Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7600,2,Mod(1,7600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7600, 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("7600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7600.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: | \(60.6863055362\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.56310016.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 9x^{4} + 14x^{2} - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 380) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.23277\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7600.1 |
$q$-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 | ||||||||
\(3\) | −1.62236 | −0.936672 | −0.468336 | − | 0.883551i | \(-0.655146\pi\) | ||||
−0.468336 | + | 0.883551i | \(0.655146\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.74397 | −1.79305 | −0.896525 | − | 0.442993i | \(-0.853917\pi\) | ||||
−0.896525 | + | 0.442993i | \(0.853917\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.367938 | −0.122646 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.48028 | −1.35085 | −0.675427 | − | 0.737426i | \(-0.736041\pi\) | ||||
−0.675427 | + | 0.737426i | \(0.736041\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.843176 | 0.233855 | 0.116928 | − | 0.993140i | \(-0.462695\pi\) | ||||
0.116928 | + | 0.993140i | \(0.462695\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.52315 | 1.33956 | 0.669781 | − | 0.742559i | \(-0.266388\pi\) | ||||
0.669781 | + | 0.742559i | \(0.266388\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.69643 | 1.67950 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.779187 | 0.162472 | 0.0812358 | − | 0.996695i | \(-0.474113\pi\) | ||||
0.0812358 | + | 0.996695i | \(0.474113\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.46402 | 1.05155 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.6570 | −1.97895 | −0.989477 | − | 0.144691i | \(-0.953781\pi\) | ||||
−0.989477 | + | 0.144691i | \(0.953781\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.65699 | 1.55484 | 0.777421 | − | 0.628981i | \(-0.216528\pi\) | ||||
0.777421 | + | 0.628981i | \(0.216528\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.26864 | 1.26531 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.62236 | 0.266715 | 0.133357 | − | 0.991068i | \(-0.457424\pi\) | ||||
0.133357 | + | 0.991068i | \(0.457424\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.36794 | −0.219045 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.73588 | 0.739620 | 0.369810 | − | 0.929107i | \(-0.379423\pi\) | ||||
0.369810 | + | 0.929107i | \(0.379423\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.67504 | 1.47543 | 0.737715 | − | 0.675112i | \(-0.235905\pi\) | ||||
0.737715 | + | 0.675112i | \(0.235905\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.18559 | −0.464666 | −0.232333 | − | 0.972636i | \(-0.574636\pi\) | ||||
−0.232333 | + | 0.972636i | \(0.574636\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.5052 | 2.21503 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.96056 | −1.25473 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.17922 | −0.848780 | −0.424390 | − | 0.905479i | \(-0.639512\pi\) | ||||
−0.424390 | + | 0.905479i | \(0.639512\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.62236 | 0.214887 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.6964 | −1.52275 | −0.761373 | − | 0.648314i | \(-0.775474\pi\) | ||||
−0.761373 | + | 0.648314i | \(0.775474\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.48028 | 0.829715 | 0.414857 | − | 0.909886i | \(-0.363831\pi\) | ||||
0.414857 | + | 0.909886i | \(0.363831\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.74549 | 0.219911 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.8880 | 1.81885 | 0.909427 | − | 0.415864i | \(-0.136521\pi\) | ||||
0.909427 | + | 0.415864i | \(0.136521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.26412 | −0.152183 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.303566 | −0.0360266 | −0.0180133 | − | 0.999838i | \(-0.505734\pi\) | ||||
−0.0180133 | + | 0.999838i | \(0.505734\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0800 | 1.17978 | 0.589888 | − | 0.807485i | \(-0.299172\pi\) | ||||
0.589888 | + | 0.807485i | \(0.299172\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 21.2543 | 2.42215 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.76081 | −0.862312 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.779187 | −0.0855268 | −0.0427634 | − | 0.999085i | \(-0.513616\pi\) | ||||
−0.0427634 | + | 0.999085i | \(0.513616\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 17.2895 | 1.85363 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.69643 | −0.603821 | −0.301910 | − | 0.953336i | \(-0.597624\pi\) | ||||
−0.301910 | + | 0.953336i | \(0.597624\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.0448 | −1.45638 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.17922 | −0.627404 | −0.313702 | − | 0.949521i | \(-0.601569\pi\) | ||||
−0.313702 | + | 0.949521i | \(0.601569\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.64847 | 0.165677 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.36794 | 0.335122 | 0.167561 | − | 0.985862i | \(-0.446411\pi\) | ||||
0.167561 | + | 0.985862i | \(0.446411\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.71368 | −0.365919 | −0.182960 | − | 0.983120i | \(-0.558568\pi\) | ||||
−0.182960 | + | 0.983120i | \(0.558568\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.2031 | 0.986374 | 0.493187 | − | 0.869923i | \(-0.335832\pi\) | ||||
0.493187 | + | 0.869923i | \(0.335832\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.96056 | 0.283570 | 0.141785 | − | 0.989897i | \(-0.454716\pi\) | ||||
0.141785 | + | 0.989897i | \(0.454716\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.63206 | −0.249824 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.08638 | 0.666631 | 0.333315 | − | 0.942815i | \(-0.391833\pi\) | ||||
0.333315 | + | 0.942815i | \(0.391833\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.310237 | −0.0286814 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −26.2016 | −2.40190 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.07290 | 0.824809 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.68331 | −0.692781 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.79817 | 0.869447 | 0.434723 | − | 0.900564i | \(-0.356846\pi\) | ||||
0.434723 | + | 0.900564i | \(0.356846\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.6964 | −1.38199 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.5841 | −1.09948 | −0.549739 | − | 0.835337i | \(-0.685273\pi\) | ||||
−0.549739 | + | 0.835337i | \(0.685273\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.74397 | 0.411354 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.89586 | −0.760024 | −0.380012 | − | 0.924981i | \(-0.624080\pi\) | ||||
−0.380012 | + | 0.924981i | \(0.624080\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.25560 | −0.530593 | −0.265296 | − | 0.964167i | \(-0.585470\pi\) | ||||
−0.265296 | + | 0.964167i | \(0.585470\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.16819 | 0.435240 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.77767 | −0.315904 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −25.1551 | −2.07476 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.48028 | 0.203192 | 0.101596 | − | 0.994826i | \(-0.467605\pi\) | ||||
0.101596 | + | 0.994826i | \(0.467605\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.69643 | −0.300812 | −0.150406 | − | 0.988624i | \(-0.548058\pi\) | ||||
−0.150406 | + | 0.988624i | \(0.548058\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.03218 | −0.164292 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.8479 | −1.50422 | −0.752112 | − | 0.659035i | \(-0.770965\pi\) | ||||
−0.752112 | + | 0.659035i | \(0.770965\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.0249 | 0.795029 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.69643 | −0.291320 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.46554 | 0.193116 | 0.0965580 | − | 0.995327i | \(-0.469217\pi\) | ||||
0.0965580 | + | 0.995327i | \(0.469217\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.49134 | −0.579697 | −0.289849 | − | 0.957072i | \(-0.593605\pi\) | ||||
−0.289849 | + | 0.957072i | \(0.593605\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2891 | −0.945312 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.367938 | 0.0281369 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.0653 | 1.52554 | 0.762768 | − | 0.646673i | \(-0.223840\pi\) | ||||
0.762768 | + | 0.646673i | \(0.223840\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18.9759 | 1.42631 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.69643 | 0.276284 | 0.138142 | − | 0.990412i | \(-0.455887\pi\) | ||||
0.138142 | + | 0.990412i | \(0.455887\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.5134 | −0.777170 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.7453 | −1.80955 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −25.9211 | −1.88548 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.887659 | −0.0642288 | −0.0321144 | − | 0.999484i | \(-0.510224\pi\) | ||||
−0.0321144 | + | 0.999484i | \(0.510224\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.1581 | −1.37903 | −0.689516 | − | 0.724271i | \(-0.742177\pi\) | ||||
−0.689516 | + | 0.724271i | \(0.742177\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.37271 | −0.240295 | −0.120148 | − | 0.992756i | \(-0.538337\pi\) | ||||
−0.120148 | + | 0.992756i | \(0.538337\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.58409 | −0.324958 | −0.162479 | − | 0.986712i | \(-0.551949\pi\) | ||||
−0.162479 | + | 0.986712i | \(0.551949\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −24.1537 | −1.70367 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 50.5564 | 3.54836 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.286693 | −0.0199265 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.48028 | 0.309907 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.8817 | 1.02450 | 0.512248 | − | 0.858837i | \(-0.328813\pi\) | ||||
0.512248 | + | 0.858837i | \(0.328813\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.492494 | 0.0337451 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −41.0685 | −2.78791 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.3534 | −1.10506 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.65699 | 0.313263 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.7839 | 1.25786 | 0.628931 | − | 0.777461i | \(-0.283493\pi\) | ||||
0.628931 | + | 0.777461i | \(0.283493\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.843176 | −0.0559636 | −0.0279818 | − | 0.999608i | \(-0.508908\pi\) | ||||
−0.0279818 | + | 0.999608i | \(0.508908\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.86273 | −0.321338 | −0.160669 | − | 0.987008i | \(-0.551365\pi\) | ||||
−0.160669 | + | 0.987008i | \(0.551365\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −34.4822 | −2.26876 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.90268 | 0.321185 | 0.160593 | − | 0.987021i | \(-0.448659\pi\) | ||||
0.160593 | + | 0.987021i | \(0.448659\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.48945 | 0.421535 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.20164 | 0.401151 | 0.200575 | − | 0.979678i | \(-0.435719\pi\) | ||||
0.200575 | + | 0.979678i | \(0.435719\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.26412 | −0.210261 | −0.105130 | − | 0.994458i | \(-0.533526\pi\) | ||||
−0.105130 | + | 0.994458i | \(0.533526\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.80121 | −0.243848 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.843176 | −0.0536500 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.26412 | 0.0801106 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.4263 | −1.79425 | −0.897127 | − | 0.441773i | \(-0.854350\pi\) | ||||
−0.897127 | + | 0.441773i | \(0.854350\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.49097 | −0.219476 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.55192 | 0.595832 | 0.297916 | − | 0.954592i | \(-0.403708\pi\) | ||||
0.297916 | + | 0.954592i | \(0.403708\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.69643 | −0.478233 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.92112 | 0.242711 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.54706 | −0.588697 | −0.294349 | − | 0.955698i | \(-0.595103\pi\) | ||||
−0.294349 | + | 0.955698i | \(0.595103\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.24168 | 0.565582 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.3534 | −0.875144 | −0.437572 | − | 0.899183i | \(-0.644161\pi\) | ||||
−0.437572 | + | 0.899183i | \(0.644161\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.1038 | 0.735254 | 0.367627 | − | 0.929973i | \(-0.380170\pi\) | ||||
0.367627 | + | 0.929973i | \(0.380170\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.48945 | 0.392760 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.59055 | −0.215735 | −0.107868 | − | 0.994165i | \(-0.534402\pi\) | ||||
−0.107868 | + | 0.994165i | \(0.534402\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.18524 | −0.190695 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.7069 | 1.59320 | 0.796599 | − | 0.604509i | \(-0.206631\pi\) | ||||
0.796599 | + | 0.604509i | \(0.206631\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.4751 | −1.21712 | −0.608559 | − | 0.793508i | \(-0.708252\pi\) | ||||
−0.608559 | + | 0.793508i | \(0.708252\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.4668 | −1.32618 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5052 | 0.794424 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.0249 | 0.587672 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.1581 | −1.11923 | −0.559615 | − | 0.828753i | \(-0.689051\pi\) | ||||
−0.559615 | + | 0.828753i | \(0.689051\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −24.4803 | −1.42049 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.656992 | 0.0379948 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −45.8981 | −2.64552 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.46402 | −0.313900 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.0495 | −1.82916 | −0.914580 | − | 0.404404i | \(-0.867479\pi\) | ||||
−0.914580 | + | 0.404404i | \(0.867479\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.02493 | 0.342746 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.5301 | 1.16416 | 0.582079 | − | 0.813132i | \(-0.302240\pi\) | ||||
0.582079 | + | 0.813132i | \(0.302240\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.7932 | −0.836163 | −0.418082 | − | 0.908409i | \(-0.637297\pi\) | ||||
−0.418082 | + | 0.908409i | \(0.637297\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.9485 | −0.951925 | −0.475962 | − | 0.879466i | \(-0.657900\pi\) | ||||
−0.475962 | + | 0.879466i | \(0.657900\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 47.7463 | 2.67328 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.5532 | −0.923908 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.52315 | −0.307316 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.80310 | −0.265612 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.1123 | 0.833170 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.1287 | 1.21631 | 0.608153 | − | 0.793820i | \(-0.291911\pi\) | ||||
0.608153 | + | 0.793820i | \(0.291911\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.596929 | −0.0327115 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.9948 | 1.52498 | 0.762488 | − | 0.647002i | \(-0.223978\pi\) | ||||
0.762488 | + | 0.647002i | \(0.223978\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.4967 | −0.624414 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −38.7857 | −2.10037 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −40.3484 | −2.17861 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.1024 | 0.918105 | 0.459052 | − | 0.888409i | \(-0.348189\pi\) | ||||
0.459052 | + | 0.888409i | \(0.348189\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.2411 | −1.02995 | −0.514976 | − | 0.857205i | \(-0.672199\pi\) | ||||
−0.514976 | + | 0.857205i | \(0.672199\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.60713 | 0.245910 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.42735 | 0.395318 | 0.197659 | − | 0.980271i | \(-0.436666\pi\) | ||||
0.197659 | + | 0.980271i | \(0.436666\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 42.5086 | 2.24979 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.1767 | −1.48711 | −0.743555 | − | 0.668675i | \(-0.766862\pi\) | ||||
−0.743555 | + | 0.668675i | \(0.766862\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.7195 | −0.772575 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.1165 | 1.36327 | 0.681636 | − | 0.731692i | \(-0.261269\pi\) | ||||
0.681636 | + | 0.731692i | \(0.261269\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.74251 | −0.0907115 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.3140 | 1.52191 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.438217 | −0.0226900 | −0.0113450 | − | 0.999936i | \(-0.503611\pi\) | ||||
−0.0113450 | + | 0.999936i | \(0.503611\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.98572 | −0.462788 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.7753 | 0.707591 | 0.353795 | − | 0.935323i | \(-0.384891\pi\) | ||||
0.353795 | + | 0.935323i | \(0.384891\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.8962 | −0.814386 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.3153 | 1.14026 | 0.570130 | − | 0.821555i | \(-0.306893\pi\) | ||||
0.570130 | + | 0.821555i | \(0.306893\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.55982 | −0.180956 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.4263 | 0.731444 | 0.365722 | − | 0.930724i | \(-0.380822\pi\) | ||||
0.365722 | + | 0.930724i | \(0.380822\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.30357 | 0.217641 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.4160 | 1.02985 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.4512 | −0.825662 | −0.412831 | − | 0.910808i | \(-0.635460\pi\) | ||||
−0.412831 | + | 0.910808i | \(0.635460\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.69643 | −0.385304 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.96056 | 0.147843 | 0.0739216 | − | 0.997264i | \(-0.476449\pi\) | ||||
0.0739216 | + | 0.997264i | \(0.476449\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.29937 | 0.363608 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.26864 | −0.360293 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.0893 | 0.845012 | 0.422506 | − | 0.906360i | \(-0.361151\pi\) | ||||
0.422506 | + | 0.906360i | \(0.361151\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.4323 | 0.711893 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 55.4875 | 2.73036 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.1489 | 0.496991 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.3929 | 0.751991 | 0.375995 | − | 0.926622i | \(-0.377301\pi\) | ||||
0.375995 | + | 0.926622i | \(0.377301\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.4323 | −0.800862 | −0.400431 | − | 0.916327i | \(-0.631140\pi\) | ||||
−0.400431 | + | 0.916327i | \(0.631140\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.17210 | 0.0569895 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.7422 | −1.48772 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.12874 | 0.295899 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.1852 | −0.731447 | −0.365724 | − | 0.930724i | \(-0.619178\pi\) | ||||
−0.365724 | + | 0.930724i | \(0.619178\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.4380 | 1.12636 | 0.563179 | − | 0.826335i | \(-0.309578\pi\) | ||||
0.563179 | + | 0.826335i | \(0.309578\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.779187 | −0.0372735 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.511196 | −0.0243980 | −0.0121990 | − | 0.999926i | \(-0.503883\pi\) | ||||
−0.0121990 | + | 0.999926i | \(0.503883\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.70496 | −0.271665 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.7834 | 0.939940 | 0.469970 | − | 0.882682i | \(-0.344265\pi\) | ||||
0.469970 | + | 0.882682i | \(0.344265\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.02391 | −0.190325 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.1682 | 1.47092 | 0.735459 | − | 0.677569i | \(-0.236967\pi\) | ||||
0.735459 | + | 0.677569i | \(0.236967\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.2180 | −0.999119 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.99696 | 0.281762 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.20950 | −0.337246 | −0.168623 | − | 0.985681i | \(-0.553932\pi\) | ||||
−0.168623 | + | 0.985681i | \(0.553932\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 30.1786 | 1.40862 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.41591 | −0.252244 | −0.126122 | − | 0.992015i | \(-0.540253\pi\) | ||||
−0.126122 | + | 0.992015i | \(0.540253\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.73715 | −0.406050 | −0.203025 | − | 0.979174i | \(-0.565077\pi\) | ||||
−0.203025 | + | 0.979174i | \(0.565077\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.3584 | 0.803249 | 0.401624 | − | 0.915804i | \(-0.368446\pi\) | ||||
0.401624 | + | 0.915804i | \(0.368446\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −70.6280 | −3.26130 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 30.5781 | 1.40896 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −43.3469 | −1.99309 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.27357 | 0.104100 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.44682 | −0.340254 | −0.170127 | − | 0.985422i | \(-0.554418\pi\) | ||||
−0.170127 | + | 0.985422i | \(0.554418\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.36794 | 0.0623726 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.99696 | 0.272871 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.15530 | −0.0976661 | −0.0488330 | − | 0.998807i | \(-0.515550\pi\) | ||||
−0.0488330 | + | 0.998807i | \(0.515550\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.3140 | −1.32292 | −0.661461 | − | 0.749980i | \(-0.730063\pi\) | ||||
−0.661461 | + | 0.749980i | \(0.730063\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −58.8602 | −2.65093 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.44011 | 0.0645976 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.5696 | 1.05512 | 0.527560 | − | 0.849518i | \(-0.323107\pi\) | ||||
0.527560 | + | 0.849518i | \(0.323107\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.1537 | 0.542986 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.08297 | 0.404990 | 0.202495 | − | 0.979283i | \(-0.435095\pi\) | ||||
0.202495 | + | 0.979283i | \(0.435095\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.9373 | 0.885447 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.5112 | −0.820494 | −0.410247 | − | 0.911974i | \(-0.634558\pi\) | ||||
−0.410247 | + | 0.911974i | \(0.634558\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −47.8192 | −2.11540 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.46402 | −0.241242 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.2723 | 0.627697 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.5532 | −1.42893 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.0893 | −1.09918 | −0.549591 | − | 0.835434i | \(-0.685216\pi\) | ||||
−0.549591 | + | 0.835434i | \(0.685216\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.5181 | −1.24701 | −0.623504 | − | 0.781820i | \(-0.714292\pi\) | ||||
−0.623504 | + | 0.781820i | \(0.714292\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 47.8139 | 2.08281 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3929 | −0.973603 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.30357 | 0.186759 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.99318 | 0.172964 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.99696 | −0.258788 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −69.4677 | −2.99218 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.6485 | −0.672780 | −0.336390 | − | 0.941723i | \(-0.609206\pi\) | ||||
−0.336390 | + | 0.941723i | \(0.609206\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.24473 | 0.139245 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.8543 | −0.464098 | −0.232049 | − | 0.972704i | \(-0.574543\pi\) | ||||
−0.232049 | + | 0.972704i | \(0.574543\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.38434 | −0.101761 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.6570 | 0.454003 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.9759 | 0.806936 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.8763 | −0.799814 | −0.399907 | − | 0.916556i | \(-0.630958\pi\) | ||||
−0.399907 | + | 0.916556i | \(0.630958\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.15777 | 0.345037 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.1458 | 1.69496 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.2846 | −0.939183 | −0.469591 | − | 0.882884i | \(-0.655599\pi\) | ||||
−0.469591 | + | 0.882884i | \(0.655599\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 36.8170 | 1.54617 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.11833 | −0.298416 | −0.149208 | − | 0.988806i | \(-0.547672\pi\) | ||||
−0.149208 | + | 0.988806i | \(0.547672\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.21017 | −0.0506440 | −0.0253220 | − | 0.999679i | \(-0.508061\pi\) | ||||
−0.0253220 | + | 0.999679i | \(0.508061\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.44011 | 0.0601613 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.4143 | 1.72410 | 0.862050 | − | 0.506823i | \(-0.169180\pi\) | ||||
0.862050 | + | 0.506823i | \(0.169180\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 31.0814 | 1.29170 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.69643 | 0.153354 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.6846 | 1.14658 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.0591336 | −0.00244071 | −0.00122035 | − | 0.999999i | \(-0.500388\pi\) | ||||
−0.00122035 | + | 0.999999i | \(0.500388\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.65699 | −0.356705 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.47175 | 0.225078 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −42.8828 | −1.76099 | −0.880493 | − | 0.474059i | \(-0.842788\pi\) | ||||
−0.880493 | + | 0.474059i | \(0.842788\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.43706 | 0.304379 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.3430 | −0.626898 | −0.313449 | − | 0.949605i | \(-0.601485\pi\) | ||||
−0.313449 | + | 0.949605i | \(0.601485\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.5781 | −0.513072 | −0.256536 | − | 0.966535i | \(-0.582581\pi\) | ||||
−0.256536 | + | 0.966535i | \(0.582581\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.47785 | −0.223075 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.65751 | 0.107865 | 0.0539325 | − | 0.998545i | \(-0.482824\pi\) | ||||
0.0539325 | + | 0.998545i | \(0.482824\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −82.0208 | −3.32365 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.68602 | −0.108665 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.1052 | −1.37750 | −0.688748 | − | 0.725001i | \(-0.741839\pi\) | ||||
−0.688748 | + | 0.725001i | \(0.741839\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.9226 | −1.20464 | −0.602319 | − | 0.798255i | \(-0.705756\pi\) | ||||
−0.602319 | + | 0.798255i | \(0.705756\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.2102 | −0.691735 | −0.345868 | − | 0.938283i | \(-0.612415\pi\) | ||||
−0.345868 | + | 0.938283i | \(0.612415\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.25749 | 0.170847 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.0237 | 1.08268 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.26864 | −0.290281 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.96056 | 0.357281 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.36195 | 0.133837 | 0.0669186 | − | 0.997758i | \(-0.478683\pi\) | ||||
0.0669186 | + | 0.997758i | \(0.478683\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.1435 | −0.959617 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.0736 | 0.517996 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.111693 | 0.00441853 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.2745 | −0.642806 | −0.321403 | − | 0.946943i | \(-0.604154\pi\) | ||||
−0.321403 | + | 0.946943i | \(0.604154\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.7040 | 1.40803 | 0.704015 | − | 0.710185i | \(-0.251389\pi\) | ||||
0.704015 | + | 0.710185i | \(0.251389\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.2881 | 0.601036 | 0.300518 | − | 0.953776i | \(-0.402840\pi\) | ||||
0.300518 | + | 0.953776i | \(0.402840\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 52.4033 | 2.05701 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 66.6280 | 2.61136 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.4512 | −0.643785 | −0.321892 | − | 0.946776i | \(-0.604319\pi\) | ||||
−0.321892 | + | 0.946776i | \(0.604319\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.70882 | −0.144695 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.03944 | −0.274218 | −0.137109 | − | 0.990556i | \(-0.543781\pi\) | ||||
−0.137109 | + | 0.990556i | \(0.543781\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.35343 | 0.247120 | 0.123560 | − | 0.992337i | \(-0.460569\pi\) | ||||
0.123560 | + | 0.992337i | \(0.460569\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.55533 | −0.293425 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.30378 | −0.321524 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −30.4743 | −1.17820 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.0335 | −1.12082 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.08638 | −0.273160 | −0.136580 | − | 0.990629i | \(-0.543611\pi\) | ||||
−0.136580 | + | 0.990629i | \(0.543611\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.6095 | 0.676786 | 0.338393 | − | 0.941005i | \(-0.390117\pi\) | ||||
0.338393 | + | 0.941005i | \(0.390117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.3140 | 1.12497 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.36794 | 0.0524195 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.5855 | −1.01726 | −0.508632 | − | 0.860984i | \(-0.669849\pi\) | ||||
−0.508632 | + | 0.860984i | \(0.669849\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.88911 | 0.300988 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.21017 | −0.198492 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −49.4907 | −1.88271 | −0.941357 | − | 0.337411i | \(-0.890449\pi\) | ||||
−0.941357 | + | 0.337411i | \(0.890449\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.82027 | −0.297067 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.1570 | 0.990766 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.95392 | −0.300845 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.3389 | 1.10812 | 0.554058 | − | 0.832478i | \(-0.313079\pi\) | ||||
0.554058 | + | 0.832478i | \(0.313079\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.62236 | −0.0611886 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.9774 | −0.600891 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.7359 | 0.928975 | 0.464488 | − | 0.885580i | \(-0.346238\pi\) | ||||
0.464488 | + | 0.885580i | \(0.346238\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.47175 | 0.0551951 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.74541 | 0.252618 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.0613 | −0.375747 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.7548 | −0.997786 | −0.498893 | − | 0.866663i | \(-0.666260\pi\) | ||||
−0.498893 | + | 0.866663i | \(0.666260\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.6175 | 0.656112 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.29559 | 0.196945 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.2108 | 1.00919 | 0.504596 | − | 0.863355i | \(-0.331641\pi\) | ||||
0.504596 | + | 0.863355i | \(0.331641\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.4494 | 1.09072 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 53.4367 | 1.97643 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.0026 | 1.47753 | 0.738765 | − | 0.673963i | \(-0.235409\pi\) | ||||
0.738765 | + | 0.673963i | \(0.235409\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −66.7022 | −2.45701 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.1123 | −1.29163 | −0.645814 | − | 0.763495i | \(-0.723482\pi\) | ||||
−0.645814 | + | 0.763495i | \(0.723482\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.36794 | 0.0502525 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.6476 | −0.940918 | −0.470459 | − | 0.882422i | \(-0.655912\pi\) | ||||
−0.470459 | + | 0.882422i | \(0.655912\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.286693 | 0.0104895 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −48.4033 | −1.76862 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.2641 | 0.484015 | 0.242007 | − | 0.970274i | \(-0.422194\pi\) | ||||
0.242007 | + | 0.970274i | \(0.422194\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 46.1178 | 1.68063 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.77092 | 0.100711 | 0.0503554 | − | 0.998731i | \(-0.483965\pi\) | ||||
0.0503554 | + | 0.998731i | \(0.483965\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.66363 | 0.205577 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.7838 | 0.390914 | 0.195457 | − | 0.980712i | \(-0.437381\pi\) | ||||
0.195457 | + | 0.980712i | \(0.437381\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.0448 | −0.508455 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.86216 | −0.356102 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.6090 | −1.46440 | −0.732199 | − | 0.681090i | \(-0.761506\pi\) | ||||
−0.732199 | + | 0.681090i | \(0.761506\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.4967 | −0.558099 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.4410 | −0.627310 | −0.313655 | − | 0.949537i | \(-0.601554\pi\) | ||||
−0.313655 | + | 0.949537i | \(0.601554\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.4864 | 0.447947 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.73588 | −0.169680 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.36006 | 0.0486668 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −58.2300 | −2.08097 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.8346 | −1.09914 | −0.549568 | − | 0.835449i | \(-0.685208\pi\) | ||||
−0.549568 | + | 0.835449i | \(0.685208\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.4888 | 0.551416 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33.6175 | −1.19530 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.46402 | 0.194033 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38.1340 | −1.35077 | −0.675387 | − | 0.737463i | \(-0.736024\pi\) | ||||
−0.675387 | + | 0.737463i | \(0.736024\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.5945 | −0.622449 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.09594 | 0.0740563 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −45.1612 | −1.59371 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.2865 | 0.819722 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.7917 | 1.08258 | 0.541290 | − | 0.840836i | \(-0.317936\pi\) | ||||
0.541290 | + | 0.840836i | \(0.317936\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.0275 | 0.668145 | 0.334072 | − | 0.942547i | \(-0.391577\pi\) | ||||
0.334072 | + | 0.942547i | \(0.391577\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.6368 | −0.688692 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.67504 | −0.338487 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.47175 | 0.0514272 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.1228 | −1.47009 | −0.735047 | − | 0.678016i | \(-0.762840\pi\) | ||||
−0.735047 | + | 0.678016i | \(0.762840\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.6298 | 1.45112 | 0.725562 | − | 0.688157i | \(-0.241580\pi\) | ||||
0.725562 | + | 0.688157i | \(0.241580\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.54814 | −0.262475 | −0.131237 | − | 0.991351i | \(-0.541895\pi\) | ||||
−0.131237 | + | 0.991351i | \(0.541895\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.6674 | 1.79448 | 0.897242 | − | 0.441540i | \(-0.145568\pi\) | ||||
0.897242 | + | 0.441540i | \(0.145568\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.82518 | 0.202073 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 85.6376 | 2.96717 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 47.3020 | 1.63500 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.1682 | −1.55938 | −0.779689 | − | 0.626166i | \(-0.784623\pi\) | ||||
−0.779689 | + | 0.626166i | \(0.784623\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 84.5715 | 2.91626 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −43.3282 | −1.49230 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43.0415 | −1.47892 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 33.2180 | 1.14004 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.26412 | 0.0433336 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.6721 | 0.365405 | 0.182702 | − | 0.983168i | \(-0.441515\pi\) | ||||
0.182702 | + | 0.983168i | \(0.441515\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.7119 | 1.01494 | 0.507470 | − | 0.861669i | \(-0.330581\pi\) | ||||
0.507470 | + | 0.861669i | \(0.330581\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.6734 | 0.534769 | 0.267385 | − | 0.963590i | \(-0.413841\pi\) | ||||
0.267385 | + | 0.963590i | \(0.413841\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36.4494 | 1.24219 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.5741 | −1.34712 | −0.673559 | − | 0.739134i | \(-0.735235\pi\) | ||||
−0.673559 | + | 0.739134i | \(0.735235\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.9104 | −0.744115 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.9211 | 0.607932 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.5532 | 0.425348 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.27357 | 0.0769487 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.9393 | −1.61880 | −0.809398 | − | 0.587260i | \(-0.800207\pi\) | ||||
−0.809398 | + | 0.587260i | \(0.800207\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.0814 | 1.04835 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.32251 | −0.0782473 | −0.0391237 | − | 0.999234i | \(-0.512457\pi\) | ||||
−0.0391237 | + | 0.999234i | \(0.512457\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.3919 | 1.15738 | 0.578690 | − | 0.815548i | \(-0.303564\pi\) | ||||
0.578690 | + | 0.815548i | \(0.303564\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.1002 | −1.48074 | −0.740370 | − | 0.672200i | \(-0.765350\pi\) | ||||
−0.740370 | + | 0.672200i | \(0.765350\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −46.4822 | −1.55896 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 34.7706 | 1.16486 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.18559 | 0.106602 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.06588 | −0.0355887 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −92.2575 | −3.07696 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.1287 | −1.13699 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 74.4633 | 2.47798 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.3706 | 0.842417 | 0.421208 | − | 0.906964i | \(-0.361606\pi\) | ||||
0.421208 | + | 0.906964i | \(0.361606\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.23919 | −0.0411015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.8252 | −0.988152 | −0.494076 | − | 0.869419i | \(-0.664494\pi\) | ||||
−0.494076 | + | 0.869419i | \(0.664494\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.49097 | 0.115534 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 59.6985 | 1.97142 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.8422 | 0.522587 | 0.261293 | − | 0.965259i | \(-0.415851\pi\) | ||||
0.261293 | + | 0.965259i | \(0.415851\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 51.9959 | 1.71332 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.255960 | −0.00842501 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.36640 | 0.0448786 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.97098 | −0.261519 | −0.130760 | − | 0.991414i | \(-0.541742\pi\) | ||||
−0.130760 | + | 0.991414i | \(0.541742\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.5052 | −0.508163 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33.3073 | −1.09043 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.848033 | −0.0277040 | −0.0138520 | − | 0.999904i | \(-0.504409\pi\) | ||||
−0.0138520 | + | 0.999904i | \(0.504409\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.0000 | 0.783210 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.3140 | 1.02081 | 0.510403 | − | 0.859935i | \(-0.329496\pi\) | ||||
0.510403 | + | 0.859935i | \(0.329496\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.69013 | 0.120167 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.9885 | −0.844514 | −0.422257 | − | 0.906476i | \(-0.638762\pi\) | ||||
−0.422257 | + | 0.906476i | \(0.638762\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.49922 | 0.275896 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 27.4967 | 0.891641 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.6347 | −1.34868 | −0.674340 | − | 0.738421i | \(-0.735572\pi\) | ||||
−0.674340 | + | 0.738421i | \(0.735572\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −77.4618 | −2.50399 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 42.2016 | 1.36276 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43.9435 | 1.41753 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.75412 | −0.120975 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.2656 | 0.426593 | 0.213296 | − | 0.976988i | \(-0.431580\pi\) | ||||
0.213296 | + | 0.976988i | \(0.431580\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.96056 | 0.287855 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.3140 | −0.812364 | −0.406182 | − | 0.913792i | \(-0.633140\pi\) | ||||
−0.406182 | + | 0.913792i | \(0.633140\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.6763 | 0.951380 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.7694 | 1.62426 | 0.812128 | − | 0.583479i | \(-0.198309\pi\) | ||||
0.812128 | + | 0.583479i | \(0.198309\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.5216 | 0.815674 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.08930 | −0.0347788 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.4123 | 1.44843 | 0.724214 | − | 0.689575i | \(-0.242203\pi\) | ||||
0.724214 | + | 0.689575i | \(0.242203\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.5177 | −0.780407 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.53866 | 0.239716 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.6175 | −1.44909 | −0.724545 | − | 0.689228i | \(-0.757950\pi\) | ||||
−0.724545 | + | 0.689228i | \(0.757950\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −35.9009 | −1.13928 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −59.5705 | −1.88662 | −0.943309 | − | 0.331917i | \(-0.892305\pi\) | ||||
−0.943309 | + | 0.331917i | \(0.892305\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.86462 | 0.280464 |
(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 | 7600.2.a.cj.1.2 | 6 | ||
4.3 | odd | 2 | 1900.2.a.k.1.5 | 6 | |||
5.2 | odd | 4 | 1520.2.d.i.609.5 | 6 | |||
5.3 | odd | 4 | 1520.2.d.i.609.2 | 6 | |||
5.4 | even | 2 | inner | 7600.2.a.cj.1.5 | 6 | ||
20.3 | even | 4 | 380.2.c.b.229.5 | yes | 6 | ||
20.7 | even | 4 | 380.2.c.b.229.2 | ✓ | 6 | ||
20.19 | odd | 2 | 1900.2.a.k.1.2 | 6 | |||
60.23 | odd | 4 | 3420.2.f.c.1369.6 | 6 | |||
60.47 | odd | 4 | 3420.2.f.c.1369.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.c.b.229.2 | ✓ | 6 | 20.7 | even | 4 | ||
380.2.c.b.229.5 | yes | 6 | 20.3 | even | 4 | ||
1520.2.d.i.609.2 | 6 | 5.3 | odd | 4 | |||
1520.2.d.i.609.5 | 6 | 5.2 | odd | 4 | |||
1900.2.a.k.1.2 | 6 | 20.19 | odd | 2 | |||
1900.2.a.k.1.5 | 6 | 4.3 | odd | 2 | |||
3420.2.f.c.1369.5 | 6 | 60.47 | odd | 4 | |||
3420.2.f.c.1369.6 | 6 | 60.23 | odd | 4 | |||
7600.2.a.cj.1.2 | 6 | 1.1 | even | 1 | trivial | ||
7600.2.a.cj.1.5 | 6 | 5.4 | even | 2 | inner |