Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(431,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("864.431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.f (of order \(2\), degree \(1\), not 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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.170772624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 431.7 | ||
Root | \(1.41203 - 0.0786378i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 864.431 |
Dual form | 864.2.f.b.431.8 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.42703 | 1.53262 | 0.766308 | − | 0.642473i | \(-0.222092\pi\) | ||||
0.766308 | + | 0.642473i | \(0.222092\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 0.505408i | − 0.191026i | −0.995428 | − | 0.0955132i | \(-0.969551\pi\) | ||||
0.995428 | − | 0.0955132i | \(-0.0304492\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.31662i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.43039i | 1.50612i | 0.657952 | + | 0.753059i | \(0.271423\pi\) | ||||
−0.657952 | + | 0.753059i | \(0.728577\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 1.58457i | − 0.384316i | −0.981364 | − | 0.192158i | \(-0.938451\pi\) | ||||
0.981364 | − | 0.192158i | \(-0.0615486\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.74456 | 1.54731 | 0.773654 | − | 0.633608i | \(-0.218427\pi\) | ||||
0.773654 | + | 0.633608i | \(0.218427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.30243 | −0.897118 | −0.448559 | − | 0.893753i | \(-0.648063\pi\) | ||||
−0.448559 | + | 0.893753i | \(0.648063\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.74456 | 1.34891 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.55164 | −0.473828 | −0.236914 | − | 0.971531i | \(-0.576136\pi\) | ||||
−0.236914 | + | 0.971531i | \(0.576136\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.92498i | 0.884553i | 0.896879 | + | 0.442276i | \(0.145829\pi\) | ||||
−0.896879 | + | 0.442276i | \(0.854171\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.73205i | − 0.292770i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 7.45202i | − 1.22510i | −0.790430 | − | 0.612552i | \(-0.790143\pi\) | ||||
0.790430 | − | 0.612552i | \(-0.209857\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 8.51278i | − 1.32947i | −0.747078 | − | 0.664736i | \(-0.768544\pi\) | ||||
0.747078 | − | 0.664736i | \(-0.231456\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.10328 | −0.744390 | −0.372195 | − | 0.928154i | \(-0.621395\pi\) | ||||
−0.372195 | + | 0.928154i | \(0.621395\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.74456 | 0.963509 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.875393 | −0.120244 | −0.0601222 | − | 0.998191i | \(-0.519149\pi\) | ||||
−0.0601222 | + | 0.998191i | \(0.519149\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.3662i | 1.53262i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 6.63325i | − 0.863576i | −0.901975 | − | 0.431788i | \(-0.857883\pi\) | ||||
0.901975 | − | 0.431788i | \(-0.142117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8608i | 1.39058i | 0.718729 | + | 0.695290i | \(0.244724\pi\) | ||||
−0.718729 | + | 0.695290i | \(0.755276\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18.6101i | 2.30830i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.40571 | 1.11625 | 0.558126 | − | 0.829756i | \(-0.311520\pi\) | ||||
0.558126 | + | 0.829756i | \(0.311520\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.74456 | −0.438268 | −0.219134 | − | 0.975695i | \(-0.570323\pi\) | ||||
−0.219134 | + | 0.975695i | \(0.570323\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.67625 | 0.191026 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 6.44121i | − 0.724692i | −0.932044 | − | 0.362346i | \(-0.881976\pi\) | ||||
0.932044 | − | 0.362346i | \(-0.118024\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.2448i | 1.12452i | 0.826962 | + | 0.562258i | \(0.190067\pi\) | ||||
−0.826962 | + | 0.562258i | \(0.809933\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 5.43039i | − 0.589008i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 3.75906i | − 0.398459i | −0.979953 | − | 0.199230i | \(-0.936156\pi\) | ||||
0.979953 | − | 0.199230i | \(-0.0638439\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.74456 | 0.287708 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 23.1138 | 2.37143 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | −0.101535 | −0.0507673 | − | 0.998711i | \(-0.516167\pi\) | ||||
−0.0507673 | + | 0.998711i | \(0.516167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.0820 | −1.10270 | −0.551348 | − | 0.834275i | \(-0.685886\pi\) | ||||
−0.551348 | + | 0.834275i | \(0.685886\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 17.3020i | − 1.70482i | −0.522878 | − | 0.852408i | \(-0.675142\pi\) | ||||
0.522878 | − | 0.852408i | \(-0.324858\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 8.36530i | − 0.808704i | −0.914603 | − | 0.404352i | \(-0.867497\pi\) | ||||
0.914603 | − | 0.404352i | \(-0.132503\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.45202i | 0.713774i | 0.934148 | + | 0.356887i | \(0.116162\pi\) | ||||
−0.934148 | + | 0.356887i | \(0.883838\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.34363i | 0.502686i | 0.967898 | + | 0.251343i | \(0.0808723\pi\) | ||||
−0.967898 | + | 0.251343i | \(0.919128\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.7446 | −1.37494 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.800857 | −0.0734144 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.97868 | 0.534749 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.51622i | 0.134543i | 0.997735 | + | 0.0672716i | \(0.0214294\pi\) | ||||
−0.997735 | + | 0.0672716i | \(0.978571\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 15.2935i | − 1.33620i | −0.744072 | − | 0.668100i | \(-0.767108\pi\) | ||||
0.744072 | − | 0.668100i | \(-0.232892\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3.40876i | − 0.295577i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 3.75906i | − 0.321158i | −0.987023 | − | 0.160579i | \(-0.948664\pi\) | ||||
0.987023 | − | 0.160579i | \(-0.0513361\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00000 | −0.678551 | −0.339276 | − | 0.940687i | \(-0.610182\pi\) | ||||
−0.339276 | + | 0.940687i | \(0.610182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.0106 | −1.50612 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.74456 | −0.726196 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.48025 | −0.776652 | −0.388326 | − | 0.921522i | \(-0.626947\pi\) | ||||
−0.388326 | + | 0.921522i | \(0.626947\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.94661i | 0.565307i | 0.959222 | + | 0.282654i | \(0.0912147\pi\) | ||||
−0.959222 | + | 0.282654i | \(0.908785\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.8781i | 1.35568i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 10.8608i | − 0.866784i | −0.901205 | − | 0.433392i | \(-0.857316\pi\) | ||||
0.901205 | − | 0.433392i | \(-0.142684\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.17448i | 0.171373i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.2337 | −1.27152 | −0.635760 | − | 0.771887i | \(-0.719313\pi\) | ||||
−0.635760 | + | 0.771887i | \(0.719313\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.7081 | −1.06077 | −0.530384 | − | 0.847758i | \(-0.677952\pi\) | ||||
−0.530384 | + | 0.847758i | \(0.677952\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −16.4891 | −1.26839 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.67625 | −0.127443 | −0.0637214 | − | 0.997968i | \(-0.520297\pi\) | ||||
−0.0637214 | + | 0.997968i | \(0.520297\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 3.40876i | − 0.257678i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1.43710i | − 0.107414i | −0.998557 | − | 0.0537068i | \(-0.982896\pi\) | ||||
0.998557 | − | 0.0537068i | \(-0.0171036\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 25.5383i | − 1.87762i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.25544 | 0.384316 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.0106 | −1.30320 | −0.651599 | − | 0.758563i | \(-0.725902\pi\) | ||||
−0.651599 | + | 0.758563i | \(0.725902\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.2337 | −1.52843 | −0.764217 | − | 0.644959i | \(-0.776874\pi\) | ||||
−0.764217 | + | 0.644959i | \(0.776874\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0319 | 0.857236 | 0.428618 | − | 0.903486i | \(-0.359001\pi\) | ||||
0.428618 | + | 0.903486i | \(0.359001\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 22.2270i | − 1.57563i | −0.615913 | − | 0.787814i | \(-0.711213\pi\) | ||||
0.615913 | − | 0.787814i | \(-0.288787\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.28962i | 0.0905136i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 29.1736i | − 2.03757i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.3692i | 1.54731i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.25544 | 0.0864279 | 0.0432139 | − | 0.999066i | \(-0.486240\pi\) | ||||
0.0432139 | + | 0.999066i | \(0.486240\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.7081 | 0.934887 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.48913 | 0.168973 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.60485 | 0.578825 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.46284i | 0.566714i | 0.959015 | + | 0.283357i | \(0.0914481\pi\) | ||||
−0.959015 | + | 0.283357i | \(0.908552\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.87419i | 0.190767i | 0.995441 | + | 0.0953835i | \(0.0304077\pi\) | ||||
−0.995441 | + | 0.0953835i | \(0.969592\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.8824i | 0.851294i | 0.904889 | + | 0.425647i | \(0.139953\pi\) | ||||
−0.904889 | + | 0.425647i | \(0.860047\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 27.1229i | − 1.77688i | −0.458992 | − | 0.888440i | \(-0.651789\pi\) | ||||
0.458992 | − | 0.888440i | \(-0.348211\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.4891 | −1.14086 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.5090 | 0.938509 | 0.469254 | − | 0.883063i | \(-0.344523\pi\) | ||||
0.469254 | + | 0.883063i | \(0.344523\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23.1138 | 1.47669 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 36.6256i | 2.33043i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.7306i | 1.05603i | 0.849236 | + | 0.528013i | \(0.177063\pi\) | ||||
−0.849236 | + | 0.528013i | \(0.822937\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 14.2695i | − 0.897118i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.2718i | 0.765496i | 0.923853 | + | 0.382748i | \(0.125022\pi\) | ||||
−0.923853 | + | 0.382748i | \(0.874978\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.76631 | −0.234027 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.30243 | 0.265299 | 0.132649 | − | 0.991163i | \(-0.457652\pi\) | ||||
0.132649 | + | 0.991163i | \(0.457652\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.00000 | −0.184289 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.1565 | −0.680223 | −0.340112 | − | 0.940385i | \(-0.610465\pi\) | ||||
−0.340112 | + | 0.940385i | \(0.610465\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 20.8398i | − 1.26593i | −0.774180 | − | 0.632965i | \(-0.781838\pi\) | ||||
0.774180 | − | 0.632965i | \(-0.218162\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.3692i | 1.34891i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.8608i | 0.652561i | 0.945273 | + | 0.326280i | \(0.105795\pi\) | ||||
−0.945273 | + | 0.326280i | \(0.894205\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 15.4410i | − 0.921132i | −0.887626 | − | 0.460566i | \(-0.847647\pi\) | ||||
0.887626 | − | 0.460566i | \(-0.152353\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.7446 | −1.35202 | −0.676012 | − | 0.736891i | \(-0.736293\pi\) | ||||
−0.676012 | + | 0.736891i | \(0.736293\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.30243 | −0.253964 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.4891 | 0.852301 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.8646 | 1.45261 | 0.726304 | − | 0.687374i | \(-0.241237\pi\) | ||||
0.726304 | + | 0.687374i | \(0.241237\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 22.7324i | − 1.32353i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 23.3639i | − 1.35117i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 2.02163i | − 0.116525i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 37.2203i | 2.13123i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.7446 | 1.06981 | 0.534904 | − | 0.844913i | \(-0.320348\pi\) | ||||
0.534904 | + | 0.844913i | \(0.320348\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.1138 | −1.31067 | −0.655333 | − | 0.755340i | \(-0.727472\pi\) | ||||
−0.655333 | + | 0.755340i | \(0.727472\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.23369 | −0.521919 | −0.260959 | − | 0.965350i | \(-0.584039\pi\) | ||||
−0.260959 | + | 0.965350i | \(0.584039\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.5835 | −0.819093 | −0.409546 | − | 0.912289i | \(-0.634313\pi\) | ||||
−0.409546 | + | 0.912289i | \(0.634313\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 8.46284i | − 0.473828i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 10.6873i | − 0.594655i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 36.6256i | 2.03162i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.57924i | 0.142198i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.4891 | 1.84073 | 0.920364 | − | 0.391062i | \(-0.127892\pi\) | ||||
0.920364 | + | 0.391062i | \(0.127892\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.7081 | 0.748955 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.3343 | −0.884553 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 6.94661i | − 0.375082i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 6.19082i | − 0.332341i | −0.986097 | − | 0.166170i | \(-0.946860\pi\) | ||||
0.986097 | − | 0.166170i | \(-0.0531401\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.40876i | 0.182467i | 0.995830 | + | 0.0912333i | \(0.0290809\pi\) | ||||
−0.995830 | + | 0.0912333i | \(0.970919\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 18.0202i | − 0.959120i | −0.877509 | − | 0.479560i | \(-0.840796\pi\) | ||||
0.877509 | − | 0.479560i | \(-0.159204\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 32.2337 | 1.71079 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.50157 | 0.184806 | 0.0924029 | − | 0.995722i | \(-0.470545\pi\) | ||||
0.0924029 | + | 0.995722i | \(0.470545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.4891 | 1.39416 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.8327 | −0.671697 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.7858i | 0.824010i | 0.911182 | + | 0.412005i | \(0.135171\pi\) | ||||
−0.911182 | + | 0.412005i | \(0.864829\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.442430i | 0.0229698i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.43039i | 0.281175i | 0.990068 | + | 0.140587i | \(0.0448991\pi\) | ||||
−0.990068 | + | 0.140587i | \(0.955101\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 13.8564i | − 0.713641i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.4891 | −0.692890 | −0.346445 | − | 0.938070i | \(-0.612611\pi\) | ||||
−0.346445 | + | 0.938070i | \(0.612611\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.6123 | −1.00214 | −0.501070 | − | 0.865407i | \(-0.667060\pi\) | ||||
−0.501070 | + | 0.865407i | \(0.667060\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.74456 | 0.292770 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −36.8965 | −1.87073 | −0.935364 | − | 0.353687i | \(-0.884928\pi\) | ||||
−0.935364 | + | 0.353687i | \(0.884928\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.81751i | 0.344776i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 22.0742i | − 1.11068i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.38712i | 0.0696178i | 0.999394 | + | 0.0348089i | \(0.0110823\pi\) | ||||
−0.999394 | + | 0.0348089i | \(0.988918\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.0256i | 0.850216i | 0.905143 | + | 0.425108i | \(0.139764\pi\) | ||||
−0.905143 | + | 0.425108i | \(0.860236\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.7446 | −1.33224 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.7156 | 1.22510 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.0000 | 0.543915 | 0.271957 | − | 0.962309i | \(-0.412329\pi\) | ||||
0.271957 | + | 0.962309i | \(0.412329\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.35250 | −0.164966 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 35.1094i | 1.72345i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 20.4897i | − 1.00099i | −0.865741 | − | 0.500493i | \(-0.833152\pi\) | ||||
0.865741 | − | 0.500493i | \(-0.166848\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 4.04326i | − 0.197057i | −0.995134 | − | 0.0985283i | \(-0.968586\pi\) | ||||
0.995134 | − | 0.0985283i | \(-0.0314135\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 10.6873i | − 0.518408i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.48913 | 0.265637 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.3130 | 1.07478 | 0.537389 | − | 0.843334i | \(-0.319411\pi\) | ||||
0.537389 | + | 0.843334i | \(0.319411\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.48913 | 0.215734 | 0.107867 | − | 0.994165i | \(-0.465598\pi\) | ||||
0.107867 | + | 0.994165i | \(0.465598\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −29.0180 | −1.38812 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.0769i | 1.53095i | 0.643467 | + | 0.765474i | \(0.277495\pi\) | ||||
−0.643467 | + | 0.765474i | \(0.722505\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 6.63325i | − 0.315155i | −0.987507 | − | 0.157578i | \(-0.949632\pi\) | ||||
0.987507 | − | 0.157578i | \(-0.0503684\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 12.8824i | − 0.610685i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.7075i | 1.35479i | 0.735620 | + | 0.677395i | \(0.236891\pi\) | ||||
−0.735620 | + | 0.677395i | \(0.763109\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.2337 | 1.32947 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.40571 | 0.440946 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.4674 | 1.28487 | 0.642435 | − | 0.766340i | \(-0.277924\pi\) | ||||
0.642435 | + | 0.766340i | \(0.277924\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.8507 | 1.94918 | 0.974591 | − | 0.223990i | \(-0.0719084\pi\) | ||||
0.974591 | + | 0.223990i | \(0.0719084\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 12.7533i | − 0.592697i | −0.955080 | − | 0.296348i | \(-0.904231\pi\) | ||||
0.955080 | − | 0.296348i | \(-0.0957689\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 37.9576i | 1.75647i | 0.478229 | + | 0.878235i | \(0.341279\pi\) | ||||
−0.478229 | + | 0.878235i | \(0.658721\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 2.02163i | − 0.0933503i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.2665i | 0.609994i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 45.4891 | 2.08718 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.7081 | 0.626341 | 0.313170 | − | 0.949697i | \(-0.398609\pi\) | ||||
0.313170 | + | 0.949697i | \(0.398609\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 40.4674 | 1.84515 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.42703 | −0.155614 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.41957i | 0.200270i | 0.994974 | + | 0.100135i | \(0.0319275\pi\) | ||||
−0.994974 | + | 0.100135i | \(0.968073\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.3624i | 1.73127i | 0.500675 | + | 0.865635i | \(0.333085\pi\) | ||||
−0.500675 | + | 0.865635i | \(0.666915\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.04326i | 0.182099i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 4.75372i | − 0.213234i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.0000 | 1.25345 | 0.626726 | − | 0.779240i | \(-0.284395\pi\) | ||||
0.626726 | + | 0.779240i | \(0.284395\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.9073 | −0.575507 | −0.287754 | − | 0.957704i | \(-0.592908\pi\) | ||||
−0.287754 | + | 0.957704i | \(0.592908\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −37.9783 | −1.69001 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.0745360 | −0.00330375 | −0.00165187 | − | 0.999999i | \(-0.500526\pi\) | ||||
−0.00165187 | + | 0.999999i | \(0.500526\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.89253i | 0.0837207i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 59.2945i | − 2.61283i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 16.9257i | − 0.744390i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 1.58457i | − 0.0694214i | −0.999397 | − | 0.0347107i | \(-0.988949\pi\) | ||||
0.999397 | − | 0.0347107i | \(-0.0110510\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.233688 | 0.0102185 | 0.00510923 | − | 0.999987i | \(-0.498374\pi\) | ||||
0.00510923 | + | 0.999987i | \(0.498374\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.80400 | 0.339947 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.48913 | −0.195179 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 46.2277 | 2.00234 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 28.6682i | − 1.23943i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.3692i | 0.963509i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.6783i | 0.760049i | 0.924976 | + | 0.380025i | \(0.124084\pi\) | ||||
−0.924976 | + | 0.380025i | \(0.875916\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 25.5383i | 1.09394i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40.2337 | −1.72027 | −0.860134 | − | 0.510068i | \(-0.829620\pi\) | ||||
−0.860134 | + | 0.510068i | \(0.829620\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.2097 | −0.733158 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.25544 | −0.138435 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.4376 | 0.908340 | 0.454170 | − | 0.890915i | \(-0.349936\pi\) | ||||
0.454170 | + | 0.890915i | \(0.349936\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.7216i | 0.918724i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.6087i | 1.41644i | 0.705993 | + | 0.708218i | \(0.250501\pi\) | ||||
−0.705993 | + | 0.708218i | \(0.749499\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.3128i | 0.770425i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 34.0511i | − 1.42750i | −0.700402 | − | 0.713748i | \(-0.746996\pi\) | ||||
0.700402 | − | 0.713748i | \(-0.253004\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.233688 | 0.00977954 | 0.00488977 | − | 0.999988i | \(-0.498444\pi\) | ||||
0.00488977 | + | 0.999988i | \(0.498444\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −29.0180 | −1.21013 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.97825 | −0.373769 | −0.186885 | − | 0.982382i | \(-0.559839\pi\) | ||||
−0.186885 | + | 0.982382i | \(0.559839\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.17782 | 0.214812 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 2.90335i | − 0.120244i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 12.7143i | − 0.524774i | −0.964963 | − | 0.262387i | \(-0.915490\pi\) | ||||
0.964963 | − | 0.262387i | \(-0.0845097\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.2168i | 1.36868i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 13.2665i | − 0.544790i | −0.962186 | − | 0.272395i | \(-0.912184\pi\) | ||||
0.962186 | − | 0.272395i | \(-0.0878157\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.74456 | −0.112516 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.9178 | 1.26327 | 0.631634 | − | 0.775266i | \(-0.282384\pi\) | ||||
0.631634 | + | 0.775266i | \(0.282384\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.2337 | 1.27405 | 0.637024 | − | 0.770844i | \(-0.280165\pi\) | ||||
0.637024 | + | 0.770844i | \(0.280165\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.376308i | 0.0152739i | 0.999971 | + | 0.00763694i | \(0.00243094\pi\) | ||||
−0.999971 | + | 0.00763694i | \(0.997569\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 27.7128i | − 1.12114i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 41.4215i | − 1.67300i | −0.547969 | − | 0.836499i | \(-0.684599\pi\) | ||||
0.547969 | − | 0.836499i | \(-0.315401\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 18.0202i | − 0.725467i | −0.931893 | − | 0.362733i | \(-0.881844\pi\) | ||||
0.931893 | − | 0.362733i | \(-0.118156\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.76631 | 0.312154 | 0.156077 | − | 0.987745i | \(-0.450115\pi\) | ||||
0.156077 | + | 0.987745i | \(0.450115\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.89986 | −0.0761162 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.2337 | −0.529348 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.8083 | −0.470827 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.2594i | 1.00556i | 0.864414 | + | 0.502781i | \(0.167690\pi\) | ||||
−0.864414 | + | 0.502781i | \(0.832310\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.19615i | 0.206203i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36.6256i | 1.45116i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 8.51278i | − 0.336234i | −0.985767 | − | 0.168117i | \(-0.946231\pi\) | ||||
0.985767 | − | 0.168117i | \(-0.0537687\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.4674 | −0.964899 | −0.482450 | − | 0.875924i | \(-0.660253\pi\) | ||||
−0.482450 | + | 0.875924i | \(0.660253\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −44.6260 | −1.75443 | −0.877214 | − | 0.480099i | \(-0.840601\pi\) | ||||
−0.877214 | + | 0.480099i | \(0.840601\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.0000 | 0.863576 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30.6942 | −1.20116 | −0.600579 | − | 0.799565i | \(-0.705063\pi\) | ||||
−0.600579 | + | 0.799565i | \(0.705063\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 52.4114i | − 2.04788i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.2757i | 1.02356i | 0.859118 | + | 0.511778i | \(0.171013\pi\) | ||||
−0.859118 | + | 0.511778i | \(0.828987\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 3.40876i | − 0.132585i | −0.997800 | − | 0.0662926i | \(-0.978883\pi\) | ||||
0.997800 | − | 0.0662926i | \(-0.0211171\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 11.6819i | − 0.453006i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.9783 | 0.425080 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36.0211 | −1.39058 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.4891 | −1.17527 | −0.587635 | − | 0.809126i | \(-0.699941\pi\) | ||||
−0.587635 | + | 0.809126i | \(0.699941\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.55478 | −0.367220 | −0.183610 | − | 0.982999i | \(-0.558778\pi\) | ||||
−0.183610 | + | 0.982999i | \(0.558778\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.505408i | 0.0193958i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.7306i | 0.640179i | 0.947387 | + | 0.320089i | \(0.103713\pi\) | ||||
−0.947387 | + | 0.320089i | \(0.896287\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 12.8824i | − 0.492212i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 4.75372i | − 0.181102i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.5109 | −1.00852 | −0.504261 | − | 0.863552i | \(-0.668235\pi\) | ||||
−0.504261 | + | 0.863552i | \(0.668235\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.4163 | −1.03996 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.4891 | −0.510937 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.53032 | 0.322186 | 0.161093 | − | 0.986939i | \(-0.448498\pi\) | ||||
0.161093 | + | 0.986939i | \(0.448498\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 50.2606i | − 1.89562i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.60091i | 0.210644i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 36.6256i | − 1.37550i | −0.725946 | − | 0.687752i | \(-0.758598\pi\) | ||||
0.725946 | − | 0.687752i | \(-0.241402\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 21.1894i | − 0.793548i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −61.7228 | −2.30830 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.8114 | 0.701548 | 0.350774 | − | 0.936460i | \(-0.385919\pi\) | ||||
0.350774 | + | 0.936460i | \(0.385919\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.74456 | −0.325665 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.2097 | −0.639152 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 47.9918i | − 1.77992i | −0.456042 | − | 0.889958i | \(-0.650733\pi\) | ||||
0.456042 | − | 0.889958i | \(-0.349267\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 6.33830i | − 0.234430i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.4953i | 0.424588i | 0.977206 | + | 0.212294i | \(0.0680935\pi\) | ||||
−0.977206 | + | 0.212294i | \(0.931907\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.2665i | 0.488678i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.7446 | 0.689530 | 0.344765 | − | 0.938689i | \(-0.387959\pi\) | ||||
0.344765 | + | 0.938689i | \(0.387959\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.800857 | −0.0293806 | −0.0146903 | − | 0.999892i | \(-0.504676\pi\) | ||||
−0.0146903 | + | 0.999892i | \(0.504676\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.4891 | −1.19031 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.22789 | −0.154484 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.4114i | 1.91252i | 0.292522 | + | 0.956259i | \(0.405506\pi\) | ||||
−0.292522 | + | 0.956259i | \(0.594494\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23.8063i | 0.866399i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 41.4215i | − 1.50549i | −0.658313 | − | 0.752745i | \(-0.728729\pi\) | ||||
0.658313 | − | 0.752745i | \(-0.271271\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.3894i | 1.46411i | 0.681243 | + | 0.732057i | \(0.261440\pi\) | ||||
−0.681243 | + | 0.732057i | \(0.738560\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.76631 | 0.136350 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.0211 | 1.30065 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.2554 | −0.369821 | −0.184910 | − | 0.982755i | \(-0.559199\pi\) | ||||
−0.184910 | + | 0.982755i | \(0.559199\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 45.2778 | 1.62853 | 0.814264 | − | 0.580495i | \(-0.197141\pi\) | ||||
0.814264 | + | 0.580495i | \(0.197141\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33.2168i | 1.19318i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 57.4150i | − 2.05710i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.1952i | 1.11625i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 37.2203i | − 1.32845i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.4891 | 0.766005 | 0.383002 | − | 0.923747i | \(-0.374890\pi\) | ||||
0.383002 | + | 0.923747i | \(0.374890\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.70071 | 0.0960263 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −58.9783 | −2.09438 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.7400 | 0.911758 | 0.455879 | − | 0.890042i | \(-0.349325\pi\) | ||||
0.455879 | + | 0.890042i | \(0.349325\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.08653i | 0.286081i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 12.4193i | − 0.438268i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.45202i | 0.262649i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.9686i | 1.51070i | 0.655323 | + | 0.755349i | \(0.272532\pi\) | ||||
−0.655323 | + | 0.755349i | \(0.727468\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.74456 | 0.236834 | 0.118417 | − | 0.992964i | \(-0.462218\pi\) | ||||
0.118417 | + | 0.992964i | \(0.462218\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −55.6334 | −1.94875 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.9783 | 0.943850 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.0743 | 1.46840 | 0.734202 | − | 0.678931i | \(-0.237556\pi\) | ||||
0.734202 | + | 0.678931i | \(0.237556\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 21.5925i | − 0.752666i | −0.926485 | − | 0.376333i | \(-0.877185\pi\) | ||||
0.926485 | − | 0.376333i | \(-0.122815\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 6.63325i | − 0.230661i | −0.993327 | − | 0.115330i | \(-0.963207\pi\) | ||||
0.993327 | − | 0.115330i | \(-0.0367927\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 23.7432i | − 0.824635i | −0.911040 | − | 0.412318i | \(-0.864719\pi\) | ||||
0.911040 | − | 0.412318i | \(-0.135281\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 10.6873i | − 0.370292i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −46.9783 | −1.62575 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45.4268 | 1.56831 | 0.784154 | − | 0.620566i | \(-0.213097\pi\) | ||||
0.784154 | + | 0.620566i | \(0.213097\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.4891 | −0.775487 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −56.5088 | −1.94396 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.0618i | 1.09906i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 45.4647i | − 1.55668i | −0.627841 | − | 0.778342i | \(-0.716061\pi\) | ||||
0.627841 | − | 0.778342i | \(-0.283939\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.6357i | 1.21729i | 0.793442 | + | 0.608646i | \(0.208287\pi\) | ||||
−0.793442 | + | 0.608646i | \(0.791713\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.4674 | −1.65369 | −0.826843 | − | 0.562433i | \(-0.809865\pi\) | ||||
−0.826843 | + | 0.562433i | \(0.809865\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 56.4343 | 1.92104 | 0.960522 | − | 0.278203i | \(-0.0897389\pi\) | ||||
0.960522 | + | 0.278203i | \(0.0897389\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.74456 | −0.195321 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.3631 | 0.724692 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.7216i | 0.736007i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 3.02167i | − 0.102151i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.02163i | − 0.0682657i | −0.999417 | − | 0.0341328i | \(-0.989133\pi\) | ||||
0.999417 | − | 0.0341328i | \(-0.0108669\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 38.8048i | − 1.30737i | −0.756768 | − | 0.653684i | \(-0.773223\pi\) | ||||
0.756768 | − | 0.653684i | \(-0.226777\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.7228 | −1.13486 | −0.567432 | − | 0.823421i | \(-0.692063\pi\) | ||||
−0.567432 | + | 0.823421i | \(0.692063\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 55.6334 | 1.86799 | 0.933993 | − | 0.357290i | \(-0.116299\pi\) | ||||
0.933993 | + | 0.357290i | \(0.116299\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.766312 | 0.0257013 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −34.4194 | −1.15180 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 4.92498i | − 0.164624i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 12.5668i | − 0.419126i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.38712i | 0.0462118i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.7663 | 0.656330 | 0.328165 | − | 0.944620i | \(-0.393570\pi\) | ||||
0.328165 | + | 0.944620i | \(0.393570\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.10328 | −0.169079 | −0.0845397 | − | 0.996420i | \(-0.526942\pi\) | ||||
−0.0845397 | + | 0.996420i | \(0.526942\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.9783 | −1.12452 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.72946 | −0.255249 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 44.5830i | − 1.47066i | −0.677710 | − | 0.735329i | \(-0.737028\pi\) | ||||
0.677710 | − | 0.735329i | \(-0.262972\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 51.0767i | 1.68121i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 50.2606i | − 1.65256i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49.8968i | 1.63706i | 0.574462 | + | 0.818531i | \(0.305211\pi\) | ||||
−0.574462 | + | 0.818531i | \(0.694789\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.4891 | 1.49085 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.0106 | 0.589008 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.0000 | 1.14340 | 0.571700 | − | 0.820463i | \(-0.306284\pi\) | ||||
0.571700 | + | 0.820463i | \(0.306284\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.8327 | 0.418335 | 0.209168 | − | 0.977880i | \(-0.432925\pi\) | ||||
0.209168 | + | 0.977880i | \(0.432925\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.6256i | 1.19269i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.43710i | − 0.0466994i | −0.999727 | − | 0.0233497i | \(-0.992567\pi\) | ||||
0.999727 | − | 0.0233497i | \(-0.00743311\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 20.3344i | − 0.660084i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.7384i | 1.44922i | 0.689160 | + | 0.724609i | \(0.257980\pi\) | ||||
−0.689160 | + | 0.724609i | \(0.742020\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −61.7228 | −1.99730 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.89986 | −0.0613496 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.74456 | 0.217567 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −72.7686 | −2.34250 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 3.91416i | − 0.125871i | −0.998018 | − | 0.0629355i | \(-0.979954\pi\) | ||||
0.998018 | − | 0.0629355i | \(-0.0200462\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 47.7600i | − 1.53269i | −0.642428 | − | 0.766346i | \(-0.722073\pi\) | ||||
0.642428 | − | 0.766346i | \(-0.277927\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.04326i | 0.129621i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.74839i | 0.183907i | 0.995763 | + | 0.0919536i | \(0.0293112\pi\) | ||||
−0.995763 | + | 0.0919536i | \(0.970689\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.4674 | 0.398459 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.7261 | −1.36275 | −0.681376 | − | 0.731934i | \(-0.738618\pi\) | ||||
−0.681376 | + | 0.731934i | \(0.738618\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.2337 | 1.31381 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.2097 | −0.547237 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 13.3878i | − 0.425278i | −0.977131 | − | 0.212639i | \(-0.931794\pi\) | ||||
0.977131 | − | 0.212639i | \(-0.0682058\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 76.1726i | − 2.41483i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.9600i | 1.80394i | 0.431796 | + | 0.901971i | \(0.357880\pi\) | ||||
−0.431796 | + | 0.901971i | \(0.642120\pi\) | |||||||
\(998\) | 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 | 864.2.f.b.431.7 | 8 | ||
3.2 | odd | 2 | inner | 864.2.f.b.431.1 | 8 | ||
4.3 | odd | 2 | 216.2.f.b.107.6 | yes | 8 | ||
8.3 | odd | 2 | inner | 864.2.f.b.431.2 | 8 | ||
8.5 | even | 2 | 216.2.f.b.107.4 | yes | 8 | ||
9.2 | odd | 6 | 2592.2.p.d.2159.4 | 8 | |||
9.4 | even | 3 | 2592.2.p.d.431.1 | 8 | |||
9.5 | odd | 6 | 2592.2.p.e.431.4 | 8 | |||
9.7 | even | 3 | 2592.2.p.e.2159.1 | 8 | |||
12.11 | even | 2 | 216.2.f.b.107.3 | ✓ | 8 | ||
24.5 | odd | 2 | 216.2.f.b.107.5 | yes | 8 | ||
24.11 | even | 2 | inner | 864.2.f.b.431.8 | 8 | ||
36.7 | odd | 6 | 648.2.l.e.539.3 | 8 | |||
36.11 | even | 6 | 648.2.l.d.539.2 | 8 | |||
36.23 | even | 6 | 648.2.l.e.107.4 | 8 | |||
36.31 | odd | 6 | 648.2.l.d.107.1 | 8 | |||
72.5 | odd | 6 | 648.2.l.e.107.3 | 8 | |||
72.11 | even | 6 | 2592.2.p.d.2159.1 | 8 | |||
72.13 | even | 6 | 648.2.l.d.107.2 | 8 | |||
72.29 | odd | 6 | 648.2.l.d.539.1 | 8 | |||
72.43 | odd | 6 | 2592.2.p.e.2159.4 | 8 | |||
72.59 | even | 6 | 2592.2.p.e.431.1 | 8 | |||
72.61 | even | 6 | 648.2.l.e.539.4 | 8 | |||
72.67 | odd | 6 | 2592.2.p.d.431.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.f.b.107.3 | ✓ | 8 | 12.11 | even | 2 | ||
216.2.f.b.107.4 | yes | 8 | 8.5 | even | 2 | ||
216.2.f.b.107.5 | yes | 8 | 24.5 | odd | 2 | ||
216.2.f.b.107.6 | yes | 8 | 4.3 | odd | 2 | ||
648.2.l.d.107.1 | 8 | 36.31 | odd | 6 | |||
648.2.l.d.107.2 | 8 | 72.13 | even | 6 | |||
648.2.l.d.539.1 | 8 | 72.29 | odd | 6 | |||
648.2.l.d.539.2 | 8 | 36.11 | even | 6 | |||
648.2.l.e.107.3 | 8 | 72.5 | odd | 6 | |||
648.2.l.e.107.4 | 8 | 36.23 | even | 6 | |||
648.2.l.e.539.3 | 8 | 36.7 | odd | 6 | |||
648.2.l.e.539.4 | 8 | 72.61 | even | 6 | |||
864.2.f.b.431.1 | 8 | 3.2 | odd | 2 | inner | ||
864.2.f.b.431.2 | 8 | 8.3 | odd | 2 | inner | ||
864.2.f.b.431.7 | 8 | 1.1 | even | 1 | trivial | ||
864.2.f.b.431.8 | 8 | 24.11 | even | 2 | inner | ||
2592.2.p.d.431.1 | 8 | 9.4 | even | 3 | |||
2592.2.p.d.431.4 | 8 | 72.67 | odd | 6 | |||
2592.2.p.d.2159.1 | 8 | 72.11 | even | 6 | |||
2592.2.p.d.2159.4 | 8 | 9.2 | odd | 6 | |||
2592.2.p.e.431.1 | 8 | 72.59 | even | 6 | |||
2592.2.p.e.431.4 | 8 | 9.5 | odd | 6 | |||
2592.2.p.e.2159.1 | 8 | 9.7 | even | 3 | |||
2592.2.p.e.2159.4 | 8 | 72.43 | odd | 6 |