Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(1,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, 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("4600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.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: | \(36.7311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.13955077.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 14x^{3} - x^{2} + 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-3.36002\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.1 |
$q$-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 | ||||||||
\(3\) | 3.36002 | 1.93991 | 0.969954 | − | 0.243287i | \(-0.0782256\pi\) | ||||
0.969954 | + | 0.243287i | \(0.0782256\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.90754 | 0.720984 | 0.360492 | − | 0.932762i | \(-0.382609\pi\) | ||||
0.360492 | + | 0.932762i | \(0.382609\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.28974 | 2.76325 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.48021 | −1.65234 | −0.826172 | − | 0.563418i | \(-0.809486\pi\) | ||||
−0.826172 | + | 0.563418i | \(0.809486\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.04937 | 0.291041 | 0.145521 | − | 0.989355i | \(-0.453514\pi\) | ||||
0.145521 | + | 0.989355i | \(0.453514\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.74222 | 1.63523 | 0.817614 | − | 0.575767i | \(-0.195297\pi\) | ||||
0.817614 | + | 0.575767i | \(0.195297\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.55049 | −0.355707 | −0.177853 | − | 0.984057i | \(-0.556915\pi\) | ||||
−0.177853 | + | 0.984057i | \(0.556915\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.40939 | 1.39864 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 17.7736 | 3.42054 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.38219 | −0.628058 | −0.314029 | − | 0.949413i | \(-0.601679\pi\) | ||||
−0.314029 | + | 0.949413i | \(0.601679\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.9327 | 1.96357 | 0.981784 | − | 0.190000i | \(-0.0608489\pi\) | ||||
0.981784 | + | 0.190000i | \(0.0608489\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −18.4136 | −3.20540 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.26201 | −0.865069 | −0.432534 | − | 0.901617i | \(-0.642381\pi\) | ||||
−0.432534 | + | 0.901617i | \(0.642381\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.52589 | 0.564594 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.09801 | 0.952350 | 0.476175 | − | 0.879351i | \(-0.342023\pi\) | ||||
0.476175 | + | 0.879351i | \(0.342023\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.403830 | −0.0589046 | −0.0294523 | − | 0.999566i | \(-0.509376\pi\) | ||||
−0.0294523 | + | 0.999566i | \(0.509376\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.36128 | −0.480183 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 22.6540 | 3.17219 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.88332 | −0.808136 | −0.404068 | − | 0.914729i | \(-0.632404\pi\) | ||||
−0.404068 | + | 0.914729i | \(0.632404\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.20968 | −0.690039 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.60111 | 1.24996 | 0.624979 | − | 0.780641i | \(-0.285107\pi\) | ||||
0.624979 | + | 0.780641i | \(0.285107\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.09927 | −0.908968 | −0.454484 | − | 0.890755i | \(-0.650176\pi\) | ||||
−0.454484 | + | 0.890755i | \(0.650176\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.8130 | 1.99226 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.7971 | −1.68559 | −0.842794 | − | 0.538236i | \(-0.819091\pi\) | ||||
−0.842794 | + | 0.538236i | \(0.819091\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.36002 | 0.404499 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.478950 | 0.0568409 | 0.0284205 | − | 0.999596i | \(-0.490952\pi\) | ||||
0.0284205 | + | 0.999596i | \(0.490952\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.40383 | −0.281347 | −0.140673 | − | 0.990056i | \(-0.544927\pi\) | ||||
−0.140673 | + | 0.990056i | \(0.544927\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.4537 | −1.19131 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.24037 | −0.477079 | −0.238540 | − | 0.971133i | \(-0.576669\pi\) | ||||
−0.238540 | + | 0.971133i | \(0.576669\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 34.8505 | 3.87228 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.2620 | 1.23617 | 0.618083 | − | 0.786113i | \(-0.287910\pi\) | ||||
0.618083 | + | 0.786113i | \(0.287910\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.3642 | −1.21837 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.90495 | 0.519924 | 0.259962 | − | 0.965619i | \(-0.416290\pi\) | ||||
0.259962 | + | 0.965619i | \(0.416290\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00171 | 0.209836 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 36.7340 | 3.80914 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3433 | 1.25327 | 0.626637 | − | 0.779311i | \(-0.284431\pi\) | ||||
0.626637 | + | 0.779311i | \(0.284431\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −45.4295 | −4.56583 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.44692 | −0.143974 | −0.0719870 | − | 0.997406i | \(-0.522934\pi\) | ||||
−0.0719870 | + | 0.997406i | \(0.522934\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.76385 | 0.764995 | 0.382497 | − | 0.923957i | \(-0.375064\pi\) | ||||
0.382497 | + | 0.923957i | \(0.375064\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.54197 | 0.439089 | 0.219544 | − | 0.975603i | \(-0.429543\pi\) | ||||
0.219544 | + | 0.975603i | \(0.429543\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.4136 | 1.18901 | 0.594504 | − | 0.804093i | \(-0.297348\pi\) | ||||
0.594504 | + | 0.804093i | \(0.297348\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.6805 | −1.67815 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.27312 | −0.872342 | −0.436171 | − | 0.899864i | \(-0.643666\pi\) | ||||
−0.436171 | + | 0.899864i | \(0.643666\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.69896 | 0.804219 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.8611 | 1.17897 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.0327 | 1.73024 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20.4894 | 1.84747 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.4149 | −1.10165 | −0.550824 | − | 0.834621i | \(-0.685686\pi\) | ||||
−0.550824 | + | 0.834621i | \(0.685686\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.55434 | 0.834766 | 0.417383 | − | 0.908731i | \(-0.362947\pi\) | ||||
0.417383 | + | 0.908731i | \(0.362947\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.95763 | −0.256459 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.36558 | 0.287541 | 0.143770 | − | 0.989611i | \(-0.454077\pi\) | ||||
0.143770 | + | 0.989611i | \(0.454077\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.7361 | −1.75881 | −0.879406 | − | 0.476072i | \(-0.842060\pi\) | ||||
−0.879406 | + | 0.476072i | \(0.842060\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.35688 | −0.114270 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.75074 | −0.480901 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.2940 | −0.931510 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.9399 | −1.63354 | −0.816769 | − | 0.576965i | \(-0.804237\pi\) | ||||
−0.816769 | + | 0.576965i | \(0.804237\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.7979 | 1.93664 | 0.968321 | − | 0.249709i | \(-0.0803349\pi\) | ||||
0.968321 | + | 0.249709i | \(0.0803349\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 55.8912 | 4.51854 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.3175 | −1.06285 | −0.531425 | − | 0.847105i | \(-0.678343\pi\) | ||||
−0.531425 | + | 0.847105i | \(0.678343\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.7681 | −1.56771 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.90754 | 0.150335 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.1529 | −1.26519 | −0.632595 | − | 0.774483i | \(-0.718010\pi\) | ||||
−0.632595 | + | 0.774483i | \(0.718010\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.6782 | 1.60013 | 0.800064 | − | 0.599915i | \(-0.204799\pi\) | ||||
0.800064 | + | 0.599915i | \(0.204799\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8988 | −0.915295 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.8532 | −0.982905 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.72058 | −0.586985 | −0.293492 | − | 0.955961i | \(-0.594818\pi\) | ||||
−0.293492 | + | 0.955961i | \(0.594818\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 32.2599 | 2.42480 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.88683 | 0.738976 | 0.369488 | − | 0.929236i | \(-0.379533\pi\) | ||||
0.369488 | + | 0.929236i | \(0.379533\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.9883 | −1.78304 | −0.891519 | − | 0.452983i | \(-0.850360\pi\) | ||||
−0.891519 | + | 0.452983i | \(0.850360\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.8537 | −1.76332 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −36.9487 | −2.70196 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 33.9040 | 2.46615 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.72004 | 0.486245 | 0.243123 | − | 0.969996i | \(-0.421828\pi\) | ||||
0.243123 | + | 0.969996i | \(0.421828\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.95007 | −0.644240 | −0.322120 | − | 0.946699i | \(-0.604395\pi\) | ||||
−0.322120 | + | 0.946699i | \(0.604395\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.65109 | 0.473871 | 0.236935 | − | 0.971525i | \(-0.423857\pi\) | ||||
0.236935 | + | 0.971525i | \(0.423857\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.9050 | −0.773032 | −0.386516 | − | 0.922283i | \(-0.626322\pi\) | ||||
−0.386516 | + | 0.922283i | \(0.626322\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −46.3587 | −3.26989 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.45168 | −0.452819 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.28974 | 0.576177 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.49700 | 0.587750 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.21874 | −0.0839014 | −0.0419507 | − | 0.999120i | \(-0.513357\pi\) | ||||
−0.0419507 | + | 0.999120i | \(0.513357\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.60928 | 0.110266 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.8546 | 1.41570 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.07692 | −0.545787 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.07505 | 0.475919 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.1542 | −0.947835 | −0.473917 | − | 0.880569i | \(-0.657160\pi\) | ||||
−0.473917 | + | 0.880569i | \(0.657160\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.89902 | 0.325159 | 0.162580 | − | 0.986695i | \(-0.448019\pi\) | ||||
0.162580 | + | 0.986695i | \(0.448019\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.3946 | 0.819056 | 0.409528 | − | 0.912298i | \(-0.365693\pi\) | ||||
0.409528 | + | 0.912298i | \(0.365693\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −35.1248 | −2.31104 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.882062 | −0.0577858 | −0.0288929 | − | 0.999583i | \(-0.509198\pi\) | ||||
−0.0288929 | + | 0.999583i | \(0.509198\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.2477 | −0.925490 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.9506 | −1.29049 | −0.645247 | − | 0.763974i | \(-0.723246\pi\) | ||||
−0.645247 | + | 0.763974i | \(0.723246\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.81877 | −0.181573 | −0.0907865 | − | 0.995870i | \(-0.528938\pi\) | ||||
−0.0907865 | + | 0.995870i | \(0.528938\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 63.7777 | 4.09134 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.62703 | −0.103525 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 37.8406 | 2.39805 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.9883 | 1.13541 | 0.567706 | − | 0.823231i | \(-0.307831\pi\) | ||||
0.567706 | + | 0.823231i | \(0.307831\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.48021 | −0.344538 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.1705 | 0.883930 | 0.441965 | − | 0.897032i | \(-0.354282\pi\) | ||||
0.441965 | + | 0.897032i | \(0.354282\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.0375 | −0.623701 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −28.0375 | −1.73548 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.88386 | 0.424477 | 0.212238 | − | 0.977218i | \(-0.431925\pi\) | ||||
0.212238 | + | 0.977218i | \(0.431925\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.4807 | 1.00861 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.3463 | −1.42345 | −0.711724 | − | 0.702459i | \(-0.752085\pi\) | ||||
−0.711724 | + | 0.702459i | \(0.752085\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.9519 | 0.847517 | 0.423759 | − | 0.905775i | \(-0.360711\pi\) | ||||
0.423759 | + | 0.905775i | \(0.360711\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.72579 | 0.407063 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.69490 | −0.222005 | −0.111003 | − | 0.993820i | \(-0.535406\pi\) | ||||
−0.111003 | + | 0.993820i | \(0.535406\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 90.6291 | 5.42582 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.9582 | 0.951984 | 0.475992 | − | 0.879450i | \(-0.342089\pi\) | ||||
0.475992 | + | 0.879450i | \(0.342089\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.21649 | 0.488420 | 0.244210 | − | 0.969722i | \(-0.421471\pi\) | ||||
0.244210 | + | 0.969722i | \(0.421471\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.6322 | 0.686628 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.4575 | 1.67397 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 41.4738 | 2.43124 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.0878 | −1.29038 | −0.645191 | − | 0.764021i | \(-0.723222\pi\) | ||||
−0.645191 | + | 0.764021i | \(0.723222\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −97.4032 | −5.65191 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.04937 | 0.0606863 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.86168 | −0.279296 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.2091 | −0.868030 | −0.434015 | − | 0.900906i | \(-0.642903\pi\) | ||||
−0.434015 | + | 0.900906i | \(0.642903\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.0867 | 1.48402 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.254818 | 0.0144494 | 0.00722471 | − | 0.999974i | \(-0.497700\pi\) | ||||
0.00722471 | + | 0.999974i | \(0.497700\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.57095 | −0.201842 | −0.100921 | − | 0.994894i | \(-0.532179\pi\) | ||||
−0.100921 | + | 0.994894i | \(0.532179\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.3235 | −0.692155 | −0.346078 | − | 0.938206i | \(-0.612487\pi\) | ||||
−0.346078 | + | 0.938206i | \(0.612487\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.5351 | 1.03777 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.2611 | 0.851792 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.4537 | −0.581661 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 41.7100 | 2.30657 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.770323 | −0.0424693 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.1082 | 1.43503 | 0.717517 | − | 0.696541i | \(-0.245278\pi\) | ||||
0.717517 | + | 0.696541i | \(0.245278\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −43.6207 | −2.39040 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.68246 | −0.527437 | −0.263718 | − | 0.964600i | \(-0.584949\pi\) | ||||
−0.263718 | + | 0.964600i | \(0.584949\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −31.1579 | −1.69226 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −59.9134 | −3.24449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.7646 | −1.06719 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.9747 | −1.34071 | −0.670355 | − | 0.742040i | \(-0.733858\pi\) | ||||
−0.670355 | + | 0.742040i | \(0.733858\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.3019 | −1.88967 | −0.944835 | − | 0.327547i | \(-0.893778\pi\) | ||||
−0.944835 | + | 0.327547i | \(0.893778\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.6510 | 0.995518 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.0326 | 0.533980 | 0.266990 | − | 0.963699i | \(-0.413971\pi\) | ||||
0.266990 | + | 0.963699i | \(0.413971\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 43.2135 | 2.28710 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.8691 | −1.62921 | −0.814603 | − | 0.580019i | \(-0.803045\pi\) | ||||
−0.814603 | + | 0.580019i | \(0.803045\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.5960 | −0.873473 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 63.9502 | 3.35651 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.3234 | −1.73947 | −0.869734 | − | 0.493521i | \(-0.835709\pi\) | ||||
−0.869734 | + | 0.493521i | \(0.835709\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 50.5509 | 2.63158 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.2227 | −0.582653 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.62023 | −0.239227 | −0.119613 | − | 0.992821i | \(-0.538165\pi\) | ||||
−0.119613 | + | 0.992821i | \(0.538165\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.54916 | −0.182791 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.0020 | 0.770600 | 0.385300 | − | 0.922791i | \(-0.374098\pi\) | ||||
0.385300 | + | 0.922791i | \(0.374098\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −41.7145 | −2.13710 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.87882 | −0.0960033 | −0.0480016 | − | 0.998847i | \(-0.515285\pi\) | ||||
−0.0480016 | + | 0.998847i | \(0.515285\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.48539 | −0.0753121 | −0.0376560 | − | 0.999291i | \(-0.511989\pi\) | ||||
−0.0376560 | + | 0.999291i | \(0.511989\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.74222 | 0.340968 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 32.1028 | 1.61937 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.26722 | −0.264354 | −0.132177 | − | 0.991226i | \(-0.542197\pi\) | ||||
−0.132177 | + | 0.991226i | \(0.542197\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.93769 | −0.497507 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.1490 | 1.30582 | 0.652910 | − | 0.757436i | \(-0.273548\pi\) | ||||
0.652910 | + | 0.757436i | \(0.273548\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.4724 | 0.571480 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.8369 | 1.42939 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.7503 | −0.729355 | −0.364677 | − | 0.931134i | \(-0.618821\pi\) | ||||
−0.364677 | + | 0.931134i | \(0.618821\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.3084 | 0.557803 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.3145 | 0.901200 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −69.6737 | −3.41194 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.10616 | 0.0540394 | 0.0270197 | − | 0.999635i | \(-0.491398\pi\) | ||||
0.0270197 | + | 0.999635i | \(0.491398\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.16362 | 0.446607 | 0.223304 | − | 0.974749i | \(-0.428316\pi\) | ||||
0.223304 | + | 0.974749i | \(0.428316\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.34764 | −0.162768 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.5422 | −0.655351 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19.3226 | −0.932904 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.1712 | −1.54963 | −0.774817 | − | 0.632186i | \(-0.782158\pi\) | ||||
−0.774817 | + | 0.632186i | \(0.782158\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.37861 | 0.402650 | 0.201325 | − | 0.979524i | \(-0.435475\pi\) | ||||
0.201325 | + | 0.979524i | \(0.435475\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.55049 | −0.0741700 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.3093 | −0.730673 | −0.365336 | − | 0.930876i | \(-0.619046\pi\) | ||||
−0.365336 | + | 0.930876i | \(0.619046\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −27.8641 | −1.32686 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.24129 | 0.153998 | 0.0769992 | − | 0.997031i | \(-0.475466\pi\) | ||||
0.0769992 | + | 0.997031i | \(0.475466\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −66.9984 | −3.16892 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.02215 | −0.425782 | −0.212891 | − | 0.977076i | \(-0.568288\pi\) | ||||
−0.212891 | + | 0.977076i | \(0.568288\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −33.4184 | −1.57361 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 79.9613 | 3.75691 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.03526 | −0.329096 | −0.164548 | − | 0.986369i | \(-0.552616\pi\) | ||||
−0.164548 | + | 0.986369i | \(0.552616\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 119.834 | 5.59336 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.59617 | −0.0743411 | −0.0371705 | − | 0.999309i | \(-0.511834\pi\) | ||||
−0.0371705 | + | 0.999309i | \(0.511834\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.61655 | −0.446919 | −0.223459 | − | 0.974713i | \(-0.571735\pi\) | ||||
−0.223459 | + | 0.974713i | \(0.571735\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.4764 | −1.13263 | −0.566317 | − | 0.824188i | \(-0.691632\pi\) | ||||
−0.566317 | + | 0.824188i | \(0.691632\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.3186 | −1.21528 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −44.7470 | −2.06183 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −48.7712 | −2.23308 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.2108 | −0.603618 | −0.301809 | − | 0.953368i | \(-0.597590\pi\) | ||||
−0.301809 | + | 0.953368i | \(0.597590\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.52177 | −0.251771 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.40939 | 0.291637 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.7078 | 1.07431 | 0.537153 | − | 0.843485i | \(-0.319500\pi\) | ||||
0.537153 | + | 0.843485i | \(0.319500\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −54.2739 | −2.45435 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.5930 | 0.839091 | 0.419546 | − | 0.907734i | \(-0.362189\pi\) | ||||
0.419546 | + | 0.907734i | \(0.362189\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.8035 | −1.02702 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.913618 | 0.0409814 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.9121 | 0.801858 | 0.400929 | − | 0.916109i | \(-0.368687\pi\) | ||||
0.400929 | + | 0.916109i | \(0.368687\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 69.4792 | 3.10410 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.24890 | −0.0556855 | −0.0278428 | − | 0.999612i | \(-0.508864\pi\) | ||||
−0.0278428 | + | 0.999612i | \(0.508864\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −39.9803 | −1.77559 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.8757 | 0.703679 | 0.351839 | − | 0.936060i | \(-0.385556\pi\) | ||||
0.351839 | + | 0.936060i | \(0.385556\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.58541 | −0.202847 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −27.5578 | −1.21671 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.21307 | 0.0973307 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.9413 | −1.13870 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.5488 | 1.16312 | 0.581561 | − | 0.813503i | \(-0.302442\pi\) | ||||
0.581561 | + | 0.813503i | \(0.302442\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.0258 | −1.35666 | −0.678331 | − | 0.734757i | \(-0.737296\pi\) | ||||
−0.678331 | + | 0.734757i | \(0.737296\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 73.7105 | 3.21088 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 79.5907 | 3.45394 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.39904 | 0.277173 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 33.2199 | 1.43355 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.4205 | 0.793427 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.4123 | 0.963579 | 0.481790 | − | 0.876287i | \(-0.339987\pi\) | ||||
0.481790 | + | 0.876287i | \(0.339987\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −80.6013 | −3.45893 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.3980 | 1.85556 | 0.927782 | − | 0.373122i | \(-0.121713\pi\) | ||||
0.927782 | + | 0.373122i | \(0.121713\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −58.8511 | −2.51170 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.24406 | 0.223404 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.08870 | −0.343966 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.2690 | 0.901197 | 0.450599 | − | 0.892727i | \(-0.351211\pi\) | ||||
0.450599 | + | 0.892727i | \(0.351211\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −124.149 | −5.24155 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.6629 | −0.449389 | −0.224694 | − | 0.974429i | \(-0.572138\pi\) | ||||
−0.224694 | + | 0.974429i | \(0.572138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 66.4789 | 2.79185 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.8986 | 1.33726 | 0.668630 | − | 0.743596i | \(-0.266881\pi\) | ||||
0.668630 | + | 0.743596i | \(0.266881\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.87477 | −0.329549 | −0.164774 | − | 0.986331i | \(-0.552690\pi\) | ||||
−0.164774 | + | 0.986331i | \(0.552690\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.5795 | 0.943271 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.7070 | −1.69466 | −0.847328 | − | 0.531070i | \(-0.821790\pi\) | ||||
−0.847328 | + | 0.531070i | \(0.821790\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −30.0724 | −1.24977 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.4828 | 0.891256 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.2418 | 1.33532 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.9321 | 0.946508 | 0.473254 | − | 0.880926i | \(-0.343079\pi\) | ||||
0.473254 | + | 0.880926i | \(0.343079\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.9510 | −0.698454 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.3478 | 0.919266 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.6250 | −1.13442 | −0.567211 | − | 0.823572i | \(-0.691978\pi\) | ||||
−0.567211 | + | 0.823572i | \(0.691978\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −36.6409 | −1.49961 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.2139 | −0.744199 | −0.372099 | − | 0.928193i | \(-0.621362\pi\) | ||||
−0.372099 | + | 0.928193i | \(0.621362\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.0407 | −0.980640 | −0.490320 | − | 0.871543i | \(-0.663120\pi\) | ||||
−0.490320 | + | 0.871543i | \(0.663120\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −114.375 | −4.65770 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.52878 | −0.224406 | −0.112203 | − | 0.993685i | \(-0.535791\pi\) | ||||
−0.112203 | + | 0.993685i | \(0.535791\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.6778 | −0.878428 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.423765 | −0.0171437 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.1205 | 0.853050 | 0.426525 | − | 0.904476i | \(-0.359738\pi\) | ||||
0.426525 | + | 0.904476i | \(0.359738\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.6523 | −0.791174 | −0.395587 | − | 0.918429i | \(-0.629459\pi\) | ||||
−0.395587 | + | 0.918429i | \(0.629459\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.9931 | 1.64765 | 0.823826 | − | 0.566843i | \(-0.191836\pi\) | ||||
0.823826 | + | 0.566843i | \(0.191836\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.7736 | 0.713231 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.35641 | 0.374857 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 28.5501 | 1.14018 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −35.4776 | −1.41458 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.5595 | −1.81369 | −0.906847 | − | 0.421461i | \(-0.861517\pi\) | ||||
−0.906847 | + | 0.421461i | \(0.861517\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.09499 | −0.162761 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.52721 | −0.139753 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.97037 | 0.157065 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.97997 | 0.354688 | 0.177344 | − | 0.984149i | \(-0.443250\pi\) | ||||
0.177344 | + | 0.984149i | \(0.443250\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.69616 | −0.106326 | −0.0531630 | − | 0.998586i | \(-0.516930\pi\) | ||||
−0.0531630 | + | 0.998586i | \(0.516930\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.12638 | −0.358795 | −0.179398 | − | 0.983777i | \(-0.557415\pi\) | ||||
−0.179398 | + | 0.983777i | \(0.557415\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −52.6161 | −2.06536 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 70.0718 | 2.74633 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −41.5497 | −1.62596 | −0.812982 | − | 0.582289i | \(-0.802157\pi\) | ||||
−0.812982 | + | 0.582289i | \(0.802157\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −19.9271 | −0.777431 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.9256 | 0.815145 | 0.407573 | − | 0.913173i | \(-0.366375\pi\) | ||||
0.407573 | + | 0.913173i | \(0.366375\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.25688 | 0.204469 | 0.102234 | − | 0.994760i | \(-0.467401\pi\) | ||||
0.102234 | + | 0.994760i | \(0.467401\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.7723 | 0.923240 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.38219 | −0.130959 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −47.5584 | −1.83871 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.9055 | 1.50193 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.1900 | −1.47212 | −0.736059 | − | 0.676918i | \(-0.763315\pi\) | ||||
−0.736059 | + | 0.676918i | \(0.763315\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.83529 | 0.185835 | 0.0929176 | − | 0.995674i | \(-0.470381\pi\) | ||||
0.0929176 | + | 0.995674i | \(0.470381\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.5454 | 0.903591 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.4608 | 0.630780 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 50.3044 | 1.92484 | 0.962422 | − | 0.271559i | \(-0.0875391\pi\) | ||||
0.962422 | + | 0.271559i | \(0.0875391\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.6460 | 1.58889 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.17375 | −0.235201 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.6298 | 0.784793 | 0.392396 | − | 0.919796i | \(-0.371646\pi\) | ||||
0.392396 | + | 0.919796i | \(0.371646\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −86.6587 | −3.29189 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 41.1141 | 1.55731 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.96375 | −0.112099 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.9598 | −0.867182 | −0.433591 | − | 0.901110i | \(-0.642754\pi\) | ||||
−0.433591 | + | 0.901110i | \(0.642754\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.15869 | 0.307711 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.76006 | −0.103803 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.9069 | 0.447174 | 0.223587 | − | 0.974684i | \(-0.428223\pi\) | ||||
0.223587 | + | 0.974684i | \(0.428223\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −35.1516 | −1.31829 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.9327 | 0.409432 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −67.0343 | −2.50344 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.5244 | 0.914604 | 0.457302 | − | 0.889311i | \(-0.348816\pi\) | ||||
0.457302 | + | 0.889311i | \(0.348816\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.8099 | 0.551549 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.47113 | −0.352235 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.4034 | −0.422928 | −0.211464 | − | 0.977386i | \(-0.567823\pi\) | ||||
−0.211464 | + | 0.977386i | \(0.567823\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 109.743 | 4.06454 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.8722 | −1.32497 | −0.662484 | − | 0.749076i | \(-0.730498\pi\) | ||||
−0.662484 | + | 0.749076i | \(0.730498\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 75.6112 | 2.78517 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.1503 | −0.630883 | −0.315441 | − | 0.948945i | \(-0.602153\pi\) | ||||
−0.315441 | + | 0.948945i | \(0.602153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.46685 | −0.200830 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.7242 | −1.01710 | −0.508552 | − | 0.861031i | \(-0.669819\pi\) | ||||
−0.508552 | + | 0.861031i | \(0.669819\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 93.3591 | 3.41583 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.66400 | 0.316576 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.80173 | −0.102236 | −0.0511182 | − | 0.998693i | \(-0.516279\pi\) | ||||
−0.0511182 | + | 0.998693i | \(0.516279\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 60.4411 | 2.20260 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.6710 | 1.51456 | 0.757278 | − | 0.653092i | \(-0.226529\pi\) | ||||
0.757278 | + | 0.653092i | \(0.226529\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.4136 | −0.668372 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.4285 | −1.28428 | −0.642141 | − | 0.766587i | \(-0.721954\pi\) | ||||
−0.642141 | + | 0.766587i | \(0.721954\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.6795 | 0.857255 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.0751 | 0.363790 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.8731 | 0.860885 | 0.430442 | − | 0.902618i | \(-0.358358\pi\) | ||||
0.430442 | + | 0.902618i | \(0.358358\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 47.6131 | 1.71474 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.3403 | −0.407881 | −0.203941 | − | 0.978983i | \(-0.565375\pi\) | ||||
−0.203941 | + | 0.978983i | \(0.565375\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −33.7262 | −1.20992 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.45490 | −0.338757 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.62475 | −0.0939208 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −60.1139 | −2.14829 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.1906 | 0.933595 | 0.466797 | − | 0.884364i | \(-0.345408\pi\) | ||||
0.466797 | + | 0.884364i | \(0.345408\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.1299 | 0.823446 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.6889 | −0.628944 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.44973 | −0.264547 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.48133 | 0.158737 | 0.0793684 | − | 0.996845i | \(-0.474710\pi\) | ||||
0.0793684 | + | 0.996845i | \(0.474710\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.72271 | −0.0963224 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 40.6608 | 1.43668 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.1735 | 0.464882 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −78.4440 | −2.76136 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.4608 | −1.14126 | −0.570630 | − | 0.821207i | \(-0.693301\pi\) | ||||
−0.570630 | + | 0.821207i | \(0.693301\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.3500 | 0.398554 | 0.199277 | − | 0.979943i | \(-0.436141\pi\) | ||||
0.199277 | + | 0.979943i | \(0.436141\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 46.8786 | 1.64411 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.5936 | 0.579829 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.2070 | 1.68244 | 0.841218 | − | 0.540697i | \(-0.181839\pi\) | ||||
0.841218 | + | 0.540697i | \(0.181839\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.7179 | 1.31476 | 0.657381 | − | 0.753558i | \(-0.271664\pi\) | ||||
0.657381 | + | 0.753558i | \(0.271664\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.89736 | 0.309392 | 0.154696 | − | 0.987962i | \(-0.450560\pi\) | ||||
0.154696 | + | 0.987962i | \(0.450560\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.9058 | 1.07340 | 0.536702 | − | 0.843772i | \(-0.319670\pi\) | ||||
0.536702 | + | 0.843772i | \(0.319670\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.4149 | −0.430670 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.6625 | −0.785208 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 194.313 | 6.71646 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.34387 | 0.0463954 | 0.0231977 | − | 0.999731i | \(-0.492615\pi\) | ||||
0.0231977 | + | 0.999731i | \(0.492615\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.5608 | −0.605543 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 53.6198 | 1.84676 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36.3056 | 1.24748 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.6076 | 0.947489 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.26201 | −0.180379 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.3940 | 0.903713 | 0.451857 | − | 0.892091i | \(-0.350762\pi\) | ||||
0.451857 | + | 0.892091i | \(0.350762\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.5048 | 0.597953 | 0.298976 | − | 0.954260i | \(-0.403355\pi\) | ||||
0.298976 | + | 0.954260i | \(0.403355\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.7199 | 0.399877 | 0.199938 | − | 0.979808i | \(-0.435926\pi\) | ||||
0.199938 | + | 0.979808i | \(0.435926\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 39.0845 | 1.33200 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.6578 | −0.907443 | −0.453722 | − | 0.891144i | \(-0.649904\pi\) | ||||
−0.453722 | + | 0.891144i | \(0.649904\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 95.6177 | 3.24735 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.2381 | 0.788299 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.4782 | −0.490576 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 102.323 | 3.46311 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.9574 | −0.673912 | −0.336956 | − | 0.941520i | \(-0.609397\pi\) | ||||
−0.336956 | + | 0.941520i | \(0.609397\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −74.2154 | −2.50322 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.7297 | −0.698402 | −0.349201 | − | 0.937048i | \(-0.613547\pi\) | ||||
−0.349201 | + | 0.937048i | \(0.613547\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.31093 | −0.0777690 | −0.0388845 | − | 0.999244i | \(-0.512380\pi\) | ||||
−0.0388845 | + | 0.999244i | \(0.512380\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.6924 | 0.392592 | 0.196296 | − | 0.980545i | \(-0.437109\pi\) | ||||
0.196296 | + | 0.980545i | \(0.437109\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.6820 | −0.794270 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −190.988 | −6.39835 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.626134 | 0.0209528 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.52589 | 0.117726 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −36.9765 | −1.23323 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.6666 | −1.32149 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.5061 | −1.07935 | −0.539673 | − | 0.841875i | \(-0.681452\pi\) | ||||
−0.539673 | + | 0.841875i | \(0.681452\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.9946 | −0.397836 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.7518 | 0.356224 | 0.178112 | − | 0.984010i | \(-0.443001\pi\) | ||||
0.178112 | + | 0.984010i | \(0.443001\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −61.7181 | −2.04257 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.2253 | 0.601853 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.2758 | −0.800785 | −0.400392 | − | 0.916344i | \(-0.631126\pi\) | ||||
−0.400392 | + | 0.916344i | \(0.631126\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −51.1029 | −1.68390 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.502594 | 0.0165431 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 64.3603 | 2.11387 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.18842 | 0.268653 | 0.134327 | − | 0.990937i | \(-0.457113\pi\) | ||||
0.134327 | + | 0.990937i | \(0.457113\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.21163 | 0.170804 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.856194 | 0.0280305 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.2312 | −0.856936 | −0.428468 | − | 0.903557i | \(-0.640947\pi\) | ||||
−0.428468 | + | 0.903557i | \(0.640947\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.9985 | −0.391556 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.6292 | 0.770291 | 0.385145 | − | 0.922856i | \(-0.374151\pi\) | ||||
0.385145 | + | 0.922856i | \(0.374151\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.09801 | 0.198579 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.9026 | 0.516765 | 0.258383 | − | 0.966043i | \(-0.416810\pi\) | ||||
0.258383 | + | 0.966043i | \(0.416810\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.52249 | −0.0818836 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −41.4071 | −1.34272 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.9451 | −0.678478 | −0.339239 | − | 0.940700i | \(-0.610169\pi\) | ||||
−0.339239 | + | 0.940700i | \(0.610169\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 62.2784 | 2.01318 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.41998 | 0.207312 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 88.5236 | 2.85560 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 37.6517 | 1.21331 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.0732 | 0.452563 | 0.226281 | − | 0.974062i | \(-0.427343\pi\) | ||||
0.226281 | + | 0.974062i | \(0.427343\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −35.1248 | −1.12837 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.4404 | −0.367139 | −0.183569 | − | 0.983007i | \(-0.558765\pi\) | ||||
−0.183569 | + | 0.983007i | \(0.558765\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −39.5550 | −1.26808 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.9119 | −1.40487 | −0.702433 | − | 0.711750i | \(-0.747903\pi\) | ||||
−0.702433 | + | 0.711750i | \(0.747903\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.8802 | −0.859094 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 102.906 | 3.28552 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.0420 | 1.37283 | 0.686413 | − | 0.727212i | \(-0.259184\pi\) | ||||
0.686413 | + | 0.727212i | \(0.259184\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.58830 | −0.0823865 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.5288 | 1.38274 | 0.691369 | − | 0.722501i | \(-0.257008\pi\) | ||||
0.691369 | + | 0.722501i | \(0.257008\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 87.7240 | 2.78384 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.4448 | −0.837517 | −0.418758 | − | 0.908098i | \(-0.637535\pi\) | ||||
−0.418758 | + | 0.908098i | \(0.637535\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −93.5250 | −2.95900 |
(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 | 4600.2.a.be.1.5 | 5 | ||
4.3 | odd | 2 | 9200.2.a.cu.1.1 | 5 | |||
5.2 | odd | 4 | 4600.2.e.u.4049.1 | 10 | |||
5.3 | odd | 4 | 4600.2.e.u.4049.10 | 10 | |||
5.4 | even | 2 | 920.2.a.j.1.1 | ✓ | 5 | ||
15.14 | odd | 2 | 8280.2.a.bs.1.3 | 5 | |||
20.19 | odd | 2 | 1840.2.a.v.1.5 | 5 | |||
40.19 | odd | 2 | 7360.2.a.cp.1.1 | 5 | |||
40.29 | even | 2 | 7360.2.a.co.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.j.1.1 | ✓ | 5 | 5.4 | even | 2 | ||
1840.2.a.v.1.5 | 5 | 20.19 | odd | 2 | |||
4600.2.a.be.1.5 | 5 | 1.1 | even | 1 | trivial | ||
4600.2.e.u.4049.1 | 10 | 5.2 | odd | 4 | |||
4600.2.e.u.4049.10 | 10 | 5.3 | odd | 4 | |||
7360.2.a.co.1.5 | 5 | 40.29 | even | 2 | |||
7360.2.a.cp.1.1 | 5 | 40.19 | odd | 2 | |||
8280.2.a.bs.1.3 | 5 | 15.14 | odd | 2 | |||
9200.2.a.cu.1.1 | 5 | 4.3 | odd | 2 |