Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,5,Mod(161,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.161");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.3279120261\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 8x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.2 | ||
Root | \(1.16372i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.161 |
Dual form | 216.5.e.a.161.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | − 16.7931i | − 0.671724i | −0.941911 | − | 0.335862i | \(-0.890972\pi\) | ||||
0.941911 | − | 0.335862i | \(-0.109028\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −54.4980 | −1.11220 | −0.556102 | − | 0.831114i | \(-0.687704\pi\) | ||||
−0.556102 | + | 0.831114i | \(0.687704\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 27.7519i | − 0.229354i | −0.993403 | − | 0.114677i | \(-0.963417\pi\) | ||||
0.993403 | − | 0.114677i | \(-0.0365833\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 70.4980 | 0.417148 | 0.208574 | − | 0.978007i | \(-0.433118\pi\) | ||||
0.208574 | + | 0.978007i | \(0.433118\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 522.715i | 1.80870i | 0.426787 | + | 0.904352i | \(0.359645\pi\) | ||||
−0.426787 | + | 0.904352i | \(0.640355\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −157.996 | −0.437662 | −0.218831 | − | 0.975763i | \(-0.570224\pi\) | ||||
−0.218831 | + | 0.975763i | \(0.570224\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 368.583i | 0.696754i | 0.937354 | + | 0.348377i | \(0.113267\pi\) | ||||
−0.937354 | + | 0.348377i | \(0.886733\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 342.992 | 0.548787 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 61.1828i | 0.0727501i | 0.999338 | + | 0.0363750i | \(0.0115811\pi\) | ||||
−0.999338 | + | 0.0363750i | \(0.988419\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 683.961 | 0.711718 | 0.355859 | − | 0.934540i | \(-0.384188\pi\) | ||||
0.355859 | + | 0.934540i | \(0.384188\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 915.190i | 0.747094i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −344.467 | −0.251619 | −0.125810 | − | 0.992054i | \(-0.540153\pi\) | ||||
−0.125810 | + | 0.992054i | \(0.540153\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2251.07i | 1.33913i | 0.742755 | + | 0.669564i | \(0.233519\pi\) | ||||
−0.742755 | + | 0.669564i | \(0.766481\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2331.94 | −1.26119 | −0.630596 | − | 0.776111i | \(-0.717190\pi\) | ||||
−0.630596 | + | 0.776111i | \(0.717190\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2827.47i | 1.27998i | 0.768384 | + | 0.639989i | \(0.221061\pi\) | ||||
−0.768384 | + | 0.639989i | \(0.778939\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 569.035 | 0.236999 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2258.17i | 0.803906i | 0.915660 | + | 0.401953i | \(0.131668\pi\) | ||||
−0.915660 | + | 0.401953i | \(0.868332\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −466.039 | −0.154063 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5556.56i | 1.59625i | 0.602489 | + | 0.798127i | \(0.294176\pi\) | ||||
−0.602489 | + | 0.798127i | \(0.705824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5151.41 | 1.38441 | 0.692207 | − | 0.721699i | \(-0.256638\pi\) | ||||
0.692207 | + | 0.721699i | \(0.256638\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 1183.88i | − 0.280208i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7004.90 | −1.56046 | −0.780229 | − | 0.625494i | \(-0.784898\pi\) | ||||
−0.780229 | + | 0.625494i | \(0.784898\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 936.775i | − 0.185831i | −0.995674 | − | 0.0929155i | \(-0.970381\pi\) | ||||
0.995674 | − | 0.0929155i | \(-0.0296187\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5613.87 | 1.05346 | 0.526728 | − | 0.850034i | \(-0.323419\pi\) | ||||
0.526728 | + | 0.850034i | \(0.323419\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1512.42i | 0.255089i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1495.60 | −0.239641 | −0.119820 | − | 0.992796i | \(-0.538232\pi\) | ||||
−0.119820 | + | 0.992796i | \(0.538232\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 11070.7i | − 1.60701i | −0.595296 | − | 0.803506i | \(-0.702965\pi\) | ||||
0.595296 | − | 0.803506i | \(-0.297035\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8778.01 | 1.21495 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8524.75i | 1.07622i | 0.842874 | + | 0.538110i | \(0.180862\pi\) | ||||
−0.842874 | + | 0.538110i | \(0.819138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3842.00 | −0.463954 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2653.24i | 0.293988i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6355.67 | −0.675488 | −0.337744 | − | 0.941238i | \(-0.609664\pi\) | ||||
−0.337744 | + | 0.941238i | \(0.609664\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 18722.7i | − 1.83538i | −0.397296 | − | 0.917691i | \(-0.630051\pi\) | ||||
0.397296 | − | 0.917691i | \(-0.369949\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12421.4 | −1.17084 | −0.585420 | − | 0.810731i | \(-0.699070\pi\) | ||||
−0.585420 | + | 0.810731i | \(0.699070\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6532.11i | 0.570540i | 0.958447 | + | 0.285270i | \(0.0920833\pi\) | ||||
−0.958447 | + | 0.285270i | \(0.907917\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1100.20 | 0.0926014 | 0.0463007 | − | 0.998928i | \(-0.485257\pi\) | ||||
0.0463007 | + | 0.998928i | \(0.485257\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4380.56i | 0.343062i | 0.985179 | + | 0.171531i | \(0.0548713\pi\) | ||||
−0.985179 | + | 0.171531i | \(0.945129\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6189.65 | 0.468026 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 28487.0i | − 2.01165i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13870.8 | 0.947397 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 16255.6i | − 1.04036i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9545.65 | −0.591832 | −0.295916 | − | 0.955214i | \(-0.595625\pi\) | ||||
−0.295916 | + | 0.955214i | \(0.595625\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 13920.6i | − 0.811177i | −0.914056 | − | 0.405588i | \(-0.867067\pi\) | ||||
0.914056 | − | 0.405588i | \(-0.132933\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8610.47 | 0.486770 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 32465.5i | − 1.72974i | −0.501994 | − | 0.864871i | \(-0.667400\pi\) | ||||
0.501994 | − | 0.864871i | \(-0.332600\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10915.3 | −0.564943 | −0.282472 | − | 0.959276i | \(-0.591154\pi\) | ||||
−0.282472 | + | 0.959276i | \(0.591154\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1956.45i | − 0.0956747i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1027.45 | 0.0488680 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16681.0i | 0.751363i | 0.926749 | + | 0.375682i | \(0.122591\pi\) | ||||
−0.926749 | + | 0.375682i | \(0.877409\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14388.9 | −0.631064 | −0.315532 | − | 0.948915i | \(-0.602183\pi\) | ||||
−0.315532 | + | 0.948915i | \(0.602183\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 11485.8i | − 0.478078i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 47631.3 | 1.93238 | 0.966191 | − | 0.257829i | \(-0.0830070\pi\) | ||||
0.966191 | + | 0.257829i | \(0.0830070\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 20087.0i | − 0.774933i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20759.8 | 0.781353 | 0.390677 | − | 0.920528i | \(-0.372241\pi\) | ||||
0.390677 | + | 0.920528i | \(0.372241\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 51588.7i | 1.84979i | 0.380226 | + | 0.924893i | \(0.375846\pi\) | ||||
−0.380226 | + | 0.924893i | \(0.624154\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23591.0 | −0.825987 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1946.18i | 0.0650264i | 0.999471 | + | 0.0325132i | \(0.0103511\pi\) | ||||
−0.999471 | + | 0.0325132i | \(0.989649\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18692.4 | −0.610364 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10628.6i | 0.331718i | 0.986149 | + | 0.165859i | \(0.0530397\pi\) | ||||
−0.986149 | + | 0.165859i | \(0.946960\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −50545.9 | −1.54287 | −0.771434 | − | 0.636309i | \(-0.780460\pi\) | ||||
−0.771434 | + | 0.636309i | \(0.780460\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5784.66i | 0.169018i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14506.3 | 0.414834 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 56168.5i | − 1.53967i | −0.638246 | − | 0.769833i | \(-0.720340\pi\) | ||||
0.638246 | − | 0.769833i | \(-0.279660\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −53259.2 | −1.42982 | −0.714908 | − | 0.699219i | \(-0.753531\pi\) | ||||
−0.714908 | + | 0.699219i | \(0.753531\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 58910.9i | 1.51797i | 0.651109 | + | 0.758984i | \(0.274304\pi\) | ||||
−0.651109 | + | 0.758984i | \(0.725696\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 55975.9 | 1.41350 | 0.706748 | − | 0.707465i | \(-0.250161\pi\) | ||||
0.706748 | + | 0.707465i | \(0.250161\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 3334.34i | − 0.0809130i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 37802.5 | 0.899523 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4384.68i | 0.100380i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6355.39 | −0.142750 | −0.0713752 | − | 0.997450i | \(-0.522739\pi\) | ||||
−0.0713752 | + | 0.997450i | \(0.522739\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 39160.6i | 0.847173i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −37274.5 | −0.791576 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 36850.4i | 0.754497i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 46703.3 | 0.939156 | 0.469578 | − | 0.882891i | \(-0.344406\pi\) | ||||
0.469578 | + | 0.882891i | \(0.344406\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 45773.4i | 0.888304i | 0.895952 | + | 0.444152i | \(0.146495\pi\) | ||||
−0.895952 | + | 0.444152i | \(0.853505\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28850.9 | 0.550159 | 0.275079 | − | 0.961422i | \(-0.411296\pi\) | ||||
0.275079 | + | 0.961422i | \(0.411296\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 52269.2i | 0.962796i | 0.876502 | + | 0.481398i | \(0.159871\pi\) | ||||
−0.876502 | + | 0.481398i | \(0.840129\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 47482.0 | 0.859792 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28580.2i | 0.500345i | 0.968201 | + | 0.250172i | \(0.0804873\pi\) | ||||
−0.968201 | + | 0.250172i | \(0.919513\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −105372. | −1.81423 | −0.907115 | − | 0.420882i | \(-0.861721\pi\) | ||||
−0.907115 | + | 0.420882i | \(0.861721\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 9555.86i | − 0.159198i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11138.4 | −0.182570 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 52937.9i | 0.840271i | 0.907461 | + | 0.420135i | \(0.138017\pi\) | ||||
−0.907461 | + | 0.420135i | \(0.861983\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10228.9 | 0.159803 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 48237.2i | 0.730324i | 0.930944 | + | 0.365162i | \(0.118986\pi\) | ||||
−0.930944 | + | 0.365162i | \(0.881014\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18772.7 | 0.279852 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 84023.0i | 1.21475i | 0.794415 | + | 0.607375i | \(0.207777\pi\) | ||||
−0.794415 | + | 0.607375i | \(0.792223\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37921.7 | 0.540003 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 11092.5i | − 0.153294i | −0.997058 | − | 0.0766470i | \(-0.975579\pi\) | ||||
0.997058 | − | 0.0766470i | \(-0.0244215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 72287.5 | 0.984293 | 0.492147 | − | 0.870512i | \(-0.336212\pi\) | ||||
0.492147 | + | 0.870512i | \(0.336212\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 9518.67i | − 0.125867i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18391.1 | −0.239689 | −0.119845 | − | 0.992793i | \(-0.538240\pi\) | ||||
−0.119845 | + | 0.992793i | \(0.538240\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23661.1i | 0.299656i | 0.988712 | + | 0.149828i | \(0.0478720\pi\) | ||||
−0.988712 | + | 0.149828i | \(0.952128\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −110406. | −1.37854 | −0.689269 | − | 0.724505i | \(-0.742068\pi\) | ||||
−0.689269 | + | 0.724505i | \(0.742068\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 122679.i | − 1.48938i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −189710. | −2.27141 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 84688.1i | − 0.986478i | −0.869894 | − | 0.493239i | \(-0.835813\pi\) | ||||
0.869894 | − | 0.493239i | \(-0.164187\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 93311.8 | 1.07224 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 25984.4i | 0.290650i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 127086. | 1.40270 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 86508.0i | − 0.929944i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16361.1 | −0.173595 | −0.0867973 | − | 0.996226i | \(-0.527663\pi\) | ||||
−0.0867973 | + | 0.996226i | \(0.527663\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 14948.3i | − 0.154550i | −0.997010 | − | 0.0772752i | \(-0.975378\pi\) | ||||
0.997010 | − | 0.0772752i | \(-0.0246220\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −134060. | −1.36839 | −0.684196 | − | 0.729298i | \(-0.739847\pi\) | ||||
−0.684196 | + | 0.729298i | \(0.739847\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 86061.7i | 0.856429i | 0.903677 | + | 0.428214i | \(0.140857\pi\) | ||||
−0.903677 | + | 0.428214i | \(0.859143\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1697.94 | 0.0166855 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 82587.0i | − 0.791601i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24180.3 | 0.228926 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 154092.i | − 1.42360i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 149207. | 1.36187 | 0.680933 | − | 0.732346i | \(-0.261575\pi\) | ||||
0.680933 | + | 0.732346i | \(0.261575\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 117634.i | 1.04820i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 36926.1 | 0.325142 | 0.162571 | − | 0.986697i | \(-0.448021\pi\) | ||||
0.162571 | + | 0.986697i | \(0.448021\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 18981.2i | − 0.163235i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 99838.5 | 0.848613 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 88812.4i | − 0.737590i | −0.929511 | − | 0.368795i | \(-0.879770\pi\) | ||||
0.929511 | − | 0.368795i | \(-0.120230\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14758.3 | −0.121167 | −0.0605835 | − | 0.998163i | \(-0.519296\pi\) | ||||
−0.0605835 | + | 0.998163i | \(0.519296\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 77766.3i | 0.624083i | 0.950069 | + | 0.312041i | \(0.101013\pi\) | ||||
−0.950069 | + | 0.312041i | \(0.898987\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15731.3 | −0.124827 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 114321.i | − 0.887025i | −0.896268 | − | 0.443513i | \(-0.853732\pi\) | ||||
0.896268 | − | 0.443513i | \(-0.146268\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −105358. | −0.808452 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 94274.2i | − 0.707632i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −200142. | −1.48596 | −0.742978 | − | 0.669316i | \(-0.766587\pi\) | ||||
−0.742978 | + | 0.669316i | \(0.766587\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 123066.i | − 0.894108i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 173908. | 1.24997 | 0.624987 | − | 0.780635i | \(-0.285104\pi\) | ||||
0.624987 | + | 0.780635i | \(0.285104\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4313.27i | 0.0303476i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 52888.6 | 0.368200 | 0.184100 | − | 0.982908i | \(-0.441063\pi\) | ||||
0.184100 | + | 0.982908i | \(0.441063\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 284885.i | − 1.94210i | −0.238872 | − | 0.971051i | \(-0.576778\pi\) | ||||
0.238872 | − | 0.971051i | \(-0.423222\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25398.2 | 0.171349 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 76777.6i | − 0.507382i | −0.967285 | − | 0.253691i | \(-0.918355\pi\) | ||||
0.967285 | − | 0.253691i | \(-0.0816447\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −192664. | −1.26022 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25115.7i | 0.160972i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 207521. | 1.31668 | 0.658342 | − | 0.752719i | \(-0.271258\pi\) | ||||
0.658342 | + | 0.752719i | \(0.271258\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 26074.8i | − 0.162156i | −0.996708 | − | 0.0810778i | \(-0.974164\pi\) | ||||
0.996708 | − | 0.0810778i | \(-0.0258362\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 48217.9 | 0.296892 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9559.58i | 0.0577099i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −103331. | −0.617708 | −0.308854 | − | 0.951109i | \(-0.599946\pi\) | ||||
−0.308854 | + | 0.951109i | \(0.599946\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 302822.i | − 1.77536i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −185911. | −1.07947 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 111666.i | − 0.636053i | −0.948082 | − | 0.318027i | \(-0.896980\pi\) | ||||
0.948082 | − | 0.318027i | \(-0.103020\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 244363. | 1.37870 | 0.689352 | − | 0.724427i | \(-0.257895\pi\) | ||||
0.689352 | + | 0.724427i | \(0.257895\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 179287.i | 0.992594i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −280742. | −1.53975 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 225431.i | 1.21356i | 0.794871 | + | 0.606778i | \(0.207538\pi\) | ||||
−0.794871 | + | 0.606778i | \(0.792462\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −156965. | −0.837196 | −0.418598 | − | 0.908172i | \(-0.637478\pi\) | ||||
−0.418598 | + | 0.908172i | \(0.637478\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 58234.6i | − 0.304943i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −135624. | −0.703734 | −0.351867 | − | 0.936050i | \(-0.614453\pi\) | ||||
−0.351867 | + | 0.936050i | \(0.614453\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 296902.i | 1.51289i | 0.654060 | + | 0.756443i | \(0.273065\pi\) | ||||
−0.654060 | + | 0.756443i | \(0.726935\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 143157. | 0.722923 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33504.9i | 0.166194i | 0.996541 | + | 0.0830970i | \(0.0264811\pi\) | ||||
−0.996541 | + | 0.0830970i | \(0.973519\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 62471.4 | 0.307134 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 64519.1i | 0.311649i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 105859. | 0.506867 | 0.253433 | − | 0.967353i | \(-0.418440\pi\) | ||||
0.253433 | + | 0.967353i | \(0.418440\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 252698.i | 1.18905i | 0.804078 | + | 0.594524i | \(0.202659\pi\) | ||||
−0.804078 | + | 0.594524i | \(0.797341\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 138659. | 0.646824 | 0.323412 | − | 0.946258i | \(-0.395170\pi\) | ||||
0.323412 | + | 0.946258i | \(0.395170\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 93323.7i | − 0.427916i | −0.976843 | − | 0.213958i | \(-0.931364\pi\) | ||||
0.976843 | − | 0.213958i | \(-0.0686355\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 381753. | 1.73555 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 64715.8i | 0.289260i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −54191.4 | −0.240184 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11792.8i | 0.0513981i | 0.999670 | + | 0.0256991i | \(0.00818117\pi\) | ||||
−0.999670 | + | 0.0256991i | \(0.991819\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24284.2 | −0.104962 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 106731.i | 0.453741i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 82751.4 | 0.348913 | 0.174457 | − | 0.984665i | \(-0.444183\pi\) | ||||
0.174457 | + | 0.984665i | \(0.444183\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 139655.i | 0.579285i | 0.957135 | + | 0.289643i | \(0.0935364\pi\) | ||||
−0.957135 | + | 0.289643i | \(0.906464\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31981.2 | −0.131583 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 51052.4i | 0.206682i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 89055.0 | 0.357649 | 0.178825 | − | 0.983881i | \(-0.442771\pi\) | ||||
0.178825 | + | 0.983881i | \(0.442771\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 16199.6i | − 0.0640277i | −0.999487 | − | 0.0320139i | \(-0.989808\pi\) | ||||
0.999487 | − | 0.0320139i | \(-0.0101921\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −314412. | −1.23287 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 45421.9i | 0.175319i | 0.996150 | + | 0.0876597i | \(0.0279388\pi\) | ||||
−0.996150 | + | 0.0876597i | \(0.972061\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −305945. | −1.17166 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 208594.i | 0.786480i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 78467.6 | 0.293568 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 148324.i | − 0.546433i | −0.961953 | − | 0.273217i | \(-0.911912\pi\) | ||||
0.961953 | − | 0.273217i | \(-0.0880876\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −220169. | −0.804922 | −0.402461 | − | 0.915437i | \(-0.631845\pi\) | ||||
−0.402461 | + | 0.915437i | \(0.631845\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 357517.i | 1.28729i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 143988. | 0.514534 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 158696.i | 0.558614i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 109694. | 0.383245 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 15791.8i | − 0.0543568i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 104022. | 0.355410 | 0.177705 | − | 0.984084i | \(-0.443133\pi\) | ||||
0.177705 | + | 0.984084i | \(0.443133\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 18475.7i | − 0.0622025i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 106892. | 0.357249 | 0.178624 | − | 0.983917i | \(-0.442835\pi\) | ||||
0.178624 | + | 0.983917i | \(0.442835\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 9666.65i | − 0.0318400i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 81507.1 | 0.266529 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 528557.i | 1.70366i | 0.523822 | + | 0.851828i | \(0.324506\pi\) | ||||
−0.523822 | + | 0.851828i | \(0.675494\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −164398. | −0.526104 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 81419.0i | 0.256867i | 0.991718 | + | 0.128434i | \(0.0409949\pi\) | ||||
−0.991718 | + | 0.128434i | \(0.959005\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 73563.1 | 0.230443 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 187928.i | − 0.580452i | −0.956958 | − | 0.290226i | \(-0.906270\pi\) | ||||
0.956958 | − | 0.290226i | \(-0.0937305\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −417033. | −1.27908 | −0.639540 | − | 0.768758i | \(-0.720875\pi\) | ||||
−0.639540 | + | 0.768758i | \(0.720875\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 126421.i | 0.382370i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 227914. | 0.684571 | 0.342286 | − | 0.939596i | \(-0.388799\pi\) | ||||
0.342286 | + | 0.939596i | \(0.388799\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 603332.i | 1.78733i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 62668.5 | 0.184379 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 166988.i | − 0.484628i | −0.970198 | − | 0.242314i | \(-0.922094\pi\) | ||||
0.970198 | − | 0.242314i | \(-0.0779064\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −108063. | −0.311492 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 318532.i | 0.905824i | 0.891555 | + | 0.452912i | \(0.149615\pi\) | ||||
−0.891555 | + | 0.452912i | \(0.850385\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −478384. | −1.35127 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 302637.i | − 0.843468i | −0.906720 | − | 0.421734i | \(-0.861422\pi\) | ||||
0.906720 | − | 0.421734i | \(-0.138578\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −422926. | −1.17089 | −0.585445 | − | 0.810712i | \(-0.699080\pi\) | ||||
−0.585445 | + | 0.810712i | \(0.699080\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 232934.i | − 0.636389i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 520864. | 1.41367 | 0.706833 | − | 0.707381i | \(-0.250123\pi\) | ||||
0.706833 | + | 0.707381i | \(0.250123\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 199331.i | 0.533941i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 178145. | 0.474080 | 0.237040 | − | 0.971500i | \(-0.423823\pi\) | ||||
0.237040 | + | 0.971500i | \(0.423823\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 137889.i | 0.362208i | 0.983464 | + | 0.181104i | \(0.0579671\pi\) | ||||
−0.983464 | + | 0.181104i | \(0.942033\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 251133. | 0.655425 | 0.327713 | − | 0.944777i | \(-0.393722\pi\) | ||||
0.327713 | + | 0.944777i | \(0.393722\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 464582.i | − 1.19698i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −58611.3 | −0.150045 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 180058.i | − 0.455104i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 445643. | 1.11925 | 0.559626 | − | 0.828745i | \(-0.310945\pi\) | ||||
0.559626 | + | 0.828745i | \(0.310945\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 160301.i | 0.397547i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 40115.9 | 0.0988638 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 775880.i | − 1.88833i | −0.329467 | − | 0.944167i | \(-0.606869\pi\) | ||||
0.329467 | − | 0.944167i | \(-0.393131\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 409296. | 0.989955 | 0.494977 | − | 0.868906i | \(-0.335176\pi\) | ||||
0.494977 | + | 0.868906i | \(0.335176\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 443379.i | 1.05917i | 0.848256 | + | 0.529586i | \(0.177653\pi\) | ||||
−0.848256 | + | 0.529586i | \(0.822347\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 154205. | 0.366108 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 601542.i | − 1.41072i | −0.708851 | − | 0.705359i | \(-0.750786\pi\) | ||||
0.708851 | − | 0.705359i | \(-0.249214\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −233770. | −0.544887 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 489818.i | − 1.12788i | −0.825814 | − | 0.563942i | \(-0.809284\pi\) | ||||
0.825814 | − | 0.563942i | \(-0.190716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −331368. | −0.758417 | −0.379209 | − | 0.925311i | \(-0.623804\pi\) | ||||
−0.379209 | + | 0.925311i | \(0.623804\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 144596.i | − 0.326975i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22550.9 | −0.0506889 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 142961.i | − 0.317521i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −253335. | −0.559326 | −0.279663 | − | 0.960098i | \(-0.590223\pi\) | ||||
−0.279663 | + | 0.960098i | \(0.590223\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 696282.i | − 1.51917i | −0.650406 | − | 0.759587i | \(-0.725401\pi\) | ||||
0.650406 | − | 0.759587i | \(-0.274599\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 346371. | 0.751281 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 733575.i | − 1.57254i | −0.617880 | − | 0.786272i | \(-0.712008\pi\) | ||||
0.617880 | − | 0.786272i | \(-0.287992\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −545197. | −1.16191 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 159197.i | 0.335348i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 737689. | 1.54496 | 0.772480 | − | 0.635039i | \(-0.219016\pi\) | ||||
0.772480 | + | 0.635039i | \(0.219016\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 183301.i | 0.379486i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.17667e6 | −2.42209 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30577.8i | 0.0622258i | 0.999516 | + | 0.0311129i | \(0.00990514\pi\) | ||||
−0.999516 | + | 0.0311129i | \(0.990095\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 54424.4 | 0.110124 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.02035e6i | 2.04132i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 147706. | 0.293836 | 0.146918 | − | 0.989149i | \(-0.453065\pi\) | ||||
0.146918 | + | 0.989149i | \(0.453065\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 252096.i | 0.495892i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −32854.9 | −0.0642669 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 636542.i | − 1.23131i | −0.788014 | − | 0.615657i | \(-0.788891\pi\) | ||||
0.788014 | − | 0.615657i | \(-0.211109\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 676944. | 1.30221 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20985.2i | 0.0399243i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −190722. | −0.360853 | −0.180427 | − | 0.983588i | \(-0.557748\pi\) | ||||
−0.180427 | + | 0.983588i | \(0.557748\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1.21894e6i | − 2.28112i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −650363. | −1.21045 | −0.605226 | − | 0.796054i | \(-0.706917\pi\) | ||||
−0.605226 | + | 0.796054i | \(0.706917\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 194399.i | 0.357898i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −183014. | −0.335117 | −0.167558 | − | 0.985862i | \(-0.553588\pi\) | ||||
−0.167558 | + | 0.985862i | \(0.553588\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 20638.0i | − 0.0373844i | −0.999825 | − | 0.0186922i | \(-0.994050\pi\) | ||||
0.999825 | − | 0.0186922i | \(-0.00595025\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 280126. | 0.504709 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 355987.i | − 0.634557i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 593868. | 1.05296 | 0.526478 | − | 0.850189i | \(-0.323512\pi\) | ||||
0.526478 | + | 0.850189i | \(0.323512\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 241634.i | 0.423901i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −463873. | −0.809483 | −0.404741 | − | 0.914431i | \(-0.632638\pi\) | ||||
−0.404741 | + | 0.914431i | \(0.632638\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 324294.i | − 0.559977i | −0.960003 | − | 0.279989i | \(-0.909669\pi\) | ||||
0.960003 | − | 0.279989i | \(-0.0903307\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −59958.6 | −0.102992 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 391727.i | 0.665874i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −323637. | −0.547275 | −0.273638 | − | 0.961833i | \(-0.588227\pi\) | ||||
−0.273638 | + | 0.961833i | \(0.588227\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 542127.i | − 0.907282i | −0.891185 | − | 0.453641i | \(-0.850125\pi\) | ||||
0.891185 | − | 0.453641i | \(-0.149875\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 234593. | 0.390582 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 355661.i | − 0.586085i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25997.2 | −0.0426211 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 799876.i | − 1.29803i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.00397e6 | 1.62096 | 0.810481 | − | 0.585765i | \(-0.199206\pi\) | ||||
0.810481 | + | 0.585765i | \(0.199206\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 238732.i | − 0.381555i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 363164. | 0.577506 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.01967e6i | 1.60526i | 0.596480 | + | 0.802628i | \(0.296565\pi\) | ||||
−0.596480 | + | 0.802628i | \(0.703435\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.47796e6 | −2.31510 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 155795.i | − 0.241615i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −337324. | −0.520541 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 323388.i | − 0.494114i | −0.969001 | − | 0.247057i | \(-0.920536\pi\) | ||||
0.969001 | − | 0.247057i | \(-0.0794635\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 98256.1 | 0.149389 | 0.0746944 | − | 0.997206i | \(-0.476202\pi\) | ||||
0.0746944 | + | 0.997206i | \(0.476202\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 348621.i | − 0.524853i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 368438. | 0.551976 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 221130.i | 0.328067i | 0.986455 | + | 0.164033i | \(0.0524505\pi\) | ||||
−0.986455 | + | 0.164033i | \(0.947550\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.09099e6 | 1.61072 | 0.805359 | − | 0.592787i | \(-0.201973\pi\) | ||||
0.805359 | + | 0.592787i | \(0.201973\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.00999e6i | 1.47675i | 0.674392 | + | 0.738373i | \(0.264406\pi\) | ||||
−0.674392 | + | 0.738373i | \(0.735594\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 91383.0 | 0.132971 | 0.0664854 | − | 0.997787i | \(-0.478821\pi\) | ||||
0.0664854 | + | 0.997787i | \(0.478821\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 297444.i | 0.428662i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 866334. | 1.24255 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1.09255e6i | − 1.55209i | −0.630677 | − | 0.776045i | \(-0.717223\pi\) | ||||
0.630677 | − | 0.776045i | \(-0.282777\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 703538. | 0.994707 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 396166.i | 0.554835i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −755933. | −1.05370 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 126964.i | − 0.175317i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −128093. | −0.176047 | −0.0880233 | − | 0.996118i | \(-0.528055\pi\) | ||||
−0.0880233 | + | 0.996118i | \(0.528055\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.29528e6i | 1.76361i | 0.471610 | + | 0.881807i | \(0.343673\pi\) | ||||
−0.471610 | + | 0.881807i | \(0.656327\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −530958. | −0.719571 | −0.359785 | − | 0.933035i | \(-0.617150\pi\) | ||||
−0.359785 | + | 0.933035i | \(0.617150\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.28810e6i | 1.72953i | 0.502177 | + | 0.864765i | \(0.332533\pi\) | ||||
−0.502177 | + | 0.864765i | \(0.667467\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32682.3 | 0.0436798 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41505.6i | 0.0549625i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −493831. | −0.650942 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 885897.i | 1.15709i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.12511e6 | −1.46284 | −0.731418 | − | 0.681930i | \(-0.761141\pi\) | ||||
−0.731418 | + | 0.681930i | \(0.761141\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 584300.i | 0.752807i | 0.926456 | + | 0.376404i | \(0.122839\pi\) | ||||
−0.926456 | + | 0.376404i | \(0.877161\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −278108. | −0.356692 | −0.178346 | − | 0.983968i | \(-0.557075\pi\) | ||||
−0.178346 | + | 0.983968i | \(0.557075\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 309151.i | 0.392938i | 0.980510 | + | 0.196469i | \(0.0629475\pi\) | ||||
−0.980510 | + | 0.196469i | \(0.937052\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 520219. | 0.658238 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 446730.i | − 0.560198i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 178487. | 0.222823 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 41846.6i | 0.0517775i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.18038e6 | −1.45403 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 848822.i | 1.03638i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 727666. | 0.884540 | 0.442270 | − | 0.896882i | \(-0.354173\pi\) | ||||
0.442270 | + | 0.896882i | \(0.354173\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 587369.i | 0.707740i | 0.935295 | + | 0.353870i | \(0.115135\pi\) | ||||
−0.935295 | + | 0.353870i | \(0.884865\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −307233. | −0.368575 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 758646.i | 0.902195i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 324267. | 0.383947 | 0.191974 | − | 0.981400i | \(-0.438511\pi\) | ||||
0.191974 | + | 0.981400i | \(0.438511\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 66040.8i | − 0.0775191i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −118149. | −0.138085 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 421994.i | 0.488962i | 0.969654 | + | 0.244481i | \(0.0786175\pi\) | ||||
−0.969654 | + | 0.244481i | \(0.921382\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −89905.4 | −0.103726 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 243606.i | − 0.278654i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.56511e6 | 1.78265 | 0.891327 | − | 0.453362i | \(-0.149775\pi\) | ||||
0.891327 | + | 0.453362i | \(0.149775\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1.69092e6i | − 1.90961i | −0.297234 | − | 0.954805i | \(-0.596064\pi\) | ||||
0.297234 | − | 0.954805i | \(-0.403936\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −829707. | −0.933042 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 810385.i | 0.903632i | 0.892111 | + | 0.451816i | \(0.149224\pi\) | ||||
−0.892111 | + | 0.451816i | \(0.850776\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 395767. | 0.439447 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 639808.i | − 0.704472i | −0.935911 | − | 0.352236i | \(-0.885421\pi\) | ||||
0.935911 | − | 0.352236i | \(-0.114579\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −943243. | −1.03423 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.76931e6i | 1.92383i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −455719. | −0.493458 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 894386.i | 0.960441i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.20128e6 | 1.28467 | 0.642337 | − | 0.766422i | \(-0.277965\pi\) | ||||
0.642337 | + | 0.766422i | \(0.277965\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 280285.i | − 0.297278i | −0.988892 | − | 0.148639i | \(-0.952511\pi\) | ||||
0.988892 | − | 0.148639i | \(-0.0474892\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 594861. | 0.628333 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 432819.i | 0.453437i | 0.973960 | + | 0.226719i | \(0.0727998\pi\) | ||||
−0.973960 | + | 0.226719i | \(0.927200\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 236577. | 0.246836 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 261450.i | 0.270571i | 0.990807 | + | 0.135285i | \(0.0431951\pi\) | ||||
−0.990807 | + | 0.135285i | \(0.956805\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 989295. | 1.01966 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 859515.i | − 0.878741i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −982664. | −1.00059 | −0.500297 | − | 0.865854i | \(-0.666776\pi\) | ||||
−0.500297 | + | 0.865854i | \(0.666776\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 940008.i | − 0.949479i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.04183e6 | −1.04811 | −0.524053 | − | 0.851686i | \(-0.675580\pi\) | ||||
−0.524053 | + | 0.851686i | \(0.675580\pi\) | |||||||
\(998\) | 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 | 216.5.e.a.161.2 | ✓ | 4 | |
3.2 | odd | 2 | inner | 216.5.e.a.161.3 | yes | 4 | |
4.3 | odd | 2 | 432.5.e.j.161.2 | 4 | |||
9.2 | odd | 6 | 648.5.m.d.377.2 | 8 | |||
9.4 | even | 3 | 648.5.m.d.593.2 | 8 | |||
9.5 | odd | 6 | 648.5.m.d.593.3 | 8 | |||
9.7 | even | 3 | 648.5.m.d.377.3 | 8 | |||
12.11 | even | 2 | 432.5.e.j.161.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.5.e.a.161.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
216.5.e.a.161.3 | yes | 4 | 3.2 | odd | 2 | inner | |
432.5.e.j.161.2 | 4 | 4.3 | odd | 2 | |||
432.5.e.j.161.3 | 4 | 12.11 | even | 2 | |||
648.5.m.d.377.2 | 8 | 9.2 | odd | 6 | |||
648.5.m.d.377.3 | 8 | 9.7 | even | 3 | |||
648.5.m.d.593.2 | 8 | 9.4 | even | 3 | |||
648.5.m.d.593.3 | 8 | 9.5 | odd | 6 |