Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.4642000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 8x^{4} + 5x^{3} + 14x^{2} - 9x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.0970464\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.0970464 | 0.0560298 | 0.0280149 | − | 0.999608i | \(-0.491081\pi\) | ||||
0.0280149 | + | 0.999608i | \(0.491081\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.0970464 | −0.0396190 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.99058 | −0.996861 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.0970464 | 0.0280149 | ||||||||
\(13\) | 4.32646 | 1.19994 | 0.599972 | − | 0.800021i | \(-0.295178\pi\) | ||||
0.599972 | + | 0.800021i | \(0.295178\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0.0970464 | 0.0250573 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.12295 | −0.514891 | −0.257445 | − | 0.966293i | \(-0.582881\pi\) | ||||
−0.257445 | + | 0.966293i | \(0.582881\pi\) | |||||||
\(18\) | 2.99058 | 0.704887 | ||||||||
\(19\) | −5.51022 | −1.26413 | −0.632066 | − | 0.774915i | \(-0.717793\pi\) | ||||
−0.632066 | + | 0.774915i | \(0.717793\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0.0970464 | 0.0211773 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.922019 | 0.192254 | 0.0961271 | − | 0.995369i | \(-0.469354\pi\) | ||||
0.0961271 | + | 0.995369i | \(0.469354\pi\) | |||||||
\(24\) | −0.0970464 | −0.0198095 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.32646 | −0.848489 | ||||||||
\(27\) | −0.581365 | −0.111884 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 8.02820 | 1.49080 | 0.745399 | − | 0.666618i | \(-0.232259\pi\) | ||||
0.745399 | + | 0.666618i | \(0.232259\pi\) | |||||||
\(30\) | −0.0970464 | −0.0177182 | ||||||||
\(31\) | 1.21552 | 0.218314 | 0.109157 | − | 0.994024i | \(-0.465185\pi\) | ||||
0.109157 | + | 0.994024i | \(0.465185\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.12295 | 0.364083 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −2.99058 | −0.498430 | ||||||||
\(37\) | −5.01306 | −0.824142 | −0.412071 | − | 0.911152i | \(-0.635194\pi\) | ||||
−0.412071 | + | 0.911152i | \(0.635194\pi\) | |||||||
\(38\) | 5.51022 | 0.893876 | ||||||||
\(39\) | 0.419868 | 0.0672326 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 1.92806 | 0.301113 | 0.150556 | − | 0.988601i | \(-0.451893\pi\) | ||||
0.150556 | + | 0.988601i | \(0.451893\pi\) | |||||||
\(42\) | −0.0970464 | −0.0149746 | ||||||||
\(43\) | −3.75423 | −0.572514 | −0.286257 | − | 0.958153i | \(-0.592411\pi\) | ||||
−0.286257 | + | 0.958153i | \(0.592411\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.99058 | −0.445810 | ||||||||
\(46\) | −0.922019 | −0.135944 | ||||||||
\(47\) | −0.865052 | −0.126181 | −0.0630904 | − | 0.998008i | \(-0.520096\pi\) | ||||
−0.0630904 | + | 0.998008i | \(0.520096\pi\) | |||||||
\(48\) | 0.0970464 | 0.0140074 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −0.206025 | −0.0288492 | ||||||||
\(52\) | 4.32646 | 0.599972 | ||||||||
\(53\) | −0.729158 | −0.100158 | −0.0500788 | − | 0.998745i | \(-0.515947\pi\) | ||||
−0.0500788 | + | 0.998745i | \(0.515947\pi\) | |||||||
\(54\) | 0.581365 | 0.0791137 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −0.534747 | −0.0708290 | ||||||||
\(58\) | −8.02820 | −1.05415 | ||||||||
\(59\) | −0.178208 | −0.0232008 | −0.0116004 | − | 0.999933i | \(-0.503693\pi\) | ||||
−0.0116004 | + | 0.999933i | \(0.503693\pi\) | |||||||
\(60\) | 0.0970464 | 0.0125286 | ||||||||
\(61\) | 13.0127 | 1.66610 | 0.833051 | − | 0.553195i | \(-0.186592\pi\) | ||||
0.833051 | + | 0.553195i | \(0.186592\pi\) | |||||||
\(62\) | −1.21552 | −0.154372 | ||||||||
\(63\) | −2.99058 | −0.376778 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.32646 | 0.536631 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.55383 | −0.434169 | −0.217085 | − | 0.976153i | \(-0.569655\pi\) | ||||
−0.217085 | + | 0.976153i | \(0.569655\pi\) | |||||||
\(68\) | −2.12295 | −0.257445 | ||||||||
\(69\) | 0.0894787 | 0.0107720 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | 5.96038 | 0.707367 | 0.353683 | − | 0.935365i | \(-0.384929\pi\) | ||||
0.353683 | + | 0.935365i | \(0.384929\pi\) | |||||||
\(72\) | 2.99058 | 0.352443 | ||||||||
\(73\) | 14.8292 | 1.73562 | 0.867811 | − | 0.496895i | \(-0.165526\pi\) | ||||
0.867811 | + | 0.496895i | \(0.165526\pi\) | |||||||
\(74\) | 5.01306 | 0.582756 | ||||||||
\(75\) | 0.0970464 | 0.0112060 | ||||||||
\(76\) | −5.51022 | −0.632066 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.419868 | −0.0475406 | ||||||||
\(79\) | −13.1971 | −1.48479 | −0.742394 | − | 0.669964i | \(-0.766310\pi\) | ||||
−0.742394 | + | 0.669964i | \(0.766310\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 8.91533 | 0.990592 | ||||||||
\(82\) | −1.92806 | −0.212919 | ||||||||
\(83\) | −2.63016 | −0.288698 | −0.144349 | − | 0.989527i | \(-0.546109\pi\) | ||||
−0.144349 | + | 0.989527i | \(0.546109\pi\) | |||||||
\(84\) | 0.0970464 | 0.0105886 | ||||||||
\(85\) | −2.12295 | −0.230266 | ||||||||
\(86\) | 3.75423 | 0.404829 | ||||||||
\(87\) | 0.779108 | 0.0835291 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18.4678 | −1.95758 | −0.978791 | − | 0.204861i | \(-0.934326\pi\) | ||||
−0.978791 | + | 0.204861i | \(0.934326\pi\) | |||||||
\(90\) | 2.99058 | 0.315235 | ||||||||
\(91\) | 4.32646 | 0.453536 | ||||||||
\(92\) | 0.922019 | 0.0961271 | ||||||||
\(93\) | 0.117962 | 0.0122321 | ||||||||
\(94\) | 0.865052 | 0.0892233 | ||||||||
\(95\) | −5.51022 | −0.565337 | ||||||||
\(96\) | −0.0970464 | −0.00990476 | ||||||||
\(97\) | 0.0855815 | 0.00868949 | 0.00434474 | − | 0.999991i | \(-0.498617\pi\) | ||||
0.00434474 | + | 0.999991i | \(0.498617\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 7.57523 | 0.753763 | 0.376882 | − | 0.926261i | \(-0.376996\pi\) | ||||
0.376882 | + | 0.926261i | \(0.376996\pi\) | |||||||
\(102\) | 0.206025 | 0.0203995 | ||||||||
\(103\) | −3.76181 | −0.370663 | −0.185331 | − | 0.982676i | \(-0.559336\pi\) | ||||
−0.185331 | + | 0.982676i | \(0.559336\pi\) | |||||||
\(104\) | −4.32646 | −0.424244 | ||||||||
\(105\) | 0.0970464 | 0.00947076 | ||||||||
\(106\) | 0.729158 | 0.0708221 | ||||||||
\(107\) | 13.3165 | 1.28735 | 0.643677 | − | 0.765297i | \(-0.277408\pi\) | ||||
0.643677 | + | 0.765297i | \(0.277408\pi\) | |||||||
\(108\) | −0.581365 | −0.0559418 | ||||||||
\(109\) | 8.04563 | 0.770631 | 0.385316 | − | 0.922785i | \(-0.374093\pi\) | ||||
0.385316 | + | 0.922785i | \(0.374093\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.486499 | −0.0461765 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 9.17493 | 0.863104 | 0.431552 | − | 0.902088i | \(-0.357966\pi\) | ||||
0.431552 | + | 0.902088i | \(0.357966\pi\) | |||||||
\(114\) | 0.534747 | 0.0500837 | ||||||||
\(115\) | 0.922019 | 0.0859787 | ||||||||
\(116\) | 8.02820 | 0.745399 | ||||||||
\(117\) | −12.9386 | −1.19618 | ||||||||
\(118\) | 0.178208 | 0.0164054 | ||||||||
\(119\) | −2.12295 | −0.194610 | ||||||||
\(120\) | −0.0970464 | −0.00885909 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −13.0127 | −1.17811 | ||||||||
\(123\) | 0.187112 | 0.0168713 | ||||||||
\(124\) | 1.21552 | 0.109157 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.99058 | 0.266422 | ||||||||
\(127\) | 8.63204 | 0.765970 | 0.382985 | − | 0.923755i | \(-0.374896\pi\) | ||||
0.382985 | + | 0.923755i | \(0.374896\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.364335 | −0.0320779 | ||||||||
\(130\) | −4.32646 | −0.379456 | ||||||||
\(131\) | −5.01748 | −0.438379 | −0.219189 | − | 0.975682i | \(-0.570341\pi\) | ||||
−0.219189 | + | 0.975682i | \(0.570341\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.51022 | −0.477797 | ||||||||
\(134\) | 3.55383 | 0.307004 | ||||||||
\(135\) | −0.581365 | −0.0500359 | ||||||||
\(136\) | 2.12295 | 0.182041 | ||||||||
\(137\) | −9.38739 | −0.802018 | −0.401009 | − | 0.916074i | \(-0.631340\pi\) | ||||
−0.401009 | + | 0.916074i | \(0.631340\pi\) | |||||||
\(138\) | −0.0894787 | −0.00761693 | ||||||||
\(139\) | 6.96159 | 0.590474 | 0.295237 | − | 0.955424i | \(-0.404601\pi\) | ||||
0.295237 | + | 0.955424i | \(0.404601\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | −0.0839502 | −0.00706988 | ||||||||
\(142\) | −5.96038 | −0.500184 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.99058 | −0.249215 | ||||||||
\(145\) | 8.02820 | 0.666706 | ||||||||
\(146\) | −14.8292 | −1.22727 | ||||||||
\(147\) | 0.0970464 | 0.00800426 | ||||||||
\(148\) | −5.01306 | −0.412071 | ||||||||
\(149\) | 19.8855 | 1.62908 | 0.814542 | − | 0.580105i | \(-0.196989\pi\) | ||||
0.814542 | + | 0.580105i | \(0.196989\pi\) | |||||||
\(150\) | −0.0970464 | −0.00792381 | ||||||||
\(151\) | 6.91156 | 0.562455 | 0.281227 | − | 0.959641i | \(-0.409258\pi\) | ||||
0.281227 | + | 0.959641i | \(0.409258\pi\) | |||||||
\(152\) | 5.51022 | 0.446938 | ||||||||
\(153\) | 6.34886 | 0.513275 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.21552 | 0.0976332 | ||||||||
\(156\) | 0.419868 | 0.0336163 | ||||||||
\(157\) | 9.00126 | 0.718378 | 0.359189 | − | 0.933265i | \(-0.383053\pi\) | ||||
0.359189 | + | 0.933265i | \(0.383053\pi\) | |||||||
\(158\) | 13.1971 | 1.04990 | ||||||||
\(159\) | −0.0707622 | −0.00561181 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0.922019 | 0.0726653 | ||||||||
\(162\) | −8.91533 | −0.700454 | ||||||||
\(163\) | −7.07107 | −0.553849 | −0.276924 | − | 0.960892i | \(-0.589315\pi\) | ||||
−0.276924 | + | 0.960892i | \(0.589315\pi\) | |||||||
\(164\) | 1.92806 | 0.150556 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.63016 | 0.204140 | ||||||||
\(167\) | 19.7421 | 1.52769 | 0.763846 | − | 0.645398i | \(-0.223309\pi\) | ||||
0.763846 | + | 0.645398i | \(0.223309\pi\) | |||||||
\(168\) | −0.0970464 | −0.00748730 | ||||||||
\(169\) | 5.71826 | 0.439866 | ||||||||
\(170\) | 2.12295 | 0.162823 | ||||||||
\(171\) | 16.4788 | 1.26016 | ||||||||
\(172\) | −3.75423 | −0.286257 | ||||||||
\(173\) | −13.9142 | −1.05787 | −0.528937 | − | 0.848661i | \(-0.677409\pi\) | ||||
−0.528937 | + | 0.848661i | \(0.677409\pi\) | |||||||
\(174\) | −0.779108 | −0.0590640 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.0172945 | −0.00129993 | ||||||||
\(178\) | 18.4678 | 1.38422 | ||||||||
\(179\) | −3.61007 | −0.269829 | −0.134915 | − | 0.990857i | \(-0.543076\pi\) | ||||
−0.134915 | + | 0.990857i | \(0.543076\pi\) | |||||||
\(180\) | −2.99058 | −0.222905 | ||||||||
\(181\) | −1.95017 | −0.144955 | −0.0724776 | − | 0.997370i | \(-0.523091\pi\) | ||||
−0.0724776 | + | 0.997370i | \(0.523091\pi\) | |||||||
\(182\) | −4.32646 | −0.320699 | ||||||||
\(183\) | 1.26283 | 0.0933514 | ||||||||
\(184\) | −0.922019 | −0.0679722 | ||||||||
\(185\) | −5.01306 | −0.368567 | ||||||||
\(186\) | −0.117962 | −0.00864941 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.865052 | −0.0630904 | ||||||||
\(189\) | −0.581365 | −0.0422881 | ||||||||
\(190\) | 5.51022 | 0.399753 | ||||||||
\(191\) | 12.7463 | 0.922288 | 0.461144 | − | 0.887325i | \(-0.347439\pi\) | ||||
0.461144 | + | 0.887325i | \(0.347439\pi\) | |||||||
\(192\) | 0.0970464 | 0.00700372 | ||||||||
\(193\) | 14.5920 | 1.05035 | 0.525176 | − | 0.850994i | \(-0.323999\pi\) | ||||
0.525176 | + | 0.850994i | \(0.323999\pi\) | |||||||
\(194\) | −0.0855815 | −0.00614439 | ||||||||
\(195\) | 0.419868 | 0.0300673 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −24.4598 | −1.74269 | −0.871346 | − | 0.490669i | \(-0.836752\pi\) | ||||
−0.871346 | + | 0.490669i | \(0.836752\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.4998 | −0.744315 | −0.372157 | − | 0.928170i | \(-0.621382\pi\) | ||||
−0.372157 | + | 0.928170i | \(0.621382\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −0.344887 | −0.0243264 | ||||||||
\(202\) | −7.57523 | −0.532991 | ||||||||
\(203\) | 8.02820 | 0.563469 | ||||||||
\(204\) | −0.206025 | −0.0144246 | ||||||||
\(205\) | 1.92806 | 0.134662 | ||||||||
\(206\) | 3.76181 | 0.262098 | ||||||||
\(207\) | −2.75737 | −0.191651 | ||||||||
\(208\) | 4.32646 | 0.299986 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.0970464 | −0.00669684 | ||||||||
\(211\) | −14.9790 | −1.03120 | −0.515600 | − | 0.856830i | \(-0.672431\pi\) | ||||
−0.515600 | + | 0.856830i | \(0.672431\pi\) | |||||||
\(212\) | −0.729158 | −0.0500788 | ||||||||
\(213\) | 0.578434 | 0.0396336 | ||||||||
\(214\) | −13.3165 | −0.910296 | ||||||||
\(215\) | −3.75423 | −0.256036 | ||||||||
\(216\) | 0.581365 | 0.0395569 | ||||||||
\(217\) | 1.21552 | 0.0825151 | ||||||||
\(218\) | −8.04563 | −0.544919 | ||||||||
\(219\) | 1.43912 | 0.0972465 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.18486 | −0.617840 | ||||||||
\(222\) | 0.486499 | 0.0326517 | ||||||||
\(223\) | −6.98647 | −0.467848 | −0.233924 | − | 0.972255i | \(-0.575157\pi\) | ||||
−0.233924 | + | 0.972255i | \(0.575157\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −2.99058 | −0.199372 | ||||||||
\(226\) | −9.17493 | −0.610307 | ||||||||
\(227\) | 23.6112 | 1.56713 | 0.783565 | − | 0.621309i | \(-0.213399\pi\) | ||||
0.783565 | + | 0.621309i | \(0.213399\pi\) | |||||||
\(228\) | −0.534747 | −0.0354145 | ||||||||
\(229\) | 21.0574 | 1.39151 | 0.695755 | − | 0.718279i | \(-0.255070\pi\) | ||||
0.695755 | + | 0.718279i | \(0.255070\pi\) | |||||||
\(230\) | −0.922019 | −0.0607961 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.02820 | −0.527077 | ||||||||
\(233\) | 29.7941 | 1.95187 | 0.975937 | − | 0.218052i | \(-0.0699702\pi\) | ||||
0.975937 | + | 0.218052i | \(0.0699702\pi\) | |||||||
\(234\) | 12.9386 | 0.845825 | ||||||||
\(235\) | −0.865052 | −0.0564298 | ||||||||
\(236\) | −0.178208 | −0.0116004 | ||||||||
\(237\) | −1.28073 | −0.0831923 | ||||||||
\(238\) | 2.12295 | 0.137610 | ||||||||
\(239\) | 18.4084 | 1.19074 | 0.595370 | − | 0.803452i | \(-0.297005\pi\) | ||||
0.595370 | + | 0.803452i | \(0.297005\pi\) | |||||||
\(240\) | 0.0970464 | 0.00626432 | ||||||||
\(241\) | 2.15635 | 0.138903 | 0.0694513 | − | 0.997585i | \(-0.477875\pi\) | ||||
0.0694513 | + | 0.997585i | \(0.477875\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.60929 | 0.167386 | ||||||||
\(244\) | 13.0127 | 0.833051 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −0.187112 | −0.0119298 | ||||||||
\(247\) | −23.8398 | −1.51689 | ||||||||
\(248\) | −1.21552 | −0.0771858 | ||||||||
\(249\) | −0.255248 | −0.0161757 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 19.6172 | 1.23823 | 0.619114 | − | 0.785301i | \(-0.287492\pi\) | ||||
0.619114 | + | 0.785301i | \(0.287492\pi\) | |||||||
\(252\) | −2.99058 | −0.188389 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −8.63204 | −0.541622 | ||||||||
\(255\) | −0.206025 | −0.0129018 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.06003 | −0.315636 | −0.157818 | − | 0.987468i | \(-0.550446\pi\) | ||||
−0.157818 | + | 0.987468i | \(0.550446\pi\) | |||||||
\(258\) | 0.364335 | 0.0226825 | ||||||||
\(259\) | −5.01306 | −0.311496 | ||||||||
\(260\) | 4.32646 | 0.268316 | ||||||||
\(261\) | −24.0090 | −1.48612 | ||||||||
\(262\) | 5.01748 | 0.309981 | ||||||||
\(263\) | 16.0394 | 0.989031 | 0.494516 | − | 0.869169i | \(-0.335345\pi\) | ||||
0.494516 | + | 0.869169i | \(0.335345\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.729158 | −0.0447918 | ||||||||
\(266\) | 5.51022 | 0.337853 | ||||||||
\(267\) | −1.79223 | −0.109683 | ||||||||
\(268\) | −3.55383 | −0.217085 | ||||||||
\(269\) | 7.45344 | 0.454444 | 0.227222 | − | 0.973843i | \(-0.427036\pi\) | ||||
0.227222 | + | 0.973843i | \(0.427036\pi\) | |||||||
\(270\) | 0.581365 | 0.0353807 | ||||||||
\(271\) | −19.3298 | −1.17420 | −0.587102 | − | 0.809513i | \(-0.699731\pi\) | ||||
−0.587102 | + | 0.809513i | \(0.699731\pi\) | |||||||
\(272\) | −2.12295 | −0.128723 | ||||||||
\(273\) | 0.419868 | 0.0254115 | ||||||||
\(274\) | 9.38739 | 0.567113 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.0894787 | 0.00538598 | ||||||||
\(277\) | −21.9563 | −1.31923 | −0.659614 | − | 0.751605i | \(-0.729280\pi\) | ||||
−0.659614 | + | 0.751605i | \(0.729280\pi\) | |||||||
\(278\) | −6.96159 | −0.417528 | ||||||||
\(279\) | −3.63512 | −0.217629 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −0.172162 | −0.0102703 | −0.00513515 | − | 0.999987i | \(-0.501635\pi\) | ||||
−0.00513515 | + | 0.999987i | \(0.501635\pi\) | |||||||
\(282\) | 0.0839502 | 0.00499916 | ||||||||
\(283\) | 14.5989 | 0.867817 | 0.433909 | − | 0.900957i | \(-0.357134\pi\) | ||||
0.433909 | + | 0.900957i | \(0.357134\pi\) | |||||||
\(284\) | 5.96038 | 0.353683 | ||||||||
\(285\) | −0.534747 | −0.0316757 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.92806 | 0.113810 | ||||||||
\(288\) | 2.99058 | 0.176222 | ||||||||
\(289\) | −12.4931 | −0.734887 | ||||||||
\(290\) | −8.02820 | −0.471432 | ||||||||
\(291\) | 0.00830538 | 0.000486870 0 | ||||||||
\(292\) | 14.8292 | 0.867811 | ||||||||
\(293\) | 4.99491 | 0.291806 | 0.145903 | − | 0.989299i | \(-0.453391\pi\) | ||||
0.145903 | + | 0.989299i | \(0.453391\pi\) | |||||||
\(294\) | −0.0970464 | −0.00565986 | ||||||||
\(295\) | −0.178208 | −0.0103757 | ||||||||
\(296\) | 5.01306 | 0.291378 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.8855 | −1.15194 | ||||||||
\(299\) | 3.98908 | 0.230694 | ||||||||
\(300\) | 0.0970464 | 0.00560298 | ||||||||
\(301\) | −3.75423 | −0.216390 | ||||||||
\(302\) | −6.91156 | −0.397716 | ||||||||
\(303\) | 0.735149 | 0.0422332 | ||||||||
\(304\) | −5.51022 | −0.316033 | ||||||||
\(305\) | 13.0127 | 0.745104 | ||||||||
\(306\) | −6.34886 | −0.362940 | ||||||||
\(307\) | −12.1296 | −0.692270 | −0.346135 | − | 0.938185i | \(-0.612506\pi\) | ||||
−0.346135 | + | 0.938185i | \(0.612506\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.365071 | −0.0207681 | ||||||||
\(310\) | −1.21552 | −0.0690371 | ||||||||
\(311\) | −5.79026 | −0.328335 | −0.164168 | − | 0.986432i | \(-0.552494\pi\) | ||||
−0.164168 | + | 0.986432i | \(0.552494\pi\) | |||||||
\(312\) | −0.419868 | −0.0237703 | ||||||||
\(313\) | −8.21454 | −0.464313 | −0.232157 | − | 0.972678i | \(-0.574578\pi\) | ||||
−0.232157 | + | 0.972678i | \(0.574578\pi\) | |||||||
\(314\) | −9.00126 | −0.507970 | ||||||||
\(315\) | −2.99058 | −0.168500 | ||||||||
\(316\) | −13.1971 | −0.742394 | ||||||||
\(317\) | −9.85272 | −0.553384 | −0.276692 | − | 0.960959i | \(-0.589238\pi\) | ||||
−0.276692 | + | 0.960959i | \(0.589238\pi\) | |||||||
\(318\) | 0.0707622 | 0.00396815 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 1.29232 | 0.0721301 | ||||||||
\(322\) | −0.922019 | −0.0513821 | ||||||||
\(323\) | 11.6979 | 0.650890 | ||||||||
\(324\) | 8.91533 | 0.495296 | ||||||||
\(325\) | 4.32646 | 0.239989 | ||||||||
\(326\) | 7.07107 | 0.391630 | ||||||||
\(327\) | 0.780799 | 0.0431783 | ||||||||
\(328\) | −1.92806 | −0.106459 | ||||||||
\(329\) | −0.865052 | −0.0476919 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.71671 | −0.314219 | −0.157109 | − | 0.987581i | \(-0.550218\pi\) | ||||
−0.157109 | + | 0.987581i | \(0.550218\pi\) | |||||||
\(332\) | −2.63016 | −0.144349 | ||||||||
\(333\) | 14.9920 | 0.821554 | ||||||||
\(334\) | −19.7421 | −1.08024 | ||||||||
\(335\) | −3.55383 | −0.194166 | ||||||||
\(336\) | 0.0970464 | 0.00529432 | ||||||||
\(337\) | 29.1366 | 1.58717 | 0.793585 | − | 0.608459i | \(-0.208212\pi\) | ||||
0.793585 | + | 0.608459i | \(0.208212\pi\) | |||||||
\(338\) | −5.71826 | −0.311032 | ||||||||
\(339\) | 0.890394 | 0.0483596 | ||||||||
\(340\) | −2.12295 | −0.115133 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −16.4788 | −0.891070 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 3.75423 | 0.202414 | ||||||||
\(345\) | 0.0894787 | 0.00481737 | ||||||||
\(346\) | 13.9142 | 0.748030 | ||||||||
\(347\) | −9.51730 | −0.510915 | −0.255458 | − | 0.966820i | \(-0.582226\pi\) | ||||
−0.255458 | + | 0.966820i | \(0.582226\pi\) | |||||||
\(348\) | 0.779108 | 0.0417646 | ||||||||
\(349\) | 8.24510 | 0.441350 | 0.220675 | − | 0.975347i | \(-0.429174\pi\) | ||||
0.220675 | + | 0.975347i | \(0.429174\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −2.51525 | −0.134254 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.6347 | 1.57730 | 0.788649 | − | 0.614843i | \(-0.210781\pi\) | ||||
0.788649 | + | 0.614843i | \(0.210781\pi\) | |||||||
\(354\) | 0.0172945 | 0.000919192 0 | ||||||||
\(355\) | 5.96038 | 0.316344 | ||||||||
\(356\) | −18.4678 | −0.978791 | ||||||||
\(357\) | −0.206025 | −0.0109040 | ||||||||
\(358\) | 3.61007 | 0.190798 | ||||||||
\(359\) | 24.7795 | 1.30781 | 0.653907 | − | 0.756575i | \(-0.273129\pi\) | ||||
0.653907 | + | 0.756575i | \(0.273129\pi\) | |||||||
\(360\) | 2.99058 | 0.157618 | ||||||||
\(361\) | 11.3625 | 0.598028 | ||||||||
\(362\) | 1.95017 | 0.102499 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.32646 | 0.226768 | ||||||||
\(365\) | 14.8292 | 0.776194 | ||||||||
\(366\) | −1.26283 | −0.0660094 | ||||||||
\(367\) | 12.8613 | 0.671352 | 0.335676 | − | 0.941977i | \(-0.391035\pi\) | ||||
0.335676 | + | 0.941977i | \(0.391035\pi\) | |||||||
\(368\) | 0.922019 | 0.0480636 | ||||||||
\(369\) | −5.76603 | −0.300167 | ||||||||
\(370\) | 5.01306 | 0.260616 | ||||||||
\(371\) | −0.729158 | −0.0378560 | ||||||||
\(372\) | 0.117962 | 0.00611606 | ||||||||
\(373\) | −22.7708 | −1.17903 | −0.589514 | − | 0.807758i | \(-0.700681\pi\) | ||||
−0.589514 | + | 0.807758i | \(0.700681\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.0970464 | 0.00501146 | ||||||||
\(376\) | 0.865052 | 0.0446117 | ||||||||
\(377\) | 34.7337 | 1.78888 | ||||||||
\(378\) | 0.581365 | 0.0299022 | ||||||||
\(379\) | 11.0712 | 0.568691 | 0.284346 | − | 0.958722i | \(-0.408224\pi\) | ||||
0.284346 | + | 0.958722i | \(0.408224\pi\) | |||||||
\(380\) | −5.51022 | −0.282668 | ||||||||
\(381\) | 0.837709 | 0.0429171 | ||||||||
\(382\) | −12.7463 | −0.652156 | ||||||||
\(383\) | 28.6974 | 1.46637 | 0.733184 | − | 0.680030i | \(-0.238033\pi\) | ||||
0.733184 | + | 0.680030i | \(0.238033\pi\) | |||||||
\(384\) | −0.0970464 | −0.00495238 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.5920 | −0.742711 | ||||||||
\(387\) | 11.2273 | 0.570717 | ||||||||
\(388\) | 0.0855815 | 0.00434474 | ||||||||
\(389\) | 1.68387 | 0.0853754 | 0.0426877 | − | 0.999088i | \(-0.486408\pi\) | ||||
0.0426877 | + | 0.999088i | \(0.486408\pi\) | |||||||
\(390\) | −0.419868 | −0.0212608 | ||||||||
\(391\) | −1.95740 | −0.0989900 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −0.486928 | −0.0245623 | ||||||||
\(394\) | 24.4598 | 1.23227 | ||||||||
\(395\) | −13.1971 | −0.664017 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.9399 | 0.850189 | 0.425095 | − | 0.905149i | \(-0.360241\pi\) | ||||
0.425095 | + | 0.905149i | \(0.360241\pi\) | |||||||
\(398\) | 10.4998 | 0.526310 | ||||||||
\(399\) | −0.534747 | −0.0267709 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −15.0165 | −0.749889 | −0.374944 | − | 0.927047i | \(-0.622338\pi\) | ||||
−0.374944 | + | 0.927047i | \(0.622338\pi\) | |||||||
\(402\) | 0.344887 | 0.0172014 | ||||||||
\(403\) | 5.25891 | 0.261965 | ||||||||
\(404\) | 7.57523 | 0.376882 | ||||||||
\(405\) | 8.91533 | 0.443006 | ||||||||
\(406\) | −8.02820 | −0.398433 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.206025 | 0.0101997 | ||||||||
\(409\) | −33.7143 | −1.66707 | −0.833533 | − | 0.552469i | \(-0.813686\pi\) | ||||
−0.833533 | + | 0.552469i | \(0.813686\pi\) | |||||||
\(410\) | −1.92806 | −0.0952202 | ||||||||
\(411\) | −0.911012 | −0.0449369 | ||||||||
\(412\) | −3.76181 | −0.185331 | ||||||||
\(413\) | −0.178208 | −0.00876907 | ||||||||
\(414\) | 2.75737 | 0.135518 | ||||||||
\(415\) | −2.63016 | −0.129109 | ||||||||
\(416\) | −4.32646 | −0.212122 | ||||||||
\(417\) | 0.675598 | 0.0330842 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.7859 | −0.868900 | −0.434450 | − | 0.900696i | \(-0.643057\pi\) | ||||
−0.434450 | + | 0.900696i | \(0.643057\pi\) | |||||||
\(420\) | 0.0970464 | 0.00473538 | ||||||||
\(421\) | 18.2534 | 0.889619 | 0.444809 | − | 0.895625i | \(-0.353271\pi\) | ||||
0.444809 | + | 0.895625i | \(0.353271\pi\) | |||||||
\(422\) | 14.9790 | 0.729168 | ||||||||
\(423\) | 2.58701 | 0.125785 | ||||||||
\(424\) | 0.729158 | 0.0354111 | ||||||||
\(425\) | −2.12295 | −0.102978 | ||||||||
\(426\) | −0.578434 | −0.0280252 | ||||||||
\(427\) | 13.0127 | 0.629728 | ||||||||
\(428\) | 13.3165 | 0.643677 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.75423 | 0.181045 | ||||||||
\(431\) | −27.5547 | −1.32726 | −0.663632 | − | 0.748059i | \(-0.730986\pi\) | ||||
−0.663632 | + | 0.748059i | \(0.730986\pi\) | |||||||
\(432\) | −0.581365 | −0.0279709 | ||||||||
\(433\) | −3.18070 | −0.152855 | −0.0764273 | − | 0.997075i | \(-0.524351\pi\) | ||||
−0.0764273 | + | 0.997075i | \(0.524351\pi\) | |||||||
\(434\) | −1.21552 | −0.0583470 | ||||||||
\(435\) | 0.779108 | 0.0373554 | ||||||||
\(436\) | 8.04563 | 0.385316 | ||||||||
\(437\) | −5.08053 | −0.243035 | ||||||||
\(438\) | −1.43912 | −0.0687637 | ||||||||
\(439\) | −39.0123 | −1.86196 | −0.930978 | − | 0.365076i | \(-0.881043\pi\) | ||||
−0.930978 | + | 0.365076i | \(0.881043\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.99058 | −0.142409 | ||||||||
\(442\) | 9.18486 | 0.436879 | ||||||||
\(443\) | 5.00748 | 0.237912 | 0.118956 | − | 0.992900i | \(-0.462045\pi\) | ||||
0.118956 | + | 0.992900i | \(0.462045\pi\) | |||||||
\(444\) | −0.486499 | −0.0230882 | ||||||||
\(445\) | −18.4678 | −0.875457 | ||||||||
\(446\) | 6.98647 | 0.330819 | ||||||||
\(447\) | 1.92982 | 0.0912772 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 12.5770 | 0.593546 | 0.296773 | − | 0.954948i | \(-0.404090\pi\) | ||||
0.296773 | + | 0.954948i | \(0.404090\pi\) | |||||||
\(450\) | 2.99058 | 0.140977 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 9.17493 | 0.431552 | ||||||||
\(453\) | 0.670742 | 0.0315142 | ||||||||
\(454\) | −23.6112 | −1.10813 | ||||||||
\(455\) | 4.32646 | 0.202828 | ||||||||
\(456\) | 0.534747 | 0.0250418 | ||||||||
\(457\) | 36.1549 | 1.69125 | 0.845627 | − | 0.533775i | \(-0.179227\pi\) | ||||
0.845627 | + | 0.533775i | \(0.179227\pi\) | |||||||
\(458\) | −21.0574 | −0.983946 | ||||||||
\(459\) | 1.23421 | 0.0576079 | ||||||||
\(460\) | 0.922019 | 0.0429894 | ||||||||
\(461\) | −26.0248 | −1.21209 | −0.606047 | − | 0.795429i | \(-0.707246\pi\) | ||||
−0.606047 | + | 0.795429i | \(0.707246\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.55526 | 0.118753 | 0.0593766 | − | 0.998236i | \(-0.481089\pi\) | ||||
0.0593766 | + | 0.998236i | \(0.481089\pi\) | |||||||
\(464\) | 8.02820 | 0.372700 | ||||||||
\(465\) | 0.117962 | 0.00547037 | ||||||||
\(466\) | −29.7941 | −1.38018 | ||||||||
\(467\) | 14.4176 | 0.667169 | 0.333585 | − | 0.942720i | \(-0.391742\pi\) | ||||
0.333585 | + | 0.942720i | \(0.391742\pi\) | |||||||
\(468\) | −12.9386 | −0.598089 | ||||||||
\(469\) | −3.55383 | −0.164101 | ||||||||
\(470\) | 0.865052 | 0.0399019 | ||||||||
\(471\) | 0.873540 | 0.0402506 | ||||||||
\(472\) | 0.178208 | 0.00820271 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 1.28073 | 0.0588259 | ||||||||
\(475\) | −5.51022 | −0.252826 | ||||||||
\(476\) | −2.12295 | −0.0973052 | ||||||||
\(477\) | 2.18061 | 0.0998432 | ||||||||
\(478\) | −18.4084 | −0.841981 | ||||||||
\(479\) | −32.6066 | −1.48984 | −0.744918 | − | 0.667156i | \(-0.767511\pi\) | ||||
−0.744918 | + | 0.667156i | \(0.767511\pi\) | |||||||
\(480\) | −0.0970464 | −0.00442954 | ||||||||
\(481\) | −21.6888 | −0.988924 | ||||||||
\(482\) | −2.15635 | −0.0982190 | ||||||||
\(483\) | 0.0894787 | 0.00407142 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.0855815 | 0.00388606 | ||||||||
\(486\) | −2.60929 | −0.118360 | ||||||||
\(487\) | 16.9041 | 0.765997 | 0.382999 | − | 0.923749i | \(-0.374891\pi\) | ||||
0.382999 | + | 0.923749i | \(0.374891\pi\) | |||||||
\(488\) | −13.0127 | −0.589056 | ||||||||
\(489\) | −0.686222 | −0.0310320 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 38.7664 | 1.74950 | 0.874752 | − | 0.484571i | \(-0.161024\pi\) | ||||
0.874752 | + | 0.484571i | \(0.161024\pi\) | |||||||
\(492\) | 0.187112 | 0.00843564 | ||||||||
\(493\) | −17.0435 | −0.767599 | ||||||||
\(494\) | 23.8398 | 1.07260 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.21552 | 0.0545786 | ||||||||
\(497\) | 5.96038 | 0.267360 | ||||||||
\(498\) | 0.255248 | 0.0114379 | ||||||||
\(499\) | −37.6575 | −1.68578 | −0.842890 | − | 0.538086i | \(-0.819148\pi\) | ||||
−0.842890 | + | 0.538086i | \(0.819148\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 1.91590 | 0.0855963 | ||||||||
\(502\) | −19.6172 | −0.875559 | ||||||||
\(503\) | −28.4963 | −1.27059 | −0.635294 | − | 0.772270i | \(-0.719121\pi\) | ||||
−0.635294 | + | 0.772270i | \(0.719121\pi\) | |||||||
\(504\) | 2.99058 | 0.133211 | ||||||||
\(505\) | 7.57523 | 0.337093 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.554937 | 0.0246456 | ||||||||
\(508\) | 8.63204 | 0.382985 | ||||||||
\(509\) | 21.2554 | 0.942130 | 0.471065 | − | 0.882099i | \(-0.343870\pi\) | ||||
0.471065 | + | 0.882099i | \(0.343870\pi\) | |||||||
\(510\) | 0.206025 | 0.00912293 | ||||||||
\(511\) | 14.8292 | 0.656003 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.20345 | 0.141436 | ||||||||
\(514\) | 5.06003 | 0.223189 | ||||||||
\(515\) | −3.76181 | −0.165765 | ||||||||
\(516\) | −0.364335 | −0.0160389 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 5.01306 | 0.220261 | ||||||||
\(519\) | −1.35032 | −0.0592724 | ||||||||
\(520\) | −4.32646 | −0.189728 | ||||||||
\(521\) | 9.47858 | 0.415264 | 0.207632 | − | 0.978207i | \(-0.433424\pi\) | ||||
0.207632 | + | 0.978207i | \(0.433424\pi\) | |||||||
\(522\) | 24.0090 | 1.05084 | ||||||||
\(523\) | 21.3021 | 0.931475 | 0.465737 | − | 0.884923i | \(-0.345789\pi\) | ||||
0.465737 | + | 0.884923i | \(0.345789\pi\) | |||||||
\(524\) | −5.01748 | −0.219189 | ||||||||
\(525\) | 0.0970464 | 0.00423545 | ||||||||
\(526\) | −16.0394 | −0.699351 | ||||||||
\(527\) | −2.58050 | −0.112408 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.1499 | −0.963038 | ||||||||
\(530\) | 0.729158 | 0.0316726 | ||||||||
\(531\) | 0.532947 | 0.0231279 | ||||||||
\(532\) | −5.51022 | −0.238898 | ||||||||
\(533\) | 8.34169 | 0.361319 | ||||||||
\(534\) | 1.79223 | 0.0775575 | ||||||||
\(535\) | 13.3165 | 0.575722 | ||||||||
\(536\) | 3.55383 | 0.153502 | ||||||||
\(537\) | −0.350344 | −0.0151185 | ||||||||
\(538\) | −7.45344 | −0.321341 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.581365 | −0.0250180 | ||||||||
\(541\) | 43.2284 | 1.85853 | 0.929267 | − | 0.369408i | \(-0.120440\pi\) | ||||
0.929267 | + | 0.369408i | \(0.120440\pi\) | |||||||
\(542\) | 19.3298 | 0.830287 | ||||||||
\(543\) | −0.189257 | −0.00812181 | ||||||||
\(544\) | 2.12295 | 0.0910207 | ||||||||
\(545\) | 8.04563 | 0.344637 | ||||||||
\(546\) | −0.419868 | −0.0179687 | ||||||||
\(547\) | 22.1833 | 0.948491 | 0.474245 | − | 0.880393i | \(-0.342721\pi\) | ||||
0.474245 | + | 0.880393i | \(0.342721\pi\) | |||||||
\(548\) | −9.38739 | −0.401009 | ||||||||
\(549\) | −38.9155 | −1.66087 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −44.2372 | −1.88457 | ||||||||
\(552\) | −0.0894787 | −0.00380847 | ||||||||
\(553\) | −13.1971 | −0.561197 | ||||||||
\(554\) | 21.9563 | 0.932835 | ||||||||
\(555\) | −0.486499 | −0.0206507 | ||||||||
\(556\) | 6.96159 | 0.295237 | ||||||||
\(557\) | −3.41806 | −0.144828 | −0.0724140 | − | 0.997375i | \(-0.523070\pi\) | ||||
−0.0724140 | + | 0.997375i | \(0.523070\pi\) | |||||||
\(558\) | 3.63512 | 0.153887 | ||||||||
\(559\) | −16.2425 | −0.686985 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.172162 | 0.00726220 | ||||||||
\(563\) | 16.7614 | 0.706411 | 0.353205 | − | 0.935546i | \(-0.385092\pi\) | ||||
0.353205 | + | 0.935546i | \(0.385092\pi\) | |||||||
\(564\) | −0.0839502 | −0.00353494 | ||||||||
\(565\) | 9.17493 | 0.385992 | ||||||||
\(566\) | −14.5989 | −0.613640 | ||||||||
\(567\) | 8.91533 | 0.374409 | ||||||||
\(568\) | −5.96038 | −0.250092 | ||||||||
\(569\) | −30.7237 | −1.28800 | −0.644001 | − | 0.765024i | \(-0.722727\pi\) | ||||
−0.644001 | + | 0.765024i | \(0.722727\pi\) | |||||||
\(570\) | 0.534747 | 0.0223981 | ||||||||
\(571\) | −26.7892 | −1.12109 | −0.560546 | − | 0.828123i | \(-0.689409\pi\) | ||||
−0.560546 | + | 0.828123i | \(0.689409\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.23698 | 0.0516756 | ||||||||
\(574\) | −1.92806 | −0.0804758 | ||||||||
\(575\) | 0.922019 | 0.0384509 | ||||||||
\(576\) | −2.99058 | −0.124608 | ||||||||
\(577\) | 8.18950 | 0.340933 | 0.170467 | − | 0.985363i | \(-0.445472\pi\) | ||||
0.170467 | + | 0.985363i | \(0.445472\pi\) | |||||||
\(578\) | 12.4931 | 0.519644 | ||||||||
\(579\) | 1.41610 | 0.0588510 | ||||||||
\(580\) | 8.02820 | 0.333353 | ||||||||
\(581\) | −2.63016 | −0.109117 | ||||||||
\(582\) | −0.00830538 | −0.000344269 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −14.8292 | −0.613635 | ||||||||
\(585\) | −12.9386 | −0.534947 | ||||||||
\(586\) | −4.99491 | −0.206338 | ||||||||
\(587\) | −19.3228 | −0.797537 | −0.398768 | − | 0.917052i | \(-0.630562\pi\) | ||||
−0.398768 | + | 0.917052i | \(0.630562\pi\) | |||||||
\(588\) | 0.0970464 | 0.00400213 | ||||||||
\(589\) | −6.69780 | −0.275978 | ||||||||
\(590\) | 0.178208 | 0.00733673 | ||||||||
\(591\) | −2.37374 | −0.0976427 | ||||||||
\(592\) | −5.01306 | −0.206035 | ||||||||
\(593\) | 46.6962 | 1.91758 | 0.958792 | − | 0.284109i | \(-0.0916979\pi\) | ||||
0.958792 | + | 0.284109i | \(0.0916979\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.12295 | −0.0870325 | ||||||||
\(596\) | 19.8855 | 0.814542 | ||||||||
\(597\) | −1.01897 | −0.0417038 | ||||||||
\(598\) | −3.98908 | −0.163126 | ||||||||
\(599\) | −20.0821 | −0.820533 | −0.410267 | − | 0.911966i | \(-0.634564\pi\) | ||||
−0.410267 | + | 0.911966i | \(0.634564\pi\) | |||||||
\(600\) | −0.0970464 | −0.00396190 | ||||||||
\(601\) | 19.0105 | 0.775456 | 0.387728 | − | 0.921774i | \(-0.373260\pi\) | ||||
0.387728 | + | 0.921774i | \(0.373260\pi\) | |||||||
\(602\) | 3.75423 | 0.153011 | ||||||||
\(603\) | 10.6280 | 0.432806 | ||||||||
\(604\) | 6.91156 | 0.281227 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.735149 | −0.0298634 | ||||||||
\(607\) | −27.4450 | −1.11396 | −0.556979 | − | 0.830526i | \(-0.688040\pi\) | ||||
−0.556979 | + | 0.830526i | \(0.688040\pi\) | |||||||
\(608\) | 5.51022 | 0.223469 | ||||||||
\(609\) | 0.779108 | 0.0315711 | ||||||||
\(610\) | −13.0127 | −0.526868 | ||||||||
\(611\) | −3.74261 | −0.151410 | ||||||||
\(612\) | 6.34886 | 0.256637 | ||||||||
\(613\) | −9.50074 | −0.383731 | −0.191866 | − | 0.981421i | \(-0.561454\pi\) | ||||
−0.191866 | + | 0.981421i | \(0.561454\pi\) | |||||||
\(614\) | 12.1296 | 0.489509 | ||||||||
\(615\) | 0.187112 | 0.00754507 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.6314 | 1.35395 | 0.676974 | − | 0.736007i | \(-0.263291\pi\) | ||||
0.676974 | + | 0.736007i | \(0.263291\pi\) | |||||||
\(618\) | 0.365071 | 0.0146853 | ||||||||
\(619\) | 27.2183 | 1.09400 | 0.546998 | − | 0.837134i | \(-0.315770\pi\) | ||||
0.546998 | + | 0.837134i | \(0.315770\pi\) | |||||||
\(620\) | 1.21552 | 0.0488166 | ||||||||
\(621\) | −0.536029 | −0.0215101 | ||||||||
\(622\) | 5.79026 | 0.232168 | ||||||||
\(623\) | −18.4678 | −0.739896 | ||||||||
\(624\) | 0.419868 | 0.0168082 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 8.21454 | 0.328319 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.00126 | 0.359189 | ||||||||
\(629\) | 10.6425 | 0.424343 | ||||||||
\(630\) | 2.99058 | 0.119148 | ||||||||
\(631\) | 28.1766 | 1.12169 | 0.560846 | − | 0.827920i | \(-0.310476\pi\) | ||||
0.560846 | + | 0.827920i | \(0.310476\pi\) | |||||||
\(632\) | 13.1971 | 0.524952 | ||||||||
\(633\) | −1.45366 | −0.0577779 | ||||||||
\(634\) | 9.85272 | 0.391301 | ||||||||
\(635\) | 8.63204 | 0.342552 | ||||||||
\(636\) | −0.0707622 | −0.00280590 | ||||||||
\(637\) | 4.32646 | 0.171421 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.8250 | −0.705146 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 9.40813 | 0.371599 | 0.185799 | − | 0.982588i | \(-0.440513\pi\) | ||||
0.185799 | + | 0.982588i | \(0.440513\pi\) | |||||||
\(642\) | −1.29232 | −0.0510037 | ||||||||
\(643\) | −41.8999 | −1.65237 | −0.826185 | − | 0.563398i | \(-0.809494\pi\) | ||||
−0.826185 | + | 0.563398i | \(0.809494\pi\) | |||||||
\(644\) | 0.922019 | 0.0363326 | ||||||||
\(645\) | −0.364335 | −0.0143457 | ||||||||
\(646\) | −11.6979 | −0.460249 | ||||||||
\(647\) | 17.5282 | 0.689105 | 0.344553 | − | 0.938767i | \(-0.388031\pi\) | ||||
0.344553 | + | 0.938767i | \(0.388031\pi\) | |||||||
\(648\) | −8.91533 | −0.350227 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.32646 | −0.169698 | ||||||||
\(651\) | 0.117962 | 0.00462330 | ||||||||
\(652\) | −7.07107 | −0.276924 | ||||||||
\(653\) | 47.2120 | 1.84755 | 0.923775 | − | 0.382937i | \(-0.125087\pi\) | ||||
0.923775 | + | 0.382937i | \(0.125087\pi\) | |||||||
\(654\) | −0.780799 | −0.0305317 | ||||||||
\(655\) | −5.01748 | −0.196049 | ||||||||
\(656\) | 1.92806 | 0.0752782 | ||||||||
\(657\) | −44.3478 | −1.73017 | ||||||||
\(658\) | 0.865052 | 0.0337232 | ||||||||
\(659\) | 4.53445 | 0.176637 | 0.0883185 | − | 0.996092i | \(-0.471851\pi\) | ||||
0.0883185 | + | 0.996092i | \(0.471851\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.2581 | −1.29359 | −0.646794 | − | 0.762664i | \(-0.723891\pi\) | ||||
−0.646794 | + | 0.762664i | \(0.723891\pi\) | |||||||
\(662\) | 5.71671 | 0.222186 | ||||||||
\(663\) | −0.891358 | −0.0346175 | ||||||||
\(664\) | 2.63016 | 0.102070 | ||||||||
\(665\) | −5.51022 | −0.213677 | ||||||||
\(666\) | −14.9920 | −0.580927 | ||||||||
\(667\) | 7.40215 | 0.286612 | ||||||||
\(668\) | 19.7421 | 0.763846 | ||||||||
\(669\) | −0.678012 | −0.0262134 | ||||||||
\(670\) | 3.55383 | 0.137296 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.0970464 | −0.00374365 | ||||||||
\(673\) | −3.32610 | −0.128212 | −0.0641059 | − | 0.997943i | \(-0.520420\pi\) | ||||
−0.0641059 | + | 0.997943i | \(0.520420\pi\) | |||||||
\(674\) | −29.1366 | −1.12230 | ||||||||
\(675\) | −0.581365 | −0.0223767 | ||||||||
\(676\) | 5.71826 | 0.219933 | ||||||||
\(677\) | −8.90346 | −0.342188 | −0.171094 | − | 0.985255i | \(-0.554730\pi\) | ||||
−0.171094 | + | 0.985255i | \(0.554730\pi\) | |||||||
\(678\) | −0.890394 | −0.0341954 | ||||||||
\(679\) | 0.0855815 | 0.00328432 | ||||||||
\(680\) | 2.12295 | 0.0814114 | ||||||||
\(681\) | 2.29138 | 0.0878060 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.5881 | 1.01736 | 0.508682 | − | 0.860954i | \(-0.330133\pi\) | ||||
0.508682 | + | 0.860954i | \(0.330133\pi\) | |||||||
\(684\) | 16.4788 | 0.630081 | ||||||||
\(685\) | −9.38739 | −0.358674 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 2.04354 | 0.0779660 | ||||||||
\(688\) | −3.75423 | −0.143129 | ||||||||
\(689\) | −3.15468 | −0.120184 | ||||||||
\(690\) | −0.0894787 | −0.00340639 | ||||||||
\(691\) | −28.8459 | −1.09735 | −0.548674 | − | 0.836036i | \(-0.684867\pi\) | ||||
−0.548674 | + | 0.836036i | \(0.684867\pi\) | |||||||
\(692\) | −13.9142 | −0.528937 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.51730 | 0.361272 | ||||||||
\(695\) | 6.96159 | 0.264068 | ||||||||
\(696\) | −0.779108 | −0.0295320 | ||||||||
\(697\) | −4.09318 | −0.155040 | ||||||||
\(698\) | −8.24510 | −0.312082 | ||||||||
\(699\) | 2.89141 | 0.109363 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −10.9136 | −0.412203 | −0.206101 | − | 0.978531i | \(-0.566078\pi\) | ||||
−0.206101 | + | 0.978531i | \(0.566078\pi\) | |||||||
\(702\) | 2.51525 | 0.0949320 | ||||||||
\(703\) | 27.6231 | 1.04182 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.0839502 | −0.00316175 | ||||||||
\(706\) | −29.6347 | −1.11532 | ||||||||
\(707\) | 7.57523 | 0.284896 | ||||||||
\(708\) | −0.0172945 | −0.000649967 0 | ||||||||
\(709\) | −35.0191 | −1.31517 | −0.657584 | − | 0.753381i | \(-0.728422\pi\) | ||||
−0.657584 | + | 0.753381i | \(0.728422\pi\) | |||||||
\(710\) | −5.96038 | −0.223689 | ||||||||
\(711\) | 39.4670 | 1.48013 | ||||||||
\(712\) | 18.4678 | 0.692110 | ||||||||
\(713\) | 1.12074 | 0.0419719 | ||||||||
\(714\) | 0.206025 | 0.00771028 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.61007 | −0.134915 | ||||||||
\(717\) | 1.78647 | 0.0667169 | ||||||||
\(718\) | −24.7795 | −0.924765 | ||||||||
\(719\) | 43.4663 | 1.62102 | 0.810510 | − | 0.585725i | \(-0.199190\pi\) | ||||
0.810510 | + | 0.585725i | \(0.199190\pi\) | |||||||
\(720\) | −2.99058 | −0.111452 | ||||||||
\(721\) | −3.76181 | −0.140097 | ||||||||
\(722\) | −11.3625 | −0.422870 | ||||||||
\(723\) | 0.209266 | 0.00778269 | ||||||||
\(724\) | −1.95017 | −0.0724776 | ||||||||
\(725\) | 8.02820 | 0.298160 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −52.4475 | −1.94517 | −0.972585 | − | 0.232548i | \(-0.925294\pi\) | ||||
−0.972585 | + | 0.232548i | \(0.925294\pi\) | |||||||
\(728\) | −4.32646 | −0.160349 | ||||||||
\(729\) | −26.4928 | −0.981213 | ||||||||
\(730\) | −14.8292 | −0.548852 | ||||||||
\(731\) | 7.97004 | 0.294783 | ||||||||
\(732\) | 1.26283 | 0.0466757 | ||||||||
\(733\) | 26.2363 | 0.969059 | 0.484529 | − | 0.874775i | \(-0.338991\pi\) | ||||
0.484529 | + | 0.874775i | \(0.338991\pi\) | |||||||
\(734\) | −12.8613 | −0.474718 | ||||||||
\(735\) | 0.0970464 | 0.00357961 | ||||||||
\(736\) | −0.922019 | −0.0339861 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 5.76603 | 0.212250 | ||||||||
\(739\) | 29.8531 | 1.09816 | 0.549081 | − | 0.835769i | \(-0.314978\pi\) | ||||
0.549081 | + | 0.835769i | \(0.314978\pi\) | |||||||
\(740\) | −5.01306 | −0.184284 | ||||||||
\(741\) | −2.31356 | −0.0849909 | ||||||||
\(742\) | 0.729158 | 0.0267682 | ||||||||
\(743\) | 39.8331 | 1.46133 | 0.730667 | − | 0.682734i | \(-0.239209\pi\) | ||||
0.730667 | + | 0.682734i | \(0.239209\pi\) | |||||||
\(744\) | −0.117962 | −0.00432471 | ||||||||
\(745\) | 19.8855 | 0.728548 | ||||||||
\(746\) | 22.7708 | 0.833698 | ||||||||
\(747\) | 7.86571 | 0.287791 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.3165 | 0.486574 | ||||||||
\(750\) | −0.0970464 | −0.00354363 | ||||||||
\(751\) | 48.2801 | 1.76177 | 0.880884 | − | 0.473333i | \(-0.156949\pi\) | ||||
0.880884 | + | 0.473333i | \(0.156949\pi\) | |||||||
\(752\) | −0.865052 | −0.0315452 | ||||||||
\(753\) | 1.90378 | 0.0693776 | ||||||||
\(754\) | −34.7337 | −1.26493 | ||||||||
\(755\) | 6.91156 | 0.251537 | ||||||||
\(756\) | −0.581365 | −0.0211440 | ||||||||
\(757\) | −8.61332 | −0.313056 | −0.156528 | − | 0.987673i | \(-0.550030\pi\) | ||||
−0.156528 | + | 0.987673i | \(0.550030\pi\) | |||||||
\(758\) | −11.0712 | −0.402125 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.51022 | 0.199877 | ||||||||
\(761\) | 0.634416 | 0.0229975 | 0.0114988 | − | 0.999934i | \(-0.496340\pi\) | ||||
0.0114988 | + | 0.999934i | \(0.496340\pi\) | |||||||
\(762\) | −0.837709 | −0.0303470 | ||||||||
\(763\) | 8.04563 | 0.291271 | ||||||||
\(764\) | 12.7463 | 0.461144 | ||||||||
\(765\) | 6.34886 | 0.229543 | ||||||||
\(766\) | −28.6974 | −1.03688 | ||||||||
\(767\) | −0.771012 | −0.0278396 | ||||||||
\(768\) | 0.0970464 | 0.00350186 | ||||||||
\(769\) | 34.4997 | 1.24409 | 0.622046 | − | 0.782981i | \(-0.286302\pi\) | ||||
0.622046 | + | 0.782981i | \(0.286302\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.491058 | −0.0176850 | ||||||||
\(772\) | 14.5920 | 0.525176 | ||||||||
\(773\) | −32.9878 | −1.18649 | −0.593244 | − | 0.805023i | \(-0.702153\pi\) | ||||
−0.593244 | + | 0.805023i | \(0.702153\pi\) | |||||||
\(774\) | −11.2273 | −0.403558 | ||||||||
\(775\) | 1.21552 | 0.0436629 | ||||||||
\(776\) | −0.0855815 | −0.00307220 | ||||||||
\(777\) | −0.486499 | −0.0174531 | ||||||||
\(778\) | −1.68387 | −0.0603695 | ||||||||
\(779\) | −10.6241 | −0.380646 | ||||||||
\(780\) | 0.419868 | 0.0150337 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.95740 | 0.0699965 | ||||||||
\(783\) | −4.66731 | −0.166796 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 9.00126 | 0.321269 | ||||||||
\(786\) | 0.486928 | 0.0173682 | ||||||||
\(787\) | 33.6231 | 1.19853 | 0.599266 | − | 0.800550i | \(-0.295459\pi\) | ||||
0.599266 | + | 0.800550i | \(0.295459\pi\) | |||||||
\(788\) | −24.4598 | −0.871346 | ||||||||
\(789\) | 1.55657 | 0.0554152 | ||||||||
\(790\) | 13.1971 | 0.469531 | ||||||||
\(791\) | 9.17493 | 0.326223 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 56.2988 | 1.99923 | ||||||||
\(794\) | −16.9399 | −0.601175 | ||||||||
\(795\) | −0.0707622 | −0.00250968 | ||||||||
\(796\) | −10.4998 | −0.372157 | ||||||||
\(797\) | 45.0594 | 1.59609 | 0.798043 | − | 0.602600i | \(-0.205869\pi\) | ||||
0.798043 | + | 0.602600i | \(0.205869\pi\) | |||||||
\(798\) | 0.534747 | 0.0189299 | ||||||||
\(799\) | 1.83646 | 0.0649694 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 55.2294 | 1.95144 | ||||||||
\(802\) | 15.0165 | 0.530252 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.344887 | −0.0121632 | ||||||||
\(805\) | 0.922019 | 0.0324969 | ||||||||
\(806\) | −5.25891 | −0.185237 | ||||||||
\(807\) | 0.723330 | 0.0254624 | ||||||||
\(808\) | −7.57523 | −0.266496 | ||||||||
\(809\) | 12.1005 | 0.425432 | 0.212716 | − | 0.977114i | \(-0.431769\pi\) | ||||
0.212716 | + | 0.977114i | \(0.431769\pi\) | |||||||
\(810\) | −8.91533 | −0.313253 | ||||||||
\(811\) | 19.6540 | 0.690147 | 0.345073 | − | 0.938576i | \(-0.387854\pi\) | ||||
0.345073 | + | 0.938576i | \(0.387854\pi\) | |||||||
\(812\) | 8.02820 | 0.281735 | ||||||||
\(813\) | −1.87589 | −0.0657904 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.07107 | −0.247689 | ||||||||
\(816\) | −0.206025 | −0.00721231 | ||||||||
\(817\) | 20.6866 | 0.723734 | ||||||||
\(818\) | 33.7143 | 1.17879 | ||||||||
\(819\) | −12.9386 | −0.452113 | ||||||||
\(820\) | 1.92806 | 0.0673309 | ||||||||
\(821\) | −5.45071 | −0.190231 | −0.0951156 | − | 0.995466i | \(-0.530322\pi\) | ||||
−0.0951156 | + | 0.995466i | \(0.530322\pi\) | |||||||
\(822\) | 0.911012 | 0.0317752 | ||||||||
\(823\) | 34.8782 | 1.21578 | 0.607889 | − | 0.794022i | \(-0.292016\pi\) | ||||
0.607889 | + | 0.794022i | \(0.292016\pi\) | |||||||
\(824\) | 3.76181 | 0.131049 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.178208 | 0.00620067 | ||||||||
\(827\) | 16.7849 | 0.583670 | 0.291835 | − | 0.956469i | \(-0.405734\pi\) | ||||
0.291835 | + | 0.956469i | \(0.405734\pi\) | |||||||
\(828\) | −2.75737 | −0.0958254 | ||||||||
\(829\) | −7.98157 | −0.277211 | −0.138606 | − | 0.990348i | \(-0.544262\pi\) | ||||
−0.138606 | + | 0.990348i | \(0.544262\pi\) | |||||||
\(830\) | 2.63016 | 0.0912942 | ||||||||
\(831\) | −2.13078 | −0.0739160 | ||||||||
\(832\) | 4.32646 | 0.149993 | ||||||||
\(833\) | −2.12295 | −0.0735558 | ||||||||
\(834\) | −0.675598 | −0.0233940 | ||||||||
\(835\) | 19.7421 | 0.683205 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.706662 | −0.0244258 | ||||||||
\(838\) | 17.7859 | 0.614405 | ||||||||
\(839\) | −6.47669 | −0.223600 | −0.111800 | − | 0.993731i | \(-0.535662\pi\) | ||||
−0.111800 | + | 0.993731i | \(0.535662\pi\) | |||||||
\(840\) | −0.0970464 | −0.00334842 | ||||||||
\(841\) | 35.4520 | 1.22248 | ||||||||
\(842\) | −18.2534 | −0.629055 | ||||||||
\(843\) | −0.0167077 | −0.000575443 0 | ||||||||
\(844\) | −14.9790 | −0.515600 | ||||||||
\(845\) | 5.71826 | 0.196714 | ||||||||
\(846\) | −2.58701 | −0.0889432 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.729158 | −0.0250394 | ||||||||
\(849\) | 1.41678 | 0.0486236 | ||||||||
\(850\) | 2.12295 | 0.0728166 | ||||||||
\(851\) | −4.62213 | −0.158445 | ||||||||
\(852\) | 0.578434 | 0.0198168 | ||||||||
\(853\) | 11.1007 | 0.380081 | 0.190040 | − | 0.981776i | \(-0.439138\pi\) | ||||
0.190040 | + | 0.981776i | \(0.439138\pi\) | |||||||
\(854\) | −13.0127 | −0.445285 | ||||||||
\(855\) | 16.4788 | 0.563562 | ||||||||
\(856\) | −13.3165 | −0.455148 | ||||||||
\(857\) | 21.2871 | 0.727154 | 0.363577 | − | 0.931564i | \(-0.381555\pi\) | ||||
0.363577 | + | 0.931564i | \(0.381555\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.8904 | 0.508053 | 0.254027 | − | 0.967197i | \(-0.418245\pi\) | ||||
0.254027 | + | 0.967197i | \(0.418245\pi\) | |||||||
\(860\) | −3.75423 | −0.128018 | ||||||||
\(861\) | 0.187112 | 0.00637675 | ||||||||
\(862\) | 27.5547 | 0.938518 | ||||||||
\(863\) | −47.6345 | −1.62150 | −0.810748 | − | 0.585395i | \(-0.800939\pi\) | ||||
−0.810748 | + | 0.585395i | \(0.800939\pi\) | |||||||
\(864\) | 0.581365 | 0.0197784 | ||||||||
\(865\) | −13.9142 | −0.473095 | ||||||||
\(866\) | 3.18070 | 0.108084 | ||||||||
\(867\) | −1.21241 | −0.0411756 | ||||||||
\(868\) | 1.21552 | 0.0412576 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.779108 | −0.0264142 | ||||||||
\(871\) | −15.3755 | −0.520979 | ||||||||
\(872\) | −8.04563 | −0.272459 | ||||||||
\(873\) | −0.255939 | −0.00866221 | ||||||||
\(874\) | 5.08053 | 0.171851 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 1.43912 | 0.0486233 | ||||||||
\(877\) | −36.4415 | −1.23054 | −0.615270 | − | 0.788316i | \(-0.710953\pi\) | ||||
−0.615270 | + | 0.788316i | \(0.710953\pi\) | |||||||
\(878\) | 39.0123 | 1.31660 | ||||||||
\(879\) | 0.484738 | 0.0163498 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.4724 | 1.76784 | 0.883920 | − | 0.467639i | \(-0.154895\pi\) | ||||
0.883920 | + | 0.467639i | \(0.154895\pi\) | |||||||
\(882\) | 2.99058 | 0.100698 | ||||||||
\(883\) | −6.85399 | −0.230655 | −0.115328 | − | 0.993328i | \(-0.536792\pi\) | ||||
−0.115328 | + | 0.993328i | \(0.536792\pi\) | |||||||
\(884\) | −9.18486 | −0.308920 | ||||||||
\(885\) | −0.0172945 | −0.000581348 0 | ||||||||
\(886\) | −5.00748 | −0.168229 | ||||||||
\(887\) | 23.4947 | 0.788876 | 0.394438 | − | 0.918922i | \(-0.370939\pi\) | ||||
0.394438 | + | 0.918922i | \(0.370939\pi\) | |||||||
\(888\) | 0.486499 | 0.0163258 | ||||||||
\(889\) | 8.63204 | 0.289509 | ||||||||
\(890\) | 18.4678 | 0.619042 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.98647 | −0.233924 | ||||||||
\(893\) | 4.76663 | 0.159509 | ||||||||
\(894\) | −1.92982 | −0.0645427 | ||||||||
\(895\) | −3.61007 | −0.120671 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0.387126 | 0.0129258 | ||||||||
\(898\) | −12.5770 | −0.419700 | ||||||||
\(899\) | 9.75846 | 0.325463 | ||||||||
\(900\) | −2.99058 | −0.0996861 | ||||||||
\(901\) | 1.54797 | 0.0515702 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.364335 | −0.0121243 | ||||||||
\(904\) | −9.17493 | −0.305153 | ||||||||
\(905\) | −1.95017 | −0.0648260 | ||||||||
\(906\) | −0.670742 | −0.0222839 | ||||||||
\(907\) | 33.9046 | 1.12578 | 0.562892 | − | 0.826530i | \(-0.309689\pi\) | ||||
0.562892 | + | 0.826530i | \(0.309689\pi\) | |||||||
\(908\) | 23.6112 | 0.783565 | ||||||||
\(909\) | −22.6543 | −0.751397 | ||||||||
\(910\) | −4.32646 | −0.143421 | ||||||||
\(911\) | −48.8133 | −1.61726 | −0.808628 | − | 0.588320i | \(-0.799790\pi\) | ||||
−0.808628 | + | 0.588320i | \(0.799790\pi\) | |||||||
\(912\) | −0.534747 | −0.0177073 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −36.1549 | −1.19590 | ||||||||
\(915\) | 1.26283 | 0.0417480 | ||||||||
\(916\) | 21.0574 | 0.695755 | ||||||||
\(917\) | −5.01748 | −0.165692 | ||||||||
\(918\) | −1.23421 | −0.0407349 | ||||||||
\(919\) | −16.4073 | −0.541228 | −0.270614 | − | 0.962688i | \(-0.587227\pi\) | ||||
−0.270614 | + | 0.962688i | \(0.587227\pi\) | |||||||
\(920\) | −0.922019 | −0.0303981 | ||||||||
\(921\) | −1.17713 | −0.0387878 | ||||||||
\(922\) | 26.0248 | 0.857080 | ||||||||
\(923\) | 25.7873 | 0.848801 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.01306 | −0.164828 | ||||||||
\(926\) | −2.55526 | −0.0839711 | ||||||||
\(927\) | 11.2500 | 0.369499 | ||||||||
\(928\) | −8.02820 | −0.263539 | ||||||||
\(929\) | −18.9935 | −0.623157 | −0.311579 | − | 0.950220i | \(-0.600858\pi\) | ||||
−0.311579 | + | 0.950220i | \(0.600858\pi\) | |||||||
\(930\) | −0.117962 | −0.00386813 | ||||||||
\(931\) | −5.51022 | −0.180590 | ||||||||
\(932\) | 29.7941 | 0.975937 | ||||||||
\(933\) | −0.561924 | −0.0183966 | ||||||||
\(934\) | −14.4176 | −0.471760 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.9386 | 0.422913 | ||||||||
\(937\) | −5.26363 | −0.171955 | −0.0859777 | − | 0.996297i | \(-0.527401\pi\) | ||||
−0.0859777 | + | 0.996297i | \(0.527401\pi\) | |||||||
\(938\) | 3.55383 | 0.116037 | ||||||||
\(939\) | −0.797192 | −0.0260154 | ||||||||
\(940\) | −0.865052 | −0.0282149 | ||||||||
\(941\) | −36.6208 | −1.19380 | −0.596901 | − | 0.802315i | \(-0.703602\pi\) | ||||
−0.596901 | + | 0.802315i | \(0.703602\pi\) | |||||||
\(942\) | −0.873540 | −0.0284615 | ||||||||
\(943\) | 1.77771 | 0.0578902 | ||||||||
\(944\) | −0.178208 | −0.00580019 | ||||||||
\(945\) | −0.581365 | −0.0189118 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.3320 | 1.27812 | 0.639060 | − | 0.769157i | \(-0.279324\pi\) | ||||
0.639060 | + | 0.769157i | \(0.279324\pi\) | |||||||
\(948\) | −1.28073 | −0.0415962 | ||||||||
\(949\) | 64.1578 | 2.08265 | ||||||||
\(950\) | 5.51022 | 0.178775 | ||||||||
\(951\) | −0.956171 | −0.0310060 | ||||||||
\(952\) | 2.12295 | 0.0688052 | ||||||||
\(953\) | 30.1849 | 0.977784 | 0.488892 | − | 0.872344i | \(-0.337401\pi\) | ||||
0.488892 | + | 0.872344i | \(0.337401\pi\) | |||||||
\(954\) | −2.18061 | −0.0705998 | ||||||||
\(955\) | 12.7463 | 0.412460 | ||||||||
\(956\) | 18.4084 | 0.595370 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 32.6066 | 1.05347 | ||||||||
\(959\) | −9.38739 | −0.303134 | ||||||||
\(960\) | 0.0970464 | 0.00313216 | ||||||||
\(961\) | −29.5225 | −0.952339 | ||||||||
\(962\) | 21.6888 | 0.699275 | ||||||||
\(963\) | −39.8241 | −1.28331 | ||||||||
\(964\) | 2.15635 | 0.0694513 | ||||||||
\(965\) | 14.5920 | 0.469732 | ||||||||
\(966\) | −0.0894787 | −0.00287893 | ||||||||
\(967\) | 52.3303 | 1.68283 | 0.841414 | − | 0.540391i | \(-0.181724\pi\) | ||||
0.841414 | + | 0.540391i | \(0.181724\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.13524 | 0.0364692 | ||||||||
\(970\) | −0.0855815 | −0.00274786 | ||||||||
\(971\) | 34.1707 | 1.09659 | 0.548294 | − | 0.836285i | \(-0.315277\pi\) | ||||
0.548294 | + | 0.836285i | \(0.315277\pi\) | |||||||
\(972\) | 2.60929 | 0.0836932 | ||||||||
\(973\) | 6.96159 | 0.223178 | ||||||||
\(974\) | −16.9041 | −0.541642 | ||||||||
\(975\) | 0.419868 | 0.0134465 | ||||||||
\(976\) | 13.0127 | 0.416526 | ||||||||
\(977\) | −43.2069 | −1.38231 | −0.691156 | − | 0.722706i | \(-0.742898\pi\) | ||||
−0.691156 | + | 0.722706i | \(0.742898\pi\) | |||||||
\(978\) | 0.686222 | 0.0219430 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −24.0611 | −0.768212 | ||||||||
\(982\) | −38.7664 | −1.23709 | ||||||||
\(983\) | 43.9672 | 1.40233 | 0.701167 | − | 0.712997i | \(-0.252663\pi\) | ||||
0.701167 | + | 0.712997i | \(0.252663\pi\) | |||||||
\(984\) | −0.187112 | −0.00596490 | ||||||||
\(985\) | −24.4598 | −0.779356 | ||||||||
\(986\) | 17.0435 | 0.542774 | ||||||||
\(987\) | −0.0839502 | −0.00267216 | ||||||||
\(988\) | −23.8398 | −0.758444 | ||||||||
\(989\) | −3.46147 | −0.110068 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.0881 | 0.352224 | 0.176112 | − | 0.984370i | \(-0.443648\pi\) | ||||
0.176112 | + | 0.984370i | \(0.443648\pi\) | |||||||
\(992\) | −1.21552 | −0.0385929 | ||||||||
\(993\) | −0.554786 | −0.0176056 | ||||||||
\(994\) | −5.96038 | −0.189052 | ||||||||
\(995\) | −10.4998 | −0.332868 | ||||||||
\(996\) | −0.255248 | −0.00808783 | ||||||||
\(997\) | −14.3365 | −0.454042 | −0.227021 | − | 0.973890i | \(-0.572899\pi\) | ||||
−0.227021 | + | 0.973890i | \(0.572899\pi\) | |||||||
\(998\) | 37.6575 | 1.19203 | ||||||||
\(999\) | 2.91441 | 0.0922080 |
(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 | 8470.2.a.cv.1.4 | 6 | ||
11.7 | odd | 10 | 770.2.n.g.71.2 | ✓ | 12 | ||
11.8 | odd | 10 | 770.2.n.g.141.2 | yes | 12 | ||
11.10 | odd | 2 | 8470.2.a.db.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.g.71.2 | ✓ | 12 | 11.7 | odd | 10 | ||
770.2.n.g.141.2 | yes | 12 | 11.8 | odd | 10 | ||
8470.2.a.cv.1.4 | 6 | 1.1 | even | 1 | trivial | ||
8470.2.a.db.1.4 | 6 | 11.10 | odd | 2 |