Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7942,2,Mod(1,7942)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7942, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("7942.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7942 = 2 \cdot 11 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7942.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: | \(63.4171892853\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 14x^{6} + 29x^{5} + 64x^{4} - 50x^{3} - 36x^{2} + 30x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.725465\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7942.1 |
$q$-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 | ||||||||
\(3\) | 0.274535 | 0.158503 | 0.0792516 | − | 0.996855i | \(-0.474747\pi\) | ||||
0.0792516 | + | 0.996855i | \(0.474747\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.892569 | 0.399169 | 0.199585 | − | 0.979881i | \(-0.436041\pi\) | ||||
0.199585 | + | 0.979881i | \(0.436041\pi\) | |||||||
\(6\) | −0.274535 | −0.112079 | ||||||||
\(7\) | 2.55547 | 0.965876 | 0.482938 | − | 0.875654i | \(-0.339570\pi\) | ||||
0.482938 | + | 0.875654i | \(0.339570\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.92463 | −0.974877 | ||||||||
\(10\) | −0.892569 | −0.282255 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0.274535 | 0.0792516 | ||||||||
\(13\) | 2.80434 | 0.777784 | 0.388892 | − | 0.921283i | \(-0.372858\pi\) | ||||
0.388892 | + | 0.921283i | \(0.372858\pi\) | |||||||
\(14\) | −2.55547 | −0.682978 | ||||||||
\(15\) | 0.245042 | 0.0632696 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.51680 | 0.610414 | 0.305207 | − | 0.952286i | \(-0.401274\pi\) | ||||
0.305207 | + | 0.952286i | \(0.401274\pi\) | |||||||
\(18\) | 2.92463 | 0.689342 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0.892569 | 0.199585 | ||||||||
\(21\) | 0.701567 | 0.153094 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −4.65781 | −0.971220 | −0.485610 | − | 0.874176i | \(-0.661402\pi\) | ||||
−0.485610 | + | 0.874176i | \(0.661402\pi\) | |||||||
\(24\) | −0.274535 | −0.0560393 | ||||||||
\(25\) | −4.20332 | −0.840664 | ||||||||
\(26\) | −2.80434 | −0.549976 | ||||||||
\(27\) | −1.62652 | −0.313024 | ||||||||
\(28\) | 2.55547 | 0.482938 | ||||||||
\(29\) | 4.95536 | 0.920187 | 0.460094 | − | 0.887870i | \(-0.347816\pi\) | ||||
0.460094 | + | 0.887870i | \(0.347816\pi\) | |||||||
\(30\) | −0.245042 | −0.0447383 | ||||||||
\(31\) | −6.85998 | −1.23209 | −0.616044 | − | 0.787712i | \(-0.711266\pi\) | ||||
−0.616044 | + | 0.787712i | \(0.711266\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.274535 | −0.0477905 | ||||||||
\(34\) | −2.51680 | −0.431628 | ||||||||
\(35\) | 2.28093 | 0.385548 | ||||||||
\(36\) | −2.92463 | −0.487438 | ||||||||
\(37\) | 6.39092 | 1.05066 | 0.525330 | − | 0.850898i | \(-0.323942\pi\) | ||||
0.525330 | + | 0.850898i | \(0.323942\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.769891 | 0.123281 | ||||||||
\(40\) | −0.892569 | −0.141128 | ||||||||
\(41\) | 11.0881 | 1.73167 | 0.865837 | − | 0.500325i | \(-0.166786\pi\) | ||||
0.865837 | + | 0.500325i | \(0.166786\pi\) | |||||||
\(42\) | −0.701567 | −0.108254 | ||||||||
\(43\) | −0.288970 | −0.0440675 | −0.0220338 | − | 0.999757i | \(-0.507014\pi\) | ||||
−0.0220338 | + | 0.999757i | \(0.507014\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −2.61044 | −0.389141 | ||||||||
\(46\) | 4.65781 | 0.686756 | ||||||||
\(47\) | −4.66995 | −0.681182 | −0.340591 | − | 0.940212i | \(-0.610627\pi\) | ||||
−0.340591 | + | 0.940212i | \(0.610627\pi\) | |||||||
\(48\) | 0.274535 | 0.0396258 | ||||||||
\(49\) | −0.469582 | −0.0670831 | ||||||||
\(50\) | 4.20332 | 0.594439 | ||||||||
\(51\) | 0.690951 | 0.0967525 | ||||||||
\(52\) | 2.80434 | 0.388892 | ||||||||
\(53\) | 12.4197 | 1.70597 | 0.852985 | − | 0.521935i | \(-0.174790\pi\) | ||||
0.852985 | + | 0.521935i | \(0.174790\pi\) | |||||||
\(54\) | 1.62652 | 0.221341 | ||||||||
\(55\) | −0.892569 | −0.120354 | ||||||||
\(56\) | −2.55547 | −0.341489 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.95536 | −0.650671 | ||||||||
\(59\) | −6.23658 | −0.811934 | −0.405967 | − | 0.913888i | \(-0.633065\pi\) | ||||
−0.405967 | + | 0.913888i | \(0.633065\pi\) | |||||||
\(60\) | 0.245042 | 0.0316348 | ||||||||
\(61\) | 3.39707 | 0.434950 | 0.217475 | − | 0.976066i | \(-0.430218\pi\) | ||||
0.217475 | + | 0.976066i | \(0.430218\pi\) | |||||||
\(62\) | 6.85998 | 0.871218 | ||||||||
\(63\) | −7.47380 | −0.941610 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.50307 | 0.310467 | ||||||||
\(66\) | 0.274535 | 0.0337930 | ||||||||
\(67\) | −7.74670 | −0.946410 | −0.473205 | − | 0.880952i | \(-0.656903\pi\) | ||||
−0.473205 | + | 0.880952i | \(0.656903\pi\) | |||||||
\(68\) | 2.51680 | 0.305207 | ||||||||
\(69\) | −1.27873 | −0.153941 | ||||||||
\(70\) | −2.28093 | −0.272624 | ||||||||
\(71\) | −2.71375 | −0.322063 | −0.161032 | − | 0.986949i | \(-0.551482\pi\) | ||||
−0.161032 | + | 0.986949i | \(0.551482\pi\) | |||||||
\(72\) | 2.92463 | 0.344671 | ||||||||
\(73\) | 6.41177 | 0.750441 | 0.375221 | − | 0.926936i | \(-0.377567\pi\) | ||||
0.375221 | + | 0.926936i | \(0.377567\pi\) | |||||||
\(74\) | −6.39092 | −0.742929 | ||||||||
\(75\) | −1.15396 | −0.133248 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.55547 | −0.291223 | ||||||||
\(78\) | −0.769891 | −0.0871730 | ||||||||
\(79\) | 14.5145 | 1.63301 | 0.816505 | − | 0.577338i | \(-0.195909\pi\) | ||||
0.816505 | + | 0.577338i | \(0.195909\pi\) | |||||||
\(80\) | 0.892569 | 0.0997923 | ||||||||
\(81\) | 8.32735 | 0.925261 | ||||||||
\(82\) | −11.0881 | −1.22448 | ||||||||
\(83\) | −3.05634 | −0.335477 | −0.167738 | − | 0.985832i | \(-0.553646\pi\) | ||||
−0.167738 | + | 0.985832i | \(0.553646\pi\) | |||||||
\(84\) | 0.701567 | 0.0765472 | ||||||||
\(85\) | 2.24642 | 0.243658 | ||||||||
\(86\) | 0.288970 | 0.0311604 | ||||||||
\(87\) | 1.36042 | 0.145853 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −0.997910 | −0.105778 | −0.0528891 | − | 0.998600i | \(-0.516843\pi\) | ||||
−0.0528891 | + | 0.998600i | \(0.516843\pi\) | |||||||
\(90\) | 2.61044 | 0.275164 | ||||||||
\(91\) | 7.16640 | 0.751243 | ||||||||
\(92\) | −4.65781 | −0.485610 | ||||||||
\(93\) | −1.88331 | −0.195290 | ||||||||
\(94\) | 4.66995 | 0.481668 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.274535 | −0.0280197 | ||||||||
\(97\) | 13.2525 | 1.34559 | 0.672793 | − | 0.739831i | \(-0.265095\pi\) | ||||
0.672793 | + | 0.739831i | \(0.265095\pi\) | |||||||
\(98\) | 0.469582 | 0.0474349 | ||||||||
\(99\) | 2.92463 | 0.293936 | ||||||||
\(100\) | −4.20332 | −0.420332 | ||||||||
\(101\) | 10.9736 | 1.09192 | 0.545958 | − | 0.837813i | \(-0.316166\pi\) | ||||
0.545958 | + | 0.837813i | \(0.316166\pi\) | |||||||
\(102\) | −0.690951 | −0.0684143 | ||||||||
\(103\) | −11.9597 | −1.17843 | −0.589214 | − | 0.807977i | \(-0.700562\pi\) | ||||
−0.589214 | + | 0.807977i | \(0.700562\pi\) | |||||||
\(104\) | −2.80434 | −0.274988 | ||||||||
\(105\) | 0.626197 | 0.0611106 | ||||||||
\(106\) | −12.4197 | −1.20630 | ||||||||
\(107\) | 7.69689 | 0.744086 | 0.372043 | − | 0.928215i | \(-0.378657\pi\) | ||||
0.372043 | + | 0.928215i | \(0.378657\pi\) | |||||||
\(108\) | −1.62652 | −0.156512 | ||||||||
\(109\) | −4.32954 | −0.414695 | −0.207347 | − | 0.978267i | \(-0.566483\pi\) | ||||
−0.207347 | + | 0.978267i | \(0.566483\pi\) | |||||||
\(110\) | 0.892569 | 0.0851032 | ||||||||
\(111\) | 1.75453 | 0.166533 | ||||||||
\(112\) | 2.55547 | 0.241469 | ||||||||
\(113\) | 17.2931 | 1.62680 | 0.813401 | − | 0.581703i | \(-0.197614\pi\) | ||||
0.813401 | + | 0.581703i | \(0.197614\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.15742 | −0.387681 | ||||||||
\(116\) | 4.95536 | 0.460094 | ||||||||
\(117\) | −8.20166 | −0.758244 | ||||||||
\(118\) | 6.23658 | 0.574124 | ||||||||
\(119\) | 6.43160 | 0.589584 | ||||||||
\(120\) | −0.245042 | −0.0223692 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −3.39707 | −0.307556 | ||||||||
\(123\) | 3.04408 | 0.274476 | ||||||||
\(124\) | −6.85998 | −0.616044 | ||||||||
\(125\) | −8.21460 | −0.734736 | ||||||||
\(126\) | 7.47380 | 0.665819 | ||||||||
\(127\) | 4.44325 | 0.394275 | 0.197137 | − | 0.980376i | \(-0.436836\pi\) | ||||
0.197137 | + | 0.980376i | \(0.436836\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.0793325 | −0.00698484 | ||||||||
\(130\) | −2.50307 | −0.219534 | ||||||||
\(131\) | 12.8733 | 1.12474 | 0.562372 | − | 0.826884i | \(-0.309889\pi\) | ||||
0.562372 | + | 0.826884i | \(0.309889\pi\) | |||||||
\(132\) | −0.274535 | −0.0238952 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.74670 | 0.669213 | ||||||||
\(135\) | −1.45178 | −0.124950 | ||||||||
\(136\) | −2.51680 | −0.215814 | ||||||||
\(137\) | −4.65730 | −0.397900 | −0.198950 | − | 0.980010i | \(-0.563753\pi\) | ||||
−0.198950 | + | 0.980010i | \(0.563753\pi\) | |||||||
\(138\) | 1.27873 | 0.108853 | ||||||||
\(139\) | 1.05322 | 0.0893331 | 0.0446665 | − | 0.999002i | \(-0.485777\pi\) | ||||
0.0446665 | + | 0.999002i | \(0.485777\pi\) | |||||||
\(140\) | 2.28093 | 0.192774 | ||||||||
\(141\) | −1.28207 | −0.107969 | ||||||||
\(142\) | 2.71375 | 0.227733 | ||||||||
\(143\) | −2.80434 | −0.234511 | ||||||||
\(144\) | −2.92463 | −0.243719 | ||||||||
\(145\) | 4.42300 | 0.367310 | ||||||||
\(146\) | −6.41177 | −0.530642 | ||||||||
\(147\) | −0.128917 | −0.0106329 | ||||||||
\(148\) | 6.39092 | 0.525330 | ||||||||
\(149\) | −19.6886 | −1.61296 | −0.806478 | − | 0.591264i | \(-0.798629\pi\) | ||||
−0.806478 | + | 0.591264i | \(0.798629\pi\) | |||||||
\(150\) | 1.15396 | 0.0942205 | ||||||||
\(151\) | −6.41598 | −0.522125 | −0.261063 | − | 0.965322i | \(-0.584073\pi\) | ||||
−0.261063 | + | 0.965322i | \(0.584073\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.36071 | −0.595078 | ||||||||
\(154\) | 2.55547 | 0.205926 | ||||||||
\(155\) | −6.12300 | −0.491812 | ||||||||
\(156\) | 0.769891 | 0.0616406 | ||||||||
\(157\) | 9.84280 | 0.785541 | 0.392770 | − | 0.919637i | \(-0.371517\pi\) | ||||
0.392770 | + | 0.919637i | \(0.371517\pi\) | |||||||
\(158\) | −14.5145 | −1.15471 | ||||||||
\(159\) | 3.40963 | 0.270402 | ||||||||
\(160\) | −0.892569 | −0.0705638 | ||||||||
\(161\) | −11.9029 | −0.938078 | ||||||||
\(162\) | −8.32735 | −0.654259 | ||||||||
\(163\) | −19.1942 | −1.50340 | −0.751701 | − | 0.659504i | \(-0.770766\pi\) | ||||
−0.751701 | + | 0.659504i | \(0.770766\pi\) | |||||||
\(164\) | 11.0881 | 0.865837 | ||||||||
\(165\) | −0.245042 | −0.0190765 | ||||||||
\(166\) | 3.05634 | 0.237218 | ||||||||
\(167\) | 16.4737 | 1.27477 | 0.637387 | − | 0.770544i | \(-0.280015\pi\) | ||||
0.637387 | + | 0.770544i | \(0.280015\pi\) | |||||||
\(168\) | −0.701567 | −0.0541270 | ||||||||
\(169\) | −5.13568 | −0.395052 | ||||||||
\(170\) | −2.24642 | −0.172292 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.288970 | −0.0220338 | ||||||||
\(173\) | 20.3003 | 1.54340 | 0.771702 | − | 0.635984i | \(-0.219405\pi\) | ||||
0.771702 | + | 0.635984i | \(0.219405\pi\) | |||||||
\(174\) | −1.36042 | −0.103133 | ||||||||
\(175\) | −10.7415 | −0.811977 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −1.71216 | −0.128694 | ||||||||
\(178\) | 0.997910 | 0.0747966 | ||||||||
\(179\) | 5.57802 | 0.416921 | 0.208460 | − | 0.978031i | \(-0.433155\pi\) | ||||
0.208460 | + | 0.978031i | \(0.433155\pi\) | |||||||
\(180\) | −2.61044 | −0.194570 | ||||||||
\(181\) | 3.25681 | 0.242077 | 0.121038 | − | 0.992648i | \(-0.461378\pi\) | ||||
0.121038 | + | 0.992648i | \(0.461378\pi\) | |||||||
\(182\) | −7.16640 | −0.531209 | ||||||||
\(183\) | 0.932616 | 0.0689409 | ||||||||
\(184\) | 4.65781 | 0.343378 | ||||||||
\(185\) | 5.70434 | 0.419391 | ||||||||
\(186\) | 1.88331 | 0.138091 | ||||||||
\(187\) | −2.51680 | −0.184047 | ||||||||
\(188\) | −4.66995 | −0.340591 | ||||||||
\(189\) | −4.15652 | −0.302343 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.6232 | 1.20281 | 0.601407 | − | 0.798943i | \(-0.294607\pi\) | ||||
0.601407 | + | 0.798943i | \(0.294607\pi\) | |||||||
\(192\) | 0.274535 | 0.0198129 | ||||||||
\(193\) | −1.55689 | −0.112068 | −0.0560339 | − | 0.998429i | \(-0.517845\pi\) | ||||
−0.0560339 | + | 0.998429i | \(0.517845\pi\) | |||||||
\(194\) | −13.2525 | −0.951472 | ||||||||
\(195\) | 0.687181 | 0.0492101 | ||||||||
\(196\) | −0.469582 | −0.0335416 | ||||||||
\(197\) | 0.246728 | 0.0175786 | 0.00878931 | − | 0.999961i | \(-0.497202\pi\) | ||||
0.00878931 | + | 0.999961i | \(0.497202\pi\) | |||||||
\(198\) | −2.92463 | −0.207844 | ||||||||
\(199\) | 20.0230 | 1.41939 | 0.709696 | − | 0.704508i | \(-0.248832\pi\) | ||||
0.709696 | + | 0.704508i | \(0.248832\pi\) | |||||||
\(200\) | 4.20332 | 0.297220 | ||||||||
\(201\) | −2.12674 | −0.150009 | ||||||||
\(202\) | −10.9736 | −0.772101 | ||||||||
\(203\) | 12.6633 | 0.888787 | ||||||||
\(204\) | 0.690951 | 0.0483762 | ||||||||
\(205\) | 9.89693 | 0.691231 | ||||||||
\(206\) | 11.9597 | 0.833274 | ||||||||
\(207\) | 13.6224 | 0.946820 | ||||||||
\(208\) | 2.80434 | 0.194446 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.626197 | −0.0432117 | ||||||||
\(211\) | 13.1424 | 0.904760 | 0.452380 | − | 0.891825i | \(-0.350575\pi\) | ||||
0.452380 | + | 0.891825i | \(0.350575\pi\) | |||||||
\(212\) | 12.4197 | 0.852985 | ||||||||
\(213\) | −0.745021 | −0.0510480 | ||||||||
\(214\) | −7.69689 | −0.526148 | ||||||||
\(215\) | −0.257926 | −0.0175904 | ||||||||
\(216\) | 1.62652 | 0.110671 | ||||||||
\(217\) | −17.5304 | −1.19004 | ||||||||
\(218\) | 4.32954 | 0.293234 | ||||||||
\(219\) | 1.76026 | 0.118947 | ||||||||
\(220\) | −0.892569 | −0.0601770 | ||||||||
\(221\) | 7.05797 | 0.474770 | ||||||||
\(222\) | −1.75453 | −0.117757 | ||||||||
\(223\) | −3.35906 | −0.224939 | −0.112470 | − | 0.993655i | \(-0.535876\pi\) | ||||
−0.112470 | + | 0.993655i | \(0.535876\pi\) | |||||||
\(224\) | −2.55547 | −0.170744 | ||||||||
\(225\) | 12.2932 | 0.819544 | ||||||||
\(226\) | −17.2931 | −1.15032 | ||||||||
\(227\) | −16.3860 | −1.08758 | −0.543789 | − | 0.839222i | \(-0.683011\pi\) | ||||
−0.543789 | + | 0.839222i | \(0.683011\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.2509 | 0.941728 | 0.470864 | − | 0.882206i | \(-0.343942\pi\) | ||||
0.470864 | + | 0.882206i | \(0.343942\pi\) | |||||||
\(230\) | 4.15742 | 0.274132 | ||||||||
\(231\) | −0.701567 | −0.0461597 | ||||||||
\(232\) | −4.95536 | −0.325335 | ||||||||
\(233\) | 24.8755 | 1.62965 | 0.814823 | − | 0.579710i | \(-0.196834\pi\) | ||||
0.814823 | + | 0.579710i | \(0.196834\pi\) | |||||||
\(234\) | 8.20166 | 0.536159 | ||||||||
\(235\) | −4.16825 | −0.271907 | ||||||||
\(236\) | −6.23658 | −0.405967 | ||||||||
\(237\) | 3.98475 | 0.258837 | ||||||||
\(238\) | −6.43160 | −0.416899 | ||||||||
\(239\) | 4.31856 | 0.279345 | 0.139672 | − | 0.990198i | \(-0.455395\pi\) | ||||
0.139672 | + | 0.990198i | \(0.455395\pi\) | |||||||
\(240\) | 0.245042 | 0.0158174 | ||||||||
\(241\) | −20.7016 | −1.33351 | −0.666753 | − | 0.745279i | \(-0.732316\pi\) | ||||
−0.666753 | + | 0.745279i | \(0.732316\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 7.16572 | 0.459681 | ||||||||
\(244\) | 3.39707 | 0.217475 | ||||||||
\(245\) | −0.419134 | −0.0267775 | ||||||||
\(246\) | −3.04408 | −0.194084 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.85998 | 0.435609 | ||||||||
\(249\) | −0.839073 | −0.0531741 | ||||||||
\(250\) | 8.21460 | 0.519537 | ||||||||
\(251\) | −9.10965 | −0.574996 | −0.287498 | − | 0.957781i | \(-0.592823\pi\) | ||||
−0.287498 | + | 0.957781i | \(0.592823\pi\) | |||||||
\(252\) | −7.47380 | −0.470805 | ||||||||
\(253\) | 4.65781 | 0.292834 | ||||||||
\(254\) | −4.44325 | −0.278794 | ||||||||
\(255\) | 0.616722 | 0.0386206 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.4988 | −0.654899 | −0.327450 | − | 0.944869i | \(-0.606189\pi\) | ||||
−0.327450 | + | 0.944869i | \(0.606189\pi\) | |||||||
\(258\) | 0.0793325 | 0.00493902 | ||||||||
\(259\) | 16.3318 | 1.01481 | ||||||||
\(260\) | 2.50307 | 0.155234 | ||||||||
\(261\) | −14.4926 | −0.897069 | ||||||||
\(262\) | −12.8733 | −0.795314 | ||||||||
\(263\) | 5.40330 | 0.333182 | 0.166591 | − | 0.986026i | \(-0.446724\pi\) | ||||
0.166591 | + | 0.986026i | \(0.446724\pi\) | |||||||
\(264\) | 0.274535 | 0.0168965 | ||||||||
\(265\) | 11.0854 | 0.680971 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.273962 | −0.0167662 | ||||||||
\(268\) | −7.74670 | −0.473205 | ||||||||
\(269\) | 16.8668 | 1.02839 | 0.514194 | − | 0.857674i | \(-0.328091\pi\) | ||||
0.514194 | + | 0.857674i | \(0.328091\pi\) | |||||||
\(270\) | 1.45178 | 0.0883527 | ||||||||
\(271\) | 18.4177 | 1.11880 | 0.559399 | − | 0.828898i | \(-0.311032\pi\) | ||||
0.559399 | + | 0.828898i | \(0.311032\pi\) | |||||||
\(272\) | 2.51680 | 0.152603 | ||||||||
\(273\) | 1.96743 | 0.119074 | ||||||||
\(274\) | 4.65730 | 0.281358 | ||||||||
\(275\) | 4.20332 | 0.253470 | ||||||||
\(276\) | −1.27873 | −0.0769707 | ||||||||
\(277\) | −20.3493 | −1.22267 | −0.611335 | − | 0.791372i | \(-0.709367\pi\) | ||||
−0.611335 | + | 0.791372i | \(0.709367\pi\) | |||||||
\(278\) | −1.05322 | −0.0631680 | ||||||||
\(279\) | 20.0629 | 1.20113 | ||||||||
\(280\) | −2.28093 | −0.136312 | ||||||||
\(281\) | 18.9213 | 1.12875 | 0.564375 | − | 0.825518i | \(-0.309117\pi\) | ||||
0.564375 | + | 0.825518i | \(0.309117\pi\) | |||||||
\(282\) | 1.28207 | 0.0763459 | ||||||||
\(283\) | 14.3130 | 0.850822 | 0.425411 | − | 0.905000i | \(-0.360129\pi\) | ||||
0.425411 | + | 0.905000i | \(0.360129\pi\) | |||||||
\(284\) | −2.71375 | −0.161032 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.80434 | 0.165824 | ||||||||
\(287\) | 28.3354 | 1.67258 | ||||||||
\(288\) | 2.92463 | 0.172335 | ||||||||
\(289\) | −10.6657 | −0.627395 | ||||||||
\(290\) | −4.42300 | −0.259728 | ||||||||
\(291\) | 3.63827 | 0.213279 | ||||||||
\(292\) | 6.41177 | 0.375221 | ||||||||
\(293\) | −7.78857 | −0.455013 | −0.227506 | − | 0.973777i | \(-0.573057\pi\) | ||||
−0.227506 | + | 0.973777i | \(0.573057\pi\) | |||||||
\(294\) | 0.128917 | 0.00751858 | ||||||||
\(295\) | −5.56658 | −0.324099 | ||||||||
\(296\) | −6.39092 | −0.371465 | ||||||||
\(297\) | 1.62652 | 0.0943803 | ||||||||
\(298\) | 19.6886 | 1.14053 | ||||||||
\(299\) | −13.0621 | −0.755399 | ||||||||
\(300\) | −1.15396 | −0.0666239 | ||||||||
\(301\) | −0.738453 | −0.0425638 | ||||||||
\(302\) | 6.41598 | 0.369198 | ||||||||
\(303\) | 3.01265 | 0.173072 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.03212 | 0.173619 | ||||||||
\(306\) | 7.36071 | 0.420784 | ||||||||
\(307\) | 8.08339 | 0.461343 | 0.230672 | − | 0.973032i | \(-0.425908\pi\) | ||||
0.230672 | + | 0.973032i | \(0.425908\pi\) | |||||||
\(308\) | −2.55547 | −0.145611 | ||||||||
\(309\) | −3.28337 | −0.186784 | ||||||||
\(310\) | 6.12300 | 0.347763 | ||||||||
\(311\) | 24.4319 | 1.38540 | 0.692702 | − | 0.721224i | \(-0.256420\pi\) | ||||
0.692702 | + | 0.721224i | \(0.256420\pi\) | |||||||
\(312\) | −0.769891 | −0.0435865 | ||||||||
\(313\) | −10.4738 | −0.592013 | −0.296006 | − | 0.955186i | \(-0.595655\pi\) | ||||
−0.296006 | + | 0.955186i | \(0.595655\pi\) | |||||||
\(314\) | −9.84280 | −0.555461 | ||||||||
\(315\) | −6.67089 | −0.375862 | ||||||||
\(316\) | 14.5145 | 0.816505 | ||||||||
\(317\) | −18.5843 | −1.04380 | −0.521899 | − | 0.853007i | \(-0.674776\pi\) | ||||
−0.521899 | + | 0.853007i | \(0.674776\pi\) | |||||||
\(318\) | −3.40963 | −0.191203 | ||||||||
\(319\) | −4.95536 | −0.277447 | ||||||||
\(320\) | 0.892569 | 0.0498961 | ||||||||
\(321\) | 2.11307 | 0.117940 | ||||||||
\(322\) | 11.9029 | 0.663322 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 8.32735 | 0.462631 | ||||||||
\(325\) | −11.7875 | −0.653855 | ||||||||
\(326\) | 19.1942 | 1.06307 | ||||||||
\(327\) | −1.18861 | −0.0657304 | ||||||||
\(328\) | −11.0881 | −0.612240 | ||||||||
\(329\) | −11.9339 | −0.657938 | ||||||||
\(330\) | 0.245042 | 0.0134891 | ||||||||
\(331\) | −21.0755 | −1.15841 | −0.579206 | − | 0.815181i | \(-0.696638\pi\) | ||||
−0.579206 | + | 0.815181i | \(0.696638\pi\) | |||||||
\(332\) | −3.05634 | −0.167738 | ||||||||
\(333\) | −18.6911 | −1.02426 | ||||||||
\(334\) | −16.4737 | −0.901401 | ||||||||
\(335\) | −6.91446 | −0.377778 | ||||||||
\(336\) | 0.701567 | 0.0382736 | ||||||||
\(337\) | 13.4832 | 0.734476 | 0.367238 | − | 0.930127i | \(-0.380303\pi\) | ||||
0.367238 | + | 0.930127i | \(0.380303\pi\) | |||||||
\(338\) | 5.13568 | 0.279344 | ||||||||
\(339\) | 4.74758 | 0.257853 | ||||||||
\(340\) | 2.24642 | 0.121829 | ||||||||
\(341\) | 6.85998 | 0.371488 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.0883 | −1.03067 | ||||||||
\(344\) | 0.288970 | 0.0155802 | ||||||||
\(345\) | −1.14136 | −0.0614487 | ||||||||
\(346\) | −20.3003 | −1.09135 | ||||||||
\(347\) | −15.9885 | −0.858306 | −0.429153 | − | 0.903232i | \(-0.641188\pi\) | ||||
−0.429153 | + | 0.903232i | \(0.641188\pi\) | |||||||
\(348\) | 1.36042 | 0.0729263 | ||||||||
\(349\) | −32.0957 | −1.71804 | −0.859022 | − | 0.511939i | \(-0.828927\pi\) | ||||
−0.859022 | + | 0.511939i | \(0.828927\pi\) | |||||||
\(350\) | 10.7415 | 0.574155 | ||||||||
\(351\) | −4.56132 | −0.243465 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 10.1485 | 0.540148 | 0.270074 | − | 0.962840i | \(-0.412952\pi\) | ||||
0.270074 | + | 0.962840i | \(0.412952\pi\) | |||||||
\(354\) | 1.71216 | 0.0910004 | ||||||||
\(355\) | −2.42221 | −0.128558 | ||||||||
\(356\) | −0.997910 | −0.0528891 | ||||||||
\(357\) | 1.76570 | 0.0934509 | ||||||||
\(358\) | −5.57802 | −0.294808 | ||||||||
\(359\) | −5.98929 | −0.316103 | −0.158051 | − | 0.987431i | \(-0.550521\pi\) | ||||
−0.158051 | + | 0.987431i | \(0.550521\pi\) | |||||||
\(360\) | 2.61044 | 0.137582 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −3.25681 | −0.171174 | ||||||||
\(363\) | 0.274535 | 0.0144094 | ||||||||
\(364\) | 7.16640 | 0.375622 | ||||||||
\(365\) | 5.72295 | 0.299553 | ||||||||
\(366\) | −0.932616 | −0.0487486 | ||||||||
\(367\) | −18.8213 | −0.982464 | −0.491232 | − | 0.871029i | \(-0.663453\pi\) | ||||
−0.491232 | + | 0.871029i | \(0.663453\pi\) | |||||||
\(368\) | −4.65781 | −0.242805 | ||||||||
\(369\) | −32.4287 | −1.68817 | ||||||||
\(370\) | −5.70434 | −0.296554 | ||||||||
\(371\) | 31.7380 | 1.64776 | ||||||||
\(372\) | −1.88331 | −0.0976449 | ||||||||
\(373\) | −6.91364 | −0.357975 | −0.178987 | − | 0.983851i | \(-0.557282\pi\) | ||||
−0.178987 | + | 0.983851i | \(0.557282\pi\) | |||||||
\(374\) | 2.51680 | 0.130141 | ||||||||
\(375\) | −2.25520 | −0.116458 | ||||||||
\(376\) | 4.66995 | 0.240834 | ||||||||
\(377\) | 13.8965 | 0.715707 | ||||||||
\(378\) | 4.15652 | 0.213788 | ||||||||
\(379\) | 22.2824 | 1.14457 | 0.572284 | − | 0.820056i | \(-0.306058\pi\) | ||||
0.572284 | + | 0.820056i | \(0.306058\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.21983 | 0.0624938 | ||||||||
\(382\) | −16.6232 | −0.850519 | ||||||||
\(383\) | −22.3408 | −1.14156 | −0.570780 | − | 0.821103i | \(-0.693359\pi\) | ||||
−0.570780 | + | 0.821103i | \(0.693359\pi\) | |||||||
\(384\) | −0.274535 | −0.0140098 | ||||||||
\(385\) | −2.28093 | −0.116247 | ||||||||
\(386\) | 1.55689 | 0.0792439 | ||||||||
\(387\) | 0.845130 | 0.0429604 | ||||||||
\(388\) | 13.2525 | 0.672793 | ||||||||
\(389\) | 25.1591 | 1.27562 | 0.637808 | − | 0.770195i | \(-0.279841\pi\) | ||||
0.637808 | + | 0.770195i | \(0.279841\pi\) | |||||||
\(390\) | −0.687181 | −0.0347968 | ||||||||
\(391\) | −11.7228 | −0.592846 | ||||||||
\(392\) | 0.469582 | 0.0237175 | ||||||||
\(393\) | 3.53417 | 0.178275 | ||||||||
\(394\) | −0.246728 | −0.0124300 | ||||||||
\(395\) | 12.9552 | 0.651847 | ||||||||
\(396\) | 2.92463 | 0.146968 | ||||||||
\(397\) | 5.11918 | 0.256924 | 0.128462 | − | 0.991714i | \(-0.458996\pi\) | ||||
0.128462 | + | 0.991714i | \(0.458996\pi\) | |||||||
\(398\) | −20.0230 | −1.00366 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.20332 | −0.210166 | ||||||||
\(401\) | −3.83325 | −0.191424 | −0.0957118 | − | 0.995409i | \(-0.530513\pi\) | ||||
−0.0957118 | + | 0.995409i | \(0.530513\pi\) | |||||||
\(402\) | 2.12674 | 0.106072 | ||||||||
\(403\) | −19.2377 | −0.958298 | ||||||||
\(404\) | 10.9736 | 0.545958 | ||||||||
\(405\) | 7.43274 | 0.369336 | ||||||||
\(406\) | −12.6633 | −0.628467 | ||||||||
\(407\) | −6.39092 | −0.316786 | ||||||||
\(408\) | −0.690951 | −0.0342072 | ||||||||
\(409\) | −4.42842 | −0.218971 | −0.109486 | − | 0.993988i | \(-0.534920\pi\) | ||||
−0.109486 | + | 0.993988i | \(0.534920\pi\) | |||||||
\(410\) | −9.89693 | −0.488774 | ||||||||
\(411\) | −1.27859 | −0.0630684 | ||||||||
\(412\) | −11.9597 | −0.589214 | ||||||||
\(413\) | −15.9374 | −0.784228 | ||||||||
\(414\) | −13.6224 | −0.669503 | ||||||||
\(415\) | −2.72799 | −0.133912 | ||||||||
\(416\) | −2.80434 | −0.137494 | ||||||||
\(417\) | 0.289147 | 0.0141596 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.2640 | −0.599137 | −0.299568 | − | 0.954075i | \(-0.596843\pi\) | ||||
−0.299568 | + | 0.954075i | \(0.596843\pi\) | |||||||
\(420\) | 0.626197 | 0.0305553 | ||||||||
\(421\) | −29.8939 | −1.45694 | −0.728470 | − | 0.685078i | \(-0.759768\pi\) | ||||
−0.728470 | + | 0.685078i | \(0.759768\pi\) | |||||||
\(422\) | −13.1424 | −0.639762 | ||||||||
\(423\) | 13.6579 | 0.664069 | ||||||||
\(424\) | −12.4197 | −0.603152 | ||||||||
\(425\) | −10.5789 | −0.513153 | ||||||||
\(426\) | 0.745021 | 0.0360964 | ||||||||
\(427\) | 8.68110 | 0.420108 | ||||||||
\(428\) | 7.69689 | 0.372043 | ||||||||
\(429\) | −0.769891 | −0.0371707 | ||||||||
\(430\) | 0.257926 | 0.0124383 | ||||||||
\(431\) | 17.0662 | 0.822051 | 0.411026 | − | 0.911624i | \(-0.365171\pi\) | ||||
0.411026 | + | 0.911624i | \(0.365171\pi\) | |||||||
\(432\) | −1.62652 | −0.0782560 | ||||||||
\(433\) | 12.1572 | 0.584236 | 0.292118 | − | 0.956382i | \(-0.405640\pi\) | ||||
0.292118 | + | 0.956382i | \(0.405640\pi\) | |||||||
\(434\) | 17.5304 | 0.841488 | ||||||||
\(435\) | 1.21427 | 0.0582198 | ||||||||
\(436\) | −4.32954 | −0.207347 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −1.76026 | −0.0841084 | ||||||||
\(439\) | 35.3669 | 1.68797 | 0.843986 | − | 0.536365i | \(-0.180203\pi\) | ||||
0.843986 | + | 0.536365i | \(0.180203\pi\) | |||||||
\(440\) | 0.892569 | 0.0425516 | ||||||||
\(441\) | 1.37335 | 0.0653978 | ||||||||
\(442\) | −7.05797 | −0.335713 | ||||||||
\(443\) | −34.1995 | −1.62487 | −0.812434 | − | 0.583053i | \(-0.801858\pi\) | ||||
−0.812434 | + | 0.583053i | \(0.801858\pi\) | |||||||
\(444\) | 1.75453 | 0.0832665 | ||||||||
\(445\) | −0.890704 | −0.0422234 | ||||||||
\(446\) | 3.35906 | 0.159056 | ||||||||
\(447\) | −5.40523 | −0.255658 | ||||||||
\(448\) | 2.55547 | 0.120735 | ||||||||
\(449\) | 33.9412 | 1.60178 | 0.800892 | − | 0.598808i | \(-0.204359\pi\) | ||||
0.800892 | + | 0.598808i | \(0.204359\pi\) | |||||||
\(450\) | −12.2932 | −0.579505 | ||||||||
\(451\) | −11.0881 | −0.522120 | ||||||||
\(452\) | 17.2931 | 0.813401 | ||||||||
\(453\) | −1.76141 | −0.0827584 | ||||||||
\(454\) | 16.3860 | 0.769033 | ||||||||
\(455\) | 6.39651 | 0.299873 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.5228 | 1.10035 | 0.550176 | − | 0.835049i | \(-0.314561\pi\) | ||||
0.550176 | + | 0.835049i | \(0.314561\pi\) | |||||||
\(458\) | −14.2509 | −0.665902 | ||||||||
\(459\) | −4.09363 | −0.191074 | ||||||||
\(460\) | −4.15742 | −0.193841 | ||||||||
\(461\) | 27.9047 | 1.29965 | 0.649827 | − | 0.760082i | \(-0.274841\pi\) | ||||
0.649827 | + | 0.760082i | \(0.274841\pi\) | |||||||
\(462\) | 0.701567 | 0.0326398 | ||||||||
\(463\) | −30.3458 | −1.41029 | −0.705145 | − | 0.709063i | \(-0.749118\pi\) | ||||
−0.705145 | + | 0.709063i | \(0.749118\pi\) | |||||||
\(464\) | 4.95536 | 0.230047 | ||||||||
\(465\) | −1.68098 | −0.0779537 | ||||||||
\(466\) | −24.8755 | −1.15233 | ||||||||
\(467\) | 24.6301 | 1.13975 | 0.569874 | − | 0.821732i | \(-0.306992\pi\) | ||||
0.569874 | + | 0.821732i | \(0.306992\pi\) | |||||||
\(468\) | −8.20166 | −0.379122 | ||||||||
\(469\) | −19.7964 | −0.914114 | ||||||||
\(470\) | 4.16825 | 0.192267 | ||||||||
\(471\) | 2.70220 | 0.124511 | ||||||||
\(472\) | 6.23658 | 0.287062 | ||||||||
\(473\) | 0.288970 | 0.0132869 | ||||||||
\(474\) | −3.98475 | −0.183026 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.43160 | 0.294792 | ||||||||
\(477\) | −36.3229 | −1.66311 | ||||||||
\(478\) | −4.31856 | −0.197526 | ||||||||
\(479\) | −29.0486 | −1.32726 | −0.663632 | − | 0.748059i | \(-0.730986\pi\) | ||||
−0.663632 | + | 0.748059i | \(0.730986\pi\) | |||||||
\(480\) | −0.245042 | −0.0111846 | ||||||||
\(481\) | 17.9223 | 0.817187 | ||||||||
\(482\) | 20.7016 | 0.942930 | ||||||||
\(483\) | −3.26776 | −0.148688 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 11.8288 | 0.537116 | ||||||||
\(486\) | −7.16572 | −0.325043 | ||||||||
\(487\) | 9.40209 | 0.426049 | 0.213025 | − | 0.977047i | \(-0.431669\pi\) | ||||
0.213025 | + | 0.977047i | \(0.431669\pi\) | |||||||
\(488\) | −3.39707 | −0.153778 | ||||||||
\(489\) | −5.26948 | −0.238294 | ||||||||
\(490\) | 0.419134 | 0.0189346 | ||||||||
\(491\) | 17.5251 | 0.790895 | 0.395448 | − | 0.918489i | \(-0.370589\pi\) | ||||
0.395448 | + | 0.918489i | \(0.370589\pi\) | |||||||
\(492\) | 3.04408 | 0.137238 | ||||||||
\(493\) | 12.4717 | 0.561695 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.61044 | 0.117330 | ||||||||
\(496\) | −6.85998 | −0.308022 | ||||||||
\(497\) | −6.93491 | −0.311073 | ||||||||
\(498\) | 0.839073 | 0.0375998 | ||||||||
\(499\) | 16.0414 | 0.718111 | 0.359056 | − | 0.933316i | \(-0.383099\pi\) | ||||
0.359056 | + | 0.933316i | \(0.383099\pi\) | |||||||
\(500\) | −8.21460 | −0.367368 | ||||||||
\(501\) | 4.52261 | 0.202056 | ||||||||
\(502\) | 9.10965 | 0.406583 | ||||||||
\(503\) | −5.65371 | −0.252086 | −0.126043 | − | 0.992025i | \(-0.540228\pi\) | ||||
−0.126043 | + | 0.992025i | \(0.540228\pi\) | |||||||
\(504\) | 7.47380 | 0.332910 | ||||||||
\(505\) | 9.79472 | 0.435859 | ||||||||
\(506\) | −4.65781 | −0.207065 | ||||||||
\(507\) | −1.40992 | −0.0626170 | ||||||||
\(508\) | 4.44325 | 0.197137 | ||||||||
\(509\) | −12.4761 | −0.552993 | −0.276497 | − | 0.961015i | \(-0.589173\pi\) | ||||
−0.276497 | + | 0.961015i | \(0.589173\pi\) | |||||||
\(510\) | −0.616722 | −0.0273089 | ||||||||
\(511\) | 16.3851 | 0.724833 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.4988 | 0.463084 | ||||||||
\(515\) | −10.6749 | −0.470392 | ||||||||
\(516\) | −0.0793325 | −0.00349242 | ||||||||
\(517\) | 4.66995 | 0.205384 | ||||||||
\(518\) | −16.3318 | −0.717578 | ||||||||
\(519\) | 5.57316 | 0.244634 | ||||||||
\(520\) | −2.50307 | −0.109767 | ||||||||
\(521\) | 1.96422 | 0.0860542 | 0.0430271 | − | 0.999074i | \(-0.486300\pi\) | ||||
0.0430271 | + | 0.999074i | \(0.486300\pi\) | |||||||
\(522\) | 14.4926 | 0.634324 | ||||||||
\(523\) | −25.6587 | −1.12198 | −0.560988 | − | 0.827824i | \(-0.689579\pi\) | ||||
−0.560988 | + | 0.827824i | \(0.689579\pi\) | |||||||
\(524\) | 12.8733 | 0.562372 | ||||||||
\(525\) | −2.94891 | −0.128701 | ||||||||
\(526\) | −5.40330 | −0.235595 | ||||||||
\(527\) | −17.2652 | −0.752083 | ||||||||
\(528\) | −0.274535 | −0.0119476 | ||||||||
\(529\) | −1.30483 | −0.0567316 | ||||||||
\(530\) | −11.0854 | −0.481519 | ||||||||
\(531\) | 18.2397 | 0.791535 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.0949 | 1.34687 | ||||||||
\(534\) | 0.273962 | 0.0118555 | ||||||||
\(535\) | 6.87001 | 0.297016 | ||||||||
\(536\) | 7.74670 | 0.334606 | ||||||||
\(537\) | 1.53136 | 0.0660833 | ||||||||
\(538\) | −16.8668 | −0.727180 | ||||||||
\(539\) | 0.469582 | 0.0202263 | ||||||||
\(540\) | −1.45178 | −0.0624748 | ||||||||
\(541\) | −40.2006 | −1.72836 | −0.864180 | − | 0.503183i | \(-0.832162\pi\) | ||||
−0.864180 | + | 0.503183i | \(0.832162\pi\) | |||||||
\(542\) | −18.4177 | −0.791110 | ||||||||
\(543\) | 0.894110 | 0.0383699 | ||||||||
\(544\) | −2.51680 | −0.107907 | ||||||||
\(545\) | −3.86442 | −0.165533 | ||||||||
\(546\) | −1.96743 | −0.0841983 | ||||||||
\(547\) | −23.1690 | −0.990635 | −0.495318 | − | 0.868712i | \(-0.664948\pi\) | ||||
−0.495318 | + | 0.868712i | \(0.664948\pi\) | |||||||
\(548\) | −4.65730 | −0.198950 | ||||||||
\(549\) | −9.93517 | −0.424023 | ||||||||
\(550\) | −4.20332 | −0.179230 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 1.27873 | 0.0544265 | ||||||||
\(553\) | 37.0914 | 1.57729 | ||||||||
\(554\) | 20.3493 | 0.864558 | ||||||||
\(555\) | 1.56604 | 0.0664748 | ||||||||
\(556\) | 1.05322 | 0.0446665 | ||||||||
\(557\) | 0.295914 | 0.0125383 | 0.00626914 | − | 0.999980i | \(-0.498004\pi\) | ||||
0.00626914 | + | 0.999980i | \(0.498004\pi\) | |||||||
\(558\) | −20.0629 | −0.849330 | ||||||||
\(559\) | −0.810370 | −0.0342750 | ||||||||
\(560\) | 2.28093 | 0.0963870 | ||||||||
\(561\) | −0.690951 | −0.0291720 | ||||||||
\(562\) | −18.9213 | −0.798147 | ||||||||
\(563\) | 37.7508 | 1.59101 | 0.795504 | − | 0.605948i | \(-0.207206\pi\) | ||||
0.795504 | + | 0.605948i | \(0.207206\pi\) | |||||||
\(564\) | −1.28207 | −0.0539847 | ||||||||
\(565\) | 15.4353 | 0.649369 | ||||||||
\(566\) | −14.3130 | −0.601622 | ||||||||
\(567\) | 21.2803 | 0.893688 | ||||||||
\(568\) | 2.71375 | 0.113866 | ||||||||
\(569\) | 42.4122 | 1.77801 | 0.889006 | − | 0.457896i | \(-0.151397\pi\) | ||||
0.889006 | + | 0.457896i | \(0.151397\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0643 | −0.839664 | −0.419832 | − | 0.907602i | \(-0.637911\pi\) | ||||
−0.419832 | + | 0.907602i | \(0.637911\pi\) | |||||||
\(572\) | −2.80434 | −0.117255 | ||||||||
\(573\) | 4.56367 | 0.190650 | ||||||||
\(574\) | −28.3354 | −1.18270 | ||||||||
\(575\) | 19.5783 | 0.816470 | ||||||||
\(576\) | −2.92463 | −0.121860 | ||||||||
\(577\) | −3.91059 | −0.162800 | −0.0814000 | − | 0.996682i | \(-0.525939\pi\) | ||||
−0.0814000 | + | 0.996682i | \(0.525939\pi\) | |||||||
\(578\) | 10.6657 | 0.443635 | ||||||||
\(579\) | −0.427423 | −0.0177631 | ||||||||
\(580\) | 4.42300 | 0.183655 | ||||||||
\(581\) | −7.81037 | −0.324029 | ||||||||
\(582\) | −3.63827 | −0.150811 | ||||||||
\(583\) | −12.4197 | −0.514369 | ||||||||
\(584\) | −6.41177 | −0.265321 | ||||||||
\(585\) | −7.32055 | −0.302667 | ||||||||
\(586\) | 7.78857 | 0.321743 | ||||||||
\(587\) | 38.5196 | 1.58988 | 0.794938 | − | 0.606691i | \(-0.207504\pi\) | ||||
0.794938 | + | 0.606691i | \(0.207504\pi\) | |||||||
\(588\) | −0.128917 | −0.00531644 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 5.56658 | 0.229173 | ||||||||
\(591\) | 0.0677355 | 0.00278627 | ||||||||
\(592\) | 6.39092 | 0.262665 | ||||||||
\(593\) | −0.961362 | −0.0394784 | −0.0197392 | − | 0.999805i | \(-0.506284\pi\) | ||||
−0.0197392 | + | 0.999805i | \(0.506284\pi\) | |||||||
\(594\) | −1.62652 | −0.0667370 | ||||||||
\(595\) | 5.74065 | 0.235344 | ||||||||
\(596\) | −19.6886 | −0.806478 | ||||||||
\(597\) | 5.49702 | 0.224978 | ||||||||
\(598\) | 13.0621 | 0.534148 | ||||||||
\(599\) | 13.2725 | 0.542299 | 0.271150 | − | 0.962537i | \(-0.412596\pi\) | ||||
0.271150 | + | 0.962537i | \(0.412596\pi\) | |||||||
\(600\) | 1.15396 | 0.0471102 | ||||||||
\(601\) | 27.4695 | 1.12051 | 0.560253 | − | 0.828322i | \(-0.310704\pi\) | ||||
0.560253 | + | 0.828322i | \(0.310704\pi\) | |||||||
\(602\) | 0.738453 | 0.0300971 | ||||||||
\(603\) | 22.6562 | 0.922633 | ||||||||
\(604\) | −6.41598 | −0.261063 | ||||||||
\(605\) | 0.892569 | 0.0362881 | ||||||||
\(606\) | −3.01265 | −0.122380 | ||||||||
\(607\) | 14.8642 | 0.603320 | 0.301660 | − | 0.953416i | \(-0.402459\pi\) | ||||
0.301660 | + | 0.953416i | \(0.402459\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.47651 | 0.140875 | ||||||||
\(610\) | −3.03212 | −0.122767 | ||||||||
\(611\) | −13.0961 | −0.529813 | ||||||||
\(612\) | −7.36071 | −0.297539 | ||||||||
\(613\) | −14.0513 | −0.567525 | −0.283762 | − | 0.958895i | \(-0.591583\pi\) | ||||
−0.283762 | + | 0.958895i | \(0.591583\pi\) | |||||||
\(614\) | −8.08339 | −0.326219 | ||||||||
\(615\) | 2.71706 | 0.109562 | ||||||||
\(616\) | 2.55547 | 0.102963 | ||||||||
\(617\) | 1.66750 | 0.0671311 | 0.0335656 | − | 0.999437i | \(-0.489314\pi\) | ||||
0.0335656 | + | 0.999437i | \(0.489314\pi\) | |||||||
\(618\) | 3.28337 | 0.132076 | ||||||||
\(619\) | 21.6054 | 0.868394 | 0.434197 | − | 0.900818i | \(-0.357032\pi\) | ||||
0.434197 | + | 0.900818i | \(0.357032\pi\) | |||||||
\(620\) | −6.12300 | −0.245906 | ||||||||
\(621\) | 7.57602 | 0.304015 | ||||||||
\(622\) | −24.4319 | −0.979629 | ||||||||
\(623\) | −2.55013 | −0.102169 | ||||||||
\(624\) | 0.769891 | 0.0308203 | ||||||||
\(625\) | 13.6845 | 0.547380 | ||||||||
\(626\) | 10.4738 | 0.418616 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.84280 | 0.392770 | ||||||||
\(629\) | 16.0847 | 0.641338 | ||||||||
\(630\) | 6.67089 | 0.265774 | ||||||||
\(631\) | 11.2648 | 0.448445 | 0.224223 | − | 0.974538i | \(-0.428016\pi\) | ||||
0.224223 | + | 0.974538i | \(0.428016\pi\) | |||||||
\(632\) | −14.5145 | −0.577356 | ||||||||
\(633\) | 3.60805 | 0.143407 | ||||||||
\(634\) | 18.5843 | 0.738077 | ||||||||
\(635\) | 3.96591 | 0.157382 | ||||||||
\(636\) | 3.40963 | 0.135201 | ||||||||
\(637\) | −1.31687 | −0.0521762 | ||||||||
\(638\) | 4.95536 | 0.196185 | ||||||||
\(639\) | 7.93672 | 0.313972 | ||||||||
\(640\) | −0.892569 | −0.0352819 | ||||||||
\(641\) | 29.8776 | 1.18009 | 0.590046 | − | 0.807370i | \(-0.299110\pi\) | ||||
0.590046 | + | 0.807370i | \(0.299110\pi\) | |||||||
\(642\) | −2.11307 | −0.0833962 | ||||||||
\(643\) | −12.8767 | −0.507806 | −0.253903 | − | 0.967230i | \(-0.581714\pi\) | ||||
−0.253903 | + | 0.967230i | \(0.581714\pi\) | |||||||
\(644\) | −11.9029 | −0.469039 | ||||||||
\(645\) | −0.0708097 | −0.00278813 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.3391 | −0.485100 | −0.242550 | − | 0.970139i | \(-0.577984\pi\) | ||||
−0.242550 | + | 0.970139i | \(0.577984\pi\) | |||||||
\(648\) | −8.32735 | −0.327129 | ||||||||
\(649\) | 6.23658 | 0.244807 | ||||||||
\(650\) | 11.7875 | 0.462345 | ||||||||
\(651\) | −4.81273 | −0.188626 | ||||||||
\(652\) | −19.1942 | −0.751701 | ||||||||
\(653\) | −9.35777 | −0.366198 | −0.183099 | − | 0.983095i | \(-0.558613\pi\) | ||||
−0.183099 | + | 0.983095i | \(0.558613\pi\) | |||||||
\(654\) | 1.18861 | 0.0464784 | ||||||||
\(655\) | 11.4903 | 0.448963 | ||||||||
\(656\) | 11.0881 | 0.432919 | ||||||||
\(657\) | −18.7521 | −0.731588 | ||||||||
\(658\) | 11.9339 | 0.465232 | ||||||||
\(659\) | 3.19319 | 0.124389 | 0.0621946 | − | 0.998064i | \(-0.480190\pi\) | ||||
0.0621946 | + | 0.998064i | \(0.480190\pi\) | |||||||
\(660\) | −0.245042 | −0.00953824 | ||||||||
\(661\) | 2.98717 | 0.116187 | 0.0580937 | − | 0.998311i | \(-0.481498\pi\) | ||||
0.0580937 | + | 0.998311i | \(0.481498\pi\) | |||||||
\(662\) | 21.0755 | 0.819122 | ||||||||
\(663\) | 1.93766 | 0.0752525 | ||||||||
\(664\) | 3.05634 | 0.118609 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18.6911 | 0.724264 | ||||||||
\(667\) | −23.0811 | −0.893704 | ||||||||
\(668\) | 16.4737 | 0.637387 | ||||||||
\(669\) | −0.922181 | −0.0356536 | ||||||||
\(670\) | 6.91446 | 0.267129 | ||||||||
\(671\) | −3.39707 | −0.131142 | ||||||||
\(672\) | −0.701567 | −0.0270635 | ||||||||
\(673\) | 16.1728 | 0.623414 | 0.311707 | − | 0.950178i | \(-0.399099\pi\) | ||||
0.311707 | + | 0.950178i | \(0.399099\pi\) | |||||||
\(674\) | −13.4832 | −0.519353 | ||||||||
\(675\) | 6.83679 | 0.263148 | ||||||||
\(676\) | −5.13568 | −0.197526 | ||||||||
\(677\) | −37.6666 | −1.44765 | −0.723823 | − | 0.689986i | \(-0.757617\pi\) | ||||
−0.723823 | + | 0.689986i | \(0.757617\pi\) | |||||||
\(678\) | −4.74758 | −0.182330 | ||||||||
\(679\) | 33.8663 | 1.29967 | ||||||||
\(680\) | −2.24642 | −0.0861462 | ||||||||
\(681\) | −4.49854 | −0.172384 | ||||||||
\(682\) | −6.85998 | −0.262682 | ||||||||
\(683\) | 33.2423 | 1.27198 | 0.635991 | − | 0.771697i | \(-0.280592\pi\) | ||||
0.635991 | + | 0.771697i | \(0.280592\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.15697 | −0.158830 | ||||||||
\(686\) | 19.0883 | 0.728794 | ||||||||
\(687\) | 3.91239 | 0.149267 | ||||||||
\(688\) | −0.288970 | −0.0110169 | ||||||||
\(689\) | 34.8289 | 1.32688 | ||||||||
\(690\) | 1.14136 | 0.0434508 | ||||||||
\(691\) | 44.4889 | 1.69244 | 0.846219 | − | 0.532835i | \(-0.178873\pi\) | ||||
0.846219 | + | 0.532835i | \(0.178873\pi\) | |||||||
\(692\) | 20.3003 | 0.771702 | ||||||||
\(693\) | 7.47380 | 0.283906 | ||||||||
\(694\) | 15.9885 | 0.606914 | ||||||||
\(695\) | 0.940073 | 0.0356590 | ||||||||
\(696\) | −1.36042 | −0.0515667 | ||||||||
\(697\) | 27.9066 | 1.05704 | ||||||||
\(698\) | 32.0957 | 1.21484 | ||||||||
\(699\) | 6.82920 | 0.258304 | ||||||||
\(700\) | −10.7415 | −0.405989 | ||||||||
\(701\) | 11.6656 | 0.440605 | 0.220303 | − | 0.975432i | \(-0.429296\pi\) | ||||
0.220303 | + | 0.975432i | \(0.429296\pi\) | |||||||
\(702\) | 4.56132 | 0.172156 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −1.14433 | −0.0430981 | ||||||||
\(706\) | −10.1485 | −0.381942 | ||||||||
\(707\) | 28.0427 | 1.05466 | ||||||||
\(708\) | −1.71216 | −0.0643470 | ||||||||
\(709\) | −1.81477 | −0.0681552 | −0.0340776 | − | 0.999419i | \(-0.510849\pi\) | ||||
−0.0340776 | + | 0.999419i | \(0.510849\pi\) | |||||||
\(710\) | 2.42221 | 0.0909040 | ||||||||
\(711\) | −42.4496 | −1.59198 | ||||||||
\(712\) | 0.997910 | 0.0373983 | ||||||||
\(713\) | 31.9524 | 1.19663 | ||||||||
\(714\) | −1.76570 | −0.0660798 | ||||||||
\(715\) | −2.50307 | −0.0936094 | ||||||||
\(716\) | 5.57802 | 0.208460 | ||||||||
\(717\) | 1.18560 | 0.0442770 | ||||||||
\(718\) | 5.98929 | 0.223518 | ||||||||
\(719\) | −43.9083 | −1.63750 | −0.818752 | − | 0.574147i | \(-0.805334\pi\) | ||||
−0.818752 | + | 0.574147i | \(0.805334\pi\) | |||||||
\(720\) | −2.61044 | −0.0972852 | ||||||||
\(721\) | −30.5627 | −1.13821 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.68331 | −0.211365 | ||||||||
\(724\) | 3.25681 | 0.121038 | ||||||||
\(725\) | −20.8290 | −0.773568 | ||||||||
\(726\) | −0.274535 | −0.0101890 | ||||||||
\(727\) | −29.9225 | −1.10976 | −0.554882 | − | 0.831929i | \(-0.687237\pi\) | ||||
−0.554882 | + | 0.831929i | \(0.687237\pi\) | |||||||
\(728\) | −7.16640 | −0.265605 | ||||||||
\(729\) | −23.0148 | −0.852401 | ||||||||
\(730\) | −5.72295 | −0.211816 | ||||||||
\(731\) | −0.727280 | −0.0268994 | ||||||||
\(732\) | 0.932616 | 0.0344705 | ||||||||
\(733\) | 21.2241 | 0.783928 | 0.391964 | − | 0.919980i | \(-0.371796\pi\) | ||||
0.391964 | + | 0.919980i | \(0.371796\pi\) | |||||||
\(734\) | 18.8213 | 0.694707 | ||||||||
\(735\) | −0.115067 | −0.00424432 | ||||||||
\(736\) | 4.65781 | 0.171689 | ||||||||
\(737\) | 7.74670 | 0.285353 | ||||||||
\(738\) | 32.4287 | 1.19372 | ||||||||
\(739\) | 34.7099 | 1.27683 | 0.638413 | − | 0.769694i | \(-0.279591\pi\) | ||||
0.638413 | + | 0.769694i | \(0.279591\pi\) | |||||||
\(740\) | 5.70434 | 0.209696 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −31.7380 | −1.16514 | ||||||||
\(743\) | −13.2728 | −0.486932 | −0.243466 | − | 0.969909i | \(-0.578284\pi\) | ||||
−0.243466 | + | 0.969909i | \(0.578284\pi\) | |||||||
\(744\) | 1.88331 | 0.0690454 | ||||||||
\(745\) | −17.5735 | −0.643842 | ||||||||
\(746\) | 6.91364 | 0.253126 | ||||||||
\(747\) | 8.93866 | 0.327048 | ||||||||
\(748\) | −2.51680 | −0.0920233 | ||||||||
\(749\) | 19.6692 | 0.718695 | ||||||||
\(750\) | 2.25520 | 0.0823482 | ||||||||
\(751\) | 17.9408 | 0.654669 | 0.327335 | − | 0.944909i | \(-0.393850\pi\) | ||||
0.327335 | + | 0.944909i | \(0.393850\pi\) | |||||||
\(752\) | −4.66995 | −0.170296 | ||||||||
\(753\) | −2.50092 | −0.0911386 | ||||||||
\(754\) | −13.8965 | −0.506081 | ||||||||
\(755\) | −5.72671 | −0.208416 | ||||||||
\(756\) | −4.15652 | −0.151171 | ||||||||
\(757\) | −20.3788 | −0.740682 | −0.370341 | − | 0.928896i | \(-0.620759\pi\) | ||||
−0.370341 | + | 0.928896i | \(0.620759\pi\) | |||||||
\(758\) | −22.2824 | −0.809332 | ||||||||
\(759\) | 1.27873 | 0.0464151 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.7074 | 0.569394 | 0.284697 | − | 0.958618i | \(-0.408107\pi\) | ||||
0.284697 | + | 0.958618i | \(0.408107\pi\) | |||||||
\(762\) | −1.21983 | −0.0441898 | ||||||||
\(763\) | −11.0640 | −0.400544 | ||||||||
\(764\) | 16.6232 | 0.601407 | ||||||||
\(765\) | −6.56995 | −0.237537 | ||||||||
\(766\) | 22.3408 | 0.807205 | ||||||||
\(767\) | −17.4895 | −0.631509 | ||||||||
\(768\) | 0.274535 | 0.00990644 | ||||||||
\(769\) | 30.4053 | 1.09644 | 0.548221 | − | 0.836334i | \(-0.315305\pi\) | ||||
0.548221 | + | 0.836334i | \(0.315305\pi\) | |||||||
\(770\) | 2.28093 | 0.0821991 | ||||||||
\(771\) | −2.88230 | −0.103804 | ||||||||
\(772\) | −1.55689 | −0.0560339 | ||||||||
\(773\) | 28.6877 | 1.03182 | 0.515912 | − | 0.856642i | \(-0.327453\pi\) | ||||
0.515912 | + | 0.856642i | \(0.327453\pi\) | |||||||
\(774\) | −0.845130 | −0.0303776 | ||||||||
\(775\) | 28.8347 | 1.03577 | ||||||||
\(776\) | −13.2525 | −0.475736 | ||||||||
\(777\) | 4.48365 | 0.160850 | ||||||||
\(778\) | −25.1591 | −0.901997 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0.687181 | 0.0246050 | ||||||||
\(781\) | 2.71375 | 0.0971057 | ||||||||
\(782\) | 11.7228 | 0.419206 | ||||||||
\(783\) | −8.06000 | −0.288041 | ||||||||
\(784\) | −0.469582 | −0.0167708 | ||||||||
\(785\) | 8.78538 | 0.313564 | ||||||||
\(786\) | −3.53417 | −0.126060 | ||||||||
\(787\) | −42.5311 | −1.51607 | −0.758036 | − | 0.652213i | \(-0.773841\pi\) | ||||
−0.758036 | + | 0.652213i | \(0.773841\pi\) | |||||||
\(788\) | 0.246728 | 0.00878931 | ||||||||
\(789\) | 1.48340 | 0.0528104 | ||||||||
\(790\) | −12.9552 | −0.460926 | ||||||||
\(791\) | 44.1921 | 1.57129 | ||||||||
\(792\) | −2.92463 | −0.103922 | ||||||||
\(793\) | 9.52653 | 0.338297 | ||||||||
\(794\) | −5.11918 | −0.181673 | ||||||||
\(795\) | 3.04334 | 0.107936 | ||||||||
\(796\) | 20.0230 | 0.709696 | ||||||||
\(797\) | 32.8831 | 1.16478 | 0.582390 | − | 0.812909i | \(-0.302118\pi\) | ||||
0.582390 | + | 0.812909i | \(0.302118\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.7533 | −0.415803 | ||||||||
\(800\) | 4.20332 | 0.148610 | ||||||||
\(801\) | 2.91852 | 0.103121 | ||||||||
\(802\) | 3.83325 | 0.135357 | ||||||||
\(803\) | −6.41177 | −0.226267 | ||||||||
\(804\) | −2.12674 | −0.0750044 | ||||||||
\(805\) | −10.6241 | −0.374452 | ||||||||
\(806\) | 19.2377 | 0.677619 | ||||||||
\(807\) | 4.63054 | 0.163003 | ||||||||
\(808\) | −10.9736 | −0.386051 | ||||||||
\(809\) | 22.0675 | 0.775851 | 0.387925 | − | 0.921691i | \(-0.373192\pi\) | ||||
0.387925 | + | 0.921691i | \(0.373192\pi\) | |||||||
\(810\) | −7.43274 | −0.261160 | ||||||||
\(811\) | 26.4855 | 0.930032 | 0.465016 | − | 0.885302i | \(-0.346049\pi\) | ||||
0.465016 | + | 0.885302i | \(0.346049\pi\) | |||||||
\(812\) | 12.6633 | 0.444393 | ||||||||
\(813\) | 5.05632 | 0.177333 | ||||||||
\(814\) | 6.39092 | 0.224002 | ||||||||
\(815\) | −17.1321 | −0.600112 | ||||||||
\(816\) | 0.690951 | 0.0241881 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 4.42842 | 0.154836 | ||||||||
\(819\) | −20.9591 | −0.732369 | ||||||||
\(820\) | 9.89693 | 0.345616 | ||||||||
\(821\) | −33.3961 | −1.16553 | −0.582766 | − | 0.812640i | \(-0.698029\pi\) | ||||
−0.582766 | + | 0.812640i | \(0.698029\pi\) | |||||||
\(822\) | 1.27859 | 0.0445961 | ||||||||
\(823\) | 52.6240 | 1.83436 | 0.917179 | − | 0.398477i | \(-0.130461\pi\) | ||||
0.917179 | + | 0.398477i | \(0.130461\pi\) | |||||||
\(824\) | 11.9597 | 0.416637 | ||||||||
\(825\) | 1.15396 | 0.0401757 | ||||||||
\(826\) | 15.9374 | 0.554533 | ||||||||
\(827\) | 17.2375 | 0.599407 | 0.299704 | − | 0.954032i | \(-0.403112\pi\) | ||||
0.299704 | + | 0.954032i | \(0.403112\pi\) | |||||||
\(828\) | 13.6224 | 0.473410 | ||||||||
\(829\) | −54.9443 | −1.90829 | −0.954147 | − | 0.299339i | \(-0.903234\pi\) | ||||
−0.954147 | + | 0.299339i | \(0.903234\pi\) | |||||||
\(830\) | 2.72799 | 0.0946900 | ||||||||
\(831\) | −5.58660 | −0.193797 | ||||||||
\(832\) | 2.80434 | 0.0972230 | ||||||||
\(833\) | −1.18184 | −0.0409485 | ||||||||
\(834\) | −0.289147 | −0.0100123 | ||||||||
\(835\) | 14.7039 | 0.508850 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.1579 | 0.385673 | ||||||||
\(838\) | 12.2640 | 0.423654 | ||||||||
\(839\) | −27.2997 | −0.942492 | −0.471246 | − | 0.882002i | \(-0.656196\pi\) | ||||
−0.471246 | + | 0.882002i | \(0.656196\pi\) | |||||||
\(840\) | −0.626197 | −0.0216058 | ||||||||
\(841\) | −4.44441 | −0.153256 | ||||||||
\(842\) | 29.8939 | 1.03021 | ||||||||
\(843\) | 5.19457 | 0.178910 | ||||||||
\(844\) | 13.1424 | 0.452380 | ||||||||
\(845\) | −4.58395 | −0.157693 | ||||||||
\(846\) | −13.6579 | −0.469567 | ||||||||
\(847\) | 2.55547 | 0.0878069 | ||||||||
\(848\) | 12.4197 | 0.426493 | ||||||||
\(849\) | 3.92944 | 0.134858 | ||||||||
\(850\) | 10.5789 | 0.362854 | ||||||||
\(851\) | −29.7677 | −1.02042 | ||||||||
\(852\) | −0.745021 | −0.0255240 | ||||||||
\(853\) | 23.3089 | 0.798082 | 0.399041 | − | 0.916933i | \(-0.369343\pi\) | ||||
0.399041 | + | 0.916933i | \(0.369343\pi\) | |||||||
\(854\) | −8.68110 | −0.297061 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.69689 | −0.263074 | ||||||||
\(857\) | −35.3421 | −1.20726 | −0.603632 | − | 0.797263i | \(-0.706281\pi\) | ||||
−0.603632 | + | 0.797263i | \(0.706281\pi\) | |||||||
\(858\) | 0.769891 | 0.0262836 | ||||||||
\(859\) | 4.57419 | 0.156069 | 0.0780347 | − | 0.996951i | \(-0.475136\pi\) | ||||
0.0780347 | + | 0.996951i | \(0.475136\pi\) | |||||||
\(860\) | −0.257926 | −0.00879519 | ||||||||
\(861\) | 7.77906 | 0.265110 | ||||||||
\(862\) | −17.0662 | −0.581278 | ||||||||
\(863\) | 3.06254 | 0.104250 | 0.0521250 | − | 0.998641i | \(-0.483401\pi\) | ||||
0.0521250 | + | 0.998641i | \(0.483401\pi\) | |||||||
\(864\) | 1.62652 | 0.0553354 | ||||||||
\(865\) | 18.1194 | 0.616080 | ||||||||
\(866\) | −12.1572 | −0.413118 | ||||||||
\(867\) | −2.92812 | −0.0994441 | ||||||||
\(868\) | −17.5304 | −0.595022 | ||||||||
\(869\) | −14.5145 | −0.492371 | ||||||||
\(870\) | −1.21427 | −0.0411676 | ||||||||
\(871\) | −21.7244 | −0.736102 | ||||||||
\(872\) | 4.32954 | 0.146617 | ||||||||
\(873\) | −38.7586 | −1.31178 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −20.9922 | −0.709664 | ||||||||
\(876\) | 1.76026 | 0.0594736 | ||||||||
\(877\) | 18.9114 | 0.638591 | 0.319296 | − | 0.947655i | \(-0.396554\pi\) | ||||
0.319296 | + | 0.947655i | \(0.396554\pi\) | |||||||
\(878\) | −35.3669 | −1.19358 | ||||||||
\(879\) | −2.13824 | −0.0721210 | ||||||||
\(880\) | −0.892569 | −0.0300885 | ||||||||
\(881\) | 21.1597 | 0.712889 | 0.356445 | − | 0.934316i | \(-0.383989\pi\) | ||||
0.356445 | + | 0.934316i | \(0.383989\pi\) | |||||||
\(882\) | −1.37335 | −0.0462432 | ||||||||
\(883\) | 45.7789 | 1.54058 | 0.770292 | − | 0.637691i | \(-0.220110\pi\) | ||||
0.770292 | + | 0.637691i | \(0.220110\pi\) | |||||||
\(884\) | 7.05797 | 0.237385 | ||||||||
\(885\) | −1.52822 | −0.0513707 | ||||||||
\(886\) | 34.1995 | 1.14896 | ||||||||
\(887\) | 9.25059 | 0.310604 | 0.155302 | − | 0.987867i | \(-0.450365\pi\) | ||||
0.155302 | + | 0.987867i | \(0.450365\pi\) | |||||||
\(888\) | −1.75453 | −0.0588783 | ||||||||
\(889\) | 11.3546 | 0.380820 | ||||||||
\(890\) | 0.890704 | 0.0298565 | ||||||||
\(891\) | −8.32735 | −0.278977 | ||||||||
\(892\) | −3.35906 | −0.112470 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 5.40523 | 0.180778 | ||||||||
\(895\) | 4.97877 | 0.166422 | ||||||||
\(896\) | −2.55547 | −0.0853722 | ||||||||
\(897\) | −3.58600 | −0.119733 | ||||||||
\(898\) | −33.9412 | −1.13263 | ||||||||
\(899\) | −33.9936 | −1.13375 | ||||||||
\(900\) | 12.2932 | 0.409772 | ||||||||
\(901\) | 31.2578 | 1.04135 | ||||||||
\(902\) | 11.0881 | 0.369194 | ||||||||
\(903\) | −0.202732 | −0.00674649 | ||||||||
\(904\) | −17.2931 | −0.575161 | ||||||||
\(905\) | 2.90693 | 0.0966296 | ||||||||
\(906\) | 1.76141 | 0.0585191 | ||||||||
\(907\) | −1.43404 | −0.0476167 | −0.0238083 | − | 0.999717i | \(-0.507579\pi\) | ||||
−0.0238083 | + | 0.999717i | \(0.507579\pi\) | |||||||
\(908\) | −16.3860 | −0.543789 | ||||||||
\(909\) | −32.0938 | −1.06448 | ||||||||
\(910\) | −6.39651 | −0.212042 | ||||||||
\(911\) | −55.0525 | −1.82397 | −0.911985 | − | 0.410223i | \(-0.865451\pi\) | ||||
−0.911985 | + | 0.410223i | \(0.865451\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.05634 | 0.101150 | ||||||||
\(914\) | −23.5228 | −0.778066 | ||||||||
\(915\) | 0.832424 | 0.0275191 | ||||||||
\(916\) | 14.2509 | 0.470864 | ||||||||
\(917\) | 32.8973 | 1.08636 | ||||||||
\(918\) | 4.09363 | 0.135110 | ||||||||
\(919\) | 29.9768 | 0.988842 | 0.494421 | − | 0.869223i | \(-0.335380\pi\) | ||||
0.494421 | + | 0.869223i | \(0.335380\pi\) | |||||||
\(920\) | 4.15742 | 0.137066 | ||||||||
\(921\) | 2.21918 | 0.0731243 | ||||||||
\(922\) | −27.9047 | −0.918994 | ||||||||
\(923\) | −7.61028 | −0.250496 | ||||||||
\(924\) | −0.701567 | −0.0230798 | ||||||||
\(925\) | −26.8631 | −0.883252 | ||||||||
\(926\) | 30.3458 | 0.997225 | ||||||||
\(927\) | 34.9778 | 1.14882 | ||||||||
\(928\) | −4.95536 | −0.162668 | ||||||||
\(929\) | 13.6036 | 0.446318 | 0.223159 | − | 0.974782i | \(-0.428363\pi\) | ||||
0.223159 | + | 0.974782i | \(0.428363\pi\) | |||||||
\(930\) | 1.68098 | 0.0551216 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 24.8755 | 0.814823 | ||||||||
\(933\) | 6.70742 | 0.219591 | ||||||||
\(934\) | −24.6301 | −0.805923 | ||||||||
\(935\) | −2.24642 | −0.0734658 | ||||||||
\(936\) | 8.20166 | 0.268080 | ||||||||
\(937\) | 12.7388 | 0.416159 | 0.208079 | − | 0.978112i | \(-0.433279\pi\) | ||||
0.208079 | + | 0.978112i | \(0.433279\pi\) | |||||||
\(938\) | 19.7964 | 0.646377 | ||||||||
\(939\) | −2.87542 | −0.0938358 | ||||||||
\(940\) | −4.16825 | −0.135953 | ||||||||
\(941\) | 12.5791 | 0.410068 | 0.205034 | − | 0.978755i | \(-0.434270\pi\) | ||||
0.205034 | + | 0.978755i | \(0.434270\pi\) | |||||||
\(942\) | −2.70220 | −0.0880423 | ||||||||
\(943\) | −51.6464 | −1.68184 | ||||||||
\(944\) | −6.23658 | −0.202983 | ||||||||
\(945\) | −3.70999 | −0.120686 | ||||||||
\(946\) | −0.288970 | −0.00939522 | ||||||||
\(947\) | −58.6889 | −1.90713 | −0.953567 | − | 0.301181i | \(-0.902619\pi\) | ||||
−0.953567 | + | 0.301181i | \(0.902619\pi\) | |||||||
\(948\) | 3.98475 | 0.129419 | ||||||||
\(949\) | 17.9808 | 0.583681 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.10205 | −0.165445 | ||||||||
\(952\) | −6.43160 | −0.208449 | ||||||||
\(953\) | 22.6435 | 0.733494 | 0.366747 | − | 0.930321i | \(-0.380471\pi\) | ||||
0.366747 | + | 0.930321i | \(0.380471\pi\) | |||||||
\(954\) | 36.3229 | 1.17600 | ||||||||
\(955\) | 14.8374 | 0.480127 | ||||||||
\(956\) | 4.31856 | 0.139672 | ||||||||
\(957\) | −1.36042 | −0.0439762 | ||||||||
\(958\) | 29.0486 | 0.938517 | ||||||||
\(959\) | −11.9016 | −0.384322 | ||||||||
\(960\) | 0.245042 | 0.00790869 | ||||||||
\(961\) | 16.0593 | 0.518041 | ||||||||
\(962\) | −17.9223 | −0.577838 | ||||||||
\(963\) | −22.5106 | −0.725392 | ||||||||
\(964\) | −20.7016 | −0.666753 | ||||||||
\(965\) | −1.38964 | −0.0447340 | ||||||||
\(966\) | 3.26776 | 0.105139 | ||||||||
\(967\) | 38.2819 | 1.23106 | 0.615531 | − | 0.788112i | \(-0.288941\pi\) | ||||
0.615531 | + | 0.788112i | \(0.288941\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.8288 | −0.379798 | ||||||||
\(971\) | −21.9845 | −0.705516 | −0.352758 | − | 0.935715i | \(-0.614756\pi\) | ||||
−0.352758 | + | 0.935715i | \(0.614756\pi\) | |||||||
\(972\) | 7.16572 | 0.229840 | ||||||||
\(973\) | 2.69147 | 0.0862847 | ||||||||
\(974\) | −9.40209 | −0.301262 | ||||||||
\(975\) | −3.23610 | −0.103638 | ||||||||
\(976\) | 3.39707 | 0.108737 | ||||||||
\(977\) | −22.0839 | −0.706527 | −0.353264 | − | 0.935524i | \(-0.614928\pi\) | ||||
−0.353264 | + | 0.935524i | \(0.614928\pi\) | |||||||
\(978\) | 5.26948 | 0.168499 | ||||||||
\(979\) | 0.997910 | 0.0318934 | ||||||||
\(980\) | −0.419134 | −0.0133888 | ||||||||
\(981\) | 12.6623 | 0.404276 | ||||||||
\(982\) | −17.5251 | −0.559247 | ||||||||
\(983\) | 1.58991 | 0.0507102 | 0.0253551 | − | 0.999679i | \(-0.491928\pi\) | ||||
0.0253551 | + | 0.999679i | \(0.491928\pi\) | |||||||
\(984\) | −3.04408 | −0.0970419 | ||||||||
\(985\) | 0.220222 | 0.00701685 | ||||||||
\(986\) | −12.4717 | −0.397178 | ||||||||
\(987\) | −3.27628 | −0.104285 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.34597 | 0.0427992 | ||||||||
\(990\) | −2.61044 | −0.0829651 | ||||||||
\(991\) | 18.1634 | 0.576979 | 0.288490 | − | 0.957483i | \(-0.406847\pi\) | ||||
0.288490 | + | 0.957483i | \(0.406847\pi\) | |||||||
\(992\) | 6.85998 | 0.217804 | ||||||||
\(993\) | −5.78597 | −0.183612 | ||||||||
\(994\) | 6.93491 | 0.219962 | ||||||||
\(995\) | 17.8719 | 0.566577 | ||||||||
\(996\) | −0.839073 | −0.0265870 | ||||||||
\(997\) | −54.3199 | −1.72033 | −0.860164 | − | 0.510018i | \(-0.829639\pi\) | ||||
−0.860164 | + | 0.510018i | \(0.829639\pi\) | |||||||
\(998\) | −16.0414 | −0.507781 | ||||||||
\(999\) | −10.3950 | −0.328882 |
(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 | 7942.2.a.bo.1.3 | ✓ | 8 | |
19.18 | odd | 2 | 7942.2.a.bp.1.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7942.2.a.bo.1.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
7942.2.a.bp.1.6 | yes | 8 | 19.18 | odd | 2 |