Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2169,2,Mod(1,2169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2169, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2169.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2169 = 3^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2169.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(17.3195521984\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | 7.7.31056073.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 3x^{5} + 11x^{4} + x^{3} - 9x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 241) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.60363\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2169.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.60363 | 1.84104 | 0.920521 | − | 0.390694i | \(-0.127765\pi\) | ||||
0.920521 | + | 0.390694i | \(0.127765\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.77887 | 2.38943 | ||||||||
\(5\) | 1.69135 | 0.756395 | 0.378197 | − | 0.925725i | \(-0.376544\pi\) | ||||
0.378197 | + | 0.925725i | \(0.376544\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.30586 | −0.493569 | −0.246785 | − | 0.969070i | \(-0.579374\pi\) | ||||
−0.246785 | + | 0.969070i | \(0.579374\pi\) | |||||||
\(8\) | 7.23513 | 2.55801 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.40364 | 1.39255 | ||||||||
\(11\) | 3.27094 | 0.986226 | 0.493113 | − | 0.869965i | \(-0.335859\pi\) | ||||
0.493113 | + | 0.869965i | \(0.335859\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.30649 | 1.19441 | 0.597203 | − | 0.802090i | \(-0.296279\pi\) | ||||
0.597203 | + | 0.802090i | \(0.296279\pi\) | |||||||
\(14\) | −3.39998 | −0.908682 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9.27984 | 2.31996 | ||||||||
\(17\) | 1.02456 | 0.248493 | 0.124247 | − | 0.992251i | \(-0.460349\pi\) | ||||
0.124247 | + | 0.992251i | \(0.460349\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.01250 | −1.60878 | −0.804388 | − | 0.594104i | \(-0.797507\pi\) | ||||
−0.804388 | + | 0.594104i | \(0.797507\pi\) | |||||||
\(20\) | 8.08274 | 1.80736 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.51631 | 1.81568 | ||||||||
\(23\) | −0.835873 | −0.174292 | −0.0871458 | − | 0.996196i | \(-0.527775\pi\) | ||||
−0.0871458 | + | 0.996196i | \(0.527775\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.13934 | −0.427867 | ||||||||
\(26\) | 11.2125 | 2.19895 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.24054 | −1.17935 | ||||||||
\(29\) | 1.11761 | 0.207535 | 0.103767 | − | 0.994602i | \(-0.466910\pi\) | ||||
0.103767 | + | 0.994602i | \(0.466910\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.97344 | −0.713652 | −0.356826 | − | 0.934171i | \(-0.616141\pi\) | ||||
−0.356826 | + | 0.934171i | \(0.616141\pi\) | |||||||
\(32\) | 9.69098 | 1.71314 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.66758 | 0.457486 | ||||||||
\(35\) | −2.20867 | −0.373333 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.3098 | −1.85932 | −0.929658 | − | 0.368423i | \(-0.879898\pi\) | ||||
−0.929658 | + | 0.368423i | \(0.879898\pi\) | |||||||
\(38\) | −18.2579 | −2.96182 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.2371 | 1.93486 | ||||||||
\(41\) | −1.22869 | −0.191890 | −0.0959448 | − | 0.995387i | \(-0.530587\pi\) | ||||
−0.0959448 | + | 0.995387i | \(0.530587\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.8406 | 1.65318 | 0.826591 | − | 0.562804i | \(-0.190277\pi\) | ||||
0.826591 | + | 0.562804i | \(0.190277\pi\) | |||||||
\(44\) | 15.6314 | 2.35652 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.17630 | −0.320878 | ||||||||
\(47\) | 0.151820 | 0.0221453 | 0.0110726 | − | 0.999939i | \(-0.496475\pi\) | ||||
0.0110726 | + | 0.999939i | \(0.496475\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.29473 | −0.756389 | ||||||||
\(50\) | −5.57003 | −0.787721 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 20.5801 | 2.85395 | ||||||||
\(53\) | −3.02053 | −0.414902 | −0.207451 | − | 0.978245i | \(-0.566517\pi\) | ||||
−0.207451 | + | 0.978245i | \(0.566517\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.53231 | 0.745976 | ||||||||
\(56\) | −9.44808 | −1.26255 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.90984 | 0.382080 | ||||||||
\(59\) | 4.15373 | 0.540769 | 0.270385 | − | 0.962752i | \(-0.412849\pi\) | ||||
0.270385 | + | 0.962752i | \(0.412849\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.62714 | 0.720482 | 0.360241 | − | 0.932859i | \(-0.382694\pi\) | ||||
0.360241 | + | 0.932859i | \(0.382694\pi\) | |||||||
\(62\) | −10.3454 | −1.31386 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.67199 | 0.833999 | ||||||||
\(65\) | 7.28378 | 0.903442 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.9934 | 1.58740 | 0.793700 | − | 0.608309i | \(-0.208152\pi\) | ||||
0.793700 | + | 0.608309i | \(0.208152\pi\) | |||||||
\(68\) | 4.89626 | 0.593758 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.75055 | −0.687322 | ||||||||
\(71\) | 11.2862 | 1.33942 | 0.669711 | − | 0.742622i | \(-0.266418\pi\) | ||||
0.669711 | + | 0.742622i | \(0.266418\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.7148 | 1.37112 | 0.685560 | − | 0.728017i | \(-0.259558\pi\) | ||||
0.685560 | + | 0.728017i | \(0.259558\pi\) | |||||||
\(74\) | −29.4464 | −3.42308 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −33.5118 | −3.84407 | ||||||||
\(77\) | −4.27140 | −0.486771 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.66517 | −0.187346 | −0.0936732 | − | 0.995603i | \(-0.529861\pi\) | ||||
−0.0936732 | + | 0.995603i | \(0.529861\pi\) | |||||||
\(80\) | 15.6955 | 1.75481 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.19906 | −0.353277 | ||||||||
\(83\) | 2.34322 | 0.257201 | 0.128601 | − | 0.991696i | \(-0.458951\pi\) | ||||
0.128601 | + | 0.991696i | \(0.458951\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.73290 | 0.187959 | ||||||||
\(86\) | 28.2250 | 3.04358 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 23.6657 | 2.52277 | ||||||||
\(89\) | −18.1099 | −1.91965 | −0.959825 | − | 0.280598i | \(-0.909467\pi\) | ||||
−0.959825 | + | 0.280598i | \(0.909467\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.62368 | −0.589522 | ||||||||
\(92\) | −3.99453 | −0.416458 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.395283 | 0.0407703 | ||||||||
\(95\) | −11.8606 | −1.21687 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.17873 | −0.728890 | −0.364445 | − | 0.931225i | \(-0.618741\pi\) | ||||
−0.364445 | + | 0.931225i | \(0.618741\pi\) | |||||||
\(98\) | −13.7855 | −1.39254 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10.2236 | −1.02236 | ||||||||
\(101\) | 5.48113 | 0.545393 | 0.272696 | − | 0.962100i | \(-0.412085\pi\) | ||||
0.272696 | + | 0.962100i | \(0.412085\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.7371 | −1.55062 | −0.775311 | − | 0.631580i | \(-0.782407\pi\) | ||||
−0.775311 | + | 0.631580i | \(0.782407\pi\) | |||||||
\(104\) | 31.1580 | 3.05530 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.86433 | −0.763851 | ||||||||
\(107\) | 11.1816 | 1.08097 | 0.540483 | − | 0.841355i | \(-0.318242\pi\) | ||||
0.540483 | + | 0.841355i | \(0.318242\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.296424 | −0.0283922 | −0.0141961 | − | 0.999899i | \(-0.504519\pi\) | ||||
−0.0141961 | + | 0.999899i | \(0.504519\pi\) | |||||||
\(110\) | 14.4041 | 1.37337 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.1182 | −1.14506 | ||||||||
\(113\) | −10.5881 | −0.996045 | −0.498023 | − | 0.867164i | \(-0.665940\pi\) | ||||
−0.498023 | + | 0.867164i | \(0.665940\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.41375 | −0.131833 | ||||||||
\(116\) | 5.34091 | 0.495891 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.8147 | 0.995578 | ||||||||
\(119\) | −1.33794 | −0.122649 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.300940 | −0.0273582 | ||||||||
\(122\) | 14.6510 | 1.32644 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −18.9886 | −1.70522 | ||||||||
\(125\) | −12.0751 | −1.08003 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6989 | 1.30432 | 0.652160 | − | 0.758081i | \(-0.273863\pi\) | ||||
0.652160 | + | 0.758081i | \(0.273863\pi\) | |||||||
\(128\) | −2.01059 | −0.177713 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 18.9642 | 1.66327 | ||||||||
\(131\) | −9.63853 | −0.842122 | −0.421061 | − | 0.907032i | \(-0.638342\pi\) | ||||
−0.421061 | + | 0.907032i | \(0.638342\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.15735 | 0.794043 | ||||||||
\(134\) | 33.8300 | 2.92247 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.41286 | 0.635647 | ||||||||
\(137\) | −23.2376 | −1.98532 | −0.992661 | − | 0.120933i | \(-0.961411\pi\) | ||||
−0.992661 | + | 0.120933i | \(0.961411\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.29376 | −0.109736 | −0.0548678 | − | 0.998494i | \(-0.517474\pi\) | ||||
−0.0548678 | + | 0.998494i | \(0.517474\pi\) | |||||||
\(140\) | −10.5549 | −0.892055 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 29.3850 | 2.46593 | ||||||||
\(143\) | 14.0863 | 1.17795 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.89027 | 0.156978 | ||||||||
\(146\) | 30.5011 | 2.52429 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −54.0480 | −4.44271 | ||||||||
\(149\) | −17.5316 | −1.43625 | −0.718123 | − | 0.695916i | \(-0.754998\pi\) | ||||
−0.718123 | + | 0.695916i | \(0.754998\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.26990 | 0.428858 | 0.214429 | − | 0.976740i | \(-0.431211\pi\) | ||||
0.214429 | + | 0.976740i | \(0.431211\pi\) | |||||||
\(152\) | −50.7363 | −4.11526 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11.1211 | −0.896166 | ||||||||
\(155\) | −6.72048 | −0.539802 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.2165 | −1.13460 | −0.567299 | − | 0.823512i | \(-0.692012\pi\) | ||||
−0.567299 | + | 0.823512i | \(0.692012\pi\) | |||||||
\(158\) | −4.33548 | −0.344912 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 16.3908 | 1.29581 | ||||||||
\(161\) | 1.09153 | 0.0860250 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.9688 | −1.25077 | −0.625386 | − | 0.780315i | \(-0.715059\pi\) | ||||
−0.625386 | + | 0.780315i | \(0.715059\pi\) | |||||||
\(164\) | −5.87176 | −0.458508 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.10086 | 0.473518 | ||||||||
\(167\) | 21.5275 | 1.66585 | 0.832925 | − | 0.553386i | \(-0.186665\pi\) | ||||
0.832925 | + | 0.553386i | \(0.186665\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.54585 | 0.426604 | ||||||||
\(170\) | 4.51181 | 0.346040 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 51.8060 | 3.95017 | ||||||||
\(173\) | 5.82531 | 0.442890 | 0.221445 | − | 0.975173i | \(-0.428923\pi\) | ||||
0.221445 | + | 0.975173i | \(0.428923\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.79368 | 0.211182 | ||||||||
\(176\) | 30.3538 | 2.28801 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −47.1515 | −3.53416 | ||||||||
\(179\) | 6.03932 | 0.451400 | 0.225700 | − | 0.974197i | \(-0.427533\pi\) | ||||
0.225700 | + | 0.974197i | \(0.427533\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.03706 | −0.300073 | −0.150036 | − | 0.988680i | \(-0.547939\pi\) | ||||
−0.150036 | + | 0.988680i | \(0.547939\pi\) | |||||||
\(182\) | −14.6420 | −1.08533 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.04765 | −0.445839 | ||||||||
\(185\) | −19.1288 | −1.40638 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.35129 | 0.245071 | ||||||||
\(188\) | 0.725529 | 0.0529146 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −30.8805 | −2.24031 | ||||||||
\(191\) | 16.4803 | 1.19247 | 0.596235 | − | 0.802810i | \(-0.296663\pi\) | ||||
0.596235 | + | 0.802810i | \(0.296663\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.0631 | −1.66012 | −0.830060 | − | 0.557674i | \(-0.811694\pi\) | ||||
−0.830060 | + | 0.557674i | \(0.811694\pi\) | |||||||
\(194\) | −18.6907 | −1.34192 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −25.3028 | −1.80734 | ||||||||
\(197\) | 13.5540 | 0.965680 | 0.482840 | − | 0.875709i | \(-0.339605\pi\) | ||||
0.482840 | + | 0.875709i | \(0.339605\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.6725 | −1.81988 | −0.909938 | − | 0.414745i | \(-0.863871\pi\) | ||||
−0.909938 | + | 0.414745i | \(0.863871\pi\) | |||||||
\(200\) | −15.4784 | −1.09449 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.2708 | 1.00409 | ||||||||
\(203\) | −1.45944 | −0.102433 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.07815 | −0.145144 | ||||||||
\(206\) | −40.9735 | −2.85476 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 39.9635 | 2.77097 | ||||||||
\(209\) | −22.9375 | −1.58662 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.18301 | 0.356813 | 0.178407 | − | 0.983957i | \(-0.442906\pi\) | ||||
0.178407 | + | 0.983957i | \(0.442906\pi\) | |||||||
\(212\) | −14.4347 | −0.991380 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 29.1127 | 1.99010 | ||||||||
\(215\) | 18.3353 | 1.25046 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.18877 | 0.352237 | ||||||||
\(218\) | −0.771777 | −0.0522713 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 26.4382 | 1.78246 | ||||||||
\(221\) | 4.41227 | 0.296802 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.50914 | −0.435884 | −0.217942 | − | 0.975962i | \(-0.569934\pi\) | ||||
−0.217942 | + | 0.975962i | \(0.569934\pi\) | |||||||
\(224\) | −12.6551 | −0.845553 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −27.5675 | −1.83376 | ||||||||
\(227\) | −11.0460 | −0.733150 | −0.366575 | − | 0.930389i | \(-0.619470\pi\) | ||||
−0.366575 | + | 0.930389i | \(0.619470\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.95679 | 0.591881 | 0.295941 | − | 0.955206i | \(-0.404367\pi\) | ||||
0.295941 | + | 0.955206i | \(0.404367\pi\) | |||||||
\(230\) | −3.68089 | −0.242710 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.08605 | 0.530875 | ||||||||
\(233\) | 6.46647 | 0.423632 | 0.211816 | − | 0.977310i | \(-0.432062\pi\) | ||||
0.211816 | + | 0.977310i | \(0.432062\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.256781 | 0.0167506 | ||||||||
\(236\) | 19.8501 | 1.29213 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.48349 | −0.225801 | ||||||||
\(239\) | 25.0588 | 1.62092 | 0.810460 | − | 0.585794i | \(-0.199217\pi\) | ||||
0.810460 | + | 0.585794i | \(0.199217\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | −0.783536 | −0.0503676 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 26.8914 | 1.72154 | ||||||||
\(245\) | −8.95523 | −0.572129 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.1992 | −1.92153 | ||||||||
\(248\) | −28.7484 | −1.82552 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −31.4391 | −1.98838 | ||||||||
\(251\) | 12.5611 | 0.792847 | 0.396424 | − | 0.918068i | \(-0.370251\pi\) | ||||
0.396424 | + | 0.918068i | \(0.370251\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.73409 | −0.171891 | ||||||||
\(254\) | 38.2706 | 2.40131 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −18.5788 | −1.16117 | ||||||||
\(257\) | −16.0367 | −1.00034 | −0.500171 | − | 0.865927i | \(-0.666730\pi\) | ||||
−0.500171 | + | 0.865927i | \(0.666730\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.7690 | 0.917702 | ||||||||
\(260\) | 34.8082 | 2.15871 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −25.0951 | −1.55038 | ||||||||
\(263\) | −3.33210 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.10877 | −0.313829 | ||||||||
\(266\) | 23.8423 | 1.46187 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 62.0939 | 3.79299 | ||||||||
\(269\) | 7.44101 | 0.453686 | 0.226843 | − | 0.973931i | \(-0.427160\pi\) | ||||
0.226843 | + | 0.973931i | \(0.427160\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.6031 | −1.25155 | −0.625774 | − | 0.780005i | \(-0.715217\pi\) | ||||
−0.625774 | + | 0.780005i | \(0.715217\pi\) | |||||||
\(272\) | 9.50779 | 0.576495 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −60.5020 | −3.65506 | ||||||||
\(275\) | −6.99764 | −0.421974 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.17667 | 0.311036 | 0.155518 | − | 0.987833i | \(-0.450295\pi\) | ||||
0.155518 | + | 0.987833i | \(0.450295\pi\) | |||||||
\(278\) | −3.36848 | −0.202028 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −15.9800 | −0.954988 | ||||||||
\(281\) | 14.1821 | 0.846031 | 0.423015 | − | 0.906123i | \(-0.360972\pi\) | ||||
0.423015 | + | 0.906123i | \(0.360972\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.05196 | −0.419196 | −0.209598 | − | 0.977788i | \(-0.567215\pi\) | ||||
−0.209598 | + | 0.977788i | \(0.567215\pi\) | |||||||
\(284\) | 53.9351 | 3.20046 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 36.6754 | 2.16866 | ||||||||
\(287\) | 1.60450 | 0.0947109 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9503 | −0.938251 | ||||||||
\(290\) | 4.92155 | 0.289004 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 55.9837 | 3.27620 | ||||||||
\(293\) | 2.78966 | 0.162974 | 0.0814869 | − | 0.996674i | \(-0.474033\pi\) | ||||
0.0814869 | + | 0.996674i | \(0.474033\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.02540 | 0.409035 | ||||||||
\(296\) | −81.8278 | −4.75614 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −45.6458 | −2.64419 | ||||||||
\(299\) | −3.59968 | −0.208175 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.1564 | −0.815960 | ||||||||
\(302\) | 13.7208 | 0.789546 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −65.0749 | −3.73230 | ||||||||
\(305\) | 9.51747 | 0.544969 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.8285 | 1.13167 | 0.565837 | − | 0.824517i | \(-0.308553\pi\) | ||||
0.565837 | + | 0.824517i | \(0.308553\pi\) | |||||||
\(308\) | −20.4124 | −1.16311 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.4976 | −0.993798 | ||||||||
\(311\) | −33.5109 | −1.90023 | −0.950114 | − | 0.311902i | \(-0.899034\pi\) | ||||
−0.950114 | + | 0.311902i | \(0.899034\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.4152 | 1.09741 | 0.548705 | − | 0.836016i | \(-0.315121\pi\) | ||||
0.548705 | + | 0.836016i | \(0.315121\pi\) | |||||||
\(314\) | −37.0144 | −2.08884 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.95763 | −0.447652 | ||||||||
\(317\) | 11.7255 | 0.658569 | 0.329284 | − | 0.944231i | \(-0.393193\pi\) | ||||
0.329284 | + | 0.944231i | \(0.393193\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.65564 | 0.204676 | ||||||||
\(320\) | 11.2847 | 0.630832 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.84195 | 0.158376 | ||||||||
\(323\) | −7.18475 | −0.399770 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.21303 | −0.511047 | ||||||||
\(326\) | −41.5768 | −2.30272 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.88976 | −0.490855 | ||||||||
\(329\) | −0.198256 | −0.0109302 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.93072 | 0.271017 | 0.135509 | − | 0.990776i | \(-0.456733\pi\) | ||||
0.135509 | + | 0.990776i | \(0.456733\pi\) | |||||||
\(332\) | 11.1979 | 0.614566 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 56.0496 | 3.06690 | ||||||||
\(335\) | 21.9764 | 1.20070 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.4425 | 1.87620 | 0.938100 | − | 0.346364i | \(-0.112584\pi\) | ||||
0.938100 | + | 0.346364i | \(0.112584\pi\) | |||||||
\(338\) | 14.4393 | 0.785395 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.28128 | 0.449116 | ||||||||
\(341\) | −12.9969 | −0.703822 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.0552 | 0.866900 | ||||||||
\(344\) | 78.4334 | 4.22885 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.1669 | 0.815378 | ||||||||
\(347\) | 23.4553 | 1.25915 | 0.629574 | − | 0.776940i | \(-0.283229\pi\) | ||||
0.629574 | + | 0.776940i | \(0.283229\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.8727 | 0.849648 | 0.424824 | − | 0.905276i | \(-0.360336\pi\) | ||||
0.424824 | + | 0.905276i | \(0.360336\pi\) | |||||||
\(350\) | 7.27369 | 0.388795 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 31.6986 | 1.68954 | ||||||||
\(353\) | 28.4598 | 1.51476 | 0.757382 | − | 0.652972i | \(-0.226478\pi\) | ||||
0.757382 | + | 0.652972i | \(0.226478\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.0889 | 1.01313 | ||||||||
\(356\) | −86.5450 | −4.58688 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.7241 | 0.831047 | ||||||||
\(359\) | 0.772338 | 0.0407625 | 0.0203812 | − | 0.999792i | \(-0.493512\pi\) | ||||
0.0203812 | + | 0.999792i | \(0.493512\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.1751 | 1.58816 | ||||||||
\(362\) | −10.5110 | −0.552446 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −26.8748 | −1.40862 | ||||||||
\(365\) | 19.8139 | 1.03711 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.3631 | −1.21954 | −0.609772 | − | 0.792577i | \(-0.708739\pi\) | ||||
−0.609772 | + | 0.792577i | \(0.708739\pi\) | |||||||
\(368\) | −7.75677 | −0.404350 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −49.8042 | −2.58920 | ||||||||
\(371\) | 3.94439 | 0.204783 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.7831 | 1.43855 | 0.719277 | − | 0.694724i | \(-0.244473\pi\) | ||||
0.719277 | + | 0.694724i | \(0.244473\pi\) | |||||||
\(374\) | 8.72550 | 0.451185 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.09844 | 0.0566477 | ||||||||
\(377\) | 4.81297 | 0.247881 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.33328 | 0.376685 | 0.188343 | − | 0.982103i | \(-0.439688\pi\) | ||||
0.188343 | + | 0.982103i | \(0.439688\pi\) | |||||||
\(380\) | −56.6802 | −2.90763 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 42.9084 | 2.19539 | ||||||||
\(383\) | 33.4931 | 1.71142 | 0.855708 | − | 0.517459i | \(-0.173122\pi\) | ||||
0.855708 | + | 0.517459i | \(0.173122\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.22443 | −0.368191 | ||||||||
\(386\) | −60.0477 | −3.05635 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −34.3062 | −1.74163 | ||||||||
\(389\) | −15.6882 | −0.795425 | −0.397713 | − | 0.917510i | \(-0.630196\pi\) | ||||
−0.397713 | + | 0.917510i | \(0.630196\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.856405 | −0.0433103 | ||||||||
\(392\) | −38.3080 | −1.93485 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 35.2894 | 1.77786 | ||||||||
\(395\) | −2.81639 | −0.141708 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.34483 | 0.418815 | 0.209408 | − | 0.977828i | \(-0.432846\pi\) | ||||
0.209408 | + | 0.977828i | \(0.432846\pi\) | |||||||
\(398\) | −66.8416 | −3.35047 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19.8527 | −0.992635 | ||||||||
\(401\) | 38.5766 | 1.92642 | 0.963211 | − | 0.268747i | \(-0.0866094\pi\) | ||||
0.963211 | + | 0.268747i | \(0.0866094\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.1116 | −0.852389 | ||||||||
\(404\) | 26.1936 | 1.30318 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.79985 | −0.188583 | ||||||||
\(407\) | −36.9936 | −1.83371 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.5415 | −0.966266 | −0.483133 | − | 0.875547i | \(-0.660501\pi\) | ||||
−0.483133 | + | 0.875547i | \(0.660501\pi\) | |||||||
\(410\) | −5.41073 | −0.267217 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −75.2055 | −3.70511 | ||||||||
\(413\) | −5.42419 | −0.266907 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.96320 | 0.194546 | ||||||||
\(416\) | 41.7341 | 2.04618 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −59.7206 | −2.92103 | ||||||||
\(419\) | 29.7748 | 1.45459 | 0.727297 | − | 0.686323i | \(-0.240776\pi\) | ||||
0.727297 | + | 0.686323i | \(0.240776\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.78920 | −0.233411 | −0.116706 | − | 0.993167i | \(-0.537233\pi\) | ||||
−0.116706 | + | 0.993167i | \(0.537233\pi\) | |||||||
\(422\) | 13.4946 | 0.656908 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −21.8539 | −1.06132 | ||||||||
\(425\) | −2.19189 | −0.106322 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.34827 | −0.355608 | ||||||||
\(428\) | 53.4354 | 2.58290 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 47.7383 | 2.30214 | ||||||||
\(431\) | −5.35939 | −0.258153 | −0.129076 | − | 0.991635i | \(-0.541201\pi\) | ||||
−0.129076 | + | 0.991635i | \(0.541201\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.5028 | 1.03336 | 0.516680 | − | 0.856179i | \(-0.327168\pi\) | ||||
0.516680 | + | 0.856179i | \(0.327168\pi\) | |||||||
\(434\) | 13.5096 | 0.648482 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.41657 | −0.0678414 | ||||||||
\(437\) | 5.86156 | 0.280396 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.22306 | 0.201556 | 0.100778 | − | 0.994909i | \(-0.467867\pi\) | ||||
0.100778 | + | 0.994909i | \(0.467867\pi\) | |||||||
\(440\) | 40.0270 | 1.90821 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.4879 | 0.546424 | ||||||||
\(443\) | −8.34030 | −0.396260 | −0.198130 | − | 0.980176i | \(-0.563487\pi\) | ||||
−0.198130 | + | 0.980176i | \(0.563487\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.6303 | −1.45201 | ||||||||
\(446\) | −16.9474 | −0.802481 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.71269 | −0.411636 | ||||||||
\(449\) | −15.7796 | −0.744684 | −0.372342 | − | 0.928096i | \(-0.621445\pi\) | ||||
−0.372342 | + | 0.928096i | \(0.621445\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.01898 | −0.189247 | ||||||||
\(452\) | −50.5992 | −2.37998 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −28.7597 | −1.34976 | ||||||||
\(455\) | −9.51161 | −0.445911 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.71419 | −0.407633 | −0.203816 | − | 0.979009i | \(-0.565335\pi\) | ||||
−0.203816 | + | 0.979009i | \(0.565335\pi\) | |||||||
\(458\) | 23.3201 | 1.08968 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.75614 | −0.315007 | ||||||||
\(461\) | −24.9140 | −1.16036 | −0.580181 | − | 0.814487i | \(-0.697018\pi\) | ||||
−0.580181 | + | 0.814487i | \(0.697018\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.87272 | −0.133507 | −0.0667534 | − | 0.997770i | \(-0.521264\pi\) | ||||
−0.0667534 | + | 0.997770i | \(0.521264\pi\) | |||||||
\(464\) | 10.3712 | 0.481473 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.8363 | 0.779925 | ||||||||
\(467\) | −4.87474 | −0.225576 | −0.112788 | − | 0.993619i | \(-0.535978\pi\) | ||||
−0.112788 | + | 0.993619i | \(0.535978\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.9676 | −0.783492 | ||||||||
\(470\) | 0.668562 | 0.0308385 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 30.0528 | 1.38329 | ||||||||
\(473\) | 35.4591 | 1.63041 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.0021 | 0.688343 | ||||||||
\(476\) | −6.39383 | −0.293061 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 65.2438 | 2.98418 | ||||||||
\(479\) | −0.194055 | −0.00886661 | −0.00443331 | − | 0.999990i | \(-0.501411\pi\) | ||||
−0.00443331 | + | 0.999990i | \(0.501411\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.7055 | −2.22078 | ||||||||
\(482\) | −2.60363 | −0.118592 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.43815 | −0.0653707 | ||||||||
\(485\) | −12.1417 | −0.551328 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.7592 | −1.39383 | −0.696915 | − | 0.717154i | \(-0.745445\pi\) | ||||
−0.696915 | + | 0.717154i | \(0.745445\pi\) | |||||||
\(488\) | 40.7131 | 1.84300 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −23.3161 | −1.05331 | ||||||||
\(491\) | 21.5528 | 0.972663 | 0.486332 | − | 0.873774i | \(-0.338335\pi\) | ||||
0.486332 | + | 0.873774i | \(0.338335\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.14506 | 0.0515710 | ||||||||
\(494\) | −78.6275 | −3.53762 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −36.8729 | −1.65564 | ||||||||
\(497\) | −14.7382 | −0.661097 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.8992 | 0.980341 | 0.490170 | − | 0.871627i | \(-0.336935\pi\) | ||||
0.490170 | + | 0.871627i | \(0.336935\pi\) | |||||||
\(500\) | −57.7054 | −2.58066 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 32.7043 | 1.45966 | ||||||||
\(503\) | −4.44114 | −0.198021 | −0.0990104 | − | 0.995086i | \(-0.531568\pi\) | ||||
−0.0990104 | + | 0.995086i | \(0.531568\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.27050 | 0.412532 | ||||||||
\(506\) | −7.11855 | −0.316458 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 70.2443 | 3.11659 | ||||||||
\(509\) | −29.6966 | −1.31628 | −0.658140 | − | 0.752895i | \(-0.728657\pi\) | ||||
−0.658140 | + | 0.752895i | \(0.728657\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.2980 | −0.676742 | ||||||||
\(512\) | −44.3511 | −1.96006 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −41.7536 | −1.84167 | ||||||||
\(515\) | −26.6169 | −1.17288 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.496595 | 0.0218402 | ||||||||
\(518\) | 38.4530 | 1.68953 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 52.6991 | 2.31101 | ||||||||
\(521\) | 32.5336 | 1.42532 | 0.712661 | − | 0.701509i | \(-0.247490\pi\) | ||||
0.712661 | + | 0.701509i | \(0.247490\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.6812 | −0.948053 | −0.474027 | − | 0.880510i | \(-0.657200\pi\) | ||||
−0.474027 | + | 0.880510i | \(0.657200\pi\) | |||||||
\(524\) | −46.0612 | −2.01219 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.67555 | −0.378272 | ||||||||
\(527\) | −4.07105 | −0.177338 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3013 | −0.969622 | ||||||||
\(530\) | −13.3013 | −0.577773 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 43.7618 | 1.89731 | ||||||||
\(533\) | −5.29135 | −0.229194 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.9120 | 0.817637 | ||||||||
\(536\) | 94.0092 | 4.06058 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19.3736 | 0.835255 | ||||||||
\(539\) | −17.3187 | −0.745971 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.08311 | 0.261533 | 0.130767 | − | 0.991413i | \(-0.458256\pi\) | ||||
0.130767 | + | 0.991413i | \(0.458256\pi\) | |||||||
\(542\) | −53.6427 | −2.30415 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.92903 | 0.425703 | ||||||||
\(545\) | −0.501356 | −0.0214757 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.1956 | −0.521447 | −0.260723 | − | 0.965414i | \(-0.583961\pi\) | ||||
−0.260723 | + | 0.965414i | \(0.583961\pi\) | |||||||
\(548\) | −111.049 | −4.74379 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −18.2192 | −0.776871 | ||||||||
\(551\) | −7.83723 | −0.333877 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.17448 | 0.0924684 | ||||||||
\(554\) | 13.4781 | 0.572630 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.18273 | −0.262206 | ||||||||
\(557\) | 37.5982 | 1.59309 | 0.796544 | − | 0.604581i | \(-0.206659\pi\) | ||||
0.796544 | + | 0.604581i | \(0.206659\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.6851 | 1.97457 | ||||||||
\(560\) | −20.4961 | −0.866118 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 36.9248 | 1.55758 | ||||||||
\(563\) | −20.6037 | −0.868342 | −0.434171 | − | 0.900830i | \(-0.642959\pi\) | ||||
−0.434171 | + | 0.900830i | \(0.642959\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.9082 | −0.753403 | ||||||||
\(566\) | −18.3607 | −0.771756 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 81.6569 | 3.42625 | ||||||||
\(569\) | −20.5762 | −0.862601 | −0.431301 | − | 0.902208i | \(-0.641945\pi\) | ||||
−0.431301 | + | 0.902208i | \(0.641945\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.1320 | 1.55392 | 0.776962 | − | 0.629547i | \(-0.216760\pi\) | ||||
0.776962 | + | 0.629547i | \(0.216760\pi\) | |||||||
\(572\) | 67.3165 | 2.81464 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.17753 | 0.174367 | ||||||||
\(575\) | 1.78821 | 0.0745736 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.7064 | −1.44484 | −0.722422 | − | 0.691452i | \(-0.756971\pi\) | ||||
−0.722422 | + | 0.691452i | \(0.756971\pi\) | |||||||
\(578\) | −41.5285 | −1.72736 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.03335 | 0.375089 | ||||||||
\(581\) | −3.05992 | −0.126947 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.87998 | −0.409187 | ||||||||
\(584\) | 84.7585 | 3.50733 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.26324 | 0.300042 | ||||||||
\(587\) | 1.14455 | 0.0472405 | 0.0236203 | − | 0.999721i | \(-0.492481\pi\) | ||||
0.0236203 | + | 0.999721i | \(0.492481\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.8638 | 1.14811 | ||||||||
\(590\) | 18.2915 | 0.753050 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −104.953 | −4.31354 | ||||||||
\(593\) | −3.60735 | −0.148136 | −0.0740680 | − | 0.997253i | \(-0.523598\pi\) | ||||
−0.0740680 | + | 0.997253i | \(0.523598\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.26292 | −0.0927708 | ||||||||
\(596\) | −83.7813 | −3.43181 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.37222 | −0.383258 | ||||||||
\(599\) | 31.6723 | 1.29410 | 0.647048 | − | 0.762449i | \(-0.276003\pi\) | ||||
0.647048 | + | 0.762449i | \(0.276003\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.55665 | 0.267451 | 0.133726 | − | 0.991018i | \(-0.457306\pi\) | ||||
0.133726 | + | 0.991018i | \(0.457306\pi\) | |||||||
\(602\) | −36.8579 | −1.50222 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 25.1841 | 1.02473 | ||||||||
\(605\) | −0.508996 | −0.0206936 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.16648 | −0.372056 | −0.186028 | − | 0.982544i | \(-0.559562\pi\) | ||||
−0.186028 | + | 0.982544i | \(0.559562\pi\) | |||||||
\(608\) | −67.9579 | −2.75606 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 24.7799 | 1.00331 | ||||||||
\(611\) | 0.653812 | 0.0264504 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.92345 | 0.320025 | 0.160012 | − | 0.987115i | \(-0.448847\pi\) | ||||
0.160012 | + | 0.987115i | \(0.448847\pi\) | |||||||
\(614\) | 51.6260 | 2.08346 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −30.9041 | −1.24516 | ||||||||
\(617\) | −16.5959 | −0.668126 | −0.334063 | − | 0.942551i | \(-0.608420\pi\) | ||||
−0.334063 | + | 0.942551i | \(0.608420\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.49086 | 0.180503 | 0.0902514 | − | 0.995919i | \(-0.471233\pi\) | ||||
0.0902514 | + | 0.995919i | \(0.471233\pi\) | |||||||
\(620\) | −32.1163 | −1.28982 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −87.2498 | −3.49840 | ||||||||
\(623\) | 23.6491 | 0.947481 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.72656 | −0.389063 | ||||||||
\(626\) | 50.5499 | 2.02038 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −67.9387 | −2.71105 | ||||||||
\(629\) | −11.5876 | −0.462028 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.96553 | −0.237484 | −0.118742 | − | 0.992925i | \(-0.537886\pi\) | ||||
−0.118742 | + | 0.992925i | \(0.537886\pi\) | |||||||
\(632\) | −12.0477 | −0.479233 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30.5288 | 1.21245 | ||||||||
\(635\) | 24.8611 | 0.986581 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.8017 | −0.903435 | ||||||||
\(638\) | 9.51791 | 0.376818 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.40061 | −0.134421 | ||||||||
\(641\) | 1.73375 | 0.0684789 | 0.0342395 | − | 0.999414i | \(-0.489099\pi\) | ||||
0.0342395 | + | 0.999414i | \(0.489099\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.3312 | 1.51163 | 0.755817 | − | 0.654783i | \(-0.227240\pi\) | ||||
0.755817 | + | 0.654783i | \(0.227240\pi\) | |||||||
\(644\) | 5.21630 | 0.205551 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.7064 | −0.735994 | ||||||||
\(647\) | −29.2098 | −1.14836 | −0.574178 | − | 0.818730i | \(-0.694678\pi\) | ||||
−0.574178 | + | 0.818730i | \(0.694678\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.5866 | 0.533321 | ||||||||
\(650\) | −23.9873 | −0.940858 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −76.3127 | −2.98864 | ||||||||
\(653\) | 42.7952 | 1.67471 | 0.837353 | − | 0.546662i | \(-0.184102\pi\) | ||||
0.837353 | + | 0.546662i | \(0.184102\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.3021 | −0.636976 | ||||||||
\(656\) | −11.4021 | −0.445177 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.516185 | −0.0201230 | ||||||||
\(659\) | 23.7004 | 0.923238 | 0.461619 | − | 0.887078i | \(-0.347269\pi\) | ||||
0.461619 | + | 0.887078i | \(0.347269\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.1228 | 0.938268 | 0.469134 | − | 0.883127i | \(-0.344566\pi\) | ||||
0.469134 | + | 0.883127i | \(0.344566\pi\) | |||||||
\(662\) | 12.8378 | 0.498954 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.9535 | 0.657923 | ||||||||
\(665\) | 15.4883 | 0.600610 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.934180 | −0.0361716 | ||||||||
\(668\) | 102.877 | 3.98044 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 57.2184 | 2.21054 | ||||||||
\(671\) | 18.4061 | 0.710558 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.67522 | −0.141669 | −0.0708346 | − | 0.997488i | \(-0.522566\pi\) | ||||
−0.0708346 | + | 0.997488i | \(0.522566\pi\) | |||||||
\(674\) | 89.6753 | 3.45416 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 26.5029 | 1.01934 | ||||||||
\(677\) | −45.7769 | −1.75935 | −0.879675 | − | 0.475575i | \(-0.842240\pi\) | ||||
−0.879675 | + | 0.475575i | \(0.842240\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.37443 | 0.359758 | ||||||||
\(680\) | 12.5377 | 0.480800 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −33.8391 | −1.29577 | ||||||||
\(683\) | 1.52419 | 0.0583215 | 0.0291608 | − | 0.999575i | \(-0.490717\pi\) | ||||
0.0291608 | + | 0.999575i | \(0.490717\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −39.3029 | −1.50169 | ||||||||
\(686\) | 41.8018 | 1.59600 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 100.599 | 3.83532 | ||||||||
\(689\) | −13.0079 | −0.495561 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.3036 | 0.772386 | 0.386193 | − | 0.922418i | \(-0.373790\pi\) | ||||
0.386193 | + | 0.922418i | \(0.373790\pi\) | |||||||
\(692\) | 27.8384 | 1.05826 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 61.0689 | 2.31814 | ||||||||
\(695\) | −2.18821 | −0.0830034 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.25888 | −0.0476833 | ||||||||
\(698\) | 41.3267 | 1.56424 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 13.3506 | 0.504606 | ||||||||
\(701\) | 10.3863 | 0.392285 | 0.196143 | − | 0.980575i | \(-0.437158\pi\) | ||||
0.196143 | + | 0.980575i | \(0.437158\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 79.3098 | 2.99123 | ||||||||
\(704\) | 21.8237 | 0.822511 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 74.0988 | 2.78874 | ||||||||
\(707\) | −7.15759 | −0.269189 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.9053 | 1.31090 | 0.655448 | − | 0.755240i | \(-0.272480\pi\) | ||||
0.655448 | + | 0.755240i | \(0.272480\pi\) | |||||||
\(710\) | 49.7002 | 1.86522 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −131.028 | −4.91048 | ||||||||
\(713\) | 3.32129 | 0.124383 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.8248 | 0.890998 | ||||||||
\(716\) | 28.8611 | 1.07859 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.01088 | 0.0750454 | ||||||||
\(719\) | −5.17696 | −0.193068 | −0.0965341 | − | 0.995330i | \(-0.530776\pi\) | ||||
−0.0965341 | + | 0.995330i | \(0.530776\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.5505 | 0.765339 | ||||||||
\(722\) | 78.5646 | 2.92387 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.2926 | −0.717003 | ||||||||
\(725\) | −2.39094 | −0.0887974 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.00384 | −0.259758 | −0.129879 | − | 0.991530i | \(-0.541459\pi\) | ||||
−0.129879 | + | 0.991530i | \(0.541459\pi\) | |||||||
\(728\) | −40.6881 | −1.50800 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 51.5880 | 1.90936 | ||||||||
\(731\) | 11.1069 | 0.410804 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.22518 | −0.0452530 | −0.0226265 | − | 0.999744i | \(-0.507203\pi\) | ||||
−0.0226265 | + | 0.999744i | \(0.507203\pi\) | |||||||
\(734\) | −60.8288 | −2.24523 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.10042 | −0.298586 | ||||||||
\(737\) | 42.5008 | 1.56554 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.4569 | −1.15716 | −0.578580 | − | 0.815625i | \(-0.696393\pi\) | ||||
−0.578580 | + | 0.815625i | \(0.696393\pi\) | |||||||
\(740\) | −91.4140 | −3.36045 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.2697 | 0.377014 | ||||||||
\(743\) | −17.5176 | −0.642659 | −0.321330 | − | 0.946967i | \(-0.604130\pi\) | ||||
−0.321330 | + | 0.946967i | \(0.604130\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.6521 | −1.08637 | ||||||||
\(746\) | 72.3368 | 2.64844 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16.0154 | 0.585580 | ||||||||
\(749\) | −14.6016 | −0.533532 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.2893 | −1.28773 | −0.643863 | − | 0.765141i | \(-0.722669\pi\) | ||||
−0.643863 | + | 0.765141i | \(0.722669\pi\) | |||||||
\(752\) | 1.40887 | 0.0513761 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.5312 | 0.456359 | ||||||||
\(755\) | 8.91324 | 0.324386 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.2974 | −0.628686 | −0.314343 | − | 0.949309i | \(-0.601784\pi\) | ||||
−0.314343 | + | 0.949309i | \(0.601784\pi\) | |||||||
\(758\) | 19.0931 | 0.693493 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −85.8129 | −3.11276 | ||||||||
\(761\) | −9.53250 | −0.345553 | −0.172776 | − | 0.984961i | \(-0.555274\pi\) | ||||
−0.172776 | + | 0.984961i | \(0.555274\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.387088 | 0.0140135 | ||||||||
\(764\) | 78.7570 | 2.84933 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 87.2034 | 3.15079 | ||||||||
\(767\) | 17.8880 | 0.645897 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.0399 | −1.33569 | −0.667847 | − | 0.744299i | \(-0.732784\pi\) | ||||
−0.667847 | + | 0.744299i | \(0.732784\pi\) | |||||||
\(770\) | −18.8097 | −0.677855 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −110.216 | −3.96675 | ||||||||
\(773\) | 6.97450 | 0.250855 | 0.125428 | − | 0.992103i | \(-0.459970\pi\) | ||||
0.125428 | + | 0.992103i | \(0.459970\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.50053 | 0.305348 | ||||||||
\(776\) | −51.9391 | −1.86450 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −40.8463 | −1.46441 | ||||||||
\(779\) | 8.61621 | 0.308708 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.9164 | 1.32097 | ||||||||
\(782\) | −2.22976 | −0.0797360 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −49.1342 | −1.75479 | ||||||||
\(785\) | −24.0450 | −0.858204 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.9359 | 1.06710 | 0.533550 | − | 0.845768i | \(-0.320857\pi\) | ||||
0.533550 | + | 0.845768i | \(0.320857\pi\) | |||||||
\(788\) | 64.7726 | 2.30743 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.33281 | −0.260890 | ||||||||
\(791\) | 13.8266 | 0.491617 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.2332 | 0.860547 | ||||||||
\(794\) | 21.7268 | 0.771056 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −122.685 | −4.34847 | ||||||||
\(797\) | 10.7103 | 0.379380 | 0.189690 | − | 0.981844i | \(-0.439252\pi\) | ||||
0.189690 | + | 0.981844i | \(0.439252\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.155550 | 0.00550295 | ||||||||
\(800\) | −20.7323 | −0.732996 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 100.439 | 3.54662 | ||||||||
\(803\) | 38.3186 | 1.35223 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.84617 | 0.0650688 | ||||||||
\(806\) | −44.5522 | −1.56928 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 39.6567 | 1.39512 | ||||||||
\(809\) | 30.4625 | 1.07100 | 0.535502 | − | 0.844534i | \(-0.320122\pi\) | ||||
0.535502 | + | 0.844534i | \(0.320122\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.38159 | −0.224088 | −0.112044 | − | 0.993703i | \(-0.535740\pi\) | ||||
−0.112044 | + | 0.993703i | \(0.535740\pi\) | |||||||
\(812\) | −6.97449 | −0.244757 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −96.3176 | −3.37593 | ||||||||
\(815\) | −27.0088 | −0.946077 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −76.0199 | −2.65960 | ||||||||
\(818\) | −50.8788 | −1.77894 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.93121 | −0.346813 | ||||||||
\(821\) | 31.3814 | 1.09522 | 0.547609 | − | 0.836734i | \(-0.315538\pi\) | ||||
0.547609 | + | 0.836734i | \(0.315538\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.61720 | −0.300377 | −0.150188 | − | 0.988657i | \(-0.547988\pi\) | ||||
−0.150188 | + | 0.988657i | \(0.547988\pi\) | |||||||
\(824\) | −113.860 | −3.96650 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.1226 | −0.491387 | ||||||||
\(827\) | 18.2047 | 0.633039 | 0.316520 | − | 0.948586i | \(-0.397486\pi\) | ||||
0.316520 | + | 0.948586i | \(0.397486\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.0162 | 1.32036 | 0.660179 | − | 0.751108i | \(-0.270480\pi\) | ||||
0.660179 | + | 0.751108i | \(0.270480\pi\) | |||||||
\(830\) | 10.3187 | 0.358167 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 28.7328 | 0.996132 | ||||||||
\(833\) | −5.42479 | −0.187958 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36.4106 | 1.26004 | ||||||||
\(836\) | −109.615 | −3.79112 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 77.5224 | 2.67797 | ||||||||
\(839\) | −45.6228 | −1.57507 | −0.787537 | − | 0.616267i | \(-0.788644\pi\) | ||||
−0.787537 | + | 0.616267i | \(0.788644\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7509 | −0.956929 | ||||||||
\(842\) | −12.4693 | −0.429720 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 24.7689 | 0.852582 | ||||||||
\(845\) | 9.37997 | 0.322681 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.392987 | 0.0135032 | ||||||||
\(848\) | −28.0300 | −0.962556 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.70685 | −0.195743 | ||||||||
\(851\) | 9.45354 | 0.324063 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.2406 | 0.590307 | 0.295153 | − | 0.955450i | \(-0.404629\pi\) | ||||
0.295153 | + | 0.955450i | \(0.404629\pi\) | |||||||
\(854\) | −19.1321 | −0.654689 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 80.9003 | 2.76512 | ||||||||
\(857\) | −9.87638 | −0.337371 | −0.168685 | − | 0.985670i | \(-0.553952\pi\) | ||||
−0.168685 | + | 0.985670i | \(0.553952\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.8904 | 0.883369 | 0.441685 | − | 0.897170i | \(-0.354381\pi\) | ||||
0.441685 | + | 0.897170i | \(0.354381\pi\) | |||||||
\(860\) | 87.6220 | 2.98789 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.9538 | −0.475270 | ||||||||
\(863\) | 14.8445 | 0.505311 | 0.252656 | − | 0.967556i | \(-0.418696\pi\) | ||||
0.252656 | + | 0.967556i | \(0.418696\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.85263 | 0.334999 | ||||||||
\(866\) | 55.9853 | 1.90246 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 24.7964 | 0.841646 | ||||||||
\(869\) | −5.44668 | −0.184766 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.9561 | 1.89600 | ||||||||
\(872\) | −2.14467 | −0.0726275 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 15.2613 | 0.516221 | ||||||||
\(875\) | 15.7684 | 0.533070 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.0781 | 1.42088 | 0.710439 | − | 0.703759i | \(-0.248497\pi\) | ||||
0.710439 | + | 0.703759i | \(0.248497\pi\) | |||||||
\(878\) | 10.9953 | 0.371072 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 51.3389 | 1.73064 | ||||||||
\(881\) | 19.0418 | 0.641534 | 0.320767 | − | 0.947158i | \(-0.396059\pi\) | ||||
0.320767 | + | 0.947158i | \(0.396059\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.51087 | 0.219108 | 0.109554 | − | 0.993981i | \(-0.465058\pi\) | ||||
0.109554 | + | 0.993981i | \(0.465058\pi\) | |||||||
\(884\) | 21.0857 | 0.709188 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.7150 | −0.729531 | ||||||||
\(887\) | −5.59140 | −0.187741 | −0.0938704 | − | 0.995584i | \(-0.529924\pi\) | ||||
−0.0938704 | + | 0.995584i | \(0.529924\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.1948 | −0.643773 | ||||||||
\(890\) | −79.7497 | −2.67322 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −31.1063 | −1.04152 | ||||||||
\(893\) | −1.06464 | −0.0356268 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.2146 | 0.341437 | ||||||||
\(896\) | 2.62555 | 0.0877135 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −41.0841 | −1.37099 | ||||||||
\(899\) | −4.44076 | −0.148108 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.09473 | −0.103100 | ||||||||
\(902\) | −10.4639 | −0.348411 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −76.6063 | −2.54789 | ||||||||
\(905\) | −6.82809 | −0.226973 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.3915 | 0.610681 | 0.305340 | − | 0.952243i | \(-0.401230\pi\) | ||||
0.305340 | + | 0.952243i | \(0.401230\pi\) | |||||||
\(908\) | −52.7874 | −1.75181 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −24.7647 | −0.820941 | ||||||||
\(911\) | 38.2665 | 1.26783 | 0.633913 | − | 0.773404i | \(-0.281448\pi\) | ||||
0.633913 | + | 0.773404i | \(0.281448\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.66452 | 0.253659 | ||||||||
\(914\) | −22.6885 | −0.750469 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 42.8033 | 1.41426 | ||||||||
\(917\) | 12.5866 | 0.415646 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.89962 | −0.161624 | −0.0808118 | − | 0.996729i | \(-0.525751\pi\) | ||||
−0.0808118 | + | 0.996729i | \(0.525751\pi\) | |||||||
\(920\) | −10.2287 | −0.337230 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −64.8669 | −2.13628 | ||||||||
\(923\) | 48.6038 | 1.59981 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.1954 | 0.795541 | ||||||||
\(926\) | −7.47949 | −0.245791 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.8307 | 0.355536 | ||||||||
\(929\) | −17.9381 | −0.588528 | −0.294264 | − | 0.955724i | \(-0.595075\pi\) | ||||
−0.294264 | + | 0.955724i | \(0.595075\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.1292 | 1.21686 | ||||||||
\(932\) | 30.9024 | 1.01224 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.6920 | −0.415295 | ||||||||
\(935\) | 5.66820 | 0.185370 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.8369 | 0.974730 | 0.487365 | − | 0.873198i | \(-0.337958\pi\) | ||||
0.487365 | + | 0.873198i | \(0.337958\pi\) | |||||||
\(938\) | −44.1773 | −1.44244 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.22712 | 0.0400243 | ||||||||
\(941\) | −26.8047 | −0.873809 | −0.436904 | − | 0.899508i | \(-0.643925\pi\) | ||||
−0.436904 | + | 0.899508i | \(0.643925\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.02703 | 0.0334448 | ||||||||
\(944\) | 38.5459 | 1.25456 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 92.3222 | 3.00165 | ||||||||
\(947\) | −2.94622 | −0.0957393 | −0.0478697 | − | 0.998854i | \(-0.515243\pi\) | ||||
−0.0478697 | + | 0.998854i | \(0.515243\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.4499 | 1.63767 | ||||||||
\(950\) | 39.0598 | 1.26727 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.68017 | −0.313736 | ||||||||
\(953\) | 4.62861 | 0.149935 | 0.0749676 | − | 0.997186i | \(-0.476115\pi\) | ||||
0.0749676 | + | 0.997186i | \(0.476115\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.8739 | 0.901978 | ||||||||
\(956\) | 119.753 | 3.87308 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.505247 | −0.0163238 | ||||||||
\(959\) | 30.3451 | 0.979894 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.2117 | −0.490702 | ||||||||
\(962\) | −126.811 | −4.08854 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.77887 | −0.153917 | ||||||||
\(965\) | −39.0078 | −1.25571 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.1721 | 0.648689 | 0.324345 | − | 0.945939i | \(-0.394856\pi\) | ||||
0.324345 | + | 0.945939i | \(0.394856\pi\) | |||||||
\(968\) | −2.17734 | −0.0699825 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −31.6126 | −1.01502 | ||||||||
\(971\) | −30.0251 | −0.963550 | −0.481775 | − | 0.876295i | \(-0.660008\pi\) | ||||
−0.481775 | + | 0.876295i | \(0.660008\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.68948 | 0.0541621 | ||||||||
\(974\) | −80.0853 | −2.56610 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 52.2190 | 1.67149 | ||||||||
\(977\) | −57.7096 | −1.84629 | −0.923147 | − | 0.384448i | \(-0.874392\pi\) | ||||
−0.923147 | + | 0.384448i | \(0.874392\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −59.2366 | −1.89321 | ||||||||
\(980\) | −42.7959 | −1.36706 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 56.1154 | 1.79071 | ||||||||
\(983\) | 3.33817 | 0.106471 | 0.0532356 | − | 0.998582i | \(-0.483047\pi\) | ||||
0.0532356 | + | 0.998582i | \(0.483047\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.9245 | 0.730435 | ||||||||
\(986\) | 2.98132 | 0.0949444 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −144.318 | −4.59137 | ||||||||
\(989\) | −9.06139 | −0.288136 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.48757 | 0.142552 | 0.0712762 | − | 0.997457i | \(-0.477293\pi\) | ||||
0.0712762 | + | 0.997457i | \(0.477293\pi\) | |||||||
\(992\) | −38.5065 | −1.22258 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −38.3727 | −1.21711 | ||||||||
\(995\) | −43.4212 | −1.37654 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47.4116 | −1.50154 | −0.750770 | − | 0.660564i | \(-0.770317\pi\) | ||||
−0.750770 | + | 0.660564i | \(0.770317\pi\) | |||||||
\(998\) | 57.0172 | 1.80485 | ||||||||
\(999\) | 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 | 2169.2.a.e.1.7 | 7 | ||
3.2 | odd | 2 | 241.2.a.a.1.1 | ✓ | 7 | ||
12.11 | even | 2 | 3856.2.a.j.1.2 | 7 | |||
15.14 | odd | 2 | 6025.2.a.f.1.7 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
241.2.a.a.1.1 | ✓ | 7 | 3.2 | odd | 2 | ||
2169.2.a.e.1.7 | 7 | 1.1 | even | 1 | trivial | ||
3856.2.a.j.1.2 | 7 | 12.11 | even | 2 | |||
6025.2.a.f.1.7 | 7 | 15.14 | odd | 2 |