Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(64,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, 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("105.64");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(6.19520055060\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9}\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.2 | ||
Root | \(-1.37042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.64 |
Dual form | 105.4.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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | \(-0.332254\pi\) | |||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | −15.9059 | −1.98823 | ||||||||
\(5\) | −9.63020 | + | 5.67972i | −0.861351 | + | 0.508010i | ||||
\(6\) | 14.6681 | 0.998037 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | 38.6546i | 1.70831i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 27.7702 | + | 47.0855i | 0.878171 | + | 1.48898i | ||||
\(11\) | 54.9009 | 1.50484 | 0.752420 | − | 0.658684i | \(-0.228887\pi\) | ||||
0.752420 | + | 0.658684i | \(0.228887\pi\) | |||||||
\(12\) | − | 47.7176i | − | 1.14791i | ||||||
\(13\) | 49.7580i | 1.06157i | 0.847507 | + | 0.530784i | \(0.178103\pi\) | ||||
−0.847507 | + | 0.530784i | \(0.821897\pi\) | |||||||
\(14\) | 34.2255 | 0.653368 | ||||||||
\(15\) | −17.0392 | − | 28.8906i | −0.293300 | − | 0.497301i | ||||
\(16\) | 61.7496 | 0.964837 | ||||||||
\(17\) | 133.661i | 1.90692i | 0.301517 | + | 0.953461i | \(0.402507\pi\) | ||||
−0.301517 | + | 0.953461i | \(0.597493\pi\) | |||||||
\(18\) | 44.0043i | 0.576217i | ||||||||
\(19\) | −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 | ||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | − | 268.430i | − | 2.60134i | ||||||
\(23\) | − | 7.32751i | − | 0.0664301i | −0.999448 | − | 0.0332150i | \(-0.989425\pi\) | ||
0.999448 | − | 0.0332150i | \(-0.0105746\pi\) | |||||||
\(24\) | −115.964 | −0.986293 | ||||||||
\(25\) | 60.4815 | − | 109.394i | 0.483852 | − | 0.875150i | ||||
\(26\) | 243.285 | 1.83508 | ||||||||
\(27\) | − | 27.0000i | − | 0.192450i | ||||||
\(28\) | − | 111.341i | − | 0.751481i | ||||||
\(29\) | −87.2408 | −0.558628 | −0.279314 | − | 0.960200i | \(-0.590107\pi\) | ||||
−0.279314 | + | 0.960200i | \(0.590107\pi\) | |||||||
\(30\) | −141.257 | + | 83.3106i | −0.859660 | + | 0.507012i | ||||
\(31\) | −209.479 | −1.21366 | −0.606831 | − | 0.794831i | \(-0.707560\pi\) | ||||
−0.606831 | + | 0.794831i | \(0.707560\pi\) | |||||||
\(32\) | 7.32107i | 0.0404436i | ||||||||
\(33\) | 164.703i | 0.868820i | ||||||||
\(34\) | 653.519 | 3.29640 | ||||||||
\(35\) | −39.7580 | − | 67.4114i | −0.192010 | − | 0.325560i | ||||
\(36\) | 143.153 | 0.662744 | ||||||||
\(37\) | − | 67.9041i | − | 0.301713i | −0.988556 | − | 0.150856i | \(-0.951797\pi\) | ||
0.988556 | − | 0.150856i | \(-0.0482031\pi\) | |||||||
\(38\) | 679.555i | 2.90101i | ||||||||
\(39\) | −149.274 | −0.612897 | ||||||||
\(40\) | −219.547 | − | 372.252i | −0.867838 | − | 1.47145i | ||||
\(41\) | 77.6804 | 0.295894 | 0.147947 | − | 0.988995i | \(-0.452734\pi\) | ||||
0.147947 | + | 0.988995i | \(0.452734\pi\) | |||||||
\(42\) | 102.677i | 0.377222i | ||||||||
\(43\) | 197.692i | 0.701112i | 0.936542 | + | 0.350556i | \(0.114007\pi\) | ||||
−0.936542 | + | 0.350556i | \(0.885993\pi\) | |||||||
\(44\) | −873.246 | −2.99197 | ||||||||
\(45\) | 86.6718 | − | 51.1175i | 0.287117 | − | 0.169337i | ||||
\(46\) | −35.8269 | −0.114834 | ||||||||
\(47\) | 4.97613i | 0.0154435i | 0.999970 | + | 0.00772173i | \(0.00245793\pi\) | ||||
−0.999970 | + | 0.00772173i | \(0.997542\pi\) | |||||||
\(48\) | 185.249i | 0.557049i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | −534.865 | − | 295.716i | −1.51283 | − | 0.836412i | ||||
\(51\) | −400.984 | −1.10096 | ||||||||
\(52\) | − | 791.444i | − | 2.11065i | ||||||
\(53\) | 53.0843i | 0.137579i | 0.997631 | + | 0.0687895i | \(0.0219137\pi\) | ||||
−0.997631 | + | 0.0687895i | \(0.978086\pi\) | |||||||
\(54\) | −132.013 | −0.332679 | ||||||||
\(55\) | −528.706 | + | 311.822i | −1.29620 | + | 0.764473i | ||||
\(56\) | −270.582 | −0.645680 | ||||||||
\(57\) | − | 416.959i | − | 0.968905i | ||||||
\(58\) | 426.552i | 0.965673i | ||||||||
\(59\) | 683.950 | 1.50920 | 0.754599 | − | 0.656186i | \(-0.227831\pi\) | ||||
0.754599 | + | 0.656186i | \(0.227831\pi\) | |||||||
\(60\) | 271.023 | + | 459.530i | 0.583148 | + | 0.988751i | ||||
\(61\) | −26.8658 | −0.0563904 | −0.0281952 | − | 0.999602i | \(-0.508976\pi\) | ||||
−0.0281952 | + | 0.999602i | \(0.508976\pi\) | |||||||
\(62\) | 1024.22i | 2.09800i | ||||||||
\(63\) | − | 63.0000i | − | 0.125988i | ||||||
\(64\) | 529.792 | 1.03475 | ||||||||
\(65\) | −282.612 | − | 479.180i | −0.539287 | − | 0.914383i | ||||
\(66\) | 805.291 | 1.50189 | ||||||||
\(67\) | 149.300i | 0.272237i | 0.990693 | + | 0.136119i | \(0.0434628\pi\) | ||||
−0.990693 | + | 0.136119i | \(0.956537\pi\) | |||||||
\(68\) | − | 2126.00i | − | 3.79140i | ||||||
\(69\) | 21.9825 | 0.0383534 | ||||||||
\(70\) | −329.599 | + | 194.391i | −0.562780 | + | 0.331918i | ||||
\(71\) | 6.15571 | 0.0102894 | 0.00514470 | − | 0.999987i | \(-0.498362\pi\) | ||||
0.00514470 | + | 0.999987i | \(0.498362\pi\) | |||||||
\(72\) | − | 347.892i | − | 0.569436i | ||||||
\(73\) | − | 294.545i | − | 0.472245i | −0.971723 | − | 0.236123i | \(-0.924123\pi\) | ||
0.971723 | − | 0.236123i | \(-0.0758767\pi\) | |||||||
\(74\) | −332.008 | −0.521556 | ||||||||
\(75\) | 328.181 | + | 181.445i | 0.505268 | + | 0.279352i | ||||
\(76\) | 2210.70 | 3.33664 | ||||||||
\(77\) | 384.306i | 0.568776i | ||||||||
\(78\) | 729.855i | 1.05948i | ||||||||
\(79\) | 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 | ||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | − | 379.807i | − | 0.511496i | ||||||
\(83\) | − | 784.907i | − | 1.03801i | −0.854772 | − | 0.519004i | \(-0.826303\pi\) | ||
0.854772 | − | 0.519004i | \(-0.173697\pi\) | |||||||
\(84\) | 334.023 | 0.433868 | ||||||||
\(85\) | −759.160 | − | 1287.19i | −0.968735 | − | 1.64253i | ||||
\(86\) | 966.590 | 1.21198 | ||||||||
\(87\) | − | 261.722i | − | 0.322524i | ||||||
\(88\) | 2122.17i | 2.57073i | ||||||||
\(89\) | −275.928 | −0.328633 | −0.164316 | − | 0.986408i | \(-0.552542\pi\) | ||||
−0.164316 | + | 0.986408i | \(0.552542\pi\) | |||||||
\(90\) | −249.932 | − | 423.770i | −0.292724 | − | 0.496325i | ||||
\(91\) | −348.306 | −0.401235 | ||||||||
\(92\) | 116.550i | 0.132078i | ||||||||
\(93\) | − | 628.437i | − | 0.700708i | ||||||
\(94\) | 24.3301 | 0.0266963 | ||||||||
\(95\) | 1338.47 | − | 789.404i | 1.44551 | − | 0.852538i | ||||
\(96\) | −21.9632 | −0.0233501 | ||||||||
\(97\) | 1165.27i | 1.21975i | 0.792499 | + | 0.609873i | \(0.208780\pi\) | ||||
−0.792499 | + | 0.609873i | \(0.791220\pi\) | |||||||
\(98\) | 239.579i | 0.246950i | ||||||||
\(99\) | −494.108 | −0.501613 | ||||||||
\(100\) | −962.011 | + | 1740.00i | −0.962011 | + | 1.74000i | ||||
\(101\) | −0.162999 | −0.000160584 | −8.02919e−5 | − | 1.00000i | \(-0.500026\pi\) | ||||
−8.02919e−5 | 1.00000i | \(0.500026\pi\) | ||||||||
\(102\) | 1960.56i | 1.90318i | ||||||||
\(103\) | − | 1300.78i | − | 1.24437i | −0.782871 | − | 0.622184i | \(-0.786245\pi\) | ||
0.782871 | − | 0.622184i | \(-0.213755\pi\) | |||||||
\(104\) | −1923.38 | −1.81349 | ||||||||
\(105\) | 202.234 | − | 119.274i | 0.187962 | − | 0.110857i | ||||
\(106\) | 259.548 | 0.237826 | ||||||||
\(107\) | 1531.63i | 1.38382i | 0.721985 | + | 0.691908i | \(0.243230\pi\) | ||||
−0.721985 | + | 0.691908i | \(0.756770\pi\) | |||||||
\(108\) | 429.458i | 0.382636i | ||||||||
\(109\) | −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 | ||||
\(111\) | 203.712 | 0.174194 | ||||||||
\(112\) | 432.247i | 0.364674i | ||||||||
\(113\) | 262.817i | 0.218794i | 0.993998 | + | 0.109397i | \(0.0348920\pi\) | ||||
−0.993998 | + | 0.109397i | \(0.965108\pi\) | |||||||
\(114\) | −2038.66 | −1.67490 | ||||||||
\(115\) | 41.6182 | + | 70.5654i | 0.0337471 | + | 0.0572196i | ||||
\(116\) | 1387.64 | 1.11068 | ||||||||
\(117\) | − | 447.822i | − | 0.353856i | ||||||
\(118\) | − | 3344.08i | − | 2.60888i | ||||||
\(119\) | −935.630 | −0.720749 | ||||||||
\(120\) | 1116.76 | − | 658.642i | 0.849545 | − | 0.501046i | ||||
\(121\) | 1683.11 | 1.26454 | ||||||||
\(122\) | 131.357i | 0.0974793i | ||||||||
\(123\) | 233.041i | 0.170834i | ||||||||
\(124\) | 3331.94 | 2.41304 | ||||||||
\(125\) | 38.8765 | + | 1397.00i | 0.0278177 | + | 0.999613i | ||||
\(126\) | −308.030 | −0.217789 | ||||||||
\(127\) | 569.649i | 0.398017i | 0.979998 | + | 0.199009i | \(0.0637722\pi\) | ||||
−0.979998 | + | 0.199009i | \(0.936228\pi\) | |||||||
\(128\) | − | 2531.78i | − | 1.74828i | ||||||
\(129\) | −593.077 | −0.404787 | ||||||||
\(130\) | −2342.88 | + | 1381.79i | −1.58065 | + | 0.932239i | ||||
\(131\) | 984.808 | 0.656817 | 0.328409 | − | 0.944536i | \(-0.393488\pi\) | ||||
0.328409 | + | 0.944536i | \(0.393488\pi\) | |||||||
\(132\) | − | 2619.74i | − | 1.72742i | ||||||
\(133\) | − | 972.905i | − | 0.634297i | ||||||
\(134\) | 729.982 | 0.470603 | ||||||||
\(135\) | 153.352 | + | 260.015i | 0.0977665 | + | 0.165767i | ||||
\(136\) | −5166.63 | −3.25761 | ||||||||
\(137\) | − | 1377.35i | − | 0.858942i | −0.903081 | − | 0.429471i | \(-0.858700\pi\) | ||
0.903081 | − | 0.429471i | \(-0.141300\pi\) | |||||||
\(138\) | − | 107.481i | − | 0.0662997i | ||||||
\(139\) | −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 | ||||
\(141\) | −14.9284 | −0.00891629 | ||||||||
\(142\) | − | 30.0975i | − | 0.0177868i | ||||||
\(143\) | 2731.76i | 1.59749i | ||||||||
\(144\) | −555.746 | −0.321612 | ||||||||
\(145\) | 840.147 | − | 495.504i | 0.481175 | − | 0.283788i | ||||
\(146\) | −1440.14 | −0.816347 | ||||||||
\(147\) | − | 147.000i | − | 0.0824786i | ||||||
\(148\) | 1080.07i | 0.599875i | ||||||||
\(149\) | 1470.33 | 0.808416 | 0.404208 | − | 0.914667i | \(-0.367547\pi\) | ||||
0.404208 | + | 0.914667i | \(0.367547\pi\) | |||||||
\(150\) | 887.148 | − | 1604.60i | 0.482902 | − | 0.873432i | ||||
\(151\) | −1695.79 | −0.913916 | −0.456958 | − | 0.889488i | \(-0.651061\pi\) | ||||
−0.456958 | + | 0.889488i | \(0.651061\pi\) | |||||||
\(152\) | − | 5372.47i | − | 2.86687i | ||||||
\(153\) | − | 1202.95i | − | 0.635641i | ||||||
\(154\) | 1879.01 | 0.983215 | ||||||||
\(155\) | 2017.32 | − | 1189.78i | 1.04539 | − | 0.616552i | ||||
\(156\) | 2374.33 | 1.21858 | ||||||||
\(157\) | 959.433i | 0.487714i | 0.969811 | + | 0.243857i | \(0.0784127\pi\) | ||||
−0.969811 | + | 0.243857i | \(0.921587\pi\) | |||||||
\(158\) | − | 4589.49i | − | 2.31089i | ||||||
\(159\) | −159.253 | −0.0794312 | ||||||||
\(160\) | −41.5816 | − | 70.5033i | −0.0205457 | − | 0.0348361i | ||||
\(161\) | 51.2926 | 0.0251082 | ||||||||
\(162\) | − | 396.038i | − | 0.192072i | ||||||
\(163\) | 3865.27i | 1.85737i | 0.370869 | + | 0.928685i | \(0.379060\pi\) | ||||
−0.370869 | + | 0.928685i | \(0.620940\pi\) | |||||||
\(164\) | −1235.57 | −0.588305 | ||||||||
\(165\) | −935.465 | − | 1586.12i | −0.441369 | − | 0.748359i | ||||
\(166\) | −3837.69 | −1.79435 | ||||||||
\(167\) | − | 465.084i | − | 0.215505i | −0.994178 | − | 0.107752i | \(-0.965635\pi\) | ||
0.994178 | − | 0.107752i | \(-0.0343653\pi\) | |||||||
\(168\) | − | 811.747i | − | 0.372784i | ||||||
\(169\) | −278.860 | −0.126927 | ||||||||
\(170\) | −6293.52 | + | 3711.81i | −2.83936 | + | 1.67460i | ||||
\(171\) | 1250.88 | 0.559398 | ||||||||
\(172\) | − | 3144.47i | − | 1.39397i | ||||||
\(173\) | − | 2048.04i | − | 0.900057i | −0.893014 | − | 0.450028i | \(-0.851414\pi\) | ||
0.893014 | − | 0.450028i | \(-0.148586\pi\) | |||||||
\(174\) | −1279.66 | −0.557531 | ||||||||
\(175\) | 765.756 | + | 423.371i | 0.330775 | + | 0.182879i | ||||
\(176\) | 3390.10 | 1.45192 | ||||||||
\(177\) | 2051.85i | 0.871336i | ||||||||
\(178\) | 1349.11i | 0.568091i | ||||||||
\(179\) | 911.856 | 0.380756 | 0.190378 | − | 0.981711i | \(-0.439029\pi\) | ||||
0.190378 | + | 0.981711i | \(0.439029\pi\) | |||||||
\(180\) | −1378.59 | + | 813.068i | −0.570856 | + | 0.336681i | ||||
\(181\) | −2029.81 | −0.833562 | −0.416781 | − | 0.909007i | \(-0.636842\pi\) | ||||
−0.416781 | + | 0.909007i | \(0.636842\pi\) | |||||||
\(182\) | 1702.99i | 0.693595i | ||||||||
\(183\) | − | 80.5975i | − | 0.0325570i | ||||||
\(184\) | 283.242 | 0.113483 | ||||||||
\(185\) | 385.677 | + | 653.930i | 0.153273 | + | 0.259881i | ||||
\(186\) | −3072.66 | −1.21128 | ||||||||
\(187\) | 7338.13i | 2.86961i | ||||||||
\(188\) | − | 79.1496i | − | 0.0307052i | ||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | −3859.68 | − | 6544.25i | −1.47374 | − | 2.49879i | ||||
\(191\) | 4984.11 | 1.88815 | 0.944077 | − | 0.329725i | \(-0.106956\pi\) | ||||
0.944077 | + | 0.329725i | \(0.106956\pi\) | |||||||
\(192\) | 1589.38i | 0.597413i | ||||||||
\(193\) | 3393.44i | 1.26562i | 0.774306 | + | 0.632811i | \(0.218099\pi\) | ||||
−0.774306 | + | 0.632811i | \(0.781901\pi\) | |||||||
\(194\) | 5697.43 | 2.10852 | ||||||||
\(195\) | 1437.54 | − | 847.835i | 0.527919 | − | 0.311358i | ||||
\(196\) | 779.387 | 0.284033 | ||||||||
\(197\) | 762.475i | 0.275757i | 0.990449 | + | 0.137878i | \(0.0440283\pi\) | ||||
−0.990449 | + | 0.137878i | \(0.955972\pi\) | |||||||
\(198\) | 2415.87i | 0.867114i | ||||||||
\(199\) | 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 | ||||
\(201\) | −447.900 | −0.157176 | ||||||||
\(202\) | 0.796959i | 0.000277593i | ||||||||
\(203\) | − | 610.686i | − | 0.211142i | ||||||
\(204\) | 6378.00 | 2.18897 | ||||||||
\(205\) | −748.077 | + | 441.203i | −0.254868 | + | 0.150317i | ||||
\(206\) | −6360.00 | −2.15108 | ||||||||
\(207\) | 65.9476i | 0.0221434i | ||||||||
\(208\) | 3072.53i | 1.02424i | ||||||||
\(209\) | −7630.47 | −2.52541 | ||||||||
\(210\) | −583.174 | − | 988.796i | −0.191633 | − | 0.324921i | ||||
\(211\) | 2010.72 | 0.656035 | 0.328017 | − | 0.944672i | \(-0.393620\pi\) | ||||
0.328017 | + | 0.944672i | \(0.393620\pi\) | |||||||
\(212\) | − | 844.351i | − | 0.273539i | ||||||
\(213\) | 18.4671i | 0.00594059i | ||||||||
\(214\) | 7488.70 | 2.39214 | ||||||||
\(215\) | −1122.84 | − | 1903.82i | −0.356172 | − | 0.603904i | ||||
\(216\) | 1043.67 | 0.328764 | ||||||||
\(217\) | − | 1466.35i | − | 0.458721i | ||||||
\(218\) | 9638.85i | 2.99461i | ||||||||
\(219\) | 883.635 | 0.272651 | ||||||||
\(220\) | 8409.53 | − | 4959.79i | 2.57714 | − | 1.51995i | ||||
\(221\) | −6650.73 | −2.02433 | ||||||||
\(222\) | − | 996.024i | − | 0.301120i | ||||||
\(223\) | − | 1516.44i | − | 0.455374i | −0.973734 | − | 0.227687i | \(-0.926884\pi\) | ||
0.973734 | − | 0.227687i | \(-0.0731163\pi\) | |||||||
\(224\) | −51.2475 | −0.0152862 | ||||||||
\(225\) | −544.334 | + | 984.543i | −0.161284 | + | 0.291717i | ||||
\(226\) | 1285.01 | 0.378219 | ||||||||
\(227\) | 4101.17i | 1.19914i | 0.800323 | + | 0.599568i | \(0.204661\pi\) | ||||
−0.800323 | + | 0.599568i | \(0.795339\pi\) | |||||||
\(228\) | 6632.10i | 1.92641i | ||||||||
\(229\) | 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 | ||||
\(231\) | −1152.92 | −0.328383 | ||||||||
\(232\) | − | 3372.26i | − | 0.954309i | ||||||
\(233\) | − | 5578.41i | − | 1.56847i | −0.620463 | − | 0.784236i | \(-0.713055\pi\) | ||
0.620463 | − | 0.784236i | \(-0.286945\pi\) | |||||||
\(234\) | −2189.56 | −0.611694 | ||||||||
\(235\) | −28.2630 | − | 47.9211i | −0.00784543 | − | 0.0133022i | ||||
\(236\) | −10878.8 | −3.00064 | ||||||||
\(237\) | 2816.01i | 0.771812i | ||||||||
\(238\) | 4574.64i | 1.24592i | ||||||||
\(239\) | −5389.67 | −1.45870 | −0.729348 | − | 0.684142i | \(-0.760177\pi\) | ||||
−0.729348 | + | 0.684142i | \(0.760177\pi\) | |||||||
\(240\) | −1052.16 | − | 1783.98i | −0.282986 | − | 0.479815i | ||||
\(241\) | 3976.27 | 1.06280 | 0.531399 | − | 0.847122i | \(-0.321667\pi\) | ||||
0.531399 | + | 0.847122i | \(0.321667\pi\) | |||||||
\(242\) | − | 8229.31i | − | 2.18595i | ||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 427.324 | 0.112117 | ||||||||
\(245\) | 471.880 | − | 278.306i | 0.123050 | − | 0.0725728i | ||||
\(246\) | 1139.42 | 0.295313 | ||||||||
\(247\) | − | 6915.69i | − | 1.78152i | ||||||
\(248\) | − | 8097.33i | − | 2.07331i | ||||||
\(249\) | 2354.72 | 0.599294 | ||||||||
\(250\) | 6830.45 | − | 190.081i | 1.72798 | − | 0.0480871i | ||||
\(251\) | 7095.76 | 1.78438 | 0.892192 | − | 0.451655i | \(-0.149166\pi\) | ||||
0.892192 | + | 0.451655i | \(0.149166\pi\) | |||||||
\(252\) | 1002.07i | 0.250494i | ||||||||
\(253\) | − | 402.287i | − | 0.0999666i | ||||||
\(254\) | 2785.22 | 0.688033 | ||||||||
\(255\) | 3861.56 | − | 2277.48i | 0.948315 | − | 0.559299i | ||||
\(256\) | −8140.43 | −1.98741 | ||||||||
\(257\) | − | 2526.56i | − | 0.613239i | −0.951832 | − | 0.306619i | \(-0.900802\pi\) | ||
0.951832 | − | 0.306619i | \(-0.0991979\pi\) | |||||||
\(258\) | 2899.77i | 0.699735i | ||||||||
\(259\) | 475.329 | 0.114037 | ||||||||
\(260\) | 4495.18 | + | 7621.77i | 1.07223 | + | 1.81801i | ||||
\(261\) | 785.167 | 0.186209 | ||||||||
\(262\) | − | 4815.08i | − | 1.13541i | ||||||
\(263\) | 3842.34i | 0.900871i | 0.892809 | + | 0.450435i | \(0.148731\pi\) | ||||
−0.892809 | + | 0.450435i | \(0.851269\pi\) | |||||||
\(264\) | −6366.52 | −1.48421 | ||||||||
\(265\) | −301.504 | − | 511.212i | −0.0698914 | − | 0.118504i | ||||
\(266\) | −4756.88 | −1.09648 | ||||||||
\(267\) | − | 827.784i | − | 0.189736i | ||||||
\(268\) | − | 2374.75i | − | 0.541271i | ||||||
\(269\) | 8411.04 | 1.90643 | 0.953216 | − | 0.302291i | \(-0.0977514\pi\) | ||||
0.953216 | + | 0.302291i | \(0.0977514\pi\) | |||||||
\(270\) | 1271.31 | − | 749.796i | 0.286553 | − | 0.169004i | ||||
\(271\) | 5659.73 | 1.26865 | 0.634325 | − | 0.773067i | \(-0.281278\pi\) | ||||
0.634325 | + | 0.773067i | \(0.281278\pi\) | |||||||
\(272\) | 8253.54i | 1.83987i | ||||||||
\(273\) | − | 1044.92i | − | 0.231653i | ||||||
\(274\) | −6734.37 | −1.48481 | ||||||||
\(275\) | 3320.49 | − | 6005.81i | 0.728120 | − | 1.31696i | ||||
\(276\) | −349.651 | −0.0762555 | ||||||||
\(277\) | − | 881.409i | − | 0.191187i | −0.995420 | − | 0.0955934i | \(-0.969525\pi\) | ||
0.995420 | − | 0.0955934i | \(-0.0304749\pi\) | |||||||
\(278\) | 4105.47i | 0.885718i | ||||||||
\(279\) | 1885.31 | 0.404554 | ||||||||
\(280\) | 2605.76 | − | 1536.83i | 0.556157 | − | 0.328012i | ||||
\(281\) | −3853.71 | −0.818124 | −0.409062 | − | 0.912506i | \(-0.634144\pi\) | ||||
−0.409062 | + | 0.912506i | \(0.634144\pi\) | |||||||
\(282\) | 72.9902i | 0.0154131i | ||||||||
\(283\) | 1891.60i | 0.397328i | 0.980068 | + | 0.198664i | \(0.0636603\pi\) | ||||
−0.980068 | + | 0.198664i | \(0.936340\pi\) | |||||||
\(284\) | −97.9118 | −0.0204577 | ||||||||
\(285\) | 2368.21 | + | 4015.40i | 0.492213 | + | 0.834568i | ||||
\(286\) | 13356.6 | 2.76150 | ||||||||
\(287\) | 543.763i | 0.111837i | ||||||||
\(288\) | − | 65.8896i | − | 0.0134812i | ||||||
\(289\) | −12952.4 | −2.63635 | ||||||||
\(290\) | −2422.70 | − | 4107.78i | −0.490571 | − | 0.831784i | ||||
\(291\) | −3495.81 | −0.704221 | ||||||||
\(292\) | 4684.99i | 0.938933i | ||||||||
\(293\) | 4076.18i | 0.812742i | 0.913708 | + | 0.406371i | \(0.133206\pi\) | ||||
−0.913708 | + | 0.406371i | \(0.866794\pi\) | |||||||
\(294\) | −718.736 | −0.142577 | ||||||||
\(295\) | −6586.58 | + | 3884.65i | −1.29995 | + | 0.766687i | ||||
\(296\) | 2624.81 | 0.515419 | ||||||||
\(297\) | − | 1482.32i | − | 0.289607i | ||||||
\(298\) | − | 7188.97i | − | 1.39747i | ||||||
\(299\) | 364.602 | 0.0705201 | ||||||||
\(300\) | −5220.00 | − | 2886.03i | −1.00459 | − | 0.555417i | ||||
\(301\) | −1383.85 | −0.264995 | ||||||||
\(302\) | 8291.33i | 1.57984i | ||||||||
\(303\) | − | 0.488996i | − | 9.27131e-5i | ||||||
\(304\) | −8582.35 | −1.61918 | ||||||||
\(305\) | 258.723 | − | 152.590i | 0.0485720 | − | 0.0286469i | ||||
\(306\) | −5881.67 | −1.09880 | ||||||||
\(307\) | 6201.87i | 1.15296i | 0.817110 | + | 0.576481i | \(0.195575\pi\) | ||||
−0.817110 | + | 0.576481i | \(0.804425\pi\) | |||||||
\(308\) | − | 6112.72i | − | 1.13086i | ||||||
\(309\) | 3902.35 | 0.718437 | ||||||||
\(310\) | −5817.28 | − | 9863.43i | −1.06580 | − | 1.80711i | ||||
\(311\) | −6601.95 | −1.20374 | −0.601868 | − | 0.798595i | \(-0.705577\pi\) | ||||
−0.601868 | + | 0.798595i | \(0.705577\pi\) | |||||||
\(312\) | − | 5770.13i | − | 1.04702i | ||||||
\(313\) | − | 2291.01i | − | 0.413724i | −0.978370 | − | 0.206862i | \(-0.933675\pi\) | ||
0.978370 | − | 0.206862i | \(-0.0663251\pi\) | |||||||
\(314\) | 4691.02 | 0.843087 | ||||||||
\(315\) | 357.822 | + | 606.703i | 0.0640032 | + | 0.108520i | ||||
\(316\) | −14930.3 | −2.65790 | ||||||||
\(317\) | 3124.07i | 0.553517i | 0.960939 | + | 0.276759i | \(0.0892603\pi\) | ||||
−0.960939 | + | 0.276759i | \(0.910740\pi\) | |||||||
\(318\) | 778.644i | 0.137309i | ||||||||
\(319\) | −4789.60 | −0.840646 | ||||||||
\(320\) | −5102.00 | + | 3009.07i | −0.891283 | + | 0.525663i | ||||
\(321\) | −4594.89 | −0.798947 | ||||||||
\(322\) | − | 250.788i | − | 0.0434033i | ||||||
\(323\) | − | 18577.1i | − | 3.20018i | ||||||
\(324\) | −1288.37 | −0.220915 | ||||||||
\(325\) | 5443.21 | + | 3009.44i | 0.929031 | + | 0.513642i | ||||
\(326\) | 18898.7 | 3.21074 | ||||||||
\(327\) | − | 5914.18i | − | 1.00017i | ||||||
\(328\) | 3002.70i | 0.505478i | ||||||||
\(329\) | −34.8329 | −0.00583708 | ||||||||
\(330\) | −7755.11 | + | 4573.83i | −1.29365 | + | 0.762972i | ||||
\(331\) | 9825.49 | 1.63159 | 0.815797 | − | 0.578338i | \(-0.196298\pi\) | ||||
0.815797 | + | 0.578338i | \(0.196298\pi\) | |||||||
\(332\) | 12484.6i | 2.06380i | ||||||||
\(333\) | 611.137i | 0.100571i | ||||||||
\(334\) | −2273.96 | −0.372532 | ||||||||
\(335\) | −847.983 | − | 1437.79i | −0.138299 | − | 0.234492i | ||||
\(336\) | −1296.74 | −0.210545 | ||||||||
\(337\) | − | 8526.35i | − | 1.37822i | −0.724657 | − | 0.689110i | \(-0.758002\pi\) | ||
0.724657 | − | 0.689110i | \(-0.241998\pi\) | |||||||
\(338\) | 1363.45i | 0.219413i | ||||||||
\(339\) | −788.451 | −0.126321 | ||||||||
\(340\) | 12075.1 | + | 20473.8i | 1.92607 | + | 3.26573i | ||||
\(341\) | −11500.6 | −1.82637 | ||||||||
\(342\) | − | 6115.99i | − | 0.967003i | ||||||
\(343\) | − | 343.000i | − | 0.0539949i | ||||||
\(344\) | −7641.73 | −1.19772 | ||||||||
\(345\) | −211.696 | + | 124.855i | −0.0330358 | + | 0.0194839i | ||||
\(346\) | −10013.6 | −1.55588 | ||||||||
\(347\) | 4164.54i | 0.644277i | 0.946693 | + | 0.322138i | \(0.104402\pi\) | ||||
−0.946693 | + | 0.322138i | \(0.895598\pi\) | |||||||
\(348\) | 4162.92i | 0.641253i | ||||||||
\(349\) | −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 | ||||
\(351\) | 1343.47 | 0.204299 | ||||||||
\(352\) | 401.933i | 0.0608611i | ||||||||
\(353\) | − | 4199.25i | − | 0.633154i | −0.948567 | − | 0.316577i | \(-0.897466\pi\) | ||
0.948567 | − | 0.316577i | \(-0.102534\pi\) | |||||||
\(354\) | 10032.2 | 1.50624 | ||||||||
\(355\) | −59.2807 | + | 34.9627i | −0.00886280 | + | 0.00522712i | ||||
\(356\) | 4388.87 | 0.653398 | ||||||||
\(357\) | − | 2806.89i | − | 0.416124i | ||||||
\(358\) | − | 4458.39i | − | 0.658194i | ||||||
\(359\) | 990.277 | 0.145584 | 0.0727922 | − | 0.997347i | \(-0.476809\pi\) | ||||
0.0727922 | + | 0.997347i | \(0.476809\pi\) | |||||||
\(360\) | 1975.93 | + | 3350.27i | 0.289279 | + | 0.490485i | ||||
\(361\) | 12458.2 | 1.81633 | ||||||||
\(362\) | 9924.48i | 1.44094i | ||||||||
\(363\) | 5049.32i | 0.730084i | ||||||||
\(364\) | 5540.11 | 0.797749 | ||||||||
\(365\) | 1672.93 | + | 2836.53i | 0.239905 | + | 0.406769i | ||||
\(366\) | −394.070 | −0.0562797 | ||||||||
\(367\) | 4179.24i | 0.594427i | 0.954811 | + | 0.297213i | \(0.0960573\pi\) | ||||
−0.954811 | + | 0.297213i | \(0.903943\pi\) | |||||||
\(368\) | − | 452.471i | − | 0.0640942i | ||||||
\(369\) | −699.123 | −0.0986312 | ||||||||
\(370\) | 3197.30 | − | 1885.71i | 0.449243 | − | 0.264955i | ||||
\(371\) | −371.590 | −0.0519999 | ||||||||
\(372\) | 9995.83i | 1.39317i | ||||||||
\(373\) | 7365.36i | 1.02242i | 0.859455 | + | 0.511212i | \(0.170803\pi\) | ||||
−0.859455 | + | 0.511212i | \(0.829197\pi\) | |||||||
\(374\) | 35878.8 | 4.96056 | ||||||||
\(375\) | −4191.00 | + | 116.629i | −0.577127 | + | 0.0160606i | ||||
\(376\) | −192.350 | −0.0263822 | ||||||||
\(377\) | − | 4340.93i | − | 0.593022i | ||||||
\(378\) | − | 924.089i | − | 0.125741i | ||||||
\(379\) | 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 | ||||
\(381\) | −1708.95 | −0.229795 | ||||||||
\(382\) | − | 24369.1i | − | 3.26396i | ||||||
\(383\) | 1755.04i | 0.234148i | 0.993123 | + | 0.117074i | \(0.0373514\pi\) | ||||
−0.993123 | + | 0.117074i | \(0.962649\pi\) | |||||||
\(384\) | 7595.33 | 1.00937 | ||||||||
\(385\) | −2182.75 | − | 3700.94i | −0.288944 | − | 0.489916i | ||||
\(386\) | 16591.7 | 2.18782 | ||||||||
\(387\) | − | 1779.23i | − | 0.233704i | ||||||
\(388\) | − | 18534.6i | − | 2.42514i | ||||||
\(389\) | −8805.69 | −1.14773 | −0.573864 | − | 0.818950i | \(-0.694556\pi\) | ||||
−0.573864 | + | 0.818950i | \(0.694556\pi\) | |||||||
\(390\) | −4145.37 | − | 7028.65i | −0.538228 | − | 0.912588i | ||||
\(391\) | 979.406 | 0.126677 | ||||||||
\(392\) | − | 1894.08i | − | 0.244044i | ||||||
\(393\) | 2954.42i | 0.379214i | ||||||||
\(394\) | 3728.01 | 0.476687 | ||||||||
\(395\) | −9039.57 | + | 5331.38i | −1.15147 | + | 0.679116i | ||||
\(396\) | 7859.21 | 0.997324 | ||||||||
\(397\) | − | 13717.2i | − | 1.73413i | −0.498199 | − | 0.867063i | \(-0.666005\pi\) | ||
0.498199 | − | 0.867063i | \(-0.333995\pi\) | |||||||
\(398\) | − | 6220.82i | − | 0.783471i | ||||||
\(399\) | 2918.71 | 0.366212 | ||||||||
\(400\) | 3734.71 | − | 6755.01i | 0.466838 | − | 0.844377i | ||||
\(401\) | 307.220 | 0.0382590 | 0.0191295 | − | 0.999817i | \(-0.493911\pi\) | ||||
0.0191295 | + | 0.999817i | \(0.493911\pi\) | |||||||
\(402\) | 2189.95i | 0.271703i | ||||||||
\(403\) | − | 10423.3i | − | 1.28839i | ||||||
\(404\) | 2.59263 | 0.000319278 | ||||||||
\(405\) | −780.046 | + | 460.057i | −0.0957057 | + | 0.0564455i | ||||
\(406\) | −2985.86 | −0.364990 | ||||||||
\(407\) | − | 3728.00i | − | 0.454029i | ||||||
\(408\) | − | 15499.9i | − | 1.88078i | ||||||
\(409\) | −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 | ||||
\(411\) | 4132.05 | 0.495910 | ||||||||
\(412\) | 20690.1i | 2.47409i | ||||||||
\(413\) | 4787.65i | 0.570423i | ||||||||
\(414\) | 322.442 | 0.0382781 | ||||||||
\(415\) | 4458.05 | + | 7558.81i | 0.527318 | + | 0.894090i | ||||
\(416\) | −364.282 | −0.0429336 | ||||||||
\(417\) | − | 2519.02i | − | 0.295820i | ||||||
\(418\) | 37308.2i | 4.36555i | ||||||||
\(419\) | −2664.10 | −0.310620 | −0.155310 | − | 0.987866i | \(-0.549638\pi\) | ||||
−0.155310 | + | 0.987866i | \(0.549638\pi\) | |||||||
\(420\) | −3216.71 | + | 1897.16i | −0.373713 | + | 0.220409i | ||||
\(421\) | −6851.11 | −0.793118 | −0.396559 | − | 0.918009i | \(-0.629796\pi\) | ||||
−0.396559 | + | 0.918009i | \(0.629796\pi\) | |||||||
\(422\) | − | 9831.12i | − | 1.13406i | ||||||
\(423\) | − | 44.7851i | − | 0.00514782i | ||||||
\(424\) | −2051.95 | −0.235027 | ||||||||
\(425\) | 14621.7 | + | 8084.05i | 1.66884 | + | 0.922668i | ||||
\(426\) | 90.2924 | 0.0102692 | ||||||||
\(427\) | − | 188.061i | − | 0.0213136i | ||||||
\(428\) | − | 24361.9i | − | 2.75135i | ||||||
\(429\) | −8195.27 | −0.922311 | ||||||||
\(430\) | −9308.45 | + | 5489.96i | −1.04394 | + | 0.615696i | ||||
\(431\) | −7651.38 | −0.855114 | −0.427557 | − | 0.903988i | \(-0.640626\pi\) | ||||
−0.427557 | + | 0.903988i | \(0.640626\pi\) | |||||||
\(432\) | − | 1667.24i | − | 0.185683i | ||||||
\(433\) | − | 691.572i | − | 0.0767548i | −0.999263 | − | 0.0383774i | \(-0.987781\pi\) | ||
0.999263 | − | 0.0383774i | \(-0.0122189\pi\) | |||||||
\(434\) | −7169.53 | −0.792969 | ||||||||
\(435\) | 1486.51 | + | 2520.44i | 0.163845 | + | 0.277807i | ||||
\(436\) | 31356.7 | 3.44430 | ||||||||
\(437\) | 1018.42i | 0.111483i | ||||||||
\(438\) | − | 4320.41i | − | 0.471318i | ||||||
\(439\) | −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 | ||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 32517.8i | 3.49936i | ||||||||
\(443\) | 3133.67i | 0.336084i | 0.985780 | + | 0.168042i | \(0.0537444\pi\) | ||||
−0.985780 | + | 0.168042i | \(0.946256\pi\) | |||||||
\(444\) | −3240.22 | −0.346338 | ||||||||
\(445\) | 2657.24 | − | 1567.19i | 0.283068 | − | 0.166949i | ||||
\(446\) | −7414.43 | −0.787182 | ||||||||
\(447\) | 4410.99i | 0.466739i | ||||||||
\(448\) | 3708.54i | 0.391099i | ||||||||
\(449\) | 9144.92 | 0.961192 | 0.480596 | − | 0.876942i | \(-0.340420\pi\) | ||||
0.480596 | + | 0.876942i | \(0.340420\pi\) | |||||||
\(450\) | 4813.79 | + | 2661.45i | 0.504276 | + | 0.278804i | ||||
\(451\) | 4264.72 | 0.445272 | ||||||||
\(452\) | − | 4180.33i | − | 0.435014i | ||||||
\(453\) | − | 5087.37i | − | 0.527650i | ||||||
\(454\) | 20052.1 | 2.07289 | ||||||||
\(455\) | 3354.26 | − | 1978.28i | 0.345604 | − | 0.203831i | ||||
\(456\) | 16117.4 | 1.65519 | ||||||||
\(457\) | − | 8142.60i | − | 0.833468i | −0.909029 | − | 0.416734i | \(-0.863175\pi\) | ||
0.909029 | − | 0.416734i | \(-0.136825\pi\) | |||||||
\(458\) | − | 5032.32i | − | 0.513417i | ||||||
\(459\) | 3608.86 | 0.366987 | ||||||||
\(460\) | −661.974 | − | 1122.40i | −0.0670971 | − | 0.113766i | ||||
\(461\) | −9287.29 | −0.938291 | −0.469145 | − | 0.883121i | \(-0.655438\pi\) | ||||
−0.469145 | + | 0.883121i | \(0.655438\pi\) | |||||||
\(462\) | 5637.04i | 0.567659i | ||||||||
\(463\) | 2440.53i | 0.244970i | 0.992470 | + | 0.122485i | \(0.0390864\pi\) | ||||
−0.992470 | + | 0.122485i | \(0.960914\pi\) | |||||||
\(464\) | −5387.08 | −0.538985 | ||||||||
\(465\) | 3569.35 | + | 6051.97i | 0.355967 | + | 0.603556i | ||||
\(466\) | −27274.9 | −2.71134 | ||||||||
\(467\) | 12066.3i | 1.19564i | 0.801632 | + | 0.597818i | \(0.203966\pi\) | ||||
−0.801632 | + | 0.597818i | \(0.796034\pi\) | |||||||
\(468\) | 7123.00i | 0.703548i | ||||||||
\(469\) | −1045.10 | −0.102896 | ||||||||
\(470\) | −234.304 | + | 138.188i | −0.0229949 | + | 0.0135620i | ||||
\(471\) | −2878.30 | −0.281582 | ||||||||
\(472\) | 26437.8i | 2.57818i | ||||||||
\(473\) | 10853.5i | 1.05506i | ||||||||
\(474\) | 13768.5 | 1.33419 | ||||||||
\(475\) | −8406.11 | + | 15204.2i | −0.811998 | + | 1.46867i | ||||
\(476\) | 14882.0 | 1.43302 | ||||||||
\(477\) | − | 477.758i | − | 0.0458596i | ||||||
\(478\) | 26352.0i | 2.52158i | ||||||||
\(479\) | −395.211 | −0.0376987 | −0.0188493 | − | 0.999822i | \(-0.506000\pi\) | ||||
−0.0188493 | + | 0.999822i | \(0.506000\pi\) | |||||||
\(480\) | 211.510 | − | 124.745i | 0.0201126 | − | 0.0118621i | ||||
\(481\) | 3378.77 | 0.320289 | ||||||||
\(482\) | − | 19441.4i | − | 1.83721i | ||||||
\(483\) | 153.878i | 0.0144962i | ||||||||
\(484\) | −26771.2 | −2.51420 | ||||||||
\(485\) | −6618.42 | − | 11221.8i | −0.619643 | − | 1.05063i | ||||
\(486\) | 1188.11 | 0.110893 | ||||||||
\(487\) | 9609.06i | 0.894102i | 0.894508 | + | 0.447051i | \(0.147526\pi\) | ||||
−0.894508 | + | 0.447051i | \(0.852474\pi\) | |||||||
\(488\) | − | 1038.49i | − | 0.0963323i | ||||||
\(489\) | −11595.8 | −1.07235 | ||||||||
\(490\) | −1360.74 | − | 2307.19i | −0.125453 | − | 0.212711i | ||||
\(491\) | 10941.0 | 1.00562 | 0.502810 | − | 0.864397i | \(-0.332299\pi\) | ||||
0.502810 | + | 0.864397i | \(0.332299\pi\) | |||||||
\(492\) | − | 3706.72i | − | 0.339658i | ||||||
\(493\) | − | 11660.7i | − | 1.06526i | ||||||
\(494\) | −33813.3 | −3.07962 | ||||||||
\(495\) | 4758.36 | − | 2806.39i | 0.432065 | − | 0.254824i | ||||
\(496\) | −12935.2 | −1.17099 | ||||||||
\(497\) | 43.0899i | 0.00388903i | ||||||||
\(498\) | − | 11513.1i | − | 1.03597i | ||||||
\(499\) | −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 | ||||
\(501\) | 1395.25 | 0.124422 | ||||||||
\(502\) | − | 34693.8i | − | 3.08458i | ||||||
\(503\) | 15085.4i | 1.33723i | 0.743609 | + | 0.668615i | \(0.233112\pi\) | ||||
−0.743609 | + | 0.668615i | \(0.766888\pi\) | |||||||
\(504\) | 2435.24 | 0.215227 | ||||||||
\(505\) | 1.56971 | − | 0.925787i | 0.000138319 | − | 8.15781e-5i | ||||
\(506\) | −1966.93 | −0.172807 | ||||||||
\(507\) | − | 836.579i | − | 0.0732816i | ||||||
\(508\) | − | 9060.76i | − | 0.791351i | ||||||
\(509\) | −8650.44 | −0.753289 | −0.376645 | − | 0.926358i | \(-0.622922\pi\) | ||||
−0.376645 | + | 0.926358i | \(0.622922\pi\) | |||||||
\(510\) | −11135.4 | − | 18880.6i | −0.966833 | − | 1.63931i | ||||
\(511\) | 2061.82 | 0.178492 | ||||||||
\(512\) | 19547.3i | 1.68726i | ||||||||
\(513\) | 3752.63i | 0.322968i | ||||||||
\(514\) | −12353.3 | −1.06008 | ||||||||
\(515\) | 7388.09 | + | 12526.8i | 0.632151 | + | 1.07184i | ||||
\(516\) | 9433.40 | 0.804811 | ||||||||
\(517\) | 273.194i | 0.0232399i | ||||||||
\(518\) | − | 2324.06i | − | 0.197130i | ||||||
\(519\) | 6144.13 | 0.519648 | ||||||||
\(520\) | 18522.5 | − | 10924.2i | 1.56205 | − | 0.921269i | ||||
\(521\) | 10661.6 | 0.896535 | 0.448268 | − | 0.893899i | \(-0.352041\pi\) | ||||
0.448268 | + | 0.893899i | \(0.352041\pi\) | |||||||
\(522\) | − | 3838.97i | − | 0.321891i | ||||||
\(523\) | 3449.22i | 0.288382i | 0.989550 | + | 0.144191i | \(0.0460580\pi\) | ||||
−0.989550 | + | 0.144191i | \(0.953942\pi\) | |||||||
\(524\) | −15664.2 | −1.30591 | ||||||||
\(525\) | −1270.11 | + | 2297.27i | −0.105585 | + | 0.190973i | ||||
\(526\) | 18786.6 | 1.55729 | ||||||||
\(527\) | − | 27999.3i | − | 2.31436i | ||||||
\(528\) | 10170.3i | 0.838269i | ||||||||
\(529\) | 12113.3 | 0.995587 | ||||||||
\(530\) | −2499.50 | + | 1474.16i | −0.204852 | + | 0.120818i | ||||
\(531\) | −6155.55 | −0.503066 | ||||||||
\(532\) | 15474.9i | 1.26113i | ||||||||
\(533\) | 3865.22i | 0.314111i | ||||||||
\(534\) | −4047.34 | −0.327988 | ||||||||
\(535\) | −8699.24 | − | 14749.9i | −0.702992 | − | 1.19195i | ||||
\(536\) | −5771.14 | −0.465066 | ||||||||
\(537\) | 2735.57i | 0.219829i | ||||||||
\(538\) | − | 41124.6i | − | 3.29555i | ||||||
\(539\) | −2690.14 | −0.214977 | ||||||||
\(540\) | −2439.20 | − | 4135.77i | −0.194383 | − | 0.329584i | ||||
\(541\) | 13403.2 | 1.06516 | 0.532578 | − | 0.846381i | \(-0.321223\pi\) | ||||
0.532578 | + | 0.846381i | \(0.321223\pi\) | |||||||
\(542\) | − | 27672.5i | − | 2.19305i | ||||||
\(543\) | − | 6089.43i | − | 0.481257i | ||||||
\(544\) | −978.544 | −0.0771227 | ||||||||
\(545\) | 18984.9 | − | 11197.0i | 1.49215 | − | 0.880046i | ||||
\(546\) | −5108.98 | −0.400447 | ||||||||
\(547\) | − | 3670.29i | − | 0.286893i | −0.989658 | − | 0.143446i | \(-0.954182\pi\) | ||
0.989658 | − | 0.143446i | \(-0.0458184\pi\) | |||||||
\(548\) | 21907.9i | 1.70778i | ||||||||
\(549\) | 241.792 | 0.0187968 | ||||||||
\(550\) | −29364.6 | − | 16235.1i | −2.27656 | − | 1.25867i | ||||
\(551\) | 12125.3 | 0.937486 | ||||||||
\(552\) | 849.727i | 0.0655195i | ||||||||
\(553\) | 6570.69i | 0.505269i | ||||||||
\(554\) | −4309.53 | −0.330495 | ||||||||
\(555\) | −1961.79 | + | 1157.03i | −0.150042 | + | 0.0884922i | ||||
\(556\) | 13355.7 | 1.01872 | ||||||||
\(557\) | 521.169i | 0.0396456i | 0.999804 | + | 0.0198228i | \(0.00631021\pi\) | ||||
−0.999804 | + | 0.0198228i | \(0.993690\pi\) | |||||||
\(558\) | − | 9217.97i | − | 0.699333i | ||||||
\(559\) | −9836.78 | −0.744278 | ||||||||
\(560\) | −2455.04 | − | 4162.62i | −0.185258 | − | 0.314112i | ||||
\(561\) | −22014.4 | −1.65677 | ||||||||
\(562\) | 18842.2i | 1.41425i | ||||||||
\(563\) | 17970.2i | 1.34521i | 0.740000 | + | 0.672606i | \(0.234825\pi\) | ||||
−0.740000 | + | 0.672606i | \(0.765175\pi\) | |||||||
\(564\) | 237.449 | 0.0177277 | ||||||||
\(565\) | −1492.73 | − | 2530.98i | −0.111150 | − | 0.188459i | ||||
\(566\) | 9248.71 | 0.686842 | ||||||||
\(567\) | 567.000i | 0.0419961i | ||||||||
\(568\) | 237.947i | 0.0175775i | ||||||||
\(569\) | 21808.6 | 1.60679 | 0.803396 | − | 0.595445i | \(-0.203024\pi\) | ||||
0.803396 | + | 0.595445i | \(0.203024\pi\) | |||||||
\(570\) | 19632.7 | − | 11579.0i | 1.44268 | − | 0.850865i | ||||
\(571\) | 6604.75 | 0.484064 | 0.242032 | − | 0.970268i | \(-0.422186\pi\) | ||||
0.242032 | + | 0.970268i | \(0.422186\pi\) | |||||||
\(572\) | − | 43451.0i | − | 3.17618i | ||||||
\(573\) | 14952.3i | 1.09013i | ||||||||
\(574\) | 2658.65 | 0.193327 | ||||||||
\(575\) | −801.584 | − | 443.179i | −0.0581363 | − | 0.0321423i | ||||
\(576\) | −4768.13 | −0.344916 | ||||||||
\(577\) | − | 25886.9i | − | 1.86774i | −0.357618 | − | 0.933868i | \(-0.616411\pi\) | ||
0.357618 | − | 0.933868i | \(-0.383589\pi\) | |||||||
\(578\) | 63328.9i | 4.55733i | ||||||||
\(579\) | −10180.3 | −0.730707 | ||||||||
\(580\) | −13363.3 | + | 7881.41i | −0.956688 | + | 0.564238i | ||||
\(581\) | 5494.35 | 0.392330 | ||||||||
\(582\) | 17092.3i | 1.21735i | ||||||||
\(583\) | 2914.37i | 0.207034i | ||||||||
\(584\) | 11385.5 | 0.806741 | ||||||||
\(585\) | 2543.50 | + | 4312.62i | 0.179762 | + | 0.304794i | ||||
\(586\) | 19929.9 | 1.40495 | ||||||||
\(587\) | − | 4949.88i | − | 0.348046i | −0.984742 | − | 0.174023i | \(-0.944323\pi\) | ||
0.984742 | − | 0.174023i | \(-0.0556768\pi\) | |||||||
\(588\) | 2338.16i | 0.163987i | ||||||||
\(589\) | 29114.7 | 2.03676 | ||||||||
\(590\) | 18993.4 | + | 32204.2i | 1.32533 | + | 2.24716i | ||||
\(591\) | −2287.42 | −0.159208 | ||||||||
\(592\) | − | 4193.05i | − | 0.291104i | ||||||
\(593\) | − | 31.3988i | − | 0.00217436i | −0.999999 | − | 0.00108718i | \(-0.999654\pi\) | ||
0.999999 | − | 0.00108718i | \(-0.000346059\pi\) | |||||||
\(594\) | −7247.62 | −0.500628 | ||||||||
\(595\) | 9010.31 | − | 5314.12i | 0.620818 | − | 0.366147i | ||||
\(596\) | −23386.8 | −1.60732 | ||||||||
\(597\) | 3816.95i | 0.261671i | ||||||||
\(598\) | − | 1782.67i | − | 0.121905i | ||||||
\(599\) | 11870.4 | 0.809704 | 0.404852 | − | 0.914382i | \(-0.367323\pi\) | ||||
0.404852 | + | 0.914382i | \(0.367323\pi\) | |||||||
\(600\) | −7013.67 | + | 12685.7i | −0.477220 | + | 0.863154i | ||||
\(601\) | −967.320 | −0.0656536 | −0.0328268 | − | 0.999461i | \(-0.510451\pi\) | ||||
−0.0328268 | + | 0.999461i | \(0.510451\pi\) | |||||||
\(602\) | 6766.13i | 0.458084i | ||||||||
\(603\) | − | 1343.70i | − | 0.0907458i | ||||||
\(604\) | 26973.0 | 1.81708 | ||||||||
\(605\) | −16208.6 | + | 9559.57i | −1.08922 | + | 0.642400i | ||||
\(606\) | −2.39088 | −0.000160269 | ||||||||
\(607\) | − | 9518.28i | − | 0.636466i | −0.948013 | − | 0.318233i | \(-0.896911\pi\) | ||
0.948013 | − | 0.318233i | \(-0.103089\pi\) | |||||||
\(608\) | − | 1017.53i | − | 0.0678721i | ||||||
\(609\) | 1832.06 | 0.121903 | ||||||||
\(610\) | −746.070 | − | 1264.99i | −0.0495205 | − | 0.0839640i | ||||
\(611\) | −247.602 | −0.0163943 | ||||||||
\(612\) | 19134.0i | 1.26380i | ||||||||
\(613\) | 3607.19i | 0.237672i | 0.992914 | + | 0.118836i | \(0.0379163\pi\) | ||||
−0.992914 | + | 0.118836i | \(0.962084\pi\) | |||||||
\(614\) | 30323.2 | 1.99307 | ||||||||
\(615\) | −1323.61 | − | 2244.23i | −0.0867854 | − | 0.147148i | ||||
\(616\) | −14855.2 | −0.971645 | ||||||||
\(617\) | 22473.2i | 1.46635i | 0.680042 | + | 0.733173i | \(0.261962\pi\) | ||||
−0.680042 | + | 0.733173i | \(0.738038\pi\) | |||||||
\(618\) | − | 19080.0i | − | 1.24193i | ||||||
\(619\) | −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 | ||||
\(621\) | −197.843 | −0.0127845 | ||||||||
\(622\) | 32279.3i | 2.08084i | ||||||||
\(623\) | − | 1931.50i | − | 0.124211i | ||||||
\(624\) | −9217.60 | −0.591345 | ||||||||
\(625\) | −8308.97 | − | 13232.6i | −0.531774 | − | 0.846886i | ||||
\(626\) | −11201.6 | −0.715184 | ||||||||
\(627\) | − | 22891.4i | − | 1.45805i | ||||||
\(628\) | − | 15260.6i | − | 0.969689i | ||||||
\(629\) | 9076.17 | 0.575343 | ||||||||
\(630\) | 2966.39 | − | 1749.52i | 0.187593 | − | 0.110639i | ||||
\(631\) | −6980.64 | −0.440404 | −0.220202 | − | 0.975454i | \(-0.570672\pi\) | ||||
−0.220202 | + | 0.975454i | \(0.570672\pi\) | |||||||
\(632\) | 36283.9i | 2.28370i | ||||||||
\(633\) | 6032.15i | 0.378762i | ||||||||
\(634\) | 15274.7 | 0.956838 | ||||||||
\(635\) | −3235.45 | − | 5485.83i | −0.202197 | − | 0.342833i | ||||
\(636\) | 2533.05 | 0.157928 | ||||||||
\(637\) | − | 2438.14i | − | 0.151653i | ||||||
\(638\) | 23418.1i | 1.45318i | ||||||||
\(639\) | −55.4014 | −0.00342980 | ||||||||
\(640\) | 14379.8 | + | 24381.5i | 0.888142 | + | 1.50588i | ||||
\(641\) | −1083.82 | −0.0667837 | −0.0333919 | − | 0.999442i | \(-0.510631\pi\) | ||||
−0.0333919 | + | 0.999442i | \(0.510631\pi\) | |||||||
\(642\) | 22466.1i | 1.38110i | ||||||||
\(643\) | − | 4151.42i | − | 0.254613i | −0.991863 | − | 0.127307i | \(-0.959367\pi\) | ||
0.991863 | − | 0.127307i | \(-0.0406332\pi\) | |||||||
\(644\) | −815.853 | −0.0499210 | ||||||||
\(645\) | 5711.45 | − | 3368.51i | 0.348664 | − | 0.205636i | ||||
\(646\) | −90830.3 | −5.53200 | ||||||||
\(647\) | 3014.99i | 0.183202i | 0.995796 | + | 0.0916008i | \(0.0291984\pi\) | ||||
−0.995796 | + | 0.0916008i | \(0.970802\pi\) | |||||||
\(648\) | 3131.02i | 0.189812i | ||||||||
\(649\) | 37549.4 | 2.27110 | ||||||||
\(650\) | 14714.2 | − | 26613.8i | 0.887908 | − | 1.60597i | ||||
\(651\) | 4399.06 | 0.264843 | ||||||||
\(652\) | − | 61480.5i | − | 3.69288i | ||||||
\(653\) | − | 21130.7i | − | 1.26632i | −0.774019 | − | 0.633162i | \(-0.781757\pi\) | ||
0.774019 | − | 0.633162i | \(-0.218243\pi\) | |||||||
\(654\) | −28916.6 | −1.72894 | ||||||||
\(655\) | −9483.90 | + | 5593.44i | −0.565751 | + | 0.333670i | ||||
\(656\) | 4796.73 | 0.285489 | ||||||||
\(657\) | 2650.91i | 0.157415i | ||||||||
\(658\) | 170.311i | 0.0100903i | ||||||||
\(659\) | 9961.24 | 0.588824 | 0.294412 | − | 0.955679i | \(-0.404876\pi\) | ||||
0.294412 | + | 0.955679i | \(0.404876\pi\) | |||||||
\(660\) | 14879.4 | + | 25228.6i | 0.877544 | + | 1.48791i | ||||
\(661\) | 1581.43 | 0.0930569 | 0.0465285 | − | 0.998917i | \(-0.485184\pi\) | ||||
0.0465285 | + | 0.998917i | \(0.485184\pi\) | |||||||
\(662\) | − | 48040.4i | − | 2.82046i | ||||||
\(663\) | − | 19952.2i | − | 1.16875i | ||||||
\(664\) | 30340.3 | 1.77324 | ||||||||
\(665\) | 5525.83 | + | 9369.27i | 0.322229 | + | 0.546353i | ||||
\(666\) | 2988.07 | 0.173852 | ||||||||
\(667\) | 639.258i | 0.0371097i | ||||||||
\(668\) | 7397.56i | 0.428473i | ||||||||
\(669\) | 4549.32 | 0.262910 | ||||||||
\(670\) | −7029.87 | + | 4146.09i | −0.405355 | + | 0.239071i | ||||
\(671\) | −1474.96 | −0.0848586 | ||||||||
\(672\) | − | 153.742i | − | 0.00882551i | ||||||
\(673\) | 11101.6i | 0.635865i | 0.948113 | + | 0.317932i | \(0.102988\pi\) | ||||
−0.948113 | + | 0.317932i | \(0.897012\pi\) | |||||||
\(674\) | −41688.4 | −2.38246 | ||||||||
\(675\) | −2953.63 | − | 1633.00i | −0.168423 | − | 0.0931174i | ||||
\(676\) | 4435.50 | 0.252361 | ||||||||
\(677\) | 18249.8i | 1.03603i | 0.855370 | + | 0.518017i | \(0.173330\pi\) | ||||
−0.855370 | + | 0.518017i | \(0.826670\pi\) | |||||||
\(678\) | 3855.02i | 0.218365i | ||||||||
\(679\) | −8156.90 | −0.461021 | ||||||||
\(680\) | 49755.7 | − | 29345.0i | 2.80595 | − | 1.65490i | ||||
\(681\) | −12303.5 | −0.692322 | ||||||||
\(682\) | 56230.5i | 3.15715i | ||||||||
\(683\) | − | 14144.2i | − | 0.792403i | −0.918164 | − | 0.396202i | \(-0.870328\pi\) | ||
0.918164 | − | 0.396202i | \(-0.129672\pi\) | |||||||
\(684\) | −19896.3 | −1.11221 | ||||||||
\(685\) | 7822.97 | + | 13264.2i | 0.436351 | + | 0.739851i | ||||
\(686\) | −1677.05 | −0.0933384 | ||||||||
\(687\) | 3087.71i | 0.171475i | ||||||||
\(688\) | 12207.4i | 0.676458i | ||||||||
\(689\) | −2641.37 | −0.146049 | ||||||||
\(690\) | 610.460 | + | 1035.06i | 0.0336809 | + | 0.0571073i | ||||
\(691\) | 19621.7 | 1.08024 | 0.540120 | − | 0.841588i | \(-0.318379\pi\) | ||||
0.540120 | + | 0.841588i | \(0.318379\pi\) | |||||||
\(692\) | 32575.9i | 1.78952i | ||||||||
\(693\) | − | 3458.75i | − | 0.189592i | ||||||
\(694\) | 20361.9 | 1.11373 | ||||||||
\(695\) | 8086.22 | − | 4769.11i | 0.441335 | − | 0.260292i | ||||
\(696\) | 10116.8 | 0.550971 | ||||||||
\(697\) | 10382.9i | 0.564246i | ||||||||
\(698\) | 12637.1i | 0.685272i | ||||||||
\(699\) | 16735.2 | 0.905557 | ||||||||
\(700\) | −12180.0 | − | 6734.08i | −0.657659 | − | 0.363606i | ||||
\(701\) | 21609.1 | 1.16428 | 0.582142 | − | 0.813087i | \(-0.302215\pi\) | ||||
0.582142 | + | 0.813087i | \(0.302215\pi\) | |||||||
\(702\) | − | 6568.69i | − | 0.353161i | ||||||
\(703\) | 9437.75i | 0.506332i | ||||||||
\(704\) | 29086.0 | 1.55713 | ||||||||
\(705\) | 143.763 | − | 84.7890i | 0.00768005 | − | 0.00452956i | ||||
\(706\) | −20531.6 | −1.09450 | ||||||||
\(707\) | − | 1.14099i | − | 6.06950e-5i | ||||||
\(708\) | − | 32636.4i | − | 1.73242i | ||||||
\(709\) | 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 | ||||
\(711\) | −8448.02 | −0.445606 | ||||||||
\(712\) | − | 10665.9i | − | 0.561406i | ||||||
\(713\) | 1534.96i | 0.0806237i | ||||||||
\(714\) | −13723.9 | −0.719334 | ||||||||
\(715\) | −15515.6 | − | 26307.4i | −0.811540 | − | 1.37600i | ||||
\(716\) | −14503.9 | −0.757031 | ||||||||
\(717\) | − | 16169.0i | − | 0.842179i | ||||||
\(718\) | − | 4841.82i | − | 0.251665i | ||||||
\(719\) | −36151.9 | −1.87516 | −0.937580 | − | 0.347771i | \(-0.886939\pi\) | ||||
−0.937580 | + | 0.347771i | \(0.886939\pi\) | |||||||
\(720\) | 5351.95 | − | 3156.48i | 0.277021 | − | 0.163382i | ||||
\(721\) | 9105.48 | 0.470327 | ||||||||
\(722\) | − | 60912.8i | − | 3.13980i | ||||||
\(723\) | 11928.8i | 0.613606i | ||||||||
\(724\) | 32285.9 | 1.65731 | ||||||||
\(725\) | −5276.46 | + | 9543.60i | −0.270293 | + | 0.488883i | ||||
\(726\) | 24687.9 | 1.26206 | ||||||||
\(727\) | − | 12007.2i | − | 0.612550i | −0.951943 | − | 0.306275i | \(-0.900917\pi\) | ||
0.951943 | − | 0.306275i | \(-0.0990828\pi\) | |||||||
\(728\) | − | 13463.6i | − | 0.685434i | ||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 13868.8 | − | 8179.58i | 0.703162 | − | 0.414712i | ||||
\(731\) | −26423.9 | −1.33697 | ||||||||
\(732\) | 1281.97i | 0.0647310i | ||||||||
\(733\) | − | 15920.2i | − | 0.802220i | −0.916030 | − | 0.401110i | \(-0.868625\pi\) | ||
0.916030 | − | 0.401110i | \(-0.131375\pi\) | |||||||
\(734\) | 20433.8 | 1.02756 | ||||||||
\(735\) | 834.919 | + | 1415.64i | 0.0418999 | + | 0.0710431i | ||||
\(736\) | 53.6452 | 0.00268667 | ||||||||
\(737\) | 8196.70i | 0.409674i | ||||||||
\(738\) | 3418.27i | 0.170499i | ||||||||
\(739\) | 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 | ||||
\(741\) | 20747.1 | 1.02856 | ||||||||
\(742\) | 1816.84i | 0.0898897i | ||||||||
\(743\) | − | 6601.38i | − | 0.325950i | −0.986630 | − | 0.162975i | \(-0.947891\pi\) | ||
0.986630 | − | 0.162975i | \(-0.0521090\pi\) | |||||||
\(744\) | 24292.0 | 1.19703 | ||||||||
\(745\) | −14159.6 | + | 8351.06i | −0.696330 | + | 0.410683i | ||||
\(746\) | 36011.9 | 1.76741 | ||||||||
\(747\) | 7064.16i | 0.346003i | ||||||||
\(748\) | − | 116719.i | − | 5.70546i | ||||||
\(749\) | −10721.4 | −0.523034 | ||||||||
\(750\) | 570.243 | + | 20491.3i | 0.0277631 | + | 0.997651i | ||||
\(751\) | −29809.6 | −1.44842 | −0.724212 | − | 0.689578i | \(-0.757796\pi\) | ||||
−0.724212 | + | 0.689578i | \(0.757796\pi\) | |||||||
\(752\) | 307.274i | 0.0149004i | ||||||||
\(753\) | 21287.3i | 1.03022i | ||||||||
\(754\) | −21224.4 | −1.02513 | ||||||||
\(755\) | 16330.8 | − | 9631.61i | 0.787203 | − | 0.464278i | ||||
\(756\) | −3006.21 | −0.144623 | ||||||||
\(757\) | 8179.09i | 0.392700i | 0.980534 | + | 0.196350i | \(0.0629089\pi\) | ||||
−0.980534 | + | 0.196350i | \(0.937091\pi\) | |||||||
\(758\) | − | 30383.2i | − | 1.45589i | ||||||
\(759\) | 1206.86 | 0.0577158 | ||||||||
\(760\) | 30514.1 | + | 51737.9i | 1.45640 | + | 2.46938i | ||||
\(761\) | −31616.8 | −1.50605 | −0.753027 | − | 0.657990i | \(-0.771407\pi\) | ||||
−0.753027 | + | 0.657990i | \(0.771407\pi\) | |||||||
\(762\) | 8355.66i | 0.397236i | ||||||||
\(763\) | − | 13799.8i | − | 0.654763i | ||||||
\(764\) | −79276.5 | −3.75409 | ||||||||
\(765\) | 6832.44 | + | 11584.7i | 0.322912 | + | 0.547510i | ||||
\(766\) | 8581.05 | 0.404760 | ||||||||
\(767\) | 34032.0i | 1.60212i | ||||||||
\(768\) | − | 24421.3i | − | 1.14743i | ||||||
\(769\) | −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 | ||||
\(771\) | 7579.67 | 0.354054 | ||||||||
\(772\) | − | 53975.6i | − | 2.51635i | ||||||
\(773\) | − | 7888.63i | − | 0.367056i | −0.983015 | − | 0.183528i | \(-0.941248\pi\) | ||
0.983015 | − | 0.183528i | \(-0.0587518\pi\) | |||||||
\(774\) | −8699.31 | −0.403992 | ||||||||
\(775\) | −12669.6 | + | 22915.7i | −0.587233 | + | 1.06214i | ||||
\(776\) | −45043.1 | −2.08370 | ||||||||
\(777\) | 1425.99i | 0.0658391i | ||||||||
\(778\) | 43054.2i | 1.98402i | ||||||||
\(779\) | −10796.5 | −0.496566 | ||||||||
\(780\) | −22865.3 | + | 13485.5i | −1.04963 | + | 0.619051i | ||||
\(781\) | 337.954 | 0.0154839 | ||||||||
\(782\) | − | 4788.67i | − | 0.218980i | ||||||
\(783\) | 2355.50i | 0.107508i | ||||||||
\(784\) | −3025.73 | −0.137834 | ||||||||
\(785\) | −5449.31 | − | 9239.53i | −0.247763 | − | 0.420093i | ||||
\(786\) | 14445.2 | 0.655528 | ||||||||
\(787\) | 8592.94i | 0.389206i | 0.980882 | + | 0.194603i | \(0.0623419\pi\) | ||||
−0.980882 | + | 0.194603i | \(0.937658\pi\) | |||||||
\(788\) | − | 12127.8i | − | 0.548268i | ||||||
\(789\) | −11527.0 | −0.520118 | ||||||||
\(790\) | 26067.1 | + | 44197.8i | 1.17395 | + | 1.99049i | ||||
\(791\) | −1839.72 | −0.0826964 | ||||||||
\(792\) | − | 19099.6i | − | 0.856910i | ||||||
\(793\) | − | 1336.79i | − | 0.0598623i | ||||||
\(794\) | −67068.5 | −2.99770 | ||||||||
\(795\) | 1533.64 | − | 904.511i | 0.0684182 | − | 0.0403518i | ||||
\(796\) | −20237.3 | −0.901120 | ||||||||
\(797\) | 37498.1i | 1.66656i | 0.552848 | + | 0.833282i | \(0.313541\pi\) | ||||
−0.552848 | + | 0.833282i | \(0.686459\pi\) | |||||||
\(798\) | − | 14270.7i | − | 0.633052i | ||||||
\(799\) | −665.116 | −0.0294495 | ||||||||
\(800\) | 800.878 | + | 442.789i | 0.0353942 | + | 0.0195687i | ||||
\(801\) | 2483.35 | 0.109544 | ||||||||
\(802\) | − | 1502.11i | − | 0.0661364i | ||||||
\(803\) | − | 16170.8i | − | 0.710653i | ||||||
\(804\) | 7124.24 | 0.312503 | ||||||||
\(805\) | −493.958 | + | 291.328i | −0.0216270 | + | 0.0127552i | ||||
\(806\) | −50963.1 | −2.22717 | ||||||||
\(807\) | 25233.1i | 1.10068i | ||||||||
\(808\) | − | 6.30065i | − | 0.000274327i | ||||||
\(809\) | −33834.0 | −1.47039 | −0.735193 | − | 0.677858i | \(-0.762908\pi\) | ||||
−0.735193 | + | 0.677858i | \(0.762908\pi\) | |||||||
\(810\) | 2249.39 | + | 3813.93i | 0.0975746 | + | 0.165442i | ||||
\(811\) | 16234.0 | 0.702899 | 0.351450 | − | 0.936207i | \(-0.385689\pi\) | ||||
0.351450 | + | 0.936207i | \(0.385689\pi\) | |||||||
\(812\) | 9713.48i | 0.419799i | ||||||||
\(813\) | 16979.2i | 0.732455i | ||||||||
\(814\) | −18227.5 | −0.784858 | ||||||||
\(815\) | −21953.7 | − | 37223.3i | −0.943562 | − | 1.59985i | ||||
\(816\) | −24760.6 | −1.06225 | ||||||||
\(817\) | − | 27476.6i | − | 1.17660i | ||||||
\(818\) | 60582.5i | 2.58951i | ||||||||
\(819\) | 3134.75 | 0.133745 | ||||||||
\(820\) | 11898.8 | − | 7017.71i | 0.506737 | − | 0.298865i | ||||
\(821\) | −26551.4 | −1.12868 | −0.564342 | − | 0.825541i | \(-0.690870\pi\) | ||||
−0.564342 | + | 0.825541i | \(0.690870\pi\) | |||||||
\(822\) | − | 20203.1i | − | 0.857255i | ||||||
\(823\) | 651.954i | 0.0276132i | 0.999905 | + | 0.0138066i | \(0.00439492\pi\) | ||||
−0.999905 | + | 0.0138066i | \(0.995605\pi\) | |||||||
\(824\) | 50281.3 | 2.12577 | ||||||||
\(825\) | 18017.4 | + | 9961.47i | 0.760347 | + | 0.420380i | ||||
\(826\) | 23408.6 | 0.986063 | ||||||||
\(827\) | − | 13248.0i | − | 0.557046i | −0.960430 | − | 0.278523i | \(-0.910155\pi\) | ||
0.960430 | − | 0.278523i | \(-0.0898448\pi\) | |||||||
\(828\) | − | 1048.95i | − | 0.0440262i | ||||||
\(829\) | 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 | ||||
\(831\) | 2644.23 | 0.110382 | ||||||||
\(832\) | 26361.4i | 1.09846i | ||||||||
\(833\) | − | 6549.41i | − | 0.272417i | ||||||
\(834\) | −12316.4 | −0.511369 | ||||||||
\(835\) | 2641.55 | + | 4478.85i | 0.109478 | + | 0.185625i | ||||
\(836\) | 121369. | 5.02111 | ||||||||
\(837\) | 5655.93i | 0.233569i | ||||||||
\(838\) | 13025.7i | 0.536953i | ||||||||
\(839\) | 10641.5 | 0.437884 | 0.218942 | − | 0.975738i | \(-0.429739\pi\) | ||||
0.218942 | + | 0.975738i | \(0.429739\pi\) | |||||||
\(840\) | 4610.50 | + | 7817.29i | 0.189378 | + | 0.321098i | ||||
\(841\) | −16778.0 | −0.687935 | ||||||||
\(842\) | 33497.6i | 1.37102i | ||||||||
\(843\) | − | 11561.1i | − | 0.472344i | ||||||
\(844\) | −31982.2 | −1.30435 | ||||||||
\(845\) | 2685.47 | − | 1583.84i | 0.109329 | − | 0.0644804i | ||||
\(846\) | −218.971 | −0.00889878 | ||||||||
\(847\) | 11781.7i | 0.477952i | ||||||||
\(848\) | 3277.93i | 0.132741i | ||||||||
\(849\) | −5674.80 | −0.229398 | ||||||||
\(850\) | 39525.9 | − | 71490.9i | 1.59497 | − | 2.88484i | ||||
\(851\) | −497.568 | −0.0200428 | ||||||||
\(852\) | − | 293.735i | − | 0.0118113i | ||||||
\(853\) | 2819.13i | 0.113160i | 0.998398 | + | 0.0565799i | \(0.0180196\pi\) | ||||
−0.998398 | + | 0.0565799i | \(0.981980\pi\) | |||||||
\(854\) | −919.497 | −0.0368437 | ||||||||
\(855\) | −12046.2 | + | 7104.64i | −0.481838 | + | 0.284179i | ||||
\(856\) | −59204.6 | −2.36399 | ||||||||
\(857\) | 38853.9i | 1.54869i | 0.632766 | + | 0.774343i | \(0.281919\pi\) | ||||
−0.632766 | + | 0.774343i | \(0.718081\pi\) | |||||||
\(858\) | 40069.7i | 1.59435i | ||||||||
\(859\) | −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 | ||||
\(861\) | −1631.29 | −0.0645693 | ||||||||
\(862\) | 37410.4i | 1.47819i | ||||||||
\(863\) | − | 32649.8i | − | 1.28785i | −0.765090 | − | 0.643924i | \(-0.777305\pi\) | ||
0.765090 | − | 0.643924i | \(-0.222695\pi\) | |||||||
\(864\) | 197.669 | 0.00778337 | ||||||||
\(865\) | 11632.3 | + | 19723.1i | 0.457238 | + | 0.775265i | ||||
\(866\) | −3381.35 | −0.132682 | ||||||||
\(867\) | − | 38857.2i | − | 1.52210i | ||||||
\(868\) | 23323.6i | 0.912045i | ||||||||
\(869\) | 51533.8 | 2.01170 | ||||||||
\(870\) | 12323.3 | − | 7268.09i | 0.480230 | − | 0.283231i | ||||
\(871\) | −7428.87 | −0.288999 | ||||||||
\(872\) | − | 76203.5i | − | 2.95937i | ||||||
\(873\) | − | 10487.4i | − | 0.406582i | ||||||
\(874\) | 4979.45 | 0.192714 | ||||||||
\(875\) | −9779.01 | + | 272.135i | −0.377818 | + | 0.0105141i | ||||
\(876\) | −14055.0 | −0.542093 | ||||||||
\(877\) | 20229.3i | 0.778899i | 0.921048 | + | 0.389450i | \(0.127335\pi\) | ||||
−0.921048 | + | 0.389450i | \(0.872665\pi\) | |||||||
\(878\) | 51933.5i | 1.99621i | ||||||||
\(879\) | −12228.6 | −0.469237 | ||||||||
\(880\) | −32647.4 | + | 19254.8i | −1.25062 | + | 0.737592i | ||||
\(881\) | 4356.08 | 0.166584 | 0.0832918 | − | 0.996525i | \(-0.473457\pi\) | ||||
0.0832918 | + | 0.996525i | \(0.473457\pi\) | |||||||
\(882\) | − | 2156.21i | − | 0.0823167i | ||||||
\(883\) | 43349.9i | 1.65214i | 0.563567 | + | 0.826070i | \(0.309429\pi\) | ||||
−0.563567 | + | 0.826070i | \(0.690571\pi\) | |||||||
\(884\) | 105786. | 4.02484 | ||||||||
\(885\) | −11653.9 | − | 19759.7i | −0.442647 | − | 0.750526i | ||||
\(886\) | 15321.6 | 0.580971 | ||||||||
\(887\) | 9754.67i | 0.369256i | 0.982809 | + | 0.184628i | \(0.0591080\pi\) | ||||
−0.982809 | + | 0.184628i | \(0.940892\pi\) | |||||||
\(888\) | 7874.43i | 0.297577i | ||||||||
\(889\) | −3987.54 | −0.150436 | ||||||||
\(890\) | −7662.58 | − | 12992.2i | −0.288596 | − | 0.489326i | ||||
\(891\) | 4446.97 | 0.167204 | ||||||||
\(892\) | 24120.3i | 0.905389i | ||||||||
\(893\) | − | 691.614i | − | 0.0259171i | ||||||
\(894\) | 21566.9 | 0.806829 | ||||||||
\(895\) | −8781.35 | + | 5179.09i | −0.327965 | + | 0.193428i | ||||
\(896\) | 17722.4 | 0.660786 | ||||||||
\(897\) | 1093.81i | 0.0407148i | ||||||||
\(898\) | − | 44712.8i | − | 1.66157i | ||||||
\(899\) | 18275.1 | 0.677986 | ||||||||
\(900\) | 8658.10 | − | 15660.0i | 0.320670 | − | 0.580000i | ||||
\(901\) | −7095.32 | −0.262352 | ||||||||
\(902\) | − | 20851.8i | − | 0.769720i | ||||||
\(903\) | − | 4151.54i | − | 0.152995i | ||||||
\(904\) | −10159.1 | −0.373768 | ||||||||
\(905\) | 19547.5 | − | 11528.8i | 0.717989 | − | 0.423457i | ||||
\(906\) | −24874.0 | −0.912122 | ||||||||
\(907\) | 7155.16i | 0.261944i | 0.991386 | + | 0.130972i | \(0.0418098\pi\) | ||||
−0.991386 | + | 0.130972i | \(0.958190\pi\) | |||||||
\(908\) | − | 65232.6i | − | 2.38416i | ||||||
\(909\) | 1.46699 | 5.35279e−5 | ||||||||
\(910\) | −9672.53 | − | 16400.2i | −0.352353 | − | 0.597429i | ||||
\(911\) | −47255.4 | −1.71860 | −0.859298 | − | 0.511475i | \(-0.829099\pi\) | ||||
−0.859298 | + | 0.511475i | \(0.829099\pi\) | |||||||
\(912\) | − | 25747.0i | − | 0.934835i | ||||||
\(913\) | − | 43092.1i | − | 1.56204i | ||||||
\(914\) | −39812.1 | −1.44077 | ||||||||
\(915\) | 457.771 | + | 776.170i | 0.0165393 | + | 0.0280430i | ||||
\(916\) | −16370.9 | −0.590514 | ||||||||
\(917\) | 6893.66i | 0.248254i | ||||||||
\(918\) | − | 17645.0i | − | 0.634393i | ||||||
\(919\) | −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 | ||||
\(921\) | −18605.6 | −0.665663 | ||||||||
\(922\) | 45408.9i | 1.62198i | ||||||||
\(923\) | 306.296i | 0.0109229i | ||||||||
\(924\) | 18338.2 | 0.652902 | ||||||||
\(925\) | −7428.29 | − | 4106.95i | −0.264044 | − | 0.145984i | ||||
\(926\) | 11932.6 | 0.423468 | ||||||||
\(927\) | 11707.0i | 0.414790i | ||||||||
\(928\) | − | 638.696i | − | 0.0225929i | ||||||
\(929\) | −12147.4 | −0.429004 | −0.214502 | − | 0.976724i | \(-0.568813\pi\) | ||||
−0.214502 | + | 0.976724i | \(0.568813\pi\) | |||||||
\(930\) | 29590.3 | − | 17451.8i | 1.04334 | − | 0.615342i | ||||
\(931\) | 6810.33 | 0.239742 | ||||||||
\(932\) | 88729.4i | 3.11849i | ||||||||
\(933\) | − | 19805.8i | − | 0.694978i | ||||||
\(934\) | 58996.6 | 2.06684 | ||||||||
\(935\) | −41678.5 | − | 70667.7i | −1.45779 | − | 2.47174i | ||||
\(936\) | 17310.4 | 0.604496 | ||||||||
\(937\) | 13388.6i | 0.466794i | 0.972381 | + | 0.233397i | \(0.0749842\pi\) | ||||
−0.972381 | + | 0.233397i | \(0.925016\pi\) | |||||||
\(938\) | 5109.87i | 0.177871i | ||||||||
\(939\) | 6873.03 | 0.238864 | ||||||||
\(940\) | 449.548 | + | 762.226i | 0.0155985 | + | 0.0264480i | ||||
\(941\) | −8035.36 | −0.278369 | −0.139184 | − | 0.990266i | \(-0.544448\pi\) | ||||
−0.139184 | + | 0.990266i | \(0.544448\pi\) | |||||||
\(942\) | 14073.0i | 0.486757i | ||||||||
\(943\) | − | 569.204i | − | 0.0196562i | ||||||
\(944\) | 42233.6 | 1.45613 | ||||||||
\(945\) | −1820.11 | + | 1073.47i | −0.0626541 | + | 0.0369523i | ||||
\(946\) | 53066.6 | 1.82383 | ||||||||
\(947\) | − | 17647.7i | − | 0.605567i | −0.953059 | − | 0.302784i | \(-0.902084\pi\) | ||
0.953059 | − | 0.302784i | \(-0.0979160\pi\) | |||||||
\(948\) | − | 44791.0i | − | 1.53454i | ||||||
\(949\) | 14656.0 | 0.501321 | ||||||||
\(950\) | 74339.0 | + | 41100.5i | 2.53882 | + | 1.40366i | ||||
\(951\) | −9372.20 | −0.319573 | ||||||||
\(952\) | − | 36166.4i | − | 1.23126i | ||||||
\(953\) | 35629.1i | 1.21106i | 0.795823 | + | 0.605529i | \(0.207039\pi\) | ||||
−0.795823 | + | 0.605529i | \(0.792961\pi\) | |||||||
\(954\) | −2335.93 | −0.0792753 | ||||||||
\(955\) | −47998.0 | + | 28308.3i | −1.62636 | + | 0.959200i | ||||
\(956\) | 85727.3 | 2.90023 | ||||||||
\(957\) | − | 14368.8i | − | 0.485347i | ||||||
\(958\) | 1932.33i | 0.0651679i | ||||||||
\(959\) | 9641.45 | 0.324649 | ||||||||
\(960\) | −9027.21 | − | 15306.0i | −0.303492 | − | 0.514582i | ||||
\(961\) | 14090.4 | 0.472977 | ||||||||
\(962\) | − | 16520.1i | − | 0.553667i | ||||||
\(963\) | − | 13784.7i | − | 0.461272i | ||||||
\(964\) | −63246.0 | −2.11309 | ||||||||
\(965\) | −19273.8 | − | 32679.5i | −0.642948 | − | 1.09015i | ||||
\(966\) | 752.364 | 0.0250589 | ||||||||
\(967\) | − | 35954.1i | − | 1.19566i | −0.801622 | − | 0.597831i | \(-0.796029\pi\) | ||
0.801622 | − | 0.597831i | \(-0.203971\pi\) | |||||||
\(968\) | 65059.8i | 2.16023i | ||||||||
\(969\) | 55731.4 | 1.84763 | ||||||||
\(970\) | −54867.4 | + | 32359.8i | −1.81617 | + | 1.07115i | ||||
\(971\) | 59266.0 | 1.95874 | 0.979370 | − | 0.202074i | \(-0.0647680\pi\) | ||||
0.979370 | + | 0.202074i | \(0.0647680\pi\) | |||||||
\(972\) | − | 3865.12i | − | 0.127545i | ||||||
\(973\) | − | 5877.71i | − | 0.193660i | ||||||
\(974\) | 46982.2 | 1.54559 | ||||||||
\(975\) | −9028.32 | + | 16329.6i | −0.296552 | + | 0.536376i | ||||
\(976\) | −1658.95 | −0.0544076 | ||||||||
\(977\) | − | 35518.9i | − | 1.16310i | −0.813510 | − | 0.581551i | \(-0.802446\pi\) | ||
0.813510 | − | 0.581551i | \(-0.197554\pi\) | |||||||
\(978\) | 56696.1i | 1.85372i | ||||||||
\(979\) | −15148.7 | −0.494540 | ||||||||
\(980\) | −7505.66 | + | 4426.70i | −0.244652 | + | 0.144292i | ||||
\(981\) | 17742.5 | 0.577447 | ||||||||
\(982\) | − | 53494.4i | − | 1.73837i | ||||||
\(983\) | − | 37683.6i | − | 1.22271i | −0.791358 | − | 0.611353i | \(-0.790626\pi\) | ||
0.791358 | − | 0.611353i | \(-0.209374\pi\) | |||||||
\(984\) | −9008.11 | −0.291838 | ||||||||
\(985\) | −4330.64 | − | 7342.78i | −0.140087 | − | 0.237523i | ||||
\(986\) | −57013.6 | −1.84146 | ||||||||
\(987\) | − | 104.499i | − | 0.00337004i | ||||||
\(988\) | 110000.i | 3.54207i | ||||||||
\(989\) | 1448.59 | 0.0465749 | ||||||||
\(990\) | −13721.5 | − | 23265.3i | −0.440502 | − | 0.746890i | ||||
\(991\) | 21371.1 | 0.685041 | 0.342521 | − | 0.939510i | \(-0.388719\pi\) | ||||
0.342521 | + | 0.939510i | \(0.388719\pi\) | |||||||
\(992\) | − | 1533.61i | − | 0.0490848i | ||||||
\(993\) | 29476.5i | 0.942002i | ||||||||
\(994\) | 210.682 | 0.00672278 | ||||||||
\(995\) | −12252.7 | + | 7226.40i | −0.390387 | + | 0.230244i | ||||
\(996\) | −37453.8 | −1.19154 | ||||||||
\(997\) | − | 42934.0i | − | 1.36383i | −0.731434 | − | 0.681913i | \(-0.761148\pi\) | ||
0.731434 | − | 0.681913i | \(-0.238852\pi\) | |||||||
\(998\) | 45323.9i | 1.43758i | ||||||||
\(999\) | −1833.41 | −0.0580646 |
(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 | 105.4.d.b.64.2 | ✓ | 10 | |
3.2 | odd | 2 | 315.4.d.b.64.9 | 10 | |||
5.2 | odd | 4 | 525.4.a.w.1.5 | 5 | |||
5.3 | odd | 4 | 525.4.a.x.1.1 | 5 | |||
5.4 | even | 2 | inner | 105.4.d.b.64.9 | yes | 10 | |
15.2 | even | 4 | 1575.4.a.bp.1.1 | 5 | |||
15.8 | even | 4 | 1575.4.a.bo.1.5 | 5 | |||
15.14 | odd | 2 | 315.4.d.b.64.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.d.b.64.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
105.4.d.b.64.9 | yes | 10 | 5.4 | even | 2 | inner | |
315.4.d.b.64.2 | 10 | 15.14 | odd | 2 | |||
315.4.d.b.64.9 | 10 | 3.2 | odd | 2 | |||
525.4.a.w.1.5 | 5 | 5.2 | odd | 4 | |||
525.4.a.x.1.1 | 5 | 5.3 | odd | 4 | |||
1575.4.a.bo.1.5 | 5 | 15.8 | even | 4 | |||
1575.4.a.bp.1.1 | 5 | 15.2 | even | 4 |