Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,2,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2151.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(17.1758214748\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 21 x^{18} + 96 x^{17} + 164 x^{16} - 936 x^{15} - 540 x^{14} + 4804 x^{13} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.67404\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.67404 | −1.89083 | −0.945416 | − | 0.325865i | \(-0.894344\pi\) | ||||
−0.945416 | + | 0.325865i | \(0.894344\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.15050 | 2.57525 | ||||||||
\(5\) | −0.519163 | −0.232177 | −0.116088 | − | 0.993239i | \(-0.537036\pi\) | ||||
−0.116088 | + | 0.993239i | \(0.537036\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.02094 | 0.385881 | 0.192940 | − | 0.981211i | \(-0.438198\pi\) | ||||
0.192940 | + | 0.981211i | \(0.438198\pi\) | |||||||
\(8\) | −8.42455 | −2.97853 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.38826 | 0.439008 | ||||||||
\(11\) | −5.14954 | −1.55265 | −0.776323 | − | 0.630336i | \(-0.782917\pi\) | ||||
−0.776323 | + | 0.630336i | \(0.782917\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.29568 | −0.636708 | −0.318354 | − | 0.947972i | \(-0.603130\pi\) | ||||
−0.318354 | + | 0.947972i | \(0.603130\pi\) | |||||||
\(14\) | −2.73005 | −0.729635 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.2266 | 3.05665 | ||||||||
\(17\) | 1.92182 | 0.466109 | 0.233054 | − | 0.972464i | \(-0.425128\pi\) | ||||
0.233054 | + | 0.972464i | \(0.425128\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.15077 | 0.722835 | 0.361418 | − | 0.932404i | \(-0.382293\pi\) | ||||
0.361418 | + | 0.932404i | \(0.382293\pi\) | |||||||
\(20\) | −2.67395 | −0.597913 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 13.7701 | 2.93579 | ||||||||
\(23\) | 6.68812 | 1.39457 | 0.697284 | − | 0.716795i | \(-0.254391\pi\) | ||||
0.697284 | + | 0.716795i | \(0.254391\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.73047 | −0.946094 | ||||||||
\(26\) | 6.13875 | 1.20391 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.25837 | 0.993738 | ||||||||
\(29\) | 7.68981 | 1.42796 | 0.713981 | − | 0.700165i | \(-0.246890\pi\) | ||||
0.713981 | + | 0.700165i | \(0.246890\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.20467 | −0.216365 | −0.108182 | − | 0.994131i | \(-0.534503\pi\) | ||||
−0.108182 | + | 0.994131i | \(0.534503\pi\) | |||||||
\(32\) | −15.8454 | −2.80109 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.13902 | −0.881334 | ||||||||
\(35\) | −0.530037 | −0.0895926 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.791859 | −0.130181 | −0.0650904 | − | 0.997879i | \(-0.520734\pi\) | ||||
−0.0650904 | + | 0.997879i | \(0.520734\pi\) | |||||||
\(38\) | −8.42528 | −1.36676 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.37372 | 0.691546 | ||||||||
\(41\) | −2.49631 | −0.389858 | −0.194929 | − | 0.980817i | \(-0.562448\pi\) | ||||
−0.194929 | + | 0.980817i | \(0.562448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.15197 | 0.175674 | 0.0878370 | − | 0.996135i | \(-0.472005\pi\) | ||||
0.0878370 | + | 0.996135i | \(0.472005\pi\) | |||||||
\(44\) | −26.5227 | −3.99845 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −17.8843 | −2.63690 | ||||||||
\(47\) | −8.92862 | −1.30237 | −0.651187 | − | 0.758918i | \(-0.725728\pi\) | ||||
−0.651187 | + | 0.758918i | \(0.725728\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.95767 | −0.851096 | ||||||||
\(50\) | 12.6495 | 1.78891 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −11.8239 | −1.63968 | ||||||||
\(53\) | 7.62842 | 1.04784 | 0.523922 | − | 0.851766i | \(-0.324468\pi\) | ||||
0.523922 | + | 0.851766i | \(0.324468\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.67345 | 0.360488 | ||||||||
\(56\) | −8.60100 | −1.14936 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −20.5629 | −2.70004 | ||||||||
\(59\) | −9.24454 | −1.20354 | −0.601768 | − | 0.798671i | \(-0.705537\pi\) | ||||
−0.601768 | + | 0.798671i | \(0.705537\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.23081 | 0.285626 | 0.142813 | − | 0.989750i | \(-0.454385\pi\) | ||||
0.142813 | + | 0.989750i | \(0.454385\pi\) | |||||||
\(62\) | 3.22134 | 0.409110 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 17.9179 | 2.23974 | ||||||||
\(65\) | 1.19183 | 0.147829 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.8406 | 1.81307 | 0.906535 | − | 0.422130i | \(-0.138717\pi\) | ||||
0.906535 | + | 0.422130i | \(0.138717\pi\) | |||||||
\(68\) | 9.89831 | 1.20035 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.41734 | 0.169405 | ||||||||
\(71\) | 4.46542 | 0.529948 | 0.264974 | − | 0.964256i | \(-0.414637\pi\) | ||||
0.264974 | + | 0.964256i | \(0.414637\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.29621 | −0.268751 | −0.134376 | − | 0.990930i | \(-0.542903\pi\) | ||||
−0.134376 | + | 0.990930i | \(0.542903\pi\) | |||||||
\(74\) | 2.11746 | 0.246150 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 16.2280 | 1.86148 | ||||||||
\(77\) | −5.25739 | −0.599136 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.20506 | −1.03565 | −0.517825 | − | 0.855487i | \(-0.673258\pi\) | ||||
−0.517825 | + | 0.855487i | \(0.673258\pi\) | |||||||
\(80\) | −6.34761 | −0.709684 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.67524 | 0.737157 | ||||||||
\(83\) | −13.9566 | −1.53193 | −0.765967 | − | 0.642880i | \(-0.777739\pi\) | ||||
−0.765967 | + | 0.642880i | \(0.777739\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.997737 | −0.108220 | ||||||||
\(86\) | −3.08042 | −0.332170 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 43.3826 | 4.62460 | ||||||||
\(89\) | −7.81208 | −0.828079 | −0.414039 | − | 0.910259i | \(-0.635882\pi\) | ||||
−0.414039 | + | 0.910259i | \(0.635882\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.34376 | −0.245693 | ||||||||
\(92\) | 34.4471 | 3.59136 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 23.8755 | 2.46257 | ||||||||
\(95\) | −1.63576 | −0.167826 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.25925 | −0.432461 | −0.216231 | − | 0.976342i | \(-0.569376\pi\) | ||||
−0.216231 | + | 0.976342i | \(0.569376\pi\) | |||||||
\(98\) | 15.9311 | 1.60928 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −24.3643 | −2.43643 | ||||||||
\(101\) | −16.5592 | −1.64770 | −0.823851 | − | 0.566807i | \(-0.808179\pi\) | ||||
−0.823851 | + | 0.566807i | \(0.808179\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.0011 | −1.28103 | −0.640517 | − | 0.767944i | \(-0.721280\pi\) | ||||
−0.640517 | + | 0.767944i | \(0.721280\pi\) | |||||||
\(104\) | 19.3401 | 1.89645 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.3987 | −1.98130 | ||||||||
\(107\) | 5.26519 | 0.509005 | 0.254503 | − | 0.967072i | \(-0.418088\pi\) | ||||
0.254503 | + | 0.967072i | \(0.418088\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.9722 | −1.05095 | −0.525475 | − | 0.850809i | \(-0.676112\pi\) | ||||
−0.525475 | + | 0.850809i | \(0.676112\pi\) | |||||||
\(110\) | −7.14892 | −0.681623 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.4827 | 1.17950 | ||||||||
\(113\) | 8.33557 | 0.784144 | 0.392072 | − | 0.919934i | \(-0.371758\pi\) | ||||
0.392072 | + | 0.919934i | \(0.371758\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.47223 | −0.323787 | ||||||||
\(116\) | 39.6064 | 3.67736 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 24.7203 | 2.27569 | ||||||||
\(119\) | 1.96207 | 0.179862 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.5178 | 1.41071 | ||||||||
\(122\) | −5.96527 | −0.540070 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.20464 | −0.557193 | ||||||||
\(125\) | 5.05170 | 0.451838 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2324 | 0.907979 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(128\) | −16.2225 | −1.43388 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.18702 | −0.279520 | ||||||||
\(131\) | 11.8436 | 1.03478 | 0.517389 | − | 0.855750i | \(-0.326904\pi\) | ||||
0.517389 | + | 0.855750i | \(0.326904\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.21676 | 0.278928 | ||||||||
\(134\) | −39.6844 | −3.42821 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −16.1904 | −1.38832 | ||||||||
\(137\) | 18.1801 | 1.55323 | 0.776614 | − | 0.629977i | \(-0.216936\pi\) | ||||
0.776614 | + | 0.629977i | \(0.216936\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.89676 | 0.330519 | 0.165259 | − | 0.986250i | \(-0.447154\pi\) | ||||
0.165259 | + | 0.986250i | \(0.447154\pi\) | |||||||
\(140\) | −2.72995 | −0.230723 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.9407 | −1.00204 | ||||||||
\(143\) | 11.8217 | 0.988582 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.99227 | −0.331540 | ||||||||
\(146\) | 6.14016 | 0.508163 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.07846 | −0.335248 | ||||||||
\(149\) | −2.58671 | −0.211911 | −0.105956 | − | 0.994371i | \(-0.533790\pi\) | ||||
−0.105956 | + | 0.994371i | \(0.533790\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.0193 | −1.38501 | −0.692506 | − | 0.721412i | \(-0.743494\pi\) | ||||
−0.692506 | + | 0.721412i | \(0.743494\pi\) | |||||||
\(152\) | −26.5438 | −2.15299 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.0585 | 1.13286 | ||||||||
\(155\) | 0.625420 | 0.0502350 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.59695 | −0.765920 | −0.382960 | − | 0.923765i | \(-0.625095\pi\) | ||||
−0.382960 | + | 0.923765i | \(0.625095\pi\) | |||||||
\(158\) | 24.6147 | 1.95824 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.22633 | 0.650349 | ||||||||
\(161\) | 6.82819 | 0.538137 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.07845 | −0.0844708 | −0.0422354 | − | 0.999108i | \(-0.513448\pi\) | ||||
−0.0422354 | + | 0.999108i | \(0.513448\pi\) | |||||||
\(164\) | −12.8572 | −1.00398 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 37.3205 | 2.89663 | ||||||||
\(167\) | −11.9566 | −0.925230 | −0.462615 | − | 0.886559i | \(-0.653089\pi\) | ||||
−0.462615 | + | 0.886559i | \(0.653089\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.72984 | −0.594603 | ||||||||
\(170\) | 2.66799 | 0.204625 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.93322 | 0.452404 | ||||||||
\(173\) | −16.3039 | −1.23956 | −0.619780 | − | 0.784776i | \(-0.712778\pi\) | ||||
−0.619780 | + | 0.784776i | \(0.712778\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.82954 | −0.365079 | ||||||||
\(176\) | −62.9615 | −4.74590 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 20.8898 | 1.56576 | ||||||||
\(179\) | 0.105075 | 0.00785365 | 0.00392682 | − | 0.999992i | \(-0.498750\pi\) | ||||
0.00392682 | + | 0.999992i | \(0.498750\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.0099 | −1.33866 | −0.669332 | − | 0.742963i | \(-0.733420\pi\) | ||||
−0.669332 | + | 0.742963i | \(0.733420\pi\) | |||||||
\(182\) | 6.26732 | 0.464565 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −56.3444 | −4.15376 | ||||||||
\(185\) | 0.411104 | 0.0302250 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.89647 | −0.723702 | ||||||||
\(188\) | −45.9868 | −3.35393 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.37410 | 0.317330 | ||||||||
\(191\) | 1.54242 | 0.111606 | 0.0558028 | − | 0.998442i | \(-0.482228\pi\) | ||||
0.0558028 | + | 0.998442i | \(0.482228\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.49555 | 0.683505 | 0.341752 | − | 0.939790i | \(-0.388980\pi\) | ||||
0.341752 | + | 0.939790i | \(0.388980\pi\) | |||||||
\(194\) | 11.3894 | 0.817712 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −30.6850 | −2.19178 | ||||||||
\(197\) | −4.42454 | −0.315235 | −0.157618 | − | 0.987500i | \(-0.550381\pi\) | ||||
−0.157618 | + | 0.987500i | \(0.550381\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.1893 | −1.00585 | −0.502927 | − | 0.864329i | \(-0.667744\pi\) | ||||
−0.502927 | + | 0.864329i | \(0.667744\pi\) | |||||||
\(200\) | 39.8521 | 2.81797 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 44.2800 | 3.11553 | ||||||||
\(203\) | 7.85087 | 0.551023 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.29599 | 0.0905161 | ||||||||
\(206\) | 34.7654 | 2.42222 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −28.0684 | −1.94620 | ||||||||
\(209\) | −16.2250 | −1.12231 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.0479471 | 0.00330081 | 0.00165041 | − | 0.999999i | \(-0.499475\pi\) | ||||
0.00165041 | + | 0.999999i | \(0.499475\pi\) | |||||||
\(212\) | 39.2901 | 2.69846 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.0793 | −0.962444 | ||||||||
\(215\) | −0.598061 | −0.0407874 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.22990 | −0.0834910 | ||||||||
\(218\) | 29.3402 | 1.98717 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 13.7696 | 0.928347 | ||||||||
\(221\) | −4.41188 | −0.296775 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.1434 | −1.48283 | −0.741415 | − | 0.671047i | \(-0.765845\pi\) | ||||
−0.741415 | + | 0.671047i | \(0.765845\pi\) | |||||||
\(224\) | −16.1772 | −1.08089 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −22.2896 | −1.48269 | ||||||||
\(227\) | −25.9911 | −1.72509 | −0.862546 | − | 0.505978i | \(-0.831132\pi\) | ||||
−0.862546 | + | 0.505978i | \(0.831132\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.4825 | −1.08919 | −0.544596 | − | 0.838699i | \(-0.683317\pi\) | ||||
−0.544596 | + | 0.838699i | \(0.683317\pi\) | |||||||
\(230\) | 9.28487 | 0.612226 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −64.7833 | −4.25323 | ||||||||
\(233\) | −8.28328 | −0.542656 | −0.271328 | − | 0.962487i | \(-0.587463\pi\) | ||||
−0.271328 | + | 0.962487i | \(0.587463\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.63541 | 0.302381 | ||||||||
\(236\) | −47.6140 | −3.09940 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.24665 | −0.340090 | ||||||||
\(239\) | −1.00000 | −0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.7517 | 1.20790 | 0.603951 | − | 0.797021i | \(-0.293592\pi\) | ||||
0.603951 | + | 0.797021i | \(0.293592\pi\) | |||||||
\(242\) | −41.4952 | −2.66741 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.4898 | 0.735557 | ||||||||
\(245\) | 3.09301 | 0.197605 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.23316 | −0.460235 | ||||||||
\(248\) | 10.1488 | 0.644450 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13.5085 | −0.854350 | ||||||||
\(251\) | −8.36672 | −0.528103 | −0.264051 | − | 0.964509i | \(-0.585059\pi\) | ||||
−0.264051 | + | 0.964509i | \(0.585059\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −34.4407 | −2.16527 | ||||||||
\(254\) | −27.3619 | −1.71684 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.54385 | 0.471491 | ||||||||
\(257\) | 8.28841 | 0.517017 | 0.258509 | − | 0.966009i | \(-0.416769\pi\) | ||||
0.258509 | + | 0.966009i | \(0.416769\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.808443 | −0.0502342 | ||||||||
\(260\) | 6.13854 | 0.380696 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −31.6702 | −1.95659 | ||||||||
\(263\) | 12.7232 | 0.784543 | 0.392272 | − | 0.919849i | \(-0.371689\pi\) | ||||
0.392272 | + | 0.919849i | \(0.371689\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.96040 | −0.243285 | ||||||||
\(266\) | −8.60174 | −0.527406 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 76.4366 | 4.66911 | ||||||||
\(269\) | −7.72368 | −0.470921 | −0.235461 | − | 0.971884i | \(-0.575660\pi\) | ||||
−0.235461 | + | 0.971884i | \(0.575660\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.2037 | 1.40953 | 0.704764 | − | 0.709442i | \(-0.251053\pi\) | ||||
0.704764 | + | 0.709442i | \(0.251053\pi\) | |||||||
\(272\) | 23.4973 | 1.42473 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −48.6142 | −2.93689 | ||||||||
\(275\) | 24.3597 | 1.46895 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.69405 | −0.342123 | −0.171061 | − | 0.985260i | \(-0.554720\pi\) | ||||
−0.171061 | + | 0.985260i | \(0.554720\pi\) | |||||||
\(278\) | −10.4201 | −0.624956 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.46532 | 0.266854 | ||||||||
\(281\) | −26.2890 | −1.56827 | −0.784134 | − | 0.620592i | \(-0.786892\pi\) | ||||
−0.784134 | + | 0.620592i | \(0.786892\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.4629 | 1.27584 | 0.637918 | − | 0.770104i | \(-0.279796\pi\) | ||||
0.637918 | + | 0.770104i | \(0.279796\pi\) | |||||||
\(284\) | 22.9991 | 1.36475 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −31.6118 | −1.86924 | ||||||||
\(287\) | −2.54859 | −0.150439 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.3066 | −0.782742 | ||||||||
\(290\) | 10.6755 | 0.626887 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.8266 | −0.692101 | ||||||||
\(293\) | 15.8224 | 0.924356 | 0.462178 | − | 0.886787i | \(-0.347068\pi\) | ||||
0.462178 | + | 0.886787i | \(0.347068\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.79943 | 0.279433 | ||||||||
\(296\) | 6.67106 | 0.387747 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.91696 | 0.400689 | ||||||||
\(299\) | −15.3538 | −0.887933 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.17610 | 0.0677891 | ||||||||
\(302\) | 45.5104 | 2.61883 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 38.5232 | 2.20946 | ||||||||
\(305\) | −1.15815 | −0.0663157 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.3738 | −0.649137 | −0.324569 | − | 0.945862i | \(-0.605219\pi\) | ||||
−0.324569 | + | 0.945862i | \(0.605219\pi\) | |||||||
\(308\) | −27.0782 | −1.54292 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.67240 | −0.0949859 | ||||||||
\(311\) | −19.7338 | −1.11900 | −0.559501 | − | 0.828830i | \(-0.689007\pi\) | ||||
−0.559501 | + | 0.828830i | \(0.689007\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.24433 | 0.409474 | 0.204737 | − | 0.978817i | \(-0.434366\pi\) | ||||
0.204737 | + | 0.978817i | \(0.434366\pi\) | |||||||
\(314\) | 25.6626 | 1.44823 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −47.4106 | −2.66705 | ||||||||
\(317\) | −11.0779 | −0.622199 | −0.311099 | − | 0.950377i | \(-0.600697\pi\) | ||||
−0.311099 | + | 0.950377i | \(0.600697\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −39.5990 | −2.21712 | ||||||||
\(320\) | −9.30233 | −0.520016 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −18.2589 | −1.01753 | ||||||||
\(323\) | 6.05519 | 0.336920 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.8597 | 0.602386 | ||||||||
\(326\) | 2.88382 | 0.159720 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 21.0303 | 1.16120 | ||||||||
\(329\) | −9.11562 | −0.502560 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.7234 | 0.644374 | 0.322187 | − | 0.946676i | \(-0.395582\pi\) | ||||
0.322187 | + | 0.946676i | \(0.395582\pi\) | |||||||
\(332\) | −71.8833 | −3.94511 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 31.9724 | 1.74945 | ||||||||
\(335\) | −7.70471 | −0.420953 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.6376 | −1.55999 | −0.779995 | − | 0.625786i | \(-0.784778\pi\) | ||||
−0.779995 | + | 0.625786i | \(0.784778\pi\) | |||||||
\(338\) | 20.6699 | 1.12429 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.13884 | −0.278693 | ||||||||
\(341\) | 6.20349 | 0.335938 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.2291 | −0.714302 | ||||||||
\(344\) | −9.70484 | −0.523250 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 43.5972 | 2.34380 | ||||||||
\(347\) | 1.96621 | 0.105552 | 0.0527760 | − | 0.998606i | \(-0.483193\pi\) | ||||
0.0527760 | + | 0.998606i | \(0.483193\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.25673 | −0.0672713 | −0.0336357 | − | 0.999434i | \(-0.510709\pi\) | ||||
−0.0336357 | + | 0.999434i | \(0.510709\pi\) | |||||||
\(350\) | 12.9144 | 0.690304 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 81.5963 | 4.34910 | ||||||||
\(353\) | −21.0991 | −1.12299 | −0.561495 | − | 0.827480i | \(-0.689774\pi\) | ||||
−0.561495 | + | 0.827480i | \(0.689774\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.31828 | −0.123042 | ||||||||
\(356\) | −40.2361 | −2.13251 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.280974 | −0.0148499 | ||||||||
\(359\) | −17.5335 | −0.925382 | −0.462691 | − | 0.886520i | \(-0.653116\pi\) | ||||
−0.462691 | + | 0.886520i | \(0.653116\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.07267 | −0.477509 | ||||||||
\(362\) | 48.1592 | 2.53119 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.0715 | −0.632721 | ||||||||
\(365\) | 1.19211 | 0.0623978 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.4166 | 1.48334 | 0.741668 | − | 0.670767i | \(-0.234035\pi\) | ||||
0.741668 | + | 0.670767i | \(0.234035\pi\) | |||||||
\(368\) | 81.7730 | 4.26271 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.09931 | −0.0571503 | ||||||||
\(371\) | 7.78819 | 0.404343 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.4497 | 1.16240 | 0.581201 | − | 0.813760i | \(-0.302583\pi\) | ||||
0.581201 | + | 0.813760i | \(0.302583\pi\) | |||||||
\(374\) | 26.4636 | 1.36840 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 75.2197 | 3.87916 | ||||||||
\(377\) | −17.6534 | −0.909195 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.8689 | 0.866499 | 0.433250 | − | 0.901274i | \(-0.357367\pi\) | ||||
0.433250 | + | 0.901274i | \(0.357367\pi\) | |||||||
\(380\) | −8.42499 | −0.432193 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.12449 | −0.211027 | ||||||||
\(383\) | 15.0924 | 0.771184 | 0.385592 | − | 0.922669i | \(-0.373997\pi\) | ||||
0.385592 | + | 0.922669i | \(0.373997\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.72945 | 0.139105 | ||||||||
\(386\) | −25.3915 | −1.29239 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −21.9373 | −1.11370 | ||||||||
\(389\) | −4.28146 | −0.217079 | −0.108539 | − | 0.994092i | \(-0.534617\pi\) | ||||
−0.108539 | + | 0.994092i | \(0.534617\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.8533 | 0.650021 | ||||||||
\(392\) | 50.1907 | 2.53502 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.8314 | 0.596057 | ||||||||
\(395\) | 4.77893 | 0.240454 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.2285 | −1.31637 | −0.658186 | − | 0.752855i | \(-0.728676\pi\) | ||||
−0.658186 | + | 0.752855i | \(0.728676\pi\) | |||||||
\(398\) | 37.9429 | 1.90190 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −57.8376 | −2.89188 | ||||||||
\(401\) | 1.34368 | 0.0671001 | 0.0335500 | − | 0.999437i | \(-0.489319\pi\) | ||||
0.0335500 | + | 0.999437i | \(0.489319\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.76554 | 0.137761 | ||||||||
\(404\) | −85.2881 | −4.24324 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.9935 | −1.04189 | ||||||||
\(407\) | 4.07771 | 0.202124 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.8377 | 0.733677 | 0.366838 | − | 0.930285i | \(-0.380440\pi\) | ||||
0.366838 | + | 0.930285i | \(0.380440\pi\) | |||||||
\(410\) | −3.46554 | −0.171151 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −66.9620 | −3.29898 | ||||||||
\(413\) | −9.43816 | −0.464421 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.24575 | 0.355680 | ||||||||
\(416\) | 36.3759 | 1.78348 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 43.3863 | 2.12209 | ||||||||
\(419\) | −33.9802 | −1.66004 | −0.830021 | − | 0.557731i | \(-0.811672\pi\) | ||||
−0.830021 | + | 0.557731i | \(0.811672\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 40.1479 | 1.95669 | 0.978344 | − | 0.206985i | \(-0.0663652\pi\) | ||||
0.978344 | + | 0.206985i | \(0.0663652\pi\) | |||||||
\(422\) | −0.128213 | −0.00624129 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −64.2660 | −3.12103 | ||||||||
\(425\) | −9.09109 | −0.440983 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.27753 | 0.110217 | ||||||||
\(428\) | 27.1183 | 1.31081 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.59924 | 0.0771222 | ||||||||
\(431\) | −25.2309 | −1.21533 | −0.607665 | − | 0.794194i | \(-0.707894\pi\) | ||||
−0.607665 | + | 0.794194i | \(0.707894\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.2782 | −1.50313 | −0.751567 | − | 0.659657i | \(-0.770702\pi\) | ||||
−0.751567 | + | 0.659657i | \(0.770702\pi\) | |||||||
\(434\) | 3.28880 | 0.157868 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −56.5124 | −2.70645 | ||||||||
\(437\) | 21.0727 | 1.00804 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.15467 | −0.198291 | −0.0991457 | − | 0.995073i | \(-0.531611\pi\) | ||||
−0.0991457 | + | 0.995073i | \(0.531611\pi\) | |||||||
\(440\) | −22.5227 | −1.07373 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.7976 | 0.561152 | ||||||||
\(443\) | 20.0339 | 0.951840 | 0.475920 | − | 0.879489i | \(-0.342115\pi\) | ||||
0.475920 | + | 0.879489i | \(0.342115\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.05575 | 0.192261 | ||||||||
\(446\) | 59.2123 | 2.80378 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18.2932 | 0.864272 | ||||||||
\(449\) | −15.7631 | −0.743906 | −0.371953 | − | 0.928252i | \(-0.621312\pi\) | ||||
−0.371953 | + | 0.928252i | \(0.621312\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.8549 | 0.605312 | ||||||||
\(452\) | 42.9323 | 2.01937 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 69.5014 | 3.26186 | ||||||||
\(455\) | 1.21680 | 0.0570443 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.3920 | 0.673227 | 0.336614 | − | 0.941643i | \(-0.390718\pi\) | ||||
0.336614 | + | 0.941643i | \(0.390718\pi\) | |||||||
\(458\) | 44.0748 | 2.05948 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −17.8837 | −0.833831 | ||||||||
\(461\) | −9.25187 | −0.430903 | −0.215451 | − | 0.976515i | \(-0.569122\pi\) | ||||
−0.215451 | + | 0.976515i | \(0.569122\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.95525 | 0.462660 | 0.231330 | − | 0.972875i | \(-0.425692\pi\) | ||||
0.231330 | + | 0.972875i | \(0.425692\pi\) | |||||||
\(464\) | 94.0204 | 4.36479 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.1498 | 1.02607 | ||||||||
\(467\) | 18.9730 | 0.877964 | 0.438982 | − | 0.898496i | \(-0.355339\pi\) | ||||
0.438982 | + | 0.898496i | \(0.355339\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.1514 | 0.699629 | ||||||||
\(470\) | −12.3953 | −0.571752 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 77.8811 | 3.58477 | ||||||||
\(473\) | −5.93212 | −0.272759 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.9046 | −0.683870 | ||||||||
\(476\) | 10.1056 | 0.463190 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.67404 | 0.122308 | ||||||||
\(479\) | 33.1598 | 1.51511 | 0.757555 | − | 0.652771i | \(-0.226394\pi\) | ||||
0.757555 | + | 0.652771i | \(0.226394\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.81786 | 0.0828871 | ||||||||
\(482\) | −50.1428 | −2.28394 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 79.9242 | 3.63292 | ||||||||
\(485\) | 2.21125 | 0.100408 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.0030 | −1.67677 | −0.838384 | − | 0.545080i | \(-0.816499\pi\) | ||||
−0.838384 | + | 0.545080i | \(0.816499\pi\) | |||||||
\(488\) | −18.7936 | −0.850745 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.27083 | −0.373638 | ||||||||
\(491\) | 15.5770 | 0.702980 | 0.351490 | − | 0.936192i | \(-0.385675\pi\) | ||||
0.351490 | + | 0.936192i | \(0.385675\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.7784 | 0.665586 | ||||||||
\(494\) | 19.3418 | 0.870227 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.7290 | −0.661353 | ||||||||
\(497\) | 4.55895 | 0.204497 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.63382 | −0.162672 | −0.0813360 | − | 0.996687i | \(-0.525919\pi\) | ||||
−0.0813360 | + | 0.996687i | \(0.525919\pi\) | |||||||
\(500\) | 26.0188 | 1.16360 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22.3730 | 0.998554 | ||||||||
\(503\) | 42.5761 | 1.89838 | 0.949188 | − | 0.314710i | \(-0.101907\pi\) | ||||
0.949188 | + | 0.314710i | \(0.101907\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.59693 | 0.382558 | ||||||||
\(506\) | 92.0959 | 4.09416 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 52.7020 | 2.33827 | ||||||||
\(509\) | −35.1080 | −1.55614 | −0.778068 | − | 0.628180i | \(-0.783800\pi\) | ||||
−0.778068 | + | 0.628180i | \(0.783800\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.34430 | −0.103706 | ||||||||
\(512\) | 12.2725 | 0.542371 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.1636 | −0.977593 | ||||||||
\(515\) | 6.74968 | 0.297426 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.9783 | 2.02212 | ||||||||
\(518\) | 2.16181 | 0.0949845 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.0407 | −0.440313 | ||||||||
\(521\) | −36.0412 | −1.57899 | −0.789497 | − | 0.613754i | \(-0.789659\pi\) | ||||
−0.789497 | + | 0.613754i | \(0.789659\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.568975 | 0.0248795 | 0.0124398 | − | 0.999923i | \(-0.496040\pi\) | ||||
0.0124398 | + | 0.999923i | \(0.496040\pi\) | |||||||
\(524\) | 61.0003 | 2.66481 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −34.0222 | −1.48344 | ||||||||
\(527\) | −2.31515 | −0.100850 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.7309 | 0.944822 | ||||||||
\(530\) | 10.5903 | 0.460012 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16.5679 | 0.718309 | ||||||||
\(533\) | 5.73074 | 0.248226 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.73349 | −0.118179 | ||||||||
\(536\) | −125.026 | −5.40029 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.6534 | 0.890433 | ||||||||
\(539\) | 30.6793 | 1.32145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.1080 | 0.520565 | 0.260283 | − | 0.965533i | \(-0.416184\pi\) | ||||
0.260283 | + | 0.965533i | \(0.416184\pi\) | |||||||
\(542\) | −62.0478 | −2.66518 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −30.4519 | −1.30561 | ||||||||
\(545\) | 5.69638 | 0.244006 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.4919 | 1.73131 | 0.865654 | − | 0.500642i | \(-0.166903\pi\) | ||||
0.865654 | + | 0.500642i | \(0.166903\pi\) | |||||||
\(548\) | 93.6363 | 3.99995 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −65.1390 | −2.77753 | ||||||||
\(551\) | 24.2288 | 1.03218 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.39785 | −0.399637 | ||||||||
\(554\) | 15.2261 | 0.646896 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.0702 | 0.851168 | ||||||||
\(557\) | 26.3904 | 1.11820 | 0.559098 | − | 0.829101i | \(-0.311147\pi\) | ||||
0.559098 | + | 0.829101i | \(0.311147\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.64456 | −0.111853 | ||||||||
\(560\) | −6.48055 | −0.273853 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 70.2977 | 2.96533 | ||||||||
\(563\) | 30.2542 | 1.27506 | 0.637532 | − | 0.770424i | \(-0.279955\pi\) | ||||
0.637532 | + | 0.770424i | \(0.279955\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.32752 | −0.182060 | ||||||||
\(566\) | −57.3927 | −2.41239 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −37.6192 | −1.57847 | ||||||||
\(569\) | −4.56920 | −0.191551 | −0.0957754 | − | 0.995403i | \(-0.530533\pi\) | ||||
−0.0957754 | + | 0.995403i | \(0.530533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.4991 | −0.439375 | −0.219687 | − | 0.975570i | \(-0.570504\pi\) | ||||
−0.219687 | + | 0.975570i | \(0.570504\pi\) | |||||||
\(572\) | 60.8877 | 2.54584 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.81505 | 0.284455 | ||||||||
\(575\) | −31.6379 | −1.31939 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.62882 | −0.151070 | −0.0755349 | − | 0.997143i | \(-0.524066\pi\) | ||||
−0.0755349 | + | 0.997143i | \(0.524066\pi\) | |||||||
\(578\) | 35.5825 | 1.48003 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −20.5622 | −0.853798 | ||||||||
\(581\) | −14.2489 | −0.591143 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −39.2829 | −1.62693 | ||||||||
\(584\) | 19.3446 | 0.800483 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −42.3098 | −1.74780 | ||||||||
\(587\) | −22.5623 | −0.931244 | −0.465622 | − | 0.884984i | \(-0.654169\pi\) | ||||
−0.465622 | + | 0.884984i | \(0.654169\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.79563 | −0.156396 | ||||||||
\(590\) | −12.8339 | −0.528362 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.68175 | −0.397917 | ||||||||
\(593\) | 26.6646 | 1.09498 | 0.547492 | − | 0.836811i | \(-0.315583\pi\) | ||||
0.547492 | + | 0.836811i | \(0.315583\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.01863 | −0.0417599 | ||||||||
\(596\) | −13.3228 | −0.545724 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 41.0567 | 1.67893 | ||||||||
\(599\) | −29.4480 | −1.20321 | −0.601605 | − | 0.798793i | \(-0.705472\pi\) | ||||
−0.601605 | + | 0.798793i | \(0.705472\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.9235 | −1.38377 | −0.691884 | − | 0.722009i | \(-0.743219\pi\) | ||||
−0.691884 | + | 0.722009i | \(0.743219\pi\) | |||||||
\(602\) | −3.14493 | −0.128178 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −87.6579 | −3.56675 | ||||||||
\(605\) | −8.05626 | −0.327534 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.484162 | 0.0196515 | 0.00982577 | − | 0.999952i | \(-0.496872\pi\) | ||||
0.00982577 | + | 0.999952i | \(0.496872\pi\) | |||||||
\(608\) | −49.9250 | −2.02473 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.09695 | 0.125392 | ||||||||
\(611\) | 20.4973 | 0.829231 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.8655 | −0.842750 | −0.421375 | − | 0.906886i | \(-0.638452\pi\) | ||||
−0.421375 | + | 0.906886i | \(0.638452\pi\) | |||||||
\(614\) | 30.4140 | 1.22741 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 44.2912 | 1.78454 | ||||||||
\(617\) | 13.7272 | 0.552637 | 0.276319 | − | 0.961066i | \(-0.410885\pi\) | ||||
0.276319 | + | 0.961066i | \(0.410885\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −45.3078 | −1.82107 | −0.910536 | − | 0.413429i | \(-0.864331\pi\) | ||||
−0.910536 | + | 0.413429i | \(0.864331\pi\) | |||||||
\(620\) | 3.22122 | 0.129367 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 52.7690 | 2.11585 | ||||||||
\(623\) | −7.97569 | −0.319539 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.0297 | 0.841187 | ||||||||
\(626\) | −19.3716 | −0.774247 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −49.4290 | −1.97243 | ||||||||
\(629\) | −1.52181 | −0.0606784 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.0302 | 1.07605 | 0.538027 | − | 0.842927i | \(-0.319170\pi\) | ||||
0.538027 | + | 0.842927i | \(0.319170\pi\) | |||||||
\(632\) | 77.5485 | 3.08471 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 29.6228 | 1.17647 | ||||||||
\(635\) | −5.31229 | −0.210812 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.6769 | 0.541900 | ||||||||
\(638\) | 105.889 | 4.19220 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.42214 | 0.332914 | ||||||||
\(641\) | −44.9994 | −1.77737 | −0.888684 | − | 0.458520i | \(-0.848380\pi\) | ||||
−0.888684 | + | 0.458520i | \(0.848380\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.2140 | −1.70419 | −0.852097 | − | 0.523384i | \(-0.824669\pi\) | ||||
−0.852097 | + | 0.523384i | \(0.824669\pi\) | |||||||
\(644\) | 35.1686 | 1.38584 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.1918 | −0.637059 | ||||||||
\(647\) | −17.6690 | −0.694642 | −0.347321 | − | 0.937746i | \(-0.612909\pi\) | ||||
−0.347321 | + | 0.937746i | \(0.612909\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 47.6051 | 1.86867 | ||||||||
\(650\) | −29.0392 | −1.13901 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.55456 | −0.217533 | ||||||||
\(653\) | −38.1713 | −1.49376 | −0.746879 | − | 0.664960i | \(-0.768449\pi\) | ||||
−0.746879 | + | 0.664960i | \(0.768449\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.14876 | −0.240252 | ||||||||
\(656\) | −30.5214 | −1.19166 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24.3755 | 0.950258 | ||||||||
\(659\) | −13.7251 | −0.534655 | −0.267328 | − | 0.963606i | \(-0.586141\pi\) | ||||
−0.267328 | + | 0.963606i | \(0.586141\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.8679 | 1.23952 | 0.619759 | − | 0.784793i | \(-0.287231\pi\) | ||||
0.619759 | + | 0.784793i | \(0.287231\pi\) | |||||||
\(662\) | −31.3488 | −1.21840 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 117.578 | 4.56291 | ||||||||
\(665\) | −1.67002 | −0.0647607 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 51.4304 | 1.99139 | ||||||||
\(668\) | −61.5824 | −2.38270 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 20.6027 | 0.795952 | ||||||||
\(671\) | −11.4876 | −0.443475 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.3721 | −1.28640 | −0.643200 | − | 0.765698i | \(-0.722394\pi\) | ||||
−0.643200 | + | 0.765698i | \(0.722394\pi\) | |||||||
\(674\) | 76.5781 | 2.94968 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −39.8125 | −1.53125 | ||||||||
\(677\) | 36.3936 | 1.39872 | 0.699359 | − | 0.714770i | \(-0.253469\pi\) | ||||
0.699359 | + | 0.714770i | \(0.253469\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.34846 | −0.166878 | ||||||||
\(680\) | 8.40549 | 0.322336 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.5884 | −0.635203 | ||||||||
\(683\) | −22.4689 | −0.859748 | −0.429874 | − | 0.902889i | \(-0.641442\pi\) | ||||
−0.429874 | + | 0.902889i | \(0.641442\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.43842 | −0.360624 | ||||||||
\(686\) | 35.3750 | 1.35063 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 14.0847 | 0.536974 | ||||||||
\(689\) | −17.5124 | −0.667171 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.7002 | −0.749430 | −0.374715 | − | 0.927140i | \(-0.622260\pi\) | ||||
−0.374715 | + | 0.927140i | \(0.622260\pi\) | |||||||
\(692\) | −83.9730 | −3.19217 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.25774 | −0.199581 | ||||||||
\(695\) | −2.02305 | −0.0767388 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.79745 | −0.181716 | ||||||||
\(698\) | 3.36055 | 0.127199 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −24.8745 | −0.940169 | ||||||||
\(701\) | 26.1013 | 0.985833 | 0.492917 | − | 0.870077i | \(-0.335931\pi\) | ||||
0.492917 | + | 0.870077i | \(0.335931\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.49496 | −0.0940992 | ||||||||
\(704\) | −92.2690 | −3.47752 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 56.4197 | 2.12339 | ||||||||
\(707\) | −16.9060 | −0.635816 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.7834 | 1.45654 | 0.728270 | − | 0.685291i | \(-0.240325\pi\) | ||||
0.728270 | + | 0.685291i | \(0.240325\pi\) | |||||||
\(710\) | 6.19919 | 0.232651 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 65.8133 | 2.46646 | ||||||||
\(713\) | −8.05697 | −0.301736 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.13740 | −0.229526 | ||||||||
\(716\) | 0.541186 | 0.0202251 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 46.8852 | 1.74974 | ||||||||
\(719\) | 28.2950 | 1.05522 | 0.527612 | − | 0.849485i | \(-0.323087\pi\) | ||||
0.527612 | + | 0.849485i | \(0.323087\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.2734 | −0.494326 | ||||||||
\(722\) | 24.2607 | 0.902890 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −92.7598 | −3.44739 | ||||||||
\(725\) | −36.3764 | −1.35099 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.95426 | −0.220831 | −0.110416 | − | 0.993886i | \(-0.535218\pi\) | ||||
−0.110416 | + | 0.993886i | \(0.535218\pi\) | |||||||
\(728\) | 19.7452 | 0.731805 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.18775 | −0.117984 | ||||||||
\(731\) | 2.21388 | 0.0818832 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.6216 | 1.42652 | 0.713260 | − | 0.700900i | \(-0.247218\pi\) | ||||
0.713260 | + | 0.700900i | \(0.247218\pi\) | |||||||
\(734\) | −75.9873 | −2.80474 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −105.976 | −3.90631 | ||||||||
\(737\) | −76.4224 | −2.81506 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 52.1755 | 1.91931 | 0.959654 | − | 0.281183i | \(-0.0907266\pi\) | ||||
0.959654 | + | 0.281183i | \(0.0907266\pi\) | |||||||
\(740\) | 2.11739 | 0.0778368 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20.8259 | −0.764544 | ||||||||
\(743\) | −10.6094 | −0.389223 | −0.194611 | − | 0.980880i | \(-0.562345\pi\) | ||||
−0.194611 | + | 0.980880i | \(0.562345\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.34292 | 0.0492009 | ||||||||
\(746\) | −60.0315 | −2.19791 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −50.9717 | −1.86371 | ||||||||
\(749\) | 5.37546 | 0.196415 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.96839 | 0.0718277 | 0.0359139 | − | 0.999355i | \(-0.488566\pi\) | ||||
0.0359139 | + | 0.999355i | \(0.488566\pi\) | |||||||
\(752\) | −109.167 | −3.98090 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 47.2059 | 1.71914 | ||||||||
\(755\) | 8.83581 | 0.321568 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.9685 | 1.56172 | 0.780859 | − | 0.624707i | \(-0.214782\pi\) | ||||
0.780859 | + | 0.624707i | \(0.214782\pi\) | |||||||
\(758\) | −45.1082 | −1.63840 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.7806 | 0.499874 | ||||||||
\(761\) | −4.94581 | −0.179285 | −0.0896427 | − | 0.995974i | \(-0.528573\pi\) | ||||
−0.0896427 | + | 0.995974i | \(0.528573\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.2020 | −0.405541 | ||||||||
\(764\) | 7.94423 | 0.287412 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −40.3576 | −1.45818 | ||||||||
\(767\) | 21.2225 | 0.766301 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.4312 | −0.736769 | −0.368385 | − | 0.929674i | \(-0.620089\pi\) | ||||
−0.368385 | + | 0.929674i | \(0.620089\pi\) | |||||||
\(770\) | −7.29865 | −0.263025 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 48.9068 | 1.76019 | ||||||||
\(773\) | 5.93494 | 0.213465 | 0.106733 | − | 0.994288i | \(-0.465961\pi\) | ||||
0.106733 | + | 0.994288i | \(0.465961\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.69865 | 0.204702 | ||||||||
\(776\) | 35.8823 | 1.28810 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.4488 | 0.410460 | ||||||||
\(779\) | −7.86529 | −0.281803 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.9949 | −0.822821 | ||||||||
\(782\) | −34.3703 | −1.22908 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −72.8422 | −2.60151 | ||||||||
\(785\) | 4.98238 | 0.177829 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.9085 | 0.959184 | 0.479592 | − | 0.877492i | \(-0.340785\pi\) | ||||
0.479592 | + | 0.877492i | \(0.340785\pi\) | |||||||
\(788\) | −22.7886 | −0.811809 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.7790 | −0.454658 | ||||||||
\(791\) | 8.51015 | 0.302586 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.12123 | −0.181860 | ||||||||
\(794\) | 70.1362 | 2.48904 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −73.0821 | −2.59033 | ||||||||
\(797\) | 0.527733 | 0.0186933 | 0.00934663 | − | 0.999956i | \(-0.497025\pi\) | ||||
0.00934663 | + | 0.999956i | \(0.497025\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.1592 | −0.607048 | ||||||||
\(800\) | 74.9560 | 2.65009 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.59305 | −0.126875 | ||||||||
\(803\) | 11.8244 | 0.417275 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.54495 | −0.124943 | ||||||||
\(806\) | −7.39517 | −0.260484 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 139.504 | 4.90773 | ||||||||
\(809\) | −29.8806 | −1.05055 | −0.525273 | − | 0.850934i | \(-0.676037\pi\) | ||||
−0.525273 | + | 0.850934i | \(0.676037\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.241148 | −0.00846783 | −0.00423392 | − | 0.999991i | \(-0.501348\pi\) | ||||
−0.00423392 | + | 0.999991i | \(0.501348\pi\) | |||||||
\(812\) | 40.4359 | 1.41902 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.9040 | −0.382184 | ||||||||
\(815\) | 0.559893 | 0.0196122 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.62959 | 0.126983 | ||||||||
\(818\) | −39.6766 | −1.38726 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.67501 | 0.233101 | ||||||||
\(821\) | 12.4693 | 0.435183 | 0.217592 | − | 0.976040i | \(-0.430180\pi\) | ||||
0.217592 | + | 0.976040i | \(0.430180\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.5737 | −0.612582 | −0.306291 | − | 0.951938i | \(-0.599088\pi\) | ||||
−0.306291 | + | 0.951938i | \(0.599088\pi\) | |||||||
\(824\) | 109.528 | 3.81560 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 25.2380 | 0.878143 | ||||||||
\(827\) | −27.0166 | −0.939458 | −0.469729 | − | 0.882811i | \(-0.655648\pi\) | ||||
−0.469729 | + | 0.882811i | \(0.655648\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.3187 | −1.19194 | −0.595969 | − | 0.803008i | \(-0.703232\pi\) | ||||
−0.595969 | + | 0.803008i | \(0.703232\pi\) | |||||||
\(830\) | −19.3754 | −0.672531 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −41.1339 | −1.42606 | ||||||||
\(833\) | −11.4496 | −0.396704 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.20743 | 0.214817 | ||||||||
\(836\) | −83.5668 | −2.89022 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 90.8645 | 3.13886 | ||||||||
\(839\) | 57.5893 | 1.98820 | 0.994101 | − | 0.108454i | \(-0.0345901\pi\) | ||||
0.994101 | + | 0.108454i | \(0.0345901\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.1332 | 1.03908 | ||||||||
\(842\) | −107.357 | −3.69977 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.246951 | 0.00850042 | ||||||||
\(845\) | 4.01305 | 0.138053 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.8428 | 0.544364 | ||||||||
\(848\) | 93.2697 | 3.20290 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 24.3100 | 0.833825 | ||||||||
\(851\) | −5.29604 | −0.181546 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.45708 | 0.152607 | 0.0763037 | − | 0.997085i | \(-0.475688\pi\) | ||||
0.0763037 | + | 0.997085i | \(0.475688\pi\) | |||||||
\(854\) | −6.09021 | −0.208403 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −44.3569 | −1.51609 | ||||||||
\(857\) | −14.3007 | −0.488503 | −0.244252 | − | 0.969712i | \(-0.578542\pi\) | ||||
−0.244252 | + | 0.969712i | \(0.578542\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 56.6289 | 1.93215 | 0.966077 | − | 0.258256i | \(-0.0831477\pi\) | ||||
0.966077 | + | 0.258256i | \(0.0831477\pi\) | |||||||
\(860\) | −3.08031 | −0.105038 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 67.4685 | 2.29799 | ||||||||
\(863\) | −21.5070 | −0.732106 | −0.366053 | − | 0.930594i | \(-0.619291\pi\) | ||||
−0.366053 | + | 0.930594i | \(0.619291\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.46437 | 0.287797 | ||||||||
\(866\) | 83.6392 | 2.84217 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.33459 | −0.215010 | ||||||||
\(869\) | 47.4018 | 1.60800 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.0694 | −1.15440 | ||||||||
\(872\) | 92.4362 | 3.13028 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −56.3492 | −1.90604 | ||||||||
\(875\) | 5.15751 | 0.174356 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.70284 | −0.327642 | −0.163821 | − | 0.986490i | \(-0.552382\pi\) | ||||
−0.163821 | + | 0.986490i | \(0.552382\pi\) | |||||||
\(878\) | 11.1098 | 0.374936 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 32.6873 | 1.10189 | ||||||||
\(881\) | −10.7139 | −0.360960 | −0.180480 | − | 0.983579i | \(-0.557765\pi\) | ||||
−0.180480 | + | 0.983579i | \(0.557765\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.9553 | 0.570592 | 0.285296 | − | 0.958440i | \(-0.407908\pi\) | ||||
0.285296 | + | 0.958440i | \(0.407908\pi\) | |||||||
\(884\) | −22.7234 | −0.764270 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −53.5715 | −1.79977 | ||||||||
\(887\) | −13.5417 | −0.454687 | −0.227343 | − | 0.973815i | \(-0.573004\pi\) | ||||
−0.227343 | + | 0.973815i | \(0.573004\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.4467 | 0.350371 | ||||||||
\(890\) | −10.8452 | −0.363533 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −114.049 | −3.81865 | ||||||||
\(893\) | −28.1320 | −0.941401 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.0545509 | −0.00182344 | ||||||||
\(896\) | −16.5623 | −0.553307 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 42.1511 | 1.40660 | ||||||||
\(899\) | −9.26368 | −0.308961 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.6604 | 0.488409 | ||||||||
\(902\) | −34.3744 | −1.14454 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −70.2234 | −2.33560 | ||||||||
\(905\) | 9.35007 | 0.310807 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.47529 | 0.215008 | 0.107504 | − | 0.994205i | \(-0.465714\pi\) | ||||
0.107504 | + | 0.994205i | \(0.465714\pi\) | |||||||
\(908\) | −133.867 | −4.44254 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.25376 | −0.107861 | ||||||||
\(911\) | −32.6698 | −1.08240 | −0.541199 | − | 0.840895i | \(-0.682029\pi\) | ||||
−0.541199 | + | 0.840895i | \(0.682029\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 71.8700 | 2.37855 | ||||||||
\(914\) | −38.4847 | −1.27296 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −84.8928 | −2.80494 | ||||||||
\(917\) | 12.0916 | 0.399301 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.45226 | −0.0479055 | −0.0239527 | − | 0.999713i | \(-0.507625\pi\) | ||||
−0.0239527 | + | 0.999713i | \(0.507625\pi\) | |||||||
\(920\) | 29.2520 | 0.964408 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 24.7399 | 0.814765 | ||||||||
\(923\) | −10.2512 | −0.337422 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.74586 | 0.123163 | ||||||||
\(926\) | −26.6207 | −0.874812 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −121.848 | −3.99985 | ||||||||
\(929\) | 37.4415 | 1.22842 | 0.614208 | − | 0.789144i | \(-0.289476\pi\) | ||||
0.614208 | + | 0.789144i | \(0.289476\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.7712 | −0.615202 | ||||||||
\(932\) | −42.6630 | −1.39747 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −50.7345 | −1.66008 | ||||||||
\(935\) | 5.13789 | 0.168027 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.6947 | −0.512724 | −0.256362 | − | 0.966581i | \(-0.582524\pi\) | ||||
−0.256362 | + | 0.966581i | \(0.582524\pi\) | |||||||
\(938\) | −40.5156 | −1.32288 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 23.8747 | 0.778706 | ||||||||
\(941\) | −25.7719 | −0.840140 | −0.420070 | − | 0.907492i | \(-0.637994\pi\) | ||||
−0.420070 | + | 0.907492i | \(0.637994\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.6956 | −0.543684 | ||||||||
\(944\) | −113.029 | −3.67879 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.8627 | 0.515742 | ||||||||
\(947\) | 53.4780 | 1.73780 | 0.868900 | − | 0.494988i | \(-0.164827\pi\) | ||||
0.868900 | + | 0.494988i | \(0.164827\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.27137 | 0.171116 | ||||||||
\(950\) | 39.8555 | 1.29308 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −16.5295 | −0.535725 | ||||||||
\(953\) | 24.6066 | 0.797085 | 0.398542 | − | 0.917150i | \(-0.369516\pi\) | ||||
0.398542 | + | 0.917150i | \(0.369516\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.800768 | −0.0259122 | ||||||||
\(956\) | −5.15050 | −0.166579 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −88.6707 | −2.86482 | ||||||||
\(959\) | 18.5608 | 0.599360 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5488 | −0.953186 | ||||||||
\(962\) | −4.86102 | −0.156726 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 96.5805 | 3.11065 | ||||||||
\(965\) | −4.92974 | −0.158694 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.5510 | −0.725192 | −0.362596 | − | 0.931946i | \(-0.618110\pi\) | ||||
−0.362596 | + | 0.931946i | \(0.618110\pi\) | |||||||
\(968\) | −130.730 | −4.20183 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.91297 | −0.189854 | ||||||||
\(971\) | −2.61563 | −0.0839396 | −0.0419698 | − | 0.999119i | \(-0.513363\pi\) | ||||
−0.0419698 | + | 0.999119i | \(0.513363\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.97837 | 0.127541 | ||||||||
\(974\) | 98.9477 | 3.17049 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 27.2752 | 0.873059 | ||||||||
\(977\) | −44.8697 | −1.43551 | −0.717755 | − | 0.696296i | \(-0.754830\pi\) | ||||
−0.717755 | + | 0.696296i | \(0.754830\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.2286 | 1.28571 | ||||||||
\(980\) | 15.9305 | 0.508882 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −41.6536 | −1.32922 | ||||||||
\(983\) | −27.0373 | −0.862355 | −0.431177 | − | 0.902267i | \(-0.641902\pi\) | ||||
−0.431177 | + | 0.902267i | \(0.641902\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.29706 | 0.0731903 | ||||||||
\(986\) | −39.5181 | −1.25851 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −37.2544 | −1.18522 | ||||||||
\(989\) | 7.70452 | 0.244989 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.3172 | −0.931293 | −0.465646 | − | 0.884971i | \(-0.654178\pi\) | ||||
−0.465646 | + | 0.884971i | \(0.654178\pi\) | |||||||
\(992\) | 19.0884 | 0.606058 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.1908 | −0.386669 | ||||||||
\(995\) | 7.36658 | 0.233536 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57.2679 | 1.81369 | 0.906847 | − | 0.421460i | \(-0.138482\pi\) | ||||
0.906847 | + | 0.421460i | \(0.138482\pi\) | |||||||
\(998\) | 9.71698 | 0.307585 | ||||||||
\(999\) | 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 | 2151.2.a.j.1.1 | ✓ | 20 | |
3.2 | odd | 2 | 2151.2.a.k.1.20 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.2.a.j.1.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
2151.2.a.k.1.20 | yes | 20 | 3.2 | odd | 2 |