Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1352,2,Mod(1,1352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1352.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1352 = 2^{3} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1352.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: | \(10.7957743533\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
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 | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1352.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.44504 | −0.834295 | −0.417148 | − | 0.908839i | \(-0.636970\pi\) | ||||
−0.417148 | + | 0.908839i | \(0.636970\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.44504 | −0.646242 | −0.323121 | − | 0.946358i | \(-0.604732\pi\) | ||||
−0.323121 | + | 0.946358i | \(0.604732\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.445042 | −0.168210 | −0.0841050 | − | 0.996457i | \(-0.526803\pi\) | ||||
−0.0841050 | + | 0.996457i | \(0.526803\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.911854 | −0.303951 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.33513 | 0.704067 | 0.352033 | − | 0.935987i | \(-0.385490\pi\) | ||||
0.352033 | + | 0.935987i | \(0.385490\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.08815 | 0.539157 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.89977 | 1.67344 | 0.836720 | − | 0.547630i | \(-0.184470\pi\) | ||||
0.836720 | + | 0.547630i | \(0.184470\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.74094 | 1.54648 | 0.773239 | − | 0.634115i | \(-0.218635\pi\) | ||||
0.773239 | + | 0.634115i | \(0.218635\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.643104 | 0.140337 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.71379 | −1.19141 | −0.595704 | − | 0.803204i | \(-0.703127\pi\) | ||||
−0.595704 | + | 0.803204i | \(0.703127\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.91185 | −0.582371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65279 | 1.08788 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.14675 | −1.51281 | −0.756407 | − | 0.654101i | \(-0.773047\pi\) | ||||
−0.756407 | + | 0.654101i | \(0.773047\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.54288 | −0.815925 | −0.407962 | − | 0.912999i | \(-0.633761\pi\) | ||||
−0.407962 | + | 0.912999i | \(0.633761\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.37435 | −0.587400 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.643104 | 0.108704 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.07069 | −1.32681 | −0.663406 | − | 0.748259i | \(-0.730890\pi\) | ||||
−0.663406 | + | 0.748259i | \(0.730890\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.71379 | 0.267649 | 0.133825 | − | 0.991005i | \(-0.457274\pi\) | ||||
0.133825 | + | 0.991005i | \(0.457274\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.86294 | −0.589092 | −0.294546 | − | 0.955637i | \(-0.595168\pi\) | ||||
−0.294546 | + | 0.955637i | \(0.595168\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.31767 | 0.196426 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.829085 | −0.120934 | −0.0604672 | − | 0.998170i | \(-0.519259\pi\) | ||||
−0.0604672 | + | 0.998170i | \(0.519259\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.80194 | −0.971705 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.97046 | −1.39614 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.02715 | −0.965253 | −0.482626 | − | 0.875826i | \(-0.660317\pi\) | ||||
−0.482626 | + | 0.875826i | \(0.660317\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.37435 | −0.454998 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.74094 | −1.29022 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.59179 | −0.467612 | −0.233806 | − | 0.972283i | \(-0.575118\pi\) | ||||
−0.233806 | + | 0.972283i | \(0.575118\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.65519 | −0.211925 | −0.105962 | − | 0.994370i | \(-0.533792\pi\) | ||||
−0.105962 | + | 0.994370i | \(0.533792\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.405813 | 0.0511277 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.3448 | 1.63033 | 0.815164 | − | 0.579230i | \(-0.196647\pi\) | ||||
0.815164 | + | 0.579230i | \(0.196647\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.25667 | 0.993986 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.4916 | 1.71983 | 0.859916 | − | 0.510435i | \(-0.170516\pi\) | ||||
0.859916 | + | 0.510435i | \(0.170516\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.35690 | −0.744018 | −0.372009 | − | 0.928229i | \(-0.621331\pi\) | ||||
−0.372009 | + | 0.928229i | \(0.621331\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.20775 | 0.485869 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.03923 | −0.118431 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.47219 | −0.728178 | −0.364089 | − | 0.931364i | \(-0.618620\pi\) | ||||
−0.364089 | + | 0.931364i | \(0.618620\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.43296 | −0.603662 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.41789 | 0.265398 | 0.132699 | − | 0.991156i | \(-0.457636\pi\) | ||||
0.132699 | + | 0.991156i | \(0.457636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.97046 | −1.08145 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.7724 | 1.26213 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.2295 | −1.40233 | −0.701163 | − | 0.713001i | \(-0.747336\pi\) | ||||
−0.701163 | + | 0.713001i | \(0.747336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.56465 | 0.680722 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.74094 | −0.999399 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.0368 | −1.12062 | −0.560310 | − | 0.828283i | \(-0.689318\pi\) | ||||
−0.560310 | + | 0.828283i | \(0.689318\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.12929 | −0.214002 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.89977 | −0.587049 | −0.293525 | − | 0.955952i | \(-0.594828\pi\) | ||||
−0.293525 | + | 0.955952i | \(0.594828\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.4426 | −1.91574 | −0.957871 | − | 0.287200i | \(-0.907275\pi\) | ||||
−0.957871 | + | 0.287200i | \(0.907275\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.929312 | −0.0906916 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.18598 | −0.791369 | −0.395684 | − | 0.918387i | \(-0.629493\pi\) | ||||
−0.395684 | + | 0.918387i | \(0.629493\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.0858 | 1.44495 | 0.722477 | − | 0.691395i | \(-0.243004\pi\) | ||||
0.722477 | + | 0.691395i | \(0.243004\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.6625 | 1.10695 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.9119 | −1.02650 | −0.513250 | − | 0.858239i | \(-0.671559\pi\) | ||||
−0.513250 | + | 0.858239i | \(0.671559\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.25667 | 0.769938 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.07069 | −0.281489 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.54719 | −0.504290 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.47650 | −0.223299 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.4330 | 1.02260 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.53079 | 0.402043 | 0.201022 | − | 0.979587i | \(-0.435574\pi\) | ||||
0.201022 | + | 0.979587i | \(0.435574\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.58211 | 0.491477 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.1032 | 0.882722 | 0.441361 | − | 0.897330i | \(-0.354496\pi\) | ||||
0.441361 | + | 0.897330i | \(0.354496\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | −0.260133 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.16852 | −0.703034 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.21983 | −0.531396 | −0.265698 | − | 0.964056i | \(-0.585602\pi\) | ||||
−0.265698 | + | 0.964056i | \(0.585602\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.9541 | −0.929112 | −0.464556 | − | 0.885544i | \(-0.653786\pi\) | ||||
−0.464556 | + | 0.885544i | \(0.653786\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.19806 | 0.100895 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.7724 | 0.977644 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.82908 | 0.810689 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.40581 | 0.360938 | 0.180469 | − | 0.983581i | \(-0.442238\pi\) | ||||
0.180469 | + | 0.983581i | \(0.442238\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.3056 | −1.32693 | −0.663465 | − | 0.748207i | \(-0.730915\pi\) | ||||
−0.663465 | + | 0.748207i | \(0.730915\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.29159 | −0.508645 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.56465 | 0.527285 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.2131 | −0.894905 | −0.447453 | − | 0.894308i | \(-0.647669\pi\) | ||||
−0.447453 | + | 0.894308i | \(0.647669\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.1545 | 0.805306 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.54288 | 0.200407 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.41789 | 0.267710 | 0.133855 | − | 0.991001i | \(-0.457264\pi\) | ||||
0.133855 | + | 0.991001i | \(0.457264\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.87608 | 0.379603 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.32975 | 0.412428 | 0.206214 | − | 0.978507i | \(-0.433886\pi\) | ||||
0.206214 | + | 0.978507i | \(0.433886\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.14675 | −0.470054 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.63533 | 0.656532 | 0.328266 | − | 0.944585i | \(-0.393536\pi\) | ||||
0.328266 | + | 0.944585i | \(0.393536\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.29590 | 0.0979606 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.19029 | 0.390126 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.6920 | 1.39711 | 0.698554 | − | 0.715558i | \(-0.253827\pi\) | ||||
0.698554 | + | 0.715558i | \(0.253827\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.8092 | 1.47241 | 0.736204 | − | 0.676759i | \(-0.236616\pi\) | ||||
0.736204 | + | 0.676759i | \(0.236616\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.39181 | 0.176808 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.6625 | 0.857443 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.1118 | 1.17821 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.51573 | −0.182992 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.4547 | 0.756478 | 0.378239 | − | 0.925708i | \(-0.376530\pi\) | ||||
0.378239 | + | 0.925708i | \(0.376530\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.72587 | 0.268194 | 0.134097 | − | 0.990968i | \(-0.457187\pi\) | ||||
0.134097 | + | 0.990968i | \(0.457187\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.8310 | −1.55539 | −0.777697 | − | 0.628639i | \(-0.783612\pi\) | ||||
−0.777697 | + | 0.628639i | \(0.783612\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.3013 | −1.01379 | −0.506895 | − | 0.862008i | \(-0.669207\pi\) | ||||
−0.506895 | + | 0.862008i | \(0.669207\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.2838 | −1.36018 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.62565 | 0.254470 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.47650 | −0.172966 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.21014 | 0.362130 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.7409 | 1.08882 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.18300 | −0.150284 | −0.0751418 | − | 0.997173i | \(-0.523941\pi\) | ||||
−0.0751418 | + | 0.997173i | \(0.523941\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −20.9409 | −1.43485 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.58211 | 0.380696 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.02177 | 0.137247 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.18598 | 0.620731 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.0489 | −1.87829 | −0.939147 | − | 0.343515i | \(-0.888382\pi\) | ||||
−0.939147 | + | 0.343515i | \(0.888382\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.65519 | 0.177012 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.76510 | 0.382643 | 0.191322 | − | 0.981527i | \(-0.438723\pi\) | ||||
0.191322 | + | 0.981527i | \(0.438723\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.1323 | 1.06605 | 0.533025 | − | 0.846099i | \(-0.321055\pi\) | ||||
0.533025 | + | 0.846099i | \(0.321055\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.50173 | 0.0988065 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.13169 | 0.598237 | 0.299118 | − | 0.954216i | \(-0.403307\pi\) | ||||
0.299118 | + | 0.954216i | \(0.403307\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.19806 | 0.0781530 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.35258 | 0.607516 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.4179 | −0.738562 | −0.369281 | − | 0.929318i | \(-0.620396\pi\) | ||||
−0.369281 | + | 0.929318i | \(0.620396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3666 | 0.732186 | 0.366093 | − | 0.930578i | \(-0.380695\pi\) | ||||
0.366093 | + | 0.930578i | \(0.380695\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.10752 | −0.584248 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.82908 | 0.627957 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.49396 | −0.221421 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.61596 | 0.291357 | 0.145678 | − | 0.989332i | \(-0.453464\pi\) | ||||
0.145678 | + | 0.989332i | \(0.453464\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.3424 | −0.838831 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.4077 | 0.902247 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.24459 | −0.264770 | −0.132385 | − | 0.991198i | \(-0.542264\pi\) | ||||
−0.132385 | + | 0.991198i | \(0.542264\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.59179 | 0.223183 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.42865 | 0.459822 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 31.0780 | 1.91635 | 0.958175 | − | 0.286182i | \(-0.0923862\pi\) | ||||
0.958175 | + | 0.286182i | \(0.0923862\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.1545 | 0.623787 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.1172 | 1.16995 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.88471 | 0.358797 | 0.179398 | − | 0.983776i | \(-0.442585\pi\) | ||||
0.179398 | + | 0.983776i | \(0.442585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −32.5827 | −1.97926 | −0.989629 | − | 0.143647i | \(-0.954117\pi\) | ||||
−0.989629 | + | 0.143647i | \(0.954117\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.79954 | −0.410028 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.0465 | −1.02423 | −0.512113 | − | 0.858918i | \(-0.671137\pi\) | ||||
−0.512113 | + | 0.858918i | \(0.671137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.14244 | 0.248001 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.6920 | −0.757143 | −0.378571 | − | 0.925572i | \(-0.623585\pi\) | ||||
−0.378571 | + | 0.925572i | \(0.623585\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.15346 | 0.306341 | 0.153171 | − | 0.988200i | \(-0.451052\pi\) | ||||
0.153171 | + | 0.988200i | \(0.451052\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.0761 | 0.833794 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.762709 | −0.0450213 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.6069 | 1.80040 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.9487 | 0.934929 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.3696 | 0.897900 | 0.448950 | − | 0.893557i | \(-0.351798\pi\) | ||||
0.448950 | + | 0.893557i | \(0.351798\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.19029 | 0.302191 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.2000 | 0.765941 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.71917 | 0.0990912 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.52542 | 0.489772 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.39181 | 0.136955 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.9651 | −1.02532 | −0.512661 | − | 0.858591i | \(-0.671340\pi\) | ||||
−0.512661 | + | 0.858591i | \(0.671340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.0954 | 1.59829 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.3230 | 1.37923 | 0.689617 | − | 0.724175i | \(-0.257779\pi\) | ||||
0.689617 | + | 0.724175i | \(0.257779\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.6625 | −1.39401 | −0.697003 | − | 0.717068i | \(-0.745484\pi\) | ||||
−0.697003 | + | 0.717068i | \(0.745484\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.586417 | −0.0330409 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.6896 | 0.712721 | 0.356360 | − | 0.934349i | \(-0.384018\pi\) | ||||
0.356360 | + | 0.934349i | \(0.384018\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.0237 | −1.06512 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.8291 | 0.660235 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 46.5109 | 2.58794 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.7995 | −1.20552 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.368977 | 0.0203424 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.8374 | −1.58505 | −0.792525 | − | 0.609840i | \(-0.791234\pi\) | ||||
−0.792525 | + | 0.609840i | \(0.791234\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.35929 | 0.403287 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.2838 | −1.05359 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.80194 | −0.533946 | −0.266973 | − | 0.963704i | \(-0.586023\pi\) | ||||
−0.266973 | + | 0.963704i | \(0.586023\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.7681 | 0.856405 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.6082 | −0.574466 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.14244 | 0.331661 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.9312 | −0.642356 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.1879 | −0.922695 | −0.461347 | − | 0.887220i | \(-0.652634\pi\) | ||||
−0.461347 | + | 0.887220i | \(0.652634\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.3556 | −0.661378 | −0.330689 | − | 0.943740i | \(-0.607281\pi\) | ||||
−0.330689 | + | 0.943740i | \(0.607281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.4209 | −1.29979 | −0.649896 | − | 0.760023i | \(-0.725188\pi\) | ||||
−0.649896 | + | 0.760023i | \(0.725188\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.9409 | −1.11143 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.43727 | 0.234845 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.1293 | 0.640160 | 0.320080 | − | 0.947391i | \(-0.396290\pi\) | ||||
0.320080 | + | 0.947391i | \(0.396290\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.4403 | 1.39159 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.01592 | 0.420727 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.18598 | 0.480816 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.96615 | 0.311430 | 0.155715 | − | 0.987802i | \(-0.450232\pi\) | ||||
0.155715 | + | 0.987802i | \(0.450232\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.56273 | −0.0813524 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.12737 | 0.162365 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.09352 | −0.315511 | −0.157755 | − | 0.987478i | \(-0.550426\pi\) | ||||
−0.157755 | + | 0.987478i | \(0.550426\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −16.5211 | −0.853146 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.9627 | 1.69318 | 0.846590 | − | 0.532246i | \(-0.178652\pi\) | ||||
0.846590 | + | 0.532246i | \(0.178652\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.54719 | −0.335423 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.4155 | −1.24757 | −0.623787 | − | 0.781594i | \(-0.714407\pi\) | ||||
−0.623787 | + | 0.781594i | \(0.714407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.50173 | 0.0765352 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.52243 | 0.179055 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.78746 | −0.445542 | −0.222771 | − | 0.974871i | \(-0.571510\pi\) | ||||
−0.222771 | + | 0.974871i | \(0.571510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −39.4239 | −1.99375 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.5996 | −0.736451 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.35258 | 0.470580 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.4964 | 0.727551 | 0.363776 | − | 0.931487i | \(-0.381488\pi\) | ||||
0.363776 | + | 0.931487i | \(0.381488\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.33513 | 0.217028 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.08038 | −0.103889 | −0.0519445 | − | 0.998650i | \(-0.516542\pi\) | ||||
−0.0519445 | + | 0.998650i | \(0.516542\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.85086 | 0.390112 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.8461 | −0.934165 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.951083 | 0.0470280 | 0.0235140 | − | 0.999724i | \(-0.492515\pi\) | ||||
0.0235140 | + | 0.999724i | \(0.492515\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.98792 | 0.443341 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.59850 | 0.0786570 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.49396 | −0.171512 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.8291 | 0.775154 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.30665 | −0.405806 | −0.202903 | − | 0.979199i | \(-0.565038\pi\) | ||||
−0.202903 | + | 0.979199i | \(0.565038\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.4077 | 1.33577 | 0.667886 | − | 0.744264i | \(-0.267200\pi\) | ||||
0.667886 | + | 0.744264i | \(0.267200\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.756004 | 0.0367582 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.0911 | −0.974563 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.736627 | 0.0356479 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.0930 | 1.01602 | 0.508008 | − | 0.861352i | \(-0.330382\pi\) | ||||
0.508008 | + | 0.861352i | \(0.330382\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.0175 | −0.673636 | −0.336818 | − | 0.941570i | \(-0.609351\pi\) | ||||
−0.336818 | + | 0.941570i | \(0.609351\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.0116 | −0.815644 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −38.5163 | −1.84249 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.1377 | 1.24748 | 0.623741 | − | 0.781631i | \(-0.285612\pi\) | ||||
0.623741 | + | 0.781631i | \(0.285612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.20237 | 0.295351 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.1884 | −0.531576 | −0.265788 | − | 0.964032i | \(-0.585632\pi\) | ||||
−0.265788 | + | 0.964032i | \(0.585632\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.1172 | 0.906243 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.36658 | −0.301129 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.7060 | 1.02437 | 0.512185 | − | 0.858875i | \(-0.328836\pi\) | ||||
0.512185 | + | 0.858875i | \(0.328836\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00192 | 0.188443 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.5623 | 1.10705 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.7657 | 0.597154 | 0.298577 | − | 0.954386i | \(-0.403488\pi\) | ||||
0.298577 | + | 0.954386i | \(0.403488\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 39.0030 | 1.82050 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.80864 | −0.0842369 | −0.0421184 | − | 0.999113i | \(-0.513411\pi\) | ||||
−0.0421184 | + | 0.999113i | \(0.513411\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.39911 | 0.297392 | 0.148696 | − | 0.988883i | \(-0.452492\pi\) | ||||
0.148696 | + | 0.988883i | \(0.452492\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.48619 | −0.439912 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.3817 | 0.943150 | 0.471575 | − | 0.881826i | \(-0.343686\pi\) | ||||
0.471575 | + | 0.881826i | \(0.343686\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.93900 | −0.274238 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.2034 | 0.746615 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.02044 | −0.414760 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.6286 | −0.900623 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.40773 | 0.293390 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.8092 | −1.54478 | −0.772392 | − | 0.635147i | \(-0.780940\pi\) | ||||
−0.772392 | + | 0.635147i | \(0.780940\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.67456 | −0.167198 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.9487 | 0.724193 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.47650 | 0.338793 | 0.169396 | − | 0.985548i | \(-0.445818\pi\) | ||||
0.169396 | + | 0.985548i | \(0.445818\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.93900 | −0.223349 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.7885 | −1.52485 | −0.762427 | − | 0.647074i | \(-0.775993\pi\) | ||||
−0.762427 | + | 0.647074i | \(0.775993\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −56.2107 | −2.53160 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.07692 | 0.138297 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.44935 | −0.289293 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.9855 | 1.02897 | 0.514487 | − | 0.857498i | \(-0.327982\pi\) | ||||
0.514487 | + | 0.857498i | \(0.327982\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.70171 | −0.344087 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.1726 | 0.988626 | 0.494313 | − | 0.869284i | \(-0.335420\pi\) | ||||
0.494313 | + | 0.869284i | \(0.335420\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.52542 | 0.379376 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.0258 | −0.444387 | −0.222193 | − | 0.975003i | \(-0.571322\pi\) | ||||
−0.222193 | + | 0.975003i | \(0.571322\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.82908 | 0.125151 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 38.1051 | 1.68238 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.0954 | 1.23803 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.93602 | −0.0851459 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.4784 | −0.547742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.02284 | 0.263865 | 0.131933 | − | 0.991259i | \(-0.457882\pi\) | ||||
0.131933 | + | 0.991259i | \(0.457882\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −45.5056 | −1.98982 | −0.994910 | − | 0.100770i | \(-0.967869\pi\) | ||||
−0.994910 | + | 0.100770i | \(0.967869\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.87263 | −0.0817281 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −31.3448 | −1.36540 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.64742 | 0.419453 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.27519 | 0.142131 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.8291 | 0.511416 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −27.0108 | −1.16560 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.8834 | −0.684146 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.1051 | −0.950374 | −0.475187 | − | 0.879885i | \(-0.657620\pi\) | ||||
−0.475187 | + | 0.879885i | \(0.657620\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −28.6252 | −1.22842 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21.7995 | −0.933790 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.77240 | −0.332324 | −0.166162 | − | 0.986098i | \(-0.553137\pi\) | ||||
−0.166162 | + | 0.986098i | \(0.553137\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.50929 | 0.0644148 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −54.9168 | −2.33953 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.88040 | 0.122487 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.8528 | −0.715360 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.2959 | −0.902336 | −0.451168 | − | 0.892439i | \(-0.648992\pi\) | ||||
−0.451168 | + | 0.892439i | \(0.648992\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23.2823 | −0.982978 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.7144 | 0.493702 | 0.246851 | − | 0.969053i | \(-0.420604\pi\) | ||||
0.246851 | + | 0.969053i | \(0.420604\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.7681 | 0.663368 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.41789 | 0.101542 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.9474 | 1.25546 | 0.627729 | − | 0.778432i | \(-0.283984\pi\) | ||||
0.627729 | + | 0.778432i | \(0.283984\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.1967 | 0.468569 | 0.234284 | − | 0.972168i | \(-0.424725\pi\) | ||||
0.234284 | + | 0.972168i | \(0.424725\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.1075 | −0.631126 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.6377 | 0.693841 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.89785 | 0.287161 | 0.143581 | − | 0.989639i | \(-0.454138\pi\) | ||||
0.143581 | + | 0.989639i | \(0.454138\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.38404 | −0.223753 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.07606 | −0.0446427 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.4093 | −0.679603 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.4765 | 1.01025 | 0.505127 | − | 0.863045i | \(-0.331446\pi\) | ||||
0.505127 | + | 0.863045i | \(0.331446\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.6233 | −1.26181 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 31.5467 | 1.29766 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.5496 | 0.638545 | 0.319272 | − | 0.947663i | \(-0.396562\pi\) | ||||
0.319272 | + | 0.947663i | \(0.396562\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.43727 | 0.181910 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.6659 | 0.845801 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.2978 | 1.68738 | 0.843692 | − | 0.536828i | \(-0.180378\pi\) | ||||
0.843692 | + | 0.536828i | \(0.180378\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −47.1909 | −1.92496 | −0.962478 | − | 0.271359i | \(-0.912527\pi\) | ||||
−0.962478 | + | 0.271359i | \(0.912527\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.1685 | −0.495541 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.01592 | 0.325893 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.51706 | −0.142753 | −0.0713765 | − | 0.997449i | \(-0.522739\pi\) | ||||
−0.0713765 | + | 0.997449i | \(0.522739\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.23921 | −0.212303 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.6926 | 0.795377 | 0.397689 | − | 0.917520i | \(-0.369812\pi\) | ||||
0.397689 | + | 0.917520i | \(0.369812\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.57865 | 0.144305 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.7827 | 1.52107 | 0.760537 | − | 0.649295i | \(-0.224936\pi\) | ||||
0.760537 | + | 0.649295i | \(0.224936\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.4440 | −0.500166 | −0.250083 | − | 0.968224i | \(-0.580458\pi\) | ||||
−0.250083 | + | 0.968224i | \(0.580458\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −32.2989 | −1.29611 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.88769 | 0.235885 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.96184 | −0.0784735 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −22.7463 | −0.908400 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −55.6859 | −2.22034 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.3696 | 0.890518 | 0.445259 | − | 0.895402i | \(-0.353112\pi\) | ||||
0.445259 | + | 0.895402i | \(0.353112\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.15452 | 0.125381 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.54719 | −0.259817 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.2142 | −0.522745 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 47.6564 | 1.88231 | 0.941157 | − | 0.337971i | \(-0.109740\pi\) | ||||
0.941157 | + | 0.337971i | \(0.109740\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.7071 | −0.934916 | −0.467458 | − | 0.884015i | \(-0.654830\pi\) | ||||
−0.467458 | + | 0.884015i | \(0.654830\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.06638 | −0.317613 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.4155 | −1.19576 | −0.597878 | − | 0.801587i | \(-0.703989\pi\) | ||||
−0.597878 | + | 0.801587i | \(0.703989\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.38729 | −0.329230 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.92154 | −0.114504 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.87561 | 0.269063 | 0.134532 | − | 0.990909i | \(-0.457047\pi\) | ||||
0.134532 | + | 0.990909i | \(0.457047\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.5996 | −0.570452 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.79656 | 0.226145 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.2218 | −0.670864 | −0.335432 | − | 0.942064i | \(-0.608882\pi\) | ||||
−0.335432 | + | 0.942064i | \(0.608882\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.3967 | 1.14340 | 0.571700 | − | 0.820463i | \(-0.306284\pi\) | ||||
0.571700 | + | 0.820463i | \(0.306284\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.33513 | 0.168109 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 46.5488 | 1.80238 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 40.5319 | 1.56705 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.86507 | −0.149209 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.8823 | −1.03624 | −0.518119 | − | 0.855309i | \(-0.673367\pi\) | ||||
−0.518119 | + | 0.855309i | \(0.673367\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.4601 | −0.633550 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.4215 | 1.63039 | 0.815195 | − | 0.579187i | \(-0.196630\pi\) | ||||
0.815195 | + | 0.579187i | \(0.196630\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.91185 | 0.188500 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.33081 | −0.319237 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −35.6176 | −1.36287 | −0.681435 | − | 0.731879i | \(-0.738644\pi\) | ||||
−0.681435 | + | 0.731879i | \(0.738644\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.98792 | 0.343411 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.3118 | −0.889401 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.21552 | 0.350575 | 0.175287 | − | 0.984517i | \(-0.443915\pi\) | ||||
0.175287 | + | 0.984517i | \(0.443915\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.947625 | 0.0359973 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.8291 | 0.600431 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.8248 | 0.447895 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.1957 | −0.499106 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.1473 | −1.47857 | −0.739287 | − | 0.673390i | \(-0.764837\pi\) | ||||
−0.739287 | + | 0.673390i | \(0.764837\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −54.4040 | −2.05189 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.73125 | −0.0652027 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.62565 | 0.0987476 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −48.4389 | −1.81916 | −0.909581 | − | 0.415527i | \(-0.863597\pi\) | ||||
−0.909581 | + | 0.415527i | \(0.863597\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.90169 | 0.221331 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.9571 | 0.972099 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.4993 | 0.616179 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.8968 | 0.704731 | 0.352366 | − | 0.935862i | \(-0.385377\pi\) | ||||
0.352366 | + | 0.935862i | \(0.385377\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.65279 | 0.322247 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.4252 | −0.610859 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23.7222 | 0.881019 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.7976 | −0.771341 | −0.385671 | − | 0.922637i | \(-0.626030\pi\) | ||||
−0.385671 | + | 0.922637i | \(0.626030\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.4596 | 1.09110 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.6534 | −0.985811 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.44994 | −0.238234 | −0.119117 | − | 0.992880i | \(-0.538006\pi\) | ||||
−0.119117 | + | 0.992880i | \(0.538006\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.2034 | −0.523902 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.1618 | 1.14786 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.9772 | −0.698086 | −0.349043 | − | 0.937107i | \(-0.613493\pi\) | ||||
−0.349043 | + | 0.937107i | \(0.613493\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.8933 | −0.473010 | −0.236505 | − | 0.971630i | \(-0.576002\pi\) | ||||
−0.236505 | + | 0.971630i | \(0.576002\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.36658 | −0.233254 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.20477 | −0.0806682 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.64310 | 0.133116 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.48321 | −0.236576 | −0.118288 | − | 0.992979i | \(-0.537741\pi\) | ||||
−0.118288 | + | 0.992979i | \(0.537741\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.67025 | −0.243077 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23.5623 | 0.857518 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.0543 | −0.765231 | −0.382616 | − | 0.923908i | \(-0.624977\pi\) | ||||
−0.382616 | + | 0.923908i | \(0.624977\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 19.2804 | 0.699833 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.37973 | 0.158765 | 0.0793826 | − | 0.996844i | \(-0.474705\pi\) | ||||
0.0793826 | + | 0.996844i | \(0.474705\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.71379 | −0.243056 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.09160 | 0.328708 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.1075 | 1.84298 | 0.921492 | − | 0.388397i | \(-0.126971\pi\) | ||||
0.921492 | + | 0.388397i | \(0.126971\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.13361 | 0.220896 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.9487 | −0.681537 | −0.340768 | − | 0.940147i | \(-0.610687\pi\) | ||||
−0.340768 | + | 0.940147i | \(0.610687\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.2282 | 0.475171 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.19029 | −0.186201 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.5526 | 0.413914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.8396 | 1.21088 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −46.0519 | −1.64576 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.2034 | 0.578326 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.8877 | 0.851504 | 0.425752 | − | 0.904840i | \(-0.360010\pi\) | ||||
0.425752 | + | 0.904840i | \(0.360010\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −44.9090 | −1.59880 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.85623 | 0.172668 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.6737 | −0.520423 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.3338 | 0.578573 | 0.289286 | − | 0.957243i | \(-0.406582\pi\) | ||||
0.289286 | + | 0.957243i | \(0.406582\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.72050 | −0.202377 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.0634 | 0.426239 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.8442 | −0.523839 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.67456 | −0.129511 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.50365 | −0.299343 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.66296 | 0.0584664 | 0.0292332 | − | 0.999573i | \(-0.490693\pi\) | ||||
0.0292332 | + | 0.999573i | \(0.490693\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.99462 | 0.210500 | 0.105250 | − | 0.994446i | \(-0.466436\pi\) | ||||
0.105250 | + | 0.994446i | \(0.466436\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 47.0834 | 1.65129 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.93900 | −0.173006 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.0398 | −0.911018 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.19136 | 0.250980 | 0.125490 | − | 0.992095i | \(-0.459950\pi\) | ||||
0.125490 | + | 0.992095i | \(0.459950\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.54229 | −0.0537607 | −0.0268803 | − | 0.999639i | \(-0.508557\pi\) | ||||
−0.0268803 | + | 0.999639i | \(0.508557\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.82563 | 0.342084 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.3308 | 0.706972 | 0.353486 | − | 0.935440i | \(-0.384996\pi\) | ||||
0.353486 | + | 0.935440i | \(0.384996\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.16123 | −0.318183 | −0.159091 | − | 0.987264i | \(-0.550856\pi\) | ||||
−0.159091 | + | 0.987264i | \(0.550856\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.6329 | 0.854507 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −46.9318 | −1.62609 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.70171 | −0.266529 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.6799 | −0.887629 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.6582 | −0.402485 | −0.201242 | − | 0.979541i | \(-0.564498\pi\) | ||||
−0.201242 | + | 0.979541i | \(0.564498\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.3696 | 1.28861 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.3405 | 0.631680 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.46873 | 0.0848266 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.44696 | −0.255579 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 46.1142 | 1.58078 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.56033 | −0.258861 | −0.129430 | − | 0.991589i | \(-0.541315\pi\) | ||||
−0.129430 | + | 0.991589i | \(0.541315\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.88231 | 0.303769 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.96077 | 0.135297 | 0.0676487 | − | 0.997709i | \(-0.478450\pi\) | ||||
0.0676487 | + | 0.997709i | \(0.478450\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.0388 | 0.751953 | 0.375976 | − | 0.926629i | \(-0.377307\pi\) | ||||
0.375976 | + | 0.926629i | \(0.377307\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.10215 | 0.0375611 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.6668 | −0.431183 | −0.215591 | − | 0.976484i | \(-0.569168\pi\) | ||||
−0.215591 | + | 0.976484i | \(0.569168\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.4784 | −0.424279 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −44.2282 | −1.50207 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.1134 | −0.512686 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.0640 | 0.340614 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.08815 | −0.172011 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.5972 | −0.898123 | −0.449061 | − | 0.893501i | \(-0.648242\pi\) | ||||
−0.449061 | + | 0.893501i | \(0.648242\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.2097 | −0.749114 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.47544 | 0.184472 | 0.0922361 | − | 0.995737i | \(-0.470599\pi\) | ||||
0.0922361 | + | 0.995737i | \(0.470599\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.6015 | −1.33270 | −0.666348 | − | 0.745641i | \(-0.732143\pi\) | ||||
−0.666348 | + | 0.745641i | \(0.732143\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.50019 | −0.252116 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.0519 | −0.639700 | −0.319850 | − | 0.947468i | \(-0.603633\pi\) | ||||
−0.319850 | + | 0.947468i | \(0.603633\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.01639 | −0.0676277 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.6866 | −0.425019 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.58881 | −0.187022 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.0108 | −0.902870 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.0097 | 1.23434 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.4857 | −1.61529 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.48427 | −0.0826713 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.6252 | −0.951533 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.0127 | 1.49462 | 0.747311 | − | 0.664475i | \(-0.231345\pi\) | ||||
0.747311 | + | 0.664475i | \(0.231345\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.37973 | 0.178434 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.3884 | −0.774891 | −0.387445 | − | 0.921893i | \(-0.626642\pi\) | ||||
−0.387445 | + | 0.921893i | \(0.626642\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.64609 | 0.186858 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.45627 | −0.114261 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.49635 | −0.148483 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.6732 | −0.451038 | −0.225519 | − | 0.974239i | \(-0.572408\pi\) | ||||
−0.225519 | + | 0.974239i | \(0.572408\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.9603 | 0.855421 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.5007 | 0.772697 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.7289 | 0.582292 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.47086 | 0.0810663 | 0.0405332 | − | 0.999178i | \(-0.487094\pi\) | ||||
0.0405332 | + | 0.999178i | \(0.487094\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.8514 | −1.50272 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −35.1478 | −1.15069 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −23.2823 | −0.761412 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −58.1390 | −1.89932 | −0.949659 | − | 0.313286i | \(-0.898570\pi\) | ||||
−0.949659 | + | 0.313286i | \(0.898570\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35.6383 | 1.16301 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.9154 | 1.36640 | 0.683202 | − | 0.730229i | \(-0.260587\pi\) | ||||
0.683202 | + | 0.730229i | \(0.260587\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.79225 | −0.318880 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.63533 | 0.118257 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.8745 | 1.03578 | 0.517892 | − | 0.855446i | \(-0.326717\pi\) | ||||
0.517892 | + | 0.855446i | \(0.326717\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.3370 | −0.594619 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.2360 | −0.525934 | −0.262967 | − | 0.964805i | \(-0.584701\pi\) | ||||
−0.262967 | + | 0.964805i | \(0.584701\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.1075 | −0.488868 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.4900 | 0.888626 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.76809 | 0.0893862 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.3623 | −0.334267 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.46442 | 0.240538 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.38404 | −0.173318 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.35881 | −0.0436965 | −0.0218483 | − | 0.999761i | \(-0.506955\pi\) | ||||
−0.0218483 | + | 0.999761i | \(0.506955\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −67.2103 | −2.15910 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.3236 | 1.06941 | 0.534703 | − | 0.845040i | \(-0.320423\pi\) | ||||
0.534703 | + | 0.845040i | \(0.320423\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.87502 | 0.156286 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.3314 | −1.09836 | −0.549179 | − | 0.835704i | \(-0.685060\pi\) | ||||
−0.549179 | + | 0.835704i | \(0.685060\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.8926 | −0.987332 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.7560 | −0.439195 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.3739 | −0.586036 | −0.293018 | − | 0.956107i | \(-0.594660\pi\) | ||||
−0.293018 | + | 0.956107i | \(0.594660\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.5467 | 1.00516 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.533188 | −0.0169716 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.0720 | 0.701849 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.8133 | 1.74120 | 0.870601 | − | 0.491990i | \(-0.163730\pi\) | ||||
0.870601 | + | 0.491990i | \(0.163730\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 41.6713 | 1.32240 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.6659 | 0.655154 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.1976 | 1.24140 | 0.620700 | − | 0.784048i | \(-0.286848\pi\) | ||||
0.620700 | + | 0.784048i | \(0.286848\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −45.6219 | −1.44341 |
(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 | 1352.2.a.i.1.2 | ✓ | 3 | |
4.3 | odd | 2 | 2704.2.a.bb.1.2 | 3 | |||
13.2 | odd | 12 | 1352.2.o.g.1161.4 | 12 | |||
13.3 | even | 3 | 1352.2.i.i.529.2 | 6 | |||
13.4 | even | 6 | 1352.2.i.j.1329.2 | 6 | |||
13.5 | odd | 4 | 1352.2.f.e.337.4 | 6 | |||
13.6 | odd | 12 | 1352.2.o.g.361.4 | 12 | |||
13.7 | odd | 12 | 1352.2.o.g.361.3 | 12 | |||
13.8 | odd | 4 | 1352.2.f.e.337.3 | 6 | |||
13.9 | even | 3 | 1352.2.i.i.1329.2 | 6 | |||
13.10 | even | 6 | 1352.2.i.j.529.2 | 6 | |||
13.11 | odd | 12 | 1352.2.o.g.1161.3 | 12 | |||
13.12 | even | 2 | 1352.2.a.j.1.2 | yes | 3 | ||
52.31 | even | 4 | 2704.2.f.p.337.4 | 6 | |||
52.47 | even | 4 | 2704.2.f.p.337.3 | 6 | |||
52.51 | odd | 2 | 2704.2.a.bc.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1352.2.a.i.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1352.2.a.j.1.2 | yes | 3 | 13.12 | even | 2 | ||
1352.2.f.e.337.3 | 6 | 13.8 | odd | 4 | |||
1352.2.f.e.337.4 | 6 | 13.5 | odd | 4 | |||
1352.2.i.i.529.2 | 6 | 13.3 | even | 3 | |||
1352.2.i.i.1329.2 | 6 | 13.9 | even | 3 | |||
1352.2.i.j.529.2 | 6 | 13.10 | even | 6 | |||
1352.2.i.j.1329.2 | 6 | 13.4 | even | 6 | |||
1352.2.o.g.361.3 | 12 | 13.7 | odd | 12 | |||
1352.2.o.g.361.4 | 12 | 13.6 | odd | 12 | |||
1352.2.o.g.1161.3 | 12 | 13.11 | odd | 12 | |||
1352.2.o.g.1161.4 | 12 | 13.2 | odd | 12 | |||
2704.2.a.bb.1.2 | 3 | 4.3 | odd | 2 | |||
2704.2.a.bc.1.2 | 3 | 52.51 | odd | 2 | |||
2704.2.f.p.337.3 | 6 | 52.47 | even | 4 | |||
2704.2.f.p.337.4 | 6 | 52.31 | even | 4 |