Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(10.4433380710\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 34x^{5} + 25x^{4} + 315x^{3} - 146x^{2} - 736x + 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.775001\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.77500 | −0.627558 | −0.313779 | − | 0.949496i | \(-0.601595\pi\) | ||||
−0.313779 | + | 0.949496i | \(0.601595\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −4.84937 | −0.606171 | ||||||||
\(5\) | 6.23028 | 0.557253 | 0.278627 | − | 0.960399i | \(-0.410121\pi\) | ||||
0.278627 | + | 0.960399i | \(0.410121\pi\) | |||||||
\(6\) | −5.32500 | −0.362321 | ||||||||
\(7\) | −18.0779 | −0.976114 | −0.488057 | − | 0.872812i | \(-0.662294\pi\) | ||||
−0.488057 | + | 0.872812i | \(0.662294\pi\) | |||||||
\(8\) | 22.8076 | 1.00797 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −11.0588 | −0.349709 | ||||||||
\(11\) | 13.3400 | 0.365650 | 0.182825 | − | 0.983145i | \(-0.441476\pi\) | ||||
0.182825 | + | 0.983145i | \(0.441476\pi\) | |||||||
\(12\) | −14.5481 | −0.349973 | ||||||||
\(13\) | −66.3734 | −1.41605 | −0.708026 | − | 0.706187i | \(-0.750414\pi\) | ||||
−0.708026 | + | 0.706187i | \(0.750414\pi\) | |||||||
\(14\) | 32.0883 | 0.612568 | ||||||||
\(15\) | 18.6908 | 0.321730 | ||||||||
\(16\) | −1.68865 | −0.0263851 | ||||||||
\(17\) | −97.6720 | −1.39347 | −0.696733 | − | 0.717330i | \(-0.745364\pi\) | ||||
−0.696733 | + | 0.717330i | \(0.745364\pi\) | |||||||
\(18\) | −15.9750 | −0.209186 | ||||||||
\(19\) | 109.769 | 1.32540 | 0.662702 | − | 0.748883i | \(-0.269409\pi\) | ||||
0.662702 | + | 0.748883i | \(0.269409\pi\) | |||||||
\(20\) | −30.2129 | −0.337791 | ||||||||
\(21\) | −54.2336 | −0.563559 | ||||||||
\(22\) | −23.6785 | −0.229466 | ||||||||
\(23\) | −147.736 | −1.33935 | −0.669674 | − | 0.742655i | \(-0.733566\pi\) | ||||
−0.669674 | + | 0.742655i | \(0.733566\pi\) | |||||||
\(24\) | 68.4229 | 0.581949 | ||||||||
\(25\) | −86.1836 | −0.689469 | ||||||||
\(26\) | 117.813 | 0.888654 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 87.6663 | 0.591692 | ||||||||
\(29\) | −173.639 | −1.11186 | −0.555931 | − | 0.831228i | \(-0.687638\pi\) | ||||
−0.555931 | + | 0.831228i | \(0.687638\pi\) | |||||||
\(30\) | −33.1763 | −0.201904 | ||||||||
\(31\) | 148.613 | 0.861024 | 0.430512 | − | 0.902585i | \(-0.358333\pi\) | ||||
0.430512 | + | 0.902585i | \(0.358333\pi\) | |||||||
\(32\) | −179.464 | −0.991407 | ||||||||
\(33\) | 40.0199 | 0.211108 | ||||||||
\(34\) | 173.368 | 0.874481 | ||||||||
\(35\) | −112.630 | −0.543943 | ||||||||
\(36\) | −43.6443 | −0.202057 | ||||||||
\(37\) | −446.332 | −1.98315 | −0.991574 | − | 0.129539i | \(-0.958650\pi\) | ||||
−0.991574 | + | 0.129539i | \(0.958650\pi\) | |||||||
\(38\) | −194.840 | −0.831768 | ||||||||
\(39\) | −199.120 | −0.817557 | ||||||||
\(40\) | 142.098 | 0.561692 | ||||||||
\(41\) | 182.883 | 0.696622 | 0.348311 | − | 0.937379i | \(-0.386755\pi\) | ||||
0.348311 | + | 0.937379i | \(0.386755\pi\) | |||||||
\(42\) | 96.2648 | 0.353666 | ||||||||
\(43\) | −223.613 | −0.793040 | −0.396520 | − | 0.918026i | \(-0.629782\pi\) | ||||
−0.396520 | + | 0.918026i | \(0.629782\pi\) | |||||||
\(44\) | −64.6904 | −0.221647 | ||||||||
\(45\) | 56.0725 | 0.185751 | ||||||||
\(46\) | 262.231 | 0.840519 | ||||||||
\(47\) | −529.113 | −1.64211 | −0.821053 | − | 0.570851i | \(-0.806613\pi\) | ||||
−0.821053 | + | 0.570851i | \(0.806613\pi\) | |||||||
\(48\) | −5.06595 | −0.0152335 | ||||||||
\(49\) | −16.1904 | −0.0472023 | ||||||||
\(50\) | 152.976 | 0.432681 | ||||||||
\(51\) | −293.016 | −0.804518 | ||||||||
\(52\) | 321.869 | 0.858369 | ||||||||
\(53\) | 398.029 | 1.03157 | 0.515787 | − | 0.856717i | \(-0.327500\pi\) | ||||
0.515787 | + | 0.856717i | \(0.327500\pi\) | |||||||
\(54\) | −47.9250 | −0.120774 | ||||||||
\(55\) | 83.1117 | 0.203760 | ||||||||
\(56\) | −412.314 | −0.983889 | ||||||||
\(57\) | 329.306 | 0.765223 | ||||||||
\(58\) | 308.210 | 0.697758 | ||||||||
\(59\) | −59.0000 | −0.130189 | ||||||||
\(60\) | −90.6388 | −0.195024 | ||||||||
\(61\) | 788.427 | 1.65488 | 0.827440 | − | 0.561554i | \(-0.189796\pi\) | ||||
0.827440 | + | 0.561554i | \(0.189796\pi\) | |||||||
\(62\) | −263.789 | −0.540342 | ||||||||
\(63\) | −162.701 | −0.325371 | ||||||||
\(64\) | 332.058 | 0.648550 | ||||||||
\(65\) | −413.525 | −0.789099 | ||||||||
\(66\) | −71.0354 | −0.132483 | ||||||||
\(67\) | 288.375 | 0.525829 | 0.262915 | − | 0.964819i | \(-0.415316\pi\) | ||||
0.262915 | + | 0.964819i | \(0.415316\pi\) | |||||||
\(68\) | 473.648 | 0.844680 | ||||||||
\(69\) | −443.207 | −0.773273 | ||||||||
\(70\) | 199.919 | 0.341355 | ||||||||
\(71\) | −139.803 | −0.233684 | −0.116842 | − | 0.993150i | \(-0.537277\pi\) | ||||
−0.116842 | + | 0.993150i | \(0.537277\pi\) | |||||||
\(72\) | 205.269 | 0.335988 | ||||||||
\(73\) | 549.077 | 0.880336 | 0.440168 | − | 0.897915i | \(-0.354919\pi\) | ||||
0.440168 | + | 0.897915i | \(0.354919\pi\) | |||||||
\(74\) | 792.240 | 1.24454 | ||||||||
\(75\) | −258.551 | −0.398065 | ||||||||
\(76\) | −532.310 | −0.803422 | ||||||||
\(77\) | −241.158 | −0.356916 | ||||||||
\(78\) | 353.439 | 0.513065 | ||||||||
\(79\) | −190.617 | −0.271469 | −0.135735 | − | 0.990745i | \(-0.543339\pi\) | ||||
−0.135735 | + | 0.990745i | \(0.543339\pi\) | |||||||
\(80\) | −10.5208 | −0.0147032 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −324.617 | −0.437171 | ||||||||
\(83\) | 410.618 | 0.543026 | 0.271513 | − | 0.962435i | \(-0.412476\pi\) | ||||
0.271513 | + | 0.962435i | \(0.412476\pi\) | |||||||
\(84\) | 262.999 | 0.341614 | ||||||||
\(85\) | −608.524 | −0.776514 | ||||||||
\(86\) | 396.914 | 0.497679 | ||||||||
\(87\) | −520.918 | −0.641934 | ||||||||
\(88\) | 304.253 | 0.368562 | ||||||||
\(89\) | 1291.81 | 1.53856 | 0.769281 | − | 0.638911i | \(-0.220615\pi\) | ||||
0.769281 | + | 0.638911i | \(0.220615\pi\) | |||||||
\(90\) | −99.5288 | −0.116570 | ||||||||
\(91\) | 1199.89 | 1.38223 | ||||||||
\(92\) | 716.425 | 0.811875 | ||||||||
\(93\) | 445.840 | 0.497112 | ||||||||
\(94\) | 939.176 | 1.03052 | ||||||||
\(95\) | 683.891 | 0.738586 | ||||||||
\(96\) | −538.392 | −0.572389 | ||||||||
\(97\) | 1488.11 | 1.55768 | 0.778839 | − | 0.627225i | \(-0.215809\pi\) | ||||
0.778839 | + | 0.627225i | \(0.215809\pi\) | |||||||
\(98\) | 28.7380 | 0.0296222 | ||||||||
\(99\) | 120.060 | 0.121883 | ||||||||
\(100\) | 417.936 | 0.417936 | ||||||||
\(101\) | −1287.68 | −1.26861 | −0.634303 | − | 0.773085i | \(-0.718713\pi\) | ||||
−0.634303 | + | 0.773085i | \(0.718713\pi\) | |||||||
\(102\) | 520.104 | 0.504882 | ||||||||
\(103\) | −469.022 | −0.448680 | −0.224340 | − | 0.974511i | \(-0.572023\pi\) | ||||
−0.224340 | + | 0.974511i | \(0.572023\pi\) | |||||||
\(104\) | −1513.82 | −1.42733 | ||||||||
\(105\) | −337.891 | −0.314045 | ||||||||
\(106\) | −706.501 | −0.647372 | ||||||||
\(107\) | −1237.22 | −1.11782 | −0.558908 | − | 0.829230i | \(-0.688779\pi\) | ||||
−0.558908 | + | 0.829230i | \(0.688779\pi\) | |||||||
\(108\) | −130.933 | −0.116658 | ||||||||
\(109\) | 2145.12 | 1.88500 | 0.942501 | − | 0.334204i | \(-0.108468\pi\) | ||||
0.942501 | + | 0.334204i | \(0.108468\pi\) | |||||||
\(110\) | −147.523 | −0.127871 | ||||||||
\(111\) | −1339.00 | −1.14497 | ||||||||
\(112\) | 30.5272 | 0.0257549 | ||||||||
\(113\) | 1114.62 | 0.927919 | 0.463960 | − | 0.885856i | \(-0.346428\pi\) | ||||
0.463960 | + | 0.885856i | \(0.346428\pi\) | |||||||
\(114\) | −584.519 | −0.480222 | ||||||||
\(115\) | −920.435 | −0.746357 | ||||||||
\(116\) | 842.041 | 0.673979 | ||||||||
\(117\) | −597.360 | −0.472017 | ||||||||
\(118\) | 104.725 | 0.0817011 | ||||||||
\(119\) | 1765.70 | 1.36018 | ||||||||
\(120\) | 426.294 | 0.324293 | ||||||||
\(121\) | −1153.05 | −0.866300 | ||||||||
\(122\) | −1399.46 | −1.03853 | ||||||||
\(123\) | 548.649 | 0.402195 | ||||||||
\(124\) | −720.681 | −0.521928 | ||||||||
\(125\) | −1315.73 | −0.941462 | ||||||||
\(126\) | 288.794 | 0.204189 | ||||||||
\(127\) | −1267.75 | −0.885782 | −0.442891 | − | 0.896576i | \(-0.646047\pi\) | ||||
−0.442891 | + | 0.896576i | \(0.646047\pi\) | |||||||
\(128\) | 846.308 | 0.584404 | ||||||||
\(129\) | −670.840 | −0.457862 | ||||||||
\(130\) | 734.007 | 0.495205 | ||||||||
\(131\) | −2119.49 | −1.41359 | −0.706796 | − | 0.707418i | \(-0.749860\pi\) | ||||
−0.706796 | + | 0.707418i | \(0.749860\pi\) | |||||||
\(132\) | −194.071 | −0.127968 | ||||||||
\(133\) | −1984.39 | −1.29375 | ||||||||
\(134\) | −511.865 | −0.329988 | ||||||||
\(135\) | 168.218 | 0.107243 | ||||||||
\(136\) | −2227.67 | −1.40457 | ||||||||
\(137\) | −845.583 | −0.527322 | −0.263661 | − | 0.964615i | \(-0.584930\pi\) | ||||
−0.263661 | + | 0.964615i | \(0.584930\pi\) | |||||||
\(138\) | 786.693 | 0.485274 | ||||||||
\(139\) | −1390.93 | −0.848754 | −0.424377 | − | 0.905486i | \(-0.639507\pi\) | ||||
−0.424377 | + | 0.905486i | \(0.639507\pi\) | |||||||
\(140\) | 546.186 | 0.329722 | ||||||||
\(141\) | −1587.34 | −0.948071 | ||||||||
\(142\) | 248.151 | 0.146650 | ||||||||
\(143\) | −885.418 | −0.517779 | ||||||||
\(144\) | −15.1978 | −0.00879504 | ||||||||
\(145\) | −1081.82 | −0.619589 | ||||||||
\(146\) | −974.612 | −0.552462 | ||||||||
\(147\) | −48.5712 | −0.0272523 | ||||||||
\(148\) | 2164.43 | 1.20213 | ||||||||
\(149\) | −1007.80 | −0.554110 | −0.277055 | − | 0.960854i | \(-0.589358\pi\) | ||||
−0.277055 | + | 0.960854i | \(0.589358\pi\) | |||||||
\(150\) | 458.928 | 0.249809 | ||||||||
\(151\) | −1926.18 | −1.03808 | −0.519041 | − | 0.854750i | \(-0.673711\pi\) | ||||
−0.519041 | + | 0.854750i | \(0.673711\pi\) | |||||||
\(152\) | 2503.57 | 1.33596 | ||||||||
\(153\) | −879.048 | −0.464489 | ||||||||
\(154\) | 428.056 | 0.223985 | ||||||||
\(155\) | 925.903 | 0.479808 | ||||||||
\(156\) | 965.607 | 0.495580 | ||||||||
\(157\) | −1235.58 | −0.628092 | −0.314046 | − | 0.949408i | \(-0.601685\pi\) | ||||
−0.314046 | + | 0.949408i | \(0.601685\pi\) | |||||||
\(158\) | 338.345 | 0.170363 | ||||||||
\(159\) | 1194.09 | 0.595580 | ||||||||
\(160\) | −1118.11 | −0.552465 | ||||||||
\(161\) | 2670.75 | 1.30736 | ||||||||
\(162\) | −143.775 | −0.0697286 | ||||||||
\(163\) | 3664.53 | 1.76091 | 0.880454 | − | 0.474131i | \(-0.157238\pi\) | ||||
0.880454 | + | 0.474131i | \(0.157238\pi\) | |||||||
\(164\) | −886.867 | −0.422272 | ||||||||
\(165\) | 249.335 | 0.117641 | ||||||||
\(166\) | −728.847 | −0.340780 | ||||||||
\(167\) | 3953.29 | 1.83183 | 0.915913 | − | 0.401377i | \(-0.131468\pi\) | ||||
0.915913 | + | 0.401377i | \(0.131468\pi\) | |||||||
\(168\) | −1236.94 | −0.568048 | ||||||||
\(169\) | 2208.43 | 1.00520 | ||||||||
\(170\) | 1080.13 | 0.487307 | ||||||||
\(171\) | 987.919 | 0.441802 | ||||||||
\(172\) | 1084.38 | 0.480718 | ||||||||
\(173\) | −2225.27 | −0.977945 | −0.488973 | − | 0.872299i | \(-0.662628\pi\) | ||||
−0.488973 | + | 0.872299i | \(0.662628\pi\) | |||||||
\(174\) | 924.630 | 0.402851 | ||||||||
\(175\) | 1558.02 | 0.673000 | ||||||||
\(176\) | −22.5265 | −0.00964772 | ||||||||
\(177\) | −177.000 | −0.0751646 | ||||||||
\(178\) | −2292.97 | −0.965536 | ||||||||
\(179\) | −2130.61 | −0.889662 | −0.444831 | − | 0.895615i | \(-0.646736\pi\) | ||||
−0.444831 | + | 0.895615i | \(0.646736\pi\) | |||||||
\(180\) | −271.917 | −0.112597 | ||||||||
\(181\) | 1429.58 | 0.587072 | 0.293536 | − | 0.955948i | \(-0.405168\pi\) | ||||
0.293536 | + | 0.955948i | \(0.405168\pi\) | |||||||
\(182\) | −2129.81 | −0.867427 | ||||||||
\(183\) | 2365.28 | 0.955446 | ||||||||
\(184\) | −3369.50 | −1.35002 | ||||||||
\(185\) | −2780.77 | −1.10512 | ||||||||
\(186\) | −791.366 | −0.311967 | ||||||||
\(187\) | −1302.94 | −0.509521 | ||||||||
\(188\) | 2565.86 | 0.995398 | ||||||||
\(189\) | −488.103 | −0.187853 | ||||||||
\(190\) | −1213.91 | −0.463506 | ||||||||
\(191\) | −920.502 | −0.348718 | −0.174359 | − | 0.984682i | \(-0.555785\pi\) | ||||
−0.174359 | + | 0.984682i | \(0.555785\pi\) | |||||||
\(192\) | 996.173 | 0.374441 | ||||||||
\(193\) | −1870.05 | −0.697458 | −0.348729 | − | 0.937224i | \(-0.613387\pi\) | ||||
−0.348729 | + | 0.937224i | \(0.613387\pi\) | |||||||
\(194\) | −2641.40 | −0.977532 | ||||||||
\(195\) | −1240.57 | −0.455587 | ||||||||
\(196\) | 78.5132 | 0.0286127 | ||||||||
\(197\) | −476.512 | −0.172335 | −0.0861676 | − | 0.996281i | \(-0.527462\pi\) | ||||
−0.0861676 | + | 0.996281i | \(0.527462\pi\) | |||||||
\(198\) | −213.106 | −0.0764888 | ||||||||
\(199\) | 4164.08 | 1.48334 | 0.741668 | − | 0.670767i | \(-0.234035\pi\) | ||||
0.741668 | + | 0.670767i | \(0.234035\pi\) | |||||||
\(200\) | −1965.64 | −0.694960 | ||||||||
\(201\) | 865.124 | 0.303588 | ||||||||
\(202\) | 2285.64 | 0.796123 | ||||||||
\(203\) | 3139.03 | 1.08530 | ||||||||
\(204\) | 1420.94 | 0.487676 | ||||||||
\(205\) | 1139.41 | 0.388195 | ||||||||
\(206\) | 832.514 | 0.281573 | ||||||||
\(207\) | −1329.62 | −0.446450 | ||||||||
\(208\) | 112.081 | 0.0373627 | ||||||||
\(209\) | 1464.31 | 0.484634 | ||||||||
\(210\) | 599.757 | 0.197082 | ||||||||
\(211\) | −2499.21 | −0.815415 | −0.407707 | − | 0.913113i | \(-0.633672\pi\) | ||||
−0.407707 | + | 0.913113i | \(0.633672\pi\) | |||||||
\(212\) | −1930.19 | −0.625311 | ||||||||
\(213\) | −419.410 | −0.134918 | ||||||||
\(214\) | 2196.06 | 0.701494 | ||||||||
\(215\) | −1393.18 | −0.441924 | ||||||||
\(216\) | 615.807 | 0.193983 | ||||||||
\(217\) | −2686.61 | −0.840457 | ||||||||
\(218\) | −3807.59 | −1.18295 | ||||||||
\(219\) | 1647.23 | 0.508262 | ||||||||
\(220\) | −403.040 | −0.123513 | ||||||||
\(221\) | 6482.82 | 1.97322 | ||||||||
\(222\) | 2376.72 | 0.718536 | ||||||||
\(223\) | 2567.55 | 0.771013 | 0.385506 | − | 0.922705i | \(-0.374027\pi\) | ||||
0.385506 | + | 0.922705i | \(0.374027\pi\) | |||||||
\(224\) | 3244.33 | 0.967726 | ||||||||
\(225\) | −775.652 | −0.229823 | ||||||||
\(226\) | −1978.46 | −0.582323 | ||||||||
\(227\) | −969.018 | −0.283330 | −0.141665 | − | 0.989915i | \(-0.545246\pi\) | ||||
−0.141665 | + | 0.989915i | \(0.545246\pi\) | |||||||
\(228\) | −1596.93 | −0.463856 | ||||||||
\(229\) | 4217.16 | 1.21693 | 0.608467 | − | 0.793579i | \(-0.291785\pi\) | ||||
0.608467 | + | 0.793579i | \(0.291785\pi\) | |||||||
\(230\) | 1633.77 | 0.468382 | ||||||||
\(231\) | −723.475 | −0.206065 | ||||||||
\(232\) | −3960.30 | −1.12072 | ||||||||
\(233\) | 382.087 | 0.107431 | 0.0537154 | − | 0.998556i | \(-0.482894\pi\) | ||||
0.0537154 | + | 0.998556i | \(0.482894\pi\) | |||||||
\(234\) | 1060.32 | 0.296218 | ||||||||
\(235\) | −3296.52 | −0.915070 | ||||||||
\(236\) | 286.113 | 0.0789168 | ||||||||
\(237\) | −571.851 | −0.156733 | ||||||||
\(238\) | −3134.12 | −0.853593 | ||||||||
\(239\) | −4069.70 | −1.10145 | −0.550726 | − | 0.834686i | \(-0.685649\pi\) | ||||
−0.550726 | + | 0.834686i | \(0.685649\pi\) | |||||||
\(240\) | −31.5623 | −0.00848890 | ||||||||
\(241\) | 4573.11 | 1.22232 | 0.611162 | − | 0.791506i | \(-0.290703\pi\) | ||||
0.611162 | + | 0.791506i | \(0.290703\pi\) | |||||||
\(242\) | 2046.66 | 0.543653 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −3823.37 | −1.00314 | ||||||||
\(245\) | −100.871 | −0.0263036 | ||||||||
\(246\) | −973.852 | −0.252401 | ||||||||
\(247\) | −7285.73 | −1.87684 | ||||||||
\(248\) | 3389.52 | 0.867882 | ||||||||
\(249\) | 1231.85 | 0.313516 | ||||||||
\(250\) | 2335.43 | 0.590822 | ||||||||
\(251\) | 4263.66 | 1.07219 | 0.536095 | − | 0.844158i | \(-0.319899\pi\) | ||||
0.536095 | + | 0.844158i | \(0.319899\pi\) | |||||||
\(252\) | 788.997 | 0.197231 | ||||||||
\(253\) | −1970.79 | −0.489733 | ||||||||
\(254\) | 2250.25 | 0.555879 | ||||||||
\(255\) | −1825.57 | −0.448321 | ||||||||
\(256\) | −4158.66 | −1.01530 | ||||||||
\(257\) | 3758.60 | 0.912277 | 0.456138 | − | 0.889909i | \(-0.349232\pi\) | ||||
0.456138 | + | 0.889909i | \(0.349232\pi\) | |||||||
\(258\) | 1190.74 | 0.287335 | ||||||||
\(259\) | 8068.73 | 1.93578 | ||||||||
\(260\) | 2005.34 | 0.478329 | ||||||||
\(261\) | −1562.75 | −0.370621 | ||||||||
\(262\) | 3762.09 | 0.887110 | ||||||||
\(263\) | −2832.72 | −0.664157 | −0.332078 | − | 0.943252i | \(-0.607750\pi\) | ||||
−0.332078 | + | 0.943252i | \(0.607750\pi\) | |||||||
\(264\) | 912.760 | 0.212790 | ||||||||
\(265\) | 2479.83 | 0.574848 | ||||||||
\(266\) | 3522.29 | 0.811900 | ||||||||
\(267\) | 3875.44 | 0.888289 | ||||||||
\(268\) | −1398.44 | −0.318743 | ||||||||
\(269\) | −7351.53 | −1.66629 | −0.833143 | − | 0.553058i | \(-0.813461\pi\) | ||||
−0.833143 | + | 0.553058i | \(0.813461\pi\) | |||||||
\(270\) | −298.587 | −0.0673015 | ||||||||
\(271\) | −4053.05 | −0.908507 | −0.454253 | − | 0.890872i | \(-0.650094\pi\) | ||||
−0.454253 | + | 0.890872i | \(0.650094\pi\) | |||||||
\(272\) | 164.934 | 0.0367668 | ||||||||
\(273\) | 3599.67 | 0.798029 | ||||||||
\(274\) | 1500.91 | 0.330925 | ||||||||
\(275\) | −1149.69 | −0.252104 | ||||||||
\(276\) | 2149.28 | 0.468736 | ||||||||
\(277\) | 3054.14 | 0.662475 | 0.331238 | − | 0.943547i | \(-0.392534\pi\) | ||||
0.331238 | + | 0.943547i | \(0.392534\pi\) | |||||||
\(278\) | 2468.90 | 0.532642 | ||||||||
\(279\) | 1337.52 | 0.287008 | ||||||||
\(280\) | −2568.83 | −0.548275 | ||||||||
\(281\) | −3512.24 | −0.745632 | −0.372816 | − | 0.927905i | \(-0.621608\pi\) | ||||
−0.372816 | + | 0.927905i | \(0.621608\pi\) | |||||||
\(282\) | 2817.53 | 0.594969 | ||||||||
\(283\) | −7955.47 | −1.67104 | −0.835518 | − | 0.549463i | \(-0.814832\pi\) | ||||
−0.835518 | + | 0.549463i | \(0.814832\pi\) | |||||||
\(284\) | 677.958 | 0.141653 | ||||||||
\(285\) | 2051.67 | 0.426423 | ||||||||
\(286\) | 1571.62 | 0.324936 | ||||||||
\(287\) | −3306.13 | −0.679982 | ||||||||
\(288\) | −1615.17 | −0.330469 | ||||||||
\(289\) | 4626.82 | 0.941750 | ||||||||
\(290\) | 1920.24 | 0.388828 | ||||||||
\(291\) | 4464.33 | 0.899325 | ||||||||
\(292\) | −2662.68 | −0.533635 | ||||||||
\(293\) | 4933.26 | 0.983632 | 0.491816 | − | 0.870699i | \(-0.336333\pi\) | ||||
0.491816 | + | 0.870699i | \(0.336333\pi\) | |||||||
\(294\) | 86.2139 | 0.0171024 | ||||||||
\(295\) | −367.587 | −0.0725482 | ||||||||
\(296\) | −10179.8 | −1.99895 | ||||||||
\(297\) | 360.179 | 0.0703694 | ||||||||
\(298\) | 1788.85 | 0.347736 | ||||||||
\(299\) | 9805.72 | 1.89659 | ||||||||
\(300\) | 1253.81 | 0.241296 | ||||||||
\(301\) | 4042.46 | 0.774098 | ||||||||
\(302\) | 3418.97 | 0.651456 | ||||||||
\(303\) | −3863.05 | −0.732430 | ||||||||
\(304\) | −185.361 | −0.0349710 | ||||||||
\(305\) | 4912.12 | 0.922188 | ||||||||
\(306\) | 1560.31 | 0.291494 | ||||||||
\(307\) | −4362.63 | −0.811037 | −0.405518 | − | 0.914087i | \(-0.632909\pi\) | ||||
−0.405518 | + | 0.914087i | \(0.632909\pi\) | |||||||
\(308\) | 1169.47 | 0.216352 | ||||||||
\(309\) | −1407.07 | −0.259046 | ||||||||
\(310\) | −1643.48 | −0.301107 | ||||||||
\(311\) | −3542.33 | −0.645875 | −0.322937 | − | 0.946420i | \(-0.604670\pi\) | ||||
−0.322937 | + | 0.946420i | \(0.604670\pi\) | |||||||
\(312\) | −4541.46 | −0.824069 | ||||||||
\(313\) | −1808.65 | −0.326616 | −0.163308 | − | 0.986575i | \(-0.552216\pi\) | ||||
−0.163308 | + | 0.986575i | \(0.552216\pi\) | |||||||
\(314\) | 2193.16 | 0.394164 | ||||||||
\(315\) | −1013.67 | −0.181314 | ||||||||
\(316\) | 924.372 | 0.164557 | ||||||||
\(317\) | 302.078 | 0.0535217 | 0.0267609 | − | 0.999642i | \(-0.491481\pi\) | ||||
0.0267609 | + | 0.999642i | \(0.491481\pi\) | |||||||
\(318\) | −2119.50 | −0.373761 | ||||||||
\(319\) | −2316.34 | −0.406552 | ||||||||
\(320\) | 2068.81 | 0.361407 | ||||||||
\(321\) | −3711.65 | −0.645371 | ||||||||
\(322\) | −4740.58 | −0.820442 | ||||||||
\(323\) | −10721.3 | −1.84691 | ||||||||
\(324\) | −392.799 | −0.0673524 | ||||||||
\(325\) | 5720.30 | 0.976323 | ||||||||
\(326\) | −6504.54 | −1.10507 | ||||||||
\(327\) | 6435.36 | 1.08831 | ||||||||
\(328\) | 4171.13 | 0.702171 | ||||||||
\(329\) | 9565.23 | 1.60288 | ||||||||
\(330\) | −442.570 | −0.0738263 | ||||||||
\(331\) | −4133.17 | −0.686343 | −0.343172 | − | 0.939273i | \(-0.611501\pi\) | ||||
−0.343172 | + | 0.939273i | \(0.611501\pi\) | |||||||
\(332\) | −1991.24 | −0.329167 | ||||||||
\(333\) | −4016.99 | −0.661050 | ||||||||
\(334\) | −7017.10 | −1.14958 | ||||||||
\(335\) | 1796.66 | 0.293020 | ||||||||
\(336\) | 91.5815 | 0.0148696 | ||||||||
\(337\) | −3246.37 | −0.524750 | −0.262375 | − | 0.964966i | \(-0.584506\pi\) | ||||
−0.262375 | + | 0.964966i | \(0.584506\pi\) | |||||||
\(338\) | −3919.96 | −0.630821 | ||||||||
\(339\) | 3343.87 | 0.535734 | ||||||||
\(340\) | 2950.96 | 0.470701 | ||||||||
\(341\) | 1982.50 | 0.314833 | ||||||||
\(342\) | −1753.56 | −0.277256 | ||||||||
\(343\) | 6493.40 | 1.02219 | ||||||||
\(344\) | −5100.10 | −0.799357 | ||||||||
\(345\) | −2761.31 | −0.430909 | ||||||||
\(346\) | 3949.87 | 0.613717 | ||||||||
\(347\) | 463.911 | 0.0717696 | 0.0358848 | − | 0.999356i | \(-0.488575\pi\) | ||||
0.0358848 | + | 0.999356i | \(0.488575\pi\) | |||||||
\(348\) | 2526.12 | 0.389122 | ||||||||
\(349\) | −6606.06 | −1.01322 | −0.506611 | − | 0.862175i | \(-0.669102\pi\) | ||||
−0.506611 | + | 0.862175i | \(0.669102\pi\) | |||||||
\(350\) | −2765.48 | −0.422346 | ||||||||
\(351\) | −1792.08 | −0.272519 | ||||||||
\(352\) | −2394.04 | −0.362508 | ||||||||
\(353\) | −6284.55 | −0.947572 | −0.473786 | − | 0.880640i | \(-0.657113\pi\) | ||||
−0.473786 | + | 0.880640i | \(0.657113\pi\) | |||||||
\(354\) | 314.175 | 0.0471701 | ||||||||
\(355\) | −871.014 | −0.130221 | ||||||||
\(356\) | −6264.48 | −0.932632 | ||||||||
\(357\) | 5297.11 | 0.785301 | ||||||||
\(358\) | 3781.84 | 0.558314 | ||||||||
\(359\) | 5773.93 | 0.848848 | 0.424424 | − | 0.905464i | \(-0.360477\pi\) | ||||
0.424424 | + | 0.905464i | \(0.360477\pi\) | |||||||
\(360\) | 1278.88 | 0.187231 | ||||||||
\(361\) | 5190.19 | 0.756698 | ||||||||
\(362\) | −2537.51 | −0.368421 | ||||||||
\(363\) | −3459.14 | −0.500159 | ||||||||
\(364\) | −5818.71 | −0.837866 | ||||||||
\(365\) | 3420.90 | 0.490570 | ||||||||
\(366\) | −4198.38 | −0.599597 | ||||||||
\(367\) | −669.964 | −0.0952911 | −0.0476456 | − | 0.998864i | \(-0.515172\pi\) | ||||
−0.0476456 | + | 0.998864i | \(0.515172\pi\) | |||||||
\(368\) | 249.474 | 0.0353389 | ||||||||
\(369\) | 1645.95 | 0.232207 | ||||||||
\(370\) | 4935.88 | 0.693524 | ||||||||
\(371\) | −7195.51 | −1.00693 | ||||||||
\(372\) | −2162.04 | −0.301335 | ||||||||
\(373\) | 3345.79 | 0.464446 | 0.232223 | − | 0.972663i | \(-0.425400\pi\) | ||||
0.232223 | + | 0.972663i | \(0.425400\pi\) | |||||||
\(374\) | 2312.72 | 0.319754 | ||||||||
\(375\) | −3947.20 | −0.543553 | ||||||||
\(376\) | −12067.8 | −1.65519 | ||||||||
\(377\) | 11525.0 | 1.57445 | ||||||||
\(378\) | 866.383 | 0.117889 | ||||||||
\(379\) | 6881.01 | 0.932595 | 0.466298 | − | 0.884628i | \(-0.345588\pi\) | ||||
0.466298 | + | 0.884628i | \(0.345588\pi\) | |||||||
\(380\) | −3316.44 | −0.447710 | ||||||||
\(381\) | −3803.24 | −0.511406 | ||||||||
\(382\) | 1633.89 | 0.218841 | ||||||||
\(383\) | −4080.85 | −0.544444 | −0.272222 | − | 0.962235i | \(-0.587758\pi\) | ||||
−0.272222 | + | 0.962235i | \(0.587758\pi\) | |||||||
\(384\) | 2538.92 | 0.337406 | ||||||||
\(385\) | −1502.48 | −0.198893 | ||||||||
\(386\) | 3319.35 | 0.437695 | ||||||||
\(387\) | −2012.52 | −0.264347 | ||||||||
\(388\) | −7216.40 | −0.944219 | ||||||||
\(389\) | −4698.80 | −0.612439 | −0.306220 | − | 0.951961i | \(-0.599064\pi\) | ||||
−0.306220 | + | 0.951961i | \(0.599064\pi\) | |||||||
\(390\) | 2202.02 | 0.285907 | ||||||||
\(391\) | 14429.6 | 1.86634 | ||||||||
\(392\) | −369.265 | −0.0475783 | ||||||||
\(393\) | −6358.46 | −0.816138 | ||||||||
\(394\) | 845.809 | 0.108150 | ||||||||
\(395\) | −1187.60 | −0.151277 | ||||||||
\(396\) | −582.214 | −0.0738822 | ||||||||
\(397\) | 10293.0 | 1.30124 | 0.650620 | − | 0.759404i | \(-0.274509\pi\) | ||||
0.650620 | + | 0.759404i | \(0.274509\pi\) | |||||||
\(398\) | −7391.25 | −0.930879 | ||||||||
\(399\) | −5953.16 | −0.746944 | ||||||||
\(400\) | 145.534 | 0.0181917 | ||||||||
\(401\) | 7673.35 | 0.955583 | 0.477792 | − | 0.878473i | \(-0.341437\pi\) | ||||
0.477792 | + | 0.878473i | \(0.341437\pi\) | |||||||
\(402\) | −1535.60 | −0.190519 | ||||||||
\(403\) | −9863.97 | −1.21925 | ||||||||
\(404\) | 6244.45 | 0.768992 | ||||||||
\(405\) | 504.653 | 0.0619170 | ||||||||
\(406\) | −5571.78 | −0.681091 | ||||||||
\(407\) | −5954.05 | −0.725138 | ||||||||
\(408\) | −6683.01 | −0.810927 | ||||||||
\(409\) | 3707.61 | 0.448239 | 0.224119 | − | 0.974562i | \(-0.428049\pi\) | ||||
0.224119 | + | 0.974562i | \(0.428049\pi\) | |||||||
\(410\) | −2022.46 | −0.243615 | ||||||||
\(411\) | −2536.75 | −0.304449 | ||||||||
\(412\) | 2274.46 | 0.271977 | ||||||||
\(413\) | 1066.59 | 0.127079 | ||||||||
\(414\) | 2360.08 | 0.280173 | ||||||||
\(415\) | 2558.27 | 0.302603 | ||||||||
\(416\) | 11911.6 | 1.40388 | ||||||||
\(417\) | −4172.78 | −0.490029 | ||||||||
\(418\) | −2599.16 | −0.304136 | ||||||||
\(419\) | −11357.0 | −1.32416 | −0.662082 | − | 0.749431i | \(-0.730327\pi\) | ||||
−0.662082 | + | 0.749431i | \(0.730327\pi\) | |||||||
\(420\) | 1638.56 | 0.190365 | ||||||||
\(421\) | 3814.03 | 0.441531 | 0.220766 | − | 0.975327i | \(-0.429144\pi\) | ||||
0.220766 | + | 0.975327i | \(0.429144\pi\) | |||||||
\(422\) | 4436.10 | 0.511720 | ||||||||
\(423\) | −4762.01 | −0.547369 | ||||||||
\(424\) | 9078.10 | 1.03979 | ||||||||
\(425\) | 8417.72 | 0.960752 | ||||||||
\(426\) | 744.453 | 0.0846687 | ||||||||
\(427\) | −14253.1 | −1.61535 | ||||||||
\(428\) | 5999.72 | 0.677588 | ||||||||
\(429\) | −2656.26 | −0.298940 | ||||||||
\(430\) | 2472.89 | 0.277333 | ||||||||
\(431\) | −1307.09 | −0.146079 | −0.0730396 | − | 0.997329i | \(-0.523270\pi\) | ||||
−0.0730396 | + | 0.997329i | \(0.523270\pi\) | |||||||
\(432\) | −45.5935 | −0.00507782 | ||||||||
\(433\) | 7915.74 | 0.878536 | 0.439268 | − | 0.898356i | \(-0.355238\pi\) | ||||
0.439268 | + | 0.898356i | \(0.355238\pi\) | |||||||
\(434\) | 4768.74 | 0.527435 | ||||||||
\(435\) | −3245.47 | −0.357720 | ||||||||
\(436\) | −10402.5 | −1.14263 | ||||||||
\(437\) | −16216.8 | −1.77518 | ||||||||
\(438\) | −2923.83 | −0.318964 | ||||||||
\(439\) | 2570.45 | 0.279456 | 0.139728 | − | 0.990190i | \(-0.455377\pi\) | ||||
0.139728 | + | 0.990190i | \(0.455377\pi\) | |||||||
\(440\) | 1895.58 | 0.205383 | ||||||||
\(441\) | −145.713 | −0.0157341 | ||||||||
\(442\) | −11507.0 | −1.23831 | ||||||||
\(443\) | −633.121 | −0.0679017 | −0.0339509 | − | 0.999424i | \(-0.510809\pi\) | ||||
−0.0339509 | + | 0.999424i | \(0.510809\pi\) | |||||||
\(444\) | 6493.29 | 0.694049 | ||||||||
\(445\) | 8048.36 | 0.857369 | ||||||||
\(446\) | −4557.40 | −0.483855 | ||||||||
\(447\) | −3023.41 | −0.319915 | ||||||||
\(448\) | −6002.90 | −0.633059 | ||||||||
\(449\) | 10146.6 | 1.06648 | 0.533238 | − | 0.845965i | \(-0.320975\pi\) | ||||
0.533238 | + | 0.845965i | \(0.320975\pi\) | |||||||
\(450\) | 1376.78 | 0.144227 | ||||||||
\(451\) | 2439.65 | 0.254720 | ||||||||
\(452\) | −5405.22 | −0.562478 | ||||||||
\(453\) | −5778.54 | −0.599336 | ||||||||
\(454\) | 1720.01 | 0.177806 | ||||||||
\(455\) | 7475.65 | 0.770250 | ||||||||
\(456\) | 7510.71 | 0.771318 | ||||||||
\(457\) | −7173.92 | −0.734315 | −0.367157 | − | 0.930159i | \(-0.619669\pi\) | ||||
−0.367157 | + | 0.930159i | \(0.619669\pi\) | |||||||
\(458\) | −7485.47 | −0.763697 | ||||||||
\(459\) | −2637.14 | −0.268173 | ||||||||
\(460\) | 4463.53 | 0.452420 | ||||||||
\(461\) | −15959.8 | −1.61242 | −0.806208 | − | 0.591632i | \(-0.798484\pi\) | ||||
−0.806208 | + | 0.591632i | \(0.798484\pi\) | |||||||
\(462\) | 1284.17 | 0.129318 | ||||||||
\(463\) | 10486.8 | 1.05262 | 0.526308 | − | 0.850294i | \(-0.323576\pi\) | ||||
0.526308 | + | 0.850294i | \(0.323576\pi\) | |||||||
\(464\) | 293.216 | 0.0293366 | ||||||||
\(465\) | 2777.71 | 0.277018 | ||||||||
\(466\) | −678.205 | −0.0674190 | ||||||||
\(467\) | −11871.2 | −1.17630 | −0.588150 | − | 0.808752i | \(-0.700144\pi\) | ||||
−0.588150 | + | 0.808752i | \(0.700144\pi\) | |||||||
\(468\) | 2896.82 | 0.286123 | ||||||||
\(469\) | −5213.20 | −0.513269 | ||||||||
\(470\) | 5851.33 | 0.574259 | ||||||||
\(471\) | −3706.75 | −0.362629 | ||||||||
\(472\) | −1345.65 | −0.131226 | ||||||||
\(473\) | −2983.00 | −0.289975 | ||||||||
\(474\) | 1015.04 | 0.0983590 | ||||||||
\(475\) | −9460.27 | −0.913825 | ||||||||
\(476\) | −8562.54 | −0.824503 | ||||||||
\(477\) | 3582.26 | 0.343858 | ||||||||
\(478\) | 7223.72 | 0.691225 | ||||||||
\(479\) | −9570.85 | −0.912950 | −0.456475 | − | 0.889736i | \(-0.650888\pi\) | ||||
−0.456475 | + | 0.889736i | \(0.650888\pi\) | |||||||
\(480\) | −3354.33 | −0.318966 | ||||||||
\(481\) | 29624.6 | 2.80824 | ||||||||
\(482\) | −8117.28 | −0.767078 | ||||||||
\(483\) | 8012.24 | 0.754803 | ||||||||
\(484\) | 5591.54 | 0.525126 | ||||||||
\(485\) | 9271.34 | 0.868021 | ||||||||
\(486\) | −431.325 | −0.0402578 | ||||||||
\(487\) | 11208.2 | 1.04290 | 0.521451 | − | 0.853281i | \(-0.325391\pi\) | ||||
0.521451 | + | 0.853281i | \(0.325391\pi\) | |||||||
\(488\) | 17982.2 | 1.66806 | ||||||||
\(489\) | 10993.6 | 1.01666 | ||||||||
\(490\) | 179.046 | 0.0165071 | ||||||||
\(491\) | 7720.19 | 0.709587 | 0.354793 | − | 0.934945i | \(-0.384551\pi\) | ||||
0.354793 | + | 0.934945i | \(0.384551\pi\) | |||||||
\(492\) | −2660.60 | −0.243799 | ||||||||
\(493\) | 16959.7 | 1.54934 | ||||||||
\(494\) | 12932.2 | 1.17783 | ||||||||
\(495\) | 748.006 | 0.0679199 | ||||||||
\(496\) | −250.956 | −0.0227182 | ||||||||
\(497\) | 2527.35 | 0.228103 | ||||||||
\(498\) | −2186.54 | −0.196750 | ||||||||
\(499\) | −3679.73 | −0.330115 | −0.165057 | − | 0.986284i | \(-0.552781\pi\) | ||||
−0.165057 | + | 0.986284i | \(0.552781\pi\) | |||||||
\(500\) | 6380.48 | 0.570687 | ||||||||
\(501\) | 11859.9 | 1.05761 | ||||||||
\(502\) | −7568.00 | −0.672861 | ||||||||
\(503\) | 15306.9 | 1.35686 | 0.678431 | − | 0.734664i | \(-0.262660\pi\) | ||||
0.678431 | + | 0.734664i | \(0.262660\pi\) | |||||||
\(504\) | −3710.82 | −0.327963 | ||||||||
\(505\) | −8022.62 | −0.706935 | ||||||||
\(506\) | 3498.15 | 0.307336 | ||||||||
\(507\) | 6625.28 | 0.580353 | ||||||||
\(508\) | 6147.77 | 0.536935 | ||||||||
\(509\) | −9361.34 | −0.815195 | −0.407597 | − | 0.913162i | \(-0.633633\pi\) | ||||
−0.407597 | + | 0.913162i | \(0.633633\pi\) | |||||||
\(510\) | 3240.39 | 0.281347 | ||||||||
\(511\) | −9926.14 | −0.859308 | ||||||||
\(512\) | 611.164 | 0.0527537 | ||||||||
\(513\) | 2963.76 | 0.255074 | ||||||||
\(514\) | −6671.52 | −0.572506 | ||||||||
\(515\) | −2922.14 | −0.250029 | ||||||||
\(516\) | 3253.15 | 0.277543 | ||||||||
\(517\) | −7058.34 | −0.600436 | ||||||||
\(518\) | −14322.0 | −1.21481 | ||||||||
\(519\) | −6675.82 | −0.564617 | ||||||||
\(520\) | −9431.53 | −0.795385 | ||||||||
\(521\) | −5933.23 | −0.498924 | −0.249462 | − | 0.968385i | \(-0.580254\pi\) | ||||
−0.249462 | + | 0.968385i | \(0.580254\pi\) | |||||||
\(522\) | 2773.89 | 0.232586 | ||||||||
\(523\) | 17269.3 | 1.44385 | 0.721925 | − | 0.691972i | \(-0.243258\pi\) | ||||
0.721925 | + | 0.691972i | \(0.243258\pi\) | |||||||
\(524\) | 10278.2 | 0.856879 | ||||||||
\(525\) | 4674.05 | 0.388557 | ||||||||
\(526\) | 5028.09 | 0.416797 | ||||||||
\(527\) | −14515.4 | −1.19981 | ||||||||
\(528\) | −67.5795 | −0.00557012 | ||||||||
\(529\) | 9658.83 | 0.793855 | ||||||||
\(530\) | −4401.70 | −0.360750 | ||||||||
\(531\) | −531.000 | −0.0433963 | ||||||||
\(532\) | 9623.03 | 0.784231 | ||||||||
\(533\) | −12138.6 | −0.986453 | ||||||||
\(534\) | −6878.91 | −0.557453 | ||||||||
\(535\) | −7708.21 | −0.622907 | ||||||||
\(536\) | 6577.15 | 0.530018 | ||||||||
\(537\) | −6391.84 | −0.513647 | ||||||||
\(538\) | 13049.0 | 1.04569 | ||||||||
\(539\) | −215.979 | −0.0172595 | ||||||||
\(540\) | −815.750 | −0.0650079 | ||||||||
\(541\) | −1132.58 | −0.0900067 | −0.0450034 | − | 0.998987i | \(-0.514330\pi\) | ||||
−0.0450034 | + | 0.998987i | \(0.514330\pi\) | |||||||
\(542\) | 7194.17 | 0.570141 | ||||||||
\(543\) | 4288.75 | 0.338946 | ||||||||
\(544\) | 17528.6 | 1.38149 | ||||||||
\(545\) | 13364.7 | 1.05042 | ||||||||
\(546\) | −6389.42 | −0.500809 | ||||||||
\(547\) | 8546.77 | 0.668069 | 0.334034 | − | 0.942561i | \(-0.391590\pi\) | ||||
0.334034 | + | 0.942561i | \(0.391590\pi\) | |||||||
\(548\) | 4100.55 | 0.319647 | ||||||||
\(549\) | 7095.84 | 0.551627 | ||||||||
\(550\) | 2040.69 | 0.158210 | ||||||||
\(551\) | −19060.2 | −1.47367 | ||||||||
\(552\) | −10108.5 | −0.779433 | ||||||||
\(553\) | 3445.95 | 0.264985 | ||||||||
\(554\) | −5421.11 | −0.415741 | ||||||||
\(555\) | −8342.32 | −0.638039 | ||||||||
\(556\) | 6745.12 | 0.514490 | ||||||||
\(557\) | −16689.2 | −1.26956 | −0.634778 | − | 0.772695i | \(-0.718908\pi\) | ||||
−0.634778 | + | 0.772695i | \(0.718908\pi\) | |||||||
\(558\) | −2374.10 | −0.180114 | ||||||||
\(559\) | 14842.0 | 1.12299 | ||||||||
\(560\) | 190.193 | 0.0143520 | ||||||||
\(561\) | −3908.82 | −0.294172 | ||||||||
\(562\) | 6234.23 | 0.467927 | ||||||||
\(563\) | −6844.25 | −0.512346 | −0.256173 | − | 0.966631i | \(-0.582462\pi\) | ||||
−0.256173 | + | 0.966631i | \(0.582462\pi\) | |||||||
\(564\) | 7697.59 | 0.574693 | ||||||||
\(565\) | 6944.41 | 0.517086 | ||||||||
\(566\) | 14121.0 | 1.04867 | ||||||||
\(567\) | −1464.31 | −0.108457 | ||||||||
\(568\) | −3188.58 | −0.235546 | ||||||||
\(569\) | −12047.3 | −0.887611 | −0.443806 | − | 0.896123i | \(-0.646372\pi\) | ||||
−0.443806 | + | 0.896123i | \(0.646372\pi\) | |||||||
\(570\) | −3641.72 | −0.267605 | ||||||||
\(571\) | −14990.8 | −1.09868 | −0.549338 | − | 0.835600i | \(-0.685120\pi\) | ||||
−0.549338 | + | 0.835600i | \(0.685120\pi\) | |||||||
\(572\) | 4293.72 | 0.313863 | ||||||||
\(573\) | −2761.51 | −0.201333 | ||||||||
\(574\) | 5868.39 | 0.426728 | ||||||||
\(575\) | 12732.4 | 0.923439 | ||||||||
\(576\) | 2988.52 | 0.216183 | ||||||||
\(577\) | −5773.70 | −0.416572 | −0.208286 | − | 0.978068i | \(-0.566788\pi\) | ||||
−0.208286 | + | 0.978068i | \(0.566788\pi\) | |||||||
\(578\) | −8212.61 | −0.591002 | ||||||||
\(579\) | −5610.16 | −0.402677 | ||||||||
\(580\) | 5246.16 | 0.375577 | ||||||||
\(581\) | −7423.10 | −0.530055 | ||||||||
\(582\) | −7924.19 | −0.564379 | ||||||||
\(583\) | 5309.69 | 0.377195 | ||||||||
\(584\) | 12523.1 | 0.887348 | ||||||||
\(585\) | −3721.72 | −0.263033 | ||||||||
\(586\) | −8756.54 | −0.617286 | ||||||||
\(587\) | −1595.79 | −0.112207 | −0.0561034 | − | 0.998425i | \(-0.517868\pi\) | ||||
−0.0561034 | + | 0.998425i | \(0.517868\pi\) | |||||||
\(588\) | 235.540 | 0.0165195 | ||||||||
\(589\) | 16313.1 | 1.14121 | ||||||||
\(590\) | 652.467 | 0.0455282 | ||||||||
\(591\) | −1429.53 | −0.0994978 | ||||||||
\(592\) | 753.698 | 0.0523256 | ||||||||
\(593\) | 5301.19 | 0.367106 | 0.183553 | − | 0.983010i | \(-0.441240\pi\) | ||||
0.183553 | + | 0.983010i | \(0.441240\pi\) | |||||||
\(594\) | −639.318 | −0.0441608 | ||||||||
\(595\) | 11000.8 | 0.757966 | ||||||||
\(596\) | 4887.20 | 0.335885 | ||||||||
\(597\) | 12492.2 | 0.856405 | ||||||||
\(598\) | −17405.2 | −1.19022 | ||||||||
\(599\) | 12610.9 | 0.860211 | 0.430105 | − | 0.902779i | \(-0.358476\pi\) | ||||
0.430105 | + | 0.902779i | \(0.358476\pi\) | |||||||
\(600\) | −5896.93 | −0.401236 | ||||||||
\(601\) | −27751.9 | −1.88357 | −0.941783 | − | 0.336221i | \(-0.890851\pi\) | ||||
−0.941783 | + | 0.336221i | \(0.890851\pi\) | |||||||
\(602\) | −7175.37 | −0.485791 | ||||||||
\(603\) | 2595.37 | 0.175276 | ||||||||
\(604\) | 9340.76 | 0.629255 | ||||||||
\(605\) | −7183.80 | −0.482749 | ||||||||
\(606\) | 6856.91 | 0.459642 | ||||||||
\(607\) | −20229.0 | −1.35267 | −0.676334 | − | 0.736595i | \(-0.736433\pi\) | ||||
−0.676334 | + | 0.736595i | \(0.736433\pi\) | |||||||
\(608\) | −19699.5 | −1.31402 | ||||||||
\(609\) | 9417.09 | 0.626601 | ||||||||
\(610\) | −8719.02 | −0.578726 | ||||||||
\(611\) | 35119.0 | 2.32531 | ||||||||
\(612\) | 4262.83 | 0.281560 | ||||||||
\(613\) | −21903.1 | −1.44316 | −0.721580 | − | 0.692331i | \(-0.756584\pi\) | ||||
−0.721580 | + | 0.692331i | \(0.756584\pi\) | |||||||
\(614\) | 7743.67 | 0.508972 | ||||||||
\(615\) | 3418.24 | 0.224125 | ||||||||
\(616\) | −5500.25 | −0.359759 | ||||||||
\(617\) | 8023.42 | 0.523519 | 0.261759 | − | 0.965133i | \(-0.415697\pi\) | ||||
0.261759 | + | 0.965133i | \(0.415697\pi\) | |||||||
\(618\) | 2497.54 | 0.162566 | ||||||||
\(619\) | −6262.61 | −0.406649 | −0.203324 | − | 0.979111i | \(-0.565175\pi\) | ||||
−0.203324 | + | 0.979111i | \(0.565175\pi\) | |||||||
\(620\) | −4490.05 | −0.290846 | ||||||||
\(621\) | −3988.86 | −0.257758 | ||||||||
\(622\) | 6287.64 | 0.405324 | ||||||||
\(623\) | −23353.2 | −1.50181 | ||||||||
\(624\) | 336.244 | 0.0215714 | ||||||||
\(625\) | 2575.56 | 0.164836 | ||||||||
\(626\) | 3210.35 | 0.204970 | ||||||||
\(627\) | 4392.93 | 0.279804 | ||||||||
\(628\) | 5991.81 | 0.380731 | ||||||||
\(629\) | 43594.1 | 2.76345 | ||||||||
\(630\) | 1799.27 | 0.113785 | ||||||||
\(631\) | −6018.53 | −0.379705 | −0.189852 | − | 0.981813i | \(-0.560801\pi\) | ||||
−0.189852 | + | 0.981813i | \(0.560801\pi\) | |||||||
\(632\) | −4347.53 | −0.273632 | ||||||||
\(633\) | −7497.62 | −0.470780 | ||||||||
\(634\) | −536.189 | −0.0335880 | ||||||||
\(635\) | −7898.42 | −0.493605 | ||||||||
\(636\) | −5790.56 | −0.361023 | ||||||||
\(637\) | 1074.61 | 0.0668409 | ||||||||
\(638\) | 4111.51 | 0.255135 | ||||||||
\(639\) | −1258.23 | −0.0778948 | ||||||||
\(640\) | 5272.74 | 0.325661 | ||||||||
\(641\) | 3669.06 | 0.226083 | 0.113041 | − | 0.993590i | \(-0.463941\pi\) | ||||
0.113041 | + | 0.993590i | \(0.463941\pi\) | |||||||
\(642\) | 6588.19 | 0.405008 | ||||||||
\(643\) | −9099.99 | −0.558116 | −0.279058 | − | 0.960274i | \(-0.590022\pi\) | ||||
−0.279058 | + | 0.960274i | \(0.590022\pi\) | |||||||
\(644\) | −12951.4 | −0.792482 | ||||||||
\(645\) | −4179.53 | −0.255145 | ||||||||
\(646\) | 19030.4 | 1.15904 | ||||||||
\(647\) | −1873.56 | −0.113844 | −0.0569222 | − | 0.998379i | \(-0.518129\pi\) | ||||
−0.0569222 | + | 0.998379i | \(0.518129\pi\) | |||||||
\(648\) | 1847.42 | 0.111996 | ||||||||
\(649\) | −787.058 | −0.0476036 | ||||||||
\(650\) | −10153.5 | −0.612699 | ||||||||
\(651\) | −8059.84 | −0.485238 | ||||||||
\(652\) | −17770.7 | −1.06741 | ||||||||
\(653\) | −23009.5 | −1.37892 | −0.689458 | − | 0.724325i | \(-0.742151\pi\) | ||||
−0.689458 | + | 0.724325i | \(0.742151\pi\) | |||||||
\(654\) | −11422.8 | −0.682975 | ||||||||
\(655\) | −13205.0 | −0.787729 | ||||||||
\(656\) | −308.825 | −0.0183805 | ||||||||
\(657\) | 4941.69 | 0.293445 | ||||||||
\(658\) | −16978.3 | −1.00590 | ||||||||
\(659\) | −10038.1 | −0.593368 | −0.296684 | − | 0.954976i | \(-0.595881\pi\) | ||||
−0.296684 | + | 0.954976i | \(0.595881\pi\) | |||||||
\(660\) | −1209.12 | −0.0713104 | ||||||||
\(661\) | −21406.5 | −1.25963 | −0.629816 | − | 0.776744i | \(-0.716870\pi\) | ||||
−0.629816 | + | 0.776744i | \(0.716870\pi\) | |||||||
\(662\) | 7336.38 | 0.430720 | ||||||||
\(663\) | 19448.5 | 1.13924 | ||||||||
\(664\) | 9365.23 | 0.547351 | ||||||||
\(665\) | −12363.3 | −0.720944 | ||||||||
\(666\) | 7130.16 | 0.414847 | ||||||||
\(667\) | 25652.7 | 1.48917 | ||||||||
\(668\) | −19171.0 | −1.11040 | ||||||||
\(669\) | 7702.65 | 0.445144 | ||||||||
\(670\) | −3189.07 | −0.183887 | ||||||||
\(671\) | 10517.6 | 0.605107 | ||||||||
\(672\) | 9732.98 | 0.558717 | ||||||||
\(673\) | −934.831 | −0.0535439 | −0.0267720 | − | 0.999642i | \(-0.508523\pi\) | ||||
−0.0267720 | + | 0.999642i | \(0.508523\pi\) | |||||||
\(674\) | 5762.30 | 0.329311 | ||||||||
\(675\) | −2326.96 | −0.132688 | ||||||||
\(676\) | −10709.5 | −0.609324 | ||||||||
\(677\) | −3937.51 | −0.223531 | −0.111766 | − | 0.993735i | \(-0.535651\pi\) | ||||
−0.111766 | + | 0.993735i | \(0.535651\pi\) | |||||||
\(678\) | −5935.37 | −0.336204 | ||||||||
\(679\) | −26901.9 | −1.52047 | ||||||||
\(680\) | −13879.0 | −0.782699 | ||||||||
\(681\) | −2907.05 | −0.163581 | ||||||||
\(682\) | −3518.93 | −0.197576 | ||||||||
\(683\) | −12374.6 | −0.693268 | −0.346634 | − | 0.938001i | \(-0.612675\pi\) | ||||
−0.346634 | + | 0.938001i | \(0.612675\pi\) | |||||||
\(684\) | −4790.79 | −0.267807 | ||||||||
\(685\) | −5268.22 | −0.293852 | ||||||||
\(686\) | −11525.8 | −0.641482 | ||||||||
\(687\) | 12651.5 | 0.702598 | ||||||||
\(688\) | 377.605 | 0.0209245 | ||||||||
\(689\) | −26418.5 | −1.46076 | ||||||||
\(690\) | 4901.32 | 0.270420 | ||||||||
\(691\) | −5887.06 | −0.324102 | −0.162051 | − | 0.986782i | \(-0.551811\pi\) | ||||
−0.162051 | + | 0.986782i | \(0.551811\pi\) | |||||||
\(692\) | 10791.2 | 0.592802 | ||||||||
\(693\) | −2170.42 | −0.118972 | ||||||||
\(694\) | −823.443 | −0.0450396 | ||||||||
\(695\) | −8665.87 | −0.472971 | ||||||||
\(696\) | −11880.9 | −0.647047 | ||||||||
\(697\) | −17862.5 | −0.970720 | ||||||||
\(698\) | 11725.8 | 0.635855 | ||||||||
\(699\) | 1146.26 | 0.0620252 | ||||||||
\(700\) | −7555.40 | −0.407953 | ||||||||
\(701\) | 7809.40 | 0.420766 | 0.210383 | − | 0.977619i | \(-0.432529\pi\) | ||||
0.210383 | + | 0.977619i | \(0.432529\pi\) | |||||||
\(702\) | 3180.95 | 0.171022 | ||||||||
\(703\) | −48993.3 | −2.62847 | ||||||||
\(704\) | 4429.64 | 0.237142 | ||||||||
\(705\) | −9889.56 | −0.528316 | ||||||||
\(706\) | 11155.1 | 0.594656 | ||||||||
\(707\) | 23278.6 | 1.23830 | ||||||||
\(708\) | 858.339 | 0.0455626 | ||||||||
\(709\) | 13649.5 | 0.723018 | 0.361509 | − | 0.932369i | \(-0.382262\pi\) | ||||
0.361509 | + | 0.932369i | \(0.382262\pi\) | |||||||
\(710\) | 1546.05 | 0.0817215 | ||||||||
\(711\) | −1715.55 | −0.0904898 | ||||||||
\(712\) | 29463.2 | 1.55082 | ||||||||
\(713\) | −21955.5 | −1.15321 | ||||||||
\(714\) | −9402.37 | −0.492822 | ||||||||
\(715\) | −5516.41 | −0.288534 | ||||||||
\(716\) | 10332.1 | 0.539288 | ||||||||
\(717\) | −12209.1 | −0.635923 | ||||||||
\(718\) | −10248.7 | −0.532701 | ||||||||
\(719\) | 475.869 | 0.0246828 | 0.0123414 | − | 0.999924i | \(-0.496072\pi\) | ||||
0.0123414 | + | 0.999924i | \(0.496072\pi\) | |||||||
\(720\) | −94.6868 | −0.00490107 | ||||||||
\(721\) | 8478.92 | 0.437963 | ||||||||
\(722\) | −9212.60 | −0.474872 | ||||||||
\(723\) | 13719.3 | 0.705709 | ||||||||
\(724\) | −6932.57 | −0.355866 | ||||||||
\(725\) | 14964.9 | 0.766594 | ||||||||
\(726\) | 6139.97 | 0.313878 | ||||||||
\(727\) | −8057.43 | −0.411050 | −0.205525 | − | 0.978652i | \(-0.565890\pi\) | ||||
−0.205525 | + | 0.978652i | \(0.565890\pi\) | |||||||
\(728\) | 27366.7 | 1.39324 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −6072.11 | −0.307861 | ||||||||
\(731\) | 21840.8 | 1.10508 | ||||||||
\(732\) | −11470.1 | −0.579164 | ||||||||
\(733\) | 28918.2 | 1.45719 | 0.728594 | − | 0.684946i | \(-0.240174\pi\) | ||||
0.728594 | + | 0.684946i | \(0.240174\pi\) | |||||||
\(734\) | 1189.19 | 0.0598007 | ||||||||
\(735\) | −302.612 | −0.0151864 | ||||||||
\(736\) | 26513.2 | 1.32784 | ||||||||
\(737\) | 3846.91 | 0.192270 | ||||||||
\(738\) | −2921.56 | −0.145724 | ||||||||
\(739\) | −25403.3 | −1.26451 | −0.632256 | − | 0.774760i | \(-0.717871\pi\) | ||||
−0.632256 | + | 0.774760i | \(0.717871\pi\) | |||||||
\(740\) | 13485.0 | 0.669890 | ||||||||
\(741\) | −21857.2 | −1.08359 | ||||||||
\(742\) | 12772.0 | 0.631909 | ||||||||
\(743\) | −30468.3 | −1.50441 | −0.752204 | − | 0.658930i | \(-0.771009\pi\) | ||||
−0.752204 | + | 0.658930i | \(0.771009\pi\) | |||||||
\(744\) | 10168.6 | 0.501072 | ||||||||
\(745\) | −6278.89 | −0.308779 | ||||||||
\(746\) | −5938.77 | −0.291466 | ||||||||
\(747\) | 3695.56 | 0.181009 | ||||||||
\(748\) | 6318.44 | 0.308857 | ||||||||
\(749\) | 22366.3 | 1.09112 | ||||||||
\(750\) | 7006.29 | 0.341111 | ||||||||
\(751\) | −1951.23 | −0.0948088 | −0.0474044 | − | 0.998876i | \(-0.515095\pi\) | ||||
−0.0474044 | + | 0.998876i | \(0.515095\pi\) | |||||||
\(752\) | 893.485 | 0.0433272 | ||||||||
\(753\) | 12791.0 | 0.619029 | ||||||||
\(754\) | −20456.9 | −0.988061 | ||||||||
\(755\) | −12000.6 | −0.578474 | ||||||||
\(756\) | 2366.99 | 0.113871 | ||||||||
\(757\) | 13529.5 | 0.649588 | 0.324794 | − | 0.945785i | \(-0.394705\pi\) | ||||
0.324794 | + | 0.945785i | \(0.394705\pi\) | |||||||
\(758\) | −12213.8 | −0.585257 | ||||||||
\(759\) | −5912.37 | −0.282747 | ||||||||
\(760\) | 15597.9 | 0.744469 | ||||||||
\(761\) | 31379.5 | 1.49475 | 0.747376 | − | 0.664402i | \(-0.231314\pi\) | ||||
0.747376 | + | 0.664402i | \(0.231314\pi\) | |||||||
\(762\) | 6750.75 | 0.320937 | ||||||||
\(763\) | −38779.2 | −1.83998 | ||||||||
\(764\) | 4463.86 | 0.211383 | ||||||||
\(765\) | −5476.72 | −0.258838 | ||||||||
\(766\) | 7243.52 | 0.341670 | ||||||||
\(767\) | 3916.03 | 0.184354 | ||||||||
\(768\) | −12476.0 | −0.586182 | ||||||||
\(769\) | −1805.38 | −0.0846604 | −0.0423302 | − | 0.999104i | \(-0.513478\pi\) | ||||
−0.0423302 | + | 0.999104i | \(0.513478\pi\) | |||||||
\(770\) | 2666.91 | 0.124817 | ||||||||
\(771\) | 11275.8 | 0.526703 | ||||||||
\(772\) | 9068.58 | 0.422779 | ||||||||
\(773\) | 27743.2 | 1.29089 | 0.645443 | − | 0.763808i | \(-0.276673\pi\) | ||||
0.645443 | + | 0.763808i | \(0.276673\pi\) | |||||||
\(774\) | 3572.23 | 0.165893 | ||||||||
\(775\) | −12808.0 | −0.593649 | ||||||||
\(776\) | 33940.3 | 1.57008 | ||||||||
\(777\) | 24206.2 | 1.11762 | ||||||||
\(778\) | 8340.38 | 0.384341 | ||||||||
\(779\) | 20074.8 | 0.923306 | ||||||||
\(780\) | 6016.01 | 0.276164 | ||||||||
\(781\) | −1864.97 | −0.0854467 | ||||||||
\(782\) | −25612.6 | −1.17123 | ||||||||
\(783\) | −4688.26 | −0.213978 | ||||||||
\(784\) | 27.3399 | 0.00124544 | ||||||||
\(785\) | −7698.04 | −0.350006 | ||||||||
\(786\) | 11286.3 | 0.512173 | ||||||||
\(787\) | −2980.67 | −0.135005 | −0.0675027 | − | 0.997719i | \(-0.521503\pi\) | ||||
−0.0675027 | + | 0.997719i | \(0.521503\pi\) | |||||||
\(788\) | 2310.78 | 0.104465 | ||||||||
\(789\) | −8498.17 | −0.383451 | ||||||||
\(790\) | 2107.99 | 0.0949352 | ||||||||
\(791\) | −20150.0 | −0.905755 | ||||||||
\(792\) | 2738.28 | 0.122854 | ||||||||
\(793\) | −52330.6 | −2.34340 | ||||||||
\(794\) | −18270.1 | −0.816603 | ||||||||
\(795\) | 7439.49 | 0.331889 | ||||||||
\(796\) | −20193.2 | −0.899156 | ||||||||
\(797\) | 26151.2 | 1.16226 | 0.581131 | − | 0.813810i | \(-0.302610\pi\) | ||||
0.581131 | + | 0.813810i | \(0.302610\pi\) | |||||||
\(798\) | 10566.9 | 0.468751 | ||||||||
\(799\) | 51679.5 | 2.28822 | ||||||||
\(800\) | 15466.8 | 0.683544 | ||||||||
\(801\) | 11626.3 | 0.512854 | ||||||||
\(802\) | −13620.2 | −0.599684 | ||||||||
\(803\) | 7324.66 | 0.321895 | ||||||||
\(804\) | −4195.31 | −0.184026 | ||||||||
\(805\) | 16639.5 | 0.728529 | ||||||||
\(806\) | 17508.6 | 0.765152 | ||||||||
\(807\) | −22054.6 | −0.962030 | ||||||||
\(808\) | −29369.0 | −1.27871 | ||||||||
\(809\) | −30368.8 | −1.31979 | −0.659895 | − | 0.751358i | \(-0.729399\pi\) | ||||
−0.659895 | + | 0.751358i | \(0.729399\pi\) | |||||||
\(810\) | −895.760 | −0.0388565 | ||||||||
\(811\) | −5497.72 | −0.238041 | −0.119020 | − | 0.992892i | \(-0.537975\pi\) | ||||
−0.119020 | + | 0.992892i | \(0.537975\pi\) | |||||||
\(812\) | −15222.3 | −0.657880 | ||||||||
\(813\) | −12159.2 | −0.524527 | ||||||||
\(814\) | 10568.4 | 0.455066 | ||||||||
\(815\) | 22831.0 | 0.981272 | ||||||||
\(816\) | 494.801 | 0.0212273 | ||||||||
\(817\) | −24545.8 | −1.05110 | ||||||||
\(818\) | −6581.02 | −0.281296 | ||||||||
\(819\) | 10799.0 | 0.460742 | ||||||||
\(820\) | −5525.43 | −0.235313 | ||||||||
\(821\) | −33287.7 | −1.41504 | −0.707521 | − | 0.706692i | \(-0.750186\pi\) | ||||
−0.707521 | + | 0.706692i | \(0.750186\pi\) | |||||||
\(822\) | 4502.74 | 0.191060 | ||||||||
\(823\) | −13109.6 | −0.555253 | −0.277626 | − | 0.960689i | \(-0.589548\pi\) | ||||
−0.277626 | + | 0.960689i | \(0.589548\pi\) | |||||||
\(824\) | −10697.3 | −0.452254 | ||||||||
\(825\) | −3449.06 | −0.145552 | ||||||||
\(826\) | −1893.21 | −0.0797495 | ||||||||
\(827\) | 31629.7 | 1.32995 | 0.664977 | − | 0.746864i | \(-0.268441\pi\) | ||||
0.664977 | + | 0.746864i | \(0.268441\pi\) | |||||||
\(828\) | 6447.83 | 0.270625 | ||||||||
\(829\) | 23175.2 | 0.970938 | 0.485469 | − | 0.874254i | \(-0.338649\pi\) | ||||
0.485469 | + | 0.874254i | \(0.338649\pi\) | |||||||
\(830\) | −4540.92 | −0.189901 | ||||||||
\(831\) | 9162.42 | 0.382480 | ||||||||
\(832\) | −22039.8 | −0.918380 | ||||||||
\(833\) | 1581.35 | 0.0657748 | ||||||||
\(834\) | 7406.69 | 0.307521 | ||||||||
\(835\) | 24630.1 | 1.02079 | ||||||||
\(836\) | −7100.99 | −0.293771 | ||||||||
\(837\) | 4012.56 | 0.165704 | ||||||||
\(838\) | 20158.7 | 0.830990 | ||||||||
\(839\) | 24731.6 | 1.01767 | 0.508837 | − | 0.860863i | \(-0.330076\pi\) | ||||
0.508837 | + | 0.860863i | \(0.330076\pi\) | |||||||
\(840\) | −7706.50 | −0.316547 | ||||||||
\(841\) | 5761.61 | 0.236238 | ||||||||
\(842\) | −6769.91 | −0.277086 | ||||||||
\(843\) | −10536.7 | −0.430491 | ||||||||
\(844\) | 12119.6 | 0.494281 | ||||||||
\(845\) | 13759.1 | 0.560151 | ||||||||
\(846\) | 8452.58 | 0.343506 | ||||||||
\(847\) | 20844.6 | 0.845607 | ||||||||
\(848\) | −672.130 | −0.0272182 | ||||||||
\(849\) | −23866.4 | −0.964773 | ||||||||
\(850\) | −14941.5 | −0.602927 | ||||||||
\(851\) | 65939.1 | 2.65613 | ||||||||
\(852\) | 2033.87 | 0.0817833 | ||||||||
\(853\) | 26779.6 | 1.07493 | 0.537466 | − | 0.843285i | \(-0.319382\pi\) | ||||
0.537466 | + | 0.843285i | \(0.319382\pi\) | |||||||
\(854\) | 25299.2 | 1.01373 | ||||||||
\(855\) | 6155.02 | 0.246195 | ||||||||
\(856\) | −28218.0 | −1.12672 | ||||||||
\(857\) | 32339.7 | 1.28904 | 0.644518 | − | 0.764589i | \(-0.277058\pi\) | ||||
0.644518 | + | 0.764589i | \(0.277058\pi\) | |||||||
\(858\) | 4714.86 | 0.187602 | ||||||||
\(859\) | 41682.2 | 1.65562 | 0.827810 | − | 0.561009i | \(-0.189587\pi\) | ||||
0.827810 | + | 0.561009i | \(0.189587\pi\) | |||||||
\(860\) | 6756.02 | 0.267882 | ||||||||
\(861\) | −9918.40 | −0.392588 | ||||||||
\(862\) | 2320.08 | 0.0916732 | ||||||||
\(863\) | −15307.7 | −0.603802 | −0.301901 | − | 0.953339i | \(-0.597621\pi\) | ||||
−0.301901 | + | 0.953339i | \(0.597621\pi\) | |||||||
\(864\) | −4845.52 | −0.190796 | ||||||||
\(865\) | −13864.1 | −0.544963 | ||||||||
\(866\) | −14050.4 | −0.551332 | ||||||||
\(867\) | 13880.5 | 0.543720 | ||||||||
\(868\) | 13028.4 | 0.509461 | ||||||||
\(869\) | −2542.82 | −0.0992628 | ||||||||
\(870\) | 5760.71 | 0.224490 | ||||||||
\(871\) | −19140.4 | −0.744601 | ||||||||
\(872\) | 48925.1 | 1.90002 | ||||||||
\(873\) | 13393.0 | 0.519226 | ||||||||
\(874\) | 28784.8 | 1.11403 | ||||||||
\(875\) | 23785.7 | 0.918974 | ||||||||
\(876\) | −7988.03 | −0.308094 | ||||||||
\(877\) | −42064.0 | −1.61961 | −0.809807 | − | 0.586696i | \(-0.800428\pi\) | ||||
−0.809807 | + | 0.586696i | \(0.800428\pi\) | |||||||
\(878\) | −4562.56 | −0.175374 | ||||||||
\(879\) | 14799.8 | 0.567900 | ||||||||
\(880\) | −140.346 | −0.00537623 | ||||||||
\(881\) | −983.391 | −0.0376065 | −0.0188032 | − | 0.999823i | \(-0.505986\pi\) | ||||
−0.0188032 | + | 0.999823i | \(0.505986\pi\) | |||||||
\(882\) | 258.642 | 0.00987405 | ||||||||
\(883\) | 3067.46 | 0.116906 | 0.0584531 | − | 0.998290i | \(-0.481383\pi\) | ||||
0.0584531 | + | 0.998290i | \(0.481383\pi\) | |||||||
\(884\) | −31437.6 | −1.19611 | ||||||||
\(885\) | −1102.76 | −0.0418857 | ||||||||
\(886\) | 1123.79 | 0.0426123 | ||||||||
\(887\) | 15178.8 | 0.574583 | 0.287291 | − | 0.957843i | \(-0.407245\pi\) | ||||
0.287291 | + | 0.957843i | \(0.407245\pi\) | |||||||
\(888\) | −30539.3 | −1.15409 | ||||||||
\(889\) | 22918.2 | 0.864624 | ||||||||
\(890\) | −14285.9 | −0.538048 | ||||||||
\(891\) | 1080.54 | 0.0406278 | ||||||||
\(892\) | −12451.0 | −0.467366 | ||||||||
\(893\) | −58080.1 | −2.17646 | ||||||||
\(894\) | 5366.55 | 0.200765 | ||||||||
\(895\) | −13274.3 | −0.495767 | ||||||||
\(896\) | −15299.4 | −0.570445 | ||||||||
\(897\) | 29417.1 | 1.09499 | ||||||||
\(898\) | −18010.2 | −0.669275 | ||||||||
\(899\) | −25805.1 | −0.957340 | ||||||||
\(900\) | 3761.42 | 0.139312 | ||||||||
\(901\) | −38876.2 | −1.43746 | ||||||||
\(902\) | −4330.38 | −0.159851 | ||||||||
\(903\) | 12127.4 | 0.446925 | ||||||||
\(904\) | 25421.9 | 0.935310 | ||||||||
\(905\) | 8906.70 | 0.327148 | ||||||||
\(906\) | 10256.9 | 0.376118 | ||||||||
\(907\) | −2893.09 | −0.105914 | −0.0529568 | − | 0.998597i | \(-0.516865\pi\) | ||||
−0.0529568 | + | 0.998597i | \(0.516865\pi\) | |||||||
\(908\) | 4699.13 | 0.171747 | ||||||||
\(909\) | −11589.1 | −0.422869 | ||||||||
\(910\) | −13269.3 | −0.483377 | ||||||||
\(911\) | −2299.05 | −0.0836124 | −0.0418062 | − | 0.999126i | \(-0.513311\pi\) | ||||
−0.0418062 | + | 0.999126i | \(0.513311\pi\) | |||||||
\(912\) | −556.083 | −0.0201905 | ||||||||
\(913\) | 5477.63 | 0.198557 | ||||||||
\(914\) | 12733.7 | 0.460825 | ||||||||
\(915\) | 14736.4 | 0.532425 | ||||||||
\(916\) | −20450.6 | −0.737671 | ||||||||
\(917\) | 38315.8 | 1.37983 | ||||||||
\(918\) | 4680.93 | 0.168294 | ||||||||
\(919\) | −45794.9 | −1.64378 | −0.821891 | − | 0.569645i | \(-0.807081\pi\) | ||||
−0.821891 | + | 0.569645i | \(0.807081\pi\) | |||||||
\(920\) | −20993.0 | −0.752301 | ||||||||
\(921\) | −13087.9 | −0.468252 | ||||||||
\(922\) | 28328.7 | 1.01188 | ||||||||
\(923\) | 9279.22 | 0.330909 | ||||||||
\(924\) | 3508.40 | 0.124911 | ||||||||
\(925\) | 38466.5 | 1.36732 | ||||||||
\(926\) | −18614.0 | −0.660578 | ||||||||
\(927\) | −4221.20 | −0.149560 | ||||||||
\(928\) | 31162.0 | 1.10231 | ||||||||
\(929\) | −43137.0 | −1.52344 | −0.761721 | − | 0.647905i | \(-0.775646\pi\) | ||||
−0.761721 | + | 0.647905i | \(0.775646\pi\) | |||||||
\(930\) | −4930.44 | −0.173844 | ||||||||
\(931\) | −1777.20 | −0.0625621 | ||||||||
\(932\) | −1852.88 | −0.0651214 | ||||||||
\(933\) | −10627.0 | −0.372896 | ||||||||
\(934\) | 21071.4 | 0.738197 | ||||||||
\(935\) | −8117.69 | −0.283932 | ||||||||
\(936\) | −13624.4 | −0.475777 | ||||||||
\(937\) | 20420.6 | 0.711966 | 0.355983 | − | 0.934492i | \(-0.384146\pi\) | ||||
0.355983 | + | 0.934492i | \(0.384146\pi\) | |||||||
\(938\) | 9253.44 | 0.322106 | ||||||||
\(939\) | −5425.94 | −0.188572 | ||||||||
\(940\) | 15986.1 | 0.554689 | ||||||||
\(941\) | −21235.7 | −0.735668 | −0.367834 | − | 0.929892i | \(-0.619900\pi\) | ||||
−0.367834 | + | 0.929892i | \(0.619900\pi\) | |||||||
\(942\) | 6579.49 | 0.227571 | ||||||||
\(943\) | −27018.3 | −0.933020 | ||||||||
\(944\) | 99.6303 | 0.00343505 | ||||||||
\(945\) | −3041.02 | −0.104682 | ||||||||
\(946\) | 5294.82 | 0.181976 | ||||||||
\(947\) | −21631.9 | −0.742283 | −0.371141 | − | 0.928576i | \(-0.621034\pi\) | ||||
−0.371141 | + | 0.928576i | \(0.621034\pi\) | |||||||
\(948\) | 2773.12 | 0.0950070 | ||||||||
\(949\) | −36444.1 | −1.24660 | ||||||||
\(950\) | 16792.0 | 0.573478 | ||||||||
\(951\) | 906.234 | 0.0309008 | ||||||||
\(952\) | 40271.5 | 1.37102 | ||||||||
\(953\) | 869.752 | 0.0295635 | 0.0147818 | − | 0.999891i | \(-0.495295\pi\) | ||||
0.0147818 | + | 0.999891i | \(0.495295\pi\) | |||||||
\(954\) | −6358.51 | −0.215791 | ||||||||
\(955\) | −5734.99 | −0.194324 | ||||||||
\(956\) | 19735.5 | 0.667668 | ||||||||
\(957\) | −6949.03 | −0.234723 | ||||||||
\(958\) | 16988.3 | 0.572929 | ||||||||
\(959\) | 15286.4 | 0.514726 | ||||||||
\(960\) | 6206.44 | 0.208658 | ||||||||
\(961\) | −7705.09 | −0.258638 | ||||||||
\(962\) | −52583.6 | −1.76233 | ||||||||
\(963\) | −11135.0 | −0.372605 | ||||||||
\(964\) | −22176.7 | −0.740937 | ||||||||
\(965\) | −11651.0 | −0.388661 | ||||||||
\(966\) | −14221.7 | −0.473682 | ||||||||
\(967\) | 45869.5 | 1.52540 | 0.762700 | − | 0.646752i | \(-0.223873\pi\) | ||||
0.762700 | + | 0.646752i | \(0.223873\pi\) | |||||||
\(968\) | −26298.3 | −0.873200 | ||||||||
\(969\) | −32164.0 | −1.06631 | ||||||||
\(970\) | −16456.6 | −0.544733 | ||||||||
\(971\) | 4456.05 | 0.147272 | 0.0736361 | − | 0.997285i | \(-0.476540\pi\) | ||||
0.0736361 | + | 0.997285i | \(0.476540\pi\) | |||||||
\(972\) | −1178.40 | −0.0388859 | ||||||||
\(973\) | 25145.0 | 0.828481 | ||||||||
\(974\) | −19894.6 | −0.654481 | ||||||||
\(975\) | 17160.9 | 0.563680 | ||||||||
\(976\) | −1331.38 | −0.0436642 | ||||||||
\(977\) | −34528.0 | −1.13065 | −0.565326 | − | 0.824867i | \(-0.691250\pi\) | ||||
−0.565326 | + | 0.824867i | \(0.691250\pi\) | |||||||
\(978\) | −19513.6 | −0.638013 | ||||||||
\(979\) | 17232.7 | 0.562575 | ||||||||
\(980\) | 489.159 | 0.0159445 | ||||||||
\(981\) | 19306.1 | 0.628334 | ||||||||
\(982\) | −13703.3 | −0.445307 | ||||||||
\(983\) | 17284.8 | 0.560834 | 0.280417 | − | 0.959878i | \(-0.409527\pi\) | ||||
0.280417 | + | 0.959878i | \(0.409527\pi\) | |||||||
\(984\) | 12513.4 | 0.405399 | ||||||||
\(985\) | −2968.80 | −0.0960344 | ||||||||
\(986\) | −30103.5 | −0.972303 | ||||||||
\(987\) | 28695.7 | 0.925425 | ||||||||
\(988\) | 35331.2 | 1.13769 | ||||||||
\(989\) | 33035.7 | 1.06216 | ||||||||
\(990\) | −1327.71 | −0.0426237 | ||||||||
\(991\) | −49628.1 | −1.59081 | −0.795403 | − | 0.606081i | \(-0.792741\pi\) | ||||
−0.795403 | + | 0.606081i | \(0.792741\pi\) | |||||||
\(992\) | −26670.7 | −0.853625 | ||||||||
\(993\) | −12399.5 | −0.396260 | ||||||||
\(994\) | −4486.04 | −0.143148 | ||||||||
\(995\) | 25943.4 | 0.826594 | ||||||||
\(996\) | −5973.71 | −0.190045 | ||||||||
\(997\) | −1153.92 | −0.0366549 | −0.0183274 | − | 0.999832i | \(-0.505834\pi\) | ||||
−0.0183274 | + | 0.999832i | \(0.505834\pi\) | |||||||
\(998\) | 6531.53 | 0.207166 | ||||||||
\(999\) | −12051.0 | −0.381657 |
(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 | 177.4.a.a.1.4 | ✓ | 7 | |
3.2 | odd | 2 | 531.4.a.d.1.4 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.a.a.1.4 | ✓ | 7 | 1.1 | even | 1 | trivial | |
531.4.a.d.1.4 | 7 | 3.2 | odd | 2 |