Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,2,Mod(575,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.3975326257\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 575.2 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.575 |
Dual form | 2304.2.l.g.1727.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.517638 | + | 0.517638i | −0.231495 | + | 0.231495i | −0.813316 | − | 0.581822i | \(-0.802340\pi\) |
0.581822 | + | 0.813316i | \(0.302340\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41421 | −0.534522 | −0.267261 | − | 0.963624i | \(-0.586119\pi\) | ||||
−0.267261 | + | 0.963624i | \(0.586119\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.73205 | + | 2.73205i | 0.823744 | + | 0.823744i | 0.986643 | − | 0.162899i | \(-0.0520843\pi\) |
−0.162899 | + | 0.986643i | \(0.552084\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.73205 | + | 1.73205i | −0.480384 | + | 0.480384i | −0.905254 | − | 0.424870i | \(-0.860320\pi\) |
0.424870 | + | 0.905254i | \(0.360320\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.378937i | − | 0.0919058i | −0.998944 | − | 0.0459529i | \(-0.985368\pi\) | ||
0.998944 | − | 0.0459529i | \(-0.0146324\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.378937 | + | 0.378937i | 0.0869342 | + | 0.0869342i | 0.749237 | − | 0.662302i | \(-0.230421\pi\) |
−0.662302 | + | 0.749237i | \(0.730421\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.46410i | − | 0.722315i | −0.932505 | − | 0.361158i | \(-0.882382\pi\) | ||
0.932505 | − | 0.361158i | \(-0.117618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.46410i | 0.892820i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.76028 | − | 4.76028i | −0.883962 | − | 0.883962i | 0.109973 | − | 0.993935i | \(-0.464924\pi\) |
−0.993935 | + | 0.109973i | \(0.964924\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.656339i | 0.117882i | 0.998261 | + | 0.0589410i | \(0.0187724\pi\) | ||||
−0.998261 | + | 0.0589410i | \(0.981228\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.732051 | − | 0.732051i | 0.123739 | − | 0.123739i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.46410 | + | 4.46410i | 0.733894 | + | 0.733894i | 0.971389 | − | 0.237495i | \(-0.0763263\pi\) |
−0.237495 | + | 0.971389i | \(0.576326\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.1769 | −1.58936 | −0.794682 | − | 0.607026i | \(-0.792362\pi\) | ||||
−0.794682 | + | 0.607026i | \(0.792362\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.31319 | − | 6.31319i | 0.962753 | − | 0.962753i | −0.0365779 | − | 0.999331i | \(-0.511646\pi\) |
0.999331 | + | 0.0365779i | \(0.0116457\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.3923 | −1.51587 | −0.757937 | − | 0.652328i | \(-0.773792\pi\) | ||||
−0.757937 | + | 0.652328i | \(0.773792\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.00240 | + | 4.00240i | −0.549772 | + | 0.549772i | −0.926375 | − | 0.376602i | \(-0.877092\pi\) |
0.376602 | + | 0.926375i | \(0.377092\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.82843 | −0.381385 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.92820 | + | 4.92820i | 0.641597 | + | 0.641597i | 0.950948 | − | 0.309351i | \(-0.100112\pi\) |
−0.309351 | + | 0.950948i | \(0.600112\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | + | 3.00000i | −0.384111 | + | 0.384111i | −0.872581 | − | 0.488470i | \(-0.837555\pi\) |
0.488470 | + | 0.872581i | \(0.337555\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1.79315i | − | 0.222413i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.03528 | + | 1.03528i | 0.126479 | + | 0.126479i | 0.767513 | − | 0.641034i | \(-0.221494\pi\) |
−0.641034 | + | 0.767513i | \(0.721494\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.0000i | − | 1.66149i | −0.556650 | − | 0.830747i | \(-0.687914\pi\) | ||
0.556650 | − | 0.830747i | \(-0.312086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.92820i | 1.04497i | 0.852649 | + | 0.522484i | \(0.174994\pi\) | ||||
−0.852649 | + | 0.522484i | \(0.825006\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.86370 | − | 3.86370i | −0.440310 | − | 0.440310i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.9700i | 1.34674i | 0.739308 | + | 0.673368i | \(0.235153\pi\) | ||||
−0.739308 | + | 0.673368i | \(0.764847\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.26795 | + | 7.26795i | −0.797761 | + | 0.797761i | −0.982742 | − | 0.184981i | \(-0.940778\pi\) |
0.184981 | + | 0.982742i | \(0.440778\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.196152 | + | 0.196152i | 0.0212757 | + | 0.0212757i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.2827 | −1.40797 | −0.703983 | − | 0.710217i | \(-0.748597\pi\) | ||||
−0.703983 | + | 0.710217i | \(0.748597\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.44949 | − | 2.44949i | 0.256776 | − | 0.256776i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.392305 | −0.0402496 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.39230 | 0.242902 | 0.121451 | − | 0.992597i | \(-0.461245\pi\) | ||||
0.121451 | + | 0.992597i | \(0.461245\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.65926 | + | 9.65926i | −0.961132 | + | 0.961132i | −0.999272 | − | 0.0381403i | \(-0.987857\pi\) |
0.0381403 | + | 0.999272i | \(0.487857\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.9396 | −1.86617 | −0.933086 | − | 0.359653i | \(-0.882895\pi\) | ||||
−0.933086 | + | 0.359653i | \(0.882895\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.4641 | + | 13.4641i | 1.30162 | + | 1.30162i | 0.927297 | + | 0.374327i | \(0.122126\pi\) |
0.374327 | + | 0.927297i | \(0.377874\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.26795 | + | 4.26795i | −0.408795 | + | 0.408795i | −0.881318 | − | 0.472523i | \(-0.843343\pi\) |
0.472523 | + | 0.881318i | \(0.343343\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.24264i | − | 0.399114i | −0.979886 | − | 0.199557i | \(-0.936050\pi\) | ||
0.979886 | − | 0.199557i | \(-0.0639503\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.79315 | + | 1.79315i | 0.167212 | + | 0.167212i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.535898i | 0.0491257i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.92820i | 0.357109i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.89898 | − | 4.89898i | −0.438178 | − | 0.438178i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.55532i | 0.492955i | 0.969149 | + | 0.246477i | \(0.0792731\pi\) | ||||
−0.969149 | + | 0.246477i | \(0.920727\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.92820 | − | 6.92820i | 0.605320 | − | 0.605320i | −0.336399 | − | 0.941719i | \(-0.609209\pi\) |
0.941719 | + | 0.336399i | \(0.109209\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.535898 | − | 0.535898i | −0.0464683 | − | 0.0464683i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.10634 | −0.692572 | −0.346286 | − | 0.938129i | \(-0.612557\pi\) | ||||
−0.346286 | + | 0.938129i | \(0.612557\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.76268 | − | 8.76268i | 0.743241 | − | 0.743241i | −0.229959 | − | 0.973200i | \(-0.573859\pi\) |
0.973200 | + | 0.229959i | \(0.0738593\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.46410 | −0.791428 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.92820 | 0.409265 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.55291 | + | 1.55291i | −0.127220 | + | 0.127220i | −0.767850 | − | 0.640630i | \(-0.778673\pi\) |
0.640630 | + | 0.767850i | \(0.278673\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.14162 | 0.743934 | 0.371967 | − | 0.928246i | \(-0.378683\pi\) | ||||
0.371967 | + | 0.928246i | \(0.378683\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.339746 | − | 0.339746i | −0.0272891 | − | 0.0272891i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.92820 | + | 9.92820i | −0.792357 | + | 0.792357i | −0.981877 | − | 0.189520i | \(-0.939307\pi\) |
0.189520 | + | 0.981877i | \(0.439307\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.89898i | 0.386094i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.14162 | − | 9.14162i | −0.716027 | − | 0.716027i | 0.251762 | − | 0.967789i | \(-0.418990\pi\) |
−0.967789 | + | 0.251762i | \(0.918990\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 13.4641i | − | 1.04188i | −0.853592 | − | 0.520942i | \(-0.825581\pi\) | ||
0.853592 | − | 0.520942i | \(-0.174419\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000i | 0.538462i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.8666 | − | 12.8666i | −0.978231 | − | 0.978231i | 0.0215368 | − | 0.999768i | \(-0.493144\pi\) |
−0.999768 | + | 0.0215368i | \(0.993144\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 6.31319i | − | 0.477233i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.00000 | + | 6.00000i | −0.448461 | + | 0.448461i | −0.894843 | − | 0.446382i | \(-0.852712\pi\) |
0.446382 | + | 0.894843i | \(0.352712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.1962 | + | 11.1962i | 0.832203 | + | 0.832203i | 0.987818 | − | 0.155614i | \(-0.0497357\pi\) |
−0.155614 | + | 0.987818i | \(0.549736\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.62158 | −0.339785 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.03528 | − | 1.03528i | 0.0757069 | − | 0.0757069i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.53590 | 0.472921 | 0.236461 | − | 0.971641i | \(-0.424013\pi\) | ||||
0.236461 | + | 0.971641i | \(0.424013\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.7846 | −1.35215 | −0.676073 | − | 0.736835i | \(-0.736320\pi\) | ||||
−0.676073 | + | 0.736835i | \(0.736320\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.48288 | − | 4.48288i | 0.319392 | − | 0.319392i | −0.529142 | − | 0.848533i | \(-0.677486\pi\) |
0.848533 | + | 0.529142i | \(0.177486\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.101536 | −0.00719769 | −0.00359885 | − | 0.999994i | \(-0.501146\pi\) | ||||
−0.00359885 | + | 0.999994i | \(0.501146\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.73205 | + | 6.73205i | 0.472497 | + | 0.472497i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.26795 | − | 5.26795i | 0.367930 | − | 0.367930i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.07055i | 0.143223i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.1774 | + | 15.1774i | 1.04486 | + | 1.04486i | 0.998946 | + | 0.0459106i | \(0.0146189\pi\) |
0.0459106 | + | 0.998946i | \(0.485381\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.53590i | 0.445745i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.928203i | − | 0.0630105i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.656339 | + | 0.656339i | 0.0441501 | + | 0.0441501i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 12.7279i | − | 0.852325i | −0.904647 | − | 0.426162i | \(-0.859865\pi\) | ||
0.904647 | − | 0.426162i | \(-0.140135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.2679 | − | 11.2679i | 0.747880 | − | 0.747880i | −0.226201 | − | 0.974081i | \(-0.572631\pi\) |
0.974081 | + | 0.226201i | \(0.0726305\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.19615 | − | 3.19615i | −0.211208 | − | 0.211208i | 0.593573 | − | 0.804780i | \(-0.297717\pi\) |
−0.804780 | + | 0.593573i | \(0.797717\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.6574 | 0.698188 | 0.349094 | − | 0.937088i | \(-0.386489\pi\) | ||||
0.349094 | + | 0.937088i | \(0.386489\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.37945 | − | 5.37945i | 0.350917 | − | 0.350917i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.5359 | −0.940249 | −0.470125 | − | 0.882600i | \(-0.655791\pi\) | ||||
−0.470125 | + | 0.882600i | \(0.655791\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.4641 | 0.867299 | 0.433650 | − | 0.901082i | \(-0.357226\pi\) | ||||
0.433650 | + | 0.901082i | \(0.357226\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.58819 | − | 2.58819i | 0.165353 | − | 0.165353i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.31268 | −0.0835237 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.66025 | − | 9.66025i | −0.609750 | − | 0.609750i | 0.333131 | − | 0.942881i | \(-0.391895\pi\) |
−0.942881 | + | 0.333131i | \(0.891895\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.46410 | − | 9.46410i | 0.595003 | − | 0.595003i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2.17209i | − | 0.135491i | −0.997703 | − | 0.0677456i | \(-0.978419\pi\) | ||
0.997703 | − | 0.0677456i | \(-0.0215806\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.31319 | − | 6.31319i | −0.392283 | − | 0.392283i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 10.9282i | − | 0.673862i | −0.941529 | − | 0.336931i | \(-0.890611\pi\) | ||
0.941529 | − | 0.336931i | \(-0.109389\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.14359i | − | 0.254539i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.2808 | + | 14.2808i | 0.870718 | + | 0.870718i | 0.992551 | − | 0.121833i | \(-0.0388771\pi\) |
−0.121833 | + | 0.992551i | \(0.538877\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.5259i | 1.36835i | 0.729318 | + | 0.684175i | \(0.239838\pi\) | ||||
−0.729318 | + | 0.684175i | \(0.760162\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.1962 | + | 12.1962i | −0.735456 | + | 0.735456i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.803848 | + | 0.803848i | 0.0482985 | + | 0.0482985i | 0.730844 | − | 0.682545i | \(-0.239127\pi\) |
−0.682545 | + | 0.730844i | \(0.739127\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.656339 | 0.0391539 | 0.0195769 | − | 0.999808i | \(-0.493768\pi\) | ||||
0.0195769 | + | 0.999808i | \(0.493768\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.7990 | + | 19.7990i | −1.17693 | + | 1.17693i | −0.196405 | + | 0.980523i | \(0.562927\pi\) |
−0.980523 | + | 0.196405i | \(0.937073\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.3923 | 0.849551 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8564 | 0.991553 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.65445 | + | 1.65445i | −0.0966540 | + | 0.0966540i | −0.753780 | − | 0.657126i | \(-0.771772\pi\) |
0.657126 | + | 0.753780i | \(0.271772\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.10205 | −0.297053 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.00000 | + | 6.00000i | 0.346989 | + | 0.346989i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.92820 | + | 8.92820i | −0.514613 | + | 0.514613i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3.10583i | − | 0.177839i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.86370 | − | 3.86370i | −0.220513 | − | 0.220513i | 0.588201 | − | 0.808715i | \(-0.299836\pi\) |
−0.808715 | + | 0.588201i | \(0.799836\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.8564i | 1.69300i | 0.532388 | + | 0.846501i | \(0.321295\pi\) | ||||
−0.532388 | + | 0.846501i | \(0.678705\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.00000i | 0.113047i | 0.998401 | + | 0.0565233i | \(0.0180015\pi\) | ||||
−0.998401 | + | 0.0565233i | \(0.981998\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.1798 | + | 19.1798i | 1.07725 | + | 1.07725i | 0.996755 | + | 0.0804904i | \(0.0256486\pi\) |
0.0804904 | + | 0.996755i | \(0.474351\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 26.0106i | − | 1.45632i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.143594 | − | 0.143594i | 0.00798976 | − | 0.00798976i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.73205 | − | 7.73205i | −0.428897 | − | 0.428897i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.6969 | 0.810268 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00481 | + | 8.00481i | −0.439984 | + | 0.439984i | −0.892007 | − | 0.452022i | \(-0.850703\pi\) |
0.452022 | + | 0.892007i | \(0.350703\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.07180 | −0.0585585 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.7846 | −1.02326 | −0.511631 | − | 0.859205i | \(-0.670959\pi\) | ||||
−0.511631 | + | 0.859205i | \(0.670959\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.79315 | + | 1.79315i | −0.0971046 | + | 0.0971046i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.1244 | − | 25.1244i | −1.34875 | − | 1.34875i | −0.887025 | − | 0.461721i | \(-0.847232\pi\) |
−0.461721 | − | 0.887025i | \(-0.652768\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.39230 | − | 7.39230i | 0.395701 | − | 0.395701i | −0.481013 | − | 0.876714i | \(-0.659731\pi\) |
0.876714 | + | 0.481013i | \(0.159731\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 17.4238i | − | 0.927377i | −0.885998 | − | 0.463688i | \(-0.846526\pi\) | ||
0.885998 | − | 0.463688i | \(-0.153474\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.24693 | + | 7.24693i | 0.384627 | + | 0.384627i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.85641i | 0.203533i | 0.994808 | + | 0.101767i | \(0.0324495\pi\) | ||||
−0.994808 | + | 0.101767i | \(0.967550\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.7128i | − | 0.984885i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.62158 | − | 4.62158i | −0.241904 | − | 0.241904i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.3848i | 0.959678i | 0.877357 | + | 0.479839i | \(0.159305\pi\) | ||||
−0.877357 | + | 0.479839i | \(0.840695\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.66025 | − | 5.66025i | 0.293866 | − | 0.293866i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.8564 | − | 22.8564i | −1.18346 | − | 1.18346i | −0.978842 | − | 0.204618i | \(-0.934405\pi\) |
−0.204618 | − | 0.978842i | \(-0.565595\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.4901 | 0.849283 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.10634 | + | 8.10634i | −0.416395 | + | 0.416395i | −0.883959 | − | 0.467564i | \(-0.845132\pi\) |
0.467564 | + | 0.883959i | \(0.345132\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.4641 | 1.30115 | 0.650577 | − | 0.759440i | \(-0.274527\pi\) | ||||
0.650577 | + | 0.759440i | \(0.274527\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.6999 | − | 23.6999i | 1.20163 | − | 1.20163i | 0.227960 | − | 0.973670i | \(-0.426794\pi\) |
0.973670 | − | 0.227960i | \(-0.0732055\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.31268 | −0.0663850 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.19615 | − | 6.19615i | −0.311762 | − | 0.311762i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.3205 | − | 16.3205i | 0.819103 | − | 0.819103i | −0.166875 | − | 0.985978i | \(-0.553368\pi\) |
0.985978 | + | 0.166875i | \(0.0533677\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.3495i | 0.866393i | 0.901300 | + | 0.433196i | \(0.142614\pi\) | ||||
−0.901300 | + | 0.433196i | \(0.857386\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.13681 | − | 1.13681i | −0.0566286 | − | 0.0566286i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.3923i | 1.20908i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 14.3923i | − | 0.711654i | −0.934552 | − | 0.355827i | \(-0.884199\pi\) | ||
0.934552 | − | 0.355827i | \(-0.115801\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.96953 | − | 6.96953i | −0.342948 | − | 0.342948i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 7.52433i | − | 0.369355i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.26795 | − | 7.26795i | 0.355063 | − | 0.355063i | −0.506927 | − | 0.861989i | \(-0.669219\pi\) |
0.861989 | + | 0.506927i | \(0.169219\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.7321 | + | 17.7321i | 0.864207 | + | 0.864207i | 0.991824 | − | 0.127616i | \(-0.0407326\pi\) |
−0.127616 | + | 0.991824i | \(0.540733\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.69161 | 0.0820554 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.24264 | − | 4.24264i | 0.205316 | − | 0.205316i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.67949 | −0.129067 | −0.0645333 | − | 0.997916i | \(-0.520556\pi\) | ||||
−0.0645333 | + | 0.997916i | \(0.520556\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.07180 | −0.0515073 | −0.0257536 | − | 0.999668i | \(-0.508199\pi\) | ||||
−0.0257536 | + | 0.999668i | \(0.508199\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.31268 | − | 1.31268i | 0.0627939 | − | 0.0627939i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.6985 | 1.41743 | 0.708716 | − | 0.705494i | \(-0.249275\pi\) | ||||
0.708716 | + | 0.705494i | \(0.249275\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.5885 | − | 26.5885i | −1.26326 | − | 1.26326i | −0.949506 | − | 0.313750i | \(-0.898415\pi\) |
−0.313750 | − | 0.949506i | \(-0.601585\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.87564 | − | 6.87564i | 0.325937 | − | 0.325937i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.6622i | 0.880723i | 0.897821 | + | 0.440361i | \(0.145150\pi\) | ||||
−0.897821 | + | 0.440361i | \(0.854850\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.8038 | − | 27.8038i | −1.30923 | − | 1.30923i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.53590i | 0.118885i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 21.3205i | − | 0.997331i | −0.866794 | − | 0.498666i | \(-0.833824\pi\) | ||
0.866794 | − | 0.498666i | \(-0.166176\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.2156 | + | 25.2156i | 1.17441 | + | 1.17441i | 0.981147 | + | 0.193260i | \(0.0619062\pi\) |
0.193260 | + | 0.981147i | \(0.438094\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 35.1523i | − | 1.63366i | −0.576875 | − | 0.816832i | \(-0.695728\pi\) | ||
0.576875 | − | 0.816832i | \(-0.304272\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.33975 | + | 4.33975i | −0.200819 | + | 0.200819i | −0.800351 | − | 0.599532i | \(-0.795354\pi\) |
0.599532 | + | 0.800351i | \(0.295354\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.46410 | − | 1.46410i | −0.0676059 | − | 0.0676059i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 34.4959 | 1.58612 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.69161 | + | 1.69161i | −0.0776166 | + | 0.0776166i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.7846 | 1.40658 | 0.703292 | − | 0.710901i | \(-0.251712\pi\) | ||||
0.703292 | + | 0.710901i | \(0.251712\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.4641 | −0.705102 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.23835 | + | 1.23835i | −0.0562305 | + | 0.0562305i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.9091 | 1.17405 | 0.587027 | − | 0.809567i | \(-0.300298\pi\) | ||||
0.587027 | + | 0.809567i | \(0.300298\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.143594 | + | 0.143594i | 0.00648029 | + | 0.00648029i | 0.710340 | − | 0.703859i | \(-0.248541\pi\) |
−0.703859 | + | 0.710340i | \(0.748541\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.80385 | + | 1.80385i | −0.0812412 | + | 0.0812412i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.7990i | 0.888106i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.3233 | + | 27.3233i | 1.22316 | + | 1.22316i | 0.966502 | + | 0.256658i | \(0.0826213\pi\) |
0.256658 | + | 0.966502i | \(0.417379\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.0718i | 0.493667i | 0.969058 | + | 0.246834i | \(0.0793901\pi\) | ||||
−0.969058 | + | 0.246834i | \(0.920610\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 10.0000i | − | 0.444994i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.1750 | + | 11.1750i | 0.495324 | + | 0.495324i | 0.909979 | − | 0.414655i | \(-0.136098\pi\) |
−0.414655 | + | 0.909979i | \(0.636098\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 12.6264i | − | 0.558558i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.80385 | − | 9.80385i | 0.432009 | − | 0.432009i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.3923 | − | 28.3923i | −1.24869 | − | 1.24869i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.2875 | 0.932624 | 0.466312 | − | 0.884620i | \(-0.345582\pi\) | ||||
0.466312 | + | 0.884620i | \(0.345582\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.13681 | − | 1.13681i | 0.0497093 | − | 0.0497093i | −0.681815 | − | 0.731524i | \(-0.738809\pi\) |
0.731524 | + | 0.681815i | \(0.238809\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.248711 | 0.0108340 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | 0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.6269 | − | 17.6269i | 0.763506 | − | 0.763506i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.9391 | −0.602638 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.6603 | − | 13.6603i | −0.588389 | − | 0.588389i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0526 | − | 11.0526i | 0.475187 | − | 0.475187i | −0.428402 | − | 0.903588i | \(-0.640923\pi\) |
0.903588 | + | 0.428402i | \(0.140923\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 4.41851i | − | 0.189268i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.1112 | − | 16.1112i | −0.688863 | − | 0.688863i | 0.273118 | − | 0.961981i | \(-0.411945\pi\) |
−0.961981 | + | 0.273118i | \(0.911945\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 3.60770i | − | 0.153693i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 16.9282i | − | 0.719860i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.83032 | + | 1.83032i | 0.0775530 | + | 0.0775530i | 0.744819 | − | 0.667266i | \(-0.232536\pi\) |
−0.667266 | + | 0.744819i | \(0.732536\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.8695i | 0.924983i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.0526 | + | 18.0526i | −0.760825 | + | 0.760825i | −0.976471 | − | 0.215647i | \(-0.930814\pi\) |
0.215647 | + | 0.976471i | \(0.430814\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.19615 | + | 2.19615i | 0.0923928 | + | 0.0923928i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.0759 | 0.632014 | 0.316007 | − | 0.948757i | \(-0.397658\pi\) | ||||
0.316007 | + | 0.948757i | \(0.397658\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.7990 | + | 19.7990i | −0.828562 | + | 0.828562i | −0.987318 | − | 0.158756i | \(-0.949252\pi\) |
0.158756 | + | 0.987318i | \(0.449252\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.4641 | 0.644898 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.9282 | 1.62060 | 0.810301 | − | 0.586014i | \(-0.199304\pi\) | ||||
0.810301 | + | 0.586014i | \(0.199304\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.2784 | − | 10.2784i | 0.426421 | − | 0.426421i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.8695 | −0.905744 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.07180 | + | 3.07180i | 0.126787 | + | 0.126787i | 0.767653 | − | 0.640866i | \(-0.221425\pi\) |
−0.640866 | + | 0.767653i | \(0.721425\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.248711 | + | 0.248711i | −0.0102480 | + | 0.0102480i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 32.3238i | − | 1.32738i | −0.748007 | − | 0.663691i | \(-0.768989\pi\) | ||
0.748007 | − | 0.663691i | \(-0.231011\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.277401 | − | 0.277401i | −0.0113723 | − | 0.0113723i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.3205i | 1.36144i | 0.732544 | + | 0.680720i | \(0.238333\pi\) | ||||
−0.732544 | + | 0.680720i | \(0.761667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12.7846i | − | 0.521495i | −0.965407 | − | 0.260748i | \(-0.916031\pi\) | ||
0.965407 | − | 0.260748i | \(-0.0839690\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.03339 | − | 2.03339i | −0.0826690 | − | 0.0826690i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 17.6269i | − | 0.715454i | −0.933826 | − | 0.357727i | \(-0.883552\pi\) | ||
0.933826 | − | 0.357727i | \(-0.116448\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0000 | − | 18.0000i | 0.728202 | − | 0.728202i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.6077 | + | 12.6077i | 0.509220 | + | 0.509220i | 0.914287 | − | 0.405067i | \(-0.132752\pi\) |
−0.405067 | + | 0.914287i | \(0.632752\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.07107 | 0.284670 | 0.142335 | − | 0.989819i | \(-0.454539\pi\) | ||||
0.142335 | + | 0.989819i | \(0.454539\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.3538 | + | 20.3538i | −0.818088 | + | 0.818088i | −0.985831 | − | 0.167743i | \(-0.946352\pi\) |
0.167743 | + | 0.985831i | \(0.446352\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.7846 | 0.752589 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.2487 | −0.689948 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.69161 | − | 1.69161i | 0.0674491 | − | 0.0674491i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.2923 | 1.16611 | 0.583055 | − | 0.812433i | \(-0.301857\pi\) | ||||
0.583055 | + | 0.812433i | \(0.301857\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.87564 | − | 2.87564i | −0.114116 | − | 0.114116i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.66025 | − | 8.66025i | 0.343132 | − | 0.343132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.4896i | 0.453811i | 0.973917 | + | 0.226905i | \(0.0728608\pi\) | ||||
−0.973917 | + | 0.226905i | \(0.927139\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.9091 | + | 25.9091i | 1.02176 | + | 1.02176i | 0.999758 | + | 0.0219976i | \(0.00700261\pi\) |
0.0219976 | + | 0.999758i | \(0.492997\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.3923i | 0.723076i | 0.932357 | + | 0.361538i | \(0.117748\pi\) | ||||
−0.932357 | + | 0.361538i | \(0.882252\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.9282i | 1.05702i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.0392 | + | 20.0392i | 0.784196 | + | 0.784196i | 0.980536 | − | 0.196340i | \(-0.0629057\pi\) |
−0.196340 | + | 0.980536i | \(0.562906\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.17260i | 0.280257i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.39230 | + | 6.39230i | −0.249009 | + | 0.249009i | −0.820564 | − | 0.571555i | \(-0.806340\pi\) |
0.571555 | + | 0.820564i | \(0.306340\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.7846 | − | 21.7846i | −0.847323 | − | 0.847323i | 0.142475 | − | 0.989798i | \(-0.454494\pi\) |
−0.989798 | + | 0.142475i | \(0.954494\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.554803 | 0.0215143 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.4901 | + | 16.4901i | −0.638499 | + | 0.638499i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.3923 | −0.632818 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.78461 | −0.338622 | −0.169311 | − | 0.985563i | \(-0.554154\pi\) | ||||
−0.169311 | + | 0.985563i | \(0.554154\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.9077 | + | 31.9077i | −1.22631 | + | 1.22631i | −0.260966 | + | 0.965348i | \(0.584041\pi\) |
−0.965348 | + | 0.260966i | \(0.915959\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.38323 | −0.129836 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.2679 | − | 11.2679i | −0.431156 | − | 0.431156i | 0.457865 | − | 0.889022i | \(-0.348614\pi\) |
−0.889022 | + | 0.457865i | \(0.848614\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.19615 | − | 4.19615i | 0.160327 | − | 0.160327i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 13.8647i | − | 0.528204i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.8386 | − | 23.8386i | −0.906862 | − | 0.906862i | 0.0891562 | − | 0.996018i | \(-0.471583\pi\) |
−0.996018 | + | 0.0891562i | \(0.971583\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.07180i | 0.344113i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.85641i | 0.146072i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.9062 | + | 16.9062i | 0.638538 | + | 0.638538i | 0.950195 | − | 0.311657i | \(-0.100884\pi\) |
−0.311657 | + | 0.950195i | \(0.600884\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.38323i | 0.127601i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.6603 | − | 13.6603i | 0.513747 | − | 0.513747i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.19615 | − | 5.19615i | −0.195146 | − | 0.195146i | 0.602770 | − | 0.797915i | \(-0.294064\pi\) |
−0.797915 | + | 0.602770i | \(0.794064\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.27362 | 0.0851479 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.89898 | − | 4.89898i | 0.183211 | − | 0.183211i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.7128 | −0.958926 | −0.479463 | − | 0.877562i | \(-0.659169\pi\) | ||||
−0.479463 | + | 0.877562i | \(0.659169\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.7846 | 0.997511 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.2504 | − | 21.2504i | 0.789219 | − | 0.789219i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.9396 | 0.702430 | 0.351215 | − | 0.936295i | \(-0.385769\pi\) | ||||
0.351215 | + | 0.936295i | \(0.385769\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.39230 | − | 2.39230i | −0.0884826 | − | 0.0884826i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.4449 | + | 37.4449i | −1.38306 | + | 1.38306i | −0.543921 | + | 0.839136i | \(0.683061\pi\) |
−0.839136 | + | 0.543921i | \(0.816939\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.65685i | 0.208373i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.6264 | − | 12.6264i | −0.464469 | − | 0.464469i | 0.435648 | − | 0.900117i | \(-0.356519\pi\) |
−0.900117 | + | 0.435648i | \(0.856519\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 40.1051i | − | 1.47131i | −0.677354 | − | 0.735657i | \(-0.736874\pi\) | ||
0.677354 | − | 0.735657i | \(-0.263126\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1.60770i | − | 0.0589014i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.0411 | − | 19.0411i | −0.695747 | − | 0.695747i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 14.7985i | − | 0.540004i | −0.962860 | − | 0.270002i | \(-0.912976\pi\) | ||
0.962860 | − | 0.270002i | \(-0.0870244\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.73205 | + | 4.73205i | −0.172217 | + | 0.172217i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.6603 | + | 34.6603i | 1.25975 | + | 1.25975i | 0.951213 | + | 0.308536i | \(0.0998389\pi\) |
0.308536 | + | 0.951213i | \(0.400161\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.1464 | −0.621558 | −0.310779 | − | 0.950482i | \(-0.600590\pi\) | ||||
−0.310779 | + | 0.950482i | \(0.600590\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.03579 | − | 6.03579i | 0.218510 | − | 0.218510i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.0718 | −0.616427 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −45.7128 | −1.64845 | −0.824223 | − | 0.566265i | \(-0.808388\pi\) | ||||
−0.824223 | + | 0.566265i | \(0.808388\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.3572 | − | 34.3572i | 1.23574 | − | 1.23574i | 0.274019 | − | 0.961724i | \(-0.411647\pi\) |
0.961724 | − | 0.274019i | \(-0.0883533\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.92996 | −0.105247 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.85641 | − | 3.85641i | −0.138170 | − | 0.138170i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.2487 | − | 38.2487i | 1.36865 | − | 1.36865i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 10.2784i | − | 0.366853i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.3190 | + | 24.3190i | 0.866880 | + | 0.866880i | 0.992126 | − | 0.125246i | \(-0.0399720\pi\) |
−0.125246 | + | 0.992126i | \(0.539972\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.00000i | 0.213335i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 10.3923i | − | 0.369042i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.76079 | − | 9.76079i | −0.345745 | − | 0.345745i | 0.512777 | − | 0.858522i | \(-0.328617\pi\) |
−0.858522 | + | 0.512777i | \(0.828617\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.93803i | 0.139318i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.3923 | + | 24.3923i | −0.860786 | + | 0.860786i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.53590 | − | 2.53590i | −0.0893787 | − | 0.0893787i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.4505 | −0.437737 | −0.218868 | − | 0.975754i | \(-0.570237\pi\) | ||||
−0.218868 | + | 0.975754i | \(0.570237\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.4906 | − | 21.4906i | 0.754637 | − | 0.754637i | −0.220704 | − | 0.975341i | \(-0.570835\pi\) |
0.975341 | + | 0.220704i | \(0.0708354\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.46410 | 0.331513 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.78461 | 0.167392 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.5582 | + | 14.5582i | −0.508086 | + | 0.508086i | −0.913939 | − | 0.405853i | \(-0.866975\pi\) |
0.405853 | + | 0.913939i | \(0.366975\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.4238 | −0.607357 | −0.303678 | − | 0.952775i | \(-0.598215\pi\) | ||||
−0.303678 | + | 0.952775i | \(0.598215\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.39230 | + | 4.39230i | 0.152735 | + | 0.152735i | 0.779339 | − | 0.626603i | \(-0.215555\pi\) |
−0.626603 | + | 0.779339i | \(0.715555\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.1962 | − | 15.1962i | 0.527784 | − | 0.527784i | −0.392127 | − | 0.919911i | \(-0.628261\pi\) |
0.919911 | + | 0.392127i | \(0.128261\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.89469i | 0.0656470i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.96953 | + | 6.96953i | 0.241191 | + | 0.241191i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 9.21539i | − | 0.318151i | −0.987266 | − | 0.159075i | \(-0.949149\pi\) | ||
0.987266 | − | 0.159075i | \(-0.0508513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.3205i | 0.562776i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.62347 | − | 3.62347i | −0.124651 | − | 0.124651i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 5.55532i | − | 0.190883i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.4641 | − | 15.4641i | 0.530103 | − | 0.530103i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.78461 | + | 5.78461i | 0.198061 | + | 0.198061i | 0.799168 | − | 0.601107i | \(-0.205274\pi\) |
−0.601107 | + | 0.799168i | \(0.705274\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.62209 | 0.328684 | 0.164342 | − | 0.986403i | \(-0.447450\pi\) | ||||
0.164342 | + | 0.986403i | \(0.447450\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.4238 | − | 17.4238i | 0.594493 | − | 0.594493i | −0.344349 | − | 0.938842i | \(-0.611900\pi\) |
0.938842 | + | 0.344349i | \(0.111900\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.3923 | 1.10265 | 0.551323 | − | 0.834292i | \(-0.314123\pi\) | ||||
0.551323 | + | 0.834292i | \(0.314123\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.3205 | 0.452911 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.7028 | + | 32.7028i | −1.10937 | + | 1.10937i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.58630 | −0.121517 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.92820 | + | 6.92820i | 0.234216 | + | 0.234216i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.4641 | + | 18.4641i | −0.623488 | + | 0.623488i | −0.946422 | − | 0.322933i | \(-0.895331\pi\) |
0.322933 | + | 0.946422i | \(0.395331\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.4249i | 0.923967i | 0.886889 | + | 0.461984i | \(0.152862\pi\) | ||||
−0.886889 | + | 0.461984i | \(0.847138\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.58682 | + | 8.58682i | 0.288969 | + | 0.288969i | 0.836673 | − | 0.547703i | \(-0.184498\pi\) |
−0.547703 | + | 0.836673i | \(0.684498\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 33.0718i | − | 1.11044i | −0.831703 | − | 0.555221i | \(-0.812634\pi\) | ||
0.831703 | − | 0.555221i | \(-0.187366\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 7.85641i | − | 0.263495i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.93803 | − | 3.93803i | −0.131781 | − | 0.131781i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 6.21166i | − | 0.207633i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.12436 | − | 3.12436i | 0.104203 | − | 0.104203i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.51666 | + | 1.51666i | 0.0505273 | + | 0.0505273i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.5911 | −0.385302 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.38375 | − | 8.38375i | 0.278378 | − | 0.278378i | −0.554083 | − | 0.832461i | \(-0.686931\pi\) |
0.832461 | + | 0.554083i | \(0.186931\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.1769 | −1.62930 | −0.814652 | − | 0.579950i | \(-0.803072\pi\) | ||||
−0.814652 | + | 0.579950i | \(0.803072\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.7128 | −1.31430 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.79796 | + | 9.79796i | −0.323557 | + | 0.323557i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.92996 | −0.0966506 | −0.0483253 | − | 0.998832i | \(-0.515388\pi\) | ||||
−0.0483253 | + | 0.998832i | \(0.515388\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.2487 | + | 24.2487i | 0.798156 | + | 0.798156i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.9282 | + | 19.9282i | −0.655235 | + | 0.655235i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.1464i | 0.562556i | 0.959626 | + | 0.281278i | \(0.0907583\pi\) | ||||
−0.959626 | + | 0.281278i | \(0.909242\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.89469 | − | 1.89469i | −0.0620959 | − | 0.0620959i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.07180i | 0.0350515i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0000i | 0.980057i | 0.871706 | + | 0.490029i | \(0.163014\pi\) | ||||
−0.871706 | + | 0.490029i | \(0.836986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.2108 | − | 17.2108i | −0.561056 | − | 0.561056i | 0.368551 | − | 0.929607i | \(-0.379854\pi\) |
−0.929607 | + | 0.368551i | \(0.879854\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.2538i | 1.14802i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.60770 | + | 9.60770i | −0.312208 | + | 0.312208i | −0.845765 | − | 0.533556i | \(-0.820855\pi\) |
0.533556 | + | 0.845765i | \(0.320855\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.4641 | − | 15.4641i | −0.501986 | − | 0.501986i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.2581 | −1.23930 | −0.619651 | − | 0.784878i | \(-0.712726\pi\) | ||||
−0.619651 | + | 0.784878i | \(0.712726\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.38323 | + | 3.38323i | −0.109479 | + | 0.109479i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.4641 | 0.370195 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.5692 | 0.986104 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.72363 | − | 9.72363i | 0.313015 | − | 0.313015i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.2923 | −0.941978 | −0.470989 | − | 0.882139i | \(-0.656103\pi\) | ||||
−0.470989 | + | 0.882139i | \(0.656103\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.9808 | + | 34.9808i | 1.12259 | + | 1.12259i | 0.991351 | + | 0.131235i | \(0.0418942\pi\) |
0.131235 | + | 0.991351i | \(0.458106\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.3923 | + | 12.3923i | −0.397279 | + | 0.397279i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.0053i | 0.416077i | 0.978121 | + | 0.208039i | \(0.0667080\pi\) | ||||
−0.978121 | + | 0.208039i | \(0.933292\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.2891 | − | 36.2891i | −1.15980 | − | 1.15980i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 30.6410i | − | 0.977297i | −0.872481 | − | 0.488648i | \(-0.837490\pi\) | ||
0.872481 | − | 0.488648i | \(-0.162510\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.64102i | 0.147875i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.8695 | − | 21.8695i | −0.695411 | − | 0.695411i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.7081i | 1.45197i | 0.687713 | + | 0.725983i | \(0.258615\pi\) | ||||
−0.687713 | + | 0.725983i | \(0.741385\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.0525589 | − | 0.0525589i | 0.00166623 | − | 0.00166623i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.0000 | + | 21.0000i | 0.665077 | + | 0.665077i | 0.956572 | − | 0.291496i | \(-0.0941528\pi\) |
−0.291496 | + | 0.956572i | \(0.594153\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2304.2.l.g.575.2 | yes | 8 | |
3.2 | odd | 2 | 2304.2.l.c.575.3 | yes | 8 | ||
4.3 | odd | 2 | 2304.2.l.c.575.2 | yes | 8 | ||
8.3 | odd | 2 | 2304.2.l.f.575.3 | yes | 8 | ||
8.5 | even | 2 | 2304.2.l.b.575.3 | yes | 8 | ||
12.11 | even | 2 | inner | 2304.2.l.g.575.3 | yes | 8 | |
16.3 | odd | 4 | 2304.2.l.c.1727.3 | yes | 8 | ||
16.5 | even | 4 | 2304.2.l.b.1727.2 | yes | 8 | ||
16.11 | odd | 4 | 2304.2.l.f.1727.2 | yes | 8 | ||
16.13 | even | 4 | inner | 2304.2.l.g.1727.3 | yes | 8 | |
24.5 | odd | 2 | 2304.2.l.f.575.2 | yes | 8 | ||
24.11 | even | 2 | 2304.2.l.b.575.2 | ✓ | 8 | ||
48.5 | odd | 4 | 2304.2.l.f.1727.3 | yes | 8 | ||
48.11 | even | 4 | 2304.2.l.b.1727.3 | yes | 8 | ||
48.29 | odd | 4 | 2304.2.l.c.1727.2 | yes | 8 | ||
48.35 | even | 4 | inner | 2304.2.l.g.1727.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2304.2.l.b.575.2 | ✓ | 8 | 24.11 | even | 2 | ||
2304.2.l.b.575.3 | yes | 8 | 8.5 | even | 2 | ||
2304.2.l.b.1727.2 | yes | 8 | 16.5 | even | 4 | ||
2304.2.l.b.1727.3 | yes | 8 | 48.11 | even | 4 | ||
2304.2.l.c.575.2 | yes | 8 | 4.3 | odd | 2 | ||
2304.2.l.c.575.3 | yes | 8 | 3.2 | odd | 2 | ||
2304.2.l.c.1727.2 | yes | 8 | 48.29 | odd | 4 | ||
2304.2.l.c.1727.3 | yes | 8 | 16.3 | odd | 4 | ||
2304.2.l.f.575.2 | yes | 8 | 24.5 | odd | 2 | ||
2304.2.l.f.575.3 | yes | 8 | 8.3 | odd | 2 | ||
2304.2.l.f.1727.2 | yes | 8 | 16.11 | odd | 4 | ||
2304.2.l.f.1727.3 | yes | 8 | 48.5 | odd | 4 | ||
2304.2.l.g.575.2 | yes | 8 | 1.1 | even | 1 | trivial | |
2304.2.l.g.575.3 | yes | 8 | 12.11 | even | 2 | inner | |
2304.2.l.g.1727.2 | yes | 8 | 48.35 | even | 4 | inner | |
2304.2.l.g.1727.3 | yes | 8 | 16.13 | even | 4 | inner |