Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(865,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.s (of order \(3\), degree \(2\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.9391935744.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 12x^{5} - 76x^{4} + 84x^{3} + 245x^{2} - 1372x + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1297.1 | ||
Root | \(2.61033 + 0.431486i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.1297 |
Dual form | 1512.2.s.m.865.1 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.36603 | + | 2.36603i | −0.610905 | + | 1.05812i | 0.380183 | + | 0.924911i | \(0.375861\pi\) |
−0.991088 | + | 0.133207i | \(0.957472\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.931486 | − | 2.47635i | −0.352069 | − | 0.935974i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.17884 | + | 2.04182i | 0.355435 | + | 0.615631i | 0.987192 | − | 0.159535i | \(-0.0509996\pi\) |
−0.631758 | + | 0.775166i | \(0.717666\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.68476 | 1.85402 | 0.927009 | − | 0.375038i | \(-0.122370\pi\) | ||||
0.927009 | + | 0.375038i | \(0.122370\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.09808 | − | 3.63397i | −0.508858 | − | 0.881368i | −0.999947 | − | 0.0102590i | \(-0.996734\pi\) |
0.491089 | − | 0.871109i | \(-0.336599\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.80056 | + | 3.11867i | −0.413078 | + | 0.715472i | −0.995225 | − | 0.0976120i | \(-0.968880\pi\) |
0.582147 | + | 0.813084i | \(0.302213\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.40784 | + | 5.90255i | −0.710584 | + | 1.23077i | 0.254054 | + | 0.967190i | \(0.418236\pi\) |
−0.964638 | + | 0.263578i | \(0.915097\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.23205 | − | 2.13397i | −0.246410 | − | 0.426795i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00610 | 0.186829 | 0.0934145 | − | 0.995627i | \(-0.470222\pi\) | ||||
0.0934145 | + | 0.995627i | \(0.470222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.05321 | − | 1.82421i | −0.189162 | − | 0.327638i | 0.755809 | − | 0.654792i | \(-0.227244\pi\) |
−0.944971 | + | 0.327154i | \(0.893910\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.13155 | + | 1.17884i | 1.20545 | + | 0.199261i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.47941 | − | 4.29446i | 0.407612 | − | 0.706005i | −0.587010 | − | 0.809580i | \(-0.699695\pi\) |
0.994622 | + | 0.103575i | \(0.0330282\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.91152 | 1.39175 | 0.695873 | − | 0.718165i | \(-0.255018\pi\) | ||||
0.695873 | + | 0.718165i | \(0.255018\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.25127 | −0.343315 | −0.171658 | − | 0.985157i | \(-0.554912\pi\) | ||||
−0.171658 | + | 0.985157i | \(0.554912\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.85463 | + | 10.1405i | −0.853986 | + | 1.47915i | 0.0235965 | + | 0.999722i | \(0.492488\pi\) |
−0.877583 | + | 0.479426i | \(0.840845\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.26467 | + | 4.61338i | −0.752095 | + | 0.659055i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.13989 | + | 7.17050i | 0.568658 | + | 0.984944i | 0.996699 | + | 0.0811851i | \(0.0258705\pi\) |
−0.428041 | + | 0.903759i | \(0.640796\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.44132 | −0.868547 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.91089 | + | 10.2380i | 0.769533 | + | 1.33287i | 0.937817 | + | 0.347131i | \(0.112844\pi\) |
−0.168284 | + | 0.985739i | \(0.553822\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00592 | + | 10.4026i | −0.768979 | + | 1.33191i | 0.169138 | + | 0.985592i | \(0.445902\pi\) |
−0.938117 | + | 0.346318i | \(0.887432\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.13155 | + | 15.8163i | −1.13263 | + | 1.96177i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.03262 | + | 5.25264i | 0.370493 | + | 0.641713i | 0.989641 | − | 0.143561i | \(-0.0458554\pi\) |
−0.619149 | + | 0.785274i | \(0.712522\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.89358 | 0.580762 | 0.290381 | − | 0.956911i | \(-0.406218\pi\) | ||||
0.290381 | + | 0.956911i | \(0.406218\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.28917 | + | 3.96496i | 0.267927 | + | 0.464064i | 0.968326 | − | 0.249688i | \(-0.0803279\pi\) |
−0.700399 | + | 0.713751i | \(0.746995\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.95818 | − | 4.82116i | 0.451077 | − | 0.549422i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.252644 | − | 0.437591i | 0.0284246 | − | 0.0492329i | −0.851463 | − | 0.524414i | \(-0.824284\pi\) |
0.879888 | + | 0.475182i | \(0.157618\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.1900 | −1.22827 | −0.614134 | − | 0.789202i | \(-0.710494\pi\) | ||||
−0.614134 | + | 0.789202i | \(0.710494\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.4641 | 1.24346 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.22900 | + | 7.32484i | −0.448273 | + | 0.776431i | −0.998274 | − | 0.0587326i | \(-0.981294\pi\) |
0.550001 | + | 0.835164i | \(0.314627\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.22676 | − | 16.5538i | −0.652742 | − | 1.73531i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.91923 | − | 8.52036i | −0.504703 | − | 0.874171i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.25127 | 0.228582 | 0.114291 | − | 0.993447i | \(-0.463540\pi\) | ||||
0.114291 | + | 0.993447i | \(0.463540\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.53653 | + | 6.12545i | 0.351898 | + | 0.609505i | 0.986582 | − | 0.163267i | \(-0.0522031\pi\) |
−0.634684 | + | 0.772772i | \(0.718870\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.87828 | + | 4.98532i | −0.283605 | + | 0.491219i | −0.972270 | − | 0.233861i | \(-0.924864\pi\) |
0.688665 | + | 0.725080i | \(0.258197\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.04245 | − | 15.6620i | 0.874166 | − | 1.51410i | 0.0165180 | − | 0.999864i | \(-0.494742\pi\) |
0.857648 | − | 0.514237i | \(-0.171925\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00592 | + | 13.8667i | 0.766828 | + | 1.32818i | 0.939275 | + | 0.343166i | \(0.111499\pi\) |
−0.172447 | + | 0.985019i | \(0.555167\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.84457 | −0.267595 | −0.133797 | − | 0.991009i | \(-0.542717\pi\) | ||||
−0.133797 | + | 0.991009i | \(0.542717\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.31040 | − | 16.1261i | −0.868199 | − | 1.50376i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.04468 | + | 8.58058i | −0.645785 | + | 0.786580i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.72066 | − | 4.71232i | 0.247333 | − | 0.428393i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.92820 | −0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.64231 | −0.411939 | −0.205969 | − | 0.978558i | \(-0.566035\pi\) | ||||
−0.205969 | + | 0.978558i | \(0.566035\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.27692 | − | 5.67579i | 0.286306 | − | 0.495896i | −0.686619 | − | 0.727017i | \(-0.740906\pi\) |
0.972925 | + | 0.231121i | \(0.0742394\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.40013 | + | 1.55384i | 0.815095 | + | 0.134735i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.78221 | − | 10.0151i | −0.494007 | − | 0.855646i | 0.505969 | − | 0.862552i | \(-0.331135\pi\) |
−0.999976 | + | 0.00690610i | \(0.997802\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.5065 | −1.06079 | −0.530396 | − | 0.847750i | \(-0.677957\pi\) | ||||
−0.530396 | + | 0.847750i | \(0.677957\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.88028 | + | 13.6490i | 0.658982 | + | 1.14139i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.37436 | + | 2.38047i | −0.114135 | + | 0.197687i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.36603 | + | 5.83013i | −0.275756 | + | 0.477623i | −0.970325 | − | 0.241803i | \(-0.922261\pi\) |
0.694570 | + | 0.719425i | \(0.255595\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.41089 | + | 4.17579i | 0.196196 | + | 0.339821i | 0.947292 | − | 0.320372i | \(-0.103808\pi\) |
−0.751096 | + | 0.660193i | \(0.770475\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.75483 | 0.462239 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.5538 | − | 18.2798i | −0.842288 | − | 1.45889i | −0.887956 | − | 0.459929i | \(-0.847875\pi\) |
0.0456678 | − | 0.998957i | \(-0.485458\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.7912 | + | 2.94087i | 1.40214 | + | 0.231773i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.36297 | − | 11.0210i | 0.498387 | − | 0.863231i | −0.501612 | − | 0.865093i | \(-0.667259\pi\) |
0.999998 | + | 0.00186211i | \(0.000592727\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.4535 | −0.963683 | −0.481841 | − | 0.876258i | \(-0.660032\pi\) | ||||
−0.481841 | + | 0.876258i | \(0.660032\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.6860 | 2.43739 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.81282 | + | 16.9963i | −0.746055 | + | 1.29220i | 0.203646 | + | 0.979045i | \(0.434721\pi\) |
−0.949700 | + | 0.313160i | \(0.898612\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.13684 | + | 5.03876i | −0.312716 | + | 0.380895i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.50305 | − | 11.2636i | −0.486061 | − | 0.841882i | 0.513811 | − | 0.857904i | \(-0.328233\pi\) |
−0.999872 | + | 0.0160213i | \(0.994900\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.7684 | 1.17206 | 0.586028 | − | 0.810291i | \(-0.300691\pi\) | ||||
0.586028 | + | 0.810291i | \(0.300691\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.77387 | + | 11.7327i | 0.498025 | + | 0.862604i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.94660 | − | 8.56777i | 0.361732 | − | 0.626537i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.47244 | − | 4.28239i | 0.178900 | − | 0.309863i | −0.762604 | − | 0.646865i | \(-0.776080\pi\) |
0.941504 | + | 0.337002i | \(0.109413\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.92620 | − | 8.53243i | −0.354596 | − | 0.614178i | 0.632453 | − | 0.774599i | \(-0.282048\pi\) |
−0.987049 | + | 0.160421i | \(0.948715\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 27.0955 | 1.93047 | 0.965236 | − | 0.261380i | \(-0.0841775\pi\) | ||||
0.965236 | + | 0.261380i | \(0.0841775\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.7441 | + | 23.8054i | 0.974292 | + | 1.68752i | 0.682253 | + | 0.731116i | \(0.261000\pi\) |
0.292038 | + | 0.956407i | \(0.405667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.937173 | − | 2.49147i | −0.0657767 | − | 0.174867i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.1734 | + | 21.0849i | −0.850225 | + | 1.47263i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.49033 | −0.587288 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.66636 | 0.114717 | 0.0573584 | − | 0.998354i | \(-0.481732\pi\) | ||||
0.0573584 | + | 0.998354i | \(0.481732\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.07529 | − | 5.32656i | 0.209733 | − | 0.363269i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.53634 | + | 4.30734i | −0.240062 | + | 0.292401i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.0251 | − | 24.2922i | −0.943433 | − | 1.63407i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.19005 | 0.347551 | 0.173776 | − | 0.984785i | \(-0.444403\pi\) | ||||
0.173776 | + | 0.984785i | \(0.444403\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.05016 | − | 1.81892i | −0.0697013 | − | 0.120726i | 0.829069 | − | 0.559147i | \(-0.188871\pi\) |
−0.898770 | + | 0.438421i | \(0.855538\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6316 | − | 21.8785i | 0.834716 | − | 1.44577i | −0.0595446 | − | 0.998226i | \(-0.518965\pi\) |
0.894261 | − | 0.447546i | \(-0.147702\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.9862 | − | 19.0286i | 0.719729 | − | 1.24661i | −0.241378 | − | 0.970431i | \(-0.577599\pi\) |
0.961107 | − | 0.276176i | \(-0.0890673\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.9952 | − | 27.7044i | −1.04341 | − | 1.80724i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.3038 | 1.37803 | 0.689015 | − | 0.724747i | \(-0.258043\pi\) | ||||
0.689015 | + | 0.724747i | \(0.258043\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.17866 | + | 10.7017i | 0.398002 | + | 0.689360i | 0.993479 | − | 0.114012i | \(-0.0363703\pi\) |
−0.595477 | + | 0.803372i | \(0.703037\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.72371 | − | 18.7583i | −0.237899 | − | 1.19843i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.0363 | + | 20.8476i | −0.765854 | + | 1.32650i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.35158 | 0.0853110 | 0.0426555 | − | 0.999090i | \(-0.486418\pi\) | ||||
0.0426555 | + | 0.999090i | \(0.486418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.0692 | −1.01026 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.59502 | − | 9.69087i | 0.349008 | − | 0.604500i | −0.637066 | − | 0.770810i | \(-0.719852\pi\) |
0.986074 | + | 0.166310i | \(0.0531853\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.9441 | − | 2.13966i | −0.804310 | − | 0.132952i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.93540 | − | 12.0125i | −0.427655 | − | 0.740720i | 0.569009 | − | 0.822331i | \(-0.307327\pi\) |
−0.996664 | + | 0.0816108i | \(0.973994\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.6208 | −1.38958 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.9115 | − | 22.3634i | −0.787230 | − | 1.36352i | −0.927658 | − | 0.373431i | \(-0.878181\pi\) |
0.140429 | − | 0.990091i | \(-0.455152\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0895 | + | 20.9397i | −0.734388 | + | 1.27200i | 0.220604 | + | 0.975364i | \(0.429197\pi\) |
−0.954991 | + | 0.296633i | \(0.904136\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.90479 | − | 5.03124i | 0.175165 | − | 0.303395i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.03653 | + | 10.4556i | 0.362700 | + | 0.628215i | 0.988404 | − | 0.151846i | \(-0.0485217\pi\) |
−0.625704 | + | 0.780060i | \(0.715188\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.6554 | −0.635648 | −0.317824 | − | 0.948150i | \(-0.602952\pi\) | ||||
−0.317824 | + | 0.948150i | \(0.602952\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.23205 | − | 2.13397i | −0.0732378 | − | 0.126852i | 0.827081 | − | 0.562083i | \(-0.190000\pi\) |
−0.900319 | + | 0.435231i | \(0.856667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.30096 | − | 22.0681i | −0.489990 | − | 1.30264i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.303848 | + | 0.526279i | −0.0178734 | + | 0.0309576i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.38047 | −0.314330 | −0.157165 | − | 0.987572i | \(-0.550236\pi\) | ||||
−0.157165 | + | 0.987572i | \(0.550236\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −32.2977 | −1.88045 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −22.7806 | + | 39.4572i | −1.31744 | + | 2.28187i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.09703 | + | 5.57494i | 0.120871 | + | 0.321334i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.4085 | − | 28.4203i | −0.939546 | − | 1.62734i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.3083 | 1.04491 | 0.522455 | − | 0.852667i | \(-0.325016\pi\) | ||||
0.522455 | + | 0.852667i | \(0.325016\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.00063 | − | 1.73314i | −0.0567405 | − | 0.0982775i | 0.836260 | − | 0.548333i | \(-0.184737\pi\) |
−0.893000 | + | 0.450056i | \(0.851404\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.04401 | − | 3.54032i | 0.115534 | − | 0.200111i | −0.802459 | − | 0.596707i | \(-0.796475\pi\) |
0.917993 | + | 0.396596i | \(0.129809\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.88639 | + | 8.46347i | −0.274447 | + | 0.475356i | −0.969995 | − | 0.243123i | \(-0.921828\pi\) |
0.695549 | + | 0.718479i | \(0.255161\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.18604 | + | 2.05428i | 0.0664055 | + | 0.115018i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.1109 | 0.840792 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.23596 | − | 14.2651i | −0.456849 | − | 0.791286i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.5650 | + | 5.05239i | 1.68511 | + | 0.278547i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.8369 | − | 29.1624i | 0.925440 | − | 1.60291i | 0.134588 | − | 0.990902i | \(-0.457029\pi\) |
0.790852 | − | 0.612008i | \(-0.209638\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.5705 | −0.905344 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.7790 | 1.34980 | 0.674898 | − | 0.737911i | \(-0.264188\pi\) | ||||
0.674898 | + | 0.737911i | \(0.264188\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.48313 | − | 4.30091i | 0.134469 | − | 0.232908i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.3283 | + | 8.73988i | 0.881647 | + | 0.471909i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.53590 | − | 14.7846i | −0.458231 | − | 0.793679i | 0.540637 | − | 0.841256i | \(-0.318183\pi\) |
−0.998868 | + | 0.0475768i | \(0.984850\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.0714 | −0.592640 | −0.296320 | − | 0.955089i | \(-0.595759\pi\) | ||||
−0.296320 | + | 0.955089i | \(0.595759\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.0670 | − | 17.4365i | −0.535810 | − | 0.928050i | −0.999124 | − | 0.0418556i | \(-0.986673\pi\) |
0.463314 | − | 0.886194i | \(-0.346660\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.68476 | + | 11.5783i | −0.354790 | + | 0.614515i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.04245 | + | 15.6620i | −0.477242 | + | 0.826607i | −0.999660 | − | 0.0260822i | \(-0.991697\pi\) |
0.522418 | + | 0.852690i | \(0.325030\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.01594 | + | 5.22375i | 0.158733 | + | 0.274934i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.5083 | −0.654713 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.60441 | + | 4.51097i | 0.135949 | + | 0.235471i | 0.925960 | − | 0.377622i | \(-0.123258\pi\) |
−0.790010 | + | 0.613093i | \(0.789925\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.9005 | − | 16.9311i | 0.721676 | − | 0.879017i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.3299 | + | 17.8919i | −0.534862 | + | 0.926408i | 0.464308 | + | 0.885674i | \(0.346303\pi\) |
−0.999170 | + | 0.0407341i | \(0.987030\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.72557 | 0.346385 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.9829 | −1.43738 | −0.718691 | − | 0.695329i | \(-0.755259\pi\) | ||||
−0.718691 | + | 0.695329i | \(0.755259\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.11424 | − | 14.0543i | 0.414618 | − | 0.718140i | −0.580770 | − | 0.814068i | \(-0.697248\pi\) |
0.995388 | + | 0.0959276i | \(0.0305817\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | + | 15.9510i | 0.305788 | + | 0.812938i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.72434 | + | 8.18280i | 0.239534 | + | 0.414884i | 0.960581 | − | 0.278002i | \(-0.0896721\pi\) |
−0.721047 | + | 0.692886i | \(0.756339\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.5996 | 1.44635 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.690235 | + | 1.19552i | 0.0347295 | + | 0.0601532i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.64823 | − | 14.9792i | 0.434042 | − | 0.751783i | −0.563175 | − | 0.826338i | \(-0.690420\pi\) |
0.997217 | + | 0.0745546i | \(0.0237535\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.46347 | + | 4.26686i | −0.123020 | + | 0.213077i | −0.920957 | − | 0.389664i | \(-0.872591\pi\) |
0.797937 | + | 0.602740i | \(0.205925\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.04044 | − | 12.1944i | −0.350709 | − | 0.607447i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.6913 | 0.579518 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.63374 | + | 4.56178i | 0.130230 | + | 0.225565i | 0.923765 | − | 0.382959i | \(-0.125095\pi\) |
−0.793535 | + | 0.608525i | \(0.791762\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.8469 | − | 24.1740i | 0.976603 | − | 1.18952i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.2859 | − | 26.4759i | 0.750355 | − | 1.29965i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.06569 | −0.198622 | −0.0993110 | − | 0.995056i | \(-0.531664\pi\) | ||||
−0.0993110 | + | 0.995056i | \(0.531664\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.9479 | −0.874725 | −0.437363 | − | 0.899285i | \(-0.644087\pi\) | ||||
−0.437363 | + | 0.899285i | \(0.644087\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.16987 | + | 8.95448i | −0.250776 | + | 0.434356i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.3548 | + | 5.18294i | 1.51737 | + | 0.250820i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.4892 | − | 30.2922i | −0.842427 | − | 1.45913i | −0.887837 | − | 0.460158i | \(-0.847793\pi\) |
0.0454101 | − | 0.998968i | \(-0.485541\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6314 | −0.799252 | −0.399626 | − | 0.916678i | \(-0.630860\pi\) | ||||
−0.399626 | + | 0.916678i | \(0.630860\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.2721 | − | 21.2559i | −0.587053 | − | 1.01681i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.1550 | − | 17.5889i | 0.484670 | − | 0.839473i | −0.515175 | − | 0.857085i | \(-0.672273\pi\) |
0.999845 | + | 0.0176119i | \(0.00560632\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.65739 | − | 14.9950i | 0.411325 | − | 0.712436i | −0.583710 | − | 0.811962i | \(-0.698399\pi\) |
0.995035 | + | 0.0995265i | \(0.0317328\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.5538 | − | 20.0118i | −0.547704 | − | 0.948652i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.85030 | −0.417672 | −0.208836 | − | 0.977951i | \(-0.566967\pi\) | ||||
−0.208836 | + | 0.977951i | \(0.566967\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.5053 | + | 18.1957i | 0.494675 | + | 0.856802i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 47.6727 | + | 7.88028i | 2.23493 | + | 0.369433i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.51668 | + | 6.09107i | −0.164503 | + | 0.284928i | −0.936479 | − | 0.350724i | \(-0.885935\pi\) |
0.771975 | + | 0.635652i | \(0.219269\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.0452 | 0.514426 | 0.257213 | − | 0.966355i | \(-0.417196\pi\) | ||||
0.257213 | + | 0.966355i | \(0.417196\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.49597 | 0.115998 | 0.0579989 | − | 0.998317i | \(-0.481528\pi\) | ||||
0.0579989 | + | 0.998317i | \(0.481528\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.66135 | + | 15.0019i | −0.400799 | + | 0.694205i | −0.993823 | − | 0.110981i | \(-0.964601\pi\) |
0.593023 | + | 0.805185i | \(0.297934\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.1826 | − | 12.4026i | 0.470187 | − | 0.572699i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.65389 | − | 4.59668i | −0.122026 | − | 0.211356i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.87355 | 0.407146 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.44966 | − | 12.9032i | −0.340384 | − | 0.589562i | 0.644120 | − | 0.764924i | \(-0.277224\pi\) |
−0.984504 | + | 0.175363i | \(0.943890\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.5742 | − | 28.7074i | 0.755720 | − | 1.30895i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.07529 | + | 5.32656i | −0.139642 | + | 0.241867i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.0637 | + | 27.8231i | 0.727914 | + | 1.26078i | 0.957763 | + | 0.287558i | \(0.0928435\pi\) |
−0.229849 | + | 0.973226i | \(0.573823\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.3099 | −1.18735 | −0.593675 | − | 0.804705i | \(-0.702324\pi\) | ||||
−0.593675 | + | 0.804705i | \(0.702324\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.11088 | − | 3.65616i | −0.0950695 | − | 0.164665i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.55831 | − | 12.1183i | −0.204468 | − | 0.543578i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.94132 | − | 5.09451i | 0.131671 | − | 0.228062i | −0.792650 | − | 0.609678i | \(-0.791299\pi\) |
0.924321 | + | 0.381616i | \(0.124632\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.7798 | 1.50617 | 0.753083 | − | 0.657926i | \(-0.228566\pi\) | ||||
0.753083 | + | 0.657926i | \(0.228566\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.3240 | −0.859905 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.5902 | + | 28.7350i | −0.735347 | + | 1.27366i | 0.219224 | + | 0.975674i | \(0.429647\pi\) |
−0.954571 | + | 0.297983i | \(0.903686\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.68632 | − | 9.36211i | 0.340023 | − | 0.414155i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.86360 | − | 13.6202i | −0.346512 | − | 0.600176i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.6068 | −1.21414 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.8642 | + | 36.1379i | 0.914079 | + | 1.58323i | 0.808245 | + | 0.588847i | \(0.200418\pi\) |
0.105834 | + | 0.994384i | \(0.466249\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.9319 | − | 25.8629i | 0.652928 | − | 1.13090i | −0.329481 | − | 0.944162i | \(-0.606874\pi\) |
0.982409 | − | 0.186742i | \(-0.0597928\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.41942 | + | 7.65466i | −0.192513 | + | 0.333442i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.7268 | − | 20.3114i | −0.509859 | − | 0.883102i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 59.5714 | 2.58032 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.7044 | + | 42.7893i | 1.06807 | + | 1.84994i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.6259 | − | 5.31103i | −0.673055 | − | 0.228762i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.8903 | + | 20.5946i | −0.511204 | + | 0.885431i | 0.488712 | + | 0.872445i | \(0.337467\pi\) |
−0.999916 | + | 0.0129859i | \(0.995866\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −43.7451 | −1.87384 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.03499 | −0.343552 | −0.171776 | − | 0.985136i | \(-0.554950\pi\) | ||||
−0.171776 | + | 0.985136i | \(0.554950\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.81156 | + | 3.13771i | −0.0771749 | + | 0.133671i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.31897 | − | 0.218025i | −0.0560881 | − | 0.00927135i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.38397 | + | 16.2535i | 0.397611 | + | 0.688683i | 0.993431 | − | 0.114435i | \(-0.0365059\pi\) |
−0.595819 | + | 0.803119i | \(0.703173\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.0492 | −0.636513 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.0335 | + | 22.5746i | 0.549296 | + | 0.951408i | 0.998323 | + | 0.0578898i | \(0.0184372\pi\) |
−0.449027 | + | 0.893518i | \(0.648229\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.88576 | − | 6.73033i | 0.163475 | − | 0.283147i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.04792 | + | 8.74326i | −0.211620 | + | 0.366536i | −0.952222 | − | 0.305408i | \(-0.901207\pi\) |
0.740602 | + | 0.671944i | \(0.234541\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.50983 | + | 16.4715i | 0.397974 | + | 0.689311i | 0.993476 | − | 0.114043i | \(-0.0363801\pi\) |
−0.595502 | + | 0.803354i | \(0.703047\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.7945 | 0.700380 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.960818 | + | 1.66419i | 0.0399994 | + | 0.0692810i | 0.885332 | − | 0.464959i | \(-0.153931\pi\) |
−0.845333 | + | 0.534240i | \(0.820598\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.4234 | + | 27.7105i | 0.432435 | + | 1.14963i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.76056 | + | 16.9058i | −0.404241 | + | 0.700166i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.1471 | −0.418817 | −0.209409 | − | 0.977828i | \(-0.567154\pi\) | ||||
−0.209409 | + | 0.977828i | \(0.567154\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.58547 | 0.312554 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.85177 | + | 4.93941i | −0.117108 | + | 0.202837i | −0.918620 | − | 0.395141i | \(-0.870696\pi\) |
0.801512 | + | 0.597978i | \(0.204029\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.6787 | − | 28.3892i | −0.437782 | − | 1.16384i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.3833 | − | 28.3768i | −0.669405 | − | 1.15944i | −0.978071 | − | 0.208273i | \(-0.933216\pi\) |
0.308666 | − | 0.951171i | \(-0.400118\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.3712 | −1.36124 | −0.680619 | − | 0.732638i | \(-0.738289\pi\) | ||||
−0.680619 | + | 0.732638i | \(0.738289\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.43298 | + | 12.8743i | 0.302194 | + | 0.523415i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.5037 | + | 26.8532i | −0.629277 | + | 1.08994i | 0.358420 | + | 0.933560i | \(0.383315\pi\) |
−0.987697 | + | 0.156379i | \(0.950018\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39.1368 | + | 67.7870i | −1.58331 | + | 2.74237i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.394215 | − | 0.682800i | −0.0159222 | − | 0.0275780i | 0.857955 | − | 0.513726i | \(-0.171735\pi\) |
−0.873877 | + | 0.486148i | \(0.838402\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.534638 | −0.0215237 | −0.0107619 | − | 0.999942i | \(-0.503426\pi\) | ||||
−0.0107619 | + | 0.999942i | \(0.503426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.8238 | + | 18.7474i | 0.435045 | + | 0.753520i | 0.997299 | − | 0.0734444i | \(-0.0233992\pi\) |
−0.562254 | + | 0.826964i | \(0.690066\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.0782 | + | 3.64951i | 0.884543 | + | 0.146215i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.6244 | − | 27.0622i | 0.624974 | − | 1.08249i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.8079 | −0.829667 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.7378 | −0.785749 | −0.392874 | − | 0.919592i | \(-0.628519\pi\) | ||||
−0.392874 | + | 0.919592i | \(0.628519\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.34152 | − | 10.9838i | 0.251656 | − | 0.435880i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −35.1930 | + | 30.8394i | −1.39440 | + | 1.22190i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.6580 | − | 27.1205i | −0.618455 | − | 1.07119i | −0.989768 | − | 0.142687i | \(-0.954426\pi\) |
0.371313 | − | 0.928508i | \(-0.378908\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.2846 | 0.563331 | 0.281665 | − | 0.959513i | \(-0.409113\pi\) | ||||
0.281665 | + | 0.959513i | \(0.409113\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.10642 | − | 1.91637i | −0.0434977 | − | 0.0753402i | 0.843457 | − | 0.537197i | \(-0.180517\pi\) |
−0.886955 | + | 0.461857i | \(0.847183\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.9360 | + | 24.1379i | −0.547037 | + | 0.947496i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.1578 | − | 31.4503i | 0.710571 | − | 1.23074i | −0.254072 | − | 0.967185i | \(-0.581770\pi\) |
0.964643 | − | 0.263560i | \(-0.0848966\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.95271 | + | 15.5065i | 0.349811 | + | 0.605891i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.37474 | 0.287279 | 0.143640 | − | 0.989630i | \(-0.454119\pi\) | ||||
0.143640 | + | 0.989630i | \(0.454119\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0943 | − | 29.6082i | −0.664890 | − | 1.15162i | −0.979315 | − | 0.202342i | \(-0.935145\pi\) |
0.314425 | − | 0.949282i | \(-0.398188\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.5172 | + | 20.1184i | −0.640511 | + | 0.780157i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.42865 | + | 5.93859i | −0.132758 | + | 0.229943i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.3201 | −1.09329 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.7219 | 0.875866 | 0.437933 | − | 0.899008i | \(-0.355711\pi\) | ||||
0.437933 | + | 0.899008i | \(0.355711\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.7606 | + | 37.6904i | −0.836326 | + | 1.44856i | 0.0566194 | + | 0.998396i | \(0.481968\pi\) |
−0.892946 | + | 0.450164i | \(0.851365\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.09703 | − | 5.57494i | −0.0804765 | − | 0.213947i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.71875 | − | 13.3693i | −0.295350 | − | 0.511561i | 0.679716 | − | 0.733475i | \(-0.262103\pi\) |
−0.975066 | + | 0.221914i | \(0.928769\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.5946 | 1.20717 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.6742 | + | 47.9331i | 1.05430 | + | 1.82611i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.726764 | − | 1.25879i | 0.0276474 | − | 0.0478867i | −0.851871 | − | 0.523752i | \(-0.824532\pi\) |
0.879518 | + | 0.475866i | \(0.157865\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.0843 | − | 29.5908i | 0.648043 | − | 1.12244i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.6971 | − | 32.3843i | −0.708202 | − | 1.22664i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.25700 | −0.0474762 | −0.0237381 | − | 0.999718i | \(-0.507557\pi\) | ||||
−0.0237381 | + | 0.999718i | \(0.507557\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.92866 | + | 15.4649i | 0.336751 | + | 0.583270i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.8746 | − | 14.4635i | 0.446589 | − | 0.543955i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.971298 | + | 1.68234i | −0.0364779 | + | 0.0631815i | −0.883688 | − | 0.468076i | \(-0.844947\pi\) |
0.847210 | + | 0.531258i | \(0.178281\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.3567 | 0.537661 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −43.0587 | −1.61030 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.7817 | + | 34.2629i | −0.737733 | + | 1.27779i | 0.215781 | + | 0.976442i | \(0.430770\pi\) |
−0.953514 | + | 0.301349i | \(0.902563\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.0265 | + | 2.48388i | 0.559616 | + | 0.0925044i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.23957 | − | 2.14700i | −0.0460366 | − | 0.0797377i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.6317 | 0.431397 | 0.215699 | − | 0.976460i | \(-0.430797\pi\) | ||||
0.215699 | + | 0.976460i | \(0.430797\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.72334 | + | 8.18106i | 0.174699 | + | 0.302587i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.636397 | − | 1.10227i | 0.0235058 | − | 0.0407133i | −0.854033 | − | 0.520219i | \(-0.825850\pi\) |
0.877539 | + | 0.479505i | \(0.159184\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.14995 | + | 12.3841i | −0.263372 | + | 0.456174i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.279341 | − | 0.483833i | −0.0102757 | − | 0.0177981i | 0.860842 | − | 0.508873i | \(-0.169938\pi\) |
−0.871118 | + | 0.491075i | \(0.836604\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.2067 | −0.484508 | −0.242254 | − | 0.970213i | \(-0.577887\pi\) | ||||
−0.242254 | + | 0.970213i | \(0.577887\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.19615 | − | 15.9282i | −0.336921 | − | 0.583564i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −47.2075 | − | 7.80339i | −1.72493 | − | 0.285130i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.6281 | + | 35.7289i | −0.752729 | + | 1.30377i | 0.193766 | + | 0.981048i | \(0.437930\pi\) |
−0.946495 | + | 0.322718i | \(0.895404\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.1734 | −0.479428 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.7615 | 1.51785 | 0.758923 | − | 0.651181i | \(-0.225726\pi\) | ||||
0.758923 | + | 0.651181i | \(0.225726\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.3695 | − | 43.9413i | 0.919644 | − | 1.59287i | 0.119689 | − | 0.992811i | \(-0.461810\pi\) |
0.799955 | − | 0.600059i | \(-0.204856\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.8814 | − | 32.7421i | 0.973170 | − | 1.18534i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 39.5129 | + | 68.4384i | 1.42673 | + | 2.47117i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.16070 | 0.150039 | 0.0750193 | − | 0.997182i | \(-0.476098\pi\) | ||||
0.0750193 | + | 0.997182i | \(0.476098\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.0926 | + | 17.4809i | 0.363006 | + | 0.628744i | 0.988454 | − | 0.151521i | \(-0.0484172\pi\) |
−0.625448 | + | 0.780266i | \(0.715084\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.59521 | + | 4.49504i | −0.0932227 | + | 0.161467i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.0458 | + | 27.7921i | −0.574899 | + | 0.995755i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.76877 | + | 9.99180i | 0.206423 | + | 0.357535i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 57.6672 | 2.05823 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.0902 | − | 24.4049i | −0.502261 | − | 0.869941i | −0.999997 | − | 0.00261235i | \(-0.999168\pi\) |
0.497736 | − | 0.867329i | \(-0.334165\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.64968 | + | 7.04417i | 0.0942118 | + | 0.250462i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.1481 | + | 69.5386i | −1.42570 | + | 2.46939i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.44006 | −0.157275 | −0.0786374 | − | 0.996903i | \(-0.525057\pi\) | ||||
−0.0786374 | + | 0.996903i | \(0.525057\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 49.1339 | 1.73823 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.39715 | + | 9.34814i | −0.190461 | + | 0.329889i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.2614 | + | 38.0771i | −1.10182 | + | 1.34204i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.49918 | − | 2.59666i | −0.0527084 | − | 0.0912937i | 0.838467 | − | 0.544952i | \(-0.183452\pi\) |
−0.891176 | + | 0.453658i | \(0.850119\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.34674 | 0.152635 | 0.0763173 | − | 0.997084i | \(-0.475684\pi\) | ||||
0.0763173 | + | 0.997084i | \(0.475684\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.3840 | + | 30.1099i | 0.608934 | + | 1.05470i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.05356 | − | 7.02097i | 0.141816 | − | 0.245633i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.9601 | − | 32.8398i | 0.661711 | − | 1.14612i | −0.318455 | − | 0.947938i | \(-0.603164\pi\) |
0.980166 | − | 0.198179i | \(-0.0635028\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.8917 | + | 22.3290i | 0.449376 | + | 0.778341i | 0.998345 | − | 0.0575009i | \(-0.0183132\pi\) |
−0.548970 | + | 0.835842i | \(0.684980\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.4404 | 1.33670 | 0.668352 | − | 0.743845i | \(-0.267000\pi\) | ||||
0.668352 | + | 0.743845i | \(0.267000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.6224 | − | 47.8433i | −0.959364 | − | 1.66167i | −0.724050 | − | 0.689748i | \(-0.757721\pi\) |
−0.235314 | − | 0.971919i | \(-0.575612\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.8106 | + | 9.45244i | 0.963580 | + | 0.327507i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.0118 | − | 29.4654i | 0.588719 | − | 1.01969i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.23562 | 0.180754 | 0.0903768 | − | 0.995908i | \(-0.471193\pi\) | ||||
0.0903768 | + | 0.995908i | \(0.471193\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9878 | −0.965095 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −43.2839 | + | 74.9699i | −1.48901 | + | 2.57904i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.2036 | − | 2.34785i | −0.488043 | − | 0.0806732i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.8989 | + | 29.2697i | 0.579285 | + | 1.00335i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.99343 | 0.273690 | 0.136845 | − | 0.990592i | \(-0.456304\pi\) | ||||
0.136845 | + | 0.990592i | \(0.456304\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.7126 | + | 18.5548i | 0.365937 | + | 0.633821i | 0.988926 | − | 0.148409i | \(-0.0474152\pi\) |
−0.622989 | + | 0.782231i | \(0.714082\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.8589 | − | 27.4685i | 0.541100 | − | 0.937213i | −0.457741 | − | 0.889086i | \(-0.651341\pi\) |
0.998841 | − | 0.0481275i | \(-0.0153254\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.1823 | − | 22.8325i | 0.448732 | − | 0.777227i | −0.549572 | − | 0.835447i | \(-0.685209\pi\) |
0.998304 | + | 0.0582199i | \(0.0185424\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.8091 | − | 46.4348i | −0.911537 | − | 1.57883i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.19131 | 0.0404124 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.2723 | + | 35.1127i | 0.686901 | + | 1.18975i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.45353 | + | 17.1567i | 0.218169 | + | 0.580002i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.8868 | − | 36.1771i | 0.705298 | − | 1.22161i | −0.261286 | − | 0.965262i | \(-0.584146\pi\) |
0.966584 | − | 0.256351i | \(-0.0825202\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.3035 | −1.29048 | −0.645238 | − | 0.763982i | \(-0.723242\pi\) | ||||
−0.645238 | + | 0.763982i | \(0.723242\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.7097 | 1.67286 | 0.836432 | − | 0.548070i | \(-0.184637\pi\) | ||||
0.836432 | + | 0.548070i | \(0.184637\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.2338 | + | 38.5100i | −0.746536 | + | 1.29304i | 0.202937 | + | 0.979192i | \(0.434951\pi\) |
−0.949473 | + | 0.313847i | \(0.898382\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.32425 | + | 11.4960i | 0.145031 | + | 0.385564i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.0833 | − | 36.5173i | −0.705525 | − | 1.22201i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 35.5333 | 1.18775 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.05964 | − | 1.83535i | −0.0353409 | − | 0.0612122i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.3716 | − | 30.0885i | 0.578733 | − | 1.00239i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.5400 | + | 37.3084i | −0.716015 | + | 1.24017i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.51466 | − | 16.4799i | −0.315929 | − | 0.547205i | 0.663706 | − | 0.747994i | \(-0.268983\pi\) |
−0.979635 | + | 0.200789i | \(0.935649\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.7811 | 1.08609 | 0.543043 | − | 0.839705i | \(-0.317272\pi\) | ||||
0.543043 | + | 0.839705i | \(0.317272\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.1913 | − | 22.8480i | −0.436569 | − | 0.756159i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.1077 | − | 2.82789i | −0.564945 | − | 0.0933852i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.5944 | − | 51.2590i | 0.976228 | − | 1.69088i | 0.300408 | − | 0.953811i | \(-0.402877\pi\) |
0.675821 | − | 0.737066i | \(-0.263789\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.7124 | 1.07674 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.2190 | −0.401759 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.82001 | + | 10.0806i | −0.190948 | + | 0.330732i | −0.945565 | − | 0.325434i | \(-0.894490\pi\) |
0.754616 | + | 0.656166i | \(0.227823\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.90824 | − | 24.7254i | −0.160861 | − | 0.810344i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.5144 | + | 23.4076i | 0.441967 | + | 0.765510i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.7562 | −0.939424 | −0.469712 | − | 0.882820i | \(-0.655642\pi\) | ||||
−0.469712 | + | 0.882820i | \(0.655642\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.3947 | + | 47.4489i | 0.893040 | + | 1.54679i | 0.836211 | + | 0.548407i | \(0.184766\pi\) |
0.0568289 | + | 0.998384i | \(0.481901\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.3691 | + | 52.6008i | −0.988953 | + | 1.71292i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.96888 | − | 13.8025i | 0.258954 | − | 0.448521i | −0.707008 | − | 0.707205i | \(-0.749956\pi\) |
0.965962 | + | 0.258684i | \(0.0832890\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.3026 | + | 26.5048i | 0.496742 | + | 0.860383i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.6599 | −0.474880 | −0.237440 | − | 0.971402i | \(-0.576308\pi\) | ||||
−0.237440 | + | 0.971402i | \(0.576308\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.75483 | + | 11.6997i | 0.218581 | + | 0.378594i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.4148 | + | 23.6477i | −0.626938 | + | 0.763624i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.2815 | − | 23.0042i | 0.428436 | − | 0.742072i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.9173 | 0.866497 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.70591 | −0.215647 | −0.107824 | − | 0.994170i | \(-0.534388\pi\) | ||||
−0.107824 | + | 0.994170i | \(0.534388\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.7121 | − | 18.5540i | 0.343769 | − | 0.595425i | −0.641361 | − | 0.767240i | \(-0.721630\pi\) |
0.985129 | + | 0.171815i | \(0.0549631\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.6497 | + | 30.9706i | 0.373472 | + | 0.992873i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.1979 | − | 31.5196i | −0.582202 | − | 1.00840i | −0.995218 | − | 0.0976791i | \(-0.968858\pi\) |
0.413016 | − | 0.910724i | \(-0.364475\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.9413 | −0.637327 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.5055 | − | 47.6408i | −0.877288 | − | 1.51951i | −0.854306 | − | 0.519771i | \(-0.826017\pi\) |
−0.0229823 | − | 0.999736i | \(-0.507316\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −37.0131 | + | 64.1086i | −1.17934 | + | 2.04267i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.67197 | − | 13.2882i | 0.243954 | − | 0.422542i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.2596 | + | 47.2151i | 0.865931 | + | 1.49984i | 0.866120 | + | 0.499836i | \(0.166606\pi\) |
−0.000189141 | 1.00000i | \(0.500060\pi\) | ||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −75.0990 | −2.38080 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.975306 | + | 1.68928i | 0.0308883 | + | 0.0535000i | 0.881056 | − | 0.473011i | \(-0.156833\pi\) |
−0.850168 | + | 0.526511i | \(0.823500\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1512.2.s.m.1297.1 | yes | 8 | |
3.2 | odd | 2 | 1512.2.s.p.1297.3 | yes | 8 | ||
7.4 | even | 3 | inner | 1512.2.s.m.865.1 | ✓ | 8 | |
21.11 | odd | 6 | 1512.2.s.p.865.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.s.m.865.1 | ✓ | 8 | 7.4 | even | 3 | inner | |
1512.2.s.m.1297.1 | yes | 8 | 1.1 | even | 1 | trivial | |
1512.2.s.p.865.3 | yes | 8 | 21.11 | odd | 6 | ||
1512.2.s.p.1297.3 | yes | 8 | 3.2 | odd | 2 |