Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [619,2,Mod(1,619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(619, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 619.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(4.94273988512\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 619.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.993756 | 0.702692 | 0.351346 | − | 0.936246i | \(-0.385724\pi\) | ||||
0.351346 | + | 0.936246i | \(0.385724\pi\) | |||||||
\(3\) | 2.38151 | 1.37496 | 0.687482 | − | 0.726201i | \(-0.258716\pi\) | ||||
0.687482 | + | 0.726201i | \(0.258716\pi\) | |||||||
\(4\) | −1.01245 | −0.506224 | ||||||||
\(5\) | 2.26626 | 1.01350 | 0.506751 | − | 0.862092i | \(-0.330846\pi\) | ||||
0.506751 | + | 0.862092i | \(0.330846\pi\) | |||||||
\(6\) | 2.36664 | 0.966176 | ||||||||
\(7\) | 3.26853 | 1.23539 | 0.617693 | − | 0.786419i | \(-0.288067\pi\) | ||||
0.617693 | + | 0.786419i | \(0.288067\pi\) | |||||||
\(8\) | −2.99364 | −1.05841 | ||||||||
\(9\) | 2.67158 | 0.890528 | ||||||||
\(10\) | 2.25211 | 0.712180 | ||||||||
\(11\) | −3.48891 | −1.05195 | −0.525973 | − | 0.850501i | \(-0.676299\pi\) | ||||
−0.525973 | + | 0.850501i | \(0.676299\pi\) | |||||||
\(12\) | −2.41115 | −0.696040 | ||||||||
\(13\) | −0.0423457 | −0.0117446 | −0.00587229 | − | 0.999983i | \(-0.501869\pi\) | ||||
−0.00587229 | + | 0.999983i | \(0.501869\pi\) | |||||||
\(14\) | 3.24812 | 0.868096 | ||||||||
\(15\) | 5.39712 | 1.39353 | ||||||||
\(16\) | −0.950051 | −0.237513 | ||||||||
\(17\) | 0.559856 | 0.135785 | 0.0678925 | − | 0.997693i | \(-0.478373\pi\) | ||||
0.0678925 | + | 0.997693i | \(0.478373\pi\) | |||||||
\(18\) | 2.65490 | 0.625766 | ||||||||
\(19\) | 1.62574 | 0.372969 | 0.186485 | − | 0.982458i | \(-0.440291\pi\) | ||||
0.186485 | + | 0.982458i | \(0.440291\pi\) | |||||||
\(20\) | −2.29447 | −0.513060 | ||||||||
\(21\) | 7.78402 | 1.69861 | ||||||||
\(22\) | −3.46712 | −0.739193 | ||||||||
\(23\) | 4.81952 | 1.00494 | 0.502469 | − | 0.864595i | \(-0.332425\pi\) | ||||
0.502469 | + | 0.864595i | \(0.332425\pi\) | |||||||
\(24\) | −7.12938 | −1.45528 | ||||||||
\(25\) | 0.135941 | 0.0271882 | ||||||||
\(26\) | −0.0420813 | −0.00825282 | ||||||||
\(27\) | −0.782128 | −0.150521 | ||||||||
\(28\) | −3.30921 | −0.625383 | ||||||||
\(29\) | −6.07768 | −1.12860 | −0.564299 | − | 0.825571i | \(-0.690853\pi\) | ||||
−0.564299 | + | 0.825571i | \(0.690853\pi\) | |||||||
\(30\) | 5.36342 | 0.979223 | ||||||||
\(31\) | −6.33396 | −1.13761 | −0.568807 | − | 0.822471i | \(-0.692595\pi\) | ||||
−0.568807 | + | 0.822471i | \(0.692595\pi\) | |||||||
\(32\) | 5.04316 | 0.891513 | ||||||||
\(33\) | −8.30887 | −1.44639 | ||||||||
\(34\) | 0.556360 | 0.0954150 | ||||||||
\(35\) | 7.40733 | 1.25207 | ||||||||
\(36\) | −2.70484 | −0.450807 | ||||||||
\(37\) | −9.01381 | −1.48186 | −0.740931 | − | 0.671581i | \(-0.765615\pi\) | ||||
−0.740931 | + | 0.671581i | \(0.765615\pi\) | |||||||
\(38\) | 1.61558 | 0.262082 | ||||||||
\(39\) | −0.100847 | −0.0161484 | ||||||||
\(40\) | −6.78437 | −1.07270 | ||||||||
\(41\) | 7.61121 | 1.18867 | 0.594336 | − | 0.804217i | \(-0.297415\pi\) | ||||
0.594336 | + | 0.804217i | \(0.297415\pi\) | |||||||
\(42\) | 7.73542 | 1.19360 | ||||||||
\(43\) | −1.05671 | −0.161146 | −0.0805732 | − | 0.996749i | \(-0.525675\pi\) | ||||
−0.0805732 | + | 0.996749i | \(0.525675\pi\) | |||||||
\(44\) | 3.53234 | 0.532520 | ||||||||
\(45\) | 6.05451 | 0.902552 | ||||||||
\(46\) | 4.78942 | 0.706162 | ||||||||
\(47\) | 2.17333 | 0.317013 | 0.158506 | − | 0.987358i | \(-0.449332\pi\) | ||||
0.158506 | + | 0.987358i | \(0.449332\pi\) | |||||||
\(48\) | −2.26255 | −0.326572 | ||||||||
\(49\) | 3.68326 | 0.526180 | ||||||||
\(50\) | 0.135092 | 0.0191049 | ||||||||
\(51\) | 1.33330 | 0.186700 | ||||||||
\(52\) | 0.0428728 | 0.00594539 | ||||||||
\(53\) | 4.67404 | 0.642029 | 0.321014 | − | 0.947074i | \(-0.395976\pi\) | ||||
0.321014 | + | 0.947074i | \(0.395976\pi\) | |||||||
\(54\) | −0.777245 | −0.105770 | ||||||||
\(55\) | −7.90678 | −1.06615 | ||||||||
\(56\) | −9.78479 | −1.30755 | ||||||||
\(57\) | 3.87170 | 0.512820 | ||||||||
\(58\) | −6.03973 | −0.793056 | ||||||||
\(59\) | −6.68730 | −0.870612 | −0.435306 | − | 0.900283i | \(-0.643360\pi\) | ||||
−0.435306 | + | 0.900283i | \(0.643360\pi\) | |||||||
\(60\) | −5.46431 | −0.705439 | ||||||||
\(61\) | 8.79056 | 1.12552 | 0.562758 | − | 0.826622i | \(-0.309740\pi\) | ||||
0.562758 | + | 0.826622i | \(0.309740\pi\) | |||||||
\(62\) | −6.29442 | −0.799392 | ||||||||
\(63\) | 8.73214 | 1.10015 | ||||||||
\(64\) | 6.91177 | 0.863972 | ||||||||
\(65\) | −0.0959664 | −0.0119032 | ||||||||
\(66\) | −8.25699 | −1.01636 | ||||||||
\(67\) | 15.4972 | 1.89329 | 0.946643 | − | 0.322285i | \(-0.104451\pi\) | ||||
0.946643 | + | 0.322285i | \(0.104451\pi\) | |||||||
\(68\) | −0.566825 | −0.0687377 | ||||||||
\(69\) | 11.4777 | 1.38175 | ||||||||
\(70\) | 7.36108 | 0.879818 | ||||||||
\(71\) | −4.11028 | −0.487800 | −0.243900 | − | 0.969800i | \(-0.578427\pi\) | ||||
−0.243900 | + | 0.969800i | \(0.578427\pi\) | |||||||
\(72\) | −7.99776 | −0.942545 | ||||||||
\(73\) | −6.53747 | −0.765153 | −0.382577 | − | 0.923924i | \(-0.624963\pi\) | ||||
−0.382577 | + | 0.923924i | \(0.624963\pi\) | |||||||
\(74\) | −8.95753 | −1.04129 | ||||||||
\(75\) | 0.323744 | 0.0373828 | ||||||||
\(76\) | −1.64597 | −0.188806 | ||||||||
\(77\) | −11.4036 | −1.29956 | ||||||||
\(78\) | −0.100217 | −0.0113473 | ||||||||
\(79\) | −12.7015 | −1.42903 | −0.714516 | − | 0.699619i | \(-0.753353\pi\) | ||||
−0.714516 | + | 0.699619i | \(0.753353\pi\) | |||||||
\(80\) | −2.15306 | −0.240720 | ||||||||
\(81\) | −9.87739 | −1.09749 | ||||||||
\(82\) | 7.56369 | 0.835270 | ||||||||
\(83\) | −6.39009 | −0.701404 | −0.350702 | − | 0.936487i | \(-0.614057\pi\) | ||||
−0.350702 | + | 0.936487i | \(0.614057\pi\) | |||||||
\(84\) | −7.88092 | −0.859879 | ||||||||
\(85\) | 1.26878 | 0.137619 | ||||||||
\(86\) | −1.05011 | −0.113236 | ||||||||
\(87\) | −14.4741 | −1.55178 | ||||||||
\(88\) | 10.4445 | 1.11339 | ||||||||
\(89\) | 10.4798 | 1.11086 | 0.555430 | − | 0.831563i | \(-0.312554\pi\) | ||||
0.555430 | + | 0.831563i | \(0.312554\pi\) | |||||||
\(90\) | 6.01670 | 0.634216 | ||||||||
\(91\) | −0.138408 | −0.0145091 | ||||||||
\(92\) | −4.87951 | −0.508724 | ||||||||
\(93\) | −15.0844 | −1.56418 | ||||||||
\(94\) | 2.15976 | 0.222762 | ||||||||
\(95\) | 3.68434 | 0.378005 | ||||||||
\(96\) | 12.0103 | 1.22580 | ||||||||
\(97\) | 2.73737 | 0.277938 | 0.138969 | − | 0.990297i | \(-0.455621\pi\) | ||||
0.138969 | + | 0.990297i | \(0.455621\pi\) | |||||||
\(98\) | 3.66026 | 0.369742 | ||||||||
\(99\) | −9.32091 | −0.936787 | ||||||||
\(100\) | −0.137633 | −0.0137633 | ||||||||
\(101\) | −2.53899 | −0.252639 | −0.126320 | − | 0.991990i | \(-0.540317\pi\) | ||||
−0.126320 | + | 0.991990i | \(0.540317\pi\) | |||||||
\(102\) | 1.32498 | 0.131192 | ||||||||
\(103\) | 4.72956 | 0.466017 | 0.233008 | − | 0.972475i | \(-0.425143\pi\) | ||||
0.233008 | + | 0.972475i | \(0.425143\pi\) | |||||||
\(104\) | 0.126768 | 0.0124306 | ||||||||
\(105\) | 17.6406 | 1.72155 | ||||||||
\(106\) | 4.64486 | 0.451148 | ||||||||
\(107\) | −1.10752 | −0.107068 | −0.0535338 | − | 0.998566i | \(-0.517048\pi\) | ||||
−0.0535338 | + | 0.998566i | \(0.517048\pi\) | |||||||
\(108\) | 0.791864 | 0.0761972 | ||||||||
\(109\) | −11.8815 | −1.13804 | −0.569021 | − | 0.822323i | \(-0.692678\pi\) | ||||
−0.569021 | + | 0.822323i | \(0.692678\pi\) | |||||||
\(110\) | −7.85741 | −0.749175 | ||||||||
\(111\) | −21.4665 | −2.03751 | ||||||||
\(112\) | −3.10527 | −0.293420 | ||||||||
\(113\) | −8.27758 | −0.778689 | −0.389345 | − | 0.921092i | \(-0.627298\pi\) | ||||
−0.389345 | + | 0.921092i | \(0.627298\pi\) | |||||||
\(114\) | 3.84753 | 0.360354 | ||||||||
\(115\) | 10.9223 | 1.01851 | ||||||||
\(116\) | 6.15334 | 0.571323 | ||||||||
\(117\) | −0.113130 | −0.0104589 | ||||||||
\(118\) | −6.64554 | −0.611772 | ||||||||
\(119\) | 1.82990 | 0.167747 | ||||||||
\(120\) | −16.1570 | −1.47493 | ||||||||
\(121\) | 1.17248 | 0.106589 | ||||||||
\(122\) | 8.73568 | 0.790891 | ||||||||
\(123\) | 18.1262 | 1.63438 | ||||||||
\(124\) | 6.41281 | 0.575888 | ||||||||
\(125\) | −11.0232 | −0.985948 | ||||||||
\(126\) | 8.67762 | 0.773063 | ||||||||
\(127\) | −9.64782 | −0.856106 | −0.428053 | − | 0.903754i | \(-0.640800\pi\) | ||||
−0.428053 | + | 0.903754i | \(0.640800\pi\) | |||||||
\(128\) | −3.21770 | −0.284407 | ||||||||
\(129\) | −2.51656 | −0.221571 | ||||||||
\(130\) | −0.0953672 | −0.00836426 | ||||||||
\(131\) | 15.5141 | 1.35547 | 0.677735 | − | 0.735306i | \(-0.262961\pi\) | ||||
0.677735 | + | 0.735306i | \(0.262961\pi\) | |||||||
\(132\) | 8.41230 | 0.732197 | ||||||||
\(133\) | 5.31376 | 0.460761 | ||||||||
\(134\) | 15.4004 | 1.33040 | ||||||||
\(135\) | −1.77251 | −0.152553 | ||||||||
\(136\) | −1.67601 | −0.143716 | ||||||||
\(137\) | 0.728793 | 0.0622650 | 0.0311325 | − | 0.999515i | \(-0.490089\pi\) | ||||
0.0311325 | + | 0.999515i | \(0.490089\pi\) | |||||||
\(138\) | 11.4061 | 0.970948 | ||||||||
\(139\) | −12.4402 | −1.05516 | −0.527581 | − | 0.849505i | \(-0.676901\pi\) | ||||
−0.527581 | + | 0.849505i | \(0.676901\pi\) | |||||||
\(140\) | −7.49954 | −0.633827 | ||||||||
\(141\) | 5.17580 | 0.435881 | ||||||||
\(142\) | −4.08461 | −0.342773 | ||||||||
\(143\) | 0.147740 | 0.0123547 | ||||||||
\(144\) | −2.53814 | −0.211512 | ||||||||
\(145\) | −13.7736 | −1.14384 | ||||||||
\(146\) | −6.49665 | −0.537667 | ||||||||
\(147\) | 8.77171 | 0.723479 | ||||||||
\(148\) | 9.12602 | 0.750154 | ||||||||
\(149\) | 3.71652 | 0.304470 | 0.152235 | − | 0.988344i | \(-0.451353\pi\) | ||||
0.152235 | + | 0.988344i | \(0.451353\pi\) | |||||||
\(150\) | 0.321723 | 0.0262686 | ||||||||
\(151\) | −9.93395 | −0.808413 | −0.404207 | − | 0.914668i | \(-0.632452\pi\) | ||||
−0.404207 | + | 0.914668i | \(0.632452\pi\) | |||||||
\(152\) | −4.86687 | −0.394755 | ||||||||
\(153\) | 1.49570 | 0.120920 | ||||||||
\(154\) | −11.3324 | −0.913190 | ||||||||
\(155\) | −14.3544 | −1.15297 | ||||||||
\(156\) | 0.102102 | 0.00817470 | ||||||||
\(157\) | 21.8988 | 1.74772 | 0.873859 | − | 0.486180i | \(-0.161610\pi\) | ||||
0.873859 | + | 0.486180i | \(0.161610\pi\) | |||||||
\(158\) | −12.6222 | −1.00417 | ||||||||
\(159\) | 11.1313 | 0.882767 | ||||||||
\(160\) | 11.4291 | 0.903551 | ||||||||
\(161\) | 15.7527 | 1.24149 | ||||||||
\(162\) | −9.81572 | −0.771196 | ||||||||
\(163\) | 16.5248 | 1.29433 | 0.647163 | − | 0.762352i | \(-0.275955\pi\) | ||||
0.647163 | + | 0.762352i | \(0.275955\pi\) | |||||||
\(164\) | −7.70596 | −0.601735 | ||||||||
\(165\) | −18.8301 | −1.46592 | ||||||||
\(166\) | −6.35019 | −0.492871 | ||||||||
\(167\) | 18.4365 | 1.42666 | 0.713330 | − | 0.700829i | \(-0.247186\pi\) | ||||
0.713330 | + | 0.700829i | \(0.247186\pi\) | |||||||
\(168\) | −23.3026 | −1.79783 | ||||||||
\(169\) | −12.9982 | −0.999862 | ||||||||
\(170\) | 1.26086 | 0.0967034 | ||||||||
\(171\) | 4.34329 | 0.332139 | ||||||||
\(172\) | 1.06986 | 0.0815762 | ||||||||
\(173\) | 4.62720 | 0.351799 | 0.175900 | − | 0.984408i | \(-0.443717\pi\) | ||||
0.175900 | + | 0.984408i | \(0.443717\pi\) | |||||||
\(174\) | −14.3837 | −1.09042 | ||||||||
\(175\) | 0.444326 | 0.0335879 | ||||||||
\(176\) | 3.31464 | 0.249850 | ||||||||
\(177\) | −15.9259 | −1.19706 | ||||||||
\(178\) | 10.4144 | 0.780592 | ||||||||
\(179\) | 8.34650 | 0.623847 | 0.311924 | − | 0.950107i | \(-0.399027\pi\) | ||||
0.311924 | + | 0.950107i | \(0.399027\pi\) | |||||||
\(180\) | −6.12987 | −0.456894 | ||||||||
\(181\) | 13.3973 | 0.995813 | 0.497907 | − | 0.867231i | \(-0.334102\pi\) | ||||
0.497907 | + | 0.867231i | \(0.334102\pi\) | |||||||
\(182\) | −0.137544 | −0.0101954 | ||||||||
\(183\) | 20.9348 | 1.54755 | ||||||||
\(184\) | −14.4279 | −1.06364 | ||||||||
\(185\) | −20.4277 | −1.50187 | ||||||||
\(186\) | −14.9902 | −1.09914 | ||||||||
\(187\) | −1.95329 | −0.142838 | ||||||||
\(188\) | −2.20038 | −0.160480 | ||||||||
\(189\) | −2.55641 | −0.185951 | ||||||||
\(190\) | 3.66134 | 0.265621 | ||||||||
\(191\) | −6.08952 | −0.440622 | −0.220311 | − | 0.975430i | \(-0.570707\pi\) | ||||
−0.220311 | + | 0.975430i | \(0.570707\pi\) | |||||||
\(192\) | 16.4604 | 1.18793 | ||||||||
\(193\) | −7.50218 | −0.540019 | −0.270009 | − | 0.962858i | \(-0.587027\pi\) | ||||
−0.270009 | + | 0.962858i | \(0.587027\pi\) | |||||||
\(194\) | 2.72028 | 0.195305 | ||||||||
\(195\) | −0.228545 | −0.0163664 | ||||||||
\(196\) | −3.72911 | −0.266365 | ||||||||
\(197\) | 8.24651 | 0.587540 | 0.293770 | − | 0.955876i | \(-0.405090\pi\) | ||||
0.293770 | + | 0.955876i | \(0.405090\pi\) | |||||||
\(198\) | −9.26271 | −0.658272 | ||||||||
\(199\) | 8.50919 | 0.603200 | 0.301600 | − | 0.953435i | \(-0.402479\pi\) | ||||
0.301600 | + | 0.953435i | \(0.402479\pi\) | |||||||
\(200\) | −0.406958 | −0.0287763 | ||||||||
\(201\) | 36.9067 | 2.60320 | ||||||||
\(202\) | −2.52314 | −0.177528 | ||||||||
\(203\) | −19.8651 | −1.39425 | ||||||||
\(204\) | −1.34990 | −0.0945119 | ||||||||
\(205\) | 17.2490 | 1.20472 | ||||||||
\(206\) | 4.70002 | 0.327466 | ||||||||
\(207\) | 12.8757 | 0.894925 | ||||||||
\(208\) | 0.0402306 | 0.00278949 | ||||||||
\(209\) | −5.67204 | −0.392343 | ||||||||
\(210\) | 17.5305 | 1.20972 | ||||||||
\(211\) | −5.91072 | −0.406910 | −0.203455 | − | 0.979084i | \(-0.565217\pi\) | ||||
−0.203455 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(212\) | −4.73223 | −0.325011 | ||||||||
\(213\) | −9.78866 | −0.670708 | ||||||||
\(214\) | −1.10060 | −0.0752356 | ||||||||
\(215\) | −2.39478 | −0.163322 | ||||||||
\(216\) | 2.34141 | 0.159313 | ||||||||
\(217\) | −20.7027 | −1.40539 | ||||||||
\(218\) | −11.8073 | −0.799693 | ||||||||
\(219\) | −15.5690 | −1.05206 | ||||||||
\(220\) | 8.00521 | 0.539711 | ||||||||
\(221\) | −0.0237075 | −0.00159474 | ||||||||
\(222\) | −21.3324 | −1.43174 | ||||||||
\(223\) | −10.2228 | −0.684567 | −0.342283 | − | 0.939597i | \(-0.611200\pi\) | ||||
−0.342283 | + | 0.939597i | \(0.611200\pi\) | |||||||
\(224\) | 16.4837 | 1.10136 | ||||||||
\(225\) | 0.363177 | 0.0242118 | ||||||||
\(226\) | −8.22590 | −0.547179 | ||||||||
\(227\) | 25.7805 | 1.71111 | 0.855555 | − | 0.517713i | \(-0.173216\pi\) | ||||
0.855555 | + | 0.517713i | \(0.173216\pi\) | |||||||
\(228\) | −3.91990 | −0.259602 | ||||||||
\(229\) | 3.62202 | 0.239350 | 0.119675 | − | 0.992813i | \(-0.461815\pi\) | ||||
0.119675 | + | 0.992813i | \(0.461815\pi\) | |||||||
\(230\) | 10.8541 | 0.715697 | ||||||||
\(231\) | −27.1577 | −1.78685 | ||||||||
\(232\) | 18.1944 | 1.19452 | ||||||||
\(233\) | −8.02271 | −0.525585 | −0.262792 | − | 0.964852i | \(-0.584643\pi\) | ||||
−0.262792 | + | 0.964852i | \(0.584643\pi\) | |||||||
\(234\) | −0.112424 | −0.00734937 | ||||||||
\(235\) | 4.92533 | 0.321293 | ||||||||
\(236\) | 6.77054 | 0.440725 | ||||||||
\(237\) | −30.2488 | −1.96487 | ||||||||
\(238\) | 1.81848 | 0.117874 | ||||||||
\(239\) | −17.3902 | −1.12488 | −0.562438 | − | 0.826839i | \(-0.690136\pi\) | ||||
−0.562438 | + | 0.826839i | \(0.690136\pi\) | |||||||
\(240\) | −5.12754 | −0.330981 | ||||||||
\(241\) | 10.2145 | 0.657974 | 0.328987 | − | 0.944334i | \(-0.393293\pi\) | ||||
0.328987 | + | 0.944334i | \(0.393293\pi\) | |||||||
\(242\) | 1.16516 | 0.0748995 | ||||||||
\(243\) | −21.1767 | −1.35849 | ||||||||
\(244\) | −8.89999 | −0.569764 | ||||||||
\(245\) | 8.34723 | 0.533285 | ||||||||
\(246\) | 18.0130 | 1.14847 | ||||||||
\(247\) | −0.0688429 | −0.00438037 | ||||||||
\(248\) | 18.9616 | 1.20406 | ||||||||
\(249\) | −15.2181 | −0.964405 | ||||||||
\(250\) | −10.9544 | −0.692817 | ||||||||
\(251\) | 8.85928 | 0.559193 | 0.279596 | − | 0.960118i | \(-0.409799\pi\) | ||||
0.279596 | + | 0.960118i | \(0.409799\pi\) | |||||||
\(252\) | −8.84084 | −0.556921 | ||||||||
\(253\) | −16.8148 | −1.05714 | ||||||||
\(254\) | −9.58758 | −0.601578 | ||||||||
\(255\) | 3.02161 | 0.189221 | ||||||||
\(256\) | −17.0212 | −1.06382 | ||||||||
\(257\) | 29.5926 | 1.84594 | 0.922968 | − | 0.384877i | \(-0.125756\pi\) | ||||
0.922968 | + | 0.384877i | \(0.125756\pi\) | |||||||
\(258\) | −2.50085 | −0.155696 | ||||||||
\(259\) | −29.4619 | −1.83067 | ||||||||
\(260\) | 0.0971611 | 0.00602567 | ||||||||
\(261\) | −16.2370 | −1.00505 | ||||||||
\(262\) | 15.4172 | 0.952478 | ||||||||
\(263\) | 13.1829 | 0.812893 | 0.406446 | − | 0.913675i | \(-0.366768\pi\) | ||||
0.406446 | + | 0.913675i | \(0.366768\pi\) | |||||||
\(264\) | 24.8737 | 1.53087 | ||||||||
\(265\) | 10.5926 | 0.650698 | ||||||||
\(266\) | 5.28058 | 0.323773 | ||||||||
\(267\) | 24.9578 | 1.52739 | ||||||||
\(268\) | −15.6901 | −0.958427 | ||||||||
\(269\) | 6.16528 | 0.375904 | 0.187952 | − | 0.982178i | \(-0.439815\pi\) | ||||
0.187952 | + | 0.982178i | \(0.439815\pi\) | |||||||
\(270\) | −1.76144 | −0.107198 | ||||||||
\(271\) | −7.42818 | −0.451230 | −0.225615 | − | 0.974217i | \(-0.572439\pi\) | ||||
−0.225615 | + | 0.974217i | \(0.572439\pi\) | |||||||
\(272\) | −0.531892 | −0.0322507 | ||||||||
\(273\) | −0.329620 | −0.0199495 | ||||||||
\(274\) | 0.724242 | 0.0437531 | ||||||||
\(275\) | −0.474285 | −0.0286005 | ||||||||
\(276\) | −11.6206 | −0.699478 | ||||||||
\(277\) | 28.4319 | 1.70831 | 0.854155 | − | 0.520019i | \(-0.174075\pi\) | ||||
0.854155 | + | 0.520019i | \(0.174075\pi\) | |||||||
\(278\) | −12.3625 | −0.741454 | ||||||||
\(279\) | −16.9217 | −1.01308 | ||||||||
\(280\) | −22.1749 | −1.32520 | ||||||||
\(281\) | −1.93121 | −0.115206 | −0.0576031 | − | 0.998340i | \(-0.518346\pi\) | ||||
−0.0576031 | + | 0.998340i | \(0.518346\pi\) | |||||||
\(282\) | 5.14349 | 0.306290 | ||||||||
\(283\) | −4.39718 | −0.261385 | −0.130693 | − | 0.991423i | \(-0.541720\pi\) | ||||
−0.130693 | + | 0.991423i | \(0.541720\pi\) | |||||||
\(284\) | 4.16144 | 0.246936 | ||||||||
\(285\) | 8.77429 | 0.519744 | ||||||||
\(286\) | 0.146818 | 0.00868152 | ||||||||
\(287\) | 24.8774 | 1.46847 | ||||||||
\(288\) | 13.4732 | 0.793917 | ||||||||
\(289\) | −16.6866 | −0.981562 | ||||||||
\(290\) | −13.6876 | −0.803765 | ||||||||
\(291\) | 6.51908 | 0.382155 | ||||||||
\(292\) | 6.61885 | 0.387339 | ||||||||
\(293\) | 28.4616 | 1.66274 | 0.831371 | − | 0.555717i | \(-0.187556\pi\) | ||||
0.831371 | + | 0.555717i | \(0.187556\pi\) | |||||||
\(294\) | 8.71695 | 0.508383 | ||||||||
\(295\) | −15.1552 | −0.882368 | ||||||||
\(296\) | 26.9841 | 1.56842 | ||||||||
\(297\) | 2.72877 | 0.158339 | ||||||||
\(298\) | 3.69332 | 0.213948 | ||||||||
\(299\) | −0.204086 | −0.0118026 | ||||||||
\(300\) | −0.327774 | −0.0189241 | ||||||||
\(301\) | −3.45388 | −0.199078 | ||||||||
\(302\) | −9.87192 | −0.568065 | ||||||||
\(303\) | −6.04664 | −0.347370 | ||||||||
\(304\) | −1.54453 | −0.0885850 | ||||||||
\(305\) | 19.9217 | 1.14071 | ||||||||
\(306\) | 1.48636 | 0.0849697 | ||||||||
\(307\) | 31.7094 | 1.80975 | 0.904874 | − | 0.425679i | \(-0.139965\pi\) | ||||
0.904874 | + | 0.425679i | \(0.139965\pi\) | |||||||
\(308\) | 11.5455 | 0.657868 | ||||||||
\(309\) | 11.2635 | 0.640757 | ||||||||
\(310\) | −14.2648 | −0.810186 | ||||||||
\(311\) | −17.5426 | −0.994748 | −0.497374 | − | 0.867536i | \(-0.665702\pi\) | ||||
−0.497374 | + | 0.867536i | \(0.665702\pi\) | |||||||
\(312\) | 0.301898 | 0.0170916 | ||||||||
\(313\) | 24.0671 | 1.36035 | 0.680175 | − | 0.733049i | \(-0.261904\pi\) | ||||
0.680175 | + | 0.733049i | \(0.261904\pi\) | |||||||
\(314\) | 21.7621 | 1.22811 | ||||||||
\(315\) | 19.7893 | 1.11500 | ||||||||
\(316\) | 12.8596 | 0.723411 | ||||||||
\(317\) | 30.3259 | 1.70327 | 0.851636 | − | 0.524134i | \(-0.175611\pi\) | ||||
0.851636 | + | 0.524134i | \(0.175611\pi\) | |||||||
\(318\) | 11.0618 | 0.620313 | ||||||||
\(319\) | 21.2045 | 1.18722 | ||||||||
\(320\) | 15.6639 | 0.875638 | ||||||||
\(321\) | −2.63756 | −0.147214 | ||||||||
\(322\) | 15.6544 | 0.872383 | ||||||||
\(323\) | 0.910178 | 0.0506436 | ||||||||
\(324\) | 10.0004 | 0.555575 | ||||||||
\(325\) | −0.00575651 | −0.000319314 0 | ||||||||
\(326\) | 16.4217 | 0.909512 | ||||||||
\(327\) | −28.2959 | −1.56477 | ||||||||
\(328\) | −22.7852 | −1.25810 | ||||||||
\(329\) | 7.10358 | 0.391633 | ||||||||
\(330\) | −18.7125 | −1.03009 | ||||||||
\(331\) | −14.1141 | −0.775783 | −0.387892 | − | 0.921705i | \(-0.626797\pi\) | ||||
−0.387892 | + | 0.921705i | \(0.626797\pi\) | |||||||
\(332\) | 6.46964 | 0.355067 | ||||||||
\(333\) | −24.0811 | −1.31964 | ||||||||
\(334\) | 18.3214 | 1.00250 | ||||||||
\(335\) | 35.1207 | 1.91885 | ||||||||
\(336\) | −7.39522 | −0.403442 | ||||||||
\(337\) | 33.3303 | 1.81562 | 0.907810 | − | 0.419382i | \(-0.137753\pi\) | ||||
0.907810 | + | 0.419382i | \(0.137753\pi\) | |||||||
\(338\) | −12.9170 | −0.702595 | ||||||||
\(339\) | −19.7131 | −1.07067 | ||||||||
\(340\) | −1.28457 | −0.0696658 | ||||||||
\(341\) | 22.0986 | 1.19671 | ||||||||
\(342\) | 4.31617 | 0.233392 | ||||||||
\(343\) | −10.8409 | −0.585351 | ||||||||
\(344\) | 3.16340 | 0.170559 | ||||||||
\(345\) | 26.0115 | 1.40041 | ||||||||
\(346\) | 4.59830 | 0.247206 | ||||||||
\(347\) | −1.57665 | −0.0846392 | −0.0423196 | − | 0.999104i | \(-0.513475\pi\) | ||||
−0.0423196 | + | 0.999104i | \(0.513475\pi\) | |||||||
\(348\) | 14.6542 | 0.785549 | ||||||||
\(349\) | −5.53888 | −0.296490 | −0.148245 | − | 0.988951i | \(-0.547362\pi\) | ||||
−0.148245 | + | 0.988951i | \(0.547362\pi\) | |||||||
\(350\) | 0.441552 | 0.0236019 | ||||||||
\(351\) | 0.0331198 | 0.00176780 | ||||||||
\(352\) | −17.5951 | −0.937823 | ||||||||
\(353\) | −11.6547 | −0.620317 | −0.310158 | − | 0.950685i | \(-0.600382\pi\) | ||||
−0.310158 | + | 0.950685i | \(0.600382\pi\) | |||||||
\(354\) | −15.8264 | −0.841165 | ||||||||
\(355\) | −9.31496 | −0.494387 | ||||||||
\(356\) | −10.6103 | −0.562344 | ||||||||
\(357\) | 4.35793 | 0.230646 | ||||||||
\(358\) | 8.29439 | 0.438372 | ||||||||
\(359\) | 19.8234 | 1.04624 | 0.523120 | − | 0.852259i | \(-0.324768\pi\) | ||||
0.523120 | + | 0.852259i | \(0.324768\pi\) | |||||||
\(360\) | −18.1250 | −0.955272 | ||||||||
\(361\) | −16.3570 | −0.860894 | ||||||||
\(362\) | 13.3137 | 0.699750 | ||||||||
\(363\) | 2.79228 | 0.146557 | ||||||||
\(364\) | 0.140131 | 0.00734486 | ||||||||
\(365\) | −14.8156 | −0.775485 | ||||||||
\(366\) | 20.8041 | 1.08745 | ||||||||
\(367\) | −11.5005 | −0.600323 | −0.300161 | − | 0.953888i | \(-0.597041\pi\) | ||||
−0.300161 | + | 0.953888i | \(0.597041\pi\) | |||||||
\(368\) | −4.57878 | −0.238686 | ||||||||
\(369\) | 20.3340 | 1.05855 | ||||||||
\(370\) | −20.3001 | −1.05535 | ||||||||
\(371\) | 15.2772 | 0.793154 | ||||||||
\(372\) | 15.2722 | 0.791825 | ||||||||
\(373\) | −36.0734 | −1.86781 | −0.933905 | − | 0.357521i | \(-0.883622\pi\) | ||||
−0.933905 | + | 0.357521i | \(0.883622\pi\) | |||||||
\(374\) | −1.94109 | −0.100371 | ||||||||
\(375\) | −26.2519 | −1.35564 | ||||||||
\(376\) | −6.50617 | −0.335530 | ||||||||
\(377\) | 0.257364 | 0.0132549 | ||||||||
\(378\) | −2.54044 | −0.130666 | ||||||||
\(379\) | −3.58163 | −0.183976 | −0.0919880 | − | 0.995760i | \(-0.529322\pi\) | ||||
−0.0919880 | + | 0.995760i | \(0.529322\pi\) | |||||||
\(380\) | −3.73021 | −0.191356 | ||||||||
\(381\) | −22.9764 | −1.17711 | ||||||||
\(382\) | −6.05149 | −0.309621 | ||||||||
\(383\) | 21.0537 | 1.07579 | 0.537897 | − | 0.843011i | \(-0.319219\pi\) | ||||
0.537897 | + | 0.843011i | \(0.319219\pi\) | |||||||
\(384\) | −7.66298 | −0.391050 | ||||||||
\(385\) | −25.8435 | −1.31711 | ||||||||
\(386\) | −7.45534 | −0.379467 | ||||||||
\(387\) | −2.82308 | −0.143505 | ||||||||
\(388\) | −2.77145 | −0.140699 | ||||||||
\(389\) | −8.55454 | −0.433733 | −0.216866 | − | 0.976201i | \(-0.569584\pi\) | ||||
−0.216866 | + | 0.976201i | \(0.569584\pi\) | |||||||
\(390\) | −0.227118 | −0.0115006 | ||||||||
\(391\) | 2.69823 | 0.136456 | ||||||||
\(392\) | −11.0264 | −0.556915 | ||||||||
\(393\) | 36.9469 | 1.86372 | ||||||||
\(394\) | 8.19502 | 0.412859 | ||||||||
\(395\) | −28.7850 | −1.44833 | ||||||||
\(396\) | 9.43694 | 0.474224 | ||||||||
\(397\) | 20.4403 | 1.02587 | 0.512934 | − | 0.858428i | \(-0.328559\pi\) | ||||
0.512934 | + | 0.858428i | \(0.328559\pi\) | |||||||
\(398\) | 8.45606 | 0.423864 | ||||||||
\(399\) | 12.6548 | 0.633530 | ||||||||
\(400\) | −0.129151 | −0.00645753 | ||||||||
\(401\) | −17.1022 | −0.854042 | −0.427021 | − | 0.904242i | \(-0.640437\pi\) | ||||
−0.427021 | + | 0.904242i | \(0.640437\pi\) | |||||||
\(402\) | 36.6763 | 1.82925 | ||||||||
\(403\) | 0.268216 | 0.0133608 | ||||||||
\(404\) | 2.57060 | 0.127892 | ||||||||
\(405\) | −22.3848 | −1.11231 | ||||||||
\(406\) | −19.7410 | −0.979731 | ||||||||
\(407\) | 31.4484 | 1.55884 | ||||||||
\(408\) | −3.99143 | −0.197605 | ||||||||
\(409\) | 8.28369 | 0.409602 | 0.204801 | − | 0.978804i | \(-0.434345\pi\) | ||||
0.204801 | + | 0.978804i | \(0.434345\pi\) | |||||||
\(410\) | 17.1413 | 0.846549 | ||||||||
\(411\) | 1.73563 | 0.0856121 | ||||||||
\(412\) | −4.78843 | −0.235909 | ||||||||
\(413\) | −21.8576 | −1.07554 | ||||||||
\(414\) | 12.7953 | 0.628857 | ||||||||
\(415\) | −14.4816 | −0.710875 | ||||||||
\(416\) | −0.213556 | −0.0104704 | ||||||||
\(417\) | −29.6264 | −1.45081 | ||||||||
\(418\) | −5.63663 | −0.275696 | ||||||||
\(419\) | −23.9904 | −1.17201 | −0.586004 | − | 0.810308i | \(-0.699300\pi\) | ||||
−0.586004 | + | 0.810308i | \(0.699300\pi\) | |||||||
\(420\) | −17.8602 | −0.871490 | ||||||||
\(421\) | −13.8202 | −0.673556 | −0.336778 | − | 0.941584i | \(-0.609337\pi\) | ||||
−0.336778 | + | 0.941584i | \(0.609337\pi\) | |||||||
\(422\) | −5.87381 | −0.285933 | ||||||||
\(423\) | 5.80623 | 0.282309 | ||||||||
\(424\) | −13.9924 | −0.679531 | ||||||||
\(425\) | 0.0761073 | 0.00369175 | ||||||||
\(426\) | −9.72754 | −0.471301 | ||||||||
\(427\) | 28.7322 | 1.39045 | ||||||||
\(428\) | 1.12130 | 0.0542002 | ||||||||
\(429\) | 0.351845 | 0.0169872 | ||||||||
\(430\) | −2.37982 | −0.114765 | ||||||||
\(431\) | 19.1258 | 0.921258 | 0.460629 | − | 0.887593i | \(-0.347624\pi\) | ||||
0.460629 | + | 0.887593i | \(0.347624\pi\) | |||||||
\(432\) | 0.743061 | 0.0357506 | ||||||||
\(433\) | −16.3174 | −0.784166 | −0.392083 | − | 0.919930i | \(-0.628245\pi\) | ||||
−0.392083 | + | 0.919930i | \(0.628245\pi\) | |||||||
\(434\) | −20.5735 | −0.987558 | ||||||||
\(435\) | −32.8020 | −1.57273 | ||||||||
\(436\) | 12.0294 | 0.576105 | ||||||||
\(437\) | 7.83526 | 0.374811 | ||||||||
\(438\) | −15.4718 | −0.739273 | ||||||||
\(439\) | 29.5061 | 1.40825 | 0.704124 | − | 0.710077i | \(-0.251340\pi\) | ||||
0.704124 | + | 0.710077i | \(0.251340\pi\) | |||||||
\(440\) | 23.6700 | 1.12843 | ||||||||
\(441\) | 9.84013 | 0.468578 | ||||||||
\(442\) | −0.0235595 | −0.00112061 | ||||||||
\(443\) | 7.94549 | 0.377502 | 0.188751 | − | 0.982025i | \(-0.439556\pi\) | ||||
0.188751 | + | 0.982025i | \(0.439556\pi\) | |||||||
\(444\) | 21.7337 | 1.03144 | ||||||||
\(445\) | 23.7500 | 1.12586 | ||||||||
\(446\) | −10.1589 | −0.481040 | ||||||||
\(447\) | 8.85094 | 0.418635 | ||||||||
\(448\) | 22.5913 | 1.06734 | ||||||||
\(449\) | −37.2956 | −1.76009 | −0.880045 | − | 0.474890i | \(-0.842488\pi\) | ||||
−0.880045 | + | 0.474890i | \(0.842488\pi\) | |||||||
\(450\) | 0.360910 | 0.0170134 | ||||||||
\(451\) | −26.5548 | −1.25042 | ||||||||
\(452\) | 8.38062 | 0.394191 | ||||||||
\(453\) | −23.6578 | −1.11154 | ||||||||
\(454\) | 25.6195 | 1.20238 | ||||||||
\(455\) | −0.313669 | −0.0147050 | ||||||||
\(456\) | −11.5905 | −0.542774 | ||||||||
\(457\) | 17.0381 | 0.797007 | 0.398503 | − | 0.917167i | \(-0.369530\pi\) | ||||
0.398503 | + | 0.917167i | \(0.369530\pi\) | |||||||
\(458\) | 3.59940 | 0.168189 | ||||||||
\(459\) | −0.437879 | −0.0204384 | ||||||||
\(460\) | −11.0582 | −0.515593 | ||||||||
\(461\) | 36.9778 | 1.72223 | 0.861113 | − | 0.508413i | \(-0.169768\pi\) | ||||
0.861113 | + | 0.508413i | \(0.169768\pi\) | |||||||
\(462\) | −26.9882 | −1.25560 | ||||||||
\(463\) | −42.0166 | −1.95268 | −0.976339 | − | 0.216245i | \(-0.930619\pi\) | ||||
−0.976339 | + | 0.216245i | \(0.930619\pi\) | |||||||
\(464\) | 5.77411 | 0.268056 | ||||||||
\(465\) | −34.1852 | −1.58530 | ||||||||
\(466\) | −7.97261 | −0.369324 | ||||||||
\(467\) | −11.6484 | −0.539022 | −0.269511 | − | 0.962997i | \(-0.586862\pi\) | ||||
−0.269511 | + | 0.962997i | \(0.586862\pi\) | |||||||
\(468\) | 0.114538 | 0.00529454 | ||||||||
\(469\) | 50.6530 | 2.33894 | ||||||||
\(470\) | 4.89458 | 0.225770 | ||||||||
\(471\) | 52.1523 | 2.40305 | ||||||||
\(472\) | 20.0194 | 0.921466 | ||||||||
\(473\) | 3.68676 | 0.169517 | ||||||||
\(474\) | −30.0599 | −1.38070 | ||||||||
\(475\) | 0.221004 | 0.0101403 | ||||||||
\(476\) | −1.85268 | −0.0849176 | ||||||||
\(477\) | 12.4871 | 0.571744 | ||||||||
\(478\) | −17.2816 | −0.790441 | ||||||||
\(479\) | −11.2345 | −0.513319 | −0.256659 | − | 0.966502i | \(-0.582622\pi\) | ||||
−0.256659 | + | 0.966502i | \(0.582622\pi\) | |||||||
\(480\) | 27.2185 | 1.24235 | ||||||||
\(481\) | 0.381696 | 0.0174038 | ||||||||
\(482\) | 10.1507 | 0.462353 | ||||||||
\(483\) | 37.5152 | 1.70700 | ||||||||
\(484\) | −1.18708 | −0.0539582 | ||||||||
\(485\) | 6.20360 | 0.281691 | ||||||||
\(486\) | −21.0445 | −0.954597 | ||||||||
\(487\) | −12.7952 | −0.579806 | −0.289903 | − | 0.957056i | \(-0.593623\pi\) | ||||
−0.289903 | + | 0.957056i | \(0.593623\pi\) | |||||||
\(488\) | −26.3158 | −1.19126 | ||||||||
\(489\) | 39.3540 | 1.77965 | ||||||||
\(490\) | 8.29511 | 0.374735 | ||||||||
\(491\) | −25.8706 | −1.16753 | −0.583763 | − | 0.811924i | \(-0.698420\pi\) | ||||
−0.583763 | + | 0.811924i | \(0.698420\pi\) | |||||||
\(492\) | −18.3518 | −0.827364 | ||||||||
\(493\) | −3.40263 | −0.153247 | ||||||||
\(494\) | −0.0684131 | −0.00307805 | ||||||||
\(495\) | −21.1236 | −0.949436 | ||||||||
\(496\) | 6.01759 | 0.270198 | ||||||||
\(497\) | −13.4345 | −0.602622 | ||||||||
\(498\) | −15.1230 | −0.677679 | ||||||||
\(499\) | −39.9900 | −1.79020 | −0.895099 | − | 0.445867i | \(-0.852895\pi\) | ||||
−0.895099 | + | 0.445867i | \(0.852895\pi\) | |||||||
\(500\) | 11.1605 | 0.499111 | ||||||||
\(501\) | 43.9067 | 1.96161 | ||||||||
\(502\) | 8.80396 | 0.392940 | ||||||||
\(503\) | 23.6258 | 1.05342 | 0.526712 | − | 0.850044i | \(-0.323425\pi\) | ||||
0.526712 | + | 0.850044i | \(0.323425\pi\) | |||||||
\(504\) | −26.1409 | −1.16441 | ||||||||
\(505\) | −5.75402 | −0.256051 | ||||||||
\(506\) | −16.7099 | −0.742844 | ||||||||
\(507\) | −30.9553 | −1.37477 | ||||||||
\(508\) | 9.76792 | 0.433381 | ||||||||
\(509\) | 30.6346 | 1.35786 | 0.678928 | − | 0.734204i | \(-0.262445\pi\) | ||||
0.678928 | + | 0.734204i | \(0.262445\pi\) | |||||||
\(510\) | 3.00274 | 0.132964 | ||||||||
\(511\) | −21.3679 | −0.945260 | ||||||||
\(512\) | −10.4795 | −0.463132 | ||||||||
\(513\) | −1.27153 | −0.0561396 | ||||||||
\(514\) | 29.4078 | 1.29712 | ||||||||
\(515\) | 10.7184 | 0.472310 | ||||||||
\(516\) | 2.54789 | 0.112164 | ||||||||
\(517\) | −7.58255 | −0.333480 | ||||||||
\(518\) | −29.2779 | −1.28640 | ||||||||
\(519\) | 11.0197 | 0.483711 | ||||||||
\(520\) | 0.287289 | 0.0125984 | ||||||||
\(521\) | −8.18590 | −0.358631 | −0.179315 | − | 0.983792i | \(-0.557388\pi\) | ||||
−0.179315 | + | 0.983792i | \(0.557388\pi\) | |||||||
\(522\) | −16.1357 | −0.706238 | ||||||||
\(523\) | −15.6310 | −0.683497 | −0.341749 | − | 0.939791i | \(-0.611019\pi\) | ||||
−0.341749 | + | 0.939791i | \(0.611019\pi\) | |||||||
\(524\) | −15.7072 | −0.686172 | ||||||||
\(525\) | 1.05817 | 0.0461822 | ||||||||
\(526\) | 13.1006 | 0.571213 | ||||||||
\(527\) | −3.54611 | −0.154471 | ||||||||
\(528\) | 7.89385 | 0.343536 | ||||||||
\(529\) | 0.227726 | 0.00990113 | ||||||||
\(530\) | 10.5265 | 0.457240 | ||||||||
\(531\) | −17.8657 | −0.775304 | ||||||||
\(532\) | −5.37991 | −0.233249 | ||||||||
\(533\) | −0.322302 | −0.0139605 | ||||||||
\(534\) | 24.8020 | 1.07329 | ||||||||
\(535\) | −2.50992 | −0.108513 | ||||||||
\(536\) | −46.3931 | −2.00387 | ||||||||
\(537\) | 19.8773 | 0.857768 | ||||||||
\(538\) | 6.12679 | 0.264144 | ||||||||
\(539\) | −12.8506 | −0.553513 | ||||||||
\(540\) | 1.79457 | 0.0772261 | ||||||||
\(541\) | 23.7414 | 1.02072 | 0.510360 | − | 0.859961i | \(-0.329512\pi\) | ||||
0.510360 | + | 0.859961i | \(0.329512\pi\) | |||||||
\(542\) | −7.38180 | −0.317075 | ||||||||
\(543\) | 31.9058 | 1.36921 | ||||||||
\(544\) | 2.82344 | 0.121054 | ||||||||
\(545\) | −26.9266 | −1.15341 | ||||||||
\(546\) | −0.327562 | −0.0140183 | ||||||||
\(547\) | −15.5980 | −0.666922 | −0.333461 | − | 0.942764i | \(-0.608217\pi\) | ||||
−0.333461 | + | 0.942764i | \(0.608217\pi\) | |||||||
\(548\) | −0.737865 | −0.0315200 | ||||||||
\(549\) | 23.4847 | 1.00230 | ||||||||
\(550\) | −0.471324 | −0.0200973 | ||||||||
\(551\) | −9.88070 | −0.420932 | ||||||||
\(552\) | −34.3601 | −1.46246 | ||||||||
\(553\) | −41.5152 | −1.76541 | ||||||||
\(554\) | 28.2544 | 1.20041 | ||||||||
\(555\) | −48.6486 | −2.06502 | ||||||||
\(556\) | 12.5950 | 0.534149 | ||||||||
\(557\) | 35.0308 | 1.48430 | 0.742151 | − | 0.670233i | \(-0.233806\pi\) | ||||
0.742151 | + | 0.670233i | \(0.233806\pi\) | |||||||
\(558\) | −16.8161 | −0.711880 | ||||||||
\(559\) | 0.0447470 | 0.00189260 | ||||||||
\(560\) | −7.03734 | −0.297382 | ||||||||
\(561\) | −4.65177 | −0.196398 | ||||||||
\(562\) | −1.91915 | −0.0809545 | ||||||||
\(563\) | 24.0930 | 1.01540 | 0.507700 | − | 0.861534i | \(-0.330496\pi\) | ||||
0.507700 | + | 0.861534i | \(0.330496\pi\) | |||||||
\(564\) | −5.24023 | −0.220654 | ||||||||
\(565\) | −18.7592 | −0.789204 | ||||||||
\(566\) | −4.36972 | −0.183673 | ||||||||
\(567\) | −32.2845 | −1.35582 | ||||||||
\(568\) | 12.3047 | 0.516293 | ||||||||
\(569\) | −9.18857 | −0.385205 | −0.192603 | − | 0.981277i | \(-0.561693\pi\) | ||||
−0.192603 | + | 0.981277i | \(0.561693\pi\) | |||||||
\(570\) | 8.71951 | 0.365220 | ||||||||
\(571\) | −16.9178 | −0.707989 | −0.353994 | − | 0.935248i | \(-0.615177\pi\) | ||||
−0.353994 | + | 0.935248i | \(0.615177\pi\) | |||||||
\(572\) | −0.149579 | −0.00625423 | ||||||||
\(573\) | −14.5022 | −0.605840 | ||||||||
\(574\) | 24.7221 | 1.03188 | ||||||||
\(575\) | 0.655169 | 0.0273224 | ||||||||
\(576\) | 18.4654 | 0.769391 | ||||||||
\(577\) | 25.3727 | 1.05628 | 0.528141 | − | 0.849157i | \(-0.322889\pi\) | ||||
0.528141 | + | 0.849157i | \(0.322889\pi\) | |||||||
\(578\) | −16.5824 | −0.689736 | ||||||||
\(579\) | −17.8665 | −0.742507 | ||||||||
\(580\) | 13.9451 | 0.579038 | ||||||||
\(581\) | −20.8862 | −0.866504 | ||||||||
\(582\) | 6.47838 | 0.268537 | ||||||||
\(583\) | −16.3073 | −0.675379 | ||||||||
\(584\) | 19.5708 | 0.809847 | ||||||||
\(585\) | −0.256382 | −0.0106001 | ||||||||
\(586\) | 28.2839 | 1.16840 | ||||||||
\(587\) | −42.0228 | −1.73447 | −0.867233 | − | 0.497902i | \(-0.834104\pi\) | ||||
−0.867233 | + | 0.497902i | \(0.834104\pi\) | |||||||
\(588\) | −8.88091 | −0.366242 | ||||||||
\(589\) | −10.2974 | −0.424295 | ||||||||
\(590\) | −15.0605 | −0.620033 | ||||||||
\(591\) | 19.6391 | 0.807846 | ||||||||
\(592\) | 8.56358 | 0.351961 | ||||||||
\(593\) | −4.55651 | −0.187114 | −0.0935568 | − | 0.995614i | \(-0.529824\pi\) | ||||
−0.0935568 | + | 0.995614i | \(0.529824\pi\) | |||||||
\(594\) | 2.71174 | 0.111264 | ||||||||
\(595\) | 4.14704 | 0.170012 | ||||||||
\(596\) | −3.76279 | −0.154130 | ||||||||
\(597\) | 20.2647 | 0.829379 | ||||||||
\(598\) | −0.202811 | −0.00829358 | ||||||||
\(599\) | −29.9219 | −1.22258 | −0.611288 | − | 0.791409i | \(-0.709348\pi\) | ||||
−0.611288 | + | 0.791409i | \(0.709348\pi\) | |||||||
\(600\) | −0.969173 | −0.0395663 | ||||||||
\(601\) | 18.2493 | 0.744404 | 0.372202 | − | 0.928152i | \(-0.378603\pi\) | ||||
0.372202 | + | 0.928152i | \(0.378603\pi\) | |||||||
\(602\) | −3.43231 | −0.139891 | ||||||||
\(603\) | 41.4021 | 1.68602 | ||||||||
\(604\) | 10.0576 | 0.409238 | ||||||||
\(605\) | 2.65715 | 0.108029 | ||||||||
\(606\) | −6.00888 | −0.244094 | ||||||||
\(607\) | −36.9675 | −1.50046 | −0.750232 | − | 0.661174i | \(-0.770058\pi\) | ||||
−0.750232 | + | 0.661174i | \(0.770058\pi\) | |||||||
\(608\) | 8.19884 | 0.332507 | ||||||||
\(609\) | −47.3088 | −1.91705 | ||||||||
\(610\) | 19.7973 | 0.801570 | ||||||||
\(611\) | −0.0920311 | −0.00372318 | ||||||||
\(612\) | −1.51432 | −0.0612128 | ||||||||
\(613\) | 7.11423 | 0.287341 | 0.143670 | − | 0.989626i | \(-0.454109\pi\) | ||||
0.143670 | + | 0.989626i | \(0.454109\pi\) | |||||||
\(614\) | 31.5114 | 1.27170 | ||||||||
\(615\) | 41.0786 | 1.65645 | ||||||||
\(616\) | 34.1382 | 1.37547 | ||||||||
\(617\) | −21.3061 | −0.857751 | −0.428876 | − | 0.903364i | \(-0.641090\pi\) | ||||
−0.428876 | + | 0.903364i | \(0.641090\pi\) | |||||||
\(618\) | 11.1931 | 0.450255 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | 14.5331 | 0.583664 | ||||||||
\(621\) | −3.76948 | −0.151264 | ||||||||
\(622\) | −17.4330 | −0.699001 | ||||||||
\(623\) | 34.2536 | 1.37234 | ||||||||
\(624\) | 0.0958094 | 0.00383545 | ||||||||
\(625\) | −25.6612 | −1.02645 | ||||||||
\(626\) | 23.9168 | 0.955907 | ||||||||
\(627\) | −13.5080 | −0.539458 | ||||||||
\(628\) | −22.1714 | −0.884737 | ||||||||
\(629\) | −5.04644 | −0.201215 | ||||||||
\(630\) | 19.6657 | 0.783502 | ||||||||
\(631\) | −22.2473 | −0.885650 | −0.442825 | − | 0.896608i | \(-0.646024\pi\) | ||||
−0.442825 | + | 0.896608i | \(0.646024\pi\) | |||||||
\(632\) | 38.0238 | 1.51250 | ||||||||
\(633\) | −14.0764 | −0.559487 | ||||||||
\(634\) | 30.1365 | 1.19687 | ||||||||
\(635\) | −21.8645 | −0.867665 | ||||||||
\(636\) | −11.2698 | −0.446878 | ||||||||
\(637\) | −0.155970 | −0.00617976 | ||||||||
\(638\) | 21.0721 | 0.834252 | ||||||||
\(639\) | −10.9809 | −0.434400 | ||||||||
\(640\) | −7.29215 | −0.288248 | ||||||||
\(641\) | 28.1342 | 1.11124 | 0.555618 | − | 0.831438i | \(-0.312482\pi\) | ||||
0.555618 | + | 0.831438i | \(0.312482\pi\) | |||||||
\(642\) | −2.62109 | −0.103446 | ||||||||
\(643\) | −32.9969 | −1.30127 | −0.650636 | − | 0.759390i | \(-0.725498\pi\) | ||||
−0.650636 | + | 0.759390i | \(0.725498\pi\) | |||||||
\(644\) | −15.9488 | −0.628471 | ||||||||
\(645\) | −5.70318 | −0.224562 | ||||||||
\(646\) | 0.904495 | 0.0355869 | ||||||||
\(647\) | −41.0699 | −1.61463 | −0.807313 | − | 0.590124i | \(-0.799079\pi\) | ||||
−0.807313 | + | 0.590124i | \(0.799079\pi\) | |||||||
\(648\) | 29.5694 | 1.16159 | ||||||||
\(649\) | 23.3314 | 0.915836 | ||||||||
\(650\) | −0.00572057 | −0.000224379 0 | ||||||||
\(651\) | −49.3037 | −1.93237 | ||||||||
\(652\) | −16.7306 | −0.655219 | ||||||||
\(653\) | 39.9591 | 1.56372 | 0.781860 | − | 0.623454i | \(-0.214271\pi\) | ||||
0.781860 | + | 0.623454i | \(0.214271\pi\) | |||||||
\(654\) | −28.1193 | −1.09955 | ||||||||
\(655\) | 35.1589 | 1.37377 | ||||||||
\(656\) | −7.23104 | −0.282325 | ||||||||
\(657\) | −17.4654 | −0.681390 | ||||||||
\(658\) | 7.05923 | 0.275197 | ||||||||
\(659\) | 26.4314 | 1.02962 | 0.514811 | − | 0.857304i | \(-0.327862\pi\) | ||||
0.514811 | + | 0.857304i | \(0.327862\pi\) | |||||||
\(660\) | 19.0645 | 0.742083 | ||||||||
\(661\) | 17.4319 | 0.678024 | 0.339012 | − | 0.940782i | \(-0.389907\pi\) | ||||
0.339012 | + | 0.940782i | \(0.389907\pi\) | |||||||
\(662\) | −14.0260 | −0.545137 | ||||||||
\(663\) | −0.0564596 | −0.00219271 | ||||||||
\(664\) | 19.1296 | 0.742374 | ||||||||
\(665\) | 12.0424 | 0.466983 | ||||||||
\(666\) | −23.9308 | −0.927299 | ||||||||
\(667\) | −29.2915 | −1.13417 | ||||||||
\(668\) | −18.6660 | −0.722209 | ||||||||
\(669\) | −24.3456 | −0.941255 | ||||||||
\(670\) | 34.9014 | 1.34836 | ||||||||
\(671\) | −30.6695 | −1.18398 | ||||||||
\(672\) | 39.2561 | 1.51434 | ||||||||
\(673\) | 41.7040 | 1.60757 | 0.803785 | − | 0.594919i | \(-0.202816\pi\) | ||||
0.803785 | + | 0.594919i | \(0.202816\pi\) | |||||||
\(674\) | 33.1222 | 1.27582 | ||||||||
\(675\) | −0.106323 | −0.00409238 | ||||||||
\(676\) | 13.1600 | 0.506154 | ||||||||
\(677\) | −6.10189 | −0.234515 | −0.117257 | − | 0.993102i | \(-0.537410\pi\) | ||||
−0.117257 | + | 0.993102i | \(0.537410\pi\) | |||||||
\(678\) | −19.5900 | −0.752351 | ||||||||
\(679\) | 8.94718 | 0.343361 | ||||||||
\(680\) | −3.79827 | −0.145657 | ||||||||
\(681\) | 61.3964 | 2.35271 | ||||||||
\(682\) | 21.9606 | 0.840917 | ||||||||
\(683\) | −0.724917 | −0.0277382 | −0.0138691 | − | 0.999904i | \(-0.504415\pi\) | ||||
−0.0138691 | + | 0.999904i | \(0.504415\pi\) | |||||||
\(684\) | −4.39735 | −0.168137 | ||||||||
\(685\) | 1.65164 | 0.0631057 | ||||||||
\(686\) | −10.7732 | −0.411321 | ||||||||
\(687\) | 8.62587 | 0.329097 | ||||||||
\(688\) | 1.00393 | 0.0382743 | ||||||||
\(689\) | −0.197925 | −0.00754036 | ||||||||
\(690\) | 25.8491 | 0.984058 | ||||||||
\(691\) | −33.3019 | −1.26686 | −0.633432 | − | 0.773798i | \(-0.718354\pi\) | ||||
−0.633432 | + | 0.773798i | \(0.718354\pi\) | |||||||
\(692\) | −4.68480 | −0.178089 | ||||||||
\(693\) | −30.4656 | −1.15729 | ||||||||
\(694\) | −1.56681 | −0.0594753 | ||||||||
\(695\) | −28.1927 | −1.06941 | ||||||||
\(696\) | 43.3301 | 1.64242 | ||||||||
\(697\) | 4.26118 | 0.161404 | ||||||||
\(698\) | −5.50430 | −0.208341 | ||||||||
\(699\) | −19.1061 | −0.722661 | ||||||||
\(700\) | −0.449857 | −0.0170030 | ||||||||
\(701\) | −22.5695 | −0.852438 | −0.426219 | − | 0.904620i | \(-0.640155\pi\) | ||||
−0.426219 | + | 0.904620i | \(0.640155\pi\) | |||||||
\(702\) | 0.0329130 | 0.00124222 | ||||||||
\(703\) | −14.6541 | −0.552689 | ||||||||
\(704\) | −24.1145 | −0.908851 | ||||||||
\(705\) | 11.7297 | 0.441767 | ||||||||
\(706\) | −11.5819 | −0.435892 | ||||||||
\(707\) | −8.29877 | −0.312107 | ||||||||
\(708\) | 16.1241 | 0.605981 | ||||||||
\(709\) | −9.58864 | −0.360109 | −0.180054 | − | 0.983657i | \(-0.557627\pi\) | ||||
−0.180054 | + | 0.983657i | \(0.557627\pi\) | |||||||
\(710\) | −9.25680 | −0.347402 | ||||||||
\(711\) | −33.9332 | −1.27259 | ||||||||
\(712\) | −31.3729 | −1.17575 | ||||||||
\(713\) | −30.5266 | −1.14323 | ||||||||
\(714\) | 4.33072 | 0.162073 | ||||||||
\(715\) | 0.334818 | 0.0125215 | ||||||||
\(716\) | −8.45041 | −0.315807 | ||||||||
\(717\) | −41.4148 | −1.54666 | ||||||||
\(718\) | 19.6996 | 0.735184 | ||||||||
\(719\) | −6.38603 | −0.238159 | −0.119079 | − | 0.992885i | \(-0.537994\pi\) | ||||
−0.119079 | + | 0.992885i | \(0.537994\pi\) | |||||||
\(720\) | −5.75209 | −0.214368 | ||||||||
\(721\) | 15.4587 | 0.575711 | ||||||||
\(722\) | −16.2549 | −0.604943 | ||||||||
\(723\) | 24.3259 | 0.904691 | ||||||||
\(724\) | −13.5641 | −0.504105 | ||||||||
\(725\) | −0.826205 | −0.0306845 | ||||||||
\(726\) | 2.77485 | 0.102984 | ||||||||
\(727\) | 34.5236 | 1.28041 | 0.640204 | − | 0.768205i | \(-0.278850\pi\) | ||||
0.640204 | + | 0.768205i | \(0.278850\pi\) | |||||||
\(728\) | 0.414344 | 0.0153566 | ||||||||
\(729\) | −20.8003 | −0.770383 | ||||||||
\(730\) | −14.7231 | −0.544927 | ||||||||
\(731\) | −0.591604 | −0.0218813 | ||||||||
\(732\) | −21.1954 | −0.783405 | ||||||||
\(733\) | 3.21274 | 0.118665 | 0.0593325 | − | 0.998238i | \(-0.481103\pi\) | ||||
0.0593325 | + | 0.998238i | \(0.481103\pi\) | |||||||
\(734\) | −11.4287 | −0.421842 | ||||||||
\(735\) | 19.8790 | 0.733248 | ||||||||
\(736\) | 24.3056 | 0.895916 | ||||||||
\(737\) | −54.0683 | −1.99163 | ||||||||
\(738\) | 20.2070 | 0.743831 | ||||||||
\(739\) | −34.8845 | −1.28325 | −0.641623 | − | 0.767020i | \(-0.721738\pi\) | ||||
−0.641623 | + | 0.767020i | \(0.721738\pi\) | |||||||
\(740\) | 20.6819 | 0.760284 | ||||||||
\(741\) | −0.163950 | −0.00602285 | ||||||||
\(742\) | 15.1818 | 0.557343 | ||||||||
\(743\) | 47.5785 | 1.74549 | 0.872743 | − | 0.488181i | \(-0.162339\pi\) | ||||
0.872743 | + | 0.488181i | \(0.162339\pi\) | |||||||
\(744\) | 45.1572 | 1.65554 | ||||||||
\(745\) | 8.42262 | 0.308581 | ||||||||
\(746\) | −35.8482 | −1.31250 | ||||||||
\(747\) | −17.0717 | −0.624619 | ||||||||
\(748\) | 1.97760 | 0.0723083 | ||||||||
\(749\) | −3.61995 | −0.132270 | ||||||||
\(750\) | −26.0880 | −0.952599 | ||||||||
\(751\) | 21.7473 | 0.793569 | 0.396785 | − | 0.917912i | \(-0.370126\pi\) | ||||
0.396785 | + | 0.917912i | \(0.370126\pi\) | |||||||
\(752\) | −2.06477 | −0.0752946 | ||||||||
\(753\) | 21.0985 | 0.768870 | ||||||||
\(754\) | 0.255757 | 0.00931411 | ||||||||
\(755\) | −22.5129 | −0.819329 | ||||||||
\(756\) | 2.58823 | 0.0941330 | ||||||||
\(757\) | 25.0202 | 0.909375 | 0.454687 | − | 0.890651i | \(-0.349751\pi\) | ||||
0.454687 | + | 0.890651i | \(0.349751\pi\) | |||||||
\(758\) | −3.55927 | −0.129278 | ||||||||
\(759\) | −40.0447 | −1.45353 | ||||||||
\(760\) | −11.0296 | −0.400085 | ||||||||
\(761\) | −21.1523 | −0.766769 | −0.383384 | − | 0.923589i | \(-0.625242\pi\) | ||||
−0.383384 | + | 0.923589i | \(0.625242\pi\) | |||||||
\(762\) | −22.8329 | −0.827149 | ||||||||
\(763\) | −38.8350 | −1.40592 | ||||||||
\(764\) | 6.16532 | 0.223054 | ||||||||
\(765\) | 3.38965 | 0.122553 | ||||||||
\(766\) | 20.9222 | 0.755951 | ||||||||
\(767\) | 0.283178 | 0.0102250 | ||||||||
\(768\) | −40.5360 | −1.46272 | ||||||||
\(769\) | −24.5196 | −0.884200 | −0.442100 | − | 0.896966i | \(-0.645766\pi\) | ||||
−0.442100 | + | 0.896966i | \(0.645766\pi\) | |||||||
\(770\) | −25.6821 | −0.925520 | ||||||||
\(771\) | 70.4750 | 2.53810 | ||||||||
\(772\) | 7.59557 | 0.273371 | ||||||||
\(773\) | −0.751017 | −0.0270122 | −0.0135061 | − | 0.999909i | \(-0.504299\pi\) | ||||
−0.0135061 | + | 0.999909i | \(0.504299\pi\) | |||||||
\(774\) | −2.80546 | −0.100840 | ||||||||
\(775\) | −0.861044 | −0.0309296 | ||||||||
\(776\) | −8.19471 | −0.294173 | ||||||||
\(777\) | −70.1637 | −2.51711 | ||||||||
\(778\) | −8.50113 | −0.304780 | ||||||||
\(779\) | 12.3738 | 0.443338 | ||||||||
\(780\) | 0.231390 | 0.00828509 | ||||||||
\(781\) | 14.3404 | 0.513139 | ||||||||
\(782\) | 2.68139 | 0.0958862 | ||||||||
\(783\) | 4.75353 | 0.169877 | ||||||||
\(784\) | −3.49928 | −0.124974 | ||||||||
\(785\) | 49.6285 | 1.77132 | ||||||||
\(786\) | 36.7162 | 1.30962 | ||||||||
\(787\) | −32.7650 | −1.16795 | −0.583973 | − | 0.811773i | \(-0.698503\pi\) | ||||
−0.583973 | + | 0.811773i | \(0.698503\pi\) | |||||||
\(788\) | −8.34917 | −0.297427 | ||||||||
\(789\) | 31.3952 | 1.11770 | ||||||||
\(790\) | −28.6052 | −1.01773 | ||||||||
\(791\) | −27.0555 | −0.961982 | ||||||||
\(792\) | 27.9034 | 0.991506 | ||||||||
\(793\) | −0.372243 | −0.0132187 | ||||||||
\(794\) | 20.3126 | 0.720868 | ||||||||
\(795\) | 25.2264 | 0.894687 | ||||||||
\(796\) | −8.61511 | −0.305355 | ||||||||
\(797\) | −18.9303 | −0.670547 | −0.335274 | − | 0.942121i | \(-0.608829\pi\) | ||||
−0.335274 | + | 0.942121i | \(0.608829\pi\) | |||||||
\(798\) | 12.5757 | 0.445177 | ||||||||
\(799\) | 1.21675 | 0.0430456 | ||||||||
\(800\) | 0.685571 | 0.0242386 | ||||||||
\(801\) | 27.9978 | 0.989252 | ||||||||
\(802\) | −16.9954 | −0.600128 | ||||||||
\(803\) | 22.8086 | 0.804899 | ||||||||
\(804\) | −37.3662 | −1.31780 | ||||||||
\(805\) | 35.6998 | 1.25825 | ||||||||
\(806\) | 0.266541 | 0.00938852 | ||||||||
\(807\) | 14.6827 | 0.516854 | ||||||||
\(808\) | 7.60083 | 0.267396 | ||||||||
\(809\) | −34.3026 | −1.20601 | −0.603007 | − | 0.797736i | \(-0.706031\pi\) | ||||
−0.603007 | + | 0.797736i | \(0.706031\pi\) | |||||||
\(810\) | −22.2450 | −0.781609 | ||||||||
\(811\) | −38.1606 | −1.34000 | −0.669999 | − | 0.742362i | \(-0.733706\pi\) | ||||
−0.669999 | + | 0.742362i | \(0.733706\pi\) | |||||||
\(812\) | 20.1123 | 0.705805 | ||||||||
\(813\) | −17.6903 | −0.620425 | ||||||||
\(814\) | 31.2520 | 1.09538 | ||||||||
\(815\) | 37.4496 | 1.31180 | ||||||||
\(816\) | −1.26670 | −0.0443435 | ||||||||
\(817\) | −1.71793 | −0.0601027 | ||||||||
\(818\) | 8.23197 | 0.287824 | ||||||||
\(819\) | −0.369768 | −0.0129208 | ||||||||
\(820\) | −17.4637 | −0.609860 | ||||||||
\(821\) | −36.9014 | −1.28787 | −0.643935 | − | 0.765081i | \(-0.722699\pi\) | ||||
−0.643935 | + | 0.765081i | \(0.722699\pi\) | |||||||
\(822\) | 1.72479 | 0.0601589 | ||||||||
\(823\) | −2.42438 | −0.0845085 | −0.0422543 | − | 0.999107i | \(-0.513454\pi\) | ||||
−0.0422543 | + | 0.999107i | \(0.513454\pi\) | |||||||
\(824\) | −14.1586 | −0.493238 | ||||||||
\(825\) | −1.12951 | −0.0393246 | ||||||||
\(826\) | −21.7211 | −0.755775 | ||||||||
\(827\) | 2.08456 | 0.0724874 | 0.0362437 | − | 0.999343i | \(-0.488461\pi\) | ||||
0.0362437 | + | 0.999343i | \(0.488461\pi\) | |||||||
\(828\) | −13.0360 | −0.453033 | ||||||||
\(829\) | −46.0254 | −1.59853 | −0.799264 | − | 0.600980i | \(-0.794777\pi\) | ||||
−0.799264 | + | 0.600980i | \(0.794777\pi\) | |||||||
\(830\) | −14.3912 | −0.499526 | ||||||||
\(831\) | 67.7109 | 2.34886 | ||||||||
\(832\) | −0.292684 | −0.0101470 | ||||||||
\(833\) | 2.06209 | 0.0714474 | ||||||||
\(834\) | −29.4414 | −1.01947 | ||||||||
\(835\) | 41.7819 | 1.44592 | ||||||||
\(836\) | 5.74265 | 0.198614 | ||||||||
\(837\) | 4.95397 | 0.171234 | ||||||||
\(838\) | −23.8406 | −0.823560 | ||||||||
\(839\) | −8.54263 | −0.294924 | −0.147462 | − | 0.989068i | \(-0.547110\pi\) | ||||
−0.147462 | + | 0.989068i | \(0.547110\pi\) | |||||||
\(840\) | −52.8097 | −1.82211 | ||||||||
\(841\) | 7.93822 | 0.273732 | ||||||||
\(842\) | −13.7339 | −0.473302 | ||||||||
\(843\) | −4.59919 | −0.158405 | ||||||||
\(844\) | 5.98430 | 0.205988 | ||||||||
\(845\) | −29.4573 | −1.01336 | ||||||||
\(846\) | 5.76998 | 0.198376 | ||||||||
\(847\) | 3.83229 | 0.131679 | ||||||||
\(848\) | −4.44058 | −0.152490 | ||||||||
\(849\) | −10.4719 | −0.359395 | ||||||||
\(850\) | 0.0756321 | 0.00259416 | ||||||||
\(851\) | −43.4422 | −1.48918 | ||||||||
\(852\) | 9.91052 | 0.339529 | ||||||||
\(853\) | −24.5758 | −0.841461 | −0.420730 | − | 0.907186i | \(-0.638226\pi\) | ||||
−0.420730 | + | 0.907186i | \(0.638226\pi\) | |||||||
\(854\) | 28.5528 | 0.977056 | ||||||||
\(855\) | 9.84302 | 0.336624 | ||||||||
\(856\) | 3.31550 | 0.113322 | ||||||||
\(857\) | 49.6423 | 1.69575 | 0.847874 | − | 0.530198i | \(-0.177882\pi\) | ||||
0.847874 | + | 0.530198i | \(0.177882\pi\) | |||||||
\(858\) | 0.349648 | 0.0119368 | ||||||||
\(859\) | −30.2314 | −1.03148 | −0.515740 | − | 0.856745i | \(-0.672483\pi\) | ||||
−0.515740 | + | 0.856745i | \(0.672483\pi\) | |||||||
\(860\) | 2.42459 | 0.0826777 | ||||||||
\(861\) | 59.2459 | 2.01909 | ||||||||
\(862\) | 19.0064 | 0.647360 | ||||||||
\(863\) | −27.9588 | −0.951728 | −0.475864 | − | 0.879519i | \(-0.657865\pi\) | ||||
−0.475864 | + | 0.879519i | \(0.657865\pi\) | |||||||
\(864\) | −3.94440 | −0.134191 | ||||||||
\(865\) | 10.4864 | 0.356549 | ||||||||
\(866\) | −16.2156 | −0.551027 | ||||||||
\(867\) | −39.7392 | −1.34961 | ||||||||
\(868\) | 20.9604 | 0.711444 | ||||||||
\(869\) | 44.3144 | 1.50326 | ||||||||
\(870\) | −32.5972 | −1.10515 | ||||||||
\(871\) | −0.656240 | −0.0222358 | ||||||||
\(872\) | 35.5690 | 1.20452 | ||||||||
\(873\) | 7.31312 | 0.247512 | ||||||||
\(874\) | 7.78633 | 0.263377 | ||||||||
\(875\) | −36.0297 | −1.21803 | ||||||||
\(876\) | 15.7629 | 0.532577 | ||||||||
\(877\) | −8.94803 | −0.302153 | −0.151077 | − | 0.988522i | \(-0.548274\pi\) | ||||
−0.151077 | + | 0.988522i | \(0.548274\pi\) | |||||||
\(878\) | 29.3218 | 0.989564 | ||||||||
\(879\) | 67.7815 | 2.28621 | ||||||||
\(880\) | 7.51184 | 0.253224 | ||||||||
\(881\) | 52.7351 | 1.77669 | 0.888345 | − | 0.459176i | \(-0.151855\pi\) | ||||
0.888345 | + | 0.459176i | \(0.151855\pi\) | |||||||
\(882\) | 9.77869 | 0.329266 | ||||||||
\(883\) | −12.0557 | −0.405707 | −0.202854 | − | 0.979209i | \(-0.565022\pi\) | ||||
−0.202854 | + | 0.979209i | \(0.565022\pi\) | |||||||
\(884\) | 0.0240026 | 0.000807295 0 | ||||||||
\(885\) | −36.0922 | −1.21322 | ||||||||
\(886\) | 7.89588 | 0.265267 | ||||||||
\(887\) | 13.3652 | 0.448760 | 0.224380 | − | 0.974502i | \(-0.427964\pi\) | ||||
0.224380 | + | 0.974502i | \(0.427964\pi\) | |||||||
\(888\) | 64.2629 | 2.15652 | ||||||||
\(889\) | −31.5341 | −1.05762 | ||||||||
\(890\) | 23.6018 | 0.791133 | ||||||||
\(891\) | 34.4613 | 1.15450 | ||||||||
\(892\) | 10.3500 | 0.346544 | ||||||||
\(893\) | 3.53326 | 0.118236 | ||||||||
\(894\) | 8.79567 | 0.294171 | ||||||||
\(895\) | 18.9154 | 0.632271 | ||||||||
\(896\) | −10.5171 | −0.351353 | ||||||||
\(897\) | −0.486032 | −0.0162281 | ||||||||
\(898\) | −37.0628 | −1.23680 | ||||||||
\(899\) | 38.4958 | 1.28391 | ||||||||
\(900\) | −0.367698 | −0.0122566 | ||||||||
\(901\) | 2.61679 | 0.0871779 | ||||||||
\(902\) | −26.3890 | −0.878659 | ||||||||
\(903\) | −8.22544 | −0.273725 | ||||||||
\(904\) | 24.7801 | 0.824174 | ||||||||
\(905\) | 30.3618 | 1.00926 | ||||||||
\(906\) | −23.5101 | −0.781070 | ||||||||
\(907\) | −17.4678 | −0.580007 | −0.290004 | − | 0.957026i | \(-0.593657\pi\) | ||||
−0.290004 | + | 0.957026i | \(0.593657\pi\) | |||||||
\(908\) | −26.1014 | −0.866205 | ||||||||
\(909\) | −6.78313 | −0.224982 | ||||||||
\(910\) | −0.311710 | −0.0103331 | ||||||||
\(911\) | 47.8184 | 1.58429 | 0.792147 | − | 0.610331i | \(-0.208964\pi\) | ||||
0.792147 | + | 0.610331i | \(0.208964\pi\) | |||||||
\(912\) | −3.67831 | −0.121801 | ||||||||
\(913\) | 22.2944 | 0.737838 | ||||||||
\(914\) | 16.9317 | 0.560050 | ||||||||
\(915\) | 47.4437 | 1.56844 | ||||||||
\(916\) | −3.66711 | −0.121165 | ||||||||
\(917\) | 50.7081 | 1.67453 | ||||||||
\(918\) | −0.435145 | −0.0143619 | ||||||||
\(919\) | 0.0733749 | 0.00242041 | 0.00121021 | − | 0.999999i | \(-0.499615\pi\) | ||||
0.00121021 | + | 0.999999i | \(0.499615\pi\) | |||||||
\(920\) | −32.6974 | −1.07800 | ||||||||
\(921\) | 75.5161 | 2.48834 | ||||||||
\(922\) | 36.7469 | 1.21019 | ||||||||
\(923\) | 0.174053 | 0.00572901 | ||||||||
\(924\) | 27.4958 | 0.904546 | ||||||||
\(925\) | −1.22534 | −0.0402891 | ||||||||
\(926\) | −41.7543 | −1.37213 | ||||||||
\(927\) | 12.6354 | 0.415001 | ||||||||
\(928\) | −30.6507 | −1.00616 | ||||||||
\(929\) | 37.0409 | 1.21527 | 0.607636 | − | 0.794216i | \(-0.292118\pi\) | ||||
0.607636 | + | 0.794216i | \(0.292118\pi\) | |||||||
\(930\) | −33.9717 | −1.11398 | ||||||||
\(931\) | 5.98801 | 0.196249 | ||||||||
\(932\) | 8.12258 | 0.266064 | ||||||||
\(933\) | −41.7778 | −1.36774 | ||||||||
\(934\) | −11.5756 | −0.378766 | ||||||||
\(935\) | −4.42666 | −0.144767 | ||||||||
\(936\) | 0.338671 | 0.0110698 | ||||||||
\(937\) | 37.6030 | 1.22844 | 0.614219 | − | 0.789136i | \(-0.289471\pi\) | ||||
0.614219 | + | 0.789136i | \(0.289471\pi\) | |||||||
\(938\) | 50.3368 | 1.64355 | ||||||||
\(939\) | 57.3159 | 1.87043 | ||||||||
\(940\) | −4.98665 | −0.162646 | ||||||||
\(941\) | 37.0302 | 1.20715 | 0.603576 | − | 0.797306i | \(-0.293742\pi\) | ||||
0.603576 | + | 0.797306i | \(0.293742\pi\) | |||||||
\(942\) | 51.8266 | 1.68860 | ||||||||
\(943\) | 36.6824 | 1.19454 | ||||||||
\(944\) | 6.35327 | 0.206781 | ||||||||
\(945\) | −5.79348 | −0.188462 | ||||||||
\(946\) | 3.66374 | 0.119118 | ||||||||
\(947\) | 4.21444 | 0.136951 | 0.0684754 | − | 0.997653i | \(-0.478187\pi\) | ||||
0.0684754 | + | 0.997653i | \(0.478187\pi\) | |||||||
\(948\) | 30.6253 | 0.994665 | ||||||||
\(949\) | 0.276834 | 0.00898640 | ||||||||
\(950\) | 0.219624 | 0.00712554 | ||||||||
\(951\) | 72.2213 | 2.34194 | ||||||||
\(952\) | −5.47807 | −0.177545 | ||||||||
\(953\) | 27.4562 | 0.889392 | 0.444696 | − | 0.895682i | \(-0.353312\pi\) | ||||
0.444696 | + | 0.895682i | \(0.353312\pi\) | |||||||
\(954\) | 12.4091 | 0.401760 | ||||||||
\(955\) | −13.8004 | −0.446572 | ||||||||
\(956\) | 17.6066 | 0.569440 | ||||||||
\(957\) | 50.4986 | 1.63239 | ||||||||
\(958\) | −11.1644 | −0.360705 | ||||||||
\(959\) | 2.38208 | 0.0769213 | ||||||||
\(960\) | 37.3037 | 1.20397 | ||||||||
\(961\) | 9.11911 | 0.294165 | ||||||||
\(962\) | 0.379313 | 0.0122295 | ||||||||
\(963\) | −2.95882 | −0.0953467 | ||||||||
\(964\) | −10.3417 | −0.333082 | ||||||||
\(965\) | −17.0019 | −0.547311 | ||||||||
\(966\) | 37.2810 | 1.19950 | ||||||||
\(967\) | −17.0797 | −0.549246 | −0.274623 | − | 0.961552i | \(-0.588553\pi\) | ||||
−0.274623 | + | 0.961552i | \(0.588553\pi\) | |||||||
\(968\) | −3.50999 | −0.112815 | ||||||||
\(969\) | 2.16760 | 0.0696332 | ||||||||
\(970\) | 6.16487 | 0.197942 | ||||||||
\(971\) | −18.9414 | −0.607859 | −0.303929 | − | 0.952695i | \(-0.598299\pi\) | ||||
−0.303929 | + | 0.952695i | \(0.598299\pi\) | |||||||
\(972\) | 21.4403 | 0.687699 | ||||||||
\(973\) | −40.6611 | −1.30353 | ||||||||
\(974\) | −12.7153 | −0.407425 | ||||||||
\(975\) | −0.0137092 | −0.000439045 0 | ||||||||
\(976\) | −8.35148 | −0.267324 | ||||||||
\(977\) | −52.5608 | −1.68157 | −0.840785 | − | 0.541369i | \(-0.817906\pi\) | ||||
−0.840785 | + | 0.541369i | \(0.817906\pi\) | |||||||
\(978\) | 39.1083 | 1.25055 | ||||||||
\(979\) | −36.5632 | −1.16856 | ||||||||
\(980\) | −8.45114 | −0.269962 | ||||||||
\(981\) | −31.7425 | −1.01346 | ||||||||
\(982\) | −25.7091 | −0.820411 | ||||||||
\(983\) | −47.3712 | −1.51091 | −0.755453 | − | 0.655203i | \(-0.772583\pi\) | ||||
−0.755453 | + | 0.655203i | \(0.772583\pi\) | |||||||
\(984\) | −54.2632 | −1.72985 | ||||||||
\(985\) | 18.6887 | 0.595473 | ||||||||
\(986\) | −3.38138 | −0.107685 | ||||||||
\(987\) | 16.9172 | 0.538482 | ||||||||
\(988\) | 0.0696999 | 0.00221745 | ||||||||
\(989\) | −5.09282 | −0.161942 | ||||||||
\(990\) | −20.9917 | −0.667161 | ||||||||
\(991\) | −31.7535 | −1.00868 | −0.504342 | − | 0.863504i | \(-0.668265\pi\) | ||||
−0.504342 | + | 0.863504i | \(0.668265\pi\) | |||||||
\(992\) | −31.9432 | −1.01420 | ||||||||
\(993\) | −33.6129 | −1.06667 | ||||||||
\(994\) | −13.3507 | −0.423457 | ||||||||
\(995\) | 19.2840 | 0.611345 | ||||||||
\(996\) | 15.4075 | 0.488205 | ||||||||
\(997\) | −44.9981 | −1.42510 | −0.712552 | − | 0.701619i | \(-0.752461\pi\) | ||||
−0.712552 | + | 0.701619i | \(0.752461\pi\) | |||||||
\(998\) | −39.7403 | −1.25796 | ||||||||
\(999\) | 7.04996 | 0.223051 |
(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 | 619.2.a.b.1.18 | ✓ | 30 | |
3.2 | odd | 2 | 5571.2.a.g.1.13 | 30 | |||
4.3 | odd | 2 | 9904.2.a.n.1.6 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
619.2.a.b.1.18 | ✓ | 30 | 1.1 | even | 1 | trivial | |
5571.2.a.g.1.13 | 30 | 3.2 | odd | 2 | |||
9904.2.a.n.1.6 | 30 | 4.3 | odd | 2 |