Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, 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("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 966) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.414214 | 0.185242 | 0.0926210 | − | 0.995701i | \(-0.470476\pi\) | ||||
0.0926210 | + | 0.995701i | \(0.470476\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.414214 | −0.130986 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.82843 | −0.507114 | −0.253557 | − | 0.967320i | \(-0.581601\pi\) | ||||
−0.253557 | + | 0.967320i | \(0.581601\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.414214 | 0.106949 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.24264 | −0.786456 | −0.393228 | − | 0.919441i | \(-0.628642\pi\) | ||||
−0.393228 | + | 0.919441i | \(0.628642\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 3.65685 | 0.838940 | 0.419470 | − | 0.907769i | \(-0.362216\pi\) | ||||
0.419470 | + | 0.907769i | \(0.362216\pi\) | |||||||
\(20\) | 0.414214 | 0.0926210 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.82843 | −0.965685 | ||||||||
\(26\) | 1.82843 | 0.358584 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.17157 | −0.217556 | −0.108778 | − | 0.994066i | \(-0.534694\pi\) | ||||
−0.108778 | + | 0.994066i | \(0.534694\pi\) | |||||||
\(30\) | −0.414214 | −0.0756247 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 3.24264 | 0.556108 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.17157 | −0.521403 | −0.260702 | − | 0.965419i | \(-0.583954\pi\) | ||||
−0.260702 | + | 0.965419i | \(0.583954\pi\) | |||||||
\(38\) | −3.65685 | −0.593220 | ||||||||
\(39\) | −1.82843 | −0.292783 | ||||||||
\(40\) | −0.414214 | −0.0654929 | ||||||||
\(41\) | −10.8284 | −1.69112 | −0.845558 | − | 0.533883i | \(-0.820732\pi\) | ||||
−0.845558 | + | 0.533883i | \(0.820732\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.6569 | −1.77765 | −0.888827 | − | 0.458243i | \(-0.848479\pi\) | ||||
−0.888827 | + | 0.458243i | \(0.848479\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | 0.414214 | 0.0617473 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 9.00000 | 1.31278 | 0.656392 | − | 0.754420i | \(-0.272082\pi\) | ||||
0.656392 | + | 0.754420i | \(0.272082\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.82843 | 0.682843 | ||||||||
\(51\) | −3.24264 | −0.454061 | ||||||||
\(52\) | −1.82843 | −0.253557 | ||||||||
\(53\) | −10.0711 | −1.38337 | −0.691684 | − | 0.722200i | \(-0.743131\pi\) | ||||
−0.691684 | + | 0.722200i | \(0.743131\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0.828427 | 0.111705 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.65685 | 0.484362 | ||||||||
\(58\) | 1.17157 | 0.153835 | ||||||||
\(59\) | 1.65685 | 0.215704 | 0.107852 | − | 0.994167i | \(-0.465603\pi\) | ||||
0.107852 | + | 0.994167i | \(0.465603\pi\) | |||||||
\(60\) | 0.414214 | 0.0534747 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.757359 | −0.0939389 | ||||||||
\(66\) | −2.00000 | −0.246183 | ||||||||
\(67\) | 14.8995 | 1.82026 | 0.910132 | − | 0.414319i | \(-0.135980\pi\) | ||||
0.910132 | + | 0.414319i | \(0.135980\pi\) | |||||||
\(68\) | −3.24264 | −0.393228 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.82843 | −1.16642 | −0.583210 | − | 0.812322i | \(-0.698203\pi\) | ||||
−0.583210 | + | 0.812322i | \(0.698203\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −10.6569 | −1.24729 | −0.623645 | − | 0.781708i | \(-0.714349\pi\) | ||||
−0.623645 | + | 0.781708i | \(0.714349\pi\) | |||||||
\(74\) | 3.17157 | 0.368688 | ||||||||
\(75\) | −4.82843 | −0.557539 | ||||||||
\(76\) | 3.65685 | 0.419470 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.82843 | 0.207029 | ||||||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 0.414214 | 0.0463105 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.8284 | 1.19580 | ||||||||
\(83\) | 12.8284 | 1.40810 | 0.704051 | − | 0.710149i | \(-0.251372\pi\) | ||||
0.704051 | + | 0.710149i | \(0.251372\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.34315 | −0.145685 | ||||||||
\(86\) | 11.6569 | 1.25699 | ||||||||
\(87\) | −1.17157 | −0.125606 | ||||||||
\(88\) | −2.00000 | −0.213201 | ||||||||
\(89\) | 1.17157 | 0.124186 | 0.0620932 | − | 0.998070i | \(-0.480222\pi\) | ||||
0.0620932 | + | 0.998070i | \(0.480222\pi\) | |||||||
\(90\) | −0.414214 | −0.0436619 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −2.00000 | −0.207390 | ||||||||
\(94\) | −9.00000 | −0.928279 | ||||||||
\(95\) | 1.51472 | 0.155407 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −9.65685 | −0.980505 | −0.490252 | − | 0.871580i | \(-0.663095\pi\) | ||||
−0.490252 | + | 0.871580i | \(0.663095\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | −4.82843 | −0.482843 | ||||||||
\(101\) | 3.17157 | 0.315583 | 0.157792 | − | 0.987472i | \(-0.449563\pi\) | ||||
0.157792 | + | 0.987472i | \(0.449563\pi\) | |||||||
\(102\) | 3.24264 | 0.321069 | ||||||||
\(103\) | −8.89949 | −0.876893 | −0.438447 | − | 0.898757i | \(-0.644471\pi\) | ||||
−0.438447 | + | 0.898757i | \(0.644471\pi\) | |||||||
\(104\) | 1.82843 | 0.179292 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.0711 | 0.978189 | ||||||||
\(107\) | 5.65685 | 0.546869 | 0.273434 | − | 0.961891i | \(-0.411840\pi\) | ||||
0.273434 | + | 0.961891i | \(0.411840\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 14.8284 | 1.42031 | 0.710153 | − | 0.704048i | \(-0.248626\pi\) | ||||
0.710153 | + | 0.704048i | \(0.248626\pi\) | |||||||
\(110\) | −0.828427 | −0.0789874 | ||||||||
\(111\) | −3.17157 | −0.301032 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.7279 | −1.29141 | −0.645707 | − | 0.763585i | \(-0.723437\pi\) | ||||
−0.645707 | + | 0.763585i | \(0.723437\pi\) | |||||||
\(114\) | −3.65685 | −0.342496 | ||||||||
\(115\) | 0.414214 | 0.0386256 | ||||||||
\(116\) | −1.17157 | −0.108778 | ||||||||
\(117\) | −1.82843 | −0.169038 | ||||||||
\(118\) | −1.65685 | −0.152526 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.414214 | −0.0378124 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 2.00000 | 0.181071 | ||||||||
\(123\) | −10.8284 | −0.976366 | ||||||||
\(124\) | −2.00000 | −0.179605 | ||||||||
\(125\) | −4.07107 | −0.364127 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.82843 | 0.428454 | 0.214227 | − | 0.976784i | \(-0.431277\pi\) | ||||
0.214227 | + | 0.976784i | \(0.431277\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −11.6569 | −1.02633 | ||||||||
\(130\) | 0.757359 | 0.0664248 | ||||||||
\(131\) | 19.1421 | 1.67246 | 0.836228 | − | 0.548382i | \(-0.184756\pi\) | ||||
0.836228 | + | 0.548382i | \(0.184756\pi\) | |||||||
\(132\) | 2.00000 | 0.174078 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −14.8995 | −1.28712 | ||||||||
\(135\) | 0.414214 | 0.0356498 | ||||||||
\(136\) | 3.24264 | 0.278054 | ||||||||
\(137\) | −10.4142 | −0.889746 | −0.444873 | − | 0.895594i | \(-0.646751\pi\) | ||||
−0.444873 | + | 0.895594i | \(0.646751\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −13.3137 | −1.12925 | −0.564627 | − | 0.825346i | \(-0.690980\pi\) | ||||
−0.564627 | + | 0.825346i | \(0.690980\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.00000 | 0.757937 | ||||||||
\(142\) | 9.82843 | 0.824783 | ||||||||
\(143\) | −3.65685 | −0.305802 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.485281 | −0.0403004 | ||||||||
\(146\) | 10.6569 | 0.881968 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.17157 | −0.260702 | ||||||||
\(149\) | 0.757359 | 0.0620453 | 0.0310226 | − | 0.999519i | \(-0.490124\pi\) | ||||
0.0310226 | + | 0.999519i | \(0.490124\pi\) | |||||||
\(150\) | 4.82843 | 0.394239 | ||||||||
\(151\) | 14.1421 | 1.15087 | 0.575435 | − | 0.817847i | \(-0.304833\pi\) | ||||
0.575435 | + | 0.817847i | \(0.304833\pi\) | |||||||
\(152\) | −3.65685 | −0.296610 | ||||||||
\(153\) | −3.24264 | −0.262152 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.828427 | −0.0665409 | ||||||||
\(156\) | −1.82843 | −0.146391 | ||||||||
\(157\) | −4.34315 | −0.346621 | −0.173310 | − | 0.984867i | \(-0.555446\pi\) | ||||
−0.173310 | + | 0.984867i | \(0.555446\pi\) | |||||||
\(158\) | 10.0000 | 0.795557 | ||||||||
\(159\) | −10.0711 | −0.798688 | ||||||||
\(160\) | −0.414214 | −0.0327465 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −9.65685 | −0.756383 | −0.378192 | − | 0.925727i | \(-0.623454\pi\) | ||||
−0.378192 | + | 0.925727i | \(0.623454\pi\) | |||||||
\(164\) | −10.8284 | −0.845558 | ||||||||
\(165\) | 0.828427 | 0.0644930 | ||||||||
\(166\) | −12.8284 | −0.995679 | ||||||||
\(167\) | −14.7990 | −1.14518 | −0.572590 | − | 0.819842i | \(-0.694061\pi\) | ||||
−0.572590 | + | 0.819842i | \(0.694061\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.65685 | −0.742835 | ||||||||
\(170\) | 1.34315 | 0.103015 | ||||||||
\(171\) | 3.65685 | 0.279647 | ||||||||
\(172\) | −11.6569 | −0.888827 | ||||||||
\(173\) | 15.3137 | 1.16428 | 0.582140 | − | 0.813089i | \(-0.302216\pi\) | ||||
0.582140 | + | 0.813089i | \(0.302216\pi\) | |||||||
\(174\) | 1.17157 | 0.0888167 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 1.65685 | 0.124537 | ||||||||
\(178\) | −1.17157 | −0.0878131 | ||||||||
\(179\) | 11.9706 | 0.894722 | 0.447361 | − | 0.894354i | \(-0.352364\pi\) | ||||
0.447361 | + | 0.894354i | \(0.352364\pi\) | |||||||
\(180\) | 0.414214 | 0.0308737 | ||||||||
\(181\) | 13.3137 | 0.989600 | 0.494800 | − | 0.869007i | \(-0.335241\pi\) | ||||
0.494800 | + | 0.869007i | \(0.335241\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −1.31371 | −0.0965858 | ||||||||
\(186\) | 2.00000 | 0.146647 | ||||||||
\(187\) | −6.48528 | −0.474251 | ||||||||
\(188\) | 9.00000 | 0.656392 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.51472 | −0.109889 | ||||||||
\(191\) | −10.8284 | −0.783517 | −0.391759 | − | 0.920068i | \(-0.628133\pi\) | ||||
−0.391759 | + | 0.920068i | \(0.628133\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 11.4853 | 0.826729 | 0.413364 | − | 0.910566i | \(-0.364354\pi\) | ||||
0.413364 | + | 0.910566i | \(0.364354\pi\) | |||||||
\(194\) | 9.65685 | 0.693322 | ||||||||
\(195\) | −0.757359 | −0.0542356 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.17157 | −0.510953 | −0.255477 | − | 0.966815i | \(-0.582232\pi\) | ||||
−0.255477 | + | 0.966815i | \(0.582232\pi\) | |||||||
\(198\) | −2.00000 | −0.142134 | ||||||||
\(199\) | −16.3431 | −1.15853 | −0.579267 | − | 0.815138i | \(-0.696661\pi\) | ||||
−0.579267 | + | 0.815138i | \(0.696661\pi\) | |||||||
\(200\) | 4.82843 | 0.341421 | ||||||||
\(201\) | 14.8995 | 1.05093 | ||||||||
\(202\) | −3.17157 | −0.223151 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.24264 | −0.227030 | ||||||||
\(205\) | −4.48528 | −0.313266 | ||||||||
\(206\) | 8.89949 | 0.620057 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −1.82843 | −0.126779 | ||||||||
\(209\) | 7.31371 | 0.505900 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.8284 | −1.15852 | −0.579258 | − | 0.815144i | \(-0.696658\pi\) | ||||
−0.579258 | + | 0.815144i | \(0.696658\pi\) | |||||||
\(212\) | −10.0711 | −0.691684 | ||||||||
\(213\) | −9.82843 | −0.673433 | ||||||||
\(214\) | −5.65685 | −0.386695 | ||||||||
\(215\) | −4.82843 | −0.329296 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −14.8284 | −1.00431 | ||||||||
\(219\) | −10.6569 | −0.720123 | ||||||||
\(220\) | 0.828427 | 0.0558525 | ||||||||
\(221\) | 5.92893 | 0.398823 | ||||||||
\(222\) | 3.17157 | 0.212862 | ||||||||
\(223\) | 4.48528 | 0.300357 | 0.150178 | − | 0.988659i | \(-0.452015\pi\) | ||||
0.150178 | + | 0.988659i | \(0.452015\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.82843 | −0.321895 | ||||||||
\(226\) | 13.7279 | 0.913168 | ||||||||
\(227\) | 22.9706 | 1.52461 | 0.762305 | − | 0.647218i | \(-0.224068\pi\) | ||||
0.762305 | + | 0.647218i | \(0.224068\pi\) | |||||||
\(228\) | 3.65685 | 0.242181 | ||||||||
\(229\) | −26.1421 | −1.72752 | −0.863760 | − | 0.503903i | \(-0.831897\pi\) | ||||
−0.863760 | + | 0.503903i | \(0.831897\pi\) | |||||||
\(230\) | −0.414214 | −0.0273124 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.17157 | 0.0769175 | ||||||||
\(233\) | −8.00000 | −0.524097 | −0.262049 | − | 0.965055i | \(-0.584398\pi\) | ||||
−0.262049 | + | 0.965055i | \(0.584398\pi\) | |||||||
\(234\) | 1.82843 | 0.119528 | ||||||||
\(235\) | 3.72792 | 0.243183 | ||||||||
\(236\) | 1.65685 | 0.107852 | ||||||||
\(237\) | −10.0000 | −0.649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.6569 | 1.40087 | 0.700433 | − | 0.713718i | \(-0.252990\pi\) | ||||
0.700433 | + | 0.713718i | \(0.252990\pi\) | |||||||
\(240\) | 0.414214 | 0.0267374 | ||||||||
\(241\) | −7.17157 | −0.461962 | −0.230981 | − | 0.972958i | \(-0.574193\pi\) | ||||
−0.230981 | + | 0.972958i | \(0.574193\pi\) | |||||||
\(242\) | 7.00000 | 0.449977 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.8284 | 0.690395 | ||||||||
\(247\) | −6.68629 | −0.425439 | ||||||||
\(248\) | 2.00000 | 0.127000 | ||||||||
\(249\) | 12.8284 | 0.812969 | ||||||||
\(250\) | 4.07107 | 0.257477 | ||||||||
\(251\) | −5.31371 | −0.335398 | −0.167699 | − | 0.985838i | \(-0.553634\pi\) | ||||
−0.167699 | + | 0.985838i | \(0.553634\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000 | 0.125739 | ||||||||
\(254\) | −4.82843 | −0.302962 | ||||||||
\(255\) | −1.34315 | −0.0841110 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.4853 | 1.40259 | 0.701297 | − | 0.712870i | \(-0.252605\pi\) | ||||
0.701297 | + | 0.712870i | \(0.252605\pi\) | |||||||
\(258\) | 11.6569 | 0.725724 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.757359 | −0.0469694 | ||||||||
\(261\) | −1.17157 | −0.0725185 | ||||||||
\(262\) | −19.1421 | −1.18261 | ||||||||
\(263\) | −3.31371 | −0.204332 | −0.102166 | − | 0.994767i | \(-0.532577\pi\) | ||||
−0.102166 | + | 0.994767i | \(0.532577\pi\) | |||||||
\(264\) | −2.00000 | −0.123091 | ||||||||
\(265\) | −4.17157 | −0.256258 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.17157 | 0.0716991 | ||||||||
\(268\) | 14.8995 | 0.910132 | ||||||||
\(269\) | −12.0000 | −0.731653 | −0.365826 | − | 0.930683i | \(-0.619214\pi\) | ||||
−0.365826 | + | 0.930683i | \(0.619214\pi\) | |||||||
\(270\) | −0.414214 | −0.0252082 | ||||||||
\(271\) | 26.2843 | 1.59666 | 0.798328 | − | 0.602223i | \(-0.205718\pi\) | ||||
0.798328 | + | 0.602223i | \(0.205718\pi\) | |||||||
\(272\) | −3.24264 | −0.196614 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.4142 | 0.629146 | ||||||||
\(275\) | −9.65685 | −0.582330 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | −31.2843 | −1.87969 | −0.939845 | − | 0.341602i | \(-0.889031\pi\) | ||||
−0.939845 | + | 0.341602i | \(0.889031\pi\) | |||||||
\(278\) | 13.3137 | 0.798503 | ||||||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.4142 | −0.979190 | −0.489595 | − | 0.871950i | \(-0.662855\pi\) | ||||
−0.489595 | + | 0.871950i | \(0.662855\pi\) | |||||||
\(282\) | −9.00000 | −0.535942 | ||||||||
\(283\) | 7.38478 | 0.438979 | 0.219490 | − | 0.975615i | \(-0.429561\pi\) | ||||
0.219490 | + | 0.975615i | \(0.429561\pi\) | |||||||
\(284\) | −9.82843 | −0.583210 | ||||||||
\(285\) | 1.51472 | 0.0897242 | ||||||||
\(286\) | 3.65685 | 0.216234 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −6.48528 | −0.381487 | ||||||||
\(290\) | 0.485281 | 0.0284967 | ||||||||
\(291\) | −9.65685 | −0.566095 | ||||||||
\(292\) | −10.6569 | −0.623645 | ||||||||
\(293\) | −6.41421 | −0.374722 | −0.187361 | − | 0.982291i | \(-0.559993\pi\) | ||||
−0.187361 | + | 0.982291i | \(0.559993\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.686292 | 0.0399574 | ||||||||
\(296\) | 3.17157 | 0.184344 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | −0.757359 | −0.0438726 | ||||||||
\(299\) | −1.82843 | −0.105741 | ||||||||
\(300\) | −4.82843 | −0.278769 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −14.1421 | −0.813788 | ||||||||
\(303\) | 3.17157 | 0.182202 | ||||||||
\(304\) | 3.65685 | 0.209735 | ||||||||
\(305\) | −0.828427 | −0.0474356 | ||||||||
\(306\) | 3.24264 | 0.185369 | ||||||||
\(307\) | 14.1421 | 0.807134 | 0.403567 | − | 0.914950i | \(-0.367770\pi\) | ||||
0.403567 | + | 0.914950i | \(0.367770\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.89949 | −0.506275 | ||||||||
\(310\) | 0.828427 | 0.0470515 | ||||||||
\(311\) | 6.31371 | 0.358018 | 0.179009 | − | 0.983847i | \(-0.442711\pi\) | ||||
0.179009 | + | 0.983847i | \(0.442711\pi\) | |||||||
\(312\) | 1.82843 | 0.103514 | ||||||||
\(313\) | −0.970563 | −0.0548595 | −0.0274297 | − | 0.999624i | \(-0.508732\pi\) | ||||
−0.0274297 | + | 0.999624i | \(0.508732\pi\) | |||||||
\(314\) | 4.34315 | 0.245098 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | 12.6274 | 0.709226 | 0.354613 | − | 0.935013i | \(-0.384613\pi\) | ||||
0.354613 | + | 0.935013i | \(0.384613\pi\) | |||||||
\(318\) | 10.0711 | 0.564757 | ||||||||
\(319\) | −2.34315 | −0.131191 | ||||||||
\(320\) | 0.414214 | 0.0231552 | ||||||||
\(321\) | 5.65685 | 0.315735 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.8579 | −0.659789 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 8.82843 | 0.489713 | ||||||||
\(326\) | 9.65685 | 0.534844 | ||||||||
\(327\) | 14.8284 | 0.820014 | ||||||||
\(328\) | 10.8284 | 0.597900 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.828427 | −0.0456034 | ||||||||
\(331\) | −17.5147 | −0.962696 | −0.481348 | − | 0.876530i | \(-0.659853\pi\) | ||||
−0.481348 | + | 0.876530i | \(0.659853\pi\) | |||||||
\(332\) | 12.8284 | 0.704051 | ||||||||
\(333\) | −3.17157 | −0.173801 | ||||||||
\(334\) | 14.7990 | 0.809765 | ||||||||
\(335\) | 6.17157 | 0.337189 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | 9.65685 | 0.525264 | ||||||||
\(339\) | −13.7279 | −0.745598 | ||||||||
\(340\) | −1.34315 | −0.0728423 | ||||||||
\(341\) | −4.00000 | −0.216612 | ||||||||
\(342\) | −3.65685 | −0.197740 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11.6569 | 0.628495 | ||||||||
\(345\) | 0.414214 | 0.0223005 | ||||||||
\(346\) | −15.3137 | −0.823270 | ||||||||
\(347\) | −21.3431 | −1.14576 | −0.572880 | − | 0.819639i | \(-0.694174\pi\) | ||||
−0.572880 | + | 0.819639i | \(0.694174\pi\) | |||||||
\(348\) | −1.17157 | −0.0628029 | ||||||||
\(349\) | 3.14214 | 0.168195 | 0.0840973 | − | 0.996458i | \(-0.473199\pi\) | ||||
0.0840973 | + | 0.996458i | \(0.473199\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.82843 | −0.0975942 | ||||||||
\(352\) | −2.00000 | −0.106600 | ||||||||
\(353\) | −26.1421 | −1.39141 | −0.695703 | − | 0.718330i | \(-0.744907\pi\) | ||||
−0.695703 | + | 0.718330i | \(0.744907\pi\) | |||||||
\(354\) | −1.65685 | −0.0880608 | ||||||||
\(355\) | −4.07107 | −0.216070 | ||||||||
\(356\) | 1.17157 | 0.0620932 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.9706 | −0.632664 | ||||||||
\(359\) | −6.97056 | −0.367892 | −0.183946 | − | 0.982936i | \(-0.558887\pi\) | ||||
−0.183946 | + | 0.982936i | \(0.558887\pi\) | |||||||
\(360\) | −0.414214 | −0.0218310 | ||||||||
\(361\) | −5.62742 | −0.296180 | ||||||||
\(362\) | −13.3137 | −0.699753 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.41421 | −0.231050 | ||||||||
\(366\) | 2.00000 | 0.104542 | ||||||||
\(367\) | −32.6985 | −1.70685 | −0.853424 | − | 0.521218i | \(-0.825478\pi\) | ||||
−0.853424 | + | 0.521218i | \(0.825478\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −10.8284 | −0.563705 | ||||||||
\(370\) | 1.31371 | 0.0682965 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.00000 | −0.103695 | ||||||||
\(373\) | −11.6569 | −0.603569 | −0.301785 | − | 0.953376i | \(-0.597582\pi\) | ||||
−0.301785 | + | 0.953376i | \(0.597582\pi\) | |||||||
\(374\) | 6.48528 | 0.335346 | ||||||||
\(375\) | −4.07107 | −0.210229 | ||||||||
\(376\) | −9.00000 | −0.464140 | ||||||||
\(377\) | 2.14214 | 0.110326 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.899495 | 0.0462040 | 0.0231020 | − | 0.999733i | \(-0.492646\pi\) | ||||
0.0231020 | + | 0.999733i | \(0.492646\pi\) | |||||||
\(380\) | 1.51472 | 0.0777034 | ||||||||
\(381\) | 4.82843 | 0.247368 | ||||||||
\(382\) | 10.8284 | 0.554031 | ||||||||
\(383\) | −7.65685 | −0.391247 | −0.195623 | − | 0.980679i | \(-0.562673\pi\) | ||||
−0.195623 | + | 0.980679i | \(0.562673\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.4853 | −0.584585 | ||||||||
\(387\) | −11.6569 | −0.592551 | ||||||||
\(388\) | −9.65685 | −0.490252 | ||||||||
\(389\) | 13.4558 | 0.682238 | 0.341119 | − | 0.940020i | \(-0.389194\pi\) | ||||
0.341119 | + | 0.940020i | \(0.389194\pi\) | |||||||
\(390\) | 0.757359 | 0.0383504 | ||||||||
\(391\) | −3.24264 | −0.163987 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.1421 | 0.965593 | ||||||||
\(394\) | 7.17157 | 0.361299 | ||||||||
\(395\) | −4.14214 | −0.208413 | ||||||||
\(396\) | 2.00000 | 0.100504 | ||||||||
\(397\) | 2.65685 | 0.133344 | 0.0666718 | − | 0.997775i | \(-0.478762\pi\) | ||||
0.0666718 | + | 0.997775i | \(0.478762\pi\) | |||||||
\(398\) | 16.3431 | 0.819208 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.82843 | −0.241421 | ||||||||
\(401\) | 26.6985 | 1.33326 | 0.666629 | − | 0.745389i | \(-0.267736\pi\) | ||||
0.666629 | + | 0.745389i | \(0.267736\pi\) | |||||||
\(402\) | −14.8995 | −0.743119 | ||||||||
\(403\) | 3.65685 | 0.182161 | ||||||||
\(404\) | 3.17157 | 0.157792 | ||||||||
\(405\) | 0.414214 | 0.0205824 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.34315 | −0.314418 | ||||||||
\(408\) | 3.24264 | 0.160535 | ||||||||
\(409\) | 12.7990 | 0.632869 | 0.316435 | − | 0.948614i | \(-0.397514\pi\) | ||||
0.316435 | + | 0.948614i | \(0.397514\pi\) | |||||||
\(410\) | 4.48528 | 0.221512 | ||||||||
\(411\) | −10.4142 | −0.513695 | ||||||||
\(412\) | −8.89949 | −0.438447 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 5.31371 | 0.260840 | ||||||||
\(416\) | 1.82843 | 0.0896460 | ||||||||
\(417\) | −13.3137 | −0.651975 | ||||||||
\(418\) | −7.31371 | −0.357725 | ||||||||
\(419\) | 24.4853 | 1.19618 | 0.598092 | − | 0.801427i | \(-0.295926\pi\) | ||||
0.598092 | + | 0.801427i | \(0.295926\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.3137 | 0.746344 | 0.373172 | − | 0.927762i | \(-0.378270\pi\) | ||||
0.373172 | + | 0.927762i | \(0.378270\pi\) | |||||||
\(422\) | 16.8284 | 0.819195 | ||||||||
\(423\) | 9.00000 | 0.437595 | ||||||||
\(424\) | 10.0711 | 0.489094 | ||||||||
\(425\) | 15.6569 | 0.759469 | ||||||||
\(426\) | 9.82843 | 0.476189 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.65685 | 0.273434 | ||||||||
\(429\) | −3.65685 | −0.176555 | ||||||||
\(430\) | 4.82843 | 0.232847 | ||||||||
\(431\) | −4.68629 | −0.225731 | −0.112865 | − | 0.993610i | \(-0.536003\pi\) | ||||
−0.112865 | + | 0.993610i | \(0.536003\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.485281 | −0.0232675 | ||||||||
\(436\) | 14.8284 | 0.710153 | ||||||||
\(437\) | 3.65685 | 0.174931 | ||||||||
\(438\) | 10.6569 | 0.509204 | ||||||||
\(439\) | −2.97056 | −0.141777 | −0.0708886 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708886 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(440\) | −0.828427 | −0.0394937 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.92893 | −0.282011 | ||||||||
\(443\) | −17.1421 | −0.814447 | −0.407224 | − | 0.913328i | \(-0.633503\pi\) | ||||
−0.407224 | + | 0.913328i | \(0.633503\pi\) | |||||||
\(444\) | −3.17157 | −0.150516 | ||||||||
\(445\) | 0.485281 | 0.0230045 | ||||||||
\(446\) | −4.48528 | −0.212384 | ||||||||
\(447\) | 0.757359 | 0.0358219 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.4853 | 1.24992 | 0.624959 | − | 0.780658i | \(-0.285116\pi\) | ||||
0.624959 | + | 0.780658i | \(0.285116\pi\) | |||||||
\(450\) | 4.82843 | 0.227614 | ||||||||
\(451\) | −21.6569 | −1.01978 | ||||||||
\(452\) | −13.7279 | −0.645707 | ||||||||
\(453\) | 14.1421 | 0.664455 | ||||||||
\(454\) | −22.9706 | −1.07806 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.65685 | −0.171248 | ||||||||
\(457\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(458\) | 26.1421 | 1.22154 | ||||||||
\(459\) | −3.24264 | −0.151354 | ||||||||
\(460\) | 0.414214 | 0.0193128 | ||||||||
\(461\) | 14.0000 | 0.652045 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6274 | 0.493898 | 0.246949 | − | 0.969028i | \(-0.420572\pi\) | ||||
0.246949 | + | 0.969028i | \(0.420572\pi\) | |||||||
\(464\) | −1.17157 | −0.0543889 | ||||||||
\(465\) | −0.828427 | −0.0384174 | ||||||||
\(466\) | 8.00000 | 0.370593 | ||||||||
\(467\) | 10.3431 | 0.478624 | 0.239312 | − | 0.970943i | \(-0.423078\pi\) | ||||
0.239312 | + | 0.970943i | \(0.423078\pi\) | |||||||
\(468\) | −1.82843 | −0.0845191 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.72792 | −0.171956 | ||||||||
\(471\) | −4.34315 | −0.200122 | ||||||||
\(472\) | −1.65685 | −0.0762629 | ||||||||
\(473\) | −23.3137 | −1.07197 | ||||||||
\(474\) | 10.0000 | 0.459315 | ||||||||
\(475\) | −17.6569 | −0.810152 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.0711 | −0.461123 | ||||||||
\(478\) | −21.6569 | −0.990561 | ||||||||
\(479\) | 34.1421 | 1.55999 | 0.779997 | − | 0.625783i | \(-0.215221\pi\) | ||||
0.779997 | + | 0.625783i | \(0.215221\pi\) | |||||||
\(480\) | −0.414214 | −0.0189062 | ||||||||
\(481\) | 5.79899 | 0.264411 | ||||||||
\(482\) | 7.17157 | 0.326656 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | −4.00000 | −0.181631 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −32.7696 | −1.48493 | −0.742465 | − | 0.669885i | \(-0.766343\pi\) | ||||
−0.742465 | + | 0.669885i | \(0.766343\pi\) | |||||||
\(488\) | 2.00000 | 0.0905357 | ||||||||
\(489\) | −9.65685 | −0.436698 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.3431 | −0.511909 | −0.255955 | − | 0.966689i | \(-0.582390\pi\) | ||||
−0.255955 | + | 0.966689i | \(0.582390\pi\) | |||||||
\(492\) | −10.8284 | −0.488183 | ||||||||
\(493\) | 3.79899 | 0.171098 | ||||||||
\(494\) | 6.68629 | 0.300830 | ||||||||
\(495\) | 0.828427 | 0.0372350 | ||||||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −12.8284 | −0.574856 | ||||||||
\(499\) | 1.17157 | 0.0524468 | 0.0262234 | − | 0.999656i | \(-0.491652\pi\) | ||||
0.0262234 | + | 0.999656i | \(0.491652\pi\) | |||||||
\(500\) | −4.07107 | −0.182064 | ||||||||
\(501\) | −14.7990 | −0.661170 | ||||||||
\(502\) | 5.31371 | 0.237162 | ||||||||
\(503\) | 43.6569 | 1.94656 | 0.973281 | − | 0.229615i | \(-0.0737468\pi\) | ||||
0.973281 | + | 0.229615i | \(0.0737468\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.31371 | 0.0584593 | ||||||||
\(506\) | −2.00000 | −0.0889108 | ||||||||
\(507\) | −9.65685 | −0.428876 | ||||||||
\(508\) | 4.82843 | 0.214227 | ||||||||
\(509\) | 15.8579 | 0.702887 | 0.351444 | − | 0.936209i | \(-0.385691\pi\) | ||||
0.351444 | + | 0.936209i | \(0.385691\pi\) | |||||||
\(510\) | 1.34315 | 0.0594755 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.65685 | 0.161454 | ||||||||
\(514\) | −22.4853 | −0.991783 | ||||||||
\(515\) | −3.68629 | −0.162437 | ||||||||
\(516\) | −11.6569 | −0.513164 | ||||||||
\(517\) | 18.0000 | 0.791639 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.3137 | 0.672197 | ||||||||
\(520\) | 0.757359 | 0.0332124 | ||||||||
\(521\) | 25.5858 | 1.12093 | 0.560467 | − | 0.828177i | \(-0.310622\pi\) | ||||
0.560467 | + | 0.828177i | \(0.310622\pi\) | |||||||
\(522\) | 1.17157 | 0.0512784 | ||||||||
\(523\) | −14.0711 | −0.615285 | −0.307642 | − | 0.951502i | \(-0.599540\pi\) | ||||
−0.307642 | + | 0.951502i | \(0.599540\pi\) | |||||||
\(524\) | 19.1421 | 0.836228 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.31371 | 0.144485 | ||||||||
\(527\) | 6.48528 | 0.282503 | ||||||||
\(528\) | 2.00000 | 0.0870388 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 4.17157 | 0.181202 | ||||||||
\(531\) | 1.65685 | 0.0719014 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.7990 | 0.857589 | ||||||||
\(534\) | −1.17157 | −0.0506989 | ||||||||
\(535\) | 2.34315 | 0.101303 | ||||||||
\(536\) | −14.8995 | −0.643560 | ||||||||
\(537\) | 11.9706 | 0.516568 | ||||||||
\(538\) | 12.0000 | 0.517357 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.414214 | 0.0178249 | ||||||||
\(541\) | 12.8579 | 0.552803 | 0.276401 | − | 0.961042i | \(-0.410858\pi\) | ||||
0.276401 | + | 0.961042i | \(0.410858\pi\) | |||||||
\(542\) | −26.2843 | −1.12901 | ||||||||
\(543\) | 13.3137 | 0.571346 | ||||||||
\(544\) | 3.24264 | 0.139027 | ||||||||
\(545\) | 6.14214 | 0.263100 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.2843 | −1.46589 | −0.732945 | − | 0.680288i | \(-0.761855\pi\) | ||||
−0.732945 | + | 0.680288i | \(0.761855\pi\) | |||||||
\(548\) | −10.4142 | −0.444873 | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | 9.65685 | 0.411770 | ||||||||
\(551\) | −4.28427 | −0.182516 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 31.2843 | 1.32914 | ||||||||
\(555\) | −1.31371 | −0.0557638 | ||||||||
\(556\) | −13.3137 | −0.564627 | ||||||||
\(557\) | −23.7990 | −1.00840 | −0.504198 | − | 0.863588i | \(-0.668212\pi\) | ||||
−0.504198 | + | 0.863588i | \(0.668212\pi\) | |||||||
\(558\) | 2.00000 | 0.0846668 | ||||||||
\(559\) | 21.3137 | 0.901474 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.48528 | −0.273809 | ||||||||
\(562\) | 16.4142 | 0.692392 | ||||||||
\(563\) | −5.45584 | −0.229936 | −0.114968 | − | 0.993369i | \(-0.536677\pi\) | ||||
−0.114968 | + | 0.993369i | \(0.536677\pi\) | |||||||
\(564\) | 9.00000 | 0.378968 | ||||||||
\(565\) | −5.68629 | −0.239224 | ||||||||
\(566\) | −7.38478 | −0.310405 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.82843 | 0.412392 | ||||||||
\(569\) | 10.4142 | 0.436587 | 0.218293 | − | 0.975883i | \(-0.429951\pi\) | ||||
0.218293 | + | 0.975883i | \(0.429951\pi\) | |||||||
\(570\) | −1.51472 | −0.0634446 | ||||||||
\(571\) | −20.8995 | −0.874617 | −0.437308 | − | 0.899312i | \(-0.644068\pi\) | ||||
−0.437308 | + | 0.899312i | \(0.644068\pi\) | |||||||
\(572\) | −3.65685 | −0.152901 | ||||||||
\(573\) | −10.8284 | −0.452364 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.82843 | −0.201359 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −31.9411 | −1.32973 | −0.664863 | − | 0.746965i | \(-0.731510\pi\) | ||||
−0.664863 | + | 0.746965i | \(0.731510\pi\) | |||||||
\(578\) | 6.48528 | 0.269752 | ||||||||
\(579\) | 11.4853 | 0.477312 | ||||||||
\(580\) | −0.485281 | −0.0201502 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 9.65685 | 0.400289 | ||||||||
\(583\) | −20.1421 | −0.834202 | ||||||||
\(584\) | 10.6569 | 0.440984 | ||||||||
\(585\) | −0.757359 | −0.0313130 | ||||||||
\(586\) | 6.41421 | 0.264969 | ||||||||
\(587\) | 1.14214 | 0.0471410 | 0.0235705 | − | 0.999722i | \(-0.492497\pi\) | ||||
0.0235705 | + | 0.999722i | \(0.492497\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.31371 | −0.301356 | ||||||||
\(590\) | −0.686292 | −0.0282542 | ||||||||
\(591\) | −7.17157 | −0.294999 | ||||||||
\(592\) | −3.17157 | −0.130351 | ||||||||
\(593\) | −3.85786 | −0.158424 | −0.0792118 | − | 0.996858i | \(-0.525240\pi\) | ||||
−0.0792118 | + | 0.996858i | \(0.525240\pi\) | |||||||
\(594\) | −2.00000 | −0.0820610 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.757359 | 0.0310226 | ||||||||
\(597\) | −16.3431 | −0.668880 | ||||||||
\(598\) | 1.82843 | 0.0747699 | ||||||||
\(599\) | −6.17157 | −0.252164 | −0.126082 | − | 0.992020i | \(-0.540240\pi\) | ||||
−0.126082 | + | 0.992020i | \(0.540240\pi\) | |||||||
\(600\) | 4.82843 | 0.197120 | ||||||||
\(601\) | −14.2843 | −0.582668 | −0.291334 | − | 0.956621i | \(-0.594099\pi\) | ||||
−0.291334 | + | 0.956621i | \(0.594099\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.8995 | 0.606754 | ||||||||
\(604\) | 14.1421 | 0.575435 | ||||||||
\(605\) | −2.89949 | −0.117881 | ||||||||
\(606\) | −3.17157 | −0.128836 | ||||||||
\(607\) | 36.1421 | 1.46696 | 0.733482 | − | 0.679709i | \(-0.237894\pi\) | ||||
0.733482 | + | 0.679709i | \(0.237894\pi\) | |||||||
\(608\) | −3.65685 | −0.148305 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.828427 | 0.0335420 | ||||||||
\(611\) | −16.4558 | −0.665732 | ||||||||
\(612\) | −3.24264 | −0.131076 | ||||||||
\(613\) | −17.7990 | −0.718894 | −0.359447 | − | 0.933165i | \(-0.617035\pi\) | ||||
−0.359447 | + | 0.933165i | \(0.617035\pi\) | |||||||
\(614\) | −14.1421 | −0.570730 | ||||||||
\(615\) | −4.48528 | −0.180864 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.0711 | −1.45217 | −0.726083 | − | 0.687607i | \(-0.758661\pi\) | ||||
−0.726083 | + | 0.687607i | \(0.758661\pi\) | |||||||
\(618\) | 8.89949 | 0.357990 | ||||||||
\(619\) | 29.9289 | 1.20295 | 0.601473 | − | 0.798893i | \(-0.294581\pi\) | ||||
0.601473 | + | 0.798893i | \(0.294581\pi\) | |||||||
\(620\) | −0.828427 | −0.0332704 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −6.31371 | −0.253157 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.82843 | −0.0731957 | ||||||||
\(625\) | 22.4558 | 0.898234 | ||||||||
\(626\) | 0.970563 | 0.0387915 | ||||||||
\(627\) | 7.31371 | 0.292081 | ||||||||
\(628\) | −4.34315 | −0.173310 | ||||||||
\(629\) | 10.2843 | 0.410061 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.5563 | −1.85338 | −0.926689 | − | 0.375828i | \(-0.877358\pi\) | ||||
−0.926689 | + | 0.375828i | \(0.877358\pi\) | |||||||
\(632\) | 10.0000 | 0.397779 | ||||||||
\(633\) | −16.8284 | −0.668870 | ||||||||
\(634\) | −12.6274 | −0.501499 | ||||||||
\(635\) | 2.00000 | 0.0793676 | ||||||||
\(636\) | −10.0711 | −0.399344 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.34315 | 0.0927660 | ||||||||
\(639\) | −9.82843 | −0.388807 | ||||||||
\(640\) | −0.414214 | −0.0163732 | ||||||||
\(641\) | −10.6152 | −0.419276 | −0.209638 | − | 0.977779i | \(-0.567229\pi\) | ||||
−0.209638 | + | 0.977779i | \(0.567229\pi\) | |||||||
\(642\) | −5.65685 | −0.223258 | ||||||||
\(643\) | 6.68629 | 0.263682 | 0.131841 | − | 0.991271i | \(-0.457911\pi\) | ||||
0.131841 | + | 0.991271i | \(0.457911\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.82843 | −0.190119 | ||||||||
\(646\) | 11.8579 | 0.466541 | ||||||||
\(647\) | −21.6569 | −0.851419 | −0.425709 | − | 0.904860i | \(-0.639975\pi\) | ||||
−0.425709 | + | 0.904860i | \(0.639975\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 3.31371 | 0.130074 | ||||||||
\(650\) | −8.82843 | −0.346279 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.65685 | −0.378192 | ||||||||
\(653\) | −31.9411 | −1.24995 | −0.624976 | − | 0.780644i | \(-0.714891\pi\) | ||||
−0.624976 | + | 0.780644i | \(0.714891\pi\) | |||||||
\(654\) | −14.8284 | −0.579837 | ||||||||
\(655\) | 7.92893 | 0.309809 | ||||||||
\(656\) | −10.8284 | −0.422779 | ||||||||
\(657\) | −10.6569 | −0.415763 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.4558 | 1.06953 | 0.534764 | − | 0.845002i | \(-0.320401\pi\) | ||||
0.534764 | + | 0.845002i | \(0.320401\pi\) | |||||||
\(660\) | 0.828427 | 0.0322465 | ||||||||
\(661\) | 17.4558 | 0.678954 | 0.339477 | − | 0.940614i | \(-0.389750\pi\) | ||||
0.339477 | + | 0.940614i | \(0.389750\pi\) | |||||||
\(662\) | 17.5147 | 0.680729 | ||||||||
\(663\) | 5.92893 | 0.230261 | ||||||||
\(664\) | −12.8284 | −0.497840 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.17157 | 0.122896 | ||||||||
\(667\) | −1.17157 | −0.0453635 | ||||||||
\(668\) | −14.7990 | −0.572590 | ||||||||
\(669\) | 4.48528 | 0.173411 | ||||||||
\(670\) | −6.17157 | −0.238429 | ||||||||
\(671\) | −4.00000 | −0.154418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.3137 | −1.12996 | −0.564980 | − | 0.825104i | \(-0.691116\pi\) | ||||
−0.564980 | + | 0.825104i | \(0.691116\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.82843 | −0.185846 | ||||||||
\(676\) | −9.65685 | −0.371417 | ||||||||
\(677\) | −20.2721 | −0.779119 | −0.389560 | − | 0.921001i | \(-0.627373\pi\) | ||||
−0.389560 | + | 0.921001i | \(0.627373\pi\) | |||||||
\(678\) | 13.7279 | 0.527218 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.34315 | 0.0515073 | ||||||||
\(681\) | 22.9706 | 0.880234 | ||||||||
\(682\) | 4.00000 | 0.153168 | ||||||||
\(683\) | −45.1421 | −1.72732 | −0.863658 | − | 0.504078i | \(-0.831832\pi\) | ||||
−0.863658 | + | 0.504078i | \(0.831832\pi\) | |||||||
\(684\) | 3.65685 | 0.139823 | ||||||||
\(685\) | −4.31371 | −0.164818 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.1421 | −0.997385 | ||||||||
\(688\) | −11.6569 | −0.444413 | ||||||||
\(689\) | 18.4142 | 0.701526 | ||||||||
\(690\) | −0.414214 | −0.0157688 | ||||||||
\(691\) | 16.1421 | 0.614076 | 0.307038 | − | 0.951697i | \(-0.400662\pi\) | ||||
0.307038 | + | 0.951697i | \(0.400662\pi\) | |||||||
\(692\) | 15.3137 | 0.582140 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.3431 | 0.810175 | ||||||||
\(695\) | −5.51472 | −0.209185 | ||||||||
\(696\) | 1.17157 | 0.0444084 | ||||||||
\(697\) | 35.1127 | 1.32999 | ||||||||
\(698\) | −3.14214 | −0.118932 | ||||||||
\(699\) | −8.00000 | −0.302588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.3848 | 1.71416 | 0.857080 | − | 0.515184i | \(-0.172276\pi\) | ||||
0.857080 | + | 0.515184i | \(0.172276\pi\) | |||||||
\(702\) | 1.82843 | 0.0690095 | ||||||||
\(703\) | −11.5980 | −0.437426 | ||||||||
\(704\) | 2.00000 | 0.0753778 | ||||||||
\(705\) | 3.72792 | 0.140402 | ||||||||
\(706\) | 26.1421 | 0.983872 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.65685 | 0.0622684 | ||||||||
\(709\) | −38.1421 | −1.43246 | −0.716229 | − | 0.697865i | \(-0.754133\pi\) | ||||
−0.716229 | + | 0.697865i | \(0.754133\pi\) | |||||||
\(710\) | 4.07107 | 0.152784 | ||||||||
\(711\) | −10.0000 | −0.375029 | ||||||||
\(712\) | −1.17157 | −0.0439065 | ||||||||
\(713\) | −2.00000 | −0.0749006 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.51472 | −0.0566473 | ||||||||
\(716\) | 11.9706 | 0.447361 | ||||||||
\(717\) | 21.6569 | 0.808790 | ||||||||
\(718\) | 6.97056 | 0.260139 | ||||||||
\(719\) | 3.34315 | 0.124678 | 0.0623391 | − | 0.998055i | \(-0.480144\pi\) | ||||
0.0623391 | + | 0.998055i | \(0.480144\pi\) | |||||||
\(720\) | 0.414214 | 0.0154368 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.62742 | 0.209431 | ||||||||
\(723\) | −7.17157 | −0.266714 | ||||||||
\(724\) | 13.3137 | 0.494800 | ||||||||
\(725\) | 5.65685 | 0.210090 | ||||||||
\(726\) | 7.00000 | 0.259794 | ||||||||
\(727\) | −42.0000 | −1.55769 | −0.778847 | − | 0.627214i | \(-0.784195\pi\) | ||||
−0.778847 | + | 0.627214i | \(0.784195\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.41421 | 0.163377 | ||||||||
\(731\) | 37.7990 | 1.39805 | ||||||||
\(732\) | −2.00000 | −0.0739221 | ||||||||
\(733\) | 8.48528 | 0.313411 | 0.156706 | − | 0.987645i | \(-0.449913\pi\) | ||||
0.156706 | + | 0.987645i | \(0.449913\pi\) | |||||||
\(734\) | 32.6985 | 1.20692 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 29.7990 | 1.09766 | ||||||||
\(738\) | 10.8284 | 0.398600 | ||||||||
\(739\) | 45.2548 | 1.66473 | 0.832363 | − | 0.554231i | \(-0.186988\pi\) | ||||
0.832363 | + | 0.554231i | \(0.186988\pi\) | |||||||
\(740\) | −1.31371 | −0.0482929 | ||||||||
\(741\) | −6.68629 | −0.245627 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.4558 | −1.30075 | −0.650374 | − | 0.759614i | \(-0.725388\pi\) | ||||
−0.650374 | + | 0.759614i | \(0.725388\pi\) | |||||||
\(744\) | 2.00000 | 0.0733236 | ||||||||
\(745\) | 0.313708 | 0.0114934 | ||||||||
\(746\) | 11.6569 | 0.426788 | ||||||||
\(747\) | 12.8284 | 0.469368 | ||||||||
\(748\) | −6.48528 | −0.237125 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4.07107 | 0.148654 | ||||||||
\(751\) | −41.5980 | −1.51793 | −0.758966 | − | 0.651130i | \(-0.774295\pi\) | ||||
−0.758966 | + | 0.651130i | \(0.774295\pi\) | |||||||
\(752\) | 9.00000 | 0.328196 | ||||||||
\(753\) | −5.31371 | −0.193642 | ||||||||
\(754\) | −2.14214 | −0.0780120 | ||||||||
\(755\) | 5.85786 | 0.213190 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.97056 | −0.180658 | −0.0903291 | − | 0.995912i | \(-0.528792\pi\) | ||||
−0.0903291 | + | 0.995912i | \(0.528792\pi\) | |||||||
\(758\) | −0.899495 | −0.0326711 | ||||||||
\(759\) | 2.00000 | 0.0725954 | ||||||||
\(760\) | −1.51472 | −0.0549446 | ||||||||
\(761\) | −10.3431 | −0.374939 | −0.187469 | − | 0.982270i | \(-0.560029\pi\) | ||||
−0.187469 | + | 0.982270i | \(0.560029\pi\) | |||||||
\(762\) | −4.82843 | −0.174915 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.8284 | −0.391759 | ||||||||
\(765\) | −1.34315 | −0.0485615 | ||||||||
\(766\) | 7.65685 | 0.276653 | ||||||||
\(767\) | −3.02944 | −0.109387 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 10.6863 | 0.385358 | 0.192679 | − | 0.981262i | \(-0.438282\pi\) | ||||
0.192679 | + | 0.981262i | \(0.438282\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.4853 | 0.809788 | ||||||||
\(772\) | 11.4853 | 0.413364 | ||||||||
\(773\) | −9.24264 | −0.332435 | −0.166217 | − | 0.986089i | \(-0.553155\pi\) | ||||
−0.166217 | + | 0.986089i | \(0.553155\pi\) | |||||||
\(774\) | 11.6569 | 0.418997 | ||||||||
\(775\) | 9.65685 | 0.346884 | ||||||||
\(776\) | 9.65685 | 0.346661 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13.4558 | −0.482415 | ||||||||
\(779\) | −39.5980 | −1.41874 | ||||||||
\(780\) | −0.757359 | −0.0271178 | ||||||||
\(781\) | −19.6569 | −0.703378 | ||||||||
\(782\) | 3.24264 | 0.115957 | ||||||||
\(783\) | −1.17157 | −0.0418686 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.79899 | −0.0642087 | ||||||||
\(786\) | −19.1421 | −0.682777 | ||||||||
\(787\) | 11.0416 | 0.393592 | 0.196796 | − | 0.980444i | \(-0.436946\pi\) | ||||
0.196796 | + | 0.980444i | \(0.436946\pi\) | |||||||
\(788\) | −7.17157 | −0.255477 | ||||||||
\(789\) | −3.31371 | −0.117971 | ||||||||
\(790\) | 4.14214 | 0.147371 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.00000 | −0.0710669 | ||||||||
\(793\) | 3.65685 | 0.129859 | ||||||||
\(794\) | −2.65685 | −0.0942882 | ||||||||
\(795\) | −4.17157 | −0.147950 | ||||||||
\(796\) | −16.3431 | −0.579267 | ||||||||
\(797\) | 13.8701 | 0.491303 | 0.245651 | − | 0.969358i | \(-0.420998\pi\) | ||||
0.245651 | + | 0.969358i | \(0.420998\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.1838 | −1.03245 | ||||||||
\(800\) | 4.82843 | 0.170711 | ||||||||
\(801\) | 1.17157 | 0.0413955 | ||||||||
\(802\) | −26.6985 | −0.942756 | ||||||||
\(803\) | −21.3137 | −0.752144 | ||||||||
\(804\) | 14.8995 | 0.525465 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.65685 | −0.128807 | ||||||||
\(807\) | −12.0000 | −0.422420 | ||||||||
\(808\) | −3.17157 | −0.111576 | ||||||||
\(809\) | 4.14214 | 0.145630 | 0.0728149 | − | 0.997345i | \(-0.476802\pi\) | ||||
0.0728149 | + | 0.997345i | \(0.476802\pi\) | |||||||
\(810\) | −0.414214 | −0.0145540 | ||||||||
\(811\) | −41.1127 | −1.44366 | −0.721831 | − | 0.692069i | \(-0.756699\pi\) | ||||
−0.721831 | + | 0.692069i | \(0.756699\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.2843 | 0.921830 | ||||||||
\(814\) | 6.34315 | 0.222327 | ||||||||
\(815\) | −4.00000 | −0.140114 | ||||||||
\(816\) | −3.24264 | −0.113515 | ||||||||
\(817\) | −42.6274 | −1.49134 | ||||||||
\(818\) | −12.7990 | −0.447506 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.48528 | −0.156633 | ||||||||
\(821\) | 54.2843 | 1.89453 | 0.947267 | − | 0.320445i | \(-0.103832\pi\) | ||||
0.947267 | + | 0.320445i | \(0.103832\pi\) | |||||||
\(822\) | 10.4142 | 0.363237 | ||||||||
\(823\) | 25.7990 | 0.899296 | 0.449648 | − | 0.893206i | \(-0.351549\pi\) | ||||
0.449648 | + | 0.893206i | \(0.351549\pi\) | |||||||
\(824\) | 8.89949 | 0.310029 | ||||||||
\(825\) | −9.65685 | −0.336209 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.62742 | 0.0913642 | 0.0456821 | − | 0.998956i | \(-0.485454\pi\) | ||||
0.0456821 | + | 0.998956i | \(0.485454\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | 21.8284 | 0.758133 | 0.379066 | − | 0.925370i | \(-0.376245\pi\) | ||||
0.379066 | + | 0.925370i | \(0.376245\pi\) | |||||||
\(830\) | −5.31371 | −0.184442 | ||||||||
\(831\) | −31.2843 | −1.08524 | ||||||||
\(832\) | −1.82843 | −0.0633893 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 13.3137 | 0.461016 | ||||||||
\(835\) | −6.12994 | −0.212135 | ||||||||
\(836\) | 7.31371 | 0.252950 | ||||||||
\(837\) | −2.00000 | −0.0691301 | ||||||||
\(838\) | −24.4853 | −0.845830 | ||||||||
\(839\) | −8.97056 | −0.309698 | −0.154849 | − | 0.987938i | \(-0.549489\pi\) | ||||
−0.154849 | + | 0.987938i | \(0.549489\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6274 | −0.952670 | ||||||||
\(842\) | −15.3137 | −0.527745 | ||||||||
\(843\) | −16.4142 | −0.565336 | ||||||||
\(844\) | −16.8284 | −0.579258 | ||||||||
\(845\) | −4.00000 | −0.137604 | ||||||||
\(846\) | −9.00000 | −0.309426 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.0711 | −0.345842 | ||||||||
\(849\) | 7.38478 | 0.253445 | ||||||||
\(850\) | −15.6569 | −0.537026 | ||||||||
\(851\) | −3.17157 | −0.108720 | ||||||||
\(852\) | −9.82843 | −0.336716 | ||||||||
\(853\) | 48.9117 | 1.67470 | 0.837352 | − | 0.546664i | \(-0.184102\pi\) | ||||
0.837352 | + | 0.546664i | \(0.184102\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.51472 | 0.0518023 | ||||||||
\(856\) | −5.65685 | −0.193347 | ||||||||
\(857\) | 44.6274 | 1.52444 | 0.762222 | − | 0.647316i | \(-0.224109\pi\) | ||||
0.762222 | + | 0.647316i | \(0.224109\pi\) | |||||||
\(858\) | 3.65685 | 0.124843 | ||||||||
\(859\) | −12.6863 | −0.432851 | −0.216425 | − | 0.976299i | \(-0.569440\pi\) | ||||
−0.216425 | + | 0.976299i | \(0.569440\pi\) | |||||||
\(860\) | −4.82843 | −0.164648 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.68629 | 0.159616 | ||||||||
\(863\) | 31.3431 | 1.06693 | 0.533467 | − | 0.845821i | \(-0.320889\pi\) | ||||
0.533467 | + | 0.845821i | \(0.320889\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 6.34315 | 0.215673 | ||||||||
\(866\) | 14.0000 | 0.475739 | ||||||||
\(867\) | −6.48528 | −0.220252 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.0000 | −0.678454 | ||||||||
\(870\) | 0.485281 | 0.0164526 | ||||||||
\(871\) | −27.2426 | −0.923082 | ||||||||
\(872\) | −14.8284 | −0.502154 | ||||||||
\(873\) | −9.65685 | −0.326835 | ||||||||
\(874\) | −3.65685 | −0.123695 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.6569 | −0.360062 | ||||||||
\(877\) | −40.3137 | −1.36130 | −0.680649 | − | 0.732610i | \(-0.738302\pi\) | ||||
−0.680649 | + | 0.732610i | \(0.738302\pi\) | |||||||
\(878\) | 2.97056 | 0.100252 | ||||||||
\(879\) | −6.41421 | −0.216346 | ||||||||
\(880\) | 0.828427 | 0.0279263 | ||||||||
\(881\) | −31.7279 | −1.06894 | −0.534470 | − | 0.845187i | \(-0.679489\pi\) | ||||
−0.534470 | + | 0.845187i | \(0.679489\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.2843 | 0.413399 | 0.206699 | − | 0.978405i | \(-0.433728\pi\) | ||||
0.206699 | + | 0.978405i | \(0.433728\pi\) | |||||||
\(884\) | 5.92893 | 0.199412 | ||||||||
\(885\) | 0.686292 | 0.0230694 | ||||||||
\(886\) | 17.1421 | 0.575901 | ||||||||
\(887\) | 7.02944 | 0.236025 | 0.118013 | − | 0.993012i | \(-0.462348\pi\) | ||||
0.118013 | + | 0.993012i | \(0.462348\pi\) | |||||||
\(888\) | 3.17157 | 0.106431 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.485281 | −0.0162667 | ||||||||
\(891\) | 2.00000 | 0.0670025 | ||||||||
\(892\) | 4.48528 | 0.150178 | ||||||||
\(893\) | 32.9117 | 1.10135 | ||||||||
\(894\) | −0.757359 | −0.0253299 | ||||||||
\(895\) | 4.95837 | 0.165740 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.82843 | −0.0610494 | ||||||||
\(898\) | −26.4853 | −0.883825 | ||||||||
\(899\) | 2.34315 | 0.0781483 | ||||||||
\(900\) | −4.82843 | −0.160948 | ||||||||
\(901\) | 32.6569 | 1.08796 | ||||||||
\(902\) | 21.6569 | 0.721094 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.7279 | 0.456584 | ||||||||
\(905\) | 5.51472 | 0.183315 | ||||||||
\(906\) | −14.1421 | −0.469841 | ||||||||
\(907\) | 23.1005 | 0.767040 | 0.383520 | − | 0.923533i | \(-0.374712\pi\) | ||||
0.383520 | + | 0.923533i | \(0.374712\pi\) | |||||||
\(908\) | 22.9706 | 0.762305 | ||||||||
\(909\) | 3.17157 | 0.105194 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.48528 | −0.281130 | −0.140565 | − | 0.990071i | \(-0.544892\pi\) | ||||
−0.140565 | + | 0.990071i | \(0.544892\pi\) | |||||||
\(912\) | 3.65685 | 0.121091 | ||||||||
\(913\) | 25.6569 | 0.849118 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.828427 | −0.0273870 | ||||||||
\(916\) | −26.1421 | −0.863760 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.24264 | 0.107023 | ||||||||
\(919\) | 1.72792 | 0.0569989 | 0.0284994 | − | 0.999594i | \(-0.490927\pi\) | ||||
0.0284994 | + | 0.999594i | \(0.490927\pi\) | |||||||
\(920\) | −0.414214 | −0.0136562 | ||||||||
\(921\) | 14.1421 | 0.465999 | ||||||||
\(922\) | −14.0000 | −0.461065 | ||||||||
\(923\) | 17.9706 | 0.591508 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.3137 | 0.503512 | ||||||||
\(926\) | −10.6274 | −0.349239 | ||||||||
\(927\) | −8.89949 | −0.292298 | ||||||||
\(928\) | 1.17157 | 0.0384588 | ||||||||
\(929\) | −50.6274 | −1.66103 | −0.830516 | − | 0.556995i | \(-0.811954\pi\) | ||||
−0.830516 | + | 0.556995i | \(0.811954\pi\) | |||||||
\(930\) | 0.828427 | 0.0271652 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8.00000 | −0.262049 | ||||||||
\(933\) | 6.31371 | 0.206702 | ||||||||
\(934\) | −10.3431 | −0.338438 | ||||||||
\(935\) | −2.68629 | −0.0878511 | ||||||||
\(936\) | 1.82843 | 0.0597640 | ||||||||
\(937\) | −12.4853 | −0.407876 | −0.203938 | − | 0.978984i | \(-0.565374\pi\) | ||||
−0.203938 | + | 0.978984i | \(0.565374\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.970563 | −0.0316731 | ||||||||
\(940\) | 3.72792 | 0.121591 | ||||||||
\(941\) | 48.4853 | 1.58058 | 0.790288 | − | 0.612736i | \(-0.209931\pi\) | ||||
0.790288 | + | 0.612736i | \(0.209931\pi\) | |||||||
\(942\) | 4.34315 | 0.141507 | ||||||||
\(943\) | −10.8284 | −0.352622 | ||||||||
\(944\) | 1.65685 | 0.0539260 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.3137 | 0.757994 | ||||||||
\(947\) | −34.3137 | −1.11505 | −0.557523 | − | 0.830162i | \(-0.688248\pi\) | ||||
−0.557523 | + | 0.830162i | \(0.688248\pi\) | |||||||
\(948\) | −10.0000 | −0.324785 | ||||||||
\(949\) | 19.4853 | 0.632519 | ||||||||
\(950\) | 17.6569 | 0.572864 | ||||||||
\(951\) | 12.6274 | 0.409472 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.7990 | −0.900498 | −0.450249 | − | 0.892903i | \(-0.648665\pi\) | ||||
−0.450249 | + | 0.892903i | \(0.648665\pi\) | |||||||
\(954\) | 10.0711 | 0.326063 | ||||||||
\(955\) | −4.48528 | −0.145140 | ||||||||
\(956\) | 21.6569 | 0.700433 | ||||||||
\(957\) | −2.34315 | −0.0757431 | ||||||||
\(958\) | −34.1421 | −1.10308 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.414214 | 0.0133687 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −5.79899 | −0.186967 | ||||||||
\(963\) | 5.65685 | 0.182290 | ||||||||
\(964\) | −7.17157 | −0.230981 | ||||||||
\(965\) | 4.75736 | 0.153145 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.17157 | −0.166307 | −0.0831533 | − | 0.996537i | \(-0.526499\pi\) | ||||
−0.0831533 | + | 0.996537i | \(0.526499\pi\) | |||||||
\(968\) | 7.00000 | 0.224989 | ||||||||
\(969\) | −11.8579 | −0.380929 | ||||||||
\(970\) | 4.00000 | 0.128432 | ||||||||
\(971\) | 2.34315 | 0.0751951 | 0.0375976 | − | 0.999293i | \(-0.488030\pi\) | ||||
0.0375976 | + | 0.999293i | \(0.488030\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 32.7696 | 1.05000 | ||||||||
\(975\) | 8.82843 | 0.282736 | ||||||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | −46.3553 | −1.48304 | −0.741519 | − | 0.670931i | \(-0.765894\pi\) | ||||
−0.741519 | + | 0.670931i | \(0.765894\pi\) | |||||||
\(978\) | 9.65685 | 0.308792 | ||||||||
\(979\) | 2.34315 | 0.0748873 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.8284 | 0.473435 | ||||||||
\(982\) | 11.3431 | 0.361974 | ||||||||
\(983\) | 51.4558 | 1.64119 | 0.820593 | − | 0.571513i | \(-0.193643\pi\) | ||||
0.820593 | + | 0.571513i | \(0.193643\pi\) | |||||||
\(984\) | 10.8284 | 0.345198 | ||||||||
\(985\) | −2.97056 | −0.0946500 | ||||||||
\(986\) | −3.79899 | −0.120984 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.68629 | −0.212719 | ||||||||
\(989\) | −11.6569 | −0.370666 | ||||||||
\(990\) | −0.828427 | −0.0263291 | ||||||||
\(991\) | −47.9411 | −1.52290 | −0.761450 | − | 0.648224i | \(-0.775512\pi\) | ||||
−0.761450 | + | 0.648224i | \(0.775512\pi\) | |||||||
\(992\) | 2.00000 | 0.0635001 | ||||||||
\(993\) | −17.5147 | −0.555813 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.76955 | −0.214609 | ||||||||
\(996\) | 12.8284 | 0.406484 | ||||||||
\(997\) | 20.6274 | 0.653277 | 0.326638 | − | 0.945149i | \(-0.394084\pi\) | ||||
0.326638 | + | 0.945149i | \(0.394084\pi\) | |||||||
\(998\) | −1.17157 | −0.0370855 | ||||||||
\(999\) | −3.17157 | −0.100344 |
(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 | 6762.2.a.bv.1.2 | 2 | ||
7.2 | even | 3 | 966.2.i.j.277.1 | ✓ | 4 | ||
7.4 | even | 3 | 966.2.i.j.415.1 | yes | 4 | ||
7.6 | odd | 2 | 6762.2.a.bt.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.j.277.1 | ✓ | 4 | 7.2 | even | 3 | ||
966.2.i.j.415.1 | yes | 4 | 7.4 | even | 3 | ||
6762.2.a.bt.1.1 | 2 | 7.6 | odd | 2 | |||
6762.2.a.bv.1.2 | 2 | 1.1 | even | 1 | trivial |