Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [575,2,Mod(1,575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(575, 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("575.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 575 = 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 575.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: | \(4.59139811622\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5744.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 115) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.92022\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.92022 | 1.35780 | 0.678901 | − | 0.734230i | \(-0.262457\pi\) | ||||
0.678901 | + | 0.734230i | \(0.262457\pi\) | |||||||
\(3\) | −1.39945 | −0.807971 | −0.403986 | − | 0.914765i | \(-0.632375\pi\) | ||||
−0.403986 | + | 0.914765i | \(0.632375\pi\) | |||||||
\(4\) | 1.68725 | 0.843624 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.68725 | −1.09706 | ||||||||
\(7\) | −4.60747 | −1.74146 | −0.870730 | − | 0.491762i | \(-0.836353\pi\) | ||||
−0.870730 | + | 0.491762i | \(0.836353\pi\) | |||||||
\(8\) | −0.600553 | −0.212327 | ||||||||
\(9\) | −1.04155 | −0.347182 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.56592 | 0.472143 | 0.236072 | − | 0.971736i | \(-0.424140\pi\) | ||||
0.236072 | + | 0.971736i | \(0.424140\pi\) | |||||||
\(12\) | −2.36122 | −0.681624 | ||||||||
\(13\) | −2.60055 | −0.721264 | −0.360632 | − | 0.932708i | \(-0.617439\pi\) | ||||
−0.360632 | + | 0.932708i | \(0.617439\pi\) | |||||||
\(14\) | −8.84736 | −2.36456 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.52769 | −1.13192 | ||||||||
\(17\) | −0.559006 | −0.135579 | −0.0677894 | − | 0.997700i | \(-0.521595\pi\) | ||||
−0.0677894 | + | 0.997700i | \(0.521595\pi\) | |||||||
\(18\) | −2.00000 | −0.471405 | ||||||||
\(19\) | −1.16647 | −0.267608 | −0.133804 | − | 0.991008i | \(-0.542719\pi\) | ||||
−0.133804 | + | 0.991008i | \(0.542719\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.44791 | 1.40705 | ||||||||
\(22\) | 3.00692 | 0.641077 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0.840442 | 0.171554 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.99364 | −0.979332 | ||||||||
\(27\) | 5.65593 | 1.08848 | ||||||||
\(28\) | −7.77394 | −1.46914 | ||||||||
\(29\) | −3.17339 | −0.589284 | −0.294642 | − | 0.955608i | \(-0.595200\pi\) | ||||
−0.294642 | + | 0.955608i | \(0.595200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0554 | 1.80600 | 0.903000 | − | 0.429641i | \(-0.141360\pi\) | ||||
0.903000 | + | 0.429641i | \(0.141360\pi\) | |||||||
\(32\) | −7.49306 | −1.32460 | ||||||||
\(33\) | −2.19143 | −0.381478 | ||||||||
\(34\) | −1.07341 | −0.184089 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.75735 | −0.292891 | ||||||||
\(37\) | −5.07341 | −0.834064 | −0.417032 | − | 0.908892i | \(-0.636930\pi\) | ||||
−0.417032 | + | 0.908892i | \(0.636930\pi\) | |||||||
\(38\) | −2.23989 | −0.363358 | ||||||||
\(39\) | 3.63934 | 0.582760 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.8127 | −1.84484 | −0.922419 | − | 0.386190i | \(-0.873791\pi\) | ||||
−0.922419 | + | 0.386190i | \(0.873791\pi\) | |||||||
\(42\) | 12.3814 | 1.91049 | ||||||||
\(43\) | 2.76426 | 0.421546 | 0.210773 | − | 0.977535i | \(-0.432402\pi\) | ||||
0.210773 | + | 0.977535i | \(0.432402\pi\) | |||||||
\(44\) | 2.64210 | 0.398311 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.92022 | 0.283121 | ||||||||
\(47\) | −9.32298 | −1.35990 | −0.679948 | − | 0.733260i | \(-0.737998\pi\) | ||||
−0.679948 | + | 0.733260i | \(0.737998\pi\) | |||||||
\(48\) | 6.33626 | 0.914561 | ||||||||
\(49\) | 14.2288 | 2.03268 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.782299 | 0.109544 | ||||||||
\(52\) | −4.38778 | −0.608475 | ||||||||
\(53\) | 5.54789 | 0.762061 | 0.381030 | − | 0.924562i | \(-0.375569\pi\) | ||||
0.381030 | + | 0.924562i | \(0.375569\pi\) | |||||||
\(54\) | 10.8606 | 1.47795 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.76703 | 0.369760 | ||||||||
\(57\) | 1.63242 | 0.216219 | ||||||||
\(58\) | −6.09361 | −0.800130 | ||||||||
\(59\) | 3.84044 | 0.499983 | 0.249991 | − | 0.968248i | \(-0.419572\pi\) | ||||
0.249991 | + | 0.968248i | \(0.419572\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.29832 | −0.550343 | −0.275172 | − | 0.961395i | \(-0.588735\pi\) | ||||
−0.275172 | + | 0.961395i | \(0.588735\pi\) | |||||||
\(62\) | 19.3086 | 2.45219 | ||||||||
\(63\) | 4.79889 | 0.604604 | ||||||||
\(64\) | −5.33295 | −0.666619 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.20802 | −0.517972 | ||||||||
\(67\) | −2.60747 | −0.318553 | −0.159277 | − | 0.987234i | \(-0.550916\pi\) | ||||
−0.159277 | + | 0.987234i | \(0.550916\pi\) | |||||||
\(68\) | −0.943181 | −0.114378 | ||||||||
\(69\) | −1.39945 | −0.168474 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.89582 | 0.937062 | 0.468531 | − | 0.883447i | \(-0.344783\pi\) | ||||
0.468531 | + | 0.883447i | \(0.344783\pi\) | |||||||
\(72\) | 0.625504 | 0.0737163 | ||||||||
\(73\) | −9.90579 | −1.15938 | −0.579692 | − | 0.814835i | \(-0.696827\pi\) | ||||
−0.579692 | + | 0.814835i | \(0.696827\pi\) | |||||||
\(74\) | −9.74208 | −1.13249 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.96813 | −0.225760 | ||||||||
\(77\) | −7.21494 | −0.822219 | ||||||||
\(78\) | 6.98833 | 0.791273 | ||||||||
\(79\) | 12.0485 | 1.35556 | 0.677779 | − | 0.735266i | \(-0.262943\pi\) | ||||
0.677779 | + | 0.735266i | \(0.262943\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.79054 | −0.532282 | ||||||||
\(82\) | −22.6830 | −2.50492 | ||||||||
\(83\) | −13.3856 | −1.46926 | −0.734628 | − | 0.678470i | \(-0.762643\pi\) | ||||
−0.734628 | + | 0.678470i | \(0.762643\pi\) | |||||||
\(84\) | 10.8792 | 1.18702 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.30800 | 0.572376 | ||||||||
\(87\) | 4.44099 | 0.476125 | ||||||||
\(88\) | −0.940419 | −0.100249 | ||||||||
\(89\) | −7.71551 | −0.817843 | −0.408921 | − | 0.912570i | \(-0.634095\pi\) | ||||
−0.408921 | + | 0.912570i | \(0.634095\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.9820 | 1.25605 | ||||||||
\(92\) | 1.68725 | 0.175908 | ||||||||
\(93\) | −14.0720 | −1.45920 | ||||||||
\(94\) | −17.9022 | −1.84647 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 10.4861 | 1.07024 | ||||||||
\(97\) | 2.62130 | 0.266153 | 0.133076 | − | 0.991106i | \(-0.457514\pi\) | ||||
0.133076 | + | 0.991106i | \(0.457514\pi\) | |||||||
\(98\) | 27.3224 | 2.75998 | ||||||||
\(99\) | −1.63098 | −0.163920 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.88199 | −0.883791 | −0.441895 | − | 0.897067i | \(-0.645694\pi\) | ||||
−0.441895 | + | 0.897067i | \(0.645694\pi\) | |||||||
\(102\) | 1.50219 | 0.148739 | ||||||||
\(103\) | 8.65593 | 0.852894 | 0.426447 | − | 0.904512i | \(-0.359765\pi\) | ||||
0.426447 | + | 0.904512i | \(0.359765\pi\) | |||||||
\(104\) | 1.56177 | 0.153144 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.6532 | 1.03473 | ||||||||
\(107\) | 6.91662 | 0.668655 | 0.334327 | − | 0.942457i | \(-0.391491\pi\) | ||||
0.334327 | + | 0.942457i | \(0.391491\pi\) | |||||||
\(108\) | 9.54296 | 0.918272 | ||||||||
\(109\) | −6.84736 | −0.655858 | −0.327929 | − | 0.944702i | \(-0.606351\pi\) | ||||
−0.327929 | + | 0.944702i | \(0.606351\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.09998 | 0.673900 | ||||||||
\(112\) | 20.8612 | 1.97120 | ||||||||
\(113\) | 4.60747 | 0.433434 | 0.216717 | − | 0.976234i | \(-0.430465\pi\) | ||||
0.216717 | + | 0.976234i | \(0.430465\pi\) | |||||||
\(114\) | 3.13461 | 0.293583 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.35430 | −0.497134 | ||||||||
\(117\) | 2.70860 | 0.250410 | ||||||||
\(118\) | 7.37450 | 0.678877 | ||||||||
\(119\) | 2.57560 | 0.236105 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.54789 | −0.777081 | ||||||||
\(122\) | −8.25372 | −0.747257 | ||||||||
\(123\) | 16.5313 | 1.49058 | ||||||||
\(124\) | 16.9659 | 1.52358 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 9.21494 | 0.820932 | ||||||||
\(127\) | −11.5324 | −1.02334 | −0.511669 | − | 0.859182i | \(-0.670973\pi\) | ||||
−0.511669 | + | 0.859182i | \(0.670973\pi\) | |||||||
\(128\) | 4.74568 | 0.419463 | ||||||||
\(129\) | −3.86844 | −0.340597 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.9639 | −1.13266 | −0.566332 | − | 0.824177i | \(-0.691638\pi\) | ||||
−0.566332 | + | 0.824177i | \(0.691638\pi\) | |||||||
\(132\) | −3.69748 | −0.321824 | ||||||||
\(133\) | 5.37450 | 0.466028 | ||||||||
\(134\) | −5.00692 | −0.432532 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.335712 | 0.0287871 | ||||||||
\(137\) | 17.1457 | 1.46485 | 0.732427 | − | 0.680846i | \(-0.238388\pi\) | ||||
0.732427 | + | 0.680846i | \(0.238388\pi\) | |||||||
\(138\) | −2.68725 | −0.228754 | ||||||||
\(139\) | −19.4798 | −1.65225 | −0.826127 | − | 0.563485i | \(-0.809460\pi\) | ||||
−0.826127 | + | 0.563485i | \(0.809460\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.0470 | 1.09876 | ||||||||
\(142\) | 15.1617 | 1.27234 | ||||||||
\(143\) | −4.07226 | −0.340540 | ||||||||
\(144\) | 4.71580 | 0.392983 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −19.0213 | −1.57421 | ||||||||
\(147\) | −19.9124 | −1.64235 | ||||||||
\(148\) | −8.56011 | −0.703637 | ||||||||
\(149\) | 13.2288 | 1.08374 | 0.541872 | − | 0.840461i | \(-0.317716\pi\) | ||||
0.541872 | + | 0.840461i | \(0.317716\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.50749 | −0.204057 | −0.102028 | − | 0.994781i | \(-0.532533\pi\) | ||||
−0.102028 | + | 0.994781i | \(0.532533\pi\) | |||||||
\(152\) | 0.700529 | 0.0568204 | ||||||||
\(153\) | 0.582231 | 0.0470706 | ||||||||
\(154\) | −13.8543 | −1.11641 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.14046 | 0.491631 | ||||||||
\(157\) | 8.52824 | 0.680628 | 0.340314 | − | 0.940312i | \(-0.389467\pi\) | ||||
0.340314 | + | 0.940312i | \(0.389467\pi\) | |||||||
\(158\) | 23.1357 | 1.84058 | ||||||||
\(159\) | −7.76398 | −0.615723 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.60747 | −0.363119 | ||||||||
\(162\) | −9.19889 | −0.722733 | ||||||||
\(163\) | 7.73240 | 0.605648 | 0.302824 | − | 0.953046i | \(-0.402071\pi\) | ||||
0.302824 | + | 0.953046i | \(0.402071\pi\) | |||||||
\(164\) | −19.9310 | −1.55635 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −25.7032 | −1.99496 | ||||||||
\(167\) | 14.3064 | 1.10706 | 0.553531 | − | 0.832829i | \(-0.313280\pi\) | ||||
0.553531 | + | 0.832829i | \(0.313280\pi\) | |||||||
\(168\) | −3.87231 | −0.298755 | ||||||||
\(169\) | −6.23713 | −0.479779 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.21494 | 0.0929086 | ||||||||
\(172\) | 4.66400 | 0.355627 | ||||||||
\(173\) | −15.4714 | −1.17627 | −0.588135 | − | 0.808763i | \(-0.700138\pi\) | ||||
−0.588135 | + | 0.808763i | \(0.700138\pi\) | |||||||
\(174\) | 8.52769 | 0.646483 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.09001 | −0.534430 | ||||||||
\(177\) | −5.37450 | −0.403972 | ||||||||
\(178\) | −14.8155 | −1.11047 | ||||||||
\(179\) | 5.98612 | 0.447424 | 0.223712 | − | 0.974655i | \(-0.428183\pi\) | ||||
0.223712 | + | 0.974655i | \(0.428183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.69892 | −0.423597 | −0.211799 | − | 0.977313i | \(-0.567932\pi\) | ||||
−0.211799 | + | 0.977313i | \(0.567932\pi\) | |||||||
\(182\) | 23.0080 | 1.70547 | ||||||||
\(183\) | 6.01527 | 0.444662 | ||||||||
\(184\) | −0.600553 | −0.0442733 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −27.0213 | −1.98130 | ||||||||
\(187\) | −0.875359 | −0.0640126 | ||||||||
\(188\) | −15.7302 | −1.14724 | ||||||||
\(189\) | −26.0595 | −1.89555 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.34402 | −0.603752 | −0.301876 | − | 0.953347i | \(-0.597613\pi\) | ||||
−0.301876 | + | 0.953347i | \(0.597613\pi\) | |||||||
\(192\) | 7.46318 | 0.538609 | ||||||||
\(193\) | −16.0250 | −1.15350 | −0.576751 | − | 0.816920i | \(-0.695680\pi\) | ||||
−0.576751 | + | 0.816920i | \(0.695680\pi\) | |||||||
\(194\) | 5.03348 | 0.361383 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 24.0075 | 1.71482 | ||||||||
\(197\) | −5.78893 | −0.412444 | −0.206222 | − | 0.978505i | \(-0.566117\pi\) | ||||
−0.206222 | + | 0.978505i | \(0.566117\pi\) | |||||||
\(198\) | −3.13184 | −0.222570 | ||||||||
\(199\) | −18.8085 | −1.33330 | −0.666651 | − | 0.745370i | \(-0.732273\pi\) | ||||
−0.666651 | + | 0.745370i | \(0.732273\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.64902 | 0.257382 | ||||||||
\(202\) | −17.0554 | −1.20001 | ||||||||
\(203\) | 14.6213 | 1.02621 | ||||||||
\(204\) | 1.31993 | 0.0924138 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 16.6213 | 1.15806 | ||||||||
\(207\) | −1.04155 | −0.0723925 | ||||||||
\(208\) | 11.7745 | 0.816414 | ||||||||
\(209\) | −1.82661 | −0.126349 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.88199 | −0.336090 | −0.168045 | − | 0.985779i | \(-0.553745\pi\) | ||||
−0.168045 | + | 0.985779i | \(0.553745\pi\) | |||||||
\(212\) | 9.36066 | 0.642893 | ||||||||
\(213\) | −11.0498 | −0.757119 | ||||||||
\(214\) | 13.2814 | 0.907900 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.39668 | −0.231115 | ||||||||
\(217\) | −46.3299 | −3.14508 | ||||||||
\(218\) | −13.1484 | −0.890525 | ||||||||
\(219\) | 13.8626 | 0.936750 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.45372 | 0.0977880 | ||||||||
\(222\) | 13.6335 | 0.915022 | ||||||||
\(223\) | 13.4786 | 0.902596 | 0.451298 | − | 0.892373i | \(-0.350961\pi\) | ||||
0.451298 | + | 0.892373i | \(0.350961\pi\) | |||||||
\(224\) | 34.5240 | 2.30673 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.84736 | 0.588518 | ||||||||
\(227\) | −13.6894 | −0.908598 | −0.454299 | − | 0.890849i | \(-0.650110\pi\) | ||||
−0.454299 | + | 0.890849i | \(0.650110\pi\) | |||||||
\(228\) | 2.75430 | 0.182408 | ||||||||
\(229\) | 27.3964 | 1.81040 | 0.905202 | − | 0.424981i | \(-0.139719\pi\) | ||||
0.905202 | + | 0.424981i | \(0.139719\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.0969 | 0.664329 | ||||||||
\(232\) | 1.90579 | 0.125121 | ||||||||
\(233\) | 0.0387841 | 0.00254083 | 0.00127041 | − | 0.999999i | \(-0.499596\pi\) | ||||
0.00127041 | + | 0.999999i | \(0.499596\pi\) | |||||||
\(234\) | 5.20111 | 0.340007 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.47978 | 0.421798 | ||||||||
\(237\) | −16.8612 | −1.09525 | ||||||||
\(238\) | 4.94572 | 0.320584 | ||||||||
\(239\) | −13.9030 | −0.899312 | −0.449656 | − | 0.893202i | \(-0.648453\pi\) | ||||
−0.449656 | + | 0.893202i | \(0.648453\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.9972 | −0.772810 | −0.386405 | − | 0.922329i | \(-0.626283\pi\) | ||||
−0.386405 | + | 0.922329i | \(0.626283\pi\) | |||||||
\(242\) | −16.4138 | −1.05512 | ||||||||
\(243\) | −10.2637 | −0.658416 | ||||||||
\(244\) | −7.25233 | −0.464283 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 31.7437 | 2.02391 | ||||||||
\(247\) | 3.03348 | 0.193016 | ||||||||
\(248\) | −6.03878 | −0.383463 | ||||||||
\(249\) | 18.7324 | 1.18712 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.7806 | −1.12230 | −0.561150 | − | 0.827714i | \(-0.689641\pi\) | ||||
−0.561150 | + | 0.827714i | \(0.689641\pi\) | |||||||
\(252\) | 8.09693 | 0.510058 | ||||||||
\(253\) | 1.56592 | 0.0984487 | ||||||||
\(254\) | −22.1448 | −1.38949 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.7786 | 1.23617 | ||||||||
\(257\) | −10.2315 | −0.638226 | −0.319113 | − | 0.947717i | \(-0.603385\pi\) | ||||
−0.319113 | + | 0.947717i | \(0.603385\pi\) | |||||||
\(258\) | −7.42826 | −0.462464 | ||||||||
\(259\) | 23.3756 | 1.45249 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.30524 | 0.204589 | ||||||||
\(262\) | −24.8936 | −1.53793 | ||||||||
\(263\) | 3.99856 | 0.246562 | 0.123281 | − | 0.992372i | \(-0.460658\pi\) | ||||
0.123281 | + | 0.992372i | \(0.460658\pi\) | |||||||
\(264\) | 1.31607 | 0.0809983 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 10.3202 | 0.632773 | ||||||||
\(267\) | 10.7975 | 0.660794 | ||||||||
\(268\) | −4.39945 | −0.268739 | ||||||||
\(269\) | −2.88084 | −0.175648 | −0.0878239 | − | 0.996136i | \(-0.527991\pi\) | ||||
−0.0878239 | + | 0.996136i | \(0.527991\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.1944 | 0.862250 | 0.431125 | − | 0.902292i | \(-0.358117\pi\) | ||||
0.431125 | + | 0.902292i | \(0.358117\pi\) | |||||||
\(272\) | 2.53100 | 0.153465 | ||||||||
\(273\) | −16.7681 | −1.01485 | ||||||||
\(274\) | 32.9235 | 1.98898 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.36122 | −0.142128 | ||||||||
\(277\) | −9.13576 | −0.548915 | −0.274457 | − | 0.961599i | \(-0.588498\pi\) | ||||
−0.274457 | + | 0.961599i | \(0.588498\pi\) | |||||||
\(278\) | −37.4055 | −2.24343 | ||||||||
\(279\) | −10.4731 | −0.627011 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.8640 | 0.886709 | 0.443355 | − | 0.896346i | \(-0.353788\pi\) | ||||
0.443355 | + | 0.896346i | \(0.353788\pi\) | |||||||
\(282\) | 25.0532 | 1.49189 | ||||||||
\(283\) | −3.03878 | −0.180637 | −0.0903185 | − | 0.995913i | \(-0.528788\pi\) | ||||
−0.0903185 | + | 0.995913i | \(0.528788\pi\) | |||||||
\(284\) | 13.3222 | 0.790528 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.81964 | −0.462385 | ||||||||
\(287\) | 54.4268 | 3.21271 | ||||||||
\(288\) | 7.80437 | 0.459877 | ||||||||
\(289\) | −16.6875 | −0.981618 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.66837 | −0.215044 | ||||||||
\(292\) | −16.7135 | −0.978085 | ||||||||
\(293\) | 19.2288 | 1.12336 | 0.561678 | − | 0.827356i | \(-0.310156\pi\) | ||||
0.561678 | + | 0.827356i | \(0.310156\pi\) | |||||||
\(294\) | −38.2362 | −2.22998 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.04685 | 0.177095 | ||||||||
\(297\) | 8.85675 | 0.513921 | ||||||||
\(298\) | 25.4022 | 1.47151 | ||||||||
\(299\) | −2.60055 | −0.150394 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.7363 | −0.734106 | ||||||||
\(302\) | −4.81494 | −0.277069 | ||||||||
\(303\) | 12.4299 | 0.714078 | ||||||||
\(304\) | 5.28144 | 0.302911 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.11801 | 0.0639125 | ||||||||
\(307\) | 20.5395 | 1.17225 | 0.586127 | − | 0.810220i | \(-0.300652\pi\) | ||||
0.586127 | + | 0.810220i | \(0.300652\pi\) | |||||||
\(308\) | −12.1734 | −0.693643 | ||||||||
\(309\) | −12.1135 | −0.689114 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.83929 | −0.557935 | −0.278967 | − | 0.960301i | \(-0.589992\pi\) | ||||
−0.278967 | + | 0.960301i | \(0.589992\pi\) | |||||||
\(312\) | −2.18561 | −0.123736 | ||||||||
\(313\) | −22.4659 | −1.26985 | −0.634925 | − | 0.772574i | \(-0.718969\pi\) | ||||
−0.634925 | + | 0.772574i | \(0.718969\pi\) | |||||||
\(314\) | 16.3761 | 0.924157 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.3287 | 1.14358 | ||||||||
\(317\) | 17.8404 | 1.00202 | 0.501010 | − | 0.865442i | \(-0.332962\pi\) | ||||
0.501010 | + | 0.865442i | \(0.332962\pi\) | |||||||
\(318\) | −14.9086 | −0.836030 | ||||||||
\(319\) | −4.96928 | −0.278226 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.67944 | −0.540254 | ||||||||
\(322\) | −8.84736 | −0.493044 | ||||||||
\(323\) | 0.652066 | 0.0362819 | ||||||||
\(324\) | −8.08283 | −0.449046 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.8479 | 0.822350 | ||||||||
\(327\) | 9.58252 | 0.529914 | ||||||||
\(328\) | 7.09416 | 0.391710 | ||||||||
\(329\) | 42.9554 | 2.36821 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.3130 | 0.731750 | 0.365875 | − | 0.930664i | \(-0.380770\pi\) | ||||
0.365875 | + | 0.930664i | \(0.380770\pi\) | |||||||
\(332\) | −22.5848 | −1.23950 | ||||||||
\(333\) | 5.28420 | 0.289572 | ||||||||
\(334\) | 27.4714 | 1.50317 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −29.1941 | −1.59267 | ||||||||
\(337\) | −3.08338 | −0.167962 | −0.0839812 | − | 0.996467i | \(-0.526764\pi\) | ||||
−0.0839812 | + | 0.996467i | \(0.526764\pi\) | |||||||
\(338\) | −11.9767 | −0.651444 | ||||||||
\(339\) | −6.44791 | −0.350202 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.7459 | 0.852691 | ||||||||
\(342\) | 2.33295 | 0.126151 | ||||||||
\(343\) | −33.3063 | −1.79837 | ||||||||
\(344\) | −1.66009 | −0.0895058 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −29.7085 | −1.59714 | ||||||||
\(347\) | −11.5617 | −0.620666 | −0.310333 | − | 0.950628i | \(-0.600441\pi\) | ||||
−0.310333 | + | 0.950628i | \(0.600441\pi\) | |||||||
\(348\) | 7.49306 | 0.401670 | ||||||||
\(349\) | −16.4980 | −0.883117 | −0.441558 | − | 0.897232i | \(-0.645574\pi\) | ||||
−0.441558 | + | 0.897232i | \(0.645574\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.7085 | −0.785084 | ||||||||
\(352\) | −11.7335 | −0.625400 | ||||||||
\(353\) | −13.7252 | −0.730518 | −0.365259 | − | 0.930906i | \(-0.619020\pi\) | ||||
−0.365259 | + | 0.930906i | \(0.619020\pi\) | |||||||
\(354\) | −10.3202 | −0.548514 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −13.0180 | −0.689952 | ||||||||
\(357\) | −3.60442 | −0.190766 | ||||||||
\(358\) | 11.4947 | 0.607512 | ||||||||
\(359\) | 15.1442 | 0.799282 | 0.399641 | − | 0.916672i | \(-0.369135\pi\) | ||||
0.399641 | + | 0.916672i | \(0.369135\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6393 | −0.928386 | ||||||||
\(362\) | −10.9432 | −0.575161 | ||||||||
\(363\) | 11.9623 | 0.627859 | ||||||||
\(364\) | 20.2165 | 1.05964 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.5507 | 0.603762 | ||||||||
\(367\) | −11.2719 | −0.588390 | −0.294195 | − | 0.955745i | \(-0.595051\pi\) | ||||
−0.294195 | + | 0.955745i | \(0.595051\pi\) | |||||||
\(368\) | −4.52769 | −0.236022 | ||||||||
\(369\) | 12.3035 | 0.640495 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −25.5617 | −1.32710 | ||||||||
\(372\) | −23.7429 | −1.23101 | ||||||||
\(373\) | 35.3296 | 1.82930 | 0.914648 | − | 0.404252i | \(-0.132468\pi\) | ||||
0.914648 | + | 0.404252i | \(0.132468\pi\) | |||||||
\(374\) | −1.68088 | −0.0869164 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.59894 | 0.288743 | ||||||||
\(377\) | 8.25257 | 0.425029 | ||||||||
\(378\) | −50.0401 | −2.57378 | ||||||||
\(379\) | −36.8598 | −1.89336 | −0.946679 | − | 0.322178i | \(-0.895585\pi\) | ||||
−0.946679 | + | 0.322178i | \(0.895585\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.1390 | 0.826828 | ||||||||
\(382\) | −16.0224 | −0.819775 | ||||||||
\(383\) | 4.27065 | 0.218220 | 0.109110 | − | 0.994030i | \(-0.465200\pi\) | ||||
0.109110 | + | 0.994030i | \(0.465200\pi\) | |||||||
\(384\) | −6.64133 | −0.338914 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −30.7714 | −1.56623 | ||||||||
\(387\) | −2.87911 | −0.146353 | ||||||||
\(388\) | 4.42279 | 0.224533 | ||||||||
\(389\) | −6.42988 | −0.326008 | −0.163004 | − | 0.986625i | \(-0.552118\pi\) | ||||
−0.163004 | + | 0.986625i | \(0.552118\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.559006 | −0.0282701 | ||||||||
\(392\) | −8.54512 | −0.431594 | ||||||||
\(393\) | 18.1423 | 0.915160 | ||||||||
\(394\) | −11.1160 | −0.560017 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.75187 | −0.138287 | ||||||||
\(397\) | 33.9539 | 1.70410 | 0.852049 | − | 0.523462i | \(-0.175360\pi\) | ||||
0.852049 | + | 0.523462i | \(0.175360\pi\) | |||||||
\(398\) | −36.1165 | −1.81036 | ||||||||
\(399\) | −7.52133 | −0.376537 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.6421 | 1.38038 | 0.690189 | − | 0.723629i | \(-0.257527\pi\) | ||||
0.690189 | + | 0.723629i | \(0.257527\pi\) | |||||||
\(402\) | 7.00692 | 0.349473 | ||||||||
\(403\) | −26.1495 | −1.30260 | ||||||||
\(404\) | −14.9861 | −0.745587 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 28.0761 | 1.39339 | ||||||||
\(407\) | −7.94457 | −0.393798 | ||||||||
\(408\) | −0.469812 | −0.0232591 | ||||||||
\(409\) | −13.2161 | −0.653494 | −0.326747 | − | 0.945112i | \(-0.605952\pi\) | ||||
−0.326747 | + | 0.945112i | \(0.605952\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.9945 | −1.18356 | ||||||||
\(412\) | 14.6047 | 0.719522 | ||||||||
\(413\) | −17.6947 | −0.870700 | ||||||||
\(414\) | −2.00000 | −0.0982946 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 19.4861 | 0.955384 | ||||||||
\(417\) | 27.2609 | 1.33497 | ||||||||
\(418\) | −3.50749 | −0.171557 | ||||||||
\(419\) | 23.4772 | 1.14694 | 0.573468 | − | 0.819228i | \(-0.305598\pi\) | ||||
0.573468 | + | 0.819228i | \(0.305598\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.1138 | 1.12650 | 0.563249 | − | 0.826287i | \(-0.309551\pi\) | ||||
0.563249 | + | 0.826287i | \(0.309551\pi\) | |||||||
\(422\) | −9.37450 | −0.456343 | ||||||||
\(423\) | 9.71032 | 0.472132 | ||||||||
\(424\) | −3.33180 | −0.161806 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −21.2180 | −1.02802 | ||||||||
\(427\) | 19.8044 | 0.958401 | ||||||||
\(428\) | 11.6701 | 0.564093 | ||||||||
\(429\) | 5.69892 | 0.275146 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.52709 | −0.458904 | −0.229452 | − | 0.973320i | \(-0.573693\pi\) | ||||
−0.229452 | + | 0.973320i | \(0.573693\pi\) | |||||||
\(432\) | −25.6083 | −1.23208 | ||||||||
\(433\) | −2.79445 | −0.134293 | −0.0671464 | − | 0.997743i | \(-0.521389\pi\) | ||||
−0.0671464 | + | 0.997743i | \(0.521389\pi\) | |||||||
\(434\) | −88.9635 | −4.27039 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.5532 | −0.553298 | ||||||||
\(437\) | −1.16647 | −0.0558001 | ||||||||
\(438\) | 26.6193 | 1.27192 | ||||||||
\(439\) | 2.09578 | 0.100026 | 0.0500129 | − | 0.998749i | \(-0.484074\pi\) | ||||
0.0500129 | + | 0.998749i | \(0.484074\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.8199 | −0.705711 | ||||||||
\(442\) | 2.79147 | 0.132777 | ||||||||
\(443\) | 27.0870 | 1.28694 | 0.643470 | − | 0.765471i | \(-0.277494\pi\) | ||||
0.643470 | + | 0.765471i | \(0.277494\pi\) | |||||||
\(444\) | 11.9794 | 0.568518 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 25.8819 | 1.22555 | ||||||||
\(447\) | −18.5130 | −0.875633 | ||||||||
\(448\) | 24.5714 | 1.16089 | ||||||||
\(449\) | −0.470272 | −0.0221935 | −0.0110967 | − | 0.999938i | \(-0.503532\pi\) | ||||
−0.0110967 | + | 0.999938i | \(0.503532\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.4978 | −0.871028 | ||||||||
\(452\) | 7.77394 | 0.365656 | ||||||||
\(453\) | 3.50910 | 0.164872 | ||||||||
\(454\) | −26.2867 | −1.23370 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.980354 | −0.0459093 | ||||||||
\(457\) | −5.83768 | −0.273075 | −0.136538 | − | 0.990635i | \(-0.543597\pi\) | ||||
−0.136538 | + | 0.990635i | \(0.543597\pi\) | |||||||
\(458\) | 52.6071 | 2.45817 | ||||||||
\(459\) | −3.16170 | −0.147575 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.8487 | 0.505277 | 0.252638 | − | 0.967561i | \(-0.418702\pi\) | ||||
0.252638 | + | 0.967561i | \(0.418702\pi\) | |||||||
\(462\) | 19.3883 | 0.902027 | ||||||||
\(463\) | −1.06258 | −0.0493825 | −0.0246912 | − | 0.999695i | \(-0.507860\pi\) | ||||
−0.0246912 | + | 0.999695i | \(0.507860\pi\) | |||||||
\(464\) | 14.3681 | 0.667024 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.0744740 | 0.00344994 | ||||||||
\(467\) | 4.99885 | 0.231319 | 0.115660 | − | 0.993289i | \(-0.463102\pi\) | ||||
0.115660 | + | 0.993289i | \(0.463102\pi\) | |||||||
\(468\) | 4.57008 | 0.211252 | ||||||||
\(469\) | 12.0138 | 0.554747 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.9348 | −0.549928 | ||||||||
\(472\) | −2.30639 | −0.106160 | ||||||||
\(473\) | 4.32862 | 0.199030 | ||||||||
\(474\) | −32.3772 | −1.48713 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.34568 | 0.199184 | ||||||||
\(477\) | −5.77838 | −0.264574 | ||||||||
\(478\) | −26.6969 | −1.22109 | ||||||||
\(479\) | 33.4283 | 1.52738 | 0.763688 | − | 0.645585i | \(-0.223387\pi\) | ||||
0.763688 | + | 0.645585i | \(0.223387\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.1937 | 0.601580 | ||||||||
\(482\) | −23.0373 | −1.04932 | ||||||||
\(483\) | 6.44791 | 0.293390 | ||||||||
\(484\) | −14.4224 | −0.655564 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.7085 | −0.893998 | ||||||||
\(487\) | 10.7901 | 0.488945 | 0.244473 | − | 0.969656i | \(-0.421385\pi\) | ||||
0.244473 | + | 0.969656i | \(0.421385\pi\) | |||||||
\(488\) | 2.58137 | 0.116853 | ||||||||
\(489\) | −10.8211 | −0.489346 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.8127 | 0.713618 | 0.356809 | − | 0.934177i | \(-0.383865\pi\) | ||||
0.356809 | + | 0.934177i | \(0.383865\pi\) | |||||||
\(492\) | 27.8924 | 1.25749 | ||||||||
\(493\) | 1.77394 | 0.0798944 | ||||||||
\(494\) | 5.82495 | 0.262077 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −45.5276 | −2.04425 | ||||||||
\(497\) | −36.3798 | −1.63185 | ||||||||
\(498\) | 35.9703 | 1.61187 | ||||||||
\(499\) | 12.9711 | 0.580668 | 0.290334 | − | 0.956925i | \(-0.406234\pi\) | ||||
0.290334 | + | 0.956925i | \(0.406234\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.0210 | −0.894474 | ||||||||
\(502\) | −34.1426 | −1.52386 | ||||||||
\(503\) | 0.998849 | 0.0445365 | 0.0222682 | − | 0.999752i | \(-0.492911\pi\) | ||||
0.0222682 | + | 0.999752i | \(0.492911\pi\) | |||||||
\(504\) | −2.88199 | −0.128374 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.00692 | 0.133674 | ||||||||
\(507\) | 8.72853 | 0.387648 | ||||||||
\(508\) | −19.4581 | −0.863313 | ||||||||
\(509\) | −20.6936 | −0.917228 | −0.458614 | − | 0.888636i | \(-0.651654\pi\) | ||||
−0.458614 | + | 0.888636i | \(0.651654\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 45.6406 | 2.01902 | ||||||||
\(512\) | 28.4880 | 1.25900 | ||||||||
\(513\) | −6.59750 | −0.291287 | ||||||||
\(514\) | −19.6468 | −0.866583 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.52702 | −0.287336 | ||||||||
\(517\) | −14.5991 | −0.642066 | ||||||||
\(518\) | 44.8863 | 1.97219 | ||||||||
\(519\) | 21.6514 | 0.950393 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.2620 | 1.72010 | 0.860049 | − | 0.510212i | \(-0.170433\pi\) | ||||
0.860049 | + | 0.510212i | \(0.170433\pi\) | |||||||
\(522\) | 6.34678 | 0.277791 | ||||||||
\(523\) | 1.74162 | 0.0761556 | 0.0380778 | − | 0.999275i | \(-0.487877\pi\) | ||||
0.0380778 | + | 0.999275i | \(0.487877\pi\) | |||||||
\(524\) | −21.8734 | −0.955543 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.67812 | 0.334782 | ||||||||
\(527\) | −5.62101 | −0.244855 | ||||||||
\(528\) | 9.92210 | 0.431804 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 9.06811 | 0.393152 | ||||||||
\(533\) | 30.7196 | 1.33061 | ||||||||
\(534\) | 20.7335 | 0.897226 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.56592 | 0.0676375 | ||||||||
\(537\) | −8.37726 | −0.361505 | ||||||||
\(538\) | −5.53184 | −0.238495 | ||||||||
\(539\) | 22.2811 | 0.959717 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.18117 | −0.351736 | −0.175868 | − | 0.984414i | \(-0.556273\pi\) | ||||
−0.175868 | + | 0.984414i | \(0.556273\pi\) | |||||||
\(542\) | 27.2564 | 1.17076 | ||||||||
\(543\) | 7.97534 | 0.342254 | ||||||||
\(544\) | 4.18866 | 0.179587 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −32.1985 | −1.37797 | ||||||||
\(547\) | 24.2470 | 1.03673 | 0.518364 | − | 0.855160i | \(-0.326541\pi\) | ||||
0.518364 | + | 0.855160i | \(0.326541\pi\) | |||||||
\(548\) | 28.9290 | 1.23579 | ||||||||
\(549\) | 4.47690 | 0.191069 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.70168 | 0.157697 | ||||||||
\(552\) | 0.840442 | 0.0357716 | ||||||||
\(553\) | −55.5129 | −2.36065 | ||||||||
\(554\) | −17.5427 | −0.745317 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −32.8672 | −1.39388 | ||||||||
\(557\) | 35.0966 | 1.48709 | 0.743546 | − | 0.668685i | \(-0.233142\pi\) | ||||
0.743546 | + | 0.668685i | \(0.233142\pi\) | |||||||
\(558\) | −20.1108 | −0.851356 | ||||||||
\(559\) | −7.18862 | −0.304046 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.22502 | 0.0517204 | ||||||||
\(562\) | 28.5421 | 1.20397 | ||||||||
\(563\) | 6.98179 | 0.294247 | 0.147124 | − | 0.989118i | \(-0.452998\pi\) | ||||
0.147124 | + | 0.989118i | \(0.452998\pi\) | |||||||
\(564\) | 22.0136 | 0.926938 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.83514 | −0.245269 | ||||||||
\(567\) | 22.0723 | 0.926948 | ||||||||
\(568\) | −4.74186 | −0.198964 | ||||||||
\(569\) | 21.7280 | 0.910886 | 0.455443 | − | 0.890265i | \(-0.349481\pi\) | ||||
0.455443 | + | 0.890265i | \(0.349481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.71016 | −0.197114 | −0.0985570 | − | 0.995131i | \(-0.531423\pi\) | ||||
−0.0985570 | + | 0.995131i | \(0.531423\pi\) | |||||||
\(572\) | −6.87092 | −0.287288 | ||||||||
\(573\) | 11.6770 | 0.487814 | ||||||||
\(574\) | 104.511 | 4.36222 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.55452 | 0.231438 | ||||||||
\(577\) | 9.49085 | 0.395109 | 0.197555 | − | 0.980292i | \(-0.436700\pi\) | ||||
0.197555 | + | 0.980292i | \(0.436700\pi\) | |||||||
\(578\) | −32.0437 | −1.33284 | ||||||||
\(579\) | 22.4261 | 0.931996 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 61.6736 | 2.55865 | ||||||||
\(582\) | −7.04409 | −0.291987 | ||||||||
\(583\) | 8.68756 | 0.359802 | ||||||||
\(584\) | 5.94895 | 0.246169 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36.9235 | 1.52530 | ||||||||
\(587\) | −10.4952 | −0.433184 | −0.216592 | − | 0.976262i | \(-0.569494\pi\) | ||||
−0.216592 | + | 0.976262i | \(0.569494\pi\) | |||||||
\(588\) | −33.5972 | −1.38552 | ||||||||
\(589\) | −11.7293 | −0.483299 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.10130 | 0.333243 | ||||||||
\(592\) | 22.9708 | 0.944096 | ||||||||
\(593\) | 18.2138 | 0.747951 | 0.373975 | − | 0.927439i | \(-0.377994\pi\) | ||||
0.373975 | + | 0.927439i | \(0.377994\pi\) | |||||||
\(594\) | 17.0069 | 0.697802 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.3202 | 0.914272 | ||||||||
\(597\) | 26.3215 | 1.07727 | ||||||||
\(598\) | −4.99364 | −0.204205 | ||||||||
\(599\) | −20.8055 | −0.850091 | −0.425045 | − | 0.905172i | \(-0.639742\pi\) | ||||
−0.425045 | + | 0.905172i | \(0.639742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −47.4004 | −1.93350 | −0.966752 | − | 0.255716i | \(-0.917689\pi\) | ||||
−0.966752 | + | 0.255716i | \(0.917689\pi\) | |||||||
\(602\) | −24.4564 | −0.996770 | ||||||||
\(603\) | 2.71580 | 0.110596 | ||||||||
\(604\) | −4.23076 | −0.172147 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 23.8681 | 0.969576 | ||||||||
\(607\) | 5.77118 | 0.234245 | 0.117123 | − | 0.993117i | \(-0.462633\pi\) | ||||
0.117123 | + | 0.993117i | \(0.462633\pi\) | |||||||
\(608\) | 8.74046 | 0.354473 | ||||||||
\(609\) | −20.4617 | −0.829152 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.2449 | 0.980844 | ||||||||
\(612\) | 0.982368 | 0.0397099 | ||||||||
\(613\) | −38.9329 | −1.57248 | −0.786242 | − | 0.617919i | \(-0.787976\pi\) | ||||
−0.786242 | + | 0.617919i | \(0.787976\pi\) | |||||||
\(614\) | 39.4404 | 1.59169 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.33295 | 0.174580 | ||||||||
\(617\) | −10.1653 | −0.409241 | −0.204620 | − | 0.978841i | \(-0.565596\pi\) | ||||
−0.204620 | + | 0.978841i | \(0.565596\pi\) | |||||||
\(618\) | −23.2606 | −0.935680 | ||||||||
\(619\) | 2.09923 | 0.0843752 | 0.0421876 | − | 0.999110i | \(-0.486567\pi\) | ||||
0.0421876 | + | 0.999110i | \(0.486567\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.65593 | 0.226965 | ||||||||
\(622\) | −18.8936 | −0.757565 | ||||||||
\(623\) | 35.5490 | 1.42424 | ||||||||
\(624\) | −16.4778 | −0.659639 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −43.1396 | −1.72420 | ||||||||
\(627\) | 2.55624 | 0.102087 | ||||||||
\(628\) | 14.3893 | 0.574194 | ||||||||
\(629\) | 2.83607 | 0.113081 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.3066 | −1.28611 | −0.643053 | − | 0.765821i | \(-0.722333\pi\) | ||||
−0.643053 | + | 0.765821i | \(0.722333\pi\) | |||||||
\(632\) | −7.23574 | −0.287822 | ||||||||
\(633\) | 6.83209 | 0.271551 | ||||||||
\(634\) | 34.2576 | 1.36054 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −13.0998 | −0.519439 | ||||||||
\(637\) | −37.0027 | −1.46610 | ||||||||
\(638\) | −9.54212 | −0.377776 | ||||||||
\(639\) | −8.22387 | −0.325331 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.5758 | 0.575711 | 0.287856 | − | 0.957674i | \(-0.407058\pi\) | ||||
0.287856 | + | 0.957674i | \(0.407058\pi\) | |||||||
\(642\) | −18.5867 | −0.733557 | ||||||||
\(643\) | 42.5090 | 1.67639 | 0.838196 | − | 0.545369i | \(-0.183611\pi\) | ||||
0.838196 | + | 0.545369i | \(0.183611\pi\) | |||||||
\(644\) | −7.77394 | −0.306336 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.25211 | 0.0492636 | ||||||||
\(647\) | 3.04979 | 0.119900 | 0.0599498 | − | 0.998201i | \(-0.480906\pi\) | ||||
0.0599498 | + | 0.998201i | \(0.480906\pi\) | |||||||
\(648\) | 2.87697 | 0.113018 | ||||||||
\(649\) | 6.01383 | 0.236064 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 64.8362 | 2.54113 | ||||||||
\(652\) | 13.0465 | 0.510939 | ||||||||
\(653\) | −17.9600 | −0.702830 | −0.351415 | − | 0.936220i | \(-0.614299\pi\) | ||||
−0.351415 | + | 0.936220i | \(0.614299\pi\) | |||||||
\(654\) | 18.4006 | 0.719518 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 53.4844 | 2.08821 | ||||||||
\(657\) | 10.3173 | 0.402518 | ||||||||
\(658\) | 82.4838 | 3.21555 | ||||||||
\(659\) | 46.3411 | 1.80519 | 0.902597 | − | 0.430486i | \(-0.141658\pi\) | ||||
0.902597 | + | 0.430486i | \(0.141658\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.23165 | 0.0479056 | 0.0239528 | − | 0.999713i | \(-0.492375\pi\) | ||||
0.0239528 | + | 0.999713i | \(0.492375\pi\) | |||||||
\(662\) | 25.5639 | 0.993570 | ||||||||
\(663\) | −2.03441 | −0.0790099 | ||||||||
\(664\) | 8.03874 | 0.311963 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.1468 | 0.393182 | ||||||||
\(667\) | −3.17339 | −0.122874 | ||||||||
\(668\) | 24.1384 | 0.933944 | ||||||||
\(669\) | −18.8626 | −0.729271 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.73083 | −0.259841 | ||||||||
\(672\) | −48.3146 | −1.86378 | ||||||||
\(673\) | −42.4664 | −1.63696 | −0.818479 | − | 0.574537i | \(-0.805182\pi\) | ||||
−0.818479 | + | 0.574537i | \(0.805182\pi\) | |||||||
\(674\) | −5.92077 | −0.228060 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.5236 | −0.404753 | ||||||||
\(677\) | −1.41777 | −0.0544893 | −0.0272447 | − | 0.999629i | \(-0.508673\pi\) | ||||
−0.0272447 | + | 0.999629i | \(0.508673\pi\) | |||||||
\(678\) | −12.3814 | −0.475505 | ||||||||
\(679\) | −12.0776 | −0.463495 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.1576 | 0.734121 | ||||||||
\(682\) | 30.2357 | 1.15778 | ||||||||
\(683\) | −4.60886 | −0.176353 | −0.0881766 | − | 0.996105i | \(-0.528104\pi\) | ||||
−0.0881766 | + | 0.996105i | \(0.528104\pi\) | |||||||
\(684\) | 2.04990 | 0.0783800 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −63.9555 | −2.44183 | ||||||||
\(687\) | −38.3398 | −1.46276 | ||||||||
\(688\) | −12.5157 | −0.477158 | ||||||||
\(689\) | −14.4276 | −0.549647 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.8903 | −0.642537 | −0.321269 | − | 0.946988i | \(-0.604109\pi\) | ||||
−0.321269 | + | 0.946988i | \(0.604109\pi\) | |||||||
\(692\) | −26.1041 | −0.992330 | ||||||||
\(693\) | 7.51470 | 0.285460 | ||||||||
\(694\) | −22.2011 | −0.842741 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.66705 | −0.101094 | ||||||||
\(697\) | 6.60338 | 0.250121 | ||||||||
\(698\) | −31.6798 | −1.19910 | ||||||||
\(699\) | −0.0542763 | −0.00205292 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.9543 | −0.451508 | −0.225754 | − | 0.974184i | \(-0.572484\pi\) | ||||
−0.225754 | + | 0.974184i | \(0.572484\pi\) | |||||||
\(702\) | −28.2437 | −1.06599 | ||||||||
\(703\) | 5.91801 | 0.223202 | ||||||||
\(704\) | −8.35098 | −0.314740 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.3554 | −0.991899 | ||||||||
\(707\) | 40.9235 | 1.53909 | ||||||||
\(708\) | −9.06811 | −0.340800 | ||||||||
\(709\) | −12.6755 | −0.476040 | −0.238020 | − | 0.971260i | \(-0.576498\pi\) | ||||
−0.238020 | + | 0.971260i | \(0.576498\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.5490 | −0.470626 | ||||||||
\(712\) | 4.63357 | 0.173650 | ||||||||
\(713\) | 10.0554 | 0.376577 | ||||||||
\(714\) | −6.92128 | −0.259022 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.1001 | 0.377457 | ||||||||
\(717\) | 19.4566 | 0.726618 | ||||||||
\(718\) | 29.0803 | 1.08527 | ||||||||
\(719\) | −34.7351 | −1.29540 | −0.647700 | − | 0.761896i | \(-0.724269\pi\) | ||||
−0.647700 | + | 0.761896i | \(0.724269\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39.8819 | −1.48528 | ||||||||
\(722\) | −33.8714 | −1.26056 | ||||||||
\(723\) | 16.7895 | 0.624408 | ||||||||
\(724\) | −9.61549 | −0.357357 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 22.9703 | 0.852508 | ||||||||
\(727\) | −27.6631 | −1.02597 | −0.512984 | − | 0.858398i | \(-0.671460\pi\) | ||||
−0.512984 | + | 0.858398i | \(0.671460\pi\) | |||||||
\(728\) | −7.19580 | −0.266694 | ||||||||
\(729\) | 28.7351 | 1.06426 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.54524 | −0.0571528 | ||||||||
\(732\) | 10.1493 | 0.375127 | ||||||||
\(733\) | 2.14239 | 0.0791309 | 0.0395654 | − | 0.999217i | \(-0.487403\pi\) | ||||
0.0395654 | + | 0.999217i | \(0.487403\pi\) | |||||||
\(734\) | −21.6446 | −0.798917 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.49306 | −0.276198 | ||||||||
\(737\) | −4.08309 | −0.150403 | ||||||||
\(738\) | 23.6255 | 0.869665 | ||||||||
\(739\) | −42.6249 | −1.56798 | −0.783991 | − | 0.620772i | \(-0.786819\pi\) | ||||
−0.783991 | + | 0.620772i | \(0.786819\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.24519 | −0.155951 | ||||||||
\(742\) | −49.0841 | −1.80194 | ||||||||
\(743\) | −23.4687 | −0.860982 | −0.430491 | − | 0.902595i | \(-0.641660\pi\) | ||||
−0.430491 | + | 0.902595i | \(0.641660\pi\) | |||||||
\(744\) | 8.45096 | 0.309827 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 67.8406 | 2.48382 | ||||||||
\(747\) | 13.9417 | 0.510100 | ||||||||
\(748\) | −1.47695 | −0.0540026 | ||||||||
\(749\) | −31.8681 | −1.16444 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.2579 | −0.994654 | −0.497327 | − | 0.867563i | \(-0.665685\pi\) | ||||
−0.497327 | + | 0.867563i | \(0.665685\pi\) | |||||||
\(752\) | 42.2116 | 1.53930 | ||||||||
\(753\) | 24.8830 | 0.906786 | ||||||||
\(754\) | 15.8468 | 0.577105 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −43.9689 | −1.59913 | ||||||||
\(757\) | 12.7382 | 0.462976 | 0.231488 | − | 0.972838i | \(-0.425641\pi\) | ||||
0.231488 | + | 0.972838i | \(0.425641\pi\) | |||||||
\(758\) | −70.7789 | −2.57080 | ||||||||
\(759\) | −2.19143 | −0.0795437 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.61715 | 0.239871 | 0.119936 | − | 0.992782i | \(-0.461731\pi\) | ||||
0.119936 | + | 0.992782i | \(0.461731\pi\) | |||||||
\(762\) | 30.9905 | 1.12267 | ||||||||
\(763\) | 31.5490 | 1.14215 | ||||||||
\(764\) | −14.0784 | −0.509340 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.20060 | 0.296300 | ||||||||
\(767\) | −9.98727 | −0.360619 | ||||||||
\(768\) | −27.6792 | −0.998786 | ||||||||
\(769\) | −27.2116 | −0.981275 | −0.490638 | − | 0.871364i | \(-0.663236\pi\) | ||||
−0.490638 | + | 0.871364i | \(0.663236\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.3185 | 0.515668 | ||||||||
\(772\) | −27.0381 | −0.973121 | ||||||||
\(773\) | −22.9249 | −0.824552 | −0.412276 | − | 0.911059i | \(-0.635266\pi\) | ||||
−0.412276 | + | 0.911059i | \(0.635266\pi\) | |||||||
\(774\) | −5.52853 | −0.198719 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.57423 | −0.0565116 | ||||||||
\(777\) | −32.7129 | −1.17357 | ||||||||
\(778\) | −12.3468 | −0.442654 | ||||||||
\(779\) | 13.7792 | 0.493693 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.3642 | 0.442427 | ||||||||
\(782\) | −1.07341 | −0.0383852 | ||||||||
\(783\) | −17.9485 | −0.641427 | ||||||||
\(784\) | −64.4235 | −2.30084 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 34.8373 | 1.24261 | ||||||||
\(787\) | −13.0620 | −0.465610 | −0.232805 | − | 0.972523i | \(-0.574790\pi\) | ||||
−0.232805 | + | 0.972523i | \(0.574790\pi\) | |||||||
\(788\) | −9.76736 | −0.347948 | ||||||||
\(789\) | −5.59578 | −0.199215 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.2288 | −0.754808 | ||||||||
\(792\) | 0.979490 | 0.0348047 | ||||||||
\(793\) | 11.1780 | 0.396943 | ||||||||
\(794\) | 65.1990 | 2.31383 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −31.7347 | −1.12480 | ||||||||
\(797\) | −20.9305 | −0.741395 | −0.370697 | − | 0.928754i | \(-0.620881\pi\) | ||||
−0.370697 | + | 0.928754i | \(0.620881\pi\) | |||||||
\(798\) | −14.4426 | −0.511263 | ||||||||
\(799\) | 5.21160 | 0.184373 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.03607 | 0.283941 | ||||||||
\(802\) | 53.0788 | 1.87428 | ||||||||
\(803\) | −15.5117 | −0.547396 | ||||||||
\(804\) | 6.15680 | 0.217133 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −50.2129 | −1.76867 | ||||||||
\(807\) | 4.03158 | 0.141918 | ||||||||
\(808\) | 5.33410 | 0.187653 | ||||||||
\(809\) | 18.0664 | 0.635180 | 0.317590 | − | 0.948228i | \(-0.397126\pi\) | ||||
0.317590 | + | 0.948228i | \(0.397126\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.8658 | 1.22430 | 0.612152 | − | 0.790740i | \(-0.290304\pi\) | ||||
0.612152 | + | 0.790740i | \(0.290304\pi\) | |||||||
\(812\) | 24.6698 | 0.865739 | ||||||||
\(813\) | −19.8644 | −0.696673 | ||||||||
\(814\) | −15.2553 | −0.534699 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.54201 | −0.123995 | ||||||||
\(817\) | −3.22444 | −0.112809 | ||||||||
\(818\) | −25.3778 | −0.887314 | ||||||||
\(819\) | −12.4798 | −0.436079 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.5989 | 0.509507 | 0.254753 | − | 0.967006i | \(-0.418006\pi\) | ||||
0.254753 | + | 0.967006i | \(0.418006\pi\) | |||||||
\(822\) | −46.0747 | −1.60704 | ||||||||
\(823\) | −25.8126 | −0.899771 | −0.449886 | − | 0.893086i | \(-0.648535\pi\) | ||||
−0.449886 | + | 0.893086i | \(0.648535\pi\) | |||||||
\(824\) | −5.19834 | −0.181093 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −33.9778 | −1.18224 | ||||||||
\(827\) | −54.9097 | −1.90940 | −0.954698 | − | 0.297577i | \(-0.903822\pi\) | ||||
−0.954698 | + | 0.297577i | \(0.903822\pi\) | |||||||
\(828\) | −1.75735 | −0.0610721 | ||||||||
\(829\) | −27.4809 | −0.954452 | −0.477226 | − | 0.878781i | \(-0.658358\pi\) | ||||
−0.477226 | + | 0.878781i | \(0.658358\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.7850 | 0.443507 | ||||||||
\(832\) | 13.8686 | 0.480808 | ||||||||
\(833\) | −7.95396 | −0.275589 | ||||||||
\(834\) | 52.3470 | 1.81263 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.08194 | −0.106591 | ||||||||
\(837\) | 56.8725 | 1.96580 | ||||||||
\(838\) | 45.0814 | 1.55731 | ||||||||
\(839\) | −1.46577 | −0.0506041 | −0.0253020 | − | 0.999680i | \(-0.508055\pi\) | ||||
−0.0253020 | + | 0.999680i | \(0.508055\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9296 | −0.652744 | ||||||||
\(842\) | 44.3836 | 1.52956 | ||||||||
\(843\) | −20.8013 | −0.716436 | ||||||||
\(844\) | −8.23713 | −0.283534 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 18.6460 | 0.641062 | ||||||||
\(847\) | 39.3841 | 1.35325 | ||||||||
\(848\) | −25.1191 | −0.862594 | ||||||||
\(849\) | 4.25262 | 0.145949 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.07341 | −0.173914 | ||||||||
\(852\) | −18.6437 | −0.638724 | ||||||||
\(853\) | −35.8044 | −1.22592 | −0.612959 | − | 0.790115i | \(-0.710021\pi\) | ||||
−0.612959 | + | 0.790115i | \(0.710021\pi\) | |||||||
\(854\) | 38.0288 | 1.30132 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.15379 | −0.141974 | ||||||||
\(857\) | −28.1663 | −0.962141 | −0.481070 | − | 0.876682i | \(-0.659752\pi\) | ||||
−0.481070 | + | 0.876682i | \(0.659752\pi\) | |||||||
\(858\) | 10.9432 | 0.373594 | ||||||||
\(859\) | 20.3185 | 0.693258 | 0.346629 | − | 0.938002i | \(-0.387326\pi\) | ||||
0.346629 | + | 0.938002i | \(0.387326\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −76.1674 | −2.59578 | ||||||||
\(862\) | −18.2941 | −0.623100 | ||||||||
\(863\) | 15.1357 | 0.515224 | 0.257612 | − | 0.966248i | \(-0.417064\pi\) | ||||
0.257612 | + | 0.966248i | \(0.417064\pi\) | |||||||
\(864\) | −42.3802 | −1.44180 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.36597 | −0.182343 | ||||||||
\(867\) | 23.3533 | 0.793120 | ||||||||
\(868\) | −78.1700 | −2.65326 | ||||||||
\(869\) | 18.8670 | 0.640018 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.78086 | 0.229761 | ||||||||
\(872\) | 4.11220 | 0.139257 | ||||||||
\(873\) | −2.73021 | −0.0924036 | ||||||||
\(874\) | −2.23989 | −0.0757654 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 23.3897 | 0.790265 | ||||||||
\(877\) | −12.9668 | −0.437856 | −0.218928 | − | 0.975741i | \(-0.570256\pi\) | ||||
−0.218928 | + | 0.975741i | \(0.570256\pi\) | |||||||
\(878\) | 4.02435 | 0.135815 | ||||||||
\(879\) | −26.9097 | −0.907640 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.3573 | −1.15753 | −0.578763 | − | 0.815496i | \(-0.696464\pi\) | ||||
−0.578763 | + | 0.815496i | \(0.696464\pi\) | |||||||
\(882\) | −28.4575 | −0.958215 | ||||||||
\(883\) | 14.7201 | 0.495372 | 0.247686 | − | 0.968840i | \(-0.420330\pi\) | ||||
0.247686 | + | 0.968840i | \(0.420330\pi\) | |||||||
\(884\) | 2.45279 | 0.0824963 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 52.0129 | 1.74741 | ||||||||
\(887\) | −20.9401 | −0.703101 | −0.351550 | − | 0.936169i | \(-0.614345\pi\) | ||||
−0.351550 | + | 0.936169i | \(0.614345\pi\) | |||||||
\(888\) | −4.26391 | −0.143087 | ||||||||
\(889\) | 53.1354 | 1.78210 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.50161 | −0.251313 | ||||||||
\(892\) | 22.7418 | 0.761451 | ||||||||
\(893\) | 10.8750 | 0.363919 | ||||||||
\(894\) | −35.5490 | −1.18894 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −21.8656 | −0.730477 | ||||||||
\(897\) | 3.63934 | 0.121514 | ||||||||
\(898\) | −0.903025 | −0.0301343 | ||||||||
\(899\) | −31.9097 | −1.06425 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.10130 | −0.103319 | ||||||||
\(902\) | −35.5199 | −1.18268 | ||||||||
\(903\) | 17.8237 | 0.593137 | ||||||||
\(904\) | −2.76703 | −0.0920300 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.73825 | 0.223863 | ||||||||
\(907\) | 40.2008 | 1.33485 | 0.667423 | − | 0.744679i | \(-0.267397\pi\) | ||||
0.667423 | + | 0.744679i | \(0.267397\pi\) | |||||||
\(908\) | −23.0974 | −0.766515 | ||||||||
\(909\) | 9.25101 | 0.306837 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.6058 | 1.80917 | 0.904586 | − | 0.426292i | \(-0.140180\pi\) | ||||
0.904586 | + | 0.426292i | \(0.140180\pi\) | |||||||
\(912\) | −7.39109 | −0.244744 | ||||||||
\(913\) | −20.9608 | −0.693700 | ||||||||
\(914\) | −11.2096 | −0.370782 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 46.2245 | 1.52730 | ||||||||
\(917\) | 59.7309 | 1.97249 | ||||||||
\(918\) | −6.07116 | −0.200378 | ||||||||
\(919\) | 13.8019 | 0.455284 | 0.227642 | − | 0.973745i | \(-0.426898\pi\) | ||||
0.227642 | + | 0.973745i | \(0.426898\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.7440 | −0.947147 | ||||||||
\(922\) | 20.8320 | 0.686065 | ||||||||
\(923\) | −20.5335 | −0.675868 | ||||||||
\(924\) | 17.0360 | 0.560444 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.04040 | −0.0670516 | ||||||||
\(927\) | −9.01556 | −0.296110 | ||||||||
\(928\) | 23.7784 | 0.780565 | ||||||||
\(929\) | 19.2775 | 0.632475 | 0.316237 | − | 0.948680i | \(-0.397580\pi\) | ||||
0.316237 | + | 0.948680i | \(0.397580\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.5975 | −0.543961 | ||||||||
\(932\) | 0.0654384 | 0.00214350 | ||||||||
\(933\) | 13.7696 | 0.450795 | ||||||||
\(934\) | 9.59889 | 0.314085 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.62666 | −0.0531689 | ||||||||
\(937\) | −48.0855 | −1.57089 | −0.785443 | − | 0.618934i | \(-0.787565\pi\) | ||||
−0.785443 | + | 0.618934i | \(0.787565\pi\) | |||||||
\(938\) | 23.0692 | 0.753237 | ||||||||
\(939\) | 31.4399 | 1.02600 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.6853 | −1.00031 | −0.500156 | − | 0.865935i | \(-0.666724\pi\) | ||||
−0.500156 | + | 0.865935i | \(0.666724\pi\) | |||||||
\(942\) | −22.9175 | −0.746693 | ||||||||
\(943\) | −11.8127 | −0.384675 | ||||||||
\(944\) | −17.3883 | −0.565942 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.31191 | 0.270244 | ||||||||
\(947\) | 12.9280 | 0.420103 | 0.210051 | − | 0.977690i | \(-0.432637\pi\) | ||||
0.210051 | + | 0.977690i | \(0.432637\pi\) | |||||||
\(948\) | −28.4490 | −0.923981 | ||||||||
\(949\) | 25.7605 | 0.836222 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.9668 | −0.809603 | ||||||||
\(952\) | −1.54678 | −0.0501316 | ||||||||
\(953\) | 6.38285 | 0.206761 | 0.103380 | − | 0.994642i | \(-0.467034\pi\) | ||||
0.103380 | + | 0.994642i | \(0.467034\pi\) | |||||||
\(954\) | −11.0958 | −0.359239 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −23.4579 | −0.758681 | ||||||||
\(957\) | 6.95425 | 0.224799 | ||||||||
\(958\) | 64.1897 | 2.07387 | ||||||||
\(959\) | −78.9982 | −2.55098 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 70.1107 | 2.26163 | ||||||||
\(962\) | 25.3348 | 0.816826 | ||||||||
\(963\) | −7.20398 | −0.232145 | ||||||||
\(964\) | −20.2423 | −0.651961 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 12.3814 | 0.398365 | ||||||||
\(967\) | 38.6028 | 1.24138 | 0.620691 | − | 0.784056i | \(-0.286852\pi\) | ||||
0.620691 | + | 0.784056i | \(0.286852\pi\) | |||||||
\(968\) | 5.13346 | 0.164996 | ||||||||
\(969\) | −0.912532 | −0.0293148 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.0216 | −0.770889 | −0.385444 | − | 0.922731i | \(-0.625952\pi\) | ||||
−0.385444 | + | 0.922731i | \(0.625952\pi\) | |||||||
\(972\) | −17.3174 | −0.555456 | ||||||||
\(973\) | 89.7525 | 2.87733 | ||||||||
\(974\) | 20.7193 | 0.663890 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19.4615 | 0.622946 | ||||||||
\(977\) | −45.5558 | −1.45746 | −0.728730 | − | 0.684801i | \(-0.759889\pi\) | ||||
−0.728730 | + | 0.684801i | \(0.759889\pi\) | |||||||
\(978\) | −20.7789 | −0.664435 | ||||||||
\(979\) | −12.0819 | −0.386139 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.13184 | 0.227702 | ||||||||
\(982\) | 30.3639 | 0.968952 | ||||||||
\(983\) | 29.1396 | 0.929408 | 0.464704 | − | 0.885466i | \(-0.346161\pi\) | ||||
0.464704 | + | 0.885466i | \(0.346161\pi\) | |||||||
\(984\) | −9.92791 | −0.316490 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.40636 | 0.108481 | ||||||||
\(987\) | −60.1138 | −1.91344 | ||||||||
\(988\) | 5.11823 | 0.162833 | ||||||||
\(989\) | 2.76426 | 0.0878985 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.0415 | −0.636639 | −0.318320 | − | 0.947983i | \(-0.603119\pi\) | ||||
−0.318320 | + | 0.947983i | \(0.603119\pi\) | |||||||
\(992\) | −75.3456 | −2.39222 | ||||||||
\(993\) | −18.6309 | −0.591233 | ||||||||
\(994\) | −69.8572 | −2.21573 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 31.6062 | 1.00148 | ||||||||
\(997\) | −0.340153 | −0.0107728 | −0.00538638 | − | 0.999985i | \(-0.501715\pi\) | ||||
−0.00538638 | + | 0.999985i | \(0.501715\pi\) | |||||||
\(998\) | 24.9074 | 0.788431 | ||||||||
\(999\) | −28.6949 | −0.907866 |
(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 | 575.2.a.i.1.4 | 4 | ||
3.2 | odd | 2 | 5175.2.a.bv.1.1 | 4 | |||
4.3 | odd | 2 | 9200.2.a.cq.1.3 | 4 | |||
5.2 | odd | 4 | 115.2.b.b.24.7 | yes | 8 | ||
5.3 | odd | 4 | 115.2.b.b.24.2 | ✓ | 8 | ||
5.4 | even | 2 | 575.2.a.j.1.1 | 4 | |||
15.2 | even | 4 | 1035.2.b.e.829.2 | 8 | |||
15.8 | even | 4 | 1035.2.b.e.829.7 | 8 | |||
15.14 | odd | 2 | 5175.2.a.bw.1.4 | 4 | |||
20.3 | even | 4 | 1840.2.e.d.369.6 | 8 | |||
20.7 | even | 4 | 1840.2.e.d.369.3 | 8 | |||
20.19 | odd | 2 | 9200.2.a.ck.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.b.b.24.2 | ✓ | 8 | 5.3 | odd | 4 | ||
115.2.b.b.24.7 | yes | 8 | 5.2 | odd | 4 | ||
575.2.a.i.1.4 | 4 | 1.1 | even | 1 | trivial | ||
575.2.a.j.1.1 | 4 | 5.4 | even | 2 | |||
1035.2.b.e.829.2 | 8 | 15.2 | even | 4 | |||
1035.2.b.e.829.7 | 8 | 15.8 | even | 4 | |||
1840.2.e.d.369.3 | 8 | 20.7 | even | 4 | |||
1840.2.e.d.369.6 | 8 | 20.3 | even | 4 | |||
5175.2.a.bv.1.1 | 4 | 3.2 | odd | 2 | |||
5175.2.a.bw.1.4 | 4 | 15.14 | odd | 2 | |||
9200.2.a.ck.1.2 | 4 | 20.19 | odd | 2 | |||
9200.2.a.cq.1.3 | 4 | 4.3 | odd | 2 |