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: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) 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 | ||||||||
\(3\) | −1.73205 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.73205 | 0.707107 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.73205 | −0.500000 | ||||||||
\(13\) | 1.73205 | 0.480384 | 0.240192 | − | 0.970725i | \(-0.422790\pi\) | ||||
0.240192 | + | 0.970725i | \(0.422790\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.73205 | 0.447214 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.26795 | 0.307523 | 0.153761 | − | 0.988108i | \(-0.450861\pi\) | ||||
0.153761 | + | 0.988108i | \(0.450861\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.73205 | −0.397360 | −0.198680 | − | 0.980064i | \(-0.563665\pi\) | ||||
−0.198680 | + | 0.980064i | \(0.563665\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 1.73205 | 0.377964 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.46410 | 0.513801 | 0.256900 | − | 0.966438i | \(-0.417299\pi\) | ||||
0.256900 | + | 0.966438i | \(0.417299\pi\) | |||||||
\(24\) | 1.73205 | 0.353553 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.73205 | −0.339683 | ||||||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 2.53590 | 0.470905 | 0.235452 | − | 0.971886i | \(-0.424343\pi\) | ||||
0.235452 | + | 0.971886i | \(0.424343\pi\) | |||||||
\(30\) | −1.73205 | −0.316228 | ||||||||
\(31\) | −3.26795 | −0.586941 | −0.293471 | − | 0.955968i | \(-0.594810\pi\) | ||||
−0.293471 | + | 0.955968i | \(0.594810\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.26795 | −0.217451 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.46410 | −1.22709 | −0.613545 | − | 0.789659i | \(-0.710257\pi\) | ||||
−0.613545 | + | 0.789659i | \(0.710257\pi\) | |||||||
\(38\) | 1.73205 | 0.280976 | ||||||||
\(39\) | −3.00000 | −0.480384 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −6.73205 | −1.05137 | −0.525685 | − | 0.850679i | \(-0.676191\pi\) | ||||
−0.525685 | + | 0.850679i | \(0.676191\pi\) | |||||||
\(42\) | −1.73205 | −0.267261 | ||||||||
\(43\) | −7.66025 | −1.16818 | −0.584089 | − | 0.811690i | \(-0.698548\pi\) | ||||
−0.584089 | + | 0.811690i | \(0.698548\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.46410 | −0.363312 | ||||||||
\(47\) | −2.73205 | −0.398511 | −0.199255 | − | 0.979948i | \(-0.563852\pi\) | ||||
−0.199255 | + | 0.979948i | \(0.563852\pi\) | |||||||
\(48\) | −1.73205 | −0.250000 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −2.19615 | −0.307523 | ||||||||
\(52\) | 1.73205 | 0.240192 | ||||||||
\(53\) | −1.26795 | −0.174166 | −0.0870831 | − | 0.996201i | \(-0.527755\pi\) | ||||
−0.0870831 | + | 0.996201i | \(0.527755\pi\) | |||||||
\(54\) | −5.19615 | −0.707107 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 3.00000 | 0.397360 | ||||||||
\(58\) | −2.53590 | −0.332980 | ||||||||
\(59\) | −1.00000 | −0.130189 | −0.0650945 | − | 0.997879i | \(-0.520735\pi\) | ||||
−0.0650945 | + | 0.997879i | \(0.520735\pi\) | |||||||
\(60\) | 1.73205 | 0.223607 | ||||||||
\(61\) | 4.00000 | 0.512148 | 0.256074 | − | 0.966657i | \(-0.417571\pi\) | ||||
0.256074 | + | 0.966657i | \(0.417571\pi\) | |||||||
\(62\) | 3.26795 | 0.415030 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.73205 | −0.214834 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.1962 | 1.73434 | 0.867168 | − | 0.498016i | \(-0.165938\pi\) | ||||
0.867168 | + | 0.498016i | \(0.165938\pi\) | |||||||
\(68\) | 1.26795 | 0.153761 | ||||||||
\(69\) | −4.26795 | −0.513801 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | 2.92820 | 0.347514 | 0.173757 | − | 0.984789i | \(-0.444409\pi\) | ||||
0.173757 | + | 0.984789i | \(0.444409\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.66025 | 1.13065 | 0.565324 | − | 0.824869i | \(-0.308751\pi\) | ||||
0.565324 | + | 0.824869i | \(0.308751\pi\) | |||||||
\(74\) | 7.46410 | 0.867684 | ||||||||
\(75\) | −1.73205 | −0.200000 | ||||||||
\(76\) | −1.73205 | −0.198680 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.00000 | 0.339683 | ||||||||
\(79\) | −0.0717968 | −0.00807777 | −0.00403888 | − | 0.999992i | \(-0.501286\pi\) | ||||
−0.00403888 | + | 0.999992i | \(0.501286\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 6.73205 | 0.743431 | ||||||||
\(83\) | 11.9282 | 1.30929 | 0.654645 | − | 0.755936i | \(-0.272818\pi\) | ||||
0.654645 | + | 0.755936i | \(0.272818\pi\) | |||||||
\(84\) | 1.73205 | 0.188982 | ||||||||
\(85\) | −1.26795 | −0.137528 | ||||||||
\(86\) | 7.66025 | 0.826026 | ||||||||
\(87\) | −4.39230 | −0.470905 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.73205 | −0.501596 | −0.250798 | − | 0.968039i | \(-0.580693\pi\) | ||||
−0.250798 | + | 0.968039i | \(0.580693\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.73205 | −0.181568 | ||||||||
\(92\) | 2.46410 | 0.256900 | ||||||||
\(93\) | 5.66025 | 0.586941 | ||||||||
\(94\) | 2.73205 | 0.281790 | ||||||||
\(95\) | 1.73205 | 0.177705 | ||||||||
\(96\) | 1.73205 | 0.176777 | ||||||||
\(97\) | 1.46410 | 0.148657 | 0.0743285 | − | 0.997234i | \(-0.476319\pi\) | ||||
0.0743285 | + | 0.997234i | \(0.476319\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 7.92820 | 0.788886 | 0.394443 | − | 0.918920i | \(-0.370938\pi\) | ||||
0.394443 | + | 0.918920i | \(0.370938\pi\) | |||||||
\(102\) | 2.19615 | 0.217451 | ||||||||
\(103\) | 1.80385 | 0.177738 | 0.0888692 | − | 0.996043i | \(-0.471675\pi\) | ||||
0.0888692 | + | 0.996043i | \(0.471675\pi\) | |||||||
\(104\) | −1.73205 | −0.169842 | ||||||||
\(105\) | −1.73205 | −0.169031 | ||||||||
\(106\) | 1.26795 | 0.123154 | ||||||||
\(107\) | 0.535898 | 0.0518073 | 0.0259036 | − | 0.999664i | \(-0.491754\pi\) | ||||
0.0259036 | + | 0.999664i | \(0.491754\pi\) | |||||||
\(108\) | 5.19615 | 0.500000 | ||||||||
\(109\) | 0.196152 | 0.0187880 | 0.00939400 | − | 0.999956i | \(-0.497010\pi\) | ||||
0.00939400 | + | 0.999956i | \(0.497010\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.9282 | 1.22709 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −4.66025 | −0.438400 | −0.219200 | − | 0.975680i | \(-0.570345\pi\) | ||||
−0.219200 | + | 0.975680i | \(0.570345\pi\) | |||||||
\(114\) | −3.00000 | −0.280976 | ||||||||
\(115\) | −2.46410 | −0.229779 | ||||||||
\(116\) | 2.53590 | 0.235452 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | −1.26795 | −0.116233 | ||||||||
\(120\) | −1.73205 | −0.158114 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −4.00000 | −0.362143 | ||||||||
\(123\) | 11.6603 | 1.05137 | ||||||||
\(124\) | −3.26795 | −0.293471 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.1962 | 1.17097 | 0.585485 | − | 0.810684i | \(-0.300904\pi\) | ||||
0.585485 | + | 0.810684i | \(0.300904\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 13.2679 | 1.16818 | ||||||||
\(130\) | 1.73205 | 0.151911 | ||||||||
\(131\) | 4.26795 | 0.372892 | 0.186446 | − | 0.982465i | \(-0.440303\pi\) | ||||
0.186446 | + | 0.982465i | \(0.440303\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.73205 | 0.150188 | ||||||||
\(134\) | −14.1962 | −1.22636 | ||||||||
\(135\) | −5.19615 | −0.447214 | ||||||||
\(136\) | −1.26795 | −0.108726 | ||||||||
\(137\) | 12.1244 | 1.03585 | 0.517927 | − | 0.855425i | \(-0.326704\pi\) | ||||
0.517927 | + | 0.855425i | \(0.326704\pi\) | |||||||
\(138\) | 4.26795 | 0.363312 | ||||||||
\(139\) | 1.33975 | 0.113636 | 0.0568179 | − | 0.998385i | \(-0.481905\pi\) | ||||
0.0568179 | + | 0.998385i | \(0.481905\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 4.73205 | 0.398511 | ||||||||
\(142\) | −2.92820 | −0.245729 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.53590 | −0.210595 | ||||||||
\(146\) | −9.66025 | −0.799488 | ||||||||
\(147\) | −1.73205 | −0.142857 | ||||||||
\(148\) | −7.46410 | −0.613545 | ||||||||
\(149\) | 0.928203 | 0.0760414 | 0.0380207 | − | 0.999277i | \(-0.487895\pi\) | ||||
0.0380207 | + | 0.999277i | \(0.487895\pi\) | |||||||
\(150\) | 1.73205 | 0.141421 | ||||||||
\(151\) | −13.0000 | −1.05792 | −0.528962 | − | 0.848645i | \(-0.677419\pi\) | ||||
−0.528962 | + | 0.848645i | \(0.677419\pi\) | |||||||
\(152\) | 1.73205 | 0.140488 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.26795 | 0.262488 | ||||||||
\(156\) | −3.00000 | −0.240192 | ||||||||
\(157\) | −10.4641 | −0.835126 | −0.417563 | − | 0.908648i | \(-0.637116\pi\) | ||||
−0.417563 | + | 0.908648i | \(0.637116\pi\) | |||||||
\(158\) | 0.0717968 | 0.00571184 | ||||||||
\(159\) | 2.19615 | 0.174166 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −2.46410 | −0.194198 | ||||||||
\(162\) | 9.00000 | 0.707107 | ||||||||
\(163\) | 8.92820 | 0.699311 | 0.349655 | − | 0.936878i | \(-0.386299\pi\) | ||||
0.349655 | + | 0.936878i | \(0.386299\pi\) | |||||||
\(164\) | −6.73205 | −0.525685 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.9282 | −0.925808 | ||||||||
\(167\) | 6.73205 | 0.520942 | 0.260471 | − | 0.965482i | \(-0.416122\pi\) | ||||
0.260471 | + | 0.965482i | \(0.416122\pi\) | |||||||
\(168\) | −1.73205 | −0.133631 | ||||||||
\(169\) | −10.0000 | −0.769231 | ||||||||
\(170\) | 1.26795 | 0.0972473 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.66025 | −0.584089 | ||||||||
\(173\) | −10.0000 | −0.760286 | −0.380143 | − | 0.924928i | \(-0.624125\pi\) | ||||
−0.380143 | + | 0.924928i | \(0.624125\pi\) | |||||||
\(174\) | 4.39230 | 0.332980 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.73205 | 0.130189 | ||||||||
\(178\) | 4.73205 | 0.354682 | ||||||||
\(179\) | −9.12436 | −0.681986 | −0.340993 | − | 0.940066i | \(-0.610763\pi\) | ||||
−0.340993 | + | 0.940066i | \(0.610763\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.12436 | −0.306561 | −0.153280 | − | 0.988183i | \(-0.548984\pi\) | ||||
−0.153280 | + | 0.988183i | \(0.548984\pi\) | |||||||
\(182\) | 1.73205 | 0.128388 | ||||||||
\(183\) | −6.92820 | −0.512148 | ||||||||
\(184\) | −2.46410 | −0.181656 | ||||||||
\(185\) | 7.46410 | 0.548772 | ||||||||
\(186\) | −5.66025 | −0.415030 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2.73205 | −0.199255 | ||||||||
\(189\) | −5.19615 | −0.377964 | ||||||||
\(190\) | −1.73205 | −0.125656 | ||||||||
\(191\) | −18.2679 | −1.32182 | −0.660911 | − | 0.750464i | \(-0.729830\pi\) | ||||
−0.660911 | + | 0.750464i | \(0.729830\pi\) | |||||||
\(192\) | −1.73205 | −0.125000 | ||||||||
\(193\) | 21.7846 | 1.56809 | 0.784045 | − | 0.620704i | \(-0.213153\pi\) | ||||
0.784045 | + | 0.620704i | \(0.213153\pi\) | |||||||
\(194\) | −1.46410 | −0.105116 | ||||||||
\(195\) | 3.00000 | 0.214834 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −24.0000 | −1.70993 | −0.854965 | − | 0.518686i | \(-0.826421\pi\) | ||||
−0.854965 | + | 0.518686i | \(0.826421\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.39230 | 0.594915 | 0.297457 | − | 0.954735i | \(-0.403861\pi\) | ||||
0.297457 | + | 0.954735i | \(0.403861\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −24.5885 | −1.73434 | ||||||||
\(202\) | −7.92820 | −0.557826 | ||||||||
\(203\) | −2.53590 | −0.177985 | ||||||||
\(204\) | −2.19615 | −0.153761 | ||||||||
\(205\) | 6.73205 | 0.470187 | ||||||||
\(206\) | −1.80385 | −0.125680 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.73205 | 0.120096 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.73205 | 0.119523 | ||||||||
\(211\) | 1.46410 | 0.100793 | 0.0503965 | − | 0.998729i | \(-0.483952\pi\) | ||||
0.0503965 | + | 0.998729i | \(0.483952\pi\) | |||||||
\(212\) | −1.26795 | −0.0870831 | ||||||||
\(213\) | −5.07180 | −0.347514 | ||||||||
\(214\) | −0.535898 | −0.0366333 | ||||||||
\(215\) | 7.66025 | 0.522425 | ||||||||
\(216\) | −5.19615 | −0.353553 | ||||||||
\(217\) | 3.26795 | 0.221843 | ||||||||
\(218\) | −0.196152 | −0.0132851 | ||||||||
\(219\) | −16.7321 | −1.13065 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.19615 | 0.147729 | ||||||||
\(222\) | −12.9282 | −0.867684 | ||||||||
\(223\) | 11.1244 | 0.744942 | 0.372471 | − | 0.928044i | \(-0.378511\pi\) | ||||
0.372471 | + | 0.928044i | \(0.378511\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.66025 | 0.309995 | ||||||||
\(227\) | 7.46410 | 0.495410 | 0.247705 | − | 0.968836i | \(-0.420324\pi\) | ||||
0.247705 | + | 0.968836i | \(0.420324\pi\) | |||||||
\(228\) | 3.00000 | 0.198680 | ||||||||
\(229\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(230\) | 2.46410 | 0.162478 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.53590 | −0.166490 | ||||||||
\(233\) | 22.8564 | 1.49737 | 0.748686 | − | 0.662924i | \(-0.230685\pi\) | ||||
0.748686 | + | 0.662924i | \(0.230685\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.73205 | 0.178219 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | 0.124356 | 0.00807777 | ||||||||
\(238\) | 1.26795 | 0.0821889 | ||||||||
\(239\) | 2.46410 | 0.159389 | 0.0796947 | − | 0.996819i | \(-0.474605\pi\) | ||||
0.0796947 | + | 0.996819i | \(0.474605\pi\) | |||||||
\(240\) | 1.73205 | 0.111803 | ||||||||
\(241\) | 10.9282 | 0.703947 | 0.351974 | − | 0.936010i | \(-0.385511\pi\) | ||||
0.351974 | + | 0.936010i | \(0.385511\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.00000 | 0.256074 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −11.6603 | −0.743431 | ||||||||
\(247\) | −3.00000 | −0.190885 | ||||||||
\(248\) | 3.26795 | 0.207515 | ||||||||
\(249\) | −20.6603 | −1.30929 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −10.3923 | −0.655956 | −0.327978 | − | 0.944685i | \(-0.606367\pi\) | ||||
−0.327978 | + | 0.944685i | \(0.606367\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −13.1962 | −0.828000 | ||||||||
\(255\) | 2.19615 | 0.137528 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.2679 | −1.20190 | −0.600951 | − | 0.799286i | \(-0.705211\pi\) | ||||
−0.600951 | + | 0.799286i | \(0.705211\pi\) | |||||||
\(258\) | −13.2679 | −0.826026 | ||||||||
\(259\) | 7.46410 | 0.463797 | ||||||||
\(260\) | −1.73205 | −0.107417 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.26795 | −0.263675 | ||||||||
\(263\) | 17.7321 | 1.09341 | 0.546703 | − | 0.837327i | \(-0.315883\pi\) | ||||
0.546703 | + | 0.837327i | \(0.315883\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.26795 | 0.0778895 | ||||||||
\(266\) | −1.73205 | −0.106199 | ||||||||
\(267\) | 8.19615 | 0.501596 | ||||||||
\(268\) | 14.1962 | 0.867168 | ||||||||
\(269\) | 16.5167 | 1.00704 | 0.503519 | − | 0.863984i | \(-0.332038\pi\) | ||||
0.503519 | + | 0.863984i | \(0.332038\pi\) | |||||||
\(270\) | 5.19615 | 0.316228 | ||||||||
\(271\) | 32.3923 | 1.96769 | 0.983846 | − | 0.179016i | \(-0.0572913\pi\) | ||||
0.983846 | + | 0.179016i | \(0.0572913\pi\) | |||||||
\(272\) | 1.26795 | 0.0768807 | ||||||||
\(273\) | 3.00000 | 0.181568 | ||||||||
\(274\) | −12.1244 | −0.732459 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.26795 | −0.256900 | ||||||||
\(277\) | −4.58846 | −0.275694 | −0.137847 | − | 0.990454i | \(-0.544018\pi\) | ||||
−0.137847 | + | 0.990454i | \(0.544018\pi\) | |||||||
\(278\) | −1.33975 | −0.0803526 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −7.73205 | −0.461255 | −0.230628 | − | 0.973042i | \(-0.574078\pi\) | ||||
−0.230628 | + | 0.973042i | \(0.574078\pi\) | |||||||
\(282\) | −4.73205 | −0.281790 | ||||||||
\(283\) | 17.7846 | 1.05719 | 0.528593 | − | 0.848876i | \(-0.322720\pi\) | ||||
0.528593 | + | 0.848876i | \(0.322720\pi\) | |||||||
\(284\) | 2.92820 | 0.173757 | ||||||||
\(285\) | −3.00000 | −0.177705 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.73205 | 0.397380 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.3923 | −0.905430 | ||||||||
\(290\) | 2.53590 | 0.148913 | ||||||||
\(291\) | −2.53590 | −0.148657 | ||||||||
\(292\) | 9.66025 | 0.565324 | ||||||||
\(293\) | 5.33975 | 0.311951 | 0.155976 | − | 0.987761i | \(-0.450148\pi\) | ||||
0.155976 | + | 0.987761i | \(0.450148\pi\) | |||||||
\(294\) | 1.73205 | 0.101015 | ||||||||
\(295\) | 1.00000 | 0.0582223 | ||||||||
\(296\) | 7.46410 | 0.433842 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.928203 | −0.0537694 | ||||||||
\(299\) | 4.26795 | 0.246822 | ||||||||
\(300\) | −1.73205 | −0.100000 | ||||||||
\(301\) | 7.66025 | 0.441530 | ||||||||
\(302\) | 13.0000 | 0.748066 | ||||||||
\(303\) | −13.7321 | −0.788886 | ||||||||
\(304\) | −1.73205 | −0.0993399 | ||||||||
\(305\) | −4.00000 | −0.229039 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.07180 | −0.175317 | −0.0876584 | − | 0.996151i | \(-0.527938\pi\) | ||||
−0.0876584 | + | 0.996151i | \(0.527938\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.12436 | −0.177738 | ||||||||
\(310\) | −3.26795 | −0.185607 | ||||||||
\(311\) | −32.1962 | −1.82568 | −0.912838 | − | 0.408322i | \(-0.866114\pi\) | ||||
−0.912838 | + | 0.408322i | \(0.866114\pi\) | |||||||
\(312\) | 3.00000 | 0.169842 | ||||||||
\(313\) | −16.5359 | −0.934664 | −0.467332 | − | 0.884082i | \(-0.654785\pi\) | ||||
−0.467332 | + | 0.884082i | \(0.654785\pi\) | |||||||
\(314\) | 10.4641 | 0.590523 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.0717968 | −0.00403888 | ||||||||
\(317\) | 21.6603 | 1.21656 | 0.608281 | − | 0.793722i | \(-0.291860\pi\) | ||||
0.608281 | + | 0.793722i | \(0.291860\pi\) | |||||||
\(318\) | −2.19615 | −0.123154 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −0.928203 | −0.0518073 | ||||||||
\(322\) | 2.46410 | 0.137319 | ||||||||
\(323\) | −2.19615 | −0.122197 | ||||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 1.73205 | 0.0960769 | ||||||||
\(326\) | −8.92820 | −0.494487 | ||||||||
\(327\) | −0.339746 | −0.0187880 | ||||||||
\(328\) | 6.73205 | 0.371715 | ||||||||
\(329\) | 2.73205 | 0.150623 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.80385 | −0.0991484 | −0.0495742 | − | 0.998770i | \(-0.515786\pi\) | ||||
−0.0495742 | + | 0.998770i | \(0.515786\pi\) | |||||||
\(332\) | 11.9282 | 0.654645 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.73205 | −0.368361 | ||||||||
\(335\) | −14.1962 | −0.775619 | ||||||||
\(336\) | 1.73205 | 0.0944911 | ||||||||
\(337\) | −15.7846 | −0.859842 | −0.429921 | − | 0.902866i | \(-0.641459\pi\) | ||||
−0.429921 | + | 0.902866i | \(0.641459\pi\) | |||||||
\(338\) | 10.0000 | 0.543928 | ||||||||
\(339\) | 8.07180 | 0.438400 | ||||||||
\(340\) | −1.26795 | −0.0687642 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 7.66025 | 0.413013 | ||||||||
\(345\) | 4.26795 | 0.229779 | ||||||||
\(346\) | 10.0000 | 0.537603 | ||||||||
\(347\) | −8.53590 | −0.458231 | −0.229116 | − | 0.973399i | \(-0.573583\pi\) | ||||
−0.229116 | + | 0.973399i | \(0.573583\pi\) | |||||||
\(348\) | −4.39230 | −0.235452 | ||||||||
\(349\) | −3.00000 | −0.160586 | −0.0802932 | − | 0.996771i | \(-0.525586\pi\) | ||||
−0.0802932 | + | 0.996771i | \(0.525586\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 9.00000 | 0.480384 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.66025 | 0.407714 | 0.203857 | − | 0.979001i | \(-0.434652\pi\) | ||||
0.203857 | + | 0.979001i | \(0.434652\pi\) | |||||||
\(354\) | −1.73205 | −0.0920575 | ||||||||
\(355\) | −2.92820 | −0.155413 | ||||||||
\(356\) | −4.73205 | −0.250798 | ||||||||
\(357\) | 2.19615 | 0.116233 | ||||||||
\(358\) | 9.12436 | 0.482237 | ||||||||
\(359\) | −14.0000 | −0.738892 | −0.369446 | − | 0.929252i | \(-0.620452\pi\) | ||||
−0.369446 | + | 0.929252i | \(0.620452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.0000 | −0.842105 | ||||||||
\(362\) | 4.12436 | 0.216771 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.73205 | −0.0907841 | ||||||||
\(365\) | −9.66025 | −0.505641 | ||||||||
\(366\) | 6.92820 | 0.362143 | ||||||||
\(367\) | −4.33975 | −0.226533 | −0.113266 | − | 0.993565i | \(-0.536131\pi\) | ||||
−0.113266 | + | 0.993565i | \(0.536131\pi\) | |||||||
\(368\) | 2.46410 | 0.128450 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.46410 | −0.388040 | ||||||||
\(371\) | 1.26795 | 0.0658286 | ||||||||
\(372\) | 5.66025 | 0.293471 | ||||||||
\(373\) | −12.9282 | −0.669397 | −0.334698 | − | 0.942325i | \(-0.608634\pi\) | ||||
−0.334698 | + | 0.942325i | \(0.608634\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.73205 | 0.0894427 | ||||||||
\(376\) | 2.73205 | 0.140895 | ||||||||
\(377\) | 4.39230 | 0.226215 | ||||||||
\(378\) | 5.19615 | 0.267261 | ||||||||
\(379\) | −6.39230 | −0.328351 | −0.164175 | − | 0.986431i | \(-0.552496\pi\) | ||||
−0.164175 | + | 0.986431i | \(0.552496\pi\) | |||||||
\(380\) | 1.73205 | 0.0888523 | ||||||||
\(381\) | −22.8564 | −1.17097 | ||||||||
\(382\) | 18.2679 | 0.934670 | ||||||||
\(383\) | −26.5885 | −1.35861 | −0.679303 | − | 0.733858i | \(-0.737718\pi\) | ||||
−0.679303 | + | 0.733858i | \(0.737718\pi\) | |||||||
\(384\) | 1.73205 | 0.0883883 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −21.7846 | −1.10881 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.46410 | 0.0743285 | ||||||||
\(389\) | −10.8756 | −0.551417 | −0.275709 | − | 0.961241i | \(-0.588912\pi\) | ||||
−0.275709 | + | 0.961241i | \(0.588912\pi\) | |||||||
\(390\) | −3.00000 | −0.151911 | ||||||||
\(391\) | 3.12436 | 0.158005 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −7.39230 | −0.372892 | ||||||||
\(394\) | 24.0000 | 1.20910 | ||||||||
\(395\) | 0.0717968 | 0.00361249 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.85641 | −0.494679 | −0.247339 | − | 0.968929i | \(-0.579556\pi\) | ||||
−0.247339 | + | 0.968929i | \(0.579556\pi\) | |||||||
\(398\) | −8.39230 | −0.420668 | ||||||||
\(399\) | −3.00000 | −0.150188 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −30.2487 | −1.51055 | −0.755274 | − | 0.655409i | \(-0.772496\pi\) | ||||
−0.755274 | + | 0.655409i | \(0.772496\pi\) | |||||||
\(402\) | 24.5885 | 1.22636 | ||||||||
\(403\) | −5.66025 | −0.281957 | ||||||||
\(404\) | 7.92820 | 0.394443 | ||||||||
\(405\) | 9.00000 | 0.447214 | ||||||||
\(406\) | 2.53590 | 0.125855 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.19615 | 0.108726 | ||||||||
\(409\) | 25.1769 | 1.24492 | 0.622459 | − | 0.782652i | \(-0.286134\pi\) | ||||
0.622459 | + | 0.782652i | \(0.286134\pi\) | |||||||
\(410\) | −6.73205 | −0.332472 | ||||||||
\(411\) | −21.0000 | −1.03585 | ||||||||
\(412\) | 1.80385 | 0.0888692 | ||||||||
\(413\) | 1.00000 | 0.0492068 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.9282 | −0.585532 | ||||||||
\(416\) | −1.73205 | −0.0849208 | ||||||||
\(417\) | −2.32051 | −0.113636 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.39230 | −0.458844 | −0.229422 | − | 0.973327i | \(-0.573684\pi\) | ||||
−0.229422 | + | 0.973327i | \(0.573684\pi\) | |||||||
\(420\) | −1.73205 | −0.0845154 | ||||||||
\(421\) | −10.2487 | −0.499492 | −0.249746 | − | 0.968311i | \(-0.580347\pi\) | ||||
−0.249746 | + | 0.968311i | \(0.580347\pi\) | |||||||
\(422\) | −1.46410 | −0.0712714 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.26795 | 0.0615771 | ||||||||
\(425\) | 1.26795 | 0.0615046 | ||||||||
\(426\) | 5.07180 | 0.245729 | ||||||||
\(427\) | −4.00000 | −0.193574 | ||||||||
\(428\) | 0.535898 | 0.0259036 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.66025 | −0.369410 | ||||||||
\(431\) | −18.4641 | −0.889384 | −0.444692 | − | 0.895683i | \(-0.646687\pi\) | ||||
−0.444692 | + | 0.895683i | \(0.646687\pi\) | |||||||
\(432\) | 5.19615 | 0.250000 | ||||||||
\(433\) | 12.1962 | 0.586110 | 0.293055 | − | 0.956096i | \(-0.405328\pi\) | ||||
0.293055 | + | 0.956096i | \(0.405328\pi\) | |||||||
\(434\) | −3.26795 | −0.156867 | ||||||||
\(435\) | 4.39230 | 0.210595 | ||||||||
\(436\) | 0.196152 | 0.00939400 | ||||||||
\(437\) | −4.26795 | −0.204164 | ||||||||
\(438\) | 16.7321 | 0.799488 | ||||||||
\(439\) | −13.8038 | −0.658822 | −0.329411 | − | 0.944187i | \(-0.606850\pi\) | ||||
−0.329411 | + | 0.944187i | \(0.606850\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.19615 | −0.104460 | ||||||||
\(443\) | −18.9282 | −0.899306 | −0.449653 | − | 0.893203i | \(-0.648452\pi\) | ||||
−0.449653 | + | 0.893203i | \(0.648452\pi\) | |||||||
\(444\) | 12.9282 | 0.613545 | ||||||||
\(445\) | 4.73205 | 0.224321 | ||||||||
\(446\) | −11.1244 | −0.526754 | ||||||||
\(447\) | −1.60770 | −0.0760414 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −27.5359 | −1.29950 | −0.649750 | − | 0.760148i | \(-0.725126\pi\) | ||||
−0.649750 | + | 0.760148i | \(0.725126\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −4.66025 | −0.219200 | ||||||||
\(453\) | 22.5167 | 1.05792 | ||||||||
\(454\) | −7.46410 | −0.350308 | ||||||||
\(455\) | 1.73205 | 0.0811998 | ||||||||
\(456\) | −3.00000 | −0.140488 | ||||||||
\(457\) | −19.9282 | −0.932202 | −0.466101 | − | 0.884732i | \(-0.654342\pi\) | ||||
−0.466101 | + | 0.884732i | \(0.654342\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.58846 | 0.307523 | ||||||||
\(460\) | −2.46410 | −0.114889 | ||||||||
\(461\) | 38.2487 | 1.78142 | 0.890710 | − | 0.454572i | \(-0.150208\pi\) | ||||
0.890710 | + | 0.454572i | \(0.150208\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.0000 | 1.62659 | 0.813294 | − | 0.581853i | \(-0.197672\pi\) | ||||
0.813294 | + | 0.581853i | \(0.197672\pi\) | |||||||
\(464\) | 2.53590 | 0.117726 | ||||||||
\(465\) | −5.66025 | −0.262488 | ||||||||
\(466\) | −22.8564 | −1.05880 | ||||||||
\(467\) | −5.87564 | −0.271892 | −0.135946 | − | 0.990716i | \(-0.543407\pi\) | ||||
−0.135946 | + | 0.990716i | \(0.543407\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.1962 | −0.655517 | ||||||||
\(470\) | −2.73205 | −0.126020 | ||||||||
\(471\) | 18.1244 | 0.835126 | ||||||||
\(472\) | 1.00000 | 0.0460287 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.124356 | −0.00571184 | ||||||||
\(475\) | −1.73205 | −0.0794719 | ||||||||
\(476\) | −1.26795 | −0.0581164 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.46410 | −0.112705 | ||||||||
\(479\) | −15.2679 | −0.697610 | −0.348805 | − | 0.937195i | \(-0.613413\pi\) | ||||
−0.348805 | + | 0.937195i | \(0.613413\pi\) | |||||||
\(480\) | −1.73205 | −0.0790569 | ||||||||
\(481\) | −12.9282 | −0.589475 | ||||||||
\(482\) | −10.9282 | −0.497766 | ||||||||
\(483\) | 4.26795 | 0.194198 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.46410 | −0.0664814 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.7128 | 1.02922 | 0.514608 | − | 0.857426i | \(-0.327938\pi\) | ||||
0.514608 | + | 0.857426i | \(0.327938\pi\) | |||||||
\(488\) | −4.00000 | −0.181071 | ||||||||
\(489\) | −15.4641 | −0.699311 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −17.5167 | −0.790516 | −0.395258 | − | 0.918570i | \(-0.629345\pi\) | ||||
−0.395258 | + | 0.918570i | \(0.629345\pi\) | |||||||
\(492\) | 11.6603 | 0.525685 | ||||||||
\(493\) | 3.21539 | 0.144814 | ||||||||
\(494\) | 3.00000 | 0.134976 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.26795 | −0.146735 | ||||||||
\(497\) | −2.92820 | −0.131348 | ||||||||
\(498\) | 20.6603 | 0.925808 | ||||||||
\(499\) | 1.60770 | 0.0719703 | 0.0359852 | − | 0.999352i | \(-0.488543\pi\) | ||||
0.0359852 | + | 0.999352i | \(0.488543\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −11.6603 | −0.520942 | ||||||||
\(502\) | 10.3923 | 0.463831 | ||||||||
\(503\) | −28.9808 | −1.29219 | −0.646094 | − | 0.763258i | \(-0.723599\pi\) | ||||
−0.646094 | + | 0.763258i | \(0.723599\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.92820 | −0.352800 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.3205 | 0.769231 | ||||||||
\(508\) | 13.1962 | 0.585485 | ||||||||
\(509\) | −35.1962 | −1.56004 | −0.780021 | − | 0.625753i | \(-0.784792\pi\) | ||||
−0.780021 | + | 0.625753i | \(0.784792\pi\) | |||||||
\(510\) | −2.19615 | −0.0972473 | ||||||||
\(511\) | −9.66025 | −0.427344 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −9.00000 | −0.397360 | ||||||||
\(514\) | 19.2679 | 0.849873 | ||||||||
\(515\) | −1.80385 | −0.0794870 | ||||||||
\(516\) | 13.2679 | 0.584089 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −7.46410 | −0.327954 | ||||||||
\(519\) | 17.3205 | 0.760286 | ||||||||
\(520\) | 1.73205 | 0.0759555 | ||||||||
\(521\) | −14.5359 | −0.636829 | −0.318415 | − | 0.947952i | \(-0.603150\pi\) | ||||
−0.318415 | + | 0.947952i | \(0.603150\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.2487 | 1.36641 | 0.683205 | − | 0.730226i | \(-0.260585\pi\) | ||||
0.683205 | + | 0.730226i | \(0.260585\pi\) | |||||||
\(524\) | 4.26795 | 0.186446 | ||||||||
\(525\) | 1.73205 | 0.0755929 | ||||||||
\(526\) | −17.7321 | −0.773154 | ||||||||
\(527\) | −4.14359 | −0.180498 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.9282 | −0.736009 | ||||||||
\(530\) | −1.26795 | −0.0550762 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.73205 | 0.0750939 | ||||||||
\(533\) | −11.6603 | −0.505062 | ||||||||
\(534\) | −8.19615 | −0.354682 | ||||||||
\(535\) | −0.535898 | −0.0231689 | ||||||||
\(536\) | −14.1962 | −0.613180 | ||||||||
\(537\) | 15.8038 | 0.681986 | ||||||||
\(538\) | −16.5167 | −0.712084 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.19615 | −0.223607 | ||||||||
\(541\) | −24.2487 | −1.04253 | −0.521267 | − | 0.853394i | \(-0.674540\pi\) | ||||
−0.521267 | + | 0.853394i | \(0.674540\pi\) | |||||||
\(542\) | −32.3923 | −1.39137 | ||||||||
\(543\) | 7.14359 | 0.306561 | ||||||||
\(544\) | −1.26795 | −0.0543629 | ||||||||
\(545\) | −0.196152 | −0.00840225 | ||||||||
\(546\) | −3.00000 | −0.128388 | ||||||||
\(547\) | 26.5885 | 1.13684 | 0.568420 | − | 0.822738i | \(-0.307555\pi\) | ||||
0.568420 | + | 0.822738i | \(0.307555\pi\) | |||||||
\(548\) | 12.1244 | 0.517927 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.39230 | −0.187118 | ||||||||
\(552\) | 4.26795 | 0.181656 | ||||||||
\(553\) | 0.0717968 | 0.00305311 | ||||||||
\(554\) | 4.58846 | 0.194945 | ||||||||
\(555\) | −12.9282 | −0.548772 | ||||||||
\(556\) | 1.33975 | 0.0568179 | ||||||||
\(557\) | −40.0526 | −1.69708 | −0.848541 | − | 0.529130i | \(-0.822518\pi\) | ||||
−0.848541 | + | 0.529130i | \(0.822518\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.2679 | −0.561174 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.73205 | 0.326157 | ||||||||
\(563\) | 42.4641 | 1.78965 | 0.894824 | − | 0.446419i | \(-0.147301\pi\) | ||||
0.894824 | + | 0.446419i | \(0.147301\pi\) | |||||||
\(564\) | 4.73205 | 0.199255 | ||||||||
\(565\) | 4.66025 | 0.196058 | ||||||||
\(566\) | −17.7846 | −0.747543 | ||||||||
\(567\) | 9.00000 | 0.377964 | ||||||||
\(568\) | −2.92820 | −0.122865 | ||||||||
\(569\) | 14.1244 | 0.592124 | 0.296062 | − | 0.955169i | \(-0.404327\pi\) | ||||
0.296062 | + | 0.955169i | \(0.404327\pi\) | |||||||
\(570\) | 3.00000 | 0.125656 | ||||||||
\(571\) | 0.679492 | 0.0284359 | 0.0142179 | − | 0.999899i | \(-0.495474\pi\) | ||||
0.0142179 | + | 0.999899i | \(0.495474\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 31.6410 | 1.32182 | ||||||||
\(574\) | −6.73205 | −0.280990 | ||||||||
\(575\) | 2.46410 | 0.102760 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.1962 | 1.67339 | 0.836694 | − | 0.547671i | \(-0.184485\pi\) | ||||
0.836694 | + | 0.547671i | \(0.184485\pi\) | |||||||
\(578\) | 15.3923 | 0.640235 | ||||||||
\(579\) | −37.7321 | −1.56809 | ||||||||
\(580\) | −2.53590 | −0.105297 | ||||||||
\(581\) | −11.9282 | −0.494865 | ||||||||
\(582\) | 2.53590 | 0.105116 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −9.66025 | −0.399744 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.33975 | −0.220583 | ||||||||
\(587\) | −36.1244 | −1.49101 | −0.745506 | − | 0.666499i | \(-0.767792\pi\) | ||||
−0.745506 | + | 0.666499i | \(0.767792\pi\) | |||||||
\(588\) | −1.73205 | −0.0714286 | ||||||||
\(589\) | 5.66025 | 0.233227 | ||||||||
\(590\) | −1.00000 | −0.0411693 | ||||||||
\(591\) | 41.5692 | 1.70993 | ||||||||
\(592\) | −7.46410 | −0.306773 | ||||||||
\(593\) | −2.92820 | −0.120247 | −0.0601234 | − | 0.998191i | \(-0.519149\pi\) | ||||
−0.0601234 | + | 0.998191i | \(0.519149\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.26795 | 0.0519808 | ||||||||
\(596\) | 0.928203 | 0.0380207 | ||||||||
\(597\) | −14.5359 | −0.594915 | ||||||||
\(598\) | −4.26795 | −0.174529 | ||||||||
\(599\) | 2.66025 | 0.108695 | 0.0543475 | − | 0.998522i | \(-0.482692\pi\) | ||||
0.0543475 | + | 0.998522i | \(0.482692\pi\) | |||||||
\(600\) | 1.73205 | 0.0707107 | ||||||||
\(601\) | 5.41154 | 0.220741 | 0.110371 | − | 0.993890i | \(-0.464796\pi\) | ||||
0.110371 | + | 0.993890i | \(0.464796\pi\) | |||||||
\(602\) | −7.66025 | −0.312209 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.0000 | −0.528962 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.7321 | 0.557826 | ||||||||
\(607\) | 36.5359 | 1.48295 | 0.741473 | − | 0.670983i | \(-0.234127\pi\) | ||||
0.741473 | + | 0.670983i | \(0.234127\pi\) | |||||||
\(608\) | 1.73205 | 0.0702439 | ||||||||
\(609\) | 4.39230 | 0.177985 | ||||||||
\(610\) | 4.00000 | 0.161955 | ||||||||
\(611\) | −4.73205 | −0.191438 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.9808 | −0.685847 | −0.342923 | − | 0.939363i | \(-0.611417\pi\) | ||||
−0.342923 | + | 0.939363i | \(0.611417\pi\) | |||||||
\(614\) | 3.07180 | 0.123968 | ||||||||
\(615\) | −11.6603 | −0.470187 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.39230 | 0.0963106 | 0.0481553 | − | 0.998840i | \(-0.484666\pi\) | ||||
0.0481553 | + | 0.998840i | \(0.484666\pi\) | |||||||
\(618\) | 3.12436 | 0.125680 | ||||||||
\(619\) | −0.607695 | −0.0244253 | −0.0122127 | − | 0.999925i | \(-0.503888\pi\) | ||||
−0.0122127 | + | 0.999925i | \(0.503888\pi\) | |||||||
\(620\) | 3.26795 | 0.131244 | ||||||||
\(621\) | 12.8038 | 0.513801 | ||||||||
\(622\) | 32.1962 | 1.29095 | ||||||||
\(623\) | 4.73205 | 0.189586 | ||||||||
\(624\) | −3.00000 | −0.120096 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 16.5359 | 0.660907 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.4641 | −0.417563 | ||||||||
\(629\) | −9.46410 | −0.377358 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.53590 | 0.260190 | 0.130095 | − | 0.991502i | \(-0.458472\pi\) | ||||
0.130095 | + | 0.991502i | \(0.458472\pi\) | |||||||
\(632\) | 0.0717968 | 0.00285592 | ||||||||
\(633\) | −2.53590 | −0.100793 | ||||||||
\(634\) | −21.6603 | −0.860239 | ||||||||
\(635\) | −13.1962 | −0.523673 | ||||||||
\(636\) | 2.19615 | 0.0870831 | ||||||||
\(637\) | 1.73205 | 0.0686264 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −20.3205 | −0.802612 | −0.401306 | − | 0.915944i | \(-0.631444\pi\) | ||||
−0.401306 | + | 0.915944i | \(0.631444\pi\) | |||||||
\(642\) | 0.928203 | 0.0366333 | ||||||||
\(643\) | −40.2487 | −1.58725 | −0.793627 | − | 0.608404i | \(-0.791810\pi\) | ||||
−0.793627 | + | 0.608404i | \(0.791810\pi\) | |||||||
\(644\) | −2.46410 | −0.0970992 | ||||||||
\(645\) | −13.2679 | −0.522425 | ||||||||
\(646\) | 2.19615 | 0.0864065 | ||||||||
\(647\) | −28.4449 | −1.11828 | −0.559141 | − | 0.829072i | \(-0.688869\pi\) | ||||
−0.559141 | + | 0.829072i | \(0.688869\pi\) | |||||||
\(648\) | 9.00000 | 0.353553 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.73205 | −0.0679366 | ||||||||
\(651\) | −5.66025 | −0.221843 | ||||||||
\(652\) | 8.92820 | 0.349655 | ||||||||
\(653\) | −4.05256 | −0.158589 | −0.0792944 | − | 0.996851i | \(-0.525267\pi\) | ||||
−0.0792944 | + | 0.996851i | \(0.525267\pi\) | |||||||
\(654\) | 0.339746 | 0.0132851 | ||||||||
\(655\) | −4.26795 | −0.166763 | ||||||||
\(656\) | −6.73205 | −0.262842 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.73205 | −0.106506 | ||||||||
\(659\) | −14.8756 | −0.579473 | −0.289736 | − | 0.957106i | \(-0.593568\pi\) | ||||
−0.289736 | + | 0.957106i | \(0.593568\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.58846 | −0.217366 | −0.108683 | − | 0.994076i | \(-0.534663\pi\) | ||||
−0.108683 | + | 0.994076i | \(0.534663\pi\) | |||||||
\(662\) | 1.80385 | 0.0701085 | ||||||||
\(663\) | −3.80385 | −0.147729 | ||||||||
\(664\) | −11.9282 | −0.462904 | ||||||||
\(665\) | −1.73205 | −0.0671660 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.24871 | 0.241951 | ||||||||
\(668\) | 6.73205 | 0.260471 | ||||||||
\(669\) | −19.2679 | −0.744942 | ||||||||
\(670\) | 14.1962 | 0.548445 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.73205 | −0.0668153 | ||||||||
\(673\) | 33.7846 | 1.30230 | 0.651150 | − | 0.758949i | \(-0.274287\pi\) | ||||
0.651150 | + | 0.758949i | \(0.274287\pi\) | |||||||
\(674\) | 15.7846 | 0.608000 | ||||||||
\(675\) | 5.19615 | 0.200000 | ||||||||
\(676\) | −10.0000 | −0.384615 | ||||||||
\(677\) | −25.7321 | −0.988963 | −0.494482 | − | 0.869188i | \(-0.664642\pi\) | ||||
−0.494482 | + | 0.869188i | \(0.664642\pi\) | |||||||
\(678\) | −8.07180 | −0.309995 | ||||||||
\(679\) | −1.46410 | −0.0561871 | ||||||||
\(680\) | 1.26795 | 0.0486236 | ||||||||
\(681\) | −12.9282 | −0.495410 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.39230 | 0.168067 | 0.0840334 | − | 0.996463i | \(-0.473220\pi\) | ||||
0.0840334 | + | 0.996463i | \(0.473220\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.1244 | −0.463248 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.66025 | −0.292044 | ||||||||
\(689\) | −2.19615 | −0.0836667 | ||||||||
\(690\) | −4.26795 | −0.162478 | ||||||||
\(691\) | −18.6410 | −0.709138 | −0.354569 | − | 0.935030i | \(-0.615372\pi\) | ||||
−0.354569 | + | 0.935030i | \(0.615372\pi\) | |||||||
\(692\) | −10.0000 | −0.380143 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.53590 | 0.324018 | ||||||||
\(695\) | −1.33975 | −0.0508195 | ||||||||
\(696\) | 4.39230 | 0.166490 | ||||||||
\(697\) | −8.53590 | −0.323320 | ||||||||
\(698\) | 3.00000 | 0.113552 | ||||||||
\(699\) | −39.5885 | −1.49737 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | −7.41154 | −0.279930 | −0.139965 | − | 0.990156i | \(-0.544699\pi\) | ||||
−0.139965 | + | 0.990156i | \(0.544699\pi\) | |||||||
\(702\) | −9.00000 | −0.339683 | ||||||||
\(703\) | 12.9282 | 0.487596 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.73205 | −0.178219 | ||||||||
\(706\) | −7.66025 | −0.288297 | ||||||||
\(707\) | −7.92820 | −0.298171 | ||||||||
\(708\) | 1.73205 | 0.0650945 | ||||||||
\(709\) | 10.0000 | 0.375558 | 0.187779 | − | 0.982211i | \(-0.439871\pi\) | ||||
0.187779 | + | 0.982211i | \(0.439871\pi\) | |||||||
\(710\) | 2.92820 | 0.109894 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.73205 | 0.177341 | ||||||||
\(713\) | −8.05256 | −0.301571 | ||||||||
\(714\) | −2.19615 | −0.0821889 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.12436 | −0.340993 | ||||||||
\(717\) | −4.26795 | −0.159389 | ||||||||
\(718\) | 14.0000 | 0.522475 | ||||||||
\(719\) | 32.0000 | 1.19340 | 0.596699 | − | 0.802465i | \(-0.296479\pi\) | ||||
0.596699 | + | 0.802465i | \(0.296479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.80385 | −0.0671788 | ||||||||
\(722\) | 16.0000 | 0.595458 | ||||||||
\(723\) | −18.9282 | −0.703947 | ||||||||
\(724\) | −4.12436 | −0.153280 | ||||||||
\(725\) | 2.53590 | 0.0941809 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 51.7128 | 1.91792 | 0.958961 | − | 0.283538i | \(-0.0915082\pi\) | ||||
0.958961 | + | 0.283538i | \(0.0915082\pi\) | |||||||
\(728\) | 1.73205 | 0.0641941 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 9.66025 | 0.357542 | ||||||||
\(731\) | −9.71281 | −0.359241 | ||||||||
\(732\) | −6.92820 | −0.256074 | ||||||||
\(733\) | −26.5167 | −0.979415 | −0.489708 | − | 0.871887i | \(-0.662896\pi\) | ||||
−0.489708 | + | 0.871887i | \(0.662896\pi\) | |||||||
\(734\) | 4.33975 | 0.160183 | ||||||||
\(735\) | 1.73205 | 0.0638877 | ||||||||
\(736\) | −2.46410 | −0.0908280 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.33975 | 0.306783 | 0.153391 | − | 0.988166i | \(-0.450981\pi\) | ||||
0.153391 | + | 0.988166i | \(0.450981\pi\) | |||||||
\(740\) | 7.46410 | 0.274386 | ||||||||
\(741\) | 5.19615 | 0.190885 | ||||||||
\(742\) | −1.26795 | −0.0465479 | ||||||||
\(743\) | 23.1769 | 0.850279 | 0.425139 | − | 0.905128i | \(-0.360225\pi\) | ||||
0.425139 | + | 0.905128i | \(0.360225\pi\) | |||||||
\(744\) | −5.66025 | −0.207515 | ||||||||
\(745\) | −0.928203 | −0.0340067 | ||||||||
\(746\) | 12.9282 | 0.473335 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.535898 | −0.0195813 | ||||||||
\(750\) | −1.73205 | −0.0632456 | ||||||||
\(751\) | −30.6603 | −1.11881 | −0.559404 | − | 0.828895i | \(-0.688970\pi\) | ||||
−0.559404 | + | 0.828895i | \(0.688970\pi\) | |||||||
\(752\) | −2.73205 | −0.0996276 | ||||||||
\(753\) | 18.0000 | 0.655956 | ||||||||
\(754\) | −4.39230 | −0.159958 | ||||||||
\(755\) | 13.0000 | 0.473118 | ||||||||
\(756\) | −5.19615 | −0.188982 | ||||||||
\(757\) | −26.9808 | −0.980632 | −0.490316 | − | 0.871545i | \(-0.663119\pi\) | ||||
−0.490316 | + | 0.871545i | \(0.663119\pi\) | |||||||
\(758\) | 6.39230 | 0.232179 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.73205 | −0.0628281 | ||||||||
\(761\) | −21.5167 | −0.779978 | −0.389989 | − | 0.920819i | \(-0.627521\pi\) | ||||
−0.389989 | + | 0.920819i | \(0.627521\pi\) | |||||||
\(762\) | 22.8564 | 0.828000 | ||||||||
\(763\) | −0.196152 | −0.00710119 | ||||||||
\(764\) | −18.2679 | −0.660911 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.5885 | 0.960680 | ||||||||
\(767\) | −1.73205 | −0.0625407 | ||||||||
\(768\) | −1.73205 | −0.0625000 | ||||||||
\(769\) | −30.3923 | −1.09597 | −0.547987 | − | 0.836487i | \(-0.684606\pi\) | ||||
−0.547987 | + | 0.836487i | \(0.684606\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.3731 | 1.20190 | ||||||||
\(772\) | 21.7846 | 0.784045 | ||||||||
\(773\) | −6.60770 | −0.237662 | −0.118831 | − | 0.992914i | \(-0.537915\pi\) | ||||
−0.118831 | + | 0.992914i | \(0.537915\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.26795 | −0.117388 | ||||||||
\(776\) | −1.46410 | −0.0525582 | ||||||||
\(777\) | −12.9282 | −0.463797 | ||||||||
\(778\) | 10.8756 | 0.389911 | ||||||||
\(779\) | 11.6603 | 0.417772 | ||||||||
\(780\) | 3.00000 | 0.107417 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −3.12436 | −0.111727 | ||||||||
\(783\) | 13.1769 | 0.470905 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 10.4641 | 0.373480 | ||||||||
\(786\) | 7.39230 | 0.263675 | ||||||||
\(787\) | −25.7128 | −0.916563 | −0.458281 | − | 0.888807i | \(-0.651535\pi\) | ||||
−0.458281 | + | 0.888807i | \(0.651535\pi\) | |||||||
\(788\) | −24.0000 | −0.854965 | ||||||||
\(789\) | −30.7128 | −1.09341 | ||||||||
\(790\) | −0.0717968 | −0.00255441 | ||||||||
\(791\) | 4.66025 | 0.165700 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.92820 | 0.246028 | ||||||||
\(794\) | 9.85641 | 0.349791 | ||||||||
\(795\) | −2.19615 | −0.0778895 | ||||||||
\(796\) | 8.39230 | 0.297457 | ||||||||
\(797\) | −11.6795 | −0.413709 | −0.206854 | − | 0.978372i | \(-0.566323\pi\) | ||||
−0.206854 | + | 0.978372i | \(0.566323\pi\) | |||||||
\(798\) | 3.00000 | 0.106199 | ||||||||
\(799\) | −3.46410 | −0.122551 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 30.2487 | 1.06812 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −24.5885 | −0.867168 | ||||||||
\(805\) | 2.46410 | 0.0868482 | ||||||||
\(806\) | 5.66025 | 0.199374 | ||||||||
\(807\) | −28.6077 | −1.00704 | ||||||||
\(808\) | −7.92820 | −0.278913 | ||||||||
\(809\) | 3.85641 | 0.135584 | 0.0677920 | − | 0.997699i | \(-0.478405\pi\) | ||||
0.0677920 | + | 0.997699i | \(0.478405\pi\) | |||||||
\(810\) | −9.00000 | −0.316228 | ||||||||
\(811\) | 7.32051 | 0.257058 | 0.128529 | − | 0.991706i | \(-0.458974\pi\) | ||||
0.128529 | + | 0.991706i | \(0.458974\pi\) | |||||||
\(812\) | −2.53590 | −0.0889926 | ||||||||
\(813\) | −56.1051 | −1.96769 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.92820 | −0.312741 | ||||||||
\(816\) | −2.19615 | −0.0768807 | ||||||||
\(817\) | 13.2679 | 0.464187 | ||||||||
\(818\) | −25.1769 | −0.880290 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.73205 | 0.235093 | ||||||||
\(821\) | 10.0000 | 0.349002 | 0.174501 | − | 0.984657i | \(-0.444169\pi\) | ||||
0.174501 | + | 0.984657i | \(0.444169\pi\) | |||||||
\(822\) | 21.0000 | 0.732459 | ||||||||
\(823\) | −49.7128 | −1.73288 | −0.866440 | − | 0.499281i | \(-0.833597\pi\) | ||||
−0.866440 | + | 0.499281i | \(0.833597\pi\) | |||||||
\(824\) | −1.80385 | −0.0628400 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.00000 | −0.0347945 | ||||||||
\(827\) | −36.9808 | −1.28595 | −0.642974 | − | 0.765888i | \(-0.722299\pi\) | ||||
−0.642974 | + | 0.765888i | \(0.722299\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.3731 | 1.33275 | 0.666376 | − | 0.745616i | \(-0.267845\pi\) | ||||
0.666376 | + | 0.745616i | \(0.267845\pi\) | |||||||
\(830\) | 11.9282 | 0.414034 | ||||||||
\(831\) | 7.94744 | 0.275694 | ||||||||
\(832\) | 1.73205 | 0.0600481 | ||||||||
\(833\) | 1.26795 | 0.0439318 | ||||||||
\(834\) | 2.32051 | 0.0803526 | ||||||||
\(835\) | −6.73205 | −0.232972 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.9808 | −0.586941 | ||||||||
\(838\) | 9.39230 | 0.324452 | ||||||||
\(839\) | 5.66025 | 0.195414 | 0.0977068 | − | 0.995215i | \(-0.468849\pi\) | ||||
0.0977068 | + | 0.995215i | \(0.468849\pi\) | |||||||
\(840\) | 1.73205 | 0.0597614 | ||||||||
\(841\) | −22.5692 | −0.778249 | ||||||||
\(842\) | 10.2487 | 0.353194 | ||||||||
\(843\) | 13.3923 | 0.461255 | ||||||||
\(844\) | 1.46410 | 0.0503965 | ||||||||
\(845\) | 10.0000 | 0.344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.26795 | −0.0435416 | ||||||||
\(849\) | −30.8038 | −1.05719 | ||||||||
\(850\) | −1.26795 | −0.0434903 | ||||||||
\(851\) | −18.3923 | −0.630480 | ||||||||
\(852\) | −5.07180 | −0.173757 | ||||||||
\(853\) | −45.7321 | −1.56584 | −0.782918 | − | 0.622125i | \(-0.786269\pi\) | ||||
−0.782918 | + | 0.622125i | \(0.786269\pi\) | |||||||
\(854\) | 4.00000 | 0.136877 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.535898 | −0.0183166 | ||||||||
\(857\) | −28.3923 | −0.969863 | −0.484931 | − | 0.874552i | \(-0.661155\pi\) | ||||
−0.484931 | + | 0.874552i | \(0.661155\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.0000 | −0.341196 | −0.170598 | − | 0.985341i | \(-0.554570\pi\) | ||||
−0.170598 | + | 0.985341i | \(0.554570\pi\) | |||||||
\(860\) | 7.66025 | 0.261212 | ||||||||
\(861\) | −11.6603 | −0.397380 | ||||||||
\(862\) | 18.4641 | 0.628890 | ||||||||
\(863\) | −38.6410 | −1.31536 | −0.657678 | − | 0.753299i | \(-0.728461\pi\) | ||||
−0.657678 | + | 0.753299i | \(0.728461\pi\) | |||||||
\(864\) | −5.19615 | −0.176777 | ||||||||
\(865\) | 10.0000 | 0.340010 | ||||||||
\(866\) | −12.1962 | −0.414442 | ||||||||
\(867\) | 26.6603 | 0.905430 | ||||||||
\(868\) | 3.26795 | 0.110921 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −4.39230 | −0.148913 | ||||||||
\(871\) | 24.5885 | 0.833148 | ||||||||
\(872\) | −0.196152 | −0.00664256 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.26795 | 0.144366 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −16.7321 | −0.565324 | ||||||||
\(877\) | −19.1244 | −0.645784 | −0.322892 | − | 0.946436i | \(-0.604655\pi\) | ||||
−0.322892 | + | 0.946436i | \(0.604655\pi\) | |||||||
\(878\) | 13.8038 | 0.465857 | ||||||||
\(879\) | −9.24871 | −0.311951 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.3205 | −1.12260 | −0.561298 | − | 0.827614i | \(-0.689698\pi\) | ||||
−0.561298 | + | 0.827614i | \(0.689698\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.3923 | 1.15739 | 0.578697 | − | 0.815543i | \(-0.303562\pi\) | ||||
0.578697 | + | 0.815543i | \(0.303562\pi\) | |||||||
\(884\) | 2.19615 | 0.0738646 | ||||||||
\(885\) | −1.73205 | −0.0582223 | ||||||||
\(886\) | 18.9282 | 0.635905 | ||||||||
\(887\) | 12.9808 | 0.435851 | 0.217926 | − | 0.975965i | \(-0.430071\pi\) | ||||
0.217926 | + | 0.975965i | \(0.430071\pi\) | |||||||
\(888\) | −12.9282 | −0.433842 | ||||||||
\(889\) | −13.1962 | −0.442585 | ||||||||
\(890\) | −4.73205 | −0.158619 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.1244 | 0.372471 | ||||||||
\(893\) | 4.73205 | 0.158352 | ||||||||
\(894\) | 1.60770 | 0.0537694 | ||||||||
\(895\) | 9.12436 | 0.304994 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −7.39230 | −0.246822 | ||||||||
\(898\) | 27.5359 | 0.918885 | ||||||||
\(899\) | −8.28719 | −0.276393 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.60770 | −0.0535601 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.2679 | −0.441530 | ||||||||
\(904\) | 4.66025 | 0.154998 | ||||||||
\(905\) | 4.12436 | 0.137098 | ||||||||
\(906\) | −22.5167 | −0.748066 | ||||||||
\(907\) | −14.9282 | −0.495683 | −0.247841 | − | 0.968801i | \(-0.579721\pi\) | ||||
−0.247841 | + | 0.968801i | \(0.579721\pi\) | |||||||
\(908\) | 7.46410 | 0.247705 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.73205 | −0.0574169 | ||||||||
\(911\) | −49.7321 | −1.64770 | −0.823848 | − | 0.566811i | \(-0.808177\pi\) | ||||
−0.823848 | + | 0.566811i | \(0.808177\pi\) | |||||||
\(912\) | 3.00000 | 0.0993399 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 19.9282 | 0.659166 | ||||||||
\(915\) | 6.92820 | 0.229039 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.26795 | −0.140940 | ||||||||
\(918\) | −6.58846 | −0.217451 | ||||||||
\(919\) | 5.71281 | 0.188448 | 0.0942242 | − | 0.995551i | \(-0.469963\pi\) | ||||
0.0942242 | + | 0.995551i | \(0.469963\pi\) | |||||||
\(920\) | 2.46410 | 0.0812390 | ||||||||
\(921\) | 5.32051 | 0.175317 | ||||||||
\(922\) | −38.2487 | −1.25965 | ||||||||
\(923\) | 5.07180 | 0.166940 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.46410 | −0.245418 | ||||||||
\(926\) | −35.0000 | −1.15017 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.53590 | −0.0832449 | ||||||||
\(929\) | 31.3205 | 1.02759 | 0.513796 | − | 0.857912i | \(-0.328239\pi\) | ||||
0.513796 | + | 0.857912i | \(0.328239\pi\) | |||||||
\(930\) | 5.66025 | 0.185607 | ||||||||
\(931\) | −1.73205 | −0.0567657 | ||||||||
\(932\) | 22.8564 | 0.748686 | ||||||||
\(933\) | 55.7654 | 1.82568 | ||||||||
\(934\) | 5.87564 | 0.192257 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.6410 | −1.65437 | −0.827185 | − | 0.561930i | \(-0.810059\pi\) | ||||
−0.827185 | + | 0.561930i | \(0.810059\pi\) | |||||||
\(938\) | 14.1962 | 0.463521 | ||||||||
\(939\) | 28.6410 | 0.934664 | ||||||||
\(940\) | 2.73205 | 0.0891097 | ||||||||
\(941\) | 2.28719 | 0.0745602 | 0.0372801 | − | 0.999305i | \(-0.488131\pi\) | ||||
0.0372801 | + | 0.999305i | \(0.488131\pi\) | |||||||
\(942\) | −18.1244 | −0.590523 | ||||||||
\(943\) | −16.5885 | −0.540194 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | 5.19615 | 0.169031 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.26795 | 0.106194 | 0.0530970 | − | 0.998589i | \(-0.483091\pi\) | ||||
0.0530970 | + | 0.998589i | \(0.483091\pi\) | |||||||
\(948\) | 0.124356 | 0.00403888 | ||||||||
\(949\) | 16.7321 | 0.543145 | ||||||||
\(950\) | 1.73205 | 0.0561951 | ||||||||
\(951\) | −37.5167 | −1.21656 | ||||||||
\(952\) | 1.26795 | 0.0410945 | ||||||||
\(953\) | −6.07180 | −0.196685 | −0.0983424 | − | 0.995153i | \(-0.531354\pi\) | ||||
−0.0983424 | + | 0.995153i | \(0.531354\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.2679 | 0.591137 | ||||||||
\(956\) | 2.46410 | 0.0796947 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.2679 | 0.493285 | ||||||||
\(959\) | −12.1244 | −0.391516 | ||||||||
\(960\) | 1.73205 | 0.0559017 | ||||||||
\(961\) | −20.3205 | −0.655500 | ||||||||
\(962\) | 12.9282 | 0.416822 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.9282 | 0.351974 | ||||||||
\(965\) | −21.7846 | −0.701271 | ||||||||
\(966\) | −4.26795 | −0.137319 | ||||||||
\(967\) | −52.4974 | −1.68820 | −0.844102 | − | 0.536183i | \(-0.819866\pi\) | ||||
−0.844102 | + | 0.536183i | \(0.819866\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.80385 | 0.122197 | ||||||||
\(970\) | 1.46410 | 0.0470095 | ||||||||
\(971\) | −6.60770 | −0.212051 | −0.106026 | − | 0.994363i | \(-0.533813\pi\) | ||||
−0.106026 | + | 0.994363i | \(0.533813\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.33975 | −0.0429503 | ||||||||
\(974\) | −22.7128 | −0.727765 | ||||||||
\(975\) | −3.00000 | −0.0960769 | ||||||||
\(976\) | 4.00000 | 0.128037 | ||||||||
\(977\) | −40.5167 | −1.29624 | −0.648121 | − | 0.761537i | \(-0.724445\pi\) | ||||
−0.648121 | + | 0.761537i | \(0.724445\pi\) | |||||||
\(978\) | 15.4641 | 0.494487 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.5167 | 0.558979 | ||||||||
\(983\) | 23.0718 | 0.735876 | 0.367938 | − | 0.929850i | \(-0.380064\pi\) | ||||
0.367938 | + | 0.929850i | \(0.380064\pi\) | |||||||
\(984\) | −11.6603 | −0.371715 | ||||||||
\(985\) | 24.0000 | 0.764704 | ||||||||
\(986\) | −3.21539 | −0.102399 | ||||||||
\(987\) | −4.73205 | −0.150623 | ||||||||
\(988\) | −3.00000 | −0.0954427 | ||||||||
\(989\) | −18.8756 | −0.600211 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.5167 | 0.778797 | 0.389399 | − | 0.921069i | \(-0.372683\pi\) | ||||
0.389399 | + | 0.921069i | \(0.372683\pi\) | |||||||
\(992\) | 3.26795 | 0.103757 | ||||||||
\(993\) | 3.12436 | 0.0991484 | ||||||||
\(994\) | 2.92820 | 0.0928770 | ||||||||
\(995\) | −8.39230 | −0.266054 | ||||||||
\(996\) | −20.6603 | −0.654645 | ||||||||
\(997\) | 3.19615 | 0.101223 | 0.0506116 | − | 0.998718i | \(-0.483883\pi\) | ||||
0.0506116 | + | 0.998718i | \(0.483883\pi\) | |||||||
\(998\) | −1.60770 | −0.0508907 | ||||||||
\(999\) | −38.7846 | −1.22709 |
(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.bl.1.1 | ✓ | 2 | |
11.10 | odd | 2 | 8470.2.a.ca.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.bl.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
8470.2.a.ca.1.1 | yes | 2 | 11.10 | odd | 2 |