Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(1,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.00000 | 1.15470 | 0.577350 | − | 0.816497i | \(-0.304087\pi\) | ||||
0.577350 | + | 0.816497i | \(0.304087\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | −4.37228 | −1.65257 | −0.826284 | − | 0.563254i | \(-0.809549\pi\) | ||||
−0.826284 | + | 0.563254i | \(0.809549\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 2.37228 | 0.715270 | 0.357635 | − | 0.933862i | \(-0.383583\pi\) | ||||
0.357635 | + | 0.933862i | \(0.383583\pi\) | |||||||
\(12\) | 2.00000 | 0.577350 | ||||||||
\(13\) | 6.74456 | 1.87061 | 0.935303 | − | 0.353849i | \(-0.115127\pi\) | ||||
0.935303 | + | 0.353849i | \(0.115127\pi\) | |||||||
\(14\) | −4.37228 | −1.16854 | ||||||||
\(15\) | 2.00000 | 0.516398 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.372281 | 0.0902915 | 0.0451457 | − | 0.998980i | \(-0.485625\pi\) | ||||
0.0451457 | + | 0.998980i | \(0.485625\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −8.74456 | −1.90822 | ||||||||
\(22\) | 2.37228 | 0.505772 | ||||||||
\(23\) | −4.74456 | −0.989310 | −0.494655 | − | 0.869090i | \(-0.664706\pi\) | ||||
−0.494655 | + | 0.869090i | \(0.664706\pi\) | |||||||
\(24\) | 2.00000 | 0.408248 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 6.74456 | 1.32272 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | −4.37228 | −0.826284 | ||||||||
\(29\) | −9.11684 | −1.69296 | −0.846478 | − | 0.532424i | \(-0.821281\pi\) | ||||
−0.846478 | + | 0.532424i | \(0.821281\pi\) | |||||||
\(30\) | 2.00000 | 0.365148 | ||||||||
\(31\) | −8.37228 | −1.50371 | −0.751853 | − | 0.659331i | \(-0.770840\pi\) | ||||
−0.751853 | + | 0.659331i | \(0.770840\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.74456 | 0.825922 | ||||||||
\(34\) | 0.372281 | 0.0638457 | ||||||||
\(35\) | −4.37228 | −0.739050 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 13.4891 | 2.15999 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −0.372281 | −0.0581406 | −0.0290703 | − | 0.999577i | \(-0.509255\pi\) | ||||
−0.0290703 | + | 0.999577i | \(0.509255\pi\) | |||||||
\(42\) | −8.74456 | −1.34932 | ||||||||
\(43\) | 1.62772 | 0.248225 | 0.124112 | − | 0.992268i | \(-0.460392\pi\) | ||||
0.124112 | + | 0.992268i | \(0.460392\pi\) | |||||||
\(44\) | 2.37228 | 0.357635 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −4.74456 | −0.699548 | ||||||||
\(47\) | 2.74456 | 0.400336 | 0.200168 | − | 0.979762i | \(-0.435851\pi\) | ||||
0.200168 | + | 0.979762i | \(0.435851\pi\) | |||||||
\(48\) | 2.00000 | 0.288675 | ||||||||
\(49\) | 12.1168 | 1.73098 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0.744563 | 0.104260 | ||||||||
\(52\) | 6.74456 | 0.935303 | ||||||||
\(53\) | −4.37228 | −0.600579 | −0.300290 | − | 0.953848i | \(-0.597083\pi\) | ||||
−0.300290 | + | 0.953848i | \(0.597083\pi\) | |||||||
\(54\) | −4.00000 | −0.544331 | ||||||||
\(55\) | 2.37228 | 0.319878 | ||||||||
\(56\) | −4.37228 | −0.584271 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | −9.11684 | −1.19710 | ||||||||
\(59\) | 1.25544 | 0.163444 | 0.0817220 | − | 0.996655i | \(-0.473958\pi\) | ||||
0.0817220 | + | 0.996655i | \(0.473958\pi\) | |||||||
\(60\) | 2.00000 | 0.258199 | ||||||||
\(61\) | 0.372281 | 0.0476657 | 0.0238329 | − | 0.999716i | \(-0.492413\pi\) | ||||
0.0238329 | + | 0.999716i | \(0.492413\pi\) | |||||||
\(62\) | −8.37228 | −1.06328 | ||||||||
\(63\) | −4.37228 | −0.550856 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.74456 | 0.836560 | ||||||||
\(66\) | 4.74456 | 0.584015 | ||||||||
\(67\) | −6.74456 | −0.823979 | −0.411990 | − | 0.911188i | \(-0.635166\pi\) | ||||
−0.411990 | + | 0.911188i | \(0.635166\pi\) | |||||||
\(68\) | 0.372281 | 0.0451457 | ||||||||
\(69\) | −9.48913 | −1.14236 | ||||||||
\(70\) | −4.37228 | −0.522588 | ||||||||
\(71\) | 4.74456 | 0.563076 | 0.281538 | − | 0.959550i | \(-0.409155\pi\) | ||||
0.281538 | + | 0.959550i | \(0.409155\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −2.74456 | −0.321227 | −0.160613 | − | 0.987017i | \(-0.551347\pi\) | ||||
−0.160613 | + | 0.987017i | \(0.551347\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 2.00000 | 0.230940 | ||||||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | −10.3723 | −1.18203 | ||||||||
\(78\) | 13.4891 | 1.52734 | ||||||||
\(79\) | 6.74456 | 0.758823 | 0.379411 | − | 0.925228i | \(-0.376127\pi\) | ||||
0.379411 | + | 0.925228i | \(0.376127\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | −0.372281 | −0.0411116 | ||||||||
\(83\) | 10.7446 | 1.17937 | 0.589684 | − | 0.807634i | \(-0.299252\pi\) | ||||
0.589684 | + | 0.807634i | \(0.299252\pi\) | |||||||
\(84\) | −8.74456 | −0.954110 | ||||||||
\(85\) | 0.372281 | 0.0403796 | ||||||||
\(86\) | 1.62772 | 0.175521 | ||||||||
\(87\) | −18.2337 | −1.95486 | ||||||||
\(88\) | 2.37228 | 0.252886 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | −29.4891 | −3.09130 | ||||||||
\(92\) | −4.74456 | −0.494655 | ||||||||
\(93\) | −16.7446 | −1.73633 | ||||||||
\(94\) | 2.74456 | 0.283080 | ||||||||
\(95\) | −2.00000 | −0.205196 | ||||||||
\(96\) | 2.00000 | 0.204124 | ||||||||
\(97\) | 17.1168 | 1.73795 | 0.868976 | − | 0.494854i | \(-0.164778\pi\) | ||||
0.868976 | + | 0.494854i | \(0.164778\pi\) | |||||||
\(98\) | 12.1168 | 1.22399 | ||||||||
\(99\) | 2.37228 | 0.238423 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 11.4891 | 1.14321 | 0.571605 | − | 0.820529i | \(-0.306321\pi\) | ||||
0.571605 | + | 0.820529i | \(0.306321\pi\) | |||||||
\(102\) | 0.744563 | 0.0737227 | ||||||||
\(103\) | 13.4891 | 1.32912 | 0.664562 | − | 0.747234i | \(-0.268618\pi\) | ||||
0.664562 | + | 0.747234i | \(0.268618\pi\) | |||||||
\(104\) | 6.74456 | 0.661359 | ||||||||
\(105\) | −8.74456 | −0.853382 | ||||||||
\(106\) | −4.37228 | −0.424674 | ||||||||
\(107\) | 19.4891 | 1.88408 | 0.942042 | − | 0.335494i | \(-0.108903\pi\) | ||||
0.942042 | + | 0.335494i | \(0.108903\pi\) | |||||||
\(108\) | −4.00000 | −0.384900 | ||||||||
\(109\) | −17.1168 | −1.63950 | −0.819748 | − | 0.572724i | \(-0.805887\pi\) | ||||
−0.819748 | + | 0.572724i | \(0.805887\pi\) | |||||||
\(110\) | 2.37228 | 0.226188 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | −4.37228 | −0.413142 | ||||||||
\(113\) | 11.6277 | 1.09384 | 0.546922 | − | 0.837184i | \(-0.315799\pi\) | ||||
0.546922 | + | 0.837184i | \(0.315799\pi\) | |||||||
\(114\) | −4.00000 | −0.374634 | ||||||||
\(115\) | −4.74456 | −0.442433 | ||||||||
\(116\) | −9.11684 | −0.846478 | ||||||||
\(117\) | 6.74456 | 0.623535 | ||||||||
\(118\) | 1.25544 | 0.115572 | ||||||||
\(119\) | −1.62772 | −0.149213 | ||||||||
\(120\) | 2.00000 | 0.182574 | ||||||||
\(121\) | −5.37228 | −0.488389 | ||||||||
\(122\) | 0.372281 | 0.0337048 | ||||||||
\(123\) | −0.744563 | −0.0671350 | ||||||||
\(124\) | −8.37228 | −0.751853 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −4.37228 | −0.389514 | ||||||||
\(127\) | −5.25544 | −0.466345 | −0.233172 | − | 0.972435i | \(-0.574911\pi\) | ||||
−0.233172 | + | 0.972435i | \(0.574911\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.25544 | 0.286625 | ||||||||
\(130\) | 6.74456 | 0.591537 | ||||||||
\(131\) | −14.7446 | −1.28824 | −0.644119 | − | 0.764925i | \(-0.722776\pi\) | ||||
−0.644119 | + | 0.764925i | \(0.722776\pi\) | |||||||
\(132\) | 4.74456 | 0.412961 | ||||||||
\(133\) | 8.74456 | 0.758250 | ||||||||
\(134\) | −6.74456 | −0.582641 | ||||||||
\(135\) | −4.00000 | −0.344265 | ||||||||
\(136\) | 0.372281 | 0.0319229 | ||||||||
\(137\) | 5.25544 | 0.449002 | 0.224501 | − | 0.974474i | \(-0.427925\pi\) | ||||
0.224501 | + | 0.974474i | \(0.427925\pi\) | |||||||
\(138\) | −9.48913 | −0.807768 | ||||||||
\(139\) | −19.1168 | −1.62147 | −0.810735 | − | 0.585414i | \(-0.800932\pi\) | ||||
−0.810735 | + | 0.585414i | \(0.800932\pi\) | |||||||
\(140\) | −4.37228 | −0.369525 | ||||||||
\(141\) | 5.48913 | 0.462268 | ||||||||
\(142\) | 4.74456 | 0.398155 | ||||||||
\(143\) | 16.0000 | 1.33799 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −9.11684 | −0.757113 | ||||||||
\(146\) | −2.74456 | −0.227142 | ||||||||
\(147\) | 24.2337 | 1.99876 | ||||||||
\(148\) | 1.00000 | 0.0821995 | ||||||||
\(149\) | 11.4891 | 0.941226 | 0.470613 | − | 0.882340i | \(-0.344033\pi\) | ||||
0.470613 | + | 0.882340i | \(0.344033\pi\) | |||||||
\(150\) | 2.00000 | 0.163299 | ||||||||
\(151\) | −20.0000 | −1.62758 | −0.813788 | − | 0.581161i | \(-0.802599\pi\) | ||||
−0.813788 | + | 0.581161i | \(0.802599\pi\) | |||||||
\(152\) | −2.00000 | −0.162221 | ||||||||
\(153\) | 0.372281 | 0.0300972 | ||||||||
\(154\) | −10.3723 | −0.835822 | ||||||||
\(155\) | −8.37228 | −0.672478 | ||||||||
\(156\) | 13.4891 | 1.07999 | ||||||||
\(157\) | 11.6277 | 0.927993 | 0.463996 | − | 0.885837i | \(-0.346415\pi\) | ||||
0.463996 | + | 0.885837i | \(0.346415\pi\) | |||||||
\(158\) | 6.74456 | 0.536569 | ||||||||
\(159\) | −8.74456 | −0.693489 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 20.7446 | 1.63490 | ||||||||
\(162\) | −11.0000 | −0.864242 | ||||||||
\(163\) | 13.6277 | 1.06741 | 0.533703 | − | 0.845672i | \(-0.320800\pi\) | ||||
0.533703 | + | 0.845672i | \(0.320800\pi\) | |||||||
\(164\) | −0.372281 | −0.0290703 | ||||||||
\(165\) | 4.74456 | 0.369364 | ||||||||
\(166\) | 10.7446 | 0.833940 | ||||||||
\(167\) | −21.4891 | −1.66288 | −0.831439 | − | 0.555616i | \(-0.812483\pi\) | ||||
−0.831439 | + | 0.555616i | \(0.812483\pi\) | |||||||
\(168\) | −8.74456 | −0.674658 | ||||||||
\(169\) | 32.4891 | 2.49916 | ||||||||
\(170\) | 0.372281 | 0.0285527 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | 1.62772 | 0.124112 | ||||||||
\(173\) | −5.86141 | −0.445634 | −0.222817 | − | 0.974860i | \(-0.571525\pi\) | ||||
−0.222817 | + | 0.974860i | \(0.571525\pi\) | |||||||
\(174\) | −18.2337 | −1.38229 | ||||||||
\(175\) | −4.37228 | −0.330513 | ||||||||
\(176\) | 2.37228 | 0.178817 | ||||||||
\(177\) | 2.51087 | 0.188729 | ||||||||
\(178\) | 10.0000 | 0.749532 | ||||||||
\(179\) | 8.23369 | 0.615415 | 0.307707 | − | 0.951481i | \(-0.400438\pi\) | ||||
0.307707 | + | 0.951481i | \(0.400438\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −15.4891 | −1.15130 | −0.575649 | − | 0.817697i | \(-0.695250\pi\) | ||||
−0.575649 | + | 0.817697i | \(0.695250\pi\) | |||||||
\(182\) | −29.4891 | −2.18588 | ||||||||
\(183\) | 0.744563 | 0.0550397 | ||||||||
\(184\) | −4.74456 | −0.349774 | ||||||||
\(185\) | 1.00000 | 0.0735215 | ||||||||
\(186\) | −16.7446 | −1.22777 | ||||||||
\(187\) | 0.883156 | 0.0645828 | ||||||||
\(188\) | 2.74456 | 0.200168 | ||||||||
\(189\) | 17.4891 | 1.27215 | ||||||||
\(190\) | −2.00000 | −0.145095 | ||||||||
\(191\) | 24.3723 | 1.76352 | 0.881758 | − | 0.471702i | \(-0.156360\pi\) | ||||
0.881758 | + | 0.471702i | \(0.156360\pi\) | |||||||
\(192\) | 2.00000 | 0.144338 | ||||||||
\(193\) | 2.00000 | 0.143963 | 0.0719816 | − | 0.997406i | \(-0.477068\pi\) | ||||
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | 17.1168 | 1.22892 | ||||||||
\(195\) | 13.4891 | 0.965976 | ||||||||
\(196\) | 12.1168 | 0.865489 | ||||||||
\(197\) | 4.51087 | 0.321387 | 0.160693 | − | 0.987004i | \(-0.448627\pi\) | ||||
0.160693 | + | 0.987004i | \(0.448627\pi\) | |||||||
\(198\) | 2.37228 | 0.168591 | ||||||||
\(199\) | −22.7446 | −1.61232 | −0.806160 | − | 0.591698i | \(-0.798458\pi\) | ||||
−0.806160 | + | 0.591698i | \(0.798458\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −13.4891 | −0.951450 | ||||||||
\(202\) | 11.4891 | 0.808372 | ||||||||
\(203\) | 39.8614 | 2.79772 | ||||||||
\(204\) | 0.744563 | 0.0521298 | ||||||||
\(205\) | −0.372281 | −0.0260013 | ||||||||
\(206\) | 13.4891 | 0.939832 | ||||||||
\(207\) | −4.74456 | −0.329770 | ||||||||
\(208\) | 6.74456 | 0.467651 | ||||||||
\(209\) | −4.74456 | −0.328188 | ||||||||
\(210\) | −8.74456 | −0.603432 | ||||||||
\(211\) | 3.11684 | 0.214572 | 0.107286 | − | 0.994228i | \(-0.465784\pi\) | ||||
0.107286 | + | 0.994228i | \(0.465784\pi\) | |||||||
\(212\) | −4.37228 | −0.300290 | ||||||||
\(213\) | 9.48913 | 0.650184 | ||||||||
\(214\) | 19.4891 | 1.33225 | ||||||||
\(215\) | 1.62772 | 0.111009 | ||||||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | 36.6060 | 2.48498 | ||||||||
\(218\) | −17.1168 | −1.15930 | ||||||||
\(219\) | −5.48913 | −0.370921 | ||||||||
\(220\) | 2.37228 | 0.159939 | ||||||||
\(221\) | 2.51087 | 0.168900 | ||||||||
\(222\) | 2.00000 | 0.134231 | ||||||||
\(223\) | 4.37228 | 0.292790 | 0.146395 | − | 0.989226i | \(-0.453233\pi\) | ||||
0.146395 | + | 0.989226i | \(0.453233\pi\) | |||||||
\(224\) | −4.37228 | −0.292135 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 11.6277 | 0.773464 | ||||||||
\(227\) | −5.62772 | −0.373525 | −0.186762 | − | 0.982405i | \(-0.559799\pi\) | ||||
−0.186762 | + | 0.982405i | \(0.559799\pi\) | |||||||
\(228\) | −4.00000 | −0.264906 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | −4.74456 | −0.312847 | ||||||||
\(231\) | −20.7446 | −1.36489 | ||||||||
\(232\) | −9.11684 | −0.598550 | ||||||||
\(233\) | −28.2337 | −1.84965 | −0.924825 | − | 0.380392i | \(-0.875789\pi\) | ||||
−0.924825 | + | 0.380392i | \(0.875789\pi\) | |||||||
\(234\) | 6.74456 | 0.440906 | ||||||||
\(235\) | 2.74456 | 0.179036 | ||||||||
\(236\) | 1.25544 | 0.0817220 | ||||||||
\(237\) | 13.4891 | 0.876213 | ||||||||
\(238\) | −1.62772 | −0.105509 | ||||||||
\(239\) | −22.6060 | −1.46226 | −0.731129 | − | 0.682239i | \(-0.761006\pi\) | ||||
−0.731129 | + | 0.682239i | \(0.761006\pi\) | |||||||
\(240\) | 2.00000 | 0.129099 | ||||||||
\(241\) | 24.2337 | 1.56103 | 0.780515 | − | 0.625138i | \(-0.214957\pi\) | ||||
0.780515 | + | 0.625138i | \(0.214957\pi\) | |||||||
\(242\) | −5.37228 | −0.345343 | ||||||||
\(243\) | −10.0000 | −0.641500 | ||||||||
\(244\) | 0.372281 | 0.0238329 | ||||||||
\(245\) | 12.1168 | 0.774117 | ||||||||
\(246\) | −0.744563 | −0.0474716 | ||||||||
\(247\) | −13.4891 | −0.858292 | ||||||||
\(248\) | −8.37228 | −0.531640 | ||||||||
\(249\) | 21.4891 | 1.36182 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −11.4891 | −0.725187 | −0.362594 | − | 0.931947i | \(-0.618109\pi\) | ||||
−0.362594 | + | 0.931947i | \(0.618109\pi\) | |||||||
\(252\) | −4.37228 | −0.275428 | ||||||||
\(253\) | −11.2554 | −0.707623 | ||||||||
\(254\) | −5.25544 | −0.329755 | ||||||||
\(255\) | 0.744563 | 0.0466263 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.9783 | 1.55810 | 0.779050 | − | 0.626962i | \(-0.215702\pi\) | ||||
0.779050 | + | 0.626962i | \(0.215702\pi\) | |||||||
\(258\) | 3.25544 | 0.202675 | ||||||||
\(259\) | −4.37228 | −0.271680 | ||||||||
\(260\) | 6.74456 | 0.418280 | ||||||||
\(261\) | −9.11684 | −0.564318 | ||||||||
\(262\) | −14.7446 | −0.910922 | ||||||||
\(263\) | −17.1168 | −1.05547 | −0.527735 | − | 0.849409i | \(-0.676959\pi\) | ||||
−0.527735 | + | 0.849409i | \(0.676959\pi\) | |||||||
\(264\) | 4.74456 | 0.292008 | ||||||||
\(265\) | −4.37228 | −0.268587 | ||||||||
\(266\) | 8.74456 | 0.536164 | ||||||||
\(267\) | 20.0000 | 1.22398 | ||||||||
\(268\) | −6.74456 | −0.411990 | ||||||||
\(269\) | 10.0000 | 0.609711 | 0.304855 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304855 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(270\) | −4.00000 | −0.243432 | ||||||||
\(271\) | 4.74456 | 0.288212 | 0.144106 | − | 0.989562i | \(-0.453969\pi\) | ||||
0.144106 | + | 0.989562i | \(0.453969\pi\) | |||||||
\(272\) | 0.372281 | 0.0225729 | ||||||||
\(273\) | −58.9783 | −3.56953 | ||||||||
\(274\) | 5.25544 | 0.317493 | ||||||||
\(275\) | 2.37228 | 0.143054 | ||||||||
\(276\) | −9.48913 | −0.571178 | ||||||||
\(277\) | −10.7446 | −0.645578 | −0.322789 | − | 0.946471i | \(-0.604620\pi\) | ||||
−0.322789 | + | 0.946471i | \(0.604620\pi\) | |||||||
\(278\) | −19.1168 | −1.14655 | ||||||||
\(279\) | −8.37228 | −0.501235 | ||||||||
\(280\) | −4.37228 | −0.261294 | ||||||||
\(281\) | 13.2554 | 0.790753 | 0.395377 | − | 0.918519i | \(-0.370614\pi\) | ||||
0.395377 | + | 0.918519i | \(0.370614\pi\) | |||||||
\(282\) | 5.48913 | 0.326873 | ||||||||
\(283\) | −17.4891 | −1.03962 | −0.519810 | − | 0.854282i | \(-0.673997\pi\) | ||||
−0.519810 | + | 0.854282i | \(0.673997\pi\) | |||||||
\(284\) | 4.74456 | 0.281538 | ||||||||
\(285\) | −4.00000 | −0.236940 | ||||||||
\(286\) | 16.0000 | 0.946100 | ||||||||
\(287\) | 1.62772 | 0.0960812 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.8614 | −0.991847 | ||||||||
\(290\) | −9.11684 | −0.535360 | ||||||||
\(291\) | 34.2337 | 2.00681 | ||||||||
\(292\) | −2.74456 | −0.160613 | ||||||||
\(293\) | 9.86141 | 0.576110 | 0.288055 | − | 0.957614i | \(-0.406991\pi\) | ||||
0.288055 | + | 0.957614i | \(0.406991\pi\) | |||||||
\(294\) | 24.2337 | 1.41334 | ||||||||
\(295\) | 1.25544 | 0.0730944 | ||||||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | −9.48913 | −0.550615 | ||||||||
\(298\) | 11.4891 | 0.665547 | ||||||||
\(299\) | −32.0000 | −1.85061 | ||||||||
\(300\) | 2.00000 | 0.115470 | ||||||||
\(301\) | −7.11684 | −0.410208 | ||||||||
\(302\) | −20.0000 | −1.15087 | ||||||||
\(303\) | 22.9783 | 1.32007 | ||||||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | 0.372281 | 0.0213168 | ||||||||
\(306\) | 0.372281 | 0.0212819 | ||||||||
\(307\) | −0.510875 | −0.0291572 | −0.0145786 | − | 0.999894i | \(-0.504641\pi\) | ||||
−0.0145786 | + | 0.999894i | \(0.504641\pi\) | |||||||
\(308\) | −10.3723 | −0.591016 | ||||||||
\(309\) | 26.9783 | 1.53474 | ||||||||
\(310\) | −8.37228 | −0.475514 | ||||||||
\(311\) | 4.37228 | 0.247929 | 0.123965 | − | 0.992287i | \(-0.460439\pi\) | ||||
0.123965 | + | 0.992287i | \(0.460439\pi\) | |||||||
\(312\) | 13.4891 | 0.763671 | ||||||||
\(313\) | 19.4891 | 1.10159 | 0.550795 | − | 0.834640i | \(-0.314325\pi\) | ||||
0.550795 | + | 0.834640i | \(0.314325\pi\) | |||||||
\(314\) | 11.6277 | 0.656190 | ||||||||
\(315\) | −4.37228 | −0.246350 | ||||||||
\(316\) | 6.74456 | 0.379411 | ||||||||
\(317\) | 19.6277 | 1.10240 | 0.551201 | − | 0.834372i | \(-0.314170\pi\) | ||||
0.551201 | + | 0.834372i | \(0.314170\pi\) | |||||||
\(318\) | −8.74456 | −0.490371 | ||||||||
\(319\) | −21.6277 | −1.21092 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 38.9783 | 2.17555 | ||||||||
\(322\) | 20.7446 | 1.15605 | ||||||||
\(323\) | −0.744563 | −0.0414286 | ||||||||
\(324\) | −11.0000 | −0.611111 | ||||||||
\(325\) | 6.74456 | 0.374121 | ||||||||
\(326\) | 13.6277 | 0.754770 | ||||||||
\(327\) | −34.2337 | −1.89313 | ||||||||
\(328\) | −0.372281 | −0.0205558 | ||||||||
\(329\) | −12.0000 | −0.661581 | ||||||||
\(330\) | 4.74456 | 0.261180 | ||||||||
\(331\) | 0.510875 | 0.0280802 | 0.0140401 | − | 0.999901i | \(-0.495531\pi\) | ||||
0.0140401 | + | 0.999901i | \(0.495531\pi\) | |||||||
\(332\) | 10.7446 | 0.589684 | ||||||||
\(333\) | 1.00000 | 0.0547997 | ||||||||
\(334\) | −21.4891 | −1.17583 | ||||||||
\(335\) | −6.74456 | −0.368495 | ||||||||
\(336\) | −8.74456 | −0.477055 | ||||||||
\(337\) | −18.7446 | −1.02108 | −0.510541 | − | 0.859854i | \(-0.670555\pi\) | ||||
−0.510541 | + | 0.859854i | \(0.670555\pi\) | |||||||
\(338\) | 32.4891 | 1.76718 | ||||||||
\(339\) | 23.2554 | 1.26306 | ||||||||
\(340\) | 0.372281 | 0.0201898 | ||||||||
\(341\) | −19.8614 | −1.07556 | ||||||||
\(342\) | −2.00000 | −0.108148 | ||||||||
\(343\) | −22.3723 | −1.20799 | ||||||||
\(344\) | 1.62772 | 0.0877607 | ||||||||
\(345\) | −9.48913 | −0.510877 | ||||||||
\(346\) | −5.86141 | −0.315111 | ||||||||
\(347\) | 22.9783 | 1.23354 | 0.616769 | − | 0.787145i | \(-0.288441\pi\) | ||||
0.616769 | + | 0.787145i | \(0.288441\pi\) | |||||||
\(348\) | −18.2337 | −0.977428 | ||||||||
\(349\) | −22.0000 | −1.17763 | −0.588817 | − | 0.808267i | \(-0.700406\pi\) | ||||
−0.588817 | + | 0.808267i | \(0.700406\pi\) | |||||||
\(350\) | −4.37228 | −0.233708 | ||||||||
\(351\) | −26.9783 | −1.43999 | ||||||||
\(352\) | 2.37228 | 0.126443 | ||||||||
\(353\) | 5.86141 | 0.311971 | 0.155986 | − | 0.987759i | \(-0.450145\pi\) | ||||
0.155986 | + | 0.987759i | \(0.450145\pi\) | |||||||
\(354\) | 2.51087 | 0.133451 | ||||||||
\(355\) | 4.74456 | 0.251815 | ||||||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | −3.25544 | −0.172296 | ||||||||
\(358\) | 8.23369 | 0.435164 | ||||||||
\(359\) | 14.9783 | 0.790522 | 0.395261 | − | 0.918569i | \(-0.370654\pi\) | ||||
0.395261 | + | 0.918569i | \(0.370654\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | −15.4891 | −0.814090 | ||||||||
\(363\) | −10.7446 | −0.563943 | ||||||||
\(364\) | −29.4891 | −1.54565 | ||||||||
\(365\) | −2.74456 | −0.143657 | ||||||||
\(366\) | 0.744563 | 0.0389189 | ||||||||
\(367\) | 21.1168 | 1.10229 | 0.551145 | − | 0.834409i | \(-0.314191\pi\) | ||||
0.551145 | + | 0.834409i | \(0.314191\pi\) | |||||||
\(368\) | −4.74456 | −0.247327 | ||||||||
\(369\) | −0.372281 | −0.0193802 | ||||||||
\(370\) | 1.00000 | 0.0519875 | ||||||||
\(371\) | 19.1168 | 0.992497 | ||||||||
\(372\) | −16.7446 | −0.868165 | ||||||||
\(373\) | −8.51087 | −0.440676 | −0.220338 | − | 0.975424i | \(-0.570716\pi\) | ||||
−0.220338 | + | 0.975424i | \(0.570716\pi\) | |||||||
\(374\) | 0.883156 | 0.0456669 | ||||||||
\(375\) | 2.00000 | 0.103280 | ||||||||
\(376\) | 2.74456 | 0.141540 | ||||||||
\(377\) | −61.4891 | −3.16685 | ||||||||
\(378\) | 17.4891 | 0.899544 | ||||||||
\(379\) | −8.00000 | −0.410932 | −0.205466 | − | 0.978664i | \(-0.565871\pi\) | ||||
−0.205466 | + | 0.978664i | \(0.565871\pi\) | |||||||
\(380\) | −2.00000 | −0.102598 | ||||||||
\(381\) | −10.5109 | −0.538488 | ||||||||
\(382\) | 24.3723 | 1.24699 | ||||||||
\(383\) | 9.48913 | 0.484872 | 0.242436 | − | 0.970167i | \(-0.422054\pi\) | ||||
0.242436 | + | 0.970167i | \(0.422054\pi\) | |||||||
\(384\) | 2.00000 | 0.102062 | ||||||||
\(385\) | −10.3723 | −0.528620 | ||||||||
\(386\) | 2.00000 | 0.101797 | ||||||||
\(387\) | 1.62772 | 0.0827416 | ||||||||
\(388\) | 17.1168 | 0.868976 | ||||||||
\(389\) | −13.8614 | −0.702801 | −0.351401 | − | 0.936225i | \(-0.614294\pi\) | ||||
−0.351401 | + | 0.936225i | \(0.614294\pi\) | |||||||
\(390\) | 13.4891 | 0.683048 | ||||||||
\(391\) | −1.76631 | −0.0893262 | ||||||||
\(392\) | 12.1168 | 0.611993 | ||||||||
\(393\) | −29.4891 | −1.48753 | ||||||||
\(394\) | 4.51087 | 0.227255 | ||||||||
\(395\) | 6.74456 | 0.339356 | ||||||||
\(396\) | 2.37228 | 0.119212 | ||||||||
\(397\) | −20.9783 | −1.05287 | −0.526434 | − | 0.850216i | \(-0.676471\pi\) | ||||
−0.526434 | + | 0.850216i | \(0.676471\pi\) | |||||||
\(398\) | −22.7446 | −1.14008 | ||||||||
\(399\) | 17.4891 | 0.875551 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 10.0000 | 0.499376 | 0.249688 | − | 0.968326i | \(-0.419672\pi\) | ||||
0.249688 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(402\) | −13.4891 | −0.672776 | ||||||||
\(403\) | −56.4674 | −2.81284 | ||||||||
\(404\) | 11.4891 | 0.571605 | ||||||||
\(405\) | −11.0000 | −0.546594 | ||||||||
\(406\) | 39.8614 | 1.97829 | ||||||||
\(407\) | 2.37228 | 0.117590 | ||||||||
\(408\) | 0.744563 | 0.0368613 | ||||||||
\(409\) | −28.2337 | −1.39607 | −0.698033 | − | 0.716066i | \(-0.745941\pi\) | ||||
−0.698033 | + | 0.716066i | \(0.745941\pi\) | |||||||
\(410\) | −0.372281 | −0.0183857 | ||||||||
\(411\) | 10.5109 | 0.518463 | ||||||||
\(412\) | 13.4891 | 0.664562 | ||||||||
\(413\) | −5.48913 | −0.270102 | ||||||||
\(414\) | −4.74456 | −0.233183 | ||||||||
\(415\) | 10.7446 | 0.527430 | ||||||||
\(416\) | 6.74456 | 0.330679 | ||||||||
\(417\) | −38.2337 | −1.87231 | ||||||||
\(418\) | −4.74456 | −0.232064 | ||||||||
\(419\) | −9.48913 | −0.463574 | −0.231787 | − | 0.972767i | \(-0.574457\pi\) | ||||
−0.231787 | + | 0.972767i | \(0.574457\pi\) | |||||||
\(420\) | −8.74456 | −0.426691 | ||||||||
\(421\) | 15.4891 | 0.754894 | 0.377447 | − | 0.926031i | \(-0.376802\pi\) | ||||
0.377447 | + | 0.926031i | \(0.376802\pi\) | |||||||
\(422\) | 3.11684 | 0.151726 | ||||||||
\(423\) | 2.74456 | 0.133445 | ||||||||
\(424\) | −4.37228 | −0.212337 | ||||||||
\(425\) | 0.372281 | 0.0180583 | ||||||||
\(426\) | 9.48913 | 0.459750 | ||||||||
\(427\) | −1.62772 | −0.0787708 | ||||||||
\(428\) | 19.4891 | 0.942042 | ||||||||
\(429\) | 32.0000 | 1.54497 | ||||||||
\(430\) | 1.62772 | 0.0784956 | ||||||||
\(431\) | 4.37228 | 0.210605 | 0.105303 | − | 0.994440i | \(-0.466419\pi\) | ||||
0.105303 | + | 0.994440i | \(0.466419\pi\) | |||||||
\(432\) | −4.00000 | −0.192450 | ||||||||
\(433\) | −32.9783 | −1.58483 | −0.792417 | − | 0.609980i | \(-0.791177\pi\) | ||||
−0.792417 | + | 0.609980i | \(0.791177\pi\) | |||||||
\(434\) | 36.6060 | 1.75714 | ||||||||
\(435\) | −18.2337 | −0.874238 | ||||||||
\(436\) | −17.1168 | −0.819748 | ||||||||
\(437\) | 9.48913 | 0.453926 | ||||||||
\(438\) | −5.48913 | −0.262281 | ||||||||
\(439\) | −7.62772 | −0.364051 | −0.182026 | − | 0.983294i | \(-0.558265\pi\) | ||||
−0.182026 | + | 0.983294i | \(0.558265\pi\) | |||||||
\(440\) | 2.37228 | 0.113094 | ||||||||
\(441\) | 12.1168 | 0.576993 | ||||||||
\(442\) | 2.51087 | 0.119430 | ||||||||
\(443\) | 28.9783 | 1.37680 | 0.688399 | − | 0.725332i | \(-0.258314\pi\) | ||||
0.688399 | + | 0.725332i | \(0.258314\pi\) | |||||||
\(444\) | 2.00000 | 0.0949158 | ||||||||
\(445\) | 10.0000 | 0.474045 | ||||||||
\(446\) | 4.37228 | 0.207034 | ||||||||
\(447\) | 22.9783 | 1.08683 | ||||||||
\(448\) | −4.37228 | −0.206571 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −0.883156 | −0.0415862 | ||||||||
\(452\) | 11.6277 | 0.546922 | ||||||||
\(453\) | −40.0000 | −1.87936 | ||||||||
\(454\) | −5.62772 | −0.264122 | ||||||||
\(455\) | −29.4891 | −1.38247 | ||||||||
\(456\) | −4.00000 | −0.187317 | ||||||||
\(457\) | −9.86141 | −0.461297 | −0.230649 | − | 0.973037i | \(-0.574085\pi\) | ||||
−0.230649 | + | 0.973037i | \(0.574085\pi\) | |||||||
\(458\) | −10.0000 | −0.467269 | ||||||||
\(459\) | −1.48913 | −0.0695064 | ||||||||
\(460\) | −4.74456 | −0.221216 | ||||||||
\(461\) | 24.0951 | 1.12222 | 0.561110 | − | 0.827741i | \(-0.310374\pi\) | ||||
0.561110 | + | 0.827741i | \(0.310374\pi\) | |||||||
\(462\) | −20.7446 | −0.965124 | ||||||||
\(463\) | 17.4891 | 0.812789 | 0.406394 | − | 0.913698i | \(-0.366786\pi\) | ||||
0.406394 | + | 0.913698i | \(0.366786\pi\) | |||||||
\(464\) | −9.11684 | −0.423239 | ||||||||
\(465\) | −16.7446 | −0.776510 | ||||||||
\(466\) | −28.2337 | −1.30790 | ||||||||
\(467\) | −21.3505 | −0.987985 | −0.493992 | − | 0.869466i | \(-0.664463\pi\) | ||||
−0.493992 | + | 0.869466i | \(0.664463\pi\) | |||||||
\(468\) | 6.74456 | 0.311768 | ||||||||
\(469\) | 29.4891 | 1.36168 | ||||||||
\(470\) | 2.74456 | 0.126597 | ||||||||
\(471\) | 23.2554 | 1.07155 | ||||||||
\(472\) | 1.25544 | 0.0577862 | ||||||||
\(473\) | 3.86141 | 0.177548 | ||||||||
\(474\) | 13.4891 | 0.619576 | ||||||||
\(475\) | −2.00000 | −0.0917663 | ||||||||
\(476\) | −1.62772 | −0.0746064 | ||||||||
\(477\) | −4.37228 | −0.200193 | ||||||||
\(478\) | −22.6060 | −1.03397 | ||||||||
\(479\) | 14.7446 | 0.673696 | 0.336848 | − | 0.941559i | \(-0.390639\pi\) | ||||
0.336848 | + | 0.941559i | \(0.390639\pi\) | |||||||
\(480\) | 2.00000 | 0.0912871 | ||||||||
\(481\) | 6.74456 | 0.307526 | ||||||||
\(482\) | 24.2337 | 1.10381 | ||||||||
\(483\) | 41.4891 | 1.88782 | ||||||||
\(484\) | −5.37228 | −0.244195 | ||||||||
\(485\) | 17.1168 | 0.777236 | ||||||||
\(486\) | −10.0000 | −0.453609 | ||||||||
\(487\) | 19.7228 | 0.893726 | 0.446863 | − | 0.894602i | \(-0.352541\pi\) | ||||
0.446863 | + | 0.894602i | \(0.352541\pi\) | |||||||
\(488\) | 0.372281 | 0.0168524 | ||||||||
\(489\) | 27.2554 | 1.23253 | ||||||||
\(490\) | 12.1168 | 0.547383 | ||||||||
\(491\) | −30.9783 | −1.39803 | −0.699014 | − | 0.715108i | \(-0.746378\pi\) | ||||
−0.699014 | + | 0.715108i | \(0.746378\pi\) | |||||||
\(492\) | −0.744563 | −0.0335675 | ||||||||
\(493\) | −3.39403 | −0.152859 | ||||||||
\(494\) | −13.4891 | −0.606904 | ||||||||
\(495\) | 2.37228 | 0.106626 | ||||||||
\(496\) | −8.37228 | −0.375927 | ||||||||
\(497\) | −20.7446 | −0.930521 | ||||||||
\(498\) | 21.4891 | 0.962951 | ||||||||
\(499\) | 20.9783 | 0.939115 | 0.469558 | − | 0.882902i | \(-0.344413\pi\) | ||||
0.469558 | + | 0.882902i | \(0.344413\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −42.9783 | −1.92013 | ||||||||
\(502\) | −11.4891 | −0.512785 | ||||||||
\(503\) | 6.51087 | 0.290306 | 0.145153 | − | 0.989409i | \(-0.453633\pi\) | ||||
0.145153 | + | 0.989409i | \(0.453633\pi\) | |||||||
\(504\) | −4.37228 | −0.194757 | ||||||||
\(505\) | 11.4891 | 0.511259 | ||||||||
\(506\) | −11.2554 | −0.500365 | ||||||||
\(507\) | 64.9783 | 2.88579 | ||||||||
\(508\) | −5.25544 | −0.233172 | ||||||||
\(509\) | −22.7446 | −1.00814 | −0.504068 | − | 0.863664i | \(-0.668164\pi\) | ||||
−0.504068 | + | 0.863664i | \(0.668164\pi\) | |||||||
\(510\) | 0.744563 | 0.0329698 | ||||||||
\(511\) | 12.0000 | 0.530849 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 8.00000 | 0.353209 | ||||||||
\(514\) | 24.9783 | 1.10174 | ||||||||
\(515\) | 13.4891 | 0.594402 | ||||||||
\(516\) | 3.25544 | 0.143313 | ||||||||
\(517\) | 6.51087 | 0.286348 | ||||||||
\(518\) | −4.37228 | −0.192107 | ||||||||
\(519\) | −11.7228 | −0.514574 | ||||||||
\(520\) | 6.74456 | 0.295769 | ||||||||
\(521\) | −36.0951 | −1.58135 | −0.790677 | − | 0.612233i | \(-0.790271\pi\) | ||||
−0.790677 | + | 0.612233i | \(0.790271\pi\) | |||||||
\(522\) | −9.11684 | −0.399033 | ||||||||
\(523\) | 28.0000 | 1.22435 | 0.612177 | − | 0.790721i | \(-0.290294\pi\) | ||||
0.612177 | + | 0.790721i | \(0.290294\pi\) | |||||||
\(524\) | −14.7446 | −0.644119 | ||||||||
\(525\) | −8.74456 | −0.381644 | ||||||||
\(526\) | −17.1168 | −0.746330 | ||||||||
\(527\) | −3.11684 | −0.135772 | ||||||||
\(528\) | 4.74456 | 0.206481 | ||||||||
\(529\) | −0.489125 | −0.0212663 | ||||||||
\(530\) | −4.37228 | −0.189920 | ||||||||
\(531\) | 1.25544 | 0.0544813 | ||||||||
\(532\) | 8.74456 | 0.379125 | ||||||||
\(533\) | −2.51087 | −0.108758 | ||||||||
\(534\) | 20.0000 | 0.865485 | ||||||||
\(535\) | 19.4891 | 0.842588 | ||||||||
\(536\) | −6.74456 | −0.291321 | ||||||||
\(537\) | 16.4674 | 0.710620 | ||||||||
\(538\) | 10.0000 | 0.431131 | ||||||||
\(539\) | 28.7446 | 1.23812 | ||||||||
\(540\) | −4.00000 | −0.172133 | ||||||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | 4.74456 | 0.203796 | ||||||||
\(543\) | −30.9783 | −1.32940 | ||||||||
\(544\) | 0.372281 | 0.0159614 | ||||||||
\(545\) | −17.1168 | −0.733205 | ||||||||
\(546\) | −58.9783 | −2.52404 | ||||||||
\(547\) | 33.6277 | 1.43782 | 0.718909 | − | 0.695104i | \(-0.244642\pi\) | ||||
0.718909 | + | 0.695104i | \(0.244642\pi\) | |||||||
\(548\) | 5.25544 | 0.224501 | ||||||||
\(549\) | 0.372281 | 0.0158886 | ||||||||
\(550\) | 2.37228 | 0.101154 | ||||||||
\(551\) | 18.2337 | 0.776781 | ||||||||
\(552\) | −9.48913 | −0.403884 | ||||||||
\(553\) | −29.4891 | −1.25401 | ||||||||
\(554\) | −10.7446 | −0.456493 | ||||||||
\(555\) | 2.00000 | 0.0848953 | ||||||||
\(556\) | −19.1168 | −0.810735 | ||||||||
\(557\) | −2.74456 | −0.116291 | −0.0581454 | − | 0.998308i | \(-0.518519\pi\) | ||||
−0.0581454 | + | 0.998308i | \(0.518519\pi\) | |||||||
\(558\) | −8.37228 | −0.354427 | ||||||||
\(559\) | 10.9783 | 0.464331 | ||||||||
\(560\) | −4.37228 | −0.184763 | ||||||||
\(561\) | 1.76631 | 0.0745738 | ||||||||
\(562\) | 13.2554 | 0.559147 | ||||||||
\(563\) | −30.0951 | −1.26836 | −0.634179 | − | 0.773187i | \(-0.718662\pi\) | ||||
−0.634179 | + | 0.773187i | \(0.718662\pi\) | |||||||
\(564\) | 5.48913 | 0.231134 | ||||||||
\(565\) | 11.6277 | 0.489182 | ||||||||
\(566\) | −17.4891 | −0.735123 | ||||||||
\(567\) | 48.0951 | 2.01980 | ||||||||
\(568\) | 4.74456 | 0.199077 | ||||||||
\(569\) | 12.9783 | 0.544077 | 0.272038 | − | 0.962286i | \(-0.412302\pi\) | ||||
0.272038 | + | 0.962286i | \(0.412302\pi\) | |||||||
\(570\) | −4.00000 | −0.167542 | ||||||||
\(571\) | 12.6060 | 0.527543 | 0.263772 | − | 0.964585i | \(-0.415033\pi\) | ||||
0.263772 | + | 0.964585i | \(0.415033\pi\) | |||||||
\(572\) | 16.0000 | 0.668994 | ||||||||
\(573\) | 48.7446 | 2.03633 | ||||||||
\(574\) | 1.62772 | 0.0679397 | ||||||||
\(575\) | −4.74456 | −0.197862 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 15.4891 | 0.644821 | 0.322410 | − | 0.946600i | \(-0.395507\pi\) | ||||
0.322410 | + | 0.946600i | \(0.395507\pi\) | |||||||
\(578\) | −16.8614 | −0.701342 | ||||||||
\(579\) | 4.00000 | 0.166234 | ||||||||
\(580\) | −9.11684 | −0.378556 | ||||||||
\(581\) | −46.9783 | −1.94899 | ||||||||
\(582\) | 34.2337 | 1.41903 | ||||||||
\(583\) | −10.3723 | −0.429576 | ||||||||
\(584\) | −2.74456 | −0.113571 | ||||||||
\(585\) | 6.74456 | 0.278853 | ||||||||
\(586\) | 9.86141 | 0.407371 | ||||||||
\(587\) | −26.8397 | −1.10779 | −0.553896 | − | 0.832586i | \(-0.686859\pi\) | ||||
−0.553896 | + | 0.832586i | \(0.686859\pi\) | |||||||
\(588\) | 24.2337 | 0.999380 | ||||||||
\(589\) | 16.7446 | 0.689948 | ||||||||
\(590\) | 1.25544 | 0.0516855 | ||||||||
\(591\) | 9.02175 | 0.371105 | ||||||||
\(592\) | 1.00000 | 0.0410997 | ||||||||
\(593\) | 24.2337 | 0.995158 | 0.497579 | − | 0.867419i | \(-0.334222\pi\) | ||||
0.497579 | + | 0.867419i | \(0.334222\pi\) | |||||||
\(594\) | −9.48913 | −0.389344 | ||||||||
\(595\) | −1.62772 | −0.0667300 | ||||||||
\(596\) | 11.4891 | 0.470613 | ||||||||
\(597\) | −45.4891 | −1.86175 | ||||||||
\(598\) | −32.0000 | −1.30858 | ||||||||
\(599\) | −5.48913 | −0.224280 | −0.112140 | − | 0.993692i | \(-0.535770\pi\) | ||||
−0.112140 | + | 0.993692i | \(0.535770\pi\) | |||||||
\(600\) | 2.00000 | 0.0816497 | ||||||||
\(601\) | 0.372281 | 0.0151857 | 0.00759284 | − | 0.999971i | \(-0.497583\pi\) | ||||
0.00759284 | + | 0.999971i | \(0.497583\pi\) | |||||||
\(602\) | −7.11684 | −0.290061 | ||||||||
\(603\) | −6.74456 | −0.274660 | ||||||||
\(604\) | −20.0000 | −0.813788 | ||||||||
\(605\) | −5.37228 | −0.218414 | ||||||||
\(606\) | 22.9783 | 0.933428 | ||||||||
\(607\) | −39.7228 | −1.61230 | −0.806150 | − | 0.591712i | \(-0.798452\pi\) | ||||
−0.806150 | + | 0.591712i | \(0.798452\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | 79.7228 | 3.23053 | ||||||||
\(610\) | 0.372281 | 0.0150732 | ||||||||
\(611\) | 18.5109 | 0.748870 | ||||||||
\(612\) | 0.372281 | 0.0150486 | ||||||||
\(613\) | −20.0951 | −0.811633 | −0.405817 | − | 0.913955i | \(-0.633013\pi\) | ||||
−0.405817 | + | 0.913955i | \(0.633013\pi\) | |||||||
\(614\) | −0.510875 | −0.0206172 | ||||||||
\(615\) | −0.744563 | −0.0300237 | ||||||||
\(616\) | −10.3723 | −0.417911 | ||||||||
\(617\) | 25.7228 | 1.03556 | 0.517781 | − | 0.855513i | \(-0.326758\pi\) | ||||
0.517781 | + | 0.855513i | \(0.326758\pi\) | |||||||
\(618\) | 26.9783 | 1.08522 | ||||||||
\(619\) | 12.8832 | 0.517818 | 0.258909 | − | 0.965902i | \(-0.416637\pi\) | ||||
0.258909 | + | 0.965902i | \(0.416637\pi\) | |||||||
\(620\) | −8.37228 | −0.336239 | ||||||||
\(621\) | 18.9783 | 0.761571 | ||||||||
\(622\) | 4.37228 | 0.175313 | ||||||||
\(623\) | −43.7228 | −1.75172 | ||||||||
\(624\) | 13.4891 | 0.539997 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 19.4891 | 0.778942 | ||||||||
\(627\) | −9.48913 | −0.378959 | ||||||||
\(628\) | 11.6277 | 0.463996 | ||||||||
\(629\) | 0.372281 | 0.0148438 | ||||||||
\(630\) | −4.37228 | −0.174196 | ||||||||
\(631\) | 44.0951 | 1.75540 | 0.877699 | − | 0.479212i | \(-0.159078\pi\) | ||||
0.877699 | + | 0.479212i | \(0.159078\pi\) | |||||||
\(632\) | 6.74456 | 0.268284 | ||||||||
\(633\) | 6.23369 | 0.247767 | ||||||||
\(634\) | 19.6277 | 0.779516 | ||||||||
\(635\) | −5.25544 | −0.208556 | ||||||||
\(636\) | −8.74456 | −0.346744 | ||||||||
\(637\) | 81.7228 | 3.23798 | ||||||||
\(638\) | −21.6277 | −0.856250 | ||||||||
\(639\) | 4.74456 | 0.187692 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −9.39403 | −0.371042 | −0.185521 | − | 0.982640i | \(-0.559397\pi\) | ||||
−0.185521 | + | 0.982640i | \(0.559397\pi\) | |||||||
\(642\) | 38.9783 | 1.53835 | ||||||||
\(643\) | −2.37228 | −0.0935536 | −0.0467768 | − | 0.998905i | \(-0.514895\pi\) | ||||
−0.0467768 | + | 0.998905i | \(0.514895\pi\) | |||||||
\(644\) | 20.7446 | 0.817450 | ||||||||
\(645\) | 3.25544 | 0.128183 | ||||||||
\(646\) | −0.744563 | −0.0292944 | ||||||||
\(647\) | 9.48913 | 0.373056 | 0.186528 | − | 0.982450i | \(-0.440276\pi\) | ||||
0.186528 | + | 0.982450i | \(0.440276\pi\) | |||||||
\(648\) | −11.0000 | −0.432121 | ||||||||
\(649\) | 2.97825 | 0.116907 | ||||||||
\(650\) | 6.74456 | 0.264544 | ||||||||
\(651\) | 73.2119 | 2.86940 | ||||||||
\(652\) | 13.6277 | 0.533703 | ||||||||
\(653\) | 23.4891 | 0.919201 | 0.459600 | − | 0.888126i | \(-0.347993\pi\) | ||||
0.459600 | + | 0.888126i | \(0.347993\pi\) | |||||||
\(654\) | −34.2337 | −1.33864 | ||||||||
\(655\) | −14.7446 | −0.576118 | ||||||||
\(656\) | −0.372281 | −0.0145351 | ||||||||
\(657\) | −2.74456 | −0.107076 | ||||||||
\(658\) | −12.0000 | −0.467809 | ||||||||
\(659\) | 12.0000 | 0.467454 | 0.233727 | − | 0.972302i | \(-0.424908\pi\) | ||||
0.233727 | + | 0.972302i | \(0.424908\pi\) | |||||||
\(660\) | 4.74456 | 0.184682 | ||||||||
\(661\) | −47.3505 | −1.84172 | −0.920861 | − | 0.389891i | \(-0.872513\pi\) | ||||
−0.920861 | + | 0.389891i | \(0.872513\pi\) | |||||||
\(662\) | 0.510875 | 0.0198557 | ||||||||
\(663\) | 5.02175 | 0.195029 | ||||||||
\(664\) | 10.7446 | 0.416970 | ||||||||
\(665\) | 8.74456 | 0.339100 | ||||||||
\(666\) | 1.00000 | 0.0387492 | ||||||||
\(667\) | 43.2554 | 1.67486 | ||||||||
\(668\) | −21.4891 | −0.831439 | ||||||||
\(669\) | 8.74456 | 0.338084 | ||||||||
\(670\) | −6.74456 | −0.260565 | ||||||||
\(671\) | 0.883156 | 0.0340939 | ||||||||
\(672\) | −8.74456 | −0.337329 | ||||||||
\(673\) | −31.4891 | −1.21382 | −0.606908 | − | 0.794772i | \(-0.707590\pi\) | ||||
−0.606908 | + | 0.794772i | \(0.707590\pi\) | |||||||
\(674\) | −18.7446 | −0.722014 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 32.4891 | 1.24958 | ||||||||
\(677\) | −42.0000 | −1.61419 | −0.807096 | − | 0.590421i | \(-0.798962\pi\) | ||||
−0.807096 | + | 0.590421i | \(0.798962\pi\) | |||||||
\(678\) | 23.2554 | 0.893120 | ||||||||
\(679\) | −74.8397 | −2.87208 | ||||||||
\(680\) | 0.372281 | 0.0142763 | ||||||||
\(681\) | −11.2554 | −0.431309 | ||||||||
\(682\) | −19.8614 | −0.760533 | ||||||||
\(683\) | 14.3723 | 0.549940 | 0.274970 | − | 0.961453i | \(-0.411332\pi\) | ||||
0.274970 | + | 0.961453i | \(0.411332\pi\) | |||||||
\(684\) | −2.00000 | −0.0764719 | ||||||||
\(685\) | 5.25544 | 0.200800 | ||||||||
\(686\) | −22.3723 | −0.854178 | ||||||||
\(687\) | −20.0000 | −0.763048 | ||||||||
\(688\) | 1.62772 | 0.0620562 | ||||||||
\(689\) | −29.4891 | −1.12345 | ||||||||
\(690\) | −9.48913 | −0.361245 | ||||||||
\(691\) | −29.3505 | −1.11655 | −0.558273 | − | 0.829657i | \(-0.688536\pi\) | ||||
−0.558273 | + | 0.829657i | \(0.688536\pi\) | |||||||
\(692\) | −5.86141 | −0.222817 | ||||||||
\(693\) | −10.3723 | −0.394010 | ||||||||
\(694\) | 22.9783 | 0.872242 | ||||||||
\(695\) | −19.1168 | −0.725143 | ||||||||
\(696\) | −18.2337 | −0.691146 | ||||||||
\(697\) | −0.138593 | −0.00524960 | ||||||||
\(698\) | −22.0000 | −0.832712 | ||||||||
\(699\) | −56.4674 | −2.13579 | ||||||||
\(700\) | −4.37228 | −0.165257 | ||||||||
\(701\) | 42.4674 | 1.60397 | 0.801985 | − | 0.597344i | \(-0.203777\pi\) | ||||
0.801985 | + | 0.597344i | \(0.203777\pi\) | |||||||
\(702\) | −26.9783 | −1.01823 | ||||||||
\(703\) | −2.00000 | −0.0754314 | ||||||||
\(704\) | 2.37228 | 0.0894087 | ||||||||
\(705\) | 5.48913 | 0.206732 | ||||||||
\(706\) | 5.86141 | 0.220597 | ||||||||
\(707\) | −50.2337 | −1.88923 | ||||||||
\(708\) | 2.51087 | 0.0943645 | ||||||||
\(709\) | 22.8832 | 0.859395 | 0.429697 | − | 0.902973i | \(-0.358620\pi\) | ||||
0.429697 | + | 0.902973i | \(0.358620\pi\) | |||||||
\(710\) | 4.74456 | 0.178060 | ||||||||
\(711\) | 6.74456 | 0.252941 | ||||||||
\(712\) | 10.0000 | 0.374766 | ||||||||
\(713\) | 39.7228 | 1.48763 | ||||||||
\(714\) | −3.25544 | −0.121832 | ||||||||
\(715\) | 16.0000 | 0.598366 | ||||||||
\(716\) | 8.23369 | 0.307707 | ||||||||
\(717\) | −45.2119 | −1.68847 | ||||||||
\(718\) | 14.9783 | 0.558983 | ||||||||
\(719\) | −23.2554 | −0.867281 | −0.433641 | − | 0.901086i | \(-0.642771\pi\) | ||||
−0.433641 | + | 0.901086i | \(0.642771\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −58.9783 | −2.19646 | ||||||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | 48.4674 | 1.80252 | ||||||||
\(724\) | −15.4891 | −0.575649 | ||||||||
\(725\) | −9.11684 | −0.338591 | ||||||||
\(726\) | −10.7446 | −0.398768 | ||||||||
\(727\) | −48.0000 | −1.78022 | −0.890111 | − | 0.455744i | \(-0.849373\pi\) | ||||
−0.890111 | + | 0.455744i | \(0.849373\pi\) | |||||||
\(728\) | −29.4891 | −1.09294 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −2.74456 | −0.101581 | ||||||||
\(731\) | 0.605969 | 0.0224126 | ||||||||
\(732\) | 0.744563 | 0.0275198 | ||||||||
\(733\) | −23.6277 | −0.872710 | −0.436355 | − | 0.899775i | \(-0.643731\pi\) | ||||
−0.436355 | + | 0.899775i | \(0.643731\pi\) | |||||||
\(734\) | 21.1168 | 0.779437 | ||||||||
\(735\) | 24.2337 | 0.893873 | ||||||||
\(736\) | −4.74456 | −0.174887 | ||||||||
\(737\) | −16.0000 | −0.589368 | ||||||||
\(738\) | −0.372281 | −0.0137039 | ||||||||
\(739\) | −8.13859 | −0.299383 | −0.149691 | − | 0.988733i | \(-0.547828\pi\) | ||||
−0.149691 | + | 0.988733i | \(0.547828\pi\) | |||||||
\(740\) | 1.00000 | 0.0367607 | ||||||||
\(741\) | −26.9783 | −0.991071 | ||||||||
\(742\) | 19.1168 | 0.701801 | ||||||||
\(743\) | 0.372281 | 0.0136577 | 0.00682884 | − | 0.999977i | \(-0.497826\pi\) | ||||
0.00682884 | + | 0.999977i | \(0.497826\pi\) | |||||||
\(744\) | −16.7446 | −0.613885 | ||||||||
\(745\) | 11.4891 | 0.420929 | ||||||||
\(746\) | −8.51087 | −0.311605 | ||||||||
\(747\) | 10.7446 | 0.393123 | ||||||||
\(748\) | 0.883156 | 0.0322914 | ||||||||
\(749\) | −85.2119 | −3.11358 | ||||||||
\(750\) | 2.00000 | 0.0730297 | ||||||||
\(751\) | −0.744563 | −0.0271695 | −0.0135847 | − | 0.999908i | \(-0.504324\pi\) | ||||
−0.0135847 | + | 0.999908i | \(0.504324\pi\) | |||||||
\(752\) | 2.74456 | 0.100084 | ||||||||
\(753\) | −22.9783 | −0.837374 | ||||||||
\(754\) | −61.4891 | −2.23930 | ||||||||
\(755\) | −20.0000 | −0.727875 | ||||||||
\(756\) | 17.4891 | 0.636073 | ||||||||
\(757\) | −47.9565 | −1.74301 | −0.871504 | − | 0.490388i | \(-0.836855\pi\) | ||||
−0.871504 | + | 0.490388i | \(0.836855\pi\) | |||||||
\(758\) | −8.00000 | −0.290573 | ||||||||
\(759\) | −22.5109 | −0.817093 | ||||||||
\(760\) | −2.00000 | −0.0725476 | ||||||||
\(761\) | −0.372281 | −0.0134952 | −0.00674759 | − | 0.999977i | \(-0.502148\pi\) | ||||
−0.00674759 | + | 0.999977i | \(0.502148\pi\) | |||||||
\(762\) | −10.5109 | −0.380769 | ||||||||
\(763\) | 74.8397 | 2.70938 | ||||||||
\(764\) | 24.3723 | 0.881758 | ||||||||
\(765\) | 0.372281 | 0.0134599 | ||||||||
\(766\) | 9.48913 | 0.342856 | ||||||||
\(767\) | 8.46738 | 0.305739 | ||||||||
\(768\) | 2.00000 | 0.0721688 | ||||||||
\(769\) | 11.7663 | 0.424304 | 0.212152 | − | 0.977237i | \(-0.431953\pi\) | ||||
0.212152 | + | 0.977237i | \(0.431953\pi\) | |||||||
\(770\) | −10.3723 | −0.373791 | ||||||||
\(771\) | 49.9565 | 1.79914 | ||||||||
\(772\) | 2.00000 | 0.0719816 | ||||||||
\(773\) | 27.3505 | 0.983730 | 0.491865 | − | 0.870671i | \(-0.336315\pi\) | ||||
0.491865 | + | 0.870671i | \(0.336315\pi\) | |||||||
\(774\) | 1.62772 | 0.0585071 | ||||||||
\(775\) | −8.37228 | −0.300741 | ||||||||
\(776\) | 17.1168 | 0.614459 | ||||||||
\(777\) | −8.74456 | −0.313709 | ||||||||
\(778\) | −13.8614 | −0.496956 | ||||||||
\(779\) | 0.744563 | 0.0266767 | ||||||||
\(780\) | 13.4891 | 0.482988 | ||||||||
\(781\) | 11.2554 | 0.402751 | ||||||||
\(782\) | −1.76631 | −0.0631632 | ||||||||
\(783\) | 36.4674 | 1.30324 | ||||||||
\(784\) | 12.1168 | 0.432744 | ||||||||
\(785\) | 11.6277 | 0.415011 | ||||||||
\(786\) | −29.4891 | −1.05184 | ||||||||
\(787\) | −22.0000 | −0.784215 | −0.392108 | − | 0.919919i | \(-0.628254\pi\) | ||||
−0.392108 | + | 0.919919i | \(0.628254\pi\) | |||||||
\(788\) | 4.51087 | 0.160693 | ||||||||
\(789\) | −34.2337 | −1.21875 | ||||||||
\(790\) | 6.74456 | 0.239961 | ||||||||
\(791\) | −50.8397 | −1.80765 | ||||||||
\(792\) | 2.37228 | 0.0842953 | ||||||||
\(793\) | 2.51087 | 0.0891638 | ||||||||
\(794\) | −20.9783 | −0.744490 | ||||||||
\(795\) | −8.74456 | −0.310138 | ||||||||
\(796\) | −22.7446 | −0.806160 | ||||||||
\(797\) | −4.51087 | −0.159783 | −0.0798917 | − | 0.996804i | \(-0.525457\pi\) | ||||
−0.0798917 | + | 0.996804i | \(0.525457\pi\) | |||||||
\(798\) | 17.4891 | 0.619108 | ||||||||
\(799\) | 1.02175 | 0.0361469 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 10.0000 | 0.353333 | ||||||||
\(802\) | 10.0000 | 0.353112 | ||||||||
\(803\) | −6.51087 | −0.229764 | ||||||||
\(804\) | −13.4891 | −0.475725 | ||||||||
\(805\) | 20.7446 | 0.731150 | ||||||||
\(806\) | −56.4674 | −1.98898 | ||||||||
\(807\) | 20.0000 | 0.704033 | ||||||||
\(808\) | 11.4891 | 0.404186 | ||||||||
\(809\) | −28.5109 | −1.00239 | −0.501194 | − | 0.865335i | \(-0.667106\pi\) | ||||
−0.501194 | + | 0.865335i | \(0.667106\pi\) | |||||||
\(810\) | −11.0000 | −0.386501 | ||||||||
\(811\) | 26.5109 | 0.930923 | 0.465461 | − | 0.885068i | \(-0.345888\pi\) | ||||
0.465461 | + | 0.885068i | \(0.345888\pi\) | |||||||
\(812\) | 39.8614 | 1.39886 | ||||||||
\(813\) | 9.48913 | 0.332798 | ||||||||
\(814\) | 2.37228 | 0.0831484 | ||||||||
\(815\) | 13.6277 | 0.477358 | ||||||||
\(816\) | 0.744563 | 0.0260649 | ||||||||
\(817\) | −3.25544 | −0.113893 | ||||||||
\(818\) | −28.2337 | −0.987168 | ||||||||
\(819\) | −29.4891 | −1.03043 | ||||||||
\(820\) | −0.372281 | −0.0130006 | ||||||||
\(821\) | −21.2554 | −0.741820 | −0.370910 | − | 0.928669i | \(-0.620954\pi\) | ||||
−0.370910 | + | 0.928669i | \(0.620954\pi\) | |||||||
\(822\) | 10.5109 | 0.366609 | ||||||||
\(823\) | 17.7228 | 0.617778 | 0.308889 | − | 0.951098i | \(-0.400043\pi\) | ||||
0.308889 | + | 0.951098i | \(0.400043\pi\) | |||||||
\(824\) | 13.4891 | 0.469916 | ||||||||
\(825\) | 4.74456 | 0.165184 | ||||||||
\(826\) | −5.48913 | −0.190991 | ||||||||
\(827\) | −2.64947 | −0.0921310 | −0.0460655 | − | 0.998938i | \(-0.514668\pi\) | ||||
−0.0460655 | + | 0.998938i | \(0.514668\pi\) | |||||||
\(828\) | −4.74456 | −0.164885 | ||||||||
\(829\) | 11.3505 | 0.394220 | 0.197110 | − | 0.980381i | \(-0.436844\pi\) | ||||
0.197110 | + | 0.980381i | \(0.436844\pi\) | |||||||
\(830\) | 10.7446 | 0.372949 | ||||||||
\(831\) | −21.4891 | −0.745449 | ||||||||
\(832\) | 6.74456 | 0.233826 | ||||||||
\(833\) | 4.51087 | 0.156293 | ||||||||
\(834\) | −38.2337 | −1.32392 | ||||||||
\(835\) | −21.4891 | −0.743662 | ||||||||
\(836\) | −4.74456 | −0.164094 | ||||||||
\(837\) | 33.4891 | 1.15755 | ||||||||
\(838\) | −9.48913 | −0.327796 | ||||||||
\(839\) | −6.51087 | −0.224780 | −0.112390 | − | 0.993664i | \(-0.535851\pi\) | ||||
−0.112390 | + | 0.993664i | \(0.535851\pi\) | |||||||
\(840\) | −8.74456 | −0.301716 | ||||||||
\(841\) | 54.1168 | 1.86610 | ||||||||
\(842\) | 15.4891 | 0.533791 | ||||||||
\(843\) | 26.5109 | 0.913083 | ||||||||
\(844\) | 3.11684 | 0.107286 | ||||||||
\(845\) | 32.4891 | 1.11766 | ||||||||
\(846\) | 2.74456 | 0.0943600 | ||||||||
\(847\) | 23.4891 | 0.807096 | ||||||||
\(848\) | −4.37228 | −0.150145 | ||||||||
\(849\) | −34.9783 | −1.20045 | ||||||||
\(850\) | 0.372281 | 0.0127691 | ||||||||
\(851\) | −4.74456 | −0.162642 | ||||||||
\(852\) | 9.48913 | 0.325092 | ||||||||
\(853\) | 12.5109 | 0.428364 | 0.214182 | − | 0.976794i | \(-0.431291\pi\) | ||||
0.214182 | + | 0.976794i | \(0.431291\pi\) | |||||||
\(854\) | −1.62772 | −0.0556994 | ||||||||
\(855\) | −2.00000 | −0.0683986 | ||||||||
\(856\) | 19.4891 | 0.666125 | ||||||||
\(857\) | −57.8614 | −1.97651 | −0.988254 | − | 0.152820i | \(-0.951164\pi\) | ||||
−0.988254 | + | 0.152820i | \(0.951164\pi\) | |||||||
\(858\) | 32.0000 | 1.09246 | ||||||||
\(859\) | 37.7228 | 1.28709 | 0.643543 | − | 0.765410i | \(-0.277464\pi\) | ||||
0.643543 | + | 0.765410i | \(0.277464\pi\) | |||||||
\(860\) | 1.62772 | 0.0555047 | ||||||||
\(861\) | 3.25544 | 0.110945 | ||||||||
\(862\) | 4.37228 | 0.148920 | ||||||||
\(863\) | −20.8397 | −0.709390 | −0.354695 | − | 0.934982i | \(-0.615415\pi\) | ||||
−0.354695 | + | 0.934982i | \(0.615415\pi\) | |||||||
\(864\) | −4.00000 | −0.136083 | ||||||||
\(865\) | −5.86141 | −0.199294 | ||||||||
\(866\) | −32.9783 | −1.12065 | ||||||||
\(867\) | −33.7228 | −1.14529 | ||||||||
\(868\) | 36.6060 | 1.24249 | ||||||||
\(869\) | 16.0000 | 0.542763 | ||||||||
\(870\) | −18.2337 | −0.618180 | ||||||||
\(871\) | −45.4891 | −1.54134 | ||||||||
\(872\) | −17.1168 | −0.579649 | ||||||||
\(873\) | 17.1168 | 0.579317 | ||||||||
\(874\) | 9.48913 | 0.320974 | ||||||||
\(875\) | −4.37228 | −0.147810 | ||||||||
\(876\) | −5.48913 | −0.185460 | ||||||||
\(877\) | 43.6277 | 1.47320 | 0.736602 | − | 0.676327i | \(-0.236429\pi\) | ||||
0.736602 | + | 0.676327i | \(0.236429\pi\) | |||||||
\(878\) | −7.62772 | −0.257423 | ||||||||
\(879\) | 19.7228 | 0.665234 | ||||||||
\(880\) | 2.37228 | 0.0799696 | ||||||||
\(881\) | −4.37228 | −0.147306 | −0.0736530 | − | 0.997284i | \(-0.523466\pi\) | ||||
−0.0736530 | + | 0.997284i | \(0.523466\pi\) | |||||||
\(882\) | 12.1168 | 0.407995 | ||||||||
\(883\) | −5.62772 | −0.189388 | −0.0946939 | − | 0.995506i | \(-0.530187\pi\) | ||||
−0.0946939 | + | 0.995506i | \(0.530187\pi\) | |||||||
\(884\) | 2.51087 | 0.0844499 | ||||||||
\(885\) | 2.51087 | 0.0844021 | ||||||||
\(886\) | 28.9783 | 0.973543 | ||||||||
\(887\) | −19.6277 | −0.659034 | −0.329517 | − | 0.944150i | \(-0.606886\pi\) | ||||
−0.329517 | + | 0.944150i | \(0.606886\pi\) | |||||||
\(888\) | 2.00000 | 0.0671156 | ||||||||
\(889\) | 22.9783 | 0.770666 | ||||||||
\(890\) | 10.0000 | 0.335201 | ||||||||
\(891\) | −26.0951 | −0.874219 | ||||||||
\(892\) | 4.37228 | 0.146395 | ||||||||
\(893\) | −5.48913 | −0.183687 | ||||||||
\(894\) | 22.9783 | 0.768508 | ||||||||
\(895\) | 8.23369 | 0.275222 | ||||||||
\(896\) | −4.37228 | −0.146068 | ||||||||
\(897\) | −64.0000 | −2.13690 | ||||||||
\(898\) | 18.0000 | 0.600668 | ||||||||
\(899\) | 76.3288 | 2.54571 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −1.62772 | −0.0542272 | ||||||||
\(902\) | −0.883156 | −0.0294059 | ||||||||
\(903\) | −14.2337 | −0.473667 | ||||||||
\(904\) | 11.6277 | 0.386732 | ||||||||
\(905\) | −15.4891 | −0.514876 | ||||||||
\(906\) | −40.0000 | −1.32891 | ||||||||
\(907\) | −28.4674 | −0.945244 | −0.472622 | − | 0.881265i | \(-0.656692\pi\) | ||||
−0.472622 | + | 0.881265i | \(0.656692\pi\) | |||||||
\(908\) | −5.62772 | −0.186762 | ||||||||
\(909\) | 11.4891 | 0.381070 | ||||||||
\(910\) | −29.4891 | −0.977555 | ||||||||
\(911\) | 52.2337 | 1.73058 | 0.865290 | − | 0.501272i | \(-0.167134\pi\) | ||||
0.865290 | + | 0.501272i | \(0.167134\pi\) | |||||||
\(912\) | −4.00000 | −0.132453 | ||||||||
\(913\) | 25.4891 | 0.843567 | ||||||||
\(914\) | −9.86141 | −0.326186 | ||||||||
\(915\) | 0.744563 | 0.0246145 | ||||||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | 64.4674 | 2.12890 | ||||||||
\(918\) | −1.48913 | −0.0491485 | ||||||||
\(919\) | −49.7228 | −1.64020 | −0.820102 | − | 0.572217i | \(-0.806083\pi\) | ||||
−0.820102 | + | 0.572217i | \(0.806083\pi\) | |||||||
\(920\) | −4.74456 | −0.156424 | ||||||||
\(921\) | −1.02175 | −0.0336678 | ||||||||
\(922\) | 24.0951 | 0.793530 | ||||||||
\(923\) | 32.0000 | 1.05329 | ||||||||
\(924\) | −20.7446 | −0.682446 | ||||||||
\(925\) | 1.00000 | 0.0328798 | ||||||||
\(926\) | 17.4891 | 0.574728 | ||||||||
\(927\) | 13.4891 | 0.443041 | ||||||||
\(928\) | −9.11684 | −0.299275 | ||||||||
\(929\) | −32.0951 | −1.05301 | −0.526503 | − | 0.850173i | \(-0.676497\pi\) | ||||
−0.526503 | + | 0.850173i | \(0.676497\pi\) | |||||||
\(930\) | −16.7446 | −0.549076 | ||||||||
\(931\) | −24.2337 | −0.794227 | ||||||||
\(932\) | −28.2337 | −0.924825 | ||||||||
\(933\) | 8.74456 | 0.286284 | ||||||||
\(934\) | −21.3505 | −0.698611 | ||||||||
\(935\) | 0.883156 | 0.0288823 | ||||||||
\(936\) | 6.74456 | 0.220453 | ||||||||
\(937\) | −8.97825 | −0.293307 | −0.146653 | − | 0.989188i | \(-0.546850\pi\) | ||||
−0.146653 | + | 0.989188i | \(0.546850\pi\) | |||||||
\(938\) | 29.4891 | 0.962854 | ||||||||
\(939\) | 38.9783 | 1.27201 | ||||||||
\(940\) | 2.74456 | 0.0895178 | ||||||||
\(941\) | 18.0000 | 0.586783 | 0.293392 | − | 0.955992i | \(-0.405216\pi\) | ||||
0.293392 | + | 0.955992i | \(0.405216\pi\) | |||||||
\(942\) | 23.2554 | 0.757703 | ||||||||
\(943\) | 1.76631 | 0.0575190 | ||||||||
\(944\) | 1.25544 | 0.0408610 | ||||||||
\(945\) | 17.4891 | 0.568921 | ||||||||
\(946\) | 3.86141 | 0.125545 | ||||||||
\(947\) | −26.0951 | −0.847977 | −0.423988 | − | 0.905668i | \(-0.639370\pi\) | ||||
−0.423988 | + | 0.905668i | \(0.639370\pi\) | |||||||
\(948\) | 13.4891 | 0.438106 | ||||||||
\(949\) | −18.5109 | −0.600888 | ||||||||
\(950\) | −2.00000 | −0.0648886 | ||||||||
\(951\) | 39.2554 | 1.27294 | ||||||||
\(952\) | −1.62772 | −0.0527547 | ||||||||
\(953\) | 11.7663 | 0.381148 | 0.190574 | − | 0.981673i | \(-0.438965\pi\) | ||||
0.190574 | + | 0.981673i | \(0.438965\pi\) | |||||||
\(954\) | −4.37228 | −0.141558 | ||||||||
\(955\) | 24.3723 | 0.788669 | ||||||||
\(956\) | −22.6060 | −0.731129 | ||||||||
\(957\) | −43.2554 | −1.39825 | ||||||||
\(958\) | 14.7446 | 0.476375 | ||||||||
\(959\) | −22.9783 | −0.742006 | ||||||||
\(960\) | 2.00000 | 0.0645497 | ||||||||
\(961\) | 39.0951 | 1.26113 | ||||||||
\(962\) | 6.74456 | 0.217453 | ||||||||
\(963\) | 19.4891 | 0.628028 | ||||||||
\(964\) | 24.2337 | 0.780515 | ||||||||
\(965\) | 2.00000 | 0.0643823 | ||||||||
\(966\) | 41.4891 | 1.33489 | ||||||||
\(967\) | −28.0000 | −0.900419 | −0.450210 | − | 0.892923i | \(-0.648651\pi\) | ||||
−0.450210 | + | 0.892923i | \(0.648651\pi\) | |||||||
\(968\) | −5.37228 | −0.172672 | ||||||||
\(969\) | −1.48913 | −0.0478376 | ||||||||
\(970\) | 17.1168 | 0.549589 | ||||||||
\(971\) | 20.6060 | 0.661277 | 0.330639 | − | 0.943757i | \(-0.392736\pi\) | ||||
0.330639 | + | 0.943757i | \(0.392736\pi\) | |||||||
\(972\) | −10.0000 | −0.320750 | ||||||||
\(973\) | 83.5842 | 2.67959 | ||||||||
\(974\) | 19.7228 | 0.631960 | ||||||||
\(975\) | 13.4891 | 0.431998 | ||||||||
\(976\) | 0.372281 | 0.0119164 | ||||||||
\(977\) | −29.1168 | −0.931530 | −0.465765 | − | 0.884908i | \(-0.654221\pi\) | ||||
−0.465765 | + | 0.884908i | \(0.654221\pi\) | |||||||
\(978\) | 27.2554 | 0.871533 | ||||||||
\(979\) | 23.7228 | 0.758184 | ||||||||
\(980\) | 12.1168 | 0.387058 | ||||||||
\(981\) | −17.1168 | −0.546499 | ||||||||
\(982\) | −30.9783 | −0.988556 | ||||||||
\(983\) | 2.13859 | 0.0682105 | 0.0341053 | − | 0.999418i | \(-0.489142\pi\) | ||||
0.0341053 | + | 0.999418i | \(0.489142\pi\) | |||||||
\(984\) | −0.744563 | −0.0237358 | ||||||||
\(985\) | 4.51087 | 0.143728 | ||||||||
\(986\) | −3.39403 | −0.108088 | ||||||||
\(987\) | −24.0000 | −0.763928 | ||||||||
\(988\) | −13.4891 | −0.429146 | ||||||||
\(989\) | −7.72281 | −0.245571 | ||||||||
\(990\) | 2.37228 | 0.0753960 | ||||||||
\(991\) | −14.6060 | −0.463974 | −0.231987 | − | 0.972719i | \(-0.574523\pi\) | ||||
−0.231987 | + | 0.972719i | \(0.574523\pi\) | |||||||
\(992\) | −8.37228 | −0.265820 | ||||||||
\(993\) | 1.02175 | 0.0324242 | ||||||||
\(994\) | −20.7446 | −0.657978 | ||||||||
\(995\) | −22.7446 | −0.721051 | ||||||||
\(996\) | 21.4891 | 0.680909 | ||||||||
\(997\) | −8.23369 | −0.260764 | −0.130382 | − | 0.991464i | \(-0.541620\pi\) | ||||
−0.130382 | + | 0.991464i | \(0.541620\pi\) | |||||||
\(998\) | 20.9783 | 0.664055 | ||||||||
\(999\) | −4.00000 | −0.126554 |
(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 | 370.2.a.f.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 3330.2.a.bb.1.1 | 2 | |||
4.3 | odd | 2 | 2960.2.a.o.1.2 | 2 | |||
5.2 | odd | 4 | 1850.2.b.m.149.3 | 4 | |||
5.3 | odd | 4 | 1850.2.b.m.149.2 | 4 | |||
5.4 | even | 2 | 1850.2.a.q.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.a.f.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1850.2.a.q.1.2 | 2 | 5.4 | even | 2 | |||
1850.2.b.m.149.2 | 4 | 5.3 | odd | 4 | |||
1850.2.b.m.149.3 | 4 | 5.2 | odd | 4 | |||
2960.2.a.o.1.2 | 2 | 4.3 | odd | 2 | |||
3330.2.a.bb.1.1 | 2 | 3.2 | odd | 2 |