Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2025,4,Mod(1,2025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2025, 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("2025.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2025 = 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2025.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: | \(119.478867762\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 64 x^{10} + 241 x^{9} + 1452 x^{8} - 5130 x^{7} - 13834 x^{6} + 45247 x^{5} + \cdots + 73008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 225) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.63978\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.63978 | −1.28686 | −0.643429 | − | 0.765506i | \(-0.722489\pi\) | ||||
−0.643429 | + | 0.765506i | \(0.722489\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.24803 | 0.656004 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.72054 | 0.200890 | 0.100445 | − | 0.994943i | \(-0.467973\pi\) | ||||
0.100445 | + | 0.994943i | \(0.467973\pi\) | |||||||
\(8\) | 10.0166 | 0.442674 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 28.0133 | 0.767847 | 0.383923 | − | 0.923365i | \(-0.374573\pi\) | ||||
0.383923 | + | 0.923365i | \(0.374573\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 43.6420 | 0.931086 | 0.465543 | − | 0.885025i | \(-0.345859\pi\) | ||||
0.465543 | + | 0.885025i | \(0.345859\pi\) | |||||||
\(14\) | −13.5420 | −0.258517 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −78.4424 | −1.22566 | ||||||||
\(17\) | −87.3128 | −1.24567 | −0.622837 | − | 0.782351i | \(-0.714020\pi\) | ||||
−0.622837 | + | 0.782351i | \(0.714020\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 38.5062 | 0.464944 | 0.232472 | − | 0.972603i | \(-0.425319\pi\) | ||||
0.232472 | + | 0.972603i | \(0.425319\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −101.962 | −0.988110 | ||||||||
\(23\) | 115.947 | 1.05115 | 0.525577 | − | 0.850746i | \(-0.323849\pi\) | ||||
0.525577 | + | 0.850746i | \(0.323849\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −158.848 | −1.19818 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 19.5255 | 0.131785 | ||||||||
\(29\) | −196.049 | −1.25536 | −0.627679 | − | 0.778472i | \(-0.715995\pi\) | ||||
−0.627679 | + | 0.778472i | \(0.715995\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 173.535 | 1.00541 | 0.502707 | − | 0.864457i | \(-0.332338\pi\) | ||||
0.502707 | + | 0.864457i | \(0.332338\pi\) | |||||||
\(32\) | 205.381 | 1.13458 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 317.800 | 1.60301 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −181.738 | −0.807499 | −0.403749 | − | 0.914870i | \(-0.632293\pi\) | ||||
−0.403749 | + | 0.914870i | \(0.632293\pi\) | |||||||
\(38\) | −140.154 | −0.598317 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 249.785 | 0.951460 | 0.475730 | − | 0.879591i | \(-0.342184\pi\) | ||||
0.475730 | + | 0.879591i | \(0.342184\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −460.708 | −1.63389 | −0.816945 | − | 0.576715i | \(-0.804334\pi\) | ||||
−0.816945 | + | 0.576715i | \(0.804334\pi\) | |||||||
\(44\) | 147.015 | 0.503711 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −422.021 | −1.35269 | ||||||||
\(47\) | −328.392 | −1.01917 | −0.509583 | − | 0.860421i | \(-0.670200\pi\) | ||||
−0.509583 | + | 0.860421i | \(0.670200\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −329.158 | −0.959643 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 229.035 | 0.610797 | ||||||||
\(53\) | −667.821 | −1.73080 | −0.865399 | − | 0.501083i | \(-0.832935\pi\) | ||||
−0.865399 | + | 0.501083i | \(0.832935\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 37.2671 | 0.0889289 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 713.577 | 1.61547 | ||||||||
\(59\) | −111.117 | −0.245191 | −0.122595 | − | 0.992457i | \(-0.539122\pi\) | ||||
−0.122595 | + | 0.992457i | \(0.539122\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 437.946 | 0.919233 | 0.459617 | − | 0.888117i | \(-0.347987\pi\) | ||||
0.459617 | + | 0.888117i | \(0.347987\pi\) | |||||||
\(62\) | −631.630 | −1.29382 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −120.003 | −0.234381 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 154.845 | 0.282348 | 0.141174 | − | 0.989985i | \(-0.454912\pi\) | ||||
0.141174 | + | 0.989985i | \(0.454912\pi\) | |||||||
\(68\) | −458.221 | −0.817168 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −912.989 | −1.52608 | −0.763041 | − | 0.646350i | \(-0.776295\pi\) | ||||
−0.763041 | + | 0.646350i | \(0.776295\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 975.779 | 1.56447 | 0.782234 | − | 0.622984i | \(-0.214080\pi\) | ||||
0.782234 | + | 0.622984i | \(0.214080\pi\) | |||||||
\(74\) | 661.485 | 1.03914 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 202.082 | 0.305005 | ||||||||
\(77\) | 104.225 | 0.154253 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 856.040 | 1.21914 | 0.609570 | − | 0.792733i | \(-0.291342\pi\) | ||||
0.609570 | + | 0.792733i | \(0.291342\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −909.164 | −1.22439 | ||||||||
\(83\) | −68.4209 | −0.0904840 | −0.0452420 | − | 0.998976i | \(-0.514406\pi\) | ||||
−0.0452420 | + | 0.998976i | \(0.514406\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1676.88 | 2.10259 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 280.597 | 0.339906 | ||||||||
\(89\) | −665.452 | −0.792559 | −0.396280 | − | 0.918130i | \(-0.629699\pi\) | ||||
−0.396280 | + | 0.918130i | \(0.629699\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 162.372 | 0.187046 | ||||||||
\(92\) | 608.492 | 0.689562 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1195.27 | 1.31152 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1403.67 | −1.46929 | −0.734646 | − | 0.678450i | \(-0.762652\pi\) | ||||
−0.734646 | + | 0.678450i | \(0.762652\pi\) | |||||||
\(98\) | 1198.06 | 1.23492 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 655.178 | 0.645472 | 0.322736 | − | 0.946489i | \(-0.395397\pi\) | ||||
0.322736 | + | 0.946489i | \(0.395397\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 253.523 | 0.242528 | 0.121264 | − | 0.992620i | \(-0.461305\pi\) | ||||
0.121264 | + | 0.992620i | \(0.461305\pi\) | |||||||
\(104\) | 437.143 | 0.412168 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2430.73 | 2.22729 | ||||||||
\(107\) | −1132.73 | −1.02341 | −0.511706 | − | 0.859161i | \(-0.670986\pi\) | ||||
−0.511706 | + | 0.859161i | \(0.670986\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1514.68 | 1.33101 | 0.665506 | − | 0.746392i | \(-0.268216\pi\) | ||||
0.665506 | + | 0.746392i | \(0.268216\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −291.848 | −0.246224 | ||||||||
\(113\) | −1672.03 | −1.39196 | −0.695980 | − | 0.718061i | \(-0.745030\pi\) | ||||
−0.695980 | + | 0.718061i | \(0.745030\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1028.87 | −0.823521 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 404.443 | 0.315526 | ||||||||
\(119\) | −324.851 | −0.250244 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −546.258 | −0.410411 | ||||||||
\(122\) | −1594.03 | −1.18292 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 910.718 | 0.659555 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −547.016 | −0.382203 | −0.191102 | − | 0.981570i | \(-0.561206\pi\) | ||||
−0.191102 | + | 0.981570i | \(0.561206\pi\) | |||||||
\(128\) | −1206.26 | −0.832965 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1267.97 | −0.845673 | −0.422836 | − | 0.906206i | \(-0.638965\pi\) | ||||
−0.422836 | + | 0.906206i | \(0.638965\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 143.264 | 0.0934028 | ||||||||
\(134\) | −563.602 | −0.363342 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −874.575 | −0.551428 | ||||||||
\(137\) | −930.444 | −0.580242 | −0.290121 | − | 0.956990i | \(-0.593696\pi\) | ||||
−0.290121 | + | 0.956990i | \(0.593696\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3130.27 | 1.91011 | 0.955057 | − | 0.296423i | \(-0.0957939\pi\) | ||||
0.955057 | + | 0.296423i | \(0.0957939\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3323.08 | 1.96385 | ||||||||
\(143\) | 1222.56 | 0.714932 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3551.62 | −2.01325 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −953.765 | −0.529723 | ||||||||
\(149\) | 1631.36 | 0.896953 | 0.448476 | − | 0.893795i | \(-0.351967\pi\) | ||||
0.448476 | + | 0.893795i | \(0.351967\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1821.64 | 0.981739 | 0.490870 | − | 0.871233i | \(-0.336679\pi\) | ||||
0.490870 | + | 0.871233i | \(0.336679\pi\) | |||||||
\(152\) | 385.700 | 0.205819 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −379.355 | −0.198502 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2835.18 | −1.44122 | −0.720612 | − | 0.693338i | \(-0.756139\pi\) | ||||
−0.720612 | + | 0.693338i | \(0.756139\pi\) | |||||||
\(158\) | −3115.80 | −1.56886 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 431.385 | 0.211167 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3048.62 | 1.46495 | 0.732473 | − | 0.680796i | \(-0.238366\pi\) | ||||
0.732473 | + | 0.680796i | \(0.238366\pi\) | |||||||
\(164\) | 1310.88 | 0.624162 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 249.037 | 0.116440 | ||||||||
\(167\) | 2837.92 | 1.31500 | 0.657500 | − | 0.753454i | \(-0.271614\pi\) | ||||
0.657500 | + | 0.753454i | \(0.271614\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −292.373 | −0.133078 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2417.81 | −1.07184 | ||||||||
\(173\) | −510.534 | −0.224365 | −0.112183 | − | 0.993688i | \(-0.535784\pi\) | ||||
−0.112183 | + | 0.993688i | \(0.535784\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2197.43 | −0.941121 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2422.10 | 1.01991 | ||||||||
\(179\) | 2274.36 | 0.949687 | 0.474843 | − | 0.880070i | \(-0.342505\pi\) | ||||
0.474843 | + | 0.880070i | \(0.342505\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −975.489 | −0.400594 | −0.200297 | − | 0.979735i | \(-0.564191\pi\) | ||||
−0.200297 | + | 0.979735i | \(0.564191\pi\) | |||||||
\(182\) | −590.999 | −0.240702 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1161.39 | 0.465319 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2445.92 | −0.956487 | ||||||||
\(188\) | −1723.41 | −0.668578 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1880.03 | 0.712219 | 0.356110 | − | 0.934444i | \(-0.384103\pi\) | ||||
0.356110 | + | 0.934444i | \(0.384103\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −613.562 | −0.228835 | −0.114418 | − | 0.993433i | \(-0.536500\pi\) | ||||
−0.114418 | + | 0.993433i | \(0.536500\pi\) | |||||||
\(194\) | 5109.07 | 1.89077 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1727.43 | −0.629530 | ||||||||
\(197\) | 68.3454 | 0.0247178 | 0.0123589 | − | 0.999924i | \(-0.496066\pi\) | ||||
0.0123589 | + | 0.999924i | \(0.496066\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2174.87 | 0.774736 | 0.387368 | − | 0.921925i | \(-0.373384\pi\) | ||||
0.387368 | + | 0.921925i | \(0.373384\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2384.71 | −0.830630 | ||||||||
\(203\) | −729.409 | −0.252190 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −922.769 | −0.312099 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3423.39 | −1.14120 | ||||||||
\(209\) | 1078.69 | 0.357006 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −475.041 | −0.154991 | −0.0774957 | − | 0.996993i | \(-0.524692\pi\) | ||||
−0.0774957 | + | 0.996993i | \(0.524692\pi\) | |||||||
\(212\) | −3504.75 | −1.13541 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4122.89 | 1.31699 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 645.644 | 0.201978 | ||||||||
\(218\) | −5513.12 | −1.71282 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3810.51 | −1.15983 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2966.35 | 0.890768 | 0.445384 | − | 0.895340i | \(-0.353067\pi\) | ||||
0.445384 | + | 0.895340i | \(0.353067\pi\) | |||||||
\(224\) | 764.129 | 0.227926 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6085.84 | 1.79126 | ||||||||
\(227\) | −2832.23 | −0.828113 | −0.414056 | − | 0.910251i | \(-0.635888\pi\) | ||||
−0.414056 | + | 0.910251i | \(0.635888\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4292.45 | −1.23866 | −0.619330 | − | 0.785131i | \(-0.712596\pi\) | ||||
−0.619330 | + | 0.785131i | \(0.712596\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1963.74 | −0.555715 | ||||||||
\(233\) | −4267.52 | −1.19989 | −0.599945 | − | 0.800041i | \(-0.704811\pi\) | ||||
−0.599945 | + | 0.800041i | \(0.704811\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −583.148 | −0.160846 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1182.39 | 0.322029 | ||||||||
\(239\) | −2585.03 | −0.699631 | −0.349816 | − | 0.936819i | \(-0.613756\pi\) | ||||
−0.349816 | + | 0.936819i | \(0.613756\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3904.99 | −1.04374 | −0.521872 | − | 0.853024i | \(-0.674766\pi\) | ||||
−0.521872 | + | 0.853024i | \(0.674766\pi\) | |||||||
\(242\) | 1988.26 | 0.528141 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2298.36 | 0.603021 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1680.49 | 0.432903 | ||||||||
\(248\) | 1738.22 | 0.445070 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1466.63 | −0.368815 | −0.184408 | − | 0.982850i | \(-0.559037\pi\) | ||||
−0.184408 | + | 0.982850i | \(0.559037\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3248.04 | 0.807126 | ||||||||
\(254\) | 1991.02 | 0.491842 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5350.56 | 1.30629 | ||||||||
\(257\) | 4447.35 | 1.07945 | 0.539723 | − | 0.841842i | \(-0.318529\pi\) | ||||
0.539723 | + | 0.841842i | \(0.318529\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −676.162 | −0.162219 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4615.14 | 1.08826 | ||||||||
\(263\) | 1755.14 | 0.411509 | 0.205754 | − | 0.978604i | \(-0.434035\pi\) | ||||
0.205754 | + | 0.978604i | \(0.434035\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −521.451 | −0.120196 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 812.632 | 0.185222 | ||||||||
\(269\) | 3412.93 | 0.773569 | 0.386785 | − | 0.922170i | \(-0.373586\pi\) | ||||
0.386785 | + | 0.922170i | \(0.373586\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 206.271 | 0.0462365 | 0.0231183 | − | 0.999733i | \(-0.492641\pi\) | ||||
0.0231183 | + | 0.999733i | \(0.492641\pi\) | |||||||
\(272\) | 6849.03 | 1.52678 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3386.62 | 0.746689 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5303.65 | −1.15042 | −0.575208 | − | 0.818007i | \(-0.695079\pi\) | ||||
−0.575208 | + | 0.818007i | \(0.695079\pi\) | |||||||
\(278\) | −11393.5 | −2.45805 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2849.15 | −0.604862 | −0.302431 | − | 0.953171i | \(-0.597798\pi\) | ||||
−0.302431 | + | 0.953171i | \(0.597798\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8075.05 | 1.69615 | 0.848077 | − | 0.529873i | \(-0.177760\pi\) | ||||
0.848077 | + | 0.529873i | \(0.177760\pi\) | |||||||
\(284\) | −4791.40 | −1.00112 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4449.84 | −0.920016 | ||||||||
\(287\) | 929.336 | 0.191139 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2710.53 | 0.551705 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5120.92 | 1.02630 | ||||||||
\(293\) | 2622.85 | 0.522964 | 0.261482 | − | 0.965208i | \(-0.415789\pi\) | ||||
0.261482 | + | 0.965208i | \(0.415789\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1820.39 | −0.357459 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5937.79 | −1.15425 | ||||||||
\(299\) | 5060.15 | 0.978716 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1714.08 | −0.328233 | ||||||||
\(302\) | −6630.36 | −1.26336 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3020.52 | −0.569865 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1699.16 | −0.315883 | −0.157941 | − | 0.987448i | \(-0.550486\pi\) | ||||
−0.157941 | + | 0.987448i | \(0.550486\pi\) | |||||||
\(308\) | 546.974 | 0.101191 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4818.93 | −0.878639 | −0.439319 | − | 0.898331i | \(-0.644780\pi\) | ||||
−0.439319 | + | 0.898331i | \(0.644780\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6016.46 | −1.08649 | −0.543243 | − | 0.839575i | \(-0.682804\pi\) | ||||
−0.543243 | + | 0.839575i | \(0.682804\pi\) | |||||||
\(314\) | 10319.5 | 1.85465 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4492.52 | 0.799760 | ||||||||
\(317\) | −7276.72 | −1.28928 | −0.644639 | − | 0.764487i | \(-0.722992\pi\) | ||||
−0.644639 | + | 0.764487i | \(0.722992\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5491.97 | −0.963923 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1570.15 | −0.271742 | ||||||||
\(323\) | −3362.09 | −0.579169 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11096.3 | −1.88518 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2501.99 | 0.421187 | ||||||||
\(329\) | −1221.80 | −0.204741 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1594.18 | −0.264725 | −0.132362 | − | 0.991201i | \(-0.542256\pi\) | ||||
−0.132362 | + | 0.991201i | \(0.542256\pi\) | |||||||
\(332\) | −359.075 | −0.0593579 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10329.4 | −1.69222 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8396.93 | 1.35730 | 0.678650 | − | 0.734462i | \(-0.262565\pi\) | ||||
0.678650 | + | 0.734462i | \(0.262565\pi\) | |||||||
\(338\) | 1064.17 | 0.171253 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4861.28 | 0.772003 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2500.79 | −0.393673 | ||||||||
\(344\) | −4614.71 | −0.723281 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1858.23 | 0.288726 | ||||||||
\(347\) | −10420.9 | −1.61217 | −0.806083 | − | 0.591802i | \(-0.798417\pi\) | ||||
−0.806083 | + | 0.591802i | \(0.798417\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7907.42 | −1.21282 | −0.606411 | − | 0.795152i | \(-0.707391\pi\) | ||||
−0.606411 | + | 0.795152i | \(0.707391\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5753.39 | 0.871184 | ||||||||
\(353\) | −5003.97 | −0.754488 | −0.377244 | − | 0.926114i | \(-0.623128\pi\) | ||||
−0.377244 | + | 0.926114i | \(0.623128\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3492.31 | −0.519922 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8278.19 | −1.22211 | ||||||||
\(359\) | 2385.12 | 0.350646 | 0.175323 | − | 0.984511i | \(-0.443903\pi\) | ||||
0.175323 | + | 0.984511i | \(0.443903\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5376.27 | −0.783827 | ||||||||
\(362\) | 3550.57 | 0.515508 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 852.134 | 0.122703 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1808.01 | 0.257159 | 0.128580 | − | 0.991699i | \(-0.458958\pi\) | ||||
0.128580 | + | 0.991699i | \(0.458958\pi\) | |||||||
\(368\) | −9095.14 | −1.28836 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2484.66 | −0.347701 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12533.7 | −1.73987 | −0.869933 | − | 0.493170i | \(-0.835838\pi\) | ||||
−0.869933 | + | 0.493170i | \(0.835838\pi\) | |||||||
\(374\) | 8902.61 | 1.23086 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3289.36 | −0.451159 | ||||||||
\(377\) | −8555.98 | −1.16885 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5221.98 | 0.707745 | 0.353872 | − | 0.935294i | \(-0.384865\pi\) | ||||
0.353872 | + | 0.935294i | \(0.384865\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6842.89 | −0.916525 | ||||||||
\(383\) | −8557.69 | −1.14172 | −0.570859 | − | 0.821048i | \(-0.693390\pi\) | ||||
−0.570859 | + | 0.821048i | \(0.693390\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2233.23 | 0.294478 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7366.52 | −0.963862 | ||||||||
\(389\) | 5461.33 | 0.711826 | 0.355913 | − | 0.934519i | \(-0.384170\pi\) | ||||
0.355913 | + | 0.934519i | \(0.384170\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10123.6 | −1.30940 | ||||||||
\(392\) | −3297.03 | −0.424809 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −248.763 | −0.0318083 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1998.55 | 0.252656 | 0.126328 | − | 0.991989i | \(-0.459681\pi\) | ||||
0.126328 | + | 0.991989i | \(0.459681\pi\) | |||||||
\(398\) | −7916.06 | −0.996975 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 492.166 | 0.0612907 | 0.0306454 | − | 0.999530i | \(-0.490244\pi\) | ||||
0.0306454 | + | 0.999530i | \(0.490244\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7573.42 | 0.936126 | ||||||||
\(404\) | 3438.40 | 0.423432 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2654.89 | 0.324532 | ||||||||
\(407\) | −5091.06 | −0.620035 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8000.45 | −0.967230 | −0.483615 | − | 0.875281i | \(-0.660676\pi\) | ||||
−0.483615 | + | 0.875281i | \(0.660676\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1330.50 | 0.159099 | ||||||||
\(413\) | −413.417 | −0.0492565 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 8963.24 | 1.05639 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3926.18 | −0.459416 | ||||||||
\(419\) | −5504.93 | −0.641846 | −0.320923 | − | 0.947105i | \(-0.603993\pi\) | ||||
−0.320923 | + | 0.947105i | \(0.603993\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10404.6 | −1.20448 | −0.602241 | − | 0.798314i | \(-0.705726\pi\) | ||||
−0.602241 | + | 0.798314i | \(0.705726\pi\) | |||||||
\(422\) | 1729.05 | 0.199452 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6689.28 | −0.766179 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1629.40 | 0.184665 | ||||||||
\(428\) | −5944.60 | −0.671362 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6446.05 | −0.720406 | −0.360203 | − | 0.932874i | \(-0.617293\pi\) | ||||
−0.360203 | + | 0.932874i | \(0.617293\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6307.26 | −0.700018 | −0.350009 | − | 0.936746i | \(-0.613821\pi\) | ||||
−0.350009 | + | 0.936746i | \(0.613821\pi\) | |||||||
\(434\) | −2350.01 | −0.259917 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7949.11 | 0.873150 | ||||||||
\(437\) | 4464.67 | 0.488728 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7894.27 | −0.858253 | −0.429127 | − | 0.903244i | \(-0.641179\pi\) | ||||
−0.429127 | + | 0.903244i | \(0.641179\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13869.4 | 1.49254 | ||||||||
\(443\) | −8779.17 | −0.941560 | −0.470780 | − | 0.882251i | \(-0.656027\pi\) | ||||
−0.470780 | + | 0.882251i | \(0.656027\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10796.9 | −1.14629 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −446.477 | −0.0470850 | ||||||||
\(449\) | −16514.2 | −1.73575 | −0.867874 | − | 0.496784i | \(-0.834514\pi\) | ||||
−0.867874 | + | 0.496784i | \(0.834514\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6997.29 | 0.730576 | ||||||||
\(452\) | −8774.88 | −0.913132 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10308.7 | 1.06566 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15496.9 | 1.58624 | 0.793121 | − | 0.609064i | \(-0.208455\pi\) | ||||
0.793121 | + | 0.609064i | \(0.208455\pi\) | |||||||
\(458\) | 15623.6 | 1.59398 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15282.9 | 1.54402 | 0.772012 | − | 0.635608i | \(-0.219250\pi\) | ||||
0.772012 | + | 0.635608i | \(0.219250\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13649.7 | −1.37010 | −0.685051 | − | 0.728495i | \(-0.740220\pi\) | ||||
−0.685051 | + | 0.728495i | \(0.740220\pi\) | |||||||
\(464\) | 15378.6 | 1.53865 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15532.8 | 1.54409 | ||||||||
\(467\) | 6841.24 | 0.677891 | 0.338945 | − | 0.940806i | \(-0.389930\pi\) | ||||
0.338945 | + | 0.940806i | \(0.389930\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 576.107 | 0.0567210 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1113.01 | −0.108540 | ||||||||
\(473\) | −12905.9 | −1.25458 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1704.83 | −0.164161 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9408.96 | 0.900326 | ||||||||
\(479\) | 5777.26 | 0.551085 | 0.275542 | − | 0.961289i | \(-0.411143\pi\) | ||||
0.275542 | + | 0.961289i | \(0.411143\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7931.39 | −0.751851 | ||||||||
\(482\) | 14213.3 | 1.34315 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2866.78 | −0.269232 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17699.8 | −1.64693 | −0.823463 | − | 0.567370i | \(-0.807961\pi\) | ||||
−0.823463 | + | 0.567370i | \(0.807961\pi\) | |||||||
\(488\) | 4386.72 | 0.406921 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12091.0 | 1.11132 | 0.555661 | − | 0.831409i | \(-0.312465\pi\) | ||||
0.555661 | + | 0.831409i | \(0.312465\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17117.6 | 1.56377 | ||||||||
\(494\) | −6116.63 | −0.557085 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13612.5 | −1.23230 | ||||||||
\(497\) | −3396.81 | −0.306575 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16307.4 | −1.46296 | −0.731481 | − | 0.681862i | \(-0.761171\pi\) | ||||
−0.731481 | + | 0.681862i | \(0.761171\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5338.20 | 0.474613 | ||||||||
\(503\) | 8574.88 | 0.760109 | 0.380054 | − | 0.924964i | \(-0.375905\pi\) | ||||
0.380054 | + | 0.924964i | \(0.375905\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11822.2 | −1.03866 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2870.76 | −0.250727 | ||||||||
\(509\) | −4054.42 | −0.353063 | −0.176532 | − | 0.984295i | \(-0.556488\pi\) | ||||
−0.176532 | + | 0.984295i | \(0.556488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3630.43 | 0.314287 | ||||||||
\(512\) | −9824.79 | −0.848044 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −16187.4 | −1.38909 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9199.32 | −0.782564 | ||||||||
\(518\) | 2461.08 | 0.208753 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22757.9 | 1.91371 | 0.956854 | − | 0.290570i | \(-0.0938448\pi\) | ||||
0.956854 | + | 0.290570i | \(0.0938448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12468.0 | 1.04242 | 0.521211 | − | 0.853428i | \(-0.325480\pi\) | ||||
0.521211 | + | 0.853428i | \(0.325480\pi\) | |||||||
\(524\) | −6654.35 | −0.554765 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6388.35 | −0.529554 | ||||||||
\(527\) | −15151.8 | −1.25242 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1276.64 | 0.104926 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 751.855 | 0.0612726 | ||||||||
\(533\) | 10901.1 | 0.885892 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1551.01 | 0.124988 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12422.3 | −0.995474 | ||||||||
\(539\) | −9220.77 | −0.736859 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22965.1 | −1.82504 | −0.912519 | − | 0.409034i | \(-0.865866\pi\) | ||||
−0.912519 | + | 0.409034i | \(0.865866\pi\) | |||||||
\(542\) | −750.783 | −0.0594998 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17932.4 | −1.41332 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10183.0 | 0.795966 | 0.397983 | − | 0.917393i | \(-0.369710\pi\) | ||||
0.397983 | + | 0.917393i | \(0.369710\pi\) | |||||||
\(548\) | −4883.00 | −0.380641 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7549.12 | −0.583672 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3184.93 | 0.244913 | ||||||||
\(554\) | 19304.1 | 1.48042 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16427.7 | 1.25304 | ||||||||
\(557\) | −4498.86 | −0.342231 | −0.171116 | − | 0.985251i | \(-0.554737\pi\) | ||||
−0.171116 | + | 0.985251i | \(0.554737\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20106.2 | −1.52129 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10370.3 | 0.778371 | ||||||||
\(563\) | −12042.2 | −0.901452 | −0.450726 | − | 0.892662i | \(-0.648835\pi\) | ||||
−0.450726 | + | 0.892662i | \(0.648835\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −29391.4 | −2.18271 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9145.01 | −0.675557 | ||||||||
\(569\) | −3491.33 | −0.257231 | −0.128615 | − | 0.991695i | \(-0.541053\pi\) | ||||
−0.128615 | + | 0.991695i | \(0.541053\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16100.2 | −1.17999 | −0.589993 | − | 0.807408i | \(-0.700870\pi\) | ||||
−0.589993 | + | 0.807408i | \(0.700870\pi\) | |||||||
\(572\) | 6416.01 | 0.468998 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3382.58 | −0.245969 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5196.41 | −0.374921 | −0.187460 | − | 0.982272i | \(-0.560026\pi\) | ||||
−0.187460 | + | 0.982272i | \(0.560026\pi\) | |||||||
\(578\) | −9865.74 | −0.709966 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −254.563 | −0.0181774 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18707.8 | −1.32899 | ||||||||
\(584\) | 9773.95 | 0.692550 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9546.61 | −0.672981 | ||||||||
\(587\) | 3897.19 | 0.274028 | 0.137014 | − | 0.990569i | \(-0.456249\pi\) | ||||
0.137014 | + | 0.990569i | \(0.456249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6682.18 | 0.467461 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14255.9 | 0.989721 | ||||||||
\(593\) | 3023.70 | 0.209390 | 0.104695 | − | 0.994504i | \(-0.466613\pi\) | ||||
0.104695 | + | 0.994504i | \(0.466613\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8561.41 | 0.588405 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −18417.9 | −1.25947 | ||||||||
\(599\) | −16629.5 | −1.13433 | −0.567164 | − | 0.823605i | \(-0.691959\pi\) | ||||
−0.567164 | + | 0.823605i | \(0.691959\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2958.68 | −0.200810 | −0.100405 | − | 0.994947i | \(-0.532014\pi\) | ||||
−0.100405 | + | 0.994947i | \(0.532014\pi\) | |||||||
\(602\) | 6238.89 | 0.422389 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9560.01 | 0.644025 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7012.36 | 0.468901 | 0.234451 | − | 0.972128i | \(-0.424671\pi\) | ||||
0.234451 | + | 0.972128i | \(0.424671\pi\) | |||||||
\(608\) | 7908.45 | 0.527516 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14331.7 | −0.948932 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8462.75 | 0.557597 | 0.278799 | − | 0.960350i | \(-0.410064\pi\) | ||||
0.278799 | + | 0.960350i | \(0.410064\pi\) | |||||||
\(614\) | 6184.57 | 0.406496 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1043.97 | 0.0682838 | ||||||||
\(617\) | 8413.43 | 0.548966 | 0.274483 | − | 0.961592i | \(-0.411493\pi\) | ||||
0.274483 | + | 0.961592i | \(0.411493\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1120.47 | −0.0727549 | −0.0363775 | − | 0.999338i | \(-0.511582\pi\) | ||||
−0.0363775 | + | 0.999338i | \(0.511582\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17539.9 | 1.13068 | ||||||||
\(623\) | −2475.84 | −0.159218 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 21898.6 | 1.39815 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14879.1 | −0.945450 | ||||||||
\(629\) | 15868.0 | 1.00588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7709.69 | 0.486399 | 0.243200 | − | 0.969976i | \(-0.421803\pi\) | ||||
0.243200 | + | 0.969976i | \(0.421803\pi\) | |||||||
\(632\) | 8574.58 | 0.539681 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 26485.7 | 1.65912 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14365.1 | −0.893511 | ||||||||
\(638\) | 19989.6 | 1.24043 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20299.6 | −1.25084 | −0.625419 | − | 0.780289i | \(-0.715072\pi\) | ||||
−0.625419 | + | 0.780289i | \(0.715072\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31865.2 | 1.95434 | 0.977169 | − | 0.212462i | \(-0.0681481\pi\) | ||||
0.977169 | + | 0.212462i | \(0.0681481\pi\) | |||||||
\(644\) | 2263.92 | 0.138526 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12237.3 | 0.745309 | ||||||||
\(647\) | −22400.4 | −1.36113 | −0.680563 | − | 0.732689i | \(-0.738265\pi\) | ||||
−0.680563 | + | 0.732689i | \(0.738265\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3112.76 | −0.188269 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15999.3 | 0.961011 | ||||||||
\(653\) | −10342.2 | −0.619791 | −0.309895 | − | 0.950771i | \(-0.600294\pi\) | ||||
−0.309895 | + | 0.950771i | \(0.600294\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −19593.7 | −1.16617 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4447.07 | 0.263472 | ||||||||
\(659\) | −237.410 | −0.0140336 | −0.00701682 | − | 0.999975i | \(-0.502234\pi\) | ||||
−0.00701682 | + | 0.999975i | \(0.502234\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28823.7 | 1.69608 | 0.848042 | − | 0.529930i | \(-0.177782\pi\) | ||||
0.848042 | + | 0.529930i | \(0.177782\pi\) | |||||||
\(662\) | 5802.46 | 0.340663 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −685.342 | −0.0400549 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22731.2 | −1.31958 | ||||||||
\(668\) | 14893.5 | 0.862646 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12268.3 | 0.705830 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7760.84 | −0.444515 | −0.222257 | − | 0.974988i | \(-0.571342\pi\) | ||||
−0.222257 | + | 0.974988i | \(0.571342\pi\) | |||||||
\(674\) | −30563.0 | −1.74665 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1534.38 | −0.0872998 | ||||||||
\(677\) | 23593.3 | 1.33939 | 0.669693 | − | 0.742638i | \(-0.266426\pi\) | ||||
0.669693 | + | 0.742638i | \(0.266426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5222.43 | −0.295167 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −17694.0 | −0.993459 | ||||||||
\(683\) | −4383.39 | −0.245572 | −0.122786 | − | 0.992433i | \(-0.539183\pi\) | ||||
−0.122786 | + | 0.992433i | \(0.539183\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9102.34 | 0.506602 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 36139.0 | 2.00260 | ||||||||
\(689\) | −29145.1 | −1.61152 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17752.5 | −0.977333 | −0.488667 | − | 0.872471i | \(-0.662517\pi\) | ||||
−0.488667 | + | 0.872471i | \(0.662517\pi\) | |||||||
\(692\) | −2679.30 | −0.147185 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 37929.7 | 2.07463 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21809.4 | −1.18521 | ||||||||
\(698\) | 28781.3 | 1.56073 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15650.2 | −0.843223 | −0.421611 | − | 0.906777i | \(-0.638535\pi\) | ||||
−0.421611 | + | 0.906777i | \(0.638535\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6998.03 | −0.375442 | ||||||||
\(704\) | −3361.68 | −0.179969 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18213.4 | 0.970920 | ||||||||
\(707\) | 2437.62 | 0.129669 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13217.6 | 0.700137 | 0.350069 | − | 0.936724i | \(-0.386158\pi\) | ||||
0.350069 | + | 0.936724i | \(0.386158\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6665.54 | −0.350845 | ||||||||
\(713\) | 20120.8 | 1.05684 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11935.9 | 0.622998 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8681.34 | −0.451232 | ||||||||
\(719\) | 14824.5 | 0.768932 | 0.384466 | − | 0.923139i | \(-0.374386\pi\) | ||||
0.384466 | + | 0.923139i | \(0.374386\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 943.243 | 0.0487215 | ||||||||
\(722\) | 19568.5 | 1.00867 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5119.40 | −0.262791 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7220.09 | −0.368333 | −0.184167 | − | 0.982895i | \(-0.558959\pi\) | ||||
−0.184167 | + | 0.982895i | \(0.558959\pi\) | |||||||
\(728\) | 1626.41 | 0.0828005 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 40225.7 | 2.03530 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1861.96 | −0.0938242 | −0.0469121 | − | 0.998899i | \(-0.514938\pi\) | ||||
−0.0469121 | + | 0.998899i | \(0.514938\pi\) | |||||||
\(734\) | −6580.77 | −0.330927 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 23813.2 | 1.19262 | ||||||||
\(737\) | 4337.71 | 0.216800 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29412.7 | −1.46409 | −0.732046 | − | 0.681255i | \(-0.761434\pi\) | ||||
−0.732046 | + | 0.681255i | \(0.761434\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9043.62 | 0.447442 | ||||||||
\(743\) | 34422.1 | 1.69963 | 0.849816 | − | 0.527080i | \(-0.176713\pi\) | ||||
0.849816 | + | 0.527080i | \(0.176713\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 45619.9 | 2.23896 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12836.3 | −0.627460 | ||||||||
\(749\) | −4214.37 | −0.205594 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29376.4 | −1.42738 | −0.713689 | − | 0.700462i | \(-0.752977\pi\) | ||||
−0.713689 | + | 0.700462i | \(0.752977\pi\) | |||||||
\(752\) | 25759.8 | 1.24915 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 31141.9 | 1.50414 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6235.27 | −0.299372 | −0.149686 | − | 0.988734i | \(-0.547826\pi\) | ||||
−0.149686 | + | 0.988734i | \(0.547826\pi\) | |||||||
\(758\) | −19006.9 | −0.910767 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27970.2 | 1.33235 | 0.666176 | − | 0.745795i | \(-0.267930\pi\) | ||||
0.666176 | + | 0.745795i | \(0.267930\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5635.44 | 0.267388 | ||||||||
\(764\) | 9866.44 | 0.467219 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 31148.2 | 1.46923 | ||||||||
\(767\) | −4849.39 | −0.228294 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9068.10 | −0.425233 | −0.212616 | − | 0.977136i | \(-0.568198\pi\) | ||||
−0.212616 | + | 0.977136i | \(0.568198\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3219.99 | −0.150117 | ||||||||
\(773\) | −31339.8 | −1.45823 | −0.729117 | − | 0.684389i | \(-0.760069\pi\) | ||||
−0.729117 | + | 0.684389i | \(0.760069\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14060.0 | −0.650418 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19878.1 | −0.916019 | ||||||||
\(779\) | 9618.28 | 0.442376 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25575.8 | −1.17180 | ||||||||
\(782\) | 36847.8 | 1.68501 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 25819.9 | 1.17620 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10079.4 | −0.456533 | −0.228267 | − | 0.973599i | \(-0.573306\pi\) | ||||
−0.228267 | + | 0.973599i | \(0.573306\pi\) | |||||||
\(788\) | 358.679 | 0.0162150 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6220.87 | −0.279632 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19112.9 | 0.855886 | ||||||||
\(794\) | −7274.29 | −0.325132 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11413.8 | 0.508230 | ||||||||
\(797\) | −7630.80 | −0.339143 | −0.169571 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169571 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28672.8 | 1.26955 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1791.38 | −0.0788725 | ||||||||
\(803\) | 27334.7 | 1.20127 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −27565.6 | −1.20466 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6562.63 | 0.285733 | ||||||||
\(809\) | 2066.39 | 0.0898028 | 0.0449014 | − | 0.998991i | \(-0.485703\pi\) | ||||
0.0449014 | + | 0.998991i | \(0.485703\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27700.4 | −1.19937 | −0.599687 | − | 0.800235i | \(-0.704708\pi\) | ||||
−0.599687 | + | 0.800235i | \(0.704708\pi\) | |||||||
\(812\) | −3827.96 | −0.165437 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 18530.4 | 0.797898 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17740.1 | −0.759668 | ||||||||
\(818\) | 29119.9 | 1.24469 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17103.1 | −0.727042 | −0.363521 | − | 0.931586i | \(-0.618426\pi\) | ||||
−0.363521 | + | 0.931586i | \(0.618426\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9190.15 | 0.389245 | 0.194623 | − | 0.980878i | \(-0.437652\pi\) | ||||
0.194623 | + | 0.980878i | \(0.437652\pi\) | |||||||
\(824\) | 2539.43 | 0.107361 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1504.75 | 0.0633861 | ||||||||
\(827\) | 9902.35 | 0.416371 | 0.208185 | − | 0.978089i | \(-0.433244\pi\) | ||||
0.208185 | + | 0.978089i | \(0.433244\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26858.5 | 1.12525 | 0.562626 | − | 0.826711i | \(-0.309791\pi\) | ||||
0.562626 | + | 0.826711i | \(0.309791\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5237.19 | −0.218229 | ||||||||
\(833\) | 28739.7 | 1.19540 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5660.98 | 0.234197 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 20036.8 | 0.825965 | ||||||||
\(839\) | 9300.55 | 0.382706 | 0.191353 | − | 0.981521i | \(-0.438712\pi\) | ||||
0.191353 | + | 0.981521i | \(0.438712\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14046.3 | 0.575926 | ||||||||
\(842\) | 37870.4 | 1.55000 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2493.03 | −0.101675 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2032.37 | −0.0824477 | ||||||||
\(848\) | 52385.5 | 2.12137 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21071.9 | −0.848806 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22214.6 | 0.891691 | 0.445845 | − | 0.895110i | \(-0.352903\pi\) | ||||
0.445845 | + | 0.895110i | \(0.352903\pi\) | |||||||
\(854\) | −5930.65 | −0.237638 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11346.1 | −0.453037 | ||||||||
\(857\) | −34347.9 | −1.36908 | −0.684541 | − | 0.728974i | \(-0.739997\pi\) | ||||
−0.684541 | + | 0.728974i | \(0.739997\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11178.2 | 0.444001 | 0.222001 | − | 0.975047i | \(-0.428741\pi\) | ||||
0.222001 | + | 0.975047i | \(0.428741\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 23462.2 | 0.927061 | ||||||||
\(863\) | 33684.0 | 1.32864 | 0.664321 | − | 0.747448i | \(-0.268721\pi\) | ||||
0.664321 | + | 0.747448i | \(0.268721\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 22957.1 | 0.900824 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3388.36 | 0.132498 | ||||||||
\(869\) | 23980.5 | 0.936112 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6757.75 | 0.262890 | ||||||||
\(872\) | 15171.9 | 0.589204 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −16250.4 | −0.628924 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5409.31 | 0.208278 | 0.104139 | − | 0.994563i | \(-0.466791\pi\) | ||||
0.104139 | + | 0.994563i | \(0.466791\pi\) | |||||||
\(878\) | 28733.5 | 1.10445 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41501.3 | 1.58708 | 0.793538 | − | 0.608520i | \(-0.208237\pi\) | ||||
0.793538 | + | 0.608520i | \(0.208237\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10532.8 | 0.401423 | 0.200711 | − | 0.979650i | \(-0.435675\pi\) | ||||
0.200711 | + | 0.979650i | \(0.435675\pi\) | |||||||
\(884\) | −19997.7 | −0.760854 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31954.3 | 1.21165 | ||||||||
\(887\) | −30002.5 | −1.13572 | −0.567861 | − | 0.823125i | \(-0.692229\pi\) | ||||
−0.567861 | + | 0.823125i | \(0.692229\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2035.20 | −0.0767810 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15567.5 | 0.584347 | ||||||||
\(893\) | −12645.1 | −0.473856 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4487.95 | −0.167335 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 60108.0 | 2.23366 | ||||||||
\(899\) | −34021.4 | −1.26215 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58309.4 | 2.15601 | ||||||||
\(902\) | −25468.6 | −0.940147 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16748.0 | −0.616185 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1098.35 | 0.0402096 | 0.0201048 | − | 0.999798i | \(-0.493600\pi\) | ||||
0.0201048 | + | 0.999798i | \(0.493600\pi\) | |||||||
\(908\) | −14863.6 | −0.543245 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36841.5 | 1.33986 | 0.669931 | − | 0.742423i | \(-0.266324\pi\) | ||||
0.669931 | + | 0.742423i | \(0.266324\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1916.69 | −0.0694778 | ||||||||
\(914\) | −56405.3 | −2.04127 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22526.9 | −0.812566 | ||||||||
\(917\) | −4717.54 | −0.169888 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46004.8 | 1.65131 | 0.825657 | − | 0.564172i | \(-0.190804\pi\) | ||||
0.825657 | + | 0.564172i | \(0.190804\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −55626.4 | −1.98694 | ||||||||
\(923\) | −39844.7 | −1.42091 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 49682.1 | 1.76313 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −40264.8 | −1.42431 | ||||||||
\(929\) | −50902.9 | −1.79771 | −0.898853 | − | 0.438251i | \(-0.855598\pi\) | ||||
−0.898853 | + | 0.438251i | \(0.855598\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12674.6 | −0.446180 | ||||||||
\(932\) | −22396.1 | −0.787133 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −24900.7 | −0.872349 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26913.6 | 0.938343 | 0.469172 | − | 0.883107i | \(-0.344553\pi\) | ||||
0.469172 | + | 0.883107i | \(0.344553\pi\) | |||||||
\(938\) | −2096.91 | −0.0729919 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21560.9 | −0.746935 | −0.373468 | − | 0.927643i | \(-0.621831\pi\) | ||||
−0.373468 | + | 0.927643i | \(0.621831\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28961.8 | 1.00013 | ||||||||
\(944\) | 8716.32 | 0.300521 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 46974.8 | 1.61446 | ||||||||
\(947\) | 28569.0 | 0.980326 | 0.490163 | − | 0.871631i | \(-0.336937\pi\) | ||||
0.490163 | + | 0.871631i | \(0.336937\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42585.0 | 1.45666 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3253.89 | −0.110777 | ||||||||
\(953\) | −3807.33 | −0.129414 | −0.0647069 | − | 0.997904i | \(-0.520611\pi\) | ||||
−0.0647069 | + | 0.997904i | \(0.520611\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13566.3 | −0.458961 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21028.0 | −0.709168 | ||||||||
\(959\) | −3461.76 | −0.116565 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 323.400 | 0.0108556 | ||||||||
\(962\) | 28868.6 | 0.967526 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20493.5 | −0.684701 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17905.3 | −0.595447 | −0.297723 | − | 0.954652i | \(-0.596227\pi\) | ||||
−0.297723 | + | 0.954652i | \(0.596227\pi\) | |||||||
\(968\) | −5471.62 | −0.181678 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8567.95 | 0.283170 | 0.141585 | − | 0.989926i | \(-0.454780\pi\) | ||||
0.141585 | + | 0.989926i | \(0.454780\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11646.3 | 0.383723 | ||||||||
\(974\) | 64423.3 | 2.11936 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34353.5 | −1.12667 | ||||||||
\(977\) | −19620.3 | −0.642488 | −0.321244 | − | 0.946997i | \(-0.604101\pi\) | ||||
−0.321244 | + | 0.946997i | \(0.604101\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18641.5 | −0.608564 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −44008.6 | −1.43011 | ||||||||
\(983\) | −47336.3 | −1.53590 | −0.767951 | − | 0.640508i | \(-0.778724\pi\) | ||||
−0.767951 | + | 0.640508i | \(0.778724\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −62304.4 | −2.01235 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8819.27 | 0.283986 | ||||||||
\(989\) | −53417.6 | −1.71747 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13735.8 | 0.440294 | 0.220147 | − | 0.975467i | \(-0.429346\pi\) | ||||
0.220147 | + | 0.975467i | \(0.429346\pi\) | |||||||
\(992\) | 35640.8 | 1.14072 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12363.7 | 0.394519 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35872.6 | −1.13952 | −0.569758 | − | 0.821813i | \(-0.692963\pi\) | ||||
−0.569758 | + | 0.821813i | \(0.692963\pi\) | |||||||
\(998\) | 59355.3 | 1.88262 | ||||||||
\(999\) | 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 | 2025.4.a.be.1.3 | 12 | ||
3.2 | odd | 2 | 2025.4.a.bi.1.10 | 12 | |||
5.4 | even | 2 | 2025.4.a.bj.1.10 | 12 | |||
9.2 | odd | 6 | 225.4.e.e.76.3 | ✓ | 24 | ||
9.5 | odd | 6 | 225.4.e.e.151.3 | yes | 24 | ||
15.14 | odd | 2 | 2025.4.a.bf.1.3 | 12 | |||
45.2 | even | 12 | 225.4.k.e.49.19 | 48 | |||
45.14 | odd | 6 | 225.4.e.f.151.10 | yes | 24 | ||
45.23 | even | 12 | 225.4.k.e.124.19 | 48 | |||
45.29 | odd | 6 | 225.4.e.f.76.10 | yes | 24 | ||
45.32 | even | 12 | 225.4.k.e.124.6 | 48 | |||
45.38 | even | 12 | 225.4.k.e.49.6 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.4.e.e.76.3 | ✓ | 24 | 9.2 | odd | 6 | ||
225.4.e.e.151.3 | yes | 24 | 9.5 | odd | 6 | ||
225.4.e.f.76.10 | yes | 24 | 45.29 | odd | 6 | ||
225.4.e.f.151.10 | yes | 24 | 45.14 | odd | 6 | ||
225.4.k.e.49.6 | 48 | 45.38 | even | 12 | |||
225.4.k.e.49.19 | 48 | 45.2 | even | 12 | |||
225.4.k.e.124.6 | 48 | 45.32 | even | 12 | |||
225.4.k.e.124.19 | 48 | 45.23 | even | 12 | |||
2025.4.a.be.1.3 | 12 | 1.1 | even | 1 | trivial | ||
2025.4.a.bf.1.3 | 12 | 15.14 | odd | 2 | |||
2025.4.a.bi.1.10 | 12 | 3.2 | odd | 2 | |||
2025.4.a.bj.1.10 | 12 | 5.4 | even | 2 |