Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,4,Mod(95,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.95");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.k (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: | \(22.6567334422\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 95.13 | ||
Character | \(\chi\) | \(=\) | 384.95 |
Dual form | 384.4.k.b.287.13 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.13522 | + | 5.07063i | 0.218474 | + | 0.975843i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −11.2665 | − | 11.2665i | −1.00771 | − | 1.00771i | −0.999970 | − | 0.00773900i | \(-0.997537\pi\) |
−0.00773900 | − | 0.999970i | \(-0.502463\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 30.2121 | 1.63130 | 0.815649 | − | 0.578547i | \(-0.196380\pi\) | ||||
0.815649 | + | 0.578547i | \(0.196380\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −24.4225 | + | 11.5126i | −0.904538 | + | 0.426393i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.9799 | + | 14.9799i | −0.410601 | + | 0.410601i | −0.881948 | − | 0.471347i | \(-0.843768\pi\) |
0.471347 | + | 0.881948i | \(0.343768\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.4733 | − | 10.4733i | −0.223444 | − | 0.223444i | 0.586503 | − | 0.809947i | \(-0.300504\pi\) |
−0.809947 | + | 0.586503i | \(0.800504\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 44.3383 | − | 69.9184i | 0.763207 | − | 1.20352i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 69.5806i | − | 0.992693i | −0.868124 | − | 0.496347i | \(-0.834675\pi\) | ||
0.868124 | − | 0.496347i | \(-0.165325\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 36.4354 | − | 36.4354i | 0.439940 | − | 0.439940i | −0.452052 | − | 0.891992i | \(-0.649308\pi\) |
0.891992 | + | 0.452052i | \(0.149308\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 34.2975 | + | 153.194i | 0.356396 | + | 1.59189i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.28579i | − | 0.0116568i | −0.999983 | − | 0.00582838i | \(-0.998145\pi\) | ||
0.999983 | − | 0.00582838i | \(-0.00185524\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 128.869i | 1.03096i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −86.1012 | − | 110.768i | −0.613710 | − | 0.789531i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 119.373 | − | 119.373i | 0.764382 | − | 0.764382i | −0.212729 | − | 0.977111i | \(-0.568235\pi\) |
0.977111 | + | 0.212729i | \(0.0682352\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 172.615i | − | 1.00008i | −0.866002 | − | 0.500041i | \(-0.833318\pi\) | ||
0.866002 | − | 0.500041i | \(-0.166682\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −92.9630 | − | 58.9519i | −0.490387 | − | 0.310976i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −340.385 | − | 340.385i | −1.64387 | − | 1.64387i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 235.193 | − | 235.193i | 1.04501 | − | 1.04501i | 0.0460739 | − | 0.998938i | \(-0.485329\pi\) |
0.998938 | − | 0.0460739i | \(-0.0146710\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 41.2167 | − | 64.9958i | 0.169230 | − | 0.266863i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 19.9510 | 0.0759957 | 0.0379979 | − | 0.999278i | \(-0.487902\pi\) | ||||
0.0379979 | + | 0.999278i | \(0.487902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 294.812 | + | 294.812i | 1.04554 | + | 1.04554i | 0.998912 | + | 0.0466324i | \(0.0148489\pi\) |
0.0466324 | + | 0.998912i | \(0.485151\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 404.864 | + | 145.450i | 1.34119 | + | 0.481832i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 69.5052 | 0.215710 | 0.107855 | − | 0.994167i | \(-0.465602\pi\) | ||||
0.107855 | + | 0.994167i | \(0.465602\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 569.769 | 1.66113 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 352.818 | − | 78.9896i | 0.968713 | − | 0.216878i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −122.813 | − | 122.813i | −0.318295 | − | 0.318295i | 0.529817 | − | 0.848112i | \(-0.322261\pi\) |
−0.848112 | + | 0.529817i | \(0.822261\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 337.543 | 0.827532 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 226.113 | + | 143.388i | 0.525427 | + | 0.333196i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 63.2396 | − | 63.2396i | 0.139544 | − | 0.139544i | −0.633884 | − | 0.773428i | \(-0.718540\pi\) |
0.773428 | + | 0.633884i | \(0.218540\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 352.521 | + | 352.521i | 0.739928 | + | 0.739928i | 0.972564 | − | 0.232636i | \(-0.0747349\pi\) |
−0.232636 | + | 0.972564i | \(0.574735\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −737.855 | + | 347.819i | −1.47557 | + | 0.695574i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 235.996i | 0.450334i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 228.455 | − | 228.455i | 0.416570 | − | 0.416570i | −0.467450 | − | 0.884020i | \(-0.654827\pi\) |
0.884020 | + | 0.467450i | \(0.154827\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.51976 | − | 1.45966i | 0.0113752 | − | 0.00254670i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 524.753i | − | 0.877137i | −0.898698 | − | 0.438568i | \(-0.855486\pi\) | ||
0.898698 | − | 0.438568i | \(-0.144514\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 578.802i | 0.927994i | 0.885837 | + | 0.463997i | \(0.153585\pi\) | ||||
−0.885837 | + | 0.463997i | \(0.846415\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −653.449 | + | 146.296i | −1.00605 | + | 0.225237i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −452.573 | + | 452.573i | −0.669812 | + | 0.669812i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 745.229i | − | 1.06133i | −0.847583 | − | 0.530664i | \(-0.821943\pi\) | ||
0.847583 | − | 0.530664i | \(-0.178057\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 463.920 | − | 562.334i | 0.636379 | − | 0.771377i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 286.237 | + | 286.237i | 0.378537 | + | 0.378537i | 0.870574 | − | 0.492037i | \(-0.163748\pi\) |
−0.492037 | + | 0.870574i | \(0.663748\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −783.932 | + | 783.932i | −1.00035 | + | 1.00035i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 740.814 | + | 469.783i | 0.912914 | + | 0.578919i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 203.128 | 0.241927 | 0.120964 | − | 0.992657i | \(-0.461402\pi\) | ||||
0.120964 | + | 0.992657i | \(0.461402\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −316.421 | − | 316.421i | −0.364504 | − | 0.364504i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 875.266 | − | 195.957i | 0.975923 | − | 0.218492i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −821.001 | −0.886662 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −39.4244 | −0.0412674 | −0.0206337 | − | 0.999787i | \(-0.506568\pi\) | ||||
−0.0206337 | + | 0.999787i | \(0.506568\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 193.389 | − | 538.304i | 0.196327 | − | 0.546481i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −477.063 | − | 477.063i | −0.469996 | − | 0.469996i | 0.431917 | − | 0.901913i | \(-0.357837\pi\) |
−0.901913 | + | 0.431917i | \(0.857837\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1080.92 | −1.03404 | −0.517022 | − | 0.855972i | \(-0.672960\pi\) | ||||
−0.517022 | + | 0.855972i | \(0.672960\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1339.55 | − | 2112.38i | 1.24502 | − | 1.96331i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1267.21 | − | 1267.21i | 1.14491 | − | 1.14491i | 0.157374 | − | 0.987539i | \(-0.449697\pi\) |
0.987539 | − | 0.157374i | \(-0.0503029\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1252.27 | − | 1252.27i | −1.10042 | − | 1.10042i | −0.994360 | − | 0.106058i | \(-0.966177\pi\) |
−0.106058 | − | 0.994360i | \(-0.533823\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1459.57 | + | 925.578i | 1.24808 | + | 0.791459i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 644.877i | − | 0.536858i | −0.963299 | − | 0.268429i | \(-0.913496\pi\) | ||
0.963299 | − | 0.268429i | \(-0.0865045\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.4864 | + | 14.4864i | −0.0117466 | + | 0.0117466i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 376.360 | + | 135.210i | 0.297389 | + | 0.106839i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2102.18i | − | 1.61938i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 882.206i | 0.662814i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 22.6489 | + | 101.164i | 0.0166031 | + | 0.0741599i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 43.5945 | − | 43.5945i | 0.0311937 | − | 0.0311937i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 713.342i | − | 0.498417i | −0.968450 | − | 0.249208i | \(-0.919830\pi\) | ||
0.968450 | − | 0.249208i | \(-0.0801704\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1160.20 | + | 1829.56i | −0.791863 | + | 1.24871i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −342.230 | − | 342.230i | −0.228250 | − | 0.228250i | 0.583711 | − | 0.811961i | \(-0.301600\pi\) |
−0.811961 | + | 0.583711i | \(0.801600\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1100.79 | − | 1100.79i | 0.717673 | − | 0.717673i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −277.912 | + | 2218.03i | −0.177177 | + | 1.41406i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3148.95 | −1.96374 | −0.981872 | − | 0.189546i | \(-0.939299\pi\) | ||||
−0.981872 | + | 0.189546i | \(0.939299\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 308.310 | + | 308.310i | 0.188133 | + | 0.188133i | 0.794889 | − | 0.606755i | \(-0.207529\pi\) |
−0.606755 | + | 0.794889i | \(0.707529\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 78.9040 | + | 352.435i | 0.0471271 | + | 0.210499i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 313.778 | 0.183493 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2689.85 | −1.54055 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 646.816 | + | 2889.09i | 0.362915 | + | 1.62101i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −397.287 | − | 397.287i | −0.218437 | − | 0.218437i | 0.589403 | − | 0.807839i | \(-0.299363\pi\) |
−0.807839 | + | 0.589403i | \(0.799363\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1028.33 | −0.554200 | −0.277100 | − | 0.960841i | \(-0.589373\pi\) | ||||
−0.277100 | + | 0.960841i | \(0.589373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 801.054 | + | 1699.34i | 0.423277 | + | 0.897929i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1944.77 | + | 1944.77i | −1.00779 | + | 1.00779i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −154.961 | − | 154.961i | −0.0787721 | − | 0.0787721i | 0.666623 | − | 0.745395i | \(-0.267739\pi\) |
−0.745395 | + | 0.666623i | \(0.767739\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 483.318 | − | 762.159i | 0.241067 | − | 0.380145i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 38.8464i | − | 0.0190157i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1541.10 | + | 1541.10i | −0.740540 | + | 0.740540i | −0.972682 | − | 0.232142i | \(-0.925427\pi\) |
0.232142 | + | 0.972682i | \(0.425427\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 383.187 | + | 1711.55i | 0.180794 | + | 0.807541i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2839.46i | 1.31571i | 0.753143 | + | 0.657856i | \(0.228537\pi\) | ||||
−0.753143 | + | 0.657856i | \(0.771463\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1977.62i | − | 0.900145i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −470.378 | + | 1309.31i | −0.210355 | + | 0.585529i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2220.59 | + | 2220.59i | −0.975885 | + | 0.975885i | −0.999716 | − | 0.0238309i | \(-0.992414\pi\) |
0.0238309 | + | 0.999716i | \(0.492414\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3893.41i | 1.68180i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 392.456 | + | 248.873i | 0.166660 | + | 0.105686i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1986.85 | − | 1986.85i | −0.829630 | − | 0.829630i | 0.157835 | − | 0.987465i | \(-0.449549\pi\) |
−0.987465 | + | 0.157835i | \(0.949549\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.17608 | + | 8.17608i | −0.00335759 | + | 0.00335759i | −0.708784 | − | 0.705426i | \(-0.750756\pi\) |
0.705426 | + | 0.708784i | \(0.250756\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1387.31 | + | 2187.69i | −0.560399 | + | 0.883709i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5299.61 | −2.10614 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1042.31 | + | 1042.31i | 0.407600 | + | 0.407600i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2601.29 | − | 3346.54i | −1.00114 | − | 1.28796i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3114.07 | 1.17972 | 0.589860 | − | 0.807506i | \(-0.299183\pi\) | ||||
0.589860 | + | 0.807506i | \(0.299183\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4424.82 | 1.65029 | 0.825144 | − | 0.564922i | \(-0.191094\pi\) | ||||
0.825144 | + | 0.564922i | \(0.191094\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1196.65 | + | 267.908i | −0.439455 | + | 0.0983862i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1951.27 | + | 1951.27i | 0.705697 | + | 0.705697i | 0.965627 | − | 0.259931i | \(-0.0836997\pi\) |
−0.259931 | + | 0.965627i | \(0.583700\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2770.53 | 0.986922 | 0.493461 | − | 0.869768i | \(-0.335731\pi\) | ||||
0.493461 | + | 0.869768i | \(0.335731\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1417.76 | + | 899.062i | 0.497517 | + | 0.315497i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3606.52 | − | 3606.52i | 1.24694 | − | 1.24694i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −224.779 | − | 224.779i | −0.0765816 | − | 0.0765816i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.8028 | + | 31.4022i | 0.00497036 | + | 0.0105440i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1091.60i | 0.361279i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3424.36 | + | 3424.36i | −1.11726 | + | 1.11726i | −0.125124 | + | 0.992141i | \(0.539933\pi\) |
−0.992141 | + | 0.125124i | \(0.960067\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2660.83 | − | 595.712i | 0.855947 | − | 0.191632i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 6643.02i | − | 2.10721i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 5215.06i | − | 1.63143i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2934.89 | + | 657.070i | −0.905577 | + | 0.202743i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −728.740 | + | 728.740i | −0.221812 | + | 0.221812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1568.26i | 0.470934i | 0.971882 | + | 0.235467i | \(0.0756619\pi\) | ||||
−0.971882 | + | 0.235467i | \(0.924338\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1483.62 | − | 3147.32i | −0.439592 | − | 0.932538i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2298.97 | + | 2298.97i | 0.672193 | + | 0.672193i | 0.958221 | − | 0.286028i | \(-0.0923351\pi\) |
−0.286028 | + | 0.958221i | \(0.592335\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 844.364 | − | 844.364i | 0.243656 | − | 0.243656i | −0.574705 | − | 0.818361i | \(-0.694883\pi\) |
0.818361 | + | 0.574705i | \(0.194883\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2808.60 | − | 1781.06i | −0.799968 | − | 0.507295i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7011.40 | 1.97138 | 0.985692 | − | 0.168558i | \(-0.0539111\pi\) | ||||
0.985692 | + | 0.168558i | \(0.0539111\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −783.083 | − | 783.083i | −0.217373 | − | 0.217373i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3778.78 | − | 846.002i | 1.03569 | − | 0.231872i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1850.30 | −0.500779 | −0.250389 | − | 0.968145i | \(-0.580559\pi\) | ||||
−0.250389 | + | 0.968145i | \(0.580559\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5628.68 | −1.50446 | −0.752231 | − | 0.658900i | \(-0.771022\pi\) | ||||
−0.752231 | + | 0.658900i | \(0.771022\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3378.04 | + | 1713.99i | 0.891775 | + | 0.452480i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6419.32 | − | 6419.32i | −1.67394 | − | 1.67394i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −763.199 | −0.196604 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1126.46 | + | 1776.34i | −0.286692 | + | 0.452093i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 598.579 | − | 598.579i | 0.150526 | − | 0.150526i | −0.627827 | − | 0.778353i | \(-0.716056\pi\) |
0.778353 | + | 0.627827i | \(0.216056\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.2610 | + | 19.2610i | 0.00478628 | + | 0.00478628i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4864.97 | − | 3085.09i | −1.19473 | − | 0.757631i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6418.48i | 1.55787i | 0.627102 | + | 0.778937i | \(0.284241\pi\) | ||||
−0.627102 | + | 0.778937i | \(0.715759\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7105.66 | − | 7105.66i | 1.70473 | − | 1.70473i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1541.10 | + | 4289.70i | −0.365486 | + | 1.01734i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3467.23i | 0.812922i | 0.913668 | + | 0.406461i | \(0.133237\pi\) | ||||
−0.913668 | + | 0.406461i | \(0.866763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2767.35i | 0.641498i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 230.596 | + | 1029.99i | 0.0528548 | + | 0.236083i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2049.90 | + | 2049.90i | −0.464627 | + | 0.464627i | −0.900169 | − | 0.435542i | \(-0.856557\pi\) |
0.435542 | + | 0.900169i | \(0.356557\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2445.74i | − | 0.548223i | −0.961698 | − | 0.274111i | \(-0.911616\pi\) | ||
0.961698 | − | 0.274111i | \(-0.0883837\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1245.24 | − | 1963.66i | 0.276064 | − | 0.435334i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1930.45 | − | 1930.45i | −0.423311 | − | 0.423311i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4784.71 | + | 4784.71i | −1.03785 | + | 1.03785i | −0.0385995 | + | 0.999255i | \(0.512290\pi\) |
−0.999255 | + | 0.0385995i | \(0.987710\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1987.25 | + | 4215.69i | 0.426428 | + | 0.904613i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1716.06 | −0.364312 | −0.182156 | − | 0.983270i | \(-0.558308\pi\) | ||||
−0.182156 | + | 0.983270i | \(0.558308\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4822.50 | − | 4822.50i | −1.01296 | − | 1.01296i | −0.999915 | − | 0.0130454i | \(-0.995847\pi\) |
−0.0130454 | − | 0.999915i | \(-0.504153\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −932.020 | − | 4162.99i | −0.193713 | − | 0.865243i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 602.761 | 0.123972 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 71.5338 | 0.0145601 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −44.7555 | − | 199.906i | −0.00901586 | − | 0.0402705i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −768.551 | − | 768.551i | −0.153240 | − | 0.153240i | 0.626324 | − | 0.779563i | \(-0.284559\pi\) |
−0.779563 | + | 0.626324i | \(0.784559\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1424.98 | −0.281239 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2949.08 | + | 369.509i | 0.576172 | + | 0.0721923i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.4665 | + | 13.4665i | −0.00260464 | + | 0.00260464i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8906.88 | + | 8906.88i | 1.70560 | + | 1.70560i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1877.44 | − | 2960.59i | 0.355960 | − | 0.561324i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 7943.37i | − | 1.49127i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5562.98 | − | 5562.98i | 1.03419 | − | 1.03419i | 0.0347941 | − | 0.999395i | \(-0.488922\pi\) |
0.999395 | − | 0.0347941i | \(-0.0110775\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1227.09 | − | 5480.96i | −0.225912 | − | 1.00906i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 907.726i | 0.165506i | 0.996570 | + | 0.0827531i | \(0.0263713\pi\) | ||||
−0.996570 | + | 0.0827531i | \(0.973629\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1022.22i | 0.184599i | 0.995731 | + | 0.0922993i | \(0.0294217\pi\) | ||||
−0.995731 | + | 0.0922993i | \(0.970578\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12231.8 | + | 4394.35i | 2.18788 | + | 0.786011i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4180.59 | − | 4180.59i | 0.740711 | − | 0.740711i | −0.232004 | − | 0.972715i | \(-0.574528\pi\) |
0.972715 | + | 0.232004i | \(0.0745282\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3576.40i | 0.627712i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7864.11 | + | 4986.98i | 1.36739 | + | 0.867122i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2535.20 | − | 2535.20i | −0.436725 | − | 0.436725i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1349.69 | − | 1349.69i | 0.230361 | − | 0.230361i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4928.18 | − | 7771.39i | 0.833422 | − | 1.31425i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2099.90 | 0.351888 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1915.71 | − | 1915.71i | −0.318117 | − | 0.318117i | 0.529926 | − | 0.848044i | \(-0.322220\pi\) |
−0.848044 | + | 0.529926i | \(0.822220\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3036.32 | + | 8451.68i | −0.499668 | + | 1.39084i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5147.78 | −0.839563 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3088.80 | 0.499281 | 0.249641 | − | 0.968339i | \(-0.419687\pi\) | ||||
0.249641 | + | 0.968339i | \(0.419687\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3269.93 | − | 732.080i | 0.523889 | − | 0.117290i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2585.75 | + | 2585.75i | 0.410635 | + | 0.410635i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6851.17 | 1.07851 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −89.9004 | − | 57.0098i | −0.0140292 | − | 0.00889653i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2015.99 | + | 2015.99i | −0.311884 | + | 0.311884i | −0.845639 | − | 0.533755i | \(-0.820780\pi\) |
0.533755 | + | 0.845639i | \(0.320780\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2106.10 | − | 2106.10i | −0.323029 | − | 0.323029i | 0.526899 | − | 0.849928i | \(-0.323355\pi\) |
−0.849928 | + | 0.526899i | \(0.823355\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −258.346 | + | 2061.87i | −0.0392862 | + | 0.313546i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 6982.94i | − | 1.05287i | −0.850214 | − | 0.526437i | \(-0.823528\pi\) | ||
0.850214 | − | 0.526437i | \(-0.176472\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5912.14 | + | 5912.14i | −0.883898 | + | 0.883898i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10659.3 | − | 2386.44i | 1.58026 | − | 0.353792i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 8753.09i | − | 1.28683i | −0.765519 | − | 0.643413i | \(-0.777518\pi\) | ||
0.765519 | − | 0.643413i | \(-0.222482\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4203.93i | 0.612906i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4473.34 | + | 1001.50i | −0.646803 | + | 0.144808i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6521.08 | − | 6521.08i | 0.935148 | − | 0.935148i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 8242.34i | − | 1.17233i | −0.810190 | − | 0.586167i | \(-0.800636\pi\) | ||
0.810190 | − | 0.586167i | \(-0.199364\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −487.254 | + | 229.688i | −0.0687410 | + | 0.0324040i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3710.43 | − | 3710.43i | −0.519234 | − | 0.519234i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 298.350 | − | 298.350i | 0.0414154 | − | 0.0414154i | −0.686096 | − | 0.727511i | \(-0.740677\pi\) |
0.727511 | + | 0.686096i | \(0.240677\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 270.541 | + | 171.562i | 0.0372552 | + | 0.0236251i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2500.47 | −0.341594 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1059.78 | + | 1059.78i | 0.143633 | + | 0.143633i | 0.775267 | − | 0.631634i | \(-0.217615\pi\) |
−0.631634 | + | 0.775267i | \(0.717615\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3617.09 | − | 809.804i | 0.486376 | − | 0.108891i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4404.31 | −0.587597 | −0.293799 | − | 0.955867i | \(-0.594920\pi\) | ||||
−0.293799 | + | 0.955867i | \(0.594920\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10197.9 | 1.34995 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10594.1 | − | 3806.00i | −1.39155 | − | 0.499923i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9687.95 | + | 9687.95i | 1.26272 | + | 1.26272i | 0.949769 | + | 0.312953i | \(0.101318\pi\) |
0.312953 | + | 0.949769i | \(0.398682\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −89.4661 | −0.0115716 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1346.81 | − | 2123.83i | 0.172869 | − | 0.272603i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8396.15 | + | 8396.15i | −1.06951 | + | 1.06951i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −73.0707 | − | 73.0707i | −0.00923757 | − | 0.00923757i | 0.702473 | − | 0.711710i | \(-0.252079\pi\) |
−0.711710 | + | 0.702473i | \(0.752079\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6831.33 | + | 4332.05i | 0.857129 | + | 0.543543i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 340.273i | − | 0.0423751i | −0.999776 | − | 0.0211875i | \(-0.993255\pi\) | ||
0.999776 | − | 0.0211875i | \(-0.00674471\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1807.85 | + | 1807.85i | −0.223463 | + | 0.223463i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11562.3 | + | 1108.78i | −1.41861 | + | 0.136039i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7046.32i | 0.858165i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10873.6i | 1.31458i | 0.753636 | + | 0.657291i | \(0.228298\pi\) | ||||
−0.753636 | + | 0.657291i | \(0.771702\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3574.76 | − | 15967.2i | −0.429027 | − | 1.91631i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1910.60 | − | 1910.60i | 0.227638 | − | 0.227638i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 6449.80i | − | 0.762911i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1213.32 | + | 1913.33i | −0.142486 | + | 0.224691i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5701.01 | + | 5701.01i | 0.664708 | + | 0.664708i | 0.956486 | − | 0.291778i | \(-0.0942468\pi\) |
−0.291778 | + | 0.956486i | \(0.594247\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1062.79 | − | 1062.79i | 0.123034 | − | 0.123034i | −0.642909 | − | 0.765943i | \(-0.722273\pi\) |
0.765943 | + | 0.642909i | \(0.222273\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1697.49 | + | 800.186i | −0.195118 | + | 0.0919772i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8966.82 | 1.02342 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10650.4 | + | 10650.4i | 1.20704 | + | 1.20704i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 356.209 | + | 1591.05i | 0.0400884 | + | 0.179060i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2350.06 | 0.262641 | 0.131321 | − | 0.991340i | \(-0.458078\pi\) | ||||
0.131321 | + | 0.991340i | \(0.458078\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8617.75 | −0.956450 | −0.478225 | − | 0.878237i | \(-0.658720\pi\) | ||||
−0.478225 | + | 0.878237i | \(0.658720\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3053.58 | − | 13639.2i | −0.336570 | − | 1.50333i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −46.8482 | − | 46.8482i | −0.00512827 | − | 0.00512827i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4948.07 | −0.537947 | −0.268973 | − | 0.963148i | \(-0.586684\pi\) | ||||
−0.268973 | + | 0.963148i | \(0.586684\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13915.2 | + | 6559.52i | −1.50256 | + | 0.708295i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6128.78 | − | 6128.78i | 0.657307 | − | 0.657307i | −0.297435 | − | 0.954742i | \(-0.596131\pi\) |
0.954742 | + | 0.297435i | \(0.0961311\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2288.55 | − | 2288.55i | −0.243792 | − | 0.243792i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1563.49 | − | 2465.51i | 0.165437 | − | 0.260882i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13057.1i | 1.37239i | 0.727416 | + | 0.686197i | \(0.240721\pi\) | ||||
−0.727416 | + | 0.686197i | \(0.759279\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −298.864 | + | 298.864i | −0.0312039 | + | 0.0312039i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1167.38 | − | 5214.27i | −0.121078 | − | 0.540812i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7129.92i | 0.734628i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 16737.3i | − | 1.71321i | −0.515973 | − | 0.856605i | \(-0.672570\pi\) | ||
0.515973 | − | 0.856605i | \(-0.327430\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7707.32 | + | 5990.97i | −0.783762 | + | 0.609226i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11008.3 | + | 11008.3i | −1.11216 | + | 1.11216i | −0.119306 | + | 0.992857i | \(0.538067\pi\) |
−0.992857 | + | 0.119306i | \(0.961933\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1019.62i | − | 0.102345i | −0.998690 | − | 0.0511723i | \(-0.983704\pi\) | ||
0.998690 | − | 0.0511723i | \(-0.0162958\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12069.0 | − | 7653.46i | −1.20362 | − | 0.763270i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9386.52 | + | 9386.52i | 0.930099 | + | 0.930099i | 0.997712 | − | 0.0676128i | \(-0.0215383\pi\) |
−0.0676128 | + | 0.997712i | \(0.521538\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6902.09 | − | 6902.09i | 0.679550 | − | 0.679550i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 609.833 | − | 961.664i | 0.0596595 | − | 0.0940788i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8832.50 | −0.858602 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4695.41 | + | 4695.41i | 0.453558 | + | 0.453558i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4413.30 | + | 1585.51i | 0.423629 | + | 0.152191i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19141.8 | 1.82592 | 0.912958 | − | 0.408054i | \(-0.133793\pi\) | ||||
0.912958 | + | 0.408054i | \(0.133793\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4926.49 | −0.467004 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 196.975 | − | 44.0993i | 0.0185563 | − | 0.00415443i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 444.176 | + | 444.176i | 0.0415856 | + | 0.0415856i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9857.78 | 0.917246 | 0.458623 | − | 0.888631i | \(-0.348343\pi\) | ||||
0.458623 | + | 0.888631i | \(0.348343\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9563.82 | − | 6064.84i | −0.884440 | − | 0.560862i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2235.97 | − | 2235.97i | 0.205515 | − | 0.205515i | −0.596843 | − | 0.802358i | \(-0.703578\pi\) |
0.802358 | + | 0.596843i | \(0.203578\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8306.08 | − | 8306.08i | −0.758797 | − | 0.758797i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8243.65 | + | 3885.99i | −0.748534 | + | 0.352853i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 15853.9i | − | 1.43087i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1879.08 | − | 1879.08i | 0.168576 | − | 0.168576i | −0.617777 | − | 0.786353i | \(-0.711967\pi\) |
0.786353 | + | 0.617777i | \(0.211967\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14397.8 | + | 3223.42i | −1.28393 | + | 0.287449i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18597.9i | 1.64859i | 0.566161 | + | 0.824295i | \(0.308428\pi\) | ||||
−0.566161 | + | 0.824295i | \(0.691572\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10749.7i | 0.947238i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10027.8 | − | 2245.04i | 0.878400 | − | 0.196658i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12280.3 | − | 12280.3i | 1.06938 | − | 1.06938i | 0.0719701 | − | 0.997407i | \(-0.477071\pi\) |
0.997407 | − | 0.0719701i | \(-0.0229286\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17486.8i | 1.51384i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7173.01 | − | 898.753i | −0.617341 | − | 0.0773507i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12178.3 | + | 12178.3i | 1.04202 | + | 1.04202i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1041.18 | + | 1041.18i | −0.0885707 | + | 0.0885707i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13780.6 | − | 8738.91i | −1.16552 | − | 0.739105i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9893.24 | 0.831921 | 0.415961 | − | 0.909383i | \(-0.363445\pi\) | ||||
0.415961 | + | 0.909383i | \(0.363445\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7608.31 | − | 7608.31i | −0.636115 | − | 0.636115i | 0.313480 | − | 0.949595i | \(-0.398505\pi\) |
−0.949595 | + | 0.313480i | \(0.898505\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −19742.0 | + | 4419.89i | −1.64117 | + | 0.367429i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12010.7 | −0.992775 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12165.3 | 0.999864 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −816.419 | + | 2272.52i | −0.0667223 | + | 0.185723i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −208.953 | − | 208.953i | −0.0169808 | − | 0.0169808i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28554.1 | −2.30748 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7819.04 | − | 12330.1i | 0.628336 | − | 0.990841i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8535.08 | + | 8535.08i | −0.682063 | + | 0.682063i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9518.30 | − | 9518.30i | −0.756421 | − | 0.756421i | 0.219248 | − | 0.975669i | \(-0.429639\pi\) |
−0.975669 | + | 0.219248i | \(0.929639\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −50.7396 | − | 32.1762i | −0.00401002 | − | 0.00254293i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28217.4i | 2.21780i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3126.99 | + | 3126.99i | −0.244425 | + | 0.244425i | −0.818678 | − | 0.574253i | \(-0.805293\pi\) |
0.574253 | + | 0.818678i | \(0.305293\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12667.9 | − | 4551.02i | −0.984794 | − | 0.353794i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 8698.83i | − | 0.672564i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 22514.9i | − | 1.73134i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6016.25 | − | 26872.4i | −0.460136 | − | 2.05526i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8497.54 | + | 8497.54i | −0.646414 | + | 0.646414i | −0.952124 | − | 0.305711i | \(-0.901106\pi\) |
0.305711 | + | 0.952124i | \(0.401106\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6175.32i | − | 0.467242i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4101.91 | + | 6468.42i | −0.308704 | + | 0.486804i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3772.00 | − | 3772.00i | −0.282364 | − | 0.282364i | 0.551687 | − | 0.834051i | \(-0.313984\pi\) |
−0.834051 | + | 0.551687i | \(0.813984\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7265.53 | + | 7265.53i | −0.540997 | + | 0.540997i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14016.0 | − | 16989.3i | 1.03812 | − | 1.25835i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21830.1 | 1.60838 | 0.804189 | − | 0.594374i | \(-0.202600\pi\) | ||||
0.804189 | + | 0.594374i | \(0.202600\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 189.972 | + | 189.972i | 0.0139231 | + | 0.0139231i | 0.714034 | − | 0.700111i | \(-0.246866\pi\) |
−0.700111 | + | 0.714034i | \(0.746866\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3535.17 | + | 15790.3i | 0.257738 | + | 1.15122i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 165.699 | 0.0120176 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20253.3 | −1.46127 | −0.730637 | − | 0.682766i | \(-0.760777\pi\) | ||||
−0.730637 | + | 0.682766i | \(0.760777\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5023.17 | + | 22436.6i | 0.360545 | + | 1.61042i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8647.81 | + | 8647.81i | 0.617507 | + | 0.617507i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3679.45 | 0.261384 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2716.93 | − | 5763.62i | −0.192019 | − | 0.407344i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.1015 | + | 19.1015i | −0.00134311 | + | 0.00134311i | −0.707778 | − | 0.706435i | \(-0.750302\pi\) |
0.706435 | + | 0.707778i | \(0.250302\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6289.29 | − | 6289.29i | −0.439976 | − | 0.439976i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7679.04 | + | 12109.3i | −0.534473 | + | 0.842825i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 2075.52i | − | 0.143729i | −0.997414 | − | 0.0718646i | \(-0.977105\pi\) | ||
0.997414 | − | 0.0718646i | \(-0.0228950\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23684.2 | + | 23684.2i | −1.63186 | + | 1.63186i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3145.17 | + | 14048.3i | 0.215617 | + | 0.963081i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2373.75i | 0.161918i | 0.996717 | + | 0.0809589i | \(0.0257982\pi\) | ||||
−0.996717 | + | 0.0809589i | \(0.974202\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18198.0i | 1.23512i | 0.786522 | + | 0.617562i | \(0.211880\pi\) | ||||
−0.786522 | + | 0.617562i | \(0.788120\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2949.34 | + | 8209.55i | −0.199181 | + | 0.554426i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9939.40 | − | 9939.40i | 0.667924 | − | 0.667924i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6359.38i | 0.425238i | 0.977135 | + | 0.212619i | \(0.0681993\pi\) | ||||
−0.977135 | + | 0.212619i | \(0.931801\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22381.5 | + | 14193.1i | 1.48924 | + | 0.944390i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −727.950 | − | 727.950i | −0.0481992 | − | 0.0481992i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14688.4 | − | 14688.4i | 0.967796 | − | 0.967796i | −0.0317012 | − | 0.999497i | \(-0.510092\pi\) |
0.999497 | + | 0.0317012i | \(0.0100925\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 884.595 | − | 1394.94i | 0.0580005 | − | 0.0914627i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8344.93 | 0.544496 | 0.272248 | − | 0.962227i | \(-0.412233\pi\) | ||||
0.272248 | + | 0.962227i | \(0.412233\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7771.63 | + | 7771.63i | 0.504634 | + | 0.504634i | 0.912874 | − | 0.408241i | \(-0.133858\pi\) |
−0.408241 | + | 0.912874i | \(0.633858\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −142.425 | + | 110.708i | −0.00920338 | + | 0.00715388i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6136.91 | 0.394655 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15126.4 | 0.968087 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5535.08 | + | 1239.21i | −0.352551 | + | 0.0789300i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16364.9 | − | 16364.9i | −1.03738 | − | 1.03738i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2424.40 | 0.152954 | 0.0764768 | − | 0.997071i | \(-0.475633\pi\) | ||||
0.0764768 | + | 0.997071i | \(0.475633\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21251.1 | − | 13476.3i | −1.33437 | − | 0.846182i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8036.89 | + | 8036.89i | −0.502259 | + | 0.502259i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5967.37 | − | 5967.37i | −0.371171 | − | 0.371171i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6041.27 | + | 12815.8i | 0.374005 | + | 0.793404i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 17744.2i | − | 1.09338i | −0.837337 | − | 0.546688i | \(-0.815889\pi\) | ||
0.837337 | − | 0.546688i | \(-0.184111\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18580.6 | − | 18580.6i | 1.13958 | − | 1.13958i | 0.151052 | − | 0.988526i | \(-0.451734\pi\) |
0.988526 | − | 0.151052i | \(-0.0482661\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 33684.3 | − | 7541.31i | 2.05630 | − | 0.460370i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32732.6i | 1.98895i | 0.104958 | + | 0.994477i | \(0.466529\pi\) | ||||
−0.104958 | + | 0.994477i | \(0.533471\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1894.64i | 0.114594i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26443.6 | − | 5920.26i | 1.59202 | − | 0.356426i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10271.0 | + | 10271.0i | −0.615522 | + | 0.615522i | −0.944380 | − | 0.328858i | \(-0.893336\pi\) |
0.328858 | + | 0.944380i | \(0.393336\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7711.48i | 0.460019i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6663.51 | − | 14135.8i | −0.395690 | − | 0.839406i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2233.64 | − | 2233.64i | −0.132034 | − | 0.132034i | 0.638001 | − | 0.770035i | \(-0.279761\pi\) |
−0.770035 | + | 0.638001i | \(0.779761\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15832.2 | + | 15832.2i | −0.931622 | + | 0.931622i | −0.997807 | − | 0.0661854i | \(-0.978917\pi\) |
0.0661854 | + | 0.997807i | \(0.478917\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4522.45 | − | 2867.89i | −0.264913 | − | 0.167993i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −24804.1 | −1.44641 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −153.489 | − | 153.489i | −0.00891023 | − | 0.00891023i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7952.05 | + | 1780.32i | −0.459557 | + | 0.102887i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10561.4 | −0.607630 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7290.78 | 0.417591 | 0.208796 | − | 0.977959i | \(-0.433046\pi\) | ||||
0.208796 | + | 0.977959i | \(0.433046\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14274.6 | − | 11095.8i | 0.813971 | − | 0.632708i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6254.52 | − | 6254.52i | −0.355067 | − | 0.355067i | 0.506924 | − | 0.861991i | \(-0.330783\pi\) |
−0.861991 | + | 0.506924i | \(0.830783\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1191.09 | −0.0673195 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9047.37 | + | 14267.1i | −0.509098 | + | 0.802812i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11670.1 | + | 11670.1i | −0.653798 | + | 0.653798i | −0.953905 | − | 0.300108i | \(-0.902977\pi\) |
0.300108 | + | 0.953905i | \(0.402977\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35477.7 | + | 35477.7i | 1.97888 | + | 1.97888i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5240.00 | + | 3322.91i | 0.291002 | + | 0.184537i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2572.52i | 0.142242i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2970.42 | − | 2970.42i | 0.163531 | − | 0.163531i | −0.620598 | − | 0.784129i | \(-0.713110\pi\) |
0.784129 | + | 0.620598i | \(0.213110\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5842.69 | − | 16263.3i | 0.320268 | − | 0.891474i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 6947.17i | − | 0.379167i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1388.20i | − | 0.0754405i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7959.52 | + | 35552.2i | 0.430696 | + | 1.92376i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2674.46 | + | 2674.46i | −0.144099 | + | 0.144099i | −0.775476 | − | 0.631377i | \(-0.782490\pi\) |
0.631377 | + | 0.775476i | \(0.282490\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 17138.7i | − | 0.919484i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3081.75 | − | 4859.69i | 0.164632 | − | 0.259612i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14413.1 | − | 14413.1i | −0.766704 | − | 0.766704i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14743.1 | + | 14743.1i | −0.780942 | + | 0.780942i | −0.979990 | − | 0.199048i | \(-0.936215\pi\) |
0.199048 | + | 0.979990i | \(0.436215\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8579.53 | + | 18200.4i | 0.452542 | + | 0.960011i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −221.947 | −0.0116577 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3535.19 | − | 3535.19i | −0.184907 | − | 0.184907i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2100.51 | − | 9382.19i | −0.109407 | − | 0.488681i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2860.53 | 0.148372 | 0.0741861 | − | 0.997244i | \(-0.476364\pi\) | ||||
0.0741861 | + | 0.997244i | \(0.476364\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32656.9 | −1.68684 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6389.82 | − | 28540.9i | −0.328686 | − | 1.46812i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15383.6 | + | 15383.6i | 0.788044 | + | 0.788044i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4158.25 | −0.212133 | −0.106067 | − | 0.994359i | \(-0.533826\pi\) | ||||
−0.106067 | + | 0.994359i | \(0.533826\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4856.18 | + | 19074.5i | −0.246720 | + | 0.969087i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20513.2 | − | 20513.2i | 1.03790 | − | 1.03790i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5464.41 | − | 5464.41i | −0.275351 | − | 0.275351i | 0.555899 | − | 0.831250i | \(-0.312374\pi\) |
−0.831250 | + | 0.555899i | \(0.812374\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 25262.6 | − | 39837.4i | 1.26779 | − | 1.99922i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6844.45i | 0.342088i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12274.6 | + | 12274.6i | −0.611002 | + | 0.611002i | −0.943207 | − | 0.332205i | \(-0.892207\pi\) |
0.332205 | + | 0.943207i | \(0.392207\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −866.402 | − | 3869.90i | −0.0429528 | − | 0.191854i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 17013.3i | − | 0.840052i | −0.907512 | − | 0.420026i | \(-0.862021\pi\) | ||
0.907512 | − | 0.420026i | \(-0.137979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8952.10i | 0.440241i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10286.0 | − | 3695.30i | −0.503807 | − | 0.180996i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 38285.0 | − | 38285.0i | 1.86770 | − | 1.86770i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 28248.5i | − | 1.37257i | −0.727332 | − | 0.686286i | \(-0.759240\pi\) | ||
0.727332 | − | 0.686286i | \(-0.240760\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3714.69 | + | 2355.65i | 0.179775 | + | 0.114003i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11585.7 | + | 11585.7i | 0.558472 | + | 0.558472i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16064.6 | − | 16064.6i | 0.771306 | − | 0.771306i | −0.207029 | − | 0.978335i | \(-0.566379\pi\) |
0.978335 | + | 0.207029i | \(0.0663793\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −75.7997 | + | 119.531i | −0.00362498 | + | 0.00571633i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23115.8 | 1.10111 | 0.550557 | − | 0.834798i | \(-0.314415\pi\) | ||||
0.550557 | + | 0.834798i | \(0.314415\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −37833.6 | − | 37833.6i | −1.79511 | − | 1.79511i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10120.5 | − | 28170.7i | 0.478311 | − | 1.33139i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1324.66 | −0.0623606 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6409.50 | −0.300562 | −0.150281 | − | 0.988643i | \(-0.548018\pi\) | ||||
−0.150281 | + | 0.988643i | \(0.548018\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −32545.7 | + | 7286.41i | −1.52024 | + | 0.340355i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15617.9 | + | 15617.9i | 0.726699 | + | 0.726699i | 0.969961 | − | 0.243262i | \(-0.0782175\pi\) |
−0.243262 | + | 0.969961i | \(0.578218\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22244.8 | 1.03104 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 44096.7 | + | 27963.6i | 2.03598 | + | 1.29111i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 726.923 | − | 726.923i | 0.0334335 | − | 0.0334335i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7860.74 | + | 7860.74i | 0.360153 | + | 0.360153i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −23501.0 | − | 2944.59i | −1.07261 | − | 0.134395i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3491.74i | 0.158759i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24107.2 | − | 24107.2i | 1.09190 | − | 1.09190i | 0.0965795 | − | 0.995325i | \(-0.469210\pi\) |
0.995325 | − | 0.0965795i | \(-0.0307902\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −17581.0 | + | 3936.08i | −0.793284 | + | 0.177602i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 19483.1i | − | 0.875776i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 7384.12i | − | 0.330666i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14032.2 | + | 3141.56i | −0.626001 | + | 0.140151i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10177.6 | + | 10177.6i | −0.452335 | + | 0.452335i | −0.896129 | − | 0.443794i | \(-0.853632\pi\) |
0.443794 | + | 0.896129i | \(0.353632\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4836.22i | − | 0.214134i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4960.90 | + | 2338.53i | −0.218832 | + | 0.103156i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8670.38 | − | 8670.38i | −0.381035 | − | 0.381035i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −437.664 | + | 437.664i | −0.0191623 | + | 0.0191623i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12721.4 | − | 8067.18i | −0.554912 | − | 0.351894i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15986.6 | −0.694759 | −0.347380 | − | 0.937725i | \(-0.612928\pi\) | ||||
−0.347380 | + | 0.937725i | \(0.612928\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13233.6 | + | 13233.6i | 0.572990 | + | 0.572990i | 0.932963 | − | 0.359973i | \(-0.117214\pi\) |
−0.359973 | + | 0.932963i | \(0.617214\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12401.5 | − | 2776.47i | 0.534979 | − | 0.119772i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 34725.6 | 1.49250 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21483.2 | 0.919953 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11370.6 | + | 4084.97i | 0.485130 | + | 0.174286i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6092.12 | − | 6092.12i | −0.258972 | − | 0.258972i | 0.565664 | − | 0.824636i | \(-0.308620\pi\) |
−0.824636 | + | 0.565664i | \(0.808620\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28908.7 | 1.22442 | 0.612208 | − | 0.790697i | \(-0.290281\pi\) | ||||
0.612208 | + | 0.790697i | \(0.290281\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7597.10 | − | 11980.1i | 0.320602 | − | 0.505567i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8950.54 | − | 8950.54i | 0.376349 | − | 0.376349i | −0.493434 | − | 0.869783i | \(-0.664259\pi\) |
0.869783 | + | 0.493434i | \(0.164259\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5252.07 | + | 5252.07i | 0.220038 | + | 0.220038i | 0.808515 | − | 0.588476i | \(-0.200272\pi\) |
−0.588476 | + | 0.808515i | \(0.700272\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29693.2 | − | 18829.8i | −1.23953 | − | 0.786038i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 39644.9i | − | 1.64900i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31990.9 | − | 31990.9i | 1.32586 | − | 1.32586i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19120.2 | + | 14862.3i | −0.789597 | + | 0.613761i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 26507.2i | − | 1.09074i | −0.838195 | − | 0.545370i | \(-0.816389\pi\) | ||
0.838195 | − | 0.545370i | \(-0.183611\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 4111.02i | − | 0.168560i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1948.11 | − | 8701.50i | −0.0795926 | − | 0.355511i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22280.9 | + | 22280.9i | −0.907085 | + | 0.907085i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26653.3i | 1.08125i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18978.5 | − | 29927.7i | 0.767184 | − | 1.20980i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −302.408 | − | 302.408i | −0.0121815 | − | 0.0121815i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11291.0 | − | 11291.0i | 0.453222 | − | 0.453222i | −0.443201 | − | 0.896422i | \(-0.646157\pi\) |
0.896422 | + | 0.443201i | \(0.146157\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20050.9 | − | 9451.85i | 0.802020 | − | 0.378066i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37764.6 | −1.50527 | −0.752634 | − | 0.658439i | \(-0.771217\pi\) | ||||
−0.752634 | + | 0.658439i | \(0.771217\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10557.9 | + | 10557.9i | 0.419359 | + | 0.419359i | 0.884983 | − | 0.465624i | \(-0.154170\pi\) |
−0.465624 | + | 0.884983i | \(0.654170\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 684.269 | + | 3056.38i | 0.0270846 | + | 0.120977i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42832.2 | −1.68949 | −0.844743 | − | 0.535173i | \(-0.820247\pi\) | ||||
−0.844743 | + | 0.535173i | \(0.820247\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 50036.6 | 1.96682 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 81.2069 | + | 362.721i | 0.00318100 | + | 0.0142084i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11163.5 | + | 11163.5i | 0.435782 | + | 0.435782i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4785.36 | −0.186160 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 962.844 | − | 453.877i | 0.0373280 | − | 0.0175961i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1317.08 | − | 1317.08i | 0.0508863 | − | 0.0508863i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2791.16 | − | 2791.16i | −0.107469 | − | 0.107469i | 0.651327 | − | 0.758797i | \(-0.274212\pi\) |
−0.758797 | + | 0.651327i | \(0.774212\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3024.56 | − | 4769.51i | 0.116059 | − | 0.183017i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 8537.89i | − | 0.326503i | −0.986585 | − | 0.163251i | \(-0.947802\pi\) | ||
0.986585 | − | 0.163251i | \(-0.0521981\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28914.0 | + | 28914.0i | −1.10196 | + | 1.10196i | −0.107791 | + | 0.994174i | \(0.534378\pi\) |
−0.994174 | + | 0.107791i | \(0.965622\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1617.67 | − | 7225.55i | −0.0614435 | − | 0.274445i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3233.15i | 0.122389i | 0.998126 | + | 0.0611943i | \(0.0194909\pi\) | ||||
−0.998126 | + | 0.0611943i | \(0.980509\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 21551.5i | − | 0.813066i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1474.22 | + | 15373.2i | 0.0554302 | + | 0.578025i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2532.45 | − | 2532.45i | 0.0948994 | − | 0.0948994i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 44769.7i | 1.67205i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −83.5710 | − | 52.9960i | −0.00311076 | − | 0.00197267i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20605.6 | − | 20605.6i | −0.764445 | − | 0.764445i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8545.40 | + | 8545.40i | −0.315970 | + | 0.315970i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −35052.2 | + | 55274.8i | −1.29176 | + | 2.03702i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 184.232 | 0.00676694 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24455.2 | + | 24455.2i | 0.895284 | + | 0.895284i | 0.995014 | − | 0.0997307i | \(-0.0317981\pi\) |
−0.0997307 | + | 0.995014i | \(0.531798\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17143.3 | + | 6158.86i | 0.625532 | + | 0.224727i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26302.8 | 0.956589 | 0.478294 | − | 0.878200i | \(-0.341255\pi\) | ||||
0.478294 | + | 0.878200i | \(0.341255\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8575.60 | −0.310855 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 40277.9 | − | 9017.50i | 1.45524 | − | 0.325803i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10339.5 | − | 10339.5i | −0.372344 | − | 0.372344i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14271.1 | 0.512252 | 0.256126 | − | 0.966643i | \(-0.417554\pi\) | ||||
0.256126 | + | 0.966643i | \(0.417554\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 34523.0 | + | 21892.6i | 1.23515 | + | 0.783262i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5495.90 | + | 5495.90i | −0.195991 | + | 0.195991i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30309.1 | + | 30309.1i | 1.07736 | + | 1.07736i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26398.9 | − | 12444.2i | 0.935333 | − | 0.440909i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14189.2i | 0.501113i | 0.968102 | + | 0.250556i | \(0.0806135\pi\) | ||||
−0.968102 | + | 0.250556i | \(0.919386\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20759.8 | − | 20759.8i | 0.730799 | − | 0.730799i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4602.74 | + | 1030.47i | −0.161508 | + | 0.0361588i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 23486.4i | − | 0.821485i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37715.2i | 1.31494i | 0.753479 | + | 0.657472i | \(0.228374\pi\) | ||||
−0.753479 | + | 0.657472i | \(0.771626\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5183.30 | + | 1160.45i | −0.180139 | + | 0.0403300i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20871.8 | + | 20871.8i | −0.723062 | + | 0.723062i | −0.969228 | − | 0.246166i | \(-0.920829\pi\) |
0.246166 | + | 0.969228i | \(0.420829\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 25.6528i | − | 0.000885865i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8396.29 | + | 67011.4i | −0.289028 | + | 2.30675i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35217.3 | + | 35217.3i | 1.20846 | + | 1.20846i | 0.971526 | + | 0.236931i | \(0.0761415\pi\) |
0.236931 | + | 0.971526i | \(0.423858\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6061.97 | − | 6061.97i | 0.207355 | − | 0.207355i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25944.1 | + | 16452.3i | 0.884644 | + | 0.560991i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8998.22 | 0.305856 | 0.152928 | − | 0.988237i | \(-0.451130\pi\) | ||||
0.152928 | + | 0.988237i | \(0.451130\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35084.8 | − | 35084.8i | −1.18881 | − | 1.18881i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18134.6 | + | 4060.02i | −0.612548 | + | 0.137139i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −95136.3 | −3.20345 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.92611 | −0.000165356 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16359.6 | + | 45537.3i | −0.547435 | + | 1.52380i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −49852.4 | − | 49852.4i | −1.66301 | − | 1.66301i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27956.6 | 0.929702 | 0.464851 | − | 0.885389i | \(-0.346108\pi\) | ||||
0.464851 | + | 0.885389i | \(0.346108\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9977.03 | − | 15733.1i | 0.330762 | − | 0.521588i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10274.5 | − | 10274.5i | 0.339571 | − | 0.339571i | −0.516635 | − | 0.856206i | \(-0.672816\pi\) |
0.856206 | + | 0.516635i | \(0.172816\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9314.69 | + | 9314.69i | 0.306901 | + | 0.306901i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8375.97 | + | 5311.57i | 0.275124 | + | 0.174468i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50724.0i | 1.66101i | 0.557013 | + | 0.830504i | \(0.311947\pi\) | ||||
−0.557013 | + | 0.830504i | \(0.688053\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3042.83 | + | 3042.83i | −0.0993354 | + | 0.0993354i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45000.4 | + | 16166.7i | 1.46458 | + | 0.526160i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8090.00i | 0.262493i | 0.991350 | + | 0.131247i | \(0.0418980\pi\) | ||||
−0.991350 | + | 0.131247i | \(0.958102\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 43968.1i | − | 1.42227i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2383.85 | + | 10647.8i | 0.0768783 | + | 0.343387i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 379.066 | − | 379.066i | 0.0121877 | − | 0.0121877i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35268.5i | 1.13052i | 0.824914 | + | 0.565258i | \(0.191223\pi\) | ||||
−0.824914 | + | 0.565258i | \(0.808777\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7539.08 | − | 11888.6i | 0.240932 | − | 0.379933i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −31214.2 | − | 31214.2i | −0.994531 | − | 0.994531i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17738.4 | + | 17738.4i | −0.563473 | + | 0.563473i | −0.930292 | − | 0.366820i | \(-0.880447\pi\) |
0.366820 | + | 0.930292i | \(0.380447\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −46302.2 | − | 5801.51i | −1.46640 | − | 0.183735i |
(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 | 384.4.k.b.95.13 | 44 | ||
3.2 | odd | 2 | inner | 384.4.k.b.95.2 | 44 | ||
4.3 | odd | 2 | 384.4.k.a.95.10 | 44 | |||
8.3 | odd | 2 | 192.4.k.a.47.13 | 44 | |||
8.5 | even | 2 | 48.4.k.a.35.8 | yes | 44 | ||
12.11 | even | 2 | 384.4.k.a.95.21 | 44 | |||
16.3 | odd | 4 | 48.4.k.a.11.15 | yes | 44 | ||
16.5 | even | 4 | 384.4.k.a.287.21 | 44 | |||
16.11 | odd | 4 | inner | 384.4.k.b.287.2 | 44 | ||
16.13 | even | 4 | 192.4.k.a.143.2 | 44 | |||
24.5 | odd | 2 | 48.4.k.a.35.15 | yes | 44 | ||
24.11 | even | 2 | 192.4.k.a.47.2 | 44 | |||
48.5 | odd | 4 | 384.4.k.a.287.10 | 44 | |||
48.11 | even | 4 | inner | 384.4.k.b.287.13 | 44 | ||
48.29 | odd | 4 | 192.4.k.a.143.13 | 44 | |||
48.35 | even | 4 | 48.4.k.a.11.8 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.4.k.a.11.8 | ✓ | 44 | 48.35 | even | 4 | ||
48.4.k.a.11.15 | yes | 44 | 16.3 | odd | 4 | ||
48.4.k.a.35.8 | yes | 44 | 8.5 | even | 2 | ||
48.4.k.a.35.15 | yes | 44 | 24.5 | odd | 2 | ||
192.4.k.a.47.2 | 44 | 24.11 | even | 2 | |||
192.4.k.a.47.13 | 44 | 8.3 | odd | 2 | |||
192.4.k.a.143.2 | 44 | 16.13 | even | 4 | |||
192.4.k.a.143.13 | 44 | 48.29 | odd | 4 | |||
384.4.k.a.95.10 | 44 | 4.3 | odd | 2 | |||
384.4.k.a.95.21 | 44 | 12.11 | even | 2 | |||
384.4.k.a.287.10 | 44 | 48.5 | odd | 4 | |||
384.4.k.a.287.21 | 44 | 16.5 | even | 4 | |||
384.4.k.b.95.2 | 44 | 3.2 | odd | 2 | inner | ||
384.4.k.b.95.13 | 44 | 1.1 | even | 1 | trivial | ||
384.4.k.b.287.2 | 44 | 16.11 | odd | 4 | inner | ||
384.4.k.b.287.13 | 44 | 48.11 | even | 4 | inner |