Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(251,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.b (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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.4 | ||
Root | \(1.93185i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.251 |
Dual form | 315.2.b.a.251.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.93185i | 1.36603i | 0.730406 | + | 0.683013i | \(0.239331\pi\) | ||||
−0.730406 | + | 0.683013i | \(0.760669\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.73205 | −0.866025 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | + | 2.44949i | 0.377964 | + | 0.925820i | ||||
\(8\) | 0.517638i | 0.183013i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 1.93185i | − | 0.610905i | ||||||
\(11\) | 5.27792i | 1.59135i | 0.605723 | + | 0.795676i | \(0.292884\pi\) | ||||
−0.605723 | + | 0.795676i | \(0.707116\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.69213i | − | 1.85606i | −0.372502 | − | 0.928032i | \(-0.621500\pi\) | ||
0.372502 | − | 0.928032i | \(-0.378500\pi\) | |||||||
\(14\) | −4.73205 | + | 1.93185i | −1.26469 | + | 0.516309i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.46410 | −1.11603 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.69213i | 1.53528i | 0.640881 | + | 0.767640i | \(0.278569\pi\) | ||||
−0.640881 | + | 0.767640i | \(0.721431\pi\) | |||||||
\(20\) | 1.73205 | 0.387298 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10.1962 | −2.17383 | ||||||||
\(23\) | − | 1.41421i | − | 0.294884i | −0.989071 | − | 0.147442i | \(-0.952896\pi\) | ||
0.989071 | − | 0.147442i | \(-0.0471040\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 12.9282 | 2.53543 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.73205 | − | 4.24264i | −0.327327 | − | 0.801784i | ||||
\(29\) | − | 1.41421i | − | 0.262613i | −0.991342 | − | 0.131306i | \(-0.958083\pi\) | ||
0.991342 | − | 0.131306i | \(-0.0419172\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.79315i | 0.322059i | 0.986950 | + | 0.161030i | \(0.0514815\pi\) | ||||
−0.986950 | + | 0.161030i | \(0.948519\pi\) | |||||||
\(32\) | − | 7.58871i | − | 1.34151i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.69213i | − | 1.14769i | ||||||
\(35\) | −1.00000 | − | 2.44949i | −0.169031 | − | 0.414039i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.46410 | 0.898293 | 0.449146 | − | 0.893458i | \(-0.351728\pi\) | ||||
0.449146 | + | 0.893458i | \(0.351728\pi\) | |||||||
\(38\) | −12.9282 | −2.09723 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 0.517638i | − | 0.0818458i | ||||||
\(41\) | 10.3923 | 1.62301 | 0.811503 | − | 0.584349i | \(-0.198650\pi\) | ||||
0.811503 | + | 0.584349i | \(0.198650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.92820 | 1.36154 | 0.680769 | − | 0.732498i | \(-0.261646\pi\) | ||||
0.680769 | + | 0.732498i | \(0.261646\pi\) | |||||||
\(44\) | − | 9.14162i | − | 1.37815i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.73205 | 0.402819 | ||||||||
\(47\) | 2.53590 | 0.369899 | 0.184949 | − | 0.982748i | \(-0.440788\pi\) | ||||
0.184949 | + | 0.982748i | \(0.440788\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | + | 4.89898i | −0.714286 | + | 0.699854i | ||||
\(50\) | 1.93185i | 0.273205i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 11.5911i | 1.60740i | ||||||||
\(53\) | − | 4.52004i | − | 0.620876i | −0.950594 | − | 0.310438i | \(-0.899524\pi\) | ||
0.950594 | − | 0.310438i | \(-0.100476\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.27792i | − | 0.711674i | ||||||
\(56\) | −1.26795 | + | 0.517638i | −0.169437 | + | 0.0691723i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.73205 | 0.358736 | ||||||||
\(59\) | 2.53590 | 0.330146 | 0.165073 | − | 0.986281i | \(-0.447214\pi\) | ||||
0.165073 | + | 0.986281i | \(0.447214\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.58630i | 0.459179i | 0.973288 | + | 0.229589i | \(0.0737383\pi\) | ||||
−0.973288 | + | 0.229589i | \(0.926262\pi\) | |||||||
\(62\) | −3.46410 | −0.439941 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.73205 | 0.716506 | ||||||||
\(65\) | 6.69213i | 0.830057i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.92820 | 0.357737 | 0.178868 | − | 0.983873i | \(-0.442756\pi\) | ||||
0.178868 | + | 0.983873i | \(0.442756\pi\) | |||||||
\(68\) | 6.00000 | 0.727607 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.73205 | − | 1.93185i | 0.565588 | − | 0.230900i | ||||
\(71\) | − | 9.41902i | − | 1.11783i | −0.829224 | − | 0.558916i | \(-0.811217\pi\) | ||
0.829224 | − | 0.558916i | \(-0.188783\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.69213i | 0.783255i | 0.920124 | + | 0.391627i | \(0.128088\pi\) | ||||
−0.920124 | + | 0.391627i | \(0.871912\pi\) | |||||||
\(74\) | 10.5558i | 1.22709i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 11.5911i | − | 1.32959i | ||||||
\(77\) | −12.9282 | + | 5.27792i | −1.47331 | + | 0.601474i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.92820 | 0.329449 | 0.164724 | − | 0.986340i | \(-0.447327\pi\) | ||||
0.164724 | + | 0.986340i | \(0.447327\pi\) | |||||||
\(80\) | 4.46410 | 0.499102 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 20.0764i | 2.21707i | ||||||||
\(83\) | −2.53590 | −0.278351 | −0.139176 | − | 0.990268i | \(-0.544445\pi\) | ||||
−0.139176 | + | 0.990268i | \(0.544445\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.46410 | 0.375735 | ||||||||
\(86\) | 17.2480i | 1.85990i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.73205 | −0.291238 | ||||||||
\(89\) | −0.928203 | −0.0983893 | −0.0491947 | − | 0.998789i | \(-0.515665\pi\) | ||||
−0.0491947 | + | 0.998789i | \(0.515665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.3923 | − | 6.69213i | 1.71838 | − | 0.701526i | ||||
\(92\) | 2.44949i | 0.255377i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.89898i | 0.505291i | ||||||||
\(95\) | − | 6.69213i | − | 0.686598i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.2784i | − | 1.04362i | −0.853063 | − | 0.521808i | \(-0.825258\pi\) | ||
0.853063 | − | 0.521808i | \(-0.174742\pi\) | |||||||
\(98\) | −9.46410 | − | 9.65926i | −0.956019 | − | 0.975732i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.73205 | −0.173205 | ||||||||
\(101\) | 10.3923 | 1.03407 | 0.517036 | − | 0.855963i | \(-0.327035\pi\) | ||||
0.517036 | + | 0.855963i | \(0.327035\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.58630i | 0.353369i | 0.984268 | + | 0.176684i | \(0.0565372\pi\) | ||||
−0.984268 | + | 0.176684i | \(0.943463\pi\) | |||||||
\(104\) | 3.46410 | 0.339683 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.73205 | 0.848132 | ||||||||
\(107\) | − | 16.1112i | − | 1.55752i | −0.627320 | − | 0.778762i | \(-0.715848\pi\) | ||
0.627320 | − | 0.778762i | \(-0.284152\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000 | 0.766261 | 0.383131 | − | 0.923694i | \(-0.374846\pi\) | ||||
0.383131 | + | 0.923694i | \(0.374846\pi\) | |||||||
\(110\) | 10.1962 | 0.972165 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.46410 | − | 10.9348i | −0.421818 | − | 1.03324i | ||||
\(113\) | 15.0759i | 1.41822i | 0.705098 | + | 0.709110i | \(0.250903\pi\) | ||||
−0.705098 | + | 0.709110i | \(0.749097\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.41421i | 0.131876i | ||||||||
\(116\) | 2.44949i | 0.227429i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.89898i | 0.450988i | ||||||||
\(119\) | −3.46410 | − | 8.48528i | −0.317554 | − | 0.777844i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.8564 | −1.53240 | ||||||||
\(122\) | −6.92820 | −0.627250 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 3.10583i | − | 0.278912i | ||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.9282 | −0.969721 | −0.484861 | − | 0.874591i | \(-0.661130\pi\) | ||||
−0.484861 | + | 0.874591i | \(0.661130\pi\) | |||||||
\(128\) | − | 4.10394i | − | 0.362740i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.9282 | −1.13388 | ||||||||
\(131\) | −9.46410 | −0.826882 | −0.413441 | − | 0.910531i | \(-0.635673\pi\) | ||||
−0.413441 | + | 0.910531i | \(0.635673\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.3923 | + | 6.69213i | −1.42139 | + | 0.580281i | ||||
\(134\) | 5.65685i | 0.488678i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 1.79315i | − | 0.153761i | ||||||
\(137\) | − | 6.79367i | − | 0.580422i | −0.956963 | − | 0.290211i | \(-0.906274\pi\) | ||
0.956963 | − | 0.290211i | \(-0.0937255\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00481i | 0.678959i | 0.940613 | + | 0.339479i | \(0.110251\pi\) | ||||
−0.940613 | + | 0.339479i | \(0.889749\pi\) | |||||||
\(140\) | 1.73205 | + | 4.24264i | 0.146385 | + | 0.358569i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 18.1962 | 1.52699 | ||||||||
\(143\) | 35.3205 | 2.95365 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.41421i | 0.117444i | ||||||||
\(146\) | −12.9282 | −1.06995 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.46410 | −0.777944 | ||||||||
\(149\) | − | 5.00052i | − | 0.409658i | −0.978798 | − | 0.204829i | \(-0.934336\pi\) | ||
0.978798 | − | 0.204829i | \(-0.0656639\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.46410 | −0.607420 | −0.303710 | − | 0.952765i | \(-0.598225\pi\) | ||||
−0.303710 | + | 0.952765i | \(0.598225\pi\) | |||||||
\(152\) | −3.46410 | −0.280976 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.1962 | − | 24.9754i | −0.821629 | − | 2.01257i | ||||
\(155\) | − | 1.79315i | − | 0.144029i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 11.5911i | − | 0.925071i | −0.886601 | − | 0.462536i | \(-0.846940\pi\) | ||
0.886601 | − | 0.462536i | \(-0.153060\pi\) | |||||||
\(158\) | 5.65685i | 0.450035i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.58871i | 0.599940i | ||||||||
\(161\) | 3.46410 | − | 1.41421i | 0.273009 | − | 0.111456i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | −18.0000 | −1.40556 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 4.89898i | − | 0.380235i | ||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −31.7846 | −2.44497 | ||||||||
\(170\) | 6.69213i | 0.513263i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −15.4641 | −1.17913 | ||||||||
\(173\) | 6.00000 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | + | 2.44949i | 0.0755929 | + | 0.185164i | ||||
\(176\) | − | 23.5612i | − | 1.77599i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 1.79315i | − | 0.134402i | ||||||
\(179\) | 3.96524i | 0.296376i | 0.988959 | + | 0.148188i | \(0.0473441\pi\) | ||||
−0.988959 | + | 0.148188i | \(0.952656\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.8695i | − | 1.62555i | −0.582578 | − | 0.812775i | \(-0.697956\pi\) | ||
0.582578 | − | 0.812775i | \(-0.302044\pi\) | |||||||
\(182\) | 12.9282 | + | 31.6675i | 0.958302 | + | 2.34735i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.732051 | 0.0539675 | ||||||||
\(185\) | −5.46410 | −0.401729 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 18.2832i | − | 1.33700i | ||||||
\(188\) | −4.39230 | −0.320342 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.9282 | 0.937910 | ||||||||
\(191\) | 1.69161i | 0.122401i | 0.998125 | + | 0.0612005i | \(0.0194929\pi\) | ||||
−0.998125 | + | 0.0612005i | \(0.980507\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.60770 | 0.259688 | 0.129844 | − | 0.991534i | \(-0.458552\pi\) | ||||
0.129844 | + | 0.991534i | \(0.458552\pi\) | |||||||
\(194\) | 19.8564 | 1.42561 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.66025 | − | 8.48528i | 0.618590 | − | 0.606092i | ||||
\(197\) | − | 3.20736i | − | 0.228515i | −0.993451 | − | 0.114258i | \(-0.963551\pi\) | ||
0.993451 | − | 0.114258i | \(-0.0364489\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.2784i | 0.728619i | 0.931278 | + | 0.364309i | \(0.118695\pi\) | ||||
−0.931278 | + | 0.364309i | \(0.881305\pi\) | |||||||
\(200\) | 0.517638i | 0.0366025i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.0764i | 1.41257i | ||||||||
\(203\) | 3.46410 | − | 1.41421i | 0.243132 | − | 0.0992583i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.3923 | −0.725830 | ||||||||
\(206\) | −6.92820 | −0.482711 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 29.8744i | 2.07141i | ||||||||
\(209\) | −35.3205 | −2.44317 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.3923 | 1.26618 | 0.633089 | − | 0.774079i | \(-0.281787\pi\) | ||||
0.633089 | + | 0.774079i | \(0.281787\pi\) | |||||||
\(212\) | 7.82894i | 0.537694i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 31.1244 | 2.12762 | ||||||||
\(215\) | −8.92820 | −0.608898 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.39230 | + | 1.79315i | −0.298169 | + | 0.121727i | ||||
\(218\) | 15.4548i | 1.04673i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.14162i | 0.616328i | ||||||||
\(221\) | 23.1822i | 1.55940i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.89898i | 0.328060i | 0.986455 | + | 0.164030i | \(0.0524494\pi\) | ||||
−0.986455 | + | 0.164030i | \(0.947551\pi\) | |||||||
\(224\) | 18.5885 | − | 7.58871i | 1.24199 | − | 0.507042i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −29.1244 | −1.93732 | ||||||||
\(227\) | 23.3205 | 1.54784 | 0.773918 | − | 0.633286i | \(-0.218294\pi\) | ||||
0.773918 | + | 0.633286i | \(0.218294\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.6969i | 0.971201i | 0.874181 | + | 0.485601i | \(0.161399\pi\) | ||||
−0.874181 | + | 0.485601i | \(0.838601\pi\) | |||||||
\(230\) | −2.73205 | −0.180146 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.732051 | 0.0480615 | ||||||||
\(233\) | 18.6622i | 1.22260i | 0.791399 | + | 0.611300i | \(0.209353\pi\) | ||||
−0.791399 | + | 0.611300i | \(0.790647\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.53590 | −0.165424 | ||||||||
\(236\) | −4.39230 | −0.285915 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 16.3923 | − | 6.69213i | 1.06256 | − | 0.433786i | ||||
\(239\) | 18.6622i | 1.20716i | 0.797304 | + | 0.603578i | \(0.206259\pi\) | ||||
−0.797304 | + | 0.603578i | \(0.793741\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 18.2832i | − | 1.17773i | −0.808232 | − | 0.588864i | \(-0.799576\pi\) | ||
0.808232 | − | 0.588864i | \(-0.200424\pi\) | |||||||
\(242\) | − | 32.5641i | − | 2.09330i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 6.21166i | − | 0.397661i | ||||||
\(245\) | 5.00000 | − | 4.89898i | 0.319438 | − | 0.312984i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 44.7846 | 2.84958 | ||||||||
\(248\) | −0.928203 | −0.0589410 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 1.93185i | − | 0.122181i | ||||||
\(251\) | −23.3205 | −1.47198 | −0.735989 | − | 0.676994i | \(-0.763282\pi\) | ||||
−0.735989 | + | 0.676994i | \(0.763282\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.46410 | 0.469264 | ||||||||
\(254\) | − | 21.1117i | − | 1.32466i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.3923 | 1.21202 | ||||||||
\(257\) | −8.53590 | −0.532455 | −0.266227 | − | 0.963910i | \(-0.585777\pi\) | ||||
−0.266227 | + | 0.963910i | \(0.585777\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.46410 | + | 13.3843i | 0.339523 | + | 0.831658i | ||||
\(260\) | − | 11.5911i | − | 0.718850i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 18.2832i | − | 1.12954i | ||||||
\(263\) | 2.17209i | 0.133937i | 0.997755 | + | 0.0669684i | \(0.0213327\pi\) | ||||
−0.997755 | + | 0.0669684i | \(0.978667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.52004i | 0.277664i | ||||||||
\(266\) | −12.9282 | − | 31.6675i | −0.792679 | − | 1.94166i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.07180 | −0.309809 | ||||||||
\(269\) | 15.4641 | 0.942863 | 0.471431 | − | 0.881903i | \(-0.343737\pi\) | ||||
0.471431 | + | 0.881903i | \(0.343737\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.8028i | 1.08144i | 0.841202 | + | 0.540721i | \(0.181848\pi\) | ||||
−0.841202 | + | 0.540721i | \(0.818152\pi\) | |||||||
\(272\) | 15.4641 | 0.937649 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.1244 | 0.792871 | ||||||||
\(275\) | 5.27792i | 0.318270i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.0000 | −1.32185 | −0.660926 | − | 0.750451i | \(-0.729836\pi\) | ||||
−0.660926 | + | 0.750451i | \(0.729836\pi\) | |||||||
\(278\) | −15.4641 | −0.927475 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.26795 | − | 0.517638i | 0.0757745 | − | 0.0309348i | ||||
\(281\) | − | 6.31319i | − | 0.376614i | −0.982110 | − | 0.188307i | \(-0.939700\pi\) | ||
0.982110 | − | 0.188307i | \(-0.0602999\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 24.4949i | − | 1.45607i | −0.685540 | − | 0.728035i | \(-0.740434\pi\) | ||
0.685540 | − | 0.728035i | \(-0.259566\pi\) | |||||||
\(284\) | 16.3142i | 0.968071i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 68.2340i | 4.03476i | ||||||||
\(287\) | 10.3923 | + | 25.4558i | 0.613438 | + | 1.50261i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | −2.73205 | −0.160432 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 11.5911i | − | 0.678318i | ||||||
\(293\) | 10.3923 | 0.607125 | 0.303562 | − | 0.952812i | \(-0.401824\pi\) | ||||
0.303562 | + | 0.952812i | \(0.401824\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.53590 | −0.147646 | ||||||||
\(296\) | 2.82843i | 0.164399i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.66025 | 0.559603 | ||||||||
\(299\) | −9.46410 | −0.547323 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.92820 | + | 21.8695i | 0.514613 | + | 1.26054i | ||||
\(302\) | − | 14.4195i | − | 0.829751i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 29.8744i | − | 1.71341i | ||||||
\(305\) | − | 3.58630i | − | 0.205351i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 14.6969i | − | 0.838799i | −0.907802 | − | 0.419399i | \(-0.862241\pi\) | ||
0.907802 | − | 0.419399i | \(-0.137759\pi\) | |||||||
\(308\) | 22.3923 | − | 9.14162i | 1.27592 | − | 0.520892i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.46410 | 0.196748 | ||||||||
\(311\) | 7.60770 | 0.431393 | 0.215696 | − | 0.976460i | \(-0.430798\pi\) | ||||
0.215696 | + | 0.976460i | \(0.430798\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 15.1774i | − | 0.857878i | −0.903333 | − | 0.428939i | \(-0.858888\pi\) | ||
0.903333 | − | 0.428939i | \(-0.141112\pi\) | |||||||
\(314\) | 22.3923 | 1.26367 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.07180 | −0.285311 | ||||||||
\(317\) | 12.4505i | 0.699291i | 0.936882 | + | 0.349645i | \(0.113698\pi\) | ||||
−0.936882 | + | 0.349645i | \(0.886302\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.46410 | 0.417909 | ||||||||
\(320\) | −5.73205 | −0.320431 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.73205 | + | 6.69213i | 0.152251 | + | 0.372938i | ||||
\(323\) | − | 23.1822i | − | 1.28989i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 6.69213i | − | 0.371213i | ||||||
\(326\) | − | 7.72741i | − | 0.427981i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.37945i | 0.297031i | ||||||||
\(329\) | 2.53590 | + | 6.21166i | 0.139809 | + | 0.342460i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.3923 | −1.45065 | −0.725326 | − | 0.688405i | \(-0.758311\pi\) | ||||
−0.725326 | + | 0.688405i | \(0.758311\pi\) | |||||||
\(332\) | 4.39230 | 0.241059 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 23.1822i | − | 1.26847i | ||||||
\(335\) | −2.92820 | −0.159985 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.39230 | −0.457158 | −0.228579 | − | 0.973525i | \(-0.573408\pi\) | ||||
−0.228579 | + | 0.973525i | \(0.573408\pi\) | |||||||
\(338\) | − | 61.4032i | − | 3.33989i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.00000 | −0.325396 | ||||||||
\(341\) | −9.46410 | −0.512510 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | − | 7.34847i | −0.917914 | − | 0.396780i | ||||
\(344\) | 4.62158i | 0.249179i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.5911i | 0.623142i | ||||||||
\(347\) | − | 8.58682i | − | 0.460965i | −0.973077 | − | 0.230482i | \(-0.925970\pi\) | ||
0.973077 | − | 0.230482i | \(-0.0740304\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | −4.73205 | + | 1.93185i | −0.252939 | + | 0.103262i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 40.0526 | 2.13481 | ||||||||
\(353\) | −30.0000 | −1.59674 | −0.798369 | − | 0.602168i | \(-0.794304\pi\) | ||||
−0.798369 | + | 0.602168i | \(0.794304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.41902i | 0.499910i | ||||||||
\(356\) | 1.60770 | 0.0852077 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.66025 | −0.404857 | ||||||||
\(359\) | − | 25.0769i | − | 1.32351i | −0.749721 | − | 0.661754i | \(-0.769812\pi\) | ||
0.749721 | − | 0.661754i | \(-0.230188\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −25.7846 | −1.35708 | ||||||||
\(362\) | 42.2487 | 2.22054 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −28.3923 | + | 11.5911i | −1.48816 | + | 0.607539i | ||||
\(365\) | − | 6.69213i | − | 0.350282i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.0716i | 0.630132i | 0.949070 | + | 0.315066i | \(0.102027\pi\) | ||||
−0.949070 | + | 0.315066i | \(0.897973\pi\) | |||||||
\(368\) | 6.31319i | 0.329098i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 10.5558i | − | 0.548772i | ||||||
\(371\) | 11.0718 | − | 4.52004i | 0.574819 | − | 0.234669i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.9282 | 1.08362 | 0.541811 | − | 0.840501i | \(-0.317739\pi\) | ||||
0.541811 | + | 0.840501i | \(0.317739\pi\) | |||||||
\(374\) | 35.3205 | 1.82638 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.31268i | 0.0676962i | ||||||||
\(377\) | −9.46410 | −0.487426 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.53590 | 0.232993 | 0.116497 | − | 0.993191i | \(-0.462834\pi\) | ||||
0.116497 | + | 0.993191i | \(0.462834\pi\) | |||||||
\(380\) | 11.5911i | 0.594611i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.26795 | −0.167203 | ||||||||
\(383\) | −17.0718 | −0.872328 | −0.436164 | − | 0.899867i | \(-0.643663\pi\) | ||||
−0.436164 | + | 0.899867i | \(0.643663\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.9282 | − | 5.27792i | 0.658882 | − | 0.268988i | ||||
\(386\) | 6.96953i | 0.354740i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.8028i | 0.903799i | ||||||||
\(389\) | 0.859411i | 0.0435739i | 0.999763 | + | 0.0217869i | \(0.00693554\pi\) | ||||
−0.999763 | + | 0.0217869i | \(0.993064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.89898i | 0.247752i | ||||||||
\(392\) | −2.53590 | − | 2.58819i | −0.128082 | − | 0.130723i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.19615 | 0.312158 | ||||||||
\(395\) | −2.92820 | −0.147334 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.3891i | 1.07349i | 0.843746 | + | 0.536743i | \(0.180346\pi\) | ||||
−0.843746 | + | 0.536743i | \(0.819654\pi\) | |||||||
\(398\) | −19.8564 | −0.995312 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.46410 | −0.223205 | ||||||||
\(401\) | 18.1817i | 0.907951i | 0.891014 | + | 0.453975i | \(0.149995\pi\) | ||||
−0.891014 | + | 0.453975i | \(0.850005\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0000 | 0.597763 | ||||||||
\(404\) | −18.0000 | −0.895533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.73205 | + | 6.69213i | 0.135589 | + | 0.332125i | ||||
\(407\) | 28.8391i | 1.42950i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 2.27362i | − | 0.112423i | −0.998419 | − | 0.0562117i | \(-0.982098\pi\) | ||
0.998419 | − | 0.0562117i | \(-0.0179022\pi\) | |||||||
\(410\) | − | 20.0764i | − | 0.991502i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 6.21166i | − | 0.306026i | ||||||
\(413\) | 2.53590 | + | 6.21166i | 0.124783 | + | 0.305656i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.53590 | 0.124482 | ||||||||
\(416\) | −50.7846 | −2.48992 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 68.2340i | − | 3.33743i | ||||||
\(419\) | 37.8564 | 1.84941 | 0.924703 | − | 0.380689i | \(-0.124313\pi\) | ||||
0.924703 | + | 0.380689i | \(0.124313\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.8564 | 1.35764 | 0.678819 | − | 0.734306i | \(-0.262492\pi\) | ||||
0.678819 | + | 0.734306i | \(0.262492\pi\) | |||||||
\(422\) | 35.5312i | 1.72963i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.33975 | 0.113628 | ||||||||
\(425\) | −3.46410 | −0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.78461 | + | 3.58630i | −0.425117 | + | 0.173553i | ||||
\(428\) | 27.9053i | 1.34886i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 17.2480i | − | 0.831771i | ||||||
\(431\) | − | 21.4906i | − | 1.03517i | −0.855633 | − | 0.517583i | \(-0.826832\pi\) | ||
0.855633 | − | 0.517583i | \(-0.173168\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 24.9754i | − | 1.20024i | −0.799910 | − | 0.600120i | \(-0.795120\pi\) | ||
0.799910 | − | 0.600120i | \(-0.204880\pi\) | |||||||
\(434\) | −3.46410 | − | 8.48528i | −0.166282 | − | 0.407307i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.8564 | −0.663602 | ||||||||
\(437\) | 9.46410 | 0.452729 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 33.4607i | − | 1.59699i | −0.602002 | − | 0.798495i | \(-0.705630\pi\) | ||
0.602002 | − | 0.798495i | \(-0.294370\pi\) | |||||||
\(440\) | 2.73205 | 0.130245 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −44.7846 | −2.13019 | ||||||||
\(443\) | 15.5563i | 0.739104i | 0.929210 | + | 0.369552i | \(0.120489\pi\) | ||||
−0.929210 | + | 0.369552i | \(0.879511\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.928203 | 0.0440011 | ||||||||
\(446\) | −9.46410 | −0.448138 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.73205 | + | 14.0406i | 0.270814 | + | 0.663356i | ||||
\(449\) | 26.6670i | 1.25849i | 0.777206 | + | 0.629246i | \(0.216636\pi\) | ||||
−0.777206 | + | 0.629246i | \(0.783364\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 54.8497i | 2.58277i | ||||||||
\(452\) | − | 26.1122i | − | 1.22821i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 45.0518i | 2.11438i | ||||||||
\(455\) | −16.3923 | + | 6.69213i | −0.768483 | + | 0.313732i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.2487 | −1.04075 | −0.520375 | − | 0.853938i | \(-0.674208\pi\) | ||||
−0.520375 | + | 0.853938i | \(0.674208\pi\) | |||||||
\(458\) | −28.3923 | −1.32669 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 2.44949i | − | 0.114208i | ||||||
\(461\) | 19.8564 | 0.924805 | 0.462403 | − | 0.886670i | \(-0.346988\pi\) | ||||
0.462403 | + | 0.886670i | \(0.346988\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 6.31319i | 0.293083i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −36.0526 | −1.67010 | ||||||||
\(467\) | −7.60770 | −0.352042 | −0.176021 | − | 0.984386i | \(-0.556323\pi\) | ||||
−0.176021 | + | 0.984386i | \(0.556323\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.92820 | + | 7.17260i | 0.135212 | + | 0.331200i | ||||
\(470\) | − | 4.89898i | − | 0.225973i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.31268i | 0.0604209i | ||||||||
\(473\) | 47.1223i | 2.16669i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.69213i | 0.307056i | ||||||||
\(476\) | 6.00000 | + | 14.6969i | 0.275010 | + | 0.673633i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −36.0526 | −1.64901 | ||||||||
\(479\) | −21.4641 | −0.980720 | −0.490360 | − | 0.871520i | \(-0.663135\pi\) | ||||
−0.490360 | + | 0.871520i | \(0.663135\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 36.5665i | − | 1.66729i | ||||||
\(482\) | 35.3205 | 1.60881 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 29.1962 | 1.32710 | ||||||||
\(485\) | 10.2784i | 0.466720i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.8564 | 0.718522 | 0.359261 | − | 0.933237i | \(-0.383029\pi\) | ||||
0.359261 | + | 0.933237i | \(0.383029\pi\) | |||||||
\(488\) | −1.85641 | −0.0840356 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.46410 | + | 9.65926i | 0.427545 | + | 0.436361i | ||||
\(491\) | 1.69161i | 0.0763415i | 0.999271 | + | 0.0381708i | \(0.0121531\pi\) | ||||
−0.999271 | + | 0.0381708i | \(0.987847\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.89898i | 0.220639i | ||||||||
\(494\) | 86.5172i | 3.89259i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.00481i | − | 0.359426i | ||||||
\(497\) | 23.0718 | − | 9.41902i | 1.03491 | − | 0.422501i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.3923 | −1.71868 | −0.859338 | − | 0.511408i | \(-0.829124\pi\) | ||||
−0.859338 | + | 0.511408i | \(0.829124\pi\) | |||||||
\(500\) | 1.73205 | 0.0774597 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 45.0518i | − | 2.01076i | ||||||
\(503\) | 6.92820 | 0.308913 | 0.154457 | − | 0.988000i | \(-0.450637\pi\) | ||||
0.154457 | + | 0.988000i | \(0.450637\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.3923 | −0.462451 | ||||||||
\(506\) | 14.4195i | 0.641027i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.9282 | 0.839803 | ||||||||
\(509\) | −34.3923 | −1.52441 | −0.762206 | − | 0.647334i | \(-0.775884\pi\) | ||||
−0.762206 | + | 0.647334i | \(0.775884\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.3923 | + | 6.69213i | −0.725153 | + | 0.296042i | ||||
\(512\) | 29.2552i | 1.29291i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 16.4901i | − | 0.727347i | ||||||
\(515\) | − | 3.58630i | − | 0.158031i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.3843i | 0.588639i | ||||||||
\(518\) | −25.8564 | + | 10.5558i | −1.13607 | + | 0.463797i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.46410 | −0.151911 | ||||||||
\(521\) | 10.3923 | 0.455295 | 0.227648 | − | 0.973744i | \(-0.426897\pi\) | ||||
0.227648 | + | 0.973744i | \(0.426897\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 10.7589i | − | 0.470454i | −0.971940 | − | 0.235227i | \(-0.924417\pi\) | ||
0.971940 | − | 0.235227i | \(-0.0755834\pi\) | |||||||
\(524\) | 16.3923 | 0.716101 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.19615 | −0.182961 | ||||||||
\(527\) | − | 6.21166i | − | 0.270584i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.0000 | 0.913043 | ||||||||
\(530\) | −8.73205 | −0.379296 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 28.3923 | − | 11.5911i | 1.23096 | − | 0.502538i | ||||
\(533\) | − | 69.5467i | − | 3.01240i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.1112i | 0.696546i | ||||||||
\(536\) | 1.51575i | 0.0654704i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 29.8744i | 1.28797i | ||||||||
\(539\) | −25.8564 | − | 26.3896i | −1.11371 | − | 1.13668i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.8564 | 0.681720 | 0.340860 | − | 0.940114i | \(-0.389282\pi\) | ||||
0.340860 | + | 0.940114i | \(0.389282\pi\) | |||||||
\(542\) | −34.3923 | −1.47728 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 26.2880i | 1.12709i | ||||||||
\(545\) | −8.00000 | −0.342682 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.14359 | −0.0916534 | −0.0458267 | − | 0.998949i | \(-0.514592\pi\) | ||||
−0.0458267 | + | 0.998949i | \(0.514592\pi\) | |||||||
\(548\) | 11.7670i | 0.502660i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10.1962 | −0.434765 | ||||||||
\(551\) | 9.46410 | 0.403184 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.92820 | + | 7.17260i | 0.124520 | + | 0.305010i | ||||
\(554\) | − | 42.5007i | − | 1.80568i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 13.8647i | − | 0.587996i | ||||||
\(557\) | − | 33.5622i | − | 1.42208i | −0.703154 | − | 0.711038i | \(-0.748225\pi\) | ||
0.703154 | − | 0.711038i | \(-0.251775\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 59.7487i | − | 2.52710i | ||||||
\(560\) | 4.46410 | + | 10.9348i | 0.188643 | + | 0.462078i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.1962 | 0.514464 | ||||||||
\(563\) | 17.0718 | 0.719490 | 0.359745 | − | 0.933051i | \(-0.382864\pi\) | ||||
0.359745 | + | 0.933051i | \(0.382864\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 15.0759i | − | 0.634247i | ||||||
\(566\) | 47.3205 | 1.98903 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.87564 | 0.204577 | ||||||||
\(569\) | − | 36.6680i | − | 1.53720i | −0.639728 | − | 0.768602i | \(-0.720953\pi\) | ||
0.639728 | − | 0.768602i | \(-0.279047\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | −61.1769 | −2.55794 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −49.1769 | + | 20.0764i | −2.05260 | + | 0.837972i | ||||
\(575\) | − | 1.41421i | − | 0.0589768i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.8028i | 0.741139i | 0.928805 | + | 0.370569i | \(0.120837\pi\) | ||||
−0.928805 | + | 0.370569i | \(0.879163\pi\) | |||||||
\(578\) | − | 9.65926i | − | 0.401772i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 2.44949i | − | 0.101710i | ||||||
\(581\) | −2.53590 | − | 6.21166i | −0.105207 | − | 0.257703i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.8564 | 0.988031 | ||||||||
\(584\) | −3.46410 | −0.143346 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.0764i | 0.829348i | ||||||||
\(587\) | 39.7128 | 1.63912 | 0.819562 | − | 0.572991i | \(-0.194217\pi\) | ||||
0.819562 | + | 0.572991i | \(0.194217\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | − | 4.89898i | − | 0.201688i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24.3923 | −1.00252 | ||||||||
\(593\) | 45.7128 | 1.87720 | 0.938600 | − | 0.345007i | \(-0.112123\pi\) | ||||
0.938600 | + | 0.345007i | \(0.112123\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.46410 | + | 8.48528i | 0.142014 | + | 0.347863i | ||||
\(596\) | 8.66115i | 0.354774i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 18.2832i | − | 0.747657i | ||||||
\(599\) | − | 37.5002i | − | 1.53222i | −0.642711 | − | 0.766109i | \(-0.722190\pi\) | ||
0.642711 | − | 0.766109i | \(-0.277810\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.5959i | − | 0.799334i | −0.916660 | − | 0.399667i | \(-0.869126\pi\) | ||
0.916660 | − | 0.399667i | \(-0.130874\pi\) | |||||||
\(602\) | −42.2487 | + | 17.2480i | −1.72193 | + | 0.702975i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.9282 | 0.526041 | ||||||||
\(605\) | 16.8564 | 0.685310 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 18.2832i | − | 0.742094i | −0.928614 | − | 0.371047i | \(-0.878999\pi\) | ||
0.928614 | − | 0.371047i | \(-0.121001\pi\) | |||||||
\(608\) | 50.7846 | 2.05959 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.92820 | 0.280515 | ||||||||
\(611\) | − | 16.9706i | − | 0.686555i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.0718 | −0.608744 | −0.304372 | − | 0.952553i | \(-0.598447\pi\) | ||||
−0.304372 | + | 0.952553i | \(0.598447\pi\) | |||||||
\(614\) | 28.3923 | 1.14582 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.73205 | − | 6.69213i | −0.110077 | − | 0.269634i | ||||
\(617\) | 1.69161i | 0.0681019i | 0.999420 | + | 0.0340509i | \(0.0108408\pi\) | ||||
−0.999420 | + | 0.0340509i | \(0.989159\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.9459i | 1.68595i | 0.537953 | + | 0.842975i | \(0.319198\pi\) | ||||
−0.537953 | + | 0.842975i | \(0.680802\pi\) | |||||||
\(620\) | 3.10583i | 0.124733i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.6969i | 0.589294i | ||||||||
\(623\) | −0.928203 | − | 2.27362i | −0.0371877 | − | 0.0910908i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 29.3205 | 1.17188 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.0764i | 0.801135i | ||||||||
\(629\) | −18.9282 | −0.754717 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.7846 | 0.668185 | 0.334092 | − | 0.942540i | \(-0.391570\pi\) | ||||
0.334092 | + | 0.942540i | \(0.391570\pi\) | |||||||
\(632\) | 1.51575i | 0.0602933i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −24.0526 | −0.955249 | ||||||||
\(635\) | 10.9282 | 0.433673 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.7846 | + | 33.4607i | 1.29897 | + | 1.32576i | ||||
\(638\) | 14.4195i | 0.570875i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.10394i | 0.162222i | ||||||||
\(641\) | − | 8.93855i | − | 0.353051i | −0.984296 | − | 0.176526i | \(-0.943514\pi\) | ||
0.984296 | − | 0.176526i | \(-0.0564859\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11.1106i | − | 0.438161i | −0.975707 | − | 0.219080i | \(-0.929694\pi\) | ||
0.975707 | − | 0.219080i | \(-0.0703057\pi\) | |||||||
\(644\) | −6.00000 | + | 2.44949i | −0.236433 | + | 0.0965234i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 44.7846 | 1.76203 | ||||||||
\(647\) | −8.78461 | −0.345359 | −0.172679 | − | 0.984978i | \(-0.555242\pi\) | ||||
−0.172679 | + | 0.984978i | \(0.555242\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.3843i | 0.525378i | ||||||||
\(650\) | 12.9282 | 0.507086 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.92820 | 0.271329 | ||||||||
\(653\) | − | 36.1875i | − | 1.41613i | −0.706148 | − | 0.708064i | \(-0.749569\pi\) | ||
0.706148 | − | 0.708064i | \(-0.250431\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.46410 | 0.369793 | ||||||||
\(656\) | −46.3923 | −1.81132 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.0000 | + | 4.89898i | −0.467809 | + | 0.190982i | ||||
\(659\) | 3.96524i | 0.154464i | 0.997013 | + | 0.0772319i | \(0.0246082\pi\) | ||||
−0.997013 | + | 0.0772319i | \(0.975392\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 32.9802i | − | 1.28278i | −0.767215 | − | 0.641390i | \(-0.778358\pi\) | ||
0.767215 | − | 0.641390i | \(-0.221642\pi\) | |||||||
\(662\) | − | 50.9860i | − | 1.98163i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 1.31268i | − | 0.0509418i | ||||||
\(665\) | 16.3923 | − | 6.69213i | 0.635666 | − | 0.259510i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.00000 | −0.0774403 | ||||||||
\(668\) | 20.7846 | 0.804181 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 5.65685i | − | 0.218543i | ||||||
\(671\) | −18.9282 | −0.730715 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.3923 | −1.71120 | −0.855599 | − | 0.517640i | \(-0.826811\pi\) | ||||
−0.855599 | + | 0.517640i | \(0.826811\pi\) | |||||||
\(674\) | − | 16.2127i | − | 0.624489i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 55.0526 | 2.11741 | ||||||||
\(677\) | 6.67949 | 0.256714 | 0.128357 | − | 0.991728i | \(-0.459030\pi\) | ||||
0.128357 | + | 0.991728i | \(0.459030\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.1769 | − | 10.2784i | 0.966201 | − | 0.394450i | ||||
\(680\) | 1.79315i | 0.0687642i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 18.2832i | − | 0.700101i | ||||||
\(683\) | 33.8396i | 1.29484i | 0.762135 | + | 0.647418i | \(0.224151\pi\) | ||||
−0.762135 | + | 0.647418i | \(0.775849\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.79367i | 0.259573i | ||||||||
\(686\) | 14.1962 | − | 32.8415i | 0.542012 | − | 1.25389i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −39.8564 | −1.51951 | ||||||||
\(689\) | −30.2487 | −1.15238 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 41.9459i | − | 1.59570i | −0.602857 | − | 0.797849i | \(-0.705971\pi\) | ||
0.602857 | − | 0.797849i | \(-0.294029\pi\) | |||||||
\(692\) | −10.3923 | −0.395056 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.5885 | 0.629689 | ||||||||
\(695\) | − | 8.00481i | − | 0.303640i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −36.0000 | −1.36360 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.73205 | − | 4.24264i | −0.0654654 | − | 0.160357i | ||||
\(701\) | 32.5269i | 1.22852i | 0.789102 | + | 0.614262i | \(0.210546\pi\) | ||||
−0.789102 | + | 0.614262i | \(0.789454\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.5665i | 1.37913i | ||||||||
\(704\) | 30.2533i | 1.14021i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 57.9555i | − | 2.18119i | ||||||
\(707\) | 10.3923 | + | 25.4558i | 0.390843 | + | 0.957366i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.5692 | 1.41094 | 0.705471 | − | 0.708739i | \(-0.250736\pi\) | ||||
0.705471 | + | 0.708739i | \(0.250736\pi\) | |||||||
\(710\) | −18.1962 | −0.682889 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 0.480473i | − | 0.0180065i | ||||||
\(713\) | 2.53590 | 0.0949701 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −35.3205 | −1.32091 | ||||||||
\(716\) | − | 6.86800i | − | 0.256669i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 48.4449 | 1.80795 | ||||||||
\(719\) | 16.3923 | 0.611330 | 0.305665 | − | 0.952139i | \(-0.401121\pi\) | ||||
0.305665 | + | 0.952139i | \(0.401121\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.78461 | + | 3.58630i | −0.327156 | + | 0.133561i | ||||
\(722\) | − | 49.8120i | − | 1.85381i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 37.8792i | 1.40777i | ||||||||
\(725\) | − | 1.41421i | − | 0.0525226i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.5959i | 0.726772i | 0.931639 | + | 0.363386i | \(0.118379\pi\) | ||||
−0.931639 | + | 0.363386i | \(0.881621\pi\) | |||||||
\(728\) | 3.46410 | + | 8.48528i | 0.128388 | + | 0.314485i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.9282 | 0.478494 | ||||||||
\(731\) | −30.9282 | −1.14392 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.2490i | 1.00646i | 0.864151 | + | 0.503232i | \(0.167856\pi\) | ||||
−0.864151 | + | 0.503232i | \(0.832144\pi\) | |||||||
\(734\) | −23.3205 | −0.860776 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10.7321 | −0.395589 | ||||||||
\(737\) | 15.4548i | 0.569285i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.9282 | 1.43200 | 0.715999 | − | 0.698102i | \(-0.245972\pi\) | ||||
0.715999 | + | 0.698102i | \(0.245972\pi\) | |||||||
\(740\) | 9.46410 | 0.347907 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.73205 | + | 21.3891i | 0.320564 | + | 0.785217i | ||||
\(743\) | − | 16.1112i | − | 0.591061i | −0.955333 | − | 0.295530i | \(-0.904504\pi\) | ||
0.955333 | − | 0.295530i | \(-0.0954964\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.00052i | 0.183205i | ||||||||
\(746\) | 40.4302i | 1.48025i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 31.6675i | 1.15788i | ||||||||
\(749\) | 39.4641 | − | 16.1112i | 1.44199 | − | 0.588689i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.60770 | −0.204628 | −0.102314 | − | 0.994752i | \(-0.532625\pi\) | ||||
−0.102314 | + | 0.994752i | \(0.532625\pi\) | |||||||
\(752\) | −11.3205 | −0.412816 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 18.2832i | − | 0.665836i | ||||||
\(755\) | 7.46410 | 0.271646 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.1769 | 1.64198 | 0.820991 | − | 0.570940i | \(-0.193421\pi\) | ||||
0.820991 | + | 0.570940i | \(0.193421\pi\) | |||||||
\(758\) | 8.76268i | 0.318275i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.46410 | 0.125656 | ||||||||
\(761\) | 47.5692 | 1.72438 | 0.862191 | − | 0.506583i | \(-0.169091\pi\) | ||||
0.862191 | + | 0.506583i | \(0.169091\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00000 | + | 19.5959i | 0.289619 | + | 0.709420i | ||||
\(764\) | − | 2.92996i | − | 0.106002i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 32.9802i | − | 1.19162i | ||||||
\(767\) | − | 16.9706i | − | 0.612772i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.1918i | 1.41329i | 0.707566 | + | 0.706647i | \(0.249793\pi\) | ||||
−0.707566 | + | 0.706647i | \(0.750207\pi\) | |||||||
\(770\) | 10.1962 | + | 24.9754i | 0.367444 | + | 0.900050i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.24871 | −0.224896 | ||||||||
\(773\) | −21.7128 | −0.780956 | −0.390478 | − | 0.920612i | \(-0.627690\pi\) | ||||
−0.390478 | + | 0.920612i | \(0.627690\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.79315i | 0.0644119i | ||||||||
\(776\) | 5.32051 | 0.190995 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.66025 | −0.0595230 | ||||||||
\(779\) | 69.5467i | 2.49177i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.7128 | 1.77886 | ||||||||
\(782\) | −9.46410 | −0.338436 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 22.3205 | − | 21.8695i | 0.797161 | − | 0.781055i | ||||
\(785\) | 11.5911i | 0.413704i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 2.62536i | − | 0.0935838i | −0.998905 | − | 0.0467919i | \(-0.985100\pi\) | ||
0.998905 | − | 0.0467919i | \(-0.0148998\pi\) | |||||||
\(788\) | 5.55532i | 0.197900i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 5.65685i | − | 0.201262i | ||||||
\(791\) | −36.9282 | + | 15.0759i | −1.31302 | + | 0.536036i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0000 | 0.852265 | ||||||||
\(794\) | −41.3205 | −1.46641 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 17.8028i | − | 0.631002i | ||||||
\(797\) | −42.4974 | −1.50534 | −0.752668 | − | 0.658400i | \(-0.771233\pi\) | ||||
−0.752668 | + | 0.658400i | \(0.771233\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.78461 | −0.310777 | ||||||||
\(800\) | − | 7.58871i | − | 0.268301i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −35.1244 | −1.24028 | ||||||||
\(803\) | −35.3205 | −1.24643 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.46410 | + | 1.41421i | −0.122094 | + | 0.0498445i | ||||
\(806\) | 23.1822i | 0.816559i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.37945i | 0.189248i | ||||||||
\(809\) | 2.17209i | 0.0763666i | 0.999271 | + | 0.0381833i | \(0.0121571\pi\) | ||||
−0.999271 | + | 0.0381833i | \(0.987843\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.9754i | 0.877004i | 0.898730 | + | 0.438502i | \(0.144491\pi\) | ||||
−0.898730 | + | 0.438502i | \(0.855509\pi\) | |||||||
\(812\) | −6.00000 | + | 2.44949i | −0.210559 | + | 0.0859602i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −55.7128 | −1.95273 | ||||||||
\(815\) | 4.00000 | 0.140114 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 59.7487i | 2.09034i | ||||||||
\(818\) | 4.39230 | 0.153573 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18.0000 | 0.628587 | ||||||||
\(821\) | − | 47.7787i | − | 1.66749i | −0.552152 | − | 0.833743i | \(-0.686193\pi\) | ||
0.552152 | − | 0.833743i | \(-0.313807\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.7846 | −0.863937 | −0.431969 | − | 0.901889i | \(-0.642181\pi\) | ||||
−0.431969 | + | 0.901889i | \(0.642181\pi\) | |||||||
\(824\) | −1.85641 | −0.0646710 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.0000 | + | 4.89898i | −0.417533 | + | 0.170457i | ||||
\(827\) | − | 31.7690i | − | 1.10472i | −0.833606 | − | 0.552359i | \(-0.813728\pi\) | ||
0.833606 | − | 0.552359i | \(-0.186272\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 45.0518i | − | 1.56471i | −0.622831 | − | 0.782356i | \(-0.714018\pi\) | ||
0.622831 | − | 0.782356i | \(-0.285982\pi\) | |||||||
\(830\) | 4.89898i | 0.170046i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 38.3596i | − | 1.32988i | ||||||
\(833\) | 17.3205 | − | 16.9706i | 0.600120 | − | 0.587995i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0000 | 0.415277 | ||||||||
\(836\) | 61.1769 | 2.11585 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 73.1330i | 2.52634i | ||||||||
\(839\) | 6.92820 | 0.239188 | 0.119594 | − | 0.992823i | \(-0.461841\pi\) | ||||
0.119594 | + | 0.992823i | \(0.461841\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000 | 0.931034 | ||||||||
\(842\) | 53.8144i | 1.85457i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −31.8564 | −1.09654 | ||||||||
\(845\) | 31.7846 | 1.09342 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.8564 | − | 41.2896i | −0.579193 | − | 1.41873i | ||||
\(848\) | 20.1779i | 0.692913i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 6.69213i | − | 0.229538i | ||||||
\(851\) | − | 7.72741i | − | 0.264892i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 8.96575i | − | 0.306982i | −0.988150 | − | 0.153491i | \(-0.950948\pi\) | ||
0.988150 | − | 0.153491i | \(-0.0490515\pi\) | |||||||
\(854\) | −6.92820 | − | 16.9706i | −0.237078 | − | 0.580721i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.33975 | 0.285047 | ||||||||
\(857\) | −50.7846 | −1.73477 | −0.867385 | − | 0.497638i | \(-0.834201\pi\) | ||||
−0.867385 | + | 0.497638i | \(0.834201\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 37.0470i | − | 1.26403i | −0.774958 | − | 0.632013i | \(-0.782229\pi\) | ||
0.774958 | − | 0.632013i | \(-0.217771\pi\) | |||||||
\(860\) | 15.4641 | 0.527321 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 41.5167 | 1.41406 | ||||||||
\(863\) | 25.3543i | 0.863071i | 0.902096 | + | 0.431535i | \(0.142028\pi\) | ||||
−0.902096 | + | 0.431535i | \(0.857972\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | 48.2487 | 1.63956 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.60770 | − | 3.10583i | 0.258222 | − | 0.105419i | ||||
\(869\) | 15.4548i | 0.524269i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 19.5959i | − | 0.663982i | ||||||
\(872\) | 4.14110i | 0.140236i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.2832i | 0.618440i | ||||||||
\(875\) | −1.00000 | − | 2.44949i | −0.0338062 | − | 0.0828079i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.0000 | −0.742887 | −0.371444 | − | 0.928456i | \(-0.621137\pi\) | ||||
−0.371444 | + | 0.928456i | \(0.621137\pi\) | |||||||
\(878\) | 64.6410 | 2.18153 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 23.5612i | 0.794246i | ||||||||
\(881\) | −9.21539 | −0.310474 | −0.155237 | − | 0.987877i | \(-0.549614\pi\) | ||||
−0.155237 | + | 0.987877i | \(0.549614\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.8564 | 1.34127 | 0.670637 | − | 0.741785i | \(-0.266021\pi\) | ||||
0.670637 | + | 0.741785i | \(0.266021\pi\) | |||||||
\(884\) | − | 40.1528i | − | 1.35048i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30.0526 | −1.00964 | ||||||||
\(887\) | 30.2487 | 1.01565 | 0.507826 | − | 0.861460i | \(-0.330449\pi\) | ||||
0.507826 | + | 0.861460i | \(0.330449\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.9282 | − | 26.7685i | −0.366520 | − | 0.897787i | ||||
\(890\) | 1.79315i | 0.0601066i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 8.48528i | − | 0.284108i | ||||||
\(893\) | 16.9706i | 0.567898i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.96524i | − | 0.132543i | ||||||
\(896\) | 10.0526 | − | 4.10394i | 0.335832 | − | 0.137103i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −51.5167 | −1.71913 | ||||||||
\(899\) | 2.53590 | 0.0845769 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.6579i | 0.521640i | ||||||||
\(902\) | −105.962 | −3.52813 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.80385 | −0.259552 | ||||||||
\(905\) | 21.8695i | 0.726968i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.7846 | −1.02219 | −0.511093 | − | 0.859525i | \(-0.670759\pi\) | ||||
−0.511093 | + | 0.859525i | \(0.670759\pi\) | |||||||
\(908\) | −40.3923 | −1.34047 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.9282 | − | 31.6675i | −0.428566 | − | 1.04977i | ||||
\(911\) | 33.3591i | 1.10524i | 0.833434 | + | 0.552618i | \(0.186371\pi\) | ||||
−0.833434 | + | 0.552618i | \(0.813629\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 13.3843i | − | 0.442954i | ||||||
\(914\) | − | 42.9812i | − | 1.42169i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 25.4558i | − | 0.841085i | ||||||
\(917\) | −9.46410 | − | 23.1822i | −0.312532 | − | 0.765544i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.1051 | −1.38892 | −0.694460 | − | 0.719531i | \(-0.744357\pi\) | ||||
−0.694460 | + | 0.719531i | \(0.744357\pi\) | |||||||
\(920\) | −0.732051 | −0.0241350 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 38.3596i | 1.26331i | ||||||||
\(923\) | −63.0333 | −2.07477 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.46410 | 0.179659 | ||||||||
\(926\) | 15.4548i | 0.507877i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −10.7321 | −0.352297 | ||||||||
\(929\) | 23.0718 | 0.756961 | 0.378481 | − | 0.925609i | \(-0.376447\pi\) | ||||
0.378481 | + | 0.925609i | \(0.376447\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.7846 | − | 33.4607i | −1.07447 | − | 1.09663i | ||||
\(932\) | − | 32.3238i | − | 1.05880i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 14.6969i | − | 0.480899i | ||||||
\(935\) | 18.2832i | 0.597926i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 15.1774i | − | 0.495824i | −0.968783 | − | 0.247912i | \(-0.920256\pi\) | ||
0.968783 | − | 0.247912i | \(-0.0797445\pi\) | |||||||
\(938\) | −13.8564 | + | 5.65685i | −0.452428 | + | 0.184703i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.39230 | 0.143261 | ||||||||
\(941\) | 0.928203 | 0.0302586 | 0.0151293 | − | 0.999886i | \(-0.495184\pi\) | ||||
0.0151293 | + | 0.999886i | \(0.495184\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 14.6969i | − | 0.478598i | ||||||
\(944\) | −11.3205 | −0.368451 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −91.0333 | −2.95975 | ||||||||
\(947\) | 19.4944i | 0.633482i | 0.948512 | + | 0.316741i | \(0.102589\pi\) | ||||
−0.948512 | + | 0.316741i | \(0.897411\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.7846 | 1.45377 | ||||||||
\(950\) | −12.9282 | −0.419446 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.39230 | − | 1.79315i | 0.142355 | − | 0.0581164i | ||||
\(953\) | − | 6.79367i | − | 0.220068i | −0.993928 | − | 0.110034i | \(-0.964904\pi\) | ||
0.993928 | − | 0.110034i | \(-0.0350960\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.69161i | − | 0.0547394i | ||||||
\(956\) | − | 32.3238i | − | 1.04543i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 41.4655i | − | 1.33969i | ||||||
\(959\) | 16.6410 | − | 6.79367i | 0.537366 | − | 0.219379i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.7846 | 0.896278 | ||||||||
\(962\) | 70.6410 | 2.27756 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 31.6675i | 1.01994i | ||||||||
\(965\) | −3.60770 | −0.116136 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.7846 | −0.411125 | −0.205563 | − | 0.978644i | \(-0.565902\pi\) | ||||
−0.205563 | + | 0.978644i | \(0.565902\pi\) | |||||||
\(968\) | − | 8.72552i | − | 0.280449i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19.8564 | −0.637551 | ||||||||
\(971\) | 5.07180 | 0.162762 | 0.0813809 | − | 0.996683i | \(-0.474067\pi\) | ||||
0.0813809 | + | 0.996683i | \(0.474067\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.6077 | + | 8.00481i | −0.628594 | + | 0.256622i | ||||
\(974\) | 30.6322i | 0.981520i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 16.0096i | − | 0.512455i | ||||||
\(977\) | 31.0855i | 0.994513i | 0.867604 | + | 0.497256i | \(0.165659\pi\) | ||||
−0.867604 | + | 0.497256i | \(0.834341\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 4.89898i | − | 0.156572i | ||||||
\(980\) | −8.66025 | + | 8.48528i | −0.276642 | + | 0.271052i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.26795 | −0.104284 | ||||||||
\(983\) | −2.53590 | −0.0808826 | −0.0404413 | − | 0.999182i | \(-0.512876\pi\) | ||||
−0.0404413 | + | 0.999182i | \(0.512876\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.20736i | 0.102195i | ||||||||
\(986\) | −9.46410 | −0.301398 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −77.5692 | −2.46781 | ||||||||
\(989\) | − | 12.6264i | − | 0.401496i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.3205 | −0.677268 | −0.338634 | − | 0.940918i | \(-0.609965\pi\) | ||||
−0.338634 | + | 0.940918i | \(0.609965\pi\) | |||||||
\(992\) | 13.6077 | 0.432045 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18.1962 | + | 44.5713i | 0.577147 | + | 1.41372i | ||||
\(995\) | − | 10.2784i | − | 0.325848i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.8124i | 1.07085i | 0.844583 | + | 0.535424i | \(0.179848\pi\) | ||||
−0.844583 | + | 0.535424i | \(0.820152\pi\) | |||||||
\(998\) | − | 74.1682i | − | 2.34775i | ||||||
\(999\) | 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 | 315.2.b.a.251.4 | yes | 4 | |
3.2 | odd | 2 | 315.2.b.b.251.1 | yes | 4 | ||
4.3 | odd | 2 | 5040.2.f.a.881.1 | 4 | |||
5.2 | odd | 4 | 1575.2.g.c.1574.2 | 8 | |||
5.3 | odd | 4 | 1575.2.g.c.1574.7 | 8 | |||
5.4 | even | 2 | 1575.2.b.b.251.1 | 4 | |||
7.6 | odd | 2 | 315.2.b.b.251.4 | yes | 4 | ||
12.11 | even | 2 | 5040.2.f.c.881.2 | 4 | |||
15.2 | even | 4 | 1575.2.g.a.1574.8 | 8 | |||
15.8 | even | 4 | 1575.2.g.a.1574.1 | 8 | |||
15.14 | odd | 2 | 1575.2.b.c.251.4 | 4 | |||
21.20 | even | 2 | inner | 315.2.b.a.251.1 | ✓ | 4 | |
28.27 | even | 2 | 5040.2.f.c.881.3 | 4 | |||
35.13 | even | 4 | 1575.2.g.a.1574.7 | 8 | |||
35.27 | even | 4 | 1575.2.g.a.1574.2 | 8 | |||
35.34 | odd | 2 | 1575.2.b.c.251.1 | 4 | |||
84.83 | odd | 2 | 5040.2.f.a.881.4 | 4 | |||
105.62 | odd | 4 | 1575.2.g.c.1574.8 | 8 | |||
105.83 | odd | 4 | 1575.2.g.c.1574.1 | 8 | |||
105.104 | even | 2 | 1575.2.b.b.251.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.b.a.251.1 | ✓ | 4 | 21.20 | even | 2 | inner | |
315.2.b.a.251.4 | yes | 4 | 1.1 | even | 1 | trivial | |
315.2.b.b.251.1 | yes | 4 | 3.2 | odd | 2 | ||
315.2.b.b.251.4 | yes | 4 | 7.6 | odd | 2 | ||
1575.2.b.b.251.1 | 4 | 5.4 | even | 2 | |||
1575.2.b.b.251.4 | 4 | 105.104 | even | 2 | |||
1575.2.b.c.251.1 | 4 | 35.34 | odd | 2 | |||
1575.2.b.c.251.4 | 4 | 15.14 | odd | 2 | |||
1575.2.g.a.1574.1 | 8 | 15.8 | even | 4 | |||
1575.2.g.a.1574.2 | 8 | 35.27 | even | 4 | |||
1575.2.g.a.1574.7 | 8 | 35.13 | even | 4 | |||
1575.2.g.a.1574.8 | 8 | 15.2 | even | 4 | |||
1575.2.g.c.1574.1 | 8 | 105.83 | odd | 4 | |||
1575.2.g.c.1574.2 | 8 | 5.2 | odd | 4 | |||
1575.2.g.c.1574.7 | 8 | 5.3 | odd | 4 | |||
1575.2.g.c.1574.8 | 8 | 105.62 | odd | 4 | |||
5040.2.f.a.881.1 | 4 | 4.3 | odd | 2 | |||
5040.2.f.a.881.4 | 4 | 84.83 | odd | 2 | |||
5040.2.f.c.881.2 | 4 | 12.11 | even | 2 | |||
5040.2.f.c.881.3 | 4 | 28.27 | even | 2 |