Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.44 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | 2.79702 | 1.61486 | 0.807431 | − | 0.589962i | \(-0.200857\pi\) | ||||
0.807431 | + | 0.589962i | \(0.200857\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.61938 | −1.17142 | −0.585712 | − | 0.810519i | \(-0.699185\pi\) | ||||
−0.585712 | + | 0.810519i | \(0.699185\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0133665 | 0.00505208 | 0.00252604 | − | 0.999997i | \(-0.499196\pi\) | ||||
0.00252604 | + | 0.999997i | \(0.499196\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.82334 | 1.60778 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.228502 | 0.0688958 | 0.0344479 | − | 0.999406i | \(-0.489033\pi\) | ||||
0.0344479 | + | 0.999406i | \(0.489033\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.688069 | 0.190836 | 0.0954180 | − | 0.995437i | \(-0.469581\pi\) | ||||
0.0954180 | + | 0.995437i | \(0.469581\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.32648 | −1.89169 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.16498 | −0.282549 | −0.141275 | − | 0.989970i | \(-0.545120\pi\) | ||||
−0.141275 | + | 0.989970i | \(0.545120\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.379935 | −0.0871632 | −0.0435816 | − | 0.999050i | \(-0.513877\pi\) | ||||
−0.0435816 | + | 0.999050i | \(0.513877\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0373865 | 0.00815841 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.37001 | 1.53675 | 0.768376 | − | 0.639998i | \(-0.221065\pi\) | ||||
0.768376 | + | 0.639998i | \(0.221065\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.86117 | 0.372234 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.09993 | 0.981483 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.16069 | −0.772620 | −0.386310 | − | 0.922369i | \(-0.626251\pi\) | ||||
−0.386310 | + | 0.922369i | \(0.626251\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.39262 | 0.968542 | 0.484271 | − | 0.874918i | \(-0.339085\pi\) | ||||
0.484271 | + | 0.874918i | \(0.339085\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.639124 | 0.111257 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0350121 | −0.00591813 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.04431 | 1.32248 | 0.661238 | − | 0.750176i | \(-0.270031\pi\) | ||||
0.661238 | + | 0.750176i | \(0.270031\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.92455 | 0.308174 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.81652 | 0.752214 | 0.376107 | − | 0.926576i | \(-0.377263\pi\) | ||||
0.376107 | + | 0.926576i | \(0.377263\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.53393 | −0.691417 | −0.345709 | − | 0.938342i | \(-0.612361\pi\) | ||||
−0.345709 | + | 0.938342i | \(0.612361\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −12.6342 | −1.88339 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.68239 | 0.828862 | 0.414431 | − | 0.910081i | \(-0.363981\pi\) | ||||
0.414431 | + | 0.910081i | \(0.363981\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99982 | −0.999974 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.25848 | −0.456278 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.16875 | 0.984703 | 0.492352 | − | 0.870396i | \(-0.336137\pi\) | ||||
0.492352 | + | 0.870396i | \(0.336137\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.598533 | −0.0807062 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.06269 | −0.140757 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.9962 | −1.56178 | −0.780888 | − | 0.624671i | \(-0.785233\pi\) | ||||
−0.780888 | + | 0.624671i | \(0.785233\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.14696 | 0.402927 | 0.201464 | − | 0.979496i | \(-0.435430\pi\) | ||||
0.201464 | + | 0.979496i | \(0.435430\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0644714 | 0.00812263 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.80232 | −0.223550 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4676 | 1.52316 | 0.761578 | − | 0.648074i | \(-0.224425\pi\) | ||||
0.761578 | + | 0.648074i | \(0.224425\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 20.6141 | 2.48164 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.7784 | −1.39784 | −0.698918 | − | 0.715202i | \(-0.746335\pi\) | ||||
−0.698918 | + | 0.715202i | \(0.746335\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.77458 | −0.324740 | −0.162370 | − | 0.986730i | \(-0.551914\pi\) | ||||
−0.162370 | + | 0.986730i | \(0.551914\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.20574 | 0.601108 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.00305428 | 0.000348067 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.8738 | 1.56092 | 0.780460 | − | 0.625205i | \(-0.214985\pi\) | ||||
0.780460 | + | 0.625205i | \(0.214985\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.205392 | −0.0228213 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.29311 | 0.690759 | 0.345379 | − | 0.938463i | \(-0.387750\pi\) | ||||
0.345379 | + | 0.938463i | \(0.387750\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.05153 | 0.330985 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.6375 | −1.24768 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.77038 | 0.929658 | 0.464829 | − | 0.885400i | \(-0.346116\pi\) | ||||
0.464829 | + | 0.885400i | \(0.346116\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.00919710 | 0.000964119 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.0833 | 1.56406 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.995197 | 0.102105 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.10175 | −0.518004 | −0.259002 | − | 0.965877i | \(-0.583394\pi\) | ||||
−0.259002 | + | 0.965877i | \(0.583394\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.10214 | 0.110769 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.42910 | 0.241705 | 0.120852 | − | 0.992671i | \(-0.461437\pi\) | ||||
0.120852 | + | 0.992671i | \(0.461437\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.55877 | 0.744788 | 0.372394 | − | 0.928075i | \(-0.378537\pi\) | ||||
0.372394 | + | 0.928075i | \(0.378537\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.0979297 | −0.00955696 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.9024 | 1.15064 | 0.575322 | − | 0.817927i | \(-0.304877\pi\) | ||||
0.575322 | + | 0.817927i | \(0.304877\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.6601 | 1.40418 | 0.702092 | − | 0.712087i | \(-0.252250\pi\) | ||||
0.702092 | + | 0.712087i | \(0.252250\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 22.5001 | 2.13562 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.64470 | −0.531009 | −0.265504 | − | 0.964110i | \(-0.585538\pi\) | ||||
−0.265504 | + | 0.964110i | \(0.585538\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −19.3049 | −1.80019 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.31879 | 0.306823 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.0155717 | −0.00142746 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9478 | −0.995253 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.4719 | 1.21472 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.22179 | 0.735380 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0316 | 1.06763 | 0.533815 | − | 0.845601i | \(-0.320758\pi\) | ||||
0.533815 | + | 0.845601i | \(0.320758\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.6815 | −1.11654 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.3128 | 1.25052 | 0.625259 | − | 0.780417i | \(-0.284993\pi\) | ||||
0.625259 | + | 0.780417i | \(0.284993\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.00507842 | −0.000440355 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.3587 | −1.14973 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.20046 | −0.529741 | −0.264871 | − | 0.964284i | \(-0.585329\pi\) | ||||
−0.264871 | + | 0.964284i | \(0.585329\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.0479 | 1.27634 | 0.638172 | − | 0.769894i | \(-0.279691\pi\) | ||||
0.638172 | + | 0.769894i | \(0.279691\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.8938 | 1.33850 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.157225 | 0.0131478 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.8984 | 0.905066 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −19.5787 | −1.61482 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.36010 | 0.521040 | 0.260520 | − | 0.965468i | \(-0.416106\pi\) | ||||
0.260520 | + | 0.965468i | \(0.416106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.21352 | 0.261513 | 0.130756 | − | 0.991415i | \(-0.458259\pi\) | ||||
0.130756 | + | 0.991415i | \(0.458259\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.61910 | −0.454277 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.1253 | −1.13457 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.11889 | −0.727767 | −0.363883 | − | 0.931445i | \(-0.618549\pi\) | ||||
−0.363883 | + | 0.931445i | \(0.618549\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 20.0512 | 1.59016 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0985115 | 0.00776380 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.60236 | 0.125507 | 0.0627533 | − | 0.998029i | \(-0.480012\pi\) | ||||
0.0627533 | + | 0.998029i | \(0.480012\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.67411 | −0.130329 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.18609 | −0.323929 | −0.161965 | − | 0.986797i | \(-0.551783\pi\) | ||||
−0.161965 | + | 0.986797i | \(0.551783\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5266 | −0.963582 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.83256 | −0.140139 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.5003 | −1.17846 | −0.589232 | − | 0.807964i | \(-0.700569\pi\) | ||||
−0.589232 | + | 0.807964i | \(0.700569\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0248774 | 0.00188056 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −33.5537 | −2.52205 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.0062 | 1.34585 | 0.672925 | − | 0.739711i | \(-0.265038\pi\) | ||||
0.672925 | + | 0.739711i | \(0.265038\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.2099 | 1.27920 | 0.639600 | − | 0.768708i | \(-0.279100\pi\) | ||||
0.639600 | + | 0.768708i | \(0.279100\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.80213 | 0.650672 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.0711 | −1.54918 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.266200 | −0.0194664 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.0681685 | 0.00495853 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.53668 | 0.255905 | 0.127953 | − | 0.991780i | \(-0.459159\pi\) | ||||
0.127953 | + | 0.991780i | \(0.459159\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.44314 | −0.319824 | −0.159912 | − | 0.987131i | \(-0.551121\pi\) | ||||
−0.159912 | + | 0.987131i | \(0.551121\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.04112 | −0.361002 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.0182 | −1.49749 | −0.748744 | − | 0.662859i | \(-0.769343\pi\) | ||||
−0.748744 | + | 0.662859i | \(0.769343\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.41409 | −0.242018 | −0.121009 | − | 0.992651i | \(-0.538613\pi\) | ||||
−0.121009 | + | 0.992651i | \(0.538613\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 34.8721 | 2.45969 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.0556140 | −0.00390334 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.6163 | −0.881161 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 35.5481 | 2.47076 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0868158 | −0.00600518 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.66210 | 0.389795 | 0.194898 | − | 0.980824i | \(-0.437563\pi\) | ||||
0.194898 | + | 0.980824i | \(0.437563\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −32.9444 | −2.25731 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.8761 | 0.809943 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.0720806 | 0.00489315 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.76056 | −0.524410 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.801586 | −0.0539205 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.1060 | 1.21247 | 0.606234 | − | 0.795287i | \(-0.292680\pi\) | ||||
0.606234 | + | 0.795287i | \(0.292680\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.97707 | 0.598472 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.1140 | −1.13589 | −0.567946 | − | 0.823066i | \(-0.692262\pi\) | ||||
−0.567946 | + | 0.823066i | \(0.692262\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.7678 | −1.04196 | −0.520982 | − | 0.853567i | \(-0.674434\pi\) | ||||
−0.520982 | + | 0.853567i | \(0.674434\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.00854288 | 0.000562080 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.18223 | 0.601548 | 0.300774 | − | 0.953695i | \(-0.402755\pi\) | ||||
0.300774 | + | 0.953695i | \(0.402755\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.8844 | −0.970949 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 38.8053 | 2.52067 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.42482 | 0.156849 | 0.0784244 | − | 0.996920i | \(-0.475011\pi\) | ||||
0.0784244 | + | 0.996920i | \(0.475011\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.97634 | 0.256138 | 0.128069 | − | 0.991765i | \(-0.459122\pi\) | ||||
0.128069 | + | 0.991765i | \(0.459122\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.8743 | −1.01834 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18.3352 | 1.17139 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.261422 | −0.0166339 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.6020 | 1.11548 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.00201 | −0.189485 | −0.0947425 | − | 0.995502i | \(-0.530203\pi\) | ||||
−0.0947425 | + | 0.995502i | \(0.530203\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.68406 | 0.105876 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.53520 | 0.534495 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.5002 | 0.966874 | 0.483437 | − | 0.875379i | \(-0.339388\pi\) | ||||
0.483437 | + | 0.875379i | \(0.339388\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.107525 | 0.00668125 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.0684 | −1.24220 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.5926 | −1.51644 | −0.758221 | − | 0.651998i | \(-0.773931\pi\) | ||||
−0.758221 | + | 0.651998i | \(0.773931\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.7777 | −1.15350 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.5310 | 1.50127 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.5263 | 1.55637 | 0.778185 | − | 0.628036i | \(-0.216141\pi\) | ||||
0.778185 | + | 0.628036i | \(0.216141\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.4498 | 1.42447 | 0.712237 | − | 0.701939i | \(-0.247682\pi\) | ||||
0.712237 | + | 0.701939i | \(0.247682\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0257245 | 0.00155692 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.425281 | 0.0256454 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.9730 | 0.719386 | 0.359693 | − | 0.933071i | \(-0.382881\pi\) | ||||
0.359693 | + | 0.933071i | \(0.382881\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 26.0104 | 1.55720 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.1916 | −0.906254 | −0.453127 | − | 0.891446i | \(-0.649692\pi\) | ||||
−0.453127 | + | 0.891446i | \(0.649692\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.4437 | 1.33414 | 0.667070 | − | 0.744995i | \(-0.267548\pi\) | ||||
0.667070 | + | 0.744995i | \(0.267548\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.78359 | 0.164886 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.0643802 | 0.00380024 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6428 | −0.920166 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.2697 | −0.836505 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.9534 | −1.57463 | −0.787317 | − | 0.616549i | \(-0.788530\pi\) | ||||
−0.787317 | + | 0.616549i | \(0.788530\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 31.4227 | 1.82950 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.16534 | 0.0676201 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.07108 | 0.293268 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0606029 | −0.00349309 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.79425 | 0.390320 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.24311 | −0.471999 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.26500 | 0.243417 | 0.121708 | − | 0.992566i | \(-0.461163\pi\) | ||||
0.121708 | + | 0.992566i | \(0.461163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.1421 | 1.20273 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.3339 | −0.699389 | −0.349695 | − | 0.936864i | \(-0.613715\pi\) | ||||
−0.349695 | + | 0.936864i | \(0.613715\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.9379 | −1.29653 | −0.648264 | − | 0.761416i | \(-0.724505\pi\) | ||||
−0.648264 | + | 0.761416i | \(0.724505\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.168875 | −0.00951505 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 34.3786 | 1.93090 | 0.965448 | − | 0.260595i | \(-0.0839188\pi\) | ||||
0.965448 | + | 0.260595i | \(0.0839188\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.950724 | −0.0532303 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 33.2912 | 1.85813 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.442617 | 0.0246279 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.28062 | 0.0710358 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 41.0047 | 2.26756 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.0759540 | 0.00418748 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.53098 | 0.413940 | 0.206970 | − | 0.978347i | \(-0.433640\pi\) | ||||
0.206970 | + | 0.978347i | \(0.433640\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 38.8005 | 2.12625 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −32.6573 | −1.78426 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.9185 | −1.13950 | −0.569751 | − | 0.821817i | \(-0.692960\pi\) | ||||
−0.569751 | + | 0.821817i | \(0.692960\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.7884 | −0.857506 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.23222 | 0.0667285 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.187129 | −0.0101040 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −53.9962 | −2.90706 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.8732 | −1.54999 | −0.774996 | − | 0.631966i | \(-0.782248\pi\) | ||||
−0.774996 | + | 0.631966i | \(0.782248\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.9850 | 1.01624 | 0.508121 | − | 0.861286i | \(-0.330340\pi\) | ||||
0.508121 | + | 0.861286i | \(0.330340\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.50911 | 0.187302 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.0690 | 1.60041 | 0.800205 | − | 0.599727i | \(-0.204724\pi\) | ||||
0.800205 | + | 0.599727i | \(0.204724\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.8521 | 1.63746 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0435545 | −0.00230515 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.67072 | −0.140955 | −0.0704775 | − | 0.997513i | \(-0.522452\pi\) | ||||
−0.0704775 | + | 0.997513i | \(0.522452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8556 | −0.992403 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −30.6212 | −1.60720 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.26769 | 0.380408 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.7441 | −0.926237 | −0.463118 | − | 0.886296i | \(-0.653270\pi\) | ||||
−0.463118 | + | 0.886296i | \(0.653270\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 23.2317 | 1.20939 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.0958214 | 0.00497480 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.09717 | 0.160365 | 0.0801827 | − | 0.996780i | \(-0.474450\pi\) | ||||
0.0801827 | + | 0.996780i | \(0.474450\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 22.9966 | 1.18754 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.86284 | −0.147444 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.477841 | 0.0245450 | 0.0122725 | − | 0.999925i | \(-0.496093\pi\) | ||||
0.0122725 | + | 0.999925i | \(0.496093\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 33.6526 | 1.72408 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.35113 | −0.222332 | −0.111166 | − | 0.993802i | \(-0.535459\pi\) | ||||
−0.111166 | + | 0.993802i | \(0.535459\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.00800032 | −0.000407734 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −21.8687 | −1.11165 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.4169 | −0.984475 | −0.492237 | − | 0.870461i | \(-0.663821\pi\) | ||||
−0.492237 | + | 0.870461i | \(0.663821\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.58591 | −0.434208 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 40.0334 | 2.01942 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −36.3407 | −1.82850 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.874016 | 0.0438656 | 0.0219328 | − | 0.999759i | \(-0.493018\pi\) | ||||
0.0219328 | + | 0.999759i | \(0.493018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0142045 | −0.000711113 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.27785 | 0.413376 | 0.206688 | − | 0.978407i | \(-0.433732\pi\) | ||||
0.206688 | + | 0.978407i | \(0.433732\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.71049 | 0.184833 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.538000 | 0.0267335 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.83814 | 0.0911131 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.0121 | 1.28622 | 0.643109 | − | 0.765775i | \(-0.277644\pi\) | ||||
0.643109 | + | 0.765775i | \(0.277644\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.3428 | −0.855460 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.160348 | −0.00789021 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.4841 | −0.809171 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 42.0893 | 2.06112 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.93898 | 0.0947253 | 0.0473626 | − | 0.998878i | \(-0.484918\pi\) | ||||
0.0473626 | + | 0.998878i | \(0.484918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.9456 | 1.21577 | 0.607886 | − | 0.794024i | \(-0.292018\pi\) | ||||
0.607886 | + | 0.794024i | \(0.292018\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 27.4081 | 1.33263 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.16823 | −0.105174 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0420640 | 0.00203562 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.439762 | 0.0212319 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.5025 | −0.746727 | −0.373363 | − | 0.927685i | \(-0.621796\pi\) | ||||
−0.373363 | + | 0.927685i | \(0.621796\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.1305 | 0.967412 | 0.483706 | − | 0.875231i | \(-0.339290\pi\) | ||||
0.483706 | + | 0.875231i | \(0.339290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 30.4832 | 1.46156 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.80013 | −0.133948 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.9259 | −1.18965 | −0.594824 | − | 0.803856i | \(-0.702778\pi\) | ||||
−0.594824 | + | 0.803856i | \(0.702778\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −33.7625 | −1.60774 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.52679 | −0.405120 | −0.202560 | − | 0.979270i | \(-0.564926\pi\) | ||||
−0.202560 | + | 0.979270i | \(0.564926\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.9730 | −1.08902 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.7894 | 0.841407 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.52352 | 0.119092 | 0.0595460 | − | 0.998226i | \(-0.481035\pi\) | ||||
0.0595460 | + | 0.998226i | \(0.481035\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.10058 | 0.0518244 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.98829 | 0.422307 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0240907 | −0.00112939 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.6375 | −0.637935 | −0.318967 | − | 0.947766i | \(-0.603336\pi\) | ||||
−0.318967 | + | 0.947766i | \(0.603336\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.94132 | −0.277317 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.0818 | −0.795580 | −0.397790 | − | 0.917477i | \(-0.630223\pi\) | ||||
−0.397790 | + | 0.917477i | \(0.630223\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.4036 | 1.22708 | 0.613540 | − | 0.789664i | \(-0.289745\pi\) | ||||
0.613540 | + | 0.789664i | \(0.289745\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −39.5089 | −1.83218 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.9657 | −0.970176 | −0.485088 | − | 0.874465i | \(-0.661212\pi\) | ||||
−0.485088 | + | 0.874465i | \(0.661212\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.166648 | 0.00769510 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.5058 | −1.17524 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.03601 | −0.0476358 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.707125 | −0.0324451 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 34.5773 | 1.58319 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.05097 | −0.0937114 | −0.0468557 | − | 0.998902i | \(-0.514920\pi\) | ||||
−0.0468557 | + | 0.998902i | \(0.514920\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.53504 | 0.252376 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.275539 | 0.0125375 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.3634 | 0.606802 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.2267 | −1.55096 | −0.775480 | − | 0.631372i | \(-0.782492\pi\) | ||||
−0.775480 | + | 0.631372i | \(0.782492\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.48184 | 0.202676 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.1369 | −0.999026 | −0.499513 | − | 0.866306i | \(-0.666488\pi\) | ||||
−0.499513 | + | 0.866306i | \(0.666488\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.84712 | 0.218303 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.88693 | −0.129758 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.157436 | −0.00706198 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.1745 | 1.70892 | 0.854462 | − | 0.519513i | \(-0.173887\pi\) | ||||
0.854462 | + | 0.519513i | \(0.173887\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.7086 | −0.523102 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −38.1811 | −1.70241 | −0.851207 | − | 0.524831i | \(-0.824129\pi\) | ||||
−0.851207 | + | 0.524831i | \(0.824129\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.36275 | −0.283139 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −35.0371 | −1.55605 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.91801 | −0.129338 | −0.0646692 | − | 0.997907i | \(-0.520599\pi\) | ||||
−0.0646692 | + | 0.997907i | \(0.520599\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0370865 | −0.00164061 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.93765 | −0.0855491 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.7993 | −0.872462 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.29844 | 0.0571052 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −43.3546 | −1.90306 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.53808 | 0.374060 | 0.187030 | − | 0.982354i | \(-0.440114\pi\) | ||||
0.187030 | + | 0.982354i | \(0.440114\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.70731 | −0.424471 | −0.212235 | − | 0.977219i | \(-0.568074\pi\) | ||||
−0.212235 | + | 0.977219i | \(0.568074\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.0695828 | 0.00303684 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.28229 | −0.273661 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31.3170 | 1.36161 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −57.8619 | −2.51099 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.31410 | 0.143549 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −31.1768 | −1.34789 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 50.3639 | 2.17336 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.59947 | −0.0688941 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0739 | −0.433113 | −0.216556 | − | 0.976270i | \(-0.569482\pi\) | ||||
−0.216556 | + | 0.976270i | \(0.569482\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 48.1364 | 2.06573 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −38.4004 | −1.64489 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.00527 | −0.214010 | −0.107005 | − | 0.994258i | \(-0.534126\pi\) | ||||
−0.107005 | + | 0.994258i | \(0.534126\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.1789 | 0.647819 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.58079 | 0.0673440 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.185444 | 0.00788589 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −58.9365 | −2.50171 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.3178 | −1.36935 | −0.684675 | − | 0.728849i | \(-0.740056\pi\) | ||||
−0.684675 | + | 0.728849i | \(0.740056\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.11965 | −0.131947 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.744567 | −0.0314356 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.63057 | −0.279445 | −0.139723 | − | 0.990191i | \(-0.544621\pi\) | ||||
−0.139723 | + | 0.990191i | \(0.544621\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.7856 | 0.622036 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.00274538 | −0.000115295 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.4748 | −1.06796 | −0.533980 | − | 0.845497i | \(-0.679304\pi\) | ||||
−0.533980 | + | 0.845497i | \(0.679304\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.20036 | −0.259477 | −0.129739 | − | 0.991548i | \(-0.541414\pi\) | ||||
−0.129739 | + | 0.991548i | \(0.541414\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.89217 | 0.413251 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.7169 | 0.572032 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.1128 | −1.21198 | −0.605990 | − | 0.795472i | \(-0.707223\pi\) | ||||
−0.605990 | + | 0.795472i | \(0.707223\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.4276 | −0.516472 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.0841171 | 0.00348977 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.63807 | 0.0678419 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.69319 | −0.359419 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.9788 | 0.453144 | 0.226572 | − | 0.973994i | \(-0.427248\pi\) | ||||
0.226572 | + | 0.973994i | \(0.427248\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.04885 | −0.0844212 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −58.7885 | −2.41824 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.39094 | −0.385640 | −0.192820 | − | 0.981234i | \(-0.561763\pi\) | ||||
−0.192820 | + | 0.981234i | \(0.561763\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0407884 | 0.00167216 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.54929 | −0.390827 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.6012 | −0.678306 | −0.339153 | − | 0.940731i | \(-0.610140\pi\) | ||||
−0.339153 | + | 0.940731i | \(0.610140\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.6927 | −1.04803 | −0.524013 | − | 0.851710i | \(-0.675566\pi\) | ||||
−0.524013 | + | 0.851710i | \(0.675566\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 60.1353 | 2.44890 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 28.6765 | 1.16586 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −44.3433 | −1.79984 | −0.899920 | − | 0.436056i | \(-0.856375\pi\) | ||||
−0.899920 | + | 0.436056i | \(0.856375\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.155554 | −0.00630335 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.90988 | 0.158177 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.0207 | 1.41447 | 0.707237 | − | 0.706976i | \(-0.249941\pi\) | ||||
0.707237 | + | 0.706976i | \(0.249941\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −35.2881 | −1.42295 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.5618 | −0.827786 | −0.413893 | − | 0.910326i | \(-0.635831\pi\) | ||||
−0.413893 | + | 0.910326i | \(0.635831\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.416231 | −0.0167297 | −0.00836486 | − | 0.999965i | \(-0.502663\pi\) | ||||
−0.00836486 | + | 0.999965i | \(0.502663\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 37.5866 | 1.50830 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.117230 | 0.00469671 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.8419 | −1.23368 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.242826 | −0.00969754 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.37145 | −0.373664 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.24035 | −0.248424 | −0.124212 | − | 0.992256i | \(-0.539640\pi\) | ||||
−0.124212 | + | 0.992256i | \(0.539640\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.8370 | 0.629466 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −31.5154 | −1.25065 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.81636 | −0.190831 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −56.8111 | −2.24741 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.8218 | 0.743416 | 0.371708 | − | 0.928350i | \(-0.378772\pi\) | ||||
0.371708 | + | 0.928350i | \(0.378772\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.73031 | −0.265418 | −0.132709 | − | 0.991155i | \(-0.542368\pi\) | ||||
−0.132709 | + | 0.991155i | \(0.542368\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 33.2177 | 1.30795 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.9280 | 1.13728 | 0.568639 | − | 0.822587i | \(-0.307470\pi\) | ||||
0.568639 | + | 0.822587i | \(0.307470\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.74116 | −0.107600 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.201611 | 0.00790177 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.42094 | −0.290404 | −0.145202 | − | 0.989402i | \(-0.546383\pi\) | ||||
−0.145202 | + | 0.989402i | \(0.546383\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −37.4908 | −1.46489 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.3827 | −0.522111 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.7466 | 0.457581 | 0.228790 | − | 0.973476i | \(-0.426523\pi\) | ||||
0.228790 | + | 0.973476i | \(0.426523\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.2584 | −0.476798 | −0.238399 | − | 0.971167i | \(-0.576623\pi\) | ||||
−0.238399 | + | 0.971167i | \(0.576623\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.24206 | −0.0870742 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.0133023 | 0.000515843 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.6643 | −1.18733 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 50.6429 | 1.95797 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.719086 | 0.0277600 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.91363 | 0.227954 | 0.113977 | − | 0.993483i | \(-0.463641\pi\) | ||||
0.113977 | + | 0.993483i | \(0.463641\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.49186 | 0.365342 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.0064 | −0.922641 | −0.461320 | − | 0.887234i | \(-0.652624\pi\) | ||||
−0.461320 | + | 0.887234i | \(0.652624\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0681927 | −0.00261700 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −47.8681 | −1.83431 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.59259 | −0.213994 | −0.106997 | − | 0.994259i | \(-0.534124\pi\) | ||||
−0.106997 | + | 0.994259i | \(0.534124\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.2414 | 0.620552 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −44.1029 | −1.68263 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.93259 | 0.187917 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.923589 | 0.0351350 | 0.0175675 | − | 0.999846i | \(-0.494408\pi\) | ||||
0.0175675 | + | 0.999846i | \(0.494408\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0147318 | 0.000559616 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −39.4162 | −1.49514 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.61114 | −0.212537 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.6829 | 0.971417 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.36440 | −0.278150 | −0.139075 | − | 0.990282i | \(-0.544413\pi\) | ||||
−0.139075 | + | 0.990282i | \(0.544413\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.05632 | −0.115271 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −41.6319 | −1.56795 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.0324687 | 0.00122111 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.0693 | 0.415715 | 0.207857 | − | 0.978159i | \(-0.433351\pi\) | ||||
0.207857 | + | 0.978159i | \(0.433351\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 66.9179 | 2.50962 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 39.7436 | 1.48841 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.411832 | −0.0154017 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.78229 | 0.253289 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.3083 | −0.533608 | −0.266804 | − | 0.963751i | \(-0.585968\pi\) | ||||
−0.266804 | + | 0.963751i | \(0.585968\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.101035 | 0.00376273 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.1219 | 0.413628 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.74376 | −0.287596 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.7350 | 1.32534 | 0.662669 | − | 0.748913i | \(-0.269424\pi\) | ||||
0.662669 | + | 0.748913i | \(0.269424\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.28193 | 0.195359 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.467268 | −0.0172589 | −0.00862947 | − | 0.999963i | \(-0.502747\pi\) | ||||
−0.00862947 | + | 0.999963i | \(0.502747\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 51.2840 | 1.89164 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.84886 | 0.104939 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.6771 | −1.12847 | −0.564237 | − | 0.825613i | \(-0.690830\pi\) | ||||
−0.564237 | + | 0.825613i | \(0.690830\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.731203 | −0.0268614 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.3966 | 1.73881 | 0.869406 | − | 0.494098i | \(-0.164502\pi\) | ||||
0.869406 | + | 0.494098i | \(0.164502\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.6595 | −0.610358 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.3538 | 1.11059 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.159093 | 0.00581314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.39668 | −0.305992 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.41744 | −0.306342 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.9824 | −1.45318 | −0.726592 | − | 0.687069i | \(-0.758897\pi\) | ||||
−0.726592 | + | 0.687069i | \(0.758897\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.71035 | 0.170975 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.9031 | 1.59148 | 0.795742 | − | 0.605635i | \(-0.207081\pi\) | ||||
0.795742 | + | 0.605635i | \(0.207081\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.195955 | 0.00709404 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.7186 | 0.532151 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.25423 | −0.298043 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.5042 | 1.46062 | 0.730310 | − | 0.683116i | \(-0.239376\pi\) | ||||
0.730310 | + | 0.683116i | \(0.239376\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 43.3543 | 1.56137 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.2429 | −1.08776 | −0.543880 | − | 0.839163i | \(-0.683045\pi\) | ||||
−0.543880 | + | 0.839163i | \(0.683045\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.0366 | 0.360525 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.300749 | 0.0107893 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.82997 | −0.0655653 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.69138 | −0.0963050 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.2192 | −0.758313 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.8859 | 0.852523 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.4649 | 1.12160 | 0.560802 | − | 0.827950i | \(-0.310493\pi\) | ||||
0.560802 | + | 0.827950i | \(0.310493\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −68.7860 | −2.44885 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.0754501 | −0.00268270 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.16533 | 0.0768931 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −52.5217 | −1.86275 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.94633 | −0.316895 | −0.158448 | − | 0.987367i | \(-0.550649\pi\) | ||||
−0.158448 | + | 0.987367i | \(0.550649\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.61987 | −0.234194 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 42.3025 | 1.49469 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.633996 | −0.0223732 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.258040 | −0.00909470 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 71.3978 | 2.51332 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.4742 | −0.930783 | −0.465392 | − | 0.885105i | \(-0.654087\pi\) | ||||
−0.465392 | + | 0.885105i | \(0.654087\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.3607 | −0.644732 | −0.322366 | − | 0.946615i | \(-0.604478\pi\) | ||||
−0.322366 | + | 0.946615i | \(0.604478\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 65.5897 | 2.30033 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.19720 | −0.147021 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.72260 | 0.0602661 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.0443608 | 0.00155009 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.0586 | 1.36316 | 0.681578 | − | 0.731745i | \(-0.261294\pi\) | ||||
0.681578 | + | 0.731745i | \(0.261294\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.5048 | 0.993616 | 0.496808 | − | 0.867861i | \(-0.334505\pi\) | ||||
0.496808 | + | 0.867861i | \(0.334505\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.18952 | 0.0414138 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.1765 | −1.60571 | −0.802856 | − | 0.596173i | \(-0.796687\pi\) | ||||
−0.802856 | + | 0.596173i | \(0.796687\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.8007 | 1.48653 | 0.743264 | − | 0.668998i | \(-0.233277\pi\) | ||||
0.743264 | + | 0.668998i | \(0.233277\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.4887 | 1.16171 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.15465 | 0.282542 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.9650 | 0.379459 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27.5020 | 0.950607 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.7301 | −0.370443 | −0.185221 | − | 0.982697i | \(-0.559300\pi\) | ||||
−0.185221 | + | 0.982697i | \(0.559300\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.6887 | −0.403058 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −42.4912 | −1.46347 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 32.8119 | 1.12876 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.146334 | −0.00502810 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 62.7756 | 2.15445 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 59.2866 | 2.03232 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.8526 | 1.12485 | 0.562425 | − | 0.826848i | \(-0.309868\pi\) | ||||
0.562425 | + | 0.826848i | \(0.309868\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.80017 | 0.164163 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.3586 | −0.558800 | −0.279400 | − | 0.960175i | \(-0.590136\pi\) | ||||
−0.279400 | + | 0.960175i | \(0.590136\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.23860 | 0.0763801 | 0.0381900 | − | 0.999270i | \(-0.487841\pi\) | ||||
0.0381900 | + | 0.999270i | \(0.487841\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.180073 | 0.00613687 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.2864 | 0.894801 | 0.447400 | − | 0.894334i | \(-0.352350\pi\) | ||||
0.447400 | + | 0.894334i | \(0.352350\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.6011 | 1.38048 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −43.7534 | −1.48594 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.17018 | 0.107541 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.57855 | 0.290673 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −24.6075 | −0.832837 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.109897 | 0.00371520 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.8001 | −0.634835 | −0.317417 | − | 0.948286i | \(-0.602816\pi\) | ||||
−0.317417 | + | 0.948286i | \(0.602816\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −75.3892 | −2.54282 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.8722 | −1.47809 | −0.739046 | − | 0.673655i | \(-0.764723\pi\) | ||||
−0.739046 | + | 0.673655i | \(0.764723\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.3456 | 0.751989 | 0.375994 | − | 0.926622i | \(-0.377301\pi\) | ||||
0.375994 | + | 0.926622i | \(0.377301\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 87.8901 | 2.95439 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.5006 | −1.09126 | −0.545632 | − | 0.838025i | \(-0.683711\pi\) | ||||
−0.545632 | + | 0.838025i | \(0.683711\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.160821 | 0.00539375 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.0469324 | −0.00157229 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.15894 | −0.0722463 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −47.1653 | −1.57656 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.1839 | 0.473587 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22.4370 | −0.748315 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.35144 | −0.278227 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.169508 | −0.00564087 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −45.0793 | −1.49849 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.7498 | 0.888214 | 0.444107 | − | 0.895974i | \(-0.353521\pi\) | ||||
0.444107 | + | 0.895974i | \(0.353521\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.7164 | 0.388608 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.8806 | −0.989988 | −0.494994 | − | 0.868896i | \(-0.664830\pi\) | ||||
−0.494994 | + | 0.868896i | \(0.664830\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.43799 | 0.0475904 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23.0562 | −0.762213 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.191313 | 0.00631772 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.7725 | 0.388338 | 0.194169 | − | 0.980968i | \(-0.437799\pi\) | ||||
0.194169 | + | 0.980968i | \(0.437799\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.9293 | 0.393084 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.10433 | −0.266757 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.9718 | 0.492271 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 36.4585 | 1.19746 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 54.9523 | 1.80293 | 0.901464 | − | 0.432855i | \(-0.142494\pi\) | ||||
0.901464 | + | 0.432855i | \(0.142494\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.65948 | 0.0871609 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −34.4981 | −1.12942 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.697279 | 0.0228035 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.3117 | 0.402206 | 0.201103 | − | 0.979570i | \(-0.435547\pi\) | ||||
0.201103 | + | 0.979570i | \(0.435547\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −64.1579 | −2.09371 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.73503 | 0.284754 | 0.142377 | − | 0.989813i | \(-0.454526\pi\) | ||||
0.142377 | + | 0.989813i | \(0.454526\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.4978 | 1.15597 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.178559 | −0.00580854 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.1736 | −1.30547 | −0.652733 | − | 0.757588i | \(-0.726378\pi\) | ||||
−0.652733 | + | 0.757588i | \(0.726378\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.90910 | −0.0619721 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 96.1579 | 3.11813 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.7400 | −0.542261 | −0.271130 | − | 0.962543i | \(-0.587397\pi\) | ||||
−0.271130 | + | 0.962543i | \(0.587397\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.26392 | −0.299773 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.65920 | −0.0859596 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.0828788 | −0.00267630 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.91970 | −0.0619259 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 57.4091 | 1.84998 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.6383 | 0.374650 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.0724 | −1.03138 | −0.515689 | − | 0.856776i | \(-0.672464\pi\) | ||||
−0.515689 | + | 0.856776i | \(0.672464\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.23801 | 0.0397706 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.0992 | 1.83240 | 0.916201 | − | 0.400719i | \(-0.131240\pi\) | ||||
0.916201 | + | 0.400719i | \(0.131240\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.201138 | 0.00644819 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.58191 | 0.114713 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.17595 | 0.229579 | 0.114790 | − | 0.993390i | \(-0.463381\pi\) | ||||
0.114790 | + | 0.993390i | \(0.463381\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.00405 | 0.0640496 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 70.7107 | 2.25762 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48.5615 | −1.54887 | −0.774436 | − | 0.632652i | \(-0.781966\pi\) | ||||
−0.774436 | + | 0.632652i | \(0.781966\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 55.0549 | 1.75419 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.212445 | 0.00676220 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.4151 | −1.06254 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.8539 | −0.630681 | −0.315341 | − | 0.948979i | \(-0.602119\pi\) | ||||
−0.315341 | + | 0.948979i | \(0.602119\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.0643 | 0.668456 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.94281 | 0.283506 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.31953 | 0.136801 | 0.0684005 | − | 0.997658i | \(-0.478210\pi\) | ||||
0.0684005 | + | 0.997658i | \(0.478210\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 41.0254 | 1.29799 |
(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 | 6008.2.a.e.1.44 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.44 | ✓ | 50 | 1.1 | even | 1 | trivial |