Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3381,2,Mod(1,3381)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, 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("3381.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3381 = 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3381.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: | \(26.9974209234\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 13x^{8} + 41x^{7} + 47x^{6} - 165x^{5} - 45x^{4} + 207x^{3} + 12x^{2} - 76x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 483) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.73999\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3381.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73999 | −1.93747 | −0.968733 | − | 0.248105i | \(-0.920192\pi\) | ||||
−0.968733 | + | 0.248105i | \(0.920192\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.50755 | 2.75378 | ||||||||
\(5\) | −3.38181 | −1.51239 | −0.756197 | − | 0.654345i | \(-0.772945\pi\) | ||||
−0.756197 | + | 0.654345i | \(0.772945\pi\) | |||||||
\(6\) | 2.73999 | 1.11860 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −9.61066 | −3.39788 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 9.26614 | 2.93021 | ||||||||
\(11\) | 1.88341 | 0.567870 | 0.283935 | − | 0.958844i | \(-0.408360\pi\) | ||||
0.283935 | + | 0.958844i | \(0.408360\pi\) | |||||||
\(12\) | −5.50755 | −1.58989 | ||||||||
\(13\) | 1.76938 | 0.490736 | 0.245368 | − | 0.969430i | \(-0.421091\pi\) | ||||
0.245368 | + | 0.969430i | \(0.421091\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.38181 | 0.873181 | ||||||||
\(16\) | 15.3180 | 3.82950 | ||||||||
\(17\) | −5.89595 | −1.42998 | −0.714989 | − | 0.699135i | \(-0.753569\pi\) | ||||
−0.714989 | + | 0.699135i | \(0.753569\pi\) | |||||||
\(18\) | −2.73999 | −0.645822 | ||||||||
\(19\) | −6.62660 | −1.52025 | −0.760123 | − | 0.649779i | \(-0.774862\pi\) | ||||
−0.760123 | + | 0.649779i | \(0.774862\pi\) | |||||||
\(20\) | −18.6255 | −4.16479 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.16053 | −1.10023 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 9.61066 | 1.96177 | ||||||||
\(25\) | 6.43667 | 1.28733 | ||||||||
\(26\) | −4.84807 | −0.950785 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.24468 | 1.53100 | 0.765500 | − | 0.643436i | \(-0.222492\pi\) | ||||
0.765500 | + | 0.643436i | \(0.222492\pi\) | |||||||
\(30\) | −9.26614 | −1.69176 | ||||||||
\(31\) | 2.94359 | 0.528684 | 0.264342 | − | 0.964429i | \(-0.414845\pi\) | ||||
0.264342 | + | 0.964429i | \(0.414845\pi\) | |||||||
\(32\) | −22.7499 | −4.02165 | ||||||||
\(33\) | −1.88341 | −0.327860 | ||||||||
\(34\) | 16.1549 | 2.77054 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.50755 | 0.917925 | ||||||||
\(37\) | −4.43562 | −0.729212 | −0.364606 | − | 0.931162i | \(-0.618796\pi\) | ||||
−0.364606 | + | 0.931162i | \(0.618796\pi\) | |||||||
\(38\) | 18.1568 | 2.94543 | ||||||||
\(39\) | −1.76938 | −0.283327 | ||||||||
\(40\) | 32.5015 | 5.13893 | ||||||||
\(41\) | −5.90495 | −0.922198 | −0.461099 | − | 0.887349i | \(-0.652545\pi\) | ||||
−0.461099 | + | 0.887349i | \(0.652545\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.669028 | 0.102026 | 0.0510129 | − | 0.998698i | \(-0.483755\pi\) | ||||
0.0510129 | + | 0.998698i | \(0.483755\pi\) | |||||||
\(44\) | 10.3730 | 1.56379 | ||||||||
\(45\) | −3.38181 | −0.504131 | ||||||||
\(46\) | −2.73999 | −0.403990 | ||||||||
\(47\) | 1.79517 | 0.261852 | 0.130926 | − | 0.991392i | \(-0.458205\pi\) | ||||
0.130926 | + | 0.991392i | \(0.458205\pi\) | |||||||
\(48\) | −15.3180 | −2.21096 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −17.6364 | −2.49416 | ||||||||
\(51\) | 5.89595 | 0.825599 | ||||||||
\(52\) | 9.74492 | 1.35138 | ||||||||
\(53\) | −9.68500 | −1.33034 | −0.665169 | − | 0.746693i | \(-0.731640\pi\) | ||||
−0.665169 | + | 0.746693i | \(0.731640\pi\) | |||||||
\(54\) | 2.73999 | 0.372866 | ||||||||
\(55\) | −6.36935 | −0.858843 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.62660 | 0.877715 | ||||||||
\(58\) | −22.5904 | −2.96626 | ||||||||
\(59\) | 1.36723 | 0.177998 | 0.0889988 | − | 0.996032i | \(-0.471633\pi\) | ||||
0.0889988 | + | 0.996032i | \(0.471633\pi\) | |||||||
\(60\) | 18.6255 | 2.40454 | ||||||||
\(61\) | 9.36339 | 1.19886 | 0.599430 | − | 0.800427i | \(-0.295394\pi\) | ||||
0.599430 | + | 0.800427i | \(0.295394\pi\) | |||||||
\(62\) | −8.06540 | −1.02431 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 31.6985 | 3.96231 | ||||||||
\(65\) | −5.98370 | −0.742186 | ||||||||
\(66\) | 5.16053 | 0.635218 | ||||||||
\(67\) | −8.17894 | −0.999216 | −0.499608 | − | 0.866252i | \(-0.666523\pi\) | ||||
−0.499608 | + | 0.866252i | \(0.666523\pi\) | |||||||
\(68\) | −32.4723 | −3.93784 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.295052 | −0.0350162 | −0.0175081 | − | 0.999847i | \(-0.505573\pi\) | ||||
−0.0175081 | + | 0.999847i | \(0.505573\pi\) | |||||||
\(72\) | −9.61066 | −1.13263 | ||||||||
\(73\) | −4.45751 | −0.521712 | −0.260856 | − | 0.965378i | \(-0.584005\pi\) | ||||
−0.260856 | + | 0.965378i | \(0.584005\pi\) | |||||||
\(74\) | 12.1536 | 1.41282 | ||||||||
\(75\) | −6.43667 | −0.743242 | ||||||||
\(76\) | −36.4963 | −4.18642 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.84807 | 0.548936 | ||||||||
\(79\) | −3.02768 | −0.340641 | −0.170320 | − | 0.985389i | \(-0.554480\pi\) | ||||
−0.170320 | + | 0.985389i | \(0.554480\pi\) | |||||||
\(80\) | −51.8027 | −5.79171 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 16.1795 | 1.78673 | ||||||||
\(83\) | −10.5300 | −1.15582 | −0.577910 | − | 0.816100i | \(-0.696132\pi\) | ||||
−0.577910 | + | 0.816100i | \(0.696132\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.9390 | 2.16269 | ||||||||
\(86\) | −1.83313 | −0.197672 | ||||||||
\(87\) | −8.24468 | −0.883923 | ||||||||
\(88\) | −18.1008 | −1.92955 | ||||||||
\(89\) | −10.7196 | −1.13628 | −0.568138 | − | 0.822933i | \(-0.692336\pi\) | ||||
−0.568138 | + | 0.822933i | \(0.692336\pi\) | |||||||
\(90\) | 9.26614 | 0.976737 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.50755 | 0.574202 | ||||||||
\(93\) | −2.94359 | −0.305236 | ||||||||
\(94\) | −4.91874 | −0.507329 | ||||||||
\(95\) | 22.4099 | 2.29921 | ||||||||
\(96\) | 22.7499 | 2.32190 | ||||||||
\(97\) | 15.6290 | 1.58688 | 0.793441 | − | 0.608648i | \(-0.208288\pi\) | ||||
0.793441 | + | 0.608648i | \(0.208288\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.88341 | 0.189290 | ||||||||
\(100\) | 35.4503 | 3.54503 | ||||||||
\(101\) | 7.56916 | 0.753159 | 0.376580 | − | 0.926384i | \(-0.377100\pi\) | ||||
0.376580 | + | 0.926384i | \(0.377100\pi\) | |||||||
\(102\) | −16.1549 | −1.59957 | ||||||||
\(103\) | −2.62127 | −0.258281 | −0.129141 | − | 0.991626i | \(-0.541222\pi\) | ||||
−0.129141 | + | 0.991626i | \(0.541222\pi\) | |||||||
\(104\) | −17.0049 | −1.66746 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 26.5368 | 2.57748 | ||||||||
\(107\) | 17.3322 | 1.67557 | 0.837783 | − | 0.546004i | \(-0.183852\pi\) | ||||
0.837783 | + | 0.546004i | \(0.183852\pi\) | |||||||
\(108\) | −5.50755 | −0.529964 | ||||||||
\(109\) | −13.3681 | −1.28043 | −0.640214 | − | 0.768197i | \(-0.721154\pi\) | ||||
−0.640214 | + | 0.768197i | \(0.721154\pi\) | |||||||
\(110\) | 17.4520 | 1.66398 | ||||||||
\(111\) | 4.43562 | 0.421011 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.18709 | −0.111672 | −0.0558360 | − | 0.998440i | \(-0.517782\pi\) | ||||
−0.0558360 | + | 0.998440i | \(0.517782\pi\) | |||||||
\(114\) | −18.1568 | −1.70054 | ||||||||
\(115\) | −3.38181 | −0.315356 | ||||||||
\(116\) | 45.4080 | 4.21603 | ||||||||
\(117\) | 1.76938 | 0.163579 | ||||||||
\(118\) | −3.74618 | −0.344864 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −32.5015 | −2.96696 | ||||||||
\(121\) | −7.45276 | −0.677523 | ||||||||
\(122\) | −25.6556 | −2.32275 | ||||||||
\(123\) | 5.90495 | 0.532431 | ||||||||
\(124\) | 16.2120 | 1.45588 | ||||||||
\(125\) | −4.85853 | −0.434560 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.2311 | −1.08533 | −0.542667 | − | 0.839948i | \(-0.682585\pi\) | ||||
−0.542667 | + | 0.839948i | \(0.682585\pi\) | |||||||
\(128\) | −41.3538 | −3.65519 | ||||||||
\(129\) | −0.669028 | −0.0589046 | ||||||||
\(130\) | 16.3953 | 1.43796 | ||||||||
\(131\) | −6.05670 | −0.529176 | −0.264588 | − | 0.964362i | \(-0.585236\pi\) | ||||
−0.264588 | + | 0.964362i | \(0.585236\pi\) | |||||||
\(132\) | −10.3730 | −0.902853 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 22.4102 | 1.93595 | ||||||||
\(135\) | 3.38181 | 0.291060 | ||||||||
\(136\) | 56.6640 | 4.85890 | ||||||||
\(137\) | −14.2926 | −1.22110 | −0.610550 | − | 0.791978i | \(-0.709052\pi\) | ||||
−0.610550 | + | 0.791978i | \(0.709052\pi\) | |||||||
\(138\) | 2.73999 | 0.233244 | ||||||||
\(139\) | −16.4290 | −1.39349 | −0.696743 | − | 0.717321i | \(-0.745368\pi\) | ||||
−0.696743 | + | 0.717321i | \(0.745368\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.79517 | −0.151180 | ||||||||
\(142\) | 0.808440 | 0.0678427 | ||||||||
\(143\) | 3.33246 | 0.278675 | ||||||||
\(144\) | 15.3180 | 1.27650 | ||||||||
\(145\) | −27.8820 | −2.31547 | ||||||||
\(146\) | 12.2135 | 1.01080 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −24.4294 | −2.00809 | ||||||||
\(149\) | 13.8036 | 1.13084 | 0.565418 | − | 0.824805i | \(-0.308715\pi\) | ||||
0.565418 | + | 0.824805i | \(0.308715\pi\) | |||||||
\(150\) | 17.6364 | 1.44001 | ||||||||
\(151\) | −4.24714 | −0.345628 | −0.172814 | − | 0.984955i | \(-0.555286\pi\) | ||||
−0.172814 | + | 0.984955i | \(0.555286\pi\) | |||||||
\(152\) | 63.6860 | 5.16562 | ||||||||
\(153\) | −5.89595 | −0.476660 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.95467 | −0.799578 | ||||||||
\(156\) | −9.74492 | −0.780218 | ||||||||
\(157\) | −0.667792 | −0.0532956 | −0.0266478 | − | 0.999645i | \(-0.508483\pi\) | ||||
−0.0266478 | + | 0.999645i | \(0.508483\pi\) | |||||||
\(158\) | 8.29583 | 0.659980 | ||||||||
\(159\) | 9.68500 | 0.768071 | ||||||||
\(160\) | 76.9359 | 6.08232 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.73999 | −0.215274 | ||||||||
\(163\) | −0.727180 | −0.0569572 | −0.0284786 | − | 0.999594i | \(-0.509066\pi\) | ||||
−0.0284786 | + | 0.999594i | \(0.509066\pi\) | |||||||
\(164\) | −32.5218 | −2.53952 | ||||||||
\(165\) | 6.36935 | 0.495853 | ||||||||
\(166\) | 28.8522 | 2.23936 | ||||||||
\(167\) | 9.42526 | 0.729349 | 0.364674 | − | 0.931135i | \(-0.381180\pi\) | ||||
0.364674 | + | 0.931135i | \(0.381180\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.86931 | −0.759178 | ||||||||
\(170\) | −54.6327 | −4.19014 | ||||||||
\(171\) | −6.62660 | −0.506749 | ||||||||
\(172\) | 3.68470 | 0.280956 | ||||||||
\(173\) | 10.8514 | 0.825014 | 0.412507 | − | 0.910954i | \(-0.364653\pi\) | ||||
0.412507 | + | 0.910954i | \(0.364653\pi\) | |||||||
\(174\) | 22.5904 | 1.71257 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 28.8501 | 2.17466 | ||||||||
\(177\) | −1.36723 | −0.102767 | ||||||||
\(178\) | 29.3716 | 2.20150 | ||||||||
\(179\) | −9.94360 | −0.743220 | −0.371610 | − | 0.928389i | \(-0.621194\pi\) | ||||
−0.371610 | + | 0.928389i | \(0.621194\pi\) | |||||||
\(180\) | −18.6255 | −1.38826 | ||||||||
\(181\) | −0.975614 | −0.0725168 | −0.0362584 | − | 0.999342i | \(-0.511544\pi\) | ||||
−0.0362584 | + | 0.999342i | \(0.511544\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.36339 | −0.692162 | ||||||||
\(184\) | −9.61066 | −0.708507 | ||||||||
\(185\) | 15.0004 | 1.10285 | ||||||||
\(186\) | 8.06540 | 0.591384 | ||||||||
\(187\) | −11.1045 | −0.812042 | ||||||||
\(188\) | 9.88696 | 0.721081 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −61.4030 | −4.45464 | ||||||||
\(191\) | 7.00670 | 0.506987 | 0.253494 | − | 0.967337i | \(-0.418420\pi\) | ||||
0.253494 | + | 0.967337i | \(0.418420\pi\) | |||||||
\(192\) | −31.6985 | −2.28764 | ||||||||
\(193\) | 12.5202 | 0.901225 | 0.450613 | − | 0.892720i | \(-0.351206\pi\) | ||||
0.450613 | + | 0.892720i | \(0.351206\pi\) | |||||||
\(194\) | −42.8232 | −3.07453 | ||||||||
\(195\) | 5.98370 | 0.428502 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.3287 | −1.80459 | −0.902296 | − | 0.431116i | \(-0.858120\pi\) | ||||
−0.902296 | + | 0.431116i | \(0.858120\pi\) | |||||||
\(198\) | −5.16053 | −0.366743 | ||||||||
\(199\) | 0.648559 | 0.0459751 | 0.0229876 | − | 0.999736i | \(-0.492682\pi\) | ||||
0.0229876 | + | 0.999736i | \(0.492682\pi\) | |||||||
\(200\) | −61.8606 | −4.37420 | ||||||||
\(201\) | 8.17894 | 0.576898 | ||||||||
\(202\) | −20.7394 | −1.45922 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 32.4723 | 2.27351 | ||||||||
\(205\) | 19.9694 | 1.39473 | ||||||||
\(206\) | 7.18225 | 0.500411 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 27.1033 | 1.87928 | ||||||||
\(209\) | −12.4806 | −0.863303 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.4647 | 0.995790 | 0.497895 | − | 0.867237i | \(-0.334106\pi\) | ||||
0.497895 | + | 0.867237i | \(0.334106\pi\) | |||||||
\(212\) | −53.3406 | −3.66345 | ||||||||
\(213\) | 0.295052 | 0.0202166 | ||||||||
\(214\) | −47.4900 | −3.24635 | ||||||||
\(215\) | −2.26253 | −0.154303 | ||||||||
\(216\) | 9.61066 | 0.653922 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 36.6284 | 2.48079 | ||||||||
\(219\) | 4.45751 | 0.301210 | ||||||||
\(220\) | −35.0795 | −2.36506 | ||||||||
\(221\) | −10.4322 | −0.701743 | ||||||||
\(222\) | −12.1536 | −0.815694 | ||||||||
\(223\) | −29.7327 | −1.99105 | −0.995525 | − | 0.0945015i | \(-0.969874\pi\) | ||||
−0.995525 | + | 0.0945015i | \(0.969874\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.43667 | 0.429111 | ||||||||
\(226\) | 3.25261 | 0.216361 | ||||||||
\(227\) | −6.49019 | −0.430769 | −0.215385 | − | 0.976529i | \(-0.569101\pi\) | ||||
−0.215385 | + | 0.976529i | \(0.569101\pi\) | |||||||
\(228\) | 36.4963 | 2.41703 | ||||||||
\(229\) | −1.23608 | −0.0816824 | −0.0408412 | − | 0.999166i | \(-0.513004\pi\) | ||||
−0.0408412 | + | 0.999166i | \(0.513004\pi\) | |||||||
\(230\) | 9.26614 | 0.610991 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −79.2368 | −5.20215 | ||||||||
\(233\) | 24.3562 | 1.59563 | 0.797814 | − | 0.602904i | \(-0.205990\pi\) | ||||
0.797814 | + | 0.602904i | \(0.205990\pi\) | |||||||
\(234\) | −4.84807 | −0.316928 | ||||||||
\(235\) | −6.07091 | −0.396023 | ||||||||
\(236\) | 7.53006 | 0.490165 | ||||||||
\(237\) | 3.02768 | 0.196669 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.2471 | 0.986251 | 0.493126 | − | 0.869958i | \(-0.335854\pi\) | ||||
0.493126 | + | 0.869958i | \(0.335854\pi\) | |||||||
\(240\) | 51.8027 | 3.34385 | ||||||||
\(241\) | 4.12703 | 0.265845 | 0.132923 | − | 0.991126i | \(-0.457564\pi\) | ||||
0.132923 | + | 0.991126i | \(0.457564\pi\) | |||||||
\(242\) | 20.4205 | 1.31268 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 51.5694 | 3.30139 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −16.1795 | −1.03157 | ||||||||
\(247\) | −11.7249 | −0.746040 | ||||||||
\(248\) | −28.2898 | −1.79640 | ||||||||
\(249\) | 10.5300 | 0.667314 | ||||||||
\(250\) | 13.3123 | 0.841946 | ||||||||
\(251\) | 4.82682 | 0.304666 | 0.152333 | − | 0.988329i | \(-0.451321\pi\) | ||||
0.152333 | + | 0.988329i | \(0.451321\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.88341 | 0.118409 | ||||||||
\(254\) | 33.5131 | 2.10280 | ||||||||
\(255\) | −19.9390 | −1.24863 | ||||||||
\(256\) | 49.9120 | 3.11950 | ||||||||
\(257\) | −4.75140 | −0.296384 | −0.148192 | − | 0.988959i | \(-0.547345\pi\) | ||||
−0.148192 | + | 0.988959i | \(0.547345\pi\) | |||||||
\(258\) | 1.83313 | 0.114126 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −32.9555 | −2.04381 | ||||||||
\(261\) | 8.24468 | 0.510333 | ||||||||
\(262\) | 16.5953 | 1.02526 | ||||||||
\(263\) | −16.1415 | −0.995326 | −0.497663 | − | 0.867370i | \(-0.665808\pi\) | ||||
−0.497663 | + | 0.867370i | \(0.665808\pi\) | |||||||
\(264\) | 18.1008 | 1.11403 | ||||||||
\(265\) | 32.7529 | 2.01199 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.7196 | 0.656030 | ||||||||
\(268\) | −45.0459 | −2.75162 | ||||||||
\(269\) | 9.59563 | 0.585056 | 0.292528 | − | 0.956257i | \(-0.405504\pi\) | ||||
0.292528 | + | 0.956257i | \(0.405504\pi\) | |||||||
\(270\) | −9.26614 | −0.563919 | ||||||||
\(271\) | 20.9621 | 1.27335 | 0.636677 | − | 0.771130i | \(-0.280308\pi\) | ||||
0.636677 | + | 0.771130i | \(0.280308\pi\) | |||||||
\(272\) | −90.3143 | −5.47611 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 39.1616 | 2.36584 | ||||||||
\(275\) | 12.1229 | 0.731038 | ||||||||
\(276\) | −5.50755 | −0.331516 | ||||||||
\(277\) | 14.5824 | 0.876169 | 0.438085 | − | 0.898934i | \(-0.355657\pi\) | ||||
0.438085 | + | 0.898934i | \(0.355657\pi\) | |||||||
\(278\) | 45.0152 | 2.69983 | ||||||||
\(279\) | 2.94359 | 0.176228 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.2706 | −0.612694 | −0.306347 | − | 0.951920i | \(-0.599107\pi\) | ||||
−0.306347 | + | 0.951920i | \(0.599107\pi\) | |||||||
\(282\) | 4.91874 | 0.292907 | ||||||||
\(283\) | 17.0930 | 1.01607 | 0.508037 | − | 0.861335i | \(-0.330371\pi\) | ||||
0.508037 | + | 0.861335i | \(0.330371\pi\) | |||||||
\(284\) | −1.62501 | −0.0964268 | ||||||||
\(285\) | −22.4099 | −1.32745 | ||||||||
\(286\) | −9.13092 | −0.539923 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −22.7499 | −1.34055 | ||||||||
\(289\) | 17.7623 | 1.04484 | ||||||||
\(290\) | 76.3964 | 4.48615 | ||||||||
\(291\) | −15.6290 | −0.916186 | ||||||||
\(292\) | −24.5499 | −1.43668 | ||||||||
\(293\) | 10.9029 | 0.636955 | 0.318478 | − | 0.947930i | \(-0.396828\pi\) | ||||
0.318478 | + | 0.947930i | \(0.396828\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.62370 | −0.269202 | ||||||||
\(296\) | 42.6292 | 2.47777 | ||||||||
\(297\) | −1.88341 | −0.109287 | ||||||||
\(298\) | −37.8218 | −2.19096 | ||||||||
\(299\) | 1.76938 | 0.102326 | ||||||||
\(300\) | −35.4503 | −2.04672 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.6371 | 0.669642 | ||||||||
\(303\) | −7.56916 | −0.434837 | ||||||||
\(304\) | −101.506 | −5.82179 | ||||||||
\(305\) | −31.6653 | −1.81315 | ||||||||
\(306\) | 16.1549 | 0.923512 | ||||||||
\(307\) | 26.7973 | 1.52940 | 0.764700 | − | 0.644386i | \(-0.222887\pi\) | ||||
0.764700 | + | 0.644386i | \(0.222887\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.62127 | 0.149119 | ||||||||
\(310\) | 27.2757 | 1.54916 | ||||||||
\(311\) | 17.8615 | 1.01283 | 0.506417 | − | 0.862289i | \(-0.330970\pi\) | ||||
0.506417 | + | 0.862289i | \(0.330970\pi\) | |||||||
\(312\) | 17.0049 | 0.962711 | ||||||||
\(313\) | −29.1299 | −1.64652 | −0.823260 | − | 0.567665i | \(-0.807847\pi\) | ||||
−0.823260 | + | 0.567665i | \(0.807847\pi\) | |||||||
\(314\) | 1.82975 | 0.103258 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.6751 | −0.938049 | ||||||||
\(317\) | 21.9373 | 1.23212 | 0.616062 | − | 0.787698i | \(-0.288727\pi\) | ||||
0.616062 | + | 0.787698i | \(0.288727\pi\) | |||||||
\(318\) | −26.5368 | −1.48811 | ||||||||
\(319\) | 15.5281 | 0.869409 | ||||||||
\(320\) | −107.198 | −5.99257 | ||||||||
\(321\) | −17.3322 | −0.967388 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.0701 | 2.17392 | ||||||||
\(324\) | 5.50755 | 0.305975 | ||||||||
\(325\) | 11.3889 | 0.631741 | ||||||||
\(326\) | 1.99247 | 0.110353 | ||||||||
\(327\) | 13.3681 | 0.739255 | ||||||||
\(328\) | 56.7504 | 3.13352 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −17.4520 | −0.960699 | ||||||||
\(331\) | −5.63045 | −0.309477 | −0.154739 | − | 0.987955i | \(-0.549454\pi\) | ||||
−0.154739 | + | 0.987955i | \(0.549454\pi\) | |||||||
\(332\) | −57.9947 | −3.18287 | ||||||||
\(333\) | −4.43562 | −0.243071 | ||||||||
\(334\) | −25.8251 | −1.41309 | ||||||||
\(335\) | 27.6596 | 1.51121 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.7330 | 1.18387 | 0.591936 | − | 0.805985i | \(-0.298364\pi\) | ||||
0.591936 | + | 0.805985i | \(0.298364\pi\) | |||||||
\(338\) | 27.0418 | 1.47088 | ||||||||
\(339\) | 1.18709 | 0.0644738 | ||||||||
\(340\) | 109.815 | 5.95556 | ||||||||
\(341\) | 5.54399 | 0.300224 | ||||||||
\(342\) | 18.1568 | 0.981809 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.42980 | −0.346671 | ||||||||
\(345\) | 3.38181 | 0.182071 | ||||||||
\(346\) | −29.7326 | −1.59844 | ||||||||
\(347\) | 32.4805 | 1.74364 | 0.871822 | − | 0.489822i | \(-0.162938\pi\) | ||||
0.871822 | + | 0.489822i | \(0.162938\pi\) | |||||||
\(348\) | −45.4080 | −2.43412 | ||||||||
\(349\) | 0.230635 | 0.0123456 | 0.00617281 | − | 0.999981i | \(-0.498035\pi\) | ||||
0.00617281 | + | 0.999981i | \(0.498035\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.76938 | −0.0944423 | ||||||||
\(352\) | −42.8474 | −2.28378 | ||||||||
\(353\) | 27.8964 | 1.48478 | 0.742388 | − | 0.669970i | \(-0.233693\pi\) | ||||
0.742388 | + | 0.669970i | \(0.233693\pi\) | |||||||
\(354\) | 3.74618 | 0.199107 | ||||||||
\(355\) | 0.997811 | 0.0529583 | ||||||||
\(356\) | −59.0388 | −3.12905 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 27.2454 | 1.43996 | ||||||||
\(359\) | 16.3625 | 0.863581 | 0.431790 | − | 0.901974i | \(-0.357882\pi\) | ||||
0.431790 | + | 0.901974i | \(0.357882\pi\) | |||||||
\(360\) | 32.5015 | 1.71298 | ||||||||
\(361\) | 24.9119 | 1.31115 | ||||||||
\(362\) | 2.67317 | 0.140499 | ||||||||
\(363\) | 7.45276 | 0.391168 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.0745 | 0.789033 | ||||||||
\(366\) | 25.6556 | 1.34104 | ||||||||
\(367\) | 15.4796 | 0.808031 | 0.404016 | − | 0.914752i | \(-0.367614\pi\) | ||||
0.404016 | + | 0.914752i | \(0.367614\pi\) | |||||||
\(368\) | 15.3180 | 0.798507 | ||||||||
\(369\) | −5.90495 | −0.307399 | ||||||||
\(370\) | −41.1011 | −2.13674 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −16.2120 | −0.840551 | ||||||||
\(373\) | −29.4072 | −1.52265 | −0.761325 | − | 0.648371i | \(-0.775451\pi\) | ||||
−0.761325 | + | 0.648371i | \(0.775451\pi\) | |||||||
\(374\) | 30.4263 | 1.57330 | ||||||||
\(375\) | 4.85853 | 0.250894 | ||||||||
\(376\) | −17.2527 | −0.889741 | ||||||||
\(377\) | 14.5879 | 0.751317 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.7449 | 1.21969 | 0.609846 | − | 0.792520i | \(-0.291231\pi\) | ||||
0.609846 | + | 0.792520i | \(0.291231\pi\) | |||||||
\(380\) | 123.424 | 6.33151 | ||||||||
\(381\) | 12.2311 | 0.626618 | ||||||||
\(382\) | −19.1983 | −0.982270 | ||||||||
\(383\) | 4.79000 | 0.244758 | 0.122379 | − | 0.992483i | \(-0.460948\pi\) | ||||
0.122379 | + | 0.992483i | \(0.460948\pi\) | |||||||
\(384\) | 41.3538 | 2.11033 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −34.3053 | −1.74609 | ||||||||
\(387\) | 0.669028 | 0.0340086 | ||||||||
\(388\) | 86.0773 | 4.36991 | ||||||||
\(389\) | 22.5553 | 1.14360 | 0.571798 | − | 0.820394i | \(-0.306246\pi\) | ||||
0.571798 | + | 0.820394i | \(0.306246\pi\) | |||||||
\(390\) | −16.3953 | −0.830207 | ||||||||
\(391\) | −5.89595 | −0.298171 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.05670 | 0.305520 | ||||||||
\(394\) | 69.4003 | 3.49634 | ||||||||
\(395\) | 10.2391 | 0.515183 | ||||||||
\(396\) | 10.3730 | 0.521262 | ||||||||
\(397\) | 3.58874 | 0.180114 | 0.0900570 | − | 0.995937i | \(-0.471295\pi\) | ||||
0.0900570 | + | 0.995937i | \(0.471295\pi\) | |||||||
\(398\) | −1.77705 | −0.0890753 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 98.5969 | 4.92985 | ||||||||
\(401\) | 10.6336 | 0.531015 | 0.265508 | − | 0.964109i | \(-0.414460\pi\) | ||||
0.265508 | + | 0.964109i | \(0.414460\pi\) | |||||||
\(402\) | −22.4102 | −1.11772 | ||||||||
\(403\) | 5.20831 | 0.259444 | ||||||||
\(404\) | 41.6875 | 2.07403 | ||||||||
\(405\) | −3.38181 | −0.168044 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.35410 | −0.414098 | ||||||||
\(408\) | −56.6640 | −2.80529 | ||||||||
\(409\) | 14.5323 | 0.718575 | 0.359288 | − | 0.933227i | \(-0.383020\pi\) | ||||
0.359288 | + | 0.933227i | \(0.383020\pi\) | |||||||
\(410\) | −54.7161 | −2.70223 | ||||||||
\(411\) | 14.2926 | 0.705002 | ||||||||
\(412\) | −14.4368 | −0.711248 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.73999 | −0.134663 | ||||||||
\(415\) | 35.6106 | 1.74806 | ||||||||
\(416\) | −40.2531 | −1.97357 | ||||||||
\(417\) | 16.4290 | 0.804529 | ||||||||
\(418\) | 34.1968 | 1.67262 | ||||||||
\(419\) | −28.8287 | −1.40837 | −0.704187 | − | 0.710015i | \(-0.748688\pi\) | ||||
−0.704187 | + | 0.710015i | \(0.748688\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.2897 | 1.23254 | 0.616271 | − | 0.787534i | \(-0.288643\pi\) | ||||
0.616271 | + | 0.787534i | \(0.288643\pi\) | |||||||
\(422\) | −39.6331 | −1.92931 | ||||||||
\(423\) | 1.79517 | 0.0872839 | ||||||||
\(424\) | 93.0792 | 4.52033 | ||||||||
\(425\) | −37.9503 | −1.84086 | ||||||||
\(426\) | −0.808440 | −0.0391690 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 95.4579 | 4.61413 | ||||||||
\(429\) | −3.33246 | −0.160893 | ||||||||
\(430\) | 6.19931 | 0.298957 | ||||||||
\(431\) | −1.33330 | −0.0642226 | −0.0321113 | − | 0.999484i | \(-0.510223\pi\) | ||||
−0.0321113 | + | 0.999484i | \(0.510223\pi\) | |||||||
\(432\) | −15.3180 | −0.736988 | ||||||||
\(433\) | −12.4620 | −0.598887 | −0.299444 | − | 0.954114i | \(-0.596801\pi\) | ||||
−0.299444 | + | 0.954114i | \(0.596801\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 27.8820 | 1.33684 | ||||||||
\(436\) | −73.6253 | −3.52601 | ||||||||
\(437\) | −6.62660 | −0.316993 | ||||||||
\(438\) | −12.2135 | −0.583585 | ||||||||
\(439\) | 13.7656 | 0.656994 | 0.328497 | − | 0.944505i | \(-0.393458\pi\) | ||||
0.328497 | + | 0.944505i | \(0.393458\pi\) | |||||||
\(440\) | 61.2136 | 2.91825 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 28.5840 | 1.35960 | ||||||||
\(443\) | −7.06812 | −0.335816 | −0.167908 | − | 0.985803i | \(-0.553701\pi\) | ||||
−0.167908 | + | 0.985803i | \(0.553701\pi\) | |||||||
\(444\) | 24.4294 | 1.15937 | ||||||||
\(445\) | 36.2517 | 1.71850 | ||||||||
\(446\) | 81.4674 | 3.85759 | ||||||||
\(447\) | −13.8036 | −0.652888 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.4140 | −1.05778 | −0.528892 | − | 0.848689i | \(-0.677392\pi\) | ||||
−0.528892 | + | 0.848689i | \(0.677392\pi\) | |||||||
\(450\) | −17.6364 | −0.831388 | ||||||||
\(451\) | −11.1214 | −0.523689 | ||||||||
\(452\) | −6.53795 | −0.307519 | ||||||||
\(453\) | 4.24714 | 0.199548 | ||||||||
\(454\) | 17.7831 | 0.834601 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −63.6860 | −2.98237 | ||||||||
\(457\) | −2.69034 | −0.125849 | −0.0629244 | − | 0.998018i | \(-0.520043\pi\) | ||||
−0.0629244 | + | 0.998018i | \(0.520043\pi\) | |||||||
\(458\) | 3.38684 | 0.158257 | ||||||||
\(459\) | 5.89595 | 0.275200 | ||||||||
\(460\) | −18.6255 | −0.868419 | ||||||||
\(461\) | 30.1064 | 1.40220 | 0.701098 | − | 0.713065i | \(-0.252693\pi\) | ||||
0.701098 | + | 0.713065i | \(0.252693\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0463 | −0.652787 | −0.326394 | − | 0.945234i | \(-0.605834\pi\) | ||||
−0.326394 | + | 0.945234i | \(0.605834\pi\) | |||||||
\(464\) | 126.292 | 5.86296 | ||||||||
\(465\) | 9.95467 | 0.461637 | ||||||||
\(466\) | −66.7358 | −3.09148 | ||||||||
\(467\) | −10.6041 | −0.490699 | −0.245350 | − | 0.969435i | \(-0.578903\pi\) | ||||
−0.245350 | + | 0.969435i | \(0.578903\pi\) | |||||||
\(468\) | 9.74492 | 0.450459 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 16.6343 | 0.767281 | ||||||||
\(471\) | 0.667792 | 0.0307703 | ||||||||
\(472\) | −13.1399 | −0.604814 | ||||||||
\(473\) | 1.26006 | 0.0579374 | ||||||||
\(474\) | −8.29583 | −0.381040 | ||||||||
\(475\) | −42.6532 | −1.95706 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.68500 | −0.443446 | ||||||||
\(478\) | −41.7768 | −1.91083 | ||||||||
\(479\) | −11.2639 | −0.514661 | −0.257331 | − | 0.966323i | \(-0.582843\pi\) | ||||
−0.257331 | + | 0.966323i | \(0.582843\pi\) | |||||||
\(480\) | −76.9359 | −3.51163 | ||||||||
\(481\) | −7.84828 | −0.357851 | ||||||||
\(482\) | −11.3080 | −0.515066 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −41.0464 | −1.86575 | ||||||||
\(485\) | −52.8543 | −2.39999 | ||||||||
\(486\) | 2.73999 | 0.124289 | ||||||||
\(487\) | 1.90335 | 0.0862488 | 0.0431244 | − | 0.999070i | \(-0.486269\pi\) | ||||
0.0431244 | + | 0.999070i | \(0.486269\pi\) | |||||||
\(488\) | −89.9884 | −4.07358 | ||||||||
\(489\) | 0.727180 | 0.0328842 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.8742 | 0.942040 | 0.471020 | − | 0.882123i | \(-0.343886\pi\) | ||||
0.471020 | + | 0.882123i | \(0.343886\pi\) | |||||||
\(492\) | 32.5218 | 1.46620 | ||||||||
\(493\) | −48.6103 | −2.18930 | ||||||||
\(494\) | 32.1262 | 1.44543 | ||||||||
\(495\) | −6.36935 | −0.286281 | ||||||||
\(496\) | 45.0899 | 2.02460 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −28.8522 | −1.29290 | ||||||||
\(499\) | −37.0935 | −1.66053 | −0.830266 | − | 0.557368i | \(-0.811811\pi\) | ||||
−0.830266 | + | 0.557368i | \(0.811811\pi\) | |||||||
\(500\) | −26.7586 | −1.19668 | ||||||||
\(501\) | −9.42526 | −0.421090 | ||||||||
\(502\) | −13.2254 | −0.590280 | ||||||||
\(503\) | 0.702967 | 0.0313437 | 0.0156719 | − | 0.999877i | \(-0.495011\pi\) | ||||
0.0156719 | + | 0.999877i | \(0.495011\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.5975 | −1.13907 | ||||||||
\(506\) | −5.16053 | −0.229414 | ||||||||
\(507\) | 9.86931 | 0.438311 | ||||||||
\(508\) | −67.3633 | −2.98876 | ||||||||
\(509\) | 18.9239 | 0.838785 | 0.419393 | − | 0.907805i | \(-0.362243\pi\) | ||||
0.419393 | + | 0.907805i | \(0.362243\pi\) | |||||||
\(510\) | 54.6327 | 2.41918 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −54.0509 | −2.38874 | ||||||||
\(513\) | 6.62660 | 0.292572 | ||||||||
\(514\) | 13.0188 | 0.574234 | ||||||||
\(515\) | 8.86464 | 0.390623 | ||||||||
\(516\) | −3.68470 | −0.162210 | ||||||||
\(517\) | 3.38104 | 0.148698 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.8514 | −0.476322 | ||||||||
\(520\) | 57.5073 | 2.52186 | ||||||||
\(521\) | 19.1445 | 0.838737 | 0.419369 | − | 0.907816i | \(-0.362251\pi\) | ||||
0.419369 | + | 0.907816i | \(0.362251\pi\) | |||||||
\(522\) | −22.5904 | −0.988753 | ||||||||
\(523\) | 13.9178 | 0.608581 | 0.304291 | − | 0.952579i | \(-0.401581\pi\) | ||||
0.304291 | + | 0.952579i | \(0.401581\pi\) | |||||||
\(524\) | −33.3576 | −1.45723 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 44.2275 | 1.92841 | ||||||||
\(527\) | −17.3553 | −0.756007 | ||||||||
\(528\) | −28.8501 | −1.25554 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −89.7426 | −3.89817 | ||||||||
\(531\) | 1.36723 | 0.0593325 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.4481 | −0.452556 | ||||||||
\(534\) | −29.3716 | −1.27104 | ||||||||
\(535\) | −58.6142 | −2.53411 | ||||||||
\(536\) | 78.6049 | 3.39522 | ||||||||
\(537\) | 9.94360 | 0.429098 | ||||||||
\(538\) | −26.2919 | −1.13353 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 18.6255 | 0.801514 | ||||||||
\(541\) | 28.7511 | 1.23611 | 0.618053 | − | 0.786136i | \(-0.287922\pi\) | ||||
0.618053 | + | 0.786136i | \(0.287922\pi\) | |||||||
\(542\) | −57.4359 | −2.46708 | ||||||||
\(543\) | 0.975614 | 0.0418676 | ||||||||
\(544\) | 134.132 | 5.75088 | ||||||||
\(545\) | 45.2083 | 1.93651 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.9067 | 1.10769 | 0.553845 | − | 0.832620i | \(-0.313160\pi\) | ||||
0.553845 | + | 0.832620i | \(0.313160\pi\) | |||||||
\(548\) | −78.7172 | −3.36263 | ||||||||
\(549\) | 9.36339 | 0.399620 | ||||||||
\(550\) | −33.2166 | −1.41636 | ||||||||
\(551\) | −54.6342 | −2.32750 | ||||||||
\(552\) | 9.61066 | 0.409057 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −39.9555 | −1.69755 | ||||||||
\(555\) | −15.0004 | −0.636733 | ||||||||
\(556\) | −90.4833 | −3.83735 | ||||||||
\(557\) | −4.63598 | −0.196433 | −0.0982164 | − | 0.995165i | \(-0.531314\pi\) | ||||
−0.0982164 | + | 0.995165i | \(0.531314\pi\) | |||||||
\(558\) | −8.06540 | −0.341436 | ||||||||
\(559\) | 1.18376 | 0.0500678 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.1045 | 0.468833 | ||||||||
\(562\) | 28.1414 | 1.18707 | ||||||||
\(563\) | 5.23116 | 0.220467 | 0.110233 | − | 0.993906i | \(-0.464840\pi\) | ||||
0.110233 | + | 0.993906i | \(0.464840\pi\) | |||||||
\(564\) | −9.88696 | −0.416316 | ||||||||
\(565\) | 4.01451 | 0.168892 | ||||||||
\(566\) | −46.8347 | −1.96861 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.83564 | 0.118981 | ||||||||
\(569\) | 7.71135 | 0.323277 | 0.161638 | − | 0.986850i | \(-0.448322\pi\) | ||||
0.161638 | + | 0.986850i | \(0.448322\pi\) | |||||||
\(570\) | 61.4030 | 2.57189 | ||||||||
\(571\) | 17.5515 | 0.734508 | 0.367254 | − | 0.930121i | \(-0.380298\pi\) | ||||
0.367254 | + | 0.930121i | \(0.380298\pi\) | |||||||
\(572\) | 18.3537 | 0.767407 | ||||||||
\(573\) | −7.00670 | −0.292709 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.43667 | 0.268427 | ||||||||
\(576\) | 31.6985 | 1.32077 | ||||||||
\(577\) | 15.6526 | 0.651628 | 0.325814 | − | 0.945434i | \(-0.394362\pi\) | ||||
0.325814 | + | 0.945434i | \(0.394362\pi\) | |||||||
\(578\) | −48.6685 | −2.02434 | ||||||||
\(579\) | −12.5202 | −0.520323 | ||||||||
\(580\) | −153.561 | −6.37629 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 42.8232 | 1.77508 | ||||||||
\(583\) | −18.2409 | −0.755459 | ||||||||
\(584\) | 42.8396 | 1.77271 | ||||||||
\(585\) | −5.98370 | −0.247395 | ||||||||
\(586\) | −29.8739 | −1.23408 | ||||||||
\(587\) | 29.3900 | 1.21305 | 0.606527 | − | 0.795063i | \(-0.292562\pi\) | ||||
0.606527 | + | 0.795063i | \(0.292562\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.5060 | −0.803730 | ||||||||
\(590\) | 12.6689 | 0.521570 | ||||||||
\(591\) | 25.3287 | 1.04188 | ||||||||
\(592\) | −67.9449 | −2.79252 | ||||||||
\(593\) | −18.0072 | −0.739469 | −0.369734 | − | 0.929137i | \(-0.620551\pi\) | ||||
−0.369734 | + | 0.929137i | \(0.620551\pi\) | |||||||
\(594\) | 5.16053 | 0.211739 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 76.0241 | 3.11407 | ||||||||
\(597\) | −0.648559 | −0.0265438 | ||||||||
\(598\) | −4.84807 | −0.198252 | ||||||||
\(599\) | −12.3391 | −0.504162 | −0.252081 | − | 0.967706i | \(-0.581115\pi\) | ||||
−0.252081 | + | 0.967706i | \(0.581115\pi\) | |||||||
\(600\) | 61.8606 | 2.52545 | ||||||||
\(601\) | 0.594459 | 0.0242485 | 0.0121243 | − | 0.999926i | \(-0.496141\pi\) | ||||
0.0121243 | + | 0.999926i | \(0.496141\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.17894 | −0.333072 | ||||||||
\(604\) | −23.3914 | −0.951781 | ||||||||
\(605\) | 25.2038 | 1.02468 | ||||||||
\(606\) | 20.7394 | 0.842481 | ||||||||
\(607\) | −0.0677745 | −0.00275088 | −0.00137544 | − | 0.999999i | \(-0.500438\pi\) | ||||
−0.00137544 | + | 0.999999i | \(0.500438\pi\) | |||||||
\(608\) | 150.755 | 6.11390 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 86.7625 | 3.51291 | ||||||||
\(611\) | 3.17632 | 0.128500 | ||||||||
\(612\) | −32.4723 | −1.31261 | ||||||||
\(613\) | 21.5033 | 0.868508 | 0.434254 | − | 0.900790i | \(-0.357012\pi\) | ||||
0.434254 | + | 0.900790i | \(0.357012\pi\) | |||||||
\(614\) | −73.4243 | −2.96316 | ||||||||
\(615\) | −19.9694 | −0.805245 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.0024 | 0.402683 | 0.201341 | − | 0.979521i | \(-0.435470\pi\) | ||||
0.201341 | + | 0.979521i | \(0.435470\pi\) | |||||||
\(618\) | −7.18225 | −0.288912 | ||||||||
\(619\) | −13.1494 | −0.528518 | −0.264259 | − | 0.964452i | \(-0.585127\pi\) | ||||
−0.264259 | + | 0.964452i | \(0.585127\pi\) | |||||||
\(620\) | −54.8258 | −2.20186 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −48.9404 | −1.96233 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −27.1033 | −1.08500 | ||||||||
\(625\) | −15.7527 | −0.630107 | ||||||||
\(626\) | 79.8157 | 3.19008 | ||||||||
\(627\) | 12.4806 | 0.498428 | ||||||||
\(628\) | −3.67790 | −0.146764 | ||||||||
\(629\) | 26.1522 | 1.04276 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.0831 | 1.07816 | 0.539081 | − | 0.842254i | \(-0.318772\pi\) | ||||
0.539081 | + | 0.842254i | \(0.318772\pi\) | |||||||
\(632\) | 29.0980 | 1.15746 | ||||||||
\(633\) | −14.4647 | −0.574920 | ||||||||
\(634\) | −60.1081 | −2.38720 | ||||||||
\(635\) | 41.3633 | 1.64145 | ||||||||
\(636\) | 53.3406 | 2.11509 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −42.5469 | −1.68445 | ||||||||
\(639\) | −0.295052 | −0.0116721 | ||||||||
\(640\) | 139.851 | 5.52809 | ||||||||
\(641\) | −37.6596 | −1.48747 | −0.743733 | − | 0.668477i | \(-0.766947\pi\) | ||||
−0.743733 | + | 0.668477i | \(0.766947\pi\) | |||||||
\(642\) | 47.4900 | 1.87428 | ||||||||
\(643\) | 0.584100 | 0.0230347 | 0.0115173 | − | 0.999934i | \(-0.496334\pi\) | ||||
0.0115173 | + | 0.999934i | \(0.496334\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.26253 | 0.0890869 | ||||||||
\(646\) | −107.052 | −4.21190 | ||||||||
\(647\) | 5.80803 | 0.228337 | 0.114169 | − | 0.993461i | \(-0.463580\pi\) | ||||
0.114169 | + | 0.993461i | \(0.463580\pi\) | |||||||
\(648\) | −9.61066 | −0.377542 | ||||||||
\(649\) | 2.57505 | 0.101080 | ||||||||
\(650\) | −31.2054 | −1.22398 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00498 | −0.156847 | ||||||||
\(653\) | 24.7043 | 0.966756 | 0.483378 | − | 0.875412i | \(-0.339410\pi\) | ||||
0.483378 | + | 0.875412i | \(0.339410\pi\) | |||||||
\(654\) | −36.6284 | −1.43228 | ||||||||
\(655\) | 20.4826 | 0.800323 | ||||||||
\(656\) | −90.4520 | −3.53156 | ||||||||
\(657\) | −4.45751 | −0.173904 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.0716 | 0.937697 | 0.468848 | − | 0.883279i | \(-0.344669\pi\) | ||||
0.468848 | + | 0.883279i | \(0.344669\pi\) | |||||||
\(660\) | 35.0795 | 1.36547 | ||||||||
\(661\) | 10.1639 | 0.395330 | 0.197665 | − | 0.980270i | \(-0.436664\pi\) | ||||
0.197665 | + | 0.980270i | \(0.436664\pi\) | |||||||
\(662\) | 15.4274 | 0.599602 | ||||||||
\(663\) | 10.4322 | 0.405151 | ||||||||
\(664\) | 101.200 | 3.92734 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.1536 | 0.470941 | ||||||||
\(667\) | 8.24468 | 0.319235 | ||||||||
\(668\) | 51.9101 | 2.00846 | ||||||||
\(669\) | 29.7327 | 1.14953 | ||||||||
\(670\) | −75.7872 | −2.92791 | ||||||||
\(671\) | 17.6351 | 0.680797 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.4374 | 0.826350 | 0.413175 | − | 0.910652i | \(-0.364420\pi\) | ||||
0.413175 | + | 0.910652i | \(0.364420\pi\) | |||||||
\(674\) | −59.5482 | −2.29371 | ||||||||
\(675\) | −6.43667 | −0.247747 | ||||||||
\(676\) | −54.3557 | −2.09060 | ||||||||
\(677\) | 29.1868 | 1.12174 | 0.560869 | − | 0.827905i | \(-0.310467\pi\) | ||||
0.560869 | + | 0.827905i | \(0.310467\pi\) | |||||||
\(678\) | −3.25261 | −0.124916 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −191.627 | −7.34856 | ||||||||
\(681\) | 6.49019 | 0.248705 | ||||||||
\(682\) | −15.1905 | −0.581674 | ||||||||
\(683\) | −49.6777 | −1.90086 | −0.950432 | − | 0.310934i | \(-0.899358\pi\) | ||||
−0.950432 | + | 0.310934i | \(0.899358\pi\) | |||||||
\(684\) | −36.4963 | −1.39547 | ||||||||
\(685\) | 48.3349 | 1.84678 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.23608 | 0.0471593 | ||||||||
\(688\) | 10.2482 | 0.390708 | ||||||||
\(689\) | −17.1364 | −0.652845 | ||||||||
\(690\) | −9.26614 | −0.352756 | ||||||||
\(691\) | 7.22139 | 0.274715 | 0.137357 | − | 0.990522i | \(-0.456139\pi\) | ||||
0.137357 | + | 0.990522i | \(0.456139\pi\) | |||||||
\(692\) | 59.7644 | 2.27190 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −88.9963 | −3.37825 | ||||||||
\(695\) | 55.5597 | 2.10750 | ||||||||
\(696\) | 79.2368 | 3.00346 | ||||||||
\(697\) | 34.8153 | 1.31872 | ||||||||
\(698\) | −0.631938 | −0.0239192 | ||||||||
\(699\) | −24.3562 | −0.921236 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.4759 | −1.64206 | −0.821031 | − | 0.570884i | \(-0.806601\pi\) | ||||
−0.821031 | + | 0.570884i | \(0.806601\pi\) | |||||||
\(702\) | 4.84807 | 0.182979 | ||||||||
\(703\) | 29.3931 | 1.10858 | ||||||||
\(704\) | 59.7013 | 2.25008 | ||||||||
\(705\) | 6.07091 | 0.228644 | ||||||||
\(706\) | −76.4359 | −2.87670 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.53006 | −0.282997 | ||||||||
\(709\) | 23.2264 | 0.872286 | 0.436143 | − | 0.899877i | \(-0.356344\pi\) | ||||
0.436143 | + | 0.899877i | \(0.356344\pi\) | |||||||
\(710\) | −2.73399 | −0.102605 | ||||||||
\(711\) | −3.02768 | −0.113547 | ||||||||
\(712\) | 103.022 | 3.86093 | ||||||||
\(713\) | 2.94359 | 0.110238 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.2698 | −0.421466 | ||||||||
\(716\) | −54.7649 | −2.04666 | ||||||||
\(717\) | −15.2471 | −0.569412 | ||||||||
\(718\) | −44.8332 | −1.67316 | ||||||||
\(719\) | 39.8039 | 1.48444 | 0.742218 | − | 0.670158i | \(-0.233774\pi\) | ||||
0.742218 | + | 0.670158i | \(0.233774\pi\) | |||||||
\(720\) | −51.8027 | −1.93057 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −68.2582 | −2.54031 | ||||||||
\(723\) | −4.12703 | −0.153486 | ||||||||
\(724\) | −5.37324 | −0.199695 | ||||||||
\(725\) | 53.0683 | 1.97091 | ||||||||
\(726\) | −20.4205 | −0.757875 | ||||||||
\(727\) | −22.3786 | −0.829978 | −0.414989 | − | 0.909826i | \(-0.636215\pi\) | ||||
−0.414989 | + | 0.909826i | \(0.636215\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −41.3039 | −1.52872 | ||||||||
\(731\) | −3.94456 | −0.145895 | ||||||||
\(732\) | −51.5694 | −1.90606 | ||||||||
\(733\) | −31.2261 | −1.15336 | −0.576681 | − | 0.816970i | \(-0.695652\pi\) | ||||
−0.576681 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(734\) | −42.4141 | −1.56553 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −22.7499 | −0.838572 | ||||||||
\(737\) | −15.4043 | −0.567425 | ||||||||
\(738\) | 16.1795 | 0.595576 | ||||||||
\(739\) | 34.6438 | 1.27439 | 0.637197 | − | 0.770701i | \(-0.280094\pi\) | ||||
0.637197 | + | 0.770701i | \(0.280094\pi\) | |||||||
\(740\) | 82.6157 | 3.03701 | ||||||||
\(741\) | 11.7249 | 0.430727 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.7961 | −0.872996 | −0.436498 | − | 0.899705i | \(-0.643781\pi\) | ||||
−0.436498 | + | 0.899705i | \(0.643781\pi\) | |||||||
\(744\) | 28.2898 | 1.03715 | ||||||||
\(745\) | −46.6812 | −1.71027 | ||||||||
\(746\) | 80.5756 | 2.95008 | ||||||||
\(747\) | −10.5300 | −0.385274 | ||||||||
\(748\) | −61.1587 | −2.23618 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −13.3123 | −0.486098 | ||||||||
\(751\) | −2.54860 | −0.0929997 | −0.0464999 | − | 0.998918i | \(-0.514807\pi\) | ||||
−0.0464999 | + | 0.998918i | \(0.514807\pi\) | |||||||
\(752\) | 27.4984 | 1.00276 | ||||||||
\(753\) | −4.82682 | −0.175899 | ||||||||
\(754\) | −39.9708 | −1.45565 | ||||||||
\(755\) | 14.3630 | 0.522725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.5043 | −1.29042 | −0.645212 | − | 0.764004i | \(-0.723231\pi\) | ||||
−0.645212 | + | 0.764004i | \(0.723231\pi\) | |||||||
\(758\) | −65.0607 | −2.36311 | ||||||||
\(759\) | −1.88341 | −0.0683635 | ||||||||
\(760\) | −215.374 | −7.81244 | ||||||||
\(761\) | −30.0000 | −1.08750 | −0.543749 | − | 0.839248i | \(-0.682996\pi\) | ||||
−0.543749 | + | 0.839248i | \(0.682996\pi\) | |||||||
\(762\) | −33.5131 | −1.21405 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 38.5898 | 1.39613 | ||||||||
\(765\) | 19.9390 | 0.720897 | ||||||||
\(766\) | −13.1246 | −0.474209 | ||||||||
\(767\) | 2.41913 | 0.0873499 | ||||||||
\(768\) | −49.9120 | −1.80105 | ||||||||
\(769\) | 39.7222 | 1.43242 | 0.716210 | − | 0.697885i | \(-0.245875\pi\) | ||||
0.716210 | + | 0.697885i | \(0.245875\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.75140 | 0.171117 | ||||||||
\(772\) | 68.9558 | 2.48177 | ||||||||
\(773\) | 11.9933 | 0.431369 | 0.215684 | − | 0.976463i | \(-0.430802\pi\) | ||||
0.215684 | + | 0.976463i | \(0.430802\pi\) | |||||||
\(774\) | −1.83313 | −0.0658905 | ||||||||
\(775\) | 18.9469 | 0.680592 | ||||||||
\(776\) | −150.205 | −5.39203 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −61.8012 | −2.21568 | ||||||||
\(779\) | 39.1297 | 1.40197 | ||||||||
\(780\) | 32.9555 | 1.18000 | ||||||||
\(781\) | −0.555704 | −0.0198847 | ||||||||
\(782\) | 16.1549 | 0.577697 | ||||||||
\(783\) | −8.24468 | −0.294641 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.25835 | 0.0806040 | ||||||||
\(786\) | −16.5953 | −0.591935 | ||||||||
\(787\) | −8.04112 | −0.286635 | −0.143318 | − | 0.989677i | \(-0.545777\pi\) | ||||
−0.143318 | + | 0.989677i | \(0.545777\pi\) | |||||||
\(788\) | −139.499 | −4.96944 | ||||||||
\(789\) | 16.1415 | 0.574652 | ||||||||
\(790\) | −28.0549 | −0.998150 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −18.1008 | −0.643185 | ||||||||
\(793\) | 16.5674 | 0.588324 | ||||||||
\(794\) | −9.83313 | −0.348965 | ||||||||
\(795\) | −32.7529 | −1.16162 | ||||||||
\(796\) | 3.57197 | 0.126605 | ||||||||
\(797\) | −27.9672 | −0.990651 | −0.495325 | − | 0.868708i | \(-0.664951\pi\) | ||||
−0.495325 | + | 0.868708i | \(0.664951\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.5842 | −0.374443 | ||||||||
\(800\) | −146.433 | −5.17721 | ||||||||
\(801\) | −10.7196 | −0.378759 | ||||||||
\(802\) | −29.1359 | −1.02882 | ||||||||
\(803\) | −8.39532 | −0.296264 | ||||||||
\(804\) | 45.0459 | 1.58865 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.2707 | −0.502665 | ||||||||
\(807\) | −9.59563 | −0.337782 | ||||||||
\(808\) | −72.7446 | −2.55914 | ||||||||
\(809\) | 9.31700 | 0.327568 | 0.163784 | − | 0.986496i | \(-0.447630\pi\) | ||||
0.163784 | + | 0.986496i | \(0.447630\pi\) | |||||||
\(810\) | 9.26614 | 0.325579 | ||||||||
\(811\) | −18.5550 | −0.651553 | −0.325776 | − | 0.945447i | \(-0.605626\pi\) | ||||
−0.325776 | + | 0.945447i | \(0.605626\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.9621 | −0.735172 | ||||||||
\(814\) | 22.8902 | 0.802300 | ||||||||
\(815\) | 2.45919 | 0.0861416 | ||||||||
\(816\) | 90.3143 | 3.16163 | ||||||||
\(817\) | −4.43338 | −0.155104 | ||||||||
\(818\) | −39.8183 | −1.39222 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 109.983 | 3.84076 | ||||||||
\(821\) | −21.6775 | −0.756549 | −0.378275 | − | 0.925693i | \(-0.623483\pi\) | ||||
−0.378275 | + | 0.925693i | \(0.623483\pi\) | |||||||
\(822\) | −39.1616 | −1.36592 | ||||||||
\(823\) | 3.22962 | 0.112578 | 0.0562888 | − | 0.998415i | \(-0.482073\pi\) | ||||
0.0562888 | + | 0.998415i | \(0.482073\pi\) | |||||||
\(824\) | 25.1921 | 0.877609 | ||||||||
\(825\) | −12.1229 | −0.422065 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.5890 | 1.20278 | 0.601388 | − | 0.798957i | \(-0.294614\pi\) | ||||
0.601388 | + | 0.798957i | \(0.294614\pi\) | |||||||
\(828\) | 5.50755 | 0.191401 | ||||||||
\(829\) | 17.1078 | 0.594179 | 0.297090 | − | 0.954850i | \(-0.403984\pi\) | ||||
0.297090 | + | 0.954850i | \(0.403984\pi\) | |||||||
\(830\) | −97.5727 | −3.38680 | ||||||||
\(831\) | −14.5824 | −0.505856 | ||||||||
\(832\) | 56.0865 | 1.94445 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −45.0152 | −1.55875 | ||||||||
\(835\) | −31.8745 | −1.10306 | ||||||||
\(836\) | −68.7377 | −2.37734 | ||||||||
\(837\) | −2.94359 | −0.101745 | ||||||||
\(838\) | 78.9904 | 2.72868 | ||||||||
\(839\) | −16.7696 | −0.578951 | −0.289476 | − | 0.957185i | \(-0.593481\pi\) | ||||
−0.289476 | + | 0.957185i | \(0.593481\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.9748 | 1.34396 | ||||||||
\(842\) | −69.2934 | −2.38801 | ||||||||
\(843\) | 10.2706 | 0.353739 | ||||||||
\(844\) | 79.6650 | 2.74218 | ||||||||
\(845\) | 33.3762 | 1.14818 | ||||||||
\(846\) | −4.91874 | −0.169110 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −148.355 | −5.09453 | ||||||||
\(849\) | −17.0930 | −0.586631 | ||||||||
\(850\) | 103.983 | 3.56660 | ||||||||
\(851\) | −4.43562 | −0.152051 | ||||||||
\(852\) | 1.62501 | 0.0556720 | ||||||||
\(853\) | 51.7879 | 1.77318 | 0.886591 | − | 0.462554i | \(-0.153067\pi\) | ||||
0.886591 | + | 0.462554i | \(0.153067\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22.4099 | 0.766404 | ||||||||
\(856\) | −166.574 | −5.69337 | ||||||||
\(857\) | −43.1996 | −1.47567 | −0.737835 | − | 0.674982i | \(-0.764152\pi\) | ||||
−0.737835 | + | 0.674982i | \(0.764152\pi\) | |||||||
\(858\) | 9.13092 | 0.311724 | ||||||||
\(859\) | −2.30553 | −0.0786636 | −0.0393318 | − | 0.999226i | \(-0.512523\pi\) | ||||
−0.0393318 | + | 0.999226i | \(0.512523\pi\) | |||||||
\(860\) | −12.4610 | −0.424916 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.65322 | 0.124429 | ||||||||
\(863\) | −25.4718 | −0.867069 | −0.433535 | − | 0.901137i | \(-0.642734\pi\) | ||||
−0.433535 | + | 0.901137i | \(0.642734\pi\) | |||||||
\(864\) | 22.7499 | 0.773967 | ||||||||
\(865\) | −36.6973 | −1.24775 | ||||||||
\(866\) | 34.1459 | 1.16032 | ||||||||
\(867\) | −17.7623 | −0.603238 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.70238 | −0.193440 | ||||||||
\(870\) | −76.3964 | −2.59008 | ||||||||
\(871\) | −14.4716 | −0.490352 | ||||||||
\(872\) | 128.476 | 4.35074 | ||||||||
\(873\) | 15.6290 | 0.528960 | ||||||||
\(874\) | 18.1568 | 0.614164 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 24.5499 | 0.829465 | ||||||||
\(877\) | −7.10061 | −0.239771 | −0.119885 | − | 0.992788i | \(-0.538253\pi\) | ||||
−0.119885 | + | 0.992788i | \(0.538253\pi\) | |||||||
\(878\) | −37.7175 | −1.27290 | ||||||||
\(879\) | −10.9029 | −0.367746 | ||||||||
\(880\) | −97.5658 | −3.28894 | ||||||||
\(881\) | −29.0434 | −0.978497 | −0.489249 | − | 0.872144i | \(-0.662729\pi\) | ||||
−0.489249 | + | 0.872144i | \(0.662729\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.2662 | −1.01854 | −0.509269 | − | 0.860608i | \(-0.670084\pi\) | ||||
−0.509269 | + | 0.860608i | \(0.670084\pi\) | |||||||
\(884\) | −57.4556 | −1.93244 | ||||||||
\(885\) | 4.62370 | 0.155424 | ||||||||
\(886\) | 19.3666 | 0.650633 | ||||||||
\(887\) | −31.3757 | −1.05349 | −0.526746 | − | 0.850023i | \(-0.676588\pi\) | ||||
−0.526746 | + | 0.850023i | \(0.676588\pi\) | |||||||
\(888\) | −42.6292 | −1.43054 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −99.3294 | −3.32953 | ||||||||
\(891\) | 1.88341 | 0.0630967 | ||||||||
\(892\) | −163.754 | −5.48290 | ||||||||
\(893\) | −11.8958 | −0.398079 | ||||||||
\(894\) | 37.8218 | 1.26495 | ||||||||
\(895\) | 33.6274 | 1.12404 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.76938 | −0.0590777 | ||||||||
\(898\) | 61.4143 | 2.04942 | ||||||||
\(899\) | 24.2689 | 0.809415 | ||||||||
\(900\) | 35.4503 | 1.18168 | ||||||||
\(901\) | 57.1023 | 1.90235 | ||||||||
\(902\) | 30.4727 | 1.01463 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.4087 | 0.379448 | ||||||||
\(905\) | 3.29934 | 0.109674 | ||||||||
\(906\) | −11.6371 | −0.386618 | ||||||||
\(907\) | 22.5635 | 0.749208 | 0.374604 | − | 0.927185i | \(-0.377779\pi\) | ||||
0.374604 | + | 0.927185i | \(0.377779\pi\) | |||||||
\(908\) | −35.7451 | −1.18624 | ||||||||
\(909\) | 7.56916 | 0.251053 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.2986 | 1.83212 | 0.916062 | − | 0.401038i | \(-0.131350\pi\) | ||||
0.916062 | + | 0.401038i | \(0.131350\pi\) | |||||||
\(912\) | 101.506 | 3.36121 | ||||||||
\(913\) | −19.8324 | −0.656356 | ||||||||
\(914\) | 7.37151 | 0.243828 | ||||||||
\(915\) | 31.6653 | 1.04682 | ||||||||
\(916\) | −6.80776 | −0.224935 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −16.1549 | −0.533190 | ||||||||
\(919\) | 25.4246 | 0.838682 | 0.419341 | − | 0.907829i | \(-0.362261\pi\) | ||||
0.419341 | + | 0.907829i | \(0.362261\pi\) | |||||||
\(920\) | 32.5015 | 1.07154 | ||||||||
\(921\) | −26.7973 | −0.883000 | ||||||||
\(922\) | −82.4914 | −2.71671 | ||||||||
\(923\) | −0.522058 | −0.0171837 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.5506 | −0.938738 | ||||||||
\(926\) | 38.4868 | 1.26475 | ||||||||
\(927\) | −2.62127 | −0.0860937 | ||||||||
\(928\) | −187.566 | −6.15715 | ||||||||
\(929\) | −34.2563 | −1.12391 | −0.561956 | − | 0.827167i | \(-0.689951\pi\) | ||||
−0.561956 | + | 0.827167i | \(0.689951\pi\) | |||||||
\(930\) | −27.2757 | −0.894405 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 134.143 | 4.39400 | ||||||||
\(933\) | −17.8615 | −0.584760 | ||||||||
\(934\) | 29.0552 | 0.950714 | ||||||||
\(935\) | 37.5534 | 1.22813 | ||||||||
\(936\) | −17.0049 | −0.555821 | ||||||||
\(937\) | 54.0699 | 1.76639 | 0.883193 | − | 0.469010i | \(-0.155389\pi\) | ||||
0.883193 | + | 0.469010i | \(0.155389\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.1299 | 0.950619 | ||||||||
\(940\) | −33.4359 | −1.09056 | ||||||||
\(941\) | −17.0577 | −0.556064 | −0.278032 | − | 0.960572i | \(-0.589682\pi\) | ||||
−0.278032 | + | 0.960572i | \(0.589682\pi\) | |||||||
\(942\) | −1.82975 | −0.0596163 | ||||||||
\(943\) | −5.90495 | −0.192291 | ||||||||
\(944\) | 20.9432 | 0.681642 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.45254 | −0.112252 | ||||||||
\(947\) | 33.9477 | 1.10315 | 0.551575 | − | 0.834125i | \(-0.314027\pi\) | ||||
0.551575 | + | 0.834125i | \(0.314027\pi\) | |||||||
\(948\) | 16.6751 | 0.541583 | ||||||||
\(949\) | −7.88700 | −0.256023 | ||||||||
\(950\) | 116.869 | 3.79174 | ||||||||
\(951\) | −21.9373 | −0.711367 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.1762 | −0.718358 | −0.359179 | − | 0.933269i | \(-0.616943\pi\) | ||||
−0.359179 | + | 0.933269i | \(0.616943\pi\) | |||||||
\(954\) | 26.5368 | 0.859161 | ||||||||
\(955\) | −23.6954 | −0.766764 | ||||||||
\(956\) | 83.9740 | 2.71591 | ||||||||
\(957\) | −15.5281 | −0.501953 | ||||||||
\(958\) | 30.8630 | 0.997139 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 107.198 | 3.45981 | ||||||||
\(961\) | −22.3353 | −0.720493 | ||||||||
\(962\) | 21.5042 | 0.693324 | ||||||||
\(963\) | 17.3322 | 0.558522 | ||||||||
\(964\) | 22.7298 | 0.732078 | ||||||||
\(965\) | −42.3411 | −1.36301 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.9540 | 0.513045 | 0.256523 | − | 0.966538i | \(-0.417423\pi\) | ||||
0.256523 | + | 0.966538i | \(0.417423\pi\) | |||||||
\(968\) | 71.6259 | 2.30214 | ||||||||
\(969\) | −39.0701 | −1.25511 | ||||||||
\(970\) | 144.820 | 4.64990 | ||||||||
\(971\) | 37.3099 | 1.19733 | 0.598665 | − | 0.800999i | \(-0.295698\pi\) | ||||
0.598665 | + | 0.800999i | \(0.295698\pi\) | |||||||
\(972\) | −5.50755 | −0.176655 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −5.21515 | −0.167104 | ||||||||
\(975\) | −11.3889 | −0.364736 | ||||||||
\(976\) | 143.429 | 4.59104 | ||||||||
\(977\) | −37.1289 | −1.18786 | −0.593930 | − | 0.804517i | \(-0.702424\pi\) | ||||
−0.593930 | + | 0.804517i | \(0.702424\pi\) | |||||||
\(978\) | −1.99247 | −0.0637121 | ||||||||
\(979\) | −20.1894 | −0.645258 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.3681 | −0.426809 | ||||||||
\(982\) | −57.1951 | −1.82517 | ||||||||
\(983\) | −20.0403 | −0.639188 | −0.319594 | − | 0.947555i | \(-0.603546\pi\) | ||||
−0.319594 | + | 0.947555i | \(0.603546\pi\) | |||||||
\(984\) | −56.7504 | −1.80914 | ||||||||
\(985\) | 85.6568 | 2.72925 | ||||||||
\(986\) | 133.192 | 4.24169 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −64.5757 | −2.05443 | ||||||||
\(989\) | 0.669028 | 0.0212738 | ||||||||
\(990\) | 17.4520 | 0.554660 | ||||||||
\(991\) | 40.3456 | 1.28162 | 0.640810 | − | 0.767699i | \(-0.278598\pi\) | ||||
0.640810 | + | 0.767699i | \(0.278598\pi\) | |||||||
\(992\) | −66.9663 | −2.12618 | ||||||||
\(993\) | 5.63045 | 0.178677 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.19331 | −0.0695325 | ||||||||
\(996\) | 57.9947 | 1.83763 | ||||||||
\(997\) | 4.57100 | 0.144765 | 0.0723826 | − | 0.997377i | \(-0.476940\pi\) | ||||
0.0723826 | + | 0.997377i | \(0.476940\pi\) | |||||||
\(998\) | 101.636 | 3.21722 | ||||||||
\(999\) | 4.43562 | 0.140337 |
(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 | 3381.2.a.bi.1.1 | 10 | ||
7.2 | even | 3 | 483.2.i.h.277.10 | ✓ | 20 | ||
7.4 | even | 3 | 483.2.i.h.415.10 | yes | 20 | ||
7.6 | odd | 2 | 3381.2.a.bj.1.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.h.277.10 | ✓ | 20 | 7.2 | even | 3 | ||
483.2.i.h.415.10 | yes | 20 | 7.4 | even | 3 | ||
3381.2.a.bi.1.1 | 10 | 1.1 | even | 1 | trivial | ||
3381.2.a.bj.1.1 | 10 | 7.6 | odd | 2 |