Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 100 x^{16} + 4066 x^{14} - 86197 x^{12} + 1016064 x^{10} - 6594119 x^{8} + 22251817 x^{6} - 37096332 x^{4} + 27824160 x^{2} - 6889792 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7\cdot 13^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.85886\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.85886 | −1.71787 | −0.858933 | − | 0.512088i | \(-0.828872\pi\) | ||||
−0.858933 | + | 0.512088i | \(0.828872\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 15.6085 | 1.95106 | ||||||||
\(5\) | −14.8714 | −1.33014 | −0.665071 | − | 0.746780i | \(-0.731599\pi\) | ||||
−0.665071 | + | 0.746780i | \(0.731599\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −29.6598 | −1.60148 | −0.800741 | − | 0.599011i | \(-0.795560\pi\) | ||||
−0.800741 | + | 0.599011i | \(0.795560\pi\) | |||||||
\(8\) | −36.9687 | −1.63380 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 72.2582 | 2.28501 | ||||||||
\(11\) | 60.0283 | 1.64538 | 0.822691 | − | 0.568488i | \(-0.192471\pi\) | ||||
0.822691 | + | 0.568488i | \(0.192471\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 144.113 | 2.75113 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 54.7574 | 0.855585 | ||||||||
\(17\) | 49.0713 | 0.700091 | 0.350046 | − | 0.936733i | \(-0.386166\pi\) | ||||
0.350046 | + | 0.936733i | \(0.386166\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −96.7335 | −1.16801 | −0.584005 | − | 0.811750i | \(-0.698515\pi\) | ||||
−0.584005 | + | 0.811750i | \(0.698515\pi\) | |||||||
\(20\) | −232.121 | −2.59519 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −291.669 | −2.82655 | ||||||||
\(23\) | −42.4461 | −0.384810 | −0.192405 | − | 0.981316i | \(-0.561629\pi\) | ||||
−0.192405 | + | 0.981316i | \(0.561629\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 96.1597 | 0.769278 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −462.946 | −3.12459 | ||||||||
\(29\) | −176.826 | −1.13227 | −0.566133 | − | 0.824314i | \(-0.691561\pi\) | ||||
−0.566133 | + | 0.824314i | \(0.691561\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −269.559 | −1.56175 | −0.780875 | − | 0.624688i | \(-0.785226\pi\) | ||||
−0.780875 | + | 0.624688i | \(0.785226\pi\) | |||||||
\(32\) | 29.6906 | 0.164019 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −238.431 | −1.20266 | ||||||||
\(35\) | 441.085 | 2.13020 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −186.663 | −0.829383 | −0.414691 | − | 0.909962i | \(-0.636110\pi\) | ||||
−0.414691 | + | 0.909962i | \(0.636110\pi\) | |||||||
\(38\) | 470.014 | 2.00648 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 549.777 | 2.17319 | ||||||||
\(41\) | 52.7630 | 0.200981 | 0.100490 | − | 0.994938i | \(-0.467959\pi\) | ||||
0.100490 | + | 0.994938i | \(0.467959\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 527.456 | 1.87061 | 0.935306 | − | 0.353839i | \(-0.115124\pi\) | ||||
0.935306 | + | 0.353839i | \(0.115124\pi\) | |||||||
\(44\) | 936.952 | 3.21025 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 206.240 | 0.661052 | ||||||||
\(47\) | 61.3270 | 0.190329 | 0.0951644 | − | 0.995462i | \(-0.469662\pi\) | ||||
0.0951644 | + | 0.995462i | \(0.469662\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 536.706 | 1.56474 | ||||||||
\(50\) | −467.226 | −1.32152 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 340.468 | 0.882394 | 0.441197 | − | 0.897410i | \(-0.354554\pi\) | ||||
0.441197 | + | 0.897410i | \(0.354554\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −892.707 | −2.18859 | ||||||||
\(56\) | 1096.48 | 2.61650 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 859.172 | 1.94508 | ||||||||
\(59\) | 595.111 | 1.31317 | 0.656583 | − | 0.754254i | \(-0.272001\pi\) | ||||
0.656583 | + | 0.754254i | \(0.272001\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −415.671 | −0.872480 | −0.436240 | − | 0.899830i | \(-0.643690\pi\) | ||||
−0.436240 | + | 0.899830i | \(0.643690\pi\) | |||||||
\(62\) | 1309.75 | 2.68288 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −582.322 | −1.13735 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 640.901 | 1.16864 | 0.584318 | − | 0.811525i | \(-0.301362\pi\) | ||||
0.584318 | + | 0.811525i | \(0.301362\pi\) | |||||||
\(68\) | 765.930 | 1.36592 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2143.17 | −3.65939 | ||||||||
\(71\) | 551.454 | 0.921768 | 0.460884 | − | 0.887461i | \(-0.347533\pi\) | ||||
0.460884 | + | 0.887461i | \(0.347533\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 431.954 | 0.692553 | 0.346276 | − | 0.938133i | \(-0.387446\pi\) | ||||
0.346276 | + | 0.938133i | \(0.387446\pi\) | |||||||
\(74\) | 906.968 | 1.42477 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1509.86 | −2.27886 | ||||||||
\(77\) | −1780.43 | −2.63505 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 998.743 | 1.42237 | 0.711186 | − | 0.703004i | \(-0.248159\pi\) | ||||
0.711186 | + | 0.703004i | \(0.248159\pi\) | |||||||
\(80\) | −814.322 | −1.13805 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −256.368 | −0.345258 | ||||||||
\(83\) | 461.462 | 0.610265 | 0.305133 | − | 0.952310i | \(-0.401299\pi\) | ||||
0.305133 | + | 0.952310i | \(0.401299\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −729.762 | −0.931221 | ||||||||
\(86\) | −2562.84 | −3.21346 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2219.17 | −2.68823 | ||||||||
\(89\) | −1025.25 | −1.22108 | −0.610541 | − | 0.791985i | \(-0.709048\pi\) | ||||
−0.610541 | + | 0.791985i | \(0.709048\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −662.520 | −0.750788 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −297.979 | −0.326959 | ||||||||
\(95\) | 1438.57 | 1.55362 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 261.585 | 0.273813 | 0.136907 | − | 0.990584i | \(-0.456284\pi\) | ||||
0.136907 | + | 0.990584i | \(0.456284\pi\) | |||||||
\(98\) | −2607.78 | −2.68802 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1500.91 | 1.50091 | ||||||||
\(101\) | −290.237 | −0.285937 | −0.142969 | − | 0.989727i | \(-0.545665\pi\) | ||||
−0.142969 | + | 0.989727i | \(0.545665\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −198.640 | −0.190025 | −0.0950123 | − | 0.995476i | \(-0.530289\pi\) | ||||
−0.0950123 | + | 0.995476i | \(0.530289\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1654.29 | −1.51583 | ||||||||
\(107\) | −684.251 | −0.618216 | −0.309108 | − | 0.951027i | \(-0.600030\pi\) | ||||
−0.309108 | + | 0.951027i | \(0.600030\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1725.33 | 1.51612 | 0.758059 | − | 0.652186i | \(-0.226148\pi\) | ||||
0.758059 | + | 0.652186i | \(0.226148\pi\) | |||||||
\(110\) | 4337.54 | 3.75971 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1624.10 | −1.37020 | ||||||||
\(113\) | 2032.55 | 1.69209 | 0.846045 | − | 0.533111i | \(-0.178977\pi\) | ||||
0.846045 | + | 0.533111i | \(0.178977\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 631.235 | 0.511852 | ||||||||
\(116\) | −2759.99 | −2.20912 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2891.56 | −2.25584 | ||||||||
\(119\) | −1455.45 | −1.12118 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2272.40 | 1.70728 | ||||||||
\(122\) | 2019.69 | 1.49880 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4207.41 | −3.04707 | ||||||||
\(125\) | 428.897 | 0.306894 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1074.21 | −0.750559 | −0.375279 | − | 0.926912i | \(-0.622453\pi\) | ||||
−0.375279 | + | 0.926912i | \(0.622453\pi\) | |||||||
\(128\) | 2591.90 | 1.78979 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1969.09 | −1.31328 | −0.656641 | − | 0.754203i | \(-0.728023\pi\) | ||||
−0.656641 | + | 0.754203i | \(0.728023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2869.10 | 1.87054 | ||||||||
\(134\) | −3114.05 | −2.00756 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1814.10 | −1.14381 | ||||||||
\(137\) | 0.346542 | 0.000216110 0 | 0.000108055 | − | 1.00000i | \(-0.499966\pi\) | ||||
0.000108055 | 1.00000i | \(0.499966\pi\) | ||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1863.25 | −1.13697 | −0.568486 | − | 0.822693i | \(-0.692471\pi\) | ||||
−0.568486 | + | 0.822693i | \(0.692471\pi\) | |||||||
\(140\) | 6884.67 | 4.15615 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2679.43 | −1.58347 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2629.65 | 1.50608 | ||||||||
\(146\) | −2098.80 | −1.18971 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2913.53 | −1.61818 | ||||||||
\(149\) | −24.6640 | −0.0135608 | −0.00678038 | − | 0.999977i | \(-0.502158\pi\) | ||||
−0.00678038 | + | 0.999977i | \(0.502158\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 447.901 | 0.241388 | 0.120694 | − | 0.992690i | \(-0.461488\pi\) | ||||
0.120694 | + | 0.992690i | \(0.461488\pi\) | |||||||
\(152\) | 3576.11 | 1.90829 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8650.86 | 4.52666 | ||||||||
\(155\) | 4008.73 | 2.07735 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −547.454 | −0.278290 | −0.139145 | − | 0.990272i | \(-0.544435\pi\) | ||||
−0.139145 | + | 0.990272i | \(0.544435\pi\) | |||||||
\(158\) | −4852.75 | −2.44344 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −441.542 | −0.218169 | ||||||||
\(161\) | 1258.94 | 0.616266 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −190.029 | −0.0913143 | −0.0456572 | − | 0.998957i | \(-0.514538\pi\) | ||||
−0.0456572 | + | 0.998957i | \(0.514538\pi\) | |||||||
\(164\) | 823.552 | 0.392126 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2242.18 | −1.04835 | ||||||||
\(167\) | −851.170 | −0.394404 | −0.197202 | − | 0.980363i | \(-0.563186\pi\) | ||||
−0.197202 | + | 0.980363i | \(0.563186\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3545.81 | 1.59971 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8232.81 | 3.64968 | ||||||||
\(173\) | 2688.72 | 1.18162 | 0.590809 | − | 0.806811i | \(-0.298809\pi\) | ||||
0.590809 | + | 0.806811i | \(0.298809\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2852.08 | −1.23198 | ||||||||
\(176\) | 3287.00 | 1.40776 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4981.54 | 2.09765 | ||||||||
\(179\) | 991.338 | 0.413944 | 0.206972 | − | 0.978347i | \(-0.433639\pi\) | ||||
0.206972 | + | 0.978347i | \(0.433639\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 225.981 | 0.0928011 | 0.0464006 | − | 0.998923i | \(-0.485225\pi\) | ||||
0.0464006 | + | 0.998923i | \(0.485225\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1569.18 | 0.628702 | ||||||||
\(185\) | 2775.94 | 1.10320 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2945.67 | 1.15192 | ||||||||
\(188\) | 957.222 | 0.371344 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6989.79 | −2.66891 | ||||||||
\(191\) | 2265.08 | 0.858090 | 0.429045 | − | 0.903283i | \(-0.358850\pi\) | ||||
0.429045 | + | 0.903283i | \(0.358850\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.6018 | −0.00768369 | −0.00384184 | − | 0.999993i | \(-0.501223\pi\) | ||||
−0.00384184 | + | 0.999993i | \(0.501223\pi\) | |||||||
\(194\) | −1271.00 | −0.470375 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8377.19 | 3.05291 | ||||||||
\(197\) | −72.6929 | −0.0262901 | −0.0131451 | − | 0.999914i | \(-0.504184\pi\) | ||||
−0.0131451 | + | 0.999914i | \(0.504184\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3599.20 | −1.28211 | −0.641057 | − | 0.767494i | \(-0.721504\pi\) | ||||
−0.641057 | + | 0.767494i | \(0.721504\pi\) | |||||||
\(200\) | −3554.90 | −1.25685 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1410.22 | 0.491202 | ||||||||
\(203\) | 5244.63 | 1.81330 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −784.662 | −0.267333 | ||||||||
\(206\) | 965.161 | 0.326437 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5806.74 | −1.92182 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −340.466 | −0.111084 | −0.0555419 | − | 0.998456i | \(-0.517689\pi\) | ||||
−0.0555419 | + | 0.998456i | \(0.517689\pi\) | |||||||
\(212\) | 5314.20 | 1.72161 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3324.68 | 1.06201 | ||||||||
\(215\) | −7844.04 | −2.48818 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7995.08 | 2.50111 | ||||||||
\(218\) | −8383.14 | −2.60449 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −13933.8 | −4.27008 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1963.17 | −0.589522 | −0.294761 | − | 0.955571i | \(-0.595240\pi\) | ||||
−0.294761 | + | 0.955571i | \(0.595240\pi\) | |||||||
\(224\) | −880.620 | −0.262674 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9875.87 | −2.90678 | ||||||||
\(227\) | −610.759 | −0.178579 | −0.0892897 | − | 0.996006i | \(-0.528460\pi\) | ||||
−0.0892897 | + | 0.996006i | \(0.528460\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4357.13 | −1.25732 | −0.628662 | − | 0.777679i | \(-0.716397\pi\) | ||||
−0.628662 | + | 0.777679i | \(0.716397\pi\) | |||||||
\(230\) | −3067.08 | −0.879292 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6537.01 | 1.84990 | ||||||||
\(233\) | −2776.38 | −0.780630 | −0.390315 | − | 0.920681i | \(-0.627634\pi\) | ||||
−0.390315 | + | 0.920681i | \(0.627634\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −912.020 | −0.253164 | ||||||||
\(236\) | 9288.79 | 2.56207 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7071.82 | 1.92604 | ||||||||
\(239\) | −2740.18 | −0.741622 | −0.370811 | − | 0.928708i | \(-0.620920\pi\) | ||||
−0.370811 | + | 0.928708i | \(0.620920\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1734.06 | 0.463489 | 0.231745 | − | 0.972777i | \(-0.425557\pi\) | ||||
0.231745 | + | 0.972777i | \(0.425557\pi\) | |||||||
\(242\) | −11041.3 | −2.93289 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6488.01 | −1.70226 | ||||||||
\(245\) | −7981.60 | −2.08133 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 9965.24 | 2.55159 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2083.95 | −0.527202 | ||||||||
\(251\) | −1183.57 | −0.297635 | −0.148817 | − | 0.988865i | \(-0.547547\pi\) | ||||
−0.148817 | + | 0.988865i | \(0.547547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2547.97 | −0.633159 | ||||||||
\(254\) | 5219.45 | 1.28936 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7935.08 | −1.93727 | ||||||||
\(257\) | −7585.34 | −1.84109 | −0.920546 | − | 0.390635i | \(-0.872255\pi\) | ||||
−0.920546 | + | 0.390635i | \(0.872255\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5536.39 | 1.32824 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9567.52 | 2.25604 | ||||||||
\(263\) | 4698.49 | 1.10160 | 0.550801 | − | 0.834637i | \(-0.314322\pi\) | ||||
0.550801 | + | 0.834637i | \(0.314322\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5063.25 | −1.17371 | ||||||||
\(266\) | −13940.5 | −3.21335 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10003.5 | 2.28008 | ||||||||
\(269\) | −7395.94 | −1.67635 | −0.838175 | − | 0.545401i | \(-0.816378\pi\) | ||||
−0.838175 | + | 0.545401i | \(0.816378\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1931.83 | −0.433028 | −0.216514 | − | 0.976280i | \(-0.569469\pi\) | ||||
−0.216514 | + | 0.976280i | \(0.569469\pi\) | |||||||
\(272\) | 2687.02 | 0.598987 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.68380 | −0.000371248 0 | ||||||||
\(275\) | 5772.30 | 1.26576 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1830.40 | 0.397032 | 0.198516 | − | 0.980098i | \(-0.436388\pi\) | ||||
0.198516 | + | 0.980098i | \(0.436388\pi\) | |||||||
\(278\) | 9053.29 | 1.95317 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −16306.3 | −3.48031 | ||||||||
\(281\) | −273.145 | −0.0579875 | −0.0289938 | − | 0.999580i | \(-0.509230\pi\) | ||||
−0.0289938 | + | 0.999580i | \(0.509230\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1147.91 | −0.241116 | −0.120558 | − | 0.992706i | \(-0.538468\pi\) | ||||
−0.120558 | + | 0.992706i | \(0.538468\pi\) | |||||||
\(284\) | 8607.37 | 1.79843 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1564.94 | −0.321867 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2505.00 | −0.509872 | ||||||||
\(290\) | −12777.1 | −2.58724 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6742.15 | 1.35121 | ||||||||
\(293\) | 7106.25 | 1.41690 | 0.708450 | − | 0.705761i | \(-0.249395\pi\) | ||||
0.708450 | + | 0.705761i | \(0.249395\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8850.15 | −1.74670 | ||||||||
\(296\) | 6900.67 | 1.35504 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 119.839 | 0.0232956 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15644.3 | −2.99575 | ||||||||
\(302\) | −2176.29 | −0.414673 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5296.88 | −0.999331 | ||||||||
\(305\) | 6181.63 | 1.16052 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7964.11 | −1.48057 | −0.740287 | − | 0.672291i | \(-0.765310\pi\) | ||||
−0.740287 | + | 0.672291i | \(0.765310\pi\) | |||||||
\(308\) | −27789.9 | −5.14115 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −19477.9 | −3.56861 | ||||||||
\(311\) | 7003.74 | 1.27700 | 0.638498 | − | 0.769623i | \(-0.279556\pi\) | ||||
0.638498 | + | 0.769623i | \(0.279556\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1848.21 | −0.333761 | −0.166881 | − | 0.985977i | \(-0.553369\pi\) | ||||
−0.166881 | + | 0.985977i | \(0.553369\pi\) | |||||||
\(314\) | 2660.00 | 0.478065 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15588.9 | 2.77514 | ||||||||
\(317\) | −2266.75 | −0.401619 | −0.200810 | − | 0.979630i | \(-0.564357\pi\) | ||||
−0.200810 | + | 0.979630i | \(0.564357\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10614.6 | −1.86301 | ||||||||
\(320\) | 8659.97 | 1.51283 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6117.03 | −1.05866 | ||||||||
\(323\) | −4746.84 | −0.817713 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 923.325 | 0.156866 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1950.58 | −0.328362 | ||||||||
\(329\) | −1818.95 | −0.304808 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8471.48 | 1.40675 | 0.703376 | − | 0.710818i | \(-0.251675\pi\) | ||||
0.703376 | + | 0.710818i | \(0.251675\pi\) | |||||||
\(332\) | 7202.73 | 1.19067 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4135.71 | 0.677533 | ||||||||
\(335\) | −9531.13 | −1.55445 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 642.992 | 0.103935 | 0.0519674 | − | 0.998649i | \(-0.483451\pi\) | ||||
0.0519674 | + | 0.998649i | \(0.483451\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11390.5 | −1.81687 | ||||||||
\(341\) | −16181.2 | −2.56968 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5745.30 | −0.904423 | ||||||||
\(344\) | −19499.4 | −3.05621 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13064.1 | −2.02986 | ||||||||
\(347\) | 11357.5 | 1.75706 | 0.878531 | − | 0.477686i | \(-0.158524\pi\) | ||||
0.878531 | + | 0.477686i | \(0.158524\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7539.82 | −1.15644 | −0.578219 | − | 0.815881i | \(-0.696252\pi\) | ||||
−0.578219 | + | 0.815881i | \(0.696252\pi\) | |||||||
\(350\) | 13857.9 | 2.11638 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1782.28 | 0.269874 | ||||||||
\(353\) | 11978.3 | 1.80607 | 0.903033 | − | 0.429572i | \(-0.141336\pi\) | ||||
0.903033 | + | 0.429572i | \(0.141336\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8200.91 | −1.22608 | ||||||||
\(356\) | −16002.6 | −2.38241 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4816.77 | −0.711101 | ||||||||
\(359\) | 8585.68 | 1.26221 | 0.631107 | − | 0.775696i | \(-0.282601\pi\) | ||||
0.631107 | + | 0.775696i | \(0.282601\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2498.36 | 0.364246 | ||||||||
\(362\) | −1098.01 | −0.159420 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6423.77 | −0.921193 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2302.65 | 0.327514 | 0.163757 | − | 0.986501i | \(-0.447639\pi\) | ||||
0.163757 | + | 0.986501i | \(0.447639\pi\) | |||||||
\(368\) | −2324.24 | −0.329237 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −13487.9 | −1.89514 | ||||||||
\(371\) | −10098.2 | −1.41314 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8961.58 | −1.24400 | −0.622002 | − | 0.783016i | \(-0.713680\pi\) | ||||
−0.622002 | + | 0.783016i | \(0.713680\pi\) | |||||||
\(374\) | −14312.6 | −1.97884 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2267.18 | −0.310959 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4627.11 | −0.627120 | −0.313560 | − | 0.949568i | \(-0.601522\pi\) | ||||
−0.313560 | + | 0.949568i | \(0.601522\pi\) | |||||||
\(380\) | 22453.9 | 3.03121 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11005.7 | −1.47408 | ||||||||
\(383\) | 2130.00 | 0.284172 | 0.142086 | − | 0.989854i | \(-0.454619\pi\) | ||||
0.142086 | + | 0.989854i | \(0.454619\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26477.6 | 3.50499 | ||||||||
\(386\) | 100.101 | 0.0131995 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4082.94 | 0.534227 | ||||||||
\(389\) | −5935.17 | −0.773586 | −0.386793 | − | 0.922167i | \(-0.626417\pi\) | ||||
−0.386793 | + | 0.922167i | \(0.626417\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2082.89 | −0.269402 | ||||||||
\(392\) | −19841.3 | −2.55647 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 353.204 | 0.0451629 | ||||||||
\(395\) | −14852.7 | −1.89196 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11708.6 | 1.48019 | 0.740095 | − | 0.672502i | \(-0.234781\pi\) | ||||
0.740095 | + | 0.672502i | \(0.234781\pi\) | |||||||
\(398\) | 17488.0 | 2.20250 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5265.46 | 0.658182 | ||||||||
\(401\) | 4600.01 | 0.572852 | 0.286426 | − | 0.958102i | \(-0.407533\pi\) | ||||
0.286426 | + | 0.958102i | \(0.407533\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −4530.16 | −0.557881 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −25482.9 | −3.11501 | ||||||||
\(407\) | −11205.0 | −1.36465 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −544.220 | −0.0657945 | −0.0328972 | − | 0.999459i | \(-0.510473\pi\) | ||||
−0.0328972 | + | 0.999459i | \(0.510473\pi\) | |||||||
\(410\) | 3812.56 | 0.459242 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3100.47 | −0.370750 | ||||||||
\(413\) | −17650.9 | −2.10301 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6862.60 | −0.811739 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 28214.2 | 3.30143 | ||||||||
\(419\) | −10617.4 | −1.23793 | −0.618965 | − | 0.785418i | \(-0.712448\pi\) | ||||
−0.618965 | + | 0.785418i | \(0.712448\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1404.23 | 0.162560 | 0.0812801 | − | 0.996691i | \(-0.474099\pi\) | ||||
0.0812801 | + | 0.996691i | \(0.474099\pi\) | |||||||
\(422\) | 1654.28 | 0.190827 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12586.6 | −1.44165 | ||||||||
\(425\) | 4718.69 | 0.538564 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12328.8 | 1.39726 | ||||||||
\(428\) | −10680.1 | −1.20618 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 38113.1 | 4.27436 | ||||||||
\(431\) | 1352.99 | 0.151209 | 0.0756046 | − | 0.997138i | \(-0.475911\pi\) | ||||
0.0756046 | + | 0.997138i | \(0.475911\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12465.1 | 1.38346 | 0.691728 | − | 0.722158i | \(-0.256850\pi\) | ||||
0.691728 | + | 0.722158i | \(0.256850\pi\) | |||||||
\(434\) | −38847.0 | −4.29658 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 26929.8 | 2.95804 | ||||||||
\(437\) | 4105.96 | 0.449461 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4202.96 | 0.456939 | 0.228470 | − | 0.973551i | \(-0.426628\pi\) | ||||
0.228470 | + | 0.973551i | \(0.426628\pi\) | |||||||
\(440\) | 33002.2 | 3.57572 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8198.85 | 0.879321 | 0.439661 | − | 0.898164i | \(-0.355099\pi\) | ||||
0.439661 | + | 0.898164i | \(0.355099\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15246.9 | 1.62421 | ||||||||
\(446\) | 9538.75 | 1.01272 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 17271.6 | 1.82144 | ||||||||
\(449\) | −642.438 | −0.0675245 | −0.0337623 | − | 0.999430i | \(-0.510749\pi\) | ||||
−0.0337623 | + | 0.999430i | \(0.510749\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3167.27 | 0.330690 | ||||||||
\(452\) | 31725.1 | 3.30138 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2967.59 | 0.306775 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1925.81 | 0.197124 | 0.0985620 | − | 0.995131i | \(-0.468576\pi\) | ||||
0.0985620 | + | 0.995131i | \(0.468576\pi\) | |||||||
\(458\) | 21170.7 | 2.15991 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9852.63 | 0.998655 | ||||||||
\(461\) | −9658.81 | −0.975826 | −0.487913 | − | 0.872892i | \(-0.662242\pi\) | ||||
−0.487913 | + | 0.872892i | \(0.662242\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12025.9 | −1.20711 | −0.603556 | − | 0.797320i | \(-0.706250\pi\) | ||||
−0.603556 | + | 0.797320i | \(0.706250\pi\) | |||||||
\(464\) | −9682.53 | −0.968750 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13490.0 | 1.34102 | ||||||||
\(467\) | 2470.93 | 0.244842 | 0.122421 | − | 0.992478i | \(-0.460934\pi\) | ||||
0.122421 | + | 0.992478i | \(0.460934\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19009.0 | −1.87155 | ||||||||
\(470\) | 4431.38 | 0.434903 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −22000.4 | −2.14545 | ||||||||
\(473\) | 31662.3 | 3.07787 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9301.86 | −0.898523 | ||||||||
\(476\) | −22717.4 | −2.18750 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13314.2 | 1.27401 | ||||||||
\(479\) | −5606.05 | −0.534754 | −0.267377 | − | 0.963592i | \(-0.586157\pi\) | ||||
−0.267377 | + | 0.963592i | \(0.586157\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −8425.58 | −0.796213 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 35468.7 | 3.33102 | ||||||||
\(485\) | −3890.14 | −0.364211 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −778.566 | −0.0724440 | −0.0362220 | − | 0.999344i | \(-0.511532\pi\) | ||||
−0.0362220 | + | 0.999344i | \(0.511532\pi\) | |||||||
\(488\) | 15366.8 | 1.42546 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 38781.5 | 3.57544 | ||||||||
\(491\) | −9336.64 | −0.858160 | −0.429080 | − | 0.903266i | \(-0.641162\pi\) | ||||
−0.429080 | + | 0.903266i | \(0.641162\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8677.08 | −0.792690 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14760.4 | −1.33621 | ||||||||
\(497\) | −16356.0 | −1.47619 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16615.2 | 1.49057 | 0.745287 | − | 0.666744i | \(-0.232312\pi\) | ||||
0.745287 | + | 0.666744i | \(0.232312\pi\) | |||||||
\(500\) | 6694.44 | 0.598769 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5750.80 | 0.511296 | ||||||||
\(503\) | −7494.12 | −0.664307 | −0.332153 | − | 0.943225i | \(-0.607775\pi\) | ||||
−0.332153 | + | 0.943225i | \(0.607775\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4316.24 | 0.380337 | ||||||||
\(506\) | 12380.2 | 1.08768 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16766.9 | −1.46439 | ||||||||
\(509\) | −11882.9 | −1.03478 | −0.517388 | − | 0.855751i | \(-0.673096\pi\) | ||||
−0.517388 | + | 0.855751i | \(0.673096\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12811.7 | −1.10911 | ||||||||
\(512\) | 17820.3 | 1.53819 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 36856.1 | 3.16275 | ||||||||
\(515\) | 2954.06 | 0.252760 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3681.35 | 0.313164 | ||||||||
\(518\) | −26900.5 | −2.28174 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20244.7 | −1.70237 | −0.851186 | − | 0.524864i | \(-0.824116\pi\) | ||||
−0.851186 | + | 0.524864i | \(0.824116\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15231.8 | −1.27350 | −0.636748 | − | 0.771072i | \(-0.719721\pi\) | ||||
−0.636748 | + | 0.771072i | \(0.719721\pi\) | |||||||
\(524\) | −30734.5 | −2.56230 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22829.3 | −1.89240 | ||||||||
\(527\) | −13227.6 | −1.09337 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10365.3 | −0.851921 | ||||||||
\(530\) | 24601.6 | 2.01628 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 44782.4 | 3.64955 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10175.8 | 0.822315 | ||||||||
\(536\) | −23693.3 | −1.90932 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 35935.8 | 2.87975 | ||||||||
\(539\) | 32217.6 | 2.57460 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3599.15 | −0.286025 | −0.143013 | − | 0.989721i | \(-0.545679\pi\) | ||||
−0.143013 | + | 0.989721i | \(0.545679\pi\) | |||||||
\(542\) | 9386.51 | 0.743884 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1456.96 | 0.114828 | ||||||||
\(545\) | −25658.2 | −2.01665 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9212.26 | −0.720087 | −0.360044 | − | 0.932936i | \(-0.617238\pi\) | ||||
−0.360044 | + | 0.932936i | \(0.617238\pi\) | |||||||
\(548\) | 5.40900 | 0.000421644 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −28046.8 | −2.17440 | ||||||||
\(551\) | 17105.0 | 1.32250 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −29622.6 | −2.27790 | ||||||||
\(554\) | −8893.64 | −0.682048 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −29082.6 | −2.21830 | ||||||||
\(557\) | −25245.0 | −1.92040 | −0.960202 | − | 0.279306i | \(-0.909896\pi\) | ||||
−0.960202 | + | 0.279306i | \(0.909896\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 24152.7 | 1.82256 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1327.18 | 0.0996148 | ||||||||
\(563\) | 1694.84 | 0.126872 | 0.0634359 | − | 0.997986i | \(-0.479794\pi\) | ||||
0.0634359 | + | 0.997986i | \(0.479794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30226.9 | −2.25072 | ||||||||
\(566\) | 5577.51 | 0.414206 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −20386.5 | −1.50598 | ||||||||
\(569\) | −494.893 | −0.0364622 | −0.0182311 | − | 0.999834i | \(-0.505803\pi\) | ||||
−0.0182311 | + | 0.999834i | \(0.505803\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1750.91 | −0.128325 | −0.0641623 | − | 0.997939i | \(-0.520438\pi\) | ||||
−0.0641623 | + | 0.997939i | \(0.520438\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7603.84 | 0.552924 | ||||||||
\(575\) | −4081.60 | −0.296025 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8535.56 | −0.615841 | −0.307920 | − | 0.951412i | \(-0.599633\pi\) | ||||
−0.307920 | + | 0.951412i | \(0.599633\pi\) | |||||||
\(578\) | 12171.5 | 0.875892 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 41045.0 | 2.93845 | ||||||||
\(581\) | −13686.9 | −0.977328 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20437.7 | 1.45188 | ||||||||
\(584\) | −15968.7 | −1.13149 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −34528.3 | −2.43404 | ||||||||
\(587\) | 19499.0 | 1.37105 | 0.685527 | − | 0.728047i | \(-0.259572\pi\) | ||||
0.685527 | + | 0.728047i | \(0.259572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26075.4 | 1.82414 | ||||||||
\(590\) | 43001.6 | 3.00059 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10221.2 | −0.709607 | ||||||||
\(593\) | −7599.31 | −0.526250 | −0.263125 | − | 0.964762i | \(-0.584753\pi\) | ||||
−0.263125 | + | 0.964762i | \(0.584753\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21644.6 | 1.49133 | ||||||||
\(596\) | −384.968 | −0.0264579 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26240.9 | −1.78994 | −0.894971 | − | 0.446124i | \(-0.852804\pi\) | ||||
−0.894971 | + | 0.446124i | \(0.852804\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20319.6 | 1.37912 | 0.689561 | − | 0.724227i | \(-0.257803\pi\) | ||||
0.689561 | + | 0.724227i | \(0.257803\pi\) | |||||||
\(602\) | 76013.3 | 5.14630 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6991.06 | 0.470964 | ||||||||
\(605\) | −33793.8 | −2.27093 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1361.39 | 0.0910333 | 0.0455166 | − | 0.998964i | \(-0.485507\pi\) | ||||
0.0455166 | + | 0.998964i | \(0.485507\pi\) | |||||||
\(608\) | −2872.08 | −0.191576 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −30035.7 | −1.99362 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13883.5 | 0.914764 | 0.457382 | − | 0.889270i | \(-0.348787\pi\) | ||||
0.457382 | + | 0.889270i | \(0.348787\pi\) | |||||||
\(614\) | 38696.5 | 2.54343 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 65820.1 | 4.30514 | ||||||||
\(617\) | −15316.8 | −0.999403 | −0.499701 | − | 0.866198i | \(-0.666557\pi\) | ||||
−0.499701 | + | 0.866198i | \(0.666557\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10325.0 | 0.670432 | 0.335216 | − | 0.942141i | \(-0.391191\pi\) | ||||
0.335216 | + | 0.942141i | \(0.391191\pi\) | |||||||
\(620\) | 62570.3 | 4.05304 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −34030.2 | −2.19371 | ||||||||
\(623\) | 30408.7 | 1.95554 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18398.3 | −1.17749 | ||||||||
\(626\) | 8980.21 | 0.573357 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8544.93 | −0.542962 | ||||||||
\(629\) | −9159.79 | −0.580643 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20967.7 | −1.32284 | −0.661420 | − | 0.750016i | \(-0.730046\pi\) | ||||
−0.661420 | + | 0.750016i | \(0.730046\pi\) | |||||||
\(632\) | −36922.2 | −2.32387 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11013.8 | 0.689928 | ||||||||
\(635\) | 15975.1 | 0.998349 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 51574.6 | 3.20041 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −38545.2 | −2.38068 | ||||||||
\(641\) | 20292.1 | 1.25037 | 0.625187 | − | 0.780475i | \(-0.285023\pi\) | ||||
0.625187 | + | 0.780475i | \(0.285023\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9106.14 | −0.558493 | −0.279247 | − | 0.960219i | \(-0.590085\pi\) | ||||
−0.279247 | + | 0.960219i | \(0.590085\pi\) | |||||||
\(644\) | 19650.2 | 1.20237 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 23064.2 | 1.40472 | ||||||||
\(647\) | 15251.4 | 0.926732 | 0.463366 | − | 0.886167i | \(-0.346641\pi\) | ||||
0.463366 | + | 0.886167i | \(0.346641\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35723.5 | 2.16066 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2966.07 | −0.178160 | ||||||||
\(653\) | −14421.0 | −0.864220 | −0.432110 | − | 0.901821i | \(-0.642231\pi\) | ||||
−0.432110 | + | 0.901821i | \(0.642231\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29283.2 | 1.74685 | ||||||||
\(656\) | 2889.17 | 0.171956 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8838.01 | 0.523619 | ||||||||
\(659\) | 11890.9 | 0.702892 | 0.351446 | − | 0.936208i | \(-0.385690\pi\) | ||||
0.351446 | + | 0.936208i | \(0.385690\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3696.05 | 0.217488 | 0.108744 | − | 0.994070i | \(-0.465317\pi\) | ||||
0.108744 | + | 0.994070i | \(0.465317\pi\) | |||||||
\(662\) | −41161.7 | −2.41661 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17059.6 | −0.997051 | ||||||||
\(665\) | −42667.6 | −2.48809 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7505.57 | 0.435707 | ||||||||
\(668\) | −13285.5 | −0.769507 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 46310.4 | 2.67034 | ||||||||
\(671\) | −24952.0 | −1.43556 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9587.03 | −0.549112 | −0.274556 | − | 0.961571i | \(-0.588531\pi\) | ||||
−0.274556 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(674\) | −3124.21 | −0.178546 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12413.6 | 0.704718 | 0.352359 | − | 0.935865i | \(-0.385380\pi\) | ||||
0.352359 | + | 0.935865i | \(0.385380\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7758.56 | −0.438507 | ||||||||
\(680\) | 26978.3 | 1.52143 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 78622.0 | 4.41436 | ||||||||
\(683\) | −23012.6 | −1.28924 | −0.644622 | − | 0.764502i | \(-0.722985\pi\) | ||||
−0.644622 | + | 0.764502i | \(0.722985\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.15357 | −0.000287457 0 | ||||||||
\(686\) | 27915.6 | 1.55368 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 28882.2 | 1.60047 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30604.2 | −1.68486 | −0.842431 | − | 0.538804i | \(-0.818876\pi\) | ||||
−0.842431 | + | 0.538804i | \(0.818876\pi\) | |||||||
\(692\) | 41967.0 | 2.30541 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −55184.3 | −3.01840 | ||||||||
\(695\) | 27709.3 | 1.51233 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2589.15 | 0.140705 | ||||||||
\(698\) | 36634.9 | 1.98661 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −44516.7 | −2.40368 | ||||||||
\(701\) | 4042.16 | 0.217789 | 0.108895 | − | 0.994053i | \(-0.465269\pi\) | ||||
0.108895 | + | 0.994053i | \(0.465269\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18056.5 | 0.968727 | ||||||||
\(704\) | −34955.8 | −1.87137 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −58200.9 | −3.10258 | ||||||||
\(707\) | 8608.38 | 0.457923 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33867.3 | 1.79395 | 0.896977 | − | 0.442077i | \(-0.145758\pi\) | ||||
0.896977 | + | 0.442077i | \(0.145758\pi\) | |||||||
\(710\) | 39847.1 | 2.10624 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 37902.1 | 1.99500 | ||||||||
\(713\) | 11441.7 | 0.600976 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15473.3 | 0.807632 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −41716.6 | −2.16831 | ||||||||
\(719\) | −7082.45 | −0.367358 | −0.183679 | − | 0.982986i | \(-0.558801\pi\) | ||||
−0.183679 | + | 0.982986i | \(0.558801\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5891.62 | 0.304321 | ||||||||
\(722\) | −12139.2 | −0.625725 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3527.22 | 0.181061 | ||||||||
\(725\) | −17003.5 | −0.871027 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29511.0 | 1.50551 | 0.752754 | − | 0.658302i | \(-0.228725\pi\) | ||||
0.752754 | + | 0.658302i | \(0.228725\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 31212.2 | 1.58249 | ||||||||
\(731\) | 25883.0 | 1.30960 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19353.4 | −0.975217 | −0.487608 | − | 0.873062i | \(-0.662131\pi\) | ||||
−0.487608 | + | 0.873062i | \(0.662131\pi\) | |||||||
\(734\) | −11188.3 | −0.562625 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1260.25 | −0.0631162 | ||||||||
\(737\) | 38472.2 | 1.92285 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35578.3 | −1.77100 | −0.885500 | − | 0.464639i | \(-0.846184\pi\) | ||||
−0.885500 | + | 0.464639i | \(0.846184\pi\) | |||||||
\(740\) | 43328.3 | 2.15241 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 49065.9 | 2.42758 | ||||||||
\(743\) | 12875.1 | 0.635722 | 0.317861 | − | 0.948137i | \(-0.397036\pi\) | ||||
0.317861 | + | 0.948137i | \(0.397036\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 366.789 | 0.0180377 | ||||||||
\(746\) | 43543.1 | 2.13703 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 45977.5 | 2.24747 | ||||||||
\(749\) | 20294.8 | 0.990061 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37817.4 | −1.83752 | −0.918758 | − | 0.394821i | \(-0.870807\pi\) | ||||
−0.918758 | + | 0.394821i | \(0.870807\pi\) | |||||||
\(752\) | 3358.11 | 0.162843 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6660.93 | −0.321081 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6185.73 | 0.296994 | 0.148497 | − | 0.988913i | \(-0.452557\pi\) | ||||
0.148497 | + | 0.988913i | \(0.452557\pi\) | |||||||
\(758\) | 22482.4 | 1.07731 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −53181.8 | −2.53830 | ||||||||
\(761\) | −15728.3 | −0.749213 | −0.374607 | − | 0.927184i | \(-0.622222\pi\) | ||||
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −51173.1 | −2.42803 | ||||||||
\(764\) | 35354.5 | 1.67419 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10349.4 | −0.488169 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8203.97 | −0.384711 | −0.192356 | − | 0.981325i | \(-0.561613\pi\) | ||||
−0.192356 | + | 0.981325i | \(0.561613\pi\) | |||||||
\(770\) | −128651. | −6.02110 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −321.564 | −0.0149914 | ||||||||
\(773\) | −3418.73 | −0.159073 | −0.0795363 | − | 0.996832i | \(-0.525344\pi\) | ||||
−0.0795363 | + | 0.996832i | \(0.525344\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25920.7 | −1.20142 | ||||||||
\(776\) | −9670.43 | −0.447356 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28838.1 | 1.32892 | ||||||||
\(779\) | −5103.95 | −0.234747 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33102.8 | 1.51666 | ||||||||
\(782\) | 10120.5 | 0.462796 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 29388.7 | 1.33877 | ||||||||
\(785\) | 8141.42 | 0.370165 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26092.8 | −1.18184 | −0.590921 | − | 0.806730i | \(-0.701235\pi\) | ||||
−0.590921 | + | 0.806730i | \(0.701235\pi\) | |||||||
\(788\) | −1134.63 | −0.0512937 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 72167.4 | 3.25013 | ||||||||
\(791\) | −60285.1 | −2.70985 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −56890.2 | −2.54277 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −56178.1 | −2.50148 | ||||||||
\(797\) | −18636.4 | −0.828275 | −0.414138 | − | 0.910214i | \(-0.635917\pi\) | ||||
−0.414138 | + | 0.910214i | \(0.635917\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3009.40 | 0.133248 | ||||||||
\(800\) | 2855.04 | 0.126176 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22350.8 | −0.984083 | ||||||||
\(803\) | 25929.4 | 1.13951 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18722.3 | −0.819721 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10729.7 | 0.467164 | ||||||||
\(809\) | −9074.08 | −0.394348 | −0.197174 | − | 0.980368i | \(-0.563176\pi\) | ||||
−0.197174 | + | 0.980368i | \(0.563176\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20112.2 | 0.870818 | 0.435409 | − | 0.900233i | \(-0.356604\pi\) | ||||
0.435409 | + | 0.900233i | \(0.356604\pi\) | |||||||
\(812\) | 81860.8 | 3.53787 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 54443.7 | 2.34429 | ||||||||
\(815\) | 2826.01 | 0.121461 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −51022.7 | −2.18489 | ||||||||
\(818\) | 2644.29 | 0.113026 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12247.4 | −0.521583 | ||||||||
\(821\) | 29190.8 | 1.24089 | 0.620443 | − | 0.784252i | \(-0.286953\pi\) | ||||
0.620443 | + | 0.784252i | \(0.286953\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27556.8 | 1.16716 | 0.583579 | − | 0.812056i | \(-0.301652\pi\) | ||||
0.583579 | + | 0.812056i | \(0.301652\pi\) | |||||||
\(824\) | 7343.44 | 0.310462 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 85763.2 | 3.61269 | ||||||||
\(827\) | 16596.0 | 0.697822 | 0.348911 | − | 0.937156i | \(-0.386552\pi\) | ||||
0.348911 | + | 0.937156i | \(0.386552\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20877.6 | 0.874681 | 0.437340 | − | 0.899296i | \(-0.355920\pi\) | ||||
0.437340 | + | 0.899296i | \(0.355920\pi\) | |||||||
\(830\) | 33344.4 | 1.39446 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26336.9 | 1.09546 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12658.1 | 0.524613 | ||||||||
\(836\) | −90634.6 | −3.74960 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 51588.3 | 2.12660 | ||||||||
\(839\) | 31026.1 | 1.27669 | 0.638343 | − | 0.769752i | \(-0.279620\pi\) | ||||
0.638343 | + | 0.769752i | \(0.279620\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6878.38 | 0.282028 | ||||||||
\(842\) | −6822.94 | −0.279257 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5314.17 | −0.216731 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −67398.9 | −2.73418 | ||||||||
\(848\) | 18643.2 | 0.754963 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −22927.4 | −0.925181 | ||||||||
\(851\) | 7923.10 | 0.319154 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24134.3 | 0.968748 | 0.484374 | − | 0.874861i | \(-0.339047\pi\) | ||||
0.484374 | + | 0.874861i | \(0.339047\pi\) | |||||||
\(854\) | −59903.7 | −2.40031 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25295.9 | 1.01004 | ||||||||
\(857\) | 4872.72 | 0.194223 | 0.0971114 | − | 0.995274i | \(-0.469040\pi\) | ||||
0.0971114 | + | 0.995274i | \(0.469040\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17690.2 | 0.702658 | 0.351329 | − | 0.936252i | \(-0.385730\pi\) | ||||
0.351329 | + | 0.936252i | \(0.385730\pi\) | |||||||
\(860\) | −122434. | −4.85460 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6573.98 | −0.259757 | ||||||||
\(863\) | −32855.1 | −1.29595 | −0.647973 | − | 0.761664i | \(-0.724383\pi\) | ||||
−0.647973 | + | 0.761664i | \(0.724383\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39985.2 | −1.57172 | ||||||||
\(866\) | −60566.4 | −2.37659 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 124791. | 4.87983 | ||||||||
\(869\) | 59952.8 | 2.34035 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −63783.2 | −2.47703 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −19950.3 | −0.772114 | ||||||||
\(875\) | −12721.0 | −0.491484 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10874.1 | −0.418691 | −0.209346 | − | 0.977842i | \(-0.567133\pi\) | ||||
−0.209346 | + | 0.977842i | \(0.567133\pi\) | |||||||
\(878\) | −20421.6 | −0.784960 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −48882.4 | −1.87253 | ||||||||
\(881\) | −7130.10 | −0.272667 | −0.136333 | − | 0.990663i | \(-0.543532\pi\) | ||||
−0.136333 | + | 0.990663i | \(0.543532\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12029.0 | 0.458446 | 0.229223 | − | 0.973374i | \(-0.426381\pi\) | ||||
0.229223 | + | 0.973374i | \(0.426381\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −39837.1 | −1.51056 | ||||||||
\(887\) | 40837.9 | 1.54589 | 0.772944 | − | 0.634474i | \(-0.218783\pi\) | ||||
0.772944 | + | 0.634474i | \(0.218783\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31861.0 | 1.20201 | ||||||||
\(890\) | −74082.7 | −2.79018 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −30642.1 | −1.15019 | ||||||||
\(893\) | −5932.37 | −0.222306 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14742.6 | −0.550605 | ||||||||
\(896\) | −76875.2 | −2.86632 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3121.52 | 0.115998 | ||||||||
\(899\) | 47665.0 | 1.76832 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16707.2 | 0.617756 | ||||||||
\(902\) | −15389.3 | −0.568081 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −75140.7 | −2.76454 | ||||||||
\(905\) | −3360.66 | −0.123439 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19247.0 | −0.704616 | −0.352308 | − | 0.935884i | \(-0.614603\pi\) | ||||
−0.352308 | + | 0.935884i | \(0.614603\pi\) | |||||||
\(908\) | −9533.04 | −0.348420 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11860.9 | 0.431359 | 0.215680 | − | 0.976464i | \(-0.430803\pi\) | ||||
0.215680 | + | 0.976464i | \(0.430803\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27700.8 | 1.00412 | ||||||||
\(914\) | −9357.25 | −0.338633 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −68008.3 | −2.45312 | ||||||||
\(917\) | 58402.8 | 2.10320 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21211.9 | −0.761390 | −0.380695 | − | 0.924701i | \(-0.624315\pi\) | ||||
−0.380695 | + | 0.924701i | \(0.624315\pi\) | |||||||
\(920\) | −23335.9 | −0.836263 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 46930.8 | 1.67634 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17949.4 | −0.638025 | ||||||||
\(926\) | 58432.4 | 2.07366 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5250.07 | −0.185713 | ||||||||
\(929\) | 37450.9 | 1.32263 | 0.661316 | − | 0.750108i | \(-0.269998\pi\) | ||||
0.661316 | + | 0.750108i | \(0.269998\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −51917.5 | −1.82763 | ||||||||
\(932\) | −43335.2 | −1.52306 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12005.9 | −0.420605 | ||||||||
\(935\) | −43806.3 | −1.53221 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45853.2 | −1.59868 | −0.799338 | − | 0.600882i | \(-0.794816\pi\) | ||||
−0.799338 | + | 0.600882i | \(0.794816\pi\) | |||||||
\(938\) | 92362.2 | 3.21507 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −14235.3 | −0.493940 | ||||||||
\(941\) | −14680.3 | −0.508569 | −0.254285 | − | 0.967129i | \(-0.581840\pi\) | ||||
−0.254285 | + | 0.967129i | \(0.581840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2239.59 | −0.0773393 | ||||||||
\(944\) | 32586.7 | 1.12353 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −153843. | −5.28738 | ||||||||
\(947\) | −34542.6 | −1.18531 | −0.592653 | − | 0.805458i | \(-0.701919\pi\) | ||||
−0.592653 | + | 0.805458i | \(0.701919\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 45196.4 | 1.54354 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 53806.0 | 1.83179 | ||||||||
\(953\) | 44993.2 | 1.52935 | 0.764677 | − | 0.644414i | \(-0.222899\pi\) | ||||
0.764677 | + | 0.644414i | \(0.222899\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33684.9 | −1.14138 | ||||||||
\(956\) | −42770.1 | −1.44695 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27239.0 | 0.918636 | ||||||||
\(959\) | −10.2784 | −0.000346096 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 42871.1 | 1.43906 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 27066.2 | 0.904297 | ||||||||
\(965\) | 306.379 | 0.0102204 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38006.9 | −1.26393 | −0.631964 | − | 0.774997i | \(-0.717751\pi\) | ||||
−0.631964 | + | 0.774997i | \(0.717751\pi\) | |||||||
\(968\) | −84007.4 | −2.78936 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 18901.6 | 0.625665 | ||||||||
\(971\) | −29954.2 | −0.989987 | −0.494993 | − | 0.868897i | \(-0.664829\pi\) | ||||
−0.494993 | + | 0.868897i | \(0.664829\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 55263.8 | 1.82084 | ||||||||
\(974\) | 3782.94 | 0.124449 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22761.1 | −0.746481 | ||||||||
\(977\) | −43605.7 | −1.42791 | −0.713957 | − | 0.700190i | \(-0.753099\pi\) | ||||
−0.713957 | + | 0.700190i | \(0.753099\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −61544.0 | −2.00915 | ||||||||
\(980\) | −124581. | −4.06080 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 45365.4 | 1.47420 | ||||||||
\(983\) | −45624.8 | −1.48037 | −0.740185 | − | 0.672403i | \(-0.765262\pi\) | ||||
−0.740185 | + | 0.672403i | \(0.765262\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1081.05 | 0.0349696 | ||||||||
\(986\) | 42160.7 | 1.36173 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22388.5 | −0.719830 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34882.4 | 1.11814 | 0.559069 | − | 0.829121i | \(-0.311159\pi\) | ||||
0.559069 | + | 0.829121i | \(0.311159\pi\) | |||||||
\(992\) | −8003.38 | −0.256157 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 79471.6 | 2.53590 | ||||||||
\(995\) | 53525.3 | 1.70539 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18448.4 | −0.586024 | −0.293012 | − | 0.956109i | \(-0.594658\pi\) | ||||
−0.293012 | + | 0.956109i | \(0.594658\pi\) | |||||||
\(998\) | −80730.7 | −2.56061 | ||||||||
\(999\) | 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 | 1521.4.a.bm.1.1 | ✓ | 18 | |
3.2 | odd | 2 | inner | 1521.4.a.bm.1.18 | yes | 18 | |
13.12 | even | 2 | 1521.4.a.bn.1.18 | yes | 18 | ||
39.38 | odd | 2 | 1521.4.a.bn.1.1 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1521.4.a.bm.1.1 | ✓ | 18 | 1.1 | even | 1 | trivial | |
1521.4.a.bm.1.18 | yes | 18 | 3.2 | odd | 2 | inner | |
1521.4.a.bn.1.1 | yes | 18 | 39.38 | odd | 2 | ||
1521.4.a.bn.1.18 | yes | 18 | 13.12 | even | 2 |