Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8005,2,Mod(1,8005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8005, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8005 = 5 \cdot 1601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8005.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: | \(63.9202468180\) |
Analytic rank: | \(1\) |
Dimension: | \(126\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.36778 | −1.67428 | −0.837138 | − | 0.546992i | \(-0.815773\pi\) | ||||
−0.837138 | + | 0.546992i | \(0.815773\pi\) | |||||||
\(3\) | 2.79221 | 1.61208 | 0.806042 | − | 0.591859i | \(-0.201606\pi\) | ||||
0.806042 | + | 0.591859i | \(0.201606\pi\) | |||||||
\(4\) | 3.60639 | 1.80320 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −6.61135 | −2.69907 | ||||||||
\(7\) | −4.83880 | −1.82889 | −0.914447 | − | 0.404707i | \(-0.867374\pi\) | ||||
−0.914447 | + | 0.404707i | \(0.867374\pi\) | |||||||
\(8\) | −3.80359 | −1.34477 | ||||||||
\(9\) | 4.79644 | 1.59881 | ||||||||
\(10\) | −2.36778 | −0.748759 | ||||||||
\(11\) | 2.26162 | 0.681905 | 0.340953 | − | 0.940080i | \(-0.389250\pi\) | ||||
0.340953 | + | 0.940080i | \(0.389250\pi\) | |||||||
\(12\) | 10.0698 | 2.90690 | ||||||||
\(13\) | 3.53108 | 0.979347 | 0.489673 | − | 0.871906i | \(-0.337116\pi\) | ||||
0.489673 | + | 0.871906i | \(0.337116\pi\) | |||||||
\(14\) | 11.4572 | 3.06207 | ||||||||
\(15\) | 2.79221 | 0.720946 | ||||||||
\(16\) | 1.79329 | 0.448323 | ||||||||
\(17\) | −4.02121 | −0.975287 | −0.487644 | − | 0.873043i | \(-0.662143\pi\) | ||||
−0.487644 | + | 0.873043i | \(0.662143\pi\) | |||||||
\(18\) | −11.3569 | −2.67685 | ||||||||
\(19\) | −2.95196 | −0.677225 | −0.338613 | − | 0.940926i | \(-0.609958\pi\) | ||||
−0.338613 | + | 0.940926i | \(0.609958\pi\) | |||||||
\(20\) | 3.60639 | 0.806414 | ||||||||
\(21\) | −13.5109 | −2.94833 | ||||||||
\(22\) | −5.35503 | −1.14170 | ||||||||
\(23\) | −7.54734 | −1.57373 | −0.786865 | − | 0.617125i | \(-0.788297\pi\) | ||||
−0.786865 | + | 0.617125i | \(0.788297\pi\) | |||||||
\(24\) | −10.6204 | −2.16789 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −8.36084 | −1.63970 | ||||||||
\(27\) | 5.01604 | 0.965337 | ||||||||
\(28\) | −17.4506 | −3.29786 | ||||||||
\(29\) | 8.91566 | 1.65560 | 0.827798 | − | 0.561026i | \(-0.189593\pi\) | ||||
0.827798 | + | 0.561026i | \(0.189593\pi\) | |||||||
\(30\) | −6.61135 | −1.20706 | ||||||||
\(31\) | −8.58965 | −1.54275 | −0.771374 | − | 0.636383i | \(-0.780430\pi\) | ||||
−0.771374 | + | 0.636383i | \(0.780430\pi\) | |||||||
\(32\) | 3.36106 | 0.594157 | ||||||||
\(33\) | 6.31493 | 1.09929 | ||||||||
\(34\) | 9.52136 | 1.63290 | ||||||||
\(35\) | −4.83880 | −0.817906 | ||||||||
\(36\) | 17.2979 | 2.88298 | ||||||||
\(37\) | −0.979194 | −0.160979 | −0.0804893 | − | 0.996755i | \(-0.525648\pi\) | ||||
−0.0804893 | + | 0.996755i | \(0.525648\pi\) | |||||||
\(38\) | 6.98959 | 1.13386 | ||||||||
\(39\) | 9.85953 | 1.57879 | ||||||||
\(40\) | −3.80359 | −0.601401 | ||||||||
\(41\) | 5.91401 | 0.923614 | 0.461807 | − | 0.886981i | \(-0.347201\pi\) | ||||
0.461807 | + | 0.886981i | \(0.347201\pi\) | |||||||
\(42\) | 31.9910 | 4.93631 | ||||||||
\(43\) | 2.18281 | 0.332875 | 0.166438 | − | 0.986052i | \(-0.446774\pi\) | ||||
0.166438 | + | 0.986052i | \(0.446774\pi\) | |||||||
\(44\) | 8.15631 | 1.22961 | ||||||||
\(45\) | 4.79644 | 0.715011 | ||||||||
\(46\) | 17.8705 | 2.63486 | ||||||||
\(47\) | −1.98949 | −0.290197 | −0.145099 | − | 0.989417i | \(-0.546350\pi\) | ||||
−0.145099 | + | 0.989417i | \(0.546350\pi\) | |||||||
\(48\) | 5.00725 | 0.722734 | ||||||||
\(49\) | 16.4140 | 2.34485 | ||||||||
\(50\) | −2.36778 | −0.334855 | ||||||||
\(51\) | −11.2281 | −1.57224 | ||||||||
\(52\) | 12.7345 | 1.76596 | ||||||||
\(53\) | 2.46344 | 0.338379 | 0.169190 | − | 0.985584i | \(-0.445885\pi\) | ||||
0.169190 | + | 0.985584i | \(0.445885\pi\) | |||||||
\(54\) | −11.8769 | −1.61624 | ||||||||
\(55\) | 2.26162 | 0.304957 | ||||||||
\(56\) | 18.4048 | 2.45945 | ||||||||
\(57\) | −8.24249 | −1.09174 | ||||||||
\(58\) | −21.1103 | −2.77192 | ||||||||
\(59\) | −4.16140 | −0.541769 | −0.270884 | − | 0.962612i | \(-0.587316\pi\) | ||||
−0.270884 | + | 0.962612i | \(0.587316\pi\) | |||||||
\(60\) | 10.0698 | 1.30001 | ||||||||
\(61\) | −4.48728 | −0.574537 | −0.287269 | − | 0.957850i | \(-0.592747\pi\) | ||||
−0.287269 | + | 0.957850i | \(0.592747\pi\) | |||||||
\(62\) | 20.3384 | 2.58298 | ||||||||
\(63\) | −23.2090 | −2.92406 | ||||||||
\(64\) | −11.5448 | −1.44311 | ||||||||
\(65\) | 3.53108 | 0.437977 | ||||||||
\(66\) | −14.9524 | −1.84051 | ||||||||
\(67\) | 4.14563 | 0.506470 | 0.253235 | − | 0.967405i | \(-0.418505\pi\) | ||||
0.253235 | + | 0.967405i | \(0.418505\pi\) | |||||||
\(68\) | −14.5021 | −1.75863 | ||||||||
\(69\) | −21.0738 | −2.53698 | ||||||||
\(70\) | 11.4572 | 1.36940 | ||||||||
\(71\) | 8.70692 | 1.03332 | 0.516661 | − | 0.856190i | \(-0.327175\pi\) | ||||
0.516661 | + | 0.856190i | \(0.327175\pi\) | |||||||
\(72\) | −18.2437 | −2.15004 | ||||||||
\(73\) | −9.88283 | −1.15670 | −0.578349 | − | 0.815790i | \(-0.696303\pi\) | ||||
−0.578349 | + | 0.815790i | \(0.696303\pi\) | |||||||
\(74\) | 2.31852 | 0.269522 | ||||||||
\(75\) | 2.79221 | 0.322417 | ||||||||
\(76\) | −10.6459 | −1.22117 | ||||||||
\(77\) | −10.9435 | −1.24713 | ||||||||
\(78\) | −23.3452 | −2.64333 | ||||||||
\(79\) | 13.3332 | 1.50010 | 0.750052 | − | 0.661379i | \(-0.230029\pi\) | ||||
0.750052 | + | 0.661379i | \(0.230029\pi\) | |||||||
\(80\) | 1.79329 | 0.200496 | ||||||||
\(81\) | −0.383485 | −0.0426095 | ||||||||
\(82\) | −14.0031 | −1.54638 | ||||||||
\(83\) | 12.2918 | 1.34920 | 0.674598 | − | 0.738185i | \(-0.264317\pi\) | ||||
0.674598 | + | 0.738185i | \(0.264317\pi\) | |||||||
\(84\) | −48.7258 | −5.31642 | ||||||||
\(85\) | −4.02121 | −0.436162 | ||||||||
\(86\) | −5.16842 | −0.557325 | ||||||||
\(87\) | 24.8944 | 2.66896 | ||||||||
\(88\) | −8.60230 | −0.917008 | ||||||||
\(89\) | −11.6996 | −1.24016 | −0.620078 | − | 0.784540i | \(-0.712899\pi\) | ||||
−0.620078 | + | 0.784540i | \(0.712899\pi\) | |||||||
\(90\) | −11.3569 | −1.19713 | ||||||||
\(91\) | −17.0862 | −1.79112 | ||||||||
\(92\) | −27.2187 | −2.83774 | ||||||||
\(93\) | −23.9841 | −2.48704 | ||||||||
\(94\) | 4.71068 | 0.485870 | ||||||||
\(95\) | −2.95196 | −0.302864 | ||||||||
\(96\) | 9.38479 | 0.957831 | ||||||||
\(97\) | −2.59114 | −0.263091 | −0.131545 | − | 0.991310i | \(-0.541994\pi\) | ||||
−0.131545 | + | 0.991310i | \(0.541994\pi\) | |||||||
\(98\) | −38.8647 | −3.92592 | ||||||||
\(99\) | 10.8477 | 1.09024 | ||||||||
\(100\) | 3.60639 | 0.360639 | ||||||||
\(101\) | −6.37806 | −0.634641 | −0.317320 | − | 0.948318i | \(-0.602783\pi\) | ||||
−0.317320 | + | 0.948318i | \(0.602783\pi\) | |||||||
\(102\) | 26.5856 | 2.63237 | ||||||||
\(103\) | −17.1180 | −1.68669 | −0.843343 | − | 0.537376i | \(-0.819416\pi\) | ||||
−0.843343 | + | 0.537376i | \(0.819416\pi\) | |||||||
\(104\) | −13.4308 | −1.31700 | ||||||||
\(105\) | −13.5109 | −1.31853 | ||||||||
\(106\) | −5.83288 | −0.566540 | ||||||||
\(107\) | −14.3219 | −1.38455 | −0.692276 | − | 0.721633i | \(-0.743392\pi\) | ||||
−0.692276 | + | 0.721633i | \(0.743392\pi\) | |||||||
\(108\) | 18.0898 | 1.74069 | ||||||||
\(109\) | 0.953522 | 0.0913309 | 0.0456654 | − | 0.998957i | \(-0.485459\pi\) | ||||
0.0456654 | + | 0.998957i | \(0.485459\pi\) | |||||||
\(110\) | −5.35503 | −0.510582 | ||||||||
\(111\) | −2.73412 | −0.259511 | ||||||||
\(112\) | −8.67737 | −0.819935 | ||||||||
\(113\) | −9.38097 | −0.882487 | −0.441244 | − | 0.897387i | \(-0.645463\pi\) | ||||
−0.441244 | + | 0.897387i | \(0.645463\pi\) | |||||||
\(114\) | 19.5164 | 1.82788 | ||||||||
\(115\) | −7.54734 | −0.703793 | ||||||||
\(116\) | 32.1534 | 2.98537 | ||||||||
\(117\) | 16.9366 | 1.56579 | ||||||||
\(118\) | 9.85330 | 0.907070 | ||||||||
\(119\) | 19.4578 | 1.78370 | ||||||||
\(120\) | −10.6204 | −0.969508 | ||||||||
\(121\) | −5.88506 | −0.535005 | ||||||||
\(122\) | 10.6249 | 0.961934 | ||||||||
\(123\) | 16.5132 | 1.48894 | ||||||||
\(124\) | −30.9777 | −2.78188 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 54.9539 | 4.89568 | ||||||||
\(127\) | −18.4810 | −1.63992 | −0.819961 | − | 0.572419i | \(-0.806005\pi\) | ||||
−0.819961 | + | 0.572419i | \(0.806005\pi\) | |||||||
\(128\) | 20.6136 | 1.82200 | ||||||||
\(129\) | 6.09487 | 0.536623 | ||||||||
\(130\) | −8.36084 | −0.733294 | ||||||||
\(131\) | −15.9517 | −1.39370 | −0.696851 | − | 0.717215i | \(-0.745416\pi\) | ||||
−0.696851 | + | 0.717215i | \(0.745416\pi\) | |||||||
\(132\) | 22.7741 | 1.98223 | ||||||||
\(133\) | 14.2839 | 1.23857 | ||||||||
\(134\) | −9.81596 | −0.847970 | ||||||||
\(135\) | 5.01604 | 0.431712 | ||||||||
\(136\) | 15.2951 | 1.31154 | ||||||||
\(137\) | −1.38198 | −0.118070 | −0.0590352 | − | 0.998256i | \(-0.518802\pi\) | ||||
−0.0590352 | + | 0.998256i | \(0.518802\pi\) | |||||||
\(138\) | 49.8981 | 4.24761 | ||||||||
\(139\) | 3.28084 | 0.278277 | 0.139138 | − | 0.990273i | \(-0.455567\pi\) | ||||
0.139138 | + | 0.990273i | \(0.455567\pi\) | |||||||
\(140\) | −17.4506 | −1.47485 | ||||||||
\(141\) | −5.55508 | −0.467822 | ||||||||
\(142\) | −20.6161 | −1.73006 | ||||||||
\(143\) | 7.98599 | 0.667822 | ||||||||
\(144\) | 8.60141 | 0.716784 | ||||||||
\(145\) | 8.91566 | 0.740405 | ||||||||
\(146\) | 23.4004 | 1.93663 | ||||||||
\(147\) | 45.8312 | 3.78009 | ||||||||
\(148\) | −3.53136 | −0.290276 | ||||||||
\(149\) | 12.6329 | 1.03493 | 0.517464 | − | 0.855705i | \(-0.326876\pi\) | ||||
0.517464 | + | 0.855705i | \(0.326876\pi\) | |||||||
\(150\) | −6.61135 | −0.539814 | ||||||||
\(151\) | 15.9896 | 1.30121 | 0.650607 | − | 0.759415i | \(-0.274515\pi\) | ||||
0.650607 | + | 0.759415i | \(0.274515\pi\) | |||||||
\(152\) | 11.2280 | 0.910714 | ||||||||
\(153\) | −19.2875 | −1.55930 | ||||||||
\(154\) | 25.9119 | 2.08804 | ||||||||
\(155\) | −8.58965 | −0.689938 | ||||||||
\(156\) | 35.5574 | 2.84687 | ||||||||
\(157\) | 2.87493 | 0.229444 | 0.114722 | − | 0.993398i | \(-0.463402\pi\) | ||||
0.114722 | + | 0.993398i | \(0.463402\pi\) | |||||||
\(158\) | −31.5701 | −2.51159 | ||||||||
\(159\) | 6.87844 | 0.545496 | ||||||||
\(160\) | 3.36106 | 0.265715 | ||||||||
\(161\) | 36.5201 | 2.87818 | ||||||||
\(162\) | 0.908009 | 0.0713399 | ||||||||
\(163\) | 1.25288 | 0.0981328 | 0.0490664 | − | 0.998796i | \(-0.484375\pi\) | ||||
0.0490664 | + | 0.998796i | \(0.484375\pi\) | |||||||
\(164\) | 21.3283 | 1.66546 | ||||||||
\(165\) | 6.31493 | 0.491617 | ||||||||
\(166\) | −29.1042 | −2.25893 | ||||||||
\(167\) | 8.65766 | 0.669950 | 0.334975 | − | 0.942227i | \(-0.391272\pi\) | ||||
0.334975 | + | 0.942227i | \(0.391272\pi\) | |||||||
\(168\) | 51.3901 | 3.96483 | ||||||||
\(169\) | −0.531441 | −0.0408801 | ||||||||
\(170\) | 9.52136 | 0.730255 | ||||||||
\(171\) | −14.1589 | −1.08276 | ||||||||
\(172\) | 7.87207 | 0.600240 | ||||||||
\(173\) | −21.1658 | −1.60921 | −0.804604 | − | 0.593812i | \(-0.797622\pi\) | ||||
−0.804604 | + | 0.593812i | \(0.797622\pi\) | |||||||
\(174\) | −58.9445 | −4.46857 | ||||||||
\(175\) | −4.83880 | −0.365779 | ||||||||
\(176\) | 4.05575 | 0.305714 | ||||||||
\(177\) | −11.6195 | −0.873376 | ||||||||
\(178\) | 27.7021 | 2.07636 | ||||||||
\(179\) | −26.1898 | −1.95752 | −0.978760 | − | 0.205010i | \(-0.934277\pi\) | ||||
−0.978760 | + | 0.205010i | \(0.934277\pi\) | |||||||
\(180\) | 17.2979 | 1.28931 | ||||||||
\(181\) | −10.2734 | −0.763616 | −0.381808 | − | 0.924242i | \(-0.624698\pi\) | ||||
−0.381808 | + | 0.924242i | \(0.624698\pi\) | |||||||
\(182\) | 40.4564 | 2.99883 | ||||||||
\(183\) | −12.5294 | −0.926202 | ||||||||
\(184\) | 28.7070 | 2.11631 | ||||||||
\(185\) | −0.979194 | −0.0719918 | ||||||||
\(186\) | 56.7892 | 4.16398 | ||||||||
\(187\) | −9.09447 | −0.665053 | ||||||||
\(188\) | −7.17489 | −0.523283 | ||||||||
\(189\) | −24.2716 | −1.76550 | ||||||||
\(190\) | 6.98959 | 0.507078 | ||||||||
\(191\) | 5.52518 | 0.399788 | 0.199894 | − | 0.979818i | \(-0.435940\pi\) | ||||
0.199894 | + | 0.979818i | \(0.435940\pi\) | |||||||
\(192\) | −32.2356 | −2.32641 | ||||||||
\(193\) | 3.63674 | 0.261779 | 0.130889 | − | 0.991397i | \(-0.458217\pi\) | ||||
0.130889 | + | 0.991397i | \(0.458217\pi\) | |||||||
\(194\) | 6.13526 | 0.440486 | ||||||||
\(195\) | 9.85953 | 0.706056 | ||||||||
\(196\) | 59.1952 | 4.22823 | ||||||||
\(197\) | 13.0962 | 0.933064 | 0.466532 | − | 0.884504i | \(-0.345503\pi\) | ||||
0.466532 | + | 0.884504i | \(0.345503\pi\) | |||||||
\(198\) | −25.6851 | −1.82536 | ||||||||
\(199\) | −4.53308 | −0.321342 | −0.160671 | − | 0.987008i | \(-0.551366\pi\) | ||||
−0.160671 | + | 0.987008i | \(0.551366\pi\) | |||||||
\(200\) | −3.80359 | −0.268955 | ||||||||
\(201\) | 11.5755 | 0.816472 | ||||||||
\(202\) | 15.1019 | 1.06256 | ||||||||
\(203\) | −43.1411 | −3.02791 | ||||||||
\(204\) | −40.4928 | −2.83507 | ||||||||
\(205\) | 5.91401 | 0.413053 | ||||||||
\(206\) | 40.5317 | 2.82398 | ||||||||
\(207\) | −36.2004 | −2.51610 | ||||||||
\(208\) | 6.33226 | 0.439063 | ||||||||
\(209\) | −6.67622 | −0.461804 | ||||||||
\(210\) | 31.9910 | 2.20759 | ||||||||
\(211\) | −20.4709 | −1.40927 | −0.704636 | − | 0.709569i | \(-0.748890\pi\) | ||||
−0.704636 | + | 0.709569i | \(0.748890\pi\) | |||||||
\(212\) | 8.88413 | 0.610164 | ||||||||
\(213\) | 24.3115 | 1.66580 | ||||||||
\(214\) | 33.9112 | 2.31812 | ||||||||
\(215\) | 2.18281 | 0.148866 | ||||||||
\(216\) | −19.0790 | −1.29816 | ||||||||
\(217\) | 41.5636 | 2.82152 | ||||||||
\(218\) | −2.25773 | −0.152913 | ||||||||
\(219\) | −27.5949 | −1.86469 | ||||||||
\(220\) | 8.15631 | 0.549898 | ||||||||
\(221\) | −14.1992 | −0.955144 | ||||||||
\(222\) | 6.47379 | 0.434493 | ||||||||
\(223\) | −10.0042 | −0.669932 | −0.334966 | − | 0.942230i | \(-0.608725\pi\) | ||||
−0.334966 | + | 0.942230i | \(0.608725\pi\) | |||||||
\(224\) | −16.2635 | −1.08665 | ||||||||
\(225\) | 4.79644 | 0.319763 | ||||||||
\(226\) | 22.2121 | 1.47753 | ||||||||
\(227\) | −22.2921 | −1.47958 | −0.739789 | − | 0.672839i | \(-0.765075\pi\) | ||||
−0.739789 | + | 0.672839i | \(0.765075\pi\) | |||||||
\(228\) | −29.7257 | −1.96863 | ||||||||
\(229\) | −6.42255 | −0.424414 | −0.212207 | − | 0.977225i | \(-0.568065\pi\) | ||||
−0.212207 | + | 0.977225i | \(0.568065\pi\) | |||||||
\(230\) | 17.8705 | 1.17834 | ||||||||
\(231\) | −30.5567 | −2.01048 | ||||||||
\(232\) | −33.9115 | −2.22640 | ||||||||
\(233\) | −3.10920 | −0.203690 | −0.101845 | − | 0.994800i | \(-0.532475\pi\) | ||||
−0.101845 | + | 0.994800i | \(0.532475\pi\) | |||||||
\(234\) | −40.1023 | −2.62157 | ||||||||
\(235\) | −1.98949 | −0.129780 | ||||||||
\(236\) | −15.0077 | −0.976916 | ||||||||
\(237\) | 37.2291 | 2.41829 | ||||||||
\(238\) | −46.0719 | −2.98640 | ||||||||
\(239\) | 16.8554 | 1.09029 | 0.545143 | − | 0.838343i | \(-0.316475\pi\) | ||||
0.545143 | + | 0.838343i | \(0.316475\pi\) | |||||||
\(240\) | 5.00725 | 0.323216 | ||||||||
\(241\) | −16.1099 | −1.03773 | −0.518865 | − | 0.854856i | \(-0.673645\pi\) | ||||
−0.518865 | + | 0.854856i | \(0.673645\pi\) | |||||||
\(242\) | 13.9345 | 0.895746 | ||||||||
\(243\) | −16.1189 | −1.03403 | ||||||||
\(244\) | −16.1829 | −1.03600 | ||||||||
\(245\) | 16.4140 | 1.04865 | ||||||||
\(246\) | −39.0996 | −2.49290 | ||||||||
\(247\) | −10.4236 | −0.663238 | ||||||||
\(248\) | 32.6715 | 2.07464 | ||||||||
\(249\) | 34.3212 | 2.17502 | ||||||||
\(250\) | −2.36778 | −0.149752 | ||||||||
\(251\) | 2.31475 | 0.146106 | 0.0730530 | − | 0.997328i | \(-0.476726\pi\) | ||||
0.0730530 | + | 0.997328i | \(0.476726\pi\) | |||||||
\(252\) | −83.7008 | −5.27265 | ||||||||
\(253\) | −17.0693 | −1.07313 | ||||||||
\(254\) | 43.7590 | 2.74568 | ||||||||
\(255\) | −11.2281 | −0.703129 | ||||||||
\(256\) | −25.7187 | −1.60742 | ||||||||
\(257\) | −23.4867 | −1.46506 | −0.732529 | − | 0.680736i | \(-0.761660\pi\) | ||||
−0.732529 | + | 0.680736i | \(0.761660\pi\) | |||||||
\(258\) | −14.4313 | −0.898454 | ||||||||
\(259\) | 4.73812 | 0.294413 | ||||||||
\(260\) | 12.7345 | 0.789759 | ||||||||
\(261\) | 42.7634 | 2.64699 | ||||||||
\(262\) | 37.7701 | 2.33344 | ||||||||
\(263\) | −7.22512 | −0.445520 | −0.222760 | − | 0.974873i | \(-0.571507\pi\) | ||||
−0.222760 | + | 0.974873i | \(0.571507\pi\) | |||||||
\(264\) | −24.0194 | −1.47829 | ||||||||
\(265\) | 2.46344 | 0.151328 | ||||||||
\(266\) | −33.8212 | −2.07371 | ||||||||
\(267\) | −32.6678 | −1.99923 | ||||||||
\(268\) | 14.9508 | 0.913265 | ||||||||
\(269\) | 27.7863 | 1.69416 | 0.847080 | − | 0.531465i | \(-0.178358\pi\) | ||||
0.847080 | + | 0.531465i | \(0.178358\pi\) | |||||||
\(270\) | −11.8769 | −0.722804 | ||||||||
\(271\) | 19.2702 | 1.17058 | 0.585290 | − | 0.810824i | \(-0.300981\pi\) | ||||
0.585290 | + | 0.810824i | \(0.300981\pi\) | |||||||
\(272\) | −7.21120 | −0.437243 | ||||||||
\(273\) | −47.7083 | −2.88744 | ||||||||
\(274\) | 3.27223 | 0.197682 | ||||||||
\(275\) | 2.26162 | 0.136381 | ||||||||
\(276\) | −76.0003 | −4.57468 | ||||||||
\(277\) | −6.33992 | −0.380929 | −0.190465 | − | 0.981694i | \(-0.560999\pi\) | ||||
−0.190465 | + | 0.981694i | \(0.560999\pi\) | |||||||
\(278\) | −7.76831 | −0.465912 | ||||||||
\(279\) | −41.1998 | −2.46656 | ||||||||
\(280\) | 18.4048 | 1.09990 | ||||||||
\(281\) | −4.22013 | −0.251752 | −0.125876 | − | 0.992046i | \(-0.540174\pi\) | ||||
−0.125876 | + | 0.992046i | \(0.540174\pi\) | |||||||
\(282\) | 13.1532 | 0.783263 | ||||||||
\(283\) | 15.4029 | 0.915605 | 0.457802 | − | 0.889054i | \(-0.348637\pi\) | ||||
0.457802 | + | 0.889054i | \(0.348637\pi\) | |||||||
\(284\) | 31.4006 | 1.86328 | ||||||||
\(285\) | −8.24249 | −0.488243 | ||||||||
\(286\) | −18.9091 | −1.11812 | ||||||||
\(287\) | −28.6167 | −1.68919 | ||||||||
\(288\) | 16.1211 | 0.949947 | ||||||||
\(289\) | −0.829856 | −0.0488150 | ||||||||
\(290\) | −21.1103 | −1.23964 | ||||||||
\(291\) | −7.23501 | −0.424124 | ||||||||
\(292\) | −35.6414 | −2.08575 | ||||||||
\(293\) | −12.9770 | −0.758124 | −0.379062 | − | 0.925371i | \(-0.623753\pi\) | ||||
−0.379062 | + | 0.925371i | \(0.623753\pi\) | |||||||
\(294\) | −108.518 | −6.32892 | ||||||||
\(295\) | −4.16140 | −0.242286 | ||||||||
\(296\) | 3.72446 | 0.216480 | ||||||||
\(297\) | 11.3444 | 0.658268 | ||||||||
\(298\) | −29.9120 | −1.73276 | ||||||||
\(299\) | −26.6503 | −1.54123 | ||||||||
\(300\) | 10.0698 | 0.581381 | ||||||||
\(301\) | −10.5622 | −0.608794 | ||||||||
\(302\) | −37.8599 | −2.17859 | ||||||||
\(303\) | −17.8089 | −1.02309 | ||||||||
\(304\) | −5.29372 | −0.303616 | ||||||||
\(305\) | −4.48728 | −0.256941 | ||||||||
\(306\) | 45.6686 | 2.61070 | ||||||||
\(307\) | 6.91601 | 0.394717 | 0.197359 | − | 0.980331i | \(-0.436764\pi\) | ||||
0.197359 | + | 0.980331i | \(0.436764\pi\) | |||||||
\(308\) | −39.4667 | −2.24882 | ||||||||
\(309\) | −47.7970 | −2.71908 | ||||||||
\(310\) | 20.3384 | 1.15515 | ||||||||
\(311\) | −2.39808 | −0.135983 | −0.0679914 | − | 0.997686i | \(-0.521659\pi\) | ||||
−0.0679914 | + | 0.997686i | \(0.521659\pi\) | |||||||
\(312\) | −37.5016 | −2.12311 | ||||||||
\(313\) | 18.8629 | 1.06619 | 0.533097 | − | 0.846054i | \(-0.321028\pi\) | ||||
0.533097 | + | 0.846054i | \(0.321028\pi\) | |||||||
\(314\) | −6.80721 | −0.384153 | ||||||||
\(315\) | −23.2090 | −1.30768 | ||||||||
\(316\) | 48.0848 | 2.70498 | ||||||||
\(317\) | −1.85221 | −0.104030 | −0.0520152 | − | 0.998646i | \(-0.516564\pi\) | ||||
−0.0520152 | + | 0.998646i | \(0.516564\pi\) | |||||||
\(318\) | −16.2866 | −0.913310 | ||||||||
\(319\) | 20.1639 | 1.12896 | ||||||||
\(320\) | −11.5448 | −0.645376 | ||||||||
\(321\) | −39.9898 | −2.23201 | ||||||||
\(322\) | −86.4716 | −4.81887 | ||||||||
\(323\) | 11.8704 | 0.660489 | ||||||||
\(324\) | −1.38300 | −0.0768332 | ||||||||
\(325\) | 3.53108 | 0.195869 | ||||||||
\(326\) | −2.96654 | −0.164301 | ||||||||
\(327\) | 2.66243 | 0.147233 | ||||||||
\(328\) | −22.4945 | −1.24205 | ||||||||
\(329\) | 9.62674 | 0.530740 | ||||||||
\(330\) | −14.9524 | −0.823102 | ||||||||
\(331\) | −11.9931 | −0.659200 | −0.329600 | − | 0.944121i | \(-0.606914\pi\) | ||||
−0.329600 | + | 0.944121i | \(0.606914\pi\) | |||||||
\(332\) | 44.3290 | 2.43287 | ||||||||
\(333\) | −4.69665 | −0.257375 | ||||||||
\(334\) | −20.4995 | −1.12168 | ||||||||
\(335\) | 4.14563 | 0.226500 | ||||||||
\(336\) | −24.2290 | −1.32180 | ||||||||
\(337\) | −11.9385 | −0.650333 | −0.325166 | − | 0.945657i | \(-0.605420\pi\) | ||||
−0.325166 | + | 0.945657i | \(0.605420\pi\) | |||||||
\(338\) | 1.25834 | 0.0684445 | ||||||||
\(339\) | −26.1936 | −1.42264 | ||||||||
\(340\) | −14.5021 | −0.786485 | ||||||||
\(341\) | −19.4266 | −1.05201 | ||||||||
\(342\) | 33.5252 | 1.81283 | ||||||||
\(343\) | −45.5522 | −2.45959 | ||||||||
\(344\) | −8.30252 | −0.447642 | ||||||||
\(345\) | −21.0738 | −1.13457 | ||||||||
\(346\) | 50.1161 | 2.69426 | ||||||||
\(347\) | −33.9129 | −1.82054 | −0.910269 | − | 0.414017i | \(-0.864125\pi\) | ||||
−0.910269 | + | 0.414017i | \(0.864125\pi\) | |||||||
\(348\) | 89.7790 | 4.81266 | ||||||||
\(349\) | −2.94951 | −0.157884 | −0.0789419 | − | 0.996879i | \(-0.525154\pi\) | ||||
−0.0789419 | + | 0.996879i | \(0.525154\pi\) | |||||||
\(350\) | 11.4572 | 0.612414 | ||||||||
\(351\) | 17.7121 | 0.945400 | ||||||||
\(352\) | 7.60146 | 0.405159 | ||||||||
\(353\) | 0.634803 | 0.0337872 | 0.0168936 | − | 0.999857i | \(-0.494622\pi\) | ||||
0.0168936 | + | 0.999857i | \(0.494622\pi\) | |||||||
\(354\) | 27.5125 | 1.46227 | ||||||||
\(355\) | 8.70692 | 0.462115 | ||||||||
\(356\) | −42.1934 | −2.23624 | ||||||||
\(357\) | 54.3303 | 2.87547 | ||||||||
\(358\) | 62.0118 | 3.27743 | ||||||||
\(359\) | 8.63389 | 0.455679 | 0.227840 | − | 0.973699i | \(-0.426834\pi\) | ||||
0.227840 | + | 0.973699i | \(0.426834\pi\) | |||||||
\(360\) | −18.2437 | −0.961528 | ||||||||
\(361\) | −10.2860 | −0.541366 | ||||||||
\(362\) | 24.3252 | 1.27850 | ||||||||
\(363\) | −16.4323 | −0.862473 | ||||||||
\(364\) | −61.6196 | −3.22974 | ||||||||
\(365\) | −9.88283 | −0.517291 | ||||||||
\(366\) | 29.6670 | 1.55072 | ||||||||
\(367\) | −6.41382 | −0.334799 | −0.167399 | − | 0.985889i | \(-0.553537\pi\) | ||||
−0.167399 | + | 0.985889i | \(0.553537\pi\) | |||||||
\(368\) | −13.5346 | −0.705539 | ||||||||
\(369\) | 28.3662 | 1.47669 | ||||||||
\(370\) | 2.31852 | 0.120534 | ||||||||
\(371\) | −11.9201 | −0.618859 | ||||||||
\(372\) | −86.4962 | −4.48462 | ||||||||
\(373\) | 0.950354 | 0.0492075 | 0.0246037 | − | 0.999697i | \(-0.492168\pi\) | ||||
0.0246037 | + | 0.999697i | \(0.492168\pi\) | |||||||
\(374\) | 21.5337 | 1.11348 | ||||||||
\(375\) | 2.79221 | 0.144189 | ||||||||
\(376\) | 7.56721 | 0.390249 | ||||||||
\(377\) | 31.4820 | 1.62140 | ||||||||
\(378\) | 57.4698 | 2.95593 | ||||||||
\(379\) | −18.4614 | −0.948301 | −0.474150 | − | 0.880444i | \(-0.657245\pi\) | ||||
−0.474150 | + | 0.880444i | \(0.657245\pi\) | |||||||
\(380\) | −10.6459 | −0.546124 | ||||||||
\(381\) | −51.6028 | −2.64369 | ||||||||
\(382\) | −13.0824 | −0.669355 | ||||||||
\(383\) | 6.69875 | 0.342290 | 0.171145 | − | 0.985246i | \(-0.445253\pi\) | ||||
0.171145 | + | 0.985246i | \(0.445253\pi\) | |||||||
\(384\) | 57.5574 | 2.93721 | ||||||||
\(385\) | −10.9435 | −0.557734 | ||||||||
\(386\) | −8.61102 | −0.438289 | ||||||||
\(387\) | 10.4697 | 0.532206 | ||||||||
\(388\) | −9.34468 | −0.474404 | ||||||||
\(389\) | 35.9446 | 1.82246 | 0.911232 | − | 0.411894i | \(-0.135133\pi\) | ||||
0.911232 | + | 0.411894i | \(0.135133\pi\) | |||||||
\(390\) | −23.3452 | −1.18213 | ||||||||
\(391\) | 30.3495 | 1.53484 | ||||||||
\(392\) | −62.4320 | −3.15329 | ||||||||
\(393\) | −44.5404 | −2.24677 | ||||||||
\(394\) | −31.0089 | −1.56221 | ||||||||
\(395\) | 13.3332 | 0.670867 | ||||||||
\(396\) | 39.1212 | 1.96592 | ||||||||
\(397\) | 25.8728 | 1.29852 | 0.649259 | − | 0.760567i | \(-0.275079\pi\) | ||||
0.649259 | + | 0.760567i | \(0.275079\pi\) | |||||||
\(398\) | 10.7333 | 0.538014 | ||||||||
\(399\) | 39.8837 | 1.99668 | ||||||||
\(400\) | 1.79329 | 0.0896646 | ||||||||
\(401\) | 24.4433 | 1.22064 | 0.610321 | − | 0.792154i | \(-0.291041\pi\) | ||||
0.610321 | + | 0.792154i | \(0.291041\pi\) | |||||||
\(402\) | −27.4082 | −1.36700 | ||||||||
\(403\) | −30.3308 | −1.51088 | ||||||||
\(404\) | −23.0018 | −1.14438 | ||||||||
\(405\) | −0.383485 | −0.0190555 | ||||||||
\(406\) | 102.149 | 5.06955 | ||||||||
\(407\) | −2.21457 | −0.109772 | ||||||||
\(408\) | 42.7070 | 2.11431 | ||||||||
\(409\) | 15.2936 | 0.756219 | 0.378110 | − | 0.925761i | \(-0.376574\pi\) | ||||
0.378110 | + | 0.925761i | \(0.376574\pi\) | |||||||
\(410\) | −14.0031 | −0.691564 | ||||||||
\(411\) | −3.85878 | −0.190339 | ||||||||
\(412\) | −61.7342 | −3.04143 | ||||||||
\(413\) | 20.1362 | 0.990837 | ||||||||
\(414\) | 85.7146 | 4.21264 | ||||||||
\(415\) | 12.2918 | 0.603379 | ||||||||
\(416\) | 11.8682 | 0.581886 | ||||||||
\(417\) | 9.16078 | 0.448606 | ||||||||
\(418\) | 15.8078 | 0.773186 | ||||||||
\(419\) | −20.6955 | −1.01104 | −0.505522 | − | 0.862814i | \(-0.668700\pi\) | ||||
−0.505522 | + | 0.862814i | \(0.668700\pi\) | |||||||
\(420\) | −48.7258 | −2.37757 | ||||||||
\(421\) | 4.28882 | 0.209024 | 0.104512 | − | 0.994524i | \(-0.466672\pi\) | ||||
0.104512 | + | 0.994524i | \(0.466672\pi\) | |||||||
\(422\) | 48.4705 | 2.35951 | ||||||||
\(423\) | −9.54247 | −0.463971 | ||||||||
\(424\) | −9.36991 | −0.455043 | ||||||||
\(425\) | −4.02121 | −0.195057 | ||||||||
\(426\) | −57.5645 | −2.78901 | ||||||||
\(427\) | 21.7130 | 1.05077 | ||||||||
\(428\) | −51.6505 | −2.49662 | ||||||||
\(429\) | 22.2986 | 1.07658 | ||||||||
\(430\) | −5.16842 | −0.249243 | ||||||||
\(431\) | 10.5839 | 0.509811 | 0.254905 | − | 0.966966i | \(-0.417956\pi\) | ||||
0.254905 | + | 0.966966i | \(0.417956\pi\) | |||||||
\(432\) | 8.99522 | 0.432783 | ||||||||
\(433\) | 3.88275 | 0.186593 | 0.0932966 | − | 0.995638i | \(-0.470260\pi\) | ||||
0.0932966 | + | 0.995638i | \(0.470260\pi\) | |||||||
\(434\) | −98.4135 | −4.72400 | ||||||||
\(435\) | 24.8944 | 1.19360 | ||||||||
\(436\) | 3.43878 | 0.164688 | ||||||||
\(437\) | 22.2794 | 1.06577 | ||||||||
\(438\) | 65.3388 | 3.12201 | ||||||||
\(439\) | −26.1598 | −1.24854 | −0.624269 | − | 0.781210i | \(-0.714603\pi\) | ||||
−0.624269 | + | 0.781210i | \(0.714603\pi\) | |||||||
\(440\) | −8.60230 | −0.410098 | ||||||||
\(441\) | 78.7285 | 3.74898 | ||||||||
\(442\) | 33.6207 | 1.59917 | ||||||||
\(443\) | −17.2850 | −0.821236 | −0.410618 | − | 0.911808i | \(-0.634687\pi\) | ||||
−0.410618 | + | 0.911808i | \(0.634687\pi\) | |||||||
\(444\) | −9.86030 | −0.467949 | ||||||||
\(445\) | −11.6996 | −0.554614 | ||||||||
\(446\) | 23.6878 | 1.12165 | ||||||||
\(447\) | 35.2738 | 1.66839 | ||||||||
\(448\) | 55.8632 | 2.63929 | ||||||||
\(449\) | −28.8368 | −1.36089 | −0.680447 | − | 0.732797i | \(-0.738214\pi\) | ||||
−0.680447 | + | 0.732797i | \(0.738214\pi\) | |||||||
\(450\) | −11.3569 | −0.535371 | ||||||||
\(451\) | 13.3753 | 0.629817 | ||||||||
\(452\) | −33.8315 | −1.59130 | ||||||||
\(453\) | 44.6463 | 2.09767 | ||||||||
\(454\) | 52.7828 | 2.47722 | ||||||||
\(455\) | −17.0862 | −0.801013 | ||||||||
\(456\) | 31.3511 | 1.46815 | ||||||||
\(457\) | 38.2656 | 1.78999 | 0.894994 | − | 0.446078i | \(-0.147179\pi\) | ||||
0.894994 | + | 0.446078i | \(0.147179\pi\) | |||||||
\(458\) | 15.2072 | 0.710586 | ||||||||
\(459\) | −20.1706 | −0.941481 | ||||||||
\(460\) | −27.2187 | −1.26908 | ||||||||
\(461\) | −20.8037 | −0.968927 | −0.484463 | − | 0.874812i | \(-0.660985\pi\) | ||||
−0.484463 | + | 0.874812i | \(0.660985\pi\) | |||||||
\(462\) | 72.3515 | 3.36610 | ||||||||
\(463\) | 42.4374 | 1.97223 | 0.986116 | − | 0.166059i | \(-0.0531042\pi\) | ||||
0.986116 | + | 0.166059i | \(0.0531042\pi\) | |||||||
\(464\) | 15.9884 | 0.742242 | ||||||||
\(465\) | −23.9841 | −1.11224 | ||||||||
\(466\) | 7.36191 | 0.341034 | ||||||||
\(467\) | −24.1492 | −1.11749 | −0.558745 | − | 0.829340i | \(-0.688717\pi\) | ||||
−0.558745 | + | 0.829340i | \(0.688717\pi\) | |||||||
\(468\) | 61.0802 | 2.82343 | ||||||||
\(469\) | −20.0599 | −0.926279 | ||||||||
\(470\) | 4.71068 | 0.217288 | ||||||||
\(471\) | 8.02741 | 0.369884 | ||||||||
\(472\) | 15.8283 | 0.728556 | ||||||||
\(473\) | 4.93670 | 0.226990 | ||||||||
\(474\) | −88.1505 | −4.04889 | ||||||||
\(475\) | −2.95196 | −0.135445 | ||||||||
\(476\) | 70.1726 | 3.21636 | ||||||||
\(477\) | 11.8157 | 0.541005 | ||||||||
\(478\) | −39.9099 | −1.82544 | ||||||||
\(479\) | −18.1033 | −0.827161 | −0.413581 | − | 0.910467i | \(-0.635722\pi\) | ||||
−0.413581 | + | 0.910467i | \(0.635722\pi\) | |||||||
\(480\) | 9.38479 | 0.428355 | ||||||||
\(481\) | −3.45762 | −0.157654 | ||||||||
\(482\) | 38.1447 | 1.73745 | ||||||||
\(483\) | 101.972 | 4.63987 | ||||||||
\(484\) | −21.2238 | −0.964720 | ||||||||
\(485\) | −2.59114 | −0.117658 | ||||||||
\(486\) | 38.1660 | 1.73125 | ||||||||
\(487\) | −6.15594 | −0.278952 | −0.139476 | − | 0.990225i | \(-0.544542\pi\) | ||||
−0.139476 | + | 0.990225i | \(0.544542\pi\) | |||||||
\(488\) | 17.0678 | 0.772622 | ||||||||
\(489\) | 3.49829 | 0.158198 | ||||||||
\(490\) | −38.8647 | −1.75573 | ||||||||
\(491\) | 29.8563 | 1.34740 | 0.673699 | − | 0.739006i | \(-0.264705\pi\) | ||||
0.673699 | + | 0.739006i | \(0.264705\pi\) | |||||||
\(492\) | 59.5530 | 2.68486 | ||||||||
\(493\) | −35.8518 | −1.61468 | ||||||||
\(494\) | 24.6808 | 1.11044 | ||||||||
\(495\) | 10.8477 | 0.487570 | ||||||||
\(496\) | −15.4037 | −0.691649 | ||||||||
\(497\) | −42.1310 | −1.88983 | ||||||||
\(498\) | −81.2651 | −3.64158 | ||||||||
\(499\) | −13.6988 | −0.613244 | −0.306622 | − | 0.951831i | \(-0.599199\pi\) | ||||
−0.306622 | + | 0.951831i | \(0.599199\pi\) | |||||||
\(500\) | 3.60639 | 0.161283 | ||||||||
\(501\) | 24.1740 | 1.08001 | ||||||||
\(502\) | −5.48084 | −0.244622 | ||||||||
\(503\) | 6.47760 | 0.288822 | 0.144411 | − | 0.989518i | \(-0.453871\pi\) | ||||
0.144411 | + | 0.989518i | \(0.453871\pi\) | |||||||
\(504\) | 88.2776 | 3.93220 | ||||||||
\(505\) | −6.37806 | −0.283820 | ||||||||
\(506\) | 40.4163 | 1.79672 | ||||||||
\(507\) | −1.48389 | −0.0659021 | ||||||||
\(508\) | −66.6497 | −2.95710 | ||||||||
\(509\) | 4.86666 | 0.215711 | 0.107855 | − | 0.994167i | \(-0.465602\pi\) | ||||
0.107855 | + | 0.994167i | \(0.465602\pi\) | |||||||
\(510\) | 26.5856 | 1.17723 | ||||||||
\(511\) | 47.8210 | 2.11548 | ||||||||
\(512\) | 19.6693 | 0.869267 | ||||||||
\(513\) | −14.8071 | −0.653751 | ||||||||
\(514\) | 55.6113 | 2.45291 | ||||||||
\(515\) | −17.1180 | −0.754309 | ||||||||
\(516\) | 21.9805 | 0.967637 | ||||||||
\(517\) | −4.49948 | −0.197887 | ||||||||
\(518\) | −11.2188 | −0.492928 | ||||||||
\(519\) | −59.0994 | −2.59418 | ||||||||
\(520\) | −13.4308 | −0.588980 | ||||||||
\(521\) | 23.8258 | 1.04383 | 0.521914 | − | 0.852998i | \(-0.325218\pi\) | ||||
0.521914 | + | 0.852998i | \(0.325218\pi\) | |||||||
\(522\) | −101.255 | −4.43179 | ||||||||
\(523\) | 32.2397 | 1.40974 | 0.704872 | − | 0.709334i | \(-0.251004\pi\) | ||||
0.704872 | + | 0.709334i | \(0.251004\pi\) | |||||||
\(524\) | −57.5280 | −2.51312 | ||||||||
\(525\) | −13.5109 | −0.589666 | ||||||||
\(526\) | 17.1075 | 0.745923 | ||||||||
\(527\) | 34.5408 | 1.50462 | ||||||||
\(528\) | 11.3245 | 0.492836 | ||||||||
\(529\) | 33.9624 | 1.47663 | ||||||||
\(530\) | −5.83288 | −0.253364 | ||||||||
\(531\) | −19.9599 | −0.866187 | ||||||||
\(532\) | 51.5134 | 2.23339 | ||||||||
\(533\) | 20.8829 | 0.904538 | ||||||||
\(534\) | 77.3501 | 3.34727 | ||||||||
\(535\) | −14.3219 | −0.619190 | ||||||||
\(536\) | −15.7683 | −0.681087 | ||||||||
\(537\) | −73.1275 | −3.15569 | ||||||||
\(538\) | −65.7919 | −2.83649 | ||||||||
\(539\) | 37.1222 | 1.59897 | ||||||||
\(540\) | 18.0898 | 0.778462 | ||||||||
\(541\) | 26.0818 | 1.12135 | 0.560673 | − | 0.828037i | \(-0.310542\pi\) | ||||
0.560673 | + | 0.828037i | \(0.310542\pi\) | |||||||
\(542\) | −45.6276 | −1.95987 | ||||||||
\(543\) | −28.6855 | −1.23101 | ||||||||
\(544\) | −13.5155 | −0.579474 | ||||||||
\(545\) | 0.953522 | 0.0408444 | ||||||||
\(546\) | 112.963 | 4.83436 | ||||||||
\(547\) | 44.1205 | 1.88646 | 0.943228 | − | 0.332147i | \(-0.107773\pi\) | ||||
0.943228 | + | 0.332147i | \(0.107773\pi\) | |||||||
\(548\) | −4.98396 | −0.212904 | ||||||||
\(549\) | −21.5230 | −0.918578 | ||||||||
\(550\) | −5.35503 | −0.228339 | ||||||||
\(551\) | −26.3186 | −1.12121 | ||||||||
\(552\) | 80.1560 | 3.41167 | ||||||||
\(553\) | −64.5167 | −2.74353 | ||||||||
\(554\) | 15.0116 | 0.637780 | ||||||||
\(555\) | −2.73412 | −0.116057 | ||||||||
\(556\) | 11.8320 | 0.501788 | ||||||||
\(557\) | −21.3819 | −0.905982 | −0.452991 | − | 0.891515i | \(-0.649643\pi\) | ||||
−0.452991 | + | 0.891515i | \(0.649643\pi\) | |||||||
\(558\) | 97.5521 | 4.12971 | ||||||||
\(559\) | 7.70769 | 0.326000 | ||||||||
\(560\) | −8.67737 | −0.366686 | ||||||||
\(561\) | −25.3937 | −1.07212 | ||||||||
\(562\) | 9.99235 | 0.421502 | ||||||||
\(563\) | −39.9369 | −1.68314 | −0.841570 | − | 0.540148i | \(-0.818368\pi\) | ||||
−0.841570 | + | 0.540148i | \(0.818368\pi\) | |||||||
\(564\) | −20.0338 | −0.843575 | ||||||||
\(565\) | −9.38097 | −0.394660 | ||||||||
\(566\) | −36.4706 | −1.53297 | ||||||||
\(567\) | 1.85561 | 0.0779281 | ||||||||
\(568\) | −33.1176 | −1.38958 | ||||||||
\(569\) | −43.5671 | −1.82643 | −0.913214 | − | 0.407480i | \(-0.866408\pi\) | ||||
−0.913214 | + | 0.407480i | \(0.866408\pi\) | |||||||
\(570\) | 19.5164 | 0.817453 | ||||||||
\(571\) | −14.8029 | −0.619481 | −0.309740 | − | 0.950821i | \(-0.600242\pi\) | ||||
−0.309740 | + | 0.950821i | \(0.600242\pi\) | |||||||
\(572\) | 28.8006 | 1.20421 | ||||||||
\(573\) | 15.4275 | 0.644491 | ||||||||
\(574\) | 67.7581 | 2.82817 | ||||||||
\(575\) | −7.54734 | −0.314746 | ||||||||
\(576\) | −55.3742 | −2.30726 | ||||||||
\(577\) | 30.9771 | 1.28959 | 0.644796 | − | 0.764355i | \(-0.276942\pi\) | ||||
0.644796 | + | 0.764355i | \(0.276942\pi\) | |||||||
\(578\) | 1.96492 | 0.0817298 | ||||||||
\(579\) | 10.1546 | 0.422009 | ||||||||
\(580\) | 32.1534 | 1.33510 | ||||||||
\(581\) | −59.4774 | −2.46754 | ||||||||
\(582\) | 17.1309 | 0.710100 | ||||||||
\(583\) | 5.57137 | 0.230743 | ||||||||
\(584\) | 37.5902 | 1.55550 | ||||||||
\(585\) | 16.9366 | 0.700244 | ||||||||
\(586\) | 30.7267 | 1.26931 | ||||||||
\(587\) | −26.5565 | −1.09610 | −0.548051 | − | 0.836445i | \(-0.684630\pi\) | ||||
−0.548051 | + | 0.836445i | \(0.684630\pi\) | |||||||
\(588\) | 165.285 | 6.81626 | ||||||||
\(589\) | 25.3563 | 1.04479 | ||||||||
\(590\) | 9.85330 | 0.405654 | ||||||||
\(591\) | 36.5673 | 1.50418 | ||||||||
\(592\) | −1.75598 | −0.0721704 | ||||||||
\(593\) | 7.24201 | 0.297394 | 0.148697 | − | 0.988883i | \(-0.452492\pi\) | ||||
0.148697 | + | 0.988883i | \(0.452492\pi\) | |||||||
\(594\) | −26.8611 | −1.10212 | ||||||||
\(595\) | 19.4578 | 0.797693 | ||||||||
\(596\) | 45.5593 | 1.86618 | ||||||||
\(597\) | −12.6573 | −0.518029 | ||||||||
\(598\) | 63.1021 | 2.58044 | ||||||||
\(599\) | −17.4361 | −0.712418 | −0.356209 | − | 0.934406i | \(-0.615931\pi\) | ||||
−0.356209 | + | 0.934406i | \(0.615931\pi\) | |||||||
\(600\) | −10.6204 | −0.433577 | ||||||||
\(601\) | 4.09401 | 0.166998 | 0.0834991 | − | 0.996508i | \(-0.473390\pi\) | ||||
0.0834991 | + | 0.996508i | \(0.473390\pi\) | |||||||
\(602\) | 25.0089 | 1.01929 | ||||||||
\(603\) | 19.8843 | 0.809751 | ||||||||
\(604\) | 57.6647 | 2.34635 | ||||||||
\(605\) | −5.88506 | −0.239262 | ||||||||
\(606\) | 42.1676 | 1.71294 | ||||||||
\(607\) | 23.3676 | 0.948460 | 0.474230 | − | 0.880401i | \(-0.342727\pi\) | ||||
0.474230 | + | 0.880401i | \(0.342727\pi\) | |||||||
\(608\) | −9.92171 | −0.402378 | ||||||||
\(609\) | −120.459 | −4.88124 | ||||||||
\(610\) | 10.6249 | 0.430190 | ||||||||
\(611\) | −7.02506 | −0.284204 | ||||||||
\(612\) | −69.5583 | −2.81173 | ||||||||
\(613\) | 29.4024 | 1.18755 | 0.593775 | − | 0.804631i | \(-0.297637\pi\) | ||||
0.593775 | + | 0.804631i | \(0.297637\pi\) | |||||||
\(614\) | −16.3756 | −0.660866 | ||||||||
\(615\) | 16.5132 | 0.665875 | ||||||||
\(616\) | 41.6248 | 1.67711 | ||||||||
\(617\) | −32.7587 | −1.31881 | −0.659407 | − | 0.751786i | \(-0.729193\pi\) | ||||
−0.659407 | + | 0.751786i | \(0.729193\pi\) | |||||||
\(618\) | 113.173 | 4.55249 | ||||||||
\(619\) | −19.6423 | −0.789491 | −0.394746 | − | 0.918790i | \(-0.629167\pi\) | ||||
−0.394746 | + | 0.918790i | \(0.629167\pi\) | |||||||
\(620\) | −30.9777 | −1.24409 | ||||||||
\(621\) | −37.8578 | −1.51918 | ||||||||
\(622\) | 5.67814 | 0.227673 | ||||||||
\(623\) | 56.6120 | 2.26811 | ||||||||
\(624\) | 17.6810 | 0.707807 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −44.6633 | −1.78510 | ||||||||
\(627\) | −18.6414 | −0.744466 | ||||||||
\(628\) | 10.3681 | 0.413734 | ||||||||
\(629\) | 3.93755 | 0.157000 | ||||||||
\(630\) | 54.9539 | 2.18941 | ||||||||
\(631\) | −25.0025 | −0.995332 | −0.497666 | − | 0.867369i | \(-0.665810\pi\) | ||||
−0.497666 | + | 0.867369i | \(0.665810\pi\) | |||||||
\(632\) | −50.7141 | −2.01730 | ||||||||
\(633\) | −57.1589 | −2.27186 | ||||||||
\(634\) | 4.38562 | 0.174175 | ||||||||
\(635\) | −18.4810 | −0.733396 | ||||||||
\(636\) | 24.8064 | 0.983636 | ||||||||
\(637\) | 57.9591 | 2.29642 | ||||||||
\(638\) | −47.7437 | −1.89019 | ||||||||
\(639\) | 41.7622 | 1.65209 | ||||||||
\(640\) | 20.6136 | 0.814822 | ||||||||
\(641\) | −21.4298 | −0.846428 | −0.423214 | − | 0.906030i | \(-0.639098\pi\) | ||||
−0.423214 | + | 0.906030i | \(0.639098\pi\) | |||||||
\(642\) | 94.6871 | 3.73700 | ||||||||
\(643\) | −31.2499 | −1.23238 | −0.616188 | − | 0.787599i | \(-0.711324\pi\) | ||||
−0.616188 | + | 0.787599i | \(0.711324\pi\) | |||||||
\(644\) | 131.706 | 5.18993 | ||||||||
\(645\) | 6.09487 | 0.239985 | ||||||||
\(646\) | −28.1066 | −1.10584 | ||||||||
\(647\) | −40.4840 | −1.59159 | −0.795795 | − | 0.605567i | \(-0.792947\pi\) | ||||
−0.795795 | + | 0.605567i | \(0.792947\pi\) | |||||||
\(648\) | 1.45862 | 0.0573000 | ||||||||
\(649\) | −9.41153 | −0.369435 | ||||||||
\(650\) | −8.36084 | −0.327939 | ||||||||
\(651\) | 116.054 | 4.54853 | ||||||||
\(652\) | 4.51837 | 0.176953 | ||||||||
\(653\) | 6.54743 | 0.256221 | 0.128110 | − | 0.991760i | \(-0.459109\pi\) | ||||
0.128110 | + | 0.991760i | \(0.459109\pi\) | |||||||
\(654\) | −6.30407 | −0.246508 | ||||||||
\(655\) | −15.9517 | −0.623283 | ||||||||
\(656\) | 10.6055 | 0.414077 | ||||||||
\(657\) | −47.4024 | −1.84934 | ||||||||
\(658\) | −22.7940 | −0.888604 | ||||||||
\(659\) | 34.2884 | 1.33569 | 0.667844 | − | 0.744301i | \(-0.267217\pi\) | ||||
0.667844 | + | 0.744301i | \(0.267217\pi\) | |||||||
\(660\) | 22.7741 | 0.886482 | ||||||||
\(661\) | −6.84087 | −0.266079 | −0.133039 | − | 0.991111i | \(-0.542474\pi\) | ||||
−0.133039 | + | 0.991111i | \(0.542474\pi\) | |||||||
\(662\) | 28.3970 | 1.10368 | ||||||||
\(663\) | −39.6473 | −1.53977 | ||||||||
\(664\) | −46.7529 | −1.81436 | ||||||||
\(665\) | 14.2839 | 0.553907 | ||||||||
\(666\) | 11.1206 | 0.430916 | ||||||||
\(667\) | −67.2896 | −2.60546 | ||||||||
\(668\) | 31.2229 | 1.20805 | ||||||||
\(669\) | −27.9339 | −1.07999 | ||||||||
\(670\) | −9.81596 | −0.379224 | ||||||||
\(671\) | −10.1485 | −0.391780 | ||||||||
\(672\) | −45.4111 | −1.75177 | ||||||||
\(673\) | 48.1673 | 1.85671 | 0.928356 | − | 0.371693i | \(-0.121223\pi\) | ||||
0.928356 | + | 0.371693i | \(0.121223\pi\) | |||||||
\(674\) | 28.2678 | 1.08884 | ||||||||
\(675\) | 5.01604 | 0.193067 | ||||||||
\(676\) | −1.91658 | −0.0737148 | ||||||||
\(677\) | −9.32497 | −0.358388 | −0.179194 | − | 0.983814i | \(-0.557349\pi\) | ||||
−0.179194 | + | 0.983814i | \(0.557349\pi\) | |||||||
\(678\) | 62.0208 | 2.38190 | ||||||||
\(679\) | 12.5380 | 0.481165 | ||||||||
\(680\) | 15.2951 | 0.586538 | ||||||||
\(681\) | −62.2442 | −2.38520 | ||||||||
\(682\) | 45.9979 | 1.76135 | ||||||||
\(683\) | −25.8000 | −0.987210 | −0.493605 | − | 0.869686i | \(-0.664321\pi\) | ||||
−0.493605 | + | 0.869686i | \(0.664321\pi\) | |||||||
\(684\) | −51.0625 | −1.95242 | ||||||||
\(685\) | −1.38198 | −0.0528027 | ||||||||
\(686\) | 107.858 | 4.11803 | ||||||||
\(687\) | −17.9331 | −0.684191 | ||||||||
\(688\) | 3.91441 | 0.149236 | ||||||||
\(689\) | 8.69861 | 0.331391 | ||||||||
\(690\) | 49.8981 | 1.89959 | ||||||||
\(691\) | 31.4749 | 1.19736 | 0.598680 | − | 0.800988i | \(-0.295692\pi\) | ||||
0.598680 | + | 0.800988i | \(0.295692\pi\) | |||||||
\(692\) | −76.3323 | −2.90172 | ||||||||
\(693\) | −52.4900 | −1.99393 | ||||||||
\(694\) | 80.2983 | 3.04808 | ||||||||
\(695\) | 3.28084 | 0.124449 | ||||||||
\(696\) | −94.6882 | −3.58915 | ||||||||
\(697\) | −23.7815 | −0.900789 | ||||||||
\(698\) | 6.98381 | 0.264341 | ||||||||
\(699\) | −8.68154 | −0.328366 | ||||||||
\(700\) | −17.4506 | −0.659571 | ||||||||
\(701\) | 21.9338 | 0.828426 | 0.414213 | − | 0.910180i | \(-0.364057\pi\) | ||||
0.414213 | + | 0.910180i | \(0.364057\pi\) | |||||||
\(702\) | −41.9383 | −1.58286 | ||||||||
\(703\) | 2.89054 | 0.109019 | ||||||||
\(704\) | −26.1101 | −0.984061 | ||||||||
\(705\) | −5.55508 | −0.209216 | ||||||||
\(706\) | −1.50308 | −0.0565690 | ||||||||
\(707\) | 30.8621 | 1.16069 | ||||||||
\(708\) | −41.9046 | −1.57487 | ||||||||
\(709\) | −36.1334 | −1.35702 | −0.678508 | − | 0.734593i | \(-0.737373\pi\) | ||||
−0.678508 | + | 0.734593i | \(0.737373\pi\) | |||||||
\(710\) | −20.6161 | −0.773708 | ||||||||
\(711\) | 63.9519 | 2.39839 | ||||||||
\(712\) | 44.5005 | 1.66773 | ||||||||
\(713\) | 64.8291 | 2.42787 | ||||||||
\(714\) | −128.642 | −4.81432 | ||||||||
\(715\) | 7.98599 | 0.298659 | ||||||||
\(716\) | −94.4509 | −3.52979 | ||||||||
\(717\) | 47.0638 | 1.75763 | ||||||||
\(718\) | −20.4432 | −0.762933 | ||||||||
\(719\) | −29.0564 | −1.08362 | −0.541811 | − | 0.840500i | \(-0.682261\pi\) | ||||
−0.541811 | + | 0.840500i | \(0.682261\pi\) | |||||||
\(720\) | 8.60141 | 0.320556 | ||||||||
\(721\) | 82.8305 | 3.08477 | ||||||||
\(722\) | 24.3549 | 0.906395 | ||||||||
\(723\) | −44.9822 | −1.67291 | ||||||||
\(724\) | −37.0499 | −1.37695 | ||||||||
\(725\) | 8.91566 | 0.331119 | ||||||||
\(726\) | 38.9082 | 1.44402 | ||||||||
\(727\) | −10.4347 | −0.387001 | −0.193501 | − | 0.981100i | \(-0.561984\pi\) | ||||
−0.193501 | + | 0.981100i | \(0.561984\pi\) | |||||||
\(728\) | 64.9889 | 2.40865 | ||||||||
\(729\) | −43.8569 | −1.62433 | ||||||||
\(730\) | 23.4004 | 0.866087 | ||||||||
\(731\) | −8.77754 | −0.324649 | ||||||||
\(732\) | −45.1861 | −1.67013 | ||||||||
\(733\) | −43.2357 | −1.59695 | −0.798474 | − | 0.602030i | \(-0.794359\pi\) | ||||
−0.798474 | + | 0.602030i | \(0.794359\pi\) | |||||||
\(734\) | 15.1865 | 0.560545 | ||||||||
\(735\) | 45.8312 | 1.69051 | ||||||||
\(736\) | −25.3671 | −0.935043 | ||||||||
\(737\) | 9.37586 | 0.345364 | ||||||||
\(738\) | −67.1650 | −2.47238 | ||||||||
\(739\) | −26.9322 | −0.990718 | −0.495359 | − | 0.868688i | \(-0.664963\pi\) | ||||
−0.495359 | + | 0.868688i | \(0.664963\pi\) | |||||||
\(740\) | −3.53136 | −0.129815 | ||||||||
\(741\) | −29.1049 | −1.06920 | ||||||||
\(742\) | 28.2241 | 1.03614 | ||||||||
\(743\) | −33.5079 | −1.22929 | −0.614643 | − | 0.788806i | \(-0.710700\pi\) | ||||
−0.614643 | + | 0.788806i | \(0.710700\pi\) | |||||||
\(744\) | 91.2258 | 3.34450 | ||||||||
\(745\) | 12.6329 | 0.462834 | ||||||||
\(746\) | −2.25023 | −0.0823868 | ||||||||
\(747\) | 58.9567 | 2.15711 | ||||||||
\(748\) | −32.7982 | −1.19922 | ||||||||
\(749\) | 69.3008 | 2.53220 | ||||||||
\(750\) | −6.61135 | −0.241412 | ||||||||
\(751\) | 28.0379 | 1.02312 | 0.511559 | − | 0.859248i | \(-0.329068\pi\) | ||||
0.511559 | + | 0.859248i | \(0.329068\pi\) | |||||||
\(752\) | −3.56774 | −0.130102 | ||||||||
\(753\) | 6.46328 | 0.235535 | ||||||||
\(754\) | −74.5424 | −2.71468 | ||||||||
\(755\) | 15.9896 | 0.581921 | ||||||||
\(756\) | −87.5329 | −3.18354 | ||||||||
\(757\) | −31.7709 | −1.15473 | −0.577366 | − | 0.816485i | \(-0.695920\pi\) | ||||
−0.577366 | + | 0.816485i | \(0.695920\pi\) | |||||||
\(758\) | 43.7127 | 1.58772 | ||||||||
\(759\) | −47.6609 | −1.72998 | ||||||||
\(760\) | 11.2280 | 0.407284 | ||||||||
\(761\) | 2.57964 | 0.0935118 | 0.0467559 | − | 0.998906i | \(-0.485112\pi\) | ||||
0.0467559 | + | 0.998906i | \(0.485112\pi\) | |||||||
\(762\) | 122.184 | 4.42627 | ||||||||
\(763\) | −4.61390 | −0.167034 | ||||||||
\(764\) | 19.9260 | 0.720896 | ||||||||
\(765\) | −19.2875 | −0.697341 | ||||||||
\(766\) | −15.8612 | −0.573088 | ||||||||
\(767\) | −14.6943 | −0.530579 | ||||||||
\(768\) | −71.8121 | −2.59130 | ||||||||
\(769\) | −6.93037 | −0.249916 | −0.124958 | − | 0.992162i | \(-0.539880\pi\) | ||||
−0.124958 | + | 0.992162i | \(0.539880\pi\) | |||||||
\(770\) | 25.9119 | 0.933801 | ||||||||
\(771\) | −65.5797 | −2.36179 | ||||||||
\(772\) | 13.1155 | 0.472038 | ||||||||
\(773\) | 0.936234 | 0.0336740 | 0.0168370 | − | 0.999858i | \(-0.494640\pi\) | ||||
0.0168370 | + | 0.999858i | \(0.494640\pi\) | |||||||
\(774\) | −24.7900 | −0.891059 | ||||||||
\(775\) | −8.58965 | −0.308549 | ||||||||
\(776\) | 9.85565 | 0.353797 | ||||||||
\(777\) | 13.2298 | 0.474618 | ||||||||
\(778\) | −85.1090 | −3.05131 | ||||||||
\(779\) | −17.4579 | −0.625495 | ||||||||
\(780\) | 35.5574 | 1.27316 | ||||||||
\(781\) | 19.6918 | 0.704627 | ||||||||
\(782\) | −71.8609 | −2.56974 | ||||||||
\(783\) | 44.7213 | 1.59821 | ||||||||
\(784\) | 29.4350 | 1.05125 | ||||||||
\(785\) | 2.87493 | 0.102611 | ||||||||
\(786\) | 105.462 | 3.76170 | ||||||||
\(787\) | −8.72173 | −0.310896 | −0.155448 | − | 0.987844i | \(-0.549682\pi\) | ||||
−0.155448 | + | 0.987844i | \(0.549682\pi\) | |||||||
\(788\) | 47.2300 | 1.68250 | ||||||||
\(789\) | −20.1740 | −0.718215 | ||||||||
\(790\) | −31.5701 | −1.12322 | ||||||||
\(791\) | 45.3926 | 1.61397 | ||||||||
\(792\) | −41.2604 | −1.46612 | ||||||||
\(793\) | −15.8450 | −0.562671 | ||||||||
\(794\) | −61.2611 | −2.17408 | ||||||||
\(795\) | 6.87844 | 0.243953 | ||||||||
\(796\) | −16.3481 | −0.579442 | ||||||||
\(797\) | 2.10910 | 0.0747083 | 0.0373541 | − | 0.999302i | \(-0.488107\pi\) | ||||
0.0373541 | + | 0.999302i | \(0.488107\pi\) | |||||||
\(798\) | −94.4360 | −3.34300 | ||||||||
\(799\) | 8.00017 | 0.283025 | ||||||||
\(800\) | 3.36106 | 0.118831 | ||||||||
\(801\) | −56.1164 | −1.98278 | ||||||||
\(802\) | −57.8765 | −2.04369 | ||||||||
\(803\) | −22.3512 | −0.788758 | ||||||||
\(804\) | 41.7457 | 1.47226 | ||||||||
\(805\) | 36.5201 | 1.28716 | ||||||||
\(806\) | 71.8167 | 2.52964 | ||||||||
\(807\) | 77.5852 | 2.73113 | ||||||||
\(808\) | 24.2595 | 0.853448 | ||||||||
\(809\) | 10.3546 | 0.364049 | 0.182024 | − | 0.983294i | \(-0.441735\pi\) | ||||
0.182024 | + | 0.983294i | \(0.441735\pi\) | |||||||
\(810\) | 0.908009 | 0.0319042 | ||||||||
\(811\) | 27.6983 | 0.972619 | 0.486310 | − | 0.873787i | \(-0.338343\pi\) | ||||
0.486310 | + | 0.873787i | \(0.338343\pi\) | |||||||
\(812\) | −155.584 | −5.45992 | ||||||||
\(813\) | 53.8064 | 1.88707 | ||||||||
\(814\) | 5.24362 | 0.183789 | ||||||||
\(815\) | 1.25288 | 0.0438863 | ||||||||
\(816\) | −20.1352 | −0.704873 | ||||||||
\(817\) | −6.44356 | −0.225432 | ||||||||
\(818\) | −36.2119 | −1.26612 | ||||||||
\(819\) | −81.9529 | −2.86367 | ||||||||
\(820\) | 21.3283 | 0.744815 | ||||||||
\(821\) | −14.6702 | −0.511995 | −0.255997 | − | 0.966677i | \(-0.582404\pi\) | ||||
−0.255997 | + | 0.966677i | \(0.582404\pi\) | |||||||
\(822\) | 9.13674 | 0.318680 | ||||||||
\(823\) | 53.3549 | 1.85984 | 0.929918 | − | 0.367767i | \(-0.119877\pi\) | ||||
0.929918 | + | 0.367767i | \(0.119877\pi\) | |||||||
\(824\) | 65.1099 | 2.26821 | ||||||||
\(825\) | 6.31493 | 0.219858 | ||||||||
\(826\) | −47.6781 | −1.65893 | ||||||||
\(827\) | 3.87862 | 0.134873 | 0.0674363 | − | 0.997724i | \(-0.478518\pi\) | ||||
0.0674363 | + | 0.997724i | \(0.478518\pi\) | |||||||
\(828\) | −130.553 | −4.53702 | ||||||||
\(829\) | 32.4421 | 1.12676 | 0.563381 | − | 0.826197i | \(-0.309500\pi\) | ||||
0.563381 | + | 0.826197i | \(0.309500\pi\) | |||||||
\(830\) | −29.1042 | −1.01022 | ||||||||
\(831\) | −17.7024 | −0.614089 | ||||||||
\(832\) | −40.7658 | −1.41330 | ||||||||
\(833\) | −66.0040 | −2.28690 | ||||||||
\(834\) | −21.6907 | −0.751089 | ||||||||
\(835\) | 8.65766 | 0.299611 | ||||||||
\(836\) | −24.0771 | −0.832723 | ||||||||
\(837\) | −43.0860 | −1.48927 | ||||||||
\(838\) | 49.0026 | 1.69277 | ||||||||
\(839\) | −4.25650 | −0.146951 | −0.0734753 | − | 0.997297i | \(-0.523409\pi\) | ||||
−0.0734753 | + | 0.997297i | \(0.523409\pi\) | |||||||
\(840\) | 51.3901 | 1.77313 | ||||||||
\(841\) | 50.4890 | 1.74100 | ||||||||
\(842\) | −10.1550 | −0.349964 | ||||||||
\(843\) | −11.7835 | −0.405845 | ||||||||
\(844\) | −73.8260 | −2.54120 | ||||||||
\(845\) | −0.531441 | −0.0182821 | ||||||||
\(846\) | 22.5945 | 0.776815 | ||||||||
\(847\) | 28.4766 | 0.978467 | ||||||||
\(848\) | 4.41766 | 0.151703 | ||||||||
\(849\) | 43.0080 | 1.47603 | ||||||||
\(850\) | 9.52136 | 0.326580 | ||||||||
\(851\) | 7.39032 | 0.253337 | ||||||||
\(852\) | 87.6770 | 3.00377 | ||||||||
\(853\) | −18.1012 | −0.619774 | −0.309887 | − | 0.950773i | \(-0.600291\pi\) | ||||
−0.309887 | + | 0.950773i | \(0.600291\pi\) | |||||||
\(854\) | −51.4118 | −1.75927 | ||||||||
\(855\) | −14.1589 | −0.484224 | ||||||||
\(856\) | 54.4747 | 1.86191 | ||||||||
\(857\) | 19.8436 | 0.677844 | 0.338922 | − | 0.940815i | \(-0.389938\pi\) | ||||
0.338922 | + | 0.940815i | \(0.389938\pi\) | |||||||
\(858\) | −52.7981 | −1.80250 | ||||||||
\(859\) | −4.33114 | −0.147777 | −0.0738883 | − | 0.997267i | \(-0.523541\pi\) | ||||
−0.0738883 | + | 0.997267i | \(0.523541\pi\) | |||||||
\(860\) | 7.87207 | 0.268435 | ||||||||
\(861\) | −79.9039 | −2.72312 | ||||||||
\(862\) | −25.0605 | −0.853564 | ||||||||
\(863\) | −24.3887 | −0.830200 | −0.415100 | − | 0.909776i | \(-0.636253\pi\) | ||||
−0.415100 | + | 0.909776i | \(0.636253\pi\) | |||||||
\(864\) | 16.8592 | 0.573562 | ||||||||
\(865\) | −21.1658 | −0.719659 | ||||||||
\(866\) | −9.19351 | −0.312408 | ||||||||
\(867\) | −2.31713 | −0.0786939 | ||||||||
\(868\) | 149.895 | 5.08776 | ||||||||
\(869\) | 30.1547 | 1.02293 | ||||||||
\(870\) | −58.9445 | −1.99841 | ||||||||
\(871\) | 14.6386 | 0.496009 | ||||||||
\(872\) | −3.62681 | −0.122819 | ||||||||
\(873\) | −12.4283 | −0.420633 | ||||||||
\(874\) | −52.7528 | −1.78439 | ||||||||
\(875\) | −4.83880 | −0.163581 | ||||||||
\(876\) | −99.5182 | −3.36241 | ||||||||
\(877\) | 11.0874 | 0.374396 | 0.187198 | − | 0.982322i | \(-0.440059\pi\) | ||||
0.187198 | + | 0.982322i | \(0.440059\pi\) | |||||||
\(878\) | 61.9406 | 2.09040 | ||||||||
\(879\) | −36.2345 | −1.22216 | ||||||||
\(880\) | 4.05575 | 0.136719 | ||||||||
\(881\) | 49.9000 | 1.68117 | 0.840586 | − | 0.541678i | \(-0.182211\pi\) | ||||
0.840586 | + | 0.541678i | \(0.182211\pi\) | |||||||
\(882\) | −186.412 | −6.27682 | ||||||||
\(883\) | −10.1601 | −0.341914 | −0.170957 | − | 0.985279i | \(-0.554686\pi\) | ||||
−0.170957 | + | 0.985279i | \(0.554686\pi\) | |||||||
\(884\) | −51.2081 | −1.72231 | ||||||||
\(885\) | −11.6195 | −0.390586 | ||||||||
\(886\) | 40.9272 | 1.37497 | ||||||||
\(887\) | 16.0136 | 0.537684 | 0.268842 | − | 0.963184i | \(-0.413359\pi\) | ||||
0.268842 | + | 0.963184i | \(0.413359\pi\) | |||||||
\(888\) | 10.3995 | 0.348983 | ||||||||
\(889\) | 89.4257 | 2.99924 | ||||||||
\(890\) | 27.7021 | 0.928577 | ||||||||
\(891\) | −0.867299 | −0.0290556 | ||||||||
\(892\) | −36.0792 | −1.20802 | ||||||||
\(893\) | 5.87289 | 0.196529 | ||||||||
\(894\) | −83.5206 | −2.79335 | ||||||||
\(895\) | −26.1898 | −0.875429 | ||||||||
\(896\) | −99.7448 | −3.33224 | ||||||||
\(897\) | −74.4133 | −2.48459 | ||||||||
\(898\) | 68.2793 | 2.27851 | ||||||||
\(899\) | −76.5824 | −2.55417 | ||||||||
\(900\) | 17.2979 | 0.576595 | ||||||||
\(901\) | −9.90600 | −0.330017 | ||||||||
\(902\) | −31.6697 | −1.05449 | ||||||||
\(903\) | −29.4918 | −0.981426 | ||||||||
\(904\) | 35.6814 | 1.18674 | ||||||||
\(905\) | −10.2734 | −0.341499 | ||||||||
\(906\) | −105.713 | −3.51207 | ||||||||
\(907\) | 35.9530 | 1.19380 | 0.596901 | − | 0.802315i | \(-0.296399\pi\) | ||||
0.596901 | + | 0.802315i | \(0.296399\pi\) | |||||||
\(908\) | −80.3940 | −2.66797 | ||||||||
\(909\) | −30.5920 | −1.01467 | ||||||||
\(910\) | 40.4564 | 1.34112 | ||||||||
\(911\) | 24.0272 | 0.796055 | 0.398028 | − | 0.917373i | \(-0.369695\pi\) | ||||
0.398028 | + | 0.917373i | \(0.369695\pi\) | |||||||
\(912\) | −14.7812 | −0.489454 | ||||||||
\(913\) | 27.7994 | 0.920024 | ||||||||
\(914\) | −90.6046 | −2.99693 | ||||||||
\(915\) | −12.5294 | −0.414210 | ||||||||
\(916\) | −23.1622 | −0.765302 | ||||||||
\(917\) | 77.1868 | 2.54893 | ||||||||
\(918\) | 47.7595 | 1.57630 | ||||||||
\(919\) | 25.1177 | 0.828557 | 0.414279 | − | 0.910150i | \(-0.364034\pi\) | ||||
0.414279 | + | 0.910150i | \(0.364034\pi\) | |||||||
\(920\) | 28.7070 | 0.946442 | ||||||||
\(921\) | 19.3110 | 0.636317 | ||||||||
\(922\) | 49.2587 | 1.62225 | ||||||||
\(923\) | 30.7449 | 1.01198 | ||||||||
\(924\) | −110.199 | −3.62529 | ||||||||
\(925\) | −0.979194 | −0.0321957 | ||||||||
\(926\) | −100.482 | −3.30206 | ||||||||
\(927\) | −82.1054 | −2.69670 | ||||||||
\(928\) | 29.9661 | 0.983685 | ||||||||
\(929\) | 35.5277 | 1.16563 | 0.582813 | − | 0.812606i | \(-0.301952\pi\) | ||||
0.582813 | + | 0.812606i | \(0.301952\pi\) | |||||||
\(930\) | 56.7892 | 1.86219 | ||||||||
\(931\) | −48.4533 | −1.58799 | ||||||||
\(932\) | −11.2130 | −0.367294 | ||||||||
\(933\) | −6.69595 | −0.219216 | ||||||||
\(934\) | 57.1800 | 1.87099 | ||||||||
\(935\) | −9.09447 | −0.297421 | ||||||||
\(936\) | −64.4201 | −2.10564 | ||||||||
\(937\) | −24.5818 | −0.803052 | −0.401526 | − | 0.915848i | \(-0.631520\pi\) | ||||
−0.401526 | + | 0.915848i | \(0.631520\pi\) | |||||||
\(938\) | 47.4974 | 1.55085 | ||||||||
\(939\) | 52.6692 | 1.71880 | ||||||||
\(940\) | −7.17489 | −0.234019 | ||||||||
\(941\) | −0.231228 | −0.00753783 | −0.00376891 | − | 0.999993i | \(-0.501200\pi\) | ||||
−0.00376891 | + | 0.999993i | \(0.501200\pi\) | |||||||
\(942\) | −19.0072 | −0.619287 | ||||||||
\(943\) | −44.6351 | −1.45352 | ||||||||
\(944\) | −7.46261 | −0.242887 | ||||||||
\(945\) | −24.2716 | −0.789555 | ||||||||
\(946\) | −11.6890 | −0.380043 | ||||||||
\(947\) | −28.9559 | −0.940940 | −0.470470 | − | 0.882416i | \(-0.655916\pi\) | ||||
−0.470470 | + | 0.882416i | \(0.655916\pi\) | |||||||
\(948\) | 134.263 | 4.36066 | ||||||||
\(949\) | −34.8971 | −1.13281 | ||||||||
\(950\) | 6.98959 | 0.226772 | ||||||||
\(951\) | −5.17175 | −0.167706 | ||||||||
\(952\) | −74.0096 | −2.39867 | ||||||||
\(953\) | −0.843160 | −0.0273126 | −0.0136563 | − | 0.999907i | \(-0.504347\pi\) | ||||
−0.0136563 | + | 0.999907i | \(0.504347\pi\) | |||||||
\(954\) | −27.9771 | −0.905791 | ||||||||
\(955\) | 5.52518 | 0.178791 | ||||||||
\(956\) | 60.7872 | 1.96600 | ||||||||
\(957\) | 56.3018 | 1.81998 | ||||||||
\(958\) | 42.8647 | 1.38490 | ||||||||
\(959\) | 6.68711 | 0.215938 | ||||||||
\(960\) | −32.2356 | −1.04040 | ||||||||
\(961\) | 42.7821 | 1.38007 | ||||||||
\(962\) | 8.18689 | 0.263956 | ||||||||
\(963\) | −68.6942 | −2.21364 | ||||||||
\(964\) | −58.0987 | −1.87123 | ||||||||
\(965\) | 3.63674 | 0.117071 | ||||||||
\(966\) | −241.447 | −7.76842 | ||||||||
\(967\) | 53.0160 | 1.70488 | 0.852440 | − | 0.522824i | \(-0.175122\pi\) | ||||
0.852440 | + | 0.522824i | \(0.175122\pi\) | |||||||
\(968\) | 22.3844 | 0.719460 | ||||||||
\(969\) | 33.1448 | 1.06476 | ||||||||
\(970\) | 6.13526 | 0.196991 | ||||||||
\(971\) | −27.6344 | −0.886832 | −0.443416 | − | 0.896316i | \(-0.646233\pi\) | ||||
−0.443416 | + | 0.896316i | \(0.646233\pi\) | |||||||
\(972\) | −58.1311 | −1.86455 | ||||||||
\(973\) | −15.8753 | −0.508939 | ||||||||
\(974\) | 14.5759 | 0.467042 | ||||||||
\(975\) | 9.85953 | 0.315758 | ||||||||
\(976\) | −8.04700 | −0.257578 | ||||||||
\(977\) | −28.7830 | −0.920851 | −0.460425 | − | 0.887698i | \(-0.652303\pi\) | ||||
−0.460425 | + | 0.887698i | \(0.652303\pi\) | |||||||
\(978\) | −8.28320 | −0.264868 | ||||||||
\(979\) | −26.4601 | −0.845668 | ||||||||
\(980\) | 59.1952 | 1.89092 | ||||||||
\(981\) | 4.57351 | 0.146021 | ||||||||
\(982\) | −70.6933 | −2.25591 | ||||||||
\(983\) | 12.0374 | 0.383934 | 0.191967 | − | 0.981401i | \(-0.438513\pi\) | ||||
0.191967 | + | 0.981401i | \(0.438513\pi\) | |||||||
\(984\) | −62.8094 | −2.00229 | ||||||||
\(985\) | 13.0962 | 0.417279 | ||||||||
\(986\) | 84.8892 | 2.70342 | ||||||||
\(987\) | 26.8799 | 0.855596 | ||||||||
\(988\) | −37.5916 | −1.19595 | ||||||||
\(989\) | −16.4744 | −0.523856 | ||||||||
\(990\) | −25.6851 | −0.816326 | ||||||||
\(991\) | −51.7046 | −1.64245 | −0.821226 | − | 0.570603i | \(-0.806710\pi\) | ||||
−0.821226 | + | 0.570603i | \(0.806710\pi\) | |||||||
\(992\) | −28.8703 | −0.916634 | ||||||||
\(993\) | −33.4872 | −1.06268 | ||||||||
\(994\) | 99.7571 | 3.16410 | ||||||||
\(995\) | −4.53308 | −0.143708 | ||||||||
\(996\) | 123.776 | 3.92199 | ||||||||
\(997\) | −39.3223 | −1.24535 | −0.622675 | − | 0.782481i | \(-0.713954\pi\) | ||||
−0.622675 | + | 0.782481i | \(0.713954\pi\) | |||||||
\(998\) | 32.4358 | 1.02674 | ||||||||
\(999\) | −4.91168 | −0.155399 |
(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 | 8005.2.a.e.1.15 | ✓ | 126 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8005.2.a.e.1.15 | ✓ | 126 | 1.1 | even | 1 | trivial |