Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,4,Mod(64,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.64");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.5856016518\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 37x^{8} + 398x^{6} + 1149x^{4} + 1040x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.2 | ||
Root | \(-1.37042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.64 |
Dual form | 315.4.d.b.64.9 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.88936i | − | 1.72865i | −0.502933 | − | 0.864325i | \(-0.667746\pi\) | ||
0.502933 | − | 0.864325i | \(-0.332254\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −15.9059 | −1.98823 | ||||||||
\(5\) | 9.63020 | + | 5.67972i | 0.861351 | + | 0.508010i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.00000i | − | 0.377964i | ||||||
\(8\) | 38.6546i | 1.70831i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 27.7702 | − | 47.0855i | 0.878171 | − | 1.48898i | ||||
\(11\) | −54.9009 | −1.50484 | −0.752420 | − | 0.658684i | \(-0.771113\pi\) | ||||
−0.752420 | + | 0.658684i | \(0.771113\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 49.7580i | − | 1.06157i | −0.847507 | − | 0.530784i | \(-0.821897\pi\) | ||
0.847507 | − | 0.530784i | \(-0.178103\pi\) | |||||||
\(14\) | −34.2255 | −0.653368 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 61.7496 | 0.964837 | ||||||||
\(17\) | 133.661i | 1.90692i | 0.301517 | + | 0.953461i | \(0.402507\pi\) | ||||
−0.301517 | + | 0.953461i | \(0.597493\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −138.986 | −1.67819 | −0.839097 | − | 0.543983i | \(-0.816916\pi\) | ||||
−0.839097 | + | 0.543983i | \(0.816916\pi\) | |||||||
\(20\) | −153.177 | − | 90.3409i | −1.71257 | − | 1.01004i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 268.430i | 2.60134i | ||||||||
\(23\) | − | 7.32751i | − | 0.0664301i | −0.999448 | − | 0.0332150i | \(-0.989425\pi\) | ||
0.999448 | − | 0.0332150i | \(-0.0105746\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 60.4815 | + | 109.394i | 0.483852 | + | 0.875150i | ||||
\(26\) | −243.285 | −1.83508 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 111.341i | 0.751481i | ||||||||
\(29\) | 87.2408 | 0.558628 | 0.279314 | − | 0.960200i | \(-0.409893\pi\) | ||||
0.279314 | + | 0.960200i | \(0.409893\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −209.479 | −1.21366 | −0.606831 | − | 0.794831i | \(-0.707560\pi\) | ||||
−0.606831 | + | 0.794831i | \(0.707560\pi\) | |||||||
\(32\) | 7.32107i | 0.0404436i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 653.519 | 3.29640 | ||||||||
\(35\) | 39.7580 | − | 67.4114i | 0.192010 | − | 0.325560i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 67.9041i | 0.301713i | 0.988556 | + | 0.150856i | \(0.0482031\pi\) | ||||
−0.988556 | + | 0.150856i | \(0.951797\pi\) | |||||||
\(38\) | 679.555i | 2.90101i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −219.547 | + | 372.252i | −0.867838 | + | 1.47145i | ||||
\(41\) | −77.6804 | −0.295894 | −0.147947 | − | 0.988995i | \(-0.547266\pi\) | ||||
−0.147947 | + | 0.988995i | \(0.547266\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 197.692i | − | 0.701112i | −0.936542 | − | 0.350556i | \(-0.885993\pi\) | ||
0.936542 | − | 0.350556i | \(-0.114007\pi\) | |||||||
\(44\) | 873.246 | 2.99197 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −35.8269 | −0.114834 | ||||||||
\(47\) | 4.97613i | 0.0154435i | 0.999970 | + | 0.00772173i | \(0.00245793\pi\) | ||||
−0.999970 | + | 0.00772173i | \(0.997542\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 534.865 | − | 295.716i | 1.51283 | − | 0.836412i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 791.444i | 2.11065i | ||||||||
\(53\) | 53.0843i | 0.137579i | 0.997631 | + | 0.0687895i | \(0.0219137\pi\) | ||||
−0.997631 | + | 0.0687895i | \(0.978086\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −528.706 | − | 311.822i | −1.29620 | − | 0.764473i | ||||
\(56\) | 270.582 | 0.645680 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 426.552i | − | 0.965673i | ||||||
\(59\) | −683.950 | −1.50920 | −0.754599 | − | 0.656186i | \(-0.772169\pi\) | ||||
−0.754599 | + | 0.656186i | \(0.772169\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −26.8658 | −0.0563904 | −0.0281952 | − | 0.999602i | \(-0.508976\pi\) | ||||
−0.0281952 | + | 0.999602i | \(0.508976\pi\) | |||||||
\(62\) | 1024.22i | 2.09800i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 529.792 | 1.03475 | ||||||||
\(65\) | 282.612 | − | 479.180i | 0.539287 | − | 0.914383i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 149.300i | − | 0.272237i | −0.990693 | − | 0.136119i | \(-0.956537\pi\) | ||
0.990693 | − | 0.136119i | \(-0.0434628\pi\) | |||||||
\(68\) | − | 2126.00i | − | 3.79140i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −329.599 | − | 194.391i | −0.562780 | − | 0.331918i | ||||
\(71\) | −6.15571 | −0.0102894 | −0.00514470 | − | 0.999987i | \(-0.501638\pi\) | ||||
−0.00514470 | + | 0.999987i | \(0.501638\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 294.545i | 0.472245i | 0.971723 | + | 0.236123i | \(0.0758767\pi\) | ||||
−0.971723 | + | 0.236123i | \(0.924123\pi\) | |||||||
\(74\) | 332.008 | 0.521556 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2210.70 | 3.33664 | ||||||||
\(77\) | 384.306i | 0.568776i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 938.669 | 1.33682 | 0.668409 | − | 0.743794i | \(-0.266976\pi\) | ||||
0.668409 | + | 0.743794i | \(0.266976\pi\) | |||||||
\(80\) | 594.661 | + | 350.720i | 0.831063 | + | 0.490146i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 379.807i | 0.511496i | ||||||||
\(83\) | − | 784.907i | − | 1.03801i | −0.854772 | − | 0.519004i | \(-0.826303\pi\) | ||
0.854772 | − | 0.519004i | \(-0.173697\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −759.160 | + | 1287.19i | −0.968735 | + | 1.64253i | ||||
\(86\) | −966.590 | −1.21198 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 2122.17i | − | 2.57073i | ||||||
\(89\) | 275.928 | 0.328633 | 0.164316 | − | 0.986408i | \(-0.447458\pi\) | ||||
0.164316 | + | 0.986408i | \(0.447458\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −348.306 | −0.401235 | ||||||||
\(92\) | 116.550i | 0.132078i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 24.3301 | 0.0266963 | ||||||||
\(95\) | −1338.47 | − | 789.404i | −1.44551 | − | 0.852538i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1165.27i | − | 1.21975i | −0.792499 | − | 0.609873i | \(-0.791220\pi\) | ||
0.792499 | − | 0.609873i | \(-0.208780\pi\) | |||||||
\(98\) | 239.579i | 0.246950i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −962.011 | − | 1740.00i | −0.962011 | − | 1.74000i | ||||
\(101\) | 0.162999 | 0.000160584 | 8.02919e−5 | − | 1.00000i | \(-0.499974\pi\) | ||||
8.02919e−5 | 1.00000i | \(0.499974\pi\) | ||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1300.78i | 1.24437i | 0.782871 | + | 0.622184i | \(0.213755\pi\) | ||||
−0.782871 | + | 0.622184i | \(0.786245\pi\) | |||||||
\(104\) | 1923.38 | 1.81349 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 259.548 | 0.237826 | ||||||||
\(107\) | 1531.63i | 1.38382i | 0.721985 | + | 0.691908i | \(0.243230\pi\) | ||||
−0.721985 | + | 0.691908i | \(0.756770\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1971.39 | −1.73234 | −0.866171 | − | 0.499748i | \(-0.833426\pi\) | ||||
−0.866171 | + | 0.499748i | \(0.833426\pi\) | |||||||
\(110\) | −1524.61 | + | 2585.04i | −1.32151 | + | 2.24067i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 432.247i | − | 0.364674i | ||||||
\(113\) | 262.817i | 0.218794i | 0.993998 | + | 0.109397i | \(0.0348920\pi\) | ||||
−0.993998 | + | 0.109397i | \(0.965108\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 41.6182 | − | 70.5654i | 0.0337471 | − | 0.0572196i | ||||
\(116\) | −1387.64 | −1.11068 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3344.08i | 2.60888i | ||||||||
\(119\) | 935.630 | 0.720749 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1683.11 | 1.26454 | ||||||||
\(122\) | 131.357i | 0.0974793i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3331.94 | 2.41304 | ||||||||
\(125\) | −38.8765 | + | 1397.00i | −0.0278177 | + | 0.999613i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 569.649i | − | 0.398017i | −0.979998 | − | 0.199009i | \(-0.936228\pi\) | ||
0.979998 | − | 0.199009i | \(-0.0637722\pi\) | |||||||
\(128\) | − | 2531.78i | − | 1.74828i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2342.88 | − | 1381.79i | −1.58065 | − | 0.932239i | ||||
\(131\) | −984.808 | −0.656817 | −0.328409 | − | 0.944536i | \(-0.606512\pi\) | ||||
−0.328409 | + | 0.944536i | \(0.606512\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 972.905i | 0.634297i | ||||||||
\(134\) | −729.982 | −0.470603 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5166.63 | −3.25761 | ||||||||
\(137\) | − | 1377.35i | − | 0.858942i | −0.903081 | − | 0.429471i | \(-0.858700\pi\) | ||
0.903081 | − | 0.429471i | \(-0.141300\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −839.673 | −0.512375 | −0.256188 | − | 0.966627i | \(-0.582466\pi\) | ||||
−0.256188 | + | 0.966627i | \(0.582466\pi\) | |||||||
\(140\) | −632.386 | + | 1072.24i | −0.381760 | + | 0.647289i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 30.0975i | 0.0177868i | ||||||||
\(143\) | 2731.76i | 1.59749i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 840.147 | + | 495.504i | 0.481175 | + | 0.283788i | ||||
\(146\) | 1440.14 | 0.816347 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1080.07i | − | 0.599875i | ||||||
\(149\) | −1470.33 | −0.808416 | −0.404208 | − | 0.914667i | \(-0.632453\pi\) | ||||
−0.404208 | + | 0.914667i | \(0.632453\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1695.79 | −0.913916 | −0.456958 | − | 0.889488i | \(-0.651061\pi\) | ||||
−0.456958 | + | 0.889488i | \(0.651061\pi\) | |||||||
\(152\) | − | 5372.47i | − | 2.86687i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1879.01 | 0.983215 | ||||||||
\(155\) | −2017.32 | − | 1189.78i | −1.04539 | − | 0.616552i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 959.433i | − | 0.487714i | −0.969811 | − | 0.243857i | \(-0.921587\pi\) | ||
0.969811 | − | 0.243857i | \(-0.0784127\pi\) | |||||||
\(158\) | − | 4589.49i | − | 2.31089i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −41.5816 | + | 70.5033i | −0.0205457 | + | 0.0348361i | ||||
\(161\) | −51.2926 | −0.0251082 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3865.27i | − | 1.85737i | −0.370869 | − | 0.928685i | \(-0.620940\pi\) | ||
0.370869 | − | 0.928685i | \(-0.379060\pi\) | |||||||
\(164\) | 1235.57 | 0.588305 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3837.69 | −1.79435 | ||||||||
\(167\) | − | 465.084i | − | 0.215505i | −0.994178 | − | 0.107752i | \(-0.965635\pi\) | ||
0.994178 | − | 0.107752i | \(-0.0343653\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −278.860 | −0.126927 | ||||||||
\(170\) | 6293.52 | + | 3711.81i | 2.83936 | + | 1.67460i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3144.47i | 1.39397i | ||||||||
\(173\) | − | 2048.04i | − | 0.900057i | −0.893014 | − | 0.450028i | \(-0.851414\pi\) | ||
0.893014 | − | 0.450028i | \(-0.148586\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 765.756 | − | 423.371i | 0.330775 | − | 0.182879i | ||||
\(176\) | −3390.10 | −1.45192 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 1349.11i | − | 0.568091i | ||||||
\(179\) | −911.856 | −0.380756 | −0.190378 | − | 0.981711i | \(-0.560971\pi\) | ||||
−0.190378 | + | 0.981711i | \(0.560971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2029.81 | −0.833562 | −0.416781 | − | 0.909007i | \(-0.636842\pi\) | ||||
−0.416781 | + | 0.909007i | \(0.636842\pi\) | |||||||
\(182\) | 1702.99i | 0.693595i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 283.242 | 0.113483 | ||||||||
\(185\) | −385.677 | + | 653.930i | −0.153273 | + | 0.259881i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 7338.13i | − | 2.86961i | ||||||
\(188\) | − | 79.1496i | − | 0.0307052i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3859.68 | + | 6544.25i | −1.47374 | + | 2.49879i | ||||
\(191\) | −4984.11 | −1.88815 | −0.944077 | − | 0.329725i | \(-0.893044\pi\) | ||||
−0.944077 | + | 0.329725i | \(0.893044\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 3393.44i | − | 1.26562i | −0.774306 | − | 0.632811i | \(-0.781901\pi\) | ||
0.774306 | − | 0.632811i | \(-0.218099\pi\) | |||||||
\(194\) | −5697.43 | −2.10852 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 779.387 | 0.284033 | ||||||||
\(197\) | 762.475i | 0.275757i | 0.990449 | + | 0.137878i | \(0.0440283\pi\) | ||||
−0.990449 | + | 0.137878i | \(0.955972\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1272.32 | 0.453227 | 0.226613 | − | 0.973985i | \(-0.427235\pi\) | ||||
0.226613 | + | 0.973985i | \(0.427235\pi\) | |||||||
\(200\) | −4228.57 | + | 2337.89i | −1.49503 | + | 0.826569i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 0.796959i | − | 0.000277593i | ||||||
\(203\) | − | 610.686i | − | 0.211142i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −748.077 | − | 441.203i | −0.254868 | − | 0.150317i | ||||
\(206\) | 6360.00 | 2.15108 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 3072.53i | − | 1.02424i | ||||||
\(209\) | 7630.47 | 2.52541 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2010.72 | 0.656035 | 0.328017 | − | 0.944672i | \(-0.393620\pi\) | ||||
0.328017 | + | 0.944672i | \(0.393620\pi\) | |||||||
\(212\) | − | 844.351i | − | 0.273539i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7488.70 | 2.39214 | ||||||||
\(215\) | 1122.84 | − | 1903.82i | 0.356172 | − | 0.603904i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1466.35i | 0.458721i | ||||||||
\(218\) | 9638.85i | 2.99461i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8409.53 | + | 4959.79i | 2.57714 | + | 1.51995i | ||||
\(221\) | 6650.73 | 2.02433 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1516.44i | 0.455374i | 0.973734 | + | 0.227687i | \(0.0731163\pi\) | ||||
−0.973734 | + | 0.227687i | \(0.926884\pi\) | |||||||
\(224\) | 51.2475 | 0.0152862 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1285.01 | 0.378219 | ||||||||
\(227\) | 4101.17i | 1.19914i | 0.800323 | + | 0.599568i | \(0.204661\pi\) | ||||
−0.800323 | + | 0.599568i | \(0.795339\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1029.24 | 0.297004 | 0.148502 | − | 0.988912i | \(-0.452555\pi\) | ||||
0.148502 | + | 0.988912i | \(0.452555\pi\) | |||||||
\(230\) | −345.020 | − | 203.487i | −0.0989128 | − | 0.0583370i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3372.26i | 0.954309i | ||||||||
\(233\) | − | 5578.41i | − | 1.56847i | −0.620463 | − | 0.784236i | \(-0.713055\pi\) | ||
0.620463 | − | 0.784236i | \(-0.286945\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −28.2630 | + | 47.9211i | −0.00784543 | + | 0.0133022i | ||||
\(236\) | 10878.8 | 3.00064 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 4574.64i | − | 1.24592i | ||||||
\(239\) | 5389.67 | 1.45870 | 0.729348 | − | 0.684142i | \(-0.239823\pi\) | ||||
0.729348 | + | 0.684142i | \(0.239823\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3976.27 | 1.06280 | 0.531399 | − | 0.847122i | \(-0.321667\pi\) | ||||
0.531399 | + | 0.847122i | \(0.321667\pi\) | |||||||
\(242\) | − | 8229.31i | − | 2.18595i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 427.324 | 0.112117 | ||||||||
\(245\) | −471.880 | − | 278.306i | −0.123050 | − | 0.0725728i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6915.69i | 1.78152i | ||||||||
\(248\) | − | 8097.33i | − | 2.07331i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6830.45 | + | 190.081i | 1.72798 | + | 0.0480871i | ||||
\(251\) | −7095.76 | −1.78438 | −0.892192 | − | 0.451655i | \(-0.850834\pi\) | ||||
−0.892192 | + | 0.451655i | \(0.850834\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 402.287i | 0.0999666i | ||||||||
\(254\) | −2785.22 | −0.688033 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8140.43 | −1.98741 | ||||||||
\(257\) | − | 2526.56i | − | 0.613239i | −0.951832 | − | 0.306619i | \(-0.900802\pi\) | ||
0.951832 | − | 0.306619i | \(-0.0991979\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 475.329 | 0.114037 | ||||||||
\(260\) | −4495.18 | + | 7621.77i | −1.07223 | + | 1.81801i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4815.08i | 1.13541i | ||||||||
\(263\) | 3842.34i | 0.900871i | 0.892809 | + | 0.450435i | \(0.148731\pi\) | ||||
−0.892809 | + | 0.450435i | \(0.851269\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −301.504 | + | 511.212i | −0.0698914 | + | 0.118504i | ||||
\(266\) | 4756.88 | 1.09648 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2374.75i | 0.541271i | ||||||||
\(269\) | −8411.04 | −1.90643 | −0.953216 | − | 0.302291i | \(-0.902249\pi\) | ||||
−0.953216 | + | 0.302291i | \(0.902249\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5659.73 | 1.26865 | 0.634325 | − | 0.773067i | \(-0.281278\pi\) | ||||
0.634325 | + | 0.773067i | \(0.281278\pi\) | |||||||
\(272\) | 8253.54i | 1.83987i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6734.37 | −1.48481 | ||||||||
\(275\) | −3320.49 | − | 6005.81i | −0.728120 | − | 1.31696i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 881.409i | 0.191187i | 0.995420 | + | 0.0955934i | \(0.0304749\pi\) | ||||
−0.995420 | + | 0.0955934i | \(0.969525\pi\) | |||||||
\(278\) | 4105.47i | 0.885718i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2605.76 | + | 1536.83i | 0.556157 | + | 0.328012i | ||||
\(281\) | 3853.71 | 0.818124 | 0.409062 | − | 0.912506i | \(-0.365856\pi\) | ||||
0.409062 | + | 0.912506i | \(0.365856\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1891.60i | − | 0.397328i | −0.980068 | − | 0.198664i | \(-0.936340\pi\) | ||
0.980068 | − | 0.198664i | \(-0.0636603\pi\) | |||||||
\(284\) | 97.9118 | 0.0204577 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13356.6 | 2.76150 | ||||||||
\(287\) | 543.763i | 0.111837i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12952.4 | −2.63635 | ||||||||
\(290\) | 2422.70 | − | 4107.78i | 0.490571 | − | 0.831784i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 4684.99i | − | 0.938933i | ||||||
\(293\) | 4076.18i | 0.812742i | 0.913708 | + | 0.406371i | \(0.133206\pi\) | ||||
−0.913708 | + | 0.406371i | \(0.866794\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6586.58 | − | 3884.65i | −1.29995 | − | 0.766687i | ||||
\(296\) | −2624.81 | −0.515419 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7188.97i | 1.39747i | ||||||||
\(299\) | −364.602 | −0.0705201 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1383.85 | −0.264995 | ||||||||
\(302\) | 8291.33i | 1.57984i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8582.35 | −1.61918 | ||||||||
\(305\) | −258.723 | − | 152.590i | −0.0485720 | − | 0.0286469i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6201.87i | − | 1.15296i | −0.817110 | − | 0.576481i | \(-0.804425\pi\) | ||
0.817110 | − | 0.576481i | \(-0.195575\pi\) | |||||||
\(308\) | − | 6112.72i | − | 1.13086i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5817.28 | + | 9863.43i | −1.06580 | + | 1.80711i | ||||
\(311\) | 6601.95 | 1.20374 | 0.601868 | − | 0.798595i | \(-0.294423\pi\) | ||||
0.601868 | + | 0.798595i | \(0.294423\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2291.01i | 0.413724i | 0.978370 | + | 0.206862i | \(0.0663251\pi\) | ||||
−0.978370 | + | 0.206862i | \(0.933675\pi\) | |||||||
\(314\) | −4691.02 | −0.843087 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14930.3 | −2.65790 | ||||||||
\(317\) | 3124.07i | 0.553517i | 0.960939 | + | 0.276759i | \(0.0892603\pi\) | ||||
−0.960939 | + | 0.276759i | \(0.910740\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4789.60 | −0.840646 | ||||||||
\(320\) | 5102.00 | + | 3009.07i | 0.891283 | + | 0.525663i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 250.788i | 0.0434033i | ||||||||
\(323\) | − | 18577.1i | − | 3.20018i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5443.21 | − | 3009.44i | 0.929031 | − | 0.513642i | ||||
\(326\) | −18898.7 | −3.21074 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 3002.70i | − | 0.505478i | ||||||
\(329\) | 34.8329 | 0.00583708 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9825.49 | 1.63159 | 0.815797 | − | 0.578338i | \(-0.196298\pi\) | ||||
0.815797 | + | 0.578338i | \(0.196298\pi\) | |||||||
\(332\) | 12484.6i | 2.06380i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2273.96 | −0.372532 | ||||||||
\(335\) | 847.983 | − | 1437.79i | 0.138299 | − | 0.234492i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8526.35i | 1.37822i | 0.724657 | + | 0.689110i | \(0.241998\pi\) | ||||
−0.724657 | + | 0.689110i | \(0.758002\pi\) | |||||||
\(338\) | 1363.45i | 0.219413i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12075.1 | − | 20473.8i | 1.92607 | − | 3.26573i | ||||
\(341\) | 11500.6 | 1.82637 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | 7641.73 | 1.19772 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10013.6 | −1.55588 | ||||||||
\(347\) | 4164.54i | 0.644277i | 0.946693 | + | 0.322138i | \(0.104402\pi\) | ||||
−0.946693 | + | 0.322138i | \(0.895598\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2584.60 | −0.396420 | −0.198210 | − | 0.980160i | \(-0.563513\pi\) | ||||
−0.198210 | + | 0.980160i | \(0.563513\pi\) | |||||||
\(350\) | −2070.01 | − | 3744.06i | −0.316134 | − | 0.571795i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 401.933i | − | 0.0608611i | ||||||
\(353\) | − | 4199.25i | − | 0.633154i | −0.948567 | − | 0.316577i | \(-0.897466\pi\) | ||
0.948567 | − | 0.316577i | \(-0.102534\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −59.2807 | − | 34.9627i | −0.00886280 | − | 0.00522712i | ||||
\(356\) | −4388.87 | −0.653398 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4458.39i | 0.658194i | ||||||||
\(359\) | −990.277 | −0.145584 | −0.0727922 | − | 0.997347i | \(-0.523191\pi\) | ||||
−0.0727922 | + | 0.997347i | \(0.523191\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12458.2 | 1.81633 | ||||||||
\(362\) | 9924.48i | 1.44094i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5540.11 | 0.797749 | ||||||||
\(365\) | −1672.93 | + | 2836.53i | −0.239905 | + | 0.406769i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4179.24i | − | 0.594427i | −0.954811 | − | 0.297213i | \(-0.903943\pi\) | ||
0.954811 | − | 0.297213i | \(-0.0960573\pi\) | |||||||
\(368\) | − | 452.471i | − | 0.0640942i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3197.30 | + | 1885.71i | 0.449243 | + | 0.264955i | ||||
\(371\) | 371.590 | 0.0519999 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 7365.36i | − | 1.02242i | −0.859455 | − | 0.511212i | \(-0.829197\pi\) | ||
0.859455 | − | 0.511212i | \(-0.170803\pi\) | |||||||
\(374\) | −35878.8 | −4.96056 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −192.350 | −0.0263822 | ||||||||
\(377\) | − | 4340.93i | − | 0.593022i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6214.13 | 0.842213 | 0.421106 | − | 0.907011i | \(-0.361642\pi\) | ||||
0.421106 | + | 0.907011i | \(0.361642\pi\) | |||||||
\(380\) | 21289.5 | + | 12556.2i | 2.87402 | + | 1.69504i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 24369.1i | 3.26396i | ||||||||
\(383\) | 1755.04i | 0.234148i | 0.993123 | + | 0.117074i | \(0.0373514\pi\) | ||||
−0.993123 | + | 0.117074i | \(0.962649\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2182.75 | + | 3700.94i | −0.288944 | + | 0.489916i | ||||
\(386\) | −16591.7 | −2.18782 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18534.6i | 2.42514i | ||||||||
\(389\) | 8805.69 | 1.14773 | 0.573864 | − | 0.818950i | \(-0.305444\pi\) | ||||
0.573864 | + | 0.818950i | \(0.305444\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 979.406 | 0.126677 | ||||||||
\(392\) | − | 1894.08i | − | 0.244044i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3728.01 | 0.476687 | ||||||||
\(395\) | 9039.57 | + | 5331.38i | 1.15147 | + | 0.679116i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13717.2i | 1.73413i | 0.498199 | + | 0.867063i | \(0.333995\pi\) | ||||
−0.498199 | + | 0.867063i | \(0.666005\pi\) | |||||||
\(398\) | − | 6220.82i | − | 0.783471i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3734.71 | + | 6755.01i | 0.466838 | + | 0.844377i | ||||
\(401\) | −307.220 | −0.0382590 | −0.0191295 | − | 0.999817i | \(-0.506089\pi\) | ||||
−0.0191295 | + | 0.999817i | \(0.506089\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10423.3i | 1.28839i | ||||||||
\(404\) | −2.59263 | −0.000319278 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2985.86 | −0.364990 | ||||||||
\(407\) | − | 3728.00i | − | 0.454029i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12390.7 | −1.49799 | −0.748997 | − | 0.662573i | \(-0.769464\pi\) | ||||
−0.748997 | + | 0.662573i | \(0.769464\pi\) | |||||||
\(410\) | −2157.20 | + | 3657.62i | −0.259845 | + | 0.440578i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 20690.1i | − | 2.47409i | ||||||
\(413\) | 4787.65i | 0.570423i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4458.05 | − | 7558.81i | 0.527318 | − | 0.894090i | ||||
\(416\) | 364.282 | 0.0429336 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 37308.2i | − | 4.36555i | ||||||
\(419\) | 2664.10 | 0.310620 | 0.155310 | − | 0.987866i | \(-0.450362\pi\) | ||||
0.155310 | + | 0.987866i | \(0.450362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6851.11 | −0.793118 | −0.396559 | − | 0.918009i | \(-0.629796\pi\) | ||||
−0.396559 | + | 0.918009i | \(0.629796\pi\) | |||||||
\(422\) | − | 9831.12i | − | 1.13406i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2051.95 | −0.235027 | ||||||||
\(425\) | −14621.7 | + | 8084.05i | −1.66884 | + | 0.922668i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 188.061i | 0.0213136i | ||||||||
\(428\) | − | 24361.9i | − | 2.75135i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9308.45 | − | 5489.96i | −1.04394 | − | 0.615696i | ||||
\(431\) | 7651.38 | 0.855114 | 0.427557 | − | 0.903988i | \(-0.359374\pi\) | ||||
0.427557 | + | 0.903988i | \(0.359374\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 691.572i | 0.0767548i | 0.999263 | + | 0.0383774i | \(0.0122189\pi\) | ||||
−0.999263 | + | 0.0383774i | \(0.987781\pi\) | |||||||
\(434\) | 7169.53 | 0.792969 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 31356.7 | 3.44430 | ||||||||
\(437\) | 1018.42i | 0.111483i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10621.7 | −1.15478 | −0.577389 | − | 0.816469i | \(-0.695928\pi\) | ||||
−0.577389 | + | 0.816469i | \(0.695928\pi\) | |||||||
\(440\) | 12053.3 | − | 20436.9i | 1.30596 | − | 2.21430i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 32517.8i | − | 3.49936i | ||||||
\(443\) | 3133.67i | 0.336084i | 0.985780 | + | 0.168042i | \(0.0537444\pi\) | ||||
−0.985780 | + | 0.168042i | \(0.946256\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2657.24 | + | 1567.19i | 0.283068 | + | 0.166949i | ||||
\(446\) | 7414.43 | 0.787182 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 3708.54i | − | 0.391099i | ||||||
\(449\) | −9144.92 | −0.961192 | −0.480596 | − | 0.876942i | \(-0.659580\pi\) | ||||
−0.480596 | + | 0.876942i | \(0.659580\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4264.72 | 0.445272 | ||||||||
\(452\) | − | 4180.33i | − | 0.435014i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 20052.1 | 2.07289 | ||||||||
\(455\) | −3354.26 | − | 1978.28i | −0.345604 | − | 0.203831i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8142.60i | 0.833468i | 0.909029 | + | 0.416734i | \(0.136825\pi\) | ||||
−0.909029 | + | 0.416734i | \(0.863175\pi\) | |||||||
\(458\) | − | 5032.32i | − | 0.513417i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −661.974 | + | 1122.40i | −0.0670971 | + | 0.113766i | ||||
\(461\) | 9287.29 | 0.938291 | 0.469145 | − | 0.883121i | \(-0.344562\pi\) | ||||
0.469145 | + | 0.883121i | \(0.344562\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2440.53i | − | 0.244970i | −0.992470 | − | 0.122485i | \(-0.960914\pi\) | ||
0.992470 | − | 0.122485i | \(-0.0390864\pi\) | |||||||
\(464\) | 5387.08 | 0.538985 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27274.9 | −2.71134 | ||||||||
\(467\) | 12066.3i | 1.19564i | 0.801632 | + | 0.597818i | \(0.203966\pi\) | ||||
−0.801632 | + | 0.597818i | \(0.796034\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1045.10 | −0.102896 | ||||||||
\(470\) | 234.304 | + | 138.188i | 0.0229949 | + | 0.0135620i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 26437.8i | − | 2.57818i | ||||||
\(473\) | 10853.5i | 1.05506i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8406.11 | − | 15204.2i | −0.811998 | − | 1.46867i | ||||
\(476\) | −14882.0 | −1.43302 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 26352.0i | − | 2.52158i | ||||||
\(479\) | 395.211 | 0.0376987 | 0.0188493 | − | 0.999822i | \(-0.494000\pi\) | ||||
0.0188493 | + | 0.999822i | \(0.494000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3378.77 | 0.320289 | ||||||||
\(482\) | − | 19441.4i | − | 1.83721i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −26771.2 | −2.51420 | ||||||||
\(485\) | 6618.42 | − | 11221.8i | 0.619643 | − | 1.05063i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9609.06i | − | 0.894102i | −0.894508 | − | 0.447051i | \(-0.852474\pi\) | ||
0.894508 | − | 0.447051i | \(-0.147526\pi\) | |||||||
\(488\) | − | 1038.49i | − | 0.0963323i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1360.74 | + | 2307.19i | −0.125453 | + | 0.212711i | ||||
\(491\) | −10941.0 | −1.00562 | −0.502810 | − | 0.864397i | \(-0.667701\pi\) | ||||
−0.502810 | + | 0.864397i | \(0.667701\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11660.7i | 1.06526i | ||||||||
\(494\) | 33813.3 | 3.07962 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12935.2 | −1.17099 | ||||||||
\(497\) | 43.0899i | 0.00388903i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9269.90 | −0.831618 | −0.415809 | − | 0.909452i | \(-0.636502\pi\) | ||||
−0.415809 | + | 0.909452i | \(0.636502\pi\) | |||||||
\(500\) | 618.363 | − | 22220.5i | 0.0553081 | − | 1.98746i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 34693.8i | 3.08458i | ||||||||
\(503\) | 15085.4i | 1.33723i | 0.743609 | + | 0.668615i | \(0.233112\pi\) | ||||
−0.743609 | + | 0.668615i | \(0.766888\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.56971 | + | 0.925787i | 0.000138319 | + | 8.15781e-5i | ||||
\(506\) | 1966.93 | 0.172807 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9060.76i | 0.791351i | ||||||||
\(509\) | 8650.44 | 0.753289 | 0.376645 | − | 0.926358i | \(-0.377078\pi\) | ||||
0.376645 | + | 0.926358i | \(0.377078\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2061.82 | 0.178492 | ||||||||
\(512\) | 19547.3i | 1.68726i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12353.3 | −1.06008 | ||||||||
\(515\) | −7388.09 | + | 12526.8i | −0.632151 | + | 1.07184i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 273.194i | − | 0.0232399i | ||||||
\(518\) | − | 2324.06i | − | 0.197130i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 18522.5 | + | 10924.2i | 1.56205 | + | 0.921269i | ||||
\(521\) | −10661.6 | −0.896535 | −0.448268 | − | 0.893899i | \(-0.647959\pi\) | ||||
−0.448268 | + | 0.893899i | \(0.647959\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 3449.22i | − | 0.288382i | −0.989550 | − | 0.144191i | \(-0.953942\pi\) | ||
0.989550 | − | 0.144191i | \(-0.0460580\pi\) | |||||||
\(524\) | 15664.2 | 1.30591 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18786.6 | 1.55729 | ||||||||
\(527\) | − | 27999.3i | − | 2.31436i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12113.3 | 0.995587 | ||||||||
\(530\) | 2499.50 | + | 1474.16i | 0.204852 | + | 0.120818i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 15474.9i | − | 1.26113i | ||||||
\(533\) | 3865.22i | 0.314111i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8699.24 | + | 14749.9i | −0.702992 | + | 1.19195i | ||||
\(536\) | 5771.14 | 0.465066 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 41124.6i | 3.29555i | ||||||||
\(539\) | 2690.14 | 0.214977 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13403.2 | 1.06516 | 0.532578 | − | 0.846381i | \(-0.321223\pi\) | ||||
0.532578 | + | 0.846381i | \(0.321223\pi\) | |||||||
\(542\) | − | 27672.5i | − | 2.19305i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −978.544 | −0.0771227 | ||||||||
\(545\) | −18984.9 | − | 11197.0i | −1.49215 | − | 0.880046i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3670.29i | 0.286893i | 0.989658 | + | 0.143446i | \(0.0458184\pi\) | ||||
−0.989658 | + | 0.143446i | \(0.954182\pi\) | |||||||
\(548\) | 21907.9i | 1.70778i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −29364.6 | + | 16235.1i | −2.27656 | + | 1.25867i | ||||
\(551\) | −12125.3 | −0.937486 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6570.69i | − | 0.505269i | ||||||
\(554\) | 4309.53 | 0.330495 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13355.7 | 1.01872 | ||||||||
\(557\) | 521.169i | 0.0396456i | 0.999804 | + | 0.0198228i | \(0.00631021\pi\) | ||||
−0.999804 | + | 0.0198228i | \(0.993690\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9836.78 | −0.744278 | ||||||||
\(560\) | 2455.04 | − | 4162.62i | 0.185258 | − | 0.314112i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 18842.2i | − | 1.41425i | ||||||
\(563\) | 17970.2i | 1.34521i | 0.740000 | + | 0.672606i | \(0.234825\pi\) | ||||
−0.740000 | + | 0.672606i | \(0.765175\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1492.73 | + | 2530.98i | −0.111150 | + | 0.188459i | ||||
\(566\) | −9248.71 | −0.686842 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 237.947i | − | 0.0175775i | ||||||
\(569\) | −21808.6 | −1.60679 | −0.803396 | − | 0.595445i | \(-0.796976\pi\) | ||||
−0.803396 | + | 0.595445i | \(0.796976\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6604.75 | 0.484064 | 0.242032 | − | 0.970268i | \(-0.422186\pi\) | ||||
0.242032 | + | 0.970268i | \(0.422186\pi\) | |||||||
\(572\) | − | 43451.0i | − | 3.17618i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2658.65 | 0.193327 | ||||||||
\(575\) | 801.584 | − | 443.179i | 0.0581363 | − | 0.0321423i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25886.9i | 1.86774i | 0.357618 | + | 0.933868i | \(0.383589\pi\) | ||||
−0.357618 | + | 0.933868i | \(0.616411\pi\) | |||||||
\(578\) | 63328.9i | 4.55733i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13363.3 | − | 7881.41i | −0.956688 | − | 0.564238i | ||||
\(581\) | −5494.35 | −0.392330 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2914.37i | − | 0.207034i | ||||||
\(584\) | −11385.5 | −0.806741 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19929.9 | 1.40495 | ||||||||
\(587\) | − | 4949.88i | − | 0.348046i | −0.984742 | − | 0.174023i | \(-0.944323\pi\) | ||
0.984742 | − | 0.174023i | \(-0.0556768\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29114.7 | 2.03676 | ||||||||
\(590\) | −18993.4 | + | 32204.2i | −1.32533 | + | 2.24716i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4193.05i | 0.291104i | ||||||||
\(593\) | − | 31.3988i | − | 0.00217436i | −0.999999 | − | 0.00108718i | \(-0.999654\pi\) | ||
0.999999 | − | 0.00108718i | \(-0.000346059\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9010.31 | + | 5314.12i | 0.620818 | + | 0.366147i | ||||
\(596\) | 23386.8 | 1.60732 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1782.67i | 0.121905i | ||||||||
\(599\) | −11870.4 | −0.809704 | −0.404852 | − | 0.914382i | \(-0.632677\pi\) | ||||
−0.404852 | + | 0.914382i | \(0.632677\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −967.320 | −0.0656536 | −0.0328268 | − | 0.999461i | \(-0.510451\pi\) | ||||
−0.0328268 | + | 0.999461i | \(0.510451\pi\) | |||||||
\(602\) | 6766.13i | 0.458084i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 26973.0 | 1.81708 | ||||||||
\(605\) | 16208.6 | + | 9559.57i | 1.08922 | + | 0.642400i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9518.28i | 0.636466i | 0.948013 | + | 0.318233i | \(0.103089\pi\) | ||||
−0.948013 | + | 0.318233i | \(0.896911\pi\) | |||||||
\(608\) | − | 1017.53i | − | 0.0678721i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −746.070 | + | 1264.99i | −0.0495205 | + | 0.0839640i | ||||
\(611\) | 247.602 | 0.0163943 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 3607.19i | − | 0.237672i | −0.992914 | − | 0.118836i | \(-0.962084\pi\) | ||
0.992914 | − | 0.118836i | \(-0.0379163\pi\) | |||||||
\(614\) | −30323.2 | −1.99307 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14855.2 | −0.971645 | ||||||||
\(617\) | 22473.2i | 1.46635i | 0.680042 | + | 0.733173i | \(0.261962\pi\) | ||||
−0.680042 | + | 0.733173i | \(0.738038\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19200.1 | −1.24672 | −0.623358 | − | 0.781936i | \(-0.714232\pi\) | ||||
−0.623358 | + | 0.781936i | \(0.714232\pi\) | |||||||
\(620\) | 32087.3 | + | 18924.5i | 2.07848 | + | 1.22585i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 32279.3i | − | 2.08084i | ||||||
\(623\) | − | 1931.50i | − | 0.124211i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8308.97 | + | 13232.6i | −0.531774 | + | 0.846886i | ||||
\(626\) | 11201.6 | 0.715184 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15260.6i | 0.969689i | ||||||||
\(629\) | −9076.17 | −0.575343 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6980.64 | −0.440404 | −0.220202 | − | 0.975454i | \(-0.570672\pi\) | ||||
−0.220202 | + | 0.975454i | \(0.570672\pi\) | |||||||
\(632\) | 36283.9i | 2.28370i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 15274.7 | 0.956838 | ||||||||
\(635\) | 3235.45 | − | 5485.83i | 0.202197 | − | 0.342833i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2438.14i | 0.151653i | ||||||||
\(638\) | 23418.1i | 1.45318i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14379.8 | − | 24381.5i | 0.888142 | − | 1.50588i | ||||
\(641\) | 1083.82 | 0.0667837 | 0.0333919 | − | 0.999442i | \(-0.489369\pi\) | ||||
0.0333919 | + | 0.999442i | \(0.489369\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4151.42i | 0.254613i | 0.991863 | + | 0.127307i | \(0.0406332\pi\) | ||||
−0.991863 | + | 0.127307i | \(0.959367\pi\) | |||||||
\(644\) | 815.853 | 0.0499210 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −90830.3 | −5.53200 | ||||||||
\(647\) | 3014.99i | 0.183202i | 0.995796 | + | 0.0916008i | \(0.0291984\pi\) | ||||
−0.995796 | + | 0.0916008i | \(0.970802\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 37549.4 | 2.27110 | ||||||||
\(650\) | −14714.2 | − | 26613.8i | −0.887908 | − | 1.60597i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 61480.5i | 3.69288i | ||||||||
\(653\) | − | 21130.7i | − | 1.26632i | −0.774019 | − | 0.633162i | \(-0.781757\pi\) | ||
0.774019 | − | 0.633162i | \(-0.218243\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9483.90 | − | 5593.44i | −0.565751 | − | 0.333670i | ||||
\(656\) | −4796.73 | −0.285489 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 170.311i | − | 0.0100903i | ||||||
\(659\) | −9961.24 | −0.588824 | −0.294412 | − | 0.955679i | \(-0.595124\pi\) | ||||
−0.294412 | + | 0.955679i | \(0.595124\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1581.43 | 0.0930569 | 0.0465285 | − | 0.998917i | \(-0.485184\pi\) | ||||
0.0465285 | + | 0.998917i | \(0.485184\pi\) | |||||||
\(662\) | − | 48040.4i | − | 2.82046i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 30340.3 | 1.77324 | ||||||||
\(665\) | −5525.83 | + | 9369.27i | −0.322229 | + | 0.546353i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 639.258i | − | 0.0371097i | ||||||
\(668\) | 7397.56i | 0.428473i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7029.87 | − | 4146.09i | −0.405355 | − | 0.239071i | ||||
\(671\) | 1474.96 | 0.0848586 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 11101.6i | − | 0.635865i | −0.948113 | − | 0.317932i | \(-0.897012\pi\) | ||
0.948113 | − | 0.317932i | \(-0.102988\pi\) | |||||||
\(674\) | 41688.4 | 2.38246 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4435.50 | 0.252361 | ||||||||
\(677\) | 18249.8i | 1.03603i | 0.855370 | + | 0.518017i | \(0.173330\pi\) | ||||
−0.855370 | + | 0.518017i | \(0.826670\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8156.90 | −0.461021 | ||||||||
\(680\) | −49755.7 | − | 29345.0i | −2.80595 | − | 1.65490i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 56230.5i | − | 3.15715i | ||||||
\(683\) | − | 14144.2i | − | 0.792403i | −0.918164 | − | 0.396202i | \(-0.870328\pi\) | ||
0.918164 | − | 0.396202i | \(-0.129672\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7822.97 | − | 13264.2i | 0.436351 | − | 0.739851i | ||||
\(686\) | 1677.05 | 0.0933384 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 12207.4i | − | 0.676458i | ||||||
\(689\) | 2641.37 | 0.146049 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19621.7 | 1.08024 | 0.540120 | − | 0.841588i | \(-0.318379\pi\) | ||||
0.540120 | + | 0.841588i | \(0.318379\pi\) | |||||||
\(692\) | 32575.9i | 1.78952i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20361.9 | 1.11373 | ||||||||
\(695\) | −8086.22 | − | 4769.11i | −0.441335 | − | 0.260292i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 10382.9i | − | 0.564246i | ||||||
\(698\) | 12637.1i | 0.685272i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12180.0 | + | 6734.08i | −0.657659 | + | 0.363606i | ||||
\(701\) | −21609.1 | −1.16428 | −0.582142 | − | 0.813087i | \(-0.697785\pi\) | ||||
−0.582142 | + | 0.813087i | \(0.697785\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9437.75i | − | 0.506332i | ||||||
\(704\) | −29086.0 | −1.55713 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20531.6 | −1.09450 | ||||||||
\(707\) | − | 1.14099i | − | 6.06950e-5i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12557.2 | 0.665158 | 0.332579 | − | 0.943075i | \(-0.392081\pi\) | ||||
0.332579 | + | 0.943075i | \(0.392081\pi\) | |||||||
\(710\) | −170.945 | + | 289.845i | −0.00903586 | + | 0.0153207i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10665.9i | 0.561406i | ||||||||
\(713\) | 1534.96i | 0.0806237i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15515.6 | + | 26307.4i | −0.811540 | + | 1.37600i | ||||
\(716\) | 14503.9 | 0.757031 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4841.82i | 0.251665i | ||||||||
\(719\) | 36151.9 | 1.87516 | 0.937580 | − | 0.347771i | \(-0.113061\pi\) | ||||
0.937580 | + | 0.347771i | \(0.113061\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9105.48 | 0.470327 | ||||||||
\(722\) | − | 60912.8i | − | 3.13980i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 32285.9 | 1.65731 | ||||||||
\(725\) | 5276.46 | + | 9543.60i | 0.270293 | + | 0.488883i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12007.2i | 0.612550i | 0.951943 | + | 0.306275i | \(0.0990828\pi\) | ||||
−0.951943 | + | 0.306275i | \(0.900917\pi\) | |||||||
\(728\) | − | 13463.6i | − | 0.685434i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13868.8 | + | 8179.58i | 0.703162 | + | 0.414712i | ||||
\(731\) | 26423.9 | 1.33697 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15920.2i | 0.802220i | 0.916030 | + | 0.401110i | \(0.131375\pi\) | ||||
−0.916030 | + | 0.401110i | \(0.868625\pi\) | |||||||
\(734\) | −20433.8 | −1.02756 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 53.6452 | 0.00268667 | ||||||||
\(737\) | 8196.70i | 0.409674i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26581.1 | 1.32314 | 0.661571 | − | 0.749882i | \(-0.269890\pi\) | ||||
0.661571 | + | 0.749882i | \(0.269890\pi\) | |||||||
\(740\) | 6134.52 | − | 10401.3i | 0.304742 | − | 0.516703i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 1816.84i | − | 0.0898897i | ||||||
\(743\) | − | 6601.38i | − | 0.325950i | −0.986630 | − | 0.162975i | \(-0.947891\pi\) | ||
0.986630 | − | 0.162975i | \(-0.0521090\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14159.6 | − | 8351.06i | −0.696330 | − | 0.410683i | ||||
\(746\) | −36011.9 | −1.76741 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 116719.i | 5.70546i | ||||||||
\(749\) | 10721.4 | 0.523034 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29809.6 | −1.44842 | −0.724212 | − | 0.689578i | \(-0.757796\pi\) | ||||
−0.724212 | + | 0.689578i | \(0.757796\pi\) | |||||||
\(752\) | 307.274i | 0.0149004i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −21224.4 | −1.02513 | ||||||||
\(755\) | −16330.8 | − | 9631.61i | −0.787203 | − | 0.464278i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 8179.09i | − | 0.392700i | −0.980534 | − | 0.196350i | \(-0.937091\pi\) | ||
0.980534 | − | 0.196350i | \(-0.0629089\pi\) | |||||||
\(758\) | − | 30383.2i | − | 1.45589i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 30514.1 | − | 51737.9i | 1.45640 | − | 2.46938i | ||||
\(761\) | 31616.8 | 1.50605 | 0.753027 | − | 0.657990i | \(-0.228593\pi\) | ||||
0.753027 | + | 0.657990i | \(0.228593\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13799.8i | 0.654763i | ||||||||
\(764\) | 79276.5 | 3.75409 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8581.05 | 0.404760 | ||||||||
\(767\) | 34032.0i | 1.60212i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24651.3 | −1.15598 | −0.577991 | − | 0.816043i | \(-0.696163\pi\) | ||||
−0.577991 | + | 0.816043i | \(0.696163\pi\) | |||||||
\(770\) | 18095.3 | + | 10672.3i | 0.846893 | + | 0.499483i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 53975.6i | 2.51635i | ||||||||
\(773\) | − | 7888.63i | − | 0.367056i | −0.983015 | − | 0.183528i | \(-0.941248\pi\) | ||
0.983015 | − | 0.183528i | \(-0.0587518\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12669.6 | − | 22915.7i | −0.587233 | − | 1.06214i | ||||
\(776\) | 45043.1 | 2.08370 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 43054.2i | − | 1.98402i | ||||||
\(779\) | 10796.5 | 0.496566 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 337.954 | 0.0154839 | ||||||||
\(782\) | − | 4788.67i | − | 0.218980i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3025.73 | −0.137834 | ||||||||
\(785\) | 5449.31 | − | 9239.53i | 0.247763 | − | 0.420093i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 8592.94i | − | 0.389206i | −0.980882 | − | 0.194603i | \(-0.937658\pi\) | ||
0.980882 | − | 0.194603i | \(-0.0623419\pi\) | |||||||
\(788\) | − | 12127.8i | − | 0.548268i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 26067.1 | − | 44197.8i | 1.17395 | − | 1.99049i | ||||
\(791\) | 1839.72 | 0.0826964 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1336.79i | 0.0598623i | ||||||||
\(794\) | 67068.5 | 2.99770 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20237.3 | −0.901120 | ||||||||
\(797\) | 37498.1i | 1.66656i | 0.552848 | + | 0.833282i | \(0.313541\pi\) | ||||
−0.552848 | + | 0.833282i | \(0.686459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −665.116 | −0.0294495 | ||||||||
\(800\) | −800.878 | + | 442.789i | −0.0353942 | + | 0.0195687i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1502.11i | 0.0661364i | ||||||||
\(803\) | − | 16170.8i | − | 0.710653i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −493.958 | − | 291.328i | −0.0216270 | − | 0.0127552i | ||||
\(806\) | 50963.1 | 2.22717 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.30065i | 0.000274327i | ||||||||
\(809\) | 33834.0 | 1.47039 | 0.735193 | − | 0.677858i | \(-0.237092\pi\) | ||||
0.735193 | + | 0.677858i | \(0.237092\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16234.0 | 0.702899 | 0.351450 | − | 0.936207i | \(-0.385689\pi\) | ||||
0.351450 | + | 0.936207i | \(0.385689\pi\) | |||||||
\(812\) | 9713.48i | 0.419799i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −18227.5 | −0.784858 | ||||||||
\(815\) | 21953.7 | − | 37223.3i | 0.943562 | − | 1.59985i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27476.6i | 1.17660i | ||||||||
\(818\) | 60582.5i | 2.58951i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11898.8 | + | 7017.71i | 0.506737 | + | 0.298865i | ||||
\(821\) | 26551.4 | 1.12868 | 0.564342 | − | 0.825541i | \(-0.309130\pi\) | ||||
0.564342 | + | 0.825541i | \(0.309130\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 651.954i | − | 0.0276132i | −0.999905 | − | 0.0138066i | \(-0.995605\pi\) | ||
0.999905 | − | 0.0138066i | \(-0.00439492\pi\) | |||||||
\(824\) | −50281.3 | −2.12577 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 23408.6 | 0.986063 | ||||||||
\(827\) | − | 13248.0i | − | 0.557046i | −0.960430 | − | 0.278523i | \(-0.910155\pi\) | ||
0.960430 | − | 0.278523i | \(-0.0898448\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36828.9 | 1.54297 | 0.771484 | − | 0.636248i | \(-0.219515\pi\) | ||||
0.771484 | + | 0.636248i | \(0.219515\pi\) | |||||||
\(830\) | −36957.7 | − | 21797.0i | −1.54557 | − | 0.911549i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 26361.4i | − | 1.09846i | ||||||
\(833\) | − | 6549.41i | − | 0.272417i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2641.55 | − | 4478.85i | 0.109478 | − | 0.185625i | ||||
\(836\) | −121369. | −5.02111 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 13025.7i | − | 0.536953i | ||||||
\(839\) | −10641.5 | −0.437884 | −0.218942 | − | 0.975738i | \(-0.570261\pi\) | ||||
−0.218942 | + | 0.975738i | \(0.570261\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16778.0 | −0.687935 | ||||||||
\(842\) | 33497.6i | 1.37102i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −31982.2 | −1.30435 | ||||||||
\(845\) | −2685.47 | − | 1583.84i | −0.109329 | − | 0.0644804i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 11781.7i | − | 0.477952i | ||||||
\(848\) | 3277.93i | 0.132741i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 39525.9 | + | 71490.9i | 1.59497 | + | 2.88484i | ||||
\(851\) | 497.568 | 0.0200428 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 2819.13i | − | 0.113160i | −0.998398 | − | 0.0565799i | \(-0.981980\pi\) | ||
0.998398 | − | 0.0565799i | \(-0.0180196\pi\) | |||||||
\(854\) | 919.497 | 0.0368437 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −59204.6 | −2.36399 | ||||||||
\(857\) | 38853.9i | 1.54869i | 0.632766 | + | 0.774343i | \(0.281919\pi\) | ||||
−0.632766 | + | 0.774343i | \(0.718081\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8959.42 | −0.355869 | −0.177935 | − | 0.984042i | \(-0.556942\pi\) | ||||
−0.177935 | + | 0.984042i | \(0.556942\pi\) | |||||||
\(860\) | −17859.7 | + | 30281.9i | −0.708152 | + | 1.20070i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 37410.4i | − | 1.47819i | ||||||
\(863\) | − | 32649.8i | − | 1.28785i | −0.765090 | − | 0.643924i | \(-0.777305\pi\) | ||
0.765090 | − | 0.643924i | \(-0.222695\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11632.3 | − | 19723.1i | 0.457238 | − | 0.775265i | ||||
\(866\) | 3381.35 | 0.132682 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 23323.6i | − | 0.912045i | ||||||
\(869\) | −51533.8 | −2.01170 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7428.87 | −0.288999 | ||||||||
\(872\) | − | 76203.5i | − | 2.95937i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4979.45 | 0.192714 | ||||||||
\(875\) | 9779.01 | + | 272.135i | 0.377818 | + | 0.0105141i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 20229.3i | − | 0.778899i | −0.921048 | − | 0.389450i | \(-0.872665\pi\) | ||
0.921048 | − | 0.389450i | \(-0.127335\pi\) | |||||||
\(878\) | 51933.5i | 1.99621i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −32647.4 | − | 19254.8i | −1.25062 | − | 0.737592i | ||||
\(881\) | −4356.08 | −0.166584 | −0.0832918 | − | 0.996525i | \(-0.526543\pi\) | ||||
−0.0832918 | + | 0.996525i | \(0.526543\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 43349.9i | − | 1.65214i | −0.563567 | − | 0.826070i | \(-0.690571\pi\) | ||
0.563567 | − | 0.826070i | \(-0.309429\pi\) | |||||||
\(884\) | −105786. | −4.02484 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15321.6 | 0.580971 | ||||||||
\(887\) | 9754.67i | 0.369256i | 0.982809 | + | 0.184628i | \(0.0591080\pi\) | ||||
−0.982809 | + | 0.184628i | \(0.940892\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3987.54 | −0.150436 | ||||||||
\(890\) | 7662.58 | − | 12992.2i | 0.288596 | − | 0.489326i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 24120.3i | − | 0.905389i | ||||||
\(893\) | − | 691.614i | − | 0.0259171i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8781.35 | − | 5179.09i | −0.327965 | − | 0.193428i | ||||
\(896\) | −17722.4 | −0.660786 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 44712.8i | 1.66157i | ||||||||
\(899\) | −18275.1 | −0.677986 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7095.32 | −0.262352 | ||||||||
\(902\) | − | 20851.8i | − | 0.769720i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10159.1 | −0.373768 | ||||||||
\(905\) | −19547.5 | − | 11528.8i | −0.717989 | − | 0.423457i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 7155.16i | − | 0.261944i | −0.991386 | − | 0.130972i | \(-0.958190\pi\) | ||
0.991386 | − | 0.130972i | \(-0.0418098\pi\) | |||||||
\(908\) | − | 65232.6i | − | 2.38416i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −9672.53 | + | 16400.2i | −0.352353 | + | 0.597429i | ||||
\(911\) | 47255.4 | 1.71860 | 0.859298 | − | 0.511475i | \(-0.170901\pi\) | ||||
0.859298 | + | 0.511475i | \(0.170901\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43092.1i | 1.56204i | ||||||||
\(914\) | 39812.1 | 1.44077 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16370.9 | −0.590514 | ||||||||
\(917\) | 6893.66i | 0.248254i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30942.1 | −1.11065 | −0.555324 | − | 0.831634i | \(-0.687406\pi\) | ||||
−0.555324 | + | 0.831634i | \(0.687406\pi\) | |||||||
\(920\) | 2727.68 | + | 1608.74i | 0.0977488 | + | 0.0576505i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 45408.9i | − | 1.62198i | ||||||
\(923\) | 306.296i | 0.0109229i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7428.29 | + | 4106.95i | −0.264044 | + | 0.145984i | ||||
\(926\) | −11932.6 | −0.423468 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 638.696i | 0.0225929i | ||||||||
\(929\) | 12147.4 | 0.429004 | 0.214502 | − | 0.976724i | \(-0.431187\pi\) | ||||
0.214502 | + | 0.976724i | \(0.431187\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6810.33 | 0.239742 | ||||||||
\(932\) | 88729.4i | 3.11849i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 58996.6 | 2.06684 | ||||||||
\(935\) | 41678.5 | − | 70667.7i | 1.45779 | − | 2.47174i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 13388.6i | − | 0.466794i | −0.972381 | − | 0.233397i | \(-0.925016\pi\) | ||
0.972381 | − | 0.233397i | \(-0.0749842\pi\) | |||||||
\(938\) | 5109.87i | 0.177871i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 449.548 | − | 762.226i | 0.0155985 | − | 0.0264480i | ||||
\(941\) | 8035.36 | 0.278369 | 0.139184 | − | 0.990266i | \(-0.455552\pi\) | ||||
0.139184 | + | 0.990266i | \(0.455552\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 569.204i | 0.0196562i | ||||||||
\(944\) | −42233.6 | −1.45613 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 53066.6 | 1.82383 | ||||||||
\(947\) | − | 17647.7i | − | 0.605567i | −0.953059 | − | 0.302784i | \(-0.902084\pi\) | ||
0.953059 | − | 0.302784i | \(-0.0979160\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14656.0 | 0.501321 | ||||||||
\(950\) | −74339.0 | + | 41100.5i | −2.53882 | + | 1.40366i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 36166.4i | 1.23126i | ||||||||
\(953\) | 35629.1i | 1.21106i | 0.795823 | + | 0.605529i | \(0.207039\pi\) | ||||
−0.795823 | + | 0.605529i | \(0.792961\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −47998.0 | − | 28308.3i | −1.62636 | − | 0.959200i | ||||
\(956\) | −85727.3 | −2.90023 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 1932.33i | − | 0.0651679i | ||||||
\(959\) | −9641.45 | −0.324649 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14090.4 | 0.472977 | ||||||||
\(962\) | − | 16520.1i | − | 0.553667i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −63246.0 | −2.11309 | ||||||||
\(965\) | 19273.8 | − | 32679.5i | 0.642948 | − | 1.09015i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35954.1i | 1.19566i | 0.801622 | + | 0.597831i | \(0.203971\pi\) | ||||
−0.801622 | + | 0.597831i | \(0.796029\pi\) | |||||||
\(968\) | 65059.8i | 2.16023i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −54867.4 | − | 32359.8i | −1.81617 | − | 1.07115i | ||||
\(971\) | −59266.0 | −1.95874 | −0.979370 | − | 0.202074i | \(-0.935232\pi\) | ||||
−0.979370 | + | 0.202074i | \(0.935232\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5877.71i | 0.193660i | ||||||||
\(974\) | −46982.2 | −1.54559 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1658.95 | −0.0544076 | ||||||||
\(977\) | − | 35518.9i | − | 1.16310i | −0.813510 | − | 0.581551i | \(-0.802446\pi\) | ||
0.813510 | − | 0.581551i | \(-0.197554\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15148.7 | −0.494540 | ||||||||
\(980\) | 7505.66 | + | 4426.70i | 0.244652 | + | 0.144292i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 53494.4i | 1.73837i | ||||||||
\(983\) | − | 37683.6i | − | 1.22271i | −0.791358 | − | 0.611353i | \(-0.790626\pi\) | ||
0.791358 | − | 0.611353i | \(-0.209374\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4330.64 | + | 7342.78i | −0.140087 | + | 0.237523i | ||||
\(986\) | 57013.6 | 1.84146 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 110000.i | − | 3.54207i | ||||||
\(989\) | −1448.59 | −0.0465749 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21371.1 | 0.685041 | 0.342521 | − | 0.939510i | \(-0.388719\pi\) | ||||
0.342521 | + | 0.939510i | \(0.388719\pi\) | |||||||
\(992\) | − | 1533.61i | − | 0.0490848i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 210.682 | 0.00672278 | ||||||||
\(995\) | 12252.7 | + | 7226.40i | 0.390387 | + | 0.230244i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42934.0i | 1.36383i | 0.731434 | + | 0.681913i | \(0.238852\pi\) | ||||
−0.731434 | + | 0.681913i | \(0.761148\pi\) | |||||||
\(998\) | 45323.9i | 1.43758i | ||||||||
\(999\) | 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 | 315.4.d.b.64.2 | 10 | ||
3.2 | odd | 2 | 105.4.d.b.64.9 | yes | 10 | ||
5.2 | odd | 4 | 1575.4.a.bo.1.5 | 5 | |||
5.3 | odd | 4 | 1575.4.a.bp.1.1 | 5 | |||
5.4 | even | 2 | inner | 315.4.d.b.64.9 | 10 | ||
15.2 | even | 4 | 525.4.a.x.1.1 | 5 | |||
15.8 | even | 4 | 525.4.a.w.1.5 | 5 | |||
15.14 | odd | 2 | 105.4.d.b.64.2 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.d.b.64.2 | ✓ | 10 | 15.14 | odd | 2 | ||
105.4.d.b.64.9 | yes | 10 | 3.2 | odd | 2 | ||
315.4.d.b.64.2 | 10 | 1.1 | even | 1 | trivial | ||
315.4.d.b.64.9 | 10 | 5.4 | even | 2 | inner | ||
525.4.a.w.1.5 | 5 | 15.8 | even | 4 | |||
525.4.a.x.1.1 | 5 | 15.2 | even | 4 | |||
1575.4.a.bo.1.5 | 5 | 5.2 | odd | 4 | |||
1575.4.a.bp.1.1 | 5 | 5.3 | odd | 4 |