Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, 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("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 9x^{5} + 10x^{4} + 16x^{3} - 15x^{2} - 6x + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.835360\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.835360 | −0.590689 | −0.295344 | − | 0.955391i | \(-0.595434\pi\) | ||||
−0.295344 | + | 0.955391i | \(0.595434\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.30217 | −0.651087 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.835360 | −0.341034 | ||||||||
\(7\) | 1.49880 | 0.566493 | 0.283246 | − | 0.959047i | \(-0.408589\pi\) | ||||
0.283246 | + | 0.959047i | \(0.408589\pi\) | |||||||
\(8\) | 2.75850 | 0.975279 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.60705 | 1.08757 | 0.543784 | − | 0.839225i | \(-0.316991\pi\) | ||||
0.543784 | + | 0.839225i | \(0.316991\pi\) | |||||||
\(12\) | −1.30217 | −0.375905 | ||||||||
\(13\) | 3.45073 | 0.957059 | 0.478530 | − | 0.878071i | \(-0.341170\pi\) | ||||
0.478530 | + | 0.878071i | \(0.341170\pi\) | |||||||
\(14\) | −1.25204 | −0.334621 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.300002 | 0.0750004 | ||||||||
\(17\) | 0.431873 | 0.104745 | 0.0523724 | − | 0.998628i | \(-0.483322\pi\) | ||||
0.0523724 | + | 0.998628i | \(0.483322\pi\) | |||||||
\(18\) | −0.835360 | −0.196896 | ||||||||
\(19\) | 6.45616 | 1.48114 | 0.740572 | − | 0.671977i | \(-0.234555\pi\) | ||||
0.740572 | + | 0.671977i | \(0.234555\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.49880 | 0.327065 | ||||||||
\(22\) | −3.01319 | −0.642414 | ||||||||
\(23\) | 2.41668 | 0.503912 | 0.251956 | − | 0.967739i | \(-0.418926\pi\) | ||||
0.251956 | + | 0.967739i | \(0.418926\pi\) | |||||||
\(24\) | 2.75850 | 0.563077 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.88260 | −0.565324 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.95170 | −0.368836 | ||||||||
\(29\) | 6.34012 | 1.17733 | 0.588666 | − | 0.808377i | \(-0.299653\pi\) | ||||
0.588666 | + | 0.808377i | \(0.299653\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.92114 | −0.524652 | −0.262326 | − | 0.964979i | \(-0.584490\pi\) | ||||
−0.262326 | + | 0.964979i | \(0.584490\pi\) | |||||||
\(32\) | −5.76762 | −1.01958 | ||||||||
\(33\) | 3.60705 | 0.627908 | ||||||||
\(34\) | −0.360770 | −0.0618715 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.30217 | −0.217029 | ||||||||
\(37\) | −6.28033 | −1.03248 | −0.516240 | − | 0.856444i | \(-0.672669\pi\) | ||||
−0.516240 | + | 0.856444i | \(0.672669\pi\) | |||||||
\(38\) | −5.39322 | −0.874895 | ||||||||
\(39\) | 3.45073 | 0.552558 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.66349 | −0.259794 | −0.129897 | − | 0.991527i | \(-0.541465\pi\) | ||||
−0.129897 | + | 0.991527i | \(0.541465\pi\) | |||||||
\(42\) | −1.25204 | −0.193194 | ||||||||
\(43\) | 4.44949 | 0.678541 | 0.339270 | − | 0.940689i | \(-0.389820\pi\) | ||||
0.339270 | + | 0.940689i | \(0.389820\pi\) | |||||||
\(44\) | −4.69701 | −0.708101 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.01880 | −0.297655 | ||||||||
\(47\) | 1.00000 | 0.145865 | ||||||||
\(48\) | 0.300002 | 0.0433015 | ||||||||
\(49\) | −4.75360 | −0.679086 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.431873 | 0.0604744 | ||||||||
\(52\) | −4.49344 | −0.623128 | ||||||||
\(53\) | 6.04735 | 0.830667 | 0.415334 | − | 0.909669i | \(-0.363665\pi\) | ||||
0.415334 | + | 0.909669i | \(0.363665\pi\) | |||||||
\(54\) | −0.835360 | −0.113678 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.13444 | 0.552488 | ||||||||
\(57\) | 6.45616 | 0.855139 | ||||||||
\(58\) | −5.29629 | −0.695437 | ||||||||
\(59\) | −11.9353 | −1.55385 | −0.776924 | − | 0.629595i | \(-0.783221\pi\) | ||||
−0.776924 | + | 0.629595i | \(0.783221\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.57141 | −0.201199 | −0.100599 | − | 0.994927i | \(-0.532076\pi\) | ||||
−0.100599 | + | 0.994927i | \(0.532076\pi\) | |||||||
\(62\) | 2.44020 | 0.309906 | ||||||||
\(63\) | 1.49880 | 0.188831 | ||||||||
\(64\) | 4.21804 | 0.527254 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.01319 | −0.370898 | ||||||||
\(67\) | −5.12322 | −0.625901 | −0.312951 | − | 0.949769i | \(-0.601317\pi\) | ||||
−0.312951 | + | 0.949769i | \(0.601317\pi\) | |||||||
\(68\) | −0.562374 | −0.0681979 | ||||||||
\(69\) | 2.41668 | 0.290934 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.60553 | 0.190541 | 0.0952704 | − | 0.995451i | \(-0.469628\pi\) | ||||
0.0952704 | + | 0.995451i | \(0.469628\pi\) | |||||||
\(72\) | 2.75850 | 0.325093 | ||||||||
\(73\) | 4.19855 | 0.491403 | 0.245702 | − | 0.969346i | \(-0.420982\pi\) | ||||
0.245702 | + | 0.969346i | \(0.420982\pi\) | |||||||
\(74\) | 5.24634 | 0.609875 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.40703 | −0.964353 | ||||||||
\(77\) | 5.40625 | 0.616099 | ||||||||
\(78\) | −2.88260 | −0.326390 | ||||||||
\(79\) | −3.89653 | −0.438394 | −0.219197 | − | 0.975681i | \(-0.570344\pi\) | ||||
−0.219197 | + | 0.975681i | \(0.570344\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.38962 | 0.153458 | ||||||||
\(83\) | 5.80304 | 0.636967 | 0.318483 | − | 0.947928i | \(-0.396827\pi\) | ||||
0.318483 | + | 0.947928i | \(0.396827\pi\) | |||||||
\(84\) | −1.95170 | −0.212948 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.71693 | −0.400807 | ||||||||
\(87\) | 6.34012 | 0.679733 | ||||||||
\(88\) | 9.95008 | 1.06068 | ||||||||
\(89\) | −9.97189 | −1.05702 | −0.528509 | − | 0.848928i | \(-0.677249\pi\) | ||||
−0.528509 | + | 0.848928i | \(0.677249\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.17194 | 0.542167 | ||||||||
\(92\) | −3.14693 | −0.328090 | ||||||||
\(93\) | −2.92114 | −0.302908 | ||||||||
\(94\) | −0.835360 | −0.0861608 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.76762 | −0.588655 | ||||||||
\(97\) | 3.19957 | 0.324868 | 0.162434 | − | 0.986719i | \(-0.448066\pi\) | ||||
0.162434 | + | 0.986719i | \(0.448066\pi\) | |||||||
\(98\) | 3.97097 | 0.401128 | ||||||||
\(99\) | 3.60705 | 0.362523 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.86233 | −0.384317 | −0.192158 | − | 0.981364i | \(-0.561549\pi\) | ||||
−0.192158 | + | 0.981364i | \(0.561549\pi\) | |||||||
\(102\) | −0.360770 | −0.0357215 | ||||||||
\(103\) | 13.2030 | 1.30093 | 0.650467 | − | 0.759534i | \(-0.274573\pi\) | ||||
0.650467 | + | 0.759534i | \(0.274573\pi\) | |||||||
\(104\) | 9.51884 | 0.933399 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.05171 | −0.490666 | ||||||||
\(107\) | −6.16832 | −0.596314 | −0.298157 | − | 0.954517i | \(-0.596372\pi\) | ||||
−0.298157 | + | 0.954517i | \(0.596372\pi\) | |||||||
\(108\) | −1.30217 | −0.125302 | ||||||||
\(109\) | 13.8020 | 1.32199 | 0.660997 | − | 0.750388i | \(-0.270133\pi\) | ||||
0.660997 | + | 0.750388i | \(0.270133\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.28033 | −0.596103 | ||||||||
\(112\) | 0.449642 | 0.0424872 | ||||||||
\(113\) | −3.38313 | −0.318258 | −0.159129 | − | 0.987258i | \(-0.550869\pi\) | ||||
−0.159129 | + | 0.987258i | \(0.550869\pi\) | |||||||
\(114\) | −5.39322 | −0.505121 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.25594 | −0.766545 | ||||||||
\(117\) | 3.45073 | 0.319020 | ||||||||
\(118\) | 9.97030 | 0.917840 | ||||||||
\(119\) | 0.647292 | 0.0593371 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.01084 | 0.182804 | ||||||||
\(122\) | 1.31270 | 0.118846 | ||||||||
\(123\) | −1.66349 | −0.149992 | ||||||||
\(124\) | 3.80383 | 0.341594 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.25204 | −0.111540 | ||||||||
\(127\) | −19.9308 | −1.76858 | −0.884288 | − | 0.466943i | \(-0.845355\pi\) | ||||
−0.884288 | + | 0.466943i | \(0.845355\pi\) | |||||||
\(128\) | 8.01166 | 0.708137 | ||||||||
\(129\) | 4.44949 | 0.391756 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.01344 | −0.0885446 | −0.0442723 | − | 0.999020i | \(-0.514097\pi\) | ||||
−0.0442723 | + | 0.999020i | \(0.514097\pi\) | |||||||
\(132\) | −4.69701 | −0.408822 | ||||||||
\(133\) | 9.67648 | 0.839058 | ||||||||
\(134\) | 4.27974 | 0.369713 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.19132 | 0.102155 | ||||||||
\(137\) | 23.0985 | 1.97344 | 0.986720 | − | 0.162433i | \(-0.0519340\pi\) | ||||
0.986720 | + | 0.162433i | \(0.0519340\pi\) | |||||||
\(138\) | −2.01880 | −0.171851 | ||||||||
\(139\) | −17.1927 | −1.45827 | −0.729135 | − | 0.684370i | \(-0.760077\pi\) | ||||
−0.729135 | + | 0.684370i | \(0.760077\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.00000 | 0.0842152 | ||||||||
\(142\) | −1.34119 | −0.112550 | ||||||||
\(143\) | 12.4470 | 1.04087 | ||||||||
\(144\) | 0.300002 | 0.0250001 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.50730 | −0.290266 | ||||||||
\(147\) | −4.75360 | −0.392070 | ||||||||
\(148\) | 8.17808 | 0.672234 | ||||||||
\(149\) | −6.10498 | −0.500139 | −0.250070 | − | 0.968228i | \(-0.580454\pi\) | ||||
−0.250070 | + | 0.968228i | \(0.580454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.6212 | −1.02710 | −0.513549 | − | 0.858060i | \(-0.671669\pi\) | ||||
−0.513549 | + | 0.858060i | \(0.671669\pi\) | |||||||
\(152\) | 17.8093 | 1.44453 | ||||||||
\(153\) | 0.431873 | 0.0349149 | ||||||||
\(154\) | −4.51617 | −0.363923 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.49344 | −0.359763 | ||||||||
\(157\) | −5.27493 | −0.420986 | −0.210493 | − | 0.977595i | \(-0.567507\pi\) | ||||
−0.210493 | + | 0.977595i | \(0.567507\pi\) | |||||||
\(158\) | 3.25501 | 0.258955 | ||||||||
\(159\) | 6.04735 | 0.479586 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.62211 | 0.285463 | ||||||||
\(162\) | −0.835360 | −0.0656321 | ||||||||
\(163\) | 1.41749 | 0.111026 | 0.0555130 | − | 0.998458i | \(-0.482321\pi\) | ||||
0.0555130 | + | 0.998458i | \(0.482321\pi\) | |||||||
\(164\) | 2.16616 | 0.169149 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.84763 | −0.376249 | ||||||||
\(167\) | 21.0197 | 1.62655 | 0.813277 | − | 0.581877i | \(-0.197682\pi\) | ||||
0.813277 | + | 0.581877i | \(0.197682\pi\) | |||||||
\(168\) | 4.13444 | 0.318979 | ||||||||
\(169\) | −1.09249 | −0.0840380 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.45616 | 0.493715 | ||||||||
\(172\) | −5.79401 | −0.441789 | ||||||||
\(173\) | −7.69708 | −0.585198 | −0.292599 | − | 0.956235i | \(-0.594520\pi\) | ||||
−0.292599 | + | 0.956235i | \(0.594520\pi\) | |||||||
\(174\) | −5.29629 | −0.401511 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.08212 | 0.0815680 | ||||||||
\(177\) | −11.9353 | −0.897114 | ||||||||
\(178\) | 8.33012 | 0.624369 | ||||||||
\(179\) | 13.3669 | 0.999089 | 0.499545 | − | 0.866288i | \(-0.333501\pi\) | ||||
0.499545 | + | 0.866288i | \(0.333501\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.49768 | 0.334310 | 0.167155 | − | 0.985931i | \(-0.446542\pi\) | ||||
0.167155 | + | 0.985931i | \(0.446542\pi\) | |||||||
\(182\) | −4.32044 | −0.320252 | ||||||||
\(183\) | −1.57141 | −0.116162 | ||||||||
\(184\) | 6.66641 | 0.491455 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.44020 | 0.178924 | ||||||||
\(187\) | 1.55779 | 0.113917 | ||||||||
\(188\) | −1.30217 | −0.0949707 | ||||||||
\(189\) | 1.49880 | 0.109022 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.40415 | −0.391031 | −0.195515 | − | 0.980701i | \(-0.562638\pi\) | ||||
−0.195515 | + | 0.980701i | \(0.562638\pi\) | |||||||
\(192\) | 4.21804 | 0.304411 | ||||||||
\(193\) | 21.4252 | 1.54222 | 0.771110 | − | 0.636702i | \(-0.219702\pi\) | ||||
0.771110 | + | 0.636702i | \(0.219702\pi\) | |||||||
\(194\) | −2.67280 | −0.191896 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.19001 | 0.442144 | ||||||||
\(197\) | 13.6662 | 0.973677 | 0.486839 | − | 0.873492i | \(-0.338150\pi\) | ||||
0.486839 | + | 0.873492i | \(0.338150\pi\) | |||||||
\(198\) | −3.01319 | −0.214138 | ||||||||
\(199\) | 14.2123 | 1.00748 | 0.503741 | − | 0.863855i | \(-0.331957\pi\) | ||||
0.503741 | + | 0.863855i | \(0.331957\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.12322 | −0.361364 | ||||||||
\(202\) | 3.22644 | 0.227012 | ||||||||
\(203\) | 9.50257 | 0.666950 | ||||||||
\(204\) | −0.562374 | −0.0393741 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.0293 | −0.768448 | ||||||||
\(207\) | 2.41668 | 0.167971 | ||||||||
\(208\) | 1.03522 | 0.0717798 | ||||||||
\(209\) | 23.2877 | 1.61084 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.76216 | −0.327840 | −0.163920 | − | 0.986474i | \(-0.552414\pi\) | ||||
−0.163920 | + | 0.986474i | \(0.552414\pi\) | |||||||
\(212\) | −7.87469 | −0.540836 | ||||||||
\(213\) | 1.60553 | 0.110009 | ||||||||
\(214\) | 5.15277 | 0.352236 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.75850 | 0.187692 | ||||||||
\(217\) | −4.37820 | −0.297212 | ||||||||
\(218\) | −11.5297 | −0.780888 | ||||||||
\(219\) | 4.19855 | 0.283712 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.49028 | 0.100247 | ||||||||
\(222\) | 5.24634 | 0.352111 | ||||||||
\(223\) | 6.02259 | 0.403302 | 0.201651 | − | 0.979457i | \(-0.435369\pi\) | ||||
0.201651 | + | 0.979457i | \(0.435369\pi\) | |||||||
\(224\) | −8.64450 | −0.577585 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.82613 | 0.187991 | ||||||||
\(227\) | 12.2111 | 0.810478 | 0.405239 | − | 0.914211i | \(-0.367188\pi\) | ||||
0.405239 | + | 0.914211i | \(0.367188\pi\) | |||||||
\(228\) | −8.40703 | −0.556769 | ||||||||
\(229\) | −26.3687 | −1.74249 | −0.871246 | − | 0.490846i | \(-0.836688\pi\) | ||||
−0.871246 | + | 0.490846i | \(0.836688\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.40625 | 0.355705 | ||||||||
\(232\) | 17.4893 | 1.14823 | ||||||||
\(233\) | −5.02155 | −0.328972 | −0.164486 | − | 0.986379i | \(-0.552597\pi\) | ||||
−0.164486 | + | 0.986379i | \(0.552597\pi\) | |||||||
\(234\) | −2.88260 | −0.188441 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 15.5419 | 1.01169 | ||||||||
\(237\) | −3.89653 | −0.253107 | ||||||||
\(238\) | −0.540722 | −0.0350498 | ||||||||
\(239\) | −10.7625 | −0.696170 | −0.348085 | − | 0.937463i | \(-0.613168\pi\) | ||||
−0.348085 | + | 0.937463i | \(0.613168\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.25618 | 0.274165 | 0.137082 | − | 0.990560i | \(-0.456227\pi\) | ||||
0.137082 | + | 0.990560i | \(0.456227\pi\) | |||||||
\(242\) | −1.67978 | −0.107980 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.04625 | 0.130998 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.38962 | 0.0885988 | ||||||||
\(247\) | 22.2784 | 1.41754 | ||||||||
\(248\) | −8.05797 | −0.511682 | ||||||||
\(249\) | 5.80304 | 0.367753 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.9538 | 1.51195 | 0.755977 | − | 0.654599i | \(-0.227162\pi\) | ||||
0.755977 | + | 0.654599i | \(0.227162\pi\) | |||||||
\(252\) | −1.95170 | −0.122945 | ||||||||
\(253\) | 8.71709 | 0.548039 | ||||||||
\(254\) | 16.6494 | 1.04468 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.1287 | −0.945543 | ||||||||
\(257\) | 23.3416 | 1.45601 | 0.728004 | − | 0.685572i | \(-0.240448\pi\) | ||||
0.728004 | + | 0.685572i | \(0.240448\pi\) | |||||||
\(258\) | −3.71693 | −0.231406 | ||||||||
\(259\) | −9.41296 | −0.584893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.34012 | 0.392444 | ||||||||
\(262\) | 0.846587 | 0.0523023 | ||||||||
\(263\) | −3.46425 | −0.213615 | −0.106807 | − | 0.994280i | \(-0.534063\pi\) | ||||
−0.106807 | + | 0.994280i | \(0.534063\pi\) | |||||||
\(264\) | 9.95008 | 0.612385 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.08335 | −0.495622 | ||||||||
\(267\) | −9.97189 | −0.610270 | ||||||||
\(268\) | 6.67132 | 0.407516 | ||||||||
\(269\) | 14.9476 | 0.911371 | 0.455685 | − | 0.890141i | \(-0.349394\pi\) | ||||
0.455685 | + | 0.890141i | \(0.349394\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.1187 | −1.46511 | −0.732554 | − | 0.680709i | \(-0.761672\pi\) | ||||
−0.732554 | + | 0.680709i | \(0.761672\pi\) | |||||||
\(272\) | 0.129563 | 0.00785589 | ||||||||
\(273\) | 5.17194 | 0.313020 | ||||||||
\(274\) | −19.2956 | −1.16569 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.14693 | −0.189423 | ||||||||
\(277\) | 0.682813 | 0.0410263 | 0.0205131 | − | 0.999790i | \(-0.493470\pi\) | ||||
0.0205131 | + | 0.999790i | \(0.493470\pi\) | |||||||
\(278\) | 14.3621 | 0.861383 | ||||||||
\(279\) | −2.92114 | −0.174884 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.795242 | 0.0474402 | 0.0237201 | − | 0.999719i | \(-0.492449\pi\) | ||||
0.0237201 | + | 0.999719i | \(0.492449\pi\) | |||||||
\(282\) | −0.835360 | −0.0497450 | ||||||||
\(283\) | −29.0426 | −1.72640 | −0.863201 | − | 0.504861i | \(-0.831544\pi\) | ||||
−0.863201 | + | 0.504861i | \(0.831544\pi\) | |||||||
\(284\) | −2.09067 | −0.124059 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.3977 | −0.614828 | ||||||||
\(287\) | −2.49324 | −0.147172 | ||||||||
\(288\) | −5.76762 | −0.339860 | ||||||||
\(289\) | −16.8135 | −0.989029 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.19957 | 0.187562 | ||||||||
\(292\) | −5.46724 | −0.319946 | ||||||||
\(293\) | −1.78518 | −0.104292 | −0.0521458 | − | 0.998639i | \(-0.516606\pi\) | ||||
−0.0521458 | + | 0.998639i | \(0.516606\pi\) | |||||||
\(294\) | 3.97097 | 0.231592 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −17.3243 | −1.00696 | ||||||||
\(297\) | 3.60705 | 0.209303 | ||||||||
\(298\) | 5.09986 | 0.295427 | ||||||||
\(299\) | 8.33929 | 0.482274 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.66889 | 0.384389 | ||||||||
\(302\) | 10.5432 | 0.606695 | ||||||||
\(303\) | −3.86233 | −0.221885 | ||||||||
\(304\) | 1.93686 | 0.111086 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.360770 | −0.0206238 | ||||||||
\(307\) | 2.76651 | 0.157893 | 0.0789467 | − | 0.996879i | \(-0.474844\pi\) | ||||
0.0789467 | + | 0.996879i | \(0.474844\pi\) | |||||||
\(308\) | −7.03988 | −0.401134 | ||||||||
\(309\) | 13.2030 | 0.751095 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.3933 | 1.78015 | 0.890076 | − | 0.455813i | \(-0.150651\pi\) | ||||
0.890076 | + | 0.455813i | \(0.150651\pi\) | |||||||
\(312\) | 9.51884 | 0.538898 | ||||||||
\(313\) | −15.3171 | −0.865774 | −0.432887 | − | 0.901448i | \(-0.642505\pi\) | ||||
−0.432887 | + | 0.901448i | \(0.642505\pi\) | |||||||
\(314\) | 4.40647 | 0.248671 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.07396 | 0.285433 | ||||||||
\(317\) | −12.1597 | −0.682956 | −0.341478 | − | 0.939890i | \(-0.610928\pi\) | ||||
−0.341478 | + | 0.939890i | \(0.610928\pi\) | |||||||
\(318\) | −5.05171 | −0.283286 | ||||||||
\(319\) | 22.8692 | 1.28043 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.16832 | −0.344282 | ||||||||
\(322\) | −3.02577 | −0.168620 | ||||||||
\(323\) | 2.78824 | 0.155142 | ||||||||
\(324\) | −1.30217 | −0.0723430 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.18411 | −0.0655818 | ||||||||
\(327\) | 13.8020 | 0.763254 | ||||||||
\(328\) | −4.58876 | −0.253372 | ||||||||
\(329\) | 1.49880 | 0.0826315 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.9978 | −1.42897 | −0.714484 | − | 0.699651i | \(-0.753339\pi\) | ||||
−0.714484 | + | 0.699651i | \(0.753339\pi\) | |||||||
\(332\) | −7.55657 | −0.414721 | ||||||||
\(333\) | −6.28033 | −0.344160 | ||||||||
\(334\) | −17.5590 | −0.960787 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.449642 | 0.0245300 | ||||||||
\(337\) | −6.03799 | −0.328910 | −0.164455 | − | 0.986385i | \(-0.552587\pi\) | ||||
−0.164455 | + | 0.986385i | \(0.552587\pi\) | |||||||
\(338\) | 0.912626 | 0.0496403 | ||||||||
\(339\) | −3.38313 | −0.183746 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.5367 | −0.570595 | ||||||||
\(342\) | −5.39322 | −0.291632 | ||||||||
\(343\) | −17.6163 | −0.951190 | ||||||||
\(344\) | 12.2739 | 0.661766 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.42984 | 0.345670 | ||||||||
\(347\) | −4.10637 | −0.220441 | −0.110221 | − | 0.993907i | \(-0.535156\pi\) | ||||
−0.110221 | + | 0.993907i | \(0.535156\pi\) | |||||||
\(348\) | −8.25594 | −0.442565 | ||||||||
\(349\) | −9.88265 | −0.529006 | −0.264503 | − | 0.964385i | \(-0.585208\pi\) | ||||
−0.264503 | + | 0.964385i | \(0.585208\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.45073 | 0.184186 | ||||||||
\(352\) | −20.8041 | −1.10886 | ||||||||
\(353\) | 0.277318 | 0.0147601 | 0.00738007 | − | 0.999973i | \(-0.497651\pi\) | ||||
0.00738007 | + | 0.999973i | \(0.497651\pi\) | |||||||
\(354\) | 9.97030 | 0.529915 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.9851 | 0.688210 | ||||||||
\(357\) | 0.647292 | 0.0342583 | ||||||||
\(358\) | −11.1662 | −0.590151 | ||||||||
\(359\) | 12.8277 | 0.677020 | 0.338510 | − | 0.940963i | \(-0.390077\pi\) | ||||
0.338510 | + | 0.940963i | \(0.390077\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.6820 | 1.19379 | ||||||||
\(362\) | −3.75718 | −0.197473 | ||||||||
\(363\) | 2.01084 | 0.105542 | ||||||||
\(364\) | −6.73477 | −0.352998 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.31270 | 0.0686157 | ||||||||
\(367\) | 13.9591 | 0.728661 | 0.364331 | − | 0.931270i | \(-0.381298\pi\) | ||||
0.364331 | + | 0.931270i | \(0.381298\pi\) | |||||||
\(368\) | 0.725007 | 0.0377936 | ||||||||
\(369\) | −1.66349 | −0.0865981 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.06376 | 0.470567 | ||||||||
\(372\) | 3.80383 | 0.197219 | ||||||||
\(373\) | 17.1264 | 0.886771 | 0.443386 | − | 0.896331i | \(-0.353777\pi\) | ||||
0.443386 | + | 0.896331i | \(0.353777\pi\) | |||||||
\(374\) | −1.30132 | −0.0672895 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.75850 | 0.142259 | ||||||||
\(377\) | 21.8780 | 1.12678 | ||||||||
\(378\) | −1.25204 | −0.0643979 | ||||||||
\(379\) | −25.2685 | −1.29795 | −0.648977 | − | 0.760808i | \(-0.724803\pi\) | ||||
−0.648977 | + | 0.760808i | \(0.724803\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.9308 | −1.02109 | ||||||||
\(382\) | 4.51441 | 0.230978 | ||||||||
\(383\) | 6.33708 | 0.323810 | 0.161905 | − | 0.986806i | \(-0.448236\pi\) | ||||
0.161905 | + | 0.986806i | \(0.448236\pi\) | |||||||
\(384\) | 8.01166 | 0.408843 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.8978 | −0.910972 | ||||||||
\(387\) | 4.44949 | 0.226180 | ||||||||
\(388\) | −4.16640 | −0.211517 | ||||||||
\(389\) | 18.2354 | 0.924570 | 0.462285 | − | 0.886731i | \(-0.347030\pi\) | ||||
0.462285 | + | 0.886731i | \(0.347030\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.04370 | 0.0527821 | ||||||||
\(392\) | −13.1128 | −0.662298 | ||||||||
\(393\) | −1.01344 | −0.0511212 | ||||||||
\(394\) | −11.4162 | −0.575140 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.69701 | −0.236034 | ||||||||
\(397\) | −26.7157 | −1.34082 | −0.670411 | − | 0.741990i | \(-0.733882\pi\) | ||||
−0.670411 | + | 0.741990i | \(0.733882\pi\) | |||||||
\(398\) | −11.8724 | −0.595108 | ||||||||
\(399\) | 9.67648 | 0.484430 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.13261 | 0.156435 | 0.0782176 | − | 0.996936i | \(-0.475077\pi\) | ||||
0.0782176 | + | 0.996936i | \(0.475077\pi\) | |||||||
\(402\) | 4.27974 | 0.213454 | ||||||||
\(403\) | −10.0800 | −0.502123 | ||||||||
\(404\) | 5.02943 | 0.250223 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.93807 | −0.393960 | ||||||||
\(407\) | −22.6535 | −1.12289 | ||||||||
\(408\) | 1.19132 | 0.0589794 | ||||||||
\(409\) | 24.5146 | 1.21217 | 0.606084 | − | 0.795401i | \(-0.292740\pi\) | ||||
0.606084 | + | 0.795401i | \(0.292740\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.0985 | 1.13937 | ||||||||
\(412\) | −17.1927 | −0.847021 | ||||||||
\(413\) | −17.8887 | −0.880244 | ||||||||
\(414\) | −2.01880 | −0.0992184 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −19.9025 | −0.975799 | ||||||||
\(417\) | −17.1927 | −0.841932 | ||||||||
\(418\) | −19.4536 | −0.951508 | ||||||||
\(419\) | −3.61047 | −0.176383 | −0.0881914 | − | 0.996104i | \(-0.528109\pi\) | ||||
−0.0881914 | + | 0.996104i | \(0.528109\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.4964 | 0.755249 | 0.377624 | − | 0.925959i | \(-0.376741\pi\) | ||||
0.377624 | + | 0.925959i | \(0.376741\pi\) | |||||||
\(422\) | 3.97812 | 0.193652 | ||||||||
\(423\) | 1.00000 | 0.0486217 | ||||||||
\(424\) | 16.6816 | 0.810132 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.34119 | −0.0649810 | ||||||||
\(427\) | −2.35523 | −0.113978 | ||||||||
\(428\) | 8.03222 | 0.388252 | ||||||||
\(429\) | 12.4470 | 0.600945 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.9485 | −1.29806 | −0.649032 | − | 0.760761i | \(-0.724826\pi\) | ||||
−0.649032 | + | 0.760761i | \(0.724826\pi\) | |||||||
\(432\) | 0.300002 | 0.0144338 | ||||||||
\(433\) | −5.45210 | −0.262011 | −0.131006 | − | 0.991382i | \(-0.541821\pi\) | ||||
−0.131006 | + | 0.991382i | \(0.541821\pi\) | |||||||
\(434\) | 3.65737 | 0.175560 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.9726 | −0.860733 | ||||||||
\(437\) | 15.6024 | 0.746366 | ||||||||
\(438\) | −3.50730 | −0.167585 | ||||||||
\(439\) | −25.3547 | −1.21011 | −0.605057 | − | 0.796182i | \(-0.706850\pi\) | ||||
−0.605057 | + | 0.796182i | \(0.706850\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.75360 | −0.226362 | ||||||||
\(442\) | −1.24492 | −0.0592147 | ||||||||
\(443\) | 27.1808 | 1.29140 | 0.645699 | − | 0.763592i | \(-0.276566\pi\) | ||||
0.645699 | + | 0.763592i | \(0.276566\pi\) | |||||||
\(444\) | 8.17808 | 0.388115 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.03103 | −0.238226 | ||||||||
\(447\) | −6.10498 | −0.288756 | ||||||||
\(448\) | 6.32199 | 0.298686 | ||||||||
\(449\) | 7.15431 | 0.337633 | 0.168816 | − | 0.985648i | \(-0.446005\pi\) | ||||
0.168816 | + | 0.985648i | \(0.446005\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00032 | −0.282544 | ||||||||
\(452\) | 4.40542 | 0.207214 | ||||||||
\(453\) | −12.6212 | −0.592995 | ||||||||
\(454\) | −10.2007 | −0.478740 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 17.8093 | 0.833999 | ||||||||
\(457\) | 20.5543 | 0.961488 | 0.480744 | − | 0.876861i | \(-0.340367\pi\) | ||||
0.480744 | + | 0.876861i | \(0.340367\pi\) | |||||||
\(458\) | 22.0274 | 1.02927 | ||||||||
\(459\) | 0.431873 | 0.0201581 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.0983 | 0.796346 | 0.398173 | − | 0.917310i | \(-0.369644\pi\) | ||||
0.398173 | + | 0.917310i | \(0.369644\pi\) | |||||||
\(462\) | −4.51617 | −0.210111 | ||||||||
\(463\) | −15.6746 | −0.728460 | −0.364230 | − | 0.931309i | \(-0.618668\pi\) | ||||
−0.364230 | + | 0.931309i | \(0.618668\pi\) | |||||||
\(464\) | 1.90205 | 0.0883003 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.19480 | 0.194320 | ||||||||
\(467\) | 1.16729 | 0.0540159 | 0.0270080 | − | 0.999635i | \(-0.491402\pi\) | ||||
0.0270080 | + | 0.999635i | \(0.491402\pi\) | |||||||
\(468\) | −4.49344 | −0.207709 | ||||||||
\(469\) | −7.67868 | −0.354569 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.27493 | −0.243056 | ||||||||
\(472\) | −32.9237 | −1.51543 | ||||||||
\(473\) | 16.0496 | 0.737959 | ||||||||
\(474\) | 3.25501 | 0.149508 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.842886 | −0.0386336 | ||||||||
\(477\) | 6.04735 | 0.276889 | ||||||||
\(478\) | 8.99058 | 0.411220 | ||||||||
\(479\) | −11.9790 | −0.547334 | −0.273667 | − | 0.961824i | \(-0.588237\pi\) | ||||
−0.273667 | + | 0.961824i | \(0.588237\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.6717 | −0.988145 | ||||||||
\(482\) | −3.55545 | −0.161946 | ||||||||
\(483\) | 3.62211 | 0.164812 | ||||||||
\(484\) | −2.61847 | −0.119021 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.835360 | −0.0378927 | ||||||||
\(487\) | 17.0359 | 0.771971 | 0.385986 | − | 0.922505i | \(-0.373861\pi\) | ||||
0.385986 | + | 0.922505i | \(0.373861\pi\) | |||||||
\(488\) | −4.33475 | −0.196225 | ||||||||
\(489\) | 1.41749 | 0.0641009 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.1337 | 0.547584 | 0.273792 | − | 0.961789i | \(-0.411722\pi\) | ||||
0.273792 | + | 0.961789i | \(0.411722\pi\) | |||||||
\(492\) | 2.16616 | 0.0976580 | ||||||||
\(493\) | 2.73813 | 0.123319 | ||||||||
\(494\) | −18.6105 | −0.837326 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.876346 | −0.0393491 | ||||||||
\(497\) | 2.40636 | 0.107940 | ||||||||
\(498\) | −4.84763 | −0.217228 | ||||||||
\(499\) | 39.8307 | 1.78307 | 0.891533 | − | 0.452955i | \(-0.149630\pi\) | ||||
0.891533 | + | 0.452955i | \(0.149630\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.0197 | 0.939091 | ||||||||
\(502\) | −20.0101 | −0.893094 | ||||||||
\(503\) | −8.32208 | −0.371063 | −0.185532 | − | 0.982638i | \(-0.559401\pi\) | ||||
−0.185532 | + | 0.982638i | \(0.559401\pi\) | |||||||
\(504\) | 4.13444 | 0.184163 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.28191 | −0.323720 | ||||||||
\(507\) | −1.09249 | −0.0485194 | ||||||||
\(508\) | 25.9534 | 1.15150 | ||||||||
\(509\) | −22.8230 | −1.01161 | −0.505807 | − | 0.862647i | \(-0.668805\pi\) | ||||
−0.505807 | + | 0.862647i | \(0.668805\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.29278 | 0.278376 | ||||||||
\(512\) | −3.38541 | −0.149615 | ||||||||
\(513\) | 6.45616 | 0.285046 | ||||||||
\(514\) | −19.4986 | −0.860048 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.79401 | −0.255067 | ||||||||
\(517\) | 3.60705 | 0.158638 | ||||||||
\(518\) | 7.86321 | 0.345490 | ||||||||
\(519\) | −7.69708 | −0.337864 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.71854 | 0.250534 | 0.125267 | − | 0.992123i | \(-0.460021\pi\) | ||||
0.125267 | + | 0.992123i | \(0.460021\pi\) | |||||||
\(522\) | −5.29629 | −0.231812 | ||||||||
\(523\) | 42.5714 | 1.86152 | 0.930759 | − | 0.365632i | \(-0.119147\pi\) | ||||
0.930759 | + | 0.365632i | \(0.119147\pi\) | |||||||
\(524\) | 1.31967 | 0.0576502 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.89390 | 0.126180 | ||||||||
\(527\) | −1.26156 | −0.0549545 | ||||||||
\(528\) | 1.08212 | 0.0470933 | ||||||||
\(529\) | −17.1597 | −0.746073 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.9353 | −0.517949 | ||||||||
\(532\) | −12.6005 | −0.546299 | ||||||||
\(533\) | −5.74026 | −0.248638 | ||||||||
\(534\) | 8.33012 | 0.360480 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14.1324 | −0.610428 | ||||||||
\(537\) | 13.3669 | 0.576825 | ||||||||
\(538\) | −12.4866 | −0.538337 | ||||||||
\(539\) | −17.1465 | −0.738552 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.967751 | 0.0416069 | 0.0208034 | − | 0.999784i | \(-0.493378\pi\) | ||||
0.0208034 | + | 0.999784i | \(0.493378\pi\) | |||||||
\(542\) | 20.1478 | 0.865423 | ||||||||
\(543\) | 4.49768 | 0.193014 | ||||||||
\(544\) | −2.49088 | −0.106796 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.32044 | −0.184898 | ||||||||
\(547\) | −8.53981 | −0.365136 | −0.182568 | − | 0.983193i | \(-0.558441\pi\) | ||||
−0.182568 | + | 0.983193i | \(0.558441\pi\) | |||||||
\(548\) | −30.0783 | −1.28488 | ||||||||
\(549\) | −1.57141 | −0.0670663 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 40.9328 | 1.74380 | ||||||||
\(552\) | 6.66641 | 0.283741 | ||||||||
\(553\) | −5.84012 | −0.248347 | ||||||||
\(554\) | −0.570395 | −0.0242338 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.3879 | 0.949459 | ||||||||
\(557\) | −28.8759 | −1.22351 | −0.611756 | − | 0.791046i | \(-0.709537\pi\) | ||||
−0.611756 | + | 0.791046i | \(0.709537\pi\) | |||||||
\(558\) | 2.44020 | 0.103302 | ||||||||
\(559\) | 15.3540 | 0.649404 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.55779 | 0.0657700 | ||||||||
\(562\) | −0.664314 | −0.0280224 | ||||||||
\(563\) | −43.3713 | −1.82788 | −0.913942 | − | 0.405845i | \(-0.866977\pi\) | ||||
−0.913942 | + | 0.405845i | \(0.866977\pi\) | |||||||
\(564\) | −1.30217 | −0.0548314 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.2610 | 1.01977 | ||||||||
\(567\) | 1.49880 | 0.0629437 | ||||||||
\(568\) | 4.42885 | 0.185830 | ||||||||
\(569\) | 8.48746 | 0.355813 | 0.177906 | − | 0.984047i | \(-0.443068\pi\) | ||||
0.177906 | + | 0.984047i | \(0.443068\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.4422 | −1.56691 | −0.783453 | − | 0.621451i | \(-0.786543\pi\) | ||||
−0.783453 | + | 0.621451i | \(0.786543\pi\) | |||||||
\(572\) | −16.2081 | −0.677694 | ||||||||
\(573\) | −5.40415 | −0.225762 | ||||||||
\(574\) | 2.08276 | 0.0869326 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.21804 | 0.175751 | ||||||||
\(577\) | 3.64145 | 0.151596 | 0.0757978 | − | 0.997123i | \(-0.475850\pi\) | ||||
0.0757978 | + | 0.997123i | \(0.475850\pi\) | |||||||
\(578\) | 14.0453 | 0.584208 | ||||||||
\(579\) | 21.4252 | 0.890401 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.69760 | 0.360837 | ||||||||
\(582\) | −2.67280 | −0.110791 | ||||||||
\(583\) | 21.8131 | 0.903407 | ||||||||
\(584\) | 11.5817 | 0.479255 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.49127 | 0.0616038 | ||||||||
\(587\) | 40.2475 | 1.66119 | 0.830596 | − | 0.556876i | \(-0.188000\pi\) | ||||
0.830596 | + | 0.556876i | \(0.188000\pi\) | |||||||
\(588\) | 6.19001 | 0.255272 | ||||||||
\(589\) | −18.8593 | −0.777085 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.6662 | 0.562153 | ||||||||
\(592\) | −1.88411 | −0.0774364 | ||||||||
\(593\) | 10.5073 | 0.431482 | 0.215741 | − | 0.976451i | \(-0.430783\pi\) | ||||
0.215741 | + | 0.976451i | \(0.430783\pi\) | |||||||
\(594\) | −3.01319 | −0.123633 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.94974 | 0.325634 | ||||||||
\(597\) | 14.2123 | 0.581670 | ||||||||
\(598\) | −6.96631 | −0.284874 | ||||||||
\(599\) | −34.1199 | −1.39410 | −0.697052 | − | 0.717021i | \(-0.745505\pi\) | ||||
−0.697052 | + | 0.717021i | \(0.745505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.46985 | 0.304701 | 0.152351 | − | 0.988327i | \(-0.451316\pi\) | ||||
0.152351 | + | 0.988327i | \(0.451316\pi\) | |||||||
\(602\) | −5.57093 | −0.227054 | ||||||||
\(603\) | −5.12322 | −0.208634 | ||||||||
\(604\) | 16.4350 | 0.668729 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.22644 | 0.131065 | ||||||||
\(607\) | 25.5358 | 1.03646 | 0.518232 | − | 0.855240i | \(-0.326590\pi\) | ||||
0.518232 | + | 0.855240i | \(0.326590\pi\) | |||||||
\(608\) | −37.2366 | −1.51015 | ||||||||
\(609\) | 9.50257 | 0.385064 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.45073 | 0.139601 | ||||||||
\(612\) | −0.562374 | −0.0227326 | ||||||||
\(613\) | −46.6096 | −1.88254 | −0.941272 | − | 0.337651i | \(-0.890368\pi\) | ||||
−0.941272 | + | 0.337651i | \(0.890368\pi\) | |||||||
\(614\) | −2.31104 | −0.0932658 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.9132 | 0.600869 | ||||||||
\(617\) | −14.0084 | −0.563955 | −0.281978 | − | 0.959421i | \(-0.590990\pi\) | ||||
−0.281978 | + | 0.959421i | \(0.590990\pi\) | |||||||
\(618\) | −11.0293 | −0.443664 | ||||||||
\(619\) | −16.3881 | −0.658694 | −0.329347 | − | 0.944209i | \(-0.606829\pi\) | ||||
−0.329347 | + | 0.944209i | \(0.606829\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.41668 | 0.0969779 | ||||||||
\(622\) | −26.2247 | −1.05152 | ||||||||
\(623\) | −14.9459 | −0.598793 | ||||||||
\(624\) | 1.03522 | 0.0414421 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.7953 | 0.511403 | ||||||||
\(627\) | 23.2877 | 0.930022 | ||||||||
\(628\) | 6.86888 | 0.274098 | ||||||||
\(629\) | −2.71231 | −0.108147 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.9798 | 1.51195 | 0.755976 | − | 0.654600i | \(-0.227163\pi\) | ||||
0.755976 | + | 0.654600i | \(0.227163\pi\) | |||||||
\(632\) | −10.7486 | −0.427557 | ||||||||
\(633\) | −4.76216 | −0.189279 | ||||||||
\(634\) | 10.1577 | 0.403415 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.87469 | −0.312252 | ||||||||
\(637\) | −16.4034 | −0.649925 | ||||||||
\(638\) | −19.1040 | −0.756335 | ||||||||
\(639\) | 1.60553 | 0.0635136 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.9073 | 0.509808 | 0.254904 | − | 0.966966i | \(-0.417956\pi\) | ||||
0.254904 | + | 0.966966i | \(0.417956\pi\) | |||||||
\(642\) | 5.15277 | 0.203364 | ||||||||
\(643\) | 45.0333 | 1.77594 | 0.887970 | − | 0.459901i | \(-0.152115\pi\) | ||||
0.887970 | + | 0.459901i | \(0.152115\pi\) | |||||||
\(644\) | −4.71662 | −0.185861 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.32919 | −0.0916407 | ||||||||
\(647\) | 12.0805 | 0.474933 | 0.237467 | − | 0.971396i | \(-0.423683\pi\) | ||||
0.237467 | + | 0.971396i | \(0.423683\pi\) | |||||||
\(648\) | 2.75850 | 0.108364 | ||||||||
\(649\) | −43.0514 | −1.68991 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.37820 | −0.171595 | ||||||||
\(652\) | −1.84581 | −0.0722875 | ||||||||
\(653\) | −21.6763 | −0.848260 | −0.424130 | − | 0.905601i | \(-0.639420\pi\) | ||||
−0.424130 | + | 0.905601i | \(0.639420\pi\) | |||||||
\(654\) | −11.5297 | −0.450846 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.499051 | −0.0194847 | ||||||||
\(657\) | 4.19855 | 0.163801 | ||||||||
\(658\) | −1.25204 | −0.0488095 | ||||||||
\(659\) | 11.1348 | 0.433751 | 0.216876 | − | 0.976199i | \(-0.430413\pi\) | ||||
0.216876 | + | 0.976199i | \(0.430413\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.3437 | −1.18023 | −0.590116 | − | 0.807318i | \(-0.700918\pi\) | ||||
−0.590116 | + | 0.807318i | \(0.700918\pi\) | |||||||
\(662\) | 21.7175 | 0.844076 | ||||||||
\(663\) | 1.49028 | 0.0578776 | ||||||||
\(664\) | 16.0077 | 0.621220 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.24634 | 0.203292 | ||||||||
\(667\) | 15.3220 | 0.593271 | ||||||||
\(668\) | −27.3713 | −1.05903 | ||||||||
\(669\) | 6.02259 | 0.232847 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.66817 | −0.218817 | ||||||||
\(672\) | −8.64450 | −0.333469 | ||||||||
\(673\) | −5.10678 | −0.196852 | −0.0984260 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984260 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(674\) | 5.04390 | 0.194284 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.42262 | 0.0547160 | ||||||||
\(677\) | −48.5544 | −1.86610 | −0.933048 | − | 0.359753i | \(-0.882861\pi\) | ||||
−0.933048 | + | 0.359753i | \(0.882861\pi\) | |||||||
\(678\) | 2.82613 | 0.108537 | ||||||||
\(679\) | 4.79552 | 0.184035 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.2111 | 0.467930 | ||||||||
\(682\) | 8.80194 | 0.337044 | ||||||||
\(683\) | −28.1169 | −1.07586 | −0.537932 | − | 0.842988i | \(-0.680794\pi\) | ||||
−0.537932 | + | 0.842988i | \(0.680794\pi\) | |||||||
\(684\) | −8.40703 | −0.321451 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 14.7159 | 0.561857 | ||||||||
\(687\) | −26.3687 | −1.00603 | ||||||||
\(688\) | 1.33485 | 0.0508908 | ||||||||
\(689\) | 20.8677 | 0.794997 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.0245 | 0.457433 | 0.228717 | − | 0.973493i | \(-0.426547\pi\) | ||||
0.228717 | + | 0.973493i | \(0.426547\pi\) | |||||||
\(692\) | 10.0229 | 0.381015 | ||||||||
\(693\) | 5.40625 | 0.205366 | ||||||||
\(694\) | 3.43030 | 0.130212 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 17.4893 | 0.662929 | ||||||||
\(697\) | −0.718419 | −0.0272121 | ||||||||
\(698\) | 8.25557 | 0.312478 | ||||||||
\(699\) | −5.02155 | −0.189932 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.3441 | 1.33493 | 0.667464 | − | 0.744642i | \(-0.267380\pi\) | ||||
0.667464 | + | 0.744642i | \(0.267380\pi\) | |||||||
\(702\) | −2.88260 | −0.108797 | ||||||||
\(703\) | −40.5468 | −1.52925 | ||||||||
\(704\) | 15.2147 | 0.573425 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.231660 | −0.00871865 | ||||||||
\(707\) | −5.78886 | −0.217713 | ||||||||
\(708\) | 15.5419 | 0.584099 | ||||||||
\(709\) | 4.51395 | 0.169525 | 0.0847624 | − | 0.996401i | \(-0.472987\pi\) | ||||
0.0847624 | + | 0.996401i | \(0.472987\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.89653 | −0.146131 | ||||||||
\(712\) | −27.5075 | −1.03089 | ||||||||
\(713\) | −7.05945 | −0.264378 | ||||||||
\(714\) | −0.540722 | −0.0202360 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.4060 | −0.650494 | ||||||||
\(717\) | −10.7625 | −0.401934 | ||||||||
\(718\) | −10.7157 | −0.399908 | ||||||||
\(719\) | −32.4057 | −1.20853 | −0.604264 | − | 0.796784i | \(-0.706533\pi\) | ||||
−0.604264 | + | 0.796784i | \(0.706533\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.7887 | 0.736970 | ||||||||
\(722\) | −18.9476 | −0.705157 | ||||||||
\(723\) | 4.25618 | 0.158289 | ||||||||
\(724\) | −5.85676 | −0.217665 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.67978 | −0.0623425 | ||||||||
\(727\) | 24.3094 | 0.901584 | 0.450792 | − | 0.892629i | \(-0.351142\pi\) | ||||
0.450792 | + | 0.892629i | \(0.351142\pi\) | |||||||
\(728\) | 14.2668 | 0.528764 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.92162 | 0.0710736 | ||||||||
\(732\) | 2.04625 | 0.0756317 | ||||||||
\(733\) | 11.1733 | 0.412696 | 0.206348 | − | 0.978479i | \(-0.433842\pi\) | ||||
0.206348 | + | 0.978479i | \(0.433842\pi\) | |||||||
\(734\) | −11.6609 | −0.430412 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.9385 | −0.513779 | ||||||||
\(737\) | −18.4797 | −0.680710 | ||||||||
\(738\) | 1.38962 | 0.0511525 | ||||||||
\(739\) | −32.4670 | −1.19432 | −0.597160 | − | 0.802122i | \(-0.703704\pi\) | ||||
−0.597160 | + | 0.802122i | \(0.703704\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.2784 | 0.818418 | ||||||||
\(742\) | −7.57151 | −0.277959 | ||||||||
\(743\) | 13.1450 | 0.482245 | 0.241123 | − | 0.970495i | \(-0.422484\pi\) | ||||
0.241123 | + | 0.970495i | \(0.422484\pi\) | |||||||
\(744\) | −8.05797 | −0.295420 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14.3067 | −0.523806 | ||||||||
\(747\) | 5.80304 | 0.212322 | ||||||||
\(748\) | −2.02851 | −0.0741698 | ||||||||
\(749\) | −9.24507 | −0.337808 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.83639 | 0.358935 | 0.179468 | − | 0.983764i | \(-0.442563\pi\) | ||||
0.179468 | + | 0.983764i | \(0.442563\pi\) | |||||||
\(752\) | 0.300002 | 0.0109399 | ||||||||
\(753\) | 23.9538 | 0.872927 | ||||||||
\(754\) | −18.2760 | −0.665574 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.95170 | −0.0709825 | ||||||||
\(757\) | −25.9609 | −0.943567 | −0.471783 | − | 0.881715i | \(-0.656390\pi\) | ||||
−0.471783 | + | 0.881715i | \(0.656390\pi\) | |||||||
\(758\) | 21.1083 | 0.766688 | ||||||||
\(759\) | 8.71709 | 0.316410 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 52.7826 | 1.91337 | 0.956684 | − | 0.291129i | \(-0.0940307\pi\) | ||||
0.956684 | + | 0.291129i | \(0.0940307\pi\) | |||||||
\(762\) | 16.6494 | 0.603145 | ||||||||
\(763\) | 20.6865 | 0.748901 | ||||||||
\(764\) | 7.03714 | 0.254595 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.29374 | −0.191271 | ||||||||
\(767\) | −41.1855 | −1.48712 | ||||||||
\(768\) | −15.1287 | −0.545910 | ||||||||
\(769\) | −51.6994 | −1.86433 | −0.932165 | − | 0.362035i | \(-0.882082\pi\) | ||||
−0.932165 | + | 0.362035i | \(0.882082\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.3416 | 0.840627 | ||||||||
\(772\) | −27.8993 | −1.00412 | ||||||||
\(773\) | −29.3029 | −1.05395 | −0.526975 | − | 0.849881i | \(-0.676674\pi\) | ||||
−0.526975 | + | 0.849881i | \(0.676674\pi\) | |||||||
\(774\) | −3.71693 | −0.133602 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.82604 | 0.316836 | ||||||||
\(777\) | −9.41296 | −0.337688 | ||||||||
\(778\) | −15.2331 | −0.546133 | ||||||||
\(779\) | −10.7398 | −0.384793 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.79122 | 0.207226 | ||||||||
\(782\) | −0.871864 | −0.0311778 | ||||||||
\(783\) | 6.34012 | 0.226578 | ||||||||
\(784\) | −1.42609 | −0.0509317 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.846587 | 0.0301967 | ||||||||
\(787\) | −40.5942 | −1.44703 | −0.723514 | − | 0.690310i | \(-0.757474\pi\) | ||||
−0.723514 | + | 0.690310i | \(0.757474\pi\) | |||||||
\(788\) | −17.7958 | −0.633948 | ||||||||
\(789\) | −3.46425 | −0.123331 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.07063 | −0.180291 | ||||||||
\(792\) | 9.95008 | 0.353561 | ||||||||
\(793\) | −5.42252 | −0.192559 | ||||||||
\(794\) | 22.3172 | 0.792008 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.5068 | −0.655957 | ||||||||
\(797\) | −12.7079 | −0.450138 | −0.225069 | − | 0.974343i | \(-0.572261\pi\) | ||||
−0.225069 | + | 0.974343i | \(0.572261\pi\) | |||||||
\(798\) | −8.08335 | −0.286147 | ||||||||
\(799\) | 0.431873 | 0.0152786 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.97189 | −0.352339 | ||||||||
\(802\) | −2.61686 | −0.0924045 | ||||||||
\(803\) | 15.1444 | 0.534434 | ||||||||
\(804\) | 6.67132 | 0.235279 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.42047 | 0.296598 | ||||||||
\(807\) | 14.9476 | 0.526180 | ||||||||
\(808\) | −10.6543 | −0.374816 | ||||||||
\(809\) | 47.9537 | 1.68596 | 0.842981 | − | 0.537944i | \(-0.180799\pi\) | ||||
0.842981 | + | 0.537944i | \(0.180799\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.8214 | −1.01205 | −0.506027 | − | 0.862517i | \(-0.668887\pi\) | ||||
−0.506027 | + | 0.862517i | \(0.668887\pi\) | |||||||
\(812\) | −12.3740 | −0.434242 | ||||||||
\(813\) | −24.1187 | −0.845881 | ||||||||
\(814\) | 18.9238 | 0.663280 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.129563 | 0.00453560 | ||||||||
\(817\) | 28.7266 | 1.00502 | ||||||||
\(818\) | −20.4785 | −0.716014 | ||||||||
\(819\) | 5.17194 | 0.180722 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.1851 | 1.68167 | 0.840835 | − | 0.541291i | \(-0.182064\pi\) | ||||
0.840835 | + | 0.541291i | \(0.182064\pi\) | |||||||
\(822\) | −19.2956 | −0.673011 | ||||||||
\(823\) | −1.05231 | −0.0366812 | −0.0183406 | − | 0.999832i | \(-0.505838\pi\) | ||||
−0.0183406 | + | 0.999832i | \(0.505838\pi\) | |||||||
\(824\) | 36.4207 | 1.26877 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.9435 | 0.519950 | ||||||||
\(827\) | −4.58539 | −0.159450 | −0.0797249 | − | 0.996817i | \(-0.525404\pi\) | ||||
−0.0797249 | + | 0.996817i | \(0.525404\pi\) | |||||||
\(828\) | −3.14693 | −0.109363 | ||||||||
\(829\) | −22.6716 | −0.787419 | −0.393709 | − | 0.919235i | \(-0.628808\pi\) | ||||
−0.393709 | + | 0.919235i | \(0.628808\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.682813 | 0.0236865 | ||||||||
\(832\) | 14.5553 | 0.504614 | ||||||||
\(833\) | −2.05295 | −0.0711306 | ||||||||
\(834\) | 14.3621 | 0.497320 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −30.3246 | −1.04880 | ||||||||
\(837\) | −2.92114 | −0.100969 | ||||||||
\(838\) | 3.01604 | 0.104187 | ||||||||
\(839\) | −36.5409 | −1.26153 | −0.630766 | − | 0.775973i | \(-0.717259\pi\) | ||||
−0.630766 | + | 0.775973i | \(0.717259\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.1972 | 0.386109 | ||||||||
\(842\) | −12.9451 | −0.446117 | ||||||||
\(843\) | 0.795242 | 0.0273896 | ||||||||
\(844\) | 6.20115 | 0.213453 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.835360 | −0.0287203 | ||||||||
\(847\) | 3.01385 | 0.103557 | ||||||||
\(848\) | 1.81421 | 0.0623004 | ||||||||
\(849\) | −29.0426 | −0.996738 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.1775 | −0.520279 | ||||||||
\(852\) | −2.09067 | −0.0716253 | ||||||||
\(853\) | 6.57318 | 0.225061 | 0.112531 | − | 0.993648i | \(-0.464104\pi\) | ||||
0.112531 | + | 0.993648i | \(0.464104\pi\) | |||||||
\(854\) | 1.96747 | 0.0673254 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.0153 | −0.581572 | ||||||||
\(857\) | 33.9335 | 1.15915 | 0.579573 | − | 0.814920i | \(-0.303219\pi\) | ||||
0.579573 | + | 0.814920i | \(0.303219\pi\) | |||||||
\(858\) | −10.3977 | −0.354971 | ||||||||
\(859\) | −34.1505 | −1.16520 | −0.582601 | − | 0.812759i | \(-0.697965\pi\) | ||||
−0.582601 | + | 0.812759i | \(0.697965\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.49324 | −0.0849696 | ||||||||
\(862\) | 22.5117 | 0.766752 | ||||||||
\(863\) | −1.17710 | −0.0400690 | −0.0200345 | − | 0.999799i | \(-0.506378\pi\) | ||||
−0.0200345 | + | 0.999799i | \(0.506378\pi\) | |||||||
\(864\) | −5.76762 | −0.196218 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.55447 | 0.154767 | ||||||||
\(867\) | −16.8135 | −0.571016 | ||||||||
\(868\) | 5.70117 | 0.193510 | ||||||||
\(869\) | −14.0550 | −0.476784 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.6788 | −0.599024 | ||||||||
\(872\) | 38.0730 | 1.28931 | ||||||||
\(873\) | 3.19957 | 0.108289 | ||||||||
\(874\) | −13.0337 | −0.440870 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.46724 | −0.184721 | ||||||||
\(877\) | 23.3347 | 0.787957 | 0.393978 | − | 0.919120i | \(-0.371098\pi\) | ||||
0.393978 | + | 0.919120i | \(0.371098\pi\) | |||||||
\(878\) | 21.1803 | 0.714801 | ||||||||
\(879\) | −1.78518 | −0.0602127 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.8127 | 1.57716 | 0.788580 | − | 0.614932i | \(-0.210817\pi\) | ||||
0.788580 | + | 0.614932i | \(0.210817\pi\) | |||||||
\(882\) | 3.97097 | 0.133709 | ||||||||
\(883\) | 35.0578 | 1.17979 | 0.589895 | − | 0.807480i | \(-0.299169\pi\) | ||||
0.589895 | + | 0.807480i | \(0.299169\pi\) | |||||||
\(884\) | −1.94060 | −0.0652694 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −22.7058 | −0.762815 | ||||||||
\(887\) | −41.0751 | −1.37917 | −0.689583 | − | 0.724206i | \(-0.742206\pi\) | ||||
−0.689583 | + | 0.724206i | \(0.742206\pi\) | |||||||
\(888\) | −17.3243 | −0.581366 | ||||||||
\(889\) | −29.8723 | −1.00189 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.60705 | 0.120841 | ||||||||
\(892\) | −7.84246 | −0.262585 | ||||||||
\(893\) | 6.45616 | 0.216047 | ||||||||
\(894\) | 5.09986 | 0.170565 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 12.0079 | 0.401155 | ||||||||
\(897\) | 8.33929 | 0.278441 | ||||||||
\(898\) | −5.97643 | −0.199436 | ||||||||
\(899\) | −18.5204 | −0.617689 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.61169 | 0.0870080 | ||||||||
\(902\) | 5.01243 | 0.166896 | ||||||||
\(903\) | 6.66889 | 0.221927 | ||||||||
\(904\) | −9.33238 | −0.310390 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10.5432 | 0.350276 | ||||||||
\(907\) | 46.5063 | 1.54422 | 0.772109 | − | 0.635490i | \(-0.219202\pi\) | ||||
0.772109 | + | 0.635490i | \(0.219202\pi\) | |||||||
\(908\) | −15.9009 | −0.527691 | ||||||||
\(909\) | −3.86233 | −0.128106 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.2207 | −1.36570 | −0.682851 | − | 0.730558i | \(-0.739260\pi\) | ||||
−0.682851 | + | 0.730558i | \(0.739260\pi\) | |||||||
\(912\) | 1.93686 | 0.0641358 | ||||||||
\(913\) | 20.9319 | 0.692745 | ||||||||
\(914\) | −17.1702 | −0.567940 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 34.3366 | 1.13451 | ||||||||
\(917\) | −1.51894 | −0.0501599 | ||||||||
\(918\) | −0.360770 | −0.0119072 | ||||||||
\(919\) | −21.2777 | −0.701887 | −0.350944 | − | 0.936397i | \(-0.614139\pi\) | ||||
−0.350944 | + | 0.936397i | \(0.614139\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.76651 | 0.0911598 | ||||||||
\(922\) | −14.2832 | −0.470393 | ||||||||
\(923\) | 5.54023 | 0.182359 | ||||||||
\(924\) | −7.03988 | −0.231595 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 13.0939 | 0.430293 | ||||||||
\(927\) | 13.2030 | 0.433645 | ||||||||
\(928\) | −36.5674 | −1.20038 | ||||||||
\(929\) | −32.3268 | −1.06061 | −0.530304 | − | 0.847808i | \(-0.677922\pi\) | ||||
−0.530304 | + | 0.847808i | \(0.677922\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.6900 | −1.00582 | ||||||||
\(932\) | 6.53892 | 0.214190 | ||||||||
\(933\) | 31.3933 | 1.02777 | ||||||||
\(934\) | −0.975111 | −0.0319066 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.51884 | 0.311133 | ||||||||
\(937\) | −6.47728 | −0.211603 | −0.105802 | − | 0.994387i | \(-0.533741\pi\) | ||||
−0.105802 | + | 0.994387i | \(0.533741\pi\) | |||||||
\(938\) | 6.41447 | 0.209440 | ||||||||
\(939\) | −15.3171 | −0.499855 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.2304 | −0.594294 | −0.297147 | − | 0.954832i | \(-0.596035\pi\) | ||||
−0.297147 | + | 0.954832i | \(0.596035\pi\) | |||||||
\(942\) | 4.40647 | 0.143571 | ||||||||
\(943\) | −4.02013 | −0.130913 | ||||||||
\(944\) | −3.58062 | −0.116539 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.4072 | −0.435904 | ||||||||
\(947\) | 31.6821 | 1.02953 | 0.514765 | − | 0.857331i | \(-0.327879\pi\) | ||||
0.514765 | + | 0.857331i | \(0.327879\pi\) | |||||||
\(948\) | 5.07396 | 0.164795 | ||||||||
\(949\) | 14.4880 | 0.470302 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.1597 | −0.394305 | ||||||||
\(952\) | 1.78556 | 0.0578702 | ||||||||
\(953\) | −20.2485 | −0.655915 | −0.327957 | − | 0.944693i | \(-0.606360\pi\) | ||||
−0.327957 | + | 0.944693i | \(0.606360\pi\) | |||||||
\(954\) | −5.05171 | −0.163555 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.0147 | 0.453267 | ||||||||
\(957\) | 22.8692 | 0.739255 | ||||||||
\(958\) | 10.0068 | 0.323304 | ||||||||
\(959\) | 34.6200 | 1.11794 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.4670 | −0.724740 | ||||||||
\(962\) | 18.1037 | 0.583686 | ||||||||
\(963\) | −6.16832 | −0.198771 | ||||||||
\(964\) | −5.54229 | −0.178505 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.02577 | −0.0973526 | ||||||||
\(967\) | 36.4479 | 1.17209 | 0.586043 | − | 0.810280i | \(-0.300685\pi\) | ||||
0.586043 | + | 0.810280i | \(0.300685\pi\) | |||||||
\(968\) | 5.54692 | 0.178285 | ||||||||
\(969\) | 2.78824 | 0.0895713 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.0132 | −0.449704 | −0.224852 | − | 0.974393i | \(-0.572190\pi\) | ||||
−0.224852 | + | 0.974393i | \(0.572190\pi\) | |||||||
\(972\) | −1.30217 | −0.0417672 | ||||||||
\(973\) | −25.7685 | −0.826099 | ||||||||
\(974\) | −14.2311 | −0.455995 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.471426 | −0.0150900 | ||||||||
\(977\) | −10.7799 | −0.344881 | −0.172440 | − | 0.985020i | \(-0.555165\pi\) | ||||
−0.172440 | + | 0.985020i | \(0.555165\pi\) | |||||||
\(978\) | −1.18411 | −0.0378637 | ||||||||
\(979\) | −35.9691 | −1.14958 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.8020 | 0.440665 | ||||||||
\(982\) | −10.1360 | −0.323452 | ||||||||
\(983\) | 33.0650 | 1.05461 | 0.527304 | − | 0.849677i | \(-0.323203\pi\) | ||||
0.527304 | + | 0.849677i | \(0.323203\pi\) | |||||||
\(984\) | −4.58876 | −0.146284 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.28733 | −0.0728433 | ||||||||
\(987\) | 1.49880 | 0.0477073 | ||||||||
\(988\) | −29.0104 | −0.922943 | ||||||||
\(989\) | 10.7530 | 0.341925 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.1188 | −1.14735 | −0.573675 | − | 0.819083i | \(-0.694483\pi\) | ||||
−0.573675 | + | 0.819083i | \(0.694483\pi\) | |||||||
\(992\) | 16.8480 | 0.534925 | ||||||||
\(993\) | −25.9978 | −0.825016 | ||||||||
\(994\) | −2.01018 | −0.0637590 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.55657 | −0.239439 | ||||||||
\(997\) | −6.21095 | −0.196703 | −0.0983515 | − | 0.995152i | \(-0.531357\pi\) | ||||
−0.0983515 | + | 0.995152i | \(0.531357\pi\) | |||||||
\(998\) | −33.2730 | −1.05324 | ||||||||
\(999\) | −6.28033 | −0.198701 |
(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 | 3525.2.a.z.1.3 | ✓ | 7 | |
5.4 | even | 2 | 3525.2.a.ba.1.5 | yes | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3525.2.a.z.1.3 | ✓ | 7 | 1.1 | even | 1 | trivial | |
3525.2.a.ba.1.5 | yes | 7 | 5.4 | even | 2 |