Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.81361\) 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 | ||||||||
\(3\) | 3.10278 | 1.79139 | 0.895694 | − | 0.444671i | \(-0.146679\pi\) | ||||
0.895694 | + | 0.444671i | \(0.146679\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 3.10278 | 1.26670 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.62721 | 2.20907 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.10278 | 0.895694 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 3.10278 | 0.801133 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.62721 | 1.36480 | 0.682400 | − | 0.730979i | \(-0.260936\pi\) | ||||
0.682400 | + | 0.730979i | \(0.260936\pi\) | |||||||
\(18\) | 6.62721 | 1.56205 | ||||||||
\(19\) | −4.72999 | −1.08513 | −0.542567 | − | 0.840013i | \(-0.682547\pi\) | ||||
−0.542567 | + | 0.840013i | \(0.682547\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 3.10278 | 0.677081 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.52444 | 0.943411 | 0.471705 | − | 0.881756i | \(-0.343639\pi\) | ||||
0.471705 | + | 0.881756i | \(0.343639\pi\) | |||||||
\(24\) | 3.10278 | 0.633351 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.2544 | 2.16592 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −2.52444 | −0.468776 | −0.234388 | − | 0.972143i | \(-0.575309\pi\) | ||||
−0.234388 | + | 0.972143i | \(0.575309\pi\) | |||||||
\(30\) | 3.10278 | 0.566487 | ||||||||
\(31\) | −3.04888 | −0.547594 | −0.273797 | − | 0.961787i | \(-0.588280\pi\) | ||||
−0.273797 | + | 0.961787i | \(0.588280\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.62721 | 0.965059 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 6.62721 | 1.10454 | ||||||||
\(37\) | 4.52444 | 0.743813 | 0.371907 | − | 0.928270i | \(-0.378704\pi\) | ||||
0.371907 | + | 0.928270i | \(0.378704\pi\) | |||||||
\(38\) | −4.72999 | −0.767305 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −7.30833 | −1.14137 | −0.570684 | − | 0.821170i | \(-0.693322\pi\) | ||||
−0.570684 | + | 0.821170i | \(0.693322\pi\) | |||||||
\(42\) | 3.10278 | 0.478769 | ||||||||
\(43\) | 0.578337 | 0.0881956 | 0.0440978 | − | 0.999027i | \(-0.485959\pi\) | ||||
0.0440978 | + | 0.999027i | \(0.485959\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.62721 | 0.987927 | ||||||||
\(46\) | 4.52444 | 0.667092 | ||||||||
\(47\) | 11.8328 | 1.72599 | 0.862993 | − | 0.505216i | \(-0.168587\pi\) | ||||
0.862993 | + | 0.505216i | \(0.168587\pi\) | |||||||
\(48\) | 3.10278 | 0.447847 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 17.4600 | 2.44489 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.57331 | −0.765554 | −0.382777 | − | 0.923841i | \(-0.625032\pi\) | ||||
−0.382777 | + | 0.923841i | \(0.625032\pi\) | |||||||
\(54\) | 11.2544 | 1.53153 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −14.6761 | −1.94390 | ||||||||
\(58\) | −2.52444 | −0.331475 | ||||||||
\(59\) | −7.62721 | −0.992979 | −0.496489 | − | 0.868043i | \(-0.665378\pi\) | ||||
−0.496489 | + | 0.868043i | \(0.665378\pi\) | |||||||
\(60\) | 3.10278 | 0.400567 | ||||||||
\(61\) | −9.83276 | −1.25896 | −0.629478 | − | 0.777018i | \(-0.716731\pi\) | ||||
−0.629478 | + | 0.777018i | \(0.716731\pi\) | |||||||
\(62\) | −3.04888 | −0.387208 | ||||||||
\(63\) | 6.62721 | 0.834950 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.2544 | −1.61929 | −0.809643 | − | 0.586923i | \(-0.800339\pi\) | ||||
−0.809643 | + | 0.586923i | \(0.800339\pi\) | |||||||
\(68\) | 5.62721 | 0.682400 | ||||||||
\(69\) | 14.0383 | 1.69001 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | −8.41110 | −0.998214 | −0.499107 | − | 0.866540i | \(-0.666339\pi\) | ||||
−0.499107 | + | 0.866540i | \(0.666339\pi\) | |||||||
\(72\) | 6.62721 | 0.781025 | ||||||||
\(73\) | −4.57834 | −0.535854 | −0.267927 | − | 0.963439i | \(-0.586339\pi\) | ||||
−0.267927 | + | 0.963439i | \(0.586339\pi\) | |||||||
\(74\) | 4.52444 | 0.525955 | ||||||||
\(75\) | 3.10278 | 0.358278 | ||||||||
\(76\) | −4.72999 | −0.542567 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.77886 | 1.10021 | 0.550104 | − | 0.835096i | \(-0.314588\pi\) | ||||
0.550104 | + | 0.835096i | \(0.314588\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 15.0383 | 1.67092 | ||||||||
\(82\) | −7.30833 | −0.807069 | ||||||||
\(83\) | −7.25443 | −0.796277 | −0.398138 | − | 0.917325i | \(-0.630344\pi\) | ||||
−0.398138 | + | 0.917325i | \(0.630344\pi\) | |||||||
\(84\) | 3.10278 | 0.338541 | ||||||||
\(85\) | 5.62721 | 0.610357 | ||||||||
\(86\) | 0.578337 | 0.0623637 | ||||||||
\(87\) | −7.83276 | −0.839760 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.4111 | 1.52757 | 0.763787 | − | 0.645469i | \(-0.223338\pi\) | ||||
0.763787 | + | 0.645469i | \(0.223338\pi\) | |||||||
\(90\) | 6.62721 | 0.698570 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.52444 | 0.471705 | ||||||||
\(93\) | −9.45998 | −0.980954 | ||||||||
\(94\) | 11.8328 | 1.22046 | ||||||||
\(95\) | −4.72999 | −0.485287 | ||||||||
\(96\) | 3.10278 | 0.316676 | ||||||||
\(97\) | 16.5244 | 1.67780 | 0.838901 | − | 0.544284i | \(-0.183198\pi\) | ||||
0.838901 | + | 0.544284i | \(0.183198\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −5.42166 | −0.539476 | −0.269738 | − | 0.962934i | \(-0.586937\pi\) | ||||
−0.269738 | + | 0.962934i | \(0.586937\pi\) | |||||||
\(102\) | 17.4600 | 1.72880 | ||||||||
\(103\) | −5.62721 | −0.554466 | −0.277233 | − | 0.960803i | \(-0.589417\pi\) | ||||
−0.277233 | + | 0.960803i | \(0.589417\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.10278 | 0.302800 | ||||||||
\(106\) | −5.57331 | −0.541328 | ||||||||
\(107\) | −11.8328 | −1.14392 | −0.571958 | − | 0.820283i | \(-0.693816\pi\) | ||||
−0.571958 | + | 0.820283i | \(0.693816\pi\) | |||||||
\(108\) | 11.2544 | 1.08296 | ||||||||
\(109\) | 5.88666 | 0.563840 | 0.281920 | − | 0.959438i | \(-0.409029\pi\) | ||||
0.281920 | + | 0.959438i | \(0.409029\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.0383 | 1.33246 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −5.25443 | −0.494295 | −0.247147 | − | 0.968978i | \(-0.579493\pi\) | ||||
−0.247147 | + | 0.968978i | \(0.579493\pi\) | |||||||
\(114\) | −14.6761 | −1.37454 | ||||||||
\(115\) | 4.52444 | 0.421906 | ||||||||
\(116\) | −2.52444 | −0.234388 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.62721 | −0.702142 | ||||||||
\(119\) | 5.62721 | 0.515846 | ||||||||
\(120\) | 3.10278 | 0.283243 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −9.83276 | −0.890217 | ||||||||
\(123\) | −22.6761 | −2.04463 | ||||||||
\(124\) | −3.04888 | −0.273797 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 6.62721 | 0.590399 | ||||||||
\(127\) | −20.7144 | −1.83811 | −0.919053 | − | 0.394134i | \(-0.871045\pi\) | ||||
−0.919053 | + | 0.394134i | \(0.871045\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.79445 | 0.157993 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.7789 | 1.55335 | 0.776673 | − | 0.629904i | \(-0.216906\pi\) | ||||
0.776673 | + | 0.629904i | \(0.216906\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.72999 | −0.410142 | ||||||||
\(134\) | −13.2544 | −1.14501 | ||||||||
\(135\) | 11.2544 | 0.968627 | ||||||||
\(136\) | 5.62721 | 0.482530 | ||||||||
\(137\) | −6.41110 | −0.547737 | −0.273869 | − | 0.961767i | \(-0.588303\pi\) | ||||
−0.273869 | + | 0.961767i | \(0.588303\pi\) | |||||||
\(138\) | 14.0383 | 1.19502 | ||||||||
\(139\) | 9.77886 | 0.829432 | 0.414716 | − | 0.909951i | \(-0.363881\pi\) | ||||
0.414716 | + | 0.909951i | \(0.363881\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 36.7144 | 3.09191 | ||||||||
\(142\) | −8.41110 | −0.705844 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.62721 | 0.552268 | ||||||||
\(145\) | −2.52444 | −0.209643 | ||||||||
\(146\) | −4.57834 | −0.378906 | ||||||||
\(147\) | 3.10278 | 0.255913 | ||||||||
\(148\) | 4.52444 | 0.371907 | ||||||||
\(149\) | −1.88666 | −0.154561 | −0.0772807 | − | 0.997009i | \(-0.524624\pi\) | ||||
−0.0772807 | + | 0.997009i | \(0.524624\pi\) | |||||||
\(150\) | 3.10278 | 0.253341 | ||||||||
\(151\) | 19.9844 | 1.62631 | 0.813154 | − | 0.582048i | \(-0.197749\pi\) | ||||
0.813154 | + | 0.582048i | \(0.197749\pi\) | |||||||
\(152\) | −4.72999 | −0.383653 | ||||||||
\(153\) | 37.2927 | 3.01494 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.04888 | −0.244892 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.36222 | 0.747187 | 0.373593 | − | 0.927593i | \(-0.378126\pi\) | ||||
0.373593 | + | 0.927593i | \(0.378126\pi\) | |||||||
\(158\) | 9.77886 | 0.777965 | ||||||||
\(159\) | −17.2927 | −1.37140 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 4.52444 | 0.356576 | ||||||||
\(162\) | 15.0383 | 1.18152 | ||||||||
\(163\) | 17.2544 | 1.35147 | 0.675735 | − | 0.737144i | \(-0.263826\pi\) | ||||
0.675735 | + | 0.737144i | \(0.263826\pi\) | |||||||
\(164\) | −7.30833 | −0.570684 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.25443 | −0.563053 | ||||||||
\(167\) | −17.5678 | −1.35944 | −0.679718 | − | 0.733474i | \(-0.737898\pi\) | ||||
−0.679718 | + | 0.733474i | \(0.737898\pi\) | |||||||
\(168\) | 3.10278 | 0.239384 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 5.62721 | 0.431588 | ||||||||
\(171\) | −31.3466 | −2.39714 | ||||||||
\(172\) | 0.578337 | 0.0440978 | ||||||||
\(173\) | −10.6761 | −0.811688 | −0.405844 | − | 0.913942i | \(-0.633022\pi\) | ||||
−0.405844 | + | 0.913942i | \(0.633022\pi\) | |||||||
\(174\) | −7.83276 | −0.593800 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −23.6655 | −1.77881 | ||||||||
\(178\) | 14.4111 | 1.08016 | ||||||||
\(179\) | −4.47054 | −0.334144 | −0.167072 | − | 0.985945i | \(-0.553431\pi\) | ||||
−0.167072 | + | 0.985945i | \(0.553431\pi\) | |||||||
\(180\) | 6.62721 | 0.493963 | ||||||||
\(181\) | −10.4111 | −0.773851 | −0.386925 | − | 0.922111i | \(-0.626463\pi\) | ||||
−0.386925 | + | 0.922111i | \(0.626463\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −30.5089 | −2.25528 | ||||||||
\(184\) | 4.52444 | 0.333546 | ||||||||
\(185\) | 4.52444 | 0.332643 | ||||||||
\(186\) | −9.45998 | −0.693639 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 11.8328 | 0.862993 | ||||||||
\(189\) | 11.2544 | 0.818639 | ||||||||
\(190\) | −4.72999 | −0.343149 | ||||||||
\(191\) | 14.6167 | 1.05762 | 0.528812 | − | 0.848739i | \(-0.322638\pi\) | ||||
0.528812 | + | 0.848739i | \(0.322638\pi\) | |||||||
\(192\) | 3.10278 | 0.223924 | ||||||||
\(193\) | 25.4983 | 1.83541 | 0.917704 | − | 0.397266i | \(-0.130041\pi\) | ||||
0.917704 | + | 0.397266i | \(0.130041\pi\) | |||||||
\(194\) | 16.5244 | 1.18639 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −5.89220 | −0.419802 | −0.209901 | − | 0.977723i | \(-0.567314\pi\) | ||||
−0.209901 | + | 0.977723i | \(0.567314\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.9305 | 1.12928 | 0.564642 | − | 0.825336i | \(-0.309014\pi\) | ||||
0.564642 | + | 0.825336i | \(0.309014\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −41.1255 | −2.90077 | ||||||||
\(202\) | −5.42166 | −0.381467 | ||||||||
\(203\) | −2.52444 | −0.177181 | ||||||||
\(204\) | 17.4600 | 1.22244 | ||||||||
\(205\) | −7.30833 | −0.510436 | ||||||||
\(206\) | −5.62721 | −0.392067 | ||||||||
\(207\) | 29.9844 | 2.08406 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.10278 | 0.214112 | ||||||||
\(211\) | −17.5678 | −1.20942 | −0.604708 | − | 0.796447i | \(-0.706710\pi\) | ||||
−0.604708 | + | 0.796447i | \(0.706710\pi\) | |||||||
\(212\) | −5.57331 | −0.382777 | ||||||||
\(213\) | −26.0978 | −1.78819 | ||||||||
\(214\) | −11.8328 | −0.808871 | ||||||||
\(215\) | 0.578337 | 0.0394423 | ||||||||
\(216\) | 11.2544 | 0.765767 | ||||||||
\(217\) | −3.04888 | −0.206971 | ||||||||
\(218\) | 5.88666 | 0.398695 | ||||||||
\(219\) | −14.2056 | −0.959922 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 14.0383 | 0.942190 | ||||||||
\(223\) | 9.62721 | 0.644686 | 0.322343 | − | 0.946623i | \(-0.395530\pi\) | ||||
0.322343 | + | 0.946623i | \(0.395530\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 6.62721 | 0.441814 | ||||||||
\(226\) | −5.25443 | −0.349519 | ||||||||
\(227\) | −18.6167 | −1.23563 | −0.617815 | − | 0.786323i | \(-0.711982\pi\) | ||||
−0.617815 | + | 0.786323i | \(0.711982\pi\) | |||||||
\(228\) | −14.6761 | −0.971948 | ||||||||
\(229\) | −10.8816 | −0.719079 | −0.359539 | − | 0.933130i | \(-0.617066\pi\) | ||||
−0.359539 | + | 0.933130i | \(0.617066\pi\) | |||||||
\(230\) | 4.52444 | 0.298333 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.52444 | −0.165737 | ||||||||
\(233\) | −12.8433 | −0.841394 | −0.420697 | − | 0.907201i | \(-0.638214\pi\) | ||||
−0.420697 | + | 0.907201i | \(0.638214\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.8328 | 0.771884 | ||||||||
\(236\) | −7.62721 | −0.496489 | ||||||||
\(237\) | 30.3416 | 1.97090 | ||||||||
\(238\) | 5.62721 | 0.364758 | ||||||||
\(239\) | 25.8867 | 1.67447 | 0.837234 | − | 0.546844i | \(-0.184171\pi\) | ||||
0.837234 | + | 0.546844i | \(0.184171\pi\) | |||||||
\(240\) | 3.10278 | 0.200283 | ||||||||
\(241\) | −13.5139 | −0.870505 | −0.435253 | − | 0.900308i | \(-0.643341\pi\) | ||||
−0.435253 | + | 0.900308i | \(0.643341\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.8972 | 0.827357 | ||||||||
\(244\) | −9.83276 | −0.629478 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −22.6761 | −1.44577 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.04888 | −0.193604 | ||||||||
\(249\) | −22.5089 | −1.42644 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 26.9894 | 1.70356 | 0.851779 | − | 0.523901i | \(-0.175524\pi\) | ||||
0.851779 | + | 0.523901i | \(0.175524\pi\) | |||||||
\(252\) | 6.62721 | 0.417475 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −20.7144 | −1.29974 | ||||||||
\(255\) | 17.4600 | 1.09339 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.83779 | −0.177016 | −0.0885081 | − | 0.996075i | \(-0.528210\pi\) | ||||
−0.0885081 | + | 0.996075i | \(0.528210\pi\) | |||||||
\(258\) | 1.79445 | 0.111718 | ||||||||
\(259\) | 4.52444 | 0.281135 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.7300 | −1.03556 | ||||||||
\(262\) | 17.7789 | 1.09838 | ||||||||
\(263\) | 2.95112 | 0.181974 | 0.0909871 | − | 0.995852i | \(-0.470998\pi\) | ||||
0.0909871 | + | 0.995852i | \(0.470998\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.57331 | −0.342366 | ||||||||
\(266\) | −4.72999 | −0.290014 | ||||||||
\(267\) | 44.7144 | 2.73648 | ||||||||
\(268\) | −13.2544 | −0.809643 | ||||||||
\(269\) | −2.88164 | −0.175697 | −0.0878483 | − | 0.996134i | \(-0.527999\pi\) | ||||
−0.0878483 | + | 0.996134i | \(0.527999\pi\) | |||||||
\(270\) | 11.2544 | 0.684923 | ||||||||
\(271\) | 16.3033 | 0.990355 | 0.495178 | − | 0.868792i | \(-0.335103\pi\) | ||||
0.495178 | + | 0.868792i | \(0.335103\pi\) | |||||||
\(272\) | 5.62721 | 0.341200 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.41110 | −0.387309 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 14.0383 | 0.845007 | ||||||||
\(277\) | −13.3622 | −0.802858 | −0.401429 | − | 0.915890i | \(-0.631486\pi\) | ||||
−0.401429 | + | 0.915890i | \(0.631486\pi\) | |||||||
\(278\) | 9.77886 | 0.586497 | ||||||||
\(279\) | −20.2056 | −1.20967 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 27.5577 | 1.64396 | 0.821978 | − | 0.569519i | \(-0.192871\pi\) | ||||
0.821978 | + | 0.569519i | \(0.192871\pi\) | |||||||
\(282\) | 36.7144 | 2.18631 | ||||||||
\(283\) | 11.8922 | 0.706918 | 0.353459 | − | 0.935450i | \(-0.385005\pi\) | ||||
0.353459 | + | 0.935450i | \(0.385005\pi\) | |||||||
\(284\) | −8.41110 | −0.499107 | ||||||||
\(285\) | −14.6761 | −0.869336 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.30833 | −0.431397 | ||||||||
\(288\) | 6.62721 | 0.390512 | ||||||||
\(289\) | 14.6655 | 0.862678 | ||||||||
\(290\) | −2.52444 | −0.148240 | ||||||||
\(291\) | 51.2716 | 3.00560 | ||||||||
\(292\) | −4.57834 | −0.267927 | ||||||||
\(293\) | −14.3133 | −0.836195 | −0.418097 | − | 0.908402i | \(-0.637303\pi\) | ||||
−0.418097 | + | 0.908402i | \(0.637303\pi\) | |||||||
\(294\) | 3.10278 | 0.180958 | ||||||||
\(295\) | −7.62721 | −0.444074 | ||||||||
\(296\) | 4.52444 | 0.262978 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.88666 | −0.109291 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 3.10278 | 0.179139 | ||||||||
\(301\) | 0.578337 | 0.0333348 | ||||||||
\(302\) | 19.9844 | 1.14997 | ||||||||
\(303\) | −16.8222 | −0.966410 | ||||||||
\(304\) | −4.72999 | −0.271283 | ||||||||
\(305\) | −9.83276 | −0.563022 | ||||||||
\(306\) | 37.2927 | 2.13188 | ||||||||
\(307\) | 20.3033 | 1.15877 | 0.579385 | − | 0.815054i | \(-0.303293\pi\) | ||||
0.579385 | + | 0.815054i | \(0.303293\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.4600 | −0.993263 | ||||||||
\(310\) | −3.04888 | −0.173165 | ||||||||
\(311\) | −0.951124 | −0.0539333 | −0.0269666 | − | 0.999636i | \(-0.508585\pi\) | ||||
−0.0269666 | + | 0.999636i | \(0.508585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0922 | −0.570446 | −0.285223 | − | 0.958461i | \(-0.592068\pi\) | ||||
−0.285223 | + | 0.958461i | \(0.592068\pi\) | |||||||
\(314\) | 9.36222 | 0.528341 | ||||||||
\(315\) | 6.62721 | 0.373401 | ||||||||
\(316\) | 9.77886 | 0.550104 | ||||||||
\(317\) | −5.98441 | −0.336118 | −0.168059 | − | 0.985777i | \(-0.553750\pi\) | ||||
−0.168059 | + | 0.985777i | \(0.553750\pi\) | |||||||
\(318\) | −17.2927 | −0.969729 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −36.7144 | −2.04920 | ||||||||
\(322\) | 4.52444 | 0.252137 | ||||||||
\(323\) | −26.6167 | −1.48099 | ||||||||
\(324\) | 15.0383 | 0.835462 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.2544 | 0.955634 | ||||||||
\(327\) | 18.2650 | 1.01006 | ||||||||
\(328\) | −7.30833 | −0.403535 | ||||||||
\(329\) | 11.8328 | 0.652361 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.2927 | 0.950495 | 0.475247 | − | 0.879852i | \(-0.342359\pi\) | ||||
0.475247 | + | 0.879852i | \(0.342359\pi\) | |||||||
\(332\) | −7.25443 | −0.398138 | ||||||||
\(333\) | 29.9844 | 1.64314 | ||||||||
\(334\) | −17.5678 | −0.961266 | ||||||||
\(335\) | −13.2544 | −0.724167 | ||||||||
\(336\) | 3.10278 | 0.169270 | ||||||||
\(337\) | −27.1567 | −1.47932 | −0.739659 | − | 0.672982i | \(-0.765013\pi\) | ||||
−0.739659 | + | 0.672982i | \(0.765013\pi\) | |||||||
\(338\) | −13.0000 | −0.707107 | ||||||||
\(339\) | −16.3033 | −0.885474 | ||||||||
\(340\) | 5.62721 | 0.305178 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −31.3466 | −1.69503 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.578337 | 0.0311818 | ||||||||
\(345\) | 14.0383 | 0.755797 | ||||||||
\(346\) | −10.6761 | −0.573950 | ||||||||
\(347\) | −31.0872 | −1.66885 | −0.834424 | − | 0.551123i | \(-0.814199\pi\) | ||||
−0.834424 | + | 0.551123i | \(0.814199\pi\) | |||||||
\(348\) | −7.83276 | −0.419880 | ||||||||
\(349\) | −21.7250 | −1.16291 | −0.581455 | − | 0.813578i | \(-0.697516\pi\) | ||||
−0.581455 | + | 0.813578i | \(0.697516\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.22114 | 0.437567 | 0.218783 | − | 0.975773i | \(-0.429791\pi\) | ||||
0.218783 | + | 0.975773i | \(0.429791\pi\) | |||||||
\(354\) | −23.6655 | −1.25781 | ||||||||
\(355\) | −8.41110 | −0.446415 | ||||||||
\(356\) | 14.4111 | 0.763787 | ||||||||
\(357\) | 17.4600 | 0.924080 | ||||||||
\(358\) | −4.47054 | −0.236275 | ||||||||
\(359\) | −14.8277 | −0.782578 | −0.391289 | − | 0.920268i | \(-0.627971\pi\) | ||||
−0.391289 | + | 0.920268i | \(0.627971\pi\) | |||||||
\(360\) | 6.62721 | 0.349285 | ||||||||
\(361\) | 3.37279 | 0.177515 | ||||||||
\(362\) | −10.4111 | −0.547195 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.57834 | −0.239641 | ||||||||
\(366\) | −30.5089 | −1.59472 | ||||||||
\(367\) | −23.9406 | −1.24969 | −0.624844 | − | 0.780750i | \(-0.714837\pi\) | ||||
−0.624844 | + | 0.780750i | \(0.714837\pi\) | |||||||
\(368\) | 4.52444 | 0.235853 | ||||||||
\(369\) | −48.4338 | −2.52136 | ||||||||
\(370\) | 4.52444 | 0.235214 | ||||||||
\(371\) | −5.57331 | −0.289352 | ||||||||
\(372\) | −9.45998 | −0.490477 | ||||||||
\(373\) | 3.04888 | 0.157865 | 0.0789324 | − | 0.996880i | \(-0.474849\pi\) | ||||
0.0789324 | + | 0.996880i | \(0.474849\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.10278 | 0.160227 | ||||||||
\(376\) | 11.8328 | 0.610228 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 11.2544 | 0.578865 | ||||||||
\(379\) | −27.6655 | −1.42108 | −0.710541 | − | 0.703655i | \(-0.751550\pi\) | ||||
−0.710541 | + | 0.703655i | \(0.751550\pi\) | |||||||
\(380\) | −4.72999 | −0.242643 | ||||||||
\(381\) | −64.2721 | −3.29276 | ||||||||
\(382\) | 14.6167 | 0.747853 | ||||||||
\(383\) | −7.52946 | −0.384737 | −0.192369 | − | 0.981323i | \(-0.561617\pi\) | ||||
−0.192369 | + | 0.981323i | \(0.561617\pi\) | |||||||
\(384\) | 3.10278 | 0.158338 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.4983 | 1.29783 | ||||||||
\(387\) | 3.83276 | 0.194830 | ||||||||
\(388\) | 16.5244 | 0.838901 | ||||||||
\(389\) | −27.4600 | −1.39228 | −0.696138 | − | 0.717908i | \(-0.745100\pi\) | ||||
−0.696138 | + | 0.717908i | \(0.745100\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.4600 | 1.28757 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 55.1638 | 2.78265 | ||||||||
\(394\) | −5.89220 | −0.296845 | ||||||||
\(395\) | 9.77886 | 0.492028 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.4600 | 1.37818 | 0.689088 | − | 0.724677i | \(-0.258011\pi\) | ||||
0.689088 | + | 0.724677i | \(0.258011\pi\) | |||||||
\(398\) | 15.9305 | 0.798525 | ||||||||
\(399\) | −14.6761 | −0.734723 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 1.52946 | 0.0763776 | 0.0381888 | − | 0.999271i | \(-0.487841\pi\) | ||||
0.0381888 | + | 0.999271i | \(0.487841\pi\) | |||||||
\(402\) | −41.1255 | −2.05115 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5.42166 | −0.269738 | ||||||||
\(405\) | 15.0383 | 0.747260 | ||||||||
\(406\) | −2.52444 | −0.125286 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 17.4600 | 0.864398 | ||||||||
\(409\) | 34.6705 | 1.71435 | 0.857174 | − | 0.515027i | \(-0.172218\pi\) | ||||
0.857174 | + | 0.515027i | \(0.172218\pi\) | |||||||
\(410\) | −7.30833 | −0.360932 | ||||||||
\(411\) | −19.8922 | −0.981210 | ||||||||
\(412\) | −5.62721 | −0.277233 | ||||||||
\(413\) | −7.62721 | −0.375311 | ||||||||
\(414\) | 29.9844 | 1.47365 | ||||||||
\(415\) | −7.25443 | −0.356106 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.3416 | 1.48584 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.4217 | 1.24193 | 0.620965 | − | 0.783838i | \(-0.286741\pi\) | ||||
0.620965 | + | 0.783838i | \(0.286741\pi\) | |||||||
\(420\) | 3.10278 | 0.151400 | ||||||||
\(421\) | −13.7733 | −0.671271 | −0.335635 | − | 0.941992i | \(-0.608951\pi\) | ||||
−0.335635 | + | 0.941992i | \(0.608951\pi\) | |||||||
\(422\) | −17.5678 | −0.855186 | ||||||||
\(423\) | 78.4182 | 3.81283 | ||||||||
\(424\) | −5.57331 | −0.270664 | ||||||||
\(425\) | 5.62721 | 0.272960 | ||||||||
\(426\) | −26.0978 | −1.26444 | ||||||||
\(427\) | −9.83276 | −0.475841 | ||||||||
\(428\) | −11.8328 | −0.571958 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.578337 | 0.0278899 | ||||||||
\(431\) | −29.2489 | −1.40887 | −0.704435 | − | 0.709769i | \(-0.748799\pi\) | ||||
−0.704435 | + | 0.709769i | \(0.748799\pi\) | |||||||
\(432\) | 11.2544 | 0.541479 | ||||||||
\(433\) | −9.04334 | −0.434595 | −0.217298 | − | 0.976105i | \(-0.569724\pi\) | ||||
−0.217298 | + | 0.976105i | \(0.569724\pi\) | |||||||
\(434\) | −3.04888 | −0.146351 | ||||||||
\(435\) | −7.83276 | −0.375552 | ||||||||
\(436\) | 5.88666 | 0.281920 | ||||||||
\(437\) | −21.4005 | −1.02373 | ||||||||
\(438\) | −14.2056 | −0.678767 | ||||||||
\(439\) | −36.7144 | −1.75228 | −0.876141 | − | 0.482054i | \(-0.839891\pi\) | ||||
−0.876141 | + | 0.482054i | \(0.839891\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.62721 | 0.315582 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.6655 | −0.649269 | −0.324634 | − | 0.945840i | \(-0.605241\pi\) | ||||
−0.324634 | + | 0.945840i | \(0.605241\pi\) | |||||||
\(444\) | 14.0383 | 0.666229 | ||||||||
\(445\) | 14.4111 | 0.683152 | ||||||||
\(446\) | 9.62721 | 0.455862 | ||||||||
\(447\) | −5.85389 | −0.276879 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −18.3517 | −0.866068 | −0.433034 | − | 0.901377i | \(-0.642557\pi\) | ||||
−0.433034 | + | 0.901377i | \(0.642557\pi\) | |||||||
\(450\) | 6.62721 | 0.312410 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −5.25443 | −0.247147 | ||||||||
\(453\) | 62.0071 | 2.91335 | ||||||||
\(454\) | −18.6167 | −0.873723 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −14.6761 | −0.687271 | ||||||||
\(457\) | 15.1567 | 0.708999 | 0.354500 | − | 0.935056i | \(-0.384651\pi\) | ||||
0.354500 | + | 0.935056i | \(0.384651\pi\) | |||||||
\(458\) | −10.8816 | −0.508466 | ||||||||
\(459\) | 63.3311 | 2.95604 | ||||||||
\(460\) | 4.52444 | 0.210953 | ||||||||
\(461\) | 9.52946 | 0.443831 | 0.221916 | − | 0.975066i | \(-0.428769\pi\) | ||||
0.221916 | + | 0.975066i | \(0.428769\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.9355 | 0.787061 | 0.393531 | − | 0.919312i | \(-0.371254\pi\) | ||||
0.393531 | + | 0.919312i | \(0.371254\pi\) | |||||||
\(464\) | −2.52444 | −0.117194 | ||||||||
\(465\) | −9.45998 | −0.438696 | ||||||||
\(466\) | −12.8433 | −0.594956 | ||||||||
\(467\) | 16.0439 | 0.742421 | 0.371210 | − | 0.928549i | \(-0.378943\pi\) | ||||
0.371210 | + | 0.928549i | \(0.378943\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.2544 | −0.612033 | ||||||||
\(470\) | 11.8328 | 0.545805 | ||||||||
\(471\) | 29.0489 | 1.33850 | ||||||||
\(472\) | −7.62721 | −0.351071 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 30.3416 | 1.39364 | ||||||||
\(475\) | −4.72999 | −0.217027 | ||||||||
\(476\) | 5.62721 | 0.257923 | ||||||||
\(477\) | −36.9355 | −1.69116 | ||||||||
\(478\) | 25.8867 | 1.18403 | ||||||||
\(479\) | −12.4111 | −0.567078 | −0.283539 | − | 0.958961i | \(-0.591508\pi\) | ||||
−0.283539 | + | 0.958961i | \(0.591508\pi\) | |||||||
\(480\) | 3.10278 | 0.141622 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −13.5139 | −0.615540 | ||||||||
\(483\) | 14.0383 | 0.638765 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.5244 | 0.750336 | ||||||||
\(486\) | 12.8972 | 0.585030 | ||||||||
\(487\) | 1.37781 | 0.0624345 | 0.0312173 | − | 0.999513i | \(-0.490062\pi\) | ||||
0.0312173 | + | 0.999513i | \(0.490062\pi\) | |||||||
\(488\) | −9.83276 | −0.445108 | ||||||||
\(489\) | 53.5366 | 2.42101 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 6.31335 | 0.284917 | 0.142459 | − | 0.989801i | \(-0.454499\pi\) | ||||
0.142459 | + | 0.989801i | \(0.454499\pi\) | |||||||
\(492\) | −22.6761 | −1.02232 | ||||||||
\(493\) | −14.2056 | −0.639786 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.04888 | −0.136899 | ||||||||
\(497\) | −8.41110 | −0.377289 | ||||||||
\(498\) | −22.5089 | −1.00865 | ||||||||
\(499\) | 10.9794 | 0.491505 | 0.245753 | − | 0.969333i | \(-0.420965\pi\) | ||||
0.245753 | + | 0.969333i | \(0.420965\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −54.5089 | −2.43528 | ||||||||
\(502\) | 26.9894 | 1.20460 | ||||||||
\(503\) | 34.1744 | 1.52376 | 0.761880 | − | 0.647718i | \(-0.224277\pi\) | ||||
0.761880 | + | 0.647718i | \(0.224277\pi\) | |||||||
\(504\) | 6.62721 | 0.295200 | ||||||||
\(505\) | −5.42166 | −0.241261 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −40.3361 | −1.79139 | ||||||||
\(508\) | −20.7144 | −0.919053 | ||||||||
\(509\) | −19.5678 | −0.867326 | −0.433663 | − | 0.901075i | \(-0.642779\pi\) | ||||
−0.433663 | + | 0.901075i | \(0.642779\pi\) | |||||||
\(510\) | 17.4600 | 0.773141 | ||||||||
\(511\) | −4.57834 | −0.202534 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −53.2333 | −2.35031 | ||||||||
\(514\) | −2.83779 | −0.125169 | ||||||||
\(515\) | −5.62721 | −0.247965 | ||||||||
\(516\) | 1.79445 | 0.0789963 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 4.52444 | 0.198792 | ||||||||
\(519\) | −33.1255 | −1.45405 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0278 | 0.570756 | 0.285378 | − | 0.958415i | \(-0.407881\pi\) | ||||
0.285378 | + | 0.958415i | \(0.407881\pi\) | |||||||
\(522\) | −16.7300 | −0.732252 | ||||||||
\(523\) | 33.6555 | 1.47165 | 0.735826 | − | 0.677171i | \(-0.236794\pi\) | ||||
0.735826 | + | 0.677171i | \(0.236794\pi\) | |||||||
\(524\) | 17.7789 | 0.776673 | ||||||||
\(525\) | 3.10278 | 0.135416 | ||||||||
\(526\) | 2.95112 | 0.128675 | ||||||||
\(527\) | −17.1567 | −0.747356 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.52946 | −0.109977 | ||||||||
\(530\) | −5.57331 | −0.242089 | ||||||||
\(531\) | −50.5472 | −2.19356 | ||||||||
\(532\) | −4.72999 | −0.205071 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 44.7144 | 1.93498 | ||||||||
\(535\) | −11.8328 | −0.511575 | ||||||||
\(536\) | −13.2544 | −0.572504 | ||||||||
\(537\) | −13.8711 | −0.598581 | ||||||||
\(538\) | −2.88164 | −0.124236 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 11.2544 | 0.484313 | ||||||||
\(541\) | 6.29776 | 0.270762 | 0.135381 | − | 0.990794i | \(-0.456774\pi\) | ||||
0.135381 | + | 0.990794i | \(0.456774\pi\) | |||||||
\(542\) | 16.3033 | 0.700287 | ||||||||
\(543\) | −32.3033 | −1.38627 | ||||||||
\(544\) | 5.62721 | 0.241265 | ||||||||
\(545\) | 5.88666 | 0.252157 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.6867 | 0.756227 | 0.378113 | − | 0.925759i | \(-0.376573\pi\) | ||||
0.378113 | + | 0.925759i | \(0.376573\pi\) | |||||||
\(548\) | −6.41110 | −0.273869 | ||||||||
\(549\) | −65.1638 | −2.78112 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.9406 | 0.508685 | ||||||||
\(552\) | 14.0383 | 0.597510 | ||||||||
\(553\) | 9.77886 | 0.415840 | ||||||||
\(554\) | −13.3622 | −0.567707 | ||||||||
\(555\) | 14.0383 | 0.595893 | ||||||||
\(556\) | 9.77886 | 0.414716 | ||||||||
\(557\) | 6.94108 | 0.294103 | 0.147051 | − | 0.989129i | \(-0.453022\pi\) | ||||
0.147051 | + | 0.989129i | \(0.453022\pi\) | |||||||
\(558\) | −20.2056 | −0.855369 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.5577 | 1.16245 | ||||||||
\(563\) | 27.1355 | 1.14363 | 0.571814 | − | 0.820384i | \(-0.306240\pi\) | ||||
0.571814 | + | 0.820384i | \(0.306240\pi\) | |||||||
\(564\) | 36.7144 | 1.54596 | ||||||||
\(565\) | −5.25443 | −0.221055 | ||||||||
\(566\) | 11.8922 | 0.499867 | ||||||||
\(567\) | 15.0383 | 0.631550 | ||||||||
\(568\) | −8.41110 | −0.352922 | ||||||||
\(569\) | −6.31335 | −0.264669 | −0.132335 | − | 0.991205i | \(-0.542247\pi\) | ||||
−0.132335 | + | 0.991205i | \(0.542247\pi\) | |||||||
\(570\) | −14.6761 | −0.614714 | ||||||||
\(571\) | 37.5366 | 1.57086 | 0.785429 | − | 0.618952i | \(-0.212442\pi\) | ||||
0.785429 | + | 0.618952i | \(0.212442\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 45.3522 | 1.89461 | ||||||||
\(574\) | −7.30833 | −0.305044 | ||||||||
\(575\) | 4.52444 | 0.188682 | ||||||||
\(576\) | 6.62721 | 0.276134 | ||||||||
\(577\) | −8.11334 | −0.337763 | −0.168881 | − | 0.985636i | \(-0.554015\pi\) | ||||
−0.168881 | + | 0.985636i | \(0.554015\pi\) | |||||||
\(578\) | 14.6655 | 0.610005 | ||||||||
\(579\) | 79.1155 | 3.28793 | ||||||||
\(580\) | −2.52444 | −0.104822 | ||||||||
\(581\) | −7.25443 | −0.300964 | ||||||||
\(582\) | 51.2716 | 2.12528 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −4.57834 | −0.189453 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.3133 | −0.591279 | ||||||||
\(587\) | −45.7961 | −1.89021 | −0.945103 | − | 0.326774i | \(-0.894039\pi\) | ||||
−0.945103 | + | 0.326774i | \(0.894039\pi\) | |||||||
\(588\) | 3.10278 | 0.127956 | ||||||||
\(589\) | 14.4211 | 0.594213 | ||||||||
\(590\) | −7.62721 | −0.314007 | ||||||||
\(591\) | −18.2822 | −0.752028 | ||||||||
\(592\) | 4.52444 | 0.185953 | ||||||||
\(593\) | 46.3416 | 1.90302 | 0.951511 | − | 0.307615i | \(-0.0995308\pi\) | ||||
0.951511 | + | 0.307615i | \(0.0995308\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.62721 | 0.230693 | ||||||||
\(596\) | −1.88666 | −0.0772807 | ||||||||
\(597\) | 49.4288 | 2.02299 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.5889 | 0.636945 | 0.318473 | − | 0.947932i | \(-0.396830\pi\) | ||||
0.318473 | + | 0.947932i | \(0.396830\pi\) | |||||||
\(600\) | 3.10278 | 0.126670 | ||||||||
\(601\) | −23.9461 | −0.976782 | −0.488391 | − | 0.872625i | \(-0.662416\pi\) | ||||
−0.488391 | + | 0.872625i | \(0.662416\pi\) | |||||||
\(602\) | 0.578337 | 0.0235713 | ||||||||
\(603\) | −87.8399 | −3.57712 | ||||||||
\(604\) | 19.9844 | 0.813154 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −16.8222 | −0.683355 | ||||||||
\(607\) | −8.24386 | −0.334608 | −0.167304 | − | 0.985905i | \(-0.553506\pi\) | ||||
−0.167304 | + | 0.985905i | \(0.553506\pi\) | |||||||
\(608\) | −4.72999 | −0.191826 | ||||||||
\(609\) | −7.83276 | −0.317400 | ||||||||
\(610\) | −9.83276 | −0.398117 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 37.2927 | 1.50747 | ||||||||
\(613\) | −27.0177 | −1.09123 | −0.545617 | − | 0.838034i | \(-0.683705\pi\) | ||||
−0.545617 | + | 0.838034i | \(0.683705\pi\) | |||||||
\(614\) | 20.3033 | 0.819375 | ||||||||
\(615\) | −22.6761 | −0.914388 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.4011 | 0.660282 | 0.330141 | − | 0.943932i | \(-0.392904\pi\) | ||||
0.330141 | + | 0.943932i | \(0.392904\pi\) | |||||||
\(618\) | −17.4600 | −0.702343 | ||||||||
\(619\) | −0.146111 | −0.00587272 | −0.00293636 | − | 0.999996i | \(-0.500935\pi\) | ||||
−0.00293636 | + | 0.999996i | \(0.500935\pi\) | |||||||
\(620\) | −3.04888 | −0.122446 | ||||||||
\(621\) | 50.9200 | 2.04335 | ||||||||
\(622\) | −0.951124 | −0.0381366 | ||||||||
\(623\) | 14.4111 | 0.577369 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −10.0922 | −0.403366 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.36222 | 0.373593 | ||||||||
\(629\) | 25.4600 | 1.01516 | ||||||||
\(630\) | 6.62721 | 0.264034 | ||||||||
\(631\) | 44.6832 | 1.77881 | 0.889406 | − | 0.457119i | \(-0.151119\pi\) | ||||
0.889406 | + | 0.457119i | \(0.151119\pi\) | |||||||
\(632\) | 9.77886 | 0.388982 | ||||||||
\(633\) | −54.5089 | −2.16653 | ||||||||
\(634\) | −5.98441 | −0.237671 | ||||||||
\(635\) | −20.7144 | −0.822026 | ||||||||
\(636\) | −17.2927 | −0.685702 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −55.7422 | −2.20513 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −37.1355 | −1.46677 | −0.733383 | − | 0.679816i | \(-0.762060\pi\) | ||||
−0.733383 | + | 0.679816i | \(0.762060\pi\) | |||||||
\(642\) | −36.7144 | −1.44900 | ||||||||
\(643\) | −28.1205 | −1.10896 | −0.554482 | − | 0.832196i | \(-0.687083\pi\) | ||||
−0.554482 | + | 0.832196i | \(0.687083\pi\) | |||||||
\(644\) | 4.52444 | 0.178288 | ||||||||
\(645\) | 1.79445 | 0.0706564 | ||||||||
\(646\) | −26.6167 | −1.04722 | ||||||||
\(647\) | −30.4494 | −1.19709 | −0.598545 | − | 0.801089i | \(-0.704254\pi\) | ||||
−0.598545 | + | 0.801089i | \(0.704254\pi\) | |||||||
\(648\) | 15.0383 | 0.590761 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.45998 | −0.370766 | ||||||||
\(652\) | 17.2544 | 0.675735 | ||||||||
\(653\) | 32.9355 | 1.28887 | 0.644434 | − | 0.764660i | \(-0.277093\pi\) | ||||
0.644434 | + | 0.764660i | \(0.277093\pi\) | |||||||
\(654\) | 18.2650 | 0.714218 | ||||||||
\(655\) | 17.7789 | 0.694678 | ||||||||
\(656\) | −7.30833 | −0.285342 | ||||||||
\(657\) | −30.3416 | −1.18374 | ||||||||
\(658\) | 11.8328 | 0.461289 | ||||||||
\(659\) | −27.8922 | −1.08653 | −0.543263 | − | 0.839563i | \(-0.682811\pi\) | ||||
−0.543263 | + | 0.839563i | \(0.682811\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.0388 | −1.12948 | −0.564740 | − | 0.825269i | \(-0.691023\pi\) | ||||
−0.564740 | + | 0.825269i | \(0.691023\pi\) | |||||||
\(662\) | 17.2927 | 0.672101 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.25443 | −0.281526 | ||||||||
\(665\) | −4.72999 | −0.183421 | ||||||||
\(666\) | 29.9844 | 1.16187 | ||||||||
\(667\) | −11.4217 | −0.442249 | ||||||||
\(668\) | −17.5678 | −0.679718 | ||||||||
\(669\) | 29.8711 | 1.15488 | ||||||||
\(670\) | −13.2544 | −0.512063 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.10278 | 0.119692 | ||||||||
\(673\) | 11.6867 | 0.450487 | 0.225244 | − | 0.974302i | \(-0.427682\pi\) | ||||
0.225244 | + | 0.974302i | \(0.427682\pi\) | |||||||
\(674\) | −27.1567 | −1.04604 | ||||||||
\(675\) | 11.2544 | 0.433183 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | 31.1638 | 1.19772 | 0.598861 | − | 0.800853i | \(-0.295620\pi\) | ||||
0.598861 | + | 0.800853i | \(0.295620\pi\) | |||||||
\(678\) | −16.3033 | −0.626125 | ||||||||
\(679\) | 16.5244 | 0.634150 | ||||||||
\(680\) | 5.62721 | 0.215794 | ||||||||
\(681\) | −57.7633 | −2.21349 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.5400 | 0.479831 | 0.239915 | − | 0.970794i | \(-0.422880\pi\) | ||||
0.239915 | + | 0.970794i | \(0.422880\pi\) | |||||||
\(684\) | −31.3466 | −1.19857 | ||||||||
\(685\) | −6.41110 | −0.244956 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −33.7633 | −1.28815 | ||||||||
\(688\) | 0.578337 | 0.0220489 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 14.0383 | 0.534429 | ||||||||
\(691\) | −25.1638 | −0.957277 | −0.478638 | − | 0.878012i | \(-0.658869\pi\) | ||||
−0.478638 | + | 0.878012i | \(0.658869\pi\) | |||||||
\(692\) | −10.6761 | −0.405844 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −31.0872 | −1.18005 | ||||||||
\(695\) | 9.77886 | 0.370933 | ||||||||
\(696\) | −7.83276 | −0.296900 | ||||||||
\(697\) | −41.1255 | −1.55774 | ||||||||
\(698\) | −21.7250 | −0.822302 | ||||||||
\(699\) | −39.8500 | −1.50726 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 13.1411 | 0.496332 | 0.248166 | − | 0.968718i | \(-0.420172\pi\) | ||||
0.248166 | + | 0.968718i | \(0.420172\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.4005 | −0.807137 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 36.7144 | 1.38274 | ||||||||
\(706\) | 8.22114 | 0.309407 | ||||||||
\(707\) | −5.42166 | −0.203903 | ||||||||
\(708\) | −23.6655 | −0.889405 | ||||||||
\(709\) | 25.3311 | 0.951328 | 0.475664 | − | 0.879627i | \(-0.342208\pi\) | ||||
0.475664 | + | 0.879627i | \(0.342208\pi\) | |||||||
\(710\) | −8.41110 | −0.315663 | ||||||||
\(711\) | 64.8066 | 2.43044 | ||||||||
\(712\) | 14.4111 | 0.540079 | ||||||||
\(713\) | −13.7944 | −0.516606 | ||||||||
\(714\) | 17.4600 | 0.653423 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.47054 | −0.167072 | ||||||||
\(717\) | 80.3205 | 2.99962 | ||||||||
\(718\) | −14.8277 | −0.553366 | ||||||||
\(719\) | −43.2616 | −1.61338 | −0.806692 | − | 0.590972i | \(-0.798744\pi\) | ||||
−0.806692 | + | 0.590972i | \(0.798744\pi\) | |||||||
\(720\) | 6.62721 | 0.246982 | ||||||||
\(721\) | −5.62721 | −0.209568 | ||||||||
\(722\) | 3.37279 | 0.125522 | ||||||||
\(723\) | −41.9305 | −1.55941 | ||||||||
\(724\) | −10.4111 | −0.386925 | ||||||||
\(725\) | −2.52444 | −0.0937553 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −47.6938 | −1.76886 | −0.884432 | − | 0.466668i | \(-0.845454\pi\) | ||||
−0.884432 | + | 0.466668i | \(0.845454\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.09775 | −0.188806 | ||||||||
\(730\) | −4.57834 | −0.169452 | ||||||||
\(731\) | 3.25443 | 0.120369 | ||||||||
\(732\) | −30.5089 | −1.12764 | ||||||||
\(733\) | −32.7738 | −1.21053 | −0.605265 | − | 0.796024i | \(-0.706933\pi\) | ||||
−0.605265 | + | 0.796024i | \(0.706933\pi\) | |||||||
\(734\) | −23.9406 | −0.883662 | ||||||||
\(735\) | 3.10278 | 0.114448 | ||||||||
\(736\) | 4.52444 | 0.166773 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −48.4338 | −1.78287 | ||||||||
\(739\) | 34.5089 | 1.26943 | 0.634714 | − | 0.772747i | \(-0.281118\pi\) | ||||
0.634714 | + | 0.772747i | \(0.281118\pi\) | |||||||
\(740\) | 4.52444 | 0.166322 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.57331 | −0.204603 | ||||||||
\(743\) | 34.2822 | 1.25769 | 0.628846 | − | 0.777530i | \(-0.283528\pi\) | ||||
0.628846 | + | 0.777530i | \(0.283528\pi\) | |||||||
\(744\) | −9.45998 | −0.346820 | ||||||||
\(745\) | −1.88666 | −0.0691220 | ||||||||
\(746\) | 3.04888 | 0.111627 | ||||||||
\(747\) | −48.0766 | −1.75903 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.8328 | −0.432360 | ||||||||
\(750\) | 3.10278 | 0.113297 | ||||||||
\(751\) | −39.1355 | −1.42808 | −0.714038 | − | 0.700107i | \(-0.753136\pi\) | ||||
−0.714038 | + | 0.700107i | \(0.753136\pi\) | |||||||
\(752\) | 11.8328 | 0.431496 | ||||||||
\(753\) | 83.7422 | 3.05173 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.9844 | 0.727307 | ||||||||
\(756\) | 11.2544 | 0.409320 | ||||||||
\(757\) | −25.7577 | −0.936181 | −0.468090 | − | 0.883681i | \(-0.655058\pi\) | ||||
−0.468090 | + | 0.883681i | \(0.655058\pi\) | |||||||
\(758\) | −27.6655 | −1.00486 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.72999 | −0.171575 | ||||||||
\(761\) | −1.74055 | −0.0630949 | −0.0315475 | − | 0.999502i | \(-0.510044\pi\) | ||||
−0.0315475 | + | 0.999502i | \(0.510044\pi\) | |||||||
\(762\) | −64.2721 | −2.32833 | ||||||||
\(763\) | 5.88666 | 0.213111 | ||||||||
\(764\) | 14.6167 | 0.528812 | ||||||||
\(765\) | 37.2927 | 1.34832 | ||||||||
\(766\) | −7.52946 | −0.272050 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 3.10278 | 0.111962 | ||||||||
\(769\) | 36.8449 | 1.32866 | 0.664331 | − | 0.747438i | \(-0.268717\pi\) | ||||
0.664331 | + | 0.747438i | \(0.268717\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.80501 | −0.317105 | ||||||||
\(772\) | 25.4983 | 0.917704 | ||||||||
\(773\) | −33.4499 | −1.20311 | −0.601555 | − | 0.798831i | \(-0.705452\pi\) | ||||
−0.601555 | + | 0.798831i | \(0.705452\pi\) | |||||||
\(774\) | 3.83276 | 0.137766 | ||||||||
\(775\) | −3.04888 | −0.109519 | ||||||||
\(776\) | 16.5244 | 0.593193 | ||||||||
\(777\) | 14.0383 | 0.503622 | ||||||||
\(778\) | −27.4600 | −0.984488 | ||||||||
\(779\) | 34.5683 | 1.23854 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 25.4600 | 0.910447 | ||||||||
\(783\) | −28.4111 | −1.01533 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 9.36222 | 0.334152 | ||||||||
\(786\) | 55.1638 | 1.96763 | ||||||||
\(787\) | −6.72445 | −0.239701 | −0.119850 | − | 0.992792i | \(-0.538241\pi\) | ||||
−0.119850 | + | 0.992792i | \(0.538241\pi\) | |||||||
\(788\) | −5.89220 | −0.209901 | ||||||||
\(789\) | 9.15667 | 0.325986 | ||||||||
\(790\) | 9.77886 | 0.347916 | ||||||||
\(791\) | −5.25443 | −0.186826 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 27.4600 | 0.974518 | ||||||||
\(795\) | −17.2927 | −0.613310 | ||||||||
\(796\) | 15.9305 | 0.564642 | ||||||||
\(797\) | −31.2444 | −1.10673 | −0.553366 | − | 0.832938i | \(-0.686657\pi\) | ||||
−0.553366 | + | 0.832938i | \(0.686657\pi\) | |||||||
\(798\) | −14.6761 | −0.519528 | ||||||||
\(799\) | 66.5855 | 2.35562 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 95.5054 | 3.37452 | ||||||||
\(802\) | 1.52946 | 0.0540072 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −41.1255 | −1.45038 | ||||||||
\(805\) | 4.52444 | 0.159465 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.94108 | −0.314741 | ||||||||
\(808\) | −5.42166 | −0.190733 | ||||||||
\(809\) | 44.7910 | 1.57477 | 0.787384 | − | 0.616462i | \(-0.211435\pi\) | ||||
0.787384 | + | 0.616462i | \(0.211435\pi\) | |||||||
\(810\) | 15.0383 | 0.528392 | ||||||||
\(811\) | 15.3466 | 0.538893 | 0.269447 | − | 0.963015i | \(-0.413159\pi\) | ||||
0.269447 | + | 0.963015i | \(0.413159\pi\) | |||||||
\(812\) | −2.52444 | −0.0885904 | ||||||||
\(813\) | 50.5855 | 1.77411 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.2544 | 0.604396 | ||||||||
\(816\) | 17.4600 | 0.611221 | ||||||||
\(817\) | −2.73553 | −0.0957040 | ||||||||
\(818\) | 34.6705 | 1.21223 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.30833 | −0.255218 | ||||||||
\(821\) | 10.0822 | 0.351870 | 0.175935 | − | 0.984402i | \(-0.443705\pi\) | ||||
0.175935 | + | 0.984402i | \(0.443705\pi\) | |||||||
\(822\) | −19.8922 | −0.693820 | ||||||||
\(823\) | 17.2388 | 0.600908 | 0.300454 | − | 0.953796i | \(-0.402862\pi\) | ||||
0.300454 | + | 0.953796i | \(0.402862\pi\) | |||||||
\(824\) | −5.62721 | −0.196033 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.62721 | −0.265385 | ||||||||
\(827\) | −55.7422 | −1.93834 | −0.969172 | − | 0.246384i | \(-0.920758\pi\) | ||||
−0.969172 | + | 0.246384i | \(0.920758\pi\) | |||||||
\(828\) | 29.9844 | 1.04203 | ||||||||
\(829\) | −32.8605 | −1.14129 | −0.570646 | − | 0.821196i | \(-0.693307\pi\) | ||||
−0.570646 | + | 0.821196i | \(0.693307\pi\) | |||||||
\(830\) | −7.25443 | −0.251805 | ||||||||
\(831\) | −41.4600 | −1.43823 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.62721 | 0.194971 | ||||||||
\(834\) | 30.3416 | 1.05064 | ||||||||
\(835\) | −17.5678 | −0.607958 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34.3133 | −1.18604 | ||||||||
\(838\) | 25.4217 | 0.878177 | ||||||||
\(839\) | 6.71440 | 0.231807 | 0.115903 | − | 0.993260i | \(-0.463024\pi\) | ||||
0.115903 | + | 0.993260i | \(0.463024\pi\) | |||||||
\(840\) | 3.10278 | 0.107056 | ||||||||
\(841\) | −22.6272 | −0.780249 | ||||||||
\(842\) | −13.7733 | −0.474660 | ||||||||
\(843\) | 85.5054 | 2.94496 | ||||||||
\(844\) | −17.5678 | −0.604708 | ||||||||
\(845\) | −13.0000 | −0.447214 | ||||||||
\(846\) | 78.4182 | 2.69607 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.57331 | −0.191388 | ||||||||
\(849\) | 36.8988 | 1.26636 | ||||||||
\(850\) | 5.62721 | 0.193012 | ||||||||
\(851\) | 20.4705 | 0.701721 | ||||||||
\(852\) | −26.0978 | −0.894094 | ||||||||
\(853\) | −3.01056 | −0.103080 | −0.0515399 | − | 0.998671i | \(-0.516413\pi\) | ||||
−0.0515399 | + | 0.998671i | \(0.516413\pi\) | |||||||
\(854\) | −9.83276 | −0.336470 | ||||||||
\(855\) | −31.3466 | −1.07203 | ||||||||
\(856\) | −11.8328 | −0.404436 | ||||||||
\(857\) | −17.8116 | −0.608434 | −0.304217 | − | 0.952603i | \(-0.598395\pi\) | ||||
−0.304217 | + | 0.952603i | \(0.598395\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.3416 | −1.51292 | −0.756458 | − | 0.654042i | \(-0.773072\pi\) | ||||
−0.756458 | + | 0.654042i | \(0.773072\pi\) | |||||||
\(860\) | 0.578337 | 0.0197211 | ||||||||
\(861\) | −22.6761 | −0.772799 | ||||||||
\(862\) | −29.2489 | −0.996221 | ||||||||
\(863\) | −27.1099 | −0.922832 | −0.461416 | − | 0.887184i | \(-0.652658\pi\) | ||||
−0.461416 | + | 0.887184i | \(0.652658\pi\) | |||||||
\(864\) | 11.2544 | 0.382883 | ||||||||
\(865\) | −10.6761 | −0.362998 | ||||||||
\(866\) | −9.04334 | −0.307305 | ||||||||
\(867\) | 45.5038 | 1.54539 | ||||||||
\(868\) | −3.04888 | −0.103486 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −7.83276 | −0.265556 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 5.88666 | 0.199348 | ||||||||
\(873\) | 109.511 | 3.70638 | ||||||||
\(874\) | −21.4005 | −0.723884 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −14.2056 | −0.479961 | ||||||||
\(877\) | −40.9511 | −1.38282 | −0.691411 | − | 0.722462i | \(-0.743010\pi\) | ||||
−0.691411 | + | 0.722462i | \(0.743010\pi\) | |||||||
\(878\) | −36.7144 | −1.23905 | ||||||||
\(879\) | −44.4111 | −1.49795 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 53.3311 | 1.79677 | 0.898384 | − | 0.439210i | \(-0.144742\pi\) | ||||
0.898384 | + | 0.439210i | \(0.144742\pi\) | |||||||
\(882\) | 6.62721 | 0.223150 | ||||||||
\(883\) | 27.7944 | 0.935358 | 0.467679 | − | 0.883898i | \(-0.345090\pi\) | ||||
0.467679 | + | 0.883898i | \(0.345090\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23.6655 | −0.795508 | ||||||||
\(886\) | −13.6655 | −0.459102 | ||||||||
\(887\) | −30.2933 | −1.01715 | −0.508574 | − | 0.861018i | \(-0.669827\pi\) | ||||
−0.508574 | + | 0.861018i | \(0.669827\pi\) | |||||||
\(888\) | 14.0383 | 0.471095 | ||||||||
\(889\) | −20.7144 | −0.694739 | ||||||||
\(890\) | 14.4111 | 0.483061 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.62721 | 0.322343 | ||||||||
\(893\) | −55.9688 | −1.87293 | ||||||||
\(894\) | −5.85389 | −0.195783 | ||||||||
\(895\) | −4.47054 | −0.149434 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.3517 | −0.612403 | ||||||||
\(899\) | 7.69670 | 0.256699 | ||||||||
\(900\) | 6.62721 | 0.220907 | ||||||||
\(901\) | −31.3622 | −1.04483 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.79445 | 0.0597156 | ||||||||
\(904\) | −5.25443 | −0.174760 | ||||||||
\(905\) | −10.4111 | −0.346077 | ||||||||
\(906\) | 62.0071 | 2.06005 | ||||||||
\(907\) | −39.8711 | −1.32390 | −0.661949 | − | 0.749549i | \(-0.730270\pi\) | ||||
−0.661949 | + | 0.749549i | \(0.730270\pi\) | |||||||
\(908\) | −18.6167 | −0.617815 | ||||||||
\(909\) | −35.9305 | −1.19174 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.7733 | 0.655119 | 0.327560 | − | 0.944830i | \(-0.393774\pi\) | ||||
0.327560 | + | 0.944830i | \(0.393774\pi\) | |||||||
\(912\) | −14.6761 | −0.485974 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 15.1567 | 0.501338 | ||||||||
\(915\) | −30.5089 | −1.00859 | ||||||||
\(916\) | −10.8816 | −0.359539 | ||||||||
\(917\) | 17.7789 | 0.587110 | ||||||||
\(918\) | 63.3311 | 2.09024 | ||||||||
\(919\) | 17.8100 | 0.587499 | 0.293749 | − | 0.955882i | \(-0.405097\pi\) | ||||
0.293749 | + | 0.955882i | \(0.405097\pi\) | |||||||
\(920\) | 4.52444 | 0.149166 | ||||||||
\(921\) | 62.9966 | 2.07581 | ||||||||
\(922\) | 9.52946 | 0.313836 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.52444 | 0.148763 | ||||||||
\(926\) | 16.9355 | 0.556536 | ||||||||
\(927\) | −37.2927 | −1.22485 | ||||||||
\(928\) | −2.52444 | −0.0828687 | ||||||||
\(929\) | 24.7355 | 0.811546 | 0.405773 | − | 0.913974i | \(-0.367002\pi\) | ||||
0.405773 | + | 0.913974i | \(0.367002\pi\) | |||||||
\(930\) | −9.45998 | −0.310205 | ||||||||
\(931\) | −4.72999 | −0.155019 | ||||||||
\(932\) | −12.8433 | −0.420697 | ||||||||
\(933\) | −2.95112 | −0.0966155 | ||||||||
\(934\) | 16.0439 | 0.524971 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.52946 | 0.115302 | 0.0576512 | − | 0.998337i | \(-0.481639\pi\) | ||||
0.0576512 | + | 0.998337i | \(0.481639\pi\) | |||||||
\(938\) | −13.2544 | −0.432772 | ||||||||
\(939\) | −31.3139 | −1.02189 | ||||||||
\(940\) | 11.8328 | 0.385942 | ||||||||
\(941\) | −49.4217 | −1.61110 | −0.805550 | − | 0.592528i | \(-0.798130\pi\) | ||||
−0.805550 | + | 0.592528i | \(0.798130\pi\) | |||||||
\(942\) | 29.0489 | 0.946464 | ||||||||
\(943\) | −33.0661 | −1.07678 | ||||||||
\(944\) | −7.62721 | −0.248245 | ||||||||
\(945\) | 11.2544 | 0.366107 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.7144 | 0.998084 | 0.499042 | − | 0.866578i | \(-0.333685\pi\) | ||||
0.499042 | + | 0.866578i | \(0.333685\pi\) | |||||||
\(948\) | 30.3416 | 0.985450 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4.72999 | −0.153461 | ||||||||
\(951\) | −18.5683 | −0.602118 | ||||||||
\(952\) | 5.62721 | 0.182379 | ||||||||
\(953\) | 24.7527 | 0.801819 | 0.400910 | − | 0.916118i | \(-0.368694\pi\) | ||||
0.400910 | + | 0.916118i | \(0.368694\pi\) | |||||||
\(954\) | −36.9355 | −1.19583 | ||||||||
\(955\) | 14.6167 | 0.472984 | ||||||||
\(956\) | 25.8867 | 0.837234 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.4111 | −0.400984 | ||||||||
\(959\) | −6.41110 | −0.207025 | ||||||||
\(960\) | 3.10278 | 0.100142 | ||||||||
\(961\) | −21.7044 | −0.700141 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −78.4182 | −2.52699 | ||||||||
\(964\) | −13.5139 | −0.435253 | ||||||||
\(965\) | 25.4983 | 0.820819 | ||||||||
\(966\) | 14.0383 | 0.451675 | ||||||||
\(967\) | 34.2822 | 1.10244 | 0.551220 | − | 0.834360i | \(-0.314162\pi\) | ||||
0.551220 | + | 0.834360i | \(0.314162\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −82.5855 | −2.65303 | ||||||||
\(970\) | 16.5244 | 0.530568 | ||||||||
\(971\) | −48.0383 | −1.54162 | −0.770811 | − | 0.637063i | \(-0.780149\pi\) | ||||
−0.770811 | + | 0.637063i | \(0.780149\pi\) | |||||||
\(972\) | 12.8972 | 0.413679 | ||||||||
\(973\) | 9.77886 | 0.313496 | ||||||||
\(974\) | 1.37781 | 0.0441479 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.83276 | −0.314739 | ||||||||
\(977\) | 27.5678 | 0.881971 | 0.440986 | − | 0.897514i | \(-0.354629\pi\) | ||||
0.440986 | + | 0.897514i | \(0.354629\pi\) | |||||||
\(978\) | 53.5366 | 1.71191 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 39.0122 | 1.24556 | ||||||||
\(982\) | 6.31335 | 0.201467 | ||||||||
\(983\) | 56.3316 | 1.79670 | 0.898349 | − | 0.439282i | \(-0.144767\pi\) | ||||
0.898349 | + | 0.439282i | \(0.144767\pi\) | |||||||
\(984\) | −22.6761 | −0.722887 | ||||||||
\(985\) | −5.89220 | −0.187741 | ||||||||
\(986\) | −14.2056 | −0.452397 | ||||||||
\(987\) | 36.7144 | 1.16863 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.61665 | 0.0832046 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.37993 | 0.139133 | 0.0695665 | − | 0.997577i | \(-0.477838\pi\) | ||||
0.0695665 | + | 0.997577i | \(0.477838\pi\) | |||||||
\(992\) | −3.04888 | −0.0968019 | ||||||||
\(993\) | 53.6555 | 1.70271 | ||||||||
\(994\) | −8.41110 | −0.266784 | ||||||||
\(995\) | 15.9305 | 0.505031 | ||||||||
\(996\) | −22.5089 | −0.713220 | ||||||||
\(997\) | −27.7139 | −0.877708 | −0.438854 | − | 0.898558i | \(-0.644615\pi\) | ||||
−0.438854 | + | 0.898558i | \(0.644615\pi\) | |||||||
\(998\) | 10.9794 | 0.347547 | ||||||||
\(999\) | 50.9200 | 1.61104 |
(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.cn.1.3 | yes | 3 | |
11.10 | odd | 2 | 8470.2.a.ch.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.ch.1.3 | ✓ | 3 | 11.10 | odd | 2 | ||
8470.2.a.cn.1.3 | yes | 3 | 1.1 | even | 1 | trivial |