Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(307,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.e (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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.12745506816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 23x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 307.2 | ||
Root | \(0.323042 + 0.323042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.307 |
Dual form | 1386.2.e.b.307.7 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 0.646084i | − | 0.288937i | −0.989509 | − | 0.144469i | \(-0.953853\pi\) | ||
0.989509 | − | 0.144469i | \(-0.0461473\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.44949 | − | 1.00000i | 0.925820 | − | 0.377964i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.646084 | −0.204310 | ||||||||
\(11\) | −2.79129 | + | 1.79129i | −0.841605 | + | 0.540094i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.09557 | −0.858558 | −0.429279 | − | 0.903172i | \(-0.641232\pi\) | ||||
−0.429279 | + | 0.903172i | \(0.641232\pi\) | |||||||
\(14\) | −1.00000 | − | 2.44949i | −0.267261 | − | 0.654654i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.74166 | −0.907485 | −0.453743 | − | 0.891133i | \(-0.649911\pi\) | ||||
−0.453743 | + | 0.891133i | \(0.649911\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.54506 | −1.27212 | −0.636062 | − | 0.771638i | \(-0.719438\pi\) | ||||
−0.636062 | + | 0.771638i | \(0.719438\pi\) | |||||||
\(20\) | 0.646084i | 0.144469i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.79129 | + | 2.79129i | 0.381904 | + | 0.595105i | ||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.58258 | 0.916515 | ||||||||
\(26\) | 3.09557i | 0.607092i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.44949 | + | 1.00000i | −0.462910 | + | 0.188982i | ||||
\(29\) | − | 7.58258i | − | 1.40805i | −0.710176 | − | 0.704024i | \(-0.751385\pi\) | ||
0.710176 | − | 0.704024i | \(-0.248615\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.15732i | 0.207861i | 0.994585 | + | 0.103931i | \(0.0331420\pi\) | ||||
−0.994585 | + | 0.103931i | \(0.966858\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.74166i | 0.641689i | ||||||||
\(35\) | −0.646084 | − | 1.58258i | −0.109208 | − | 0.267504i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.58258 | −0.917770 | −0.458885 | − | 0.888496i | \(-0.651751\pi\) | ||||
−0.458885 | + | 0.888496i | \(0.651751\pi\) | |||||||
\(38\) | 5.54506i | 0.899528i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.646084 | 0.102155 | ||||||||
\(41\) | −5.03383 | −0.786151 | −0.393076 | − | 0.919506i | \(-0.628589\pi\) | ||||
−0.393076 | + | 0.919506i | \(0.628589\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.1652i | − | 1.70267i | −0.524623 | − | 0.851335i | \(-0.675794\pi\) | ||
0.524623 | − | 0.851335i | \(-0.324206\pi\) | |||||||
\(44\) | 2.79129 | − | 1.79129i | 0.420802 | − | 0.270047i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000i | 0.589768i | ||||||||
\(47\) | 5.03383i | 0.734259i | 0.930170 | + | 0.367129i | \(0.119659\pi\) | ||||
−0.930170 | + | 0.367129i | \(0.880341\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | − | 4.89898i | 0.714286 | − | 0.699854i | ||||
\(50\) | − | 4.58258i | − | 0.648074i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.09557 | 0.429279 | ||||||||
\(53\) | 2.41742 | 0.332059 | 0.166029 | − | 0.986121i | \(-0.446905\pi\) | ||||
0.166029 | + | 0.986121i | \(0.446905\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.15732 | + | 1.80341i | 0.156053 | + | 0.243171i | ||||
\(56\) | 1.00000 | + | 2.44949i | 0.133631 | + | 0.327327i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.58258 | −0.995641 | ||||||||
\(59\) | 3.09557i | 0.403009i | 0.979488 | + | 0.201505i | \(0.0645831\pi\) | ||||
−0.979488 | + | 0.201505i | \(0.935417\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.28672 | −1.18904 | −0.594521 | − | 0.804080i | \(-0.702658\pi\) | ||||
−0.594521 | + | 0.804080i | \(0.702658\pi\) | |||||||
\(62\) | 1.15732 | 0.146980 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.00000i | 0.248069i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.58258 | 0.193342 | 0.0966712 | − | 0.995316i | \(-0.469180\pi\) | ||||
0.0966712 | + | 0.995316i | \(0.469180\pi\) | |||||||
\(68\) | 3.74166 | 0.453743 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.58258 | + | 0.646084i | −0.189154 | + | 0.0772218i | ||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.32599 | −0.740401 | −0.370201 | − | 0.928952i | \(-0.620711\pi\) | ||||
−0.370201 | + | 0.928952i | \(0.620711\pi\) | |||||||
\(74\) | 5.58258i | 0.648961i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.54506 | 0.636062 | ||||||||
\(77\) | −5.04594 | + | 7.17903i | −0.575039 | + | 0.818126i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000i | 0.450035i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | − | 0.646084i | − | 0.0722344i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.03383i | 0.555893i | ||||||||
\(83\) | −9.15188 | −1.00455 | −0.502274 | − | 0.864708i | \(-0.667503\pi\) | ||||
−0.502274 | + | 0.864708i | \(0.667503\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.41742i | 0.262206i | ||||||||
\(86\) | −11.1652 | −1.20397 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.79129 | − | 2.79129i | −0.190952 | − | 0.297552i | ||||
\(89\) | 9.79796i | 1.03858i | 0.854598 | + | 0.519291i | \(0.173804\pi\) | ||||
−0.854598 | + | 0.519291i | \(0.826196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.58258 | + | 3.09557i | −0.794870 | + | 0.324504i | ||||
\(92\) | 4.00000 | 0.417029 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.03383 | 0.519199 | ||||||||
\(95\) | 3.58258i | 0.367565i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.9891i | 1.62345i | 0.584041 | + | 0.811724i | \(0.301471\pi\) | ||||
−0.584041 | + | 0.811724i | \(0.698529\pi\) | |||||||
\(98\) | −4.89898 | − | 5.00000i | −0.494872 | − | 0.505076i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.58258 | −0.458258 | ||||||||
\(101\) | 0.511238 | 0.0508701 | 0.0254351 | − | 0.999676i | \(-0.491903\pi\) | ||||
0.0254351 | + | 0.999676i | \(0.491903\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 13.5396i | − | 1.33410i | −0.745014 | − | 0.667049i | \(-0.767557\pi\) | ||
0.745014 | − | 0.667049i | \(-0.232443\pi\) | |||||||
\(104\) | − | 3.09557i | − | 0.303546i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 2.41742i | − | 0.234801i | ||||||
\(107\) | 8.41742i | 0.813743i | 0.913485 | + | 0.406872i | \(0.133380\pi\) | ||||
−0.913485 | + | 0.406872i | \(0.866620\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.16515i | 0.111601i | 0.998442 | + | 0.0558006i | \(0.0177711\pi\) | ||||
−0.998442 | + | 0.0558006i | \(0.982229\pi\) | |||||||
\(110\) | 1.80341 | − | 1.15732i | 0.171948 | − | 0.110346i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.44949 | − | 1.00000i | 0.231455 | − | 0.0944911i | ||||
\(113\) | 16.7477 | 1.57549 | 0.787747 | − | 0.615999i | \(-0.211248\pi\) | ||||
0.787747 | + | 0.615999i | \(0.211248\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.58434i | 0.240991i | ||||||||
\(116\) | 7.58258i | 0.704024i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.09557 | 0.284971 | ||||||||
\(119\) | −9.16515 | + | 3.74166i | −0.840168 | + | 0.342997i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.58258 | − | 10.0000i | 0.416598 | − | 0.909091i | ||||
\(122\) | 9.28672i | 0.840780i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 1.15732i | − | 0.103931i | ||||||
\(125\) | − | 6.19115i | − | 0.553753i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 5.58258i | − | 0.495373i | −0.968840 | − | 0.247687i | \(-0.920330\pi\) | ||
0.968840 | − | 0.247687i | \(-0.0796704\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | 0.175412 | ||||||||
\(131\) | −9.42157 | −0.823166 | −0.411583 | − | 0.911372i | \(-0.635024\pi\) | ||||
−0.411583 | + | 0.911372i | \(0.635024\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.5826 | + | 5.54506i | −1.17776 | + | 0.480818i | ||||
\(134\) | − | 1.58258i | − | 0.136714i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 3.74166i | − | 0.320844i | ||||||
\(137\) | −15.1652 | −1.29565 | −0.647823 | − | 0.761791i | \(-0.724320\pi\) | ||||
−0.647823 | + | 0.761791i | \(0.724320\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.23042 | 0.274001 | 0.137000 | − | 0.990571i | \(-0.456254\pi\) | ||||
0.137000 | + | 0.990571i | \(0.456254\pi\) | |||||||
\(140\) | 0.646084 | + | 1.58258i | 0.0546040 | + | 0.133752i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.00000i | 0.167836i | ||||||||
\(143\) | 8.64064 | − | 5.54506i | 0.722566 | − | 0.463701i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.89898 | −0.406838 | ||||||||
\(146\) | 6.32599i | 0.523543i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.58258 | 0.458885 | ||||||||
\(149\) | − | 14.0000i | − | 1.14692i | −0.819232 | − | 0.573462i | \(-0.805600\pi\) | ||
0.819232 | − | 0.573462i | \(-0.194400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.58258i | 0.291546i | 0.989318 | + | 0.145773i | \(0.0465669\pi\) | ||||
−0.989318 | + | 0.145773i | \(0.953433\pi\) | |||||||
\(152\) | − | 5.54506i | − | 0.449764i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.17903 | + | 5.04594i | 0.578503 | + | 0.406614i | ||||
\(155\) | 0.747727 | 0.0600589 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 20.5117i | − | 1.63701i | −0.574498 | − | 0.818506i | \(-0.694803\pi\) | ||
0.574498 | − | 0.818506i | \(-0.305197\pi\) | |||||||
\(158\) | 4.00000 | 0.318223 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.646084 | −0.0510774 | ||||||||
\(161\) | −9.79796 | + | 4.00000i | −0.772187 | + | 0.315244i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | 5.03383 | 0.393076 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.15188i | 0.710323i | ||||||||
\(167\) | 6.19115 | 0.479085 | 0.239543 | − | 0.970886i | \(-0.423002\pi\) | ||||
0.239543 | + | 0.970886i | \(0.423002\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.41742 | −0.262879 | ||||||||
\(170\) | 2.41742 | 0.185408 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.1652i | 0.851335i | ||||||||
\(173\) | 22.9612 | 1.74571 | 0.872853 | − | 0.487983i | \(-0.162267\pi\) | ||||
0.872853 | + | 0.487983i | \(0.162267\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.2250 | − | 4.58258i | 0.848528 | − | 0.346410i | ||||
\(176\) | −2.79129 | + | 1.79129i | −0.210401 | + | 0.135023i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.79796 | 0.734388 | ||||||||
\(179\) | 7.16515 | 0.535549 | 0.267774 | − | 0.963482i | \(-0.413712\pi\) | ||||
0.267774 | + | 0.963482i | \(0.413712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 16.6352i | − | 1.23648i | −0.785988 | − | 0.618242i | \(-0.787845\pi\) | ||
0.785988 | − | 0.618242i | \(-0.212155\pi\) | |||||||
\(182\) | 3.09557 | + | 7.58258i | 0.229459 | + | 0.562058i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 4.00000i | − | 0.294884i | ||||||
\(185\) | 3.60681i | 0.265178i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.4440 | − | 6.70239i | 0.763744 | − | 0.490127i | ||||
\(188\) | − | 5.03383i | − | 0.367129i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.58258 | 0.259907 | ||||||||
\(191\) | 18.0000 | 1.30243 | 0.651217 | − | 0.758891i | \(-0.274259\pi\) | ||||
0.651217 | + | 0.758891i | \(0.274259\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.3303i | 1.46341i | 0.681623 | + | 0.731704i | \(0.261274\pi\) | ||||
−0.681623 | + | 0.731704i | \(0.738726\pi\) | |||||||
\(194\) | 15.9891 | 1.14795 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.00000 | + | 4.89898i | −0.357143 | + | 0.349927i | ||||
\(197\) | − | 18.7477i | − | 1.33572i | −0.744287 | − | 0.667860i | \(-0.767210\pi\) | ||
0.744287 | − | 0.667860i | \(-0.232790\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.6297i | 1.74596i | 0.487759 | + | 0.872978i | \(0.337814\pi\) | ||||
−0.487759 | + | 0.872978i | \(0.662186\pi\) | |||||||
\(200\) | 4.58258i | 0.324037i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 0.511238i | − | 0.0359706i | ||||||
\(203\) | −7.58258 | − | 18.5734i | −0.532192 | − | 1.30360i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.25227i | 0.227149i | ||||||||
\(206\) | −13.5396 | −0.943350 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.09557 | −0.214639 | ||||||||
\(209\) | 15.4779 | − | 9.93280i | 1.07063 | − | 0.687066i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.7477i | 0.739904i | 0.929051 | + | 0.369952i | \(0.120626\pi\) | ||||
−0.929051 | + | 0.369952i | \(0.879374\pi\) | |||||||
\(212\) | −2.41742 | −0.166029 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.41742 | 0.575403 | ||||||||
\(215\) | −7.21362 | −0.491965 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.15732 | + | 2.83485i | 0.0785641 | + | 0.192442i | ||||
\(218\) | 1.16515 | 0.0789140 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.15732 | − | 1.80341i | −0.0780266 | − | 0.121586i | ||||
\(221\) | 11.5826 | 0.779128 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.32599i | 0.423620i | 0.977311 | + | 0.211810i | \(0.0679358\pi\) | ||||
−0.977311 | + | 0.211810i | \(0.932064\pi\) | |||||||
\(224\) | −1.00000 | − | 2.44949i | −0.0668153 | − | 0.163663i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 16.7477i | − | 1.11404i | ||||||
\(227\) | 11.7362 | 0.778960 | 0.389480 | − | 0.921035i | \(-0.372655\pi\) | ||||
0.389480 | + | 0.921035i | \(0.372655\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 13.0284i | − | 0.860939i | −0.902605 | − | 0.430470i | \(-0.858348\pi\) | ||
0.902605 | − | 0.430470i | \(-0.141652\pi\) | |||||||
\(230\) | 2.58434 | 0.170406 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.58258 | 0.497820 | ||||||||
\(233\) | − | 8.83485i | − | 0.578790i | −0.957210 | − | 0.289395i | \(-0.906546\pi\) | ||
0.957210 | − | 0.289395i | \(-0.0934541\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.25227 | 0.212155 | ||||||||
\(236\) | − | 3.09557i | − | 0.201505i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.74166 | + | 9.16515i | 0.242536 | + | 0.594089i | ||||
\(239\) | − | 17.5826i | − | 1.13732i | −0.822572 | − | 0.568661i | \(-0.807462\pi\) | ||
0.822572 | − | 0.568661i | \(-0.192538\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.9219 | −1.66978 | −0.834889 | − | 0.550419i | \(-0.814468\pi\) | ||||
−0.834889 | + | 0.550419i | \(0.814468\pi\) | |||||||
\(242\) | −10.0000 | − | 4.58258i | −0.642824 | − | 0.294579i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.28672 | 0.594521 | ||||||||
\(245\) | −3.16515 | − | 3.23042i | −0.202214 | − | 0.206384i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.1652 | 1.09219 | ||||||||
\(248\) | −1.15732 | −0.0734900 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.19115 | −0.391563 | ||||||||
\(251\) | − | 2.07310i | − | 0.130853i | −0.997857 | − | 0.0654264i | \(-0.979159\pi\) | ||
0.997857 | − | 0.0654264i | \(-0.0208407\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.1652 | − | 7.16515i | 0.701947 | − | 0.450469i | ||||
\(254\) | −5.58258 | −0.350282 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 4.89898i | − | 0.305590i | −0.988258 | − | 0.152795i | \(-0.951173\pi\) | ||
0.988258 | − | 0.152795i | \(-0.0488274\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.6745 | + | 5.58258i | −0.849690 | + | 0.346884i | ||||
\(260\) | − | 2.00000i | − | 0.124035i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.42157i | 0.582066i | ||||||||
\(263\) | 28.3303i | 1.74692i | 0.486895 | + | 0.873461i | \(0.338130\pi\) | ||||
−0.486895 | + | 0.873461i | \(0.661870\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.56186i | − | 0.0959442i | ||||||
\(266\) | 5.54506 | + | 13.5826i | 0.339990 | + | 0.832801i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.58258 | −0.0966712 | ||||||||
\(269\) | − | 20.2420i | − | 1.23418i | −0.786894 | − | 0.617088i | \(-0.788312\pi\) | ||
0.786894 | − | 0.617088i | \(-0.211688\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.89898 | −0.297592 | −0.148796 | − | 0.988868i | \(-0.547540\pi\) | ||||
−0.148796 | + | 0.988868i | \(0.547540\pi\) | |||||||
\(272\) | −3.74166 | −0.226871 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.1652i | 0.916160i | ||||||||
\(275\) | −12.7913 | + | 8.20871i | −0.771344 | + | 0.495004i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.00000i | − | 0.120168i | −0.998193 | − | 0.0600842i | \(-0.980863\pi\) | ||
0.998193 | − | 0.0600842i | \(-0.0191369\pi\) | |||||||
\(278\) | − | 3.23042i | − | 0.193748i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.58258 | − | 0.646084i | 0.0945770 | − | 0.0386109i | ||||
\(281\) | − | 7.16515i | − | 0.427437i | −0.976895 | − | 0.213719i | \(-0.931442\pi\) | ||
0.976895 | − | 0.213719i | \(-0.0685575\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.6127 | 0.928079 | 0.464040 | − | 0.885814i | \(-0.346399\pi\) | ||||
0.464040 | + | 0.885814i | \(0.346399\pi\) | |||||||
\(284\) | 2.00000 | 0.118678 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.54506 | − | 8.64064i | −0.327886 | − | 0.510932i | ||||
\(287\) | −12.3303 | + | 5.03383i | −0.727835 | + | 0.297137i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.00000 | −0.176471 | ||||||||
\(290\) | 4.89898i | 0.287678i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.32599 | 0.370201 | ||||||||
\(293\) | −21.3993 | −1.25016 | −0.625081 | − | 0.780560i | \(-0.714934\pi\) | ||||
−0.625081 | + | 0.780560i | \(0.714934\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.00000 | 0.116445 | ||||||||
\(296\) | − | 5.58258i | − | 0.324481i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.0000 | −0.810998 | ||||||||
\(299\) | 12.3823 | 0.716087 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.1652 | − | 27.3489i | −0.643549 | − | 1.57637i | ||||
\(302\) | 3.58258 | 0.206154 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.54506 | −0.318031 | ||||||||
\(305\) | 6.00000i | 0.343559i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.12940 | 0.463969 | 0.231985 | − | 0.972719i | \(-0.425478\pi\) | ||||
0.231985 | + | 0.972719i | \(0.425478\pi\) | |||||||
\(308\) | 5.04594 | − | 7.17903i | 0.287519 | − | 0.409063i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 0.747727i | − | 0.0424680i | ||||||
\(311\) | − | 9.93280i | − | 0.563238i | −0.959526 | − | 0.281619i | \(-0.909129\pi\) | ||
0.959526 | − | 0.281619i | \(-0.0908714\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.02248i | 0.0577938i | 0.999582 | + | 0.0288969i | \(0.00919945\pi\) | ||||
−0.999582 | + | 0.0288969i | \(0.990801\pi\) | |||||||
\(314\) | −20.5117 | −1.15754 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 4.00000i | − | 0.225018i | ||||||
\(317\) | 9.16515 | 0.514766 | 0.257383 | − | 0.966309i | \(-0.417140\pi\) | ||||
0.257383 | + | 0.966309i | \(0.417140\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.5826 | + | 21.1652i | 0.760478 | + | 1.18502i | ||||
\(320\) | 0.646084i | 0.0361172i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.00000 | + | 9.79796i | 0.222911 | + | 0.546019i | ||||
\(323\) | 20.7477 | 1.15443 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.1857 | −0.786881 | ||||||||
\(326\) | − | 4.00000i | − | 0.221540i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 5.03383i | − | 0.277946i | ||||||
\(329\) | 5.03383 | + | 12.3303i | 0.277524 | + | 0.679792i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.4174 | −0.792453 | −0.396227 | − | 0.918153i | \(-0.629681\pi\) | ||||
−0.396227 | + | 0.918153i | \(0.629681\pi\) | |||||||
\(332\) | 9.15188 | 0.502274 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 6.19115i | − | 0.338764i | ||||||
\(335\) | − | 1.02248i | − | 0.0558639i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 29.1652i | − | 1.58873i | −0.607443 | − | 0.794364i | \(-0.707805\pi\) | ||
0.607443 | − | 0.794364i | \(-0.292195\pi\) | |||||||
\(338\) | 3.41742i | 0.185883i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 2.41742i | − | 0.131103i | ||||||
\(341\) | −2.07310 | − | 3.23042i | −0.112264 | − | 0.174937i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.34847 | − | 17.0000i | 0.396780 | − | 0.917914i | ||||
\(344\) | 11.1652 | 0.601985 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 22.9612i | − | 1.23440i | ||||||
\(347\) | − | 0.834849i | − | 0.0448170i | −0.999749 | − | 0.0224085i | \(-0.992867\pi\) | ||
0.999749 | − | 0.0224085i | \(-0.00713345\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.07310 | −0.110970 | −0.0554852 | − | 0.998460i | \(-0.517671\pi\) | ||||
−0.0554852 | + | 0.998460i | \(0.517671\pi\) | |||||||
\(350\) | −4.58258 | − | 11.2250i | −0.244949 | − | 0.600000i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.79129 | + | 2.79129i | 0.0954760 | + | 0.148776i | ||||
\(353\) | − | 7.48331i | − | 0.398297i | −0.979969 | − | 0.199148i | \(-0.936182\pi\) | ||
0.979969 | − | 0.199148i | \(-0.0638176\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.29217i | 0.0685811i | ||||||||
\(356\) | − | 9.79796i | − | 0.519291i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 7.16515i | − | 0.378690i | ||||||
\(359\) | − | 0.417424i | − | 0.0220308i | −0.999939 | − | 0.0110154i | \(-0.996494\pi\) | ||
0.999939 | − | 0.0110154i | \(-0.00350638\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.7477 | 0.618301 | ||||||||
\(362\) | −16.6352 | −0.874326 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.58258 | − | 3.09557i | 0.397435 | − | 0.162252i | ||||
\(365\) | 4.08712i | 0.213930i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.42701i | 0.0744895i | 0.999306 | + | 0.0372447i | \(0.0118581\pi\) | ||||
−0.999306 | + | 0.0372447i | \(0.988142\pi\) | |||||||
\(368\) | −4.00000 | −0.208514 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.60681 | 0.187509 | ||||||||
\(371\) | 5.92146 | − | 2.41742i | 0.307427 | − | 0.125506i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 0.417424i | − | 0.0216134i | −0.999942 | − | 0.0108067i | \(-0.996560\pi\) | ||
0.999942 | − | 0.0108067i | \(-0.00343995\pi\) | |||||||
\(374\) | −6.70239 | − | 10.4440i | −0.346572 | − | 0.540049i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.03383 | −0.259600 | ||||||||
\(377\) | 23.4724i | 1.20889i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.3303 | 0.736098 | 0.368049 | − | 0.929806i | \(-0.380026\pi\) | ||||
0.368049 | + | 0.929806i | \(0.380026\pi\) | |||||||
\(380\) | − | 3.58258i | − | 0.183782i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 18.0000i | − | 0.920960i | ||||||
\(383\) | 4.76413i | 0.243436i | 0.992565 | + | 0.121718i | \(0.0388403\pi\) | ||||
−0.992565 | + | 0.121718i | \(0.961160\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.63825 | + | 3.26010i | 0.236387 | + | 0.166150i | ||||
\(386\) | 20.3303 | 1.03479 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 15.9891i | − | 0.811724i | ||||||
\(389\) | −10.0000 | −0.507020 | −0.253510 | − | 0.967333i | \(-0.581585\pi\) | ||||
−0.253510 | + | 0.967333i | \(0.581585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.9666 | 0.756895 | ||||||||
\(392\) | 4.89898 | + | 5.00000i | 0.247436 | + | 0.252538i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.7477 | −0.944497 | ||||||||
\(395\) | 2.58434 | 0.130032 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.8488i | 1.19694i | 0.801146 | + | 0.598469i | \(0.204224\pi\) | ||||
−0.801146 | + | 0.598469i | \(0.795776\pi\) | |||||||
\(398\) | 24.6297 | 1.23458 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.58258 | 0.229129 | ||||||||
\(401\) | 1.58258 | 0.0790301 | 0.0395150 | − | 0.999219i | \(-0.487419\pi\) | ||||
0.0395150 | + | 0.999219i | \(0.487419\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 3.58258i | − | 0.178461i | ||||||
\(404\) | −0.511238 | −0.0254351 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.5734 | + | 7.58258i | −0.921784 | + | 0.376317i | ||||
\(407\) | 15.5826 | − | 10.0000i | 0.772400 | − | 0.495682i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.93280 | 0.491146 | 0.245573 | − | 0.969378i | \(-0.421024\pi\) | ||||
0.245573 | + | 0.969378i | \(0.421024\pi\) | |||||||
\(410\) | 3.25227 | 0.160618 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.5396i | 0.667049i | ||||||||
\(413\) | 3.09557 | + | 7.58258i | 0.152323 | + | 0.373114i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.91288i | 0.290252i | ||||||||
\(416\) | 3.09557i | 0.151773i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.93280 | − | 15.4779i | −0.485829 | − | 0.757047i | ||||
\(419\) | − | 5.67991i | − | 0.277482i | −0.990329 | − | 0.138741i | \(-0.955694\pi\) | ||
0.990329 | − | 0.138741i | \(-0.0443055\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.58258 | −0.0771300 | −0.0385650 | − | 0.999256i | \(-0.512279\pi\) | ||||
−0.0385650 | + | 0.999256i | \(0.512279\pi\) | |||||||
\(422\) | 10.7477 | 0.523191 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.41742i | 0.117401i | ||||||||
\(425\) | −17.1464 | −0.831724 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.7477 | + | 9.28672i | −1.10084 | + | 0.449416i | ||||
\(428\) | − | 8.41742i | − | 0.406872i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.21362i | 0.347872i | ||||||||
\(431\) | 17.9129i | 0.862833i | 0.902153 | + | 0.431416i | \(0.141986\pi\) | ||||
−0.902153 | + | 0.431416i | \(0.858014\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 28.1017i | − | 1.35048i | −0.737597 | − | 0.675241i | \(-0.764040\pi\) | ||
0.737597 | − | 0.675241i | \(-0.235960\pi\) | |||||||
\(434\) | 2.83485 | − | 1.15732i | 0.136077 | − | 0.0555532i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 1.16515i | − | 0.0558006i | ||||||
\(437\) | 22.1803 | 1.06103 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.31464 | 0.110472 | 0.0552360 | − | 0.998473i | \(-0.482409\pi\) | ||||
0.0552360 | + | 0.998473i | \(0.482409\pi\) | |||||||
\(440\) | −1.80341 | + | 1.15732i | −0.0859740 | + | 0.0551732i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 11.5826i | − | 0.550927i | ||||||
\(443\) | 3.16515 | 0.150381 | 0.0751904 | − | 0.997169i | \(-0.476044\pi\) | ||||
0.0751904 | + | 0.997169i | \(0.476044\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.33030 | 0.300085 | ||||||||
\(446\) | 6.32599 | 0.299544 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.44949 | + | 1.00000i | −0.115728 | + | 0.0472456i | ||||
\(449\) | −12.8348 | −0.605714 | −0.302857 | − | 0.953036i | \(-0.597940\pi\) | ||||
−0.302857 | + | 0.953036i | \(0.597940\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.0509 | − | 9.01703i | 0.661629 | − | 0.424595i | ||||
\(452\) | −16.7477 | −0.787747 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 11.7362i | − | 0.550808i | ||||||
\(455\) | 2.00000 | + | 4.89898i | 0.0937614 | + | 0.229668i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 14.8348i | − | 0.693945i | −0.937875 | − | 0.346972i | \(-0.887210\pi\) | ||
0.937875 | − | 0.346972i | \(-0.112790\pi\) | |||||||
\(458\) | −13.0284 | −0.608776 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 2.58434i | − | 0.120495i | ||||||
\(461\) | −26.2983 | −1.22483 | −0.612417 | − | 0.790535i | \(-0.709803\pi\) | ||||
−0.612417 | + | 0.790535i | \(0.709803\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.1652 | −0.611836 | −0.305918 | − | 0.952058i | \(-0.598963\pi\) | ||||
−0.305918 | + | 0.952058i | \(0.598963\pi\) | |||||||
\(464\) | − | 7.58258i | − | 0.352012i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.83485 | −0.409266 | ||||||||
\(467\) | − | 0.511238i | − | 0.0236573i | −0.999930 | − | 0.0118286i | \(-0.996235\pi\) | ||
0.999930 | − | 0.0118286i | \(-0.00376526\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.87650 | − | 1.58258i | 0.179000 | − | 0.0730766i | ||||
\(470\) | − | 3.25227i | − | 0.150016i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.09557 | −0.142485 | ||||||||
\(473\) | 20.0000 | + | 31.1652i | 0.919601 | + | 1.43298i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.4107 | −1.16592 | ||||||||
\(476\) | 9.16515 | − | 3.74166i | 0.420084 | − | 0.171499i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.5826 | −0.804208 | ||||||||
\(479\) | 6.46084 | 0.295203 | 0.147602 | − | 0.989047i | \(-0.452845\pi\) | ||||
0.147602 | + | 0.989047i | \(0.452845\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.2813 | 0.787958 | ||||||||
\(482\) | 25.9219i | 1.18071i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.58258 | + | 10.0000i | −0.208299 | + | 0.454545i | ||||
\(485\) | 10.3303 | 0.469075 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.4955 | −1.51782 | −0.758912 | − | 0.651193i | \(-0.774269\pi\) | ||||
−0.758912 | + | 0.651193i | \(0.774269\pi\) | |||||||
\(488\) | − | 9.28672i | − | 0.420390i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.23042 | + | 3.16515i | −0.145935 | + | 0.142987i | ||||
\(491\) | − | 21.4955i | − | 0.970076i | −0.874493 | − | 0.485038i | \(-0.838806\pi\) | ||
0.874493 | − | 0.485038i | \(-0.161194\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.3714i | 1.27778i | ||||||||
\(494\) | − | 17.1652i | − | 0.772297i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.15732i | 0.0519653i | ||||||||
\(497\) | −4.89898 | + | 2.00000i | −0.219749 | + | 0.0897123i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.9129 | 1.24955 | 0.624776 | − | 0.780804i | \(-0.285190\pi\) | ||||
0.624776 | + | 0.780804i | \(0.285190\pi\) | |||||||
\(500\) | 6.19115i | 0.276877i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.07310 | −0.0925268 | ||||||||
\(503\) | 31.9782 | 1.42584 | 0.712919 | − | 0.701246i | \(-0.247373\pi\) | ||||
0.712919 | + | 0.701246i | \(0.247373\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.330303i | − | 0.0146983i | ||||||
\(506\) | −7.16515 | − | 11.1652i | −0.318530 | − | 0.496352i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.58258i | 0.247687i | ||||||||
\(509\) | − | 17.9274i | − | 0.794616i | −0.917685 | − | 0.397308i | \(-0.869944\pi\) | ||
0.917685 | − | 0.397308i | \(-0.130056\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.4955 | + | 6.32599i | −0.685479 | + | 0.279845i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.89898 | −0.216085 | ||||||||
\(515\) | −8.74773 | −0.385471 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.01703 | − | 14.0509i | −0.396569 | − | 0.617956i | ||||
\(518\) | 5.58258 | + | 13.6745i | 0.245284 | + | 0.600821i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.00000 | −0.0877058 | ||||||||
\(521\) | − | 35.5850i | − | 1.55901i | −0.626397 | − | 0.779504i | \(-0.715471\pi\) | ||
0.626397 | − | 0.779504i | \(-0.284529\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.7028 | 1.16763 | 0.583817 | − | 0.811885i | \(-0.301559\pi\) | ||||
0.583817 | + | 0.811885i | \(0.301559\pi\) | |||||||
\(524\) | 9.42157 | 0.411583 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.3303 | 1.23526 | ||||||||
\(527\) | − | 4.33030i | − | 0.188631i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −1.56186 | −0.0678428 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13.5826 | − | 5.54506i | 0.588879 | − | 0.240409i | ||||
\(533\) | 15.5826 | 0.674956 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.43836 | 0.235121 | ||||||||
\(536\) | 1.58258i | 0.0683569i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.2420 | −0.872695 | ||||||||
\(539\) | −5.18096 | + | 22.6309i | −0.223160 | + | 0.974782i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.25227i | 0.397786i | 0.980021 | + | 0.198893i | \(0.0637347\pi\) | ||||
−0.980021 | + | 0.198893i | \(0.936265\pi\) | |||||||
\(542\) | 4.89898i | 0.210429i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.74166i | 0.160422i | ||||||||
\(545\) | 0.752785 | 0.0322458 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2.74773i | − | 0.117484i | −0.998273 | − | 0.0587422i | \(-0.981291\pi\) | ||
0.998273 | − | 0.0587422i | \(-0.0187090\pi\) | |||||||
\(548\) | 15.1652 | 0.647823 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.20871 | + | 12.7913i | 0.350021 | + | 0.545422i | ||||
\(551\) | 42.0459i | 1.79121i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | + | 9.79796i | 0.170097 | + | 0.416652i | ||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.23042 | −0.137000 | ||||||||
\(557\) | 9.91288i | 0.420022i | 0.977699 | + | 0.210011i | \(0.0673500\pi\) | ||||
−0.977699 | + | 0.210011i | \(0.932650\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.5625i | 1.46184i | ||||||||
\(560\) | −0.646084 | − | 1.58258i | −0.0273020 | − | 0.0668760i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.16515 | −0.302244 | ||||||||
\(563\) | −42.4223 | −1.78788 | −0.893942 | − | 0.448182i | \(-0.852072\pi\) | ||||
−0.893942 | + | 0.448182i | \(0.852072\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 10.8204i | − | 0.455219i | ||||||
\(566\) | − | 15.6127i | − | 0.656251i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.00000i | − | 0.0839181i | ||||||
\(569\) | − | 15.4955i | − | 0.649603i | −0.945782 | − | 0.324802i | \(-0.894702\pi\) | ||
0.945782 | − | 0.324802i | \(-0.105298\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 3.58258i | − | 0.149926i | −0.997186 | − | 0.0749631i | \(-0.976116\pi\) | ||
0.997186 | − | 0.0749631i | \(-0.0238839\pi\) | |||||||
\(572\) | −8.64064 | + | 5.54506i | −0.361283 | + | 0.231851i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.03383 | + | 12.3303i | 0.210108 | + | 0.514657i | ||||
\(575\) | −18.3303 | −0.764426 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.269691i | 0.0112274i | 0.999984 | + | 0.00561369i | \(0.00178690\pi\) | ||||
−0.999984 | + | 0.00561369i | \(0.998213\pi\) | |||||||
\(578\) | 3.00000i | 0.124784i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.89898 | 0.203419 | ||||||||
\(581\) | −22.4174 | + | 9.15188i | −0.930031 | + | 0.379684i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.74773 | + | 4.33030i | −0.279462 | + | 0.179343i | ||||
\(584\) | − | 6.32599i | − | 0.261771i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.3993i | 0.883998i | ||||||||
\(587\) | 17.0397i | 0.703305i | 0.936131 | + | 0.351652i | \(0.114380\pi\) | ||||
−0.936131 | + | 0.351652i | \(0.885620\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 6.41742i | − | 0.264425i | ||||||
\(590\) | − | 2.00000i | − | 0.0823387i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.58258 | −0.229442 | ||||||||
\(593\) | −0.134846 | −0.00553744 | −0.00276872 | − | 0.999996i | \(-0.500881\pi\) | ||||
−0.00276872 | + | 0.999996i | \(0.500881\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.41742 | + | 5.92146i | 0.0991047 | + | 0.242756i | ||||
\(596\) | 14.0000i | 0.573462i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 12.3823i | − | 0.506350i | ||||||
\(599\) | 2.83485 | 0.115829 | 0.0579144 | − | 0.998322i | \(-0.481555\pi\) | ||||
0.0579144 | + | 0.998322i | \(0.481555\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.42701 | −0.0582091 | −0.0291045 | − | 0.999576i | \(-0.509266\pi\) | ||||
−0.0291045 | + | 0.999576i | \(0.509266\pi\) | |||||||
\(602\) | −27.3489 | + | 11.1652i | −1.11466 | + | 0.455058i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 3.58258i | − | 0.145773i | ||||||
\(605\) | −6.46084 | − | 2.96073i | −0.262670 | − | 0.120371i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.9448 | 1.90543 | 0.952716 | − | 0.303862i | \(-0.0982761\pi\) | ||||
0.952716 | + | 0.303862i | \(0.0982761\pi\) | |||||||
\(608\) | 5.54506i | 0.224882i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | − | 15.5826i | − | 0.630404i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.9129i | 0.561936i | 0.959717 | + | 0.280968i | \(0.0906555\pi\) | ||||
−0.959717 | + | 0.280968i | \(0.909345\pi\) | |||||||
\(614\) | − | 8.12940i | − | 0.328076i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.17903 | − | 5.04594i | −0.289251 | − | 0.203307i | ||||
\(617\) | −25.9129 | −1.04321 | −0.521607 | − | 0.853186i | \(-0.674667\pi\) | ||||
−0.521607 | + | 0.853186i | \(0.674667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 0.780929i | − | 0.0313882i | −0.999877 | − | 0.0156941i | \(-0.995004\pi\) | ||
0.999877 | − | 0.0156941i | \(-0.00499579\pi\) | |||||||
\(620\) | −0.747727 | −0.0300294 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.93280 | −0.398269 | ||||||||
\(623\) | 9.79796 | + | 24.0000i | 0.392547 | + | 0.961540i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.9129 | 0.756515 | ||||||||
\(626\) | 1.02248 | 0.0408664 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.5117i | 0.818506i | ||||||||
\(629\) | 20.8881 | 0.832863 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.16515 | −0.205621 | −0.102811 | − | 0.994701i | \(-0.532784\pi\) | ||||
−0.102811 | + | 0.994701i | \(0.532784\pi\) | |||||||
\(632\) | −4.00000 | −0.159111 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 9.16515i | − | 0.363995i | ||||||
\(635\) | −3.60681 | −0.143132 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.4779 | + | 15.1652i | −0.613255 | + | 0.600865i | ||||
\(638\) | 21.1652 | − | 13.5826i | 0.837936 | − | 0.537739i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.646084 | 0.0255387 | ||||||||
\(641\) | −29.9129 | −1.18149 | −0.590744 | − | 0.806859i | \(-0.701166\pi\) | ||||
−0.590744 | + | 0.806859i | \(0.701166\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 16.7700i | − | 0.661346i | −0.943745 | − | 0.330673i | \(-0.892724\pi\) | ||
0.943745 | − | 0.330673i | \(-0.107276\pi\) | |||||||
\(644\) | 9.79796 | − | 4.00000i | 0.386094 | − | 0.157622i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − | 20.7477i | − | 0.816308i | ||||||
\(647\) | 44.7650i | 1.75990i | 0.475071 | + | 0.879948i | \(0.342423\pi\) | ||||
−0.475071 | + | 0.879948i | \(0.657577\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.54506 | − | 8.64064i | −0.217663 | − | 0.339175i | ||||
\(650\) | 14.1857i | 0.556409i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | 6.00000 | 0.234798 | 0.117399 | − | 0.993085i | \(-0.462544\pi\) | ||||
0.117399 | + | 0.993085i | \(0.462544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.08712i | 0.237844i | ||||||||
\(656\) | −5.03383 | −0.196538 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.3303 | − | 5.03383i | 0.480685 | − | 0.196239i | ||||
\(659\) | 30.3303i | 1.18150i | 0.806854 | + | 0.590750i | \(0.201168\pi\) | ||||
−0.806854 | + | 0.590750i | \(0.798832\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.4107i | 0.988361i | 0.869359 | + | 0.494180i | \(0.164532\pi\) | ||||
−0.869359 | + | 0.494180i | \(0.835468\pi\) | |||||||
\(662\) | 14.4174i | 0.560349i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 9.15188i | − | 0.355162i | ||||||
\(665\) | 3.58258 | + | 8.77548i | 0.138926 | + | 0.340299i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.3303i | 1.17439i | ||||||||
\(668\) | −6.19115 | −0.239543 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.02248 | −0.0395017 | ||||||||
\(671\) | 25.9219 | − | 16.6352i | 1.00070 | − | 0.642194i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 18.3303i | − | 0.706581i | −0.935514 | − | 0.353291i | \(-0.885063\pi\) | ||
0.935514 | − | 0.353291i | \(-0.114937\pi\) | |||||||
\(674\) | −29.1652 | −1.12340 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.41742 | 0.131439 | ||||||||
\(677\) | −31.4670 | −1.20937 | −0.604687 | − | 0.796463i | \(-0.706702\pi\) | ||||
−0.604687 | + | 0.796463i | \(0.706702\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.9891 | + | 39.1652i | 0.613606 | + | 1.50302i | ||||
\(680\) | −2.41742 | −0.0927040 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.23042 | + | 2.07310i | −0.123699 | + | 0.0793830i | ||||
\(683\) | −45.4955 | −1.74084 | −0.870418 | − | 0.492314i | \(-0.836151\pi\) | ||||
−0.870418 | + | 0.492314i | \(0.836151\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.79796i | 0.374361i | ||||||||
\(686\) | −17.0000 | − | 7.34847i | −0.649063 | − | 0.280566i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 11.1652i | − | 0.425667i | ||||||
\(689\) | −7.48331 | −0.285092 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.6581i | 1.43258i | 0.697801 | + | 0.716291i | \(0.254162\pi\) | ||||
−0.697801 | + | 0.716291i | \(0.745838\pi\) | |||||||
\(692\) | −22.9612 | −0.872853 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.834849 | −0.0316904 | ||||||||
\(695\) | − | 2.08712i | − | 0.0791690i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.8348 | 0.713421 | ||||||||
\(698\) | 2.07310i | 0.0784679i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.2250 | + | 4.58258i | −0.424264 | + | 0.173205i | ||||
\(701\) | − | 24.3303i | − | 0.918943i | −0.888193 | − | 0.459471i | \(-0.848039\pi\) | ||
0.888193 | − | 0.459471i | \(-0.151961\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.9557 | 1.16752 | ||||||||
\(704\) | 2.79129 | − | 1.79129i | 0.105201 | − | 0.0675117i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.48331 | −0.281638 | ||||||||
\(707\) | 1.25227 | − | 0.511238i | 0.0470966 | − | 0.0192271i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.6697 | 0.588488 | 0.294244 | − | 0.955730i | \(-0.404932\pi\) | ||||
0.294244 | + | 0.955730i | \(0.404932\pi\) | |||||||
\(710\) | 1.29217 | 0.0484942 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.79796 | −0.367194 | ||||||||
\(713\) | − | 4.62929i | − | 0.173368i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.58258 | − | 5.58258i | −0.133981 | − | 0.208776i | ||||
\(716\) | −7.16515 | −0.267774 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.417424 | −0.0155781 | ||||||||
\(719\) | − | 15.8543i | − | 0.591264i | −0.955302 | − | 0.295632i | \(-0.904470\pi\) | ||
0.955302 | − | 0.295632i | \(-0.0955302\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.5396 | − | 33.1652i | −0.504242 | − | 1.23513i | ||||
\(722\) | − | 11.7477i | − | 0.437205i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.6352i | 0.618242i | ||||||||
\(725\) | − | 34.7477i | − | 1.29050i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 52.2484i | 1.93778i | 0.247483 | + | 0.968892i | \(0.420396\pi\) | ||||
−0.247483 | + | 0.968892i | \(0.579604\pi\) | |||||||
\(728\) | −3.09557 | − | 7.58258i | −0.114730 | − | 0.281029i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.08712 | 0.151271 | ||||||||
\(731\) | 41.7762i | 1.54515i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.9612 | −0.848091 | −0.424045 | − | 0.905641i | \(-0.639390\pi\) | ||||
−0.424045 | + | 0.905641i | \(0.639390\pi\) | |||||||
\(734\) | 1.42701 | 0.0526720 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000i | 0.147442i | ||||||||
\(737\) | −4.41742 | + | 2.83485i | −0.162718 | + | 0.104423i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.58258i | 0.278930i | 0.990227 | + | 0.139465i | \(0.0445382\pi\) | ||||
−0.990227 | + | 0.139465i | \(0.955462\pi\) | |||||||
\(740\) | − | 3.60681i | − | 0.132589i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.41742 | − | 5.92146i | −0.0887464 | − | 0.217383i | ||||
\(743\) | − | 43.9129i | − | 1.61101i | −0.592591 | − | 0.805504i | \(-0.701895\pi\) | ||
0.592591 | − | 0.805504i | \(-0.298105\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.04517 | −0.331390 | ||||||||
\(746\) | −0.417424 | −0.0152830 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.4440 | + | 6.70239i | −0.381872 | + | 0.245063i | ||||
\(749\) | 8.41742 | + | 20.6184i | 0.307566 | + | 0.753380i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.4955 | 0.492456 | 0.246228 | − | 0.969212i | \(-0.420809\pi\) | ||||
0.246228 | + | 0.969212i | \(0.420809\pi\) | |||||||
\(752\) | 5.03383i | 0.183565i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 23.4724 | 0.854815 | ||||||||
\(755\) | 2.31464 | 0.0842385 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.1652 | −1.78694 | −0.893469 | − | 0.449125i | \(-0.851736\pi\) | ||||
−0.893469 | + | 0.449125i | \(0.851736\pi\) | |||||||
\(758\) | − | 14.3303i | − | 0.520500i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.58258 | −0.129954 | ||||||||
\(761\) | −20.7532 | −0.752304 | −0.376152 | − | 0.926558i | \(-0.622753\pi\) | ||||
−0.376152 | + | 0.926558i | \(0.622753\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.16515 | + | 2.85403i | 0.0421813 | + | 0.103323i | ||||
\(764\) | −18.0000 | −0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.76413 | 0.172135 | ||||||||
\(767\) | − | 9.58258i | − | 0.346007i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.7984 | 1.07456 | 0.537279 | − | 0.843404i | \(-0.319452\pi\) | ||||
0.537279 | + | 0.843404i | \(0.319452\pi\) | |||||||
\(770\) | 3.26010 | − | 4.63825i | 0.117486 | − | 0.167151i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 20.3303i | − | 0.731704i | ||||||
\(773\) | 51.1977i | 1.84145i | 0.390207 | + | 0.920727i | \(0.372404\pi\) | ||||
−0.390207 | + | 0.920727i | \(0.627596\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.30352i | 0.190508i | ||||||||
\(776\) | −15.9891 | −0.573975 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.0000i | 0.358517i | ||||||||
\(779\) | 27.9129 | 1.00008 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.58258 | − | 3.58258i | 0.199760 | − | 0.128195i | ||||
\(782\) | − | 14.9666i | − | 0.535206i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.00000 | − | 4.89898i | 0.178571 | − | 0.174964i | ||||
\(785\) | −13.2523 | −0.472994 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.3773 | −1.43930 | −0.719648 | − | 0.694339i | \(-0.755697\pi\) | ||||
−0.719648 | + | 0.694339i | \(0.755697\pi\) | |||||||
\(788\) | 18.7477i | 0.667860i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 2.58434i | − | 0.0919465i | ||||||
\(791\) | 41.0234 | − | 16.7477i | 1.45862 | − | 0.595481i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.7477 | 1.02086 | ||||||||
\(794\) | 23.8488 | 0.846363 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 24.6297i | − | 0.872978i | ||||||
\(797\) | 36.2311i | 1.28337i | 0.766968 | + | 0.641686i | \(0.221765\pi\) | ||||
−0.766968 | + | 0.641686i | \(0.778235\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 18.8348i | − | 0.666329i | ||||||
\(800\) | − | 4.58258i | − | 0.162019i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 1.58258i | − | 0.0558827i | ||||||
\(803\) | 17.6577 | − | 11.3317i | 0.623126 | − | 0.399886i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.58434 | + | 6.33030i | 0.0910859 | + | 0.223114i | ||||
\(806\) | −3.58258 | −0.126191 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.511238i | 0.0179853i | ||||||||
\(809\) | 33.1652i | 1.16602i | 0.812463 | + | 0.583012i | \(0.198126\pi\) | ||||
−0.812463 | + | 0.583012i | \(0.801874\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.3097 | −1.06432 | −0.532158 | − | 0.846645i | \(-0.678619\pi\) | ||||
−0.532158 | + | 0.846645i | \(0.678619\pi\) | |||||||
\(812\) | 7.58258 | + | 18.5734i | 0.266096 | + | 0.651800i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.0000 | − | 15.5826i | −0.350500 | − | 0.546169i | ||||
\(815\) | − | 2.58434i | − | 0.0905253i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 61.9115i | 2.16601i | ||||||||
\(818\) | − | 9.93280i | − | 0.347292i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 3.25227i | − | 0.113574i | ||||||
\(821\) | 11.4955i | 0.401194i | 0.979674 | + | 0.200597i | \(0.0642882\pi\) | ||||
−0.979674 | + | 0.200597i | \(0.935712\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.3303 | −1.40583 | −0.702913 | − | 0.711276i | \(-0.748118\pi\) | ||||
−0.702913 | + | 0.711276i | \(0.748118\pi\) | |||||||
\(824\) | 13.5396 | 0.471675 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.58258 | − | 3.09557i | 0.263832 | − | 0.107709i | ||||
\(827\) | − | 15.1652i | − | 0.527344i | −0.964612 | − | 0.263672i | \(-0.915066\pi\) | ||
0.964612 | − | 0.263672i | \(-0.0849337\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 4.25290i | − | 0.147709i | −0.997269 | − | 0.0738546i | \(-0.976470\pi\) | ||
0.997269 | − | 0.0738546i | \(-0.0235301\pi\) | |||||||
\(830\) | 5.91288 | 0.205239 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.09557 | 0.107320 | ||||||||
\(833\) | −18.7083 | + | 18.3303i | −0.648204 | + | 0.635107i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 4.00000i | − | 0.138426i | ||||||
\(836\) | −15.4779 | + | 9.93280i | −0.535313 | + | 0.343533i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.67991 | −0.196209 | ||||||||
\(839\) | − | 24.6297i | − | 0.850313i | −0.905120 | − | 0.425157i | \(-0.860219\pi\) | ||
0.905120 | − | 0.425157i | \(-0.139781\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4955 | −0.982602 | ||||||||
\(842\) | 1.58258i | 0.0545392i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 10.7477i | − | 0.369952i | ||||||
\(845\) | 2.20794i | 0.0759555i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.22497 | − | 29.0775i | 0.0420905 | − | 0.999114i | ||||
\(848\) | 2.41742 | 0.0830147 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17.1464i | 0.588118i | ||||||||
\(851\) | 22.3303 | 0.765473 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.1748 | 1.03317 | 0.516583 | − | 0.856237i | \(-0.327204\pi\) | ||||
0.516583 | + | 0.856237i | \(0.327204\pi\) | |||||||
\(854\) | 9.28672 | + | 22.7477i | 0.317785 | + | 0.778411i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.41742 | −0.287702 | ||||||||
\(857\) | −21.2926 | −0.727342 | −0.363671 | − | 0.931527i | \(-0.618477\pi\) | ||||
−0.363671 | + | 0.931527i | \(0.618477\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 31.7367i | − | 1.08284i | −0.840752 | − | 0.541421i | \(-0.817887\pi\) | ||
0.840752 | − | 0.541421i | \(-0.182113\pi\) | |||||||
\(860\) | 7.21362 | 0.245983 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.9129 | 0.610115 | ||||||||
\(863\) | 33.1652 | 1.12895 | 0.564477 | − | 0.825448i | \(-0.309078\pi\) | ||||
0.564477 | + | 0.825448i | \(0.309078\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 14.8348i | − | 0.504400i | ||||||
\(866\) | −28.1017 | −0.954935 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.15732 | − | 2.83485i | −0.0392821 | − | 0.0962210i | ||||
\(869\) | −7.16515 | − | 11.1652i | −0.243061 | − | 0.378752i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.89898 | −0.165996 | ||||||||
\(872\) | −1.16515 | −0.0394570 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 22.1803i | − | 0.750258i | ||||||
\(875\) | −6.19115 | − | 15.1652i | −0.209299 | − | 0.512676i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.1652i | 0.849767i | 0.905248 | + | 0.424883i | \(0.139685\pi\) | ||||
−0.905248 | + | 0.424883i | \(0.860315\pi\) | |||||||
\(878\) | − | 2.31464i | − | 0.0781155i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.15732 | + | 1.80341i | 0.0390133 | + | 0.0607928i | ||||
\(881\) | 22.1803i | 0.747272i | 0.927575 | + | 0.373636i | \(0.121889\pi\) | ||||
−0.927575 | + | 0.373636i | \(0.878111\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.1652 | 1.04879 | 0.524395 | − | 0.851475i | \(-0.324291\pi\) | ||||
0.524395 | + | 0.851475i | \(0.324291\pi\) | |||||||
\(884\) | −11.5826 | −0.389564 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 3.16515i | − | 0.106335i | ||||||
\(887\) | −28.9108 | −0.970729 | −0.485365 | − | 0.874312i | \(-0.661313\pi\) | ||||
−0.485365 | + | 0.874312i | \(0.661313\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.58258 | − | 13.6745i | −0.187234 | − | 0.458627i | ||||
\(890\) | − | 6.33030i | − | 0.212192i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 6.32599i | − | 0.211810i | ||||||
\(893\) | − | 27.9129i | − | 0.934069i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 4.62929i | − | 0.154740i | ||||||
\(896\) | 1.00000 | + | 2.44949i | 0.0334077 | + | 0.0818317i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.8348i | 0.428304i | ||||||||
\(899\) | 8.77548 | 0.292679 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.04517 | −0.301338 | ||||||||
\(902\) | −9.01703 | − | 14.0509i | −0.300234 | − | 0.467842i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.7477i | 0.557021i | ||||||||
\(905\) | −10.7477 | −0.357267 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.9129 | −1.32529 | −0.662643 | − | 0.748936i | \(-0.730565\pi\) | ||||
−0.662643 | + | 0.748936i | \(0.730565\pi\) | |||||||
\(908\) | −11.7362 | −0.389480 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.89898 | − | 2.00000i | 0.162400 | − | 0.0662994i | ||||
\(911\) | 15.1652 | 0.502444 | 0.251222 | − | 0.967930i | \(-0.419168\pi\) | ||||
0.251222 | + | 0.967930i | \(0.419168\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.5455 | − | 16.3936i | 0.845433 | − | 0.542550i | ||||
\(914\) | −14.8348 | −0.490693 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.0284i | 0.430470i | ||||||||
\(917\) | −23.0780 | + | 9.42157i | −0.762104 | + | 0.311128i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.4955i | 1.17089i | 0.810713 | + | 0.585443i | \(0.199080\pi\) | ||||
−0.810713 | + | 0.585443i | \(0.800920\pi\) | |||||||
\(920\) | −2.58434 | −0.0852030 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 26.2983i | 0.866088i | ||||||||
\(923\) | 6.19115 | 0.203784 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.5826 | −0.841150 | ||||||||
\(926\) | 13.1652i | 0.432634i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.58258 | −0.248910 | ||||||||
\(929\) | − | 38.7087i | − | 1.26999i | −0.772515 | − | 0.634996i | \(-0.781002\pi\) | ||
0.772515 | − | 0.634996i | \(-0.218998\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.7253 | + | 27.1652i | −0.908661 | + | 0.890302i | ||||
\(932\) | 8.83485i | 0.289395i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.511238 | −0.0167282 | ||||||||
\(935\) | −4.33030 | − | 6.74773i | −0.141616 | − | 0.220674i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.7650 | −1.46241 | −0.731205 | − | 0.682158i | \(-0.761042\pi\) | ||||
−0.731205 | + | 0.682158i | \(0.761042\pi\) | |||||||
\(938\) | −1.58258 | − | 3.87650i | −0.0516729 | − | 0.126572i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.25227 | −0.106077 | ||||||||
\(941\) | 31.4670 | 1.02579 | 0.512897 | − | 0.858450i | \(-0.328572\pi\) | ||||
0.512897 | + | 0.858450i | \(0.328572\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.1353 | 0.655696 | ||||||||
\(944\) | 3.09557i | 0.100752i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31.1652 | − | 20.0000i | 1.01327 | − | 0.650256i | ||||
\(947\) | 5.58258 | 0.181409 | 0.0907047 | − | 0.995878i | \(-0.471088\pi\) | ||||
0.0907047 | + | 0.995878i | \(0.471088\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.5826 | 0.635677 | ||||||||
\(950\) | 25.4107i | 0.824431i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.74166 | − | 9.16515i | −0.121268 | − | 0.297044i | ||||
\(953\) | 18.3303i | 0.593777i | 0.954912 | + | 0.296888i | \(0.0959489\pi\) | ||||
−0.954912 | + | 0.296888i | \(0.904051\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 11.6295i | − | 0.376322i | ||||||
\(956\) | 17.5826i | 0.568661i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 6.46084i | − | 0.208740i | ||||||
\(959\) | −37.1469 | + | 15.1652i | −1.19954 | + | 0.489708i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.6606 | 0.956794 | ||||||||
\(962\) | − | 17.2813i | − | 0.557171i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25.9219 | 0.834889 | ||||||||
\(965\) | 13.1351 | 0.422833 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.5826i | 1.01563i | 0.861467 | + | 0.507814i | \(0.169546\pi\) | ||||
−0.861467 | + | 0.507814i | \(0.830454\pi\) | |||||||
\(968\) | 10.0000 | + | 4.58258i | 0.321412 | + | 0.147290i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 10.3303i | − | 0.331686i | ||||||
\(971\) | 17.7925i | 0.570989i | 0.958380 | + | 0.285494i | \(0.0921578\pi\) | ||||
−0.958380 | + | 0.285494i | \(0.907842\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.91288 | − | 3.23042i | 0.253675 | − | 0.103562i | ||||
\(974\) | 33.4955i | 1.07326i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.28672 | −0.297261 | ||||||||
\(977\) | 9.16515 | 0.293219 | 0.146610 | − | 0.989194i | \(-0.453164\pi\) | ||||
0.146610 | + | 0.989194i | \(0.453164\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.5510 | − | 27.3489i | −0.560931 | − | 0.874075i | ||||
\(980\) | 3.16515 | + | 3.23042i | 0.101107 | + | 0.103192i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.4955 | −0.685948 | ||||||||
\(983\) | − | 1.69670i | − | 0.0541165i | −0.999634 | − | 0.0270582i | \(-0.991386\pi\) | ||
0.999634 | − | 0.0270582i | \(-0.00861395\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.1126 | −0.385940 | ||||||||
\(986\) | 28.3714 | 0.903529 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.1652 | −0.546096 | ||||||||
\(989\) | 44.6606i | 1.42012i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.6606 | −0.846902 | −0.423451 | − | 0.905919i | \(-0.639181\pi\) | ||||
−0.423451 | + | 0.905919i | \(0.639181\pi\) | |||||||
\(992\) | 1.15732 | 0.0367450 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.00000 | + | 4.89898i | 0.0634361 | + | 0.155386i | ||||
\(995\) | 15.9129 | 0.504472 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.7816 | 1.06987 | 0.534937 | − | 0.844892i | \(-0.320335\pi\) | ||||
0.534937 | + | 0.844892i | \(0.320335\pi\) | |||||||
\(998\) | − | 27.9129i | − | 0.883567i | ||||||
\(999\) | 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 | 1386.2.e.b.307.2 | 8 | ||
3.2 | odd | 2 | 154.2.c.a.153.8 | yes | 8 | ||
7.6 | odd | 2 | inner | 1386.2.e.b.307.3 | 8 | ||
11.10 | odd | 2 | inner | 1386.2.e.b.307.6 | 8 | ||
12.11 | even | 2 | 1232.2.e.e.769.1 | 8 | |||
21.2 | odd | 6 | 1078.2.i.b.1011.5 | 16 | |||
21.5 | even | 6 | 1078.2.i.b.1011.8 | 16 | |||
21.11 | odd | 6 | 1078.2.i.b.901.4 | 16 | |||
21.17 | even | 6 | 1078.2.i.b.901.1 | 16 | |||
21.20 | even | 2 | 154.2.c.a.153.5 | yes | 8 | ||
33.32 | even | 2 | 154.2.c.a.153.4 | yes | 8 | ||
77.76 | even | 2 | inner | 1386.2.e.b.307.7 | 8 | ||
84.83 | odd | 2 | 1232.2.e.e.769.8 | 8 | |||
132.131 | odd | 2 | 1232.2.e.e.769.2 | 8 | |||
231.32 | even | 6 | 1078.2.i.b.901.8 | 16 | |||
231.65 | even | 6 | 1078.2.i.b.1011.1 | 16 | |||
231.131 | odd | 6 | 1078.2.i.b.1011.4 | 16 | |||
231.164 | odd | 6 | 1078.2.i.b.901.5 | 16 | |||
231.230 | odd | 2 | 154.2.c.a.153.1 | ✓ | 8 | ||
924.923 | even | 2 | 1232.2.e.e.769.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.c.a.153.1 | ✓ | 8 | 231.230 | odd | 2 | ||
154.2.c.a.153.4 | yes | 8 | 33.32 | even | 2 | ||
154.2.c.a.153.5 | yes | 8 | 21.20 | even | 2 | ||
154.2.c.a.153.8 | yes | 8 | 3.2 | odd | 2 | ||
1078.2.i.b.901.1 | 16 | 21.17 | even | 6 | |||
1078.2.i.b.901.4 | 16 | 21.11 | odd | 6 | |||
1078.2.i.b.901.5 | 16 | 231.164 | odd | 6 | |||
1078.2.i.b.901.8 | 16 | 231.32 | even | 6 | |||
1078.2.i.b.1011.1 | 16 | 231.65 | even | 6 | |||
1078.2.i.b.1011.4 | 16 | 231.131 | odd | 6 | |||
1078.2.i.b.1011.5 | 16 | 21.2 | odd | 6 | |||
1078.2.i.b.1011.8 | 16 | 21.5 | even | 6 | |||
1232.2.e.e.769.1 | 8 | 12.11 | even | 2 | |||
1232.2.e.e.769.2 | 8 | 132.131 | odd | 2 | |||
1232.2.e.e.769.7 | 8 | 924.923 | even | 2 | |||
1232.2.e.e.769.8 | 8 | 84.83 | odd | 2 | |||
1386.2.e.b.307.2 | 8 | 1.1 | even | 1 | trivial | ||
1386.2.e.b.307.3 | 8 | 7.6 | odd | 2 | inner | ||
1386.2.e.b.307.6 | 8 | 11.10 | odd | 2 | inner | ||
1386.2.e.b.307.7 | 8 | 77.76 | even | 2 | inner |