Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4655,2,Mod(1,4655)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4655, 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("4655.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4655 = 5 \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4655.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: | \(37.1703621409\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.48119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4655.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.48119 | −1.04736 | −0.523681 | − | 0.851914i | \(-0.675442\pi\) | ||||
−0.523681 | + | 0.851914i | \(0.675442\pi\) | |||||||
\(3\) | −0.806063 | −0.465381 | −0.232690 | − | 0.972551i | \(-0.574753\pi\) | ||||
−0.232690 | + | 0.972551i | \(0.574753\pi\) | |||||||
\(4\) | 0.193937 | 0.0969683 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.19394 | 0.487423 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.67513 | 0.945802 | ||||||||
\(9\) | −2.35026 | −0.783421 | ||||||||
\(10\) | 1.48119 | 0.468395 | ||||||||
\(11\) | 0.962389 | 0.290171 | 0.145086 | − | 0.989419i | \(-0.453654\pi\) | ||||
0.145086 | + | 0.989419i | \(0.453654\pi\) | |||||||
\(12\) | −0.156325 | −0.0451272 | ||||||||
\(13\) | −6.15633 | −1.70746 | −0.853729 | − | 0.520718i | \(-0.825664\pi\) | ||||
−0.853729 | + | 0.520718i | \(0.825664\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.806063 | 0.208125 | ||||||||
\(16\) | −4.35026 | −1.08757 | ||||||||
\(17\) | 6.31265 | 1.53104 | 0.765521 | − | 0.643411i | \(-0.222481\pi\) | ||||
0.765521 | + | 0.643411i | \(0.222481\pi\) | |||||||
\(18\) | 3.48119 | 0.820525 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −0.193937 | −0.0433655 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.42548 | −0.303914 | ||||||||
\(23\) | −4.96239 | −1.03473 | −0.517365 | − | 0.855765i | \(-0.673087\pi\) | ||||
−0.517365 | + | 0.855765i | \(0.673087\pi\) | |||||||
\(24\) | −2.15633 | −0.440158 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 9.11871 | 1.78833 | ||||||||
\(27\) | 4.31265 | 0.829970 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.61213 | −0.670755 | −0.335378 | − | 0.942084i | \(-0.608864\pi\) | ||||
−0.335378 | + | 0.942084i | \(0.608864\pi\) | |||||||
\(30\) | −1.19394 | −0.217982 | ||||||||
\(31\) | 5.92478 | 1.06412 | 0.532061 | − | 0.846706i | \(-0.321418\pi\) | ||||
0.532061 | + | 0.846706i | \(0.321418\pi\) | |||||||
\(32\) | 1.09332 | 0.193274 | ||||||||
\(33\) | −0.775746 | −0.135040 | ||||||||
\(34\) | −9.35026 | −1.60356 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.455802 | −0.0759669 | ||||||||
\(37\) | 10.1563 | 1.66969 | 0.834845 | − | 0.550485i | \(-0.185557\pi\) | ||||
0.834845 | + | 0.550485i | \(0.185557\pi\) | |||||||
\(38\) | −1.48119 | −0.240281 | ||||||||
\(39\) | 4.96239 | 0.794618 | ||||||||
\(40\) | −2.67513 | −0.422975 | ||||||||
\(41\) | −6.31265 | −0.985870 | −0.492935 | − | 0.870066i | \(-0.664076\pi\) | ||||
−0.492935 | + | 0.870066i | \(0.664076\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.12601 | −0.629210 | −0.314605 | − | 0.949223i | \(-0.601872\pi\) | ||||
−0.314605 | + | 0.949223i | \(0.601872\pi\) | |||||||
\(44\) | 0.186642 | 0.0281374 | ||||||||
\(45\) | 2.35026 | 0.350356 | ||||||||
\(46\) | 7.35026 | 1.08374 | ||||||||
\(47\) | −3.35026 | −0.488686 | −0.244343 | − | 0.969689i | \(-0.578572\pi\) | ||||
−0.244343 | + | 0.969689i | \(0.578572\pi\) | |||||||
\(48\) | 3.50659 | 0.506132 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.48119 | −0.209473 | ||||||||
\(51\) | −5.08840 | −0.712518 | ||||||||
\(52\) | −1.19394 | −0.165569 | ||||||||
\(53\) | 1.84367 | 0.253248 | 0.126624 | − | 0.991951i | \(-0.459586\pi\) | ||||
0.126624 | + | 0.991951i | \(0.459586\pi\) | |||||||
\(54\) | −6.38787 | −0.869279 | ||||||||
\(55\) | −0.962389 | −0.129768 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.806063 | −0.106766 | ||||||||
\(58\) | 5.35026 | 0.702524 | ||||||||
\(59\) | 6.38787 | 0.831630 | 0.415815 | − | 0.909449i | \(-0.363496\pi\) | ||||
0.415815 | + | 0.909449i | \(0.363496\pi\) | |||||||
\(60\) | 0.156325 | 0.0201815 | ||||||||
\(61\) | 11.2750 | 1.44362 | 0.721810 | − | 0.692091i | \(-0.243310\pi\) | ||||
0.721810 | + | 0.692091i | \(0.243310\pi\) | |||||||
\(62\) | −8.77575 | −1.11452 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.08110 | 0.885138 | ||||||||
\(65\) | 6.15633 | 0.763598 | ||||||||
\(66\) | 1.14903 | 0.141436 | ||||||||
\(67\) | −6.73084 | −0.822303 | −0.411152 | − | 0.911567i | \(-0.634873\pi\) | ||||
−0.411152 | + | 0.911567i | \(0.634873\pi\) | |||||||
\(68\) | 1.22425 | 0.148463 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.775746 | −0.0920641 | −0.0460321 | − | 0.998940i | \(-0.514658\pi\) | ||||
−0.0460321 | + | 0.998940i | \(0.514658\pi\) | |||||||
\(72\) | −6.28726 | −0.740960 | ||||||||
\(73\) | −0.387873 | −0.0453971 | −0.0226986 | − | 0.999742i | \(-0.507226\pi\) | ||||
−0.0226986 | + | 0.999742i | \(0.507226\pi\) | |||||||
\(74\) | −15.0435 | −1.74877 | ||||||||
\(75\) | −0.806063 | −0.0930762 | ||||||||
\(76\) | 0.193937 | 0.0222460 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.35026 | −0.832253 | ||||||||
\(79\) | −0.836381 | −0.0941002 | −0.0470501 | − | 0.998893i | \(-0.514982\pi\) | ||||
−0.0470501 | + | 0.998893i | \(0.514982\pi\) | |||||||
\(80\) | 4.35026 | 0.486374 | ||||||||
\(81\) | 3.57452 | 0.397168 | ||||||||
\(82\) | 9.35026 | 1.03256 | ||||||||
\(83\) | 7.03761 | 0.772478 | 0.386239 | − | 0.922399i | \(-0.373774\pi\) | ||||
0.386239 | + | 0.922399i | \(0.373774\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.31265 | −0.684703 | ||||||||
\(86\) | 6.11142 | 0.659011 | ||||||||
\(87\) | 2.91160 | 0.312157 | ||||||||
\(88\) | 2.57452 | 0.274444 | ||||||||
\(89\) | −7.08840 | −0.751369 | −0.375684 | − | 0.926748i | \(-0.622592\pi\) | ||||
−0.375684 | + | 0.926748i | \(0.622592\pi\) | |||||||
\(90\) | −3.48119 | −0.366950 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.962389 | −0.100336 | ||||||||
\(93\) | −4.77575 | −0.495222 | ||||||||
\(94\) | 4.96239 | 0.511831 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | −0.881286 | −0.0899459 | ||||||||
\(97\) | −10.9927 | −1.11614 | −0.558070 | − | 0.829794i | \(-0.688458\pi\) | ||||
−0.558070 | + | 0.829794i | \(0.688458\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.26187 | −0.227326 | ||||||||
\(100\) | 0.193937 | 0.0193937 | ||||||||
\(101\) | 2.64974 | 0.263659 | 0.131829 | − | 0.991272i | \(-0.457915\pi\) | ||||
0.131829 | + | 0.991272i | \(0.457915\pi\) | |||||||
\(102\) | 7.53690 | 0.746265 | ||||||||
\(103\) | 10.7308 | 1.05734 | 0.528671 | − | 0.848827i | \(-0.322691\pi\) | ||||
0.528671 | + | 0.848827i | \(0.322691\pi\) | |||||||
\(104\) | −16.4690 | −1.61492 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.73084 | −0.265243 | ||||||||
\(107\) | 4.80606 | 0.464620 | 0.232310 | − | 0.972642i | \(-0.425372\pi\) | ||||
0.232310 | + | 0.972642i | \(0.425372\pi\) | |||||||
\(108\) | 0.836381 | 0.0804808 | ||||||||
\(109\) | −2.77575 | −0.265868 | −0.132934 | − | 0.991125i | \(-0.542440\pi\) | ||||
−0.132934 | + | 0.991125i | \(0.542440\pi\) | |||||||
\(110\) | 1.42548 | 0.135915 | ||||||||
\(111\) | −8.18664 | −0.777042 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.99271 | 0.657818 | 0.328909 | − | 0.944362i | \(-0.393319\pi\) | ||||
0.328909 | + | 0.944362i | \(0.393319\pi\) | |||||||
\(114\) | 1.19394 | 0.111822 | ||||||||
\(115\) | 4.96239 | 0.462745 | ||||||||
\(116\) | −0.700523 | −0.0650420 | ||||||||
\(117\) | 14.4690 | 1.33766 | ||||||||
\(118\) | −9.46168 | −0.871018 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.15633 | 0.196845 | ||||||||
\(121\) | −10.0738 | −0.915801 | ||||||||
\(122\) | −16.7005 | −1.51199 | ||||||||
\(123\) | 5.08840 | 0.458805 | ||||||||
\(124\) | 1.14903 | 0.103186 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.4314 | 1.19184 | 0.595920 | − | 0.803043i | \(-0.296787\pi\) | ||||
0.595920 | + | 0.803043i | \(0.296787\pi\) | |||||||
\(128\) | −12.6751 | −1.12033 | ||||||||
\(129\) | 3.32582 | 0.292822 | ||||||||
\(130\) | −9.11871 | −0.799764 | ||||||||
\(131\) | −20.6253 | −1.80204 | −0.901020 | − | 0.433777i | \(-0.857181\pi\) | ||||
−0.901020 | + | 0.433777i | \(0.857181\pi\) | |||||||
\(132\) | −0.150446 | −0.0130946 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.96968 | 0.861249 | ||||||||
\(135\) | −4.31265 | −0.371174 | ||||||||
\(136\) | 16.8872 | 1.44806 | ||||||||
\(137\) | 20.2374 | 1.72900 | 0.864500 | − | 0.502633i | \(-0.167635\pi\) | ||||
0.864500 | + | 0.502633i | \(0.167635\pi\) | |||||||
\(138\) | −5.92478 | −0.504351 | ||||||||
\(139\) | 17.5877 | 1.49177 | 0.745884 | − | 0.666076i | \(-0.232027\pi\) | ||||
0.745884 | + | 0.666076i | \(0.232027\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.70052 | 0.227425 | ||||||||
\(142\) | 1.14903 | 0.0964245 | ||||||||
\(143\) | −5.92478 | −0.495455 | ||||||||
\(144\) | 10.2243 | 0.852021 | ||||||||
\(145\) | 3.61213 | 0.299971 | ||||||||
\(146\) | 0.574515 | 0.0475472 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.96968 | 0.161907 | ||||||||
\(149\) | −7.42548 | −0.608319 | −0.304160 | − | 0.952621i | \(-0.598376\pi\) | ||||
−0.304160 | + | 0.952621i | \(0.598376\pi\) | |||||||
\(150\) | 1.19394 | 0.0974845 | ||||||||
\(151\) | −1.61213 | −0.131193 | −0.0655965 | − | 0.997846i | \(-0.520895\pi\) | ||||
−0.0655965 | + | 0.997846i | \(0.520895\pi\) | |||||||
\(152\) | 2.67513 | 0.216982 | ||||||||
\(153\) | −14.8364 | −1.19945 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.92478 | −0.475890 | ||||||||
\(156\) | 0.962389 | 0.0770528 | ||||||||
\(157\) | −4.38787 | −0.350190 | −0.175095 | − | 0.984552i | \(-0.556023\pi\) | ||||
−0.175095 | + | 0.984552i | \(0.556023\pi\) | |||||||
\(158\) | 1.23884 | 0.0985570 | ||||||||
\(159\) | −1.48612 | −0.117857 | ||||||||
\(160\) | −1.09332 | −0.0864346 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.29455 | −0.415979 | ||||||||
\(163\) | −0.649738 | −0.0508914 | −0.0254457 | − | 0.999676i | \(-0.508100\pi\) | ||||
−0.0254457 | + | 0.999676i | \(0.508100\pi\) | |||||||
\(164\) | −1.22425 | −0.0955982 | ||||||||
\(165\) | 0.775746 | 0.0603918 | ||||||||
\(166\) | −10.4241 | −0.809065 | ||||||||
\(167\) | 15.3561 | 1.18829 | 0.594147 | − | 0.804357i | \(-0.297490\pi\) | ||||
0.594147 | + | 0.804357i | \(0.297490\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.9003 | 1.91541 | ||||||||
\(170\) | 9.35026 | 0.717132 | ||||||||
\(171\) | −2.35026 | −0.179729 | ||||||||
\(172\) | −0.800184 | −0.0610134 | ||||||||
\(173\) | −3.24472 | −0.246692 | −0.123346 | − | 0.992364i | \(-0.539362\pi\) | ||||
−0.123346 | + | 0.992364i | \(0.539362\pi\) | |||||||
\(174\) | −4.31265 | −0.326941 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.18664 | −0.315580 | ||||||||
\(177\) | −5.14903 | −0.387025 | ||||||||
\(178\) | 10.4993 | 0.786955 | ||||||||
\(179\) | 15.0132 | 1.12214 | 0.561069 | − | 0.827769i | \(-0.310390\pi\) | ||||
0.561069 | + | 0.827769i | \(0.310390\pi\) | |||||||
\(180\) | 0.455802 | 0.0339735 | ||||||||
\(181\) | −9.22425 | −0.685633 | −0.342817 | − | 0.939402i | \(-0.611381\pi\) | ||||
−0.342817 | + | 0.939402i | \(0.611381\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.08840 | −0.671834 | ||||||||
\(184\) | −13.2750 | −0.978649 | ||||||||
\(185\) | −10.1563 | −0.746708 | ||||||||
\(186\) | 7.07381 | 0.518677 | ||||||||
\(187\) | 6.07522 | 0.444264 | ||||||||
\(188\) | −0.649738 | −0.0473870 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.48119 | 0.107457 | ||||||||
\(191\) | −21.7743 | −1.57554 | −0.787768 | − | 0.615972i | \(-0.788763\pi\) | ||||
−0.787768 | + | 0.615972i | \(0.788763\pi\) | |||||||
\(192\) | −5.70782 | −0.411926 | ||||||||
\(193\) | 12.5442 | 0.902951 | 0.451476 | − | 0.892283i | \(-0.350898\pi\) | ||||
0.451476 | + | 0.892283i | \(0.350898\pi\) | |||||||
\(194\) | 16.2823 | 1.16900 | ||||||||
\(195\) | −4.96239 | −0.355364 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.5501 | 1.74912 | 0.874560 | − | 0.484917i | \(-0.161150\pi\) | ||||
0.874560 | + | 0.484917i | \(0.161150\pi\) | |||||||
\(198\) | 3.35026 | 0.238093 | ||||||||
\(199\) | −23.0738 | −1.63566 | −0.817829 | − | 0.575461i | \(-0.804823\pi\) | ||||
−0.817829 | + | 0.575461i | \(0.804823\pi\) | |||||||
\(200\) | 2.67513 | 0.189160 | ||||||||
\(201\) | 5.42548 | 0.382684 | ||||||||
\(202\) | −3.92478 | −0.276146 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.986826 | −0.0690917 | ||||||||
\(205\) | 6.31265 | 0.440895 | ||||||||
\(206\) | −15.8945 | −1.10742 | ||||||||
\(207\) | 11.6629 | 0.810628 | ||||||||
\(208\) | 26.7816 | 1.85697 | ||||||||
\(209\) | 0.962389 | 0.0665698 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.9380 | −1.44143 | −0.720714 | − | 0.693233i | \(-0.756186\pi\) | ||||
−0.720714 | + | 0.693233i | \(0.756186\pi\) | |||||||
\(212\) | 0.357556 | 0.0245570 | ||||||||
\(213\) | 0.625301 | 0.0428449 | ||||||||
\(214\) | −7.11871 | −0.486625 | ||||||||
\(215\) | 4.12601 | 0.281391 | ||||||||
\(216\) | 11.5369 | 0.784987 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.11142 | 0.278460 | ||||||||
\(219\) | 0.312650 | 0.0211270 | ||||||||
\(220\) | −0.186642 | −0.0125834 | ||||||||
\(221\) | −38.8627 | −2.61419 | ||||||||
\(222\) | 12.1260 | 0.813844 | ||||||||
\(223\) | 0.0303172 | 0.00203019 | 0.00101509 | − | 0.999999i | \(-0.499677\pi\) | ||||
0.00101509 | + | 0.999999i | \(0.499677\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.35026 | −0.156684 | ||||||||
\(226\) | −10.3576 | −0.688974 | ||||||||
\(227\) | −4.80606 | −0.318990 | −0.159495 | − | 0.987199i | \(-0.550987\pi\) | ||||
−0.159495 | + | 0.987199i | \(0.550987\pi\) | |||||||
\(228\) | −0.156325 | −0.0103529 | ||||||||
\(229\) | −1.87399 | −0.123837 | −0.0619184 | − | 0.998081i | \(-0.519722\pi\) | ||||
−0.0619184 | + | 0.998081i | \(0.519722\pi\) | |||||||
\(230\) | −7.35026 | −0.484662 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.66291 | −0.634401 | ||||||||
\(233\) | −11.1490 | −0.730397 | −0.365199 | − | 0.930930i | \(-0.618999\pi\) | ||||
−0.365199 | + | 0.930930i | \(0.618999\pi\) | |||||||
\(234\) | −21.4314 | −1.40101 | ||||||||
\(235\) | 3.35026 | 0.218547 | ||||||||
\(236\) | 1.23884 | 0.0806418 | ||||||||
\(237\) | 0.674176 | 0.0437924 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.29948 | 0.601533 | 0.300767 | − | 0.953698i | \(-0.402757\pi\) | ||||
0.300767 | + | 0.953698i | \(0.402757\pi\) | |||||||
\(240\) | −3.50659 | −0.226349 | ||||||||
\(241\) | 2.31265 | 0.148971 | 0.0744855 | − | 0.997222i | \(-0.476269\pi\) | ||||
0.0744855 | + | 0.997222i | \(0.476269\pi\) | |||||||
\(242\) | 14.9213 | 0.959175 | ||||||||
\(243\) | −15.8192 | −1.01480 | ||||||||
\(244\) | 2.18664 | 0.139985 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.53690 | −0.480535 | ||||||||
\(247\) | −6.15633 | −0.391718 | ||||||||
\(248\) | 15.8496 | 1.00645 | ||||||||
\(249\) | −5.67276 | −0.359497 | ||||||||
\(250\) | 1.48119 | 0.0936790 | ||||||||
\(251\) | −24.1016 | −1.52128 | −0.760639 | − | 0.649175i | \(-0.775114\pi\) | ||||
−0.760639 | + | 0.649175i | \(0.775114\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.77575 | −0.300249 | ||||||||
\(254\) | −19.8945 | −1.24829 | ||||||||
\(255\) | 5.08840 | 0.318648 | ||||||||
\(256\) | 4.61213 | 0.288258 | ||||||||
\(257\) | 13.3199 | 0.830875 | 0.415438 | − | 0.909622i | \(-0.363628\pi\) | ||||
0.415438 | + | 0.909622i | \(0.363628\pi\) | |||||||
\(258\) | −4.92619 | −0.306691 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.19394 | 0.0740448 | ||||||||
\(261\) | 8.48944 | 0.525483 | ||||||||
\(262\) | 30.5501 | 1.88739 | ||||||||
\(263\) | 12.9624 | 0.799295 | 0.399648 | − | 0.916669i | \(-0.369133\pi\) | ||||
0.399648 | + | 0.916669i | \(0.369133\pi\) | |||||||
\(264\) | −2.07522 | −0.127721 | ||||||||
\(265\) | −1.84367 | −0.113256 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.71370 | 0.349673 | ||||||||
\(268\) | −1.30536 | −0.0797373 | ||||||||
\(269\) | 11.4010 | 0.695134 | 0.347567 | − | 0.937655i | \(-0.387008\pi\) | ||||
0.347567 | + | 0.937655i | \(0.387008\pi\) | |||||||
\(270\) | 6.38787 | 0.388754 | ||||||||
\(271\) | −16.8119 | −1.02125 | −0.510626 | − | 0.859803i | \(-0.670586\pi\) | ||||
−0.510626 | + | 0.859803i | \(0.670586\pi\) | |||||||
\(272\) | −27.4617 | −1.66511 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −29.9756 | −1.81089 | ||||||||
\(275\) | 0.962389 | 0.0580342 | ||||||||
\(276\) | 0.775746 | 0.0466944 | ||||||||
\(277\) | −29.7889 | −1.78984 | −0.894921 | − | 0.446224i | \(-0.852769\pi\) | ||||
−0.894921 | + | 0.446224i | \(0.852769\pi\) | |||||||
\(278\) | −26.0508 | −1.56242 | ||||||||
\(279\) | −13.9248 | −0.833655 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.6121 | −0.692721 | −0.346361 | − | 0.938101i | \(-0.612583\pi\) | ||||
−0.346361 | + | 0.938101i | \(0.612583\pi\) | |||||||
\(282\) | −4.00000 | −0.238197 | ||||||||
\(283\) | −2.26187 | −0.134454 | −0.0672270 | − | 0.997738i | \(-0.521415\pi\) | ||||
−0.0672270 | + | 0.997738i | \(0.521415\pi\) | |||||||
\(284\) | −0.150446 | −0.00892730 | ||||||||
\(285\) | 0.806063 | 0.0477471 | ||||||||
\(286\) | 8.77575 | 0.518921 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.56959 | −0.151415 | ||||||||
\(289\) | 22.8496 | 1.34409 | ||||||||
\(290\) | −5.35026 | −0.314178 | ||||||||
\(291\) | 8.86082 | 0.519430 | ||||||||
\(292\) | −0.0752228 | −0.00440208 | ||||||||
\(293\) | −1.84367 | −0.107709 | −0.0538543 | − | 0.998549i | \(-0.517151\pi\) | ||||
−0.0538543 | + | 0.998549i | \(0.517151\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.38787 | −0.371916 | ||||||||
\(296\) | 27.1695 | 1.57920 | ||||||||
\(297\) | 4.15045 | 0.240833 | ||||||||
\(298\) | 10.9986 | 0.637131 | ||||||||
\(299\) | 30.5501 | 1.76676 | ||||||||
\(300\) | −0.156325 | −0.00902544 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.38787 | 0.137407 | ||||||||
\(303\) | −2.13586 | −0.122702 | ||||||||
\(304\) | −4.35026 | −0.249505 | ||||||||
\(305\) | −11.2750 | −0.645607 | ||||||||
\(306\) | 21.9756 | 1.25626 | ||||||||
\(307\) | −26.2071 | −1.49572 | −0.747859 | − | 0.663857i | \(-0.768918\pi\) | ||||
−0.747859 | + | 0.663857i | \(0.768918\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.64974 | −0.492066 | ||||||||
\(310\) | 8.77575 | 0.498429 | ||||||||
\(311\) | −6.51388 | −0.369368 | −0.184684 | − | 0.982798i | \(-0.559126\pi\) | ||||
−0.184684 | + | 0.982798i | \(0.559126\pi\) | |||||||
\(312\) | 13.2750 | 0.751551 | ||||||||
\(313\) | −16.0752 | −0.908625 | −0.454313 | − | 0.890842i | \(-0.650115\pi\) | ||||
−0.454313 | + | 0.890842i | \(0.650115\pi\) | |||||||
\(314\) | 6.49929 | 0.366776 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.162205 | −0.00912473 | ||||||||
\(317\) | −5.69323 | −0.319764 | −0.159882 | − | 0.987136i | \(-0.551111\pi\) | ||||
−0.159882 | + | 0.987136i | \(0.551111\pi\) | |||||||
\(318\) | 2.20123 | 0.123439 | ||||||||
\(319\) | −3.47627 | −0.194634 | ||||||||
\(320\) | −7.08110 | −0.395846 | ||||||||
\(321\) | −3.87399 | −0.216225 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.31265 | 0.351245 | ||||||||
\(324\) | 0.693229 | 0.0385127 | ||||||||
\(325\) | −6.15633 | −0.341491 | ||||||||
\(326\) | 0.962389 | 0.0533018 | ||||||||
\(327\) | 2.23743 | 0.123730 | ||||||||
\(328\) | −16.8872 | −0.932438 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.14903 | −0.0632521 | ||||||||
\(331\) | −12.3127 | −0.676764 | −0.338382 | − | 0.941009i | \(-0.609880\pi\) | ||||
−0.338382 | + | 0.941009i | \(0.609880\pi\) | |||||||
\(332\) | 1.36485 | 0.0749059 | ||||||||
\(333\) | −23.8700 | −1.30807 | ||||||||
\(334\) | −22.7454 | −1.24457 | ||||||||
\(335\) | 6.73084 | 0.367745 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.76845 | 0.205281 | 0.102640 | − | 0.994719i | \(-0.467271\pi\) | ||||
0.102640 | + | 0.994719i | \(0.467271\pi\) | |||||||
\(338\) | −36.8822 | −2.00613 | ||||||||
\(339\) | −5.63656 | −0.306136 | ||||||||
\(340\) | −1.22425 | −0.0663945 | ||||||||
\(341\) | 5.70194 | 0.308777 | ||||||||
\(342\) | 3.48119 | 0.188241 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −11.0376 | −0.595108 | ||||||||
\(345\) | −4.00000 | −0.215353 | ||||||||
\(346\) | 4.80606 | 0.258376 | ||||||||
\(347\) | −22.3634 | −1.20053 | −0.600266 | − | 0.799800i | \(-0.704939\pi\) | ||||
−0.600266 | + | 0.799800i | \(0.704939\pi\) | |||||||
\(348\) | 0.564666 | 0.0302693 | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.5501 | −1.41714 | ||||||||
\(352\) | 1.05220 | 0.0560824 | ||||||||
\(353\) | −5.53690 | −0.294700 | −0.147350 | − | 0.989084i | \(-0.547074\pi\) | ||||
−0.147350 | + | 0.989084i | \(0.547074\pi\) | |||||||
\(354\) | 7.62672 | 0.405355 | ||||||||
\(355\) | 0.775746 | 0.0411723 | ||||||||
\(356\) | −1.37470 | −0.0728589 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.2374 | −1.17528 | ||||||||
\(359\) | −10.3634 | −0.546961 | −0.273481 | − | 0.961878i | \(-0.588175\pi\) | ||||
−0.273481 | + | 0.961878i | \(0.588175\pi\) | |||||||
\(360\) | 6.28726 | 0.331368 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 13.6629 | 0.718107 | ||||||||
\(363\) | 8.12013 | 0.426196 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.387873 | 0.0203022 | ||||||||
\(366\) | 13.4617 | 0.703653 | ||||||||
\(367\) | −3.35026 | −0.174882 | −0.0874411 | − | 0.996170i | \(-0.527869\pi\) | ||||
−0.0874411 | + | 0.996170i | \(0.527869\pi\) | |||||||
\(368\) | 21.5877 | 1.12534 | ||||||||
\(369\) | 14.8364 | 0.772351 | ||||||||
\(370\) | 15.0435 | 0.782074 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.926192 | −0.0480208 | ||||||||
\(373\) | −12.6048 | −0.652653 | −0.326327 | − | 0.945257i | \(-0.605811\pi\) | ||||
−0.326327 | + | 0.945257i | \(0.605811\pi\) | |||||||
\(374\) | −8.99859 | −0.465306 | ||||||||
\(375\) | 0.806063 | 0.0416249 | ||||||||
\(376\) | −8.96239 | −0.462200 | ||||||||
\(377\) | 22.2374 | 1.14529 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.2506 | −1.91343 | −0.956717 | − | 0.291018i | \(-0.906006\pi\) | ||||
−0.956717 | + | 0.291018i | \(0.906006\pi\) | |||||||
\(380\) | −0.193937 | −0.00994874 | ||||||||
\(381\) | −10.8265 | −0.554660 | ||||||||
\(382\) | 32.2520 | 1.65016 | ||||||||
\(383\) | −30.8324 | −1.57546 | −0.787731 | − | 0.616019i | \(-0.788744\pi\) | ||||
−0.787731 | + | 0.616019i | \(0.788744\pi\) | |||||||
\(384\) | 10.2170 | 0.521382 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.5804 | −0.945717 | ||||||||
\(387\) | 9.69720 | 0.492936 | ||||||||
\(388\) | −2.13189 | −0.108230 | ||||||||
\(389\) | −1.37470 | −0.0697000 | −0.0348500 | − | 0.999393i | \(-0.511095\pi\) | ||||
−0.0348500 | + | 0.999393i | \(0.511095\pi\) | |||||||
\(390\) | 7.35026 | 0.372195 | ||||||||
\(391\) | −31.3258 | −1.58422 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.6253 | 0.838635 | ||||||||
\(394\) | −36.3634 | −1.83196 | ||||||||
\(395\) | 0.836381 | 0.0420829 | ||||||||
\(396\) | −0.438658 | −0.0220434 | ||||||||
\(397\) | 9.38646 | 0.471093 | 0.235546 | − | 0.971863i | \(-0.424312\pi\) | ||||
0.235546 | + | 0.971863i | \(0.424312\pi\) | |||||||
\(398\) | 34.1768 | 1.71313 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.35026 | −0.217513 | ||||||||
\(401\) | 14.1016 | 0.704199 | 0.352099 | − | 0.935963i | \(-0.385468\pi\) | ||||
0.352099 | + | 0.935963i | \(0.385468\pi\) | |||||||
\(402\) | −8.03620 | −0.400809 | ||||||||
\(403\) | −36.4749 | −1.81694 | ||||||||
\(404\) | 0.513881 | 0.0255665 | ||||||||
\(405\) | −3.57452 | −0.177619 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.77433 | 0.484496 | ||||||||
\(408\) | −13.6121 | −0.673901 | ||||||||
\(409\) | −35.1490 | −1.73801 | −0.869004 | − | 0.494805i | \(-0.835239\pi\) | ||||
−0.869004 | + | 0.494805i | \(0.835239\pi\) | |||||||
\(410\) | −9.35026 | −0.461777 | ||||||||
\(411\) | −16.3127 | −0.804644 | ||||||||
\(412\) | 2.08110 | 0.102529 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −17.2750 | −0.849022 | ||||||||
\(415\) | −7.03761 | −0.345463 | ||||||||
\(416\) | −6.73084 | −0.330007 | ||||||||
\(417\) | −14.1768 | −0.694241 | ||||||||
\(418\) | −1.42548 | −0.0697227 | ||||||||
\(419\) | −9.02776 | −0.441035 | −0.220518 | − | 0.975383i | \(-0.570775\pi\) | ||||
−0.220518 | + | 0.975383i | \(0.570775\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.2097 | 0.741274 | 0.370637 | − | 0.928778i | \(-0.379139\pi\) | ||||
0.370637 | + | 0.928778i | \(0.379139\pi\) | |||||||
\(422\) | 31.0132 | 1.50970 | ||||||||
\(423\) | 7.87399 | 0.382847 | ||||||||
\(424\) | 4.93207 | 0.239523 | ||||||||
\(425\) | 6.31265 | 0.306209 | ||||||||
\(426\) | −0.926192 | −0.0448741 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.932071 | 0.0450534 | ||||||||
\(429\) | 4.77575 | 0.230575 | ||||||||
\(430\) | −6.11142 | −0.294719 | ||||||||
\(431\) | 16.3127 | 0.785753 | 0.392876 | − | 0.919591i | \(-0.371480\pi\) | ||||
0.392876 | + | 0.919591i | \(0.371480\pi\) | |||||||
\(432\) | −18.7612 | −0.902647 | ||||||||
\(433\) | −11.1432 | −0.535506 | −0.267753 | − | 0.963488i | \(-0.586281\pi\) | ||||
−0.267753 | + | 0.963488i | \(0.586281\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.91160 | −0.139601 | ||||||||
\(436\) | −0.538319 | −0.0257808 | ||||||||
\(437\) | −4.96239 | −0.237383 | ||||||||
\(438\) | −0.463096 | −0.0221276 | ||||||||
\(439\) | −27.3865 | −1.30708 | −0.653542 | − | 0.756890i | \(-0.726718\pi\) | ||||
−0.653542 | + | 0.756890i | \(0.726718\pi\) | |||||||
\(440\) | −2.57452 | −0.122735 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 57.5633 | 2.73800 | ||||||||
\(443\) | 19.5125 | 0.927065 | 0.463533 | − | 0.886080i | \(-0.346582\pi\) | ||||
0.463533 | + | 0.886080i | \(0.346582\pi\) | |||||||
\(444\) | −1.58769 | −0.0753484 | ||||||||
\(445\) | 7.08840 | 0.336022 | ||||||||
\(446\) | −0.0449056 | −0.00212634 | ||||||||
\(447\) | 5.98541 | 0.283100 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.1016 | −1.04304 | −0.521519 | − | 0.853240i | \(-0.674634\pi\) | ||||
−0.521519 | + | 0.853240i | \(0.674634\pi\) | |||||||
\(450\) | 3.48119 | 0.164105 | ||||||||
\(451\) | −6.07522 | −0.286071 | ||||||||
\(452\) | 1.35614 | 0.0637875 | ||||||||
\(453\) | 1.29948 | 0.0610547 | ||||||||
\(454\) | 7.11871 | 0.334098 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.15633 | −0.100979 | ||||||||
\(457\) | −17.8496 | −0.834967 | −0.417483 | − | 0.908685i | \(-0.637088\pi\) | ||||
−0.417483 | + | 0.908685i | \(0.637088\pi\) | |||||||
\(458\) | 2.77575 | 0.129702 | ||||||||
\(459\) | 27.2243 | 1.27072 | ||||||||
\(460\) | 0.962389 | 0.0448716 | ||||||||
\(461\) | 35.2506 | 1.64178 | 0.820892 | − | 0.571083i | \(-0.193477\pi\) | ||||
0.820892 | + | 0.571083i | \(0.193477\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.3634 | −1.22521 | −0.612606 | − | 0.790388i | \(-0.709879\pi\) | ||||
−0.612606 | + | 0.790388i | \(0.709879\pi\) | |||||||
\(464\) | 15.7137 | 0.729490 | ||||||||
\(465\) | 4.77575 | 0.221470 | ||||||||
\(466\) | 16.5139 | 0.764991 | ||||||||
\(467\) | 6.78560 | 0.314000 | 0.157000 | − | 0.987599i | \(-0.449818\pi\) | ||||
0.157000 | + | 0.987599i | \(0.449818\pi\) | |||||||
\(468\) | 2.80606 | 0.129710 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.96239 | −0.228898 | ||||||||
\(471\) | 3.53690 | 0.162972 | ||||||||
\(472\) | 17.0884 | 0.786557 | ||||||||
\(473\) | −3.97082 | −0.182579 | ||||||||
\(474\) | −0.998585 | −0.0458665 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.33312 | −0.198400 | ||||||||
\(478\) | −13.7743 | −0.630023 | ||||||||
\(479\) | −12.7104 | −0.580752 | −0.290376 | − | 0.956913i | \(-0.593780\pi\) | ||||
−0.290376 | + | 0.956913i | \(0.593780\pi\) | |||||||
\(480\) | 0.881286 | 0.0402250 | ||||||||
\(481\) | −62.5256 | −2.85092 | ||||||||
\(482\) | −3.42548 | −0.156027 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.95368 | −0.0888036 | ||||||||
\(485\) | 10.9927 | 0.499153 | ||||||||
\(486\) | 23.4314 | 1.06287 | ||||||||
\(487\) | −15.7586 | −0.714090 | −0.357045 | − | 0.934087i | \(-0.616216\pi\) | ||||
−0.357045 | + | 0.934087i | \(0.616216\pi\) | |||||||
\(488\) | 30.1622 | 1.36538 | ||||||||
\(489\) | 0.523730 | 0.0236839 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.5501 | −0.656636 | −0.328318 | − | 0.944567i | \(-0.606482\pi\) | ||||
−0.328318 | + | 0.944567i | \(0.606482\pi\) | |||||||
\(492\) | 0.986826 | 0.0444896 | ||||||||
\(493\) | −22.8021 | −1.02695 | ||||||||
\(494\) | 9.11871 | 0.410270 | ||||||||
\(495\) | 2.26187 | 0.101663 | ||||||||
\(496\) | −25.7743 | −1.15730 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.40246 | 0.376523 | ||||||||
\(499\) | −5.48612 | −0.245592 | −0.122796 | − | 0.992432i | \(-0.539186\pi\) | ||||
−0.122796 | + | 0.992432i | \(0.539186\pi\) | |||||||
\(500\) | −0.193937 | −0.00867311 | ||||||||
\(501\) | −12.3780 | −0.553009 | ||||||||
\(502\) | 35.6991 | 1.59333 | ||||||||
\(503\) | 36.6615 | 1.63466 | 0.817328 | − | 0.576173i | \(-0.195455\pi\) | ||||
0.817328 | + | 0.576173i | \(0.195455\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.64974 | −0.117912 | ||||||||
\(506\) | 7.07381 | 0.314469 | ||||||||
\(507\) | −20.0713 | −0.891396 | ||||||||
\(508\) | 2.60483 | 0.115571 | ||||||||
\(509\) | −39.1900 | −1.73706 | −0.868532 | − | 0.495632i | \(-0.834936\pi\) | ||||
−0.868532 | + | 0.495632i | \(0.834936\pi\) | |||||||
\(510\) | −7.53690 | −0.333740 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 18.5188 | 0.818423 | ||||||||
\(513\) | 4.31265 | 0.190408 | ||||||||
\(514\) | −19.7294 | −0.870228 | ||||||||
\(515\) | −10.7308 | −0.472857 | ||||||||
\(516\) | 0.644999 | 0.0283945 | ||||||||
\(517\) | −3.22425 | −0.141803 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.61545 | 0.114806 | ||||||||
\(520\) | 16.4690 | 0.722212 | ||||||||
\(521\) | 17.7283 | 0.776690 | 0.388345 | − | 0.921514i | \(-0.373047\pi\) | ||||
0.388345 | + | 0.921514i | \(0.373047\pi\) | |||||||
\(522\) | −12.5745 | −0.550372 | ||||||||
\(523\) | 40.7572 | 1.78219 | 0.891094 | − | 0.453819i | \(-0.149939\pi\) | ||||
0.891094 | + | 0.453819i | \(0.149939\pi\) | |||||||
\(524\) | −4.00000 | −0.174741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.1998 | −0.837152 | ||||||||
\(527\) | 37.4010 | 1.62922 | ||||||||
\(528\) | 3.37470 | 0.146865 | ||||||||
\(529\) | 1.62530 | 0.0706652 | ||||||||
\(530\) | 2.73084 | 0.118620 | ||||||||
\(531\) | −15.0132 | −0.651516 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 38.8627 | 1.68333 | ||||||||
\(534\) | −8.46310 | −0.366234 | ||||||||
\(535\) | −4.80606 | −0.207784 | ||||||||
\(536\) | −18.0059 | −0.777736 | ||||||||
\(537\) | −12.1016 | −0.522221 | ||||||||
\(538\) | −16.8872 | −0.728057 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.836381 | −0.0359921 | ||||||||
\(541\) | 23.9003 | 1.02756 | 0.513778 | − | 0.857923i | \(-0.328246\pi\) | ||||
0.513778 | + | 0.857923i | \(0.328246\pi\) | |||||||
\(542\) | 24.9018 | 1.06962 | ||||||||
\(543\) | 7.43533 | 0.319081 | ||||||||
\(544\) | 6.90175 | 0.295910 | ||||||||
\(545\) | 2.77575 | 0.118900 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.55405 | 0.365745 | 0.182872 | − | 0.983137i | \(-0.441461\pi\) | ||||
0.182872 | + | 0.983137i | \(0.441461\pi\) | |||||||
\(548\) | 3.92478 | 0.167658 | ||||||||
\(549\) | −26.4993 | −1.13096 | ||||||||
\(550\) | −1.42548 | −0.0607829 | ||||||||
\(551\) | −3.61213 | −0.153882 | ||||||||
\(552\) | 10.7005 | 0.455445 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 44.1232 | 1.87461 | ||||||||
\(555\) | 8.18664 | 0.347504 | ||||||||
\(556\) | 3.41090 | 0.144654 | ||||||||
\(557\) | −4.23743 | −0.179546 | −0.0897728 | − | 0.995962i | \(-0.528614\pi\) | ||||
−0.0897728 | + | 0.995962i | \(0.528614\pi\) | |||||||
\(558\) | 20.6253 | 0.873139 | ||||||||
\(559\) | 25.4010 | 1.07435 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.89701 | −0.206752 | ||||||||
\(562\) | 17.1998 | 0.725530 | ||||||||
\(563\) | −16.4934 | −0.695114 | −0.347557 | − | 0.937659i | \(-0.612989\pi\) | ||||
−0.347557 | + | 0.937659i | \(0.612989\pi\) | |||||||
\(564\) | 0.523730 | 0.0220530 | ||||||||
\(565\) | −6.99271 | −0.294185 | ||||||||
\(566\) | 3.35026 | 0.140822 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.07522 | −0.0870744 | ||||||||
\(569\) | −10.0000 | −0.419222 | −0.209611 | − | 0.977785i | \(-0.567220\pi\) | ||||
−0.209611 | + | 0.977785i | \(0.567220\pi\) | |||||||
\(570\) | −1.19394 | −0.0500085 | ||||||||
\(571\) | −26.2619 | −1.09902 | −0.549512 | − | 0.835486i | \(-0.685186\pi\) | ||||
−0.549512 | + | 0.835486i | \(0.685186\pi\) | |||||||
\(572\) | −1.14903 | −0.0480434 | ||||||||
\(573\) | 17.5515 | 0.733224 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.96239 | −0.206946 | ||||||||
\(576\) | −16.6424 | −0.693435 | ||||||||
\(577\) | −30.1016 | −1.25314 | −0.626572 | − | 0.779363i | \(-0.715543\pi\) | ||||
−0.626572 | + | 0.779363i | \(0.715543\pi\) | |||||||
\(578\) | −33.8446 | −1.40775 | ||||||||
\(579\) | −10.1114 | −0.420216 | ||||||||
\(580\) | 0.700523 | 0.0290877 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13.1246 | −0.544032 | ||||||||
\(583\) | 1.77433 | 0.0734853 | ||||||||
\(584\) | −1.03761 | −0.0429367 | ||||||||
\(585\) | −14.4690 | −0.598219 | ||||||||
\(586\) | 2.73084 | 0.112810 | ||||||||
\(587\) | 35.1392 | 1.45035 | 0.725175 | − | 0.688565i | \(-0.241759\pi\) | ||||
0.725175 | + | 0.688565i | \(0.241759\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.92478 | 0.244126 | ||||||||
\(590\) | 9.46168 | 0.389531 | ||||||||
\(591\) | −19.7889 | −0.814007 | ||||||||
\(592\) | −44.1827 | −1.81590 | ||||||||
\(593\) | −34.3244 | −1.40953 | −0.704767 | − | 0.709439i | \(-0.748949\pi\) | ||||
−0.704767 | + | 0.709439i | \(0.748949\pi\) | |||||||
\(594\) | −6.14762 | −0.252240 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.44007 | −0.0589877 | ||||||||
\(597\) | 18.5990 | 0.761204 | ||||||||
\(598\) | −45.2506 | −1.85043 | ||||||||
\(599\) | 14.6107 | 0.596978 | 0.298489 | − | 0.954413i | \(-0.403517\pi\) | ||||
0.298489 | + | 0.954413i | \(0.403517\pi\) | |||||||
\(600\) | −2.15633 | −0.0880316 | ||||||||
\(601\) | −23.5633 | −0.961165 | −0.480583 | − | 0.876949i | \(-0.659575\pi\) | ||||
−0.480583 | + | 0.876949i | \(0.659575\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.8192 | 0.644209 | ||||||||
\(604\) | −0.312650 | −0.0127216 | ||||||||
\(605\) | 10.0738 | 0.409559 | ||||||||
\(606\) | 3.16362 | 0.128513 | ||||||||
\(607\) | 8.80606 | 0.357427 | 0.178714 | − | 0.983901i | \(-0.442806\pi\) | ||||
0.178714 | + | 0.983901i | \(0.442806\pi\) | |||||||
\(608\) | 1.09332 | 0.0443400 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.7005 | 0.676184 | ||||||||
\(611\) | 20.6253 | 0.834410 | ||||||||
\(612\) | −2.87732 | −0.116309 | ||||||||
\(613\) | 10.4142 | 0.420626 | 0.210313 | − | 0.977634i | \(-0.432552\pi\) | ||||
0.210313 | + | 0.977634i | \(0.432552\pi\) | |||||||
\(614\) | 38.8178 | 1.56656 | ||||||||
\(615\) | −5.08840 | −0.205184 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.2849 | −0.695863 | −0.347932 | − | 0.937520i | \(-0.613116\pi\) | ||||
−0.347932 | + | 0.937520i | \(0.613116\pi\) | |||||||
\(618\) | 12.8119 | 0.515372 | ||||||||
\(619\) | 10.6351 | 0.427463 | 0.213731 | − | 0.976892i | \(-0.431438\pi\) | ||||
0.213731 | + | 0.976892i | \(0.431438\pi\) | |||||||
\(620\) | −1.14903 | −0.0461462 | ||||||||
\(621\) | −21.4010 | −0.858794 | ||||||||
\(622\) | 9.64832 | 0.386863 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −21.5877 | −0.864199 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 23.8105 | 0.951660 | ||||||||
\(627\) | −0.775746 | −0.0309803 | ||||||||
\(628\) | −0.850969 | −0.0339574 | ||||||||
\(629\) | 64.1133 | 2.55637 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.5599 | −0.659240 | −0.329620 | − | 0.944114i | \(-0.606921\pi\) | ||||
−0.329620 | + | 0.944114i | \(0.606921\pi\) | |||||||
\(632\) | −2.23743 | −0.0890001 | ||||||||
\(633\) | 16.8773 | 0.670813 | ||||||||
\(634\) | 8.43278 | 0.334908 | ||||||||
\(635\) | −13.4314 | −0.533007 | ||||||||
\(636\) | −0.288213 | −0.0114284 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.14903 | 0.203852 | ||||||||
\(639\) | 1.82321 | 0.0721249 | ||||||||
\(640\) | 12.6751 | 0.501029 | ||||||||
\(641\) | −16.7612 | −0.662026 | −0.331013 | − | 0.943626i | \(-0.607390\pi\) | ||||
−0.331013 | + | 0.943626i | \(0.607390\pi\) | |||||||
\(642\) | 5.73813 | 0.226466 | ||||||||
\(643\) | −5.73813 | −0.226290 | −0.113145 | − | 0.993578i | \(-0.536092\pi\) | ||||
−0.113145 | + | 0.993578i | \(0.536092\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.32582 | −0.130954 | ||||||||
\(646\) | −9.35026 | −0.367881 | ||||||||
\(647\) | 37.2144 | 1.46305 | 0.731525 | − | 0.681815i | \(-0.238809\pi\) | ||||
0.731525 | + | 0.681815i | \(0.238809\pi\) | |||||||
\(648\) | 9.56230 | 0.375642 | ||||||||
\(649\) | 6.14762 | 0.241315 | ||||||||
\(650\) | 9.11871 | 0.357665 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.126008 | −0.00493485 | ||||||||
\(653\) | 11.7626 | 0.460305 | 0.230153 | − | 0.973155i | \(-0.426077\pi\) | ||||
0.230153 | + | 0.973155i | \(0.426077\pi\) | |||||||
\(654\) | −3.31406 | −0.129590 | ||||||||
\(655\) | 20.6253 | 0.805897 | ||||||||
\(656\) | 27.4617 | 1.07220 | ||||||||
\(657\) | 0.911603 | 0.0355650 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.23884 | 0.0482584 | 0.0241292 | − | 0.999709i | \(-0.492319\pi\) | ||||
0.0241292 | + | 0.999709i | \(0.492319\pi\) | |||||||
\(660\) | 0.150446 | 0.00585609 | ||||||||
\(661\) | 9.53690 | 0.370943 | 0.185471 | − | 0.982650i | \(-0.440619\pi\) | ||||
0.185471 | + | 0.982650i | \(0.440619\pi\) | |||||||
\(662\) | 18.2374 | 0.708818 | ||||||||
\(663\) | 31.3258 | 1.21659 | ||||||||
\(664\) | 18.8265 | 0.730611 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 35.3561 | 1.37002 | ||||||||
\(667\) | 17.9248 | 0.694050 | ||||||||
\(668\) | 2.97812 | 0.115227 | ||||||||
\(669\) | −0.0244376 | −0.000944811 0 | ||||||||
\(670\) | −9.96968 | −0.385162 | ||||||||
\(671\) | 10.8510 | 0.418897 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.9307 | 1.53921 | 0.769607 | − | 0.638518i | \(-0.220452\pi\) | ||||
0.769607 | + | 0.638518i | \(0.220452\pi\) | |||||||
\(674\) | −5.58181 | −0.215003 | ||||||||
\(675\) | 4.31265 | 0.165994 | ||||||||
\(676\) | 4.82909 | 0.185734 | ||||||||
\(677\) | 3.05334 | 0.117349 | 0.0586747 | − | 0.998277i | \(-0.481313\pi\) | ||||
0.0586747 | + | 0.998277i | \(0.481313\pi\) | |||||||
\(678\) | 8.34885 | 0.320636 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −16.8872 | −0.647593 | ||||||||
\(681\) | 3.87399 | 0.148452 | ||||||||
\(682\) | −8.44568 | −0.323402 | ||||||||
\(683\) | 29.2692 | 1.11995 | 0.559977 | − | 0.828508i | \(-0.310810\pi\) | ||||
0.559977 | + | 0.828508i | \(0.310810\pi\) | |||||||
\(684\) | −0.455802 | −0.0174280 | ||||||||
\(685\) | −20.2374 | −0.773232 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.51056 | 0.0576313 | ||||||||
\(688\) | 17.9492 | 0.684307 | ||||||||
\(689\) | −11.3503 | −0.432411 | ||||||||
\(690\) | 5.92478 | 0.225552 | ||||||||
\(691\) | −2.63515 | −0.100246 | −0.0501229 | − | 0.998743i | \(-0.515961\pi\) | ||||
−0.0501229 | + | 0.998743i | \(0.515961\pi\) | |||||||
\(692\) | −0.629270 | −0.0239213 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.1246 | 1.25739 | ||||||||
\(695\) | −17.5877 | −0.667139 | ||||||||
\(696\) | 7.78892 | 0.295238 | ||||||||
\(697\) | −39.8496 | −1.50941 | ||||||||
\(698\) | −14.8119 | −0.560640 | ||||||||
\(699\) | 8.98683 | 0.339913 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.0494 | −0.946102 | −0.473051 | − | 0.881035i | \(-0.656847\pi\) | ||||
−0.473051 | + | 0.881035i | \(0.656847\pi\) | |||||||
\(702\) | 39.3258 | 1.48426 | ||||||||
\(703\) | 10.1563 | 0.383053 | ||||||||
\(704\) | 6.81477 | 0.256841 | ||||||||
\(705\) | −2.70052 | −0.101708 | ||||||||
\(706\) | 8.20123 | 0.308657 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.998585 | −0.0375291 | ||||||||
\(709\) | −41.6991 | −1.56604 | −0.783021 | − | 0.621995i | \(-0.786323\pi\) | ||||
−0.783021 | + | 0.621995i | \(0.786323\pi\) | |||||||
\(710\) | −1.14903 | −0.0431224 | ||||||||
\(711\) | 1.96571 | 0.0737200 | ||||||||
\(712\) | −18.9624 | −0.710646 | ||||||||
\(713\) | −29.4010 | −1.10108 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.92478 | 0.221574 | ||||||||
\(716\) | 2.91160 | 0.108812 | ||||||||
\(717\) | −7.49597 | −0.279942 | ||||||||
\(718\) | 15.3503 | 0.572867 | ||||||||
\(719\) | −30.6351 | −1.14250 | −0.571249 | − | 0.820777i | \(-0.693541\pi\) | ||||
−0.571249 | + | 0.820777i | \(0.693541\pi\) | |||||||
\(720\) | −10.2243 | −0.381035 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.48119 | −0.0551243 | ||||||||
\(723\) | −1.86414 | −0.0693282 | ||||||||
\(724\) | −1.78892 | −0.0664847 | ||||||||
\(725\) | −3.61213 | −0.134151 | ||||||||
\(726\) | −12.0275 | −0.446382 | ||||||||
\(727\) | −7.50071 | −0.278186 | −0.139093 | − | 0.990279i | \(-0.544419\pi\) | ||||
−0.139093 | + | 0.990279i | \(0.544419\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.02776 | 0.0751023 | ||||||||
\(730\) | −0.574515 | −0.0212638 | ||||||||
\(731\) | −26.0460 | −0.963348 | ||||||||
\(732\) | −1.76257 | −0.0651466 | ||||||||
\(733\) | −9.84955 | −0.363802 | −0.181901 | − | 0.983317i | \(-0.558225\pi\) | ||||
−0.181901 | + | 0.983317i | \(0.558225\pi\) | |||||||
\(734\) | 4.96239 | 0.183165 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.42548 | −0.199986 | ||||||||
\(737\) | −6.47768 | −0.238609 | ||||||||
\(738\) | −21.9756 | −0.808932 | ||||||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | −1.96968 | −0.0724070 | ||||||||
\(741\) | 4.96239 | 0.182298 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.7177 | −0.576625 | −0.288313 | − | 0.957536i | \(-0.593094\pi\) | ||||
−0.288313 | + | 0.957536i | \(0.593094\pi\) | |||||||
\(744\) | −12.7757 | −0.468382 | ||||||||
\(745\) | 7.42548 | 0.272049 | ||||||||
\(746\) | 18.6702 | 0.683565 | ||||||||
\(747\) | −16.5402 | −0.605175 | ||||||||
\(748\) | 1.17821 | 0.0430795 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.19394 | −0.0435964 | ||||||||
\(751\) | −43.7400 | −1.59610 | −0.798048 | − | 0.602593i | \(-0.794134\pi\) | ||||
−0.798048 | + | 0.602593i | \(0.794134\pi\) | |||||||
\(752\) | 14.5745 | 0.531478 | ||||||||
\(753\) | 19.4274 | 0.707974 | ||||||||
\(754\) | −32.9380 | −1.19953 | ||||||||
\(755\) | 1.61213 | 0.0586713 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.7743 | −0.573328 | −0.286664 | − | 0.958031i | \(-0.592546\pi\) | ||||
−0.286664 | + | 0.958031i | \(0.592546\pi\) | |||||||
\(758\) | 55.1754 | 2.00406 | ||||||||
\(759\) | 3.84955 | 0.139730 | ||||||||
\(760\) | −2.67513 | −0.0970372 | ||||||||
\(761\) | −43.2262 | −1.56695 | −0.783474 | − | 0.621425i | \(-0.786554\pi\) | ||||
−0.783474 | + | 0.621425i | \(0.786554\pi\) | |||||||
\(762\) | 16.0362 | 0.580930 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.22284 | −0.152777 | ||||||||
\(765\) | 14.8364 | 0.536410 | ||||||||
\(766\) | 45.6688 | 1.65008 | ||||||||
\(767\) | −39.3258 | −1.41997 | ||||||||
\(768\) | −3.71767 | −0.134150 | ||||||||
\(769\) | 19.1246 | 0.689650 | 0.344825 | − | 0.938667i | \(-0.387938\pi\) | ||||
0.344825 | + | 0.938667i | \(0.387938\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.7367 | −0.386674 | ||||||||
\(772\) | 2.43278 | 0.0875576 | ||||||||
\(773\) | −25.8846 | −0.931005 | −0.465502 | − | 0.885047i | \(-0.654126\pi\) | ||||
−0.465502 | + | 0.885047i | \(0.654126\pi\) | |||||||
\(774\) | −14.3634 | −0.516283 | ||||||||
\(775\) | 5.92478 | 0.212824 | ||||||||
\(776\) | −29.4069 | −1.05565 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.03620 | 0.0730012 | ||||||||
\(779\) | −6.31265 | −0.226174 | ||||||||
\(780\) | −0.962389 | −0.0344590 | ||||||||
\(781\) | −0.746569 | −0.0267144 | ||||||||
\(782\) | 46.3996 | 1.65925 | ||||||||
\(783\) | −15.5778 | −0.556707 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.38787 | 0.156610 | ||||||||
\(786\) | −24.6253 | −0.878355 | ||||||||
\(787\) | −19.9814 | −0.712261 | −0.356131 | − | 0.934436i | \(-0.615904\pi\) | ||||
−0.356131 | + | 0.934436i | \(0.615904\pi\) | |||||||
\(788\) | 4.76116 | 0.169609 | ||||||||
\(789\) | −10.4485 | −0.371977 | ||||||||
\(790\) | −1.23884 | −0.0440760 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.05079 | −0.215005 | ||||||||
\(793\) | −69.4128 | −2.46492 | ||||||||
\(794\) | −13.9032 | −0.493405 | ||||||||
\(795\) | 1.48612 | 0.0527072 | ||||||||
\(796\) | −4.47486 | −0.158607 | ||||||||
\(797\) | −28.6458 | −1.01469 | −0.507343 | − | 0.861744i | \(-0.669372\pi\) | ||||
−0.507343 | + | 0.861744i | \(0.669372\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.1490 | −0.748199 | ||||||||
\(800\) | 1.09332 | 0.0386547 | ||||||||
\(801\) | 16.6596 | 0.588638 | ||||||||
\(802\) | −20.8872 | −0.737551 | ||||||||
\(803\) | −0.373285 | −0.0131729 | ||||||||
\(804\) | 1.05220 | 0.0371082 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 54.0263 | 1.90300 | ||||||||
\(807\) | −9.18997 | −0.323502 | ||||||||
\(808\) | 7.08840 | 0.249369 | ||||||||
\(809\) | −17.2243 | −0.605573 | −0.302786 | − | 0.953058i | \(-0.597917\pi\) | ||||
−0.302786 | + | 0.953058i | \(0.597917\pi\) | |||||||
\(810\) | 5.29455 | 0.186032 | ||||||||
\(811\) | 15.6267 | 0.548728 | 0.274364 | − | 0.961626i | \(-0.411533\pi\) | ||||
0.274364 | + | 0.961626i | \(0.411533\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.5515 | 0.475272 | ||||||||
\(814\) | −14.4777 | −0.507443 | ||||||||
\(815\) | 0.649738 | 0.0227593 | ||||||||
\(816\) | 22.1359 | 0.774910 | ||||||||
\(817\) | −4.12601 | −0.144351 | ||||||||
\(818\) | 52.0625 | 1.82032 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.22425 | 0.0427528 | ||||||||
\(821\) | 39.2506 | 1.36986 | 0.684928 | − | 0.728611i | \(-0.259834\pi\) | ||||
0.684928 | + | 0.728611i | \(0.259834\pi\) | |||||||
\(822\) | 24.1622 | 0.842754 | ||||||||
\(823\) | −45.5271 | −1.58697 | −0.793487 | − | 0.608588i | \(-0.791736\pi\) | ||||
−0.793487 | + | 0.608588i | \(0.791736\pi\) | |||||||
\(824\) | 28.7064 | 1.00003 | ||||||||
\(825\) | −0.775746 | −0.0270080 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.0698 | 0.593576 | 0.296788 | − | 0.954943i | \(-0.404084\pi\) | ||||
0.296788 | + | 0.954943i | \(0.404084\pi\) | |||||||
\(828\) | 2.26187 | 0.0786052 | ||||||||
\(829\) | −1.69911 | −0.0590125 | −0.0295062 | − | 0.999565i | \(-0.509393\pi\) | ||||
−0.0295062 | + | 0.999565i | \(0.509393\pi\) | |||||||
\(830\) | 10.4241 | 0.361825 | ||||||||
\(831\) | 24.0118 | 0.832959 | ||||||||
\(832\) | −43.5936 | −1.51134 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 20.9986 | 0.727122 | ||||||||
\(835\) | −15.3561 | −0.531421 | ||||||||
\(836\) | 0.186642 | 0.00645516 | ||||||||
\(837\) | 25.5515 | 0.883189 | ||||||||
\(838\) | 13.3719 | 0.461924 | ||||||||
\(839\) | 50.5910 | 1.74660 | 0.873298 | − | 0.487187i | \(-0.161977\pi\) | ||||
0.873298 | + | 0.487187i | \(0.161977\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9525 | −0.550088 | ||||||||
\(842\) | −22.5285 | −0.776382 | ||||||||
\(843\) | 9.36011 | 0.322379 | ||||||||
\(844\) | −4.06063 | −0.139773 | ||||||||
\(845\) | −24.9003 | −0.856598 | ||||||||
\(846\) | −11.6629 | −0.400979 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.02047 | −0.275424 | ||||||||
\(849\) | 1.82321 | 0.0625723 | ||||||||
\(850\) | −9.35026 | −0.320711 | ||||||||
\(851\) | −50.3996 | −1.72768 | ||||||||
\(852\) | 0.121269 | 0.00415460 | ||||||||
\(853\) | 22.5237 | 0.771198 | 0.385599 | − | 0.922667i | \(-0.373995\pi\) | ||||
0.385599 | + | 0.922667i | \(0.373995\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.35026 | 0.0803773 | ||||||||
\(856\) | 12.8568 | 0.439438 | ||||||||
\(857\) | 23.6180 | 0.806776 | 0.403388 | − | 0.915029i | \(-0.367833\pi\) | ||||
0.403388 | + | 0.915029i | \(0.367833\pi\) | |||||||
\(858\) | −7.07381 | −0.241496 | ||||||||
\(859\) | −15.1754 | −0.517777 | −0.258889 | − | 0.965907i | \(-0.583356\pi\) | ||||
−0.258889 | + | 0.965907i | \(0.583356\pi\) | |||||||
\(860\) | 0.800184 | 0.0272860 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.1622 | −0.822968 | ||||||||
\(863\) | 30.1055 | 1.02480 | 0.512402 | − | 0.858746i | \(-0.328756\pi\) | ||||
0.512402 | + | 0.858746i | \(0.328756\pi\) | |||||||
\(864\) | 4.71511 | 0.160411 | ||||||||
\(865\) | 3.24472 | 0.110324 | ||||||||
\(866\) | 16.5052 | 0.560869 | ||||||||
\(867\) | −18.4182 | −0.625515 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.804923 | −0.0273051 | ||||||||
\(870\) | 4.31265 | 0.146213 | ||||||||
\(871\) | 41.4372 | 1.40405 | ||||||||
\(872\) | −7.42548 | −0.251459 | ||||||||
\(873\) | 25.8357 | 0.874407 | ||||||||
\(874\) | 7.35026 | 0.248626 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.0606343 | 0.00204864 | ||||||||
\(877\) | −5.53102 | −0.186769 | −0.0933847 | − | 0.995630i | \(-0.529769\pi\) | ||||
−0.0933847 | + | 0.995630i | \(0.529769\pi\) | |||||||
\(878\) | 40.5647 | 1.36899 | ||||||||
\(879\) | 1.48612 | 0.0501255 | ||||||||
\(880\) | 4.18664 | 0.141132 | ||||||||
\(881\) | −20.8265 | −0.701664 | −0.350832 | − | 0.936438i | \(-0.614101\pi\) | ||||
−0.350832 | + | 0.936438i | \(0.614101\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.1509 | 1.45214 | 0.726072 | − | 0.687618i | \(-0.241344\pi\) | ||||
0.726072 | + | 0.687618i | \(0.241344\pi\) | |||||||
\(884\) | −7.53690 | −0.253494 | ||||||||
\(885\) | 5.14903 | 0.173083 | ||||||||
\(886\) | −28.9018 | −0.970973 | ||||||||
\(887\) | 44.5461 | 1.49571 | 0.747856 | − | 0.663861i | \(-0.231083\pi\) | ||||
0.747856 | + | 0.663861i | \(0.231083\pi\) | |||||||
\(888\) | −21.9003 | −0.734927 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −10.4993 | −0.351937 | ||||||||
\(891\) | 3.44007 | 0.115247 | ||||||||
\(892\) | 0.00587961 | 0.000196864 0 | ||||||||
\(893\) | −3.35026 | −0.112112 | ||||||||
\(894\) | −8.86556 | −0.296509 | ||||||||
\(895\) | −15.0132 | −0.501835 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.6253 | −0.822215 | ||||||||
\(898\) | 32.7367 | 1.09244 | ||||||||
\(899\) | −21.4010 | −0.713765 | ||||||||
\(900\) | −0.455802 | −0.0151934 | ||||||||
\(901\) | 11.6385 | 0.387734 | ||||||||
\(902\) | 8.99859 | 0.299620 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.7064 | 0.622166 | ||||||||
\(905\) | 9.22425 | 0.306625 | ||||||||
\(906\) | −1.92478 | −0.0639464 | ||||||||
\(907\) | 53.7558 | 1.78493 | 0.892466 | − | 0.451115i | \(-0.148974\pi\) | ||||
0.892466 | + | 0.451115i | \(0.148974\pi\) | |||||||
\(908\) | −0.932071 | −0.0309319 | ||||||||
\(909\) | −6.22758 | −0.206556 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.28630 | −0.0757486 | −0.0378743 | − | 0.999283i | \(-0.512059\pi\) | ||||
−0.0378743 | + | 0.999283i | \(0.512059\pi\) | |||||||
\(912\) | 3.50659 | 0.116115 | ||||||||
\(913\) | 6.77292 | 0.224151 | ||||||||
\(914\) | 26.4387 | 0.874513 | ||||||||
\(915\) | 9.08840 | 0.300453 | ||||||||
\(916\) | −0.363436 | −0.0120082 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −40.3244 | −1.33090 | ||||||||
\(919\) | −34.8510 | −1.14963 | −0.574814 | − | 0.818284i | \(-0.694925\pi\) | ||||
−0.574814 | + | 0.818284i | \(0.694925\pi\) | |||||||
\(920\) | 13.2750 | 0.437665 | ||||||||
\(921\) | 21.1246 | 0.696079 | ||||||||
\(922\) | −52.2130 | −1.71954 | ||||||||
\(923\) | 4.77575 | 0.157196 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.1563 | 0.333938 | ||||||||
\(926\) | 39.0494 | 1.28324 | ||||||||
\(927\) | −25.2203 | −0.828343 | ||||||||
\(928\) | −3.94921 | −0.129639 | ||||||||
\(929\) | −41.6991 | −1.36810 | −0.684052 | − | 0.729434i | \(-0.739784\pi\) | ||||
−0.684052 | + | 0.729434i | \(0.739784\pi\) | |||||||
\(930\) | −7.07381 | −0.231959 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.16220 | −0.0708254 | ||||||||
\(933\) | 5.25060 | 0.171897 | ||||||||
\(934\) | −10.0508 | −0.328872 | ||||||||
\(935\) | −6.07522 | −0.198681 | ||||||||
\(936\) | 38.7064 | 1.26516 | ||||||||
\(937\) | −21.9102 | −0.715775 | −0.357887 | − | 0.933765i | \(-0.616503\pi\) | ||||
−0.357887 | + | 0.933765i | \(0.616503\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.9576 | 0.422857 | ||||||||
\(940\) | 0.649738 | 0.0211921 | ||||||||
\(941\) | 3.55149 | 0.115775 | 0.0578877 | − | 0.998323i | \(-0.481563\pi\) | ||||
0.0578877 | + | 0.998323i | \(0.481563\pi\) | |||||||
\(942\) | −5.23884 | −0.170691 | ||||||||
\(943\) | 31.3258 | 1.02011 | ||||||||
\(944\) | −27.7889 | −0.904452 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.88156 | 0.191226 | ||||||||
\(947\) | 38.3634 | 1.24664 | 0.623322 | − | 0.781965i | \(-0.285783\pi\) | ||||
0.623322 | + | 0.781965i | \(0.285783\pi\) | |||||||
\(948\) | 0.130747 | 0.00424648 | ||||||||
\(949\) | 2.38787 | 0.0775136 | ||||||||
\(950\) | −1.48119 | −0.0480563 | ||||||||
\(951\) | 4.58910 | 0.148812 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.8714 | −0.740879 | −0.370439 | − | 0.928857i | \(-0.620793\pi\) | ||||
−0.370439 | + | 0.928857i | \(0.620793\pi\) | |||||||
\(954\) | 6.41819 | 0.207797 | ||||||||
\(955\) | 21.7743 | 0.704601 | ||||||||
\(956\) | 1.80351 | 0.0583296 | ||||||||
\(957\) | 2.80209 | 0.0905788 | ||||||||
\(958\) | 18.8265 | 0.608258 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 5.70782 | 0.184219 | ||||||||
\(961\) | 4.10299 | 0.132354 | ||||||||
\(962\) | 92.6126 | 2.98595 | ||||||||
\(963\) | −11.2955 | −0.363993 | ||||||||
\(964\) | 0.448507 | 0.0144455 | ||||||||
\(965\) | −12.5442 | −0.403812 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.6629 | 0.889579 | 0.444790 | − | 0.895635i | \(-0.353278\pi\) | ||||
0.444790 | + | 0.895635i | \(0.353278\pi\) | |||||||
\(968\) | −26.9488 | −0.866166 | ||||||||
\(969\) | −5.08840 | −0.163463 | ||||||||
\(970\) | −16.2823 | −0.522794 | ||||||||
\(971\) | 42.1768 | 1.35352 | 0.676759 | − | 0.736205i | \(-0.263384\pi\) | ||||
0.676759 | + | 0.736205i | \(0.263384\pi\) | |||||||
\(972\) | −3.06793 | −0.0984039 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 23.3416 | 0.747912 | ||||||||
\(975\) | 4.96239 | 0.158924 | ||||||||
\(976\) | −49.0494 | −1.57003 | ||||||||
\(977\) | 0.856849 | 0.0274130 | 0.0137065 | − | 0.999906i | \(-0.495637\pi\) | ||||
0.0137065 | + | 0.999906i | \(0.495637\pi\) | |||||||
\(978\) | −0.775746 | −0.0248056 | ||||||||
\(979\) | −6.82179 | −0.218025 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.52373 | 0.208287 | ||||||||
\(982\) | 21.5515 | 0.687736 | ||||||||
\(983\) | −45.2809 | −1.44424 | −0.722119 | − | 0.691769i | \(-0.756831\pi\) | ||||
−0.722119 | + | 0.691769i | \(0.756831\pi\) | |||||||
\(984\) | 13.6121 | 0.433939 | ||||||||
\(985\) | −24.5501 | −0.782231 | ||||||||
\(986\) | 33.7743 | 1.07559 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.19394 | −0.0379842 | ||||||||
\(989\) | 20.4749 | 0.651063 | ||||||||
\(990\) | −3.35026 | −0.106478 | ||||||||
\(991\) | 47.0132 | 1.49342 | 0.746711 | − | 0.665148i | \(-0.231632\pi\) | ||||
0.746711 | + | 0.665148i | \(0.231632\pi\) | |||||||
\(992\) | 6.47768 | 0.205667 | ||||||||
\(993\) | 9.92478 | 0.314953 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.0738 | 0.731489 | ||||||||
\(996\) | −1.10016 | −0.0348598 | ||||||||
\(997\) | −13.6873 | −0.433483 | −0.216741 | − | 0.976229i | \(-0.569543\pi\) | ||||
−0.216741 | + | 0.976229i | \(0.569543\pi\) | |||||||
\(998\) | 8.12601 | 0.257224 | ||||||||
\(999\) | 43.8007 | 1.38579 |
(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 | 4655.2.a.u.1.1 | 3 | ||
7.6 | odd | 2 | 95.2.a.a.1.1 | ✓ | 3 | ||
21.20 | even | 2 | 855.2.a.i.1.3 | 3 | |||
28.27 | even | 2 | 1520.2.a.p.1.2 | 3 | |||
35.13 | even | 4 | 475.2.b.d.324.5 | 6 | |||
35.27 | even | 4 | 475.2.b.d.324.2 | 6 | |||
35.34 | odd | 2 | 475.2.a.f.1.3 | 3 | |||
56.13 | odd | 2 | 6080.2.a.bo.1.2 | 3 | |||
56.27 | even | 2 | 6080.2.a.by.1.2 | 3 | |||
105.104 | even | 2 | 4275.2.a.bk.1.1 | 3 | |||
133.132 | even | 2 | 1805.2.a.f.1.3 | 3 | |||
140.139 | even | 2 | 7600.2.a.bx.1.2 | 3 | |||
665.664 | even | 2 | 9025.2.a.bb.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.a.a.1.1 | ✓ | 3 | 7.6 | odd | 2 | ||
475.2.a.f.1.3 | 3 | 35.34 | odd | 2 | |||
475.2.b.d.324.2 | 6 | 35.27 | even | 4 | |||
475.2.b.d.324.5 | 6 | 35.13 | even | 4 | |||
855.2.a.i.1.3 | 3 | 21.20 | even | 2 | |||
1520.2.a.p.1.2 | 3 | 28.27 | even | 2 | |||
1805.2.a.f.1.3 | 3 | 133.132 | even | 2 | |||
4275.2.a.bk.1.1 | 3 | 105.104 | even | 2 | |||
4655.2.a.u.1.1 | 3 | 1.1 | even | 1 | trivial | ||
6080.2.a.bo.1.2 | 3 | 56.13 | odd | 2 | |||
6080.2.a.by.1.2 | 3 | 56.27 | even | 2 | |||
7600.2.a.bx.1.2 | 3 | 140.139 | even | 2 | |||
9025.2.a.bb.1.1 | 3 | 665.664 | even | 2 |