Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,2,Mod(575,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.l (of order \(4\), degree \(2\), 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: | \(18.3975326257\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.157351936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1727.3 | ||
Root | \(-0.581861 - 1.28897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1727 |
Dual form | 2304.2.l.d.575.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.16372 | + | 1.16372i | 0.520432 | + | 0.520432i | 0.917702 | − | 0.397270i | \(-0.130042\pi\) |
−0.397270 | + | 0.917702i | \(0.630042\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.74166 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.64575 | − | 1.64575i | 0.496213 | − | 0.496213i | −0.414044 | − | 0.910257i | \(-0.635884\pi\) |
0.910257 | + | 0.414044i | \(0.135884\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.645751 | − | 0.645751i | −0.179099 | − | 0.179099i | 0.611864 | − | 0.790963i | \(-0.290420\pi\) |
−0.790963 | + | 0.611864i | \(0.790420\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.57008i | − | 1.59348i | −0.604323 | − | 0.796740i | \(-0.706556\pi\) | ||
0.604323 | − | 0.796740i | \(-0.293444\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.41421 | + | 1.41421i | −0.324443 | + | 0.324443i | −0.850469 | − | 0.526026i | \(-0.823682\pi\) |
0.526026 | + | 0.850469i | \(0.323682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.00000i | − | 1.25109i | −0.780189 | − | 0.625543i | \(-0.784877\pi\) | ||
0.780189 | − | 0.625543i | \(-0.215123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 2.29150i | − | 0.458301i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.40636 | − | 5.40636i | 1.00394 | − | 1.00394i | 0.00394411 | − | 0.999992i | \(-0.498745\pi\) |
0.999992 | − | 0.00394411i | \(-0.00125545\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.913230i | 0.164021i | 0.996631 | + | 0.0820105i | \(0.0261341\pi\) | ||||
−0.996631 | + | 0.0820105i | \(0.973866\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.35425 | + | 4.35425i | 0.736002 | + | 0.736002i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | − | 1.00000i | 0.164399 | − | 0.164399i | −0.620113 | − | 0.784512i | \(-0.712913\pi\) |
0.784512 | + | 0.620113i | \(0.212913\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.57008 | 1.02607 | 0.513037 | − | 0.858366i | \(-0.328520\pi\) | ||||
0.513037 | + | 0.858366i | \(0.328520\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.74166 | − | 3.74166i | −0.570597 | − | 0.570597i | 0.361698 | − | 0.932295i | \(-0.382197\pi\) |
−0.932295 | + | 0.361698i | \(0.882197\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.73381 | − | 7.73381i | −1.06232 | − | 1.06232i | −0.997924 | − | 0.0643956i | \(-0.979488\pi\) |
−0.0643956 | − | 0.997924i | \(-0.520512\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.83039 | 0.516490 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.29150 | + | 9.29150i | −1.20965 | + | 1.20965i | −0.238511 | + | 0.971140i | \(0.576659\pi\) |
−0.971140 | + | 0.238511i | \(0.923341\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.2915 | + | 10.2915i | 1.31769 | + | 1.31769i | 0.915599 | + | 0.402093i | \(0.131717\pi\) |
0.402093 | + | 0.915599i | \(0.368283\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1.50295i | − | 0.186418i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.8127 | + | 10.8127i | −1.32098 | + | 1.32098i | −0.408005 | + | 0.912980i | \(0.633775\pi\) |
−0.912980 | + | 0.408005i | \(0.866225\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.70850i | − | 0.321440i | −0.987000 | − | 0.160720i | \(-0.948618\pi\) | ||
0.987000 | − | 0.160720i | \(-0.0513815\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.5830i | 1.47273i | 0.676585 | + | 0.736365i | \(0.263459\pi\) | ||||
−0.676585 | + | 0.736365i | \(0.736541\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.15784 | − | 6.15784i | 0.701751 | − | 0.701751i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 14.0534i | − | 1.58113i | −0.612378 | − | 0.790565i | \(-0.709787\pi\) | ||
0.612378 | − | 0.790565i | \(-0.290213\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.9373 | + | 10.9373i | 1.20052 | + | 1.20052i | 0.974009 | + | 0.226511i | \(0.0727319\pi\) |
0.226511 | + | 0.974009i | \(0.427268\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.64575 | − | 7.64575i | 0.829298 | − | 0.829298i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.412247 | −0.0436981 | −0.0218490 | − | 0.999761i | \(-0.506955\pi\) | ||||
−0.0218490 | + | 0.999761i | \(0.506955\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.41618 | − | 2.41618i | −0.253285 | − | 0.253285i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.29150 | −0.337701 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.70850 | 0.275006 | 0.137503 | − | 0.990501i | \(-0.456092\pi\) | ||||
0.137503 | + | 0.990501i | \(0.456092\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.07892 | − | 3.07892i | −0.306364 | − | 0.306364i | 0.537133 | − | 0.843497i | \(-0.319507\pi\) |
−0.843497 | + | 0.537133i | \(0.819507\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.913230 | −0.0899833 | −0.0449916 | − | 0.998987i | \(-0.514326\pi\) | ||||
−0.0449916 | + | 0.998987i | \(0.514326\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.29150 | + | 3.29150i | −0.318202 | + | 0.318202i | −0.848076 | − | 0.529874i | \(-0.822239\pi\) |
0.529874 | + | 0.848076i | \(0.322239\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.64575 | + | 6.64575i | 0.636548 | + | 0.636548i | 0.949702 | − | 0.313155i | \(-0.101386\pi\) |
−0.313155 | + | 0.949702i | \(0.601386\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.7279i | − | 1.19734i | −0.800995 | − | 0.598671i | \(-0.795696\pi\) | ||
0.800995 | − | 0.598671i | \(-0.204304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.98233 | − | 6.98233i | 0.651106 | − | 0.651106i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 24.5830i | − | 2.25352i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.58301i | 0.507546i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.48528 | − | 8.48528i | 0.758947 | − | 0.758947i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.39851i | 0.833983i | 0.908910 | + | 0.416992i | \(0.136916\pi\) | ||||
−0.908910 | + | 0.416992i | \(0.863084\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | + | 12.0000i | 1.04844 | + | 1.04844i | 0.998765 | + | 0.0496797i | \(0.0158200\pi\) |
0.0496797 | + | 0.998765i | \(0.484180\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.29150 | + | 5.29150i | −0.458831 | + | 0.458831i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.91520 | 0.163626 | 0.0818132 | − | 0.996648i | \(-0.473929\pi\) | ||||
0.0818132 | + | 0.996648i | \(0.473929\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8127 | + | 10.8127i | 0.917123 | + | 0.917123i | 0.996819 | − | 0.0796958i | \(-0.0253949\pi\) |
−0.0796958 | + | 0.996819i | \(0.525395\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.12549 | −0.177743 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.5830 | 1.04496 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.49117 | + | 3.49117i | 0.286007 | + | 0.286007i | 0.835499 | − | 0.549492i | \(-0.185179\pi\) |
−0.549492 | + | 0.835499i | \(0.685179\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.8838 | 1.45536 | 0.727681 | − | 0.685915i | \(-0.240598\pi\) | ||||
0.727681 | + | 0.685915i | \(0.240598\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.06275 | + | 1.06275i | −0.0853618 | + | 0.0853618i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.29150 | − | 4.29150i | −0.342499 | − | 0.342499i | 0.514807 | − | 0.857306i | \(-0.327864\pi\) |
−0.857306 | + | 0.514807i | \(0.827864\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 22.4499i | − | 1.76930i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.39851 | + | 9.39851i | −0.736148 | + | 0.736148i | −0.971830 | − | 0.235682i | \(-0.924268\pi\) |
0.235682 | + | 0.971830i | \(0.424268\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3.29150i | − | 0.254704i | −0.991858 | − | 0.127352i | \(-0.959352\pi\) | ||
0.991858 | − | 0.127352i | \(-0.0406478\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.1660i | − | 0.935847i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.16372 | + | 1.16372i | −0.0884761 | + | 0.0884761i | −0.749960 | − | 0.661484i | \(-0.769927\pi\) |
0.661484 | + | 0.749960i | \(0.269927\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 8.57402i | − | 0.648135i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.8745 | − | 15.8745i | −1.18652 | − | 1.18652i | −0.978024 | − | 0.208492i | \(-0.933144\pi\) |
−0.208492 | − | 0.978024i | \(-0.566856\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.64575 | + | 6.64575i | −0.493975 | + | 0.493975i | −0.909556 | − | 0.415581i | \(-0.863578\pi\) |
0.415581 | + | 0.909556i | \(0.363578\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.32744 | 0.171117 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.8127 | − | 10.8127i | −0.790705 | − | 0.790705i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.70850 | 0.630125 | 0.315062 | − | 0.949071i | \(-0.397975\pi\) | ||||
0.315062 | + | 0.949071i | \(0.397975\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.5830 | 1.19367 | 0.596835 | − | 0.802364i | \(-0.296425\pi\) | ||||
0.596835 | + | 0.802364i | \(0.296425\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.751475 | + | 0.751475i | 0.0535404 | + | 0.0535404i | 0.733370 | − | 0.679830i | \(-0.237946\pi\) |
−0.679830 | + | 0.733370i | \(0.737946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.56812 | 0.394713 | 0.197357 | − | 0.980332i | \(-0.436764\pi\) | ||||
0.197357 | + | 0.980332i | \(0.436764\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.2288 | − | 20.2288i | 1.41978 | − | 1.41978i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.64575 | + | 7.64575i | 0.534002 | + | 0.534002i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.65489i | 0.321985i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.98233 | + | 6.98233i | −0.480684 | + | 0.480684i | −0.905350 | − | 0.424666i | \(-0.860391\pi\) |
0.424666 | + | 0.905350i | \(0.360391\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 8.70850i | − | 0.593915i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.41699i | 0.231961i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.24264 | + | 4.24264i | −0.285391 | + | 0.285391i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.57205i | 0.507062i | 0.967327 | + | 0.253531i | \(0.0815920\pi\) | ||||
−0.967327 | + | 0.253531i | \(0.918408\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.64575 | + | 7.64575i | 0.507466 | + | 0.507466i | 0.913748 | − | 0.406282i | \(-0.133175\pi\) |
−0.406282 | + | 0.913748i | \(0.633175\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.6458 | − | 14.6458i | 0.967818 | − | 0.967818i | −0.0316796 | − | 0.999498i | \(-0.510086\pi\) |
0.999498 | + | 0.0316796i | \(0.0100856\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.412247 | 0.0270072 | 0.0135036 | − | 0.999909i | \(-0.495702\pi\) | ||||
0.0135036 | + | 0.999909i | \(0.495702\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.98233 | − | 6.98233i | −0.455477 | − | 0.455477i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.8745 | −1.41494 | −0.707472 | − | 0.706741i | \(-0.750165\pi\) | ||||
−0.707472 | + | 0.706741i | \(0.750165\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.8745 | −1.15140 | −0.575699 | − | 0.817662i | \(-0.695270\pi\) | ||||
−0.575699 | + | 0.817662i | \(0.695270\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.14605 | + | 8.14605i | 0.520432 | + | 0.520432i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.82646 | 0.116215 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.6458 | + | 13.6458i | −0.861312 | + | 0.861312i | −0.991491 | − | 0.130178i | \(-0.958445\pi\) |
0.130178 | + | 0.991491i | \(0.458445\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.87451 | − | 9.87451i | −0.620805 | − | 0.620805i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.89753i | 0.555013i | 0.960724 | + | 0.277506i | \(0.0895079\pi\) | ||||
−0.960724 | + | 0.277506i | \(0.910492\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.74166 | − | 3.74166i | 0.232495 | − | 0.232495i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 30.5830i | 1.88583i | 0.333035 | + | 0.942914i | \(0.391927\pi\) | ||||
−0.333035 | + | 0.942914i | \(0.608073\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 18.0000i | − | 1.10573i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.7161 | − | 14.7161i | 0.897259 | − | 0.897259i | −0.0979341 | − | 0.995193i | \(-0.531223\pi\) |
0.995193 | + | 0.0979341i | \(0.0312235\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.39851i | 0.570919i | 0.958391 | + | 0.285459i | \(0.0921462\pi\) | ||||
−0.958391 | + | 0.285459i | \(0.907854\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.77124 | − | 3.77124i | −0.227415 | − | 0.227415i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.35425 | + | 5.35425i | −0.321706 | + | 0.321706i | −0.849421 | − | 0.527716i | \(-0.823049\pi\) |
0.527716 | + | 0.849421i | \(0.323049\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.2073 | 1.08616 | 0.543078 | − | 0.839682i | \(-0.317259\pi\) | ||||
0.543078 | + | 0.839682i | \(0.317259\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.83039 | + | 3.83039i | 0.227693 | + | 0.227693i | 0.811728 | − | 0.584035i | \(-0.198527\pi\) |
−0.584035 | + | 0.811728i | \(0.698527\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.5830 | 1.45109 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −26.1660 | −1.53918 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.5465 | − | 18.5465i | −1.08350 | − | 1.08350i | −0.996180 | − | 0.0873196i | \(-0.972170\pi\) |
−0.0873196 | − | 0.996180i | \(-0.527830\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.6255 | −1.25908 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.87451 | + | 3.87451i | −0.224069 | + | 0.224069i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.0000 | − | 14.0000i | −0.806947 | − | 0.806947i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 23.9529i | 1.37154i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.6431 | − | 14.6431i | 0.835727 | − | 0.835727i | −0.152566 | − | 0.988293i | \(-0.548754\pi\) |
0.988293 | + | 0.152566i | \(0.0487538\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.1660i | 0.746576i | 0.927716 | + | 0.373288i | \(0.121770\pi\) | ||||
−0.927716 | + | 0.373288i | \(0.878230\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.1660i | 0.857234i | 0.903486 | + | 0.428617i | \(0.140999\pi\) | ||||
−0.903486 | + | 0.428617i | \(0.859001\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.73381 | + | 7.73381i | −0.434374 | + | 0.434374i | −0.890113 | − | 0.455739i | \(-0.849375\pi\) |
0.455739 | + | 0.890113i | \(0.349375\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 17.7951i | − | 0.996332i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.29150 | + | 9.29150i | 0.516993 | + | 0.516993i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.47974 | + | 1.47974i | −0.0820813 | + | 0.0820813i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.4499 | −1.23771 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.98233 | + | 6.98233i | 0.383784 | + | 0.383784i | 0.872463 | − | 0.488680i | \(-0.162521\pi\) |
−0.488680 | + | 0.872463i | \(0.662521\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.1660 | −1.37497 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.5830 | −0.685440 | −0.342720 | − | 0.939438i | \(-0.611348\pi\) | ||||
−0.342720 | + | 0.939438i | \(0.611348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.50295 | + | 1.50295i | 0.0813893 | + | 0.0813893i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.64575 | + | 7.64575i | −0.410445 | + | 0.410445i | −0.881894 | − | 0.471448i | \(-0.843731\pi\) |
0.471448 | + | 0.881894i | \(0.343731\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.416995 | − | 0.416995i | −0.0223212 | − | 0.0223212i | 0.695858 | − | 0.718179i | \(-0.255024\pi\) |
−0.718179 | + | 0.695858i | \(0.755024\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.07303i | 0.429684i | 0.976649 | + | 0.214842i | \(0.0689237\pi\) | ||||
−0.976649 | + | 0.214842i | \(0.931076\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.15194 | − | 3.15194i | 0.167287 | − | 0.167287i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.7085i | 1.40962i | 0.709396 | + | 0.704810i | \(0.248968\pi\) | ||||
−0.709396 | + | 0.704810i | \(0.751032\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000i | 0.789474i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.6431 | + | 14.6431i | −0.766456 | + | 0.766456i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.74166i | 0.195313i | 0.995220 | + | 0.0976565i | \(0.0311346\pi\) | ||||
−0.995220 | + | 0.0976565i | \(0.968865\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.9373 | − | 28.9373i | −1.50235 | − | 1.50235i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.7085 | − | 13.7085i | 0.709799 | − | 0.709799i | −0.256694 | − | 0.966493i | \(-0.582633\pi\) |
0.966493 | + | 0.256694i | \(0.0826332\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.98233 | −0.359608 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.2112 | − | 20.2112i | −1.03818 | − | 1.03818i | −0.999242 | − | 0.0389399i | \(-0.987602\pi\) |
−0.0389399 | − | 0.999242i | \(-0.512398\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.4575 | 1.45411 | 0.727055 | − | 0.686579i | \(-0.240888\pi\) | ||||
0.727055 | + | 0.686579i | \(0.240888\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.3320 | 0.730427 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.8068 | + | 15.8068i | 0.801439 | + | 0.801439i | 0.983320 | − | 0.181882i | \(-0.0582188\pi\) |
−0.181882 | + | 0.983320i | \(0.558219\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −39.4205 | −1.99358 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.3542 | − | 16.3542i | 0.822872 | − | 0.822872i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.5830 | + | 13.5830i | 0.681711 | + | 0.681711i | 0.960386 | − | 0.278674i | \(-0.0898950\pi\) |
−0.278674 | + | 0.960386i | \(0.589895\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.5406i | 1.17556i | 0.809019 | + | 0.587782i | \(0.199999\pi\) | ||||
−0.809019 | + | 0.587782i | \(0.800001\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.589720 | − | 0.589720i | 0.0293760 | − | 0.0293760i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.29150i | − | 0.163154i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 33.2915i | − | 1.64616i | −0.567926 | − | 0.823079i | \(-0.692254\pi\) | ||
0.567926 | − | 0.823079i | \(-0.307746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −34.7656 | + | 34.7656i | −1.71070 | + | 1.71070i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.4558i | 1.24958i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.9373 | − | 10.9373i | −0.534320 | − | 0.534320i | 0.387535 | − | 0.921855i | \(-0.373327\pi\) |
−0.921855 | + | 0.387535i | \(0.873327\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.93725 | + | 9.93725i | −0.484312 | + | 0.484312i | −0.906506 | − | 0.422194i | \(-0.861260\pi\) |
0.422194 | + | 0.906506i | \(0.361260\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.0554 | −0.730293 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 38.5073 | + | 38.5073i | 1.86350 | + | 1.86350i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.5830 | 0.606102 | 0.303051 | − | 0.952974i | \(-0.401995\pi\) | ||||
0.303051 | + | 0.952974i | \(0.401995\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.41699 | −0.260324 | −0.130162 | − | 0.991493i | \(-0.541550\pi\) | ||||
−0.130162 | + | 0.991493i | \(0.541550\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.48528 | + | 8.48528i | 0.405906 | + | 0.405906i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.57205 | 0.361394 | 0.180697 | − | 0.983539i | \(-0.442165\pi\) | ||||
0.180697 | + | 0.983539i | \(0.442165\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.64575 | − | 7.64575i | 0.363261 | − | 0.363261i | −0.501751 | − | 0.865012i | \(-0.667311\pi\) |
0.865012 | + | 0.501751i | \(0.167311\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.479741 | − | 0.479741i | −0.0227419 | − | 0.0227419i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.0554i | 0.710507i | 0.934770 | + | 0.355253i | \(0.115605\pi\) | ||||
−0.934770 | + | 0.355253i | \(0.884395\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.8127 | − | 10.8127i | 0.509151 | − | 0.509151i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 5.62352i | − | 0.263635i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.4575i | 1.05052i | 0.850942 | + | 0.525259i | \(0.176032\pi\) | ||||
−0.850942 | + | 0.525259i | \(0.823968\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.4735 | + | 10.4735i | −0.487799 | + | 0.487799i | −0.907611 | − | 0.419812i | \(-0.862096\pi\) |
0.419812 | + | 0.907611i | \(0.362096\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 30.1995i | − | 1.40349i | −0.712429 | − | 0.701744i | \(-0.752405\pi\) | ||
0.712429 | − | 0.701744i | \(-0.247595\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.6458 | − | 19.6458i | −0.909097 | − | 0.909097i | 0.0871024 | − | 0.996199i | \(-0.472239\pi\) |
−0.996199 | + | 0.0871024i | \(0.972239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.4575 | + | 40.4575i | −1.86815 | + | 1.86815i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.3157 | −0.566275 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.24067 | + | 3.24067i | 0.148692 | + | 0.148692i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.7085 | 0.672048 | 0.336024 | − | 0.941853i | \(-0.390918\pi\) | ||||
0.336024 | + | 0.941853i | \(0.390918\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.29150 | −0.0588875 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.15194 | + | 3.15194i | 0.143122 | + | 0.143122i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.2269 | −0.554055 | −0.277028 | − | 0.960862i | \(-0.589349\pi\) | ||||
−0.277028 | + | 0.960862i | \(0.589349\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.29150 | − | 9.29150i | 0.419320 | − | 0.419320i | −0.465650 | − | 0.884969i | \(-0.654179\pi\) |
0.884969 | + | 0.465650i | \(0.154179\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.5203 | − | 35.5203i | −1.59975 | − | 1.59975i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 10.1343i | − | 0.454584i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.6255 | − | 21.6255i | 0.968088 | − | 0.968088i | −0.0314182 | − | 0.999506i | \(-0.510002\pi\) |
0.999506 | + | 0.0314182i | \(0.0100024\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 3.87451i | − | 0.172756i | −0.996262 | − | 0.0863779i | \(-0.972471\pi\) | ||
0.996262 | − | 0.0863779i | \(-0.0275292\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 7.16601i | − | 0.318883i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.73381 | − | 7.73381i | 0.342795 | − | 0.342795i | −0.514622 | − | 0.857417i | \(-0.672068\pi\) |
0.857417 | + | 0.514622i | \(0.172068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 47.0813i | 2.08275i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.06275 | − | 1.06275i | −0.0468302 | − | 0.0468302i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.87451 | + | 9.87451i | −0.434280 | + | 0.434280i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.91520 | 0.0839063 | 0.0419531 | − | 0.999120i | \(-0.486642\pi\) | ||||
0.0419531 | + | 0.999120i | \(0.486642\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.3808 | + | 16.3808i | 0.716284 | + | 0.716284i | 0.967842 | − | 0.251558i | \(-0.0809429\pi\) |
−0.251558 | + | 0.967842i | \(0.580943\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.00000 | 0.261364 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.24264 | − | 4.24264i | −0.183769 | − | 0.183769i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.66079 | −0.331205 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.5203 | − | 11.5203i | 0.496213 | − | 0.496213i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.64575 | − | 8.64575i | −0.371710 | − | 0.371710i | 0.496390 | − | 0.868100i | \(-0.334659\pi\) |
−0.868100 | + | 0.496390i | \(0.834659\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.4676i | 0.662560i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.0887363 | − | 0.0887363i | 0.00379409 | − | 0.00379409i | −0.705207 | − | 0.709001i | \(-0.749146\pi\) |
0.709001 | + | 0.705207i | \(0.249146\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.2915i | 0.651440i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 52.5830i | − | 2.23606i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.6196 | + | 26.6196i | −1.12791 | + | 1.12791i | −0.137390 | + | 0.990517i | \(0.543871\pi\) |
−0.990517 | + | 0.137390i | \(0.956129\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.83236i | 0.204387i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.3542 | − | 10.3542i | −0.436380 | − | 0.436380i | 0.454412 | − | 0.890792i | \(-0.349849\pi\) |
−0.890792 | + | 0.454412i | \(0.849849\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.8118 | − | 14.8118i | 0.623136 | − | 0.623136i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.0200 | −1.21658 | −0.608291 | − | 0.793714i | \(-0.708145\pi\) | ||||
−0.608291 | + | 0.793714i | \(0.708145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.83039 | + | 3.83039i | 0.160297 | + | 0.160297i | 0.782698 | − | 0.622401i | \(-0.213843\pi\) |
−0.622401 | + | 0.782698i | \(0.713843\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.7490 | −0.573374 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.5830 | −1.27319 | −0.636594 | − | 0.771199i | \(-0.719657\pi\) | ||||
−0.636594 | + | 0.771199i | \(0.719657\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.9235 | + | 40.9235i | 1.69779 | + | 1.69779i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.4558 | −1.05427 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.70850 | − | 2.70850i | 0.111792 | − | 0.111792i | −0.648998 | − | 0.760790i | \(-0.724812\pi\) |
0.760790 | + | 0.648998i | \(0.224812\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.29150 | − | 1.29150i | −0.0532154 | − | 0.0532154i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 4.24264i | − | 0.174224i | −0.996199 | − | 0.0871122i | \(-0.972236\pi\) | ||
0.996199 | − | 0.0871122i | \(-0.0277639\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.6078 | − | 28.6078i | 1.17280 | − | 1.17280i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.1660i | 0.783102i | 0.920156 | + | 0.391551i | \(0.128061\pi\) | ||||
−0.920156 | + | 0.391551i | \(0.871939\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.5830i | 1.24751i | 0.781621 | + | 0.623753i | \(0.214393\pi\) | ||||
−0.781621 | + | 0.623753i | \(0.785607\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.49707 | + | 6.49707i | −0.264143 | + | 0.264143i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 38.5073i | − | 1.56296i | −0.623929 | − | 0.781481i | \(-0.714465\pi\) | ||
0.623929 | − | 0.781481i | \(-0.285535\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.87451 | + | 3.87451i | 0.156746 | + | 0.156746i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.5830 | − | 13.5830i | 0.548612 | − | 0.548612i | −0.377427 | − | 0.926039i | \(-0.623191\pi\) |
0.926039 | + | 0.377427i | \(0.123191\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.3475 | 1.26200 | 0.631001 | − | 0.775782i | \(-0.282644\pi\) | ||||
0.631001 | + | 0.775782i | \(0.282644\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.7951 | − | 17.7951i | −0.715244 | − | 0.715244i | 0.252384 | − | 0.967627i | \(-0.418786\pi\) |
−0.967627 | + | 0.252384i | \(0.918786\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.54249 | −0.0617984 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.29150 | 0.331660 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.57008 | − | 6.57008i | −0.261966 | − | 0.261966i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.1916 | 1.04267 | 0.521336 | − | 0.853352i | \(-0.325434\pi\) | ||||
0.521336 | + | 0.853352i | \(0.325434\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.9373 | + | 10.9373i | −0.434032 | + | 0.434032i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.52026 | − | 4.52026i | −0.179099 | − | 0.179099i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.0259i | 1.26495i | 0.774582 | + | 0.632474i | \(0.217961\pi\) | ||||
−0.774582 | + | 0.632474i | \(0.782039\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.7122 | + | 20.7122i | −0.816810 | + | 0.816810i | −0.985644 | − | 0.168834i | \(-0.946000\pi\) |
0.168834 | + | 0.985644i | \(0.446000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.3320i | 1.74287i | 0.490510 | + | 0.871436i | \(0.336811\pi\) | ||||
−0.490510 | + | 0.871436i | \(0.663189\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.5830i | 1.20049i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.16372 | − | 1.16372i | 0.0455400 | − | 0.0455400i | −0.683970 | − | 0.729510i | \(-0.739748\pi\) |
0.729510 | + | 0.683970i | \(0.239748\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.9293i | 1.09129i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.1660 | − | 19.1660i | −0.746602 | − | 0.746602i | 0.227238 | − | 0.973839i | \(-0.427031\pi\) |
−0.973839 | + | 0.227238i | \(0.927031\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.4575 | − | 29.4575i | 1.14576 | − | 1.14576i | 0.158387 | − | 0.987377i | \(-0.449371\pi\) |
0.987377 | − | 0.158387i | \(-0.0506295\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.3157 | −0.477581 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −32.4382 | − | 32.4382i | −1.25601 | − | 1.25601i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.8745 | 1.30771 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.7490 | −0.761269 | −0.380634 | − | 0.924726i | \(-0.624294\pi\) | ||||
−0.380634 | + | 0.924726i | \(0.624294\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.4441 | − | 27.4441i | −1.05476 | − | 1.05476i | −0.998411 | − | 0.0563498i | \(-0.982054\pi\) |
−0.0563498 | − | 0.998411i | \(-0.517946\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.1343 | 0.388918 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.3542 | − | 16.3542i | 0.625778 | − | 0.625778i | −0.321225 | − | 0.947003i | \(-0.604095\pi\) |
0.947003 | + | 0.321225i | \(0.104095\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.22876 | + | 2.22876i | 0.0851564 | + | 0.0851564i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.98823i | 0.380521i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.5367 | + | 21.5367i | −0.819295 | + | 0.819295i | −0.986006 | − | 0.166711i | \(-0.946685\pi\) |
0.166711 | + | 0.986006i | \(0.446685\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.1660i | 0.954601i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 43.1660i | − | 1.63503i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.6867 | − | 31.6867i | 1.19679 | − | 1.19679i | 0.221668 | − | 0.975122i | \(-0.428850\pi\) |
0.975122 | − | 0.221668i | \(-0.0711501\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.82843i | 0.106676i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.5203 | − | 11.5203i | −0.433264 | − | 0.433264i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.3542 | + | 23.3542i | −0.877087 | + | 0.877087i | −0.993232 | − | 0.116145i | \(-0.962946\pi\) |
0.116145 | + | 0.993232i | \(0.462946\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.47938 | 0.205204 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.47348 | − | 2.47348i | −0.0925030 | − | 0.0925030i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.4575 | −1.28505 | −0.642524 | − | 0.766265i | \(-0.722113\pi\) | ||||
−0.642524 | + | 0.766265i | \(0.722113\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.41699 | −0.127256 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.3887 | − | 12.3887i | −0.460105 | − | 0.460105i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.39261 | −0.237089 | −0.118544 | − | 0.992949i | \(-0.537823\pi\) | ||||
−0.118544 | + | 0.992949i | \(0.537823\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.5830 | + | 24.5830i | −0.909235 | + | 0.909235i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.06275 | − | 6.06275i | −0.223933 | − | 0.223933i | 0.586220 | − | 0.810152i | \(-0.300616\pi\) |
−0.810152 | + | 0.586220i | \(0.800616\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.5901i | 1.31098i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.83039 | − | 3.83039i | 0.140903 | − | 0.140903i | −0.633137 | − | 0.774040i | \(-0.718233\pi\) |
0.774040 | + | 0.633137i | \(0.218233\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.0405i | 1.28551i | 0.766071 | + | 0.642756i | \(0.222209\pi\) | ||||
−0.766071 | + | 0.642756i | \(0.777791\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.12549i | 0.297695i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.3157 | + | 12.3157i | −0.450005 | + | 0.450005i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 34.6769i | − | 1.26538i | −0.774406 | − | 0.632689i | \(-0.781951\pi\) | ||
0.774406 | − | 0.632689i | \(-0.218049\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.8118 | + | 20.8118i | 0.757418 | + | 0.757418i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.35425 | + | 9.35425i | −0.339986 | + | 0.339986i | −0.856362 | − | 0.516376i | \(-0.827281\pi\) |
0.516376 | + | 0.856362i | \(0.327281\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.7162 | 0.823460 | 0.411730 | − | 0.911306i | \(-0.364925\pi\) | ||||
0.411730 | + | 0.911306i | \(0.364925\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.8661 | + | 24.8661i | 0.900214 | + | 0.900214i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.0000 | 0.433295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.1660 | −0.402657 | −0.201328 | − | 0.979524i | \(-0.564526\pi\) | ||||
−0.201328 | + | 0.979524i | \(0.564526\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.73381 | + | 7.73381i | 0.278166 | + | 0.278166i | 0.832376 | − | 0.554211i | \(-0.186980\pi\) |
−0.554211 | + | 0.832376i | \(0.686980\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.09267 | 0.0751709 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.29150 | + | 9.29150i | −0.332903 | + | 0.332903i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.45751 | − | 4.45751i | −0.159502 | − | 0.159502i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 9.98823i | − | 0.356495i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.06910 | − | 6.06910i | 0.216340 | − | 0.216340i | −0.590614 | − | 0.806954i | \(-0.701114\pi\) |
0.806954 | + | 0.590614i | \(0.201114\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 47.6235i | − | 1.69330i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 13.2915i | − | 0.471995i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.81861 | − | 5.81861i | 0.206106 | − | 0.206106i | −0.596504 | − | 0.802610i | \(-0.703444\pi\) |
0.802610 | + | 0.596504i | \(0.203444\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39.4205i | 1.39460i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.7085 | + | 20.7085i | 0.730787 | + | 0.730787i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.1255 | − | 26.1255i | 0.920803 | − | 0.920803i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.0495 | 0.423637 | 0.211818 | − | 0.977309i | \(-0.432061\pi\) | ||||
0.211818 | + | 0.977309i | \(0.432061\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.0416 | − | 24.0416i | −0.844216 | − | 0.844216i | 0.145188 | − | 0.989404i | \(-0.453621\pi\) |
−0.989404 | + | 0.145188i | \(0.953621\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.8745 | −0.766231 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.5830 | 0.370252 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.55830 | − | 8.55830i | −0.298687 | − | 0.298687i | 0.541813 | − | 0.840499i | \(-0.317738\pi\) |
−0.840499 | + | 0.541813i | \(0.817738\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.1641 | −1.53946 | −0.769732 | − | 0.638367i | \(-0.779610\pi\) | ||||
−0.769732 | + | 0.638367i | \(0.779610\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.12549 | + | 2.12549i | −0.0739106 | + | 0.0739106i | −0.743096 | − | 0.669185i | \(-0.766643\pi\) |
0.669185 | + | 0.743096i | \(0.266643\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.9373 | + | 23.9373i | 0.831375 | + | 0.831375i | 0.987705 | − | 0.156330i | \(-0.0499662\pi\) |
−0.156330 | + | 0.987705i | \(0.549966\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 45.9906i | − | 1.59348i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.83039 | − | 3.83039i | 0.132556 | − | 0.132556i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 27.8745i | − | 0.962335i | −0.876629 | − | 0.481167i | \(-0.840213\pi\) | ||
0.876629 | − | 0.481167i | \(-0.159787\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 29.4575i | − | 1.01578i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.1579 | − | 14.1579i | 0.487045 | − | 0.487045i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.8897i | 0.717778i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | − | 6.00000i | −0.205677 | − | 0.205677i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.70850 | − | 7.70850i | 0.263934 | − | 0.263934i | −0.562716 | − | 0.826650i | \(-0.690244\pi\) |
0.826650 | + | 0.562716i | \(0.190244\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.74559 | 0.196266 | 0.0981328 | − | 0.995173i | \(-0.468713\pi\) | ||||
0.0981328 | + | 0.995173i | \(0.468713\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.7083 | + | 18.7083i | 0.638319 | + | 0.638319i | 0.950141 | − | 0.311822i | \(-0.100939\pi\) |
−0.311822 | + | 0.950141i | \(0.600939\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −47.0405 | −1.60128 | −0.800639 | − | 0.599147i | \(-0.795506\pi\) | ||||
−0.800639 | + | 0.599147i | \(0.795506\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.70850 | −0.0920917 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.1284 | − | 23.1284i | −0.784577 | − | 0.784577i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.9647 | 0.473175 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.7490 | − | 31.7490i | 1.07331 | − | 1.07331i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.4170 | − | 12.4170i | −0.419292 | − | 0.419292i | 0.465668 | − | 0.884960i | \(-0.345814\pi\) |
−0.884960 | + | 0.465668i | \(0.845814\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 7.24854i | − | 0.244210i | −0.992517 | − | 0.122105i | \(-0.961036\pi\) | ||
0.992517 | − | 0.122105i | \(-0.0389644\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.2269 | + | 12.2269i | −0.411469 | + | 0.411469i | −0.882250 | − | 0.470781i | \(-0.843972\pi\) |
0.470781 | + | 0.882250i | \(0.343972\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 49.1660i | − | 1.65083i | −0.564524 | − | 0.825417i | \(-0.690940\pi\) | ||
0.564524 | − | 0.825417i | \(-0.309060\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.1660i | 1.17943i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.48528 | − | 8.48528i | 0.283949 | − | 0.283949i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 36.9470i | − | 1.23500i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.93725 | + | 4.93725i | 0.164667 | + | 0.164667i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −50.8118 | + | 50.8118i | −1.69279 | + | 1.69279i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.4676 | −0.514161 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.7142 | − | 21.7142i | −0.721008 | − | 0.721008i | 0.247803 | − | 0.968811i | \(-0.420292\pi\) |
−0.968811 | + | 0.247803i | \(0.920292\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.6235 | 1.77663 | 0.888313 | − | 0.459238i | \(-0.151877\pi\) | ||||
0.888313 | + | 0.459238i | \(0.151877\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.0000 | 1.19143 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 44.8999 | + | 44.8999i | 1.48272 | + | 1.48272i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.09267 | 0.0690308 | 0.0345154 | − | 0.999404i | \(-0.489011\pi\) | ||||
0.0345154 | + | 0.999404i | \(0.489011\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.74902 | + | 1.74902i | −0.0575696 | + | 0.0575696i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.29150 | − | 2.29150i | −0.0753441 | − | 0.0753441i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 45.1661i | − | 1.48185i | −0.671587 | − | 0.740926i | \(-0.734387\pi\) | ||
0.671587 | − | 0.740926i | \(-0.265613\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.89949 | + | 9.89949i | −0.324443 | + | 0.324443i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 25.1660i | − | 0.823017i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.3320i | 1.70961i | 0.518947 | + | 0.854806i | \(0.326324\pi\) | ||||
−0.518947 | + | 0.854806i | \(0.673676\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.9588 | + | 18.9588i | −0.618039 | + | 0.618039i | −0.945028 | − | 0.326989i | \(-0.893966\pi\) |
0.326989 | + | 0.945028i | \(0.393966\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 39.4205i | − | 1.28371i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.5830 | + | 12.5830i | 0.408893 | + | 0.408893i | 0.881352 | − | 0.472460i | \(-0.156634\pi\) |
−0.472460 | + | 0.881352i | \(0.656634\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.12549 | − | 8.12549i | 0.263765 | − | 0.263765i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.8858 | −0.611770 | −0.305885 | − | 0.952069i | \(-0.598952\pi\) | ||||
−0.305885 | + | 0.952069i | \(0.598952\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.1343 | + | 10.1343i | 0.327937 | + | 0.327937i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.16601 | 0.231403 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.1660 | 0.973097 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.2980 | + | 19.2980i | 0.621225 | + | 0.621225i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.3023 | 1.81056 | 0.905280 | − | 0.424814i | \(-0.139661\pi\) | ||||
0.905280 | + | 0.424814i | \(0.139661\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.9373 | + | 34.9373i | −1.12119 | + | 1.12119i | −0.129627 | + | 0.991563i | \(0.541378\pi\) |
−0.991563 | + | 0.129627i | \(0.958622\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 40.4575 | + | 40.4575i | 1.29701 | + | 1.29701i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 20.5347i | − | 0.656965i | −0.944510 | − | 0.328482i | \(-0.893463\pi\) | ||
0.944510 | − | 0.328482i | \(-0.106537\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.678456 | + | 0.678456i | −0.0216835 | + | 0.0216835i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 6.58301i | − | 0.209965i | −0.994474 | − | 0.104983i | \(-0.966521\pi\) | ||
0.994474 | − | 0.104983i | \(-0.0334787\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.74902i | 0.0557283i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.4499 | + | 22.4499i | −0.713867 | + | 0.713867i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0573i | 0.510078i | 0.966931 | + | 0.255039i | \(0.0820883\pi\) | ||||
−0.966931 | + | 0.255039i | \(0.917912\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.47974 | + | 6.47974i | 0.205422 | + | 0.205422i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.2915 | − | 10.2915i | 0.325935 | − | 0.325935i | −0.525103 | − | 0.851038i | \(-0.675973\pi\) |
0.851038 | + | 0.525103i | \(0.175973\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2304.2.l.d.1727.3 | yes | 8 | |
3.2 | odd | 2 | 2304.2.l.h.1727.2 | yes | 8 | ||
4.3 | odd | 2 | 2304.2.l.h.1727.3 | yes | 8 | ||
8.3 | odd | 2 | 2304.2.l.a.1727.2 | yes | 8 | ||
8.5 | even | 2 | 2304.2.l.e.1727.2 | yes | 8 | ||
12.11 | even | 2 | inner | 2304.2.l.d.1727.2 | yes | 8 | |
16.3 | odd | 4 | 2304.2.l.a.575.3 | yes | 8 | ||
16.5 | even | 4 | inner | 2304.2.l.d.575.2 | yes | 8 | |
16.11 | odd | 4 | 2304.2.l.h.575.2 | yes | 8 | ||
16.13 | even | 4 | 2304.2.l.e.575.3 | yes | 8 | ||
24.5 | odd | 2 | 2304.2.l.a.1727.3 | yes | 8 | ||
24.11 | even | 2 | 2304.2.l.e.1727.3 | yes | 8 | ||
48.5 | odd | 4 | 2304.2.l.h.575.3 | yes | 8 | ||
48.11 | even | 4 | inner | 2304.2.l.d.575.3 | yes | 8 | |
48.29 | odd | 4 | 2304.2.l.a.575.2 | ✓ | 8 | ||
48.35 | even | 4 | 2304.2.l.e.575.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2304.2.l.a.575.2 | ✓ | 8 | 48.29 | odd | 4 | ||
2304.2.l.a.575.3 | yes | 8 | 16.3 | odd | 4 | ||
2304.2.l.a.1727.2 | yes | 8 | 8.3 | odd | 2 | ||
2304.2.l.a.1727.3 | yes | 8 | 24.5 | odd | 2 | ||
2304.2.l.d.575.2 | yes | 8 | 16.5 | even | 4 | inner | |
2304.2.l.d.575.3 | yes | 8 | 48.11 | even | 4 | inner | |
2304.2.l.d.1727.2 | yes | 8 | 12.11 | even | 2 | inner | |
2304.2.l.d.1727.3 | yes | 8 | 1.1 | even | 1 | trivial | |
2304.2.l.e.575.2 | yes | 8 | 48.35 | even | 4 | ||
2304.2.l.e.575.3 | yes | 8 | 16.13 | even | 4 | ||
2304.2.l.e.1727.2 | yes | 8 | 8.5 | even | 2 | ||
2304.2.l.e.1727.3 | yes | 8 | 24.11 | even | 2 | ||
2304.2.l.h.575.2 | yes | 8 | 16.11 | odd | 4 | ||
2304.2.l.h.575.3 | yes | 8 | 48.5 | odd | 4 | ||
2304.2.l.h.1727.2 | yes | 8 | 3.2 | odd | 2 | ||
2304.2.l.h.1727.3 | yes | 8 | 4.3 | odd | 2 |