Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(49,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.s (of order \(6\), degree \(2\), not 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: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.49 |
Dual form | 1900.2.s.b.349.1 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.73205 | − | 1.00000i | −1.00000 | − | 0.577350i | −0.0917517 | − | 0.995782i | \(-0.529247\pi\) |
−0.908248 | + | 0.418432i | \(0.862580\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.00000i | 1.51186i | 0.654654 | + | 0.755929i | \(0.272814\pi\) | ||||
−0.654654 | + | 0.755929i | \(0.727186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.19615 | − | 3.00000i | 1.44115 | − | 0.832050i | 0.443227 | − | 0.896410i | \(-0.353834\pi\) |
0.997927 | + | 0.0643593i | \(0.0205004\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.73205 | + | 1.00000i | 0.420084 | + | 0.242536i | 0.695113 | − | 0.718900i | \(-0.255354\pi\) |
−0.275029 | + | 0.961436i | \(0.588688\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | − | 2.59808i | −0.802955 | − | 0.596040i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | − | 6.92820i | 0.872872 | − | 1.51186i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.46410 | − | 2.00000i | 0.722315 | − | 0.417029i | −0.0932891 | − | 0.995639i | \(-0.529738\pi\) |
0.815604 | + | 0.578610i | \(0.196405\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.500000 | + | 0.866025i | 0.0928477 | + | 0.160817i | 0.908708 | − | 0.417432i | \(-0.137070\pi\) |
−0.815861 | + | 0.578249i | \(0.803736\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.00000 | −0.898027 | −0.449013 | − | 0.893525i | \(-0.648224\pi\) | ||||
−0.449013 | + | 0.893525i | \(0.648224\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.19615 | + | 3.00000i | 0.904534 | + | 0.522233i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000i | 0.657596i | 0.944400 | + | 0.328798i | \(0.106644\pi\) | ||||
−0.944400 | + | 0.328798i | \(0.893356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.0000 | −1.92154 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | + | 1.73205i | −0.156174 | + | 0.270501i | −0.933486 | − | 0.358614i | \(-0.883249\pi\) |
0.777312 | + | 0.629115i | \(0.216583\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.19615 | + | 3.00000i | −0.757937 | + | 0.437595i | −0.828554 | − | 0.559908i | \(-0.810836\pi\) |
0.0706177 | + | 0.997503i | \(0.477503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.00000 | −1.28571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | − | 3.46410i | −0.280056 | − | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.19615 | + | 3.00000i | −0.713746 | + | 0.412082i | −0.812447 | − | 0.583036i | \(-0.801865\pi\) |
0.0987002 | + | 0.995117i | \(0.468532\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.46410 | + | 8.00000i | 0.458831 | + | 1.05963i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.500000 | + | 0.866025i | −0.0650945 | + | 0.112747i | −0.896736 | − | 0.442566i | \(-0.854068\pi\) |
0.831641 | + | 0.555313i | \(0.187402\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50000 | + | 6.06218i | 0.448129 | + | 0.776182i | 0.998264 | − | 0.0588933i | \(-0.0187572\pi\) |
−0.550135 | + | 0.835076i | \(0.685424\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.46410 | + | 2.00000i | −0.436436 | + | 0.251976i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.1244 | − | 7.00000i | 1.48123 | − | 0.855186i | 0.481452 | − | 0.876472i | \(-0.340109\pi\) |
0.999773 | + | 0.0212861i | \(0.00677610\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.00000 | −0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.50000 | + | 12.9904i | −0.890086 | + | 1.54167i | −0.0503155 | + | 0.998733i | \(0.516023\pi\) |
−0.839771 | + | 0.542941i | \(0.817311\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.3923 | − | 6.00000i | −1.21633 | − | 0.702247i | −0.252197 | − | 0.967676i | \(-0.581153\pi\) |
−0.964130 | + | 0.265429i | \(0.914486\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 12.0000i | − | 1.36753i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.500000 | + | 0.866025i | −0.0562544 | + | 0.0974355i | −0.892781 | − | 0.450490i | \(-0.851249\pi\) |
0.836527 | + | 0.547926i | \(0.184582\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.50000 | − | 9.52628i | 0.611111 | − | 1.05848i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.0000i | 1.75623i | 0.478451 | + | 0.878114i | \(0.341198\pi\) | ||||
−0.478451 | + | 0.878114i | \(0.658802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 2.00000i | − | 0.214423i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.50000 | + | 14.7224i | 0.900998 | + | 1.56057i | 0.826201 | + | 0.563376i | \(0.190498\pi\) |
0.0747975 | + | 0.997199i | \(0.476169\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | + | 20.7846i | 1.25794 | + | 2.17882i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.66025 | + | 5.00000i | 0.898027 | + | 0.518476i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3923 | + | 6.00000i | 1.05518 | + | 0.609208i | 0.924095 | − | 0.382164i | \(-0.124821\pi\) |
0.131084 | + | 0.991371i | \(0.458154\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.50000 | − | 2.59808i | −0.150756 | − | 0.261116i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.50000 | − | 9.52628i | −0.547270 | − | 0.947900i | −0.998460 | − | 0.0554722i | \(-0.982334\pi\) |
0.451190 | − | 0.892428i | \(-0.351000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000i | 1.16008i | 0.814587 | + | 0.580042i | \(0.196964\pi\) | ||||
−0.814587 | + | 0.580042i | \(0.803036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.50000 | − | 6.06218i | 0.335239 | − | 0.580651i | −0.648292 | − | 0.761392i | \(-0.724516\pi\) |
0.983531 | + | 0.180741i | \(0.0578495\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | − | 6.92820i | 0.379663 | − | 0.657596i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000i | 1.31701i | 0.752577 | + | 0.658505i | \(0.228811\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.19615 | + | 3.00000i | 0.480384 | + | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.00000 | + | 6.92820i | −0.366679 | + | 0.635107i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.46410 | − | 2.00000i | 0.312348 | − | 0.180334i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.5885 | + | 9.00000i | −1.38325 | + | 0.798621i | −0.992543 | − | 0.121894i | \(-0.961103\pi\) |
−0.390709 | + | 0.920514i | \(0.627770\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0000 | − | 17.3205i | 0.873704 | − | 1.51330i | 0.0155672 | − | 0.999879i | \(-0.495045\pi\) |
0.858137 | − | 0.513421i | \(-0.171622\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.3923 | − | 14.0000i | 0.901127 | − | 1.21395i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.3923 | + | 6.00000i | −0.887875 | + | 0.512615i | −0.873247 | − | 0.487278i | \(-0.837990\pi\) |
−0.0146279 | + | 0.999893i | \(0.504656\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0000 | 1.01058 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.5885 | + | 9.00000i | −1.30357 | + | 0.752618i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.5885 | + | 9.00000i | 1.28571 | + | 0.742307i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.50000 | + | 14.7224i | −0.696347 | + | 1.20611i | 0.273377 | + | 0.961907i | \(0.411859\pi\) |
−0.969724 | + | 0.244202i | \(0.921474\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.00000 | 0.244137 | 0.122068 | − | 0.992522i | \(-0.461047\pi\) | ||||
0.122068 | + | 0.992522i | \(0.461047\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000i | 0.161690i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.5885 | + | 9.00000i | 1.24409 | + | 0.718278i | 0.969925 | − | 0.243403i | \(-0.0782638\pi\) |
0.274169 | + | 0.961681i | \(0.411597\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.0000 | 0.951662 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.00000 | + | 13.8564i | 0.630488 | + | 1.09204i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.0000i | 1.40987i | 0.709273 | + | 0.704934i | \(0.249024\pi\) | ||||
−0.709273 | + | 0.704934i | \(0.750976\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.92820 | + | 4.00000i | −0.536120 | + | 0.309529i | −0.743505 | − | 0.668730i | \(-0.766838\pi\) |
0.207385 | + | 0.978259i | \(0.433505\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | − | 19.9186i | 0.884615 | − | 1.53220i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.500000 | − | 4.33013i | 0.0382360 | − | 0.331133i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.73205 | − | 1.00000i | 0.130189 | − | 0.0751646i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.0000 | 1.12115 | 0.560576 | − | 0.828103i | \(-0.310580\pi\) | ||||
0.560576 | + | 0.828103i | \(0.310580\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.00000 | − | 1.73205i | −0.0743294 | − | 0.128742i | 0.826465 | − | 0.562988i | \(-0.190348\pi\) |
−0.900794 | + | 0.434246i | \(0.857015\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 14.0000i | − | 1.03491i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.19615 | − | 3.00000i | −0.379980 | − | 0.219382i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −16.0000 | −1.16383 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.0000 | −0.940647 | −0.470323 | − | 0.882494i | \(-0.655863\pi\) | ||||
−0.470323 | + | 0.882494i | \(0.655863\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.8564 | − | 8.00000i | −0.997406 | − | 0.575853i | −0.0899262 | − | 0.995948i | \(-0.528663\pi\) |
−0.907480 | + | 0.420096i | \(0.861996\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.00000i | − | 0.142494i | −0.997459 | − | 0.0712470i | \(-0.977302\pi\) | ||
0.997459 | − | 0.0712470i | \(-0.0226979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.5000 | + | 19.9186i | 0.815213 | + | 1.41199i | 0.909175 | + | 0.416415i | \(0.136714\pi\) |
−0.0939612 | + | 0.995576i | \(0.529953\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −28.0000 | −1.97497 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.46410 | + | 2.00000i | −0.243132 | + | 0.140372i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.46410 | + | 2.00000i | 0.240772 | + | 0.139010i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.5000 | + | 7.79423i | 0.726300 | + | 0.539138i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.500000 | − | 0.866025i | 0.0344214 | − | 0.0596196i | −0.848301 | − | 0.529514i | \(-0.822374\pi\) |
0.882723 | + | 0.469894i | \(0.155708\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 25.9808 | − | 15.0000i | 1.78017 | − | 1.02778i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 20.0000i | − | 1.35769i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.0000 | + | 20.7846i | 0.810885 | + | 1.40449i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.92820 | − | 4.00000i | −0.463947 | − | 0.267860i | 0.249756 | − | 0.968309i | \(-0.419650\pi\) |
−0.713702 | + | 0.700449i | \(0.752983\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.00000i | 0.265489i | 0.991150 | + | 0.132745i | \(0.0423790\pi\) | ||||
−0.991150 | + | 0.132745i | \(0.957621\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.0000 | −1.38772 | −0.693860 | − | 0.720110i | \(-0.744091\pi\) | ||||
−0.693860 | + | 0.720110i | \(0.744091\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.0000 | + | 20.7846i | −0.789542 | + | 1.36753i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.66025 | + | 5.00000i | 0.567352 | + | 0.327561i | 0.756091 | − | 0.654466i | \(-0.227107\pi\) |
−0.188739 | + | 0.982027i | \(0.560440\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.73205 | − | 1.00000i | 0.112509 | − | 0.0649570i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.0000 | −0.970269 | −0.485135 | − | 0.874439i | \(-0.661229\pi\) | ||||
−0.485135 | + | 0.874439i | \(0.661229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.50000 | − | 4.33013i | −0.161039 | − | 0.278928i | 0.774202 | − | 0.632938i | \(-0.218151\pi\) |
−0.935242 | + | 0.354010i | \(0.884818\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.66025 | + | 5.00000i | −0.555556 | + | 0.320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.9808 | − | 3.00000i | −1.65312 | − | 0.190885i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.0000 | − | 27.7128i | 1.01396 | − | 1.75623i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.5000 | − | 26.8468i | −0.978351 | − | 1.69455i | −0.668400 | − | 0.743802i | \(-0.733021\pi\) |
−0.309951 | − | 0.950753i | \(-0.600313\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.3923 | + | 6.00000i | −0.653359 | + | 0.377217i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.5885 | + | 9.00000i | −0.972381 | + | 0.561405i | −0.899961 | − | 0.435970i | \(-0.856405\pi\) |
−0.0724199 | + | 0.997374i | \(0.523072\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.0000 | −0.994192 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.500000 | + | 0.866025i | −0.0309492 | + | 0.0536056i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.66025 | − | 5.00000i | −0.534014 | − | 0.308313i | 0.208635 | − | 0.977993i | \(-0.433098\pi\) |
−0.742650 | + | 0.669680i | \(0.766431\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 34.0000i | − | 2.08077i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.500000 | + | 0.866025i | −0.0304855 | + | 0.0528025i | −0.880866 | − | 0.473366i | \(-0.843039\pi\) |
0.850380 | + | 0.526169i | \(0.176372\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.50000 | + | 14.7224i | −0.516338 | + | 0.894324i | 0.483482 | + | 0.875354i | \(0.339372\pi\) |
−0.999820 | + | 0.0189696i | \(0.993961\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 48.0000i | − | 2.90509i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 16.0000i | − | 0.961347i | −0.876900 | − | 0.480673i | \(-0.840392\pi\) | ||
0.876900 | − | 0.480673i | \(-0.159608\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.50000 | − | 4.33013i | −0.149671 | − | 0.259238i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.0000 | + | 22.5167i | 0.775515 | + | 1.34323i | 0.934505 | + | 0.355951i | \(0.115843\pi\) |
−0.158990 | + | 0.987280i | \(0.550824\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.5167 | + | 13.0000i | 1.33848 | + | 0.772770i | 0.986581 | − | 0.163270i | \(-0.0522041\pi\) |
0.351895 | + | 0.936039i | \(0.385537\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.92820 | − | 4.00000i | −0.408959 | − | 0.236113i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.50000 | − | 11.2583i | −0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.0000 | − | 20.7846i | −0.703452 | − | 1.21842i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.0000i | 0.934730i | 0.884064 | + | 0.467365i | \(0.154797\pi\) | ||||
−0.884064 | + | 0.467365i | \(0.845203\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 12.0000i | − | 0.696311i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.0000 | − | 20.7846i | 0.693978 | − | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.0000i | 1.26387i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.1244 | − | 7.00000i | −0.691974 | − | 0.399511i | 0.112377 | − | 0.993666i | \(-0.464153\pi\) |
−0.804351 | + | 0.594154i | \(0.797487\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.4449 | − | 17.0000i | 1.66432 | − | 0.960897i | 0.693708 | − | 0.720257i | \(-0.255976\pi\) |
0.970614 | − | 0.240640i | \(-0.0773574\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.3923 | − | 6.00000i | 0.583690 | − | 0.336994i | −0.178908 | − | 0.983866i | \(-0.557257\pi\) |
0.762598 | + | 0.646872i | \(0.223923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.50000 | − | 2.59808i | −0.0839839 | − | 0.145464i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0000 | − | 20.7846i | 0.669775 | − | 1.16008i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.46410 | − | 8.00000i | −0.192748 | − | 0.445132i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.1244 | + | 7.00000i | −0.670478 | + | 0.387101i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.0000 | − | 20.7846i | −0.661581 | − | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0000 | −1.09930 | −0.549650 | − | 0.835395i | \(-0.685239\pi\) | ||||
−0.549650 | + | 0.835395i | \(0.685239\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.46410 | + | 2.00000i | −0.189832 | + | 0.109599i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.46410 | + | 2.00000i | 0.188702 | + | 0.108947i | 0.591375 | − | 0.806397i | \(-0.298585\pi\) |
−0.402673 | + | 0.915344i | \(0.631919\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.0000 | − | 24.2487i | 0.760376 | − | 1.31701i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.0000 | 0.812296 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.00000i | − | 0.431959i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.3923 | + | 6.00000i | 0.557888 | + | 0.322097i | 0.752297 | − | 0.658824i | \(-0.228946\pi\) |
−0.194409 | + | 0.980921i | \(0.562279\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.0000 | + | 20.7846i | 0.640513 | + | 1.10940i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 36.0000i | − | 1.91609i | −0.286623 | − | 0.958043i | \(-0.592533\pi\) | ||
0.286623 | − | 0.958043i | \(-0.407467\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.8564 | − | 8.00000i | 0.733359 | − | 0.423405i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | + | 18.1865i | 0.289474 | + | 0.957186i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.46410 | + | 2.00000i | 0.181818 | + | 0.104973i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.2487 | − | 14.0000i | 1.26577 | − | 0.730794i | 0.291587 | − | 0.956544i | \(-0.405817\pi\) |
0.974185 | + | 0.225750i | \(0.0724833\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | − | 20.7846i | −0.623009 | − | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 12.0000i | − | 0.621336i | −0.950518 | − | 0.310668i | \(-0.899447\pi\) | ||
0.950518 | − | 0.310668i | \(-0.100553\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.19615 | + | 3.00000i | 0.267615 | + | 0.154508i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.0000 | 0.975964 | 0.487982 | − | 0.872854i | \(-0.337733\pi\) | ||||
0.487982 | + | 0.872854i | \(0.337733\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 36.0000 | 1.84434 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.5885 | + | 9.00000i | 0.796533 | + | 0.459879i | 0.842257 | − | 0.539076i | \(-0.181226\pi\) |
−0.0457244 | + | 0.998954i | \(0.514560\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.5000 | − | 18.1865i | −0.532371 | − | 0.922094i | −0.999286 | − | 0.0377914i | \(-0.987968\pi\) |
0.466915 | − | 0.884302i | \(-0.345366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −34.6410 | + | 20.0000i | −1.74741 | + | 1.00887i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.92820 | − | 4.00000i | −0.347717 | − | 0.200754i | 0.315963 | − | 0.948772i | \(-0.397673\pi\) |
−0.663679 | + | 0.748017i | \(0.731006\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −32.0000 | + | 13.8564i | −1.60200 | + | 0.693688i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.50000 | + | 12.9904i | −0.374532 | + | 0.648709i | −0.990257 | − | 0.139253i | \(-0.955530\pi\) |
0.615725 | + | 0.787961i | \(0.288863\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.9808 | + | 15.0000i | −1.29419 | + | 0.747203i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 12.0000i | − | 0.594818i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.500000 | − | 0.866025i | −0.0247234 | − | 0.0428222i | 0.853399 | − | 0.521258i | \(-0.174537\pi\) |
−0.878122 | + | 0.478436i | \(0.841204\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.0000 | 1.18383 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.46410 | − | 2.00000i | −0.170457 | − | 0.0984136i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.00000 | 0.244266 | 0.122133 | − | 0.992514i | \(-0.461027\pi\) | ||||
0.122133 | + | 0.992514i | \(0.461027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.5000 | + | 21.6506i | −0.609213 | + | 1.05519i | 0.382158 | + | 0.924097i | \(0.375181\pi\) |
−0.991370 | + | 0.131090i | \(0.958152\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.19615 | − | 3.00000i | −0.252646 | − | 0.145865i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.2487 | + | 14.0000i | −1.17348 | + | 0.677507i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 36.0000 | 1.73810 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.5000 | − | 23.3827i | −0.650272 | − | 1.12630i | −0.983057 | − | 0.183301i | \(-0.941322\pi\) |
0.332785 | − | 0.943003i | \(-0.392012\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −17.3205 | − | 2.00000i | −0.828552 | − | 0.0956730i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.500000 | − | 0.866025i | 0.0238637 | − | 0.0413331i | −0.853847 | − | 0.520524i | \(-0.825737\pi\) |
0.877711 | + | 0.479191i | \(0.159070\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.50000 | − | 7.79423i | −0.214286 | − | 0.371154i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.3923 | + | 6.00000i | −0.493753 | + | 0.285069i | −0.726130 | − | 0.687557i | \(-0.758683\pi\) |
0.232377 | + | 0.972626i | \(0.425350\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 29.4449 | − | 17.0000i | 1.39269 | − | 0.804072i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.00000 | 0.0471929 | 0.0235965 | − | 0.999722i | \(-0.492488\pi\) | ||||
0.0235965 | + | 0.999722i | \(0.492488\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.00000 | − | 5.19615i | 0.141264 | − | 0.244677i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.19615 | − | 3.00000i | −0.244137 | − | 0.140952i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.00000i | 0.0935561i | 0.998905 | + | 0.0467780i | \(0.0148953\pi\) | ||||
−0.998905 | + | 0.0467780i | \(0.985105\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.00000 | + | 6.92820i | −0.186704 | + | 0.323381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.5000 | + | 30.3109i | −0.815056 | + | 1.41172i | 0.0942312 | + | 0.995550i | \(0.469961\pi\) |
−0.909288 | + | 0.416169i | \(0.863373\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.00000i | − | 0.371792i | −0.982569 | − | 0.185896i | \(-0.940481\pi\) | ||
0.982569 | − | 0.185896i | \(-0.0595187\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.0000i | 0.925490i | 0.886492 | + | 0.462745i | \(0.153135\pi\) | ||||
−0.886492 | + | 0.462745i | \(0.846865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.0000 | + | 48.4974i | 1.29292 | + | 2.23940i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.0000 | − | 31.1769i | −0.829396 | − | 1.43656i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.19615 | − | 3.00000i | −0.237915 | − | 0.137361i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.50000 | − | 2.59808i | −0.0685367 | − | 0.118709i | 0.829721 | − | 0.558179i | \(-0.188500\pi\) |
−0.898257 | + | 0.439470i | \(0.855166\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | + | 20.7846i | 0.547153 | + | 0.947697i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 32.0000i | − | 1.45605i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 34.0000i | − | 1.54069i | −0.637629 | − | 0.770344i | \(-0.720085\pi\) | ||
0.637629 | − | 0.770344i | \(-0.279915\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.0000 | − | 31.1769i | 0.813988 | − | 1.40987i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.5000 | − | 21.6506i | 0.564117 | − | 0.977079i | −0.433014 | − | 0.901387i | \(-0.642550\pi\) |
0.997131 | − | 0.0756923i | \(-0.0241167\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.00000i | 0.0900755i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −51.9615 | − | 30.0000i | −2.33079 | − | 1.34568i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.0000 | − | 31.1769i | 0.805791 | − | 1.39567i | −0.109965 | − | 0.993935i | \(-0.535074\pi\) |
0.915756 | − | 0.401735i | \(-0.131593\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.0000 | 0.714827 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.0526 | − | 11.0000i | 0.849512 | − | 0.490466i | −0.0109744 | − | 0.999940i | \(-0.503493\pi\) |
0.860486 | + | 0.509474i | \(0.170160\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −39.8372 | + | 23.0000i | −1.76923 | + | 1.02147i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.0000 | + | 25.9808i | 0.664863 | + | 1.15158i | 0.979322 | + | 0.202306i | \(0.0648436\pi\) |
−0.314459 | + | 0.949271i | \(0.601823\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.0000 | − | 41.5692i | 1.06170 | − | 1.83891i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.3923 | − | 14.0000i | 0.458831 | − | 0.618115i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.5885 | − | 9.00000i | 0.685580 | − | 0.395820i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −45.0000 | −1.97149 | −0.985743 | − | 0.168259i | \(-0.946186\pi\) | ||||
−0.985743 | + | 0.168259i | \(0.946186\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.66025 | + | 5.00000i | −0.378686 | + | 0.218635i | −0.677247 | − | 0.735756i | \(-0.736827\pi\) |
0.298560 | + | 0.954391i | \(0.403494\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.66025 | − | 5.00000i | −0.377247 | − | 0.217803i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.50000 | + | 6.06218i | −0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000i | 0.519778i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −25.9808 | − | 15.0000i | −1.12115 | − | 0.647298i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.0000 | 1.16297 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5000 | + | 21.6506i | 0.537417 | + | 0.930834i | 0.999042 | + | 0.0437584i | \(0.0139332\pi\) |
−0.461625 | + | 0.887075i | \(0.652733\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.00000i | 0.171656i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.92820 | − | 4.00000i | 0.296229 | − | 0.171028i | −0.344519 | − | 0.938779i | \(-0.611958\pi\) |
0.640747 | + | 0.767752i | \(0.278625\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.50000 | + | 6.06218i | −0.149376 | + | 0.258727i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.500000 | − | 4.33013i | 0.0213007 | − | 0.184470i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.46410 | − | 2.00000i | −0.147309 | − | 0.0850487i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.6410 | − | 20.0000i | 1.46779 | − | 0.847427i | 0.468438 | − | 0.883497i | \(-0.344817\pi\) |
0.999349 | + | 0.0360693i | \(0.0114837\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.00000 | + | 10.3923i | 0.253320 | + | 0.438763i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.0000i | 0.421450i | 0.977545 | + | 0.210725i | \(0.0675824\pi\) | ||||
−0.977545 | + | 0.210725i | \(0.932418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 38.1051 | + | 22.0000i | 1.60026 | + | 0.923913i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.0000 | 0.712677 | 0.356339 | − | 0.934357i | \(-0.384025\pi\) | ||||
0.356339 | + | 0.934357i | \(0.384025\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.0000 | −0.711428 | −0.355714 | − | 0.934595i | \(-0.615762\pi\) | ||||
−0.355714 | + | 0.934595i | \(0.615762\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.5167 | + | 13.0000i | 0.940647 | + | 0.543083i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.0000i | 0.832611i | 0.909225 | + | 0.416305i | \(0.136675\pi\) | ||||
−0.909225 | + | 0.416305i | \(0.863325\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.0000 | + | 27.7128i | 0.664937 | + | 1.15171i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −64.0000 | −2.65517 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.5885 | − | 9.00000i | 0.645608 | − | 0.372742i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.3923 | − | 6.00000i | −0.428936 | − | 0.247647i | 0.269957 | − | 0.962872i | \(-0.412990\pi\) |
−0.698893 | + | 0.715226i | \(0.746324\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.5000 | + | 12.9904i | 0.721075 | + | 0.535259i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.00000 | + | 3.46410i | −0.0822690 | + | 0.142494i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.46410 | + | 2.00000i | −0.142254 | + | 0.0821302i | −0.569438 | − | 0.822035i | \(-0.692839\pi\) |
0.427184 | + | 0.904165i | \(0.359506\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 46.0000i | − | 1.88265i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.0000 | − | 20.7846i | −0.490307 | − | 0.849236i | 0.509631 | − | 0.860393i | \(-0.329782\pi\) |
−0.999938 | + | 0.0111569i | \(0.996449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0000 | 0.693444 | 0.346722 | − | 0.937968i | \(-0.387295\pi\) | ||||
0.346722 | + | 0.937968i | \(0.387295\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.1244 | + | 7.00000i | 0.493742 | + | 0.285062i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.0000i | 0.568242i | 0.958788 | + | 0.284121i | \(0.0917018\pi\) | ||||
−0.958788 | + | 0.284121i | \(0.908298\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.00000 | 0.324176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.0000 | + | 31.1769i | −0.728202 | + | 1.26128i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.0526 | + | 11.0000i | 0.769526 | + | 0.444286i | 0.832705 | − | 0.553716i | \(-0.186791\pi\) |
−0.0631797 | + | 0.998002i | \(0.520124\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.92820 | − | 4.00000i | 0.278919 | − | 0.161034i | −0.354015 | − | 0.935240i | \(-0.615184\pi\) |
0.632934 | + | 0.774206i | \(0.281850\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.0000 | 0.803868 | 0.401934 | − | 0.915669i | \(-0.368338\pi\) | ||||
0.401934 | + | 0.915669i | \(0.368338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.00000 | + | 13.8564i | 0.321029 | + | 0.556038i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −58.8897 | + | 34.0000i | −2.35937 | + | 1.36218i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.3923 | − | 24.0000i | −0.415029 | − | 0.958468i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.00000 | + | 6.92820i | −0.159490 | + | 0.276246i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.5000 | + | 28.5788i | 0.656855 | + | 1.13771i | 0.981425 | + | 0.191844i | \(0.0614468\pi\) |
−0.324571 | + | 0.945861i | \(0.605220\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.73205 | + | 1.00000i | −0.0688428 | + | 0.0397464i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −46.7654 | + | 27.0000i | −1.85291 | + | 1.06978i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.0000 | −0.593391 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.50000 | + | 7.79423i | −0.177739 | + | 0.307854i | −0.941106 | − | 0.338112i | \(-0.890212\pi\) |
0.763367 | + | 0.645966i | \(0.223545\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.73205 | + | 1.00000i | 0.0683054 | + | 0.0394362i | 0.533764 | − | 0.845634i | \(-0.320777\pi\) |
−0.465458 | + | 0.885070i | \(0.654110\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.0000i | 1.17942i | 0.807614 | + | 0.589711i | \(0.200758\pi\) | ||||
−0.807614 | + | 0.589711i | \(0.799242\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.50000 | − | 2.59808i | 0.0588802 | − | 0.101983i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.0000 | + | 34.6410i | −0.783862 | + | 1.35769i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.0000i | 0.469596i | 0.972044 | + | 0.234798i | \(0.0754429\pi\) | ||||
−0.972044 | + | 0.234798i | \(0.924557\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 12.0000i | − | 0.468165i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.0000 | − | 31.1769i | −0.701180 | − | 1.21448i | −0.968052 | − | 0.250748i | \(-0.919323\pi\) |
0.266872 | − | 0.963732i | \(-0.414010\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.5000 | − | 35.5070i | −0.797358 | − | 1.38106i | −0.921331 | − | 0.388778i | \(-0.872897\pi\) |
0.123974 | − | 0.992286i | \(-0.460436\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −20.7846 | − | 12.0000i | −0.807207 | − | 0.466041i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.46410 | + | 2.00000i | 0.134131 | + | 0.0774403i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.00000 | + | 13.8564i | 0.309298 | + | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.5000 | − | 18.1865i | −0.405348 | − | 0.702083i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 28.0000i | − | 1.07932i | −0.841883 | − | 0.539660i | \(-0.818553\pi\) | ||
0.841883 | − | 0.539660i | \(-0.181447\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.0000i | 1.22986i | 0.788582 | + | 0.614930i | \(0.210816\pi\) | ||||
−0.788582 | + | 0.614930i | \(0.789184\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.0000 | + | 41.5692i | −0.921035 | + | 1.59528i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.00000 | − | 6.92820i | 0.153280 | − | 0.265489i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.00000i | 0.229584i | 0.993390 | + | 0.114792i | \(0.0366201\pi\) | ||||
−0.993390 | + | 0.114792i | \(0.963380\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 36.3731 | + | 21.0000i | 1.38772 | + | 0.801200i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.0000 | + | 31.1769i | −0.685745 | + | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.0000 | 1.40755 | 0.703773 | − | 0.710425i | \(-0.251497\pi\) | ||||
0.703773 | + | 0.710425i | \(0.251497\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.3923 | − | 6.00000i | 0.394771 | − | 0.227921i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.46410 | + | 2.00000i | −0.131212 | + | 0.0757554i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.0000 | − | 17.3205i | −0.378235 | − | 0.655122i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.0000 | − | 36.3731i | 0.793159 | − | 1.37379i | −0.130843 | − | 0.991403i | \(-0.541768\pi\) |
0.924002 | − | 0.382389i | \(-0.124898\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.3923 | − | 14.0000i | 0.391953 | − | 0.528020i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.1051 | − | 22.0000i | 1.43309 | − | 0.827395i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.50000 | + | 4.33013i | 0.0938895 | + | 0.162621i | 0.909145 | − | 0.416481i | \(-0.136737\pi\) |
−0.815255 | + | 0.579102i | \(0.803403\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.00000 | −0.0375029 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.3205 | + | 10.0000i | −0.648658 | + | 0.374503i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.9808 | + | 15.0000i | 0.970269 | + | 0.560185i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.5000 | − | 25.1147i | 0.540759 | − | 0.936622i | −0.458102 | − | 0.888900i | \(-0.651471\pi\) |
0.998861 | − | 0.0477220i | \(-0.0151961\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.0000i | 0.371904i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.5167 | + | 13.0000i | 0.835097 | + | 0.482143i | 0.855595 | − | 0.517647i | \(-0.173192\pi\) |
−0.0204978 | + | 0.999790i | \(0.506525\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 12.0000i | − | 0.443230i | −0.975134 | − | 0.221615i | \(-0.928867\pi\) | ||
0.975134 | − | 0.221615i | \(-0.0711328\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −36.3731 | + | 21.0000i | −1.33982 | + | 0.773545i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.50000 | + | 16.4545i | −0.349463 | + | 0.605288i | −0.986154 | − | 0.165831i | \(-0.946969\pi\) |
0.636691 | + | 0.771119i | \(0.280303\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 42.0000 | + | 31.1769i | 1.54291 | + | 1.14531i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.0333 | − | 26.0000i | −1.65211 | − | 0.953847i | −0.976202 | − | 0.216864i | \(-0.930417\pi\) |
−0.675910 | − | 0.736984i | \(-0.736249\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.8564 | + | 8.00000i | −0.506979 | + | 0.292705i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −48.0000 | −1.75388 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.50000 | − | 16.4545i | −0.346660 | − | 0.600433i | 0.638994 | − | 0.769212i | \(-0.279351\pi\) |
−0.985654 | + | 0.168779i | \(0.946018\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 62.0000i | 2.25941i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.1244 | − | 7.00000i | −0.440667 | − | 0.254419i | 0.263213 | − | 0.964738i | \(-0.415218\pi\) |
−0.703881 | + | 0.710318i | \(0.748551\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 24.0000 | 0.871145 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 54.0000 | 1.95750 | 0.978749 | − | 0.205061i | \(-0.0657392\pi\) | ||||
0.978749 | + | 0.205061i | \(0.0657392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.2487 | + | 14.0000i | 0.877862 | + | 0.506834i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.00000i | 0.216647i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.50000 | + | 11.2583i | 0.234396 | + | 0.405986i | 0.959097 | − | 0.283078i | \(-0.0913554\pi\) |
−0.724701 | + | 0.689063i | \(0.758022\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.0000 | 1.29651 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −46.7654 | + | 27.0000i | −1.68203 | + | 0.971123i | −0.721726 | + | 0.692179i | \(0.756651\pi\) |
−0.960307 | + | 0.278944i | \(0.910016\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 27.7128 | + | 16.0000i | 0.994192 | + | 0.573997i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.00000 | − | 3.46410i | 0.286630 | − | 0.124114i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.5000 | − | 38.9711i | 0.805113 | − | 1.39450i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.46410 | + | 2.00000i | −0.123797 | + | 0.0714742i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 38.0000i | − | 1.35455i | −0.735728 | − | 0.677277i | \(-0.763160\pi\) | ||
0.735728 | − | 0.677277i | \(-0.236840\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.0000 | + | 17.3205i | 0.356009 | + | 0.616626i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −56.0000 | −1.99113 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.3731 | + | 21.0000i | 1.29165 | + | 0.745732i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.0000i | 0.779280i | 0.920967 | + | 0.389640i | \(0.127401\pi\) | ||||
−0.920967 | + | 0.389640i | \(0.872599\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.0000 | −0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.50000 | + | 14.7224i | −0.300333 | + | 0.520192i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.1769 | + | 18.0000i | 1.10021 | + | 0.635206i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.73205 | − | 1.00000i | 0.0609711 | − | 0.0352017i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.0000 | −1.58212 | −0.791058 | − | 0.611741i | \(-0.790469\pi\) | ||||
−0.791058 | + | 0.611741i | \(0.790469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.50000 | + | 11.2583i | 0.228246 | + | 0.395333i | 0.957288 | − | 0.289135i | \(-0.0933677\pi\) |
−0.729042 | + | 0.684468i | \(0.760034\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.4449 | − | 17.0000i | 1.03268 | − | 0.596216i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.0000 | + | 20.7846i | −0.419314 | + | 0.726273i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.5000 | − | 21.6506i | −0.436253 | − | 0.755612i | 0.561144 | − | 0.827718i | \(-0.310361\pi\) |
−0.997397 | + | 0.0721058i | \(0.977028\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.5167 | − | 13.0000i | 0.784881 | − | 0.453152i | −0.0532760 | − | 0.998580i | \(-0.516966\pi\) |
0.838157 | + | 0.545428i | \(0.183633\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.5885 | − | 9.00000i | 0.542064 | − | 0.312961i | −0.203851 | − | 0.979002i | \(-0.565346\pi\) |
0.745915 | + | 0.666041i | \(0.232013\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.0000 | 1.04194 | 0.520972 | − | 0.853574i | \(-0.325570\pi\) | ||||
0.520972 | + | 0.853574i | \(0.325570\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.0000 | + | 27.7128i | −0.555034 | + | 0.961347i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.5885 | − | 9.00000i | −0.540108 | − | 0.311832i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 20.0000i | − | 0.691301i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0000 | − | 24.2487i | 0.482759 | − | 0.836162i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 52.0000i | − | 1.79098i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 8.00000i | − | 0.274883i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.0000 | − | 45.0333i | −0.892318 | − | 1.54554i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.00000 | + | 13.8564i | 0.274236 | + | 0.474991i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.9090 | − | 19.0000i | −1.12678 | − | 0.650548i | −0.183658 | − | 0.982990i | \(-0.558794\pi\) |
−0.943123 | + | 0.332443i | \(0.892127\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.500000 | − | 0.866025i | −0.0170598 | − | 0.0295484i | 0.857369 | − | 0.514701i | \(-0.172097\pi\) |
−0.874429 | + | 0.485153i | \(0.838764\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.00000 | + | 13.8564i | 0.272639 | + | 0.472225i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 18.0000i | − | 0.612727i | −0.951915 | − | 0.306364i | \(-0.900888\pi\) | ||
0.951915 | − | 0.306364i | \(-0.0991123\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.0000i | 0.883006i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.50000 | − | 2.59808i | 0.0508840 | − | 0.0881337i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42.0000 | − | 72.7461i | 1.42312 | − | 2.46491i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.0000i | 0.406138i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.6410 | + | 20.0000i | 1.16974 | + | 0.675352i | 0.953620 | − | 0.301014i | \(-0.0973250\pi\) |
0.216124 | + | 0.976366i | \(0.430658\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.0000 | − | 27.7128i | 0.539667 | − | 0.934730i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.00000 | −0.235836 | −0.117918 | − | 0.993023i | \(-0.537622\pi\) | ||||
−0.117918 | + | 0.993023i | \(0.537622\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.92820 | − | 4.00000i | 0.233153 | − | 0.134611i | −0.378873 | − | 0.925449i | \(-0.623688\pi\) |
0.612026 | + | 0.790838i | \(0.290355\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.2487 | + | 14.0000i | −0.814192 | + | 0.470074i | −0.848410 | − | 0.529340i | \(-0.822439\pi\) |
0.0342175 | + | 0.999414i | \(0.489106\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.0000 | − | 62.3538i | −1.20740 | − | 2.09128i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.5000 | + | 28.5788i | −0.552771 | + | 0.957427i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.9808 | + | 3.00000i | 0.869413 | + | 0.100391i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −41.5692 | + | 24.0000i | −1.38796 | + | 0.801337i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.50000 | − | 4.33013i | −0.0833797 | − | 0.144418i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.7128 | + | 16.0000i | 0.920189 | + | 0.531271i | 0.883695 | − | 0.468063i | \(-0.155048\pi\) |
0.0364935 | + | 0.999334i | \(0.488381\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.50000 | − | 9.52628i | 0.182423 | − | 0.315967i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.00000 | 0.231920 | 0.115960 | − | 0.993254i | \(-0.463006\pi\) | ||||
0.115960 | + | 0.993254i | \(0.463006\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 48.0000i | − | 1.58857i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 69.2820 | + | 40.0000i | 2.28789 | + | 1.32092i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.00000 | −0.263896 | −0.131948 | − | 0.991257i | \(-0.542123\pi\) | ||||
−0.131948 | + | 0.991257i | \(0.542123\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0000 | + | 24.2487i | 0.461316 | + | 0.799022i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 90.0000i | 2.96239i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.5000 | + | 18.1865i | −0.344494 | + | 0.596681i | −0.985262 | − | 0.171054i | \(-0.945283\pi\) |
0.640768 | + | 0.767735i | \(0.278616\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.5000 | + | 23.3827i | 1.03237 | + | 0.766337i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.73205 | + | 1.00000i | −0.0565836 | + | 0.0326686i | −0.528025 | − | 0.849229i | \(-0.677067\pi\) |
0.471441 | + | 0.881897i | \(0.343734\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −68.0000 | −2.21910 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.5000 | − | 30.3109i | −0.570484 | − | 0.988107i | −0.996516 | − | 0.0833989i | \(-0.973422\pi\) |
0.426033 | − | 0.904708i | \(-0.359911\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.00000i | 0.260516i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.66025 | − | 5.00000i | −0.281420 | − | 0.162478i | 0.352646 | − | 0.935757i | \(-0.385282\pi\) |
−0.634066 | + | 0.773279i | \(0.718615\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −72.0000 | −2.33722 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.0000 | −0.778253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.2487 | + | 14.0000i | 0.785493 | + | 0.453504i | 0.838373 | − | 0.545096i | \(-0.183507\pi\) |
−0.0528806 | + | 0.998601i | \(0.516840\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.00000i | 0.193952i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.0000 | − | 41.5692i | −0.775000 | − | 1.34234i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.00000 | −0.193548 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.3923 | + | 6.00000i | −0.334887 | + | 0.193347i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.3923 | − | 6.00000i | −0.334194 | − | 0.192947i | 0.323508 | − | 0.946226i | \(-0.395138\pi\) |
−0.657702 | + | 0.753279i | \(0.728471\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.00000 | + | 17.3205i | −0.0642493 | + | 0.556415i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.0000 | + | 51.9615i | −0.962746 | + | 1.66752i | −0.247193 | + | 0.968966i | \(0.579508\pi\) |
−0.715553 | + | 0.698558i | \(0.753825\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 12.0000i | − | 0.383914i | −0.981403 | − | 0.191957i | \(-0.938517\pi\) | ||
0.981403 | − | 0.191957i | \(-0.0614834\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.5000 | − | 44.1673i | −0.814984 | − | 1.41159i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.00000 | 0.223493 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.1769 | + | 18.0000i | 0.994389 | + | 0.574111i | 0.906583 | − | 0.422027i | \(-0.138681\pi\) |
0.0878058 | + | 0.996138i | \(0.472015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 48.0000i | 1.52786i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | + | 27.7128i | −0.508257 | + | 0.880327i | 0.491698 | + | 0.870766i | \(0.336377\pi\) |
−0.999954 | + | 0.00956046i | \(0.996957\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 34.6410 | + | 20.0000i | 1.09930 | + | 0.634681i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.66025 | − | 5.00000i | 0.274273 | − | 0.158352i | −0.356555 | − | 0.934274i | \(-0.616049\pi\) |
0.630828 | + | 0.775923i | \(0.282715\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.0000 | −0.506218 |
(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 | 1900.2.s.b.49.1 | 4 | ||
5.2 | odd | 4 | 380.2.i.a.201.1 | yes | 2 | ||
5.3 | odd | 4 | 1900.2.i.b.201.1 | 2 | |||
5.4 | even | 2 | inner | 1900.2.s.b.49.2 | 4 | ||
15.2 | even | 4 | 3420.2.t.b.3241.1 | 2 | |||
19.7 | even | 3 | inner | 1900.2.s.b.349.2 | 4 | ||
20.7 | even | 4 | 1520.2.q.g.961.1 | 2 | |||
95.7 | odd | 12 | 380.2.i.a.121.1 | ✓ | 2 | ||
95.27 | even | 12 | 7220.2.a.a.1.1 | 1 | |||
95.64 | even | 6 | inner | 1900.2.s.b.349.1 | 4 | ||
95.83 | odd | 12 | 1900.2.i.b.501.1 | 2 | |||
95.87 | odd | 12 | 7220.2.a.e.1.1 | 1 | |||
285.197 | even | 12 | 3420.2.t.b.1261.1 | 2 | |||
380.7 | even | 12 | 1520.2.q.g.881.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.i.a.121.1 | ✓ | 2 | 95.7 | odd | 12 | ||
380.2.i.a.201.1 | yes | 2 | 5.2 | odd | 4 | ||
1520.2.q.g.881.1 | 2 | 380.7 | even | 12 | |||
1520.2.q.g.961.1 | 2 | 20.7 | even | 4 | |||
1900.2.i.b.201.1 | 2 | 5.3 | odd | 4 | |||
1900.2.i.b.501.1 | 2 | 95.83 | odd | 12 | |||
1900.2.s.b.49.1 | 4 | 1.1 | even | 1 | trivial | ||
1900.2.s.b.49.2 | 4 | 5.4 | even | 2 | inner | ||
1900.2.s.b.349.1 | 4 | 95.64 | even | 6 | inner | ||
1900.2.s.b.349.2 | 4 | 19.7 | even | 3 | inner | ||
3420.2.t.b.1261.1 | 2 | 285.197 | even | 12 | |||
3420.2.t.b.3241.1 | 2 | 15.2 | even | 4 | |||
7220.2.a.a.1.1 | 1 | 95.27 | even | 12 | |||
7220.2.a.e.1.1 | 1 | 95.87 | odd | 12 |