Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6384,2,Mod(1,6384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6384.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6384 = 2^{4} \cdot 3 \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6384.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: | \(50.9764966504\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.9248.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 3192) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.662153\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6384.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.69614 | −0.758537 | −0.379269 | − | 0.925287i | \(-0.623824\pi\) | ||||
−0.379269 | + | 0.925287i | \(0.623824\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.32431 | 0.399294 | 0.199647 | − | 0.979868i | \(-0.436021\pi\) | ||||
0.199647 | + | 0.979868i | \(0.436021\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.69614 | −0.437942 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.14355 | 1.49003 | 0.745015 | − | 0.667047i | \(-0.232442\pi\) | ||||
0.745015 | + | 0.667047i | \(0.232442\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.91779 | −0.608401 | −0.304201 | − | 0.952608i | \(-0.598389\pi\) | ||||
−0.304201 | + | 0.952608i | \(0.598389\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.12311 | −0.424621 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.42696 | −0.264981 | −0.132490 | − | 0.991184i | \(-0.542297\pi\) | ||||
−0.132490 | + | 0.991184i | \(0.542297\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.32431 | 0.597063 | 0.298532 | − | 0.954400i | \(-0.403503\pi\) | ||||
0.298532 | + | 0.954400i | \(0.403503\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.32431 | 0.230532 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.69614 | −0.286700 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.83969 | 1.61764 | 0.808818 | − | 0.588059i | \(-0.200108\pi\) | ||||
0.808818 | + | 0.588059i | \(0.200108\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.04090 | −1.25578 | −0.627888 | − | 0.778303i | \(-0.716081\pi\) | ||||
−0.627888 | + | 0.778303i | \(0.716081\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.16400 | −1.09250 | −0.546250 | − | 0.837622i | \(-0.683945\pi\) | ||||
−0.546250 | + | 0.837622i | \(0.683945\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.69614 | −0.252846 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.66906 | 1.11865 | 0.559324 | − | 0.828949i | \(-0.311061\pi\) | ||||
0.559324 | + | 0.828949i | \(0.311061\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.14355 | 0.860270 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.81925 | 1.21142 | 0.605708 | − | 0.795687i | \(-0.292890\pi\) | ||||
0.605708 | + | 0.795687i | \(0.292890\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.24621 | −0.302879 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.43318 | −1.22810 | −0.614048 | − | 0.789269i | \(-0.710460\pi\) | ||||
−0.614048 | + | 0.789269i | \(0.710460\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.64861 | 0.595194 | 0.297597 | − | 0.954692i | \(-0.403815\pi\) | ||||
0.297597 | + | 0.954692i | \(0.403815\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.5705 | 1.41356 | 0.706782 | − | 0.707432i | \(-0.250146\pi\) | ||||
0.706782 | + | 0.707432i | \(0.250146\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.91779 | −0.351261 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.22165 | 0.382339 | 0.191170 | − | 0.981557i | \(-0.438772\pi\) | ||||
0.191170 | + | 0.981557i | \(0.438772\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.04090 | −0.941116 | −0.470558 | − | 0.882369i | \(-0.655947\pi\) | ||||
−0.470558 | + | 0.882369i | \(0.655947\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.12311 | −0.245155 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.32431 | 0.150919 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3101 | 1.15997 | 0.579987 | − | 0.814626i | \(-0.303058\pi\) | ||||
0.579987 | + | 0.814626i | \(0.303058\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.77835 | 0.524492 | 0.262246 | − | 0.965001i | \(-0.415537\pi\) | ||||
0.262246 | + | 0.965001i | \(0.415537\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.4203 | −1.13024 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.42696 | −0.152987 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.6385 | −1.23368 | −0.616839 | − | 0.787089i | \(-0.711587\pi\) | ||||
−0.616839 | + | 0.787089i | \(0.711587\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.32431 | 0.344715 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.69614 | −0.174020 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.71659 | −0.681966 | −0.340983 | − | 0.940069i | \(-0.610760\pi\) | ||||
−0.340983 | + | 0.940069i | \(0.610760\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.32431 | 0.133098 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.7779 | 1.37096 | 0.685478 | − | 0.728094i | \(-0.259593\pi\) | ||||
0.685478 | + | 0.728094i | \(0.259593\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.1911 | 1.29976 | 0.649878 | − | 0.760039i | \(-0.274820\pi\) | ||||
0.649878 | + | 0.760039i | \(0.274820\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.69614 | −0.165526 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.46786 | −0.528598 | −0.264299 | − | 0.964441i | \(-0.585141\pi\) | ||||
−0.264299 | + | 0.964441i | \(0.585141\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.5292 | −1.39165 | −0.695823 | − | 0.718214i | \(-0.744960\pi\) | ||||
−0.695823 | + | 0.718214i | \(0.744960\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.83969 | 0.933942 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.77835 | −0.261365 | −0.130683 | − | 0.991424i | \(-0.541717\pi\) | ||||
−0.130683 | + | 0.991424i | \(0.541717\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.94898 | 0.461495 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.14355 | 0.563179 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.24621 | −0.840565 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.04090 | −0.725023 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0818 | 1.08063 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.16400 | −0.103288 | −0.0516442 | − | 0.998666i | \(-0.516446\pi\) | ||||
−0.0516442 | + | 0.998666i | \(0.516446\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.16400 | −0.630755 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.573035 | 0.0500663 | 0.0250332 | − | 0.999687i | \(-0.492031\pi\) | ||||
0.0250332 | + | 0.999687i | \(0.492031\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | 0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.69614 | −0.145981 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.83558 | −0.327696 | −0.163848 | − | 0.986486i | \(-0.552391\pi\) | ||||
−0.163848 | + | 0.986486i | \(0.552391\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.8255 | 1.76639 | 0.883196 | − | 0.469004i | \(-0.155387\pi\) | ||||
0.883196 | + | 0.469004i | \(0.155387\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.66906 | 0.645852 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.42033 | 0.200998 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.63438 | −0.133894 | −0.0669468 | − | 0.997757i | \(-0.521326\pi\) | ||||
−0.0669468 | + | 0.997757i | \(0.521326\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.08221 | 0.413584 | 0.206792 | − | 0.978385i | \(-0.433698\pi\) | ||||
0.206792 | + | 0.978385i | \(0.433698\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.14355 | 0.496677 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.63849 | −0.452895 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.24621 | 0.338885 | 0.169442 | − | 0.985540i | \(-0.445803\pi\) | ||||
0.169442 | + | 0.985540i | \(0.445803\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.81925 | 0.699412 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.91779 | −0.229954 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.9486 | 1.71914 | 0.859572 | − | 0.511014i | \(-0.170730\pi\) | ||||
0.859572 | + | 0.511014i | \(0.170730\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.24621 | −0.174867 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.20532 | 0.634946 | 0.317473 | − | 0.948267i | \(-0.397166\pi\) | ||||
0.317473 | + | 0.948267i | \(0.397166\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.39228 | 0.105853 | 0.0529266 | − | 0.998598i | \(-0.483145\pi\) | ||||
0.0529266 | + | 0.998598i | \(0.483145\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.12311 | −0.160492 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.43318 | −0.709041 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.1064 | −1.42808 | −0.714038 | − | 0.700107i | \(-0.753136\pi\) | ||||
−0.714038 | + | 0.700107i | \(0.753136\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.9895 | 1.48580 | 0.742902 | − | 0.669400i | \(-0.233449\pi\) | ||||
0.742902 | + | 0.669400i | \(0.233449\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.64861 | 0.343635 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.6895 | −1.22704 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.13595 | 0.594960 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.70235 | 0.412608 | 0.206304 | − | 0.978488i | \(-0.433856\pi\) | ||||
0.206304 | + | 0.978488i | \(0.433856\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.9766 | 1.65389 | 0.826947 | − | 0.562281i | \(-0.190076\pi\) | ||||
0.826947 | + | 0.562281i | \(0.190076\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.24210 | −0.444731 | −0.222366 | − | 0.974963i | \(-0.571378\pi\) | ||||
−0.222366 | + | 0.974963i | \(0.571378\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.7203 | −1.25616 | −0.628079 | − | 0.778150i | \(-0.716158\pi\) | ||||
−0.628079 | + | 0.778150i | \(0.716158\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.5705 | 0.816121 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.42696 | −0.100153 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.6385 | 0.952554 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.91779 | −0.202800 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.32431 | 0.0916042 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.8268 | 1.02072 | 0.510361 | − | 0.859960i | \(-0.329512\pi\) | ||||
0.510361 | + | 0.859960i | \(0.329512\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.22165 | 0.220744 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.1512 | 0.828702 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.32431 | 0.225669 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.04090 | −0.543353 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.9219 | 1.26710 | 0.633552 | − | 0.773700i | \(-0.281596\pi\) | ||||
0.633552 | + | 0.773700i | \(0.281596\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.12311 | −0.141540 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.3381 | 0.752538 | 0.376269 | − | 0.926511i | \(-0.377207\pi\) | ||||
0.376269 | + | 0.926511i | \(0.377207\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.9867 | −1.05643 | −0.528217 | − | 0.849110i | \(-0.677139\pi\) | ||||
−0.528217 | + | 0.849110i | \(0.677139\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.32431 | 0.0871330 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.87648 | 0.647029 | 0.323515 | − | 0.946223i | \(-0.395135\pi\) | ||||
0.323515 | + | 0.946223i | \(0.395135\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.0078 | −0.848536 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.3101 | 0.669711 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.6155 | 0.751346 | 0.375673 | − | 0.926752i | \(-0.377412\pi\) | ||||
0.375673 | + | 0.926752i | \(0.377412\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.3142 | −0.922058 | −0.461029 | − | 0.887385i | \(-0.652520\pi\) | ||||
−0.461029 | + | 0.887385i | \(0.652520\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.69614 | −0.108362 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.77835 | 0.302816 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.0779 | 1.58290 | 0.791451 | − | 0.611233i | \(-0.209326\pi\) | ||||
0.791451 | + | 0.611233i | \(0.209326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.86405 | −0.242931 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.4203 | −0.652547 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.7304 | −1.79215 | −0.896077 | − | 0.443899i | \(-0.853595\pi\) | ||||
−0.896077 | + | 0.443899i | \(0.853595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.83969 | 0.611409 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.42696 | −0.0883269 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.09464 | 0.314149 | 0.157074 | − | 0.987587i | \(-0.449794\pi\) | ||||
0.157074 | + | 0.987587i | \(0.449794\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.9587 | −0.918905 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.6385 | −0.712264 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.1410 | −0.801223 | −0.400612 | − | 0.916248i | \(-0.631202\pi\) | ||||
−0.400612 | + | 0.916248i | \(0.631202\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.2972 | 0.807749 | 0.403875 | − | 0.914814i | \(-0.367663\pi\) | ||||
0.403875 | + | 0.914814i | \(0.367663\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.81164 | −0.169548 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.2049 | 1.39425 | 0.697124 | − | 0.716951i | \(-0.254463\pi\) | ||||
0.697124 | + | 0.716951i | \(0.254463\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.32431 | 0.199021 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.4036 | 1.57511 | 0.787553 | − | 0.616247i | \(-0.211348\pi\) | ||||
0.787553 | + | 0.616247i | \(0.211348\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.7795 | 1.71077 | 0.855383 | − | 0.517997i | \(-0.173322\pi\) | ||||
0.855383 | + | 0.517997i | \(0.173322\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.69614 | −0.100471 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.04090 | −0.474639 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.7433 | 1.22019 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.71659 | −0.393733 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.3689 | −1.54049 | −0.770244 | − | 0.637750i | \(-0.779865\pi\) | ||||
−0.770244 | + | 0.637750i | \(0.779865\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.0000 | 0.931556 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.32431 | 0.0768441 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.16400 | −0.412926 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.7779 | 0.791522 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.88470 | −0.451477 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.73082 | 0.555367 | 0.277684 | − | 0.960673i | \(-0.410433\pi\) | ||||
0.277684 | + | 0.960673i | \(0.410433\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.1911 | 0.750414 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.4844 | −1.55850 | −0.779249 | − | 0.626715i | \(-0.784399\pi\) | ||||
−0.779249 | + | 0.626715i | \(0.784399\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.9766 | 1.29872 | 0.649358 | − | 0.760483i | \(-0.275038\pi\) | ||||
0.649358 | + | 0.760483i | \(0.275038\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.69614 | −0.0955667 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.1983 | 1.69610 | 0.848052 | − | 0.529913i | \(-0.177776\pi\) | ||||
0.848052 | + | 0.529913i | \(0.177776\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.88974 | −0.105805 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.46786 | −0.305186 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.14355 | 0.341836 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.5292 | −0.803467 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.66906 | 0.422809 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.3266 | 1.33711 | 0.668556 | − | 0.743662i | \(-0.266913\pi\) | ||||
0.668556 | + | 0.743662i | \(0.266913\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.83969 | 0.539212 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.6252 | −1.07224 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.3689 | 0.782724 | 0.391362 | − | 0.920237i | \(-0.372004\pi\) | ||||
0.391362 | + | 0.920237i | \(0.372004\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.77835 | −0.150899 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.40240 | 0.238403 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.94898 | 0.266444 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.0138 | −0.967032 | −0.483516 | − | 0.875335i | \(-0.660641\pi\) | ||||
−0.483516 | + | 0.875335i | \(0.660641\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.4924 | −0.561646 | −0.280823 | − | 0.959760i | \(-0.590607\pi\) | ||||
−0.280823 | + | 0.959760i | \(0.590607\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.6562 | −0.673622 | −0.336811 | − | 0.941572i | \(-0.609348\pi\) | ||||
−0.336811 | + | 0.941572i | \(0.609348\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.46437 | −0.290019 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.14355 | 0.325151 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −36.3050 | −1.91611 | −0.958053 | − | 0.286590i | \(-0.907478\pi\) | ||||
−0.958053 | + | 0.286590i | \(0.907478\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.24621 | −0.485300 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.6385 | 0.713871 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.0634 | 1.20390 | 0.601951 | − | 0.798533i | \(-0.294390\pi\) | ||||
0.601951 | + | 0.798533i | \(0.294390\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.04090 | −0.418592 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.81925 | 0.457872 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.1369 | −0.783760 | −0.391880 | − | 0.920016i | \(-0.628175\pi\) | ||||
−0.391880 | + | 0.920016i | \(0.628175\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.0818 | 0.623901 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.42948 | 0.227527 | 0.113764 | − | 0.993508i | \(-0.463709\pi\) | ||||
0.113764 | + | 0.993508i | \(0.463709\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.16400 | −0.0596336 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.98674 | −0.305908 | −0.152954 | − | 0.988233i | \(-0.548879\pi\) | ||||
−0.152954 | + | 0.988233i | \(0.548879\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.24621 | −0.114478 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.16400 | −0.364167 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.9858 | 1.36823 | 0.684116 | − | 0.729373i | \(-0.260188\pi\) | ||||
0.684116 | + | 0.729373i | \(0.260188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.9256 | −0.906537 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.573035 | 0.0289058 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.4873 | −0.879883 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.1360 | −0.709463 | −0.354732 | − | 0.934968i | \(-0.615428\pi\) | ||||
−0.354732 | + | 0.934968i | \(0.615428\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.00000 | 0.0500626 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.33505 | 0.216482 | 0.108241 | − | 0.994125i | \(-0.465478\pi\) | ||||
0.108241 | + | 0.994125i | \(0.465478\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.69614 | −0.0842819 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.0308 | 0.645912 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.5191 | 0.965157 | 0.482578 | − | 0.875853i | \(-0.339700\pi\) | ||||
0.482578 | + | 0.875853i | \(0.339700\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.83558 | −0.189195 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.43318 | −0.464176 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.10476 | −0.397847 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.8255 | 1.01983 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.9552 | 0.535196 | 0.267598 | − | 0.963531i | \(-0.413770\pi\) | ||||
0.267598 | + | 0.963531i | \(0.413770\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.49843 | −0.0730290 | −0.0365145 | − | 0.999333i | \(-0.511626\pi\) | ||||
−0.0365145 | + | 0.999333i | \(0.511626\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.66906 | 0.372883 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.0434 | −0.632698 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.64861 | 0.224962 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.64471 | 0.368233 | 0.184116 | − | 0.982904i | \(-0.441058\pi\) | ||||
0.184116 | + | 0.982904i | \(0.441058\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.3418 | −1.26591 | −0.632954 | − | 0.774190i | \(-0.718158\pi\) | ||||
−0.632954 | + | 0.774190i | \(0.718158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.42033 | 0.116046 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.91779 | −0.139577 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.29584 | −0.252757 | −0.126378 | − | 0.991982i | \(-0.540335\pi\) | ||||
−0.126378 | + | 0.991982i | \(0.540335\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.9118 | 0.565946 | 0.282973 | − | 0.959128i | \(-0.408679\pi\) | ||||
0.282973 | + | 0.959128i | \(0.408679\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.7405 | 0.935791 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.63438 | −0.0773035 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.8091 | −0.934850 | −0.467425 | − | 0.884033i | \(-0.654818\pi\) | ||||
−0.467425 | + | 0.884033i | \(0.654818\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.6486 | −0.501424 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.08221 | 0.238783 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.9077 | 0.837685 | 0.418843 | − | 0.908059i | \(-0.362436\pi\) | ||||
0.418843 | + | 0.908059i | \(0.362436\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.14355 | 0.286757 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.49083 | −0.0694347 | −0.0347173 | − | 0.999397i | \(-0.511053\pi\) | ||||
−0.0347173 | + | 0.999397i | \(0.511053\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.7028 | 0.869192 | 0.434596 | − | 0.900626i | \(-0.356891\pi\) | ||||
0.434596 | + | 0.900626i | \(0.356891\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.63849 | −0.261479 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.1574 | −1.02532 | −0.512660 | − | 0.858591i | \(-0.671340\pi\) | ||||
−0.512660 | + | 0.858591i | \(0.671340\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.5705 | 0.534277 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.24621 | 0.195655 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.48734 | −0.436228 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.12311 | −0.0974148 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.81925 | 0.403806 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.9387 | −0.773947 | −0.386973 | − | 0.922091i | \(-0.626480\pi\) | ||||
−0.386973 | + | 0.922091i | \(0.626480\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.91779 | −0.132764 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.3923 | 0.517297 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.4460 | −0.473354 | −0.236677 | − | 0.971588i | \(-0.576058\pi\) | ||||
−0.236677 | + | 0.971588i | \(0.576058\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.9486 | 0.992548 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.66557 | 0.255684 | 0.127842 | − | 0.991795i | \(-0.459195\pi\) | ||||
0.127842 | + | 0.991795i | \(0.459195\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.76663 | −0.394829 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.24621 | −0.100960 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.22165 | 0.144511 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.8438 | −1.33599 | −0.667996 | − | 0.744165i | \(-0.732848\pi\) | ||||
−0.667996 | + | 0.744165i | \(0.732848\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.20532 | 0.366586 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.02868 | −0.402569 | −0.201284 | − | 0.979533i | \(-0.564512\pi\) | ||||
−0.201284 | + | 0.979533i | \(0.564512\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.3693 | −1.03992 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.0000 | −0.577350 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.9256 | 1.06048 | 0.530242 | − | 0.847846i | \(-0.322101\pi\) | ||||
0.530242 | + | 0.847846i | \(0.322101\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.04090 | −0.355708 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.3739 | −0.985913 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.1562 | 0.446669 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.39228 | 0.0611144 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.5742 | 1.16424 | 0.582119 | − | 0.813104i | \(-0.302224\pi\) | ||||
0.582119 | + | 0.813104i | \(0.302224\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.73082 | 0.425499 | 0.212750 | − | 0.977107i | \(-0.431758\pi\) | ||||
0.212750 | + | 0.977107i | \(0.431758\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.12311 | −0.0926599 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.4231 | 0.889642 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.4865 | −0.629848 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.43318 | −0.409365 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.27426 | 0.400961 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.1064 | −0.824500 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.32431 | 0.0570419 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.49242 | −0.107158 | −0.0535788 | − | 0.998564i | \(-0.517063\pi\) | ||||
−0.0535788 | + | 0.998564i | \(0.517063\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.9895 | 0.857830 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.6436 | 1.05561 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.12722 | 0.219224 | 0.109612 | − | 0.993974i | \(-0.465039\pi\) | ||||
0.109612 | + | 0.993974i | \(0.465039\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.64861 | 0.198398 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.42696 | −0.0607907 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.3101 | 0.438429 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.6895 | −0.708430 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.96238 | −0.337377 | −0.168688 | − | 0.985669i | \(-0.553953\pi\) | ||||
−0.168688 | + | 0.985669i | \(0.553953\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.13595 | 0.343500 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.9899 | −0.800328 | −0.400164 | − | 0.916444i | \(-0.631047\pi\) | ||||
−0.400164 | + | 0.916444i | \(0.631047\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.71247 | 0.198255 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.71407 | −0.407235 | −0.203618 | − | 0.979051i | \(-0.565270\pi\) | ||||
−0.203618 | + | 0.979051i | \(0.565270\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.7079 | −0.741051 | −0.370525 | − | 0.928822i | \(-0.620822\pi\) | ||||
−0.370525 | + | 0.928822i | \(0.620822\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.70235 | 0.238219 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.19478 | 0.258340 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.1636 | −1.58877 | −0.794385 | − | 0.607414i | \(-0.792207\pi\) | ||||
−0.794385 | + | 0.607414i | \(0.792207\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.9766 | 0.954876 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.77835 | 0.198239 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.6794 | 0.483711 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.9186 | 1.73016 | 0.865082 | − | 0.501631i | \(-0.167266\pi\) | ||||
0.865082 | + | 0.501631i | \(0.167266\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.32431 | 0.136976 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.24210 | −0.256766 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.0200 | −0.904254 | −0.452127 | − | 0.891954i | \(-0.649335\pi\) | ||||
−0.452127 | + | 0.891954i | \(0.649335\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.4203 | −0.427192 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.7203 | −0.725243 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.0880 | 0.575620 | 0.287810 | − | 0.957687i | \(-0.407073\pi\) | ||||
0.287810 | + | 0.957687i | \(0.407073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.01696 | −0.204646 | −0.102323 | − | 0.994751i | \(-0.532628\pi\) | ||||
−0.102323 | + | 0.994751i | \(0.532628\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.5705 | 0.471188 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.6829 | 0.637600 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.9215 | 1.45801 | 0.729004 | − | 0.684509i | \(-0.239984\pi\) | ||||
0.729004 | + | 0.684509i | \(0.239984\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.42696 | −0.0578235 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.5053 | 1.19171 | 0.595853 | − | 0.803093i | \(-0.296814\pi\) | ||||
0.595853 | + | 0.803093i | \(0.296814\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.6385 | 0.549957 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.3822 | −0.498487 | −0.249244 | − | 0.968441i | \(-0.580182\pi\) | ||||
−0.249244 | + | 0.968441i | \(0.580182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.5333 | −1.06646 | −0.533232 | − | 0.845969i | \(-0.679023\pi\) | ||||
−0.533232 | + | 0.845969i | \(0.679023\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.91779 | −0.117087 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.6385 | −0.466286 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.87689 | −0.395076 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.32431 | 0.0528877 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 60.4507 | 2.41033 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0588 | −0.798529 | −0.399265 | − | 0.916836i | \(-0.630735\pi\) | ||||
−0.399265 | + | 0.916836i | \(0.630735\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.8268 | 0.589314 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.97431 | 0.0783481 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.22165 | 0.127446 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.0237 | 1.69934 | 0.849668 | − | 0.527319i | \(-0.176803\pi\) | ||||
0.849668 | + | 0.527319i | \(0.176803\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.9665 | −1.26064 | −0.630318 | − | 0.776337i | \(-0.717075\pi\) | ||||
−0.630318 | + | 0.776337i | \(0.717075\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.1512 | 0.478451 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.3820 | −0.604727 | −0.302364 | − | 0.953193i | \(-0.597776\pi\) | ||||
−0.302364 | + | 0.953193i | \(0.597776\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.4924 | −0.490370 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.32431 | 0.130290 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.3013 | −0.677054 | −0.338527 | − | 0.940957i | \(-0.609929\pi\) | ||||
−0.338527 | + | 0.940957i | \(0.609929\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.971949 | −0.0379772 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.04090 | −0.313705 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.0421 | −1.79354 | −0.896772 | − | 0.442492i | \(-0.854094\pi\) | ||||
−0.896772 | + | 0.442492i | \(0.854094\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.69963 | 0.221690 | 0.110845 | − | 0.993838i | \(-0.464644\pi\) | ||||
0.110845 | + | 0.993838i | \(0.464644\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.69614 | −0.0657735 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.16358 | 0.161215 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.9219 | 0.731563 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.15619 | 0.237657 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.2095 | −0.701925 | −0.350963 | − | 0.936389i | \(-0.614146\pi\) | ||||
−0.350963 | + | 0.936389i | \(0.614146\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.12311 | −0.0817184 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −43.1126 | −1.65695 | −0.828475 | − | 0.560026i | \(-0.810791\pi\) | ||||
−0.828475 | + | 0.560026i | \(0.810791\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.71659 | −0.257759 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.3381 | 0.434478 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.60381 | 0.0613681 | 0.0306841 | − | 0.999529i | \(-0.490231\pi\) | ||||
0.0306841 | + | 0.999529i | \(0.490231\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.50569 | 0.248569 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.9867 | −0.609932 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.3739 | 0.698977 | 0.349489 | − | 0.936941i | \(-0.386355\pi\) | ||||
0.349489 | + | 0.936941i | \(0.386355\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.32431 | 0.0503063 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −35.3229 | −1.33987 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −49.3997 | −1.87115 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.87648 | 0.373563 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.5958 | −1.15559 | −0.577794 | − | 0.816183i | \(-0.696086\pi\) | ||||
−0.577794 | + | 0.816183i | \(0.696086\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.83969 | 0.371111 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.0078 | −0.489902 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.7779 | 0.518172 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.2334 | 0.947659 | 0.473829 | − | 0.880617i | \(-0.342871\pi\) | ||||
0.473829 | + | 0.880617i | \(0.342871\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.3101 | 0.386658 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.69963 | −0.363254 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.6155 | 0.433790 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.8459 | −0.814715 | −0.407357 | − | 0.913269i | \(-0.633550\pi\) | ||||
−0.407357 | + | 0.913269i | \(0.633550\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.1911 | 0.491262 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.3142 | −0.532350 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.02960 | 0.112516 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.8889 | −1.47940 | −0.739699 | − | 0.672938i | \(-0.765032\pi\) | ||||
−0.739699 | + | 0.672938i | \(0.765032\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −44.0124 | −1.62786 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.7713 | −1.28431 | −0.642154 | − | 0.766576i | \(-0.721959\pi\) | ||||
−0.642154 | + | 0.766576i | \(0.721959\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.69614 | −0.0625631 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.3229 | 0.564427 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.02805 | 0.111389 | 0.0556943 | − | 0.998448i | \(-0.482263\pi\) | ||||
0.0556943 | + | 0.998448i | \(0.482263\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.0737 | −0.919864 | −0.459932 | − | 0.887954i | \(-0.652126\pi\) | ||||
−0.459932 | + | 0.887954i | \(0.652126\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.77214 | 0.101563 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.77835 | 0.174831 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.46786 | −0.199791 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.7616 | −0.465677 | −0.232839 | − | 0.972515i | \(-0.574801\pi\) | ||||
−0.232839 | + | 0.972515i | \(0.574801\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.0779 | 0.913889 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.62014 | −0.313719 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.3198 | 0.593152 | 0.296576 | − | 0.955009i | \(-0.404155\pi\) | ||||
0.296576 | + | 0.955009i | \(0.404155\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.86405 | −0.140256 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.6492 | −0.893534 | −0.446767 | − | 0.894650i | \(-0.647425\pi\) | ||||
−0.446767 | + | 0.894650i | \(0.647425\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.5292 | −0.525993 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.4203 | −0.376748 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.1103 | 0.436707 | 0.218354 | − | 0.975870i | \(-0.429931\pi\) | ||||
0.218354 | + | 0.975870i | \(0.429931\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.7304 | −1.03470 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.4456 | −1.27489 | −0.637445 | − | 0.770496i | \(-0.720009\pi\) | ||||
−0.637445 | + | 0.770496i | \(0.720009\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.05785 | −0.253526 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.83969 | 0.352997 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.04090 | −0.288095 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.26645 | 0.152666 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.42696 | −0.0509956 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.20217 | −0.257057 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.5890 | −0.876501 | −0.438251 | − | 0.898853i | \(-0.644402\pi\) | ||||
−0.438251 | + | 0.898853i | \(0.644402\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.09464 | 0.181374 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.77835 | −0.0987868 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.9587 | −0.530530 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.85393 | −0.313622 | −0.156811 | − | 0.987629i | \(-0.550121\pi\) | ||||
−0.156811 | + | 0.987629i | \(0.550121\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.1153 | 1.66682 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.6385 | −0.411226 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.6486 | −0.375781 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.94898 | 0.174429 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.1410 | −0.462586 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.05924 | −0.177874 | −0.0889368 | − | 0.996037i | \(-0.528347\pi\) | ||||
−0.0889368 | + | 0.996037i | \(0.528347\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.2095 | −0.850111 | −0.425056 | − | 0.905167i | \(-0.639745\pi\) | ||||
−0.425056 | + | 0.905167i | \(0.639745\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.2972 | 0.466354 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −37.2279 | −1.30404 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.16400 | −0.250637 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.3372 | 1.12857 | 0.564287 | − | 0.825579i | \(-0.309151\pi\) | ||||
0.564287 | + | 0.825579i | \(0.309151\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.2734 | −1.50842 | −0.754208 | − | 0.656635i | \(-0.771979\pi\) | ||||
−0.754208 | + | 0.656635i | \(0.771979\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.81164 | −0.0978889 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.975438 | 0.0339193 | 0.0169597 | − | 0.999856i | \(-0.494601\pi\) | ||||
0.0169597 | + | 0.999856i | \(0.494601\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.0436 | −0.696144 | −0.348072 | − | 0.937468i | \(-0.613163\pi\) | ||||
−0.348072 | + | 0.937468i | \(0.613163\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.2049 | 0.804969 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.14355 | 0.212862 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.9174 | −0.481631 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.32431 | 0.114905 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 47.4947 | 1.63970 | 0.819850 | − | 0.572578i | \(-0.194057\pi\) | ||||
0.819850 | + | 0.572578i | \(0.194057\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.9638 | −0.929785 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26.4036 | 0.909388 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.0498 | 0.758537 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.24621 | −0.317704 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.7795 | 0.987711 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.7102 | −0.984172 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.64861 | 0.159166 | 0.0795828 | − | 0.996828i | \(-0.474641\pi\) | ||||
0.0795828 | + | 0.996828i | \(0.474641\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.69614 | −0.0580068 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.3974 | −0.696761 | −0.348380 | − | 0.937353i | \(-0.613268\pi\) | ||||
−0.348380 | + | 0.937353i | \(0.613268\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.07949 | −0.173310 | −0.0866549 | − | 0.996238i | \(-0.527618\pi\) | ||||
−0.0866549 | + | 0.996238i | \(0.527618\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.04090 | −0.274033 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.5119 | −0.425910 | −0.212955 | − | 0.977062i | \(-0.568309\pi\) | ||||
−0.212955 | + | 0.977062i | \(0.568309\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.36151 | −0.0802936 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20.7433 | 0.704478 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.6537 | 0.463170 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.71659 | −0.227322 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.0818 | 0.408439 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.6601 | 1.77821 | 0.889103 | − | 0.457707i | \(-0.151329\pi\) | ||||
0.889103 | + | 0.457707i | \(0.151329\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.3689 | −0.889401 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.5892 | 0.794739 | 0.397369 | − | 0.917659i | \(-0.369923\pi\) | ||||
0.397369 | + | 0.917659i | \(0.369923\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.9256 | 1.41091 | 0.705454 | − | 0.708755i | \(-0.250743\pi\) | ||||
0.705454 | + | 0.708755i | \(0.250743\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.0000 | 0.537834 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.31280 | −0.0776561 | −0.0388281 | − | 0.999246i | \(-0.512362\pi\) | ||||
−0.0388281 | + | 0.999246i | \(0.512362\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.16400 | −0.0390394 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.32431 | 0.0443660 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.66906 | 0.256635 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.4071 | 1.08325 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.74367 | −0.158210 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 54.1815 | 1.80505 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.16400 | −0.238403 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.9049 | −1.12704 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.4980 | 0.481399 | 0.240699 | − | 0.970600i | \(-0.422623\pi\) | ||||
0.240699 | + | 0.970600i | \(0.422623\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.7779 | 0.456985 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.1320 | 0.832662 | 0.416331 | − | 0.909213i | \(-0.363316\pi\) | ||||
0.416331 | + | 0.909213i | \(0.363316\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.32800 | 0.209426 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.88470 | −0.260660 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.573035 | 0.0189233 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.17874 | −0.236805 | −0.118402 | − | 0.992966i | \(-0.537777\pi\) | ||||
−0.118402 | + | 0.992966i | \(0.537777\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.73082 | 0.320642 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.8907 | −0.686882 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.1911 | 0.433252 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.1334 | −1.48078 | −0.740390 | − | 0.672178i | \(-0.765359\pi\) | ||||
−0.740390 | + | 0.672178i | \(0.765359\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | 0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27.4844 | −0.899799 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.7997 | −0.451299 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.4916 | 1.71483 | 0.857413 | − | 0.514629i | \(-0.172071\pi\) | ||||
0.857413 | + | 0.514629i | \(0.172071\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.9766 | 0.749814 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.3055 | −1.15092 | −0.575462 | − | 0.817828i | \(-0.695178\pi\) | ||||
−0.575462 | + | 0.817828i | \(0.695178\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.4616 | 0.764016 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.69614 | −0.0551755 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.7800 | 0.772747 | 0.386374 | − | 0.922342i | \(-0.373728\pi\) | ||||
0.386374 | + | 0.922342i | \(0.373728\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.1983 | 0.979246 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.6957 | −0.540828 | −0.270414 | − | 0.962744i | \(-0.587160\pi\) | ||||
−0.270414 | + | 0.962744i | \(0.587160\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.67200 | −0.312978 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.88974 | −0.0610866 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.83558 | −0.123857 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.9490 | −0.643516 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.46786 | −0.176199 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −38.9716 | −1.25454 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.7300 | 1.53489 | 0.767446 | − | 0.641113i | \(-0.221527\pi\) | ||||
0.767446 | + | 0.641113i | \(0.221527\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.14355 | 0.197359 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.6486 | −0.598462 | −0.299231 | − | 0.954181i | \(-0.596730\pi\) | ||||
−0.299231 | + | 0.954181i | \(0.596730\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.8255 | 0.667634 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.3728 | −0.811748 | −0.405874 | − | 0.913929i | \(-0.633033\pi\) | ||||
−0.405874 | + | 0.913929i | \(0.633033\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.4129 | −0.492600 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.5292 | −0.463882 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −44.3841 | −1.41563 | −0.707817 | − | 0.706396i | \(-0.750320\pi\) | ||||
−0.707817 | + | 0.706396i | \(0.750320\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.5875 | 0.337345 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.66906 | 0.244109 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.9031 | 0.664678 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.7483 | 1.10382 | 0.551909 | − | 0.833905i | \(-0.313900\pi\) | ||||
0.551909 | + | 0.833905i | \(0.313900\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.3266 | 0.771982 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.0561 | 0.952843 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.32292 | −0.0418972 | −0.0209486 | − | 0.999781i | \(-0.506669\pi\) | ||||
−0.0209486 | + | 0.999781i | \(0.506669\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.83969 | 0.311314 |
(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 | 6384.2.a.cb.1.2 | 4 | ||
4.3 | odd | 2 | 3192.2.a.x.1.2 | ✓ | 4 | ||
12.11 | even | 2 | 9576.2.a.cj.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3192.2.a.x.1.2 | ✓ | 4 | 4.3 | odd | 2 | ||
6384.2.a.cb.1.2 | 4 | 1.1 | even | 1 | trivial | ||
9576.2.a.cj.1.3 | 4 | 12.11 | even | 2 |