Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, 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("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1477718538\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1129.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 7x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.39766\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.39766 | −1.51948 | −0.759740 | − | 0.650227i | \(-0.774674\pi\) | ||||
−0.759740 | + | 0.650227i | \(0.774674\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −4.14644 | −1.56721 | −0.783604 | − | 0.621261i | \(-0.786621\pi\) | ||||
−0.783604 | + | 0.621261i | \(0.786621\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.39766 | −1.07443 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 3.54410 | 0.982958 | 0.491479 | − | 0.870890i | \(-0.336457\pi\) | ||||
0.491479 | + | 0.870890i | \(0.336457\pi\) | |||||||
\(14\) | −4.14644 | −1.10818 | ||||||||
\(15\) | 3.39766 | 0.877272 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | 0.121268 | − | 0.992620i | \(-0.461304\pi\) | ||||
0.121268 | + | 0.992620i | \(0.461304\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 6.54410 | 1.50132 | 0.750660 | − | 0.660688i | \(-0.229736\pi\) | ||||
0.750660 | + | 0.660688i | \(0.229736\pi\) | |||||||
\(20\) | −3.39766 | −0.759740 | ||||||||
\(21\) | 4.14644 | 0.904828 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 4.54410 | 0.947511 | 0.473756 | − | 0.880656i | \(-0.342898\pi\) | ||||
0.473756 | + | 0.880656i | \(0.342898\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 6.54410 | 1.30882 | ||||||||
\(26\) | 3.54410 | 0.695056 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.14644 | −0.783604 | ||||||||
\(29\) | −1.35112 | −0.250897 | −0.125448 | − | 0.992100i | \(-0.540037\pi\) | ||||
−0.125448 | + | 0.992100i | \(0.540037\pi\) | |||||||
\(30\) | 3.39766 | 0.620325 | ||||||||
\(31\) | −9.14644 | −1.64275 | −0.821375 | − | 0.570389i | \(-0.806793\pi\) | ||||
−0.821375 | + | 0.570389i | \(0.806793\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 14.0882 | 2.38134 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.74878 | −0.945094 | −0.472547 | − | 0.881306i | \(-0.656665\pi\) | ||||
−0.472547 | + | 0.881306i | \(0.656665\pi\) | |||||||
\(38\) | 6.54410 | 1.06159 | ||||||||
\(39\) | −3.54410 | −0.567511 | ||||||||
\(40\) | −3.39766 | −0.537217 | ||||||||
\(41\) | 0.497562 | 0.0777061 | 0.0388530 | − | 0.999245i | \(-0.487630\pi\) | ||||
0.0388530 | + | 0.999245i | \(0.487630\pi\) | |||||||
\(42\) | 4.14644 | 0.639810 | ||||||||
\(43\) | −2.39766 | −0.365640 | −0.182820 | − | 0.983146i | \(-0.558523\pi\) | ||||
−0.182820 | + | 0.983146i | \(0.558523\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −3.39766 | −0.506493 | ||||||||
\(46\) | 4.54410 | 0.669992 | ||||||||
\(47\) | −1.90010 | −0.277158 | −0.138579 | − | 0.990351i | \(-0.544253\pi\) | ||||
−0.138579 | + | 0.990351i | \(0.544253\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 10.1930 | 1.45614 | ||||||||
\(50\) | 6.54410 | 0.925476 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 3.54410 | 0.491479 | ||||||||
\(53\) | −6.69055 | −0.919017 | −0.459509 | − | 0.888173i | \(-0.651974\pi\) | ||||
−0.459509 | + | 0.888173i | \(0.651974\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −3.39766 | −0.458141 | ||||||||
\(56\) | −4.14644 | −0.554092 | ||||||||
\(57\) | −6.54410 | −0.866788 | ||||||||
\(58\) | −1.35112 | −0.177411 | ||||||||
\(59\) | 10.4442 | 1.35972 | 0.679860 | − | 0.733342i | \(-0.262041\pi\) | ||||
0.679860 | + | 0.733342i | \(0.262041\pi\) | |||||||
\(60\) | 3.39766 | 0.438636 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −9.14644 | −1.16160 | ||||||||
\(63\) | −4.14644 | −0.522403 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.0417 | −1.49358 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | 9.14644 | 1.11742 | 0.558708 | − | 0.829365i | \(-0.311297\pi\) | ||||
0.558708 | + | 0.829365i | \(0.311297\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | −4.54410 | −0.547046 | ||||||||
\(70\) | 14.0882 | 1.68386 | ||||||||
\(71\) | −9.14644 | −1.08548 | −0.542742 | − | 0.839900i | \(-0.682614\pi\) | ||||
−0.542742 | + | 0.839900i | \(0.682614\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 4.64888 | 0.544110 | 0.272055 | − | 0.962282i | \(-0.412297\pi\) | ||||
0.272055 | + | 0.962282i | \(0.412297\pi\) | |||||||
\(74\) | −5.74878 | −0.668282 | ||||||||
\(75\) | −6.54410 | −0.755648 | ||||||||
\(76\) | 6.54410 | 0.750660 | ||||||||
\(77\) | −4.14644 | −0.472531 | ||||||||
\(78\) | −3.54410 | −0.401291 | ||||||||
\(79\) | 3.54410 | 0.398743 | 0.199371 | − | 0.979924i | \(-0.436110\pi\) | ||||
0.199371 | + | 0.979924i | \(0.436110\pi\) | |||||||
\(80\) | −3.39766 | −0.379870 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.497562 | 0.0549465 | ||||||||
\(83\) | −17.7371 | −1.94690 | −0.973449 | − | 0.228903i | \(-0.926486\pi\) | ||||
−0.973449 | + | 0.228903i | \(0.926486\pi\) | |||||||
\(84\) | 4.14644 | 0.452414 | ||||||||
\(85\) | −3.39766 | −0.368528 | ||||||||
\(86\) | −2.39766 | −0.258546 | ||||||||
\(87\) | 1.35112 | 0.144855 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −12.6954 | −1.34571 | −0.672856 | − | 0.739773i | \(-0.734933\pi\) | ||||
−0.672856 | + | 0.739773i | \(0.734933\pi\) | |||||||
\(90\) | −3.39766 | −0.358145 | ||||||||
\(91\) | −14.6954 | −1.54050 | ||||||||
\(92\) | 4.54410 | 0.473756 | ||||||||
\(93\) | 9.14644 | 0.948442 | ||||||||
\(94\) | −1.90010 | −0.195980 | ||||||||
\(95\) | −22.2347 | −2.28123 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 10.7371 | 1.09019 | 0.545093 | − | 0.838376i | \(-0.316494\pi\) | ||||
0.545093 | + | 0.838376i | \(0.316494\pi\) | |||||||
\(98\) | 10.1930 | 1.02965 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 6.54410 | 0.654410 | ||||||||
\(101\) | −10.9883 | −1.09338 | −0.546689 | − | 0.837336i | \(-0.684112\pi\) | ||||
−0.546689 | + | 0.837336i | \(0.684112\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | −12.1930 | −1.20141 | −0.600705 | − | 0.799471i | \(-0.705113\pi\) | ||||
−0.600705 | + | 0.799471i | \(0.705113\pi\) | |||||||
\(104\) | 3.54410 | 0.347528 | ||||||||
\(105\) | −14.0882 | −1.37487 | ||||||||
\(106\) | −6.69055 | −0.649843 | ||||||||
\(107\) | 5.04167 | 0.487396 | 0.243698 | − | 0.969851i | \(-0.421639\pi\) | ||||
0.243698 | + | 0.969851i | \(0.421639\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −18.5392 | −1.77574 | −0.887868 | − | 0.460098i | \(-0.847814\pi\) | ||||
−0.887868 | + | 0.460098i | \(0.847814\pi\) | |||||||
\(110\) | −3.39766 | −0.323954 | ||||||||
\(111\) | 5.74878 | 0.545650 | ||||||||
\(112\) | −4.14644 | −0.391802 | ||||||||
\(113\) | 7.19298 | 0.676659 | 0.338330 | − | 0.941028i | \(-0.390138\pi\) | ||||
0.338330 | + | 0.941028i | \(0.390138\pi\) | |||||||
\(114\) | −6.54410 | −0.612911 | ||||||||
\(115\) | −15.4393 | −1.43972 | ||||||||
\(116\) | −1.35112 | −0.125448 | ||||||||
\(117\) | 3.54410 | 0.327653 | ||||||||
\(118\) | 10.4442 | 0.961467 | ||||||||
\(119\) | −4.14644 | −0.380104 | ||||||||
\(120\) | 3.39766 | 0.310163 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | −0.497562 | −0.0448636 | ||||||||
\(124\) | −9.14644 | −0.821375 | ||||||||
\(125\) | −5.24634 | −0.469247 | ||||||||
\(126\) | −4.14644 | −0.369394 | ||||||||
\(127\) | 5.79532 | 0.514252 | 0.257126 | − | 0.966378i | \(-0.417224\pi\) | ||||
0.257126 | + | 0.966378i | \(0.417224\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.39766 | 0.211102 | ||||||||
\(130\) | −12.0417 | −1.05612 | ||||||||
\(131\) | −8.90010 | −0.777605 | −0.388803 | − | 0.921321i | \(-0.627111\pi\) | ||||
−0.388803 | + | 0.921321i | \(0.627111\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | −27.1348 | −2.35288 | ||||||||
\(134\) | 9.14644 | 0.790132 | ||||||||
\(135\) | 3.39766 | 0.292424 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −13.7953 | −1.17861 | −0.589307 | − | 0.807909i | \(-0.700599\pi\) | ||||
−0.589307 | + | 0.807909i | \(0.700599\pi\) | |||||||
\(138\) | −4.54410 | −0.386820 | ||||||||
\(139\) | −20.6323 | −1.75001 | −0.875005 | − | 0.484114i | \(-0.839142\pi\) | ||||
−0.875005 | + | 0.484114i | \(0.839142\pi\) | |||||||
\(140\) | 14.0882 | 1.19067 | ||||||||
\(141\) | 1.90010 | 0.160017 | ||||||||
\(142\) | −9.14644 | −0.767552 | ||||||||
\(143\) | 3.54410 | 0.296373 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.59065 | 0.381232 | ||||||||
\(146\) | 4.64888 | 0.384744 | ||||||||
\(147\) | −10.1930 | −0.840703 | ||||||||
\(148\) | −5.74878 | −0.472547 | ||||||||
\(149\) | −21.3860 | −1.75201 | −0.876003 | − | 0.482305i | \(-0.839800\pi\) | ||||
−0.876003 | + | 0.482305i | \(0.839800\pi\) | |||||||
\(150\) | −6.54410 | −0.534324 | ||||||||
\(151\) | 15.5906 | 1.26875 | 0.634374 | − | 0.773026i | \(-0.281258\pi\) | ||||
0.634374 | + | 0.773026i | \(0.281258\pi\) | |||||||
\(152\) | 6.54410 | 0.530797 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −4.14644 | −0.334130 | ||||||||
\(155\) | 31.0765 | 2.49613 | ||||||||
\(156\) | −3.54410 | −0.283755 | ||||||||
\(157\) | 3.44420 | 0.274877 | 0.137439 | − | 0.990510i | \(-0.456113\pi\) | ||||
0.137439 | + | 0.990510i | \(0.456113\pi\) | |||||||
\(158\) | 3.54410 | 0.281954 | ||||||||
\(159\) | 6.69055 | 0.530595 | ||||||||
\(160\) | −3.39766 | −0.268609 | ||||||||
\(161\) | −18.8419 | −1.48495 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 12.1464 | 0.951383 | 0.475691 | − | 0.879612i | \(-0.342198\pi\) | ||||
0.475691 | + | 0.879612i | \(0.342198\pi\) | |||||||
\(164\) | 0.497562 | 0.0388530 | ||||||||
\(165\) | 3.39766 | 0.264508 | ||||||||
\(166\) | −17.7371 | −1.37667 | ||||||||
\(167\) | −2.10478 | −0.162873 | −0.0814363 | − | 0.996679i | \(-0.525951\pi\) | ||||
−0.0814363 | + | 0.996679i | \(0.525951\pi\) | |||||||
\(168\) | 4.14644 | 0.319905 | ||||||||
\(169\) | −0.439327 | −0.0337944 | ||||||||
\(170\) | −3.39766 | −0.260589 | ||||||||
\(171\) | 6.54410 | 0.500440 | ||||||||
\(172\) | −2.39766 | −0.182820 | ||||||||
\(173\) | −3.35112 | −0.254781 | −0.127390 | − | 0.991853i | \(-0.540660\pi\) | ||||
−0.127390 | + | 0.991853i | \(0.540660\pi\) | |||||||
\(174\) | 1.35112 | 0.102428 | ||||||||
\(175\) | −27.1348 | −2.05119 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −10.4442 | −0.785034 | ||||||||
\(178\) | −12.6954 | −0.951562 | ||||||||
\(179\) | 20.6857 | 1.54612 | 0.773060 | − | 0.634333i | \(-0.218725\pi\) | ||||
0.773060 | + | 0.634333i | \(0.218725\pi\) | |||||||
\(180\) | −3.39766 | −0.253247 | ||||||||
\(181\) | −15.0931 | −1.12186 | −0.560930 | − | 0.827863i | \(-0.689556\pi\) | ||||
−0.560930 | + | 0.827863i | \(0.689556\pi\) | |||||||
\(182\) | −14.6954 | −1.08930 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 4.54410 | 0.334996 | ||||||||
\(185\) | 19.5324 | 1.43605 | ||||||||
\(186\) | 9.14644 | 0.670650 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −1.90010 | −0.138579 | ||||||||
\(189\) | 4.14644 | 0.301609 | ||||||||
\(190\) | −22.2347 | −1.61307 | ||||||||
\(191\) | 8.24634 | 0.596684 | 0.298342 | − | 0.954459i | \(-0.403566\pi\) | ||||
0.298342 | + | 0.954459i | \(0.403566\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 23.4393 | 1.68720 | 0.843600 | − | 0.536972i | \(-0.180432\pi\) | ||||
0.843600 | + | 0.536972i | \(0.180432\pi\) | |||||||
\(194\) | 10.7371 | 0.770878 | ||||||||
\(195\) | 12.0417 | 0.862322 | ||||||||
\(196\) | 10.1930 | 0.728070 | ||||||||
\(197\) | −9.64400 | −0.687107 | −0.343553 | − | 0.939133i | \(-0.611631\pi\) | ||||
−0.343553 | + | 0.939133i | \(0.611631\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | −6.70224 | −0.475109 | −0.237555 | − | 0.971374i | \(-0.576346\pi\) | ||||
−0.237555 | + | 0.971374i | \(0.576346\pi\) | |||||||
\(200\) | 6.54410 | 0.462738 | ||||||||
\(201\) | −9.14644 | −0.645140 | ||||||||
\(202\) | −10.9883 | −0.773135 | ||||||||
\(203\) | 5.60234 | 0.393207 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | −1.69055 | −0.118073 | ||||||||
\(206\) | −12.1930 | −0.849525 | ||||||||
\(207\) | 4.54410 | 0.315837 | ||||||||
\(208\) | 3.54410 | 0.245739 | ||||||||
\(209\) | 6.54410 | 0.452665 | ||||||||
\(210\) | −14.0882 | −0.972179 | ||||||||
\(211\) | −16.8787 | −1.16197 | −0.580987 | − | 0.813913i | \(-0.697333\pi\) | ||||
−0.580987 | + | 0.813913i | \(0.697333\pi\) | |||||||
\(212\) | −6.69055 | −0.459509 | ||||||||
\(213\) | 9.14644 | 0.626704 | ||||||||
\(214\) | 5.04167 | 0.344641 | ||||||||
\(215\) | 8.14644 | 0.555583 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 37.9252 | 2.57453 | ||||||||
\(218\) | −18.5392 | −1.25563 | ||||||||
\(219\) | −4.64888 | −0.314142 | ||||||||
\(220\) | −3.39766 | −0.229070 | ||||||||
\(221\) | 3.54410 | 0.238402 | ||||||||
\(222\) | 5.74878 | 0.385833 | ||||||||
\(223\) | 20.3977 | 1.36593 | 0.682964 | − | 0.730452i | \(-0.260690\pi\) | ||||
0.682964 | + | 0.730452i | \(0.260690\pi\) | |||||||
\(224\) | −4.14644 | −0.277046 | ||||||||
\(225\) | 6.54410 | 0.436274 | ||||||||
\(226\) | 7.19298 | 0.478470 | ||||||||
\(227\) | −0.765350 | −0.0507980 | −0.0253990 | − | 0.999677i | \(-0.508086\pi\) | ||||
−0.0253990 | + | 0.999677i | \(0.508086\pi\) | |||||||
\(228\) | −6.54410 | −0.433394 | ||||||||
\(229\) | −5.95833 | −0.393738 | −0.196869 | − | 0.980430i | \(-0.563077\pi\) | ||||
−0.196869 | + | 0.980430i | \(0.563077\pi\) | |||||||
\(230\) | −15.4393 | −1.01804 | ||||||||
\(231\) | 4.14644 | 0.272816 | ||||||||
\(232\) | −1.35112 | −0.0887053 | ||||||||
\(233\) | −21.7904 | −1.42754 | −0.713770 | − | 0.700380i | \(-0.753014\pi\) | ||||
−0.713770 | + | 0.700380i | \(0.753014\pi\) | |||||||
\(234\) | 3.54410 | 0.231685 | ||||||||
\(235\) | 6.45590 | 0.421136 | ||||||||
\(236\) | 10.4442 | 0.679860 | ||||||||
\(237\) | −3.54410 | −0.230214 | ||||||||
\(238\) | −4.14644 | −0.268774 | ||||||||
\(239\) | 17.1881 | 1.11181 | 0.555903 | − | 0.831247i | \(-0.312373\pi\) | ||||
0.555903 | + | 0.831247i | \(0.312373\pi\) | |||||||
\(240\) | 3.39766 | 0.219318 | ||||||||
\(241\) | −3.33943 | −0.215111 | −0.107556 | − | 0.994199i | \(-0.534302\pi\) | ||||
−0.107556 | + | 0.994199i | \(0.534302\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | −34.6323 | −2.21258 | ||||||||
\(246\) | −0.497562 | −0.0317234 | ||||||||
\(247\) | 23.1930 | 1.47573 | ||||||||
\(248\) | −9.14644 | −0.580800 | ||||||||
\(249\) | 17.7371 | 1.12404 | ||||||||
\(250\) | −5.24634 | −0.331808 | ||||||||
\(251\) | −30.3229 | −1.91396 | −0.956981 | − | 0.290151i | \(-0.906295\pi\) | ||||
−0.956981 | + | 0.290151i | \(0.906295\pi\) | |||||||
\(252\) | −4.14644 | −0.261201 | ||||||||
\(253\) | 4.54410 | 0.285685 | ||||||||
\(254\) | 5.79532 | 0.363631 | ||||||||
\(255\) | 3.39766 | 0.212770 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.2395 | 0.950616 | 0.475308 | − | 0.879820i | \(-0.342337\pi\) | ||||
0.475308 | + | 0.879820i | \(0.342337\pi\) | |||||||
\(258\) | 2.39766 | 0.149272 | ||||||||
\(259\) | 23.8370 | 1.48116 | ||||||||
\(260\) | −12.0417 | −0.746792 | ||||||||
\(261\) | −1.35112 | −0.0836322 | ||||||||
\(262\) | −8.90010 | −0.549850 | ||||||||
\(263\) | −19.9466 | −1.22996 | −0.614981 | − | 0.788542i | \(-0.710836\pi\) | ||||
−0.614981 | + | 0.788542i | \(0.710836\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | 22.7322 | 1.39643 | ||||||||
\(266\) | −27.1348 | −1.66374 | ||||||||
\(267\) | 12.6954 | 0.776947 | ||||||||
\(268\) | 9.14644 | 0.558708 | ||||||||
\(269\) | −21.0000 | −1.28039 | −0.640196 | − | 0.768211i | \(-0.721147\pi\) | ||||
−0.640196 | + | 0.768211i | \(0.721147\pi\) | |||||||
\(270\) | 3.39766 | 0.206775 | ||||||||
\(271\) | −18.5441 | −1.12647 | −0.563237 | − | 0.826295i | \(-0.690444\pi\) | ||||
−0.563237 | + | 0.826295i | \(0.690444\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 14.6954 | 0.889407 | ||||||||
\(274\) | −13.7953 | −0.833406 | ||||||||
\(275\) | 6.54410 | 0.394624 | ||||||||
\(276\) | −4.54410 | −0.273523 | ||||||||
\(277\) | −6.54898 | −0.393490 | −0.196745 | − | 0.980455i | \(-0.563037\pi\) | ||||
−0.196745 | + | 0.980455i | \(0.563037\pi\) | |||||||
\(278\) | −20.6323 | −1.23744 | ||||||||
\(279\) | −9.14644 | −0.547583 | ||||||||
\(280\) | 14.0882 | 0.841931 | ||||||||
\(281\) | −15.7371 | −0.938796 | −0.469398 | − | 0.882987i | \(-0.655529\pi\) | ||||
−0.469398 | + | 0.882987i | \(0.655529\pi\) | |||||||
\(282\) | 1.90010 | 0.113149 | ||||||||
\(283\) | 13.6023 | 0.808575 | 0.404288 | − | 0.914632i | \(-0.367520\pi\) | ||||
0.404288 | + | 0.914632i | \(0.367520\pi\) | |||||||
\(284\) | −9.14644 | −0.542742 | ||||||||
\(285\) | 22.2347 | 1.31707 | ||||||||
\(286\) | 3.54410 | 0.209567 | ||||||||
\(287\) | −2.06311 | −0.121782 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 4.59065 | 0.269572 | ||||||||
\(291\) | −10.7371 | −0.629419 | ||||||||
\(292\) | 4.64888 | 0.272055 | ||||||||
\(293\) | 4.80702 | 0.280829 | 0.140414 | − | 0.990093i | \(-0.455157\pi\) | ||||
0.140414 | + | 0.990093i | \(0.455157\pi\) | |||||||
\(294\) | −10.1930 | −0.594467 | ||||||||
\(295\) | −35.4859 | −2.06607 | ||||||||
\(296\) | −5.74878 | −0.334141 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −21.3860 | −1.23886 | ||||||||
\(299\) | 16.1048 | 0.931363 | ||||||||
\(300\) | −6.54410 | −0.377824 | ||||||||
\(301\) | 9.94177 | 0.573034 | ||||||||
\(302\) | 15.5906 | 0.897141 | ||||||||
\(303\) | 10.9883 | 0.631262 | ||||||||
\(304\) | 6.54410 | 0.375330 | ||||||||
\(305\) | 3.39766 | 0.194550 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 14.5441 | 0.830076 | 0.415038 | − | 0.909804i | \(-0.363768\pi\) | ||||
0.415038 | + | 0.909804i | \(0.363768\pi\) | |||||||
\(308\) | −4.14644 | −0.236265 | ||||||||
\(309\) | 12.1930 | 0.693635 | ||||||||
\(310\) | 31.0765 | 1.76503 | ||||||||
\(311\) | −11.9486 | −0.677542 | −0.338771 | − | 0.940869i | \(-0.610011\pi\) | ||||
−0.338771 | + | 0.940869i | \(0.610011\pi\) | |||||||
\(312\) | −3.54410 | −0.200645 | ||||||||
\(313\) | −13.0368 | −0.736883 | −0.368441 | − | 0.929651i | \(-0.620108\pi\) | ||||
−0.368441 | + | 0.929651i | \(0.620108\pi\) | |||||||
\(314\) | 3.44420 | 0.194368 | ||||||||
\(315\) | 14.0882 | 0.793781 | ||||||||
\(316\) | 3.54410 | 0.199371 | ||||||||
\(317\) | 30.3743 | 1.70599 | 0.852995 | − | 0.521920i | \(-0.174784\pi\) | ||||
0.852995 | + | 0.521920i | \(0.174784\pi\) | |||||||
\(318\) | 6.69055 | 0.375187 | ||||||||
\(319\) | −1.35112 | −0.0756482 | ||||||||
\(320\) | −3.39766 | −0.189935 | ||||||||
\(321\) | −5.04167 | −0.281398 | ||||||||
\(322\) | −18.8419 | −1.05002 | ||||||||
\(323\) | 6.54410 | 0.364124 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 23.1930 | 1.28652 | ||||||||
\(326\) | 12.1464 | 0.672729 | ||||||||
\(327\) | 18.5392 | 1.02522 | ||||||||
\(328\) | 0.497562 | 0.0274733 | ||||||||
\(329\) | 7.87865 | 0.434364 | ||||||||
\(330\) | 3.39766 | 0.187035 | ||||||||
\(331\) | 7.23953 | 0.397920 | 0.198960 | − | 0.980008i | \(-0.436244\pi\) | ||||
0.198960 | + | 0.980008i | \(0.436244\pi\) | |||||||
\(332\) | −17.7371 | −0.973449 | ||||||||
\(333\) | −5.74878 | −0.315031 | ||||||||
\(334\) | −2.10478 | −0.115168 | ||||||||
\(335\) | −31.0765 | −1.69789 | ||||||||
\(336\) | 4.14644 | 0.226207 | ||||||||
\(337\) | 29.5809 | 1.61137 | 0.805687 | − | 0.592342i | \(-0.201796\pi\) | ||||
0.805687 | + | 0.592342i | \(0.201796\pi\) | |||||||
\(338\) | −0.439327 | −0.0238963 | ||||||||
\(339\) | −7.19298 | −0.390669 | ||||||||
\(340\) | −3.39766 | −0.184264 | ||||||||
\(341\) | −9.14644 | −0.495308 | ||||||||
\(342\) | 6.54410 | 0.353865 | ||||||||
\(343\) | −13.2395 | −0.714867 | ||||||||
\(344\) | −2.39766 | −0.129273 | ||||||||
\(345\) | 15.4393 | 0.831225 | ||||||||
\(346\) | −3.35112 | −0.180157 | ||||||||
\(347\) | −2.48587 | −0.133448 | −0.0667242 | − | 0.997771i | \(-0.521255\pi\) | ||||
−0.0667242 | + | 0.997771i | \(0.521255\pi\) | |||||||
\(348\) | 1.35112 | 0.0724276 | ||||||||
\(349\) | 18.8884 | 1.01107 | 0.505537 | − | 0.862805i | \(-0.331295\pi\) | ||||
0.505537 | + | 0.862805i | \(0.331295\pi\) | |||||||
\(350\) | −27.1348 | −1.45041 | ||||||||
\(351\) | −3.54410 | −0.189170 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −31.1348 | −1.65714 | −0.828568 | − | 0.559889i | \(-0.810844\pi\) | ||||
−0.828568 | + | 0.559889i | \(0.810844\pi\) | |||||||
\(354\) | −10.4442 | −0.555103 | ||||||||
\(355\) | 31.0765 | 1.64937 | ||||||||
\(356\) | −12.6954 | −0.672856 | ||||||||
\(357\) | 4.14644 | 0.219453 | ||||||||
\(358\) | 20.6857 | 1.09327 | ||||||||
\(359\) | 15.1764 | 0.800981 | 0.400490 | − | 0.916301i | \(-0.368840\pi\) | ||||
0.400490 | + | 0.916301i | \(0.368840\pi\) | |||||||
\(360\) | −3.39766 | −0.179072 | ||||||||
\(361\) | 23.8253 | 1.25396 | ||||||||
\(362\) | −15.0931 | −0.793275 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −14.6954 | −0.770249 | ||||||||
\(365\) | −15.7953 | −0.826765 | ||||||||
\(366\) | 1.00000 | 0.0522708 | ||||||||
\(367\) | −26.6740 | −1.39237 | −0.696185 | − | 0.717862i | \(-0.745121\pi\) | ||||
−0.696185 | + | 0.717862i | \(0.745121\pi\) | |||||||
\(368\) | 4.54410 | 0.236878 | ||||||||
\(369\) | 0.497562 | 0.0259020 | ||||||||
\(370\) | 19.5324 | 1.01544 | ||||||||
\(371\) | 27.7420 | 1.44029 | ||||||||
\(372\) | 9.14644 | 0.474221 | ||||||||
\(373\) | −1.43933 | −0.0745255 | −0.0372628 | − | 0.999306i | \(-0.511864\pi\) | ||||
−0.0372628 | + | 0.999306i | \(0.511864\pi\) | |||||||
\(374\) | 1.00000 | 0.0517088 | ||||||||
\(375\) | 5.24634 | 0.270920 | ||||||||
\(376\) | −1.90010 | −0.0979902 | ||||||||
\(377\) | −4.78851 | −0.246621 | ||||||||
\(378\) | 4.14644 | 0.213270 | ||||||||
\(379\) | −6.80020 | −0.349303 | −0.174651 | − | 0.984630i | \(-0.555880\pi\) | ||||
−0.174651 | + | 0.984630i | \(0.555880\pi\) | |||||||
\(380\) | −22.2347 | −1.14061 | ||||||||
\(381\) | −5.79532 | −0.296903 | ||||||||
\(382\) | 8.24634 | 0.421920 | ||||||||
\(383\) | 24.5906 | 1.25652 | 0.628262 | − | 0.778002i | \(-0.283767\pi\) | ||||
0.628262 | + | 0.778002i | \(0.283767\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 14.0882 | 0.718002 | ||||||||
\(386\) | 23.4393 | 1.19303 | ||||||||
\(387\) | −2.39766 | −0.121880 | ||||||||
\(388\) | 10.7371 | 0.545093 | ||||||||
\(389\) | 28.1464 | 1.42708 | 0.713541 | − | 0.700614i | \(-0.247090\pi\) | ||||
0.713541 | + | 0.700614i | \(0.247090\pi\) | |||||||
\(390\) | 12.0417 | 0.609753 | ||||||||
\(391\) | 4.54410 | 0.229805 | ||||||||
\(392\) | 10.1930 | 0.514823 | ||||||||
\(393\) | 8.90010 | 0.448951 | ||||||||
\(394\) | −9.64400 | −0.485858 | ||||||||
\(395\) | −12.0417 | −0.605882 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | 4.03485 | 0.202503 | 0.101252 | − | 0.994861i | \(-0.467715\pi\) | ||||
0.101252 | + | 0.994861i | \(0.467715\pi\) | |||||||
\(398\) | −6.70224 | −0.335953 | ||||||||
\(399\) | 27.1348 | 1.35844 | ||||||||
\(400\) | 6.54410 | 0.327205 | ||||||||
\(401\) | −4.29288 | −0.214376 | −0.107188 | − | 0.994239i | \(-0.534185\pi\) | ||||
−0.107188 | + | 0.994239i | \(0.534185\pi\) | |||||||
\(402\) | −9.14644 | −0.456183 | ||||||||
\(403\) | −32.4159 | −1.61475 | ||||||||
\(404\) | −10.9883 | −0.546689 | ||||||||
\(405\) | −3.39766 | −0.168831 | ||||||||
\(406\) | 5.60234 | 0.278039 | ||||||||
\(407\) | −5.74878 | −0.284956 | ||||||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | −21.2298 | −1.04974 | −0.524872 | − | 0.851181i | \(-0.675887\pi\) | ||||
−0.524872 | + | 0.851181i | \(0.675887\pi\) | |||||||
\(410\) | −1.69055 | −0.0834901 | ||||||||
\(411\) | 13.7953 | 0.680473 | ||||||||
\(412\) | −12.1930 | −0.600705 | ||||||||
\(413\) | −43.3063 | −2.13096 | ||||||||
\(414\) | 4.54410 | 0.223331 | ||||||||
\(415\) | 60.2646 | 2.95827 | ||||||||
\(416\) | 3.54410 | 0.173764 | ||||||||
\(417\) | 20.6323 | 1.01037 | ||||||||
\(418\) | 6.54410 | 0.320083 | ||||||||
\(419\) | 5.83699 | 0.285156 | 0.142578 | − | 0.989784i | \(-0.454461\pi\) | ||||
0.142578 | + | 0.989784i | \(0.454461\pi\) | |||||||
\(420\) | −14.0882 | −0.687434 | ||||||||
\(421\) | 21.5392 | 1.04976 | 0.524879 | − | 0.851177i | \(-0.324111\pi\) | ||||
0.524879 | + | 0.851177i | \(0.324111\pi\) | |||||||
\(422\) | −16.8787 | −0.821640 | ||||||||
\(423\) | −1.90010 | −0.0923860 | ||||||||
\(424\) | −6.69055 | −0.324922 | ||||||||
\(425\) | 6.54410 | 0.317436 | ||||||||
\(426\) | 9.14644 | 0.443147 | ||||||||
\(427\) | 4.14644 | 0.200660 | ||||||||
\(428\) | 5.04167 | 0.243698 | ||||||||
\(429\) | −3.54410 | −0.171111 | ||||||||
\(430\) | 8.14644 | 0.392856 | ||||||||
\(431\) | −14.4976 | −0.698323 | −0.349161 | − | 0.937063i | \(-0.613534\pi\) | ||||
−0.349161 | + | 0.937063i | \(0.613534\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −25.8884 | −1.24412 | −0.622059 | − | 0.782971i | \(-0.713704\pi\) | ||||
−0.622059 | + | 0.782971i | \(0.713704\pi\) | |||||||
\(434\) | 37.9252 | 1.82047 | ||||||||
\(435\) | −4.59065 | −0.220105 | ||||||||
\(436\) | −18.5392 | −0.887868 | ||||||||
\(437\) | 29.7371 | 1.42252 | ||||||||
\(438\) | −4.64888 | −0.222132 | ||||||||
\(439\) | −12.7488 | −0.608466 | −0.304233 | − | 0.952598i | \(-0.598400\pi\) | ||||
−0.304233 | + | 0.952598i | \(0.598400\pi\) | |||||||
\(440\) | −3.39766 | −0.161977 | ||||||||
\(441\) | 10.1930 | 0.485380 | ||||||||
\(442\) | 3.54410 | 0.168576 | ||||||||
\(443\) | −40.0017 | −1.90054 | −0.950269 | − | 0.311429i | \(-0.899192\pi\) | ||||
−0.950269 | + | 0.311429i | \(0.899192\pi\) | |||||||
\(444\) | 5.74878 | 0.272825 | ||||||||
\(445\) | 43.1348 | 2.04478 | ||||||||
\(446\) | 20.3977 | 0.965857 | ||||||||
\(447\) | 21.3860 | 1.01152 | ||||||||
\(448\) | −4.14644 | −0.195901 | ||||||||
\(449\) | −27.8884 | −1.31614 | −0.658068 | − | 0.752959i | \(-0.728626\pi\) | ||||
−0.658068 | + | 0.752959i | \(0.728626\pi\) | |||||||
\(450\) | 6.54410 | 0.308492 | ||||||||
\(451\) | 0.497562 | 0.0234293 | ||||||||
\(452\) | 7.19298 | 0.338330 | ||||||||
\(453\) | −15.5906 | −0.732512 | ||||||||
\(454\) | −0.765350 | −0.0359196 | ||||||||
\(455\) | 49.9301 | 2.34076 | ||||||||
\(456\) | −6.54410 | −0.306456 | ||||||||
\(457\) | −10.6440 | −0.497906 | −0.248953 | − | 0.968516i | \(-0.580086\pi\) | ||||
−0.248953 | + | 0.968516i | \(0.580086\pi\) | |||||||
\(458\) | −5.95833 | −0.278415 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −15.4393 | −0.719862 | ||||||||
\(461\) | 2.20955 | 0.102909 | 0.0514546 | − | 0.998675i | \(-0.483614\pi\) | ||||
0.0514546 | + | 0.998675i | \(0.483614\pi\) | |||||||
\(462\) | 4.14644 | 0.192910 | ||||||||
\(463\) | 0.163011 | 0.00757577 | 0.00378789 | − | 0.999993i | \(-0.498794\pi\) | ||||
0.00378789 | + | 0.999993i | \(0.498794\pi\) | |||||||
\(464\) | −1.35112 | −0.0627241 | ||||||||
\(465\) | −31.0765 | −1.44114 | ||||||||
\(466\) | −21.7904 | −1.00942 | ||||||||
\(467\) | 16.3443 | 0.756324 | 0.378162 | − | 0.925739i | \(-0.376556\pi\) | ||||
0.378162 | + | 0.925739i | \(0.376556\pi\) | |||||||
\(468\) | 3.54410 | 0.163826 | ||||||||
\(469\) | −37.9252 | −1.75122 | ||||||||
\(470\) | 6.45590 | 0.297788 | ||||||||
\(471\) | −3.44420 | −0.158701 | ||||||||
\(472\) | 10.4442 | 0.480733 | ||||||||
\(473\) | −2.39766 | −0.110245 | ||||||||
\(474\) | −3.54410 | −0.162786 | ||||||||
\(475\) | 42.8253 | 1.96496 | ||||||||
\(476\) | −4.14644 | −0.190052 | ||||||||
\(477\) | −6.69055 | −0.306339 | ||||||||
\(478\) | 17.1881 | 0.786166 | ||||||||
\(479\) | −11.4859 | −0.524803 | −0.262401 | − | 0.964959i | \(-0.584514\pi\) | ||||
−0.262401 | + | 0.964959i | \(0.584514\pi\) | |||||||
\(480\) | 3.39766 | 0.155081 | ||||||||
\(481\) | −20.3743 | −0.928987 | ||||||||
\(482\) | −3.33943 | −0.152107 | ||||||||
\(483\) | 18.8419 | 0.857335 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −36.4810 | −1.65652 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 28.6489 | 1.29820 | 0.649102 | − | 0.760701i | \(-0.275145\pi\) | ||||
0.649102 | + | 0.760701i | \(0.275145\pi\) | |||||||
\(488\) | −1.00000 | −0.0452679 | ||||||||
\(489\) | −12.1464 | −0.549281 | ||||||||
\(490\) | −34.6323 | −1.56453 | ||||||||
\(491\) | 7.98831 | 0.360507 | 0.180254 | − | 0.983620i | \(-0.442308\pi\) | ||||
0.180254 | + | 0.983620i | \(0.442308\pi\) | |||||||
\(492\) | −0.497562 | −0.0224318 | ||||||||
\(493\) | −1.35112 | −0.0608514 | ||||||||
\(494\) | 23.1930 | 1.04350 | ||||||||
\(495\) | −3.39766 | −0.152714 | ||||||||
\(496\) | −9.14644 | −0.410687 | ||||||||
\(497\) | 37.9252 | 1.70118 | ||||||||
\(498\) | 17.7371 | 0.794818 | ||||||||
\(499\) | 31.5441 | 1.41211 | 0.706054 | − | 0.708158i | \(-0.250474\pi\) | ||||
0.706054 | + | 0.708158i | \(0.250474\pi\) | |||||||
\(500\) | −5.24634 | −0.234624 | ||||||||
\(501\) | 2.10478 | 0.0940345 | ||||||||
\(502\) | −30.3229 | −1.35338 | ||||||||
\(503\) | −31.2298 | −1.39247 | −0.696233 | − | 0.717815i | \(-0.745142\pi\) | ||||
−0.696233 | + | 0.717815i | \(0.745142\pi\) | |||||||
\(504\) | −4.14644 | −0.184697 | ||||||||
\(505\) | 37.3346 | 1.66137 | ||||||||
\(506\) | 4.54410 | 0.202010 | ||||||||
\(507\) | 0.439327 | 0.0195112 | ||||||||
\(508\) | 5.79532 | 0.257126 | ||||||||
\(509\) | 21.0134 | 0.931403 | 0.465701 | − | 0.884942i | \(-0.345802\pi\) | ||||
0.465701 | + | 0.884942i | \(0.345802\pi\) | |||||||
\(510\) | 3.39766 | 0.150451 | ||||||||
\(511\) | −19.2763 | −0.852734 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.54410 | −0.288929 | ||||||||
\(514\) | 15.2395 | 0.672187 | ||||||||
\(515\) | 41.4276 | 1.82552 | ||||||||
\(516\) | 2.39766 | 0.105551 | ||||||||
\(517\) | −1.90010 | −0.0835663 | ||||||||
\(518\) | 23.8370 | 1.04734 | ||||||||
\(519\) | 3.35112 | 0.147098 | ||||||||
\(520\) | −12.0417 | −0.528062 | ||||||||
\(521\) | −28.4393 | −1.24595 | −0.622975 | − | 0.782242i | \(-0.714076\pi\) | ||||
−0.622975 | + | 0.782242i | \(0.714076\pi\) | |||||||
\(522\) | −1.35112 | −0.0591369 | ||||||||
\(523\) | 32.1784 | 1.40706 | 0.703531 | − | 0.710665i | \(-0.251606\pi\) | ||||
0.703531 | + | 0.710665i | \(0.251606\pi\) | |||||||
\(524\) | −8.90010 | −0.388803 | ||||||||
\(525\) | 27.1348 | 1.18426 | ||||||||
\(526\) | −19.9466 | −0.869715 | ||||||||
\(527\) | −9.14644 | −0.398425 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −2.35112 | −0.102223 | ||||||||
\(530\) | 22.7322 | 0.987424 | ||||||||
\(531\) | 10.4442 | 0.453240 | ||||||||
\(532\) | −27.1348 | −1.17644 | ||||||||
\(533\) | 1.76341 | 0.0763818 | ||||||||
\(534\) | 12.6954 | 0.549385 | ||||||||
\(535\) | −17.1299 | −0.740589 | ||||||||
\(536\) | 9.14644 | 0.395066 | ||||||||
\(537\) | −20.6857 | −0.892653 | ||||||||
\(538\) | −21.0000 | −0.905374 | ||||||||
\(539\) | 10.1930 | 0.439043 | ||||||||
\(540\) | 3.39766 | 0.146212 | ||||||||
\(541\) | 26.8903 | 1.15611 | 0.578053 | − | 0.815999i | \(-0.303813\pi\) | ||||
0.578053 | + | 0.815999i | \(0.303813\pi\) | |||||||
\(542\) | −18.5441 | −0.796537 | ||||||||
\(543\) | 15.0931 | 0.647706 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 62.9900 | 2.69820 | ||||||||
\(546\) | 14.6954 | 0.628906 | ||||||||
\(547\) | −12.6323 | −0.540119 | −0.270059 | − | 0.962844i | \(-0.587043\pi\) | ||||
−0.270059 | + | 0.962844i | \(0.587043\pi\) | |||||||
\(548\) | −13.7953 | −0.589307 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | 6.54410 | 0.279042 | ||||||||
\(551\) | −8.84187 | −0.376676 | ||||||||
\(552\) | −4.54410 | −0.193410 | ||||||||
\(553\) | −14.6954 | −0.624913 | ||||||||
\(554\) | −6.54898 | −0.278240 | ||||||||
\(555\) | −19.5324 | −0.829105 | ||||||||
\(556\) | −20.6323 | −0.875005 | ||||||||
\(557\) | −20.4442 | −0.866249 | −0.433124 | − | 0.901334i | \(-0.642589\pi\) | ||||
−0.433124 | + | 0.901334i | \(0.642589\pi\) | |||||||
\(558\) | −9.14644 | −0.387200 | ||||||||
\(559\) | −8.49756 | −0.359409 | ||||||||
\(560\) | 14.0882 | 0.595335 | ||||||||
\(561\) | −1.00000 | −0.0422200 | ||||||||
\(562\) | −15.7371 | −0.663829 | ||||||||
\(563\) | −38.0551 | −1.60383 | −0.801915 | − | 0.597438i | \(-0.796185\pi\) | ||||
−0.801915 | + | 0.597438i | \(0.796185\pi\) | |||||||
\(564\) | 1.90010 | 0.0800086 | ||||||||
\(565\) | −24.4393 | −1.02817 | ||||||||
\(566\) | 13.6023 | 0.571749 | ||||||||
\(567\) | −4.14644 | −0.174134 | ||||||||
\(568\) | −9.14644 | −0.383776 | ||||||||
\(569\) | −18.1182 | −0.759554 | −0.379777 | − | 0.925078i | \(-0.623999\pi\) | ||||
−0.379777 | + | 0.925078i | \(0.623999\pi\) | |||||||
\(570\) | 22.2347 | 0.931307 | ||||||||
\(571\) | −3.28119 | −0.137314 | −0.0686568 | − | 0.997640i | \(-0.521871\pi\) | ||||
−0.0686568 | + | 0.997640i | \(0.521871\pi\) | |||||||
\(572\) | 3.54410 | 0.148186 | ||||||||
\(573\) | −8.24634 | −0.344496 | ||||||||
\(574\) | −2.06311 | −0.0861126 | ||||||||
\(575\) | 29.7371 | 1.24012 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −43.6089 | −1.81546 | −0.907732 | − | 0.419551i | \(-0.862187\pi\) | ||||
−0.907732 | + | 0.419551i | \(0.862187\pi\) | |||||||
\(578\) | −16.0000 | −0.665512 | ||||||||
\(579\) | −23.4393 | −0.974105 | ||||||||
\(580\) | 4.59065 | 0.190616 | ||||||||
\(581\) | 73.5458 | 3.05119 | ||||||||
\(582\) | −10.7371 | −0.445067 | ||||||||
\(583\) | −6.69055 | −0.277094 | ||||||||
\(584\) | 4.64888 | 0.192372 | ||||||||
\(585\) | −12.0417 | −0.497862 | ||||||||
\(586\) | 4.80702 | 0.198576 | ||||||||
\(587\) | −25.7088 | −1.06112 | −0.530558 | − | 0.847648i | \(-0.678018\pi\) | ||||
−0.530558 | + | 0.847648i | \(0.678018\pi\) | |||||||
\(588\) | −10.1930 | −0.420352 | ||||||||
\(589\) | −59.8553 | −2.46629 | ||||||||
\(590\) | −35.4859 | −1.46093 | ||||||||
\(591\) | 9.64400 | 0.396701 | ||||||||
\(592\) | −5.74878 | −0.236273 | ||||||||
\(593\) | −0.314330 | −0.0129080 | −0.00645400 | − | 0.999979i | \(-0.502054\pi\) | ||||
−0.00645400 | + | 0.999979i | \(0.502054\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 14.0882 | 0.577560 | ||||||||
\(596\) | −21.3860 | −0.876003 | ||||||||
\(597\) | 6.70224 | 0.274304 | ||||||||
\(598\) | 16.1048 | 0.658573 | ||||||||
\(599\) | 7.75366 | 0.316806 | 0.158403 | − | 0.987375i | \(-0.449366\pi\) | ||||
0.158403 | + | 0.987375i | \(0.449366\pi\) | |||||||
\(600\) | −6.54410 | −0.267162 | ||||||||
\(601\) | −11.9951 | −0.489291 | −0.244646 | − | 0.969613i | \(-0.578672\pi\) | ||||
−0.244646 | + | 0.969613i | \(0.578672\pi\) | |||||||
\(602\) | 9.94177 | 0.405196 | ||||||||
\(603\) | 9.14644 | 0.372472 | ||||||||
\(604\) | 15.5906 | 0.634374 | ||||||||
\(605\) | −3.39766 | −0.138135 | ||||||||
\(606\) | 10.9883 | 0.446369 | ||||||||
\(607\) | −12.9981 | −0.527575 | −0.263788 | − | 0.964581i | \(-0.584972\pi\) | ||||
−0.263788 | + | 0.964581i | \(0.584972\pi\) | |||||||
\(608\) | 6.54410 | 0.265398 | ||||||||
\(609\) | −5.60234 | −0.227018 | ||||||||
\(610\) | 3.39766 | 0.137567 | ||||||||
\(611\) | −6.73415 | −0.272435 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | 18.6274 | 0.752355 | 0.376178 | − | 0.926548i | \(-0.377238\pi\) | ||||
0.376178 | + | 0.926548i | \(0.377238\pi\) | |||||||
\(614\) | 14.5441 | 0.586952 | ||||||||
\(615\) | 1.69055 | 0.0681694 | ||||||||
\(616\) | −4.14644 | −0.167065 | ||||||||
\(617\) | −44.7088 | −1.79991 | −0.899955 | − | 0.435983i | \(-0.856401\pi\) | ||||
−0.899955 | + | 0.435983i | \(0.856401\pi\) | |||||||
\(618\) | 12.1930 | 0.490474 | ||||||||
\(619\) | −14.5926 | −0.586526 | −0.293263 | − | 0.956032i | \(-0.594741\pi\) | ||||
−0.293263 | + | 0.956032i | \(0.594741\pi\) | |||||||
\(620\) | 31.0765 | 1.24806 | ||||||||
\(621\) | −4.54410 | −0.182349 | ||||||||
\(622\) | −11.9486 | −0.479094 | ||||||||
\(623\) | 52.6408 | 2.10901 | ||||||||
\(624\) | −3.54410 | −0.141878 | ||||||||
\(625\) | −14.8952 | −0.595809 | ||||||||
\(626\) | −13.0368 | −0.521055 | ||||||||
\(627\) | −6.54410 | −0.261346 | ||||||||
\(628\) | 3.44420 | 0.137439 | ||||||||
\(629\) | −5.74878 | −0.229219 | ||||||||
\(630\) | 14.0882 | 0.561288 | ||||||||
\(631\) | 13.3462 | 0.531306 | 0.265653 | − | 0.964069i | \(-0.414413\pi\) | ||||
0.265653 | + | 0.964069i | \(0.414413\pi\) | |||||||
\(632\) | 3.54410 | 0.140977 | ||||||||
\(633\) | 16.8787 | 0.670866 | ||||||||
\(634\) | 30.3743 | 1.20632 | ||||||||
\(635\) | −19.6905 | −0.781395 | ||||||||
\(636\) | 6.69055 | 0.265297 | ||||||||
\(637\) | 36.1250 | 1.43132 | ||||||||
\(638\) | −1.35112 | −0.0534913 | ||||||||
\(639\) | −9.14644 | −0.361828 | ||||||||
\(640\) | −3.39766 | −0.134304 | ||||||||
\(641\) | 16.3957 | 0.647592 | 0.323796 | − | 0.946127i | \(-0.395041\pi\) | ||||
0.323796 | + | 0.946127i | \(0.395041\pi\) | |||||||
\(642\) | −5.04167 | −0.198979 | ||||||||
\(643\) | 4.60234 | 0.181499 | 0.0907493 | − | 0.995874i | \(-0.471074\pi\) | ||||
0.0907493 | + | 0.995874i | \(0.471074\pi\) | |||||||
\(644\) | −18.8419 | −0.742474 | ||||||||
\(645\) | −8.14644 | −0.320766 | ||||||||
\(646\) | 6.54410 | 0.257474 | ||||||||
\(647\) | −18.4907 | −0.726946 | −0.363473 | − | 0.931605i | \(-0.618409\pi\) | ||||
−0.363473 | + | 0.931605i | \(0.618409\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 10.4442 | 0.409971 | ||||||||
\(650\) | 23.1930 | 0.909704 | ||||||||
\(651\) | −37.9252 | −1.48641 | ||||||||
\(652\) | 12.1464 | 0.475691 | ||||||||
\(653\) | 0.707115 | 0.0276716 | 0.0138358 | − | 0.999904i | \(-0.495596\pi\) | ||||
0.0138358 | + | 0.999904i | \(0.495596\pi\) | |||||||
\(654\) | 18.5392 | 0.724941 | ||||||||
\(655\) | 30.2395 | 1.18156 | ||||||||
\(656\) | 0.497562 | 0.0194265 | ||||||||
\(657\) | 4.64888 | 0.181370 | ||||||||
\(658\) | 7.87865 | 0.307142 | ||||||||
\(659\) | 41.4742 | 1.61560 | 0.807802 | − | 0.589454i | \(-0.200657\pi\) | ||||
0.807802 | + | 0.589454i | \(0.200657\pi\) | |||||||
\(660\) | 3.39766 | 0.132254 | ||||||||
\(661\) | 36.8136 | 1.43188 | 0.715942 | − | 0.698160i | \(-0.245998\pi\) | ||||
0.715942 | + | 0.698160i | \(0.245998\pi\) | |||||||
\(662\) | 7.23953 | 0.281372 | ||||||||
\(663\) | −3.54410 | −0.137642 | ||||||||
\(664\) | −17.7371 | −0.688333 | ||||||||
\(665\) | 92.1947 | 3.57516 | ||||||||
\(666\) | −5.74878 | −0.222761 | ||||||||
\(667\) | −6.13963 | −0.237727 | ||||||||
\(668\) | −2.10478 | −0.0814363 | ||||||||
\(669\) | −20.3977 | −0.788619 | ||||||||
\(670\) | −31.0765 | −1.20059 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 4.14644 | 0.159952 | ||||||||
\(673\) | 5.59746 | 0.215766 | 0.107883 | − | 0.994164i | \(-0.465593\pi\) | ||||
0.107883 | + | 0.994164i | \(0.465593\pi\) | |||||||
\(674\) | 29.5809 | 1.13941 | ||||||||
\(675\) | −6.54410 | −0.251883 | ||||||||
\(676\) | −0.439327 | −0.0168972 | ||||||||
\(677\) | −1.80702 | −0.0694492 | −0.0347246 | − | 0.999397i | \(-0.511055\pi\) | ||||
−0.0347246 | + | 0.999397i | \(0.511055\pi\) | |||||||
\(678\) | −7.19298 | −0.276245 | ||||||||
\(679\) | −44.5207 | −1.70855 | ||||||||
\(680\) | −3.39766 | −0.130294 | ||||||||
\(681\) | 0.765350 | 0.0293283 | ||||||||
\(682\) | −9.14644 | −0.350235 | ||||||||
\(683\) | −26.2695 | −1.00517 | −0.502587 | − | 0.864526i | \(-0.667618\pi\) | ||||
−0.502587 | + | 0.864526i | \(0.667618\pi\) | |||||||
\(684\) | 6.54410 | 0.250220 | ||||||||
\(685\) | 46.8718 | 1.79088 | ||||||||
\(686\) | −13.2395 | −0.505487 | ||||||||
\(687\) | 5.95833 | 0.227325 | ||||||||
\(688\) | −2.39766 | −0.0914100 | ||||||||
\(689\) | −23.7120 | −0.903355 | ||||||||
\(690\) | 15.4393 | 0.587765 | ||||||||
\(691\) | −12.5509 | −0.477459 | −0.238730 | − | 0.971086i | \(-0.576731\pi\) | ||||
−0.238730 | + | 0.971086i | \(0.576731\pi\) | |||||||
\(692\) | −3.35112 | −0.127390 | ||||||||
\(693\) | −4.14644 | −0.157510 | ||||||||
\(694\) | −2.48587 | −0.0943623 | ||||||||
\(695\) | 70.1016 | 2.65911 | ||||||||
\(696\) | 1.35112 | 0.0512140 | ||||||||
\(697\) | 0.497562 | 0.0188465 | ||||||||
\(698\) | 18.8884 | 0.714937 | ||||||||
\(699\) | 21.7904 | 0.824190 | ||||||||
\(700\) | −27.1348 | −1.02560 | ||||||||
\(701\) | −33.1299 | −1.25130 | −0.625649 | − | 0.780105i | \(-0.715166\pi\) | ||||
−0.625649 | + | 0.780105i | \(0.715166\pi\) | |||||||
\(702\) | −3.54410 | −0.133764 | ||||||||
\(703\) | −37.6206 | −1.41889 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −6.45590 | −0.243143 | ||||||||
\(706\) | −31.1348 | −1.17177 | ||||||||
\(707\) | 45.5624 | 1.71355 | ||||||||
\(708\) | −10.4442 | −0.392517 | ||||||||
\(709\) | 3.32115 | 0.124728 | 0.0623641 | − | 0.998053i | \(-0.480136\pi\) | ||||
0.0623641 | + | 0.998053i | \(0.480136\pi\) | |||||||
\(710\) | 31.0765 | 1.16628 | ||||||||
\(711\) | 3.54410 | 0.132914 | ||||||||
\(712\) | −12.6954 | −0.475781 | ||||||||
\(713\) | −41.5624 | −1.55652 | ||||||||
\(714\) | 4.14644 | 0.155177 | ||||||||
\(715\) | −12.0417 | −0.450333 | ||||||||
\(716\) | 20.6857 | 0.773060 | ||||||||
\(717\) | −17.1881 | −0.641902 | ||||||||
\(718\) | 15.1764 | 0.566379 | ||||||||
\(719\) | −22.9252 | −0.854966 | −0.427483 | − | 0.904023i | \(-0.640600\pi\) | ||||
−0.427483 | + | 0.904023i | \(0.640600\pi\) | |||||||
\(720\) | −3.39766 | −0.126623 | ||||||||
\(721\) | 50.5575 | 1.88286 | ||||||||
\(722\) | 23.8253 | 0.886686 | ||||||||
\(723\) | 3.33943 | 0.124195 | ||||||||
\(724\) | −15.0931 | −0.560930 | ||||||||
\(725\) | −8.84187 | −0.328379 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | −29.6391 | −1.09925 | −0.549627 | − | 0.835410i | \(-0.685230\pi\) | ||||
−0.549627 | + | 0.835410i | \(0.685230\pi\) | |||||||
\(728\) | −14.6954 | −0.544649 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −15.7953 | −0.584611 | ||||||||
\(731\) | −2.39766 | −0.0886807 | ||||||||
\(732\) | 1.00000 | 0.0369611 | ||||||||
\(733\) | 30.8302 | 1.13874 | 0.569369 | − | 0.822082i | \(-0.307187\pi\) | ||||
0.569369 | + | 0.822082i | \(0.307187\pi\) | |||||||
\(734\) | −26.6740 | −0.984554 | ||||||||
\(735\) | 34.6323 | 1.27743 | ||||||||
\(736\) | 4.54410 | 0.167498 | ||||||||
\(737\) | 9.14644 | 0.336914 | ||||||||
\(738\) | 0.497562 | 0.0183155 | ||||||||
\(739\) | 46.4228 | 1.70769 | 0.853844 | − | 0.520528i | \(-0.174265\pi\) | ||||
0.853844 | + | 0.520528i | \(0.174265\pi\) | |||||||
\(740\) | 19.5324 | 0.718026 | ||||||||
\(741\) | −23.1930 | −0.852016 | ||||||||
\(742\) | 27.7420 | 1.01844 | ||||||||
\(743\) | −4.09308 | −0.150161 | −0.0750804 | − | 0.997177i | \(-0.523921\pi\) | ||||
−0.0750804 | + | 0.997177i | \(0.523921\pi\) | |||||||
\(744\) | 9.14644 | 0.335325 | ||||||||
\(745\) | 72.6623 | 2.66214 | ||||||||
\(746\) | −1.43933 | −0.0526975 | ||||||||
\(747\) | −17.7371 | −0.648966 | ||||||||
\(748\) | 1.00000 | 0.0365636 | ||||||||
\(749\) | −20.9050 | −0.763851 | ||||||||
\(750\) | 5.24634 | 0.191569 | ||||||||
\(751\) | −39.4674 | −1.44018 | −0.720092 | − | 0.693878i | \(-0.755901\pi\) | ||||
−0.720092 | + | 0.693878i | \(0.755901\pi\) | |||||||
\(752\) | −1.90010 | −0.0692895 | ||||||||
\(753\) | 30.3229 | 1.10503 | ||||||||
\(754\) | −4.78851 | −0.174387 | ||||||||
\(755\) | −52.9717 | −1.92784 | ||||||||
\(756\) | 4.14644 | 0.150805 | ||||||||
\(757\) | −19.3414 | −0.702974 | −0.351487 | − | 0.936193i | \(-0.614324\pi\) | ||||
−0.351487 | + | 0.936193i | \(0.614324\pi\) | |||||||
\(758\) | −6.80020 | −0.246994 | ||||||||
\(759\) | −4.54410 | −0.164941 | ||||||||
\(760\) | −22.2347 | −0.806536 | ||||||||
\(761\) | −52.1162 | −1.88921 | −0.944606 | − | 0.328206i | \(-0.893556\pi\) | ||||
−0.944606 | + | 0.328206i | \(0.893556\pi\) | |||||||
\(762\) | −5.79532 | −0.209942 | ||||||||
\(763\) | 76.8718 | 2.78295 | ||||||||
\(764\) | 8.24634 | 0.298342 | ||||||||
\(765\) | −3.39766 | −0.122843 | ||||||||
\(766\) | 24.5906 | 0.888496 | ||||||||
\(767\) | 37.0153 | 1.33655 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −45.8185 | −1.65226 | −0.826128 | − | 0.563482i | \(-0.809461\pi\) | ||||
−0.826128 | + | 0.563482i | \(0.809461\pi\) | |||||||
\(770\) | 14.0882 | 0.507704 | ||||||||
\(771\) | −15.2395 | −0.548838 | ||||||||
\(772\) | 23.4393 | 0.843600 | ||||||||
\(773\) | 11.0417 | 0.397141 | 0.198571 | − | 0.980087i | \(-0.436370\pi\) | ||||
0.198571 | + | 0.980087i | \(0.436370\pi\) | |||||||
\(774\) | −2.39766 | −0.0861822 | ||||||||
\(775\) | −59.8553 | −2.15006 | ||||||||
\(776\) | 10.7371 | 0.385439 | ||||||||
\(777\) | −23.8370 | −0.855147 | ||||||||
\(778\) | 28.1464 | 1.00910 | ||||||||
\(779\) | 3.25610 | 0.116662 | ||||||||
\(780\) | 12.0417 | 0.431161 | ||||||||
\(781\) | −9.14644 | −0.327285 | ||||||||
\(782\) | 4.54410 | 0.162497 | ||||||||
\(783\) | 1.35112 | 0.0482851 | ||||||||
\(784\) | 10.1930 | 0.364035 | ||||||||
\(785\) | −11.7022 | −0.417671 | ||||||||
\(786\) | 8.90010 | 0.317456 | ||||||||
\(787\) | 49.5741 | 1.76713 | 0.883563 | − | 0.468313i | \(-0.155138\pi\) | ||||
0.883563 | + | 0.468313i | \(0.155138\pi\) | |||||||
\(788\) | −9.64400 | −0.343553 | ||||||||
\(789\) | 19.9466 | 0.710119 | ||||||||
\(790\) | −12.0417 | −0.428423 | ||||||||
\(791\) | −29.8253 | −1.06047 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | −3.54410 | −0.125855 | ||||||||
\(794\) | 4.03485 | 0.143191 | ||||||||
\(795\) | −22.7322 | −0.806228 | ||||||||
\(796\) | −6.70224 | −0.237555 | ||||||||
\(797\) | −14.7585 | −0.522774 | −0.261387 | − | 0.965234i | \(-0.584180\pi\) | ||||
−0.261387 | + | 0.965234i | \(0.584180\pi\) | |||||||
\(798\) | 27.1348 | 0.960560 | ||||||||
\(799\) | −1.90010 | −0.0672207 | ||||||||
\(800\) | 6.54410 | 0.231369 | ||||||||
\(801\) | −12.6954 | −0.448571 | ||||||||
\(802\) | −4.29288 | −0.151587 | ||||||||
\(803\) | 4.64888 | 0.164055 | ||||||||
\(804\) | −9.14644 | −0.322570 | ||||||||
\(805\) | 64.0183 | 2.25635 | ||||||||
\(806\) | −32.4159 | −1.14180 | ||||||||
\(807\) | 21.0000 | 0.739235 | ||||||||
\(808\) | −10.9883 | −0.386567 | ||||||||
\(809\) | −44.7953 | −1.57492 | −0.787460 | − | 0.616366i | \(-0.788604\pi\) | ||||
−0.787460 | + | 0.616366i | \(0.788604\pi\) | |||||||
\(810\) | −3.39766 | −0.119382 | ||||||||
\(811\) | −5.14157 | −0.180545 | −0.0902724 | − | 0.995917i | \(-0.528774\pi\) | ||||
−0.0902724 | + | 0.995917i | \(0.528774\pi\) | |||||||
\(812\) | 5.60234 | 0.196604 | ||||||||
\(813\) | 18.5441 | 0.650370 | ||||||||
\(814\) | −5.74878 | −0.201495 | ||||||||
\(815\) | −41.2695 | −1.44561 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | −15.6905 | −0.548943 | ||||||||
\(818\) | −21.2298 | −0.742282 | ||||||||
\(819\) | −14.6954 | −0.513500 | ||||||||
\(820\) | −1.69055 | −0.0590364 | ||||||||
\(821\) | −33.9815 | −1.18596 | −0.592981 | − | 0.805216i | \(-0.702049\pi\) | ||||
−0.592981 | + | 0.805216i | \(0.702049\pi\) | |||||||
\(822\) | 13.7953 | 0.481167 | ||||||||
\(823\) | 38.7885 | 1.35208 | 0.676041 | − | 0.736864i | \(-0.263694\pi\) | ||||
0.676041 | + | 0.736864i | \(0.263694\pi\) | |||||||
\(824\) | −12.1930 | −0.424763 | ||||||||
\(825\) | −6.54410 | −0.227836 | ||||||||
\(826\) | −43.3063 | −1.50682 | ||||||||
\(827\) | 17.8467 | 0.620592 | 0.310296 | − | 0.950640i | \(-0.399572\pi\) | ||||
0.310296 | + | 0.950640i | \(0.399572\pi\) | |||||||
\(828\) | 4.54410 | 0.157919 | ||||||||
\(829\) | 1.15620 | 0.0401563 | 0.0200782 | − | 0.999798i | \(-0.493608\pi\) | ||||
0.0200782 | + | 0.999798i | \(0.493608\pi\) | |||||||
\(830\) | 60.2646 | 2.09182 | ||||||||
\(831\) | 6.54898 | 0.227182 | ||||||||
\(832\) | 3.54410 | 0.122870 | ||||||||
\(833\) | 10.1930 | 0.353166 | ||||||||
\(834\) | 20.6323 | 0.714439 | ||||||||
\(835\) | 7.15132 | 0.247482 | ||||||||
\(836\) | 6.54410 | 0.226333 | ||||||||
\(837\) | 9.14644 | 0.316147 | ||||||||
\(838\) | 5.83699 | 0.201635 | ||||||||
\(839\) | −18.0833 | −0.624306 | −0.312153 | − | 0.950032i | \(-0.601050\pi\) | ||||
−0.312153 | + | 0.950032i | \(0.601050\pi\) | |||||||
\(840\) | −14.0882 | −0.486089 | ||||||||
\(841\) | −27.1745 | −0.937051 | ||||||||
\(842\) | 21.5392 | 0.742291 | ||||||||
\(843\) | 15.7371 | 0.542014 | ||||||||
\(844\) | −16.8787 | −0.580987 | ||||||||
\(845\) | 1.49269 | 0.0513499 | ||||||||
\(846\) | −1.90010 | −0.0653268 | ||||||||
\(847\) | −4.14644 | −0.142473 | ||||||||
\(848\) | −6.69055 | −0.229754 | ||||||||
\(849\) | −13.6023 | −0.466831 | ||||||||
\(850\) | 6.54410 | 0.224461 | ||||||||
\(851\) | −26.1231 | −0.895487 | ||||||||
\(852\) | 9.14644 | 0.313352 | ||||||||
\(853\) | −26.4276 | −0.904865 | −0.452432 | − | 0.891799i | \(-0.649444\pi\) | ||||
−0.452432 | + | 0.891799i | \(0.649444\pi\) | |||||||
\(854\) | 4.14644 | 0.141888 | ||||||||
\(855\) | −22.2347 | −0.760409 | ||||||||
\(856\) | 5.04167 | 0.172321 | ||||||||
\(857\) | −7.10478 | −0.242695 | −0.121347 | − | 0.992610i | \(-0.538721\pi\) | ||||
−0.121347 | + | 0.992610i | \(0.538721\pi\) | |||||||
\(858\) | −3.54410 | −0.120994 | ||||||||
\(859\) | −46.4228 | −1.58392 | −0.791962 | − | 0.610570i | \(-0.790940\pi\) | ||||
−0.791962 | + | 0.610570i | \(0.790940\pi\) | |||||||
\(860\) | 8.14644 | 0.277791 | ||||||||
\(861\) | 2.06311 | 0.0703106 | ||||||||
\(862\) | −14.4976 | −0.493789 | ||||||||
\(863\) | 42.4761 | 1.44590 | 0.722952 | − | 0.690898i | \(-0.242785\pi\) | ||||
0.722952 | + | 0.690898i | \(0.242785\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 11.3860 | 0.387135 | ||||||||
\(866\) | −25.8884 | −0.879724 | ||||||||
\(867\) | 16.0000 | 0.543388 | ||||||||
\(868\) | 37.9252 | 1.28727 | ||||||||
\(869\) | 3.54410 | 0.120225 | ||||||||
\(870\) | −4.59065 | −0.155637 | ||||||||
\(871\) | 32.4159 | 1.09837 | ||||||||
\(872\) | −18.5392 | −0.627817 | ||||||||
\(873\) | 10.7371 | 0.363395 | ||||||||
\(874\) | 29.7371 | 1.00587 | ||||||||
\(875\) | 21.7537 | 0.735408 | ||||||||
\(876\) | −4.64888 | −0.157071 | ||||||||
\(877\) | −2.19298 | −0.0740518 | −0.0370259 | − | 0.999314i | \(-0.511788\pi\) | ||||
−0.0370259 | + | 0.999314i | \(0.511788\pi\) | |||||||
\(878\) | −12.7488 | −0.430251 | ||||||||
\(879\) | −4.80702 | −0.162137 | ||||||||
\(880\) | −3.39766 | −0.114535 | ||||||||
\(881\) | −4.10965 | −0.138458 | −0.0692289 | − | 0.997601i | \(-0.522054\pi\) | ||||
−0.0692289 | + | 0.997601i | \(0.522054\pi\) | |||||||
\(882\) | 10.1930 | 0.343216 | ||||||||
\(883\) | −22.0280 | −0.741302 | −0.370651 | − | 0.928772i | \(-0.620865\pi\) | ||||
−0.370651 | + | 0.928772i | \(0.620865\pi\) | |||||||
\(884\) | 3.54410 | 0.119201 | ||||||||
\(885\) | 35.4859 | 1.19284 | ||||||||
\(886\) | −40.0017 | −1.34388 | ||||||||
\(887\) | 27.6274 | 0.927638 | 0.463819 | − | 0.885930i | \(-0.346479\pi\) | ||||
0.463819 | + | 0.885930i | \(0.346479\pi\) | |||||||
\(888\) | 5.74878 | 0.192916 | ||||||||
\(889\) | −24.0300 | −0.805939 | ||||||||
\(890\) | 43.1348 | 1.44588 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 20.3977 | 0.682964 | ||||||||
\(893\) | −12.4345 | −0.416103 | ||||||||
\(894\) | 21.3860 | 0.715254 | ||||||||
\(895\) | −70.2829 | −2.34930 | ||||||||
\(896\) | −4.14644 | −0.138523 | ||||||||
\(897\) | −16.1048 | −0.537723 | ||||||||
\(898\) | −27.8884 | −0.930648 | ||||||||
\(899\) | 12.3579 | 0.412160 | ||||||||
\(900\) | 6.54410 | 0.218137 | ||||||||
\(901\) | −6.69055 | −0.222894 | ||||||||
\(902\) | 0.497562 | 0.0165670 | ||||||||
\(903\) | −9.94177 | −0.330841 | ||||||||
\(904\) | 7.19298 | 0.239235 | ||||||||
\(905\) | 51.2812 | 1.70464 | ||||||||
\(906\) | −15.5906 | −0.517965 | ||||||||
\(907\) | 44.1162 | 1.46486 | 0.732428 | − | 0.680845i | \(-0.238387\pi\) | ||||
0.732428 | + | 0.680845i | \(0.238387\pi\) | |||||||
\(908\) | −0.765350 | −0.0253990 | ||||||||
\(909\) | −10.9883 | −0.364459 | ||||||||
\(910\) | 49.9301 | 1.65517 | ||||||||
\(911\) | 17.6720 | 0.585501 | 0.292750 | − | 0.956189i | \(-0.405430\pi\) | ||||
0.292750 | + | 0.956189i | \(0.405430\pi\) | |||||||
\(912\) | −6.54410 | −0.216697 | ||||||||
\(913\) | −17.7371 | −0.587012 | ||||||||
\(914\) | −10.6440 | −0.352072 | ||||||||
\(915\) | −3.39766 | −0.112323 | ||||||||
\(916\) | −5.95833 | −0.196869 | ||||||||
\(917\) | 36.9038 | 1.21867 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | −12.5422 | −0.413728 | −0.206864 | − | 0.978370i | \(-0.566326\pi\) | ||||
−0.206864 | + | 0.978370i | \(0.566326\pi\) | |||||||
\(920\) | −15.4393 | −0.509020 | ||||||||
\(921\) | −14.5441 | −0.479245 | ||||||||
\(922\) | 2.20955 | 0.0727678 | ||||||||
\(923\) | −32.4159 | −1.06698 | ||||||||
\(924\) | 4.14644 | 0.136408 | ||||||||
\(925\) | −37.6206 | −1.23696 | ||||||||
\(926\) | 0.163011 | 0.00535688 | ||||||||
\(927\) | −12.1930 | −0.400470 | ||||||||
\(928\) | −1.35112 | −0.0443527 | ||||||||
\(929\) | 38.5906 | 1.26612 | 0.633059 | − | 0.774104i | \(-0.281799\pi\) | ||||
0.633059 | + | 0.774104i | \(0.281799\pi\) | |||||||
\(930\) | −31.0765 | −1.01904 | ||||||||
\(931\) | 66.7040 | 2.18613 | ||||||||
\(932\) | −21.7904 | −0.713770 | ||||||||
\(933\) | 11.9486 | 0.391179 | ||||||||
\(934\) | 16.3443 | 0.534802 | ||||||||
\(935\) | −3.39766 | −0.111115 | ||||||||
\(936\) | 3.54410 | 0.115843 | ||||||||
\(937\) | 40.0465 | 1.30826 | 0.654132 | − | 0.756381i | \(-0.273034\pi\) | ||||
0.654132 | + | 0.756381i | \(0.273034\pi\) | |||||||
\(938\) | −37.9252 | −1.23830 | ||||||||
\(939\) | 13.0368 | 0.425440 | ||||||||
\(940\) | 6.45590 | 0.210568 | ||||||||
\(941\) | 37.5858 | 1.22526 | 0.612631 | − | 0.790369i | \(-0.290111\pi\) | ||||
0.612631 | + | 0.790369i | \(0.290111\pi\) | |||||||
\(942\) | −3.44420 | −0.112218 | ||||||||
\(943\) | 2.26097 | 0.0736274 | ||||||||
\(944\) | 10.4442 | 0.339930 | ||||||||
\(945\) | −14.0882 | −0.458289 | ||||||||
\(946\) | −2.39766 | −0.0779547 | ||||||||
\(947\) | 4.72540 | 0.153555 | 0.0767774 | − | 0.997048i | \(-0.475537\pi\) | ||||
0.0767774 | + | 0.997048i | \(0.475537\pi\) | |||||||
\(948\) | −3.54410 | −0.115107 | ||||||||
\(949\) | 16.4761 | 0.534837 | ||||||||
\(950\) | 42.8253 | 1.38944 | ||||||||
\(951\) | −30.3743 | −0.984953 | ||||||||
\(952\) | −4.14644 | −0.134387 | ||||||||
\(953\) | −46.5275 | −1.50717 | −0.753587 | − | 0.657348i | \(-0.771678\pi\) | ||||
−0.753587 | + | 0.657348i | \(0.771678\pi\) | |||||||
\(954\) | −6.69055 | −0.216614 | ||||||||
\(955\) | −28.0183 | −0.906650 | ||||||||
\(956\) | 17.1881 | 0.555903 | ||||||||
\(957\) | 1.35112 | 0.0436755 | ||||||||
\(958\) | −11.4859 | −0.371092 | ||||||||
\(959\) | 57.2015 | 1.84713 | ||||||||
\(960\) | 3.39766 | 0.109659 | ||||||||
\(961\) | 52.6574 | 1.69863 | ||||||||
\(962\) | −20.3743 | −0.656893 | ||||||||
\(963\) | 5.04167 | 0.162465 | ||||||||
\(964\) | −3.33943 | −0.107556 | ||||||||
\(965\) | −79.6389 | −2.56367 | ||||||||
\(966\) | 18.8419 | 0.606227 | ||||||||
\(967\) | −27.1182 | −0.872062 | −0.436031 | − | 0.899932i | \(-0.643616\pi\) | ||||
−0.436031 | + | 0.899932i | \(0.643616\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −6.54410 | −0.210227 | ||||||||
\(970\) | −36.4810 | −1.17133 | ||||||||
\(971\) | −11.3462 | −0.364118 | −0.182059 | − | 0.983288i | \(-0.558276\pi\) | ||||
−0.182059 | + | 0.983288i | \(0.558276\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 85.5507 | 2.74263 | ||||||||
\(974\) | 28.6489 | 0.917969 | ||||||||
\(975\) | −23.1930 | −0.742770 | ||||||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | 31.3411 | 1.00269 | 0.501346 | − | 0.865247i | \(-0.332838\pi\) | ||||
0.501346 | + | 0.865247i | \(0.332838\pi\) | |||||||
\(978\) | −12.1464 | −0.388400 | ||||||||
\(979\) | −12.6954 | −0.405747 | ||||||||
\(980\) | −34.6323 | −1.10629 | ||||||||
\(981\) | −18.5392 | −0.591912 | ||||||||
\(982\) | 7.98831 | 0.254917 | ||||||||
\(983\) | 50.1396 | 1.59921 | 0.799603 | − | 0.600529i | \(-0.205043\pi\) | ||||
0.799603 | + | 0.600529i | \(0.205043\pi\) | |||||||
\(984\) | −0.497562 | −0.0158617 | ||||||||
\(985\) | 32.7671 | 1.04405 | ||||||||
\(986\) | −1.35112 | −0.0430284 | ||||||||
\(987\) | −7.87865 | −0.250780 | ||||||||
\(988\) | 23.1930 | 0.737867 | ||||||||
\(989\) | −10.8952 | −0.346448 | ||||||||
\(990\) | −3.39766 | −0.107985 | ||||||||
\(991\) | 30.3063 | 0.962711 | 0.481356 | − | 0.876525i | \(-0.340145\pi\) | ||||
0.481356 | + | 0.876525i | \(0.340145\pi\) | |||||||
\(992\) | −9.14644 | −0.290400 | ||||||||
\(993\) | −7.23953 | −0.229739 | ||||||||
\(994\) | 37.9252 | 1.20291 | ||||||||
\(995\) | 22.7719 | 0.721919 | ||||||||
\(996\) | 17.7371 | 0.562021 | ||||||||
\(997\) | 44.1084 | 1.39693 | 0.698464 | − | 0.715645i | \(-0.253867\pi\) | ||||
0.698464 | + | 0.715645i | \(0.253867\pi\) | |||||||
\(998\) | 31.5441 | 0.998511 | ||||||||
\(999\) | 5.74878 | 0.181883 |
(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 | 4026.2.a.o.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.o.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial |