Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4640,2,Mod(1,4640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4640.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4640 = 2^{5} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4640.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: | \(37.0505865379\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4640.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.618034 | 0.356822 | 0.178411 | − | 0.983956i | \(-0.442904\pi\) | ||||
0.178411 | + | 0.983956i | \(0.442904\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.85410 | −1.07875 | −0.539375 | − | 0.842066i | \(-0.681339\pi\) | ||||
−0.539375 | + | 0.842066i | \(0.681339\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.61803 | −0.872678 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.23607 | −0.975711 | −0.487856 | − | 0.872924i | \(-0.662221\pi\) | ||||
−0.487856 | + | 0.872924i | \(0.662221\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.09017 | −1.41176 | −0.705880 | − | 0.708332i | \(-0.749448\pi\) | ||||
−0.705880 | + | 0.708332i | \(0.749448\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.618034 | −0.159576 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.61803 | −0.877502 | −0.438751 | − | 0.898609i | \(-0.644579\pi\) | ||||
−0.438751 | + | 0.898609i | \(0.644579\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.76393 | 0.634089 | 0.317045 | − | 0.948411i | \(-0.397309\pi\) | ||||
0.317045 | + | 0.948411i | \(0.397309\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.76393 | −0.384922 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.85410 | 1.22066 | 0.610332 | − | 0.792145i | \(-0.291036\pi\) | ||||
0.610332 | + | 0.792145i | \(0.291036\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.47214 | −0.668213 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.61803 | −0.290607 | −0.145304 | − | 0.989387i | \(-0.546416\pi\) | ||||
−0.145304 | + | 0.989387i | \(0.546416\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00000 | −0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.85410 | 0.482431 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.23607 | 1.51840 | 0.759200 | − | 0.650857i | \(-0.225590\pi\) | ||||
0.759200 | + | 0.650857i | \(0.225590\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.14590 | −0.503747 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.70820 | −0.579124 | −0.289562 | − | 0.957159i | \(-0.593510\pi\) | ||||
−0.289562 | + | 0.957159i | \(0.593510\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.61803 | −1.16174 | −0.580870 | − | 0.813997i | \(-0.697287\pi\) | ||||
−0.580870 | + | 0.813997i | \(0.697287\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.61803 | 0.390273 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.14590 | 0.163700 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.23607 | −0.313112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.32624 | 1.28106 | 0.640529 | − | 0.767934i | \(-0.278715\pi\) | ||||
0.640529 | + | 0.767934i | \(0.278715\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.23607 | 0.436351 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.70820 | 0.226257 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.38197 | −1.22143 | −0.610714 | − | 0.791851i | \(-0.709117\pi\) | ||||
−0.610714 | + | 0.791851i | \(0.709117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.14590 | 0.274754 | 0.137377 | − | 0.990519i | \(-0.456133\pi\) | ||||
0.137377 | + | 0.990519i | \(0.456133\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.47214 | 0.941401 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.09017 | 0.631358 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.47214 | −0.302019 | −0.151010 | − | 0.988532i | \(-0.548252\pi\) | ||||
−0.151010 | + | 0.988532i | \(0.548252\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.61803 | 0.435560 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.9443 | 1.53620 | 0.768101 | − | 0.640328i | \(-0.221202\pi\) | ||||
0.768101 | + | 0.640328i | \(0.221202\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.90983 | 0.223529 | 0.111764 | − | 0.993735i | \(-0.464350\pi\) | ||||
0.111764 | + | 0.993735i | \(0.464350\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.618034 | 0.0713644 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.23607 | 1.05255 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.90983 | −0.327381 | −0.163691 | − | 0.986512i | \(-0.552340\pi\) | ||||
−0.163691 | + | 0.986512i | \(0.552340\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.70820 | 0.634245 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.7082 | 1.72420 | 0.862100 | − | 0.506739i | \(-0.169149\pi\) | ||||
0.862100 | + | 0.506739i | \(0.169149\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.61803 | 0.392431 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.618034 | 0.0662602 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.70820 | −0.181069 | −0.0905346 | − | 0.995893i | \(-0.528858\pi\) | ||||
−0.0905346 | + | 0.995893i | \(0.528858\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.5279 | 1.52293 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.76393 | −0.283573 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.79837 | 0.893340 | 0.446670 | − | 0.894699i | \(-0.352610\pi\) | ||||
0.446670 | + | 0.894699i | \(0.352610\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.47214 | 0.851482 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.09017 | −0.705498 | −0.352749 | − | 0.935718i | \(-0.614753\pi\) | ||||
−0.352749 | + | 0.935718i | \(0.614753\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.94427 | 0.881305 | 0.440653 | − | 0.897678i | \(-0.354747\pi\) | ||||
0.440653 | + | 0.897678i | \(0.354747\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.76393 | 0.172142 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.291796 | 0.0282090 | 0.0141045 | − | 0.999901i | \(-0.495510\pi\) | ||||
0.0141045 | + | 0.999901i | \(0.495510\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.7082 | 1.12144 | 0.560721 | − | 0.828005i | \(-0.310524\pi\) | ||||
0.560721 | + | 0.828005i | \(0.310524\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.70820 | 0.541799 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.79837 | 0.827681 | 0.413841 | − | 0.910349i | \(-0.364187\pi\) | ||||
0.413841 | + | 0.910349i | \(0.364187\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.85410 | −0.545898 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.3262 | 1.23201 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.3262 | 0.946605 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.527864 | −0.0479876 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.29180 | −0.206644 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.944272 | −0.0837906 | −0.0418953 | − | 0.999122i | \(-0.513340\pi\) | ||||
−0.0418953 | + | 0.999122i | \(0.513340\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.70820 | −0.414534 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.9443 | −1.65517 | −0.827584 | − | 0.561341i | \(-0.810285\pi\) | ||||
−0.827584 | + | 0.561341i | \(0.810285\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.88854 | −0.684023 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.47214 | 0.298834 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.145898 | −0.0124649 | −0.00623246 | − | 0.999981i | \(-0.501984\pi\) | ||||
−0.00623246 | + | 0.999981i | \(0.501984\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.61803 | 0.476515 | 0.238258 | − | 0.971202i | \(-0.423424\pi\) | ||||
0.238258 | + | 0.971202i | \(0.423424\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.94427 | −0.416383 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.4721 | 1.37747 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.00000 | −0.0830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.708204 | 0.0584117 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.1803 | 1.32555 | 0.662773 | − | 0.748821i | \(-0.269380\pi\) | ||||
0.662773 | + | 0.748821i | \(0.269380\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.23607 | 0.100590 | 0.0502949 | − | 0.998734i | \(-0.483984\pi\) | ||||
0.0502949 | + | 0.998734i | \(0.483984\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.47214 | 0.765777 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.61803 | 0.129964 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.05573 | 0.403491 | 0.201746 | − | 0.979438i | \(-0.435339\pi\) | ||||
0.201746 | + | 0.979438i | \(0.435339\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.76393 | 0.457110 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.7082 | −1.31679 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.5279 | −1.05958 | −0.529792 | − | 0.848128i | \(-0.677730\pi\) | ||||
−0.529792 | + | 0.848128i | \(0.677730\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.00000 | 0.155700 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.38197 | −0.339087 | −0.169543 | − | 0.985523i | \(-0.554229\pi\) | ||||
−0.169543 | + | 0.985523i | \(0.554229\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9098 | 0.993064 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.23607 | −0.553356 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.79837 | −0.364814 | −0.182407 | − | 0.983223i | \(-0.558389\pi\) | ||||
−0.182407 | + | 0.983223i | \(0.558389\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.85410 | −0.215750 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.79837 | −0.435832 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.09017 | −0.0814831 | −0.0407416 | − | 0.999170i | \(-0.512972\pi\) | ||||
−0.0407416 | + | 0.999170i | \(0.512972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.291796 | 0.0216890 | 0.0108445 | − | 0.999941i | \(-0.496548\pi\) | ||||
0.0108445 | + | 0.999941i | \(0.496548\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.32624 | 0.0980383 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.23607 | −0.679049 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.7082 | 0.856189 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.90983 | 0.720834 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.8541 | −1.50895 | −0.754475 | − | 0.656329i | \(-0.772108\pi\) | ||||
−0.754475 | + | 0.656329i | \(0.772108\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.145898 | 0.0105020 | 0.00525099 | − | 0.999986i | \(-0.498329\pi\) | ||||
0.00525099 | + | 0.999986i | \(0.498329\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.14590 | 0.225282 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.8541 | 1.34330 | 0.671650 | − | 0.740869i | \(-0.265586\pi\) | ||||
0.671650 | + | 0.740869i | \(0.265586\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.76393 | −0.621259 | −0.310629 | − | 0.950531i | \(-0.600540\pi\) | ||||
−0.310629 | + | 0.950531i | \(0.600540\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.52786 | −0.107767 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.85410 | −0.200319 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.70820 | 0.258992 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.3262 | −1.06525 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.94427 | −0.618688 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.2361 | 1.04889 | 0.524447 | − | 0.851443i | \(-0.324272\pi\) | ||||
0.524447 | + | 0.851443i | \(0.324272\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.00000 | 0.548151 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.61803 | 0.519546 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.61803 | 0.313493 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.18034 | 0.0797600 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.4164 | 1.23882 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.9787 | −1.67270 | −0.836349 | − | 0.548197i | \(-0.815314\pi\) | ||||
−0.836349 | + | 0.548197i | \(0.815314\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.61803 | −0.174536 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.00000 | 0.132745 | 0.0663723 | − | 0.997795i | \(-0.478857\pi\) | ||||
0.0663723 | + | 0.997795i | \(0.478857\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.09017 | 0.270286 | 0.135143 | − | 0.990826i | \(-0.456851\pi\) | ||||
0.135143 | + | 0.990826i | \(0.456851\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.70820 | 0.375572 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.4721 | 1.07913 | 0.539563 | − | 0.841945i | \(-0.318590\pi\) | ||||
0.539563 | + | 0.841945i | \(0.318590\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000 | 0.521862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.79837 | −0.116817 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.5279 | 0.745676 | 0.372838 | − | 0.927897i | \(-0.378385\pi\) | ||||
0.372838 | + | 0.927897i | \(0.378385\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.20163 | −0.0774035 | −0.0387018 | − | 0.999251i | \(-0.512322\pi\) | ||||
−0.0387018 | + | 0.999251i | \(0.512322\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.9443 | 0.894525 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.14590 | −0.0732087 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.0689 | −0.895182 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.70820 | 0.615232 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.1803 | −1.14753 | −0.573766 | − | 0.819019i | \(-0.694518\pi\) | ||||
−0.573766 | + | 0.819019i | \(0.694518\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.9443 | −1.19102 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.23607 | 0.140028 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.0689 | −1.75089 | −0.875444 | − | 0.483319i | \(-0.839431\pi\) | ||||
−0.875444 | + | 0.483319i | \(0.839431\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −26.3607 | −1.63797 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.61803 | −0.162052 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.5279 | −1.08081 | −0.540407 | − | 0.841404i | \(-0.681730\pi\) | ||||
−0.540407 | + | 0.841404i | \(0.681730\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.32624 | −0.572906 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.05573 | −0.0646095 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.5623 | 1.61953 | 0.809766 | − | 0.586753i | \(-0.199594\pi\) | ||||
0.809766 | + | 0.586753i | \(0.199594\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.4164 | −0.936480 | −0.468240 | − | 0.883601i | \(-0.655112\pi\) | ||||
−0.468240 | + | 0.883601i | \(0.655112\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.97871 | 0.543416 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.23607 | −0.195142 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.0000 | 1.80253 | 0.901263 | − | 0.433273i | \(-0.142641\pi\) | ||||
0.901263 | + | 0.433273i | \(0.142641\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.23607 | 0.253607 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.85410 | −0.289571 | −0.144786 | − | 0.989463i | \(-0.546249\pi\) | ||||
−0.144786 | + | 0.989463i | \(0.546249\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.1803 | 1.31848 | 0.659242 | − | 0.751931i | \(-0.270877\pi\) | ||||
0.659242 | + | 0.751931i | \(0.270877\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.70820 | −0.101185 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.5836 | 0.624730 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.90983 | −0.229990 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.43769 | 0.318763 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.1803 | 0.828424 | 0.414212 | − | 0.910180i | \(-0.364057\pi\) | ||||
0.414212 | + | 0.910180i | \(0.364057\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.38197 | 0.546239 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.2361 | 0.651983 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −29.7984 | −1.72328 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.7426 | 1.25323 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.38197 | −0.251737 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.14590 | −0.122874 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.52786 | −0.543784 | −0.271892 | − | 0.962328i | \(-0.587649\pi\) | ||||
−0.271892 | + | 0.962328i | \(0.587649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.52786 | 0.314469 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.32624 | 0.358728 | 0.179364 | − | 0.983783i | \(-0.442596\pi\) | ||||
0.179364 | + | 0.983783i | \(0.442596\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.88854 | −0.219793 | −0.109897 | − | 0.993943i | \(-0.535052\pi\) | ||||
−0.109897 | + | 0.993943i | \(0.535052\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.47214 | −0.421007 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.76393 | −0.267569 | −0.133785 | − | 0.991010i | \(-0.542713\pi\) | ||||
−0.133785 | + | 0.991010i | \(0.542713\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.23607 | −0.181185 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.180340 | 0.0100656 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.0000 | −0.556415 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.09017 | −0.282352 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.23607 | 0.400155 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.8328 | 1.25881 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.2918 | −0.565688 | −0.282844 | − | 0.959166i | \(-0.591278\pi\) | ||||
−0.282844 | + | 0.959166i | \(0.591278\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −24.1803 | −1.32507 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.47214 | 0.135067 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.1459 | 0.933997 | 0.466998 | − | 0.884258i | \(-0.345335\pi\) | ||||
0.466998 | + | 0.884258i | \(0.345335\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.43769 | 0.295335 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.23607 | 0.283549 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.7082 | 0.902158 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.61803 | −0.194788 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.7639 | 1.65149 | 0.825747 | − | 0.564040i | \(-0.190754\pi\) | ||||
0.825747 | + | 0.564040i | \(0.190754\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.9443 | −0.692891 | −0.346445 | − | 0.938070i | \(-0.612611\pi\) | ||||
−0.346445 | + | 0.938070i | \(0.612611\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.6738 | 0.943356 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.4721 | −0.983173 | −0.491586 | − | 0.870829i | \(-0.663583\pi\) | ||||
−0.491586 | + | 0.870829i | \(0.663583\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.9443 | −0.687011 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.38197 | 0.337769 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.9098 | 0.786911 | 0.393455 | − | 0.919344i | \(-0.371280\pi\) | ||||
0.393455 | + | 0.919344i | \(0.371280\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.3607 | −0.597931 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.326238 | −0.0171231 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.90983 | −0.0999651 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.1803 | −0.949006 | −0.474503 | − | 0.880254i | \(-0.657372\pi\) | ||||
−0.474503 | + | 0.880254i | \(0.657372\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.70820 | 0.505389 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.6180 | −1.38194 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.2705 | 1.36024 | 0.680118 | − | 0.733103i | \(-0.261929\pi\) | ||||
0.680118 | + | 0.733103i | \(0.261929\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.618034 | −0.0319151 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.09017 | −0.262157 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 38.0689 | 1.95547 | 0.977734 | − | 0.209850i | \(-0.0672975\pi\) | ||||
0.977734 | + | 0.209850i | \(0.0672975\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.583592 | −0.0298983 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.2705 | −1.34236 | −0.671180 | − | 0.741294i | \(-0.734212\pi\) | ||||
−0.671180 | + | 0.741294i | \(0.734212\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.23607 | −0.470714 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 19.9443 | 1.01382 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.1803 | −1.07114 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.7082 | −0.590601 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.90983 | 0.146409 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.14590 | 0.258265 | 0.129133 | − | 0.991627i | \(-0.458781\pi\) | ||||
0.129133 | + | 0.991627i | \(0.458781\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.87539 | −0.244075 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.32624 | 0.415792 | 0.207896 | − | 0.978151i | \(-0.433338\pi\) | ||||
0.207896 | + | 0.978151i | \(0.433338\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.23607 | 0.410268 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.70820 | −0.283643 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −29.8885 | −1.48152 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.41641 | 0.366718 | 0.183359 | − | 0.983046i | \(-0.441303\pi\) | ||||
0.183359 | + | 0.983046i | \(0.441303\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0901699 | −0.00444776 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.7771 | 1.31761 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.7082 | −0.771085 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.47214 | 0.170031 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.90983 | 0.191008 | 0.0955038 | − | 0.995429i | \(-0.469554\pi\) | ||||
0.0955038 | + | 0.995429i | \(0.469554\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.52786 | 0.366886 | 0.183443 | − | 0.983030i | \(-0.441276\pi\) | ||||
0.183443 | + | 0.983030i | \(0.441276\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.9443 | 1.01835 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.61803 | −0.175500 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.12461 | −0.296391 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.1803 | 0.491511 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.7082 | 1.14198 | 0.570992 | − | 0.820956i | \(-0.306559\pi\) | ||||
0.570992 | + | 0.820956i | \(0.306559\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.47214 | 0.214917 | 0.107459 | − | 0.994210i | \(-0.465729\pi\) | ||||
0.107459 | + | 0.994210i | \(0.465729\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.618034 | −0.0296325 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.1803 | 0.774011 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.00000 | 0.286364 | 0.143182 | − | 0.989696i | \(-0.454267\pi\) | ||||
0.143182 | + | 0.989696i | \(0.454267\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.2705 | 1.20064 | 0.600319 | − | 0.799761i | \(-0.295040\pi\) | ||||
0.600319 | + | 0.799761i | \(0.295040\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.70820 | 0.0809766 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.0000 | 0.472984 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.0689 | −1.13588 | −0.567940 | − | 0.823070i | \(-0.692260\pi\) | ||||
−0.567940 | + | 0.823070i | \(0.692260\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | 0.565058 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.763932 | 0.0358927 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.5279 | −0.681077 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0000 | 1.02912 | 0.514558 | − | 0.857455i | \(-0.327956\pi\) | ||||
0.514558 | + | 0.857455i | \(0.327956\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.5623 | 0.586358 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.3262 | −0.900113 | −0.450056 | − | 0.893000i | \(-0.648596\pi\) | ||||
−0.450056 | + | 0.893000i | \(0.648596\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.8328 | −1.80471 | −0.902357 | − | 0.430989i | \(-0.858165\pi\) | ||||
−0.902357 | + | 0.430989i | \(0.858165\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.00000 | 0.0463739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.6738 | −1.04922 | −0.524608 | − | 0.851344i | \(-0.675788\pi\) | ||||
−0.524608 | + | 0.851344i | \(0.675788\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.05573 | 0.325803 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.12461 | 0.143975 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.6525 | 1.13352 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.76393 | 0.126818 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.4164 | −1.11795 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.673762 | 0.0307850 | 0.0153925 | − | 0.999882i | \(-0.495100\pi\) | ||||
0.0153925 | + | 0.999882i | \(0.495100\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −47.0132 | −2.14362 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.3262 | −0.469860 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.79837 | −0.399514 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.2705 | −0.963859 | −0.481929 | − | 0.876210i | \(-0.660064\pi\) | ||||
−0.481929 | + | 0.876210i | \(0.660064\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.36068 | −0.378083 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.3050 | −1.86407 | −0.932033 | − | 0.362373i | \(-0.881967\pi\) | ||||
−0.932033 | + | 0.362373i | \(0.881967\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.61803 | −0.162948 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.47214 | −0.380794 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −36.9443 | −1.65718 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.67376 | −0.0749279 | −0.0374639 | − | 0.999298i | \(-0.511928\pi\) | ||||
−0.0374639 | + | 0.999298i | \(0.511928\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.70820 | −0.120994 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.0000 | 0.891756 | 0.445878 | − | 0.895094i | \(-0.352892\pi\) | ||||
0.445878 | + | 0.895094i | \(0.352892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.09017 | 0.315508 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.97871 | 0.354347 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.70820 | −0.164363 | −0.0821816 | − | 0.996617i | \(-0.526189\pi\) | ||||
−0.0821816 | + | 0.996617i | \(0.526189\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.45085 | −0.241131 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.59675 | −0.423707 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.94427 | −0.394132 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.8885 | 1.13858 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.96556 | −0.130174 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.3262 | −1.54767 | −0.773835 | − | 0.633387i | \(-0.781664\pi\) | ||||
−0.773835 | + | 0.633387i | \(0.781664\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.1803 | −0.445155 | −0.222578 | − | 0.974915i | \(-0.571447\pi\) | ||||
−0.222578 | + | 0.974915i | \(0.571447\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.76393 | −0.0769843 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.85410 | 0.255009 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2705 | 0.490022 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.5623 | 1.06591 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.8754 | 0.817584 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.291796 | −0.0126154 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.673762 | −0.0290750 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.70820 | −0.159724 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.03444 | 0.216448 | 0.108224 | − | 0.994127i | \(-0.465484\pi\) | ||||
0.108224 | + | 0.994127i | \(0.465484\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.180340 | 0.00773913 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.7082 | −0.501524 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.1246 | 0.817709 | 0.408855 | − | 0.912600i | \(-0.365928\pi\) | ||||
0.408855 | + | 0.912600i | \(0.365928\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.61803 | −0.239772 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.76393 | 0.117747 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.30495 | 0.353162 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.70820 | −0.242300 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.1459 | 1.02309 | 0.511547 | − | 0.859255i | \(-0.329073\pi\) | ||||
0.511547 | + | 0.859255i | \(0.329073\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.7771 | 1.64010 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.23607 | 0.305507 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.3951 | 1.19671 | 0.598356 | − | 0.801230i | \(-0.295821\pi\) | ||||
0.598356 | + | 0.801230i | \(0.295821\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.79837 | −0.370150 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.2918 | −0.684191 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.3607 | 1.35663 | 0.678315 | − | 0.734771i | \(-0.262710\pi\) | ||||
0.678315 | + | 0.734771i | \(0.262710\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.1459 | −0.843080 | −0.421540 | − | 0.906810i | \(-0.638510\pi\) | ||||
−0.421540 | + | 0.906810i | \(0.638510\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.8885 | −0.538427 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.85410 | 0.244133 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.7426 | 0.530483 | 0.265242 | − | 0.964182i | \(-0.414548\pi\) | ||||
0.265242 | + | 0.964182i | \(0.414548\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.0901699 | 0.00374733 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −44.8328 | −1.85998 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.1803 | −1.24994 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.3262 | −0.550972 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.83282 | −0.364569 | −0.182285 | − | 0.983246i | \(-0.558349\pi\) | ||||
−0.182285 | + | 0.983246i | \(0.558349\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.47214 | −0.184271 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.6525 | 0.479319 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.65248 | −0.273184 | −0.136592 | − | 0.990627i | \(-0.543615\pi\) | ||||
−0.136592 | + | 0.990627i | \(0.543615\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.3262 | −0.423334 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.41641 | −0.221679 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.673762 | −0.0275292 | −0.0137646 | − | 0.999905i | \(-0.504382\pi\) | ||||
−0.0137646 | + | 0.999905i | \(0.504382\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.5410 | 0.837886 | 0.418943 | − | 0.908013i | \(-0.362401\pi\) | ||||
0.418943 | + | 0.908013i | \(0.362401\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.47214 | 0.263566 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.527864 | 0.0214607 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.47214 | −0.100341 | −0.0501705 | − | 0.998741i | \(-0.515976\pi\) | ||||
−0.0501705 | + | 0.998741i | \(0.515976\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.76393 | −0.0714781 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 40.7214 | 1.64741 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.7426 | 1.32246 | 0.661232 | − | 0.750182i | \(-0.270034\pi\) | ||||
0.661232 | + | 0.750182i | \(0.270034\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.29180 | 0.0924141 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.7984 | −1.28015 | −0.640077 | − | 0.768311i | \(-0.721098\pi\) | ||||
−0.640077 | + | 0.768311i | \(0.721098\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.7771 | 1.67916 | 0.839581 | − | 0.543234i | \(-0.182800\pi\) | ||||
0.839581 | + | 0.543234i | \(0.182800\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.3262 | −0.815664 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.87539 | 0.195328 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.52786 | −0.220762 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33.4164 | −1.33240 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.3607 | 1.52711 | 0.763557 | − | 0.645740i | \(-0.223451\pi\) | ||||
0.763557 | + | 0.645740i | \(0.223451\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.41641 | 0.374269 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.944272 | 0.0374723 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.83282 | −0.231105 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −33.8885 | −1.34061 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.7639 | −1.53108 | −0.765542 | − | 0.643386i | \(-0.777529\pi\) | ||||
−0.765542 | + | 0.643386i | \(0.777529\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.7082 | −1.01383 | −0.506916 | − | 0.861995i | \(-0.669215\pi\) | ||||
−0.506916 | + | 0.861995i | \(0.669215\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.70820 | 0.185385 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.3050 | 1.46661 | 0.733304 | − | 0.679900i | \(-0.237977\pi\) | ||||
0.733304 | + | 0.679900i | \(0.237977\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.3607 | 1.19176 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.85410 | 0.111861 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.5967 | 1.54954 | 0.774770 | − | 0.632243i | \(-0.217866\pi\) | ||||
0.774770 | + | 0.632243i | \(0.217866\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.9443 | 0.740214 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.00000 | −0.195069 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.8197 | −0.616246 | −0.308123 | − | 0.951346i | \(-0.599701\pi\) | ||||
−0.308123 | + | 0.951346i | \(0.599701\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.5967 | 1.07339 | 0.536695 | − | 0.843777i | \(-0.319673\pi\) | ||||
0.536695 | + | 0.843777i | \(0.319673\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.3820 | 0.442039 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.88854 | 0.305905 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.85410 | 0.226672 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.4377 | −0.596856 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.94427 | −0.268081 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.7639 | 0.723296 | 0.361648 | − | 0.932315i | \(-0.382214\pi\) | ||||
0.361648 | + | 0.932315i | \(0.382214\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.47214 | −0.133643 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.8885 | −0.533780 | −0.266890 | − | 0.963727i | \(-0.585996\pi\) | ||||
−0.266890 | + | 0.963727i | \(0.585996\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.1115 | −0.963689 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.23607 | 0.0473662 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.3475 | 0.587257 | 0.293628 | − | 0.955920i | \(-0.405137\pi\) | ||||
0.293628 | + | 0.955920i | \(0.405137\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.145898 | 0.00557448 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.52786 | 0.0964440 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −47.4721 | −1.80854 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.0344 | 0.495854 | 0.247927 | − | 0.968779i | \(-0.420251\pi\) | ||||
0.247927 | + | 0.968779i | \(0.420251\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −24.1803 | −0.918535 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.61803 | −0.213104 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.4164 | 0.508183 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.1803 | 0.385056 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.1246 | −0.495710 | −0.247855 | − | 0.968797i | \(-0.579726\pi\) | ||||
−0.247855 | + | 0.968797i | \(0.579726\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.5279 | 0.962802 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.94427 | 0.186212 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.2361 | 0.761056 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.2918 | −0.686963 | −0.343481 | − | 0.939159i | \(-0.611606\pi\) | ||||
−0.343481 | + | 0.939159i | \(0.611606\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.61803 | 0.285699 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.47214 | −0.354734 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.4721 | −0.616023 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.12461 | 0.266074 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.6525 | 0.770207 | 0.385104 | − | 0.922873i | \(-0.374166\pi\) | ||||
0.385104 | + | 0.922873i | \(0.374166\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.5279 | −0.950707 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.742646 | −0.0276193 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.00000 | 0.0371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.7639 | 1.66020 | 0.830101 | − | 0.557613i | \(-0.188283\pi\) | ||||
0.830101 | + | 0.557613i | \(0.188283\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.50658 | −0.315058 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.5623 | 1.01943 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.7771 | 1.32146 | 0.660728 | − | 0.750625i | \(-0.270247\pi\) | ||||
0.660728 | + | 0.750625i | \(0.270247\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.708204 | −0.0261225 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.00000 | 0.294684 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.41641 | −0.125675 | −0.0628373 | − | 0.998024i | \(-0.520015\pi\) | ||||
−0.0628373 | + | 0.998024i | \(0.520015\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.69505 | −0.319421 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.41641 | −0.272082 | −0.136041 | − | 0.990703i | \(-0.543438\pi\) | ||||
−0.136041 | + | 0.990703i | \(0.543438\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.1803 | −0.592802 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −41.1246 | −1.50467 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.832816 | −0.0304304 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.0000 | −1.45962 | −0.729810 | − | 0.683650i | \(-0.760392\pi\) | ||||
−0.729810 | + | 0.683650i | \(0.760392\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.2361 | −0.409465 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.23607 | −0.0449851 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.1803 | 0.806158 | 0.403079 | − | 0.915165i | \(-0.367940\pi\) | ||||
0.403079 | + | 0.915165i | \(0.367940\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.7082 | −0.424981 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.0344 | −0.907498 | −0.453749 | − | 0.891130i | \(-0.649914\pi\) | ||||
−0.453749 | + | 0.891130i | \(0.649914\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.4164 | −1.20976 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.47214 | −0.342466 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 47.7558 | 1.72436 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.6525 | 1.82657 | 0.913287 | − | 0.407316i | \(-0.133535\pi\) | ||||
0.913287 | + | 0.407316i | \(0.133535\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.3475 | −0.624756 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −52.8328 | −1.90026 | −0.950132 | − | 0.311848i | \(-0.899052\pi\) | ||||
−0.950132 | + | 0.311848i | \(0.899052\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.61803 | −0.0581215 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.2918 | −0.584465 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.2492 | −0.367217 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −41.8885 | −1.49889 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.47214 | −0.124084 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.05573 | −0.180447 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.6525 | −1.59169 | −0.795844 | − | 0.605501i | \(-0.792973\pi\) | ||||
−0.795844 | + | 0.605501i | \(0.792973\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.8328 | −0.385658 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.1115 | −0.892861 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.9230 | −0.387887 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.76393 | −0.204426 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.8328 | 1.09215 | 0.546077 | − | 0.837735i | \(-0.316121\pi\) | ||||
0.546077 | + | 0.837735i | \(0.316121\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.9443 | 1.02397 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.47214 | 0.158015 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.18034 | −0.218099 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.7082 | 0.588887 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.4164 | 0.577885 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.4164 | 0.401380 | 0.200690 | − | 0.979655i | \(-0.435682\pi\) | ||||
0.200690 | + | 0.979655i | \(0.435682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.673762 | −0.0236590 | −0.0118295 | − | 0.999930i | \(-0.503766\pi\) | ||||
−0.0118295 | + | 0.999930i | \(0.503766\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.52786 | −0.334157 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.5279 | 0.473860 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.0557 | −0.736647 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −38.0344 | −1.32903 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.0689 | −1.18901 | −0.594506 | − | 0.804091i | \(-0.702652\pi\) | ||||
−0.594506 | + | 0.804091i | \(0.702652\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −45.7771 | −1.59569 | −0.797844 | − | 0.602863i | \(-0.794026\pi\) | ||||
−0.797844 | + | 0.602863i | \(0.794026\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.00000 | −0.0696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.90983 | −0.0664113 | −0.0332056 | − | 0.999449i | \(-0.510572\pi\) | ||||
−0.0332056 | + | 0.999449i | \(0.510572\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.7984 | −1.59064 | −0.795322 | − | 0.606188i | \(-0.792698\pi\) | ||||
−0.795322 | + | 0.606188i | \(0.792698\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.5410 | 0.643181 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.14590 | −0.143647 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.38197 | 0.151644 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.61803 | 0.194188 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.3607 | −0.979119 | −0.489560 | − | 0.871970i | \(-0.662842\pi\) | ||||
−0.489560 | + | 0.871970i | \(0.662842\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.00000 | −0.103325 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.9098 | −0.444112 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.50658 | 0.0517666 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.7082 | 0.470464 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 54.0689 | 1.85346 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.81966 | 0.0623040 | 0.0311520 | − | 0.999515i | \(-0.490082\pi\) | ||||
0.0311520 | + | 0.999515i | \(0.490082\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.23607 | 0.247468 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.7082 | 1.15145 | 0.575725 | − | 0.817643i | \(-0.304720\pi\) | ||||
0.575725 | + | 0.817643i | \(0.304720\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.6525 | −0.568175 | −0.284088 | − | 0.958798i | \(-0.591691\pi\) | ||||
−0.284088 | + | 0.958798i | \(0.591691\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.54102 | 0.222917 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.03444 | 0.137334 | 0.0686670 | − | 0.997640i | \(-0.478125\pi\) | ||||
0.0686670 | + | 0.997640i | \(0.478125\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.79837 | 0.163150 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.41641 | −0.0820655 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.41641 | 0.319430 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.5836 | 0.426379 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −23.0344 | −0.779598 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.85410 | 0.0964863 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.6180 | 1.70925 | 0.854625 | − | 0.519246i | \(-0.173787\pi\) | ||||
0.854625 | + | 0.519246i | \(0.173787\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.76393 | 0.295600 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.1803 | 0.342984 | 0.171492 | − | 0.985185i | \(-0.445141\pi\) | ||||
0.171492 | + | 0.985185i | \(0.445141\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.5967 | 0.726788 | 0.363394 | − | 0.931635i | \(-0.381618\pi\) | ||||
0.363394 | + | 0.931635i | \(0.381618\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.79837 | 0.194910 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.4164 | 1.05486 | 0.527430 | − | 0.849599i | \(-0.323156\pi\) | ||||
0.527430 | + | 0.849599i | \(0.323156\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.69505 | 0.0903890 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.4721 | −0.618840 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.1115 | −0.739932 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.09017 | 0.0364404 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.4164 | −0.614906 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.61803 | −0.0539645 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.7426 | −1.12413 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13.4377 | 0.447178 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.291796 | −0.00969963 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.9098 | −0.860322 | −0.430161 | − | 0.902752i | \(-0.641543\pi\) | ||||
−0.430161 | + | 0.902752i | \(0.641543\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.5623 | 0.615673 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.2705 | 1.30109 | 0.650545 | − | 0.759468i | \(-0.274541\pi\) | ||||
0.650545 | + | 0.759468i | \(0.274541\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −50.8328 | −1.68232 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.32624 | −0.0438441 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 54.0689 | 1.78551 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.4721 | 0.873235 | 0.436618 | − | 0.899647i | \(-0.356176\pi\) | ||||
0.436618 | + | 0.899647i | \(0.356176\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.88854 | −0.194034 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −65.8885 | −2.16875 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.23607 | 0.303680 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23.4164 | −0.769096 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −44.4508 | −1.45839 | −0.729193 | − | 0.684309i | \(-0.760104\pi\) | ||||
−0.729193 | + | 0.684309i | \(0.760104\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.16718 | 0.103800 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.90983 | 0.128002 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.7082 | −0.382899 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.1246 | 1.40882 | 0.704410 | − | 0.709793i | \(-0.251212\pi\) | ||||
0.704410 | + | 0.709793i | \(0.251212\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.40325 | −0.0784272 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.3607 | 1.05493 | 0.527464 | − | 0.849577i | \(-0.323143\pi\) | ||||
0.527464 | + | 0.849577i | \(0.323143\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.7082 | −0.706916 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.90983 | −0.322367 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 55.0902 | 1.79019 | 0.895095 | − | 0.445875i | \(-0.147108\pi\) | ||||
0.895095 | + | 0.445875i | \(0.147108\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.72136 | −0.315569 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.94427 | −0.0954746 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.8328 | 0.415696 | 0.207848 | − | 0.978161i | \(-0.433354\pi\) | ||||
0.207848 | + | 0.978161i | \(0.433354\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.8541 | 0.674823 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.00000 | −0.0646508 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.416408 | 0.0134465 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.3820 | −0.915547 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.763932 | −0.0246174 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.145898 | −0.00469662 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.5967 | −0.758820 | −0.379410 | − | 0.925229i | \(-0.623873\pi\) | ||||
−0.379410 | + | 0.925229i | \(0.623873\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.18034 | −0.198541 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.0689 | 1.67097 | 0.835485 | − | 0.549513i | \(-0.185187\pi\) | ||||
0.835485 | + | 0.549513i | \(0.185187\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.0344 | −0.514041 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.14590 | −0.100749 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.6525 | 0.340803 | 0.170401 | − | 0.985375i | \(-0.445494\pi\) | ||||
0.170401 | + | 0.985375i | \(0.445494\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.52786 | 0.176671 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.6525 | −0.978658 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.0557 | −0.416413 | −0.208207 | − | 0.978085i | \(-0.566763\pi\) | ||||
−0.208207 | + | 0.978085i | \(0.566763\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.8541 | −0.600742 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.1115 | 0.449173 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.5967 | −1.41809 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.0689 | −0.319849 | −0.159924 | − | 0.987129i | \(-0.551125\pi\) | ||||
−0.159924 | + | 0.987129i | \(0.551125\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.36068 | −0.201850 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.76393 | 0.277835 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.1803 | 1.39921 | 0.699603 | − | 0.714532i | \(-0.253360\pi\) | ||||
0.699603 | + | 0.714532i | \(0.253360\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −32.0689 | −1.01461 |
(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 | 4640.2.a.g.1.2 | ✓ | 2 | |
4.3 | odd | 2 | 4640.2.a.i.1.1 | yes | 2 | ||
8.3 | odd | 2 | 9280.2.a.y.1.2 | 2 | |||
8.5 | even | 2 | 9280.2.a.bd.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4640.2.a.g.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
4640.2.a.i.1.1 | yes | 2 | 4.3 | odd | 2 | ||
9280.2.a.y.1.2 | 2 | 8.3 | odd | 2 | |||
9280.2.a.bd.1.1 | 2 | 8.5 | even | 2 |