000 | −1.13208 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −43.8617 | −1.54785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.31534 | −0.152096 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.1231 | −0.531700 | −0.265850 | − | 0.964014i | \(-0.585653\pi\) | ||||
−0.265850 | + | 0.964014i | \(0.585653\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.56155 | −0.0899483 | −0.0449741 | − | 0.998988i | \(-0.514321\pi\) | ||||
−0.0449741 | + | 0.998988i | \(0.514321\pi\) | |||||||
\(812\) | 8.24621 | 0.289385 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.4536 | −0.366174 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 48.9848 | 1.71376 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.0152 | −0.384666 | ||||||||
\(821\) | 47.0000 | 1.64031 | 0.820156 | − | 0.572140i | \(-0.193887\pi\) | ||||
0.820156 | + | 0.572140i | \(0.193887\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.4233 | −1.23478 | −0.617389 | − | 0.786658i | \(-0.711810\pi\) | ||||
−0.617389 | + | 0.786658i | \(0.711810\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.0000 | 1.07798 | 0.538988 | − | 0.842314i | \(-0.318807\pi\) | ||||
0.538988 | + | 0.842314i | \(0.318807\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −53.2311 | −1.84879 | −0.924396 | − | 0.381435i | \(-0.875430\pi\) | ||||
−0.924396 | + | 0.381435i | \(0.875430\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.49242 | −0.155747 | ||||||||
\(833\) | −2.43845 | −0.0844872 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.50758 | −0.121385 | ||||||||
\(836\) | −40.9848 | −1.41749 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.4233 | 0.359852 | 0.179926 | − | 0.983680i | \(-0.442414\pi\) | ||||
0.179926 | + | 0.983680i | \(0.442414\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.0000 | −0.413793 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 32.6307 | 1.12319 | ||||||||
\(845\) | 7.12311 | 0.245042 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.2462 | −0.523866 | ||||||||
\(848\) | 44.0000 | 1.51097 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 77.7926 | 2.66670 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.5616 | −0.395860 | −0.197930 | − | 0.980216i | \(-0.563422\pi\) | ||||
−0.197930 | + | 0.980216i | \(0.563422\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.9460 | −0.647184 | −0.323592 | − | 0.946197i | \(-0.604890\pi\) | ||||
−0.323592 | + | 0.946197i | \(0.604890\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −55.9157 | −1.90782 | −0.953910 | − | 0.300094i | \(-0.902982\pi\) | ||||
−0.953910 | + | 0.300094i | \(0.902982\pi\) | |||||||
\(860\) | 13.7538 | 0.469000 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.8769 | −1.01702 | −0.508511 | − | 0.861056i | \(-0.669804\pi\) | ||||
−0.508511 | + | 0.861056i | \(0.669804\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.1231 | 0.446199 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −15.3693 | −0.521669 | ||||||||
\(869\) | −64.9848 | −2.20446 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.12311 | −0.0380550 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.43845 | −0.183853 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.5464 | −0.693803 | −0.346901 | − | 0.937902i | \(-0.612766\pi\) | ||||
−0.346901 | + | 0.937902i | \(0.612766\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −11.5076 | −0.387920 | ||||||||
\(881\) | −18.0691 | −0.608764 | −0.304382 | − | 0.952550i | \(-0.598450\pi\) | ||||
−0.304382 | + | 0.952550i | \(0.598450\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.93087 | −0.199590 | −0.0997948 | − | 0.995008i | \(-0.531819\pi\) | ||||
−0.0997948 | + | 0.995008i | \(0.531819\pi\) | |||||||
\(884\) | 2.73863 | 0.0921102 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.5616 | −1.02616 | −0.513078 | − | 0.858342i | \(-0.671495\pi\) | ||||
−0.513078 | + | 0.858342i | \(0.671495\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.6155 | −0.656776 | ||||||||
\(893\) | 52.4924 | 1.75659 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.24621 | −0.208788 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31.6847 | −1.05674 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.8229 | −0.893601 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.3693 | 0.444411 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.50758 | −0.149672 | −0.0748358 | − | 0.997196i | \(-0.523843\pi\) | ||||
−0.0748358 | + | 0.997196i | \(0.523843\pi\) | |||||||
\(908\) | 22.7386 | 0.754608 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.3693 | 0.840523 | 0.420261 | − | 0.907403i | \(-0.361938\pi\) | ||||
0.420261 | + | 0.907403i | \(0.361938\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.3845 | 0.476057 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27.1231 | 0.896173 | ||||||||
\(917\) | 1.31534 | 0.0434364 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.8617 | −1.74375 | −0.871874 | − | 0.489730i | \(-0.837095\pi\) | ||||
−0.871874 | + | 0.489730i | \(0.837095\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.73863 | 0.0901432 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 47.4233 | 1.55927 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −37.6155 | −1.23413 | −0.617063 | − | 0.786914i | \(-0.711678\pi\) | ||||
−0.617063 | + | 0.786914i | \(0.711678\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000 | 0.131095 | ||||||||
\(932\) | −0.738634 | −0.0241948 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.01515 | 0.229420 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.12311 | 0.232702 | 0.116351 | − | 0.993208i | \(-0.462880\pi\) | ||||
0.116351 | + | 0.993208i | \(0.462880\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 14.7386 | 0.480721 | ||||||||
\(941\) | −0.0539753 | −0.00175954 | −0.000879772 | − | 1.00000i | \(-0.500280\pi\) | ||||
−0.000879772 | 1.00000i | \(0.500280\pi\) | ||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 75.3693 | 2.45436 | ||||||||
\(944\) | 34.2462 | 1.11462 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.4233 | −0.761155 | −0.380577 | − | 0.924749i | \(-0.624275\pi\) | ||||
−0.380577 | + | 0.924749i | \(0.624275\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.80776 | −0.156067 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.7386 | 0.801363 | 0.400681 | − | 0.916217i | \(-0.368773\pi\) | ||||
0.400681 | + | 0.916217i | \(0.368773\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.01515 | −0.0975681 | ||||||||
\(956\) | 56.7386 | 1.83506 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.4384 | −0.498533 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0540 | 0.904967 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.1231 | 0.615914 | ||||||||
\(965\) | 0.630683 | 0.0203024 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.3542 | 1.29770 | 0.648851 | − | 0.760915i | \(-0.275250\pi\) | ||||
0.648851 | + | 0.760915i | \(0.275250\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.63068 | −0.148606 | −0.0743028 | − | 0.997236i | \(-0.523673\pi\) | ||||
−0.0743028 | + | 0.997236i | \(0.523673\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.43845 | −0.270524 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −21.7538 | −0.696322 | ||||||||
\(977\) | −12.9848 | −0.415422 | −0.207711 | − | 0.978190i | \(-0.566601\pi\) | ||||
−0.207711 | + | 0.978190i | \(0.566601\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 65.6155 | 2.09708 | ||||||||
\(980\) | 1.12311 | 0.0358763 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.80776 | −0.312819 | −0.156410 | − | 0.987692i | \(-0.549992\pi\) | ||||
−0.156410 | + | 0.987692i | \(0.549992\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.47727 | −0.0470697 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.49242 | −0.142923 | ||||||||
\(989\) | −94.1080 | −2.99246 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.05398 | 0.0968175 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.0000 | 0.823428 | 0.411714 | − | 0.911313i | \(-0.364930\pi\) | ||||
0.411714 | + | 0.911313i | \(0.364930\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 8001.2.a.i.1.1 | 2 | ||
3.2 | odd | 2 | 2667.2.a.f.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.f.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
8001.2.a.i.1.1 | 2 | 1.1 | even | 1 | trivial |