Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, 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("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(0\) |
Dimension: | \(59\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.11618 | −1.80884 | −0.904421 | − | 0.426642i | \(-0.859696\pi\) | ||||
−0.904421 | + | 0.426642i | \(0.859696\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 18.1753 | 2.27191 | ||||||||
\(5\) | 6.15957 | 0.550928 | 0.275464 | − | 0.961311i | \(-0.411168\pi\) | ||||
0.275464 | + | 0.961311i | \(0.411168\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 24.2123 | 1.30734 | 0.653669 | − | 0.756780i | \(-0.273229\pi\) | ||||
0.653669 | + | 0.756780i | \(0.273229\pi\) | |||||||
\(8\) | −52.0584 | −2.30068 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −31.5134 | −0.996542 | ||||||||
\(11\) | 60.5329 | 1.65921 | 0.829607 | − | 0.558348i | \(-0.188564\pi\) | ||||
0.829607 | + | 0.558348i | \(0.188564\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.25761 | −0.0481652 | −0.0240826 | − | 0.999710i | \(-0.507666\pi\) | ||||
−0.0240826 | + | 0.999710i | \(0.507666\pi\) | |||||||
\(14\) | −123.874 | −2.36477 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 120.938 | 1.88965 | ||||||||
\(17\) | 114.457 | 1.63294 | 0.816468 | − | 0.577391i | \(-0.195929\pi\) | ||||
0.816468 | + | 0.577391i | \(0.195929\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −56.9025 | −0.687070 | −0.343535 | − | 0.939140i | \(-0.611624\pi\) | ||||
−0.343535 | + | 0.939140i | \(0.611624\pi\) | |||||||
\(20\) | 111.952 | 1.25166 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −309.697 | −3.00126 | ||||||||
\(23\) | 11.1459 | 0.101047 | 0.0505235 | − | 0.998723i | \(-0.483911\pi\) | ||||
0.0505235 | + | 0.998723i | \(0.483911\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −87.0598 | −0.696478 | ||||||||
\(26\) | 11.5503 | 0.0871231 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 440.064 | 2.97015 | ||||||||
\(29\) | 177.408 | 1.13600 | 0.567998 | − | 0.823030i | \(-0.307718\pi\) | ||||
0.567998 | + | 0.823030i | \(0.307718\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −199.533 | −1.15604 | −0.578020 | − | 0.816022i | \(-0.696175\pi\) | ||||
−0.578020 | + | 0.816022i | \(0.696175\pi\) | |||||||
\(32\) | −202.272 | −1.11741 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −585.582 | −2.95372 | ||||||||
\(35\) | 149.137 | 0.720250 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 267.387 | 1.18806 | 0.594028 | − | 0.804444i | \(-0.297537\pi\) | ||||
0.594028 | + | 0.804444i | \(0.297537\pi\) | |||||||
\(38\) | 291.123 | 1.24280 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −320.657 | −1.26751 | ||||||||
\(41\) | 475.722 | 1.81208 | 0.906040 | − | 0.423192i | \(-0.139090\pi\) | ||||
0.906040 | + | 0.423192i | \(0.139090\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −207.667 | −0.736487 | −0.368244 | − | 0.929729i | \(-0.620041\pi\) | ||||
−0.368244 | + | 0.929729i | \(0.620041\pi\) | |||||||
\(44\) | 1100.20 | 3.76958 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −57.0244 | −0.182778 | ||||||||
\(47\) | −598.232 | −1.85662 | −0.928309 | − | 0.371809i | \(-0.878737\pi\) | ||||
−0.928309 | + | 0.371809i | \(0.878737\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 243.233 | 0.709135 | ||||||||
\(50\) | 445.413 | 1.25982 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −41.0325 | −0.109427 | ||||||||
\(53\) | −275.859 | −0.714947 | −0.357473 | − | 0.933923i | \(-0.616362\pi\) | ||||
−0.357473 | + | 0.933923i | \(0.616362\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 372.856 | 0.914108 | ||||||||
\(56\) | −1260.45 | −3.00777 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −907.651 | −2.05484 | ||||||||
\(59\) | 25.8847 | 0.0571169 | 0.0285585 | − | 0.999592i | \(-0.490908\pi\) | ||||
0.0285585 | + | 0.999592i | \(0.490908\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 247.309 | 0.519092 | 0.259546 | − | 0.965731i | \(-0.416427\pi\) | ||||
0.259546 | + | 0.965731i | \(0.416427\pi\) | |||||||
\(62\) | 1020.85 | 2.09109 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 67.3571 | 0.131557 | ||||||||
\(65\) | −13.9059 | −0.0265355 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −24.8585 | −0.0453276 | −0.0226638 | − | 0.999743i | \(-0.507215\pi\) | ||||
−0.0226638 | + | 0.999743i | \(0.507215\pi\) | |||||||
\(68\) | 2080.29 | 3.70988 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −763.011 | −1.30282 | ||||||||
\(71\) | 260.252 | 0.435017 | 0.217509 | − | 0.976058i | \(-0.430207\pi\) | ||||
0.217509 | + | 0.976058i | \(0.430207\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1076.96 | 1.72670 | 0.863349 | − | 0.504607i | \(-0.168363\pi\) | ||||
0.863349 | + | 0.504607i | \(0.168363\pi\) | |||||||
\(74\) | −1368.00 | −2.14900 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1034.22 | −1.56096 | ||||||||
\(77\) | 1465.64 | 2.16915 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 644.964 | 0.918533 | 0.459266 | − | 0.888299i | \(-0.348112\pi\) | ||||
0.459266 | + | 0.888299i | \(0.348112\pi\) | |||||||
\(80\) | 744.925 | 1.04106 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2433.88 | −3.27777 | ||||||||
\(83\) | −276.207 | −0.365274 | −0.182637 | − | 0.983180i | \(-0.558463\pi\) | ||||
−0.182637 | + | 0.983180i | \(0.558463\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 705.006 | 0.899631 | ||||||||
\(86\) | 1062.46 | 1.33219 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3151.25 | −3.81732 | ||||||||
\(89\) | 446.913 | 0.532278 | 0.266139 | − | 0.963935i | \(-0.414252\pi\) | ||||
0.266139 | + | 0.963935i | \(0.414252\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −54.6617 | −0.0629682 | ||||||||
\(92\) | 202.580 | 0.229570 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3060.66 | 3.35833 | ||||||||
\(95\) | −350.494 | −0.378526 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1294.37 | 1.35488 | 0.677438 | − | 0.735580i | \(-0.263090\pi\) | ||||
0.677438 | + | 0.735580i | \(0.263090\pi\) | |||||||
\(98\) | −1244.42 | −1.28271 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1582.33 | −1.58233 | ||||||||
\(101\) | 973.935 | 0.959506 | 0.479753 | − | 0.877404i | \(-0.340726\pi\) | ||||
0.479753 | + | 0.877404i | \(0.340726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 478.119 | 0.457383 | 0.228692 | − | 0.973499i | \(-0.426555\pi\) | ||||
0.228692 | + | 0.973499i | \(0.426555\pi\) | |||||||
\(104\) | 117.527 | 0.110812 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1411.34 | 1.29323 | ||||||||
\(107\) | −337.772 | −0.305174 | −0.152587 | − | 0.988290i | \(-0.548760\pi\) | ||||
−0.152587 | + | 0.988290i | \(0.548760\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −71.4379 | −0.0627754 | −0.0313877 | − | 0.999507i | \(-0.509993\pi\) | ||||
−0.0313877 | + | 0.999507i | \(0.509993\pi\) | |||||||
\(110\) | −1907.60 | −1.65348 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2928.18 | 2.47042 | ||||||||
\(113\) | 952.662 | 0.793088 | 0.396544 | − | 0.918016i | \(-0.370209\pi\) | ||||
0.396544 | + | 0.918016i | \(0.370209\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 68.6539 | 0.0556697 | ||||||||
\(116\) | 3224.44 | 2.58088 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −132.431 | −0.103315 | ||||||||
\(119\) | 2771.26 | 2.13480 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2333.23 | 1.75299 | ||||||||
\(122\) | −1265.27 | −0.938955 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3626.57 | −2.62642 | ||||||||
\(125\) | −1306.20 | −0.934638 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −565.205 | −0.394912 | −0.197456 | − | 0.980312i | \(-0.563268\pi\) | ||||
−0.197456 | + | 0.980312i | \(0.563268\pi\) | |||||||
\(128\) | 1273.57 | 0.879441 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 71.1449 | 0.0479986 | ||||||||
\(131\) | 1729.24 | 1.15331 | 0.576657 | − | 0.816986i | \(-0.304357\pi\) | ||||
0.576657 | + | 0.816986i | \(0.304357\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1377.74 | −0.898233 | ||||||||
\(134\) | 127.181 | 0.0819905 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5958.45 | −3.75686 | ||||||||
\(137\) | 1709.34 | 1.06597 | 0.532987 | − | 0.846123i | \(-0.321069\pi\) | ||||
0.532987 | + | 0.846123i | \(0.321069\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2291.12 | −1.39806 | −0.699030 | − | 0.715092i | \(-0.746385\pi\) | ||||
−0.699030 | + | 0.715092i | \(0.746385\pi\) | |||||||
\(140\) | 2710.60 | 1.63634 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1331.49 | −0.786877 | ||||||||
\(143\) | −136.659 | −0.0799163 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1092.76 | 0.625852 | ||||||||
\(146\) | −5509.93 | −3.12332 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4859.82 | 2.69915 | ||||||||
\(149\) | −2879.38 | −1.58314 | −0.791570 | − | 0.611079i | \(-0.790736\pi\) | ||||
−0.791570 | + | 0.611079i | \(0.790736\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −869.813 | −0.468771 | −0.234385 | − | 0.972144i | \(-0.575308\pi\) | ||||
−0.234385 | + | 0.972144i | \(0.575308\pi\) | |||||||
\(152\) | 2962.25 | 1.58073 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7498.46 | −3.92366 | ||||||||
\(155\) | −1229.04 | −0.636896 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −61.0278 | −0.0310226 | −0.0155113 | − | 0.999880i | \(-0.504938\pi\) | ||||
−0.0155113 | + | 0.999880i | \(0.504938\pi\) | |||||||
\(158\) | −3299.75 | −1.66148 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1245.91 | −0.615611 | ||||||||
\(161\) | 269.868 | 0.132103 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −566.997 | −0.272458 | −0.136229 | − | 0.990677i | \(-0.543498\pi\) | ||||
−0.136229 | + | 0.990677i | \(0.543498\pi\) | |||||||
\(164\) | 8646.37 | 4.11688 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1413.13 | 0.660722 | ||||||||
\(167\) | −833.335 | −0.386140 | −0.193070 | − | 0.981185i | \(-0.561844\pi\) | ||||
−0.193070 | + | 0.981185i | \(0.561844\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2191.90 | −0.997680 | ||||||||
\(170\) | −3606.93 | −1.62729 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3774.40 | −1.67323 | ||||||||
\(173\) | 2726.65 | 1.19829 | 0.599143 | − | 0.800642i | \(-0.295508\pi\) | ||||
0.599143 | + | 0.800642i | \(0.295508\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2107.91 | −0.910533 | ||||||||
\(176\) | 7320.72 | 3.13534 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2286.49 | −0.962806 | ||||||||
\(179\) | −2310.94 | −0.964958 | −0.482479 | − | 0.875907i | \(-0.660264\pi\) | ||||
−0.482479 | + | 0.875907i | \(0.660264\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −258.541 | −0.106173 | −0.0530863 | − | 0.998590i | \(-0.516906\pi\) | ||||
−0.0530863 | + | 0.998590i | \(0.516906\pi\) | |||||||
\(182\) | 279.659 | 0.113899 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −580.238 | −0.232477 | ||||||||
\(185\) | 1646.98 | 0.654534 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6928.42 | 2.70939 | ||||||||
\(188\) | −10873.0 | −4.21806 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1793.19 | 0.684694 | ||||||||
\(191\) | −3180.80 | −1.20500 | −0.602499 | − | 0.798119i | \(-0.705828\pi\) | ||||
−0.602499 | + | 0.798119i | \(0.705828\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1964.34 | 0.732624 | 0.366312 | − | 0.930492i | \(-0.380620\pi\) | ||||
0.366312 | + | 0.930492i | \(0.380620\pi\) | |||||||
\(194\) | −6622.20 | −2.45075 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4420.82 | 1.61109 | ||||||||
\(197\) | −3229.80 | −1.16809 | −0.584045 | − | 0.811721i | \(-0.698531\pi\) | ||||
−0.584045 | + | 0.811721i | \(0.698531\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1069.53 | −0.380991 | −0.190495 | − | 0.981688i | \(-0.561009\pi\) | ||||
−0.190495 | + | 0.981688i | \(0.561009\pi\) | |||||||
\(200\) | 4532.19 | 1.60237 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4982.82 | −1.73559 | ||||||||
\(203\) | 4295.45 | 1.48513 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2930.24 | 0.998326 | ||||||||
\(206\) | −2446.14 | −0.827334 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −273.030 | −0.0910155 | ||||||||
\(209\) | −3444.47 | −1.14000 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3260.16 | 1.06369 | 0.531845 | − | 0.846842i | \(-0.321499\pi\) | ||||
0.531845 | + | 0.846842i | \(0.321499\pi\) | |||||||
\(212\) | −5013.81 | −1.62429 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1728.10 | 0.552012 | ||||||||
\(215\) | −1279.14 | −0.405752 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4831.15 | −1.51134 | ||||||||
\(218\) | 365.489 | 0.113551 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6776.76 | 2.07677 | ||||||||
\(221\) | −258.399 | −0.0786506 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5181.92 | −1.55609 | −0.778043 | − | 0.628211i | \(-0.783787\pi\) | ||||
−0.778043 | + | 0.628211i | \(0.783787\pi\) | |||||||
\(224\) | −4897.46 | −1.46083 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4873.99 | −1.43457 | ||||||||
\(227\) | −3885.67 | −1.13613 | −0.568064 | − | 0.822984i | \(-0.692307\pi\) | ||||
−0.568064 | + | 0.822984i | \(0.692307\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −996.362 | −0.287517 | −0.143759 | − | 0.989613i | \(-0.545919\pi\) | ||||
−0.143759 | + | 0.989613i | \(0.545919\pi\) | |||||||
\(230\) | −351.246 | −0.100698 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9235.58 | −2.61356 | ||||||||
\(233\) | 4588.29 | 1.29008 | 0.645040 | − | 0.764149i | \(-0.276841\pi\) | ||||
0.645040 | + | 0.764149i | \(0.276841\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3684.85 | −1.02286 | ||||||||
\(236\) | 470.461 | 0.129764 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −14178.3 | −3.86151 | ||||||||
\(239\) | −239.000 | −0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −862.038 | −0.230410 | −0.115205 | − | 0.993342i | \(-0.536752\pi\) | ||||
−0.115205 | + | 0.993342i | \(0.536752\pi\) | |||||||
\(242\) | −11937.2 | −3.17088 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4494.90 | 1.17933 | ||||||||
\(245\) | 1498.21 | 0.390682 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 128.463 | 0.0330928 | ||||||||
\(248\) | 10387.4 | 2.65968 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6682.73 | 1.69061 | ||||||||
\(251\) | 2970.96 | 0.747113 | 0.373557 | − | 0.927607i | \(-0.378138\pi\) | ||||
0.373557 | + | 0.927607i | \(0.378138\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 674.694 | 0.167659 | ||||||||
\(254\) | 2891.69 | 0.714334 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7054.65 | −1.72233 | ||||||||
\(257\) | −3291.02 | −0.798787 | −0.399393 | − | 0.916780i | \(-0.630779\pi\) | ||||
−0.399393 | + | 0.916780i | \(0.630779\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6474.03 | 1.55319 | ||||||||
\(260\) | −252.743 | −0.0602863 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −8847.09 | −2.08616 | ||||||||
\(263\) | 5559.72 | 1.30353 | 0.651763 | − | 0.758423i | \(-0.274030\pi\) | ||||
0.651763 | + | 0.758423i | \(0.274030\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1699.17 | −0.393884 | ||||||||
\(266\) | 7048.74 | 1.62476 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −451.810 | −0.102980 | ||||||||
\(269\) | −4835.44 | −1.09599 | −0.547996 | − | 0.836481i | \(-0.684609\pi\) | ||||
−0.547996 | + | 0.836481i | \(0.684609\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4159.85 | 0.932447 | 0.466223 | − | 0.884667i | \(-0.345614\pi\) | ||||
0.466223 | + | 0.884667i | \(0.345614\pi\) | |||||||
\(272\) | 13842.2 | 3.08568 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8745.27 | −1.92818 | ||||||||
\(275\) | −5269.98 | −1.15561 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1547.96 | −0.335768 | −0.167884 | − | 0.985807i | \(-0.553693\pi\) | ||||
−0.167884 | + | 0.985807i | \(0.553693\pi\) | |||||||
\(278\) | 11721.8 | 2.52887 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7763.83 | −1.65706 | ||||||||
\(281\) | 6222.21 | 1.32095 | 0.660474 | − | 0.750849i | \(-0.270356\pi\) | ||||
0.660474 | + | 0.750849i | \(0.270356\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7453.16 | −1.56553 | −0.782764 | − | 0.622319i | \(-0.786191\pi\) | ||||
−0.782764 | + | 0.622319i | \(0.786191\pi\) | |||||||
\(284\) | 4730.15 | 0.988319 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 699.173 | 0.144556 | ||||||||
\(287\) | 11518.3 | 2.36900 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8187.41 | 1.66648 | ||||||||
\(290\) | −5590.74 | −1.13207 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19574.1 | 3.92290 | ||||||||
\(293\) | 9507.05 | 1.89559 | 0.947795 | − | 0.318881i | \(-0.103307\pi\) | ||||
0.947795 | + | 0.318881i | \(0.103307\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 159.438 | 0.0314673 | ||||||||
\(296\) | −13919.7 | −2.73333 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14731.4 | 2.86365 | ||||||||
\(299\) | −25.1631 | −0.00486695 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5028.09 | −0.962838 | ||||||||
\(302\) | 4450.12 | 0.847932 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6881.66 | −1.29832 | ||||||||
\(305\) | 1523.31 | 0.285982 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4201.33 | −0.781051 | −0.390526 | − | 0.920592i | \(-0.627707\pi\) | ||||
−0.390526 | + | 0.920592i | \(0.627707\pi\) | |||||||
\(308\) | 26638.3 | 4.92812 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6287.98 | 1.15204 | ||||||||
\(311\) | −1055.44 | −0.192438 | −0.0962190 | − | 0.995360i | \(-0.530675\pi\) | ||||
−0.0962190 | + | 0.995360i | \(0.530675\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9121.61 | −1.64723 | −0.823617 | − | 0.567147i | \(-0.808047\pi\) | ||||
−0.823617 | + | 0.567147i | \(0.808047\pi\) | |||||||
\(314\) | 312.229 | 0.0561149 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11722.4 | 2.08682 | ||||||||
\(317\) | −5793.06 | −1.02641 | −0.513203 | − | 0.858267i | \(-0.671541\pi\) | ||||
−0.513203 | + | 0.858267i | \(0.671541\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10739.0 | 1.88486 | ||||||||
\(320\) | 414.891 | 0.0724784 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1380.69 | −0.238953 | ||||||||
\(323\) | −6512.89 | −1.12194 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 196.547 | 0.0335460 | ||||||||
\(326\) | 2900.86 | 0.492833 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −24765.3 | −4.16901 | ||||||||
\(329\) | −14484.5 | −2.42723 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3979.44 | −0.660815 | −0.330408 | − | 0.943838i | \(-0.607186\pi\) | ||||
−0.330408 | + | 0.943838i | \(0.607186\pi\) | |||||||
\(332\) | −5020.14 | −0.829868 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4263.49 | 0.698466 | ||||||||
\(335\) | −153.118 | −0.0249723 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2938.64 | 0.475009 | 0.237504 | − | 0.971386i | \(-0.423671\pi\) | ||||
0.237504 | + | 0.971386i | \(0.423671\pi\) | |||||||
\(338\) | 11214.2 | 1.80465 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12813.7 | 2.04388 | ||||||||
\(341\) | −12078.3 | −1.91812 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2415.58 | −0.380260 | ||||||||
\(344\) | 10810.8 | 1.69442 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13950.0 | −2.16751 | ||||||||
\(347\) | −3152.37 | −0.487688 | −0.243844 | − | 0.969814i | \(-0.578409\pi\) | ||||
−0.243844 | + | 0.969814i | \(0.578409\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4348.01 | −0.666887 | −0.333444 | − | 0.942770i | \(-0.608211\pi\) | ||||
−0.333444 | + | 0.942770i | \(0.608211\pi\) | |||||||
\(350\) | 10784.5 | 1.64701 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12244.1 | −1.85402 | ||||||||
\(353\) | 10646.0 | 1.60518 | 0.802589 | − | 0.596532i | \(-0.203455\pi\) | ||||
0.802589 | + | 0.596532i | \(0.203455\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1603.04 | 0.239663 | ||||||||
\(356\) | 8122.76 | 1.20929 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11823.2 | 1.74546 | ||||||||
\(359\) | 7666.22 | 1.12704 | 0.563520 | − | 0.826102i | \(-0.309447\pi\) | ||||
0.563520 | + | 0.826102i | \(0.309447\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3621.11 | −0.527935 | ||||||||
\(362\) | 1322.74 | 0.192049 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −993.490 | −0.143058 | ||||||||
\(365\) | 6633.62 | 0.951287 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9305.91 | −1.32361 | −0.661805 | − | 0.749676i | \(-0.730209\pi\) | ||||
−0.661805 | + | 0.749676i | \(0.730209\pi\) | |||||||
\(368\) | 1347.96 | 0.190944 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8426.26 | −1.18395 | ||||||||
\(371\) | −6679.17 | −0.934678 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13038.1 | 1.80989 | 0.904943 | − | 0.425533i | \(-0.139913\pi\) | ||||
0.904943 | + | 0.425533i | \(0.139913\pi\) | |||||||
\(374\) | −35447.0 | −4.90086 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 31143.0 | 4.27148 | ||||||||
\(377\) | −400.518 | −0.0547154 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7405.15 | 1.00363 | 0.501816 | − | 0.864974i | \(-0.332665\pi\) | ||||
0.501816 | + | 0.864974i | \(0.332665\pi\) | |||||||
\(380\) | −6370.33 | −0.859976 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16273.5 | 2.17965 | ||||||||
\(383\) | −8586.05 | −1.14550 | −0.572750 | − | 0.819730i | \(-0.694123\pi\) | ||||
−0.572750 | + | 0.819730i | \(0.694123\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9027.69 | 1.19505 | ||||||||
\(386\) | −10049.9 | −1.32520 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 23525.4 | 3.07815 | ||||||||
\(389\) | −6051.43 | −0.788740 | −0.394370 | − | 0.918952i | \(-0.629037\pi\) | ||||
−0.394370 | + | 0.918952i | \(0.629037\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1275.73 | 0.165003 | ||||||||
\(392\) | −12662.3 | −1.63149 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16524.2 | 2.11289 | ||||||||
\(395\) | 3972.70 | 0.506046 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5248.00 | −0.663450 | −0.331725 | − | 0.943376i | \(-0.607631\pi\) | ||||
−0.331725 | + | 0.943376i | \(0.607631\pi\) | |||||||
\(398\) | 5471.91 | 0.689151 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10528.8 | −1.31610 | ||||||||
\(401\) | −10290.3 | −1.28147 | −0.640737 | − | 0.767760i | \(-0.721371\pi\) | ||||
−0.640737 | + | 0.767760i | \(0.721371\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 450.468 | 0.0556809 | ||||||||
\(404\) | 17701.5 | 2.17991 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −21976.3 | −2.68637 | ||||||||
\(407\) | 16185.7 | 1.97124 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8720.00 | 1.05422 | 0.527111 | − | 0.849797i | \(-0.323275\pi\) | ||||
0.527111 | + | 0.849797i | \(0.323275\pi\) | |||||||
\(410\) | −14991.6 | −1.80581 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8689.94 | 1.03913 | ||||||||
\(413\) | 626.726 | 0.0746712 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1701.32 | −0.201240 | ||||||||
\(416\) | 456.651 | 0.0538201 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 17622.5 | 2.06207 | ||||||||
\(419\) | 7078.88 | 0.825361 | 0.412680 | − | 0.910876i | \(-0.364593\pi\) | ||||
0.412680 | + | 0.910876i | \(0.364593\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14011.5 | 1.62203 | 0.811017 | − | 0.585022i | \(-0.198914\pi\) | ||||
0.811017 | + | 0.585022i | \(0.198914\pi\) | |||||||
\(422\) | −16679.5 | −1.92405 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 14360.8 | 1.64486 | ||||||||
\(425\) | −9964.60 | −1.13730 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5987.90 | 0.678629 | ||||||||
\(428\) | −6139.09 | −0.693327 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6544.30 | 0.733940 | ||||||||
\(431\) | 15783.4 | 1.76394 | 0.881970 | − | 0.471305i | \(-0.156217\pi\) | ||||
0.881970 | + | 0.471305i | \(0.156217\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11461.2 | 1.27203 | 0.636014 | − | 0.771677i | \(-0.280582\pi\) | ||||
0.636014 | + | 0.771677i | \(0.280582\pi\) | |||||||
\(434\) | 24717.0 | 2.73377 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1298.40 | −0.142620 | ||||||||
\(437\) | −634.230 | −0.0694264 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6354.81 | 0.690885 | 0.345442 | − | 0.938440i | \(-0.387729\pi\) | ||||
0.345442 | + | 0.938440i | \(0.387729\pi\) | |||||||
\(440\) | −19410.3 | −2.10307 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1322.01 | 0.142266 | ||||||||
\(443\) | 1129.37 | 0.121124 | 0.0605619 | − | 0.998164i | \(-0.480711\pi\) | ||||
0.0605619 | + | 0.998164i | \(0.480711\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2752.79 | 0.293247 | ||||||||
\(446\) | 26511.6 | 2.81471 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1630.87 | 0.171989 | ||||||||
\(449\) | −5699.02 | −0.599006 | −0.299503 | − | 0.954095i | \(-0.596821\pi\) | ||||
−0.299503 | + | 0.954095i | \(0.596821\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28796.8 | 3.00663 | ||||||||
\(452\) | 17314.9 | 1.80182 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19879.8 | 2.05508 | ||||||||
\(455\) | −336.692 | −0.0346909 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9585.31 | −0.981142 | −0.490571 | − | 0.871401i | \(-0.663212\pi\) | ||||
−0.490571 | + | 0.871401i | \(0.663212\pi\) | |||||||
\(458\) | 5097.57 | 0.520073 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1247.80 | 0.126476 | ||||||||
\(461\) | 15284.2 | 1.54416 | 0.772078 | − | 0.635527i | \(-0.219217\pi\) | ||||
0.772078 | + | 0.635527i | \(0.219217\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3329.90 | 0.334241 | 0.167121 | − | 0.985936i | \(-0.446553\pi\) | ||||
0.167121 | + | 0.985936i | \(0.446553\pi\) | |||||||
\(464\) | 21455.4 | 2.14664 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23474.5 | −2.33355 | ||||||||
\(467\) | −459.551 | −0.0455364 | −0.0227682 | − | 0.999741i | \(-0.507248\pi\) | ||||
−0.0227682 | + | 0.999741i | \(0.507248\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −601.881 | −0.0592586 | ||||||||
\(470\) | 18852.3 | 1.85020 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1347.51 | −0.131408 | ||||||||
\(473\) | −12570.7 | −1.22199 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4953.92 | 0.478529 | ||||||||
\(476\) | 50368.4 | 4.85007 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1222.77 | 0.117004 | ||||||||
\(479\) | −4162.34 | −0.397040 | −0.198520 | − | 0.980097i | \(-0.563613\pi\) | ||||
−0.198520 | + | 0.980097i | \(0.563613\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −603.653 | −0.0572229 | ||||||||
\(482\) | 4410.34 | 0.416775 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 42407.1 | 3.98263 | ||||||||
\(485\) | 7972.73 | 0.746439 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6565.21 | −0.610879 | −0.305439 | − | 0.952211i | \(-0.598803\pi\) | ||||
−0.305439 | + | 0.952211i | \(0.598803\pi\) | |||||||
\(488\) | −12874.5 | −1.19426 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7665.11 | −0.706682 | ||||||||
\(491\) | 6302.45 | 0.579278 | 0.289639 | − | 0.957136i | \(-0.406465\pi\) | ||||
0.289639 | + | 0.957136i | \(0.406465\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20305.6 | 1.85501 | ||||||||
\(494\) | −657.241 | −0.0598596 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24131.1 | −2.18452 | ||||||||
\(497\) | 6301.29 | 0.568715 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10128.2 | 0.908620 | 0.454310 | − | 0.890844i | \(-0.349886\pi\) | ||||
0.454310 | + | 0.890844i | \(0.349886\pi\) | |||||||
\(500\) | −23740.4 | −2.12341 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15200.0 | −1.35141 | ||||||||
\(503\) | 10440.7 | 0.925499 | 0.462750 | − | 0.886489i | \(-0.346863\pi\) | ||||
0.462750 | + | 0.886489i | \(0.346863\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5999.01 | 0.528619 | ||||||||
\(506\) | −3451.85 | −0.303268 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10272.8 | −0.897204 | ||||||||
\(509\) | 7114.47 | 0.619535 | 0.309767 | − | 0.950812i | \(-0.399749\pi\) | ||||
0.309767 | + | 0.950812i | \(0.399749\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26075.7 | 2.25738 | ||||||||
\(512\) | 25904.3 | 2.23597 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16837.4 | 1.44488 | ||||||||
\(515\) | 2945.01 | 0.251985 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36212.7 | −3.08053 | ||||||||
\(518\) | −33122.3 | −2.80948 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 723.917 | 0.0610497 | ||||||||
\(521\) | 17164.2 | 1.44333 | 0.721665 | − | 0.692242i | \(-0.243377\pi\) | ||||
0.721665 | + | 0.692242i | \(0.243377\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7814.01 | 0.653313 | 0.326657 | − | 0.945143i | \(-0.394078\pi\) | ||||
0.326657 | + | 0.945143i | \(0.394078\pi\) | |||||||
\(524\) | 31429.3 | 2.62022 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28444.5 | −2.35787 | ||||||||
\(527\) | −22838.0 | −1.88774 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12042.8 | −0.989789 | ||||||||
\(530\) | 8693.27 | 0.712474 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −25040.7 | −2.04070 | ||||||||
\(533\) | −1073.99 | −0.0872791 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2080.53 | −0.168129 | ||||||||
\(536\) | 1294.09 | 0.104284 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24739.0 | 1.98248 | ||||||||
\(539\) | 14723.6 | 1.17661 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5367.07 | −0.426522 | −0.213261 | − | 0.976995i | \(-0.568409\pi\) | ||||
−0.213261 | + | 0.976995i | \(0.568409\pi\) | |||||||
\(542\) | −21282.5 | −1.68665 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −23151.5 | −1.82465 | ||||||||
\(545\) | −440.027 | −0.0345847 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21500.9 | 1.68064 | 0.840322 | − | 0.542088i | \(-0.182366\pi\) | ||||
0.840322 | + | 0.542088i | \(0.182366\pi\) | |||||||
\(548\) | 31067.6 | 2.42180 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 26962.1 | 2.09031 | ||||||||
\(551\) | −10095.0 | −0.780508 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15616.0 | 1.20083 | ||||||||
\(554\) | 7919.61 | 0.607350 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −41641.7 | −3.17626 | ||||||||
\(557\) | −17048.6 | −1.29690 | −0.648449 | − | 0.761258i | \(-0.724582\pi\) | ||||
−0.648449 | + | 0.761258i | \(0.724582\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 468.831 | 0.0354730 | ||||||||
\(560\) | 18036.3 | 1.36102 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −31833.9 | −2.38938 | ||||||||
\(563\) | −613.122 | −0.0458970 | −0.0229485 | − | 0.999737i | \(-0.507305\pi\) | ||||
−0.0229485 | + | 0.999737i | \(0.507305\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5867.99 | 0.436935 | ||||||||
\(566\) | 38131.7 | 2.83179 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13548.3 | −1.00083 | ||||||||
\(569\) | −16212.2 | −1.19446 | −0.597232 | − | 0.802069i | \(-0.703733\pi\) | ||||
−0.597232 | + | 0.802069i | \(0.703733\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16513.8 | −1.21030 | −0.605150 | − | 0.796112i | \(-0.706887\pi\) | ||||
−0.605150 | + | 0.796112i | \(0.706887\pi\) | |||||||
\(572\) | −2483.82 | −0.181562 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −58929.7 | −4.28515 | ||||||||
\(575\) | −970.360 | −0.0703771 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1929.46 | −0.139210 | −0.0696051 | − | 0.997575i | \(-0.522174\pi\) | ||||
−0.0696051 | + | 0.997575i | \(0.522174\pi\) | |||||||
\(578\) | −41888.2 | −3.01440 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 19861.1 | 1.42188 | ||||||||
\(581\) | −6687.60 | −0.477536 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16698.6 | −1.18625 | ||||||||
\(584\) | −56065.0 | −3.97258 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −48639.7 | −3.42882 | ||||||||
\(587\) | −7835.41 | −0.550941 | −0.275470 | − | 0.961310i | \(-0.588834\pi\) | ||||
−0.275470 | + | 0.961310i | \(0.588834\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11353.9 | 0.794281 | ||||||||
\(590\) | −815.715 | −0.0569194 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 32337.2 | 2.24501 | ||||||||
\(593\) | −11655.4 | −0.807131 | −0.403566 | − | 0.914951i | \(-0.632229\pi\) | ||||
−0.403566 | + | 0.914951i | \(0.632229\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17069.8 | 1.17612 | ||||||||
\(596\) | −52333.4 | −3.59675 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 128.739 | 0.00880354 | ||||||||
\(599\) | 8154.09 | 0.556205 | 0.278103 | − | 0.960551i | \(-0.410294\pi\) | ||||
0.278103 | + | 0.960551i | \(0.410294\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3889.65 | −0.263997 | −0.131999 | − | 0.991250i | \(-0.542139\pi\) | ||||
−0.131999 | + | 0.991250i | \(0.542139\pi\) | |||||||
\(602\) | 25724.6 | 1.74162 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15809.1 | −1.06500 | ||||||||
\(605\) | 14371.7 | 0.965773 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15961.4 | −1.06730 | −0.533651 | − | 0.845705i | \(-0.679180\pi\) | ||||
−0.533651 | + | 0.845705i | \(0.679180\pi\) | |||||||
\(608\) | 11509.8 | 0.767736 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7793.54 | −0.517297 | ||||||||
\(611\) | 1350.57 | 0.0894243 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8958.59 | −0.590268 | −0.295134 | − | 0.955456i | \(-0.595364\pi\) | ||||
−0.295134 | + | 0.955456i | \(0.595364\pi\) | |||||||
\(614\) | 21494.8 | 1.41280 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −76298.7 | −4.99053 | ||||||||
\(617\) | −25935.8 | −1.69228 | −0.846139 | − | 0.532962i | \(-0.821079\pi\) | ||||
−0.846139 | + | 0.532962i | \(0.821079\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28793.1 | 1.86962 | 0.934810 | − | 0.355149i | \(-0.115570\pi\) | ||||
0.934810 | + | 0.355149i | \(0.115570\pi\) | |||||||
\(620\) | −22338.1 | −1.44697 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5399.79 | 0.348090 | ||||||||
\(623\) | 10820.8 | 0.695867 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2836.87 | 0.181560 | ||||||||
\(626\) | 46667.8 | 2.97958 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1109.20 | −0.0704804 | ||||||||
\(629\) | 30604.3 | 1.94002 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10699.7 | −0.675034 | −0.337517 | − | 0.941319i | \(-0.609587\pi\) | ||||
−0.337517 | + | 0.941319i | \(0.609587\pi\) | |||||||
\(632\) | −33575.8 | −2.11325 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 29638.3 | 1.85661 | ||||||||
\(635\) | −3481.42 | −0.217568 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −549.124 | −0.0341556 | ||||||||
\(638\) | −54942.8 | −3.40941 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7844.61 | 0.484509 | ||||||||
\(641\) | −18742.7 | −1.15490 | −0.577450 | − | 0.816426i | \(-0.695952\pi\) | ||||
−0.577450 | + | 0.816426i | \(0.695952\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1338.90 | −0.0821166 | −0.0410583 | − | 0.999157i | \(-0.513073\pi\) | ||||
−0.0410583 | + | 0.999157i | \(0.513073\pi\) | |||||||
\(644\) | 4904.91 | 0.300125 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 33321.1 | 2.02941 | ||||||||
\(647\) | −14253.8 | −0.866112 | −0.433056 | − | 0.901367i | \(-0.642565\pi\) | ||||
−0.433056 | + | 0.901367i | \(0.642565\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1566.87 | 0.0947692 | ||||||||
\(650\) | −1005.57 | −0.0606793 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10305.3 | −0.618999 | ||||||||
\(653\) | 7106.59 | 0.425884 | 0.212942 | − | 0.977065i | \(-0.431695\pi\) | ||||
0.212942 | + | 0.977065i | \(0.431695\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10651.4 | 0.635394 | ||||||||
\(656\) | 57532.8 | 3.42420 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 74105.4 | 4.39047 | ||||||||
\(659\) | 32587.0 | 1.92627 | 0.963133 | − | 0.269024i | \(-0.0867011\pi\) | ||||
0.963133 | + | 0.269024i | \(0.0867011\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29315.3 | −1.72501 | −0.862506 | − | 0.506046i | \(-0.831106\pi\) | ||||
−0.862506 | + | 0.506046i | \(0.831106\pi\) | |||||||
\(662\) | 20359.5 | 1.19531 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14378.9 | 0.840377 | ||||||||
\(665\) | −8486.26 | −0.494862 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1977.37 | 0.114789 | ||||||||
\(668\) | −15146.1 | −0.877275 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 783.377 | 0.0451709 | ||||||||
\(671\) | 14970.3 | 0.861285 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4257.99 | 0.243884 | 0.121942 | − | 0.992537i | \(-0.461088\pi\) | ||||
0.121942 | + | 0.992537i | \(0.461088\pi\) | |||||||
\(674\) | −15034.6 | −0.859215 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −39838.4 | −2.26664 | ||||||||
\(677\) | −10449.7 | −0.593227 | −0.296613 | − | 0.954998i | \(-0.595857\pi\) | ||||
−0.296613 | + | 0.954998i | \(0.595857\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31339.5 | 1.77128 | ||||||||
\(680\) | −36701.5 | −2.06976 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 61794.9 | 3.46957 | ||||||||
\(683\) | 20866.7 | 1.16902 | 0.584510 | − | 0.811386i | \(-0.301287\pi\) | ||||
0.584510 | + | 0.811386i | \(0.301287\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10528.8 | 0.587276 | ||||||||
\(686\) | 12358.5 | 0.687829 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −25114.8 | −1.39171 | ||||||||
\(689\) | 622.781 | 0.0344355 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31753.3 | 1.74812 | 0.874061 | − | 0.485815i | \(-0.161477\pi\) | ||||
0.874061 | + | 0.485815i | \(0.161477\pi\) | |||||||
\(692\) | 49557.6 | 2.72239 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16128.1 | 0.882151 | ||||||||
\(695\) | −14112.3 | −0.770231 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 54449.7 | 2.95901 | ||||||||
\(698\) | 22245.2 | 1.20629 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −38311.9 | −2.06865 | ||||||||
\(701\) | 33086.2 | 1.78266 | 0.891332 | − | 0.453350i | \(-0.149771\pi\) | ||||
0.891332 | + | 0.453350i | \(0.149771\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15215.0 | −0.816277 | ||||||||
\(704\) | 4077.32 | 0.218281 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −54466.7 | −2.90351 | ||||||||
\(707\) | 23581.2 | 1.25440 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13001.5 | 0.688689 | 0.344345 | − | 0.938843i | \(-0.388101\pi\) | ||||
0.344345 | + | 0.938843i | \(0.388101\pi\) | |||||||
\(710\) | −8201.43 | −0.433513 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −23265.6 | −1.22460 | ||||||||
\(713\) | −2223.98 | −0.116815 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −841.762 | −0.0440281 | ||||||||
\(716\) | −42001.9 | −2.19230 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −39221.7 | −2.03864 | ||||||||
\(719\) | −22832.0 | −1.18427 | −0.592136 | − | 0.805838i | \(-0.701715\pi\) | ||||
−0.592136 | + | 0.805838i | \(0.701715\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11576.3 | 0.597955 | ||||||||
\(722\) | 18526.2 | 0.954951 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4699.05 | −0.241214 | ||||||||
\(725\) | −15445.1 | −0.791196 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12675.4 | −0.646634 | −0.323317 | − | 0.946291i | \(-0.604798\pi\) | ||||
−0.323317 | + | 0.946291i | \(0.604798\pi\) | |||||||
\(728\) | 2845.60 | 0.144869 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −33938.8 | −1.72073 | ||||||||
\(731\) | −23769.0 | −1.20264 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12531.2 | 0.631448 | 0.315724 | − | 0.948851i | \(-0.397753\pi\) | ||||
0.315724 | + | 0.948851i | \(0.397753\pi\) | |||||||
\(734\) | 47610.7 | 2.39420 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2254.51 | −0.112911 | ||||||||
\(737\) | −1504.76 | −0.0752082 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28474.9 | 1.41741 | 0.708706 | − | 0.705504i | \(-0.249279\pi\) | ||||
0.708706 | + | 0.705504i | \(0.249279\pi\) | |||||||
\(740\) | 29934.4 | 1.48704 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 34171.8 | 1.69068 | ||||||||
\(743\) | −33823.3 | −1.67006 | −0.835032 | − | 0.550202i | \(-0.814551\pi\) | ||||
−0.835032 | + | 0.550202i | \(0.814551\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17735.7 | −0.872196 | ||||||||
\(746\) | −66705.2 | −3.27380 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 125926. | 6.15548 | ||||||||
\(749\) | −8178.22 | −0.398966 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32411.1 | −1.57483 | −0.787414 | − | 0.616424i | \(-0.788581\pi\) | ||||
−0.787414 | + | 0.616424i | \(0.788581\pi\) | |||||||
\(752\) | −72348.8 | −3.50837 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2049.12 | 0.0989715 | ||||||||
\(755\) | −5357.67 | −0.258259 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19616.4 | −0.941834 | −0.470917 | − | 0.882178i | \(-0.656077\pi\) | ||||
−0.470917 | + | 0.882178i | \(0.656077\pi\) | |||||||
\(758\) | −37886.0 | −1.81541 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 18246.2 | 0.870866 | ||||||||
\(761\) | 11000.9 | 0.524025 | 0.262012 | − | 0.965065i | \(-0.415614\pi\) | ||||
0.262012 | + | 0.965065i | \(0.415614\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1729.67 | −0.0820687 | ||||||||
\(764\) | −57811.9 | −2.73764 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 43927.7 | 2.07203 | ||||||||
\(767\) | −58.4374 | −0.00275104 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23498.7 | 1.10193 | 0.550966 | − | 0.834528i | \(-0.314260\pi\) | ||||
0.550966 | + | 0.834528i | \(0.314260\pi\) | |||||||
\(770\) | −46187.3 | −2.16165 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 35702.4 | 1.66445 | ||||||||
\(773\) | −20105.2 | −0.935489 | −0.467745 | − | 0.883864i | \(-0.654933\pi\) | ||||
−0.467745 | + | 0.883864i | \(0.654933\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17371.3 | 0.805157 | ||||||||
\(776\) | −67382.6 | −3.11713 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30960.2 | 1.42670 | ||||||||
\(779\) | −27069.8 | −1.24503 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15753.8 | 0.721787 | ||||||||
\(782\) | −6526.85 | −0.298465 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 29416.1 | 1.34002 | ||||||||
\(785\) | −375.904 | −0.0170912 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34093.2 | −1.54421 | −0.772103 | − | 0.635497i | \(-0.780795\pi\) | ||||
−0.772103 | + | 0.635497i | \(0.780795\pi\) | |||||||
\(788\) | −58702.5 | −2.65379 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −20325.0 | −0.915356 | ||||||||
\(791\) | 23066.1 | 1.03683 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −558.325 | −0.0250021 | ||||||||
\(794\) | 26849.7 | 1.20008 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19439.0 | −0.865575 | ||||||||
\(797\) | −9128.51 | −0.405707 | −0.202853 | − | 0.979209i | \(-0.565021\pi\) | ||||
−0.202853 | + | 0.979209i | \(0.565021\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −68471.8 | −3.03174 | ||||||||
\(800\) | 17609.8 | 0.778249 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 52646.8 | 2.31798 | ||||||||
\(803\) | 65191.7 | 2.86496 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1662.27 | 0.0727791 | ||||||||
\(806\) | −2304.67 | −0.100718 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −50701.5 | −2.20751 | ||||||||
\(809\) | −8581.63 | −0.372947 | −0.186474 | − | 0.982460i | \(-0.559706\pi\) | ||||
−0.186474 | + | 0.982460i | \(0.559706\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7419.25 | −0.321239 | −0.160620 | − | 0.987016i | \(-0.551349\pi\) | ||||
−0.160620 | + | 0.987016i | \(0.551349\pi\) | |||||||
\(812\) | 78070.9 | 3.37408 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −82808.8 | −3.56566 | ||||||||
\(815\) | −3492.46 | −0.150105 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11816.8 | 0.506018 | ||||||||
\(818\) | −44613.1 | −1.90692 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 53257.9 | 2.26810 | ||||||||
\(821\) | −395.175 | −0.0167987 | −0.00839933 | − | 0.999965i | \(-0.502674\pi\) | ||||
−0.00839933 | + | 0.999965i | \(0.502674\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13815.4 | −0.585145 | −0.292572 | − | 0.956243i | \(-0.594511\pi\) | ||||
−0.292572 | + | 0.956243i | \(0.594511\pi\) | |||||||
\(824\) | −24890.1 | −1.05229 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3206.44 | −0.135068 | ||||||||
\(827\) | −4972.77 | −0.209093 | −0.104547 | − | 0.994520i | \(-0.533339\pi\) | ||||
−0.104547 | + | 0.994520i | \(0.533339\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2223.76 | −0.0931656 | −0.0465828 | − | 0.998914i | \(-0.514833\pi\) | ||||
−0.0465828 | + | 0.998914i | \(0.514833\pi\) | |||||||
\(830\) | 8704.24 | 0.364010 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −152.066 | −0.00633646 | ||||||||
\(833\) | 27839.7 | 1.15797 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5132.98 | −0.212736 | ||||||||
\(836\) | −62604.1 | −2.58996 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −36216.8 | −1.49295 | ||||||||
\(839\) | 6945.72 | 0.285808 | 0.142904 | − | 0.989737i | \(-0.454356\pi\) | ||||
0.142904 | + | 0.989737i | \(0.454356\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7084.65 | 0.290486 | ||||||||
\(842\) | −71685.1 | −2.93400 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 59254.2 | 2.41660 | ||||||||
\(845\) | −13501.2 | −0.549650 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 56492.8 | 2.29175 | ||||||||
\(848\) | −33361.8 | −1.35100 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 50980.7 | 2.05720 | ||||||||
\(851\) | 2980.27 | 0.120050 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21002.3 | −0.843029 | −0.421515 | − | 0.906822i | \(-0.638501\pi\) | ||||
−0.421515 | + | 0.906822i | \(0.638501\pi\) | |||||||
\(854\) | −30635.1 | −1.22753 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17583.9 | 0.702107 | ||||||||
\(857\) | 17224.3 | 0.686545 | 0.343273 | − | 0.939236i | \(-0.388465\pi\) | ||||
0.343273 | + | 0.939236i | \(0.388465\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39760.0 | −1.57927 | −0.789635 | − | 0.613576i | \(-0.789730\pi\) | ||||
−0.789635 | + | 0.613576i | \(0.789730\pi\) | |||||||
\(860\) | −23248.7 | −0.921830 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −80750.5 | −3.19069 | ||||||||
\(863\) | 32018.9 | 1.26296 | 0.631480 | − | 0.775392i | \(-0.282448\pi\) | ||||
0.631480 | + | 0.775392i | \(0.282448\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16795.0 | 0.660170 | ||||||||
\(866\) | −58637.3 | −2.30090 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −87807.5 | −3.43362 | ||||||||
\(869\) | 39041.5 | 1.52404 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56.1207 | 0.00218321 | ||||||||
\(872\) | 3718.94 | 0.144426 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3244.83 | 0.125581 | ||||||||
\(875\) | −31625.9 | −1.22189 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24682.8 | 0.950376 | 0.475188 | − | 0.879884i | \(-0.342380\pi\) | ||||
0.475188 | + | 0.879884i | \(0.342380\pi\) | |||||||
\(878\) | −32512.3 | −1.24970 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 45092.4 | 1.72735 | ||||||||
\(881\) | 11864.7 | 0.453726 | 0.226863 | − | 0.973927i | \(-0.427153\pi\) | ||||
0.226863 | + | 0.973927i | \(0.427153\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16157.7 | 0.615797 | 0.307899 | − | 0.951419i | \(-0.400374\pi\) | ||||
0.307899 | + | 0.951419i | \(0.400374\pi\) | |||||||
\(884\) | −4696.46 | −0.178687 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5778.04 | −0.219094 | ||||||||
\(887\) | 26782.5 | 1.01383 | 0.506916 | − | 0.861995i | \(-0.330785\pi\) | ||||
0.506916 | + | 0.861995i | \(0.330785\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13684.9 | −0.516284 | ||||||||
\(890\) | −14083.8 | −0.530437 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −94182.7 | −3.53528 | ||||||||
\(893\) | 34040.9 | 1.27563 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14234.4 | −0.531623 | ||||||||
\(896\) | 30835.9 | 1.14973 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29157.2 | 1.08351 | ||||||||
\(899\) | −35398.9 | −1.31326 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31574.0 | −1.16746 | ||||||||
\(902\) | −147330. | −5.43852 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −49594.1 | −1.82464 | ||||||||
\(905\) | −1592.50 | −0.0584934 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16780.3 | −0.614312 | −0.307156 | − | 0.951659i | \(-0.599377\pi\) | ||||
−0.307156 | + | 0.951659i | \(0.599377\pi\) | |||||||
\(908\) | −70623.1 | −2.58118 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1722.58 | 0.0627504 | ||||||||
\(911\) | 47243.2 | 1.71815 | 0.859076 | − | 0.511848i | \(-0.171039\pi\) | ||||
0.859076 | + | 0.511848i | \(0.171039\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16719.6 | −0.606067 | ||||||||
\(914\) | 49040.1 | 1.77473 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18109.1 | −0.653213 | ||||||||
\(917\) | 41868.8 | 1.50777 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16832.5 | 0.604191 | 0.302095 | − | 0.953278i | \(-0.402314\pi\) | ||||
0.302095 | + | 0.953278i | \(0.402314\pi\) | |||||||
\(920\) | −3574.01 | −0.128078 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −78196.7 | −2.79313 | ||||||||
\(923\) | −587.546 | −0.0209527 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23278.6 | −0.827455 | ||||||||
\(926\) | −17036.4 | −0.604590 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −35884.7 | −1.26937 | ||||||||
\(929\) | 44392.4 | 1.56778 | 0.783890 | − | 0.620900i | \(-0.213233\pi\) | ||||
0.783890 | + | 0.620900i | \(0.213233\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13840.6 | −0.487225 | ||||||||
\(932\) | 83393.3 | 2.93094 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2351.14 | 0.0823681 | ||||||||
\(935\) | 42676.0 | 1.49268 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26352.9 | 0.918797 | 0.459399 | − | 0.888230i | \(-0.348065\pi\) | ||||
0.459399 | + | 0.888230i | \(0.348065\pi\) | |||||||
\(938\) | 3079.33 | 0.107189 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −66973.0 | −2.32385 | ||||||||
\(941\) | −12263.8 | −0.424853 | −0.212427 | − | 0.977177i | \(-0.568137\pi\) | ||||
−0.212427 | + | 0.977177i | \(0.568137\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5302.35 | 0.183105 | ||||||||
\(944\) | 3130.44 | 0.107931 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 64313.9 | 2.21039 | ||||||||
\(947\) | 19599.5 | 0.672542 | 0.336271 | − | 0.941765i | \(-0.390834\pi\) | ||||
0.336271 | + | 0.941765i | \(0.390834\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2431.36 | −0.0831667 | ||||||||
\(950\) | −25345.1 | −0.865583 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −144267. | −4.91149 | ||||||||
\(953\) | 26505.2 | 0.900932 | 0.450466 | − | 0.892794i | \(-0.351258\pi\) | ||||
0.450466 | + | 0.892794i | \(0.351258\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19592.4 | −0.663868 | ||||||||
\(956\) | −4343.89 | −0.146957 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21295.3 | 0.718183 | ||||||||
\(959\) | 41386.9 | 1.39359 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10022.6 | 0.336430 | ||||||||
\(962\) | 3088.40 | 0.103507 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15667.8 | −0.523470 | ||||||||
\(965\) | 12099.5 | 0.403623 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2628.01 | 0.0873951 | 0.0436976 | − | 0.999045i | \(-0.486086\pi\) | ||||
0.0436976 | + | 0.999045i | \(0.486086\pi\) | |||||||
\(968\) | −121464. | −4.03307 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −40789.9 | −1.35019 | ||||||||
\(971\) | −4466.94 | −0.147632 | −0.0738161 | − | 0.997272i | \(-0.523518\pi\) | ||||
−0.0738161 | + | 0.997272i | \(0.523518\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −55473.2 | −1.82774 | ||||||||
\(974\) | 33588.8 | 1.10498 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29909.0 | 0.980904 | ||||||||
\(977\) | 4528.27 | 0.148283 | 0.0741413 | − | 0.997248i | \(-0.476378\pi\) | ||||
0.0741413 | + | 0.997248i | \(0.476378\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27053.0 | 0.883163 | ||||||||
\(980\) | 27230.4 | 0.887594 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −32244.4 | −1.04782 | ||||||||
\(983\) | −37570.4 | −1.21903 | −0.609517 | − | 0.792773i | \(-0.708637\pi\) | ||||
−0.609517 | + | 0.792773i | \(0.708637\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19894.2 | −0.643534 | ||||||||
\(986\) | −103887. | −3.35541 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2334.85 | 0.0751838 | ||||||||
\(989\) | −2314.64 | −0.0744199 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30386.3 | 0.974018 | 0.487009 | − | 0.873397i | \(-0.338088\pi\) | ||||
0.487009 | + | 0.873397i | \(0.338088\pi\) | |||||||
\(992\) | 40360.1 | 1.29177 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −32238.5 | −1.02871 | ||||||||
\(995\) | −6587.85 | −0.209898 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30865.5 | −0.980462 | −0.490231 | − | 0.871593i | \(-0.663088\pi\) | ||||
−0.490231 | + | 0.871593i | \(0.663088\pi\) | |||||||
\(998\) | −51817.8 | −1.64355 | ||||||||
\(999\) | 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 | 2151.4.a.h.1.4 | yes | 59 | |
3.2 | odd | 2 | 2151.4.a.g.1.56 | ✓ | 59 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.4.a.g.1.56 | ✓ | 59 | 3.2 | odd | 2 | ||
2151.4.a.h.1.4 | yes | 59 | 1.1 | even | 1 | trivial |