Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.244558277.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 13x^{4} + 11x^{3} + 29x^{2} + 5x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.676795\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.676795 | 0.390748 | 0.195374 | − | 0.980729i | \(-0.437408\pi\) | ||||
0.195374 | + | 0.980729i | \(0.437408\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.59312 | 1.60689 | 0.803447 | − | 0.595376i | \(-0.202997\pi\) | ||||
0.803447 | + | 0.595376i | \(0.202997\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.54195 | −0.847316 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.43181 | 0.627890 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.62384 | −1.36398 | −0.681991 | − | 0.731360i | \(-0.738886\pi\) | ||||
−0.681991 | + | 0.731360i | \(0.738886\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.78115 | −1.32629 | −0.663143 | − | 0.748493i | \(-0.730778\pi\) | ||||
−0.663143 | + | 0.748493i | \(0.730778\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.676795 | 0.147689 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.70173 | 1.81444 | 0.907218 | − | 0.420661i | \(-0.138202\pi\) | ||||
0.907218 | + | 0.420661i | \(0.138202\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.91054 | 1.58211 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.75076 | −0.721835 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.58734 | 1.78032 | 0.890162 | − | 0.455644i | \(-0.150591\pi\) | ||||
0.890162 | + | 0.455644i | \(0.150591\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.11439 | 0.559361 | 0.279680 | − | 0.960093i | \(-0.409771\pi\) | ||||
0.279680 | + | 0.960093i | \(0.409771\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.676795 | −0.117815 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.59312 | 0.607349 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.39931 | −0.887642 | −0.443821 | − | 0.896116i | \(-0.646377\pi\) | ||||
−0.443821 | + | 0.896116i | \(0.646377\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.676795 | −0.108374 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.94093 | 1.39634 | 0.698169 | − | 0.715933i | \(-0.253998\pi\) | ||||
0.698169 | + | 0.715933i | \(0.253998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.02493 | −0.613797 | −0.306898 | − | 0.951742i | \(-0.599291\pi\) | ||||
−0.306898 | + | 0.951742i | \(0.599291\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.13354 | −1.36155 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.80586 | 0.263411 | 0.131706 | − | 0.991289i | \(-0.457955\pi\) | ||||
0.131706 | + | 0.991289i | \(0.457955\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.80619 | −0.532973 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.67067 | −0.641566 | −0.320783 | − | 0.947153i | \(-0.603946\pi\) | ||||
−0.320783 | + | 0.947153i | \(0.603946\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.59312 | −0.484497 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.91265 | −0.518244 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.19237 | 0.415611 | 0.207806 | − | 0.978170i | \(-0.433368\pi\) | ||||
0.207806 | + | 0.978170i | \(0.433368\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.66345 | 1.23728 | 0.618639 | − | 0.785676i | \(-0.287684\pi\) | ||||
0.618639 | + | 0.785676i | \(0.287684\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.54195 | −0.320255 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.59312 | −0.445672 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3992 | 1.39263 | 0.696317 | − | 0.717734i | \(-0.254821\pi\) | ||||
0.696317 | + | 0.717734i | \(0.254821\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.88929 | 0.708987 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.18836 | −0.497067 | −0.248533 | − | 0.968623i | \(-0.579949\pi\) | ||||
−0.248533 | + | 0.968623i | \(0.579949\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.6610 | 1.48185 | 0.740927 | − | 0.671585i | \(-0.234386\pi\) | ||||
0.740927 | + | 0.671585i | \(0.234386\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.35382 | 0.618205 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.1859 | 1.25851 | 0.629257 | − | 0.777197i | \(-0.283359\pi\) | ||||
0.629257 | + | 0.777197i | \(0.283359\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.08735 | 0.565261 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.112281 | −0.0123244 | −0.00616220 | − | 0.999981i | \(-0.501962\pi\) | ||||
−0.00616220 | + | 0.999981i | \(0.501962\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.2072 | −2.19178 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.48866 | 0.695658 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.6256 | 1.12631 | 0.563157 | − | 0.826350i | \(-0.309587\pi\) | ||||
0.563157 | + | 0.826350i | \(0.309587\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.10780 | 0.218569 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −20.7724 | −2.13120 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.7285 | 1.69853 | 0.849263 | − | 0.527971i | \(-0.177047\pi\) | ||||
0.849263 | + | 0.527971i | \(0.177047\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.54195 | 0.255475 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.2870 | −1.72012 | −0.860058 | − | 0.510196i | \(-0.829573\pi\) | ||||
−0.860058 | + | 0.510196i | \(0.829573\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.43181 | 0.237320 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.79615 | −0.560335 | −0.280168 | − | 0.959951i | \(-0.590390\pi\) | ||||
−0.280168 | + | 0.959951i | \(0.590390\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.19381 | −0.210129 | −0.105064 | − | 0.994465i | \(-0.533505\pi\) | ||||
−0.105064 | + | 0.994465i | \(0.533505\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.65423 | −0.346844 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.35215 | 0.785704 | 0.392852 | − | 0.919602i | \(-0.371488\pi\) | ||||
0.392852 | + | 0.919602i | \(0.371488\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 31.2664 | 2.91561 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.54195 | 0.235003 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.62384 | −0.515537 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.05118 | 0.545616 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.4579 | 0.935387 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6650 | 1.03510 | 0.517550 | − | 0.855653i | \(-0.326844\pi\) | ||||
0.517550 | + | 0.855653i | \(0.326844\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.72405 | −0.239840 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.6828 | 0.933361 | 0.466681 | − | 0.884426i | \(-0.345450\pi\) | ||||
0.466681 | + | 0.884426i | \(0.345450\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.78115 | −0.501289 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.4770 | −1.15991 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.11439 | 0.778695 | 0.389347 | − | 0.921091i | \(-0.372701\pi\) | ||||
0.389347 | + | 0.921091i | \(0.372701\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.83266 | −0.325082 | −0.162541 | − | 0.986702i | \(-0.551969\pi\) | ||||
−0.162541 | + | 0.986702i | \(0.551969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.22219 | 0.102927 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 34.4485 | 2.86079 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.676795 | 0.0558211 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.90099 | 0.729198 | 0.364599 | − | 0.931165i | \(-0.381206\pi\) | ||||
0.364599 | + | 0.931165i | \(0.381206\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.34140 | −0.353298 | −0.176649 | − | 0.984274i | \(-0.556526\pi\) | ||||
−0.176649 | + | 0.984274i | \(0.556526\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.2955 | 1.15572 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.1904 | 0.898834 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0712 | 0.803768 | 0.401884 | − | 0.915690i | \(-0.368355\pi\) | ||||
0.401884 | + | 0.915690i | \(0.368355\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.16109 | −0.250691 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.70173 | 0.685792 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.80552 | 0.298071 | 0.149036 | − | 0.988832i | \(-0.452383\pi\) | ||||
0.149036 | + | 0.988832i | \(0.452383\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.43181 | −0.189316 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.8820 | 1.22898 | 0.614492 | − | 0.788923i | \(-0.289361\pi\) | ||||
0.614492 | + | 0.788923i | \(0.289361\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.6954 | 1.12378 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.4883 | −0.797413 | −0.398706 | − | 0.917079i | \(-0.630541\pi\) | ||||
−0.398706 | + | 0.917079i | \(0.630541\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.91054 | 0.597981 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.16058 | 0.162399 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.2756 | 0.917521 | 0.458761 | − | 0.888560i | \(-0.348294\pi\) | ||||
0.458761 | + | 0.888560i | \(0.348294\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.1320 | 1.49640 | 0.748199 | − | 0.663474i | \(-0.230919\pi\) | ||||
0.748199 | + | 0.663474i | \(0.230919\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.54017 | 0.483464 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −19.4004 | −1.42635 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.62384 | 0.411256 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.75076 | −0.272828 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.80150 | −0.709211 | −0.354606 | − | 0.935016i | \(-0.615385\pi\) | ||||
−0.354606 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.00779 | 0.216505 | 0.108253 | − | 0.994123i | \(-0.465474\pi\) | ||||
0.108253 | + | 0.994123i | \(0.465474\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.43181 | −0.174145 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.2336 | −1.15660 | −0.578299 | − | 0.815825i | \(-0.696283\pi\) | ||||
−0.578299 | + | 0.815825i | \(0.696283\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.8354 | −1.33520 | −0.667602 | − | 0.744519i | \(-0.732679\pi\) | ||||
−0.667602 | + | 0.744519i | \(0.732679\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.71493 | 0.544169 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.58734 | 0.672899 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 32.1259 | 2.24377 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −22.1193 | −1.53740 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.78115 | 0.399890 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.6591 | −1.83529 | −0.917644 | − | 0.397403i | \(-0.869911\pi\) | ||||
−0.917644 | + | 0.397403i | \(0.869911\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.83466 | −0.194228 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.4621 | −0.986306 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.11439 | 0.211419 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.56888 | 0.579031 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.62384 | 0.378301 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.1514 | −0.679789 | −0.339894 | − | 0.940464i | \(-0.610391\pi\) | ||||
−0.339894 | + | 0.940464i | \(0.610391\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −20.1082 | −1.34055 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.5691 | −1.43159 | −0.715796 | − | 0.698309i | \(-0.753936\pi\) | ||||
−0.715796 | + | 0.698309i | \(0.753936\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.89330 | −0.191194 | −0.0955972 | − | 0.995420i | \(-0.530476\pi\) | ||||
−0.0955972 | + | 0.995420i | \(0.530476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.676795 | −0.0445298 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.3688 | 1.00684 | 0.503422 | − | 0.864040i | \(-0.332074\pi\) | ||||
0.503422 | + | 0.864040i | \(0.332074\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.48866 | 0.423274 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.57057 | 0.491761 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.1509 | −1.17408 | −0.587042 | − | 0.809556i | \(-0.699708\pi\) | ||||
−0.587042 | + | 0.809556i | \(0.699708\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.04429 | −0.196100 | −0.0980501 | − | 0.995181i | \(-0.531261\pi\) | ||||
−0.0980501 | + | 0.995181i | \(0.531261\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.6954 | 0.942709 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.59312 | 0.229556 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.78115 | 0.367846 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.0759910 | −0.00481573 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.8103 | −0.997939 | −0.498970 | − | 0.866619i | \(-0.666288\pi\) | ||||
−0.498970 | + | 0.866619i | \(0.666288\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.70173 | −0.547073 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.6761 | −0.856431 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.07424 | −0.503657 | −0.251829 | − | 0.967772i | \(-0.581032\pi\) | ||||
−0.251829 | + | 0.967772i | \(0.581032\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.39931 | −0.335497 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24.3705 | −1.50850 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.60516 | 0.407292 | 0.203646 | − | 0.979045i | \(-0.434721\pi\) | ||||
0.203646 | + | 0.979045i | \(0.434721\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.7823 | −1.03093 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.19137 | 0.440104 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.85703 | −0.357110 | −0.178555 | − | 0.983930i | \(-0.557142\pi\) | ||||
−0.178555 | + | 0.983930i | \(0.557142\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.6007 | −0.826184 | −0.413092 | − | 0.910689i | \(-0.635551\pi\) | ||||
−0.413092 | + | 0.910689i | \(0.635551\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.676795 | −0.0409615 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.91054 | −0.477024 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.244652 | 0.0146997 | 0.00734985 | − | 0.999973i | \(-0.497660\pi\) | ||||
0.00734985 | + | 0.999973i | \(0.497660\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.91662 | −0.473956 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.7613 | −0.940239 | −0.470120 | − | 0.882603i | \(-0.655789\pi\) | ||||
−0.470120 | + | 0.882603i | \(0.655789\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.5368 | −1.28023 | −0.640116 | − | 0.768278i | \(-0.721114\pi\) | ||||
−0.640116 | + | 0.768278i | \(0.721114\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.0586 | −0.832762 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.94093 | 0.527766 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.6276 | 0.860448 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.3218 | 0.663695 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.6207 | 1.43836 | 0.719179 | − | 0.694825i | \(-0.244518\pi\) | ||||
0.719179 | + | 0.694825i | \(0.244518\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.4706 | 0.667843 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.75076 | 0.217641 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.70173 | −0.503234 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.02493 | −0.231993 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.6997 | −0.672132 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 34.7220 | 1.98817 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.0388 | −1.37197 | −0.685984 | − | 0.727616i | \(-0.740628\pi\) | ||||
−0.685984 | + | 0.727616i | \(0.740628\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.41436 | 0.308012 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.6375 | −0.886723 | −0.443362 | − | 0.896343i | \(-0.646214\pi\) | ||||
−0.443362 | + | 0.896343i | \(0.646214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.49347 | 0.480080 | 0.240040 | − | 0.970763i | \(-0.422840\pi\) | ||||
0.240040 | + | 0.970763i | \(0.422840\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.13354 | −0.514617 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −35.1209 | −1.97259 | −0.986293 | − | 0.165005i | \(-0.947236\pi\) | ||||
−0.986293 | + | 0.165005i | \(0.947236\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.58734 | −0.536788 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.92281 | −0.218950 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 32.5123 | 1.80903 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.91054 | −0.438798 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.48476 | −0.0821074 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.80586 | 0.0995600 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.5645 | −1.40515 | −0.702577 | − | 0.711608i | \(-0.747967\pi\) | ||||
−0.702577 | + | 0.711608i | \(0.747967\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.7248 | 0.752113 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 40.9588 | 2.23782 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.9641 | 1.30541 | 0.652703 | − | 0.757614i | \(-0.273635\pi\) | ||||
0.652703 | + | 0.757614i | \(0.273635\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.65269 | 0.307012 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.11439 | −0.168654 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 21.1609 | 1.13927 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −31.0331 | −1.66595 | −0.832973 | − | 0.553314i | \(-0.813363\pi\) | ||||
−0.832973 | + | 0.553314i | \(0.813363\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.0480 | 1.87608 | 0.938039 | − | 0.346530i | \(-0.112640\pi\) | ||||
0.938039 | + | 0.346530i | \(0.112640\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.75076 | 0.200201 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.15133 | −0.114504 | −0.0572519 | − | 0.998360i | \(-0.518234\pi\) | ||||
−0.0572519 | + | 0.998360i | \(0.518234\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.0493 | −0.798734 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.80619 | −0.201445 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.61897 | 0.243780 | 0.121890 | − | 0.992544i | \(-0.461105\pi\) | ||||
0.121890 | + | 0.992544i | \(0.461105\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.4217 | 0.759036 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.676795 | 0.0355225 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 45.4924 | 2.38118 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.2909 | 0.954779 | 0.477390 | − | 0.878692i | \(-0.341583\pi\) | ||||
0.477390 | + | 0.878692i | \(0.341583\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −22.7274 | −1.18314 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.67067 | −0.242489 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.59338 | −0.496726 | −0.248363 | − | 0.968667i | \(-0.579893\pi\) | ||||
−0.248363 | + | 0.968667i | \(0.579893\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.07788 | 0.365500 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.58734 | −0.493773 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.93124 | −0.510133 | −0.255067 | − | 0.966923i | \(-0.582097\pi\) | ||||
−0.255067 | + | 0.966923i | \(0.582097\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.89480 | 0.404463 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.9342 | −0.967491 | −0.483745 | − | 0.875209i | \(-0.660724\pi\) | ||||
−0.483745 | + | 0.875209i | \(0.660724\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.59312 | −0.183123 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.2312 | 0.520080 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.41346 | 0.477281 | 0.238641 | − | 0.971108i | \(-0.423298\pi\) | ||||
0.238641 | + | 0.971108i | \(0.423298\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −48.9372 | −2.47486 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.23007 | 0.364709 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 40.1924 | 2.02230 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.77670 | −0.0891702 | −0.0445851 | − | 0.999006i | \(-0.514197\pi\) | ||||
−0.0445851 | + | 0.999006i | \(0.514197\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.91265 | −0.195878 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.37013 | −0.268172 | −0.134086 | − | 0.990970i | \(-0.542810\pi\) | ||||
−0.134086 | + | 0.990970i | \(0.542810\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.11439 | −0.155139 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.2795 | 0.908314 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.39931 | 0.267634 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.0341 | −1.18841 | −0.594204 | − | 0.804314i | \(-0.702533\pi\) | ||||
−0.594204 | + | 0.804314i | \(0.702533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.16857 | 0.304273 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.19237 | 0.157086 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.403438 | −0.0198040 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.59392 | −0.127025 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.9227 | 0.729022 | 0.364511 | − | 0.931199i | \(-0.381236\pi\) | ||||
0.364511 | + | 0.931199i | \(0.381236\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.18689 | 0.0578455 | 0.0289227 | − | 0.999582i | \(-0.490792\pi\) | ||||
0.0289227 | + | 0.999582i | \(0.490792\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.59039 | −0.223192 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −44.4877 | −2.15797 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.66345 | 0.467647 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.676795 | 0.0326760 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.1150 | −1.73960 | −0.869798 | − | 0.493407i | \(-0.835751\pi\) | ||||
−0.869798 | + | 0.493407i | \(0.835751\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.0523 | −0.963650 | −0.481825 | − | 0.876267i | \(-0.660026\pi\) | ||||
−0.481825 | + | 0.876267i | \(0.660026\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.3146 | 1.11785 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −50.3060 | −2.40646 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.3196 | 0.635711 | 0.317855 | − | 0.948139i | \(-0.397037\pi\) | ||||
0.317855 | + | 0.948139i | \(0.397037\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.54195 | −0.121045 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.4034 | 1.63456 | 0.817278 | − | 0.576243i | \(-0.195482\pi\) | ||||
0.817278 | + | 0.576243i | \(0.195482\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 38.1792 | 1.80987 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.02415 | 0.284932 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.8444 | 0.794934 | 0.397467 | − | 0.917616i | \(-0.369889\pi\) | ||||
0.397467 | + | 0.917616i | \(0.369889\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.94093 | −0.421012 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.93823 | −0.138050 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.59312 | −0.168448 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.3150 | −1.65197 | −0.825983 | − | 0.563695i | \(-0.809379\pi\) | ||||
−0.825983 | + | 0.563695i | \(0.809379\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.0937 | 0.984570 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.0321 | 0.513814 | 0.256907 | − | 0.966436i | \(-0.417297\pi\) | ||||
0.256907 | + | 0.966436i | \(0.417297\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.28844 | −0.338723 | −0.169361 | − | 0.985554i | \(-0.554170\pi\) | ||||
−0.169361 | + | 0.985554i | \(0.554170\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.57360 | 0.351217 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.03039 | 0.279053 | 0.139526 | − | 0.990218i | \(-0.455442\pi\) | ||||
0.139526 | + | 0.990218i | \(0.455442\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.3992 | 0.526366 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.81613 | 0.314071 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.02493 | 0.185067 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −45.7320 | −2.09833 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.8726 | 0.543610 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.5920 | −0.621032 | −0.310516 | − | 0.950568i | \(-0.600502\pi\) | ||||
−0.310516 | + | 0.950568i | \(0.600502\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.39931 | 0.246188 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.88929 | 0.267972 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 60.1077 | 2.72935 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.55386 | 0.342298 | 0.171149 | − | 0.985245i | \(-0.445252\pi\) | ||||
0.171149 | + | 0.985245i | \(0.445252\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.57556 | 0.116471 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.5708 | 0.838088 | 0.419044 | − | 0.907966i | \(-0.362365\pi\) | ||||
0.419044 | + | 0.907966i | \(0.362365\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −53.9177 | −2.42833 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.13354 | 0.410522 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.18836 | −0.187874 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.8928 | 1.15912 | 0.579559 | − | 0.814930i | \(-0.303225\pi\) | ||||
0.579559 | + | 0.814930i | \(0.303225\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.7488 | 0.480223 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.66225 | 0.163291 | 0.0816457 | − | 0.996661i | \(-0.473982\pi\) | ||||
0.0816457 | + | 0.996661i | \(0.473982\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −62.1142 | −2.76405 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.676795 | 0.0300575 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.9982 | 1.46262 | 0.731310 | − | 0.682045i | \(-0.238909\pi\) | ||||
0.731310 | + | 0.682045i | \(0.238909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.6610 | 0.560088 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21.6837 | 0.957360 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.7450 | 1.26666 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.80586 | −0.0794214 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.09845 | −0.311587 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.4607 | 1.24689 | 0.623443 | − | 0.781869i | \(-0.285733\pi\) | ||||
0.623443 | + | 0.781869i | \(0.285733\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.1522 | 0.968649 | 0.484324 | − | 0.874888i | \(-0.339065\pi\) | ||||
0.484324 | + | 0.874888i | \(0.339065\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.35382 | 0.233660 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.5148 | −0.762959 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 52.7201 | 2.29218 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.11484 | −0.352154 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.94093 | −0.387275 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.8263 | −0.900399 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.30806 | 0.358519 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.8923 | −1.07020 | −0.535101 | − | 0.844788i | \(-0.679726\pi\) | ||||
−0.535101 | + | 0.844788i | \(0.679726\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.6252 | 0.584715 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.88263 | −0.337655 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.6048 | −0.795485 | −0.397743 | − | 0.917497i | \(-0.630206\pi\) | ||||
−0.397743 | + | 0.917497i | \(0.630206\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.5640 | −1.04837 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −55.4258 | −2.36122 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.1859 | 0.475673 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.1301 | −0.557342 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.8700 | 0.587692 | 0.293846 | − | 0.955853i | \(-0.405065\pi\) | ||||
0.293846 | + | 0.955853i | \(0.405065\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.02493 | 0.170237 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.80619 | 0.160697 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.4856 | −1.20052 | −0.600262 | − | 0.799803i | \(-0.704937\pi\) | ||||
−0.600262 | + | 0.799803i | \(0.704937\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.0103 | 1.26254 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.08735 | 0.213649 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.1583 | −1.26430 | −0.632150 | − | 0.774846i | \(-0.717827\pi\) | ||||
−0.632150 | + | 0.774846i | \(0.717827\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.48529 | −0.229552 | −0.114776 | − | 0.993391i | \(-0.536615\pi\) | ||||
−0.114776 | + | 0.993391i | \(0.536615\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.63360 | −0.277123 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 68.8354 | 2.87063 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.9648 | 1.41397 | 0.706986 | − | 0.707228i | \(-0.250055\pi\) | ||||
0.706986 | + | 0.707228i | \(0.250055\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.03566 | 0.0845990 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.112281 | −0.00465818 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.67067 | 0.193440 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.13354 | 0.377625 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.0359 | 1.11589 | 0.557946 | − | 0.829877i | \(-0.311590\pi\) | ||||
0.557946 | + | 0.829877i | \(0.311590\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.0048 | −0.741873 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.9868 | −0.451939 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.4237 | −0.592309 | −0.296155 | − | 0.955140i | \(-0.595704\pi\) | ||||
−0.296155 | + | 0.955140i | \(0.595704\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.2072 | −0.828413 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.7477 | −0.521728 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.67784 | 0.109414 | 0.0547068 | − | 0.998502i | \(-0.482578\pi\) | ||||
0.0547068 | + | 0.998502i | \(0.482578\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.2928 | −0.786969 | −0.393484 | − | 0.919331i | \(-0.628730\pi\) | ||||
−0.393484 | + | 0.919331i | \(0.628730\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −28.9762 | −1.18000 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.59312 | 0.146081 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.6095 | 0.755334 | 0.377667 | − | 0.925941i | \(-0.376726\pi\) | ||||
0.377667 | + | 0.925941i | \(0.376726\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.48866 | 0.262934 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.80586 | −0.0730571 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.4517 | 1.31071 | 0.655356 | − | 0.755320i | \(-0.272519\pi\) | ||||
0.655356 | + | 0.755320i | \(0.272519\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 21.7426 | 0.876747 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.435725 | 0.0175416 | 0.00877081 | − | 0.999962i | \(-0.497208\pi\) | ||||
0.00877081 | + | 0.999962i | \(0.497208\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.9744 | −1.64690 | −0.823450 | − | 0.567388i | \(-0.807954\pi\) | ||||
−0.823450 | + | 0.567388i | \(0.807954\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −32.6381 | −1.30972 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.6256 | 0.425706 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.97602 | −0.0790409 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.91265 | 0.156256 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30.3649 | 1.21073 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.35558 | 0.332630 | 0.166315 | − | 0.986073i | \(-0.446813\pi\) | ||||
0.166315 | + | 0.986073i | \(0.446813\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.0427 | −0.717135 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 41.9137 | 1.66330 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.6466 | 0.421173 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.2121 | −1.15381 | −0.576905 | − | 0.816811i | \(-0.695740\pi\) | ||||
−0.576905 | + | 0.816811i | \(0.695740\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.46796 | −0.215635 | −0.107818 | − | 0.994171i | \(-0.534386\pi\) | ||||
−0.107818 | + | 0.994171i | \(0.534386\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.78787 | −0.385397 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.5057 | −1.39588 | −0.697938 | − | 0.716159i | \(-0.745899\pi\) | ||||
−0.697938 | + | 0.716159i | \(0.745899\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.19237 | −0.125311 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.10780 | 0.0826113 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.4593 | −0.526703 | −0.263352 | − | 0.964700i | \(-0.584828\pi\) | ||||
−0.263352 | + | 0.964700i | \(0.584828\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 38.3847 | 1.49981 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −32.1835 | −1.25560 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.4237 | 0.445002 | 0.222501 | − | 0.974932i | \(-0.428578\pi\) | ||||
0.222501 | + | 0.974932i | \(0.428578\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.5377 | −1.42115 | −0.710576 | − | 0.703621i | \(-0.751565\pi\) | ||||
−0.710576 | + | 0.703621i | \(0.751565\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.80619 | 0.147820 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.7724 | −0.805519 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 83.4264 | 3.23028 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.87042 | −0.265626 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.66345 | −0.373053 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.9767 | −1.57954 | −0.789768 | − | 0.613406i | \(-0.789799\pi\) | ||||
−0.789768 | + | 0.613406i | \(0.789799\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −29.6706 | −1.14202 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.97586 | −0.191238 | −0.0956190 | − | 0.995418i | \(-0.530483\pi\) | ||||
−0.0956190 | + | 0.995418i | \(0.530483\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.7285 | 0.641982 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.5979 | −0.559392 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.526478 | −0.0201451 | −0.0100726 | − | 0.999949i | \(-0.503206\pi\) | ||||
−0.0100726 | + | 0.999949i | \(0.503206\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.7491 | 1.25128 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.95817 | −0.0747088 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.67067 | 0.177939 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.68151 | −0.292218 | −0.146109 | − | 0.989268i | \(-0.546675\pi\) | ||||
−0.146109 | + | 0.989268i | \(0.546675\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.54195 | 0.0965606 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.7712 | −0.522372 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −50.2824 | −1.90458 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.4015 | 0.393422 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.29151 | 0.124319 | 0.0621593 | − | 0.998066i | \(-0.480201\pi\) | ||||
0.0621593 | + | 0.998066i | \(0.480201\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.2142 | 1.17727 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.39149 | 0.165393 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.2870 | −0.650143 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.4374 | 1.40599 | 0.702995 | − | 0.711194i | \(-0.251845\pi\) | ||||
0.702995 | + | 0.711194i | \(0.251845\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −28.4340 | −1.06636 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.1006 | 1.01492 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.59312 | 0.134375 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.2844 | −0.458771 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.8954 | −1.33867 | −0.669335 | − | 0.742960i | \(-0.733421\pi\) | ||||
−0.669335 | + | 0.742960i | \(0.733421\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | 0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.06036 | −0.0766257 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 75.8411 | 2.81667 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.15310 | 0.0427661 | 0.0213831 | − | 0.999771i | \(-0.493193\pi\) | ||||
0.0213831 | + | 0.999771i | \(0.493193\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.31628 | −0.196899 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.6356 | 0.837208 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.5439 | −0.906550 | −0.453275 | − | 0.891371i | \(-0.649745\pi\) | ||||
−0.453275 | + | 0.891371i | \(0.649745\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.43181 | 0.0896986 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.3992 | −0.419895 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.0467 | 1.76743 | 0.883714 | − | 0.468027i | \(-0.155035\pi\) | ||||
0.883714 | + | 0.468027i | \(0.155035\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.91265 | 0.143735 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.9216 | −0.950970 | −0.475485 | − | 0.879724i | \(-0.657727\pi\) | ||||
−0.475485 | + | 0.879724i | \(0.657727\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.9824 | 1.17174 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.285412 | 0.0104427 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.79615 | −0.211787 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.0776 | 0.440718 | 0.220359 | − | 0.975419i | \(-0.429277\pi\) | ||||
0.220359 | + | 0.975419i | \(0.429277\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.7004 | −0.389943 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.5992 | −0.567712 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.3929 | 0.414081 | 0.207041 | − | 0.978332i | \(-0.433617\pi\) | ||||
0.207041 | + | 0.978332i | \(0.433617\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.88929 | −0.213768 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.5386 | 0.853273 | 0.426637 | − | 0.904423i | \(-0.359698\pi\) | ||||
0.426637 | + | 0.904423i | \(0.359698\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.19381 | −0.0794213 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 51.3656 | 1.85713 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.19237 | −0.115270 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.2843 | 0.803592 | 0.401796 | − | 0.915729i | \(-0.368386\pi\) | ||||
0.401796 | + | 0.915729i | \(0.368386\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.46460 | −0.196803 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.3364 | 0.803384 | 0.401692 | − | 0.915775i | \(-0.368422\pi\) | ||||
0.401692 | + | 0.915775i | \(0.368422\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.6365 | 0.884970 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.65423 | −0.131095 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −51.6888 | −1.85194 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.18836 | 0.149871 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −35.9598 | −1.28510 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.1870 | 1.29157 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −47.3562 | −1.68806 | −0.844032 | − | 0.536292i | \(-0.819824\pi\) | ||||
−0.844032 | + | 0.536292i | \(0.819824\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.47034 | 0.159148 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.35215 | 0.296968 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.66345 | −0.343159 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.3582 | −0.402833 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.23258 | −0.220769 | −0.110385 | − | 0.993889i | \(-0.535208\pi\) | ||||
−0.110385 | + | 0.993889i | \(0.535208\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.1558 | −0.359288 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27.0098 | −0.954344 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.6610 | −0.446796 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 31.2664 | 1.10200 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.96401 | −0.139540 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.55541 | 0.160160 | 0.0800799 | − | 0.996788i | \(-0.474482\pi\) | ||||
0.0800799 | + | 0.996788i | \(0.474482\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.57597 | 0.160684 | 0.0803421 | − | 0.996767i | \(-0.474399\pi\) | ||||
0.0803421 | + | 0.996767i | \(0.474399\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.20489 | −0.322829 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.6737 | 0.478969 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.2687 | 0.814070 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.54195 | 0.0888229 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.2506 | 0.916153 | 0.458076 | − | 0.888913i | \(-0.348539\pi\) | ||||
0.458076 | + | 0.888913i | \(0.348539\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.5873 | 0.403907 | 0.201953 | − | 0.979395i | \(-0.435271\pi\) | ||||
0.201953 | + | 0.979395i | \(0.435271\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.35382 | −0.186396 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.9718 | −1.14654 | −0.573271 | − | 0.819366i | \(-0.694326\pi\) | ||||
−0.573271 | + | 0.819366i | \(0.694326\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.36535 | 0.255809 | 0.127905 | − | 0.991786i | \(-0.459175\pi\) | ||||
0.127905 | + | 0.991786i | \(0.459175\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.165579 | 0.00574388 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.62384 | −0.194855 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 57.0659 | 1.97485 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.6813 | −0.403766 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.74972 | 0.0949307 | 0.0474654 | − | 0.998873i | \(-0.484886\pi\) | ||||
0.0474654 | + | 0.998873i | \(0.484886\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 62.9171 | 2.16955 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.6672 | −0.367396 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.59312 | 0.123607 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.5760 | −0.500248 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −46.9834 | −1.61057 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.0998 | −0.722443 | −0.361222 | − | 0.932480i | \(-0.617640\pi\) | ||||
−0.361222 | + | 0.932480i | \(0.617640\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 52.8023 | 1.80580 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.65459 | 0.158998 | 0.0794989 | − | 0.996835i | \(-0.474668\pi\) | ||||
0.0794989 | + | 0.996835i | \(0.474668\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.1289 | −1.30094 | −0.650471 | − | 0.759531i | \(-0.725428\pi\) | ||||
−0.650471 | + | 0.759531i | \(0.725428\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.05118 | 0.206224 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.2902 | −0.894929 | −0.447464 | − | 0.894302i | \(-0.647673\pi\) | ||||
−0.447464 | + | 0.894302i | \(0.647673\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37.6859 | −1.28136 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.89990 | 0.336218 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.1859 | −0.379456 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.3992 | −0.386247 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −42.5231 | −1.43919 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.4579 | 0.353543 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.9230 | 0.740288 | 0.370144 | − | 0.928974i | \(-0.379308\pi\) | ||||
0.370144 | + | 0.928974i | \(0.379308\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.6632 | 0.562035 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.8363 | 1.17366 | 0.586832 | − | 0.809709i | \(-0.300375\pi\) | ||||
0.586832 | + | 0.809709i | \(0.300375\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 57.2116 | 1.92532 | 0.962662 | − | 0.270707i | \(-0.0872573\pi\) | ||||
0.962662 | + | 0.270707i | \(0.0872573\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.76323 | 0.260958 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.5586 | 0.757444 | 0.378722 | − | 0.925510i | \(-0.376364\pi\) | ||||
0.378722 | + | 0.925510i | \(0.376364\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.6650 | 0.391231 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.08735 | −0.170433 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.4399 | −0.349359 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 44.1077 | 1.47436 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.88929 | −0.196638 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 29.8587 | 0.995844 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.2671 | 0.875085 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.72405 | −0.0906509 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 72.3367 | 2.40455 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.6878 | −0.886152 | −0.443076 | − | 0.896484i | \(-0.646113\pi\) | ||||
−0.443076 | + | 0.896484i | \(0.646113\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 43.9426 | 1.45748 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.47959 | −0.0490211 | −0.0245106 | − | 0.999700i | \(-0.507803\pi\) | ||||
−0.0245106 | + | 0.999700i | \(0.507803\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.112281 | 0.00371595 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 23.4997 | 0.776875 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.6828 | 0.352777 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.1529 | 1.29154 | 0.645768 | − | 0.763534i | \(-0.276537\pi\) | ||||
0.645768 | + | 0.763534i | \(0.276537\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.2694 | −0.536094 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.18836 | 0.137861 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −42.7115 | −1.40435 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.3356 | −0.667908 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 53.2474 | 1.74699 | 0.873495 | − | 0.486834i | \(-0.161848\pi\) | ||||
0.873495 | + | 0.486834i | \(0.161848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.78115 | −0.189469 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.5834 | −0.346485 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.2072 | 0.660845 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.0294 | 0.458322 | 0.229161 | − | 0.973389i | \(-0.426402\pi\) | ||||
0.229161 | + | 0.973389i | \(0.426402\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.74834 | 0.187590 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 59.0549 | 1.92513 | 0.962567 | − | 0.271044i | \(-0.0873688\pi\) | ||||
0.962567 | + | 0.271044i | \(0.0873688\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 77.8015 | 2.53357 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.4770 | −0.438406 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.9227 | −0.452428 | −0.226214 | − | 0.974078i | \(-0.572635\pi\) | ||||
−0.226214 | + | 0.974078i | \(0.572635\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.6610 | −0.410993 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.7696 | −0.770783 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.7030 | −1.22132 | −0.610659 | − | 0.791893i | \(-0.709096\pi\) | ||||
−0.610659 | + | 0.791893i | \(0.709096\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35.2180 | −1.13963 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.48866 | −0.209749 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.11439 | 0.294319 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.3006 | −0.687115 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.7335 | 0.474781 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.8074 | 0.347901 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.5027 | −1.36679 | −0.683397 | − | 0.730047i | \(-0.739498\pi\) | ||||
−0.683397 | + | 0.730047i | \(0.739498\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22.0041 | 0.706875 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.4572 | 1.84389 | 0.921945 | − | 0.387320i | \(-0.126599\pi\) | ||||
0.921945 | + | 0.387320i | \(0.126599\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.83266 | −0.122869 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.35382 | −0.171459 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.6200 | −0.659691 | −0.329845 | − | 0.944035i | \(-0.606997\pi\) | ||||
−0.329845 | + | 0.944035i | \(0.606997\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.6256 | −0.339596 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.57655 | 0.178046 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.2574 | −1.06075 | −0.530373 | − | 0.847764i | \(-0.677948\pi\) | ||||
−0.530373 | + | 0.847764i | \(0.677948\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −58.3295 | −1.85853 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.22219 | 0.0389029 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.0239 | −1.11369 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.6901 | 0.561946 | 0.280973 | − | 0.959716i | \(-0.409343\pi\) | ||||
0.280973 | + | 0.959716i | \(0.409343\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.3019 | −0.549061 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −67.6778 | −2.14553 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.4947 | 0.902437 | 0.451218 | − | 0.892414i | \(-0.350990\pi\) | ||||
0.451218 | + | 0.892414i | \(0.350990\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.2515 | 0.640731 |
(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 | 8008.2.a.k.1.4 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.k.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial |