Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, 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("225.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.70156 | −0.601593 | −0.300797 | − | 0.953688i | \(-0.597253\pi\) | ||||
−0.300797 | + | 0.953688i | \(0.597253\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.10469 | −0.638086 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −22.2094 | −1.19919 | −0.599597 | − | 0.800302i | \(-0.704672\pi\) | ||||
−0.599597 | + | 0.800302i | \(0.704672\pi\) | |||||||
\(8\) | 22.2984 | 0.985461 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.79063 | 0.0490813 | 0.0245407 | − | 0.999699i | \(-0.492188\pi\) | ||||
0.0245407 | + | 0.999699i | \(0.492188\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −58.2094 | −1.24188 | −0.620938 | − | 0.783860i | \(-0.713248\pi\) | ||||
−0.620938 | + | 0.783860i | \(0.713248\pi\) | |||||||
\(14\) | 37.7906 | 0.721426 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.89531 | 0.0452393 | ||||||||
\(17\) | 18.9844 | 0.270846 | 0.135423 | − | 0.990788i | \(-0.456761\pi\) | ||||
0.135423 | + | 0.990788i | \(0.456761\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 104.837 | 1.26586 | 0.632931 | − | 0.774208i | \(-0.281852\pi\) | ||||
0.632931 | + | 0.774208i | \(0.281852\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.04686 | −0.0295270 | ||||||||
\(23\) | −49.6125 | −0.449779 | −0.224890 | − | 0.974384i | \(-0.572202\pi\) | ||||
−0.224890 | + | 0.974384i | \(0.572202\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 99.0469 | 0.747103 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 113.372 | 0.765188 | ||||||||
\(29\) | 293.466 | 1.87914 | 0.939572 | − | 0.342350i | \(-0.111223\pi\) | ||||
0.939572 | + | 0.342350i | \(0.111223\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 64.4187 | 0.373224 | 0.186612 | − | 0.982434i | \(-0.440249\pi\) | ||||
0.186612 | + | 0.982434i | \(0.440249\pi\) | |||||||
\(32\) | −183.314 | −1.01268 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −32.3031 | −0.162939 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 19.8844 | 0.0883505 | 0.0441752 | − | 0.999024i | \(-0.485934\pi\) | ||||
0.0441752 | + | 0.999024i | \(0.485934\pi\) | |||||||
\(38\) | −178.388 | −0.761534 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 165.581 | 0.630718 | 0.315359 | − | 0.948972i | \(-0.397875\pi\) | ||||
0.315359 | + | 0.948972i | \(0.397875\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 247.350 | 0.877221 | 0.438611 | − | 0.898677i | \(-0.355471\pi\) | ||||
0.438611 | + | 0.898677i | \(0.355471\pi\) | |||||||
\(44\) | −9.14059 | −0.0313181 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 84.4187 | 0.270584 | ||||||||
\(47\) | 384.544 | 1.19344 | 0.596718 | − | 0.802451i | \(-0.296471\pi\) | ||||
0.596718 | + | 0.802451i | \(0.296471\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 150.256 | 0.438065 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 297.141 | 0.792423 | ||||||||
\(53\) | 463.528 | 1.20133 | 0.600665 | − | 0.799501i | \(-0.294903\pi\) | ||||
0.600665 | + | 0.799501i | \(0.294903\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −495.234 | −1.18176 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −499.350 | −1.13048 | ||||||||
\(59\) | 73.7906 | 0.162826 | 0.0814129 | − | 0.996680i | \(-0.474057\pi\) | ||||
0.0814129 | + | 0.996680i | \(0.474057\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −137.350 | −0.288293 | −0.144146 | − | 0.989556i | \(-0.546044\pi\) | ||||
−0.144146 | + | 0.989556i | \(0.546044\pi\) | |||||||
\(62\) | −109.612 | −0.224529 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 288.758 | 0.563980 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −173.906 | −0.317105 | −0.158552 | − | 0.987351i | \(-0.550683\pi\) | ||||
−0.158552 | + | 0.987351i | \(0.550683\pi\) | |||||||
\(68\) | −96.9093 | −0.172823 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 594.281 | 0.993355 | 0.496677 | − | 0.867935i | \(-0.334553\pi\) | ||||
0.496677 | + | 0.867935i | \(0.334553\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −320.231 | −0.513428 | −0.256714 | − | 0.966487i | \(-0.582640\pi\) | ||||
−0.256714 | + | 0.966487i | \(0.582640\pi\) | |||||||
\(74\) | −33.8345 | −0.0531510 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −535.163 | −0.807728 | ||||||||
\(77\) | −39.7687 | −0.0588580 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −770.469 | −1.09727 | −0.548636 | − | 0.836061i | \(-0.684853\pi\) | ||||
−0.548636 | + | 0.836061i | \(0.684853\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −281.747 | −0.379436 | ||||||||
\(83\) | 173.925 | 0.230009 | 0.115004 | − | 0.993365i | \(-0.463312\pi\) | ||||
0.115004 | + | 0.993365i | \(0.463312\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −420.881 | −0.527730 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 39.9282 | 0.0483677 | ||||||||
\(89\) | −1019.02 | −1.21367 | −0.606834 | − | 0.794829i | \(-0.707561\pi\) | ||||
−0.606834 | + | 0.794829i | \(0.707561\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1292.79 | 1.48925 | ||||||||
\(92\) | 253.256 | 0.286998 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −654.325 | −0.717962 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −384.375 | −0.402344 | −0.201172 | − | 0.979556i | \(-0.564475\pi\) | ||||
−0.201172 | + | 0.979556i | \(0.564475\pi\) | |||||||
\(98\) | −255.670 | −0.263537 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −34.4906 | −0.0339796 | −0.0169898 | − | 0.999856i | \(-0.505408\pi\) | ||||
−0.0169898 | + | 0.999856i | \(0.505408\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1756.30 | 1.68013 | 0.840066 | − | 0.542484i | \(-0.182516\pi\) | ||||
0.840066 | + | 0.542484i | \(0.182516\pi\) | |||||||
\(104\) | −1297.98 | −1.22382 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −788.722 | −0.722712 | ||||||||
\(107\) | −1361.74 | −1.23032 | −0.615159 | − | 0.788403i | \(-0.710908\pi\) | ||||
−0.615159 | + | 0.788403i | \(0.710908\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 321.119 | 0.282180 | 0.141090 | − | 0.989997i | \(-0.454939\pi\) | ||||
0.141090 | + | 0.989997i | \(0.454939\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −64.3031 | −0.0542506 | ||||||||
\(113\) | −1582.25 | −1.31721 | −0.658607 | − | 0.752487i | \(-0.728854\pi\) | ||||
−0.658607 | + | 0.752487i | \(0.728854\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1498.05 | −1.19906 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −125.559 | −0.0979549 | ||||||||
\(119\) | −421.631 | −0.324797 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1327.79 | −0.997591 | ||||||||
\(122\) | 233.709 | 0.173435 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −328.837 | −0.238149 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1197.14 | 0.836449 | 0.418225 | − | 0.908344i | \(-0.362652\pi\) | ||||
0.418225 | + | 0.908344i | \(0.362652\pi\) | |||||||
\(128\) | 975.173 | 0.673390 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 321.647 | 0.214522 | 0.107261 | − | 0.994231i | \(-0.465792\pi\) | ||||
0.107261 | + | 0.994231i | \(0.465792\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2328.37 | −1.51801 | ||||||||
\(134\) | 295.912 | 0.190768 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 423.322 | 0.266909 | ||||||||
\(137\) | 354.291 | 0.220942 | 0.110471 | − | 0.993879i | \(-0.464764\pi\) | ||||
0.110471 | + | 0.993879i | \(0.464764\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 77.2562 | 0.0471424 | 0.0235712 | − | 0.999722i | \(-0.492496\pi\) | ||||
0.0235712 | + | 0.999722i | \(0.492496\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1011.21 | −0.597595 | ||||||||
\(143\) | −104.231 | −0.0609529 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 544.893 | 0.308875 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −101.503 | −0.0563752 | ||||||||
\(149\) | 1705.38 | 0.937651 | 0.468826 | − | 0.883291i | \(-0.344677\pi\) | ||||
0.468826 | + | 0.883291i | \(0.344677\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 758.281 | 0.408663 | 0.204331 | − | 0.978902i | \(-0.434498\pi\) | ||||
0.204331 | + | 0.978902i | \(0.434498\pi\) | |||||||
\(152\) | 2337.71 | 1.24746 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 67.6689 | 0.0354086 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1769.05 | 0.899273 | 0.449636 | − | 0.893212i | \(-0.351554\pi\) | ||||
0.449636 | + | 0.893212i | \(0.351554\pi\) | |||||||
\(158\) | 1311.00 | 0.660111 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1101.86 | 0.539372 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 881.719 | 0.423690 | 0.211845 | − | 0.977303i | \(-0.432053\pi\) | ||||
0.211845 | + | 0.977303i | \(0.432053\pi\) | |||||||
\(164\) | −845.240 | −0.402452 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −295.944 | −0.138372 | ||||||||
\(167\) | −216.900 | −0.100504 | −0.0502522 | − | 0.998737i | \(-0.516003\pi\) | ||||
−0.0502522 | + | 0.998737i | \(0.516003\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1191.33 | 0.542254 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1262.64 | −0.559742 | ||||||||
\(173\) | 4125.91 | 1.81322 | 0.906610 | − | 0.421970i | \(-0.138661\pi\) | ||||
0.906610 | + | 0.421970i | \(0.138661\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.18443 | 0.00222040 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1733.93 | 0.730134 | ||||||||
\(179\) | 3213.14 | 1.34168 | 0.670842 | − | 0.741600i | \(-0.265933\pi\) | ||||
0.670842 | + | 0.741600i | \(0.265933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3394.42 | 1.39395 | 0.696976 | − | 0.717095i | \(-0.254529\pi\) | ||||
0.696976 | + | 0.717095i | \(0.254529\pi\) | |||||||
\(182\) | −2199.77 | −0.895921 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1106.28 | −0.443240 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 33.9939 | 0.0132935 | ||||||||
\(188\) | −1962.98 | −0.761514 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3467.49 | 1.31361 | 0.656804 | − | 0.754062i | \(-0.271908\pi\) | ||||
0.656804 | + | 0.754062i | \(0.271908\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1792.14 | −0.668401 | −0.334200 | − | 0.942502i | \(-0.608466\pi\) | ||||
−0.334200 | + | 0.942502i | \(0.608466\pi\) | |||||||
\(194\) | 654.038 | 0.242047 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −767.011 | −0.279523 | ||||||||
\(197\) | 1678.19 | 0.606935 | 0.303467 | − | 0.952842i | \(-0.401856\pi\) | ||||
0.303467 | + | 0.952842i | \(0.401856\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3108.23 | 1.10722 | 0.553610 | − | 0.832776i | \(-0.313250\pi\) | ||||
0.553610 | + | 0.832776i | \(0.313250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 58.6878 | 0.0204419 | ||||||||
\(203\) | −6517.69 | −2.25346 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2988.46 | −1.01076 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −168.534 | −0.0561815 | ||||||||
\(209\) | 187.725 | 0.0621301 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4473.27 | −1.45949 | −0.729745 | − | 0.683719i | \(-0.760361\pi\) | ||||
−0.729745 | + | 0.683719i | \(0.760361\pi\) | |||||||
\(212\) | −2366.17 | −0.766551 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2317.08 | 0.740151 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1430.70 | −0.447568 | ||||||||
\(218\) | −546.403 | −0.169757 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1105.07 | −0.336357 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1753.42 | 0.526535 | 0.263268 | − | 0.964723i | \(-0.415200\pi\) | ||||
0.263268 | + | 0.964723i | \(0.415200\pi\) | |||||||
\(224\) | 4071.29 | 1.21440 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2692.29 | 0.792427 | ||||||||
\(227\) | −936.900 | −0.273939 | −0.136970 | − | 0.990575i | \(-0.543736\pi\) | ||||
−0.136970 | + | 0.990575i | \(0.543736\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2582.06 | −0.745096 | −0.372548 | − | 0.928013i | \(-0.621516\pi\) | ||||
−0.372548 | + | 0.928013i | \(0.621516\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6543.82 | 1.85182 | ||||||||
\(233\) | 2295.01 | 0.645284 | 0.322642 | − | 0.946521i | \(-0.395429\pi\) | ||||
0.322642 | + | 0.946521i | \(0.395429\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −376.678 | −0.103897 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 717.432 | 0.195396 | ||||||||
\(239\) | 2294.01 | 0.620866 | 0.310433 | − | 0.950595i | \(-0.399526\pi\) | ||||
0.310433 | + | 0.950595i | \(0.399526\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 382.287 | 0.102180 | 0.0510898 | − | 0.998694i | \(-0.483731\pi\) | ||||
0.0510898 | + | 0.998694i | \(0.483731\pi\) | |||||||
\(242\) | 2259.32 | 0.600144 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 701.128 | 0.183956 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6102.52 | −1.57204 | ||||||||
\(248\) | 1436.44 | 0.367798 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2259.98 | 0.568322 | 0.284161 | − | 0.958777i | \(-0.408285\pi\) | ||||
0.284161 | + | 0.958777i | \(0.408285\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −88.8375 | −0.0220758 | ||||||||
\(254\) | −2037.01 | −0.503202 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3969.38 | −0.969087 | ||||||||
\(257\) | −92.7843 | −0.0225203 | −0.0112602 | − | 0.999937i | \(-0.503584\pi\) | ||||
−0.0112602 | + | 0.999937i | \(0.503584\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −441.619 | −0.105949 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −547.302 | −0.129055 | ||||||||
\(263\) | −568.312 | −0.133246 | −0.0666229 | − | 0.997778i | \(-0.521222\pi\) | ||||
−0.0666229 | + | 0.997778i | \(0.521222\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3961.87 | 0.913226 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 887.737 | 0.202340 | ||||||||
\(269\) | −7582.41 | −1.71862 | −0.859309 | − | 0.511458i | \(-0.829106\pi\) | ||||
−0.859309 | + | 0.511458i | \(0.829106\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7943.69 | 1.78061 | 0.890304 | − | 0.455366i | \(-0.150492\pi\) | ||||
0.890304 | + | 0.455366i | \(0.150492\pi\) | |||||||
\(272\) | 54.9657 | 0.0122529 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −602.847 | −0.132917 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6823.00 | −1.47998 | −0.739990 | − | 0.672618i | \(-0.765170\pi\) | ||||
−0.739990 | + | 0.672618i | \(0.765170\pi\) | |||||||
\(278\) | −131.456 | −0.0283605 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3315.86 | −0.703942 | −0.351971 | − | 0.936011i | \(-0.614488\pi\) | ||||
−0.351971 | + | 0.936011i | \(0.614488\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6602.76 | −1.38690 | −0.693451 | − | 0.720504i | \(-0.743910\pi\) | ||||
−0.693451 | + | 0.720504i | \(0.743910\pi\) | |||||||
\(284\) | −3033.62 | −0.633846 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 177.356 | 0.0366688 | ||||||||
\(287\) | −3677.46 | −0.756353 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4552.59 | −0.926642 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1634.68 | 0.327611 | ||||||||
\(293\) | 5814.14 | 1.15927 | 0.579634 | − | 0.814877i | \(-0.303195\pi\) | ||||
0.579634 | + | 0.814877i | \(0.303195\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 443.390 | 0.0870660 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2901.81 | −0.564084 | ||||||||
\(299\) | 2887.91 | 0.558570 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5493.49 | −1.05196 | ||||||||
\(302\) | −1290.26 | −0.245849 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 303.537 | 0.0572667 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8124.86 | 1.51046 | 0.755229 | − | 0.655462i | \(-0.227526\pi\) | ||||
0.755229 | + | 0.655462i | \(0.227526\pi\) | |||||||
\(308\) | 203.007 | 0.0375564 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7336.26 | −1.33762 | −0.668812 | − | 0.743432i | \(-0.733197\pi\) | ||||
−0.668812 | + | 0.743432i | \(0.733197\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2202.66 | 0.397768 | 0.198884 | − | 0.980023i | \(-0.436268\pi\) | ||||
0.198884 | + | 0.980023i | \(0.436268\pi\) | |||||||
\(314\) | −3010.15 | −0.540996 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3933.00 | 0.700154 | ||||||||
\(317\) | 10008.9 | 1.77336 | 0.886679 | − | 0.462386i | \(-0.153007\pi\) | ||||
0.886679 | + | 0.462386i | \(0.153007\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 525.488 | 0.0922309 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1874.89 | −0.324483 | ||||||||
\(323\) | 1990.27 | 0.342854 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1500.30 | −0.254889 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3692.20 | 0.621548 | ||||||||
\(329\) | −8540.47 | −1.43116 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8695.94 | −1.44402 | −0.722012 | − | 0.691881i | \(-0.756782\pi\) | ||||
−0.722012 | + | 0.691881i | \(0.756782\pi\) | |||||||
\(332\) | −887.832 | −0.146765 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 369.069 | 0.0604627 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7400.61 | 1.19625 | 0.598126 | − | 0.801402i | \(-0.295912\pi\) | ||||
0.598126 | + | 0.801402i | \(0.295912\pi\) | |||||||
\(338\) | −2027.12 | −0.326216 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 115.350 | 0.0183183 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4280.72 | 0.673869 | ||||||||
\(344\) | 5515.52 | 0.864467 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7020.49 | −1.09082 | ||||||||
\(347\) | 7841.44 | 1.21311 | 0.606557 | − | 0.795040i | \(-0.292550\pi\) | ||||
0.606557 | + | 0.795040i | \(0.292550\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4961.26 | −0.760946 | −0.380473 | − | 0.924792i | \(-0.624239\pi\) | ||||
−0.380473 | + | 0.924792i | \(0.624239\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −328.247 | −0.0497035 | ||||||||
\(353\) | −12163.0 | −1.83392 | −0.916959 | − | 0.398981i | \(-0.869364\pi\) | ||||
−0.916959 | + | 0.398981i | \(0.869364\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5201.80 | 0.774424 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5467.36 | −0.807148 | ||||||||
\(359\) | −5193.79 | −0.763559 | −0.381779 | − | 0.924253i | \(-0.624689\pi\) | ||||
−0.381779 | + | 0.924253i | \(0.624689\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4131.90 | 0.602406 | ||||||||
\(362\) | −5775.81 | −0.838591 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6599.31 | −0.950268 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6086.09 | 0.865644 | 0.432822 | − | 0.901479i | \(-0.357518\pi\) | ||||
0.432822 | + | 0.901479i | \(0.357518\pi\) | |||||||
\(368\) | −143.644 | −0.0203477 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10294.7 | −1.44063 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10581.9 | 1.46893 | 0.734466 | − | 0.678646i | \(-0.237433\pi\) | ||||
0.734466 | + | 0.678646i | \(0.237433\pi\) | |||||||
\(374\) | −57.8428 | −0.00799727 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8574.72 | 1.17608 | ||||||||
\(377\) | −17082.4 | −2.33366 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11655.2 | 1.57964 | 0.789822 | − | 0.613336i | \(-0.210173\pi\) | ||||
0.789822 | + | 0.613336i | \(0.210173\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5900.16 | −0.790257 | ||||||||
\(383\) | 6364.97 | 0.849177 | 0.424588 | − | 0.905387i | \(-0.360419\pi\) | ||||
0.424588 | + | 0.905387i | \(0.360419\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3049.44 | 0.402105 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1962.11 | 0.256730 | ||||||||
\(389\) | −6134.33 | −0.799545 | −0.399773 | − | 0.916614i | \(-0.630911\pi\) | ||||
−0.399773 | + | 0.916614i | \(0.630911\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −941.862 | −0.121821 | ||||||||
\(392\) | 3350.48 | 0.431696 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2855.55 | −0.365128 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9746.46 | −1.23214 | −0.616072 | − | 0.787690i | \(-0.711277\pi\) | ||||
−0.616072 | + | 0.787690i | \(0.711277\pi\) | |||||||
\(398\) | −5288.85 | −0.666096 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1306.44 | 0.162695 | 0.0813474 | − | 0.996686i | \(-0.474078\pi\) | ||||
0.0813474 | + | 0.996686i | \(0.474078\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3749.77 | −0.463498 | ||||||||
\(404\) | 176.063 | 0.0216819 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11090.2 | 1.35566 | ||||||||
\(407\) | 35.6055 | 0.00433636 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3876.93 | −0.468709 | −0.234354 | − | 0.972151i | \(-0.575298\pi\) | ||||
−0.234354 | + | 0.972151i | \(0.575298\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8965.38 | −1.07207 | ||||||||
\(413\) | −1638.84 | −0.195260 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10670.6 | 1.25762 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −319.426 | −0.0373771 | ||||||||
\(419\) | 16022.5 | 1.86814 | 0.934071 | − | 0.357088i | \(-0.116230\pi\) | ||||
0.934071 | + | 0.357088i | \(0.116230\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8119.73 | −0.939980 | −0.469990 | − | 0.882672i | \(-0.655742\pi\) | ||||
−0.469990 | + | 0.882672i | \(0.655742\pi\) | |||||||
\(422\) | 7611.54 | 0.878019 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10336.0 | 1.18386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3050.46 | 0.345719 | ||||||||
\(428\) | 6951.24 | 0.785049 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5713.99 | 0.638592 | 0.319296 | − | 0.947655i | \(-0.396554\pi\) | ||||
0.319296 | + | 0.947655i | \(0.396554\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6251.34 | −0.693811 | −0.346906 | − | 0.937900i | \(-0.612768\pi\) | ||||
−0.346906 | + | 0.937900i | \(0.612768\pi\) | |||||||
\(434\) | 2434.42 | 0.269254 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1639.21 | −0.180055 | ||||||||
\(437\) | −5201.25 | −0.569358 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4230.97 | −0.459984 | −0.229992 | − | 0.973192i | \(-0.573870\pi\) | ||||
−0.229992 | + | 0.973192i | \(0.573870\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1880.34 | 0.202350 | ||||||||
\(443\) | 6314.29 | 0.677203 | 0.338601 | − | 0.940930i | \(-0.390046\pi\) | ||||
0.338601 | + | 0.940930i | \(0.390046\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2983.55 | −0.316760 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6413.13 | −0.676321 | ||||||||
\(449\) | 9349.71 | 0.982717 | 0.491358 | − | 0.870957i | \(-0.336501\pi\) | ||||
0.491358 | + | 0.870957i | \(0.336501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 296.494 | 0.0309565 | ||||||||
\(452\) | 8076.87 | 0.840496 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1594.19 | 0.164800 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9547.46 | 0.977268 | 0.488634 | − | 0.872489i | \(-0.337495\pi\) | ||||
0.488634 | + | 0.872489i | \(0.337495\pi\) | |||||||
\(458\) | 4393.53 | 0.448245 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6237.23 | −0.630145 | −0.315073 | − | 0.949068i | \(-0.602029\pi\) | ||||
−0.315073 | + | 0.949068i | \(0.602029\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6469.98 | −0.649428 | −0.324714 | − | 0.945812i | \(-0.605268\pi\) | ||||
−0.324714 | + | 0.945812i | \(0.605268\pi\) | |||||||
\(464\) | 849.675 | 0.0850111 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3905.10 | −0.388198 | ||||||||
\(467\) | 7206.64 | 0.714097 | 0.357049 | − | 0.934086i | \(-0.383783\pi\) | ||||
0.357049 | + | 0.934086i | \(0.383783\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3862.35 | 0.380270 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1645.42 | 0.160458 | ||||||||
\(473\) | 442.912 | 0.0430552 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2152.29 | 0.207248 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3903.39 | −0.373509 | ||||||||
\(479\) | 10851.8 | 1.03514 | 0.517571 | − | 0.855640i | \(-0.326836\pi\) | ||||
0.517571 | + | 0.855640i | \(0.326836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1157.46 | −0.109720 | ||||||||
\(482\) | −650.485 | −0.0614705 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6777.97 | 0.636549 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12757.1 | −1.18702 | −0.593510 | − | 0.804827i | \(-0.702258\pi\) | ||||
−0.593510 | + | 0.804827i | \(0.702258\pi\) | |||||||
\(488\) | −3062.69 | −0.284101 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7016.52 | 0.644911 | 0.322455 | − | 0.946585i | \(-0.395492\pi\) | ||||
0.322455 | + | 0.946585i | \(0.395492\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5571.26 | 0.508960 | ||||||||
\(494\) | 10383.8 | 0.945729 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 186.512 | 0.0168844 | ||||||||
\(497\) | −13198.6 | −1.19122 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11372.3 | 1.02023 | 0.510113 | − | 0.860107i | \(-0.329604\pi\) | ||||
0.510113 | + | 0.860107i | \(0.329604\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3845.50 | −0.341899 | ||||||||
\(503\) | −5587.37 | −0.495285 | −0.247643 | − | 0.968851i | \(-0.579656\pi\) | ||||
−0.247643 | + | 0.968851i | \(0.579656\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 151.163 | 0.0132806 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6111.03 | −0.533726 | ||||||||
\(509\) | −16256.7 | −1.41565 | −0.707825 | − | 0.706388i | \(-0.750324\pi\) | ||||
−0.707825 | + | 0.706388i | \(0.750324\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7112.14 | 0.615699 | ||||||||
\(512\) | −1047.24 | −0.0903943 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 157.878 | 0.0135481 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 688.574 | 0.0585754 | ||||||||
\(518\) | 751.442 | 0.0637384 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19748.4 | −1.66064 | −0.830320 | − | 0.557286i | \(-0.811843\pi\) | ||||
−0.830320 | + | 0.557286i | \(0.811843\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7843.44 | 0.655774 | 0.327887 | − | 0.944717i | \(-0.393663\pi\) | ||||
0.327887 | + | 0.944717i | \(0.393663\pi\) | |||||||
\(524\) | −1641.91 | −0.136884 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 967.019 | 0.0801597 | ||||||||
\(527\) | 1222.95 | 0.101086 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9705.60 | −0.797699 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11885.6 | 0.968622 | ||||||||
\(533\) | −9638.38 | −0.783273 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3877.84 | −0.312495 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12902.0 | 1.03391 | ||||||||
\(539\) | 269.053 | 0.0215008 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7383.29 | 0.586751 | 0.293376 | − | 0.955997i | \(-0.405221\pi\) | ||||
0.293376 | + | 0.955997i | \(0.405221\pi\) | |||||||
\(542\) | −13516.7 | −1.07120 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3480.10 | −0.274280 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3354.90 | 0.262240 | 0.131120 | − | 0.991367i | \(-0.458143\pi\) | ||||
0.131120 | + | 0.991367i | \(0.458143\pi\) | |||||||
\(548\) | −1808.54 | −0.140980 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30766.2 | 2.37874 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17111.6 | 1.31584 | ||||||||
\(554\) | 11609.8 | 0.890346 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −394.369 | −0.0300809 | ||||||||
\(557\) | 20771.8 | 1.58012 | 0.790061 | − | 0.613028i | \(-0.210049\pi\) | ||||
0.790061 | + | 0.613028i | \(0.210049\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14398.1 | −1.08940 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5642.15 | 0.423487 | ||||||||
\(563\) | 7194.86 | 0.538592 | 0.269296 | − | 0.963057i | \(-0.413209\pi\) | ||||
0.269296 | + | 0.963057i | \(0.413209\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11235.0 | 0.834350 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13251.5 | 0.978913 | ||||||||
\(569\) | −11549.5 | −0.850931 | −0.425466 | − | 0.904975i | \(-0.639890\pi\) | ||||
−0.425466 | + | 0.904975i | \(0.639890\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1482.54 | 0.108655 | 0.0543277 | − | 0.998523i | \(-0.482698\pi\) | ||||
0.0543277 | + | 0.998523i | \(0.482698\pi\) | |||||||
\(572\) | 532.068 | 0.0388932 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6257.42 | 0.455017 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15264.0 | 1.10130 | 0.550649 | − | 0.834737i | \(-0.314380\pi\) | ||||
0.550649 | + | 0.834737i | \(0.314380\pi\) | |||||||
\(578\) | 7746.52 | 0.557462 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3862.76 | −0.275825 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 830.006 | 0.0589628 | ||||||||
\(584\) | −7140.66 | −0.505963 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9893.12 | −0.697408 | ||||||||
\(587\) | 1736.89 | 0.122128 | 0.0610639 | − | 0.998134i | \(-0.480551\pi\) | ||||
0.0610639 | + | 0.998134i | \(0.480551\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6753.50 | 0.472450 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 57.5714 | 0.00399691 | ||||||||
\(593\) | −11764.8 | −0.814707 | −0.407353 | − | 0.913271i | \(-0.633548\pi\) | ||||
−0.407353 | + | 0.913271i | \(0.633548\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8705.42 | −0.598302 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4913.96 | −0.336032 | ||||||||
\(599\) | 9451.99 | 0.644737 | 0.322369 | − | 0.946614i | \(-0.395521\pi\) | ||||
0.322369 | + | 0.946614i | \(0.395521\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3131.93 | −0.212569 | −0.106285 | − | 0.994336i | \(-0.533895\pi\) | ||||
−0.106285 | + | 0.994336i | \(0.533895\pi\) | |||||||
\(602\) | 9347.51 | 0.632851 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3870.79 | −0.260762 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22700.8 | −1.51795 | −0.758975 | − | 0.651120i | \(-0.774300\pi\) | ||||
−0.758975 | + | 0.651120i | \(0.774300\pi\) | |||||||
\(608\) | −19218.2 | −1.28191 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22384.0 | −1.48210 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28911.6 | −1.90494 | −0.952471 | − | 0.304629i | \(-0.901468\pi\) | ||||
−0.952471 | + | 0.304629i | \(0.901468\pi\) | |||||||
\(614\) | −13825.0 | −0.908681 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −886.780 | −0.0580023 | ||||||||
\(617\) | −5566.87 | −0.363231 | −0.181616 | − | 0.983370i | \(-0.558133\pi\) | ||||
−0.181616 | + | 0.983370i | \(0.558133\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4150.32 | 0.269492 | 0.134746 | − | 0.990880i | \(-0.456978\pi\) | ||||
0.134746 | + | 0.990880i | \(0.456978\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12483.1 | 0.804705 | ||||||||
\(623\) | 22631.9 | 1.45542 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3747.96 | −0.239295 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9030.46 | −0.573813 | ||||||||
\(629\) | 377.492 | 0.0239294 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4090.09 | −0.258041 | −0.129021 | − | 0.991642i | \(-0.541183\pi\) | ||||
−0.129021 | + | 0.991642i | \(0.541183\pi\) | |||||||
\(632\) | −17180.2 | −1.08132 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17030.7 | −1.06684 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8746.32 | −0.544022 | ||||||||
\(638\) | −894.150 | −0.0554855 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3909.35 | −0.240890 | −0.120445 | − | 0.992720i | \(-0.538432\pi\) | ||||
−0.120445 | + | 0.992720i | \(0.538432\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30539.5 | −1.87303 | −0.936516 | − | 0.350624i | \(-0.885969\pi\) | ||||
−0.936516 | + | 0.350624i | \(0.885969\pi\) | |||||||
\(644\) | −5624.66 | −0.344166 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3386.58 | −0.206259 | ||||||||
\(647\) | −12707.7 | −0.772167 | −0.386083 | − | 0.922464i | \(-0.626172\pi\) | ||||
−0.386083 | + | 0.922464i | \(0.626172\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 132.132 | 0.00799170 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4500.90 | −0.270351 | ||||||||
\(653\) | 12777.6 | 0.765737 | 0.382869 | − | 0.923803i | \(-0.374936\pi\) | ||||
0.382869 | + | 0.923803i | \(0.374936\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 479.410 | 0.0285332 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14532.1 | 0.860976 | ||||||||
\(659\) | −23563.5 | −1.39287 | −0.696435 | − | 0.717620i | \(-0.745232\pi\) | ||||
−0.696435 | + | 0.717620i | \(0.745232\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4361.31 | −0.256634 | −0.128317 | − | 0.991733i | \(-0.540958\pi\) | ||||
−0.128317 | + | 0.991733i | \(0.540958\pi\) | |||||||
\(662\) | 14796.7 | 0.868715 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3878.25 | 0.226665 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14559.6 | −0.845200 | ||||||||
\(668\) | 1107.21 | 0.0641304 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −245.943 | −0.0141498 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8203.52 | 0.469870 | 0.234935 | − | 0.972011i | \(-0.424512\pi\) | ||||
0.234935 | + | 0.972011i | \(0.424512\pi\) | |||||||
\(674\) | −12592.6 | −0.719657 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6081.37 | −0.346004 | ||||||||
\(677\) | 28057.1 | 1.59279 | 0.796397 | − | 0.604774i | \(-0.206737\pi\) | ||||
0.796397 | + | 0.604774i | \(0.206737\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8536.73 | 0.482488 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −196.275 | −0.0110202 | ||||||||
\(683\) | −3344.62 | −0.187377 | −0.0936885 | − | 0.995602i | \(-0.529866\pi\) | ||||
−0.0936885 | + | 0.995602i | \(0.529866\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7283.91 | −0.405395 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 716.156 | 0.0396849 | ||||||||
\(689\) | −26981.7 | −1.49190 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12964.8 | 0.713757 | 0.356879 | − | 0.934151i | \(-0.383841\pi\) | ||||
0.356879 | + | 0.934151i | \(0.383841\pi\) | |||||||
\(692\) | −21061.5 | −1.15699 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13342.7 | −0.729801 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3143.46 | 0.170828 | ||||||||
\(698\) | 8441.90 | 0.457780 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16162.1 | 0.870806 | 0.435403 | − | 0.900236i | \(-0.356606\pi\) | ||||
0.435403 | + | 0.900236i | \(0.356606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2084.63 | 0.111839 | ||||||||
\(704\) | 517.058 | 0.0276809 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20696.2 | 1.10327 | ||||||||
\(707\) | 766.014 | 0.0407481 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14244.4 | −0.754529 | −0.377265 | − | 0.926105i | \(-0.623135\pi\) | ||||
−0.377265 | + | 0.926105i | \(0.623135\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −22722.7 | −1.19602 | ||||||||
\(713\) | −3195.97 | −0.167868 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16402.1 | −0.856109 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8837.55 | 0.459352 | ||||||||
\(719\) | 27638.5 | 1.43358 | 0.716790 | − | 0.697289i | \(-0.245611\pi\) | ||||
0.716790 | + | 0.697289i | \(0.245611\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39006.4 | −2.01480 | ||||||||
\(722\) | −7030.68 | −0.362403 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17327.4 | −0.889460 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2525.52 | 0.128840 | 0.0644199 | − | 0.997923i | \(-0.479480\pi\) | ||||
0.0644199 | + | 0.997923i | \(0.479480\pi\) | |||||||
\(728\) | 28827.3 | 1.46760 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4695.79 | 0.237592 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8400.27 | 0.423289 | 0.211645 | − | 0.977347i | \(-0.432118\pi\) | ||||
0.211645 | + | 0.977347i | \(0.432118\pi\) | |||||||
\(734\) | −10355.9 | −0.520765 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9094.67 | 0.455481 | ||||||||
\(737\) | −311.401 | −0.0155639 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19689.1 | −0.980074 | −0.490037 | − | 0.871702i | \(-0.663017\pi\) | ||||
−0.490037 | + | 0.871702i | \(0.663017\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17517.0 | 0.866671 | ||||||||
\(743\) | −22526.6 | −1.11227 | −0.556137 | − | 0.831091i | \(-0.687717\pi\) | ||||
−0.556137 | + | 0.831091i | \(0.687717\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −18005.8 | −0.883699 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −173.528 | −0.00848239 | ||||||||
\(749\) | 30243.3 | 1.47539 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34691.1 | 1.68562 | 0.842808 | − | 0.538215i | \(-0.180901\pi\) | ||||
0.842808 | + | 0.538215i | \(0.180901\pi\) | |||||||
\(752\) | 1113.37 | 0.0539902 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 29066.8 | 1.40392 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6619.98 | −0.317843 | −0.158922 | − | 0.987291i | \(-0.550802\pi\) | ||||
−0.158922 | + | 0.987291i | \(0.550802\pi\) | |||||||
\(758\) | −19832.0 | −0.950303 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29368.7 | 1.39897 | 0.699483 | − | 0.714649i | \(-0.253414\pi\) | ||||
0.699483 | + | 0.714649i | \(0.253414\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7131.84 | −0.338388 | ||||||||
\(764\) | −17700.5 | −0.838194 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10830.4 | −0.510859 | ||||||||
\(767\) | −4295.31 | −0.202209 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32677.4 | 1.53235 | 0.766174 | − | 0.642633i | \(-0.222158\pi\) | ||||
0.766174 | + | 0.642633i | \(0.222158\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9148.33 | 0.426497 | ||||||||
\(773\) | −28047.5 | −1.30504 | −0.652522 | − | 0.757770i | \(-0.726289\pi\) | ||||
−0.652522 | + | 0.757770i | \(0.726289\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8570.96 | −0.396494 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10438.0 | 0.481001 | ||||||||
\(779\) | 17359.1 | 0.798402 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1064.14 | 0.0487552 | ||||||||
\(782\) | 1602.64 | 0.0732867 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 435.039 | 0.0198177 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22172.1 | 1.00426 | 0.502128 | − | 0.864793i | \(-0.332551\pi\) | ||||
0.502128 | + | 0.864793i | \(0.332551\pi\) | |||||||
\(788\) | −8566.64 | −0.387276 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35140.7 | 1.57960 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7995.06 | 0.358024 | ||||||||
\(794\) | 16584.2 | 0.741249 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15866.5 | −0.706501 | ||||||||
\(797\) | −24170.3 | −1.07422 | −0.537112 | − | 0.843511i | \(-0.680485\pi\) | ||||
−0.537112 | + | 0.843511i | \(0.680485\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7300.32 | 0.323238 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2222.99 | −0.0978761 | ||||||||
\(803\) | −573.415 | −0.0251997 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6380.47 | 0.278837 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −769.085 | −0.0334856 | ||||||||
\(809\) | −15304.2 | −0.665102 | −0.332551 | − | 0.943085i | \(-0.607909\pi\) | ||||
−0.332551 | + | 0.943085i | \(0.607909\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27002.2 | −1.16914 | −0.584572 | − | 0.811342i | \(-0.698738\pi\) | ||||
−0.584572 | + | 0.811342i | \(0.698738\pi\) | |||||||
\(812\) | 33270.7 | 1.43790 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −60.5849 | −0.00260872 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25931.5 | 1.11044 | ||||||||
\(818\) | 6596.84 | 0.281972 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25061.4 | −1.06535 | −0.532673 | − | 0.846321i | \(-0.678812\pi\) | ||||
−0.532673 | + | 0.846321i | \(0.678812\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24896.4 | 1.05448 | 0.527238 | − | 0.849718i | \(-0.323228\pi\) | ||||
0.527238 | + | 0.849718i | \(0.323228\pi\) | |||||||
\(824\) | 39162.8 | 1.65571 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2788.59 | 0.117467 | ||||||||
\(827\) | −20063.2 | −0.843612 | −0.421806 | − | 0.906686i | \(-0.638604\pi\) | ||||
−0.421806 | + | 0.906686i | \(0.638604\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13884.2 | −0.581687 | −0.290844 | − | 0.956771i | \(-0.593936\pi\) | ||||
−0.290844 | + | 0.956771i | \(0.593936\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −16808.4 | −0.700393 | ||||||||
\(833\) | 2852.52 | 0.118648 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −958.277 | −0.0396444 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27263.3 | −1.12386 | ||||||||
\(839\) | 13678.1 | 0.562838 | 0.281419 | − | 0.959585i | \(-0.409195\pi\) | ||||
0.281419 | + | 0.959585i | \(0.409195\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 61733.1 | 2.53118 | ||||||||
\(842\) | 13816.2 | 0.565485 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 22834.6 | 0.931280 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29489.5 | 1.19630 | ||||||||
\(848\) | 1342.06 | 0.0543473 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −986.512 | −0.0397382 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29802.9 | −1.19629 | −0.598143 | − | 0.801390i | \(-0.704094\pi\) | ||||
−0.598143 | + | 0.801390i | \(0.704094\pi\) | |||||||
\(854\) | −5190.54 | −0.207982 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −30364.6 | −1.21243 | ||||||||
\(857\) | 22045.2 | 0.878706 | 0.439353 | − | 0.898314i | \(-0.355208\pi\) | ||||
0.439353 | + | 0.898314i | \(0.355208\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33609.5 | 1.33497 | 0.667487 | − | 0.744622i | \(-0.267370\pi\) | ||||
0.667487 | + | 0.744622i | \(0.267370\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9722.70 | −0.384172 | ||||||||
\(863\) | 33775.6 | 1.33226 | 0.666128 | − | 0.745838i | \(-0.267951\pi\) | ||||
0.666128 | + | 0.745838i | \(0.267951\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10637.0 | 0.417392 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7303.27 | 0.285587 | ||||||||
\(869\) | −1379.62 | −0.0538556 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10123.0 | 0.393805 | ||||||||
\(872\) | 7160.44 | 0.278077 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8850.25 | 0.342522 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12637.0 | −0.486570 | −0.243285 | − | 0.969955i | \(-0.578225\pi\) | ||||
−0.243285 | + | 0.969955i | \(0.578225\pi\) | |||||||
\(878\) | 7199.25 | 0.276723 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6579.45 | 0.251609 | 0.125804 | − | 0.992055i | \(-0.459849\pi\) | ||||
0.125804 | + | 0.992055i | \(0.459849\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50442.1 | 1.92244 | 0.961219 | − | 0.275786i | \(-0.0889382\pi\) | ||||
0.961219 | + | 0.275786i | \(0.0889382\pi\) | |||||||
\(884\) | 5641.03 | 0.214625 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10744.2 | −0.407401 | ||||||||
\(887\) | 984.823 | 0.0372797 | 0.0186399 | − | 0.999826i | \(-0.494066\pi\) | ||||
0.0186399 | + | 0.999826i | \(0.494066\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26587.7 | −1.00306 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8950.64 | −0.335975 | ||||||||
\(893\) | 40314.6 | 1.51072 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −21658.0 | −0.807525 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15909.1 | −0.591196 | ||||||||
\(899\) | 18904.7 | 0.701342 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8799.79 | 0.325376 | ||||||||
\(902\) | −504.503 | −0.0186232 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −35281.6 | −1.29806 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43679.9 | −1.59908 | −0.799541 | − | 0.600612i | \(-0.794924\pi\) | ||||
−0.799541 | + | 0.600612i | \(0.794924\pi\) | |||||||
\(908\) | 4782.58 | 0.174797 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10364.3 | 0.376930 | 0.188465 | − | 0.982080i | \(-0.439649\pi\) | ||||
0.188465 | + | 0.982080i | \(0.439649\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 311.435 | 0.0112891 | ||||||||
\(914\) | −16245.6 | −0.587918 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13180.6 | 0.475435 | ||||||||
\(917\) | −7143.58 | −0.257254 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11451.9 | 0.411059 | 0.205530 | − | 0.978651i | \(-0.434108\pi\) | ||||
0.205530 | + | 0.978651i | \(0.434108\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10613.0 | 0.379091 | ||||||||
\(923\) | −34592.7 | −1.23362 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11009.1 | 0.390692 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −53796.4 | −1.90297 | ||||||||
\(929\) | 27701.8 | 0.978326 | 0.489163 | − | 0.872192i | \(-0.337302\pi\) | ||||
0.489163 | + | 0.872192i | \(0.337302\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15752.5 | 0.554529 | ||||||||
\(932\) | −11715.3 | −0.411746 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12262.5 | −0.429596 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5878.01 | 0.204937 | 0.102469 | − | 0.994736i | \(-0.467326\pi\) | ||||
0.102469 | + | 0.994736i | \(0.467326\pi\) | |||||||
\(938\) | −6572.03 | −0.228768 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28786.0 | 0.997234 | 0.498617 | − | 0.866823i | \(-0.333841\pi\) | ||||
0.498617 | + | 0.866823i | \(0.333841\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8214.90 | −0.283684 | ||||||||
\(944\) | 213.647 | 0.00736612 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −753.642 | −0.0259017 | ||||||||
\(947\) | −1695.04 | −0.0581641 | −0.0290821 | − | 0.999577i | \(-0.509258\pi\) | ||||
−0.0290821 | + | 0.999577i | \(0.509258\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18640.5 | 0.637613 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9401.72 | −0.320075 | ||||||||
\(953\) | 31929.4 | 1.08530 | 0.542651 | − | 0.839958i | \(-0.317420\pi\) | ||||
0.542651 | + | 0.839958i | \(0.317420\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −11710.2 | −0.396166 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18465.1 | −0.622735 | ||||||||
\(959\) | −7868.57 | −0.264952 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25641.2 | −0.860704 | ||||||||
\(962\) | 1969.48 | 0.0660069 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1951.46 | −0.0651994 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10897.1 | 0.362385 | 0.181193 | − | 0.983448i | \(-0.442004\pi\) | ||||
0.181193 | + | 0.983448i | \(0.442004\pi\) | |||||||
\(968\) | −29607.7 | −0.983087 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7041.97 | −0.232737 | −0.116368 | − | 0.993206i | \(-0.537125\pi\) | ||||
−0.116368 | + | 0.993206i | \(0.537125\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1715.81 | −0.0565328 | ||||||||
\(974\) | 21707.0 | 0.714103 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −397.671 | −0.0130422 | ||||||||
\(977\) | −37607.6 | −1.23150 | −0.615749 | − | 0.787943i | \(-0.711146\pi\) | ||||
−0.615749 | + | 0.787943i | \(0.711146\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1824.69 | −0.0595684 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −11939.0 | −0.387974 | ||||||||
\(983\) | −25297.7 | −0.820826 | −0.410413 | − | 0.911900i | \(-0.634615\pi\) | ||||
−0.410413 | + | 0.911900i | \(0.634615\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9479.85 | −0.306187 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 31151.5 | 1.00310 | ||||||||
\(989\) | −12271.6 | −0.394556 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41686.5 | −1.33624 | −0.668120 | − | 0.744053i | \(-0.732901\pi\) | ||||
−0.668120 | + | 0.744053i | \(0.732901\pi\) | |||||||
\(992\) | −11808.9 | −0.377955 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 22458.3 | 0.716633 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25465.9 | −0.808939 | −0.404470 | − | 0.914551i | \(-0.632544\pi\) | ||||
−0.404470 | + | 0.914551i | \(0.632544\pi\) | |||||||
\(998\) | −19350.6 | −0.613761 | ||||||||
\(999\) | 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 | 225.4.a.o.1.1 | 2 | ||
3.2 | odd | 2 | 75.4.a.c.1.2 | 2 | |||
5.2 | odd | 4 | 45.4.b.b.19.2 | 4 | |||
5.3 | odd | 4 | 45.4.b.b.19.3 | 4 | |||
5.4 | even | 2 | 225.4.a.i.1.2 | 2 | |||
12.11 | even | 2 | 1200.4.a.bt.1.2 | 2 | |||
15.2 | even | 4 | 15.4.b.a.4.3 | yes | 4 | ||
15.8 | even | 4 | 15.4.b.a.4.2 | ✓ | 4 | ||
15.14 | odd | 2 | 75.4.a.f.1.1 | 2 | |||
20.3 | even | 4 | 720.4.f.j.289.3 | 4 | |||
20.7 | even | 4 | 720.4.f.j.289.4 | 4 | |||
60.23 | odd | 4 | 240.4.f.f.49.3 | 4 | |||
60.47 | odd | 4 | 240.4.f.f.49.1 | 4 | |||
60.59 | even | 2 | 1200.4.a.bn.1.1 | 2 | |||
120.53 | even | 4 | 960.4.f.q.769.4 | 4 | |||
120.77 | even | 4 | 960.4.f.q.769.2 | 4 | |||
120.83 | odd | 4 | 960.4.f.p.769.2 | 4 | |||
120.107 | odd | 4 | 960.4.f.p.769.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.4.b.a.4.2 | ✓ | 4 | 15.8 | even | 4 | ||
15.4.b.a.4.3 | yes | 4 | 15.2 | even | 4 | ||
45.4.b.b.19.2 | 4 | 5.2 | odd | 4 | |||
45.4.b.b.19.3 | 4 | 5.3 | odd | 4 | |||
75.4.a.c.1.2 | 2 | 3.2 | odd | 2 | |||
75.4.a.f.1.1 | 2 | 15.14 | odd | 2 | |||
225.4.a.i.1.2 | 2 | 5.4 | even | 2 | |||
225.4.a.o.1.1 | 2 | 1.1 | even | 1 | trivial | ||
240.4.f.f.49.1 | 4 | 60.47 | odd | 4 | |||
240.4.f.f.49.3 | 4 | 60.23 | odd | 4 | |||
720.4.f.j.289.3 | 4 | 20.3 | even | 4 | |||
720.4.f.j.289.4 | 4 | 20.7 | even | 4 | |||
960.4.f.p.769.2 | 4 | 120.83 | odd | 4 | |||
960.4.f.p.769.4 | 4 | 120.107 | odd | 4 | |||
960.4.f.q.769.2 | 4 | 120.77 | even | 4 | |||
960.4.f.q.769.4 | 4 | 120.53 | even | 4 | |||
1200.4.a.bn.1.1 | 2 | 60.59 | even | 2 | |||
1200.4.a.bt.1.2 | 2 | 12.11 | even | 2 |