Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.4642000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 8x^{4} + 5x^{3} + 14x^{2} - 9x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.92474\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.92474 | 1.11125 | 0.555623 | − | 0.831434i | \(-0.312480\pi\) | ||||
0.555623 | + | 0.831434i | \(0.312480\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.92474 | −0.785770 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.704605 | 0.234868 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.92474 | 0.555623 | ||||||||
\(13\) | 5.24489 | 1.45467 | 0.727335 | − | 0.686283i | \(-0.240759\pi\) | ||||
0.727335 | + | 0.686283i | \(0.240759\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 1.92474 | 0.496964 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.30919 | 1.04513 | 0.522566 | − | 0.852599i | \(-0.324975\pi\) | ||||
0.522566 | + | 0.852599i | \(0.324975\pi\) | |||||||
\(18\) | −0.704605 | −0.166077 | ||||||||
\(19\) | 0.740633 | 0.169913 | 0.0849564 | − | 0.996385i | \(-0.472925\pi\) | ||||
0.0849564 | + | 0.996385i | \(0.472925\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.92474 | 0.420012 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.856965 | −0.178689 | −0.0893447 | − | 0.996001i | \(-0.528477\pi\) | ||||
−0.0893447 | + | 0.996001i | \(0.528477\pi\) | |||||||
\(24\) | −1.92474 | −0.392885 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.24489 | −1.02861 | ||||||||
\(27\) | −4.41803 | −0.850250 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 8.37564 | 1.55532 | 0.777658 | − | 0.628687i | \(-0.216407\pi\) | ||||
0.777658 | + | 0.628687i | \(0.216407\pi\) | |||||||
\(30\) | −1.92474 | −0.351407 | ||||||||
\(31\) | 1.10298 | 0.198101 | 0.0990506 | − | 0.995082i | \(-0.468419\pi\) | ||||
0.0990506 | + | 0.995082i | \(0.468419\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.30919 | −0.739020 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0.704605 | 0.117434 | ||||||||
\(37\) | −1.77921 | −0.292500 | −0.146250 | − | 0.989248i | \(-0.546720\pi\) | ||||
−0.146250 | + | 0.989248i | \(0.546720\pi\) | |||||||
\(38\) | −0.740633 | −0.120146 | ||||||||
\(39\) | 10.0950 | 1.61650 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 10.7200 | 1.67418 | 0.837090 | − | 0.547065i | \(-0.184255\pi\) | ||||
0.837090 | + | 0.547065i | \(0.184255\pi\) | |||||||
\(42\) | −1.92474 | −0.296993 | ||||||||
\(43\) | −1.13472 | −0.173044 | −0.0865218 | − | 0.996250i | \(-0.527575\pi\) | ||||
−0.0865218 | + | 0.996250i | \(0.527575\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.704605 | 0.105036 | ||||||||
\(46\) | 0.856965 | 0.126353 | ||||||||
\(47\) | 8.40172 | 1.22552 | 0.612758 | − | 0.790271i | \(-0.290060\pi\) | ||||
0.612758 | + | 0.790271i | \(0.290060\pi\) | |||||||
\(48\) | 1.92474 | 0.277812 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 8.29405 | 1.16140 | ||||||||
\(52\) | 5.24489 | 0.727335 | ||||||||
\(53\) | −8.80661 | −1.20968 | −0.604840 | − | 0.796347i | \(-0.706763\pi\) | ||||
−0.604840 | + | 0.796347i | \(0.706763\pi\) | |||||||
\(54\) | 4.41803 | 0.601217 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 1.42552 | 0.188815 | ||||||||
\(58\) | −8.37564 | −1.09977 | ||||||||
\(59\) | −12.9838 | −1.69035 | −0.845175 | − | 0.534490i | \(-0.820504\pi\) | ||||
−0.845175 | + | 0.534490i | \(0.820504\pi\) | |||||||
\(60\) | 1.92474 | 0.248482 | ||||||||
\(61\) | −13.0887 | −1.67584 | −0.837920 | − | 0.545793i | \(-0.816228\pi\) | ||||
−0.837920 | + | 0.545793i | \(0.816228\pi\) | |||||||
\(62\) | −1.10298 | −0.140079 | ||||||||
\(63\) | 0.704605 | 0.0887719 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.24489 | 0.650548 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.93617 | 1.09173 | 0.545864 | − | 0.837874i | \(-0.316202\pi\) | ||||
0.545864 | + | 0.837874i | \(0.316202\pi\) | |||||||
\(68\) | 4.30919 | 0.522566 | ||||||||
\(69\) | −1.64943 | −0.198568 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −4.50750 | −0.534942 | −0.267471 | − | 0.963566i | \(-0.586188\pi\) | ||||
−0.267471 | + | 0.963566i | \(0.586188\pi\) | |||||||
\(72\) | −0.704605 | −0.0830385 | ||||||||
\(73\) | 3.33413 | 0.390230 | 0.195115 | − | 0.980780i | \(-0.437492\pi\) | ||||
0.195115 | + | 0.980780i | \(0.437492\pi\) | |||||||
\(74\) | 1.77921 | 0.206829 | ||||||||
\(75\) | 1.92474 | 0.222249 | ||||||||
\(76\) | 0.740633 | 0.0849564 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −10.0950 | −1.14304 | ||||||||
\(79\) | 1.56183 | 0.175719 | 0.0878597 | − | 0.996133i | \(-0.471997\pi\) | ||||
0.0878597 | + | 0.996133i | \(0.471997\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −10.6173 | −1.17971 | ||||||||
\(82\) | −10.7200 | −1.18382 | ||||||||
\(83\) | −0.609215 | −0.0668700 | −0.0334350 | − | 0.999441i | \(-0.510645\pi\) | ||||
−0.0334350 | + | 0.999441i | \(0.510645\pi\) | |||||||
\(84\) | 1.92474 | 0.210006 | ||||||||
\(85\) | 4.30919 | 0.467397 | ||||||||
\(86\) | 1.13472 | 0.122360 | ||||||||
\(87\) | 16.1209 | 1.72834 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.46836 | 0.155646 | 0.0778228 | − | 0.996967i | \(-0.475203\pi\) | ||||
0.0778228 | + | 0.996967i | \(0.475203\pi\) | |||||||
\(90\) | −0.704605 | −0.0742719 | ||||||||
\(91\) | 5.24489 | 0.549813 | ||||||||
\(92\) | −0.856965 | −0.0893447 | ||||||||
\(93\) | 2.12295 | 0.220139 | ||||||||
\(94\) | −8.40172 | −0.866571 | ||||||||
\(95\) | 0.740633 | 0.0759873 | ||||||||
\(96\) | −1.92474 | −0.196442 | ||||||||
\(97\) | 8.41705 | 0.854622 | 0.427311 | − | 0.904105i | \(-0.359461\pi\) | ||||
0.427311 | + | 0.904105i | \(0.359461\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 11.0295 | 1.09748 | 0.548740 | − | 0.835993i | \(-0.315108\pi\) | ||||
0.548740 | + | 0.835993i | \(0.315108\pi\) | |||||||
\(102\) | −8.29405 | −0.821233 | ||||||||
\(103\) | 5.86953 | 0.578342 | 0.289171 | − | 0.957277i | \(-0.406620\pi\) | ||||
0.289171 | + | 0.957277i | \(0.406620\pi\) | |||||||
\(104\) | −5.24489 | −0.514303 | ||||||||
\(105\) | 1.92474 | 0.187835 | ||||||||
\(106\) | 8.80661 | 0.855373 | ||||||||
\(107\) | −6.83162 | −0.660438 | −0.330219 | − | 0.943904i | \(-0.607123\pi\) | ||||
−0.330219 | + | 0.943904i | \(0.607123\pi\) | |||||||
\(108\) | −4.41803 | −0.425125 | ||||||||
\(109\) | 7.76784 | 0.744025 | 0.372012 | − | 0.928228i | \(-0.378668\pi\) | ||||
0.372012 | + | 0.928228i | \(0.378668\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.42451 | −0.325040 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 4.63948 | 0.436446 | 0.218223 | − | 0.975899i | \(-0.429974\pi\) | ||||
0.218223 | + | 0.975899i | \(0.429974\pi\) | |||||||
\(114\) | −1.42552 | −0.133512 | ||||||||
\(115\) | −0.856965 | −0.0799124 | ||||||||
\(116\) | 8.37564 | 0.777658 | ||||||||
\(117\) | 3.69557 | 0.341656 | ||||||||
\(118\) | 12.9838 | 1.19526 | ||||||||
\(119\) | 4.30919 | 0.395023 | ||||||||
\(120\) | −1.92474 | −0.175703 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 13.0887 | 1.18500 | ||||||||
\(123\) | 20.6331 | 1.86043 | ||||||||
\(124\) | 1.10298 | 0.0990506 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.704605 | −0.0627712 | ||||||||
\(127\) | −9.42065 | −0.835947 | −0.417974 | − | 0.908459i | \(-0.637260\pi\) | ||||
−0.417974 | + | 0.908459i | \(0.637260\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.18404 | −0.192294 | ||||||||
\(130\) | −5.24489 | −0.460007 | ||||||||
\(131\) | 0.862825 | 0.0753854 | 0.0376927 | − | 0.999289i | \(-0.487999\pi\) | ||||
0.0376927 | + | 0.999289i | \(0.487999\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.740633 | 0.0642210 | ||||||||
\(134\) | −8.93617 | −0.771968 | ||||||||
\(135\) | −4.41803 | −0.380243 | ||||||||
\(136\) | −4.30919 | −0.369510 | ||||||||
\(137\) | −17.2469 | −1.47350 | −0.736751 | − | 0.676164i | \(-0.763641\pi\) | ||||
−0.736751 | + | 0.676164i | \(0.763641\pi\) | |||||||
\(138\) | 1.64943 | 0.140409 | ||||||||
\(139\) | −20.4448 | −1.73411 | −0.867054 | − | 0.498213i | \(-0.833990\pi\) | ||||
−0.867054 | + | 0.498213i | \(0.833990\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 16.1711 | 1.36185 | ||||||||
\(142\) | 4.50750 | 0.378261 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.704605 | 0.0587171 | ||||||||
\(145\) | 8.37564 | 0.695559 | ||||||||
\(146\) | −3.33413 | −0.275934 | ||||||||
\(147\) | 1.92474 | 0.158749 | ||||||||
\(148\) | −1.77921 | −0.146250 | ||||||||
\(149\) | −1.88298 | −0.154260 | −0.0771299 | − | 0.997021i | \(-0.524576\pi\) | ||||
−0.0771299 | + | 0.997021i | \(0.524576\pi\) | |||||||
\(150\) | −1.92474 | −0.157154 | ||||||||
\(151\) | −5.45095 | −0.443592 | −0.221796 | − | 0.975093i | \(-0.571192\pi\) | ||||
−0.221796 | + | 0.975093i | \(0.571192\pi\) | |||||||
\(152\) | −0.740633 | −0.0600732 | ||||||||
\(153\) | 3.03628 | 0.245468 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.10298 | 0.0885935 | ||||||||
\(156\) | 10.0950 | 0.808248 | ||||||||
\(157\) | −11.9779 | −0.955944 | −0.477972 | − | 0.878375i | \(-0.658628\pi\) | ||||
−0.477972 | + | 0.878375i | \(0.658628\pi\) | |||||||
\(158\) | −1.56183 | −0.124252 | ||||||||
\(159\) | −16.9504 | −1.34425 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −0.856965 | −0.0675383 | ||||||||
\(162\) | 10.6173 | 0.834178 | ||||||||
\(163\) | −15.5543 | −1.21830 | −0.609152 | − | 0.793053i | \(-0.708490\pi\) | ||||
−0.609152 | + | 0.793053i | \(0.708490\pi\) | |||||||
\(164\) | 10.7200 | 0.837090 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.609215 | 0.0472843 | ||||||||
\(167\) | −18.0474 | −1.39655 | −0.698274 | − | 0.715830i | \(-0.746048\pi\) | ||||
−0.698274 | + | 0.715830i | \(0.746048\pi\) | |||||||
\(168\) | −1.92474 | −0.148497 | ||||||||
\(169\) | 14.5088 | 1.11606 | ||||||||
\(170\) | −4.30919 | −0.330500 | ||||||||
\(171\) | 0.521854 | 0.0399071 | ||||||||
\(172\) | −1.13472 | −0.0865218 | ||||||||
\(173\) | 9.60665 | 0.730380 | 0.365190 | − | 0.930933i | \(-0.381004\pi\) | ||||
0.365190 | + | 0.930933i | \(0.381004\pi\) | |||||||
\(174\) | −16.1209 | −1.22212 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −24.9904 | −1.87839 | ||||||||
\(178\) | −1.46836 | −0.110058 | ||||||||
\(179\) | 13.2673 | 0.991643 | 0.495822 | − | 0.868424i | \(-0.334867\pi\) | ||||
0.495822 | + | 0.868424i | \(0.334867\pi\) | |||||||
\(180\) | 0.704605 | 0.0525182 | ||||||||
\(181\) | 19.5835 | 1.45563 | 0.727815 | − | 0.685774i | \(-0.240536\pi\) | ||||
0.727815 | + | 0.685774i | \(0.240536\pi\) | |||||||
\(182\) | −5.24489 | −0.388777 | ||||||||
\(183\) | −25.1923 | −1.86227 | ||||||||
\(184\) | 0.856965 | 0.0631763 | ||||||||
\(185\) | −1.77921 | −0.130810 | ||||||||
\(186\) | −2.12295 | −0.155662 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.40172 | 0.612758 | ||||||||
\(189\) | −4.41803 | −0.321364 | ||||||||
\(190\) | −0.740633 | −0.0537311 | ||||||||
\(191\) | −12.7555 | −0.922954 | −0.461477 | − | 0.887152i | \(-0.652680\pi\) | ||||
−0.461477 | + | 0.887152i | \(0.652680\pi\) | |||||||
\(192\) | 1.92474 | 0.138906 | ||||||||
\(193\) | −11.8288 | −0.851459 | −0.425729 | − | 0.904851i | \(-0.639982\pi\) | ||||
−0.425729 | + | 0.904851i | \(0.639982\pi\) | |||||||
\(194\) | −8.41705 | −0.604309 | ||||||||
\(195\) | 10.0950 | 0.722919 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 21.9105 | 1.56106 | 0.780528 | − | 0.625121i | \(-0.214950\pi\) | ||||
0.780528 | + | 0.625121i | \(0.214950\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3121 | 0.731006 | 0.365503 | − | 0.930810i | \(-0.380897\pi\) | ||||
0.365503 | + | 0.930810i | \(0.380897\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 17.1998 | 1.21318 | ||||||||
\(202\) | −11.0295 | −0.776036 | ||||||||
\(203\) | 8.37564 | 0.587854 | ||||||||
\(204\) | 8.29405 | 0.580700 | ||||||||
\(205\) | 10.7200 | 0.748716 | ||||||||
\(206\) | −5.86953 | −0.408950 | ||||||||
\(207\) | −0.603822 | −0.0419685 | ||||||||
\(208\) | 5.24489 | 0.363667 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.92474 | −0.132819 | ||||||||
\(211\) | 24.8455 | 1.71043 | 0.855217 | − | 0.518270i | \(-0.173424\pi\) | ||||
0.855217 | + | 0.518270i | \(0.173424\pi\) | |||||||
\(212\) | −8.80661 | −0.604840 | ||||||||
\(213\) | −8.67574 | −0.594452 | ||||||||
\(214\) | 6.83162 | 0.467000 | ||||||||
\(215\) | −1.13472 | −0.0773875 | ||||||||
\(216\) | 4.41803 | 0.300609 | ||||||||
\(217\) | 1.10298 | 0.0748752 | ||||||||
\(218\) | −7.76784 | −0.526105 | ||||||||
\(219\) | 6.41731 | 0.433641 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.6012 | 1.52032 | ||||||||
\(222\) | 3.42451 | 0.229838 | ||||||||
\(223\) | −20.2394 | −1.35533 | −0.677667 | − | 0.735369i | \(-0.737009\pi\) | ||||
−0.677667 | + | 0.735369i | \(0.737009\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0.704605 | 0.0469737 | ||||||||
\(226\) | −4.63948 | −0.308614 | ||||||||
\(227\) | −11.8090 | −0.783792 | −0.391896 | − | 0.920009i | \(-0.628181\pi\) | ||||
−0.391896 | + | 0.920009i | \(0.628181\pi\) | |||||||
\(228\) | 1.42552 | 0.0944075 | ||||||||
\(229\) | 1.67906 | 0.110955 | 0.0554776 | − | 0.998460i | \(-0.482332\pi\) | ||||
0.0554776 | + | 0.998460i | \(0.482332\pi\) | |||||||
\(230\) | 0.856965 | 0.0565066 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.37564 | −0.549887 | ||||||||
\(233\) | 15.5220 | 1.01688 | 0.508440 | − | 0.861097i | \(-0.330222\pi\) | ||||
0.508440 | + | 0.861097i | \(0.330222\pi\) | |||||||
\(234\) | −3.69557 | −0.241587 | ||||||||
\(235\) | 8.40172 | 0.548067 | ||||||||
\(236\) | −12.9838 | −0.845175 | ||||||||
\(237\) | 3.00610 | 0.195267 | ||||||||
\(238\) | −4.30919 | −0.279323 | ||||||||
\(239\) | 22.0037 | 1.42330 | 0.711652 | − | 0.702532i | \(-0.247947\pi\) | ||||
0.711652 | + | 0.702532i | \(0.247947\pi\) | |||||||
\(240\) | 1.92474 | 0.124241 | ||||||||
\(241\) | 23.8155 | 1.53409 | 0.767047 | − | 0.641591i | \(-0.221726\pi\) | ||||
0.767047 | + | 0.641591i | \(0.221726\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.18150 | −0.460693 | ||||||||
\(244\) | −13.0887 | −0.837920 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −20.6331 | −1.31552 | ||||||||
\(247\) | 3.88453 | 0.247167 | ||||||||
\(248\) | −1.10298 | −0.0700393 | ||||||||
\(249\) | −1.17258 | −0.0743091 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 28.5083 | 1.79943 | 0.899715 | − | 0.436477i | \(-0.143774\pi\) | ||||
0.899715 | + | 0.436477i | \(0.143774\pi\) | |||||||
\(252\) | 0.704605 | 0.0443859 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 9.42065 | 0.591104 | ||||||||
\(255\) | 8.29405 | 0.519393 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 29.6194 | 1.84760 | 0.923802 | − | 0.382870i | \(-0.125064\pi\) | ||||
0.923802 | + | 0.382870i | \(0.125064\pi\) | |||||||
\(258\) | 2.18404 | 0.135973 | ||||||||
\(259\) | −1.77921 | −0.110555 | ||||||||
\(260\) | 5.24489 | 0.325274 | ||||||||
\(261\) | 5.90151 | 0.365295 | ||||||||
\(262\) | −0.862825 | −0.0533055 | ||||||||
\(263\) | −4.09184 | −0.252314 | −0.126157 | − | 0.992010i | \(-0.540264\pi\) | ||||
−0.126157 | + | 0.992010i | \(0.540264\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.80661 | −0.540986 | ||||||||
\(266\) | −0.740633 | −0.0454111 | ||||||||
\(267\) | 2.82620 | 0.172960 | ||||||||
\(268\) | 8.93617 | 0.545864 | ||||||||
\(269\) | 2.99735 | 0.182752 | 0.0913759 | − | 0.995816i | \(-0.470874\pi\) | ||||
0.0913759 | + | 0.995816i | \(0.470874\pi\) | |||||||
\(270\) | 4.41803 | 0.268873 | ||||||||
\(271\) | −24.7015 | −1.50051 | −0.750255 | − | 0.661148i | \(-0.770070\pi\) | ||||
−0.750255 | + | 0.661148i | \(0.770070\pi\) | |||||||
\(272\) | 4.30919 | 0.261283 | ||||||||
\(273\) | 10.0950 | 0.610978 | ||||||||
\(274\) | 17.2469 | 1.04192 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.64943 | −0.0992840 | ||||||||
\(277\) | −2.67858 | −0.160941 | −0.0804703 | − | 0.996757i | \(-0.525642\pi\) | ||||
−0.0804703 | + | 0.996757i | \(0.525642\pi\) | |||||||
\(278\) | 20.4448 | 1.22620 | ||||||||
\(279\) | 0.777166 | 0.0465277 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 11.6213 | 0.693271 | 0.346636 | − | 0.938000i | \(-0.387324\pi\) | ||||
0.346636 | + | 0.938000i | \(0.387324\pi\) | |||||||
\(282\) | −16.1711 | −0.962974 | ||||||||
\(283\) | −18.1362 | −1.07808 | −0.539042 | − | 0.842279i | \(-0.681214\pi\) | ||||
−0.539042 | + | 0.842279i | \(0.681214\pi\) | |||||||
\(284\) | −4.50750 | −0.267471 | ||||||||
\(285\) | 1.42552 | 0.0844406 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.7200 | 0.632781 | ||||||||
\(288\) | −0.704605 | −0.0415192 | ||||||||
\(289\) | 1.56912 | 0.0923010 | ||||||||
\(290\) | −8.37564 | −0.491834 | ||||||||
\(291\) | 16.2006 | 0.949695 | ||||||||
\(292\) | 3.33413 | 0.195115 | ||||||||
\(293\) | 22.8700 | 1.33608 | 0.668041 | − | 0.744125i | \(-0.267133\pi\) | ||||
0.668041 | + | 0.744125i | \(0.267133\pi\) | |||||||
\(294\) | −1.92474 | −0.112253 | ||||||||
\(295\) | −12.9838 | −0.755947 | ||||||||
\(296\) | 1.77921 | 0.103415 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.88298 | 0.109078 | ||||||||
\(299\) | −4.49468 | −0.259934 | ||||||||
\(300\) | 1.92474 | 0.111125 | ||||||||
\(301\) | −1.13472 | −0.0654044 | ||||||||
\(302\) | 5.45095 | 0.313667 | ||||||||
\(303\) | 21.2290 | 1.21957 | ||||||||
\(304\) | 0.740633 | 0.0424782 | ||||||||
\(305\) | −13.0887 | −0.749458 | ||||||||
\(306\) | −3.03628 | −0.173572 | ||||||||
\(307\) | 19.9326 | 1.13761 | 0.568806 | − | 0.822472i | \(-0.307406\pi\) | ||||
0.568806 | + | 0.822472i | \(0.307406\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.2973 | 0.642681 | ||||||||
\(310\) | −1.10298 | −0.0626451 | ||||||||
\(311\) | −1.28437 | −0.0728299 | −0.0364149 | − | 0.999337i | \(-0.511594\pi\) | ||||
−0.0364149 | + | 0.999337i | \(0.511594\pi\) | |||||||
\(312\) | −10.0950 | −0.571518 | ||||||||
\(313\) | −13.3964 | −0.757210 | −0.378605 | − | 0.925558i | \(-0.623596\pi\) | ||||
−0.378605 | + | 0.925558i | \(0.623596\pi\) | |||||||
\(314\) | 11.9779 | 0.675954 | ||||||||
\(315\) | 0.704605 | 0.0397000 | ||||||||
\(316\) | 1.56183 | 0.0878597 | ||||||||
\(317\) | 16.6640 | 0.935941 | 0.467971 | − | 0.883744i | \(-0.344985\pi\) | ||||
0.467971 | + | 0.883744i | \(0.344985\pi\) | |||||||
\(318\) | 16.9504 | 0.950530 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −13.1491 | −0.733909 | ||||||||
\(322\) | 0.856965 | 0.0477568 | ||||||||
\(323\) | 3.19153 | 0.177581 | ||||||||
\(324\) | −10.6173 | −0.589853 | ||||||||
\(325\) | 5.24489 | 0.290934 | ||||||||
\(326\) | 15.5543 | 0.861471 | ||||||||
\(327\) | 14.9510 | 0.826795 | ||||||||
\(328\) | −10.7200 | −0.591912 | ||||||||
\(329\) | 8.40172 | 0.463202 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.1340 | 0.611979 | 0.305989 | − | 0.952035i | \(-0.401013\pi\) | ||||
0.305989 | + | 0.952035i | \(0.401013\pi\) | |||||||
\(332\) | −0.609215 | −0.0334350 | ||||||||
\(333\) | −1.25364 | −0.0686991 | ||||||||
\(334\) | 18.0474 | 0.987509 | ||||||||
\(335\) | 8.93617 | 0.488235 | ||||||||
\(336\) | 1.92474 | 0.105003 | ||||||||
\(337\) | 6.71838 | 0.365974 | 0.182987 | − | 0.983115i | \(-0.441423\pi\) | ||||
0.182987 | + | 0.983115i | \(0.441423\pi\) | |||||||
\(338\) | −14.5088 | −0.789176 | ||||||||
\(339\) | 8.92978 | 0.484999 | ||||||||
\(340\) | 4.30919 | 0.233699 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.521854 | −0.0282186 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 1.13472 | 0.0611802 | ||||||||
\(345\) | −1.64943 | −0.0888023 | ||||||||
\(346\) | −9.60665 | −0.516456 | ||||||||
\(347\) | 19.4103 | 1.04200 | 0.520999 | − | 0.853557i | \(-0.325559\pi\) | ||||
0.520999 | + | 0.853557i | \(0.325559\pi\) | |||||||
\(348\) | 16.1209 | 0.864170 | ||||||||
\(349\) | −26.7685 | −1.43289 | −0.716444 | − | 0.697645i | \(-0.754231\pi\) | ||||
−0.716444 | + | 0.697645i | \(0.754231\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −23.1720 | −1.23683 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.9268 | −1.75252 | −0.876259 | − | 0.481841i | \(-0.839968\pi\) | ||||
−0.876259 | + | 0.481841i | \(0.839968\pi\) | |||||||
\(354\) | 24.9904 | 1.32823 | ||||||||
\(355\) | −4.50750 | −0.239233 | ||||||||
\(356\) | 1.46836 | 0.0778228 | ||||||||
\(357\) | 8.29405 | 0.438968 | ||||||||
\(358\) | −13.2673 | −0.701198 | ||||||||
\(359\) | −36.1167 | −1.90617 | −0.953083 | − | 0.302709i | \(-0.902109\pi\) | ||||
−0.953083 | + | 0.302709i | \(0.902109\pi\) | |||||||
\(360\) | −0.704605 | −0.0371359 | ||||||||
\(361\) | −18.4515 | −0.971130 | ||||||||
\(362\) | −19.5835 | −1.02929 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.24489 | 0.274907 | ||||||||
\(365\) | 3.33413 | 0.174516 | ||||||||
\(366\) | 25.1923 | 1.31682 | ||||||||
\(367\) | −8.35672 | −0.436217 | −0.218109 | − | 0.975925i | \(-0.569989\pi\) | ||||
−0.218109 | + | 0.975925i | \(0.569989\pi\) | |||||||
\(368\) | −0.856965 | −0.0446724 | ||||||||
\(369\) | 7.55335 | 0.393212 | ||||||||
\(370\) | 1.77921 | 0.0924968 | ||||||||
\(371\) | −8.80661 | −0.457216 | ||||||||
\(372\) | 2.12295 | 0.110070 | ||||||||
\(373\) | 16.0205 | 0.829509 | 0.414755 | − | 0.909933i | \(-0.363867\pi\) | ||||
0.414755 | + | 0.909933i | \(0.363867\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.92474 | 0.0993929 | ||||||||
\(376\) | −8.40172 | −0.433285 | ||||||||
\(377\) | 43.9292 | 2.26247 | ||||||||
\(378\) | 4.41803 | 0.227239 | ||||||||
\(379\) | 25.3872 | 1.30405 | 0.652027 | − | 0.758196i | \(-0.273919\pi\) | ||||
0.652027 | + | 0.758196i | \(0.273919\pi\) | |||||||
\(380\) | 0.740633 | 0.0379937 | ||||||||
\(381\) | −18.1323 | −0.928943 | ||||||||
\(382\) | 12.7555 | 0.652627 | ||||||||
\(383\) | −0.303318 | −0.0154988 | −0.00774942 | − | 0.999970i | \(-0.502467\pi\) | ||||
−0.00774942 | + | 0.999970i | \(0.502467\pi\) | |||||||
\(384\) | −1.92474 | −0.0982212 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.8288 | 0.602072 | ||||||||
\(387\) | −0.799532 | −0.0406425 | ||||||||
\(388\) | 8.41705 | 0.427311 | ||||||||
\(389\) | −6.74058 | −0.341761 | −0.170880 | − | 0.985292i | \(-0.554661\pi\) | ||||
−0.170880 | + | 0.985292i | \(0.554661\pi\) | |||||||
\(390\) | −10.0950 | −0.511181 | ||||||||
\(391\) | −3.69282 | −0.186754 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 1.66071 | 0.0837717 | ||||||||
\(394\) | −21.9105 | −1.10383 | ||||||||
\(395\) | 1.56183 | 0.0785841 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.9230 | −0.999904 | −0.499952 | − | 0.866053i | \(-0.666649\pi\) | ||||
−0.499952 | + | 0.866053i | \(0.666649\pi\) | |||||||
\(398\) | −10.3121 | −0.516899 | ||||||||
\(399\) | 1.42552 | 0.0713654 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 34.0886 | 1.70230 | 0.851151 | − | 0.524920i | \(-0.175905\pi\) | ||||
0.851151 | + | 0.524920i | \(0.175905\pi\) | |||||||
\(402\) | −17.1998 | −0.857846 | ||||||||
\(403\) | 5.78501 | 0.288172 | ||||||||
\(404\) | 11.0295 | 0.548740 | ||||||||
\(405\) | −10.6173 | −0.527580 | ||||||||
\(406\) | −8.37564 | −0.415676 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −8.29405 | −0.410617 | ||||||||
\(409\) | −8.09670 | −0.400356 | −0.200178 | − | 0.979760i | \(-0.564152\pi\) | ||||
−0.200178 | + | 0.979760i | \(0.564152\pi\) | |||||||
\(410\) | −10.7200 | −0.529422 | ||||||||
\(411\) | −33.1957 | −1.63742 | ||||||||
\(412\) | 5.86953 | 0.289171 | ||||||||
\(413\) | −12.9838 | −0.638892 | ||||||||
\(414\) | 0.603822 | 0.0296762 | ||||||||
\(415\) | −0.609215 | −0.0299052 | ||||||||
\(416\) | −5.24489 | −0.257152 | ||||||||
\(417\) | −39.3509 | −1.92702 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.0686 | −1.17583 | −0.587915 | − | 0.808923i | \(-0.700051\pi\) | ||||
−0.587915 | + | 0.808923i | \(0.700051\pi\) | |||||||
\(420\) | 1.92474 | 0.0939175 | ||||||||
\(421\) | 13.7871 | 0.671942 | 0.335971 | − | 0.941872i | \(-0.390936\pi\) | ||||
0.335971 | + | 0.941872i | \(0.390936\pi\) | |||||||
\(422\) | −24.8455 | −1.20946 | ||||||||
\(423\) | 5.91989 | 0.287835 | ||||||||
\(424\) | 8.80661 | 0.427687 | ||||||||
\(425\) | 4.30919 | 0.209026 | ||||||||
\(426\) | 8.67574 | 0.420341 | ||||||||
\(427\) | −13.0887 | −0.633408 | ||||||||
\(428\) | −6.83162 | −0.330219 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.13472 | 0.0547212 | ||||||||
\(431\) | 8.72005 | 0.420030 | 0.210015 | − | 0.977698i | \(-0.432649\pi\) | ||||
0.210015 | + | 0.977698i | \(0.432649\pi\) | |||||||
\(432\) | −4.41803 | −0.212562 | ||||||||
\(433\) | −8.51892 | −0.409393 | −0.204697 | − | 0.978825i | \(-0.565621\pi\) | ||||
−0.204697 | + | 0.978825i | \(0.565621\pi\) | |||||||
\(434\) | −1.10298 | −0.0529448 | ||||||||
\(435\) | 16.1209 | 0.772937 | ||||||||
\(436\) | 7.76784 | 0.372012 | ||||||||
\(437\) | −0.634696 | −0.0303616 | ||||||||
\(438\) | −6.41731 | −0.306631 | ||||||||
\(439\) | 22.5402 | 1.07579 | 0.537894 | − | 0.843013i | \(-0.319220\pi\) | ||||
0.537894 | + | 0.843013i | \(0.319220\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.704605 | 0.0335526 | ||||||||
\(442\) | −22.6012 | −1.07503 | ||||||||
\(443\) | 37.9089 | 1.80110 | 0.900552 | − | 0.434748i | \(-0.143163\pi\) | ||||
0.900552 | + | 0.434748i | \(0.143163\pi\) | |||||||
\(444\) | −3.42451 | −0.162520 | ||||||||
\(445\) | 1.46836 | 0.0696068 | ||||||||
\(446\) | 20.2394 | 0.958365 | ||||||||
\(447\) | −3.62424 | −0.171421 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −32.0551 | −1.51277 | −0.756387 | − | 0.654125i | \(-0.773037\pi\) | ||||
−0.756387 | + | 0.654125i | \(0.773037\pi\) | |||||||
\(450\) | −0.704605 | −0.0332154 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 4.63948 | 0.218223 | ||||||||
\(453\) | −10.4916 | −0.492940 | ||||||||
\(454\) | 11.8090 | 0.554225 | ||||||||
\(455\) | 5.24489 | 0.245884 | ||||||||
\(456\) | −1.42552 | −0.0667562 | ||||||||
\(457\) | −24.5243 | −1.14720 | −0.573600 | − | 0.819136i | \(-0.694453\pi\) | ||||
−0.573600 | + | 0.819136i | \(0.694453\pi\) | |||||||
\(458\) | −1.67906 | −0.0784572 | ||||||||
\(459\) | −19.0381 | −0.888623 | ||||||||
\(460\) | −0.856965 | −0.0399562 | ||||||||
\(461\) | 0.188328 | 0.00877132 | 0.00438566 | − | 0.999990i | \(-0.498604\pi\) | ||||
0.00438566 | + | 0.999990i | \(0.498604\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.40956 | −0.437299 | −0.218650 | − | 0.975803i | \(-0.570165\pi\) | ||||
−0.218650 | + | 0.975803i | \(0.570165\pi\) | |||||||
\(464\) | 8.37564 | 0.388829 | ||||||||
\(465\) | 2.12295 | 0.0984492 | ||||||||
\(466\) | −15.5220 | −0.719043 | ||||||||
\(467\) | 1.84720 | 0.0854781 | 0.0427390 | − | 0.999086i | \(-0.486392\pi\) | ||||
0.0427390 | + | 0.999086i | \(0.486392\pi\) | |||||||
\(468\) | 3.69557 | 0.170828 | ||||||||
\(469\) | 8.93617 | 0.412634 | ||||||||
\(470\) | −8.40172 | −0.387542 | ||||||||
\(471\) | −23.0544 | −1.06229 | ||||||||
\(472\) | 12.9838 | 0.597629 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −3.00610 | −0.138075 | ||||||||
\(475\) | 0.740633 | 0.0339826 | ||||||||
\(476\) | 4.30919 | 0.197511 | ||||||||
\(477\) | −6.20518 | −0.284116 | ||||||||
\(478\) | −22.0037 | −1.00643 | ||||||||
\(479\) | −33.3506 | −1.52383 | −0.761913 | − | 0.647679i | \(-0.775740\pi\) | ||||
−0.761913 | + | 0.647679i | \(0.775740\pi\) | |||||||
\(480\) | −1.92474 | −0.0878517 | ||||||||
\(481\) | −9.33176 | −0.425491 | ||||||||
\(482\) | −23.8155 | −1.08477 | ||||||||
\(483\) | −1.64943 | −0.0750517 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.41705 | 0.382198 | ||||||||
\(486\) | 7.18150 | 0.325759 | ||||||||
\(487\) | 14.1136 | 0.639550 | 0.319775 | − | 0.947493i | \(-0.396393\pi\) | ||||
0.319775 | + | 0.947493i | \(0.396393\pi\) | |||||||
\(488\) | 13.0887 | 0.592499 | ||||||||
\(489\) | −29.9378 | −1.35384 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 8.40881 | 0.379484 | 0.189742 | − | 0.981834i | \(-0.439235\pi\) | ||||
0.189742 | + | 0.981834i | \(0.439235\pi\) | |||||||
\(492\) | 20.6331 | 0.930213 | ||||||||
\(493\) | 36.0922 | 1.62551 | ||||||||
\(494\) | −3.88453 | −0.174773 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.10298 | 0.0495253 | ||||||||
\(497\) | −4.50750 | −0.202189 | ||||||||
\(498\) | 1.17258 | 0.0525444 | ||||||||
\(499\) | −22.8087 | −1.02106 | −0.510529 | − | 0.859860i | \(-0.670550\pi\) | ||||
−0.510529 | + | 0.859860i | \(0.670550\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −34.7364 | −1.55191 | ||||||||
\(502\) | −28.5083 | −1.27239 | ||||||||
\(503\) | 22.6508 | 1.00995 | 0.504975 | − | 0.863134i | \(-0.331502\pi\) | ||||
0.504975 | + | 0.863134i | \(0.331502\pi\) | |||||||
\(504\) | −0.704605 | −0.0313856 | ||||||||
\(505\) | 11.0295 | 0.490808 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.9256 | 1.24022 | ||||||||
\(508\) | −9.42065 | −0.417974 | ||||||||
\(509\) | −15.0533 | −0.667224 | −0.333612 | − | 0.942710i | \(-0.608268\pi\) | ||||
−0.333612 | + | 0.942710i | \(0.608268\pi\) | |||||||
\(510\) | −8.29405 | −0.367267 | ||||||||
\(511\) | 3.33413 | 0.147493 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.27214 | −0.144468 | ||||||||
\(514\) | −29.6194 | −1.30645 | ||||||||
\(515\) | 5.86953 | 0.258643 | ||||||||
\(516\) | −2.18404 | −0.0961471 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.77921 | 0.0781740 | ||||||||
\(519\) | 18.4902 | 0.811632 | ||||||||
\(520\) | −5.24489 | −0.230003 | ||||||||
\(521\) | −7.47977 | −0.327695 | −0.163847 | − | 0.986486i | \(-0.552390\pi\) | ||||
−0.163847 | + | 0.986486i | \(0.552390\pi\) | |||||||
\(522\) | −5.90151 | −0.258302 | ||||||||
\(523\) | 5.14535 | 0.224990 | 0.112495 | − | 0.993652i | \(-0.464116\pi\) | ||||
0.112495 | + | 0.993652i | \(0.464116\pi\) | |||||||
\(524\) | 0.862825 | 0.0376927 | ||||||||
\(525\) | 1.92474 | 0.0840023 | ||||||||
\(526\) | 4.09184 | 0.178413 | ||||||||
\(527\) | 4.75295 | 0.207042 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2656 | −0.968070 | ||||||||
\(530\) | 8.80661 | 0.382535 | ||||||||
\(531\) | −9.14846 | −0.397010 | ||||||||
\(532\) | 0.740633 | 0.0321105 | ||||||||
\(533\) | 56.2251 | 2.43538 | ||||||||
\(534\) | −2.82620 | −0.122302 | ||||||||
\(535\) | −6.83162 | −0.295357 | ||||||||
\(536\) | −8.93617 | −0.385984 | ||||||||
\(537\) | 25.5360 | 1.10196 | ||||||||
\(538\) | −2.99735 | −0.129225 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.41803 | −0.190122 | ||||||||
\(541\) | 1.92055 | 0.0825709 | 0.0412855 | − | 0.999147i | \(-0.486855\pi\) | ||||
0.0412855 | + | 0.999147i | \(0.486855\pi\) | |||||||
\(542\) | 24.7015 | 1.06102 | ||||||||
\(543\) | 37.6930 | 1.61756 | ||||||||
\(544\) | −4.30919 | −0.184755 | ||||||||
\(545\) | 7.76784 | 0.332738 | ||||||||
\(546\) | −10.0950 | −0.432027 | ||||||||
\(547\) | −0.260956 | −0.0111577 | −0.00557884 | − | 0.999984i | \(-0.501776\pi\) | ||||
−0.00557884 | + | 0.999984i | \(0.501776\pi\) | |||||||
\(548\) | −17.2469 | −0.736751 | ||||||||
\(549\) | −9.22238 | −0.393602 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.20327 | 0.264268 | ||||||||
\(552\) | 1.64943 | 0.0702044 | ||||||||
\(553\) | 1.56183 | 0.0664157 | ||||||||
\(554\) | 2.67858 | 0.113802 | ||||||||
\(555\) | −3.42451 | −0.145362 | ||||||||
\(556\) | −20.4448 | −0.867054 | ||||||||
\(557\) | 6.31867 | 0.267731 | 0.133865 | − | 0.991000i | \(-0.457261\pi\) | ||||
0.133865 | + | 0.991000i | \(0.457261\pi\) | |||||||
\(558\) | −0.777166 | −0.0329000 | ||||||||
\(559\) | −5.95149 | −0.251721 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.6213 | −0.490217 | ||||||||
\(563\) | −0.958697 | −0.0404043 | −0.0202021 | − | 0.999796i | \(-0.506431\pi\) | ||||
−0.0202021 | + | 0.999796i | \(0.506431\pi\) | |||||||
\(564\) | 16.1711 | 0.680925 | ||||||||
\(565\) | 4.63948 | 0.195185 | ||||||||
\(566\) | 18.1362 | 0.762321 | ||||||||
\(567\) | −10.6173 | −0.445887 | ||||||||
\(568\) | 4.50750 | 0.189130 | ||||||||
\(569\) | 7.11799 | 0.298402 | 0.149201 | − | 0.988807i | \(-0.452330\pi\) | ||||
0.149201 | + | 0.988807i | \(0.452330\pi\) | |||||||
\(570\) | −1.42552 | −0.0597085 | ||||||||
\(571\) | 27.1751 | 1.13724 | 0.568621 | − | 0.822599i | \(-0.307477\pi\) | ||||
0.568621 | + | 0.822599i | \(0.307477\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.5509 | −1.02563 | ||||||||
\(574\) | −10.7200 | −0.447443 | ||||||||
\(575\) | −0.856965 | −0.0357379 | ||||||||
\(576\) | 0.704605 | 0.0293585 | ||||||||
\(577\) | −32.3702 | −1.34759 | −0.673795 | − | 0.738918i | \(-0.735337\pi\) | ||||
−0.673795 | + | 0.738918i | \(0.735337\pi\) | |||||||
\(578\) | −1.56912 | −0.0652667 | ||||||||
\(579\) | −22.7674 | −0.946181 | ||||||||
\(580\) | 8.37564 | 0.347779 | ||||||||
\(581\) | −0.609215 | −0.0252745 | ||||||||
\(582\) | −16.2006 | −0.671536 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −3.33413 | −0.137967 | ||||||||
\(585\) | 3.69557 | 0.152793 | ||||||||
\(586\) | −22.8700 | −0.944753 | ||||||||
\(587\) | −8.04888 | −0.332213 | −0.166106 | − | 0.986108i | \(-0.553120\pi\) | ||||
−0.166106 | + | 0.986108i | \(0.553120\pi\) | |||||||
\(588\) | 1.92474 | 0.0793747 | ||||||||
\(589\) | 0.816904 | 0.0336599 | ||||||||
\(590\) | 12.9838 | 0.534535 | ||||||||
\(591\) | 42.1718 | 1.73472 | ||||||||
\(592\) | −1.77921 | −0.0731251 | ||||||||
\(593\) | 39.8151 | 1.63501 | 0.817506 | − | 0.575920i | \(-0.195356\pi\) | ||||
0.817506 | + | 0.575920i | \(0.195356\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.30919 | 0.176660 | ||||||||
\(596\) | −1.88298 | −0.0771299 | ||||||||
\(597\) | 19.8481 | 0.812327 | ||||||||
\(598\) | 4.49468 | 0.183801 | ||||||||
\(599\) | 30.7925 | 1.25815 | 0.629074 | − | 0.777346i | \(-0.283434\pi\) | ||||
0.629074 | + | 0.777346i | \(0.283434\pi\) | |||||||
\(600\) | −1.92474 | −0.0785770 | ||||||||
\(601\) | −33.3140 | −1.35891 | −0.679454 | − | 0.733718i | \(-0.737783\pi\) | ||||
−0.679454 | + | 0.733718i | \(0.737783\pi\) | |||||||
\(602\) | 1.13472 | 0.0462479 | ||||||||
\(603\) | 6.29647 | 0.256412 | ||||||||
\(604\) | −5.45095 | −0.221796 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −21.2290 | −0.862367 | ||||||||
\(607\) | 16.8748 | 0.684927 | 0.342463 | − | 0.939531i | \(-0.388739\pi\) | ||||
0.342463 | + | 0.939531i | \(0.388739\pi\) | |||||||
\(608\) | −0.740633 | −0.0300366 | ||||||||
\(609\) | 16.1209 | 0.653251 | ||||||||
\(610\) | 13.0887 | 0.529947 | ||||||||
\(611\) | 44.0660 | 1.78272 | ||||||||
\(612\) | 3.03628 | 0.122734 | ||||||||
\(613\) | −26.7574 | −1.08072 | −0.540360 | − | 0.841434i | \(-0.681712\pi\) | ||||
−0.540360 | + | 0.841434i | \(0.681712\pi\) | |||||||
\(614\) | −19.9326 | −0.804413 | ||||||||
\(615\) | 20.6331 | 0.832008 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.5387 | 1.30996 | 0.654979 | − | 0.755647i | \(-0.272677\pi\) | ||||
0.654979 | + | 0.755647i | \(0.272677\pi\) | |||||||
\(618\) | −11.2973 | −0.454444 | ||||||||
\(619\) | −13.9252 | −0.559701 | −0.279850 | − | 0.960044i | \(-0.590285\pi\) | ||||
−0.279850 | + | 0.960044i | \(0.590285\pi\) | |||||||
\(620\) | 1.10298 | 0.0442968 | ||||||||
\(621\) | 3.78609 | 0.151931 | ||||||||
\(622\) | 1.28437 | 0.0514985 | ||||||||
\(623\) | 1.46836 | 0.0588285 | ||||||||
\(624\) | 10.0950 | 0.404124 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 13.3964 | 0.535429 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.9779 | −0.477972 | ||||||||
\(629\) | −7.66696 | −0.305702 | ||||||||
\(630\) | −0.704605 | −0.0280721 | ||||||||
\(631\) | −12.8350 | −0.510954 | −0.255477 | − | 0.966815i | \(-0.582232\pi\) | ||||
−0.255477 | + | 0.966815i | \(0.582232\pi\) | |||||||
\(632\) | −1.56183 | −0.0621262 | ||||||||
\(633\) | 47.8210 | 1.90071 | ||||||||
\(634\) | −16.6640 | −0.661810 | ||||||||
\(635\) | −9.42065 | −0.373847 | ||||||||
\(636\) | −16.9504 | −0.672126 | ||||||||
\(637\) | 5.24489 | 0.207810 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.17601 | −0.125641 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −48.5629 | −1.91812 | −0.959059 | − | 0.283207i | \(-0.908602\pi\) | ||||
−0.959059 | + | 0.283207i | \(0.908602\pi\) | |||||||
\(642\) | 13.1491 | 0.518952 | ||||||||
\(643\) | −14.1751 | −0.559009 | −0.279505 | − | 0.960144i | \(-0.590170\pi\) | ||||
−0.279505 | + | 0.960144i | \(0.590170\pi\) | |||||||
\(644\) | −0.856965 | −0.0337691 | ||||||||
\(645\) | −2.18404 | −0.0859966 | ||||||||
\(646\) | −3.19153 | −0.125569 | ||||||||
\(647\) | −24.7982 | −0.974917 | −0.487459 | − | 0.873146i | \(-0.662076\pi\) | ||||
−0.487459 | + | 0.873146i | \(0.662076\pi\) | |||||||
\(648\) | 10.6173 | 0.417089 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5.24489 | −0.205721 | ||||||||
\(651\) | 2.12295 | 0.0832048 | ||||||||
\(652\) | −15.5543 | −0.609152 | ||||||||
\(653\) | −29.0557 | −1.13704 | −0.568519 | − | 0.822670i | \(-0.692483\pi\) | ||||
−0.568519 | + | 0.822670i | \(0.692483\pi\) | |||||||
\(654\) | −14.9510 | −0.584632 | ||||||||
\(655\) | 0.862825 | 0.0337134 | ||||||||
\(656\) | 10.7200 | 0.418545 | ||||||||
\(657\) | 2.34924 | 0.0916526 | ||||||||
\(658\) | −8.40172 | −0.327533 | ||||||||
\(659\) | −44.0463 | −1.71580 | −0.857899 | − | 0.513818i | \(-0.828231\pi\) | ||||
−0.857899 | + | 0.513818i | \(0.828231\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.575059 | −0.0223672 | −0.0111836 | − | 0.999937i | \(-0.503560\pi\) | ||||
−0.0111836 | + | 0.999937i | \(0.503560\pi\) | |||||||
\(662\) | −11.1340 | −0.432734 | ||||||||
\(663\) | 43.5013 | 1.68945 | ||||||||
\(664\) | 0.609215 | 0.0236421 | ||||||||
\(665\) | 0.740633 | 0.0287205 | ||||||||
\(666\) | 1.25364 | 0.0485776 | ||||||||
\(667\) | −7.17762 | −0.277919 | ||||||||
\(668\) | −18.0474 | −0.698274 | ||||||||
\(669\) | −38.9556 | −1.50611 | ||||||||
\(670\) | −8.93617 | −0.345234 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.92474 | −0.0742483 | ||||||||
\(673\) | 27.7568 | 1.06995 | 0.534974 | − | 0.844869i | \(-0.320321\pi\) | ||||
0.534974 | + | 0.844869i | \(0.320321\pi\) | |||||||
\(674\) | −6.71838 | −0.258782 | ||||||||
\(675\) | −4.41803 | −0.170050 | ||||||||
\(676\) | 14.5088 | 0.558032 | ||||||||
\(677\) | −51.1859 | −1.96723 | −0.983617 | − | 0.180272i | \(-0.942302\pi\) | ||||
−0.983617 | + | 0.180272i | \(0.942302\pi\) | |||||||
\(678\) | −8.92978 | −0.342946 | ||||||||
\(679\) | 8.41705 | 0.323017 | ||||||||
\(680\) | −4.30919 | −0.165250 | ||||||||
\(681\) | −22.7292 | −0.870986 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.55522 | −0.0595090 | −0.0297545 | − | 0.999557i | \(-0.509473\pi\) | ||||
−0.0297545 | + | 0.999557i | \(0.509473\pi\) | |||||||
\(684\) | 0.521854 | 0.0199536 | ||||||||
\(685\) | −17.2469 | −0.658970 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 3.23174 | 0.123299 | ||||||||
\(688\) | −1.13472 | −0.0432609 | ||||||||
\(689\) | −46.1896 | −1.75969 | ||||||||
\(690\) | 1.64943 | 0.0627927 | ||||||||
\(691\) | 4.60492 | 0.175179 | 0.0875896 | − | 0.996157i | \(-0.472084\pi\) | ||||
0.0875896 | + | 0.996157i | \(0.472084\pi\) | |||||||
\(692\) | 9.60665 | 0.365190 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.4103 | −0.736804 | ||||||||
\(695\) | −20.4448 | −0.775517 | ||||||||
\(696\) | −16.1209 | −0.611060 | ||||||||
\(697\) | 46.1944 | 1.74974 | ||||||||
\(698\) | 26.7685 | 1.01320 | ||||||||
\(699\) | 29.8757 | 1.13000 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 2.91484 | 0.110092 | 0.0550460 | − | 0.998484i | \(-0.482469\pi\) | ||||
0.0550460 | + | 0.998484i | \(0.482469\pi\) | |||||||
\(702\) | 23.1720 | 0.874573 | ||||||||
\(703\) | −1.31774 | −0.0496996 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.1711 | 0.609038 | ||||||||
\(706\) | 32.9268 | 1.23922 | ||||||||
\(707\) | 11.0295 | 0.414809 | ||||||||
\(708\) | −24.9904 | −0.939197 | ||||||||
\(709\) | 3.62357 | 0.136086 | 0.0680430 | − | 0.997682i | \(-0.478324\pi\) | ||||
0.0680430 | + | 0.997682i | \(0.478324\pi\) | |||||||
\(710\) | 4.50750 | 0.169163 | ||||||||
\(711\) | 1.10047 | 0.0412709 | ||||||||
\(712\) | −1.46836 | −0.0550290 | ||||||||
\(713\) | −0.945215 | −0.0353986 | ||||||||
\(714\) | −8.29405 | −0.310397 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.2673 | 0.495822 | ||||||||
\(717\) | 42.3514 | 1.58164 | ||||||||
\(718\) | 36.1167 | 1.34786 | ||||||||
\(719\) | −8.72290 | −0.325309 | −0.162655 | − | 0.986683i | \(-0.552006\pi\) | ||||
−0.162655 | + | 0.986683i | \(0.552006\pi\) | |||||||
\(720\) | 0.704605 | 0.0262591 | ||||||||
\(721\) | 5.86953 | 0.218593 | ||||||||
\(722\) | 18.4515 | 0.686692 | ||||||||
\(723\) | 45.8386 | 1.70476 | ||||||||
\(724\) | 19.5835 | 0.727815 | ||||||||
\(725\) | 8.37564 | 0.311063 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.3206 | 1.38415 | 0.692073 | − | 0.721828i | \(-0.256698\pi\) | ||||
0.692073 | + | 0.721828i | \(0.256698\pi\) | |||||||
\(728\) | −5.24489 | −0.194388 | ||||||||
\(729\) | 18.0296 | 0.667761 | ||||||||
\(730\) | −3.33413 | −0.123402 | ||||||||
\(731\) | −4.88974 | −0.180854 | ||||||||
\(732\) | −25.1923 | −0.931136 | ||||||||
\(733\) | −8.80262 | −0.325132 | −0.162566 | − | 0.986698i | \(-0.551977\pi\) | ||||
−0.162566 | + | 0.986698i | \(0.551977\pi\) | |||||||
\(734\) | 8.35672 | 0.308452 | ||||||||
\(735\) | 1.92474 | 0.0709949 | ||||||||
\(736\) | 0.856965 | 0.0315881 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −7.55335 | −0.278043 | ||||||||
\(739\) | −50.6335 | −1.86258 | −0.931292 | − | 0.364274i | \(-0.881317\pi\) | ||||
−0.931292 | + | 0.364274i | \(0.881317\pi\) | |||||||
\(740\) | −1.77921 | −0.0654051 | ||||||||
\(741\) | 7.47670 | 0.274663 | ||||||||
\(742\) | 8.80661 | 0.323301 | ||||||||
\(743\) | 50.4494 | 1.85081 | 0.925404 | − | 0.378983i | \(-0.123726\pi\) | ||||
0.925404 | + | 0.378983i | \(0.123726\pi\) | |||||||
\(744\) | −2.12295 | −0.0778310 | ||||||||
\(745\) | −1.88298 | −0.0689871 | ||||||||
\(746\) | −16.0205 | −0.586552 | ||||||||
\(747\) | −0.429256 | −0.0157057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.83162 | −0.249622 | ||||||||
\(750\) | −1.92474 | −0.0702814 | ||||||||
\(751\) | −23.9655 | −0.874512 | −0.437256 | − | 0.899337i | \(-0.644050\pi\) | ||||
−0.437256 | + | 0.899337i | \(0.644050\pi\) | |||||||
\(752\) | 8.40172 | 0.306379 | ||||||||
\(753\) | 54.8710 | 1.99961 | ||||||||
\(754\) | −43.9292 | −1.59981 | ||||||||
\(755\) | −5.45095 | −0.198380 | ||||||||
\(756\) | −4.41803 | −0.160682 | ||||||||
\(757\) | −4.87670 | −0.177247 | −0.0886233 | − | 0.996065i | \(-0.528247\pi\) | ||||
−0.0886233 | + | 0.996065i | \(0.528247\pi\) | |||||||
\(758\) | −25.3872 | −0.922105 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.740633 | −0.0268656 | ||||||||
\(761\) | 44.6872 | 1.61991 | 0.809955 | − | 0.586492i | \(-0.199491\pi\) | ||||
0.809955 | + | 0.586492i | \(0.199491\pi\) | |||||||
\(762\) | 18.1323 | 0.656862 | ||||||||
\(763\) | 7.76784 | 0.281215 | ||||||||
\(764\) | −12.7555 | −0.461477 | ||||||||
\(765\) | 3.03628 | 0.109777 | ||||||||
\(766\) | 0.303318 | 0.0109593 | ||||||||
\(767\) | −68.0986 | −2.45890 | ||||||||
\(768\) | 1.92474 | 0.0694529 | ||||||||
\(769\) | −52.9611 | −1.90983 | −0.954914 | − | 0.296884i | \(-0.904053\pi\) | ||||
−0.954914 | + | 0.296884i | \(0.904053\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 57.0094 | 2.05314 | ||||||||
\(772\) | −11.8288 | −0.425729 | ||||||||
\(773\) | 38.4372 | 1.38249 | 0.691246 | − | 0.722620i | \(-0.257062\pi\) | ||||
0.691246 | + | 0.722620i | \(0.257062\pi\) | |||||||
\(774\) | 0.799532 | 0.0287386 | ||||||||
\(775\) | 1.10298 | 0.0396202 | ||||||||
\(776\) | −8.41705 | −0.302154 | ||||||||
\(777\) | −3.42451 | −0.122854 | ||||||||
\(778\) | 6.74058 | 0.241661 | ||||||||
\(779\) | 7.93957 | 0.284465 | ||||||||
\(780\) | 10.0950 | 0.361459 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 3.69282 | 0.132055 | ||||||||
\(783\) | −37.0038 | −1.32241 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −11.9779 | −0.427511 | ||||||||
\(786\) | −1.66071 | −0.0592356 | ||||||||
\(787\) | 11.9075 | 0.424458 | 0.212229 | − | 0.977220i | \(-0.431928\pi\) | ||||
0.212229 | + | 0.977220i | \(0.431928\pi\) | |||||||
\(788\) | 21.9105 | 0.780528 | ||||||||
\(789\) | −7.87570 | −0.280383 | ||||||||
\(790\) | −1.56183 | −0.0555673 | ||||||||
\(791\) | 4.63948 | 0.164961 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −68.6489 | −2.43779 | ||||||||
\(794\) | 19.9230 | 0.707039 | ||||||||
\(795\) | −16.9504 | −0.601168 | ||||||||
\(796\) | 10.3121 | 0.365503 | ||||||||
\(797\) | −2.09798 | −0.0743142 | −0.0371571 | − | 0.999309i | \(-0.511830\pi\) | ||||
−0.0371571 | + | 0.999309i | \(0.511830\pi\) | |||||||
\(798\) | −1.42552 | −0.0504629 | ||||||||
\(799\) | 36.2046 | 1.28083 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 1.03461 | 0.0365562 | ||||||||
\(802\) | −34.0886 | −1.20371 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 17.1998 | 0.606589 | ||||||||
\(805\) | −0.856965 | −0.0302040 | ||||||||
\(806\) | −5.78501 | −0.203768 | ||||||||
\(807\) | 5.76911 | 0.203082 | ||||||||
\(808\) | −11.0295 | −0.388018 | ||||||||
\(809\) | 12.0315 | 0.423005 | 0.211503 | − | 0.977377i | \(-0.432164\pi\) | ||||
0.211503 | + | 0.977377i | \(0.432164\pi\) | |||||||
\(810\) | 10.6173 | 0.373056 | ||||||||
\(811\) | 8.52991 | 0.299526 | 0.149763 | − | 0.988722i | \(-0.452149\pi\) | ||||
0.149763 | + | 0.988722i | \(0.452149\pi\) | |||||||
\(812\) | 8.37564 | 0.293927 | ||||||||
\(813\) | −47.5439 | −1.66744 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.5543 | −0.544842 | ||||||||
\(816\) | 8.29405 | 0.290350 | ||||||||
\(817\) | −0.840413 | −0.0294023 | ||||||||
\(818\) | 8.09670 | 0.283094 | ||||||||
\(819\) | 3.69557 | 0.129134 | ||||||||
\(820\) | 10.7200 | 0.374358 | ||||||||
\(821\) | −49.8308 | −1.73911 | −0.869554 | − | 0.493839i | \(-0.835593\pi\) | ||||
−0.869554 | + | 0.493839i | \(0.835593\pi\) | |||||||
\(822\) | 33.1957 | 1.15783 | ||||||||
\(823\) | −14.8465 | −0.517516 | −0.258758 | − | 0.965942i | \(-0.583313\pi\) | ||||
−0.258758 | + | 0.965942i | \(0.583313\pi\) | |||||||
\(824\) | −5.86953 | −0.204475 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.9838 | 0.451765 | ||||||||
\(827\) | 1.52007 | 0.0528580 | 0.0264290 | − | 0.999651i | \(-0.491586\pi\) | ||||
0.0264290 | + | 0.999651i | \(0.491586\pi\) | |||||||
\(828\) | −0.603822 | −0.0209842 | ||||||||
\(829\) | −10.4514 | −0.362993 | −0.181497 | − | 0.983392i | \(-0.558094\pi\) | ||||
−0.181497 | + | 0.983392i | \(0.558094\pi\) | |||||||
\(830\) | 0.609215 | 0.0211462 | ||||||||
\(831\) | −5.15556 | −0.178845 | ||||||||
\(832\) | 5.24489 | 0.181834 | ||||||||
\(833\) | 4.30919 | 0.149305 | ||||||||
\(834\) | 39.3509 | 1.36261 | ||||||||
\(835\) | −18.0474 | −0.624555 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.87300 | −0.168435 | ||||||||
\(838\) | 24.0686 | 0.831437 | ||||||||
\(839\) | −39.9761 | −1.38013 | −0.690064 | − | 0.723748i | \(-0.742418\pi\) | ||||
−0.690064 | + | 0.723748i | \(0.742418\pi\) | |||||||
\(840\) | −1.92474 | −0.0664097 | ||||||||
\(841\) | 41.1513 | 1.41901 | ||||||||
\(842\) | −13.7871 | −0.475135 | ||||||||
\(843\) | 22.3680 | 0.770395 | ||||||||
\(844\) | 24.8455 | 0.855217 | ||||||||
\(845\) | 14.5088 | 0.499119 | ||||||||
\(846\) | −5.91989 | −0.203530 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.80661 | −0.302420 | ||||||||
\(849\) | −34.9074 | −1.19802 | ||||||||
\(850\) | −4.30919 | −0.147804 | ||||||||
\(851\) | 1.52472 | 0.0522668 | ||||||||
\(852\) | −8.67574 | −0.297226 | ||||||||
\(853\) | 22.2228 | 0.760893 | 0.380446 | − | 0.924803i | \(-0.375770\pi\) | ||||
0.380446 | + | 0.924803i | \(0.375770\pi\) | |||||||
\(854\) | 13.0887 | 0.447887 | ||||||||
\(855\) | 0.521854 | 0.0178470 | ||||||||
\(856\) | 6.83162 | 0.233500 | ||||||||
\(857\) | 15.8282 | 0.540681 | 0.270340 | − | 0.962765i | \(-0.412864\pi\) | ||||
0.270340 | + | 0.962765i | \(0.412864\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.7983 | −0.709628 | −0.354814 | − | 0.934937i | \(-0.615456\pi\) | ||||
−0.354814 | + | 0.934937i | \(0.615456\pi\) | |||||||
\(860\) | −1.13472 | −0.0386937 | ||||||||
\(861\) | 20.6331 | 0.703175 | ||||||||
\(862\) | −8.72005 | −0.297006 | ||||||||
\(863\) | −18.8317 | −0.641040 | −0.320520 | − | 0.947242i | \(-0.603858\pi\) | ||||
−0.320520 | + | 0.947242i | \(0.603858\pi\) | |||||||
\(864\) | 4.41803 | 0.150304 | ||||||||
\(865\) | 9.60665 | 0.326636 | ||||||||
\(866\) | 8.51892 | 0.289485 | ||||||||
\(867\) | 3.02013 | 0.102569 | ||||||||
\(868\) | 1.10298 | 0.0374376 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −16.1209 | −0.546549 | ||||||||
\(871\) | 46.8692 | 1.58810 | ||||||||
\(872\) | −7.76784 | −0.263052 | ||||||||
\(873\) | 5.93069 | 0.200724 | ||||||||
\(874\) | 0.634696 | 0.0214689 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 6.41731 | 0.216821 | ||||||||
\(877\) | 16.6176 | 0.561138 | 0.280569 | − | 0.959834i | \(-0.409477\pi\) | ||||
0.280569 | + | 0.959834i | \(0.409477\pi\) | |||||||
\(878\) | −22.5402 | −0.760697 | ||||||||
\(879\) | 44.0188 | 1.48472 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.6943 | 0.730901 | 0.365450 | − | 0.930831i | \(-0.380915\pi\) | ||||
0.365450 | + | 0.930831i | \(0.380915\pi\) | |||||||
\(882\) | −0.704605 | −0.0237253 | ||||||||
\(883\) | 32.8896 | 1.10682 | 0.553412 | − | 0.832907i | \(-0.313325\pi\) | ||||
0.553412 | + | 0.832907i | \(0.313325\pi\) | |||||||
\(884\) | 22.6012 | 0.760161 | ||||||||
\(885\) | −24.9904 | −0.840044 | ||||||||
\(886\) | −37.9089 | −1.27357 | ||||||||
\(887\) | −4.02388 | −0.135109 | −0.0675544 | − | 0.997716i | \(-0.521520\pi\) | ||||
−0.0675544 | + | 0.997716i | \(0.521520\pi\) | |||||||
\(888\) | 3.42451 | 0.114919 | ||||||||
\(889\) | −9.42065 | −0.315958 | ||||||||
\(890\) | −1.46836 | −0.0492194 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −20.2394 | −0.677667 | ||||||||
\(893\) | 6.22259 | 0.208231 | ||||||||
\(894\) | 3.62424 | 0.121213 | ||||||||
\(895\) | 13.2673 | 0.443476 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −8.65107 | −0.288851 | ||||||||
\(898\) | 32.0551 | 1.06969 | ||||||||
\(899\) | 9.23816 | 0.308110 | ||||||||
\(900\) | 0.704605 | 0.0234868 | ||||||||
\(901\) | −37.9493 | −1.26428 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.18404 | −0.0726804 | ||||||||
\(904\) | −4.63948 | −0.154307 | ||||||||
\(905\) | 19.5835 | 0.650977 | ||||||||
\(906\) | 10.4916 | 0.348561 | ||||||||
\(907\) | 20.4539 | 0.679162 | 0.339581 | − | 0.940577i | \(-0.389715\pi\) | ||||
0.339581 | + | 0.940577i | \(0.389715\pi\) | |||||||
\(908\) | −11.8090 | −0.391896 | ||||||||
\(909\) | 7.77147 | 0.257763 | ||||||||
\(910\) | −5.24489 | −0.173866 | ||||||||
\(911\) | 27.9283 | 0.925305 | 0.462653 | − | 0.886540i | \(-0.346898\pi\) | ||||
0.462653 | + | 0.886540i | \(0.346898\pi\) | |||||||
\(912\) | 1.42552 | 0.0472037 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 24.5243 | 0.811192 | ||||||||
\(915\) | −25.1923 | −0.832833 | ||||||||
\(916\) | 1.67906 | 0.0554776 | ||||||||
\(917\) | 0.862825 | 0.0284930 | ||||||||
\(918\) | 19.0381 | 0.628352 | ||||||||
\(919\) | 13.3202 | 0.439394 | 0.219697 | − | 0.975568i | \(-0.429493\pi\) | ||||
0.219697 | + | 0.975568i | \(0.429493\pi\) | |||||||
\(920\) | 0.856965 | 0.0282533 | ||||||||
\(921\) | 38.3649 | 1.26417 | ||||||||
\(922\) | −0.188328 | −0.00620226 | ||||||||
\(923\) | −23.6413 | −0.778163 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.77921 | −0.0585001 | ||||||||
\(926\) | 9.40956 | 0.309217 | ||||||||
\(927\) | 4.13570 | 0.135834 | ||||||||
\(928\) | −8.37564 | −0.274944 | ||||||||
\(929\) | 39.2113 | 1.28648 | 0.643240 | − | 0.765664i | \(-0.277590\pi\) | ||||
0.643240 | + | 0.765664i | \(0.277590\pi\) | |||||||
\(930\) | −2.12295 | −0.0696141 | ||||||||
\(931\) | 0.740633 | 0.0242733 | ||||||||
\(932\) | 15.5220 | 0.508440 | ||||||||
\(933\) | −2.47207 | −0.0809319 | ||||||||
\(934\) | −1.84720 | −0.0604421 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.69557 | −0.120794 | ||||||||
\(937\) | 21.7403 | 0.710225 | 0.355112 | − | 0.934824i | \(-0.384443\pi\) | ||||
0.355112 | + | 0.934824i | \(0.384443\pi\) | |||||||
\(938\) | −8.93617 | −0.291776 | ||||||||
\(939\) | −25.7846 | −0.841447 | ||||||||
\(940\) | 8.40172 | 0.274034 | ||||||||
\(941\) | −16.4125 | −0.535033 | −0.267516 | − | 0.963553i | \(-0.586203\pi\) | ||||
−0.267516 | + | 0.963553i | \(0.586203\pi\) | |||||||
\(942\) | 23.0544 | 0.751152 | ||||||||
\(943\) | −9.18665 | −0.299158 | ||||||||
\(944\) | −12.9838 | −0.422587 | ||||||||
\(945\) | −4.41803 | −0.143718 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.1297 | −1.46652 | −0.733259 | − | 0.679949i | \(-0.762002\pi\) | ||||
−0.733259 | + | 0.679949i | \(0.762002\pi\) | |||||||
\(948\) | 3.00610 | 0.0976337 | ||||||||
\(949\) | 17.4871 | 0.567655 | ||||||||
\(950\) | −0.740633 | −0.0240293 | ||||||||
\(951\) | 32.0737 | 1.04006 | ||||||||
\(952\) | −4.30919 | −0.139662 | ||||||||
\(953\) | 46.8181 | 1.51659 | 0.758294 | − | 0.651913i | \(-0.226033\pi\) | ||||
0.758294 | + | 0.651913i | \(0.226033\pi\) | |||||||
\(954\) | 6.20518 | 0.200900 | ||||||||
\(955\) | −12.7555 | −0.412758 | ||||||||
\(956\) | 22.0037 | 0.711652 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.3506 | 1.07751 | ||||||||
\(959\) | −17.2469 | −0.556931 | ||||||||
\(960\) | 1.92474 | 0.0621206 | ||||||||
\(961\) | −29.7834 | −0.960756 | ||||||||
\(962\) | 9.33176 | 0.300868 | ||||||||
\(963\) | −4.81359 | −0.155116 | ||||||||
\(964\) | 23.8155 | 0.767047 | ||||||||
\(965\) | −11.8288 | −0.380784 | ||||||||
\(966\) | 1.64943 | 0.0530695 | ||||||||
\(967\) | 57.9645 | 1.86401 | 0.932007 | − | 0.362441i | \(-0.118057\pi\) | ||||
0.932007 | + | 0.362441i | \(0.118057\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.14284 | 0.197337 | ||||||||
\(970\) | −8.41705 | −0.270255 | ||||||||
\(971\) | −10.6264 | −0.341019 | −0.170509 | − | 0.985356i | \(-0.554541\pi\) | ||||
−0.170509 | + | 0.985356i | \(0.554541\pi\) | |||||||
\(972\) | −7.18150 | −0.230347 | ||||||||
\(973\) | −20.4448 | −0.655432 | ||||||||
\(974\) | −14.1136 | −0.452230 | ||||||||
\(975\) | 10.0950 | 0.323299 | ||||||||
\(976\) | −13.0887 | −0.418960 | ||||||||
\(977\) | −33.6202 | −1.07561 | −0.537803 | − | 0.843071i | \(-0.680745\pi\) | ||||
−0.537803 | + | 0.843071i | \(0.680745\pi\) | |||||||
\(978\) | 29.9378 | 0.957307 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 5.47326 | 0.174748 | ||||||||
\(982\) | −8.40881 | −0.268336 | ||||||||
\(983\) | 38.3652 | 1.22366 | 0.611830 | − | 0.790989i | \(-0.290434\pi\) | ||||
0.611830 | + | 0.790989i | \(0.290434\pi\) | |||||||
\(984\) | −20.6331 | −0.657760 | ||||||||
\(985\) | 21.9105 | 0.698125 | ||||||||
\(986\) | −36.0922 | −1.14941 | ||||||||
\(987\) | 16.1711 | 0.514731 | ||||||||
\(988\) | 3.88453 | 0.123583 | ||||||||
\(989\) | 0.972418 | 0.0309211 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.5999 | 1.76619 | 0.883094 | − | 0.469196i | \(-0.155456\pi\) | ||||
0.883094 | + | 0.469196i | \(0.155456\pi\) | |||||||
\(992\) | −1.10298 | −0.0350197 | ||||||||
\(993\) | 21.4300 | 0.680059 | ||||||||
\(994\) | 4.50750 | 0.142969 | ||||||||
\(995\) | 10.3121 | 0.326916 | ||||||||
\(996\) | −1.17258 | −0.0371545 | ||||||||
\(997\) | −22.9698 | −0.727462 | −0.363731 | − | 0.931504i | \(-0.618497\pi\) | ||||
−0.363731 | + | 0.931504i | \(0.618497\pi\) | |||||||
\(998\) | 22.8087 | 0.721997 | ||||||||
\(999\) | 7.86060 | 0.248698 |
(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 | 8470.2.a.cv.1.6 | 6 | ||
11.2 | odd | 10 | 770.2.n.g.631.3 | yes | 12 | ||
11.6 | odd | 10 | 770.2.n.g.421.3 | ✓ | 12 | ||
11.10 | odd | 2 | 8470.2.a.db.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.g.421.3 | ✓ | 12 | 11.6 | odd | 10 | ||
770.2.n.g.631.3 | yes | 12 | 11.2 | odd | 10 | ||
8470.2.a.cv.1.6 | 6 | 1.1 | even | 1 | trivial | ||
8470.2.a.db.1.6 | 6 | 11.10 | odd | 2 |