Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9225,2,Mod(1,9225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9225 = 3^{2} \cdot 5^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9225.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: | \(73.6619958646\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 123) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.470683\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.470683 | 0.332823 | 0.166412 | − | 0.986056i | \(-0.446782\pi\) | ||||
0.166412 | + | 0.986056i | \(0.446782\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.77846 | −0.889229 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.30777 | −1.25022 | −0.625110 | − | 0.780536i | \(-0.714946\pi\) | ||||
−0.625110 | + | 0.780536i | \(0.714946\pi\) | |||||||
\(8\) | −1.77846 | −0.628780 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.47068 | 0.443428 | 0.221714 | − | 0.975112i | \(-0.428835\pi\) | ||||
0.221714 | + | 0.975112i | \(0.428835\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.249141 | 0.0690992 | 0.0345496 | − | 0.999403i | \(-0.489000\pi\) | ||||
0.0345496 | + | 0.999403i | \(0.489000\pi\) | |||||||
\(14\) | −1.55691 | −0.416103 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.71982 | 0.679956 | ||||||||
\(17\) | −5.02760 | −1.21937 | −0.609686 | − | 0.792643i | \(-0.708704\pi\) | ||||
−0.609686 | + | 0.792643i | \(0.708704\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.24914 | −0.515988 | −0.257994 | − | 0.966146i | \(-0.583062\pi\) | ||||
−0.257994 | + | 0.966146i | \(0.583062\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.692226 | 0.147583 | ||||||||
\(23\) | −6.24914 | −1.30304 | −0.651518 | − | 0.758633i | \(-0.725867\pi\) | ||||
−0.651518 | + | 0.758633i | \(0.725867\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.117266 | 0.0229978 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.88273 | 1.11173 | ||||||||
\(29\) | 2.41205 | 0.447906 | 0.223953 | − | 0.974600i | \(-0.428104\pi\) | ||||
0.223953 | + | 0.974600i | \(0.428104\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.89572 | −0.520087 | −0.260044 | − | 0.965597i | \(-0.583737\pi\) | ||||
−0.260044 | + | 0.965597i | \(0.583737\pi\) | |||||||
\(32\) | 4.83709 | 0.855085 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.36641 | −0.405835 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.71982 | −1.59793 | −0.798965 | − | 0.601378i | \(-0.794619\pi\) | ||||
−0.798965 | + | 0.601378i | \(0.794619\pi\) | |||||||
\(38\) | −1.05863 | −0.171733 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.8337 | 1.65212 | 0.826058 | − | 0.563585i | \(-0.190578\pi\) | ||||
0.826058 | + | 0.563585i | \(0.190578\pi\) | |||||||
\(44\) | −2.61555 | −0.394309 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.94137 | −0.433681 | ||||||||
\(47\) | −4.08623 | −0.596038 | −0.298019 | − | 0.954560i | \(-0.596326\pi\) | ||||
−0.298019 | + | 0.954560i | \(0.596326\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.94137 | 0.563052 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.443086 | −0.0614449 | ||||||||
\(53\) | −1.43965 | −0.197751 | −0.0988754 | − | 0.995100i | \(-0.531525\pi\) | ||||
−0.0988754 | + | 0.995100i | \(0.531525\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.88273 | 0.786113 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.13531 | 0.149074 | ||||||||
\(59\) | −2.61555 | −0.340515 | −0.170258 | − | 0.985400i | \(-0.554460\pi\) | ||||
−0.170258 | + | 0.985400i | \(0.554460\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.71982 | −0.732348 | −0.366174 | − | 0.930546i | \(-0.619333\pi\) | ||||
−0.366174 | + | 0.930546i | \(0.619333\pi\) | |||||||
\(62\) | −1.36297 | −0.173097 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.16291 | −0.395364 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.9379 | −1.94713 | −0.973564 | − | 0.228415i | \(-0.926646\pi\) | ||||
−0.973564 | + | 0.228415i | \(0.926646\pi\) | |||||||
\(68\) | 8.94137 | 1.08430 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5293 | 1.24960 | 0.624800 | − | 0.780785i | \(-0.285181\pi\) | ||||
0.624800 | + | 0.780785i | \(0.285181\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.39400 | −1.09949 | −0.549743 | − | 0.835334i | \(-0.685274\pi\) | ||||
−0.549743 | + | 0.835334i | \(0.685274\pi\) | |||||||
\(74\) | −4.57496 | −0.531828 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | −4.86469 | −0.554383 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.560352 | −0.0630445 | −0.0315223 | − | 0.999503i | \(-0.510036\pi\) | ||||
−0.0315223 | + | 0.999503i | \(0.510036\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.470683 | −0.0519783 | ||||||||
\(83\) | 3.80605 | 0.417769 | 0.208884 | − | 0.977940i | \(-0.433017\pi\) | ||||
0.208884 | + | 0.977940i | \(0.433017\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.09922 | 0.549863 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.61555 | −0.278818 | ||||||||
\(89\) | −4.11727 | −0.436429 | −0.218215 | − | 0.975901i | \(-0.570023\pi\) | ||||
−0.218215 | + | 0.975901i | \(0.570023\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.824101 | −0.0863892 | ||||||||
\(92\) | 11.1138 | 1.15870 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.92332 | −0.198375 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.19051 | 0.730085 | 0.365043 | − | 0.930991i | \(-0.381054\pi\) | ||||
0.365043 | + | 0.930991i | \(0.381054\pi\) | |||||||
\(98\) | 1.85514 | 0.187397 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.1449 | 1.10896 | 0.554478 | − | 0.832199i | \(-0.312918\pi\) | ||||
0.554478 | + | 0.832199i | \(0.312918\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.2767 | −1.30820 | −0.654098 | − | 0.756410i | \(-0.726952\pi\) | ||||
−0.654098 | + | 0.756410i | \(0.726952\pi\) | |||||||
\(104\) | −0.443086 | −0.0434481 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.677618 | −0.0658161 | ||||||||
\(107\) | 9.32238 | 0.901229 | 0.450614 | − | 0.892719i | \(-0.351205\pi\) | ||||
0.450614 | + | 0.892719i | \(0.351205\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.249141 | −0.0238633 | −0.0119317 | − | 0.999929i | \(-0.503798\pi\) | ||||
−0.0119317 | + | 0.999929i | \(0.503798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.99656 | −0.850095 | ||||||||
\(113\) | 9.24570 | 0.869763 | 0.434881 | − | 0.900488i | \(-0.356790\pi\) | ||||
0.434881 | + | 0.900488i | \(0.356790\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.28973 | −0.398291 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.23109 | −0.113331 | ||||||||
\(119\) | 16.6302 | 1.52448 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.83709 | −0.803372 | ||||||||
\(122\) | −2.69223 | −0.243743 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.14992 | 0.462476 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.824101 | 0.0731271 | 0.0365635 | − | 0.999331i | \(-0.488359\pi\) | ||||
0.0365635 | + | 0.999331i | \(0.488359\pi\) | |||||||
\(128\) | −11.1629 | −0.986671 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.13187 | −0.710485 | −0.355243 | − | 0.934774i | \(-0.615602\pi\) | ||||
−0.355243 | + | 0.934774i | \(0.615602\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.43965 | 0.645099 | ||||||||
\(134\) | −7.50172 | −0.648050 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.94137 | 0.766716 | ||||||||
\(137\) | −12.2035 | −1.04262 | −0.521308 | − | 0.853369i | \(-0.674556\pi\) | ||||
−0.521308 | + | 0.853369i | \(0.674556\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.2897 | 1.21204 | 0.606019 | − | 0.795450i | \(-0.292765\pi\) | ||||
0.606019 | + | 0.795450i | \(0.292765\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.95597 | 0.415896 | ||||||||
\(143\) | 0.366407 | 0.0306405 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.42160 | −0.365934 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.2863 | 1.42092 | ||||||||
\(149\) | 22.1104 | 1.81135 | 0.905677 | − | 0.423969i | \(-0.139363\pi\) | ||||
0.905677 | + | 0.423969i | \(0.139363\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1173 | 0.823331 | 0.411666 | − | 0.911335i | \(-0.364947\pi\) | ||||
0.411666 | + | 0.911335i | \(0.364947\pi\) | |||||||
\(152\) | 4.00000 | 0.324443 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.28973 | −0.184512 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.7620 | −1.49737 | −0.748686 | − | 0.662924i | \(-0.769315\pi\) | ||||
−0.748686 | + | 0.662924i | \(0.769315\pi\) | |||||||
\(158\) | −0.263748 | −0.0209827 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.6707 | 1.62908 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.54392 | −0.669212 | −0.334606 | − | 0.942358i | \(-0.608603\pi\) | ||||
−0.334606 | + | 0.942358i | \(0.608603\pi\) | |||||||
\(164\) | 1.77846 | 0.138874 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.79145 | 0.139043 | ||||||||
\(167\) | 5.05863 | 0.391449 | 0.195724 | − | 0.980659i | \(-0.437294\pi\) | ||||
0.195724 | + | 0.980659i | \(0.437294\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9379 | −0.995225 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −19.2672 | −1.46911 | ||||||||
\(173\) | 18.8647 | 1.43426 | 0.717128 | − | 0.696942i | \(-0.245456\pi\) | ||||
0.717128 | + | 0.696942i | \(0.245456\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.00000 | 0.301511 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.93793 | −0.145254 | ||||||||
\(179\) | 2.85514 | 0.213403 | 0.106701 | − | 0.994291i | \(-0.465971\pi\) | ||||
0.106701 | + | 0.994291i | \(0.465971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.4396 | 0.998961 | 0.499481 | − | 0.866325i | \(-0.333524\pi\) | ||||
0.499481 | + | 0.866325i | \(0.333524\pi\) | |||||||
\(182\) | −0.387890 | −0.0287524 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 11.1138 | 0.819322 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.39400 | −0.540703 | ||||||||
\(188\) | 7.26719 | 0.530014 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.4948 | −0.976453 | −0.488226 | − | 0.872717i | \(-0.662356\pi\) | ||||
−0.488226 | + | 0.872717i | \(0.662356\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.01461 | 0.576904 | 0.288452 | − | 0.957494i | \(-0.406859\pi\) | ||||
0.288452 | + | 0.957494i | \(0.406859\pi\) | |||||||
\(194\) | 3.38445 | 0.242990 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.00955 | −0.500682 | ||||||||
\(197\) | 13.9785 | 0.995928 | 0.497964 | − | 0.867198i | \(-0.334081\pi\) | ||||
0.497964 | + | 0.867198i | \(0.334081\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.86469 | −0.344849 | −0.172424 | − | 0.985023i | \(-0.555160\pi\) | ||||
−0.172424 | + | 0.985023i | \(0.555160\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.24570 | 0.369086 | ||||||||
\(203\) | −7.97852 | −0.559982 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.24914 | −0.435398 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.677618 | 0.0469844 | ||||||||
\(209\) | −3.30777 | −0.228803 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.6155 | −0.730804 | −0.365402 | − | 0.930850i | \(-0.619069\pi\) | ||||
−0.365402 | + | 0.930850i | \(0.619069\pi\) | |||||||
\(212\) | 2.56035 | 0.175846 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.38789 | 0.299950 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.57840 | 0.650224 | ||||||||
\(218\) | −0.117266 | −0.00794228 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.25258 | −0.0842575 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.9931 | 1.20491 | 0.602454 | − | 0.798153i | \(-0.294190\pi\) | ||||
0.602454 | + | 0.798153i | \(0.294190\pi\) | |||||||
\(224\) | −16.0000 | −1.06904 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.35180 | 0.289477 | ||||||||
\(227\) | −0.910331 | −0.0604208 | −0.0302104 | − | 0.999544i | \(-0.509618\pi\) | ||||
−0.0302104 | + | 0.999544i | \(0.509618\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.42504 | −0.490660 | −0.245330 | − | 0.969440i | \(-0.578896\pi\) | ||||
−0.245330 | + | 0.969440i | \(0.578896\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.28973 | −0.281634 | ||||||||
\(233\) | 14.7620 | 0.967093 | 0.483546 | − | 0.875319i | \(-0.339348\pi\) | ||||
0.483546 | + | 0.875319i | \(0.339348\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.65164 | 0.302796 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.82754 | 0.507384 | ||||||||
\(239\) | 1.38445 | 0.0895528 | 0.0447764 | − | 0.998997i | \(-0.485742\pi\) | ||||
0.0447764 | + | 0.998997i | \(0.485742\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.95436 | −0.383554 | −0.191777 | − | 0.981439i | \(-0.561425\pi\) | ||||
−0.191777 | + | 0.981439i | \(0.561425\pi\) | |||||||
\(242\) | −4.15947 | −0.267381 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.1725 | 0.651225 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.560352 | −0.0356543 | ||||||||
\(248\) | 5.14992 | 0.327020 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.70683 | −0.170854 | −0.0854269 | − | 0.996344i | \(-0.527225\pi\) | ||||
−0.0854269 | + | 0.996344i | \(0.527225\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.19051 | −0.577802 | ||||||||
\(254\) | 0.387890 | 0.0243384 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.07162 | 0.0669764 | ||||||||
\(257\) | −0.793065 | −0.0494700 | −0.0247350 | − | 0.999694i | \(-0.507874\pi\) | ||||
−0.0247350 | + | 0.999694i | \(0.507874\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 32.1510 | 1.99776 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.82754 | −0.236466 | ||||||||
\(263\) | −15.5879 | −0.961194 | −0.480597 | − | 0.876942i | \(-0.659580\pi\) | ||||
−0.480597 | + | 0.876942i | \(0.659580\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.50172 | 0.214704 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 28.3449 | 1.73144 | ||||||||
\(269\) | −3.05863 | −0.186488 | −0.0932441 | − | 0.995643i | \(-0.529724\pi\) | ||||
−0.0932441 | + | 0.995643i | \(0.529724\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.2802 | 0.745968 | 0.372984 | − | 0.927838i | \(-0.378335\pi\) | ||||
0.372984 | + | 0.927838i | \(0.378335\pi\) | |||||||
\(272\) | −13.6742 | −0.829119 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.74398 | −0.347007 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.56990 | 0.514916 | 0.257458 | − | 0.966290i | \(-0.417115\pi\) | ||||
0.257458 | + | 0.966290i | \(0.417115\pi\) | |||||||
\(278\) | 6.72594 | 0.403395 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.5845 | 0.870039 | 0.435020 | − | 0.900421i | \(-0.356741\pi\) | ||||
0.435020 | + | 0.900421i | \(0.356741\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.9509 | 1.24540 | 0.622701 | − | 0.782460i | \(-0.286035\pi\) | ||||
0.622701 | + | 0.782460i | \(0.286035\pi\) | |||||||
\(284\) | −18.7259 | −1.11118 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.172462 | 0.0101979 | ||||||||
\(287\) | 3.30777 | 0.195252 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.27674 | 0.486867 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.7068 | 0.977694 | ||||||||
\(293\) | 31.4086 | 1.83491 | 0.917455 | − | 0.397839i | \(-0.130240\pi\) | ||||
0.917455 | + | 0.397839i | \(0.130240\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 17.2863 | 1.00475 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.4070 | 0.602861 | ||||||||
\(299\) | −1.55691 | −0.0900387 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −35.8353 | −2.06551 | ||||||||
\(302\) | 4.76203 | 0.274024 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.11727 | −0.350849 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.54392 | −0.487628 | −0.243814 | − | 0.969822i | \(-0.578399\pi\) | ||||
−0.243814 | + | 0.969822i | \(0.578399\pi\) | |||||||
\(308\) | 8.65164 | 0.492973 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.49484 | 0.311584 | 0.155792 | − | 0.987790i | \(-0.450207\pi\) | ||||
0.155792 | + | 0.987790i | \(0.450207\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.48024 | −0.309761 | −0.154881 | − | 0.987933i | \(-0.549499\pi\) | ||||
−0.154881 | + | 0.987933i | \(0.549499\pi\) | |||||||
\(314\) | −8.83098 | −0.498361 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.996562 | 0.0560610 | ||||||||
\(317\) | −11.3173 | −0.635644 | −0.317822 | − | 0.948150i | \(-0.602951\pi\) | ||||
−0.317822 | + | 0.948150i | \(0.602951\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.54736 | 0.198614 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.72938 | 0.542197 | ||||||||
\(323\) | 11.3078 | 0.629181 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.02148 | −0.222729 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.77846 | 0.0981989 | ||||||||
\(329\) | 13.5163 | 0.745179 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.8613 | 1.86118 | 0.930591 | − | 0.366060i | \(-0.119293\pi\) | ||||
0.930591 | + | 0.366060i | \(0.119293\pi\) | |||||||
\(332\) | −6.76891 | −0.371492 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.38101 | 0.130283 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.77846 | 0.369246 | 0.184623 | − | 0.982809i | \(-0.440894\pi\) | ||||
0.184623 | + | 0.982809i | \(0.440894\pi\) | |||||||
\(338\) | −6.08967 | −0.331234 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.25869 | −0.230621 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.1173 | 0.546281 | ||||||||
\(344\) | −19.2672 | −1.03882 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.87930 | 0.477354 | ||||||||
\(347\) | 19.2001 | 1.03071 | 0.515357 | − | 0.856976i | \(-0.327659\pi\) | ||||
0.515357 | + | 0.856976i | \(0.327659\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.54392 | −0.350288 | −0.175144 | − | 0.984543i | \(-0.556039\pi\) | ||||
−0.175144 | + | 0.984543i | \(0.556039\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.11383 | 0.379168 | ||||||||
\(353\) | −15.9931 | −0.851228 | −0.425614 | − | 0.904905i | \(-0.639942\pi\) | ||||
−0.425614 | + | 0.904905i | \(0.639942\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.32238 | 0.388085 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.34387 | 0.0710255 | ||||||||
\(359\) | 12.1319 | 0.640296 | 0.320148 | − | 0.947368i | \(-0.396267\pi\) | ||||
0.320148 | + | 0.947368i | \(0.396267\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.9414 | −0.733756 | ||||||||
\(362\) | 6.32582 | 0.332478 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.46563 | 0.0768198 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.39744 | −0.333944 | −0.166972 | − | 0.985962i | \(-0.553399\pi\) | ||||
−0.166972 | + | 0.985962i | \(0.553399\pi\) | |||||||
\(368\) | −16.9966 | −0.886007 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.76203 | 0.247232 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.54049 | 0.390432 | 0.195216 | − | 0.980760i | \(-0.437459\pi\) | ||||
0.195216 | + | 0.980760i | \(0.437459\pi\) | |||||||
\(374\) | −3.48024 | −0.179959 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.26719 | 0.374777 | ||||||||
\(377\) | 0.600939 | 0.0309500 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.0620710 | −0.00318837 | −0.00159419 | − | 0.999999i | \(-0.500507\pi\) | ||||
−0.00159419 | + | 0.999999i | \(0.500507\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.35180 | −0.324986 | ||||||||
\(383\) | 23.9329 | 1.22291 | 0.611456 | − | 0.791278i | \(-0.290584\pi\) | ||||
0.611456 | + | 0.791278i | \(0.290584\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.77234 | 0.192007 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.7880 | −0.649213 | ||||||||
\(389\) | 23.8613 | 1.20981 | 0.604907 | − | 0.796296i | \(-0.293210\pi\) | ||||
0.604907 | + | 0.796296i | \(0.293210\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.4182 | 1.58888 | ||||||||
\(392\) | −7.00955 | −0.354036 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.57946 | 0.331468 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.6302 | −0.734266 | −0.367133 | − | 0.930168i | \(-0.619661\pi\) | ||||
−0.367133 | + | 0.930168i | \(0.619661\pi\) | |||||||
\(398\) | −2.28973 | −0.114774 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.3224 | 0.565413 | 0.282706 | − | 0.959206i | \(-0.408768\pi\) | ||||
0.282706 | + | 0.959206i | \(0.408768\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.721442 | −0.0359376 | ||||||||
\(404\) | −19.8207 | −0.986115 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.75536 | −0.186375 | ||||||||
\(407\) | −14.2948 | −0.708566 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.8923 | −1.67587 | −0.837933 | − | 0.545773i | \(-0.816236\pi\) | ||||
−0.837933 | + | 0.545773i | \(0.816236\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 23.6121 | 1.16329 | ||||||||
\(413\) | 8.65164 | 0.425719 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.20512 | 0.0590856 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.55691 | −0.0761512 | ||||||||
\(419\) | 1.98539 | 0.0969928 | 0.0484964 | − | 0.998823i | \(-0.484557\pi\) | ||||
0.0484964 | + | 0.998823i | \(0.484557\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.67418 | −0.276543 | −0.138271 | − | 0.990394i | \(-0.544155\pi\) | ||||
−0.138271 | + | 0.990394i | \(0.544155\pi\) | |||||||
\(422\) | −4.99656 | −0.243229 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.56035 | 0.124342 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.9199 | 0.915597 | ||||||||
\(428\) | −16.5795 | −0.801398 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.75086 | −0.0843359 | −0.0421680 | − | 0.999111i | \(-0.513426\pi\) | ||||
−0.0421680 | + | 0.999111i | \(0.513426\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.0647 | 1.63705 | 0.818524 | − | 0.574473i | \(-0.194793\pi\) | ||||
0.818524 | + | 0.574473i | \(0.194793\pi\) | |||||||
\(434\) | 4.50839 | 0.216410 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.443086 | 0.0212200 | ||||||||
\(437\) | 14.0552 | 0.672351 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.32582 | −0.206460 | −0.103230 | − | 0.994658i | \(-0.532918\pi\) | ||||
−0.103230 | + | 0.994658i | \(0.532918\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.589568 | −0.0280429 | ||||||||
\(443\) | 36.9966 | 1.75776 | 0.878880 | − | 0.477043i | \(-0.158291\pi\) | ||||
0.878880 | + | 0.477043i | \(0.158291\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.46907 | 0.401022 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.4622 | 0.494292 | ||||||||
\(449\) | 15.9448 | 0.752482 | 0.376241 | − | 0.926522i | \(-0.377216\pi\) | ||||
0.376241 | + | 0.926522i | \(0.377216\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.47068 | −0.0692518 | ||||||||
\(452\) | −16.4431 | −0.773418 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.428478 | −0.0201095 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.4396 | 1.37713 | 0.688564 | − | 0.725175i | \(-0.258241\pi\) | ||||
0.688564 | + | 0.725175i | \(0.258241\pi\) | |||||||
\(458\) | −3.49484 | −0.163303 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.8759 | −1.01886 | −0.509430 | − | 0.860512i | \(-0.670144\pi\) | ||||
−0.509430 | + | 0.860512i | \(0.670144\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.6561 | 0.867024 | 0.433512 | − | 0.901148i | \(-0.357274\pi\) | ||||
0.433512 | + | 0.901148i | \(0.357274\pi\) | |||||||
\(464\) | 6.56035 | 0.304557 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.94824 | 0.321871 | ||||||||
\(467\) | 8.67074 | 0.401234 | 0.200617 | − | 0.979670i | \(-0.435705\pi\) | ||||
0.200617 | + | 0.979670i | \(0.435705\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 52.7191 | 2.43434 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.65164 | 0.214109 | ||||||||
\(473\) | 15.9329 | 0.732594 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −29.5760 | −1.35561 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.651639 | 0.0298053 | ||||||||
\(479\) | 20.4312 | 0.933523 | 0.466762 | − | 0.884383i | \(-0.345421\pi\) | ||||
0.466762 | + | 0.884383i | \(0.345421\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.42160 | −0.110416 | ||||||||
\(482\) | −2.80262 | −0.127656 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.7164 | 0.714381 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.00611 | 0.317477 | 0.158739 | − | 0.987321i | \(-0.449257\pi\) | ||||
0.158739 | + | 0.987321i | \(0.449257\pi\) | |||||||
\(488\) | 10.1725 | 0.460486 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.5715 | 0.702733 | 0.351366 | − | 0.936238i | \(-0.385717\pi\) | ||||
0.351366 | + | 0.936238i | \(0.385717\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.1268 | −0.546164 | ||||||||
\(494\) | −0.263748 | −0.0118666 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.87586 | −0.353636 | ||||||||
\(497\) | −34.8286 | −1.56228 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.61899 | −0.0724757 | −0.0362379 | − | 0.999343i | \(-0.511537\pi\) | ||||
−0.0362379 | + | 0.999343i | \(0.511537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.27406 | −0.0568642 | ||||||||
\(503\) | −39.3725 | −1.75553 | −0.877767 | − | 0.479088i | \(-0.840968\pi\) | ||||
−0.877767 | + | 0.479088i | \(0.840968\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.32582 | −0.192306 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.46563 | −0.0650267 | ||||||||
\(509\) | 8.63971 | 0.382948 | 0.191474 | − | 0.981498i | \(-0.438673\pi\) | ||||
0.191474 | + | 0.981498i | \(0.438673\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.0732 | 1.37460 | ||||||||
\(512\) | 22.8302 | 1.00896 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.373283 | −0.0164648 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.00955 | −0.264300 | ||||||||
\(518\) | 15.1329 | 0.664903 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.7862 | −1.34877 | −0.674384 | − | 0.738381i | \(-0.735591\pi\) | ||||
−0.674384 | + | 0.738381i | \(0.735591\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.4036 | −0.761004 | −0.380502 | − | 0.924780i | \(-0.624249\pi\) | ||||
−0.380502 | + | 0.924780i | \(0.624249\pi\) | |||||||
\(524\) | 14.4622 | 0.631784 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.33699 | −0.319908 | ||||||||
\(527\) | 14.5585 | 0.634180 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.0518 | 0.697902 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −13.2311 | −0.573641 | ||||||||
\(533\) | −0.249141 | −0.0107915 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 28.3449 | 1.22431 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.43965 | −0.0620676 | ||||||||
\(539\) | 5.79650 | 0.249673 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.87586 | −0.424596 | −0.212298 | − | 0.977205i | \(-0.568095\pi\) | ||||
−0.212298 | + | 0.977205i | \(0.568095\pi\) | |||||||
\(542\) | 5.78008 | 0.248275 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −24.3189 | −1.04267 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.1465 | 0.775888 | 0.387944 | − | 0.921683i | \(-0.373185\pi\) | ||||
0.387944 | + | 0.921683i | \(0.373185\pi\) | |||||||
\(548\) | 21.7034 | 0.927123 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.42504 | −0.231114 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.85352 | 0.0788196 | ||||||||
\(554\) | 4.03371 | 0.171376 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −25.4137 | −1.07778 | ||||||||
\(557\) | 37.3725 | 1.58352 | 0.791762 | − | 0.610829i | \(-0.209164\pi\) | ||||
0.791762 | + | 0.610829i | \(0.209164\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.69910 | 0.114160 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.86469 | 0.289569 | ||||||||
\(563\) | 22.8742 | 0.964034 | 0.482017 | − | 0.876162i | \(-0.339904\pi\) | ||||
0.482017 | + | 0.876162i | \(0.339904\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.86125 | 0.414499 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18.7259 | −0.785723 | ||||||||
\(569\) | −34.4147 | −1.44274 | −0.721370 | − | 0.692550i | \(-0.756487\pi\) | ||||
−0.721370 | + | 0.692550i | \(0.756487\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.3449 | 1.52099 | 0.760494 | − | 0.649345i | \(-0.224957\pi\) | ||||
0.760494 | + | 0.649345i | \(0.224957\pi\) | |||||||
\(572\) | −0.651639 | −0.0272464 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.55691 | 0.0649843 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.1725 | −1.08957 | −0.544787 | − | 0.838575i | \(-0.683389\pi\) | ||||
−0.544787 | + | 0.838575i | \(0.683389\pi\) | |||||||
\(578\) | 3.89572 | 0.162041 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.5896 | −0.522303 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.11727 | −0.0876882 | ||||||||
\(584\) | 16.7068 | 0.691334 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.7835 | 0.610701 | ||||||||
\(587\) | −17.8156 | −0.735329 | −0.367664 | − | 0.929959i | \(-0.619842\pi\) | ||||
−0.367664 | + | 0.929959i | \(0.619842\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.51289 | 0.268359 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −26.4362 | −1.08652 | ||||||||
\(593\) | −32.7018 | −1.34290 | −0.671451 | − | 0.741049i | \(-0.734328\pi\) | ||||
−0.671451 | + | 0.741049i | \(0.734328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −39.3224 | −1.61071 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.732814 | −0.0299670 | ||||||||
\(599\) | −10.2784 | −0.419962 | −0.209981 | − | 0.977705i | \(-0.567340\pi\) | ||||
−0.209981 | + | 0.977705i | \(0.567340\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.8398 | 1.29877 | 0.649386 | − | 0.760459i | \(-0.275026\pi\) | ||||
0.649386 | + | 0.760459i | \(0.275026\pi\) | |||||||
\(602\) | −16.8671 | −0.687450 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17.9931 | −0.732130 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.2086 | −0.414352 | −0.207176 | − | 0.978304i | \(-0.566427\pi\) | ||||
−0.207176 | + | 0.978304i | \(0.566427\pi\) | |||||||
\(608\) | −10.8793 | −0.441214 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.01805 | −0.0411857 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.94137 | 0.199580 | 0.0997900 | − | 0.995009i | \(-0.468183\pi\) | ||||
0.0997900 | + | 0.995009i | \(0.468183\pi\) | |||||||
\(614\) | −4.02148 | −0.162294 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.65164 | 0.348584 | ||||||||
\(617\) | 15.2526 | 0.614046 | 0.307023 | − | 0.951702i | \(-0.400667\pi\) | ||||
0.307023 | + | 0.951702i | \(0.400667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.6543 | −0.830167 | −0.415084 | − | 0.909783i | \(-0.636248\pi\) | ||||
−0.415084 | + | 0.909783i | \(0.636248\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.58633 | 0.103702 | ||||||||
\(623\) | 13.6190 | 0.545633 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.57946 | −0.103096 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 33.3675 | 1.33151 | ||||||||
\(629\) | 48.8674 | 1.94847 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.83709 | 0.232371 | 0.116185 | − | 0.993228i | \(-0.462933\pi\) | ||||
0.116185 | + | 0.993228i | \(0.462933\pi\) | |||||||
\(632\) | 0.996562 | 0.0396411 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.32688 | −0.211557 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.981954 | 0.0389064 | ||||||||
\(638\) | 1.66968 | 0.0661034 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.6328 | −1.68390 | −0.841948 | − | 0.539559i | \(-0.818591\pi\) | ||||
−0.841948 | + | 0.539559i | \(0.818591\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.7259 | −1.21171 | −0.605856 | − | 0.795574i | \(-0.707169\pi\) | ||||
−0.605856 | + | 0.795574i | \(0.707169\pi\) | |||||||
\(644\) | −36.7620 | −1.44863 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.32238 | 0.209406 | ||||||||
\(647\) | 18.3595 | 0.721788 | 0.360894 | − | 0.932607i | \(-0.382472\pi\) | ||||
0.360894 | + | 0.932607i | \(0.382472\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.84664 | −0.150994 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.1950 | 0.595082 | ||||||||
\(653\) | −35.5811 | −1.39240 | −0.696198 | − | 0.717850i | \(-0.745126\pi\) | ||||
−0.696198 | + | 0.717850i | \(0.745126\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.71982 | −0.106191 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.36191 | 0.248013 | ||||||||
\(659\) | 6.38101 | 0.248569 | 0.124285 | − | 0.992247i | \(-0.460336\pi\) | ||||
0.124285 | + | 0.992247i | \(0.460336\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.9053 | 1.20208 | 0.601038 | − | 0.799220i | \(-0.294754\pi\) | ||||
0.601038 | + | 0.799220i | \(0.294754\pi\) | |||||||
\(662\) | 15.9379 | 0.619445 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.76891 | −0.262684 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.0732 | −0.583638 | ||||||||
\(668\) | −8.99656 | −0.348087 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.41205 | −0.324744 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.7259 | −1.41568 | −0.707840 | − | 0.706372i | \(-0.750330\pi\) | ||||
−0.707840 | + | 0.706372i | \(0.750330\pi\) | |||||||
\(674\) | 3.19051 | 0.122894 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.0096 | 0.884983 | ||||||||
\(677\) | −5.66281 | −0.217639 | −0.108820 | − | 0.994062i | \(-0.534707\pi\) | ||||
−0.108820 | + | 0.994062i | \(0.534707\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.7846 | −0.912768 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.00450 | −0.0767561 | ||||||||
\(683\) | −29.1690 | −1.11612 | −0.558061 | − | 0.829800i | \(-0.688454\pi\) | ||||
−0.558061 | + | 0.829800i | \(0.688454\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.76203 | 0.181815 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 29.4656 | 1.12337 | ||||||||
\(689\) | −0.358675 | −0.0136644 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.68879 | 0.0642445 | 0.0321223 | − | 0.999484i | \(-0.489773\pi\) | ||||
0.0321223 | + | 0.999484i | \(0.489773\pi\) | |||||||
\(692\) | −33.5500 | −1.27538 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.03715 | 0.343046 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.02760 | 0.190434 | ||||||||
\(698\) | −3.08012 | −0.116584 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.3810 | 0.769780 | 0.384890 | − | 0.922962i | \(-0.374239\pi\) | ||||
0.384890 | + | 0.922962i | \(0.374239\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.8613 | 0.824513 | ||||||||
\(704\) | −4.65164 | −0.175315 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.52770 | −0.283309 | ||||||||
\(707\) | −36.8647 | −1.38644 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.8363 | −1.53364 | −0.766820 | − | 0.641862i | \(-0.778162\pi\) | ||||
−0.766820 | + | 0.641862i | \(0.778162\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.32238 | 0.274418 | ||||||||
\(713\) | 18.0958 | 0.677692 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.07774 | −0.189764 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.71027 | 0.213105 | ||||||||
\(719\) | −9.14486 | −0.341046 | −0.170523 | − | 0.985354i | \(-0.554546\pi\) | ||||
−0.170523 | + | 0.985354i | \(0.554546\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43.9164 | 1.63553 | ||||||||
\(722\) | −6.56197 | −0.244211 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −23.9018 | −0.888305 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.13875 | 0.0793218 | 0.0396609 | − | 0.999213i | \(-0.487372\pi\) | ||||
0.0396609 | + | 0.999213i | \(0.487372\pi\) | |||||||
\(728\) | 1.46563 | 0.0543198 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −54.4672 | −2.01454 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.3388 | −0.566552 | −0.283276 | − | 0.959038i | \(-0.591421\pi\) | ||||
−0.283276 | + | 0.959038i | \(0.591421\pi\) | |||||||
\(734\) | −3.01117 | −0.111144 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −30.2277 | −1.11421 | ||||||||
\(737\) | −23.4396 | −0.863411 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.8111 | −0.581621 | −0.290811 | − | 0.956781i | \(-0.593925\pi\) | ||||
−0.290811 | + | 0.956781i | \(0.593925\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.24141 | 0.0822847 | ||||||||
\(743\) | −20.2017 | −0.741128 | −0.370564 | − | 0.928807i | \(-0.620836\pi\) | ||||
−0.370564 | + | 0.928807i | \(0.620836\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.54918 | 0.129945 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13.1499 | 0.480809 | ||||||||
\(749\) | −30.8363 | −1.12673 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.9053 | 1.20073 | 0.600365 | − | 0.799726i | \(-0.295022\pi\) | ||||
0.600365 | + | 0.799726i | \(0.295022\pi\) | |||||||
\(752\) | −11.1138 | −0.405280 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.282852 | 0.0103009 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.3009 | −0.410738 | −0.205369 | − | 0.978685i | \(-0.565839\pi\) | ||||
−0.205369 | + | 0.978685i | \(0.565839\pi\) | |||||||
\(758\) | −0.0292158 | −0.00106117 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.93449 | 0.106375 | 0.0531876 | − | 0.998585i | \(-0.483062\pi\) | ||||
0.0531876 | + | 0.998585i | \(0.483062\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.824101 | 0.0298344 | ||||||||
\(764\) | 24.0000 | 0.868290 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.2648 | 0.407014 | ||||||||
\(767\) | −0.651639 | −0.0235293 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.7785 | −0.821412 | −0.410706 | − | 0.911768i | \(-0.634718\pi\) | ||||
−0.410706 | + | 0.911768i | \(0.634718\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.2536 | −0.513000 | ||||||||
\(773\) | 10.5553 | 0.379648 | 0.189824 | − | 0.981818i | \(-0.439208\pi\) | ||||
0.189824 | + | 0.981818i | \(0.439208\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.7880 | −0.459063 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.2311 | 0.402654 | ||||||||
\(779\) | 2.24914 | 0.0805838 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.4853 | 0.554107 | ||||||||
\(782\) | 14.7880 | 0.528818 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.7198 | 0.382851 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.0682 | 0.822292 | 0.411146 | − | 0.911570i | \(-0.365129\pi\) | ||||
0.411146 | + | 0.911570i | \(0.365129\pi\) | |||||||
\(788\) | −24.8602 | −0.885608 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.5827 | −1.08740 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.42504 | −0.0506047 | ||||||||
\(794\) | −6.88617 | −0.244381 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.65164 | 0.306649 | ||||||||
\(797\) | 0.0360915 | 0.00127843 | 0.000639213 | − | 1.00000i | \(-0.499797\pi\) | ||||
0.000639213 | 1.00000i | \(0.499797\pi\) | ||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.5439 | 0.726792 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.32926 | 0.188183 | ||||||||
\(803\) | −13.8156 | −0.487542 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.339571 | −0.0119609 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −19.8207 | −0.697288 | ||||||||
\(809\) | −33.1430 | −1.16525 | −0.582624 | − | 0.812742i | \(-0.697974\pi\) | ||||
−0.582624 | + | 0.812742i | \(0.697974\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.10428 | −0.0387764 | −0.0193882 | − | 0.999812i | \(-0.506172\pi\) | ||||
−0.0193882 | + | 0.999812i | \(0.506172\pi\) | |||||||
\(812\) | 14.1894 | 0.497952 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.72832 | −0.235827 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.3664 | −0.852473 | ||||||||
\(818\) | −15.9525 | −0.557767 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.42504 | 0.259136 | 0.129568 | − | 0.991571i | \(-0.458641\pi\) | ||||
0.129568 | + | 0.991571i | \(0.458641\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.1656 | −1.46980 | −0.734900 | − | 0.678176i | \(-0.762771\pi\) | ||||
−0.734900 | + | 0.678176i | \(0.762771\pi\) | |||||||
\(824\) | 23.6121 | 0.822567 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.07218 | 0.141689 | ||||||||
\(827\) | −54.4863 | −1.89468 | −0.947338 | − | 0.320235i | \(-0.896238\pi\) | ||||
−0.947338 | + | 0.320235i | \(0.896238\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.0388 | 0.834901 | 0.417450 | − | 0.908700i | \(-0.362924\pi\) | ||||
0.417450 | + | 0.908700i | \(0.362924\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.788009 | −0.0273193 | ||||||||
\(833\) | −19.8156 | −0.686570 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.88273 | 0.203459 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.934491 | 0.0322815 | ||||||||
\(839\) | 13.6190 | 0.470180 | 0.235090 | − | 0.971974i | \(-0.424462\pi\) | ||||
0.235090 | + | 0.971974i | \(0.424462\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.1820 | −0.799380 | ||||||||
\(842\) | −2.67074 | −0.0920399 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.8793 | 0.649852 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.2311 | 1.00439 | ||||||||
\(848\) | −3.91559 | −0.134462 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 60.7405 | 2.08216 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.93449 | 0.237432 | 0.118716 | − | 0.992928i | \(-0.462122\pi\) | ||||
0.118716 | + | 0.992928i | \(0.462122\pi\) | |||||||
\(854\) | 8.90528 | 0.304732 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.5795 | −0.566674 | ||||||||
\(857\) | −34.9345 | −1.19334 | −0.596670 | − | 0.802487i | \(-0.703510\pi\) | ||||
−0.596670 | + | 0.802487i | \(0.703510\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.39057 | 0.149804 | 0.0749021 | − | 0.997191i | \(-0.476136\pi\) | ||||
0.0749021 | + | 0.997191i | \(0.476136\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.824101 | −0.0280690 | ||||||||
\(863\) | 15.4611 | 0.526303 | 0.263152 | − | 0.964755i | \(-0.415238\pi\) | ||||
0.263152 | + | 0.964755i | \(0.415238\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.0337 | 0.544848 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −17.0348 | −0.578198 | ||||||||
\(869\) | −0.824101 | −0.0279557 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.97078 | −0.134545 | ||||||||
\(872\) | 0.443086 | 0.0150048 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.61555 | 0.223774 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 55.2338 | 1.86511 | 0.932556 | − | 0.361025i | \(-0.117573\pi\) | ||||
0.932556 | + | 0.361025i | \(0.117573\pi\) | |||||||
\(878\) | −2.03609 | −0.0687148 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.4431 | 0.958272 | 0.479136 | − | 0.877741i | \(-0.340950\pi\) | ||||
0.479136 | + | 0.877741i | \(0.340950\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.1319 | 0.812102 | 0.406051 | − | 0.913850i | \(-0.366905\pi\) | ||||
0.406051 | + | 0.913850i | \(0.366905\pi\) | |||||||
\(884\) | 2.22766 | 0.0749242 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.4137 | 0.585024 | ||||||||
\(887\) | −2.06025 | −0.0691765 | −0.0345882 | − | 0.999402i | \(-0.511012\pi\) | ||||
−0.0345882 | + | 0.999402i | \(0.511012\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.72594 | −0.0914250 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −32.0000 | −1.07144 | ||||||||
\(893\) | 9.19051 | 0.307549 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 36.9244 | 1.23356 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.50496 | 0.250444 | ||||||||
\(899\) | −6.98463 | −0.232950 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.23797 | 0.241132 | ||||||||
\(902\) | −0.692226 | −0.0230486 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.4431 | −0.546889 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.5208 | 0.648178 | 0.324089 | − | 0.946027i | \(-0.394942\pi\) | ||||
0.324089 | + | 0.946027i | \(0.394942\pi\) | |||||||
\(908\) | 1.61899 | 0.0537279 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.9785 | 1.32455 | 0.662274 | − | 0.749262i | \(-0.269592\pi\) | ||||
0.662274 | + | 0.749262i | \(0.269592\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.59750 | 0.185250 | ||||||||
\(914\) | 13.8568 | 0.458341 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.2051 | 0.436309 | ||||||||
\(917\) | 26.8984 | 0.888263 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.4508 | −0.872532 | −0.436266 | − | 0.899818i | \(-0.643699\pi\) | ||||
−0.436266 | + | 0.899818i | \(0.643699\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.2966 | −0.339101 | ||||||||
\(923\) | 2.62328 | 0.0863463 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 8.78113 | 0.288566 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11.6673 | 0.382998 | ||||||||
\(929\) | −33.2913 | −1.09225 | −0.546127 | − | 0.837703i | \(-0.683898\pi\) | ||||
−0.546127 | + | 0.837703i | \(0.683898\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.86469 | −0.290528 | ||||||||
\(932\) | −26.2536 | −0.859966 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.08117 | 0.133540 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.7811 | 1.26692 | 0.633462 | − | 0.773774i | \(-0.281633\pi\) | ||||
0.633462 | + | 0.773774i | \(0.281633\pi\) | |||||||
\(938\) | 24.8140 | 0.810205 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.6482 | −0.510117 | −0.255058 | − | 0.966926i | \(-0.582095\pi\) | ||||
−0.255058 | + | 0.966926i | \(0.582095\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.24914 | 0.203500 | ||||||||
\(944\) | −7.11383 | −0.231535 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.49934 | 0.243825 | ||||||||
\(947\) | −47.5500 | −1.54517 | −0.772584 | − | 0.634912i | \(-0.781036\pi\) | ||||
−0.772584 | + | 0.634912i | \(0.781036\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.34043 | −0.0759735 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −29.5760 | −0.958564 | ||||||||
\(953\) | −29.6819 | −0.961491 | −0.480746 | − | 0.876860i | \(-0.659634\pi\) | ||||
−0.480746 | + | 0.876860i | \(0.659634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.46219 | −0.0796329 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.61661 | 0.310698 | ||||||||
\(959\) | 40.3664 | 1.30350 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.6148 | −0.729509 | ||||||||
\(962\) | −1.13981 | −0.0367489 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.5896 | 0.341067 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.21199 | 0.0389750 | 0.0194875 | − | 0.999810i | \(-0.493797\pi\) | ||||
0.0194875 | + | 0.999810i | \(0.493797\pi\) | |||||||
\(968\) | 15.7164 | 0.505144 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.5362 | −0.402306 | −0.201153 | − | 0.979560i | \(-0.564469\pi\) | ||||
−0.201153 | + | 0.979560i | \(0.564469\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −47.2672 | −1.51532 | ||||||||
\(974\) | 3.29766 | 0.105664 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.5569 | −0.497965 | ||||||||
\(977\) | 15.2069 | 0.486513 | 0.243256 | − | 0.969962i | \(-0.421784\pi\) | ||||
0.243256 | + | 0.969962i | \(0.421784\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.05520 | −0.193525 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.32926 | 0.233886 | ||||||||
\(983\) | 39.0303 | 1.24487 | 0.622436 | − | 0.782671i | \(-0.286143\pi\) | ||||
0.622436 | + | 0.782671i | \(0.286143\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.70789 | −0.181776 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.996562 | 0.0317049 | ||||||||
\(989\) | −67.7010 | −2.15277 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.91539 | −0.283207 | −0.141603 | − | 0.989923i | \(-0.545226\pi\) | ||||
−0.141603 | + | 0.989923i | \(0.545226\pi\) | |||||||
\(992\) | −14.0069 | −0.444719 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −16.3932 | −0.519962 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.6336 | 1.06519 | 0.532593 | − | 0.846371i | \(-0.321218\pi\) | ||||
0.532593 | + | 0.846371i | \(0.321218\pi\) | |||||||
\(998\) | −0.762030 | −0.0241216 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9225.2.a.bx.1.2 | 3 | ||
3.2 | odd | 2 | 3075.2.a.t.1.2 | 3 | |||
5.4 | even | 2 | 369.2.a.e.1.2 | 3 | |||
15.14 | odd | 2 | 123.2.a.d.1.2 | ✓ | 3 | ||
20.19 | odd | 2 | 5904.2.a.bd.1.1 | 3 | |||
60.59 | even | 2 | 1968.2.a.w.1.3 | 3 | |||
105.104 | even | 2 | 6027.2.a.s.1.2 | 3 | |||
120.29 | odd | 2 | 7872.2.a.bx.1.1 | 3 | |||
120.59 | even | 2 | 7872.2.a.bs.1.1 | 3 | |||
615.614 | odd | 2 | 5043.2.a.n.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
123.2.a.d.1.2 | ✓ | 3 | 15.14 | odd | 2 | ||
369.2.a.e.1.2 | 3 | 5.4 | even | 2 | |||
1968.2.a.w.1.3 | 3 | 60.59 | even | 2 | |||
3075.2.a.t.1.2 | 3 | 3.2 | odd | 2 | |||
5043.2.a.n.1.2 | 3 | 615.614 | odd | 2 | |||
5904.2.a.bd.1.1 | 3 | 20.19 | odd | 2 | |||
6027.2.a.s.1.2 | 3 | 105.104 | even | 2 | |||
7872.2.a.bs.1.1 | 3 | 120.59 | even | 2 | |||
7872.2.a.bx.1.1 | 3 | 120.29 | odd | 2 | |||
9225.2.a.bx.1.2 | 3 | 1.1 | even | 1 | trivial |