Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,3,Mod(91,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(6.26704608029\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.11 | ||
Root | \(-3.68124i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.91 |
Dual form | 230.3.d.a.91.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | −3.36596 | −1.12199 | −0.560993 | − | 0.827820i | \(-0.689581\pi\) | ||||
−0.560993 | + | 0.827820i | \(0.689581\pi\) | |||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | −4.76019 | −0.793364 | ||||||||
\(7\) | − | 1.16919i | − | 0.167026i | −0.996507 | − | 0.0835132i | \(-0.973386\pi\) | ||
0.996507 | − | 0.0835132i | \(-0.0266141\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 2.32968 | 0.258853 | ||||||||
\(10\) | − | 3.16228i | − | 0.316228i | ||||||
\(11\) | − | 10.6148i | − | 0.964981i | −0.875901 | − | 0.482490i | \(-0.839732\pi\) | ||
0.875901 | − | 0.482490i | \(-0.160268\pi\) | |||||||
\(12\) | −6.73192 | −0.560993 | ||||||||
\(13\) | −15.0913 | −1.16087 | −0.580436 | − | 0.814306i | \(-0.697118\pi\) | ||||
−0.580436 | + | 0.814306i | \(0.697118\pi\) | |||||||
\(14\) | − | 1.65348i | − | 0.118106i | ||||||
\(15\) | 7.52651i | 0.501768i | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 20.0887i | − | 1.18169i | −0.806787 | − | 0.590843i | \(-0.798795\pi\) | ||
0.806787 | − | 0.590843i | \(-0.201205\pi\) | |||||||
\(18\) | 3.29467 | 0.183037 | ||||||||
\(19\) | − | 22.5221i | − | 1.18537i | −0.805434 | − | 0.592686i | \(-0.798068\pi\) | ||
0.805434 | − | 0.592686i | \(-0.201932\pi\) | |||||||
\(20\) | − | 4.47214i | − | 0.223607i | ||||||
\(21\) | 3.93543i | 0.187401i | ||||||||
\(22\) | − | 15.0116i | − | 0.682344i | ||||||
\(23\) | −20.9683 | − | 9.45142i | −0.911666 | − | 0.410931i | ||||
\(24\) | −9.52037 | −0.396682 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | −21.3424 | −0.820860 | ||||||||
\(27\) | 22.4520 | 0.831556 | ||||||||
\(28\) | − | 2.33837i | − | 0.0835132i | ||||||
\(29\) | 32.5993 | 1.12411 | 0.562056 | − | 0.827099i | \(-0.310010\pi\) | ||||
0.562056 | + | 0.827099i | \(0.310010\pi\) | |||||||
\(30\) | 10.6441i | 0.354803i | ||||||||
\(31\) | −27.0975 | −0.874113 | −0.437056 | − | 0.899434i | \(-0.643979\pi\) | ||||
−0.437056 | + | 0.899434i | \(0.643979\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 35.7289i | 1.08270i | ||||||||
\(34\) | − | 28.4097i | − | 0.835578i | ||||||
\(35\) | −2.61438 | −0.0746965 | ||||||||
\(36\) | 4.65936 | 0.129427 | ||||||||
\(37\) | 53.0568i | 1.43397i | 0.697089 | + | 0.716984i | \(0.254478\pi\) | ||||
−0.697089 | + | 0.716984i | \(0.745522\pi\) | |||||||
\(38\) | − | 31.8510i | − | 0.838184i | ||||||
\(39\) | 50.7968 | 1.30248 | ||||||||
\(40\) | − | 6.32456i | − | 0.158114i | ||||||
\(41\) | 9.43720 | 0.230176 | 0.115088 | − | 0.993355i | \(-0.463285\pi\) | ||||
0.115088 | + | 0.993355i | \(0.463285\pi\) | |||||||
\(42\) | 5.56554i | 0.132513i | ||||||||
\(43\) | − | 36.4382i | − | 0.847400i | −0.905802 | − | 0.423700i | \(-0.860731\pi\) | ||
0.905802 | − | 0.423700i | \(-0.139269\pi\) | |||||||
\(44\) | − | 21.2296i | − | 0.482490i | ||||||
\(45\) | − | 5.20933i | − | 0.115763i | ||||||
\(46\) | −29.6537 | − | 13.3663i | −0.644645 | − | 0.290572i | ||||
\(47\) | −49.1365 | −1.04546 | −0.522728 | − | 0.852499i | \(-0.675086\pi\) | ||||
−0.522728 | + | 0.852499i | \(0.675086\pi\) | |||||||
\(48\) | −13.4638 | −0.280497 | ||||||||
\(49\) | 47.6330 | 0.972102 | ||||||||
\(50\) | −7.07107 | −0.141421 | ||||||||
\(51\) | 67.6176i | 1.32584i | ||||||||
\(52\) | −30.1827 | −0.580436 | ||||||||
\(53\) | 104.253i | 1.96703i | 0.180815 | + | 0.983517i | \(0.442126\pi\) | ||||
−0.180815 | + | 0.983517i | \(0.557874\pi\) | |||||||
\(54\) | 31.7520 | 0.587999 | ||||||||
\(55\) | −23.7354 | −0.431552 | ||||||||
\(56\) | − | 3.30696i | − | 0.0590528i | ||||||
\(57\) | 75.8083i | 1.32997i | ||||||||
\(58\) | 46.1023 | 0.794868 | ||||||||
\(59\) | 53.5457 | 0.907554 | 0.453777 | − | 0.891115i | \(-0.350076\pi\) | ||||
0.453777 | + | 0.891115i | \(0.350076\pi\) | |||||||
\(60\) | 15.0530i | 0.250884i | ||||||||
\(61\) | 23.5166i | 0.385518i | 0.981246 | + | 0.192759i | \(0.0617435\pi\) | ||||
−0.981246 | + | 0.192759i | \(0.938257\pi\) | |||||||
\(62\) | −38.3217 | −0.618091 | ||||||||
\(63\) | − | 2.72383i | − | 0.0432354i | ||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 33.7453i | 0.519158i | ||||||||
\(66\) | 50.5284i | 0.765581i | ||||||||
\(67\) | − | 59.4754i | − | 0.887692i | −0.896103 | − | 0.443846i | \(-0.853614\pi\) | ||
0.896103 | − | 0.443846i | \(-0.146386\pi\) | |||||||
\(68\) | − | 40.1773i | − | 0.590843i | ||||||
\(69\) | 70.5785 | + | 31.8131i | 1.02288 | + | 0.461060i | ||||
\(70\) | −3.69729 | −0.0528184 | ||||||||
\(71\) | 55.2130 | 0.777648 | 0.388824 | − | 0.921312i | \(-0.372881\pi\) | ||||
0.388824 | + | 0.921312i | \(0.372881\pi\) | |||||||
\(72\) | 6.58933 | 0.0915185 | ||||||||
\(73\) | −8.77305 | −0.120179 | −0.0600894 | − | 0.998193i | \(-0.519139\pi\) | ||||
−0.0600894 | + | 0.998193i | \(0.519139\pi\) | |||||||
\(74\) | 75.0337i | 1.01397i | ||||||||
\(75\) | 16.8298 | 0.224397 | ||||||||
\(76\) | − | 45.0441i | − | 0.592686i | ||||||
\(77\) | −12.4107 | −0.161177 | ||||||||
\(78\) | 71.8376 | 0.920994 | ||||||||
\(79\) | − | 57.0848i | − | 0.722592i | −0.932451 | − | 0.361296i | \(-0.882334\pi\) | ||
0.932451 | − | 0.361296i | \(-0.117666\pi\) | |||||||
\(80\) | − | 8.94427i | − | 0.111803i | ||||||
\(81\) | −96.5397 | −1.19185 | ||||||||
\(82\) | 13.3462 | 0.162759 | ||||||||
\(83\) | 55.1788i | 0.664805i | 0.943138 | + | 0.332403i | \(0.107859\pi\) | ||||
−0.943138 | + | 0.332403i | \(0.892141\pi\) | |||||||
\(84\) | 7.87086i | 0.0937007i | ||||||||
\(85\) | −44.9196 | −0.528466 | ||||||||
\(86\) | − | 51.5314i | − | 0.599203i | ||||||
\(87\) | −109.728 | −1.26124 | ||||||||
\(88\) | − | 30.0232i | − | 0.341172i | ||||||
\(89\) | − | 139.825i | − | 1.57107i | −0.618815 | − | 0.785536i | \(-0.712387\pi\) | ||
0.618815 | − | 0.785536i | \(-0.287613\pi\) | |||||||
\(90\) | − | 7.36710i | − | 0.0818567i | ||||||
\(91\) | 17.6446i | 0.193896i | ||||||||
\(92\) | −41.9366 | − | 18.9028i | −0.455833 | − | 0.205466i | ||||
\(93\) | 91.2091 | 0.980743 | ||||||||
\(94\) | −69.4894 | −0.739249 | ||||||||
\(95\) | −50.3608 | −0.530114 | ||||||||
\(96\) | −19.0407 | −0.198341 | ||||||||
\(97\) | 19.8635i | 0.204778i | 0.994744 | + | 0.102389i | \(0.0326487\pi\) | ||||
−0.994744 | + | 0.102389i | \(0.967351\pi\) | |||||||
\(98\) | 67.3632 | 0.687380 | ||||||||
\(99\) | − | 24.7291i | − | 0.249789i | ||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | 86.5639 | 0.857068 | 0.428534 | − | 0.903526i | \(-0.359030\pi\) | ||||
0.428534 | + | 0.903526i | \(0.359030\pi\) | |||||||
\(102\) | 95.6258i | 0.937507i | ||||||||
\(103\) | − | 144.118i | − | 1.39920i | −0.714535 | − | 0.699600i | \(-0.753361\pi\) | ||
0.714535 | − | 0.699600i | \(-0.246639\pi\) | |||||||
\(104\) | −42.6847 | −0.410430 | ||||||||
\(105\) | 8.79989 | 0.0838085 | ||||||||
\(106\) | 147.436i | 1.39090i | ||||||||
\(107\) | 10.4544i | 0.0977050i | 0.998806 | + | 0.0488525i | \(0.0155564\pi\) | ||||
−0.998806 | + | 0.0488525i | \(0.984444\pi\) | |||||||
\(108\) | 44.9040 | 0.415778 | ||||||||
\(109\) | 69.1221i | 0.634148i | 0.948401 | + | 0.317074i | \(0.102700\pi\) | ||||
−0.948401 | + | 0.317074i | \(0.897300\pi\) | |||||||
\(110\) | −33.5669 | −0.305154 | ||||||||
\(111\) | − | 178.587i | − | 1.60889i | ||||||
\(112\) | − | 4.67674i | − | 0.0417566i | ||||||
\(113\) | − | 137.264i | − | 1.21473i | −0.794423 | − | 0.607364i | \(-0.792227\pi\) | ||
0.794423 | − | 0.607364i | \(-0.207773\pi\) | |||||||
\(114\) | 107.209i | 0.940431i | ||||||||
\(115\) | −21.1340 | + | 46.8866i | −0.183774 | + | 0.407710i | ||||
\(116\) | 65.1985 | 0.562056 | ||||||||
\(117\) | −35.1580 | −0.300496 | ||||||||
\(118\) | 75.7250 | 0.641738 | ||||||||
\(119\) | −23.4874 | −0.197373 | ||||||||
\(120\) | 21.2882i | 0.177402i | ||||||||
\(121\) | 8.32629 | 0.0688123 | ||||||||
\(122\) | 33.2575i | 0.272602i | ||||||||
\(123\) | −31.7652 | −0.258254 | ||||||||
\(124\) | −54.1950 | −0.437056 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | − | 3.85208i | − | 0.0305720i | ||||||
\(127\) | 57.9697 | 0.456455 | 0.228227 | − | 0.973608i | \(-0.426707\pi\) | ||||
0.228227 | + | 0.973608i | \(0.426707\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 122.650i | 0.950772i | ||||||||
\(130\) | 47.7230i | 0.367100i | ||||||||
\(131\) | −95.0810 | −0.725809 | −0.362905 | − | 0.931826i | \(-0.618215\pi\) | ||||
−0.362905 | + | 0.931826i | \(0.618215\pi\) | |||||||
\(132\) | 71.4579i | 0.541348i | ||||||||
\(133\) | −26.3325 | −0.197988 | ||||||||
\(134\) | − | 84.1109i | − | 0.627693i | ||||||
\(135\) | − | 50.2042i | − | 0.371883i | ||||||
\(136\) | − | 56.8193i | − | 0.417789i | ||||||
\(137\) | 198.711i | 1.45045i | 0.688514 | + | 0.725223i | \(0.258263\pi\) | ||||
−0.688514 | + | 0.725223i | \(0.741737\pi\) | |||||||
\(138\) | 99.8131 | + | 44.9905i | 0.723283 | + | 0.326018i | ||||
\(139\) | −0.129480 | −0.000931508 | −0.000465754 | − | 1.00000i | \(-0.500148\pi\) | ||||
−0.000465754 | 1.00000i | \(0.500148\pi\) | ||||||||
\(140\) | −5.22876 | −0.0373483 | ||||||||
\(141\) | 165.391 | 1.17299 | ||||||||
\(142\) | 78.0830 | 0.549880 | ||||||||
\(143\) | 160.191i | 1.12022i | ||||||||
\(144\) | 9.31873 | 0.0647134 | ||||||||
\(145\) | − | 72.8942i | − | 0.502718i | ||||||
\(146\) | −12.4070 | −0.0849792 | ||||||||
\(147\) | −160.331 | −1.09069 | ||||||||
\(148\) | 106.114i | 0.716984i | ||||||||
\(149\) | 63.8745i | 0.428688i | 0.976758 | + | 0.214344i | \(0.0687613\pi\) | ||||
−0.976758 | + | 0.214344i | \(0.931239\pi\) | |||||||
\(150\) | 23.8009 | 0.158673 | ||||||||
\(151\) | −35.2673 | −0.233558 | −0.116779 | − | 0.993158i | \(-0.537257\pi\) | ||||
−0.116779 | + | 0.993158i | \(0.537257\pi\) | |||||||
\(152\) | − | 63.7020i | − | 0.419092i | ||||||
\(153\) | − | 46.8002i | − | 0.305884i | ||||||
\(154\) | −17.5513 | −0.113970 | ||||||||
\(155\) | 60.5919i | 0.390915i | ||||||||
\(156\) | 101.594 | 0.651241 | ||||||||
\(157\) | − | 289.136i | − | 1.84163i | −0.390002 | − | 0.920814i | \(-0.627526\pi\) | ||
0.390002 | − | 0.920814i | \(-0.372474\pi\) | |||||||
\(158\) | − | 80.7300i | − | 0.510950i | ||||||
\(159\) | − | 350.911i | − | 2.20699i | ||||||
\(160\) | − | 12.6491i | − | 0.0790569i | ||||||
\(161\) | −11.0505 | + | 24.5159i | −0.0686364 | + | 0.152272i | ||||
\(162\) | −136.528 | −0.842764 | ||||||||
\(163\) | −46.2536 | −0.283764 | −0.141882 | − | 0.989884i | \(-0.545315\pi\) | ||||
−0.141882 | + | 0.989884i | \(0.545315\pi\) | |||||||
\(164\) | 18.8744 | 0.115088 | ||||||||
\(165\) | 79.8923 | 0.484196 | ||||||||
\(166\) | 78.0346i | 0.470088i | ||||||||
\(167\) | −90.8735 | −0.544153 | −0.272076 | − | 0.962276i | \(-0.587710\pi\) | ||||
−0.272076 | + | 0.962276i | \(0.587710\pi\) | |||||||
\(168\) | 11.1311i | 0.0662564i | ||||||||
\(169\) | 58.7484 | 0.347624 | ||||||||
\(170\) | −63.5259 | −0.373682 | ||||||||
\(171\) | − | 52.4692i | − | 0.306837i | ||||||
\(172\) | − | 72.8764i | − | 0.423700i | ||||||
\(173\) | −90.7893 | −0.524794 | −0.262397 | − | 0.964960i | \(-0.584513\pi\) | ||||
−0.262397 | + | 0.964960i | \(0.584513\pi\) | |||||||
\(174\) | −155.179 | −0.891831 | ||||||||
\(175\) | 5.84593i | 0.0334053i | ||||||||
\(176\) | − | 42.4591i | − | 0.241245i | ||||||
\(177\) | −180.233 | −1.01826 | ||||||||
\(178\) | − | 197.743i | − | 1.11092i | ||||||
\(179\) | 301.636 | 1.68511 | 0.842557 | − | 0.538607i | \(-0.181049\pi\) | ||||
0.842557 | + | 0.538607i | \(0.181049\pi\) | |||||||
\(180\) | − | 10.4187i | − | 0.0578814i | ||||||
\(181\) | − | 248.547i | − | 1.37319i | −0.727040 | − | 0.686595i | \(-0.759105\pi\) | ||
0.727040 | − | 0.686595i | \(-0.240895\pi\) | |||||||
\(182\) | 24.9532i | 0.137105i | ||||||||
\(183\) | − | 79.1558i | − | 0.432546i | ||||||
\(184\) | −59.3074 | − | 26.7327i | −0.322323 | − | 0.145286i | ||||
\(185\) | 118.639 | 0.641290 | ||||||||
\(186\) | 128.989 | 0.693490 | ||||||||
\(187\) | −213.237 | −1.14030 | ||||||||
\(188\) | −98.2729 | −0.522728 | ||||||||
\(189\) | − | 26.2506i | − | 0.138892i | ||||||
\(190\) | −71.2210 | −0.374847 | ||||||||
\(191\) | − | 146.382i | − | 0.766397i | −0.923666 | − | 0.383199i | \(-0.874822\pi\) | ||
0.923666 | − | 0.383199i | \(-0.125178\pi\) | |||||||
\(192\) | −26.9277 | −0.140248 | ||||||||
\(193\) | −120.648 | −0.625120 | −0.312560 | − | 0.949898i | \(-0.601187\pi\) | ||||
−0.312560 | + | 0.949898i | \(0.601187\pi\) | |||||||
\(194\) | 28.0912i | 0.144800i | ||||||||
\(195\) | − | 113.585i | − | 0.582488i | ||||||
\(196\) | 95.2660 | 0.486051 | ||||||||
\(197\) | 31.6502 | 0.160661 | 0.0803305 | − | 0.996768i | \(-0.474402\pi\) | ||||
0.0803305 | + | 0.996768i | \(0.474402\pi\) | |||||||
\(198\) | − | 34.9722i | − | 0.176627i | ||||||
\(199\) | − | 37.4496i | − | 0.188189i | −0.995563 | − | 0.0940944i | \(-0.970004\pi\) | ||
0.995563 | − | 0.0940944i | \(-0.0299955\pi\) | |||||||
\(200\) | −14.1421 | −0.0707107 | ||||||||
\(201\) | 200.192i | 0.995979i | ||||||||
\(202\) | 122.420 | 0.606039 | ||||||||
\(203\) | − | 38.1146i | − | 0.187757i | ||||||
\(204\) | 135.235i | 0.662918i | ||||||||
\(205\) | − | 21.1022i | − | 0.102938i | ||||||
\(206\) | − | 203.813i | − | 0.989384i | ||||||
\(207\) | −48.8495 | − | 22.0188i | −0.235988 | − | 0.106371i | ||||
\(208\) | −60.3653 | −0.290218 | ||||||||
\(209\) | −239.067 | −1.14386 | ||||||||
\(210\) | 12.4449 | 0.0592615 | ||||||||
\(211\) | −43.6572 | −0.206906 | −0.103453 | − | 0.994634i | \(-0.532989\pi\) | ||||
−0.103453 | + | 0.994634i | \(0.532989\pi\) | |||||||
\(212\) | 208.506i | 0.983517i | ||||||||
\(213\) | −185.845 | −0.872510 | ||||||||
\(214\) | 14.7848i | 0.0690879i | ||||||||
\(215\) | −81.4783 | −0.378969 | ||||||||
\(216\) | 63.5039 | 0.294000 | ||||||||
\(217\) | 31.6820i | 0.146000i | ||||||||
\(218\) | 97.7535i | 0.448410i | ||||||||
\(219\) | 29.5297 | 0.134839 | ||||||||
\(220\) | −47.4708 | −0.215776 | ||||||||
\(221\) | 303.165i | 1.37179i | ||||||||
\(222\) | − | 252.560i | − | 1.13766i | ||||||
\(223\) | 348.623 | 1.56333 | 0.781666 | − | 0.623697i | \(-0.214370\pi\) | ||||
0.781666 | + | 0.623697i | \(0.214370\pi\) | |||||||
\(224\) | − | 6.61391i | − | 0.0295264i | ||||||
\(225\) | −11.6484 | −0.0517707 | ||||||||
\(226\) | − | 194.121i | − | 0.858943i | ||||||
\(227\) | − | 175.793i | − | 0.774421i | −0.921991 | − | 0.387210i | \(-0.873439\pi\) | ||
0.921991 | − | 0.387210i | \(-0.126561\pi\) | |||||||
\(228\) | 151.617i | 0.664985i | ||||||||
\(229\) | − | 1.44148i | − | 0.00629466i | −0.999995 | − | 0.00314733i | \(-0.998998\pi\) | ||
0.999995 | − | 0.00314733i | \(-0.00100183\pi\) | |||||||
\(230\) | −29.8880 | + | 66.3077i | −0.129948 | + | 0.288294i | ||||
\(231\) | 41.7738 | 0.180839 | ||||||||
\(232\) | 92.2047 | 0.397434 | ||||||||
\(233\) | −113.416 | −0.486763 | −0.243381 | − | 0.969931i | \(-0.578257\pi\) | ||||
−0.243381 | + | 0.969931i | \(0.578257\pi\) | |||||||
\(234\) | −49.7209 | −0.212483 | ||||||||
\(235\) | 109.872i | 0.467542i | ||||||||
\(236\) | 107.091 | 0.453777 | ||||||||
\(237\) | 192.145i | 0.810738i | ||||||||
\(238\) | −33.2162 | −0.139564 | ||||||||
\(239\) | 367.260 | 1.53665 | 0.768326 | − | 0.640059i | \(-0.221090\pi\) | ||||
0.768326 | + | 0.640059i | \(0.221090\pi\) | |||||||
\(240\) | 30.1061i | 0.125442i | ||||||||
\(241\) | − | 220.365i | − | 0.914378i | −0.889370 | − | 0.457189i | \(-0.848856\pi\) | ||
0.889370 | − | 0.457189i | \(-0.151144\pi\) | |||||||
\(242\) | 11.7752 | 0.0486577 | ||||||||
\(243\) | 122.881 | 0.505681 | ||||||||
\(244\) | 47.0332i | 0.192759i | ||||||||
\(245\) | − | 106.511i | − | 0.434737i | ||||||
\(246\) | −44.9228 | −0.182613 | ||||||||
\(247\) | 339.888i | 1.37606i | ||||||||
\(248\) | −76.6433 | −0.309046 | ||||||||
\(249\) | − | 185.730i | − | 0.745902i | ||||||
\(250\) | 15.8114i | 0.0632456i | ||||||||
\(251\) | 440.210i | 1.75382i | 0.480650 | + | 0.876912i | \(0.340401\pi\) | ||||
−0.480650 | + | 0.876912i | \(0.659599\pi\) | |||||||
\(252\) | − | 5.44766i | − | 0.0216177i | ||||||
\(253\) | −100.325 | + | 222.574i | −0.396541 | + | 0.879740i | ||||
\(254\) | 81.9816 | 0.322762 | ||||||||
\(255\) | 151.198 | 0.592932 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 491.519 | 1.91252 | 0.956262 | − | 0.292512i | \(-0.0944913\pi\) | ||||
0.956262 | + | 0.292512i | \(0.0944913\pi\) | |||||||
\(258\) | 173.453i | 0.672297i | ||||||||
\(259\) | 62.0333 | 0.239511 | ||||||||
\(260\) | 67.4905i | 0.259579i | ||||||||
\(261\) | 75.9459 | 0.290980 | ||||||||
\(262\) | −134.465 | −0.513225 | ||||||||
\(263\) | 267.833i | 1.01838i | 0.860655 | + | 0.509189i | \(0.170054\pi\) | ||||
−0.860655 | + | 0.509189i | \(0.829946\pi\) | |||||||
\(264\) | 101.057i | 0.382791i | ||||||||
\(265\) | 233.116 | 0.879684 | ||||||||
\(266\) | −37.2397 | −0.139999 | ||||||||
\(267\) | 470.647i | 1.76272i | ||||||||
\(268\) | − | 118.951i | − | 0.443846i | ||||||
\(269\) | 95.6985 | 0.355756 | 0.177878 | − | 0.984053i | \(-0.443077\pi\) | ||||
0.177878 | + | 0.984053i | \(0.443077\pi\) | |||||||
\(270\) | − | 70.9995i | − | 0.262961i | ||||||
\(271\) | −452.255 | −1.66884 | −0.834419 | − | 0.551131i | \(-0.814197\pi\) | ||||
−0.834419 | + | 0.551131i | \(0.814197\pi\) | |||||||
\(272\) | − | 80.3547i | − | 0.295422i | ||||||
\(273\) | − | 59.3909i | − | 0.217549i | ||||||
\(274\) | 281.020i | 1.02562i | ||||||||
\(275\) | 53.0739i | 0.192996i | ||||||||
\(276\) | 141.157 | + | 63.6262i | 0.511439 | + | 0.230530i | ||||
\(277\) | −87.4783 | −0.315806 | −0.157903 | − | 0.987455i | \(-0.550473\pi\) | ||||
−0.157903 | + | 0.987455i | \(0.550473\pi\) | |||||||
\(278\) | −0.183112 | −0.000658676 | ||||||||
\(279\) | −63.1285 | −0.226267 | ||||||||
\(280\) | −7.39458 | −0.0264092 | ||||||||
\(281\) | 232.157i | 0.826183i | 0.910690 | + | 0.413091i | \(0.135551\pi\) | ||||
−0.910690 | + | 0.413091i | \(0.864449\pi\) | |||||||
\(282\) | 233.899 | 0.829428 | ||||||||
\(283\) | − | 239.367i | − | 0.845820i | −0.906172 | − | 0.422910i | \(-0.861009\pi\) | ||
0.906172 | − | 0.422910i | \(-0.138991\pi\) | |||||||
\(284\) | 110.426 | 0.388824 | ||||||||
\(285\) | 169.513 | 0.594781 | ||||||||
\(286\) | 226.545i | 0.792114i | ||||||||
\(287\) | − | 11.0338i | − | 0.0384454i | ||||||
\(288\) | 13.1787 | 0.0457593 | ||||||||
\(289\) | −114.554 | −0.396382 | ||||||||
\(290\) | − | 103.088i | − | 0.355476i | ||||||
\(291\) | − | 66.8597i | − | 0.229758i | ||||||
\(292\) | −17.5461 | −0.0600894 | ||||||||
\(293\) | 581.830i | 1.98577i | 0.119092 | + | 0.992883i | \(0.462002\pi\) | ||||
−0.119092 | + | 0.992883i | \(0.537998\pi\) | |||||||
\(294\) | −226.742 | −0.771231 | ||||||||
\(295\) | − | 119.732i | − | 0.405871i | ||||||
\(296\) | 150.067i | 0.506984i | ||||||||
\(297\) | − | 238.323i | − | 0.802436i | ||||||
\(298\) | 90.3322i | 0.303128i | ||||||||
\(299\) | 316.440 | + | 142.635i | 1.05833 | + | 0.477039i | ||||
\(300\) | 33.6596 | 0.112199 | ||||||||
\(301\) | −42.6030 | −0.141538 | ||||||||
\(302\) | −49.8755 | −0.165151 | ||||||||
\(303\) | −291.370 | −0.961619 | ||||||||
\(304\) | − | 90.0882i | − | 0.296343i | ||||||
\(305\) | 52.5847 | 0.172409 | ||||||||
\(306\) | − | 66.1855i | − | 0.216292i | ||||||
\(307\) | 110.134 | 0.358742 | 0.179371 | − | 0.983782i | \(-0.442594\pi\) | ||||
0.179371 | + | 0.983782i | \(0.442594\pi\) | |||||||
\(308\) | −24.8213 | −0.0805887 | ||||||||
\(309\) | 485.094i | 1.56988i | ||||||||
\(310\) | 85.6898i | 0.276419i | ||||||||
\(311\) | −298.100 | −0.958520 | −0.479260 | − | 0.877673i | \(-0.659095\pi\) | ||||
−0.479260 | + | 0.877673i | \(0.659095\pi\) | |||||||
\(312\) | 143.675 | 0.460497 | ||||||||
\(313\) | 109.474i | 0.349758i | 0.984590 | + | 0.174879i | \(0.0559534\pi\) | ||||
−0.984590 | + | 0.174879i | \(0.944047\pi\) | |||||||
\(314\) | − | 408.900i | − | 1.30223i | ||||||
\(315\) | −6.09067 | −0.0193355 | ||||||||
\(316\) | − | 114.170i | − | 0.361296i | ||||||
\(317\) | 474.434 | 1.49664 | 0.748318 | − | 0.663340i | \(-0.230862\pi\) | ||||
0.748318 | + | 0.663340i | \(0.230862\pi\) | |||||||
\(318\) | − | 496.263i | − | 1.56057i | ||||||
\(319\) | − | 346.034i | − | 1.08475i | ||||||
\(320\) | − | 17.8885i | − | 0.0559017i | ||||||
\(321\) | − | 35.1892i | − | 0.109624i | ||||||
\(322\) | −15.6277 | + | 34.6707i | −0.0485333 | + | 0.107673i | ||||
\(323\) | −452.438 | −1.40074 | ||||||||
\(324\) | −193.079 | −0.595924 | ||||||||
\(325\) | 75.4567 | 0.232174 | ||||||||
\(326\) | −65.4124 | −0.200652 | ||||||||
\(327\) | − | 232.662i | − | 0.711506i | ||||||
\(328\) | 26.6924 | 0.0813794 | ||||||||
\(329\) | 57.4496i | 0.174619i | ||||||||
\(330\) | 112.985 | 0.342378 | ||||||||
\(331\) | 255.367 | 0.771503 | 0.385751 | − | 0.922603i | \(-0.373942\pi\) | ||||
0.385751 | + | 0.922603i | \(0.373942\pi\) | |||||||
\(332\) | 110.358i | 0.332403i | ||||||||
\(333\) | 123.606i | 0.371188i | ||||||||
\(334\) | −128.515 | −0.384774 | ||||||||
\(335\) | −132.991 | −0.396988 | ||||||||
\(336\) | 15.7417i | 0.0468504i | ||||||||
\(337\) | − | 458.486i | − | 1.36049i | −0.732983 | − | 0.680247i | \(-0.761873\pi\) | ||
0.732983 | − | 0.680247i | \(-0.238127\pi\) | |||||||
\(338\) | 83.0828 | 0.245807 | ||||||||
\(339\) | 462.026i | 1.36291i | ||||||||
\(340\) | −89.8392 | −0.264233 | ||||||||
\(341\) | 287.634i | 0.843502i | ||||||||
\(342\) | − | 74.2027i | − | 0.216967i | ||||||
\(343\) | − | 112.982i | − | 0.329393i | ||||||
\(344\) | − | 103.063i | − | 0.299601i | ||||||
\(345\) | 71.1363 | − | 157.818i | 0.206192 | − | 0.457445i | ||||
\(346\) | −128.395 | −0.371085 | ||||||||
\(347\) | 510.676 | 1.47169 | 0.735845 | − | 0.677151i | \(-0.236785\pi\) | ||||
0.735845 | + | 0.677151i | \(0.236785\pi\) | |||||||
\(348\) | −219.456 | −0.630620 | ||||||||
\(349\) | −591.870 | −1.69590 | −0.847951 | − | 0.530075i | \(-0.822164\pi\) | ||||
−0.847951 | + | 0.530075i | \(0.822164\pi\) | |||||||
\(350\) | 8.26739i | 0.0236211i | ||||||||
\(351\) | −338.831 | −0.965330 | ||||||||
\(352\) | − | 60.0463i | − | 0.170586i | ||||||
\(353\) | 168.334 | 0.476866 | 0.238433 | − | 0.971159i | \(-0.423366\pi\) | ||||
0.238433 | + | 0.971159i | \(0.423366\pi\) | |||||||
\(354\) | −254.887 | −0.720021 | ||||||||
\(355\) | − | 123.460i | − | 0.347775i | ||||||
\(356\) | − | 279.651i | − | 0.785536i | ||||||
\(357\) | 79.0575 | 0.221450 | ||||||||
\(358\) | 426.577 | 1.19156 | ||||||||
\(359\) | − | 37.5719i | − | 0.104657i | −0.998630 | − | 0.0523285i | \(-0.983336\pi\) | ||
0.998630 | − | 0.0523285i | \(-0.0166643\pi\) | |||||||
\(360\) | − | 14.7342i | − | 0.0409283i | ||||||
\(361\) | −146.243 | −0.405105 | ||||||||
\(362\) | − | 351.499i | − | 0.970992i | ||||||
\(363\) | −28.0260 | −0.0772065 | ||||||||
\(364\) | 35.2891i | 0.0969482i | ||||||||
\(365\) | 19.6171i | 0.0537456i | ||||||||
\(366\) | − | 111.943i | − | 0.305856i | ||||||
\(367\) | − | 427.036i | − | 1.16359i | −0.813337 | − | 0.581793i | \(-0.802351\pi\) | ||
0.813337 | − | 0.581793i | \(-0.197649\pi\) | |||||||
\(368\) | −83.8733 | − | 37.8057i | −0.227917 | − | 0.102733i | ||||
\(369\) | 21.9857 | 0.0595818 | ||||||||
\(370\) | 167.780 | 0.453461 | ||||||||
\(371\) | 121.891 | 0.328547 | ||||||||
\(372\) | 182.418 | 0.490371 | ||||||||
\(373\) | − | 369.980i | − | 0.991904i | −0.868350 | − | 0.495952i | \(-0.834819\pi\) | ||
0.868350 | − | 0.495952i | \(-0.165181\pi\) | |||||||
\(374\) | −301.563 | −0.806317 | ||||||||
\(375\) | − | 37.6326i | − | 0.100354i | ||||||
\(376\) | −138.979 | −0.369625 | ||||||||
\(377\) | −491.966 | −1.30495 | ||||||||
\(378\) | − | 37.1239i | − | 0.0982114i | ||||||
\(379\) | − | 78.8009i | − | 0.207918i | −0.994582 | − | 0.103959i | \(-0.966849\pi\) | ||
0.994582 | − | 0.103959i | \(-0.0331511\pi\) | |||||||
\(380\) | −100.722 | −0.265057 | ||||||||
\(381\) | −195.124 | −0.512136 | ||||||||
\(382\) | − | 207.015i | − | 0.541925i | ||||||
\(383\) | − | 254.083i | − | 0.663403i | −0.943384 | − | 0.331702i | \(-0.892377\pi\) | ||
0.943384 | − | 0.331702i | \(-0.107623\pi\) | |||||||
\(384\) | −38.0815 | −0.0991705 | ||||||||
\(385\) | 27.7511i | 0.0720807i | ||||||||
\(386\) | −170.622 | −0.442027 | ||||||||
\(387\) | − | 84.8894i | − | 0.219353i | ||||||
\(388\) | 39.7270i | 0.102389i | ||||||||
\(389\) | 322.363i | 0.828698i | 0.910118 | + | 0.414349i | \(0.135991\pi\) | ||||
−0.910118 | + | 0.414349i | \(0.864009\pi\) | |||||||
\(390\) | − | 160.634i | − | 0.411881i | ||||||
\(391\) | −189.866 | + | 421.226i | −0.485592 | + | 1.07730i | ||||
\(392\) | 134.726 | 0.343690 | ||||||||
\(393\) | 320.039 | 0.814348 | ||||||||
\(394\) | 44.7602 | 0.113605 | ||||||||
\(395\) | −127.645 | −0.323153 | ||||||||
\(396\) | − | 49.4581i | − | 0.124894i | ||||||
\(397\) | 715.832 | 1.80310 | 0.901552 | − | 0.432671i | \(-0.142429\pi\) | ||||
0.901552 | + | 0.432671i | \(0.142429\pi\) | |||||||
\(398\) | − | 52.9617i | − | 0.133070i | ||||||
\(399\) | 88.6340 | 0.222140 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | − | 441.435i | − | 1.10083i | −0.834890 | − | 0.550417i | \(-0.814469\pi\) | ||
0.834890 | − | 0.550417i | \(-0.185531\pi\) | |||||||
\(402\) | 283.114i | 0.704263i | ||||||||
\(403\) | 408.937 | 1.01473 | ||||||||
\(404\) | 173.128 | 0.428534 | ||||||||
\(405\) | 215.869i | 0.533011i | ||||||||
\(406\) | − | 53.9022i | − | 0.132764i | ||||||
\(407\) | 563.187 | 1.38375 | ||||||||
\(408\) | 191.252i | 0.468754i | ||||||||
\(409\) | −608.727 | −1.48833 | −0.744164 | − | 0.667996i | \(-0.767152\pi\) | ||||
−0.744164 | + | 0.667996i | \(0.767152\pi\) | |||||||
\(410\) | − | 29.8430i | − | 0.0727879i | ||||||
\(411\) | − | 668.853i | − | 1.62738i | ||||||
\(412\) | − | 288.235i | − | 0.699600i | ||||||
\(413\) | − | 62.6048i | − | 0.151586i | ||||||
\(414\) | −69.0836 | − | 31.1393i | −0.166869 | − | 0.0752157i | ||||
\(415\) | 123.384 | 0.297310 | ||||||||
\(416\) | −85.3695 | −0.205215 | ||||||||
\(417\) | 0.435823 | 0.00104514 | ||||||||
\(418\) | −338.091 | −0.808831 | ||||||||
\(419\) | 287.454i | 0.686047i | 0.939327 | + | 0.343023i | \(0.111451\pi\) | ||||
−0.939327 | + | 0.343023i | \(0.888549\pi\) | |||||||
\(420\) | 17.5998 | 0.0419042 | ||||||||
\(421\) | 130.848i | 0.310803i | 0.987851 | + | 0.155402i | \(0.0496672\pi\) | ||||
−0.987851 | + | 0.155402i | \(0.950333\pi\) | |||||||
\(422\) | −61.7406 | −0.146305 | ||||||||
\(423\) | −114.472 | −0.270620 | ||||||||
\(424\) | 294.871i | 0.695452i | ||||||||
\(425\) | 100.443i | 0.236337i | ||||||||
\(426\) | −262.824 | −0.616958 | ||||||||
\(427\) | 27.4952 | 0.0643917 | ||||||||
\(428\) | 20.9089i | 0.0488525i | ||||||||
\(429\) | − | 539.197i | − | 1.25687i | ||||||
\(430\) | −115.228 | −0.267972 | ||||||||
\(431\) | 239.816i | 0.556417i | 0.960521 | + | 0.278209i | \(0.0897406\pi\) | ||||
−0.960521 | + | 0.278209i | \(0.910259\pi\) | |||||||
\(432\) | 89.8081 | 0.207889 | ||||||||
\(433\) | 305.542i | 0.705640i | 0.935691 | + | 0.352820i | \(0.114777\pi\) | ||||
−0.935691 | + | 0.352820i | \(0.885223\pi\) | |||||||
\(434\) | 44.8051i | 0.103238i | ||||||||
\(435\) | 245.359i | 0.564043i | ||||||||
\(436\) | 138.244i | 0.317074i | ||||||||
\(437\) | −212.865 | + | 472.250i | −0.487106 | + | 1.08066i | ||||
\(438\) | 41.7613 | 0.0953455 | ||||||||
\(439\) | −579.018 | −1.31895 | −0.659474 | − | 0.751727i | \(-0.729221\pi\) | ||||
−0.659474 | + | 0.751727i | \(0.729221\pi\) | |||||||
\(440\) | −67.1338 | −0.152577 | ||||||||
\(441\) | 110.970 | 0.251632 | ||||||||
\(442\) | 428.740i | 0.969999i | ||||||||
\(443\) | −606.274 | −1.36856 | −0.684282 | − | 0.729217i | \(-0.739884\pi\) | ||||
−0.684282 | + | 0.729217i | \(0.739884\pi\) | |||||||
\(444\) | − | 357.174i | − | 0.804446i | ||||||
\(445\) | −312.659 | −0.702605 | ||||||||
\(446\) | 493.028 | 1.10544 | ||||||||
\(447\) | − | 214.999i | − | 0.480982i | ||||||
\(448\) | − | 9.35348i | − | 0.0208783i | ||||||
\(449\) | −202.580 | −0.451181 | −0.225590 | − | 0.974222i | \(-0.572431\pi\) | ||||
−0.225590 | + | 0.974222i | \(0.572431\pi\) | |||||||
\(450\) | −16.4733 | −0.0366074 | ||||||||
\(451\) | − | 100.174i | − | 0.222115i | ||||||
\(452\) | − | 274.529i | − | 0.607364i | ||||||
\(453\) | 118.708 | 0.262049 | ||||||||
\(454\) | − | 248.609i | − | 0.547598i | ||||||
\(455\) | 39.4545 | 0.0867131 | ||||||||
\(456\) | 214.418i | 0.470215i | ||||||||
\(457\) | − | 373.760i | − | 0.817857i | −0.912567 | − | 0.408928i | \(-0.865903\pi\) | ||
0.912567 | − | 0.408928i | \(-0.134097\pi\) | |||||||
\(458\) | − | 2.03856i | − | 0.00445100i | ||||||
\(459\) | − | 451.031i | − | 0.982639i | ||||||
\(460\) | −42.2681 | + | 93.7732i | −0.0918871 | + | 0.203855i | ||||
\(461\) | 709.377 | 1.53878 | 0.769390 | − | 0.638780i | \(-0.220561\pi\) | ||||
0.769390 | + | 0.638780i | \(0.220561\pi\) | |||||||
\(462\) | 59.0770 | 0.127872 | ||||||||
\(463\) | 266.488 | 0.575569 | 0.287785 | − | 0.957695i | \(-0.407081\pi\) | ||||
0.287785 | + | 0.957695i | \(0.407081\pi\) | |||||||
\(464\) | 130.397 | 0.281028 | ||||||||
\(465\) | − | 203.950i | − | 0.438602i | ||||||
\(466\) | −160.394 | −0.344193 | ||||||||
\(467\) | − | 686.135i | − | 1.46924i | −0.678479 | − | 0.734620i | \(-0.737361\pi\) | ||
0.678479 | − | 0.734620i | \(-0.262639\pi\) | |||||||
\(468\) | −70.3160 | −0.150248 | ||||||||
\(469\) | −69.5378 | −0.148268 | ||||||||
\(470\) | 155.383i | 0.330602i | ||||||||
\(471\) | 973.219i | 2.06628i | ||||||||
\(472\) | 151.450 | 0.320869 | ||||||||
\(473\) | −386.784 | −0.817725 | ||||||||
\(474\) | 271.734i | 0.573279i | ||||||||
\(475\) | 112.610i | 0.237074i | ||||||||
\(476\) | −46.9747 | −0.0986864 | ||||||||
\(477\) | 242.876i | 0.509174i | ||||||||
\(478\) | 519.384 | 1.08658 | ||||||||
\(479\) | 176.517i | 0.368511i | 0.982878 | + | 0.184256i | \(0.0589874\pi\) | ||||
−0.982878 | + | 0.184256i | \(0.941013\pi\) | |||||||
\(480\) | 42.5764i | 0.0887008i | ||||||||
\(481\) | − | 800.698i | − | 1.66465i | ||||||
\(482\) | − | 311.643i | − | 0.646563i | ||||||
\(483\) | 37.1954 | − | 82.5194i | 0.0770091 | − | 0.170848i | ||||
\(484\) | 16.6526 | 0.0344062 | ||||||||
\(485\) | 44.4161 | 0.0915796 | ||||||||
\(486\) | 173.779 | 0.357571 | ||||||||
\(487\) | 524.802 | 1.07762 | 0.538811 | − | 0.842427i | \(-0.318874\pi\) | ||||
0.538811 | + | 0.842427i | \(0.318874\pi\) | |||||||
\(488\) | 66.5149i | 0.136301i | ||||||||
\(489\) | 155.688 | 0.318380 | ||||||||
\(490\) | − | 150.629i | − | 0.307406i | ||||||
\(491\) | −551.047 | −1.12229 | −0.561147 | − | 0.827716i | \(-0.689640\pi\) | ||||
−0.561147 | + | 0.827716i | \(0.689640\pi\) | |||||||
\(492\) | −63.5304 | −0.129127 | ||||||||
\(493\) | − | 654.876i | − | 1.32835i | ||||||
\(494\) | 480.674i | 0.973024i | ||||||||
\(495\) | −55.2959 | −0.111709 | ||||||||
\(496\) | −108.390 | −0.218528 | ||||||||
\(497\) | − | 64.5542i | − | 0.129888i | ||||||
\(498\) | − | 262.661i | − | 0.527433i | ||||||
\(499\) | −736.739 | −1.47643 | −0.738216 | − | 0.674565i | \(-0.764331\pi\) | ||||
−0.738216 | + | 0.674565i | \(0.764331\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | 305.876 | 0.610532 | ||||||||
\(502\) | 622.551i | 1.24014i | ||||||||
\(503\) | − | 699.308i | − | 1.39027i | −0.718877 | − | 0.695137i | \(-0.755344\pi\) | ||
0.718877 | − | 0.695137i | \(-0.244656\pi\) | |||||||
\(504\) | − | 7.70415i | − | 0.0152860i | ||||||
\(505\) | − | 193.563i | − | 0.383292i | ||||||
\(506\) | −141.881 | + | 314.768i | −0.280397 | + | 0.622070i | ||||
\(507\) | −197.745 | −0.390029 | ||||||||
\(508\) | 115.939 | 0.228227 | ||||||||
\(509\) | −316.428 | −0.621666 | −0.310833 | − | 0.950464i | \(-0.600608\pi\) | ||||
−0.310833 | + | 0.950464i | \(0.600608\pi\) | |||||||
\(510\) | 213.826 | 0.419266 | ||||||||
\(511\) | 10.2573i | 0.0200730i | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | − | 505.666i | − | 0.985703i | ||||||
\(514\) | 695.112 | 1.35236 | ||||||||
\(515\) | −322.257 | −0.625741 | ||||||||
\(516\) | 245.299i | 0.475386i | ||||||||
\(517\) | 521.573i | 1.00885i | ||||||||
\(518\) | 87.7283 | 0.169360 | ||||||||
\(519\) | 305.593 | 0.588811 | ||||||||
\(520\) | 95.4460i | 0.183550i | ||||||||
\(521\) | − | 798.875i | − | 1.53335i | −0.642035 | − | 0.766675i | \(-0.721910\pi\) | ||
0.642035 | − | 0.766675i | \(-0.278090\pi\) | |||||||
\(522\) | 107.404 | 0.205754 | ||||||||
\(523\) | 819.091i | 1.56614i | 0.621934 | + | 0.783070i | \(0.286347\pi\) | ||||
−0.621934 | + | 0.783070i | \(0.713653\pi\) | |||||||
\(524\) | −190.162 | −0.362905 | ||||||||
\(525\) | − | 19.6772i | − | 0.0374803i | ||||||
\(526\) | 378.773i | 0.720101i | ||||||||
\(527\) | 544.353i | 1.03293i | ||||||||
\(528\) | 142.916i | 0.270674i | ||||||||
\(529\) | 350.341 | + | 396.361i | 0.662271 | + | 0.749265i | ||||
\(530\) | 329.676 | 0.622031 | ||||||||
\(531\) | 124.744 | 0.234924 | ||||||||
\(532\) | −52.6649 | −0.0989942 | ||||||||
\(533\) | −142.420 | −0.267204 | ||||||||
\(534\) | 665.595i | 1.24643i | ||||||||
\(535\) | 23.3768 | 0.0436950 | ||||||||
\(536\) | − | 168.222i | − | 0.313847i | ||||||
\(537\) | −1015.29 | −1.89068 | ||||||||
\(538\) | 135.338 | 0.251558 | ||||||||
\(539\) | − | 505.614i | − | 0.938060i | ||||||
\(540\) | − | 100.408i | − | 0.185942i | ||||||
\(541\) | 289.616 | 0.535335 | 0.267668 | − | 0.963511i | \(-0.413747\pi\) | ||||
0.267668 | + | 0.963511i | \(0.413747\pi\) | |||||||
\(542\) | −639.585 | −1.18005 | ||||||||
\(543\) | 836.600i | 1.54070i | ||||||||
\(544\) | − | 113.639i | − | 0.208895i | ||||||
\(545\) | 154.562 | 0.283600 | ||||||||
\(546\) | − | 83.9914i | − | 0.153830i | ||||||
\(547\) | 996.117 | 1.82106 | 0.910528 | − | 0.413448i | \(-0.135676\pi\) | ||||
0.910528 | + | 0.413448i | \(0.135676\pi\) | |||||||
\(548\) | 397.422i | 0.725223i | ||||||||
\(549\) | 54.7861i | 0.0997926i | ||||||||
\(550\) | 75.0579i | 0.136469i | ||||||||
\(551\) | − | 734.202i | − | 1.33249i | ||||||
\(552\) | 199.626 | + | 89.9811i | 0.361642 | + | 0.163009i | ||||
\(553\) | −66.7427 | −0.120692 | ||||||||
\(554\) | −123.713 | −0.223309 | ||||||||
\(555\) | −399.333 | −0.719519 | ||||||||
\(556\) | −0.258959 | −0.000465754 | ||||||||
\(557\) | − | 937.756i | − | 1.68358i | −0.539802 | − | 0.841792i | \(-0.681501\pi\) | ||
0.539802 | − | 0.841792i | \(-0.318499\pi\) | |||||||
\(558\) | −89.2772 | −0.159995 | ||||||||
\(559\) | 549.901i | 0.983723i | ||||||||
\(560\) | −10.4575 | −0.0186741 | ||||||||
\(561\) | 717.747 | 1.27941 | ||||||||
\(562\) | 328.320i | 0.584200i | ||||||||
\(563\) | 785.252i | 1.39476i | 0.716700 | + | 0.697382i | \(0.245652\pi\) | ||||
−0.716700 | + | 0.697382i | \(0.754348\pi\) | |||||||
\(564\) | 330.783 | 0.586494 | ||||||||
\(565\) | −306.932 | −0.543243 | ||||||||
\(566\) | − | 338.516i | − | 0.598085i | ||||||
\(567\) | 112.873i | 0.199070i | ||||||||
\(568\) | 156.166 | 0.274940 | ||||||||
\(569\) | − | 403.851i | − | 0.709755i | −0.934913 | − | 0.354877i | \(-0.884523\pi\) | ||
0.934913 | − | 0.354877i | \(-0.115477\pi\) | |||||||
\(570\) | 239.727 | 0.420574 | ||||||||
\(571\) | 335.474i | 0.587519i | 0.955879 | + | 0.293760i | \(0.0949065\pi\) | ||||
−0.955879 | + | 0.293760i | \(0.905093\pi\) | |||||||
\(572\) | 320.383i | 0.560110i | ||||||||
\(573\) | 492.715i | 0.859887i | ||||||||
\(574\) | − | 15.6042i | − | 0.0271850i | ||||||
\(575\) | 104.842 | + | 47.2571i | 0.182333 | + | 0.0821863i | ||||
\(576\) | 18.6375 | 0.0323567 | ||||||||
\(577\) | −152.703 | −0.264649 | −0.132325 | − | 0.991206i | \(-0.542244\pi\) | ||||
−0.132325 | + | 0.991206i | \(0.542244\pi\) | |||||||
\(578\) | −162.004 | −0.280284 | ||||||||
\(579\) | 406.097 | 0.701376 | ||||||||
\(580\) | − | 145.788i | − | 0.251359i | ||||||
\(581\) | 64.5143 | 0.111040 | ||||||||
\(582\) | − | 94.5538i | − | 0.162464i | ||||||
\(583\) | 1106.62 | 1.89815 | ||||||||
\(584\) | −24.8139 | −0.0424896 | ||||||||
\(585\) | 78.6157i | 0.134386i | ||||||||
\(586\) | 822.831i | 1.40415i | ||||||||
\(587\) | 129.262 | 0.220207 | 0.110104 | − | 0.993920i | \(-0.464882\pi\) | ||||
0.110104 | + | 0.993920i | \(0.464882\pi\) | |||||||
\(588\) | −320.662 | −0.545343 | ||||||||
\(589\) | 610.291i | 1.03615i | ||||||||
\(590\) | − | 169.326i | − | 0.286994i | ||||||
\(591\) | −106.533 | −0.180260 | ||||||||
\(592\) | 212.227i | 0.358492i | ||||||||
\(593\) | −879.853 | −1.48373 | −0.741866 | − | 0.670548i | \(-0.766059\pi\) | ||||
−0.741866 | + | 0.670548i | \(0.766059\pi\) | |||||||
\(594\) | − | 337.040i | − | 0.567408i | ||||||
\(595\) | 52.5194i | 0.0882678i | ||||||||
\(596\) | 127.749i | 0.214344i | ||||||||
\(597\) | 126.054i | 0.211145i | ||||||||
\(598\) | 447.514 | + | 201.716i | 0.748351 | + | 0.337317i | ||||
\(599\) | −709.708 | −1.18482 | −0.592411 | − | 0.805636i | \(-0.701824\pi\) | ||||
−0.592411 | + | 0.805636i | \(0.701824\pi\) | |||||||
\(600\) | 47.6019 | 0.0793364 | ||||||||
\(601\) | 238.861 | 0.397439 | 0.198719 | − | 0.980056i | \(-0.436322\pi\) | ||||
0.198719 | + | 0.980056i | \(0.436322\pi\) | |||||||
\(602\) | −60.2498 | −0.100083 | ||||||||
\(603\) | − | 138.559i | − | 0.229782i | ||||||
\(604\) | −70.5346 | −0.116779 | ||||||||
\(605\) | − | 18.6182i | − | 0.0307738i | ||||||
\(606\) | −412.060 | −0.679967 | ||||||||
\(607\) | −1082.53 | −1.78341 | −0.891703 | − | 0.452621i | \(-0.850489\pi\) | ||||
−0.891703 | + | 0.452621i | \(0.850489\pi\) | |||||||
\(608\) | − | 127.404i | − | 0.209546i | ||||||
\(609\) | 128.292i | 0.210660i | ||||||||
\(610\) | 74.3659 | 0.121911 | ||||||||
\(611\) | 741.535 | 1.21364 | ||||||||
\(612\) | − | 93.6004i | − | 0.152942i | ||||||
\(613\) | − | 54.0902i | − | 0.0882384i | −0.999026 | − | 0.0441192i | \(-0.985952\pi\) | ||
0.999026 | − | 0.0441192i | \(-0.0140481\pi\) | |||||||
\(614\) | 155.753 | 0.253669 | ||||||||
\(615\) | 71.0292i | 0.115495i | ||||||||
\(616\) | −35.1026 | −0.0569848 | ||||||||
\(617\) | 454.342i | 0.736373i | 0.929752 | + | 0.368186i | \(0.120021\pi\) | ||||
−0.929752 | + | 0.368186i | \(0.879979\pi\) | |||||||
\(618\) | 686.027i | 1.11008i | ||||||||
\(619\) | 153.676i | 0.248264i | 0.992266 | + | 0.124132i | \(0.0396147\pi\) | ||||
−0.992266 | + | 0.124132i | \(0.960385\pi\) | |||||||
\(620\) | 121.184i | 0.195458i | ||||||||
\(621\) | −470.781 | − | 212.204i | −0.758102 | − | 0.341713i | ||||
\(622\) | −421.577 | −0.677776 | ||||||||
\(623\) | −163.482 | −0.262411 | ||||||||
\(624\) | 203.187 | 0.325621 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 154.820i | 0.247316i | ||||||||
\(627\) | 804.689 | 1.28340 | ||||||||
\(628\) | − | 578.271i | − | 0.920814i | ||||||
\(629\) | 1065.84 | 1.69450 | ||||||||
\(630\) | −8.61350 | −0.0136722 | ||||||||
\(631\) | 1241.15i | 1.96696i | 0.181027 | + | 0.983478i | \(0.442058\pi\) | ||||
−0.181027 | + | 0.983478i | \(0.557942\pi\) | |||||||
\(632\) | − | 161.460i | − | 0.255475i | ||||||
\(633\) | 146.948 | 0.232146 | ||||||||
\(634\) | 670.950 | 1.05828 | ||||||||
\(635\) | − | 129.624i | − | 0.204133i | ||||||
\(636\) | − | 701.821i | − | 1.10349i | ||||||
\(637\) | −718.846 | −1.12849 | ||||||||
\(638\) | − | 489.366i | − | 0.767032i | ||||||
\(639\) | 128.629 | 0.201297 | ||||||||
\(640\) | − | 25.2982i | − | 0.0395285i | ||||||
\(641\) | − | 545.978i | − | 0.851759i | −0.904780 | − | 0.425880i | \(-0.859965\pi\) | ||
0.904780 | − | 0.425880i | \(-0.140035\pi\) | |||||||
\(642\) | − | 49.7651i | − | 0.0775157i | ||||||
\(643\) | − | 539.118i | − | 0.838441i | −0.907884 | − | 0.419221i | \(-0.862303\pi\) | ||
0.907884 | − | 0.419221i | \(-0.137697\pi\) | |||||||
\(644\) | −22.1009 | + | 49.0317i | −0.0343182 | + | 0.0761362i | ||||
\(645\) | 274.253 | 0.425198 | ||||||||
\(646\) | −639.844 | −0.990470 | ||||||||
\(647\) | 652.715 | 1.00883 | 0.504417 | − | 0.863460i | \(-0.331708\pi\) | ||||
0.504417 | + | 0.863460i | \(0.331708\pi\) | |||||||
\(648\) | −273.056 | −0.421382 | ||||||||
\(649\) | − | 568.376i | − | 0.875772i | ||||||
\(650\) | 106.712 | 0.164172 | ||||||||
\(651\) | − | 106.640i | − | 0.163810i | ||||||
\(652\) | −92.5071 | −0.141882 | ||||||||
\(653\) | 374.815 | 0.573989 | 0.286995 | − | 0.957932i | \(-0.407344\pi\) | ||||
0.286995 | + | 0.957932i | \(0.407344\pi\) | |||||||
\(654\) | − | 329.034i | − | 0.503110i | ||||||
\(655\) | 212.608i | 0.324592i | ||||||||
\(656\) | 37.7488 | 0.0575439 | ||||||||
\(657\) | −20.4384 | −0.0311087 | ||||||||
\(658\) | 81.2460i | 0.123474i | ||||||||
\(659\) | 440.090i | 0.667815i | 0.942606 | + | 0.333907i | \(0.108367\pi\) | ||||
−0.942606 | + | 0.333907i | \(0.891633\pi\) | |||||||
\(660\) | 159.785 | 0.242098 | ||||||||
\(661\) | 72.6725i | 0.109943i | 0.998488 | + | 0.0549716i | \(0.0175068\pi\) | ||||
−0.998488 | + | 0.0549716i | \(0.982493\pi\) | |||||||
\(662\) | 361.144 | 0.545535 | ||||||||
\(663\) | − | 1020.44i | − | 1.53913i | ||||||
\(664\) | 156.069i | 0.235044i | ||||||||
\(665\) | 58.8812i | 0.0885431i | ||||||||
\(666\) | 174.805i | 0.262469i | ||||||||
\(667\) | −683.552 | − | 308.110i | −1.02482 | − | 0.461933i | ||||
\(668\) | −181.747 | −0.272076 | ||||||||
\(669\) | −1173.45 | −1.75404 | ||||||||
\(670\) | −188.078 | −0.280713 | ||||||||
\(671\) | 249.623 | 0.372017 | ||||||||
\(672\) | 22.2622i | 0.0331282i | ||||||||
\(673\) | −1052.88 | −1.56445 | −0.782227 | − | 0.622993i | \(-0.785916\pi\) | ||||
−0.782227 | + | 0.622993i | \(0.785916\pi\) | |||||||
\(674\) | − | 648.398i | − | 0.962014i | ||||||
\(675\) | −112.260 | −0.166311 | ||||||||
\(676\) | 117.497 | 0.173812 | ||||||||
\(677\) | 393.587i | 0.581369i | 0.956819 | + | 0.290684i | \(0.0938830\pi\) | ||||
−0.956819 | + | 0.290684i | \(0.906117\pi\) | |||||||
\(678\) | 653.404i | 0.963722i | ||||||||
\(679\) | 23.2241 | 0.0342034 | ||||||||
\(680\) | −127.052 | −0.186841 | ||||||||
\(681\) | 591.714i | 0.868889i | ||||||||
\(682\) | 406.776i | 0.596446i | ||||||||
\(683\) | −645.240 | −0.944714 | −0.472357 | − | 0.881407i | \(-0.656597\pi\) | ||||
−0.472357 | + | 0.881407i | \(0.656597\pi\) | |||||||
\(684\) | − | 104.938i | − | 0.153419i | ||||||
\(685\) | 444.331 | 0.648659 | ||||||||
\(686\) | − | 159.781i | − | 0.232916i | ||||||
\(687\) | 4.85195i | 0.00706252i | ||||||||
\(688\) | − | 145.753i | − | 0.211850i | ||||||
\(689\) | − | 1573.31i | − | 2.28347i | ||||||
\(690\) | 100.602 | − | 223.189i | 0.145800 | − | 0.323462i | ||||
\(691\) | 548.216 | 0.793366 | 0.396683 | − | 0.917956i | \(-0.370161\pi\) | ||||
0.396683 | + | 0.917956i | \(0.370161\pi\) | |||||||
\(692\) | −181.579 | −0.262397 | ||||||||
\(693\) | −28.9129 | −0.0417213 | ||||||||
\(694\) | 722.205 | 1.04064 | ||||||||
\(695\) | 0.289525i | 0.000416583i | ||||||||
\(696\) | −310.357 | −0.445915 | ||||||||
\(697\) | − | 189.581i | − | 0.271995i | ||||||
\(698\) | −837.030 | −1.19918 | ||||||||
\(699\) | 381.753 | 0.546141 | ||||||||
\(700\) | 11.6919i | 0.0167026i | ||||||||
\(701\) | 92.2064i | 0.131536i | 0.997835 | + | 0.0657678i | \(0.0209496\pi\) | ||||
−0.997835 | + | 0.0657678i | \(0.979050\pi\) | |||||||
\(702\) | −479.179 | −0.682592 | ||||||||
\(703\) | 1194.95 | 1.69978 | ||||||||
\(704\) | − | 84.9183i | − | 0.120623i | ||||||
\(705\) | − | 369.826i | − | 0.524576i | ||||||
\(706\) | 238.060 | 0.337195 | ||||||||
\(707\) | − | 101.209i | − | 0.143153i | ||||||
\(708\) | −360.465 | −0.509132 | ||||||||
\(709\) | 922.612i | 1.30129i | 0.759384 | + | 0.650643i | \(0.225501\pi\) | ||||
−0.759384 | + | 0.650643i | \(0.774499\pi\) | |||||||
\(710\) | − | 174.599i | − | 0.245914i | ||||||
\(711\) | − | 132.989i | − | 0.187045i | ||||||
\(712\) | − | 395.486i | − | 0.555458i | ||||||
\(713\) | 568.189 | + | 256.110i | 0.796899 | + | 0.359201i | ||||
\(714\) | 111.804 | 0.156589 | ||||||||
\(715\) | 358.199 | 0.500977 | ||||||||
\(716\) | 603.271 | 0.842557 | ||||||||
\(717\) | −1236.18 | −1.72410 | ||||||||
\(718\) | − | 53.1347i | − | 0.0740037i | ||||||
\(719\) | 606.887 | 0.844071 | 0.422035 | − | 0.906579i | \(-0.361316\pi\) | ||||
0.422035 | + | 0.906579i | \(0.361316\pi\) | |||||||
\(720\) | − | 20.8373i | − | 0.0289407i | ||||||
\(721\) | −168.500 | −0.233704 | ||||||||
\(722\) | −206.819 | −0.286452 | ||||||||
\(723\) | 741.740i | 1.02592i | ||||||||
\(724\) | − | 497.095i | − | 0.686595i | ||||||
\(725\) | −162.996 | −0.224823 | ||||||||
\(726\) | −39.6347 | −0.0545932 | ||||||||
\(727\) | 787.544i | 1.08328i | 0.840611 | + | 0.541640i | \(0.182196\pi\) | ||||
−0.840611 | + | 0.541640i | \(0.817804\pi\) | |||||||
\(728\) | 49.9064i | 0.0685527i | ||||||||
\(729\) | 455.246 | 0.624481 | ||||||||
\(730\) | 27.7428i | 0.0380038i | ||||||||
\(731\) | −731.995 | −1.00136 | ||||||||
\(732\) | − | 158.312i | − | 0.216273i | ||||||
\(733\) | − | 415.085i | − | 0.566282i | −0.959078 | − | 0.283141i | \(-0.908624\pi\) | ||
0.959078 | − | 0.283141i | \(-0.0913765\pi\) | |||||||
\(734\) | − | 603.921i | − | 0.822780i | ||||||
\(735\) | 358.510i | 0.487769i | ||||||||
\(736\) | −118.615 | − | 53.4653i | −0.161161 | − | 0.0726431i | ||||
\(737\) | −631.319 | −0.856606 | ||||||||
\(738\) | 31.0924 | 0.0421307 | ||||||||
\(739\) | 639.964 | 0.865987 | 0.432993 | − | 0.901397i | \(-0.357457\pi\) | ||||
0.432993 | + | 0.901397i | \(0.357457\pi\) | |||||||
\(740\) | 237.277 | 0.320645 | ||||||||
\(741\) | − | 1144.05i | − | 1.54393i | ||||||
\(742\) | 172.380 | 0.232318 | ||||||||
\(743\) | 743.739i | 1.00099i | 0.865738 | + | 0.500497i | \(0.166849\pi\) | ||||
−0.865738 | + | 0.500497i | \(0.833151\pi\) | |||||||
\(744\) | 257.978 | 0.346745 | ||||||||
\(745\) | 142.828 | 0.191715 | ||||||||
\(746\) | − | 523.231i | − | 0.701382i | ||||||
\(747\) | 128.549i | 0.172087i | ||||||||
\(748\) | −426.474 | −0.570152 | ||||||||
\(749\) | 12.2232 | 0.0163193 | ||||||||
\(750\) | − | 53.2205i | − | 0.0709607i | ||||||
\(751\) | 517.047i | 0.688478i | 0.938882 | + | 0.344239i | \(0.111863\pi\) | ||||
−0.938882 | + | 0.344239i | \(0.888137\pi\) | |||||||
\(752\) | −196.546 | −0.261364 | ||||||||
\(753\) | − | 1481.73i | − | 1.96777i | ||||||
\(754\) | −695.746 | −0.922740 | ||||||||
\(755\) | 78.8601i | 0.104450i | ||||||||
\(756\) | − | 52.5011i | − | 0.0694460i | ||||||
\(757\) | 911.823i | 1.20452i | 0.798299 | + | 0.602261i | \(0.205733\pi\) | ||||
−0.798299 | + | 0.602261i | \(0.794267\pi\) | |||||||
\(758\) | − | 111.441i | − | 0.147020i | ||||||
\(759\) | 337.689 | − | 749.176i | 0.444914 | − | 0.987057i | ||||
\(760\) | −142.442 | −0.187424 | ||||||||
\(761\) | 954.073 | 1.25371 | 0.626855 | − | 0.779136i | \(-0.284342\pi\) | ||||
0.626855 | + | 0.779136i | \(0.284342\pi\) | |||||||
\(762\) | −275.947 | −0.362135 | ||||||||
\(763\) | 80.8166 | 0.105920 | ||||||||
\(764\) | − | 292.764i | − | 0.383199i | ||||||
\(765\) | −104.648 | −0.136795 | ||||||||
\(766\) | − | 359.328i | − | 0.469097i | ||||||
\(767\) | −808.076 | −1.05355 | ||||||||
\(768\) | −53.8553 | −0.0701242 | ||||||||
\(769\) | 276.277i | 0.359268i | 0.983734 | + | 0.179634i | \(0.0574913\pi\) | ||||
−0.983734 | + | 0.179634i | \(0.942509\pi\) | |||||||
\(770\) | 39.2459i | 0.0509687i | ||||||||
\(771\) | −1654.43 | −2.14583 | ||||||||
\(772\) | −241.296 | −0.312560 | ||||||||
\(773\) | 40.8440i | 0.0528383i | 0.999651 | + | 0.0264192i | \(0.00841046\pi\) | ||||
−0.999651 | + | 0.0264192i | \(0.991590\pi\) | |||||||
\(774\) | − | 120.052i | − | 0.155106i | ||||||
\(775\) | 135.488 | 0.174823 | ||||||||
\(776\) | 56.1824i | 0.0724000i | ||||||||
\(777\) | −208.801 | −0.268728 | ||||||||
\(778\) | 455.891i | 0.585978i | ||||||||
\(779\) | − | 212.545i | − | 0.272843i | ||||||
\(780\) | − | 227.170i | − | 0.291244i | ||||||
\(781\) | − | 586.074i | − | 0.750415i | ||||||
\(782\) | −268.512 | + | 595.703i | −0.343365 | + | 0.761768i | ||||
\(783\) | 731.919 | 0.934763 | ||||||||
\(784\) | 190.532 | 0.243026 | ||||||||
\(785\) | −646.527 | −0.823601 | ||||||||
\(786\) | 452.603 | 0.575831 | ||||||||
\(787\) | 1364.69i | 1.73404i | 0.498274 | + | 0.867019i | \(0.333967\pi\) | ||||
−0.498274 | + | 0.867019i | \(0.666033\pi\) | |||||||
\(788\) | 63.3005 | 0.0803305 | ||||||||
\(789\) | − | 901.515i | − | 1.14261i | ||||||
\(790\) | −180.518 | −0.228504 | ||||||||
\(791\) | −160.487 | −0.202892 | ||||||||
\(792\) | − | 69.9444i | − | 0.0883136i | ||||||
\(793\) | − | 354.897i | − | 0.447537i | ||||||
\(794\) | 1012.34 | 1.27499 | ||||||||
\(795\) | −784.660 | −0.986994 | ||||||||
\(796\) | − | 74.8991i | − | 0.0940944i | ||||||
\(797\) | − | 20.2192i | − | 0.0253692i | −0.999920 | − | 0.0126846i | \(-0.995962\pi\) | ||
0.999920 | − | 0.0126846i | \(-0.00403774\pi\) | |||||||
\(798\) | 125.347 | 0.157077 | ||||||||
\(799\) | 987.086i | 1.23540i | ||||||||
\(800\) | −28.2843 | −0.0353553 | ||||||||
\(801\) | − | 325.749i | − | 0.406678i | ||||||
\(802\) | − | 624.283i | − | 0.778407i | ||||||
\(803\) | 93.1240i | 0.115970i | ||||||||
\(804\) | 400.384i | 0.497989i | ||||||||
\(805\) | 54.8191 | + | 24.7096i | 0.0680983 | + | 0.0306951i | ||||
\(806\) | 578.325 | 0.717525 | ||||||||
\(807\) | −322.117 | −0.399154 | ||||||||
\(808\) | 244.840 | 0.303019 | ||||||||
\(809\) | −1032.11 | −1.27579 | −0.637894 | − | 0.770124i | \(-0.720194\pi\) | ||||
−0.637894 | + | 0.770124i | \(0.720194\pi\) | |||||||
\(810\) | 305.285i | 0.376896i | ||||||||
\(811\) | −70.2781 | −0.0866561 | −0.0433281 | − | 0.999061i | \(-0.513796\pi\) | ||||
−0.0433281 | + | 0.999061i | \(0.513796\pi\) | |||||||
\(812\) | − | 76.2292i | − | 0.0938783i | ||||||
\(813\) | 1522.27 | 1.87241 | ||||||||
\(814\) | 796.467 | 0.978460 | ||||||||
\(815\) | 103.426i | 0.126903i | ||||||||
\(816\) | 270.470i | 0.331459i | ||||||||
\(817\) | −820.663 | −1.00448 | ||||||||
\(818\) | −860.869 | −1.05241 | ||||||||
\(819\) | 41.1062i | 0.0501907i | ||||||||
\(820\) | − | 42.2044i | − | 0.0514688i | ||||||
\(821\) | 84.7400 | 0.103216 | 0.0516078 | − | 0.998667i | \(-0.483565\pi\) | ||||
0.0516078 | + | 0.998667i | \(0.483565\pi\) | |||||||
\(822\) | − | 945.901i | − | 1.15073i | ||||||
\(823\) | 46.0292 | 0.0559286 | 0.0279643 | − | 0.999609i | \(-0.491098\pi\) | ||||
0.0279643 | + | 0.999609i | \(0.491098\pi\) | |||||||
\(824\) | − | 407.626i | − | 0.494692i | ||||||
\(825\) | − | 178.645i | − | 0.216539i | ||||||
\(826\) | − | 88.5366i | − | 0.107187i | ||||||
\(827\) | − | 1283.77i | − | 1.55232i | −0.630536 | − | 0.776160i | \(-0.717165\pi\) | ||
0.630536 | − | 0.776160i | \(-0.282835\pi\) | |||||||
\(828\) | −97.6990 | − | 44.0376i | −0.117994 | − | 0.0531855i | ||||
\(829\) | −483.453 | −0.583177 | −0.291588 | − | 0.956544i | \(-0.594184\pi\) | ||||
−0.291588 | + | 0.956544i | \(0.594184\pi\) | |||||||
\(830\) | 174.491 | 0.210230 | ||||||||
\(831\) | 294.449 | 0.354330 | ||||||||
\(832\) | −120.731 | −0.145109 | ||||||||
\(833\) | − | 956.883i | − | 1.14872i | ||||||
\(834\) | 0.616347 | 0.000739025 | ||||||||
\(835\) | 203.199i | 0.243352i | ||||||||
\(836\) | −478.134 | −0.571930 | ||||||||
\(837\) | −608.394 | −0.726874 | ||||||||
\(838\) | 406.521i | 0.485108i | ||||||||
\(839\) | 1060.74i | 1.26429i | 0.774852 | + | 0.632143i | \(0.217824\pi\) | ||||
−0.774852 | + | 0.632143i | \(0.782176\pi\) | |||||||
\(840\) | 24.8898 | 0.0296308 | ||||||||
\(841\) | 221.712 | 0.263629 | ||||||||
\(842\) | 185.047i | 0.219771i | ||||||||
\(843\) | − | 781.432i | − | 0.926966i | ||||||
\(844\) | −87.3144 | −0.103453 | ||||||||
\(845\) | − | 131.365i | − | 0.155462i | ||||||
\(846\) | −161.888 | −0.191357 | ||||||||
\(847\) | − | 9.73498i | − | 0.0114935i | ||||||
\(848\) | 417.011i | 0.491759i | ||||||||
\(849\) | 805.700i | 0.948999i | ||||||||
\(850\) | 142.048i | 0.167116i | ||||||||
\(851\) | 501.463 | − | 1112.51i | 0.589263 | − | 1.30730i | ||||
\(852\) | −371.689 | −0.436255 | ||||||||
\(853\) | 1653.13 | 1.93802 | 0.969010 | − | 0.247023i | \(-0.0794522\pi\) | ||||
0.969010 | + | 0.247023i | \(0.0794522\pi\) | |||||||
\(854\) | 38.8841 | 0.0455318 | ||||||||
\(855\) | −117.325 | −0.137222 | ||||||||
\(856\) | 29.5696i | 0.0345439i | ||||||||
\(857\) | 1453.42 | 1.69593 | 0.847967 | − | 0.530048i | \(-0.177826\pi\) | ||||
0.847967 | + | 0.530048i | \(0.177826\pi\) | |||||||
\(858\) | − | 762.540i | − | 0.888742i | ||||||
\(859\) | 936.399 | 1.09010 | 0.545052 | − | 0.838402i | \(-0.316510\pi\) | ||||
0.545052 | + | 0.838402i | \(0.316510\pi\) | |||||||
\(860\) | −162.957 | −0.189484 | ||||||||
\(861\) | 37.1394i | 0.0431352i | ||||||||
\(862\) | 339.151i | 0.393446i | ||||||||
\(863\) | 961.830 | 1.11452 | 0.557259 | − | 0.830339i | \(-0.311853\pi\) | ||||
0.557259 | + | 0.830339i | \(0.311853\pi\) | |||||||
\(864\) | 127.008 | 0.147000 | ||||||||
\(865\) | 203.011i | 0.234695i | ||||||||
\(866\) | 432.102i | 0.498963i | ||||||||
\(867\) | 385.585 | 0.444735 | ||||||||
\(868\) | 63.3640i | 0.0730000i | ||||||||
\(869\) | −605.943 | −0.697287 | ||||||||
\(870\) | 346.990i | 0.398839i | ||||||||
\(871\) | 897.563i | 1.03050i | ||||||||
\(872\) | 195.507i | 0.224205i | ||||||||
\(873\) | 46.2756i | 0.0530075i | ||||||||
\(874\) | −301.037 | + | 667.862i | −0.344436 | + | 0.764144i | ||||
\(875\) | 13.0719 | 0.0149393 | ||||||||
\(876\) | 59.0594 | 0.0674194 | ||||||||
\(877\) | −1244.55 | −1.41910 | −0.709549 | − | 0.704657i | \(-0.751101\pi\) | ||||
−0.709549 | + | 0.704657i | \(0.751101\pi\) | |||||||
\(878\) | −818.855 | −0.932637 | ||||||||
\(879\) | − | 1958.41i | − | 2.22800i | ||||||
\(880\) | −94.9415 | −0.107888 | ||||||||
\(881\) | 961.719i | 1.09162i | 0.837908 | + | 0.545811i | \(0.183778\pi\) | ||||
−0.837908 | + | 0.545811i | \(0.816222\pi\) | |||||||
\(882\) | 156.935 | 0.177931 | ||||||||
\(883\) | 42.4945 | 0.0481251 | 0.0240626 | − | 0.999710i | \(-0.492340\pi\) | ||||
0.0240626 | + | 0.999710i | \(0.492340\pi\) | |||||||
\(884\) | 606.330i | 0.685893i | ||||||||
\(885\) | 403.012i | 0.455381i | ||||||||
\(886\) | −857.401 | −0.967722 | ||||||||
\(887\) | −551.962 | −0.622279 | −0.311140 | − | 0.950364i | \(-0.600711\pi\) | ||||
−0.311140 | + | 0.950364i | \(0.600711\pi\) | |||||||
\(888\) | − | 505.121i | − | 0.568830i | ||||||
\(889\) | − | 67.7774i | − | 0.0762400i | ||||||
\(890\) | −442.167 | −0.496817 | ||||||||
\(891\) | 1024.75i | 1.15011i | ||||||||
\(892\) | 697.246 | 0.781666 | ||||||||
\(893\) | 1106.65i | 1.23925i | ||||||||
\(894\) | − | 304.054i | − | 0.340106i | ||||||
\(895\) | − | 674.478i | − | 0.753606i | ||||||
\(896\) | − | 13.2278i | − | 0.0147632i | ||||||
\(897\) | −1065.12 | − | 480.102i | −1.18743 | − | 0.535231i | ||||
\(898\) | −286.492 | −0.319033 | ||||||||
\(899\) | −883.359 | −0.982601 | ||||||||
\(900\) | −23.2968 | −0.0258853 | ||||||||
\(901\) | 2094.30 | 2.32442 | ||||||||
\(902\) | − | 141.667i | − | 0.157059i | ||||||
\(903\) | 143.400 | 0.158804 | ||||||||
\(904\) | − | 388.242i | − | 0.429472i | ||||||
\(905\) | −555.769 | −0.614109 | ||||||||
\(906\) | 167.879 | 0.185297 | ||||||||
\(907\) | − | 237.524i | − | 0.261878i | −0.991390 | − | 0.130939i | \(-0.958201\pi\) | ||
0.991390 | − | 0.130939i | \(-0.0417993\pi\) | |||||||
\(908\) | − | 351.587i | − | 0.387210i | ||||||
\(909\) | 201.666 | 0.221855 | ||||||||
\(910\) | 55.7970 | 0.0613154 | ||||||||
\(911\) | 402.885i | 0.442245i | 0.975246 | + | 0.221122i | \(0.0709720\pi\) | ||||
−0.975246 | + | 0.221122i | \(0.929028\pi\) | |||||||
\(912\) | 303.233i | 0.332493i | ||||||||
\(913\) | 585.712 | 0.641524 | ||||||||
\(914\) | − | 528.577i | − | 0.578312i | ||||||
\(915\) | −176.998 | −0.193440 | ||||||||
\(916\) | − | 2.88295i | − | 0.00314733i | ||||||
\(917\) | 111.167i | 0.121229i | ||||||||
\(918\) | − | 637.854i | − | 0.694830i | ||||||
\(919\) | 1338.53i | 1.45650i | 0.685310 | + | 0.728251i | \(0.259667\pi\) | ||||
−0.685310 | + | 0.728251i | \(0.740333\pi\) | |||||||
\(920\) | −59.7761 | + | 132.615i | −0.0649740 | + | 0.144147i | ||||
\(921\) | −370.706 | −0.402503 | ||||||||
\(922\) | 1003.21 | 1.08808 | ||||||||
\(923\) | −833.238 | −0.902750 | ||||||||
\(924\) | 83.5475 | 0.0904194 | ||||||||
\(925\) | − | 265.284i | − | 0.286794i | ||||||
\(926\) | 376.872 | 0.406989 | ||||||||
\(927\) | − | 335.748i | − | 0.362188i | ||||||
\(928\) | 184.409 | 0.198717 | ||||||||
\(929\) | 621.771 | 0.669291 | 0.334646 | − | 0.942344i | \(-0.391383\pi\) | ||||
0.334646 | + | 0.942344i | \(0.391383\pi\) | |||||||
\(930\) | − | 288.428i | − | 0.310138i | ||||||
\(931\) | − | 1072.79i | − | 1.15230i | ||||||
\(932\) | −226.831 | −0.243381 | ||||||||
\(933\) | 1003.39 | 1.07545 | ||||||||
\(934\) | − | 970.341i | − | 1.03891i | ||||||
\(935\) | 476.812i | 0.509960i | ||||||||
\(936\) | −99.4419 | −0.106241 | ||||||||
\(937\) | 915.580i | 0.977140i | 0.872525 | + | 0.488570i | \(0.162481\pi\) | ||||
−0.872525 | + | 0.488570i | \(0.837519\pi\) | |||||||
\(938\) | −98.3412 | −0.104841 | ||||||||
\(939\) | − | 368.486i | − | 0.392424i | ||||||
\(940\) | 219.745i | 0.233771i | ||||||||
\(941\) | 834.255i | 0.886563i | 0.896383 | + | 0.443281i | \(0.146186\pi\) | ||||
−0.896383 | + | 0.443281i | \(0.853814\pi\) | |||||||
\(942\) | 1376.34i | 1.46108i | ||||||||
\(943\) | −197.882 | − | 89.1950i | −0.209843 | − | 0.0945864i | ||||
\(944\) | 214.183 | 0.226889 | ||||||||
\(945\) | −58.6981 | −0.0621144 | ||||||||
\(946\) | −546.995 | −0.578219 | ||||||||
\(947\) | 918.683 | 0.970099 | 0.485049 | − | 0.874487i | \(-0.338802\pi\) | ||||
0.485049 | + | 0.874487i | \(0.338802\pi\) | |||||||
\(948\) | 384.290i | 0.405369i | ||||||||
\(949\) | 132.397 | 0.139512 | ||||||||
\(950\) | 159.255i | 0.167637i | ||||||||
\(951\) | −1596.92 | −1.67921 | ||||||||
\(952\) | −66.4323 | −0.0697818 | ||||||||
\(953\) | 789.341i | 0.828270i | 0.910215 | + | 0.414135i | \(0.135916\pi\) | ||||
−0.910215 | + | 0.414135i | \(0.864084\pi\) | |||||||
\(954\) | 343.478i | 0.360040i | ||||||||
\(955\) | −327.320 | −0.342743 | ||||||||
\(956\) | 734.519 | 0.768326 | ||||||||
\(957\) | 1164.74i | 1.21707i | ||||||||
\(958\) | 249.632i | 0.260577i | ||||||||
\(959\) | 232.330 | 0.242263 | ||||||||
\(960\) | 60.2121i | 0.0627209i | ||||||||
\(961\) | −226.725 | −0.235927 | ||||||||
\(962\) | − | 1132.36i | − | 1.17709i | ||||||
\(963\) | 24.3555i | 0.0252913i | ||||||||
\(964\) | − | 440.730i | − | 0.457189i | ||||||
\(965\) | 269.778i | 0.279562i | ||||||||
\(966\) | 52.6023 | − | 116.700i | 0.0544537 | − | 0.120807i | ||||
\(967\) | 875.476 | 0.905353 | 0.452677 | − | 0.891675i | \(-0.350469\pi\) | ||||
0.452677 | + | 0.891675i | \(0.350469\pi\) | |||||||
\(968\) | 23.5503 | 0.0243288 | ||||||||
\(969\) | 1522.89 | 1.57161 | ||||||||
\(970\) | 62.8138 | 0.0647565 | ||||||||
\(971\) | − | 1232.49i | − | 1.26930i | −0.772801 | − | 0.634648i | \(-0.781145\pi\) | ||
0.772801 | − | 0.634648i | \(-0.218855\pi\) | |||||||
\(972\) | 245.761 | 0.252841 | ||||||||
\(973\) | 0.151386i | 0.000155587i | ||||||||
\(974\) | 742.182 | 0.761994 | ||||||||
\(975\) | −253.984 | −0.260497 | ||||||||
\(976\) | 94.0663i | 0.0963794i | ||||||||
\(977\) | − | 879.183i | − | 0.899880i | −0.893059 | − | 0.449940i | \(-0.851445\pi\) | ||
0.893059 | − | 0.449940i | \(-0.148555\pi\) | |||||||
\(978\) | 220.176 | 0.225128 | ||||||||
\(979\) | −1484.22 | −1.51606 | ||||||||
\(980\) | − | 213.021i | − | 0.217369i | ||||||
\(981\) | 161.033i | 0.164151i | ||||||||
\(982\) | −779.298 | −0.793582 | ||||||||
\(983\) | − | 247.090i | − | 0.251363i | −0.992071 | − | 0.125682i | \(-0.959888\pi\) | ||
0.992071 | − | 0.125682i | \(-0.0401118\pi\) | |||||||
\(984\) | −89.8456 | −0.0913065 | ||||||||
\(985\) | − | 70.7721i | − | 0.0718498i | ||||||
\(986\) | − | 926.134i | − | 0.939284i | ||||||
\(987\) | − | 193.373i | − | 0.195920i | ||||||
\(988\) | 679.776i | 0.688032i | ||||||||
\(989\) | −344.393 | + | 764.048i | −0.348223 | + | 0.772546i | ||||
\(990\) | −78.2002 | −0.0789901 | ||||||||
\(991\) | −1750.79 | −1.76669 | −0.883347 | − | 0.468721i | \(-0.844715\pi\) | ||||
−0.883347 | + | 0.468721i | \(0.844715\pi\) | |||||||
\(992\) | −153.287 | −0.154523 | ||||||||
\(993\) | −859.556 | −0.865615 | ||||||||
\(994\) | − | 91.2935i | − | 0.0918445i | ||||||
\(995\) | −83.7398 | −0.0841606 | ||||||||
\(996\) | − | 371.459i | − | 0.372951i | ||||||
\(997\) | −456.156 | −0.457529 | −0.228765 | − | 0.973482i | \(-0.573469\pi\) | ||||
−0.228765 | + | 0.973482i | \(0.573469\pi\) | |||||||
\(998\) | −1041.91 | −1.04399 | ||||||||
\(999\) | 1191.23i | 1.19243i |
(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 | 230.3.d.a.91.11 | ✓ | 16 | |
3.2 | odd | 2 | 2070.3.c.a.91.6 | 16 | |||
4.3 | odd | 2 | 1840.3.k.d.321.11 | 16 | |||
5.2 | odd | 4 | 1150.3.c.c.1149.16 | 32 | |||
5.3 | odd | 4 | 1150.3.c.c.1149.17 | 32 | |||
5.4 | even | 2 | 1150.3.d.b.551.6 | 16 | |||
23.22 | odd | 2 | inner | 230.3.d.a.91.12 | yes | 16 | |
69.68 | even | 2 | 2070.3.c.a.91.3 | 16 | |||
92.91 | even | 2 | 1840.3.k.d.321.12 | 16 | |||
115.22 | even | 4 | 1150.3.c.c.1149.18 | 32 | |||
115.68 | even | 4 | 1150.3.c.c.1149.15 | 32 | |||
115.114 | odd | 2 | 1150.3.d.b.551.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.d.a.91.11 | ✓ | 16 | 1.1 | even | 1 | trivial | |
230.3.d.a.91.12 | yes | 16 | 23.22 | odd | 2 | inner | |
1150.3.c.c.1149.15 | 32 | 115.68 | even | 4 | |||
1150.3.c.c.1149.16 | 32 | 5.2 | odd | 4 | |||
1150.3.c.c.1149.17 | 32 | 5.3 | odd | 4 | |||
1150.3.c.c.1149.18 | 32 | 115.22 | even | 4 | |||
1150.3.d.b.551.5 | 16 | 115.114 | odd | 2 | |||
1150.3.d.b.551.6 | 16 | 5.4 | even | 2 | |||
1840.3.k.d.321.11 | 16 | 4.3 | odd | 2 | |||
1840.3.k.d.321.12 | 16 | 92.91 | even | 2 | |||
2070.3.c.a.91.3 | 16 | 69.68 | even | 2 | |||
2070.3.c.a.91.6 | 16 | 3.2 | odd | 2 |