Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(649,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.f (of order \(2\), degree \(1\), 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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.1 | ||
Root | \(2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.649 |
Dual form | 1950.2.f.o.649.3 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | −3.12311 | −1.18042 | −0.590211 | − | 0.807249i | \(-0.700956\pi\) | ||||
−0.590211 | + | 0.807249i | \(0.700956\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.12311i | 1.54467i | 0.635213 | + | 0.772337i | \(0.280912\pi\) | ||||
−0.635213 | + | 0.772337i | \(0.719088\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | −0.561553 | − | 3.56155i | −0.155747 | − | 0.987797i | ||||
\(14\) | −3.12311 | −0.834685 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.00000i | 0.485071i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 6.00000i | 1.37649i | 0.725476 | + | 0.688247i | \(0.241620\pi\) | ||||
−0.725476 | + | 0.688247i | \(0.758380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.12311i | 0.681518i | ||||||||
\(22\) | 5.12311i | 1.09225i | ||||||||
\(23\) | 5.12311i | 1.06824i | 0.845408 | + | 0.534121i | \(0.179357\pi\) | ||||
−0.845408 | + | 0.534121i | \(0.820643\pi\) | |||||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.561553 | − | 3.56155i | −0.110130 | − | 0.698478i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −3.12311 | −0.590211 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.12311i | 0.560926i | 0.959865 | + | 0.280463i | \(0.0904881\pi\) | ||||
−0.959865 | + | 0.280463i | \(0.909512\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.12311 | 0.891818 | ||||||||
\(34\) | 2.00000i | 0.342997i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 5.12311 | 0.842233 | 0.421117 | − | 0.907006i | \(-0.361638\pi\) | ||||
0.421117 | + | 0.907006i | \(0.361638\pi\) | |||||||
\(38\) | 6.00000i | 0.973329i | ||||||||
\(39\) | −3.56155 | + | 0.561553i | −0.570305 | + | 0.0899204i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.876894i | 0.136948i | 0.997653 | + | 0.0684739i | \(0.0218130\pi\) | ||||
−0.997653 | + | 0.0684739i | \(0.978187\pi\) | |||||||
\(42\) | 3.12311i | 0.481906i | ||||||||
\(43\) | − | 6.24621i | − | 0.952538i | −0.879300 | − | 0.476269i | \(-0.841989\pi\) | ||
0.879300 | − | 0.476269i | \(-0.158011\pi\) | |||||||
\(44\) | 5.12311i | 0.772337i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.12311i | 0.755361i | ||||||||
\(47\) | 6.24621 | 0.911104 | 0.455552 | − | 0.890209i | \(-0.349442\pi\) | ||||
0.455552 | + | 0.890209i | \(0.349442\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 2.75379 | 0.393398 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | −0.561553 | − | 3.56155i | −0.0778734 | − | 0.493899i | ||||
\(53\) | 13.3693i | 1.83642i | 0.396098 | + | 0.918208i | \(0.370364\pi\) | ||||
−0.396098 | + | 0.918208i | \(0.629636\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.12311 | −0.417343 | ||||||||
\(57\) | 6.00000 | 0.794719 | ||||||||
\(58\) | −2.00000 | −0.262613 | ||||||||
\(59\) | 1.12311i | 0.146216i | 0.997324 | + | 0.0731079i | \(0.0232918\pi\) | ||||
−0.997324 | + | 0.0731079i | \(0.976708\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | 3.12311i | 0.396635i | ||||||||
\(63\) | 3.12311 | 0.393474 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.12311 | 0.630611 | ||||||||
\(67\) | −4.87689 | −0.595807 | −0.297904 | − | 0.954596i | \(-0.596287\pi\) | ||||
−0.297904 | + | 0.954596i | \(0.596287\pi\) | |||||||
\(68\) | 2.00000i | 0.242536i | ||||||||
\(69\) | 5.12311 | 0.616749 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.2462i | 1.21600i | 0.793936 | + | 0.608001i | \(0.208028\pi\) | ||||
−0.793936 | + | 0.608001i | \(0.791972\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −13.1231 | −1.53594 | −0.767972 | − | 0.640484i | \(-0.778734\pi\) | ||||
−0.767972 | + | 0.640484i | \(0.778734\pi\) | |||||||
\(74\) | 5.12311 | 0.595549 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.00000i | 0.688247i | ||||||||
\(77\) | − | 16.0000i | − | 1.82337i | ||||||
\(78\) | −3.56155 | + | 0.561553i | −0.403266 | + | 0.0635833i | ||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.876894i | 0.0968368i | ||||||||
\(83\) | −6.24621 | −0.685611 | −0.342805 | − | 0.939406i | \(-0.611377\pi\) | ||||
−0.342805 | + | 0.939406i | \(0.611377\pi\) | |||||||
\(84\) | 3.12311i | 0.340759i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 6.24621i | − | 0.673546i | ||||||
\(87\) | 2.00000i | 0.214423i | ||||||||
\(88\) | 5.12311i | 0.546125i | ||||||||
\(89\) | − | 3.12311i | − | 0.331049i | −0.986206 | − | 0.165524i | \(-0.947068\pi\) | ||
0.986206 | − | 0.165524i | \(-0.0529316\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.75379 | + | 11.1231i | 0.183847 | + | 1.16602i | ||||
\(92\) | 5.12311i | 0.534121i | ||||||||
\(93\) | 3.12311 | 0.323851 | ||||||||
\(94\) | 6.24621 | 0.644247 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 13.1231 | 1.33245 | 0.666225 | − | 0.745751i | \(-0.267909\pi\) | ||||
0.666225 | + | 0.745751i | \(0.267909\pi\) | |||||||
\(98\) | 2.75379 | 0.278175 | ||||||||
\(99\) | − | 5.12311i | − | 0.514891i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.2462 | −1.21854 | −0.609272 | − | 0.792961i | \(-0.708538\pi\) | ||||
−0.609272 | + | 0.792961i | \(0.708538\pi\) | |||||||
\(102\) | 2.00000 | 0.198030 | ||||||||
\(103\) | 13.1231i | 1.29306i | 0.762889 | + | 0.646529i | \(0.223780\pi\) | ||||
−0.762889 | + | 0.646529i | \(0.776220\pi\) | |||||||
\(104\) | −0.561553 | − | 3.56155i | −0.0550648 | − | 0.349239i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.3693i | 1.29854i | ||||||||
\(107\) | − | 8.00000i | − | 0.773389i | −0.922208 | − | 0.386695i | \(-0.873617\pi\) | ||
0.922208 | − | 0.386695i | \(-0.126383\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | − | 2.87689i | − | 0.275557i | −0.990463 | − | 0.137778i | \(-0.956004\pi\) | ||
0.990463 | − | 0.137778i | \(-0.0439961\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 5.12311i | − | 0.486264i | ||||||
\(112\) | −3.12311 | −0.295106 | ||||||||
\(113\) | − | 12.2462i | − | 1.15203i | −0.817440 | − | 0.576013i | \(-0.804608\pi\) | ||
0.817440 | − | 0.576013i | \(-0.195392\pi\) | |||||||
\(114\) | 6.00000 | 0.561951 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 0.561553 | + | 3.56155i | 0.0519156 | + | 0.329266i | ||||
\(118\) | 1.12311i | 0.103390i | ||||||||
\(119\) | − | 6.24621i | − | 0.572589i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.2462 | −1.38602 | ||||||||
\(122\) | 10.0000 | 0.905357 | ||||||||
\(123\) | 0.876894 | 0.0790669 | ||||||||
\(124\) | 3.12311i | 0.280463i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.12311 | 0.278228 | ||||||||
\(127\) | − | 13.1231i | − | 1.16449i | −0.813014 | − | 0.582244i | \(-0.802175\pi\) | ||
0.813014 | − | 0.582244i | \(-0.197825\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −6.24621 | −0.549948 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 5.12311 | 0.445909 | ||||||||
\(133\) | − | 18.7386i | − | 1.62485i | ||||||
\(134\) | −4.87689 | −0.421300 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000i | 0.171499i | ||||||||
\(137\) | 10.4924 | 0.896428 | 0.448214 | − | 0.893926i | \(-0.352060\pi\) | ||||
0.448214 | + | 0.893926i | \(0.352060\pi\) | |||||||
\(138\) | 5.12311 | 0.436108 | ||||||||
\(139\) | 16.4924 | 1.39887 | 0.699435 | − | 0.714697i | \(-0.253435\pi\) | ||||
0.699435 | + | 0.714697i | \(0.253435\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 6.24621i | − | 0.526026i | ||||||
\(142\) | 10.2462i | 0.859843i | ||||||||
\(143\) | 18.2462 | − | 2.87689i | 1.52582 | − | 0.240578i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.1231 | −1.08608 | ||||||||
\(147\) | − | 2.75379i | − | 0.227129i | ||||||
\(148\) | 5.12311 | 0.421117 | ||||||||
\(149\) | 14.0000i | 1.14692i | 0.819232 | + | 0.573462i | \(0.194400\pi\) | ||||
−0.819232 | + | 0.573462i | \(0.805600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.3693i | 1.08798i | 0.839092 | + | 0.543990i | \(0.183087\pi\) | ||||
−0.839092 | + | 0.543990i | \(0.816913\pi\) | |||||||
\(152\) | 6.00000i | 0.486664i | ||||||||
\(153\) | − | 2.00000i | − | 0.161690i | ||||||
\(154\) | − | 16.0000i | − | 1.28932i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.56155 | + | 0.561553i | −0.285152 | + | 0.0449602i | ||||
\(157\) | 21.3693i | 1.70546i | 0.522354 | + | 0.852729i | \(0.325054\pi\) | ||||
−0.522354 | + | 0.852729i | \(0.674946\pi\) | |||||||
\(158\) | −8.00000 | −0.636446 | ||||||||
\(159\) | 13.3693 | 1.06026 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 16.0000i | − | 1.26098i | ||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −7.12311 | −0.557925 | −0.278962 | − | 0.960302i | \(-0.589990\pi\) | ||||
−0.278962 | + | 0.960302i | \(0.589990\pi\) | |||||||
\(164\) | 0.876894i | 0.0684739i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.24621 | −0.484800 | ||||||||
\(167\) | 22.2462 | 1.72146 | 0.860732 | − | 0.509059i | \(-0.170006\pi\) | ||||
0.860732 | + | 0.509059i | \(0.170006\pi\) | |||||||
\(168\) | 3.12311i | 0.240953i | ||||||||
\(169\) | −12.3693 | + | 4.00000i | −0.951486 | + | 0.307692i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 6.00000i | − | 0.458831i | ||||||
\(172\) | − | 6.24621i | − | 0.476269i | ||||||
\(173\) | − | 23.1231i | − | 1.75802i | −0.476806 | − | 0.879009i | \(-0.658206\pi\) | ||
0.476806 | − | 0.879009i | \(-0.341794\pi\) | |||||||
\(174\) | 2.00000i | 0.151620i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.12311i | 0.386169i | ||||||||
\(177\) | 1.12311 | 0.0844178 | ||||||||
\(178\) | − | 3.12311i | − | 0.234087i | ||||||
\(179\) | −16.4924 | −1.23270 | −0.616351 | − | 0.787472i | \(-0.711390\pi\) | ||||
−0.616351 | + | 0.787472i | \(0.711390\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.2462 | −1.50489 | −0.752445 | − | 0.658656i | \(-0.771125\pi\) | ||||
−0.752445 | + | 0.658656i | \(0.771125\pi\) | |||||||
\(182\) | 1.75379 | + | 11.1231i | 0.129999 | + | 0.824499i | ||||
\(183\) | − | 10.0000i | − | 0.739221i | ||||||
\(184\) | 5.12311i | 0.377680i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.12311 | 0.228997 | ||||||||
\(187\) | −10.2462 | −0.749277 | ||||||||
\(188\) | 6.24621 | 0.455552 | ||||||||
\(189\) | − | 3.12311i | − | 0.227173i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.4924 | 1.19335 | 0.596675 | − | 0.802483i | \(-0.296488\pi\) | ||||
0.596675 | + | 0.802483i | \(0.296488\pi\) | |||||||
\(192\) | − | 1.00000i | − | 0.0721688i | ||||||
\(193\) | −25.1231 | −1.80840 | −0.904200 | − | 0.427109i | \(-0.859532\pi\) | ||||
−0.904200 | + | 0.427109i | \(0.859532\pi\) | |||||||
\(194\) | 13.1231 | 0.942184 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.75379 | 0.196699 | ||||||||
\(197\) | −16.2462 | −1.15749 | −0.578747 | − | 0.815507i | \(-0.696458\pi\) | ||||
−0.578747 | + | 0.815507i | \(0.696458\pi\) | |||||||
\(198\) | − | 5.12311i | − | 0.364083i | ||||||
\(199\) | −18.2462 | −1.29344 | −0.646720 | − | 0.762728i | \(-0.723860\pi\) | ||||
−0.646720 | + | 0.762728i | \(0.723860\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.87689i | 0.343990i | ||||||||
\(202\) | −12.2462 | −0.861640 | ||||||||
\(203\) | 6.24621 | 0.438398 | ||||||||
\(204\) | 2.00000 | 0.140028 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 13.1231i | 0.914330i | ||||||||
\(207\) | − | 5.12311i | − | 0.356080i | ||||||
\(208\) | −0.561553 | − | 3.56155i | −0.0389367 | − | 0.246949i | ||||
\(209\) | −30.7386 | −2.12624 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 13.3693i | 0.918208i | ||||||||
\(213\) | 10.2462 | 0.702059 | ||||||||
\(214\) | − | 8.00000i | − | 0.546869i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | − | 9.75379i | − | 0.662130i | ||||||
\(218\) | − | 2.87689i | − | 0.194848i | ||||||
\(219\) | 13.1231i | 0.886777i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.12311 | − | 1.12311i | 0.479152 | − | 0.0755483i | ||||
\(222\) | − | 5.12311i | − | 0.343840i | ||||||
\(223\) | 9.36932 | 0.627416 | 0.313708 | − | 0.949520i | \(-0.398429\pi\) | ||||
0.313708 | + | 0.949520i | \(0.398429\pi\) | |||||||
\(224\) | −3.12311 | −0.208671 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 12.2462i | − | 0.814606i | ||||||
\(227\) | −8.00000 | −0.530979 | −0.265489 | − | 0.964114i | \(-0.585534\pi\) | ||||
−0.265489 | + | 0.964114i | \(0.585534\pi\) | |||||||
\(228\) | 6.00000 | 0.397360 | ||||||||
\(229\) | 5.12311i | 0.338544i | 0.985569 | + | 0.169272i | \(0.0541417\pi\) | ||||
−0.985569 | + | 0.169272i | \(0.945858\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.0000 | −1.05272 | ||||||||
\(232\) | −2.00000 | −0.131306 | ||||||||
\(233\) | 7.75379i | 0.507968i | 0.967208 | + | 0.253984i | \(0.0817410\pi\) | ||||
−0.967208 | + | 0.253984i | \(0.918259\pi\) | |||||||
\(234\) | 0.561553 | + | 3.56155i | 0.0367099 | + | 0.232826i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.12311i | 0.0731079i | ||||||||
\(237\) | 8.00000i | 0.519656i | ||||||||
\(238\) | − | 6.24621i | − | 0.404882i | ||||||
\(239\) | − | 4.49242i | − | 0.290591i | −0.989388 | − | 0.145295i | \(-0.953587\pi\) | ||
0.989388 | − | 0.145295i | \(-0.0464132\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 14.2462i | − | 0.917679i | −0.888519 | − | 0.458840i | \(-0.848265\pi\) | ||
0.888519 | − | 0.458840i | \(-0.151735\pi\) | |||||||
\(242\) | −15.2462 | −0.980064 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 10.0000 | 0.640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.876894 | 0.0559087 | ||||||||
\(247\) | 21.3693 | − | 3.36932i | 1.35970 | − | 0.214384i | ||||
\(248\) | 3.12311i | 0.198317i | ||||||||
\(249\) | 6.24621i | 0.395838i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.2462 | 1.65665 | 0.828323 | − | 0.560251i | \(-0.189295\pi\) | ||||
0.828323 | + | 0.560251i | \(0.189295\pi\) | |||||||
\(252\) | 3.12311 | 0.196737 | ||||||||
\(253\) | −26.2462 | −1.65009 | ||||||||
\(254\) | − | 13.1231i | − | 0.823417i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 12.2462i | − | 0.763898i | −0.924183 | − | 0.381949i | \(-0.875253\pi\) | ||
0.924183 | − | 0.381949i | \(-0.124747\pi\) | |||||||
\(258\) | −6.24621 | −0.388872 | ||||||||
\(259\) | −16.0000 | −0.994192 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 4.00000 | 0.247121 | ||||||||
\(263\) | 27.3693i | 1.68766i | 0.536607 | + | 0.843832i | \(0.319706\pi\) | ||||
−0.536607 | + | 0.843832i | \(0.680294\pi\) | |||||||
\(264\) | 5.12311 | 0.315305 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 18.7386i | − | 1.14894i | ||||||
\(267\) | −3.12311 | −0.191131 | ||||||||
\(268\) | −4.87689 | −0.297904 | ||||||||
\(269\) | 16.2462 | 0.990549 | 0.495274 | − | 0.868737i | \(-0.335067\pi\) | ||||
0.495274 | + | 0.868737i | \(0.335067\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.1231i | 1.40463i | 0.711867 | + | 0.702314i | \(0.247850\pi\) | ||||
−0.711867 | + | 0.702314i | \(0.752150\pi\) | |||||||
\(272\) | 2.00000i | 0.121268i | ||||||||
\(273\) | 11.1231 | − | 1.75379i | 0.673201 | − | 0.106144i | ||||
\(274\) | 10.4924 | 0.633870 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.12311 | 0.308375 | ||||||||
\(277\) | − | 29.8617i | − | 1.79422i | −0.441809 | − | 0.897109i | \(-0.645663\pi\) | ||
0.441809 | − | 0.897109i | \(-0.354337\pi\) | |||||||
\(278\) | 16.4924 | 0.989150 | ||||||||
\(279\) | − | 3.12311i | − | 0.186975i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3.12311i | − | 0.186309i | −0.995652 | − | 0.0931544i | \(-0.970305\pi\) | ||
0.995652 | − | 0.0931544i | \(-0.0296950\pi\) | |||||||
\(282\) | − | 6.24621i | − | 0.371956i | ||||||
\(283\) | 4.00000i | 0.237775i | 0.992908 | + | 0.118888i | \(0.0379328\pi\) | ||||
−0.992908 | + | 0.118888i | \(0.962067\pi\) | |||||||
\(284\) | 10.2462i | 0.608001i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.2462 | − | 2.87689i | 1.07892 | − | 0.170114i | ||||
\(287\) | − | 2.73863i | − | 0.161656i | ||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 13.1231i | − | 0.769290i | ||||||
\(292\) | −13.1231 | −0.767972 | ||||||||
\(293\) | 28.7386 | 1.67893 | 0.839464 | − | 0.543415i | \(-0.182869\pi\) | ||||
0.839464 | + | 0.543415i | \(0.182869\pi\) | |||||||
\(294\) | − | 2.75379i | − | 0.160604i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.12311 | 0.297774 | ||||||||
\(297\) | −5.12311 | −0.297273 | ||||||||
\(298\) | 14.0000i | 0.810998i | ||||||||
\(299\) | 18.2462 | − | 2.87689i | 1.05521 | − | 0.166375i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.5076i | 1.12440i | ||||||||
\(302\) | 13.3693i | 0.769318i | ||||||||
\(303\) | 12.2462i | 0.703526i | ||||||||
\(304\) | 6.00000i | 0.344124i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 2.00000i | − | 0.114332i | ||||||
\(307\) | −31.1231 | −1.77629 | −0.888145 | − | 0.459564i | \(-0.848006\pi\) | ||||
−0.888145 | + | 0.459564i | \(0.848006\pi\) | |||||||
\(308\) | − | 16.0000i | − | 0.911685i | ||||||
\(309\) | 13.1231 | 0.746547 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.49242 | 0.481561 | 0.240781 | − | 0.970580i | \(-0.422597\pi\) | ||||
0.240781 | + | 0.970580i | \(0.422597\pi\) | |||||||
\(312\) | −3.56155 | + | 0.561553i | −0.201633 | + | 0.0317917i | ||||
\(313\) | − | 16.2462i | − | 0.918290i | −0.888361 | − | 0.459145i | \(-0.848156\pi\) | ||
0.888361 | − | 0.459145i | \(-0.151844\pi\) | |||||||
\(314\) | 21.3693i | 1.20594i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | −6.00000 | −0.336994 | −0.168497 | − | 0.985702i | \(-0.553891\pi\) | ||||
−0.168497 | + | 0.985702i | \(0.553891\pi\) | |||||||
\(318\) | 13.3693 | 0.749714 | ||||||||
\(319\) | − | 10.2462i | − | 0.573678i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.00000 | −0.446516 | ||||||||
\(322\) | − | 16.0000i | − | 0.891645i | ||||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.12311 | −0.394512 | ||||||||
\(327\) | −2.87689 | −0.159093 | ||||||||
\(328\) | 0.876894i | 0.0484184i | ||||||||
\(329\) | −19.5076 | −1.07549 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 7.75379i | − | 0.426187i | −0.977032 | − | 0.213093i | \(-0.931646\pi\) | ||
0.977032 | − | 0.213093i | \(-0.0683539\pi\) | |||||||
\(332\) | −6.24621 | −0.342805 | ||||||||
\(333\) | −5.12311 | −0.280744 | ||||||||
\(334\) | 22.2462 | 1.21726 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.12311i | 0.170379i | ||||||||
\(337\) | 6.00000i | 0.326841i | 0.986557 | + | 0.163420i | \(0.0522527\pi\) | ||||
−0.986557 | + | 0.163420i | \(0.947747\pi\) | |||||||
\(338\) | −12.3693 | + | 4.00000i | −0.672802 | + | 0.217571i | ||||
\(339\) | −12.2462 | −0.665123 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.0000 | −0.866449 | ||||||||
\(342\) | − | 6.00000i | − | 0.324443i | ||||||
\(343\) | 13.2614 | 0.716046 | ||||||||
\(344\) | − | 6.24621i | − | 0.336773i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 23.1231i | − | 1.24311i | ||||||
\(347\) | − | 14.2462i | − | 0.764777i | −0.924002 | − | 0.382388i | \(-0.875102\pi\) | ||
0.924002 | − | 0.382388i | \(-0.124898\pi\) | |||||||
\(348\) | 2.00000i | 0.107211i | ||||||||
\(349\) | − | 19.3693i | − | 1.03682i | −0.855133 | − | 0.518408i | \(-0.826525\pi\) | ||
0.855133 | − | 0.518408i | \(-0.173475\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.56155 | − | 0.561553i | 0.190102 | − | 0.0299735i | ||||
\(352\) | 5.12311i | 0.273062i | ||||||||
\(353\) | −12.2462 | −0.651800 | −0.325900 | − | 0.945404i | \(-0.605667\pi\) | ||||
−0.325900 | + | 0.945404i | \(0.605667\pi\) | |||||||
\(354\) | 1.12311 | 0.0596924 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 3.12311i | − | 0.165524i | ||||||
\(357\) | −6.24621 | −0.330585 | ||||||||
\(358\) | −16.4924 | −0.871652 | ||||||||
\(359\) | − | 17.7538i | − | 0.937009i | −0.883461 | − | 0.468505i | \(-0.844793\pi\) | ||
0.883461 | − | 0.468505i | \(-0.155207\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | −20.2462 | −1.06412 | ||||||||
\(363\) | 15.2462i | 0.800219i | ||||||||
\(364\) | 1.75379 | + | 11.1231i | 0.0919235 | + | 0.583009i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | − | 10.0000i | − | 0.522708i | ||||||
\(367\) | 8.63068i | 0.450518i | 0.974299 | + | 0.225259i | \(0.0723228\pi\) | ||||
−0.974299 | + | 0.225259i | \(0.927677\pi\) | |||||||
\(368\) | 5.12311i | 0.267060i | ||||||||
\(369\) | − | 0.876894i | − | 0.0456493i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 41.7538i | − | 2.16775i | ||||||
\(372\) | 3.12311 | 0.161925 | ||||||||
\(373\) | − | 7.12311i | − | 0.368820i | −0.982849 | − | 0.184410i | \(-0.940963\pi\) | ||
0.982849 | − | 0.184410i | \(-0.0590375\pi\) | |||||||
\(374\) | −10.2462 | −0.529819 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.24621 | 0.322124 | ||||||||
\(377\) | 1.12311 | + | 7.12311i | 0.0578429 | + | 0.366859i | ||||
\(378\) | − | 3.12311i | − | 0.160635i | ||||||
\(379\) | 6.00000i | 0.308199i | 0.988055 | + | 0.154100i | \(0.0492477\pi\) | ||||
−0.988055 | + | 0.154100i | \(0.950752\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.1231 | −0.672317 | ||||||||
\(382\) | 16.4924 | 0.843826 | ||||||||
\(383\) | 1.75379 | 0.0896144 | 0.0448072 | − | 0.998996i | \(-0.485733\pi\) | ||||
0.0448072 | + | 0.998996i | \(0.485733\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −25.1231 | −1.27873 | ||||||||
\(387\) | 6.24621i | 0.317513i | ||||||||
\(388\) | 13.1231 | 0.666225 | ||||||||
\(389\) | 0.246211 | 0.0124834 | 0.00624170 | − | 0.999981i | \(-0.498013\pi\) | ||||
0.00624170 | + | 0.999981i | \(0.498013\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.2462 | −0.518173 | ||||||||
\(392\) | 2.75379 | 0.139087 | ||||||||
\(393\) | − | 4.00000i | − | 0.201773i | ||||||
\(394\) | −16.2462 | −0.818472 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | − | 5.12311i | − | 0.257446i | ||||||
\(397\) | 15.3693 | 0.771364 | 0.385682 | − | 0.922632i | \(-0.373966\pi\) | ||||
0.385682 | + | 0.922632i | \(0.373966\pi\) | |||||||
\(398\) | −18.2462 | −0.914600 | ||||||||
\(399\) | −18.7386 | −0.938105 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.36932i | − | 0.0683804i | −0.999415 | − | 0.0341902i | \(-0.989115\pi\) | ||
0.999415 | − | 0.0341902i | \(-0.0108852\pi\) | |||||||
\(402\) | 4.87689i | 0.243237i | ||||||||
\(403\) | 11.1231 | − | 1.75379i | 0.554081 | − | 0.0873624i | ||||
\(404\) | −12.2462 | −0.609272 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.24621 | 0.309994 | ||||||||
\(407\) | 26.2462i | 1.30098i | ||||||||
\(408\) | 2.00000 | 0.0990148 | ||||||||
\(409\) | − | 8.49242i | − | 0.419923i | −0.977710 | − | 0.209962i | \(-0.932666\pi\) | ||
0.977710 | − | 0.209962i | \(-0.0673339\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 10.4924i | − | 0.517553i | ||||||
\(412\) | 13.1231i | 0.646529i | ||||||||
\(413\) | − | 3.50758i | − | 0.172597i | ||||||
\(414\) | − | 5.12311i | − | 0.251787i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.561553 | − | 3.56155i | −0.0275324 | − | 0.174619i | ||||
\(417\) | − | 16.4924i | − | 0.807637i | ||||||
\(418\) | −30.7386 | −1.50348 | ||||||||
\(419\) | 28.0000 | 1.36789 | 0.683945 | − | 0.729534i | \(-0.260263\pi\) | ||||
0.683945 | + | 0.729534i | \(0.260263\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 0.630683i | − | 0.0307376i | −0.999882 | − | 0.0153688i | \(-0.995108\pi\) | ||
0.999882 | − | 0.0153688i | \(-0.00489224\pi\) | |||||||
\(422\) | 4.00000 | 0.194717 | ||||||||
\(423\) | −6.24621 | −0.303701 | ||||||||
\(424\) | 13.3693i | 0.649271i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.2462 | 0.496431 | ||||||||
\(427\) | −31.2311 | −1.51138 | ||||||||
\(428\) | − | 8.00000i | − | 0.386695i | ||||||
\(429\) | −2.87689 | − | 18.2462i | −0.138898 | − | 0.880935i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 32.4924i | − | 1.56510i | −0.622585 | − | 0.782552i | \(-0.713917\pi\) | ||
0.622585 | − | 0.782552i | \(-0.286083\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 18.0000i | 0.865025i | 0.901628 | + | 0.432512i | \(0.142373\pi\) | ||||
−0.901628 | + | 0.432512i | \(0.857627\pi\) | |||||||
\(434\) | − | 9.75379i | − | 0.468197i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 2.87689i | − | 0.137778i | ||||||
\(437\) | −30.7386 | −1.47043 | ||||||||
\(438\) | 13.1231i | 0.627046i | ||||||||
\(439\) | 36.4924 | 1.74169 | 0.870844 | − | 0.491559i | \(-0.163573\pi\) | ||||
0.870844 | + | 0.491559i | \(0.163573\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.75379 | −0.131133 | ||||||||
\(442\) | 7.12311 | − | 1.12311i | 0.338812 | − | 0.0534207i | ||||
\(443\) | 3.50758i | 0.166650i | 0.996522 | + | 0.0833250i | \(0.0265540\pi\) | ||||
−0.996522 | + | 0.0833250i | \(0.973446\pi\) | |||||||
\(444\) | − | 5.12311i | − | 0.243132i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.36932 | 0.443650 | ||||||||
\(447\) | 14.0000 | 0.662177 | ||||||||
\(448\) | −3.12311 | −0.147553 | ||||||||
\(449\) | 28.8769i | 1.36278i | 0.731918 | + | 0.681392i | \(0.238625\pi\) | ||||
−0.731918 | + | 0.681392i | \(0.761375\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.49242 | −0.211540 | ||||||||
\(452\) | − | 12.2462i | − | 0.576013i | ||||||
\(453\) | 13.3693 | 0.628145 | ||||||||
\(454\) | −8.00000 | −0.375459 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.00000 | 0.280976 | ||||||||
\(457\) | −31.3693 | −1.46739 | −0.733697 | − | 0.679476i | \(-0.762207\pi\) | ||||
−0.733697 | + | 0.679476i | \(0.762207\pi\) | |||||||
\(458\) | 5.12311i | 0.239387i | ||||||||
\(459\) | −2.00000 | −0.0933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.4924i | 0.861278i | 0.902524 | + | 0.430639i | \(0.141712\pi\) | ||||
−0.902524 | + | 0.430639i | \(0.858288\pi\) | |||||||
\(462\) | −16.0000 | −0.744387 | ||||||||
\(463\) | −21.8617 | −1.01600 | −0.508001 | − | 0.861357i | \(-0.669615\pi\) | ||||
−0.508001 | + | 0.861357i | \(0.669615\pi\) | |||||||
\(464\) | −2.00000 | −0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.75379i | 0.359187i | ||||||||
\(467\) | − | 22.2462i | − | 1.02943i | −0.857361 | − | 0.514716i | \(-0.827897\pi\) | ||
0.857361 | − | 0.514716i | \(-0.172103\pi\) | |||||||
\(468\) | 0.561553 | + | 3.56155i | 0.0259578 | + | 0.164633i | ||||
\(469\) | 15.2311 | 0.703305 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.3693 | 0.984646 | ||||||||
\(472\) | 1.12311i | 0.0516951i | ||||||||
\(473\) | 32.0000 | 1.47136 | ||||||||
\(474\) | 8.00000i | 0.367452i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 6.24621i | − | 0.286295i | ||||||
\(477\) | − | 13.3693i | − | 0.612139i | ||||||
\(478\) | − | 4.49242i | − | 0.205479i | ||||||
\(479\) | 12.4924i | 0.570793i | 0.958409 | + | 0.285397i | \(0.0921253\pi\) | ||||
−0.958409 | + | 0.285397i | \(0.907875\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.87689 | − | 18.2462i | −0.131175 | − | 0.831956i | ||||
\(482\) | − | 14.2462i | − | 0.648897i | ||||||
\(483\) | −16.0000 | −0.728025 | ||||||||
\(484\) | −15.2462 | −0.693010 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −17.3693 | −0.787079 | −0.393539 | − | 0.919308i | \(-0.628750\pi\) | ||||
−0.393539 | + | 0.919308i | \(0.628750\pi\) | |||||||
\(488\) | 10.0000 | 0.452679 | ||||||||
\(489\) | 7.12311i | 0.322118i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.7386 | 1.74825 | 0.874125 | − | 0.485701i | \(-0.161436\pi\) | ||||
0.874125 | + | 0.485701i | \(0.161436\pi\) | |||||||
\(492\) | 0.876894 | 0.0395335 | ||||||||
\(493\) | − | 4.00000i | − | 0.180151i | ||||||
\(494\) | 21.3693 | − | 3.36932i | 0.961451 | − | 0.151593i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.12311i | 0.140232i | ||||||||
\(497\) | − | 32.0000i | − | 1.43540i | ||||||
\(498\) | 6.24621i | 0.279899i | ||||||||
\(499\) | − | 34.4924i | − | 1.54409i | −0.635566 | − | 0.772046i | \(-0.719233\pi\) | ||
0.635566 | − | 0.772046i | \(-0.280767\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 22.2462i | − | 0.993887i | ||||||
\(502\) | 26.2462 | 1.17143 | ||||||||
\(503\) | − | 35.3693i | − | 1.57704i | −0.615009 | − | 0.788520i | \(-0.710848\pi\) | ||
0.615009 | − | 0.788520i | \(-0.289152\pi\) | |||||||
\(504\) | 3.12311 | 0.139114 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −26.2462 | −1.16679 | ||||||||
\(507\) | 4.00000 | + | 12.3693i | 0.177646 | + | 0.549341i | ||||
\(508\) | − | 13.1231i | − | 0.582244i | ||||||
\(509\) | − | 32.2462i | − | 1.42929i | −0.699488 | − | 0.714644i | \(-0.746589\pi\) | ||
0.699488 | − | 0.714644i | \(-0.253411\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40.9848 | 1.81306 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.00000 | −0.264906 | ||||||||
\(514\) | − | 12.2462i | − | 0.540157i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.24621 | −0.274974 | ||||||||
\(517\) | 32.0000i | 1.40736i | ||||||||
\(518\) | −16.0000 | −0.703000 | ||||||||
\(519\) | −23.1231 | −1.01499 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.246211 | 0.0107867 | 0.00539336 | − | 0.999985i | \(-0.498283\pi\) | ||||
0.00539336 | + | 0.999985i | \(0.498283\pi\) | |||||||
\(522\) | 2.00000 | 0.0875376 | ||||||||
\(523\) | 26.7386i | 1.16920i | 0.811322 | + | 0.584599i | \(0.198748\pi\) | ||||
−0.811322 | + | 0.584599i | \(0.801252\pi\) | |||||||
\(524\) | 4.00000 | 0.174741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.3693i | 1.19336i | ||||||||
\(527\) | −6.24621 | −0.272089 | ||||||||
\(528\) | 5.12311 | 0.222955 | ||||||||
\(529\) | −3.24621 | −0.141140 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.12311i | − | 0.0487386i | ||||||
\(532\) | − | 18.7386i | − | 0.812423i | ||||||
\(533\) | 3.12311 | − | 0.492423i | 0.135277 | − | 0.0213292i | ||||
\(534\) | −3.12311 | −0.135150 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.87689 | −0.210650 | ||||||||
\(537\) | 16.4924i | 0.711701i | ||||||||
\(538\) | 16.2462 | 0.700424 | ||||||||
\(539\) | 14.1080i | 0.607672i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.8769i | 0.467634i | 0.972281 | + | 0.233817i | \(0.0751217\pi\) | ||||
−0.972281 | + | 0.233817i | \(0.924878\pi\) | |||||||
\(542\) | 23.1231i | 0.993222i | ||||||||
\(543\) | 20.2462i | 0.868848i | ||||||||
\(544\) | 2.00000i | 0.0857493i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.1231 | − | 1.75379i | 0.476025 | − | 0.0750552i | ||||
\(547\) | 20.9848i | 0.897247i | 0.893721 | + | 0.448624i | \(0.148086\pi\) | ||||
−0.893721 | + | 0.448624i | \(0.851914\pi\) | |||||||
\(548\) | 10.4924 | 0.448214 | ||||||||
\(549\) | −10.0000 | −0.426790 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 12.0000i | − | 0.511217i | ||||||
\(552\) | 5.12311 | 0.218054 | ||||||||
\(553\) | 24.9848 | 1.06246 | ||||||||
\(554\) | − | 29.8617i | − | 1.26870i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.4924 | 0.699435 | ||||||||
\(557\) | −11.7538 | −0.498024 | −0.249012 | − | 0.968500i | \(-0.580106\pi\) | ||||
−0.249012 | + | 0.968500i | \(0.580106\pi\) | |||||||
\(558\) | − | 3.12311i | − | 0.132212i | ||||||
\(559\) | −22.2462 | + | 3.50758i | −0.940914 | + | 0.148355i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.2462i | 0.432595i | ||||||||
\(562\) | − | 3.12311i | − | 0.131740i | ||||||
\(563\) | 32.9848i | 1.39015i | 0.718939 | + | 0.695073i | \(0.244628\pi\) | ||||
−0.718939 | + | 0.695073i | \(0.755372\pi\) | |||||||
\(564\) | − | 6.24621i | − | 0.263013i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.00000i | 0.168133i | ||||||||
\(567\) | −3.12311 | −0.131158 | ||||||||
\(568\) | 10.2462i | 0.429921i | ||||||||
\(569\) | 12.7386 | 0.534031 | 0.267016 | − | 0.963692i | \(-0.413962\pi\) | ||||
0.267016 | + | 0.963692i | \(0.413962\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.49242 | −0.355397 | −0.177698 | − | 0.984085i | \(-0.556865\pi\) | ||||
−0.177698 | + | 0.984085i | \(0.556865\pi\) | |||||||
\(572\) | 18.2462 | − | 2.87689i | 0.762912 | − | 0.120289i | ||||
\(573\) | − | 16.4924i | − | 0.688981i | ||||||
\(574\) | − | 2.73863i | − | 0.114308i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | −27.3693 | −1.13940 | −0.569700 | − | 0.821853i | \(-0.692941\pi\) | ||||
−0.569700 | + | 0.821853i | \(0.692941\pi\) | |||||||
\(578\) | 13.0000 | 0.540729 | ||||||||
\(579\) | 25.1231i | 1.04408i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.5076 | 0.809311 | ||||||||
\(582\) | − | 13.1231i | − | 0.543970i | ||||||
\(583\) | −68.4924 | −2.83667 | ||||||||
\(584\) | −13.1231 | −0.543038 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.7386 | 1.18718 | ||||||||
\(587\) | 16.4924 | 0.680715 | 0.340358 | − | 0.940296i | \(-0.389452\pi\) | ||||
0.340358 | + | 0.940296i | \(0.389452\pi\) | |||||||
\(588\) | − | 2.75379i | − | 0.113564i | ||||||
\(589\) | −18.7386 | −0.772112 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.2462i | 0.668280i | ||||||||
\(592\) | 5.12311 | 0.210558 | ||||||||
\(593\) | −5.50758 | −0.226169 | −0.113085 | − | 0.993585i | \(-0.536073\pi\) | ||||
−0.113085 | + | 0.993585i | \(0.536073\pi\) | |||||||
\(594\) | −5.12311 | −0.210204 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.0000i | 0.573462i | ||||||||
\(597\) | 18.2462i | 0.746768i | ||||||||
\(598\) | 18.2462 | − | 2.87689i | 0.746143 | − | 0.117645i | ||||
\(599\) | 36.4924 | 1.49104 | 0.745520 | − | 0.666483i | \(-0.232201\pi\) | ||||
0.745520 | + | 0.666483i | \(0.232201\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.0000 | 1.55005 | 0.775026 | − | 0.631929i | \(-0.217737\pi\) | ||||
0.775026 | + | 0.631929i | \(0.217737\pi\) | |||||||
\(602\) | 19.5076i | 0.795070i | ||||||||
\(603\) | 4.87689 | 0.198602 | ||||||||
\(604\) | 13.3693i | 0.543990i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12.2462i | 0.497468i | ||||||||
\(607\) | 15.3693i | 0.623821i | 0.950111 | + | 0.311911i | \(0.100969\pi\) | ||||
−0.950111 | + | 0.311911i | \(0.899031\pi\) | |||||||
\(608\) | 6.00000i | 0.243332i | ||||||||
\(609\) | − | 6.24621i | − | 0.253109i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.50758 | − | 22.2462i | −0.141901 | − | 0.899985i | ||||
\(612\) | − | 2.00000i | − | 0.0808452i | ||||||
\(613\) | 39.3693 | 1.59011 | 0.795056 | − | 0.606536i | \(-0.207441\pi\) | ||||
0.795056 | + | 0.606536i | \(0.207441\pi\) | |||||||
\(614\) | −31.1231 | −1.25603 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 16.0000i | − | 0.644658i | ||||||
\(617\) | 40.7386 | 1.64008 | 0.820038 | − | 0.572309i | \(-0.193952\pi\) | ||||
0.820038 | + | 0.572309i | \(0.193952\pi\) | |||||||
\(618\) | 13.1231 | 0.527889 | ||||||||
\(619\) | − | 38.9848i | − | 1.56693i | −0.621434 | − | 0.783467i | \(-0.713450\pi\) | ||
0.621434 | − | 0.783467i | \(-0.286550\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.12311 | −0.205583 | ||||||||
\(622\) | 8.49242 | 0.340515 | ||||||||
\(623\) | 9.75379i | 0.390777i | ||||||||
\(624\) | −3.56155 | + | 0.561553i | −0.142576 | + | 0.0224801i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 16.2462i | − | 0.649329i | ||||||
\(627\) | 30.7386i | 1.22758i | ||||||||
\(628\) | 21.3693i | 0.852729i | ||||||||
\(629\) | 10.2462i | 0.408543i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 35.6155i | − | 1.41783i | −0.705293 | − | 0.708916i | \(-0.749185\pi\) | ||
0.705293 | − | 0.708916i | \(-0.250815\pi\) | |||||||
\(632\) | −8.00000 | −0.318223 | ||||||||
\(633\) | − | 4.00000i | − | 0.158986i | ||||||
\(634\) | −6.00000 | −0.238290 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 13.3693 | 0.530128 | ||||||||
\(637\) | −1.54640 | − | 9.80776i | −0.0612705 | − | 0.388598i | ||||
\(638\) | − | 10.2462i | − | 0.405651i | ||||||
\(639\) | − | 10.2462i | − | 0.405334i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.00000 | −0.0789953 | −0.0394976 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394976 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(642\) | −8.00000 | −0.315735 | ||||||||
\(643\) | 17.3693 | 0.684979 | 0.342489 | − | 0.939522i | \(-0.388730\pi\) | ||||
0.342489 | + | 0.939522i | \(0.388730\pi\) | |||||||
\(644\) | − | 16.0000i | − | 0.630488i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0000 | −0.472134 | ||||||||
\(647\) | 29.6155i | 1.16431i | 0.813079 | + | 0.582153i | \(0.197790\pi\) | ||||
−0.813079 | + | 0.582153i | \(0.802210\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −5.75379 | −0.225856 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.75379 | −0.382281 | ||||||||
\(652\) | −7.12311 | −0.278962 | ||||||||
\(653\) | 13.8617i | 0.542452i | 0.962516 | + | 0.271226i | \(0.0874290\pi\) | ||||
−0.962516 | + | 0.271226i | \(0.912571\pi\) | |||||||
\(654\) | −2.87689 | −0.112495 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.876894i | 0.0342370i | ||||||||
\(657\) | 13.1231 | 0.511981 | ||||||||
\(658\) | −19.5076 | −0.760485 | ||||||||
\(659\) | 21.7538 | 0.847407 | 0.423704 | − | 0.905801i | \(-0.360730\pi\) | ||||
0.423704 | + | 0.905801i | \(0.360730\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.12311i | 0.354848i | 0.984135 | + | 0.177424i | \(0.0567763\pi\) | ||||
−0.984135 | + | 0.177424i | \(0.943224\pi\) | |||||||
\(662\) | − | 7.75379i | − | 0.301360i | ||||||
\(663\) | −1.12311 | − | 7.12311i | −0.0436178 | − | 0.276638i | ||||
\(664\) | −6.24621 | −0.242400 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.12311 | −0.198516 | ||||||||
\(667\) | − | 10.2462i | − | 0.396735i | ||||||
\(668\) | 22.2462 | 0.860732 | ||||||||
\(669\) | − | 9.36932i | − | 0.362239i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 51.2311i | 1.97775i | ||||||||
\(672\) | 3.12311i | 0.120476i | ||||||||
\(673\) | − | 26.9848i | − | 1.04019i | −0.854109 | − | 0.520095i | \(-0.825897\pi\) | ||
0.854109 | − | 0.520095i | \(-0.174103\pi\) | |||||||
\(674\) | 6.00000i | 0.231111i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.3693 | + | 4.00000i | −0.475743 | + | 0.153846i | ||||
\(677\) | 12.8769i | 0.494899i | 0.968901 | + | 0.247450i | \(0.0795925\pi\) | ||||
−0.968901 | + | 0.247450i | \(0.920408\pi\) | |||||||
\(678\) | −12.2462 | −0.470313 | ||||||||
\(679\) | −40.9848 | −1.57285 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.00000i | 0.306561i | ||||||||
\(682\) | −16.0000 | −0.612672 | ||||||||
\(683\) | −16.9848 | −0.649907 | −0.324954 | − | 0.945730i | \(-0.605349\pi\) | ||||
−0.324954 | + | 0.945730i | \(0.605349\pi\) | |||||||
\(684\) | − | 6.00000i | − | 0.229416i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 13.2614 | 0.506321 | ||||||||
\(687\) | 5.12311 | 0.195459 | ||||||||
\(688\) | − | 6.24621i | − | 0.238135i | ||||||
\(689\) | 47.6155 | − | 7.50758i | 1.81401 | − | 0.286016i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.7386i | 1.09327i | 0.837371 | + | 0.546635i | \(0.184091\pi\) | ||||
−0.837371 | + | 0.546635i | \(0.815909\pi\) | |||||||
\(692\) | − | 23.1231i | − | 0.879009i | ||||||
\(693\) | 16.0000i | 0.607790i | ||||||||
\(694\) | − | 14.2462i | − | 0.540779i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.00000i | 0.0758098i | ||||||||
\(697\) | −1.75379 | −0.0664295 | ||||||||
\(698\) | − | 19.3693i | − | 0.733139i | ||||||
\(699\) | 7.75379 | 0.293275 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.0000 | −0.528773 | −0.264386 | − | 0.964417i | \(-0.585169\pi\) | ||||
−0.264386 | + | 0.964417i | \(0.585169\pi\) | |||||||
\(702\) | 3.56155 | − | 0.561553i | 0.134422 | − | 0.0211944i | ||||
\(703\) | 30.7386i | 1.15933i | ||||||||
\(704\) | 5.12311i | 0.193084i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.2462 | −0.460892 | ||||||||
\(707\) | 38.2462 | 1.43840 | ||||||||
\(708\) | 1.12311 | 0.0422089 | ||||||||
\(709\) | 1.61553i | 0.0606724i | 0.999540 | + | 0.0303362i | \(0.00965780\pi\) | ||||
−0.999540 | + | 0.0303362i | \(0.990342\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000 | 0.300023 | ||||||||
\(712\) | − | 3.12311i | − | 0.117043i | ||||||
\(713\) | −16.0000 | −0.599205 | ||||||||
\(714\) | −6.24621 | −0.233759 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.4924 | −0.616351 | ||||||||
\(717\) | −4.49242 | −0.167773 | ||||||||
\(718\) | − | 17.7538i | − | 0.662566i | ||||||
\(719\) | 20.0000 | 0.745874 | 0.372937 | − | 0.927857i | \(-0.378351\pi\) | ||||
0.372937 | + | 0.927857i | \(0.378351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 40.9848i | − | 1.52636i | ||||||
\(722\) | −17.0000 | −0.632674 | ||||||||
\(723\) | −14.2462 | −0.529822 | ||||||||
\(724\) | −20.2462 | −0.752445 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 15.2462i | 0.565840i | ||||||||
\(727\) | 19.8617i | 0.736631i | 0.929701 | + | 0.368316i | \(0.120065\pi\) | ||||
−0.929701 | + | 0.368316i | \(0.879935\pi\) | |||||||
\(728\) | 1.75379 | + | 11.1231i | 0.0649997 | + | 0.412250i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.4924 | 0.462049 | ||||||||
\(732\) | − | 10.0000i | − | 0.369611i | ||||||
\(733\) | 35.3693 | 1.30640 | 0.653198 | − | 0.757187i | \(-0.273427\pi\) | ||||
0.653198 | + | 0.757187i | \(0.273427\pi\) | |||||||
\(734\) | 8.63068i | 0.318564i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.12311i | 0.188840i | ||||||||
\(737\) | − | 24.9848i | − | 0.920329i | ||||||
\(738\) | − | 0.876894i | − | 0.0322789i | ||||||
\(739\) | 37.2311i | 1.36957i | 0.728747 | + | 0.684783i | \(0.240103\pi\) | ||||
−0.728747 | + | 0.684783i | \(0.759897\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.36932 | − | 21.3693i | −0.123775 | − | 0.785021i | ||||
\(742\) | − | 41.7538i | − | 1.53283i | ||||||
\(743\) | −16.0000 | −0.586983 | −0.293492 | − | 0.955962i | \(-0.594817\pi\) | ||||
−0.293492 | + | 0.955962i | \(0.594817\pi\) | |||||||
\(744\) | 3.12311 | 0.114499 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 7.12311i | − | 0.260795i | ||||||
\(747\) | 6.24621 | 0.228537 | ||||||||
\(748\) | −10.2462 | −0.374639 | ||||||||
\(749\) | 24.9848i | 0.912926i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.2462 | −0.957738 | −0.478869 | − | 0.877886i | \(-0.658953\pi\) | ||||
−0.478869 | + | 0.877886i | \(0.658953\pi\) | |||||||
\(752\) | 6.24621 | 0.227776 | ||||||||
\(753\) | − | 26.2462i | − | 0.956465i | ||||||
\(754\) | 1.12311 | + | 7.12311i | 0.0409011 | + | 0.259408i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 3.12311i | − | 0.113586i | ||||||
\(757\) | − | 3.12311i | − | 0.113511i | −0.998388 | − | 0.0567556i | \(-0.981924\pi\) | ||
0.998388 | − | 0.0567556i | \(-0.0180756\pi\) | |||||||
\(758\) | 6.00000i | 0.217930i | ||||||||
\(759\) | 26.2462i | 0.952677i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3.12311i | − | 0.113212i | −0.998397 | − | 0.0566062i | \(-0.981972\pi\) | ||
0.998397 | − | 0.0566062i | \(-0.0180280\pi\) | |||||||
\(762\) | −13.1231 | −0.475400 | ||||||||
\(763\) | 8.98485i | 0.325273i | ||||||||
\(764\) | 16.4924 | 0.596675 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.75379 | 0.0633670 | ||||||||
\(767\) | 4.00000 | − | 0.630683i | 0.144432 | − | 0.0227726i | ||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 32.9848i | 1.18946i | 0.803924 | + | 0.594732i | \(0.202742\pi\) | ||||
−0.803924 | + | 0.594732i | \(0.797258\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.2462 | −0.441037 | ||||||||
\(772\) | −25.1231 | −0.904200 | ||||||||
\(773\) | −16.2462 | −0.584336 | −0.292168 | − | 0.956367i | \(-0.594377\pi\) | ||||
−0.292168 | + | 0.956367i | \(0.594377\pi\) | |||||||
\(774\) | 6.24621i | 0.224515i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 13.1231 | 0.471092 | ||||||||
\(777\) | 16.0000i | 0.573997i | ||||||||
\(778\) | 0.246211 | 0.00882710 | ||||||||
\(779\) | −5.26137 | −0.188508 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −52.4924 | −1.87833 | ||||||||
\(782\) | −10.2462 | −0.366404 | ||||||||
\(783\) | − | 2.00000i | − | 0.0714742i | ||||||
\(784\) | 2.75379 | 0.0983496 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | − | 4.00000i | − | 0.142675i | ||||||
\(787\) | 12.3845 | 0.441459 | 0.220729 | − | 0.975335i | \(-0.429156\pi\) | ||||
0.220729 | + | 0.975335i | \(0.429156\pi\) | |||||||
\(788\) | −16.2462 | −0.578747 | ||||||||
\(789\) | 27.3693 | 0.974373 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.2462i | 1.35988i | ||||||||
\(792\) | − | 5.12311i | − | 0.182042i | ||||||
\(793\) | −5.61553 | − | 35.6155i | −0.199413 | − | 1.26474i | ||||
\(794\) | 15.3693 | 0.545437 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.2462 | −0.646720 | ||||||||
\(797\) | 25.8617i | 0.916070i | 0.888934 | + | 0.458035i | \(0.151447\pi\) | ||||
−0.888934 | + | 0.458035i | \(0.848553\pi\) | |||||||
\(798\) | −18.7386 | −0.663340 | ||||||||
\(799\) | 12.4924i | 0.441950i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.12311i | 0.110350i | ||||||||
\(802\) | − | 1.36932i | − | 0.0483523i | ||||||
\(803\) | − | 67.2311i | − | 2.37253i | ||||||
\(804\) | 4.87689i | 0.171995i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.1231 | − | 1.75379i | 0.391795 | − | 0.0617746i | ||||
\(807\) | − | 16.2462i | − | 0.571894i | ||||||
\(808\) | −12.2462 | −0.430820 | ||||||||
\(809\) | 13.5076 | 0.474901 | 0.237451 | − | 0.971400i | \(-0.423688\pi\) | ||||
0.237451 | + | 0.971400i | \(0.423688\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 27.7538i | − | 0.974567i | −0.873244 | − | 0.487284i | \(-0.837988\pi\) | ||
0.873244 | − | 0.487284i | \(-0.162012\pi\) | |||||||
\(812\) | 6.24621 | 0.219199 | ||||||||
\(813\) | 23.1231 | 0.810963 | ||||||||
\(814\) | 26.2462i | 0.919929i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.00000 | 0.0700140 | ||||||||
\(817\) | 37.4773 | 1.31116 | ||||||||
\(818\) | − | 8.49242i | − | 0.296931i | ||||||
\(819\) | −1.75379 | − | 11.1231i | −0.0612823 | − | 0.388673i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.2462i | 1.54420i | 0.635499 | + | 0.772102i | \(0.280794\pi\) | ||||
−0.635499 | + | 0.772102i | \(0.719206\pi\) | |||||||
\(822\) | − | 10.4924i | − | 0.365965i | ||||||
\(823\) | 42.8769i | 1.49459i | 0.664490 | + | 0.747297i | \(0.268649\pi\) | ||||
−0.664490 | + | 0.747297i | \(0.731351\pi\) | |||||||
\(824\) | 13.1231i | 0.457165i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 3.50758i | − | 0.122044i | ||||||
\(827\) | −1.26137 | −0.0438620 | −0.0219310 | − | 0.999759i | \(-0.506981\pi\) | ||||
−0.0219310 | + | 0.999759i | \(0.506981\pi\) | |||||||
\(828\) | − | 5.12311i | − | 0.178040i | ||||||
\(829\) | 24.2462 | 0.842106 | 0.421053 | − | 0.907036i | \(-0.361661\pi\) | ||||
0.421053 | + | 0.907036i | \(0.361661\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.8617 | −1.03589 | ||||||||
\(832\) | −0.561553 | − | 3.56155i | −0.0194683 | − | 0.123475i | ||||
\(833\) | 5.50758i | 0.190826i | ||||||||
\(834\) | − | 16.4924i | − | 0.571086i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −30.7386 | −1.06312 | ||||||||
\(837\) | −3.12311 | −0.107950 | ||||||||
\(838\) | 28.0000 | 0.967244 | ||||||||
\(839\) | 46.7386i | 1.61360i | 0.590827 | + | 0.806798i | \(0.298802\pi\) | ||||
−0.590827 | + | 0.806798i | \(0.701198\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | − | 0.630683i | − | 0.0217348i | ||||||
\(843\) | −3.12311 | −0.107565 | ||||||||
\(844\) | 4.00000 | 0.137686 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.24621 | −0.214749 | ||||||||
\(847\) | 47.6155 | 1.63609 | ||||||||
\(848\) | 13.3693i | 0.459104i | ||||||||
\(849\) | 4.00000 | 0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.2462i | 0.899709i | ||||||||
\(852\) | 10.2462 | 0.351029 | ||||||||
\(853\) | 35.8617 | 1.22788 | 0.613941 | − | 0.789352i | \(-0.289583\pi\) | ||||
0.613941 | + | 0.789352i | \(0.289583\pi\) | |||||||
\(854\) | −31.2311 | −1.06870 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 8.00000i | − | 0.273434i | ||||||
\(857\) | − | 30.4924i | − | 1.04160i | −0.853678 | − | 0.520801i | \(-0.825633\pi\) | ||
0.853678 | − | 0.520801i | \(-0.174367\pi\) | |||||||
\(858\) | −2.87689 | − | 18.2462i | −0.0982156 | − | 0.622915i | ||||
\(859\) | 12.0000 | 0.409435 | 0.204717 | − | 0.978821i | \(-0.434372\pi\) | ||||
0.204717 | + | 0.978821i | \(0.434372\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.73863 | −0.0933324 | ||||||||
\(862\) | − | 32.4924i | − | 1.10670i | ||||||
\(863\) | −6.24621 | −0.212624 | −0.106312 | − | 0.994333i | \(-0.533904\pi\) | ||||
−0.106312 | + | 0.994333i | \(0.533904\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18.0000i | 0.611665i | ||||||||
\(867\) | − | 13.0000i | − | 0.441503i | ||||||
\(868\) | − | 9.75379i | − | 0.331065i | ||||||
\(869\) | − | 40.9848i | − | 1.39032i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.73863 | + | 17.3693i | 0.0927951 | + | 0.588537i | ||||
\(872\) | − | 2.87689i | − | 0.0974239i | ||||||
\(873\) | −13.1231 | −0.444150 | ||||||||
\(874\) | −30.7386 | −1.03975 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.1231i | 0.443389i | ||||||||
\(877\) | 18.8769 | 0.637427 | 0.318714 | − | 0.947851i | \(-0.396749\pi\) | ||||
0.318714 | + | 0.947851i | \(0.396749\pi\) | |||||||
\(878\) | 36.4924 | 1.23156 | ||||||||
\(879\) | − | 28.7386i | − | 0.969330i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.2462 | 0.951639 | 0.475820 | − | 0.879543i | \(-0.342152\pi\) | ||||
0.475820 | + | 0.879543i | \(0.342152\pi\) | |||||||
\(882\) | −2.75379 | −0.0927249 | ||||||||
\(883\) | 9.75379i | 0.328241i | 0.986440 | + | 0.164121i | \(0.0524786\pi\) | ||||
−0.986440 | + | 0.164121i | \(0.947521\pi\) | |||||||
\(884\) | 7.12311 | − | 1.12311i | 0.239576 | − | 0.0377741i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.50758i | 0.117839i | ||||||||
\(887\) | − | 18.8769i | − | 0.633824i | −0.948455 | − | 0.316912i | \(-0.897354\pi\) | ||
0.948455 | − | 0.316912i | \(-0.102646\pi\) | |||||||
\(888\) | − | 5.12311i | − | 0.171920i | ||||||
\(889\) | 40.9848i | 1.37459i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.12311i | 0.171630i | ||||||||
\(892\) | 9.36932 | 0.313708 | ||||||||
\(893\) | 37.4773i | 1.25413i | ||||||||
\(894\) | 14.0000 | 0.468230 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.12311 | −0.104336 | ||||||||
\(897\) | −2.87689 | − | 18.2462i | −0.0960567 | − | 0.609223i | ||||
\(898\) | 28.8769i | 0.963634i | ||||||||
\(899\) | − | 6.24621i | − | 0.208323i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.7386 | −0.890793 | ||||||||
\(902\) | −4.49242 | −0.149581 | ||||||||
\(903\) | 19.5076 | 0.649172 | ||||||||
\(904\) | − | 12.2462i | − | 0.407303i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 13.3693 | 0.444166 | ||||||||
\(907\) | 25.7538i | 0.855141i | 0.903982 | + | 0.427570i | \(0.140630\pi\) | ||||
−0.903982 | + | 0.427570i | \(0.859370\pi\) | |||||||
\(908\) | −8.00000 | −0.265489 | ||||||||
\(909\) | 12.2462 | 0.406181 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.00000 | 0.132526 | 0.0662630 | − | 0.997802i | \(-0.478892\pi\) | ||||
0.0662630 | + | 0.997802i | \(0.478892\pi\) | |||||||
\(912\) | 6.00000 | 0.198680 | ||||||||
\(913\) | − | 32.0000i | − | 1.05905i | ||||||
\(914\) | −31.3693 | −1.03760 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.12311i | 0.169272i | ||||||||
\(917\) | −12.4924 | −0.412536 | ||||||||
\(918\) | −2.00000 | −0.0660098 | ||||||||
\(919\) | 21.7538 | 0.717591 | 0.358796 | − | 0.933416i | \(-0.383187\pi\) | ||||
0.358796 | + | 0.933416i | \(0.383187\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.1231i | 1.02554i | ||||||||
\(922\) | 18.4924i | 0.609016i | ||||||||
\(923\) | 36.4924 | − | 5.75379i | 1.20116 | − | 0.189388i | ||||
\(924\) | −16.0000 | −0.526361 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −21.8617 | −0.718421 | ||||||||
\(927\) | − | 13.1231i | − | 0.431019i | ||||||
\(928\) | −2.00000 | −0.0656532 | ||||||||
\(929\) | − | 28.1080i | − | 0.922192i | −0.887350 | − | 0.461096i | \(-0.847456\pi\) | ||
0.887350 | − | 0.461096i | \(-0.152544\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.5227i | 0.541511i | ||||||||
\(932\) | 7.75379i | 0.253984i | ||||||||
\(933\) | − | 8.49242i | − | 0.278029i | ||||||
\(934\) | − | 22.2462i | − | 0.727918i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.561553 | + | 3.56155i | 0.0183549 | + | 0.116413i | ||||
\(937\) | − | 20.2462i | − | 0.661415i | −0.943733 | − | 0.330707i | \(-0.892713\pi\) | ||
0.943733 | − | 0.330707i | \(-0.107287\pi\) | |||||||
\(938\) | 15.2311 | 0.497312 | ||||||||
\(939\) | −16.2462 | −0.530175 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 14.0000i | − | 0.456387i | −0.973616 | − | 0.228193i | \(-0.926718\pi\) | ||
0.973616 | − | 0.228193i | \(-0.0732819\pi\) | |||||||
\(942\) | 21.3693 | 0.696250 | ||||||||
\(943\) | −4.49242 | −0.146293 | ||||||||
\(944\) | 1.12311i | 0.0365540i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.0000 | 1.04041 | ||||||||
\(947\) | −8.49242 | −0.275967 | −0.137983 | − | 0.990435i | \(-0.544062\pi\) | ||||
−0.137983 | + | 0.990435i | \(0.544062\pi\) | |||||||
\(948\) | 8.00000i | 0.259828i | ||||||||
\(949\) | 7.36932 | + | 46.7386i | 0.239218 | + | 1.51720i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.00000i | 0.194563i | ||||||||
\(952\) | − | 6.24621i | − | 0.202441i | ||||||
\(953\) | − | 22.9848i | − | 0.744552i | −0.928122 | − | 0.372276i | \(-0.878577\pi\) | ||
0.928122 | − | 0.372276i | \(-0.121423\pi\) | |||||||
\(954\) | − | 13.3693i | − | 0.432848i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 4.49242i | − | 0.145295i | ||||||
\(957\) | −10.2462 | −0.331213 | ||||||||
\(958\) | 12.4924i | 0.403612i | ||||||||
\(959\) | −32.7689 | −1.05816 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.2462 | 0.685362 | ||||||||
\(962\) | −2.87689 | − | 18.2462i | −0.0927548 | − | 0.588281i | ||||
\(963\) | 8.00000i | 0.257796i | ||||||||
\(964\) | − | 14.2462i | − | 0.458840i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −16.0000 | −0.514792 | ||||||||
\(967\) | 47.6155 | 1.53121 | 0.765606 | − | 0.643310i | \(-0.222439\pi\) | ||||
0.765606 | + | 0.643310i | \(0.222439\pi\) | |||||||
\(968\) | −15.2462 | −0.490032 | ||||||||
\(969\) | 12.0000i | 0.385496i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.7538 | 1.21158 | 0.605788 | − | 0.795626i | \(-0.292858\pi\) | ||||
0.605788 | + | 0.795626i | \(0.292858\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | −51.5076 | −1.65126 | ||||||||
\(974\) | −17.3693 | −0.556549 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | 4.73863 | 0.151602 | 0.0758012 | − | 0.997123i | \(-0.475849\pi\) | ||||
0.0758012 | + | 0.997123i | \(0.475849\pi\) | |||||||
\(978\) | 7.12311i | 0.227772i | ||||||||
\(979\) | 16.0000 | 0.511362 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.87689i | 0.0918522i | ||||||||
\(982\) | 38.7386 | 1.23620 | ||||||||
\(983\) | −60.4924 | −1.92941 | −0.964704 | − | 0.263335i | \(-0.915177\pi\) | ||||
−0.964704 | + | 0.263335i | \(0.915177\pi\) | |||||||
\(984\) | 0.876894 | 0.0279544 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 4.00000i | − | 0.127386i | ||||||
\(987\) | 19.5076i | 0.620933i | ||||||||
\(988\) | 21.3693 | − | 3.36932i | 0.679849 | − | 0.107192i | ||||
\(989\) | 32.0000 | 1.01754 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.7386 | −0.976445 | −0.488222 | − | 0.872719i | \(-0.662355\pi\) | ||||
−0.488222 | + | 0.872719i | \(0.662355\pi\) | |||||||
\(992\) | 3.12311i | 0.0991587i | ||||||||
\(993\) | −7.75379 | −0.246059 | ||||||||
\(994\) | − | 32.0000i | − | 1.01498i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.24621i | 0.197919i | ||||||||
\(997\) | 38.3542i | 1.21469i | 0.794439 | + | 0.607344i | \(0.207765\pi\) | ||||
−0.794439 | + | 0.607344i | \(0.792235\pi\) | |||||||
\(998\) | − | 34.4924i | − | 1.09184i | ||||||
\(999\) | 5.12311i | 0.162088i |
(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 | 1950.2.f.o.649.1 | 4 | ||
5.2 | odd | 4 | 1950.2.b.h.1351.3 | 4 | |||
5.3 | odd | 4 | 390.2.b.d.181.2 | ✓ | 4 | ||
5.4 | even | 2 | 1950.2.f.l.649.4 | 4 | |||
13.12 | even | 2 | 1950.2.f.l.649.2 | 4 | |||
15.8 | even | 4 | 1170.2.b.f.181.4 | 4 | |||
20.3 | even | 4 | 3120.2.g.o.961.3 | 4 | |||
65.8 | even | 4 | 5070.2.a.bh.1.2 | 2 | |||
65.12 | odd | 4 | 1950.2.b.h.1351.2 | 4 | |||
65.18 | even | 4 | 5070.2.a.bd.1.1 | 2 | |||
65.38 | odd | 4 | 390.2.b.d.181.3 | yes | 4 | ||
65.64 | even | 2 | inner | 1950.2.f.o.649.3 | 4 | ||
195.38 | even | 4 | 1170.2.b.f.181.1 | 4 | |||
260.103 | even | 4 | 3120.2.g.o.961.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.b.d.181.2 | ✓ | 4 | 5.3 | odd | 4 | ||
390.2.b.d.181.3 | yes | 4 | 65.38 | odd | 4 | ||
1170.2.b.f.181.1 | 4 | 195.38 | even | 4 | |||
1170.2.b.f.181.4 | 4 | 15.8 | even | 4 | |||
1950.2.b.h.1351.2 | 4 | 65.12 | odd | 4 | |||
1950.2.b.h.1351.3 | 4 | 5.2 | odd | 4 | |||
1950.2.f.l.649.2 | 4 | 13.12 | even | 2 | |||
1950.2.f.l.649.4 | 4 | 5.4 | even | 2 | |||
1950.2.f.o.649.1 | 4 | 1.1 | even | 1 | trivial | ||
1950.2.f.o.649.3 | 4 | 65.64 | even | 2 | inner | ||
3120.2.g.o.961.2 | 4 | 260.103 | even | 4 | |||
3120.2.g.o.961.3 | 4 | 20.3 | even | 4 | |||
5070.2.a.bd.1.1 | 2 | 65.18 | even | 4 | |||
5070.2.a.bh.1.2 | 2 | 65.8 | even | 4 |