Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,5,Mod(113,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, 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("304.113");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.e (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: | \(31.4244687775\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 269x^{2} + 17592 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.3 | ||
Root | \(10.5914i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.113 |
Dual form | 304.5.e.d.113.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 10.5914i | 1.17683i | 0.808561 | + | 0.588413i | \(0.200247\pi\) | ||||
−0.808561 | + | 0.588413i | \(0.799753\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −16.8215 | −0.672861 | −0.336430 | − | 0.941708i | \(-0.609220\pi\) | ||||
−0.336430 | + | 0.941708i | \(0.609220\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 38.6430 | 0.788633 | 0.394317 | − | 0.918975i | \(-0.370981\pi\) | ||||
0.394317 | + | 0.918975i | \(0.370981\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −31.1785 | −0.384920 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 70.8215 | 0.585302 | 0.292651 | − | 0.956219i | \(-0.405463\pi\) | ||||
0.292651 | + | 0.956219i | \(0.405463\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 231.121i | 1.36758i | 0.729679 | + | 0.683790i | \(0.239670\pi\) | ||||
−0.729679 | + | 0.683790i | \(0.760330\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 178.164i | − | 0.791840i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −90.4279 | −0.312899 | −0.156450 | − | 0.987686i | \(-0.550005\pi\) | ||||
−0.156450 | + | 0.987686i | \(0.550005\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 319.751 | + | 167.573i | 0.885736 | + | 0.464190i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 409.285i | 0.928084i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 285.538 | 0.539769 | 0.269885 | − | 0.962893i | \(-0.413014\pi\) | ||||
0.269885 | + | 0.962893i | \(0.413014\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −342.037 | −0.547259 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 527.681i | 0.723843i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 285.969i | − | 0.340034i | −0.985441 | − | 0.170017i | \(-0.945618\pi\) | ||
0.985441 | − | 0.170017i | \(-0.0543823\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 852.235i | 0.886821i | 0.896319 | + | 0.443410i | \(0.146232\pi\) | ||||
−0.896319 | + | 0.443410i | \(0.853768\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 750.101i | 0.688798i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −650.034 | −0.530640 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 54.8476i | 0.0400640i | 0.999799 | + | 0.0200320i | \(0.00637681\pi\) | ||||
−0.999799 | + | 0.0200320i | \(0.993623\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2447.90 | −1.60940 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 37.4456i | 0.0222758i | 0.999938 | + | 0.0111379i | \(0.00354537\pi\) | ||||
−0.999938 | + | 0.0111379i | \(0.996455\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −691.677 | −0.374082 | −0.187041 | − | 0.982352i | \(-0.559890\pi\) | ||||
−0.187041 | + | 0.982352i | \(0.559890\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 524.469 | 0.258997 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2630.47 | −1.19080 | −0.595398 | − | 0.803431i | \(-0.703006\pi\) | ||||
−0.595398 | + | 0.803431i | \(0.703006\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −907.716 | −0.378058 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 957.761i | − | 0.368228i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3833.35i | − | 1.36467i | −0.731041 | − | 0.682333i | \(-0.760965\pi\) | ||
0.731041 | − | 0.682333i | \(-0.239035\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1191.33 | −0.393826 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1774.83 | + | 3386.62i | −0.546271 | + | 1.04236i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3339.72i | 0.959414i | 0.877429 | + | 0.479707i | \(0.159257\pi\) | ||||
−0.877429 | + | 0.479707i | \(0.840743\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2877.84 | −0.773405 | −0.386702 | − | 0.922205i | \(-0.626386\pi\) | ||||
−0.386702 | + | 0.922205i | \(0.626386\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1204.83 | −0.303560 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 3887.81i | − | 0.920191i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4052.74i | 0.902815i | 0.892318 | + | 0.451408i | \(0.149078\pi\) | ||||
−0.892318 | + | 0.451408i | \(0.850922\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3024.26i | 0.635214i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3315.87i | − | 0.657780i | −0.944368 | − | 0.328890i | \(-0.893325\pi\) | ||
0.944368 | − | 0.328890i | \(-0.106675\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5544.37 | −1.04041 | −0.520207 | − | 0.854040i | \(-0.674145\pi\) | ||||
−0.520207 | + | 0.854040i | \(0.674145\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 3622.66i | − | 0.644028i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2736.76 | 0.461588 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 10304.4i | − | 1.65107i | −0.564348 | − | 0.825537i | \(-0.690872\pi\) | ||
0.564348 | − | 0.825537i | \(-0.309128\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8114.36 | −1.23676 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3541.95 | 0.514145 | 0.257073 | − | 0.966392i | \(-0.417242\pi\) | ||||
0.257073 | + | 0.966392i | \(0.417242\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1521.13 | 0.210538 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3028.82 | 0.400161 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13273.7i | 1.67576i | 0.545851 | + | 0.837882i | \(0.316207\pi\) | ||||
−0.545851 | + | 0.837882i | \(0.683793\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8931.22i | 1.07852i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9026.39 | −1.04363 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5378.69 | − | 2818.82i | −0.595977 | − | 0.312335i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4281.99i | 0.455096i | 0.973767 | + | 0.227548i | \(0.0730708\pi\) | ||||
−0.973767 | + | 0.227548i | \(0.926929\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2208.11 | −0.225294 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4391.56 | 0.430503 | 0.215252 | − | 0.976559i | \(-0.430943\pi\) | ||||
0.215252 | + | 0.976559i | \(0.430943\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13489.7i | 1.27153i | 0.771881 | + | 0.635767i | \(0.219316\pi\) | ||||
−0.771881 | + | 0.635767i | \(0.780684\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 6884.80i | − | 0.624471i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 21349.0i | 1.86470i | 0.361553 | + | 0.932352i | \(0.382247\pi\) | ||||
−0.361553 | + | 0.932352i | \(0.617753\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15145.0i | 1.27472i | 0.770564 | + | 0.637362i | \(0.219974\pi\) | ||||
−0.770564 | + | 0.637362i | \(0.780026\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −580.915 | −0.0471483 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3251.23i | − | 0.254619i | −0.991863 | − | 0.127310i | \(-0.959366\pi\) | ||
0.991863 | − | 0.127310i | \(-0.0406342\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4803.18 | −0.363189 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 7206.01i | − | 0.526409i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3494.41 | −0.246763 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9625.31 | −0.657422 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −396.602 | −0.0262147 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 16267.0 | 1.04109 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16952.7i | − | 1.05107i | −0.850772 | − | 0.525535i | \(-0.823865\pi\) | ||
0.850772 | − | 0.525535i | \(-0.176135\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 7325.85i | − | 0.440229i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2912.67 | −0.169726 | −0.0848632 | − | 0.996393i | \(-0.527045\pi\) | ||||
−0.0848632 | + | 0.996393i | \(0.527045\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12356.1 | + | 6475.51i | 0.698521 | + | 0.366076i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 8876.40i | − | 0.487045i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 35986.2 | 1.91732 | 0.958660 | − | 0.284556i | \(-0.0918460\pi\) | ||||
0.958660 | + | 0.284556i | \(0.0918460\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1155.96 | −0.0598294 | −0.0299147 | − | 0.999552i | \(-0.509524\pi\) | ||||
−0.0299147 | + | 0.999552i | \(0.509524\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 27860.4i | − | 1.40136i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16368.3i | 0.800447i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4810.43i | 0.228796i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 9614.02i | − | 0.444908i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 27655.0 | 1.24567 | 0.622833 | − | 0.782355i | \(-0.285981\pi\) | ||||
0.622833 | + | 0.782355i | \(0.285981\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10441.7i | − | 0.457949i | −0.973432 | − | 0.228975i | \(-0.926463\pi\) | ||
0.973432 | − | 0.228975i | \(-0.0735373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2819.40 | 0.120441 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 14335.9i | − | 0.596707i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −27020.1 | −1.09620 | −0.548098 | − | 0.836414i | \(-0.684648\pi\) | ||||
−0.548098 | + | 0.836414i | \(0.684648\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 40600.7 | 1.60598 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11034.0 | 0.425680 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 47347.7 | 1.78206 | 0.891032 | − | 0.453941i | \(-0.149982\pi\) | ||||
0.891032 | + | 0.453941i | \(0.149982\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 12617.8i | − | 0.463465i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9876.14i | 0.354123i | 0.984200 | + | 0.177062i | \(0.0566592\pi\) | ||||
−0.984200 | + | 0.177062i | \(0.943341\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −24856.0 | −0.870277 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9969.34 | − | 5224.66i | −0.340937 | − | 0.178676i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 43235.9i | − | 1.44462i | −0.691572 | − | 0.722308i | \(-0.743081\pi\) | ||
0.691572 | − | 0.722308i | \(-0.256919\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13217.3 | −0.431586 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −35372.4 | −1.12906 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 33775.1i | − | 1.05412i | −0.849828 | − | 0.527060i | \(-0.823294\pi\) | ||
0.849828 | − | 0.527060i | \(-0.176706\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1508.54i | 0.0460469i | 0.999735 | + | 0.0230234i | \(0.00732923\pi\) | ||||
−0.999735 | + | 0.0230234i | \(0.992671\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 30480.4i | − | 0.910163i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 922.620i | − | 0.0269575i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6404.24 | −0.183140 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 20391.2i | 0.570846i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16937.5 | −0.464284 | −0.232142 | − | 0.972682i | \(-0.574573\pi\) | ||||
−0.232142 | + | 0.972682i | \(0.574573\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15699.3i | 0.421469i | 0.977543 | + | 0.210735i | \(0.0675856\pi\) | ||||
−0.977543 | + | 0.210735i | \(0.932414\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 41177.5 | 1.08290 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16437.6 | 0.423551 | 0.211776 | − | 0.977318i | \(-0.432075\pi\) | ||||
0.211776 | + | 0.977318i | \(0.432075\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13901.6 | 0.351042 | 0.175521 | − | 0.984476i | \(-0.443839\pi\) | ||||
0.175521 | + | 0.984476i | \(0.443839\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −42924.3 | −1.06246 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 11050.7i | − | 0.268162i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 629.891i | − | 0.0149885i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8902.64 | −0.207768 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22645.2 | + | 11867.7i | 0.518423 | + | 0.271691i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 32124.3i | − | 0.721554i | −0.932652 | − | 0.360777i | \(-0.882512\pi\) | ||
0.932652 | − | 0.360777i | \(-0.117488\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 35119.8 | 0.774093 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11635.1 | 0.251705 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 32932.9i | 0.699376i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 58722.8i | − | 1.22439i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 20899.8i | − | 0.427915i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 69965.9i | 1.40694i | 0.710723 | + | 0.703472i | \(0.248368\pi\) | ||||
−0.710723 | + | 0.703472i | \(0.751632\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10664.2 | 0.210651 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 88463.3i | 1.71677i | 0.513008 | + | 0.858384i | \(0.328531\pi\) | ||||
−0.513008 | + | 0.858384i | \(0.671469\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 92563.5 | 1.76510 | 0.882549 | − | 0.470221i | \(-0.155826\pi\) | ||||
0.882549 | + | 0.470221i | \(0.155826\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 28986.2i | 0.543209i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −80439.0 | −1.48168 | −0.740841 | − | 0.671681i | \(-0.765573\pi\) | ||||
−0.740841 | + | 0.671681i | \(0.765573\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 44248.5 | 0.801240 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 109138. | 1.94303 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 87546.3 | 1.53265 | 0.766323 | − | 0.642455i | \(-0.222084\pi\) | ||||
0.766323 | + | 0.642455i | \(0.222084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 96049.6i | − | 1.65372i | −0.562409 | − | 0.826859i | \(-0.690125\pi\) | ||
0.562409 | − | 0.826859i | \(-0.309875\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 43200.5i | − | 0.731605i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15269.2 | 0.254380 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −38729.6 | + | 73901.1i | −0.634817 | + | 1.21132i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 37514.3i | 0.605059i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −92400.5 | −1.46665 | −0.733325 | − | 0.679878i | \(-0.762033\pi\) | ||||
−0.733325 | + | 0.679878i | \(0.762033\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20222.2 | 0.315928 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16111.0i | 0.247766i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 9573.31i | − | 0.144942i | −0.997371 | − | 0.0724712i | \(-0.976911\pi\) | ||
0.997371 | − | 0.0724712i | \(-0.0230886\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2119.48i | 0.0315958i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8916.07i | 0.130886i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27549.0 | −0.398285 | −0.199142 | − | 0.979971i | \(-0.563816\pi\) | ||||
−0.199142 | + | 0.979971i | \(0.563816\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 64482.7i | 0.918230i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −140588. | −1.97208 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 97069.5i | − | 1.34146i | −0.741701 | − | 0.670731i | \(-0.765981\pi\) | ||
0.741701 | − | 0.670731i | \(-0.234019\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 52509.9 | 0.714994 | 0.357497 | − | 0.933914i | \(-0.383630\pi\) | ||||
0.357497 | + | 0.933914i | \(0.383630\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −94594.4 | −1.26923 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −24223.6 | −0.320311 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31441.0 | 0.409767 | 0.204883 | − | 0.978786i | \(-0.434318\pi\) | ||||
0.204883 | + | 0.978786i | \(0.434318\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 26571.4i | − | 0.341355i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 153218.i | 1.94043i | 0.242245 | + | 0.970215i | \(0.422116\pi\) | ||||
−0.242245 | + | 0.970215i | \(0.577884\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18715.4 | 0.233682 | 0.116841 | − | 0.993151i | \(-0.462723\pi\) | ||||
0.116841 | + | 0.993151i | \(0.462723\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 29855.4 | − | 56968.0i | 0.367564 | − | 0.701361i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1447.01i | 0.0175674i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −75343.8 | −0.902094 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −45352.5 | −0.535568 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 135321.i | 1.57627i | 0.615502 | + | 0.788136i | \(0.288953\pi\) | ||||
−0.615502 | + | 0.788136i | \(0.711047\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 56179.1i | − | 0.645552i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 37371.2i | 0.423666i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 65993.8i | 0.738178i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −26728.5 | −0.295013 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 46513.0i | 0.506628i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 48409.6 | 0.520393 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8548.60i | 0.0907023i | 0.998971 | + | 0.0453512i | \(0.0144407\pi\) | ||||
−0.998971 | + | 0.0453512i | \(0.985559\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −142875. | −1.49637 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 149498. | 1.54566 | 0.772830 | − | 0.634613i | \(-0.218841\pi\) | ||||
0.772830 | + | 0.634613i | \(0.218841\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32077.5 | 0.327425 | 0.163713 | − | 0.986508i | \(-0.447653\pi\) | ||||
0.163713 | + | 0.986508i | \(0.447653\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 20267.1 | 0.204254 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 127709.i | − | 1.27087i | −0.772153 | − | 0.635437i | \(-0.780820\pi\) | ||
0.772153 | − | 0.635437i | \(-0.219180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 20252.7i | − | 0.199023i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −226116. | −2.19443 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28914.4 | − | 15153.2i | −0.277146 | − | 0.145245i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 79051.9i | − | 0.748420i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −160407. | −1.50013 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −101649. | −0.939102 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 56091.4i | − | 0.511965i | −0.966681 | − | 0.255983i | \(-0.917601\pi\) | ||
0.966681 | − | 0.255983i | \(-0.0823990\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1710.06i | − | 0.0154214i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 68173.2i | − | 0.607469i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21720.9i | 0.191257i | 0.995417 | + | 0.0956286i | \(0.0304861\pi\) | ||||
−0.995417 | + | 0.0956286i | \(0.969514\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 34435.2 | 0.299643 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 60356.6i | 0.519058i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −127859. | −1.08678 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 50872.6i | − | 0.427411i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 83039.8 | 0.689648 | 0.344824 | − | 0.938667i | \(-0.387939\pi\) | ||||
0.344824 | + | 0.938667i | \(0.387939\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −205331. | −1.68579 | −0.842895 | − | 0.538079i | \(-0.819150\pi\) | ||||
−0.842895 | + | 0.538079i | \(0.819150\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −121958. | −0.989913 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −119932. | −0.962463 | −0.481232 | − | 0.876594i | \(-0.659810\pi\) | ||||
−0.481232 | + | 0.876594i | \(0.659810\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 55778.0i | 0.442594i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 37010.8i | − | 0.290397i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 138143. | 1.07187 | 0.535933 | − | 0.844260i | \(-0.319960\pi\) | ||||
0.535933 | + | 0.844260i | \(0.319960\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 74159.9 | + | 107163.i | 0.569056 | + | 0.822299i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 101946.i | − | 0.773671i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 93264.7 | 0.700054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −138217. | −1.02619 | −0.513096 | − | 0.858331i | \(-0.671502\pi\) | ||||
−0.513096 | + | 0.858331i | \(0.671502\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1167.50i | − | 0.00857438i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 148132.i | − | 1.07622i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 151421.i | 1.08835i | 0.838972 | + | 0.544175i | \(0.183157\pi\) | ||||
−0.838972 | + | 0.544175i | \(0.816843\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 172291.i | 1.22518i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 66093.4 | 0.465024 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 117526.i | 0.818194i | 0.912491 | + | 0.409097i | \(0.134156\pi\) | ||||
−0.912491 | + | 0.409097i | \(0.865844\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 179554. | 1.23693 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 217885.i | − | 1.48535i | −0.669651 | − | 0.742676i | \(-0.733556\pi\) | ||
0.669651 | − | 0.742676i | \(-0.266444\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −46036.4 | −0.310585 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21565.5 | 0.143991 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 64818.5 | 0.428351 | 0.214175 | − | 0.976795i | \(-0.431294\pi\) | ||||
0.214175 | + | 0.976795i | \(0.431294\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25820.6 | −0.168893 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 30849.4i | − | 0.199738i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 173335.i | 1.11094i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 89625.3 | 0.568656 | 0.284328 | − | 0.958727i | \(-0.408230\pi\) | ||||
0.284328 | + | 0.958727i | \(0.408230\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −68584.9 | + | 130869.i | −0.430807 | + | 0.822037i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 123664.i | − | 0.769052i | −0.923114 | − | 0.384526i | \(-0.874365\pi\) | ||
0.923114 | − | 0.384526i | \(-0.125635\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −196970. | −1.21280 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 136496. | 0.832165 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3884.39i | 0.0234495i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 67492.8i | − | 0.403470i | −0.979440 | − | 0.201735i | \(-0.935342\pi\) | ||
0.979440 | − | 0.201735i | \(-0.0646579\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 381145.i | 2.25635i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 129057.i | 0.756626i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −59580.9 | −0.345948 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 12243.3i | − | 0.0704088i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 210278. | 1.19775 | 0.598874 | − | 0.800843i | \(-0.295615\pi\) | ||||
0.598874 | + | 0.800843i | \(0.295615\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 87195.1i | − | 0.491958i | −0.969275 | − | 0.245979i | \(-0.920891\pi\) | ||
0.969275 | − | 0.245979i | \(-0.0791094\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 82014.1 | 0.458361 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 30929.7 | 0.171237 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −111208. | −0.609933 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −173364. | −0.941987 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 285166.i | − | 1.53512i | −0.640976 | − | 0.767561i | \(-0.721470\pi\) | ||
0.640976 | − | 0.767561i | \(-0.278530\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 47714.6i | − | 0.254493i | −0.991871 | − | 0.127246i | \(-0.959386\pi\) | ||
0.991871 | − | 0.127246i | \(-0.0406139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −50949.3 | −0.269253 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 91300.9 | + | 47848.3i | 0.478093 | + | 0.250555i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 6771.27i | − | 0.0351351i | −0.999846 | − | 0.0175675i | \(-0.994408\pi\) | ||
0.999846 | − | 0.0175675i | \(-0.00559221\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 28301.2 | 0.145522 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 305876. | 1.55861 | 0.779306 | − | 0.626643i | \(-0.215572\pi\) | ||||
0.779306 | + | 0.626643i | \(0.215572\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 223284.i | − | 1.12756i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 292907.i | 1.46593i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 133235.i | 0.660883i | 0.943826 | + | 0.330442i | \(0.107198\pi\) | ||||
−0.943826 | + | 0.330442i | \(0.892802\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2651.95i | 0.0130380i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 110593. | 0.538927 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 150237.i | − | 0.725693i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 295991. | 1.41725 | 0.708625 | − | 0.705585i | \(-0.249316\pi\) | ||||
0.708625 | + | 0.705585i | \(0.249316\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 47717.1i | − | 0.226490i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −142958. | −0.672675 | −0.336337 | − | 0.941742i | \(-0.609188\pi\) | ||||
−0.336337 | + | 0.941742i | \(0.609188\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29639.1 | 0.138262 | 0.0691310 | − | 0.997608i | \(-0.477977\pi\) | ||||
0.0691310 | + | 0.997608i | \(0.477977\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 151838. | 0.702220 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 256137. | 1.17446 | 0.587231 | − | 0.809419i | \(-0.300218\pi\) | ||||
0.587231 | + | 0.809419i | \(0.300218\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 156610.i | 0.711990i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 286182.i | − | 1.29003i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −48985.6 | −0.218951 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −109366. | − | 57315.9i | −0.484727 | − | 0.254032i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 119518.i | 0.525287i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −142256. | −0.620010 | −0.310005 | − | 0.950735i | \(-0.600331\pi\) | ||||
−0.310005 | + | 0.950735i | \(0.600331\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12676.4 | −0.0547907 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 116866.i | 0.500951i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 72029.6i | − | 0.306216i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 83814.6i | 0.353396i | 0.984265 | + | 0.176698i | \(0.0565416\pi\) | ||||
−0.984265 | + | 0.176698i | \(0.943458\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 501480.i | 2.09718i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −70233.1 | −0.291326 | −0.145663 | − | 0.989334i | \(-0.546531\pi\) | ||||
−0.145663 | + | 0.989334i | \(0.546531\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25859.5i | 0.106396i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 37143.7 | 0.151592 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 128135.i | − | 0.518747i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 382202. | 1.53494 | 0.767471 | − | 0.641083i | \(-0.221515\pi\) | ||||
0.767471 | + | 0.641083i | \(0.221515\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −104602. | −0.416741 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 454164. | 1.79505 | 0.897525 | − | 0.440964i | \(-0.145363\pi\) | ||||
0.897525 | + | 0.440964i | \(0.145363\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −73872.8 | −0.289669 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 263261.i | − | 1.02416i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 300805.i | − | 1.16105i | −0.814244 | − | 0.580523i | \(-0.802848\pi\) | ||
0.814244 | − | 0.580523i | \(-0.197152\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −214251. | −0.820505 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −88424.9 | + | 168726.i | −0.336000 | + | 0.641133i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 226917.i | − | 0.855565i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −186294. | −0.696975 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 457930. | 1.70006 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 488582.i | − | 1.79996i | −0.435935 | − | 0.899978i | \(-0.643582\pi\) | ||
0.435935 | − | 0.899978i | \(-0.356418\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4829.78i | 0.0176573i | 0.999961 | + | 0.00882864i | \(0.00281028\pi\) | ||||
−0.999961 | + | 0.00882864i | \(0.997190\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 139991.i | − | 0.507902i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 77065.8i | − | 0.277486i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −198309. | −0.708649 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 104127.i | − | 0.369297i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8654.46 | −0.0304639 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 359122.i | − | 1.25469i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 357726. | 1.24052 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −64285.8 | −0.221278 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −221949. | −0.758332 | −0.379166 | − | 0.925329i | \(-0.623789\pi\) | ||||
−0.379166 | + | 0.925329i | \(0.623789\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15977.6 | −0.0541891 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 254762.i | − | 0.857712i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 505454.i | 1.68930i | 0.535318 | + | 0.844651i | \(0.320192\pi\) | ||||
−0.535318 | + | 0.844651i | \(0.679808\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 89726.6 | 0.297699 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 47920.5 | − | 91438.7i | 0.157840 | − | 0.301180i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 398191.i | − | 1.30209i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9771.86 | 0.0317243 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 389257. | 1.25466 | 0.627329 | − | 0.778754i | \(-0.284148\pi\) | ||||
0.627329 | + | 0.778754i | \(0.284148\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 159861.i | − | 0.511587i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 67830.1i | − | 0.215525i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 75812.9i | − | 0.239181i | −0.992823 | − | 0.119590i | \(-0.961842\pi\) | ||
0.992823 | − | 0.119590i | \(-0.0381581\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 54690.7i | 0.171323i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −313563. | −0.975347 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 181331.i | 0.560077i | 0.959989 | + | 0.280039i | \(0.0903473\pi\) | ||||
−0.959989 | + | 0.280039i | \(0.909653\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37223.1 | 0.114167 | 0.0570835 | − | 0.998369i | \(-0.481820\pi\) | ||||
0.0570835 | + | 0.998369i | \(0.481820\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 179393.i | − | 0.546381i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −97664.4 | −0.295393 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 148028. | 0.444624 | 0.222312 | − | 0.974976i | \(-0.428640\pi\) | ||||
0.222312 | + | 0.974976i | \(0.428640\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −166278. | −0.495996 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 136872. | 0.405472 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 271484.i | − | 0.798742i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 121216.i | 0.354200i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34520.0 | −0.100183 | −0.0500915 | − | 0.998745i | \(-0.515951\pi\) | ||||
−0.0500915 | + | 0.998745i | \(0.515951\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −142811. | + | 272503.i | −0.411653 | + | 0.785489i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 174098.i | 0.498446i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 297841. | 0.846985 | 0.423492 | − | 0.905900i | \(-0.360804\pi\) | ||||
0.423492 | + | 0.905900i | \(0.360804\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 58781.2 | 0.166037 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 147238.i | 0.413115i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 76234.7i | 0.212471i | 0.994341 | + | 0.106235i | \(0.0338797\pi\) | ||||
−0.994341 | + | 0.106235i | \(0.966120\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 103183.i | − | 0.285667i | −0.989747 | − | 0.142833i | \(-0.954379\pi\) | ||
0.989747 | − | 0.142833i | \(-0.0456213\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 126358.i | − | 0.347511i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 161912. | 0.442353 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 445896.i | 1.21020i | 0.796150 | + | 0.605099i | \(0.206866\pi\) | ||||
−0.796150 | + | 0.605099i | \(0.793134\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 117043. | 0.315580 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 607957.i | − | 1.62851i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −74724.0 | −0.198856 | −0.0994281 | − | 0.995045i | \(-0.531701\pi\) | ||||
−0.0994281 | + | 0.995045i | \(0.531701\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6671.45 | 0.0176388 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 218592. | 0.574202 | 0.287101 | − | 0.957900i | \(-0.407308\pi\) | ||||
0.287101 | + | 0.957900i | \(0.407308\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −556223. | −1.45167 | −0.725835 | − | 0.687869i | \(-0.758546\pi\) | ||||
−0.725835 | + | 0.687869i | \(0.758546\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 150673.i | 0.390708i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 512937.i | 1.32156i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −59863.0 | −0.153249 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −125696. | + | 239845.i | −0.319733 | + | 0.610093i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 4959.75i | − | 0.0125360i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 237884. | 0.597458 | 0.298729 | − | 0.954338i | \(-0.403437\pi\) | ||||
0.298729 | + | 0.954338i | \(0.403437\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 340242. | 0.849143 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 285170.i | 0.707224i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 209792.i | − | 0.517024i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 103384.i | 0.253192i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 759808.i | − | 1.84922i | −0.380919 | − | 0.924608i | \(-0.624392\pi\) | ||
0.380919 | − | 0.924608i | \(-0.375608\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 239060. | 0.578208 | 0.289104 | − | 0.957298i | \(-0.406643\pi\) | ||||
0.289104 | + | 0.957298i | \(0.406643\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 123232.i | 0.296213i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 252454. | 0.603079 | 0.301540 | − | 0.953454i | \(-0.402499\pi\) | ||||
0.301540 | + | 0.953454i | \(0.402499\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 236524.i | 0.561547i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −348807. | −0.823044 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 61290.4 | 0.143736 | 0.0718681 | − | 0.997414i | \(-0.477104\pi\) | ||||
0.0718681 | + | 0.997414i | \(0.477104\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 48995.6 | 0.114202 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 172865. | 0.400476 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 115501.i | 0.265958i | 0.991119 | + | 0.132979i | \(0.0424543\pi\) | ||||
−0.991119 | + | 0.132979i | \(0.957546\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 185699.i | 0.425018i | 0.977159 | + | 0.212509i | \(0.0681635\pi\) | ||||
−0.977159 | + | 0.212509i | \(0.931837\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 221359. | 0.503582 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −207849. | − | 108928.i | −0.470007 | − | 0.246318i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 81654.9i | − | 0.183540i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −741040. | −1.65573 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −203813. | −0.452675 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 288265.i | 0.636446i | 0.948016 | + | 0.318223i | \(0.103086\pi\) | ||||
−0.948016 | + | 0.318223i | \(0.896914\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 180486.i | − | 0.396129i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 474041.i | 1.03428i | 0.855901 | + | 0.517141i | \(0.173004\pi\) | ||||
−0.855901 | + | 0.517141i | \(0.826996\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 165469.i | 0.358904i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −936953. | −2.02034 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 167789.i | 0.359685i | 0.983695 | + | 0.179843i | \(0.0575589\pi\) | ||||
−0.983695 | + | 0.179843i | \(0.942441\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −605342. | −1.29009 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 980380.i | 2.07721i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 885968. | 1.86629 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −519893. | −1.08882 | −0.544412 | − | 0.838818i | \(-0.683247\pi\) | ||||
−0.544412 | + | 0.838818i | \(0.683247\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −85328.0 | −0.177674 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19445.1 | 0.0402569 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3386.12i | − | 0.00697007i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 851964.i | − | 1.74368i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −440143. | −0.895691 | −0.447845 | − | 0.894111i | \(-0.647808\pi\) | ||||
−0.447845 | + | 0.894111i | \(0.647808\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9190.95 | + | 17537.6i | −0.0185973 | + | 0.0354861i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 468655.i | 0.942920i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 169703. | 0.339509 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −61143.5 | −0.121635 | −0.0608174 | − | 0.998149i | \(-0.519371\pi\) | ||||
−0.0608174 | + | 0.998149i | \(0.519371\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 321274.i | 0.635531i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 243345.i | 0.478679i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 275340.i | − | 0.538590i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 927241.i | 1.80366i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −313516. | −0.606459 | −0.303229 | − | 0.952918i | \(-0.598065\pi\) | ||||
−0.303229 | + | 0.952918i | \(0.598065\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 521283.i | 1.00277i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.01730e6 | 1.94614 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 97811.8i | 0.186087i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −213177. | −0.403340 | −0.201670 | − | 0.979454i | \(-0.564637\pi\) | ||||
−0.201670 | + | 0.979454i | \(0.564637\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −199708. | −0.375785 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 62546.9 | 0.117050 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 412494. | 0.767732 | 0.383866 | − | 0.923389i | \(-0.374592\pi\) | ||||
0.383866 | + | 0.923389i | \(0.374592\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 161722.i | 0.299361i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 287021.i | 0.528419i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −331782. | −0.607524 | −0.303762 | − | 0.952748i | \(-0.598243\pi\) | ||||
−0.303762 | + | 0.952748i | \(0.598243\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −782719. | − | 410202.i | −1.42551 | − | 0.747069i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 127921.i | − | 0.231721i | −0.993266 | − | 0.115860i | \(-0.963038\pi\) | ||
0.993266 | − | 0.115860i | \(-0.0369625\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −465200. | −0.838160 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −110433. | −0.197905 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 824990.i | 1.47057i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 757273.i | − | 1.34268i | −0.741149 | − | 0.671340i | \(-0.765719\pi\) | ||
0.741149 | − | 0.671340i | \(-0.234281\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 978654.i | − | 1.72599i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 175645.i | 0.308136i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.11167e6 | −1.93991 | −0.969957 | − | 0.243275i | \(-0.921778\pi\) | ||||
−0.969957 | + | 0.243275i | \(0.921778\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 214182.i | 0.371792i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 485750. | 0.838771 | 0.419386 | − | 0.907808i | \(-0.362246\pi\) | ||||
0.419386 | + | 0.907808i | \(0.362246\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 585249.i | 1.00529i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −47426.7 | −0.0810400 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −771880. | −1.31208 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 73393.4 | 0.124109 | 0.0620546 | − | 0.998073i | \(-0.480235\pi\) | ||||
0.0620546 | + | 0.998073i | \(0.480235\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 101395. | 0.170572 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 836995.i | − | 1.40076i | −0.713770 | − | 0.700380i | \(-0.753014\pi\) | ||
0.713770 | − | 0.700380i | \(-0.246986\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 291496.i | − | 0.485320i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22448.3 | −0.0371827 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6274.85 | + | 11973.2i | −0.0103402 | + | 0.0197304i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 234835.i | − | 0.385000i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 150900. | 0.246131 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 454519. | 0.737587 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 722223.i | − | 1.16606i | −0.812450 | − | 0.583031i | \(-0.801867\pi\) | ||
0.812450 | − | 0.583031i | \(-0.198133\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 291783.i | − | 0.468712i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 125637.i | − | 0.200801i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 665129.i | − | 1.05769i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −682965. | −1.08060 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 533741.i | − | 0.840260i | −0.907464 | − | 0.420130i | \(-0.861984\pi\) | ||
0.907464 | − | 0.420130i | \(-0.138016\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 237868. | 0.372599 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 413855.i | − | 0.645035i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −392661. | −0.608956 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −185609. | −0.286423 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.02811e6 | 1.57867 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 932045. | 1.42410 | 0.712049 | − | 0.702130i | \(-0.247767\pi\) | ||||
0.712049 | + | 0.702130i | \(0.247767\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 878103.i | 1.33507i | 0.744579 | + | 0.667534i | \(0.232650\pi\) | ||||
−0.744579 | + | 0.667534i | \(0.767350\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 556155.i | 0.841424i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −796459. | −1.19908 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −221164. | − | 115906.i | −0.331338 | − | 0.173645i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 278462.i | − | 0.415143i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −698577. | −1.03640 | −0.518201 | − | 0.855259i | \(-0.673398\pi\) | ||||
−0.518201 | + | 0.855259i | \(0.673398\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 351984. | 0.519665 | 0.259833 | − | 0.965654i | \(-0.416333\pi\) | ||||
0.259833 | + | 0.965654i | \(0.416333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 256562.i | − | 0.376951i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 237628.i | 0.347445i | 0.984795 | + | 0.173723i | \(0.0555797\pi\) | ||||
−0.984795 | + | 0.173723i | \(0.944420\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 818714.i | 1.19131i | 0.803242 | + | 0.595653i | \(0.203107\pi\) | ||||
−0.803242 | + | 0.595653i | \(0.796893\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 333005.i | 0.482224i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 82082.9 | 0.118294 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 166132.i | − | 0.238275i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −449708. | −0.641919 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 78055.7i | 0.110887i | 0.998462 | + | 0.0554435i | \(0.0176573\pi\) | ||||
−0.998462 | + | 0.0554435i | \(0.982343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 625503. | 0.884377 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.62280e6 | −2.28355 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 418115. | 0.585575 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −371951. | −0.518465 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 198223.i | 0.275003i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15661.1i | 0.0216253i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 841991. | 1.15720 | 0.578602 | − | 0.815610i | \(-0.303599\pi\) | ||||
0.578602 | + | 0.815610i | \(0.303599\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 167699. | + | 87886.7i | 0.229403 | + | 0.120224i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 699074.i | − | 0.951835i | −0.879490 | − | 0.475917i | \(-0.842116\pi\) | ||
0.879490 | − | 0.475917i | \(-0.157884\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 171528. | 0.232461 | 0.116230 | − | 0.993222i | \(-0.462919\pi\) | ||||
0.116230 | + | 0.993222i | \(0.462919\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15325.9 | −0.0206738 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 674012.i | − | 0.904994i | −0.891766 | − | 0.452497i | \(-0.850533\pi\) | ||
0.891766 | − | 0.452497i | \(-0.149467\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 727293.i | 0.972025i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 797999.i | − | 1.06161i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 729770.i | − | 0.966376i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −936674. | −1.23467 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 133506.i | − | 0.175175i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 628607. | 0.821038 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 969510.i | 1.26053i | 0.776380 | + | 0.630265i | \(0.217054\pi\) | ||||
−0.776380 | + | 0.630265i | \(0.782946\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.43325e6 | −1.85500 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.14587e6 | 1.47633 | 0.738164 | − | 0.674622i | \(-0.235693\pi\) | ||||
0.738164 | + | 0.674622i | \(0.235693\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.46931e6 | 1.88449 | 0.942243 | − | 0.334930i | \(-0.108713\pi\) | ||||
0.942243 | + | 0.334930i | \(0.108713\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 595018. | 0.759702 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 336843.i | 0.428134i | 0.976819 | + | 0.214067i | \(0.0686711\pi\) | ||||
−0.976819 | + | 0.214067i | \(0.931329\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 655104.i | − | 0.828909i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −574671. | −0.723876 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −841094. | − | 440794.i | −1.05473 | − | 0.552756i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 568148.i | 0.709276i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −698969. | −0.868707 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 243713. | 0.301549 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 346642.i | 0.427003i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 283093.i | − | 0.347179i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 25375.9i | − | 0.0309831i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 977089.i | 1.18774i | 0.804563 | + | 0.593868i | \(0.202400\pi\) | ||||
−0.804563 | + | 0.593868i | \(0.797600\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −136922. | −0.165709 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 233208.i | − | 0.281001i | −0.990081 | − | 0.140500i | \(-0.955129\pi\) | ||
0.990081 | − | 0.140500i | \(-0.0448711\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 250846. | 0.300930 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 512727.i | 0.612413i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −112555. | −0.133852 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 672066. | 0.795757 | 0.397879 | − | 0.917438i | \(-0.369747\pi\) | ||||
0.397879 | + | 0.917438i | \(0.369747\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −90542.0 | −0.106741 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 766368. | 0.899568 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 18759.9i | − | 0.0219254i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 420589.i | − | 0.489438i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 199293. | 0.230919 | 0.115460 | − | 0.993312i | \(-0.463166\pi\) | ||||
0.115460 | + | 0.993312i | \(0.463166\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −290243. | − | 152108.i | −0.334859 | − | 0.175491i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.58340e6i | 1.81897i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 107729. | 0.123228 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.10180e6 | −1.25494 | −0.627471 | − | 0.778640i | \(-0.715910\pi\) | ||||
−0.627471 | + | 0.778640i | \(0.715910\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 339747.i | 0.385323i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 743721.i | 0.839906i | 0.907546 | + | 0.419953i | \(0.137953\pi\) | ||||
−0.907546 | + | 0.419953i | \(0.862047\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10692.1i | 0.0120238i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 343011.i | − | 0.384100i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 957119. | 1.06725 | 0.533625 | − | 0.845721i | \(-0.320830\pi\) | ||||
0.533625 | + | 0.845721i | \(0.320830\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.28142e6i | − | 1.42285i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.35262e6 | 1.49560 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 253186.i | 0.278775i | 0.990238 | + | 0.139387i | \(0.0445133\pi\) | ||||
−0.990238 | + | 0.139387i | \(0.955487\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 284915. | 0.312398 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 214506. | 0.234215 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.39061e6 | 1.51206 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 197217. | 0.213549 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 665629.i | − | 0.717761i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 264086.i | − | 0.283590i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −98571.4 | −0.105414 | −0.0527070 | − | 0.998610i | \(-0.516785\pi\) | ||||
−0.0527070 | + | 0.998610i | \(0.516785\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 160494. | − | 306245.i | 0.170928 | − | 0.326153i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.58528e6i | 1.68138i | 0.541515 | + | 0.840691i | \(0.317851\pi\) | ||||
−0.541515 | + | 0.840691i | \(0.682149\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44670.0 | −0.0471835 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 837273. | 0.880761 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 789090.i | 0.826680i | 0.910577 | + | 0.413340i | \(0.135638\pi\) | ||||
−0.910577 | + | 0.413340i | \(0.864362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 940066.i | 0.980828i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 472198.i | − | 0.490666i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1.54784e6i | − | 1.60184i | −0.598773 | − | 0.800919i | \(-0.704345\pi\) | ||
0.598773 | − | 0.800919i | \(-0.295655\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −276505. | −0.284991 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 1.07661e6i | − | 1.10516i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −197500. | −0.201918 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 860729.i | − | 0.876434i | −0.898869 | − | 0.438217i | \(-0.855610\pi\) | ||
0.898869 | − | 0.438217i | \(-0.144390\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 594089. | 0.602494 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −233846. | −0.236202 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 770151. | 0.774793 | 0.387396 | − | 0.921913i | \(-0.373375\pi\) | ||||
0.387396 | + | 0.921913i | \(0.373375\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28942.0 | −0.0290000 |
(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 | 304.5.e.d.113.3 | 4 | ||
4.3 | odd | 2 | 76.5.c.b.37.2 | ✓ | 4 | ||
12.11 | even | 2 | 684.5.h.c.37.4 | 4 | |||
19.18 | odd | 2 | inner | 304.5.e.d.113.2 | 4 | ||
76.75 | even | 2 | 76.5.c.b.37.3 | yes | 4 | ||
228.227 | odd | 2 | 684.5.h.c.37.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.c.b.37.2 | ✓ | 4 | 4.3 | odd | 2 | ||
76.5.c.b.37.3 | yes | 4 | 76.75 | even | 2 | ||
304.5.e.d.113.2 | 4 | 19.18 | odd | 2 | inner | ||
304.5.e.d.113.3 | 4 | 1.1 | even | 1 | trivial | ||
684.5.h.c.37.3 | 4 | 228.227 | odd | 2 | |||
684.5.h.c.37.4 | 4 | 12.11 | even | 2 |