Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(168,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.168");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 168.2 | ||
Root | \(-1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.168 |
Dual form | 169.4.b.f.168.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.56155i | − 0.552092i | −0.961144 | − | 0.276046i | \(-0.910976\pi\) | ||||
0.961144 | − | 0.276046i | \(-0.0890243\pi\) | |||||||
\(3\) | 8.68466 | 1.67136 | 0.835682 | − | 0.549214i | \(-0.185073\pi\) | ||||
0.835682 | + | 0.549214i | \(0.185073\pi\) | |||||||
\(4\) | 5.56155 | 0.695194 | ||||||||
\(5\) | − 3.56155i | − 0.318555i | −0.987234 | − | 0.159277i | \(-0.949084\pi\) | ||||
0.987234 | − | 0.159277i | \(-0.0509165\pi\) | |||||||
\(6\) | − 13.5616i | − 0.922747i | ||||||||
\(7\) | 27.1771i | 1.46742i | 0.679460 | + | 0.733712i | \(0.262214\pi\) | ||||
−0.679460 | + | 0.733712i | \(0.737786\pi\) | |||||||
\(8\) | − 21.1771i | − 0.935904i | ||||||||
\(9\) | 48.4233 | 1.79346 | ||||||||
\(10\) | −5.56155 | −0.175872 | ||||||||
\(11\) | − 15.2614i | − 0.418316i | −0.977882 | − | 0.209158i | \(-0.932928\pi\) | ||||
0.977882 | − | 0.209158i | \(-0.0670723\pi\) | |||||||
\(12\) | 48.3002 | 1.16192 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 42.4384 | 0.810154 | ||||||||
\(15\) | − 30.9309i | − 0.532421i | ||||||||
\(16\) | 11.4233 | 0.178489 | ||||||||
\(17\) | −44.5464 | −0.635535 | −0.317767 | − | 0.948169i | \(-0.602933\pi\) | ||||
−0.317767 | + | 0.948169i | \(0.602933\pi\) | |||||||
\(18\) | − 75.6155i | − 0.990153i | ||||||||
\(19\) | 23.9697i | 0.289422i | 0.989474 | + | 0.144711i | \(0.0462253\pi\) | ||||
−0.989474 | + | 0.144711i | \(0.953775\pi\) | |||||||
\(20\) | − 19.8078i | − 0.221458i | ||||||||
\(21\) | 236.024i | 2.45260i | ||||||||
\(22\) | −23.8314 | −0.230949 | ||||||||
\(23\) | −122.739 | −1.11273 | −0.556365 | − | 0.830938i | \(-0.687804\pi\) | ||||
−0.556365 | + | 0.830938i | \(0.687804\pi\) | |||||||
\(24\) | − 183.916i | − 1.56423i | ||||||||
\(25\) | 112.315 | 0.898523 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 186.054 | 1.32615 | ||||||||
\(28\) | 151.147i | 1.02014i | ||||||||
\(29\) | −219.909 | −1.40814 | −0.704071 | − | 0.710130i | \(-0.748636\pi\) | ||||
−0.704071 | + | 0.710130i | \(0.748636\pi\) | |||||||
\(30\) | −48.3002 | −0.293946 | ||||||||
\(31\) | 27.0928i | 0.156968i | 0.996915 | + | 0.0784840i | \(0.0250080\pi\) | ||||
−0.996915 | + | 0.0784840i | \(0.974992\pi\) | |||||||
\(32\) | − 187.255i | − 1.03445i | ||||||||
\(33\) | − 132.540i | − 0.699158i | ||||||||
\(34\) | 69.5616i | 0.350874i | ||||||||
\(35\) | 96.7926 | 0.467455 | ||||||||
\(36\) | 269.309 | 1.24680 | ||||||||
\(37\) | − 94.1922i | − 0.418516i | −0.977860 | − | 0.209258i | \(-0.932895\pi\) | ||||
0.977860 | − | 0.209258i | \(-0.0671049\pi\) | |||||||
\(38\) | 37.4299 | 0.159788 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −75.4233 | −0.298137 | ||||||||
\(41\) | − 160.354i | − 0.610808i | −0.952223 | − | 0.305404i | \(-0.901209\pi\) | ||||
0.952223 | − | 0.305404i | \(-0.0987914\pi\) | |||||||
\(42\) | 368.563 | 1.35406 | ||||||||
\(43\) | 151.302 | 0.536589 | 0.268295 | − | 0.963337i | \(-0.413540\pi\) | ||||
0.268295 | + | 0.963337i | \(0.413540\pi\) | |||||||
\(44\) | − 84.8769i | − 0.290811i | ||||||||
\(45\) | − 172.462i | − 0.571314i | ||||||||
\(46\) | 191.663i | 0.614329i | ||||||||
\(47\) | − 466.948i | − 1.44918i | −0.689181 | − | 0.724589i | \(-0.742030\pi\) | ||||
0.689181 | − | 0.724589i | \(-0.257970\pi\) | |||||||
\(48\) | 99.2074 | 0.298320 | ||||||||
\(49\) | −395.594 | −1.15333 | ||||||||
\(50\) | − 175.386i | − 0.496067i | ||||||||
\(51\) | −386.870 | −1.06221 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −120.847 | −0.313199 | −0.156600 | − | 0.987662i | \(-0.550053\pi\) | ||||
−0.156600 | + | 0.987662i | \(0.550053\pi\) | |||||||
\(54\) | − 290.533i | − 0.732158i | ||||||||
\(55\) | −54.3542 | −0.133257 | ||||||||
\(56\) | 575.531 | 1.37337 | ||||||||
\(57\) | 208.169i | 0.483730i | ||||||||
\(58\) | 343.400i | 0.777424i | ||||||||
\(59\) | 439.633i | 0.970090i | 0.874489 | + | 0.485045i | \(0.161197\pi\) | ||||
−0.874489 | + | 0.485045i | \(0.838803\pi\) | |||||||
\(60\) | − 172.024i | − 0.370136i | ||||||||
\(61\) | −137.305 | −0.288198 | −0.144099 | − | 0.989563i | \(-0.546028\pi\) | ||||
−0.144099 | + | 0.989563i | \(0.546028\pi\) | |||||||
\(62\) | 42.3068 | 0.0866609 | ||||||||
\(63\) | 1316.00i | 2.63176i | ||||||||
\(64\) | −201.022 | −0.392621 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −206.968 | −0.386000 | ||||||||
\(67\) | 512.280i | 0.934104i | 0.884230 | + | 0.467052i | \(0.154684\pi\) | ||||
−0.884230 | + | 0.467052i | \(0.845316\pi\) | |||||||
\(68\) | −247.747 | −0.441820 | ||||||||
\(69\) | −1065.94 | −1.85977 | ||||||||
\(70\) | − 151.147i | − 0.258078i | ||||||||
\(71\) | 410.719i | 0.686526i | 0.939239 | + | 0.343263i | \(0.111532\pi\) | ||||
−0.939239 | + | 0.343263i | \(0.888468\pi\) | |||||||
\(72\) | − 1025.46i | − 1.67850i | ||||||||
\(73\) | 308.004i | 0.493823i | 0.969038 | + | 0.246912i | \(0.0794158\pi\) | ||||
−0.969038 | + | 0.246912i | \(0.920584\pi\) | |||||||
\(74\) | −147.086 | −0.231060 | ||||||||
\(75\) | 975.420 | 1.50176 | ||||||||
\(76\) | 133.309i | 0.201205i | ||||||||
\(77\) | 414.759 | 0.613847 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −586.462 | −0.835217 | −0.417608 | − | 0.908627i | \(-0.637132\pi\) | ||||
−0.417608 | + | 0.908627i | \(0.637132\pi\) | |||||||
\(80\) | − 40.6847i | − 0.0568585i | ||||||||
\(81\) | 308.386 | 0.423027 | ||||||||
\(82\) | −250.401 | −0.337222 | ||||||||
\(83\) | 1354.20i | 1.79088i | 0.445182 | + | 0.895440i | \(0.353139\pi\) | ||||
−0.445182 | + | 0.895440i | \(0.646861\pi\) | |||||||
\(84\) | 1312.66i | 1.70503i | ||||||||
\(85\) | 158.654i | 0.202453i | ||||||||
\(86\) | − 236.266i | − 0.296247i | ||||||||
\(87\) | −1909.84 | −2.35352 | ||||||||
\(88\) | −323.191 | −0.391503 | ||||||||
\(89\) | − 439.882i | − 0.523904i | −0.965081 | − | 0.261952i | \(-0.915634\pi\) | ||||
0.965081 | − | 0.261952i | \(-0.0843662\pi\) | |||||||
\(90\) | −269.309 | −0.315418 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −682.617 | −0.773563 | ||||||||
\(93\) | 235.292i | 0.262351i | ||||||||
\(94\) | −729.164 | −0.800080 | ||||||||
\(95\) | 85.3693 | 0.0921969 | ||||||||
\(96\) | − 1626.24i | − 1.72894i | ||||||||
\(97\) | − 1511.27i | − 1.58192i | −0.611869 | − | 0.790959i | \(-0.709582\pi\) | ||||
0.611869 | − | 0.790959i | \(-0.290418\pi\) | |||||||
\(98\) | 617.740i | 0.636747i | ||||||||
\(99\) | − 739.006i | − 0.750231i | ||||||||
\(100\) | 624.648 | 0.624648 | ||||||||
\(101\) | −336.260 | −0.331278 | −0.165639 | − | 0.986186i | \(-0.552969\pi\) | ||||
−0.165639 | + | 0.986186i | \(0.552969\pi\) | |||||||
\(102\) | 604.118i | 0.586438i | ||||||||
\(103\) | −322.712 | −0.308716 | −0.154358 | − | 0.988015i | \(-0.549331\pi\) | ||||
−0.154358 | + | 0.988015i | \(0.549331\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 840.611 | 0.781288 | ||||||||
\(106\) | 188.708i | 0.172915i | ||||||||
\(107\) | 1434.62 | 1.29617 | 0.648083 | − | 0.761570i | \(-0.275571\pi\) | ||||
0.648083 | + | 0.761570i | \(0.275571\pi\) | |||||||
\(108\) | 1034.75 | 0.921933 | ||||||||
\(109\) | 849.147i | 0.746179i | 0.927795 | + | 0.373089i | \(0.121702\pi\) | ||||
−0.927795 | + | 0.373089i | \(0.878298\pi\) | |||||||
\(110\) | 84.8769i | 0.0735699i | ||||||||
\(111\) | − 818.027i | − 0.699493i | ||||||||
\(112\) | 310.452i | 0.261919i | ||||||||
\(113\) | 1614.53 | 1.34409 | 0.672044 | − | 0.740511i | \(-0.265417\pi\) | ||||
0.672044 | + | 0.740511i | \(0.265417\pi\) | |||||||
\(114\) | 325.066 | 0.267064 | ||||||||
\(115\) | 437.140i | 0.354465i | ||||||||
\(116\) | −1223.04 | −0.978931 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 686.509 | 0.535579 | ||||||||
\(119\) | − 1210.64i | − 0.932599i | ||||||||
\(120\) | −655.026 | −0.498295 | ||||||||
\(121\) | 1098.09 | 0.825012 | ||||||||
\(122\) | 214.409i | 0.159112i | ||||||||
\(123\) | − 1392.62i | − 1.02088i | ||||||||
\(124\) | 150.678i | 0.109123i | ||||||||
\(125\) | − 845.211i | − 0.604784i | ||||||||
\(126\) | 2055.01 | 1.45297 | ||||||||
\(127\) | −865.174 | −0.604502 | −0.302251 | − | 0.953228i | \(-0.597738\pi\) | ||||
−0.302251 | + | 0.953228i | \(0.597738\pi\) | |||||||
\(128\) | − 1184.13i | − 0.817683i | ||||||||
\(129\) | 1314.01 | 0.896836 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −281.400 | −0.187680 | −0.0938400 | − | 0.995587i | \(-0.529914\pi\) | ||||
−0.0938400 | + | 0.995587i | \(0.529914\pi\) | |||||||
\(132\) | − 737.127i | − 0.486050i | ||||||||
\(133\) | −651.426 | −0.424705 | ||||||||
\(134\) | 799.953 | 0.515712 | ||||||||
\(135\) | − 662.641i | − 0.422452i | ||||||||
\(136\) | 943.363i | 0.594799i | ||||||||
\(137\) | 2641.43i | 1.64725i | 0.567137 | + | 0.823624i | \(0.308051\pi\) | ||||
−0.567137 | + | 0.823624i | \(0.691949\pi\) | |||||||
\(138\) | 1664.53i | 1.02677i | ||||||||
\(139\) | −1998.64 | −1.21958 | −0.609791 | − | 0.792562i | \(-0.708747\pi\) | ||||
−0.609791 | + | 0.792562i | \(0.708747\pi\) | |||||||
\(140\) | 538.317 | 0.324972 | ||||||||
\(141\) | − 4055.28i | − 2.42210i | ||||||||
\(142\) | 641.359 | 0.379026 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 553.153 | 0.320112 | ||||||||
\(145\) | 783.218i | 0.448570i | ||||||||
\(146\) | 480.964 | 0.272636 | ||||||||
\(147\) | −3435.60 | −1.92764 | ||||||||
\(148\) | − 523.855i | − 0.290950i | ||||||||
\(149\) | − 1752.98i | − 0.963824i | −0.876220 | − | 0.481912i | \(-0.839942\pi\) | ||||
0.876220 | − | 0.481912i | \(-0.160058\pi\) | |||||||
\(150\) | − 1523.17i | − 0.829109i | ||||||||
\(151\) | 2794.64i | 1.50613i | 0.657949 | + | 0.753063i | \(0.271424\pi\) | ||||
−0.657949 | + | 0.753063i | \(0.728576\pi\) | |||||||
\(152\) | 507.608 | 0.270871 | ||||||||
\(153\) | −2157.08 | −1.13980 | ||||||||
\(154\) | − 647.669i | − 0.338900i | ||||||||
\(155\) | 96.4924 | 0.0500030 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3244.87 | 1.64949 | 0.824743 | − | 0.565508i | \(-0.191320\pi\) | ||||
0.824743 | + | 0.565508i | \(0.191320\pi\) | |||||||
\(158\) | 915.792i | 0.461117i | ||||||||
\(159\) | −1049.51 | −0.523470 | ||||||||
\(160\) | −666.918 | −0.329528 | ||||||||
\(161\) | − 3335.68i | − 1.63285i | ||||||||
\(162\) | − 481.562i | − 0.233550i | ||||||||
\(163\) | − 3281.47i | − 1.57684i | −0.615139 | − | 0.788418i | \(-0.710900\pi\) | ||||
0.615139 | − | 0.788418i | \(-0.289100\pi\) | |||||||
\(164\) | − 891.818i | − 0.424630i | ||||||||
\(165\) | −472.047 | −0.222720 | ||||||||
\(166\) | 2114.66 | 0.988731 | ||||||||
\(167\) | 3126.52i | 1.44873i | 0.689418 | + | 0.724364i | \(0.257866\pi\) | ||||
−0.689418 | + | 0.724364i | \(0.742134\pi\) | |||||||
\(168\) | 4998.29 | 2.29540 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 247.747 | 0.111773 | ||||||||
\(171\) | 1160.69i | 0.519066i | ||||||||
\(172\) | 841.474 | 0.373034 | ||||||||
\(173\) | −97.5698 | −0.0428792 | −0.0214396 | − | 0.999770i | \(-0.506825\pi\) | ||||
−0.0214396 | + | 0.999770i | \(0.506825\pi\) | |||||||
\(174\) | 2982.31i | 1.29936i | ||||||||
\(175\) | 3052.40i | 1.31851i | ||||||||
\(176\) | − 174.335i | − 0.0746648i | ||||||||
\(177\) | 3818.06i | 1.62137i | ||||||||
\(178\) | −686.900 | −0.289243 | ||||||||
\(179\) | 34.7150 | 0.0144956 | 0.00724782 | − | 0.999974i | \(-0.497693\pi\) | ||||
0.00724782 | + | 0.999974i | \(0.497693\pi\) | |||||||
\(180\) | − 959.157i | − 0.397174i | ||||||||
\(181\) | 1229.35 | 0.504843 | 0.252422 | − | 0.967617i | \(-0.418773\pi\) | ||||
0.252422 | + | 0.967617i | \(0.418773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1192.45 | −0.481684 | ||||||||
\(184\) | 2599.25i | 1.04141i | ||||||||
\(185\) | −335.471 | −0.133320 | ||||||||
\(186\) | 367.420 | 0.144842 | ||||||||
\(187\) | 679.839i | 0.265854i | ||||||||
\(188\) | − 2596.96i | − 1.00746i | ||||||||
\(189\) | 5056.40i | 1.94603i | ||||||||
\(190\) | − 133.309i | − 0.0509012i | ||||||||
\(191\) | 4280.80 | 1.62172 | 0.810858 | − | 0.585243i | \(-0.199001\pi\) | ||||
0.810858 | + | 0.585243i | \(0.199001\pi\) | |||||||
\(192\) | −1745.81 | −0.656212 | ||||||||
\(193\) | − 472.320i | − 0.176157i | −0.996114 | − | 0.0880786i | \(-0.971927\pi\) | ||||
0.996114 | − | 0.0880786i | \(-0.0280727\pi\) | |||||||
\(194\) | −2359.93 | −0.873365 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2200.12 | −0.801791 | ||||||||
\(197\) | − 4484.37i | − 1.62182i | −0.585173 | − | 0.810908i | \(-0.698974\pi\) | ||||
0.585173 | − | 0.810908i | \(-0.301026\pi\) | |||||||
\(198\) | −1154.00 | −0.414197 | ||||||||
\(199\) | 366.240 | 0.130463 | 0.0652314 | − | 0.997870i | \(-0.479221\pi\) | ||||
0.0652314 | + | 0.997870i | \(0.479221\pi\) | |||||||
\(200\) | − 2378.51i | − 0.840931i | ||||||||
\(201\) | 4448.98i | 1.56123i | ||||||||
\(202\) | 525.087i | 0.182896i | ||||||||
\(203\) | − 5976.49i | − 2.06634i | ||||||||
\(204\) | −2151.60 | −0.738442 | ||||||||
\(205\) | −571.110 | −0.194576 | ||||||||
\(206\) | 503.932i | 0.170440i | ||||||||
\(207\) | −5943.41 | −1.99563 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 365.810 | 0.121070 | ||||||||
\(210\) | − 1312.66i | − 0.431343i | ||||||||
\(211\) | 2122.55 | 0.692524 | 0.346262 | − | 0.938138i | \(-0.387451\pi\) | ||||
0.346262 | + | 0.938138i | \(0.387451\pi\) | |||||||
\(212\) | −672.095 | −0.217734 | ||||||||
\(213\) | 3566.95i | 1.14743i | ||||||||
\(214\) | − 2240.23i | − 0.715603i | ||||||||
\(215\) | − 538.870i | − 0.170933i | ||||||||
\(216\) | − 3940.08i | − 1.24115i | ||||||||
\(217\) | −736.303 | −0.230339 | ||||||||
\(218\) | 1325.99 | 0.411960 | ||||||||
\(219\) | 2674.91i | 0.825358i | ||||||||
\(220\) | −302.294 | −0.0926392 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1277.39 | −0.386185 | ||||||||
\(223\) | − 5926.42i | − 1.77965i | −0.456301 | − | 0.889826i | \(-0.650826\pi\) | ||||
0.456301 | − | 0.889826i | \(-0.349174\pi\) | |||||||
\(224\) | 5089.04 | 1.51797 | ||||||||
\(225\) | 5438.68 | 1.61146 | ||||||||
\(226\) | − 2521.17i | − 0.742060i | ||||||||
\(227\) | − 895.661i | − 0.261881i | −0.991390 | − | 0.130941i | \(-0.958200\pi\) | ||||
0.991390 | − | 0.130941i | \(-0.0417998\pi\) | |||||||
\(228\) | 1157.74i | 0.336286i | ||||||||
\(229\) | − 627.717i | − 0.181138i | −0.995890 | − | 0.0905692i | \(-0.971131\pi\) | ||||
0.995890 | − | 0.0905692i | \(-0.0288686\pi\) | |||||||
\(230\) | 682.617 | 0.195698 | ||||||||
\(231\) | 3602.04 | 1.02596 | ||||||||
\(232\) | 4657.03i | 1.31788i | ||||||||
\(233\) | −2303.72 | −0.647734 | −0.323867 | − | 0.946103i | \(-0.604983\pi\) | ||||
−0.323867 | + | 0.946103i | \(0.604983\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1663.06 | −0.461643 | ||||||||
\(236\) | 2445.04i | 0.674401i | ||||||||
\(237\) | −5093.22 | −1.39595 | ||||||||
\(238\) | −1890.48 | −0.514881 | ||||||||
\(239\) | 544.622i | 0.147400i | 0.997280 | + | 0.0737001i | \(0.0234808\pi\) | ||||
−0.997280 | + | 0.0737001i | \(0.976519\pi\) | |||||||
\(240\) | − 353.332i | − 0.0950313i | ||||||||
\(241\) | − 5426.10i | − 1.45031i | −0.688584 | − | 0.725157i | \(-0.741767\pi\) | ||||
0.688584 | − | 0.725157i | \(-0.258233\pi\) | |||||||
\(242\) | − 1714.73i | − 0.455483i | ||||||||
\(243\) | −2345.23 | −0.619121 | ||||||||
\(244\) | −763.629 | −0.200354 | ||||||||
\(245\) | 1408.93i | 0.367400i | ||||||||
\(246\) | −2174.65 | −0.563621 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 573.746 | 0.146907 | ||||||||
\(249\) | 11760.8i | 2.99321i | ||||||||
\(250\) | −1319.84 | −0.333897 | ||||||||
\(251\) | 5221.22 | 1.31299 | 0.656494 | − | 0.754331i | \(-0.272039\pi\) | ||||
0.656494 | + | 0.754331i | \(0.272039\pi\) | |||||||
\(252\) | 7319.02i | 1.82958i | ||||||||
\(253\) | 1873.16i | 0.465472i | ||||||||
\(254\) | 1351.02i | 0.333741i | ||||||||
\(255\) | 1377.86i | 0.338372i | ||||||||
\(256\) | −3457.26 | −0.844057 | ||||||||
\(257\) | −658.206 | −0.159758 | −0.0798789 | − | 0.996805i | \(-0.525453\pi\) | ||||
−0.0798789 | + | 0.996805i | \(0.525453\pi\) | |||||||
\(258\) | − 2051.89i | − 0.495136i | ||||||||
\(259\) | 2559.87 | 0.614141 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10648.7 | −2.52544 | ||||||||
\(262\) | 439.422i | 0.103617i | ||||||||
\(263\) | 3246.45 | 0.761160 | 0.380580 | − | 0.924748i | \(-0.375724\pi\) | ||||
0.380580 | + | 0.924748i | \(0.375724\pi\) | |||||||
\(264\) | −2806.81 | −0.654344 | ||||||||
\(265\) | 430.401i | 0.0997711i | ||||||||
\(266\) | 1017.24i | 0.234477i | ||||||||
\(267\) | − 3820.23i | − 0.875634i | ||||||||
\(268\) | 2849.07i | 0.649384i | ||||||||
\(269\) | −2585.80 | −0.586093 | −0.293047 | − | 0.956098i | \(-0.594669\pi\) | ||||
−0.293047 | + | 0.956098i | \(0.594669\pi\) | |||||||
\(270\) | −1034.75 | −0.233233 | ||||||||
\(271\) | − 988.933i | − 0.221673i | −0.993839 | − | 0.110836i | \(-0.964647\pi\) | ||||
0.993839 | − | 0.110836i | \(-0.0353530\pi\) | |||||||
\(272\) | −508.867 | −0.113436 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4124.74 | 0.909433 | ||||||||
\(275\) | − 1714.09i | − 0.375866i | ||||||||
\(276\) | −5928.30 | −1.29290 | ||||||||
\(277\) | −8142.40 | −1.76617 | −0.883086 | − | 0.469211i | \(-0.844538\pi\) | ||||
−0.883086 | + | 0.469211i | \(0.844538\pi\) | |||||||
\(278\) | 3120.97i | 0.673322i | ||||||||
\(279\) | 1311.92i | 0.281515i | ||||||||
\(280\) | − 2049.78i | − 0.437493i | ||||||||
\(281\) | − 1534.21i | − 0.325705i | −0.986650 | − | 0.162853i | \(-0.947930\pi\) | ||||
0.986650 | − | 0.162853i | \(-0.0520695\pi\) | |||||||
\(282\) | −6332.54 | −1.33722 | ||||||||
\(283\) | 6965.00 | 1.46299 | 0.731495 | − | 0.681847i | \(-0.238823\pi\) | ||||
0.731495 | + | 0.681847i | \(0.238823\pi\) | |||||||
\(284\) | 2284.23i | 0.477269i | ||||||||
\(285\) | 741.403 | 0.154095 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4357.96 | 0.896314 | ||||||||
\(288\) | − 9067.49i | − 1.85523i | ||||||||
\(289\) | −2928.62 | −0.596096 | ||||||||
\(290\) | 1223.04 | 0.247652 | ||||||||
\(291\) | − 13124.9i | − 2.64396i | ||||||||
\(292\) | 1712.98i | 0.343303i | ||||||||
\(293\) | − 640.029i | − 0.127614i | −0.997962 | − | 0.0638070i | \(-0.979676\pi\) | ||||
0.997962 | − | 0.0638070i | \(-0.0203242\pi\) | |||||||
\(294\) | 5364.87i | 1.06424i | ||||||||
\(295\) | 1565.77 | 0.309027 | ||||||||
\(296\) | −1994.72 | −0.391691 | ||||||||
\(297\) | − 2839.44i | − 0.554750i | ||||||||
\(298\) | −2737.37 | −0.532120 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5424.85 | 1.04401 | ||||||||
\(301\) | 4111.95i | 0.787404i | ||||||||
\(302\) | 4363.99 | 0.831520 | ||||||||
\(303\) | −2920.30 | −0.553686 | ||||||||
\(304\) | 273.813i | 0.0516587i | ||||||||
\(305\) | 489.019i | 0.0918070i | ||||||||
\(306\) | 3368.40i | 0.629276i | ||||||||
\(307\) | 100.406i | 0.0186660i | 0.999956 | + | 0.00933299i | \(0.00297083\pi\) | ||||
−0.999956 | + | 0.00933299i | \(0.997029\pi\) | |||||||
\(308\) | 2306.71 | 0.426743 | ||||||||
\(309\) | −2802.64 | −0.515977 | ||||||||
\(310\) | − 150.678i | − 0.0276062i | ||||||||
\(311\) | 3878.92 | 0.707245 | 0.353623 | − | 0.935388i | \(-0.384950\pi\) | ||||
0.353623 | + | 0.935388i | \(0.384950\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3789.39 | −0.684311 | −0.342155 | − | 0.939643i | \(-0.611157\pi\) | ||||
−0.342155 | + | 0.939643i | \(0.611157\pi\) | |||||||
\(314\) | − 5067.04i | − 0.910668i | ||||||||
\(315\) | 4687.02 | 0.838360 | ||||||||
\(316\) | −3261.64 | −0.580638 | ||||||||
\(317\) | 4406.81i | 0.780791i | 0.920647 | + | 0.390396i | \(0.127662\pi\) | ||||
−0.920647 | + | 0.390396i | \(0.872338\pi\) | |||||||
\(318\) | 1638.87i | 0.289004i | ||||||||
\(319\) | 3356.11i | 0.589048i | ||||||||
\(320\) | 715.950i | 0.125071i | ||||||||
\(321\) | 12459.2 | 2.16636 | ||||||||
\(322\) | −5208.84 | −0.901482 | ||||||||
\(323\) | − 1067.76i | − 0.183938i | ||||||||
\(324\) | 1715.11 | 0.294086 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5124.19 | −0.870559 | ||||||||
\(327\) | 7374.55i | 1.24714i | ||||||||
\(328\) | −3395.83 | −0.571657 | ||||||||
\(329\) | 12690.3 | 2.12656 | ||||||||
\(330\) | 737.127i | 0.122962i | ||||||||
\(331\) | − 4131.49i | − 0.686064i | −0.939324 | − | 0.343032i | \(-0.888546\pi\) | ||||
0.939324 | − | 0.343032i | \(-0.111454\pi\) | |||||||
\(332\) | 7531.47i | 1.24501i | ||||||||
\(333\) | − 4561.10i | − 0.750591i | ||||||||
\(334\) | 4882.23 | 0.799831 | ||||||||
\(335\) | 1824.51 | 0.297564 | ||||||||
\(336\) | 2696.17i | 0.437762i | ||||||||
\(337\) | 4560.82 | 0.737221 | 0.368611 | − | 0.929584i | \(-0.379834\pi\) | ||||
0.368611 | + | 0.929584i | \(0.379834\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14021.6 | 2.24646 | ||||||||
\(340\) | 882.365i | 0.140744i | ||||||||
\(341\) | 413.473 | 0.0656622 | ||||||||
\(342\) | 1812.48 | 0.286572 | ||||||||
\(343\) | − 1429.34i | − 0.225007i | ||||||||
\(344\) | − 3204.14i | − 0.502196i | ||||||||
\(345\) | 3796.41i | 0.592441i | ||||||||
\(346\) | 152.360i | 0.0236733i | ||||||||
\(347\) | 10069.4 | 1.55779 | 0.778896 | − | 0.627153i | \(-0.215780\pi\) | ||||
0.778896 | + | 0.627153i | \(0.215780\pi\) | |||||||
\(348\) | −10621.6 | −1.63615 | ||||||||
\(349\) | − 5879.32i | − 0.901757i | −0.892585 | − | 0.450878i | \(-0.851111\pi\) | ||||
0.892585 | − | 0.450878i | \(-0.148889\pi\) | |||||||
\(350\) | 4766.49 | 0.727942 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2857.76 | −0.432725 | ||||||||
\(353\) | − 9142.56i | − 1.37850i | −0.724525 | − | 0.689249i | \(-0.757941\pi\) | ||||
0.724525 | − | 0.689249i | \(-0.242059\pi\) | |||||||
\(354\) | 5962.10 | 0.895147 | ||||||||
\(355\) | 1462.80 | 0.218696 | ||||||||
\(356\) | − 2446.43i | − 0.364215i | ||||||||
\(357\) | − 10514.0i | − 1.55871i | ||||||||
\(358\) | − 54.2093i | − 0.00800293i | ||||||||
\(359\) | 2754.32i | 0.404924i | 0.979290 | + | 0.202462i | \(0.0648942\pi\) | ||||
−0.979290 | + | 0.202462i | \(0.935106\pi\) | |||||||
\(360\) | −3652.24 | −0.534695 | ||||||||
\(361\) | 6284.45 | 0.916235 | ||||||||
\(362\) | − 1919.69i | − 0.278720i | ||||||||
\(363\) | 9536.54 | 1.37889 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1096.97 | 0.157310 | ||||||||
\(366\) | 1862.07i | 0.265934i | ||||||||
\(367\) | 3040.19 | 0.432416 | 0.216208 | − | 0.976347i | \(-0.430631\pi\) | ||||
0.216208 | + | 0.976347i | \(0.430631\pi\) | |||||||
\(368\) | −1402.08 | −0.198610 | ||||||||
\(369\) | − 7764.88i | − 1.09546i | ||||||||
\(370\) | 523.855i | 0.0736052i | ||||||||
\(371\) | − 3284.26i | − 0.459596i | ||||||||
\(372\) | 1308.59i | 0.182385i | ||||||||
\(373\) | −5384.72 | −0.747481 | −0.373740 | − | 0.927533i | \(-0.621925\pi\) | ||||
−0.373740 | + | 0.927533i | \(0.621925\pi\) | |||||||
\(374\) | 1061.60 | 0.146776 | ||||||||
\(375\) | − 7340.37i | − 1.01081i | ||||||||
\(376\) | −9888.59 | −1.35629 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 7895.84 | 1.07439 | ||||||||
\(379\) | − 3424.27i | − 0.464097i | −0.972704 | − | 0.232049i | \(-0.925457\pi\) | ||||
0.972704 | − | 0.232049i | \(-0.0745428\pi\) | |||||||
\(380\) | 474.786 | 0.0640948 | ||||||||
\(381\) | −7513.74 | −1.01034 | ||||||||
\(382\) | − 6684.69i | − 0.895336i | ||||||||
\(383\) | − 382.985i | − 0.0510956i | −0.999674 | − | 0.0255478i | \(-0.991867\pi\) | ||||
0.999674 | − | 0.0255478i | \(-0.00813301\pi\) | |||||||
\(384\) | − 10283.8i | − 1.36665i | ||||||||
\(385\) | − 1477.19i | − 0.195544i | ||||||||
\(386\) | −737.553 | −0.0972551 | ||||||||
\(387\) | 7326.54 | 0.962349 | ||||||||
\(388\) | − 8405.00i | − 1.09974i | ||||||||
\(389\) | −8588.34 | −1.11940 | −0.559699 | − | 0.828696i | \(-0.689083\pi\) | ||||
−0.559699 | + | 0.828696i | \(0.689083\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5467.56 | 0.707178 | ||||||||
\(392\) | 8377.52i | 1.07941i | ||||||||
\(393\) | −2443.87 | −0.313681 | ||||||||
\(394\) | −7002.57 | −0.895392 | ||||||||
\(395\) | 2088.72i | 0.266063i | ||||||||
\(396\) | − 4110.02i | − 0.521556i | ||||||||
\(397\) | 7239.16i | 0.915171i | 0.889166 | + | 0.457586i | \(0.151286\pi\) | ||||
−0.889166 | + | 0.457586i | \(0.848714\pi\) | |||||||
\(398\) | − 571.904i | − 0.0720275i | ||||||||
\(399\) | −5657.41 | −0.709837 | ||||||||
\(400\) | 1283.01 | 0.160376 | ||||||||
\(401\) | − 4269.62i | − 0.531708i | −0.964013 | − | 0.265854i | \(-0.914346\pi\) | ||||
0.964013 | − | 0.265854i | \(-0.0856539\pi\) | |||||||
\(402\) | 6947.32 | 0.861942 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1870.12 | −0.230302 | ||||||||
\(405\) | − 1098.33i | − 0.134757i | ||||||||
\(406\) | −9332.60 | −1.14081 | ||||||||
\(407\) | −1437.50 | −0.175072 | ||||||||
\(408\) | 8192.78i | 0.994125i | ||||||||
\(409\) | 13562.5i | 1.63967i | 0.572602 | + | 0.819834i | \(0.305934\pi\) | ||||
−0.572602 | + | 0.819834i | \(0.694066\pi\) | |||||||
\(410\) | 891.818i | 0.107424i | ||||||||
\(411\) | 22939.9i | 2.75315i | ||||||||
\(412\) | −1794.78 | −0.214618 | ||||||||
\(413\) | −11947.9 | −1.42353 | ||||||||
\(414\) | 9280.95i | 1.10177i | ||||||||
\(415\) | 4823.06 | 0.570494 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17357.5 | −2.03837 | ||||||||
\(418\) | − 571.232i | − 0.0668418i | ||||||||
\(419\) | −14576.9 | −1.69959 | −0.849794 | − | 0.527114i | \(-0.823274\pi\) | ||||
−0.849794 | + | 0.527114i | \(0.823274\pi\) | |||||||
\(420\) | 4675.10 | 0.543147 | ||||||||
\(421\) | 15848.4i | 1.83469i | 0.398099 | + | 0.917343i | \(0.369670\pi\) | ||||
−0.398099 | + | 0.917343i | \(0.630330\pi\) | |||||||
\(422\) | − 3314.48i | − 0.382337i | ||||||||
\(423\) | − 22611.2i | − 2.59904i | ||||||||
\(424\) | 2559.18i | 0.293124i | ||||||||
\(425\) | −5003.24 | −0.571042 | ||||||||
\(426\) | 5569.98 | 0.633490 | ||||||||
\(427\) | − 3731.55i | − 0.422909i | ||||||||
\(428\) | 7978.70 | 0.901087 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −841.474 | −0.0943709 | ||||||||
\(431\) | 10694.7i | 1.19524i | 0.801781 | + | 0.597618i | \(0.203886\pi\) | ||||
−0.801781 | + | 0.597618i | \(0.796114\pi\) | |||||||
\(432\) | 2125.35 | 0.236703 | ||||||||
\(433\) | 16079.0 | 1.78454 | 0.892272 | − | 0.451498i | \(-0.149110\pi\) | ||||
0.892272 | + | 0.451498i | \(0.149110\pi\) | |||||||
\(434\) | 1149.78i | 0.127168i | ||||||||
\(435\) | 6801.98i | 0.749724i | ||||||||
\(436\) | 4722.57i | 0.518739i | ||||||||
\(437\) | − 2942.01i | − 0.322049i | ||||||||
\(438\) | 4177.01 | 0.455674 | ||||||||
\(439\) | −6035.80 | −0.656203 | −0.328101 | − | 0.944643i | \(-0.606409\pi\) | ||||
−0.328101 | + | 0.944643i | \(0.606409\pi\) | |||||||
\(440\) | 1151.06i | 0.124715i | ||||||||
\(441\) | −19156.0 | −2.06845 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10201.3 | 1.09409 | 0.547043 | − | 0.837105i | \(-0.315753\pi\) | ||||
0.547043 | + | 0.837105i | \(0.315753\pi\) | |||||||
\(444\) | − 4549.50i | − 0.486283i | ||||||||
\(445\) | −1566.66 | −0.166892 | ||||||||
\(446\) | −9254.41 | −0.982532 | ||||||||
\(447\) | − 15224.0i | − 1.61090i | ||||||||
\(448\) | − 5463.19i | − 0.576141i | ||||||||
\(449\) | 5822.54i | 0.611988i | 0.952033 | + | 0.305994i | \(0.0989888\pi\) | ||||
−0.952033 | + | 0.305994i | \(0.901011\pi\) | |||||||
\(450\) | − 8492.78i | − 0.889675i | ||||||||
\(451\) | −2447.22 | −0.255511 | ||||||||
\(452\) | 8979.27 | 0.934402 | ||||||||
\(453\) | 24270.5i | 2.51728i | ||||||||
\(454\) | −1398.62 | −0.144583 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4408.40 | 0.452724 | ||||||||
\(457\) | 4621.60i | 0.473062i | 0.971624 | + | 0.236531i | \(0.0760105\pi\) | ||||
−0.971624 | + | 0.236531i | \(0.923990\pi\) | |||||||
\(458\) | −980.213 | −0.100005 | ||||||||
\(459\) | −8288.03 | −0.842816 | ||||||||
\(460\) | 2431.18i | 0.246422i | ||||||||
\(461\) | 5127.77i | 0.518056i | 0.965870 | + | 0.259028i | \(0.0834023\pi\) | ||||
−0.965870 | + | 0.259028i | \(0.916598\pi\) | |||||||
\(462\) | − 5624.78i | − 0.566425i | ||||||||
\(463\) | − 6486.27i | − 0.651064i | −0.945531 | − | 0.325532i | \(-0.894457\pi\) | ||||
0.945531 | − | 0.325532i | \(-0.105543\pi\) | |||||||
\(464\) | −2512.09 | −0.251338 | ||||||||
\(465\) | 838.004 | 0.0835731 | ||||||||
\(466\) | 3597.39i | 0.357609i | ||||||||
\(467\) | −12978.0 | −1.28598 | −0.642990 | − | 0.765875i | \(-0.722306\pi\) | ||||
−0.642990 | + | 0.765875i | \(0.722306\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13922.3 | −1.37073 | ||||||||
\(470\) | 2596.96i | 0.254869i | ||||||||
\(471\) | 28180.6 | 2.75689 | ||||||||
\(472\) | 9310.13 | 0.907910 | ||||||||
\(473\) | − 2309.08i | − 0.224464i | ||||||||
\(474\) | 7953.34i | 0.770694i | ||||||||
\(475\) | 2692.16i | 0.260053i | ||||||||
\(476\) | − 6733.04i | − 0.648337i | ||||||||
\(477\) | −5851.79 | −0.561709 | ||||||||
\(478\) | 850.456 | 0.0813786 | ||||||||
\(479\) | 5808.96i | 0.554109i | 0.960854 | + | 0.277055i | \(0.0893583\pi\) | ||||
−0.960854 | + | 0.277055i | \(0.910642\pi\) | |||||||
\(480\) | −5791.95 | −0.550761 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −8473.14 | −0.800707 | ||||||||
\(483\) | − 28969.2i | − 2.72908i | ||||||||
\(484\) | 6107.09 | 0.573543 | ||||||||
\(485\) | −5382.46 | −0.503928 | ||||||||
\(486\) | 3662.20i | 0.341812i | ||||||||
\(487\) | − 5387.14i | − 0.501262i | −0.968083 | − | 0.250631i | \(-0.919362\pi\) | ||||
0.968083 | − | 0.250631i | \(-0.0806381\pi\) | |||||||
\(488\) | 2907.72i | 0.269726i | ||||||||
\(489\) | − 28498.4i | − 2.63547i | ||||||||
\(490\) | 2200.12 | 0.202839 | ||||||||
\(491\) | −15259.1 | −1.40251 | −0.701255 | − | 0.712911i | \(-0.747376\pi\) | ||||
−0.701255 | + | 0.712911i | \(0.747376\pi\) | |||||||
\(492\) | − 7745.14i | − 0.709711i | ||||||||
\(493\) | 9796.16 | 0.894922 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2632.01 | −0.238990 | ||||||||
\(496\) | 309.489i | 0.0280171i | ||||||||
\(497\) | −11162.1 | −1.00742 | ||||||||
\(498\) | 18365.1 | 1.65253 | ||||||||
\(499\) | 1856.04i | 0.166509i | 0.996528 | + | 0.0832544i | \(0.0265314\pi\) | ||||
−0.996528 | + | 0.0832544i | \(0.973469\pi\) | |||||||
\(500\) | − 4700.69i | − 0.420442i | ||||||||
\(501\) | 27152.8i | 2.42135i | ||||||||
\(502\) | − 8153.20i | − 0.724891i | ||||||||
\(503\) | 1049.46 | 0.0930283 | 0.0465142 | − | 0.998918i | \(-0.485189\pi\) | ||||
0.0465142 | + | 0.998918i | \(0.485189\pi\) | |||||||
\(504\) | 27869.1 | 2.46307 | ||||||||
\(505\) | 1197.61i | 0.105530i | ||||||||
\(506\) | 2925.04 | 0.256984 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4811.71 | −0.420246 | ||||||||
\(509\) | − 551.106i | − 0.0479909i | −0.999712 | − | 0.0239954i | \(-0.992361\pi\) | ||||
0.999712 | − | 0.0239954i | \(-0.00763872\pi\) | |||||||
\(510\) | 2151.60 | 0.186813 | ||||||||
\(511\) | −8370.64 | −0.724649 | ||||||||
\(512\) | − 4074.36i | − 0.351686i | ||||||||
\(513\) | 4459.66i | 0.383818i | ||||||||
\(514\) | 1027.82i | 0.0882010i | ||||||||
\(515\) | 1149.36i | 0.0983431i | ||||||||
\(516\) | 7307.92 | 0.623475 | ||||||||
\(517\) | −7126.26 | −0.606214 | ||||||||
\(518\) | − 3997.37i | − 0.339063i | ||||||||
\(519\) | −847.361 | −0.0716667 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8995.30 | −0.756413 | −0.378206 | − | 0.925721i | \(-0.623459\pi\) | ||||
−0.378206 | + | 0.925721i | \(0.623459\pi\) | |||||||
\(522\) | 16628.5i | 1.39427i | ||||||||
\(523\) | 2663.91 | 0.222724 | 0.111362 | − | 0.993780i | \(-0.464479\pi\) | ||||
0.111362 | + | 0.993780i | \(0.464479\pi\) | |||||||
\(524\) | −1565.02 | −0.130474 | ||||||||
\(525\) | 26509.1i | 2.20372i | ||||||||
\(526\) | − 5069.51i | − 0.420230i | ||||||||
\(527\) | − 1206.89i | − 0.0997586i | ||||||||
\(528\) | − 1514.04i | − 0.124792i | ||||||||
\(529\) | 2897.77 | 0.238167 | ||||||||
\(530\) | 672.095 | 0.0550829 | ||||||||
\(531\) | 21288.5i | 1.73981i | ||||||||
\(532\) | −3622.94 | −0.295253 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −5965.49 | −0.483431 | ||||||||
\(535\) | − 5109.47i | − 0.412900i | ||||||||
\(536\) | 10848.6 | 0.874232 | ||||||||
\(537\) | 301.488 | 0.0242275 | ||||||||
\(538\) | 4037.86i | 0.323577i | ||||||||
\(539\) | 6037.30i | 0.482458i | ||||||||
\(540\) | − 3685.31i | − 0.293686i | ||||||||
\(541\) | 6169.23i | 0.490270i | 0.969489 | + | 0.245135i | \(0.0788322\pi\) | ||||
−0.969489 | + | 0.245135i | \(0.921168\pi\) | |||||||
\(542\) | −1544.27 | −0.122384 | ||||||||
\(543\) | 10676.5 | 0.843776 | ||||||||
\(544\) | 8341.52i | 0.657426i | ||||||||
\(545\) | 3024.28 | 0.237699 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5140.42 | 0.401807 | 0.200904 | − | 0.979611i | \(-0.435612\pi\) | ||||
0.200904 | + | 0.979611i | \(0.435612\pi\) | |||||||
\(548\) | 14690.5i | 1.14516i | ||||||||
\(549\) | −6648.76 | −0.516871 | ||||||||
\(550\) | −2676.64 | −0.207513 | ||||||||
\(551\) | − 5271.15i | − 0.407547i | ||||||||
\(552\) | 22573.6i | 1.74057i | ||||||||
\(553\) | − 15938.3i | − 1.22562i | ||||||||
\(554\) | 12714.8i | 0.975090i | ||||||||
\(555\) | −2913.45 | −0.222827 | ||||||||
\(556\) | −11115.5 | −0.847847 | ||||||||
\(557\) | − 2778.56i | − 0.211367i | −0.994400 | − | 0.105683i | \(-0.966297\pi\) | ||||
0.994400 | − | 0.105683i | \(-0.0337030\pi\) | |||||||
\(558\) | 2048.64 | 0.155422 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1105.69 | 0.0834356 | ||||||||
\(561\) | 5904.17i | 0.444339i | ||||||||
\(562\) | −2395.75 | −0.179819 | ||||||||
\(563\) | −4906.14 | −0.367263 | −0.183632 | − | 0.982995i | \(-0.558785\pi\) | ||||
−0.183632 | + | 0.982995i | \(0.558785\pi\) | |||||||
\(564\) | − 22553.7i | − 1.68383i | ||||||||
\(565\) | − 5750.22i | − 0.428166i | ||||||||
\(566\) | − 10876.2i | − 0.807706i | ||||||||
\(567\) | 8381.04i | 0.620759i | ||||||||
\(568\) | 8697.82 | 0.642522 | ||||||||
\(569\) | 9363.15 | 0.689849 | 0.344924 | − | 0.938631i | \(-0.387905\pi\) | ||||
0.344924 | + | 0.938631i | \(0.387905\pi\) | |||||||
\(570\) | − 1157.74i | − 0.0850744i | ||||||||
\(571\) | −7199.32 | −0.527640 | −0.263820 | − | 0.964572i | \(-0.584982\pi\) | ||||
−0.263820 | + | 0.964572i | \(0.584982\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 37177.3 | 2.71048 | ||||||||
\(574\) | − 6805.18i | − 0.494848i | ||||||||
\(575\) | −13785.4 | −0.999813 | ||||||||
\(576\) | −9734.14 | −0.704148 | ||||||||
\(577\) | − 11449.6i | − 0.826086i | −0.910711 | − | 0.413043i | \(-0.864466\pi\) | ||||
0.910711 | − | 0.413043i | \(-0.135534\pi\) | |||||||
\(578\) | 4573.19i | 0.329100i | ||||||||
\(579\) | − 4101.94i | − 0.294423i | ||||||||
\(580\) | 4355.91i | 0.311843i | ||||||||
\(581\) | −36803.3 | −2.62798 | ||||||||
\(582\) | −20495.2 | −1.45971 | ||||||||
\(583\) | 1844.28i | 0.131016i | ||||||||
\(584\) | 6522.62 | 0.462171 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −999.439 | −0.0704547 | ||||||||
\(587\) | − 5439.39i | − 0.382466i | −0.981545 | − | 0.191233i | \(-0.938751\pi\) | ||||
0.981545 | − | 0.191233i | \(-0.0612487\pi\) | |||||||
\(588\) | −19107.3 | −1.34008 | ||||||||
\(589\) | −649.406 | −0.0454301 | ||||||||
\(590\) | − 2445.04i | − 0.170611i | ||||||||
\(591\) | − 38945.2i | − 2.71064i | ||||||||
\(592\) | − 1075.99i | − 0.0747006i | ||||||||
\(593\) | 28405.8i | 1.96709i | 0.180651 | + | 0.983547i | \(0.442180\pi\) | ||||
−0.180651 | + | 0.983547i | \(0.557820\pi\) | |||||||
\(594\) | −4433.93 | −0.306273 | ||||||||
\(595\) | −4311.76 | −0.297084 | ||||||||
\(596\) | − 9749.30i | − 0.670045i | ||||||||
\(597\) | 3180.67 | 0.218051 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10482.3 | −0.715020 | −0.357510 | − | 0.933909i | \(-0.616374\pi\) | ||||
−0.357510 | + | 0.933909i | \(0.616374\pi\) | |||||||
\(600\) | − 20656.6i | − 1.40550i | ||||||||
\(601\) | 3199.54 | 0.217158 | 0.108579 | − | 0.994088i | \(-0.465370\pi\) | ||||
0.108579 | + | 0.994088i | \(0.465370\pi\) | |||||||
\(602\) | 6421.02 | 0.434720 | ||||||||
\(603\) | 24806.3i | 1.67527i | ||||||||
\(604\) | 15542.6i | 1.04705i | ||||||||
\(605\) | − 3910.91i | − 0.262812i | ||||||||
\(606\) | 4560.20i | 0.305686i | ||||||||
\(607\) | 11342.8 | 0.758468 | 0.379234 | − | 0.925301i | \(-0.376188\pi\) | ||||
0.379234 | + | 0.925301i | \(0.376188\pi\) | |||||||
\(608\) | 4488.44 | 0.299392 | ||||||||
\(609\) | − 51903.7i | − 3.45361i | ||||||||
\(610\) | 763.629 | 0.0506859 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −11996.7 | −0.792384 | ||||||||
\(613\) | 14385.4i | 0.947831i | 0.880570 | + | 0.473916i | \(0.157160\pi\) | ||||
−0.880570 | + | 0.473916i | \(0.842840\pi\) | |||||||
\(614\) | 156.789 | 0.0103053 | ||||||||
\(615\) | −4959.89 | −0.325207 | ||||||||
\(616\) | − 8783.39i | − 0.574502i | ||||||||
\(617\) | 22056.8i | 1.43918i | 0.694401 | + | 0.719588i | \(0.255669\pi\) | ||||
−0.694401 | + | 0.719588i | \(0.744331\pi\) | |||||||
\(618\) | 4376.48i | 0.284867i | ||||||||
\(619\) | − 13621.4i | − 0.884477i | −0.896898 | − | 0.442238i | \(-0.854185\pi\) | ||||
0.896898 | − | 0.442238i | \(-0.145815\pi\) | |||||||
\(620\) | 536.648 | 0.0347618 | ||||||||
\(621\) | −22836.0 | −1.47565 | ||||||||
\(622\) | − 6057.14i | − 0.390465i | ||||||||
\(623\) | 11954.7 | 0.768789 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11029.2 | 0.705866 | ||||||||
\(626\) | 5917.34i | 0.377803i | ||||||||
\(627\) | 3176.94 | 0.202352 | ||||||||
\(628\) | 18046.5 | 1.14671 | ||||||||
\(629\) | 4195.92i | 0.265982i | ||||||||
\(630\) | − 7319.02i | − 0.462852i | ||||||||
\(631\) | 18737.5i | 1.18214i | 0.806622 | + | 0.591068i | \(0.201293\pi\) | ||||
−0.806622 | + | 0.591068i | \(0.798707\pi\) | |||||||
\(632\) | 12419.6i | 0.781683i | ||||||||
\(633\) | 18433.7 | 1.15746 | ||||||||
\(634\) | 6881.46 | 0.431069 | ||||||||
\(635\) | 3081.36i | 0.192567i | ||||||||
\(636\) | −5836.91 | −0.363913 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5240.75 | 0.325209 | ||||||||
\(639\) | 19888.4i | 1.23125i | ||||||||
\(640\) | −4217.35 | −0.260477 | ||||||||
\(641\) | −29798.7 | −1.83616 | −0.918081 | − | 0.396394i | \(-0.870261\pi\) | ||||
−0.918081 | + | 0.396394i | \(0.870261\pi\) | |||||||
\(642\) | − 19455.6i | − 1.19603i | ||||||||
\(643\) | − 22983.5i | − 1.40961i | −0.709399 | − | 0.704807i | \(-0.751034\pi\) | ||||
0.709399 | − | 0.704807i | \(-0.248966\pi\) | |||||||
\(644\) | − 18551.5i | − 1.13515i | ||||||||
\(645\) | − 4679.90i | − 0.285692i | ||||||||
\(646\) | −1667.37 | −0.101551 | ||||||||
\(647\) | 24905.4 | 1.51334 | 0.756672 | − | 0.653794i | \(-0.226824\pi\) | ||||
0.756672 | + | 0.653794i | \(0.226824\pi\) | |||||||
\(648\) | − 6530.72i | − 0.395912i | ||||||||
\(649\) | 6709.39 | 0.405804 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6394.54 | −0.384980 | ||||||||
\(652\) | − 18250.1i | − 1.09621i | ||||||||
\(653\) | 10077.8 | 0.603946 | 0.301973 | − | 0.953316i | \(-0.402355\pi\) | ||||
0.301973 | + | 0.953316i | \(0.402355\pi\) | |||||||
\(654\) | 11515.7 | 0.688534 | ||||||||
\(655\) | 1002.22i | 0.0597864i | ||||||||
\(656\) | − 1831.77i | − 0.109022i | ||||||||
\(657\) | 14914.6i | 0.885650i | ||||||||
\(658\) | − 19816.5i | − 1.17406i | ||||||||
\(659\) | 12334.6 | 0.729116 | 0.364558 | − | 0.931181i | \(-0.381220\pi\) | ||||
0.364558 | + | 0.931181i | \(0.381220\pi\) | |||||||
\(660\) | −2625.32 | −0.154834 | ||||||||
\(661\) | 12749.1i | 0.750202i | 0.926984 | + | 0.375101i | \(0.122392\pi\) | ||||
−0.926984 | + | 0.375101i | \(0.877608\pi\) | |||||||
\(662\) | −6451.54 | −0.378771 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 28678.1 | 1.67609 | ||||||||
\(665\) | 2320.09i | 0.135292i | ||||||||
\(666\) | −7122.40 | −0.414395 | ||||||||
\(667\) | 26991.3 | 1.56688 | ||||||||
\(668\) | 17388.3i | 1.00715i | ||||||||
\(669\) | − 51468.9i | − 2.97444i | ||||||||
\(670\) | − 2849.07i | − 0.164283i | ||||||||
\(671\) | 2095.46i | 0.120558i | ||||||||
\(672\) | 44196.5 | 2.53708 | ||||||||
\(673\) | 13618.2 | 0.780007 | 0.390004 | − | 0.920813i | \(-0.372474\pi\) | ||||
0.390004 | + | 0.920813i | \(0.372474\pi\) | |||||||
\(674\) | − 7121.96i | − 0.407014i | ||||||||
\(675\) | 20896.7 | 1.19158 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9655.67 | 0.548150 | 0.274075 | − | 0.961708i | \(-0.411628\pi\) | ||||
0.274075 | + | 0.961708i | \(0.411628\pi\) | |||||||
\(678\) | − 21895.5i | − 1.24025i | ||||||||
\(679\) | 41071.9 | 2.32135 | ||||||||
\(680\) | 3359.84 | 0.189476 | ||||||||
\(681\) | − 7778.51i | − 0.437699i | ||||||||
\(682\) | − 645.660i | − 0.0362516i | ||||||||
\(683\) | − 16316.8i | − 0.914119i | −0.889436 | − | 0.457060i | \(-0.848903\pi\) | ||||
0.889436 | − | 0.457060i | \(-0.151097\pi\) | |||||||
\(684\) | 6455.25i | 0.360852i | ||||||||
\(685\) | 9407.61 | 0.524739 | ||||||||
\(686\) | −2232.00 | −0.124225 | ||||||||
\(687\) | − 5451.51i | − 0.302748i | ||||||||
\(688\) | 1728.37 | 0.0957753 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 5928.30 | 0.327082 | ||||||||
\(691\) | 2350.84i | 0.129421i | 0.997904 | + | 0.0647106i | \(0.0206124\pi\) | ||||
−0.997904 | + | 0.0647106i | \(0.979388\pi\) | |||||||
\(692\) | −542.640 | −0.0298093 | ||||||||
\(693\) | 20084.0 | 1.10091 | ||||||||
\(694\) | − 15723.9i | − 0.860045i | ||||||||
\(695\) | 7118.24i | 0.388504i | ||||||||
\(696\) | 40444.7i | 2.20266i | ||||||||
\(697\) | 7143.20i | 0.388189i | ||||||||
\(698\) | −9180.88 | −0.497853 | ||||||||
\(699\) | −20007.1 | −1.08260 | ||||||||
\(700\) | 16976.1i | 0.916623i | ||||||||
\(701\) | 8076.90 | 0.435179 | 0.217589 | − | 0.976040i | \(-0.430181\pi\) | ||||
0.217589 | + | 0.976040i | \(0.430181\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2257.76 | 0.121128 | ||||||||
\(704\) | 3067.87i | 0.164239i | ||||||||
\(705\) | −14443.1 | −0.771573 | ||||||||
\(706\) | −14276.6 | −0.761058 | ||||||||
\(707\) | − 9138.55i | − 0.486125i | ||||||||
\(708\) | 21234.3i | 1.12717i | ||||||||
\(709\) | 13624.9i | 0.721712i | 0.932622 | + | 0.360856i | \(0.117515\pi\) | ||||
−0.932622 | + | 0.360856i | \(0.882485\pi\) | |||||||
\(710\) | − 2284.23i | − 0.120741i | ||||||||
\(711\) | −28398.4 | −1.49792 | ||||||||
\(712\) | −9315.43 | −0.490324 | ||||||||
\(713\) | − 3325.33i | − 0.174663i | ||||||||
\(714\) | −16418.2 | −0.860553 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 193.069 | 0.0100773 | ||||||||
\(717\) | 4729.86i | 0.246359i | ||||||||
\(718\) | 4301.02 | 0.223555 | ||||||||
\(719\) | −16235.8 | −0.842131 | −0.421066 | − | 0.907030i | \(-0.638344\pi\) | ||||
−0.421066 | + | 0.907030i | \(0.638344\pi\) | |||||||
\(720\) | − 1970.09i | − 0.101973i | ||||||||
\(721\) | − 8770.37i | − 0.453018i | ||||||||
\(722\) | − 9813.51i | − 0.505846i | ||||||||
\(723\) | − 47123.8i | − 2.42400i | ||||||||
\(724\) | 6837.08 | 0.350964 | ||||||||
\(725\) | −24699.2 | −1.26525 | ||||||||
\(726\) | − 14891.8i | − 0.761277i | ||||||||
\(727\) | −24181.2 | −1.23361 | −0.616803 | − | 0.787118i | \(-0.711572\pi\) | ||||
−0.616803 | + | 0.787118i | \(0.711572\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28693.9 | −1.45780 | ||||||||
\(730\) | − 1712.98i | − 0.0868496i | ||||||||
\(731\) | −6739.96 | −0.341021 | ||||||||
\(732\) | −6631.86 | −0.334864 | ||||||||
\(733\) | 3053.70i | 0.153876i | 0.997036 | + | 0.0769379i | \(0.0245143\pi\) | ||||
−0.997036 | + | 0.0769379i | \(0.975486\pi\) | |||||||
\(734\) | − 4747.41i | − 0.238733i | ||||||||
\(735\) | 12236.1i | 0.614060i | ||||||||
\(736\) | 22983.4i | 1.15106i | ||||||||
\(737\) | 7818.10 | 0.390751 | ||||||||
\(738\) | −12125.3 | −0.604793 | ||||||||
\(739\) | 8033.62i | 0.399894i | 0.979807 | + | 0.199947i | \(0.0640770\pi\) | ||||
−0.979807 | + | 0.199947i | \(0.935923\pi\) | |||||||
\(740\) | −1865.74 | −0.0926836 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5128.54 | −0.253739 | ||||||||
\(743\) | − 16139.6i | − 0.796912i | −0.917187 | − | 0.398456i | \(-0.869546\pi\) | ||||
0.917187 | − | 0.398456i | \(-0.130454\pi\) | |||||||
\(744\) | 4982.79 | 0.245535 | ||||||||
\(745\) | −6243.33 | −0.307031 | ||||||||
\(746\) | 8408.53i | 0.412678i | ||||||||
\(747\) | 65574.9i | 3.21186i | ||||||||
\(748\) | 3780.96i | 0.184820i | ||||||||
\(749\) | 38988.7i | 1.90202i | ||||||||
\(750\) | −11462.4 | −0.558062 | ||||||||
\(751\) | 18491.1 | 0.898469 | 0.449235 | − | 0.893414i | \(-0.351697\pi\) | ||||
0.449235 | + | 0.893414i | \(0.351697\pi\) | |||||||
\(752\) | − 5334.08i | − 0.258662i | ||||||||
\(753\) | 45344.5 | 2.19448 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9953.28 | 0.479784 | ||||||||
\(756\) | 28121.5i | 1.35287i | ||||||||
\(757\) | 160.630 | 0.00771227 | 0.00385613 | − | 0.999993i | \(-0.498773\pi\) | ||||
0.00385613 | + | 0.999993i | \(0.498773\pi\) | |||||||
\(758\) | −5347.17 | −0.256224 | ||||||||
\(759\) | 16267.7i | 0.777973i | ||||||||
\(760\) | − 1807.87i | − 0.0862874i | ||||||||
\(761\) | − 26799.1i | − 1.27656i | −0.769803 | − | 0.638282i | \(-0.779645\pi\) | ||||
0.769803 | − | 0.638282i | \(-0.220355\pi\) | |||||||
\(762\) | 11733.1i | 0.557803i | ||||||||
\(763\) | −23077.3 | −1.09496 | ||||||||
\(764\) | 23807.9 | 1.12741 | ||||||||
\(765\) | 7682.57i | 0.363090i | ||||||||
\(766\) | −598.052 | −0.0282095 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −30025.1 | −1.41073 | ||||||||
\(769\) | − 5145.82i | − 0.241304i | −0.992695 | − | 0.120652i | \(-0.961501\pi\) | ||||
0.992695 | − | 0.120652i | \(-0.0384986\pi\) | |||||||
\(770\) | −2306.71 | −0.107958 | ||||||||
\(771\) | −5716.29 | −0.267013 | ||||||||
\(772\) | − 2626.83i | − 0.122463i | ||||||||
\(773\) | 12810.6i | 0.596072i | 0.954555 | + | 0.298036i | \(0.0963316\pi\) | ||||
−0.954555 | + | 0.298036i | \(0.903668\pi\) | |||||||
\(774\) | − 11440.8i | − 0.531306i | ||||||||
\(775\) | 3042.94i | 0.141039i | ||||||||
\(776\) | −32004.3 | −1.48052 | ||||||||
\(777\) | 22231.6 | 1.02645 | ||||||||
\(778\) | 13411.1i | 0.618011i | ||||||||
\(779\) | 3843.64 | 0.176781 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6268.13 | 0.287185 | ||||||||
\(782\) | − 8537.89i | − 0.390428i | ||||||||
\(783\) | −40915.0 | −1.86741 | ||||||||
\(784\) | −4518.98 | −0.205857 | ||||||||
\(785\) | − 11556.8i | − 0.525452i | ||||||||
\(786\) | 3816.23i | 0.173181i | ||||||||
\(787\) | − 28073.0i | − 1.27153i | −0.771883 | − | 0.635764i | \(-0.780685\pi\) | ||||
0.771883 | − | 0.635764i | \(-0.219315\pi\) | |||||||
\(788\) | − 24940.0i | − 1.12748i | ||||||||
\(789\) | 28194.3 | 1.27217 | ||||||||
\(790\) | 3261.64 | 0.146891 | ||||||||
\(791\) | 43878.1i | 1.97235i | ||||||||
\(792\) | −15650.0 | −0.702144 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 11304.3 | 0.505259 | ||||||||
\(795\) | 3737.89i | 0.166754i | ||||||||
\(796\) | 2036.87 | 0.0906970 | ||||||||
\(797\) | −30093.1 | −1.33746 | −0.668729 | − | 0.743507i | \(-0.733161\pi\) | ||||
−0.668729 | + | 0.743507i | \(0.733161\pi\) | |||||||
\(798\) | 8834.35i | 0.391896i | ||||||||
\(799\) | 20800.8i | 0.921003i | ||||||||
\(800\) | − 21031.6i | − 0.929473i | ||||||||
\(801\) | − 21300.6i | − 0.939598i | ||||||||
\(802\) | −6667.24 | −0.293552 | ||||||||
\(803\) | 4700.56 | 0.206574 | ||||||||
\(804\) | 24743.2i | 1.08536i | ||||||||
\(805\) | −11880.2 | −0.520151 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22456.8 | −0.979575 | ||||||||
\(808\) | 7120.99i | 0.310044i | ||||||||
\(809\) | −24337.1 | −1.05766 | −0.528831 | − | 0.848727i | \(-0.677369\pi\) | ||||
−0.528831 | + | 0.848727i | \(0.677369\pi\) | |||||||
\(810\) | −1715.11 | −0.0743984 | ||||||||
\(811\) | 19078.7i | 0.826071i | 0.910715 | + | 0.413035i | \(0.135531\pi\) | ||||
−0.910715 | + | 0.413035i | \(0.864469\pi\) | |||||||
\(812\) | − 33238.5i | − 1.43651i | ||||||||
\(813\) | − 8588.54i | − 0.370496i | ||||||||
\(814\) | 2244.74i | 0.0966559i | ||||||||
\(815\) | −11687.1 | −0.502309 | ||||||||
\(816\) | −4419.33 | −0.189593 | ||||||||
\(817\) | 3626.66i | 0.155301i | ||||||||
\(818\) | 21178.6 | 0.905248 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3176.26 | −0.135268 | ||||||||
\(821\) | 2013.92i | 0.0856104i | 0.999083 | + | 0.0428052i | \(0.0136295\pi\) | ||||
−0.999083 | + | 0.0428052i | \(0.986371\pi\) | |||||||
\(822\) | 35821.9 | 1.51999 | ||||||||
\(823\) | 7692.10 | 0.325795 | 0.162898 | − | 0.986643i | \(-0.447916\pi\) | ||||
0.162898 | + | 0.986643i | \(0.447916\pi\) | |||||||
\(824\) | 6834.10i | 0.288929i | ||||||||
\(825\) | − 14886.2i | − 0.628209i | ||||||||
\(826\) | 18657.3i | 0.785922i | ||||||||
\(827\) | 4762.76i | 0.200263i | 0.994974 | + | 0.100131i | \(0.0319263\pi\) | ||||
−0.994974 | + | 0.100131i | \(0.968074\pi\) | |||||||
\(828\) | −33054.6 | −1.38735 | ||||||||
\(829\) | −19977.7 | −0.836976 | −0.418488 | − | 0.908222i | \(-0.637440\pi\) | ||||
−0.418488 | + | 0.908222i | \(0.637440\pi\) | |||||||
\(830\) | − 7531.47i | − 0.314965i | ||||||||
\(831\) | −70714.0 | −2.95191 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17622.3 | 0.732984 | ||||||||
\(834\) | 27104.6i | 1.12537i | ||||||||
\(835\) | 11135.3 | 0.461499 | ||||||||
\(836\) | 2034.47 | 0.0841671 | ||||||||
\(837\) | 5040.72i | 0.208164i | ||||||||
\(838\) | 22762.6i | 0.938330i | ||||||||
\(839\) | 30615.8i | 1.25980i | 0.776676 | + | 0.629901i | \(0.216905\pi\) | ||||
−0.776676 | + | 0.629901i | \(0.783095\pi\) | |||||||
\(840\) | − 17801.7i | − 0.731210i | ||||||||
\(841\) | 23971.0 | 0.982861 | ||||||||
\(842\) | 24748.1 | 1.01292 | ||||||||
\(843\) | − 13324.1i | − 0.544372i | ||||||||
\(844\) | 11804.7 | 0.481439 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −35308.5 | −1.43491 | ||||||||
\(847\) | 29842.9i | 1.21064i | ||||||||
\(848\) | −1380.47 | −0.0559026 | ||||||||
\(849\) | 60488.6 | 2.44519 | ||||||||
\(850\) | 7812.83i | 0.315268i | ||||||||
\(851\) | 11561.0i | 0.465696i | ||||||||
\(852\) | 19837.8i | 0.797690i | ||||||||
\(853\) | − 5660.88i | − 0.227227i | −0.993525 | − | 0.113614i | \(-0.963757\pi\) | ||||
0.993525 | − | 0.113614i | \(-0.0362426\pi\) | |||||||
\(854\) | −5827.01 | −0.233485 | ||||||||
\(855\) | 4133.86 | 0.165351 | ||||||||
\(856\) | − 30381.0i | − 1.21309i | ||||||||
\(857\) | −41346.1 | −1.64802 | −0.824012 | − | 0.566572i | \(-0.808269\pi\) | ||||
−0.824012 | + | 0.566572i | \(0.808269\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34810.5 | −1.38268 | −0.691339 | − | 0.722530i | \(-0.742979\pi\) | ||||
−0.691339 | + | 0.722530i | \(0.742979\pi\) | |||||||
\(860\) | − 2996.96i | − 0.118832i | ||||||||
\(861\) | 37847.4 | 1.49807 | ||||||||
\(862\) | 16700.4 | 0.659880 | ||||||||
\(863\) | − 8360.51i | − 0.329774i | −0.986312 | − | 0.164887i | \(-0.947274\pi\) | ||||
0.986312 | − | 0.164887i | \(-0.0527260\pi\) | |||||||
\(864\) | − 34839.5i | − 1.37183i | ||||||||
\(865\) | 347.500i | 0.0136594i | ||||||||
\(866\) | − 25108.2i | − 0.985233i | ||||||||
\(867\) | −25434.1 | −0.996293 | ||||||||
\(868\) | −4094.99 | −0.160130 | ||||||||
\(869\) | 8950.21i | 0.349385i | ||||||||
\(870\) | 10621.6 | 0.413917 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 17982.4 | 0.698352 | ||||||||
\(873\) | − 73180.6i | − 2.83710i | ||||||||
\(874\) | −4594.10 | −0.177801 | ||||||||
\(875\) | 22970.4 | 0.887475 | ||||||||
\(876\) | 14876.6i | 0.573784i | ||||||||
\(877\) | − 40579.3i | − 1.56245i | −0.624251 | − | 0.781223i | \(-0.714596\pi\) | ||||
0.624251 | − | 0.781223i | \(-0.285404\pi\) | |||||||
\(878\) | 9425.22i | 0.362285i | ||||||||
\(879\) | − 5558.43i | − 0.213289i | ||||||||
\(880\) | −620.903 | −0.0237848 | ||||||||
\(881\) | −10445.2 | −0.399442 | −0.199721 | − | 0.979853i | \(-0.564004\pi\) | ||||
−0.199721 | + | 0.979853i | \(0.564004\pi\) | |||||||
\(882\) | 29913.0i | 1.14198i | ||||||||
\(883\) | −18227.6 | −0.694685 | −0.347343 | − | 0.937738i | \(-0.612916\pi\) | ||||
−0.347343 | + | 0.937738i | \(0.612916\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13598.2 | 0.516496 | ||||||||
\(886\) | − 15929.9i | − 0.604036i | ||||||||
\(887\) | −23517.7 | −0.890245 | −0.445122 | − | 0.895470i | \(-0.646840\pi\) | ||||
−0.445122 | + | 0.895470i | \(0.646840\pi\) | |||||||
\(888\) | −17323.4 | −0.654658 | ||||||||
\(889\) | − 23512.9i | − 0.887061i | ||||||||
\(890\) | 2446.43i | 0.0921399i | ||||||||
\(891\) | − 4706.40i | − 0.176959i | ||||||||
\(892\) | − 32960.1i | − 1.23720i | ||||||||
\(893\) | 11192.6 | 0.419424 | ||||||||
\(894\) | −23773.1 | −0.889366 | ||||||||
\(895\) | − 123.639i | − 0.00461766i | ||||||||
\(896\) | 32181.2 | 1.19989 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9092.21 | 0.337874 | ||||||||
\(899\) | − 5957.95i | − 0.221033i | ||||||||
\(900\) | 30247.5 | 1.12028 | ||||||||
\(901\) | 5383.28 | 0.199049 | ||||||||
\(902\) | 3821.47i | 0.141065i | ||||||||
\(903\) | 35710.9i | 1.31604i | ||||||||
\(904\) | − 34191.0i | − 1.25794i | ||||||||
\(905\) | − 4378.38i | − 0.160820i | ||||||||
\(906\) | 37899.7 | 1.38977 | ||||||||
\(907\) | 30564.6 | 1.11894 | 0.559471 | − | 0.828850i | \(-0.311004\pi\) | ||||
0.559471 | + | 0.828850i | \(0.311004\pi\) | |||||||
\(908\) | − 4981.26i | − 0.182058i | ||||||||
\(909\) | −16282.8 | −0.594132 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32766.5 | −1.19166 | −0.595831 | − | 0.803110i | \(-0.703177\pi\) | ||||
−0.595831 | + | 0.803110i | \(0.703177\pi\) | |||||||
\(912\) | 2377.97i | 0.0863404i | ||||||||
\(913\) | 20667.0 | 0.749154 | ||||||||
\(914\) | 7216.87 | 0.261174 | ||||||||
\(915\) | 4246.96i | 0.153443i | ||||||||
\(916\) | − 3491.08i | − 0.125926i | ||||||||
\(917\) | − 7647.64i | − 0.275406i | ||||||||
\(918\) | 12942.2i | 0.465312i | ||||||||
\(919\) | 20686.7 | 0.742538 | 0.371269 | − | 0.928525i | \(-0.378923\pi\) | ||||
0.371269 | + | 0.928525i | \(0.378923\pi\) | |||||||
\(920\) | 9257.35 | 0.331745 | ||||||||
\(921\) | 871.989i | 0.0311976i | ||||||||
\(922\) | 8007.28 | 0.286015 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 20033.0 | 0.713242 | ||||||||
\(925\) | − 10579.2i | − 0.376047i | ||||||||
\(926\) | −10128.6 | −0.359447 | ||||||||
\(927\) | −15626.8 | −0.553669 | ||||||||
\(928\) | 41179.0i | 1.45665i | ||||||||
\(929\) | 45632.2i | 1.61156i | 0.592212 | + | 0.805782i | \(0.298255\pi\) | ||||
−0.592212 | + | 0.805782i | \(0.701745\pi\) | |||||||
\(930\) | − 1308.59i | − 0.0461401i | ||||||||
\(931\) | − 9482.26i | − 0.333801i | ||||||||
\(932\) | −12812.3 | −0.450301 | ||||||||
\(933\) | 33687.1 | 1.18206 | ||||||||
\(934\) | 20265.9i | 0.709979i | ||||||||
\(935\) | 2421.28 | 0.0846892 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17761.4 | −0.619253 | −0.309626 | − | 0.950858i | \(-0.600204\pi\) | ||||
−0.309626 | + | 0.950858i | \(0.600204\pi\) | |||||||
\(938\) | 21740.4i | 0.756768i | ||||||||
\(939\) | −32909.6 | −1.14373 | ||||||||
\(940\) | −9249.19 | −0.320931 | ||||||||
\(941\) | − 44888.3i | − 1.55507i | −0.628841 | − | 0.777534i | \(-0.716470\pi\) | ||||
0.628841 | − | 0.777534i | \(-0.283530\pi\) | |||||||
\(942\) | − 44005.5i | − 1.52206i | ||||||||
\(943\) | 19681.7i | 0.679664i | ||||||||
\(944\) | 5022.05i | 0.173150i | ||||||||
\(945\) | 18008.6 | 0.619917 | ||||||||
\(946\) | −3605.74 | −0.123925 | ||||||||
\(947\) | − 16069.6i | − 0.551415i | −0.961242 | − | 0.275708i | \(-0.911088\pi\) | ||||
0.961242 | − | 0.275708i | \(-0.0889122\pi\) | |||||||
\(948\) | −28326.2 | −0.970457 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4203.96 | 0.143573 | ||||||||
\(951\) | 38271.6i | 1.30499i | ||||||||
\(952\) | −25637.8 | −0.872823 | ||||||||
\(953\) | −3512.03 | −0.119377 | −0.0596883 | − | 0.998217i | \(-0.519011\pi\) | ||||
−0.0596883 | + | 0.998217i | \(0.519011\pi\) | |||||||
\(954\) | 9137.88i | 0.310115i | ||||||||
\(955\) | − 15246.3i | − 0.516605i | ||||||||
\(956\) | 3028.94i | 0.102472i | ||||||||
\(957\) | 29146.7i | 0.984513i | ||||||||
\(958\) | 9071.00 | 0.305919 | ||||||||
\(959\) | −71786.5 | −2.41721 | ||||||||
\(960\) | 6217.78i | 0.209040i | ||||||||
\(961\) | 29057.0 | 0.975361 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 69468.9 | 2.32461 | ||||||||
\(964\) | − 30177.5i | − 1.00825i | ||||||||
\(965\) | −1682.19 | −0.0561158 | ||||||||
\(966\) | −45237.0 | −1.50670 | ||||||||
\(967\) | − 37011.9i | − 1.23084i | −0.788199 | − | 0.615421i | \(-0.788986\pi\) | ||||
0.788199 | − | 0.615421i | \(-0.211014\pi\) | |||||||
\(968\) | − 23254.4i | − 0.772132i | ||||||||
\(969\) | − 9273.16i | − 0.307427i | ||||||||
\(970\) | 8405.00i | 0.278215i | ||||||||
\(971\) | 19532.3 | 0.645542 | 0.322771 | − | 0.946477i | \(-0.395386\pi\) | ||||
0.322771 | + | 0.946477i | \(0.395386\pi\) | |||||||
\(972\) | −13043.1 | −0.430409 | ||||||||
\(973\) | − 54317.1i | − 1.78965i | ||||||||
\(974\) | −8412.30 | −0.276743 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1568.47 | −0.0514402 | ||||||||
\(977\) | 30201.2i | 0.988970i | 0.869186 | + | 0.494485i | \(0.164643\pi\) | ||||
−0.869186 | + | 0.494485i | \(0.835357\pi\) | |||||||
\(978\) | −44501.8 | −1.45502 | ||||||||
\(979\) | −6713.21 | −0.219157 | ||||||||
\(980\) | 7835.83i | 0.255415i | ||||||||
\(981\) | 41118.5i | 1.33824i | ||||||||
\(982\) | 23827.8i | 0.774315i | ||||||||
\(983\) | 38774.9i | 1.25812i | 0.777359 | + | 0.629058i | \(0.216559\pi\) | ||||
−0.777359 | + | 0.629058i | \(0.783441\pi\) | |||||||
\(984\) | −29491.7 | −0.955447 | ||||||||
\(985\) | −15971.3 | −0.516638 | ||||||||
\(986\) | − 15297.2i | − 0.494080i | ||||||||
\(987\) | 110211. | 3.55425 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18570.6 | −0.597079 | ||||||||
\(990\) | 4110.02i | 0.131944i | ||||||||
\(991\) | −27728.9 | −0.888838 | −0.444419 | − | 0.895819i | \(-0.646590\pi\) | ||||
−0.444419 | + | 0.895819i | \(0.646590\pi\) | |||||||
\(992\) | 5073.25 | 0.162375 | ||||||||
\(993\) | − 35880.6i | − 1.14666i | ||||||||
\(994\) | 17430.3i | 0.556192i | ||||||||
\(995\) | − 1304.38i | − 0.0415596i | ||||||||
\(996\) | 65408.2i | 2.08086i | ||||||||
\(997\) | −48918.2 | −1.55392 | −0.776958 | − | 0.629552i | \(-0.783239\pi\) | ||||
−0.776958 | + | 0.629552i | \(0.783239\pi\) | |||||||
\(998\) | 2898.31 | 0.0919283 | ||||||||
\(999\) | − 17524.8i | − 0.555016i |
(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 | 169.4.b.f.168.2 | 4 | ||
13.2 | odd | 12 | 169.4.c.g.22.2 | 4 | |||
13.3 | even | 3 | 169.4.e.f.147.3 | 8 | |||
13.4 | even | 6 | 169.4.e.f.23.3 | 8 | |||
13.5 | odd | 4 | 13.4.a.b.1.1 | ✓ | 2 | ||
13.6 | odd | 12 | 169.4.c.g.146.2 | 4 | |||
13.7 | odd | 12 | 169.4.c.j.146.1 | 4 | |||
13.8 | odd | 4 | 169.4.a.g.1.2 | 2 | |||
13.9 | even | 3 | 169.4.e.f.23.2 | 8 | |||
13.10 | even | 6 | 169.4.e.f.147.2 | 8 | |||
13.11 | odd | 12 | 169.4.c.j.22.1 | 4 | |||
13.12 | even | 2 | inner | 169.4.b.f.168.3 | 4 | ||
39.5 | even | 4 | 117.4.a.d.1.2 | 2 | |||
39.8 | even | 4 | 1521.4.a.r.1.1 | 2 | |||
52.31 | even | 4 | 208.4.a.h.1.1 | 2 | |||
65.18 | even | 4 | 325.4.b.e.274.3 | 4 | |||
65.44 | odd | 4 | 325.4.a.f.1.2 | 2 | |||
65.57 | even | 4 | 325.4.b.e.274.2 | 4 | |||
91.83 | even | 4 | 637.4.a.b.1.1 | 2 | |||
104.5 | odd | 4 | 832.4.a.s.1.1 | 2 | |||
104.83 | even | 4 | 832.4.a.z.1.2 | 2 | |||
143.109 | even | 4 | 1573.4.a.b.1.2 | 2 | |||
156.83 | odd | 4 | 1872.4.a.bb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.a.b.1.1 | ✓ | 2 | 13.5 | odd | 4 | ||
117.4.a.d.1.2 | 2 | 39.5 | even | 4 | |||
169.4.a.g.1.2 | 2 | 13.8 | odd | 4 | |||
169.4.b.f.168.2 | 4 | 1.1 | even | 1 | trivial | ||
169.4.b.f.168.3 | 4 | 13.12 | even | 2 | inner | ||
169.4.c.g.22.2 | 4 | 13.2 | odd | 12 | |||
169.4.c.g.146.2 | 4 | 13.6 | odd | 12 | |||
169.4.c.j.22.1 | 4 | 13.11 | odd | 12 | |||
169.4.c.j.146.1 | 4 | 13.7 | odd | 12 | |||
169.4.e.f.23.2 | 8 | 13.9 | even | 3 | |||
169.4.e.f.23.3 | 8 | 13.4 | even | 6 | |||
169.4.e.f.147.2 | 8 | 13.10 | even | 6 | |||
169.4.e.f.147.3 | 8 | 13.3 | even | 3 | |||
208.4.a.h.1.1 | 2 | 52.31 | even | 4 | |||
325.4.a.f.1.2 | 2 | 65.44 | odd | 4 | |||
325.4.b.e.274.2 | 4 | 65.57 | even | 4 | |||
325.4.b.e.274.3 | 4 | 65.18 | even | 4 | |||
637.4.a.b.1.1 | 2 | 91.83 | even | 4 | |||
832.4.a.s.1.1 | 2 | 104.5 | odd | 4 | |||
832.4.a.z.1.2 | 2 | 104.83 | even | 4 | |||
1521.4.a.r.1.1 | 2 | 39.8 | even | 4 | |||
1573.4.a.b.1.2 | 2 | 143.109 | even | 4 | |||
1872.4.a.bb.1.2 | 2 | 156.83 | odd | 4 |