Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(2155,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3234.2155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.e (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: | \(25.8236200137\) |
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: | \( x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 462) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2155.1 | ||
Root | \(0.500000 + 2.40229i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.2155 |
Dual form | 3234.2.e.b.2155.16 |
$q$-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 \(\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(1079\) | \(2059\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 3.26832i | − | 1.46164i | −0.682572 | − | 0.730818i | \(-0.739139\pi\) | ||
0.682572 | − | 0.730818i | \(-0.260861\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −3.26832 | −1.03353 | ||||||||
\(11\) | 3.11438 | − | 1.14045i | 0.939021 | − | 0.343860i | ||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | −5.12518 | −1.42147 | −0.710734 | − | 0.703461i | \(-0.751637\pi\) | ||||
−0.710734 | + | 0.703461i | \(0.751637\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.26832 | 0.843876 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.32580 | 1.29170 | 0.645848 | − | 0.763466i | \(-0.276504\pi\) | ||||
0.645848 | + | 0.763466i | \(0.276504\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 4.27490 | 0.980729 | 0.490364 | − | 0.871518i | \(-0.336864\pi\) | ||||
0.490364 | + | 0.871518i | \(0.336864\pi\) | |||||||
\(20\) | 3.26832i | 0.730818i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.14045 | − | 3.11438i | −0.243145 | − | 0.663988i | ||||
\(23\) | 5.37186 | 1.12011 | 0.560055 | − | 0.828455i | \(-0.310780\pi\) | ||||
0.560055 | + | 0.828455i | \(0.310780\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −5.68190 | −1.13638 | ||||||||
\(26\) | 5.12518i | 1.00513i | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.77874i | − | 0.887389i | −0.896178 | − | 0.443695i | \(-0.853667\pi\) | ||
0.896178 | − | 0.443695i | \(-0.146333\pi\) | |||||||
\(30\) | − | 3.26832i | − | 0.596711i | ||||||
\(31\) | 6.46485i | 1.16112i | 0.814217 | + | 0.580561i | \(0.197167\pi\) | ||||
−0.814217 | + | 0.580561i | \(0.802833\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 1.14045 | + | 3.11438i | 0.198527 | + | 0.542144i | ||||
\(34\) | − | 5.32580i | − | 0.913367i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.13093 | 0.350323 | 0.175161 | − | 0.984540i | \(-0.443955\pi\) | ||||
0.175161 | + | 0.984540i | \(0.443955\pi\) | |||||||
\(38\) | − | 4.27490i | − | 0.693480i | ||||||
\(39\) | − | 5.12518i | − | 0.820685i | ||||||
\(40\) | 3.26832 | 0.516767 | ||||||||
\(41\) | 0.949652 | 0.148311 | 0.0741554 | − | 0.997247i | \(-0.476374\pi\) | ||||
0.0741554 | + | 0.997247i | \(0.476374\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.20483i | 0.946228i | 0.881001 | + | 0.473114i | \(0.156870\pi\) | ||||
−0.881001 | + | 0.473114i | \(0.843130\pi\) | |||||||
\(44\) | −3.11438 | + | 1.14045i | −0.469511 | + | 0.171930i | ||||
\(45\) | 3.26832i | 0.487212i | ||||||||
\(46\) | − | 5.37186i | − | 0.792037i | ||||||
\(47\) | − | 12.0303i | − | 1.75479i | −0.479766 | − | 0.877397i | \(-0.659278\pi\) | ||
0.479766 | − | 0.877397i | \(-0.340722\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.68190i | 0.803543i | ||||||||
\(51\) | 5.32580i | 0.745761i | ||||||||
\(52\) | 5.12518 | 0.710734 | ||||||||
\(53\) | 12.5399 | 1.72249 | 0.861246 | − | 0.508189i | \(-0.169685\pi\) | ||||
0.861246 | + | 0.508189i | \(0.169685\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −3.72736 | − | 10.1788i | −0.502598 | − | 1.37251i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.27490i | 0.566224i | ||||||||
\(58\) | −4.77874 | −0.627479 | ||||||||
\(59\) | − | 13.4844i | − | 1.75552i | −0.479105 | − | 0.877758i | \(-0.659039\pi\) | ||
0.479105 | − | 0.877758i | \(-0.340961\pi\) | |||||||
\(60\) | −3.26832 | −0.421938 | ||||||||
\(61\) | −5.34060 | −0.683793 | −0.341897 | − | 0.939738i | \(-0.611069\pi\) | ||||
−0.341897 | + | 0.939738i | \(0.611069\pi\) | |||||||
\(62\) | 6.46485 | 0.821037 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 16.7507i | 2.07767i | ||||||||
\(66\) | 3.11438 | − | 1.14045i | 0.383354 | − | 0.140380i | ||||
\(67\) | 6.19350 | 0.756656 | 0.378328 | − | 0.925672i | \(-0.376499\pi\) | ||||
0.378328 | + | 0.925672i | \(0.376499\pi\) | |||||||
\(68\) | −5.32580 | −0.645848 | ||||||||
\(69\) | 5.37186i | 0.646696i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.8061 | −1.28245 | −0.641226 | − | 0.767352i | \(-0.721574\pi\) | ||||
−0.641226 | + | 0.767352i | \(0.721574\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | −13.2295 | −1.54840 | −0.774199 | − | 0.632943i | \(-0.781847\pi\) | ||||
−0.774199 | + | 0.632943i | \(0.781847\pi\) | |||||||
\(74\) | − | 2.13093i | − | 0.247716i | ||||||
\(75\) | − | 5.68190i | − | 0.656090i | ||||||
\(76\) | −4.27490 | −0.490364 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.12518 | −0.580312 | ||||||||
\(79\) | − | 9.16702i | − | 1.03137i | −0.856778 | − | 0.515685i | \(-0.827537\pi\) | ||
0.856778 | − | 0.515685i | \(-0.172463\pi\) | |||||||
\(80\) | − | 3.26832i | − | 0.365409i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 0.949652i | − | 0.104872i | ||||||
\(83\) | 0.835847 | 0.0917462 | 0.0458731 | − | 0.998947i | \(-0.485393\pi\) | ||||
0.0458731 | + | 0.998947i | \(0.485393\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 17.4064i | − | 1.88799i | ||||||
\(86\) | 6.20483 | 0.669084 | ||||||||
\(87\) | 4.77874 | 0.512335 | ||||||||
\(88\) | 1.14045 | + | 3.11438i | 0.121573 | + | 0.331994i | ||||
\(89\) | 6.22408i | 0.659751i | 0.944024 | + | 0.329875i | \(0.107007\pi\) | ||||
−0.944024 | + | 0.329875i | \(0.892993\pi\) | |||||||
\(90\) | 3.26832 | 0.344511 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.37186 | −0.560055 | ||||||||
\(93\) | −6.46485 | −0.670374 | ||||||||
\(94\) | −12.0303 | −1.24083 | ||||||||
\(95\) | − | 13.9717i | − | 1.43347i | ||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | − | 0.624337i | − | 0.0633919i | −0.999498 | − | 0.0316959i | \(-0.989909\pi\) | ||
0.999498 | − | 0.0316959i | \(-0.0100908\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.11438 | + | 1.14045i | −0.313007 | + | 0.114620i | ||||
\(100\) | 5.68190 | 0.568190 | ||||||||
\(101\) | −13.1692 | −1.31039 | −0.655194 | − | 0.755460i | \(-0.727413\pi\) | ||||
−0.655194 | + | 0.755460i | \(0.727413\pi\) | |||||||
\(102\) | 5.32580 | 0.527332 | ||||||||
\(103\) | − | 13.2122i | − | 1.30183i | −0.759150 | − | 0.650916i | \(-0.774385\pi\) | ||
0.759150 | − | 0.650916i | \(-0.225615\pi\) | |||||||
\(104\) | − | 5.12518i | − | 0.502565i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 12.5399i | − | 1.21799i | ||||||
\(107\) | 11.1094i | 1.07399i | 0.843586 | + | 0.536994i | \(0.180440\pi\) | ||||
−0.843586 | + | 0.536994i | \(0.819560\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | 7.13138i | 0.683062i | 0.939870 | + | 0.341531i | \(0.110945\pi\) | ||||
−0.939870 | + | 0.341531i | \(0.889055\pi\) | |||||||
\(110\) | −10.1788 | + | 3.72736i | −0.970509 | + | 0.355390i | ||||
\(111\) | 2.13093i | 0.202259i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.41436 | 0.227124 | 0.113562 | − | 0.993531i | \(-0.463774\pi\) | ||||
0.113562 | + | 0.993531i | \(0.463774\pi\) | |||||||
\(114\) | 4.27490 | 0.400381 | ||||||||
\(115\) | − | 17.5569i | − | 1.63719i | ||||||
\(116\) | 4.77874i | 0.443695i | ||||||||
\(117\) | 5.12518 | 0.473823 | ||||||||
\(118\) | −13.4844 | −1.24134 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.26832i | 0.298355i | ||||||||
\(121\) | 8.39873 | − | 7.10361i | 0.763521 | − | 0.645783i | ||||
\(122\) | 5.34060i | 0.483515i | ||||||||
\(123\) | 0.949652i | 0.0856273i | ||||||||
\(124\) | − | 6.46485i | − | 0.580561i | ||||||
\(125\) | 2.22868i | 0.199339i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 13.8100i | − | 1.22544i | −0.790301 | − | 0.612719i | \(-0.790076\pi\) | ||
0.790301 | − | 0.612719i | \(-0.209924\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −6.20483 | −0.546305 | ||||||||
\(130\) | 16.7507 | 1.46913 | ||||||||
\(131\) | −11.7866 | −1.02980 | −0.514902 | − | 0.857249i | \(-0.672172\pi\) | ||||
−0.514902 | + | 0.857249i | \(0.672172\pi\) | |||||||
\(132\) | −1.14045 | − | 3.11438i | −0.0992637 | − | 0.271072i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 6.19350i | − | 0.535037i | ||||||
\(135\) | −3.26832 | −0.281292 | ||||||||
\(136\) | 5.32580i | 0.456683i | ||||||||
\(137\) | 4.86111 | 0.415312 | 0.207656 | − | 0.978202i | \(-0.433416\pi\) | ||||
0.207656 | + | 0.978202i | \(0.433416\pi\) | |||||||
\(138\) | 5.37186 | 0.457283 | ||||||||
\(139\) | 16.7827 | 1.42349 | 0.711744 | − | 0.702439i | \(-0.247906\pi\) | ||||
0.711744 | + | 0.702439i | \(0.247906\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0303 | 1.01313 | ||||||||
\(142\) | 10.8061i | 0.906830i | ||||||||
\(143\) | −15.9618 | + | 5.84502i | −1.33479 | + | 0.488785i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −15.6184 | −1.29704 | ||||||||
\(146\) | 13.2295i | 1.09488i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.13093 | −0.175161 | ||||||||
\(149\) | 7.22464i | 0.591866i | 0.955209 | + | 0.295933i | \(0.0956305\pi\) | ||||
−0.955209 | + | 0.295933i | \(0.904370\pi\) | |||||||
\(150\) | −5.68190 | −0.463926 | ||||||||
\(151\) | − | 4.88028i | − | 0.397151i | −0.980086 | − | 0.198576i | \(-0.936368\pi\) | ||
0.980086 | − | 0.198576i | \(-0.0636315\pi\) | |||||||
\(152\) | 4.27490i | 0.346740i | ||||||||
\(153\) | −5.32580 | −0.430565 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.1292 | 1.69714 | ||||||||
\(156\) | 5.12518i | 0.410343i | ||||||||
\(157\) | − | 3.30239i | − | 0.263560i | −0.991279 | − | 0.131780i | \(-0.957931\pi\) | ||
0.991279 | − | 0.131780i | \(-0.0420692\pi\) | |||||||
\(158\) | −9.16702 | −0.729289 | ||||||||
\(159\) | 12.5399i | 0.994481i | ||||||||
\(160\) | −3.26832 | −0.258383 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −4.84536 | −0.379518 | −0.189759 | − | 0.981831i | \(-0.560771\pi\) | ||||
−0.189759 | + | 0.981831i | \(0.560771\pi\) | |||||||
\(164\) | −0.949652 | −0.0741554 | ||||||||
\(165\) | 10.1788 | − | 3.72736i | 0.792418 | − | 0.290175i | ||||
\(166\) | − | 0.835847i | − | 0.0648743i | ||||||
\(167\) | 2.13922 | 0.165538 | 0.0827688 | − | 0.996569i | \(-0.473624\pi\) | ||||
0.0827688 | + | 0.996569i | \(0.473624\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.2674 | 1.02057 | ||||||||
\(170\) | −17.4064 | −1.33501 | ||||||||
\(171\) | −4.27490 | −0.326910 | ||||||||
\(172\) | − | 6.20483i | − | 0.473114i | ||||||
\(173\) | −17.7492 | −1.34944 | −0.674722 | − | 0.738072i | \(-0.735736\pi\) | ||||
−0.674722 | + | 0.738072i | \(0.735736\pi\) | |||||||
\(174\) | − | 4.77874i | − | 0.362275i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.11438 | − | 1.14045i | 0.234755 | − | 0.0859649i | ||||
\(177\) | 13.4844 | 1.01355 | ||||||||
\(178\) | 6.22408 | 0.466514 | ||||||||
\(179\) | 2.88470 | 0.215612 | 0.107806 | − | 0.994172i | \(-0.465617\pi\) | ||||
0.107806 | + | 0.994172i | \(0.465617\pi\) | |||||||
\(180\) | − | 3.26832i | − | 0.243606i | ||||||
\(181\) | − | 10.9351i | − | 0.812803i | −0.913695 | − | 0.406401i | \(-0.866783\pi\) | ||
0.913695 | − | 0.406401i | \(-0.133217\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 5.34060i | − | 0.394788i | ||||||
\(184\) | 5.37186i | 0.396019i | ||||||||
\(185\) | − | 6.96456i | − | 0.512044i | ||||||
\(186\) | 6.46485i | 0.474026i | ||||||||
\(187\) | 16.5866 | − | 6.07382i | 1.21293 | − | 0.444162i | ||||
\(188\) | 12.0303i | 0.877397i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13.9717 | −1.01362 | ||||||||
\(191\) | 12.8770 | 0.931744 | 0.465872 | − | 0.884852i | \(-0.345741\pi\) | ||||
0.465872 | + | 0.884852i | \(0.345741\pi\) | |||||||
\(192\) | − | 1.00000i | − | 0.0721688i | ||||||
\(193\) | − | 6.04479i | − | 0.435113i | −0.976048 | − | 0.217557i | \(-0.930191\pi\) | ||
0.976048 | − | 0.217557i | \(-0.0698087\pi\) | |||||||
\(194\) | −0.624337 | −0.0448248 | ||||||||
\(195\) | −16.7507 | −1.19954 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.18237i | 0.440476i | 0.975446 | + | 0.220238i | \(0.0706833\pi\) | ||||
−0.975446 | + | 0.220238i | \(0.929317\pi\) | |||||||
\(198\) | 1.14045 | + | 3.11438i | 0.0810485 | + | 0.221329i | ||||
\(199\) | − | 3.88246i | − | 0.275220i | −0.990486 | − | 0.137610i | \(-0.956058\pi\) | ||
0.990486 | − | 0.137610i | \(-0.0439421\pi\) | |||||||
\(200\) | − | 5.68190i | − | 0.401771i | ||||||
\(201\) | 6.19350i | 0.436856i | ||||||||
\(202\) | 13.1692i | 0.926585i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 5.32580i | − | 0.372880i | ||||||
\(205\) | − | 3.10377i | − | 0.216776i | ||||||
\(206\) | −13.2122 | −0.920534 | ||||||||
\(207\) | −5.37186 | −0.373370 | ||||||||
\(208\) | −5.12518 | −0.355367 | ||||||||
\(209\) | 13.3137 | − | 4.87532i | 0.920925 | − | 0.337233i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.04700i | 0.622821i | 0.950276 | + | 0.311410i | \(0.100801\pi\) | ||||
−0.950276 | + | 0.311410i | \(0.899199\pi\) | |||||||
\(212\) | −12.5399 | −0.861246 | ||||||||
\(213\) | − | 10.8061i | − | 0.740424i | ||||||
\(214\) | 11.1094 | 0.759424 | ||||||||
\(215\) | 20.2794 | 1.38304 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.13138 | 0.482998 | ||||||||
\(219\) | − | 13.2295i | − | 0.893968i | ||||||
\(220\) | 3.72736 | + | 10.1788i | 0.251299 | + | 0.686254i | ||||
\(221\) | −27.2956 | −1.83610 | ||||||||
\(222\) | 2.13093 | 0.143019 | ||||||||
\(223\) | 5.42935i | 0.363576i | 0.983338 | + | 0.181788i | \(0.0581885\pi\) | ||||
−0.983338 | + | 0.181788i | \(0.941812\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.68190 | 0.378794 | ||||||||
\(226\) | − | 2.41436i | − | 0.160601i | ||||||
\(227\) | −11.8564 | −0.786934 | −0.393467 | − | 0.919339i | \(-0.628724\pi\) | ||||
−0.393467 | + | 0.919339i | \(0.628724\pi\) | |||||||
\(228\) | − | 4.27490i | − | 0.283112i | ||||||
\(229\) | 6.42701i | 0.424708i | 0.977193 | + | 0.212354i | \(0.0681131\pi\) | ||||
−0.977193 | + | 0.212354i | \(0.931887\pi\) | |||||||
\(230\) | −17.5569 | −1.15767 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.77874 | 0.313740 | ||||||||
\(233\) | − | 2.00886i | − | 0.131605i | −0.997833 | − | 0.0658023i | \(-0.979039\pi\) | ||
0.997833 | − | 0.0658023i | \(-0.0209607\pi\) | |||||||
\(234\) | − | 5.12518i | − | 0.335043i | ||||||
\(235\) | −39.3187 | −2.56487 | ||||||||
\(236\) | 13.4844i | 0.877758i | ||||||||
\(237\) | 9.16702 | 0.595462 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.65869i | 0.301346i | 0.988584 | + | 0.150673i | \(0.0481440\pi\) | ||||
−0.988584 | + | 0.150673i | \(0.951856\pi\) | |||||||
\(240\) | 3.26832 | 0.210969 | ||||||||
\(241\) | 5.96996 | 0.384559 | 0.192279 | − | 0.981340i | \(-0.438412\pi\) | ||||
0.192279 | + | 0.981340i | \(0.438412\pi\) | |||||||
\(242\) | −7.10361 | − | 8.39873i | −0.456637 | − | 0.539891i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 5.34060 | 0.341897 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.949652 | 0.0605476 | ||||||||
\(247\) | −21.9096 | −1.39407 | ||||||||
\(248\) | −6.46485 | −0.410519 | ||||||||
\(249\) | 0.835847i | 0.0529697i | ||||||||
\(250\) | 2.22868 | 0.140954 | ||||||||
\(251\) | 1.45699i | 0.0919645i | 0.998942 | + | 0.0459822i | \(0.0146418\pi\) | ||||
−0.998942 | + | 0.0459822i | \(0.985358\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.7300 | − | 6.12635i | 1.05181 | − | 0.385161i | ||||
\(254\) | −13.8100 | −0.866516 | ||||||||
\(255\) | 17.4064 | 1.09003 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 26.3742i | − | 1.64518i | −0.568636 | − | 0.822589i | \(-0.692529\pi\) | ||
0.568636 | − | 0.822589i | \(-0.307471\pi\) | |||||||
\(258\) | 6.20483i | 0.386296i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 16.7507i | − | 1.03883i | ||||||
\(261\) | 4.77874i | 0.295796i | ||||||||
\(262\) | 11.7866i | 0.728181i | ||||||||
\(263\) | − | 31.3179i | − | 1.93114i | −0.260141 | − | 0.965571i | \(-0.583769\pi\) | ||
0.260141 | − | 0.965571i | \(-0.416231\pi\) | |||||||
\(264\) | −3.11438 | + | 1.14045i | −0.191677 | + | 0.0701900i | ||||
\(265\) | − | 40.9845i | − | 2.51766i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.22408 | −0.380907 | ||||||||
\(268\) | −6.19350 | −0.378328 | ||||||||
\(269\) | 3.05002i | 0.185963i | 0.995668 | + | 0.0929815i | \(0.0296397\pi\) | ||||
−0.995668 | + | 0.0929815i | \(0.970360\pi\) | |||||||
\(270\) | 3.26832i | 0.198904i | ||||||||
\(271\) | 22.4492 | 1.36369 | 0.681847 | − | 0.731495i | \(-0.261177\pi\) | ||||
0.681847 | + | 0.731495i | \(0.261177\pi\) | |||||||
\(272\) | 5.32580 | 0.322924 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 4.86111i | − | 0.293670i | ||||||
\(275\) | −17.6956 | + | 6.47995i | −1.06709 | + | 0.390755i | ||||
\(276\) | − | 5.37186i | − | 0.323348i | ||||||
\(277\) | − | 20.5218i | − | 1.23304i | −0.787341 | − | 0.616518i | \(-0.788543\pi\) | ||
0.787341 | − | 0.616518i | \(-0.211457\pi\) | |||||||
\(278\) | − | 16.7827i | − | 1.00656i | ||||||
\(279\) | − | 6.46485i | − | 0.387041i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 13.8822i | − | 0.828141i | −0.910245 | − | 0.414071i | \(-0.864107\pi\) | ||
0.910245 | − | 0.414071i | \(-0.135893\pi\) | |||||||
\(282\) | − | 12.0303i | − | 0.716391i | ||||||
\(283\) | −29.7862 | −1.77061 | −0.885304 | − | 0.465013i | \(-0.846050\pi\) | ||||
−0.885304 | + | 0.465013i | \(0.846050\pi\) | |||||||
\(284\) | 10.8061 | 0.641226 | ||||||||
\(285\) | 13.9717 | 0.827614 | ||||||||
\(286\) | 5.84502 | + | 15.9618i | 0.345624 | + | 0.943838i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 11.3641 | 0.668477 | ||||||||
\(290\) | 15.6184i | 0.917146i | ||||||||
\(291\) | 0.624337 | 0.0365993 | ||||||||
\(292\) | 13.2295 | 0.774199 | ||||||||
\(293\) | 10.3943 | 0.607243 | 0.303621 | − | 0.952793i | \(-0.401804\pi\) | ||||
0.303621 | + | 0.952793i | \(0.401804\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −44.0712 | −2.56593 | ||||||||
\(296\) | 2.13093i | 0.123858i | ||||||||
\(297\) | −1.14045 | − | 3.11438i | −0.0661758 | − | 0.180715i | ||||
\(298\) | 7.22464 | 0.418512 | ||||||||
\(299\) | −27.5317 | −1.59220 | ||||||||
\(300\) | 5.68190i | 0.328045i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4.88028 | −0.280828 | ||||||||
\(303\) | − | 13.1692i | − | 0.756553i | ||||||
\(304\) | 4.27490 | 0.245182 | ||||||||
\(305\) | 17.4548i | 0.999457i | ||||||||
\(306\) | 5.32580i | 0.304456i | ||||||||
\(307\) | −1.37847 | −0.0786736 | −0.0393368 | − | 0.999226i | \(-0.512525\pi\) | ||||
−0.0393368 | + | 0.999226i | \(0.512525\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.2122 | 0.751613 | ||||||||
\(310\) | − | 21.1292i | − | 1.20006i | ||||||
\(311\) | 10.5210i | 0.596594i | 0.954473 | + | 0.298297i | \(0.0964185\pi\) | ||||
−0.954473 | + | 0.298297i | \(0.903581\pi\) | |||||||
\(312\) | 5.12518 | 0.290156 | ||||||||
\(313\) | − | 2.26694i | − | 0.128135i | −0.997946 | − | 0.0640676i | \(-0.979593\pi\) | ||
0.997946 | − | 0.0640676i | \(-0.0204073\pi\) | |||||||
\(314\) | −3.30239 | −0.186365 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.16702i | 0.515685i | ||||||||
\(317\) | −4.94169 | −0.277553 | −0.138777 | − | 0.990324i | \(-0.544317\pi\) | ||||
−0.138777 | + | 0.990324i | \(0.544317\pi\) | |||||||
\(318\) | 12.5399 | 0.703204 | ||||||||
\(319\) | −5.44993 | − | 14.8828i | −0.305137 | − | 0.833277i | ||||
\(320\) | 3.26832i | 0.182705i | ||||||||
\(321\) | −11.1094 | −0.620067 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.7672 | 1.26680 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 29.1208 | 1.61533 | ||||||||
\(326\) | 4.84536i | 0.268360i | ||||||||
\(327\) | −7.13138 | −0.394366 | ||||||||
\(328\) | 0.949652i | 0.0524358i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.72736 | − | 10.1788i | −0.205185 | − | 0.560324i | ||||
\(331\) | 12.9489 | 0.711737 | 0.355869 | − | 0.934536i | \(-0.384185\pi\) | ||||
0.355869 | + | 0.934536i | \(0.384185\pi\) | |||||||
\(332\) | −0.835847 | −0.0458731 | ||||||||
\(333\) | −2.13093 | −0.116774 | ||||||||
\(334\) | − | 2.13922i | − | 0.117053i | ||||||
\(335\) | − | 20.2423i | − | 1.10596i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8.22142i | − | 0.447849i | −0.974606 | − | 0.223925i | \(-0.928113\pi\) | ||
0.974606 | − | 0.223925i | \(-0.0718869\pi\) | |||||||
\(338\) | − | 13.2674i | − | 0.721654i | ||||||
\(339\) | 2.41436i | 0.131130i | ||||||||
\(340\) | 17.4064i | 0.943994i | ||||||||
\(341\) | 7.37286 | + | 20.1340i | 0.399263 | + | 1.09032i | ||||
\(342\) | 4.27490i | 0.231160i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.20483 | −0.334542 | ||||||||
\(345\) | 17.5569 | 0.945234 | ||||||||
\(346\) | 17.7492i | 0.954201i | ||||||||
\(347\) | 31.3657i | 1.68380i | 0.539632 | + | 0.841901i | \(0.318563\pi\) | ||||
−0.539632 | + | 0.841901i | \(0.681437\pi\) | |||||||
\(348\) | −4.77874 | −0.256167 | ||||||||
\(349\) | 3.15342 | 0.168799 | 0.0843993 | − | 0.996432i | \(-0.473103\pi\) | ||||
0.0843993 | + | 0.996432i | \(0.473103\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.12518i | 0.273562i | ||||||||
\(352\) | −1.14045 | − | 3.11438i | −0.0607864 | − | 0.165997i | ||||
\(353\) | − | 8.15423i | − | 0.434006i | −0.976171 | − | 0.217003i | \(-0.930372\pi\) | ||
0.976171 | − | 0.217003i | \(-0.0696281\pi\) | |||||||
\(354\) | − | 13.4844i | − | 0.716686i | ||||||
\(355\) | 35.3179i | 1.87448i | ||||||||
\(356\) | − | 6.22408i | − | 0.329875i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 2.88470i | − | 0.152461i | ||||||
\(359\) | 9.54046i | 0.503526i | 0.967789 | + | 0.251763i | \(0.0810104\pi\) | ||||
−0.967789 | + | 0.251763i | \(0.918990\pi\) | |||||||
\(360\) | −3.26832 | −0.172256 | ||||||||
\(361\) | −0.725250 | −0.0381710 | ||||||||
\(362\) | −10.9351 | −0.574738 | ||||||||
\(363\) | 7.10361 | + | 8.39873i | 0.372843 | + | 0.440819i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 43.2383i | 2.26319i | ||||||||
\(366\) | −5.34060 | −0.279158 | ||||||||
\(367\) | − | 6.76680i | − | 0.353224i | −0.984281 | − | 0.176612i | \(-0.943486\pi\) | ||
0.984281 | − | 0.176612i | \(-0.0565138\pi\) | |||||||
\(368\) | 5.37186 | 0.280028 | ||||||||
\(369\) | −0.949652 | −0.0494369 | ||||||||
\(370\) | −6.96456 | −0.362070 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6.46485 | 0.335187 | ||||||||
\(373\) | 0.476776i | 0.0246865i | 0.999924 | + | 0.0123433i | \(0.00392908\pi\) | ||||
−0.999924 | + | 0.0123433i | \(0.996071\pi\) | |||||||
\(374\) | −6.07382 | − | 16.5866i | −0.314070 | − | 0.857670i | ||||
\(375\) | −2.22868 | −0.115089 | ||||||||
\(376\) | 12.0303 | 0.620413 | ||||||||
\(377\) | 24.4919i | 1.26140i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.2564 | −0.783669 | −0.391835 | − | 0.920036i | \(-0.628160\pi\) | ||||
−0.391835 | + | 0.920036i | \(0.628160\pi\) | |||||||
\(380\) | 13.9717i | 0.716734i | ||||||||
\(381\) | 13.8100 | 0.707507 | ||||||||
\(382\) | − | 12.8770i | − | 0.658843i | ||||||
\(383\) | − | 12.2197i | − | 0.624396i | −0.950017 | − | 0.312198i | \(-0.898935\pi\) | ||
0.950017 | − | 0.312198i | \(-0.101065\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.04479 | −0.307672 | ||||||||
\(387\) | − | 6.20483i | − | 0.315409i | ||||||
\(388\) | 0.624337i | 0.0316959i | ||||||||
\(389\) | 28.0321 | 1.42128 | 0.710641 | − | 0.703554i | \(-0.248405\pi\) | ||||
0.710641 | + | 0.703554i | \(0.248405\pi\) | |||||||
\(390\) | 16.7507i | 0.848205i | ||||||||
\(391\) | 28.6094 | 1.44684 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 11.7866i | − | 0.594557i | ||||||
\(394\) | 6.18237 | 0.311463 | ||||||||
\(395\) | −29.9607 | −1.50749 | ||||||||
\(396\) | 3.11438 | − | 1.14045i | 0.156504 | − | 0.0573099i | ||||
\(397\) | 30.1481i | 1.51309i | 0.653941 | + | 0.756546i | \(0.273114\pi\) | ||||
−0.653941 | + | 0.756546i | \(0.726886\pi\) | |||||||
\(398\) | −3.88246 | −0.194610 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.68190 | −0.284095 | ||||||||
\(401\) | −3.21065 | −0.160332 | −0.0801661 | − | 0.996782i | \(-0.525545\pi\) | ||||
−0.0801661 | + | 0.996782i | \(0.525545\pi\) | |||||||
\(402\) | 6.19350 | 0.308904 | ||||||||
\(403\) | − | 33.1335i | − | 1.65050i | ||||||
\(404\) | 13.1692 | 0.655194 | ||||||||
\(405\) | − | 3.26832i | − | 0.162404i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.63653 | − | 2.43023i | 0.328960 | − | 0.120462i | ||||
\(408\) | −5.32580 | −0.263666 | ||||||||
\(409\) | 34.3043 | 1.69624 | 0.848120 | − | 0.529805i | \(-0.177735\pi\) | ||||
0.848120 | + | 0.529805i | \(0.177735\pi\) | |||||||
\(410\) | −3.10377 | −0.153284 | ||||||||
\(411\) | 4.86111i | 0.239781i | ||||||||
\(412\) | 13.2122i | 0.650916i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.37186i | 0.264012i | ||||||||
\(415\) | − | 2.73181i | − | 0.134100i | ||||||
\(416\) | 5.12518i | 0.251282i | ||||||||
\(417\) | 16.7827i | 0.821851i | ||||||||
\(418\) | −4.87532 | − | 13.3137i | −0.238460 | − | 0.651192i | ||||
\(419\) | − | 12.7969i | − | 0.625168i | −0.949890 | − | 0.312584i | \(-0.898805\pi\) | ||
0.949890 | − | 0.312584i | \(-0.101195\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.0356 | 1.70753 | 0.853766 | − | 0.520657i | \(-0.174313\pi\) | ||||
0.853766 | + | 0.520657i | \(0.174313\pi\) | |||||||
\(422\) | 9.04700 | 0.440401 | ||||||||
\(423\) | 12.0303i | 0.584931i | ||||||||
\(424\) | 12.5399i | 0.608993i | ||||||||
\(425\) | −30.2607 | −1.46786 | ||||||||
\(426\) | −10.8061 | −0.523559 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 11.1094i | − | 0.536994i | ||||||
\(429\) | −5.84502 | − | 15.9618i | −0.282200 | − | 0.770641i | ||||
\(430\) | − | 20.2794i | − | 0.977958i | ||||||
\(431\) | 25.9217i | 1.24860i | 0.781183 | + | 0.624302i | \(0.214616\pi\) | ||||
−0.781183 | + | 0.624302i | \(0.785384\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | 29.5108i | 1.41820i | 0.705110 | + | 0.709098i | \(0.250898\pi\) | ||||
−0.705110 | + | 0.709098i | \(0.749102\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 15.6184i | − | 0.748847i | ||||||
\(436\) | − | 7.13138i | − | 0.341531i | ||||||
\(437\) | 22.9641 | 1.09852 | ||||||||
\(438\) | −13.2295 | −0.632131 | ||||||||
\(439\) | 11.4208 | 0.545085 | 0.272542 | − | 0.962144i | \(-0.412136\pi\) | ||||
0.272542 | + | 0.962144i | \(0.412136\pi\) | |||||||
\(440\) | 10.1788 | − | 3.72736i | 0.485255 | − | 0.177695i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 27.2956i | 1.29832i | ||||||||
\(443\) | 25.5212 | 1.21255 | 0.606273 | − | 0.795256i | \(-0.292664\pi\) | ||||
0.606273 | + | 0.795256i | \(0.292664\pi\) | |||||||
\(444\) | − | 2.13093i | − | 0.101129i | ||||||
\(445\) | 20.3423 | 0.964316 | ||||||||
\(446\) | 5.42935 | 0.257087 | ||||||||
\(447\) | −7.22464 | −0.341714 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.9959 | 1.22682 | 0.613412 | − | 0.789763i | \(-0.289797\pi\) | ||||
0.613412 | + | 0.789763i | \(0.289797\pi\) | |||||||
\(450\) | − | 5.68190i | − | 0.267848i | ||||||
\(451\) | 2.95758 | − | 1.08303i | 0.139267 | − | 0.0509981i | ||||
\(452\) | −2.41436 | −0.113562 | ||||||||
\(453\) | 4.88028 | 0.229295 | ||||||||
\(454\) | 11.8564i | 0.556446i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.27490 | −0.200190 | ||||||||
\(457\) | 8.03248i | 0.375743i | 0.982194 | + | 0.187872i | \(0.0601589\pi\) | ||||
−0.982194 | + | 0.187872i | \(0.939841\pi\) | |||||||
\(458\) | 6.42701 | 0.300314 | ||||||||
\(459\) | − | 5.32580i | − | 0.248587i | ||||||
\(460\) | 17.5569i | 0.818597i | ||||||||
\(461\) | −33.5115 | −1.56078 | −0.780392 | − | 0.625290i | \(-0.784981\pi\) | ||||
−0.780392 | + | 0.625290i | \(0.784981\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.7419 | −0.731587 | −0.365793 | − | 0.930696i | \(-0.619202\pi\) | ||||
−0.365793 | + | 0.930696i | \(0.619202\pi\) | |||||||
\(464\) | − | 4.77874i | − | 0.221847i | ||||||
\(465\) | 21.1292i | 0.979843i | ||||||||
\(466\) | −2.00886 | −0.0930585 | ||||||||
\(467\) | − | 10.2329i | − | 0.473521i | −0.971568 | − | 0.236760i | \(-0.923914\pi\) | ||
0.971568 | − | 0.236760i | \(-0.0760857\pi\) | |||||||
\(468\) | −5.12518 | −0.236911 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 39.3187i | 1.81364i | ||||||||
\(471\) | 3.30239 | 0.152166 | ||||||||
\(472\) | 13.4844 | 0.620668 | ||||||||
\(473\) | 7.07632 | + | 19.3242i | 0.325370 | + | 0.888528i | ||||
\(474\) | − | 9.16702i | − | 0.421055i | ||||||
\(475\) | −24.2896 | −1.11448 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.5399 | −0.574164 | ||||||||
\(478\) | 4.65869 | 0.213083 | ||||||||
\(479\) | 5.19626 | 0.237423 | 0.118712 | − | 0.992929i | \(-0.462124\pi\) | ||||
0.118712 | + | 0.992929i | \(0.462124\pi\) | |||||||
\(480\) | − | 3.26832i | − | 0.149178i | ||||||
\(481\) | −10.9214 | −0.497973 | ||||||||
\(482\) | − | 5.96996i | − | 0.271924i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.39873 | + | 7.10361i | −0.381761 | + | 0.322891i | ||||
\(485\) | −2.04053 | −0.0926558 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −31.5483 | −1.42959 | −0.714794 | − | 0.699335i | \(-0.753479\pi\) | ||||
−0.714794 | + | 0.699335i | \(0.753479\pi\) | |||||||
\(488\) | − | 5.34060i | − | 0.241758i | ||||||
\(489\) | − | 4.84536i | − | 0.219115i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7.14182i | − | 0.322306i | −0.986929 | − | 0.161153i | \(-0.948479\pi\) | ||
0.986929 | − | 0.161153i | \(-0.0515212\pi\) | |||||||
\(492\) | − | 0.949652i | − | 0.0428136i | ||||||
\(493\) | − | 25.4506i | − | 1.14624i | ||||||
\(494\) | 21.9096i | 0.985760i | ||||||||
\(495\) | 3.72736 | + | 10.1788i | 0.167533 | + | 0.457502i | ||||
\(496\) | 6.46485i | 0.290281i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.835847 | 0.0374552 | ||||||||
\(499\) | −34.7635 | −1.55623 | −0.778114 | − | 0.628123i | \(-0.783824\pi\) | ||||
−0.778114 | + | 0.628123i | \(0.783824\pi\) | |||||||
\(500\) | − | 2.22868i | − | 0.0996697i | ||||||
\(501\) | 2.13922i | 0.0955732i | ||||||||
\(502\) | 1.45699 | 0.0650287 | ||||||||
\(503\) | −3.06150 | −0.136506 | −0.0682529 | − | 0.997668i | \(-0.521742\pi\) | ||||
−0.0682529 | + | 0.997668i | \(0.521742\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 43.0413i | 1.91531i | ||||||||
\(506\) | −6.12635 | − | 16.7300i | −0.272350 | − | 0.743740i | ||||
\(507\) | 13.2674i | 0.589228i | ||||||||
\(508\) | 13.8100i | 0.612719i | ||||||||
\(509\) | 28.4354i | 1.26038i | 0.776442 | + | 0.630188i | \(0.217022\pi\) | ||||
−0.776442 | + | 0.630188i | \(0.782978\pi\) | |||||||
\(510\) | − | 17.4064i | − | 0.770768i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 4.27490i | − | 0.188741i | ||||||
\(514\) | −26.3742 | −1.16332 | ||||||||
\(515\) | −43.1815 | −1.90281 | ||||||||
\(516\) | 6.20483 | 0.273152 | ||||||||
\(517\) | −13.7199 | − | 37.4668i | −0.603402 | − | 1.64779i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 17.7492i | − | 0.779101i | ||||||
\(520\) | −16.7507 | −0.734567 | ||||||||
\(521\) | − | 3.64587i | − | 0.159728i | −0.996806 | − | 0.0798642i | \(-0.974551\pi\) | ||
0.996806 | − | 0.0798642i | \(-0.0254487\pi\) | |||||||
\(522\) | 4.77874 | 0.209160 | ||||||||
\(523\) | 23.9460 | 1.04708 | 0.523542 | − | 0.852000i | \(-0.324610\pi\) | ||||
0.523542 | + | 0.852000i | \(0.324610\pi\) | |||||||
\(524\) | 11.7866 | 0.514902 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −31.3179 | −1.36552 | ||||||||
\(527\) | 34.4305i | 1.49982i | ||||||||
\(528\) | 1.14045 | + | 3.11438i | 0.0496318 | + | 0.135536i | ||||
\(529\) | 5.85687 | 0.254647 | ||||||||
\(530\) | −40.9845 | −1.78025 | ||||||||
\(531\) | 13.4844i | 0.585172i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.86714 | −0.210819 | ||||||||
\(534\) | 6.22408i | 0.269342i | ||||||||
\(535\) | 36.3091 | 1.56978 | ||||||||
\(536\) | 6.19350i | 0.267518i | ||||||||
\(537\) | 2.88470i | 0.124484i | ||||||||
\(538\) | 3.05002 | 0.131496 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.26832 | 0.140646 | ||||||||
\(541\) | 43.0569i | 1.85116i | 0.378552 | + | 0.925580i | \(0.376422\pi\) | ||||
−0.378552 | + | 0.925580i | \(0.623578\pi\) | |||||||
\(542\) | − | 22.4492i | − | 0.964278i | ||||||
\(543\) | 10.9351 | 0.469272 | ||||||||
\(544\) | − | 5.32580i | − | 0.228342i | ||||||
\(545\) | 23.3076 | 0.998389 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00013i | 0.342061i | 0.985266 | + | 0.171030i | \(0.0547097\pi\) | ||||
−0.985266 | + | 0.171030i | \(0.945290\pi\) | |||||||
\(548\) | −4.86111 | −0.207656 | ||||||||
\(549\) | 5.34060 | 0.227931 | ||||||||
\(550\) | 6.47995 | + | 17.6956i | 0.276306 | + | 0.754544i | ||||
\(551\) | − | 20.4286i | − | 0.870288i | ||||||
\(552\) | −5.37186 | −0.228642 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −20.5218 | −0.871888 | ||||||||
\(555\) | 6.96456 | 0.295629 | ||||||||
\(556\) | −16.7827 | −0.711744 | ||||||||
\(557\) | − | 23.3405i | − | 0.988967i | −0.869187 | − | 0.494484i | \(-0.835357\pi\) | ||
0.869187 | − | 0.494484i | \(-0.164643\pi\) | |||||||
\(558\) | −6.46485 | −0.273679 | ||||||||
\(559\) | − | 31.8009i | − | 1.34503i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.07382 | + | 16.5866i | 0.256437 | + | 0.700285i | ||||
\(562\) | −13.8822 | −0.585584 | ||||||||
\(563\) | 26.4381 | 1.11423 | 0.557116 | − | 0.830435i | \(-0.311908\pi\) | ||||
0.557116 | + | 0.830435i | \(0.311908\pi\) | |||||||
\(564\) | −12.0303 | −0.506565 | ||||||||
\(565\) | − | 7.89089i | − | 0.331972i | ||||||
\(566\) | 29.7862i | 1.25201i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 10.8061i | − | 0.453415i | ||||||
\(569\) | − | 24.9986i | − | 1.04799i | −0.851720 | − | 0.523997i | \(-0.824440\pi\) | ||
0.851720 | − | 0.523997i | \(-0.175560\pi\) | |||||||
\(570\) | − | 13.9717i | − | 0.585211i | ||||||
\(571\) | 43.4852i | 1.81980i | 0.414830 | + | 0.909899i | \(0.363841\pi\) | ||||
−0.414830 | + | 0.909899i | \(0.636159\pi\) | |||||||
\(572\) | 15.9618 | − | 5.84502i | 0.667394 | − | 0.244393i | ||||
\(573\) | 12.8770i | 0.537943i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.5224 | −1.27287 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 27.7990i | 1.15729i | 0.815581 | + | 0.578643i | \(0.196418\pi\) | ||||
−0.815581 | + | 0.578643i | \(0.803582\pi\) | |||||||
\(578\) | − | 11.3641i | − | 0.472685i | ||||||
\(579\) | 6.04479 | 0.251213 | ||||||||
\(580\) | 15.6184 | 0.648520 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 0.624337i | − | 0.0258796i | ||||||
\(583\) | 39.0541 | − | 14.3012i | 1.61746 | − | 0.592295i | ||||
\(584\) | − | 13.2295i | − | 0.547441i | ||||||
\(585\) | − | 16.7507i | − | 0.692557i | ||||||
\(586\) | − | 10.3943i | − | 0.429385i | ||||||
\(587\) | 11.2683i | 0.465091i | 0.972585 | + | 0.232546i | \(0.0747055\pi\) | ||||
−0.972585 | + | 0.232546i | \(0.925294\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.6366i | 1.13875i | ||||||||
\(590\) | 44.0712i | 1.81438i | ||||||||
\(591\) | −6.18237 | −0.254309 | ||||||||
\(592\) | 2.13093 | 0.0875807 | ||||||||
\(593\) | 15.7021 | 0.644809 | 0.322405 | − | 0.946602i | \(-0.395509\pi\) | ||||
0.322405 | + | 0.946602i | \(0.395509\pi\) | |||||||
\(594\) | −3.11438 | + | 1.14045i | −0.127785 | + | 0.0467934i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 7.22464i | − | 0.295933i | ||||||
\(597\) | 3.88246 | 0.158898 | ||||||||
\(598\) | 27.5317i | 1.12586i | ||||||||
\(599\) | 9.58002 | 0.391429 | 0.195714 | − | 0.980661i | \(-0.437297\pi\) | ||||
0.195714 | + | 0.980661i | \(0.437297\pi\) | |||||||
\(600\) | 5.68190 | 0.231963 | ||||||||
\(601\) | 36.7398 | 1.49865 | 0.749324 | − | 0.662204i | \(-0.230379\pi\) | ||||
0.749324 | + | 0.662204i | \(0.230379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.19350 | −0.252219 | ||||||||
\(604\) | 4.88028i | 0.198576i | ||||||||
\(605\) | −23.2169 | − | 27.4497i | −0.943900 | − | 1.11599i | ||||
\(606\) | −13.1692 | −0.534964 | ||||||||
\(607\) | −40.4651 | −1.64243 | −0.821215 | − | 0.570619i | \(-0.806703\pi\) | ||||
−0.821215 | + | 0.570619i | \(0.806703\pi\) | |||||||
\(608\) | − | 4.27490i | − | 0.173370i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 17.4548 | 0.706723 | ||||||||
\(611\) | 61.6572i | 2.49438i | ||||||||
\(612\) | 5.32580 | 0.215283 | ||||||||
\(613\) | − | 10.4735i | − | 0.423019i | −0.977376 | − | 0.211509i | \(-0.932162\pi\) | ||
0.977376 | − | 0.211509i | \(-0.0678379\pi\) | |||||||
\(614\) | 1.37847i | 0.0556307i | ||||||||
\(615\) | 3.10377 | 0.125156 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.4244 | −0.580706 | −0.290353 | − | 0.956920i | \(-0.593773\pi\) | ||||
−0.290353 | + | 0.956920i | \(0.593773\pi\) | |||||||
\(618\) | − | 13.2122i | − | 0.531471i | ||||||
\(619\) | 44.7946i | 1.80045i | 0.435430 | + | 0.900223i | \(0.356596\pi\) | ||||
−0.435430 | + | 0.900223i | \(0.643404\pi\) | |||||||
\(620\) | −21.1292 | −0.848569 | ||||||||
\(621\) | − | 5.37186i | − | 0.215565i | ||||||
\(622\) | 10.5210 | 0.421855 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 5.12518i | − | 0.205171i | ||||||
\(625\) | −21.1255 | −0.845019 | ||||||||
\(626\) | −2.26694 | −0.0906052 | ||||||||
\(627\) | 4.87532 | + | 13.3137i | 0.194702 | + | 0.531696i | ||||
\(628\) | 3.30239i | 0.131780i | ||||||||
\(629\) | 11.3489 | 0.452510 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.1975 | 0.525383 | 0.262692 | − | 0.964880i | \(-0.415390\pi\) | ||||
0.262692 | + | 0.964880i | \(0.415390\pi\) | |||||||
\(632\) | 9.16702 | 0.364644 | ||||||||
\(633\) | −9.04700 | −0.359586 | ||||||||
\(634\) | 4.94169i | 0.196260i | ||||||||
\(635\) | −45.1354 | −1.79114 | ||||||||
\(636\) | − | 12.5399i | − | 0.497240i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.8828 | + | 5.44993i | −0.589216 | + | 0.215765i | ||||
\(639\) | 10.8061 | 0.427484 | ||||||||
\(640\) | 3.26832 | 0.129192 | ||||||||
\(641\) | 21.5850 | 0.852555 | 0.426278 | − | 0.904592i | \(-0.359825\pi\) | ||||
0.426278 | + | 0.904592i | \(0.359825\pi\) | |||||||
\(642\) | 11.1094i | 0.438454i | ||||||||
\(643\) | 28.9651i | 1.14227i | 0.820855 | + | 0.571137i | \(0.193497\pi\) | ||||
−0.820855 | + | 0.571137i | \(0.806503\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20.2794i | 0.798499i | ||||||||
\(646\) | − | 22.7672i | − | 0.895765i | ||||||
\(647\) | 29.3639i | 1.15442i | 0.816597 | + | 0.577208i | \(0.195858\pi\) | ||||
−0.816597 | + | 0.577208i | \(0.804142\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −15.3783 | − | 41.9955i | −0.603651 | − | 1.64847i | ||||
\(650\) | − | 29.1208i | − | 1.14221i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.84536 | 0.189759 | ||||||||
\(653\) | −38.2449 | −1.49664 | −0.748320 | − | 0.663338i | \(-0.769139\pi\) | ||||
−0.748320 | + | 0.663338i | \(0.769139\pi\) | |||||||
\(654\) | 7.13138i | 0.278859i | ||||||||
\(655\) | 38.5225i | 1.50520i | ||||||||
\(656\) | 0.949652 | 0.0370777 | ||||||||
\(657\) | 13.2295 | 0.516133 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.210272i | 0.00819105i | 0.999992 | + | 0.00409553i | \(0.00130365\pi\) | ||||
−0.999992 | + | 0.00409553i | \(0.998696\pi\) | |||||||
\(660\) | −10.1788 | + | 3.72736i | −0.396209 | + | 0.145087i | ||||
\(661\) | 9.32692i | 0.362775i | 0.983412 | + | 0.181388i | \(0.0580588\pi\) | ||||
−0.983412 | + | 0.181388i | \(0.941941\pi\) | |||||||
\(662\) | − | 12.9489i | − | 0.503274i | ||||||
\(663\) | − | 27.2956i | − | 1.06008i | ||||||
\(664\) | 0.835847i | 0.0324372i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.13093i | 0.0825718i | ||||||||
\(667\) | − | 25.6707i | − | 0.993974i | ||||||
\(668\) | −2.13922 | −0.0827688 | ||||||||
\(669\) | −5.42935 | −0.209911 | ||||||||
\(670\) | −20.2423 | −0.782029 | ||||||||
\(671\) | −16.6327 | + | 6.09070i | −0.642096 | + | 0.235129i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 15.7351i | − | 0.606545i | −0.952904 | − | 0.303273i | \(-0.901921\pi\) | ||
0.952904 | − | 0.303273i | \(-0.0980793\pi\) | |||||||
\(674\) | −8.22142 | −0.316677 | ||||||||
\(675\) | 5.68190i | 0.218697i | ||||||||
\(676\) | −13.2674 | −0.510286 | ||||||||
\(677\) | 13.0789 | 0.502661 | 0.251331 | − | 0.967901i | \(-0.419132\pi\) | ||||
0.251331 | + | 0.967901i | \(0.419132\pi\) | |||||||
\(678\) | 2.41436 | 0.0927229 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 17.4064 | 0.667505 | ||||||||
\(681\) | − | 11.8564i | − | 0.454337i | ||||||
\(682\) | 20.1340 | − | 7.37286i | 0.770971 | − | 0.282322i | ||||
\(683\) | −25.1709 | −0.963136 | −0.481568 | − | 0.876409i | \(-0.659933\pi\) | ||||
−0.481568 | + | 0.876409i | \(0.659933\pi\) | |||||||
\(684\) | 4.27490 | 0.163455 | ||||||||
\(685\) | − | 15.8876i | − | 0.607036i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.42701 | −0.245206 | ||||||||
\(688\) | 6.20483i | 0.236557i | ||||||||
\(689\) | −64.2693 | −2.44847 | ||||||||
\(690\) | − | 17.5569i | − | 0.668381i | ||||||
\(691\) | − | 0.792464i | − | 0.0301468i | −0.999886 | − | 0.0150734i | \(-0.995202\pi\) | ||
0.999886 | − | 0.0150734i | \(-0.00479819\pi\) | |||||||
\(692\) | 17.7492 | 0.674722 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31.3657 | 1.19063 | ||||||||
\(695\) | − | 54.8511i | − | 2.08062i | ||||||
\(696\) | 4.77874i | 0.181138i | ||||||||
\(697\) | 5.05766 | 0.191572 | ||||||||
\(698\) | − | 3.15342i | − | 0.119359i | ||||||
\(699\) | 2.00886 | 0.0759820 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.5754i | 1.49474i | 0.664406 | + | 0.747372i | \(0.268685\pi\) | ||||
−0.664406 | + | 0.747372i | \(0.731315\pi\) | |||||||
\(702\) | 5.12518 | 0.193437 | ||||||||
\(703\) | 9.10951 | 0.343572 | ||||||||
\(704\) | −3.11438 | + | 1.14045i | −0.117378 | + | 0.0429824i | ||||
\(705\) | − | 39.3187i | − | 1.48083i | ||||||
\(706\) | −8.15423 | −0.306889 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −13.4844 | −0.506774 | ||||||||
\(709\) | 36.4422 | 1.36861 | 0.684307 | − | 0.729194i | \(-0.260105\pi\) | ||||
0.684307 | + | 0.729194i | \(0.260105\pi\) | |||||||
\(710\) | 35.3179 | 1.32546 | ||||||||
\(711\) | 9.16702i | 0.343790i | ||||||||
\(712\) | −6.22408 | −0.233257 | ||||||||
\(713\) | 34.7283i | 1.30058i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.1034 | + | 52.1681i | 0.714427 | + | 1.95098i | ||||
\(716\) | −2.88470 | −0.107806 | ||||||||
\(717\) | −4.65869 | −0.173982 | ||||||||
\(718\) | 9.54046 | 0.356047 | ||||||||
\(719\) | 14.1604i | 0.528092i | 0.964510 | + | 0.264046i | \(0.0850571\pi\) | ||||
−0.964510 | + | 0.264046i | \(0.914943\pi\) | |||||||
\(720\) | 3.26832i | 0.121803i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.725250i | 0.0269910i | ||||||||
\(723\) | 5.96996i | 0.222025i | ||||||||
\(724\) | 10.9351i | 0.406401i | ||||||||
\(725\) | 27.1523i | 1.00841i | ||||||||
\(726\) | 8.39873 | − | 7.10361i | 0.311706 | − | 0.263640i | ||||
\(727\) | 8.58699i | 0.318474i | 0.987240 | + | 0.159237i | \(0.0509033\pi\) | ||||
−0.987240 | + | 0.159237i | \(0.949097\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 43.2383 | 1.60032 | ||||||||
\(731\) | 33.0457i | 1.22224i | ||||||||
\(732\) | 5.34060i | 0.197394i | ||||||||
\(733\) | 42.7196 | 1.57788 | 0.788942 | − | 0.614468i | \(-0.210629\pi\) | ||||
0.788942 | + | 0.614468i | \(0.210629\pi\) | |||||||
\(734\) | −6.76680 | −0.249767 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 5.37186i | − | 0.198009i | ||||||
\(737\) | 19.2889 | − | 7.06340i | 0.710516 | − | 0.260184i | ||||
\(738\) | 0.949652i | 0.0349572i | ||||||||
\(739\) | − | 33.2019i | − | 1.22135i | −0.791881 | − | 0.610675i | \(-0.790898\pi\) | ||
0.791881 | − | 0.610675i | \(-0.209102\pi\) | |||||||
\(740\) | 6.96456i | 0.256022i | ||||||||
\(741\) | − | 21.9096i | − | 0.804870i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.11448i | 0.297691i | 0.988860 | + | 0.148846i | \(0.0475557\pi\) | ||||
−0.988860 | + | 0.148846i | \(0.952444\pi\) | |||||||
\(744\) | − | 6.46485i | − | 0.237013i | ||||||
\(745\) | 23.6124 | 0.865093 | ||||||||
\(746\) | 0.476776 | 0.0174560 | ||||||||
\(747\) | −0.835847 | −0.0305821 | ||||||||
\(748\) | −16.5866 | + | 6.07382i | −0.606465 | + | 0.222081i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.22868i | 0.0813800i | ||||||||
\(751\) | 0.0753513 | 0.00274961 | 0.00137480 | − | 0.999999i | \(-0.499562\pi\) | ||||
0.00137480 | + | 0.999999i | \(0.499562\pi\) | |||||||
\(752\) | − | 12.0303i | − | 0.438698i | ||||||
\(753\) | −1.45699 | −0.0530957 | ||||||||
\(754\) | 24.4919 | 0.891942 | ||||||||
\(755\) | −15.9503 | −0.580491 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.134400 | −0.00488484 | −0.00244242 | − | 0.999997i | \(-0.500777\pi\) | ||||
−0.00244242 | + | 0.999997i | \(0.500777\pi\) | |||||||
\(758\) | 15.2564i | 0.554138i | ||||||||
\(759\) | 6.12635 | + | 16.7300i | 0.222373 | + | 0.607261i | ||||
\(760\) | 13.9717 | 0.506808 | ||||||||
\(761\) | 14.7028 | 0.532978 | 0.266489 | − | 0.963838i | \(-0.414136\pi\) | ||||
0.266489 | + | 0.963838i | \(0.414136\pi\) | |||||||
\(762\) | − | 13.8100i | − | 0.500283i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12.8770 | −0.465872 | ||||||||
\(765\) | 17.4064i | 0.629330i | ||||||||
\(766\) | −12.2197 | −0.441515 | ||||||||
\(767\) | 69.1098i | 2.49541i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −7.17040 | −0.258571 | −0.129286 | − | 0.991607i | \(-0.541268\pi\) | ||||
−0.129286 | + | 0.991607i | \(0.541268\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.3742 | 0.949844 | ||||||||
\(772\) | 6.04479i | 0.217557i | ||||||||
\(773\) | − | 37.2109i | − | 1.33838i | −0.743090 | − | 0.669192i | \(-0.766641\pi\) | ||
0.743090 | − | 0.669192i | \(-0.233359\pi\) | |||||||
\(774\) | −6.20483 | −0.223028 | ||||||||
\(775\) | − | 36.7327i | − | 1.31948i | ||||||
\(776\) | 0.624337 | 0.0224124 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 28.0321i | − | 1.00500i | ||||||
\(779\) | 4.05967 | 0.145453 | ||||||||
\(780\) | 16.7507 | 0.599772 | ||||||||
\(781\) | −33.6544 | + | 12.3239i | −1.20425 | + | 0.440983i | ||||
\(782\) | − | 28.6094i | − | 1.02307i | ||||||
\(783\) | −4.77874 | −0.170778 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.7933 | −0.385229 | ||||||||
\(786\) | −11.7866 | −0.420416 | ||||||||
\(787\) | 43.1199 | 1.53706 | 0.768529 | − | 0.639815i | \(-0.220989\pi\) | ||||
0.768529 | + | 0.639815i | \(0.220989\pi\) | |||||||
\(788\) | − | 6.18237i | − | 0.220238i | ||||||
\(789\) | 31.3179 | 1.11494 | ||||||||
\(790\) | 29.9607i | 1.06596i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.14045 | − | 3.11438i | −0.0405242 | − | 0.110665i | ||||
\(793\) | 27.3715 | 0.971991 | ||||||||
\(794\) | 30.1481 | 1.06992 | ||||||||
\(795\) | 40.9845 | 1.45357 | ||||||||
\(796\) | 3.88246i | 0.137610i | ||||||||
\(797\) | 30.1768i | 1.06892i | 0.845195 | + | 0.534458i | \(0.179484\pi\) | ||||
−0.845195 | + | 0.534458i | \(0.820516\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 64.0707i | − | 2.26666i | ||||||
\(800\) | 5.68190i | 0.200886i | ||||||||
\(801\) | − | 6.22408i | − | 0.219917i | ||||||
\(802\) | 3.21065i | 0.113372i | ||||||||
\(803\) | −41.2017 | + | 15.0876i | −1.45398 | + | 0.532431i | ||||
\(804\) | − | 6.19350i | − | 0.218428i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −33.1335 | −1.16708 | ||||||||
\(807\) | −3.05002 | −0.107366 | ||||||||
\(808\) | − | 13.1692i | − | 0.463292i | ||||||
\(809\) | 46.2479i | 1.62599i | 0.582270 | + | 0.812996i | \(0.302165\pi\) | ||||
−0.582270 | + | 0.812996i | \(0.697835\pi\) | |||||||
\(810\) | −3.26832 | −0.114837 | ||||||||
\(811\) | −22.9534 | −0.806003 | −0.403001 | − | 0.915199i | \(-0.632033\pi\) | ||||
−0.403001 | + | 0.915199i | \(0.632033\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.4492i | 0.787329i | ||||||||
\(814\) | −2.43023 | − | 6.63653i | −0.0851794 | − | 0.232610i | ||||
\(815\) | 15.8362i | 0.554717i | ||||||||
\(816\) | 5.32580i | 0.186440i | ||||||||
\(817\) | 26.5250i | 0.927993i | ||||||||
\(818\) | − | 34.3043i | − | 1.19942i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.10377i | 0.108388i | ||||||||
\(821\) | − | 16.4705i | − | 0.574823i | −0.957807 | − | 0.287412i | \(-0.907205\pi\) | ||
0.957807 | − | 0.287412i | \(-0.0927948\pi\) | |||||||
\(822\) | 4.86111 | 0.169551 | ||||||||
\(823\) | 12.2157 | 0.425812 | 0.212906 | − | 0.977073i | \(-0.431707\pi\) | ||||
0.212906 | + | 0.977073i | \(0.431707\pi\) | |||||||
\(824\) | 13.2122 | 0.460267 | ||||||||
\(825\) | −6.47995 | − | 17.6956i | −0.225603 | − | 0.616082i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.55524i | 0.158401i | 0.996859 | + | 0.0792007i | \(0.0252368\pi\) | ||||
−0.996859 | + | 0.0792007i | \(0.974763\pi\) | |||||||
\(828\) | 5.37186 | 0.186685 | ||||||||
\(829\) | − | 37.1759i | − | 1.29117i | −0.763688 | − | 0.645585i | \(-0.776613\pi\) | ||
0.763688 | − | 0.645585i | \(-0.223387\pi\) | |||||||
\(830\) | −2.73181 | −0.0948227 | ||||||||
\(831\) | 20.5218 | 0.711894 | ||||||||
\(832\) | 5.12518 | 0.177684 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.7827 | 0.581136 | ||||||||
\(835\) | − | 6.99164i | − | 0.241956i | ||||||
\(836\) | −13.3137 | + | 4.87532i | −0.460463 | + | 0.168616i | ||||
\(837\) | 6.46485 | 0.223458 | ||||||||
\(838\) | −12.7969 | −0.442061 | ||||||||
\(839\) | − | 39.5086i | − | 1.36399i | −0.731358 | − | 0.681994i | \(-0.761113\pi\) | ||
0.731358 | − | 0.681994i | \(-0.238887\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.16366 | 0.212540 | ||||||||
\(842\) | − | 35.0356i | − | 1.20741i | ||||||
\(843\) | 13.8822 | 0.478128 | ||||||||
\(844\) | − | 9.04700i | − | 0.311410i | ||||||
\(845\) | − | 43.3622i | − | 1.49171i | ||||||
\(846\) | 12.0303 | 0.413609 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.5399 | 0.430623 | ||||||||
\(849\) | − | 29.7862i | − | 1.02226i | ||||||
\(850\) | 30.2607i | 1.03793i | ||||||||
\(851\) | 11.4471 | 0.392400 | ||||||||
\(852\) | 10.8061i | 0.370212i | ||||||||
\(853\) | −34.2280 | −1.17194 | −0.585972 | − | 0.810331i | \(-0.699287\pi\) | ||||
−0.585972 | + | 0.810331i | \(0.699287\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.9717i | 0.477823i | ||||||||
\(856\) | −11.1094 | −0.379712 | ||||||||
\(857\) | −1.64415 | −0.0561629 | −0.0280815 | − | 0.999606i | \(-0.508940\pi\) | ||||
−0.0280815 | + | 0.999606i | \(0.508940\pi\) | |||||||
\(858\) | −15.9618 | + | 5.84502i | −0.544925 | + | 0.199546i | ||||
\(859\) | 21.9701i | 0.749610i | 0.927104 | + | 0.374805i | \(0.122290\pi\) | ||||
−0.927104 | + | 0.374805i | \(0.877710\pi\) | |||||||
\(860\) | −20.2794 | −0.691521 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25.9217 | 0.882896 | ||||||||
\(863\) | 9.52205 | 0.324134 | 0.162067 | − | 0.986780i | \(-0.448184\pi\) | ||||
0.162067 | + | 0.986780i | \(0.448184\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 58.0099i | 1.97240i | ||||||||
\(866\) | 29.5108 | 1.00282 | ||||||||
\(867\) | 11.3641i | 0.385945i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.4546 | − | 28.5496i | −0.354646 | − | 0.968478i | ||||
\(870\) | −15.6184 | −0.529515 | ||||||||
\(871\) | −31.7428 | −1.07556 | ||||||||
\(872\) | −7.13138 | −0.241499 | ||||||||
\(873\) | 0.624337i | 0.0211306i | ||||||||
\(874\) | − | 22.9641i | − | 0.776774i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.2295i | 0.446984i | ||||||||
\(877\) | − | 34.6691i | − | 1.17069i | −0.810783 | − | 0.585347i | \(-0.800958\pi\) | ||
0.810783 | − | 0.585347i | \(-0.199042\pi\) | |||||||
\(878\) | − | 11.4208i | − | 0.385433i | ||||||
\(879\) | 10.3943i | 0.350592i | ||||||||
\(880\) | −3.72736 | − | 10.1788i | −0.125649 | − | 0.343127i | ||||
\(881\) | 9.30311i | 0.313430i | 0.987644 | + | 0.156715i | \(0.0500904\pi\) | ||||
−0.987644 | + | 0.156715i | \(0.949910\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.2050 | −1.35301 | −0.676503 | − | 0.736440i | \(-0.736505\pi\) | ||||
−0.676503 | + | 0.736440i | \(0.736505\pi\) | |||||||
\(884\) | 27.2956 | 0.918052 | ||||||||
\(885\) | − | 44.0712i | − | 1.48144i | ||||||
\(886\) | − | 25.5212i | − | 0.857400i | ||||||
\(887\) | 15.0891 | 0.506643 | 0.253322 | − | 0.967382i | \(-0.418477\pi\) | ||||
0.253322 | + | 0.967382i | \(0.418477\pi\) | |||||||
\(888\) | −2.13093 | −0.0715093 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 20.3423i | − | 0.681874i | ||||||
\(891\) | 3.11438 | − | 1.14045i | 0.104336 | − | 0.0382066i | ||||
\(892\) | − | 5.42935i | − | 0.181788i | ||||||
\(893\) | − | 51.4281i | − | 1.72098i | ||||||
\(894\) | 7.22464i | 0.241628i | ||||||||
\(895\) | − | 9.42811i | − | 0.315147i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 27.5317i | − | 0.919258i | ||||||
\(898\) | − | 25.9959i | − | 0.867495i | ||||||
\(899\) | 30.8938 | 1.03037 | ||||||||
\(900\) | −5.68190 | −0.189397 | ||||||||
\(901\) | 66.7851 | 2.22493 | ||||||||
\(902\) | −1.08303 | − | 2.95758i | −0.0360611 | − | 0.0984766i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.41436i | 0.0803004i | ||||||||
\(905\) | −35.7395 | −1.18802 | ||||||||
\(906\) | − | 4.88028i | − | 0.162136i | ||||||
\(907\) | −18.5370 | −0.615512 | −0.307756 | − | 0.951465i | \(-0.599578\pi\) | ||||
−0.307756 | + | 0.951465i | \(0.599578\pi\) | |||||||
\(908\) | 11.8564 | 0.393467 | ||||||||
\(909\) | 13.1692 | 0.436796 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.6539 | −1.11500 | −0.557502 | − | 0.830176i | \(-0.688240\pi\) | ||||
−0.557502 | + | 0.830176i | \(0.688240\pi\) | |||||||
\(912\) | 4.27490i | 0.141556i | ||||||||
\(913\) | 2.60315 | − | 0.953245i | 0.0861516 | − | 0.0315478i | ||||
\(914\) | 8.03248 | 0.265691 | ||||||||
\(915\) | −17.4548 | −0.577037 | ||||||||
\(916\) | − | 6.42701i | − | 0.212354i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.32580 | −0.175777 | ||||||||
\(919\) | 13.7982i | 0.455160i | 0.973759 | + | 0.227580i | \(0.0730813\pi\) | ||||
−0.973759 | + | 0.227580i | \(0.926919\pi\) | |||||||
\(920\) | 17.5569 | 0.578835 | ||||||||
\(921\) | − | 1.37847i | − | 0.0454222i | ||||||
\(922\) | 33.5115i | 1.10364i | ||||||||
\(923\) | 55.3833 | 1.82296 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.1077 | −0.398100 | ||||||||
\(926\) | 15.7419i | 0.517310i | ||||||||
\(927\) | 13.2122i | 0.433944i | ||||||||
\(928\) | −4.77874 | −0.156870 | ||||||||
\(929\) | 31.4371i | 1.03142i | 0.856764 | + | 0.515709i | \(0.172471\pi\) | ||||
−0.856764 | + | 0.515709i | \(0.827529\pi\) | |||||||
\(930\) | 21.1292 | 0.692854 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.00886i | 0.0658023i | ||||||||
\(933\) | −10.5210 | −0.344444 | ||||||||
\(934\) | −10.2329 | −0.334830 | ||||||||
\(935\) | −19.8512 | − | 54.2102i | −0.649203 | − | 1.77286i | ||||
\(936\) | 5.12518i | 0.167522i | ||||||||
\(937\) | 13.0822 | 0.427377 | 0.213689 | − | 0.976902i | \(-0.431452\pi\) | ||||
0.213689 | + | 0.976902i | \(0.431452\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.26694 | 0.0739788 | ||||||||
\(940\) | 39.3187 | 1.28243 | ||||||||
\(941\) | 38.3447 | 1.25000 | 0.625001 | − | 0.780624i | \(-0.285099\pi\) | ||||
0.625001 | + | 0.780624i | \(0.285099\pi\) | |||||||
\(942\) | − | 3.30239i | − | 0.107598i | ||||||
\(943\) | 5.10140 | 0.166124 | ||||||||
\(944\) | − | 13.4844i | − | 0.438879i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.3242 | − | 7.07632i | 0.628284 | − | 0.230071i | ||||
\(947\) | 40.9405 | 1.33039 | 0.665193 | − | 0.746671i | \(-0.268349\pi\) | ||||
0.665193 | + | 0.746671i | \(0.268349\pi\) | |||||||
\(948\) | −9.16702 | −0.297731 | ||||||||
\(949\) | 67.8036 | 2.20100 | ||||||||
\(950\) | 24.2896i | 0.788057i | ||||||||
\(951\) | − | 4.94169i | − | 0.160245i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.7503i | 0.639776i | 0.947455 | + | 0.319888i | \(0.103645\pi\) | ||||
−0.947455 | + | 0.319888i | \(0.896355\pi\) | |||||||
\(954\) | 12.5399i | 0.405995i | ||||||||
\(955\) | − | 42.0860i | − | 1.36187i | ||||||
\(956\) | − | 4.65869i | − | 0.150673i | ||||||
\(957\) | 14.8828 | − | 5.44993i | 0.481093 | − | 0.176171i | ||||
\(958\) | − | 5.19626i | − | 0.167883i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.26832 | −0.105485 | ||||||||
\(961\) | −10.7943 | −0.348205 | ||||||||
\(962\) | 10.9214i | 0.352120i | ||||||||
\(963\) | − | 11.1094i | − | 0.357996i | ||||||
\(964\) | −5.96996 | −0.192279 | ||||||||
\(965\) | −19.7563 | −0.635977 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 36.4927i | − | 1.17352i | −0.809759 | − | 0.586762i | \(-0.800402\pi\) | ||
0.809759 | − | 0.586762i | \(-0.199598\pi\) | |||||||
\(968\) | 7.10361 | + | 8.39873i | 0.228319 | + | 0.269946i | ||||
\(969\) | 22.7672i | 0.731389i | ||||||||
\(970\) | 2.04053i | 0.0655176i | ||||||||
\(971\) | 51.4179i | 1.65008i | 0.565075 | + | 0.825039i | \(0.308847\pi\) | ||||
−0.565075 | + | 0.825039i | \(0.691153\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 31.5483i | 1.01087i | ||||||||
\(975\) | 29.1208i | 0.932611i | ||||||||
\(976\) | −5.34060 | −0.170948 | ||||||||
\(977\) | 7.81628 | 0.250065 | 0.125033 | − | 0.992153i | \(-0.460096\pi\) | ||||
0.125033 | + | 0.992153i | \(0.460096\pi\) | |||||||
\(978\) | −4.84536 | −0.154938 | ||||||||
\(979\) | 7.09827 | + | 19.3841i | 0.226862 | + | 0.619520i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 7.13138i | − | 0.227687i | ||||||
\(982\) | −7.14182 | −0.227905 | ||||||||
\(983\) | 14.7755i | 0.471264i | 0.971842 | + | 0.235632i | \(0.0757160\pi\) | ||||
−0.971842 | + | 0.235632i | \(0.924284\pi\) | |||||||
\(984\) | −0.949652 | −0.0302738 | ||||||||
\(985\) | 20.2060 | 0.643815 | ||||||||
\(986\) | −25.4506 | −0.810512 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 21.9096 | 0.697037 | ||||||||
\(989\) | 33.3315i | 1.05988i | ||||||||
\(990\) | 10.1788 | − | 3.72736i | 0.323503 | − | 0.118463i | ||||
\(991\) | −0.545492 | −0.0173281 | −0.00866407 | − | 0.999962i | \(-0.502758\pi\) | ||||
−0.00866407 | + | 0.999962i | \(0.502758\pi\) | |||||||
\(992\) | 6.46485 | 0.205259 | ||||||||
\(993\) | 12.9489i | 0.410922i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.6891 | −0.402272 | ||||||||
\(996\) | − | 0.835847i | − | 0.0264848i | ||||||
\(997\) | 37.9225 | 1.20102 | 0.600508 | − | 0.799619i | \(-0.294965\pi\) | ||||
0.600508 | + | 0.799619i | \(0.294965\pi\) | |||||||
\(998\) | 34.7635i | 1.10042i | ||||||||
\(999\) | − | 2.13093i | − | 0.0674196i |
(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 | 3234.2.e.b.2155.1 | 16 | ||
7.4 | even | 3 | 462.2.p.b.439.8 | yes | 16 | ||
7.5 | odd | 6 | 462.2.p.a.241.4 | ✓ | 16 | ||
7.6 | odd | 2 | 3234.2.e.a.2155.8 | 16 | |||
11.10 | odd | 2 | 3234.2.e.a.2155.9 | 16 | |||
21.5 | even | 6 | 1386.2.bk.a.703.5 | 16 | |||
21.11 | odd | 6 | 1386.2.bk.b.901.1 | 16 | |||
77.32 | odd | 6 | 462.2.p.a.439.4 | yes | 16 | ||
77.54 | even | 6 | 462.2.p.b.241.8 | yes | 16 | ||
77.76 | even | 2 | inner | 3234.2.e.b.2155.16 | 16 | ||
231.32 | even | 6 | 1386.2.bk.a.901.5 | 16 | |||
231.131 | odd | 6 | 1386.2.bk.b.703.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.p.a.241.4 | ✓ | 16 | 7.5 | odd | 6 | ||
462.2.p.a.439.4 | yes | 16 | 77.32 | odd | 6 | ||
462.2.p.b.241.8 | yes | 16 | 77.54 | even | 6 | ||
462.2.p.b.439.8 | yes | 16 | 7.4 | even | 3 | ||
1386.2.bk.a.703.5 | 16 | 21.5 | even | 6 | |||
1386.2.bk.a.901.5 | 16 | 231.32 | even | 6 | |||
1386.2.bk.b.703.1 | 16 | 231.131 | odd | 6 | |||
1386.2.bk.b.901.1 | 16 | 21.11 | odd | 6 | |||
3234.2.e.a.2155.8 | 16 | 7.6 | odd | 2 | |||
3234.2.e.a.2155.9 | 16 | 11.10 | odd | 2 | |||
3234.2.e.b.2155.1 | 16 | 1.1 | even | 1 | trivial | ||
3234.2.e.b.2155.16 | 16 | 77.76 | even | 2 | inner |