Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(2157,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.2157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.m (of order \(2\), degree \(1\), 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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2157.3 | ||
Character | \(\chi\) | \(=\) | 4004.2157 |
Dual form | 4004.2.m.c.2157.4 |
$q$-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 \(\left(\mathbb{Z}/4004\mathbb{Z}\right)^\times\).
\(n\) | \(365\) | \(925\) | \(2003\) | \(3433\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.10315 | −1.79160 | −0.895802 | − | 0.444453i | \(-0.853398\pi\) | ||||
−0.895802 | + | 0.444453i | \(0.853398\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.71558i | 0.767232i | 0.923493 | + | 0.383616i | \(0.125321\pi\) | ||||
−0.923493 | + | 0.383616i | \(0.874679\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.62954 | 2.20985 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.66202 | − | 3.19964i | 0.460962 | − | 0.887420i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 5.32371i | − | 1.37458i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.08192 | 1.23255 | 0.616273 | − | 0.787532i | \(-0.288642\pi\) | ||||
0.616273 | + | 0.787532i | \(0.288642\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.32222i | − | 1.67983i | −0.542717 | − | 0.839916i | \(-0.682604\pi\) | ||
0.542717 | − | 0.839916i | \(-0.317396\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 3.10315i | − | 0.677163i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.22025 | −0.671469 | −0.335735 | − | 0.941957i | \(-0.608985\pi\) | ||||
−0.335735 | + | 0.941957i | \(0.608985\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.05677 | 0.411355 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −11.2630 | −2.16757 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.04384 | −1.67940 | −0.839700 | − | 0.543051i | \(-0.817269\pi\) | ||||
−0.839700 | + | 0.543051i | \(0.817269\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.98361i | − | 0.895082i | −0.894263 | − | 0.447541i | \(-0.852300\pi\) | ||
0.894263 | − | 0.447541i | \(-0.147700\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.10315i | 0.540189i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.71558 | −0.289986 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.36062i | 0.223685i | 0.993726 | + | 0.111843i | \(0.0356753\pi\) | ||||
−0.993726 | + | 0.111843i | \(0.964325\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.15750 | + | 9.92896i | −0.825861 | + | 1.58991i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.1147i | 1.89199i | 0.324174 | + | 0.945997i | \(0.394914\pi\) | ||||
−0.324174 | + | 0.945997i | \(0.605086\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.57894 | 1.30828 | 0.654138 | − | 0.756375i | \(-0.273032\pi\) | ||||
0.654138 | + | 0.756375i | \(0.273032\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.3735i | 1.69547i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.265550i | 0.0387344i | 0.999812 | + | 0.0193672i | \(0.00616516\pi\) | ||||
−0.999812 | + | 0.0193672i | \(0.993835\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.7700 | −2.20824 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.73208 | −1.33680 | −0.668402 | − | 0.743800i | \(-0.733022\pi\) | ||||
−0.668402 | + | 0.743800i | \(0.733022\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.71558 | 0.231329 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 22.7219i | 3.00959i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.610665i | 0.0795018i | 0.999210 | + | 0.0397509i | \(0.0126564\pi\) | ||||
−0.999210 | + | 0.0397509i | \(0.987344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.47181 | −0.188446 | −0.0942229 | − | 0.995551i | \(-0.530037\pi\) | ||||
−0.0942229 | + | 0.995551i | \(0.530037\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.62954i | 0.835243i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.48925 | + | 2.85134i | 0.680857 | + | 0.353665i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.4920i | − | 1.52614i | −0.646313 | − | 0.763072i | \(-0.723690\pi\) | ||
0.646313 | − | 0.763072i | \(-0.276310\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.99293 | 1.20301 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.07609i | 0.127708i | 0.997959 | + | 0.0638541i | \(0.0203392\pi\) | ||||
−0.997959 | + | 0.0638541i | \(0.979661\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.37610i | − | 0.863307i | −0.902039 | − | 0.431654i | \(-0.857930\pi\) | ||
0.902039 | − | 0.431654i | \(-0.142070\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.38248 | −0.736985 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.6681 | −1.20026 | −0.600130 | − | 0.799902i | \(-0.704885\pi\) | ||||
−0.600130 | + | 0.799902i | \(0.704885\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 15.0622 | 1.67357 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.00686i | 0.110517i | 0.998472 | + | 0.0552584i | \(0.0175983\pi\) | ||||
−0.998472 | + | 0.0552584i | \(0.982402\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.71846i | 0.945649i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 28.0644 | 3.00882 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.76495i | 0.293084i | 0.989204 | + | 0.146542i | \(0.0468144\pi\) | ||||
−0.989204 | + | 0.146542i | \(0.953186\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.19964 | + | 1.66202i | 0.335413 | + | 0.174227i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.4649i | 1.60363i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.5619 | 1.28882 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.77103i | 0.179821i | 0.995950 | + | 0.0899107i | \(0.0286582\pi\) | ||||
−0.995950 | + | 0.0899107i | \(0.971342\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 6.62954i | − | 0.666294i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.5672 | 1.64850 | 0.824250 | − | 0.566226i | \(-0.191597\pi\) | ||||
0.824250 | + | 0.566226i | \(0.191597\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.8945 | 1.27053 | 0.635266 | − | 0.772294i | \(-0.280891\pi\) | ||||
0.635266 | + | 0.772294i | \(0.280891\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.32371 | 0.519541 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.5121 | −1.49961 | −0.749806 | − | 0.661658i | \(-0.769853\pi\) | ||||
−0.749806 | + | 0.661658i | \(0.769853\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.76650i | 0.264982i | 0.991184 | + | 0.132491i | \(0.0422976\pi\) | ||||
−0.991184 | + | 0.132491i | \(0.957702\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 4.22222i | − | 0.400756i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.63951 | −0.718665 | −0.359332 | − | 0.933210i | \(-0.616996\pi\) | ||||
−0.359332 | + | 0.933210i | \(0.616996\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5.52461i | − | 0.515173i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.0184 | − | 21.2121i | 1.01865 | − | 1.96106i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.08192i | 0.465859i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 37.5937i | − | 3.38971i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1065i | 1.08284i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.4565 | −1.81522 | −0.907612 | − | 0.419809i | \(-0.862097\pi\) | ||||
−0.907612 | + | 0.419809i | \(0.862097\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −26.6217 | −2.34391 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.1564 | −1.32422 | −0.662109 | − | 0.749408i | \(-0.730338\pi\) | ||||
−0.662109 | + | 0.749408i | \(0.730338\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.32222 | 0.634917 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 19.3226i | − | 1.66303i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 7.89611i | − | 0.674610i | −0.941395 | − | 0.337305i | \(-0.890485\pi\) | ||
0.941395 | − | 0.337305i | \(-0.109515\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.11731 | −0.773320 | −0.386660 | − | 0.922222i | \(-0.626371\pi\) | ||||
−0.386660 | + | 0.922222i | \(0.626371\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 0.824040i | − | 0.0693967i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.19964 | − | 1.66202i | −0.267567 | − | 0.138985i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 15.5155i | − | 1.28849i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.10315 | 0.255943 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 8.08924i | − | 0.662697i | −0.943509 | − | 0.331348i | \(-0.892496\pi\) | ||
0.943509 | − | 0.331348i | \(-0.107504\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.1840i | 1.64255i | 0.570535 | + | 0.821273i | \(0.306736\pi\) | ||||
−0.570535 | + | 0.821273i | \(0.693264\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 33.6908 | 2.72374 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.54979 | 0.686736 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.6475 | −1.16900 | −0.584498 | − | 0.811395i | \(-0.698709\pi\) | ||||
−0.584498 | + | 0.811395i | \(0.698709\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 30.2001 | 2.39502 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.22025i | − | 0.253791i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.8860i | 1.00931i | 0.863322 | + | 0.504653i | \(0.168380\pi\) | ||||
−0.863322 | + | 0.504653i | \(0.831620\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.32371 | −0.414450 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 17.2959i | − | 1.33840i | −0.743083 | − | 0.669200i | \(-0.766637\pi\) | ||
0.743083 | − | 0.669200i | \(-0.233363\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.47537 | − | 10.6357i | −0.575029 | − | 0.818133i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 48.5429i | − | 3.71217i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.4223 | −0.944450 | −0.472225 | − | 0.881478i | \(-0.656549\pi\) | ||||
−0.472225 | + | 0.881478i | \(0.656549\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.05677i | 0.155478i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 1.89498i | − | 0.142436i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.1096 | −0.830370 | −0.415185 | − | 0.909737i | \(-0.636283\pi\) | ||||
−0.415185 | + | 0.909737i | \(0.636283\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.5362 | 1.37779 | 0.688894 | − | 0.724862i | \(-0.258097\pi\) | ||||
0.688894 | + | 0.724862i | \(0.258097\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.56724 | 0.337620 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.33426 | −0.171619 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 5.08192i | − | 0.371627i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 11.2630i | − | 0.819263i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.5932 | −1.34535 | −0.672677 | − | 0.739936i | \(-0.734856\pi\) | ||||
−0.672677 | + | 0.739936i | \(0.734856\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 3.28669i | − | 0.236581i | −0.992979 | − | 0.118291i | \(-0.962259\pi\) | ||
0.992979 | − | 0.118291i | \(-0.0377415\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −17.0340 | − | 8.84812i | −1.21983 | − | 0.633627i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 17.4262i | − | 1.24156i | −0.783984 | − | 0.620781i | \(-0.786815\pi\) | ||
0.783984 | − | 0.620781i | \(-0.213185\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.64221 | 0.470854 | 0.235427 | − | 0.971892i | \(-0.424351\pi\) | ||||
0.235427 | + | 0.971892i | \(0.424351\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 38.7646i | 2.73425i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 9.04384i | − | 0.634753i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.7837 | −1.45160 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −21.3488 | −1.48384 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.32222 | −0.506488 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.13924 | 0.422642 | 0.211321 | − | 0.977417i | \(-0.432223\pi\) | ||||
0.211321 | + | 0.977417i | \(0.432223\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 3.33926i | − | 0.228803i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.7179i | 1.00375i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.98361 | 0.338309 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.8891i | 1.54670i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.44626 | − | 16.2603i | 0.568157 | − | 1.09379i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.90531i | − | 0.596344i | −0.954512 | − | 0.298172i | \(-0.903623\pi\) | ||
0.954512 | − | 0.298172i | \(-0.0963769\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.6355 | 0.909031 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 14.1194i | − | 0.937138i | −0.883427 | − | 0.468569i | \(-0.844770\pi\) | ||
0.883427 | − | 0.468569i | \(-0.155230\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.92634i | 0.193378i | 0.995315 | + | 0.0966890i | \(0.0308252\pi\) | ||||
−0.995315 | + | 0.0966890i | \(0.969175\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.10315 | −0.204172 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.49861 | −0.622275 | −0.311137 | − | 0.950365i | \(-0.600710\pi\) | ||||
−0.311137 | + | 0.950365i | \(0.600710\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.455573 | −0.0297183 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 33.1049 | 2.15039 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9333i | 1.09533i | 0.836699 | + | 0.547663i | \(0.184482\pi\) | ||||
−0.836699 | + | 0.547663i | \(0.815518\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.70871i | 0.367730i | 0.982951 | + | 0.183865i | \(0.0588609\pi\) | ||||
−0.982951 | + | 0.183865i | \(0.941139\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.9512 | −0.830818 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1.71558i | − | 0.109605i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.4284 | − | 12.1697i | −1.49072 | − | 0.774338i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 3.12443i | − | 0.198002i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.0766 | 1.07787 | 0.538934 | − | 0.842348i | \(-0.318827\pi\) | ||||
0.538934 | + | 0.842348i | \(0.318827\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.22025i | 0.202456i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 27.0547i | − | 1.69423i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.6369 | −1.10016 | −0.550080 | − | 0.835112i | \(-0.685403\pi\) | ||||
−0.550080 | + | 0.835112i | \(0.685403\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.36062 | −0.0845451 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −59.9565 | −3.71121 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.4613 | 1.38502 | 0.692510 | − | 0.721408i | \(-0.256505\pi\) | ||||
0.692510 | + | 0.721408i | \(0.256505\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 16.6962i | − | 1.02564i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 8.58006i | − | 0.525091i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.52344 | 0.397741 | 0.198871 | − | 0.980026i | \(-0.436273\pi\) | ||||
0.198871 | + | 0.980026i | \(0.436273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.68382i | 0.163030i | 0.996672 | + | 0.0815151i | \(0.0259759\pi\) | ||||
−0.996672 | + | 0.0815151i | \(0.974024\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.92896 | − | 5.15750i | −0.600928 | − | 0.312146i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2.05677i | − | 0.124028i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.1046 | 1.02771 | 0.513856 | − | 0.857876i | \(-0.328216\pi\) | ||||
0.513856 | + | 0.857876i | \(0.328216\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 33.0390i | − | 1.97799i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 32.5978i | − | 1.94462i | −0.233696 | − | 0.972310i | \(-0.575082\pi\) | ||
0.233696 | − | 0.972310i | \(-0.424918\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.68236 | −0.100006 | −0.0500030 | − | 0.998749i | \(-0.515923\pi\) | ||||
−0.0500030 | + | 0.998749i | \(0.515923\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −38.9814 | −2.30906 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.1147 | −0.715107 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.82590 | 0.519171 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 5.49579i | − | 0.322169i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 10.9268i | − | 0.638353i | −0.947695 | − | 0.319176i | \(-0.896594\pi\) | ||
0.947695 | − | 0.319176i | \(-0.103406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.04765 | −0.0609963 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.2630i | 0.653546i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.35213 | + | 10.3036i | −0.309522 | + | 0.595875i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.57894i | 0.494482i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −51.4106 | −2.95346 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2.52501i | − | 0.144582i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 28.4746i | − | 1.62513i | −0.582872 | − | 0.812564i | \(-0.698071\pi\) | ||
0.582872 | − | 0.812564i | \(-0.301929\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −40.0135 | −2.27629 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.49257 | −0.254750 | −0.127375 | − | 0.991855i | \(-0.540655\pi\) | ||||
−0.127375 | + | 0.991855i | \(0.540655\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.176055 | −0.00995119 | −0.00497560 | − | 0.999988i | \(-0.501584\pi\) | ||||
−0.00497560 | + | 0.999988i | \(0.501584\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.3735 | −0.640826 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 5.56199i | − | 0.312392i | −0.987726 | − | 0.156196i | \(-0.950077\pi\) | ||
0.987726 | − | 0.156196i | \(-0.0499232\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.04384i | 0.506358i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 48.1364 | 2.68671 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 37.2109i | − | 2.07047i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.41840 | − | 6.58093i | 0.189619 | − | 0.365045i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 8.58486i | − | 0.474744i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.265550 | −0.0146402 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 20.3149i | − | 1.11661i | −0.829636 | − | 0.558305i | \(-0.811452\pi\) | ||
0.829636 | − | 0.558305i | \(-0.188548\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.02031i | 0.494310i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.4311 | 1.17091 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.0083 | −1.58019 | −0.790093 | − | 0.612987i | \(-0.789968\pi\) | ||||
−0.790093 | + | 0.612987i | \(0.789968\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.7065 | 1.28756 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.98361 | −0.269877 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.1437i | 0.922986i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.8427 | −1.27995 | −0.639973 | − | 0.768397i | \(-0.721054\pi\) | ||||
−0.639973 | + | 0.768397i | \(0.721054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 29.8451i | − | 1.59757i | −0.601615 | − | 0.798786i | \(-0.705476\pi\) | ||
0.601615 | − | 0.798786i | \(-0.294524\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.7194 | + | 36.0375i | −0.999165 | + | 1.92354i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.4542i | 0.822544i | 0.911513 | + | 0.411272i | \(0.134915\pi\) | ||||
−0.911513 | + | 0.411272i | \(0.865085\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.84612 | −0.0979819 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 15.7700i | − | 0.834635i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.37938i | 0.442247i | 0.975246 | + | 0.221123i | \(0.0709723\pi\) | ||||
−0.975246 | + | 0.221123i | \(0.929028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −34.6149 | −1.82183 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.10315 | 0.162873 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.6543 | 0.662357 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.78081 | 0.301756 | 0.150878 | − | 0.988552i | \(-0.451790\pi\) | ||||
0.150878 | + | 0.988552i | \(0.451790\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 80.3147i | 4.18102i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 9.73208i | − | 0.505265i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.26380 | 0.220771 | 0.110386 | − | 0.993889i | \(-0.464791\pi\) | ||||
0.110386 | + | 0.993889i | \(0.464791\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 37.5682i | − | 1.94002i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.0311 | + | 28.9370i | −0.774139 | + | 1.49033i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 17.0712i | − | 0.876890i | −0.898758 | − | 0.438445i | \(-0.855529\pi\) | ||
0.898758 | − | 0.438445i | \(-0.144471\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 63.4797 | 3.25216 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 1.28626i | − | 0.0657250i | −0.999460 | − | 0.0328625i | \(-0.989538\pi\) | ||
0.999460 | − | 0.0328625i | \(-0.0104623\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.71558i | 0.0874342i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 56.8744 | 2.89109 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.8254 | 1.15729 | 0.578646 | − | 0.815579i | \(-0.303581\pi\) | ||||
0.578646 | + | 0.815579i | \(0.303581\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.3651 | −0.827617 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 47.0325 | 2.37247 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 18.3021i | − | 0.920878i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 9.90885i | − | 0.497311i | −0.968592 | − | 0.248656i | \(-0.920011\pi\) | ||
0.968592 | − | 0.248656i | \(-0.0799887\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −22.7219 | −1.13752 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 8.17088i | − | 0.408035i | −0.978967 | − | 0.204017i | \(-0.934600\pi\) | ||
0.978967 | − | 0.204017i | \(-0.0653999\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.9457 | − | 8.28286i | −0.794314 | − | 0.412599i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 25.8404i | 1.28402i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.36062 | 0.0674436 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 14.9797i | − | 0.740700i | −0.928892 | − | 0.370350i | \(-0.879238\pi\) | ||
0.928892 | − | 0.370350i | \(-0.120762\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.5028i | 1.20863i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.610665 | −0.0300489 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.72735 | −0.0847920 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 28.2924 | 1.38548 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.2674 | 0.843566 | 0.421783 | − | 0.906697i | \(-0.361404\pi\) | ||||
0.421783 | + | 0.906697i | \(0.361404\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.4363i | 1.48338i | 0.670746 | + | 0.741688i | \(0.265974\pi\) | ||||
−0.670746 | + | 0.741688i | \(0.734026\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.76047i | 0.0855971i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.4524 | 0.507014 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.47181i | − | 0.0712258i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.92896 | + | 5.15750i | 0.479375 | + | 0.249007i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.2055i | 1.06960i | 0.844978 | + | 0.534801i | \(0.179613\pi\) | ||||
−0.844978 | + | 0.534801i | \(0.820387\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.2497 | 1.02119 | 0.510597 | − | 0.859820i | \(-0.329425\pi\) | ||||
0.510597 | + | 0.859820i | \(0.329425\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 48.1468i | 2.30846i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.5794i | 1.12796i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.51477 | −0.215478 | −0.107739 | − | 0.994179i | \(-0.534361\pi\) | ||||
−0.107739 | + | 0.994179i | \(0.534361\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.62954 | −0.315692 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.5619 | −0.929416 | −0.464708 | − | 0.885464i | \(-0.653841\pi\) | ||||
−0.464708 | + | 0.885464i | \(0.653841\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.74351 | −0.224864 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25.1021i | 1.18729i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.2952i | 0.627439i | 0.949516 | + | 0.313720i | \(0.101575\pi\) | ||||
−0.949516 | + | 0.313720i | \(0.898425\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.1147 | 0.570458 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 62.6338i | − | 2.94279i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.85134 | + | 5.48925i | −0.133673 | + | 0.257340i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 34.9067i | − | 1.63287i | −0.577439 | − | 0.816434i | \(-0.695948\pi\) | ||
0.577439 | − | 0.816434i | \(-0.304052\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −57.2377 | −2.67163 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 34.2750i | − | 1.59635i | −0.602428 | − | 0.798173i | \(-0.705800\pi\) | ||
0.602428 | − | 0.798173i | \(-0.294200\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.9899i | 1.57964i | 0.613337 | + | 0.789822i | \(0.289827\pi\) | ||||
−0.613337 | + | 0.789822i | \(0.710173\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −26.5313 | −1.23036 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.5307 | −1.59789 | −0.798946 | − | 0.601403i | \(-0.794609\pi\) | ||||
−0.798946 | + | 0.601403i | \(0.794609\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.4920 | 0.576828 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 45.4533 | 2.09438 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 8.57894i | − | 0.394460i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 15.0601i | − | 0.691007i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −64.5192 | −2.95413 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.1076i | 0.690284i | 0.938551 | + | 0.345142i | \(0.112169\pi\) | ||||
−0.938551 | + | 0.345142i | \(0.887831\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.35351 | + | 2.26139i | 0.198503 | + | 0.103110i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.99293i | 0.454694i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.03836 | −0.137965 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 38.6163i | − | 1.74987i | −0.484239 | − | 0.874936i | \(-0.660903\pi\) | ||
0.484239 | − | 0.874936i | \(-0.339097\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 39.9871i | − | 1.80828i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.7053 | −0.528254 | −0.264127 | − | 0.964488i | \(-0.585084\pi\) | ||||
−0.264127 | + | 0.964488i | \(0.585084\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −45.9601 | −2.06994 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.3735 | 0.511202 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.07609 | −0.0482692 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.85956i | 0.0832455i | 0.999133 | + | 0.0416227i | \(0.0132528\pi\) | ||||
−0.999133 | + | 0.0416227i | \(0.986747\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 53.6719i | 2.39788i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.45118 | 0.153881 | 0.0769403 | − | 0.997036i | \(-0.475485\pi\) | ||||
0.0769403 | + | 0.997036i | \(0.475485\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.4224i | 1.26478i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.1972 | + | 33.0043i | 1.03022 | + | 1.46577i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.5030i | 1.35202i | 0.736891 | + | 0.676011i | \(0.236293\pi\) | ||||
−0.736891 | + | 0.676011i | \(0.763707\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.37610 | 0.326299 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 82.4702i | 3.64115i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.1216i | 0.974792i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.265550 | 0.0116789 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 38.5483 | 1.69208 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.3987 | 0.981307 | 0.490653 | − | 0.871355i | \(-0.336758\pi\) | ||||
0.490653 | + | 0.871355i | \(0.336758\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.09703 | 0.179151 | 0.0895753 | − | 0.995980i | \(-0.471449\pi\) | ||||
0.0895753 | + | 0.995980i | \(0.471449\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 6.38248i | − | 0.278554i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 25.3263i | − | 1.10323i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.6300 | −0.549129 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.04843i | 0.175687i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 38.7626 | + | 20.1349i | 1.67899 | + | 0.872137i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 26.6123i | − | 1.15055i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34.4747 | 1.48770 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000i | 0.0430730i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.60972i | 0.198187i | 0.995078 | + | 0.0990936i | \(0.0315943\pi\) | ||||
−0.995078 | + | 0.0990936i | \(0.968406\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −57.5207 | −2.46845 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.74616 | −0.203303 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.7361 | −1.22867 | −0.614333 | − | 0.789047i | \(-0.710575\pi\) | ||||
−0.614333 | + | 0.789047i | \(0.710575\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.75742 | −0.416436 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 66.2210i | 2.82111i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 10.6681i | − | 0.453656i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.24357 | 0.307472 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 10.8600i | − | 0.460152i | −0.973173 | − | 0.230076i | \(-0.926102\pi\) | ||
0.973173 | − | 0.230076i | \(-0.0738976\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.2584 | − | 27.4495i | 0.603065 | − | 1.16099i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.7700i | 0.665808i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.4139 | 0.986777 | 0.493388 | − | 0.869809i | \(-0.335758\pi\) | ||||
0.493388 | + | 0.869809i | \(0.335758\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 13.1062i | − | 0.551383i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.0622i | 0.632552i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.5389 | 1.11257 | 0.556285 | − | 0.830991i | \(-0.312226\pi\) | ||||
0.556285 | + | 0.830991i | \(0.312226\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.0785 | 1.30060 | 0.650298 | − | 0.759679i | \(-0.274644\pi\) | ||||
0.650298 | + | 0.759679i | \(0.274644\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 57.6974 | 2.41034 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.62333 | −0.276212 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 44.7936i | − | 1.86478i | −0.361451 | − | 0.932391i | \(-0.617719\pi\) | ||
0.361451 | − | 0.932391i | \(-0.382281\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.1991i | 0.423860i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.00686 | −0.0417714 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.73208i | 0.403062i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 36.3912 | + | 18.9030i | 1.50459 | + | 0.781545i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 31.7357i | − | 1.30987i | −0.755685 | − | 0.654935i | \(-0.772696\pi\) | ||
0.755685 | − | 0.654935i | \(-0.227304\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.4910 | −1.50359 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 54.0760i | 2.22439i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 28.3865i | − | 1.16569i | −0.812582 | − | 0.582847i | \(-0.801939\pi\) | ||
0.812582 | − | 0.582847i | \(-0.198061\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.71846 | −0.357422 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.6118 | −0.843583 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.3055 | 0.870518 | 0.435259 | − | 0.900305i | \(-0.356657\pi\) | ||||
0.435259 | + | 0.900305i | \(0.356657\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.0139 | −0.653219 | −0.326610 | − | 0.945159i | \(-0.605906\pi\) | ||||
−0.326610 | + | 0.945159i | \(0.605906\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 82.8164i | − | 3.37255i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 1.71558i | − | 0.0697484i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.8074 | −0.722782 | −0.361391 | − | 0.932414i | \(-0.617698\pi\) | ||||
−0.361391 | + | 0.932414i | \(0.617698\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 28.0644i | 1.13723i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.849663 | + | 0.441349i | 0.0343737 | + | 0.0178551i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.7247i | 1.32174i | 0.750500 | + | 0.660870i | \(0.229813\pi\) | ||||
−0.750500 | + | 0.660870i | \(0.770187\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 64.4950 | 2.60069 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.4929i | 0.422430i | 0.977440 | + | 0.211215i | \(0.0677420\pi\) | ||||
−0.977440 | + | 0.211215i | \(0.932258\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 40.5207i | − | 1.62867i | −0.580398 | − | 0.814333i | \(-0.697103\pi\) | ||
0.580398 | − | 0.814333i | \(-0.302897\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 36.2697 | 1.45545 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.76495 | −0.110775 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.4858 | −0.419432 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 22.7219 | 0.907427 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.91458i | 0.275702i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 8.34947i | − | 0.332387i | −0.986093 | − | 0.166193i | \(-0.946852\pi\) | ||
0.986093 | − | 0.166193i | \(-0.0531476\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.0510 | −0.757208 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 35.0949i | − | 1.39270i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.66202 | + | 3.19964i | −0.0658517 | + | 0.126774i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.13397i | 0.282216i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.6733 | 1.29052 | 0.645258 | − | 0.763964i | \(-0.276750\pi\) | ||||
0.645258 | + | 0.763964i | \(0.276750\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.3767i | 1.27681i | 0.769699 | + | 0.638407i | \(0.220406\pi\) | ||||
−0.769699 | + | 0.638407i | \(0.779594\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 45.6718i | − | 1.79833i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.3589 | 0.879021 | 0.439510 | − | 0.898238i | \(-0.355152\pi\) | ||||
0.439510 | + | 0.898238i | \(0.355152\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.610665 | 0.0239707 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.4649 | −0.606116 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.3370 | 0.834982 | 0.417491 | − | 0.908681i | \(-0.362910\pi\) | ||||
0.417491 | + | 0.908681i | \(0.362910\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 26.0020i | − | 1.01598i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 48.9001i | − | 1.90778i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.7806 | −1.51068 | −0.755339 | − | 0.655334i | \(-0.772528\pi\) | ||||
−0.755339 | + | 0.655334i | \(0.772528\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.3898i | 1.10423i | 0.833767 | + | 0.552117i | \(0.186180\pi\) | ||||
−0.833767 | + | 0.552117i | \(0.813820\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −26.2100 | + | 50.4582i | −1.01791 | + | 1.95963i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.5619i | 0.487128i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.1235 | 1.12766 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27.6345i | 1.06841i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.47181i | 0.0568186i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.7052 | 1.02941 | 0.514705 | − | 0.857367i | \(-0.327901\pi\) | ||||
0.514705 | + | 0.857367i | \(0.327901\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.1655 | −0.891639 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.2714 | −1.54775 | −0.773877 | − | 0.633336i | \(-0.781685\pi\) | ||||
−0.773877 | + | 0.633336i | \(0.781685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.77103 | −0.0679661 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 43.8146i | 1.67898i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 14.8735i | − | 0.569118i | −0.958658 | − | 0.284559i | \(-0.908153\pi\) | ||
0.958658 | − | 0.284559i | \(-0.0918472\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.5464 | 0.517583 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 9.08087i | − | 0.346457i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.1749 | + | 31.1391i | −0.616216 | + | 1.18631i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.5711i | 0.782562i | 0.920271 | + | 0.391281i | \(0.127968\pi\) | ||||
−0.920271 | + | 0.391281i | \(0.872032\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.62954 | 0.251835 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 15.6415i | − | 0.593316i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 61.5658i | 2.33197i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.4756 | 1.11487 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.1759 | −0.799804 | −0.399902 | − | 0.916558i | \(-0.630956\pi\) | ||||
−0.399902 | + | 0.916558i | \(0.630956\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.96279 | 0.375754 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.41371 | 0.0532434 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.5672i | 0.623074i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 32.4743i | − | 1.21960i | −0.792557 | − | 0.609798i | \(-0.791250\pi\) | ||
0.792557 | − | 0.609798i | \(-0.208750\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −70.7249 | −2.65239 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.0485i | 0.601020i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.85134 | − | 5.48925i | 0.106634 | − | 0.205286i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 52.5466i | − | 1.96239i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.7515 | −0.811195 | −0.405598 | − | 0.914052i | \(-0.632937\pi\) | ||||
−0.405598 | + | 0.914052i | \(0.632937\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.8945i | 0.480216i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 17.7150i | − | 0.658827i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.6011 | −0.690829 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −50.4648 | −1.87163 | −0.935817 | − | 0.352485i | \(-0.885337\pi\) | ||||
−0.935817 | + | 0.352485i | \(0.885337\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.99710 | −0.185078 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 43.5975 | 1.61251 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.3476i | 0.456068i | 0.973653 | + | 0.228034i | \(0.0732298\pi\) | ||||
−0.973653 | + | 0.228034i | \(0.926770\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.32371i | 0.196368i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.4920 | −0.460150 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.3855i | 1.15454i | 0.816555 | + | 0.577268i | \(0.195881\pi\) | ||||
−0.816555 | + | 0.577268i | \(0.804119\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 72.7020 | + | 37.7643i | 2.67077 | + | 1.38731i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.4254i | 1.40969i | 0.709360 | + | 0.704846i | \(0.248984\pi\) | ||||
−0.709360 | + | 0.704846i | \(0.751016\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.8778 | 0.508442 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.67499i | 0.244225i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 15.5121i | − | 0.566800i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.3811 | 1.47353 | 0.736763 | − | 0.676151i | \(-0.236353\pi\) | ||||
0.736763 | + | 0.676151i | \(0.236353\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −52.9913 | −1.93111 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −34.6273 | −1.26021 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.2675 | 0.809326 | 0.404663 | − | 0.914466i | \(-0.367389\pi\) | ||||
0.404663 | + | 0.914466i | \(0.367389\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 9.99293i | − | 0.362720i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.9937i | 0.724771i | 0.932028 | + | 0.362386i | \(0.118038\pi\) | ||||
−0.932028 | + | 0.362386i | \(0.881962\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.76650 | −0.100154 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 57.7993i | 2.08974i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.95391 | + | 1.01494i | 0.0705515 | + | 0.0366473i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.9427i | 1.33219i | 0.745868 | + | 0.666093i | \(0.232035\pi\) | ||||
−0.745868 | + | 0.666093i | \(0.767965\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 54.7299 | 1.97105 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.8776i | 1.39833i | 0.714960 | + | 0.699165i | \(0.246445\pi\) | ||||
−0.714960 | + | 0.699165i | \(0.753555\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10.2502i | − | 0.368196i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.22222 | 0.151471 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 88.7063 | 3.17823 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.07609 | 0.0385055 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 101.861 | 3.64021 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 25.1290i | − | 0.896892i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 19.8181i | − | 0.706437i | −0.935541 | − | 0.353219i | \(-0.885087\pi\) | ||
0.935541 | − | 0.353219i | \(-0.114913\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −69.7006 | −2.48141 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 7.63951i | − | 0.271630i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.44618 | + | 4.70926i | −0.0868663 | + | 0.167231i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 51.8108i | 1.83754i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.2756 | −1.10784 | −0.553918 | − | 0.832571i | \(-0.686868\pi\) | ||||
−0.553918 | + | 0.832571i | \(0.686868\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.34950i | 0.0477420i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.3304i | 0.647671i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.37610 | −0.260297 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.52461 | 0.194717 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.2432 | −0.712595 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.0574 | 0.986444 | 0.493222 | − | 0.869903i | \(-0.335819\pi\) | ||||
0.493222 | + | 0.869903i | \(0.335819\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.50469i | − | 0.0528367i | −0.999651 | − | 0.0264183i | \(-0.991590\pi\) | ||
0.999651 | − | 0.0264183i | \(-0.00841019\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 8.32828i | − | 0.292086i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.1069 | −0.774372 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 62.8168i | − | 2.19768i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21.2121 | + | 11.0184i | 0.741212 | + | 0.385015i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.71207i | 0.0597516i | 0.999554 | + | 0.0298758i | \(0.00951118\pi\) | ||||
−0.999554 | + | 0.0298758i | \(0.990489\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.5558 | 0.542240 | 0.271120 | − | 0.962546i | \(-0.412606\pi\) | ||||
0.271120 | + | 0.962546i | \(0.412606\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.38248i | 0.222209i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.9162i | 0.518688i | 0.965785 | + | 0.259344i | \(0.0835063\pi\) | ||||
−0.965785 | + | 0.259344i | \(0.916494\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.2952 | −0.635419 | −0.317709 | − | 0.948188i | \(-0.602914\pi\) | ||||
−0.317709 | + | 0.948188i | \(0.602914\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −53.0780 | −1.84126 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.08192 | −0.176078 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.6726 | 1.02686 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 56.1304i | 1.94015i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 30.6594i | − | 1.05848i | −0.848472 | − | 0.529240i | \(-0.822477\pi\) | ||
0.848472 | − | 0.529240i | \(-0.177523\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.7911 | 1.82038 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 101.156i | 3.48399i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.2465 | − | 12.8246i | 0.627698 | − | 0.441180i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.00000i | − | 0.0343604i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.22062 | 0.179171 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.38155i | − | 0.150198i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 12.4539i | − | 0.426414i | −0.977007 | − | 0.213207i | \(-0.931609\pi\) | ||
0.977007 | − | 0.213207i | \(-0.0683909\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 83.2794 | 2.84810 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.11998 | 0.243214 | 0.121607 | − | 0.992578i | \(-0.461195\pi\) | ||||
0.121607 | + | 0.992578i | \(0.461195\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.7909 | −1.56237 | −0.781183 | − | 0.624302i | \(-0.785383\pi\) | ||||
−0.781183 | + | 0.624302i | \(0.785383\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 37.5937 | 1.28119 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 13.5172i | − | 0.460132i | −0.973175 | − | 0.230066i | \(-0.926106\pi\) | ||
0.973175 | − | 0.230066i | \(-0.0738942\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 21.3115i | − | 0.724612i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −27.3881 | −0.930149 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.6681i | 0.361892i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.9700 | − | 20.7620i | −1.35433 | − | 0.703494i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.7411i | 0.397378i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.1065 | −0.409274 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 31.7379i | − | 1.07171i | −0.844309 | − | 0.535857i | \(-0.819989\pi\) | ||
0.844309 | − | 0.535857i | \(-0.180011\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 33.9076i | 1.14368i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.6781 | −0.999881 | −0.499941 | − | 0.866060i | \(-0.666645\pi\) | ||||
−0.499941 | + | 0.866060i | \(0.666645\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.0595 | 1.01158 | 0.505791 | − | 0.862656i | \(-0.331201\pi\) | ||||
0.505791 | + | 0.862656i | \(0.331201\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.25100 | 0.109281 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.0959 | −0.574023 | −0.287012 | − | 0.957927i | \(-0.592662\pi\) | ||||
−0.287012 | + | 0.957927i | \(0.592662\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 20.4565i | − | 0.686090i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 15.0622i | − | 0.504602i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.94441 | 0.0650673 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 19.0594i | − | 0.637087i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.6085 | − | 31.9738i | 0.554540 | − | 1.06757i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 45.0709i | 1.50320i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49.4577 | −1.64767 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 26.6217i | − | 0.885916i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 31.8005i | 1.05708i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.531933 | 0.0176625 | 0.00883127 | − | 0.999961i | \(-0.497189\pi\) | ||||
0.00883127 | + | 0.999961i | \(0.497189\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 109.833 | 3.64293 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.1156 | 0.368276 | 0.184138 | − | 0.982900i | \(-0.441051\pi\) | ||||
0.184138 | + | 0.982900i | \(0.441051\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.00686 | 0.0333221 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.83549i | 0.259033i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 15.1564i | − | 0.500507i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.8972 | −0.590375 | −0.295188 | − | 0.955439i | \(-0.595382\pi\) | ||||
−0.295188 | + | 0.955439i | \(0.595382\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 88.3608i | 2.91159i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.44310 | + | 1.78848i | 0.113331 | + | 0.0588686i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.79850i | 0.0920140i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 85.4845 | 2.80768 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.7219i | 0.614245i | 0.951670 | + | 0.307123i | \(0.0993662\pi\) | ||||
−0.951670 | + | 0.307123i | \(0.900634\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.32222i | 0.239976i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.9411 | 0.456411 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.71846 | 0.285124 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.6111 | 0.869348 | 0.434674 | − | 0.900588i | \(-0.356864\pi\) | ||||
0.434674 | + | 0.900588i | \(0.356864\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.546324 | 0.0178286 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 14.1803i | − | 0.462265i | −0.972922 | − | 0.231133i | \(-0.925757\pi\) | ||
0.972922 | − | 0.231133i | \(-0.0742431\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 39.0123i | − | 1.27042i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 19.3226 | 0.628565 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 10.7724i | − | 0.350057i | −0.984563 | − | 0.175029i | \(-0.943998\pi\) | ||
0.984563 | − | 0.175029i | \(-0.0560018\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.6009 | − | 12.2592i | −0.766116 | − | 0.397952i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.2597i | 0.559683i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.62221 | −0.214515 | −0.107257 | − | 0.994231i | \(-0.534207\pi\) | ||||
−0.107257 | + | 0.994231i | \(0.534207\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 31.8981i | − | 1.03220i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 28.0644i | − | 0.907193i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.89611 | 0.254979 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.16368 | 0.198828 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −102.838 | −3.31391 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.63860 | 0.181513 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17.2050i | − | 0.553275i | −0.960974 | − | 0.276638i | \(-0.910780\pi\) | ||
0.960974 | − | 0.276638i | \(-0.0892202\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 115.471i | 3.70946i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.76690 | −0.313435 | −0.156717 | − | 0.987643i | \(-0.550091\pi\) | ||||
−0.156717 | + | 0.987643i | \(0.550091\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 9.11731i | − | 0.292287i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.6078 | + | 20.4216i | −0.339722 | + | 0.654015i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 46.7229i | − | 1.49480i | −0.664375 | − | 0.747399i | \(-0.731302\pi\) | ||
0.664375 | − | 0.747399i | \(-0.268698\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.76495 | 0.0883683 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.3406i | 0.585571i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1.49831i | − | 0.0477886i | −0.999714 | − | 0.0238943i | \(-0.992393\pi\) | ||
0.999714 | − | 0.0238943i | \(-0.00760652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.8960 | 0.952567 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.824040 | 0.0262295 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.6264 | −0.878467 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.7378 | −1.42114 | −0.710571 | − | 0.703625i | \(-0.751564\pi\) | ||||
−0.710571 | + | 0.703625i | \(0.751564\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 63.0403i | 2.00052i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.3953i | 0.361254i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.4348 | −1.34392 | −0.671961 | − | 0.740586i | \(-0.734548\pi\) | ||||
−0.671961 | + | 0.740586i | \(0.734548\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 15.3247i | − | 0.484853i |
(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 | 4004.2.m.c.2157.3 | ✓ | 36 | |
13.12 | even | 2 | inner | 4004.2.m.c.2157.4 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.m.c.2157.3 | ✓ | 36 | 1.1 | even | 1 | trivial | |
4004.2.m.c.2157.4 | yes | 36 | 13.12 | even | 2 | inner |