Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2636035467\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | no (minimal twist has level 503) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.65492 | 0.955468 | 0.477734 | − | 0.878504i | \(-0.341458\pi\) | ||||
0.477734 | + | 0.878504i | \(0.341458\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.16845 | 0.522548 | 0.261274 | − | 0.965265i | \(-0.415857\pi\) | ||||
0.261274 | + | 0.965265i | \(0.415857\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.22170 | 1.97362 | 0.986809 | − | 0.161889i | \(-0.0517587\pi\) | ||||
0.986809 | + | 0.161889i | \(0.0517587\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.261242 | −0.0870806 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.87602 | 0.565640 | 0.282820 | − | 0.959173i | \(-0.408730\pi\) | ||||
0.282820 | + | 0.959173i | \(0.408730\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.59450 | 0.996934 | 0.498467 | − | 0.866909i | \(-0.333896\pi\) | ||||
0.498467 | + | 0.866909i | \(0.333896\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.93370 | 0.499278 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.39494 | −1.06593 | −0.532965 | − | 0.846137i | \(-0.678922\pi\) | ||||
−0.532965 | + | 0.846137i | \(0.678922\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.70486 | 0.849954 | 0.424977 | − | 0.905204i | \(-0.360282\pi\) | ||||
0.424977 | + | 0.905204i | \(0.360282\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.64150 | 1.88573 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.20094 | −1.50150 | −0.750750 | − | 0.660587i | \(-0.770308\pi\) | ||||
−0.750750 | + | 0.660587i | \(0.770308\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.63472 | −0.726943 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.39709 | −1.03867 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.84811 | 1.08597 | 0.542983 | − | 0.839744i | \(-0.317295\pi\) | ||||
0.542983 | + | 0.839744i | \(0.317295\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.35487 | 0.243341 | 0.121671 | − | 0.992571i | \(-0.461175\pi\) | ||||
0.121671 | + | 0.992571i | \(0.461175\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.10465 | 0.540451 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.10132 | 1.03131 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.71544 | 0.610814 | 0.305407 | − | 0.952222i | \(-0.401207\pi\) | ||||
0.305407 | + | 0.952222i | \(0.401207\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.94860 | 0.952539 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.17811 | −0.340163 | −0.170082 | − | 0.985430i | \(-0.554403\pi\) | ||||
−0.170082 | + | 0.985430i | \(0.554403\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.7599 | −1.64087 | −0.820435 | − | 0.571740i | \(-0.806269\pi\) | ||||
−0.820435 | + | 0.571740i | \(0.806269\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.305249 | −0.0455038 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.70411 | −0.394435 | −0.197218 | − | 0.980360i | \(-0.563191\pi\) | ||||
−0.197218 | + | 0.980360i | \(0.563191\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 20.2662 | 2.89517 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.27328 | −1.01846 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.6672 | 1.87734 | 0.938668 | − | 0.344823i | \(-0.112061\pi\) | ||||
0.938668 | + | 0.344823i | \(0.112061\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.19204 | 0.295574 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.13125 | 0.812104 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.8525 | 1.41288 | 0.706439 | − | 0.707774i | \(-0.250300\pi\) | ||||
0.706439 | + | 0.707774i | \(0.250300\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.7302 | 1.75797 | 0.878985 | − | 0.476849i | \(-0.158221\pi\) | ||||
0.878985 | + | 0.476849i | \(0.158221\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.36413 | −0.171864 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.20000 | 0.520946 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.91833 | −0.356531 | −0.178265 | − | 0.983982i | \(-0.557049\pi\) | ||||
−0.178265 | + | 0.983982i | \(0.557049\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.9170 | −1.43463 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.23876 | 0.621727 | 0.310863 | − | 0.950455i | \(-0.399382\pi\) | ||||
0.310863 | + | 0.950455i | \(0.399382\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.15254 | −0.720100 | −0.360050 | − | 0.932933i | \(-0.617240\pi\) | ||||
−0.360050 | + | 0.932933i | \(0.617240\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.01516 | −0.694571 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.79599 | 1.11636 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.25148 | 0.928364 | 0.464182 | − | 0.885740i | \(-0.346348\pi\) | ||||
0.464182 | + | 0.885740i | \(0.346348\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.14803 | −0.905336 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.1873 | 1.44750 | 0.723749 | − | 0.690063i | \(-0.242417\pi\) | ||||
0.723749 | + | 0.690063i | \(0.242417\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.13529 | −0.557000 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.67814 | 1.03761 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.9803 | −1.37591 | −0.687957 | − | 0.725752i | \(-0.741492\pi\) | ||||
−0.687957 | + | 0.725752i | \(0.741492\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.7694 | 1.96757 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.24219 | 0.232505 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.32896 | 0.444142 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.59794 | 0.872988 | 0.436494 | − | 0.899707i | \(-0.356220\pi\) | ||||
0.436494 | + | 0.899707i | \(0.356220\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.490093 | −0.0492562 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.7250 | 1.46519 | 0.732596 | − | 0.680663i | \(-0.238308\pi\) | ||||
0.732596 | + | 0.680663i | \(0.238308\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.8630 | −1.76010 | −0.880049 | − | 0.474883i | \(-0.842490\pi\) | ||||
−0.880049 | + | 0.474883i | \(0.842490\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.0972 | 0.985385 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.24062 | 0.409956 | 0.204978 | − | 0.978767i | \(-0.434288\pi\) | ||||
0.204978 | + | 0.978767i | \(0.434288\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.64169 | 0.731942 | 0.365971 | − | 0.930626i | \(-0.380737\pi\) | ||||
0.365971 | + | 0.930626i | \(0.380737\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.14875 | 0.583613 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.24322 | −0.587313 | −0.293656 | − | 0.955911i | \(-0.594872\pi\) | ||||
−0.293656 | + | 0.955911i | \(0.594872\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.41396 | −0.784606 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.939033 | −0.0868136 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −22.9491 | −2.10374 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.48057 | −0.680052 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.60459 | −0.325015 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.0893 | −0.902411 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.0174 | 1.59878 | 0.799392 | − | 0.600810i | \(-0.205155\pi\) | ||||
0.799392 | + | 0.600810i | \(0.205155\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −17.8068 | −1.56780 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.17633 | 0.364888 | 0.182444 | − | 0.983216i | \(-0.441599\pi\) | ||||
0.182444 | + | 0.983216i | \(0.441599\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.3457 | 1.67748 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.30625 | −0.542756 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.22839 | 0.446692 | 0.223346 | − | 0.974739i | \(-0.428302\pi\) | ||||
0.223346 | + | 0.974739i | \(0.428302\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.6668 | −1.07438 | −0.537191 | − | 0.843460i | \(-0.680515\pi\) | ||||
−0.537191 | + | 0.843460i | \(0.680515\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.47509 | −0.376870 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.74333 | 0.563906 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.83324 | 0.567470 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 33.5389 | 2.76624 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.95650 | −0.569898 | −0.284949 | − | 0.958543i | \(-0.591977\pi\) | ||||
−0.284949 | + | 0.958543i | \(0.591977\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.24542 | 0.345488 | 0.172744 | − | 0.984967i | \(-0.444737\pi\) | ||||
0.172744 | + | 0.984967i | \(0.444737\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.14814 | 0.0928218 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.58310 | 0.127157 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.7081 | 1.01421 | 0.507107 | − | 0.861883i | \(-0.330715\pi\) | ||||
0.507107 | + | 0.861883i | \(0.330715\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 22.6181 | 1.79373 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −37.6012 | −2.96339 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.2202 | −0.878831 | −0.439416 | − | 0.898284i | \(-0.644814\pi\) | ||||
−0.439416 | + | 0.898284i | \(0.644814\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.62764 | 0.282412 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.3997 | −1.88811 | −0.944054 | − | 0.329790i | \(-0.893022\pi\) | ||||
−0.944054 | + | 0.329790i | \(0.893022\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.0795839 | −0.00612184 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.967865 | −0.0740145 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.7024 | −1.19383 | −0.596916 | − | 0.802304i | \(-0.703607\pi\) | ||||
−0.596916 | + | 0.802304i | \(0.703607\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.9794 | −1.43471 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.9601 | 1.34996 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.2973 | −0.993889 | −0.496944 | − | 0.867782i | \(-0.665545\pi\) | ||||
−0.496944 | + | 0.867782i | \(0.665545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.74072 | 0.352375 | 0.176187 | − | 0.984357i | \(-0.443624\pi\) | ||||
0.176187 | + | 0.984357i | \(0.443624\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 22.7224 | 1.67968 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.34132 | 0.319180 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.24498 | −0.602933 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −28.1820 | −2.04994 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0868 | −0.874570 | −0.437285 | − | 0.899323i | \(-0.644060\pi\) | ||||
−0.437285 | + | 0.899323i | \(0.644060\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.6225 | 1.19652 | 0.598259 | − | 0.801303i | \(-0.295860\pi\) | ||||
0.598259 | + | 0.801303i | \(0.295860\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.95067 | 0.497748 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.11878 | 0.649686 | 0.324843 | − | 0.945768i | \(-0.394689\pi\) | ||||
0.324843 | + | 0.945768i | \(0.394689\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.97681 | 0.423685 | 0.211842 | − | 0.977304i | \(-0.432054\pi\) | ||||
0.211842 | + | 0.977304i | \(0.432054\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.82960 | −0.340654 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 30.5371 | 2.14328 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.54502 | −0.177752 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.88119 | 0.130751 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.95038 | 0.480768 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.05588 | −0.279218 | −0.139609 | − | 0.990207i | \(-0.544585\pi\) | ||||
−0.139609 | + | 0.990207i | \(0.544585\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.66973 | 0.594040 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.5724 | −0.857434 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.07471 | 0.480262 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.1820 | −0.688033 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.7976 | −1.06266 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.35562 | 0.157744 | 0.0788719 | − | 0.996885i | \(-0.474868\pi\) | ||||
0.0788719 | + | 0.996885i | \(0.474868\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.949540 | 0.0633026 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.87919 | −0.456588 | −0.228294 | − | 0.973592i | \(-0.573315\pi\) | ||||
−0.228294 | + | 0.973592i | \(0.573315\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.96260 | −0.129692 | −0.0648462 | − | 0.997895i | \(-0.520656\pi\) | ||||
−0.0648462 | + | 0.997895i | \(0.520656\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.2116 | 1.06664 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.7753 | −1.09899 | −0.549493 | − | 0.835499i | \(-0.685179\pi\) | ||||
−0.549493 | + | 0.835499i | \(0.685179\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.15963 | −0.206112 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.6555 | 0.887023 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.26878 | −0.276124 | −0.138062 | − | 0.990424i | \(-0.544087\pi\) | ||||
−0.138062 | + | 0.990424i | \(0.544087\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.02897 | −0.388360 | −0.194180 | − | 0.980966i | \(-0.562205\pi\) | ||||
−0.194180 | + | 0.980966i | \(0.562205\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.70695 | 0.173651 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23.6801 | 1.51286 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.3171 | 0.847349 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.8240 | 1.38304 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.4540 | −1.41728 | −0.708642 | − | 0.705568i | \(-0.750692\pi\) | ||||
−0.708642 | + | 0.705568i | \(0.750692\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.5091 | −0.849308 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.49849 | −0.532196 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.60541 | 0.349656 | 0.174828 | − | 0.984599i | \(-0.444063\pi\) | ||||
0.174828 | + | 0.984599i | \(0.444063\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.4009 | 1.20551 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.52777 | −0.0945665 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.68398 | −0.103839 | −0.0519194 | − | 0.998651i | \(-0.516534\pi\) | ||||
−0.0519194 | + | 0.998651i | \(0.516534\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.9695 | 0.980998 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.4814 | −1.31464 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.6951 | −0.713063 | −0.356532 | − | 0.934283i | \(-0.616041\pi\) | ||||
−0.356532 | + | 0.934283i | \(0.616041\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.02617 | −0.487555 | −0.243778 | − | 0.969831i | \(-0.578387\pi\) | ||||
−0.243778 | + | 0.969831i | \(0.578387\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 31.0618 | 1.87995 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.81878 | −0.411188 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.9879 | 1.50138 | 0.750689 | − | 0.660656i | \(-0.229722\pi\) | ||||
0.750689 | + | 0.660656i | \(0.229722\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.353948 | −0.0211903 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.2415 | 0.789921 | 0.394961 | − | 0.918698i | \(-0.370758\pi\) | ||||
0.394961 | + | 0.918698i | \(0.370758\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.7184 | 1.23158 | 0.615791 | − | 0.787910i | \(-0.288837\pi\) | ||||
0.615791 | + | 0.787910i | \(0.288837\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.16408 | 0.424364 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.3734 | −0.671352 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.31552 | 0.136207 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.2289 | 0.834113 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.18432 | 0.361292 | 0.180646 | − | 0.983548i | \(-0.442181\pi\) | ||||
0.180646 | + | 0.983548i | \(0.442181\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.6807 | 0.738297 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.1250 | −0.587514 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −25.8838 | −1.49690 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −56.1850 | −3.23845 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.3687 | 1.39994 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.0431 | 0.918624 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.11954 | −0.349260 | −0.174630 | − | 0.984634i | \(-0.555873\pi\) | ||||
−0.174630 | + | 0.984634i | \(0.555873\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −29.5619 | −1.68172 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.4142 | −0.647241 | −0.323621 | − | 0.946187i | \(-0.604900\pi\) | ||||
−0.323621 | + | 0.946187i | \(0.604900\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.2666 | 1.82382 | 0.911908 | − | 0.410394i | \(-0.134609\pi\) | ||||
0.911908 | + | 0.410394i | \(0.134609\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.59392 | −0.0898071 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.2640 | −0.913476 | −0.456738 | − | 0.889601i | \(-0.650982\pi\) | ||||
−0.456738 | + | 0.889601i | \(0.650982\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.9711 | 0.614266 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.01788 | 0.391700 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.2827 | −0.905992 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.0650 | −0.724715 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.6464 | 0.699347 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.1201 | −0.778465 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.1918 | −0.944945 | −0.472473 | − | 0.881345i | \(-0.656638\pi\) | ||||
−0.472473 | + | 0.881345i | \(0.656638\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.970627 | −0.0531900 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.40993 | −0.186304 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.7167 | −0.692724 | −0.346362 | − | 0.938101i | \(-0.612583\pi\) | ||||
−0.346362 | + | 0.938101i | \(0.612583\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.3320 | −0.561158 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.54175 | 0.137643 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 69.2720 | 3.74034 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.9244 | −0.749666 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.1578 | −0.598982 | −0.299491 | − | 0.954099i | \(-0.596817\pi\) | ||||
−0.299491 | + | 0.954099i | \(0.596817\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.37351 | −0.287638 | −0.143819 | − | 0.989604i | \(-0.545938\pi\) | ||||
−0.143819 | + | 0.989604i | \(0.545938\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.3998 | −1.03549 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.5118 | −0.719163 | −0.359582 | − | 0.933114i | \(-0.617081\pi\) | ||||
−0.359582 | + | 0.933114i | \(0.617081\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.12125 | 0.324882 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −37.9789 | −2.01006 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.0870 | −0.849039 | −0.424519 | − | 0.905419i | \(-0.639557\pi\) | ||||
−0.424519 | + | 0.905419i | \(0.639557\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.27398 | −0.277578 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.3797 | −0.649768 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.18896 | −0.376287 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.6750 | −0.922626 | −0.461313 | − | 0.887237i | \(-0.652622\pi\) | ||||
−0.461313 | + | 0.887237i | \(0.652622\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.569013 | 0.0296216 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 71.3661 | 3.70514 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.48505 | 0.439339 | 0.219670 | − | 0.975574i | \(-0.429502\pi\) | ||||
0.219670 | + | 0.975574i | \(0.429502\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −16.6969 | −0.862225 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.0210 | 1.08264 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.85389 | 0.506160 | 0.253080 | − | 0.967445i | \(-0.418556\pi\) | ||||
0.253080 | + | 0.967445i | \(0.418556\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.8173 | 1.52759 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.4001 | 0.531420 | 0.265710 | − | 0.964053i | \(-0.414394\pi\) | ||||
0.265710 | + | 0.964053i | \(0.414394\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.4462 | 0.583350 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.81094 | 0.142888 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.07680 | −0.0545960 | −0.0272980 | − | 0.999627i | \(-0.508690\pi\) | ||||
−0.0272980 | + | 0.999627i | \(0.508690\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.6477 | 1.60049 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.91149 | 0.348639 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.64147 | 0.485115 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0327 | −1.10579 | −0.552895 | − | 0.833251i | \(-0.686477\pi\) | ||||
−0.552895 | + | 0.833251i | \(0.686477\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 32.0156 | 1.60278 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.11136 | 0.0554988 | 0.0277494 | − | 0.999615i | \(-0.491166\pi\) | ||||
0.0277494 | + | 0.999615i | \(0.491166\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.87006 | 0.242595 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.52059 | −0.473082 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.97022 | 0.345501 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.7644 | −0.631158 | −0.315579 | − | 0.948899i | \(-0.602199\pi\) | ||||
−0.315579 | + | 0.948899i | \(0.602199\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.65257 | 0.426800 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 56.6686 | 2.78848 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.4088 | 0.756388 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.9625 | −1.02654 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.81345 | −0.137446 | −0.0687230 | − | 0.997636i | \(-0.521892\pi\) | ||||
−0.0687230 | + | 0.997636i | \(0.521892\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.340713 | 0.0166053 | 0.00830267 | − | 0.999966i | \(-0.497357\pi\) | ||||
0.00830267 | + | 0.999966i | \(0.497357\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.706427 | 0.0343477 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.9744 | 0.774871 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 71.6949 | 3.46956 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.1597 | 0.538794 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.9632 | −0.865257 | −0.432629 | − | 0.901572i | \(-0.642414\pi\) | ||||
−0.432629 | + | 0.901572i | \(0.642414\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.4246 | 0.741259 | 0.370629 | − | 0.928781i | \(-0.379142\pi\) | ||||
0.370629 | + | 0.928781i | \(0.379142\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.3085 | 0.542199 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26.6785 | −1.27621 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.69721 | −0.319640 | −0.159820 | − | 0.987146i | \(-0.551091\pi\) | ||||
−0.159820 | + | 0.987146i | \(0.551091\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.29437 | −0.252113 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −33.6219 | −1.59743 | −0.798713 | − | 0.601712i | \(-0.794486\pi\) | ||||
−0.798713 | + | 0.601712i | \(0.794486\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.1669 | −0.718981 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.5124 | −0.544520 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.8142 | 1.31263 | 0.656316 | − | 0.754486i | \(-0.272114\pi\) | ||||
0.656316 | + | 0.754486i | \(0.272114\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.08616 | −0.192410 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.02583 | 0.330102 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 21.9312 | 1.02815 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.39554 | −0.112059 | −0.0560294 | − | 0.998429i | \(-0.517844\pi\) | ||||
−0.0560294 | + | 0.998429i | \(0.517844\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 23.7199 | 1.10715 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.6862 | −1.14975 | −0.574876 | − | 0.818241i | \(-0.694950\pi\) | ||||
−0.574876 | + | 0.818241i | \(0.694950\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.5562 | −0.583537 | −0.291769 | − | 0.956489i | \(-0.594244\pi\) | ||||
−0.291769 | + | 0.956489i | \(0.594244\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.61990 | 0.121495 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.68834 | −0.170676 | −0.0853380 | − | 0.996352i | \(-0.527197\pi\) | ||||
−0.0853380 | + | 0.996352i | \(0.527197\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.2386 | −0.703655 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.0308 | 0.969049 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.1857 | −0.928141 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.4661 | −0.617868 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.57044 | −0.163479 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.22389 | 0.375759 | 0.187880 | − | 0.982192i | \(-0.439839\pi\) | ||||
0.187880 | + | 0.982192i | \(0.439839\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.3551 | 0.608942 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −62.2269 | −2.83142 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.0463 | 0.456179 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.8574 | −0.718569 | −0.359284 | − | 0.933228i | \(-0.616979\pi\) | ||||
−0.359284 | + | 0.933228i | \(0.616979\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.5685 | −0.839695 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.4948 | 1.33108 | 0.665541 | − | 0.746361i | \(-0.268201\pi\) | ||||
0.665541 | + | 0.746361i | \(0.268201\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.7021 | −1.15756 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.572651 | −0.0257388 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.3553 | 1.22705 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.8227 | −1.42458 | −0.712291 | − | 0.701884i | \(-0.752342\pi\) | ||||
−0.712291 | + | 0.701884i | \(0.752342\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −40.3796 | −1.80403 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.2055 | 0.765634 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.131705 | −0.00584923 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.5533 | −0.512092 | −0.256046 | − | 0.966665i | \(-0.582420\pi\) | ||||
−0.256046 | + | 0.966665i | \(0.582420\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.1267 | −1.42120 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.9955 | −0.882823 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.8721 | −0.919736 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.07296 | −0.223108 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.9862 | −1.14067 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.4131 | −1.20099 | −0.600494 | − | 0.799629i | \(-0.705029\pi\) | ||||
−0.600494 | + | 0.799629i | \(0.705029\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.22449 | 0.403359 | 0.201679 | − | 0.979452i | \(-0.435360\pi\) | ||||
0.201679 | + | 0.979452i | \(0.435360\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −31.4094 | −1.37082 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.95456 | −0.259385 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.8535 | 1.25450 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.83513 | −0.123034 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.82921 | −0.339121 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.95496 | 0.214222 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.0060 | −0.949629 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 38.0197 | 1.63762 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.5153 | 1.69890 | 0.849449 | − | 0.527671i | \(-0.176935\pi\) | ||||
0.849449 | + | 0.527671i | \(0.176935\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.84551 | 0.336683 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.92896 | 0.382475 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.3165 | 0.783157 | 0.391579 | − | 0.920145i | \(-0.371929\pi\) | ||||
0.391579 | + | 0.920145i | \(0.371929\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.58690 | −0.153085 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.6664 | 0.923021 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 43.0868 | 1.83224 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.18453 | 0.304966 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.84697 | 0.0782588 | 0.0391294 | − | 0.999234i | \(-0.487542\pi\) | ||||
0.0391294 | + | 0.999234i | \(0.487542\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −38.6764 | −1.63584 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.6448 | −0.576083 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.6098 | 0.784312 | 0.392156 | − | 0.919899i | \(-0.371729\pi\) | ||||
0.392156 | + | 0.919899i | \(0.371729\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.29491 | −0.306899 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −42.5466 | −1.78679 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.8106 | −0.830503 | −0.415251 | − | 0.909707i | \(-0.636306\pi\) | ||||
−0.415251 | + | 0.909707i | \(0.636306\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.9800 | −1.42202 | −0.711008 | − | 0.703183i | \(-0.751761\pi\) | ||||
−0.711008 | + | 0.703183i | \(0.751761\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.0027 | −0.835624 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.1734 | 1.09150 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.7808 | 0.532073 | 0.266037 | − | 0.963963i | \(-0.414286\pi\) | ||||
0.266037 | + | 0.963963i | \(0.414286\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.5090 | 1.14323 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 68.8604 | 2.85681 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.6399 | 1.06190 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.09722 | −0.0453643 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.4463 | 1.21538 | 0.607690 | − | 0.794174i | \(-0.292096\pi\) | ||||
0.607690 | + | 0.794174i | \(0.292096\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.01959 | 0.206829 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.0908 | 0.620754 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.7161 | −0.850706 | −0.425353 | − | 0.905027i | \(-0.639850\pi\) | ||||
−0.425353 | + | 0.905027i | \(0.639850\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −26.8149 | −1.09931 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.89114 | 0.404817 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.4780 | −1.36787 | −0.683937 | − | 0.729541i | \(-0.739734\pi\) | ||||
−0.683937 | + | 0.729541i | \(0.739734\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.6180 | −1.04498 | −0.522489 | − | 0.852646i | \(-0.674997\pi\) | ||||
−0.522489 | + | 0.852646i | \(0.674997\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.762389 | 0.0310469 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.74069 | −0.355360 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.2416 | −1.26806 | −0.634028 | − | 0.773310i | \(-0.718600\pi\) | ||||
−0.634028 | + | 0.773310i | \(0.718600\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 50.5364 | 2.04784 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.71993 | −0.393226 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.2405 | 1.62530 | 0.812650 | − | 0.582752i | \(-0.198024\pi\) | ||||
0.812650 | + | 0.582752i | \(0.198024\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.21180 | −0.169836 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.27736 | 0.373492 | 0.186746 | − | 0.982408i | \(-0.440206\pi\) | ||||
0.186746 | + | 0.982408i | \(0.440206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.92403 | −0.318494 | −0.159247 | − | 0.987239i | \(-0.550907\pi\) | ||||
−0.159247 | + | 0.987239i | \(0.550907\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 38.8641 | 1.55956 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −67.7795 | −2.71553 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.38474 | 0.255390 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.5023 | 0.459358 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.3291 | −0.651085 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.56630 | 0.380828 | 0.190414 | − | 0.981704i | \(-0.439017\pi\) | ||||
0.190414 | + | 0.981704i | \(0.439017\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.71216 | −0.266784 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.0525 | 0.835442 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 72.8467 | 2.88629 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.36858 | −0.0541403 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.1267 | −1.11094 | −0.555469 | − | 0.831538i | \(-0.687461\pi\) | ||||
−0.555469 | + | 0.831538i | \(0.687461\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.46879 | −0.136796 | −0.0683978 | − | 0.997658i | \(-0.521789\pi\) | ||||
−0.0683978 | + | 0.997658i | \(0.521789\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20.8064 | −0.819251 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.4099 | −0.566512 | −0.283256 | − | 0.959044i | \(-0.591415\pi\) | ||||
−0.283256 | + | 0.959044i | \(0.591415\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.3595 | 0.799180 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.7081 | 0.458875 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.1316 | −0.670411 | −0.335205 | − | 0.942145i | \(-0.608806\pi\) | ||||
−0.335205 | + | 0.942145i | \(0.608806\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.87985 | 0.190671 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.60730 | 0.0627067 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.66347 | −0.142709 | −0.0713543 | − | 0.997451i | \(-0.522732\pi\) | ||||
−0.0713543 | + | 0.997451i | \(0.522732\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.6530 | 1.54232 | 0.771162 | − | 0.636639i | \(-0.219676\pi\) | ||||
0.771162 | + | 0.636639i | \(0.219676\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −26.1438 | −1.01534 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.6045 | 0.876567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −42.1118 | −1.63058 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.89836 | 0.150719 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.7580 | 0.994378 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.3247 | 1.32312 | 0.661560 | − | 0.749892i | \(-0.269895\pi\) | ||||
0.661560 | + | 0.749892i | \(0.269895\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19.6169 | 0.755055 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.2805 | 0.779442 | 0.389721 | − | 0.920933i | \(-0.372572\pi\) | ||||
0.389721 | + | 0.920933i | \(0.372572\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 44.8959 | 1.72295 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.3845 | −0.436255 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.3123 | −0.930283 | −0.465141 | − | 0.885236i | \(-0.653997\pi\) | ||||
−0.465141 | + | 0.885236i | \(0.653997\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.10914 | 0.233418 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.24795 | −0.123917 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 49.1267 | 1.87158 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.3936 | −0.661684 | −0.330842 | − | 0.943686i | \(-0.607333\pi\) | ||||
−0.330842 | + | 0.943686i | \(0.607333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.55912 | −0.0972130 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.8006 | −0.561417 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.57266 | 0.362590 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27.7617 | −1.05005 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.2331 | −0.953042 | −0.476521 | − | 0.879163i | \(-0.658102\pi\) | ||||
−0.476521 | + | 0.879163i | \(0.658102\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.7652 | 0.519164 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.22893 | −0.196933 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 76.8896 | 2.89173 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.0105 | 0.976845 | 0.488422 | − | 0.872607i | \(-0.337573\pi\) | ||||
0.488422 | + | 0.872607i | \(0.337573\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.15563 | −0.0808425 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.75631 | −0.365377 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.87927 | 0.294668 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.06448 | −0.263828 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.2045 | 0.417858 | 0.208929 | − | 0.977931i | \(-0.433002\pi\) | ||||
0.208929 | + | 0.977931i | \(0.433002\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −93.2755 | −3.47376 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.97745 | −0.371065 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.2562 | −0.789436 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.1106 | 1.37636 | 0.688179 | − | 0.725541i | \(-0.258411\pi\) | ||||
0.688179 | + | 0.725541i | \(0.258411\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.9239 | 1.07125 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 47.2892 | 1.74905 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.5163 | 1.20102 | 0.600509 | − | 0.799618i | \(-0.294965\pi\) | ||||
0.600509 | + | 0.799618i | \(0.294965\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 39.1886 | 1.44549 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.47483 | −0.201668 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.9897 | 0.956046 | 0.478023 | − | 0.878347i | \(-0.341353\pi\) | ||||
0.478023 | + | 0.878347i | \(0.341353\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.0388 | 0.809615 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.63810 | 0.206842 | 0.103421 | − | 0.994638i | \(-0.467021\pi\) | ||||
0.103421 | + | 0.994638i | \(0.467021\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.12834 | −0.297799 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.44508 | −0.126049 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.1432 | 0.809096 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.6229 | −1.77428 | −0.887138 | − | 0.461504i | \(-0.847310\pi\) | ||||
−0.887138 | + | 0.461504i | \(0.847310\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −37.1595 | −1.35417 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.96058 | 0.180534 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.9095 | −1.37784 | −0.688922 | − | 0.724835i | \(-0.741916\pi\) | ||||
−0.688922 | + | 0.724835i | \(0.741916\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −22.3564 | −0.811487 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.9830 | 1.19563 | 0.597817 | − | 0.801633i | \(-0.296035\pi\) | ||||
0.597817 | + | 0.801633i | \(0.296035\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39.9026 | 1.44457 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.34155 | 0.0485039 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 39.0094 | 1.40855 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.9036 | 0.573499 | 0.286749 | − | 0.958006i | \(-0.407425\pi\) | ||||
0.286749 | + | 0.958006i | \(0.407425\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.27651 | 0.334085 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.67230 | −0.239986 | −0.119993 | − | 0.992775i | \(-0.538287\pi\) | ||||
−0.119993 | + | 0.992775i | \(0.538287\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.92455 | −0.176895 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 32.1069 | 1.15183 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.06960 | −0.289123 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.82800 | 0.351673 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −31.5628 | −1.12796 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.8488 | 0.529976 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.7383 | 0.632302 | 0.316151 | − | 0.948709i | \(-0.397609\pi\) | ||||
0.316151 | + | 0.948709i | \(0.397609\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.78685 | −0.0992146 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.6002 | −1.15913 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.3531 | 1.75258 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 26.4282 | 0.937313 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.1191 | −0.783497 | −0.391749 | − | 0.920072i | \(-0.628130\pi\) | ||||
−0.391749 | + | 0.920072i | \(0.628130\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.8844 | 0.420441 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.39101 | 0.119815 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.5423 | −0.407317 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −43.9352 | −1.54851 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.3545 | −0.681309 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.0410 | 1.47808 | 0.739042 | − | 0.673659i | \(-0.235278\pi\) | ||||
0.739042 | + | 0.673659i | \(0.235278\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.8593 | 0.662238 | 0.331119 | − | 0.943589i | \(-0.392574\pi\) | ||||
0.331119 | + | 0.943589i | \(0.392574\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.2827 | −0.465843 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.1102 | −0.459232 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −39.8640 | −1.39466 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.90335 | −0.171337 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −46.4269 | −1.62031 | −0.810155 | − | 0.586216i | \(-0.800617\pi\) | ||||
−0.810155 | + | 0.586216i | \(0.800617\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.2034 | −0.355669 | −0.177835 | − | 0.984060i | \(-0.556909\pi\) | ||||
−0.177835 | + | 0.984060i | \(0.556909\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.2845 | −0.392877 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.0611 | 0.871461 | 0.435730 | − | 0.900077i | \(-0.356490\pi\) | ||||
0.435730 | + | 0.900077i | \(0.356490\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.9198 | −0.691844 | −0.345922 | − | 0.938263i | \(-0.612434\pi\) | ||||
−0.345922 | + | 0.938263i | \(0.612434\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 41.3530 | 1.43452 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −89.0687 | −3.08605 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.5100 | −0.986628 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.31234 | −0.252751 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.0091 | −1.79555 | −0.897777 | − | 0.440451i | \(-0.854818\pi\) | ||||
−0.897777 | + | 0.440451i | \(0.854818\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.20033 | 0.179322 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.9136 | 0.754744 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.0929901 | −0.00319896 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39.0613 | −1.34216 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 34.2873 | 1.17674 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.7546 | −0.917137 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.6780 | 1.29007 | 0.645036 | − | 0.764152i | \(-0.276842\pi\) | ||||
0.645036 | + | 0.764152i | \(0.276842\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.13091 | −0.0386762 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.6052 | −1.18209 | −0.591045 | − | 0.806638i | \(-0.701285\pi\) | ||||
−0.591045 | + | 0.806638i | \(0.701285\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.9524 | 0.953723 | 0.476861 | − | 0.878978i | \(-0.341774\pi\) | ||||
0.476861 | + | 0.878978i | \(0.341774\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.8221 | −0.641456 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.2339 | −1.19938 | −0.599688 | − | 0.800234i | \(-0.704709\pi\) | ||||
−0.599688 | + | 0.800234i | \(0.704709\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.3475 | −0.623835 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.83201 | 0.130142 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.4799 | 0.525120 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.4899 | −0.355438 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.24614 | −0.0760203 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −52.6831 | −1.78102 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.6552 | −1.00139 | −0.500693 | − | 0.865625i | \(-0.666921\pi\) | ||||
−0.500693 | + | 0.865625i | \(0.666921\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.2346 | 0.345203 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.3183 | −0.819305 | −0.409653 | − | 0.912242i | \(-0.634350\pi\) | ||||
−0.409653 | + | 0.912242i | \(0.634350\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.5391 | −0.859458 | −0.429729 | − | 0.902958i | \(-0.641391\pi\) | ||||
−0.429729 | + | 0.902958i | \(0.641391\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20.9855 | 0.705419 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.9652 | 0.368177 | 0.184088 | − | 0.982910i | \(-0.441067\pi\) | ||||
0.184088 | + | 0.982910i | \(0.441067\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 94.0814 | 3.15539 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.2858 | −0.512094 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.0184 | −0.335252 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.5373 | −0.519355 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.8355 | −1.43024 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.92340 | 0.264260 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −60.0666 | −2.00111 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −92.9816 | −3.09424 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.53931 | 0.184133 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.4093 | −0.710883 | −0.355441 | − | 0.934699i | \(-0.615669\pi\) | ||||
−0.355441 | + | 0.934699i | \(0.615669\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.84679 | −0.127590 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.28839 | 0.0758178 | 0.0379089 | − | 0.999281i | \(-0.487930\pi\) | ||||
0.0379089 | + | 0.999281i | \(0.487930\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.7397 | 0.818763 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26.5500 | 0.877716 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.8076 | 0.720149 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.90496 | 0.161800 | 0.0808999 | − | 0.996722i | \(-0.474221\pi\) | ||||
0.0808999 | + | 0.996722i | \(0.474221\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.1273 | −0.333707 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.8307 | 0.619821 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.5046 | −0.444027 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.66657 | 0.153270 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.20150 | 0.0394200 | 0.0197100 | − | 0.999806i | \(-0.493726\pi\) | ||||
0.0197100 | + | 0.999806i | \(0.493726\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 75.0834 | 2.46076 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.8896 | −0.618419 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.63388 | −0.315061 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.8422 | −0.713554 | −0.356777 | − | 0.934190i | \(-0.616124\pi\) | ||||
−0.356777 | + | 0.934190i | \(0.616124\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 53.3986 | 1.74260 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.3887 | −1.61003 | −0.805013 | − | 0.593257i | \(-0.797842\pi\) | ||||
−0.805013 | + | 0.593257i | \(0.797842\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.6844 | 0.510755 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −32.9294 | −1.07119 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.09737 | 0.165642 | 0.0828211 | − | 0.996564i | \(-0.473607\pi\) | ||||
0.0828211 | + | 0.996564i | \(0.473607\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.1153 | −0.717893 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.9156 | −0.872797 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.7086 | 1.25389 | 0.626947 | − | 0.779062i | \(-0.284304\pi\) | ||||
0.626947 | + | 0.779062i | \(0.284304\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.1229 | −0.457005 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.1563 | 0.586911 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.3011 | 0.881599 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1643 | −0.940785 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.10783 | −0.0356992 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.4227 | 0.625238 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.8409 | −0.573725 | −0.286863 | − | 0.957972i | \(-0.592612\pi\) | ||||
−0.286863 | + | 0.957972i | \(0.592612\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −26.9465 | −0.865646 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.85285 | −0.284101 | −0.142051 | − | 0.989859i | \(-0.545370\pi\) | ||||
−0.142051 | + | 0.989859i | \(0.545370\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −66.1422 | −2.12042 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −21.6215 | −0.692442 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.4775 | 1.51894 | 0.759471 | − | 0.650542i | \(-0.225458\pi\) | ||||
0.759471 | + | 0.650542i | \(0.225458\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.3513 | −0.778271 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.99633 | −0.0637379 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.8880 | −0.634328 | −0.317164 | − | 0.948371i | \(-0.602731\pi\) | ||||
−0.317164 | + | 0.948371i | \(0.602731\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.6549 | 0.339492 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −23.3676 | −0.743798 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 77.4814 | 2.46376 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.7313 | 0.340890 | 0.170445 | − | 0.985367i | \(-0.445479\pi\) | ||||
0.170445 | + | 0.985367i | \(0.445479\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28.4510 | −0.902865 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.98362 | 0.221396 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 58.1899 | 1.84289 | 0.921447 | − | 0.388504i | \(-0.127008\pi\) | ||||
0.921447 | + | 0.388504i | \(0.127008\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.0526 | −0.634435 |
(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 | 8048.2.a.u.1.20 | 26 | ||
4.3 | odd | 2 | 503.2.a.f.1.7 | ✓ | 26 | ||
12.11 | even | 2 | 4527.2.a.o.1.20 | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.f.1.7 | ✓ | 26 | 4.3 | odd | 2 | ||
4527.2.a.o.1.20 | 26 | 12.11 | even | 2 | |||
8048.2.a.u.1.20 | 26 | 1.1 | even | 1 | trivial |