Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.66399 | −1.17662 | −0.588311 | − | 0.808635i | \(-0.700207\pi\) | ||||
−0.588311 | + | 0.808635i | \(0.700207\pi\) | |||||||
\(3\) | 1.84747 | 1.06664 | 0.533318 | − | 0.845915i | \(-0.320945\pi\) | ||||
0.533318 | + | 0.845915i | \(0.320945\pi\) | |||||||
\(4\) | 0.768874 | 0.384437 | ||||||||
\(5\) | 1.24336 | 0.556046 | 0.278023 | − | 0.960574i | \(-0.410321\pi\) | ||||
0.278023 | + | 0.960574i | \(0.410321\pi\) | |||||||
\(6\) | −3.07417 | −1.25503 | ||||||||
\(7\) | 0.0311850 | 0.0117868 | 0.00589340 | − | 0.999983i | \(-0.498124\pi\) | ||||
0.00589340 | + | 0.999983i | \(0.498124\pi\) | |||||||
\(8\) | 2.04859 | 0.724284 | ||||||||
\(9\) | 0.413132 | 0.137711 | ||||||||
\(10\) | −2.06894 | −0.654256 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.42047 | 0.410054 | ||||||||
\(13\) | 3.49994 | 0.970709 | 0.485355 | − | 0.874317i | \(-0.338691\pi\) | ||||
0.485355 | + | 0.874317i | \(0.338691\pi\) | |||||||
\(14\) | −0.0518916 | −0.0138686 | ||||||||
\(15\) | 2.29706 | 0.593099 | ||||||||
\(16\) | −4.94658 | −1.23665 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −0.687449 | −0.162033 | ||||||||
\(19\) | −5.25992 | −1.20671 | −0.603354 | − | 0.797473i | \(-0.706170\pi\) | ||||
−0.603354 | + | 0.797473i | \(0.706170\pi\) | |||||||
\(20\) | 0.955986 | 0.213765 | ||||||||
\(21\) | 0.0576132 | 0.0125722 | ||||||||
\(22\) | 1.66399 | 0.354765 | ||||||||
\(23\) | −4.42189 | −0.922027 | −0.461013 | − | 0.887393i | \(-0.652514\pi\) | ||||
−0.461013 | + | 0.887393i | \(0.652514\pi\) | |||||||
\(24\) | 3.78469 | 0.772547 | ||||||||
\(25\) | −3.45406 | −0.690812 | ||||||||
\(26\) | −5.82388 | −1.14216 | ||||||||
\(27\) | −4.77915 | −0.919748 | ||||||||
\(28\) | 0.0239773 | 0.00453129 | ||||||||
\(29\) | −2.78056 | −0.516336 | −0.258168 | − | 0.966100i | \(-0.583119\pi\) | ||||
−0.258168 | + | 0.966100i | \(0.583119\pi\) | |||||||
\(30\) | −3.82229 | −0.697852 | ||||||||
\(31\) | −0.289166 | −0.0519358 | −0.0259679 | − | 0.999663i | \(-0.508267\pi\) | ||||
−0.0259679 | + | 0.999663i | \(0.508267\pi\) | |||||||
\(32\) | 4.13391 | 0.730779 | ||||||||
\(33\) | −1.84747 | −0.321603 | ||||||||
\(34\) | −1.66399 | −0.285373 | ||||||||
\(35\) | 0.0387741 | 0.00655401 | ||||||||
\(36\) | 0.317647 | 0.0529411 | ||||||||
\(37\) | 10.1101 | 1.66210 | 0.831049 | − | 0.556199i | \(-0.187741\pi\) | ||||
0.831049 | + | 0.556199i | \(0.187741\pi\) | |||||||
\(38\) | 8.75248 | 1.41984 | ||||||||
\(39\) | 6.46602 | 1.03539 | ||||||||
\(40\) | 2.54712 | 0.402736 | ||||||||
\(41\) | 4.09151 | 0.638987 | 0.319494 | − | 0.947588i | \(-0.396487\pi\) | ||||
0.319494 | + | 0.947588i | \(0.396487\pi\) | |||||||
\(42\) | −0.0958679 | −0.0147927 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −0.768874 | −0.115912 | ||||||||
\(45\) | 0.513671 | 0.0765735 | ||||||||
\(46\) | 7.35799 | 1.08488 | ||||||||
\(47\) | 13.1048 | 1.91154 | 0.955769 | − | 0.294118i | \(-0.0950257\pi\) | ||||
0.955769 | + | 0.294118i | \(0.0950257\pi\) | |||||||
\(48\) | −9.13864 | −1.31905 | ||||||||
\(49\) | −6.99903 | −0.999861 | ||||||||
\(50\) | 5.74754 | 0.812824 | ||||||||
\(51\) | 1.84747 | 0.258697 | ||||||||
\(52\) | 2.69102 | 0.373177 | ||||||||
\(53\) | −5.95331 | −0.817750 | −0.408875 | − | 0.912590i | \(-0.634079\pi\) | ||||
−0.408875 | + | 0.912590i | \(0.634079\pi\) | |||||||
\(54\) | 7.95248 | 1.08220 | ||||||||
\(55\) | −1.24336 | −0.167654 | ||||||||
\(56\) | 0.0638850 | 0.00853700 | ||||||||
\(57\) | −9.71753 | −1.28712 | ||||||||
\(58\) | 4.62683 | 0.607532 | ||||||||
\(59\) | 10.5664 | 1.37563 | 0.687815 | − | 0.725886i | \(-0.258570\pi\) | ||||
0.687815 | + | 0.725886i | \(0.258570\pi\) | |||||||
\(60\) | 1.76615 | 0.228009 | ||||||||
\(61\) | −5.77116 | −0.738921 | −0.369460 | − | 0.929246i | \(-0.620457\pi\) | ||||
−0.369460 | + | 0.929246i | \(0.620457\pi\) | |||||||
\(62\) | 0.481170 | 0.0611087 | ||||||||
\(63\) | 0.0128835 | 0.00162317 | ||||||||
\(64\) | 3.01437 | 0.376796 | ||||||||
\(65\) | 4.35168 | 0.539759 | ||||||||
\(66\) | 3.07417 | 0.378404 | ||||||||
\(67\) | −13.2819 | −1.62264 | −0.811319 | − | 0.584604i | \(-0.801250\pi\) | ||||
−0.811319 | + | 0.584604i | \(0.801250\pi\) | |||||||
\(68\) | 0.768874 | 0.0932397 | ||||||||
\(69\) | −8.16928 | −0.983466 | ||||||||
\(70\) | −0.0645198 | −0.00771159 | ||||||||
\(71\) | −0.811957 | −0.0963616 | −0.0481808 | − | 0.998839i | \(-0.515342\pi\) | ||||
−0.0481808 | + | 0.998839i | \(0.515342\pi\) | |||||||
\(72\) | 0.846336 | 0.0997416 | ||||||||
\(73\) | −7.66046 | −0.896589 | −0.448295 | − | 0.893886i | \(-0.647968\pi\) | ||||
−0.448295 | + | 0.893886i | \(0.647968\pi\) | |||||||
\(74\) | −16.8232 | −1.95566 | ||||||||
\(75\) | −6.38126 | −0.736845 | ||||||||
\(76\) | −4.04422 | −0.463904 | ||||||||
\(77\) | −0.0311850 | −0.00355386 | ||||||||
\(78\) | −10.7594 | −1.21826 | ||||||||
\(79\) | 3.36894 | 0.379036 | 0.189518 | − | 0.981877i | \(-0.439308\pi\) | ||||
0.189518 | + | 0.981877i | \(0.439308\pi\) | |||||||
\(80\) | −6.15037 | −0.687632 | ||||||||
\(81\) | −10.0687 | −1.11875 | ||||||||
\(82\) | −6.80825 | −0.751846 | ||||||||
\(83\) | −0.511288 | −0.0561212 | −0.0280606 | − | 0.999606i | \(-0.508933\pi\) | ||||
−0.0280606 | + | 0.999606i | \(0.508933\pi\) | |||||||
\(84\) | 0.0442973 | 0.00483323 | ||||||||
\(85\) | 1.24336 | 0.134861 | ||||||||
\(86\) | −1.66399 | −0.179433 | ||||||||
\(87\) | −5.13699 | −0.550743 | ||||||||
\(88\) | −2.04859 | −0.218380 | ||||||||
\(89\) | −13.7370 | −1.45612 | −0.728061 | − | 0.685513i | \(-0.759578\pi\) | ||||
−0.728061 | + | 0.685513i | \(0.759578\pi\) | |||||||
\(90\) | −0.854745 | −0.0900980 | ||||||||
\(91\) | 0.109146 | 0.0114416 | ||||||||
\(92\) | −3.39987 | −0.354461 | ||||||||
\(93\) | −0.534225 | −0.0553965 | ||||||||
\(94\) | −21.8064 | −2.24916 | ||||||||
\(95\) | −6.53996 | −0.670986 | ||||||||
\(96\) | 7.63726 | 0.779474 | ||||||||
\(97\) | −9.63387 | −0.978171 | −0.489085 | − | 0.872236i | \(-0.662669\pi\) | ||||
−0.489085 | + | 0.872236i | \(0.662669\pi\) | |||||||
\(98\) | 11.6463 | 1.17646 | ||||||||
\(99\) | −0.413132 | −0.0415213 | ||||||||
\(100\) | −2.65574 | −0.265574 | ||||||||
\(101\) | −17.1787 | −1.70935 | −0.854674 | − | 0.519166i | \(-0.826243\pi\) | ||||
−0.854674 | + | 0.519166i | \(0.826243\pi\) | |||||||
\(102\) | −3.07417 | −0.304388 | ||||||||
\(103\) | 0.863988 | 0.0851313 | 0.0425656 | − | 0.999094i | \(-0.486447\pi\) | ||||
0.0425656 | + | 0.999094i | \(0.486447\pi\) | |||||||
\(104\) | 7.16993 | 0.703069 | ||||||||
\(105\) | 0.0716338 | 0.00699074 | ||||||||
\(106\) | 9.90626 | 0.962181 | ||||||||
\(107\) | −11.5026 | −1.11199 | −0.555997 | − | 0.831184i | \(-0.687663\pi\) | ||||
−0.555997 | + | 0.831184i | \(0.687663\pi\) | |||||||
\(108\) | −3.67457 | −0.353585 | ||||||||
\(109\) | 3.39601 | 0.325279 | 0.162640 | − | 0.986686i | \(-0.447999\pi\) | ||||
0.162640 | + | 0.986686i | \(0.447999\pi\) | |||||||
\(110\) | 2.06894 | 0.197266 | ||||||||
\(111\) | 18.6782 | 1.77285 | ||||||||
\(112\) | −0.154259 | −0.0145761 | ||||||||
\(113\) | 3.92016 | 0.368777 | 0.184389 | − | 0.982853i | \(-0.440970\pi\) | ||||
0.184389 | + | 0.982853i | \(0.440970\pi\) | |||||||
\(114\) | 16.1699 | 1.51445 | ||||||||
\(115\) | −5.49798 | −0.512690 | ||||||||
\(116\) | −2.13790 | −0.198499 | ||||||||
\(117\) | 1.44594 | 0.133677 | ||||||||
\(118\) | −17.5825 | −1.61860 | ||||||||
\(119\) | 0.0311850 | 0.00285872 | ||||||||
\(120\) | 4.70573 | 0.429572 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 9.60317 | 0.869430 | ||||||||
\(123\) | 7.55893 | 0.681566 | ||||||||
\(124\) | −0.222332 | −0.0199660 | ||||||||
\(125\) | −10.5114 | −0.940170 | ||||||||
\(126\) | −0.0214381 | −0.00190985 | ||||||||
\(127\) | 8.57189 | 0.760632 | 0.380316 | − | 0.924857i | \(-0.375815\pi\) | ||||
0.380316 | + | 0.924857i | \(0.375815\pi\) | |||||||
\(128\) | −13.2837 | −1.17412 | ||||||||
\(129\) | 1.84747 | 0.162660 | ||||||||
\(130\) | −7.24117 | −0.635092 | ||||||||
\(131\) | −0.973771 | −0.0850788 | −0.0425394 | − | 0.999095i | \(-0.513545\pi\) | ||||
−0.0425394 | + | 0.999095i | \(0.513545\pi\) | |||||||
\(132\) | −1.42047 | −0.123636 | ||||||||
\(133\) | −0.164030 | −0.0142232 | ||||||||
\(134\) | 22.1009 | 1.90923 | ||||||||
\(135\) | −5.94219 | −0.511423 | ||||||||
\(136\) | 2.04859 | 0.175665 | ||||||||
\(137\) | −2.45605 | −0.209834 | −0.104917 | − | 0.994481i | \(-0.533458\pi\) | ||||
−0.104917 | + | 0.994481i | \(0.533458\pi\) | |||||||
\(138\) | 13.5936 | 1.15717 | ||||||||
\(139\) | −3.68775 | −0.312791 | −0.156395 | − | 0.987695i | \(-0.549987\pi\) | ||||
−0.156395 | + | 0.987695i | \(0.549987\pi\) | |||||||
\(140\) | 0.0298124 | 0.00251961 | ||||||||
\(141\) | 24.2108 | 2.03891 | ||||||||
\(142\) | 1.35109 | 0.113381 | ||||||||
\(143\) | −3.49994 | −0.292680 | ||||||||
\(144\) | −2.04359 | −0.170299 | ||||||||
\(145\) | −3.45723 | −0.287107 | ||||||||
\(146\) | 12.7470 | 1.05495 | ||||||||
\(147\) | −12.9305 | −1.06649 | ||||||||
\(148\) | 7.77343 | 0.638972 | ||||||||
\(149\) | −9.05753 | −0.742022 | −0.371011 | − | 0.928628i | \(-0.620989\pi\) | ||||
−0.371011 | + | 0.928628i | \(0.620989\pi\) | |||||||
\(150\) | 10.6184 | 0.866987 | ||||||||
\(151\) | 2.13425 | 0.173682 | 0.0868412 | − | 0.996222i | \(-0.472323\pi\) | ||||
0.0868412 | + | 0.996222i | \(0.472323\pi\) | |||||||
\(152\) | −10.7754 | −0.874000 | ||||||||
\(153\) | 0.413132 | 0.0333997 | ||||||||
\(154\) | 0.0518916 | 0.00418154 | ||||||||
\(155\) | −0.359537 | −0.0288787 | ||||||||
\(156\) | 4.97156 | 0.398043 | ||||||||
\(157\) | 4.54706 | 0.362895 | 0.181448 | − | 0.983401i | \(-0.441922\pi\) | ||||
0.181448 | + | 0.983401i | \(0.441922\pi\) | |||||||
\(158\) | −5.60590 | −0.445981 | ||||||||
\(159\) | −10.9985 | −0.872241 | ||||||||
\(160\) | 5.13993 | 0.406347 | ||||||||
\(161\) | −0.137896 | −0.0108678 | ||||||||
\(162\) | 16.7543 | 1.31634 | ||||||||
\(163\) | 23.2936 | 1.82449 | 0.912246 | − | 0.409642i | \(-0.134346\pi\) | ||||
0.912246 | + | 0.409642i | \(0.134346\pi\) | |||||||
\(164\) | 3.14586 | 0.245650 | ||||||||
\(165\) | −2.29706 | −0.178826 | ||||||||
\(166\) | 0.850780 | 0.0660334 | ||||||||
\(167\) | 6.92118 | 0.535577 | 0.267789 | − | 0.963478i | \(-0.413707\pi\) | ||||
0.267789 | + | 0.963478i | \(0.413707\pi\) | |||||||
\(168\) | 0.118025 | 0.00910586 | ||||||||
\(169\) | −0.750407 | −0.0577236 | ||||||||
\(170\) | −2.06894 | −0.158680 | ||||||||
\(171\) | −2.17304 | −0.166177 | ||||||||
\(172\) | 0.768874 | 0.0586261 | ||||||||
\(173\) | 5.14447 | 0.391127 | 0.195563 | − | 0.980691i | \(-0.437346\pi\) | ||||
0.195563 | + | 0.980691i | \(0.437346\pi\) | |||||||
\(174\) | 8.54791 | 0.648015 | ||||||||
\(175\) | −0.107715 | −0.00814247 | ||||||||
\(176\) | 4.94658 | 0.372863 | ||||||||
\(177\) | 19.5211 | 1.46730 | ||||||||
\(178\) | 22.8583 | 1.71330 | ||||||||
\(179\) | 6.24711 | 0.466931 | 0.233466 | − | 0.972365i | \(-0.424993\pi\) | ||||
0.233466 | + | 0.972365i | \(0.424993\pi\) | |||||||
\(180\) | 0.394948 | 0.0294377 | ||||||||
\(181\) | 3.60300 | 0.267809 | 0.133904 | − | 0.990994i | \(-0.457248\pi\) | ||||
0.133904 | + | 0.990994i | \(0.457248\pi\) | |||||||
\(182\) | −0.181617 | −0.0134624 | ||||||||
\(183\) | −10.6620 | −0.788159 | ||||||||
\(184\) | −9.05861 | −0.667810 | ||||||||
\(185\) | 12.5705 | 0.924204 | ||||||||
\(186\) | 0.888946 | 0.0651807 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | 10.0760 | 0.734866 | ||||||||
\(189\) | −0.149038 | −0.0108409 | ||||||||
\(190\) | 10.8825 | 0.789496 | ||||||||
\(191\) | −11.2755 | −0.815868 | −0.407934 | − | 0.913011i | \(-0.633751\pi\) | ||||
−0.407934 | + | 0.913011i | \(0.633751\pi\) | |||||||
\(192\) | 5.56894 | 0.401904 | ||||||||
\(193\) | −24.7900 | −1.78443 | −0.892213 | − | 0.451615i | \(-0.850848\pi\) | ||||
−0.892213 | + | 0.451615i | \(0.850848\pi\) | |||||||
\(194\) | 16.0307 | 1.15094 | ||||||||
\(195\) | 8.03958 | 0.575726 | ||||||||
\(196\) | −5.38137 | −0.384384 | ||||||||
\(197\) | −14.5191 | −1.03444 | −0.517222 | − | 0.855851i | \(-0.673034\pi\) | ||||
−0.517222 | + | 0.855851i | \(0.673034\pi\) | |||||||
\(198\) | 0.687449 | 0.0488549 | ||||||||
\(199\) | −12.3326 | −0.874234 | −0.437117 | − | 0.899405i | \(-0.644001\pi\) | ||||
−0.437117 | + | 0.899405i | \(0.644001\pi\) | |||||||
\(200\) | −7.07594 | −0.500345 | ||||||||
\(201\) | −24.5378 | −1.73076 | ||||||||
\(202\) | 28.5853 | 2.01125 | ||||||||
\(203\) | −0.0867116 | −0.00608596 | ||||||||
\(204\) | 1.42047 | 0.0994528 | ||||||||
\(205\) | 5.08721 | 0.355306 | ||||||||
\(206\) | −1.43767 | −0.100167 | ||||||||
\(207\) | −1.82682 | −0.126973 | ||||||||
\(208\) | −17.3127 | −1.20042 | ||||||||
\(209\) | 5.25992 | 0.363836 | ||||||||
\(210\) | −0.119198 | −0.00822545 | ||||||||
\(211\) | −26.1271 | −1.79866 | −0.899331 | − | 0.437269i | \(-0.855946\pi\) | ||||
−0.899331 | + | 0.437269i | \(0.855946\pi\) | |||||||
\(212\) | −4.57735 | −0.314373 | ||||||||
\(213\) | −1.50006 | −0.102783 | ||||||||
\(214\) | 19.1402 | 1.30840 | ||||||||
\(215\) | 1.24336 | 0.0847963 | ||||||||
\(216\) | −9.79050 | −0.666159 | ||||||||
\(217\) | −0.00901763 | −0.000612157 0 | ||||||||
\(218\) | −5.65094 | −0.382730 | ||||||||
\(219\) | −14.1524 | −0.956333 | ||||||||
\(220\) | −0.955986 | −0.0644525 | ||||||||
\(221\) | 3.49994 | 0.235432 | ||||||||
\(222\) | −31.0803 | −2.08598 | ||||||||
\(223\) | −12.1955 | −0.816672 | −0.408336 | − | 0.912832i | \(-0.633891\pi\) | ||||
−0.408336 | + | 0.912832i | \(0.633891\pi\) | |||||||
\(224\) | 0.128916 | 0.00861355 | ||||||||
\(225\) | −1.42698 | −0.0951322 | ||||||||
\(226\) | −6.52311 | −0.433911 | ||||||||
\(227\) | −13.0764 | −0.867910 | −0.433955 | − | 0.900935i | \(-0.642882\pi\) | ||||
−0.433955 | + | 0.900935i | \(0.642882\pi\) | |||||||
\(228\) | −7.47156 | −0.494816 | ||||||||
\(229\) | 2.15431 | 0.142361 | 0.0711804 | − | 0.997463i | \(-0.477323\pi\) | ||||
0.0711804 | + | 0.997463i | \(0.477323\pi\) | |||||||
\(230\) | 9.14861 | 0.603242 | ||||||||
\(231\) | −0.0576132 | −0.00379067 | ||||||||
\(232\) | −5.69621 | −0.373974 | ||||||||
\(233\) | 5.39996 | 0.353763 | 0.176881 | − | 0.984232i | \(-0.443399\pi\) | ||||
0.176881 | + | 0.984232i | \(0.443399\pi\) | |||||||
\(234\) | −2.40603 | −0.157287 | ||||||||
\(235\) | 16.2940 | 1.06290 | ||||||||
\(236\) | 8.12425 | 0.528844 | ||||||||
\(237\) | 6.22401 | 0.404293 | ||||||||
\(238\) | −0.0518916 | −0.00336363 | ||||||||
\(239\) | −2.67730 | −0.173180 | −0.0865900 | − | 0.996244i | \(-0.527597\pi\) | ||||
−0.0865900 | + | 0.996244i | \(0.527597\pi\) | |||||||
\(240\) | −11.3626 | −0.733453 | ||||||||
\(241\) | 26.7524 | 1.72327 | 0.861636 | − | 0.507526i | \(-0.169440\pi\) | ||||
0.861636 | + | 0.507526i | \(0.169440\pi\) | |||||||
\(242\) | −1.66399 | −0.106966 | ||||||||
\(243\) | −4.26416 | −0.273546 | ||||||||
\(244\) | −4.43729 | −0.284069 | ||||||||
\(245\) | −8.70229 | −0.555969 | ||||||||
\(246\) | −12.5780 | −0.801945 | ||||||||
\(247\) | −18.4094 | −1.17136 | ||||||||
\(248\) | −0.592381 | −0.0376162 | ||||||||
\(249\) | −0.944588 | −0.0598608 | ||||||||
\(250\) | 17.4909 | 1.10622 | ||||||||
\(251\) | −7.99065 | −0.504365 | −0.252183 | − | 0.967680i | \(-0.581148\pi\) | ||||
−0.252183 | + | 0.967680i | \(0.581148\pi\) | |||||||
\(252\) | 0.00990579 | 0.000624006 0 | ||||||||
\(253\) | 4.42189 | 0.278002 | ||||||||
\(254\) | −14.2636 | −0.894976 | ||||||||
\(255\) | 2.29706 | 0.143848 | ||||||||
\(256\) | 16.0753 | 1.00470 | ||||||||
\(257\) | 0.550791 | 0.0343574 | 0.0171787 | − | 0.999852i | \(-0.494532\pi\) | ||||
0.0171787 | + | 0.999852i | \(0.494532\pi\) | |||||||
\(258\) | −3.07417 | −0.191390 | ||||||||
\(259\) | 0.315285 | 0.0195908 | ||||||||
\(260\) | 3.34589 | 0.207504 | ||||||||
\(261\) | −1.14874 | −0.0711050 | ||||||||
\(262\) | 1.62035 | 0.100105 | ||||||||
\(263\) | 1.17884 | 0.0726904 | 0.0363452 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363452 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(264\) | −3.78469 | −0.232932 | ||||||||
\(265\) | −7.40209 | −0.454707 | ||||||||
\(266\) | 0.272946 | 0.0167354 | ||||||||
\(267\) | −25.3787 | −1.55315 | ||||||||
\(268\) | −10.2121 | −0.623802 | ||||||||
\(269\) | 19.5036 | 1.18915 | 0.594577 | − | 0.804039i | \(-0.297320\pi\) | ||||
0.594577 | + | 0.804039i | \(0.297320\pi\) | |||||||
\(270\) | 9.88777 | 0.601751 | ||||||||
\(271\) | 30.6217 | 1.86013 | 0.930067 | − | 0.367391i | \(-0.119749\pi\) | ||||
0.930067 | + | 0.367391i | \(0.119749\pi\) | |||||||
\(272\) | −4.94658 | −0.299931 | ||||||||
\(273\) | 0.201643 | 0.0122040 | ||||||||
\(274\) | 4.08685 | 0.246895 | ||||||||
\(275\) | 3.45406 | 0.208288 | ||||||||
\(276\) | −6.28115 | −0.378081 | ||||||||
\(277\) | −0.644936 | −0.0387504 | −0.0193752 | − | 0.999812i | \(-0.506168\pi\) | ||||
−0.0193752 | + | 0.999812i | \(0.506168\pi\) | |||||||
\(278\) | 6.13639 | 0.368036 | ||||||||
\(279\) | −0.119464 | −0.00715211 | ||||||||
\(280\) | 0.0794319 | 0.00474697 | ||||||||
\(281\) | −27.6827 | −1.65141 | −0.825706 | − | 0.564101i | \(-0.809223\pi\) | ||||
−0.825706 | + | 0.564101i | \(0.809223\pi\) | |||||||
\(282\) | −40.2866 | −2.39903 | ||||||||
\(283\) | −21.6468 | −1.28677 | −0.643383 | − | 0.765544i | \(-0.722470\pi\) | ||||
−0.643383 | + | 0.765544i | \(0.722470\pi\) | |||||||
\(284\) | −0.624293 | −0.0370450 | ||||||||
\(285\) | −12.0824 | −0.715697 | ||||||||
\(286\) | 5.82388 | 0.344373 | ||||||||
\(287\) | 0.127594 | 0.00753162 | ||||||||
\(288\) | 1.70785 | 0.100636 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 5.75280 | 0.337816 | ||||||||
\(291\) | −17.7982 | −1.04335 | ||||||||
\(292\) | −5.88993 | −0.344682 | ||||||||
\(293\) | 30.9671 | 1.80911 | 0.904557 | − | 0.426352i | \(-0.140202\pi\) | ||||
0.904557 | + | 0.426352i | \(0.140202\pi\) | |||||||
\(294\) | 21.5162 | 1.25485 | ||||||||
\(295\) | 13.1378 | 0.764915 | ||||||||
\(296\) | 20.7115 | 1.20383 | ||||||||
\(297\) | 4.77915 | 0.277315 | ||||||||
\(298\) | 15.0717 | 0.873079 | ||||||||
\(299\) | −15.4763 | −0.895020 | ||||||||
\(300\) | −4.90639 | −0.283271 | ||||||||
\(301\) | 0.0311850 | 0.00179747 | ||||||||
\(302\) | −3.55137 | −0.204358 | ||||||||
\(303\) | −31.7371 | −1.82325 | ||||||||
\(304\) | 26.0186 | 1.49227 | ||||||||
\(305\) | −7.17561 | −0.410874 | ||||||||
\(306\) | −0.687449 | −0.0392988 | ||||||||
\(307\) | −23.6287 | −1.34856 | −0.674281 | − | 0.738475i | \(-0.735546\pi\) | ||||
−0.674281 | + | 0.738475i | \(0.735546\pi\) | |||||||
\(308\) | −0.0239773 | −0.00136623 | ||||||||
\(309\) | 1.59619 | 0.0908040 | ||||||||
\(310\) | 0.598267 | 0.0339793 | ||||||||
\(311\) | 9.27572 | 0.525978 | 0.262989 | − | 0.964799i | \(-0.415292\pi\) | ||||
0.262989 | + | 0.964799i | \(0.415292\pi\) | |||||||
\(312\) | 13.2462 | 0.749919 | ||||||||
\(313\) | −23.1126 | −1.30640 | −0.653202 | − | 0.757184i | \(-0.726575\pi\) | ||||
−0.653202 | + | 0.757184i | \(0.726575\pi\) | |||||||
\(314\) | −7.56629 | −0.426990 | ||||||||
\(315\) | 0.0160188 | 0.000902557 0 | ||||||||
\(316\) | 2.59029 | 0.145715 | ||||||||
\(317\) | 24.3691 | 1.36870 | 0.684352 | − | 0.729152i | \(-0.260085\pi\) | ||||
0.684352 | + | 0.729152i | \(0.260085\pi\) | |||||||
\(318\) | 18.3015 | 1.02630 | ||||||||
\(319\) | 2.78056 | 0.155681 | ||||||||
\(320\) | 3.74793 | 0.209516 | ||||||||
\(321\) | −21.2506 | −1.18609 | ||||||||
\(322\) | 0.229459 | 0.0127872 | ||||||||
\(323\) | −5.25992 | −0.292670 | ||||||||
\(324\) | −7.74158 | −0.430088 | ||||||||
\(325\) | −12.0890 | −0.670578 | ||||||||
\(326\) | −38.7603 | −2.14674 | ||||||||
\(327\) | 6.27402 | 0.346954 | ||||||||
\(328\) | 8.38181 | 0.462808 | ||||||||
\(329\) | 0.408674 | 0.0225309 | ||||||||
\(330\) | 3.82229 | 0.210410 | ||||||||
\(331\) | 25.7679 | 1.41633 | 0.708166 | − | 0.706046i | \(-0.249523\pi\) | ||||
0.708166 | + | 0.706046i | \(0.249523\pi\) | |||||||
\(332\) | −0.393116 | −0.0215751 | ||||||||
\(333\) | 4.17683 | 0.228889 | ||||||||
\(334\) | −11.5168 | −0.630171 | ||||||||
\(335\) | −16.5141 | −0.902261 | ||||||||
\(336\) | −0.284988 | −0.0155474 | ||||||||
\(337\) | 1.60254 | 0.0872959 | 0.0436479 | − | 0.999047i | \(-0.486102\pi\) | ||||
0.0436479 | + | 0.999047i | \(0.486102\pi\) | |||||||
\(338\) | 1.24867 | 0.0679188 | ||||||||
\(339\) | 7.24236 | 0.393351 | ||||||||
\(340\) | 0.955986 | 0.0518456 | ||||||||
\(341\) | 0.289166 | 0.0156592 | ||||||||
\(342\) | 3.61593 | 0.195527 | ||||||||
\(343\) | −0.436559 | −0.0235720 | ||||||||
\(344\) | 2.04859 | 0.110452 | ||||||||
\(345\) | −10.1573 | −0.546853 | ||||||||
\(346\) | −8.56037 | −0.460208 | ||||||||
\(347\) | −36.1877 | −1.94266 | −0.971330 | − | 0.237735i | \(-0.923595\pi\) | ||||
−0.971330 | + | 0.237735i | \(0.923595\pi\) | |||||||
\(348\) | −3.94970 | −0.211726 | ||||||||
\(349\) | 2.74523 | 0.146949 | 0.0734743 | − | 0.997297i | \(-0.476591\pi\) | ||||
0.0734743 | + | 0.997297i | \(0.476591\pi\) | |||||||
\(350\) | 0.179237 | 0.00958060 | ||||||||
\(351\) | −16.7268 | −0.892808 | ||||||||
\(352\) | −4.13391 | −0.220338 | ||||||||
\(353\) | −6.09982 | −0.324661 | −0.162330 | − | 0.986736i | \(-0.551901\pi\) | ||||
−0.162330 | + | 0.986736i | \(0.551901\pi\) | |||||||
\(354\) | −32.4830 | −1.72645 | ||||||||
\(355\) | −1.00955 | −0.0535815 | ||||||||
\(356\) | −10.5620 | −0.559787 | ||||||||
\(357\) | 0.0576132 | 0.00304921 | ||||||||
\(358\) | −10.3952 | −0.549401 | ||||||||
\(359\) | −14.7446 | −0.778189 | −0.389094 | − | 0.921198i | \(-0.627212\pi\) | ||||
−0.389094 | + | 0.921198i | \(0.627212\pi\) | |||||||
\(360\) | 1.05230 | 0.0554610 | ||||||||
\(361\) | 8.66678 | 0.456146 | ||||||||
\(362\) | −5.99537 | −0.315110 | ||||||||
\(363\) | 1.84747 | 0.0969668 | ||||||||
\(364\) | 0.0839192 | 0.00439856 | ||||||||
\(365\) | −9.52469 | −0.498545 | ||||||||
\(366\) | 17.7415 | 0.927364 | ||||||||
\(367\) | −28.4531 | −1.48524 | −0.742620 | − | 0.669713i | \(-0.766417\pi\) | ||||
−0.742620 | + | 0.669713i | \(0.766417\pi\) | |||||||
\(368\) | 21.8732 | 1.14022 | ||||||||
\(369\) | 1.69034 | 0.0879953 | ||||||||
\(370\) | −20.9173 | −1.08744 | ||||||||
\(371\) | −0.185654 | −0.00963866 | ||||||||
\(372\) | −0.410752 | −0.0212965 | ||||||||
\(373\) | −4.70699 | −0.243718 | −0.121859 | − | 0.992547i | \(-0.538886\pi\) | ||||
−0.121859 | + | 0.992547i | \(0.538886\pi\) | |||||||
\(374\) | 1.66399 | 0.0860431 | ||||||||
\(375\) | −19.4195 | −1.00282 | ||||||||
\(376\) | 26.8464 | 1.38450 | ||||||||
\(377\) | −9.73179 | −0.501213 | ||||||||
\(378\) | 0.247998 | 0.0127556 | ||||||||
\(379\) | 15.9752 | 0.820591 | 0.410295 | − | 0.911953i | \(-0.365426\pi\) | ||||
0.410295 | + | 0.911953i | \(0.365426\pi\) | |||||||
\(380\) | −5.02841 | −0.257952 | ||||||||
\(381\) | 15.8363 | 0.811317 | ||||||||
\(382\) | 18.7624 | 0.959967 | ||||||||
\(383\) | 25.7909 | 1.31786 | 0.658928 | − | 0.752206i | \(-0.271010\pi\) | ||||
0.658928 | + | 0.752206i | \(0.271010\pi\) | |||||||
\(384\) | −24.5412 | −1.25236 | ||||||||
\(385\) | −0.0387741 | −0.00197611 | ||||||||
\(386\) | 41.2505 | 2.09959 | ||||||||
\(387\) | 0.413132 | 0.0210007 | ||||||||
\(388\) | −7.40723 | −0.376045 | ||||||||
\(389\) | 24.4107 | 1.23767 | 0.618836 | − | 0.785520i | \(-0.287604\pi\) | ||||
0.618836 | + | 0.785520i | \(0.287604\pi\) | |||||||
\(390\) | −13.3778 | −0.677412 | ||||||||
\(391\) | −4.42189 | −0.223624 | ||||||||
\(392\) | −14.3381 | −0.724184 | ||||||||
\(393\) | −1.79901 | −0.0907480 | ||||||||
\(394\) | 24.1597 | 1.21715 | ||||||||
\(395\) | 4.18880 | 0.210761 | ||||||||
\(396\) | −0.317647 | −0.0159623 | ||||||||
\(397\) | −10.5607 | −0.530026 | −0.265013 | − | 0.964245i | \(-0.585376\pi\) | ||||
−0.265013 | + | 0.964245i | \(0.585376\pi\) | |||||||
\(398\) | 20.5214 | 1.02864 | ||||||||
\(399\) | −0.303041 | −0.0151710 | ||||||||
\(400\) | 17.0858 | 0.854290 | ||||||||
\(401\) | 13.9064 | 0.694454 | 0.347227 | − | 0.937781i | \(-0.387123\pi\) | ||||
0.347227 | + | 0.937781i | \(0.387123\pi\) | |||||||
\(402\) | 40.8307 | 2.03645 | ||||||||
\(403\) | −1.01206 | −0.0504145 | ||||||||
\(404\) | −13.2083 | −0.657137 | ||||||||
\(405\) | −12.5190 | −0.622075 | ||||||||
\(406\) | 0.144287 | 0.00716087 | ||||||||
\(407\) | −10.1101 | −0.501142 | ||||||||
\(408\) | 3.78469 | 0.187370 | ||||||||
\(409\) | 26.4549 | 1.30811 | 0.654055 | − | 0.756447i | \(-0.273066\pi\) | ||||
0.654055 | + | 0.756447i | \(0.273066\pi\) | |||||||
\(410\) | −8.46509 | −0.418061 | ||||||||
\(411\) | −4.53746 | −0.223817 | ||||||||
\(412\) | 0.664298 | 0.0327276 | ||||||||
\(413\) | 0.329513 | 0.0162143 | ||||||||
\(414\) | 3.03982 | 0.149399 | ||||||||
\(415\) | −0.635714 | −0.0312060 | ||||||||
\(416\) | 14.4684 | 0.709374 | ||||||||
\(417\) | −6.81299 | −0.333634 | ||||||||
\(418\) | −8.75248 | −0.428098 | ||||||||
\(419\) | −7.68294 | −0.375336 | −0.187668 | − | 0.982233i | \(-0.560093\pi\) | ||||
−0.187668 | + | 0.982233i | \(0.560093\pi\) | |||||||
\(420\) | 0.0550774 | 0.00268750 | ||||||||
\(421\) | 23.1835 | 1.12989 | 0.564947 | − | 0.825127i | \(-0.308897\pi\) | ||||
0.564947 | + | 0.825127i | \(0.308897\pi\) | |||||||
\(422\) | 43.4753 | 2.11634 | ||||||||
\(423\) | 5.41403 | 0.263239 | ||||||||
\(424\) | −12.1959 | −0.592283 | ||||||||
\(425\) | −3.45406 | −0.167547 | ||||||||
\(426\) | 2.49610 | 0.120936 | ||||||||
\(427\) | −0.179973 | −0.00870952 | ||||||||
\(428\) | −8.84402 | −0.427492 | ||||||||
\(429\) | −6.46602 | −0.312183 | ||||||||
\(430\) | −2.06894 | −0.0997731 | ||||||||
\(431\) | −22.0653 | −1.06285 | −0.531423 | − | 0.847107i | \(-0.678343\pi\) | ||||
−0.531423 | + | 0.847107i | \(0.678343\pi\) | |||||||
\(432\) | 23.6405 | 1.13740 | ||||||||
\(433\) | −2.73527 | −0.131449 | −0.0657244 | − | 0.997838i | \(-0.520936\pi\) | ||||
−0.0657244 | + | 0.997838i | \(0.520936\pi\) | |||||||
\(434\) | 0.0150053 | 0.000720276 0 | ||||||||
\(435\) | −6.38711 | −0.306238 | ||||||||
\(436\) | 2.61111 | 0.125049 | ||||||||
\(437\) | 23.2588 | 1.11262 | ||||||||
\(438\) | 23.5496 | 1.12524 | ||||||||
\(439\) | −25.9404 | −1.23807 | −0.619033 | − | 0.785365i | \(-0.712475\pi\) | ||||
−0.619033 | + | 0.785365i | \(0.712475\pi\) | |||||||
\(440\) | −2.54712 | −0.121429 | ||||||||
\(441\) | −2.89152 | −0.137692 | ||||||||
\(442\) | −5.82388 | −0.277014 | ||||||||
\(443\) | −32.1727 | −1.52857 | −0.764285 | − | 0.644878i | \(-0.776908\pi\) | ||||
−0.764285 | + | 0.644878i | \(0.776908\pi\) | |||||||
\(444\) | 14.3612 | 0.681550 | ||||||||
\(445\) | −17.0800 | −0.809671 | ||||||||
\(446\) | 20.2933 | 0.960913 | ||||||||
\(447\) | −16.7335 | −0.791467 | ||||||||
\(448\) | 0.0940029 | 0.00444122 | ||||||||
\(449\) | 30.9338 | 1.45986 | 0.729929 | − | 0.683523i | \(-0.239553\pi\) | ||||
0.729929 | + | 0.683523i | \(0.239553\pi\) | |||||||
\(450\) | 2.37449 | 0.111935 | ||||||||
\(451\) | −4.09151 | −0.192662 | ||||||||
\(452\) | 3.01411 | 0.141772 | ||||||||
\(453\) | 3.94295 | 0.185256 | ||||||||
\(454\) | 21.7590 | 1.02120 | ||||||||
\(455\) | 0.135707 | 0.00636204 | ||||||||
\(456\) | −19.9072 | −0.932239 | ||||||||
\(457\) | −26.3308 | −1.23170 | −0.615851 | − | 0.787863i | \(-0.711188\pi\) | ||||
−0.615851 | + | 0.787863i | \(0.711188\pi\) | |||||||
\(458\) | −3.58476 | −0.167505 | ||||||||
\(459\) | −4.77915 | −0.223072 | ||||||||
\(460\) | −4.22726 | −0.197097 | ||||||||
\(461\) | −18.0636 | −0.841304 | −0.420652 | − | 0.907222i | \(-0.638199\pi\) | ||||
−0.420652 | + | 0.907222i | \(0.638199\pi\) | |||||||
\(462\) | 0.0958679 | 0.00446018 | ||||||||
\(463\) | 6.04264 | 0.280825 | 0.140413 | − | 0.990093i | \(-0.455157\pi\) | ||||
0.140413 | + | 0.990093i | \(0.455157\pi\) | |||||||
\(464\) | 13.7543 | 0.638525 | ||||||||
\(465\) | −0.664232 | −0.0308030 | ||||||||
\(466\) | −8.98549 | −0.416245 | ||||||||
\(467\) | 0.893753 | 0.0413579 | 0.0206790 | − | 0.999786i | \(-0.493417\pi\) | ||||
0.0206790 | + | 0.999786i | \(0.493417\pi\) | |||||||
\(468\) | 1.11174 | 0.0513904 | ||||||||
\(469\) | −0.414194 | −0.0191257 | ||||||||
\(470\) | −27.1131 | −1.25064 | ||||||||
\(471\) | 8.40055 | 0.387077 | ||||||||
\(472\) | 21.6462 | 0.996348 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −10.3567 | −0.475700 | ||||||||
\(475\) | 18.1681 | 0.833609 | ||||||||
\(476\) | 0.0239773 | 0.00109900 | ||||||||
\(477\) | −2.45950 | −0.112613 | ||||||||
\(478\) | 4.45501 | 0.203767 | ||||||||
\(479\) | 40.0823 | 1.83141 | 0.915703 | − | 0.401856i | \(-0.131635\pi\) | ||||
0.915703 | + | 0.401856i | \(0.131635\pi\) | |||||||
\(480\) | 9.49584 | 0.433424 | ||||||||
\(481\) | 35.3849 | 1.61341 | ||||||||
\(482\) | −44.5158 | −2.02764 | ||||||||
\(483\) | −0.254759 | −0.0115919 | ||||||||
\(484\) | 0.768874 | 0.0349488 | ||||||||
\(485\) | −11.9783 | −0.543908 | ||||||||
\(486\) | 7.09554 | 0.321860 | ||||||||
\(487\) | −4.48907 | −0.203419 | −0.101710 | − | 0.994814i | \(-0.532431\pi\) | ||||
−0.101710 | + | 0.994814i | \(0.532431\pi\) | |||||||
\(488\) | −11.8227 | −0.535189 | ||||||||
\(489\) | 43.0341 | 1.94607 | ||||||||
\(490\) | 14.4806 | 0.654165 | ||||||||
\(491\) | −33.8266 | −1.52658 | −0.763288 | − | 0.646059i | \(-0.776416\pi\) | ||||
−0.763288 | + | 0.646059i | \(0.776416\pi\) | |||||||
\(492\) | 5.81187 | 0.262019 | ||||||||
\(493\) | −2.78056 | −0.125230 | ||||||||
\(494\) | 30.6332 | 1.37825 | ||||||||
\(495\) | −0.513671 | −0.0230878 | ||||||||
\(496\) | 1.43038 | 0.0642261 | ||||||||
\(497\) | −0.0253209 | −0.00113580 | ||||||||
\(498\) | 1.57179 | 0.0704335 | ||||||||
\(499\) | 18.7854 | 0.840949 | 0.420475 | − | 0.907304i | \(-0.361864\pi\) | ||||
0.420475 | + | 0.907304i | \(0.361864\pi\) | |||||||
\(500\) | −8.08196 | −0.361436 | ||||||||
\(501\) | 12.7867 | 0.571266 | ||||||||
\(502\) | 13.2964 | 0.593447 | ||||||||
\(503\) | 3.78604 | 0.168811 | 0.0844056 | − | 0.996431i | \(-0.473101\pi\) | ||||
0.0844056 | + | 0.996431i | \(0.473101\pi\) | |||||||
\(504\) | 0.0263930 | 0.00117564 | ||||||||
\(505\) | −21.3593 | −0.950476 | ||||||||
\(506\) | −7.35799 | −0.327103 | ||||||||
\(507\) | −1.38635 | −0.0615700 | ||||||||
\(508\) | 6.59070 | 0.292415 | ||||||||
\(509\) | 25.2665 | 1.11992 | 0.559960 | − | 0.828520i | \(-0.310817\pi\) | ||||
0.559960 | + | 0.828520i | \(0.310817\pi\) | |||||||
\(510\) | −3.82229 | −0.169254 | ||||||||
\(511\) | −0.238891 | −0.0105679 | ||||||||
\(512\) | −0.181728 | −0.00803132 | ||||||||
\(513\) | 25.1380 | 1.10987 | ||||||||
\(514\) | −0.916513 | −0.0404257 | ||||||||
\(515\) | 1.07425 | 0.0473369 | ||||||||
\(516\) | 1.42047 | 0.0625327 | ||||||||
\(517\) | −13.1048 | −0.576351 | ||||||||
\(518\) | −0.524632 | −0.0230510 | ||||||||
\(519\) | 9.50424 | 0.417190 | ||||||||
\(520\) | 8.91478 | 0.390939 | ||||||||
\(521\) | −44.2144 | −1.93707 | −0.968534 | − | 0.248879i | \(-0.919938\pi\) | ||||
−0.968534 | + | 0.248879i | \(0.919938\pi\) | |||||||
\(522\) | 1.91149 | 0.0836637 | ||||||||
\(523\) | 16.4916 | 0.721129 | 0.360564 | − | 0.932734i | \(-0.382584\pi\) | ||||
0.360564 | + | 0.932734i | \(0.382584\pi\) | |||||||
\(524\) | −0.748707 | −0.0327074 | ||||||||
\(525\) | −0.198999 | −0.00868505 | ||||||||
\(526\) | −1.96158 | −0.0855290 | ||||||||
\(527\) | −0.289166 | −0.0125963 | ||||||||
\(528\) | 9.13864 | 0.397708 | ||||||||
\(529\) | −3.44693 | −0.149866 | ||||||||
\(530\) | 12.3170 | 0.535018 | ||||||||
\(531\) | 4.36533 | 0.189439 | ||||||||
\(532\) | −0.126119 | −0.00546794 | ||||||||
\(533\) | 14.3201 | 0.620271 | ||||||||
\(534\) | 42.2300 | 1.82747 | ||||||||
\(535\) | −14.3018 | −0.618320 | ||||||||
\(536\) | −27.2090 | −1.17525 | ||||||||
\(537\) | 11.5413 | 0.498045 | ||||||||
\(538\) | −32.4538 | −1.39918 | ||||||||
\(539\) | 6.99903 | 0.301469 | ||||||||
\(540\) | −4.56880 | −0.196610 | ||||||||
\(541\) | 10.8329 | 0.465741 | 0.232871 | − | 0.972508i | \(-0.425188\pi\) | ||||
0.232871 | + | 0.972508i | \(0.425188\pi\) | |||||||
\(542\) | −50.9542 | −2.18867 | ||||||||
\(543\) | 6.65642 | 0.285654 | ||||||||
\(544\) | 4.13391 | 0.177240 | ||||||||
\(545\) | 4.22246 | 0.180870 | ||||||||
\(546\) | −0.335532 | −0.0143595 | ||||||||
\(547\) | −38.6904 | −1.65428 | −0.827141 | − | 0.561995i | \(-0.810034\pi\) | ||||
−0.827141 | + | 0.561995i | \(0.810034\pi\) | |||||||
\(548\) | −1.88839 | −0.0806681 | ||||||||
\(549\) | −2.38425 | −0.101757 | ||||||||
\(550\) | −5.74754 | −0.245076 | ||||||||
\(551\) | 14.6255 | 0.623068 | ||||||||
\(552\) | −16.7355 | −0.712309 | ||||||||
\(553\) | 0.105060 | 0.00446762 | ||||||||
\(554\) | 1.07317 | 0.0455946 | ||||||||
\(555\) | 23.2236 | 0.985788 | ||||||||
\(556\) | −2.83542 | −0.120248 | ||||||||
\(557\) | −15.2934 | −0.648004 | −0.324002 | − | 0.946056i | \(-0.605028\pi\) | ||||
−0.324002 | + | 0.946056i | \(0.605028\pi\) | |||||||
\(558\) | 0.198787 | 0.00841532 | ||||||||
\(559\) | 3.49994 | 0.148032 | ||||||||
\(560\) | −0.191799 | −0.00810499 | ||||||||
\(561\) | −1.84747 | −0.0780001 | ||||||||
\(562\) | 46.0638 | 1.94309 | ||||||||
\(563\) | 16.8693 | 0.710956 | 0.355478 | − | 0.934685i | \(-0.384318\pi\) | ||||
0.355478 | + | 0.934685i | \(0.384318\pi\) | |||||||
\(564\) | 18.6150 | 0.783834 | ||||||||
\(565\) | 4.87415 | 0.205057 | ||||||||
\(566\) | 36.0201 | 1.51404 | ||||||||
\(567\) | −0.313993 | −0.0131864 | ||||||||
\(568\) | −1.66336 | −0.0697932 | ||||||||
\(569\) | −8.51834 | −0.357107 | −0.178554 | − | 0.983930i | \(-0.557142\pi\) | ||||
−0.178554 | + | 0.983930i | \(0.557142\pi\) | |||||||
\(570\) | 20.1050 | 0.842105 | ||||||||
\(571\) | −29.7264 | −1.24401 | −0.622006 | − | 0.783013i | \(-0.713682\pi\) | ||||
−0.622006 | + | 0.783013i | \(0.713682\pi\) | |||||||
\(572\) | −2.69102 | −0.112517 | ||||||||
\(573\) | −20.8311 | −0.870233 | ||||||||
\(574\) | −0.212315 | −0.00886186 | ||||||||
\(575\) | 15.2735 | 0.636948 | ||||||||
\(576\) | 1.24533 | 0.0518888 | ||||||||
\(577\) | −33.1391 | −1.37960 | −0.689799 | − | 0.724001i | \(-0.742301\pi\) | ||||
−0.689799 | + | 0.724001i | \(0.742301\pi\) | |||||||
\(578\) | −1.66399 | −0.0692130 | ||||||||
\(579\) | −45.7988 | −1.90333 | ||||||||
\(580\) | −2.65817 | −0.110375 | ||||||||
\(581\) | −0.0159445 | −0.000661490 0 | ||||||||
\(582\) | 29.6162 | 1.22763 | ||||||||
\(583\) | 5.95331 | 0.246561 | ||||||||
\(584\) | −15.6931 | −0.649385 | ||||||||
\(585\) | 1.79782 | 0.0743306 | ||||||||
\(586\) | −51.5290 | −2.12864 | ||||||||
\(587\) | −34.9504 | −1.44256 | −0.721279 | − | 0.692645i | \(-0.756445\pi\) | ||||
−0.721279 | + | 0.692645i | \(0.756445\pi\) | |||||||
\(588\) | −9.94190 | −0.409997 | ||||||||
\(589\) | 1.52099 | 0.0626713 | ||||||||
\(590\) | −21.8613 | −0.900015 | ||||||||
\(591\) | −26.8236 | −1.10337 | ||||||||
\(592\) | −50.0107 | −2.05543 | ||||||||
\(593\) | 13.2137 | 0.542620 | 0.271310 | − | 0.962492i | \(-0.412543\pi\) | ||||
0.271310 | + | 0.962492i | \(0.412543\pi\) | |||||||
\(594\) | −7.95248 | −0.326294 | ||||||||
\(595\) | 0.0387741 | 0.00158958 | ||||||||
\(596\) | −6.96411 | −0.285261 | ||||||||
\(597\) | −22.7841 | −0.932489 | ||||||||
\(598\) | 25.7525 | 1.05310 | ||||||||
\(599\) | −8.14703 | −0.332879 | −0.166439 | − | 0.986052i | \(-0.553227\pi\) | ||||
−0.166439 | + | 0.986052i | \(0.553227\pi\) | |||||||
\(600\) | −13.0726 | −0.533685 | ||||||||
\(601\) | −21.6584 | −0.883466 | −0.441733 | − | 0.897147i | \(-0.645636\pi\) | ||||
−0.441733 | + | 0.897147i | \(0.645636\pi\) | |||||||
\(602\) | −0.0518916 | −0.00211494 | ||||||||
\(603\) | −5.48716 | −0.223454 | ||||||||
\(604\) | 1.64097 | 0.0667700 | ||||||||
\(605\) | 1.24336 | 0.0505497 | ||||||||
\(606\) | 52.8104 | 2.14527 | ||||||||
\(607\) | −22.1221 | −0.897908 | −0.448954 | − | 0.893555i | \(-0.648203\pi\) | ||||
−0.448954 | + | 0.893555i | \(0.648203\pi\) | |||||||
\(608\) | −21.7440 | −0.881837 | ||||||||
\(609\) | −0.160197 | −0.00649150 | ||||||||
\(610\) | 11.9402 | 0.483443 | ||||||||
\(611\) | 45.8662 | 1.85555 | ||||||||
\(612\) | 0.317647 | 0.0128401 | ||||||||
\(613\) | 34.0633 | 1.37580 | 0.687902 | − | 0.725804i | \(-0.258532\pi\) | ||||
0.687902 | + | 0.725804i | \(0.258532\pi\) | |||||||
\(614\) | 39.3180 | 1.58675 | ||||||||
\(615\) | 9.39846 | 0.378982 | ||||||||
\(616\) | −0.0638850 | −0.00257400 | ||||||||
\(617\) | 29.6929 | 1.19539 | 0.597696 | − | 0.801723i | \(-0.296083\pi\) | ||||
0.597696 | + | 0.801723i | \(0.296083\pi\) | |||||||
\(618\) | −2.65605 | −0.106842 | ||||||||
\(619\) | −9.46611 | −0.380475 | −0.190238 | − | 0.981738i | \(-0.560926\pi\) | ||||
−0.190238 | + | 0.981738i | \(0.560926\pi\) | |||||||
\(620\) | −0.276439 | −0.0111020 | ||||||||
\(621\) | 21.1329 | 0.848033 | ||||||||
\(622\) | −15.4347 | −0.618876 | ||||||||
\(623\) | −0.428388 | −0.0171630 | ||||||||
\(624\) | −31.9847 | −1.28041 | ||||||||
\(625\) | 4.20086 | 0.168034 | ||||||||
\(626\) | 38.4593 | 1.53714 | ||||||||
\(627\) | 9.71753 | 0.388081 | ||||||||
\(628\) | 3.49612 | 0.139510 | ||||||||
\(629\) | 10.1101 | 0.403118 | ||||||||
\(630\) | −0.0266552 | −0.00106197 | ||||||||
\(631\) | −10.2705 | −0.408862 | −0.204431 | − | 0.978881i | \(-0.565534\pi\) | ||||
−0.204431 | + | 0.978881i | \(0.565534\pi\) | |||||||
\(632\) | 6.90157 | 0.274530 | ||||||||
\(633\) | −48.2689 | −1.91852 | ||||||||
\(634\) | −40.5500 | −1.61045 | ||||||||
\(635\) | 10.6579 | 0.422947 | ||||||||
\(636\) | −8.45649 | −0.335322 | ||||||||
\(637\) | −24.4962 | −0.970574 | ||||||||
\(638\) | −4.62683 | −0.183178 | ||||||||
\(639\) | −0.335446 | −0.0132700 | ||||||||
\(640\) | −16.5164 | −0.652868 | ||||||||
\(641\) | 3.75266 | 0.148221 | 0.0741106 | − | 0.997250i | \(-0.476388\pi\) | ||||
0.0741106 | + | 0.997250i | \(0.476388\pi\) | |||||||
\(642\) | 35.3608 | 1.39558 | ||||||||
\(643\) | 6.56660 | 0.258962 | 0.129481 | − | 0.991582i | \(-0.458669\pi\) | ||||
0.129481 | + | 0.991582i | \(0.458669\pi\) | |||||||
\(644\) | −0.106025 | −0.00417797 | ||||||||
\(645\) | 2.29706 | 0.0904467 | ||||||||
\(646\) | 8.75248 | 0.344362 | ||||||||
\(647\) | −10.3694 | −0.407665 | −0.203832 | − | 0.979006i | \(-0.565340\pi\) | ||||
−0.203832 | + | 0.979006i | \(0.565340\pi\) | |||||||
\(648\) | −20.6266 | −0.810290 | ||||||||
\(649\) | −10.5664 | −0.414768 | ||||||||
\(650\) | 20.1160 | 0.789016 | ||||||||
\(651\) | −0.0166598 | −0.000652948 0 | ||||||||
\(652\) | 17.9098 | 0.701403 | ||||||||
\(653\) | −9.90294 | −0.387532 | −0.193766 | − | 0.981048i | \(-0.562070\pi\) | ||||
−0.193766 | + | 0.981048i | \(0.562070\pi\) | |||||||
\(654\) | −10.4399 | −0.408233 | ||||||||
\(655\) | −1.21075 | −0.0473077 | ||||||||
\(656\) | −20.2390 | −0.790200 | ||||||||
\(657\) | −3.16478 | −0.123470 | ||||||||
\(658\) | −0.680031 | −0.0265104 | ||||||||
\(659\) | −39.7314 | −1.54772 | −0.773859 | − | 0.633359i | \(-0.781676\pi\) | ||||
−0.773859 | + | 0.633359i | \(0.781676\pi\) | |||||||
\(660\) | −1.76615 | −0.0687473 | ||||||||
\(661\) | 18.5390 | 0.721085 | 0.360543 | − | 0.932743i | \(-0.382591\pi\) | ||||
0.360543 | + | 0.932743i | \(0.382591\pi\) | |||||||
\(662\) | −42.8776 | −1.66649 | ||||||||
\(663\) | 6.46602 | 0.251120 | ||||||||
\(664\) | −1.04742 | −0.0406477 | ||||||||
\(665\) | −0.203948 | −0.00790878 | ||||||||
\(666\) | −6.95021 | −0.269315 | ||||||||
\(667\) | 12.2953 | 0.476076 | ||||||||
\(668\) | 5.32152 | 0.205896 | ||||||||
\(669\) | −22.5308 | −0.871091 | ||||||||
\(670\) | 27.4793 | 1.06162 | ||||||||
\(671\) | 5.77116 | 0.222793 | ||||||||
\(672\) | 0.238168 | 0.00918751 | ||||||||
\(673\) | 6.87386 | 0.264968 | 0.132484 | − | 0.991185i | \(-0.457705\pi\) | ||||
0.132484 | + | 0.991185i | \(0.457705\pi\) | |||||||
\(674\) | −2.66662 | −0.102714 | ||||||||
\(675\) | 16.5075 | 0.635373 | ||||||||
\(676\) | −0.576969 | −0.0221911 | ||||||||
\(677\) | −15.0860 | −0.579802 | −0.289901 | − | 0.957057i | \(-0.593622\pi\) | ||||
−0.289901 | + | 0.957057i | \(0.593622\pi\) | |||||||
\(678\) | −12.0512 | −0.462825 | ||||||||
\(679\) | −0.300432 | −0.0115295 | ||||||||
\(680\) | 2.54712 | 0.0976777 | ||||||||
\(681\) | −24.1582 | −0.925743 | ||||||||
\(682\) | −0.481170 | −0.0184250 | ||||||||
\(683\) | −44.1030 | −1.68756 | −0.843778 | − | 0.536693i | \(-0.819673\pi\) | ||||
−0.843778 | + | 0.536693i | \(0.819673\pi\) | |||||||
\(684\) | −1.67080 | −0.0638845 | ||||||||
\(685\) | −3.05374 | −0.116678 | ||||||||
\(686\) | 0.726431 | 0.0277353 | ||||||||
\(687\) | 3.98002 | 0.151847 | ||||||||
\(688\) | −4.94658 | −0.188587 | ||||||||
\(689\) | −20.8362 | −0.793797 | ||||||||
\(690\) | 16.9018 | 0.643439 | ||||||||
\(691\) | 25.6350 | 0.975203 | 0.487602 | − | 0.873066i | \(-0.337872\pi\) | ||||
0.487602 | + | 0.873066i | \(0.337872\pi\) | |||||||
\(692\) | 3.95545 | 0.150364 | ||||||||
\(693\) | −0.0128835 | −0.000489404 0 | ||||||||
\(694\) | 60.2162 | 2.28577 | ||||||||
\(695\) | −4.58519 | −0.173926 | ||||||||
\(696\) | −10.5236 | −0.398894 | ||||||||
\(697\) | 4.09151 | 0.154977 | ||||||||
\(698\) | −4.56804 | −0.172903 | ||||||||
\(699\) | 9.97624 | 0.377336 | ||||||||
\(700\) | −0.0828191 | −0.00313027 | ||||||||
\(701\) | −37.8442 | −1.42935 | −0.714677 | − | 0.699454i | \(-0.753426\pi\) | ||||
−0.714677 | + | 0.699454i | \(0.753426\pi\) | |||||||
\(702\) | 27.8332 | 1.05050 | ||||||||
\(703\) | −53.1786 | −2.00567 | ||||||||
\(704\) | −3.01437 | −0.113608 | ||||||||
\(705\) | 30.1026 | 1.13373 | ||||||||
\(706\) | 10.1501 | 0.382003 | ||||||||
\(707\) | −0.535718 | −0.0201477 | ||||||||
\(708\) | 15.0093 | 0.564083 | ||||||||
\(709\) | 48.5212 | 1.82225 | 0.911125 | − | 0.412129i | \(-0.135215\pi\) | ||||
0.911125 | + | 0.412129i | \(0.135215\pi\) | |||||||
\(710\) | 1.67989 | 0.0630452 | ||||||||
\(711\) | 1.39182 | 0.0521973 | ||||||||
\(712\) | −28.1415 | −1.05465 | ||||||||
\(713\) | 1.27866 | 0.0478862 | ||||||||
\(714\) | −0.0958679 | −0.00358777 | ||||||||
\(715\) | −4.35168 | −0.162744 | ||||||||
\(716\) | 4.80324 | 0.179506 | ||||||||
\(717\) | −4.94622 | −0.184720 | ||||||||
\(718\) | 24.5349 | 0.915633 | ||||||||
\(719\) | −46.0088 | −1.71584 | −0.857920 | − | 0.513783i | \(-0.828244\pi\) | ||||
−0.857920 | + | 0.513783i | \(0.828244\pi\) | |||||||
\(720\) | −2.54091 | −0.0946943 | ||||||||
\(721\) | 0.0269434 | 0.00100343 | ||||||||
\(722\) | −14.4215 | −0.536711 | ||||||||
\(723\) | 49.4241 | 1.83810 | ||||||||
\(724\) | 2.77026 | 0.102956 | ||||||||
\(725\) | 9.60422 | 0.356692 | ||||||||
\(726\) | −3.07417 | −0.114093 | ||||||||
\(727\) | 27.4828 | 1.01928 | 0.509640 | − | 0.860388i | \(-0.329778\pi\) | ||||
0.509640 | + | 0.860388i | \(0.329778\pi\) | |||||||
\(728\) | 0.223594 | 0.00828694 | ||||||||
\(729\) | 22.3283 | 0.826972 | ||||||||
\(730\) | 15.8490 | 0.586599 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −8.19775 | −0.302998 | ||||||||
\(733\) | −11.3404 | −0.418869 | −0.209434 | − | 0.977823i | \(-0.567162\pi\) | ||||
−0.209434 | + | 0.977823i | \(0.567162\pi\) | |||||||
\(734\) | 47.3458 | 1.74757 | ||||||||
\(735\) | −16.0772 | −0.593016 | ||||||||
\(736\) | −18.2797 | −0.673798 | ||||||||
\(737\) | 13.2819 | 0.489243 | ||||||||
\(738\) | −2.81271 | −0.103537 | ||||||||
\(739\) | 7.67521 | 0.282337 | 0.141169 | − | 0.989986i | \(-0.454914\pi\) | ||||
0.141169 | + | 0.989986i | \(0.454914\pi\) | |||||||
\(740\) | 9.66516 | 0.355298 | ||||||||
\(741\) | −34.0108 | −1.24942 | ||||||||
\(742\) | 0.308926 | 0.0113410 | ||||||||
\(743\) | −37.7938 | −1.38652 | −0.693260 | − | 0.720687i | \(-0.743826\pi\) | ||||
−0.693260 | + | 0.720687i | \(0.743826\pi\) | |||||||
\(744\) | −1.09440 | −0.0401228 | ||||||||
\(745\) | −11.2618 | −0.412599 | ||||||||
\(746\) | 7.83239 | 0.286764 | ||||||||
\(747\) | −0.211230 | −0.00772849 | ||||||||
\(748\) | −0.768874 | −0.0281128 | ||||||||
\(749\) | −0.358707 | −0.0131069 | ||||||||
\(750\) | 32.3139 | 1.17994 | ||||||||
\(751\) | 34.1652 | 1.24670 | 0.623352 | − | 0.781941i | \(-0.285770\pi\) | ||||
0.623352 | + | 0.781941i | \(0.285770\pi\) | |||||||
\(752\) | −64.8242 | −2.36389 | ||||||||
\(753\) | −14.7625 | −0.537974 | ||||||||
\(754\) | 16.1936 | 0.589737 | ||||||||
\(755\) | 2.65363 | 0.0965755 | ||||||||
\(756\) | −0.114591 | −0.00416764 | ||||||||
\(757\) | 37.4914 | 1.36265 | 0.681324 | − | 0.731982i | \(-0.261404\pi\) | ||||
0.681324 | + | 0.731982i | \(0.261404\pi\) | |||||||
\(758\) | −26.5826 | −0.965524 | ||||||||
\(759\) | 8.16928 | 0.296526 | ||||||||
\(760\) | −13.3977 | −0.485985 | ||||||||
\(761\) | −12.5989 | −0.456710 | −0.228355 | − | 0.973578i | \(-0.573335\pi\) | ||||
−0.228355 | + | 0.973578i | \(0.573335\pi\) | |||||||
\(762\) | −26.3515 | −0.954612 | ||||||||
\(763\) | 0.105905 | 0.00383400 | ||||||||
\(764\) | −8.66946 | −0.313650 | ||||||||
\(765\) | 0.513671 | 0.0185718 | ||||||||
\(766\) | −42.9160 | −1.55062 | ||||||||
\(767\) | 36.9819 | 1.33534 | ||||||||
\(768\) | 29.6985 | 1.07165 | ||||||||
\(769\) | −7.05586 | −0.254441 | −0.127220 | − | 0.991874i | \(-0.540606\pi\) | ||||
−0.127220 | + | 0.991874i | \(0.540606\pi\) | |||||||
\(770\) | 0.0645198 | 0.00232513 | ||||||||
\(771\) | 1.01757 | 0.0366468 | ||||||||
\(772\) | −19.0604 | −0.686000 | ||||||||
\(773\) | 17.8294 | 0.641279 | 0.320640 | − | 0.947201i | \(-0.396102\pi\) | ||||
0.320640 | + | 0.947201i | \(0.396102\pi\) | |||||||
\(774\) | −0.687449 | −0.0247098 | ||||||||
\(775\) | 0.998797 | 0.0358779 | ||||||||
\(776\) | −19.7358 | −0.708474 | ||||||||
\(777\) | 0.582478 | 0.0208963 | ||||||||
\(778\) | −40.6193 | −1.45627 | ||||||||
\(779\) | −21.5210 | −0.771071 | ||||||||
\(780\) | 6.18143 | 0.221331 | ||||||||
\(781\) | 0.811957 | 0.0290541 | ||||||||
\(782\) | 7.35799 | 0.263121 | ||||||||
\(783\) | 13.2887 | 0.474900 | ||||||||
\(784\) | 34.6213 | 1.23647 | ||||||||
\(785\) | 5.65363 | 0.201787 | ||||||||
\(786\) | 2.99354 | 0.106776 | ||||||||
\(787\) | 43.9202 | 1.56559 | 0.782793 | − | 0.622282i | \(-0.213794\pi\) | ||||
0.782793 | + | 0.622282i | \(0.213794\pi\) | |||||||
\(788\) | −11.1634 | −0.397679 | ||||||||
\(789\) | 2.17787 | 0.0775341 | ||||||||
\(790\) | −6.97014 | −0.247986 | ||||||||
\(791\) | 0.122250 | 0.00434671 | ||||||||
\(792\) | −0.846336 | −0.0300732 | ||||||||
\(793\) | −20.1987 | −0.717277 | ||||||||
\(794\) | 17.5729 | 0.623640 | ||||||||
\(795\) | −13.6751 | −0.485006 | ||||||||
\(796\) | −9.48221 | −0.336088 | ||||||||
\(797\) | 16.7168 | 0.592139 | 0.296069 | − | 0.955166i | \(-0.404324\pi\) | ||||
0.296069 | + | 0.955166i | \(0.404324\pi\) | |||||||
\(798\) | 0.504258 | 0.0178505 | ||||||||
\(799\) | 13.1048 | 0.463616 | ||||||||
\(800\) | −14.2788 | −0.504831 | ||||||||
\(801\) | −5.67520 | −0.200523 | ||||||||
\(802\) | −23.1402 | −0.817109 | ||||||||
\(803\) | 7.66046 | 0.270332 | ||||||||
\(804\) | −18.8665 | −0.665369 | ||||||||
\(805\) | −0.171454 | −0.00604297 | ||||||||
\(806\) | 1.68407 | 0.0593188 | ||||||||
\(807\) | 36.0322 | 1.26839 | ||||||||
\(808\) | −35.1921 | −1.23805 | ||||||||
\(809\) | 24.4091 | 0.858177 | 0.429088 | − | 0.903262i | \(-0.358835\pi\) | ||||
0.429088 | + | 0.903262i | \(0.358835\pi\) | |||||||
\(810\) | 20.8316 | 0.731946 | ||||||||
\(811\) | 8.29677 | 0.291339 | 0.145669 | − | 0.989333i | \(-0.453466\pi\) | ||||
0.145669 | + | 0.989333i | \(0.453466\pi\) | |||||||
\(812\) | −0.0666703 | −0.00233967 | ||||||||
\(813\) | 56.5725 | 1.98408 | ||||||||
\(814\) | 16.8232 | 0.589654 | ||||||||
\(815\) | 28.9622 | 1.01450 | ||||||||
\(816\) | −9.13864 | −0.319916 | ||||||||
\(817\) | −5.25992 | −0.184021 | ||||||||
\(818\) | −44.0208 | −1.53915 | ||||||||
\(819\) | 0.0450915 | 0.00157562 | ||||||||
\(820\) | 3.91143 | 0.136593 | ||||||||
\(821\) | 44.5956 | 1.55640 | 0.778199 | − | 0.628018i | \(-0.216134\pi\) | ||||
0.778199 | + | 0.628018i | \(0.216134\pi\) | |||||||
\(822\) | 7.55031 | 0.263347 | ||||||||
\(823\) | 29.0932 | 1.01413 | 0.507063 | − | 0.861909i | \(-0.330731\pi\) | ||||
0.507063 | + | 0.861909i | \(0.330731\pi\) | |||||||
\(824\) | 1.76995 | 0.0616592 | ||||||||
\(825\) | 6.38126 | 0.222167 | ||||||||
\(826\) | −0.548308 | −0.0190781 | ||||||||
\(827\) | −10.3349 | −0.359381 | −0.179690 | − | 0.983723i | \(-0.557510\pi\) | ||||
−0.179690 | + | 0.983723i | \(0.557510\pi\) | |||||||
\(828\) | −1.40460 | −0.0488131 | ||||||||
\(829\) | −6.82387 | −0.237003 | −0.118501 | − | 0.992954i | \(-0.537809\pi\) | ||||
−0.118501 | + | 0.992954i | \(0.537809\pi\) | |||||||
\(830\) | 1.05782 | 0.0367176 | ||||||||
\(831\) | −1.19150 | −0.0413326 | ||||||||
\(832\) | 10.5501 | 0.365759 | ||||||||
\(833\) | −6.99903 | −0.242502 | ||||||||
\(834\) | 11.3368 | 0.392560 | ||||||||
\(835\) | 8.60551 | 0.297806 | ||||||||
\(836\) | 4.04422 | 0.139872 | ||||||||
\(837\) | 1.38197 | 0.0477678 | ||||||||
\(838\) | 12.7844 | 0.441628 | ||||||||
\(839\) | 41.8740 | 1.44565 | 0.722825 | − | 0.691031i | \(-0.242843\pi\) | ||||
0.722825 | + | 0.691031i | \(0.242843\pi\) | |||||||
\(840\) | 0.146748 | 0.00506328 | ||||||||
\(841\) | −21.2685 | −0.733397 | ||||||||
\(842\) | −38.5772 | −1.32946 | ||||||||
\(843\) | −51.1429 | −1.76145 | ||||||||
\(844\) | −20.0884 | −0.691472 | ||||||||
\(845\) | −0.933024 | −0.0320970 | ||||||||
\(846\) | −9.00891 | −0.309733 | ||||||||
\(847\) | 0.0311850 | 0.00107153 | ||||||||
\(848\) | 29.4485 | 1.01127 | ||||||||
\(849\) | −39.9917 | −1.37251 | ||||||||
\(850\) | 5.74754 | 0.197139 | ||||||||
\(851\) | −44.7059 | −1.53250 | ||||||||
\(852\) | −1.15336 | −0.0395135 | ||||||||
\(853\) | 14.3131 | 0.490071 | 0.245035 | − | 0.969514i | \(-0.421200\pi\) | ||||
0.245035 | + | 0.969514i | \(0.421200\pi\) | |||||||
\(854\) | 0.299474 | 0.0102478 | ||||||||
\(855\) | −2.70187 | −0.0924019 | ||||||||
\(856\) | −23.5640 | −0.805400 | ||||||||
\(857\) | −36.3183 | −1.24061 | −0.620305 | − | 0.784360i | \(-0.712991\pi\) | ||||
−0.620305 | + | 0.784360i | \(0.712991\pi\) | |||||||
\(858\) | 10.7594 | 0.367321 | ||||||||
\(859\) | −6.63213 | −0.226286 | −0.113143 | − | 0.993579i | \(-0.536092\pi\) | ||||
−0.113143 | + | 0.993579i | \(0.536092\pi\) | |||||||
\(860\) | 0.955986 | 0.0325988 | ||||||||
\(861\) | 0.235725 | 0.00803349 | ||||||||
\(862\) | 36.7165 | 1.25057 | ||||||||
\(863\) | 4.38558 | 0.149287 | 0.0746434 | − | 0.997210i | \(-0.476218\pi\) | ||||
0.0746434 | + | 0.997210i | \(0.476218\pi\) | |||||||
\(864\) | −19.7566 | −0.672132 | ||||||||
\(865\) | 6.39642 | 0.217485 | ||||||||
\(866\) | 4.55147 | 0.154665 | ||||||||
\(867\) | 1.84747 | 0.0627432 | ||||||||
\(868\) | −0.00693342 | −0.000235336 0 | ||||||||
\(869\) | −3.36894 | −0.114284 | ||||||||
\(870\) | 10.6281 | 0.360327 | ||||||||
\(871\) | −46.4857 | −1.57511 | ||||||||
\(872\) | 6.95702 | 0.235594 | ||||||||
\(873\) | −3.98006 | −0.134705 | ||||||||
\(874\) | −38.7024 | −1.30913 | ||||||||
\(875\) | −0.327798 | −0.0110816 | ||||||||
\(876\) | −10.8815 | −0.367650 | ||||||||
\(877\) | 38.8413 | 1.31158 | 0.655789 | − | 0.754944i | \(-0.272336\pi\) | ||||
0.655789 | + | 0.754944i | \(0.272336\pi\) | |||||||
\(878\) | 43.1646 | 1.45673 | ||||||||
\(879\) | 57.2106 | 1.92967 | ||||||||
\(880\) | 6.15037 | 0.207329 | ||||||||
\(881\) | 32.5138 | 1.09542 | 0.547709 | − | 0.836669i | \(-0.315500\pi\) | ||||
0.547709 | + | 0.836669i | \(0.315500\pi\) | |||||||
\(882\) | 4.81147 | 0.162011 | ||||||||
\(883\) | −32.7859 | −1.10333 | −0.551666 | − | 0.834065i | \(-0.686008\pi\) | ||||
−0.551666 | + | 0.834065i | \(0.686008\pi\) | |||||||
\(884\) | 2.69102 | 0.0905086 | ||||||||
\(885\) | 24.2717 | 0.815885 | ||||||||
\(886\) | 53.5351 | 1.79855 | ||||||||
\(887\) | −22.5285 | −0.756432 | −0.378216 | − | 0.925717i | \(-0.623462\pi\) | ||||
−0.378216 | + | 0.925717i | \(0.623462\pi\) | |||||||
\(888\) | 38.2638 | 1.28405 | ||||||||
\(889\) | 0.267314 | 0.00896542 | ||||||||
\(890\) | 28.4211 | 0.952676 | ||||||||
\(891\) | 10.0687 | 0.337315 | ||||||||
\(892\) | −9.37682 | −0.313959 | ||||||||
\(893\) | −68.9305 | −2.30667 | ||||||||
\(894\) | 27.8444 | 0.931257 | ||||||||
\(895\) | 7.76739 | 0.259635 | ||||||||
\(896\) | −0.414252 | −0.0138392 | ||||||||
\(897\) | −28.5920 | −0.954660 | ||||||||
\(898\) | −51.4737 | −1.71770 | ||||||||
\(899\) | 0.804043 | 0.0268163 | ||||||||
\(900\) | −1.09717 | −0.0365724 | ||||||||
\(901\) | −5.95331 | −0.198333 | ||||||||
\(902\) | 6.80825 | 0.226690 | ||||||||
\(903\) | 0.0576132 | 0.00191725 | ||||||||
\(904\) | 8.03077 | 0.267099 | ||||||||
\(905\) | 4.47982 | 0.148914 | ||||||||
\(906\) | −6.56104 | −0.217976 | ||||||||
\(907\) | −57.6261 | −1.91344 | −0.956721 | − | 0.291007i | \(-0.906010\pi\) | ||||
−0.956721 | + | 0.291007i | \(0.906010\pi\) | |||||||
\(908\) | −10.0541 | −0.333657 | ||||||||
\(909\) | −7.09708 | −0.235395 | ||||||||
\(910\) | −0.225815 | −0.00748571 | ||||||||
\(911\) | −12.9954 | −0.430557 | −0.215278 | − | 0.976553i | \(-0.569066\pi\) | ||||
−0.215278 | + | 0.976553i | \(0.569066\pi\) | |||||||
\(912\) | 48.0685 | 1.59171 | ||||||||
\(913\) | 0.511288 | 0.0169212 | ||||||||
\(914\) | 43.8142 | 1.44925 | ||||||||
\(915\) | −13.2567 | −0.438253 | ||||||||
\(916\) | 1.65639 | 0.0547288 | ||||||||
\(917\) | −0.0303670 | −0.00100281 | ||||||||
\(918\) | 7.95248 | 0.262471 | ||||||||
\(919\) | 45.4946 | 1.50073 | 0.750365 | − | 0.661024i | \(-0.229878\pi\) | ||||
0.750365 | + | 0.661024i | \(0.229878\pi\) | |||||||
\(920\) | −11.2631 | −0.371333 | ||||||||
\(921\) | −43.6532 | −1.43842 | ||||||||
\(922\) | 30.0577 | 0.989896 | ||||||||
\(923\) | −2.84180 | −0.0935391 | ||||||||
\(924\) | −0.0442973 | −0.00145727 | ||||||||
\(925\) | −34.9211 | −1.14820 | ||||||||
\(926\) | −10.0549 | −0.330425 | ||||||||
\(927\) | 0.356941 | 0.0117235 | ||||||||
\(928\) | −11.4946 | −0.377328 | ||||||||
\(929\) | 31.0361 | 1.01826 | 0.509131 | − | 0.860689i | \(-0.329967\pi\) | ||||
0.509131 | + | 0.860689i | \(0.329967\pi\) | |||||||
\(930\) | 1.10528 | 0.0362435 | ||||||||
\(931\) | 36.8143 | 1.20654 | ||||||||
\(932\) | 4.15189 | 0.136000 | ||||||||
\(933\) | 17.1366 | 0.561026 | ||||||||
\(934\) | −1.48720 | −0.0486626 | ||||||||
\(935\) | −1.24336 | −0.0406621 | ||||||||
\(936\) | 2.96213 | 0.0968201 | ||||||||
\(937\) | 29.9531 | 0.978525 | 0.489262 | − | 0.872137i | \(-0.337266\pi\) | ||||
0.489262 | + | 0.872137i | \(0.337266\pi\) | |||||||
\(938\) | 0.689216 | 0.0225037 | ||||||||
\(939\) | −42.6998 | −1.39346 | ||||||||
\(940\) | 12.5280 | 0.408620 | ||||||||
\(941\) | −16.7839 | −0.547139 | −0.273570 | − | 0.961852i | \(-0.588204\pi\) | ||||
−0.273570 | + | 0.961852i | \(0.588204\pi\) | |||||||
\(942\) | −13.9785 | −0.455443 | ||||||||
\(943\) | −18.0922 | −0.589163 | ||||||||
\(944\) | −52.2677 | −1.70117 | ||||||||
\(945\) | −0.185307 | −0.00602804 | ||||||||
\(946\) | 1.66399 | 0.0541011 | ||||||||
\(947\) | −16.7225 | −0.543409 | −0.271704 | − | 0.962381i | \(-0.587587\pi\) | ||||
−0.271704 | + | 0.962381i | \(0.587587\pi\) | |||||||
\(948\) | 4.78548 | 0.155425 | ||||||||
\(949\) | −26.8112 | −0.870327 | ||||||||
\(950\) | −30.2316 | −0.980842 | ||||||||
\(951\) | 45.0210 | 1.45991 | ||||||||
\(952\) | 0.0638850 | 0.00207053 | ||||||||
\(953\) | −23.2361 | −0.752692 | −0.376346 | − | 0.926479i | \(-0.622820\pi\) | ||||
−0.376346 | + | 0.926479i | \(0.622820\pi\) | |||||||
\(954\) | 4.09259 | 0.132503 | ||||||||
\(955\) | −14.0195 | −0.453660 | ||||||||
\(956\) | −2.05851 | −0.0665768 | ||||||||
\(957\) | 5.13699 | 0.166055 | ||||||||
\(958\) | −66.6966 | −2.15487 | ||||||||
\(959\) | −0.0765917 | −0.00247328 | ||||||||
\(960\) | 6.92418 | 0.223477 | ||||||||
\(961\) | −30.9164 | −0.997303 | ||||||||
\(962\) | −58.8803 | −1.89838 | ||||||||
\(963\) | −4.75207 | −0.153133 | ||||||||
\(964\) | 20.5692 | 0.662490 | ||||||||
\(965\) | −30.8229 | −0.992224 | ||||||||
\(966\) | 0.423917 | 0.0136393 | ||||||||
\(967\) | −43.5139 | −1.39931 | −0.699656 | − | 0.714479i | \(-0.746664\pi\) | ||||
−0.699656 | + | 0.714479i | \(0.746664\pi\) | |||||||
\(968\) | 2.04859 | 0.0658440 | ||||||||
\(969\) | −9.71753 | −0.312172 | ||||||||
\(970\) | 19.9319 | 0.639974 | ||||||||
\(971\) | −13.3176 | −0.427383 | −0.213691 | − | 0.976901i | \(-0.568549\pi\) | ||||
−0.213691 | + | 0.976901i | \(0.568549\pi\) | |||||||
\(972\) | −3.27861 | −0.105161 | ||||||||
\(973\) | −0.115002 | −0.00368680 | ||||||||
\(974\) | 7.46979 | 0.239347 | ||||||||
\(975\) | −22.3341 | −0.715262 | ||||||||
\(976\) | 28.5475 | 0.913783 | ||||||||
\(977\) | 41.2670 | 1.32025 | 0.660125 | − | 0.751156i | \(-0.270503\pi\) | ||||
0.660125 | + | 0.751156i | \(0.270503\pi\) | |||||||
\(978\) | −71.6084 | −2.28978 | ||||||||
\(979\) | 13.7370 | 0.439037 | ||||||||
\(980\) | −6.69097 | −0.213735 | ||||||||
\(981\) | 1.40300 | 0.0447944 | ||||||||
\(982\) | 56.2873 | 1.79620 | ||||||||
\(983\) | −28.9531 | −0.923459 | −0.461730 | − | 0.887021i | \(-0.652771\pi\) | ||||
−0.461730 | + | 0.887021i | \(0.652771\pi\) | |||||||
\(984\) | 15.4851 | 0.493648 | ||||||||
\(985\) | −18.0524 | −0.575199 | ||||||||
\(986\) | 4.62683 | 0.147348 | ||||||||
\(987\) | 0.755012 | 0.0240323 | ||||||||
\(988\) | −14.1545 | −0.450316 | ||||||||
\(989\) | −4.42189 | −0.140608 | ||||||||
\(990\) | 0.854745 | 0.0271656 | ||||||||
\(991\) | 15.0446 | 0.477909 | 0.238954 | − | 0.971031i | \(-0.423195\pi\) | ||||
0.238954 | + | 0.971031i | \(0.423195\pi\) | |||||||
\(992\) | −1.19539 | −0.0379535 | ||||||||
\(993\) | 47.6053 | 1.51071 | ||||||||
\(994\) | 0.0421337 | 0.00133640 | ||||||||
\(995\) | −15.3338 | −0.486115 | ||||||||
\(996\) | −0.726270 | −0.0230127 | ||||||||
\(997\) | −9.65579 | −0.305802 | −0.152901 | − | 0.988242i | \(-0.548862\pi\) | ||||
−0.152901 | + | 0.988242i | \(0.548862\pi\) | |||||||
\(998\) | −31.2587 | −0.989478 | ||||||||
\(999\) | −48.3179 | −1.52871 |
(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 | 8041.2.a.g.1.20 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.g.1.20 | ✓ | 69 | 1.1 | even | 1 | trivial |