Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 17 x^{10} + 79 x^{9} + 80 x^{8} - 536 x^{7} - 4 x^{6} + 1484 x^{5} - 682 x^{4} + \cdots - 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.39079\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | 1.39079 | 0.802976 | 0.401488 | − | 0.915864i | \(-0.368493\pi\) | ||||
0.401488 | + | 0.915864i | \(0.368493\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.208204 | 0.0931115 | 0.0465557 | − | 0.998916i | \(-0.485175\pi\) | ||||
0.0465557 | + | 0.998916i | \(0.485175\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.06569 | −0.355230 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.289568 | 0.0747662 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.42443 | 1.31562 | 0.657809 | − | 0.753185i | \(-0.271483\pi\) | ||||
0.657809 | + | 0.753185i | \(0.271483\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.55310 | 1.50338 | 0.751692 | − | 0.659514i | \(-0.229238\pi\) | ||||
0.751692 | + | 0.659514i | \(0.229238\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.39079 | 0.303496 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.74563 | 0.989532 | 0.494766 | − | 0.869026i | \(-0.335254\pi\) | ||||
0.494766 | + | 0.869026i | \(0.335254\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.95665 | −0.991330 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65454 | −1.08822 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.74178 | 0.323441 | 0.161721 | − | 0.986837i | \(-0.448296\pi\) | ||||
0.161721 | + | 0.986837i | \(0.448296\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.90117 | 1.41909 | 0.709546 | − | 0.704659i | \(-0.248900\pi\) | ||||
0.709546 | + | 0.704659i | \(0.248900\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.39079 | 0.242106 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.208204 | 0.0351928 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.54773 | 0.912041 | 0.456020 | − | 0.889969i | \(-0.349274\pi\) | ||||
0.456020 | + | 0.889969i | \(0.349274\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.39079 | 0.222705 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.83388 | 1.06727 | 0.533636 | − | 0.845714i | \(-0.320825\pi\) | ||||
0.533636 | + | 0.845714i | \(0.320825\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0581 | −1.53385 | −0.766923 | − | 0.641739i | \(-0.778213\pi\) | ||||
−0.766923 | + | 0.641739i | \(0.778213\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.221881 | −0.0330760 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.89791 | −0.568569 | −0.284284 | − | 0.958740i | \(-0.591756\pi\) | ||||
−0.284284 | + | 0.958740i | \(0.591756\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.54427 | 1.05641 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.5728 | −1.45228 | −0.726141 | − | 0.687546i | \(-0.758688\pi\) | ||||
−0.726141 | + | 0.687546i | \(0.758688\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.208204 | 0.0280742 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.11402 | 1.20718 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.484155 | −0.0630316 | −0.0315158 | − | 0.999503i | \(-0.510033\pi\) | ||||
−0.0315158 | + | 0.999503i | \(0.510033\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.7490 | −1.88841 | −0.944206 | − | 0.329354i | \(-0.893169\pi\) | ||||
−0.944206 | + | 0.329354i | \(0.893169\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.06569 | −0.134264 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.208204 | 0.0258245 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.2552 | 1.86372 | 0.931860 | − | 0.362818i | \(-0.118185\pi\) | ||||
0.931860 | + | 0.362818i | \(0.118185\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.60019 | 0.794570 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.98985 | 0.473508 | 0.236754 | − | 0.971570i | \(-0.423916\pi\) | ||||
0.236754 | + | 0.971570i | \(0.423916\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.20307 | −1.07714 | −0.538569 | − | 0.842582i | \(-0.681035\pi\) | ||||
−0.538569 | + | 0.842582i | \(0.681035\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.89368 | −0.796014 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.65906 | −0.411677 | −0.205838 | − | 0.978586i | \(-0.565992\pi\) | ||||
−0.205838 | + | 0.978586i | \(0.565992\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.66723 | −0.518581 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.791043 | −0.0868282 | −0.0434141 | − | 0.999057i | \(-0.513823\pi\) | ||||
−0.0434141 | + | 0.999057i | \(0.513823\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.12939 | 0.122499 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.42246 | 0.259715 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00581 | −0.636615 | −0.318307 | − | 0.947988i | \(-0.603114\pi\) | ||||
−0.318307 | + | 0.947988i | \(0.603114\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.9889 | 1.13950 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.36438 | 0.139982 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.36633 | 0.951007 | 0.475503 | − | 0.879714i | \(-0.342266\pi\) | ||||
0.475503 | + | 0.879714i | \(0.342266\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.06569 | −0.107106 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.07622 | −0.405599 | −0.202799 | − | 0.979220i | \(-0.565004\pi\) | ||||
−0.202799 | + | 0.979220i | \(0.565004\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.66041 | −0.360671 | −0.180336 | − | 0.983605i | \(-0.557718\pi\) | ||||
−0.180336 | + | 0.983605i | \(0.557718\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.289568 | 0.0282590 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.60076 | −0.251425 | −0.125712 | − | 0.992067i | \(-0.540122\pi\) | ||||
−0.125712 | + | 0.992067i | \(0.540122\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.64314 | 0.157384 | 0.0786921 | − | 0.996899i | \(-0.474926\pi\) | ||||
0.0786921 | + | 0.996899i | \(0.474926\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.71575 | 0.732346 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.41900 | 0.415705 | 0.207852 | − | 0.978160i | \(-0.433353\pi\) | ||||
0.207852 | + | 0.978160i | \(0.433353\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.988056 | 0.0921367 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.06569 | −0.0985231 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.42443 | 0.497257 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.50452 | 0.856993 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.07301 | −0.185416 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.21283 | 0.285092 | 0.142546 | − | 0.989788i | \(-0.454471\pi\) | ||||
0.142546 | + | 0.989788i | \(0.454471\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.9887 | −1.23164 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.0924 | −1.49337 | −0.746683 | − | 0.665180i | \(-0.768355\pi\) | ||||
−0.746683 | + | 0.665180i | \(0.768355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.55310 | 0.568226 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.17730 | −0.101325 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.0792 | 1.54461 | 0.772306 | − | 0.635251i | \(-0.219103\pi\) | ||||
0.772306 | + | 0.635251i | \(0.219103\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.3427 | 1.38617 | 0.693086 | − | 0.720855i | \(-0.256251\pi\) | ||||
0.693086 | + | 0.720855i | \(0.256251\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.42120 | −0.456547 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.362646 | 0.0301161 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.39079 | 0.114711 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.91699 | −0.320892 | −0.160446 | − | 0.987045i | \(-0.551293\pi\) | ||||
−0.160446 | + | 0.987045i | \(0.551293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.4196 | 1.90586 | 0.952930 | − | 0.303189i | \(-0.0980514\pi\) | ||||
0.952930 | + | 0.303189i | \(0.0980514\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.78077 | −0.467347 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.64505 | 0.132134 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.4827 | 0.996231 | 0.498115 | − | 0.867111i | \(-0.334026\pi\) | ||||
0.498115 | + | 0.867111i | \(0.334026\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.7046 | −1.16615 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.74563 | 0.374008 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.40362 | −0.579896 | −0.289948 | − | 0.957042i | \(-0.593638\pi\) | ||||
−0.289948 | + | 0.957042i | \(0.593638\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.289568 | 0.0225429 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.97579 | 0.462421 | 0.231210 | − | 0.972904i | \(-0.425731\pi\) | ||||
0.231210 | + | 0.972904i | \(0.425731\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.98358 | −0.534048 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.16128 | −0.0882906 | −0.0441453 | − | 0.999025i | \(-0.514056\pi\) | ||||
−0.0441453 | + | 0.999025i | \(0.514056\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.95665 | −0.374688 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.673360 | −0.0506129 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.8749 | 1.26129 | 0.630646 | − | 0.776071i | \(-0.282790\pi\) | ||||
0.630646 | + | 0.776071i | \(0.282790\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.93181 | 0.515238 | 0.257619 | − | 0.966247i | \(-0.417062\pi\) | ||||
0.257619 | + | 0.966247i | \(0.417062\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.5128 | −1.51635 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.15506 | 0.0849214 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.42443 | 0.396674 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.65454 | −0.411307 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.5709 | 1.56082 | 0.780408 | − | 0.625271i | \(-0.215011\pi\) | ||||
0.780408 | + | 0.625271i | \(0.215011\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.51773 | −0.325193 | −0.162597 | − | 0.986693i | \(-0.551987\pi\) | ||||
−0.162597 | + | 0.986693i | \(0.551987\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.289568 | 0.0207364 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.6583 | 1.18685 | 0.593426 | − | 0.804889i | \(-0.297775\pi\) | ||||
0.593426 | + | 0.804889i | \(0.297775\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.18017 | 0.579877 | 0.289938 | − | 0.957045i | \(-0.406365\pi\) | ||||
0.289938 | + | 0.957045i | \(0.406365\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.2169 | 1.49652 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.74178 | 0.122249 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.42284 | 0.0993753 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.05737 | −0.351512 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.55310 | 0.453288 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.6246 | 1.21333 | 0.606663 | − | 0.794959i | \(-0.292508\pi\) | ||||
0.606663 | + | 0.794959i | \(0.292508\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.54906 | 0.380216 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.09413 | −0.142819 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.90117 | 0.536366 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.7996 | −0.864915 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.42443 | 0.364887 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.3131 | −1.56116 | −0.780582 | − | 0.625054i | \(-0.785077\pi\) | ||||
−0.780582 | + | 0.625054i | \(0.785077\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.28226 | 0.352150 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.60090 | −0.239000 | −0.119500 | − | 0.992834i | \(-0.538129\pi\) | ||||
−0.119500 | + | 0.992834i | \(0.538129\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.6056 | 0.700838 | 0.350419 | − | 0.936593i | \(-0.386039\pi\) | ||||
0.350419 | + | 0.936593i | \(0.386039\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.39079 | 0.0915076 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.8321 | 1.23373 | 0.616866 | − | 0.787068i | \(-0.288402\pi\) | ||||
0.616866 | + | 0.787068i | \(0.288402\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.811559 | −0.0529403 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.08901 | −0.330567 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.9920 | −1.29318 | −0.646589 | − | 0.762839i | \(-0.723805\pi\) | ||||
−0.646589 | + | 0.762839i | \(0.723805\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.3611 | −0.989494 | −0.494747 | − | 0.869037i | \(-0.664739\pi\) | ||||
−0.494747 | + | 0.869037i | \(0.664739\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.4725 | 0.671809 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.208204 | 0.0133016 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.55310 | 0.416964 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.10018 | −0.0697209 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.1124 | −1.20636 | −0.603180 | − | 0.797605i | \(-0.706100\pi\) | ||||
−0.603180 | + | 0.797605i | \(0.706100\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.74563 | 0.298355 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.57074 | 0.0983639 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.2930 | 0.891571 | 0.445786 | − | 0.895140i | \(-0.352924\pi\) | ||||
0.445786 | + | 0.895140i | \(0.352924\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.54773 | 0.344719 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.85620 | −0.114896 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 31.4246 | 1.93773 | 0.968863 | − | 0.247597i | \(-0.0796410\pi\) | ||||
0.968863 | + | 0.247597i | \(0.0796410\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.20129 | −0.135224 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.35285 | −0.511186 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.23525 | 0.258228 | 0.129114 | − | 0.991630i | \(-0.458787\pi\) | ||||
0.129114 | + | 0.991630i | \(0.458787\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.06996 | 0.186487 | 0.0932433 | − | 0.995643i | \(-0.470277\pi\) | ||||
0.0932433 | + | 0.995643i | \(0.470277\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.39079 | 0.0841747 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.95665 | −0.298897 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.0234775 | 0.00141062 | 0.000705312 | − | 1.00000i | \(-0.499775\pi\) | ||||
0.000705312 | 1.00000i | \(0.499775\pi\) | ||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.42020 | −0.504104 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.3364 | −0.735931 | −0.367965 | − | 0.929840i | \(-0.619945\pi\) | ||||
−0.367965 | + | 0.929840i | \(0.619945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.5235 | 1.45777 | 0.728885 | − | 0.684636i | \(-0.240039\pi\) | ||||
0.728885 | + | 0.684636i | \(0.240039\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.89757 | 0.112402 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.83388 | 0.403391 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.4245 | 0.730852 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.0266 | 0.763635 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.4678 | 1.66310 | 0.831552 | − | 0.555447i | \(-0.187453\pi\) | ||||
0.831552 | + | 0.555447i | \(0.187453\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.100803 | −0.00586897 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.65454 | −0.328110 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.74563 | 0.274447 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0581 | −0.579739 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.66918 | −0.325686 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.07079 | −0.175833 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.5550 | 0.887772 | 0.443886 | − | 0.896083i | \(-0.353600\pi\) | ||||
0.443886 | + | 0.896083i | \(0.353600\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.09088 | −0.289610 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.11279 | −0.516739 | −0.258370 | − | 0.966046i | \(-0.583185\pi\) | ||||
−0.258370 | + | 0.966046i | \(0.583185\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.22731 | 0.295465 | 0.147733 | − | 0.989027i | \(-0.452803\pi\) | ||||
0.147733 | + | 0.989027i | \(0.452803\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.221881 | −0.0125016 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.13806 | 0.288582 | 0.144291 | − | 0.989535i | \(-0.453910\pi\) | ||||
0.144291 | + | 0.989535i | \(0.453910\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.74178 | 0.0975212 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.61712 | −0.201888 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 35.5469 | 1.97788 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.95665 | −0.274946 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.28527 | 0.126376 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.89791 | −0.214899 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.5139 | −1.45734 | −0.728668 | − | 0.684868i | \(-0.759860\pi\) | ||||
−0.728668 | + | 0.684868i | \(0.759860\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.91216 | −0.323984 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.17619 | 0.173534 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.4715 | −1.87778 | −0.938892 | − | 0.344213i | \(-0.888146\pi\) | ||||
−0.938892 | + | 0.344213i | \(0.888146\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.14592 | 0.333801 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.90117 | 0.427872 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.37418 | 0.0739836 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.6339 | −1.48347 | −0.741733 | − | 0.670696i | \(-0.765996\pi\) | ||||
−0.741733 | + | 0.670696i | \(0.765996\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.09224 | 0.111995 | 0.0559974 | − | 0.998431i | \(-0.482166\pi\) | ||||
0.0559974 | + | 0.998431i | \(0.482166\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.65454 | −0.301817 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.44579 | 0.236625 | 0.118313 | − | 0.992976i | \(-0.462251\pi\) | ||||
0.118313 | + | 0.992976i | \(0.462251\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.830701 | 0.0440890 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.54427 | 0.399285 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.1857 | 1.43481 | 0.717404 | − | 0.696658i | \(-0.245330\pi\) | ||||
0.717404 | + | 0.696658i | \(0.245330\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.9431 | 1.26017 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.39079 | 0.0729978 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.91611 | −0.100294 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.3712 | −1.89856 | −0.949282 | − | 0.314427i | \(-0.898188\pi\) | ||||
−0.949282 | + | 0.314427i | \(0.898188\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.28280 | −0.379127 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.5728 | −0.548911 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.1572 | 0.836586 | 0.418293 | − | 0.908312i | \(-0.362628\pi\) | ||||
0.418293 | + | 0.908312i | \(0.362628\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.88313 | −0.148884 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.74178 | 0.0897064 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.01019 | 0.462822 | 0.231411 | − | 0.972856i | \(-0.425666\pi\) | ||||
0.231411 | + | 0.972856i | \(0.425666\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.46838 | 0.228922 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.8182 | 0.757176 | 0.378588 | − | 0.925565i | \(-0.376410\pi\) | ||||
0.378588 | + | 0.925565i | \(0.376410\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.208204 | 0.0106110 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.7188 | 0.544868 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.03175 | −0.0523116 | −0.0261558 | − | 0.999658i | \(-0.508327\pi\) | ||||
−0.0261558 | + | 0.999658i | \(0.508327\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.7423 | 1.30185 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.7720 | −1.19914 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.761830 | −0.0383318 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.35927 | −0.218786 | −0.109393 | − | 0.993999i | \(-0.534891\pi\) | ||||
−0.109393 | + | 0.993999i | \(0.534891\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.11402 | 0.456272 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.2157 | −0.759834 | −0.379917 | − | 0.925021i | \(-0.624048\pi\) | ||||
−0.379917 | + | 0.925021i | \(0.624048\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.90117 | 0.393585 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.971734 | −0.0482859 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.54773 | 0.274991 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.3414 | −0.610245 | −0.305122 | − | 0.952313i | \(-0.598697\pi\) | ||||
−0.305122 | + | 0.952313i | \(0.598697\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.1445 | 1.24029 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.484155 | −0.0238237 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.164698 | −0.00808470 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.7294 | 1.11306 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.4939 | 0.805779 | 0.402890 | − | 0.915249i | \(-0.368006\pi\) | ||||
0.402890 | + | 0.915249i | \(0.368006\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.3207 | −1.62395 | −0.811976 | − | 0.583691i | \(-0.801608\pi\) | ||||
−0.811976 | + | 0.583691i | \(0.801608\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.15397 | 0.201973 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −26.8870 | −1.30421 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.7490 | −0.713753 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.39079 | 0.0671482 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.6817 | −1.67056 | −0.835278 | − | 0.549827i | \(-0.814693\pi\) | ||||
−0.835278 | + | 0.549827i | \(0.814693\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.8918 | −1.86902 | −0.934510 | − | 0.355938i | \(-0.884161\pi\) | ||||
−0.934510 | + | 0.355938i | \(0.884161\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.504366 | 0.0241825 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31.0986 | 1.48765 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.3349 | 0.588711 | 0.294355 | − | 0.955696i | \(-0.404895\pi\) | ||||
0.294355 | + | 0.955696i | \(0.404895\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.06569 | −0.0507472 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.3625 | −1.44256 | −0.721282 | − | 0.692642i | \(-0.756447\pi\) | ||||
−0.721282 | + | 0.692642i | \(0.756447\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.25043 | −0.0592762 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.44772 | −0.257668 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.668200 | 0.0315343 | 0.0157672 | − | 0.999876i | \(-0.494981\pi\) | ||||
0.0157672 | + | 0.999876i | \(0.494981\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.83388 | 0.321795 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 32.5719 | 1.53036 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.208204 | 0.00976073 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.6032 | 1.47834 | 0.739168 | − | 0.673521i | \(-0.235219\pi\) | ||||
0.739168 | + | 0.673521i | \(0.235219\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −30.6727 | −1.43168 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.5966 | −1.47160 | −0.735799 | − | 0.677200i | \(-0.763193\pi\) | ||||
−0.735799 | + | 0.677200i | \(0.763193\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.3479 | −0.713275 | −0.356638 | − | 0.934243i | \(-0.616077\pi\) | ||||
−0.356638 | + | 0.934243i | \(0.616077\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.28793 | 0.106100 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.1706 | −1.58123 | −0.790614 | − | 0.612315i | \(-0.790238\pi\) | ||||
−0.790614 | + | 0.612315i | \(0.790238\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.2552 | 0.704420 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.3609 | 0.799949 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.0581 | −0.462472 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −32.4814 | −1.49035 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.2673 | 0.515894 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.2760 | −1.10920 | −0.554600 | − | 0.832117i | \(-0.687129\pi\) | ||||
−0.554600 | + | 0.832117i | \(0.687129\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.54773 | 0.252955 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.60019 | 0.300319 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.95010 | 0.0885496 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.4028 | −1.51363 | −0.756813 | − | 0.653631i | \(-0.773245\pi\) | ||||
−0.756813 | + | 0.653631i | \(0.773245\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.2969 | −0.465642 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.8050 | −1.11943 | −0.559717 | − | 0.828684i | \(-0.689090\pi\) | ||||
−0.559717 | + | 0.828684i | \(0.689090\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.44819 | 0.425525 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.221881 | −0.00997279 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.98985 | 0.178969 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.9994 | −0.581934 | −0.290967 | − | 0.956733i | \(-0.593977\pi\) | ||||
−0.290967 | + | 0.956733i | \(0.593977\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.31110 | 0.371313 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.04393 | −0.180310 | −0.0901550 | − | 0.995928i | \(-0.528736\pi\) | ||||
−0.0901550 | + | 0.995928i | \(0.528736\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.848683 | −0.0377659 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.39079 | 0.0617674 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 42.6514 | 1.89049 | 0.945246 | − | 0.326359i | \(-0.105822\pi\) | ||||
0.945246 | + | 0.326359i | \(0.105822\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.20307 | −0.407120 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −37.0548 | −1.63601 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.762111 | −0.0335826 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.89791 | −0.171430 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.61510 | −0.0708952 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.63349 | −0.290618 | −0.145309 | − | 0.989386i | \(-0.546418\pi\) | ||||
−0.145309 | + | 0.989386i | \(0.546418\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.1908 | −0.707972 | −0.353986 | − | 0.935251i | \(-0.615174\pi\) | ||||
−0.353986 | + | 0.935251i | \(0.615174\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.89368 | −0.300865 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 42.8594 | 1.86698 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.479025 | −0.0208272 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.515960 | 0.0223907 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.83388 | 0.296008 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.541487 | −0.0234105 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.4696 | 1.01279 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.9655 | −0.772396 | −0.386198 | − | 0.922416i | \(-0.626212\pi\) | ||||
−0.386198 | + | 0.922416i | \(0.626212\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.64073 | 0.413723 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.342107 | 0.0146543 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.0883 | −1.02994 | −0.514972 | − | 0.857207i | \(-0.672198\pi\) | ||||
−0.514972 | + | 0.857207i | \(0.672198\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.7178 | 0.670821 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.4141 | 0.486256 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.65906 | −0.155599 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.60645 | 0.0681898 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.06009 | 0.341517 | 0.170759 | − | 0.985313i | \(-0.445378\pi\) | ||||
0.170759 | + | 0.985313i | \(0.445378\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.0581 | −0.425412 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.54427 | 0.318519 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.1517 | 0.427844 | 0.213922 | − | 0.976851i | \(-0.431376\pi\) | ||||
0.213922 | + | 0.976851i | \(0.431376\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.920052 | 0.0387069 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.66723 | −0.196005 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.4857 | 1.36187 | 0.680935 | − | 0.732344i | \(-0.261574\pi\) | ||||
0.680935 | + | 0.732344i | \(0.261574\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.3069 | 1.47755 | 0.738773 | − | 0.673954i | \(-0.235405\pi\) | ||||
0.738773 | + | 0.673954i | \(0.235405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30.0007 | 1.25330 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.5224 | −0.980953 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.2307 | 0.758952 | 0.379476 | − | 0.925202i | \(-0.376104\pi\) | ||||
0.379476 | + | 0.925202i | \(0.376104\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.28323 | −0.261122 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.791043 | −0.0328180 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.5728 | −0.437880 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.221881 | −0.00917363 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.7814 | −0.651369 | −0.325685 | − | 0.945478i | \(-0.605595\pi\) | ||||
−0.325685 | + | 0.945478i | \(0.605595\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 51.7772 | 2.13344 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.1682 | 0.953013 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.45766 | 0.265184 | 0.132592 | − | 0.991171i | \(-0.457670\pi\) | ||||
0.132592 | + | 0.991171i | \(0.457670\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.12939 | 0.0463003 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.3769 | 0.465627 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.3081 | −1.23836 | −0.619178 | − | 0.785251i | \(-0.712534\pi\) | ||||
−0.619178 | + | 0.785251i | \(0.712534\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.2159 | −0.906204 | −0.453102 | − | 0.891459i | \(-0.649683\pi\) | ||||
−0.453102 | + | 0.891459i | \(0.649683\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.2573 | −0.662050 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.208204 | 0.00846468 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.6861 | 1.44845 | 0.724227 | − | 0.689562i | \(-0.242197\pi\) | ||||
0.724227 | + | 0.689562i | \(0.242197\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.42246 | 0.0981632 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.89791 | −0.157693 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.6085 | 1.47860 | 0.739301 | − | 0.673375i | \(-0.235156\pi\) | ||||
0.739301 | + | 0.673375i | \(0.235156\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.97887 | 0.0797959 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.6155 | −0.990984 | −0.495492 | − | 0.868613i | \(-0.665012\pi\) | ||||
−0.495492 | + | 0.868613i | \(0.665012\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.0242 | −1.28716 | −0.643580 | − | 0.765379i | \(-0.722552\pi\) | ||||
−0.643580 | + | 0.765379i | \(0.722552\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26.8343 | −1.07682 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.00581 | −0.240618 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.3516 | 0.974066 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.11402 | 0.363979 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30.0933 | 1.19990 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.45031 | 0.177164 | 0.0885821 | − | 0.996069i | \(-0.471766\pi\) | ||||
0.0885821 | + | 0.996069i | \(0.471766\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.5122 | 0.974272 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.668922 | 0.0265454 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.25195 | −0.168204 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.948699 | −0.0374714 | −0.0187357 | − | 0.999824i | \(-0.505964\pi\) | ||||
−0.0187357 | + | 0.999824i | \(0.505964\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.9786 | −0.985061 | −0.492531 | − | 0.870295i | \(-0.663928\pi\) | ||||
−0.492531 | + | 0.870295i | \(0.663928\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.91251 | −0.114680 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 42.7429 | 1.68040 | 0.840198 | − | 0.542280i | \(-0.182439\pi\) | ||||
0.840198 | + | 0.542280i | \(0.182439\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.484155 | −0.0190048 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.9889 | 0.430689 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.94462 | 0.115232 | 0.0576159 | − | 0.998339i | \(-0.481650\pi\) | ||||
0.0576159 | + | 0.998339i | \(0.481650\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.55869 | −0.139050 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.80762 | 0.382632 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.6545 | −0.570857 | −0.285428 | − | 0.958400i | \(-0.592136\pi\) | ||||
−0.285428 | + | 0.958400i | \(0.592136\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.22255 | 0.358716 | 0.179358 | − | 0.983784i | \(-0.442598\pi\) | ||||
0.179358 | + | 0.983784i | \(0.442598\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.54427 | 0.292995 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.36438 | 0.0529084 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.26586 | 0.320055 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −32.4238 | −1.25358 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.7490 | −0.569378 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.64012 | −0.140316 | −0.0701582 | − | 0.997536i | \(-0.522350\pi\) | ||||
−0.0701582 | + | 0.997536i | \(0.522350\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 28.0276 | 1.07878 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.4791 | −0.518044 | −0.259022 | − | 0.965871i | \(-0.583400\pi\) | ||||
−0.259022 | + | 0.965871i | \(0.583400\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.36633 | 0.359447 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.00811 | −0.191911 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.4785 | 0.439214 | 0.219607 | − | 0.975588i | \(-0.429522\pi\) | ||||
0.219607 | + | 0.975588i | \(0.429522\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.76416 | 0.143821 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.7502 | 0.562756 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.5728 | −0.402791 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.9031 | −1.06148 | −0.530741 | − | 0.847534i | \(-0.678086\pi\) | ||||
−0.530741 | + | 0.847534i | \(0.678086\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.06569 | −0.0404822 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.40261 | 0.129068 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.0699 | 1.40412 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.1916 | 0.990657 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.7465 | 1.31236 | 0.656179 | − | 0.754605i | \(-0.272172\pi\) | ||||
0.656179 | + | 0.754605i | \(0.272172\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.3548 | 1.37115 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.12871 | −0.0425098 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.07622 | −0.153302 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.90672 | −0.372055 | −0.186027 | − | 0.982545i | \(-0.559561\pi\) | ||||
−0.186027 | + | 0.982545i | \(0.559561\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.89943 | 0.146240 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 37.4960 | 1.40424 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.208204 | 0.00778637 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.8048 | −1.03839 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.4915 | 0.876085 | 0.438043 | − | 0.898954i | \(-0.355672\pi\) | ||||
0.438043 | + | 0.898954i | \(0.355672\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.66041 | −0.136321 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.3641 | −0.794539 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.63342 | −0.320637 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.3589 | 0.680895 | 0.340447 | − | 0.940264i | \(-0.389421\pi\) | ||||
0.340447 | + | 0.940264i | \(0.389421\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.5667 | 1.05803 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −54.5595 | −2.01796 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.5726 | 0.427443 | 0.213722 | − | 0.976895i | \(-0.431441\pi\) | ||||
0.213722 | + | 0.976895i | \(0.431441\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.289568 | 0.0106809 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.2552 | 0.561933 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.0160 | −1.54558 | −0.772792 | − | 0.634659i | \(-0.781141\pi\) | ||||
−0.772792 | + | 0.634659i | \(0.781141\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.11402 | 0.334812 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.20719 | 0.264406 | 0.132203 | − | 0.991223i | \(-0.457795\pi\) | ||||
0.132203 | + | 0.991223i | \(0.457795\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.815531 | −0.0298787 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.843007 | 0.0308440 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.60076 | −0.0950296 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.5524 | −1.04189 | −0.520946 | − | 0.853589i | \(-0.674421\pi\) | ||||
−0.520946 | + | 0.853589i | \(0.674421\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26.5814 | −0.968678 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.87605 | 0.177458 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.0355 | −1.16435 | −0.582176 | − | 0.813063i | \(-0.697798\pi\) | ||||
−0.582176 | + | 0.813063i | \(0.697798\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.60019 | 0.239572 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.19483 | 0.260813 | 0.130406 | − | 0.991461i | \(-0.458372\pi\) | ||||
0.130406 | + | 0.991461i | \(0.458372\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.64314 | 0.0594856 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.20358 | −0.0435154 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.484155 | −0.0174818 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.2371 | 0.693708 | 0.346854 | − | 0.937919i | \(-0.387250\pi\) | ||||
0.346854 | + | 0.937919i | \(0.387250\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.8786 | 0.715910 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.8115 | 0.460798 | 0.230399 | − | 0.973096i | \(-0.425997\pi\) | ||||
0.230399 | + | 0.973096i | \(0.425997\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −39.1633 | −1.40679 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.71575 | 0.276801 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 44.7831 | 1.60452 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.98985 | 0.142768 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.84899 | −0.351974 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.59895 | 0.0927605 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.3702 | −1.33210 | −0.666052 | − | 0.745905i | \(-0.732017\pi\) | ||||
−0.666052 | + | 0.745905i | \(0.732017\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 43.7052 | 1.55595 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.41900 | 0.157122 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.7490 | −0.523752 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.06154 | −0.108582 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.7191 | −1.05270 | −0.526352 | − | 0.850267i | \(-0.676441\pi\) | ||||
−0.526352 | + | 0.850267i | \(0.676441\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.1440 | −0.748020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.40034 | 0.226145 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.20307 | −0.324769 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.988056 | 0.0348244 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.89037 | 0.207351 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.0320 | 0.528497 | 0.264249 | − | 0.964455i | \(-0.414876\pi\) | ||||
0.264249 | + | 0.964455i | \(0.414876\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.1443 | 0.707361 | 0.353681 | − | 0.935366i | \(-0.384930\pi\) | ||||
0.353681 | + | 0.935366i | \(0.384930\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.26968 | 0.149744 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.54146 | −0.0539950 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −65.9117 | −2.30596 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.06569 | −0.0372382 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.2104 | 0.949651 | 0.474825 | − | 0.880080i | \(-0.342511\pi\) | ||||
0.474825 | + | 0.880080i | \(0.342511\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.81900 | −0.0982640 | −0.0491320 | − | 0.998792i | \(-0.515646\pi\) | ||||
−0.0491320 | + | 0.998792i | \(0.515646\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.89368 | −0.240007 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.6686 | −0.892583 | −0.446291 | − | 0.894888i | \(-0.647256\pi\) | ||||
−0.446291 | + | 0.894888i | \(0.647256\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −56.8209 | −1.97347 | −0.986736 | − | 0.162335i | \(-0.948097\pi\) | ||||
−0.986736 | + | 0.162335i | \(0.948097\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.0326523 | 0.00113270 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.42443 | 0.187946 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.24418 | 0.0430567 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −44.6775 | −1.54428 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.7617 | 0.406059 | 0.203030 | − | 0.979173i | \(-0.434921\pi\) | ||||
0.203030 | + | 0.979173i | \(0.434921\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.9662 | −0.895386 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.1575 | −0.590934 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.208204 | 0.00716242 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 34.1071 | 1.17055 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.3274 | 0.902493 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.52472 | −0.223402 | −0.111701 | − | 0.993742i | \(-0.535630\pi\) | ||||
−0.111701 | + | 0.993742i | \(0.535630\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.45401 | −0.0497260 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −45.9601 | −1.56997 | −0.784984 | − | 0.619516i | \(-0.787329\pi\) | ||||
−0.784984 | + | 0.619516i | \(0.787329\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.56938 | −0.190025 | −0.0950125 | − | 0.995476i | \(-0.530289\pi\) | ||||
−0.0950125 | + | 0.995476i | \(0.530289\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.50452 | 0.323913 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.9813 | 1.02057 | 0.510287 | − | 0.860004i | \(-0.329539\pi\) | ||||
0.510287 | + | 0.860004i | \(0.329539\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.241783 | −0.00822087 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.2799 | 0.586857 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.65906 | −0.124125 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.2552 | 0.516903 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.98161 | −0.337826 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.07301 | −0.0700805 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.6138 | 1.30389 | 0.651947 | − | 0.758265i | \(-0.273952\pi\) | ||||
0.651947 | + | 0.758265i | \(0.273952\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 39.5928 | 1.33543 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.0991 | 0.576082 | 0.288041 | − | 0.957618i | \(-0.406996\pi\) | ||||
0.288041 | + | 0.957618i | \(0.406996\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.99297 | 0.134374 | 0.0671871 | − | 0.997740i | \(-0.478598\pi\) | ||||
0.0671871 | + | 0.997740i | \(0.478598\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.140196 | −0.00471264 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.4216 | −1.42438 | −0.712189 | − | 0.701988i | \(-0.752296\pi\) | ||||
−0.712189 | + | 0.701988i | \(0.752296\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.21283 | 0.107755 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.66723 | −0.156358 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.5434 | −0.854778 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.51342 | 0.117441 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.60019 | 0.220374 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.7621 | 0.458993 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −57.3513 | −1.91065 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.9887 | −0.465516 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.44323 | 0.0479745 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.1236 | −1.43190 | −0.715948 | − | 0.698154i | \(-0.754005\pi\) | ||||
−0.715948 | + | 0.698154i | \(0.754005\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.34399 | 0.144081 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.56379 | −0.316862 | −0.158431 | − | 0.987370i | \(-0.550644\pi\) | ||||
−0.158431 | + | 0.987370i | \(0.550644\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.791043 | −0.0261797 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.27084 | −0.141190 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.0924 | −0.564440 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.6362 | −1.01060 | −0.505298 | − | 0.862945i | \(-0.668617\pi\) | ||||
−0.505298 | + | 0.862945i | \(0.668617\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.6338 | 0.712859 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.98985 | 0.131328 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27.4981 | −0.904133 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.90087 | 0.128121 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.5312 | −0.968887 | −0.484444 | − | 0.874823i | \(-0.660978\pi\) | ||||
−0.484444 | + | 0.874823i | \(0.660978\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.55310 | 0.214769 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.6740 | −0.414929 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.12939 | 0.0369349 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.15965 | 0.266564 | 0.133282 | − | 0.991078i | \(-0.457448\pi\) | ||||
0.133282 | + | 0.991078i | \(0.457448\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.27012 | 0.237251 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.9055 | 0.811895 | 0.405948 | − | 0.913896i | \(-0.366942\pi\) | ||||
0.405948 | + | 0.913896i | \(0.366942\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.4310 | 1.05610 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.17730 | −0.0382974 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.0288 | −1.39825 | −0.699124 | − | 0.715000i | \(-0.746426\pi\) | ||||
−0.699124 | + | 0.715000i | \(0.746426\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.20307 | −0.298744 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.14599 | 0.231725 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.5632 | 1.24919 | 0.624593 | − | 0.780951i | \(-0.285265\pi\) | ||||
0.624593 | + | 0.780951i | \(0.285265\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.49114 | 0.145330 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.42246 | 0.0783071 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.0792 | 0.583808 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.4285 | 1.01382 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.77160 | 0.0893136 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.940607 | −0.0302792 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −57.3770 | −1.84512 | −0.922559 | − | 0.385855i | \(-0.873906\pi\) | ||||
−0.922559 | + | 0.385855i | \(0.873906\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 49.4384 | 1.58819 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.14845 | 0.0368556 | 0.0184278 | − | 0.999830i | \(-0.494134\pi\) | ||||
0.0184278 | + | 0.999830i | \(0.494134\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.3427 | 0.523924 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.89368 | −0.220775 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.29646 | −0.0414775 | −0.0207387 | − | 0.999785i | \(-0.506602\pi\) | ||||
−0.0207387 | + | 0.999785i | \(0.506602\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.00581 | −0.191947 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.75108 | −0.0559076 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.8576 | −0.505778 | −0.252889 | − | 0.967495i | \(-0.581381\pi\) | ||||
−0.252889 | + | 0.967495i | \(0.581381\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.46831 | 0.110510 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.42120 | −0.172559 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −47.7320 | −1.51779 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.3277 | −0.486900 | −0.243450 | − | 0.969913i | \(-0.578279\pi\) | ||||
−0.243450 | + | 0.969913i | \(0.578279\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −36.8754 | −1.17020 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.70314 | 0.0539932 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.76193 | −0.0874712 | −0.0437356 | − | 0.999043i | \(-0.513926\pi\) | ||||
−0.0437356 | + | 0.999043i | \(0.513926\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −31.3698 | −0.992498 |
(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 | 8008.2.a.x.1.8 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.x.1.8 | ✓ | 12 | 1.1 | even | 1 | trivial |