Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(199,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.199");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.b (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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.3 | ||
Root | \(2.17945 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.199 |
Dual form | 225.4.b.h.199.2 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.35890i | 1.18755i | 0.804631 | + | 0.593775i | \(0.202363\pi\) | ||||
−0.804631 | + | 0.593775i | \(0.797637\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.28220 | −0.410275 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 30.4356i | − 1.64337i | −0.569944 | − | 0.821684i | \(-0.693035\pi\) | ||||
0.569944 | − | 0.821684i | \(-0.306965\pi\) | |||||||
\(8\) | 15.8466i | 0.700328i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −31.4356 | −0.861654 | −0.430827 | − | 0.902435i | \(-0.641778\pi\) | ||||
−0.430827 | + | 0.902435i | \(0.641778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 60.7424i | − 1.29592i | −0.761676 | − | 0.647958i | \(-0.775623\pi\) | ||||
0.761676 | − | 0.647958i | \(-0.224377\pi\) | |||||||
\(14\) | 102.230 | 1.95158 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −79.4848 | −1.24195 | ||||||||
\(17\) | − 121.178i | − 1.72882i | −0.502786 | − | 0.864411i | \(-0.667692\pi\) | ||||
0.502786 | − | 0.864411i | \(-0.332308\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.4356 | 0.174303 | 0.0871514 | − | 0.996195i | \(-0.472224\pi\) | ||||
0.0871514 | + | 0.996195i | \(0.472224\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 105.589i | − 1.02326i | ||||||||
\(23\) | − 13.6932i | − 0.124141i | −0.998072 | − | 0.0620703i | \(-0.980230\pi\) | ||||
0.998072 | − | 0.0620703i | \(-0.0197703\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 204.028 | 1.53896 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 99.8958i | 0.674233i | ||||||||
\(29\) | −76.0492 | −0.486965 | −0.243482 | − | 0.969905i | \(-0.578290\pi\) | ||||
−0.243482 | + | 0.969905i | \(0.578290\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 183.049 | 1.06054 | 0.530268 | − | 0.847830i | \(-0.322091\pi\) | ||||
0.530268 | + | 0.847830i | \(0.322091\pi\) | |||||||
\(32\) | − 140.208i | − 0.774550i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 407.025 | 2.05306 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 37.3864i | 0.166116i | 0.996545 | + | 0.0830580i | \(0.0264687\pi\) | ||||
−0.996545 | + | 0.0830580i | \(0.973531\pi\) | |||||||
\(38\) | 48.4877i | 0.206993i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 30.6627 | 0.116798 | 0.0583990 | − | 0.998293i | \(-0.481400\pi\) | ||||
0.0583990 | + | 0.998293i | \(0.481400\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 327.564i | 1.16170i | 0.814011 | + | 0.580850i | \(0.197280\pi\) | ||||
−0.814011 | + | 0.580850i | \(0.802720\pi\) | |||||||
\(44\) | 103.178 | 0.353515 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 45.9941 | 0.147423 | ||||||||
\(47\) | − 449.485i | − 1.39498i | −0.716594 | − | 0.697490i | \(-0.754300\pi\) | ||||
0.716594 | − | 0.697490i | \(-0.245700\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −583.325 | −1.70066 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 199.369i | 0.531682i | ||||||||
\(53\) | 301.951i | 0.782569i | 0.920270 | + | 0.391284i | \(0.127969\pi\) | ||||
−0.920270 | + | 0.391284i | \(0.872031\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 482.301 | 1.15090 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 255.441i | − 0.578295i | ||||||||
\(59\) | 340.970 | 0.752381 | 0.376190 | − | 0.926542i | \(-0.377234\pi\) | ||||
0.376190 | + | 0.926542i | \(0.377234\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 619.098 | 1.29947 | 0.649733 | − | 0.760163i | \(-0.274881\pi\) | ||||
0.649733 | + | 0.760163i | \(0.274881\pi\) | |||||||
\(62\) | 614.844i | 1.25944i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −164.932 | −0.322133 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 256.890i | − 0.468419i | −0.972186 | − | 0.234210i | \(-0.924750\pi\) | ||||
0.972186 | − | 0.234210i | \(-0.0752502\pi\) | |||||||
\(68\) | 397.731i | 0.709293i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −499.178 | −0.834388 | −0.417194 | − | 0.908818i | \(-0.636986\pi\) | ||||
−0.417194 | + | 0.908818i | \(0.636986\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 19.1288i | − 0.0306693i | −0.999882 | − | 0.0153346i | \(-0.995119\pi\) | ||||
0.999882 | − | 0.0153346i | \(-0.00488136\pi\) | |||||||
\(74\) | −125.577 | −0.197271 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −47.3805 | −0.0715121 | ||||||||
\(77\) | 956.761i | 1.41601i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −257.424 | −0.366613 | −0.183307 | − | 0.983056i | \(-0.558680\pi\) | ||||
−0.183307 | + | 0.983056i | \(0.558680\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 102.993i | 0.138703i | ||||||||
\(83\) | − 914.909i | − 1.20993i | −0.796252 | − | 0.604965i | \(-0.793187\pi\) | ||||
0.796252 | − | 0.604965i | \(-0.206813\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1100.26 | −1.37958 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 498.148i | − 0.603440i | ||||||||
\(89\) | −1059.68 | −1.26209 | −0.631045 | − | 0.775746i | \(-0.717374\pi\) | ||||
−0.631045 | + | 0.775746i | \(0.717374\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1848.73 | −2.12967 | ||||||||
\(92\) | 44.9439i | 0.0509318i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1509.77 | 1.65661 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 521.000i | − 0.545356i | −0.962105 | − | 0.272678i | \(-0.912091\pi\) | ||||
0.962105 | − | 0.272678i | \(-0.0879094\pi\) | |||||||
\(98\) | − 1959.33i | − 2.01962i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −347.080 | −0.341938 | −0.170969 | − | 0.985276i | \(-0.554690\pi\) | ||||
−0.170969 | + | 0.985276i | \(0.554690\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 770.749i | − 0.737322i | −0.929564 | − | 0.368661i | \(-0.879816\pi\) | ||||
0.929564 | − | 0.368661i | \(-0.120184\pi\) | |||||||
\(104\) | 962.561 | 0.907566 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1014.22 | −0.929339 | ||||||||
\(107\) | − 1415.37i | − 1.27878i | −0.768883 | − | 0.639390i | \(-0.779187\pi\) | ||||
0.768883 | − | 0.639390i | \(-0.220813\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −908.386 | −0.798235 | −0.399118 | − | 0.916900i | \(-0.630683\pi\) | ||||
−0.399118 | + | 0.916900i | \(0.630683\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2419.17i | 2.04098i | ||||||||
\(113\) | 2049.94i | 1.70657i | 0.521447 | + | 0.853283i | \(0.325392\pi\) | ||||
−0.521447 | + | 0.853283i | \(0.674608\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 249.609 | 0.199790 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1145.28i | 0.893490i | ||||||||
\(119\) | −3688.12 | −2.84109 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −342.803 | −0.257553 | ||||||||
\(122\) | 2079.49i | 1.54318i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −600.804 | −0.435111 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 281.644i | − 0.196786i | −0.995148 | − | 0.0983932i | \(-0.968630\pi\) | ||||
0.995148 | − | 0.0983932i | \(-0.0313703\pi\) | |||||||
\(128\) | − 1675.66i | − 1.15710i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −243.056 | −0.162106 | −0.0810531 | − | 0.996710i | \(-0.525828\pi\) | ||||
−0.0810531 | + | 0.996710i | \(0.525828\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 439.356i | − 0.286444i | ||||||||
\(134\) | 862.867 | 0.556271 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1920.26 | 1.21074 | ||||||||
\(137\) | 909.386i | 0.567110i | 0.958956 | + | 0.283555i | \(0.0915139\pi\) | ||||
−0.958956 | + | 0.283555i | \(0.908486\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2049.52 | 1.25063 | 0.625317 | − | 0.780371i | \(-0.284970\pi\) | ||||
0.625317 | + | 0.780371i | \(0.284970\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 1676.69i | − 0.990877i | ||||||||
\(143\) | 1909.47i | 1.11663i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 64.2517 | 0.0364213 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 122.710i | − 0.0681533i | ||||||||
\(149\) | 3601.14 | 1.97998 | 0.989990 | − | 0.141136i | \(-0.0450753\pi\) | ||||
0.989990 | + | 0.141136i | \(0.0450753\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1383.38 | 0.745550 | 0.372775 | − | 0.927922i | \(-0.378406\pi\) | ||||
0.372775 | + | 0.927922i | \(0.378406\pi\) | |||||||
\(152\) | 228.755i | 0.122069i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3213.66 | −1.68159 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 131.749i | 0.0669729i | 0.999439 | + | 0.0334864i | \(0.0106611\pi\) | ||||
−0.999439 | + | 0.0334864i | \(0.989339\pi\) | |||||||
\(158\) | − 864.661i | − 0.435372i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −416.761 | −0.204009 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2897.74i | 1.39244i | 0.717827 | + | 0.696222i | \(0.245137\pi\) | ||||
−0.717827 | + | 0.696222i | \(0.754863\pi\) | |||||||
\(164\) | −100.641 | −0.0479193 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3073.09 | 1.43685 | ||||||||
\(167\) | 260.283i | 0.120607i | 0.998180 | + | 0.0603034i | \(0.0192068\pi\) | ||||
−0.998180 | + | 0.0603034i | \(0.980793\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1492.64 | −0.679398 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 1075.13i | − 0.476617i | ||||||||
\(173\) | 1935.83i | 0.850742i | 0.905019 | + | 0.425371i | \(0.139856\pi\) | ||||
−0.905019 | + | 0.425371i | \(0.860144\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2498.65 | 1.07013 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 3559.36i | − 1.49880i | ||||||||
\(179\) | 576.627 | 0.240777 | 0.120389 | − | 0.992727i | \(-0.461586\pi\) | ||||
0.120389 | + | 0.992727i | \(0.461586\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1962.04 | −0.805733 | −0.402866 | − | 0.915259i | \(-0.631986\pi\) | ||||
−0.402866 | + | 0.915259i | \(0.631986\pi\) | |||||||
\(182\) | − 6209.70i | − 2.52909i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 216.991 | 0.0869390 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3809.30i | 1.48965i | ||||||||
\(188\) | 1475.30i | 0.572326i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4318.75 | 1.63609 | 0.818047 | − | 0.575152i | \(-0.195057\pi\) | ||||
0.818047 | + | 0.575152i | \(0.195057\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.97647i | 0.00111011i | 1.00000 | 0.000555054i | \(0.000176679\pi\) | |||||
−1.00000 | 0.000555054i | \(0.999823\pi\) | ||||||||
\(194\) | 1749.99 | 0.647638 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1914.59 | 0.697738 | ||||||||
\(197\) | 569.705i | 0.206040i | 0.994679 | + | 0.103020i | \(0.0328505\pi\) | ||||
−0.994679 | + | 0.103020i | \(0.967149\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3050.73 | 1.08674 | 0.543368 | − | 0.839494i | \(-0.317149\pi\) | ||||
0.543368 | + | 0.839494i | \(0.317149\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 1165.81i | − 0.406068i | ||||||||
\(203\) | 2314.60i | 0.800262i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2588.87 | 0.875607 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4828.09i | 1.60946i | ||||||||
\(209\) | −453.792 | −0.150189 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −50.5104 | −0.0164800 | −0.00824000 | − | 0.999966i | \(-0.502623\pi\) | ||||
−0.00824000 | + | 0.999966i | \(0.502623\pi\) | |||||||
\(212\) | − 991.064i | − 0.321069i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4754.10 | 1.51862 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 5571.21i | − 1.74285i | ||||||||
\(218\) | − 3051.18i | − 0.947944i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7360.64 | −2.24041 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5453.55i | 1.63765i | 0.574040 | + | 0.818827i | \(0.305375\pi\) | ||||
−0.574040 | + | 0.818827i | \(0.694625\pi\) | |||||||
\(224\) | −4267.33 | −1.27287 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6885.54 | −2.02663 | ||||||||
\(227\) | − 4777.14i | − 1.39678i | −0.715715 | − | 0.698392i | \(-0.753899\pi\) | ||||
0.715715 | − | 0.698392i | \(-0.246101\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2085.51 | 0.601808 | 0.300904 | − | 0.953654i | \(-0.402712\pi\) | ||||
0.300904 | + | 0.953654i | \(0.402712\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 1205.12i | − 0.341035i | ||||||||
\(233\) | − 6484.53i | − 1.82324i | −0.411030 | − | 0.911622i | \(-0.634831\pi\) | ||||
0.411030 | − | 0.911622i | \(-0.365169\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1119.13 | −0.308683 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 12388.0i | − 3.37394i | ||||||||
\(239\) | 2234.62 | 0.604792 | 0.302396 | − | 0.953182i | \(-0.402214\pi\) | ||||
0.302396 | + | 0.953182i | \(0.402214\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2393.01 | −0.639616 | −0.319808 | − | 0.947482i | \(-0.603618\pi\) | ||||
−0.319808 | + | 0.947482i | \(0.603618\pi\) | |||||||
\(242\) | − 1151.44i | − 0.305857i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2032.01 | −0.533139 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 876.852i | − 0.225882i | ||||||||
\(248\) | 2900.71i | 0.742722i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 612.661 | 0.154067 | 0.0770335 | − | 0.997029i | \(-0.475455\pi\) | ||||
0.0770335 | + | 0.997029i | \(0.475455\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 430.454i | 0.106966i | ||||||||
\(254\) | 946.014 | 0.233694 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4308.91 | 1.05198 | ||||||||
\(257\) | − 306.112i | − 0.0742987i | −0.999310 | − | 0.0371493i | \(-0.988172\pi\) | ||||
0.999310 | − | 0.0371493i | \(-0.0118277\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1137.88 | 0.272990 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 816.401i | − 0.192509i | ||||||||
\(263\) | − 283.839i | − 0.0665484i | −0.999446 | − | 0.0332742i | \(-0.989407\pi\) | ||||
0.999446 | − | 0.0332742i | \(-0.0105935\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1475.75 | 0.340166 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 843.165i | 0.192181i | ||||||||
\(269\) | 2426.21 | 0.549920 | 0.274960 | − | 0.961456i | \(-0.411335\pi\) | ||||
0.274960 | + | 0.961456i | \(0.411335\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −174.946 | −0.0392148 | −0.0196074 | − | 0.999808i | \(-0.506242\pi\) | ||||
−0.0196074 | + | 0.999808i | \(0.506242\pi\) | |||||||
\(272\) | 9631.80i | 2.14711i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3054.54 | −0.673472 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7807.07i | 1.69344i | 0.532042 | + | 0.846718i | \(0.321425\pi\) | ||||
−0.532042 | + | 0.846718i | \(0.678575\pi\) | |||||||
\(278\) | 6884.14i | 1.48519i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −584.171 | −0.124017 | −0.0620084 | − | 0.998076i | \(-0.519751\pi\) | ||||
−0.0620084 | + | 0.998076i | \(0.519751\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 5897.31i | − 1.23872i | −0.785106 | − | 0.619362i | \(-0.787391\pi\) | ||||
0.785106 | − | 0.619362i | \(-0.212609\pi\) | |||||||
\(284\) | 1638.40 | 0.342329 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6413.73 | −1.32605 | ||||||||
\(287\) | − 933.239i | − 0.191942i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9771.10 | −1.98883 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 62.7846i | 0.0125828i | ||||||||
\(293\) | − 1609.73i | − 0.320960i | −0.987039 | − | 0.160480i | \(-0.948696\pi\) | ||||
0.987039 | − | 0.160480i | \(-0.0513042\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −592.448 | −0.116336 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12095.9i | 2.35133i | ||||||||
\(299\) | −831.758 | −0.160876 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9969.62 | 1.90910 | ||||||||
\(302\) | 4646.64i | 0.885378i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1147.41 | −0.216475 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 234.473i | − 0.0435898i | −0.999762 | − | 0.0217949i | \(-0.993062\pi\) | ||||
0.999762 | − | 0.0217949i | \(-0.00693809\pi\) | |||||||
\(308\) | − 3140.28i | − 0.580955i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1795.25 | 0.327329 | 0.163665 | − | 0.986516i | \(-0.447669\pi\) | ||||
0.163665 | + | 0.986516i | \(0.447669\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 8440.61i | − 1.52425i | −0.647427 | − | 0.762127i | \(-0.724155\pi\) | ||||
0.647427 | − | 0.762127i | \(-0.275845\pi\) | |||||||
\(314\) | −442.533 | −0.0795336 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 844.917 | 0.150412 | ||||||||
\(317\) | 10551.7i | 1.86953i | 0.355264 | + | 0.934766i | \(0.384391\pi\) | ||||
−0.355264 | + | 0.934766i | \(0.615609\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2390.65 | 0.419595 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 1399.86i | − 0.242270i | ||||||||
\(323\) | − 1749.28i | − 0.301339i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9733.21 | −1.65360 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 485.900i | 0.0817968i | ||||||||
\(329\) | −13680.3 | −2.29247 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6743.17 | 1.11975 | 0.559876 | − | 0.828576i | \(-0.310849\pi\) | ||||
0.559876 | + | 0.828576i | \(0.310849\pi\) | |||||||
\(332\) | 3002.91i | 0.496405i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −874.265 | −0.143227 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8437.26i | 1.36382i | 0.731437 | + | 0.681909i | \(0.238850\pi\) | ||||
−0.731437 | + | 0.681909i | \(0.761150\pi\) | |||||||
\(338\) | − 5013.62i | − 0.806819i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5754.26 | −0.913814 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7314.45i | 1.15144i | ||||||||
\(344\) | −5190.78 | −0.813571 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6502.25 | −1.01030 | ||||||||
\(347\) | − 1848.85i | − 0.286027i | −0.989721 | − | 0.143013i | \(-0.954321\pi\) | ||||
0.989721 | − | 0.143013i | \(-0.0456792\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1148.38 | 0.176136 | 0.0880678 | − | 0.996114i | \(-0.471931\pi\) | ||||
0.0880678 | + | 0.996114i | \(0.471931\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4407.54i | 0.667393i | ||||||||
\(353\) | 5753.60i | 0.867516i | 0.901029 | + | 0.433758i | \(0.142813\pi\) | ||||
−0.901029 | + | 0.433758i | \(0.857187\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3478.09 | 0.517804 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1936.83i | 0.285935i | ||||||||
\(359\) | 5452.01 | 0.801521 | 0.400761 | − | 0.916183i | \(-0.368746\pi\) | ||||
0.400761 | + | 0.916183i | \(0.368746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6650.61 | −0.969619 | ||||||||
\(362\) | − 6590.31i | − 0.956848i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6067.91 | 0.873749 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 8385.93i | − 1.19276i | −0.802703 | − | 0.596379i | \(-0.796606\pi\) | ||||
0.802703 | − | 0.596379i | \(-0.203394\pi\) | |||||||
\(368\) | 1088.40i | 0.154176i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9190.05 | 1.28605 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2728.30i | 0.378730i | 0.981907 | + | 0.189365i | \(0.0606429\pi\) | ||||
−0.981907 | + | 0.189365i | \(0.939357\pi\) | |||||||
\(374\) | −12795.1 | −1.76903 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7122.81 | 0.976944 | ||||||||
\(377\) | 4619.41i | 0.631065i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3348.99 | −0.453895 | −0.226947 | − | 0.973907i | \(-0.572875\pi\) | ||||
−0.226947 | + | 0.973907i | \(0.572875\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14506.2i | 1.94294i | ||||||||
\(383\) | − 10430.3i | − 1.39155i | −0.718261 | − | 0.695774i | \(-0.755062\pi\) | ||||
0.718261 | − | 0.695774i | \(-0.244938\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.99766 | −0.00131831 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1710.03i | 0.223746i | ||||||||
\(389\) | 9827.23 | 1.28088 | 0.640438 | − | 0.768010i | \(-0.278753\pi\) | ||||
0.640438 | + | 0.768010i | \(0.278753\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1659.32 | −0.214617 | ||||||||
\(392\) | − 9243.73i | − 1.19102i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1913.58 | −0.244682 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 436.382i | 0.0551672i | 0.999619 | + | 0.0275836i | \(0.00878125\pi\) | ||||
−0.999619 | + | 0.0275836i | \(0.991219\pi\) | |||||||
\(398\) | 10247.1i | 1.29055i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14501.5 | 1.80591 | 0.902955 | − | 0.429736i | \(-0.141393\pi\) | ||||
0.902955 | + | 0.429736i | \(0.141393\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 11118.8i | − 1.37436i | ||||||||
\(404\) | 1139.19 | 0.140289 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7774.51 | −0.950351 | ||||||||
\(407\) | − 1175.26i | − 0.143134i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12058.4 | 1.45782 | 0.728911 | − | 0.684609i | \(-0.240027\pi\) | ||||
0.728911 | + | 0.684609i | \(0.240027\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2529.76i | 0.302505i | ||||||||
\(413\) | − 10377.6i | − 1.23644i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −8516.60 | −1.00375 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 1524.24i | − 0.178356i | ||||||||
\(419\) | 6042.95 | 0.704577 | 0.352288 | − | 0.935892i | \(-0.385404\pi\) | ||||
0.352288 | + | 0.935892i | \(0.385404\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9994.67 | −1.15703 | −0.578516 | − | 0.815671i | \(-0.696368\pi\) | ||||
−0.578516 | + | 0.815671i | \(0.696368\pi\) | |||||||
\(422\) | − 169.659i | − 0.0195708i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4784.90 | −0.548054 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 18842.6i | − 2.13550i | ||||||||
\(428\) | 4645.55i | 0.524652i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9327.32 | −1.04242 | −0.521208 | − | 0.853430i | \(-0.674518\pi\) | ||||
−0.521208 | + | 0.853430i | \(0.674518\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 7861.22i | − 0.872485i | −0.899829 | − | 0.436243i | \(-0.856309\pi\) | ||||
0.899829 | − | 0.436243i | \(-0.143691\pi\) | |||||||
\(434\) | 18713.1 | 2.06972 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2981.51 | 0.327496 | ||||||||
\(437\) | − 197.670i | − 0.0216380i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7412.06 | −0.805828 | −0.402914 | − | 0.915238i | \(-0.632003\pi\) | ||||
−0.402914 | + | 0.915238i | \(0.632003\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 24723.6i | − 2.66060i | ||||||||
\(443\) | 3043.66i | 0.326430i | 0.986591 | + | 0.163215i | \(0.0521864\pi\) | ||||
−0.986591 | + | 0.163215i | \(0.947814\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −18317.9 | −1.94480 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5019.81i | 0.529383i | ||||||||
\(449\) | −9547.87 | −1.00355 | −0.501773 | − | 0.864999i | \(-0.667319\pi\) | ||||
−0.501773 | + | 0.864999i | \(0.667319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −963.902 | −0.100639 | ||||||||
\(452\) | − 6728.31i | − 0.700162i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16045.9 | 1.65875 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 13401.9i | − 1.37180i | −0.727695 | − | 0.685901i | \(-0.759408\pi\) | ||||
0.727695 | − | 0.685901i | \(-0.240592\pi\) | |||||||
\(458\) | 7005.00i | 0.714677i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4137.03 | 0.417962 | 0.208981 | − | 0.977920i | \(-0.432985\pi\) | ||||
0.208981 | + | 0.977920i | \(0.432985\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 13976.3i | − 1.40288i | −0.712729 | − | 0.701439i | \(-0.752541\pi\) | ||||
0.712729 | − | 0.701439i | \(-0.247459\pi\) | |||||||
\(464\) | 6044.75 | 0.604786 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21780.9 | 2.16519 | ||||||||
\(467\) | − 10796.5i | − 1.06982i | −0.844910 | − | 0.534908i | \(-0.820346\pi\) | ||||
0.844910 | − | 0.534908i | \(-0.179654\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7818.60 | −0.769785 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5403.21i | 0.526913i | ||||||||
\(473\) | − 10297.2i | − 1.00098i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12105.2 | 1.16563 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7505.85i | 0.718221i | ||||||||
\(479\) | 14568.4 | 1.38966 | 0.694830 | − | 0.719174i | \(-0.255479\pi\) | ||||
0.694830 | + | 0.719174i | \(0.255479\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2270.94 | 0.215272 | ||||||||
\(482\) | − 8037.89i | − 0.759577i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1125.15 | 0.105668 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11456.6i | 1.06601i | 0.846113 | + | 0.533004i | \(0.178937\pi\) | ||||
−0.846113 | + | 0.533004i | \(0.821063\pi\) | |||||||
\(488\) | 9810.61i | 0.910052i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19666.5 | 1.80761 | 0.903804 | − | 0.427948i | \(-0.140763\pi\) | ||||
0.903804 | + | 0.427948i | \(0.140763\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9215.48i | 0.841875i | ||||||||
\(494\) | 2945.26 | 0.268246 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14549.6 | −1.31713 | ||||||||
\(497\) | 15192.8i | 1.37121i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8379.31 | −0.751722 | −0.375861 | − | 0.926676i | \(-0.622653\pi\) | ||||
−0.375861 | + | 0.926676i | \(0.622653\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2057.87i | 0.182962i | ||||||||
\(503\) | 15678.1i | 1.38976i | 0.719124 | + | 0.694881i | \(0.244543\pi\) | ||||
−0.719124 | + | 0.694881i | \(0.755457\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1445.85 | −0.127028 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 924.413i | 0.0807366i | ||||||||
\(509\) | −17037.3 | −1.48363 | −0.741813 | − | 0.670606i | \(-0.766034\pi\) | ||||
−0.741813 | + | 0.670606i | \(0.766034\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −582.197 | −0.0504009 | ||||||||
\(512\) | 1067.93i | 0.0921798i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1028.20 | 0.0882334 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14129.8i | 1.20199i | ||||||||
\(518\) | 3822.02i | 0.324189i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8776.12 | 0.737982 | 0.368991 | − | 0.929433i | \(-0.379703\pi\) | ||||
0.368991 | + | 0.929433i | \(0.379703\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11120.4i | 0.929753i | 0.885375 | + | 0.464877i | \(0.153901\pi\) | ||||
−0.885375 | + | 0.464877i | \(0.846099\pi\) | |||||||
\(524\) | 797.759 | 0.0665082 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 953.385 | 0.0790296 | ||||||||
\(527\) | − 22181.5i | − 1.83348i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11979.5 | 0.984589 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1442.06i | 0.117521i | ||||||||
\(533\) | − 1862.53i | − 0.151360i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4070.83 | 0.328047 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8149.39i | 0.653058i | ||||||||
\(539\) | 18337.2 | 1.46538 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21730.6 | 1.72693 | 0.863467 | − | 0.504405i | \(-0.168288\pi\) | ||||
0.863467 | + | 0.504405i | \(0.168288\pi\) | |||||||
\(542\) | − 587.626i | − 0.0465695i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −16990.2 | −1.33906 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6926.17i | 0.541392i | 0.962665 | + | 0.270696i | \(0.0872539\pi\) | ||||
−0.962665 | + | 0.270696i | \(0.912746\pi\) | |||||||
\(548\) | − 2984.79i | − 0.232671i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1097.82 | −0.0848793 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7834.85i | 0.602480i | ||||||||
\(554\) | −26223.2 | −2.01104 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6726.95 | −0.513104 | ||||||||
\(557\) | − 6589.22i | − 0.501246i | −0.968085 | − | 0.250623i | \(-0.919364\pi\) | ||||
0.968085 | − | 0.250623i | \(-0.0806355\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19897.0 | 1.50547 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 1962.17i | − 0.147276i | ||||||||
\(563\) | − 3839.63i | − 0.287426i | −0.989619 | − | 0.143713i | \(-0.954096\pi\) | ||||
0.989619 | − | 0.143713i | \(-0.0459043\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 19808.5 | 1.47105 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 7910.28i | − 0.584345i | ||||||||
\(569\) | −20874.0 | −1.53794 | −0.768968 | − | 0.639287i | \(-0.779229\pi\) | ||||
−0.768968 | + | 0.639287i | \(0.779229\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21175.9 | 1.55199 | 0.775994 | − | 0.630740i | \(-0.217248\pi\) | ||||
0.775994 | + | 0.630740i | \(0.217248\pi\) | |||||||
\(572\) | − 6267.28i | − 0.458126i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3134.66 | 0.227941 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14924.2i | 1.07678i | 0.842695 | + | 0.538391i | \(0.180968\pi\) | ||||
−0.842695 | + | 0.538391i | \(0.819032\pi\) | |||||||
\(578\) | − 32820.1i | − 2.36183i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27845.8 | −1.98836 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 9492.00i | − 0.674303i | ||||||||
\(584\) | 303.127 | 0.0214785 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5406.92 | 0.381156 | ||||||||
\(587\) | 25218.0i | 1.77318i | 0.462552 | + | 0.886592i | \(0.346934\pi\) | ||||
−0.462552 | + | 0.886592i | \(0.653066\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2642.42 | 0.184854 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 2971.65i | − 0.206308i | ||||||||
\(593\) | − 5011.77i | − 0.347063i | −0.984828 | − | 0.173532i | \(-0.944482\pi\) | ||||
0.984828 | − | 0.173532i | \(-0.0555179\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11819.7 | −0.812337 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 2793.79i | − 0.191048i | ||||||||
\(599\) | 4943.41 | 0.337199 | 0.168600 | − | 0.985685i | \(-0.446075\pi\) | ||||
0.168600 | + | 0.985685i | \(0.446075\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24334.8 | −1.65164 | −0.825821 | − | 0.563932i | \(-0.809288\pi\) | ||||
−0.825821 | + | 0.563932i | \(0.809288\pi\) | |||||||
\(602\) | 33486.9i | 2.26715i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4540.54 | −0.305881 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 28973.8i | − 1.93741i | −0.248207 | − | 0.968707i | \(-0.579841\pi\) | ||||
0.248207 | − | 0.968707i | \(-0.420159\pi\) | |||||||
\(608\) | − 2023.99i | − 0.135006i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27302.8 | −1.80778 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15139.1i | 0.997490i | 0.866749 | + | 0.498745i | \(0.166206\pi\) | ||||
−0.866749 | + | 0.498745i | \(0.833794\pi\) | |||||||
\(614\) | 787.571 | 0.0517651 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15161.4 | −0.991673 | ||||||||
\(617\) | 13894.8i | 0.906617i | 0.891354 | + | 0.453309i | \(0.149756\pi\) | ||||
−0.891354 | + | 0.453309i | \(0.850244\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4589.69 | 0.298021 | 0.149011 | − | 0.988836i | \(-0.452391\pi\) | ||||
0.149011 | + | 0.988836i | \(0.452391\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6030.07i | 0.388720i | ||||||||
\(623\) | 32252.0i | 2.07408i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 28351.2 | 1.81013 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 432.428i | − 0.0274773i | ||||||||
\(629\) | 4530.41 | 0.287185 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3005.77 | 0.189632 | 0.0948160 | − | 0.995495i | \(-0.469774\pi\) | ||||
0.0948160 | + | 0.995495i | \(0.469774\pi\) | |||||||
\(632\) | − 4079.29i | − 0.256749i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −35442.0 | −2.22016 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 35432.6i | 2.20391i | ||||||||
\(638\) | 8029.96i | 0.498290i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5631.47 | 0.347004 | 0.173502 | − | 0.984834i | \(-0.444492\pi\) | ||||
0.173502 | + | 0.984834i | \(0.444492\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11305.1i | 0.693358i | 0.937984 | + | 0.346679i | \(0.112691\pi\) | ||||
−0.937984 | + | 0.346679i | \(0.887309\pi\) | |||||||
\(644\) | 1367.89 | 0.0836997 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5875.64 | 0.357855 | ||||||||
\(647\) | − 8614.30i | − 0.523436i | −0.965144 | − | 0.261718i | \(-0.915711\pi\) | ||||
0.965144 | − | 0.261718i | \(-0.0842891\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10718.6 | −0.648291 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 9510.96i | − 0.571285i | ||||||||
\(653\) | − 12639.8i | − 0.757479i | −0.925503 | − | 0.378739i | \(-0.876358\pi\) | ||||
0.925503 | − | 0.378739i | \(-0.123642\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2437.22 | −0.145057 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 45950.9i | − 2.72242i | ||||||||
\(659\) | 13640.4 | 0.806306 | 0.403153 | − | 0.915133i | \(-0.367914\pi\) | ||||
0.403153 | + | 0.915133i | \(0.367914\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17052.0 | −1.00340 | −0.501699 | − | 0.865042i | \(-0.667291\pi\) | ||||
−0.501699 | + | 0.865042i | \(0.667291\pi\) | |||||||
\(662\) | 22649.6i | 1.32976i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14498.2 | 0.847348 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1041.36i | 0.0604521i | ||||||||
\(668\) | − 854.302i | − 0.0494820i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19461.7 | −1.11969 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 16419.7i | − 0.940467i | −0.882542 | − | 0.470234i | \(-0.844170\pi\) | ||||
0.882542 | − | 0.470234i | \(-0.155830\pi\) | |||||||
\(674\) | −28339.9 | −1.61960 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4899.14 | 0.278740 | ||||||||
\(677\) | − 8670.47i | − 0.492221i | −0.969242 | − | 0.246110i | \(-0.920847\pi\) | ||||
0.969242 | − | 0.246110i | \(-0.0791525\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15856.9 | −0.896220 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 19328.0i | − 1.08520i | ||||||||
\(683\) | − 5973.36i | − 0.334647i | −0.985902 | − | 0.167324i | \(-0.946488\pi\) | ||||
0.985902 | − | 0.167324i | \(-0.0535125\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24568.5 | −1.36739 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 26036.4i | − 1.44277i | ||||||||
\(689\) | 18341.2 | 1.01414 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15316.3 | −0.843212 | −0.421606 | − | 0.906779i | \(-0.638533\pi\) | ||||
−0.421606 | + | 0.906779i | \(0.638533\pi\) | |||||||
\(692\) | − 6353.78i | − 0.349038i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6210.09 | 0.339671 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 3715.65i | − 0.201923i | ||||||||
\(698\) | 3857.29i | 0.209170i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34583.1 | −1.86332 | −0.931660 | − | 0.363333i | \(-0.881639\pi\) | ||||
−0.931660 | + | 0.363333i | \(0.881639\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 539.695i | 0.0289545i | ||||||||
\(704\) | 5184.74 | 0.277567 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19325.8 | −1.03022 | ||||||||
\(707\) | 10563.6i | 0.561929i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11194.1 | −0.592955 | −0.296477 | − | 0.955040i | \(-0.595812\pi\) | ||||
−0.296477 | + | 0.955040i | \(0.595812\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 16792.4i | − 0.883877i | ||||||||
\(713\) | − 2506.53i | − 0.131655i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1892.61 | −0.0987850 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18312.8i | 0.951847i | ||||||||
\(719\) | −15491.9 | −0.803549 | −0.401774 | − | 0.915739i | \(-0.631606\pi\) | ||||
−0.401774 | + | 0.915739i | \(0.631606\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23458.2 | −1.21169 | ||||||||
\(722\) | − 22338.7i | − 1.15147i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6439.83 | 0.330572 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6272.72i | 0.320003i | 0.987117 | + | 0.160002i | \(0.0511500\pi\) | ||||
−0.987117 | + | 0.160002i | \(0.948850\pi\) | |||||||
\(728\) | − 29296.1i | − 1.49146i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39693.6 | 2.00837 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24980.5i | 1.25877i | 0.777095 | + | 0.629383i | \(0.216692\pi\) | ||||
−0.777095 | + | 0.629383i | \(0.783308\pi\) | |||||||
\(734\) | 28167.5 | 1.41646 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1919.90 | −0.0961530 | ||||||||
\(737\) | 8075.49i | 0.403615i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30660.7 | 1.52621 | 0.763107 | − | 0.646272i | \(-0.223673\pi\) | ||||
0.763107 | + | 0.646272i | \(0.223673\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 30868.5i | 1.52725i | ||||||||
\(743\) | 17205.7i | 0.849551i | 0.905299 | + | 0.424776i | \(0.139647\pi\) | ||||
−0.905299 | + | 0.424776i | \(0.860353\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9164.09 | −0.449760 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 12502.9i | − 0.611165i | ||||||||
\(749\) | −43077.8 | −2.10151 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18397.1 | 0.893901 | 0.446950 | − | 0.894559i | \(-0.352510\pi\) | ||||
0.446950 | + | 0.894559i | \(0.352510\pi\) | |||||||
\(752\) | 35727.2i | 1.73250i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15516.1 | −0.749422 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 22305.1i | − 1.07093i | −0.844557 | − | 0.535465i | \(-0.820136\pi\) | ||||
0.844557 | − | 0.535465i | \(-0.179864\pi\) | |||||||
\(758\) | − 11248.9i | − 0.539023i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14458.5 | −0.688727 | −0.344364 | − | 0.938836i | \(-0.611905\pi\) | ||||
−0.344364 | + | 0.938836i | \(0.611905\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27647.3i | 1.31179i | ||||||||
\(764\) | −14175.0 | −0.671249 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 35034.3 | 1.65253 | ||||||||
\(767\) | − 20711.3i | − 0.975022i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39897.6 | 1.87093 | 0.935463 | − | 0.353424i | \(-0.114983\pi\) | ||||
0.935463 | + | 0.353424i | \(0.114983\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 9.76938i | 0 0.000455450i | ||||||||
\(773\) | − 20070.2i | − 0.933863i | −0.884294 | − | 0.466931i | \(-0.845359\pi\) | ||||
0.884294 | − | 0.466931i | \(-0.154641\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8256.08 | 0.381928 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33008.7i | 1.52110i | ||||||||
\(779\) | 442.635 | 0.0203582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15692.0 | 0.718953 | ||||||||
\(782\) | − 5573.47i | − 0.254868i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 46365.5 | 2.11213 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 10733.0i | − 0.486137i | −0.970009 | − | 0.243069i | \(-0.921846\pi\) | ||||
0.970009 | − | 0.243069i | \(-0.0781540\pi\) | |||||||
\(788\) | − 1869.89i | − 0.0845329i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 62391.1 | 2.80452 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 37605.5i | − 1.68400i | ||||||||
\(794\) | −1465.76 | −0.0655139 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10013.1 | −0.445861 | ||||||||
\(797\) | − 14335.8i | − 0.637140i | −0.947899 | − | 0.318570i | \(-0.896797\pi\) | ||||
0.947899 | − | 0.318570i | \(-0.103203\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −54467.7 | −2.41167 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 48709.0i | 2.14461i | ||||||||
\(803\) | 601.325i | 0.0264263i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 37347.1 | 1.63213 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 5500.03i | − 0.239468i | ||||||||
\(809\) | 20920.7 | 0.909187 | 0.454593 | − | 0.890699i | \(-0.349785\pi\) | ||||
0.454593 | + | 0.890699i | \(0.349785\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12816.5 | 0.554931 | 0.277465 | − | 0.960736i | \(-0.410506\pi\) | ||||
0.277465 | + | 0.960736i | \(0.410506\pi\) | |||||||
\(812\) | − 7596.99i | − 0.328328i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3947.59 | 0.169979 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4728.59i | 0.202488i | ||||||||
\(818\) | 40502.9i | 1.73124i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7253.55 | −0.308344 | −0.154172 | − | 0.988044i | \(-0.549271\pi\) | ||||
−0.154172 | + | 0.988044i | \(0.549271\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35288.1i | 1.49461i | 0.664479 | + | 0.747307i | \(0.268654\pi\) | ||||
−0.664479 | + | 0.747307i | \(0.731346\pi\) | |||||||
\(824\) | 12213.8 | 0.516367 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 34857.3 | 1.46833 | ||||||||
\(827\) | − 32205.9i | − 1.35418i | −0.735899 | − | 0.677092i | \(-0.763240\pi\) | ||||
0.735899 | − | 0.677092i | \(-0.236760\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29993.3 | −1.25659 | −0.628294 | − | 0.777976i | \(-0.716246\pi\) | ||||
−0.628294 | + | 0.777976i | \(0.716246\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 10018.4i | 0.417457i | ||||||||
\(833\) | 70686.2i | 2.94013i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1489.44 | 0.0616187 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 20297.7i | 0.836720i | ||||||||
\(839\) | −35608.7 | −1.46526 | −0.732628 | − | 0.680629i | \(-0.761706\pi\) | ||||
−0.732628 | + | 0.680629i | \(0.761706\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18605.5 | −0.762865 | ||||||||
\(842\) | − 33571.1i | − 1.37403i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 165.785 | 0.00676134 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10433.4i | 0.423255i | ||||||||
\(848\) | − 24000.5i | − 0.971911i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 511.940 | 0.0206217 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 11229.3i | − 0.450744i | −0.974273 | − | 0.225372i | \(-0.927640\pi\) | ||||
0.974273 | − | 0.225372i | \(-0.0723598\pi\) | |||||||
\(854\) | 63290.5 | 2.53601 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22428.9 | 0.895565 | ||||||||
\(857\) | 22136.1i | 0.882327i | 0.897427 | + | 0.441164i | \(0.145434\pi\) | ||||
−0.897427 | + | 0.441164i | \(0.854566\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 820.727 | 0.0325994 | 0.0162997 | − | 0.999867i | \(-0.494811\pi\) | ||||
0.0162997 | + | 0.999867i | \(0.494811\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 31329.5i | − 1.23792i | ||||||||
\(863\) | 245.223i | 0.00967264i | 0.999988 | + | 0.00483632i | \(0.00153945\pi\) | ||||
−0.999988 | + | 0.00483632i | \(0.998461\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 26405.0 | 1.03612 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18285.8i | 0.715048i | ||||||||
\(869\) | 8092.27 | 0.315894 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15604.1 | −0.607032 | ||||||||
\(872\) | − 14394.8i | − 0.559026i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 663.952 | 0.0256963 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 37727.8i | − 1.45265i | −0.687350 | − | 0.726326i | \(-0.741226\pi\) | ||||
0.687350 | − | 0.726326i | \(-0.258774\pi\) | |||||||
\(878\) | − 24896.4i | − 0.956961i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21738.8 | −0.831326 | −0.415663 | − | 0.909519i | \(-0.636450\pi\) | ||||
−0.415663 | + | 0.909519i | \(0.636450\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 44340.4i | − 1.68989i | −0.534852 | − | 0.844946i | \(-0.679632\pi\) | ||||
0.534852 | − | 0.844946i | \(-0.320368\pi\) | |||||||
\(884\) | 24159.1 | 0.919184 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10223.3 | −0.387652 | ||||||||
\(887\) | − 681.008i | − 0.0257790i | −0.999917 | − | 0.0128895i | \(-0.995897\pi\) | ||||
0.999917 | − | 0.0128895i | \(-0.00410298\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8572.00 | −0.323392 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 17899.7i | − 0.671889i | ||||||||
\(893\) | − 6488.58i | − 0.243149i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −50999.6 | −1.90154 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 32070.3i | − 1.19176i | ||||||||
\(899\) | −13920.7 | −0.516443 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36589.8 | 1.35292 | ||||||||
\(902\) | − 3237.65i | − 0.119514i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −32484.6 | −1.19516 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 5348.01i | − 0.195786i | −0.995197 | − | 0.0978929i | \(-0.968790\pi\) | ||||
0.995197 | − | 0.0978929i | \(-0.0312103\pi\) | |||||||
\(908\) | 15679.5i | 0.573066i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14488.7 | −0.526930 | −0.263465 | − | 0.964669i | \(-0.584865\pi\) | ||||
−0.263465 | + | 0.964669i | \(0.584865\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28760.7i | 1.04254i | ||||||||
\(914\) | 45015.6 | 1.62908 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6845.05 | −0.246907 | ||||||||
\(917\) | 7397.56i | 0.266400i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22546.9 | 0.809308 | 0.404654 | − | 0.914470i | \(-0.367392\pi\) | ||||
0.404654 | + | 0.914470i | \(0.367392\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13895.9i | 0.496351i | ||||||||
\(923\) | 30321.3i | 1.08130i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 46944.9 | 1.66599 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10662.7i | 0.377178i | ||||||||
\(929\) | −13980.7 | −0.493747 | −0.246874 | − | 0.969048i | \(-0.579403\pi\) | ||||
−0.246874 | + | 0.969048i | \(0.579403\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8420.65 | −0.296429 | ||||||||
\(932\) | 21283.5i | 0.748032i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 36264.5 | 1.27046 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 26362.6i | − 0.919133i | −0.888143 | − | 0.459567i | \(-0.848005\pi\) | ||||
0.888143 | − | 0.459567i | \(-0.151995\pi\) | |||||||
\(938\) | − 26261.9i | − 0.914159i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14715.6 | 0.509792 | 0.254896 | − | 0.966968i | \(-0.417959\pi\) | ||||
0.254896 | + | 0.966968i | \(0.417959\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 419.871i | − 0.0144994i | ||||||||
\(944\) | −27101.9 | −0.934419 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 34587.2 | 1.18872 | ||||||||
\(947\) | − 11818.2i | − 0.405532i | −0.979227 | − | 0.202766i | \(-0.935007\pi\) | ||||
0.979227 | − | 0.202766i | \(-0.0649931\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1161.93 | −0.0397448 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 58444.2i | − 1.98969i | ||||||||
\(953\) | 43832.3i | 1.48989i | 0.667125 | + | 0.744945i | \(0.267524\pi\) | ||||
−0.667125 | + | 0.744945i | \(0.732476\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7334.46 | −0.248131 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 48933.8i | 1.65029i | ||||||||
\(959\) | 27677.7 | 0.931971 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3716.00 | 0.124736 | ||||||||
\(962\) | 7627.86i | 0.255647i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7854.36 | 0.262419 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 10696.2i | − 0.355706i | −0.984057 | − | 0.177853i | \(-0.943085\pi\) | ||||
0.984057 | − | 0.177853i | \(-0.0569152\pi\) | |||||||
\(968\) | − 5432.27i | − 0.180372i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27933.0 | −0.923187 | −0.461593 | − | 0.887092i | \(-0.652722\pi\) | ||||
−0.461593 | + | 0.887092i | \(0.652722\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 62378.4i | − 2.05525i | ||||||||
\(974\) | −38481.4 | −1.26594 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −49208.9 | −1.61387 | ||||||||
\(977\) | 24341.7i | 0.797094i | 0.917148 | + | 0.398547i | \(0.130485\pi\) | ||||
−0.917148 | + | 0.398547i | \(0.869515\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33311.7 | 1.08748 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 66057.7i | 2.14662i | ||||||||
\(983\) | − 12553.0i | − 0.407301i | −0.979044 | − | 0.203651i | \(-0.934719\pi\) | ||||
0.979044 | − | 0.203651i | \(-0.0652807\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −30953.9 | −0.999769 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2878.01i | 0.0926737i | ||||||||
\(989\) | 4485.41 | 0.144214 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45631.8 | −1.46271 | −0.731353 | − | 0.681999i | \(-0.761111\pi\) | ||||
−0.731353 | + | 0.681999i | \(0.761111\pi\) | |||||||
\(992\) | − 25665.0i | − 0.821437i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −51031.0 | −1.62838 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34499.0i | 1.09588i | 0.836517 | + | 0.547941i | \(0.184588\pi\) | ||||
−0.836517 | + | 0.547941i | \(0.815412\pi\) | |||||||
\(998\) | − 28145.3i | − 0.892708i | ||||||||
\(999\) | 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 | 225.4.b.h.199.3 | 4 | ||
3.2 | odd | 2 | 75.4.b.c.49.2 | 4 | |||
5.2 | odd | 4 | 225.4.a.n.1.1 | 2 | |||
5.3 | odd | 4 | 225.4.a.j.1.2 | 2 | |||
5.4 | even | 2 | inner | 225.4.b.h.199.2 | 4 | ||
12.11 | even | 2 | 1200.4.f.v.49.2 | 4 | |||
15.2 | even | 4 | 75.4.a.d.1.2 | ✓ | 2 | ||
15.8 | even | 4 | 75.4.a.e.1.1 | yes | 2 | ||
15.14 | odd | 2 | 75.4.b.c.49.3 | 4 | |||
60.23 | odd | 4 | 1200.4.a.bu.1.2 | 2 | |||
60.47 | odd | 4 | 1200.4.a.bl.1.1 | 2 | |||
60.59 | even | 2 | 1200.4.f.v.49.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.a.d.1.2 | ✓ | 2 | 15.2 | even | 4 | ||
75.4.a.e.1.1 | yes | 2 | 15.8 | even | 4 | ||
75.4.b.c.49.2 | 4 | 3.2 | odd | 2 | |||
75.4.b.c.49.3 | 4 | 15.14 | odd | 2 | |||
225.4.a.j.1.2 | 2 | 5.3 | odd | 4 | |||
225.4.a.n.1.1 | 2 | 5.2 | odd | 4 | |||
225.4.b.h.199.2 | 4 | 5.4 | even | 2 | inner | ||
225.4.b.h.199.3 | 4 | 1.1 | even | 1 | trivial | ||
1200.4.a.bl.1.1 | 2 | 60.47 | odd | 4 | |||
1200.4.a.bu.1.2 | 2 | 60.23 | odd | 4 | |||
1200.4.f.v.49.2 | 4 | 12.11 | even | 2 | |||
1200.4.f.v.49.3 | 4 | 60.59 | even | 2 |