Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(1077,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.1077");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.c (of order \(2\), degree \(1\), 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: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1077.2 | ||
Root | \(0.601150 - 2.24352i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.1077 |
Dual form | 1078.2.c.b.1077.15 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | − | 2.59518i | − | 1.49833i | −0.662385 | − | 0.749163i | \(-0.730456\pi\) | ||
0.662385 | − | 0.749163i | \(-0.269544\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 3.53900i | − | 1.58269i | −0.611372 | − | 0.791344i | \(-0.709382\pi\) | ||
0.611372 | − | 0.791344i | \(-0.290618\pi\) | |||||||
\(6\) | −2.59518 | −1.05948 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −3.73495 | −1.24498 | ||||||||
\(10\) | −3.53900 | −1.11913 | ||||||||
\(11\) | −2.29457 | + | 2.39477i | −0.691839 | + | 0.722052i | ||||
\(12\) | 2.59518i | 0.749163i | ||||||||
\(13\) | 5.01680 | 1.39141 | 0.695704 | − | 0.718328i | \(-0.255092\pi\) | ||||
0.695704 | + | 0.718328i | \(0.255092\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.18432 | −2.37138 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.89362 | −0.944342 | −0.472171 | − | 0.881507i | \(-0.656529\pi\) | ||||
−0.472171 | + | 0.881507i | \(0.656529\pi\) | |||||||
\(18\) | 3.73495i | 0.880335i | ||||||||
\(19\) | −4.65637 | −1.06825 | −0.534123 | − | 0.845407i | \(-0.679358\pi\) | ||||
−0.534123 | + | 0.845407i | \(0.679358\pi\) | |||||||
\(20\) | 3.53900i | 0.791344i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.39477 | + | 2.29457i | 0.510568 | + | 0.489204i | ||||
\(23\) | −1.55962 | −0.325204 | −0.162602 | − | 0.986692i | \(-0.551989\pi\) | ||||
−0.162602 | + | 0.986692i | \(0.551989\pi\) | |||||||
\(24\) | 2.59518 | 0.529738 | ||||||||
\(25\) | −7.52450 | −1.50490 | ||||||||
\(26\) | − | 5.01680i | − | 0.983875i | ||||||
\(27\) | 1.90732i | 0.367064i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.100205i | − | 0.0186075i | −0.999957 | − | 0.00930376i | \(-0.997038\pi\) | ||
0.999957 | − | 0.00930376i | \(-0.00296152\pi\) | |||||||
\(30\) | 9.18432i | 1.67682i | ||||||||
\(31\) | 0.279729i | 0.0502408i | 0.999684 | + | 0.0251204i | \(0.00799691\pi\) | ||||
−0.999684 | + | 0.0251204i | \(0.992003\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 6.21487 | + | 5.95482i | 1.08187 | + | 1.03660i | ||||
\(34\) | 3.89362i | 0.667750i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.73495 | 0.622491 | ||||||||
\(37\) | 0.705430 | 0.115972 | 0.0579860 | − | 0.998317i | \(-0.481532\pi\) | ||||
0.0579860 | + | 0.998317i | \(0.481532\pi\) | |||||||
\(38\) | 4.65637i | 0.755364i | ||||||||
\(39\) | − | 13.0195i | − | 2.08478i | ||||||
\(40\) | 3.53900 | 0.559564 | ||||||||
\(41\) | −2.94809 | −0.460415 | −0.230207 | − | 0.973142i | \(-0.573940\pi\) | ||||
−0.230207 | + | 0.973142i | \(0.573940\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.03556i | − | 1.37791i | −0.724804 | − | 0.688955i | \(-0.758070\pi\) | ||
0.724804 | − | 0.688955i | \(-0.241930\pi\) | |||||||
\(44\) | 2.29457 | − | 2.39477i | 0.345919 | − | 0.361026i | ||||
\(45\) | 13.2180i | 1.97042i | ||||||||
\(46\) | 1.55962i | 0.229954i | ||||||||
\(47\) | 6.56949i | 0.958259i | 0.877744 | + | 0.479129i | \(0.159048\pi\) | ||||
−0.877744 | + | 0.479129i | \(0.840952\pi\) | |||||||
\(48\) | − | 2.59518i | − | 0.374582i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.52450i | 1.06412i | ||||||||
\(51\) | 10.1046i | 1.41493i | ||||||||
\(52\) | −5.01680 | −0.695704 | ||||||||
\(53\) | 5.54058 | 0.761057 | 0.380529 | − | 0.924769i | \(-0.375742\pi\) | ||||
0.380529 | + | 0.924769i | \(0.375742\pi\) | |||||||
\(54\) | 1.90732 | 0.259553 | ||||||||
\(55\) | 8.47510 | + | 8.12048i | 1.14278 | + | 1.09496i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.0841i | 1.60058i | ||||||||
\(58\) | −0.100205 | −0.0131575 | ||||||||
\(59\) | − | 14.5344i | − | 1.89222i | −0.323853 | − | 0.946108i | \(-0.604978\pi\) | ||
0.323853 | − | 0.946108i | \(-0.395022\pi\) | |||||||
\(60\) | 9.18432 | 1.18569 | ||||||||
\(61\) | 11.1272 | 1.42469 | 0.712346 | − | 0.701828i | \(-0.247633\pi\) | ||||
0.712346 | + | 0.701828i | \(0.247633\pi\) | |||||||
\(62\) | 0.279729 | 0.0355256 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 17.7544i | − | 2.20217i | ||||||
\(66\) | 5.95482 | − | 6.21487i | 0.732987 | − | 0.764997i | ||||
\(67\) | 3.98392 | 0.486713 | 0.243356 | − | 0.969937i | \(-0.421752\pi\) | ||||
0.243356 | + | 0.969937i | \(0.421752\pi\) | |||||||
\(68\) | 3.89362 | 0.472171 | ||||||||
\(69\) | 4.04750i | 0.487262i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.45381 | −1.00328 | −0.501641 | − | 0.865076i | \(-0.667270\pi\) | ||||
−0.501641 | + | 0.865076i | \(0.667270\pi\) | |||||||
\(72\) | − | 3.73495i | − | 0.440168i | ||||||
\(73\) | 3.89771 | 0.456192 | 0.228096 | − | 0.973639i | \(-0.426750\pi\) | ||||
0.228096 | + | 0.973639i | \(0.426750\pi\) | |||||||
\(74\) | − | 0.705430i | − | 0.0820045i | ||||||
\(75\) | 19.5274i | 2.25483i | ||||||||
\(76\) | 4.65637 | 0.534123 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −13.0195 | −1.47417 | ||||||||
\(79\) | − | 7.69982i | − | 0.866297i | −0.901322 | − | 0.433149i | \(-0.857402\pi\) | ||
0.901322 | − | 0.433149i | \(-0.142598\pi\) | |||||||
\(80\) | − | 3.53900i | − | 0.395672i | ||||||
\(81\) | −6.25501 | −0.695001 | ||||||||
\(82\) | 2.94809i | 0.325562i | ||||||||
\(83\) | −2.87320 | −0.315375 | −0.157687 | − | 0.987489i | \(-0.550404\pi\) | ||||
−0.157687 | + | 0.987489i | \(0.550404\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.7795i | 1.49460i | ||||||||
\(86\) | −9.03556 | −0.974330 | ||||||||
\(87\) | −0.260049 | −0.0278801 | ||||||||
\(88\) | −2.39477 | − | 2.29457i | −0.255284 | − | 0.244602i | ||||
\(89\) | − | 5.94902i | − | 0.630595i | −0.948993 | − | 0.315297i | \(-0.897896\pi\) | ||
0.948993 | − | 0.315297i | \(-0.102104\pi\) | |||||||
\(90\) | 13.2180 | 1.39330 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.55962 | 0.162602 | ||||||||
\(93\) | 0.725946 | 0.0752771 | ||||||||
\(94\) | 6.56949 | 0.677591 | ||||||||
\(95\) | 16.4789i | 1.69070i | ||||||||
\(96\) | −2.59518 | −0.264869 | ||||||||
\(97\) | − | 16.7587i | − | 1.70159i | −0.525502 | − | 0.850793i | \(-0.676122\pi\) | ||
0.525502 | − | 0.850793i | \(-0.323878\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.57010 | − | 8.94436i | 0.861327 | − | 0.898942i | ||||
\(100\) | 7.52450 | 0.752450 | ||||||||
\(101\) | 1.40290 | 0.139594 | 0.0697971 | − | 0.997561i | \(-0.477765\pi\) | ||||
0.0697971 | + | 0.997561i | \(0.477765\pi\) | |||||||
\(102\) | 10.1046 | 1.00051 | ||||||||
\(103\) | 2.06291i | 0.203264i | 0.994822 | + | 0.101632i | \(0.0324064\pi\) | ||||
−0.994822 | + | 0.101632i | \(0.967594\pi\) | |||||||
\(104\) | 5.01680i | 0.491937i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 5.54058i | − | 0.538149i | ||||||
\(107\) | 12.2655i | 1.18575i | 0.805295 | + | 0.592875i | \(0.202007\pi\) | ||||
−0.805295 | + | 0.592875i | \(0.797993\pi\) | |||||||
\(108\) | − | 1.90732i | − | 0.183532i | ||||||
\(109\) | 6.72491i | 0.644129i | 0.946718 | + | 0.322065i | \(0.104377\pi\) | ||||
−0.946718 | + | 0.322065i | \(0.895623\pi\) | |||||||
\(110\) | 8.12048 | − | 8.47510i | 0.774257 | − | 0.808069i | ||||
\(111\) | − | 1.83072i | − | 0.173764i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.9900 | −1.12792 | −0.563960 | − | 0.825802i | \(-0.690723\pi\) | ||||
−0.563960 | + | 0.825802i | \(0.690723\pi\) | |||||||
\(114\) | 12.0841 | 1.13178 | ||||||||
\(115\) | 5.51950i | 0.514696i | ||||||||
\(116\) | 0.100205i | 0.00930376i | ||||||||
\(117\) | −18.7375 | −1.73228 | ||||||||
\(118\) | −14.5344 | −1.33800 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 9.18432i | − | 0.838410i | ||||||
\(121\) | −0.469894 | − | 10.9900i | −0.0427176 | − | 0.999087i | ||||
\(122\) | − | 11.1272i | − | 1.00741i | ||||||
\(123\) | 7.65083i | 0.689852i | ||||||||
\(124\) | − | 0.279729i | − | 0.0251204i | ||||||
\(125\) | 8.93419i | 0.799098i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2199i | 1.17308i | 0.809922 | + | 0.586538i | \(0.199509\pi\) | ||||
−0.809922 | + | 0.586538i | \(0.800491\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −23.4489 | −2.06456 | ||||||||
\(130\) | −17.7544 | −1.55717 | ||||||||
\(131\) | −16.4986 | −1.44149 | −0.720746 | − | 0.693200i | \(-0.756200\pi\) | ||||
−0.720746 | + | 0.693200i | \(0.756200\pi\) | |||||||
\(132\) | −6.21487 | − | 5.95482i | −0.540935 | − | 0.518300i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 3.98392i | − | 0.344158i | ||||||
\(135\) | 6.74999 | 0.580947 | ||||||||
\(136\) | − | 3.89362i | − | 0.333875i | ||||||
\(137\) | 6.64374 | 0.567613 | 0.283807 | − | 0.958882i | \(-0.408403\pi\) | ||||
0.283807 | + | 0.958882i | \(0.408403\pi\) | |||||||
\(138\) | 4.04750 | 0.344546 | ||||||||
\(139\) | 14.3533 | 1.21743 | 0.608716 | − | 0.793388i | \(-0.291685\pi\) | ||||
0.608716 | + | 0.793388i | \(0.291685\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.0490 | 1.43578 | ||||||||
\(142\) | 8.45381i | 0.709428i | ||||||||
\(143\) | −11.5114 | + | 12.0141i | −0.962631 | + | 1.00467i | ||||
\(144\) | −3.73495 | −0.311246 | ||||||||
\(145\) | −0.354624 | −0.0294499 | ||||||||
\(146\) | − | 3.89771i | − | 0.322577i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.705430 | −0.0579860 | ||||||||
\(149\) | 2.66587i | 0.218397i | 0.994020 | + | 0.109198i | \(0.0348284\pi\) | ||||
−0.994020 | + | 0.109198i | \(0.965172\pi\) | |||||||
\(150\) | 19.5274 | 1.59441 | ||||||||
\(151\) | − | 10.3903i | − | 0.845554i | −0.906234 | − | 0.422777i | \(-0.861055\pi\) | ||
0.906234 | − | 0.422777i | \(-0.138945\pi\) | |||||||
\(152\) | − | 4.65637i | − | 0.377682i | ||||||
\(153\) | 14.5425 | 1.17569 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.989959 | 0.0795154 | ||||||||
\(156\) | 13.0195i | 1.04239i | ||||||||
\(157\) | − | 8.37473i | − | 0.668376i | −0.942506 | − | 0.334188i | \(-0.891538\pi\) | ||
0.942506 | − | 0.334188i | \(-0.108462\pi\) | |||||||
\(158\) | −7.69982 | −0.612565 | ||||||||
\(159\) | − | 14.3788i | − | 1.14031i | ||||||
\(160\) | −3.53900 | −0.279782 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 6.25501i | 0.491440i | ||||||||
\(163\) | 3.06508 | 0.240075 | 0.120038 | − | 0.992769i | \(-0.461698\pi\) | ||||
0.120038 | + | 0.992769i | \(0.461698\pi\) | |||||||
\(164\) | 2.94809 | 0.230207 | ||||||||
\(165\) | 21.0741 | − | 21.9944i | 1.64061 | − | 1.71226i | ||||
\(166\) | 2.87320i | 0.223003i | ||||||||
\(167\) | −10.0731 | −0.779482 | −0.389741 | − | 0.920925i | \(-0.627435\pi\) | ||||
−0.389741 | + | 0.920925i | \(0.627435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1682 | 0.936018 | ||||||||
\(170\) | 13.7795 | 1.05684 | ||||||||
\(171\) | 17.3913 | 1.32995 | ||||||||
\(172\) | 9.03556i | 0.688955i | ||||||||
\(173\) | −0.0766026 | −0.00582399 | −0.00291200 | − | 0.999996i | \(-0.500927\pi\) | ||||
−0.00291200 | + | 0.999996i | \(0.500927\pi\) | |||||||
\(174\) | 0.260049i | 0.0197142i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.29457 | + | 2.39477i | −0.172960 | + | 0.180513i | ||||
\(177\) | −37.7193 | −2.83516 | ||||||||
\(178\) | −5.94902 | −0.445898 | ||||||||
\(179\) | −8.97491 | −0.670817 | −0.335408 | − | 0.942073i | \(-0.608874\pi\) | ||||
−0.335408 | + | 0.942073i | \(0.608874\pi\) | |||||||
\(180\) | − | 13.2180i | − | 0.985209i | ||||||
\(181\) | − | 15.1450i | − | 1.12572i | −0.826554 | − | 0.562858i | \(-0.809702\pi\) | ||
0.826554 | − | 0.562858i | \(-0.190298\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 28.8771i | − | 2.13465i | ||||||
\(184\) | − | 1.55962i | − | 0.114977i | ||||||
\(185\) | − | 2.49651i | − | 0.183547i | ||||||
\(186\) | − | 0.725946i | − | 0.0532289i | ||||||
\(187\) | 8.93419 | − | 9.32434i | 0.653332 | − | 0.681864i | ||||
\(188\) | − | 6.56949i | − | 0.479129i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.4789 | 1.19550 | ||||||||
\(191\) | 6.00000 | 0.434145 | 0.217072 | − | 0.976156i | \(-0.430349\pi\) | ||||
0.217072 | + | 0.976156i | \(0.430349\pi\) | |||||||
\(192\) | 2.59518i | 0.187291i | ||||||||
\(193\) | 14.8281i | 1.06735i | 0.845690 | + | 0.533674i | \(0.179189\pi\) | ||||
−0.845690 | + | 0.533674i | \(0.820811\pi\) | |||||||
\(194\) | −16.7587 | −1.20320 | ||||||||
\(195\) | −46.0759 | −3.29956 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 14.4745i | − | 1.03126i | −0.856811 | − | 0.515631i | \(-0.827557\pi\) | ||
0.856811 | − | 0.515631i | \(-0.172443\pi\) | |||||||
\(198\) | −8.94436 | − | 8.57010i | −0.635648 | − | 0.609050i | ||||
\(199\) | 11.2259i | 0.795780i | 0.917433 | + | 0.397890i | \(0.130258\pi\) | ||||
−0.917433 | + | 0.397890i | \(0.869742\pi\) | |||||||
\(200\) | − | 7.52450i | − | 0.532062i | ||||||
\(201\) | − | 10.3390i | − | 0.729255i | ||||||
\(202\) | − | 1.40290i | − | 0.0987080i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 10.1046i | − | 0.707466i | ||||||
\(205\) | 10.4333i | 0.728693i | ||||||||
\(206\) | 2.06291 | 0.143729 | ||||||||
\(207\) | 5.82511 | 0.404873 | ||||||||
\(208\) | 5.01680 | 0.347852 | ||||||||
\(209\) | 10.6844 | − | 11.1510i | 0.739054 | − | 0.771329i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.44038i | 0.443374i | 0.975118 | + | 0.221687i | \(0.0711563\pi\) | ||||
−0.975118 | + | 0.221687i | \(0.928844\pi\) | |||||||
\(212\) | −5.54058 | −0.380529 | ||||||||
\(213\) | 21.9391i | 1.50324i | ||||||||
\(214\) | 12.2655 | 0.838451 | ||||||||
\(215\) | −31.9768 | −2.18080 | ||||||||
\(216\) | −1.90732 | −0.129777 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.72491 | 0.455468 | ||||||||
\(219\) | − | 10.1152i | − | 0.683525i | ||||||
\(220\) | −8.47510 | − | 8.12048i | −0.571391 | − | 0.547482i | ||||
\(221\) | −19.5335 | −1.31397 | ||||||||
\(222\) | −1.83072 | −0.122870 | ||||||||
\(223\) | − | 4.01793i | − | 0.269061i | −0.990909 | − | 0.134530i | \(-0.957047\pi\) | ||
0.990909 | − | 0.134530i | \(-0.0429526\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 28.1036 | 1.87357 | ||||||||
\(226\) | 11.9900i | 0.797560i | ||||||||
\(227\) | −12.7293 | −0.844874 | −0.422437 | − | 0.906392i | \(-0.638825\pi\) | ||||
−0.422437 | + | 0.906392i | \(0.638825\pi\) | |||||||
\(228\) | − | 12.0841i | − | 0.800290i | ||||||
\(229\) | − | 6.01345i | − | 0.397380i | −0.980062 | − | 0.198690i | \(-0.936331\pi\) | ||
0.980062 | − | 0.198690i | \(-0.0636687\pi\) | |||||||
\(230\) | 5.51950 | 0.363945 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.100205 | 0.00657875 | ||||||||
\(233\) | 6.46694i | 0.423663i | 0.977306 | + | 0.211832i | \(0.0679428\pi\) | ||||
−0.977306 | + | 0.211832i | \(0.932057\pi\) | |||||||
\(234\) | 18.7375i | 1.22491i | ||||||||
\(235\) | 23.2494 | 1.51662 | ||||||||
\(236\) | 14.5344i | 0.946108i | ||||||||
\(237\) | −19.9824 | −1.29800 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 15.5775i | − | 1.00762i | −0.863813 | − | 0.503812i | \(-0.831930\pi\) | ||
0.863813 | − | 0.503812i | \(-0.168070\pi\) | |||||||
\(240\) | −9.18432 | −0.592846 | ||||||||
\(241\) | 23.4762 | 1.51224 | 0.756119 | − | 0.654434i | \(-0.227093\pi\) | ||||
0.756119 | + | 0.654434i | \(0.227093\pi\) | |||||||
\(242\) | −10.9900 | + | 0.469894i | −0.706461 | + | 0.0302059i | ||||
\(243\) | 21.9548i | 1.40840i | ||||||||
\(244\) | −11.1272 | −0.712346 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.65083 | 0.487799 | ||||||||
\(247\) | −23.3601 | −1.48637 | ||||||||
\(248\) | −0.279729 | −0.0177628 | ||||||||
\(249\) | 7.45646i | 0.472534i | ||||||||
\(250\) | 8.93419 | 0.565048 | ||||||||
\(251\) | 18.2818i | 1.15394i | 0.816766 | + | 0.576968i | \(0.195764\pi\) | ||||
−0.816766 | + | 0.576968i | \(0.804236\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.57867 | − | 3.73495i | 0.224989 | − | 0.234814i | ||||
\(254\) | 13.2199 | 0.829489 | ||||||||
\(255\) | 35.7603 | 2.23940 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 9.61966i | − | 0.600058i | −0.953930 | − | 0.300029i | \(-0.903004\pi\) | ||
0.953930 | − | 0.300029i | \(-0.0969964\pi\) | |||||||
\(258\) | 23.4489i | 1.45986i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 17.7544i | 1.10108i | ||||||||
\(261\) | 0.374259i | 0.0231660i | ||||||||
\(262\) | 16.4986i | 1.01929i | ||||||||
\(263\) | − | 0.578666i | − | 0.0356820i | −0.999841 | − | 0.0178410i | \(-0.994321\pi\) | ||
0.999841 | − | 0.0178410i | \(-0.00567928\pi\) | |||||||
\(264\) | −5.95482 | + | 6.21487i | −0.366494 | + | 0.382499i | ||||
\(265\) | − | 19.6081i | − | 1.20452i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.4388 | −0.944837 | ||||||||
\(268\) | −3.98392 | −0.243356 | ||||||||
\(269\) | − | 22.0896i | − | 1.34683i | −0.739266 | − | 0.673413i | \(-0.764827\pi\) | ||
0.739266 | − | 0.673413i | \(-0.235173\pi\) | |||||||
\(270\) | − | 6.74999i | − | 0.410791i | ||||||
\(271\) | −4.26222 | −0.258911 | −0.129456 | − | 0.991585i | \(-0.541323\pi\) | ||||
−0.129456 | + | 0.991585i | \(0.541323\pi\) | |||||||
\(272\) | −3.89362 | −0.236085 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 6.64374i | − | 0.401363i | ||||||
\(275\) | 17.2655 | − | 18.0195i | 1.04115 | − | 1.08662i | ||||
\(276\) | − | 4.04750i | − | 0.243631i | ||||||
\(277\) | 18.3653i | 1.10346i | 0.834022 | + | 0.551731i | \(0.186032\pi\) | ||||
−0.834022 | + | 0.551731i | \(0.813968\pi\) | |||||||
\(278\) | − | 14.3533i | − | 0.860855i | ||||||
\(279\) | − | 1.04477i | − | 0.0625489i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3.72890i | − | 0.222448i | −0.993795 | − | 0.111224i | \(-0.964523\pi\) | ||
0.993795 | − | 0.111224i | \(-0.0354771\pi\) | |||||||
\(282\) | − | 17.0490i | − | 1.01525i | ||||||
\(283\) | −12.7315 | −0.756811 | −0.378405 | − | 0.925640i | \(-0.623527\pi\) | ||||
−0.378405 | + | 0.925640i | \(0.623527\pi\) | |||||||
\(284\) | 8.45381 | 0.501641 | ||||||||
\(285\) | 42.7657 | 2.53322 | ||||||||
\(286\) | 12.0141 | + | 11.5114i | 0.710408 | + | 0.680683i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.73495i | 0.220084i | ||||||||
\(289\) | −1.83972 | −0.108219 | ||||||||
\(290\) | 0.354624i | 0.0208242i | ||||||||
\(291\) | −43.4917 | −2.54953 | ||||||||
\(292\) | −3.89771 | −0.228096 | ||||||||
\(293\) | 26.2251 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −51.4371 | −2.99478 | ||||||||
\(296\) | 0.705430i | 0.0410023i | ||||||||
\(297\) | −4.56760 | − | 4.37648i | −0.265039 | − | 0.253949i | ||||
\(298\) | 2.66587 | 0.154430 | ||||||||
\(299\) | −7.82431 | −0.452492 | ||||||||
\(300\) | − | 19.5274i | − | 1.12742i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −10.3903 | −0.597897 | ||||||||
\(303\) | − | 3.64079i | − | 0.209158i | ||||||
\(304\) | −4.65637 | −0.267061 | ||||||||
\(305\) | − | 39.3791i | − | 2.25484i | ||||||
\(306\) | − | 14.5425i | − | 0.831337i | ||||||
\(307\) | −25.5942 | −1.46074 | −0.730369 | − | 0.683053i | \(-0.760652\pi\) | ||||
−0.730369 | + | 0.683053i | \(0.760652\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.35360 | 0.304556 | ||||||||
\(310\) | − | 0.989959i | − | 0.0562259i | ||||||
\(311\) | 1.90970i | 0.108289i | 0.998533 | + | 0.0541446i | \(0.0172432\pi\) | ||||
−0.998533 | + | 0.0541446i | \(0.982757\pi\) | |||||||
\(312\) | 13.0195 | 0.737083 | ||||||||
\(313\) | − | 30.4503i | − | 1.72115i | −0.509323 | − | 0.860576i | \(-0.670104\pi\) | ||
0.509323 | − | 0.860576i | \(-0.329896\pi\) | |||||||
\(314\) | −8.37473 | −0.472613 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.69982i | 0.433149i | ||||||||
\(317\) | 34.3942 | 1.93177 | 0.965885 | − | 0.258973i | \(-0.0833841\pi\) | ||||
0.965885 | + | 0.258973i | \(0.0833841\pi\) | |||||||
\(318\) | −14.3788 | −0.806323 | ||||||||
\(319\) | 0.239967 | + | 0.229926i | 0.0134356 | + | 0.0128734i | ||||
\(320\) | 3.53900i | 0.197836i | ||||||||
\(321\) | 31.8311 | 1.77664 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.1302 | 1.00879 | ||||||||
\(324\) | 6.25501 | 0.347501 | ||||||||
\(325\) | −37.7489 | −2.09393 | ||||||||
\(326\) | − | 3.06508i | − | 0.169759i | ||||||
\(327\) | 17.4523 | 0.965116 | ||||||||
\(328\) | − | 2.94809i | − | 0.162781i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −21.9944 | − | 21.0741i | −1.21075 | − | 1.16009i | ||||
\(331\) | 15.5128 | 0.852663 | 0.426332 | − | 0.904567i | \(-0.359806\pi\) | ||||
0.426332 | + | 0.904567i | \(0.359806\pi\) | |||||||
\(332\) | 2.87320 | 0.157687 | ||||||||
\(333\) | −2.63474 | −0.144383 | ||||||||
\(334\) | 10.0731i | 0.551177i | ||||||||
\(335\) | − | 14.0991i | − | 0.770314i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.70882i | 0.419926i | 0.977709 | + | 0.209963i | \(0.0673344\pi\) | ||||
−0.977709 | + | 0.209963i | \(0.932666\pi\) | |||||||
\(338\) | − | 12.1682i | − | 0.661865i | ||||||
\(339\) | 31.1161i | 1.68999i | ||||||||
\(340\) | − | 13.7795i | − | 0.747299i | ||||||
\(341\) | −0.669887 | − | 0.641857i | −0.0362764 | − | 0.0347585i | ||||
\(342\) | − | 17.3913i | − | 0.940415i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.03556 | 0.487165 | ||||||||
\(345\) | 14.3241 | 0.771183 | ||||||||
\(346\) | 0.0766026i | 0.00411818i | ||||||||
\(347\) | − | 21.7413i | − | 1.16713i | −0.812065 | − | 0.583567i | \(-0.801657\pi\) | ||
0.812065 | − | 0.583567i | \(-0.198343\pi\) | |||||||
\(348\) | 0.260049 | 0.0139401 | ||||||||
\(349\) | −13.4565 | −0.720307 | −0.360154 | − | 0.932893i | \(-0.617276\pi\) | ||||
−0.360154 | + | 0.932893i | \(0.617276\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.56862i | 0.510735i | ||||||||
\(352\) | 2.39477 | + | 2.29457i | 0.127642 | + | 0.122301i | ||||
\(353\) | − | 6.70769i | − | 0.357014i | −0.983939 | − | 0.178507i | \(-0.942873\pi\) | ||
0.983939 | − | 0.178507i | \(-0.0571267\pi\) | |||||||
\(354\) | 37.7193i | 2.00476i | ||||||||
\(355\) | 29.9180i | 1.58788i | ||||||||
\(356\) | 5.94902i | 0.315297i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.97491i | 0.474339i | ||||||||
\(359\) | − | 31.0463i | − | 1.63856i | −0.573391 | − | 0.819282i | \(-0.694373\pi\) | ||
0.573391 | − | 0.819282i | \(-0.305627\pi\) | |||||||
\(360\) | −13.2180 | −0.696648 | ||||||||
\(361\) | 2.68183 | 0.141149 | ||||||||
\(362\) | −15.1450 | −0.796002 | ||||||||
\(363\) | −28.5209 | + | 1.21946i | −1.49696 | + | 0.0640050i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 13.7940i | − | 0.722010i | ||||||
\(366\) | −28.8771 | −1.50943 | ||||||||
\(367\) | − | 29.6492i | − | 1.54768i | −0.633384 | − | 0.773838i | \(-0.718335\pi\) | ||
0.633384 | − | 0.773838i | \(-0.281665\pi\) | |||||||
\(368\) | −1.55962 | −0.0813010 | ||||||||
\(369\) | 11.0110 | 0.573208 | ||||||||
\(370\) | −2.49651 | −0.129788 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.725946 | −0.0376385 | ||||||||
\(373\) | 8.78055i | 0.454640i | 0.973820 | + | 0.227320i | \(0.0729963\pi\) | ||||
−0.973820 | + | 0.227320i | \(0.927004\pi\) | |||||||
\(374\) | −9.32434 | − | 8.93419i | −0.482150 | − | 0.461976i | ||||
\(375\) | 23.1858 | 1.19731 | ||||||||
\(376\) | −6.56949 | −0.338796 | ||||||||
\(377\) | − | 0.502706i | − | 0.0258907i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.8135 | 1.58278 | 0.791391 | − | 0.611311i | \(-0.209358\pi\) | ||||
0.791391 | + | 0.611311i | \(0.209358\pi\) | |||||||
\(380\) | − | 16.4789i | − | 0.845349i | ||||||
\(381\) | 34.3080 | 1.75765 | ||||||||
\(382\) | − | 6.00000i | − | 0.306987i | ||||||
\(383\) | 5.29482i | 0.270553i | 0.990808 | + | 0.135276i | \(0.0431922\pi\) | ||||
−0.990808 | + | 0.135276i | \(0.956808\pi\) | |||||||
\(384\) | 2.59518 | 0.132435 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.8281 | 0.754729 | ||||||||
\(387\) | 33.7473i | 1.71547i | ||||||||
\(388\) | 16.7587i | 0.850793i | ||||||||
\(389\) | 0.860237 | 0.0436158 | 0.0218079 | − | 0.999762i | \(-0.493058\pi\) | ||||
0.0218079 | + | 0.999762i | \(0.493058\pi\) | |||||||
\(390\) | 46.0759i | 2.33314i | ||||||||
\(391\) | 6.07258 | 0.307104 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 42.8168i | 2.15982i | ||||||||
\(394\) | −14.4745 | −0.729213 | ||||||||
\(395\) | −27.2496 | −1.37108 | ||||||||
\(396\) | −8.57010 | + | 8.94436i | −0.430664 | + | 0.449471i | ||||
\(397\) | 12.3473i | 0.619695i | 0.950786 | + | 0.309847i | \(0.100278\pi\) | ||||
−0.950786 | + | 0.309847i | \(0.899722\pi\) | |||||||
\(398\) | 11.2259 | 0.562702 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.52450 | −0.376225 | ||||||||
\(401\) | 33.7252 | 1.68416 | 0.842078 | − | 0.539355i | \(-0.181332\pi\) | ||||
0.842078 | + | 0.539355i | \(0.181332\pi\) | |||||||
\(402\) | −10.3390 | −0.515661 | ||||||||
\(403\) | 1.40334i | 0.0699054i | ||||||||
\(404\) | −1.40290 | −0.0697971 | ||||||||
\(405\) | 22.1365i | 1.09997i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.61866 | + | 1.68935i | −0.0802339 | + | 0.0837377i | ||||
\(408\) | −10.1046 | −0.500254 | ||||||||
\(409\) | 38.3692 | 1.89723 | 0.948616 | − | 0.316428i | \(-0.102484\pi\) | ||||
0.948616 | + | 0.316428i | \(0.102484\pi\) | |||||||
\(410\) | 10.4333 | 0.515264 | ||||||||
\(411\) | − | 17.2417i | − | 0.850470i | ||||||
\(412\) | − | 2.06291i | − | 0.101632i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 5.82511i | − | 0.286289i | ||||||
\(415\) | 10.1682i | 0.499139i | ||||||||
\(416\) | − | 5.01680i | − | 0.245969i | ||||||
\(417\) | − | 37.2494i | − | 1.82411i | ||||||
\(418\) | −11.1510 | − | 10.6844i | −0.545412 | − | 0.522590i | ||||
\(419\) | 33.5023i | 1.63670i | 0.574723 | + | 0.818348i | \(0.305110\pi\) | ||||
−0.574723 | + | 0.818348i | \(0.694890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.0155 | −1.12171 | −0.560853 | − | 0.827915i | \(-0.689527\pi\) | ||||
−0.560853 | + | 0.827915i | \(0.689527\pi\) | |||||||
\(422\) | 6.44038 | 0.313513 | ||||||||
\(423\) | − | 24.5367i | − | 1.19302i | ||||||
\(424\) | 5.54058i | 0.269074i | ||||||||
\(425\) | 29.2975 | 1.42114 | ||||||||
\(426\) | 21.9391 | 1.06295 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 12.2655i | − | 0.592875i | ||||||
\(429\) | 31.1787 | + | 29.8741i | 1.50532 | + | 1.44234i | ||||
\(430\) | 31.9768i | 1.54206i | ||||||||
\(431\) | 26.8381i | 1.29275i | 0.763021 | + | 0.646373i | \(0.223715\pi\) | ||||
−0.763021 | + | 0.646373i | \(0.776285\pi\) | |||||||
\(432\) | 1.90732i | 0.0917659i | ||||||||
\(433\) | 30.6912i | 1.47493i | 0.675387 | + | 0.737463i | \(0.263976\pi\) | ||||
−0.675387 | + | 0.737463i | \(0.736024\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.920312i | 0.0441256i | ||||||||
\(436\) | − | 6.72491i | − | 0.322065i | ||||||
\(437\) | 7.26219 | 0.347398 | ||||||||
\(438\) | −10.1152 | −0.483325 | ||||||||
\(439\) | 16.8452 | 0.803976 | 0.401988 | − | 0.915645i | \(-0.368319\pi\) | ||||
0.401988 | + | 0.915645i | \(0.368319\pi\) | |||||||
\(440\) | −8.12048 | + | 8.47510i | −0.387129 | + | 0.404035i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.5335i | 0.929114i | ||||||||
\(443\) | −0.790590 | −0.0375620 | −0.0187810 | − | 0.999824i | \(-0.505979\pi\) | ||||
−0.0187810 | + | 0.999824i | \(0.505979\pi\) | |||||||
\(444\) | 1.83072i | 0.0868819i | ||||||||
\(445\) | −21.0536 | −0.998035 | ||||||||
\(446\) | −4.01793 | −0.190255 | ||||||||
\(447\) | 6.91841 | 0.327230 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.9734 | 0.753833 | 0.376917 | − | 0.926247i | \(-0.376984\pi\) | ||||
0.376917 | + | 0.926247i | \(0.376984\pi\) | |||||||
\(450\) | − | 28.1036i | − | 1.32482i | ||||||
\(451\) | 6.76461 | − | 7.06002i | 0.318533 | − | 0.332443i | ||||
\(452\) | 11.9900 | 0.563960 | ||||||||
\(453\) | −26.9648 | −1.26692 | ||||||||
\(454\) | 12.7293i | 0.597416i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.0841 | −0.565891 | ||||||||
\(457\) | 34.9331i | 1.63410i | 0.576564 | + | 0.817052i | \(0.304393\pi\) | ||||
−0.576564 | + | 0.817052i | \(0.695607\pi\) | |||||||
\(458\) | −6.01345 | −0.280990 | ||||||||
\(459\) | − | 7.42637i | − | 0.346633i | ||||||
\(460\) | − | 5.51950i | − | 0.257348i | ||||||
\(461\) | −20.8346 | −0.970364 | −0.485182 | − | 0.874413i | \(-0.661247\pi\) | ||||
−0.485182 | + | 0.874413i | \(0.661247\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.1724 | 0.612172 | 0.306086 | − | 0.952004i | \(-0.400981\pi\) | ||||
0.306086 | + | 0.952004i | \(0.400981\pi\) | |||||||
\(464\) | − | 0.100205i | − | 0.00465188i | ||||||
\(465\) | − | 2.56912i | − | 0.119140i | ||||||
\(466\) | 6.46694 | 0.299575 | ||||||||
\(467\) | − | 16.8184i | − | 0.778262i | −0.921182 | − | 0.389131i | \(-0.872775\pi\) | ||
0.921182 | − | 0.389131i | \(-0.127225\pi\) | |||||||
\(468\) | 18.7375 | 0.866140 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 23.2494i | − | 1.07241i | ||||||
\(471\) | −21.7339 | −1.00145 | ||||||||
\(472\) | 14.5344 | 0.668999 | ||||||||
\(473\) | 21.6381 | + | 20.7327i | 0.994922 | + | 0.953292i | ||||
\(474\) | 19.9824i | 0.917822i | ||||||||
\(475\) | 35.0369 | 1.60760 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.6938 | −0.947503 | ||||||||
\(478\) | −15.5775 | −0.712498 | ||||||||
\(479\) | 22.8582 | 1.04442 | 0.522208 | − | 0.852818i | \(-0.325109\pi\) | ||||
0.522208 | + | 0.852818i | \(0.325109\pi\) | |||||||
\(480\) | 9.18432i | 0.419205i | ||||||||
\(481\) | 3.53900 | 0.161364 | ||||||||
\(482\) | − | 23.4762i | − | 1.06931i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.469894 | + | 10.9900i | 0.0213588 | + | 0.499544i | ||||
\(485\) | −59.3089 | −2.69308 | ||||||||
\(486\) | 21.9548 | 0.995891 | ||||||||
\(487\) | 31.2628 | 1.41665 | 0.708327 | − | 0.705884i | \(-0.249450\pi\) | ||||
0.708327 | + | 0.705884i | \(0.249450\pi\) | |||||||
\(488\) | 11.1272i | 0.503705i | ||||||||
\(489\) | − | 7.95442i | − | 0.359711i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.4979i | 1.01532i | 0.861558 | + | 0.507659i | \(0.169489\pi\) | ||||
−0.861558 | + | 0.507659i | \(0.830511\pi\) | |||||||
\(492\) | − | 7.65083i | − | 0.344926i | ||||||
\(493\) | 0.390159i | 0.0175719i | ||||||||
\(494\) | 23.3601i | 1.05102i | ||||||||
\(495\) | −31.6541 | − | 30.3295i | −1.42274 | − | 1.36321i | ||||
\(496\) | 0.279729i | 0.0125602i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.45646 | 0.334132 | ||||||||
\(499\) | −31.9097 | −1.42847 | −0.714236 | − | 0.699905i | \(-0.753226\pi\) | ||||
−0.714236 | + | 0.699905i | \(0.753226\pi\) | |||||||
\(500\) | − | 8.93419i | − | 0.399549i | ||||||
\(501\) | 26.1415i | 1.16792i | ||||||||
\(502\) | 18.2818 | 0.815957 | ||||||||
\(503\) | 30.2687 | 1.34962 | 0.674808 | − | 0.737994i | \(-0.264227\pi\) | ||||
0.674808 | + | 0.737994i | \(0.264227\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 4.96487i | − | 0.220934i | ||||||
\(506\) | −3.73495 | − | 3.57867i | −0.166039 | − | 0.159091i | ||||
\(507\) | − | 31.5787i | − | 1.40246i | ||||||
\(508\) | − | 13.2199i | − | 0.586538i | ||||||
\(509\) | − | 23.0542i | − | 1.02186i | −0.859622 | − | 0.510930i | \(-0.829301\pi\) | ||
0.859622 | − | 0.510930i | \(-0.170699\pi\) | |||||||
\(510\) | − | 35.7603i | − | 1.58349i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 8.88119i | − | 0.392114i | ||||||
\(514\) | −9.61966 | −0.424305 | ||||||||
\(515\) | 7.30061 | 0.321703 | ||||||||
\(516\) | 23.4489 | 1.03228 | ||||||||
\(517\) | −15.7325 | − | 15.0742i | −0.691912 | − | 0.662961i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.198797i | 0.00872624i | ||||||||
\(520\) | 17.7544 | 0.778583 | ||||||||
\(521\) | 7.98303i | 0.349743i | 0.984591 | + | 0.174872i | \(0.0559510\pi\) | ||||
−0.984591 | + | 0.174872i | \(0.944049\pi\) | |||||||
\(522\) | 0.374259 | 0.0163809 | ||||||||
\(523\) | −5.58280 | −0.244119 | −0.122059 | − | 0.992523i | \(-0.538950\pi\) | ||||
−0.122059 | + | 0.992523i | \(0.538950\pi\) | |||||||
\(524\) | 16.4986 | 0.720746 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.578666 | −0.0252310 | ||||||||
\(527\) | − | 1.08916i | − | 0.0474444i | ||||||
\(528\) | 6.21487 | + | 5.95482i | 0.270467 | + | 0.259150i | ||||
\(529\) | −20.5676 | −0.894242 | ||||||||
\(530\) | −19.6081 | −0.851721 | ||||||||
\(531\) | 54.2851i | 2.35577i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.7900 | −0.640625 | ||||||||
\(534\) | 15.4388i | 0.668101i | ||||||||
\(535\) | 43.4075 | 1.87667 | ||||||||
\(536\) | 3.98392i | 0.172079i | ||||||||
\(537\) | 23.2915i | 1.00510i | ||||||||
\(538\) | −22.0896 | −0.952350 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.74999 | −0.290473 | ||||||||
\(541\) | 13.4022i | 0.576204i | 0.957600 | + | 0.288102i | \(0.0930242\pi\) | ||||
−0.957600 | + | 0.288102i | \(0.906976\pi\) | |||||||
\(542\) | 4.26222i | 0.183078i | ||||||||
\(543\) | −39.3039 | −1.68669 | ||||||||
\(544\) | 3.89362i | 0.166938i | ||||||||
\(545\) | 23.7994 | 1.01946 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 24.5161i | − | 1.04823i | −0.851647 | − | 0.524116i | \(-0.824396\pi\) | ||
0.851647 | − | 0.524116i | \(-0.175604\pi\) | |||||||
\(548\) | −6.64374 | −0.283807 | ||||||||
\(549\) | −41.5595 | −1.77372 | ||||||||
\(550\) | −18.0195 | − | 17.2655i | −0.768353 | − | 0.736203i | ||||
\(551\) | 0.466590i | 0.0198774i | ||||||||
\(552\) | −4.04750 | −0.172273 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 18.3653 | 0.780265 | ||||||||
\(555\) | −6.47890 | −0.275014 | ||||||||
\(556\) | −14.3533 | −0.608716 | ||||||||
\(557\) | − | 3.61157i | − | 0.153027i | −0.997069 | − | 0.0765137i | \(-0.975621\pi\) | ||
0.997069 | − | 0.0765137i | \(-0.0243789\pi\) | |||||||
\(558\) | −1.04477 | −0.0442287 | ||||||||
\(559\) | − | 45.3296i | − | 1.91724i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.1983 | − | 23.1858i | −1.02165 | − | 0.978905i | ||||
\(562\) | −3.72890 | −0.157294 | ||||||||
\(563\) | −5.85803 | −0.246887 | −0.123443 | − | 0.992352i | \(-0.539394\pi\) | ||||
−0.123443 | + | 0.992352i | \(0.539394\pi\) | |||||||
\(564\) | −17.0490 | −0.717892 | ||||||||
\(565\) | 42.4324i | 1.78515i | ||||||||
\(566\) | 12.7315i | 0.535146i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 8.45381i | − | 0.354714i | ||||||
\(569\) | − | 34.6147i | − | 1.45112i | −0.688158 | − | 0.725561i | \(-0.741580\pi\) | ||
0.688158 | − | 0.725561i | \(-0.258420\pi\) | |||||||
\(570\) | − | 42.7657i | − | 1.79126i | ||||||
\(571\) | 7.96636i | 0.333382i | 0.986009 | + | 0.166691i | \(0.0533082\pi\) | ||||
−0.986009 | + | 0.166691i | \(0.946692\pi\) | |||||||
\(572\) | 11.5114 | − | 12.0141i | 0.481315 | − | 0.502335i | ||||
\(573\) | − | 15.5711i | − | 0.650491i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.7354 | 0.489399 | ||||||||
\(576\) | 3.73495 | 0.155623 | ||||||||
\(577\) | − | 18.3764i | − | 0.765018i | −0.923952 | − | 0.382509i | \(-0.875060\pi\) | ||
0.923952 | − | 0.382509i | \(-0.124940\pi\) | |||||||
\(578\) | 1.83972i | 0.0765223i | ||||||||
\(579\) | 38.4815 | 1.59924 | ||||||||
\(580\) | 0.354624 | 0.0147249 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 43.4917i | 1.80279i | ||||||||
\(583\) | −12.7133 | + | 13.2684i | −0.526529 | + | 0.549523i | ||||
\(584\) | 3.89771i | 0.161288i | ||||||||
\(585\) | 66.3118i | 2.74166i | ||||||||
\(586\) | − | 26.2251i | − | 1.08335i | ||||||
\(587\) | − | 17.2267i | − | 0.711021i | −0.934672 | − | 0.355511i | \(-0.884307\pi\) | ||
0.934672 | − | 0.355511i | \(-0.115693\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.30252i | − | 0.0536695i | ||||||
\(590\) | 51.4371i | 2.11763i | ||||||||
\(591\) | −37.5638 | −1.54517 | ||||||||
\(592\) | 0.705430 | 0.0289930 | ||||||||
\(593\) | −41.2427 | −1.69363 | −0.846817 | − | 0.531884i | \(-0.821484\pi\) | ||||
−0.846817 | + | 0.531884i | \(0.821484\pi\) | |||||||
\(594\) | −4.37648 | + | 4.56760i | −0.179569 | + | 0.187411i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 2.66587i | − | 0.109198i | ||||||
\(597\) | 29.1331 | 1.19234 | ||||||||
\(598\) | 7.82431i | 0.319960i | ||||||||
\(599\) | 9.95440 | 0.406726 | 0.203363 | − | 0.979103i | \(-0.434813\pi\) | ||||
0.203363 | + | 0.979103i | \(0.434813\pi\) | |||||||
\(600\) | −19.5274 | −0.797203 | ||||||||
\(601\) | 4.76767 | 0.194477 | 0.0972386 | − | 0.995261i | \(-0.468999\pi\) | ||||
0.0972386 | + | 0.995261i | \(0.468999\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.8797 | −0.605949 | ||||||||
\(604\) | 10.3903i | 0.422777i | ||||||||
\(605\) | −38.8934 | + | 1.66295i | −1.58124 | + | 0.0676087i | ||||
\(606\) | −3.64079 | −0.147897 | ||||||||
\(607\) | 4.55345 | 0.184819 | 0.0924094 | − | 0.995721i | \(-0.470543\pi\) | ||||
0.0924094 | + | 0.995721i | \(0.470543\pi\) | |||||||
\(608\) | 4.65637i | 0.188841i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −39.3791 | −1.59441 | ||||||||
\(611\) | 32.9578i | 1.33333i | ||||||||
\(612\) | −14.5425 | −0.587844 | ||||||||
\(613\) | − | 1.44894i | − | 0.0585223i | −0.999572 | − | 0.0292611i | \(-0.990685\pi\) | ||
0.999572 | − | 0.0292611i | \(-0.00931544\pi\) | |||||||
\(614\) | 25.5942i | 1.03290i | ||||||||
\(615\) | 27.0762 | 1.09182 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.96752 | −0.119468 | −0.0597340 | − | 0.998214i | \(-0.519025\pi\) | ||||
−0.0597340 | + | 0.998214i | \(0.519025\pi\) | |||||||
\(618\) | − | 5.35360i | − | 0.215354i | ||||||
\(619\) | 11.5475i | 0.464133i | 0.972700 | + | 0.232067i | \(0.0745488\pi\) | ||||
−0.972700 | + | 0.232067i | \(0.925451\pi\) | |||||||
\(620\) | −0.989959 | −0.0397577 | ||||||||
\(621\) | − | 2.97470i | − | 0.119371i | ||||||
\(622\) | 1.90970 | 0.0765720 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 13.0195i | − | 0.521196i | ||||||
\(625\) | −6.00443 | −0.240177 | ||||||||
\(626\) | −30.4503 | −1.21704 | ||||||||
\(627\) | −28.9387 | − | 27.7279i | −1.15570 | − | 1.10734i | ||||
\(628\) | 8.37473i | 0.334188i | ||||||||
\(629\) | −2.74668 | −0.109517 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.5215 | −1.09562 | −0.547808 | − | 0.836604i | \(-0.684537\pi\) | ||||
−0.547808 | + | 0.836604i | \(0.684537\pi\) | |||||||
\(632\) | 7.69982 | 0.306282 | ||||||||
\(633\) | 16.7139 | 0.664319 | ||||||||
\(634\) | − | 34.3942i | − | 1.36597i | ||||||
\(635\) | 46.7851 | 1.85661 | ||||||||
\(636\) | 14.3788i | 0.570156i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.229926 | − | 0.239967i | 0.00910288 | − | 0.00950040i | ||||
\(639\) | 31.5745 | 1.24907 | ||||||||
\(640\) | 3.53900 | 0.139891 | ||||||||
\(641\) | 33.6547 | 1.32928 | 0.664639 | − | 0.747164i | \(-0.268585\pi\) | ||||
0.664639 | + | 0.747164i | \(0.268585\pi\) | |||||||
\(642\) | − | 31.8311i | − | 1.25627i | ||||||
\(643\) | 5.95261i | 0.234748i | 0.993088 | + | 0.117374i | \(0.0374476\pi\) | ||||
−0.993088 | + | 0.117374i | \(0.962552\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 82.9855i | 3.26755i | ||||||||
\(646\) | − | 18.1302i | − | 0.713321i | ||||||
\(647\) | − | 11.7737i | − | 0.462873i | −0.972850 | − | 0.231437i | \(-0.925657\pi\) | ||
0.972850 | − | 0.231437i | \(-0.0743426\pi\) | |||||||
\(648\) | − | 6.25501i | − | 0.245720i | ||||||
\(649\) | 34.8066 | + | 33.3502i | 1.36628 | + | 1.30911i | ||||
\(650\) | 37.7489i | 1.48063i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.06508 | −0.120038 | ||||||||
\(653\) | 28.8670 | 1.12965 | 0.564827 | − | 0.825209i | \(-0.308943\pi\) | ||||
0.564827 | + | 0.825209i | \(0.308943\pi\) | |||||||
\(654\) | − | 17.4523i | − | 0.682440i | ||||||
\(655\) | 58.3886i | 2.28143i | ||||||||
\(656\) | −2.94809 | −0.115104 | ||||||||
\(657\) | −14.5577 | −0.567952 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.6812i | 1.74053i | 0.492581 | + | 0.870266i | \(0.336053\pi\) | ||||
−0.492581 | + | 0.870266i | \(0.663947\pi\) | |||||||
\(660\) | −21.0741 | + | 21.9944i | −0.820307 | + | 0.856130i | ||||
\(661\) | 39.6341i | 1.54159i | 0.637084 | + | 0.770794i | \(0.280140\pi\) | ||||
−0.637084 | + | 0.770794i | \(0.719860\pi\) | |||||||
\(662\) | − | 15.5128i | − | 0.602924i | ||||||
\(663\) | 50.6929i | 1.96875i | ||||||||
\(664\) | − | 2.87320i | − | 0.111502i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.63474i | 0.102094i | ||||||||
\(667\) | 0.156281i | 0.00605124i | ||||||||
\(668\) | 10.0731 | 0.389741 | ||||||||
\(669\) | −10.4272 | −0.403141 | ||||||||
\(670\) | −14.0991 | −0.544694 | ||||||||
\(671\) | −25.5321 | + | 26.6471i | −0.985657 | + | 1.02870i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 2.71886i | − | 0.104804i | −0.998626 | − | 0.0524022i | \(-0.983312\pi\) | ||
0.998626 | − | 0.0524022i | \(-0.0166878\pi\) | |||||||
\(674\) | 7.70882 | 0.296933 | ||||||||
\(675\) | − | 14.3516i | − | 0.552394i | ||||||
\(676\) | −12.1682 | −0.468009 | ||||||||
\(677\) | 6.05945 | 0.232884 | 0.116442 | − | 0.993198i | \(-0.462851\pi\) | ||||
0.116442 | + | 0.993198i | \(0.462851\pi\) | |||||||
\(678\) | 31.1161 | 1.19501 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −13.7795 | −0.528420 | ||||||||
\(681\) | 33.0348i | 1.26590i | ||||||||
\(682\) | −0.641857 | + | 0.669887i | −0.0245780 | + | 0.0256513i | ||||
\(683\) | −6.03409 | −0.230888 | −0.115444 | − | 0.993314i | \(-0.536829\pi\) | ||||
−0.115444 | + | 0.993314i | \(0.536829\pi\) | |||||||
\(684\) | −17.3913 | −0.664973 | ||||||||
\(685\) | − | 23.5122i | − | 0.898354i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.6060 | −0.595405 | ||||||||
\(688\) | − | 9.03556i | − | 0.344478i | ||||||
\(689\) | 27.7960 | 1.05894 | ||||||||
\(690\) | − | 14.3241i | − | 0.545309i | ||||||
\(691\) | − | 19.8053i | − | 0.753427i | −0.926330 | − | 0.376714i | \(-0.877054\pi\) | ||
0.926330 | − | 0.376714i | \(-0.122946\pi\) | |||||||
\(692\) | 0.0766026 | 0.00291200 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.7413 | −0.825288 | ||||||||
\(695\) | − | 50.7963i | − | 1.92681i | ||||||
\(696\) | − | 0.260049i | − | 0.00985712i | ||||||
\(697\) | 11.4788 | 0.434789 | ||||||||
\(698\) | 13.4565i | 0.509334i | ||||||||
\(699\) | 16.7828 | 0.634786 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 26.0155i | − | 0.982591i | −0.870993 | − | 0.491296i | \(-0.836524\pi\) | ||
0.870993 | − | 0.491296i | \(-0.163476\pi\) | |||||||
\(702\) | 9.56862 | 0.361144 | ||||||||
\(703\) | −3.28475 | −0.123887 | ||||||||
\(704\) | 2.29457 | − | 2.39477i | 0.0864799 | − | 0.0902565i | ||||
\(705\) | − | 60.3363i | − | 2.27240i | ||||||
\(706\) | −6.70769 | −0.252447 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 37.7193 | 1.41758 | ||||||||
\(709\) | −24.8917 | −0.934826 | −0.467413 | − | 0.884039i | \(-0.654814\pi\) | ||||
−0.467413 | + | 0.884039i | \(0.654814\pi\) | |||||||
\(710\) | 29.9180 | 1.12280 | ||||||||
\(711\) | 28.7584i | 1.07853i | ||||||||
\(712\) | 5.94902 | 0.222949 | ||||||||
\(713\) | − | 0.436271i | − | 0.0163385i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 42.5178 | + | 40.7388i | 1.59008 | + | 1.52354i | ||||
\(716\) | 8.97491 | 0.335408 | ||||||||
\(717\) | −40.4263 | −1.50975 | ||||||||
\(718\) | −31.0463 | −1.15864 | ||||||||
\(719\) | − | 13.2970i | − | 0.495895i | −0.968773 | − | 0.247948i | \(-0.920244\pi\) | ||
0.968773 | − | 0.247948i | \(-0.0797561\pi\) | |||||||
\(720\) | 13.2180i | 0.492604i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 2.68183i | − | 0.0998073i | ||||||
\(723\) | − | 60.9250i | − | 2.26583i | ||||||
\(724\) | 15.1450i | 0.562858i | ||||||||
\(725\) | 0.753989i | 0.0280025i | ||||||||
\(726\) | 1.21946 | + | 28.5209i | 0.0452583 | + | 1.05851i | ||||
\(727\) | 5.67083i | 0.210319i | 0.994455 | + | 0.105160i | \(0.0335354\pi\) | ||||
−0.994455 | + | 0.105160i | \(0.966465\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 38.2116 | 1.41525 | ||||||||
\(730\) | −13.7940 | −0.510538 | ||||||||
\(731\) | 35.1810i | 1.30122i | ||||||||
\(732\) | 28.8771i | 1.06733i | ||||||||
\(733\) | −41.3759 | −1.52825 | −0.764127 | − | 0.645066i | \(-0.776830\pi\) | ||||
−0.764127 | + | 0.645066i | \(0.776830\pi\) | |||||||
\(734\) | −29.6492 | −1.09437 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.55962i | 0.0574885i | ||||||||
\(737\) | −9.14137 | + | 9.54058i | −0.336727 | + | 0.351432i | ||||
\(738\) | − | 11.0110i | − | 0.405320i | ||||||
\(739\) | − | 41.5403i | − | 1.52808i | −0.645167 | − | 0.764042i | \(-0.723212\pi\) | ||
0.645167 | − | 0.764042i | \(-0.276788\pi\) | |||||||
\(740\) | 2.49651i | 0.0917736i | ||||||||
\(741\) | 60.6236i | 2.22706i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 39.7404i | − | 1.45793i | −0.684549 | − | 0.728967i | \(-0.740001\pi\) | ||
0.684549 | − | 0.728967i | \(-0.259999\pi\) | |||||||
\(744\) | 0.725946i | 0.0266145i | ||||||||
\(745\) | 9.43451 | 0.345654 | ||||||||
\(746\) | 8.78055 | 0.321479 | ||||||||
\(747\) | 10.7312 | 0.392636 | ||||||||
\(748\) | −8.93419 | + | 9.32434i | −0.326666 | + | 0.340932i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 23.1858i | − | 0.846626i | ||||||
\(751\) | 5.36526 | 0.195781 | 0.0978905 | − | 0.995197i | \(-0.468791\pi\) | ||||
0.0978905 | + | 0.995197i | \(0.468791\pi\) | |||||||
\(752\) | 6.56949i | 0.239565i | ||||||||
\(753\) | 47.4445 | 1.72897 | ||||||||
\(754\) | −0.502706 | −0.0183075 | ||||||||
\(755\) | −36.7714 | −1.33825 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.8962 | 0.941215 | 0.470607 | − | 0.882343i | \(-0.344035\pi\) | ||||
0.470607 | + | 0.882343i | \(0.344035\pi\) | |||||||
\(758\) | − | 30.8135i | − | 1.11920i | ||||||
\(759\) | −9.69285 | − | 9.28727i | −0.351828 | − | 0.337107i | ||||
\(760\) | −16.4789 | −0.597752 | ||||||||
\(761\) | 15.2206 | 0.551747 | 0.275873 | − | 0.961194i | \(-0.411033\pi\) | ||||
0.275873 | + | 0.961194i | \(0.411033\pi\) | |||||||
\(762\) | − | 34.3080i | − | 1.24285i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | − | 51.4657i | − | 1.86075i | ||||||
\(766\) | 5.29482 | 0.191310 | ||||||||
\(767\) | − | 72.9160i | − | 2.63284i | ||||||
\(768\) | − | 2.59518i | − | 0.0936454i | ||||||
\(769\) | 22.5146 | 0.811898 | 0.405949 | − | 0.913896i | \(-0.366941\pi\) | ||||
0.405949 | + | 0.913896i | \(0.366941\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.9647 | −0.899083 | ||||||||
\(772\) | − | 14.8281i | − | 0.533674i | ||||||
\(773\) | − | 28.0333i | − | 1.00829i | −0.863619 | − | 0.504144i | \(-0.831808\pi\) | ||
0.863619 | − | 0.504144i | \(-0.168192\pi\) | |||||||
\(774\) | 33.7473 | 1.21302 | ||||||||
\(775\) | − | 2.10482i | − | 0.0756073i | ||||||
\(776\) | 16.7587 | 0.601601 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 0.860237i | − | 0.0308410i | ||||||
\(779\) | 13.7274 | 0.491836 | ||||||||
\(780\) | 46.0759 | 1.64978 | ||||||||
\(781\) | 19.3979 | − | 20.2450i | 0.694110 | − | 0.724422i | ||||
\(782\) | − | 6.07258i | − | 0.217155i | ||||||
\(783\) | 0.191122 | 0.00683014 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −29.6381 | −1.05783 | ||||||||
\(786\) | 42.8168 | 1.52723 | ||||||||
\(787\) | 12.7432 | 0.454246 | 0.227123 | − | 0.973866i | \(-0.427068\pi\) | ||||
0.227123 | + | 0.973866i | \(0.427068\pi\) | |||||||
\(788\) | 14.4745i | 0.515631i | ||||||||
\(789\) | −1.50174 | −0.0534634 | ||||||||
\(790\) | 27.2496i | 0.969499i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 8.94436 | + | 8.57010i | 0.317824 | + | 0.304525i | ||||
\(793\) | 55.8229 | 1.98233 | ||||||||
\(794\) | 12.3473 | 0.438190 | ||||||||
\(795\) | −50.8865 | −1.80476 | ||||||||
\(796\) | − | 11.2259i | − | 0.397890i | ||||||
\(797\) | 5.63488i | 0.199598i | 0.995008 | + | 0.0997989i | \(0.0318199\pi\) | ||||
−0.995008 | + | 0.0997989i | \(0.968180\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 25.5791i | − | 0.904923i | ||||||
\(800\) | 7.52450i | 0.266031i | ||||||||
\(801\) | 22.2193i | 0.785080i | ||||||||
\(802\) | − | 33.7252i | − | 1.19088i | ||||||
\(803\) | −8.94357 | + | 9.33414i | −0.315612 | + | 0.329395i | ||||
\(804\) | 10.3390i | 0.364627i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.40334 | 0.0494306 | ||||||||
\(807\) | −57.3264 | −2.01799 | ||||||||
\(808\) | 1.40290i | 0.0493540i | ||||||||
\(809\) | 17.0401i | 0.599099i | 0.954081 | + | 0.299550i | \(0.0968364\pi\) | ||||
−0.954081 | + | 0.299550i | \(0.903164\pi\) | |||||||
\(810\) | 22.1365 | 0.777796 | ||||||||
\(811\) | 0.332109 | 0.0116619 | 0.00583097 | − | 0.999983i | \(-0.498144\pi\) | ||||
0.00583097 | + | 0.999983i | \(0.498144\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.0612i | 0.387934i | ||||||||
\(814\) | 1.68935 | + | 1.61866i | 0.0592115 | + | 0.0567339i | ||||
\(815\) | − | 10.8473i | − | 0.379964i | ||||||
\(816\) | 10.1046i | 0.353733i | ||||||||
\(817\) | 42.0730i | 1.47195i | ||||||||
\(818\) | − | 38.3692i | − | 1.34155i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 10.4333i | − | 0.364346i | ||||||
\(821\) | − | 2.28292i | − | 0.0796744i | −0.999206 | − | 0.0398372i | \(-0.987316\pi\) | ||
0.999206 | − | 0.0398372i | \(-0.0126839\pi\) | |||||||
\(822\) | −17.2417 | −0.601373 | ||||||||
\(823\) | 10.0846 | 0.351525 | 0.175763 | − | 0.984433i | \(-0.443761\pi\) | ||||
0.175763 | + | 0.984433i | \(0.443761\pi\) | |||||||
\(824\) | −2.06291 | −0.0718647 | ||||||||
\(825\) | −46.7637 | − | 44.8070i | −1.62810 | − | 1.55998i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 10.9337i | − | 0.380204i | −0.981764 | − | 0.190102i | \(-0.939118\pi\) | ||
0.981764 | − | 0.190102i | \(-0.0608818\pi\) | |||||||
\(828\) | −5.82511 | −0.202437 | ||||||||
\(829\) | 11.6257i | 0.403779i | 0.979408 | + | 0.201889i | \(0.0647081\pi\) | ||||
−0.979408 | + | 0.201889i | \(0.935292\pi\) | |||||||
\(830\) | 10.1682 | 0.352945 | ||||||||
\(831\) | 47.6611 | 1.65335 | ||||||||
\(832\) | −5.01680 | −0.173926 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −37.2494 | −1.28984 | ||||||||
\(835\) | 35.6487i | 1.23368i | ||||||||
\(836\) | −10.6844 | + | 11.1510i | −0.369527 | + | 0.385664i | ||||
\(837\) | −0.533532 | −0.0184416 | ||||||||
\(838\) | 33.5023 | 1.15732 | ||||||||
\(839\) | 23.4571i | 0.809828i | 0.914355 | + | 0.404914i | \(0.132699\pi\) | ||||
−0.914355 | + | 0.404914i | \(0.867301\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9900 | 0.999654 | ||||||||
\(842\) | 23.0155i | 0.793166i | ||||||||
\(843\) | −9.67717 | −0.333299 | ||||||||
\(844\) | − | 6.44038i | − | 0.221687i | ||||||
\(845\) | − | 43.0634i | − | 1.48142i | ||||||
\(846\) | −24.5367 | −0.843589 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.54058 | 0.190264 | ||||||||
\(849\) | 33.0406i | 1.13395i | ||||||||
\(850\) | − | 29.2975i | − | 1.00490i | ||||||
\(851\) | −1.10020 | −0.0377145 | ||||||||
\(852\) | − | 21.9391i | − | 0.751622i | ||||||
\(853\) | 38.5870 | 1.32119 | 0.660597 | − | 0.750741i | \(-0.270303\pi\) | ||||
0.660597 | + | 0.750741i | \(0.270303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 61.5478i | − | 2.10489i | ||||||
\(856\) | −12.2655 | −0.419226 | ||||||||
\(857\) | −42.6013 | −1.45523 | −0.727617 | − | 0.685984i | \(-0.759372\pi\) | ||||
−0.727617 | + | 0.685984i | \(0.759372\pi\) | |||||||
\(858\) | 29.8741 | − | 31.1787i | 1.01989 | − | 1.06442i | ||||
\(859\) | 12.3950i | 0.422913i | 0.977387 | + | 0.211457i | \(0.0678207\pi\) | ||||
−0.977387 | + | 0.211457i | \(0.932179\pi\) | |||||||
\(860\) | 31.9768 | 1.09040 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.8381 | 0.914110 | ||||||||
\(863\) | −39.2748 | −1.33693 | −0.668465 | − | 0.743744i | \(-0.733048\pi\) | ||||
−0.668465 | + | 0.743744i | \(0.733048\pi\) | |||||||
\(864\) | 1.90732 | 0.0648883 | ||||||||
\(865\) | 0.271096i | 0.00921756i | ||||||||
\(866\) | 30.6912 | 1.04293 | ||||||||
\(867\) | 4.77440i | 0.162147i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.4393 | + | 17.6678i | 0.625512 | + | 0.599338i | ||||
\(870\) | 0.920312 | 0.0312015 | ||||||||
\(871\) | 19.9865 | 0.677216 | ||||||||
\(872\) | −6.72491 | −0.227734 | ||||||||
\(873\) | 62.5927i | 2.11844i | ||||||||
\(874\) | − | 7.26219i | − | 0.245647i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.1152i | 0.341763i | ||||||||
\(877\) | − | 46.1191i | − | 1.55733i | −0.627440 | − | 0.778665i | \(-0.715897\pi\) | ||
0.627440 | − | 0.778665i | \(-0.284103\pi\) | |||||||
\(878\) | − | 16.8452i | − | 0.568497i | ||||||
\(879\) | − | 68.0589i | − | 2.29557i | ||||||
\(880\) | 8.47510 | + | 8.12048i | 0.285696 | + | 0.273741i | ||||
\(881\) | − | 14.9583i | − | 0.503957i | −0.967733 | − | 0.251978i | \(-0.918919\pi\) | ||
0.967733 | − | 0.251978i | \(-0.0810812\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.42386 | −0.283485 | −0.141743 | − | 0.989904i | \(-0.545271\pi\) | ||||
−0.141743 | + | 0.989904i | \(0.545271\pi\) | |||||||
\(884\) | 19.5335 | 0.656983 | ||||||||
\(885\) | 133.488i | 4.48717i | ||||||||
\(886\) | 0.790590i | 0.0265604i | ||||||||
\(887\) | −11.3204 | −0.380103 | −0.190052 | − | 0.981774i | \(-0.560866\pi\) | ||||
−0.190052 | + | 0.981774i | \(0.560866\pi\) | |||||||
\(888\) | 1.83072 | 0.0614348 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 21.0536i | 0.705717i | ||||||||
\(891\) | 14.3526 | − | 14.9793i | 0.480829 | − | 0.501827i | ||||
\(892\) | 4.01793i | 0.134530i | ||||||||
\(893\) | − | 30.5900i | − | 1.02366i | ||||||
\(894\) | − | 6.91841i | − | 0.231386i | ||||||
\(895\) | 31.7622i | 1.06169i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.3055i | 0.677980i | ||||||||
\(898\) | − | 15.9734i | − | 0.533041i | ||||||
\(899\) | 0.0280301 | 0.000934856 | ||||||||
\(900\) | −28.1036 | −0.936787 | ||||||||
\(901\) | −21.5729 | −0.718698 | ||||||||
\(902\) | −7.06002 | − | 6.76461i | −0.235073 | − | 0.225237i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 11.9900i | − | 0.398780i | ||||||
\(905\) | −53.5980 | −1.78166 | ||||||||
\(906\) | 26.9648i | 0.895845i | ||||||||
\(907\) | 54.8065 | 1.81982 | 0.909910 | − | 0.414805i | \(-0.136150\pi\) | ||||
0.909910 | + | 0.414805i | \(0.136150\pi\) | |||||||
\(908\) | 12.7293 | 0.422437 | ||||||||
\(909\) | −5.23977 | −0.173792 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.5914 | 1.54364 | 0.771820 | − | 0.635841i | \(-0.219347\pi\) | ||||
0.771820 | + | 0.635841i | \(0.219347\pi\) | |||||||
\(912\) | 12.0841i | 0.400145i | ||||||||
\(913\) | 6.59276 | − | 6.88066i | 0.218188 | − | 0.227717i | ||||
\(914\) | 34.9331 | 1.15549 | ||||||||
\(915\) | −102.196 | −3.37849 | ||||||||
\(916\) | 6.01345i | 0.198690i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.42637 | −0.245107 | ||||||||
\(919\) | − | 54.3073i | − | 1.79143i | −0.444627 | − | 0.895716i | \(-0.646664\pi\) | ||
0.444627 | − | 0.895716i | \(-0.353336\pi\) | |||||||
\(920\) | −5.51950 | −0.181973 | ||||||||
\(921\) | 66.4215i | 2.18866i | ||||||||
\(922\) | 20.8346i | 0.686151i | ||||||||
\(923\) | −42.4110 | −1.39598 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.30800 | −0.174526 | ||||||||
\(926\) | − | 13.1724i | − | 0.432871i | ||||||
\(927\) | − | 7.70484i | − | 0.253060i | ||||||
\(928\) | −0.100205 | −0.00328938 | ||||||||
\(929\) | − | 21.5409i | − | 0.706734i | −0.935485 | − | 0.353367i | \(-0.885037\pi\) | ||
0.935485 | − | 0.353367i | \(-0.114963\pi\) | |||||||
\(930\) | −2.56912 | −0.0842447 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 6.46694i | − | 0.211832i | ||||||
\(933\) | 4.95601 | 0.162252 | ||||||||
\(934\) | −16.8184 | −0.550314 | ||||||||
\(935\) | −32.9988 | − | 31.6181i | −1.07918 | − | 1.03402i | ||||
\(936\) | − | 18.7375i | − | 0.612453i | ||||||
\(937\) | −15.2663 | −0.498729 | −0.249364 | − | 0.968410i | \(-0.580222\pi\) | ||||
−0.249364 | + | 0.968410i | \(0.580222\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −79.0239 | −2.57885 | ||||||||
\(940\) | −23.2494 | −0.758312 | ||||||||
\(941\) | 36.1889 | 1.17973 | 0.589863 | − | 0.807503i | \(-0.299182\pi\) | ||||
0.589863 | + | 0.807503i | \(0.299182\pi\) | |||||||
\(942\) | 21.7339i | 0.708129i | ||||||||
\(943\) | 4.59792 | 0.149729 | ||||||||
\(944\) | − | 14.5344i | − | 0.473054i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.7327 | − | 21.6381i | 0.674079 | − | 0.703516i | ||||
\(947\) | 39.9218 | 1.29728 | 0.648641 | − | 0.761094i | \(-0.275338\pi\) | ||||
0.648641 | + | 0.761094i | \(0.275338\pi\) | |||||||
\(948\) | 19.9824 | 0.648998 | ||||||||
\(949\) | 19.5540 | 0.634750 | ||||||||
\(950\) | − | 35.0369i | − | 1.13675i | ||||||
\(951\) | − | 89.2590i | − | 2.89442i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 8.97831i | − | 0.290836i | −0.989370 | − | 0.145418i | \(-0.953547\pi\) | ||
0.989370 | − | 0.145418i | \(-0.0464527\pi\) | |||||||
\(954\) | 20.6938i | 0.669986i | ||||||||
\(955\) | − | 21.2340i | − | 0.687115i | ||||||
\(956\) | 15.5775i | 0.503812i | ||||||||
\(957\) | 0.596700 | − | 0.622758i | 0.0192886 | − | 0.0201309i | ||||
\(958\) | − | 22.8582i | − | 0.738513i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 9.18432 | 0.296423 | ||||||||
\(961\) | 30.9218 | 0.997476 | ||||||||
\(962\) | − | 3.53900i | − | 0.114102i | ||||||
\(963\) | − | 45.8109i | − | 1.47624i | ||||||
\(964\) | −23.4762 | −0.756119 | ||||||||
\(965\) | 52.4765 | 1.68928 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 51.5738i | − | 1.65850i | −0.558877 | − | 0.829251i | \(-0.688768\pi\) | ||
0.558877 | − | 0.829251i | \(-0.311232\pi\) | |||||||
\(968\) | 10.9900 | − | 0.469894i | 0.353231 | − | 0.0151030i | ||||
\(969\) | − | 47.0510i | − | 1.51150i | ||||||
\(970\) | 59.3089i | 1.90429i | ||||||||
\(971\) | − | 33.5695i | − | 1.07730i | −0.842530 | − | 0.538649i | \(-0.818935\pi\) | ||
0.842530 | − | 0.538649i | \(-0.181065\pi\) | |||||||
\(972\) | − | 21.9548i | − | 0.704201i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 31.2628i | − | 1.00173i | ||||||
\(975\) | 97.9650i | 3.13739i | ||||||||
\(976\) | 11.1272 | 0.356173 | ||||||||
\(977\) | −1.15259 | −0.0368746 | −0.0184373 | − | 0.999830i | \(-0.505869\pi\) | ||||
−0.0184373 | + | 0.999830i | \(0.505869\pi\) | |||||||
\(978\) | −7.95442 | −0.254354 | ||||||||
\(979\) | 14.2466 | + | 13.6504i | 0.455322 | + | 0.436270i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 25.1172i | − | 0.801929i | ||||||
\(982\) | 22.4979 | 0.717938 | ||||||||
\(983\) | 16.6099i | 0.529774i | 0.964279 | + | 0.264887i | \(0.0853346\pi\) | ||||
−0.964279 | + | 0.264887i | \(0.914665\pi\) | |||||||
\(984\) | −7.65083 | −0.243899 | ||||||||
\(985\) | −51.2251 | −1.63217 | ||||||||
\(986\) | 0.390159 | 0.0124252 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.3601 | 0.743183 | ||||||||
\(989\) | 14.0921i | 0.448102i | ||||||||
\(990\) | −30.3295 | + | 31.6541i | −0.963936 | + | 1.00603i | ||||
\(991\) | −18.4914 | −0.587399 | −0.293700 | − | 0.955898i | \(-0.594887\pi\) | ||||
−0.293700 | + | 0.955898i | \(0.594887\pi\) | |||||||
\(992\) | 0.279729 | 0.00888140 | ||||||||
\(993\) | − | 40.2586i | − | 1.27757i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.7283 | 1.25947 | ||||||||
\(996\) | − | 7.45646i | − | 0.236267i | ||||||
\(997\) | −21.1730 | −0.670555 | −0.335277 | − | 0.942119i | \(-0.608830\pi\) | ||||
−0.335277 | + | 0.942119i | \(0.608830\pi\) | |||||||
\(998\) | 31.9097i | 1.01008i | ||||||||
\(999\) | 1.34548i | 0.0425691i |
(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 | 1078.2.c.b.1077.2 | 16 | ||
7.2 | even | 3 | 154.2.i.a.87.4 | ✓ | 16 | ||
7.3 | odd | 6 | 154.2.i.a.131.8 | yes | 16 | ||
7.4 | even | 3 | 1078.2.i.c.901.5 | 16 | |||
7.5 | odd | 6 | 1078.2.i.c.1011.1 | 16 | |||
7.6 | odd | 2 | inner | 1078.2.c.b.1077.7 | 16 | ||
11.10 | odd | 2 | inner | 1078.2.c.b.1077.10 | 16 | ||
21.2 | odd | 6 | 1386.2.bk.c.703.8 | 16 | |||
21.17 | even | 6 | 1386.2.bk.c.901.4 | 16 | |||
28.3 | even | 6 | 1232.2.bn.b.593.1 | 16 | |||
28.23 | odd | 6 | 1232.2.bn.b.241.2 | 16 | |||
77.10 | even | 6 | 154.2.i.a.131.4 | yes | 16 | ||
77.32 | odd | 6 | 1078.2.i.c.901.1 | 16 | |||
77.54 | even | 6 | 1078.2.i.c.1011.5 | 16 | |||
77.65 | odd | 6 | 154.2.i.a.87.8 | yes | 16 | ||
77.76 | even | 2 | inner | 1078.2.c.b.1077.15 | 16 | ||
231.65 | even | 6 | 1386.2.bk.c.703.4 | 16 | |||
231.164 | odd | 6 | 1386.2.bk.c.901.8 | 16 | |||
308.87 | odd | 6 | 1232.2.bn.b.593.2 | 16 | |||
308.219 | even | 6 | 1232.2.bn.b.241.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.i.a.87.4 | ✓ | 16 | 7.2 | even | 3 | ||
154.2.i.a.87.8 | yes | 16 | 77.65 | odd | 6 | ||
154.2.i.a.131.4 | yes | 16 | 77.10 | even | 6 | ||
154.2.i.a.131.8 | yes | 16 | 7.3 | odd | 6 | ||
1078.2.c.b.1077.2 | 16 | 1.1 | even | 1 | trivial | ||
1078.2.c.b.1077.7 | 16 | 7.6 | odd | 2 | inner | ||
1078.2.c.b.1077.10 | 16 | 11.10 | odd | 2 | inner | ||
1078.2.c.b.1077.15 | 16 | 77.76 | even | 2 | inner | ||
1078.2.i.c.901.1 | 16 | 77.32 | odd | 6 | |||
1078.2.i.c.901.5 | 16 | 7.4 | even | 3 | |||
1078.2.i.c.1011.1 | 16 | 7.5 | odd | 6 | |||
1078.2.i.c.1011.5 | 16 | 77.54 | even | 6 | |||
1232.2.bn.b.241.1 | 16 | 308.219 | even | 6 | |||
1232.2.bn.b.241.2 | 16 | 28.23 | odd | 6 | |||
1232.2.bn.b.593.1 | 16 | 28.3 | even | 6 | |||
1232.2.bn.b.593.2 | 16 | 308.87 | odd | 6 | |||
1386.2.bk.c.703.4 | 16 | 231.65 | even | 6 | |||
1386.2.bk.c.703.8 | 16 | 21.2 | odd | 6 | |||
1386.2.bk.c.901.4 | 16 | 21.17 | even | 6 | |||
1386.2.bk.c.901.8 | 16 | 231.164 | odd | 6 |