Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7942,2,Mod(1,7942)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7942, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7942.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7942 = 2 \cdot 11 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7942.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.4171892853\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 418) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.66908\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7942.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.66908 | −1.54099 | −0.770497 | − | 0.637444i | \(-0.779992\pi\) | ||||
−0.770497 | + | 0.637444i | \(0.779992\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.12398 | −1.84430 | −0.922151 | − | 0.386831i | \(-0.873570\pi\) | ||||
−0.922151 | + | 0.386831i | \(0.873570\pi\) | |||||||
\(6\) | −2.66908 | −1.08965 | ||||||||
\(7\) | −4.21417 | −1.59281 | −0.796404 | − | 0.604765i | \(-0.793267\pi\) | ||||
−0.796404 | + | 0.604765i | \(0.793267\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.12398 | 1.37466 | ||||||||
\(10\) | −4.12398 | −1.30412 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −2.66908 | −0.770497 | ||||||||
\(13\) | 2.21417 | 0.614102 | 0.307051 | − | 0.951693i | \(-0.400658\pi\) | ||||
0.307051 | + | 0.951693i | \(0.400658\pi\) | |||||||
\(14\) | −4.21417 | −1.12629 | ||||||||
\(15\) | 11.0072 | 2.84206 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.45490 | −0.837937 | −0.418969 | − | 0.908001i | \(-0.637608\pi\) | ||||
−0.418969 | + | 0.908001i | \(0.637608\pi\) | |||||||
\(18\) | 4.12398 | 0.972032 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −4.12398 | −0.922151 | ||||||||
\(21\) | 11.2480 | 2.45451 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −5.45490 | −1.13743 | −0.568713 | − | 0.822536i | \(-0.692559\pi\) | ||||
−0.568713 | + | 0.822536i | \(0.692559\pi\) | |||||||
\(24\) | −2.66908 | −0.544823 | ||||||||
\(25\) | 12.0072 | 2.40145 | ||||||||
\(26\) | 2.21417 | 0.434235 | ||||||||
\(27\) | −3.00000 | −0.577350 | ||||||||
\(28\) | −4.21417 | −0.796404 | ||||||||
\(29\) | −5.57889 | −1.03597 | −0.517987 | − | 0.855389i | \(-0.673318\pi\) | ||||
−0.517987 | + | 0.855389i | \(0.673318\pi\) | |||||||
\(30\) | 11.0072 | 2.00964 | ||||||||
\(31\) | −7.00724 | −1.25854 | −0.629268 | − | 0.777188i | \(-0.716645\pi\) | ||||
−0.629268 | + | 0.777188i | \(0.716645\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.66908 | 0.464627 | ||||||||
\(34\) | −3.45490 | −0.592511 | ||||||||
\(35\) | 17.3792 | 2.93762 | ||||||||
\(36\) | 4.12398 | 0.687331 | ||||||||
\(37\) | 2.90981 | 0.478370 | 0.239185 | − | 0.970974i | \(-0.423120\pi\) | ||||
0.239185 | + | 0.970974i | \(0.423120\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.90981 | −0.946327 | ||||||||
\(40\) | −4.12398 | −0.652059 | ||||||||
\(41\) | 11.9170 | 1.86113 | 0.930565 | − | 0.366127i | \(-0.119316\pi\) | ||||
0.930565 | + | 0.366127i | \(0.119316\pi\) | |||||||
\(42\) | 11.2480 | 1.73560 | ||||||||
\(43\) | 1.46214 | 0.222974 | 0.111487 | − | 0.993766i | \(-0.464439\pi\) | ||||
0.111487 | + | 0.993766i | \(0.464439\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −17.0072 | −2.53529 | ||||||||
\(46\) | −5.45490 | −0.804282 | ||||||||
\(47\) | 7.58612 | 1.10655 | 0.553275 | − | 0.832999i | \(-0.313378\pi\) | ||||
0.553275 | + | 0.832999i | \(0.313378\pi\) | |||||||
\(48\) | −2.66908 | −0.385248 | ||||||||
\(49\) | 10.7593 | 1.53704 | ||||||||
\(50\) | 12.0072 | 1.69808 | ||||||||
\(51\) | 9.22141 | 1.29126 | ||||||||
\(52\) | 2.21417 | 0.307051 | ||||||||
\(53\) | 13.2214 | 1.81610 | 0.908050 | − | 0.418861i | \(-0.137571\pi\) | ||||
0.908050 | + | 0.418861i | \(0.137571\pi\) | |||||||
\(54\) | −3.00000 | −0.408248 | ||||||||
\(55\) | 4.12398 | 0.556078 | ||||||||
\(56\) | −4.21417 | −0.563143 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.57889 | −0.732544 | ||||||||
\(59\) | −4.79306 | −0.624004 | −0.312002 | − | 0.950082i | \(-0.600999\pi\) | ||||
−0.312002 | + | 0.950082i | \(0.600999\pi\) | |||||||
\(60\) | 11.0072 | 1.42103 | ||||||||
\(61\) | 8.90981 | 1.14078 | 0.570392 | − | 0.821373i | \(-0.306791\pi\) | ||||
0.570392 | + | 0.821373i | \(0.306791\pi\) | |||||||
\(62\) | −7.00724 | −0.889920 | ||||||||
\(63\) | −17.3792 | −2.18957 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.13122 | −1.13259 | ||||||||
\(66\) | 2.66908 | 0.328541 | ||||||||
\(67\) | −1.30437 | −0.159354 | −0.0796769 | − | 0.996821i | \(-0.525389\pi\) | ||||
−0.0796769 | + | 0.996821i | \(0.525389\pi\) | |||||||
\(68\) | −3.45490 | −0.418969 | ||||||||
\(69\) | 14.5596 | 1.75277 | ||||||||
\(70\) | 17.3792 | 2.07721 | ||||||||
\(71\) | 6.80030 | 0.807047 | 0.403524 | − | 0.914969i | \(-0.367785\pi\) | ||||
0.403524 | + | 0.914969i | \(0.367785\pi\) | |||||||
\(72\) | 4.12398 | 0.486016 | ||||||||
\(73\) | −1.45490 | −0.170284 | −0.0851418 | − | 0.996369i | \(-0.527134\pi\) | ||||
−0.0851418 | + | 0.996369i | \(0.527134\pi\) | |||||||
\(74\) | 2.90981 | 0.338258 | ||||||||
\(75\) | −32.0483 | −3.70061 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.21417 | 0.480250 | ||||||||
\(78\) | −5.90981 | −0.669154 | ||||||||
\(79\) | 9.15777 | 1.03033 | 0.515165 | − | 0.857091i | \(-0.327731\pi\) | ||||
0.515165 | + | 0.857091i | \(0.327731\pi\) | |||||||
\(80\) | −4.12398 | −0.461075 | ||||||||
\(81\) | −4.36471 | −0.484968 | ||||||||
\(82\) | 11.9170 | 1.31602 | ||||||||
\(83\) | −13.2142 | −1.45044 | −0.725222 | − | 0.688515i | \(-0.758263\pi\) | ||||
−0.725222 | + | 0.688515i | \(0.758263\pi\) | |||||||
\(84\) | 11.2480 | 1.22725 | ||||||||
\(85\) | 14.2480 | 1.54541 | ||||||||
\(86\) | 1.46214 | 0.157667 | ||||||||
\(87\) | 14.8905 | 1.59643 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −8.24797 | −0.874283 | −0.437141 | − | 0.899393i | \(-0.644009\pi\) | ||||
−0.437141 | + | 0.899393i | \(0.644009\pi\) | |||||||
\(90\) | −17.0072 | −1.79272 | ||||||||
\(91\) | −9.33092 | −0.978146 | ||||||||
\(92\) | −5.45490 | −0.568713 | ||||||||
\(93\) | 18.7029 | 1.93940 | ||||||||
\(94\) | 7.58612 | 0.782449 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.66908 | −0.272412 | ||||||||
\(97\) | −2.18038 | −0.221384 | −0.110692 | − | 0.993855i | \(-0.535307\pi\) | ||||
−0.110692 | + | 0.993855i | \(0.535307\pi\) | |||||||
\(98\) | 10.7593 | 1.08685 | ||||||||
\(99\) | −4.12398 | −0.414476 | ||||||||
\(100\) | 12.0072 | 1.20072 | ||||||||
\(101\) | −6.24797 | −0.621696 | −0.310848 | − | 0.950460i | \(-0.600613\pi\) | ||||
−0.310848 | + | 0.950460i | \(0.600613\pi\) | |||||||
\(102\) | 9.22141 | 0.913056 | ||||||||
\(103\) | −0.605441 | −0.0596559 | −0.0298280 | − | 0.999555i | \(-0.509496\pi\) | ||||
−0.0298280 | + | 0.999555i | \(0.509496\pi\) | |||||||
\(104\) | 2.21417 | 0.217118 | ||||||||
\(105\) | −46.3864 | −4.52685 | ||||||||
\(106\) | 13.2214 | 1.28418 | ||||||||
\(107\) | −3.88325 | −0.375408 | −0.187704 | − | 0.982226i | \(-0.560105\pi\) | ||||
−0.187704 | + | 0.982226i | \(0.560105\pi\) | |||||||
\(108\) | −3.00000 | −0.288675 | ||||||||
\(109\) | 4.97345 | 0.476370 | 0.238185 | − | 0.971220i | \(-0.423448\pi\) | ||||
0.238185 | + | 0.971220i | \(0.423448\pi\) | |||||||
\(110\) | 4.12398 | 0.393206 | ||||||||
\(111\) | −7.76651 | −0.737164 | ||||||||
\(112\) | −4.21417 | −0.398202 | ||||||||
\(113\) | 8.00000 | 0.752577 | 0.376288 | − | 0.926503i | \(-0.377200\pi\) | ||||
0.376288 | + | 0.926503i | \(0.377200\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 22.4959 | 2.09776 | ||||||||
\(116\) | −5.57889 | −0.517987 | ||||||||
\(117\) | 9.13122 | 0.844182 | ||||||||
\(118\) | −4.79306 | −0.441237 | ||||||||
\(119\) | 14.5596 | 1.33467 | ||||||||
\(120\) | 11.0072 | 1.00482 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 8.90981 | 0.806656 | ||||||||
\(123\) | −31.8075 | −2.86799 | ||||||||
\(124\) | −7.00724 | −0.629268 | ||||||||
\(125\) | −28.8977 | −2.58469 | ||||||||
\(126\) | −17.3792 | −1.54826 | ||||||||
\(127\) | 2.48146 | 0.220194 | 0.110097 | − | 0.993921i | \(-0.464884\pi\) | ||||
0.110097 | + | 0.993921i | \(0.464884\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.90257 | −0.343602 | ||||||||
\(130\) | −9.13122 | −0.800861 | ||||||||
\(131\) | 11.0072 | 0.961707 | 0.480853 | − | 0.876801i | \(-0.340327\pi\) | ||||
0.480853 | + | 0.876801i | \(0.340327\pi\) | |||||||
\(132\) | 2.66908 | 0.232314 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.30437 | −0.112680 | ||||||||
\(135\) | 12.3719 | 1.06481 | ||||||||
\(136\) | −3.45490 | −0.296256 | ||||||||
\(137\) | 6.94360 | 0.593232 | 0.296616 | − | 0.954997i | \(-0.404142\pi\) | ||||
0.296616 | + | 0.954997i | \(0.404142\pi\) | |||||||
\(138\) | 14.5596 | 1.23939 | ||||||||
\(139\) | −4.37195 | −0.370824 | −0.185412 | − | 0.982661i | \(-0.559362\pi\) | ||||
−0.185412 | + | 0.982661i | \(0.559362\pi\) | |||||||
\(140\) | 17.3792 | 1.46881 | ||||||||
\(141\) | −20.2480 | −1.70519 | ||||||||
\(142\) | 6.80030 | 0.570668 | ||||||||
\(143\) | −2.21417 | −0.185159 | ||||||||
\(144\) | 4.12398 | 0.343665 | ||||||||
\(145\) | 23.0072 | 1.91065 | ||||||||
\(146\) | −1.45490 | −0.120409 | ||||||||
\(147\) | −28.7173 | −2.36857 | ||||||||
\(148\) | 2.90981 | 0.239185 | ||||||||
\(149\) | 11.7665 | 0.963950 | 0.481975 | − | 0.876185i | \(-0.339920\pi\) | ||||
0.481975 | + | 0.876185i | \(0.339920\pi\) | |||||||
\(150\) | −32.0483 | −2.61673 | ||||||||
\(151\) | 19.5861 | 1.59390 | 0.796948 | − | 0.604048i | \(-0.206446\pi\) | ||||
0.796948 | + | 0.604048i | \(0.206446\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.2480 | −1.15188 | ||||||||
\(154\) | 4.21417 | 0.339588 | ||||||||
\(155\) | 28.8977 | 2.32112 | ||||||||
\(156\) | −5.90981 | −0.473163 | ||||||||
\(157\) | 20.6199 | 1.64565 | 0.822824 | − | 0.568296i | \(-0.192397\pi\) | ||||
0.822824 | + | 0.568296i | \(0.192397\pi\) | |||||||
\(158\) | 9.15777 | 0.728553 | ||||||||
\(159\) | −35.2890 | −2.79860 | ||||||||
\(160\) | −4.12398 | −0.326029 | ||||||||
\(161\) | 22.9879 | 1.81170 | ||||||||
\(162\) | −4.36471 | −0.342924 | ||||||||
\(163\) | −17.8341 | −1.39687 | −0.698437 | − | 0.715672i | \(-0.746121\pi\) | ||||
−0.698437 | + | 0.715672i | \(0.746121\pi\) | |||||||
\(164\) | 11.9170 | 0.930565 | ||||||||
\(165\) | −11.0072 | −0.856912 | ||||||||
\(166\) | −13.2142 | −1.02562 | ||||||||
\(167\) | −4.18038 | −0.323488 | −0.161744 | − | 0.986833i | \(-0.551712\pi\) | ||||
−0.161744 | + | 0.986833i | \(0.551712\pi\) | |||||||
\(168\) | 11.2480 | 0.867799 | ||||||||
\(169\) | −8.09743 | −0.622879 | ||||||||
\(170\) | 14.2480 | 1.09277 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.46214 | 0.111487 | ||||||||
\(173\) | −23.7101 | −1.80265 | −0.901323 | − | 0.433147i | \(-0.857403\pi\) | ||||
−0.901323 | + | 0.433147i | \(0.857403\pi\) | |||||||
\(174\) | 14.8905 | 1.12885 | ||||||||
\(175\) | −50.6006 | −3.82505 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 12.7931 | 0.961585 | ||||||||
\(178\) | −8.24797 | −0.618211 | ||||||||
\(179\) | 10.8269 | 0.809237 | 0.404619 | − | 0.914486i | \(-0.367404\pi\) | ||||
0.404619 | + | 0.914486i | \(0.367404\pi\) | |||||||
\(180\) | −17.0072 | −1.26764 | ||||||||
\(181\) | 17.8341 | 1.32560 | 0.662799 | − | 0.748798i | \(-0.269368\pi\) | ||||
0.662799 | + | 0.748798i | \(0.269368\pi\) | |||||||
\(182\) | −9.33092 | −0.691654 | ||||||||
\(183\) | −23.7810 | −1.75794 | ||||||||
\(184\) | −5.45490 | −0.402141 | ||||||||
\(185\) | −12.0000 | −0.882258 | ||||||||
\(186\) | 18.7029 | 1.37136 | ||||||||
\(187\) | 3.45490 | 0.252648 | ||||||||
\(188\) | 7.58612 | 0.553275 | ||||||||
\(189\) | 12.6425 | 0.919608 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.612679 | 0.0443319 | 0.0221659 | − | 0.999754i | \(-0.492944\pi\) | ||||
0.0221659 | + | 0.999754i | \(0.492944\pi\) | |||||||
\(192\) | −2.66908 | −0.192624 | ||||||||
\(193\) | −11.6425 | −0.838047 | −0.419024 | − | 0.907975i | \(-0.637628\pi\) | ||||
−0.419024 | + | 0.907975i | \(0.637628\pi\) | |||||||
\(194\) | −2.18038 | −0.156542 | ||||||||
\(195\) | 24.3719 | 1.74531 | ||||||||
\(196\) | 10.7593 | 0.768519 | ||||||||
\(197\) | −12.9098 | −0.919786 | −0.459893 | − | 0.887974i | \(-0.652112\pi\) | ||||
−0.459893 | + | 0.887974i | \(0.652112\pi\) | |||||||
\(198\) | −4.12398 | −0.293079 | ||||||||
\(199\) | −18.3647 | −1.30184 | −0.650920 | − | 0.759146i | \(-0.725617\pi\) | ||||
−0.650920 | + | 0.759146i | \(0.725617\pi\) | |||||||
\(200\) | 12.0072 | 0.849040 | ||||||||
\(201\) | 3.48146 | 0.245563 | ||||||||
\(202\) | −6.24797 | −0.439605 | ||||||||
\(203\) | 23.5104 | 1.65011 | ||||||||
\(204\) | 9.22141 | 0.645628 | ||||||||
\(205\) | −49.1457 | −3.43248 | ||||||||
\(206\) | −0.605441 | −0.0421831 | ||||||||
\(207\) | −22.4959 | −1.56358 | ||||||||
\(208\) | 2.21417 | 0.153525 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −46.3864 | −3.20097 | ||||||||
\(211\) | −2.13122 | −0.146719 | −0.0733596 | − | 0.997306i | \(-0.523372\pi\) | ||||
−0.0733596 | + | 0.997306i | \(0.523372\pi\) | |||||||
\(212\) | 13.2214 | 0.908050 | ||||||||
\(213\) | −18.1505 | −1.24365 | ||||||||
\(214\) | −3.88325 | −0.265454 | ||||||||
\(215\) | −6.02985 | −0.411232 | ||||||||
\(216\) | −3.00000 | −0.204124 | ||||||||
\(217\) | 29.5297 | 2.00461 | ||||||||
\(218\) | 4.97345 | 0.336844 | ||||||||
\(219\) | 3.88325 | 0.262406 | ||||||||
\(220\) | 4.12398 | 0.278039 | ||||||||
\(221\) | −7.64976 | −0.514579 | ||||||||
\(222\) | −7.76651 | −0.521254 | ||||||||
\(223\) | −6.90981 | −0.462715 | −0.231357 | − | 0.972869i | \(-0.574317\pi\) | ||||
−0.231357 | + | 0.972869i | \(0.574317\pi\) | |||||||
\(224\) | −4.21417 | −0.281571 | ||||||||
\(225\) | 49.5176 | 3.30118 | ||||||||
\(226\) | 8.00000 | 0.532152 | ||||||||
\(227\) | 2.72548 | 0.180896 | 0.0904482 | − | 0.995901i | \(-0.471170\pi\) | ||||
0.0904482 | + | 0.995901i | \(0.471170\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.48870 | 0.230539 | 0.115270 | − | 0.993334i | \(-0.463227\pi\) | ||||
0.115270 | + | 0.993334i | \(0.463227\pi\) | |||||||
\(230\) | 22.4959 | 1.48334 | ||||||||
\(231\) | −11.2480 | −0.740062 | ||||||||
\(232\) | −5.57889 | −0.366272 | ||||||||
\(233\) | −17.0902 | −1.11962 | −0.559808 | − | 0.828622i | \(-0.689125\pi\) | ||||
−0.559808 | + | 0.828622i | \(0.689125\pi\) | |||||||
\(234\) | 9.13122 | 0.596927 | ||||||||
\(235\) | −31.2850 | −2.04081 | ||||||||
\(236\) | −4.79306 | −0.312002 | ||||||||
\(237\) | −24.4428 | −1.58773 | ||||||||
\(238\) | 14.5596 | 0.943757 | ||||||||
\(239\) | 6.06035 | 0.392011 | 0.196006 | − | 0.980603i | \(-0.437203\pi\) | ||||
0.196006 | + | 0.980603i | \(0.437203\pi\) | |||||||
\(240\) | 11.0072 | 0.710514 | ||||||||
\(241\) | −4.85341 | −0.312635 | −0.156318 | − | 0.987707i | \(-0.549962\pi\) | ||||
−0.156318 | + | 0.987707i | \(0.549962\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 20.6498 | 1.32468 | ||||||||
\(244\) | 8.90981 | 0.570392 | ||||||||
\(245\) | −44.3711 | −2.83476 | ||||||||
\(246\) | −31.8075 | −2.02797 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.00724 | −0.444960 | ||||||||
\(249\) | 35.2697 | 2.23513 | ||||||||
\(250\) | −28.8977 | −1.82765 | ||||||||
\(251\) | −1.58612 | −0.100115 | −0.0500576 | − | 0.998746i | \(-0.515941\pi\) | ||||
−0.0500576 | + | 0.998746i | \(0.515941\pi\) | |||||||
\(252\) | −17.3792 | −1.09479 | ||||||||
\(253\) | 5.45490 | 0.342947 | ||||||||
\(254\) | 2.48146 | 0.155701 | ||||||||
\(255\) | −38.0289 | −2.38147 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.5185 | −1.21753 | −0.608767 | − | 0.793349i | \(-0.708335\pi\) | ||||
−0.608767 | + | 0.793349i | \(0.708335\pi\) | |||||||
\(258\) | −3.90257 | −0.242963 | ||||||||
\(259\) | −12.2624 | −0.761951 | ||||||||
\(260\) | −9.13122 | −0.566294 | ||||||||
\(261\) | −23.0072 | −1.42411 | ||||||||
\(262\) | 11.0072 | 0.680029 | ||||||||
\(263\) | −13.0483 | −0.804591 | −0.402295 | − | 0.915510i | \(-0.631787\pi\) | ||||
−0.402295 | + | 0.915510i | \(0.631787\pi\) | |||||||
\(264\) | 2.66908 | 0.164270 | ||||||||
\(265\) | −54.5249 | −3.34944 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.0145 | 1.34726 | ||||||||
\(268\) | −1.30437 | −0.0796769 | ||||||||
\(269\) | −23.6006 | −1.43895 | −0.719477 | − | 0.694516i | \(-0.755618\pi\) | ||||
−0.719477 | + | 0.694516i | \(0.755618\pi\) | |||||||
\(270\) | 12.3719 | 0.752933 | ||||||||
\(271\) | −16.4090 | −0.996778 | −0.498389 | − | 0.866954i | \(-0.666075\pi\) | ||||
−0.498389 | + | 0.866954i | \(0.666075\pi\) | |||||||
\(272\) | −3.45490 | −0.209484 | ||||||||
\(273\) | 24.9050 | 1.50732 | ||||||||
\(274\) | 6.94360 | 0.419478 | ||||||||
\(275\) | −12.0072 | −0.724064 | ||||||||
\(276\) | 14.5596 | 0.876383 | ||||||||
\(277\) | −11.5861 | −0.696143 | −0.348071 | − | 0.937468i | \(-0.613163\pi\) | ||||
−0.348071 | + | 0.937468i | \(0.613163\pi\) | |||||||
\(278\) | −4.37195 | −0.262212 | ||||||||
\(279\) | −28.8977 | −1.73006 | ||||||||
\(280\) | 17.3792 | 1.03861 | ||||||||
\(281\) | −7.03379 | −0.419601 | −0.209800 | − | 0.977744i | \(-0.567281\pi\) | ||||
−0.209800 | + | 0.977744i | \(0.567281\pi\) | |||||||
\(282\) | −20.2480 | −1.20575 | ||||||||
\(283\) | 8.33092 | 0.495222 | 0.247611 | − | 0.968860i | \(-0.420355\pi\) | ||||
0.247611 | + | 0.968860i | \(0.420355\pi\) | |||||||
\(284\) | 6.80030 | 0.403524 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.21417 | −0.130927 | ||||||||
\(287\) | −50.2205 | −2.96442 | ||||||||
\(288\) | 4.12398 | 0.243008 | ||||||||
\(289\) | −5.06364 | −0.297861 | ||||||||
\(290\) | 23.0072 | 1.35103 | ||||||||
\(291\) | 5.81962 | 0.341152 | ||||||||
\(292\) | −1.45490 | −0.0851418 | ||||||||
\(293\) | −10.2142 | −0.596718 | −0.298359 | − | 0.954454i | \(-0.596439\pi\) | ||||
−0.298359 | + | 0.954454i | \(0.596439\pi\) | |||||||
\(294\) | −28.7173 | −1.67483 | ||||||||
\(295\) | 19.7665 | 1.15085 | ||||||||
\(296\) | 2.90981 | 0.169129 | ||||||||
\(297\) | 3.00000 | 0.174078 | ||||||||
\(298\) | 11.7665 | 0.681616 | ||||||||
\(299\) | −12.0781 | −0.698495 | ||||||||
\(300\) | −32.0483 | −1.85031 | ||||||||
\(301\) | −6.16172 | −0.355156 | ||||||||
\(302\) | 19.5861 | 1.12705 | ||||||||
\(303\) | 16.6763 | 0.958029 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −36.7439 | −2.10395 | ||||||||
\(306\) | −14.2480 | −0.814502 | ||||||||
\(307\) | 1.93242 | 0.110289 | 0.0551444 | − | 0.998478i | \(-0.482438\pi\) | ||||
0.0551444 | + | 0.998478i | \(0.482438\pi\) | |||||||
\(308\) | 4.21417 | 0.240125 | ||||||||
\(309\) | 1.61597 | 0.0919294 | ||||||||
\(310\) | 28.8977 | 1.64128 | ||||||||
\(311\) | −27.7173 | −1.57171 | −0.785853 | − | 0.618413i | \(-0.787776\pi\) | ||||
−0.785853 | + | 0.618413i | \(0.787776\pi\) | |||||||
\(312\) | −5.90981 | −0.334577 | ||||||||
\(313\) | 11.5258 | 0.651476 | 0.325738 | − | 0.945460i | \(-0.394387\pi\) | ||||
0.325738 | + | 0.945460i | \(0.394387\pi\) | |||||||
\(314\) | 20.6199 | 1.16365 | ||||||||
\(315\) | 71.6715 | 4.03823 | ||||||||
\(316\) | 9.15777 | 0.515165 | ||||||||
\(317\) | 33.8977 | 1.90389 | 0.951943 | − | 0.306275i | \(-0.0990827\pi\) | ||||
0.951943 | + | 0.306275i | \(0.0990827\pi\) | |||||||
\(318\) | −35.2890 | −1.97891 | ||||||||
\(319\) | 5.57889 | 0.312358 | ||||||||
\(320\) | −4.12398 | −0.230538 | ||||||||
\(321\) | 10.3647 | 0.578502 | ||||||||
\(322\) | 22.9879 | 1.28107 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −4.36471 | −0.242484 | ||||||||
\(325\) | 26.5861 | 1.47473 | ||||||||
\(326\) | −17.8341 | −0.987739 | ||||||||
\(327\) | −13.2745 | −0.734083 | ||||||||
\(328\) | 11.9170 | 0.658009 | ||||||||
\(329\) | −31.9693 | −1.76252 | ||||||||
\(330\) | −11.0072 | −0.605928 | ||||||||
\(331\) | 16.2697 | 0.894262 | 0.447131 | − | 0.894468i | \(-0.352446\pi\) | ||||
0.447131 | + | 0.894468i | \(0.352446\pi\) | |||||||
\(332\) | −13.2142 | −0.725222 | ||||||||
\(333\) | 12.0000 | 0.657596 | ||||||||
\(334\) | −4.18038 | −0.228740 | ||||||||
\(335\) | 5.37919 | 0.293896 | ||||||||
\(336\) | 11.2480 | 0.613627 | ||||||||
\(337\) | 6.82685 | 0.371882 | 0.185941 | − | 0.982561i | \(-0.440467\pi\) | ||||
0.185941 | + | 0.982561i | \(0.440467\pi\) | |||||||
\(338\) | −8.09743 | −0.440442 | ||||||||
\(339\) | −21.3526 | −1.15972 | ||||||||
\(340\) | 14.2480 | 0.772704 | ||||||||
\(341\) | 7.00724 | 0.379463 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.8422 | −0.855400 | ||||||||
\(344\) | 1.46214 | 0.0788334 | ||||||||
\(345\) | −60.0434 | −3.23263 | ||||||||
\(346\) | −23.7101 | −1.27466 | ||||||||
\(347\) | −5.09019 | −0.273256 | −0.136628 | − | 0.990622i | \(-0.543626\pi\) | ||||
−0.136628 | + | 0.990622i | \(0.543626\pi\) | |||||||
\(348\) | 14.8905 | 0.798214 | ||||||||
\(349\) | 30.9919 | 1.65896 | 0.829478 | − | 0.558539i | \(-0.188638\pi\) | ||||
0.829478 | + | 0.558539i | \(0.188638\pi\) | |||||||
\(350\) | −50.6006 | −2.70472 | ||||||||
\(351\) | −6.64252 | −0.354552 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −17.8301 | −0.949003 | −0.474501 | − | 0.880255i | \(-0.657372\pi\) | ||||
−0.474501 | + | 0.880255i | \(0.657372\pi\) | |||||||
\(354\) | 12.7931 | 0.679944 | ||||||||
\(355\) | −28.0443 | −1.48844 | ||||||||
\(356\) | −8.24797 | −0.437141 | ||||||||
\(357\) | −38.8606 | −2.05672 | ||||||||
\(358\) | 10.8269 | 0.572217 | ||||||||
\(359\) | 24.4090 | 1.28826 | 0.644130 | − | 0.764916i | \(-0.277220\pi\) | ||||
0.644130 | + | 0.764916i | \(0.277220\pi\) | |||||||
\(360\) | −17.0072 | −0.896360 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 17.8341 | 0.937339 | ||||||||
\(363\) | −2.66908 | −0.140090 | ||||||||
\(364\) | −9.33092 | −0.489073 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | −23.7810 | −1.24305 | ||||||||
\(367\) | −26.6232 | −1.38972 | −0.694860 | − | 0.719145i | \(-0.744534\pi\) | ||||
−0.694860 | + | 0.719145i | \(0.744534\pi\) | |||||||
\(368\) | −5.45490 | −0.284357 | ||||||||
\(369\) | 49.1457 | 2.55842 | ||||||||
\(370\) | −12.0000 | −0.623850 | ||||||||
\(371\) | −55.7173 | −2.89270 | ||||||||
\(372\) | 18.7029 | 0.969699 | ||||||||
\(373\) | 12.6160 | 0.653230 | 0.326615 | − | 0.945157i | \(-0.394092\pi\) | ||||
0.326615 | + | 0.945157i | \(0.394092\pi\) | |||||||
\(374\) | 3.45490 | 0.178649 | ||||||||
\(375\) | 77.1303 | 3.98299 | ||||||||
\(376\) | 7.58612 | 0.391225 | ||||||||
\(377\) | −12.3526 | −0.636193 | ||||||||
\(378\) | 12.6425 | 0.650261 | ||||||||
\(379\) | 22.8905 | 1.17581 | 0.587903 | − | 0.808932i | \(-0.299954\pi\) | ||||
0.587903 | + | 0.808932i | \(0.299954\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.62321 | −0.339317 | ||||||||
\(382\) | 0.612679 | 0.0313474 | ||||||||
\(383\) | 0.0298464 | 0.00152508 | 0.000762539 | − | 1.00000i | \(-0.499757\pi\) | ||||
0.000762539 | 1.00000i | \(0.499757\pi\) | ||||||||
\(384\) | −2.66908 | −0.136206 | ||||||||
\(385\) | −17.3792 | −0.885725 | ||||||||
\(386\) | −11.6425 | −0.592589 | ||||||||
\(387\) | 6.02985 | 0.306514 | ||||||||
\(388\) | −2.18038 | −0.110692 | ||||||||
\(389\) | 9.22865 | 0.467911 | 0.233956 | − | 0.972247i | \(-0.424833\pi\) | ||||
0.233956 | + | 0.972247i | \(0.424833\pi\) | |||||||
\(390\) | 24.3719 | 1.23412 | ||||||||
\(391\) | 18.8462 | 0.953092 | ||||||||
\(392\) | 10.7593 | 0.543425 | ||||||||
\(393\) | −29.3792 | −1.48198 | ||||||||
\(394\) | −12.9098 | −0.650387 | ||||||||
\(395\) | −37.7665 | −1.90024 | ||||||||
\(396\) | −4.12398 | −0.207238 | ||||||||
\(397\) | 17.2697 | 0.866740 | 0.433370 | − | 0.901216i | \(-0.357324\pi\) | ||||
0.433370 | + | 0.901216i | \(0.357324\pi\) | |||||||
\(398\) | −18.3647 | −0.920540 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.0072 | 0.600362 | ||||||||
\(401\) | 13.2850 | 0.663424 | 0.331712 | − | 0.943381i | \(-0.392374\pi\) | ||||
0.331712 | + | 0.943381i | \(0.392374\pi\) | |||||||
\(402\) | 3.48146 | 0.173639 | ||||||||
\(403\) | −15.5152 | −0.772870 | ||||||||
\(404\) | −6.24797 | −0.310848 | ||||||||
\(405\) | 18.0000 | 0.894427 | ||||||||
\(406\) | 23.5104 | 1.16680 | ||||||||
\(407\) | −2.90981 | −0.144234 | ||||||||
\(408\) | 9.22141 | 0.456528 | ||||||||
\(409\) | −1.94360 | −0.0961048 | −0.0480524 | − | 0.998845i | \(-0.515301\pi\) | ||||
−0.0480524 | + | 0.998845i | \(0.515301\pi\) | |||||||
\(410\) | −49.1457 | −2.42713 | ||||||||
\(411\) | −18.5330 | −0.914166 | ||||||||
\(412\) | −0.605441 | −0.0298280 | ||||||||
\(413\) | 20.1988 | 0.993918 | ||||||||
\(414\) | −22.4959 | −1.10561 | ||||||||
\(415\) | 54.4950 | 2.67506 | ||||||||
\(416\) | 2.21417 | 0.108559 | ||||||||
\(417\) | 11.6691 | 0.571437 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.49593 | −0.121934 | −0.0609671 | − | 0.998140i | \(-0.519418\pi\) | ||||
−0.0609671 | + | 0.998140i | \(0.519418\pi\) | |||||||
\(420\) | −46.3864 | −2.26343 | ||||||||
\(421\) | −15.6353 | −0.762017 | −0.381009 | − | 0.924571i | \(-0.624423\pi\) | ||||
−0.381009 | + | 0.924571i | \(0.624423\pi\) | |||||||
\(422\) | −2.13122 | −0.103746 | ||||||||
\(423\) | 31.2850 | 1.52113 | ||||||||
\(424\) | 13.2214 | 0.642089 | ||||||||
\(425\) | −41.4839 | −2.01226 | ||||||||
\(426\) | −18.1505 | −0.879396 | ||||||||
\(427\) | −37.5475 | −1.81705 | ||||||||
\(428\) | −3.88325 | −0.187704 | ||||||||
\(429\) | 5.90981 | 0.285328 | ||||||||
\(430\) | −6.02985 | −0.290785 | ||||||||
\(431\) | −0.262441 | −0.0126413 | −0.00632067 | − | 0.999980i | \(-0.502012\pi\) | ||||
−0.00632067 | + | 0.999980i | \(0.502012\pi\) | |||||||
\(432\) | −3.00000 | −0.144338 | ||||||||
\(433\) | 32.2769 | 1.55113 | 0.775565 | − | 0.631268i | \(-0.217465\pi\) | ||||
0.775565 | + | 0.631268i | \(0.217465\pi\) | |||||||
\(434\) | 29.5297 | 1.41747 | ||||||||
\(435\) | −61.4081 | −2.94429 | ||||||||
\(436\) | 4.97345 | 0.238185 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 3.88325 | 0.185549 | ||||||||
\(439\) | 17.0902 | 0.815670 | 0.407835 | − | 0.913056i | \(-0.366284\pi\) | ||||
0.407835 | + | 0.913056i | \(0.366284\pi\) | |||||||
\(440\) | 4.12398 | 0.196603 | ||||||||
\(441\) | 44.3711 | 2.11291 | ||||||||
\(442\) | −7.64976 | −0.363862 | ||||||||
\(443\) | 16.2624 | 0.772652 | 0.386326 | − | 0.922362i | \(-0.373744\pi\) | ||||
0.386326 | + | 0.922362i | \(0.373744\pi\) | |||||||
\(444\) | −7.76651 | −0.368582 | ||||||||
\(445\) | 34.0145 | 1.61244 | ||||||||
\(446\) | −6.90981 | −0.327189 | ||||||||
\(447\) | −31.4057 | −1.48544 | ||||||||
\(448\) | −4.21417 | −0.199101 | ||||||||
\(449\) | 27.3382 | 1.29017 | 0.645084 | − | 0.764112i | \(-0.276822\pi\) | ||||
0.645084 | + | 0.764112i | \(0.276822\pi\) | |||||||
\(450\) | 49.5176 | 2.33428 | ||||||||
\(451\) | −11.9170 | −0.561152 | ||||||||
\(452\) | 8.00000 | 0.376288 | ||||||||
\(453\) | −52.2769 | −2.45618 | ||||||||
\(454\) | 2.72548 | 0.127913 | ||||||||
\(455\) | 38.4806 | 1.80400 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.4920 | 0.490794 | 0.245397 | − | 0.969423i | \(-0.421082\pi\) | ||||
0.245397 | + | 0.969423i | \(0.421082\pi\) | |||||||
\(458\) | 3.48870 | 0.163016 | ||||||||
\(459\) | 10.3647 | 0.483783 | ||||||||
\(460\) | 22.4959 | 1.04888 | ||||||||
\(461\) | 6.18038 | 0.287849 | 0.143925 | − | 0.989589i | \(-0.454028\pi\) | ||||
0.143925 | + | 0.989589i | \(0.454028\pi\) | |||||||
\(462\) | −11.2480 | −0.523303 | ||||||||
\(463\) | −11.1433 | −0.517873 | −0.258937 | − | 0.965894i | \(-0.583372\pi\) | ||||
−0.258937 | + | 0.965894i | \(0.583372\pi\) | |||||||
\(464\) | −5.57889 | −0.258993 | ||||||||
\(465\) | −77.1303 | −3.57683 | ||||||||
\(466\) | −17.0902 | −0.791688 | ||||||||
\(467\) | −34.5104 | −1.59695 | −0.798476 | − | 0.602027i | \(-0.794360\pi\) | ||||
−0.798476 | + | 0.602027i | \(0.794360\pi\) | |||||||
\(468\) | 9.13122 | 0.422091 | ||||||||
\(469\) | 5.49683 | 0.253820 | ||||||||
\(470\) | −31.2850 | −1.44307 | ||||||||
\(471\) | −55.0362 | −2.53593 | ||||||||
\(472\) | −4.79306 | −0.220619 | ||||||||
\(473\) | −1.46214 | −0.0672293 | ||||||||
\(474\) | −24.4428 | −1.12270 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 14.5596 | 0.667337 | ||||||||
\(477\) | 54.5249 | 2.49652 | ||||||||
\(478\) | 6.06035 | 0.277194 | ||||||||
\(479\) | 41.6980 | 1.90523 | 0.952616 | − | 0.304176i | \(-0.0983812\pi\) | ||||
0.952616 | + | 0.304176i | \(0.0983812\pi\) | |||||||
\(480\) | 11.0072 | 0.502409 | ||||||||
\(481\) | 6.44282 | 0.293768 | ||||||||
\(482\) | −4.85341 | −0.221067 | ||||||||
\(483\) | −61.3566 | −2.79182 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 8.99187 | 0.408300 | ||||||||
\(486\) | 20.6498 | 0.936692 | ||||||||
\(487\) | −9.10137 | −0.412423 | −0.206211 | − | 0.978507i | \(-0.566113\pi\) | ||||
−0.206211 | + | 0.978507i | \(0.566113\pi\) | |||||||
\(488\) | 8.90981 | 0.403328 | ||||||||
\(489\) | 47.6006 | 2.15257 | ||||||||
\(490\) | −44.3711 | −2.00448 | ||||||||
\(491\) | −30.8413 | −1.39185 | −0.695925 | − | 0.718115i | \(-0.745005\pi\) | ||||
−0.695925 | + | 0.718115i | \(0.745005\pi\) | |||||||
\(492\) | −31.8075 | −1.43399 | ||||||||
\(493\) | 19.2745 | 0.868081 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.0072 | 0.764418 | ||||||||
\(496\) | −7.00724 | −0.314634 | ||||||||
\(497\) | −28.6577 | −1.28547 | ||||||||
\(498\) | 35.2697 | 1.58047 | ||||||||
\(499\) | 21.7665 | 0.974403 | 0.487201 | − | 0.873290i | \(-0.338018\pi\) | ||||
0.487201 | + | 0.873290i | \(0.338018\pi\) | |||||||
\(500\) | −28.8977 | −1.29235 | ||||||||
\(501\) | 11.1578 | 0.498493 | ||||||||
\(502\) | −1.58612 | −0.0707922 | ||||||||
\(503\) | 38.0893 | 1.69832 | 0.849159 | − | 0.528138i | \(-0.177109\pi\) | ||||
0.849159 | + | 0.528138i | \(0.177109\pi\) | |||||||
\(504\) | −17.3792 | −0.774131 | ||||||||
\(505\) | 25.7665 | 1.14659 | ||||||||
\(506\) | 5.45490 | 0.242500 | ||||||||
\(507\) | 21.6127 | 0.959853 | ||||||||
\(508\) | 2.48146 | 0.110097 | ||||||||
\(509\) | −14.9388 | −0.662149 | −0.331074 | − | 0.943605i | \(-0.607411\pi\) | ||||
−0.331074 | + | 0.943605i | \(0.607411\pi\) | |||||||
\(510\) | −38.0289 | −1.68395 | ||||||||
\(511\) | 6.13122 | 0.271229 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.5185 | −0.860926 | ||||||||
\(515\) | 2.49683 | 0.110023 | ||||||||
\(516\) | −3.90257 | −0.171801 | ||||||||
\(517\) | −7.58612 | −0.333637 | ||||||||
\(518\) | −12.2624 | −0.538781 | ||||||||
\(519\) | 63.2842 | 2.77787 | ||||||||
\(520\) | −9.13122 | −0.400431 | ||||||||
\(521\) | −7.22536 | −0.316549 | −0.158274 | − | 0.987395i | \(-0.550593\pi\) | ||||
−0.158274 | + | 0.987395i | \(0.550593\pi\) | |||||||
\(522\) | −23.0072 | −1.00700 | ||||||||
\(523\) | −4.90586 | −0.214518 | −0.107259 | − | 0.994231i | \(-0.534207\pi\) | ||||
−0.107259 | + | 0.994231i | \(0.534207\pi\) | |||||||
\(524\) | 11.0072 | 0.480853 | ||||||||
\(525\) | 135.057 | 5.89437 | ||||||||
\(526\) | −13.0483 | −0.568931 | ||||||||
\(527\) | 24.2093 | 1.05458 | ||||||||
\(528\) | 2.66908 | 0.116157 | ||||||||
\(529\) | 6.75598 | 0.293738 | ||||||||
\(530\) | −54.5249 | −2.36841 | ||||||||
\(531\) | −19.7665 | −0.857793 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.3864 | 1.14292 | ||||||||
\(534\) | 22.0145 | 0.952659 | ||||||||
\(535\) | 16.0145 | 0.692366 | ||||||||
\(536\) | −1.30437 | −0.0563401 | ||||||||
\(537\) | −28.8977 | −1.24703 | ||||||||
\(538\) | −23.6006 | −1.01749 | ||||||||
\(539\) | −10.7593 | −0.463435 | ||||||||
\(540\) | 12.3719 | 0.532404 | ||||||||
\(541\) | 30.8712 | 1.32726 | 0.663628 | − | 0.748063i | \(-0.269016\pi\) | ||||
0.663628 | + | 0.748063i | \(0.269016\pi\) | |||||||
\(542\) | −16.4090 | −0.704828 | ||||||||
\(543\) | −47.6006 | −2.04274 | ||||||||
\(544\) | −3.45490 | −0.148128 | ||||||||
\(545\) | −20.5104 | −0.878569 | ||||||||
\(546\) | 24.9050 | 1.06583 | ||||||||
\(547\) | −2.54115 | −0.108652 | −0.0543259 | − | 0.998523i | \(-0.517301\pi\) | ||||
−0.0543259 | + | 0.998523i | \(0.517301\pi\) | |||||||
\(548\) | 6.94360 | 0.296616 | ||||||||
\(549\) | 36.7439 | 1.56819 | ||||||||
\(550\) | −12.0072 | −0.511990 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 14.5596 | 0.619696 | ||||||||
\(553\) | −38.5925 | −1.64112 | ||||||||
\(554\) | −11.5861 | −0.492247 | ||||||||
\(555\) | 32.0289 | 1.35955 | ||||||||
\(556\) | −4.37195 | −0.185412 | ||||||||
\(557\) | 23.9017 | 1.01275 | 0.506373 | − | 0.862314i | \(-0.330986\pi\) | ||||
0.506373 | + | 0.862314i | \(0.330986\pi\) | |||||||
\(558\) | −28.8977 | −1.22334 | ||||||||
\(559\) | 3.23744 | 0.136929 | ||||||||
\(560\) | 17.3792 | 0.734405 | ||||||||
\(561\) | −9.22141 | −0.389328 | ||||||||
\(562\) | −7.03379 | −0.296703 | ||||||||
\(563\) | 10.6232 | 0.447715 | 0.223857 | − | 0.974622i | \(-0.428135\pi\) | ||||
0.223857 | + | 0.974622i | \(0.428135\pi\) | |||||||
\(564\) | −20.2480 | −0.852593 | ||||||||
\(565\) | −32.9919 | −1.38798 | ||||||||
\(566\) | 8.33092 | 0.350175 | ||||||||
\(567\) | 18.3937 | 0.772461 | ||||||||
\(568\) | 6.80030 | 0.285334 | ||||||||
\(569\) | −29.3373 | −1.22988 | −0.614941 | − | 0.788573i | \(-0.710820\pi\) | ||||
−0.614941 | + | 0.788573i | \(0.710820\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.8639 | 0.831280 | 0.415640 | − | 0.909529i | \(-0.363558\pi\) | ||||
0.415640 | + | 0.909529i | \(0.363558\pi\) | |||||||
\(572\) | −2.21417 | −0.0925793 | ||||||||
\(573\) | −1.63529 | −0.0683151 | ||||||||
\(574\) | −50.2205 | −2.09616 | ||||||||
\(575\) | −65.4983 | −2.73147 | ||||||||
\(576\) | 4.12398 | 0.171833 | ||||||||
\(577\) | −3.17709 | −0.132264 | −0.0661320 | − | 0.997811i | \(-0.521066\pi\) | ||||
−0.0661320 | + | 0.997811i | \(0.521066\pi\) | |||||||
\(578\) | −5.06364 | −0.210620 | ||||||||
\(579\) | 31.0748 | 1.29143 | ||||||||
\(580\) | 23.0072 | 0.955324 | ||||||||
\(581\) | 55.6868 | 2.31028 | ||||||||
\(582\) | 5.81962 | 0.241231 | ||||||||
\(583\) | −13.2214 | −0.547575 | ||||||||
\(584\) | −1.45490 | −0.0602044 | ||||||||
\(585\) | −37.6570 | −1.55693 | ||||||||
\(586\) | −10.2142 | −0.421944 | ||||||||
\(587\) | 4.00000 | 0.165098 | 0.0825488 | − | 0.996587i | \(-0.473694\pi\) | ||||
0.0825488 | + | 0.996587i | \(0.473694\pi\) | |||||||
\(588\) | −28.7173 | −1.18428 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 19.7665 | 0.813774 | ||||||||
\(591\) | 34.4573 | 1.41738 | ||||||||
\(592\) | 2.90981 | 0.119592 | ||||||||
\(593\) | −3.45885 | −0.142038 | −0.0710190 | − | 0.997475i | \(-0.522625\pi\) | ||||
−0.0710190 | + | 0.997475i | \(0.522625\pi\) | |||||||
\(594\) | 3.00000 | 0.123091 | ||||||||
\(595\) | −60.0434 | −2.46154 | ||||||||
\(596\) | 11.7665 | 0.481975 | ||||||||
\(597\) | 49.0169 | 2.00613 | ||||||||
\(598\) | −12.0781 | −0.493911 | ||||||||
\(599\) | −40.3864 | −1.65014 | −0.825072 | − | 0.565027i | \(-0.808866\pi\) | ||||
−0.825072 | + | 0.565027i | \(0.808866\pi\) | |||||||
\(600\) | −32.0483 | −1.30836 | ||||||||
\(601\) | −18.3309 | −0.747734 | −0.373867 | − | 0.927482i | \(-0.621968\pi\) | ||||
−0.373867 | + | 0.927482i | \(0.621968\pi\) | |||||||
\(602\) | −6.16172 | −0.251133 | ||||||||
\(603\) | −5.37919 | −0.219057 | ||||||||
\(604\) | 19.5861 | 0.796948 | ||||||||
\(605\) | −4.12398 | −0.167664 | ||||||||
\(606\) | 16.6763 | 0.677429 | ||||||||
\(607\) | −12.4283 | −0.504451 | −0.252226 | − | 0.967668i | \(-0.581162\pi\) | ||||
−0.252226 | + | 0.967668i | \(0.581162\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −62.7511 | −2.54280 | ||||||||
\(610\) | −36.7439 | −1.48772 | ||||||||
\(611\) | 16.7970 | 0.679534 | ||||||||
\(612\) | −14.2480 | −0.575940 | ||||||||
\(613\) | −0.0531082 | −0.00214502 | −0.00107251 | − | 0.999999i | \(-0.500341\pi\) | ||||
−0.00107251 | + | 0.999999i | \(0.500341\pi\) | |||||||
\(614\) | 1.93242 | 0.0779860 | ||||||||
\(615\) | 131.174 | 5.28944 | ||||||||
\(616\) | 4.21417 | 0.169794 | ||||||||
\(617\) | −17.4887 | −0.704068 | −0.352034 | − | 0.935987i | \(-0.614510\pi\) | ||||
−0.352034 | + | 0.935987i | \(0.614510\pi\) | |||||||
\(618\) | 1.61597 | 0.0650039 | ||||||||
\(619\) | 25.2995 | 1.01687 | 0.508437 | − | 0.861099i | \(-0.330224\pi\) | ||||
0.508437 | + | 0.861099i | \(0.330224\pi\) | |||||||
\(620\) | 28.8977 | 1.16056 | ||||||||
\(621\) | 16.3647 | 0.656693 | ||||||||
\(622\) | −27.7173 | −1.11136 | ||||||||
\(623\) | 34.7584 | 1.39256 | ||||||||
\(624\) | −5.90981 | −0.236582 | ||||||||
\(625\) | 59.1376 | 2.36550 | ||||||||
\(626\) | 11.5258 | 0.460663 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.6199 | 0.822824 | ||||||||
\(629\) | −10.0531 | −0.400844 | ||||||||
\(630\) | 71.6715 | 2.85546 | ||||||||
\(631\) | 9.02261 | 0.359184 | 0.179592 | − | 0.983741i | \(-0.442522\pi\) | ||||
0.179592 | + | 0.983741i | \(0.442522\pi\) | |||||||
\(632\) | 9.15777 | 0.364277 | ||||||||
\(633\) | 5.68840 | 0.226093 | ||||||||
\(634\) | 33.8977 | 1.34625 | ||||||||
\(635\) | −10.2335 | −0.406104 | ||||||||
\(636\) | −35.2890 | −1.39930 | ||||||||
\(637\) | 23.8229 | 0.943898 | ||||||||
\(638\) | 5.57889 | 0.220870 | ||||||||
\(639\) | 28.0443 | 1.10942 | ||||||||
\(640\) | −4.12398 | −0.163015 | ||||||||
\(641\) | −30.4573 | −1.20299 | −0.601495 | − | 0.798876i | \(-0.705428\pi\) | ||||
−0.601495 | + | 0.798876i | \(0.705428\pi\) | |||||||
\(642\) | 10.3647 | 0.409063 | ||||||||
\(643\) | −36.7584 | −1.44961 | −0.724804 | − | 0.688955i | \(-0.758070\pi\) | ||||
−0.724804 | + | 0.688955i | \(0.758070\pi\) | |||||||
\(644\) | 22.9879 | 0.905851 | ||||||||
\(645\) | 16.0941 | 0.633706 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −41.0700 | −1.61463 | −0.807314 | − | 0.590122i | \(-0.799079\pi\) | ||||
−0.807314 | + | 0.590122i | \(0.799079\pi\) | |||||||
\(648\) | −4.36471 | −0.171462 | ||||||||
\(649\) | 4.79306 | 0.188144 | ||||||||
\(650\) | 26.5861 | 1.04279 | ||||||||
\(651\) | −78.8172 | −3.08909 | ||||||||
\(652\) | −17.8341 | −0.698437 | ||||||||
\(653\) | 28.4806 | 1.11453 | 0.557265 | − | 0.830335i | \(-0.311851\pi\) | ||||
0.557265 | + | 0.830335i | \(0.311851\pi\) | |||||||
\(654\) | −13.2745 | −0.519075 | ||||||||
\(655\) | −45.3937 | −1.77368 | ||||||||
\(656\) | 11.9170 | 0.465282 | ||||||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | −31.9693 | −1.24629 | ||||||||
\(659\) | 10.5740 | 0.411906 | 0.205953 | − | 0.978562i | \(-0.433971\pi\) | ||||
0.205953 | + | 0.978562i | \(0.433971\pi\) | |||||||
\(660\) | −11.0072 | −0.428456 | ||||||||
\(661\) | −7.70287 | −0.299607 | −0.149803 | − | 0.988716i | \(-0.547864\pi\) | ||||
−0.149803 | + | 0.988716i | \(0.547864\pi\) | |||||||
\(662\) | 16.2697 | 0.632339 | ||||||||
\(663\) | 20.4178 | 0.792962 | ||||||||
\(664\) | −13.2142 | −0.512809 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.0000 | 0.464991 | ||||||||
\(667\) | 30.4323 | 1.17834 | ||||||||
\(668\) | −4.18038 | −0.161744 | ||||||||
\(669\) | 18.4428 | 0.713041 | ||||||||
\(670\) | 5.37919 | 0.207816 | ||||||||
\(671\) | −8.90981 | −0.343959 | ||||||||
\(672\) | 11.2480 | 0.433900 | ||||||||
\(673\) | 31.5176 | 1.21492 | 0.607458 | − | 0.794352i | \(-0.292189\pi\) | ||||
0.607458 | + | 0.794352i | \(0.292189\pi\) | |||||||
\(674\) | 6.82685 | 0.262961 | ||||||||
\(675\) | −36.0217 | −1.38648 | ||||||||
\(676\) | −8.09743 | −0.311440 | ||||||||
\(677\) | −11.9928 | −0.460919 | −0.230460 | − | 0.973082i | \(-0.574023\pi\) | ||||
−0.230460 | + | 0.973082i | \(0.574023\pi\) | |||||||
\(678\) | −21.3526 | −0.820043 | ||||||||
\(679\) | 9.18852 | 0.352623 | ||||||||
\(680\) | 14.2480 | 0.546385 | ||||||||
\(681\) | −7.27452 | −0.278760 | ||||||||
\(682\) | 7.00724 | 0.268321 | ||||||||
\(683\) | −39.1722 | −1.49888 | −0.749442 | − | 0.662070i | \(-0.769678\pi\) | ||||
−0.749442 | + | 0.662070i | \(0.769678\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.6353 | −1.09410 | ||||||||
\(686\) | −15.8422 | −0.604859 | ||||||||
\(687\) | −9.31160 | −0.355260 | ||||||||
\(688\) | 1.46214 | 0.0557436 | ||||||||
\(689\) | 29.2745 | 1.11527 | ||||||||
\(690\) | −60.0434 | −2.28581 | ||||||||
\(691\) | −49.1722 | −1.87060 | −0.935300 | − | 0.353855i | \(-0.884871\pi\) | ||||
−0.935300 | + | 0.353855i | \(0.884871\pi\) | |||||||
\(692\) | −23.7101 | −0.901323 | ||||||||
\(693\) | 17.3792 | 0.660181 | ||||||||
\(694\) | −5.09019 | −0.193221 | ||||||||
\(695\) | 18.0298 | 0.683911 | ||||||||
\(696\) | 14.8905 | 0.564423 | ||||||||
\(697\) | −41.1722 | −1.55951 | ||||||||
\(698\) | 30.9919 | 1.17306 | ||||||||
\(699\) | 45.6151 | 1.72532 | ||||||||
\(700\) | −50.6006 | −1.91252 | ||||||||
\(701\) | 37.8486 | 1.42952 | 0.714760 | − | 0.699370i | \(-0.246536\pi\) | ||||
0.714760 | + | 0.699370i | \(0.246536\pi\) | |||||||
\(702\) | −6.64252 | −0.250706 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 83.5023 | 3.14488 | ||||||||
\(706\) | −17.8301 | −0.671046 | ||||||||
\(707\) | 26.3300 | 0.990242 | ||||||||
\(708\) | 12.7931 | 0.480793 | ||||||||
\(709\) | 27.7511 | 1.04222 | 0.521108 | − | 0.853491i | \(-0.325519\pi\) | ||||
0.521108 | + | 0.853491i | \(0.325519\pi\) | |||||||
\(710\) | −28.0443 | −1.05248 | ||||||||
\(711\) | 37.7665 | 1.41635 | ||||||||
\(712\) | −8.24797 | −0.309106 | ||||||||
\(713\) | 38.2238 | 1.43149 | ||||||||
\(714\) | −38.8606 | −1.45432 | ||||||||
\(715\) | 9.13122 | 0.341488 | ||||||||
\(716\) | 10.8269 | 0.404619 | ||||||||
\(717\) | −16.1755 | −0.604087 | ||||||||
\(718\) | 24.4090 | 0.910937 | ||||||||
\(719\) | −17.0410 | −0.635523 | −0.317762 | − | 0.948171i | \(-0.602931\pi\) | ||||
−0.317762 | + | 0.948171i | \(0.602931\pi\) | |||||||
\(720\) | −17.0072 | −0.633822 | ||||||||
\(721\) | 2.55144 | 0.0950204 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.9541 | 0.481769 | ||||||||
\(724\) | 17.8341 | 0.662799 | ||||||||
\(725\) | −66.9870 | −2.48784 | ||||||||
\(726\) | −2.66908 | −0.0990588 | ||||||||
\(727\) | 13.5225 | 0.501521 | 0.250761 | − | 0.968049i | \(-0.419319\pi\) | ||||
0.250761 | + | 0.968049i | \(0.419319\pi\) | |||||||
\(728\) | −9.33092 | −0.345827 | ||||||||
\(729\) | −42.0217 | −1.55636 | ||||||||
\(730\) | 6.00000 | 0.222070 | ||||||||
\(731\) | −5.05156 | −0.186839 | ||||||||
\(732\) | −23.7810 | −0.878970 | ||||||||
\(733\) | −25.6682 | −0.948076 | −0.474038 | − | 0.880504i | \(-0.657204\pi\) | ||||
−0.474038 | + | 0.880504i | \(0.657204\pi\) | |||||||
\(734\) | −26.6232 | −0.982681 | ||||||||
\(735\) | 118.430 | 4.36835 | ||||||||
\(736\) | −5.45490 | −0.201070 | ||||||||
\(737\) | 1.30437 | 0.0480470 | ||||||||
\(738\) | 49.1457 | 1.80908 | ||||||||
\(739\) | 21.3493 | 0.785348 | 0.392674 | − | 0.919678i | \(-0.371550\pi\) | ||||
0.392674 | + | 0.919678i | \(0.371550\pi\) | |||||||
\(740\) | −12.0000 | −0.441129 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −55.7173 | −2.04545 | ||||||||
\(743\) | 7.55718 | 0.277246 | 0.138623 | − | 0.990345i | \(-0.455732\pi\) | ||||
0.138623 | + | 0.990345i | \(0.455732\pi\) | |||||||
\(744\) | 18.7029 | 0.685680 | ||||||||
\(745\) | −48.5249 | −1.77781 | ||||||||
\(746\) | 12.6160 | 0.461904 | ||||||||
\(747\) | −54.4950 | −1.99387 | ||||||||
\(748\) | 3.45490 | 0.126324 | ||||||||
\(749\) | 16.3647 | 0.597954 | ||||||||
\(750\) | 77.1303 | 2.81640 | ||||||||
\(751\) | 53.5861 | 1.95539 | 0.977693 | − | 0.210040i | \(-0.0673595\pi\) | ||||
0.977693 | + | 0.210040i | \(0.0673595\pi\) | |||||||
\(752\) | 7.58612 | 0.276637 | ||||||||
\(753\) | 4.23349 | 0.154277 | ||||||||
\(754\) | −12.3526 | −0.449856 | ||||||||
\(755\) | −80.7728 | −2.93962 | ||||||||
\(756\) | 12.6425 | 0.459804 | ||||||||
\(757\) | −13.9436 | −0.506789 | −0.253394 | − | 0.967363i | \(-0.581547\pi\) | ||||
−0.253394 | + | 0.967363i | \(0.581547\pi\) | |||||||
\(758\) | 22.8905 | 0.831420 | ||||||||
\(759\) | −14.5596 | −0.528479 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.7994 | −1.66023 | −0.830114 | − | 0.557594i | \(-0.811724\pi\) | ||||
−0.830114 | + | 0.557594i | \(0.811724\pi\) | |||||||
\(762\) | −6.62321 | −0.239934 | ||||||||
\(763\) | −20.9590 | −0.758766 | ||||||||
\(764\) | 0.612679 | 0.0221659 | ||||||||
\(765\) | 58.7584 | 2.12441 | ||||||||
\(766\) | 0.0298464 | 0.00107839 | ||||||||
\(767\) | −10.6127 | −0.383202 | ||||||||
\(768\) | −2.66908 | −0.0963121 | ||||||||
\(769\) | −40.8751 | −1.47399 | −0.736997 | − | 0.675896i | \(-0.763757\pi\) | ||||
−0.736997 | + | 0.675896i | \(0.763757\pi\) | |||||||
\(770\) | −17.3792 | −0.626302 | ||||||||
\(771\) | 52.0965 | 1.87621 | ||||||||
\(772\) | −11.6425 | −0.419024 | ||||||||
\(773\) | −37.4983 | −1.34872 | −0.674361 | − | 0.738402i | \(-0.735581\pi\) | ||||
−0.674361 | + | 0.738402i | \(0.735581\pi\) | |||||||
\(774\) | 6.02985 | 0.216738 | ||||||||
\(775\) | −84.1376 | −3.02231 | ||||||||
\(776\) | −2.18038 | −0.0782712 | ||||||||
\(777\) | 32.7294 | 1.17416 | ||||||||
\(778\) | 9.22865 | 0.330863 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 24.3719 | 0.872656 | ||||||||
\(781\) | −6.80030 | −0.243334 | ||||||||
\(782\) | 18.8462 | 0.673938 | ||||||||
\(783\) | 16.7367 | 0.598119 | ||||||||
\(784\) | 10.7593 | 0.384260 | ||||||||
\(785\) | −85.0362 | −3.03507 | ||||||||
\(786\) | −29.3792 | −1.04792 | ||||||||
\(787\) | −8.80754 | −0.313955 | −0.156977 | − | 0.987602i | \(-0.550175\pi\) | ||||
−0.156977 | + | 0.987602i | \(0.550175\pi\) | |||||||
\(788\) | −12.9098 | −0.459893 | ||||||||
\(789\) | 34.8269 | 1.23987 | ||||||||
\(790\) | −37.7665 | −1.34367 | ||||||||
\(791\) | −33.7134 | −1.19871 | ||||||||
\(792\) | −4.12398 | −0.146539 | ||||||||
\(793\) | 19.7279 | 0.700557 | ||||||||
\(794\) | 17.2697 | 0.612878 | ||||||||
\(795\) | 145.531 | 5.16146 | ||||||||
\(796\) | −18.3647 | −0.650920 | ||||||||
\(797\) | 26.1312 | 0.925615 | 0.462808 | − | 0.886459i | \(-0.346842\pi\) | ||||
0.462808 | + | 0.886459i | \(0.346842\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.2093 | −0.927220 | ||||||||
\(800\) | 12.0072 | 0.424520 | ||||||||
\(801\) | −34.0145 | −1.20184 | ||||||||
\(802\) | 13.2850 | 0.469111 | ||||||||
\(803\) | 1.45490 | 0.0513425 | ||||||||
\(804\) | 3.48146 | 0.122782 | ||||||||
\(805\) | −94.8018 | −3.34132 | ||||||||
\(806\) | −15.5152 | −0.546501 | ||||||||
\(807\) | 62.9919 | 2.21742 | ||||||||
\(808\) | −6.24797 | −0.219803 | ||||||||
\(809\) | −6.01053 | −0.211319 | −0.105659 | − | 0.994402i | \(-0.533695\pi\) | ||||
−0.105659 | + | 0.994402i | \(0.533695\pi\) | |||||||
\(810\) | 18.0000 | 0.632456 | ||||||||
\(811\) | 40.2809 | 1.41445 | 0.707226 | − | 0.706987i | \(-0.249946\pi\) | ||||
0.707226 | + | 0.706987i | \(0.249946\pi\) | |||||||
\(812\) | 23.5104 | 0.825054 | ||||||||
\(813\) | 43.7970 | 1.53603 | ||||||||
\(814\) | −2.90981 | −0.101989 | ||||||||
\(815\) | 73.5475 | 2.57626 | ||||||||
\(816\) | 9.22141 | 0.322814 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −1.94360 | −0.0679564 | ||||||||
\(819\) | −38.4806 | −1.34462 | ||||||||
\(820\) | −49.1457 | −1.71624 | ||||||||
\(821\) | 50.1496 | 1.75023 | 0.875117 | − | 0.483911i | \(-0.160784\pi\) | ||||
0.875117 | + | 0.483911i | \(0.160784\pi\) | |||||||
\(822\) | −18.5330 | −0.646413 | ||||||||
\(823\) | −42.7400 | −1.48982 | −0.744911 | − | 0.667164i | \(-0.767508\pi\) | ||||
−0.744911 | + | 0.667164i | \(0.767508\pi\) | |||||||
\(824\) | −0.605441 | −0.0210915 | ||||||||
\(825\) | 32.0483 | 1.11578 | ||||||||
\(826\) | 20.1988 | 0.702806 | ||||||||
\(827\) | −49.0555 | −1.70583 | −0.852913 | − | 0.522052i | \(-0.825167\pi\) | ||||
−0.852913 | + | 0.522052i | \(0.825167\pi\) | |||||||
\(828\) | −22.4959 | −0.781788 | ||||||||
\(829\) | −49.9653 | −1.73537 | −0.867683 | − | 0.497117i | \(-0.834392\pi\) | ||||
−0.867683 | + | 0.497117i | \(0.834392\pi\) | |||||||
\(830\) | 54.4950 | 1.89155 | ||||||||
\(831\) | 30.9243 | 1.07275 | ||||||||
\(832\) | 2.21417 | 0.0767627 | ||||||||
\(833\) | −37.1722 | −1.28794 | ||||||||
\(834\) | 11.6691 | 0.404067 | ||||||||
\(835\) | 17.2398 | 0.596609 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.0217 | 0.726617 | ||||||||
\(838\) | −2.49593 | −0.0862206 | ||||||||
\(839\) | 52.0257 | 1.79613 | 0.898063 | − | 0.439868i | \(-0.144975\pi\) | ||||
0.898063 | + | 0.439868i | \(0.144975\pi\) | |||||||
\(840\) | −46.3864 | −1.60048 | ||||||||
\(841\) | 2.12398 | 0.0732408 | ||||||||
\(842\) | −15.6353 | −0.538828 | ||||||||
\(843\) | 18.7737 | 0.646602 | ||||||||
\(844\) | −2.13122 | −0.0733596 | ||||||||
\(845\) | 33.3937 | 1.14878 | ||||||||
\(846\) | 31.2850 | 1.07560 | ||||||||
\(847\) | −4.21417 | −0.144801 | ||||||||
\(848\) | 13.2214 | 0.454025 | ||||||||
\(849\) | −22.2359 | −0.763134 | ||||||||
\(850\) | −41.4839 | −1.42288 | ||||||||
\(851\) | −15.8727 | −0.544110 | ||||||||
\(852\) | −18.1505 | −0.621827 | ||||||||
\(853\) | 16.2335 | 0.555824 | 0.277912 | − | 0.960607i | \(-0.410358\pi\) | ||||
0.277912 | + | 0.960607i | \(0.410358\pi\) | |||||||
\(854\) | −37.5475 | −1.28485 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.88325 | −0.132727 | ||||||||
\(857\) | −9.60150 | −0.327981 | −0.163990 | − | 0.986462i | \(-0.552437\pi\) | ||||
−0.163990 | + | 0.986462i | \(0.552437\pi\) | |||||||
\(858\) | 5.90981 | 0.201758 | ||||||||
\(859\) | 19.4057 | 0.662115 | 0.331058 | − | 0.943611i | \(-0.392595\pi\) | ||||
0.331058 | + | 0.943611i | \(0.392595\pi\) | |||||||
\(860\) | −6.02985 | −0.205616 | ||||||||
\(861\) | 134.043 | 4.56816 | ||||||||
\(862\) | −0.262441 | −0.00893877 | ||||||||
\(863\) | −1.54839 | −0.0527077 | −0.0263539 | − | 0.999653i | \(-0.508390\pi\) | ||||
−0.0263539 | + | 0.999653i | \(0.508390\pi\) | |||||||
\(864\) | −3.00000 | −0.102062 | ||||||||
\(865\) | 97.7801 | 3.32462 | ||||||||
\(866\) | 32.2769 | 1.09681 | ||||||||
\(867\) | 13.5152 | 0.459002 | ||||||||
\(868\) | 29.5297 | 1.00230 | ||||||||
\(869\) | −9.15777 | −0.310656 | ||||||||
\(870\) | −61.4081 | −2.08193 | ||||||||
\(871\) | −2.88810 | −0.0978594 | ||||||||
\(872\) | 4.97345 | 0.168422 | ||||||||
\(873\) | −8.99187 | −0.304329 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 121.780 | 4.11692 | ||||||||
\(876\) | 3.88325 | 0.131203 | ||||||||
\(877\) | 12.1200 | 0.409265 | 0.204632 | − | 0.978839i | \(-0.434400\pi\) | ||||
0.204632 | + | 0.978839i | \(0.434400\pi\) | |||||||
\(878\) | 17.0902 | 0.576766 | ||||||||
\(879\) | 27.2624 | 0.919539 | ||||||||
\(880\) | 4.12398 | 0.139019 | ||||||||
\(881\) | 53.6836 | 1.80864 | 0.904322 | − | 0.426850i | \(-0.140377\pi\) | ||||
0.904322 | + | 0.426850i | \(0.140377\pi\) | |||||||
\(882\) | 44.3711 | 1.49405 | ||||||||
\(883\) | 34.4283 | 1.15861 | 0.579303 | − | 0.815112i | \(-0.303325\pi\) | ||||
0.579303 | + | 0.815112i | \(0.303325\pi\) | |||||||
\(884\) | −7.64976 | −0.257289 | ||||||||
\(885\) | −52.7584 | −1.77345 | ||||||||
\(886\) | 16.2624 | 0.546347 | ||||||||
\(887\) | 27.5330 | 0.924468 | 0.462234 | − | 0.886758i | \(-0.347048\pi\) | ||||
0.462234 | + | 0.886758i | \(0.347048\pi\) | |||||||
\(888\) | −7.76651 | −0.260627 | ||||||||
\(889\) | −10.4573 | −0.350727 | ||||||||
\(890\) | 34.0145 | 1.14017 | ||||||||
\(891\) | 4.36471 | 0.146223 | ||||||||
\(892\) | −6.90981 | −0.231357 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −31.4057 | −1.05037 | ||||||||
\(895\) | −44.6498 | −1.49248 | ||||||||
\(896\) | −4.21417 | −0.140786 | ||||||||
\(897\) | 32.2374 | 1.07638 | ||||||||
\(898\) | 27.3382 | 0.912286 | ||||||||
\(899\) | 39.0926 | 1.30381 | ||||||||
\(900\) | 49.5176 | 1.65059 | ||||||||
\(901\) | −45.6787 | −1.52178 | ||||||||
\(902\) | −11.9170 | −0.396794 | ||||||||
\(903\) | 16.4461 | 0.547292 | ||||||||
\(904\) | 8.00000 | 0.266076 | ||||||||
\(905\) | −73.5475 | −2.44480 | ||||||||
\(906\) | −52.2769 | −1.73678 | ||||||||
\(907\) | −15.5677 | −0.516917 | −0.258459 | − | 0.966022i | \(-0.583215\pi\) | ||||
−0.258459 | + | 0.966022i | \(0.583215\pi\) | |||||||
\(908\) | 2.72548 | 0.0904482 | ||||||||
\(909\) | −25.7665 | −0.854621 | ||||||||
\(910\) | 38.4806 | 1.27562 | ||||||||
\(911\) | 0.623208 | 0.0206478 | 0.0103239 | − | 0.999947i | \(-0.496714\pi\) | ||||
0.0103239 | + | 0.999947i | \(0.496714\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.2142 | 0.437325 | ||||||||
\(914\) | 10.4920 | 0.347044 | ||||||||
\(915\) | 98.0724 | 3.24217 | ||||||||
\(916\) | 3.48870 | 0.115270 | ||||||||
\(917\) | −46.3864 | −1.53181 | ||||||||
\(918\) | 10.3647 | 0.342086 | ||||||||
\(919\) | −44.4887 | −1.46755 | −0.733773 | − | 0.679394i | \(-0.762243\pi\) | ||||
−0.733773 | + | 0.679394i | \(0.762243\pi\) | |||||||
\(920\) | 22.4959 | 0.741669 | ||||||||
\(921\) | −5.15777 | −0.169954 | ||||||||
\(922\) | 6.18038 | 0.203540 | ||||||||
\(923\) | 15.0571 | 0.495609 | ||||||||
\(924\) | −11.2480 | −0.370031 | ||||||||
\(925\) | 34.9388 | 1.14878 | ||||||||
\(926\) | −11.1433 | −0.366192 | ||||||||
\(927\) | −2.49683 | −0.0820067 | ||||||||
\(928\) | −5.57889 | −0.183136 | ||||||||
\(929\) | 44.1224 | 1.44761 | 0.723805 | − | 0.690005i | \(-0.242391\pi\) | ||||
0.723805 | + | 0.690005i | \(0.242391\pi\) | |||||||
\(930\) | −77.1303 | −2.52920 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −17.0902 | −0.559808 | ||||||||
\(933\) | 73.9798 | 2.42199 | ||||||||
\(934\) | −34.5104 | −1.12922 | ||||||||
\(935\) | −14.2480 | −0.465958 | ||||||||
\(936\) | 9.13122 | 0.298463 | ||||||||
\(937\) | 24.8672 | 0.812377 | 0.406188 | − | 0.913789i | \(-0.366858\pi\) | ||||
0.406188 | + | 0.913789i | \(0.366858\pi\) | |||||||
\(938\) | 5.49683 | 0.179478 | ||||||||
\(939\) | −30.7632 | −1.00392 | ||||||||
\(940\) | −31.2850 | −1.02041 | ||||||||
\(941\) | −29.8301 | −0.972435 | −0.486217 | − | 0.873838i | \(-0.661624\pi\) | ||||
−0.486217 | + | 0.873838i | \(0.661624\pi\) | |||||||
\(942\) | −55.0362 | −1.79318 | ||||||||
\(943\) | −65.0063 | −2.11690 | ||||||||
\(944\) | −4.79306 | −0.156001 | ||||||||
\(945\) | −52.1376 | −1.69603 | ||||||||
\(946\) | −1.46214 | −0.0475383 | ||||||||
\(947\) | 9.07572 | 0.294921 | 0.147461 | − | 0.989068i | \(-0.452890\pi\) | ||||
0.147461 | + | 0.989068i | \(0.452890\pi\) | |||||||
\(948\) | −24.4428 | −0.793866 | ||||||||
\(949\) | −3.22141 | −0.104571 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −90.4757 | −2.93388 | ||||||||
\(952\) | 14.5596 | 0.471878 | ||||||||
\(953\) | −1.27058 | −0.0411580 | −0.0205790 | − | 0.999788i | \(-0.506551\pi\) | ||||
−0.0205790 | + | 0.999788i | \(0.506551\pi\) | |||||||
\(954\) | 54.5249 | 1.76531 | ||||||||
\(955\) | −2.52668 | −0.0817613 | ||||||||
\(956\) | 6.06035 | 0.196006 | ||||||||
\(957\) | −14.8905 | −0.481341 | ||||||||
\(958\) | 41.6980 | 1.34720 | ||||||||
\(959\) | −29.2615 | −0.944905 | ||||||||
\(960\) | 11.0072 | 0.355257 | ||||||||
\(961\) | 18.1014 | 0.583915 | ||||||||
\(962\) | 6.44282 | 0.207725 | ||||||||
\(963\) | −16.0145 | −0.516059 | ||||||||
\(964\) | −4.85341 | −0.156318 | ||||||||
\(965\) | 48.0136 | 1.54561 | ||||||||
\(966\) | −61.3566 | −1.97412 | ||||||||
\(967\) | 6.67632 | 0.214696 | 0.107348 | − | 0.994222i | \(-0.465764\pi\) | ||||
0.107348 | + | 0.994222i | \(0.465764\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.99187 | 0.288711 | ||||||||
\(971\) | 0.191566 | 0.00614764 | 0.00307382 | − | 0.999995i | \(-0.499022\pi\) | ||||
0.00307382 | + | 0.999995i | \(0.499022\pi\) | |||||||
\(972\) | 20.6498 | 0.662341 | ||||||||
\(973\) | 18.4242 | 0.590651 | ||||||||
\(974\) | −9.10137 | −0.291627 | ||||||||
\(975\) | −70.9605 | −2.27255 | ||||||||
\(976\) | 8.90981 | 0.285196 | ||||||||
\(977\) | −16.4959 | −0.527752 | −0.263876 | − | 0.964557i | \(-0.585001\pi\) | ||||
−0.263876 | + | 0.964557i | \(0.585001\pi\) | |||||||
\(978\) | 47.6006 | 1.52210 | ||||||||
\(979\) | 8.24797 | 0.263606 | ||||||||
\(980\) | −44.3711 | −1.41738 | ||||||||
\(981\) | 20.5104 | 0.654847 | ||||||||
\(982\) | −30.8413 | −0.984186 | ||||||||
\(983\) | 35.0072 | 1.11656 | 0.558279 | − | 0.829653i | \(-0.311462\pi\) | ||||
0.558279 | + | 0.829653i | \(0.311462\pi\) | |||||||
\(984\) | −31.8075 | −1.01399 | ||||||||
\(985\) | 53.2398 | 1.69636 | ||||||||
\(986\) | 19.2745 | 0.613826 | ||||||||
\(987\) | 85.3285 | 2.71604 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.97584 | −0.253617 | ||||||||
\(990\) | 17.0072 | 0.540525 | ||||||||
\(991\) | 11.3759 | 0.361367 | 0.180684 | − | 0.983541i | \(-0.442169\pi\) | ||||
0.180684 | + | 0.983541i | \(0.442169\pi\) | |||||||
\(992\) | −7.00724 | −0.222480 | ||||||||
\(993\) | −43.4251 | −1.37805 | ||||||||
\(994\) | −28.6577 | −0.908966 | ||||||||
\(995\) | 75.7358 | 2.40099 | ||||||||
\(996\) | 35.2697 | 1.11756 | ||||||||
\(997\) | 8.89533 | 0.281718 | 0.140859 | − | 0.990030i | \(-0.455014\pi\) | ||||
0.140859 | + | 0.990030i | \(0.455014\pi\) | |||||||
\(998\) | 21.7665 | 0.689007 | ||||||||
\(999\) | −8.72942 | −0.276187 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7942.2.a.bi.1.1 | 3 | ||
19.18 | odd | 2 | 418.2.a.g.1.3 | ✓ | 3 | ||
57.56 | even | 2 | 3762.2.a.bg.1.3 | 3 | |||
76.75 | even | 2 | 3344.2.a.q.1.1 | 3 | |||
209.208 | even | 2 | 4598.2.a.bo.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.a.g.1.3 | ✓ | 3 | 19.18 | odd | 2 | ||
3344.2.a.q.1.1 | 3 | 76.75 | even | 2 | |||
3762.2.a.bg.1.3 | 3 | 57.56 | even | 2 | |||
4598.2.a.bo.1.3 | 3 | 209.208 | even | 2 | |||
7942.2.a.bi.1.1 | 3 | 1.1 | even | 1 | trivial |