Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(1,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, 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("847.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.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: | \(6.76332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2525.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 5x + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.46673\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.46673 | 1.03714 | 0.518568 | − | 0.855036i | \(-0.326465\pi\) | ||||
0.518568 | + | 0.855036i | \(0.326465\pi\) | |||||||
\(3\) | −1.61803 | −0.934172 | −0.467086 | − | 0.884212i | \(-0.654696\pi\) | ||||
−0.467086 | + | 0.884212i | \(0.654696\pi\) | |||||||
\(4\) | 0.151302 | 0.0756511 | ||||||||
\(5\) | 0.466732 | 0.208729 | 0.104364 | − | 0.994539i | \(-0.466719\pi\) | ||||
0.104364 | + | 0.994539i | \(0.466719\pi\) | |||||||
\(6\) | −2.37322 | −0.968864 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.71154 | −0.958676 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | 0.684570 | 0.216480 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.244812 | −0.0706712 | ||||||||
\(13\) | 1.58232 | 0.438856 | 0.219428 | − | 0.975629i | \(-0.429581\pi\) | ||||
0.219428 | + | 0.975629i | \(0.429581\pi\) | |||||||
\(14\) | 1.46673 | 0.392001 | ||||||||
\(15\) | −0.755188 | −0.194989 | ||||||||
\(16\) | −4.27971 | −1.06993 | ||||||||
\(17\) | −5.22732 | −1.26781 | −0.633906 | − | 0.773410i | \(-0.718549\pi\) | ||||
−0.633906 | + | 0.773410i | \(0.718549\pi\) | |||||||
\(18\) | −0.560242 | −0.132050 | ||||||||
\(19\) | −4.22192 | −0.968575 | −0.484287 | − | 0.874909i | \(-0.660921\pi\) | ||||
−0.484287 | + | 0.874909i | \(0.660921\pi\) | |||||||
\(20\) | 0.0706175 | 0.0157906 | ||||||||
\(21\) | −1.61803 | −0.353084 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.80505 | −0.376380 | −0.188190 | − | 0.982133i | \(-0.560262\pi\) | ||||
−0.188190 | + | 0.982133i | \(0.560262\pi\) | |||||||
\(24\) | 4.38737 | 0.895568 | ||||||||
\(25\) | −4.78216 | −0.956432 | ||||||||
\(26\) | 2.32083 | 0.455153 | ||||||||
\(27\) | 5.47214 | 1.05311 | ||||||||
\(28\) | 0.151302 | 0.0285934 | ||||||||
\(29\) | −2.71947 | −0.504993 | −0.252496 | − | 0.967598i | \(-0.581252\pi\) | ||||
−0.252496 | + | 0.967598i | \(0.581252\pi\) | |||||||
\(30\) | −1.10766 | −0.202230 | ||||||||
\(31\) | 1.29386 | 0.232384 | 0.116192 | − | 0.993227i | \(-0.462931\pi\) | ||||
0.116192 | + | 0.993227i | \(0.462931\pi\) | |||||||
\(32\) | −0.854102 | −0.150985 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.66708 | −1.31489 | ||||||||
\(35\) | 0.466732 | 0.0788921 | ||||||||
\(36\) | −0.0577923 | −0.00963205 | ||||||||
\(37\) | −1.94221 | −0.319297 | −0.159648 | − | 0.987174i | \(-0.551036\pi\) | ||||
−0.159648 | + | 0.987174i | \(0.551036\pi\) | |||||||
\(38\) | −6.19242 | −1.00454 | ||||||||
\(39\) | −2.56024 | −0.409967 | ||||||||
\(40\) | −1.26556 | −0.200103 | ||||||||
\(41\) | 1.04112 | 0.162596 | 0.0812980 | − | 0.996690i | \(-0.474093\pi\) | ||||
0.0812980 | + | 0.996690i | \(0.474093\pi\) | |||||||
\(42\) | −2.37322 | −0.366196 | ||||||||
\(43\) | −8.70820 | −1.32799 | −0.663994 | − | 0.747738i | \(-0.731140\pi\) | ||||
−0.663994 | + | 0.747738i | \(0.731140\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.178276 | −0.0265758 | ||||||||
\(46\) | −2.64753 | −0.390357 | ||||||||
\(47\) | −6.39530 | −0.932850 | −0.466425 | − | 0.884561i | \(-0.654458\pi\) | ||||
−0.466425 | + | 0.884561i | \(0.654458\pi\) | |||||||
\(48\) | 6.92472 | 0.999497 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −7.01415 | −0.991950 | ||||||||
\(51\) | 8.45799 | 1.18436 | ||||||||
\(52\) | 0.239408 | 0.0331999 | ||||||||
\(53\) | −13.2044 | −1.81377 | −0.906884 | − | 0.421380i | \(-0.861546\pi\) | ||||
−0.906884 | + | 0.421380i | \(0.861546\pi\) | |||||||
\(54\) | 8.02616 | 1.09222 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.71154 | −0.362345 | ||||||||
\(57\) | 6.83121 | 0.904816 | ||||||||
\(58\) | −3.98873 | −0.523746 | ||||||||
\(59\) | −8.60389 | −1.12013 | −0.560065 | − | 0.828448i | \(-0.689224\pi\) | ||||
−0.560065 | + | 0.828448i | \(0.689224\pi\) | |||||||
\(60\) | −0.114262 | −0.0147511 | ||||||||
\(61\) | 15.2401 | 1.95130 | 0.975651 | − | 0.219331i | \(-0.0703874\pi\) | ||||
0.975651 | + | 0.219331i | \(0.0703874\pi\) | |||||||
\(62\) | 1.89775 | 0.241014 | ||||||||
\(63\) | −0.381966 | −0.0481232 | ||||||||
\(64\) | 7.30669 | 0.913336 | ||||||||
\(65\) | 0.738517 | 0.0916018 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.67583 | −0.571243 | −0.285622 | − | 0.958342i | \(-0.592200\pi\) | ||||
−0.285622 | + | 0.958342i | \(0.592200\pi\) | |||||||
\(68\) | −0.790906 | −0.0959114 | ||||||||
\(69\) | 2.92064 | 0.351604 | ||||||||
\(70\) | 0.684570 | 0.0818218 | ||||||||
\(71\) | 9.74310 | 1.15629 | 0.578147 | − | 0.815933i | \(-0.303776\pi\) | ||||
0.578147 | + | 0.815933i | \(0.303776\pi\) | |||||||
\(72\) | 1.03572 | 0.122060 | ||||||||
\(73\) | 13.3200 | 1.55899 | 0.779495 | − | 0.626408i | \(-0.215476\pi\) | ||||
0.779495 | + | 0.626408i | \(0.215476\pi\) | |||||||
\(74\) | −2.84870 | −0.331154 | ||||||||
\(75\) | 7.73770 | 0.893473 | ||||||||
\(76\) | −0.638786 | −0.0732737 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.75519 | −0.425191 | ||||||||
\(79\) | −3.58232 | −0.403042 | −0.201521 | − | 0.979484i | \(-0.564588\pi\) | ||||
−0.201521 | + | 0.979484i | \(0.564588\pi\) | |||||||
\(80\) | −1.99748 | −0.223325 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | 1.52705 | 0.168634 | ||||||||
\(83\) | 17.2589 | 1.89441 | 0.947204 | − | 0.320631i | \(-0.103895\pi\) | ||||
0.947204 | + | 0.320631i | \(0.103895\pi\) | |||||||
\(84\) | −0.244812 | −0.0267112 | ||||||||
\(85\) | −2.43976 | −0.264629 | ||||||||
\(86\) | −12.7726 | −1.37730 | ||||||||
\(87\) | 4.40020 | 0.471750 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.91982 | −0.945499 | −0.472750 | − | 0.881197i | \(-0.656738\pi\) | ||||
−0.472750 | + | 0.881197i | \(0.656738\pi\) | |||||||
\(90\) | −0.261483 | −0.0275627 | ||||||||
\(91\) | 1.58232 | 0.165872 | ||||||||
\(92\) | −0.273109 | −0.0284735 | ||||||||
\(93\) | −2.09351 | −0.217087 | ||||||||
\(94\) | −9.38018 | −0.967492 | ||||||||
\(95\) | −1.97050 | −0.202169 | ||||||||
\(96\) | 1.38197 | 0.141046 | ||||||||
\(97\) | −2.70362 | −0.274511 | −0.137255 | − | 0.990536i | \(-0.543828\pi\) | ||||
−0.137255 | + | 0.990536i | \(0.543828\pi\) | |||||||
\(98\) | 1.46673 | 0.148162 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.723551 | −0.0723551 | ||||||||
\(101\) | −0.178781 | −0.0177894 | −0.00889469 | − | 0.999960i | \(-0.502831\pi\) | ||||
−0.00889469 | + | 0.999960i | \(0.502831\pi\) | |||||||
\(102\) | 12.4056 | 1.22834 | ||||||||
\(103\) | 16.8772 | 1.66296 | 0.831481 | − | 0.555553i | \(-0.187493\pi\) | ||||
0.831481 | + | 0.555553i | \(0.187493\pi\) | |||||||
\(104\) | −4.29052 | −0.420720 | ||||||||
\(105\) | −0.755188 | −0.0736988 | ||||||||
\(106\) | −19.3674 | −1.88112 | ||||||||
\(107\) | 15.4762 | 1.49614 | 0.748071 | − | 0.663618i | \(-0.230980\pi\) | ||||
0.748071 | + | 0.663618i | \(0.230980\pi\) | |||||||
\(108\) | 0.827946 | 0.0796692 | ||||||||
\(109\) | −11.0349 | −1.05695 | −0.528476 | − | 0.848948i | \(-0.677236\pi\) | ||||
−0.528476 | + | 0.848948i | \(0.677236\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.14256 | 0.298278 | ||||||||
\(112\) | −4.27971 | −0.404395 | ||||||||
\(113\) | 1.77008 | 0.166515 | 0.0832574 | − | 0.996528i | \(-0.473468\pi\) | ||||
0.0832574 | + | 0.996528i | \(0.473468\pi\) | |||||||
\(114\) | 10.0196 | 0.938417 | ||||||||
\(115\) | −0.842476 | −0.0785613 | ||||||||
\(116\) | −0.411462 | −0.0382033 | ||||||||
\(117\) | −0.604391 | −0.0558760 | ||||||||
\(118\) | −12.6196 | −1.16173 | ||||||||
\(119\) | −5.22732 | −0.479188 | ||||||||
\(120\) | 2.04773 | 0.186931 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 22.3532 | 2.02376 | ||||||||
\(123\) | −1.68457 | −0.151893 | ||||||||
\(124\) | 0.195764 | 0.0175801 | ||||||||
\(125\) | −4.56565 | −0.408364 | ||||||||
\(126\) | −0.560242 | −0.0499103 | ||||||||
\(127\) | 8.54023 | 0.757823 | 0.378911 | − | 0.925433i | \(-0.376298\pi\) | ||||
0.378911 | + | 0.925433i | \(0.376298\pi\) | |||||||
\(128\) | 12.4252 | 1.09824 | ||||||||
\(129\) | 14.0902 | 1.24057 | ||||||||
\(130\) | 1.08321 | 0.0950035 | ||||||||
\(131\) | 9.66708 | 0.844617 | 0.422308 | − | 0.906452i | \(-0.361220\pi\) | ||||
0.422308 | + | 0.906452i | \(0.361220\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.22192 | −0.366087 | ||||||||
\(134\) | −6.85818 | −0.592457 | ||||||||
\(135\) | 2.55402 | 0.219815 | ||||||||
\(136\) | 14.1741 | 1.21542 | ||||||||
\(137\) | −14.0108 | −1.19702 | −0.598512 | − | 0.801114i | \(-0.704241\pi\) | ||||
−0.598512 | + | 0.801114i | \(0.704241\pi\) | |||||||
\(138\) | 4.28379 | 0.364661 | ||||||||
\(139\) | −9.57765 | −0.812366 | −0.406183 | − | 0.913792i | \(-0.633140\pi\) | ||||
−0.406183 | + | 0.913792i | \(0.633140\pi\) | |||||||
\(140\) | 0.0706175 | 0.00596827 | ||||||||
\(141\) | 10.3478 | 0.871443 | ||||||||
\(142\) | 14.2905 | 1.19923 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.63470 | 0.136225 | ||||||||
\(145\) | −1.26926 | −0.105407 | ||||||||
\(146\) | 19.5369 | 1.61688 | ||||||||
\(147\) | −1.61803 | −0.133453 | ||||||||
\(148\) | −0.293860 | −0.0241552 | ||||||||
\(149\) | −14.9625 | −1.22578 | −0.612888 | − | 0.790170i | \(-0.709992\pi\) | ||||
−0.612888 | + | 0.790170i | \(0.709992\pi\) | |||||||
\(150\) | 11.3491 | 0.926653 | ||||||||
\(151\) | 2.87233 | 0.233747 | 0.116874 | − | 0.993147i | \(-0.462713\pi\) | ||||
0.116874 | + | 0.993147i | \(0.462713\pi\) | |||||||
\(152\) | 11.4479 | 0.928549 | ||||||||
\(153\) | 1.99666 | 0.161420 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.603886 | 0.0485053 | ||||||||
\(156\) | −0.387370 | −0.0310144 | ||||||||
\(157\) | −18.8823 | −1.50697 | −0.753487 | − | 0.657463i | \(-0.771630\pi\) | ||||
−0.753487 | + | 0.657463i | \(0.771630\pi\) | |||||||
\(158\) | −5.25430 | −0.418009 | ||||||||
\(159\) | 21.3652 | 1.69437 | ||||||||
\(160\) | −0.398637 | −0.0315150 | ||||||||
\(161\) | −1.80505 | −0.142258 | ||||||||
\(162\) | −11.3059 | −0.888273 | ||||||||
\(163\) | 11.5951 | 0.908202 | 0.454101 | − | 0.890950i | \(-0.349961\pi\) | ||||
0.454101 | + | 0.890950i | \(0.349961\pi\) | |||||||
\(164\) | 0.157524 | 0.0123006 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 25.3142 | 1.96476 | ||||||||
\(167\) | −6.32491 | −0.489437 | −0.244718 | − | 0.969594i | \(-0.578695\pi\) | ||||
−0.244718 | + | 0.969594i | \(0.578695\pi\) | |||||||
\(168\) | 4.38737 | 0.338493 | ||||||||
\(169\) | −10.4963 | −0.807406 | ||||||||
\(170\) | −3.57847 | −0.274456 | ||||||||
\(171\) | 1.61263 | 0.123321 | ||||||||
\(172\) | −1.31757 | −0.100464 | ||||||||
\(173\) | −1.33906 | −0.101807 | −0.0509035 | − | 0.998704i | \(-0.516210\pi\) | ||||
−0.0509035 | + | 0.998704i | \(0.516210\pi\) | |||||||
\(174\) | 6.45391 | 0.489269 | ||||||||
\(175\) | −4.78216 | −0.361497 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.9214 | 1.04639 | ||||||||
\(178\) | −13.0830 | −0.980611 | ||||||||
\(179\) | 17.7888 | 1.32960 | 0.664799 | − | 0.747022i | \(-0.268517\pi\) | ||||
0.664799 | + | 0.747022i | \(0.268517\pi\) | |||||||
\(180\) | −0.0269735 | −0.00201049 | ||||||||
\(181\) | −0.963777 | −0.0716370 | −0.0358185 | − | 0.999358i | \(-0.511404\pi\) | ||||
−0.0358185 | + | 0.999358i | \(0.511404\pi\) | |||||||
\(182\) | 2.32083 | 0.172032 | ||||||||
\(183\) | −24.6591 | −1.82285 | ||||||||
\(184\) | 4.89448 | 0.360826 | ||||||||
\(185\) | −0.906490 | −0.0666465 | ||||||||
\(186\) | −3.07062 | −0.225149 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.967622 | −0.0705711 | ||||||||
\(189\) | 5.47214 | 0.398039 | ||||||||
\(190\) | −2.89020 | −0.209677 | ||||||||
\(191\) | −16.0888 | −1.16415 | −0.582074 | − | 0.813136i | \(-0.697759\pi\) | ||||
−0.582074 | + | 0.813136i | \(0.697759\pi\) | |||||||
\(192\) | −11.8225 | −0.853213 | ||||||||
\(193\) | −12.1475 | −0.874393 | −0.437197 | − | 0.899366i | \(-0.644029\pi\) | ||||
−0.437197 | + | 0.899366i | \(0.644029\pi\) | |||||||
\(194\) | −3.96548 | −0.284705 | ||||||||
\(195\) | −1.19495 | −0.0855719 | ||||||||
\(196\) | 0.151302 | 0.0108073 | ||||||||
\(197\) | 2.30179 | 0.163996 | 0.0819978 | − | 0.996633i | \(-0.473870\pi\) | ||||
0.0819978 | + | 0.996633i | \(0.473870\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.2797 | 1.43759 | 0.718795 | − | 0.695222i | \(-0.244694\pi\) | ||||
0.718795 | + | 0.695222i | \(0.244694\pi\) | |||||||
\(200\) | 12.9670 | 0.916908 | ||||||||
\(201\) | 7.56565 | 0.533640 | ||||||||
\(202\) | −0.262224 | −0.0184500 | ||||||||
\(203\) | −2.71947 | −0.190869 | ||||||||
\(204\) | 1.27971 | 0.0895978 | ||||||||
\(205\) | 0.485925 | 0.0339384 | ||||||||
\(206\) | 24.7544 | 1.72472 | ||||||||
\(207\) | 0.689469 | 0.0479214 | ||||||||
\(208\) | −6.77186 | −0.469544 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.10766 | −0.0764357 | ||||||||
\(211\) | −5.36530 | −0.369362 | −0.184681 | − | 0.982799i | \(-0.559125\pi\) | ||||
−0.184681 | + | 0.982799i | \(0.559125\pi\) | |||||||
\(212\) | −1.99786 | −0.137214 | ||||||||
\(213\) | −15.7647 | −1.08018 | ||||||||
\(214\) | 22.6995 | 1.55170 | ||||||||
\(215\) | −4.06440 | −0.277189 | ||||||||
\(216\) | −14.8379 | −1.00959 | ||||||||
\(217\) | 1.29386 | 0.0878330 | ||||||||
\(218\) | −16.1852 | −1.09620 | ||||||||
\(219\) | −21.5522 | −1.45637 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.27128 | −0.556387 | ||||||||
\(222\) | 4.60929 | 0.309355 | ||||||||
\(223\) | −25.4230 | −1.70245 | −0.851225 | − | 0.524800i | \(-0.824140\pi\) | ||||
−0.851225 | + | 0.524800i | \(0.824140\pi\) | |||||||
\(224\) | −0.854102 | −0.0570671 | ||||||||
\(225\) | 1.82662 | 0.121775 | ||||||||
\(226\) | 2.59623 | 0.172699 | ||||||||
\(227\) | 21.7098 | 1.44093 | 0.720464 | − | 0.693493i | \(-0.243929\pi\) | ||||
0.720464 | + | 0.693493i | \(0.243929\pi\) | |||||||
\(228\) | 1.03358 | 0.0684503 | ||||||||
\(229\) | 20.5307 | 1.35670 | 0.678352 | − | 0.734737i | \(-0.262694\pi\) | ||||
0.678352 | + | 0.734737i | \(0.262694\pi\) | |||||||
\(230\) | −1.23569 | −0.0814787 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.37396 | 0.484124 | ||||||||
\(233\) | −0.694056 | −0.0454691 | −0.0227345 | − | 0.999742i | \(-0.507237\pi\) | ||||
−0.0227345 | + | 0.999742i | \(0.507237\pi\) | |||||||
\(234\) | −0.886480 | −0.0579510 | ||||||||
\(235\) | −2.98489 | −0.194713 | ||||||||
\(236\) | −1.30179 | −0.0847391 | ||||||||
\(237\) | 5.79631 | 0.376511 | ||||||||
\(238\) | −7.66708 | −0.496983 | ||||||||
\(239\) | −0.346561 | −0.0224171 | −0.0112086 | − | 0.999937i | \(-0.503568\pi\) | ||||
−0.0112086 | + | 0.999937i | \(0.503568\pi\) | |||||||
\(240\) | 3.23199 | 0.208624 | ||||||||
\(241\) | 10.4372 | 0.672317 | 0.336158 | − | 0.941806i | \(-0.390872\pi\) | ||||
0.336158 | + | 0.941806i | \(0.390872\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.94427 | −0.253025 | ||||||||
\(244\) | 2.30587 | 0.147618 | ||||||||
\(245\) | 0.466732 | 0.0298184 | ||||||||
\(246\) | −2.47081 | −0.157533 | ||||||||
\(247\) | −6.68041 | −0.425064 | ||||||||
\(248\) | −3.50836 | −0.222781 | ||||||||
\(249\) | −27.9255 | −1.76970 | ||||||||
\(250\) | −6.69658 | −0.423529 | ||||||||
\(251\) | −6.99502 | −0.441522 | −0.220761 | − | 0.975328i | \(-0.570854\pi\) | ||||
−0.220761 | + | 0.975328i | \(0.570854\pi\) | |||||||
\(252\) | −0.0577923 | −0.00364057 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 12.5262 | 0.785965 | ||||||||
\(255\) | 3.94761 | 0.247209 | ||||||||
\(256\) | 3.61099 | 0.225687 | ||||||||
\(257\) | −9.94843 | −0.620566 | −0.310283 | − | 0.950644i | \(-0.600424\pi\) | ||||
−0.310283 | + | 0.950644i | \(0.600424\pi\) | |||||||
\(258\) | 20.6665 | 1.28664 | ||||||||
\(259\) | −1.94221 | −0.120683 | ||||||||
\(260\) | 0.111739 | 0.00692978 | ||||||||
\(261\) | 1.03875 | 0.0642967 | ||||||||
\(262\) | 14.1790 | 0.875983 | ||||||||
\(263\) | −14.1803 | −0.874397 | −0.437199 | − | 0.899365i | \(-0.644029\pi\) | ||||
−0.437199 | + | 0.899365i | \(0.644029\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.16293 | −0.378586 | ||||||||
\(266\) | −6.19242 | −0.379682 | ||||||||
\(267\) | 14.4326 | 0.883259 | ||||||||
\(268\) | −0.707463 | −0.0432152 | ||||||||
\(269\) | −18.4031 | −1.12206 | −0.561028 | − | 0.827797i | \(-0.689594\pi\) | ||||
−0.561028 | + | 0.827797i | \(0.689594\pi\) | |||||||
\(270\) | 3.74606 | 0.227978 | ||||||||
\(271\) | −0.730591 | −0.0443802 | −0.0221901 | − | 0.999754i | \(-0.507064\pi\) | ||||
−0.0221901 | + | 0.999754i | \(0.507064\pi\) | |||||||
\(272\) | 22.3714 | 1.35647 | ||||||||
\(273\) | −2.56024 | −0.154953 | ||||||||
\(274\) | −20.5501 | −1.24148 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.441899 | 0.0265992 | ||||||||
\(277\) | −15.0644 | −0.905132 | −0.452566 | − | 0.891731i | \(-0.649491\pi\) | ||||
−0.452566 | + | 0.891731i | \(0.649491\pi\) | |||||||
\(278\) | −14.0478 | −0.842534 | ||||||||
\(279\) | −0.494211 | −0.0295876 | ||||||||
\(280\) | −1.26556 | −0.0756319 | ||||||||
\(281\) | 10.6961 | 0.638077 | 0.319039 | − | 0.947742i | \(-0.396640\pi\) | ||||
0.319039 | + | 0.947742i | \(0.396640\pi\) | |||||||
\(282\) | 15.1775 | 0.903804 | ||||||||
\(283\) | −9.10890 | −0.541468 | −0.270734 | − | 0.962654i | \(-0.587266\pi\) | ||||
−0.270734 | + | 0.962654i | \(0.587266\pi\) | |||||||
\(284\) | 1.47415 | 0.0874749 | ||||||||
\(285\) | 3.18834 | 0.188861 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.04112 | 0.0614555 | ||||||||
\(288\) | 0.326238 | 0.0192238 | ||||||||
\(289\) | 10.3249 | 0.607348 | ||||||||
\(290\) | −1.86167 | −0.109321 | ||||||||
\(291\) | 4.37454 | 0.256440 | ||||||||
\(292\) | 2.01535 | 0.117939 | ||||||||
\(293\) | −11.8890 | −0.694563 | −0.347281 | − | 0.937761i | \(-0.612895\pi\) | ||||
−0.347281 | + | 0.937761i | \(0.612895\pi\) | |||||||
\(294\) | −2.37322 | −0.138409 | ||||||||
\(295\) | −4.01571 | −0.233804 | ||||||||
\(296\) | 5.26638 | 0.306102 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −21.9460 | −1.27130 | ||||||||
\(299\) | −2.85617 | −0.165176 | ||||||||
\(300\) | 1.17073 | 0.0675922 | ||||||||
\(301\) | −8.70820 | −0.501933 | ||||||||
\(302\) | 4.21294 | 0.242427 | ||||||||
\(303\) | 0.289274 | 0.0166183 | ||||||||
\(304\) | 18.0686 | 1.03631 | ||||||||
\(305\) | 7.11306 | 0.407293 | ||||||||
\(306\) | 2.92856 | 0.167415 | ||||||||
\(307\) | −2.22072 | −0.126743 | −0.0633716 | − | 0.997990i | \(-0.520185\pi\) | ||||
−0.0633716 | + | 0.997990i | \(0.520185\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −27.3079 | −1.55349 | ||||||||
\(310\) | 0.885738 | 0.0503066 | ||||||||
\(311\) | −21.4126 | −1.21420 | −0.607098 | − | 0.794627i | \(-0.707666\pi\) | ||||
−0.607098 | + | 0.794627i | \(0.707666\pi\) | |||||||
\(312\) | 6.94221 | 0.393025 | ||||||||
\(313\) | −31.5548 | −1.78358 | −0.891790 | − | 0.452449i | \(-0.850550\pi\) | ||||
−0.891790 | + | 0.452449i | \(0.850550\pi\) | |||||||
\(314\) | −27.6953 | −1.56294 | ||||||||
\(315\) | −0.178276 | −0.0100447 | ||||||||
\(316\) | −0.542012 | −0.0304906 | ||||||||
\(317\) | −13.2007 | −0.741423 | −0.370712 | − | 0.928748i | \(-0.620886\pi\) | ||||
−0.370712 | + | 0.928748i | \(0.620886\pi\) | |||||||
\(318\) | 31.3370 | 1.75729 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.41026 | 0.190639 | ||||||||
\(321\) | −25.0410 | −1.39765 | ||||||||
\(322\) | −2.64753 | −0.147541 | ||||||||
\(323\) | 22.0693 | 1.22797 | ||||||||
\(324\) | −1.16627 | −0.0647927 | ||||||||
\(325\) | −7.56689 | −0.419736 | ||||||||
\(326\) | 17.0070 | 0.941929 | ||||||||
\(327\) | 17.8548 | 0.987375 | ||||||||
\(328\) | −2.82305 | −0.155877 | ||||||||
\(329\) | −6.39530 | −0.352584 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.47653 | 0.520877 | 0.260439 | − | 0.965490i | \(-0.416133\pi\) | ||||
0.260439 | + | 0.965490i | \(0.416133\pi\) | |||||||
\(332\) | 2.61131 | 0.143314 | ||||||||
\(333\) | 0.741857 | 0.0406535 | ||||||||
\(334\) | −9.27695 | −0.507612 | ||||||||
\(335\) | −2.18236 | −0.119235 | ||||||||
\(336\) | 6.92472 | 0.377774 | ||||||||
\(337\) | 19.2011 | 1.04595 | 0.522975 | − | 0.852348i | \(-0.324822\pi\) | ||||
0.522975 | + | 0.852348i | \(0.324822\pi\) | |||||||
\(338\) | −15.3952 | −0.837390 | ||||||||
\(339\) | −2.86405 | −0.155554 | ||||||||
\(340\) | −0.369141 | −0.0200195 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.36530 | 0.127901 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 23.6127 | 1.27311 | ||||||||
\(345\) | 1.36315 | 0.0733898 | ||||||||
\(346\) | −1.96405 | −0.105588 | ||||||||
\(347\) | −3.04831 | −0.163642 | −0.0818208 | − | 0.996647i | \(-0.526074\pi\) | ||||
−0.0818208 | + | 0.996647i | \(0.526074\pi\) | |||||||
\(348\) | 0.665759 | 0.0356884 | ||||||||
\(349\) | −19.3961 | −1.03825 | −0.519125 | − | 0.854698i | \(-0.673742\pi\) | ||||
−0.519125 | + | 0.854698i | \(0.673742\pi\) | |||||||
\(350\) | −7.01415 | −0.374922 | ||||||||
\(351\) | 8.65865 | 0.462165 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.7585 | −0.572619 | −0.286309 | − | 0.958137i | \(-0.592428\pi\) | ||||
−0.286309 | + | 0.958137i | \(0.592428\pi\) | |||||||
\(354\) | 20.4189 | 1.08525 | ||||||||
\(355\) | 4.54742 | 0.241352 | ||||||||
\(356\) | −1.34959 | −0.0715280 | ||||||||
\(357\) | 8.45799 | 0.447644 | ||||||||
\(358\) | 26.0914 | 1.37897 | ||||||||
\(359\) | −0.607226 | −0.0320481 | −0.0160241 | − | 0.999872i | \(-0.505101\pi\) | ||||
−0.0160241 | + | 0.999872i | \(0.505101\pi\) | |||||||
\(360\) | 0.483402 | 0.0254775 | ||||||||
\(361\) | −1.17539 | −0.0618628 | ||||||||
\(362\) | −1.41360 | −0.0742973 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.239408 | 0.0125484 | ||||||||
\(365\) | 6.21688 | 0.325406 | ||||||||
\(366\) | −36.1683 | −1.89055 | ||||||||
\(367\) | 27.6628 | 1.44399 | 0.721994 | − | 0.691899i | \(-0.243226\pi\) | ||||
0.721994 | + | 0.691899i | \(0.243226\pi\) | |||||||
\(368\) | 7.72511 | 0.402699 | ||||||||
\(369\) | −0.397673 | −0.0207020 | ||||||||
\(370\) | −1.32958 | −0.0691215 | ||||||||
\(371\) | −13.2044 | −0.685540 | ||||||||
\(372\) | −0.316753 | −0.0164229 | ||||||||
\(373\) | 29.4513 | 1.52493 | 0.762465 | − | 0.647029i | \(-0.223989\pi\) | ||||
0.762465 | + | 0.647029i | \(0.223989\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.38737 | 0.381482 | ||||||||
\(376\) | 17.3411 | 0.894300 | ||||||||
\(377\) | −4.30306 | −0.221619 | ||||||||
\(378\) | 8.02616 | 0.412821 | ||||||||
\(379\) | 25.3436 | 1.30182 | 0.650908 | − | 0.759157i | \(-0.274388\pi\) | ||||
0.650908 | + | 0.759157i | \(0.274388\pi\) | |||||||
\(380\) | −0.298142 | −0.0152943 | ||||||||
\(381\) | −13.8184 | −0.707937 | ||||||||
\(382\) | −23.5980 | −1.20738 | ||||||||
\(383\) | −31.9322 | −1.63166 | −0.815829 | − | 0.578293i | \(-0.803719\pi\) | ||||
−0.815829 | + | 0.578293i | \(0.803719\pi\) | |||||||
\(384\) | −20.1043 | −1.02594 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.8171 | −0.906865 | ||||||||
\(387\) | 3.32624 | 0.169082 | ||||||||
\(388\) | −0.409063 | −0.0207670 | ||||||||
\(389\) | 17.7517 | 0.900047 | 0.450024 | − | 0.893017i | \(-0.351416\pi\) | ||||
0.450024 | + | 0.893017i | \(0.351416\pi\) | |||||||
\(390\) | −1.75267 | −0.0887497 | ||||||||
\(391\) | 9.43560 | 0.477179 | ||||||||
\(392\) | −2.71154 | −0.136954 | ||||||||
\(393\) | −15.6417 | −0.789018 | ||||||||
\(394\) | 3.37610 | 0.170086 | ||||||||
\(395\) | −1.67198 | −0.0841265 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.3047 | −0.667742 | −0.333871 | − | 0.942619i | \(-0.608355\pi\) | ||||
−0.333871 | + | 0.942619i | \(0.608355\pi\) | |||||||
\(398\) | 29.7449 | 1.49098 | ||||||||
\(399\) | 6.83121 | 0.341988 | ||||||||
\(400\) | 20.4663 | 1.02331 | ||||||||
\(401\) | −3.48962 | −0.174264 | −0.0871318 | − | 0.996197i | \(-0.527770\pi\) | ||||
−0.0871318 | + | 0.996197i | \(0.527770\pi\) | |||||||
\(402\) | 11.0968 | 0.553457 | ||||||||
\(403\) | 2.04730 | 0.101983 | ||||||||
\(404\) | −0.0270500 | −0.00134579 | ||||||||
\(405\) | −3.59766 | −0.178769 | ||||||||
\(406\) | −3.98873 | −0.197958 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −22.9342 | −1.13541 | ||||||||
\(409\) | 29.6255 | 1.46489 | 0.732443 | − | 0.680828i | \(-0.238380\pi\) | ||||
0.732443 | + | 0.680828i | \(0.238380\pi\) | |||||||
\(410\) | 0.712721 | 0.0351988 | ||||||||
\(411\) | 22.6700 | 1.11823 | ||||||||
\(412\) | 2.55356 | 0.125805 | ||||||||
\(413\) | −8.60389 | −0.423370 | ||||||||
\(414\) | 1.01127 | 0.0497010 | ||||||||
\(415\) | 8.05527 | 0.395418 | ||||||||
\(416\) | −1.35146 | −0.0662608 | ||||||||
\(417\) | 15.4970 | 0.758890 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.6452 | −0.568907 | −0.284454 | − | 0.958690i | \(-0.591812\pi\) | ||||
−0.284454 | + | 0.958690i | \(0.591812\pi\) | |||||||
\(420\) | −0.114262 | −0.00557539 | ||||||||
\(421\) | 19.8848 | 0.969128 | 0.484564 | − | 0.874756i | \(-0.338978\pi\) | ||||
0.484564 | + | 0.874756i | \(0.338978\pi\) | |||||||
\(422\) | −7.86945 | −0.383079 | ||||||||
\(423\) | 2.44279 | 0.118772 | ||||||||
\(424\) | 35.8044 | 1.73882 | ||||||||
\(425\) | 24.9979 | 1.21258 | ||||||||
\(426\) | −23.1225 | −1.12029 | ||||||||
\(427\) | 15.2401 | 0.737523 | ||||||||
\(428\) | 2.34159 | 0.113185 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.96138 | −0.287483 | ||||||||
\(431\) | −30.2464 | −1.45692 | −0.728458 | − | 0.685090i | \(-0.759763\pi\) | ||||
−0.728458 | + | 0.685090i | \(0.759763\pi\) | |||||||
\(432\) | −23.4192 | −1.12676 | ||||||||
\(433\) | −5.70719 | −0.274270 | −0.137135 | − | 0.990552i | \(-0.543789\pi\) | ||||
−0.137135 | + | 0.990552i | \(0.543789\pi\) | |||||||
\(434\) | 1.89775 | 0.0910947 | ||||||||
\(435\) | 2.05371 | 0.0984679 | ||||||||
\(436\) | −1.66960 | −0.0799596 | ||||||||
\(437\) | 7.62079 | 0.364552 | ||||||||
\(438\) | −31.6114 | −1.51045 | ||||||||
\(439\) | −6.84875 | −0.326873 | −0.163436 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163436 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.381966 | −0.0181889 | ||||||||
\(442\) | −12.1317 | −0.577048 | ||||||||
\(443\) | 0.100695 | 0.00478417 | 0.00239209 | − | 0.999997i | \(-0.499239\pi\) | ||||
0.00239209 | + | 0.999997i | \(0.499239\pi\) | |||||||
\(444\) | 0.475476 | 0.0225651 | ||||||||
\(445\) | −4.16316 | −0.197353 | ||||||||
\(446\) | −37.2887 | −1.76567 | ||||||||
\(447\) | 24.2098 | 1.14509 | ||||||||
\(448\) | 7.30669 | 0.345208 | ||||||||
\(449\) | −30.8047 | −1.45377 | −0.726883 | − | 0.686762i | \(-0.759032\pi\) | ||||
−0.726883 | + | 0.686762i | \(0.759032\pi\) | |||||||
\(450\) | 2.67917 | 0.126297 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.267817 | 0.0125970 | ||||||||
\(453\) | −4.64753 | −0.218360 | ||||||||
\(454\) | 31.8424 | 1.49444 | ||||||||
\(455\) | 0.738517 | 0.0346222 | ||||||||
\(456\) | −18.5231 | −0.867425 | ||||||||
\(457\) | −23.1356 | −1.08224 | −0.541118 | − | 0.840947i | \(-0.681999\pi\) | ||||
−0.541118 | + | 0.840947i | \(0.681999\pi\) | |||||||
\(458\) | 30.1130 | 1.40709 | ||||||||
\(459\) | −28.6046 | −1.33515 | ||||||||
\(460\) | −0.127468 | −0.00594325 | ||||||||
\(461\) | 2.77839 | 0.129403 | 0.0647013 | − | 0.997905i | \(-0.479391\pi\) | ||||
0.0647013 | + | 0.997905i | \(0.479391\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.0950 | −1.21274 | −0.606369 | − | 0.795184i | \(-0.707374\pi\) | ||||
−0.606369 | + | 0.795184i | \(0.707374\pi\) | |||||||
\(464\) | 11.6385 | 0.540306 | ||||||||
\(465\) | −0.977108 | −0.0453123 | ||||||||
\(466\) | −1.01799 | −0.0471576 | ||||||||
\(467\) | −2.65829 | −0.123011 | −0.0615055 | − | 0.998107i | \(-0.519590\pi\) | ||||
−0.0615055 | + | 0.998107i | \(0.519590\pi\) | |||||||
\(468\) | −0.0914457 | −0.00422708 | ||||||||
\(469\) | −4.67583 | −0.215910 | ||||||||
\(470\) | −4.37803 | −0.201943 | ||||||||
\(471\) | 30.5522 | 1.40777 | ||||||||
\(472\) | 23.3298 | 1.07384 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 8.50163 | 0.390493 | ||||||||
\(475\) | 20.1899 | 0.926376 | ||||||||
\(476\) | −0.790906 | −0.0362511 | ||||||||
\(477\) | 5.04364 | 0.230933 | ||||||||
\(478\) | −0.508312 | −0.0232496 | ||||||||
\(479\) | 8.28223 | 0.378425 | 0.189212 | − | 0.981936i | \(-0.439407\pi\) | ||||
0.189212 | + | 0.981936i | \(0.439407\pi\) | |||||||
\(480\) | 0.645007 | 0.0294404 | ||||||||
\(481\) | −3.07319 | −0.140125 | ||||||||
\(482\) | 15.3085 | 0.697284 | ||||||||
\(483\) | 2.92064 | 0.132894 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.26186 | −0.0572983 | ||||||||
\(486\) | −5.78519 | −0.262422 | ||||||||
\(487\) | −19.5956 | −0.887960 | −0.443980 | − | 0.896037i | \(-0.646434\pi\) | ||||
−0.443980 | + | 0.896037i | \(0.646434\pi\) | |||||||
\(488\) | −41.3243 | −1.87066 | ||||||||
\(489\) | −18.7613 | −0.848417 | ||||||||
\(490\) | 0.684570 | 0.0309257 | ||||||||
\(491\) | 28.6817 | 1.29439 | 0.647193 | − | 0.762327i | \(-0.275943\pi\) | ||||
0.647193 | + | 0.762327i | \(0.275943\pi\) | |||||||
\(492\) | −0.254879 | −0.0114908 | ||||||||
\(493\) | 14.2156 | 0.640236 | ||||||||
\(494\) | −9.79837 | −0.440850 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.53735 | −0.248634 | ||||||||
\(497\) | 9.74310 | 0.437038 | ||||||||
\(498\) | −40.9592 | −1.83542 | ||||||||
\(499\) | 27.9499 | 1.25121 | 0.625605 | − | 0.780140i | \(-0.284852\pi\) | ||||
0.625605 | + | 0.780140i | \(0.284852\pi\) | |||||||
\(500\) | −0.690792 | −0.0308932 | ||||||||
\(501\) | 10.2339 | 0.457218 | ||||||||
\(502\) | −10.2598 | −0.457918 | ||||||||
\(503\) | 8.09736 | 0.361043 | 0.180522 | − | 0.983571i | \(-0.442221\pi\) | ||||
0.180522 | + | 0.983571i | \(0.442221\pi\) | |||||||
\(504\) | 1.03572 | 0.0461345 | ||||||||
\(505\) | −0.0834428 | −0.00371316 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.9833 | 0.754256 | ||||||||
\(508\) | 1.29216 | 0.0573301 | ||||||||
\(509\) | 16.3002 | 0.722492 | 0.361246 | − | 0.932471i | \(-0.382352\pi\) | ||||
0.361246 | + | 0.932471i | \(0.382352\pi\) | |||||||
\(510\) | 5.79009 | 0.256389 | ||||||||
\(511\) | 13.3200 | 0.589243 | ||||||||
\(512\) | −19.5539 | −0.864170 | ||||||||
\(513\) | −23.1029 | −1.02002 | ||||||||
\(514\) | −14.5917 | −0.643611 | ||||||||
\(515\) | 7.87714 | 0.347108 | ||||||||
\(516\) | 2.13187 | 0.0938505 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.84870 | −0.125165 | ||||||||
\(519\) | 2.16665 | 0.0951054 | ||||||||
\(520\) | −2.00252 | −0.0878164 | ||||||||
\(521\) | 7.68605 | 0.336732 | 0.168366 | − | 0.985725i | \(-0.446151\pi\) | ||||
0.168366 | + | 0.985725i | \(0.446151\pi\) | |||||||
\(522\) | 1.52356 | 0.0666844 | ||||||||
\(523\) | −26.1229 | −1.14228 | −0.571138 | − | 0.820854i | \(-0.693498\pi\) | ||||
−0.571138 | + | 0.820854i | \(0.693498\pi\) | |||||||
\(524\) | 1.46265 | 0.0638962 | ||||||||
\(525\) | 7.73770 | 0.337701 | ||||||||
\(526\) | −20.7988 | −0.906869 | ||||||||
\(527\) | −6.76343 | −0.294619 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.7418 | −0.858338 | ||||||||
\(530\) | −9.03936 | −0.392645 | ||||||||
\(531\) | 3.28639 | 0.142617 | ||||||||
\(532\) | −0.638786 | −0.0276949 | ||||||||
\(533\) | 1.64738 | 0.0713561 | ||||||||
\(534\) | 21.1687 | 0.916060 | ||||||||
\(535\) | 7.22324 | 0.312288 | ||||||||
\(536\) | 12.6787 | 0.547637 | ||||||||
\(537\) | −28.7829 | −1.24207 | ||||||||
\(538\) | −26.9924 | −1.16372 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.386429 | 0.0166292 | ||||||||
\(541\) | 25.8777 | 1.11257 | 0.556284 | − | 0.830992i | \(-0.312227\pi\) | ||||
0.556284 | + | 0.830992i | \(0.312227\pi\) | |||||||
\(542\) | −1.07158 | −0.0460283 | ||||||||
\(543\) | 1.55942 | 0.0669213 | ||||||||
\(544\) | 4.46467 | 0.191421 | ||||||||
\(545\) | −5.15034 | −0.220616 | ||||||||
\(546\) | −3.75519 | −0.160707 | ||||||||
\(547\) | 38.0968 | 1.62890 | 0.814451 | − | 0.580232i | \(-0.197038\pi\) | ||||
0.814451 | + | 0.580232i | \(0.197038\pi\) | |||||||
\(548\) | −2.11987 | −0.0905562 | ||||||||
\(549\) | −5.82122 | −0.248444 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.4814 | 0.489123 | ||||||||
\(552\) | −7.91944 | −0.337074 | ||||||||
\(553\) | −3.58232 | −0.152336 | ||||||||
\(554\) | −22.0954 | −0.938745 | ||||||||
\(555\) | 1.46673 | 0.0622593 | ||||||||
\(556\) | −1.44912 | −0.0614564 | ||||||||
\(557\) | −34.5422 | −1.46360 | −0.731799 | − | 0.681520i | \(-0.761319\pi\) | ||||
−0.731799 | + | 0.681520i | \(0.761319\pi\) | |||||||
\(558\) | −0.724874 | −0.0306864 | ||||||||
\(559\) | −13.7791 | −0.582795 | ||||||||
\(560\) | −1.99748 | −0.0844088 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.6883 | 0.661773 | ||||||||
\(563\) | −19.4819 | −0.821066 | −0.410533 | − | 0.911846i | \(-0.634657\pi\) | ||||
−0.410533 | + | 0.911846i | \(0.634657\pi\) | |||||||
\(564\) | 1.56565 | 0.0659256 | ||||||||
\(565\) | 0.826151 | 0.0347565 | ||||||||
\(566\) | −13.3603 | −0.561576 | ||||||||
\(567\) | −7.70820 | −0.323714 | ||||||||
\(568\) | −26.4189 | −1.10851 | ||||||||
\(569\) | −17.1288 | −0.718075 | −0.359038 | − | 0.933323i | \(-0.616895\pi\) | ||||
−0.359038 | + | 0.933323i | \(0.616895\pi\) | |||||||
\(570\) | 4.67644 | 0.195875 | ||||||||
\(571\) | 3.85581 | 0.161360 | 0.0806802 | − | 0.996740i | \(-0.474291\pi\) | ||||
0.0806802 | + | 0.996740i | \(0.474291\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.0323 | 1.08751 | ||||||||
\(574\) | 1.52705 | 0.0637377 | ||||||||
\(575\) | 8.63206 | 0.359982 | ||||||||
\(576\) | −2.79091 | −0.116288 | ||||||||
\(577\) | −9.78185 | −0.407224 | −0.203612 | − | 0.979052i | \(-0.565268\pi\) | ||||
−0.203612 | + | 0.979052i | \(0.565268\pi\) | |||||||
\(578\) | 15.1439 | 0.629902 | ||||||||
\(579\) | 19.6550 | 0.816834 | ||||||||
\(580\) | −0.192042 | −0.00797412 | ||||||||
\(581\) | 17.2589 | 0.716019 | ||||||||
\(582\) | 6.41628 | 0.265964 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −36.1178 | −1.49457 | ||||||||
\(585\) | −0.282089 | −0.0116629 | ||||||||
\(586\) | −17.4380 | −0.720356 | ||||||||
\(587\) | −6.09891 | −0.251729 | −0.125865 | − | 0.992047i | \(-0.540170\pi\) | ||||
−0.125865 | + | 0.992047i | \(0.540170\pi\) | |||||||
\(588\) | −0.244812 | −0.0100959 | ||||||||
\(589\) | −5.46257 | −0.225081 | ||||||||
\(590\) | −5.88997 | −0.242486 | ||||||||
\(591\) | −3.72437 | −0.153200 | ||||||||
\(592\) | 8.31209 | 0.341625 | ||||||||
\(593\) | −13.2330 | −0.543413 | −0.271706 | − | 0.962380i | \(-0.587588\pi\) | ||||
−0.271706 | + | 0.962380i | \(0.587588\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.43976 | −0.100020 | ||||||||
\(596\) | −2.26386 | −0.0927313 | ||||||||
\(597\) | −32.8133 | −1.34296 | ||||||||
\(598\) | −4.18923 | −0.171310 | ||||||||
\(599\) | −5.92515 | −0.242095 | −0.121048 | − | 0.992647i | \(-0.538625\pi\) | ||||
−0.121048 | + | 0.992647i | \(0.538625\pi\) | |||||||
\(600\) | −20.9811 | −0.856550 | ||||||||
\(601\) | −12.7408 | −0.519708 | −0.259854 | − | 0.965648i | \(-0.583674\pi\) | ||||
−0.259854 | + | 0.965648i | \(0.583674\pi\) | |||||||
\(602\) | −12.7726 | −0.520572 | ||||||||
\(603\) | 1.78601 | 0.0727318 | ||||||||
\(604\) | 0.434590 | 0.0176832 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.424287 | 0.0172355 | ||||||||
\(607\) | −8.36141 | −0.339379 | −0.169690 | − | 0.985498i | \(-0.554276\pi\) | ||||
−0.169690 | + | 0.985498i | \(0.554276\pi\) | |||||||
\(608\) | 3.60595 | 0.146241 | ||||||||
\(609\) | 4.40020 | 0.178305 | ||||||||
\(610\) | 10.4330 | 0.422418 | ||||||||
\(611\) | −10.1194 | −0.409386 | ||||||||
\(612\) | 0.302099 | 0.0122116 | ||||||||
\(613\) | 6.68294 | 0.269921 | 0.134961 | − | 0.990851i | \(-0.456909\pi\) | ||||
0.134961 | + | 0.990851i | \(0.456909\pi\) | |||||||
\(614\) | −3.25720 | −0.131450 | ||||||||
\(615\) | −0.786243 | −0.0317044 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.8669 | 0.477741 | 0.238871 | − | 0.971051i | \(-0.423223\pi\) | ||||
0.238871 | + | 0.971051i | \(0.423223\pi\) | |||||||
\(618\) | −40.0534 | −1.61118 | ||||||||
\(619\) | 20.6206 | 0.828814 | 0.414407 | − | 0.910092i | \(-0.363989\pi\) | ||||
0.414407 | + | 0.910092i | \(0.363989\pi\) | |||||||
\(620\) | 0.0913692 | 0.00366948 | ||||||||
\(621\) | −9.87750 | −0.396370 | ||||||||
\(622\) | −31.4065 | −1.25929 | ||||||||
\(623\) | −8.91982 | −0.357365 | ||||||||
\(624\) | 10.9571 | 0.438635 | ||||||||
\(625\) | 21.7799 | 0.871195 | ||||||||
\(626\) | −46.2824 | −1.84982 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.85694 | −0.114004 | ||||||||
\(629\) | 10.1525 | 0.404809 | ||||||||
\(630\) | −0.261483 | −0.0104177 | ||||||||
\(631\) | −15.4795 | −0.616228 | −0.308114 | − | 0.951349i | \(-0.599698\pi\) | ||||
−0.308114 | + | 0.951349i | \(0.599698\pi\) | |||||||
\(632\) | 9.71361 | 0.386387 | ||||||||
\(633\) | 8.68123 | 0.345048 | ||||||||
\(634\) | −19.3618 | −0.768957 | ||||||||
\(635\) | 3.98600 | 0.158179 | ||||||||
\(636\) | 3.23260 | 0.128181 | ||||||||
\(637\) | 1.58232 | 0.0626937 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.72153 | −0.147222 | ||||||||
\(640\) | 5.79921 | 0.229234 | ||||||||
\(641\) | −23.5785 | −0.931294 | −0.465647 | − | 0.884971i | \(-0.654178\pi\) | ||||
−0.465647 | + | 0.884971i | \(0.654178\pi\) | |||||||
\(642\) | −36.7285 | −1.44956 | ||||||||
\(643\) | 28.6806 | 1.13105 | 0.565527 | − | 0.824730i | \(-0.308673\pi\) | ||||
0.565527 | + | 0.824730i | \(0.308673\pi\) | |||||||
\(644\) | −0.273109 | −0.0107620 | ||||||||
\(645\) | 6.57633 | 0.258943 | ||||||||
\(646\) | 32.3698 | 1.27357 | ||||||||
\(647\) | 5.42763 | 0.213382 | 0.106691 | − | 0.994292i | \(-0.465974\pi\) | ||||
0.106691 | + | 0.994292i | \(0.465974\pi\) | |||||||
\(648\) | 20.9011 | 0.821074 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −11.0986 | −0.435323 | ||||||||
\(651\) | −2.09351 | −0.0820511 | ||||||||
\(652\) | 1.75437 | 0.0687064 | ||||||||
\(653\) | −12.3421 | −0.482983 | −0.241492 | − | 0.970403i | \(-0.577637\pi\) | ||||
−0.241492 | + | 0.970403i | \(0.577637\pi\) | |||||||
\(654\) | 26.1883 | 1.02404 | ||||||||
\(655\) | 4.51193 | 0.176296 | ||||||||
\(656\) | −4.45570 | −0.173966 | ||||||||
\(657\) | −5.08779 | −0.198494 | ||||||||
\(658\) | −9.38018 | −0.365678 | ||||||||
\(659\) | −16.2115 | −0.631512 | −0.315756 | − | 0.948840i | \(-0.602258\pi\) | ||||
−0.315756 | + | 0.948840i | \(0.602258\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.7050 | 1.69993 | 0.849964 | − | 0.526840i | \(-0.176623\pi\) | ||||
0.849964 | + | 0.526840i | \(0.176623\pi\) | |||||||
\(662\) | 13.8995 | 0.540220 | ||||||||
\(663\) | 13.3832 | 0.519761 | ||||||||
\(664\) | −46.7982 | −1.81612 | ||||||||
\(665\) | −1.97050 | −0.0764129 | ||||||||
\(666\) | 1.08811 | 0.0421632 | ||||||||
\(667\) | 4.90879 | 0.190069 | ||||||||
\(668\) | −0.956973 | −0.0370264 | ||||||||
\(669\) | 41.1353 | 1.59038 | ||||||||
\(670\) | −3.20093 | −0.123663 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.38197 | 0.0533105 | ||||||||
\(673\) | 5.86102 | 0.225926 | 0.112963 | − | 0.993599i | \(-0.463966\pi\) | ||||
0.112963 | + | 0.993599i | \(0.463966\pi\) | |||||||
\(674\) | 28.1629 | 1.08479 | ||||||||
\(675\) | −26.1686 | −1.00723 | ||||||||
\(676\) | −1.58811 | −0.0610811 | ||||||||
\(677\) | 20.5279 | 0.788952 | 0.394476 | − | 0.918906i | \(-0.370926\pi\) | ||||
0.394476 | + | 0.918906i | \(0.370926\pi\) | |||||||
\(678\) | −4.20079 | −0.161330 | ||||||||
\(679\) | −2.70362 | −0.103755 | ||||||||
\(680\) | 6.61551 | 0.253693 | ||||||||
\(681\) | −35.1271 | −1.34607 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.7055 | 1.48103 | 0.740513 | − | 0.672042i | \(-0.234583\pi\) | ||||
0.740513 | + | 0.672042i | \(0.234583\pi\) | |||||||
\(684\) | 0.243994 | 0.00932936 | ||||||||
\(685\) | −6.53929 | −0.249853 | ||||||||
\(686\) | 1.46673 | 0.0560001 | ||||||||
\(687\) | −33.2193 | −1.26740 | ||||||||
\(688\) | 37.2686 | 1.42085 | ||||||||
\(689\) | −20.8936 | −0.795982 | ||||||||
\(690\) | 1.99938 | 0.0761152 | ||||||||
\(691\) | −23.1300 | −0.879907 | −0.439954 | − | 0.898020i | \(-0.645005\pi\) | ||||
−0.439954 | + | 0.898020i | \(0.645005\pi\) | |||||||
\(692\) | −0.202603 | −0.00770182 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.47105 | −0.169719 | ||||||||
\(695\) | −4.47020 | −0.169564 | ||||||||
\(696\) | −11.9313 | −0.452256 | ||||||||
\(697\) | −5.44228 | −0.206141 | ||||||||
\(698\) | −28.4489 | −1.07681 | ||||||||
\(699\) | 1.12301 | 0.0424760 | ||||||||
\(700\) | −0.723551 | −0.0273477 | ||||||||
\(701\) | −35.5107 | −1.34122 | −0.670610 | − | 0.741810i | \(-0.733968\pi\) | ||||
−0.670610 | + | 0.741810i | \(0.733968\pi\) | |||||||
\(702\) | 12.6999 | 0.479328 | ||||||||
\(703\) | 8.19985 | 0.309263 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.82965 | 0.181895 | ||||||||
\(706\) | −15.7799 | −0.593883 | ||||||||
\(707\) | −0.178781 | −0.00672375 | ||||||||
\(708\) | 2.10634 | 0.0791609 | ||||||||
\(709\) | 43.8045 | 1.64511 | 0.822556 | − | 0.568684i | \(-0.192547\pi\) | ||||
0.822556 | + | 0.568684i | \(0.192547\pi\) | |||||||
\(710\) | 6.66984 | 0.250315 | ||||||||
\(711\) | 1.36832 | 0.0513161 | ||||||||
\(712\) | 24.1865 | 0.906427 | ||||||||
\(713\) | −2.33549 | −0.0874647 | ||||||||
\(714\) | 12.4056 | 0.464268 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.69149 | 0.100586 | ||||||||
\(717\) | 0.560747 | 0.0209415 | ||||||||
\(718\) | −0.890637 | −0.0332383 | ||||||||
\(719\) | 15.8605 | 0.591496 | 0.295748 | − | 0.955266i | \(-0.404431\pi\) | ||||
0.295748 | + | 0.955266i | \(0.404431\pi\) | |||||||
\(720\) | 0.762969 | 0.0284342 | ||||||||
\(721\) | 16.8772 | 0.628541 | ||||||||
\(722\) | −1.72399 | −0.0641602 | ||||||||
\(723\) | −16.8877 | −0.628060 | ||||||||
\(724\) | −0.145822 | −0.00541942 | ||||||||
\(725\) | 13.0049 | 0.482992 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.7719 | 0.510770 | 0.255385 | − | 0.966839i | \(-0.417798\pi\) | ||||
0.255385 | + | 0.966839i | \(0.417798\pi\) | |||||||
\(728\) | −4.29052 | −0.159017 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | 9.11849 | 0.337490 | ||||||||
\(731\) | 45.5206 | 1.68364 | ||||||||
\(732\) | −3.73097 | −0.137901 | ||||||||
\(733\) | 19.5677 | 0.722750 | 0.361375 | − | 0.932421i | \(-0.382307\pi\) | ||||
0.361375 | + | 0.932421i | \(0.382307\pi\) | |||||||
\(734\) | 40.5740 | 1.49761 | ||||||||
\(735\) | −0.755188 | −0.0278555 | ||||||||
\(736\) | 1.54170 | 0.0568278 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.583280 | −0.0214708 | ||||||||
\(739\) | 11.1542 | 0.410313 | 0.205157 | − | 0.978729i | \(-0.434230\pi\) | ||||
0.205157 | + | 0.978729i | \(0.434230\pi\) | |||||||
\(740\) | −0.137154 | −0.00504188 | ||||||||
\(741\) | 10.8091 | 0.397083 | ||||||||
\(742\) | −19.3674 | −0.710998 | ||||||||
\(743\) | −20.6550 | −0.757757 | −0.378878 | − | 0.925446i | \(-0.623690\pi\) | ||||
−0.378878 | + | 0.925446i | \(0.623690\pi\) | |||||||
\(744\) | 5.67664 | 0.208116 | ||||||||
\(745\) | −6.98348 | −0.255855 | ||||||||
\(746\) | 43.1972 | 1.58156 | ||||||||
\(747\) | −6.59231 | −0.241200 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.4762 | 0.565489 | ||||||||
\(750\) | 10.8353 | 0.395649 | ||||||||
\(751\) | 26.5991 | 0.970614 | 0.485307 | − | 0.874344i | \(-0.338708\pi\) | ||||
0.485307 | + | 0.874344i | \(0.338708\pi\) | |||||||
\(752\) | 27.3700 | 0.998082 | ||||||||
\(753\) | 11.3182 | 0.412458 | ||||||||
\(754\) | −6.31144 | −0.229849 | ||||||||
\(755\) | 1.34061 | 0.0487897 | ||||||||
\(756\) | 0.827946 | 0.0301121 | ||||||||
\(757\) | 21.0999 | 0.766890 | 0.383445 | − | 0.923564i | \(-0.374738\pi\) | ||||
0.383445 | + | 0.923564i | \(0.374738\pi\) | |||||||
\(758\) | 37.1723 | 1.35016 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.34311 | 0.193815 | ||||||||
\(761\) | 7.99743 | 0.289907 | 0.144953 | − | 0.989438i | \(-0.453697\pi\) | ||||
0.144953 | + | 0.989438i | \(0.453697\pi\) | |||||||
\(762\) | −20.2679 | −0.734227 | ||||||||
\(763\) | −11.0349 | −0.399490 | ||||||||
\(764\) | −2.43428 | −0.0880691 | ||||||||
\(765\) | 0.931905 | 0.0336931 | ||||||||
\(766\) | −46.8360 | −1.69225 | ||||||||
\(767\) | −13.6141 | −0.491576 | ||||||||
\(768\) | −5.84271 | −0.210831 | ||||||||
\(769\) | 52.0476 | 1.87689 | 0.938443 | − | 0.345435i | \(-0.112269\pi\) | ||||
0.938443 | + | 0.345435i | \(0.112269\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.0969 | 0.579716 | ||||||||
\(772\) | −1.83794 | −0.0661488 | ||||||||
\(773\) | −1.58099 | −0.0568644 | −0.0284322 | − | 0.999596i | \(-0.509051\pi\) | ||||
−0.0284322 | + | 0.999596i | \(0.509051\pi\) | |||||||
\(774\) | 4.87870 | 0.175361 | ||||||||
\(775\) | −6.18745 | −0.222260 | ||||||||
\(776\) | 7.33098 | 0.263167 | ||||||||
\(777\) | 3.14256 | 0.112739 | ||||||||
\(778\) | 26.0370 | 0.933471 | ||||||||
\(779\) | −4.39553 | −0.157486 | ||||||||
\(780\) | −0.180798 | −0.00647361 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 13.8395 | 0.494899 | ||||||||
\(783\) | −14.8813 | −0.531815 | ||||||||
\(784\) | −4.27971 | −0.152847 | ||||||||
\(785\) | −8.81298 | −0.314549 | ||||||||
\(786\) | −22.9421 | −0.818319 | ||||||||
\(787\) | −23.3907 | −0.833789 | −0.416894 | − | 0.908955i | \(-0.636882\pi\) | ||||
−0.416894 | + | 0.908955i | \(0.636882\pi\) | |||||||
\(788\) | 0.348265 | 0.0124064 | ||||||||
\(789\) | 22.9443 | 0.816838 | ||||||||
\(790\) | −2.45235 | −0.0872506 | ||||||||
\(791\) | 1.77008 | 0.0629367 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.1147 | 0.856339 | ||||||||
\(794\) | −19.5144 | −0.692539 | ||||||||
\(795\) | 9.97183 | 0.353664 | ||||||||
\(796\) | 3.06836 | 0.108755 | ||||||||
\(797\) | −46.1518 | −1.63478 | −0.817391 | − | 0.576084i | \(-0.804580\pi\) | ||||
−0.817391 | + | 0.576084i | \(0.804580\pi\) | |||||||
\(798\) | 10.0196 | 0.354688 | ||||||||
\(799\) | 33.4303 | 1.18268 | ||||||||
\(800\) | 4.08445 | 0.144407 | ||||||||
\(801\) | 3.40707 | 0.120383 | ||||||||
\(802\) | −5.11834 | −0.180735 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.14470 | 0.0403704 | ||||||||
\(805\) | −0.842476 | −0.0296934 | ||||||||
\(806\) | 3.00283 | 0.105770 | ||||||||
\(807\) | 29.7768 | 1.04819 | ||||||||
\(808\) | 0.484773 | 0.0170542 | ||||||||
\(809\) | −33.7501 | −1.18659 | −0.593295 | − | 0.804985i | \(-0.702173\pi\) | ||||
−0.593295 | + | 0.804985i | \(0.702173\pi\) | |||||||
\(810\) | −5.27681 | −0.185408 | ||||||||
\(811\) | 30.7650 | 1.08030 | 0.540152 | − | 0.841567i | \(-0.318367\pi\) | ||||
0.540152 | + | 0.841567i | \(0.318367\pi\) | |||||||
\(812\) | −0.411462 | −0.0144395 | ||||||||
\(813\) | 1.18212 | 0.0414588 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.41182 | 0.189568 | ||||||||
\(816\) | −36.1978 | −1.26717 | ||||||||
\(817\) | 36.7653 | 1.28626 | ||||||||
\(818\) | 43.4527 | 1.51929 | ||||||||
\(819\) | −0.604391 | −0.0211191 | ||||||||
\(820\) | 0.0735215 | 0.00256748 | ||||||||
\(821\) | −12.0784 | −0.421538 | −0.210769 | − | 0.977536i | \(-0.567597\pi\) | ||||
−0.210769 | + | 0.977536i | \(0.567597\pi\) | |||||||
\(822\) | 33.2508 | 1.15975 | ||||||||
\(823\) | −24.8187 | −0.865124 | −0.432562 | − | 0.901604i | \(-0.642390\pi\) | ||||
−0.432562 | + | 0.901604i | \(0.642390\pi\) | |||||||
\(824\) | −45.7634 | −1.59424 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.6196 | −0.439092 | ||||||||
\(827\) | −5.17330 | −0.179893 | −0.0899466 | − | 0.995947i | \(-0.528670\pi\) | ||||
−0.0899466 | + | 0.995947i | \(0.528670\pi\) | |||||||
\(828\) | 0.104318 | 0.00362531 | ||||||||
\(829\) | 31.5535 | 1.09590 | 0.547949 | − | 0.836511i | \(-0.315409\pi\) | ||||
0.547949 | + | 0.836511i | \(0.315409\pi\) | |||||||
\(830\) | 11.8149 | 0.410102 | ||||||||
\(831\) | 24.3747 | 0.845549 | ||||||||
\(832\) | 11.5615 | 0.400822 | ||||||||
\(833\) | −5.22732 | −0.181116 | ||||||||
\(834\) | 22.7299 | 0.787072 | ||||||||
\(835\) | −2.95204 | −0.102160 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.08018 | 0.244727 | ||||||||
\(838\) | −17.0804 | −0.590034 | ||||||||
\(839\) | −5.83642 | −0.201496 | −0.100748 | − | 0.994912i | \(-0.532124\pi\) | ||||
−0.100748 | + | 0.994912i | \(0.532124\pi\) | |||||||
\(840\) | 2.04773 | 0.0706532 | ||||||||
\(841\) | −21.6045 | −0.744982 | ||||||||
\(842\) | 29.1657 | 1.00512 | ||||||||
\(843\) | −17.3067 | −0.596074 | ||||||||
\(844\) | −0.811781 | −0.0279427 | ||||||||
\(845\) | −4.89895 | −0.168529 | ||||||||
\(846\) | 3.58291 | 0.123183 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 56.5112 | 1.94060 | ||||||||
\(849\) | 14.7385 | 0.505825 | ||||||||
\(850\) | 36.6652 | 1.25761 | ||||||||
\(851\) | 3.50579 | 0.120177 | ||||||||
\(852\) | −2.38523 | −0.0817166 | ||||||||
\(853\) | 20.3462 | 0.696640 | 0.348320 | − | 0.937376i | \(-0.386752\pi\) | ||||
0.348320 | + | 0.937376i | \(0.386752\pi\) | |||||||
\(854\) | 22.3532 | 0.764911 | ||||||||
\(855\) | 0.752666 | 0.0257406 | ||||||||
\(856\) | −41.9644 | −1.43432 | ||||||||
\(857\) | 15.1087 | 0.516104 | 0.258052 | − | 0.966131i | \(-0.416919\pi\) | ||||
0.258052 | + | 0.966131i | \(0.416919\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.9641 | −1.15884 | −0.579420 | − | 0.815029i | \(-0.696721\pi\) | ||||
−0.579420 | + | 0.815029i | \(0.696721\pi\) | |||||||
\(860\) | −0.614952 | −0.0209697 | ||||||||
\(861\) | −1.68457 | −0.0574100 | ||||||||
\(862\) | −44.3633 | −1.51102 | ||||||||
\(863\) | −2.77734 | −0.0945417 | −0.0472709 | − | 0.998882i | \(-0.515052\pi\) | ||||
−0.0472709 | + | 0.998882i | \(0.515052\pi\) | |||||||
\(864\) | −4.67376 | −0.159005 | ||||||||
\(865\) | −0.624983 | −0.0212501 | ||||||||
\(866\) | −8.37092 | −0.284456 | ||||||||
\(867\) | −16.7061 | −0.567368 | ||||||||
\(868\) | 0.195764 | 0.00664466 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 3.01224 | 0.102125 | ||||||||
\(871\) | −7.39864 | −0.250693 | ||||||||
\(872\) | 29.9216 | 1.01327 | ||||||||
\(873\) | 1.03269 | 0.0349513 | ||||||||
\(874\) | 11.1777 | 0.378090 | ||||||||
\(875\) | −4.56565 | −0.154347 | ||||||||
\(876\) | −3.26090 | −0.110176 | ||||||||
\(877\) | −49.6783 | −1.67752 | −0.838759 | − | 0.544503i | \(-0.816718\pi\) | ||||
−0.838759 | + | 0.544503i | \(0.816718\pi\) | |||||||
\(878\) | −10.0453 | −0.339012 | ||||||||
\(879\) | 19.2368 | 0.648841 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.3064 | −0.919975 | −0.459988 | − | 0.887925i | \(-0.652146\pi\) | ||||
−0.459988 | + | 0.887925i | \(0.652146\pi\) | |||||||
\(882\) | −0.560242 | −0.0188643 | ||||||||
\(883\) | −17.8109 | −0.599386 | −0.299693 | − | 0.954036i | \(-0.596884\pi\) | ||||
−0.299693 | + | 0.954036i | \(0.596884\pi\) | |||||||
\(884\) | −1.25146 | −0.0420912 | ||||||||
\(885\) | 6.49755 | 0.218413 | ||||||||
\(886\) | 0.147693 | 0.00496184 | ||||||||
\(887\) | 16.4729 | 0.553105 | 0.276553 | − | 0.960999i | \(-0.410808\pi\) | ||||
0.276553 | + | 0.960999i | \(0.410808\pi\) | |||||||
\(888\) | −8.52118 | −0.285952 | ||||||||
\(889\) | 8.54023 | 0.286430 | ||||||||
\(890\) | −6.10625 | −0.204682 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.84656 | −0.128792 | ||||||||
\(893\) | 27.0004 | 0.903535 | ||||||||
\(894\) | 35.5093 | 1.18761 | ||||||||
\(895\) | 8.30260 | 0.277525 | ||||||||
\(896\) | 12.4252 | 0.415095 | ||||||||
\(897\) | 4.62137 | 0.154303 | ||||||||
\(898\) | −45.1823 | −1.50775 | ||||||||
\(899\) | −3.51861 | −0.117352 | ||||||||
\(900\) | 0.276372 | 0.00921240 | ||||||||
\(901\) | 69.0238 | 2.29952 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.0902 | 0.468891 | ||||||||
\(904\) | −4.79964 | −0.159634 | ||||||||
\(905\) | −0.449825 | −0.0149527 | ||||||||
\(906\) | −6.81668 | −0.226469 | ||||||||
\(907\) | 28.4877 | 0.945918 | 0.472959 | − | 0.881084i | \(-0.343186\pi\) | ||||
0.472959 | + | 0.881084i | \(0.343186\pi\) | |||||||
\(908\) | 3.28473 | 0.109008 | ||||||||
\(909\) | 0.0682883 | 0.00226498 | ||||||||
\(910\) | 1.08321 | 0.0359080 | ||||||||
\(911\) | −11.2353 | −0.372242 | −0.186121 | − | 0.982527i | \(-0.559592\pi\) | ||||
−0.186121 | + | 0.982527i | \(0.559592\pi\) | |||||||
\(912\) | −29.2356 | −0.968088 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −33.9337 | −1.12243 | ||||||||
\(915\) | −11.5092 | −0.380482 | ||||||||
\(916\) | 3.10634 | 0.102636 | ||||||||
\(917\) | 9.66708 | 0.319235 | ||||||||
\(918\) | −41.9553 | −1.38473 | ||||||||
\(919\) | −0.780457 | −0.0257449 | −0.0128724 | − | 0.999917i | \(-0.504098\pi\) | ||||
−0.0128724 | + | 0.999917i | \(0.504098\pi\) | |||||||
\(920\) | 2.28441 | 0.0753148 | ||||||||
\(921\) | 3.59320 | 0.118400 | ||||||||
\(922\) | 4.07516 | 0.134208 | ||||||||
\(923\) | 15.4167 | 0.507446 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.28795 | 0.305386 | ||||||||
\(926\) | −38.2744 | −1.25777 | ||||||||
\(927\) | −6.44653 | −0.211732 | ||||||||
\(928\) | 2.32270 | 0.0762465 | ||||||||
\(929\) | 26.5963 | 0.872597 | 0.436298 | − | 0.899802i | \(-0.356289\pi\) | ||||
0.436298 | + | 0.899802i | \(0.356289\pi\) | |||||||
\(930\) | −1.43315 | −0.0469950 | ||||||||
\(931\) | −4.22192 | −0.138368 | ||||||||
\(932\) | −0.105012 | −0.00343979 | ||||||||
\(933\) | 34.6463 | 1.13427 | ||||||||
\(934\) | −3.89900 | −0.127579 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.63883 | 0.0535669 | ||||||||
\(937\) | −41.9697 | −1.37109 | −0.685544 | − | 0.728031i | \(-0.740436\pi\) | ||||
−0.685544 | + | 0.728031i | \(0.740436\pi\) | |||||||
\(938\) | −6.85818 | −0.223928 | ||||||||
\(939\) | 51.0567 | 1.66617 | ||||||||
\(940\) | −0.451620 | −0.0147302 | ||||||||
\(941\) | 49.0330 | 1.59843 | 0.799215 | − | 0.601046i | \(-0.205249\pi\) | ||||
0.799215 | + | 0.601046i | \(0.205249\pi\) | |||||||
\(942\) | 44.8119 | 1.46005 | ||||||||
\(943\) | −1.87928 | −0.0611978 | ||||||||
\(944\) | 36.8222 | 1.19846 | ||||||||
\(945\) | 2.55402 | 0.0830823 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.2953 | −0.886978 | −0.443489 | − | 0.896280i | \(-0.646259\pi\) | ||||
−0.443489 | + | 0.896280i | \(0.646259\pi\) | |||||||
\(948\) | 0.876994 | 0.0284835 | ||||||||
\(949\) | 21.0765 | 0.684171 | ||||||||
\(950\) | 29.6132 | 0.960778 | ||||||||
\(951\) | 21.3591 | 0.692617 | ||||||||
\(952\) | 14.1741 | 0.459386 | ||||||||
\(953\) | −19.7408 | −0.639466 | −0.319733 | − | 0.947508i | \(-0.603593\pi\) | ||||
−0.319733 | + | 0.947508i | \(0.603593\pi\) | |||||||
\(954\) | 7.39767 | 0.239509 | ||||||||
\(955\) | −7.50918 | −0.242991 | ||||||||
\(956\) | −0.0524354 | −0.00169588 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.1478 | 0.392478 | ||||||||
\(959\) | −14.0108 | −0.452433 | ||||||||
\(960\) | −5.51792 | −0.178090 | ||||||||
\(961\) | −29.3259 | −0.945998 | ||||||||
\(962\) | −4.50754 | −0.145329 | ||||||||
\(963\) | −5.91139 | −0.190492 | ||||||||
\(964\) | 1.57917 | 0.0508615 | ||||||||
\(965\) | −5.66960 | −0.182511 | ||||||||
\(966\) | 4.28379 | 0.137829 | ||||||||
\(967\) | 12.6734 | 0.407551 | 0.203775 | − | 0.979018i | \(-0.434679\pi\) | ||||
0.203775 | + | 0.979018i | \(0.434679\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −35.7089 | −1.14714 | ||||||||
\(970\) | −1.85082 | −0.0594261 | ||||||||
\(971\) | 16.7036 | 0.536045 | 0.268022 | − | 0.963413i | \(-0.413630\pi\) | ||||
0.268022 | + | 0.963413i | \(0.413630\pi\) | |||||||
\(972\) | −0.596777 | −0.0191416 | ||||||||
\(973\) | −9.57765 | −0.307045 | ||||||||
\(974\) | −28.7414 | −0.920935 | ||||||||
\(975\) | 12.2435 | 0.392105 | ||||||||
\(976\) | −65.2234 | −2.08775 | ||||||||
\(977\) | 27.3452 | 0.874851 | 0.437425 | − | 0.899255i | \(-0.355890\pi\) | ||||
0.437425 | + | 0.899255i | \(0.355890\pi\) | |||||||
\(978\) | −27.5178 | −0.879924 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.0706175 | 0.00225579 | ||||||||
\(981\) | 4.21496 | 0.134573 | ||||||||
\(982\) | 42.0683 | 1.34245 | ||||||||
\(983\) | −55.0065 | −1.75443 | −0.877217 | − | 0.480093i | \(-0.840603\pi\) | ||||
−0.877217 | + | 0.480093i | \(0.840603\pi\) | |||||||
\(984\) | 4.56779 | 0.145616 | ||||||||
\(985\) | 1.07432 | 0.0342306 | ||||||||
\(986\) | 20.8504 | 0.664012 | ||||||||
\(987\) | 10.3478 | 0.329374 | ||||||||
\(988\) | −1.01076 | −0.0321566 | ||||||||
\(989\) | 15.7188 | 0.499828 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.2327 | 1.69099 | 0.845497 | − | 0.533980i | \(-0.179304\pi\) | ||||
0.845497 | + | 0.533980i | \(0.179304\pi\) | |||||||
\(992\) | −1.10509 | −0.0350866 | ||||||||
\(993\) | −15.3333 | −0.486589 | ||||||||
\(994\) | 14.2905 | 0.453268 | ||||||||
\(995\) | 9.46519 | 0.300067 | ||||||||
\(996\) | −4.22518 | −0.133880 | ||||||||
\(997\) | −32.7546 | −1.03735 | −0.518674 | − | 0.854972i | \(-0.673574\pi\) | ||||
−0.518674 | + | 0.854972i | \(0.673574\pi\) | |||||||
\(998\) | 40.9950 | 1.29767 | ||||||||
\(999\) | −10.6280 | −0.336256 |
(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 | 847.2.a.k.1.4 | 4 | ||
3.2 | odd | 2 | 7623.2.a.co.1.1 | 4 | |||
7.6 | odd | 2 | 5929.2.a.bb.1.4 | 4 | |||
11.2 | odd | 10 | 77.2.f.a.15.2 | ✓ | 8 | ||
11.3 | even | 5 | 847.2.f.s.372.2 | 8 | |||
11.4 | even | 5 | 847.2.f.s.148.2 | 8 | |||
11.5 | even | 5 | 847.2.f.q.729.1 | 8 | |||
11.6 | odd | 10 | 77.2.f.a.36.2 | yes | 8 | ||
11.7 | odd | 10 | 847.2.f.p.148.1 | 8 | |||
11.8 | odd | 10 | 847.2.f.p.372.1 | 8 | |||
11.9 | even | 5 | 847.2.f.q.323.1 | 8 | |||
11.10 | odd | 2 | 847.2.a.l.1.1 | 4 | |||
33.2 | even | 10 | 693.2.m.g.631.1 | 8 | |||
33.17 | even | 10 | 693.2.m.g.190.1 | 8 | |||
33.32 | even | 2 | 7623.2.a.ch.1.4 | 4 | |||
77.2 | odd | 30 | 539.2.q.c.312.2 | 16 | |||
77.6 | even | 10 | 539.2.f.d.344.2 | 8 | |||
77.13 | even | 10 | 539.2.f.d.246.2 | 8 | |||
77.17 | even | 30 | 539.2.q.b.520.2 | 16 | |||
77.24 | even | 30 | 539.2.q.b.422.1 | 16 | |||
77.39 | odd | 30 | 539.2.q.c.520.2 | 16 | |||
77.46 | odd | 30 | 539.2.q.c.422.1 | 16 | |||
77.61 | even | 30 | 539.2.q.b.410.1 | 16 | |||
77.68 | even | 30 | 539.2.q.b.312.2 | 16 | |||
77.72 | odd | 30 | 539.2.q.c.410.1 | 16 | |||
77.76 | even | 2 | 5929.2.a.bi.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.a.15.2 | ✓ | 8 | 11.2 | odd | 10 | ||
77.2.f.a.36.2 | yes | 8 | 11.6 | odd | 10 | ||
539.2.f.d.246.2 | 8 | 77.13 | even | 10 | |||
539.2.f.d.344.2 | 8 | 77.6 | even | 10 | |||
539.2.q.b.312.2 | 16 | 77.68 | even | 30 | |||
539.2.q.b.410.1 | 16 | 77.61 | even | 30 | |||
539.2.q.b.422.1 | 16 | 77.24 | even | 30 | |||
539.2.q.b.520.2 | 16 | 77.17 | even | 30 | |||
539.2.q.c.312.2 | 16 | 77.2 | odd | 30 | |||
539.2.q.c.410.1 | 16 | 77.72 | odd | 30 | |||
539.2.q.c.422.1 | 16 | 77.46 | odd | 30 | |||
539.2.q.c.520.2 | 16 | 77.39 | odd | 30 | |||
693.2.m.g.190.1 | 8 | 33.17 | even | 10 | |||
693.2.m.g.631.1 | 8 | 33.2 | even | 10 | |||
847.2.a.k.1.4 | 4 | 1.1 | even | 1 | trivial | ||
847.2.a.l.1.1 | 4 | 11.10 | odd | 2 | |||
847.2.f.p.148.1 | 8 | 11.7 | odd | 10 | |||
847.2.f.p.372.1 | 8 | 11.8 | odd | 10 | |||
847.2.f.q.323.1 | 8 | 11.9 | even | 5 | |||
847.2.f.q.729.1 | 8 | 11.5 | even | 5 | |||
847.2.f.s.148.2 | 8 | 11.4 | even | 5 | |||
847.2.f.s.372.2 | 8 | 11.3 | even | 5 | |||
5929.2.a.bb.1.4 | 4 | 7.6 | odd | 2 | |||
5929.2.a.bi.1.1 | 4 | 77.76 | even | 2 | |||
7623.2.a.ch.1.4 | 4 | 33.32 | even | 2 | |||
7623.2.a.co.1.1 | 4 | 3.2 | odd | 2 |