Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(1,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, 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("1323.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.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: | \(10.5642081874\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7168.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 6x^{2} + 7 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.10100\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.10100 | −1.48563 | −0.742817 | − | 0.669495i | \(-0.766511\pi\) | ||||
−0.742817 | + | 0.669495i | \(0.766511\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.41421 | 1.20711 | ||||||||
\(5\) | 2.10100 | 0.939597 | 0.469799 | − | 0.882774i | \(-0.344327\pi\) | ||||
0.469799 | + | 0.882774i | \(0.344327\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.870264 | −0.307685 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.41421 | −1.39590 | ||||||||
\(11\) | 3.84153 | 1.15827 | 0.579133 | − | 0.815233i | \(-0.303391\pi\) | ||||
0.579133 | + | 0.815233i | \(0.303391\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.82843 | −1.89386 | −0.946932 | − | 0.321433i | \(-0.895836\pi\) | ||||
−0.946932 | + | 0.321433i | \(0.895836\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.00000 | −0.750000 | ||||||||
\(17\) | 1.23074 | 0.298498 | 0.149249 | − | 0.988800i | \(-0.452314\pi\) | ||||
0.149249 | + | 0.988800i | \(0.452314\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.41421 | −1.01269 | −0.506345 | − | 0.862331i | \(-0.669004\pi\) | ||||
−0.506345 | + | 0.862331i | \(0.669004\pi\) | |||||||
\(20\) | 5.07227 | 1.13419 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.07107 | −1.72076 | ||||||||
\(23\) | −6.81280 | −1.42057 | −0.710283 | − | 0.703916i | \(-0.751433\pi\) | ||||
−0.710283 | + | 0.703916i | \(0.751433\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.585786 | −0.117157 | ||||||||
\(26\) | 14.3465 | 2.81359 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.40401 | −1.56059 | −0.780293 | − | 0.625414i | \(-0.784930\pi\) | ||||
−0.780293 | + | 0.625414i | \(0.784930\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.656854 | 0.117975 | 0.0589873 | − | 0.998259i | \(-0.481213\pi\) | ||||
0.0589873 | + | 0.998259i | \(0.481213\pi\) | |||||||
\(32\) | 8.04354 | 1.42191 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.58579 | −0.443459 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.24264 | 0.533087 | 0.266543 | − | 0.963823i | \(-0.414118\pi\) | ||||
0.266543 | + | 0.963823i | \(0.414118\pi\) | |||||||
\(38\) | 9.27428 | 1.50449 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.82843 | −0.289100 | ||||||||
\(41\) | −5.07227 | −0.792155 | −0.396078 | − | 0.918217i | \(-0.629629\pi\) | ||||
−0.396078 | + | 0.918217i | \(0.629629\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.07107 | −1.07833 | −0.539164 | − | 0.842201i | \(-0.681260\pi\) | ||||
−0.539164 | + | 0.842201i | \(0.681260\pi\) | |||||||
\(44\) | 9.27428 | 1.39815 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.3137 | 2.11044 | ||||||||
\(47\) | −10.6543 | −1.55409 | −0.777047 | − | 0.629443i | \(-0.783283\pi\) | ||||
−0.777047 | + | 0.629443i | \(0.783283\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.23074 | 0.174053 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −16.4853 | −2.28610 | ||||||||
\(53\) | 10.1445 | 1.39346 | 0.696730 | − | 0.717334i | \(-0.254638\pi\) | ||||
0.696730 | + | 0.717334i | \(0.254638\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.07107 | 1.08830 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 17.6569 | 2.31846 | ||||||||
\(59\) | 2.97127 | 0.386826 | 0.193413 | − | 0.981117i | \(-0.438044\pi\) | ||||
0.193413 | + | 0.981117i | \(0.438044\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.48528 | 0.830355 | 0.415178 | − | 0.909740i | \(-0.363719\pi\) | ||||
0.415178 | + | 0.909740i | \(0.363719\pi\) | |||||||
\(62\) | −1.38005 | −0.175267 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.8995 | −1.36244 | ||||||||
\(65\) | −14.3465 | −1.77947 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.65685 | −0.691095 | −0.345547 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345547 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(68\) | 2.97127 | 0.360319 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.7070 | 1.74540 | 0.872701 | − | 0.488255i | \(-0.162366\pi\) | ||||
0.872701 | + | 0.488255i | \(0.162366\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.4142 | −1.33593 | −0.667966 | − | 0.744192i | \(-0.732835\pi\) | ||||
−0.667966 | + | 0.744192i | \(0.732835\pi\) | |||||||
\(74\) | −6.81280 | −0.791972 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.6569 | −1.22243 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.89949 | 0.663745 | 0.331873 | − | 0.943324i | \(-0.392320\pi\) | ||||
0.331873 | + | 0.943324i | \(0.392320\pi\) | |||||||
\(80\) | −6.30301 | −0.704698 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.6569 | 1.17685 | ||||||||
\(83\) | −0.720950 | −0.0791346 | −0.0395673 | − | 0.999217i | \(-0.512598\pi\) | ||||
−0.0395673 | + | 0.999217i | \(0.512598\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.58579 | 0.280468 | ||||||||
\(86\) | 14.8563 | 1.60200 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.34315 | −0.356381 | ||||||||
\(89\) | 0.149314 | 0.0158272 | 0.00791361 | − | 0.999969i | \(-0.497481\pi\) | ||||
0.00791361 | + | 0.999969i | \(0.497481\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −16.4475 | −1.71478 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 22.3848 | 2.30881 | ||||||||
\(95\) | −9.27428 | −0.951521 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.65685 | 0.168228 | 0.0841140 | − | 0.996456i | \(-0.473194\pi\) | ||||
0.0841140 | + | 0.996456i | \(0.473194\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.41421 | −0.141421 | ||||||||
\(101\) | 2.25032 | 0.223915 | 0.111957 | − | 0.993713i | \(-0.464288\pi\) | ||||
0.111957 | + | 0.993713i | \(0.464288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.4853 | −1.32874 | −0.664372 | − | 0.747402i | \(-0.731301\pi\) | ||||
−0.664372 | + | 0.747402i | \(0.731301\pi\) | |||||||
\(104\) | 5.94253 | 0.582713 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −21.3137 | −2.07017 | ||||||||
\(107\) | 5.43275 | 0.525203 | 0.262602 | − | 0.964904i | \(-0.415419\pi\) | ||||
0.262602 | + | 0.964904i | \(0.415419\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.65685 | −0.829176 | −0.414588 | − | 0.910009i | \(-0.636074\pi\) | ||||
−0.414588 | + | 0.910009i | \(0.636074\pi\) | |||||||
\(110\) | −16.9573 | −1.61682 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.6543 | 1.00227 | 0.501137 | − | 0.865368i | \(-0.332915\pi\) | ||||
0.501137 | + | 0.865368i | \(0.332915\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.3137 | −1.33476 | ||||||||
\(116\) | −20.2891 | −1.88379 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.24264 | −0.574682 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.75736 | 0.341578 | ||||||||
\(122\) | −13.6256 | −1.23360 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.58579 | 0.142408 | ||||||||
\(125\) | −11.7358 | −1.04968 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.828427 | 0.0735110 | 0.0367555 | − | 0.999324i | \(-0.488298\pi\) | ||||
0.0367555 | + | 0.999324i | \(0.488298\pi\) | |||||||
\(128\) | 6.81280 | 0.602172 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 30.1421 | 2.64364 | ||||||||
\(131\) | −7.89422 | −0.689721 | −0.344861 | − | 0.938654i | \(-0.612074\pi\) | ||||
−0.344861 | + | 0.938654i | \(0.612074\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.8851 | 1.02671 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.07107 | −0.0918433 | ||||||||
\(137\) | −16.0871 | −1.37441 | −0.687206 | − | 0.726463i | \(-0.741163\pi\) | ||||
−0.687206 | + | 0.726463i | \(0.741163\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.17157 | 0.269009 | 0.134505 | − | 0.990913i | \(-0.457056\pi\) | ||||
0.134505 | + | 0.990913i | \(0.457056\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −30.8995 | −2.59303 | ||||||||
\(143\) | −26.2316 | −2.19360 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.6569 | −1.46632 | ||||||||
\(146\) | 23.9813 | 1.98471 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.82843 | 0.643493 | ||||||||
\(149\) | −5.43275 | −0.445068 | −0.222534 | − | 0.974925i | \(-0.571433\pi\) | ||||
−0.222534 | + | 0.974925i | \(0.571433\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.24264 | −0.345261 | −0.172631 | − | 0.984987i | \(-0.555227\pi\) | ||||
−0.172631 | + | 0.984987i | \(0.555227\pi\) | |||||||
\(152\) | 3.84153 | 0.311589 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.38005 | 0.110849 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.51472 | −0.120888 | −0.0604439 | − | 0.998172i | \(-0.519252\pi\) | ||||
−0.0604439 | + | 0.998172i | \(0.519252\pi\) | |||||||
\(158\) | −12.3949 | −0.986082 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 16.8995 | 1.33602 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.343146 | −0.0268772 | −0.0134386 | − | 0.999910i | \(-0.504278\pi\) | ||||
−0.0134386 | + | 0.999910i | \(0.504278\pi\) | |||||||
\(164\) | −12.2455 | −0.956216 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.51472 | 0.117565 | ||||||||
\(167\) | −10.6543 | −0.824457 | −0.412228 | − | 0.911081i | \(-0.635249\pi\) | ||||
−0.412228 | + | 0.911081i | \(0.635249\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.6274 | 2.58672 | ||||||||
\(170\) | −5.43275 | −0.416673 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −17.0711 | −1.30166 | ||||||||
\(173\) | −15.9378 | −1.21173 | −0.605863 | − | 0.795569i | \(-0.707172\pi\) | ||||
−0.605863 | + | 0.795569i | \(0.707172\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −11.5246 | −0.868699 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.313708 | −0.0235134 | ||||||||
\(179\) | 12.0962 | 0.904115 | 0.452057 | − | 0.891989i | \(-0.350690\pi\) | ||||
0.452057 | + | 0.891989i | \(0.350690\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.8995 | −1.77644 | −0.888218 | − | 0.459423i | \(-0.848056\pi\) | ||||
−0.888218 | + | 0.459423i | \(0.848056\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.92893 | 0.437087 | ||||||||
\(185\) | 6.81280 | 0.500887 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.72792 | 0.345740 | ||||||||
\(188\) | −25.7218 | −1.87596 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 19.4853 | 1.41361 | ||||||||
\(191\) | 2.61079 | 0.188910 | 0.0944551 | − | 0.995529i | \(-0.469889\pi\) | ||||
0.0944551 | + | 0.995529i | \(0.469889\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.3431 | 0.888479 | 0.444240 | − | 0.895908i | \(-0.353474\pi\) | ||||
0.444240 | + | 0.895908i | \(0.353474\pi\) | |||||||
\(194\) | −3.48106 | −0.249925 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.3753 | 0.810455 | 0.405228 | − | 0.914216i | \(-0.367192\pi\) | ||||
0.405228 | + | 0.914216i | \(0.367192\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.0711 | 1.28102 | 0.640512 | − | 0.767948i | \(-0.278722\pi\) | ||||
0.640512 | + | 0.767948i | \(0.278722\pi\) | |||||||
\(200\) | 0.509789 | 0.0360475 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.72792 | −0.332655 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.6569 | −0.744307 | ||||||||
\(206\) | 28.3326 | 1.97403 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20.4853 | 1.42040 | ||||||||
\(209\) | −16.9573 | −1.17296 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.242641 | 0.0167041 | 0.00835204 | − | 0.999965i | \(-0.497341\pi\) | ||||
0.00835204 | + | 0.999965i | \(0.497341\pi\) | |||||||
\(212\) | 24.4911 | 1.68205 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.4142 | −0.780260 | ||||||||
\(215\) | −14.8563 | −1.01319 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 18.1881 | 1.23185 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 19.4853 | 1.31370 | ||||||||
\(221\) | −8.40401 | −0.565315 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.7279 | −0.785360 | −0.392680 | − | 0.919675i | \(-0.628452\pi\) | ||||
−0.392680 | + | 0.919675i | \(0.628452\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −22.3848 | −1.48901 | ||||||||
\(227\) | −4.71179 | −0.312733 | −0.156366 | − | 0.987699i | \(-0.549978\pi\) | ||||
−0.156366 | + | 0.987699i | \(0.549978\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.4853 | −1.22154 | −0.610771 | − | 0.791807i | \(-0.709140\pi\) | ||||
−0.610771 | + | 0.791807i | \(0.709140\pi\) | |||||||
\(230\) | 30.0731 | 1.98296 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.31371 | 0.480168 | ||||||||
\(233\) | −8.19285 | −0.536731 | −0.268366 | − | 0.963317i | \(-0.586484\pi\) | ||||
−0.268366 | + | 0.963317i | \(0.586484\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.3848 | −1.46022 | ||||||||
\(236\) | 7.17327 | 0.466940 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.97127 | −0.192195 | −0.0960976 | − | 0.995372i | \(-0.530636\pi\) | ||||
−0.0960976 | + | 0.995372i | \(0.530636\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.727922 | −0.0468896 | −0.0234448 | − | 0.999725i | \(-0.507463\pi\) | ||||
−0.0234448 | + | 0.999725i | \(0.507463\pi\) | |||||||
\(242\) | −7.89422 | −0.507460 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 15.6569 | 1.00233 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.1421 | 1.91790 | ||||||||
\(248\) | −0.571637 | −0.0362990 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 24.6569 | 1.55944 | ||||||||
\(251\) | 27.9721 | 1.76559 | 0.882793 | − | 0.469762i | \(-0.155660\pi\) | ||||
0.882793 | + | 0.469762i | \(0.155660\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.1716 | −1.64539 | ||||||||
\(254\) | −1.74053 | −0.109210 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.48528 | 0.467830 | ||||||||
\(257\) | 29.0536 | 1.81231 | 0.906156 | − | 0.422944i | \(-0.139003\pi\) | ||||
0.906156 | + | 0.422944i | \(0.139003\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −34.6356 | −2.14801 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.5858 | 1.02467 | ||||||||
\(263\) | 31.3039 | 1.93028 | 0.965140 | − | 0.261734i | \(-0.0842943\pi\) | ||||
0.965140 | + | 0.261734i | \(0.0842943\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.3137 | 1.30929 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.6569 | −0.834225 | ||||||||
\(269\) | 5.07227 | 0.309262 | 0.154631 | − | 0.987972i | \(-0.450581\pi\) | ||||
0.154631 | + | 0.987972i | \(0.450581\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.1716 | 0.678625 | 0.339312 | − | 0.940674i | \(-0.389806\pi\) | ||||
0.339312 | + | 0.940674i | \(0.389806\pi\) | |||||||
\(272\) | −3.69222 | −0.223874 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 33.7990 | 2.04187 | ||||||||
\(275\) | −2.25032 | −0.135699 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.5563 | −1.35528 | −0.677640 | − | 0.735394i | \(-0.736997\pi\) | ||||
−0.677640 | + | 0.735394i | \(0.736997\pi\) | |||||||
\(278\) | −6.66348 | −0.399649 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.99084 | −0.238074 | −0.119037 | − | 0.992890i | \(-0.537981\pi\) | ||||
−0.119037 | + | 0.992890i | \(0.537981\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.48528 | 0.504398 | 0.252199 | − | 0.967675i | \(-0.418846\pi\) | ||||
0.252199 | + | 0.967675i | \(0.418846\pi\) | |||||||
\(284\) | 35.5059 | 2.10689 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 55.1127 | 3.25888 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.4853 | −0.910899 | ||||||||
\(290\) | 37.0971 | 2.17842 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −27.5563 | −1.61261 | ||||||||
\(293\) | −25.0009 | −1.46057 | −0.730283 | − | 0.683144i | \(-0.760612\pi\) | ||||
−0.730283 | + | 0.683144i | \(0.760612\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.24264 | 0.363461 | ||||||||
\(296\) | −2.82195 | −0.164023 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.4142 | 0.661208 | ||||||||
\(299\) | 46.5207 | 2.69036 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.91380 | 0.512932 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 13.2426 | 0.759518 | ||||||||
\(305\) | 13.6256 | 0.780199 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.0711 | 1.37381 | 0.686904 | − | 0.726748i | \(-0.258969\pi\) | ||||
0.686904 | + | 0.726748i | \(0.258969\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.89949 | −0.164680 | ||||||||
\(311\) | 13.3270 | 0.755703 | 0.377852 | − | 0.925866i | \(-0.376663\pi\) | ||||
0.377852 | + | 0.925866i | \(0.376663\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.1716 | −1.08364 | −0.541821 | − | 0.840494i | \(-0.682265\pi\) | ||||
−0.541821 | + | 0.840494i | \(0.682265\pi\) | |||||||
\(314\) | 3.18243 | 0.179595 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.2426 | 0.801211 | ||||||||
\(317\) | 26.4428 | 1.48517 | 0.742587 | − | 0.669750i | \(-0.233599\pi\) | ||||
0.742587 | + | 0.669750i | \(0.233599\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −32.2843 | −1.80757 | ||||||||
\(320\) | −22.8999 | −1.28014 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.43275 | −0.302286 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00000 | 0.221880 | ||||||||
\(326\) | 0.720950 | 0.0399297 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.41421 | 0.243734 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.9706 | 1.70230 | 0.851148 | − | 0.524926i | \(-0.175907\pi\) | ||||
0.851148 | + | 0.524926i | \(0.175907\pi\) | |||||||
\(332\) | −1.74053 | −0.0955239 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 22.3848 | 1.22484 | ||||||||
\(335\) | −11.8851 | −0.649351 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.7990 | 0.588258 | 0.294129 | − | 0.955766i | \(-0.404970\pi\) | ||||
0.294129 | + | 0.955766i | \(0.404970\pi\) | |||||||
\(338\) | −70.6513 | −3.84292 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.24264 | 0.338555 | ||||||||
\(341\) | 2.52333 | 0.136646 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.15370 | 0.331785 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 33.4853 | 1.80018 | ||||||||
\(347\) | −1.59121 | −0.0854209 | −0.0427104 | − | 0.999087i | \(-0.513599\pi\) | ||||
−0.0427104 | + | 0.999087i | \(0.513599\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.0711 | −0.699678 | −0.349839 | − | 0.936810i | \(-0.613764\pi\) | ||||
−0.349839 | + | 0.936810i | \(0.613764\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 30.8995 | 1.64695 | ||||||||
\(353\) | −17.9769 | −0.956815 | −0.478407 | − | 0.878138i | \(-0.658786\pi\) | ||||
−0.478407 | + | 0.878138i | \(0.658786\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.8995 | 1.63997 | ||||||||
\(356\) | 0.360475 | 0.0191051 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −25.4142 | −1.34318 | ||||||||
\(359\) | −14.5577 | −0.768326 | −0.384163 | − | 0.923265i | \(-0.625510\pi\) | ||||
−0.384163 | + | 0.923265i | \(0.625510\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.485281 | 0.0255411 | ||||||||
\(362\) | 50.2129 | 2.63913 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.9813 | −1.25524 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.3848 | −1.53387 | −0.766936 | − | 0.641723i | \(-0.778220\pi\) | ||||
−0.766936 | + | 0.641723i | \(0.778220\pi\) | |||||||
\(368\) | 20.4384 | 1.06542 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −14.3137 | −0.744134 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.1421 | −0.784030 | −0.392015 | − | 0.919959i | \(-0.628222\pi\) | ||||
−0.392015 | + | 0.919959i | \(0.628222\pi\) | |||||||
\(374\) | −9.93338 | −0.513643 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.27208 | 0.478171 | ||||||||
\(377\) | 57.3862 | 2.95554 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.8995 | 0.919435 | 0.459718 | − | 0.888065i | \(-0.347951\pi\) | ||||
0.459718 | + | 0.888065i | \(0.347951\pi\) | |||||||
\(380\) | −22.3901 | −1.14859 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.48528 | −0.280651 | ||||||||
\(383\) | −5.43275 | −0.277600 | −0.138800 | − | 0.990320i | \(-0.544325\pi\) | ||||
−0.138800 | + | 0.990320i | \(0.544325\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −25.9330 | −1.31995 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.00000 | 0.203069 | ||||||||
\(389\) | −6.66348 | −0.337852 | −0.168926 | − | 0.985629i | \(-0.554030\pi\) | ||||
−0.168926 | + | 0.985629i | \(0.554030\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.38478 | −0.424036 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.8995 | −1.20404 | ||||||||
\(395\) | 12.3949 | 0.623653 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.0711 | −1.15790 | −0.578952 | − | 0.815362i | \(-0.696538\pi\) | ||||
−0.578952 | + | 0.815362i | \(0.696538\pi\) | |||||||
\(398\) | −37.9674 | −1.90313 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.75736 | 0.0878680 | ||||||||
\(401\) | 11.1641 | 0.557509 | 0.278755 | − | 0.960362i | \(-0.410078\pi\) | ||||
0.278755 | + | 0.960362i | \(0.410078\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.48528 | −0.223428 | ||||||||
\(404\) | 5.43275 | 0.270289 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.4567 | 0.617456 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.07107 | −0.250748 | −0.125374 | − | 0.992110i | \(-0.540013\pi\) | ||||
−0.125374 | + | 0.992110i | \(0.540013\pi\) | |||||||
\(410\) | 22.3901 | 1.10577 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −32.5563 | −1.60394 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.51472 | −0.0743546 | ||||||||
\(416\) | −54.9247 | −2.69291 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 35.6274 | 1.74259 | ||||||||
\(419\) | 12.3949 | 0.605528 | 0.302764 | − | 0.953066i | \(-0.402091\pi\) | ||||
0.302764 | + | 0.953066i | \(0.402091\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.92893 | 0.386433 | 0.193216 | − | 0.981156i | \(-0.438108\pi\) | ||||
0.193216 | + | 0.981156i | \(0.438108\pi\) | |||||||
\(422\) | −0.509789 | −0.0248161 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.82843 | −0.428746 | ||||||||
\(425\) | −0.720950 | −0.0349712 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 13.1158 | 0.633976 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 31.2132 | 1.50523 | ||||||||
\(431\) | −0.149314 | −0.00719219 | −0.00359609 | − | 0.999994i | \(-0.501145\pi\) | ||||
−0.00359609 | + | 0.999994i | \(0.501145\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.97056 | 0.431098 | 0.215549 | − | 0.976493i | \(-0.430846\pi\) | ||||
0.215549 | + | 0.976493i | \(0.430846\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.8995 | −1.00090 | ||||||||
\(437\) | 30.0731 | 1.43859 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.7990 | 0.944954 | 0.472477 | − | 0.881343i | \(-0.343360\pi\) | ||||
0.472477 | + | 0.881343i | \(0.343360\pi\) | |||||||
\(440\) | −7.02396 | −0.334854 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.6569 | 0.839851 | ||||||||
\(443\) | −11.5246 | −0.547550 | −0.273775 | − | 0.961794i | \(-0.588272\pi\) | ||||
−0.273775 | + | 0.961794i | \(0.588272\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.313708 | 0.0148712 | ||||||||
\(446\) | 24.6404 | 1.16676 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.0009 | −1.17986 | −0.589932 | − | 0.807453i | \(-0.700846\pi\) | ||||
−0.589932 | + | 0.807453i | \(0.700846\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.4853 | −0.917526 | ||||||||
\(452\) | 25.7218 | 1.20985 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.89949 | 0.464606 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.9706 | −0.653515 | −0.326758 | − | 0.945108i | \(-0.605956\pi\) | ||||
−0.326758 | + | 0.945108i | \(0.605956\pi\) | |||||||
\(458\) | 38.8376 | 1.81476 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −34.5563 | −1.61120 | ||||||||
\(461\) | 20.8607 | 0.971580 | 0.485790 | − | 0.874075i | \(-0.338532\pi\) | ||||
0.485790 | + | 0.874075i | \(0.338532\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.89949 | −0.367121 | −0.183560 | − | 0.983008i | \(-0.558762\pi\) | ||||
−0.183560 | + | 0.983008i | \(0.558762\pi\) | |||||||
\(464\) | 25.2120 | 1.17044 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.2132 | 0.797386 | ||||||||
\(467\) | −13.1158 | −0.606927 | −0.303464 | − | 0.952843i | \(-0.598143\pi\) | ||||
−0.303464 | + | 0.952843i | \(0.598143\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 47.0305 | 2.16935 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.58579 | −0.119020 | ||||||||
\(473\) | −27.1637 | −1.24899 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.58579 | 0.118644 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.24264 | 0.285532 | ||||||||
\(479\) | 27.2512 | 1.24514 | 0.622569 | − | 0.782565i | \(-0.286089\pi\) | ||||
0.622569 | + | 0.782565i | \(0.286089\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.1421 | −1.00959 | ||||||||
\(482\) | 1.52937 | 0.0696607 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.07107 | 0.412321 | ||||||||
\(485\) | 3.48106 | 0.158067 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.4142 | 1.60477 | 0.802386 | − | 0.596806i | \(-0.203564\pi\) | ||||
0.802386 | + | 0.596806i | \(0.203564\pi\) | |||||||
\(488\) | −5.64391 | −0.255488 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.8999 | −1.03346 | −0.516728 | − | 0.856149i | \(-0.672850\pi\) | ||||
−0.516728 | + | 0.856149i | \(0.672850\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.3431 | −0.465832 | ||||||||
\(494\) | −63.3287 | −2.84929 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.97056 | −0.0884809 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.4437 | −0.467522 | −0.233761 | − | 0.972294i | \(-0.575103\pi\) | ||||
−0.233761 | + | 0.972294i | \(0.575103\pi\) | |||||||
\(500\) | −28.3326 | −1.26707 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −58.7696 | −2.62301 | ||||||||
\(503\) | 5.22158 | 0.232819 | 0.116409 | − | 0.993201i | \(-0.462862\pi\) | ||||
0.116409 | + | 0.993201i | \(0.462862\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.72792 | 0.210390 | ||||||||
\(506\) | 54.9866 | 2.44445 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.00000 | 0.0887357 | ||||||||
\(509\) | −14.8563 | −0.658495 | −0.329248 | − | 0.944244i | \(-0.606795\pi\) | ||||
−0.329248 | + | 0.944244i | \(0.606795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −29.3522 | −1.29720 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −61.0416 | −2.69243 | ||||||||
\(515\) | −28.3326 | −1.24848 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −40.9289 | −1.80005 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.4853 | 0.547516 | ||||||||
\(521\) | −30.0731 | −1.31753 | −0.658764 | − | 0.752349i | \(-0.728921\pi\) | ||||
−0.658764 | + | 0.752349i | \(0.728921\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.7696 | −1.91391 | −0.956954 | − | 0.290238i | \(-0.906265\pi\) | ||||
−0.956954 | + | 0.290238i | \(0.906265\pi\) | |||||||
\(524\) | −19.0583 | −0.832567 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −65.7696 | −2.86769 | ||||||||
\(527\) | 0.808416 | 0.0352152 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.4142 | 1.01801 | ||||||||
\(530\) | −44.7802 | −1.94513 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.6356 | 1.50024 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.4142 | 0.493479 | ||||||||
\(536\) | 4.92296 | 0.212639 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.6569 | −0.459450 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.3848 | −0.919403 | −0.459702 | − | 0.888073i | \(-0.652044\pi\) | ||||
−0.459702 | + | 0.888073i | \(0.652044\pi\) | |||||||
\(542\) | −23.4715 | −1.00819 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.89949 | 0.424437 | ||||||||
\(545\) | −18.1881 | −0.779092 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.51472 | 0.321306 | 0.160653 | − | 0.987011i | \(-0.448640\pi\) | ||||
0.160653 | + | 0.987011i | \(0.448640\pi\) | |||||||
\(548\) | −38.8376 | −1.65906 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.72792 | 0.201599 | ||||||||
\(551\) | 37.0971 | 1.58039 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 47.3910 | 2.01345 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.65685 | 0.324723 | ||||||||
\(557\) | 0.932112 | 0.0394948 | 0.0197474 | − | 0.999805i | \(-0.493714\pi\) | ||||
0.0197474 | + | 0.999805i | \(0.493714\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.2843 | 2.04221 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.38478 | 0.353690 | ||||||||
\(563\) | −8.10538 | −0.341601 | −0.170801 | − | 0.985306i | \(-0.554635\pi\) | ||||
−0.170801 | + | 0.985306i | \(0.554635\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.3848 | 0.941735 | ||||||||
\(566\) | −17.8276 | −0.749350 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.7990 | −0.537034 | ||||||||
\(569\) | 24.2799 | 1.01787 | 0.508934 | − | 0.860806i | \(-0.330040\pi\) | ||||
0.508934 | + | 0.860806i | \(0.330040\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0416 | 0.671321 | 0.335661 | − | 0.941983i | \(-0.391040\pi\) | ||||
0.335661 | + | 0.941983i | \(0.391040\pi\) | |||||||
\(572\) | −63.3287 | −2.64791 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.99084 | 0.166430 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.3553 | 1.22208 | 0.611039 | − | 0.791600i | \(-0.290752\pi\) | ||||
0.611039 | + | 0.791600i | \(0.290752\pi\) | |||||||
\(578\) | 32.5346 | 1.35326 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −42.6274 | −1.77001 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.9706 | 1.61400 | ||||||||
\(584\) | 9.93338 | 0.411046 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 52.5269 | 2.16987 | ||||||||
\(587\) | 17.0192 | 0.702457 | 0.351228 | − | 0.936290i | \(-0.385764\pi\) | ||||
0.351228 | + | 0.936290i | \(0.385764\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.89949 | −0.119472 | ||||||||
\(590\) | −13.1158 | −0.539969 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.72792 | −0.399815 | ||||||||
\(593\) | −32.5346 | −1.33604 | −0.668018 | − | 0.744145i | \(-0.732857\pi\) | ||||
−0.668018 | + | 0.744145i | \(0.732857\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.1158 | −0.537244 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −97.7401 | −3.99689 | ||||||||
\(599\) | −2.90942 | −0.118876 | −0.0594378 | − | 0.998232i | \(-0.518931\pi\) | ||||
−0.0594378 | + | 0.998232i | \(0.518931\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.6274 | −1.08615 | −0.543077 | − | 0.839683i | \(-0.682741\pi\) | ||||
−0.543077 | + | 0.839683i | \(0.682741\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.2426 | −0.416767 | ||||||||
\(605\) | 7.89422 | 0.320946 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.68629 | −0.271388 | −0.135694 | − | 0.990751i | \(-0.543326\pi\) | ||||
−0.135694 | + | 0.990751i | \(0.543326\pi\) | |||||||
\(608\) | −35.5059 | −1.43995 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −28.6274 | −1.15909 | ||||||||
\(611\) | 72.7523 | 2.94324 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.62742 | 0.227289 | 0.113645 | − | 0.993521i | \(-0.463747\pi\) | ||||
0.113645 | + | 0.993521i | \(0.463747\pi\) | |||||||
\(614\) | −50.5734 | −2.04098 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.8368 | −0.557047 | −0.278523 | − | 0.960429i | \(-0.589845\pi\) | ||||
−0.278523 | + | 0.960429i | \(0.589845\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.4558 | 1.38490 | 0.692449 | − | 0.721467i | \(-0.256532\pi\) | ||||
0.692449 | + | 0.721467i | \(0.256532\pi\) | |||||||
\(620\) | 3.33174 | 0.133806 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −28.0000 | −1.12270 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.7279 | −0.869117 | ||||||||
\(626\) | 40.2795 | 1.60989 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.65685 | −0.145924 | ||||||||
\(629\) | 3.99084 | 0.159125 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.3553 | −1.64633 | −0.823165 | − | 0.567802i | \(-0.807794\pi\) | ||||
−0.823165 | + | 0.567802i | \(0.807794\pi\) | |||||||
\(632\) | −5.13412 | −0.204224 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −55.5563 | −2.20642 | ||||||||
\(635\) | 1.74053 | 0.0690707 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 67.8294 | 2.68539 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14.3137 | 0.565799 | ||||||||
\(641\) | −25.2995 | −0.999270 | −0.499635 | − | 0.866236i | \(-0.666533\pi\) | ||||
−0.499635 | + | 0.866236i | \(0.666533\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.2426 | 0.443366 | 0.221683 | − | 0.975119i | \(-0.428845\pi\) | ||||
0.221683 | + | 0.975119i | \(0.428845\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.4142 | 0.449086 | ||||||||
\(647\) | 5.43275 | 0.213583 | 0.106792 | − | 0.994281i | \(-0.465942\pi\) | ||||
0.106792 | + | 0.994281i | \(0.465942\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.4142 | 0.448047 | ||||||||
\(650\) | −8.40401 | −0.329632 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.828427 | −0.0324437 | ||||||||
\(653\) | 21.2212 | 0.830449 | 0.415225 | − | 0.909719i | \(-0.363703\pi\) | ||||
0.415225 | + | 0.909719i | \(0.363703\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.5858 | −0.648060 | ||||||||
\(656\) | 15.2168 | 0.594117 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.1110 | −0.900278 | −0.450139 | − | 0.892958i | \(-0.648626\pi\) | ||||
−0.450139 | + | 0.892958i | \(0.648626\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.1421 | −1.17239 | −0.586197 | − | 0.810169i | \(-0.699375\pi\) | ||||
−0.586197 | + | 0.810169i | \(0.699375\pi\) | |||||||
\(662\) | −65.0692 | −2.52899 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.627417 | 0.0243485 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 57.2548 | 2.21692 | ||||||||
\(668\) | −25.7218 | −0.995207 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 24.9706 | 0.964697 | ||||||||
\(671\) | 24.9134 | 0.961771 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.8284 | 0.802877 | 0.401438 | − | 0.915886i | \(-0.368510\pi\) | ||||
0.401438 | + | 0.915886i | \(0.368510\pi\) | |||||||
\(674\) | −22.6887 | −0.873936 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 81.1838 | 3.12245 | ||||||||
\(677\) | −15.4280 | −0.592945 | −0.296473 | − | 0.955041i | \(-0.595810\pi\) | ||||
−0.296473 | + | 0.955041i | \(0.595810\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.25032 | −0.0862957 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.30152 | −0.203006 | ||||||||
\(683\) | −23.1110 | −0.884319 | −0.442160 | − | 0.896936i | \(-0.645788\pi\) | ||||
−0.442160 | + | 0.896936i | \(0.645788\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −33.7990 | −1.29139 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 21.2132 | 0.808746 | ||||||||
\(689\) | −69.2713 | −2.63902 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.1716 | 1.49016 | 0.745078 | − | 0.666977i | \(-0.232412\pi\) | ||||
0.745078 | + | 0.666977i | \(0.232412\pi\) | |||||||
\(692\) | −38.4772 | −1.46268 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.34315 | 0.126904 | ||||||||
\(695\) | 6.66348 | 0.252760 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.24264 | −0.236457 | ||||||||
\(698\) | 27.4624 | 1.03947 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.20201 | −0.158708 | −0.0793538 | − | 0.996847i | \(-0.525286\pi\) | ||||
−0.0793538 | + | 0.996847i | \(0.525286\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.3137 | −0.539852 | ||||||||
\(704\) | −41.8707 | −1.57806 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 37.7696 | 1.42148 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.6569 | 1.60201 | 0.801006 | − | 0.598656i | \(-0.204299\pi\) | ||||
0.801006 | + | 0.598656i | \(0.204299\pi\) | |||||||
\(710\) | −64.9199 | −2.43640 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.129942 | −0.00486979 | ||||||||
\(713\) | −4.47502 | −0.167591 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −55.1127 | −2.06110 | ||||||||
\(716\) | 29.2029 | 1.09136 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 30.5858 | 1.14145 | ||||||||
\(719\) | −18.7597 | −0.699619 | −0.349810 | − | 0.936821i | \(-0.613754\pi\) | ||||
−0.349810 | + | 0.936821i | \(0.613754\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.01958 | −0.0379447 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −57.6985 | −2.14435 | ||||||||
\(725\) | 4.92296 | 0.182834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.0000 | 0.964287 | 0.482143 | − | 0.876092i | \(-0.339858\pi\) | ||||
0.482143 | + | 0.876092i | \(0.339858\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 50.3848 | 1.86482 | ||||||||
\(731\) | −8.70264 | −0.321879 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.7574 | −0.582011 | −0.291006 | − | 0.956721i | \(-0.593990\pi\) | ||||
−0.291006 | + | 0.956721i | \(0.593990\pi\) | |||||||
\(734\) | 61.7375 | 2.27877 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −54.7990 | −2.01992 | ||||||||
\(737\) | −21.7310 | −0.800471 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.5563 | −1.08725 | −0.543624 | − | 0.839329i | \(-0.682948\pi\) | ||||
−0.543624 | + | 0.839329i | \(0.682948\pi\) | |||||||
\(740\) | 16.4475 | 0.604624 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.0536 | −1.06587 | −0.532936 | − | 0.846156i | \(-0.678911\pi\) | ||||
−0.532936 | + | 0.846156i | \(0.678911\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.4142 | −0.418184 | ||||||||
\(746\) | 31.8137 | 1.16478 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.4142 | 0.417345 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.1005 | −0.441554 | −0.220777 | − | 0.975324i | \(-0.570859\pi\) | ||||
−0.220777 | + | 0.975324i | \(0.570859\pi\) | |||||||
\(752\) | 31.9630 | 1.16557 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −120.569 | −4.39085 | ||||||||
\(755\) | −8.91380 | −0.324406 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.65685 | −0.350984 | −0.175492 | − | 0.984481i | \(-0.556152\pi\) | ||||
−0.175492 | + | 0.984481i | \(0.556152\pi\) | |||||||
\(758\) | −37.6069 | −1.36594 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.07107 | 0.292768 | ||||||||
\(761\) | 17.3178 | 0.627770 | 0.313885 | − | 0.949461i | \(-0.398369\pi\) | ||||
0.313885 | + | 0.949461i | \(0.398369\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.30301 | 0.228035 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.4142 | 0.412412 | ||||||||
\(767\) | −20.2891 | −0.732596 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.9706 | 0.395609 | 0.197804 | − | 0.980242i | \(-0.436619\pi\) | ||||
0.197804 | + | 0.980242i | \(0.436619\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 29.7990 | 1.07249 | ||||||||
\(773\) | 34.9961 | 1.25872 | 0.629361 | − | 0.777113i | \(-0.283317\pi\) | ||||
0.629361 | + | 0.777113i | \(0.283317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.384776 | −0.0138216 | ||||||||
\(776\) | −1.44190 | −0.0517612 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.0000 | 0.501924 | ||||||||
\(779\) | 22.3901 | 0.802208 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 56.4975 | 2.02164 | ||||||||
\(782\) | 17.6164 | 0.629963 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.18243 | −0.113586 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.34315 | 0.226109 | 0.113054 | − | 0.993589i | \(-0.463937\pi\) | ||||
0.113054 | + | 0.993589i | \(0.463937\pi\) | |||||||
\(788\) | 27.4624 | 0.978306 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −26.0416 | −0.926520 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −44.2843 | −1.57258 | ||||||||
\(794\) | 48.4724 | 1.72022 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 43.6274 | 1.54633 | ||||||||
\(797\) | 40.9386 | 1.45012 | 0.725060 | − | 0.688685i | \(-0.241812\pi\) | ||||
0.725060 | + | 0.688685i | \(0.241812\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.1127 | −0.463894 | ||||||||
\(800\) | −4.71179 | −0.166587 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23.4558 | −0.828255 | ||||||||
\(803\) | −43.8481 | −1.54736 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.42359 | 0.331932 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.95837 | −0.0688952 | ||||||||
\(809\) | 33.1937 | 1.16703 | 0.583515 | − | 0.812103i | \(-0.301677\pi\) | ||||
0.583515 | + | 0.812103i | \(0.301677\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.62742 | 0.267835 | 0.133917 | − | 0.990992i | \(-0.457244\pi\) | ||||
0.133917 | + | 0.990992i | \(0.457244\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −26.1716 | −0.917313 | ||||||||
\(815\) | −0.720950 | −0.0252538 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.2132 | 1.09201 | ||||||||
\(818\) | 10.6543 | 0.372520 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −25.7279 | −0.898458 | ||||||||
\(821\) | −5.13412 | −0.179182 | −0.0895910 | − | 0.995979i | \(-0.528556\pi\) | ||||
−0.0895910 | + | 0.995979i | \(0.528556\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.2721 | −0.880929 | −0.440465 | − | 0.897770i | \(-0.645186\pi\) | ||||
−0.440465 | + | 0.897770i | \(0.645186\pi\) | |||||||
\(824\) | 11.7358 | 0.408834 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.3418 | 0.846446 | 0.423223 | − | 0.906025i | \(-0.360899\pi\) | ||||
0.423223 | + | 0.906025i | \(0.360899\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.21320 | 0.111599 | 0.0557996 | − | 0.998442i | \(-0.482229\pi\) | ||||
0.0557996 | + | 0.998442i | \(0.482229\pi\) | |||||||
\(830\) | 3.18243 | 0.110464 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 74.4264 | 2.58027 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.3848 | −0.774657 | ||||||||
\(836\) | −40.9386 | −1.41589 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −26.0416 | −0.899593 | ||||||||
\(839\) | −3.48106 | −0.120179 | −0.0600897 | − | 0.998193i | \(-0.519139\pi\) | ||||
−0.0600897 | + | 0.998193i | \(0.519139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41.6274 | 1.43543 | ||||||||
\(842\) | −16.6587 | −0.574097 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.585786 | 0.0201636 | ||||||||
\(845\) | 70.6513 | 2.43048 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −30.4336 | −1.04509 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.51472 | 0.0519544 | ||||||||
\(851\) | −22.0915 | −0.757285 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.1716 | −1.13577 | −0.567887 | − | 0.823107i | \(-0.692239\pi\) | ||||
−0.567887 | + | 0.823107i | \(0.692239\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.72792 | −0.161597 | ||||||||
\(857\) | 34.0640 | 1.16360 | 0.581802 | − | 0.813331i | \(-0.302348\pi\) | ||||
0.581802 | + | 0.813331i | \(0.302348\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.7279 | 1.08254 | 0.541271 | − | 0.840848i | \(-0.317943\pi\) | ||||
0.541271 | + | 0.840848i | \(0.317943\pi\) | |||||||
\(860\) | −35.8664 | −1.22303 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.313708 | 0.0106850 | ||||||||
\(863\) | −33.7035 | −1.14728 | −0.573640 | − | 0.819107i | \(-0.694469\pi\) | ||||
−0.573640 | + | 0.819107i | \(0.694469\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.4853 | −1.13853 | ||||||||
\(866\) | −18.8472 | −0.640453 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.6631 | 0.768793 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.6274 | 1.30884 | ||||||||
\(872\) | 7.53375 | 0.255125 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −63.1838 | −2.13722 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.8284 | −0.905932 | −0.452966 | − | 0.891528i | \(-0.649634\pi\) | ||||
−0.452966 | + | 0.891528i | \(0.649634\pi\) | |||||||
\(878\) | −41.5977 | −1.40386 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −24.2132 | −0.816227 | ||||||||
\(881\) | 9.69660 | 0.326687 | 0.163343 | − | 0.986569i | \(-0.447772\pi\) | ||||
0.163343 | + | 0.986569i | \(0.447772\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.6274 | −1.50183 | −0.750916 | − | 0.660398i | \(-0.770388\pi\) | ||||
−0.750916 | + | 0.660398i | \(0.770388\pi\) | |||||||
\(884\) | −20.2891 | −0.682396 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.2132 | 0.813458 | ||||||||
\(887\) | 48.6835 | 1.63463 | 0.817317 | − | 0.576189i | \(-0.195461\pi\) | ||||
0.817317 | + | 0.576189i | \(0.195461\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.659102 | −0.0220932 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −28.3137 | −0.948013 | ||||||||
\(893\) | 47.0305 | 1.57382 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.4142 | 0.849503 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 52.5269 | 1.75285 | ||||||||
\(899\) | −5.52021 | −0.184109 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.4853 | 0.415945 | ||||||||
\(902\) | 40.9386 | 1.36311 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.27208 | −0.308385 | ||||||||
\(905\) | −50.2129 | −1.66913 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.2721 | 0.839146 | 0.419573 | − | 0.907722i | \(-0.362180\pi\) | ||||
0.419573 | + | 0.907722i | \(0.362180\pi\) | |||||||
\(908\) | −11.3753 | −0.377502 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.9534 | −1.72129 | −0.860647 | − | 0.509202i | \(-0.829941\pi\) | ||||
−0.860647 | + | 0.509202i | \(0.829941\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.76955 | −0.0916588 | ||||||||
\(914\) | 29.3522 | 0.970884 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −44.6274 | −1.47453 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.8284 | −0.621093 | −0.310546 | − | 0.950558i | \(-0.600512\pi\) | ||||
−0.310546 | + | 0.950558i | \(0.600512\pi\) | |||||||
\(920\) | 12.4567 | 0.410685 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −43.8284 | −1.44341 | ||||||||
\(923\) | −100.426 | −3.30556 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.89949 | −0.0624550 | ||||||||
\(926\) | 16.5969 | 0.545407 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −67.5980 | −2.21901 | ||||||||
\(929\) | 11.0767 | 0.363413 | 0.181707 | − | 0.983353i | \(-0.441838\pi\) | ||||
0.181707 | + | 0.983353i | \(0.441838\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −19.7793 | −0.647892 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27.5563 | 0.901671 | ||||||||
\(935\) | 9.93338 | 0.324856 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −59.2548 | −1.93577 | −0.967886 | − | 0.251391i | \(-0.919112\pi\) | ||||
−0.967886 | + | 0.251391i | \(0.919112\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −54.0416 | −1.76264 | ||||||||
\(941\) | 29.0536 | 0.947119 | 0.473560 | − | 0.880762i | \(-0.342969\pi\) | ||||
0.473560 | + | 0.880762i | \(0.342969\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.5563 | 1.12531 | ||||||||
\(944\) | −8.91380 | −0.290120 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 57.0711 | 1.85554 | ||||||||
\(947\) | −31.3039 | −1.01724 | −0.508620 | − | 0.860991i | \(-0.669844\pi\) | ||||
−0.508620 | + | 0.860991i | \(0.669844\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 77.9411 | 2.53008 | ||||||||
\(950\) | −5.43275 | −0.176262 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.2795 | 1.30478 | 0.652391 | − | 0.757883i | \(-0.273766\pi\) | ||||
0.652391 | + | 0.757883i | \(0.273766\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.48528 | 0.177500 | ||||||||
\(956\) | −7.17327 | −0.232000 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −57.2548 | −1.84982 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5685 | −0.986082 | ||||||||
\(962\) | 46.5207 | 1.49989 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.75736 | −0.0566007 | ||||||||
\(965\) | 25.9330 | 0.834812 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.89949 | 0.0610836 | 0.0305418 | − | 0.999533i | \(-0.490277\pi\) | ||||
0.0305418 | + | 0.999533i | \(0.490277\pi\) | |||||||
\(968\) | −3.26989 | −0.105098 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.31371 | −0.234829 | ||||||||
\(971\) | 24.4911 | 0.785956 | 0.392978 | − | 0.919548i | \(-0.371445\pi\) | ||||
0.392978 | + | 0.919548i | \(0.371445\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −74.4054 | −2.38410 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −19.4558 | −0.622766 | ||||||||
\(977\) | 53.9051 | 1.72458 | 0.862289 | − | 0.506417i | \(-0.169030\pi\) | ||||
0.862289 | + | 0.506417i | \(0.169030\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.573593 | 0.0183321 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 48.1127 | 1.53534 | ||||||||
\(983\) | −15.5773 | −0.496838 | −0.248419 | − | 0.968653i | \(-0.579911\pi\) | ||||
−0.248419 | + | 0.968653i | \(0.579911\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.8995 | 0.761501 | ||||||||
\(986\) | 21.7310 | 0.692055 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 72.7696 | 2.31511 | ||||||||
\(989\) | 48.1738 | 1.53184 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.9706 | 0.856748 | 0.428374 | − | 0.903601i | \(-0.359087\pi\) | ||||
0.428374 | + | 0.903601i | \(0.359087\pi\) | |||||||
\(992\) | 5.28343 | 0.167749 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 37.9674 | 1.20365 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52.8701 | −1.67441 | −0.837206 | − | 0.546888i | \(-0.815812\pi\) | ||||
−0.837206 | + | 0.546888i | \(0.815812\pi\) | |||||||
\(998\) | 21.9421 | 0.694566 | ||||||||
\(999\) | 0 | 0 |
(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 | 1323.2.a.bc.1.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 1323.2.a.bc.1.4 | yes | 4 | |
7.6 | odd | 2 | 1323.2.a.bd.1.1 | yes | 4 | ||
21.20 | even | 2 | 1323.2.a.bd.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1323.2.a.bc.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1323.2.a.bc.1.4 | yes | 4 | 3.2 | odd | 2 | inner | |
1323.2.a.bd.1.1 | yes | 4 | 7.6 | odd | 2 | ||
1323.2.a.bd.1.4 | yes | 4 | 21.20 | even | 2 |