Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.88694 | −1.33427 | −0.667134 | − | 0.744938i | \(-0.732479\pi\) | ||||
−0.667134 | + | 0.744938i | \(0.732479\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.56054 | 0.780270 | ||||||||
\(5\) | −0.846288 | −0.378472 | −0.189236 | − | 0.981932i | \(-0.560601\pi\) | ||||
−0.189236 | + | 0.981932i | \(0.560601\pi\) | |||||||
\(6\) | −1.88694 | −0.770340 | ||||||||
\(7\) | 3.01609 | 1.13998 | 0.569988 | − | 0.821653i | \(-0.306948\pi\) | ||||
0.569988 | + | 0.821653i | \(0.306948\pi\) | |||||||
\(8\) | 0.829236 | 0.293179 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.59689 | 0.504982 | ||||||||
\(11\) | −0.920932 | −0.277672 | −0.138836 | − | 0.990315i | \(-0.544336\pi\) | ||||
−0.138836 | + | 0.990315i | \(0.544336\pi\) | |||||||
\(12\) | 1.56054 | 0.450489 | ||||||||
\(13\) | −3.85540 | −1.06930 | −0.534648 | − | 0.845075i | \(-0.679556\pi\) | ||||
−0.534648 | + | 0.845075i | \(0.679556\pi\) | |||||||
\(14\) | −5.69118 | −1.52103 | ||||||||
\(15\) | −0.846288 | −0.218511 | ||||||||
\(16\) | −4.68580 | −1.17145 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.88694 | −0.444756 | ||||||||
\(19\) | 1.27900 | 0.293423 | 0.146711 | − | 0.989179i | \(-0.453131\pi\) | ||||
0.146711 | + | 0.989179i | \(0.453131\pi\) | |||||||
\(20\) | −1.32067 | −0.295310 | ||||||||
\(21\) | 3.01609 | 0.658165 | ||||||||
\(22\) | 1.73774 | 0.370488 | ||||||||
\(23\) | −0.718821 | −0.149885 | −0.0749423 | − | 0.997188i | \(-0.523877\pi\) | ||||
−0.0749423 | + | 0.997188i | \(0.523877\pi\) | |||||||
\(24\) | 0.829236 | 0.169267 | ||||||||
\(25\) | −4.28380 | −0.856759 | ||||||||
\(26\) | 7.27490 | 1.42673 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.70673 | 0.889488 | ||||||||
\(29\) | 4.88556 | 0.907226 | 0.453613 | − | 0.891199i | \(-0.350135\pi\) | ||||
0.453613 | + | 0.891199i | \(0.350135\pi\) | |||||||
\(30\) | 1.59689 | 0.291552 | ||||||||
\(31\) | −5.70052 | −1.02384 | −0.511922 | − | 0.859032i | \(-0.671066\pi\) | ||||
−0.511922 | + | 0.859032i | \(0.671066\pi\) | |||||||
\(32\) | 7.18334 | 1.26985 | ||||||||
\(33\) | −0.920932 | −0.160314 | ||||||||
\(34\) | −1.88694 | −0.323607 | ||||||||
\(35\) | −2.55248 | −0.431448 | ||||||||
\(36\) | 1.56054 | 0.260090 | ||||||||
\(37\) | 2.37427 | 0.390328 | 0.195164 | − | 0.980771i | \(-0.437476\pi\) | ||||
0.195164 | + | 0.980771i | \(0.437476\pi\) | |||||||
\(38\) | −2.41340 | −0.391505 | ||||||||
\(39\) | −3.85540 | −0.617358 | ||||||||
\(40\) | −0.701773 | −0.110960 | ||||||||
\(41\) | 10.5478 | 1.64729 | 0.823644 | − | 0.567107i | \(-0.191937\pi\) | ||||
0.823644 | + | 0.567107i | \(0.191937\pi\) | |||||||
\(42\) | −5.69118 | −0.878169 | ||||||||
\(43\) | −4.21626 | −0.642974 | −0.321487 | − | 0.946914i | \(-0.604183\pi\) | ||||
−0.321487 | + | 0.946914i | \(0.604183\pi\) | |||||||
\(44\) | −1.43715 | −0.216659 | ||||||||
\(45\) | −0.846288 | −0.126157 | ||||||||
\(46\) | 1.35637 | 0.199986 | ||||||||
\(47\) | 5.34685 | 0.779918 | 0.389959 | − | 0.920832i | \(-0.372489\pi\) | ||||
0.389959 | + | 0.920832i | \(0.372489\pi\) | |||||||
\(48\) | −4.68580 | −0.676336 | ||||||||
\(49\) | 2.09681 | 0.299545 | ||||||||
\(50\) | 8.08326 | 1.14315 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −6.01650 | −0.834339 | ||||||||
\(53\) | −4.27035 | −0.586577 | −0.293289 | − | 0.956024i | \(-0.594750\pi\) | ||||
−0.293289 | + | 0.956024i | \(0.594750\pi\) | |||||||
\(54\) | −1.88694 | −0.256780 | ||||||||
\(55\) | 0.779374 | 0.105091 | ||||||||
\(56\) | 2.50105 | 0.334217 | ||||||||
\(57\) | 1.27900 | 0.169408 | ||||||||
\(58\) | −9.21876 | −1.21048 | ||||||||
\(59\) | 0.996670 | 0.129755 | 0.0648777 | − | 0.997893i | \(-0.479334\pi\) | ||||
0.0648777 | + | 0.997893i | \(0.479334\pi\) | |||||||
\(60\) | −1.32067 | −0.170497 | ||||||||
\(61\) | −2.60886 | −0.334031 | −0.167015 | − | 0.985954i | \(-0.553413\pi\) | ||||
−0.167015 | + | 0.985954i | \(0.553413\pi\) | |||||||
\(62\) | 10.7565 | 1.36608 | ||||||||
\(63\) | 3.01609 | 0.379992 | ||||||||
\(64\) | −4.18293 | −0.522866 | ||||||||
\(65\) | 3.26278 | 0.404698 | ||||||||
\(66\) | 1.73774 | 0.213901 | ||||||||
\(67\) | 10.0505 | 1.22786 | 0.613931 | − | 0.789360i | \(-0.289587\pi\) | ||||
0.613931 | + | 0.789360i | \(0.289587\pi\) | |||||||
\(68\) | 1.56054 | 0.189243 | ||||||||
\(69\) | −0.718821 | −0.0865359 | ||||||||
\(70\) | 4.81638 | 0.575668 | ||||||||
\(71\) | 13.2458 | 1.57199 | 0.785996 | − | 0.618231i | \(-0.212151\pi\) | ||||
0.785996 | + | 0.618231i | \(0.212151\pi\) | |||||||
\(72\) | 0.829236 | 0.0977264 | ||||||||
\(73\) | 9.80450 | 1.14753 | 0.573765 | − | 0.819020i | \(-0.305482\pi\) | ||||
0.573765 | + | 0.819020i | \(0.305482\pi\) | |||||||
\(74\) | −4.48011 | −0.520802 | ||||||||
\(75\) | −4.28380 | −0.494650 | ||||||||
\(76\) | 1.99593 | 0.228949 | ||||||||
\(77\) | −2.77762 | −0.316539 | ||||||||
\(78\) | 7.27490 | 0.823721 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 3.96553 | 0.443360 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −19.9030 | −2.19792 | ||||||||
\(83\) | 14.1014 | 1.54783 | 0.773913 | − | 0.633292i | \(-0.218297\pi\) | ||||
0.773913 | + | 0.633292i | \(0.218297\pi\) | |||||||
\(84\) | 4.70673 | 0.513546 | ||||||||
\(85\) | −0.846288 | −0.0917928 | ||||||||
\(86\) | 7.95583 | 0.857899 | ||||||||
\(87\) | 4.88556 | 0.523787 | ||||||||
\(88\) | −0.763670 | −0.0814075 | ||||||||
\(89\) | 3.60832 | 0.382481 | 0.191240 | − | 0.981543i | \(-0.438749\pi\) | ||||
0.191240 | + | 0.981543i | \(0.438749\pi\) | |||||||
\(90\) | 1.59689 | 0.168327 | ||||||||
\(91\) | −11.6282 | −1.21897 | ||||||||
\(92\) | −1.12175 | −0.116950 | ||||||||
\(93\) | −5.70052 | −0.591117 | ||||||||
\(94\) | −10.0892 | −1.04062 | ||||||||
\(95\) | −1.08240 | −0.111052 | ||||||||
\(96\) | 7.18334 | 0.733146 | ||||||||
\(97\) | 14.0403 | 1.42558 | 0.712788 | − | 0.701380i | \(-0.247432\pi\) | ||||
0.712788 | + | 0.701380i | \(0.247432\pi\) | |||||||
\(98\) | −3.95656 | −0.399673 | ||||||||
\(99\) | −0.920932 | −0.0925572 | ||||||||
\(100\) | −6.68503 | −0.668503 | ||||||||
\(101\) | −0.778050 | −0.0774188 | −0.0387094 | − | 0.999251i | \(-0.512325\pi\) | ||||
−0.0387094 | + | 0.999251i | \(0.512325\pi\) | |||||||
\(102\) | −1.88694 | −0.186835 | ||||||||
\(103\) | −0.390840 | −0.0385106 | −0.0192553 | − | 0.999815i | \(-0.506130\pi\) | ||||
−0.0192553 | + | 0.999815i | \(0.506130\pi\) | |||||||
\(104\) | −3.19704 | −0.313495 | ||||||||
\(105\) | −2.55248 | −0.249097 | ||||||||
\(106\) | 8.05789 | 0.782651 | ||||||||
\(107\) | 2.33288 | 0.225528 | 0.112764 | − | 0.993622i | \(-0.464030\pi\) | ||||
0.112764 | + | 0.993622i | \(0.464030\pi\) | |||||||
\(108\) | 1.56054 | 0.150163 | ||||||||
\(109\) | −17.8437 | −1.70912 | −0.854558 | − | 0.519356i | \(-0.826172\pi\) | ||||
−0.854558 | + | 0.519356i | \(0.826172\pi\) | |||||||
\(110\) | −1.47063 | −0.140219 | ||||||||
\(111\) | 2.37427 | 0.225356 | ||||||||
\(112\) | −14.1328 | −1.33542 | ||||||||
\(113\) | −18.2810 | −1.71973 | −0.859867 | − | 0.510518i | \(-0.829454\pi\) | ||||
−0.859867 | + | 0.510518i | \(0.829454\pi\) | |||||||
\(114\) | −2.41340 | −0.226035 | ||||||||
\(115\) | 0.608330 | 0.0567270 | ||||||||
\(116\) | 7.62411 | 0.707881 | ||||||||
\(117\) | −3.85540 | −0.356432 | ||||||||
\(118\) | −1.88066 | −0.173128 | ||||||||
\(119\) | 3.01609 | 0.276485 | ||||||||
\(120\) | −0.701773 | −0.0640628 | ||||||||
\(121\) | −10.1519 | −0.922899 | ||||||||
\(122\) | 4.92277 | 0.445686 | ||||||||
\(123\) | 10.5478 | 0.951062 | ||||||||
\(124\) | −8.89589 | −0.798875 | ||||||||
\(125\) | 7.85677 | 0.702731 | ||||||||
\(126\) | −5.69118 | −0.507011 | ||||||||
\(127\) | −12.4803 | −1.10745 | −0.553725 | − | 0.832700i | \(-0.686794\pi\) | ||||
−0.553725 | + | 0.832700i | \(0.686794\pi\) | |||||||
\(128\) | −6.47374 | −0.572203 | ||||||||
\(129\) | −4.21626 | −0.371221 | ||||||||
\(130\) | −6.15666 | −0.539975 | ||||||||
\(131\) | −2.16959 | −0.189558 | −0.0947791 | − | 0.995498i | \(-0.530214\pi\) | ||||
−0.0947791 | + | 0.995498i | \(0.530214\pi\) | |||||||
\(132\) | −1.43715 | −0.125088 | ||||||||
\(133\) | 3.85758 | 0.334495 | ||||||||
\(134\) | −18.9646 | −1.63830 | ||||||||
\(135\) | −0.846288 | −0.0728369 | ||||||||
\(136\) | 0.829236 | 0.0711064 | ||||||||
\(137\) | 17.0324 | 1.45517 | 0.727587 | − | 0.686015i | \(-0.240642\pi\) | ||||
0.727587 | + | 0.686015i | \(0.240642\pi\) | |||||||
\(138\) | 1.35637 | 0.115462 | ||||||||
\(139\) | 3.52916 | 0.299340 | 0.149670 | − | 0.988736i | \(-0.452179\pi\) | ||||
0.149670 | + | 0.988736i | \(0.452179\pi\) | |||||||
\(140\) | −3.98325 | −0.336646 | ||||||||
\(141\) | 5.34685 | 0.450286 | ||||||||
\(142\) | −24.9941 | −2.09746 | ||||||||
\(143\) | 3.55056 | 0.296913 | ||||||||
\(144\) | −4.68580 | −0.390483 | ||||||||
\(145\) | −4.13459 | −0.343359 | ||||||||
\(146\) | −18.5005 | −1.53111 | ||||||||
\(147\) | 2.09681 | 0.172942 | ||||||||
\(148\) | 3.70514 | 0.304561 | ||||||||
\(149\) | 10.4477 | 0.855912 | 0.427956 | − | 0.903800i | \(-0.359234\pi\) | ||||
0.427956 | + | 0.903800i | \(0.359234\pi\) | |||||||
\(150\) | 8.08326 | 0.659996 | ||||||||
\(151\) | 20.4933 | 1.66772 | 0.833862 | − | 0.551972i | \(-0.186125\pi\) | ||||
0.833862 | + | 0.551972i | \(0.186125\pi\) | |||||||
\(152\) | 1.06059 | 0.0860255 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 5.24119 | 0.422347 | ||||||||
\(155\) | 4.82429 | 0.387496 | ||||||||
\(156\) | −6.01650 | −0.481706 | ||||||||
\(157\) | −5.04399 | −0.402554 | −0.201277 | − | 0.979534i | \(-0.564509\pi\) | ||||
−0.201277 | + | 0.979534i | \(0.564509\pi\) | |||||||
\(158\) | −1.88694 | −0.150117 | ||||||||
\(159\) | −4.27035 | −0.338661 | ||||||||
\(160\) | −6.07917 | −0.480601 | ||||||||
\(161\) | −2.16803 | −0.170865 | ||||||||
\(162\) | −1.88694 | −0.148252 | ||||||||
\(163\) | 19.3163 | 1.51297 | 0.756486 | − | 0.654010i | \(-0.226915\pi\) | ||||
0.756486 | + | 0.654010i | \(0.226915\pi\) | |||||||
\(164\) | 16.4602 | 1.28533 | ||||||||
\(165\) | 0.779374 | 0.0606742 | ||||||||
\(166\) | −26.6084 | −2.06521 | ||||||||
\(167\) | −22.6179 | −1.75023 | −0.875113 | − | 0.483919i | \(-0.839213\pi\) | ||||
−0.875113 | + | 0.483919i | \(0.839213\pi\) | |||||||
\(168\) | 2.50105 | 0.192960 | ||||||||
\(169\) | 1.86410 | 0.143392 | ||||||||
\(170\) | 1.59689 | 0.122476 | ||||||||
\(171\) | 1.27900 | 0.0978076 | ||||||||
\(172\) | −6.57964 | −0.501693 | ||||||||
\(173\) | −5.37195 | −0.408422 | −0.204211 | − | 0.978927i | \(-0.565463\pi\) | ||||
−0.204211 | + | 0.978927i | \(0.565463\pi\) | |||||||
\(174\) | −9.21876 | −0.698872 | ||||||||
\(175\) | −12.9203 | −0.976685 | ||||||||
\(176\) | 4.31530 | 0.325278 | ||||||||
\(177\) | 0.996670 | 0.0749143 | ||||||||
\(178\) | −6.80867 | −0.510332 | ||||||||
\(179\) | 17.5000 | 1.30801 | 0.654006 | − | 0.756490i | \(-0.273087\pi\) | ||||
0.654006 | + | 0.756490i | \(0.273087\pi\) | |||||||
\(180\) | −1.32067 | −0.0984366 | ||||||||
\(181\) | 25.4752 | 1.89356 | 0.946778 | − | 0.321889i | \(-0.104318\pi\) | ||||
0.946778 | + | 0.321889i | \(0.104318\pi\) | |||||||
\(182\) | 21.9418 | 1.62643 | ||||||||
\(183\) | −2.60886 | −0.192853 | ||||||||
\(184\) | −0.596072 | −0.0439430 | ||||||||
\(185\) | −2.00932 | −0.147728 | ||||||||
\(186\) | 10.7565 | 0.788708 | ||||||||
\(187\) | −0.920932 | −0.0673452 | ||||||||
\(188\) | 8.34397 | 0.608546 | ||||||||
\(189\) | 3.01609 | 0.219388 | ||||||||
\(190\) | 2.04243 | 0.148173 | ||||||||
\(191\) | −4.97527 | −0.359998 | −0.179999 | − | 0.983667i | \(-0.557609\pi\) | ||||
−0.179999 | + | 0.983667i | \(0.557609\pi\) | |||||||
\(192\) | −4.18293 | −0.301877 | ||||||||
\(193\) | 8.95833 | 0.644835 | 0.322417 | − | 0.946598i | \(-0.395505\pi\) | ||||
0.322417 | + | 0.946598i | \(0.395505\pi\) | |||||||
\(194\) | −26.4932 | −1.90210 | ||||||||
\(195\) | 3.26278 | 0.233652 | ||||||||
\(196\) | 3.27216 | 0.233726 | ||||||||
\(197\) | 12.5153 | 0.891678 | 0.445839 | − | 0.895113i | \(-0.352905\pi\) | ||||
0.445839 | + | 0.895113i | \(0.352905\pi\) | |||||||
\(198\) | 1.73774 | 0.123496 | ||||||||
\(199\) | −25.9024 | −1.83617 | −0.918086 | − | 0.396381i | \(-0.870266\pi\) | ||||
−0.918086 | + | 0.396381i | \(0.870266\pi\) | |||||||
\(200\) | −3.55228 | −0.251184 | ||||||||
\(201\) | 10.0505 | 0.708906 | ||||||||
\(202\) | 1.46813 | 0.103297 | ||||||||
\(203\) | 14.7353 | 1.03422 | ||||||||
\(204\) | 1.56054 | 0.109260 | ||||||||
\(205\) | −8.92647 | −0.623452 | ||||||||
\(206\) | 0.737491 | 0.0513835 | ||||||||
\(207\) | −0.718821 | −0.0499615 | ||||||||
\(208\) | 18.0656 | 1.25262 | ||||||||
\(209\) | −1.17787 | −0.0814752 | ||||||||
\(210\) | 4.81638 | 0.332362 | ||||||||
\(211\) | 12.2946 | 0.846397 | 0.423199 | − | 0.906037i | \(-0.360907\pi\) | ||||
0.423199 | + | 0.906037i | \(0.360907\pi\) | |||||||
\(212\) | −6.66404 | −0.457688 | ||||||||
\(213\) | 13.2458 | 0.907590 | ||||||||
\(214\) | −4.40201 | −0.300915 | ||||||||
\(215\) | 3.56817 | 0.243347 | ||||||||
\(216\) | 0.829236 | 0.0564224 | ||||||||
\(217\) | −17.1933 | −1.16716 | ||||||||
\(218\) | 33.6700 | 2.28042 | ||||||||
\(219\) | 9.80450 | 0.662527 | ||||||||
\(220\) | 1.21624 | 0.0819991 | ||||||||
\(221\) | −3.85540 | −0.259342 | ||||||||
\(222\) | −4.48011 | −0.300685 | ||||||||
\(223\) | 0.593490 | 0.0397430 | 0.0198715 | − | 0.999803i | \(-0.493674\pi\) | ||||
0.0198715 | + | 0.999803i | \(0.493674\pi\) | |||||||
\(224\) | 21.6656 | 1.44759 | ||||||||
\(225\) | −4.28380 | −0.285586 | ||||||||
\(226\) | 34.4952 | 2.29459 | ||||||||
\(227\) | −18.5422 | −1.23069 | −0.615344 | − | 0.788259i | \(-0.710983\pi\) | ||||
−0.615344 | + | 0.788259i | \(0.710983\pi\) | |||||||
\(228\) | 1.99593 | 0.132184 | ||||||||
\(229\) | 7.01948 | 0.463860 | 0.231930 | − | 0.972732i | \(-0.425496\pi\) | ||||
0.231930 | + | 0.972732i | \(0.425496\pi\) | |||||||
\(230\) | −1.14788 | −0.0756891 | ||||||||
\(231\) | −2.77762 | −0.182754 | ||||||||
\(232\) | 4.05128 | 0.265980 | ||||||||
\(233\) | −17.8632 | −1.17026 | −0.585130 | − | 0.810940i | \(-0.698956\pi\) | ||||
−0.585130 | + | 0.810940i | \(0.698956\pi\) | |||||||
\(234\) | 7.27490 | 0.475575 | ||||||||
\(235\) | −4.52497 | −0.295177 | ||||||||
\(236\) | 1.55534 | 0.101244 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | −5.69118 | −0.368905 | ||||||||
\(239\) | −6.45389 | −0.417467 | −0.208734 | − | 0.977973i | \(-0.566934\pi\) | ||||
−0.208734 | + | 0.977973i | \(0.566934\pi\) | |||||||
\(240\) | 3.96553 | 0.255974 | ||||||||
\(241\) | −23.6366 | −1.52257 | −0.761285 | − | 0.648418i | \(-0.775431\pi\) | ||||
−0.761285 | + | 0.648418i | \(0.775431\pi\) | |||||||
\(242\) | 19.1560 | 1.23139 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −4.07123 | −0.260634 | ||||||||
\(245\) | −1.77451 | −0.113369 | ||||||||
\(246\) | −19.9030 | −1.26897 | ||||||||
\(247\) | −4.93106 | −0.313756 | ||||||||
\(248\) | −4.72708 | −0.300170 | ||||||||
\(249\) | 14.1014 | 0.893637 | ||||||||
\(250\) | −14.8252 | −0.937630 | ||||||||
\(251\) | 15.7470 | 0.993942 | 0.496971 | − | 0.867767i | \(-0.334445\pi\) | ||||
0.496971 | + | 0.867767i | \(0.334445\pi\) | |||||||
\(252\) | 4.70673 | 0.296496 | ||||||||
\(253\) | 0.661986 | 0.0416187 | ||||||||
\(254\) | 23.5496 | 1.47763 | ||||||||
\(255\) | −0.846288 | −0.0529966 | ||||||||
\(256\) | 20.5814 | 1.28634 | ||||||||
\(257\) | 16.7472 | 1.04466 | 0.522331 | − | 0.852743i | \(-0.325063\pi\) | ||||
0.522331 | + | 0.852743i | \(0.325063\pi\) | |||||||
\(258\) | 7.95583 | 0.495308 | ||||||||
\(259\) | 7.16102 | 0.444964 | ||||||||
\(260\) | 5.09169 | 0.315773 | ||||||||
\(261\) | 4.88556 | 0.302409 | ||||||||
\(262\) | 4.09389 | 0.252921 | ||||||||
\(263\) | −9.30111 | −0.573531 | −0.286766 | − | 0.958001i | \(-0.592580\pi\) | ||||
−0.286766 | + | 0.958001i | \(0.592580\pi\) | |||||||
\(264\) | −0.763670 | −0.0470007 | ||||||||
\(265\) | 3.61394 | 0.222003 | ||||||||
\(266\) | −7.27903 | −0.446306 | ||||||||
\(267\) | 3.60832 | 0.220825 | ||||||||
\(268\) | 15.6842 | 0.958063 | ||||||||
\(269\) | 19.0596 | 1.16208 | 0.581041 | − | 0.813874i | \(-0.302646\pi\) | ||||
0.581041 | + | 0.813874i | \(0.302646\pi\) | |||||||
\(270\) | 1.59689 | 0.0971839 | ||||||||
\(271\) | 29.3396 | 1.78225 | 0.891127 | − | 0.453754i | \(-0.149915\pi\) | ||||
0.891127 | + | 0.453754i | \(0.149915\pi\) | |||||||
\(272\) | −4.68580 | −0.284118 | ||||||||
\(273\) | −11.6282 | −0.703773 | ||||||||
\(274\) | −32.1391 | −1.94159 | ||||||||
\(275\) | 3.94509 | 0.237898 | ||||||||
\(276\) | −1.12175 | −0.0675213 | ||||||||
\(277\) | 31.4076 | 1.88710 | 0.943550 | − | 0.331231i | \(-0.107464\pi\) | ||||
0.943550 | + | 0.331231i | \(0.107464\pi\) | |||||||
\(278\) | −6.65931 | −0.399399 | ||||||||
\(279\) | −5.70052 | −0.341281 | ||||||||
\(280\) | −2.11661 | −0.126492 | ||||||||
\(281\) | 17.1452 | 1.02279 | 0.511397 | − | 0.859344i | \(-0.329128\pi\) | ||||
0.511397 | + | 0.859344i | \(0.329128\pi\) | |||||||
\(282\) | −10.0892 | −0.600802 | ||||||||
\(283\) | −10.0764 | −0.598981 | −0.299490 | − | 0.954099i | \(-0.596817\pi\) | ||||
−0.299490 | + | 0.954099i | \(0.596817\pi\) | |||||||
\(284\) | 20.6707 | 1.22658 | ||||||||
\(285\) | −1.08240 | −0.0641160 | ||||||||
\(286\) | −6.69969 | −0.396161 | ||||||||
\(287\) | 31.8131 | 1.87787 | ||||||||
\(288\) | 7.18334 | 0.423282 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 7.80173 | 0.458133 | ||||||||
\(291\) | 14.0403 | 0.823056 | ||||||||
\(292\) | 15.3003 | 0.895383 | ||||||||
\(293\) | −15.1049 | −0.882438 | −0.441219 | − | 0.897399i | \(-0.645454\pi\) | ||||
−0.441219 | + | 0.897399i | \(0.645454\pi\) | |||||||
\(294\) | −3.95656 | −0.230751 | ||||||||
\(295\) | −0.843470 | −0.0491087 | ||||||||
\(296\) | 1.96883 | 0.114436 | ||||||||
\(297\) | −0.920932 | −0.0534379 | ||||||||
\(298\) | −19.7142 | −1.14202 | ||||||||
\(299\) | 2.77134 | 0.160271 | ||||||||
\(300\) | −6.68503 | −0.385960 | ||||||||
\(301\) | −12.7166 | −0.732975 | ||||||||
\(302\) | −38.6697 | −2.22519 | ||||||||
\(303\) | −0.778050 | −0.0446978 | ||||||||
\(304\) | −5.99314 | −0.343730 | ||||||||
\(305\) | 2.20785 | 0.126421 | ||||||||
\(306\) | −1.88694 | −0.107869 | ||||||||
\(307\) | −5.28167 | −0.301441 | −0.150720 | − | 0.988576i | \(-0.548159\pi\) | ||||
−0.150720 | + | 0.988576i | \(0.548159\pi\) | |||||||
\(308\) | −4.33458 | −0.246986 | ||||||||
\(309\) | −0.390840 | −0.0222341 | ||||||||
\(310\) | −9.10313 | −0.517023 | ||||||||
\(311\) | −19.8699 | −1.12672 | −0.563359 | − | 0.826213i | \(-0.690491\pi\) | ||||
−0.563359 | + | 0.826213i | \(0.690491\pi\) | |||||||
\(312\) | −3.19704 | −0.180997 | ||||||||
\(313\) | 17.3863 | 0.982734 | 0.491367 | − | 0.870953i | \(-0.336497\pi\) | ||||
0.491367 | + | 0.870953i | \(0.336497\pi\) | |||||||
\(314\) | 9.51770 | 0.537115 | ||||||||
\(315\) | −2.55248 | −0.143816 | ||||||||
\(316\) | 1.56054 | 0.0877872 | ||||||||
\(317\) | 30.2204 | 1.69735 | 0.848674 | − | 0.528916i | \(-0.177401\pi\) | ||||
0.848674 | + | 0.528916i | \(0.177401\pi\) | |||||||
\(318\) | 8.05789 | 0.451864 | ||||||||
\(319\) | −4.49927 | −0.251911 | ||||||||
\(320\) | 3.53997 | 0.197890 | ||||||||
\(321\) | 2.33288 | 0.130209 | ||||||||
\(322\) | 4.09094 | 0.227979 | ||||||||
\(323\) | 1.27900 | 0.0711655 | ||||||||
\(324\) | 1.56054 | 0.0866966 | ||||||||
\(325\) | 16.5157 | 0.916129 | ||||||||
\(326\) | −36.4487 | −2.01871 | ||||||||
\(327\) | −17.8437 | −0.986759 | ||||||||
\(328\) | 8.74661 | 0.482951 | ||||||||
\(329\) | 16.1266 | 0.889088 | ||||||||
\(330\) | −1.47063 | −0.0809556 | ||||||||
\(331\) | −24.6484 | −1.35480 | −0.677400 | − | 0.735615i | \(-0.736893\pi\) | ||||
−0.677400 | + | 0.735615i | \(0.736893\pi\) | |||||||
\(332\) | 22.0057 | 1.20772 | ||||||||
\(333\) | 2.37427 | 0.130109 | ||||||||
\(334\) | 42.6786 | 2.33527 | ||||||||
\(335\) | −8.50560 | −0.464711 | ||||||||
\(336\) | −14.1328 | −0.771007 | ||||||||
\(337\) | 2.38693 | 0.130024 | 0.0650121 | − | 0.997884i | \(-0.479291\pi\) | ||||
0.0650121 | + | 0.997884i | \(0.479291\pi\) | |||||||
\(338\) | −3.51745 | −0.191324 | ||||||||
\(339\) | −18.2810 | −0.992889 | ||||||||
\(340\) | −1.32067 | −0.0716231 | ||||||||
\(341\) | 5.24980 | 0.284292 | ||||||||
\(342\) | −2.41340 | −0.130502 | ||||||||
\(343\) | −14.7885 | −0.798502 | ||||||||
\(344\) | −3.49628 | −0.188507 | ||||||||
\(345\) | 0.608330 | 0.0327514 | ||||||||
\(346\) | 10.1365 | 0.544944 | ||||||||
\(347\) | 12.7112 | 0.682372 | 0.341186 | − | 0.939996i | \(-0.389171\pi\) | ||||
0.341186 | + | 0.939996i | \(0.389171\pi\) | |||||||
\(348\) | 7.62411 | 0.408695 | ||||||||
\(349\) | −13.8757 | −0.742747 | −0.371374 | − | 0.928484i | \(-0.621113\pi\) | ||||
−0.371374 | + | 0.928484i | \(0.621113\pi\) | |||||||
\(350\) | 24.3799 | 1.30316 | ||||||||
\(351\) | −3.85540 | −0.205786 | ||||||||
\(352\) | −6.61537 | −0.352600 | ||||||||
\(353\) | 4.35714 | 0.231907 | 0.115954 | − | 0.993255i | \(-0.463008\pi\) | ||||
0.115954 | + | 0.993255i | \(0.463008\pi\) | |||||||
\(354\) | −1.88066 | −0.0999558 | ||||||||
\(355\) | −11.2098 | −0.594954 | ||||||||
\(356\) | 5.63092 | 0.298438 | ||||||||
\(357\) | 3.01609 | 0.159629 | ||||||||
\(358\) | −33.0214 | −1.74524 | ||||||||
\(359\) | −1.47835 | −0.0780242 | −0.0390121 | − | 0.999239i | \(-0.512421\pi\) | ||||
−0.0390121 | + | 0.999239i | \(0.512421\pi\) | |||||||
\(360\) | −0.701773 | −0.0369867 | ||||||||
\(361\) | −17.3642 | −0.913903 | ||||||||
\(362\) | −48.0701 | −2.52651 | ||||||||
\(363\) | −10.1519 | −0.532836 | ||||||||
\(364\) | −18.1463 | −0.951126 | ||||||||
\(365\) | −8.29743 | −0.434308 | ||||||||
\(366\) | 4.92277 | 0.257317 | ||||||||
\(367\) | 1.22044 | 0.0637064 | 0.0318532 | − | 0.999493i | \(-0.489859\pi\) | ||||
0.0318532 | + | 0.999493i | \(0.489859\pi\) | |||||||
\(368\) | 3.36825 | 0.175582 | ||||||||
\(369\) | 10.5478 | 0.549096 | ||||||||
\(370\) | 3.79146 | 0.197109 | ||||||||
\(371\) | −12.8798 | −0.668684 | ||||||||
\(372\) | −8.89589 | −0.461230 | ||||||||
\(373\) | 30.4212 | 1.57515 | 0.787574 | − | 0.616220i | \(-0.211337\pi\) | ||||
0.787574 | + | 0.616220i | \(0.211337\pi\) | |||||||
\(374\) | 1.73774 | 0.0898566 | ||||||||
\(375\) | 7.85677 | 0.405722 | ||||||||
\(376\) | 4.43380 | 0.228656 | ||||||||
\(377\) | −18.8358 | −0.970093 | ||||||||
\(378\) | −5.69118 | −0.292723 | ||||||||
\(379\) | −29.8919 | −1.53545 | −0.767723 | − | 0.640782i | \(-0.778610\pi\) | ||||
−0.767723 | + | 0.640782i | \(0.778610\pi\) | |||||||
\(380\) | −1.68913 | −0.0866507 | ||||||||
\(381\) | −12.4803 | −0.639386 | ||||||||
\(382\) | 9.38803 | 0.480334 | ||||||||
\(383\) | 32.0422 | 1.63728 | 0.818640 | − | 0.574307i | \(-0.194728\pi\) | ||||
0.818640 | + | 0.574307i | \(0.194728\pi\) | |||||||
\(384\) | −6.47374 | −0.330362 | ||||||||
\(385\) | 2.35066 | 0.119801 | ||||||||
\(386\) | −16.9038 | −0.860382 | ||||||||
\(387\) | −4.21626 | −0.214325 | ||||||||
\(388\) | 21.9104 | 1.11233 | ||||||||
\(389\) | 35.9615 | 1.82332 | 0.911659 | − | 0.410947i | \(-0.134802\pi\) | ||||
0.911659 | + | 0.410947i | \(0.134802\pi\) | |||||||
\(390\) | −6.15666 | −0.311755 | ||||||||
\(391\) | −0.718821 | −0.0363523 | ||||||||
\(392\) | 1.73875 | 0.0878203 | ||||||||
\(393\) | −2.16959 | −0.109441 | ||||||||
\(394\) | −23.6156 | −1.18974 | ||||||||
\(395\) | −0.846288 | −0.0425814 | ||||||||
\(396\) | −1.43715 | −0.0722195 | ||||||||
\(397\) | 31.2960 | 1.57070 | 0.785351 | − | 0.619051i | \(-0.212483\pi\) | ||||
0.785351 | + | 0.619051i | \(0.212483\pi\) | |||||||
\(398\) | 48.8763 | 2.44995 | ||||||||
\(399\) | 3.85758 | 0.193121 | ||||||||
\(400\) | 20.0730 | 1.00365 | ||||||||
\(401\) | −8.29049 | −0.414007 | −0.207004 | − | 0.978340i | \(-0.566371\pi\) | ||||
−0.207004 | + | 0.978340i | \(0.566371\pi\) | |||||||
\(402\) | −18.9646 | −0.945870 | ||||||||
\(403\) | 21.9778 | 1.09479 | ||||||||
\(404\) | −1.21418 | −0.0604076 | ||||||||
\(405\) | −0.846288 | −0.0420524 | ||||||||
\(406\) | −27.8046 | −1.37992 | ||||||||
\(407\) | −2.18654 | −0.108383 | ||||||||
\(408\) | 0.829236 | 0.0410533 | ||||||||
\(409\) | −10.0389 | −0.496390 | −0.248195 | − | 0.968710i | \(-0.579837\pi\) | ||||
−0.248195 | + | 0.968710i | \(0.579837\pi\) | |||||||
\(410\) | 16.8437 | 0.831851 | ||||||||
\(411\) | 17.0324 | 0.840146 | ||||||||
\(412\) | −0.609921 | −0.0300487 | ||||||||
\(413\) | 3.00605 | 0.147918 | ||||||||
\(414\) | 1.35637 | 0.0666620 | ||||||||
\(415\) | −11.9338 | −0.585808 | ||||||||
\(416\) | −27.6946 | −1.35784 | ||||||||
\(417\) | 3.52916 | 0.172824 | ||||||||
\(418\) | 2.22257 | 0.108710 | ||||||||
\(419\) | 17.1659 | 0.838611 | 0.419305 | − | 0.907845i | \(-0.362274\pi\) | ||||
0.419305 | + | 0.907845i | \(0.362274\pi\) | |||||||
\(420\) | −3.98325 | −0.194363 | ||||||||
\(421\) | −7.71328 | −0.375922 | −0.187961 | − | 0.982176i | \(-0.560188\pi\) | ||||
−0.187961 | + | 0.982176i | \(0.560188\pi\) | |||||||
\(422\) | −23.1992 | −1.12932 | ||||||||
\(423\) | 5.34685 | 0.259973 | ||||||||
\(424\) | −3.54113 | −0.171972 | ||||||||
\(425\) | −4.28380 | −0.207795 | ||||||||
\(426\) | −24.9941 | −1.21097 | ||||||||
\(427\) | −7.86857 | −0.380787 | ||||||||
\(428\) | 3.64056 | 0.175973 | ||||||||
\(429\) | 3.55056 | 0.171423 | ||||||||
\(430\) | −6.73293 | −0.324691 | ||||||||
\(431\) | 21.7270 | 1.04655 | 0.523275 | − | 0.852164i | \(-0.324710\pi\) | ||||
0.523275 | + | 0.852164i | \(0.324710\pi\) | |||||||
\(432\) | −4.68580 | −0.225445 | ||||||||
\(433\) | 28.5630 | 1.37265 | 0.686326 | − | 0.727294i | \(-0.259222\pi\) | ||||
0.686326 | + | 0.727294i | \(0.259222\pi\) | |||||||
\(434\) | 32.4427 | 1.55730 | ||||||||
\(435\) | −4.13459 | −0.198239 | ||||||||
\(436\) | −27.8458 | −1.33357 | ||||||||
\(437\) | −0.919373 | −0.0439796 | ||||||||
\(438\) | −18.5005 | −0.883988 | ||||||||
\(439\) | −16.0063 | −0.763940 | −0.381970 | − | 0.924175i | \(-0.624754\pi\) | ||||
−0.381970 | + | 0.924175i | \(0.624754\pi\) | |||||||
\(440\) | 0.646285 | 0.0308104 | ||||||||
\(441\) | 2.09681 | 0.0998482 | ||||||||
\(442\) | 7.27490 | 0.346032 | ||||||||
\(443\) | 15.3898 | 0.731191 | 0.365596 | − | 0.930774i | \(-0.380865\pi\) | ||||
0.365596 | + | 0.930774i | \(0.380865\pi\) | |||||||
\(444\) | 3.70514 | 0.175838 | ||||||||
\(445\) | −3.05368 | −0.144758 | ||||||||
\(446\) | −1.11988 | −0.0530278 | ||||||||
\(447\) | 10.4477 | 0.494161 | ||||||||
\(448\) | −12.6161 | −0.596055 | ||||||||
\(449\) | −15.7432 | −0.742966 | −0.371483 | − | 0.928440i | \(-0.621151\pi\) | ||||
−0.371483 | + | 0.928440i | \(0.621151\pi\) | |||||||
\(450\) | 8.08326 | 0.381049 | ||||||||
\(451\) | −9.71380 | −0.457405 | ||||||||
\(452\) | −28.5283 | −1.34186 | ||||||||
\(453\) | 20.4933 | 0.962861 | ||||||||
\(454\) | 34.9880 | 1.64207 | ||||||||
\(455\) | 9.84084 | 0.461346 | ||||||||
\(456\) | 1.06059 | 0.0496668 | ||||||||
\(457\) | 34.9860 | 1.63658 | 0.818289 | − | 0.574807i | \(-0.194923\pi\) | ||||
0.818289 | + | 0.574807i | \(0.194923\pi\) | |||||||
\(458\) | −13.2453 | −0.618914 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 0.949322 | 0.0442624 | ||||||||
\(461\) | −28.0810 | −1.30786 | −0.653931 | − | 0.756554i | \(-0.726882\pi\) | ||||
−0.653931 | + | 0.756554i | \(0.726882\pi\) | |||||||
\(462\) | 5.24119 | 0.243842 | ||||||||
\(463\) | −31.6142 | −1.46923 | −0.734617 | − | 0.678482i | \(-0.762638\pi\) | ||||
−0.734617 | + | 0.678482i | \(0.762638\pi\) | |||||||
\(464\) | −22.8927 | −1.06277 | ||||||||
\(465\) | 4.82429 | 0.223721 | ||||||||
\(466\) | 33.7068 | 1.56144 | ||||||||
\(467\) | −10.2872 | −0.476037 | −0.238018 | − | 0.971261i | \(-0.576498\pi\) | ||||
−0.238018 | + | 0.971261i | \(0.576498\pi\) | |||||||
\(468\) | −6.01650 | −0.278113 | ||||||||
\(469\) | 30.3132 | 1.39973 | ||||||||
\(470\) | 8.53835 | 0.393845 | ||||||||
\(471\) | −5.04399 | −0.232415 | ||||||||
\(472\) | 0.826475 | 0.0380416 | ||||||||
\(473\) | 3.88289 | 0.178536 | ||||||||
\(474\) | −1.88694 | −0.0866700 | ||||||||
\(475\) | −5.47898 | −0.251393 | ||||||||
\(476\) | 4.70673 | 0.215733 | ||||||||
\(477\) | −4.27035 | −0.195526 | ||||||||
\(478\) | 12.1781 | 0.557013 | ||||||||
\(479\) | −8.35097 | −0.381566 | −0.190783 | − | 0.981632i | \(-0.561103\pi\) | ||||
−0.190783 | + | 0.981632i | \(0.561103\pi\) | |||||||
\(480\) | −6.07917 | −0.277475 | ||||||||
\(481\) | −9.15377 | −0.417376 | ||||||||
\(482\) | 44.6009 | 2.03152 | ||||||||
\(483\) | −2.16803 | −0.0986488 | ||||||||
\(484\) | −15.8424 | −0.720110 | ||||||||
\(485\) | −11.8821 | −0.539540 | ||||||||
\(486\) | −1.88694 | −0.0855933 | ||||||||
\(487\) | −24.0747 | −1.09093 | −0.545465 | − | 0.838134i | \(-0.683647\pi\) | ||||
−0.545465 | + | 0.838134i | \(0.683647\pi\) | |||||||
\(488\) | −2.16336 | −0.0979309 | ||||||||
\(489\) | 19.3163 | 0.873515 | ||||||||
\(490\) | 3.34839 | 0.151265 | ||||||||
\(491\) | 19.0373 | 0.859142 | 0.429571 | − | 0.903033i | \(-0.358665\pi\) | ||||
0.429571 | + | 0.903033i | \(0.358665\pi\) | |||||||
\(492\) | 16.4602 | 0.742085 | ||||||||
\(493\) | 4.88556 | 0.220035 | ||||||||
\(494\) | 9.30461 | 0.418634 | ||||||||
\(495\) | 0.779374 | 0.0350303 | ||||||||
\(496\) | 26.7115 | 1.19938 | ||||||||
\(497\) | 39.9507 | 1.79203 | ||||||||
\(498\) | −26.6084 | −1.19235 | ||||||||
\(499\) | −12.3272 | −0.551840 | −0.275920 | − | 0.961181i | \(-0.588983\pi\) | ||||
−0.275920 | + | 0.961181i | \(0.588983\pi\) | |||||||
\(500\) | 12.2608 | 0.548319 | ||||||||
\(501\) | −22.6179 | −1.01049 | ||||||||
\(502\) | −29.7136 | −1.32619 | ||||||||
\(503\) | 6.74107 | 0.300569 | 0.150285 | − | 0.988643i | \(-0.451981\pi\) | ||||
0.150285 | + | 0.988643i | \(0.451981\pi\) | |||||||
\(504\) | 2.50105 | 0.111406 | ||||||||
\(505\) | 0.658454 | 0.0293008 | ||||||||
\(506\) | −1.24913 | −0.0555304 | ||||||||
\(507\) | 1.86410 | 0.0827877 | ||||||||
\(508\) | −19.4760 | −0.864109 | ||||||||
\(509\) | 25.2221 | 1.11795 | 0.558975 | − | 0.829184i | \(-0.311195\pi\) | ||||
0.558975 | + | 0.829184i | \(0.311195\pi\) | |||||||
\(510\) | 1.59689 | 0.0707117 | ||||||||
\(511\) | 29.5713 | 1.30816 | ||||||||
\(512\) | −25.8884 | −1.14412 | ||||||||
\(513\) | 1.27900 | 0.0564693 | ||||||||
\(514\) | −31.6009 | −1.39386 | ||||||||
\(515\) | 0.330763 | 0.0145752 | ||||||||
\(516\) | −6.57964 | −0.289653 | ||||||||
\(517\) | −4.92409 | −0.216561 | ||||||||
\(518\) | −13.5124 | −0.593701 | ||||||||
\(519\) | −5.37195 | −0.235802 | ||||||||
\(520\) | 2.70561 | 0.118649 | ||||||||
\(521\) | 6.19871 | 0.271570 | 0.135785 | − | 0.990738i | \(-0.456644\pi\) | ||||
0.135785 | + | 0.990738i | \(0.456644\pi\) | |||||||
\(522\) | −9.21876 | −0.403494 | ||||||||
\(523\) | −12.1289 | −0.530361 | −0.265181 | − | 0.964199i | \(-0.585432\pi\) | ||||
−0.265181 | + | 0.964199i | \(0.585432\pi\) | |||||||
\(524\) | −3.38573 | −0.147906 | ||||||||
\(525\) | −12.9203 | −0.563889 | ||||||||
\(526\) | 17.5506 | 0.765244 | ||||||||
\(527\) | −5.70052 | −0.248319 | ||||||||
\(528\) | 4.31530 | 0.187799 | ||||||||
\(529\) | −22.4833 | −0.977535 | ||||||||
\(530\) | −6.81929 | −0.296211 | ||||||||
\(531\) | 0.996670 | 0.0432518 | ||||||||
\(532\) | 6.01991 | 0.260996 | ||||||||
\(533\) | −40.6659 | −1.76144 | ||||||||
\(534\) | −6.80867 | −0.294640 | ||||||||
\(535\) | −1.97429 | −0.0853561 | ||||||||
\(536\) | 8.33422 | 0.359983 | ||||||||
\(537\) | 17.5000 | 0.755181 | ||||||||
\(538\) | −35.9642 | −1.55053 | ||||||||
\(539\) | −1.93102 | −0.0831750 | ||||||||
\(540\) | −1.32067 | −0.0568324 | ||||||||
\(541\) | 37.1875 | 1.59881 | 0.799407 | − | 0.600789i | \(-0.205147\pi\) | ||||
0.799407 | + | 0.600789i | \(0.205147\pi\) | |||||||
\(542\) | −55.3621 | −2.37800 | ||||||||
\(543\) | 25.4752 | 1.09324 | ||||||||
\(544\) | 7.18334 | 0.307983 | ||||||||
\(545\) | 15.1009 | 0.646852 | ||||||||
\(546\) | 21.9418 | 0.939021 | ||||||||
\(547\) | 42.8321 | 1.83137 | 0.915685 | − | 0.401897i | \(-0.131649\pi\) | ||||
0.915685 | + | 0.401897i | \(0.131649\pi\) | |||||||
\(548\) | 26.5797 | 1.13543 | ||||||||
\(549\) | −2.60886 | −0.111344 | ||||||||
\(550\) | −7.44414 | −0.317419 | ||||||||
\(551\) | 6.24864 | 0.266201 | ||||||||
\(552\) | −0.596072 | −0.0253705 | ||||||||
\(553\) | 3.01609 | 0.128257 | ||||||||
\(554\) | −59.2642 | −2.51790 | ||||||||
\(555\) | −2.00932 | −0.0852908 | ||||||||
\(556\) | 5.50740 | 0.233566 | ||||||||
\(557\) | 2.89913 | 0.122840 | 0.0614201 | − | 0.998112i | \(-0.480437\pi\) | ||||
0.0614201 | + | 0.998112i | \(0.480437\pi\) | |||||||
\(558\) | 10.7565 | 0.455361 | ||||||||
\(559\) | 16.2554 | 0.687529 | ||||||||
\(560\) | 11.9604 | 0.505420 | ||||||||
\(561\) | −0.920932 | −0.0388818 | ||||||||
\(562\) | −32.3519 | −1.36468 | ||||||||
\(563\) | 13.9220 | 0.586741 | 0.293370 | − | 0.955999i | \(-0.405223\pi\) | ||||
0.293370 | + | 0.955999i | \(0.405223\pi\) | |||||||
\(564\) | 8.34397 | 0.351344 | ||||||||
\(565\) | 15.4710 | 0.650871 | ||||||||
\(566\) | 19.0136 | 0.799201 | ||||||||
\(567\) | 3.01609 | 0.126664 | ||||||||
\(568\) | 10.9839 | 0.460875 | ||||||||
\(569\) | −5.20319 | −0.218129 | −0.109065 | − | 0.994035i | \(-0.534786\pi\) | ||||
−0.109065 | + | 0.994035i | \(0.534786\pi\) | |||||||
\(570\) | 2.04243 | 0.0855479 | ||||||||
\(571\) | −19.7899 | −0.828180 | −0.414090 | − | 0.910236i | \(-0.635900\pi\) | ||||
−0.414090 | + | 0.910236i | \(0.635900\pi\) | |||||||
\(572\) | 5.54079 | 0.231672 | ||||||||
\(573\) | −4.97527 | −0.207845 | ||||||||
\(574\) | −60.0294 | −2.50558 | ||||||||
\(575\) | 3.07928 | 0.128415 | ||||||||
\(576\) | −4.18293 | −0.174289 | ||||||||
\(577\) | 14.0552 | 0.585124 | 0.292562 | − | 0.956247i | \(-0.405492\pi\) | ||||
0.292562 | + | 0.956247i | \(0.405492\pi\) | |||||||
\(578\) | −1.88694 | −0.0784863 | ||||||||
\(579\) | 8.95833 | 0.372296 | ||||||||
\(580\) | −6.45219 | −0.267913 | ||||||||
\(581\) | 42.5310 | 1.76448 | ||||||||
\(582\) | −26.4932 | −1.09818 | ||||||||
\(583\) | 3.93270 | 0.162876 | ||||||||
\(584\) | 8.13025 | 0.336432 | ||||||||
\(585\) | 3.26278 | 0.134899 | ||||||||
\(586\) | 28.5020 | 1.17741 | ||||||||
\(587\) | 30.3566 | 1.25295 | 0.626475 | − | 0.779442i | \(-0.284497\pi\) | ||||
0.626475 | + | 0.779442i | \(0.284497\pi\) | |||||||
\(588\) | 3.27216 | 0.134942 | ||||||||
\(589\) | −7.29098 | −0.300419 | ||||||||
\(590\) | 1.59158 | 0.0655242 | ||||||||
\(591\) | 12.5153 | 0.514811 | ||||||||
\(592\) | −11.1254 | −0.457249 | ||||||||
\(593\) | −14.4046 | −0.591527 | −0.295763 | − | 0.955261i | \(-0.595574\pi\) | ||||
−0.295763 | + | 0.955261i | \(0.595574\pi\) | |||||||
\(594\) | 1.73774 | 0.0713005 | ||||||||
\(595\) | −2.55248 | −0.104642 | ||||||||
\(596\) | 16.3041 | 0.667842 | ||||||||
\(597\) | −25.9024 | −1.06011 | ||||||||
\(598\) | −5.22935 | −0.213844 | ||||||||
\(599\) | 44.1246 | 1.80288 | 0.901442 | − | 0.432900i | \(-0.142510\pi\) | ||||
0.901442 | + | 0.432900i | \(0.142510\pi\) | |||||||
\(600\) | −3.55228 | −0.145021 | ||||||||
\(601\) | −12.9118 | −0.526685 | −0.263342 | − | 0.964702i | \(-0.584825\pi\) | ||||
−0.263342 | + | 0.964702i | \(0.584825\pi\) | |||||||
\(602\) | 23.9955 | 0.977985 | ||||||||
\(603\) | 10.0505 | 0.409287 | ||||||||
\(604\) | 31.9807 | 1.30127 | ||||||||
\(605\) | 8.59142 | 0.349291 | ||||||||
\(606\) | 1.46813 | 0.0596388 | ||||||||
\(607\) | 7.79738 | 0.316486 | 0.158243 | − | 0.987400i | \(-0.449417\pi\) | ||||
0.158243 | + | 0.987400i | \(0.449417\pi\) | |||||||
\(608\) | 9.18750 | 0.372602 | ||||||||
\(609\) | 14.7353 | 0.597105 | ||||||||
\(610\) | −4.16608 | −0.168680 | ||||||||
\(611\) | −20.6142 | −0.833963 | ||||||||
\(612\) | 1.56054 | 0.0630811 | ||||||||
\(613\) | 38.3292 | 1.54810 | 0.774050 | − | 0.633124i | \(-0.218228\pi\) | ||||
0.774050 | + | 0.633124i | \(0.218228\pi\) | |||||||
\(614\) | 9.96619 | 0.402203 | ||||||||
\(615\) | −8.92647 | −0.359950 | ||||||||
\(616\) | −2.30330 | −0.0928026 | ||||||||
\(617\) | 36.2737 | 1.46032 | 0.730162 | − | 0.683274i | \(-0.239444\pi\) | ||||
0.730162 | + | 0.683274i | \(0.239444\pi\) | |||||||
\(618\) | 0.737491 | 0.0296663 | ||||||||
\(619\) | 34.8928 | 1.40246 | 0.701229 | − | 0.712936i | \(-0.252635\pi\) | ||||
0.701229 | + | 0.712936i | \(0.252635\pi\) | |||||||
\(620\) | 7.52849 | 0.302351 | ||||||||
\(621\) | −0.718821 | −0.0288453 | ||||||||
\(622\) | 37.4932 | 1.50334 | ||||||||
\(623\) | 10.8830 | 0.436019 | ||||||||
\(624\) | 18.0656 | 0.723203 | ||||||||
\(625\) | 14.7699 | 0.590796 | ||||||||
\(626\) | −32.8070 | −1.31123 | ||||||||
\(627\) | −1.17787 | −0.0470397 | ||||||||
\(628\) | −7.87134 | −0.314101 | ||||||||
\(629\) | 2.37427 | 0.0946684 | ||||||||
\(630\) | 4.81638 | 0.191889 | ||||||||
\(631\) | 36.1616 | 1.43957 | 0.719786 | − | 0.694196i | \(-0.244240\pi\) | ||||
0.719786 | + | 0.694196i | \(0.244240\pi\) | |||||||
\(632\) | 0.829236 | 0.0329852 | ||||||||
\(633\) | 12.2946 | 0.488668 | ||||||||
\(634\) | −57.0241 | −2.26472 | ||||||||
\(635\) | 10.5619 | 0.419138 | ||||||||
\(636\) | −6.66404 | −0.264247 | ||||||||
\(637\) | −8.08405 | −0.320302 | ||||||||
\(638\) | 8.48985 | 0.336116 | ||||||||
\(639\) | 13.2458 | 0.523997 | ||||||||
\(640\) | 5.47865 | 0.216563 | ||||||||
\(641\) | −40.8595 | −1.61385 | −0.806926 | − | 0.590652i | \(-0.798871\pi\) | ||||
−0.806926 | + | 0.590652i | \(0.798871\pi\) | |||||||
\(642\) | −4.40201 | −0.173734 | ||||||||
\(643\) | −10.3584 | −0.408494 | −0.204247 | − | 0.978919i | \(-0.565475\pi\) | ||||
−0.204247 | + | 0.978919i | \(0.565475\pi\) | |||||||
\(644\) | −3.38330 | −0.133321 | ||||||||
\(645\) | 3.56817 | 0.140497 | ||||||||
\(646\) | −2.41340 | −0.0949538 | ||||||||
\(647\) | −43.4012 | −1.70628 | −0.853139 | − | 0.521683i | \(-0.825304\pi\) | ||||
−0.853139 | + | 0.521683i | \(0.825304\pi\) | |||||||
\(648\) | 0.829236 | 0.0325755 | ||||||||
\(649\) | −0.917866 | −0.0360294 | ||||||||
\(650\) | −31.1642 | −1.22236 | ||||||||
\(651\) | −17.1933 | −0.673859 | ||||||||
\(652\) | 30.1439 | 1.18053 | ||||||||
\(653\) | −20.2481 | −0.792370 | −0.396185 | − | 0.918171i | \(-0.629666\pi\) | ||||
−0.396185 | + | 0.918171i | \(0.629666\pi\) | |||||||
\(654\) | 33.6700 | 1.31660 | ||||||||
\(655\) | 1.83610 | 0.0717424 | ||||||||
\(656\) | −49.4248 | −1.92971 | ||||||||
\(657\) | 9.80450 | 0.382510 | ||||||||
\(658\) | −30.4299 | −1.18628 | ||||||||
\(659\) | 2.17029 | 0.0845425 | 0.0422713 | − | 0.999106i | \(-0.486541\pi\) | ||||
0.0422713 | + | 0.999106i | \(0.486541\pi\) | |||||||
\(660\) | 1.21624 | 0.0473422 | ||||||||
\(661\) | −43.3422 | −1.68582 | −0.842908 | − | 0.538057i | \(-0.819158\pi\) | ||||
−0.842908 | + | 0.538057i | \(0.819158\pi\) | |||||||
\(662\) | 46.5101 | 1.80766 | ||||||||
\(663\) | −3.85540 | −0.149731 | ||||||||
\(664\) | 11.6934 | 0.453790 | ||||||||
\(665\) | −3.26463 | −0.126597 | ||||||||
\(666\) | −4.48011 | −0.173601 | ||||||||
\(667\) | −3.51185 | −0.135979 | ||||||||
\(668\) | −35.2961 | −1.36565 | ||||||||
\(669\) | 0.593490 | 0.0229456 | ||||||||
\(670\) | 16.0495 | 0.620048 | ||||||||
\(671\) | 2.40259 | 0.0927508 | ||||||||
\(672\) | 21.6656 | 0.835769 | ||||||||
\(673\) | 32.2301 | 1.24238 | 0.621190 | − | 0.783660i | \(-0.286650\pi\) | ||||
0.621190 | + | 0.783660i | \(0.286650\pi\) | |||||||
\(674\) | −4.50399 | −0.173487 | ||||||||
\(675\) | −4.28380 | −0.164883 | ||||||||
\(676\) | 2.90900 | 0.111885 | ||||||||
\(677\) | −36.3410 | −1.39670 | −0.698348 | − | 0.715758i | \(-0.746081\pi\) | ||||
−0.698348 | + | 0.715758i | \(0.746081\pi\) | |||||||
\(678\) | 34.4952 | 1.32478 | ||||||||
\(679\) | 42.3468 | 1.62512 | ||||||||
\(680\) | −0.701773 | −0.0269118 | ||||||||
\(681\) | −18.5422 | −0.710538 | ||||||||
\(682\) | −9.90605 | −0.379322 | ||||||||
\(683\) | −27.6294 | −1.05721 | −0.528605 | − | 0.848868i | \(-0.677285\pi\) | ||||
−0.528605 | + | 0.848868i | \(0.677285\pi\) | |||||||
\(684\) | 1.99593 | 0.0763163 | ||||||||
\(685\) | −14.4143 | −0.550742 | ||||||||
\(686\) | 27.9049 | 1.06542 | ||||||||
\(687\) | 7.01948 | 0.267810 | ||||||||
\(688\) | 19.7566 | 0.753211 | ||||||||
\(689\) | 16.4639 | 0.627225 | ||||||||
\(690\) | −1.14788 | −0.0436991 | ||||||||
\(691\) | 8.03647 | 0.305722 | 0.152861 | − | 0.988248i | \(-0.451151\pi\) | ||||
0.152861 | + | 0.988248i | \(0.451151\pi\) | |||||||
\(692\) | −8.38314 | −0.318679 | ||||||||
\(693\) | −2.77762 | −0.105513 | ||||||||
\(694\) | −23.9852 | −0.910467 | ||||||||
\(695\) | −2.98669 | −0.113292 | ||||||||
\(696\) | 4.05128 | 0.153564 | ||||||||
\(697\) | 10.5478 | 0.399526 | ||||||||
\(698\) | 26.1825 | 0.991023 | ||||||||
\(699\) | −17.8632 | −0.675649 | ||||||||
\(700\) | −20.1627 | −0.762077 | ||||||||
\(701\) | 28.6491 | 1.08206 | 0.541031 | − | 0.841003i | \(-0.318034\pi\) | ||||
0.541031 | + | 0.841003i | \(0.318034\pi\) | |||||||
\(702\) | 7.27490 | 0.274574 | ||||||||
\(703\) | 3.03670 | 0.114531 | ||||||||
\(704\) | 3.85220 | 0.145185 | ||||||||
\(705\) | −4.52497 | −0.170420 | ||||||||
\(706\) | −8.22166 | −0.309426 | ||||||||
\(707\) | −2.34667 | −0.0882556 | ||||||||
\(708\) | 1.55534 | 0.0584534 | ||||||||
\(709\) | 13.2281 | 0.496793 | 0.248397 | − | 0.968658i | \(-0.420096\pi\) | ||||
0.248397 | + | 0.968658i | \(0.420096\pi\) | |||||||
\(710\) | 21.1522 | 0.793828 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | 2.99215 | 0.112135 | ||||||||
\(713\) | 4.09766 | 0.153458 | ||||||||
\(714\) | −5.69118 | −0.212987 | ||||||||
\(715\) | −3.00480 | −0.112373 | ||||||||
\(716\) | 27.3094 | 1.02060 | ||||||||
\(717\) | −6.45389 | −0.241025 | ||||||||
\(718\) | 2.78955 | 0.104105 | ||||||||
\(719\) | −1.77194 | −0.0660821 | −0.0330410 | − | 0.999454i | \(-0.510519\pi\) | ||||
−0.0330410 | + | 0.999454i | \(0.510519\pi\) | |||||||
\(720\) | 3.96553 | 0.147787 | ||||||||
\(721\) | −1.17881 | −0.0439012 | ||||||||
\(722\) | 32.7651 | 1.21939 | ||||||||
\(723\) | −23.6366 | −0.879056 | ||||||||
\(724\) | 39.7550 | 1.47748 | ||||||||
\(725\) | −20.9288 | −0.777274 | ||||||||
\(726\) | 19.1560 | 0.710945 | ||||||||
\(727\) | −38.2746 | −1.41953 | −0.709764 | − | 0.704440i | \(-0.751198\pi\) | ||||
−0.709764 | + | 0.704440i | \(0.751198\pi\) | |||||||
\(728\) | −9.64256 | −0.357377 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 15.6568 | 0.579482 | ||||||||
\(731\) | −4.21626 | −0.155944 | ||||||||
\(732\) | −4.07123 | −0.150477 | ||||||||
\(733\) | 15.2987 | 0.565069 | 0.282535 | − | 0.959257i | \(-0.408825\pi\) | ||||
0.282535 | + | 0.959257i | \(0.408825\pi\) | |||||||
\(734\) | −2.30289 | −0.0850014 | ||||||||
\(735\) | −1.77451 | −0.0654537 | ||||||||
\(736\) | −5.16354 | −0.190330 | ||||||||
\(737\) | −9.25581 | −0.340942 | ||||||||
\(738\) | −19.9030 | −0.732641 | ||||||||
\(739\) | −14.4646 | −0.532088 | −0.266044 | − | 0.963961i | \(-0.585717\pi\) | ||||
−0.266044 | + | 0.963961i | \(0.585717\pi\) | |||||||
\(740\) | −3.13562 | −0.115268 | ||||||||
\(741\) | −4.93106 | −0.181147 | ||||||||
\(742\) | 24.3033 | 0.892203 | ||||||||
\(743\) | −17.9639 | −0.659032 | −0.329516 | − | 0.944150i | \(-0.606886\pi\) | ||||
−0.329516 | + | 0.944150i | \(0.606886\pi\) | |||||||
\(744\) | −4.72708 | −0.173303 | ||||||||
\(745\) | −8.84180 | −0.323938 | ||||||||
\(746\) | −57.4029 | −2.10167 | ||||||||
\(747\) | 14.1014 | 0.515942 | ||||||||
\(748\) | −1.43715 | −0.0525474 | ||||||||
\(749\) | 7.03620 | 0.257097 | ||||||||
\(750\) | −14.8252 | −0.541341 | ||||||||
\(751\) | −10.3650 | −0.378223 | −0.189111 | − | 0.981956i | \(-0.560561\pi\) | ||||
−0.189111 | + | 0.981956i | \(0.560561\pi\) | |||||||
\(752\) | −25.0542 | −0.913634 | ||||||||
\(753\) | 15.7470 | 0.573853 | ||||||||
\(754\) | 35.5420 | 1.29436 | ||||||||
\(755\) | −17.3433 | −0.631186 | ||||||||
\(756\) | 4.70673 | 0.171182 | ||||||||
\(757\) | −27.2481 | −0.990347 | −0.495174 | − | 0.868794i | \(-0.664896\pi\) | ||||
−0.495174 | + | 0.868794i | \(0.664896\pi\) | |||||||
\(758\) | 56.4043 | 2.04870 | ||||||||
\(759\) | 0.661986 | 0.0240286 | ||||||||
\(760\) | −0.897568 | −0.0325582 | ||||||||
\(761\) | −26.0036 | −0.942630 | −0.471315 | − | 0.881965i | \(-0.656221\pi\) | ||||
−0.471315 | + | 0.881965i | \(0.656221\pi\) | |||||||
\(762\) | 23.5496 | 0.853112 | ||||||||
\(763\) | −53.8182 | −1.94835 | ||||||||
\(764\) | −7.76410 | −0.280895 | ||||||||
\(765\) | −0.846288 | −0.0305976 | ||||||||
\(766\) | −60.4617 | −2.18457 | ||||||||
\(767\) | −3.84256 | −0.138747 | ||||||||
\(768\) | 20.5814 | 0.742668 | ||||||||
\(769\) | 24.9618 | 0.900146 | 0.450073 | − | 0.892992i | \(-0.351398\pi\) | ||||
0.450073 | + | 0.892992i | \(0.351398\pi\) | |||||||
\(770\) | −4.43556 | −0.159846 | ||||||||
\(771\) | 16.7472 | 0.603136 | ||||||||
\(772\) | 13.9798 | 0.503145 | ||||||||
\(773\) | −35.7594 | −1.28617 | −0.643087 | − | 0.765793i | \(-0.722347\pi\) | ||||
−0.643087 | + | 0.765793i | \(0.722347\pi\) | |||||||
\(774\) | 7.95583 | 0.285966 | ||||||||
\(775\) | 24.4199 | 0.877188 | ||||||||
\(776\) | 11.6427 | 0.417949 | ||||||||
\(777\) | 7.16102 | 0.256900 | ||||||||
\(778\) | −67.8571 | −2.43279 | ||||||||
\(779\) | 13.4906 | 0.483352 | ||||||||
\(780\) | 5.09169 | 0.182312 | ||||||||
\(781\) | −12.1985 | −0.436497 | ||||||||
\(782\) | 1.35637 | 0.0485038 | ||||||||
\(783\) | 4.88556 | 0.174596 | ||||||||
\(784\) | −9.82524 | −0.350901 | ||||||||
\(785\) | 4.26867 | 0.152355 | ||||||||
\(786\) | 4.09389 | 0.146024 | ||||||||
\(787\) | −50.1097 | −1.78622 | −0.893109 | − | 0.449840i | \(-0.851481\pi\) | ||||
−0.893109 | + | 0.449840i | \(0.851481\pi\) | |||||||
\(788\) | 19.5306 | 0.695749 | ||||||||
\(789\) | −9.30111 | −0.331128 | ||||||||
\(790\) | 1.59689 | 0.0568149 | ||||||||
\(791\) | −55.1373 | −1.96046 | ||||||||
\(792\) | −0.763670 | −0.0271358 | ||||||||
\(793\) | 10.0582 | 0.357178 | ||||||||
\(794\) | −59.0536 | −2.09574 | ||||||||
\(795\) | 3.61394 | 0.128173 | ||||||||
\(796\) | −40.4217 | −1.43271 | ||||||||
\(797\) | −25.3853 | −0.899194 | −0.449597 | − | 0.893232i | \(-0.648432\pi\) | ||||
−0.449597 | + | 0.893232i | \(0.648432\pi\) | |||||||
\(798\) | −7.27903 | −0.257675 | ||||||||
\(799\) | 5.34685 | 0.189158 | ||||||||
\(800\) | −30.7720 | −1.08795 | ||||||||
\(801\) | 3.60832 | 0.127494 | ||||||||
\(802\) | 15.6436 | 0.552396 | ||||||||
\(803\) | −9.02928 | −0.318636 | ||||||||
\(804\) | 15.6842 | 0.553138 | ||||||||
\(805\) | 1.83478 | 0.0646675 | ||||||||
\(806\) | −41.4708 | −1.46075 | ||||||||
\(807\) | 19.0596 | 0.670928 | ||||||||
\(808\) | −0.645187 | −0.0226976 | ||||||||
\(809\) | 13.9436 | 0.490232 | 0.245116 | − | 0.969494i | \(-0.421174\pi\) | ||||
0.245116 | + | 0.969494i | \(0.421174\pi\) | |||||||
\(810\) | 1.59689 | 0.0561091 | ||||||||
\(811\) | 6.74545 | 0.236865 | 0.118432 | − | 0.992962i | \(-0.462213\pi\) | ||||
0.118432 | + | 0.992962i | \(0.462213\pi\) | |||||||
\(812\) | 22.9950 | 0.806967 | ||||||||
\(813\) | 29.3396 | 1.02898 | ||||||||
\(814\) | 4.12587 | 0.144612 | ||||||||
\(815\) | −16.3472 | −0.572617 | ||||||||
\(816\) | −4.68580 | −0.164036 | ||||||||
\(817\) | −5.39260 | −0.188663 | ||||||||
\(818\) | 18.9427 | 0.662316 | ||||||||
\(819\) | −11.6282 | −0.406324 | ||||||||
\(820\) | −13.9301 | −0.486460 | ||||||||
\(821\) | −12.7394 | −0.444609 | −0.222305 | − | 0.974977i | \(-0.571358\pi\) | ||||
−0.222305 | + | 0.974977i | \(0.571358\pi\) | |||||||
\(822\) | −32.1391 | −1.12098 | ||||||||
\(823\) | −49.2113 | −1.71540 | −0.857699 | − | 0.514151i | \(-0.828107\pi\) | ||||
−0.857699 | + | 0.514151i | \(0.828107\pi\) | |||||||
\(824\) | −0.324099 | −0.0112905 | ||||||||
\(825\) | 3.94509 | 0.137350 | ||||||||
\(826\) | −5.67223 | −0.197362 | ||||||||
\(827\) | 51.9279 | 1.80571 | 0.902855 | − | 0.429946i | \(-0.141467\pi\) | ||||
0.902855 | + | 0.429946i | \(0.141467\pi\) | |||||||
\(828\) | −1.12175 | −0.0389835 | ||||||||
\(829\) | −23.6474 | −0.821310 | −0.410655 | − | 0.911791i | \(-0.634700\pi\) | ||||
−0.410655 | + | 0.911791i | \(0.634700\pi\) | |||||||
\(830\) | 22.5184 | 0.781624 | ||||||||
\(831\) | 31.4076 | 1.08952 | ||||||||
\(832\) | 16.1269 | 0.559099 | ||||||||
\(833\) | 2.09681 | 0.0726503 | ||||||||
\(834\) | −6.65931 | −0.230593 | ||||||||
\(835\) | 19.1413 | 0.662410 | ||||||||
\(836\) | −1.83812 | −0.0635726 | ||||||||
\(837\) | −5.70052 | −0.197039 | ||||||||
\(838\) | −32.3911 | −1.11893 | ||||||||
\(839\) | 54.2295 | 1.87221 | 0.936105 | − | 0.351721i | \(-0.114403\pi\) | ||||
0.936105 | + | 0.351721i | \(0.114403\pi\) | |||||||
\(840\) | −2.11661 | −0.0730300 | ||||||||
\(841\) | −5.13128 | −0.176941 | ||||||||
\(842\) | 14.5545 | 0.501581 | ||||||||
\(843\) | 17.1452 | 0.590511 | ||||||||
\(844\) | 19.1863 | 0.660418 | ||||||||
\(845\) | −1.57757 | −0.0542700 | ||||||||
\(846\) | −10.0892 | −0.346873 | ||||||||
\(847\) | −30.6190 | −1.05208 | ||||||||
\(848\) | 20.0100 | 0.687146 | ||||||||
\(849\) | −10.0764 | −0.345822 | ||||||||
\(850\) | 8.08326 | 0.277254 | ||||||||
\(851\) | −1.70668 | −0.0585041 | ||||||||
\(852\) | 20.6707 | 0.708165 | ||||||||
\(853\) | −32.2549 | −1.10439 | −0.552193 | − | 0.833716i | \(-0.686209\pi\) | ||||
−0.552193 | + | 0.833716i | \(0.686209\pi\) | |||||||
\(854\) | 14.8475 | 0.508072 | ||||||||
\(855\) | −1.08240 | −0.0370174 | ||||||||
\(856\) | 1.93451 | 0.0661203 | ||||||||
\(857\) | −15.2326 | −0.520337 | −0.260168 | − | 0.965563i | \(-0.583778\pi\) | ||||
−0.260168 | + | 0.965563i | \(0.583778\pi\) | |||||||
\(858\) | −6.69969 | −0.228724 | ||||||||
\(859\) | −9.13714 | −0.311755 | −0.155878 | − | 0.987776i | \(-0.549821\pi\) | ||||
−0.155878 | + | 0.987776i | \(0.549821\pi\) | |||||||
\(860\) | 5.56827 | 0.189877 | ||||||||
\(861\) | 31.8131 | 1.08419 | ||||||||
\(862\) | −40.9975 | −1.39638 | ||||||||
\(863\) | 24.4648 | 0.832793 | 0.416397 | − | 0.909183i | \(-0.363293\pi\) | ||||
0.416397 | + | 0.909183i | \(0.363293\pi\) | |||||||
\(864\) | 7.18334 | 0.244382 | ||||||||
\(865\) | 4.54622 | 0.154576 | ||||||||
\(866\) | −53.8967 | −1.83148 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −26.8308 | −0.910698 | ||||||||
\(869\) | −0.920932 | −0.0312405 | ||||||||
\(870\) | 7.80173 | 0.264503 | ||||||||
\(871\) | −38.7486 | −1.31295 | ||||||||
\(872\) | −14.7966 | −0.501077 | ||||||||
\(873\) | 14.0403 | 0.475192 | ||||||||
\(874\) | 1.73480 | 0.0586805 | ||||||||
\(875\) | 23.6967 | 0.801096 | ||||||||
\(876\) | 15.3003 | 0.516950 | ||||||||
\(877\) | −50.8356 | −1.71660 | −0.858298 | − | 0.513152i | \(-0.828478\pi\) | ||||
−0.858298 | + | 0.513152i | \(0.828478\pi\) | |||||||
\(878\) | 30.2030 | 1.01930 | ||||||||
\(879\) | −15.1049 | −0.509476 | ||||||||
\(880\) | −3.65199 | −0.123108 | ||||||||
\(881\) | 42.0380 | 1.41630 | 0.708149 | − | 0.706063i | \(-0.249531\pi\) | ||||
0.708149 | + | 0.706063i | \(0.249531\pi\) | |||||||
\(882\) | −3.95656 | −0.133224 | ||||||||
\(883\) | −19.5189 | −0.656863 | −0.328432 | − | 0.944528i | \(-0.606520\pi\) | ||||
−0.328432 | + | 0.944528i | \(0.606520\pi\) | |||||||
\(884\) | −6.01650 | −0.202357 | ||||||||
\(885\) | −0.843470 | −0.0283529 | ||||||||
\(886\) | −29.0396 | −0.975605 | ||||||||
\(887\) | 4.03208 | 0.135384 | 0.0676920 | − | 0.997706i | \(-0.478436\pi\) | ||||
0.0676920 | + | 0.997706i | \(0.478436\pi\) | |||||||
\(888\) | 1.96883 | 0.0660697 | ||||||||
\(889\) | −37.6418 | −1.26247 | ||||||||
\(890\) | 5.76210 | 0.193146 | ||||||||
\(891\) | −0.920932 | −0.0308524 | ||||||||
\(892\) | 0.926164 | 0.0310103 | ||||||||
\(893\) | 6.83862 | 0.228846 | ||||||||
\(894\) | −19.7142 | −0.659343 | ||||||||
\(895\) | −14.8100 | −0.495045 | ||||||||
\(896\) | −19.5254 | −0.652298 | ||||||||
\(897\) | 2.77134 | 0.0925324 | ||||||||
\(898\) | 29.7064 | 0.991315 | ||||||||
\(899\) | −27.8503 | −0.928858 | ||||||||
\(900\) | −6.68503 | −0.222834 | ||||||||
\(901\) | −4.27035 | −0.142266 | ||||||||
\(902\) | 18.3294 | 0.610301 | ||||||||
\(903\) | −12.7166 | −0.423183 | ||||||||
\(904\) | −15.1593 | −0.504190 | ||||||||
\(905\) | −21.5593 | −0.716657 | ||||||||
\(906\) | −38.6697 | −1.28471 | ||||||||
\(907\) | 15.0180 | 0.498664 | 0.249332 | − | 0.968418i | \(-0.419789\pi\) | ||||
0.249332 | + | 0.968418i | \(0.419789\pi\) | |||||||
\(908\) | −28.9358 | −0.960269 | ||||||||
\(909\) | −0.778050 | −0.0258063 | ||||||||
\(910\) | −18.5691 | −0.615559 | ||||||||
\(911\) | −19.2566 | −0.638001 | −0.319001 | − | 0.947755i | \(-0.603347\pi\) | ||||
−0.319001 | + | 0.947755i | \(0.603347\pi\) | |||||||
\(912\) | −5.99314 | −0.198453 | ||||||||
\(913\) | −12.9864 | −0.429787 | ||||||||
\(914\) | −66.0165 | −2.18363 | ||||||||
\(915\) | 2.20785 | 0.0729893 | ||||||||
\(916\) | 10.9542 | 0.361936 | ||||||||
\(917\) | −6.54369 | −0.216092 | ||||||||
\(918\) | −1.88694 | −0.0622783 | ||||||||
\(919\) | 42.4425 | 1.40005 | 0.700024 | − | 0.714119i | \(-0.253173\pi\) | ||||
0.700024 | + | 0.714119i | \(0.253173\pi\) | |||||||
\(920\) | 0.504449 | 0.0166312 | ||||||||
\(921\) | −5.28167 | −0.174037 | ||||||||
\(922\) | 52.9871 | 1.74504 | ||||||||
\(923\) | −51.0680 | −1.68092 | ||||||||
\(924\) | −4.33458 | −0.142597 | ||||||||
\(925\) | −10.1709 | −0.334417 | ||||||||
\(926\) | 59.6540 | 1.96035 | ||||||||
\(927\) | −0.390840 | −0.0128369 | ||||||||
\(928\) | 35.0947 | 1.15204 | ||||||||
\(929\) | −16.1756 | −0.530705 | −0.265352 | − | 0.964151i | \(-0.585488\pi\) | ||||
−0.265352 | + | 0.964151i | \(0.585488\pi\) | |||||||
\(930\) | −9.10313 | −0.298504 | ||||||||
\(931\) | 2.68183 | 0.0878933 | ||||||||
\(932\) | −27.8763 | −0.913117 | ||||||||
\(933\) | −19.8699 | −0.650510 | ||||||||
\(934\) | 19.4114 | 0.635160 | ||||||||
\(935\) | 0.779374 | 0.0254883 | ||||||||
\(936\) | −3.19704 | −0.104498 | ||||||||
\(937\) | −41.0799 | −1.34202 | −0.671011 | − | 0.741448i | \(-0.734140\pi\) | ||||
−0.671011 | + | 0.741448i | \(0.734140\pi\) | |||||||
\(938\) | −57.1991 | −1.86762 | ||||||||
\(939\) | 17.3863 | 0.567382 | ||||||||
\(940\) | −7.06140 | −0.230317 | ||||||||
\(941\) | −19.5457 | −0.637171 | −0.318585 | − | 0.947894i | \(-0.603208\pi\) | ||||
−0.318585 | + | 0.947894i | \(0.603208\pi\) | |||||||
\(942\) | 9.51770 | 0.310103 | ||||||||
\(943\) | −7.58198 | −0.246903 | ||||||||
\(944\) | −4.67019 | −0.152002 | ||||||||
\(945\) | −2.55248 | −0.0830323 | ||||||||
\(946\) | −7.32678 | −0.238214 | ||||||||
\(947\) | −31.5035 | −1.02372 | −0.511862 | − | 0.859067i | \(-0.671044\pi\) | ||||
−0.511862 | + | 0.859067i | \(0.671044\pi\) | |||||||
\(948\) | 1.56054 | 0.0506840 | ||||||||
\(949\) | −37.8003 | −1.22705 | ||||||||
\(950\) | 10.3385 | 0.335425 | ||||||||
\(951\) | 30.2204 | 0.979965 | ||||||||
\(952\) | 2.50105 | 0.0810596 | ||||||||
\(953\) | −38.6397 | −1.25166 | −0.625831 | − | 0.779958i | \(-0.715240\pi\) | ||||
−0.625831 | + | 0.779958i | \(0.715240\pi\) | |||||||
\(954\) | 8.05789 | 0.260884 | ||||||||
\(955\) | 4.21051 | 0.136249 | ||||||||
\(956\) | −10.0715 | −0.325737 | ||||||||
\(957\) | −4.49927 | −0.145441 | ||||||||
\(958\) | 15.7578 | 0.509111 | ||||||||
\(959\) | 51.3712 | 1.65886 | ||||||||
\(960\) | 3.53997 | 0.114252 | ||||||||
\(961\) | 1.49598 | 0.0482575 | ||||||||
\(962\) | 17.2726 | 0.556891 | ||||||||
\(963\) | 2.33288 | 0.0751762 | ||||||||
\(964\) | −36.8859 | −1.18801 | ||||||||
\(965\) | −7.58133 | −0.244052 | ||||||||
\(966\) | 4.09094 | 0.131624 | ||||||||
\(967\) | −38.4574 | −1.23671 | −0.618353 | − | 0.785900i | \(-0.712200\pi\) | ||||
−0.618353 | + | 0.785900i | \(0.712200\pi\) | |||||||
\(968\) | −8.41831 | −0.270575 | ||||||||
\(969\) | 1.27900 | 0.0410874 | ||||||||
\(970\) | 22.4209 | 0.719890 | ||||||||
\(971\) | 15.7133 | 0.504265 | 0.252132 | − | 0.967693i | \(-0.418868\pi\) | ||||
0.252132 | + | 0.967693i | \(0.418868\pi\) | |||||||
\(972\) | 1.56054 | 0.0500543 | ||||||||
\(973\) | 10.6443 | 0.341240 | ||||||||
\(974\) | 45.4275 | 1.45559 | ||||||||
\(975\) | 16.5157 | 0.528927 | ||||||||
\(976\) | 12.2246 | 0.391300 | ||||||||
\(977\) | −55.2388 | −1.76724 | −0.883622 | − | 0.468201i | \(-0.844902\pi\) | ||||
−0.883622 | + | 0.468201i | \(0.844902\pi\) | |||||||
\(978\) | −36.4487 | −1.16550 | ||||||||
\(979\) | −3.32301 | −0.106204 | ||||||||
\(980\) | −2.76919 | −0.0884585 | ||||||||
\(981\) | −17.8437 | −0.569705 | ||||||||
\(982\) | −35.9223 | −1.14633 | ||||||||
\(983\) | −52.6483 | −1.67922 | −0.839609 | − | 0.543191i | \(-0.817216\pi\) | ||||
−0.839609 | + | 0.543191i | \(0.817216\pi\) | |||||||
\(984\) | 8.74661 | 0.278832 | ||||||||
\(985\) | −10.5915 | −0.337475 | ||||||||
\(986\) | −9.21876 | −0.293585 | ||||||||
\(987\) | 16.1266 | 0.513315 | ||||||||
\(988\) | −7.69511 | −0.244814 | ||||||||
\(989\) | 3.03074 | 0.0963719 | ||||||||
\(990\) | −1.47063 | −0.0467397 | ||||||||
\(991\) | 58.3156 | 1.85246 | 0.926228 | − | 0.376963i | \(-0.123032\pi\) | ||||
0.926228 | + | 0.376963i | \(0.123032\pi\) | |||||||
\(992\) | −40.9488 | −1.30013 | ||||||||
\(993\) | −24.6484 | −0.782194 | ||||||||
\(994\) | −75.3845 | −2.39105 | ||||||||
\(995\) | 21.9209 | 0.694939 | ||||||||
\(996\) | 22.0057 | 0.697278 | ||||||||
\(997\) | 10.1087 | 0.320147 | 0.160074 | − | 0.987105i | \(-0.448827\pi\) | ||||
0.160074 | + | 0.987105i | \(0.448827\pi\) | |||||||
\(998\) | 23.2606 | 0.736302 | ||||||||
\(999\) | 2.37427 | 0.0751186 |
(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 | 4029.2.a.k.1.6 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.k.1.6 | ✓ | 31 | 1.1 | even | 1 | trivial |