Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.756159 | −0.534685 | −0.267343 | − | 0.963602i | \(-0.586146\pi\) | ||||
−0.267343 | + | 0.963602i | \(0.586146\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.42822 | −0.714112 | ||||||||
\(5\) | −3.23827 | −1.44820 | −0.724099 | − | 0.689696i | \(-0.757744\pi\) | ||||
−0.724099 | + | 0.689696i | \(0.757744\pi\) | |||||||
\(6\) | −0.756159 | −0.308701 | ||||||||
\(7\) | 4.69700 | 1.77530 | 0.887650 | − | 0.460520i | \(-0.152337\pi\) | ||||
0.887650 | + | 0.460520i | \(0.152337\pi\) | |||||||
\(8\) | 2.59228 | 0.916510 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.44865 | 0.774330 | ||||||||
\(11\) | 3.89444 | 1.17422 | 0.587109 | − | 0.809508i | \(-0.300266\pi\) | ||||
0.587109 | + | 0.809508i | \(0.300266\pi\) | |||||||
\(12\) | −1.42822 | −0.412292 | ||||||||
\(13\) | 0.979560 | 0.271681 | 0.135841 | − | 0.990731i | \(-0.456627\pi\) | ||||
0.135841 | + | 0.990731i | \(0.456627\pi\) | |||||||
\(14\) | −3.55168 | −0.949227 | ||||||||
\(15\) | −3.23827 | −0.836117 | ||||||||
\(16\) | 0.896267 | 0.224067 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.756159 | −0.178228 | ||||||||
\(19\) | −4.21016 | −0.965878 | −0.482939 | − | 0.875654i | \(-0.660431\pi\) | ||||
−0.482939 | + | 0.875654i | \(0.660431\pi\) | |||||||
\(20\) | 4.62497 | 1.03417 | ||||||||
\(21\) | 4.69700 | 1.02497 | ||||||||
\(22\) | −2.94482 | −0.627838 | ||||||||
\(23\) | −3.94172 | −0.821905 | −0.410952 | − | 0.911657i | \(-0.634804\pi\) | ||||
−0.410952 | + | 0.911657i | \(0.634804\pi\) | |||||||
\(24\) | 2.59228 | 0.529148 | ||||||||
\(25\) | 5.48638 | 1.09728 | ||||||||
\(26\) | −0.740704 | −0.145264 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −6.70836 | −1.26776 | ||||||||
\(29\) | 5.35490 | 0.994380 | 0.497190 | − | 0.867642i | \(-0.334365\pi\) | ||||
0.497190 | + | 0.867642i | \(0.334365\pi\) | |||||||
\(30\) | 2.44865 | 0.447060 | ||||||||
\(31\) | −3.41929 | −0.614122 | −0.307061 | − | 0.951690i | \(-0.599346\pi\) | ||||
−0.307061 | + | 0.951690i | \(0.599346\pi\) | |||||||
\(32\) | −5.86229 | −1.03632 | ||||||||
\(33\) | 3.89444 | 0.677936 | ||||||||
\(34\) | 0.756159 | 0.129680 | ||||||||
\(35\) | −15.2101 | −2.57098 | ||||||||
\(36\) | −1.42822 | −0.238037 | ||||||||
\(37\) | −9.92936 | −1.63238 | −0.816188 | − | 0.577786i | \(-0.803917\pi\) | ||||
−0.816188 | + | 0.577786i | \(0.803917\pi\) | |||||||
\(38\) | 3.18355 | 0.516441 | ||||||||
\(39\) | 0.979560 | 0.156855 | ||||||||
\(40\) | −8.39451 | −1.32729 | ||||||||
\(41\) | −2.77702 | −0.433697 | −0.216848 | − | 0.976205i | \(-0.569578\pi\) | ||||
−0.216848 | + | 0.976205i | \(0.569578\pi\) | |||||||
\(42\) | −3.55168 | −0.548036 | ||||||||
\(43\) | 8.94697 | 1.36440 | 0.682200 | − | 0.731165i | \(-0.261023\pi\) | ||||
0.682200 | + | 0.731165i | \(0.261023\pi\) | |||||||
\(44\) | −5.56213 | −0.838523 | ||||||||
\(45\) | −3.23827 | −0.482732 | ||||||||
\(46\) | 2.98057 | 0.439460 | ||||||||
\(47\) | −7.88353 | −1.14993 | −0.574965 | − | 0.818178i | \(-0.694984\pi\) | ||||
−0.574965 | + | 0.818178i | \(0.694984\pi\) | |||||||
\(48\) | 0.896267 | 0.129365 | ||||||||
\(49\) | 15.0618 | 2.15169 | ||||||||
\(50\) | −4.14858 | −0.586697 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −1.39903 | −0.194011 | ||||||||
\(53\) | −12.9229 | −1.77510 | −0.887551 | − | 0.460710i | \(-0.847595\pi\) | ||||
−0.887551 | + | 0.460710i | \(0.847595\pi\) | |||||||
\(54\) | −0.756159 | −0.102900 | ||||||||
\(55\) | −12.6113 | −1.70050 | ||||||||
\(56\) | 12.1760 | 1.62708 | ||||||||
\(57\) | −4.21016 | −0.557650 | ||||||||
\(58\) | −4.04916 | −0.531681 | ||||||||
\(59\) | −8.38870 | −1.09212 | −0.546058 | − | 0.837748i | \(-0.683872\pi\) | ||||
−0.546058 | + | 0.837748i | \(0.683872\pi\) | |||||||
\(60\) | 4.62497 | 0.597081 | ||||||||
\(61\) | −2.01800 | −0.258379 | −0.129189 | − | 0.991620i | \(-0.541237\pi\) | ||||
−0.129189 | + | 0.991620i | \(0.541237\pi\) | |||||||
\(62\) | 2.58553 | 0.328362 | ||||||||
\(63\) | 4.69700 | 0.591766 | ||||||||
\(64\) | 2.64029 | 0.330036 | ||||||||
\(65\) | −3.17208 | −0.393448 | ||||||||
\(66\) | −2.94482 | −0.362482 | ||||||||
\(67\) | −9.85675 | −1.20419 | −0.602097 | − | 0.798423i | \(-0.705668\pi\) | ||||
−0.602097 | + | 0.798423i | \(0.705668\pi\) | |||||||
\(68\) | 1.42822 | 0.173197 | ||||||||
\(69\) | −3.94172 | −0.474527 | ||||||||
\(70\) | 11.5013 | 1.37467 | ||||||||
\(71\) | 3.35982 | 0.398737 | 0.199369 | − | 0.979925i | \(-0.436111\pi\) | ||||
0.199369 | + | 0.979925i | \(0.436111\pi\) | |||||||
\(72\) | 2.59228 | 0.305503 | ||||||||
\(73\) | −4.43641 | −0.519242 | −0.259621 | − | 0.965711i | \(-0.583598\pi\) | ||||
−0.259621 | + | 0.965711i | \(0.583598\pi\) | |||||||
\(74\) | 7.50818 | 0.872808 | ||||||||
\(75\) | 5.48638 | 0.633513 | ||||||||
\(76\) | 6.01305 | 0.689744 | ||||||||
\(77\) | 18.2922 | 2.08459 | ||||||||
\(78\) | −0.740704 | −0.0838682 | ||||||||
\(79\) | −7.68352 | −0.864464 | −0.432232 | − | 0.901763i | \(-0.642274\pi\) | ||||
−0.432232 | + | 0.901763i | \(0.642274\pi\) | |||||||
\(80\) | −2.90235 | −0.324493 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.09987 | 0.231891 | ||||||||
\(83\) | 1.36491 | 0.149818 | 0.0749089 | − | 0.997190i | \(-0.476133\pi\) | ||||
0.0749089 | + | 0.997190i | \(0.476133\pi\) | |||||||
\(84\) | −6.70836 | −0.731942 | ||||||||
\(85\) | 3.23827 | 0.351239 | ||||||||
\(86\) | −6.76534 | −0.729525 | ||||||||
\(87\) | 5.35490 | 0.574106 | ||||||||
\(88\) | 10.0955 | 1.07618 | ||||||||
\(89\) | 11.2296 | 1.19034 | 0.595168 | − | 0.803601i | \(-0.297086\pi\) | ||||
0.595168 | + | 0.803601i | \(0.297086\pi\) | |||||||
\(90\) | 2.44865 | 0.258110 | ||||||||
\(91\) | 4.60099 | 0.482315 | ||||||||
\(92\) | 5.62965 | 0.586932 | ||||||||
\(93\) | −3.41929 | −0.354564 | ||||||||
\(94\) | 5.96120 | 0.614851 | ||||||||
\(95\) | 13.6336 | 1.39878 | ||||||||
\(96\) | −5.86229 | −0.598317 | ||||||||
\(97\) | −9.58636 | −0.973347 | −0.486674 | − | 0.873584i | \(-0.661790\pi\) | ||||
−0.486674 | + | 0.873584i | \(0.661790\pi\) | |||||||
\(98\) | −11.3891 | −1.15048 | ||||||||
\(99\) | 3.89444 | 0.391406 | ||||||||
\(100\) | −7.83577 | −0.783577 | ||||||||
\(101\) | −9.91835 | −0.986913 | −0.493456 | − | 0.869771i | \(-0.664267\pi\) | ||||
−0.493456 | + | 0.869771i | \(0.664267\pi\) | |||||||
\(102\) | 0.756159 | 0.0748709 | ||||||||
\(103\) | 15.4652 | 1.52384 | 0.761918 | − | 0.647674i | \(-0.224258\pi\) | ||||
0.761918 | + | 0.647674i | \(0.224258\pi\) | |||||||
\(104\) | 2.53930 | 0.248999 | ||||||||
\(105\) | −15.2101 | −1.48436 | ||||||||
\(106\) | 9.77180 | 0.949121 | ||||||||
\(107\) | 3.10496 | 0.300168 | 0.150084 | − | 0.988673i | \(-0.452046\pi\) | ||||
0.150084 | + | 0.988673i | \(0.452046\pi\) | |||||||
\(108\) | −1.42822 | −0.137431 | ||||||||
\(109\) | 16.2718 | 1.55856 | 0.779278 | − | 0.626678i | \(-0.215586\pi\) | ||||
0.779278 | + | 0.626678i | \(0.215586\pi\) | |||||||
\(110\) | 9.53612 | 0.909233 | ||||||||
\(111\) | −9.92936 | −0.942453 | ||||||||
\(112\) | 4.20977 | 0.397785 | ||||||||
\(113\) | −21.1316 | −1.98790 | −0.993949 | − | 0.109842i | \(-0.964966\pi\) | ||||
−0.993949 | + | 0.109842i | \(0.964966\pi\) | |||||||
\(114\) | 3.18355 | 0.298167 | ||||||||
\(115\) | 12.7643 | 1.19028 | ||||||||
\(116\) | −7.64799 | −0.710098 | ||||||||
\(117\) | 0.979560 | 0.0905604 | ||||||||
\(118\) | 6.34319 | 0.583938 | ||||||||
\(119\) | −4.69700 | −0.430573 | ||||||||
\(120\) | −8.39451 | −0.766310 | ||||||||
\(121\) | 4.16669 | 0.378790 | ||||||||
\(122\) | 1.52593 | 0.138151 | ||||||||
\(123\) | −2.77702 | −0.250395 | ||||||||
\(124\) | 4.88350 | 0.438552 | ||||||||
\(125\) | −1.57503 | −0.140875 | ||||||||
\(126\) | −3.55168 | −0.316409 | ||||||||
\(127\) | −5.92498 | −0.525757 | −0.262879 | − | 0.964829i | \(-0.584672\pi\) | ||||
−0.262879 | + | 0.964829i | \(0.584672\pi\) | |||||||
\(128\) | 9.72809 | 0.859850 | ||||||||
\(129\) | 8.94697 | 0.787737 | ||||||||
\(130\) | 2.39860 | 0.210371 | ||||||||
\(131\) | −1.70352 | −0.148837 | −0.0744186 | − | 0.997227i | \(-0.523710\pi\) | ||||
−0.0744186 | + | 0.997227i | \(0.523710\pi\) | |||||||
\(132\) | −5.56213 | −0.484122 | ||||||||
\(133\) | −19.7751 | −1.71472 | ||||||||
\(134\) | 7.45327 | 0.643865 | ||||||||
\(135\) | −3.23827 | −0.278706 | ||||||||
\(136\) | −2.59228 | −0.222286 | ||||||||
\(137\) | −10.5268 | −0.899367 | −0.449684 | − | 0.893188i | \(-0.648463\pi\) | ||||
−0.449684 | + | 0.893188i | \(0.648463\pi\) | |||||||
\(138\) | 2.98057 | 0.253723 | ||||||||
\(139\) | 13.2214 | 1.12143 | 0.560714 | − | 0.828009i | \(-0.310527\pi\) | ||||
0.560714 | + | 0.828009i | \(0.310527\pi\) | |||||||
\(140\) | 21.7235 | 1.83597 | ||||||||
\(141\) | −7.88353 | −0.663913 | ||||||||
\(142\) | −2.54056 | −0.213199 | ||||||||
\(143\) | 3.81484 | 0.319013 | ||||||||
\(144\) | 0.896267 | 0.0746889 | ||||||||
\(145\) | −17.3406 | −1.44006 | ||||||||
\(146\) | 3.35463 | 0.277631 | ||||||||
\(147\) | 15.0618 | 1.24228 | ||||||||
\(148\) | 14.1813 | 1.16570 | ||||||||
\(149\) | 1.29815 | 0.106349 | 0.0531744 | − | 0.998585i | \(-0.483066\pi\) | ||||
0.0531744 | + | 0.998585i | \(0.483066\pi\) | |||||||
\(150\) | −4.14858 | −0.338730 | ||||||||
\(151\) | 24.2497 | 1.97341 | 0.986706 | − | 0.162516i | \(-0.0519609\pi\) | ||||
0.986706 | + | 0.162516i | \(0.0519609\pi\) | |||||||
\(152\) | −10.9139 | −0.885237 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −13.8318 | −1.11460 | ||||||||
\(155\) | 11.0726 | 0.889370 | ||||||||
\(156\) | −1.39903 | −0.112012 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | 5.80997 | 0.462216 | ||||||||
\(159\) | −12.9229 | −1.02486 | ||||||||
\(160\) | 18.9837 | 1.50079 | ||||||||
\(161\) | −18.5142 | −1.45913 | ||||||||
\(162\) | −0.756159 | −0.0594095 | ||||||||
\(163\) | −17.3444 | −1.35852 | −0.679258 | − | 0.733900i | \(-0.737698\pi\) | ||||
−0.679258 | + | 0.733900i | \(0.737698\pi\) | |||||||
\(164\) | 3.96620 | 0.309708 | ||||||||
\(165\) | −12.6113 | −0.981785 | ||||||||
\(166\) | −1.03209 | −0.0801054 | ||||||||
\(167\) | −13.2331 | −1.02401 | −0.512003 | − | 0.858984i | \(-0.671096\pi\) | ||||
−0.512003 | + | 0.858984i | \(0.671096\pi\) | |||||||
\(168\) | 12.1760 | 0.939395 | ||||||||
\(169\) | −12.0405 | −0.926189 | ||||||||
\(170\) | −2.44865 | −0.187803 | ||||||||
\(171\) | −4.21016 | −0.321959 | ||||||||
\(172\) | −12.7783 | −0.974334 | ||||||||
\(173\) | −12.4883 | −0.949465 | −0.474732 | − | 0.880130i | \(-0.657455\pi\) | ||||
−0.474732 | + | 0.880130i | \(0.657455\pi\) | |||||||
\(174\) | −4.04916 | −0.306966 | ||||||||
\(175\) | 25.7695 | 1.94799 | ||||||||
\(176\) | 3.49046 | 0.263103 | ||||||||
\(177\) | −8.38870 | −0.630533 | ||||||||
\(178\) | −8.49137 | −0.636455 | ||||||||
\(179\) | −22.5928 | −1.68867 | −0.844333 | − | 0.535819i | \(-0.820003\pi\) | ||||
−0.844333 | + | 0.535819i | \(0.820003\pi\) | |||||||
\(180\) | 4.62497 | 0.344725 | ||||||||
\(181\) | 12.5309 | 0.931411 | 0.465706 | − | 0.884940i | \(-0.345801\pi\) | ||||
0.465706 | + | 0.884940i | \(0.345801\pi\) | |||||||
\(182\) | −3.47908 | −0.257887 | ||||||||
\(183\) | −2.01800 | −0.149175 | ||||||||
\(184\) | −10.2180 | −0.753284 | ||||||||
\(185\) | 32.1539 | 2.36400 | ||||||||
\(186\) | 2.58553 | 0.189580 | ||||||||
\(187\) | −3.89444 | −0.284790 | ||||||||
\(188\) | 11.2594 | 0.821179 | ||||||||
\(189\) | 4.69700 | 0.341656 | ||||||||
\(190\) | −10.3092 | −0.747908 | ||||||||
\(191\) | 7.14709 | 0.517145 | 0.258573 | − | 0.965992i | \(-0.416748\pi\) | ||||
0.258573 | + | 0.965992i | \(0.416748\pi\) | |||||||
\(192\) | 2.64029 | 0.190546 | ||||||||
\(193\) | −5.78891 | −0.416695 | −0.208347 | − | 0.978055i | \(-0.566808\pi\) | ||||
−0.208347 | + | 0.978055i | \(0.566808\pi\) | |||||||
\(194\) | 7.24881 | 0.520435 | ||||||||
\(195\) | −3.17208 | −0.227157 | ||||||||
\(196\) | −21.5116 | −1.53654 | ||||||||
\(197\) | −18.9138 | −1.34756 | −0.673778 | − | 0.738934i | \(-0.735329\pi\) | ||||
−0.673778 | + | 0.738934i | \(0.735329\pi\) | |||||||
\(198\) | −2.94482 | −0.209279 | ||||||||
\(199\) | 19.4854 | 1.38128 | 0.690640 | − | 0.723198i | \(-0.257329\pi\) | ||||
0.690640 | + | 0.723198i | \(0.257329\pi\) | |||||||
\(200\) | 14.2222 | 1.00566 | ||||||||
\(201\) | −9.85675 | −0.695241 | ||||||||
\(202\) | 7.49985 | 0.527688 | ||||||||
\(203\) | 25.1520 | 1.76532 | ||||||||
\(204\) | 1.42822 | 0.0999956 | ||||||||
\(205\) | 8.99272 | 0.628079 | ||||||||
\(206\) | −11.6942 | −0.814773 | ||||||||
\(207\) | −3.94172 | −0.273968 | ||||||||
\(208\) | 0.877947 | 0.0608747 | ||||||||
\(209\) | −16.3962 | −1.13415 | ||||||||
\(210\) | 11.5013 | 0.793665 | ||||||||
\(211\) | 24.1833 | 1.66485 | 0.832424 | − | 0.554140i | \(-0.186953\pi\) | ||||
0.832424 | + | 0.554140i | \(0.186953\pi\) | |||||||
\(212\) | 18.4568 | 1.26762 | ||||||||
\(213\) | 3.35982 | 0.230211 | ||||||||
\(214\) | −2.34785 | −0.160496 | ||||||||
\(215\) | −28.9727 | −1.97592 | ||||||||
\(216\) | 2.59228 | 0.176383 | ||||||||
\(217\) | −16.0604 | −1.09025 | ||||||||
\(218\) | −12.3041 | −0.833338 | ||||||||
\(219\) | −4.43641 | −0.299785 | ||||||||
\(220\) | 18.0117 | 1.21435 | ||||||||
\(221\) | −0.979560 | −0.0658923 | ||||||||
\(222\) | 7.50818 | 0.503916 | ||||||||
\(223\) | 0.326609 | 0.0218713 | 0.0109357 | − | 0.999940i | \(-0.496519\pi\) | ||||
0.0109357 | + | 0.999940i | \(0.496519\pi\) | |||||||
\(224\) | −27.5352 | −1.83977 | ||||||||
\(225\) | 5.48638 | 0.365759 | ||||||||
\(226\) | 15.9789 | 1.06290 | ||||||||
\(227\) | 12.6504 | 0.839637 | 0.419818 | − | 0.907608i | \(-0.362094\pi\) | ||||
0.419818 | + | 0.907608i | \(0.362094\pi\) | |||||||
\(228\) | 6.01305 | 0.398224 | ||||||||
\(229\) | 21.6181 | 1.42856 | 0.714282 | − | 0.699858i | \(-0.246753\pi\) | ||||
0.714282 | + | 0.699858i | \(0.246753\pi\) | |||||||
\(230\) | −9.65187 | −0.636426 | ||||||||
\(231\) | 18.2922 | 1.20354 | ||||||||
\(232\) | 13.8814 | 0.911360 | ||||||||
\(233\) | 13.5577 | 0.888196 | 0.444098 | − | 0.895978i | \(-0.353524\pi\) | ||||
0.444098 | + | 0.895978i | \(0.353524\pi\) | |||||||
\(234\) | −0.740704 | −0.0484213 | ||||||||
\(235\) | 25.5290 | 1.66533 | ||||||||
\(236\) | 11.9809 | 0.779892 | ||||||||
\(237\) | −7.68352 | −0.499098 | ||||||||
\(238\) | 3.55168 | 0.230221 | ||||||||
\(239\) | 27.1640 | 1.75709 | 0.878547 | − | 0.477655i | \(-0.158513\pi\) | ||||
0.878547 | + | 0.477655i | \(0.158513\pi\) | |||||||
\(240\) | −2.90235 | −0.187346 | ||||||||
\(241\) | −8.08544 | −0.520829 | −0.260415 | − | 0.965497i | \(-0.583859\pi\) | ||||
−0.260415 | + | 0.965497i | \(0.583859\pi\) | |||||||
\(242\) | −3.15068 | −0.202533 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.88215 | 0.184511 | ||||||||
\(245\) | −48.7742 | −3.11607 | ||||||||
\(246\) | 2.09987 | 0.133883 | ||||||||
\(247\) | −4.12411 | −0.262411 | ||||||||
\(248\) | −8.86376 | −0.562849 | ||||||||
\(249\) | 1.36491 | 0.0864974 | ||||||||
\(250\) | 1.19097 | 0.0753236 | ||||||||
\(251\) | −6.95982 | −0.439300 | −0.219650 | − | 0.975579i | \(-0.570492\pi\) | ||||
−0.219650 | + | 0.975579i | \(0.570492\pi\) | |||||||
\(252\) | −6.70836 | −0.422587 | ||||||||
\(253\) | −15.3508 | −0.965096 | ||||||||
\(254\) | 4.48023 | 0.281115 | ||||||||
\(255\) | 3.23827 | 0.202788 | ||||||||
\(256\) | −12.6366 | −0.789785 | ||||||||
\(257\) | −24.2037 | −1.50978 | −0.754892 | − | 0.655849i | \(-0.772311\pi\) | ||||
−0.754892 | + | 0.655849i | \(0.772311\pi\) | |||||||
\(258\) | −6.76534 | −0.421191 | ||||||||
\(259\) | −46.6382 | −2.89796 | ||||||||
\(260\) | 4.53044 | 0.280966 | ||||||||
\(261\) | 5.35490 | 0.331460 | ||||||||
\(262\) | 1.28813 | 0.0795810 | ||||||||
\(263\) | −17.4276 | −1.07463 | −0.537316 | − | 0.843381i | \(-0.680562\pi\) | ||||
−0.537316 | + | 0.843381i | \(0.680562\pi\) | |||||||
\(264\) | 10.0955 | 0.621335 | ||||||||
\(265\) | 41.8479 | 2.57070 | ||||||||
\(266\) | 14.9532 | 0.916837 | ||||||||
\(267\) | 11.2296 | 0.687241 | ||||||||
\(268\) | 14.0776 | 0.859928 | ||||||||
\(269\) | 22.6669 | 1.38202 | 0.691011 | − | 0.722844i | \(-0.257166\pi\) | ||||
0.691011 | + | 0.722844i | \(0.257166\pi\) | |||||||
\(270\) | 2.44865 | 0.149020 | ||||||||
\(271\) | −29.4442 | −1.78861 | −0.894305 | − | 0.447458i | \(-0.852330\pi\) | ||||
−0.894305 | + | 0.447458i | \(0.852330\pi\) | |||||||
\(272\) | −0.896267 | −0.0543442 | ||||||||
\(273\) | 4.60099 | 0.278465 | ||||||||
\(274\) | 7.95996 | 0.480879 | ||||||||
\(275\) | 21.3664 | 1.28844 | ||||||||
\(276\) | 5.62965 | 0.338865 | ||||||||
\(277\) | −2.94976 | −0.177234 | −0.0886170 | − | 0.996066i | \(-0.528245\pi\) | ||||
−0.0886170 | + | 0.996066i | \(0.528245\pi\) | |||||||
\(278\) | −9.99752 | −0.599611 | ||||||||
\(279\) | −3.41929 | −0.204707 | ||||||||
\(280\) | −39.4290 | −2.35633 | ||||||||
\(281\) | −9.09540 | −0.542586 | −0.271293 | − | 0.962497i | \(-0.587451\pi\) | ||||
−0.271293 | + | 0.962497i | \(0.587451\pi\) | |||||||
\(282\) | 5.96120 | 0.354984 | ||||||||
\(283\) | −15.3680 | −0.913532 | −0.456766 | − | 0.889587i | \(-0.650992\pi\) | ||||
−0.456766 | + | 0.889587i | \(0.650992\pi\) | |||||||
\(284\) | −4.79857 | −0.284743 | ||||||||
\(285\) | 13.6336 | 0.807587 | ||||||||
\(286\) | −2.88463 | −0.170572 | ||||||||
\(287\) | −13.0436 | −0.769942 | ||||||||
\(288\) | −5.86229 | −0.345439 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 13.1123 | 0.769979 | ||||||||
\(291\) | −9.58636 | −0.561962 | ||||||||
\(292\) | 6.33618 | 0.370797 | ||||||||
\(293\) | −14.1378 | −0.825941 | −0.412970 | − | 0.910744i | \(-0.635509\pi\) | ||||
−0.412970 | + | 0.910744i | \(0.635509\pi\) | |||||||
\(294\) | −11.3891 | −0.664227 | ||||||||
\(295\) | 27.1648 | 1.58160 | ||||||||
\(296\) | −25.7397 | −1.49609 | ||||||||
\(297\) | 3.89444 | 0.225979 | ||||||||
\(298\) | −0.981610 | −0.0568632 | ||||||||
\(299\) | −3.86115 | −0.223296 | ||||||||
\(300\) | −7.83577 | −0.452399 | ||||||||
\(301\) | 42.0239 | 2.42222 | ||||||||
\(302\) | −18.3366 | −1.05515 | ||||||||
\(303\) | −9.91835 | −0.569794 | ||||||||
\(304\) | −3.77343 | −0.216421 | ||||||||
\(305\) | 6.53483 | 0.374183 | ||||||||
\(306\) | 0.756159 | 0.0432268 | ||||||||
\(307\) | 19.6604 | 1.12208 | 0.561038 | − | 0.827790i | \(-0.310402\pi\) | ||||
0.561038 | + | 0.827790i | \(0.310402\pi\) | |||||||
\(308\) | −26.1253 | −1.48863 | ||||||||
\(309\) | 15.4652 | 0.879787 | ||||||||
\(310\) | −8.37263 | −0.475533 | ||||||||
\(311\) | −12.1890 | −0.691173 | −0.345587 | − | 0.938387i | \(-0.612320\pi\) | ||||
−0.345587 | + | 0.938387i | \(0.612320\pi\) | |||||||
\(312\) | 2.53930 | 0.143759 | ||||||||
\(313\) | −2.03715 | −0.115147 | −0.0575734 | − | 0.998341i | \(-0.518336\pi\) | ||||
−0.0575734 | + | 0.998341i | \(0.518336\pi\) | |||||||
\(314\) | −0.756159 | −0.0426725 | ||||||||
\(315\) | −15.2101 | −0.856995 | ||||||||
\(316\) | 10.9738 | 0.617323 | ||||||||
\(317\) | −28.1589 | −1.58156 | −0.790782 | − | 0.612098i | \(-0.790326\pi\) | ||||
−0.790782 | + | 0.612098i | \(0.790326\pi\) | |||||||
\(318\) | 9.77180 | 0.547975 | ||||||||
\(319\) | 20.8544 | 1.16762 | ||||||||
\(320\) | −8.54996 | −0.477957 | ||||||||
\(321\) | 3.10496 | 0.173302 | ||||||||
\(322\) | 13.9997 | 0.780174 | ||||||||
\(323\) | 4.21016 | 0.234260 | ||||||||
\(324\) | −1.42822 | −0.0793457 | ||||||||
\(325\) | 5.37424 | 0.298109 | ||||||||
\(326\) | 13.1151 | 0.726378 | ||||||||
\(327\) | 16.2718 | 0.899833 | ||||||||
\(328\) | −7.19881 | −0.397488 | ||||||||
\(329\) | −37.0289 | −2.04147 | ||||||||
\(330\) | 9.53612 | 0.524946 | ||||||||
\(331\) | −16.6225 | −0.913654 | −0.456827 | − | 0.889556i | \(-0.651014\pi\) | ||||
−0.456827 | + | 0.889556i | \(0.651014\pi\) | |||||||
\(332\) | −1.94939 | −0.106987 | ||||||||
\(333\) | −9.92936 | −0.544126 | ||||||||
\(334\) | 10.0063 | 0.547521 | ||||||||
\(335\) | 31.9188 | 1.74391 | ||||||||
\(336\) | 4.20977 | 0.229662 | ||||||||
\(337\) | 15.8170 | 0.861606 | 0.430803 | − | 0.902446i | \(-0.358230\pi\) | ||||
0.430803 | + | 0.902446i | \(0.358230\pi\) | |||||||
\(338\) | 9.10451 | 0.495220 | ||||||||
\(339\) | −21.1316 | −1.14771 | ||||||||
\(340\) | −4.62497 | −0.250824 | ||||||||
\(341\) | −13.3162 | −0.721114 | ||||||||
\(342\) | 3.18355 | 0.172147 | ||||||||
\(343\) | 37.8663 | 2.04459 | ||||||||
\(344\) | 23.1931 | 1.25049 | ||||||||
\(345\) | 12.7643 | 0.687209 | ||||||||
\(346\) | 9.44311 | 0.507665 | ||||||||
\(347\) | −33.5002 | −1.79838 | −0.899192 | − | 0.437554i | \(-0.855845\pi\) | ||||
−0.899192 | + | 0.437554i | \(0.855845\pi\) | |||||||
\(348\) | −7.64799 | −0.409976 | ||||||||
\(349\) | 21.2186 | 1.13581 | 0.567904 | − | 0.823095i | \(-0.307755\pi\) | ||||
0.567904 | + | 0.823095i | \(0.307755\pi\) | |||||||
\(350\) | −19.4859 | −1.04156 | ||||||||
\(351\) | 0.979560 | 0.0522851 | ||||||||
\(352\) | −22.8303 | −1.21686 | ||||||||
\(353\) | 11.3408 | 0.603612 | 0.301806 | − | 0.953369i | \(-0.402411\pi\) | ||||
0.301806 | + | 0.953369i | \(0.402411\pi\) | |||||||
\(354\) | 6.34319 | 0.337137 | ||||||||
\(355\) | −10.8800 | −0.577450 | ||||||||
\(356\) | −16.0384 | −0.850032 | ||||||||
\(357\) | −4.69700 | −0.248592 | ||||||||
\(358\) | 17.0838 | 0.902905 | ||||||||
\(359\) | −5.53738 | −0.292252 | −0.146126 | − | 0.989266i | \(-0.546680\pi\) | ||||
−0.146126 | + | 0.989266i | \(0.546680\pi\) | |||||||
\(360\) | −8.39451 | −0.442429 | ||||||||
\(361\) | −1.27453 | −0.0670806 | ||||||||
\(362\) | −9.47533 | −0.498012 | ||||||||
\(363\) | 4.16669 | 0.218694 | ||||||||
\(364\) | −6.57125 | −0.344427 | ||||||||
\(365\) | 14.3663 | 0.751965 | ||||||||
\(366\) | 1.52593 | 0.0797616 | ||||||||
\(367\) | −32.3581 | −1.68908 | −0.844540 | − | 0.535493i | \(-0.820126\pi\) | ||||
−0.844540 | + | 0.535493i | \(0.820126\pi\) | |||||||
\(368\) | −3.53283 | −0.184162 | ||||||||
\(369\) | −2.77702 | −0.144566 | ||||||||
\(370\) | −24.3135 | −1.26400 | ||||||||
\(371\) | −60.6990 | −3.15134 | ||||||||
\(372\) | 4.88350 | 0.253198 | ||||||||
\(373\) | 12.0439 | 0.623609 | 0.311805 | − | 0.950146i | \(-0.399067\pi\) | ||||
0.311805 | + | 0.950146i | \(0.399067\pi\) | |||||||
\(374\) | 2.94482 | 0.152273 | ||||||||
\(375\) | −1.57503 | −0.0813340 | ||||||||
\(376\) | −20.4363 | −1.05392 | ||||||||
\(377\) | 5.24545 | 0.270154 | ||||||||
\(378\) | −3.55168 | −0.182679 | ||||||||
\(379\) | 20.0098 | 1.02784 | 0.513918 | − | 0.857840i | \(-0.328194\pi\) | ||||
0.513918 | + | 0.857840i | \(0.328194\pi\) | |||||||
\(380\) | −19.4719 | −0.998886 | ||||||||
\(381\) | −5.92498 | −0.303546 | ||||||||
\(382\) | −5.40434 | −0.276510 | ||||||||
\(383\) | 30.0836 | 1.53720 | 0.768600 | − | 0.639729i | \(-0.220953\pi\) | ||||
0.768600 | + | 0.639729i | \(0.220953\pi\) | |||||||
\(384\) | 9.72809 | 0.496435 | ||||||||
\(385\) | −59.2350 | −3.01890 | ||||||||
\(386\) | 4.37734 | 0.222801 | ||||||||
\(387\) | 8.94697 | 0.454800 | ||||||||
\(388\) | 13.6915 | 0.695078 | ||||||||
\(389\) | 32.8468 | 1.66540 | 0.832700 | − | 0.553724i | \(-0.186794\pi\) | ||||
0.832700 | + | 0.553724i | \(0.186794\pi\) | |||||||
\(390\) | 2.39860 | 0.121458 | ||||||||
\(391\) | 3.94172 | 0.199341 | ||||||||
\(392\) | 39.0445 | 1.97204 | ||||||||
\(393\) | −1.70352 | −0.0859312 | ||||||||
\(394\) | 14.3019 | 0.720518 | ||||||||
\(395\) | 24.8813 | 1.25191 | ||||||||
\(396\) | −5.56213 | −0.279508 | ||||||||
\(397\) | −24.3792 | −1.22355 | −0.611777 | − | 0.791030i | \(-0.709545\pi\) | ||||
−0.611777 | + | 0.791030i | \(0.709545\pi\) | |||||||
\(398\) | −14.7340 | −0.738551 | ||||||||
\(399\) | −19.7751 | −0.989995 | ||||||||
\(400\) | 4.91726 | 0.245863 | ||||||||
\(401\) | 0.373064 | 0.0186299 | 0.00931495 | − | 0.999957i | \(-0.497035\pi\) | ||||
0.00931495 | + | 0.999957i | \(0.497035\pi\) | |||||||
\(402\) | 7.45327 | 0.371735 | ||||||||
\(403\) | −3.34940 | −0.166845 | ||||||||
\(404\) | 14.1656 | 0.704766 | ||||||||
\(405\) | −3.23827 | −0.160911 | ||||||||
\(406\) | −19.0189 | −0.943892 | ||||||||
\(407\) | −38.6693 | −1.91677 | ||||||||
\(408\) | −2.59228 | −0.128337 | ||||||||
\(409\) | 25.0079 | 1.23656 | 0.618279 | − | 0.785958i | \(-0.287830\pi\) | ||||
0.618279 | + | 0.785958i | \(0.287830\pi\) | |||||||
\(410\) | −6.79993 | −0.335825 | ||||||||
\(411\) | −10.5268 | −0.519250 | ||||||||
\(412\) | −22.0878 | −1.08819 | ||||||||
\(413\) | −39.4017 | −1.93883 | ||||||||
\(414\) | 2.98057 | 0.146487 | ||||||||
\(415\) | −4.41993 | −0.216966 | ||||||||
\(416\) | −5.74246 | −0.281547 | ||||||||
\(417\) | 13.2214 | 0.647457 | ||||||||
\(418\) | 12.3982 | 0.606414 | ||||||||
\(419\) | 9.91758 | 0.484505 | 0.242253 | − | 0.970213i | \(-0.422114\pi\) | ||||
0.242253 | + | 0.970213i | \(0.422114\pi\) | |||||||
\(420\) | 21.7235 | 1.06000 | ||||||||
\(421\) | −19.2406 | −0.937728 | −0.468864 | − | 0.883270i | \(-0.655336\pi\) | ||||
−0.468864 | + | 0.883270i | \(0.655336\pi\) | |||||||
\(422\) | −18.2864 | −0.890169 | ||||||||
\(423\) | −7.88353 | −0.383310 | ||||||||
\(424\) | −33.4999 | −1.62690 | ||||||||
\(425\) | −5.48638 | −0.266128 | ||||||||
\(426\) | −2.54056 | −0.123090 | ||||||||
\(427\) | −9.47855 | −0.458699 | ||||||||
\(428\) | −4.43458 | −0.214353 | ||||||||
\(429\) | 3.81484 | 0.184182 | ||||||||
\(430\) | 21.9080 | 1.05650 | ||||||||
\(431\) | −28.0512 | −1.35118 | −0.675589 | − | 0.737279i | \(-0.736111\pi\) | ||||
−0.675589 | + | 0.737279i | \(0.736111\pi\) | |||||||
\(432\) | 0.896267 | 0.0431217 | ||||||||
\(433\) | −33.7257 | −1.62076 | −0.810378 | − | 0.585908i | \(-0.800738\pi\) | ||||
−0.810378 | + | 0.585908i | \(0.800738\pi\) | |||||||
\(434\) | 12.1442 | 0.582941 | ||||||||
\(435\) | −17.3406 | −0.831419 | ||||||||
\(436\) | −23.2398 | −1.11298 | ||||||||
\(437\) | 16.5953 | 0.793859 | ||||||||
\(438\) | 3.35463 | 0.160291 | ||||||||
\(439\) | 10.9830 | 0.524190 | 0.262095 | − | 0.965042i | \(-0.415587\pi\) | ||||
0.262095 | + | 0.965042i | \(0.415587\pi\) | |||||||
\(440\) | −32.6919 | −1.55853 | ||||||||
\(441\) | 15.0618 | 0.717229 | ||||||||
\(442\) | 0.740704 | 0.0352317 | ||||||||
\(443\) | −27.2641 | −1.29536 | −0.647678 | − | 0.761914i | \(-0.724260\pi\) | ||||
−0.647678 | + | 0.761914i | \(0.724260\pi\) | |||||||
\(444\) | 14.1813 | 0.673017 | ||||||||
\(445\) | −36.3645 | −1.72384 | ||||||||
\(446\) | −0.246968 | −0.0116943 | ||||||||
\(447\) | 1.29815 | 0.0614005 | ||||||||
\(448\) | 12.4014 | 0.585913 | ||||||||
\(449\) | −24.0886 | −1.13681 | −0.568405 | − | 0.822749i | \(-0.692439\pi\) | ||||
−0.568405 | + | 0.822749i | \(0.692439\pi\) | |||||||
\(450\) | −4.14858 | −0.195566 | ||||||||
\(451\) | −10.8149 | −0.509255 | ||||||||
\(452\) | 30.1807 | 1.41958 | ||||||||
\(453\) | 24.2497 | 1.13935 | ||||||||
\(454\) | −9.56572 | −0.448942 | ||||||||
\(455\) | −14.8993 | −0.698488 | ||||||||
\(456\) | −10.9139 | −0.511092 | ||||||||
\(457\) | 25.3801 | 1.18723 | 0.593615 | − | 0.804749i | \(-0.297700\pi\) | ||||
0.593615 | + | 0.804749i | \(0.297700\pi\) | |||||||
\(458\) | −16.3467 | −0.763832 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −18.2303 | −0.849993 | ||||||||
\(461\) | 26.8287 | 1.24954 | 0.624769 | − | 0.780809i | \(-0.285193\pi\) | ||||
0.624769 | + | 0.780809i | \(0.285193\pi\) | |||||||
\(462\) | −13.8318 | −0.643514 | ||||||||
\(463\) | −41.6174 | −1.93413 | −0.967063 | − | 0.254536i | \(-0.918077\pi\) | ||||
−0.967063 | + | 0.254536i | \(0.918077\pi\) | |||||||
\(464\) | 4.79942 | 0.222808 | ||||||||
\(465\) | 11.0726 | 0.513478 | ||||||||
\(466\) | −10.2518 | −0.474905 | ||||||||
\(467\) | 16.6046 | 0.768370 | 0.384185 | − | 0.923256i | \(-0.374482\pi\) | ||||
0.384185 | + | 0.923256i | \(0.374482\pi\) | |||||||
\(468\) | −1.39903 | −0.0646702 | ||||||||
\(469\) | −46.2972 | −2.13780 | ||||||||
\(470\) | −19.3040 | −0.890426 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −21.7459 | −1.00093 | ||||||||
\(473\) | 34.8435 | 1.60210 | ||||||||
\(474\) | 5.80997 | 0.266861 | ||||||||
\(475\) | −23.0985 | −1.05983 | ||||||||
\(476\) | 6.70836 | 0.307477 | ||||||||
\(477\) | −12.9229 | −0.591700 | ||||||||
\(478\) | −20.5403 | −0.939493 | ||||||||
\(479\) | 16.0186 | 0.731908 | 0.365954 | − | 0.930633i | \(-0.380743\pi\) | ||||
0.365954 | + | 0.930633i | \(0.380743\pi\) | |||||||
\(480\) | 18.9837 | 0.866481 | ||||||||
\(481\) | −9.72641 | −0.443486 | ||||||||
\(482\) | 6.11388 | 0.278480 | ||||||||
\(483\) | −18.5142 | −0.842427 | ||||||||
\(484\) | −5.95096 | −0.270498 | ||||||||
\(485\) | 31.0432 | 1.40960 | ||||||||
\(486\) | −0.756159 | −0.0343001 | ||||||||
\(487\) | −16.7536 | −0.759177 | −0.379589 | − | 0.925155i | \(-0.623934\pi\) | ||||
−0.379589 | + | 0.925155i | \(0.623934\pi\) | |||||||
\(488\) | −5.23123 | −0.236807 | ||||||||
\(489\) | −17.3444 | −0.784339 | ||||||||
\(490\) | 36.8811 | 1.66612 | ||||||||
\(491\) | −37.8794 | −1.70948 | −0.854738 | − | 0.519060i | \(-0.826282\pi\) | ||||
−0.854738 | + | 0.519060i | \(0.826282\pi\) | |||||||
\(492\) | 3.96620 | 0.178810 | ||||||||
\(493\) | −5.35490 | −0.241173 | ||||||||
\(494\) | 3.11848 | 0.140307 | ||||||||
\(495\) | −12.6113 | −0.566834 | ||||||||
\(496\) | −3.06459 | −0.137604 | ||||||||
\(497\) | 15.7811 | 0.707878 | ||||||||
\(498\) | −1.03209 | −0.0462489 | ||||||||
\(499\) | −28.0543 | −1.25588 | −0.627941 | − | 0.778261i | \(-0.716102\pi\) | ||||
−0.627941 | + | 0.778261i | \(0.716102\pi\) | |||||||
\(500\) | 2.24949 | 0.100600 | ||||||||
\(501\) | −13.2331 | −0.591210 | ||||||||
\(502\) | 5.26274 | 0.234887 | ||||||||
\(503\) | −27.0301 | −1.20521 | −0.602605 | − | 0.798039i | \(-0.705871\pi\) | ||||
−0.602605 | + | 0.798039i | \(0.705871\pi\) | |||||||
\(504\) | 12.1760 | 0.542360 | ||||||||
\(505\) | 32.1183 | 1.42924 | ||||||||
\(506\) | 11.6076 | 0.516023 | ||||||||
\(507\) | −12.0405 | −0.534736 | ||||||||
\(508\) | 8.46220 | 0.375449 | ||||||||
\(509\) | −7.87173 | −0.348908 | −0.174454 | − | 0.984665i | \(-0.555816\pi\) | ||||
−0.174454 | + | 0.984665i | \(0.555816\pi\) | |||||||
\(510\) | −2.44865 | −0.108428 | ||||||||
\(511\) | −20.8378 | −0.921810 | ||||||||
\(512\) | −9.90093 | −0.437563 | ||||||||
\(513\) | −4.21016 | −0.185883 | ||||||||
\(514\) | 18.3018 | 0.807260 | ||||||||
\(515\) | −50.0806 | −2.20682 | ||||||||
\(516\) | −12.7783 | −0.562532 | ||||||||
\(517\) | −30.7020 | −1.35027 | ||||||||
\(518\) | 35.2659 | 1.54950 | ||||||||
\(519\) | −12.4883 | −0.548174 | ||||||||
\(520\) | −8.22292 | −0.360599 | ||||||||
\(521\) | −26.7389 | −1.17145 | −0.585727 | − | 0.810509i | \(-0.699191\pi\) | ||||
−0.585727 | + | 0.810509i | \(0.699191\pi\) | |||||||
\(522\) | −4.04916 | −0.177227 | ||||||||
\(523\) | −27.7586 | −1.21380 | −0.606900 | − | 0.794778i | \(-0.707587\pi\) | ||||
−0.606900 | + | 0.794778i | \(0.707587\pi\) | |||||||
\(524\) | 2.43300 | 0.106286 | ||||||||
\(525\) | 25.7695 | 1.12467 | ||||||||
\(526\) | 13.1780 | 0.574590 | ||||||||
\(527\) | 3.41929 | 0.148946 | ||||||||
\(528\) | 3.49046 | 0.151903 | ||||||||
\(529\) | −7.46287 | −0.324473 | ||||||||
\(530\) | −31.6437 | −1.37451 | ||||||||
\(531\) | −8.38870 | −0.364038 | ||||||||
\(532\) | 28.2433 | 1.22450 | ||||||||
\(533\) | −2.72025 | −0.117827 | ||||||||
\(534\) | −8.49137 | −0.367458 | ||||||||
\(535\) | −10.0547 | −0.434703 | ||||||||
\(536\) | −25.5515 | −1.10366 | ||||||||
\(537\) | −22.5928 | −0.974951 | ||||||||
\(538\) | −17.1398 | −0.738947 | ||||||||
\(539\) | 58.6574 | 2.52655 | ||||||||
\(540\) | 4.62497 | 0.199027 | ||||||||
\(541\) | −4.21585 | −0.181254 | −0.0906268 | − | 0.995885i | \(-0.528887\pi\) | ||||
−0.0906268 | + | 0.995885i | \(0.528887\pi\) | |||||||
\(542\) | 22.2645 | 0.956344 | ||||||||
\(543\) | 12.5309 | 0.537751 | ||||||||
\(544\) | 5.86229 | 0.251343 | ||||||||
\(545\) | −52.6925 | −2.25710 | ||||||||
\(546\) | −3.47908 | −0.148891 | ||||||||
\(547\) | −33.5163 | −1.43305 | −0.716526 | − | 0.697560i | \(-0.754269\pi\) | ||||
−0.716526 | + | 0.697560i | \(0.754269\pi\) | |||||||
\(548\) | 15.0347 | 0.642248 | ||||||||
\(549\) | −2.01800 | −0.0861262 | ||||||||
\(550\) | −16.1564 | −0.688911 | ||||||||
\(551\) | −22.5450 | −0.960450 | ||||||||
\(552\) | −10.2180 | −0.434909 | ||||||||
\(553\) | −36.0895 | −1.53468 | ||||||||
\(554\) | 2.23049 | 0.0947644 | ||||||||
\(555\) | 32.1539 | 1.36486 | ||||||||
\(556\) | −18.8832 | −0.800825 | ||||||||
\(557\) | 8.12590 | 0.344305 | 0.172153 | − | 0.985070i | \(-0.444928\pi\) | ||||
0.172153 | + | 0.985070i | \(0.444928\pi\) | |||||||
\(558\) | 2.58553 | 0.109454 | ||||||||
\(559\) | 8.76410 | 0.370682 | ||||||||
\(560\) | −13.6324 | −0.576072 | ||||||||
\(561\) | −3.89444 | −0.164424 | ||||||||
\(562\) | 6.87757 | 0.290113 | ||||||||
\(563\) | −45.3402 | −1.91086 | −0.955431 | − | 0.295214i | \(-0.904609\pi\) | ||||
−0.955431 | + | 0.295214i | \(0.904609\pi\) | |||||||
\(564\) | 11.2594 | 0.474108 | ||||||||
\(565\) | 68.4299 | 2.87887 | ||||||||
\(566\) | 11.6206 | 0.488452 | ||||||||
\(567\) | 4.69700 | 0.197255 | ||||||||
\(568\) | 8.70960 | 0.365447 | ||||||||
\(569\) | −33.5291 | −1.40561 | −0.702806 | − | 0.711382i | \(-0.748070\pi\) | ||||
−0.702806 | + | 0.711382i | \(0.748070\pi\) | |||||||
\(570\) | −10.3092 | −0.431805 | ||||||||
\(571\) | 32.0347 | 1.34061 | 0.670305 | − | 0.742085i | \(-0.266163\pi\) | ||||
0.670305 | + | 0.742085i | \(0.266163\pi\) | |||||||
\(572\) | −5.44844 | −0.227811 | ||||||||
\(573\) | 7.14709 | 0.298574 | ||||||||
\(574\) | 9.86307 | 0.411677 | ||||||||
\(575\) | −21.6258 | −0.901856 | ||||||||
\(576\) | 2.64029 | 0.110012 | ||||||||
\(577\) | −20.9015 | −0.870141 | −0.435070 | − | 0.900396i | \(-0.643277\pi\) | ||||
−0.435070 | + | 0.900396i | \(0.643277\pi\) | |||||||
\(578\) | −0.756159 | −0.0314521 | ||||||||
\(579\) | −5.78891 | −0.240579 | ||||||||
\(580\) | 24.7663 | 1.02836 | ||||||||
\(581\) | 6.41096 | 0.265972 | ||||||||
\(582\) | 7.24881 | 0.300473 | ||||||||
\(583\) | −50.3276 | −2.08436 | ||||||||
\(584\) | −11.5004 | −0.475891 | ||||||||
\(585\) | −3.17208 | −0.131149 | ||||||||
\(586\) | 10.6904 | 0.441618 | ||||||||
\(587\) | 44.6166 | 1.84152 | 0.920761 | − | 0.390127i | \(-0.127569\pi\) | ||||
0.920761 | + | 0.390127i | \(0.127569\pi\) | |||||||
\(588\) | −21.5116 | −0.887124 | ||||||||
\(589\) | 14.3958 | 0.593167 | ||||||||
\(590\) | −20.5410 | −0.845658 | ||||||||
\(591\) | −18.9138 | −0.778011 | ||||||||
\(592\) | −8.89936 | −0.365761 | ||||||||
\(593\) | −5.89702 | −0.242162 | −0.121081 | − | 0.992643i | \(-0.538636\pi\) | ||||
−0.121081 | + | 0.992643i | \(0.538636\pi\) | |||||||
\(594\) | −2.94482 | −0.120827 | ||||||||
\(595\) | 15.2101 | 0.623555 | ||||||||
\(596\) | −1.85405 | −0.0759449 | ||||||||
\(597\) | 19.4854 | 0.797483 | ||||||||
\(598\) | 2.91964 | 0.119393 | ||||||||
\(599\) | 23.4220 | 0.956998 | 0.478499 | − | 0.878088i | \(-0.341181\pi\) | ||||
0.478499 | + | 0.878088i | \(0.341181\pi\) | |||||||
\(600\) | 14.2222 | 0.580621 | ||||||||
\(601\) | 1.21096 | 0.0493960 | 0.0246980 | − | 0.999695i | \(-0.492138\pi\) | ||||
0.0246980 | + | 0.999695i | \(0.492138\pi\) | |||||||
\(602\) | −31.7768 | −1.29513 | ||||||||
\(603\) | −9.85675 | −0.401398 | ||||||||
\(604\) | −34.6340 | −1.40924 | ||||||||
\(605\) | −13.4929 | −0.548563 | ||||||||
\(606\) | 7.49985 | 0.304661 | ||||||||
\(607\) | 28.5422 | 1.15849 | 0.579245 | − | 0.815153i | \(-0.303347\pi\) | ||||
0.579245 | + | 0.815153i | \(0.303347\pi\) | |||||||
\(608\) | 24.6812 | 1.00095 | ||||||||
\(609\) | 25.1520 | 1.01921 | ||||||||
\(610\) | −4.94137 | −0.200070 | ||||||||
\(611\) | −7.72239 | −0.312414 | ||||||||
\(612\) | 1.42822 | 0.0577325 | ||||||||
\(613\) | 11.3302 | 0.457621 | 0.228811 | − | 0.973471i | \(-0.426516\pi\) | ||||
0.228811 | + | 0.973471i | \(0.426516\pi\) | |||||||
\(614\) | −14.8664 | −0.599958 | ||||||||
\(615\) | 8.99272 | 0.362621 | ||||||||
\(616\) | 47.4186 | 1.91055 | ||||||||
\(617\) | 17.3290 | 0.697640 | 0.348820 | − | 0.937190i | \(-0.386582\pi\) | ||||
0.348820 | + | 0.937190i | \(0.386582\pi\) | |||||||
\(618\) | −11.6942 | −0.470409 | ||||||||
\(619\) | 23.0361 | 0.925901 | 0.462950 | − | 0.886384i | \(-0.346791\pi\) | ||||
0.462950 | + | 0.886384i | \(0.346791\pi\) | |||||||
\(620\) | −15.8141 | −0.635109 | ||||||||
\(621\) | −3.94172 | −0.158176 | ||||||||
\(622\) | 9.21680 | 0.369560 | ||||||||
\(623\) | 52.7454 | 2.11320 | ||||||||
\(624\) | 0.877947 | 0.0351460 | ||||||||
\(625\) | −22.3315 | −0.893262 | ||||||||
\(626\) | 1.54041 | 0.0615673 | ||||||||
\(627\) | −16.3962 | −0.654803 | ||||||||
\(628\) | −1.42822 | −0.0569923 | ||||||||
\(629\) | 9.92936 | 0.395910 | ||||||||
\(630\) | 11.5013 | 0.458223 | ||||||||
\(631\) | −44.3553 | −1.76576 | −0.882878 | − | 0.469603i | \(-0.844397\pi\) | ||||
−0.882878 | + | 0.469603i | \(0.844397\pi\) | |||||||
\(632\) | −19.9179 | −0.792290 | ||||||||
\(633\) | 24.1833 | 0.961200 | ||||||||
\(634\) | 21.2926 | 0.845639 | ||||||||
\(635\) | 19.1867 | 0.761400 | ||||||||
\(636\) | 18.4568 | 0.731861 | ||||||||
\(637\) | 14.7539 | 0.584573 | ||||||||
\(638\) | −15.7692 | −0.624310 | ||||||||
\(639\) | 3.35982 | 0.132912 | ||||||||
\(640\) | −31.5022 | −1.24523 | ||||||||
\(641\) | 31.8725 | 1.25889 | 0.629443 | − | 0.777046i | \(-0.283283\pi\) | ||||
0.629443 | + | 0.777046i | \(0.283283\pi\) | |||||||
\(642\) | −2.34785 | −0.0926621 | ||||||||
\(643\) | 38.1630 | 1.50500 | 0.752501 | − | 0.658591i | \(-0.228847\pi\) | ||||
0.752501 | + | 0.658591i | \(0.228847\pi\) | |||||||
\(644\) | 26.4425 | 1.04198 | ||||||||
\(645\) | −28.9727 | −1.14080 | ||||||||
\(646\) | −3.18355 | −0.125255 | ||||||||
\(647\) | 3.87212 | 0.152229 | 0.0761144 | − | 0.997099i | \(-0.475749\pi\) | ||||
0.0761144 | + | 0.997099i | \(0.475749\pi\) | |||||||
\(648\) | 2.59228 | 0.101834 | ||||||||
\(649\) | −32.6693 | −1.28238 | ||||||||
\(650\) | −4.06378 | −0.159395 | ||||||||
\(651\) | −16.0604 | −0.629456 | ||||||||
\(652\) | 24.7716 | 0.970131 | ||||||||
\(653\) | −31.7973 | −1.24432 | −0.622162 | − | 0.782889i | \(-0.713745\pi\) | ||||
−0.622162 | + | 0.782889i | \(0.713745\pi\) | |||||||
\(654\) | −12.3041 | −0.481128 | ||||||||
\(655\) | 5.51645 | 0.215546 | ||||||||
\(656\) | −2.48895 | −0.0971771 | ||||||||
\(657\) | −4.43641 | −0.173081 | ||||||||
\(658\) | 27.9998 | 1.09154 | ||||||||
\(659\) | 2.74720 | 0.107016 | 0.0535079 | − | 0.998567i | \(-0.482960\pi\) | ||||
0.0535079 | + | 0.998567i | \(0.482960\pi\) | |||||||
\(660\) | 18.0117 | 0.701104 | ||||||||
\(661\) | −0.404631 | −0.0157383 | −0.00786916 | − | 0.999969i | \(-0.502505\pi\) | ||||
−0.00786916 | + | 0.999969i | \(0.502505\pi\) | |||||||
\(662\) | 12.5692 | 0.488517 | ||||||||
\(663\) | −0.979560 | −0.0380430 | ||||||||
\(664\) | 3.53822 | 0.137310 | ||||||||
\(665\) | 64.0372 | 2.48326 | ||||||||
\(666\) | 7.50818 | 0.290936 | ||||||||
\(667\) | −21.1075 | −0.817286 | ||||||||
\(668\) | 18.8998 | 0.731254 | ||||||||
\(669\) | 0.326609 | 0.0126274 | ||||||||
\(670\) | −24.1357 | −0.932443 | ||||||||
\(671\) | −7.85899 | −0.303393 | ||||||||
\(672\) | −27.5352 | −1.06219 | ||||||||
\(673\) | −14.4775 | −0.558068 | −0.279034 | − | 0.960281i | \(-0.590014\pi\) | ||||
−0.279034 | + | 0.960281i | \(0.590014\pi\) | |||||||
\(674\) | −11.9602 | −0.460688 | ||||||||
\(675\) | 5.48638 | 0.211171 | ||||||||
\(676\) | 17.1965 | 0.661402 | ||||||||
\(677\) | 34.7629 | 1.33605 | 0.668023 | − | 0.744141i | \(-0.267141\pi\) | ||||
0.668023 | + | 0.744141i | \(0.267141\pi\) | |||||||
\(678\) | 15.9789 | 0.613666 | ||||||||
\(679\) | −45.0271 | −1.72798 | ||||||||
\(680\) | 8.39451 | 0.321915 | ||||||||
\(681\) | 12.6504 | 0.484765 | ||||||||
\(682\) | 10.0692 | 0.385569 | ||||||||
\(683\) | 30.2203 | 1.15635 | 0.578173 | − | 0.815914i | \(-0.303766\pi\) | ||||
0.578173 | + | 0.815914i | \(0.303766\pi\) | |||||||
\(684\) | 6.01305 | 0.229915 | ||||||||
\(685\) | 34.0887 | 1.30246 | ||||||||
\(686\) | −28.6330 | −1.09321 | ||||||||
\(687\) | 21.6181 | 0.824782 | ||||||||
\(688\) | 8.01887 | 0.305717 | ||||||||
\(689\) | −12.6588 | −0.482261 | ||||||||
\(690\) | −9.65187 | −0.367440 | ||||||||
\(691\) | 11.6763 | 0.444188 | 0.222094 | − | 0.975025i | \(-0.428711\pi\) | ||||
0.222094 | + | 0.975025i | \(0.428711\pi\) | |||||||
\(692\) | 17.8360 | 0.678024 | ||||||||
\(693\) | 18.2922 | 0.694863 | ||||||||
\(694\) | 25.3315 | 0.961570 | ||||||||
\(695\) | −42.8146 | −1.62405 | ||||||||
\(696\) | 13.8814 | 0.526174 | ||||||||
\(697\) | 2.77702 | 0.105187 | ||||||||
\(698\) | −16.0447 | −0.607300 | ||||||||
\(699\) | 13.5577 | 0.512800 | ||||||||
\(700\) | −36.8046 | −1.39108 | ||||||||
\(701\) | 44.7658 | 1.69078 | 0.845390 | − | 0.534150i | \(-0.179368\pi\) | ||||
0.845390 | + | 0.534150i | \(0.179368\pi\) | |||||||
\(702\) | −0.740704 | −0.0279561 | ||||||||
\(703\) | 41.8042 | 1.57668 | ||||||||
\(704\) | 10.2825 | 0.387535 | ||||||||
\(705\) | 25.5290 | 0.961477 | ||||||||
\(706\) | −8.57548 | −0.322742 | ||||||||
\(707\) | −46.5865 | −1.75207 | ||||||||
\(708\) | 11.9809 | 0.450271 | ||||||||
\(709\) | 32.3427 | 1.21465 | 0.607327 | − | 0.794452i | \(-0.292242\pi\) | ||||
0.607327 | + | 0.794452i | \(0.292242\pi\) | |||||||
\(710\) | 8.22701 | 0.308754 | ||||||||
\(711\) | −7.68352 | −0.288155 | ||||||||
\(712\) | 29.1103 | 1.09095 | ||||||||
\(713\) | 13.4779 | 0.504750 | ||||||||
\(714\) | 3.55168 | 0.132918 | ||||||||
\(715\) | −12.3535 | −0.461994 | ||||||||
\(716\) | 32.2676 | 1.20590 | ||||||||
\(717\) | 27.1640 | 1.01446 | ||||||||
\(718\) | 4.18714 | 0.156263 | ||||||||
\(719\) | −35.7331 | −1.33262 | −0.666310 | − | 0.745675i | \(-0.732127\pi\) | ||||
−0.666310 | + | 0.745675i | \(0.732127\pi\) | |||||||
\(720\) | −2.90235 | −0.108164 | ||||||||
\(721\) | 72.6403 | 2.70526 | ||||||||
\(722\) | 0.963749 | 0.0358670 | ||||||||
\(723\) | −8.08544 | −0.300701 | ||||||||
\(724\) | −17.8969 | −0.665132 | ||||||||
\(725\) | 29.3790 | 1.09111 | ||||||||
\(726\) | −3.15068 | −0.116933 | ||||||||
\(727\) | 38.0941 | 1.41283 | 0.706417 | − | 0.707796i | \(-0.250310\pi\) | ||||
0.706417 | + | 0.707796i | \(0.250310\pi\) | |||||||
\(728\) | 11.9271 | 0.442047 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −10.8632 | −0.402065 | ||||||||
\(731\) | −8.94697 | −0.330916 | ||||||||
\(732\) | 2.88215 | 0.106528 | ||||||||
\(733\) | 37.7330 | 1.39370 | 0.696850 | − | 0.717217i | \(-0.254584\pi\) | ||||
0.696850 | + | 0.717217i | \(0.254584\pi\) | |||||||
\(734\) | 24.4679 | 0.903126 | ||||||||
\(735\) | −48.7742 | −1.79906 | ||||||||
\(736\) | 23.1075 | 0.851753 | ||||||||
\(737\) | −38.3866 | −1.41399 | ||||||||
\(738\) | 2.09987 | 0.0772971 | ||||||||
\(739\) | 1.49855 | 0.0551249 | 0.0275624 | − | 0.999620i | \(-0.491225\pi\) | ||||
0.0275624 | + | 0.999620i | \(0.491225\pi\) | |||||||
\(740\) | −45.9230 | −1.68816 | ||||||||
\(741\) | −4.12411 | −0.151503 | ||||||||
\(742\) | 45.8981 | 1.68497 | ||||||||
\(743\) | 34.4765 | 1.26482 | 0.632410 | − | 0.774634i | \(-0.282066\pi\) | ||||
0.632410 | + | 0.774634i | \(0.282066\pi\) | |||||||
\(744\) | −8.86376 | −0.324961 | ||||||||
\(745\) | −4.20377 | −0.154014 | ||||||||
\(746\) | −9.10711 | −0.333435 | ||||||||
\(747\) | 1.36491 | 0.0499393 | ||||||||
\(748\) | 5.56213 | 0.203372 | ||||||||
\(749\) | 14.5840 | 0.532888 | ||||||||
\(750\) | 1.19097 | 0.0434881 | ||||||||
\(751\) | −51.7670 | −1.88901 | −0.944503 | − | 0.328504i | \(-0.893456\pi\) | ||||
−0.944503 | + | 0.328504i | \(0.893456\pi\) | |||||||
\(752\) | −7.06575 | −0.257661 | ||||||||
\(753\) | −6.95982 | −0.253630 | ||||||||
\(754\) | −3.96640 | −0.144448 | ||||||||
\(755\) | −78.5270 | −2.85789 | ||||||||
\(756\) | −6.70836 | −0.243981 | ||||||||
\(757\) | −9.06994 | −0.329652 | −0.164826 | − | 0.986323i | \(-0.552706\pi\) | ||||
−0.164826 | + | 0.986323i | \(0.552706\pi\) | |||||||
\(758\) | −15.1306 | −0.549569 | ||||||||
\(759\) | −15.3508 | −0.557198 | ||||||||
\(760\) | 35.3422 | 1.28200 | ||||||||
\(761\) | −25.0993 | −0.909850 | −0.454925 | − | 0.890530i | \(-0.650334\pi\) | ||||
−0.454925 | + | 0.890530i | \(0.650334\pi\) | |||||||
\(762\) | 4.48023 | 0.162302 | ||||||||
\(763\) | 76.4287 | 2.76690 | ||||||||
\(764\) | −10.2076 | −0.369300 | ||||||||
\(765\) | 3.23827 | 0.117080 | ||||||||
\(766\) | −22.7480 | −0.821919 | ||||||||
\(767\) | −8.21723 | −0.296707 | ||||||||
\(768\) | −12.6366 | −0.455983 | ||||||||
\(769\) | −12.2855 | −0.443025 | −0.221512 | − | 0.975158i | \(-0.571099\pi\) | ||||
−0.221512 | + | 0.975158i | \(0.571099\pi\) | |||||||
\(770\) | 44.7911 | 1.61416 | ||||||||
\(771\) | −24.2037 | −0.871675 | ||||||||
\(772\) | 8.26786 | 0.297567 | ||||||||
\(773\) | 31.5706 | 1.13552 | 0.567758 | − | 0.823195i | \(-0.307811\pi\) | ||||
0.567758 | + | 0.823195i | \(0.307811\pi\) | |||||||
\(774\) | −6.76534 | −0.243175 | ||||||||
\(775\) | −18.7595 | −0.673861 | ||||||||
\(776\) | −24.8506 | −0.892083 | ||||||||
\(777\) | −46.6382 | −1.67314 | ||||||||
\(778\) | −24.8374 | −0.890465 | ||||||||
\(779\) | 11.6917 | 0.418898 | ||||||||
\(780\) | 4.53044 | 0.162216 | ||||||||
\(781\) | 13.0846 | 0.468205 | ||||||||
\(782\) | −2.98057 | −0.106585 | ||||||||
\(783\) | 5.35490 | 0.191369 | ||||||||
\(784\) | 13.4994 | 0.482122 | ||||||||
\(785\) | −3.23827 | −0.115579 | ||||||||
\(786\) | 1.28813 | 0.0459461 | ||||||||
\(787\) | 51.2075 | 1.82535 | 0.912676 | − | 0.408685i | \(-0.134012\pi\) | ||||
0.912676 | + | 0.408685i | \(0.134012\pi\) | |||||||
\(788\) | 27.0132 | 0.962305 | ||||||||
\(789\) | −17.4276 | −0.620439 | ||||||||
\(790\) | −18.8142 | −0.669380 | ||||||||
\(791\) | −99.2554 | −3.52911 | ||||||||
\(792\) | 10.0955 | 0.358728 | ||||||||
\(793\) | −1.97675 | −0.0701966 | ||||||||
\(794\) | 18.4345 | 0.654217 | ||||||||
\(795\) | 41.8479 | 1.48419 | ||||||||
\(796\) | −27.8294 | −0.986389 | ||||||||
\(797\) | −40.2223 | −1.42475 | −0.712374 | − | 0.701800i | \(-0.752380\pi\) | ||||
−0.712374 | + | 0.701800i | \(0.752380\pi\) | |||||||
\(798\) | 14.9532 | 0.529336 | ||||||||
\(799\) | 7.88353 | 0.278899 | ||||||||
\(800\) | −32.1627 | −1.13712 | ||||||||
\(801\) | 11.2296 | 0.396779 | ||||||||
\(802\) | −0.282096 | −0.00996114 | ||||||||
\(803\) | −17.2773 | −0.609704 | ||||||||
\(804\) | 14.0776 | 0.496480 | ||||||||
\(805\) | 59.9541 | 2.11310 | ||||||||
\(806\) | 2.53268 | 0.0892098 | ||||||||
\(807\) | 22.6669 | 0.797911 | ||||||||
\(808\) | −25.7112 | −0.904516 | ||||||||
\(809\) | 18.3783 | 0.646147 | 0.323074 | − | 0.946374i | \(-0.395284\pi\) | ||||
0.323074 | + | 0.946374i | \(0.395284\pi\) | |||||||
\(810\) | 2.44865 | 0.0860367 | ||||||||
\(811\) | 12.1831 | 0.427807 | 0.213904 | − | 0.976855i | \(-0.431382\pi\) | ||||
0.213904 | + | 0.976855i | \(0.431382\pi\) | |||||||
\(812\) | −35.9226 | −1.26064 | ||||||||
\(813\) | −29.4442 | −1.03265 | ||||||||
\(814\) | 29.2402 | 1.02487 | ||||||||
\(815\) | 56.1657 | 1.96740 | ||||||||
\(816\) | −0.896267 | −0.0313756 | ||||||||
\(817\) | −37.6682 | −1.31784 | ||||||||
\(818\) | −18.9099 | −0.661170 | ||||||||
\(819\) | 4.60099 | 0.160772 | ||||||||
\(820\) | −12.8436 | −0.448518 | ||||||||
\(821\) | 21.8930 | 0.764071 | 0.382035 | − | 0.924148i | \(-0.375223\pi\) | ||||
0.382035 | + | 0.924148i | \(0.375223\pi\) | |||||||
\(822\) | 7.95996 | 0.277635 | ||||||||
\(823\) | 3.73740 | 0.130278 | 0.0651388 | − | 0.997876i | \(-0.479251\pi\) | ||||
0.0651388 | + | 0.997876i | \(0.479251\pi\) | |||||||
\(824\) | 40.0903 | 1.39661 | ||||||||
\(825\) | 21.3664 | 0.743882 | ||||||||
\(826\) | 29.7940 | 1.03666 | ||||||||
\(827\) | 23.0393 | 0.801155 | 0.400577 | − | 0.916263i | \(-0.368810\pi\) | ||||
0.400577 | + | 0.916263i | \(0.368810\pi\) | |||||||
\(828\) | 5.62965 | 0.195644 | ||||||||
\(829\) | 6.03791 | 0.209705 | 0.104853 | − | 0.994488i | \(-0.466563\pi\) | ||||
0.104853 | + | 0.994488i | \(0.466563\pi\) | |||||||
\(830\) | 3.34217 | 0.116008 | ||||||||
\(831\) | −2.94976 | −0.102326 | ||||||||
\(832\) | 2.58632 | 0.0896646 | ||||||||
\(833\) | −15.0618 | −0.521861 | ||||||||
\(834\) | −9.99752 | −0.346186 | ||||||||
\(835\) | 42.8522 | 1.48296 | ||||||||
\(836\) | 23.4175 | 0.809911 | ||||||||
\(837\) | −3.41929 | −0.118188 | ||||||||
\(838\) | −7.49927 | −0.259058 | ||||||||
\(839\) | 28.7538 | 0.992691 | 0.496346 | − | 0.868125i | \(-0.334675\pi\) | ||||
0.496346 | + | 0.868125i | \(0.334675\pi\) | |||||||
\(840\) | −39.4290 | −1.36043 | ||||||||
\(841\) | −0.325020 | −0.0112076 | ||||||||
\(842\) | 14.5489 | 0.501389 | ||||||||
\(843\) | −9.09540 | −0.313262 | ||||||||
\(844\) | −34.5391 | −1.18889 | ||||||||
\(845\) | 38.9902 | 1.34131 | ||||||||
\(846\) | 5.96120 | 0.204950 | ||||||||
\(847\) | 19.5709 | 0.672465 | ||||||||
\(848\) | −11.5824 | −0.397741 | ||||||||
\(849\) | −15.3680 | −0.527428 | ||||||||
\(850\) | 4.14858 | 0.142295 | ||||||||
\(851\) | 39.1387 | 1.34166 | ||||||||
\(852\) | −4.79857 | −0.164396 | ||||||||
\(853\) | −22.6825 | −0.776633 | −0.388316 | − | 0.921526i | \(-0.626943\pi\) | ||||
−0.388316 | + | 0.921526i | \(0.626943\pi\) | |||||||
\(854\) | 7.16729 | 0.245260 | ||||||||
\(855\) | 13.6336 | 0.466260 | ||||||||
\(856\) | 8.04894 | 0.275107 | ||||||||
\(857\) | 1.22525 | 0.0418539 | 0.0209269 | − | 0.999781i | \(-0.493338\pi\) | ||||
0.0209269 | + | 0.999781i | \(0.493338\pi\) | |||||||
\(858\) | −2.88463 | −0.0984796 | ||||||||
\(859\) | 0.633833 | 0.0216261 | 0.0108130 | − | 0.999942i | \(-0.496558\pi\) | ||||
0.0108130 | + | 0.999942i | \(0.496558\pi\) | |||||||
\(860\) | 41.3795 | 1.41103 | ||||||||
\(861\) | −13.0436 | −0.444526 | ||||||||
\(862\) | 21.2112 | 0.722455 | ||||||||
\(863\) | −37.0724 | −1.26196 | −0.630979 | − | 0.775800i | \(-0.717347\pi\) | ||||
−0.630979 | + | 0.775800i | \(0.717347\pi\) | |||||||
\(864\) | −5.86229 | −0.199439 | ||||||||
\(865\) | 40.4403 | 1.37501 | ||||||||
\(866\) | 25.5020 | 0.866594 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 22.9378 | 0.778560 | ||||||||
\(869\) | −29.9230 | −1.01507 | ||||||||
\(870\) | 13.1123 | 0.444547 | ||||||||
\(871\) | −9.65528 | −0.327157 | ||||||||
\(872\) | 42.1811 | 1.42843 | ||||||||
\(873\) | −9.58636 | −0.324449 | ||||||||
\(874\) | −12.5487 | −0.424465 | ||||||||
\(875\) | −7.39790 | −0.250095 | ||||||||
\(876\) | 6.33618 | 0.214080 | ||||||||
\(877\) | 4.67672 | 0.157922 | 0.0789608 | − | 0.996878i | \(-0.474840\pi\) | ||||
0.0789608 | + | 0.996878i | \(0.474840\pi\) | |||||||
\(878\) | −8.30489 | −0.280276 | ||||||||
\(879\) | −14.1378 | −0.476857 | ||||||||
\(880\) | −11.3030 | −0.381026 | ||||||||
\(881\) | 42.6505 | 1.43693 | 0.718466 | − | 0.695562i | \(-0.244844\pi\) | ||||
0.718466 | + | 0.695562i | \(0.244844\pi\) | |||||||
\(882\) | −11.3891 | −0.383492 | ||||||||
\(883\) | −22.0463 | −0.741917 | −0.370959 | − | 0.928649i | \(-0.620971\pi\) | ||||
−0.370959 | + | 0.928649i | \(0.620971\pi\) | |||||||
\(884\) | 1.39903 | 0.0470545 | ||||||||
\(885\) | 27.1648 | 0.913136 | ||||||||
\(886\) | 20.6160 | 0.692608 | ||||||||
\(887\) | 15.3039 | 0.513853 | 0.256927 | − | 0.966431i | \(-0.417290\pi\) | ||||
0.256927 | + | 0.966431i | \(0.417290\pi\) | |||||||
\(888\) | −25.7397 | −0.863768 | ||||||||
\(889\) | −27.8296 | −0.933376 | ||||||||
\(890\) | 27.4973 | 0.921713 | ||||||||
\(891\) | 3.89444 | 0.130469 | ||||||||
\(892\) | −0.466470 | −0.0156186 | ||||||||
\(893\) | 33.1909 | 1.11069 | ||||||||
\(894\) | −0.981610 | −0.0328300 | ||||||||
\(895\) | 73.1616 | 2.44552 | ||||||||
\(896\) | 45.6929 | 1.52649 | ||||||||
\(897\) | −3.86115 | −0.128920 | ||||||||
\(898\) | 18.2148 | 0.607836 | ||||||||
\(899\) | −18.3099 | −0.610671 | ||||||||
\(900\) | −7.83577 | −0.261192 | ||||||||
\(901\) | 12.9229 | 0.430525 | ||||||||
\(902\) | 8.17781 | 0.272291 | ||||||||
\(903\) | 42.0239 | 1.39847 | ||||||||
\(904\) | −54.7792 | −1.82193 | ||||||||
\(905\) | −40.5783 | −1.34887 | ||||||||
\(906\) | −18.3366 | −0.609194 | ||||||||
\(907\) | −9.19825 | −0.305423 | −0.152711 | − | 0.988271i | \(-0.548801\pi\) | ||||
−0.152711 | + | 0.988271i | \(0.548801\pi\) | |||||||
\(908\) | −18.0676 | −0.599594 | ||||||||
\(909\) | −9.91835 | −0.328971 | ||||||||
\(910\) | 11.2662 | 0.373471 | ||||||||
\(911\) | −1.93728 | −0.0641850 | −0.0320925 | − | 0.999485i | \(-0.510217\pi\) | ||||
−0.0320925 | + | 0.999485i | \(0.510217\pi\) | |||||||
\(912\) | −3.77343 | −0.124951 | ||||||||
\(913\) | 5.31555 | 0.175919 | ||||||||
\(914\) | −19.1914 | −0.634795 | ||||||||
\(915\) | 6.53483 | 0.216035 | ||||||||
\(916\) | −30.8755 | −1.02015 | ||||||||
\(917\) | −8.00143 | −0.264230 | ||||||||
\(918\) | 0.756159 | 0.0249570 | ||||||||
\(919\) | −22.1104 | −0.729355 | −0.364677 | − | 0.931134i | \(-0.618821\pi\) | ||||
−0.364677 | + | 0.931134i | \(0.618821\pi\) | |||||||
\(920\) | 33.0888 | 1.09090 | ||||||||
\(921\) | 19.6604 | 0.647831 | ||||||||
\(922\) | −20.2868 | −0.668110 | ||||||||
\(923\) | 3.29115 | 0.108329 | ||||||||
\(924\) | −26.1253 | −0.859461 | ||||||||
\(925\) | −54.4762 | −1.79117 | ||||||||
\(926\) | 31.4694 | 1.03415 | ||||||||
\(927\) | 15.4652 | 0.507945 | ||||||||
\(928\) | −31.3920 | −1.03049 | ||||||||
\(929\) | 8.65867 | 0.284082 | 0.142041 | − | 0.989861i | \(-0.454634\pi\) | ||||
0.142041 | + | 0.989861i | \(0.454634\pi\) | |||||||
\(930\) | −8.37263 | −0.274549 | ||||||||
\(931\) | −63.4127 | −2.07827 | ||||||||
\(932\) | −19.3635 | −0.634271 | ||||||||
\(933\) | −12.1890 | −0.399049 | ||||||||
\(934\) | −12.5557 | −0.410836 | ||||||||
\(935\) | 12.6113 | 0.412432 | ||||||||
\(936\) | 2.53930 | 0.0829995 | ||||||||
\(937\) | 37.2436 | 1.21669 | 0.608347 | − | 0.793671i | \(-0.291833\pi\) | ||||
0.608347 | + | 0.793671i | \(0.291833\pi\) | |||||||
\(938\) | 35.0080 | 1.14305 | ||||||||
\(939\) | −2.03715 | −0.0664800 | ||||||||
\(940\) | −36.4611 | −1.18923 | ||||||||
\(941\) | 5.93547 | 0.193491 | 0.0967455 | − | 0.995309i | \(-0.469157\pi\) | ||||
0.0967455 | + | 0.995309i | \(0.469157\pi\) | |||||||
\(942\) | −0.756159 | −0.0246370 | ||||||||
\(943\) | 10.9462 | 0.356458 | ||||||||
\(944\) | −7.51851 | −0.244707 | ||||||||
\(945\) | −15.2101 | −0.494786 | ||||||||
\(946\) | −26.3472 | −0.856622 | ||||||||
\(947\) | −20.3241 | −0.660445 | −0.330223 | − | 0.943903i | \(-0.607124\pi\) | ||||
−0.330223 | + | 0.943903i | \(0.607124\pi\) | |||||||
\(948\) | 10.9738 | 0.356412 | ||||||||
\(949\) | −4.34573 | −0.141068 | ||||||||
\(950\) | 17.4662 | 0.566678 | ||||||||
\(951\) | −28.1589 | −0.913116 | ||||||||
\(952\) | −12.1760 | −0.394625 | ||||||||
\(953\) | 13.1630 | 0.426391 | 0.213195 | − | 0.977010i | \(-0.431613\pi\) | ||||
0.213195 | + | 0.977010i | \(0.431613\pi\) | |||||||
\(954\) | 9.77180 | 0.316374 | ||||||||
\(955\) | −23.1442 | −0.748929 | ||||||||
\(956\) | −38.7963 | −1.25476 | ||||||||
\(957\) | 20.8544 | 0.674126 | ||||||||
\(958\) | −12.1126 | −0.391341 | ||||||||
\(959\) | −49.4445 | −1.59665 | ||||||||
\(960\) | −8.54996 | −0.275949 | ||||||||
\(961\) | −19.3085 | −0.622854 | ||||||||
\(962\) | 7.35471 | 0.237125 | ||||||||
\(963\) | 3.10496 | 0.100056 | ||||||||
\(964\) | 11.5478 | 0.371930 | ||||||||
\(965\) | 18.7460 | 0.603457 | ||||||||
\(966\) | 13.9997 | 0.450434 | ||||||||
\(967\) | 9.50860 | 0.305776 | 0.152888 | − | 0.988244i | \(-0.451143\pi\) | ||||
0.152888 | + | 0.988244i | \(0.451143\pi\) | |||||||
\(968\) | 10.8012 | 0.347165 | ||||||||
\(969\) | 4.21016 | 0.135250 | ||||||||
\(970\) | −23.4736 | −0.753692 | ||||||||
\(971\) | −40.5746 | −1.30210 | −0.651050 | − | 0.759035i | \(-0.725671\pi\) | ||||
−0.651050 | + | 0.759035i | \(0.725671\pi\) | |||||||
\(972\) | −1.42822 | −0.0458103 | ||||||||
\(973\) | 62.1011 | 1.99087 | ||||||||
\(974\) | 12.6684 | 0.405921 | ||||||||
\(975\) | 5.37424 | 0.172113 | ||||||||
\(976\) | −1.80867 | −0.0578940 | ||||||||
\(977\) | −0.335819 | −0.0107438 | −0.00537190 | − | 0.999986i | \(-0.501710\pi\) | ||||
−0.00537190 | + | 0.999986i | \(0.501710\pi\) | |||||||
\(978\) | 13.1151 | 0.419375 | ||||||||
\(979\) | 43.7331 | 1.39771 | ||||||||
\(980\) | 69.6604 | 2.22522 | ||||||||
\(981\) | 16.2718 | 0.519519 | ||||||||
\(982\) | 28.6429 | 0.914032 | ||||||||
\(983\) | −42.2232 | −1.34671 | −0.673356 | − | 0.739319i | \(-0.735148\pi\) | ||||
−0.673356 | + | 0.739319i | \(0.735148\pi\) | |||||||
\(984\) | −7.19881 | −0.229490 | ||||||||
\(985\) | 61.2481 | 1.95153 | ||||||||
\(986\) | 4.04916 | 0.128952 | ||||||||
\(987\) | −37.0289 | −1.17864 | ||||||||
\(988\) | 5.89015 | 0.187390 | ||||||||
\(989\) | −35.2664 | −1.12141 | ||||||||
\(990\) | 9.53612 | 0.303078 | ||||||||
\(991\) | 10.8371 | 0.344253 | 0.172127 | − | 0.985075i | \(-0.444936\pi\) | ||||
0.172127 | + | 0.985075i | \(0.444936\pi\) | |||||||
\(992\) | 20.0448 | 0.636424 | ||||||||
\(993\) | −16.6225 | −0.527498 | ||||||||
\(994\) | −11.9330 | −0.378492 | ||||||||
\(995\) | −63.0988 | −2.00037 | ||||||||
\(996\) | −1.94939 | −0.0617688 | ||||||||
\(997\) | −52.3527 | −1.65803 | −0.829013 | − | 0.559229i | \(-0.811097\pi\) | ||||
−0.829013 | + | 0.559229i | \(0.811097\pi\) | |||||||
\(998\) | 21.2135 | 0.671502 | ||||||||
\(999\) | −9.92936 | −0.314151 |
(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 | 8007.2.a.e.1.19 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.e.1.19 | ✓ | 46 | 1.1 | even | 1 | trivial |