Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 23x^{6} - 3x^{5} + 163x^{4} + 13x^{3} - 418x^{2} + 4x + 269 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(3.72373\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.72373 | 1.66530 | 0.832652 | − | 0.553797i | \(-0.186822\pi\) | ||||
0.832652 | + | 0.553797i | \(0.186822\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.07650 | −0.406878 | −0.203439 | − | 0.979088i | \(-0.565212\pi\) | ||||
−0.203439 | + | 0.979088i | \(0.565212\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.31859 | −1.00059 | −0.500296 | − | 0.865854i | \(-0.666776\pi\) | ||||
−0.500296 | + | 0.865854i | \(0.666776\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.84649 | −1.89888 | −0.949438 | − | 0.313956i | \(-0.898346\pi\) | ||||
−0.949438 | + | 0.313956i | \(0.898346\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.72373 | −0.961464 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.33263 | 1.05082 | 0.525409 | − | 0.850850i | \(-0.323912\pi\) | ||||
0.525409 | + | 0.850850i | \(0.323912\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.23962 | −0.513804 | −0.256902 | − | 0.966437i | \(-0.582702\pi\) | ||||
−0.256902 | + | 0.966437i | \(0.582702\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.07650 | 0.234911 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.07650 | 0.432980 | 0.216490 | − | 0.976285i | \(-0.430539\pi\) | ||||
0.216490 | + | 0.976285i | \(0.430539\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.86618 | 1.77324 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.1256 | 1.88028 | 0.940140 | − | 0.340788i | \(-0.110694\pi\) | ||||
0.940140 | + | 0.340788i | \(0.110694\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.37662 | −1.32488 | −0.662440 | − | 0.749115i | \(-0.730479\pi\) | ||||
−0.662440 | + | 0.749115i | \(0.730479\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.31859 | 0.577692 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.00859 | −0.677575 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.893756 | 0.146933 | 0.0734663 | − | 0.997298i | \(-0.476594\pi\) | ||||
0.0734663 | + | 0.997298i | \(0.476594\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.84649 | 1.09632 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.72354 | −0.893867 | −0.446933 | − | 0.894567i | \(-0.647484\pi\) | ||||
−0.446933 | + | 0.894567i | \(0.647484\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.02378 | −1.07112 | −0.535558 | − | 0.844499i | \(-0.679899\pi\) | ||||
−0.535558 | + | 0.844499i | \(0.679899\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.72373 | 0.555101 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.79152 | 0.261321 | 0.130660 | − | 0.991427i | \(-0.458290\pi\) | ||||
0.130660 | + | 0.991427i | \(0.458290\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.84115 | −0.834451 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.33263 | −0.606690 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.33087 | −1.00697 | −0.503486 | − | 0.864003i | \(-0.667950\pi\) | ||||
−0.503486 | + | 0.864003i | \(0.667950\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.3575 | −1.66629 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.23962 | 0.296645 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.1545 | 1.58238 | 0.791190 | − | 0.611571i | \(-0.209462\pi\) | ||||
0.791190 | + | 0.611571i | \(0.209462\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.00262 | −1.02463 | −0.512316 | − | 0.858797i | \(-0.671212\pi\) | ||||
−0.512316 | + | 0.858797i | \(0.671212\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.07650 | −0.135626 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −25.4945 | −3.16220 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.37654 | −0.168171 | −0.0840855 | − | 0.996459i | \(-0.526797\pi\) | ||||
−0.0840855 | + | 0.996459i | \(0.526797\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.07650 | −0.249981 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.4875 | −1.71935 | −0.859674 | − | 0.510842i | \(-0.829334\pi\) | ||||
−0.859674 | + | 0.510842i | \(0.829334\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.17841 | −0.606087 | −0.303044 | − | 0.952977i | \(-0.598003\pi\) | ||||
−0.303044 | + | 0.952977i | \(0.598003\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.86618 | −1.02378 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.57245 | 0.407119 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.03811 | −0.454323 | −0.227162 | − | 0.973857i | \(-0.572945\pi\) | ||||
−0.227162 | + | 0.973857i | \(0.572945\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.67767 | 0.842734 | 0.421367 | − | 0.906890i | \(-0.361550\pi\) | ||||
0.421367 | + | 0.906890i | \(0.361550\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.1336 | 1.74993 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.1256 | −1.08558 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.68508 | −0.708617 | −0.354309 | − | 0.935129i | \(-0.615284\pi\) | ||||
−0.354309 | + | 0.935129i | \(0.615284\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.37023 | 0.772610 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.37662 | 0.764920 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.33975 | −0.855640 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.78308 | −0.485648 | −0.242824 | − | 0.970070i | \(-0.578074\pi\) | ||||
−0.242824 | + | 0.970070i | \(0.578074\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.31859 | −0.333531 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.22209 | −0.420113 | −0.210057 | − | 0.977689i | \(-0.567365\pi\) | ||||
−0.210057 | + | 0.977689i | \(0.567365\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.2482 | −1.69951 | −0.849757 | − | 0.527174i | \(-0.823251\pi\) | ||||
−0.849757 | + | 0.527174i | \(0.823251\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.00859 | 0.391198 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.6131 | 1.41270 | 0.706351 | − | 0.707862i | \(-0.250340\pi\) | ||||
0.706351 | + | 0.707862i | \(0.250340\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.61554 | 0.921001 | 0.460501 | − | 0.887659i | \(-0.347670\pi\) | ||||
0.460501 | + | 0.887659i | \(0.347670\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.893756 | −0.0848316 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.5985 | 0.997023 | 0.498512 | − | 0.866883i | \(-0.333880\pi\) | ||||
0.498512 | + | 0.866883i | \(0.333880\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.73232 | 0.721042 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.84649 | −0.632958 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.66407 | −0.427554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.0130376 | 0.00118524 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.72354 | 0.516074 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 14.3966 | 1.28767 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.6534 | −1.56649 | −0.783243 | − | 0.621716i | \(-0.786436\pi\) | ||||
−0.783243 | + | 0.621716i | \(0.786436\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.02378 | 0.618409 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.2497 | −1.07026 | −0.535131 | − | 0.844769i | \(-0.679738\pi\) | ||||
−0.535131 | + | 0.844769i | \(0.679738\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.41095 | 0.209055 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.72373 | −0.320488 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.3635 | −0.970852 | −0.485426 | − | 0.874278i | \(-0.661336\pi\) | ||||
−0.485426 | + | 0.874278i | \(0.661336\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.1918 | −1.62783 | −0.813914 | − | 0.580986i | \(-0.802667\pi\) | ||||
−0.813914 | + | 0.580986i | \(0.802667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.79152 | −0.150874 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.7207 | 1.90000 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 37.7051 | 3.13124 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.84115 | 0.481770 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.7242 | 1.12433 | 0.562164 | − | 0.827026i | \(-0.309969\pi\) | ||||
0.562164 | + | 0.827026i | \(0.309969\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.7082 | 0.952796 | 0.476398 | − | 0.879230i | \(-0.341942\pi\) | ||||
0.476398 | + | 0.879230i | \(0.341942\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.33263 | 0.350273 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −27.4686 | −2.20633 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.98584 | −0.158487 | −0.0792437 | − | 0.996855i | \(-0.525251\pi\) | ||||
−0.0792437 | + | 0.996855i | \(0.525251\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.33087 | 0.581376 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.23534 | −0.176170 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.14810 | −0.168252 | −0.0841260 | − | 0.996455i | \(-0.526810\pi\) | ||||
−0.0841260 | + | 0.996455i | \(0.526810\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.3575 | 0.962033 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.8745 | 2.60573 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.23962 | −0.171268 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.8343 | 1.20386 | 0.601928 | − | 0.798550i | \(-0.294399\pi\) | ||||
0.601928 | + | 0.798550i | \(0.294399\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.54442 | −0.721490 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.1545 | −0.913587 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.27008 | 0.618134 | 0.309067 | − | 0.951040i | \(-0.399983\pi\) | ||||
0.309067 | + | 0.951040i | \(0.399983\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.4376 | −1.89076 | −0.945381 | − | 0.325968i | \(-0.894310\pi\) | ||||
−0.945381 | + | 0.325968i | \(0.894310\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00262 | 0.591571 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.32811 | 0.244687 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.3782 | −1.05144 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.07650 | 0.0783036 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.07812 | 0.295082 | 0.147541 | − | 0.989056i | \(-0.452864\pi\) | ||||
0.147541 | + | 0.989056i | \(0.452864\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.24661 | −0.377659 | −0.188830 | − | 0.982010i | \(-0.560469\pi\) | ||||
−0.188830 | + | 0.982010i | \(0.560469\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 25.4945 | 1.82570 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.2812 | −1.72997 | −0.864983 | − | 0.501801i | \(-0.832671\pi\) | ||||
−0.864983 | + | 0.501801i | \(0.832671\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.8287 | 1.47651 | 0.738254 | − | 0.674523i | \(-0.235651\pi\) | ||||
0.738254 | + | 0.674523i | \(0.235651\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.37654 | 0.0970936 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.9002 | −0.765044 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.3129 | −1.48856 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.07650 | 0.144327 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.43238 | 0.514109 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.7819 | 1.22415 | 0.612077 | − | 0.790798i | \(-0.290334\pi\) | ||||
0.612077 | + | 0.790798i | \(0.290334\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.4875 | 0.992666 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −26.1547 | −1.78373 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.94091 | 0.539064 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.17841 | 0.349925 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −29.6634 | −1.99537 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.3349 | −1.02690 | −0.513451 | − | 0.858119i | \(-0.671633\pi\) | ||||
−0.513451 | + | 0.858119i | \(0.671633\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.86618 | 0.591079 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.1663 | −1.13937 | −0.569685 | − | 0.821863i | \(-0.692935\pi\) | ||||
−0.569685 | + | 0.821863i | \(0.692935\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.93152 | −0.590211 | −0.295106 | − | 0.955465i | \(-0.595355\pi\) | ||||
−0.295106 | + | 0.955465i | \(0.595355\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.57245 | −0.235050 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.8436 | −0.710390 | −0.355195 | − | 0.934792i | \(-0.615586\pi\) | ||||
−0.355195 | + | 0.934792i | \(0.615586\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.67116 | 0.435178 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.03811 | 0.262304 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.91518 | −0.123883 | −0.0619414 | − | 0.998080i | \(-0.519729\pi\) | ||||
−0.0619414 | + | 0.998080i | \(0.519729\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.61168 | 0.232649 | 0.116325 | − | 0.993211i | \(-0.462889\pi\) | ||||
0.116325 | + | 0.993211i | \(0.462889\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −21.7509 | −1.38961 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.3335 | 0.975650 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.67767 | −0.486553 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.6131 | −0.922368 | −0.461184 | − | 0.887304i | \(-0.652575\pi\) | ||||
−0.461184 | + | 0.887304i | \(0.652575\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.89104 | −0.433236 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.1336 | −1.01032 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.65220 | −0.539709 | −0.269855 | − | 0.962901i | \(-0.586976\pi\) | ||||
−0.269855 | + | 0.962901i | \(0.586976\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.962126 | −0.0597836 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.1256 | 0.626760 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.59793 | 0.345183 | 0.172592 | − | 0.984993i | \(-0.444786\pi\) | ||||
0.172592 | + | 0.984993i | \(0.444786\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −27.2982 | −1.67692 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.68508 | 0.409120 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.3299 | 1.23953 | 0.619767 | − | 0.784786i | \(-0.287227\pi\) | ||||
0.619767 | + | 0.784786i | \(0.287227\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.7500 | −1.13898 | −0.569490 | − | 0.821998i | \(-0.692859\pi\) | ||||
−0.569490 | + | 0.821998i | \(0.692859\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.37023 | −0.446067 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −29.4232 | −1.77429 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.65272 | −0.219471 | −0.109735 | − | 0.993961i | \(-0.535000\pi\) | ||||
−0.109735 | + | 0.993961i | \(0.535000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.37662 | −0.441627 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.4647 | −0.803236 | −0.401618 | − | 0.915807i | \(-0.631552\pi\) | ||||
−0.401618 | + | 0.915807i | \(0.631552\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.8397 | −1.59546 | −0.797728 | − | 0.603018i | \(-0.793965\pi\) | ||||
−0.797728 | + | 0.603018i | \(0.793965\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.33975 | 0.494004 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.16137 | 0.363694 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.77172 | 0.104219 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.78308 | 0.280389 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.19272 | 0.186521 | 0.0932605 | − | 0.995642i | \(-0.470271\pi\) | ||||
0.0932605 | + | 0.995642i | \(0.470271\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 45.2601 | 2.63514 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.31859 | 0.192564 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.2167 | −0.822174 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.56107 | 0.435813 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.22209 | 0.242553 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −29.7996 | −1.70632 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.9132 | 1.25065 | 0.625327 | − | 0.780363i | \(-0.284966\pi\) | ||||
0.625327 | + | 0.780363i | \(0.284966\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.2482 | 0.981215 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.7314 | 1.74261 | 0.871307 | − | 0.490737i | \(-0.163273\pi\) | ||||
0.871307 | + | 0.490737i | \(0.163273\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.8911 | −1.40693 | −0.703465 | − | 0.710730i | \(-0.748365\pi\) | ||||
−0.703465 | + | 0.710730i | \(0.748365\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.00859 | −0.225858 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.2167 | 1.36014 | 0.680072 | − | 0.733145i | \(-0.261949\pi\) | ||||
0.680072 | + | 0.733145i | \(0.261949\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −33.6028 | −1.88139 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.6131 | −0.815624 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.70346 | −0.539915 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −60.7023 | −3.36716 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.61554 | −0.531740 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.92857 | −0.106326 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.7698 | 0.591963 | 0.295982 | − | 0.955194i | \(-0.404353\pi\) | ||||
0.295982 | + | 0.955194i | \(0.404353\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.893756 | 0.0489775 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.12587 | −0.280056 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.4935 | 1.60661 | 0.803307 | − | 0.595565i | \(-0.203072\pi\) | ||||
0.803307 | + | 0.595565i | \(0.203072\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.5985 | −0.575632 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.4800 | 1.32567 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.8235 | 0.746397 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.73232 | −0.416294 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.56950 | −0.0842551 | −0.0421276 | − | 0.999112i | \(-0.513414\pi\) | ||||
−0.0421276 | + | 0.999112i | \(0.513414\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.6944 | 1.10775 | 0.553873 | − | 0.832601i | \(-0.313149\pi\) | ||||
0.553873 | + | 0.832601i | \(0.313149\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.84649 | 0.365439 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.4233 | −1.19347 | −0.596735 | − | 0.802438i | \(-0.703536\pi\) | ||||
−0.596735 | + | 0.802438i | \(0.703536\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −53.9475 | −2.86324 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.66407 | 0.246849 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.85741 | −0.150808 | −0.0754041 | − | 0.997153i | \(-0.524025\pi\) | ||||
−0.0754041 | + | 0.997153i | \(0.524025\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.9841 | −0.736005 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.0130376 | −0.000684298 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.2830 | −1.00932 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.46660 | −0.128756 | −0.0643778 | − | 0.997926i | \(-0.520506\pi\) | ||||
−0.0643778 | + | 0.997926i | \(0.520506\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.72354 | −0.297956 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.89166 | 0.409715 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.4922 | −1.37171 | −0.685856 | − | 0.727737i | \(-0.740572\pi\) | ||||
−0.685856 | + | 0.727737i | \(0.740572\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.3966 | −0.743439 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −69.3250 | −3.57042 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.1738 | 1.34446 | 0.672228 | − | 0.740344i | \(-0.265337\pi\) | ||||
0.672228 | + | 0.740344i | \(0.265337\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.6534 | 0.904411 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.37212 | −0.478893 | −0.239446 | − | 0.970910i | \(-0.576966\pi\) | ||||
−0.239446 | + | 0.970910i | \(0.576966\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.3029 | 0.677976 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.02378 | −0.357039 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.1111 | 0.867566 | 0.433783 | − | 0.901017i | \(-0.357179\pi\) | ||||
0.433783 | + | 0.901017i | \(0.357179\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.99670 | 0.454983 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.2497 | 0.617916 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.0369 | −0.756586 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.12053 | 0.0562379 | 0.0281190 | − | 0.999605i | \(-0.491048\pi\) | ||||
0.0281190 | + | 0.999605i | \(0.491048\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.41095 | −0.120698 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.4021 | 1.56815 | 0.784073 | − | 0.620668i | \(-0.213139\pi\) | ||||
0.784073 | + | 0.620668i | \(0.213139\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 50.5040 | 2.51578 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.72373 | 0.185034 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.96601 | −0.147020 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.16731 | 0.255507 | 0.127754 | − | 0.991806i | \(-0.459223\pi\) | ||||
0.127754 | + | 0.991806i | \(0.459223\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.3635 | 0.560522 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.0843 | −0.643835 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.5896 | 1.40341 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.1918 | 0.939826 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.5702 | −1.24919 | −0.624593 | − | 0.780951i | \(-0.714735\pi\) | ||||
−0.624593 | + | 0.780951i | \(0.714735\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.3730 | 1.33408 | 0.667039 | − | 0.745023i | \(-0.267561\pi\) | ||||
0.667039 | + | 0.745023i | \(0.267561\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.79152 | 0.0871069 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 38.4139 | 1.86335 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.61480 | 0.416899 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −22.7207 | −1.09697 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.71846 | −0.130944 | −0.0654718 | − | 0.997854i | \(-0.520855\pi\) | ||||
−0.0654718 | + | 0.997854i | \(0.520855\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.1078 | 1.73523 | 0.867615 | − | 0.497236i | \(-0.165652\pi\) | ||||
0.867615 | + | 0.497236i | \(0.165652\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −37.7051 | −1.80782 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.65057 | −0.222467 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.10414 | −0.339062 | −0.169531 | − | 0.985525i | \(-0.554225\pi\) | ||||
−0.169531 | + | 0.985525i | \(0.554225\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.84115 | −0.278150 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.0671 | −0.478302 | −0.239151 | − | 0.970982i | \(-0.576869\pi\) | ||||
−0.239151 | + | 0.970982i | \(0.576869\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.8935 | −1.18006 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.7242 | −0.649131 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.9214 | −1.22330 | −0.611652 | − | 0.791127i | \(-0.709495\pi\) | ||||
−0.611652 | + | 0.791127i | \(0.709495\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.9941 | 0.894396 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.7082 | −0.550097 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 27.4448 | 1.28663 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.2002 | −1.08526 | −0.542629 | − | 0.839972i | \(-0.682571\pi\) | ||||
−0.542629 | + | 0.839972i | \(0.682571\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.33263 | −0.202230 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.498036 | 0.0231959 | 0.0115979 | − | 0.999933i | \(-0.496308\pi\) | ||||
0.0115979 | + | 0.999933i | \(0.496308\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.3697 | 0.481920 | 0.240960 | − | 0.970535i | \(-0.422538\pi\) | ||||
0.240960 | + | 0.970535i | \(0.422538\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 27.4686 | 1.27382 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.20405 | 0.379638 | 0.189819 | − | 0.981819i | \(-0.439210\pi\) | ||||
0.189819 | + | 0.981819i | \(0.439210\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.48184 | 0.0684250 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.98584 | 0.0915028 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.3090 | 1.07175 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.8569 | −0.911097 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.33087 | −0.335658 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.232454 | −0.0106211 | −0.00531054 | − | 0.999986i | \(-0.501690\pi\) | ||||
−0.00531054 | + | 0.999986i | \(0.501690\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.11910 | −0.279007 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.23534 | 0.101712 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.8109 | −0.808752 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.4002 | −0.697852 | −0.348926 | − | 0.937150i | \(-0.613454\pi\) | ||||
−0.348926 | + | 0.937150i | \(0.613454\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.14810 | 0.0971403 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.4386 | −0.471088 | −0.235544 | − | 0.971864i | \(-0.575687\pi\) | ||||
−0.235544 | + | 0.971864i | \(0.575687\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 43.8706 | 1.97583 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.3575 | −0.555430 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.5957 | 0.699564 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.3123 | −0.551175 | −0.275587 | − | 0.961276i | \(-0.588872\pi\) | ||||
−0.275587 | + | 0.961276i | \(0.588872\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.2914 | −0.637223 | −0.318611 | − | 0.947885i | \(-0.603216\pi\) | ||||
−0.318611 | + | 0.947885i | \(0.603216\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.7219 | −0.699616 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −33.8745 | −1.50442 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.2601 | 1.51855 | 0.759276 | − | 0.650769i | \(-0.225553\pi\) | ||||
0.759276 | + | 0.650769i | \(0.225553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.57455 | 0.246603 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.23962 | 0.0988817 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −64.2276 | −2.83021 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.94533 | −0.261475 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.8343 | −0.695047 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.5599 | −1.20742 | −0.603711 | − | 0.797204i | \(-0.706312\pi\) | ||||
−0.603711 | + | 0.797204i | \(0.706312\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.72837 | 0.119303 | 0.0596517 | − | 0.998219i | \(-0.481001\pi\) | ||||
0.0596517 | + | 0.998219i | \(0.481001\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.54442 | 0.416553 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −31.9602 | −1.39221 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.6882 | −0.812529 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.1545 | 0.527460 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 39.1862 | 1.69734 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 54.4153 | 2.35258 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.27008 | −0.356880 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.3844 | 0.834945 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.48413 | −0.149794 | −0.0748971 | − | 0.997191i | \(-0.523863\pi\) | ||||
−0.0748971 | + | 0.997191i | \(0.523863\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.4376 | 1.09163 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 35.8057 | 1.53375 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.2192 | 1.46311 | 0.731554 | − | 0.681784i | \(-0.238796\pi\) | ||||
0.731554 | + | 0.681784i | \(0.238796\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.00262 | −0.341544 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.6775 | −0.966096 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.34702 | 0.184854 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.32811 | −0.141270 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.1158 | −0.598104 | −0.299052 | − | 0.954237i | \(-0.596670\pi\) | ||||
−0.299052 | + | 0.954237i | \(0.596670\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.0882 | 2.03392 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.3782 | 0.607050 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.1826 | 1.52492 | 0.762458 | − | 0.647038i | \(-0.223992\pi\) | ||||
0.762458 | + | 0.647038i | \(0.223992\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 39.4660 | 1.66035 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.07650 | −0.0452086 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.7387 | −1.07902 | −0.539510 | − | 0.841979i | \(-0.681391\pi\) | ||||
−0.539510 | + | 0.841979i | \(0.681391\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.9185 | 1.04281 | 0.521403 | − | 0.853311i | \(-0.325409\pi\) | ||||
0.521403 | + | 0.853311i | \(0.325409\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.07812 | −0.170366 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.4106 | 0.767775 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.1844 | 1.09007 | 0.545036 | − | 0.838412i | \(-0.316516\pi\) | ||||
0.545036 | + | 0.838412i | \(0.316516\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.24661 | 0.218042 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.26499 | −0.342890 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.3282 | 1.00757 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −25.4945 | −1.05407 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 38.7805 | 1.60064 | 0.800320 | − | 0.599573i | \(-0.204663\pi\) | ||||
0.800320 | + | 0.599573i | \(0.204663\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.5208 | 0.680729 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.2812 | 0.998797 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.1868 | −1.23962 | −0.619811 | − | 0.784751i | \(-0.712791\pi\) | ||||
−0.619811 | + | 0.784751i | \(0.712791\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.3677 | −0.712008 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.8287 | −0.852462 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.46214 | 0.141459 | 0.0707296 | − | 0.997496i | \(-0.477467\pi\) | ||||
0.0707296 | + | 0.997496i | \(0.477467\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.2199 | 0.457669 | 0.228835 | − | 0.973465i | \(-0.426508\pi\) | ||||
0.228835 | + | 0.973465i | \(0.426508\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.37654 | −0.0560570 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.0485487 | 0.00197378 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.59675 | 0.348931 | 0.174466 | − | 0.984663i | \(-0.444180\pi\) | ||||
0.174466 | + | 0.984663i | \(0.444180\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.9002 | 0.441698 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.2657 | −0.496215 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.6391 | −0.995165 | −0.497582 | − | 0.867417i | \(-0.665779\pi\) | ||||
−0.497582 | + | 0.867417i | \(0.665779\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 21.3129 | 0.859420 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.9004 | 0.519352 | 0.259676 | − | 0.965696i | \(-0.416384\pi\) | ||||
0.259676 | + | 0.965696i | \(0.416384\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.6735 | −1.39364 | −0.696822 | − | 0.717244i | \(-0.745403\pi\) | ||||
−0.696822 | + | 0.717244i | \(0.745403\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.07650 | −0.0833270 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.19647 | 0.288321 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.27829 | 0.371132 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.43238 | −0.296821 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.87232 | 0.154399 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.08175 | −0.242110 | −0.121055 | − | 0.992646i | \(-0.538628\pi\) | ||||
−0.121055 | + | 0.992646i | \(0.538628\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.7819 | −0.706766 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −65.7365 | −2.60868 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 39.9914 | 1.58452 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.4875 | −0.573116 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 46.7591 | 1.84687 | 0.923437 | − | 0.383749i | \(-0.125367\pi\) | ||||
0.923437 | + | 0.383749i | \(0.125367\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.1924 | 0.954055 | 0.477027 | − | 0.878888i | \(-0.341714\pi\) | ||||
0.477027 | + | 0.878888i | \(0.341714\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 26.1547 | 1.02984 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.5727 | −1.00537 | −0.502683 | − | 0.864471i | \(-0.667654\pi\) | ||||
−0.502683 | + | 0.864471i | \(0.667654\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −40.3358 | −1.58332 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.94091 | −0.311229 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.3856 | 0.406420 | 0.203210 | − | 0.979135i | \(-0.434863\pi\) | ||||
0.203210 | + | 0.979135i | \(0.434863\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −45.6146 | −1.78231 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.17841 | −0.202029 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.3971 | 0.911420 | 0.455710 | − | 0.890128i | \(-0.349385\pi\) | ||||
0.455710 | + | 0.890128i | \(0.349385\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.3314 | 1.76319 | 0.881593 | − | 0.472010i | \(-0.156471\pi\) | ||||
0.881593 | + | 0.472010i | \(0.156471\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 29.6634 | 1.15203 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.97772 | 0.348141 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.0258 | 0.814123 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.3349 | 0.592882 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.5574 | 1.02524 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.6651 | −0.873676 | −0.436838 | − | 0.899540i | \(-0.643902\pi\) | ||||
−0.436838 | + | 0.899540i | \(0.643902\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.86618 | −0.341260 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.4358 | −1.24661 | −0.623305 | − | 0.781979i | \(-0.714210\pi\) | ||||
−0.623305 | + | 0.781979i | \(0.714210\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.14897 | 0.197599 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.1663 | 0.657816 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.10805 | 0.310246 | 0.155123 | − | 0.987895i | \(-0.450423\pi\) | ||||
0.155123 | + | 0.987895i | \(0.450423\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −42.3148 | −1.61676 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.93152 | 0.340759 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 50.1908 | 1.91212 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.826869 | −0.0314556 | −0.0157278 | − | 0.999876i | \(-0.505007\pi\) | ||||
−0.0157278 | + | 0.999876i | \(0.505007\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.57245 | 0.135706 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −71.4651 | −2.71083 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.7980 | −0.939291 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.8436 | 0.410144 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.8174 | −1.16396 | −0.581979 | − | 0.813204i | \(-0.697721\pi\) | ||||
−0.581979 | + | 0.813204i | \(0.697721\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.00168 | −0.0754946 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.67116 | −0.251250 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.54506 | 0.170935 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.2855 | 0.386281 | 0.193140 | − | 0.981171i | \(-0.438133\pi\) | ||||
0.193140 | + | 0.981171i | \(0.438133\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.03811 | −0.151441 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.3175 | −0.573646 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 84.6058 | 3.16408 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.91518 | 0.0715238 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.3383 | −0.646610 | −0.323305 | − | 0.946295i | \(-0.604794\pi\) | ||||
−0.323305 | + | 0.946295i | \(0.604794\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.5676 | 0.691494 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.61168 | −0.134320 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 89.7756 | 3.33418 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.69224 | −0.211114 | −0.105557 | − | 0.994413i | \(-0.533662\pi\) | ||||
−0.105557 | + | 0.994413i | \(0.533662\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.4315 | −1.12555 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.4431 | −0.644274 | −0.322137 | − | 0.946693i | \(-0.604401\pi\) | ||||
−0.322137 | + | 0.946693i | \(0.604401\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.7509 | 0.802294 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.56817 | 0.168271 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.8704 | −0.767731 | −0.383865 | − | 0.923389i | \(-0.625407\pi\) | ||||
−0.383865 | + | 0.923389i | \(0.625407\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.3335 | −0.563292 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.5948 | −1.08573 | −0.542863 | − | 0.839821i | \(-0.682660\pi\) | ||||
−0.542863 | + | 0.839821i | \(0.682660\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 51.1051 | 1.87235 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.67767 | 0.280911 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.7310 | −0.574797 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.6241 | 1.22696 | 0.613480 | − | 0.789710i | \(-0.289769\pi\) | ||||
0.613480 | + | 0.789710i | \(0.289769\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.6131 | 0.532530 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 43.5980 | 1.58669 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.8076 | −1.22876 | −0.614379 | − | 0.789011i | \(-0.710593\pi\) | ||||
−0.614379 | + | 0.789011i | \(0.710593\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.89104 | 0.250129 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.970756 | −0.0351899 | −0.0175949 | − | 0.999845i | \(-0.505601\pi\) | ||||
−0.0175949 | + | 0.999845i | \(0.505601\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.3511 | −0.374735 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.1336 | 0.583311 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −83.2156 | −3.00474 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.1942 | 1.48550 | 0.742750 | − | 0.669569i | \(-0.233521\pi\) | ||||
0.742750 | + | 0.669569i | \(0.233521\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.65220 | 0.311601 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.7343 | −1.17737 | −0.588686 | − | 0.808362i | \(-0.700355\pi\) | ||||
−0.588686 | + | 0.808362i | \(0.700355\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −65.4025 | −2.34933 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.962126 | 0.0345161 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.8186 | 0.459273 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 48.0780 | 1.72037 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.1256 | −0.361860 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.39474 | −0.263930 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.4249 | 0.371607 | 0.185803 | − | 0.982587i | \(-0.440511\pi\) | ||||
0.185803 | + | 0.982587i | \(0.440511\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.59793 | −0.199292 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.4093 | −0.405666 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54.7899 | 1.94565 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 27.2982 | 0.968167 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.2016 | 1.53028 | 0.765139 | − | 0.643865i | \(-0.222670\pi\) | ||||
0.765139 | + | 0.643865i | \(0.222670\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.76202 | 0.274601 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.68508 | −0.236206 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.1850 | 0.606446 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.32382 | −0.293376 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.3299 | −0.715645 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.53425 | 0.335206 | 0.167603 | − | 0.985855i | \(-0.446397\pi\) | ||||
0.167603 | + | 0.985855i | \(0.446397\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.0876 | −0.775601 | −0.387800 | − | 0.921743i | \(-0.626765\pi\) | ||||
−0.387800 | + | 0.921743i | \(0.626765\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.7500 | 0.657591 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.99894 | −0.280191 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.7306 | 0.550344 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.37023 | 0.257537 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.7235 | −1.24676 | −0.623379 | − | 0.781920i | \(-0.714241\pi\) | ||||
−0.623379 | + | 0.781920i | \(0.714241\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.9617 | 1.00954 | 0.504770 | − | 0.863254i | \(-0.331577\pi\) | ||||
0.504770 | + | 0.863254i | \(0.331577\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 29.4232 | 1.02439 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.1646 | 1.46621 | 0.733103 | − | 0.680117i | \(-0.238071\pi\) | ||||
0.733103 | + | 0.680117i | \(0.238071\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.4477 | 0.883835 | 0.441918 | − | 0.897056i | \(-0.354298\pi\) | ||||
0.441918 | + | 0.897056i | \(0.354298\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.65272 | 0.126711 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.3076 | −0.876856 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.72373 | 0.128865 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.37662 | 0.254973 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.50905 | −0.190194 | −0.0950968 | − | 0.995468i | \(-0.530316\pi\) | ||||
−0.0950968 | + | 0.995468i | \(0.530316\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 73.5281 | 2.53545 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.4647 | 0.463749 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 126.139 | 4.33933 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.0140350 | −0.000482247 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.8397 | 0.921137 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.85588 | 0.0636188 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −53.7777 | −1.84131 | −0.920657 | − | 0.390373i | \(-0.872346\pi\) | ||||
−0.920657 | + | 0.390373i | \(0.872346\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.33975 | −0.285213 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −53.2240 | −1.81810 | −0.909048 | − | 0.416691i | \(-0.863190\pi\) | ||||
−0.909048 | + | 0.416691i | \(0.863190\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.3910 | 1.20753 | 0.603763 | − | 0.797164i | \(-0.293667\pi\) | ||||
0.603763 | + | 0.797164i | \(0.293667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.16137 | −0.209979 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.8390 | 1.01573 | 0.507866 | − | 0.861436i | \(-0.330435\pi\) | ||||
0.507866 | + | 0.861436i | \(0.330435\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 58.9625 | 2.00479 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.77172 | −0.0601708 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.4008 | 0.454592 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.42447 | 0.319336 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.78308 | −0.161883 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.4979 | −0.523926 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.7015 | −1.30686 | −0.653428 | − | 0.756989i | \(-0.726670\pi\) | ||||
−0.653428 | + | 0.756989i | \(0.726670\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.19272 | −0.107688 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.1289 | 0.644470 | 0.322235 | − | 0.946660i | \(-0.395566\pi\) | ||||
0.322235 | + | 0.946660i | \(0.395566\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.4516 | −0.486334 | −0.243167 | − | 0.969984i | \(-0.578186\pi\) | ||||
−0.243167 | + | 0.969984i | \(0.578186\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −45.2601 | −1.52140 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.9764 | 0.435705 | 0.217852 | − | 0.975982i | \(-0.430095\pi\) | ||||
0.217852 | + | 0.975982i | \(0.430095\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.0038 | 0.637368 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.31859 | −0.111177 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.01234 | −0.134268 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.7955 | 1.02938 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.2167 | 0.474682 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −74.6929 | −2.49115 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.7620 | −1.05815 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.56107 | −0.251617 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −94.7228 | −3.14869 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.1886 | 1.06881 | 0.534403 | − | 0.845230i | \(-0.320537\pi\) | ||||
0.534403 | + | 0.845230i | \(0.320537\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.22209 | −0.140038 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.7360 | 1.54843 | 0.774216 | − | 0.632921i | \(-0.218144\pi\) | ||||
0.774216 | + | 0.632921i | \(0.218144\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.4790 | −0.843233 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 29.7996 | 0.985145 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.1868 | 0.435466 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.4584 | 1.00473 | 0.502366 | − | 0.864655i | \(-0.332463\pi\) | ||||
0.502366 | + | 0.864655i | \(0.332463\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.9132 | −0.722065 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 99.1885 | 3.26483 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.92421 | 0.260546 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.2482 | −0.566505 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37.9586 | 1.24538 | 0.622691 | − | 0.782468i | \(-0.286040\pi\) | ||||
0.622691 | + | 0.782468i | \(0.286040\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.0820 | 0.428744 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30.7314 | −1.00610 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −53.5407 | −1.75097 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.36515 | 0.175272 | 0.0876359 | − | 0.996153i | \(-0.472069\pi\) | ||||
0.0876359 | + | 0.996153i | \(0.472069\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.8911 | 0.812291 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.3068 | 1.02057 | 0.510287 | − | 0.860004i | \(-0.329539\pi\) | ||||
0.510287 | + | 0.860004i | \(0.329539\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.8849 | −0.387026 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.00859 | 0.130399 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.4932 | 1.31585 | 0.657926 | − | 0.753082i | \(-0.271434\pi\) | ||||
0.657926 | + | 0.753082i | \(0.271434\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35.4540 | 1.15088 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.2167 | −0.785279 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.3095 | −0.625497 | −0.312749 | − | 0.949836i | \(-0.601250\pi\) | ||||
−0.312749 | + | 0.949836i | \(0.601250\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.1858 | 0.491402 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 33.6028 | 1.08622 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.2328 | 0.395018 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.4146 | 0.755309 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.6131 | 0.470901 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.5370 | −0.628917 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.40023 | 0.109344 | 0.0546720 | − | 0.998504i | \(-0.482589\pi\) | ||||
0.0546720 | + | 0.998504i | \(0.482589\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.70346 | 0.311720 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.2669 | 0.329482 | 0.164741 | − | 0.986337i | \(-0.447321\pi\) | ||||
0.164741 | + | 0.986337i | \(0.447321\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.6599 | 0.662326 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 60.7023 | 1.94403 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.0482 | 1.15328 | 0.576642 | − | 0.816997i | \(-0.304363\pi\) | ||||
0.576642 | + | 0.816997i | \(0.304363\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.1850 | 0.709037 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.61554 | 0.307000 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.83948 | −0.186250 | −0.0931252 | − | 0.995654i | \(-0.529686\pi\) | ||||
−0.0931252 | + | 0.995654i | \(0.529686\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −90.4168 | −2.88092 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.92857 | 0.0613871 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.5848 | −0.463771 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.3983 | −1.79155 | −0.895775 | − | 0.444508i | \(-0.853379\pi\) | ||||
−0.895775 | + | 0.444508i | \(0.853379\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.7698 | −0.341770 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 77.5606 | 2.45883 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.8505 | −1.04039 | −0.520194 | − | 0.854048i | \(-0.674140\pi\) | ||||
−0.520194 | + | 0.854048i | \(0.674140\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.893756 | −0.0282772 |
(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 | 4008.2.a.h.1.8 | ✓ | 8 | |
4.3 | odd | 2 | 8016.2.a.y.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.h.1.8 | ✓ | 8 | 1.1 | even | 1 | trivial | |
8016.2.a.y.1.8 | 8 | 4.3 | odd | 2 |