Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4275,2,Mod(1,4275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4275, 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("4275.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4275 = 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4275.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: | \(34.1360468641\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 2x + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 475) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4275.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.80194 | 1.98127 | 0.990635 | − | 0.136540i | \(-0.0435982\pi\) | ||||
0.990635 | + | 0.136540i | \(0.0435982\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.85086 | 2.92543 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.04892 | 1.15238 | 0.576191 | − | 0.817315i | \(-0.304538\pi\) | ||||
0.576191 | + | 0.817315i | \(0.304538\pi\) | |||||||
\(8\) | 10.7899 | 3.81479 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.93900 | 0.886142 | 0.443071 | − | 0.896486i | \(-0.353889\pi\) | ||||
0.443071 | + | 0.896486i | \(0.353889\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.24698 | −0.900550 | −0.450275 | − | 0.892890i | \(-0.648674\pi\) | ||||
−0.450275 | + | 0.892890i | \(0.648674\pi\) | |||||||
\(14\) | 8.54288 | 2.28318 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 18.5308 | 4.63270 | ||||||||
\(17\) | −2.15883 | −0.523594 | −0.261797 | − | 0.965123i | \(-0.584315\pi\) | ||||
−0.261797 | + | 0.965123i | \(0.584315\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.23490 | 1.75569 | ||||||||
\(23\) | 1.19806 | 0.249813 | 0.124907 | − | 0.992169i | \(-0.460137\pi\) | ||||
0.124907 | + | 0.992169i | \(0.460137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.09783 | −1.78423 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 17.8388 | 3.37121 | ||||||||
\(29\) | 1.77479 | 0.329570 | 0.164785 | − | 0.986329i | \(-0.447307\pi\) | ||||
0.164785 | + | 0.986329i | \(0.447307\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.34481 | −1.67838 | −0.839189 | − | 0.543840i | \(-0.816970\pi\) | ||||
−0.839189 | + | 0.543840i | \(0.816970\pi\) | |||||||
\(32\) | 30.3424 | 5.36383 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.04892 | −1.03738 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.15883 | 0.190511 | 0.0952555 | − | 0.995453i | \(-0.469633\pi\) | ||||
0.0952555 | + | 0.995453i | \(0.469633\pi\) | |||||||
\(38\) | −2.80194 | −0.454534 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.57002 | −1.33841 | −0.669206 | − | 0.743077i | \(-0.733366\pi\) | ||||
−0.669206 | + | 0.743077i | \(0.733366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.27413 | −0.804297 | −0.402148 | − | 0.915575i | \(-0.631736\pi\) | ||||
−0.402148 | + | 0.915575i | \(0.631736\pi\) | |||||||
\(44\) | 17.1957 | 2.59234 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.35690 | 0.494947 | ||||||||
\(47\) | 2.35690 | 0.343789 | 0.171894 | − | 0.985115i | \(-0.445011\pi\) | ||||
0.171894 | + | 0.985115i | \(0.445011\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.29590 | 0.327985 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −18.9976 | −2.63449 | ||||||||
\(53\) | 8.82371 | 1.21203 | 0.606015 | − | 0.795453i | \(-0.292767\pi\) | ||||
0.606015 | + | 0.795453i | \(0.292767\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 32.8974 | 4.39610 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.97285 | 0.652968 | ||||||||
\(59\) | 5.70171 | 0.742299 | 0.371150 | − | 0.928573i | \(-0.378964\pi\) | ||||
0.371150 | + | 0.928573i | \(0.378964\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.96077 | −1.27535 | −0.637673 | − | 0.770307i | \(-0.720103\pi\) | ||||
−0.637673 | + | 0.770307i | \(0.720103\pi\) | |||||||
\(62\) | −26.1836 | −3.32532 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 47.9560 | 5.99450 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.98254 | −0.608714 | −0.304357 | − | 0.952558i | \(-0.598442\pi\) | ||||
−0.304357 | + | 0.952558i | \(0.598442\pi\) | |||||||
\(68\) | −12.6310 | −1.53174 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.70171 | −0.320634 | −0.160317 | − | 0.987066i | \(-0.551252\pi\) | ||||
−0.160317 | + | 0.987066i | \(0.551252\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.7778 | −1.61257 | −0.806283 | − | 0.591530i | \(-0.798524\pi\) | ||||
−0.806283 | + | 0.591530i | \(0.798524\pi\) | |||||||
\(74\) | 3.24698 | 0.377454 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.85086 | −0.671139 | ||||||||
\(77\) | 8.96077 | 1.02117 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.66487 | 0.637348 | 0.318674 | − | 0.947864i | \(-0.396762\pi\) | ||||
0.318674 | + | 0.947864i | \(0.396762\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −24.0127 | −2.65176 | ||||||||
\(83\) | −3.00969 | −0.330356 | −0.165178 | − | 0.986264i | \(-0.552820\pi\) | ||||
−0.165178 | + | 0.986264i | \(0.552820\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −14.7778 | −1.59353 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 31.7114 | 3.38045 | ||||||||
\(89\) | 10.2838 | 1.09008 | 0.545041 | − | 0.838409i | \(-0.316514\pi\) | ||||
0.545041 | + | 0.838409i | \(0.316514\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.89977 | −1.03778 | ||||||||
\(92\) | 7.00969 | 0.730811 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.60388 | 0.681138 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.24698 | −0.329681 | −0.164840 | − | 0.986320i | \(-0.552711\pi\) | ||||
−0.164840 | + | 0.986320i | \(0.552711\pi\) | |||||||
\(98\) | 6.43296 | 0.649827 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.09246 | −0.506718 | −0.253359 | − | 0.967372i | \(-0.581535\pi\) | ||||
−0.253359 | + | 0.967372i | \(0.581535\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.3110 | 1.41010 | 0.705051 | − | 0.709157i | \(-0.250924\pi\) | ||||
0.705051 | + | 0.709157i | \(0.250924\pi\) | |||||||
\(104\) | −35.0344 | −3.43541 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 24.7235 | 2.40136 | ||||||||
\(107\) | −8.18598 | −0.791369 | −0.395684 | − | 0.918387i | \(-0.629493\pi\) | ||||
−0.395684 | + | 0.918387i | \(0.629493\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.3274 | −1.08496 | −0.542482 | − | 0.840067i | \(-0.682515\pi\) | ||||
−0.542482 | + | 0.840067i | \(0.682515\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 56.4989 | 5.33864 | ||||||||
\(113\) | 3.43535 | 0.323171 | 0.161585 | − | 0.986859i | \(-0.448339\pi\) | ||||
0.161585 | + | 0.986859i | \(0.448339\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.3840 | 0.964134 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.9758 | 1.47069 | ||||||||
\(119\) | −6.58211 | −0.603381 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.36227 | −0.214752 | ||||||||
\(122\) | −27.9095 | −2.52680 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −54.6752 | −4.90997 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.46144 | −0.129681 | −0.0648407 | − | 0.997896i | \(-0.520654\pi\) | ||||
−0.0648407 | + | 0.997896i | \(0.520654\pi\) | |||||||
\(128\) | 73.6848 | 6.51288 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.2295 | 1.15587 | 0.577934 | − | 0.816083i | \(-0.303859\pi\) | ||||
0.577934 | + | 0.816083i | \(0.303859\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.04892 | −0.264375 | ||||||||
\(134\) | −13.9608 | −1.20603 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −23.2935 | −1.99740 | ||||||||
\(137\) | 16.1739 | 1.38183 | 0.690915 | − | 0.722936i | \(-0.257208\pi\) | ||||
0.690915 | + | 0.722936i | \(0.257208\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.0978 | 1.11094 | 0.555472 | − | 0.831535i | \(-0.312538\pi\) | ||||
0.555472 | + | 0.831535i | \(0.312538\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.57002 | −0.635262 | ||||||||
\(143\) | −9.54288 | −0.798015 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −38.6045 | −3.19493 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.78017 | 0.557326 | ||||||||
\(149\) | −11.0640 | −0.906397 | −0.453198 | − | 0.891410i | \(-0.649717\pi\) | ||||
−0.453198 | + | 0.891410i | \(0.649717\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.4426 | 0.849811 | 0.424905 | − | 0.905238i | \(-0.360307\pi\) | ||||
0.424905 | + | 0.905238i | \(0.360307\pi\) | |||||||
\(152\) | −10.7899 | −0.875173 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 25.1075 | 2.02322 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.48427 | −0.198266 | −0.0991332 | − | 0.995074i | \(-0.531607\pi\) | ||||
−0.0991332 | + | 0.995074i | \(0.531607\pi\) | |||||||
\(158\) | 15.8726 | 1.26276 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.65279 | 0.287880 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.16852 | −0.248178 | −0.124089 | − | 0.992271i | \(-0.539601\pi\) | ||||
−0.124089 | + | 0.992271i | \(0.539601\pi\) | |||||||
\(164\) | −50.1420 | −3.91543 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.43296 | −0.654525 | ||||||||
\(167\) | 4.74632 | 0.367281 | 0.183640 | − | 0.982993i | \(-0.441212\pi\) | ||||
0.183640 | + | 0.982993i | \(0.441212\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.45712 | −0.189009 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −30.8582 | −2.35291 | ||||||||
\(173\) | 3.96316 | 0.301314 | 0.150657 | − | 0.988586i | \(-0.451861\pi\) | ||||
0.150657 | + | 0.988586i | \(0.451861\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 54.4620 | 4.10523 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 28.8146 | 2.15975 | ||||||||
\(179\) | 14.0858 | 1.05282 | 0.526409 | − | 0.850231i | \(-0.323538\pi\) | ||||
0.526409 | + | 0.850231i | \(0.323538\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2513 | −0.910631 | −0.455316 | − | 0.890330i | \(-0.650474\pi\) | ||||
−0.455316 | + | 0.890330i | \(0.650474\pi\) | |||||||
\(182\) | −27.7385 | −2.05612 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.9269 | 0.952985 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.34481 | −0.463979 | ||||||||
\(188\) | 13.7899 | 1.00573 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.1468 | −1.45777 | −0.728884 | − | 0.684637i | \(-0.759961\pi\) | ||||
−0.728884 | + | 0.684637i | \(0.759961\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.52781 | 0.685827 | 0.342913 | − | 0.939367i | \(-0.388586\pi\) | ||||
0.342913 | + | 0.939367i | \(0.388586\pi\) | |||||||
\(194\) | −9.09783 | −0.653186 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.4330 | 0.959497 | ||||||||
\(197\) | 4.96316 | 0.353611 | 0.176805 | − | 0.984246i | \(-0.443424\pi\) | ||||
0.176805 | + | 0.984246i | \(0.443424\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.42221 | 0.384370 | 0.192185 | − | 0.981359i | \(-0.438443\pi\) | ||||
0.192185 | + | 0.981359i | \(0.438443\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.2687 | −1.00395 | ||||||||
\(203\) | 5.41119 | 0.379791 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 40.0984 | 2.79379 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −60.1691 | −4.17198 | ||||||||
\(209\) | −2.93900 | −0.203295 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.9638 | 1.09899 | 0.549495 | − | 0.835497i | \(-0.314820\pi\) | ||||
0.549495 | + | 0.835497i | \(0.314820\pi\) | |||||||
\(212\) | 51.6262 | 3.54570 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −22.9366 | −1.56791 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −28.4916 | −1.93413 | ||||||||
\(218\) | −31.7385 | −2.14961 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.00969 | 0.471523 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.2150 | 1.55459 | 0.777297 | − | 0.629134i | \(-0.216590\pi\) | ||||
0.777297 | + | 0.629134i | \(0.216590\pi\) | |||||||
\(224\) | 92.5115 | 6.18119 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.62565 | 0.640288 | ||||||||
\(227\) | −17.4795 | −1.16015 | −0.580077 | − | 0.814562i | \(-0.696978\pi\) | ||||
−0.580077 | + | 0.814562i | \(0.696978\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.32544 | −0.153669 | −0.0768346 | − | 0.997044i | \(-0.524481\pi\) | ||||
−0.0768346 | + | 0.997044i | \(0.524481\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.1497 | 1.25724 | ||||||||
\(233\) | −18.9342 | −1.24042 | −0.620211 | − | 0.784435i | \(-0.712953\pi\) | ||||
−0.620211 | + | 0.784435i | \(0.712953\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 33.3599 | 2.17154 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −18.4426 | −1.19546 | ||||||||
\(239\) | −11.1685 | −0.722432 | −0.361216 | − | 0.932482i | \(-0.617638\pi\) | ||||
−0.361216 | + | 0.932482i | \(0.617638\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.42998 | 0.478607 | 0.239303 | − | 0.970945i | \(-0.423081\pi\) | ||||
0.239303 | + | 0.970945i | \(0.423081\pi\) | |||||||
\(242\) | −6.61894 | −0.425482 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −58.2790 | −3.73093 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.24698 | 0.206600 | ||||||||
\(248\) | −100.829 | −6.40266 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.7409 | 0.930440 | 0.465220 | − | 0.885195i | \(-0.345975\pi\) | ||||
0.465220 | + | 0.885195i | \(0.345975\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.52111 | 0.221370 | ||||||||
\(254\) | −4.09485 | −0.256934 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 110.548 | 6.90927 | ||||||||
\(257\) | 3.34721 | 0.208793 | 0.104397 | − | 0.994536i | \(-0.466709\pi\) | ||||
0.104397 | + | 0.994536i | \(0.466709\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.53319 | 0.219542 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 37.0683 | 2.29009 | ||||||||
\(263\) | −16.6853 | −1.02886 | −0.514430 | − | 0.857532i | \(-0.671997\pi\) | ||||
−0.514430 | + | 0.857532i | \(0.671997\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.54288 | −0.523797 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −29.1521 | −1.78075 | ||||||||
\(269\) | −15.5961 | −0.950911 | −0.475456 | − | 0.879740i | \(-0.657717\pi\) | ||||
−0.475456 | + | 0.879740i | \(0.657717\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.2131 | −0.802640 | −0.401320 | − | 0.915938i | \(-0.631449\pi\) | ||||
−0.401320 | + | 0.915938i | \(0.631449\pi\) | |||||||
\(272\) | −40.0049 | −2.42565 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 45.3183 | 2.73778 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.9758 | −0.779642 | −0.389821 | − | 0.920891i | \(-0.627463\pi\) | ||||
−0.389821 | + | 0.920891i | \(0.627463\pi\) | |||||||
\(278\) | 36.6993 | 2.20108 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.8901 | −1.48482 | −0.742409 | − | 0.669947i | \(-0.766317\pi\) | ||||
−0.742409 | + | 0.669947i | \(0.766317\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.5821 | 0.807372 | 0.403686 | − | 0.914898i | \(-0.367729\pi\) | ||||
0.403686 | + | 0.914898i | \(0.367729\pi\) | |||||||
\(284\) | −15.8073 | −0.937992 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −26.7385 | −1.58108 | ||||||||
\(287\) | −26.1293 | −1.54236 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3394 | −0.725849 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −80.6118 | −4.71745 | ||||||||
\(293\) | 1.27652 | 0.0745751 | 0.0372875 | − | 0.999305i | \(-0.488128\pi\) | ||||
0.0372875 | + | 0.999305i | \(0.488128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.5036 | 0.726760 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −31.0006 | −1.79582 | ||||||||
\(299\) | −3.89008 | −0.224969 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0804 | −0.926857 | ||||||||
\(302\) | 29.2597 | 1.68370 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −18.5308 | −1.06281 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.2295 | 1.83944 | 0.919718 | − | 0.392580i | \(-0.128417\pi\) | ||||
0.919718 | + | 0.392580i | \(0.128417\pi\) | |||||||
\(308\) | 52.4282 | 2.98737 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.4983 | −0.708712 | −0.354356 | − | 0.935111i | \(-0.615300\pi\) | ||||
−0.354356 | + | 0.935111i | \(0.615300\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.9390 | 1.18354 | 0.591771 | − | 0.806106i | \(-0.298429\pi\) | ||||
0.591771 | + | 0.806106i | \(0.298429\pi\) | |||||||
\(314\) | −6.96077 | −0.392819 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 33.1444 | 1.86452 | ||||||||
\(317\) | 15.8562 | 0.890575 | 0.445287 | − | 0.895388i | \(-0.353102\pi\) | ||||
0.445287 | + | 0.895388i | \(0.353102\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.21611 | 0.292046 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.2349 | 0.570369 | ||||||||
\(323\) | 2.15883 | 0.120121 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.87800 | −0.491707 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −92.4693 | −5.10576 | ||||||||
\(329\) | 7.18598 | 0.396176 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.2349 | −0.727456 | −0.363728 | − | 0.931505i | \(-0.618496\pi\) | ||||
−0.363728 | + | 0.931505i | \(0.618496\pi\) | |||||||
\(332\) | −17.6093 | −0.966433 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.2989 | 0.727682 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.0780 | 1.42056 | 0.710279 | − | 0.703920i | \(-0.248569\pi\) | ||||
0.710279 | + | 0.703920i | \(0.248569\pi\) | |||||||
\(338\) | −6.88471 | −0.374479 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.4644 | −1.48728 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.3424 | −0.774418 | ||||||||
\(344\) | −56.9071 | −3.06822 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.1045 | 0.596984 | ||||||||
\(347\) | 8.98254 | 0.482208 | 0.241104 | − | 0.970499i | \(-0.422490\pi\) | ||||
0.241104 | + | 0.970499i | \(0.422490\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.599564 | 0.0320939 | 0.0160470 | − | 0.999871i | \(-0.494892\pi\) | ||||
0.0160470 | + | 0.999871i | \(0.494892\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 89.1764 | 4.75312 | ||||||||
\(353\) | 31.8896 | 1.69731 | 0.848656 | − | 0.528945i | \(-0.177412\pi\) | ||||
0.848656 | + | 0.528945i | \(0.177412\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 60.1691 | 3.18896 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 39.4674 | 2.08592 | ||||||||
\(359\) | 18.3763 | 0.969863 | 0.484931 | − | 0.874552i | \(-0.338845\pi\) | ||||
0.484931 | + | 0.874552i | \(0.338845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −34.3274 | −1.80421 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −57.9221 | −3.03594 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.6377 | 0.764083 | 0.382042 | − | 0.924145i | \(-0.375221\pi\) | ||||
0.382042 | + | 0.924145i | \(0.375221\pi\) | |||||||
\(368\) | 22.2010 | 1.15731 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.9028 | 1.39672 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.02715 | 0.0531837 | 0.0265918 | − | 0.999646i | \(-0.491535\pi\) | ||||
0.0265918 | + | 0.999646i | \(0.491535\pi\) | |||||||
\(374\) | −17.7778 | −0.919267 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 25.4306 | 1.31148 | ||||||||
\(377\) | −5.76271 | −0.296795 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.5284 | −1.15721 | −0.578603 | − | 0.815609i | \(-0.696402\pi\) | ||||
−0.578603 | + | 0.815609i | \(0.696402\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −56.4499 | −2.88823 | ||||||||
\(383\) | 32.6698 | 1.66935 | 0.834674 | − | 0.550745i | \(-0.185656\pi\) | ||||
0.834674 | + | 0.550745i | \(0.185656\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.6963 | 1.35881 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.9976 | −0.964457 | ||||||||
\(389\) | 8.16421 | 0.413942 | 0.206971 | − | 0.978347i | \(-0.433639\pi\) | ||||
0.206971 | + | 0.978347i | \(0.433639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.58642 | −0.130801 | ||||||||
\(392\) | 24.7724 | 1.25120 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13.9065 | 0.700598 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.5478 | −1.88447 | −0.942235 | − | 0.334954i | \(-0.891279\pi\) | ||||
−0.942235 | + | 0.334954i | \(0.891279\pi\) | |||||||
\(398\) | 15.1927 | 0.761541 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.2519 | −1.61058 | −0.805291 | − | 0.592880i | \(-0.797991\pi\) | ||||
−0.805291 | + | 0.592880i | \(0.797991\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.3424 | 1.51146 | ||||||||
\(404\) | −29.7952 | −1.48237 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.1618 | 0.752468 | ||||||||
\(407\) | 3.40581 | 0.168820 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.5459 | −1.55984 | −0.779921 | − | 0.625878i | \(-0.784741\pi\) | ||||
−0.779921 | + | 0.625878i | \(0.784741\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 83.7314 | 4.12515 | ||||||||
\(413\) | 17.3840 | 0.855413 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −98.5212 | −4.83040 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.23490 | −0.402782 | ||||||||
\(419\) | 14.6866 | 0.717490 | 0.358745 | − | 0.933436i | \(-0.383205\pi\) | ||||
0.358745 | + | 0.933436i | \(0.383205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.1142 | 0.736622 | 0.368311 | − | 0.929703i | \(-0.379936\pi\) | ||||
0.368311 | + | 0.929703i | \(0.379936\pi\) | |||||||
\(422\) | 44.7294 | 2.17740 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 95.2065 | 4.62364 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.3696 | −1.46969 | ||||||||
\(428\) | −47.8950 | −2.31509 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.67696 | −0.0807761 | −0.0403881 | − | 0.999184i | \(-0.512859\pi\) | ||||
−0.0403881 | + | 0.999184i | \(0.512859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.1545 | 0.632166 | 0.316083 | − | 0.948732i | \(-0.397632\pi\) | ||||
0.316083 | + | 0.948732i | \(0.397632\pi\) | |||||||
\(434\) | −79.8316 | −3.83204 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −66.2747 | −3.17398 | ||||||||
\(437\) | −1.19806 | −0.0573111 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.45580 | 0.308118 | 0.154059 | − | 0.988062i | \(-0.450765\pi\) | ||||
0.154059 | + | 0.988062i | \(0.450765\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.6407 | 0.934213 | ||||||||
\(443\) | −25.3709 | −1.20541 | −0.602704 | − | 0.797965i | \(-0.705910\pi\) | ||||
−0.602704 | + | 0.797965i | \(0.705910\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 65.0471 | 3.08007 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 146.214 | 6.90795 | ||||||||
\(449\) | 3.59956 | 0.169874 | 0.0849370 | − | 0.996386i | \(-0.472931\pi\) | ||||
0.0849370 | + | 0.996386i | \(0.472931\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.1873 | −1.18602 | ||||||||
\(452\) | 20.0998 | 0.945413 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −48.9764 | −2.29858 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.2784 | 0.574361 | 0.287181 | − | 0.957876i | \(-0.407282\pi\) | ||||
0.287181 | + | 0.957876i | \(0.407282\pi\) | |||||||
\(458\) | −6.51573 | −0.304460 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.4935 | −1.83939 | −0.919697 | − | 0.392628i | \(-0.871566\pi\) | ||||
−0.919697 | + | 0.392628i | \(0.871566\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.3991 | −0.855079 | −0.427540 | − | 0.903997i | \(-0.640620\pi\) | ||||
−0.427540 | + | 0.903997i | \(0.640620\pi\) | |||||||
\(464\) | 32.8883 | 1.52680 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −53.0525 | −2.45761 | ||||||||
\(467\) | −36.2282 | −1.67644 | −0.838220 | − | 0.545332i | \(-0.816404\pi\) | ||||
−0.838220 | + | 0.545332i | \(0.816404\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.1914 | −0.701472 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 61.5206 | 2.83172 | ||||||||
\(473\) | −15.5007 | −0.712721 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −38.5109 | −1.76515 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −31.2935 | −1.43133 | ||||||||
\(479\) | 34.3129 | 1.56780 | 0.783898 | − | 0.620890i | \(-0.213229\pi\) | ||||
0.783898 | + | 0.620890i | \(0.213229\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.76271 | −0.171565 | ||||||||
\(482\) | 20.8183 | 0.948249 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.8213 | −0.628242 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.4722 | 1.10894 | 0.554470 | − | 0.832203i | \(-0.312921\pi\) | ||||
0.554470 | + | 0.832203i | \(0.312921\pi\) | |||||||
\(488\) | −107.475 | −4.86518 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.3067 | −0.826168 | −0.413084 | − | 0.910693i | \(-0.635548\pi\) | ||||
−0.413084 | + | 0.910693i | \(0.635548\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.83148 | −0.172561 | ||||||||
\(494\) | 9.09783 | 0.409331 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −173.167 | −7.77542 | ||||||||
\(497\) | −8.23729 | −0.369493 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.3424 | −1.13448 | −0.567241 | − | 0.823552i | \(-0.691989\pi\) | ||||
−0.567241 | + | 0.823552i | \(0.691989\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 41.3032 | 1.84345 | ||||||||
\(503\) | 14.1105 | 0.629156 | 0.314578 | − | 0.949232i | \(-0.398137\pi\) | ||||
0.314578 | + | 0.949232i | \(0.398137\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.86592 | 0.438594 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.55065 | −0.379374 | ||||||||
\(509\) | 17.8019 | 0.789057 | 0.394529 | − | 0.918884i | \(-0.370908\pi\) | ||||
0.394529 | + | 0.918884i | \(0.370908\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −42.0073 | −1.85829 | ||||||||
\(512\) | 162.380 | 7.17625 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.37867 | 0.413675 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.92692 | 0.304646 | ||||||||
\(518\) | 9.89977 | 0.434971 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.3948 | −0.586837 | −0.293418 | − | 0.955984i | \(-0.594793\pi\) | ||||
−0.293418 | + | 0.955984i | \(0.594793\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.46921 | 0.0642439 | 0.0321219 | − | 0.999484i | \(-0.489774\pi\) | ||||
0.0321219 | + | 0.999484i | \(0.489774\pi\) | |||||||
\(524\) | 77.4040 | 3.38141 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −46.7512 | −2.03845 | ||||||||
\(527\) | 20.1739 | 0.878789 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.5646 | −0.937593 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.8388 | −0.773409 | ||||||||
\(533\) | 27.8267 | 1.20531 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −53.7609 | −2.32212 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −43.6993 | −1.88401 | ||||||||
\(539\) | 6.74764 | 0.290642 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.7144 | −1.83643 | −0.918217 | − | 0.396077i | \(-0.870371\pi\) | ||||
−0.918217 | + | 0.396077i | \(0.870371\pi\) | |||||||
\(542\) | −37.0224 | −1.59025 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −65.5042 | −2.80847 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.6866 | −0.456928 | −0.228464 | − | 0.973552i | \(-0.573370\pi\) | ||||
−0.228464 | + | 0.973552i | \(0.573370\pi\) | |||||||
\(548\) | 94.6311 | 4.04244 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.77479 | −0.0756086 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.2717 | 0.734469 | ||||||||
\(554\) | −36.3575 | −1.54468 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 76.6335 | 3.24999 | ||||||||
\(557\) | −34.2083 | −1.44945 | −0.724727 | − | 0.689036i | \(-0.758034\pi\) | ||||
−0.724727 | + | 0.689036i | \(0.758034\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.1250 | 0.724310 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −69.7405 | −2.94182 | ||||||||
\(563\) | −5.46788 | −0.230444 | −0.115222 | − | 0.993340i | \(-0.536758\pi\) | ||||
−0.115222 | + | 0.993340i | \(0.536758\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 38.0562 | 1.59962 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −29.1511 | −1.22315 | ||||||||
\(569\) | 17.4819 | 0.732878 | 0.366439 | − | 0.930442i | \(-0.380577\pi\) | ||||
0.366439 | + | 0.930442i | \(0.380577\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.21877 | −0.302096 | −0.151048 | − | 0.988526i | \(-0.548265\pi\) | ||||
−0.151048 | + | 0.988526i | \(0.548265\pi\) | |||||||
\(572\) | −55.8340 | −2.33454 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −73.2127 | −3.05584 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.80625 | −0.0751952 | −0.0375976 | − | 0.999293i | \(-0.511971\pi\) | ||||
−0.0375976 | + | 0.999293i | \(0.511971\pi\) | |||||||
\(578\) | −34.5743 | −1.43810 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.17629 | −0.380697 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.9329 | 1.07403 | ||||||||
\(584\) | −148.660 | −6.15160 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.57673 | 0.147753 | ||||||||
\(587\) | 2.39075 | 0.0986767 | 0.0493384 | − | 0.998782i | \(-0.484289\pi\) | ||||
0.0493384 | + | 0.998782i | \(0.484289\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.34481 | 0.385046 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 21.4741 | 0.882580 | ||||||||
\(593\) | −42.2650 | −1.73562 | −0.867808 | − | 0.496899i | \(-0.834472\pi\) | ||||
−0.867808 | + | 0.496899i | \(0.834472\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −64.7338 | −2.65160 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.8998 | −0.445725 | ||||||||
\(599\) | −8.95838 | −0.366029 | −0.183015 | − | 0.983110i | \(-0.558586\pi\) | ||||
−0.183015 | + | 0.983110i | \(0.558586\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.8998 | −0.811729 | −0.405864 | − | 0.913933i | \(-0.633029\pi\) | ||||
−0.405864 | + | 0.913933i | \(0.633029\pi\) | |||||||
\(602\) | −45.0562 | −1.83635 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 61.0984 | 2.48606 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.0084 | −1.05565 | −0.527823 | − | 0.849354i | \(-0.676992\pi\) | ||||
−0.527823 | + | 0.849354i | \(0.676992\pi\) | |||||||
\(608\) | −30.3424 | −1.23055 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.65279 | −0.309599 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.3763 | −1.67117 | −0.835586 | − | 0.549360i | \(-0.814872\pi\) | ||||
−0.835586 | + | 0.549360i | \(0.814872\pi\) | |||||||
\(614\) | 90.3051 | 3.64442 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 96.6854 | 3.89557 | ||||||||
\(617\) | 43.9845 | 1.77075 | 0.885374 | − | 0.464880i | \(-0.153902\pi\) | ||||
0.885374 | + | 0.464880i | \(0.153902\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.4553 | 0.942749 | 0.471374 | − | 0.881933i | \(-0.343758\pi\) | ||||
0.471374 | + | 0.881933i | \(0.343758\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −35.0194 | −1.40415 | ||||||||
\(623\) | 31.3545 | 1.25619 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 58.6698 | 2.34492 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.5351 | −0.580014 | ||||||||
\(629\) | −2.50173 | −0.0997505 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.8877 | −1.38886 | −0.694429 | − | 0.719562i | \(-0.744343\pi\) | ||||
−0.694429 | + | 0.719562i | \(0.744343\pi\) | |||||||
\(632\) | 61.1232 | 2.43135 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 44.4282 | 1.76447 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.45473 | −0.295367 | ||||||||
\(638\) | 14.6152 | 0.578622 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.5314 | 1.52190 | 0.760949 | − | 0.648812i | \(-0.224734\pi\) | ||||
0.760949 | + | 0.648812i | \(0.224734\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.6353 | 0.734906 | 0.367453 | − | 0.930042i | \(-0.380230\pi\) | ||||
0.367453 | + | 0.930042i | \(0.380230\pi\) | |||||||
\(644\) | 21.3720 | 0.842173 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.04892 | 0.237991 | ||||||||
\(647\) | 19.2282 | 0.755938 | 0.377969 | − | 0.925818i | \(-0.376623\pi\) | ||||
0.377969 | + | 0.925818i | \(0.376623\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.7573 | 0.657783 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.5386 | −0.726026 | ||||||||
\(653\) | −3.98553 | −0.155966 | −0.0779828 | − | 0.996955i | \(-0.524848\pi\) | ||||
−0.0779828 | + | 0.996955i | \(0.524848\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −158.809 | −6.20046 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 20.1347 | 0.784931 | ||||||||
\(659\) | −33.5719 | −1.30778 | −0.653889 | − | 0.756591i | \(-0.726864\pi\) | ||||
−0.653889 | + | 0.756591i | \(0.726864\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.9909 | 1.43878 | 0.719390 | − | 0.694607i | \(-0.244422\pi\) | ||||
0.719390 | + | 0.694607i | \(0.244422\pi\) | |||||||
\(662\) | −37.0834 | −1.44129 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −32.4741 | −1.26024 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.12631 | 0.0823310 | ||||||||
\(668\) | 27.7700 | 1.07445 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.2747 | −1.13014 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.0747 | −0.465447 | −0.232723 | − | 0.972543i | \(-0.574764\pi\) | ||||
−0.232723 | + | 0.972543i | \(0.574764\pi\) | |||||||
\(674\) | 73.0689 | 2.81451 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −14.3763 | −0.552934 | ||||||||
\(677\) | 41.9135 | 1.61087 | 0.805434 | − | 0.592686i | \(-0.201933\pi\) | ||||
0.805434 | + | 0.592686i | \(0.201933\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.89977 | −0.379918 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −76.9536 | −2.94671 | ||||||||
\(683\) | 9.17092 | 0.350915 | 0.175458 | − | 0.984487i | \(-0.443859\pi\) | ||||
0.175458 | + | 0.984487i | \(0.443859\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −40.1866 | −1.53433 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −97.7338 | −3.72606 | ||||||||
\(689\) | −28.6504 | −1.09149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.111244 | −0.00423193 | −0.00211596 | − | 0.999998i | \(-0.500674\pi\) | ||||
−0.00211596 | + | 0.999998i | \(0.500674\pi\) | |||||||
\(692\) | 23.1879 | 0.881472 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.1685 | 0.955384 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.5013 | 0.700785 | ||||||||
\(698\) | 1.67994 | 0.0635867 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.7832 | 1.04936 | 0.524678 | − | 0.851301i | \(-0.324186\pi\) | ||||
0.524678 | + | 0.851301i | \(0.324186\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.15883 | −0.0437062 | ||||||||
\(704\) | 140.943 | 5.31198 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 89.3527 | 3.36283 | ||||||||
\(707\) | −15.5265 | −0.583933 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.4668 | 1.40710 | 0.703548 | − | 0.710648i | \(-0.251598\pi\) | ||||
0.703548 | + | 0.710648i | \(0.251598\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 110.961 | 4.15844 | ||||||||
\(713\) | −11.1957 | −0.419281 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 82.4137 | 3.07994 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 51.4892 | 1.92156 | ||||||||
\(719\) | 21.0513 | 0.785081 | 0.392541 | − | 0.919735i | \(-0.371596\pi\) | ||||
0.392541 | + | 0.919735i | \(0.371596\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43.6329 | 1.62498 | ||||||||
\(722\) | 2.80194 | 0.104277 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −71.6805 | −2.66399 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.7023 | 1.65792 | 0.828958 | − | 0.559310i | \(-0.188934\pi\) | ||||
0.828958 | + | 0.559310i | \(0.188934\pi\) | |||||||
\(728\) | −106.817 | −3.95891 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.3860 | 0.421125 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.0301 | −0.924509 | −0.462254 | − | 0.886747i | \(-0.652959\pi\) | ||||
−0.462254 | + | 0.886747i | \(0.652959\pi\) | |||||||
\(734\) | 41.0140 | 1.51385 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.3521 | 1.33996 | ||||||||
\(737\) | −14.6437 | −0.539407 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.9982 | −0.882788 | −0.441394 | − | 0.897313i | \(-0.645516\pi\) | ||||
−0.441394 | + | 0.897313i | \(0.645516\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 75.3798 | 2.76728 | ||||||||
\(743\) | 10.4601 | 0.383744 | 0.191872 | − | 0.981420i | \(-0.438544\pi\) | ||||
0.191872 | + | 0.981420i | \(0.438544\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.87800 | 0.105371 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −37.1226 | −1.35734 | ||||||||
\(749\) | −24.9584 | −0.911959 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.9420 | −1.09260 | −0.546299 | − | 0.837590i | \(-0.683964\pi\) | ||||
−0.546299 | + | 0.837590i | \(0.683964\pi\) | |||||||
\(752\) | 43.6752 | 1.59267 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16.1468 | −0.588030 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.2174 | −0.989235 | −0.494617 | − | 0.869111i | \(-0.664692\pi\) | ||||
−0.494617 | + | 0.869111i | \(0.664692\pi\) | |||||||
\(758\) | −63.1232 | −2.29274 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.6813 | −0.677195 | −0.338598 | − | 0.940931i | \(-0.609953\pi\) | ||||
−0.338598 | + | 0.940931i | \(0.609953\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.5362 | −1.25029 | ||||||||
\(764\) | −117.876 | −4.26459 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 91.5387 | 3.30743 | ||||||||
\(767\) | −18.5133 | −0.668478 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.34780 | 0.228907 | 0.114454 | − | 0.993429i | \(-0.463488\pi\) | ||||
0.114454 | + | 0.993429i | \(0.463488\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 55.7458 | 2.00634 | ||||||||
\(773\) | 49.7851 | 1.79064 | 0.895322 | − | 0.445419i | \(-0.146945\pi\) | ||||
0.895322 | + | 0.445419i | \(0.146945\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −35.0344 | −1.25766 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.8756 | 0.820130 | ||||||||
\(779\) | 8.57002 | 0.307053 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.94033 | −0.284127 | ||||||||
\(782\) | −7.24698 | −0.259151 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 42.5448 | 1.51946 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.19865 | 0.327897 | 0.163948 | − | 0.986469i | \(-0.447577\pi\) | ||||
0.163948 | + | 0.986469i | \(0.447577\pi\) | |||||||
\(788\) | 29.0388 | 1.03446 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.4741 | 0.372416 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.3424 | 1.14851 | ||||||||
\(794\) | −105.207 | −3.73364 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 31.7245 | 1.12445 | ||||||||
\(797\) | 13.5084 | 0.478493 | 0.239247 | − | 0.970959i | \(-0.423100\pi\) | ||||
0.239247 | + | 0.970959i | \(0.423100\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.08815 | −0.180006 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −90.3678 | −3.19100 | ||||||||
\(803\) | −40.4929 | −1.42896 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 85.0176 | 2.99462 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −54.9469 | −1.93302 | ||||||||
\(809\) | −31.9560 | −1.12351 | −0.561756 | − | 0.827303i | \(-0.689874\pi\) | ||||
−0.561756 | + | 0.827303i | \(0.689874\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.7012 | 1.42921 | 0.714607 | − | 0.699526i | \(-0.246606\pi\) | ||||
0.714607 | + | 0.699526i | \(0.246606\pi\) | |||||||
\(812\) | 31.6601 | 1.11105 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.54288 | 0.334478 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.27413 | 0.184518 | ||||||||
\(818\) | −88.3895 | −3.09047 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.4300 | 0.468709 | 0.234355 | − | 0.972151i | \(-0.424702\pi\) | ||||
0.234355 | + | 0.972151i | \(0.424702\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.7275 | 0.931663 | 0.465832 | − | 0.884873i | \(-0.345755\pi\) | ||||
0.465832 | + | 0.884873i | \(0.345755\pi\) | |||||||
\(824\) | 154.413 | 5.37924 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 48.7090 | 1.69480 | ||||||||
\(827\) | 33.3435 | 1.15947 | 0.579733 | − | 0.814806i | \(-0.303157\pi\) | ||||
0.579733 | + | 0.814806i | \(0.303157\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.2849 | 0.426672 | 0.213336 | − | 0.976979i | \(-0.431567\pi\) | ||||
0.213336 | + | 0.976979i | \(0.431567\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −155.712 | −5.39835 | ||||||||
\(833\) | −4.95646 | −0.171731 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −17.1957 | −0.594725 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 41.1511 | 1.42154 | ||||||||
\(839\) | −36.9922 | −1.27711 | −0.638557 | − | 0.769575i | \(-0.720468\pi\) | ||||
−0.638557 | + | 0.769575i | \(0.720468\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.8501 | −0.891383 | ||||||||
\(842\) | 42.3491 | 1.45945 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 93.4016 | 3.21502 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.20237 | −0.247477 | ||||||||
\(848\) | 163.510 | 5.61497 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.38835 | 0.0475922 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.16959 | −0.245482 | −0.122741 | − | 0.992439i | \(-0.539168\pi\) | ||||
−0.122741 | + | 0.992439i | \(0.539168\pi\) | |||||||
\(854\) | −85.0936 | −2.91184 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −88.3256 | −3.01891 | ||||||||
\(857\) | 2.55124 | 0.0871486 | 0.0435743 | − | 0.999050i | \(-0.486125\pi\) | ||||
0.0435743 | + | 0.999050i | \(0.486125\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.9493 | 1.84073 | 0.920363 | − | 0.391065i | \(-0.127893\pi\) | ||||
0.920363 | + | 0.391065i | \(0.127893\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.69873 | −0.160039 | ||||||||
\(863\) | 21.4698 | 0.730840 | 0.365420 | − | 0.930843i | \(-0.380925\pi\) | ||||
0.365420 | + | 0.930843i | \(0.380925\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 36.8582 | 1.25249 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −166.700 | −5.65817 | ||||||||
\(869\) | 16.6491 | 0.564781 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.1782 | 0.548178 | ||||||||
\(872\) | −122.221 | −4.13891 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.35690 | −0.113549 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.9638 | 1.31571 | 0.657856 | − | 0.753144i | \(-0.271463\pi\) | ||||
0.657856 | + | 0.753144i | \(0.271463\pi\) | |||||||
\(878\) | 18.0887 | 0.610465 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.4373 | 0.452713 | 0.226357 | − | 0.974045i | \(-0.427319\pi\) | ||||
0.226357 | + | 0.974045i | \(0.427319\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.8799 | 0.938234 | 0.469117 | − | 0.883136i | \(-0.344572\pi\) | ||||
0.469117 | + | 0.883136i | \(0.344572\pi\) | |||||||
\(884\) | 41.0127 | 1.37941 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −71.0877 | −2.38824 | ||||||||
\(887\) | −28.9135 | −0.970821 | −0.485410 | − | 0.874286i | \(-0.661330\pi\) | ||||
−0.485410 | + | 0.874286i | \(0.661330\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.45580 | −0.149443 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 135.828 | 4.54785 | ||||||||
\(893\) | −2.35690 | −0.0788705 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 224.659 | 7.50533 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.0858 | 0.336566 | ||||||||
\(899\) | −16.5851 | −0.553144 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.0489 | −0.634611 | ||||||||
\(902\) | −70.5733 | −2.34983 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 37.0670 | 1.23283 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.7127 | −1.01980 | −0.509900 | − | 0.860234i | \(-0.670317\pi\) | ||||
−0.509900 | + | 0.860234i | \(0.670317\pi\) | |||||||
\(908\) | −102.270 | −3.39395 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.3690 | −1.30435 | −0.652176 | − | 0.758067i | \(-0.726144\pi\) | ||||
−0.652176 | + | 0.758067i | \(0.726144\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.84548 | −0.292743 | ||||||||
\(914\) | 34.4034 | 1.13796 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.6058 | −0.449548 | ||||||||
\(917\) | 40.3357 | 1.33200 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.87023 | −0.259615 | −0.129808 | − | 0.991539i | \(-0.541436\pi\) | ||||
−0.129808 | + | 0.991539i | \(0.541436\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −110.658 | −3.64434 | ||||||||
\(923\) | 8.77240 | 0.288747 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −51.5532 | −1.69414 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 53.8514 | 1.76776 | ||||||||
\(929\) | −39.2924 | −1.28914 | −0.644572 | − | 0.764544i | \(-0.722964\pi\) | ||||
−0.644572 | + | 0.764544i | \(0.722964\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.29590 | −0.0752450 | ||||||||
\(932\) | −110.781 | −3.62876 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −101.509 | −3.32148 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.7554 | 0.874061 | 0.437031 | − | 0.899447i | \(-0.356030\pi\) | ||||
0.437031 | + | 0.899447i | \(0.356030\pi\) | |||||||
\(938\) | −42.5652 | −1.38980 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.9191 | 1.36653 | 0.683263 | − | 0.730173i | \(-0.260560\pi\) | ||||
0.683263 | + | 0.730173i | \(0.260560\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.2674 | −0.334353 | ||||||||
\(944\) | 105.657 | 3.43885 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −43.4319 | −1.41209 | ||||||||
\(947\) | 55.4868 | 1.80308 | 0.901539 | − | 0.432698i | \(-0.142438\pi\) | ||||
0.901539 | + | 0.432698i | \(0.142438\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.7362 | 1.45220 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −71.0200 | −2.30177 | ||||||||
\(953\) | 8.48081 | 0.274720 | 0.137360 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137360 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −65.3454 | −2.11342 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 96.1426 | 3.10623 | ||||||||
\(959\) | 49.3129 | 1.59240 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56.3256 | 1.81695 | ||||||||
\(962\) | −10.5429 | −0.339916 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 43.4717 | 1.40013 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.63102 | 0.245397 | 0.122699 | − | 0.992444i | \(-0.460845\pi\) | ||||
0.122699 | + | 0.992444i | \(0.460845\pi\) | |||||||
\(968\) | −25.4886 | −0.819234 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.3599 | 0.621288 | 0.310644 | − | 0.950526i | \(-0.399455\pi\) | ||||
0.310644 | + | 0.950526i | \(0.399455\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.9342 | 1.28023 | ||||||||
\(974\) | 68.5695 | 2.19711 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −184.581 | −5.90829 | ||||||||
\(977\) | 55.8883 | 1.78802 | 0.894012 | − | 0.448042i | \(-0.147879\pi\) | ||||
0.894012 | + | 0.448042i | \(0.147879\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.2241 | 0.965968 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −51.2941 | −1.63686 | ||||||||
\(983\) | −4.58450 | −0.146223 | −0.0731114 | − | 0.997324i | \(-0.523293\pi\) | ||||
−0.0731114 | + | 0.997324i | \(0.523293\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10.7356 | −0.341890 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.9976 | 0.604394 | ||||||||
\(989\) | −6.31873 | −0.200924 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.5666 | 0.875681 | 0.437840 | − | 0.899053i | \(-0.355743\pi\) | ||||
0.437840 | + | 0.899053i | \(0.355743\pi\) | |||||||
\(992\) | −283.544 | −9.00254 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −23.0804 | −0.732065 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.9119 | −0.503933 | −0.251967 | − | 0.967736i | \(-0.581077\pi\) | ||||
−0.251967 | + | 0.967736i | \(0.581077\pi\) | |||||||
\(998\) | −71.0079 | −2.24772 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4275.2.a.bn.1.3 | 3 | ||
3.2 | odd | 2 | 475.2.a.d.1.1 | ✓ | 3 | ||
5.4 | even | 2 | 4275.2.a.z.1.1 | 3 | |||
12.11 | even | 2 | 7600.2.a.bw.1.2 | 3 | |||
15.2 | even | 4 | 475.2.b.c.324.1 | 6 | |||
15.8 | even | 4 | 475.2.b.c.324.6 | 6 | |||
15.14 | odd | 2 | 475.2.a.h.1.3 | yes | 3 | ||
57.56 | even | 2 | 9025.2.a.be.1.3 | 3 | |||
60.59 | even | 2 | 7600.2.a.bn.1.2 | 3 | |||
285.284 | even | 2 | 9025.2.a.w.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.2.a.d.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
475.2.a.h.1.3 | yes | 3 | 15.14 | odd | 2 | ||
475.2.b.c.324.1 | 6 | 15.2 | even | 4 | |||
475.2.b.c.324.6 | 6 | 15.8 | even | 4 | |||
4275.2.a.z.1.1 | 3 | 5.4 | even | 2 | |||
4275.2.a.bn.1.3 | 3 | 1.1 | even | 1 | trivial | ||
7600.2.a.bn.1.2 | 3 | 60.59 | even | 2 | |||
7600.2.a.bw.1.2 | 3 | 12.11 | even | 2 | |||
9025.2.a.w.1.1 | 3 | 285.284 | even | 2 | |||
9025.2.a.be.1.3 | 3 | 57.56 | even | 2 |