Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.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: | \(32.0679214517\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 27 x^{12} + 79 x^{11} + 274 x^{10} - 747 x^{9} - 1422 x^{8} + 3287 x^{7} + \cdots - 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1004) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.53364\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 | ||||||||
\(3\) | −2.53364 | −1.46280 | −0.731399 | − | 0.681950i | \(-0.761132\pi\) | ||||
−0.731399 | + | 0.681950i | \(0.761132\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.70770 | 1.21092 | 0.605460 | − | 0.795876i | \(-0.292989\pi\) | ||||
0.605460 | + | 0.795876i | \(0.292989\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.66309 | −0.628590 | −0.314295 | − | 0.949325i | \(-0.601768\pi\) | ||||
−0.314295 | + | 0.949325i | \(0.601768\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.41934 | 1.13978 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.22692 | −0.972954 | −0.486477 | − | 0.873693i | \(-0.661718\pi\) | ||||
−0.486477 | + | 0.873693i | \(0.661718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.30349 | −1.47092 | −0.735461 | − | 0.677567i | \(-0.763034\pi\) | ||||
−0.735461 | + | 0.677567i | \(0.763034\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.86033 | −1.77133 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.60034 | 0.873211 | 0.436606 | − | 0.899653i | \(-0.356181\pi\) | ||||
0.436606 | + | 0.899653i | \(0.356181\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.49017 | 0.571285 | 0.285642 | − | 0.958336i | \(-0.407793\pi\) | ||||
0.285642 | + | 0.958336i | \(0.407793\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.21368 | 0.919500 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.44085 | 1.96855 | 0.984276 | − | 0.176636i | \(-0.0565214\pi\) | ||||
0.984276 | + | 0.176636i | \(0.0565214\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.33163 | 0.466326 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.06245 | −0.204468 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.668304 | −0.124101 | −0.0620505 | − | 0.998073i | \(-0.519764\pi\) | ||||
−0.0620505 | + | 0.998073i | \(0.519764\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.89493 | −0.340339 | −0.170169 | − | 0.985415i | \(-0.554431\pi\) | ||||
−0.170169 | + | 0.985415i | \(0.554431\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.17586 | 1.42323 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.50315 | −0.761172 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.26565 | −0.701269 | −0.350635 | − | 0.936512i | \(-0.614034\pi\) | ||||
−0.350635 | + | 0.936512i | \(0.614034\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.4371 | 2.15166 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.63994 | 0.880811 | 0.440406 | − | 0.897799i | \(-0.354835\pi\) | ||||
0.440406 | + | 0.897799i | \(0.354835\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.45482 | 1.13685 | 0.568424 | − | 0.822736i | \(-0.307553\pi\) | ||||
0.568424 | + | 0.822736i | \(0.307553\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.25853 | 1.38018 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.38668 | −0.639863 | −0.319932 | − | 0.947441i | \(-0.603660\pi\) | ||||
−0.319932 | + | 0.947441i | \(0.603660\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.23412 | −0.604875 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.12197 | −1.27733 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.7249 | −1.88526 | −0.942631 | − | 0.333837i | \(-0.891657\pi\) | ||||
−0.942631 | + | 0.333837i | \(0.891657\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.73753 | −1.17817 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.30920 | −0.835674 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.5842 | −1.37795 | −0.688973 | − | 0.724787i | \(-0.741938\pi\) | ||||
−0.688973 | + | 0.724787i | \(0.741938\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.80848 | 0.615662 | 0.307831 | − | 0.951441i | \(-0.400397\pi\) | ||||
0.307831 | + | 0.951441i | \(0.400397\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.68667 | −0.716453 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.3602 | −1.78117 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.11901 | 0.991895 | 0.495947 | − | 0.868353i | \(-0.334821\pi\) | ||||
0.495947 | + | 0.868353i | \(0.334821\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −23.9197 | −2.87960 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.73759 | −1.03696 | −0.518481 | − | 0.855089i | \(-0.673502\pi\) | ||||
−0.518481 | + | 0.855089i | \(0.673502\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.71642 | 0.669056 | 0.334528 | − | 0.942386i | \(-0.391423\pi\) | ||||
0.334528 | + | 0.942386i | \(0.391423\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.90751 | −0.682141 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.36667 | 0.611589 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.24905 | 0.253038 | 0.126519 | − | 0.991964i | \(-0.459619\pi\) | ||||
0.126519 | + | 0.991964i | \(0.459619\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.56615 | −0.840683 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.30070 | −0.252534 | −0.126267 | − | 0.991996i | \(-0.540300\pi\) | ||||
−0.126267 | + | 0.991996i | \(0.540300\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.74864 | 1.05739 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.69324 | 0.181535 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.4266 | 1.63522 | 0.817608 | − | 0.575776i | \(-0.195300\pi\) | ||||
0.817608 | + | 0.575776i | \(0.195300\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.82019 | 0.924607 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.80106 | 0.497847 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.74264 | 0.691780 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.68637 | 0.577364 | 0.288682 | − | 0.957425i | \(-0.406783\pi\) | ||||
0.288682 | + | 0.957425i | \(0.406783\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.0339 | −1.10895 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.12873 | −0.510328 | −0.255164 | − | 0.966898i | \(-0.582129\pi\) | ||||
−0.255164 | + | 0.966898i | \(0.582129\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.79517 | −0.866614 | −0.433307 | − | 0.901246i | \(-0.642653\pi\) | ||||
−0.433307 | + | 0.901246i | \(0.642653\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.4094 | 1.11344 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.1074 | 0.977121 | 0.488560 | − | 0.872530i | \(-0.337522\pi\) | ||||
0.488560 | + | 0.872530i | \(0.337522\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.87751 | 0.754528 | 0.377264 | − | 0.926106i | \(-0.376865\pi\) | ||||
0.377264 | + | 0.926106i | \(0.376865\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.8076 | 1.02582 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.94432 | −0.559195 | −0.279597 | − | 0.960117i | \(-0.590201\pi\) | ||||
−0.279597 | + | 0.960117i | \(0.590201\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 25.5630 | 2.38376 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −18.1344 | −1.67653 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.98770 | −0.548892 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.586971 | −0.0533610 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.2896 | −1.28845 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.22514 | −0.646236 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.49541 | −0.576375 | −0.288187 | − | 0.957574i | \(-0.593053\pi\) | ||||
−0.288187 | + | 0.957574i | \(0.593053\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.8878 | −1.66298 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5751 | −0.923949 | −0.461974 | − | 0.886893i | \(-0.652859\pi\) | ||||
−0.461974 | + | 0.886893i | \(0.652859\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.14139 | −0.359104 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.87678 | −0.247594 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.8302 | −1.35246 | −0.676232 | − | 0.736689i | \(-0.736388\pi\) | ||||
−0.676232 | + | 0.736689i | \(0.736388\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.3374 | −1.38572 | −0.692861 | − | 0.721071i | \(-0.743650\pi\) | ||||
−0.692861 | + | 0.721071i | \(0.743650\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.1143 | 0.935991 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.1139 | 1.43114 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.80957 | −0.150276 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.7277 | 0.884809 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.9391 | 1.46963 | 0.734813 | − | 0.678270i | \(-0.237270\pi\) | ||||
0.734813 | + | 0.678270i | \(0.237270\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.28510 | −0.511474 | −0.255737 | − | 0.966746i | \(-0.582318\pi\) | ||||
−0.255737 | + | 0.966746i | \(0.582318\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.3108 | 0.995267 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.13089 | −0.412123 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.7510 | 1.25707 | 0.628534 | − | 0.777782i | \(-0.283655\pi\) | ||||
0.628534 | + | 0.777782i | \(0.283655\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 34.7740 | 2.75776 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.7010 | −1.23741 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.20823 | −0.172962 | −0.0864810 | − | 0.996253i | \(-0.527562\pi\) | ||||
−0.0864810 | + | 0.996253i | \(0.527562\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 22.1378 | 1.72342 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.3764 | −1.49939 | −0.749696 | − | 0.661783i | \(-0.769800\pi\) | ||||
−0.749696 | + | 0.661783i | \(0.769800\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.1270 | 1.16361 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.51474 | 0.651138 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.2171 | −1.00487 | −0.502437 | − | 0.864614i | \(-0.667563\pi\) | ||||
−0.502437 | + | 0.864614i | \(0.667563\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.87772 | −0.293128 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 26.8166 | 2.01566 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.8228 | −0.883674 | −0.441837 | − | 0.897095i | \(-0.645673\pi\) | ||||
−0.441837 | + | 0.897095i | \(0.645673\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.3008 | −1.21163 | −0.605816 | − | 0.795605i | \(-0.707153\pi\) | ||||
−0.605816 | + | 0.795605i | \(0.707153\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.1830 | −0.900590 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.5501 | −0.849180 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.6180 | −0.849594 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.76695 | 0.128526 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.8529 | 0.930004 | 0.465002 | − | 0.885310i | \(-0.346054\pi\) | ||||
0.465002 | + | 0.885310i | \(0.346054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.578921 | 0.0416717 | 0.0208358 | − | 0.999783i | \(-0.493367\pi\) | ||||
0.0208358 | + | 0.999783i | \(0.493367\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 36.3837 | 2.60549 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.4759 | −1.60134 | −0.800672 | − | 0.599104i | \(-0.795524\pi\) | ||||
−0.800672 | + | 0.599104i | \(0.795524\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.84324 | 0.130664 | 0.0653319 | − | 0.997864i | \(-0.479189\pi\) | ||||
0.0653319 | + | 0.997864i | \(0.479189\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20.5707 | −1.45094 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.11145 | 0.0780086 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.2713 | 1.06659 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 32.2814 | 2.24371 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.03559 | −0.555834 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.3880 | −1.67894 | −0.839470 | − | 0.543406i | \(-0.817134\pi\) | ||||
−0.839470 | + | 0.543406i | \(0.817134\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.1379 | 1.51687 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.1854 | 1.37663 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.15144 | 0.213934 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.4833 | −0.978694 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.0944 | −1.28443 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.7244 | 0.919055 | 0.459527 | − | 0.888164i | \(-0.348019\pi\) | ||||
0.459527 | + | 0.888164i | \(0.348019\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.97263 | 0.531508 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.0337 | −1.19694 | −0.598471 | − | 0.801145i | \(-0.704225\pi\) | ||||
−0.598471 | + | 0.801145i | \(0.704225\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.9194 | −0.919818 | −0.459909 | − | 0.887966i | \(-0.652118\pi\) | ||||
−0.459909 | + | 0.887966i | \(0.652118\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.5972 | −0.894631 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.55318 | −0.429313 | −0.214657 | − | 0.976690i | \(-0.568863\pi\) | ||||
−0.214657 | + | 0.976690i | \(0.568863\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.8778 | −0.774823 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.69829 | −0.370144 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.4466 | 1.25790 | 0.628948 | − | 0.777448i | \(-0.283486\pi\) | ||||
0.628948 | + | 0.777448i | \(0.283486\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.99253 | −0.514844 | −0.257422 | − | 0.966299i | \(-0.582873\pi\) | ||||
−0.257422 | + | 0.966299i | \(0.582873\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3572 | 1.43422 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.4647 | −0.732454 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.2066 | −0.840315 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.82914 | 0.369407 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.4649 | −1.91531 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −24.6996 | −1.54675 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.5459 | −0.657838 | −0.328919 | − | 0.944358i | \(-0.606684\pi\) | ||||
−0.328919 | + | 0.944358i | \(0.606684\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.09418 | 0.440811 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.28516 | −0.141448 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.7679 | 1.46559 | 0.732796 | − | 0.680449i | \(-0.238215\pi\) | ||||
0.732796 | + | 0.680449i | \(0.238215\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37.1629 | −2.28290 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −39.0854 | −2.39199 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.9594 | −1.52180 | −0.760902 | − | 0.648867i | \(-0.775243\pi\) | ||||
−0.760902 | + | 0.648867i | \(0.775243\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.5226 | −1.30740 | −0.653702 | − | 0.756752i | \(-0.726785\pi\) | ||||
−0.653702 | + | 0.756752i | \(0.726785\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −22.3472 | −1.35251 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.52399 | −0.453714 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.9187 | −1.43714 | −0.718569 | − | 0.695456i | \(-0.755202\pi\) | ||||
−0.718569 | + | 0.695456i | \(0.755202\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.47939 | −0.387911 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.08897 | −0.482548 | −0.241274 | − | 0.970457i | \(-0.577565\pi\) | ||||
−0.241274 | + | 0.970457i | \(0.577565\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.21337 | −0.309903 | −0.154951 | − | 0.987922i | \(-0.549522\pi\) | ||||
−0.154951 | + | 0.987922i | \(0.549522\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.0834 | −1.01193 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.37975 | −0.553669 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.03754 | −0.237502 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.4072 | −0.844566 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.4390 | 0.668274 | 0.334137 | − | 0.942525i | \(-0.391555\pi\) | ||||
0.334137 | + | 0.942525i | \(0.391555\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.6588 | −1.66858 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.42843 | 0.198938 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −50.0694 | −2.89559 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.3980 | −0.714612 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.9944 | 0.746507 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.0199 | 0.745518 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.47936 | 0.0844315 | 0.0422157 | − | 0.999109i | \(-0.486558\pi\) | ||||
0.0422157 | + | 0.999109i | \(0.486558\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.2838 | 1.26768 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0241 | 1.13546 | 0.567731 | − | 0.823214i | \(-0.307821\pi\) | ||||
0.567731 | + | 0.823214i | \(0.307821\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.2154 | 1.53830 | 0.769152 | − | 0.639066i | \(-0.220679\pi\) | ||||
0.769152 | + | 0.639066i | \(0.220679\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −15.3978 | −0.867567 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.0766 | 1.68927 | 0.844636 | − | 0.535340i | \(-0.179817\pi\) | ||||
0.844636 | + | 0.535340i | \(0.179817\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.15656 | 0.120744 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −25.6086 | −1.42933 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.96547 | 0.498852 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.3658 | −0.685929 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.9588 | −1.10372 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.29546 | 0.402212 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.7923 | 0.813058 | 0.406529 | − | 0.913638i | \(-0.366739\pi\) | ||||
0.406529 | + | 0.913638i | \(0.366739\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.5857 | −0.799291 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.9838 | 1.20110 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.0697 | −0.603003 | −0.301501 | − | 0.953466i | \(-0.597488\pi\) | ||||
−0.301501 | + | 0.953466i | \(0.597488\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.0608 | 0.817989 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.11478 | 0.331134 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.6834 | 1.00881 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −64.7674 | −3.48696 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.2353 | −0.710506 | −0.355253 | − | 0.934770i | \(-0.615605\pi\) | ||||
−0.355253 | + | 0.934770i | \(0.615605\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.8843 | −0.850269 | −0.425135 | − | 0.905130i | \(-0.639773\pi\) | ||||
−0.425135 | + | 0.905130i | \(0.639773\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.63467 | 0.300756 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.29827 | 0.0690999 | 0.0345500 | − | 0.999403i | \(-0.489000\pi\) | ||||
0.0345500 | + | 0.999403i | \(0.489000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.6588 | −1.25568 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.1707 | 0.802918 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35.5797 | −1.87782 | −0.938912 | − | 0.344158i | \(-0.888164\pi\) | ||||
−0.938912 | + | 0.344158i | \(0.888164\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.7990 | −0.673634 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.48717 | 0.0780564 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.4783 | 0.810173 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.5916 | 1.07487 | 0.537435 | − | 0.843305i | \(-0.319393\pi\) | ||||
0.537435 | + | 0.843305i | \(0.319393\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.2849 | 1.00393 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.8258 | 1.18506 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.99992 | 0.414220 | 0.207110 | − | 0.978318i | \(-0.433594\pi\) | ||||
0.207110 | + | 0.978318i | \(0.433594\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.3059 | 0.945313 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.54434 | 0.182543 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.1733 | −0.830767 | −0.415384 | − | 0.909646i | \(-0.636353\pi\) | ||||
−0.415384 | + | 0.909646i | \(0.636353\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.4570 | 0.843120 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.5230 | −1.04868 | −0.524338 | − | 0.851510i | \(-0.675687\pi\) | ||||
−0.524338 | + | 0.851510i | \(0.675687\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.5313 | 0.740585 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 25.4905 | 1.29576 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.2861 | −0.977843 | −0.488922 | − | 0.872328i | \(-0.662610\pi\) | ||||
−0.488922 | + | 0.872328i | \(0.662610\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.9903 | 1.71896 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 26.7934 | 1.35155 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.08976 | 0.306409 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.4004 | 0.672547 | 0.336273 | − | 0.941764i | \(-0.390833\pi\) | ||||
0.336273 | + | 0.941764i | \(0.390833\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.4928 | 0.525297 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.72700 | −0.485743 | −0.242872 | − | 0.970058i | \(-0.578089\pi\) | ||||
−0.242872 | + | 0.970058i | \(0.578089\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.0497 | 0.500612 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.4869 | −1.01800 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.7649 | 0.682302 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.2040 | 0.504554 | 0.252277 | − | 0.967655i | \(-0.418821\pi\) | ||||
0.252277 | + | 0.967655i | \(0.418821\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 40.1080 | 1.97838 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.6025 | 0.866163 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.22960 | −0.305799 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 41.3932 | 2.02703 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.93843 | −0.485524 | −0.242762 | − | 0.970086i | \(-0.578053\pi\) | ||||
−0.242762 | + | 0.970086i | \(0.578053\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.4701 | −0.510284 | −0.255142 | − | 0.966904i | \(-0.582122\pi\) | ||||
−0.255142 | + | 0.966904i | \(0.582122\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.9995 | −0.729302 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.39467 | 0.407201 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.99694 | −0.386999 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −43.3606 | −2.09347 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.9003 | 1.05490 | 0.527451 | − | 0.849586i | \(-0.323148\pi\) | ||||
0.527451 | + | 0.849586i | \(0.323148\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.6836 | 1.61873 | 0.809364 | − | 0.587307i | \(-0.199812\pi\) | ||||
0.809364 | + | 0.587307i | \(0.199812\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.58479 | 0.219824 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.5093 | 1.12460 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.7355 | −1.37147 | −0.685736 | − | 0.727851i | \(-0.740519\pi\) | ||||
−0.685736 | + | 0.727851i | \(0.740519\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.4779 | −0.689423 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.4373 | 0.543400 | 0.271700 | − | 0.962382i | \(-0.412414\pi\) | ||||
0.271700 | + | 0.962382i | \(0.412414\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 41.7706 | 1.98011 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −45.4512 | −2.14977 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.4037 | −0.962912 | −0.481456 | − | 0.876470i | \(-0.659892\pi\) | ||||
−0.481456 | + | 0.876470i | \(0.659892\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.1997 | −0.856988 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.9242 | 0.748183 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23.8824 | 1.11962 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.6209 | 1.38560 | 0.692802 | − | 0.721127i | \(-0.256376\pi\) | ||||
0.692802 | + | 0.721127i | \(0.256376\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.82517 | −0.178544 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.9499 | −0.929162 | −0.464581 | − | 0.885531i | \(-0.653795\pi\) | ||||
−0.464581 | + | 0.885531i | \(0.653795\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.4171 | −1.55302 | −0.776511 | − | 0.630103i | \(-0.783012\pi\) | ||||
−0.776511 | + | 0.630103i | \(0.783012\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.9998 | 0.602853 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.04101 | 0.140721 | 0.0703607 | − | 0.997522i | \(-0.477585\pi\) | ||||
0.0703607 | + | 0.997522i | \(0.477585\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.5027 | −0.623495 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −39.9075 | −1.83884 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24.0561 | −1.10610 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.80616 | 0.266405 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −46.9301 | −2.14878 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.64655 | 0.349380 | 0.174690 | − | 0.984623i | \(-0.444108\pi\) | ||||
0.174690 | + | 0.984623i | \(0.444108\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.6228 | 1.03151 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 39.7807 | 1.81008 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.3970 | 0.699141 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.7583 | −0.985961 | −0.492981 | − | 0.870040i | \(-0.664093\pi\) | ||||
−0.492981 | + | 0.870040i | \(0.664093\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.59487 | 0.253009 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.4315 | −0.515897 | −0.257949 | − | 0.966159i | \(-0.583047\pi\) | ||||
−0.257949 | + | 0.966159i | \(0.583047\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.40612 | −0.108366 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −29.8766 | −1.34285 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.5314 | 0.651824 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.0439 | −1.43448 | −0.717242 | − | 0.696824i | \(-0.754596\pi\) | ||||
−0.717242 | + | 0.696824i | \(0.754596\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 49.0929 | 2.19331 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.07414 | −0.315420 | −0.157710 | − | 0.987485i | \(-0.550411\pi\) | ||||
−0.157710 | + | 0.987485i | \(0.550411\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.8871 | −0.617966 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −38.3263 | −1.70213 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.36779 | 0.104951 | 0.0524753 | − | 0.998622i | \(-0.483289\pi\) | ||||
0.0524753 | + | 0.998622i | \(0.483289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.50693 | −0.420562 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.64567 | −0.116809 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −23.8147 | −1.04940 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.1555 | 0.622557 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 33.4873 | 1.46993 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.0997 | −0.486289 | −0.243144 | − | 0.969990i | \(-0.578179\pi\) | ||||
−0.243144 | + | 0.969990i | \(0.578179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.2177 | −0.621698 | −0.310849 | − | 0.950459i | \(-0.600613\pi\) | ||||
−0.310849 | + | 0.950459i | \(0.600613\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.82474 | 0.428787 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.82238 | −0.297188 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 66.1296 | 2.87520 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −36.1909 | −1.57055 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.9114 | −1.29560 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.3678 | 1.18321 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 29.9546 | 1.29264 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.6632 | 0.588515 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.20232 | −0.180672 | −0.0903360 | − | 0.995911i | \(-0.528794\pi\) | ||||
−0.0903360 | + | 0.995911i | \(0.528794\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 41.3005 | 1.77237 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.3299 | 0.913673 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.7693 | −1.10182 | −0.550909 | − | 0.834566i | \(-0.685719\pi\) | ||||
−0.550909 | + | 0.834566i | \(0.685719\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.4418 | 0.701719 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.66419 | −0.0708970 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.74039 | −0.159057 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 29.2638 | 1.24218 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 37.8997 | 1.60586 | 0.802931 | − | 0.596072i | \(-0.203273\pi\) | ||||
0.802931 | + | 0.596072i | \(0.203273\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −39.5365 | −1.67222 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 29.4359 | 1.24278 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.59019 | −0.235599 | −0.117799 | − | 0.993037i | \(-0.537584\pi\) | ||||
−0.117799 | + | 0.993037i | \(0.537584\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.0954 | −0.677140 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.5832 | 0.528445 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.1997 | −1.47565 | −0.737824 | − | 0.674993i | \(-0.764147\pi\) | ||||
−0.737824 | + | 0.674993i | \(0.764147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.7949 | 1.37242 | 0.686212 | − | 0.727401i | \(-0.259272\pi\) | ||||
0.686212 | + | 0.727401i | \(0.259272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −32.5647 | −1.36041 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.0126 | 0.917987 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.2433 | 0.509695 | 0.254847 | − | 0.966981i | \(-0.417975\pi\) | ||||
0.254847 | + | 0.966981i | \(0.417975\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.46678 | −0.0609572 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.82628 | 0.158741 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 44.2892 | 1.83427 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −49.1025 | −2.03014 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.3012 | 0.796647 | 0.398324 | − | 0.917245i | \(-0.369592\pi\) | ||||
0.398324 | + | 0.917245i | \(0.369592\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.71869 | −0.194430 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 56.9459 | 2.34244 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.7775 | 1.67453 | 0.837266 | − | 0.546796i | \(-0.184153\pi\) | ||||
0.837266 | + | 0.546796i | \(0.184153\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.2129 | −0.664664 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.67011 | −0.191135 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.1323 | −0.659147 | −0.329574 | − | 0.944130i | \(-0.606905\pi\) | ||||
−0.329574 | + | 0.944130i | \(0.606905\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.8646 | 1.83007 | 0.915033 | − | 0.403380i | \(-0.132165\pi\) | ||||
0.915033 | + | 0.403380i | \(0.132165\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.7616 | 1.13054 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.58934 | −0.0646159 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.0278 | −0.488192 | −0.244096 | − | 0.969751i | \(-0.578491\pi\) | ||||
−0.244096 | + | 0.969751i | \(0.578491\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.81602 | −0.114111 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.2647 | 0.941189 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.73064 | 0.110289 | 0.0551447 | − | 0.998478i | \(-0.482438\pi\) | ||||
0.0551447 | + | 0.998478i | \(0.482438\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −38.6919 | −1.56021 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.6543 | −0.710734 | −0.355367 | − | 0.934727i | \(-0.615644\pi\) | ||||
−0.355367 | + | 0.934727i | \(0.615644\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.6642 | −1.51385 | −0.756927 | − | 0.653500i | \(-0.773300\pi\) | ||||
−0.756927 | + | 0.653500i | \(0.773300\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.0304 | −0.402506 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.6559 | −1.02788 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2217 | −1.24887 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.3593 | 0.813072 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.3578 | −0.612356 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.3088 | −1.80371 | −0.901857 | − | 0.432034i | \(-0.857796\pi\) | ||||
−0.901857 | + | 0.432034i | \(0.857796\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 61.7905 | 2.45595 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.5876 | −0.697943 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.4556 | 0.889723 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −29.8768 | −1.18191 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.43529 | −0.0566904 | −0.0283452 | − | 0.999598i | \(-0.509024\pi\) | ||||
−0.0283452 | + | 0.999598i | \(0.509024\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.9682 | 1.45788 | 0.728941 | − | 0.684577i | \(-0.240013\pi\) | ||||
0.728941 | + | 0.684577i | \(0.240013\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −51.1425 | −2.01374 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.37923 | −0.0542233 | −0.0271116 | − | 0.999632i | \(-0.508631\pi\) | ||||
−0.0271116 | + | 0.999632i | \(0.508631\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.1544 | 1.34068 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.98461 | −0.312942 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.7010 | −0.614426 | −0.307213 | − | 0.951641i | \(-0.599396\pi\) | ||||
−0.307213 | + | 0.951641i | \(0.599396\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.6341 | −1.11883 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19.5463 | 0.762576 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.3353 | 0.792152 | 0.396076 | − | 0.918218i | \(-0.370372\pi\) | ||||
0.396076 | + | 0.918218i | \(0.370372\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.03223 | −0.351313 | −0.175657 | − | 0.984452i | \(-0.556205\pi\) | ||||
−0.175657 | + | 0.984452i | \(0.556205\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 48.3783 | 1.87886 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.2136 | −0.434846 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.30935 | −0.244299 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −34.7727 | −1.34439 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.5166 | −0.599011 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.9791 | 1.38689 | 0.693447 | − | 0.720508i | \(-0.256091\pi\) | ||||
0.693447 | + | 0.720508i | \(0.256091\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.47723 | −0.0953487 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.1471 | −0.543718 | −0.271859 | − | 0.962337i | \(-0.587638\pi\) | ||||
−0.271859 | + | 0.962337i | \(0.587638\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.45697 | −0.362925 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 45.6910 | 1.75088 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.98547 | −0.152500 | −0.0762499 | − | 0.997089i | \(-0.524295\pi\) | ||||
−0.0762499 | + | 0.997089i | \(0.524295\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −42.8633 | −1.63772 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 35.2667 | 1.34551 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 72.7899 | 2.77307 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.11084 | −0.0422582 | −0.0211291 | − | 0.999777i | \(-0.506726\pi\) | ||||
−0.0211291 | + | 0.999777i | \(0.506726\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.3505 | 0.697076 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −44.2368 | −1.67800 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.3057 | 0.769134 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.6034 | 0.627999 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.0636 | 1.36210 | 0.681051 | − | 0.732236i | \(-0.261523\pi\) | ||||
0.681051 | + | 0.732236i | \(0.261523\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.6222 | −0.400624 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 30.0941 | 1.13341 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.52956 | 0.320787 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.6901 | −0.889701 | −0.444850 | − | 0.895605i | \(-0.646743\pi\) | ||||
−0.444850 | + | 0.895605i | \(0.646743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.69027 | 0.288408 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.8897 | −0.669975 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 46.3394 | 1.73299 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −49.2707 | −1.84005 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.6927 | 0.473357 | 0.236679 | − | 0.971588i | \(-0.423941\pi\) | ||||
0.236679 | + | 0.971588i | \(0.423941\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.6272 | 0.544745 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.2502 | 0.753113 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.55824 | −0.0578715 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.13718 | 0.338879 | 0.169440 | − | 0.985541i | \(-0.445804\pi\) | ||||
0.169440 | + | 0.985541i | \(0.445804\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −33.9468 | −1.25729 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.8399 | 0.992709 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.0549 | −1.51640 | −0.758199 | − | 0.652023i | \(-0.773920\pi\) | ||||
−0.758199 | + | 0.652023i | \(0.773920\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 29.0475 | 1.07143 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26.1994 | −0.965068 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.7604 | 1.02118 | 0.510591 | − | 0.859824i | \(-0.329427\pi\) | ||||
0.510591 | + | 0.859824i | \(0.329427\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 33.4608 | 1.22921 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.1039 | 0.627483 | 0.313741 | − | 0.949508i | \(-0.398417\pi\) | ||||
0.313741 | + | 0.949508i | \(0.398417\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48.5736 | 1.77960 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.86686 | −0.287833 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.8096 | −0.614208 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.17031 | 0.152177 | 0.0760884 | − | 0.997101i | \(-0.475757\pi\) | ||||
0.0760884 | + | 0.997101i | \(0.475757\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.53364 | −0.0923310 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.0181 | −0.619354 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.0596 | −1.31061 | −0.655304 | − | 0.755365i | \(-0.727459\pi\) | ||||
−0.655304 | + | 0.755365i | \(0.727459\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 77.1871 | 2.80171 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.4591 | 0.741641 | 0.370820 | − | 0.928705i | \(-0.379077\pi\) | ||||
0.370820 | + | 0.928705i | \(0.379077\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.1010 | −0.474289 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 33.3339 | 1.20519 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 56.1332 | 2.02685 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −55.0624 | −1.98560 | −0.992800 | − | 0.119782i | \(-0.961780\pi\) | ||||
−0.992800 | + | 0.119782i | \(0.961780\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.7196 | 0.962284 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.6721 | −1.10320 | −0.551599 | − | 0.834109i | \(-0.685982\pi\) | ||||
−0.551599 | + | 0.834109i | \(0.685982\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.41827 | −0.158709 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.9741 | −0.644817 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.0444 | 0.503194 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.1955 | 1.00892 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.710037 | 0.0253746 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42.6490 | 1.52221 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.3280 | −0.938492 | −0.469246 | − | 0.883067i | \(-0.655474\pi\) | ||||
−0.469246 | + | 0.883067i | \(0.655474\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −60.2193 | −2.14386 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.88596 | 0.351504 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.5017 | −0.905592 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 94.1575 | 3.33942 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.58289 | 0.304022 | 0.152011 | − | 0.988379i | \(-0.451425\pi\) | ||||
0.152011 | + | 0.988379i | \(0.451425\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.7936 | −0.558736 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 52.7487 | 1.86378 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.4464 | −0.650960 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −42.5136 | −1.49841 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 63.2383 | 2.22609 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.79502 | −0.309216 | −0.154608 | − | 0.987976i | \(-0.549412\pi\) | ||||
−0.154608 | + | 0.987976i | \(0.549412\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.0607 | 1.54718 | 0.773591 | − | 0.633686i | \(-0.218459\pi\) | ||||
0.773591 | + | 0.633686i | \(0.218459\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 54.5305 | 1.91247 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.97923 | −0.209443 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.5638 | 0.649464 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 30.1592 | 1.05385 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.27900 | −0.149338 | −0.0746690 | − | 0.997208i | \(-0.523790\pi\) | ||||
−0.0746690 | + | 0.997208i | \(0.523790\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.2812 | 0.985821 | 0.492911 | − | 0.870080i | \(-0.335933\pi\) | ||||
0.492911 | + | 0.870080i | \(0.335933\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 19.0631 | 0.663692 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.4581 | −0.954810 | −0.477405 | − | 0.878683i | \(-0.658423\pi\) | ||||
−0.477405 | + | 0.878683i | \(0.658423\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 49.3263 | 1.71317 | 0.856586 | − | 0.516004i | \(-0.172581\pi\) | ||||
0.856586 | + | 0.516004i | \(0.172581\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 60.6015 | 2.10224 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.2443 | −0.528183 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −52.4655 | −1.81564 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.01326 | 0.0695883 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.8210 | −1.16763 | −0.583815 | − | 0.811887i | \(-0.698441\pi\) | ||||
−0.583815 | + | 0.811887i | \(0.698441\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5534 | −0.984599 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.4946 | 0.705870 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 40.9592 | 1.40904 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.976188 | 0.0335422 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.2088 | 0.453325 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −40.2714 | −1.38049 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.24511 | 0.179589 | 0.0897946 | − | 0.995960i | \(-0.471379\pi\) | ||||
0.0897946 | + | 0.995960i | \(0.471379\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 23.0553 | 0.788476 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.1229 | −0.926499 | −0.463250 | − | 0.886228i | \(-0.653317\pi\) | ||||
−0.463250 | + | 0.886228i | \(0.653317\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.1399 | 1.13072 | 0.565360 | − | 0.824845i | \(-0.308737\pi\) | ||||
0.565360 | + | 0.824845i | \(0.308737\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.7649 | 0.809906 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.4403 | 1.27448 | 0.637241 | − | 0.770665i | \(-0.280076\pi\) | ||||
0.637241 | + | 0.770665i | \(0.280076\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.7878 | −1.21682 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.2297 | 0.347418 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.25752 | −0.246195 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43.0590 | −1.45900 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.4436 | 0.658067 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.0161 | 0.406218 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.4431 | −0.757850 | −0.378925 | − | 0.925427i | \(-0.623706\pi\) | ||||
−0.378925 | + | 0.925427i | \(0.623706\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −28.9823 | −0.977550 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.9906 | 1.61684 | 0.808422 | − | 0.588604i | \(-0.200322\pi\) | ||||
0.808422 | + | 0.588604i | \(0.200322\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.5960 | 1.13060 | 0.565298 | − | 0.824887i | \(-0.308761\pi\) | ||||
0.565298 | + | 0.824887i | \(0.308761\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 72.6112 | 2.44080 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.9340 | 0.971508 | 0.485754 | − | 0.874096i | \(-0.338545\pi\) | ||||
0.485754 | + | 0.874096i | \(0.338545\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.8025 | 0.362303 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.4154 | 0.817946 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.9236 | −0.365544 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.0124 | −1.07006 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 126.858 | 4.23566 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.26639 | 0.0422364 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49.4144 | −1.64623 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 31.4122 | 1.04533 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −44.1378 | −1.46719 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.62901 | −0.220113 | −0.110056 | − | 0.993925i | \(-0.535103\pi\) | ||||
−0.110056 | + | 0.993925i | \(0.535103\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.5369 | −0.581661 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.9716 | 0.827345 | 0.413673 | − | 0.910426i | \(-0.364246\pi\) | ||||
0.413673 | + | 0.910426i | \(0.364246\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.42418 | 0.245704 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −32.9878 | −1.09054 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.5873 | 0.580785 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.4074 | −1.56383 | −0.781914 | − | 0.623387i | \(-0.785756\pi\) | ||||
−0.781914 | + | 0.623387i | \(0.785756\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.74816 | −0.123506 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 46.3397 | 1.52529 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.94593 | −0.327020 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.0736 | −0.987748 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.5106 | 0.410461 | 0.205231 | − | 0.978714i | \(-0.434206\pi\) | ||||
0.205231 | + | 0.978714i | \(0.434206\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.5437 | −0.345556 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −50.7339 | −1.66095 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −31.4581 | −1.02879 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.6107 | 0.738659 | 0.369329 | − | 0.929299i | \(-0.379587\pi\) | ||||
0.369329 | + | 0.929299i | \(0.379587\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −68.9540 | −2.25023 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.200768 | 0.00654485 | 0.00327242 | − | 0.999995i | \(-0.498958\pi\) | ||||
0.00327242 | + | 0.999995i | \(0.498958\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 53.2458 | 1.73392 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.78436 | 0.155635 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.2447 | 0.917829 | 0.458914 | − | 0.888481i | \(-0.348238\pi\) | ||||
0.458914 | + | 0.888481i | \(0.348238\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.3169 | −0.984129 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −76.2034 | −2.47107 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.5010 | 0.923238 | 0.461619 | − | 0.887078i | \(-0.347269\pi\) | ||||
0.461619 | + | 0.887078i | \(0.347269\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.8018 | 1.12616 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.46396 | −0.176625 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26.3271 | 0.850145 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.4093 | −0.884170 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 34.5606 | 1.11370 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.56754 | 0.0504610 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.3970 | −0.816713 | −0.408356 | − | 0.912823i | \(-0.633898\pi\) | ||||
−0.408356 | + | 0.912823i | \(0.633898\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.7153 | −0.729720 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −61.2093 | −1.96430 | −0.982149 | − | 0.188103i | \(-0.939766\pi\) | ||||
−0.982149 | + | 0.188103i | \(0.939766\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 27.1707 | 0.871052 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 31.3304 | 1.00338 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 54.3713 | 1.73949 | 0.869746 | − | 0.493500i | \(-0.164283\pi\) | ||||
0.869746 | + | 0.493500i | \(0.164283\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −49.7804 | −1.59099 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.9358 | 0.859995 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.1072 | 0.513741 | 0.256870 | − | 0.966446i | \(-0.417309\pi\) | ||||
0.256870 | + | 0.966446i | \(0.417309\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −60.8580 | −1.93910 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −18.4841 | −0.588354 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 70.3798 | 2.23795 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.5652 | 1.00270 | 0.501351 | − | 0.865244i | \(-0.332836\pi\) | ||||
0.501351 | + | 0.865244i | \(0.332836\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −37.4784 | −1.18934 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.99094 | 0.158223 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.89921 | 0.0918189 | 0.0459094 | − | 0.998946i | \(-0.485381\pi\) | ||||
0.0459094 | + | 0.998946i | \(0.485381\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.53203 | 0.143387 |
(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 | 4016.2.a.j.1.3 | 14 | ||
4.3 | odd | 2 | 1004.2.a.b.1.12 | ✓ | 14 | ||
12.11 | even | 2 | 9036.2.a.m.1.4 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1004.2.a.b.1.12 | ✓ | 14 | 4.3 | odd | 2 | ||
4016.2.a.j.1.3 | 14 | 1.1 | even | 1 | trivial | ||
9036.2.a.m.1.4 | 14 | 12.11 | even | 2 |