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: | \(3\) |
Coefficient field: | 3.3.837.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
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 | \(-2.36147\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.36147 | −1.66981 | −0.834905 | − | 0.550394i | \(-0.814478\pi\) | ||||
−0.834905 | + | 0.550394i | \(0.814478\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.57653 | 1.78827 | ||||||||
\(5\) | −3.36147 | −1.50329 | −0.751647 | − | 0.659565i | \(-0.770740\pi\) | ||||
−0.751647 | + | 0.659565i | \(0.770740\pi\) | |||||||
\(6\) | 2.36147 | 0.964066 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.72294 | −1.31626 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 7.93800 | 2.51022 | ||||||||
\(11\) | 5.93800 | 1.79038 | 0.895188 | − | 0.445689i | \(-0.147041\pi\) | ||||
0.895188 | + | 0.445689i | \(0.147041\pi\) | |||||||
\(12\) | −3.57653 | −1.03246 | ||||||||
\(13\) | −1.42347 | −0.394798 | −0.197399 | − | 0.980323i | \(-0.563249\pi\) | ||||
−0.197399 | + | 0.980323i | \(0.563249\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.36147 | 0.867928 | ||||||||
\(16\) | 1.63853 | 0.409633 | ||||||||
\(17\) | −2.78493 | −0.675446 | −0.337723 | − | 0.941246i | \(-0.609657\pi\) | ||||
−0.337723 | + | 0.941246i | \(0.609657\pi\) | |||||||
\(18\) | −2.36147 | −0.556604 | ||||||||
\(19\) | 5.93800 | 1.36227 | 0.681136 | − | 0.732157i | \(-0.261486\pi\) | ||||
0.681136 | + | 0.732157i | \(0.261486\pi\) | |||||||
\(20\) | −12.0224 | −2.68829 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −14.0224 | −2.98959 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 3.72294 | 0.759941 | ||||||||
\(25\) | 6.29947 | 1.25989 | ||||||||
\(26\) | 3.36147 | 0.659238 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.66094 | −1.23691 | −0.618453 | − | 0.785822i | \(-0.712240\pi\) | ||||
−0.618453 | + | 0.785822i | \(0.712240\pi\) | |||||||
\(30\) | −7.93800 | −1.44927 | ||||||||
\(31\) | 9.93800 | 1.78492 | 0.892459 | − | 0.451128i | \(-0.148978\pi\) | ||||
0.892459 | + | 0.451128i | \(0.148978\pi\) | |||||||
\(32\) | 3.57653 | 0.632248 | ||||||||
\(33\) | −5.93800 | −1.03367 | ||||||||
\(34\) | 6.57653 | 1.12787 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.57653 | 0.596089 | ||||||||
\(37\) | 10.6609 | 1.75265 | 0.876324 | − | 0.481722i | \(-0.159989\pi\) | ||||
0.876324 | + | 0.481722i | \(0.159989\pi\) | |||||||
\(38\) | −14.0224 | −2.27474 | ||||||||
\(39\) | 1.42347 | 0.227937 | ||||||||
\(40\) | 12.5145 | 1.97872 | ||||||||
\(41\) | 9.09107 | 1.41979 | 0.709894 | − | 0.704309i | \(-0.248743\pi\) | ||||
0.709894 | + | 0.704309i | \(0.248743\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.29947 | 0.503165 | 0.251582 | − | 0.967836i | \(-0.419049\pi\) | ||||
0.251582 | + | 0.967836i | \(0.419049\pi\) | |||||||
\(44\) | 21.2375 | 3.20167 | ||||||||
\(45\) | −3.36147 | −0.501098 | ||||||||
\(46\) | 2.36147 | 0.348180 | ||||||||
\(47\) | −9.15307 | −1.33511 | −0.667556 | − | 0.744559i | \(-0.732660\pi\) | ||||
−0.667556 | + | 0.744559i | \(0.732660\pi\) | |||||||
\(48\) | −1.63853 | −0.236502 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −14.8760 | −2.10379 | ||||||||
\(51\) | 2.78493 | 0.389969 | ||||||||
\(52\) | −5.09107 | −0.706005 | ||||||||
\(53\) | 3.36147 | 0.461733 | 0.230867 | − | 0.972985i | \(-0.425844\pi\) | ||||
0.230867 | + | 0.972985i | \(0.425844\pi\) | |||||||
\(54\) | 2.36147 | 0.321355 | ||||||||
\(55\) | −19.9604 | −2.69146 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.93800 | −0.786508 | ||||||||
\(58\) | 15.7296 | 2.06540 | ||||||||
\(59\) | −0.208399 | −0.0271313 | −0.0135656 | − | 0.999908i | \(-0.504318\pi\) | ||||
−0.0135656 | + | 0.999908i | \(0.504318\pi\) | |||||||
\(60\) | 12.0224 | 1.55209 | ||||||||
\(61\) | −5.29947 | −0.678528 | −0.339264 | − | 0.940691i | \(-0.610178\pi\) | ||||
−0.339264 | + | 0.940691i | \(0.610178\pi\) | |||||||
\(62\) | −23.4683 | −2.98048 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.7229 | −1.46537 | ||||||||
\(65\) | 4.78493 | 0.593498 | ||||||||
\(66\) | 14.0224 | 1.72604 | ||||||||
\(67\) | −10.9313 | −1.33548 | −0.667738 | − | 0.744397i | \(-0.732737\pi\) | ||||
−0.667738 | + | 0.744397i | \(0.732737\pi\) | |||||||
\(68\) | −9.96041 | −1.20788 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00667 | 0.356826 | 0.178413 | − | 0.983956i | \(-0.442904\pi\) | ||||
0.178413 | + | 0.983956i | \(0.442904\pi\) | |||||||
\(72\) | −3.72294 | −0.438752 | ||||||||
\(73\) | 1.50787 | 0.176483 | 0.0882415 | − | 0.996099i | \(-0.471875\pi\) | ||||
0.0882415 | + | 0.996099i | \(0.471875\pi\) | |||||||
\(74\) | −25.1755 | −2.92659 | ||||||||
\(75\) | −6.29947 | −0.727400 | ||||||||
\(76\) | 21.2375 | 2.43611 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.36147 | −0.380611 | ||||||||
\(79\) | −4.66094 | −0.524397 | −0.262198 | − | 0.965014i | \(-0.584447\pi\) | ||||
−0.262198 | + | 0.965014i | \(0.584447\pi\) | |||||||
\(80\) | −5.50787 | −0.615799 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −21.4683 | −2.37078 | ||||||||
\(83\) | −4.78493 | −0.525215 | −0.262607 | − | 0.964903i | \(-0.584582\pi\) | ||||
−0.262607 | + | 0.964903i | \(0.584582\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.36147 | 1.01539 | ||||||||
\(86\) | −7.79160 | −0.840190 | ||||||||
\(87\) | 6.66094 | 0.714128 | ||||||||
\(88\) | −22.1068 | −2.35659 | ||||||||
\(89\) | −6.57653 | −0.697111 | −0.348556 | − | 0.937288i | \(-0.613328\pi\) | ||||
−0.348556 | + | 0.937288i | \(0.613328\pi\) | |||||||
\(90\) | 7.93800 | 0.836739 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.57653 | −0.372880 | ||||||||
\(93\) | −9.93800 | −1.03052 | ||||||||
\(94\) | 21.6147 | 2.22938 | ||||||||
\(95\) | −19.9604 | −2.04790 | ||||||||
\(96\) | −3.57653 | −0.365029 | ||||||||
\(97\) | 9.50787 | 0.965378 | 0.482689 | − | 0.875792i | \(-0.339660\pi\) | ||||
0.482689 | + | 0.875792i | \(0.339660\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.93800 | 0.596792 | ||||||||
\(100\) | 22.5303 | 2.25303 | ||||||||
\(101\) | −5.66761 | −0.563948 | −0.281974 | − | 0.959422i | \(-0.590989\pi\) | ||||
−0.281974 | + | 0.959422i | \(0.590989\pi\) | |||||||
\(102\) | −6.57653 | −0.651174 | ||||||||
\(103\) | −13.4459 | −1.32486 | −0.662431 | − | 0.749123i | \(-0.730475\pi\) | ||||
−0.662431 | + | 0.749123i | \(0.730475\pi\) | |||||||
\(104\) | 5.29947 | 0.519656 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.93800 | −0.771007 | ||||||||
\(107\) | −11.2995 | −1.09236 | −0.546181 | − | 0.837667i | \(-0.683919\pi\) | ||||
−0.546181 | + | 0.837667i | \(0.683919\pi\) | |||||||
\(108\) | −3.57653 | −0.344152 | ||||||||
\(109\) | 6.08441 | 0.582780 | 0.291390 | − | 0.956604i | \(-0.405882\pi\) | ||||
0.291390 | + | 0.956604i | \(0.405882\pi\) | |||||||
\(110\) | 47.1359 | 4.49423 | ||||||||
\(111\) | −10.6609 | −1.01189 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.06866 | 0.288676 | 0.144338 | − | 0.989528i | \(-0.453895\pi\) | ||||
0.144338 | + | 0.989528i | \(0.453895\pi\) | |||||||
\(114\) | 14.0224 | 1.31332 | ||||||||
\(115\) | 3.36147 | 0.313459 | ||||||||
\(116\) | −23.8231 | −2.21192 | ||||||||
\(117\) | −1.42347 | −0.131599 | ||||||||
\(118\) | 0.492128 | 0.0453041 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −12.5145 | −1.14242 | ||||||||
\(121\) | 24.2599 | 2.20544 | ||||||||
\(122\) | 12.5145 | 1.13301 | ||||||||
\(123\) | −9.09107 | −0.819714 | ||||||||
\(124\) | 35.5436 | 3.19191 | ||||||||
\(125\) | −4.36814 | −0.390698 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.8984 | −1.94317 | −0.971585 | − | 0.236690i | \(-0.923937\pi\) | ||||
−0.971585 | + | 0.236690i | \(0.923937\pi\) | |||||||
\(128\) | 20.5303 | 1.81464 | ||||||||
\(129\) | −3.29947 | −0.290502 | ||||||||
\(130\) | −11.2995 | −0.991029 | ||||||||
\(131\) | 5.93800 | 0.518806 | 0.259403 | − | 0.965769i | \(-0.416474\pi\) | ||||
0.259403 | + | 0.965769i | \(0.416474\pi\) | |||||||
\(132\) | −21.2375 | −1.84848 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 25.8140 | 2.22999 | ||||||||
\(135\) | 3.36147 | 0.289309 | ||||||||
\(136\) | 10.3681 | 0.889060 | ||||||||
\(137\) | −1.33906 | −0.114404 | −0.0572018 | − | 0.998363i | \(-0.518218\pi\) | ||||
−0.0572018 | + | 0.998363i | \(0.518218\pi\) | |||||||
\(138\) | −2.36147 | −0.201022 | ||||||||
\(139\) | 17.3615 | 1.47258 | 0.736290 | − | 0.676666i | \(-0.236576\pi\) | ||||
0.736290 | + | 0.676666i | \(0.236576\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.15307 | 0.770828 | ||||||||
\(142\) | −7.10015 | −0.595831 | ||||||||
\(143\) | −8.45254 | −0.706837 | ||||||||
\(144\) | 1.63853 | 0.136544 | ||||||||
\(145\) | 22.3905 | 1.85943 | ||||||||
\(146\) | −3.56079 | −0.294693 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 38.1292 | 3.13420 | ||||||||
\(149\) | −7.02908 | −0.575844 | −0.287922 | − | 0.957654i | \(-0.592964\pi\) | ||||
−0.287922 | + | 0.957654i | \(0.592964\pi\) | |||||||
\(150\) | 14.8760 | 1.21462 | ||||||||
\(151\) | 6.59894 | 0.537014 | 0.268507 | − | 0.963278i | \(-0.413470\pi\) | ||||
0.268507 | + | 0.963278i | \(0.413470\pi\) | |||||||
\(152\) | −22.1068 | −1.79310 | ||||||||
\(153\) | −2.78493 | −0.225149 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −33.4063 | −2.68326 | ||||||||
\(156\) | 5.09107 | 0.407612 | ||||||||
\(157\) | 19.7387 | 1.57532 | 0.787659 | − | 0.616111i | \(-0.211293\pi\) | ||||
0.787659 | + | 0.616111i | \(0.211293\pi\) | |||||||
\(158\) | 11.0067 | 0.875643 | ||||||||
\(159\) | −3.36147 | −0.266582 | ||||||||
\(160\) | −12.0224 | −0.950455 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.36147 | −0.185535 | ||||||||
\(163\) | 2.93134 | 0.229600 | 0.114800 | − | 0.993389i | \(-0.463377\pi\) | ||||
0.114800 | + | 0.993389i | \(0.463377\pi\) | |||||||
\(164\) | 32.5145 | 2.53896 | ||||||||
\(165\) | 19.9604 | 1.55392 | ||||||||
\(166\) | 11.2995 | 0.877009 | ||||||||
\(167\) | 11.2599 | 0.871316 | 0.435658 | − | 0.900112i | \(-0.356516\pi\) | ||||
0.435658 | + | 0.900112i | \(0.356516\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.9737 | −0.844134 | ||||||||
\(170\) | −22.1068 | −1.69552 | ||||||||
\(171\) | 5.93800 | 0.454090 | ||||||||
\(172\) | 11.8007 | 0.899793 | ||||||||
\(173\) | −1.09107 | −0.0829527 | −0.0414764 | − | 0.999139i | \(-0.513206\pi\) | ||||
−0.0414764 | + | 0.999139i | \(0.513206\pi\) | |||||||
\(174\) | −15.7296 | −1.19246 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.72960 | 0.733397 | ||||||||
\(177\) | 0.208399 | 0.0156643 | ||||||||
\(178\) | 15.5303 | 1.16404 | ||||||||
\(179\) | −13.2375 | −0.989415 | −0.494708 | − | 0.869059i | \(-0.664725\pi\) | ||||
−0.494708 | + | 0.869059i | \(0.664725\pi\) | |||||||
\(180\) | −12.0224 | −0.896098 | ||||||||
\(181\) | −18.2441 | −1.35608 | −0.678038 | − | 0.735027i | \(-0.737170\pi\) | ||||
−0.678038 | + | 0.735027i | \(0.737170\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.29947 | 0.391748 | ||||||||
\(184\) | 3.72294 | 0.274459 | ||||||||
\(185\) | −35.8364 | −2.63475 | ||||||||
\(186\) | 23.4683 | 1.72078 | ||||||||
\(187\) | −16.5369 | −1.20930 | ||||||||
\(188\) | −32.7363 | −2.38754 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 47.1359 | 3.41960 | ||||||||
\(191\) | 1.40106 | 0.101377 | 0.0506884 | − | 0.998715i | \(-0.483858\pi\) | ||||
0.0506884 | + | 0.998715i | \(0.483858\pi\) | |||||||
\(192\) | 11.7229 | 0.846030 | ||||||||
\(193\) | 16.5989 | 1.19482 | 0.597409 | − | 0.801937i | \(-0.296197\pi\) | ||||
0.597409 | + | 0.801937i | \(0.296197\pi\) | |||||||
\(194\) | −22.4525 | −1.61200 | ||||||||
\(195\) | −4.78493 | −0.342656 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.86934 | −0.204432 | −0.102216 | − | 0.994762i | \(-0.532593\pi\) | ||||
−0.102216 | + | 0.994762i | \(0.532593\pi\) | |||||||
\(198\) | −14.0224 | −0.996529 | ||||||||
\(199\) | −18.5594 | −1.31564 | −0.657819 | − | 0.753176i | \(-0.728521\pi\) | ||||
−0.657819 | + | 0.753176i | \(0.728521\pi\) | |||||||
\(200\) | −23.4525 | −1.65835 | ||||||||
\(201\) | 10.9313 | 0.771037 | ||||||||
\(202\) | 13.3839 | 0.941686 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 9.96041 | 0.697368 | ||||||||
\(205\) | −30.5594 | −2.13436 | ||||||||
\(206\) | 31.7520 | 2.21227 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −2.33239 | −0.161722 | ||||||||
\(209\) | 35.2599 | 2.43898 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.81401 | −0.675624 | −0.337812 | − | 0.941214i | \(-0.609687\pi\) | ||||
−0.337812 | + | 0.941214i | \(0.609687\pi\) | |||||||
\(212\) | 12.0224 | 0.825702 | ||||||||
\(213\) | −3.00667 | −0.206013 | ||||||||
\(214\) | 26.6834 | 1.82404 | ||||||||
\(215\) | −11.0911 | −0.756405 | ||||||||
\(216\) | 3.72294 | 0.253314 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −14.3681 | −0.973133 | ||||||||
\(219\) | −1.50787 | −0.101893 | ||||||||
\(220\) | −71.3891 | −4.81305 | ||||||||
\(221\) | 3.96426 | 0.266665 | ||||||||
\(222\) | 25.1755 | 1.68967 | ||||||||
\(223\) | 15.6676 | 1.04918 | 0.524590 | − | 0.851355i | \(-0.324219\pi\) | ||||
0.524590 | + | 0.851355i | \(0.324219\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.29947 | 0.419965 | ||||||||
\(226\) | −7.24655 | −0.482033 | ||||||||
\(227\) | 7.96041 | 0.528351 | 0.264176 | − | 0.964475i | \(-0.414900\pi\) | ||||
0.264176 | + | 0.964475i | \(0.414900\pi\) | |||||||
\(228\) | −21.2375 | −1.40649 | ||||||||
\(229\) | 14.9447 | 0.987572 | 0.493786 | − | 0.869584i | \(-0.335613\pi\) | ||||
0.493786 | + | 0.869584i | \(0.335613\pi\) | |||||||
\(230\) | −7.93800 | −0.523416 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 24.7983 | 1.62809 | ||||||||
\(233\) | 9.83642 | 0.644405 | 0.322203 | − | 0.946671i | \(-0.395577\pi\) | ||||
0.322203 | + | 0.946671i | \(0.395577\pi\) | |||||||
\(234\) | 3.36147 | 0.219746 | ||||||||
\(235\) | 30.7678 | 2.00707 | ||||||||
\(236\) | −0.745347 | −0.0485180 | ||||||||
\(237\) | 4.66094 | 0.302761 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.8073 | 1.21655 | 0.608273 | − | 0.793728i | \(-0.291863\pi\) | ||||
0.608273 | + | 0.793728i | \(0.291863\pi\) | |||||||
\(240\) | 5.50787 | 0.355532 | ||||||||
\(241\) | 10.2441 | 0.659883 | 0.329942 | − | 0.944001i | \(-0.392971\pi\) | ||||
0.329942 | + | 0.944001i | \(0.392971\pi\) | |||||||
\(242\) | −57.2890 | −3.68267 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −18.9537 | −1.21339 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 21.4683 | 1.36877 | ||||||||
\(247\) | −8.45254 | −0.537822 | ||||||||
\(248\) | −36.9986 | −2.34941 | ||||||||
\(249\) | 4.78493 | 0.303233 | ||||||||
\(250\) | 10.3152 | 0.652392 | ||||||||
\(251\) | 12.4168 | 0.783741 | 0.391871 | − | 0.920020i | \(-0.371828\pi\) | ||||
0.391871 | + | 0.920020i | \(0.371828\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.93800 | −0.373319 | ||||||||
\(254\) | 51.7124 | 3.24473 | ||||||||
\(255\) | −9.36147 | −0.586238 | ||||||||
\(256\) | −25.0357 | −1.56473 | ||||||||
\(257\) | 5.58320 | 0.348271 | 0.174135 | − | 0.984722i | \(-0.444287\pi\) | ||||
0.174135 | + | 0.984722i | \(0.444287\pi\) | |||||||
\(258\) | 7.79160 | 0.485084 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 17.1135 | 1.06133 | ||||||||
\(261\) | −6.66094 | −0.412302 | ||||||||
\(262\) | −14.0224 | −0.866307 | ||||||||
\(263\) | 19.6767 | 1.21332 | 0.606658 | − | 0.794963i | \(-0.292510\pi\) | ||||
0.606658 | + | 0.794963i | \(0.292510\pi\) | |||||||
\(264\) | 22.1068 | 1.36058 | ||||||||
\(265\) | −11.2995 | −0.694121 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.57653 | 0.402477 | ||||||||
\(268\) | −39.0963 | −2.38819 | ||||||||
\(269\) | 0.882674 | 0.0538176 | 0.0269088 | − | 0.999638i | \(-0.491434\pi\) | ||||
0.0269088 | + | 0.999638i | \(0.491434\pi\) | |||||||
\(270\) | −7.93800 | −0.483092 | ||||||||
\(271\) | 0.784934 | 0.0476813 | 0.0238407 | − | 0.999716i | \(-0.492411\pi\) | ||||
0.0238407 | + | 0.999716i | \(0.492411\pi\) | |||||||
\(272\) | −4.56320 | −0.276685 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.16215 | 0.191032 | ||||||||
\(275\) | 37.4063 | 2.25568 | ||||||||
\(276\) | 3.57653 | 0.215282 | ||||||||
\(277\) | −21.3443 | −1.28245 | −0.641227 | − | 0.767351i | \(-0.721574\pi\) | ||||
−0.641227 | + | 0.767351i | \(0.721574\pi\) | |||||||
\(278\) | −40.9986 | −2.45893 | ||||||||
\(279\) | 9.93800 | 0.594973 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.4592 | 1.28015 | 0.640075 | − | 0.768313i | \(-0.278903\pi\) | ||||
0.640075 | + | 0.768313i | \(0.278903\pi\) | |||||||
\(282\) | −21.6147 | −1.28714 | ||||||||
\(283\) | 13.6543 | 0.811662 | 0.405831 | − | 0.913948i | \(-0.366982\pi\) | ||||
0.405831 | + | 0.913948i | \(0.366982\pi\) | |||||||
\(284\) | 10.7534 | 0.638100 | ||||||||
\(285\) | 19.9604 | 1.18235 | ||||||||
\(286\) | 19.9604 | 1.18028 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.57653 | 0.210749 | ||||||||
\(289\) | −9.24414 | −0.543773 | ||||||||
\(290\) | −52.8746 | −3.10490 | ||||||||
\(291\) | −9.50787 | −0.557361 | ||||||||
\(292\) | 5.39296 | 0.315599 | ||||||||
\(293\) | 3.32188 | 0.194066 | 0.0970332 | − | 0.995281i | \(-0.469065\pi\) | ||||
0.0970332 | + | 0.995281i | \(0.469065\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.700528 | 0.0407863 | ||||||||
\(296\) | −39.6900 | −2.30694 | ||||||||
\(297\) | −5.93800 | −0.344558 | ||||||||
\(298\) | 16.5989 | 0.961551 | ||||||||
\(299\) | 1.42347 | 0.0823211 | ||||||||
\(300\) | −22.5303 | −1.30079 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −15.5832 | −0.896712 | ||||||||
\(303\) | 5.66761 | 0.325596 | ||||||||
\(304\) | 9.72960 | 0.558031 | ||||||||
\(305\) | 17.8140 | 1.02003 | ||||||||
\(306\) | 6.57653 | 0.375955 | ||||||||
\(307\) | 2.06200 | 0.117684 | 0.0588422 | − | 0.998267i | \(-0.481259\pi\) | ||||
0.0588422 | + | 0.998267i | \(0.481259\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.4459 | 0.764909 | ||||||||
\(310\) | 78.8879 | 4.48053 | ||||||||
\(311\) | 8.45254 | 0.479300 | 0.239650 | − | 0.970859i | \(-0.422967\pi\) | ||||
0.239650 | + | 0.970859i | \(0.422967\pi\) | |||||||
\(312\) | −5.29947 | −0.300024 | ||||||||
\(313\) | −10.7363 | −0.606850 | −0.303425 | − | 0.952855i | \(-0.598130\pi\) | ||||
−0.303425 | + | 0.952855i | \(0.598130\pi\) | |||||||
\(314\) | −46.6123 | −2.63048 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.6700 | −0.937762 | ||||||||
\(317\) | 16.8073 | 0.943994 | 0.471997 | − | 0.881600i | \(-0.343533\pi\) | ||||
0.471997 | + | 0.881600i | \(0.343533\pi\) | |||||||
\(318\) | 7.93800 | 0.445141 | ||||||||
\(319\) | −39.5527 | −2.21453 | ||||||||
\(320\) | 39.4063 | 2.20288 | ||||||||
\(321\) | 11.2995 | 0.630675 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.5369 | −0.920140 | ||||||||
\(324\) | 3.57653 | 0.198696 | ||||||||
\(325\) | −8.96708 | −0.497404 | ||||||||
\(326\) | −6.92226 | −0.383389 | ||||||||
\(327\) | −6.08441 | −0.336468 | ||||||||
\(328\) | −33.8455 | −1.86880 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −47.1359 | −2.59475 | ||||||||
\(331\) | −21.5699 | −1.18559 | −0.592794 | − | 0.805354i | \(-0.701975\pi\) | ||||
−0.592794 | + | 0.805354i | \(0.701975\pi\) | |||||||
\(332\) | −17.1135 | −0.939224 | ||||||||
\(333\) | 10.6609 | 0.584216 | ||||||||
\(334\) | −26.5899 | −1.45493 | ||||||||
\(335\) | 36.7453 | 2.00761 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.42347 | 0.295435 | 0.147717 | − | 0.989030i | \(-0.452807\pi\) | ||||
0.147717 | + | 0.989030i | \(0.452807\pi\) | |||||||
\(338\) | 25.9142 | 1.40954 | ||||||||
\(339\) | −3.06866 | −0.166667 | ||||||||
\(340\) | 33.4816 | 1.81580 | ||||||||
\(341\) | 59.0119 | 3.19567 | ||||||||
\(342\) | −14.0224 | −0.758245 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −12.2837 | −0.662294 | ||||||||
\(345\) | −3.36147 | −0.180975 | ||||||||
\(346\) | 2.57653 | 0.138515 | ||||||||
\(347\) | 25.9828 | 1.39483 | 0.697416 | − | 0.716667i | \(-0.254333\pi\) | ||||
0.697416 | + | 0.716667i | \(0.254333\pi\) | |||||||
\(348\) | 23.8231 | 1.27705 | ||||||||
\(349\) | 2.50120 | 0.133886 | 0.0669432 | − | 0.997757i | \(-0.478675\pi\) | ||||
0.0669432 | + | 0.997757i | \(0.478675\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.42347 | 0.0759790 | ||||||||
\(352\) | 21.2375 | 1.13196 | ||||||||
\(353\) | −19.5212 | −1.03901 | −0.519504 | − | 0.854468i | \(-0.673883\pi\) | ||||
−0.519504 | + | 0.854468i | \(0.673883\pi\) | |||||||
\(354\) | −0.492128 | −0.0261563 | ||||||||
\(355\) | −10.1068 | −0.536414 | ||||||||
\(356\) | −23.5212 | −1.24662 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 31.2599 | 1.65214 | ||||||||
\(359\) | −37.3615 | −1.97186 | −0.985931 | − | 0.167150i | \(-0.946544\pi\) | ||||
−0.985931 | + | 0.167150i | \(0.946544\pi\) | |||||||
\(360\) | 12.5145 | 0.659574 | ||||||||
\(361\) | 16.2599 | 0.855783 | ||||||||
\(362\) | 43.0830 | 2.26439 | ||||||||
\(363\) | −24.2599 | −1.27331 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.06866 | −0.265306 | ||||||||
\(366\) | −12.5145 | −0.654145 | ||||||||
\(367\) | −0.452542 | −0.0236225 | −0.0118112 | − | 0.999930i | \(-0.503760\pi\) | ||||
−0.0118112 | + | 0.999930i | \(0.503760\pi\) | |||||||
\(368\) | −1.63853 | −0.0854143 | ||||||||
\(369\) | 9.09107 | 0.473262 | ||||||||
\(370\) | 84.6266 | 4.39953 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −35.5436 | −1.84285 | ||||||||
\(373\) | −13.0911 | −0.677830 | −0.338915 | − | 0.940817i | \(-0.610060\pi\) | ||||
−0.338915 | + | 0.940817i | \(0.610060\pi\) | |||||||
\(374\) | 39.0515 | 2.01930 | ||||||||
\(375\) | 4.36814 | 0.225570 | ||||||||
\(376\) | 34.0763 | 1.75735 | ||||||||
\(377\) | 9.48162 | 0.488328 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.0315 | 1.33715 | 0.668574 | − | 0.743646i | \(-0.266905\pi\) | ||||
0.668574 | + | 0.743646i | \(0.266905\pi\) | |||||||
\(380\) | −71.3891 | −3.66218 | ||||||||
\(381\) | 21.8984 | 1.12189 | ||||||||
\(382\) | −3.30855 | −0.169280 | ||||||||
\(383\) | 3.09107 | 0.157946 | 0.0789732 | − | 0.996877i | \(-0.474836\pi\) | ||||
0.0789732 | + | 0.996877i | \(0.474836\pi\) | |||||||
\(384\) | −20.5303 | −1.04768 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −39.1979 | −1.99512 | ||||||||
\(387\) | 3.29947 | 0.167722 | ||||||||
\(388\) | 34.0052 | 1.72635 | ||||||||
\(389\) | −4.77160 | −0.241930 | −0.120965 | − | 0.992657i | \(-0.538599\pi\) | ||||
−0.120965 | + | 0.992657i | \(0.538599\pi\) | |||||||
\(390\) | 11.2995 | 0.572171 | ||||||||
\(391\) | 2.78493 | 0.140840 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.93800 | −0.299533 | ||||||||
\(394\) | 6.77586 | 0.341363 | ||||||||
\(395\) | 15.6676 | 0.788323 | ||||||||
\(396\) | 21.2375 | 1.06722 | ||||||||
\(397\) | 9.92083 | 0.497912 | 0.248956 | − | 0.968515i | \(-0.419913\pi\) | ||||
0.248956 | + | 0.968515i | \(0.419913\pi\) | |||||||
\(398\) | 43.8273 | 2.19687 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.3219 | 0.516094 | ||||||||
\(401\) | 16.5503 | 0.826482 | 0.413241 | − | 0.910622i | \(-0.364397\pi\) | ||||
0.413241 | + | 0.910622i | \(0.364397\pi\) | |||||||
\(402\) | −25.8140 | −1.28749 | ||||||||
\(403\) | −14.1464 | −0.704683 | ||||||||
\(404\) | −20.2704 | −1.00849 | ||||||||
\(405\) | −3.36147 | −0.167033 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 63.3047 | 3.13790 | ||||||||
\(408\) | −10.3681 | −0.513299 | ||||||||
\(409\) | −12.3548 | −0.610906 | −0.305453 | − | 0.952207i | \(-0.598808\pi\) | ||||
−0.305453 | + | 0.952207i | \(0.598808\pi\) | |||||||
\(410\) | 72.1650 | 3.56397 | ||||||||
\(411\) | 1.33906 | 0.0660509 | ||||||||
\(412\) | −48.0896 | −2.36921 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.36147 | 0.116060 | ||||||||
\(415\) | 16.0844 | 0.789552 | ||||||||
\(416\) | −5.09107 | −0.249610 | ||||||||
\(417\) | −17.3615 | −0.850195 | ||||||||
\(418\) | −83.2651 | −4.07263 | ||||||||
\(419\) | 37.8231 | 1.84778 | 0.923889 | − | 0.382660i | \(-0.124992\pi\) | ||||
0.923889 | + | 0.382660i | \(0.124992\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.6189 | 1.05364 | 0.526821 | − | 0.849976i | \(-0.323384\pi\) | ||||
0.526821 | + | 0.849976i | \(0.323384\pi\) | |||||||
\(422\) | 23.1755 | 1.12816 | ||||||||
\(423\) | −9.15307 | −0.445037 | ||||||||
\(424\) | −12.5145 | −0.607760 | ||||||||
\(425\) | −17.5436 | −0.850990 | ||||||||
\(426\) | 7.10015 | 0.344003 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −40.4130 | −1.95343 | ||||||||
\(429\) | 8.45254 | 0.408093 | ||||||||
\(430\) | 26.1912 | 1.26305 | ||||||||
\(431\) | 39.6371 | 1.90925 | 0.954626 | − | 0.297808i | \(-0.0962554\pi\) | ||||
0.954626 | + | 0.297808i | \(0.0962554\pi\) | |||||||
\(432\) | −1.63853 | −0.0788339 | ||||||||
\(433\) | 25.4592 | 1.22349 | 0.611746 | − | 0.791054i | \(-0.290468\pi\) | ||||
0.611746 | + | 0.791054i | \(0.290468\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.3905 | −1.07354 | ||||||||
\(436\) | 21.7611 | 1.04217 | ||||||||
\(437\) | −5.93800 | −0.284053 | ||||||||
\(438\) | 3.56079 | 0.170141 | ||||||||
\(439\) | 25.6900 | 1.22612 | 0.613059 | − | 0.790037i | \(-0.289939\pi\) | ||||
0.613059 | + | 0.790037i | \(0.289939\pi\) | |||||||
\(440\) | 74.3114 | 3.54266 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.36147 | −0.445280 | ||||||||
\(443\) | 1.44588 | 0.0686956 | 0.0343478 | − | 0.999410i | \(-0.489065\pi\) | ||||
0.0343478 | + | 0.999410i | \(0.489065\pi\) | |||||||
\(444\) | −38.1292 | −1.80953 | ||||||||
\(445\) | 22.1068 | 1.04796 | ||||||||
\(446\) | −36.9986 | −1.75193 | ||||||||
\(447\) | 7.02908 | 0.332464 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.2532 | 0.483879 | 0.241940 | − | 0.970291i | \(-0.422216\pi\) | ||||
0.241940 | + | 0.970291i | \(0.422216\pi\) | |||||||
\(450\) | −14.8760 | −0.701262 | ||||||||
\(451\) | 53.9828 | 2.54195 | ||||||||
\(452\) | 10.9752 | 0.516229 | ||||||||
\(453\) | −6.59894 | −0.310045 | ||||||||
\(454\) | −18.7983 | −0.882246 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 22.1068 | 1.03525 | ||||||||
\(457\) | −35.5303 | −1.66204 | −0.831018 | − | 0.556245i | \(-0.812242\pi\) | ||||
−0.831018 | + | 0.556245i | \(0.812242\pi\) | |||||||
\(458\) | −35.2914 | −1.64906 | ||||||||
\(459\) | 2.78493 | 0.129990 | ||||||||
\(460\) | 12.0224 | 0.560548 | ||||||||
\(461\) | −19.9471 | −0.929028 | −0.464514 | − | 0.885566i | \(-0.653771\pi\) | ||||
−0.464514 | + | 0.885566i | \(0.653771\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.92467 | 0.182395 | 0.0911974 | − | 0.995833i | \(-0.470931\pi\) | ||||
0.0911974 | + | 0.995833i | \(0.470931\pi\) | |||||||
\(464\) | −10.9142 | −0.506677 | ||||||||
\(465\) | 33.4063 | 1.54918 | ||||||||
\(466\) | −23.2284 | −1.07603 | ||||||||
\(467\) | 15.0911 | 0.698332 | 0.349166 | − | 0.937061i | \(-0.386465\pi\) | ||||
0.349166 | + | 0.937061i | \(0.386465\pi\) | |||||||
\(468\) | −5.09107 | −0.235335 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −72.6571 | −3.35142 | ||||||||
\(471\) | −19.7387 | −0.909510 | ||||||||
\(472\) | 0.775858 | 0.0357117 | ||||||||
\(473\) | 19.5923 | 0.900854 | ||||||||
\(474\) | −11.0067 | −0.505553 | ||||||||
\(475\) | 37.4063 | 1.71632 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.36147 | 0.153911 | ||||||||
\(478\) | −44.4130 | −2.03140 | ||||||||
\(479\) | −16.1201 | −0.736548 | −0.368274 | − | 0.929717i | \(-0.620051\pi\) | ||||
−0.368274 | + | 0.929717i | \(0.620051\pi\) | |||||||
\(480\) | 12.0224 | 0.548745 | ||||||||
\(481\) | −15.1755 | −0.691942 | ||||||||
\(482\) | −24.1912 | −1.10188 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 86.7663 | 3.94392 | ||||||||
\(485\) | −31.9604 | −1.45125 | ||||||||
\(486\) | 2.36147 | 0.107118 | ||||||||
\(487\) | 15.8007 | 0.715997 | 0.357999 | − | 0.933722i | \(-0.383459\pi\) | ||||
0.357999 | + | 0.933722i | \(0.383459\pi\) | |||||||
\(488\) | 19.7296 | 0.893117 | ||||||||
\(489\) | −2.93134 | −0.132560 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.97759 | −0.0892474 | −0.0446237 | − | 0.999004i | \(-0.514209\pi\) | ||||
−0.0446237 | + | 0.999004i | \(0.514209\pi\) | |||||||
\(492\) | −32.5145 | −1.46587 | ||||||||
\(493\) | 18.5503 | 0.835463 | ||||||||
\(494\) | 19.9604 | 0.898061 | ||||||||
\(495\) | −19.9604 | −0.897154 | ||||||||
\(496\) | 16.2837 | 0.731161 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −11.2995 | −0.506341 | ||||||||
\(499\) | 20.5012 | 0.917760 | 0.458880 | − | 0.888498i | \(-0.348251\pi\) | ||||
0.458880 | + | 0.888498i | \(0.348251\pi\) | |||||||
\(500\) | −15.6228 | −0.698672 | ||||||||
\(501\) | −11.2599 | −0.503055 | ||||||||
\(502\) | −29.3219 | −1.30870 | ||||||||
\(503\) | −20.1292 | −0.897518 | −0.448759 | − | 0.893653i | \(-0.648134\pi\) | ||||
−0.448759 | + | 0.893653i | \(0.648134\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.0515 | 0.847780 | ||||||||
\(506\) | 14.0224 | 0.623372 | ||||||||
\(507\) | 10.9737 | 0.487361 | ||||||||
\(508\) | −78.3204 | −3.47491 | ||||||||
\(509\) | −2.44347 | −0.108305 | −0.0541523 | − | 0.998533i | \(-0.517246\pi\) | ||||
−0.0541523 | + | 0.998533i | \(0.517246\pi\) | |||||||
\(510\) | 22.1068 | 0.978906 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 18.0606 | 0.798172 | ||||||||
\(513\) | −5.93800 | −0.262169 | ||||||||
\(514\) | −13.1846 | −0.581546 | ||||||||
\(515\) | 45.1979 | 1.99166 | ||||||||
\(516\) | −11.8007 | −0.519496 | ||||||||
\(517\) | −54.3510 | −2.39035 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.09107 | 0.0478928 | ||||||||
\(520\) | −17.8140 | −0.781196 | ||||||||
\(521\) | 5.16640 | 0.226344 | 0.113172 | − | 0.993575i | \(-0.463899\pi\) | ||||
0.113172 | + | 0.993575i | \(0.463899\pi\) | |||||||
\(522\) | 15.7296 | 0.688466 | ||||||||
\(523\) | −34.5198 | −1.50944 | −0.754722 | − | 0.656045i | \(-0.772228\pi\) | ||||
−0.754722 | + | 0.656045i | \(0.772228\pi\) | |||||||
\(524\) | 21.2375 | 0.927763 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −46.4659 | −2.02601 | ||||||||
\(527\) | −27.6767 | −1.20562 | ||||||||
\(528\) | −9.72960 | −0.423427 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 26.6834 | 1.15905 | ||||||||
\(531\) | −0.208399 | −0.00904376 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.9408 | −0.560529 | ||||||||
\(534\) | −15.5303 | −0.672061 | ||||||||
\(535\) | 37.9828 | 1.64214 | ||||||||
\(536\) | 40.6967 | 1.75783 | ||||||||
\(537\) | 13.2375 | 0.571239 | ||||||||
\(538\) | −2.08441 | −0.0898651 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 12.0224 | 0.517362 | ||||||||
\(541\) | 43.3667 | 1.86448 | 0.932240 | − | 0.361840i | \(-0.117851\pi\) | ||||
0.932240 | + | 0.361840i | \(0.117851\pi\) | |||||||
\(542\) | −1.85360 | −0.0796188 | ||||||||
\(543\) | 18.2441 | 0.782931 | ||||||||
\(544\) | −9.96041 | −0.427049 | ||||||||
\(545\) | −20.4525 | −0.876091 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.5279 | 0.706681 | 0.353340 | − | 0.935495i | \(-0.385046\pi\) | ||||
0.353340 | + | 0.935495i | \(0.385046\pi\) | |||||||
\(548\) | −4.78919 | −0.204584 | ||||||||
\(549\) | −5.29947 | −0.226176 | ||||||||
\(550\) | −88.3338 | −3.76657 | ||||||||
\(551\) | −39.5527 | −1.68500 | ||||||||
\(552\) | −3.72294 | −0.158459 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 50.4039 | 2.14146 | ||||||||
\(555\) | 35.8364 | 1.52117 | ||||||||
\(556\) | 62.0939 | 2.63337 | ||||||||
\(557\) | 20.3510 | 0.862298 | 0.431149 | − | 0.902281i | \(-0.358108\pi\) | ||||
0.431149 | + | 0.902281i | \(0.358108\pi\) | |||||||
\(558\) | −23.4683 | −0.993492 | ||||||||
\(559\) | −4.69668 | −0.198649 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.5369 | 0.698190 | ||||||||
\(562\) | −50.6753 | −2.13761 | ||||||||
\(563\) | 29.1888 | 1.23016 | 0.615081 | − | 0.788464i | \(-0.289123\pi\) | ||||
0.615081 | + | 0.788464i | \(0.289123\pi\) | |||||||
\(564\) | 32.7363 | 1.37845 | ||||||||
\(565\) | −10.3152 | −0.433964 | ||||||||
\(566\) | −32.2441 | −1.35532 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.1936 | −0.469674 | ||||||||
\(569\) | 16.1821 | 0.678391 | 0.339195 | − | 0.940716i | \(-0.389845\pi\) | ||||
0.339195 | + | 0.940716i | \(0.389845\pi\) | |||||||
\(570\) | −47.1359 | −1.97431 | ||||||||
\(571\) | −37.1226 | −1.55353 | −0.776765 | − | 0.629790i | \(-0.783141\pi\) | ||||
−0.776765 | + | 0.629790i | \(0.783141\pi\) | |||||||
\(572\) | −30.2308 | −1.26401 | ||||||||
\(573\) | −1.40106 | −0.0585299 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.29947 | −0.262706 | ||||||||
\(576\) | −11.7229 | −0.488456 | ||||||||
\(577\) | −41.7520 | −1.73816 | −0.869080 | − | 0.494672i | \(-0.835288\pi\) | ||||
−0.869080 | + | 0.494672i | \(0.835288\pi\) | |||||||
\(578\) | 21.8298 | 0.907998 | ||||||||
\(579\) | −16.5989 | −0.689829 | ||||||||
\(580\) | 80.0806 | 3.32516 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 22.4525 | 0.930688 | ||||||||
\(583\) | 19.9604 | 0.826676 | ||||||||
\(584\) | −5.61371 | −0.232297 | ||||||||
\(585\) | 4.78493 | 0.197833 | ||||||||
\(586\) | −7.84452 | −0.324054 | ||||||||
\(587\) | 43.4683 | 1.79413 | 0.897064 | − | 0.441901i | \(-0.145696\pi\) | ||||
0.897064 | + | 0.441901i | \(0.145696\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 59.0119 | 2.43154 | ||||||||
\(590\) | −1.65427 | −0.0681054 | ||||||||
\(591\) | 2.86934 | 0.118029 | ||||||||
\(592\) | 17.4683 | 0.717942 | ||||||||
\(593\) | 4.84693 | 0.199040 | 0.0995198 | − | 0.995036i | \(-0.468269\pi\) | ||||
0.0995198 | + | 0.995036i | \(0.468269\pi\) | |||||||
\(594\) | 14.0224 | 0.575346 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −25.1397 | −1.02976 | ||||||||
\(597\) | 18.5594 | 0.759584 | ||||||||
\(598\) | −3.36147 | −0.137461 | ||||||||
\(599\) | 2.27040 | 0.0927659 | 0.0463829 | − | 0.998924i | \(-0.485231\pi\) | ||||
0.0463829 | + | 0.998924i | \(0.485231\pi\) | |||||||
\(600\) | 23.4525 | 0.957446 | ||||||||
\(601\) | 34.7940 | 1.41928 | 0.709639 | − | 0.704566i | \(-0.248858\pi\) | ||||
0.709639 | + | 0.704566i | \(0.248858\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.9313 | −0.445158 | ||||||||
\(604\) | 23.6014 | 0.960325 | ||||||||
\(605\) | −81.5488 | −3.31543 | ||||||||
\(606\) | −13.3839 | −0.543683 | ||||||||
\(607\) | −18.1912 | −0.738359 | −0.369179 | − | 0.929358i | \(-0.620361\pi\) | ||||
−0.369179 | + | 0.929358i | \(0.620361\pi\) | |||||||
\(608\) | 21.2375 | 0.861293 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −42.0672 | −1.70325 | ||||||||
\(611\) | 13.0291 | 0.527100 | ||||||||
\(612\) | −9.96041 | −0.402626 | ||||||||
\(613\) | 22.2175 | 0.897355 | 0.448678 | − | 0.893694i | \(-0.351895\pi\) | ||||
0.448678 | + | 0.893694i | \(0.351895\pi\) | |||||||
\(614\) | −4.86934 | −0.196511 | ||||||||
\(615\) | 30.5594 | 1.23227 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.5789 | −0.788219 | −0.394109 | − | 0.919064i | \(-0.628947\pi\) | ||||
−0.394109 | + | 0.919064i | \(0.628947\pi\) | |||||||
\(618\) | −31.7520 | −1.27725 | ||||||||
\(619\) | −28.4525 | −1.14360 | −0.571802 | − | 0.820392i | \(-0.693755\pi\) | ||||
−0.571802 | + | 0.820392i | \(0.693755\pi\) | |||||||
\(620\) | −119.479 | −4.79838 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −19.9604 | −0.800340 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.33239 | 0.0933704 | ||||||||
\(625\) | −16.8140 | −0.672560 | ||||||||
\(626\) | 25.3534 | 1.01332 | ||||||||
\(627\) | −35.2599 | −1.40814 | ||||||||
\(628\) | 70.5961 | 2.81709 | ||||||||
\(629\) | −29.6900 | −1.18382 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.0276 | −1.67309 | −0.836547 | − | 0.547895i | \(-0.815429\pi\) | ||||
−0.836547 | + | 0.547895i | \(0.815429\pi\) | |||||||
\(632\) | 17.3524 | 0.690241 | ||||||||
\(633\) | 9.81401 | 0.390072 | ||||||||
\(634\) | −39.6900 | −1.57629 | ||||||||
\(635\) | 73.6108 | 2.92116 | ||||||||
\(636\) | −12.0224 | −0.476720 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 93.4024 | 3.69784 | ||||||||
\(639\) | 3.00667 | 0.118942 | ||||||||
\(640\) | −69.0119 | −2.72793 | ||||||||
\(641\) | 4.85601 | 0.191801 | 0.0959004 | − | 0.995391i | \(-0.469427\pi\) | ||||
0.0959004 | + | 0.995391i | \(0.469427\pi\) | |||||||
\(642\) | −26.6834 | −1.05311 | ||||||||
\(643\) | 37.6056 | 1.48302 | 0.741510 | − | 0.670942i | \(-0.234110\pi\) | ||||
0.741510 | + | 0.670942i | \(0.234110\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.0911 | 0.436711 | ||||||||
\(646\) | 39.0515 | 1.53646 | ||||||||
\(647\) | 33.7258 | 1.32590 | 0.662948 | − | 0.748665i | \(-0.269305\pi\) | ||||
0.662948 | + | 0.748665i | \(0.269305\pi\) | |||||||
\(648\) | −3.72294 | −0.146251 | ||||||||
\(649\) | −1.23748 | −0.0485752 | ||||||||
\(650\) | 21.1755 | 0.830571 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.4840 | 0.410586 | ||||||||
\(653\) | 30.6700 | 1.20021 | 0.600105 | − | 0.799921i | \(-0.295125\pi\) | ||||
0.600105 | + | 0.799921i | \(0.295125\pi\) | |||||||
\(654\) | 14.3681 | 0.561839 | ||||||||
\(655\) | −19.9604 | −0.779918 | ||||||||
\(656\) | 14.8960 | 0.581591 | ||||||||
\(657\) | 1.50787 | 0.0588277 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.50787 | −0.292465 | −0.146233 | − | 0.989250i | \(-0.546715\pi\) | ||||
−0.146233 | + | 0.989250i | \(0.546715\pi\) | |||||||
\(660\) | 71.3891 | 2.77882 | ||||||||
\(661\) | −7.35239 | −0.285975 | −0.142987 | − | 0.989725i | \(-0.545671\pi\) | ||||
−0.142987 | + | 0.989725i | \(0.545671\pi\) | |||||||
\(662\) | 50.9366 | 1.97971 | ||||||||
\(663\) | −3.96426 | −0.153959 | ||||||||
\(664\) | 17.8140 | 0.691318 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −25.1755 | −0.975530 | ||||||||
\(667\) | 6.66094 | 0.257913 | ||||||||
\(668\) | 40.2714 | 1.55815 | ||||||||
\(669\) | −15.6676 | −0.605745 | ||||||||
\(670\) | −86.7730 | −3.35233 | ||||||||
\(671\) | −31.4683 | −1.21482 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.0119 | −0.964138 | −0.482069 | − | 0.876133i | \(-0.660115\pi\) | ||||
−0.482069 | + | 0.876133i | \(0.660115\pi\) | |||||||
\(674\) | −12.8073 | −0.493320 | ||||||||
\(675\) | −6.29947 | −0.242467 | ||||||||
\(676\) | −39.2480 | −1.50954 | ||||||||
\(677\) | −10.1597 | −0.390470 | −0.195235 | − | 0.980756i | \(-0.562547\pi\) | ||||
−0.195235 | + | 0.980756i | \(0.562547\pi\) | |||||||
\(678\) | 7.24655 | 0.278302 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −34.8522 | −1.33652 | ||||||||
\(681\) | −7.96041 | −0.305044 | ||||||||
\(682\) | −139.355 | −5.33617 | ||||||||
\(683\) | −17.9828 | −0.688094 | −0.344047 | − | 0.938953i | \(-0.611798\pi\) | ||||
−0.344047 | + | 0.938953i | \(0.611798\pi\) | |||||||
\(684\) | 21.2375 | 0.812035 | ||||||||
\(685\) | 4.50120 | 0.171982 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.9447 | −0.570175 | ||||||||
\(688\) | 5.40629 | 0.206113 | ||||||||
\(689\) | −4.78493 | −0.182291 | ||||||||
\(690\) | 7.93800 | 0.302195 | ||||||||
\(691\) | −26.7320 | −1.01693 | −0.508467 | − | 0.861082i | \(-0.669788\pi\) | ||||
−0.508467 | + | 0.861082i | \(0.669788\pi\) | |||||||
\(692\) | −3.90226 | −0.148342 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −61.3576 | −2.32910 | ||||||||
\(695\) | −58.3600 | −2.21372 | ||||||||
\(696\) | −24.7983 | −0.939976 | ||||||||
\(697\) | −25.3180 | −0.958989 | ||||||||
\(698\) | −5.90652 | −0.223565 | ||||||||
\(699\) | −9.83642 | −0.372048 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.7572 | −1.57715 | −0.788575 | − | 0.614939i | \(-0.789181\pi\) | ||||
−0.788575 | + | 0.614939i | \(0.789181\pi\) | |||||||
\(702\) | −3.36147 | −0.126870 | ||||||||
\(703\) | 63.3047 | 2.38758 | ||||||||
\(704\) | −69.6108 | −2.62356 | ||||||||
\(705\) | −30.7678 | −1.15878 | ||||||||
\(706\) | 46.0987 | 1.73495 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.745347 | 0.0280119 | ||||||||
\(709\) | −31.1621 | −1.17032 | −0.585159 | − | 0.810918i | \(-0.698968\pi\) | ||||
−0.585159 | + | 0.810918i | \(0.698968\pi\) | |||||||
\(710\) | 23.8669 | 0.895710 | ||||||||
\(711\) | −4.66094 | −0.174799 | ||||||||
\(712\) | 24.4840 | 0.917578 | ||||||||
\(713\) | −9.93800 | −0.372181 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.4130 | 1.06258 | ||||||||
\(716\) | −47.3443 | −1.76934 | ||||||||
\(717\) | −18.8073 | −0.702373 | ||||||||
\(718\) | 88.2279 | 3.29264 | ||||||||
\(719\) | 36.1650 | 1.34873 | 0.674363 | − | 0.738400i | \(-0.264418\pi\) | ||||
0.674363 | + | 0.738400i | \(0.264418\pi\) | |||||||
\(720\) | −5.50787 | −0.205266 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −38.3972 | −1.42900 | ||||||||
\(723\) | −10.2441 | −0.380984 | ||||||||
\(724\) | −65.2508 | −2.42503 | ||||||||
\(725\) | −41.9604 | −1.55837 | ||||||||
\(726\) | 57.2890 | 2.12619 | ||||||||
\(727\) | −44.3338 | −1.64425 | −0.822124 | − | 0.569308i | \(-0.807211\pi\) | ||||
−0.822124 | + | 0.569308i | \(0.807211\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.9695 | 0.443011 | ||||||||
\(731\) | −9.18881 | −0.339861 | ||||||||
\(732\) | 18.9537 | 0.700551 | ||||||||
\(733\) | 16.5989 | 0.613096 | 0.306548 | − | 0.951855i | \(-0.400826\pi\) | ||||
0.306548 | + | 0.951855i | \(0.400826\pi\) | |||||||
\(734\) | 1.06866 | 0.0394451 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.57653 | −0.131833 | ||||||||
\(737\) | −64.9103 | −2.39100 | ||||||||
\(738\) | −21.4683 | −0.790258 | ||||||||
\(739\) | 21.6900 | 0.797880 | 0.398940 | − | 0.916977i | \(-0.369378\pi\) | ||||
0.398940 | + | 0.916977i | \(0.369378\pi\) | |||||||
\(740\) | −128.170 | −4.71163 | ||||||||
\(741\) | 8.45254 | 0.310512 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.1135 | −0.481087 | −0.240544 | − | 0.970638i | \(-0.577326\pi\) | ||||
−0.240544 | + | 0.970638i | \(0.577326\pi\) | |||||||
\(744\) | 36.9986 | 1.35643 | ||||||||
\(745\) | 23.6280 | 0.865664 | ||||||||
\(746\) | 30.9142 | 1.13185 | ||||||||
\(747\) | −4.78493 | −0.175072 | ||||||||
\(748\) | −59.1450 | −2.16255 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −10.3152 | −0.376658 | ||||||||
\(751\) | −48.6700 | −1.77599 | −0.887997 | − | 0.459849i | \(-0.847904\pi\) | ||||
−0.887997 | + | 0.459849i | \(0.847904\pi\) | |||||||
\(752\) | −14.9976 | −0.546906 | ||||||||
\(753\) | −12.4168 | −0.452493 | ||||||||
\(754\) | −22.3905 | −0.815416 | ||||||||
\(755\) | −22.1821 | −0.807291 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.2308 | 1.02607 | 0.513033 | − | 0.858369i | \(-0.328522\pi\) | ||||
0.513033 | + | 0.858369i | \(0.328522\pi\) | |||||||
\(758\) | −61.4725 | −2.23278 | ||||||||
\(759\) | 5.93800 | 0.215536 | ||||||||
\(760\) | 74.3114 | 2.69556 | ||||||||
\(761\) | −25.6014 | −0.928048 | −0.464024 | − | 0.885823i | \(-0.653595\pi\) | ||||
−0.464024 | + | 0.885823i | \(0.653595\pi\) | |||||||
\(762\) | −51.7124 | −1.87334 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.01092 | 0.181289 | ||||||||
\(765\) | 9.36147 | 0.338465 | ||||||||
\(766\) | −7.29947 | −0.263741 | ||||||||
\(767\) | 0.296649 | 0.0107114 | ||||||||
\(768\) | 25.0357 | 0.903400 | ||||||||
\(769\) | 18.8784 | 0.680773 | 0.340387 | − | 0.940286i | \(-0.389442\pi\) | ||||
0.340387 | + | 0.940286i | \(0.389442\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.58320 | −0.201074 | ||||||||
\(772\) | 59.3667 | 2.13665 | ||||||||
\(773\) | −29.6319 | −1.06578 | −0.532892 | − | 0.846183i | \(-0.678895\pi\) | ||||
−0.532892 | + | 0.846183i | \(0.678895\pi\) | |||||||
\(774\) | −7.79160 | −0.280063 | ||||||||
\(775\) | 62.6042 | 2.24881 | ||||||||
\(776\) | −35.3972 | −1.27069 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.2680 | 0.403977 | ||||||||
\(779\) | 53.9828 | 1.93414 | ||||||||
\(780\) | −17.1135 | −0.612761 | ||||||||
\(781\) | 17.8536 | 0.638852 | ||||||||
\(782\) | −6.57653 | −0.235176 | ||||||||
\(783\) | 6.66094 | 0.238043 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −66.3510 | −2.36817 | ||||||||
\(786\) | 14.0224 | 0.500163 | ||||||||
\(787\) | 12.3324 | 0.439602 | 0.219801 | − | 0.975545i | \(-0.429459\pi\) | ||||
0.219801 | + | 0.975545i | \(0.429459\pi\) | |||||||
\(788\) | −10.2623 | −0.365579 | ||||||||
\(789\) | −19.6767 | −0.700509 | ||||||||
\(790\) | −36.9986 | −1.31635 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −22.1068 | −0.785532 | ||||||||
\(793\) | 7.54361 | 0.267882 | ||||||||
\(794\) | −23.4277 | −0.831419 | ||||||||
\(795\) | 11.2995 | 0.400751 | ||||||||
\(796\) | −66.3782 | −2.35271 | ||||||||
\(797\) | −9.55653 | −0.338510 | −0.169255 | − | 0.985572i | \(-0.554136\pi\) | ||||
−0.169255 | + | 0.985572i | \(0.554136\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.4907 | 0.901796 | ||||||||
\(800\) | 22.5303 | 0.796566 | ||||||||
\(801\) | −6.57653 | −0.232370 | ||||||||
\(802\) | −39.0830 | −1.38007 | ||||||||
\(803\) | 8.95375 | 0.315971 | ||||||||
\(804\) | 39.0963 | 1.37882 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 33.4063 | 1.17669 | ||||||||
\(807\) | −0.882674 | −0.0310716 | ||||||||
\(808\) | 21.1001 | 0.742301 | ||||||||
\(809\) | −40.7587 | −1.43300 | −0.716499 | − | 0.697588i | \(-0.754257\pi\) | ||||
−0.716499 | + | 0.697588i | \(0.754257\pi\) | |||||||
\(810\) | 7.93800 | 0.278913 | ||||||||
\(811\) | 6.35480 | 0.223147 | 0.111574 | − | 0.993756i | \(-0.464411\pi\) | ||||
0.111574 | + | 0.993756i | \(0.464411\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.784934 | −0.0275288 | ||||||||
\(814\) | −149.492 | −5.23969 | ||||||||
\(815\) | −9.85360 | −0.345156 | ||||||||
\(816\) | 4.56320 | 0.159744 | ||||||||
\(817\) | 19.5923 | 0.685447 | ||||||||
\(818\) | 29.1755 | 1.02010 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −109.297 | −3.81680 | ||||||||
\(821\) | 32.2270 | 1.12473 | 0.562364 | − | 0.826890i | \(-0.309892\pi\) | ||||
0.562364 | + | 0.826890i | \(0.309892\pi\) | |||||||
\(822\) | −3.16215 | −0.110293 | ||||||||
\(823\) | 5.19266 | 0.181005 | 0.0905023 | − | 0.995896i | \(-0.471153\pi\) | ||||
0.0905023 | + | 0.995896i | \(0.471153\pi\) | |||||||
\(824\) | 50.0582 | 1.74386 | ||||||||
\(825\) | −37.4063 | −1.30232 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.1268 | 1.36057 | 0.680286 | − | 0.732946i | \(-0.261855\pi\) | ||||
0.680286 | + | 0.732946i | \(0.261855\pi\) | |||||||
\(828\) | −3.57653 | −0.124293 | ||||||||
\(829\) | 11.2732 | 0.391535 | 0.195768 | − | 0.980650i | \(-0.437280\pi\) | ||||
0.195768 | + | 0.980650i | \(0.437280\pi\) | |||||||
\(830\) | −37.9828 | −1.31840 | ||||||||
\(831\) | 21.3443 | 0.740425 | ||||||||
\(832\) | 16.6872 | 0.578524 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 40.9986 | 1.41966 | ||||||||
\(835\) | −37.8498 | −1.30984 | ||||||||
\(836\) | 126.108 | 4.36154 | ||||||||
\(837\) | −9.93800 | −0.343508 | ||||||||
\(838\) | −89.3180 | −3.08544 | ||||||||
\(839\) | −26.1912 | −0.904221 | −0.452111 | − | 0.891962i | \(-0.649329\pi\) | ||||
−0.452111 | + | 0.891962i | \(0.649329\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.3681 | 0.529936 | ||||||||
\(842\) | −51.0525 | −1.75938 | ||||||||
\(843\) | −21.4592 | −0.739094 | ||||||||
\(844\) | −35.1001 | −1.20820 | ||||||||
\(845\) | 36.8879 | 1.26898 | ||||||||
\(846\) | 21.6147 | 0.743128 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.50787 | 0.189141 | ||||||||
\(849\) | −13.6543 | −0.468613 | ||||||||
\(850\) | 41.4287 | 1.42099 | ||||||||
\(851\) | −10.6609 | −0.365452 | ||||||||
\(852\) | −10.7534 | −0.368407 | ||||||||
\(853\) | −39.7387 | −1.36063 | −0.680313 | − | 0.732921i | \(-0.738156\pi\) | ||||
−0.680313 | + | 0.732921i | \(0.738156\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.9604 | −0.682632 | ||||||||
\(856\) | 42.0672 | 1.43783 | ||||||||
\(857\) | 36.9366 | 1.26173 | 0.630865 | − | 0.775893i | \(-0.282700\pi\) | ||||
0.630865 | + | 0.775893i | \(0.282700\pi\) | |||||||
\(858\) | −19.9604 | −0.681437 | ||||||||
\(859\) | −9.59653 | −0.327430 | −0.163715 | − | 0.986508i | \(-0.552348\pi\) | ||||
−0.163715 | + | 0.986508i | \(0.552348\pi\) | |||||||
\(860\) | −39.6676 | −1.35265 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −93.6018 | −3.18809 | ||||||||
\(863\) | 26.2270 | 0.892776 | 0.446388 | − | 0.894839i | \(-0.352710\pi\) | ||||
0.446388 | + | 0.894839i | \(0.352710\pi\) | |||||||
\(864\) | −3.57653 | −0.121676 | ||||||||
\(865\) | 3.66761 | 0.124702 | ||||||||
\(866\) | −60.1211 | −2.04300 | ||||||||
\(867\) | 9.24414 | 0.313948 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.6767 | −0.938867 | ||||||||
\(870\) | 52.8746 | 1.79262 | ||||||||
\(871\) | 15.5604 | 0.527243 | ||||||||
\(872\) | −22.6519 | −0.767089 | ||||||||
\(873\) | 9.50787 | 0.321793 | ||||||||
\(874\) | 14.0224 | 0.474315 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.39296 | −0.182211 | ||||||||
\(877\) | 26.1240 | 0.882145 | 0.441072 | − | 0.897472i | \(-0.354598\pi\) | ||||
0.441072 | + | 0.897472i | \(0.354598\pi\) | |||||||
\(878\) | −60.6662 | −2.04738 | ||||||||
\(879\) | −3.32188 | −0.112044 | ||||||||
\(880\) | −32.7058 | −1.10251 | ||||||||
\(881\) | 20.8469 | 0.702351 | 0.351175 | − | 0.936310i | \(-0.385782\pi\) | ||||
0.351175 | + | 0.936310i | \(0.385782\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 58.6347 | 1.97321 | 0.986607 | − | 0.163114i | \(-0.0521539\pi\) | ||||
0.986607 | + | 0.163114i | \(0.0521539\pi\) | |||||||
\(884\) | 14.1783 | 0.476868 | ||||||||
\(885\) | −0.700528 | −0.0235480 | ||||||||
\(886\) | −3.41439 | −0.114709 | ||||||||
\(887\) | −28.1597 | −0.945511 | −0.472756 | − | 0.881194i | \(-0.656741\pi\) | ||||
−0.472756 | + | 0.881194i | \(0.656741\pi\) | |||||||
\(888\) | 39.6900 | 1.33191 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −52.2046 | −1.74990 | ||||||||
\(891\) | 5.93800 | 0.198931 | ||||||||
\(892\) | 56.0357 | 1.87622 | ||||||||
\(893\) | −54.3510 | −1.81879 | ||||||||
\(894\) | −16.5989 | −0.555152 | ||||||||
\(895\) | 44.4974 | 1.48738 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.42347 | −0.0475281 | ||||||||
\(898\) | −24.2127 | −0.807987 | ||||||||
\(899\) | −66.1965 | −2.20778 | ||||||||
\(900\) | 22.5303 | 0.751009 | ||||||||
\(901\) | −9.36147 | −0.311876 | ||||||||
\(902\) | −127.479 | −4.24458 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.4244 | −0.379971 | ||||||||
\(905\) | 61.3271 | 2.03858 | ||||||||
\(906\) | 15.5832 | 0.517717 | ||||||||
\(907\) | −11.5884 | −0.384788 | −0.192394 | − | 0.981318i | \(-0.561625\pi\) | ||||
−0.192394 | + | 0.981318i | \(0.561625\pi\) | |||||||
\(908\) | 28.4707 | 0.944833 | ||||||||
\(909\) | −5.66761 | −0.187983 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.5989 | 0.483685 | 0.241842 | − | 0.970316i | \(-0.422248\pi\) | ||||
0.241842 | + | 0.970316i | \(0.422248\pi\) | |||||||
\(912\) | −9.72960 | −0.322179 | ||||||||
\(913\) | −28.4130 | −0.940332 | ||||||||
\(914\) | 83.9036 | 2.77529 | ||||||||
\(915\) | −17.8140 | −0.588913 | ||||||||
\(916\) | 53.4501 | 1.76604 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.57653 | −0.217058 | ||||||||
\(919\) | −33.9380 | −1.11951 | −0.559756 | − | 0.828658i | \(-0.689105\pi\) | ||||
−0.559756 | + | 0.828658i | \(0.689105\pi\) | |||||||
\(920\) | −12.5145 | −0.412592 | ||||||||
\(921\) | −2.06200 | −0.0679451 | ||||||||
\(922\) | 47.1044 | 1.55130 | ||||||||
\(923\) | −4.27989 | −0.140874 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 67.1583 | 2.20815 | ||||||||
\(926\) | −9.26799 | −0.304565 | ||||||||
\(927\) | −13.4459 | −0.441620 | ||||||||
\(928\) | −23.8231 | −0.782031 | ||||||||
\(929\) | 5.17932 | 0.169928 | 0.0849640 | − | 0.996384i | \(-0.472922\pi\) | ||||
0.0849640 | + | 0.996384i | \(0.472922\pi\) | |||||||
\(930\) | −78.8879 | −2.58684 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 35.1803 | 1.15237 | ||||||||
\(933\) | −8.45254 | −0.276724 | ||||||||
\(934\) | −35.6371 | −1.16608 | ||||||||
\(935\) | 55.5884 | 1.81794 | ||||||||
\(936\) | 5.29947 | 0.173219 | ||||||||
\(937\) | −28.6924 | −0.937341 | −0.468670 | − | 0.883373i | \(-0.655267\pi\) | ||||
−0.468670 | + | 0.883373i | \(0.655267\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.7363 | 0.350365 | ||||||||
\(940\) | 110.042 | 3.58917 | ||||||||
\(941\) | 31.9342 | 1.04102 | 0.520512 | − | 0.853854i | \(-0.325741\pi\) | ||||
0.520512 | + | 0.853854i | \(0.325741\pi\) | |||||||
\(942\) | 46.6123 | 1.51871 | ||||||||
\(943\) | −9.09107 | −0.296046 | ||||||||
\(944\) | −0.341469 | −0.0111139 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −46.2666 | −1.50426 | ||||||||
\(947\) | −8.46162 | −0.274966 | −0.137483 | − | 0.990504i | \(-0.543901\pi\) | ||||
−0.137483 | + | 0.990504i | \(0.543901\pi\) | |||||||
\(948\) | 16.6700 | 0.541417 | ||||||||
\(949\) | −2.14640 | −0.0696752 | ||||||||
\(950\) | −88.3338 | −2.86593 | ||||||||
\(951\) | −16.8073 | −0.545015 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.5475 | −0.697991 | −0.348995 | − | 0.937124i | \(-0.613477\pi\) | ||||
−0.348995 | + | 0.937124i | \(0.613477\pi\) | |||||||
\(954\) | −7.93800 | −0.257002 | ||||||||
\(955\) | −4.70960 | −0.152399 | ||||||||
\(956\) | 67.2651 | 2.17551 | ||||||||
\(957\) | 39.5527 | 1.27856 | ||||||||
\(958\) | 38.0672 | 1.22990 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −39.4063 | −1.27183 | ||||||||
\(961\) | 67.7639 | 2.18593 | ||||||||
\(962\) | 35.8364 | 1.15541 | ||||||||
\(963\) | −11.2995 | −0.364120 | ||||||||
\(964\) | 36.6385 | 1.18005 | ||||||||
\(965\) | −55.7968 | −1.79616 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.4883 | 1.04475 | 0.522376 | − | 0.852715i | \(-0.325046\pi\) | ||||
0.522376 | + | 0.852715i | \(0.325046\pi\) | |||||||
\(968\) | −90.3180 | −2.90293 | ||||||||
\(969\) | 16.5369 | 0.531243 | ||||||||
\(970\) | 75.4735 | 2.42331 | ||||||||
\(971\) | −17.1621 | −0.550759 | −0.275380 | − | 0.961336i | \(-0.588804\pi\) | ||||
−0.275380 | + | 0.961336i | \(0.588804\pi\) | |||||||
\(972\) | −3.57653 | −0.114717 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −37.3128 | −1.19558 | ||||||||
\(975\) | 8.96708 | 0.287176 | ||||||||
\(976\) | −8.68335 | −0.277947 | ||||||||
\(977\) | 22.3285 | 0.714354 | 0.357177 | − | 0.934037i | \(-0.383739\pi\) | ||||
0.357177 | + | 0.934037i | \(0.383739\pi\) | |||||||
\(978\) | 6.92226 | 0.221349 | ||||||||
\(979\) | −39.0515 | −1.24809 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.08441 | 0.194260 | ||||||||
\(982\) | 4.67002 | 0.149026 | ||||||||
\(983\) | −39.2151 | −1.25077 | −0.625383 | − | 0.780318i | \(-0.715057\pi\) | ||||
−0.625383 | + | 0.780318i | \(0.715057\pi\) | |||||||
\(984\) | 33.8455 | 1.07896 | ||||||||
\(985\) | 9.64520 | 0.307322 | ||||||||
\(986\) | −43.8059 | −1.39506 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −30.2308 | −0.961770 | ||||||||
\(989\) | −3.29947 | −0.104917 | ||||||||
\(990\) | 47.1359 | 1.49808 | ||||||||
\(991\) | −36.4974 | −1.15938 | −0.579688 | − | 0.814838i | \(-0.696826\pi\) | ||||
−0.579688 | + | 0.814838i | \(0.696826\pi\) | |||||||
\(992\) | 35.5436 | 1.12851 | ||||||||
\(993\) | 21.5699 | 0.684499 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 62.3867 | 1.97779 | ||||||||
\(996\) | 17.1135 | 0.542261 | ||||||||
\(997\) | −29.0644 | −0.920479 | −0.460239 | − | 0.887795i | \(-0.652236\pi\) | ||||
−0.460239 | + | 0.887795i | \(0.652236\pi\) | |||||||
\(998\) | −48.4130 | −1.53249 | ||||||||
\(999\) | −10.6609 | −0.337297 |
(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.v.1.1 | 3 | ||
7.6 | odd | 2 | 483.2.a.h.1.1 | ✓ | 3 | ||
21.20 | even | 2 | 1449.2.a.l.1.3 | 3 | |||
28.27 | even | 2 | 7728.2.a.bt.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.a.h.1.1 | ✓ | 3 | 7.6 | odd | 2 | ||
1449.2.a.l.1.3 | 3 | 21.20 | even | 2 | |||
3381.2.a.v.1.1 | 3 | 1.1 | even | 1 | trivial | ||
7728.2.a.bt.1.3 | 3 | 28.27 | even | 2 |