Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.892.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 8x + 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.31955\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.93923 | −1.69697 | −0.848484 | − | 0.529221i | \(-0.822484\pi\) | ||||
−0.848484 | + | 0.529221i | \(0.822484\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.93923 | −1.19994 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 5.63910 | 1.87970 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.93923 | −0.848484 | ||||||||
\(13\) | 5.87847 | 1.63039 | 0.815197 | − | 0.579184i | \(-0.196629\pi\) | ||||
0.815197 | + | 0.579184i | \(0.196629\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 2.93923 | 0.758907 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.63910 | 1.12515 | 0.562574 | − | 0.826747i | \(-0.309811\pi\) | ||||
0.562574 | + | 0.826747i | \(0.309811\pi\) | |||||||
\(18\) | 5.63910 | 1.32915 | ||||||||
\(19\) | 5.57834 | 1.27976 | 0.639879 | − | 0.768476i | \(-0.278984\pi\) | ||||
0.639879 | + | 0.768476i | \(0.278984\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −2.93923 | −0.641394 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.57834 | 1.16316 | 0.581582 | − | 0.813488i | \(-0.302434\pi\) | ||||
0.581582 | + | 0.813488i | \(0.302434\pi\) | |||||||
\(24\) | −2.93923 | −0.599969 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.87847 | 1.15286 | ||||||||
\(27\) | −7.75694 | −1.49282 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 9.45681 | 1.75608 | 0.878042 | − | 0.478583i | \(-0.158849\pi\) | ||||
0.878042 | + | 0.478583i | \(0.158849\pi\) | |||||||
\(30\) | 2.93923 | 0.536628 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.63910 | 0.795599 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 5.63910 | 0.939850 | ||||||||
\(37\) | 2.30013 | 0.378140 | 0.189070 | − | 0.981964i | \(-0.439453\pi\) | ||||
0.189070 | + | 0.981964i | \(0.439453\pi\) | |||||||
\(38\) | 5.57834 | 0.904926 | ||||||||
\(39\) | −17.2782 | −2.76673 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 3.06077 | 0.478011 | 0.239006 | − | 0.971018i | \(-0.423179\pi\) | ||||
0.239006 | + | 0.971018i | \(0.423179\pi\) | |||||||
\(42\) | −2.93923 | −0.453534 | ||||||||
\(43\) | −10.5176 | −1.60391 | −0.801957 | − | 0.597381i | \(-0.796208\pi\) | ||||
−0.801957 | + | 0.597381i | \(0.796208\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.63910 | −0.840628 | ||||||||
\(46\) | 5.57834 | 0.822481 | ||||||||
\(47\) | 8.51757 | 1.24242 | 0.621208 | − | 0.783646i | \(-0.286642\pi\) | ||||
0.621208 | + | 0.783646i | \(0.286642\pi\) | |||||||
\(48\) | −2.93923 | −0.424242 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −13.6354 | −1.90934 | ||||||||
\(52\) | 5.87847 | 0.815197 | ||||||||
\(53\) | −9.45681 | −1.29899 | −0.649496 | − | 0.760365i | \(-0.725020\pi\) | ||||
−0.649496 | + | 0.760365i | \(0.725020\pi\) | |||||||
\(54\) | −7.75694 | −1.05559 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −16.3960 | −2.17171 | ||||||||
\(58\) | 9.45681 | 1.24174 | ||||||||
\(59\) | 7.23937 | 0.942485 | 0.471243 | − | 0.882004i | \(-0.343806\pi\) | ||||
0.471243 | + | 0.882004i | \(0.343806\pi\) | |||||||
\(60\) | 2.93923 | 0.379454 | ||||||||
\(61\) | −14.5176 | −1.85878 | −0.929392 | − | 0.369093i | \(-0.879668\pi\) | ||||
−0.929392 | + | 0.369093i | \(0.879668\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | 5.63910 | 0.710460 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.87847 | −0.729134 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 4.63910 | 0.562574 | ||||||||
\(69\) | −16.3960 | −1.97385 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −7.15667 | −0.849341 | −0.424670 | − | 0.905348i | \(-0.639610\pi\) | ||||
−0.424670 | + | 0.905348i | \(0.639610\pi\) | |||||||
\(72\) | 5.63910 | 0.664574 | ||||||||
\(73\) | −12.3960 | −1.45085 | −0.725423 | − | 0.688303i | \(-0.758356\pi\) | ||||
−0.725423 | + | 0.688303i | \(0.758356\pi\) | |||||||
\(74\) | 2.30013 | 0.267385 | ||||||||
\(75\) | −2.93923 | −0.339394 | ||||||||
\(76\) | 5.57834 | 0.639879 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −17.2782 | −1.95637 | ||||||||
\(79\) | 10.8565 | 1.22146 | 0.610728 | − | 0.791840i | \(-0.290877\pi\) | ||||
0.610728 | + | 0.791840i | \(0.290877\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 5.88216 | 0.653574 | ||||||||
\(82\) | 3.06077 | 0.338005 | ||||||||
\(83\) | 13.8785 | 1.52336 | 0.761680 | − | 0.647953i | \(-0.224375\pi\) | ||||
0.761680 | + | 0.647953i | \(0.224375\pi\) | |||||||
\(84\) | −2.93923 | −0.320697 | ||||||||
\(85\) | −4.63910 | −0.503181 | ||||||||
\(86\) | −10.5176 | −1.13414 | ||||||||
\(87\) | −27.7958 | −2.98002 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.87847 | 0.411117 | 0.205558 | − | 0.978645i | \(-0.434099\pi\) | ||||
0.205558 | + | 0.978645i | \(0.434099\pi\) | |||||||
\(90\) | −5.63910 | −0.594414 | ||||||||
\(91\) | 5.87847 | 0.616231 | ||||||||
\(92\) | 5.57834 | 0.581582 | ||||||||
\(93\) | −17.6354 | −1.82871 | ||||||||
\(94\) | 8.51757 | 0.878520 | ||||||||
\(95\) | −5.57834 | −0.572325 | ||||||||
\(96\) | −2.93923 | −0.299984 | ||||||||
\(97\) | 7.57834 | 0.769463 | 0.384732 | − | 0.923028i | \(-0.374294\pi\) | ||||
0.384732 | + | 0.923028i | \(0.374294\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −11.7958 | −1.17372 | −0.586862 | − | 0.809687i | \(-0.699637\pi\) | ||||
−0.586862 | + | 0.809687i | \(0.699637\pi\) | |||||||
\(102\) | −13.6354 | −1.35011 | ||||||||
\(103\) | 17.1178 | 1.68667 | 0.843335 | − | 0.537388i | \(-0.180589\pi\) | ||||
0.843335 | + | 0.537388i | \(0.180589\pi\) | |||||||
\(104\) | 5.87847 | 0.576431 | ||||||||
\(105\) | 2.93923 | 0.286840 | ||||||||
\(106\) | −9.45681 | −0.918526 | ||||||||
\(107\) | −2.51757 | −0.243383 | −0.121691 | − | 0.992568i | \(-0.538832\pi\) | ||||
−0.121691 | + | 0.992568i | \(0.538832\pi\) | |||||||
\(108\) | −7.75694 | −0.746412 | ||||||||
\(109\) | −10.3001 | −0.986574 | −0.493287 | − | 0.869867i | \(-0.664205\pi\) | ||||
−0.493287 | + | 0.869867i | \(0.664205\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.76063 | −0.641691 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | −16.3960 | −1.53563 | ||||||||
\(115\) | −5.57834 | −0.520183 | ||||||||
\(116\) | 9.45681 | 0.878042 | ||||||||
\(117\) | 33.1493 | 3.06465 | ||||||||
\(118\) | 7.23937 | 0.666438 | ||||||||
\(119\) | 4.63910 | 0.425266 | ||||||||
\(120\) | 2.93923 | 0.268314 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −14.5176 | −1.31436 | ||||||||
\(123\) | −8.99631 | −0.811170 | ||||||||
\(124\) | 6.00000 | 0.538816 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 5.63910 | 0.502371 | ||||||||
\(127\) | −10.4787 | −0.929837 | −0.464919 | − | 0.885353i | \(-0.653916\pi\) | ||||
−0.464919 | + | 0.885353i | \(0.653916\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 30.9136 | 2.72179 | ||||||||
\(130\) | −5.87847 | −0.515576 | ||||||||
\(131\) | 1.57834 | 0.137900 | 0.0689499 | − | 0.997620i | \(-0.478035\pi\) | ||||
0.0689499 | + | 0.997620i | \(0.478035\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.57834 | 0.483703 | ||||||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 7.75694 | 0.667611 | ||||||||
\(136\) | 4.63910 | 0.397800 | ||||||||
\(137\) | −3.27820 | −0.280076 | −0.140038 | − | 0.990146i | \(-0.544722\pi\) | ||||
−0.140038 | + | 0.990146i | \(0.544722\pi\) | |||||||
\(138\) | −16.3960 | −1.39572 | ||||||||
\(139\) | 16.0571 | 1.36194 | 0.680972 | − | 0.732310i | \(-0.261558\pi\) | ||||
0.680972 | + | 0.732310i | \(0.261558\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −25.0351 | −2.10834 | ||||||||
\(142\) | −7.15667 | −0.600575 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 5.63910 | 0.469925 | ||||||||
\(145\) | −9.45681 | −0.785345 | ||||||||
\(146\) | −12.3960 | −1.02590 | ||||||||
\(147\) | −2.93923 | −0.242424 | ||||||||
\(148\) | 2.30013 | 0.189070 | ||||||||
\(149\) | −10.7350 | −0.879446 | −0.439723 | − | 0.898133i | \(-0.644923\pi\) | ||||
−0.439723 | + | 0.898133i | \(0.644923\pi\) | |||||||
\(150\) | −2.93923 | −0.239988 | ||||||||
\(151\) | 2.17860 | 0.177292 | 0.0886461 | − | 0.996063i | \(-0.471746\pi\) | ||||
0.0886461 | + | 0.996063i | \(0.471746\pi\) | |||||||
\(152\) | 5.57834 | 0.452463 | ||||||||
\(153\) | 26.1604 | 2.11494 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | −17.2782 | −1.38336 | ||||||||
\(157\) | −17.1567 | −1.36925 | −0.684626 | − | 0.728895i | \(-0.740034\pi\) | ||||
−0.684626 | + | 0.728895i | \(0.740034\pi\) | |||||||
\(158\) | 10.8565 | 0.863700 | ||||||||
\(159\) | 27.7958 | 2.20435 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 5.57834 | 0.439635 | ||||||||
\(162\) | 5.88216 | 0.462146 | ||||||||
\(163\) | −8.00000 | −0.626608 | −0.313304 | − | 0.949653i | \(-0.601436\pi\) | ||||
−0.313304 | + | 0.949653i | \(0.601436\pi\) | |||||||
\(164\) | 3.06077 | 0.239006 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.8785 | 1.07718 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | −2.93923 | −0.226767 | ||||||||
\(169\) | 21.5564 | 1.65819 | ||||||||
\(170\) | −4.63910 | −0.355803 | ||||||||
\(171\) | 31.4568 | 2.40556 | ||||||||
\(172\) | −10.5176 | −0.801957 | ||||||||
\(173\) | 5.48243 | 0.416821 | 0.208411 | − | 0.978041i | \(-0.433171\pi\) | ||||
0.208411 | + | 0.978041i | \(0.433171\pi\) | |||||||
\(174\) | −27.7958 | −2.10719 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.2782 | −1.59937 | ||||||||
\(178\) | 3.87847 | 0.290704 | ||||||||
\(179\) | 1.23937 | 0.0926347 | 0.0463174 | − | 0.998927i | \(-0.485251\pi\) | ||||
0.0463174 | + | 0.998927i | \(0.485251\pi\) | |||||||
\(180\) | −5.63910 | −0.420314 | ||||||||
\(181\) | 8.55641 | 0.635993 | 0.317996 | − | 0.948092i | \(-0.396990\pi\) | ||||
0.317996 | + | 0.948092i | \(0.396990\pi\) | |||||||
\(182\) | 5.87847 | 0.435741 | ||||||||
\(183\) | 42.6706 | 3.15430 | ||||||||
\(184\) | 5.57834 | 0.411240 | ||||||||
\(185\) | −2.30013 | −0.169109 | ||||||||
\(186\) | −17.6354 | −1.29309 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.51757 | 0.621208 | ||||||||
\(189\) | −7.75694 | −0.564234 | ||||||||
\(190\) | −5.57834 | −0.404695 | ||||||||
\(191\) | −1.27820 | −0.0924875 | −0.0462438 | − | 0.998930i | \(-0.514725\pi\) | ||||
−0.0462438 | + | 0.998930i | \(0.514725\pi\) | |||||||
\(192\) | −2.93923 | −0.212121 | ||||||||
\(193\) | 10.6391 | 0.765819 | 0.382910 | − | 0.923786i | \(-0.374922\pi\) | ||||
0.382910 | + | 0.923786i | \(0.374922\pi\) | |||||||
\(194\) | 7.57834 | 0.544093 | ||||||||
\(195\) | 17.2782 | 1.23732 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −7.87847 | −0.561318 | −0.280659 | − | 0.959808i | \(-0.590553\pi\) | ||||
−0.280659 | + | 0.959808i | \(0.590553\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.517571 | 0.0366897 | 0.0183448 | − | 0.999832i | \(-0.494160\pi\) | ||||
0.0183448 | + | 0.999832i | \(0.494160\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −23.5139 | −1.65854 | ||||||||
\(202\) | −11.7958 | −0.829948 | ||||||||
\(203\) | 9.45681 | 0.663738 | ||||||||
\(204\) | −13.6354 | −0.954670 | ||||||||
\(205\) | −3.06077 | −0.213773 | ||||||||
\(206\) | 17.1178 | 1.19266 | ||||||||
\(207\) | 31.4568 | 2.18640 | ||||||||
\(208\) | 5.87847 | 0.407599 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.93923 | 0.202826 | ||||||||
\(211\) | −2.72180 | −0.187376 | −0.0936881 | − | 0.995602i | \(-0.529866\pi\) | ||||
−0.0936881 | + | 0.995602i | \(0.529866\pi\) | |||||||
\(212\) | −9.45681 | −0.649496 | ||||||||
\(213\) | 21.0351 | 1.44130 | ||||||||
\(214\) | −2.51757 | −0.172098 | ||||||||
\(215\) | 10.5176 | 0.717292 | ||||||||
\(216\) | −7.75694 | −0.527793 | ||||||||
\(217\) | 6.00000 | 0.407307 | ||||||||
\(218\) | −10.3001 | −0.697613 | ||||||||
\(219\) | 36.4349 | 2.46204 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 27.2708 | 1.83443 | ||||||||
\(222\) | −6.76063 | −0.453744 | ||||||||
\(223\) | −22.3960 | −1.49975 | −0.749875 | − | 0.661580i | \(-0.769886\pi\) | ||||
−0.749875 | + | 0.661580i | \(0.769886\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 5.63910 | 0.375940 | ||||||||
\(226\) | −14.0000 | −0.931266 | ||||||||
\(227\) | −13.0351 | −0.865173 | −0.432586 | − | 0.901592i | \(-0.642399\pi\) | ||||
−0.432586 | + | 0.901592i | \(0.642399\pi\) | |||||||
\(228\) | −16.3960 | −1.08585 | ||||||||
\(229\) | −6.63910 | −0.438724 | −0.219362 | − | 0.975644i | \(-0.570398\pi\) | ||||
−0.219362 | + | 0.975644i | \(0.570398\pi\) | |||||||
\(230\) | −5.57834 | −0.367825 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.45681 | 0.620870 | ||||||||
\(233\) | −19.0351 | −1.24703 | −0.623517 | − | 0.781810i | \(-0.714297\pi\) | ||||
−0.623517 | + | 0.781810i | \(0.714297\pi\) | |||||||
\(234\) | 33.1493 | 2.16704 | ||||||||
\(235\) | −8.51757 | −0.555625 | ||||||||
\(236\) | 7.23937 | 0.471243 | ||||||||
\(237\) | −31.9099 | −2.07277 | ||||||||
\(238\) | 4.63910 | 0.300708 | ||||||||
\(239\) | −22.6135 | −1.46274 | −0.731372 | − | 0.681979i | \(-0.761120\pi\) | ||||
−0.731372 | + | 0.681979i | \(0.761120\pi\) | |||||||
\(240\) | 2.93923 | 0.189727 | ||||||||
\(241\) | 17.9744 | 1.15783 | 0.578916 | − | 0.815387i | \(-0.303476\pi\) | ||||
0.578916 | + | 0.815387i | \(0.303476\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.98176 | 0.383730 | ||||||||
\(244\) | −14.5176 | −0.929392 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −8.99631 | −0.573584 | ||||||||
\(247\) | 32.7921 | 2.08651 | ||||||||
\(248\) | 6.00000 | 0.381000 | ||||||||
\(249\) | −40.7921 | −2.58509 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 8.76063 | 0.552966 | 0.276483 | − | 0.961019i | \(-0.410831\pi\) | ||||
0.276483 | + | 0.961019i | \(0.410831\pi\) | |||||||
\(252\) | 5.63910 | 0.355230 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −10.4787 | −0.657494 | ||||||||
\(255\) | 13.6354 | 0.853882 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.09960 | −0.318104 | −0.159052 | − | 0.987270i | \(-0.550844\pi\) | ||||
−0.159052 | + | 0.987270i | \(0.550844\pi\) | |||||||
\(258\) | 30.9136 | 1.92460 | ||||||||
\(259\) | 2.30013 | 0.142923 | ||||||||
\(260\) | −5.87847 | −0.364567 | ||||||||
\(261\) | 53.3279 | 3.30091 | ||||||||
\(262\) | 1.57834 | 0.0975100 | ||||||||
\(263\) | 11.7569 | 0.724964 | 0.362482 | − | 0.931991i | \(-0.381929\pi\) | ||||
0.362482 | + | 0.931991i | \(0.381929\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.45681 | 0.580927 | ||||||||
\(266\) | 5.57834 | 0.342030 | ||||||||
\(267\) | −11.3997 | −0.697652 | ||||||||
\(268\) | 8.00000 | 0.488678 | ||||||||
\(269\) | −11.6742 | −0.711791 | −0.355896 | − | 0.934526i | \(-0.615824\pi\) | ||||
−0.355896 | + | 0.934526i | \(0.615824\pi\) | |||||||
\(270\) | 7.75694 | 0.472072 | ||||||||
\(271\) | −17.6354 | −1.07127 | −0.535637 | − | 0.844448i | \(-0.679929\pi\) | ||||
−0.535637 | + | 0.844448i | \(0.679929\pi\) | |||||||
\(272\) | 4.63910 | 0.281287 | ||||||||
\(273\) | −17.2782 | −1.04572 | ||||||||
\(274\) | −3.27820 | −0.198043 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −16.3960 | −0.986926 | ||||||||
\(277\) | −22.0000 | −1.32185 | −0.660926 | − | 0.750451i | \(-0.729836\pi\) | ||||
−0.660926 | + | 0.750451i | \(0.729836\pi\) | |||||||
\(278\) | 16.0571 | 0.963039 | ||||||||
\(279\) | 33.8346 | 2.02563 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −1.15667 | −0.0690013 | −0.0345007 | − | 0.999405i | \(-0.510984\pi\) | ||||
−0.0345007 | + | 0.999405i | \(0.510984\pi\) | |||||||
\(282\) | −25.0351 | −1.49082 | ||||||||
\(283\) | −17.2782 | −1.02708 | −0.513541 | − | 0.858065i | \(-0.671667\pi\) | ||||
−0.513541 | + | 0.858065i | \(0.671667\pi\) | |||||||
\(284\) | −7.15667 | −0.424670 | ||||||||
\(285\) | 16.3960 | 0.971218 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.06077 | 0.180671 | ||||||||
\(288\) | 5.63910 | 0.332287 | ||||||||
\(289\) | 4.52126 | 0.265957 | ||||||||
\(290\) | −9.45681 | −0.555323 | ||||||||
\(291\) | −22.2745 | −1.30575 | ||||||||
\(292\) | −12.3960 | −0.725423 | ||||||||
\(293\) | −1.87847 | −0.109741 | −0.0548707 | − | 0.998493i | \(-0.517475\pi\) | ||||
−0.0548707 | + | 0.998493i | \(0.517475\pi\) | |||||||
\(294\) | −2.93923 | −0.171420 | ||||||||
\(295\) | −7.23937 | −0.421492 | ||||||||
\(296\) | 2.30013 | 0.133693 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.7350 | −0.621862 | ||||||||
\(299\) | 32.7921 | 1.89642 | ||||||||
\(300\) | −2.93923 | −0.169697 | ||||||||
\(301\) | −10.5176 | −0.606223 | ||||||||
\(302\) | 2.17860 | 0.125365 | ||||||||
\(303\) | 34.6706 | 1.99177 | ||||||||
\(304\) | 5.57834 | 0.319940 | ||||||||
\(305\) | 14.5176 | 0.831274 | ||||||||
\(306\) | 26.1604 | 1.49549 | ||||||||
\(307\) | −8.60027 | −0.490843 | −0.245422 | − | 0.969416i | \(-0.578926\pi\) | ||||
−0.245422 | + | 0.969416i | \(0.578926\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −50.3133 | −2.86223 | ||||||||
\(310\) | −6.00000 | −0.340777 | ||||||||
\(311\) | 13.7569 | 0.780084 | 0.390042 | − | 0.920797i | \(-0.372460\pi\) | ||||
0.390042 | + | 0.920797i | \(0.372460\pi\) | |||||||
\(312\) | −17.2782 | −0.978186 | ||||||||
\(313\) | 2.90040 | 0.163940 | 0.0819701 | − | 0.996635i | \(-0.473879\pi\) | ||||
0.0819701 | + | 0.996635i | \(0.473879\pi\) | |||||||
\(314\) | −17.1567 | −0.968207 | ||||||||
\(315\) | −5.63910 | −0.317727 | ||||||||
\(316\) | 10.8565 | 0.610728 | ||||||||
\(317\) | 19.3353 | 1.08598 | 0.542989 | − | 0.839740i | \(-0.317293\pi\) | ||||
0.542989 | + | 0.839740i | \(0.317293\pi\) | |||||||
\(318\) | 27.7958 | 1.55871 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 7.39973 | 0.413013 | ||||||||
\(322\) | 5.57834 | 0.310869 | ||||||||
\(323\) | 25.8785 | 1.43992 | ||||||||
\(324\) | 5.88216 | 0.326787 | ||||||||
\(325\) | 5.87847 | 0.326079 | ||||||||
\(326\) | −8.00000 | −0.443079 | ||||||||
\(327\) | 30.2745 | 1.67418 | ||||||||
\(328\) | 3.06077 | 0.169002 | ||||||||
\(329\) | 8.51757 | 0.469589 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.5176 | 0.578098 | 0.289049 | − | 0.957314i | \(-0.406661\pi\) | ||||
0.289049 | + | 0.957314i | \(0.406661\pi\) | |||||||
\(332\) | 13.8785 | 0.761680 | ||||||||
\(333\) | 12.9707 | 0.710789 | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | −8.00000 | −0.437087 | ||||||||
\(336\) | −2.93923 | −0.160348 | ||||||||
\(337\) | −7.27820 | −0.396469 | −0.198234 | − | 0.980155i | \(-0.563521\pi\) | ||||
−0.198234 | + | 0.980155i | \(0.563521\pi\) | |||||||
\(338\) | 21.5564 | 1.17251 | ||||||||
\(339\) | 41.1493 | 2.23492 | ||||||||
\(340\) | −4.63910 | −0.251591 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 31.4568 | 1.70099 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −10.5176 | −0.567069 | ||||||||
\(345\) | 16.3960 | 0.882733 | ||||||||
\(346\) | 5.48243 | 0.294737 | ||||||||
\(347\) | 14.2745 | 0.766296 | 0.383148 | − | 0.923687i | \(-0.374840\pi\) | ||||
0.383148 | + | 0.923687i | \(0.374840\pi\) | |||||||
\(348\) | −27.7958 | −1.49001 | ||||||||
\(349\) | −0.396041 | −0.0211996 | −0.0105998 | − | 0.999944i | \(-0.503374\pi\) | ||||
−0.0105998 | + | 0.999944i | \(0.503374\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −45.5989 | −2.43389 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.09960 | −0.271424 | −0.135712 | − | 0.990748i | \(-0.543332\pi\) | ||||
−0.135712 | + | 0.990748i | \(0.543332\pi\) | |||||||
\(354\) | −21.2782 | −1.13092 | ||||||||
\(355\) | 7.15667 | 0.379837 | ||||||||
\(356\) | 3.87847 | 0.205558 | ||||||||
\(357\) | −13.6354 | −0.721662 | ||||||||
\(358\) | 1.23937 | 0.0655026 | ||||||||
\(359\) | 18.3704 | 0.969554 | 0.484777 | − | 0.874638i | \(-0.338901\pi\) | ||||
0.484777 | + | 0.874638i | \(0.338901\pi\) | |||||||
\(360\) | −5.63910 | −0.297207 | ||||||||
\(361\) | 12.1178 | 0.637781 | ||||||||
\(362\) | 8.55641 | 0.449715 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.87847 | 0.308116 | ||||||||
\(365\) | 12.3960 | 0.648838 | ||||||||
\(366\) | 42.6706 | 2.23043 | ||||||||
\(367\) | 17.1178 | 0.893544 | 0.446772 | − | 0.894648i | \(-0.352574\pi\) | ||||
0.446772 | + | 0.894648i | \(0.352574\pi\) | |||||||
\(368\) | 5.57834 | 0.290791 | ||||||||
\(369\) | 17.2600 | 0.898518 | ||||||||
\(370\) | −2.30013 | −0.119578 | ||||||||
\(371\) | −9.45681 | −0.490973 | ||||||||
\(372\) | −17.6354 | −0.914353 | ||||||||
\(373\) | 6.35721 | 0.329164 | 0.164582 | − | 0.986363i | \(-0.447373\pi\) | ||||
0.164582 | + | 0.986363i | \(0.447373\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.93923 | 0.151781 | ||||||||
\(376\) | 8.51757 | 0.439260 | ||||||||
\(377\) | 55.5915 | 2.86311 | ||||||||
\(378\) | −7.75694 | −0.398974 | ||||||||
\(379\) | −5.03514 | −0.258638 | −0.129319 | − | 0.991603i | \(-0.541279\pi\) | ||||
−0.129319 | + | 0.991603i | \(0.541279\pi\) | |||||||
\(380\) | −5.57834 | −0.286163 | ||||||||
\(381\) | 30.7995 | 1.57790 | ||||||||
\(382\) | −1.27820 | −0.0653986 | ||||||||
\(383\) | −7.43118 | −0.379716 | −0.189858 | − | 0.981812i | \(-0.560803\pi\) | ||||
−0.189858 | + | 0.981812i | \(0.560803\pi\) | |||||||
\(384\) | −2.93923 | −0.149992 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.6391 | 0.541516 | ||||||||
\(387\) | −59.3097 | −3.01488 | ||||||||
\(388\) | 7.57834 | 0.384732 | ||||||||
\(389\) | −5.15667 | −0.261454 | −0.130727 | − | 0.991418i | \(-0.541731\pi\) | ||||
−0.130727 | + | 0.991418i | \(0.541731\pi\) | |||||||
\(390\) | 17.2782 | 0.874916 | ||||||||
\(391\) | 25.8785 | 1.30873 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −4.63910 | −0.234012 | ||||||||
\(394\) | −7.87847 | −0.396912 | ||||||||
\(395\) | −10.8565 | −0.546252 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.6354 | −0.985473 | −0.492736 | − | 0.870179i | \(-0.664003\pi\) | ||||
−0.492736 | + | 0.870179i | \(0.664003\pi\) | |||||||
\(398\) | 0.517571 | 0.0259435 | ||||||||
\(399\) | −16.3960 | −0.820829 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −5.11784 | −0.255573 | −0.127786 | − | 0.991802i | \(-0.540787\pi\) | ||||
−0.127786 | + | 0.991802i | \(0.540787\pi\) | |||||||
\(402\) | −23.5139 | −1.17277 | ||||||||
\(403\) | 35.2708 | 1.75696 | ||||||||
\(404\) | −11.7958 | −0.586862 | ||||||||
\(405\) | −5.88216 | −0.292287 | ||||||||
\(406\) | 9.45681 | 0.469333 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −13.6354 | −0.675053 | ||||||||
\(409\) | −2.21744 | −0.109645 | −0.0548226 | − | 0.998496i | \(-0.517459\pi\) | ||||
−0.0548226 | + | 0.998496i | \(0.517459\pi\) | |||||||
\(410\) | −3.06077 | −0.151160 | ||||||||
\(411\) | 9.63541 | 0.475280 | ||||||||
\(412\) | 17.1178 | 0.843335 | ||||||||
\(413\) | 7.23937 | 0.356226 | ||||||||
\(414\) | 31.4568 | 1.54602 | ||||||||
\(415\) | −13.8785 | −0.681267 | ||||||||
\(416\) | 5.87847 | 0.288216 | ||||||||
\(417\) | −47.1955 | −2.31117 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.51757 | −0.220698 | −0.110349 | − | 0.993893i | \(-0.535197\pi\) | ||||
−0.110349 | + | 0.993893i | \(0.535197\pi\) | |||||||
\(420\) | 2.93923 | 0.143420 | ||||||||
\(421\) | −12.3133 | −0.600116 | −0.300058 | − | 0.953921i | \(-0.597006\pi\) | ||||
−0.300058 | + | 0.953921i | \(0.597006\pi\) | |||||||
\(422\) | −2.72180 | −0.132495 | ||||||||
\(423\) | 48.0315 | 2.33537 | ||||||||
\(424\) | −9.45681 | −0.459263 | ||||||||
\(425\) | 4.63910 | 0.225029 | ||||||||
\(426\) | 21.0351 | 1.01916 | ||||||||
\(427\) | −14.5176 | −0.702555 | ||||||||
\(428\) | −2.51757 | −0.121691 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.5176 | 0.507202 | ||||||||
\(431\) | 2.17860 | 0.104940 | 0.0524698 | − | 0.998623i | \(-0.483291\pi\) | ||||
0.0524698 | + | 0.998623i | \(0.483291\pi\) | |||||||
\(432\) | −7.75694 | −0.373206 | ||||||||
\(433\) | 5.02193 | 0.241339 | 0.120669 | − | 0.992693i | \(-0.461496\pi\) | ||||
0.120669 | + | 0.992693i | \(0.461496\pi\) | |||||||
\(434\) | 6.00000 | 0.288009 | ||||||||
\(435\) | 27.7958 | 1.33271 | ||||||||
\(436\) | −10.3001 | −0.493287 | ||||||||
\(437\) | 31.1178 | 1.48857 | ||||||||
\(438\) | 36.4349 | 1.74093 | ||||||||
\(439\) | −7.15667 | −0.341569 | −0.170785 | − | 0.985308i | \(-0.554630\pi\) | ||||
−0.170785 | + | 0.985308i | \(0.554630\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.63910 | 0.268529 | ||||||||
\(442\) | 27.2708 | 1.29714 | ||||||||
\(443\) | −19.5139 | −0.927132 | −0.463566 | − | 0.886062i | \(-0.653430\pi\) | ||||
−0.463566 | + | 0.886062i | \(0.653430\pi\) | |||||||
\(444\) | −6.76063 | −0.320845 | ||||||||
\(445\) | −3.87847 | −0.183857 | ||||||||
\(446\) | −22.3960 | −1.06048 | ||||||||
\(447\) | 31.5527 | 1.49239 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 1.36090 | 0.0642248 | 0.0321124 | − | 0.999484i | \(-0.489777\pi\) | ||||
0.0321124 | + | 0.999484i | \(0.489777\pi\) | |||||||
\(450\) | 5.63910 | 0.265830 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −14.0000 | −0.658505 | ||||||||
\(453\) | −6.40343 | −0.300859 | ||||||||
\(454\) | −13.0351 | −0.611770 | ||||||||
\(455\) | −5.87847 | −0.275587 | ||||||||
\(456\) | −16.3960 | −0.767815 | ||||||||
\(457\) | −4.47874 | −0.209506 | −0.104753 | − | 0.994498i | \(-0.533405\pi\) | ||||
−0.104753 | + | 0.994498i | \(0.533405\pi\) | |||||||
\(458\) | −6.63910 | −0.310225 | ||||||||
\(459\) | −35.9852 | −1.67965 | ||||||||
\(460\) | −5.57834 | −0.260091 | ||||||||
\(461\) | 36.1530 | 1.68381 | 0.841906 | − | 0.539624i | \(-0.181434\pi\) | ||||
0.841906 | + | 0.539624i | \(0.181434\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.0922 | 0.980238 | 0.490119 | − | 0.871655i | \(-0.336953\pi\) | ||||
0.490119 | + | 0.871655i | \(0.336953\pi\) | |||||||
\(464\) | 9.45681 | 0.439021 | ||||||||
\(465\) | 17.6354 | 0.817823 | ||||||||
\(466\) | −19.0351 | −0.881786 | ||||||||
\(467\) | 19.1311 | 0.885279 | 0.442640 | − | 0.896700i | \(-0.354042\pi\) | ||||
0.442640 | + | 0.896700i | \(0.354042\pi\) | |||||||
\(468\) | 33.1493 | 1.53233 | ||||||||
\(469\) | 8.00000 | 0.369406 | ||||||||
\(470\) | −8.51757 | −0.392886 | ||||||||
\(471\) | 50.4275 | 2.32358 | ||||||||
\(472\) | 7.23937 | 0.333219 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −31.9099 | −1.46567 | ||||||||
\(475\) | 5.57834 | 0.255952 | ||||||||
\(476\) | 4.63910 | 0.212633 | ||||||||
\(477\) | −53.3279 | −2.44172 | ||||||||
\(478\) | −22.6135 | −1.03432 | ||||||||
\(479\) | −5.27820 | −0.241167 | −0.120584 | − | 0.992703i | \(-0.538477\pi\) | ||||
−0.120584 | + | 0.992703i | \(0.538477\pi\) | |||||||
\(480\) | 2.93923 | 0.134157 | ||||||||
\(481\) | 13.5213 | 0.616517 | ||||||||
\(482\) | 17.9744 | 0.818710 | ||||||||
\(483\) | −16.3960 | −0.746046 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.57834 | −0.344115 | ||||||||
\(486\) | 5.98176 | 0.271338 | ||||||||
\(487\) | −19.8140 | −0.897859 | −0.448929 | − | 0.893567i | \(-0.648194\pi\) | ||||
−0.448929 | + | 0.893567i | \(0.648194\pi\) | |||||||
\(488\) | −14.5176 | −0.657180 | ||||||||
\(489\) | 23.5139 | 1.06333 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 6.47874 | 0.292381 | 0.146191 | − | 0.989256i | \(-0.453299\pi\) | ||||
0.146191 | + | 0.989256i | \(0.453299\pi\) | |||||||
\(492\) | −8.99631 | −0.405585 | ||||||||
\(493\) | 43.8711 | 1.97585 | ||||||||
\(494\) | 32.7921 | 1.47539 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | −7.15667 | −0.321021 | ||||||||
\(498\) | −40.7921 | −1.82794 | ||||||||
\(499\) | −21.2394 | −0.950805 | −0.475402 | − | 0.879768i | \(-0.657698\pi\) | ||||
−0.475402 | + | 0.879768i | \(0.657698\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 23.5139 | 1.05052 | ||||||||
\(502\) | 8.76063 | 0.391006 | ||||||||
\(503\) | −42.2357 | −1.88320 | −0.941598 | − | 0.336739i | \(-0.890676\pi\) | ||||
−0.941598 | + | 0.336739i | \(0.890676\pi\) | |||||||
\(504\) | 5.63910 | 0.251186 | ||||||||
\(505\) | 11.7958 | 0.524905 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −63.3593 | −2.81389 | ||||||||
\(508\) | −10.4787 | −0.464919 | ||||||||
\(509\) | 38.8698 | 1.72287 | 0.861436 | − | 0.507867i | \(-0.169566\pi\) | ||||
0.861436 | + | 0.507867i | \(0.169566\pi\) | |||||||
\(510\) | 13.6354 | 0.603786 | ||||||||
\(511\) | −12.3960 | −0.548369 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −43.2708 | −1.91045 | ||||||||
\(514\) | −5.09960 | −0.224934 | ||||||||
\(515\) | −17.1178 | −0.754302 | ||||||||
\(516\) | 30.9136 | 1.36090 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.30013 | 0.101062 | ||||||||
\(519\) | −16.1141 | −0.707332 | ||||||||
\(520\) | −5.87847 | −0.257788 | ||||||||
\(521\) | 25.9488 | 1.13684 | 0.568418 | − | 0.822740i | \(-0.307556\pi\) | ||||
0.568418 | + | 0.822740i | \(0.307556\pi\) | |||||||
\(522\) | 53.3279 | 2.33410 | ||||||||
\(523\) | −42.7482 | −1.86925 | −0.934625 | − | 0.355636i | \(-0.884264\pi\) | ||||
−0.934625 | + | 0.355636i | \(0.884264\pi\) | |||||||
\(524\) | 1.57834 | 0.0689499 | ||||||||
\(525\) | −2.93923 | −0.128279 | ||||||||
\(526\) | 11.7569 | 0.512627 | ||||||||
\(527\) | 27.8346 | 1.21249 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.11784 | 0.352949 | ||||||||
\(530\) | 9.45681 | 0.410777 | ||||||||
\(531\) | 40.8235 | 1.77159 | ||||||||
\(532\) | 5.57834 | 0.241852 | ||||||||
\(533\) | 17.9926 | 0.779347 | ||||||||
\(534\) | −11.3997 | −0.493315 | ||||||||
\(535\) | 2.51757 | 0.108844 | ||||||||
\(536\) | 8.00000 | 0.345547 | ||||||||
\(537\) | −3.64279 | −0.157198 | ||||||||
\(538\) | −11.6742 | −0.503312 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.75694 | 0.333806 | ||||||||
\(541\) | 6.73501 | 0.289561 | 0.144780 | − | 0.989464i | \(-0.453752\pi\) | ||||
0.144780 | + | 0.989464i | \(0.453752\pi\) | |||||||
\(542\) | −17.6354 | −0.757506 | ||||||||
\(543\) | −25.1493 | −1.07926 | ||||||||
\(544\) | 4.63910 | 0.198900 | ||||||||
\(545\) | 10.3001 | 0.441209 | ||||||||
\(546\) | −17.2782 | −0.739439 | ||||||||
\(547\) | −23.7569 | −1.01577 | −0.507887 | − | 0.861424i | \(-0.669573\pi\) | ||||
−0.507887 | + | 0.861424i | \(0.669573\pi\) | |||||||
\(548\) | −3.27820 | −0.140038 | ||||||||
\(549\) | −81.8661 | −3.49396 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 52.7532 | 2.24736 | ||||||||
\(552\) | −16.3960 | −0.697862 | ||||||||
\(553\) | 10.8565 | 0.461667 | ||||||||
\(554\) | −22.0000 | −0.934690 | ||||||||
\(555\) | 6.76063 | 0.286973 | ||||||||
\(556\) | 16.0571 | 0.680972 | ||||||||
\(557\) | 34.1918 | 1.44875 | 0.724377 | − | 0.689404i | \(-0.242128\pi\) | ||||
0.724377 | + | 0.689404i | \(0.242128\pi\) | |||||||
\(558\) | 33.8346 | 1.43233 | ||||||||
\(559\) | −61.8272 | −2.61501 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.15667 | −0.0487913 | ||||||||
\(563\) | 31.3485 | 1.32118 | 0.660591 | − | 0.750746i | \(-0.270306\pi\) | ||||
0.660591 | + | 0.750746i | \(0.270306\pi\) | |||||||
\(564\) | −25.0351 | −1.05417 | ||||||||
\(565\) | 14.0000 | 0.588984 | ||||||||
\(566\) | −17.2782 | −0.726257 | ||||||||
\(567\) | 5.88216 | 0.247028 | ||||||||
\(568\) | −7.15667 | −0.300287 | ||||||||
\(569\) | 38.5490 | 1.61606 | 0.808030 | − | 0.589142i | \(-0.200534\pi\) | ||||
0.808030 | + | 0.589142i | \(0.200534\pi\) | |||||||
\(570\) | 16.3960 | 0.686755 | ||||||||
\(571\) | −26.9136 | −1.12630 | −0.563150 | − | 0.826355i | \(-0.690411\pi\) | ||||
−0.563150 | + | 0.826355i | \(0.690411\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.75694 | 0.156948 | ||||||||
\(574\) | 3.06077 | 0.127754 | ||||||||
\(575\) | 5.57834 | 0.232633 | ||||||||
\(576\) | 5.63910 | 0.234963 | ||||||||
\(577\) | −15.3353 | −0.638416 | −0.319208 | − | 0.947685i | \(-0.603417\pi\) | ||||
−0.319208 | + | 0.947685i | \(0.603417\pi\) | |||||||
\(578\) | 4.52126 | 0.188060 | ||||||||
\(579\) | −31.2708 | −1.29957 | ||||||||
\(580\) | −9.45681 | −0.392673 | ||||||||
\(581\) | 13.8785 | 0.575776 | ||||||||
\(582\) | −22.2745 | −0.923308 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −12.3960 | −0.512952 | ||||||||
\(585\) | −33.1493 | −1.37055 | ||||||||
\(586\) | −1.87847 | −0.0775989 | ||||||||
\(587\) | −21.2526 | −0.877188 | −0.438594 | − | 0.898685i | \(-0.644523\pi\) | ||||
−0.438594 | + | 0.898685i | \(0.644523\pi\) | |||||||
\(588\) | −2.93923 | −0.121212 | ||||||||
\(589\) | 33.4700 | 1.37911 | ||||||||
\(590\) | −7.23937 | −0.298040 | ||||||||
\(591\) | 23.1567 | 0.952538 | ||||||||
\(592\) | 2.30013 | 0.0945349 | ||||||||
\(593\) | −19.1955 | −0.788265 | −0.394133 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394133 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.63910 | −0.190185 | ||||||||
\(596\) | −10.7350 | −0.439723 | ||||||||
\(597\) | −1.52126 | −0.0622612 | ||||||||
\(598\) | 32.7921 | 1.34097 | ||||||||
\(599\) | 3.39973 | 0.138909 | 0.0694547 | − | 0.997585i | \(-0.477874\pi\) | ||||
0.0694547 | + | 0.997585i | \(0.477874\pi\) | |||||||
\(600\) | −2.93923 | −0.119994 | ||||||||
\(601\) | 7.90409 | 0.322415 | 0.161207 | − | 0.986921i | \(-0.448461\pi\) | ||||
0.161207 | + | 0.986921i | \(0.448461\pi\) | |||||||
\(602\) | −10.5176 | −0.428664 | ||||||||
\(603\) | 45.1128 | 1.83714 | ||||||||
\(604\) | 2.17860 | 0.0886461 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 34.6706 | 1.40839 | ||||||||
\(607\) | 23.7181 | 0.962688 | 0.481344 | − | 0.876532i | \(-0.340149\pi\) | ||||
0.481344 | + | 0.876532i | \(0.340149\pi\) | |||||||
\(608\) | 5.57834 | 0.226231 | ||||||||
\(609\) | −27.7958 | −1.12634 | ||||||||
\(610\) | 14.5176 | 0.587799 | ||||||||
\(611\) | 50.0703 | 2.02563 | ||||||||
\(612\) | 26.1604 | 1.05747 | ||||||||
\(613\) | −40.9136 | −1.65249 | −0.826243 | − | 0.563314i | \(-0.809526\pi\) | ||||
−0.826243 | + | 0.563314i | \(0.809526\pi\) | |||||||
\(614\) | −8.60027 | −0.347079 | ||||||||
\(615\) | 8.99631 | 0.362766 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.3572 | −1.22214 | −0.611068 | − | 0.791578i | \(-0.709260\pi\) | ||||
−0.611068 | + | 0.791578i | \(0.709260\pi\) | |||||||
\(618\) | −50.3133 | −2.02390 | ||||||||
\(619\) | −34.9963 | −1.40662 | −0.703310 | − | 0.710883i | \(-0.748295\pi\) | ||||
−0.703310 | + | 0.710883i | \(0.748295\pi\) | |||||||
\(620\) | −6.00000 | −0.240966 | ||||||||
\(621\) | −43.2708 | −1.73640 | ||||||||
\(622\) | 13.7569 | 0.551603 | ||||||||
\(623\) | 3.87847 | 0.155388 | ||||||||
\(624\) | −17.2782 | −0.691682 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 2.90040 | 0.115923 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.1567 | −0.684626 | ||||||||
\(629\) | 10.6706 | 0.425463 | ||||||||
\(630\) | −5.63910 | −0.224667 | ||||||||
\(631\) | 38.2357 | 1.52214 | 0.761069 | − | 0.648671i | \(-0.224675\pi\) | ||||
0.761069 | + | 0.648671i | \(0.224675\pi\) | |||||||
\(632\) | 10.8565 | 0.431850 | ||||||||
\(633\) | 8.00000 | 0.317971 | ||||||||
\(634\) | 19.3353 | 0.767902 | ||||||||
\(635\) | 10.4787 | 0.415836 | ||||||||
\(636\) | 27.7958 | 1.10217 | ||||||||
\(637\) | 5.87847 | 0.232913 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −40.3572 | −1.59651 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −25.5139 | −1.00774 | −0.503869 | − | 0.863780i | \(-0.668091\pi\) | ||||
−0.503869 | + | 0.863780i | \(0.668091\pi\) | |||||||
\(642\) | 7.39973 | 0.292044 | ||||||||
\(643\) | −37.8528 | −1.49277 | −0.746385 | − | 0.665514i | \(-0.768212\pi\) | ||||
−0.746385 | + | 0.665514i | \(0.768212\pi\) | |||||||
\(644\) | 5.57834 | 0.219817 | ||||||||
\(645\) | −30.9136 | −1.21722 | ||||||||
\(646\) | 25.8785 | 1.01817 | ||||||||
\(647\) | −24.7094 | −0.971426 | −0.485713 | − | 0.874118i | \(-0.661440\pi\) | ||||
−0.485713 | + | 0.874118i | \(0.661440\pi\) | |||||||
\(648\) | 5.88216 | 0.231073 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 5.87847 | 0.230573 | ||||||||
\(651\) | −17.6354 | −0.691186 | ||||||||
\(652\) | −8.00000 | −0.313304 | ||||||||
\(653\) | 16.7789 | 0.656608 | 0.328304 | − | 0.944572i | \(-0.393523\pi\) | ||||
0.328304 | + | 0.944572i | \(0.393523\pi\) | |||||||
\(654\) | 30.2745 | 1.18383 | ||||||||
\(655\) | −1.57834 | −0.0616707 | ||||||||
\(656\) | 3.06077 | 0.119503 | ||||||||
\(657\) | −69.9025 | −2.72716 | ||||||||
\(658\) | 8.51757 | 0.332050 | ||||||||
\(659\) | −10.1215 | −0.394279 | −0.197139 | − | 0.980375i | \(-0.563165\pi\) | ||||
−0.197139 | + | 0.980375i | \(0.563165\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.1128 | 0.898984 | 0.449492 | − | 0.893284i | \(-0.351605\pi\) | ||||
0.449492 | + | 0.893284i | \(0.351605\pi\) | |||||||
\(662\) | 10.5176 | 0.408777 | ||||||||
\(663\) | −80.1553 | −3.11298 | ||||||||
\(664\) | 13.8785 | 0.538589 | ||||||||
\(665\) | −5.57834 | −0.216319 | ||||||||
\(666\) | 12.9707 | 0.502604 | ||||||||
\(667\) | 52.7532 | 2.04261 | ||||||||
\(668\) | −8.00000 | −0.309529 | ||||||||
\(669\) | 65.8272 | 2.54503 | ||||||||
\(670\) | −8.00000 | −0.309067 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.93923 | −0.113383 | ||||||||
\(673\) | −38.0000 | −1.46479 | −0.732396 | − | 0.680879i | \(-0.761598\pi\) | ||||
−0.732396 | + | 0.680879i | \(0.761598\pi\) | |||||||
\(674\) | −7.27820 | −0.280346 | ||||||||
\(675\) | −7.75694 | −0.298565 | ||||||||
\(676\) | 21.5564 | 0.829093 | ||||||||
\(677\) | −8.83092 | −0.339400 | −0.169700 | − | 0.985496i | \(-0.554280\pi\) | ||||
−0.169700 | + | 0.985496i | \(0.554280\pi\) | |||||||
\(678\) | 41.1493 | 1.58033 | ||||||||
\(679\) | 7.57834 | 0.290830 | ||||||||
\(680\) | −4.63910 | −0.177901 | ||||||||
\(681\) | 38.3133 | 1.46817 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.3997 | 0.436199 | 0.218099 | − | 0.975927i | \(-0.430014\pi\) | ||||
0.218099 | + | 0.975927i | \(0.430014\pi\) | |||||||
\(684\) | 31.4568 | 1.20278 | ||||||||
\(685\) | 3.27820 | 0.125254 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 19.5139 | 0.744501 | ||||||||
\(688\) | −10.5176 | −0.400979 | ||||||||
\(689\) | −55.5915 | −2.11787 | ||||||||
\(690\) | 16.3960 | 0.624187 | ||||||||
\(691\) | −0.0826952 | −0.00314587 | −0.00157294 | − | 0.999999i | \(-0.500501\pi\) | ||||
−0.00157294 | + | 0.999999i | \(0.500501\pi\) | |||||||
\(692\) | 5.48243 | 0.208411 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.2745 | 0.541853 | ||||||||
\(695\) | −16.0571 | −0.609079 | ||||||||
\(696\) | −27.7958 | −1.05360 | ||||||||
\(697\) | 14.1992 | 0.537833 | ||||||||
\(698\) | −0.396041 | −0.0149904 | ||||||||
\(699\) | 55.9488 | 2.11618 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −38.0571 | −1.43740 | −0.718698 | − | 0.695322i | \(-0.755262\pi\) | ||||
−0.718698 | + | 0.695322i | \(0.755262\pi\) | |||||||
\(702\) | −45.5989 | −1.72102 | ||||||||
\(703\) | 12.8309 | 0.483927 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 25.0351 | 0.942878 | ||||||||
\(706\) | −5.09960 | −0.191926 | ||||||||
\(707\) | −11.7958 | −0.443626 | ||||||||
\(708\) | −21.2782 | −0.799684 | ||||||||
\(709\) | 36.4275 | 1.36806 | 0.684032 | − | 0.729452i | \(-0.260225\pi\) | ||||
0.684032 | + | 0.729452i | \(0.260225\pi\) | |||||||
\(710\) | 7.15667 | 0.268585 | ||||||||
\(711\) | 61.2211 | 2.29597 | ||||||||
\(712\) | 3.87847 | 0.145352 | ||||||||
\(713\) | 33.4700 | 1.25346 | ||||||||
\(714\) | −13.6354 | −0.510292 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.23937 | 0.0463174 | ||||||||
\(717\) | 66.4663 | 2.48223 | ||||||||
\(718\) | 18.3704 | 0.685578 | ||||||||
\(719\) | 37.3097 | 1.39142 | 0.695708 | − | 0.718325i | \(-0.255091\pi\) | ||||
0.695708 | + | 0.718325i | \(0.255091\pi\) | |||||||
\(720\) | −5.63910 | −0.210157 | ||||||||
\(721\) | 17.1178 | 0.637502 | ||||||||
\(722\) | 12.1178 | 0.450979 | ||||||||
\(723\) | −52.8309 | −1.96480 | ||||||||
\(724\) | 8.55641 | 0.317996 | ||||||||
\(725\) | 9.45681 | 0.351217 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.23937 | 0.120142 | 0.0600708 | − | 0.998194i | \(-0.480867\pi\) | ||||
0.0600708 | + | 0.998194i | \(0.480867\pi\) | |||||||
\(728\) | 5.87847 | 0.217871 | ||||||||
\(729\) | −35.2283 | −1.30475 | ||||||||
\(730\) | 12.3960 | 0.458798 | ||||||||
\(731\) | −48.7921 | −1.80464 | ||||||||
\(732\) | 42.6706 | 1.57715 | ||||||||
\(733\) | 26.3522 | 0.973340 | 0.486670 | − | 0.873586i | \(-0.338211\pi\) | ||||
0.486670 | + | 0.873586i | \(0.338211\pi\) | |||||||
\(734\) | 17.1178 | 0.631831 | ||||||||
\(735\) | 2.93923 | 0.108415 | ||||||||
\(736\) | 5.57834 | 0.205620 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 17.2600 | 0.635348 | ||||||||
\(739\) | 11.9223 | 0.438570 | 0.219285 | − | 0.975661i | \(-0.429628\pi\) | ||||
0.219285 | + | 0.975661i | \(0.429628\pi\) | |||||||
\(740\) | −2.30013 | −0.0845546 | ||||||||
\(741\) | −96.3836 | −3.54074 | ||||||||
\(742\) | −9.45681 | −0.347170 | ||||||||
\(743\) | 26.0703 | 0.956426 | 0.478213 | − | 0.878244i | \(-0.341285\pi\) | ||||
0.478213 | + | 0.878244i | \(0.341285\pi\) | |||||||
\(744\) | −17.6354 | −0.646545 | ||||||||
\(745\) | 10.7350 | 0.393300 | ||||||||
\(746\) | 6.35721 | 0.232754 | ||||||||
\(747\) | 78.2621 | 2.86346 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.51757 | −0.0919901 | ||||||||
\(750\) | 2.93923 | 0.107326 | ||||||||
\(751\) | 36.6003 | 1.33556 | 0.667781 | − | 0.744357i | \(-0.267244\pi\) | ||||
0.667781 | + | 0.744357i | \(0.267244\pi\) | |||||||
\(752\) | 8.51757 | 0.310604 | ||||||||
\(753\) | −25.7496 | −0.938366 | ||||||||
\(754\) | 55.5915 | 2.02452 | ||||||||
\(755\) | −2.17860 | −0.0792875 | ||||||||
\(756\) | −7.75694 | −0.282117 | ||||||||
\(757\) | −43.0922 | −1.56621 | −0.783107 | − | 0.621887i | \(-0.786366\pi\) | ||||
−0.783107 | + | 0.621887i | \(0.786366\pi\) | |||||||
\(758\) | −5.03514 | −0.182885 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.57834 | −0.202348 | ||||||||
\(761\) | 44.0959 | 1.59848 | 0.799238 | − | 0.601015i | \(-0.205237\pi\) | ||||
0.799238 | + | 0.601015i | \(0.205237\pi\) | |||||||
\(762\) | 30.7995 | 1.11575 | ||||||||
\(763\) | −10.3001 | −0.372890 | ||||||||
\(764\) | −1.27820 | −0.0462438 | ||||||||
\(765\) | −26.1604 | −0.945830 | ||||||||
\(766\) | −7.43118 | −0.268500 | ||||||||
\(767\) | 42.5564 | 1.53662 | ||||||||
\(768\) | −2.93923 | −0.106061 | ||||||||
\(769\) | 8.33897 | 0.300711 | 0.150355 | − | 0.988632i | \(-0.451958\pi\) | ||||
0.150355 | + | 0.988632i | \(0.451958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.9889 | 0.539813 | ||||||||
\(772\) | 10.6391 | 0.382910 | ||||||||
\(773\) | −19.2782 | −0.693389 | −0.346694 | − | 0.937978i | \(-0.612696\pi\) | ||||
−0.346694 | + | 0.937978i | \(0.612696\pi\) | |||||||
\(774\) | −59.3097 | −2.13184 | ||||||||
\(775\) | 6.00000 | 0.215526 | ||||||||
\(776\) | 7.57834 | 0.272046 | ||||||||
\(777\) | −6.76063 | −0.242536 | ||||||||
\(778\) | −5.15667 | −0.184876 | ||||||||
\(779\) | 17.0740 | 0.611739 | ||||||||
\(780\) | 17.2782 | 0.618659 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 25.8785 | 0.925412 | ||||||||
\(783\) | −73.3559 | −2.62153 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 17.1567 | 0.612348 | ||||||||
\(786\) | −4.63910 | −0.165471 | ||||||||
\(787\) | −43.5915 | −1.55387 | −0.776935 | − | 0.629580i | \(-0.783227\pi\) | ||||
−0.776935 | + | 0.629580i | \(0.783227\pi\) | |||||||
\(788\) | −7.87847 | −0.280659 | ||||||||
\(789\) | −34.5564 | −1.23024 | ||||||||
\(790\) | −10.8565 | −0.386258 | ||||||||
\(791\) | −14.0000 | −0.497783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −85.3411 | −3.03055 | ||||||||
\(794\) | −19.6354 | −0.696835 | ||||||||
\(795\) | −27.7958 | −0.985815 | ||||||||
\(796\) | 0.517571 | 0.0183448 | ||||||||
\(797\) | −51.1493 | −1.81180 | −0.905900 | − | 0.423491i | \(-0.860805\pi\) | ||||
−0.905900 | + | 0.423491i | \(0.860805\pi\) | |||||||
\(798\) | −16.3960 | −0.580414 | ||||||||
\(799\) | 39.5139 | 1.39790 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 21.8711 | 0.772777 | ||||||||
\(802\) | −5.11784 | −0.180717 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −23.5139 | −0.829271 | ||||||||
\(805\) | −5.57834 | −0.196611 | ||||||||
\(806\) | 35.2708 | 1.24236 | ||||||||
\(807\) | 34.3133 | 1.20789 | ||||||||
\(808\) | −11.7958 | −0.414974 | ||||||||
\(809\) | −45.1567 | −1.58762 | −0.793812 | − | 0.608163i | \(-0.791907\pi\) | ||||
−0.793812 | + | 0.608163i | \(0.791907\pi\) | |||||||
\(810\) | −5.88216 | −0.206678 | ||||||||
\(811\) | −39.2914 | −1.37971 | −0.689854 | − | 0.723948i | \(-0.742325\pi\) | ||||
−0.689854 | + | 0.723948i | \(0.742325\pi\) | |||||||
\(812\) | 9.45681 | 0.331869 | ||||||||
\(813\) | 51.8346 | 1.81792 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.00000 | 0.280228 | ||||||||
\(816\) | −13.6354 | −0.477335 | ||||||||
\(817\) | −58.6706 | −2.05262 | ||||||||
\(818\) | −2.21744 | −0.0775309 | ||||||||
\(819\) | 33.1493 | 1.15833 | ||||||||
\(820\) | −3.06077 | −0.106887 | ||||||||
\(821\) | −25.6486 | −0.895143 | −0.447572 | − | 0.894248i | \(-0.647711\pi\) | ||||
−0.447572 | + | 0.894248i | \(0.647711\pi\) | |||||||
\(822\) | 9.63541 | 0.336073 | ||||||||
\(823\) | −51.6486 | −1.80036 | −0.900179 | − | 0.435520i | \(-0.856564\pi\) | ||||
−0.900179 | + | 0.435520i | \(0.856564\pi\) | |||||||
\(824\) | 17.1178 | 0.596328 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.23937 | 0.251890 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 31.4568 | 1.09320 | ||||||||
\(829\) | 5.36090 | 0.186192 | 0.0930958 | − | 0.995657i | \(-0.470324\pi\) | ||||
0.0930958 | + | 0.995657i | \(0.470324\pi\) | |||||||
\(830\) | −13.8785 | −0.481729 | ||||||||
\(831\) | 64.6632 | 2.24314 | ||||||||
\(832\) | 5.87847 | 0.203799 | ||||||||
\(833\) | 4.63910 | 0.160735 | ||||||||
\(834\) | −47.1955 | −1.63425 | ||||||||
\(835\) | 8.00000 | 0.276851 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −46.5416 | −1.60871 | ||||||||
\(838\) | −4.51757 | −0.156057 | ||||||||
\(839\) | 16.9649 | 0.585692 | 0.292846 | − | 0.956160i | \(-0.405398\pi\) | ||||
0.292846 | + | 0.956160i | \(0.405398\pi\) | |||||||
\(840\) | 2.93923 | 0.101413 | ||||||||
\(841\) | 60.4312 | 2.08383 | ||||||||
\(842\) | −12.3133 | −0.424346 | ||||||||
\(843\) | 3.39973 | 0.117093 | ||||||||
\(844\) | −2.72180 | −0.0936881 | ||||||||
\(845\) | −21.5564 | −0.741563 | ||||||||
\(846\) | 48.0315 | 1.65136 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.45681 | −0.324748 | ||||||||
\(849\) | 50.7847 | 1.74293 | ||||||||
\(850\) | 4.63910 | 0.159120 | ||||||||
\(851\) | 12.8309 | 0.439838 | ||||||||
\(852\) | 21.0351 | 0.720652 | ||||||||
\(853\) | −31.0666 | −1.06370 | −0.531850 | − | 0.846839i | \(-0.678503\pi\) | ||||
−0.531850 | + | 0.846839i | \(0.678503\pi\) | |||||||
\(854\) | −14.5176 | −0.496781 | ||||||||
\(855\) | −31.4568 | −1.07580 | ||||||||
\(856\) | −2.51757 | −0.0860488 | ||||||||
\(857\) | −37.5966 | −1.28427 | −0.642137 | − | 0.766590i | \(-0.721952\pi\) | ||||
−0.642137 | + | 0.766590i | \(0.721952\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.0388 | −0.478999 | −0.239499 | − | 0.970897i | \(-0.576983\pi\) | ||||
−0.239499 | + | 0.970897i | \(0.576983\pi\) | |||||||
\(860\) | 10.5176 | 0.358646 | ||||||||
\(861\) | −8.99631 | −0.306593 | ||||||||
\(862\) | 2.17860 | 0.0742035 | ||||||||
\(863\) | 38.8053 | 1.32095 | 0.660474 | − | 0.750849i | \(-0.270355\pi\) | ||||
0.660474 | + | 0.750849i | \(0.270355\pi\) | |||||||
\(864\) | −7.75694 | −0.263896 | ||||||||
\(865\) | −5.48243 | −0.186408 | ||||||||
\(866\) | 5.02193 | 0.170652 | ||||||||
\(867\) | −13.2891 | −0.451320 | ||||||||
\(868\) | 6.00000 | 0.203653 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 27.7958 | 0.942365 | ||||||||
\(871\) | 47.0278 | 1.59347 | ||||||||
\(872\) | −10.3001 | −0.348807 | ||||||||
\(873\) | 42.7350 | 1.44636 | ||||||||
\(874\) | 31.1178 | 1.05258 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 36.4349 | 1.23102 | ||||||||
\(877\) | −31.7131 | −1.07087 | −0.535437 | − | 0.844575i | \(-0.679853\pi\) | ||||
−0.535437 | + | 0.844575i | \(0.679853\pi\) | |||||||
\(878\) | −7.15667 | −0.241526 | ||||||||
\(879\) | 5.52126 | 0.186228 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.24306 | 0.0755706 | 0.0377853 | − | 0.999286i | \(-0.487970\pi\) | ||||
0.0377853 | + | 0.999286i | \(0.487970\pi\) | |||||||
\(882\) | 5.63910 | 0.189878 | ||||||||
\(883\) | 24.4349 | 0.822299 | 0.411150 | − | 0.911568i | \(-0.365127\pi\) | ||||
0.411150 | + | 0.911568i | \(0.365127\pi\) | |||||||
\(884\) | 27.2708 | 0.917217 | ||||||||
\(885\) | 21.2782 | 0.715259 | ||||||||
\(886\) | −19.5139 | −0.655582 | ||||||||
\(887\) | −35.5915 | −1.19505 | −0.597524 | − | 0.801851i | \(-0.703849\pi\) | ||||
−0.597524 | + | 0.801851i | \(0.703849\pi\) | |||||||
\(888\) | −6.76063 | −0.226872 | ||||||||
\(889\) | −10.4787 | −0.351446 | ||||||||
\(890\) | −3.87847 | −0.130007 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −22.3960 | −0.749875 | ||||||||
\(893\) | 47.5139 | 1.58999 | ||||||||
\(894\) | 31.5527 | 1.05528 | ||||||||
\(895\) | −1.23937 | −0.0414275 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −96.3836 | −3.21816 | ||||||||
\(898\) | 1.36090 | 0.0454138 | ||||||||
\(899\) | 56.7408 | 1.89241 | ||||||||
\(900\) | 5.63910 | 0.187970 | ||||||||
\(901\) | −43.8711 | −1.46156 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 30.9136 | 1.02874 | ||||||||
\(904\) | −14.0000 | −0.465633 | ||||||||
\(905\) | −8.55641 | −0.284425 | ||||||||
\(906\) | −6.40343 | −0.212740 | ||||||||
\(907\) | 17.3923 | 0.577503 | 0.288752 | − | 0.957404i | \(-0.406760\pi\) | ||||
0.288752 | + | 0.957404i | \(0.406760\pi\) | |||||||
\(908\) | −13.0351 | −0.432586 | ||||||||
\(909\) | −66.5176 | −2.20625 | ||||||||
\(910\) | −5.87847 | −0.194869 | ||||||||
\(911\) | 52.1141 | 1.72662 | 0.863309 | − | 0.504675i | \(-0.168388\pi\) | ||||
0.863309 | + | 0.504675i | \(0.168388\pi\) | |||||||
\(912\) | −16.3960 | −0.542927 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −4.47874 | −0.148143 | ||||||||
\(915\) | −42.6706 | −1.41064 | ||||||||
\(916\) | −6.63910 | −0.219362 | ||||||||
\(917\) | 1.57834 | 0.0521213 | ||||||||
\(918\) | −35.9852 | −1.18769 | ||||||||
\(919\) | −12.1347 | −0.400288 | −0.200144 | − | 0.979766i | \(-0.564141\pi\) | ||||
−0.200144 | + | 0.979766i | \(0.564141\pi\) | |||||||
\(920\) | −5.57834 | −0.183912 | ||||||||
\(921\) | 25.2782 | 0.832945 | ||||||||
\(922\) | 36.1530 | 1.19064 | ||||||||
\(923\) | −42.0703 | −1.38476 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.30013 | 0.0756279 | ||||||||
\(926\) | 21.0922 | 0.693133 | ||||||||
\(927\) | 96.5292 | 3.17044 | ||||||||
\(928\) | 9.45681 | 0.310435 | ||||||||
\(929\) | 23.8008 | 0.780879 | 0.390439 | − | 0.920629i | \(-0.372323\pi\) | ||||
0.390439 | + | 0.920629i | \(0.372323\pi\) | |||||||
\(930\) | 17.6354 | 0.578288 | ||||||||
\(931\) | 5.57834 | 0.182823 | ||||||||
\(932\) | −19.0351 | −0.623517 | ||||||||
\(933\) | −40.4349 | −1.32378 | ||||||||
\(934\) | 19.1311 | 0.625987 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 33.1493 | 1.08352 | ||||||||
\(937\) | −9.16170 | −0.299300 | −0.149650 | − | 0.988739i | \(-0.547815\pi\) | ||||
−0.149650 | + | 0.988739i | \(0.547815\pi\) | |||||||
\(938\) | 8.00000 | 0.261209 | ||||||||
\(939\) | −8.52496 | −0.278201 | ||||||||
\(940\) | −8.51757 | −0.277813 | ||||||||
\(941\) | −0.996308 | −0.0324787 | −0.0162393 | − | 0.999868i | \(-0.505169\pi\) | ||||
−0.0162393 | + | 0.999868i | \(0.505169\pi\) | |||||||
\(942\) | 50.4275 | 1.64302 | ||||||||
\(943\) | 17.0740 | 0.556005 | ||||||||
\(944\) | 7.23937 | 0.235621 | ||||||||
\(945\) | 7.75694 | 0.252333 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.8359 | −0.612086 | −0.306043 | − | 0.952018i | \(-0.599005\pi\) | ||||
−0.306043 | + | 0.952018i | \(0.599005\pi\) | |||||||
\(948\) | −31.9099 | −1.03639 | ||||||||
\(949\) | −72.8698 | −2.36545 | ||||||||
\(950\) | 5.57834 | 0.180985 | ||||||||
\(951\) | −56.8309 | −1.84287 | ||||||||
\(952\) | 4.63910 | 0.150354 | ||||||||
\(953\) | −21.4386 | −0.694463 | −0.347232 | − | 0.937779i | \(-0.612878\pi\) | ||||
−0.347232 | + | 0.937779i | \(0.612878\pi\) | |||||||
\(954\) | −53.3279 | −1.72655 | ||||||||
\(955\) | 1.27820 | 0.0413617 | ||||||||
\(956\) | −22.6135 | −0.731372 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.27820 | −0.170531 | ||||||||
\(959\) | −3.27820 | −0.105859 | ||||||||
\(960\) | 2.93923 | 0.0948634 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 13.5213 | 0.435943 | ||||||||
\(963\) | −14.1968 | −0.457487 | ||||||||
\(964\) | 17.9744 | 0.578916 | ||||||||
\(965\) | −10.6391 | −0.342485 | ||||||||
\(966\) | −16.3960 | −0.527534 | ||||||||
\(967\) | −31.5139 | −1.01342 | −0.506709 | − | 0.862117i | \(-0.669138\pi\) | ||||
−0.506709 | + | 0.862117i | \(0.669138\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −76.0629 | −2.44349 | ||||||||
\(970\) | −7.57834 | −0.243326 | ||||||||
\(971\) | 16.1968 | 0.519781 | 0.259891 | − | 0.965638i | \(-0.416313\pi\) | ||||
0.259891 | + | 0.965638i | \(0.416313\pi\) | |||||||
\(972\) | 5.98176 | 0.191865 | ||||||||
\(973\) | 16.0571 | 0.514766 | ||||||||
\(974\) | −19.8140 | −0.634882 | ||||||||
\(975\) | −17.2782 | −0.553345 | ||||||||
\(976\) | −14.5176 | −0.464696 | ||||||||
\(977\) | 17.5139 | 0.560319 | 0.280159 | − | 0.959954i | \(-0.409613\pi\) | ||||
0.280159 | + | 0.959954i | \(0.409613\pi\) | |||||||
\(978\) | 23.5139 | 0.751891 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −58.0835 | −1.85446 | ||||||||
\(982\) | 6.47874 | 0.206745 | ||||||||
\(983\) | 41.1178 | 1.31146 | 0.655728 | − | 0.754997i | \(-0.272362\pi\) | ||||
0.655728 | + | 0.754997i | \(0.272362\pi\) | |||||||
\(984\) | −8.99631 | −0.286792 | ||||||||
\(985\) | 7.87847 | 0.251029 | ||||||||
\(986\) | 43.8711 | 1.39714 | ||||||||
\(987\) | −25.0351 | −0.796877 | ||||||||
\(988\) | 32.7921 | 1.04326 | ||||||||
\(989\) | −58.6706 | −1.86562 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.79947 | −0.0889280 | −0.0444640 | − | 0.999011i | \(-0.514158\pi\) | ||||
−0.0444640 | + | 0.999011i | \(0.514158\pi\) | |||||||
\(992\) | 6.00000 | 0.190500 | ||||||||
\(993\) | −30.9136 | −0.981014 | ||||||||
\(994\) | −7.15667 | −0.226996 | ||||||||
\(995\) | −0.517571 | −0.0164081 | ||||||||
\(996\) | −40.7921 | −1.29255 | ||||||||
\(997\) | −11.7181 | −0.371116 | −0.185558 | − | 0.982633i | \(-0.559409\pi\) | ||||
−0.185558 | + | 0.982633i | \(0.559409\pi\) | |||||||
\(998\) | −21.2394 | −0.672320 | ||||||||
\(999\) | −17.8420 | −0.564496 |
(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 | 8470.2.a.cl.1.1 | 3 | ||
11.10 | odd | 2 | 770.2.a.l.1.1 | ✓ | 3 | ||
33.32 | even | 2 | 6930.2.a.cl.1.1 | 3 | |||
44.43 | even | 2 | 6160.2.a.bi.1.3 | 3 | |||
55.32 | even | 4 | 3850.2.c.z.1849.3 | 6 | |||
55.43 | even | 4 | 3850.2.c.z.1849.4 | 6 | |||
55.54 | odd | 2 | 3850.2.a.bu.1.3 | 3 | |||
77.76 | even | 2 | 5390.2.a.bz.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.a.l.1.1 | ✓ | 3 | 11.10 | odd | 2 | ||
3850.2.a.bu.1.3 | 3 | 55.54 | odd | 2 | |||
3850.2.c.z.1849.3 | 6 | 55.32 | even | 4 | |||
3850.2.c.z.1849.4 | 6 | 55.43 | even | 4 | |||
5390.2.a.bz.1.3 | 3 | 77.76 | even | 2 | |||
6160.2.a.bi.1.3 | 3 | 44.43 | even | 2 | |||
6930.2.a.cl.1.1 | 3 | 33.32 | even | 2 | |||
8470.2.a.cl.1.1 | 3 | 1.1 | even | 1 | trivial |