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 | 649.3 | ||
Root | \(-2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.649 |
Dual form | 1950.2.f.o.649.1 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | \(-0.719088\pi\) | ||
0.635213 | − | 0.772337i | \(-0.280912\pi\) | |||||||
\(12\) | 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 | \(-0.922021\pi\) | ||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | − | 6.00000i | − | 1.37649i | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||
0.725476 | − | 0.688247i | \(-0.241620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 3.12311i | − | 0.681518i | ||||||
\(22\) | − | 5.12311i | − | 1.09225i | ||||||
\(23\) | − | 5.12311i | − | 1.06824i | −0.845408 | − | 0.534121i | \(-0.820643\pi\) | ||
0.845408 | − | 0.534121i | \(-0.179357\pi\) | |||||||
\(24\) | 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 | \(-0.909512\pi\) | ||
0.959865 | − | 0.280463i | \(-0.0904881\pi\) | |||||||
\(32\) | 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 | \(-0.978187\pi\) | ||
0.997653 | − | 0.0684739i | \(-0.0218130\pi\) | |||||||
\(42\) | − | 3.12311i | − | 0.481906i | ||||||
\(43\) | 6.24621i | 0.952538i | 0.879300 | + | 0.476269i | \(0.158011\pi\) | ||||
−0.879300 | + | 0.476269i | \(0.841989\pi\) | |||||||
\(44\) | − | 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 | \(-0.629636\pi\) | ||
0.396098 | − | 0.918208i | \(-0.370364\pi\) | |||||||
\(54\) | − | 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 | \(-0.976708\pi\) | ||
0.997324 | − | 0.0731079i | \(-0.0232918\pi\) | |||||||
\(60\) | 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 | \(-0.791972\pi\) | ||
0.793936 | − | 0.608001i | \(-0.208028\pi\) | |||||||
\(72\) | −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 | \(0.0529316\pi\) | ||||
−0.986206 | + | 0.165524i | \(0.947068\pi\) | |||||||
\(90\) | 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 | \(-0.776220\pi\) | ||
0.762889 | − | 0.646529i | \(-0.223780\pi\) | |||||||
\(104\) | −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 | \(0.126383\pi\) | ||||
−0.922208 | + | 0.386695i | \(0.873617\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | 2.87689i | 0.275557i | 0.990463 | + | 0.137778i | \(0.0439961\pi\) | ||||
−0.990463 | + | 0.137778i | \(0.956004\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.12311i | 0.486264i | ||||||||
\(112\) | −3.12311 | −0.295106 | ||||||||
\(113\) | 12.2462i | 1.15203i | 0.817440 | + | 0.576013i | \(0.195392\pi\) | ||||
−0.817440 | + | 0.576013i | \(0.804608\pi\) | |||||||
\(114\) | 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 | \(0.197825\pi\) | ||||
−0.813014 | + | 0.582244i | \(0.802175\pi\) | |||||||
\(128\) | 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 | \(-0.805600\pi\) | ||
0.819232 | − | 0.573462i | \(-0.194400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 13.3693i | − | 1.08798i | −0.839092 | − | 0.543990i | \(-0.816913\pi\) | ||
0.839092 | − | 0.543990i | \(-0.183087\pi\) | |||||||
\(152\) | − | 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 | \(-0.674946\pi\) | ||
0.522354 | − | 0.852729i | \(-0.325054\pi\) | |||||||
\(158\) | −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 | \(0.341794\pi\) | ||||
−0.476806 | + | 0.879009i | \(0.658206\pi\) | |||||||
\(174\) | − | 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 | \(-0.945858\pi\) | ||
0.985569 | − | 0.169272i | \(-0.0541417\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.0000 | −1.05272 | ||||||||
\(232\) | −2.00000 | −0.131306 | ||||||||
\(233\) | − | 7.75379i | − | 0.507968i | −0.967208 | − | 0.253984i | \(-0.918259\pi\) | ||
0.967208 | − | 0.253984i | \(-0.0817410\pi\) | |||||||
\(234\) | 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 | \(0.0464132\pi\) | ||||
−0.989388 | + | 0.145295i | \(0.953587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.2462i | 0.917679i | 0.888519 | + | 0.458840i | \(0.151735\pi\) | ||||
−0.888519 | + | 0.458840i | \(0.848265\pi\) | |||||||
\(242\) | −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 | \(0.124747\pi\) | ||||
−0.924183 | + | 0.381949i | \(0.875253\pi\) | |||||||
\(258\) | −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 | \(-0.680294\pi\) | ||
0.536607 | − | 0.843832i | \(-0.319706\pi\) | |||||||
\(264\) | 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 | \(-0.752150\pi\) | ||
0.711867 | − | 0.702314i | \(-0.247850\pi\) | |||||||
\(272\) | − | 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 | \(0.354337\pi\) | ||||
−0.441809 | + | 0.897109i | \(0.645663\pi\) | |||||||
\(278\) | 16.4924 | 0.989150 | ||||||||
\(279\) | 3.12311i | 0.186975i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.12311i | 0.186309i | 0.995652 | + | 0.0931544i | \(0.0296950\pi\) | ||||
−0.995652 | + | 0.0931544i | \(0.970305\pi\) | |||||||
\(282\) | 6.24621i | 0.371956i | ||||||||
\(283\) | − | 4.00000i | − | 0.237775i | −0.992908 | − | 0.118888i | \(-0.962067\pi\) | ||
0.992908 | − | 0.118888i | \(-0.0379328\pi\) | |||||||
\(284\) | − | 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 | \(0.151844\pi\) | ||||
−0.888361 | + | 0.459145i | \(0.848156\pi\) | |||||||
\(314\) | − | 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 | \(0.0683539\pi\) | ||||
−0.977032 | + | 0.213093i | \(0.931646\pi\) | |||||||
\(332\) | −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 | \(-0.947747\pi\) | ||
0.986557 | − | 0.163420i | \(-0.0522527\pi\) | |||||||
\(338\) | −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 | \(0.124898\pi\) | ||||
−0.924002 | + | 0.382388i | \(0.875102\pi\) | |||||||
\(348\) | − | 2.00000i | − | 0.107211i | ||||||
\(349\) | 19.3693i | 1.03682i | 0.855133 | + | 0.518408i | \(0.173475\pi\) | ||||
−0.855133 | + | 0.518408i | \(0.826525\pi\) | |||||||
\(350\) | 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 | \(0.155207\pi\) | ||||
−0.883461 | + | 0.468505i | \(0.844793\pi\) | |||||||
\(360\) | 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 | \(-0.927677\pi\) | ||
0.974299 | − | 0.225259i | \(-0.0723228\pi\) | |||||||
\(368\) | − | 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 | \(0.0590375\pi\) | ||||
−0.982849 | + | 0.184410i | \(0.940963\pi\) | |||||||
\(374\) | −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 | \(-0.950752\pi\) | ||
0.988055 | − | 0.154100i | \(-0.0492477\pi\) | |||||||
\(380\) | 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 | \(0.0108852\pi\) | ||||
−0.999415 | + | 0.0341902i | \(0.989115\pi\) | |||||||
\(402\) | − | 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 | \(0.0673339\pi\) | ||||
−0.977710 | + | 0.209962i | \(0.932666\pi\) | |||||||
\(410\) | 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 | \(0.00489224\pi\) | ||||
−0.999882 | + | 0.0153688i | \(0.995108\pi\) | |||||||
\(422\) | 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 | \(0.286083\pi\) | ||||
−0.622585 | + | 0.782552i | \(0.713917\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | − | 18.0000i | − | 0.865025i | −0.901628 | − | 0.432512i | \(-0.857627\pi\) | ||
0.901628 | − | 0.432512i | \(-0.142373\pi\) | |||||||
\(434\) | 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 | \(-0.973446\pi\) | ||
0.996522 | − | 0.0833250i | \(-0.0265540\pi\) | |||||||
\(444\) | 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 | \(-0.761375\pi\) | ||
0.731918 | − | 0.681392i | \(-0.238625\pi\) | |||||||
\(450\) | 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 | \(-0.858288\pi\) | ||
0.902524 | − | 0.430639i | \(-0.141712\pi\) | |||||||
\(462\) | −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 | \(0.172103\pi\) | ||||
−0.857361 | + | 0.514716i | \(0.827897\pi\) | |||||||
\(468\) | 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 | \(-0.907875\pi\) | ||
0.958409 | − | 0.285397i | \(-0.0921253\pi\) | |||||||
\(480\) | 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 | \(0.280767\pi\) | ||||
−0.635566 | + | 0.772046i | \(0.719233\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.2462i | 0.993887i | ||||||||
\(502\) | 26.2462 | 1.17143 | ||||||||
\(503\) | 35.3693i | 1.57704i | 0.615009 | + | 0.788520i | \(0.289152\pi\) | ||||
−0.615009 | + | 0.788520i | \(0.710848\pi\) | |||||||
\(504\) | 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 | \(0.253411\pi\) | ||||
−0.699488 | + | 0.714644i | \(0.746589\pi\) | |||||||
\(510\) | 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 | \(-0.801252\pi\) | ||
0.811322 | − | 0.584599i | \(-0.198748\pi\) | |||||||
\(524\) | 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 | \(-0.924878\pi\) | ||
0.972281 | − | 0.233817i | \(-0.0751217\pi\) | |||||||
\(542\) | − | 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 | \(-0.851914\pi\) | ||
0.893721 | − | 0.448624i | \(-0.148086\pi\) | |||||||
\(548\) | 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 | \(-0.755372\pi\) | ||
0.718939 | − | 0.695073i | \(-0.244628\pi\) | |||||||
\(564\) | 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 | \(-0.899031\pi\) | ||
0.950111 | − | 0.311911i | \(-0.100969\pi\) | |||||||
\(608\) | − | 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 | \(0.286550\pi\) | ||||
−0.621434 | + | 0.783467i | \(0.713450\pi\) | |||||||
\(620\) | 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 | \(0.250815\pi\) | ||||
−0.705293 | + | 0.708916i | \(0.749185\pi\) | |||||||
\(632\) | −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 | \(-0.802210\pi\) | ||
0.813079 | − | 0.582153i | \(-0.197790\pi\) | |||||||
\(648\) | 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 | \(-0.912571\pi\) | ||
0.962516 | − | 0.271226i | \(-0.0874290\pi\) | |||||||
\(654\) | −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 | \(-0.943224\pi\) | ||
0.984135 | − | 0.177424i | \(-0.0567763\pi\) | |||||||
\(662\) | 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 | \(0.174103\pi\) | ||||
−0.854109 | + | 0.520095i | \(0.825897\pi\) | |||||||
\(674\) | − | 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 | \(-0.920408\pi\) | ||
0.968901 | − | 0.247450i | \(-0.0795925\pi\) | |||||||
\(678\) | −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 | \(-0.815909\pi\) | ||
0.837371 | − | 0.546635i | \(-0.184091\pi\) | |||||||
\(692\) | 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 | \(-0.990342\pi\) | ||
0.999540 | − | 0.0303362i | \(-0.00965780\pi\) | |||||||
\(710\) | 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 | \(-0.879935\pi\) | ||
0.929701 | − | 0.368316i | \(-0.120065\pi\) | |||||||
\(728\) | 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 | \(-0.759897\pi\) | ||
0.728747 | − | 0.684783i | \(-0.240103\pi\) | |||||||
\(740\) | 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 | \(0.0180756\pi\) | ||||
−0.998388 | + | 0.0567556i | \(0.981924\pi\) | |||||||
\(758\) | − | 6.00000i | − | 0.217930i | ||||||
\(759\) | − | 26.2462i | − | 0.952677i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.12311i | 0.113212i | 0.998397 | + | 0.0566062i | \(0.0180280\pi\) | ||||
−0.998397 | + | 0.0566062i | \(0.981972\pi\) | |||||||
\(762\) | −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 | \(-0.797258\pi\) | ||
0.803924 | − | 0.594732i | \(-0.202742\pi\) | |||||||
\(770\) | 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 | \(-0.848553\pi\) | ||
0.888934 | − | 0.458035i | \(-0.151447\pi\) | |||||||
\(798\) | −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 | \(0.162012\pi\) | ||||
−0.873244 | + | 0.487284i | \(0.837988\pi\) | |||||||
\(812\) | 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 | \(-0.719206\pi\) | ||
0.635499 | − | 0.772102i | \(-0.280794\pi\) | |||||||
\(822\) | 10.4924i | 0.365965i | ||||||||
\(823\) | − | 42.8769i | − | 1.49459i | −0.664490 | − | 0.747297i | \(-0.731351\pi\) | ||
0.664490 | − | 0.747297i | \(-0.268649\pi\) | |||||||
\(824\) | − | 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 | \(-0.701198\pi\) | ||
0.590827 | − | 0.806798i | \(-0.298802\pi\) | |||||||
\(840\) | 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 | \(0.174367\pi\) | ||||
−0.853678 | + | 0.520801i | \(0.825633\pi\) | |||||||
\(858\) | −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 | \(-0.947521\pi\) | ||
0.986440 | − | 0.164121i | \(-0.0524786\pi\) | |||||||
\(884\) | 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 | \(0.102646\pi\) | ||||
−0.948455 | + | 0.316912i | \(0.897354\pi\) | |||||||
\(888\) | 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 | \(-0.859370\pi\) | ||
0.903982 | − | 0.427570i | \(-0.140630\pi\) | |||||||
\(908\) | −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 | \(0.152544\pi\) | ||||
−0.887350 | + | 0.461096i | \(0.847456\pi\) | |||||||
\(930\) | 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 | \(0.107287\pi\) | ||||
−0.943733 | + | 0.330707i | \(0.892713\pi\) | |||||||
\(938\) | 15.2311 | 0.497312 | ||||||||
\(939\) | −16.2462 | −0.530175 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.0000i | 0.456387i | 0.973616 | + | 0.228193i | \(0.0732819\pi\) | ||||
−0.973616 | + | 0.228193i | \(0.926718\pi\) | |||||||
\(942\) | 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 | \(0.121423\pi\) | ||||
−0.928122 | + | 0.372276i | \(0.878577\pi\) | |||||||
\(954\) | 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 | \(-0.792235\pi\) | ||
0.794439 | − | 0.607344i | \(-0.207765\pi\) | |||||||
\(998\) | 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.649.3 | 4 | ||
5.2 | odd | 4 | 390.2.b.d.181.3 | yes | 4 | ||
5.3 | odd | 4 | 1950.2.b.h.1351.2 | 4 | |||
5.4 | even | 2 | 1950.2.f.l.649.2 | 4 | |||
13.12 | even | 2 | 1950.2.f.l.649.4 | 4 | |||
15.2 | even | 4 | 1170.2.b.f.181.1 | 4 | |||
20.7 | even | 4 | 3120.2.g.o.961.2 | 4 | |||
65.12 | odd | 4 | 390.2.b.d.181.2 | ✓ | 4 | ||
65.38 | odd | 4 | 1950.2.b.h.1351.3 | 4 | |||
65.47 | even | 4 | 5070.2.a.bd.1.1 | 2 | |||
65.57 | even | 4 | 5070.2.a.bh.1.2 | 2 | |||
65.64 | even | 2 | inner | 1950.2.f.o.649.1 | 4 | ||
195.77 | even | 4 | 1170.2.b.f.181.4 | 4 | |||
260.207 | even | 4 | 3120.2.g.o.961.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.b.d.181.2 | ✓ | 4 | 65.12 | odd | 4 | ||
390.2.b.d.181.3 | yes | 4 | 5.2 | odd | 4 | ||
1170.2.b.f.181.1 | 4 | 15.2 | even | 4 | |||
1170.2.b.f.181.4 | 4 | 195.77 | even | 4 | |||
1950.2.b.h.1351.2 | 4 | 5.3 | odd | 4 | |||
1950.2.b.h.1351.3 | 4 | 65.38 | odd | 4 | |||
1950.2.f.l.649.2 | 4 | 5.4 | even | 2 | |||
1950.2.f.l.649.4 | 4 | 13.12 | even | 2 | |||
1950.2.f.o.649.1 | 4 | 65.64 | even | 2 | inner | ||
1950.2.f.o.649.3 | 4 | 1.1 | even | 1 | trivial | ||
3120.2.g.o.961.2 | 4 | 20.7 | even | 4 | |||
3120.2.g.o.961.3 | 4 | 260.207 | even | 4 | |||
5070.2.a.bd.1.1 | 2 | 65.47 | even | 4 | |||
5070.2.a.bh.1.2 | 2 | 65.57 | even | 4 |