Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.v (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1583.20 | ||
Character | \(\chi\) | \(=\) | 4032.1583 |
Dual form | 4032.2.v.e.3599.20 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.96859 | + | 2.96859i | 1.32760 | + | 1.32760i | 0.907463 | + | 0.420133i | \(0.138017\pi\) |
0.420133 | + | 0.907463i | \(0.361983\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.569860 | − | 0.569860i | 0.171819 | − | 0.171819i | −0.615959 | − | 0.787778i | \(-0.711231\pi\) |
0.787778 | + | 0.615959i | \(0.211231\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.53650 | + | 2.53650i | 0.703498 | + | 0.703498i | 0.965160 | − | 0.261661i | \(-0.0842704\pi\) |
−0.261661 | + | 0.965160i | \(0.584270\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.03528i | − | 0.251092i | −0.992088 | − | 0.125546i | \(-0.959932\pi\) | ||
0.992088 | − | 0.125546i | \(-0.0400683\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.23568 | − | 5.23568i | 1.20115 | − | 1.20115i | 0.227329 | − | 0.973818i | \(-0.427001\pi\) |
0.973818 | − | 0.227329i | \(-0.0729993\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.71217i | 1.81661i | 0.418304 | + | 0.908307i | \(0.362625\pi\) | ||||
−0.418304 | + | 0.908307i | \(0.637375\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.6251i | 2.52502i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.05233 | + | 6.05233i | −1.12389 | + | 1.12389i | −0.132739 | + | 0.991151i | \(0.542377\pi\) |
−0.991151 | + | 0.132739i | \(0.957623\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.00413i | − | 0.539558i | −0.962922 | − | 0.269779i | \(-0.913049\pi\) | ||
0.962922 | − | 0.269779i | \(-0.0869506\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.96859 | − | 2.96859i | −0.501784 | − | 0.501784i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.149739 | + | 0.149739i | −0.0246169 | + | 0.0246169i | −0.719308 | − | 0.694691i | \(-0.755541\pi\) |
0.694691 | + | 0.719308i | \(0.255541\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.63459 | 1.34850 | 0.674248 | − | 0.738505i | \(-0.264468\pi\) | ||||
0.674248 | + | 0.738505i | \(0.264468\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.73121 | − | 1.73121i | −0.264007 | − | 0.264007i | 0.562673 | − | 0.826680i | \(-0.309773\pi\) |
−0.826680 | + | 0.562673i | \(0.809773\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.10865 | −0.599308 | −0.299654 | − | 0.954048i | \(-0.596871\pi\) | ||||
−0.299654 | + | 0.954048i | \(0.596871\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.04092 | − | 6.04092i | −0.829783 | − | 0.829783i | 0.157703 | − | 0.987487i | \(-0.449591\pi\) |
−0.987487 | + | 0.157703i | \(0.949591\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.38337 | 0.456213 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.05121 | − | 6.05121i | 0.787800 | − | 0.787800i | −0.193333 | − | 0.981133i | \(-0.561930\pi\) |
0.981133 | + | 0.193333i | \(0.0619298\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.81897 | + | 5.81897i | 0.745042 | + | 0.745042i | 0.973544 | − | 0.228501i | \(-0.0733826\pi\) |
−0.228501 | + | 0.973544i | \(0.573383\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.0597i | 1.86792i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.0256948 | + | 0.0256948i | −0.00313912 | + | 0.00313912i | −0.708675 | − | 0.705535i | \(-0.750707\pi\) |
0.705535 | + | 0.708675i | \(0.250707\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.5257i | 1.72388i | 0.507008 | + | 0.861941i | \(0.330752\pi\) | ||||
−0.507008 | + | 0.861941i | \(0.669248\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.38496i | − | 0.630261i | −0.949048 | − | 0.315131i | \(-0.897952\pi\) | ||
0.949048 | − | 0.315131i | \(-0.102048\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.569860 | + | 0.569860i | −0.0649416 | + | 0.0649416i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.89876i | − | 0.438645i | −0.975652 | − | 0.219322i | \(-0.929615\pi\) | ||
0.975652 | − | 0.219322i | \(-0.0703846\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.40691 | + | 1.40691i | 0.154428 | + | 0.154428i | 0.780092 | − | 0.625664i | \(-0.215172\pi\) |
−0.625664 | + | 0.780092i | \(0.715172\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.07333 | − | 3.07333i | 0.333349 | − | 0.333349i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.0358 | 1.80579 | 0.902897 | − | 0.429856i | \(-0.141436\pi\) | ||||
0.902897 | + | 0.429856i | \(0.141436\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.53650 | − | 2.53650i | −0.265897 | − | 0.265897i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 31.0852 | 3.18928 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.75210 | 0.380968 | 0.190484 | − | 0.981690i | \(-0.438994\pi\) | ||||
0.190484 | + | 0.981690i | \(0.438994\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.23327 | + | 1.23327i | 0.122715 | + | 0.122715i | 0.765797 | − | 0.643082i | \(-0.222345\pi\) |
−0.643082 | + | 0.765797i | \(0.722345\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.3330 | −1.41227 | −0.706134 | − | 0.708078i | \(-0.749562\pi\) | ||||
−0.706134 | + | 0.708078i | \(0.749562\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.33395 | + | 7.33395i | −0.709000 | + | 0.709000i | −0.966325 | − | 0.257325i | \(-0.917159\pi\) |
0.257325 | + | 0.966325i | \(0.417159\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.12218 | − | 4.12218i | −0.394833 | − | 0.394833i | 0.481573 | − | 0.876406i | \(-0.340066\pi\) |
−0.876406 | + | 0.481573i | \(0.840066\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.1524i | − | 1.14320i | −0.820533 | − | 0.571599i | \(-0.806323\pi\) | ||
0.820533 | − | 0.571599i | \(-0.193677\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −25.8629 | + | 25.8629i | −2.41173 | + | 2.41173i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.03528i | 0.0949040i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3505i | 0.940956i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −22.6358 | + | 22.6358i | −2.02461 | + | 2.02461i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.32089i | − | 0.117210i | −0.998281 | − | 0.0586052i | \(-0.981335\pi\) | ||
0.998281 | − | 0.0586052i | \(-0.0186653\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.67723 | − | 1.67723i | −0.146540 | − | 0.146540i | 0.630030 | − | 0.776571i | \(-0.283043\pi\) |
−0.776571 | + | 0.630030i | \(0.783043\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.23568 | + | 5.23568i | −0.453991 | + | 0.453991i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.49554 | −0.725823 | −0.362911 | − | 0.931824i | \(-0.618217\pi\) | ||||
−0.362911 | + | 0.931824i | \(0.618217\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.80995 | + | 7.80995i | 0.662432 | + | 0.662432i | 0.955953 | − | 0.293521i | \(-0.0948271\pi\) |
−0.293521 | + | 0.955953i | \(0.594827\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.89090 | 0.241749 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −35.9338 | −2.98414 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.1113 | + | 13.1113i | 1.07412 | + | 1.07412i | 0.997024 | + | 0.0770980i | \(0.0245654\pi\) |
0.0770980 | + | 0.997024i | \(0.475435\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.4389 | −1.09364 | −0.546822 | − | 0.837249i | \(-0.684162\pi\) | ||||
−0.546822 | + | 0.837249i | \(0.684162\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.91804 | − | 8.91804i | 0.716314 | − | 0.716314i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.92492 | − | 5.92492i | −0.472860 | − | 0.472860i | 0.429979 | − | 0.902839i | \(-0.358521\pi\) |
−0.902839 | + | 0.429979i | \(0.858521\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 8.71217i | − | 0.686615i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.82469 | − | 1.82469i | 0.142921 | − | 0.142921i | −0.632026 | − | 0.774947i | \(-0.717776\pi\) |
0.774947 | + | 0.632026i | \(0.217776\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.49283i | 0.425048i | 0.977156 | + | 0.212524i | \(0.0681683\pi\) | ||||
−0.977156 | + | 0.212524i | \(0.931832\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 0.132347i | − | 0.0101805i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.4180 | − | 11.4180i | 0.868093 | − | 0.868093i | −0.124168 | − | 0.992261i | \(-0.539626\pi\) |
0.992261 | + | 0.124168i | \(0.0396262\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 12.6251i | − | 0.954368i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.47860 | − | 5.47860i | −0.409490 | − | 0.409490i | 0.472071 | − | 0.881561i | \(-0.343507\pi\) |
−0.881561 | + | 0.472071i | \(0.843507\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.42734 | + | 9.42734i | −0.700728 | + | 0.700728i | −0.964567 | − | 0.263838i | \(-0.915011\pi\) |
0.263838 | + | 0.964567i | \(0.415011\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.889027 | −0.0653625 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.589965 | − | 0.589965i | −0.0431425 | − | 0.0431425i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.1433 | 0.733946 | 0.366973 | − | 0.930232i | \(-0.380394\pi\) | ||||
0.366973 | + | 0.930232i | \(0.380394\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.6529 | −0.910774 | −0.455387 | − | 0.890294i | \(-0.650499\pi\) | ||||
−0.455387 | + | 0.890294i | \(0.650499\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.32030 | + | 4.32030i | 0.307808 | + | 0.307808i | 0.844059 | − | 0.536250i | \(-0.180160\pi\) |
−0.536250 | + | 0.844059i | \(0.680160\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.22338 | −0.512052 | −0.256026 | − | 0.966670i | \(-0.582413\pi\) | ||||
−0.256026 | + | 0.966670i | \(0.582413\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.05233 | − | 6.05233i | 0.424790 | − | 0.424790i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 25.6326 | + | 25.6326i | 1.79026 | + | 1.79026i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 5.96721i | − | 0.412760i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.51875 | + | 9.51875i | −0.655298 | + | 0.655298i | −0.954264 | − | 0.298966i | \(-0.903358\pi\) |
0.298966 | + | 0.954264i | \(0.403358\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 10.2785i | − | 0.700989i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.00413i | 0.203934i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.62599 | − | 2.62599i | 0.176643 | − | 0.176643i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 16.0637i | − | 1.07571i | −0.843038 | − | 0.537853i | \(-0.819235\pi\) | ||
0.843038 | − | 0.537853i | \(-0.180765\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.5695 | + | 11.5695i | 0.767894 | + | 0.767894i | 0.977735 | − | 0.209842i | \(-0.0672949\pi\) |
−0.209842 | + | 0.977735i | \(0.567295\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.50533 | + | 4.50533i | −0.297721 | + | 0.297721i | −0.840121 | − | 0.542400i | \(-0.817516\pi\) |
0.542400 | + | 0.840121i | \(0.317516\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.2560 | 1.06496 | 0.532482 | − | 0.846442i | \(-0.321260\pi\) | ||||
0.532482 | + | 0.846442i | \(0.321260\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.1969 | − | 12.1969i | −0.795638 | − | 0.795638i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.55597 | 0.294701 | 0.147351 | − | 0.989084i | \(-0.452925\pi\) | ||||
0.147351 | + | 0.989084i | \(0.452925\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.0079 | −1.41765 | −0.708827 | − | 0.705382i | \(-0.750775\pi\) | ||||
−0.708827 | + | 0.705382i | \(0.750775\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.96859 | + | 2.96859i | 0.189657 | + | 0.189657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.5606 | 1.69001 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.15767 | − | 3.15767i | 0.199311 | − | 0.199311i | −0.600394 | − | 0.799704i | \(-0.704990\pi\) |
0.799704 | + | 0.600394i | \(0.204990\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.96472 | + | 4.96472i | 0.312129 | + | 0.312129i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.930640i | 0.0580517i | 0.999579 | + | 0.0290259i | \(0.00924052\pi\) | ||||
−0.999579 | + | 0.0290259i | \(0.990759\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.149739 | − | 0.149739i | 0.00930431 | − | 0.00930431i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 14.8926i | − | 0.918319i | −0.888354 | − | 0.459160i | \(-0.848151\pi\) | ||
0.888354 | − | 0.459160i | \(-0.151849\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 35.8660i | − | 2.20323i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.20537 | + | 7.20537i | −0.439319 | + | 0.439319i | −0.891783 | − | 0.452464i | \(-0.850545\pi\) |
0.452464 | + | 0.891783i | \(0.350545\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.2262i | 1.53238i | 0.642611 | + | 0.766192i | \(0.277851\pi\) | ||||
−0.642611 | + | 0.766192i | \(0.722149\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.19454 | + | 7.19454i | 0.433847 | + | 0.433847i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.1502 | − | 10.1502i | 0.609866 | − | 0.609866i | −0.333045 | − | 0.942911i | \(-0.608076\pi\) |
0.942911 | + | 0.333045i | \(0.108076\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.47979 | −0.565517 | −0.282758 | − | 0.959191i | \(-0.591249\pi\) | ||||
−0.282758 | + | 0.959191i | \(0.591249\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.74974 | − | 2.74974i | −0.163455 | − | 0.163455i | 0.620640 | − | 0.784095i | \(-0.286873\pi\) |
−0.784095 | + | 0.620640i | \(0.786873\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.63459 | −0.509683 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.9282 | 0.936953 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.497276 | + | 0.497276i | 0.0290512 | + | 0.0290512i | 0.721483 | − | 0.692432i | \(-0.243461\pi\) |
−0.692432 | + | 0.721483i | \(0.743461\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 35.9272 | 2.09176 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −22.0984 | + | 22.0984i | −1.27798 | + | 1.27798i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.73121 | + | 1.73121i | 0.0997853 | + | 0.0997853i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 34.5483i | 1.97823i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.0456 | + | 11.0456i | −0.630408 | + | 0.630408i | −0.948170 | − | 0.317762i | \(-0.897069\pi\) |
0.317762 | + | 0.948170i | \(0.397069\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.7421i | 1.40299i | 0.712672 | + | 0.701497i | \(0.247485\pi\) | ||||
−0.712672 | + | 0.701497i | \(0.752515\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 20.1653i | − | 1.13981i | −0.821710 | − | 0.569906i | \(-0.806980\pi\) | ||
0.821710 | − | 0.569906i | \(-0.193020\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.70522 | + | 8.70522i | −0.488934 | + | 0.488934i | −0.907970 | − | 0.419036i | \(-0.862368\pi\) |
0.419036 | + | 0.907970i | \(0.362368\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.89796i | 0.386212i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.42040 | − | 5.42040i | −0.301599 | − | 0.301599i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −32.0235 | + | 32.0235i | −1.77635 | + | 1.77635i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.10865 | 0.226517 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.78793 | + | 2.78793i | 0.153239 | + | 0.153239i | 0.779563 | − | 0.626324i | \(-0.215441\pi\) |
−0.626324 | + | 0.779563i | \(0.715441\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.152555 | −0.00833496 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.465376 | −0.0253506 | −0.0126753 | − | 0.999920i | \(-0.504035\pi\) | ||||
−0.0126753 | + | 0.999920i | \(0.504035\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.71193 | − | 1.71193i | −0.0927064 | − | 0.0927064i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.3262 | + | 21.3262i | −1.14485 | + | 1.14485i | −0.157299 | + | 0.987551i | \(0.550279\pi\) |
−0.987551 | + | 0.157299i | \(0.949721\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.11124 | + | 5.11124i | 0.273598 | + | 0.273598i | 0.830547 | − | 0.556949i | \(-0.188028\pi\) |
−0.556949 | + | 0.830547i | \(0.688028\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10.2227i | − | 0.544102i | −0.962283 | − | 0.272051i | \(-0.912298\pi\) | ||
0.962283 | − | 0.272051i | \(-0.0877019\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −43.1209 | + | 43.1209i | −2.28862 | + | 2.28862i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.90071i | 0.311427i | 0.987802 | + | 0.155714i | \(0.0497677\pi\) | ||||
−0.987802 | + | 0.155714i | \(0.950232\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 35.8247i | − | 1.88551i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.9857 | − | 15.9857i | 0.836732 | − | 0.836732i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 14.1762i | − | 0.739994i | −0.929033 | − | 0.369997i | \(-0.879359\pi\) | ||
0.929033 | − | 0.369997i | \(-0.120641\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.04092 | + | 6.04092i | 0.313629 | + | 0.313629i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.5106 | − | 21.5106i | 1.11378 | − | 1.11378i | 0.121141 | − | 0.992635i | \(-0.461345\pi\) |
0.992635 | − | 0.121141i | \(-0.0386553\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −30.7035 | −1.58131 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.15510 | + | 8.15510i | 0.418900 | + | 0.418900i | 0.884824 | − | 0.465925i | \(-0.154278\pi\) |
−0.465925 | + | 0.884824i | \(0.654278\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.06121 | 0.463006 | 0.231503 | − | 0.972834i | \(-0.425636\pi\) | ||||
0.231503 | + | 0.972834i | \(0.425636\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.38337 | −0.172432 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.1084 | − | 22.1084i | −1.12094 | − | 1.12094i | −0.991600 | − | 0.129339i | \(-0.958715\pi\) |
−0.129339 | − | 0.991600i | \(-0.541285\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.01954 | 0.456138 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.5738 | − | 11.5738i | 0.582343 | − | 0.582343i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.1321 | − | 25.1321i | −1.26134 | − | 1.26134i | −0.950443 | − | 0.310899i | \(-0.899370\pi\) |
−0.310899 | − | 0.950443i | \(-0.600630\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.54588i | − | 0.0771975i | −0.999255 | − | 0.0385987i | \(-0.987711\pi\) | ||
0.999255 | − | 0.0385987i | \(-0.0122894\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.61997 | − | 7.61997i | 0.379578 | − | 0.379578i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.170660i | 0.00845931i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.72850i | − | 0.283256i | −0.989920 | − | 0.141628i | \(-0.954766\pi\) | ||
0.989920 | − | 0.141628i | \(-0.0452337\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.05121 | + | 6.05121i | −0.297761 | + | 0.297761i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.35307i | 0.410036i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.2299 | + | 26.2299i | 1.28141 | + | 1.28141i | 0.939863 | + | 0.341551i | \(0.110952\pi\) |
0.341551 | + | 0.939863i | \(0.389048\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.38496 | − | 9.38496i | 0.457395 | − | 0.457395i | −0.440404 | − | 0.897800i | \(-0.645165\pi\) |
0.897800 | + | 0.440404i | \(0.145165\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.0705 | 0.634013 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.81897 | − | 5.81897i | −0.281599 | − | 0.281599i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.9406 | 0.767830 | 0.383915 | − | 0.923368i | \(-0.374576\pi\) | ||||
0.383915 | + | 0.923368i | \(0.374576\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.0062 | 1.20172 | 0.600862 | − | 0.799353i | \(-0.294824\pi\) | ||||
0.600862 | + | 0.799353i | \(0.294824\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 45.6141 | + | 45.6141i | 2.18202 | + | 2.18202i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.0522 | 1.67295 | 0.836474 | − | 0.548007i | \(-0.184613\pi\) | ||||
0.836474 | + | 0.548007i | \(0.184613\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.1307 | + | 17.1307i | −0.813904 | + | 0.813904i | −0.985217 | − | 0.171313i | \(-0.945199\pi\) |
0.171313 | + | 0.985217i | \(0.445199\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 50.5725 | + | 50.5725i | 2.39737 | + | 2.39737i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 14.7964i | − | 0.698286i | −0.937070 | − | 0.349143i | \(-0.886473\pi\) | ||
0.937070 | − | 0.349143i | \(-0.113527\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.92050 | − | 4.92050i | 0.231697 | − | 0.231697i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 15.0597i | − | 0.706008i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.9903i | 0.560883i | 0.959871 | + | 0.280442i | \(0.0904809\pi\) | ||||
−0.959871 | + | 0.280442i | \(0.909519\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.9493 | − | 14.9493i | 0.696260 | − | 0.696260i | −0.267342 | − | 0.963602i | \(-0.586145\pi\) |
0.963602 | + | 0.267342i | \(0.0861453\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 31.4696i | − | 1.46252i | −0.682101 | − | 0.731258i | \(-0.738933\pi\) | ||
0.682101 | − | 0.731258i | \(-0.261067\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.7699 | − | 24.7699i | −1.14621 | − | 1.14621i | −0.987291 | − | 0.158922i | \(-0.949198\pi\) |
−0.158922 | − | 0.987291i | \(-0.550802\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0256948 | − | 0.0256948i | 0.00118647 | − | 0.00118647i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.97310 | −0.0907230 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 66.1010 | + | 66.1010i | 3.03292 | + | 3.03292i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.7194 | 0.809620 | 0.404810 | − | 0.914401i | \(-0.367338\pi\) | ||||
0.404810 | + | 0.914401i | \(0.367338\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.759624 | −0.0346359 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.1385 | + | 11.1385i | 0.505772 | + | 0.505772i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.8639 | 1.53452 | 0.767260 | − | 0.641336i | \(-0.221619\pi\) | ||||
0.767260 | + | 0.641336i | \(0.221619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.3486 | + | 25.3486i | −1.14397 | + | 1.14397i | −0.156248 | + | 0.987718i | \(0.549940\pi\) |
−0.987718 | + | 0.156248i | \(0.950060\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.26586 | + | 6.26586i | 0.282200 | + | 0.282200i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 14.5257i | − | 0.651566i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.26690 | − | 7.26690i | 0.325311 | − | 0.325311i | −0.525489 | − | 0.850800i | \(-0.676118\pi\) |
0.850800 | + | 0.525489i | \(0.176118\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 12.3031i | − | 0.548567i | −0.961649 | − | 0.274284i | \(-0.911559\pi\) | ||
0.961649 | − | 0.274284i | \(-0.0884407\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.32217i | 0.325832i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0082 | − | 14.0082i | 0.620901 | − | 0.620901i | −0.324861 | − | 0.945762i | \(-0.605318\pi\) |
0.945762 | + | 0.324861i | \(0.105318\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.38496i | 0.238216i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −42.5487 | − | 42.5487i | −1.87492 | − | 1.87492i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.34135 | + | 2.34135i | −0.102973 | + | 0.102973i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.8204 | 1.61313 | 0.806566 | − | 0.591144i | \(-0.201323\pi\) | ||||
0.806566 | + | 0.591144i | \(0.201323\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.49783 | − | 2.49783i | −0.109222 | − | 0.109222i | 0.650384 | − | 0.759606i | \(-0.274608\pi\) |
−0.759606 | + | 0.650384i | \(0.774608\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.11012 | −0.135479 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −52.9020 | −2.30009 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.9016 | + | 21.9016i | 0.948664 | + | 0.948664i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −43.5431 | −1.88253 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.569860 | − | 0.569860i | 0.0245456 | − | 0.0245456i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.5049 | + | 14.5049i | 0.623613 | + | 0.623613i | 0.946453 | − | 0.322841i | \(-0.104638\pi\) |
−0.322841 | + | 0.946453i | \(0.604638\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 24.4742i | − | 1.04836i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.3072 | + | 10.3072i | −0.440704 | + | 0.440704i | −0.892249 | − | 0.451545i | \(-0.850873\pi\) |
0.451545 | + | 0.892249i | \(0.350873\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 63.3761i | 2.69991i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.89876i | 0.165792i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.62884 | − | 8.62884i | 0.365616 | − | 0.365616i | −0.500260 | − | 0.865875i | \(-0.666762\pi\) |
0.865875 | + | 0.500260i | \(0.166762\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.78243i | − | 0.371457i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.3155 | + | 10.3155i | 0.434748 | + | 0.434748i | 0.890240 | − | 0.455492i | \(-0.150537\pi\) |
−0.455492 | + | 0.890240i | \(0.650537\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 36.0755 | − | 36.0755i | 1.51771 | − | 1.51771i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.23614 | −0.135666 | −0.0678330 | − | 0.997697i | \(-0.521609\pi\) | ||||
−0.0678330 | + | 0.997697i | \(0.521609\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.7822 | − | 27.7822i | −1.16265 | − | 1.16265i | −0.983893 | − | 0.178757i | \(-0.942792\pi\) |
−0.178757 | − | 0.983893i | \(-0.557208\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −109.992 | −4.58699 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.0528 | 0.918072 | 0.459036 | − | 0.888418i | \(-0.348195\pi\) | ||||
0.459036 | + | 0.888418i | \(0.348195\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.40691 | − | 1.40691i | −0.0583684 | − | 0.0583684i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.88495 | −0.285146 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.9242 | − | 16.9242i | 0.698538 | − | 0.698538i | −0.265557 | − | 0.964095i | \(-0.585556\pi\) |
0.964095 | + | 0.265557i | \(0.0855560\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.7287 | − | 15.7287i | −0.648088 | − | 0.648088i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.14027i | 0.375346i | 0.982232 | + | 0.187673i | \(0.0600945\pi\) | ||||
−0.982232 | + | 0.187673i | \(0.939905\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.07333 | + | 3.07333i | −0.125994 | + | 0.125994i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 26.4441i | − | 1.08047i | −0.841513 | − | 0.540237i | \(-0.818334\pi\) | ||
0.841513 | − | 0.540237i | \(-0.181666\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 28.3857i | − | 1.15788i | −0.815371 | − | 0.578938i | \(-0.803467\pi\) | ||
0.815371 | − | 0.578938i | \(-0.196533\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30.7265 | + | 30.7265i | −1.24921 | + | 1.24921i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 9.53246i | − | 0.386911i | −0.981109 | − | 0.193455i | \(-0.938031\pi\) | ||
0.981109 | − | 0.193455i | \(-0.0619695\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.4216 | − | 10.4216i | −0.421612 | − | 0.421612i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.07498 | − | 1.07498i | 0.0434181 | − | 0.0434181i | −0.685064 | − | 0.728483i | \(-0.740226\pi\) |
0.728483 | + | 0.685064i | \(0.240226\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.3828 | 1.42446 | 0.712229 | − | 0.701948i | \(-0.247686\pi\) | ||||
0.712229 | + | 0.701948i | \(0.247686\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.97297 | + | 3.97297i | 0.159687 | + | 0.159687i | 0.782428 | − | 0.622741i | \(-0.213981\pi\) |
−0.622741 | + | 0.782428i | \(0.713981\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.0358 | −0.682526 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −71.2676 | −2.85070 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.155022 | + | 0.155022i | 0.00618111 | + | 0.00618111i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.6289 | 1.02027 | 0.510135 | − | 0.860095i | \(-0.329596\pi\) | ||||
0.510135 | + | 0.860095i | \(0.329596\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.92120 | − | 3.92120i | 0.155608 | − | 0.155608i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.53650 | + | 2.53650i | 0.100500 | + | 0.100500i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 10.5770i | − | 0.417766i | −0.977941 | − | 0.208883i | \(-0.933017\pi\) | ||
0.977941 | − | 0.208883i | \(-0.0669829\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.26445 | + | 8.26445i | −0.325918 | + | 0.325918i | −0.851032 | − | 0.525114i | \(-0.824023\pi\) |
0.525114 | + | 0.851032i | \(0.324023\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 23.2954i | − | 0.915835i | −0.888995 | − | 0.457917i | \(-0.848596\pi\) | ||
0.888995 | − | 0.457917i | \(-0.151404\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 6.89668i | − | 0.270718i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.0365 | + | 20.0365i | −0.784090 | + | 0.784090i | −0.980518 | − | 0.196429i | \(-0.937066\pi\) |
0.196429 | + | 0.980518i | \(0.437066\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 9.95804i | − | 0.389093i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.7397 | − | 24.7397i | −0.963723 | − | 0.963723i | 0.0356416 | − | 0.999365i | \(-0.488653\pi\) |
−0.999365 | + | 0.0356416i | \(0.988653\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.31446 | + | 6.31446i | −0.245604 | + | 0.245604i | −0.819164 | − | 0.573560i | \(-0.805562\pi\) |
0.573560 | + | 0.819164i | \(0.305562\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −31.0852 | −1.20543 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −52.7290 | − | 52.7290i | −2.04167 | − | 2.04167i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.63199 | 0.256025 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.32930 | 0.0897877 | 0.0448939 | − | 0.998992i | \(-0.485705\pi\) | ||||
0.0448939 | + | 0.998992i | \(0.485705\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.0208 | − | 17.0208i | −0.654163 | − | 0.654163i | 0.299830 | − | 0.953993i | \(-0.403070\pi\) |
−0.953993 | + | 0.299830i | \(0.903070\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.75210 | −0.143993 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.18231 | − | 5.18231i | 0.198296 | − | 0.198296i | −0.600973 | − | 0.799269i | \(-0.705220\pi\) |
0.799269 | + | 0.600973i | \(0.205220\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.2198 | − | 25.2198i | −0.963599 | − | 0.963599i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 30.6455i | − | 1.16750i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.6472 | − | 23.6472i | 0.899582 | − | 0.899582i | −0.0958169 | − | 0.995399i | \(-0.530546\pi\) |
0.995399 | + | 0.0958169i | \(0.0305463\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 46.3692i | 1.75888i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8.93922i | − | 0.338597i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.62771 | + | 4.62771i | −0.174786 | + | 0.174786i | −0.789078 | − | 0.614292i | \(-0.789442\pi\) |
0.614292 | + | 0.789078i | \(0.289442\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.56797i | 0.0591370i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.23327 | − | 1.23327i | −0.0463820 | − | 0.0463820i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.1441 | + | 27.1441i | −1.01942 | + | 1.01942i | −0.0196099 | + | 0.999808i | \(0.506242\pi\) |
−0.999808 | + | 0.0196099i | \(0.993758\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.1725 | 0.980168 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.58190 | + | 8.58190i | 0.320945 | + | 0.320945i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 39.3061 | 1.46587 | 0.732934 | − | 0.680299i | \(-0.238150\pi\) | ||||
0.732934 | + | 0.680299i | \(0.238150\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.3330 | 0.533787 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −76.4113 | − | 76.4113i | −2.83784 | − | 2.83784i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.1990 | −1.34255 | −0.671274 | − | 0.741209i | \(-0.734253\pi\) | ||||
−0.671274 | + | 0.741209i | \(0.734253\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.79229 | + | 1.79229i | −0.0662902 | + | 0.0662902i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.85554 | − | 3.85554i | −0.142408 | − | 0.142408i | 0.632309 | − | 0.774716i | \(-0.282107\pi\) |
−0.774716 | + | 0.632309i | \(0.782107\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.0292849i | 0.00107872i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.1965 | − | 20.1965i | 0.742942 | − | 0.742942i | −0.230201 | − | 0.973143i | \(-0.573939\pi\) |
0.973143 | + | 0.230201i | \(0.0739385\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 38.9110i | − | 1.42751i | −0.700398 | − | 0.713753i | \(-0.746994\pi\) | ||
0.700398 | − | 0.713753i | \(-0.253006\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 77.8444i | 2.85200i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.33395 | − | 7.33395i | 0.267977 | − | 0.267977i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.20106i | − | 0.0438274i | −0.999760 | − | 0.0219137i | \(-0.993024\pi\) | ||
0.999760 | − | 0.0219137i | \(-0.00697590\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39.8947 | − | 39.8947i | −1.45192 | − | 1.45192i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.9836 | − | 12.9836i | 0.471896 | − | 0.471896i | −0.430632 | − | 0.902528i | \(-0.641709\pi\) |
0.902528 | + | 0.430632i | \(0.141709\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.4747 | −0.597208 | −0.298604 | − | 0.954377i | \(-0.596521\pi\) | ||||
−0.298604 | + | 0.954377i | \(0.596521\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.12218 | + | 4.12218i | 0.149233 | + | 0.149233i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30.6978 | 1.10843 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.6226 | 1.21246 | 0.606231 | − | 0.795289i | \(-0.292681\pi\) | ||||
0.606231 | + | 0.795289i | \(0.292681\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.0820 | − | 20.0820i | −0.722299 | − | 0.722299i | 0.246774 | − | 0.969073i | \(-0.420629\pi\) |
−0.969073 | + | 0.246774i | \(0.920629\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37.9274 | 1.36239 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 45.2079 | − | 45.2079i | 1.61974 | − | 1.61974i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.27761 | + | 8.27761i | 0.296196 | + | 0.296196i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 35.1774i | − | 1.25553i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.75329 | − | 1.75329i | 0.0624980 | − | 0.0624980i | −0.675167 | − | 0.737665i | \(-0.735928\pi\) |
0.737665 | + | 0.675167i | \(0.235928\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.1524i | 0.432089i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.5196i | 1.04827i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.1165 | + | 16.1165i | −0.570876 | + | 0.570876i | −0.932373 | − | 0.361497i | \(-0.882266\pi\) |
0.361497 | + | 0.932373i | \(0.382266\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.25360i | 0.150482i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.06867 | − | 3.06867i | −0.108291 | − | 0.108291i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.8629 | − | 25.8629i | 0.911548 | − | 0.911548i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.3586 | 1.06735 | 0.533676 | − | 0.845689i | \(-0.320810\pi\) | ||||
0.533676 | + | 0.845689i | \(0.320810\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.3645 | − | 20.3645i | −0.715095 | − | 0.715095i | 0.252502 | − | 0.967596i | \(-0.418747\pi\) |
−0.967596 | + | 0.252502i | \(0.918747\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.8336 | 0.379483 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.1281 | −0.634223 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.3970 | − | 35.3970i | −1.23536 | − | 1.23536i | −0.961876 | − | 0.273487i | \(-0.911823\pi\) |
−0.273487 | − | 0.961876i | \(-0.588177\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.6885 | −0.860587 | −0.430294 | − | 0.902689i | \(-0.641590\pi\) | ||||
−0.430294 | + | 0.902689i | \(0.641590\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.8496 | − | 37.8496i | 1.31616 | − | 1.31616i | 0.399369 | − | 0.916790i | \(-0.369229\pi\) |
0.916790 | − | 0.399369i | \(-0.130771\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.82230 | − | 5.82230i | −0.202217 | − | 0.202217i | 0.598732 | − | 0.800949i | \(-0.295671\pi\) |
−0.800949 | + | 0.598732i | \(0.795671\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.03528i | − | 0.0358703i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.3060 | + | 16.3060i | −0.564291 | + | 0.564291i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 24.7552i | − | 0.854645i | −0.904099 | − | 0.427323i | \(-0.859457\pi\) | ||
0.904099 | − | 0.427323i | \(-0.140543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 44.2615i | − | 1.52626i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.392885 | − | 0.392885i | 0.0135156 | − | 0.0135156i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.3505i | − | 0.355648i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.30455 | − | 1.30455i | −0.0447194 | − | 0.0447194i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.64611 | − | 9.64611i | 0.330276 | − | 0.330276i | −0.522415 | − | 0.852691i | \(-0.674969\pi\) |
0.852691 | + | 0.522415i | \(0.174969\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.92127 | −0.0997886 | −0.0498943 | − | 0.998755i | \(-0.515888\pi\) | ||||
−0.0498943 | + | 0.998755i | \(0.515888\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.63800 | + | 1.63800i | 0.0558880 | + | 0.0558880i | 0.734498 | − | 0.678610i | \(-0.237418\pi\) |
−0.678610 | + | 0.734498i | \(0.737418\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 54.6506 | 1.86033 | 0.930164 | − | 0.367145i | \(-0.119665\pi\) | ||||
0.930164 | + | 0.367145i | \(0.119665\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 67.7907 | 2.30495 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.22175 | − | 2.22175i | −0.0753676 | − | 0.0753676i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.130350 | −0.00441673 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.6358 | − | 22.6358i | 0.765230 | − | 0.765230i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.8847 | − | 28.8847i | −0.975368 | − | 0.975368i | 0.0243360 | − | 0.999704i | \(-0.492253\pi\) |
−0.999704 | + | 0.0243360i | \(0.992253\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 22.1474i | − | 0.746166i | −0.927798 | − | 0.373083i | \(-0.878301\pi\) | ||
0.927798 | − | 0.373083i | \(-0.121699\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.6797 | − | 34.6797i | 1.16706 | − | 1.16706i | 0.184169 | − | 0.982895i | \(-0.441041\pi\) |
0.982895 | − | 0.184169i | \(-0.0589594\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 21.6236i | − | 0.726050i | −0.931779 | − | 0.363025i | \(-0.881744\pi\) | ||
0.931779 | − | 0.363025i | \(-0.118256\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.32089i | 0.0443014i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.5116 | + | 21.5116i | −0.719857 | + | 0.719857i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 32.5275i | − | 1.08727i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.1820 | + | 18.1820i | 0.606403 | + | 0.606403i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.25404 | + | 6.25404i | −0.208352 | + | 0.208352i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −55.9719 | −1.86057 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.3334 | + | 37.3334i | 1.23963 | + | 1.23963i | 0.960150 | + | 0.279485i | \(0.0901637\pi\) |
0.279485 | + | 0.960150i | \(0.409836\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.0091 | 0.729194 | 0.364597 | − | 0.931165i | \(-0.381207\pi\) | ||||
0.364597 | + | 0.931165i | \(0.381207\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.60348 | 0.0530674 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.67723 | + | 1.67723i | 0.0553871 | + | 0.0553871i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.8652 | −1.18308 | −0.591542 | − | 0.806274i | \(-0.701481\pi\) | ||||
−0.591542 | + | 0.806274i | \(0.701481\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36.8444 | + | 36.8444i | −1.21275 | + | 1.21275i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.89047 | − | 1.89047i | −0.0621581 | − | 0.0621581i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 16.1094i | − | 0.528531i | −0.964450 | − | 0.264265i | \(-0.914870\pi\) | ||
0.964450 | − | 0.264265i | \(-0.0851295\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.23568 | − | 5.23568i | 0.171592 | − | 0.171592i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 3.50273i | − | 0.114552i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 17.5529i | − | 0.573429i | −0.958016 | − | 0.286714i | \(-0.907437\pi\) | ||
0.958016 | − | 0.286714i | \(-0.0925630\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.41436 | + | 6.41436i | −0.209102 | + | 0.209102i | −0.803886 | − | 0.594784i | \(-0.797238\pi\) |
0.594784 | + | 0.803886i | \(0.297238\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 75.2260i | 2.44970i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.95690 | + | 7.95690i | 0.258564 | + | 0.258564i | 0.824470 | − | 0.565906i | \(-0.191473\pi\) |
−0.565906 | + | 0.824470i | \(0.691473\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.6589 | − | 13.6589i | 0.443388 | − | 0.443388i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.4471 | −1.47217 | −0.736087 | − | 0.676887i | \(-0.763329\pi\) | ||||
−0.736087 | + | 0.676887i | \(0.763329\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.1114 | + | 30.1114i | 0.974383 | + | 0.974383i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.49554 | 0.274335 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.9752 | 0.708878 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −37.5612 | − | 37.5612i | −1.20914 | − | 1.20914i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −62.0308 | −1.99478 | −0.997389 | − | 0.0722214i | \(-0.976991\pi\) | ||||
−0.997389 | + | 0.0722214i | \(0.976991\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.5203 | + | 11.5203i | −0.369704 | + | 0.369704i | −0.867369 | − | 0.497665i | \(-0.834191\pi\) |
0.497665 | + | 0.867369i | \(0.334191\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.80995 | − | 7.80995i | −0.250376 | − | 0.250376i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.9755i | 0.990995i | 0.868609 | + | 0.495498i | \(0.165014\pi\) | ||||
−0.868609 | + | 0.495498i | \(0.834986\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.70804 | − | 9.70804i | 0.310270 | − | 0.310270i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.7177i | 1.26680i | 0.773825 | + | 0.633399i | \(0.218341\pi\) | ||||
−0.773825 | + | 0.633399i | \(0.781659\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.6504i | 0.817290i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.0826 | − | 15.0826i | 0.479599 | − | 0.479599i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 44.2359i | − | 1.40520i | −0.711585 | − | 0.702600i | \(-0.752022\pi\) | ||
0.711585 | − | 0.702600i | \(-0.247978\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.4433 | − | 21.4433i | −0.679798 | − | 0.679798i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.7318 | + | 19.7318i | −0.624913 | + | 0.624913i | −0.946784 | − | 0.321871i | \(-0.895688\pi\) |
0.321871 | + | 0.946784i | \(0.395688\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4032.2.v.e.1583.20 | 40 | ||
3.2 | odd | 2 | inner | 4032.2.v.e.1583.1 | 40 | ||
4.3 | odd | 2 | 1008.2.v.e.323.9 | ✓ | 40 | ||
12.11 | even | 2 | 1008.2.v.e.323.12 | yes | 40 | ||
16.5 | even | 4 | 1008.2.v.e.827.12 | yes | 40 | ||
16.11 | odd | 4 | inner | 4032.2.v.e.3599.1 | 40 | ||
48.5 | odd | 4 | 1008.2.v.e.827.9 | yes | 40 | ||
48.11 | even | 4 | inner | 4032.2.v.e.3599.20 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.v.e.323.9 | ✓ | 40 | 4.3 | odd | 2 | ||
1008.2.v.e.323.12 | yes | 40 | 12.11 | even | 2 | ||
1008.2.v.e.827.9 | yes | 40 | 48.5 | odd | 4 | ||
1008.2.v.e.827.12 | yes | 40 | 16.5 | even | 4 | ||
4032.2.v.e.1583.1 | 40 | 3.2 | odd | 2 | inner | ||
4032.2.v.e.1583.20 | 40 | 1.1 | even | 1 | trivial | ||
4032.2.v.e.3599.1 | 40 | 16.11 | odd | 4 | inner | ||
4032.2.v.e.3599.20 | 40 | 48.11 | even | 4 | inner |