Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.228656 | 0.161684 | 0.0808419 | − | 0.996727i | \(-0.474239\pi\) | ||||
0.0808419 | + | 0.996727i | \(0.474239\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.94772 | −0.973858 | ||||||||
\(5\) | 0.872276 | 0.390094 | 0.195047 | − | 0.980794i | \(-0.437514\pi\) | ||||
0.195047 | + | 0.980794i | \(0.437514\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.27506 | −0.481927 | −0.240964 | − | 0.970534i | \(-0.577463\pi\) | ||||
−0.240964 | + | 0.970534i | \(0.577463\pi\) | |||||||
\(8\) | −0.902667 | −0.319141 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.199451 | 0.0630719 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.51971 | 1.53089 | 0.765445 | − | 0.643501i | \(-0.222519\pi\) | ||||
0.765445 | + | 0.643501i | \(0.222519\pi\) | |||||||
\(14\) | −0.291550 | −0.0779199 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.68903 | 0.922258 | ||||||||
\(17\) | −7.05471 | −1.71102 | −0.855510 | − | 0.517787i | \(-0.826756\pi\) | ||||
−0.855510 | + | 0.517787i | \(0.826756\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.53854 | −1.04121 | −0.520607 | − | 0.853797i | \(-0.674294\pi\) | ||||
−0.520607 | + | 0.853797i | \(0.674294\pi\) | |||||||
\(20\) | −1.69895 | −0.379896 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.228656 | 0.0487495 | ||||||||
\(23\) | 4.97643 | 1.03766 | 0.518829 | − | 0.854878i | \(-0.326368\pi\) | ||||
0.518829 | + | 0.854878i | \(0.326368\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.23913 | −0.847827 | ||||||||
\(26\) | 1.26211 | 0.247520 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.48346 | 0.469329 | ||||||||
\(29\) | −4.43142 | −0.822894 | −0.411447 | − | 0.911434i | \(-0.634976\pi\) | ||||
−0.411447 | + | 0.911434i | \(0.634976\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.49677 | 1.16685 | 0.583427 | − | 0.812166i | \(-0.301711\pi\) | ||||
0.583427 | + | 0.812166i | \(0.301711\pi\) | |||||||
\(32\) | 2.64885 | 0.468255 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.61310 | −0.276644 | ||||||||
\(35\) | −1.11220 | −0.187997 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.65721 | 0.765640 | 0.382820 | − | 0.923823i | \(-0.374953\pi\) | ||||
0.382820 | + | 0.923823i | \(0.374953\pi\) | |||||||
\(38\) | −1.03776 | −0.168347 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.787375 | −0.124495 | ||||||||
\(41\) | 2.47842 | 0.387065 | 0.193532 | − | 0.981094i | \(-0.438006\pi\) | ||||
0.193532 | + | 0.981094i | \(0.438006\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.76809 | −1.18462 | −0.592311 | − | 0.805709i | \(-0.701784\pi\) | ||||
−0.592311 | + | 0.805709i | \(0.701784\pi\) | |||||||
\(44\) | −1.94772 | −0.293629 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.13789 | 0.167772 | ||||||||
\(47\) | 0.452696 | 0.0660324 | 0.0330162 | − | 0.999455i | \(-0.489489\pi\) | ||||
0.0330162 | + | 0.999455i | \(0.489489\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.37422 | −0.767746 | ||||||||
\(50\) | −0.969302 | −0.137080 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10.7508 | −1.49087 | ||||||||
\(53\) | 6.10390 | 0.838435 | 0.419218 | − | 0.907886i | \(-0.362304\pi\) | ||||
0.419218 | + | 0.907886i | \(0.362304\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.872276 | 0.117618 | ||||||||
\(56\) | 1.15095 | 0.153803 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.01327 | −0.133049 | ||||||||
\(59\) | −0.139545 | −0.0181672 | −0.00908361 | − | 0.999959i | \(-0.502891\pi\) | ||||
−0.00908361 | + | 0.999959i | \(0.502891\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 1.48552 | 0.188661 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.77239 | −0.846549 | ||||||||
\(65\) | 4.81471 | 0.597191 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.75357 | 0.458572 | 0.229286 | − | 0.973359i | \(-0.426361\pi\) | ||||
0.229286 | + | 0.973359i | \(0.426361\pi\) | |||||||
\(68\) | 13.7406 | 1.66629 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.254312 | −0.0303961 | ||||||||
\(71\) | −9.37234 | −1.11229 | −0.556146 | − | 0.831085i | \(-0.687720\pi\) | ||||
−0.556146 | + | 0.831085i | \(0.687720\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.78042 | −0.208383 | −0.104191 | − | 0.994557i | \(-0.533225\pi\) | ||||
−0.104191 | + | 0.994557i | \(0.533225\pi\) | |||||||
\(74\) | 1.06490 | 0.123792 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.83980 | 1.01399 | ||||||||
\(77\) | −1.27506 | −0.145307 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.21606 | 0.249327 | 0.124663 | − | 0.992199i | \(-0.460215\pi\) | ||||
0.124663 | + | 0.992199i | \(0.460215\pi\) | |||||||
\(80\) | 3.21786 | 0.359767 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.566706 | 0.0625822 | ||||||||
\(83\) | 8.77256 | 0.962914 | 0.481457 | − | 0.876470i | \(-0.340108\pi\) | ||||
0.481457 | + | 0.876470i | \(0.340108\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.15366 | −0.667458 | ||||||||
\(86\) | −1.77622 | −0.191534 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.902667 | −0.0962246 | ||||||||
\(89\) | 1.14261 | 0.121116 | 0.0605582 | − | 0.998165i | \(-0.480712\pi\) | ||||
0.0605582 | + | 0.998165i | \(0.480712\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.03796 | −0.737778 | ||||||||
\(92\) | −9.69268 | −1.01053 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.103511 | 0.0106764 | ||||||||
\(95\) | −3.95886 | −0.406171 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.4430 | −1.46646 | −0.733232 | − | 0.679979i | \(-0.761989\pi\) | ||||
−0.733232 | + | 0.679979i | \(0.761989\pi\) | |||||||
\(98\) | −1.22885 | −0.124132 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.25663 | 0.825663 | ||||||||
\(101\) | −7.74593 | −0.770749 | −0.385375 | − | 0.922760i | \(-0.625928\pi\) | ||||
−0.385375 | + | 0.922760i | \(0.625928\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7975 | 1.06391 | 0.531954 | − | 0.846774i | \(-0.321458\pi\) | ||||
0.531954 | + | 0.846774i | \(0.321458\pi\) | |||||||
\(104\) | −4.98246 | −0.488570 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.39569 | 0.135561 | ||||||||
\(107\) | −19.0879 | −1.84529 | −0.922647 | − | 0.385645i | \(-0.873979\pi\) | ||||
−0.922647 | + | 0.385645i | \(0.873979\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.61246 | 0.824924 | 0.412462 | − | 0.910975i | \(-0.364669\pi\) | ||||
0.412462 | + | 0.910975i | \(0.364669\pi\) | |||||||
\(110\) | 0.199451 | 0.0190169 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.70374 | −0.444462 | ||||||||
\(113\) | 15.7297 | 1.47973 | 0.739864 | − | 0.672757i | \(-0.234890\pi\) | ||||
0.739864 | + | 0.672757i | \(0.234890\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.34082 | 0.404784 | ||||||||
\(116\) | 8.63115 | 0.801382 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.0319078 | −0.00293735 | ||||||||
\(119\) | 8.99518 | 0.824587 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.228656 | 0.0207015 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.6539 | −1.13635 | ||||||||
\(125\) | −8.05908 | −0.720826 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.6857 | −1.74682 | −0.873411 | − | 0.486983i | \(-0.838097\pi\) | ||||
−0.873411 | + | 0.486983i | \(0.838097\pi\) | |||||||
\(128\) | −6.84625 | −0.605129 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.10091 | 0.0965561 | ||||||||
\(131\) | −0.673702 | −0.0588616 | −0.0294308 | − | 0.999567i | \(-0.509369\pi\) | ||||
−0.0294308 | + | 0.999567i | \(0.509369\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.78692 | 0.501789 | ||||||||
\(134\) | 0.858275 | 0.0741436 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.36806 | 0.546056 | ||||||||
\(137\) | −1.45200 | −0.124053 | −0.0620265 | − | 0.998075i | \(-0.519756\pi\) | ||||
−0.0620265 | + | 0.998075i | \(0.519756\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.97052 | 0.251956 | 0.125978 | − | 0.992033i | \(-0.459793\pi\) | ||||
0.125978 | + | 0.992033i | \(0.459793\pi\) | |||||||
\(140\) | 2.16626 | 0.183082 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.14304 | −0.179840 | ||||||||
\(143\) | 5.51971 | 0.461581 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.86542 | −0.321006 | ||||||||
\(146\) | −0.407103 | −0.0336921 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.07092 | −0.745625 | ||||||||
\(149\) | −11.2111 | −0.918445 | −0.459223 | − | 0.888321i | \(-0.651872\pi\) | ||||
−0.459223 | + | 0.888321i | \(0.651872\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.09238 | −0.658549 | −0.329274 | − | 0.944234i | \(-0.606804\pi\) | ||||
−0.329274 | + | 0.944234i | \(0.606804\pi\) | |||||||
\(152\) | 4.09680 | 0.332294 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.291550 | −0.0234937 | ||||||||
\(155\) | 5.66697 | 0.455182 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.24491 | −0.338780 | −0.169390 | − | 0.985549i | \(-0.554180\pi\) | ||||
−0.169390 | + | 0.985549i | \(0.554180\pi\) | |||||||
\(158\) | 0.506715 | 0.0403121 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.31053 | 0.182663 | ||||||||
\(161\) | −6.34525 | −0.500076 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.14603 | −0.0897639 | −0.0448820 | − | 0.998992i | \(-0.514291\pi\) | ||||
−0.0448820 | + | 0.998992i | \(0.514291\pi\) | |||||||
\(164\) | −4.82727 | −0.376946 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.00590 | 0.155688 | ||||||||
\(167\) | −22.4452 | −1.73686 | −0.868432 | − | 0.495808i | \(-0.834872\pi\) | ||||
−0.868432 | + | 0.495808i | \(0.834872\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.4671 | 1.34363 | ||||||||
\(170\) | −1.40707 | −0.107917 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15.1300 | 1.15365 | ||||||||
\(173\) | −21.3279 | −1.62153 | −0.810767 | − | 0.585370i | \(-0.800949\pi\) | ||||
−0.810767 | + | 0.585370i | \(0.800949\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.40515 | 0.408591 | ||||||||
\(176\) | 3.68903 | 0.278071 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.261264 | 0.0195826 | ||||||||
\(179\) | 21.8476 | 1.63296 | 0.816482 | − | 0.577371i | \(-0.195921\pi\) | ||||
0.816482 | + | 0.577371i | \(0.195921\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.4857 | 0.853725 | 0.426862 | − | 0.904317i | \(-0.359619\pi\) | ||||
0.426862 | + | 0.904317i | \(0.359619\pi\) | |||||||
\(182\) | −1.60927 | −0.119287 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.49206 | −0.331159 | ||||||||
\(185\) | 4.06237 | 0.298672 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.05471 | −0.515892 | ||||||||
\(188\) | −0.881723 | −0.0643062 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.905216 | −0.0656713 | ||||||||
\(191\) | 4.38460 | 0.317258 | 0.158629 | − | 0.987338i | \(-0.449293\pi\) | ||||
0.158629 | + | 0.987338i | \(0.449293\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.2587 | 1.53023 | 0.765116 | − | 0.643893i | \(-0.222682\pi\) | ||||
0.765116 | + | 0.643893i | \(0.222682\pi\) | |||||||
\(194\) | −3.30247 | −0.237104 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.4675 | 0.747676 | ||||||||
\(197\) | −9.17680 | −0.653820 | −0.326910 | − | 0.945055i | \(-0.606007\pi\) | ||||
−0.326910 | + | 0.945055i | \(0.606007\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.4269 | −0.739146 | −0.369573 | − | 0.929202i | \(-0.620496\pi\) | ||||
−0.369573 | + | 0.929202i | \(0.620496\pi\) | |||||||
\(200\) | 3.82653 | 0.270576 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.77115 | −0.124618 | ||||||||
\(203\) | 5.65032 | 0.396575 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.16187 | 0.150992 | ||||||||
\(206\) | 2.46890 | 0.172017 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20.3624 | 1.41188 | ||||||||
\(209\) | −4.53854 | −0.313938 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.89024 | −0.267815 | −0.133908 | − | 0.990994i | \(-0.542753\pi\) | ||||
−0.133908 | + | 0.990994i | \(0.542753\pi\) | |||||||
\(212\) | −11.8887 | −0.816517 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.36455 | −0.298354 | ||||||||
\(215\) | −6.77592 | −0.462114 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.28377 | −0.562339 | ||||||||
\(218\) | 1.96929 | 0.133377 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.69895 | −0.114543 | ||||||||
\(221\) | −38.9399 | −2.61938 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.7363 | −0.718954 | −0.359477 | − | 0.933154i | \(-0.617045\pi\) | ||||
−0.359477 | + | 0.933154i | \(0.617045\pi\) | |||||||
\(224\) | −3.37745 | −0.225665 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.59669 | 0.239248 | ||||||||
\(227\) | −15.2522 | −1.01233 | −0.506163 | − | 0.862438i | \(-0.668936\pi\) | ||||
−0.506163 | + | 0.862438i | \(0.668936\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.4919 | 0.693322 | 0.346661 | − | 0.937990i | \(-0.387315\pi\) | ||||
0.346661 | + | 0.937990i | \(0.387315\pi\) | |||||||
\(230\) | 0.992553 | 0.0654470 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.00010 | 0.262619 | ||||||||
\(233\) | −19.5688 | −1.28199 | −0.640996 | − | 0.767544i | \(-0.721479\pi\) | ||||
−0.640996 | + | 0.767544i | \(0.721479\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.394876 | 0.0257588 | ||||||||
\(236\) | 0.271794 | 0.0176923 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.05680 | 0.133322 | ||||||||
\(239\) | −6.22136 | −0.402426 | −0.201213 | − | 0.979548i | \(-0.564488\pi\) | ||||
−0.201213 | + | 0.979548i | \(0.564488\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.10210 | −0.521902 | −0.260951 | − | 0.965352i | \(-0.584036\pi\) | ||||
−0.260951 | + | 0.965352i | \(0.584036\pi\) | |||||||
\(242\) | 0.228656 | 0.0146985 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.94772 | −0.124690 | ||||||||
\(245\) | −4.68780 | −0.299493 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.0514 | −1.59398 | ||||||||
\(248\) | −5.86442 | −0.372391 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.84275 | −0.116546 | ||||||||
\(251\) | −13.5672 | −0.856357 | −0.428178 | − | 0.903694i | \(-0.640844\pi\) | ||||
−0.428178 | + | 0.903694i | \(0.640844\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.97643 | 0.312866 | ||||||||
\(254\) | −4.50124 | −0.282433 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.9794 | 0.748709 | ||||||||
\(257\) | −10.5711 | −0.659409 | −0.329705 | − | 0.944084i | \(-0.606949\pi\) | ||||
−0.329705 | + | 0.944084i | \(0.606949\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.93822 | −0.368983 | ||||||||
\(260\) | −9.37768 | −0.581579 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.154046 | −0.00951697 | ||||||||
\(263\) | −16.1723 | −0.997226 | −0.498613 | − | 0.866825i | \(-0.666157\pi\) | ||||
−0.498613 | + | 0.866825i | \(0.666157\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.32429 | 0.327068 | ||||||||
\(266\) | 1.32321 | 0.0811312 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.31089 | −0.446584 | ||||||||
\(269\) | −26.3605 | −1.60723 | −0.803615 | − | 0.595150i | \(-0.797093\pi\) | ||||
−0.803615 | + | 0.595150i | \(0.797093\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.6166 | −0.766402 | −0.383201 | − | 0.923665i | \(-0.625178\pi\) | ||||
−0.383201 | + | 0.923665i | \(0.625178\pi\) | |||||||
\(272\) | −26.0251 | −1.57800 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.332009 | −0.0200574 | ||||||||
\(275\) | −4.23913 | −0.255629 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.4948 | 1.05116 | 0.525582 | − | 0.850743i | \(-0.323848\pi\) | ||||
0.525582 | + | 0.850743i | \(0.323848\pi\) | |||||||
\(278\) | 0.679225 | 0.0407372 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.00395 | 0.0599975 | ||||||||
\(281\) | −30.0039 | −1.78988 | −0.894940 | − | 0.446186i | \(-0.852782\pi\) | ||||
−0.894940 | + | 0.446186i | \(0.852782\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.33845 | −0.495669 | −0.247835 | − | 0.968802i | \(-0.579719\pi\) | ||||
−0.247835 | + | 0.968802i | \(0.579719\pi\) | |||||||
\(284\) | 18.2547 | 1.08321 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.26211 | 0.0746302 | ||||||||
\(287\) | −3.16014 | −0.186537 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.7690 | 1.92759 | ||||||||
\(290\) | −0.883849 | −0.0519014 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.46776 | 0.202935 | ||||||||
\(293\) | −19.7968 | −1.15654 | −0.578271 | − | 0.815845i | \(-0.696272\pi\) | ||||
−0.578271 | + | 0.815845i | \(0.696272\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.121722 | −0.00708692 | ||||||||
\(296\) | −4.20391 | −0.244347 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.56347 | −0.148498 | ||||||||
\(299\) | 27.4684 | 1.58854 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.90478 | 0.570902 | ||||||||
\(302\) | −1.85037 | −0.106477 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −16.7428 | −0.960268 | ||||||||
\(305\) | 0.872276 | 0.0499464 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.5355 | 1.40031 | 0.700157 | − | 0.713989i | \(-0.253113\pi\) | ||||
0.700157 | + | 0.713989i | \(0.253113\pi\) | |||||||
\(308\) | 2.48346 | 0.141508 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.29578 | 0.0735956 | ||||||||
\(311\) | −12.5596 | −0.712189 | −0.356095 | − | 0.934450i | \(-0.615892\pi\) | ||||
−0.356095 | + | 0.934450i | \(0.615892\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.1430 | −1.87336 | −0.936678 | − | 0.350192i | \(-0.886116\pi\) | ||||
−0.936678 | + | 0.350192i | \(0.886116\pi\) | |||||||
\(314\) | −0.970621 | −0.0547753 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.31627 | −0.242809 | ||||||||
\(317\) | −19.6616 | −1.10430 | −0.552152 | − | 0.833743i | \(-0.686193\pi\) | ||||
−0.552152 | + | 0.833743i | \(0.686193\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.43142 | −0.248112 | ||||||||
\(320\) | −5.90740 | −0.330233 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.45088 | −0.0808542 | ||||||||
\(323\) | 32.0181 | 1.78154 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −23.3988 | −1.29793 | ||||||||
\(326\) | −0.262046 | −0.0145134 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.23719 | −0.123528 | ||||||||
\(329\) | −0.577214 | −0.0318228 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.7900 | −1.25265 | −0.626327 | − | 0.779561i | \(-0.715442\pi\) | ||||
−0.626327 | + | 0.779561i | \(0.715442\pi\) | |||||||
\(332\) | −17.0865 | −0.937742 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.13223 | −0.280823 | ||||||||
\(335\) | 3.27415 | 0.178886 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.19401 | 0.119515 | 0.0597577 | − | 0.998213i | \(-0.480967\pi\) | ||||
0.0597577 | + | 0.998213i | \(0.480967\pi\) | |||||||
\(338\) | 3.99396 | 0.217243 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.9856 | 0.650009 | ||||||||
\(341\) | 6.49677 | 0.351820 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.7779 | 0.851925 | ||||||||
\(344\) | 7.01200 | 0.378062 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.87675 | −0.262176 | ||||||||
\(347\) | 17.6560 | 0.947824 | 0.473912 | − | 0.880572i | \(-0.342841\pi\) | ||||
0.473912 | + | 0.880572i | \(0.342841\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.91008 | −0.316359 | −0.158180 | − | 0.987410i | \(-0.550563\pi\) | ||||
−0.158180 | + | 0.987410i | \(0.550563\pi\) | |||||||
\(350\) | 1.23592 | 0.0660626 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.64885 | 0.141184 | ||||||||
\(353\) | 30.2566 | 1.61039 | 0.805197 | − | 0.593007i | \(-0.202059\pi\) | ||||
0.805197 | + | 0.593007i | \(0.202059\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.17527 | −0.433898 | ||||||||
\(356\) | −2.22548 | −0.117950 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.99557 | 0.264024 | ||||||||
\(359\) | −1.17480 | −0.0620035 | −0.0310018 | − | 0.999519i | \(-0.509870\pi\) | ||||
−0.0310018 | + | 0.999519i | \(0.509870\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.59839 | 0.0841256 | ||||||||
\(362\) | 2.62627 | 0.138034 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.7079 | 0.718491 | ||||||||
\(365\) | −1.55302 | −0.0812888 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.0252 | 1.25411 | 0.627053 | − | 0.778976i | \(-0.284261\pi\) | ||||
0.627053 | + | 0.778976i | \(0.284261\pi\) | |||||||
\(368\) | 18.3582 | 0.956988 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.928884 | 0.0482904 | ||||||||
\(371\) | −7.78284 | −0.404065 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.0830 | −1.45408 | −0.727041 | − | 0.686594i | \(-0.759105\pi\) | ||||
−0.727041 | + | 0.686594i | \(0.759105\pi\) | |||||||
\(374\) | −1.61310 | −0.0834114 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.408634 | −0.0210737 | ||||||||
\(377\) | −24.4601 | −1.25976 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.6191 | −1.93236 | −0.966181 | − | 0.257863i | \(-0.916982\pi\) | ||||
−0.966181 | + | 0.257863i | \(0.916982\pi\) | |||||||
\(380\) | 7.71074 | 0.395553 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.00256 | 0.0512956 | ||||||||
\(383\) | −35.7407 | −1.82627 | −0.913133 | − | 0.407662i | \(-0.866344\pi\) | ||||
−0.913133 | + | 0.407662i | \(0.866344\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.11220 | −0.0566832 | ||||||||
\(386\) | 4.86091 | 0.247414 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 28.1309 | 1.42813 | ||||||||
\(389\) | −2.59704 | −0.131675 | −0.0658375 | − | 0.997830i | \(-0.520972\pi\) | ||||
−0.0658375 | + | 0.997830i | \(0.520972\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.1073 | −1.77545 | ||||||||
\(392\) | 4.85113 | 0.245019 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.09833 | −0.105712 | ||||||||
\(395\) | 1.93302 | 0.0972608 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.903397 | −0.0453402 | −0.0226701 | − | 0.999743i | \(-0.507217\pi\) | ||||
−0.0226701 | + | 0.999743i | \(0.507217\pi\) | |||||||
\(398\) | −2.38418 | −0.119508 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −15.6383 | −0.781915 | ||||||||
\(401\) | 9.59179 | 0.478991 | 0.239496 | − | 0.970897i | \(-0.423018\pi\) | ||||
0.239496 | + | 0.970897i | \(0.423018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.8602 | 1.78633 | ||||||||
\(404\) | 15.0869 | 0.750600 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.29198 | 0.0641198 | ||||||||
\(407\) | 4.65721 | 0.230849 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.5997 | 1.51306 | 0.756530 | − | 0.653959i | \(-0.226893\pi\) | ||||
0.756530 | + | 0.653959i | \(0.226893\pi\) | |||||||
\(410\) | 0.494324 | 0.0244129 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −21.0304 | −1.03609 | ||||||||
\(413\) | 0.177928 | 0.00875528 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.65210 | 0.375627 | ||||||||
\(416\) | 14.6209 | 0.716848 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.03776 | −0.0507587 | ||||||||
\(419\) | −24.7763 | −1.21040 | −0.605200 | − | 0.796073i | \(-0.706907\pi\) | ||||
−0.605200 | + | 0.796073i | \(0.706907\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.8172 | −0.965829 | −0.482915 | − | 0.875667i | \(-0.660422\pi\) | ||||
−0.482915 | + | 0.875667i | \(0.660422\pi\) | |||||||
\(422\) | −0.889525 | −0.0433014 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.50979 | −0.267579 | ||||||||
\(425\) | 29.9059 | 1.45065 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.27506 | −0.0617045 | ||||||||
\(428\) | 37.1778 | 1.79706 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.54935 | −0.0747163 | ||||||||
\(431\) | 27.7911 | 1.33865 | 0.669326 | − | 0.742969i | \(-0.266583\pi\) | ||||
0.669326 | + | 0.742969i | \(0.266583\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.0090 | 1.82660 | 0.913298 | − | 0.407292i | \(-0.133527\pi\) | ||||
0.913298 | + | 0.407292i | \(0.133527\pi\) | |||||||
\(434\) | −1.89413 | −0.0909211 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.7746 | −0.803359 | ||||||||
\(437\) | −22.5858 | −1.08042 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.9234 | 1.76226 | 0.881129 | − | 0.472875i | \(-0.156784\pi\) | ||||
0.881129 | + | 0.472875i | \(0.156784\pi\) | |||||||
\(440\) | −0.787375 | −0.0375366 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.90383 | −0.423512 | ||||||||
\(443\) | 1.62999 | 0.0774432 | 0.0387216 | − | 0.999250i | \(-0.487671\pi\) | ||||
0.0387216 | + | 0.999250i | \(0.487671\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.996671 | 0.0472468 | ||||||||
\(446\) | −2.45491 | −0.116243 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.63521 | 0.407975 | ||||||||
\(449\) | −23.0716 | −1.08882 | −0.544409 | − | 0.838820i | \(-0.683246\pi\) | ||||
−0.544409 | + | 0.838820i | \(0.683246\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.47842 | 0.116704 | ||||||||
\(452\) | −30.6370 | −1.44104 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.48750 | −0.163677 | ||||||||
\(455\) | −6.13904 | −0.287803 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.09124 | 0.0510458 | 0.0255229 | − | 0.999674i | \(-0.491875\pi\) | ||||
0.0255229 | + | 0.999674i | \(0.491875\pi\) | |||||||
\(458\) | 2.39902 | 0.112099 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.45469 | −0.394202 | ||||||||
\(461\) | 41.4760 | 1.93173 | 0.965865 | − | 0.259045i | \(-0.0834078\pi\) | ||||
0.965865 | + | 0.259045i | \(0.0834078\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.5447 | −1.65190 | −0.825950 | − | 0.563743i | \(-0.809361\pi\) | ||||
−0.825950 | + | 0.563743i | \(0.809361\pi\) | |||||||
\(464\) | −16.3476 | −0.758920 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.47451 | −0.207277 | ||||||||
\(467\) | −11.2608 | −0.521089 | −0.260545 | − | 0.965462i | \(-0.583902\pi\) | ||||
−0.260545 | + | 0.965462i | \(0.583902\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.78603 | −0.220998 | ||||||||
\(470\) | 0.0902905 | 0.00416479 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.125963 | 0.00579791 | ||||||||
\(473\) | −7.76809 | −0.357177 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.2395 | 0.882769 | ||||||||
\(476\) | −17.5201 | −0.803031 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.42255 | −0.0650658 | ||||||||
\(479\) | 6.51581 | 0.297715 | 0.148858 | − | 0.988859i | \(-0.452440\pi\) | ||||
0.148858 | + | 0.988859i | \(0.452440\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.7064 | 1.17211 | ||||||||
\(482\) | −1.85259 | −0.0843832 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.94772 | −0.0885326 | ||||||||
\(485\) | −12.5983 | −0.572058 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.85588 | 0.265355 | 0.132678 | − | 0.991159i | \(-0.457643\pi\) | ||||
0.132678 | + | 0.991159i | \(0.457643\pi\) | |||||||
\(488\) | −0.902667 | −0.0408618 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.07189 | −0.0484232 | ||||||||
\(491\) | 26.7877 | 1.20891 | 0.604457 | − | 0.796638i | \(-0.293390\pi\) | ||||
0.604457 | + | 0.796638i | \(0.293390\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.2624 | 1.40799 | ||||||||
\(494\) | −5.72815 | −0.257722 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.9668 | 1.07614 | ||||||||
\(497\) | 11.9503 | 0.536044 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.6065 | 0.743410 | 0.371705 | − | 0.928351i | \(-0.378773\pi\) | ||||
0.371705 | + | 0.928351i | \(0.378773\pi\) | |||||||
\(500\) | 15.6968 | 0.701982 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.10222 | −0.138459 | ||||||||
\(503\) | 29.9324 | 1.33462 | 0.667311 | − | 0.744780i | \(-0.267445\pi\) | ||||
0.667311 | + | 0.744780i | \(0.267445\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.75659 | −0.300664 | ||||||||
\(506\) | 1.13789 | 0.0505853 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 38.3421 | 1.70116 | ||||||||
\(509\) | 14.6222 | 0.648115 | 0.324058 | − | 0.946037i | \(-0.394953\pi\) | ||||
0.324058 | + | 0.946037i | \(0.394953\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.27015 | 0.100425 | ||||||||
\(512\) | 16.4316 | 0.726183 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.41715 | −0.106616 | ||||||||
\(515\) | 9.41838 | 0.415023 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.452696 | 0.0199095 | ||||||||
\(518\) | −1.35781 | −0.0596586 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.34608 | −0.190588 | ||||||||
\(521\) | −14.8066 | −0.648691 | −0.324345 | − | 0.945939i | \(-0.605144\pi\) | ||||
−0.324345 | + | 0.945939i | \(0.605144\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.9722 | 0.785868 | 0.392934 | − | 0.919567i | \(-0.371460\pi\) | ||||
0.392934 | + | 0.919567i | \(0.371460\pi\) | |||||||
\(524\) | 1.31218 | 0.0573229 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.69788 | −0.161235 | ||||||||
\(527\) | −45.8328 | −1.99651 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.76487 | 0.0767333 | ||||||||
\(530\) | 1.21743 | 0.0528817 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.2713 | −0.488672 | ||||||||
\(533\) | 13.6802 | 0.592554 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.6499 | −0.719838 | ||||||||
\(536\) | −3.38822 | −0.146349 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.02748 | −0.259863 | ||||||||
\(539\) | −5.37422 | −0.231484 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.6601 | −1.70512 | −0.852560 | − | 0.522630i | \(-0.824951\pi\) | ||||
−0.852560 | + | 0.522630i | \(0.824951\pi\) | |||||||
\(542\) | −2.88485 | −0.123915 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −18.6869 | −0.801194 | ||||||||
\(545\) | 7.51244 | 0.321798 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.78206 | 0.375494 | 0.187747 | − | 0.982217i | \(-0.439882\pi\) | ||||
0.187747 | + | 0.982217i | \(0.439882\pi\) | |||||||
\(548\) | 2.82809 | 0.120810 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.969302 | −0.0413312 | ||||||||
\(551\) | 20.1122 | 0.856808 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.82562 | −0.120157 | ||||||||
\(554\) | 4.00029 | 0.169956 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.78573 | −0.245369 | ||||||||
\(557\) | −39.5326 | −1.67505 | −0.837525 | − | 0.546399i | \(-0.815998\pi\) | ||||
−0.837525 | + | 0.546399i | \(0.815998\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −42.8776 | −1.81353 | ||||||||
\(560\) | −4.10296 | −0.173382 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.86055 | −0.289395 | ||||||||
\(563\) | −27.6996 | −1.16740 | −0.583699 | − | 0.811970i | \(-0.698395\pi\) | ||||
−0.583699 | + | 0.811970i | \(0.698395\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.7207 | 0.577232 | ||||||||
\(566\) | −1.90663 | −0.0801417 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.46010 | 0.354978 | ||||||||
\(569\) | −39.6326 | −1.66149 | −0.830743 | − | 0.556657i | \(-0.812084\pi\) | ||||
−0.830743 | + | 0.556657i | \(0.812084\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.5752 | 0.902895 | 0.451448 | − | 0.892298i | \(-0.350908\pi\) | ||||
0.451448 | + | 0.892298i | \(0.350908\pi\) | |||||||
\(572\) | −10.7508 | −0.449514 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.722584 | −0.0301601 | ||||||||
\(575\) | −21.0958 | −0.879754 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.4143 | 0.724965 | 0.362483 | − | 0.931990i | \(-0.381929\pi\) | ||||
0.362483 | + | 0.931990i | \(0.381929\pi\) | |||||||
\(578\) | 7.49281 | 0.311660 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.52874 | 0.312614 | ||||||||
\(581\) | −11.1855 | −0.464055 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.10390 | 0.252798 | ||||||||
\(584\) | 1.60713 | 0.0665035 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.52665 | −0.186994 | ||||||||
\(587\) | 46.6587 | 1.92581 | 0.962905 | − | 0.269841i | \(-0.0869713\pi\) | ||||
0.962905 | + | 0.269841i | \(0.0869713\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.4859 | −1.21494 | ||||||||
\(590\) | −0.0278324 | −0.00114584 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17.1806 | 0.706118 | ||||||||
\(593\) | −33.5666 | −1.37841 | −0.689207 | − | 0.724565i | \(-0.742041\pi\) | ||||
−0.689207 | + | 0.724565i | \(0.742041\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.84628 | 0.321666 | ||||||||
\(596\) | 21.8360 | 0.894436 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.28081 | 0.256841 | ||||||||
\(599\) | −19.0292 | −0.777511 | −0.388755 | − | 0.921341i | \(-0.627095\pi\) | ||||
−0.388755 | + | 0.921341i | \(0.627095\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.94500 | −0.160920 | −0.0804599 | − | 0.996758i | \(-0.525639\pi\) | ||||
−0.0804599 | + | 0.996758i | \(0.525639\pi\) | |||||||
\(602\) | 2.26478 | 0.0923057 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 15.7617 | 0.641333 | ||||||||
\(605\) | 0.872276 | 0.0354631 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.6943 | 1.61114 | 0.805572 | − | 0.592498i | \(-0.201858\pi\) | ||||
0.805572 | + | 0.592498i | \(0.201858\pi\) | |||||||
\(608\) | −12.0219 | −0.487554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.199451 | 0.00807552 | ||||||||
\(611\) | 2.49875 | 0.101088 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.7680 | 0.758032 | 0.379016 | − | 0.925390i | \(-0.376263\pi\) | ||||
0.379016 | + | 0.925390i | \(0.376263\pi\) | |||||||
\(614\) | 5.61018 | 0.226408 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.15095 | 0.0463733 | ||||||||
\(617\) | 29.2101 | 1.17596 | 0.587978 | − | 0.808877i | \(-0.299924\pi\) | ||||
0.587978 | + | 0.808877i | \(0.299924\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.1366 | 0.568196 | 0.284098 | − | 0.958795i | \(-0.408306\pi\) | ||||
0.284098 | + | 0.958795i | \(0.408306\pi\) | |||||||
\(620\) | −11.0377 | −0.443283 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.87182 | −0.115150 | ||||||||
\(623\) | −1.45690 | −0.0583693 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.1659 | 0.566637 | ||||||||
\(626\) | −7.57834 | −0.302891 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.26788 | 0.329924 | ||||||||
\(629\) | −32.8553 | −1.31003 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.9034 | 1.62834 | 0.814168 | − | 0.580629i | \(-0.197193\pi\) | ||||
0.814168 | + | 0.580629i | \(0.197193\pi\) | |||||||
\(632\) | −2.00037 | −0.0795704 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.49573 | −0.178548 | ||||||||
\(635\) | −17.1714 | −0.681425 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.6641 | −1.17534 | ||||||||
\(638\) | −1.01327 | −0.0401157 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.97182 | −0.236057 | ||||||||
\(641\) | 6.36622 | 0.251451 | 0.125725 | − | 0.992065i | \(-0.459874\pi\) | ||||
0.125725 | + | 0.992065i | \(0.459874\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.54743 | −0.218769 | −0.109385 | − | 0.993999i | \(-0.534888\pi\) | ||||
−0.109385 | + | 0.993999i | \(0.534888\pi\) | |||||||
\(644\) | 12.3587 | 0.487003 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.32112 | 0.288046 | ||||||||
\(647\) | −28.2144 | −1.10922 | −0.554611 | − | 0.832110i | \(-0.687133\pi\) | ||||
−0.554611 | + | 0.832110i | \(0.687133\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.139545 | −0.00547762 | ||||||||
\(650\) | −5.35026 | −0.209854 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.23214 | 0.0874173 | ||||||||
\(653\) | −18.9375 | −0.741081 | −0.370541 | − | 0.928816i | \(-0.620828\pi\) | ||||
−0.370541 | + | 0.928816i | \(0.620828\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.587654 | −0.0229615 | ||||||||
\(656\) | 9.14299 | 0.356974 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.131983 | −0.00514524 | ||||||||
\(659\) | 47.8590 | 1.86432 | 0.932162 | − | 0.362042i | \(-0.117920\pi\) | ||||
0.932162 | + | 0.362042i | \(0.117920\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.723538 | 0.0281424 | 0.0140712 | − | 0.999901i | \(-0.495521\pi\) | ||||
0.0140712 | + | 0.999901i | \(0.495521\pi\) | |||||||
\(662\) | −5.21107 | −0.202534 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.91871 | −0.307305 | ||||||||
\(665\) | 5.04779 | 0.195745 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.0526 | −0.853882 | ||||||||
\(668\) | 43.7169 | 1.69146 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.748652 | 0.0289230 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.8807 | −1.19037 | −0.595183 | − | 0.803591i | \(-0.702920\pi\) | ||||
−0.595183 | + | 0.803591i | \(0.702920\pi\) | |||||||
\(674\) | 0.501673 | 0.0193237 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −34.0210 | −1.30850 | ||||||||
\(677\) | −25.9471 | −0.997229 | −0.498615 | − | 0.866824i | \(-0.666158\pi\) | ||||
−0.498615 | + | 0.866824i | \(0.666158\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.4157 | 0.706729 | ||||||||
\(680\) | 5.55470 | 0.213013 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.48552 | 0.0568836 | ||||||||
\(683\) | 12.5338 | 0.479594 | 0.239797 | − | 0.970823i | \(-0.422919\pi\) | ||||
0.239797 | + | 0.970823i | \(0.422919\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.26655 | −0.0483923 | ||||||||
\(686\) | 3.60770 | 0.137743 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −28.6567 | −1.09253 | ||||||||
\(689\) | 33.6917 | 1.28355 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.77262 | −0.333726 | −0.166863 | − | 0.985980i | \(-0.553364\pi\) | ||||
−0.166863 | + | 0.985980i | \(0.553364\pi\) | |||||||
\(692\) | 41.5408 | 1.57914 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.03714 | 0.153248 | ||||||||
\(695\) | 2.59111 | 0.0982865 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.4846 | −0.662276 | ||||||||
\(698\) | −1.35137 | −0.0511502 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10.5277 | −0.397910 | ||||||||
\(701\) | −18.7353 | −0.707621 | −0.353810 | − | 0.935317i | \(-0.615114\pi\) | ||||
−0.353810 | + | 0.935317i | \(0.615114\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.1370 | −0.797195 | ||||||||
\(704\) | −6.77239 | −0.255244 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.91833 | 0.260375 | ||||||||
\(707\) | 9.87653 | 0.371445 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.04862 | −0.264716 | −0.132358 | − | 0.991202i | \(-0.542255\pi\) | ||||
−0.132358 | + | 0.991202i | \(0.542255\pi\) | |||||||
\(710\) | −1.86932 | −0.0701543 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.03140 | −0.0386532 | ||||||||
\(713\) | 32.3307 | 1.21079 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.81471 | 0.180060 | ||||||||
\(716\) | −42.5529 | −1.59028 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.268624 | −0.0100250 | ||||||||
\(719\) | −17.4437 | −0.650540 | −0.325270 | − | 0.945621i | \(-0.605455\pi\) | ||||
−0.325270 | + | 0.945621i | \(0.605455\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.7674 | −0.512726 | ||||||||
\(722\) | 0.365480 | 0.0136018 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22.3709 | −0.831407 | ||||||||
\(725\) | 18.7854 | 0.697671 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.9461 | 1.40734 | 0.703671 | − | 0.710526i | \(-0.251543\pi\) | ||||
0.703671 | + | 0.710526i | \(0.251543\pi\) | |||||||
\(728\) | 6.35293 | 0.235455 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.355107 | −0.0131431 | ||||||||
\(731\) | 54.8016 | 2.02691 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −50.3118 | −1.85831 | −0.929154 | − | 0.369693i | \(-0.879463\pi\) | ||||
−0.929154 | + | 0.369693i | \(0.879463\pi\) | |||||||
\(734\) | 5.49350 | 0.202769 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.1818 | 0.485889 | ||||||||
\(737\) | 3.75357 | 0.138265 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.3697 | −1.30110 | −0.650549 | − | 0.759465i | \(-0.725461\pi\) | ||||
−0.650549 | + | 0.759465i | \(0.725461\pi\) | |||||||
\(740\) | −7.91235 | −0.290864 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.77959 | −0.0653308 | ||||||||
\(743\) | −2.96335 | −0.108715 | −0.0543574 | − | 0.998522i | \(-0.517311\pi\) | ||||
−0.0543574 | + | 0.998522i | \(0.517311\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.77914 | −0.358280 | ||||||||
\(746\) | −6.42133 | −0.235102 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13.7406 | 0.502405 | ||||||||
\(749\) | 24.3382 | 0.889298 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.2766 | −0.484468 | −0.242234 | − | 0.970218i | \(-0.577880\pi\) | ||||
−0.242234 | + | 0.970218i | \(0.577880\pi\) | |||||||
\(752\) | 1.67001 | 0.0608990 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.59294 | −0.203683 | ||||||||
\(755\) | −7.05879 | −0.256896 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.2374 | 0.408432 | 0.204216 | − | 0.978926i | \(-0.434536\pi\) | ||||
0.204216 | + | 0.978926i | \(0.434536\pi\) | |||||||
\(758\) | −8.60181 | −0.312432 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.57354 | 0.129626 | ||||||||
\(761\) | 0.978109 | 0.0354564 | 0.0177282 | − | 0.999843i | \(-0.494357\pi\) | ||||
0.0177282 | + | 0.999843i | \(0.494357\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.9814 | −0.397553 | ||||||||
\(764\) | −8.53996 | −0.308965 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.17232 | −0.295278 | ||||||||
\(767\) | −0.770248 | −0.0278120 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.30774 | −0.0832191 | −0.0416096 | − | 0.999134i | \(-0.513249\pi\) | ||||
−0.0416096 | + | 0.999134i | \(0.513249\pi\) | |||||||
\(770\) | −0.254312 | −0.00916476 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −41.4058 | −1.49023 | ||||||||
\(773\) | −33.6378 | −1.20987 | −0.604935 | − | 0.796275i | \(-0.706801\pi\) | ||||
−0.604935 | + | 0.796275i | \(0.706801\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.5407 | −0.989290 | ||||||||
\(776\) | 13.0372 | 0.468009 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.593827 | −0.0212897 | ||||||||
\(779\) | −11.2484 | −0.403017 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.37234 | −0.335369 | ||||||||
\(782\) | −8.02748 | −0.287062 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −19.8257 | −0.708060 | ||||||||
\(785\) | −3.70273 | −0.132156 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.3015 | 0.759318 | 0.379659 | − | 0.925126i | \(-0.376041\pi\) | ||||
0.379659 | + | 0.925126i | \(0.376041\pi\) | |||||||
\(788\) | 17.8738 | 0.636728 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.441996 | 0.0157255 | ||||||||
\(791\) | −20.0563 | −0.713121 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.51971 | 0.196010 | ||||||||
\(794\) | −0.206567 | −0.00733077 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.3087 | 0.719824 | ||||||||
\(797\) | −26.9259 | −0.953765 | −0.476882 | − | 0.878967i | \(-0.658233\pi\) | ||||
−0.476882 | + | 0.878967i | \(0.658233\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.19364 | −0.112983 | ||||||||
\(800\) | −11.2288 | −0.396999 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.19322 | 0.0774451 | ||||||||
\(803\) | −1.78042 | −0.0628297 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.53481 | −0.195076 | ||||||||
\(806\) | 8.19964 | 0.288820 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.99200 | 0.245978 | ||||||||
\(809\) | −18.6486 | −0.655648 | −0.327824 | − | 0.944739i | \(-0.606315\pi\) | ||||
−0.327824 | + | 0.944739i | \(0.606315\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.6205 | 1.81264 | 0.906321 | − | 0.422590i | \(-0.138879\pi\) | ||||
0.906321 | + | 0.422590i | \(0.138879\pi\) | |||||||
\(812\) | −11.0052 | −0.386208 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.06490 | 0.0373246 | ||||||||
\(815\) | −0.999654 | −0.0350163 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.2558 | 1.23344 | ||||||||
\(818\) | 6.99680 | 0.244637 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.21071 | −0.147044 | ||||||||
\(821\) | 43.8024 | 1.52872 | 0.764358 | − | 0.644792i | \(-0.223056\pi\) | ||||
0.764358 | + | 0.644792i | \(0.223056\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.0240 | 1.01171 | 0.505856 | − | 0.862618i | \(-0.331177\pi\) | ||||
0.505856 | + | 0.862618i | \(0.331177\pi\) | |||||||
\(824\) | −9.74653 | −0.339536 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.0406843 | 0.00141559 | ||||||||
\(827\) | −0.0272059 | −0.000946042 0 | −0.000473021 | − | 1.00000i | \(-0.500151\pi\) | ||||
−0.000473021 | 1.00000i | \(0.500151\pi\) | ||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.2095 | −0.701905 | −0.350952 | − | 0.936393i | \(-0.614142\pi\) | ||||
−0.350952 | + | 0.936393i | \(0.614142\pi\) | |||||||
\(830\) | 1.74969 | 0.0607328 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −37.3816 | −1.29597 | ||||||||
\(833\) | 37.9136 | 1.31363 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.5784 | −0.677540 | ||||||||
\(836\) | 8.83980 | 0.305731 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.66523 | −0.195702 | ||||||||
\(839\) | 2.45841 | 0.0848738 | 0.0424369 | − | 0.999099i | \(-0.486488\pi\) | ||||
0.0424369 | + | 0.999099i | \(0.486488\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.36254 | −0.322846 | ||||||||
\(842\) | −4.53130 | −0.156159 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.57708 | 0.260814 | ||||||||
\(845\) | 15.2362 | 0.524140 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.27506 | −0.0438116 | ||||||||
\(848\) | 22.5175 | 0.773254 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.83814 | 0.234546 | ||||||||
\(851\) | 23.1763 | 0.794473 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.1701 | 0.485175 | 0.242588 | − | 0.970129i | \(-0.422004\pi\) | ||||
0.242588 | + | 0.970129i | \(0.422004\pi\) | |||||||
\(854\) | −0.291550 | −0.00997662 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.2300 | 0.588909 | ||||||||
\(857\) | −2.30725 | −0.0788141 | −0.0394070 | − | 0.999223i | \(-0.512547\pi\) | ||||
−0.0394070 | + | 0.999223i | \(0.512547\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.0148953 | −0.000508220 0 | −0.000254110 | − | 1.00000i | \(-0.500081\pi\) | ||||
−0.000254110 | 1.00000i | \(0.500081\pi\) | ||||||||
\(860\) | 13.1976 | 0.450033 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.35459 | 0.216438 | ||||||||
\(863\) | 37.5589 | 1.27852 | 0.639260 | − | 0.768991i | \(-0.279241\pi\) | ||||
0.639260 | + | 0.768991i | \(0.279241\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.6039 | −0.632550 | ||||||||
\(866\) | 8.69097 | 0.295331 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.1344 | 0.547638 | ||||||||
\(869\) | 2.21606 | 0.0751748 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.7186 | 0.702023 | ||||||||
\(872\) | −7.77418 | −0.263267 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.16436 | −0.174687 | ||||||||
\(875\) | 10.2758 | 0.347386 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.1102 | 0.780378 | 0.390189 | − | 0.920735i | \(-0.372410\pi\) | ||||
0.390189 | + | 0.920735i | \(0.372410\pi\) | |||||||
\(878\) | 8.44274 | 0.284929 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.21786 | 0.108474 | ||||||||
\(881\) | −21.9178 | −0.738430 | −0.369215 | − | 0.929344i | \(-0.620373\pi\) | ||||
−0.369215 | + | 0.929344i | \(0.620373\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.0472 | −1.48231 | −0.741153 | − | 0.671336i | \(-0.765721\pi\) | ||||
−0.741153 | + | 0.671336i | \(0.765721\pi\) | |||||||
\(884\) | 75.8440 | 2.55091 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.372706 | 0.0125213 | ||||||||
\(887\) | 44.2865 | 1.48700 | 0.743498 | − | 0.668738i | \(-0.233165\pi\) | ||||
0.743498 | + | 0.668738i | \(0.233165\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.1004 | 0.841842 | ||||||||
\(890\) | 0.227894 | 0.00763904 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.9112 | 0.700159 | ||||||||
\(893\) | −2.05458 | −0.0687539 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.0571 | 0.637009 | ||||||||
\(896\) | 8.72938 | 0.291628 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.27546 | −0.176044 | ||||||||
\(899\) | −28.7899 | −0.960196 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.0613 | −1.43458 | ||||||||
\(902\) | 0.566706 | 0.0188692 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.1987 | −0.472242 | ||||||||
\(905\) | 10.0187 | 0.333033 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.7897 | −0.391471 | −0.195736 | − | 0.980657i | \(-0.562709\pi\) | ||||
−0.195736 | + | 0.980657i | \(0.562709\pi\) | |||||||
\(908\) | 29.7070 | 0.985861 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.40373 | −0.0465330 | ||||||||
\(911\) | 50.2024 | 1.66328 | 0.831640 | − | 0.555315i | \(-0.187402\pi\) | ||||
0.831640 | + | 0.555315i | \(0.187402\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.77256 | 0.290329 | ||||||||
\(914\) | 0.249517 | 0.00825329 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20.4352 | −0.675198 | ||||||||
\(917\) | 0.859010 | 0.0283670 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.09392 | −0.135046 | −0.0675230 | − | 0.997718i | \(-0.521510\pi\) | ||||
−0.0675230 | + | 0.997718i | \(0.521510\pi\) | |||||||
\(920\) | −3.91832 | −0.129183 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.48372 | 0.312330 | ||||||||
\(923\) | −51.7325 | −1.70280 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.7425 | −0.649131 | ||||||||
\(926\) | −8.12748 | −0.267086 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −11.7382 | −0.385324 | ||||||||
\(929\) | −1.87956 | −0.0616662 | −0.0308331 | − | 0.999525i | \(-0.509816\pi\) | ||||
−0.0308331 | + | 0.999525i | \(0.509816\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.3911 | 0.799387 | ||||||||
\(932\) | 38.1144 | 1.24848 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.57485 | −0.0842517 | ||||||||
\(935\) | −6.15366 | −0.201246 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.8551 | −0.713974 | −0.356987 | − | 0.934109i | \(-0.616196\pi\) | ||||
−0.356987 | + | 0.934109i | \(0.616196\pi\) | |||||||
\(938\) | −1.09435 | −0.0357319 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.769106 | −0.0250855 | ||||||||
\(941\) | −16.1328 | −0.525915 | −0.262957 | − | 0.964807i | \(-0.584698\pi\) | ||||
−0.262957 | + | 0.964807i | \(0.584698\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.3337 | 0.401641 | ||||||||
\(944\) | −0.514787 | −0.0167549 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.77622 | −0.0577498 | ||||||||
\(947\) | 3.33314 | 0.108312 | 0.0541562 | − | 0.998532i | \(-0.482753\pi\) | ||||
0.0541562 | + | 0.998532i | \(0.482753\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.82741 | −0.319011 | ||||||||
\(950\) | 4.39922 | 0.142729 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.11966 | −0.263160 | ||||||||
\(953\) | 51.2844 | 1.66126 | 0.830632 | − | 0.556822i | \(-0.187980\pi\) | ||||
0.830632 | + | 0.556822i | \(0.187980\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.82458 | 0.123761 | ||||||||
\(956\) | 12.1174 | 0.391906 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.48988 | 0.0481357 | ||||||||
\(959\) | 1.85139 | 0.0597846 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.2080 | 0.361548 | ||||||||
\(962\) | 5.87792 | 0.189512 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.7806 | 0.508259 | ||||||||
\(965\) | 18.5434 | 0.596934 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.99705 | 0.321484 | 0.160742 | − | 0.986996i | \(-0.448611\pi\) | ||||
0.160742 | + | 0.986996i | \(0.448611\pi\) | |||||||
\(968\) | −0.902667 | −0.0290128 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.88067 | −0.0924926 | ||||||||
\(971\) | −3.60803 | −0.115787 | −0.0578936 | − | 0.998323i | \(-0.518438\pi\) | ||||
−0.0578936 | + | 0.998323i | \(0.518438\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.78759 | −0.121425 | ||||||||
\(974\) | 1.33898 | 0.0429037 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.68903 | 0.118083 | ||||||||
\(977\) | −51.4571 | −1.64626 | −0.823130 | − | 0.567853i | \(-0.807774\pi\) | ||||
−0.823130 | + | 0.567853i | \(0.807774\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.14261 | 0.0365180 | ||||||||
\(980\) | 9.13052 | 0.291664 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.12516 | 0.195462 | ||||||||
\(983\) | 35.9137 | 1.14547 | 0.572734 | − | 0.819741i | \(-0.305883\pi\) | ||||
0.572734 | + | 0.819741i | \(0.305883\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.00470 | −0.255051 | ||||||||
\(986\) | 7.14832 | 0.227649 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 48.7931 | 1.55231 | ||||||||
\(989\) | −38.6574 | −1.22923 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.0440 | 0.732017 | 0.366009 | − | 0.930612i | \(-0.380724\pi\) | ||||
0.366009 | + | 0.930612i | \(0.380724\pi\) | |||||||
\(992\) | 17.2090 | 0.546386 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.73250 | 0.0866697 | ||||||||
\(995\) | −9.09517 | −0.288336 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.8343 | 1.26157 | 0.630783 | − | 0.775959i | \(-0.282734\pi\) | ||||
0.630783 | + | 0.775959i | \(0.282734\pi\) | |||||||
\(998\) | 3.79717 | 0.120197 | ||||||||
\(999\) | 0 | 0 |
(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 | 6039.2.a.m.1.14 | ✓ | 25 | |
3.2 | odd | 2 | 6039.2.a.p.1.12 | yes | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6039.2.a.m.1.14 | ✓ | 25 | 1.1 | even | 1 | trivial | |
6039.2.a.p.1.12 | yes | 25 | 3.2 | odd | 2 |