Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [810,3,Mod(809,810)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(810, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("810.809");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.0709014132\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 809.11 | ||
Character | \(\chi\) | \(=\) | 810.809 |
Dual form | 810.3.b.c.809.12 |
$q$-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 \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).
\(n\) | \(487\) | \(731\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 4.99998 | − | 0.0147805i | 0.999996 | − | 0.00295610i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 5.91951i | − | 0.845645i | −0.906213 | − | 0.422822i | \(-0.861039\pi\) | ||
0.906213 | − | 0.422822i | \(-0.138961\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.07104 | + | 0.0209028i | −0.707104 | + | 0.00209028i | ||||
\(11\) | − | 3.80976i | − | 0.346342i | −0.984892 | − | 0.173171i | \(-0.944599\pi\) | ||
0.984892 | − | 0.173171i | \(-0.0554013\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 22.2295i | 1.70996i | 0.518658 | + | 0.854982i | \(0.326432\pi\) | ||||
−0.518658 | + | 0.854982i | \(0.673568\pi\) | |||||||
\(14\) | 8.37146i | 0.597961i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −1.20411 | −0.0708299 | −0.0354150 | − | 0.999373i | \(-0.511275\pi\) | ||||
−0.0354150 | + | 0.999373i | \(0.511275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29.3606 | 1.54529 | 0.772647 | − | 0.634836i | \(-0.218932\pi\) | ||||
0.772647 | + | 0.634836i | \(0.218932\pi\) | |||||||
\(20\) | 9.99996 | − | 0.0295610i | 0.499998 | − | 0.00147805i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.38781i | 0.244901i | ||||||||
\(23\) | −16.1421 | −0.701832 | −0.350916 | − | 0.936407i | \(-0.614130\pi\) | ||||
−0.350916 | + | 0.936407i | \(0.614130\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.9996 | − | 0.147805i | 0.999983 | − | 0.00591218i | ||||
\(26\) | − | 31.4373i | − | 1.20913i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 11.8390i | − | 0.422822i | ||||||
\(29\) | 45.2869i | 1.56162i | 0.624770 | + | 0.780809i | \(0.285193\pi\) | ||||
−0.624770 | + | 0.780809i | \(0.714807\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 43.7756 | 1.41212 | 0.706059 | − | 0.708153i | \(-0.250471\pi\) | ||||
0.706059 | + | 0.708153i | \(0.250471\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.70287 | 0.0500843 | ||||||||
\(35\) | −0.0874935 | − | 29.5974i | −0.00249981 | − | 0.845641i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 48.4190i | − | 1.30862i | −0.756226 | − | 0.654311i | \(-0.772959\pi\) | ||
0.756226 | − | 0.654311i | \(-0.227041\pi\) | |||||||
\(38\) | −41.5221 | −1.09269 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −14.1421 | + | 0.0418056i | −0.353552 | + | 0.00104514i | ||||
\(41\) | 2.72108i | 0.0663677i | 0.999449 | + | 0.0331838i | \(0.0105647\pi\) | ||||
−0.999449 | + | 0.0331838i | \(0.989435\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 19.9856i | − | 0.464781i | −0.972623 | − | 0.232391i | \(-0.925345\pi\) | ||
0.972623 | − | 0.232391i | \(-0.0746548\pi\) | |||||||
\(44\) | − | 7.61952i | − | 0.173171i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 22.8284 | 0.496270 | ||||||||
\(47\) | −24.2985 | −0.516989 | −0.258495 | − | 0.966013i | \(-0.583226\pi\) | ||||
−0.258495 | + | 0.966013i | \(0.583226\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.9594 | 0.284885 | ||||||||
\(50\) | −35.3547 | + | 0.209027i | −0.707094 | + | 0.00418054i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 44.4590i | 0.854982i | ||||||||
\(53\) | −10.8425 | −0.204576 | −0.102288 | − | 0.994755i | \(-0.532616\pi\) | ||||
−0.102288 | + | 0.994755i | \(0.532616\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0563102 | − | 19.0487i | −0.00102382 | − | 0.346340i | ||||
\(56\) | 16.7429i | 0.298981i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 64.0454i | − | 1.10423i | ||||||
\(59\) | − | 19.3890i | − | 0.328626i | −0.986408 | − | 0.164313i | \(-0.947459\pi\) | ||
0.986408 | − | 0.164313i | \(-0.0525408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18.3991 | 0.301624 | 0.150812 | − | 0.988562i | \(-0.451811\pi\) | ||||
0.150812 | + | 0.988562i | \(0.451811\pi\) | |||||||
\(62\) | −61.9081 | −0.998518 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0.328564 | + | 111.147i | 0.00505483 | + | 1.70996i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 83.1289i | 1.24073i | 0.784313 | + | 0.620365i | \(0.213015\pi\) | ||||
−0.784313 | + | 0.620365i | \(0.786985\pi\) | |||||||
\(68\) | −2.40822 | −0.0354150 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.123734 | + | 41.8571i | 0.00176764 | + | 0.597959i | ||||
\(71\) | − | 121.784i | − | 1.71527i | −0.514258 | − | 0.857635i | \(-0.671933\pi\) | ||
0.514258 | − | 0.857635i | \(-0.328067\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 105.116i | 1.43994i | 0.694003 | + | 0.719972i | \(0.255845\pi\) | ||||
−0.694003 | + | 0.719972i | \(0.744155\pi\) | |||||||
\(74\) | 68.4748i | 0.925335i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 58.7212 | 0.772647 | ||||||||
\(77\) | −22.5519 | −0.292882 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 94.2105 | 1.19254 | 0.596269 | − | 0.802785i | \(-0.296649\pi\) | ||||
0.596269 | + | 0.802785i | \(0.296649\pi\) | |||||||
\(80\) | 19.9999 | − | 0.0591221i | 0.249999 | − | 0.000739026i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 3.84818i | − | 0.0469290i | ||||||
\(83\) | 94.6426 | 1.14027 | 0.570136 | − | 0.821550i | \(-0.306890\pi\) | ||||
0.570136 | + | 0.821550i | \(0.306890\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.02052 | + | 0.0177973i | −0.0708296 | + | 0.000209381i | ||||
\(86\) | 28.2639i | 0.328650i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.7756i | 0.122450i | ||||||||
\(89\) | − | 132.665i | − | 1.49062i | −0.666718 | − | 0.745310i | \(-0.732302\pi\) | ||
0.666718 | − | 0.745310i | \(-0.267698\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 131.588 | 1.44602 | ||||||||
\(92\) | −32.2843 | −0.350916 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 34.3633 | 0.365567 | ||||||||
\(95\) | 146.802 | − | 0.433965i | 1.54529 | − | 0.00456805i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 119.009i | − | 1.22689i | −0.789736 | − | 0.613447i | \(-0.789783\pi\) | ||
0.789736 | − | 0.613447i | \(-0.210217\pi\) | |||||||
\(98\) | −19.7415 | −0.201444 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 49.9991 | − | 0.295609i | 0.499991 | − | 0.00295609i | ||||
\(101\) | 23.8005i | 0.235648i | 0.993034 | + | 0.117824i | \(0.0375919\pi\) | ||||
−0.993034 | + | 0.117824i | \(0.962408\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.12865i | 0.0400840i | 0.999799 | + | 0.0200420i | \(0.00637999\pi\) | ||||
−0.999799 | + | 0.0200420i | \(0.993620\pi\) | |||||||
\(104\) | − | 62.8746i | − | 0.604563i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15.3337 | 0.144657 | ||||||||
\(107\) | 117.008 | 1.09353 | 0.546765 | − | 0.837286i | \(-0.315859\pi\) | ||||
0.546765 | + | 0.837286i | \(0.315859\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −84.3413 | −0.773774 | −0.386887 | − | 0.922127i | \(-0.626450\pi\) | ||||
−0.386887 | + | 0.922127i | \(0.626450\pi\) | |||||||
\(110\) | 0.0796347 | + | 26.9389i | 0.000723951 | + | 0.244900i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 23.6781i | − | 0.211411i | ||||||
\(113\) | 80.1454 | 0.709251 | 0.354626 | − | 0.935008i | \(-0.384608\pi\) | ||||
0.354626 | + | 0.935008i | \(0.384608\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −80.7104 | + | 0.238589i | −0.701829 | + | 0.00207469i | ||||
\(116\) | 90.5738i | 0.780809i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 27.4201i | 0.232374i | ||||||||
\(119\) | 7.12774i | 0.0598970i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 106.486 | 0.880047 | ||||||||
\(122\) | −26.0202 | −0.213281 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 87.5513 | 0.706059 | ||||||||
\(125\) | 124.995 | − | 1.10853i | 0.999961 | − | 0.00886821i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 91.3285i | − | 0.719122i | −0.933122 | − | 0.359561i | \(-0.882926\pi\) | ||
0.933122 | − | 0.359561i | \(-0.117074\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.464659 | − | 157.186i | −0.00357430 | − | 1.20912i | ||||
\(131\) | 227.949i | 1.74007i | 0.492992 | + | 0.870034i | \(0.335903\pi\) | ||||
−0.492992 | + | 0.870034i | \(0.664097\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 173.800i | − | 1.30677i | ||||||
\(134\) | − | 117.562i | − | 0.877329i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.40573 | 0.0250422 | ||||||||
\(137\) | 122.719 | 0.895758 | 0.447879 | − | 0.894094i | \(-0.352180\pi\) | ||||
0.447879 | + | 0.894094i | \(0.352180\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −38.4803 | −0.276837 | −0.138418 | − | 0.990374i | \(-0.544202\pi\) | ||||
−0.138418 | + | 0.990374i | \(0.544202\pi\) | |||||||
\(140\) | −0.174987 | − | 59.1949i | −0.00124991 | − | 0.422821i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 172.229i | 1.21288i | ||||||||
\(143\) | 84.6891 | 0.592232 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.669364 | + | 226.434i | 0.00461630 | + | 1.56161i | ||||
\(146\) | − | 148.656i | − | 1.01819i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 96.8380i | − | 0.654311i | ||||||
\(149\) | − | 7.49468i | − | 0.0502998i | −0.999684 | − | 0.0251499i | \(-0.991994\pi\) | ||
0.999684 | − | 0.0251499i | \(-0.00800631\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 217.233 | 1.43863 | 0.719315 | − | 0.694684i | \(-0.244456\pi\) | ||||
0.719315 | + | 0.694684i | \(0.244456\pi\) | |||||||
\(152\) | −83.0443 | −0.546344 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 31.8932 | 0.207099 | ||||||||
\(155\) | 218.877 | − | 0.647027i | 1.41211 | − | 0.00417437i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 177.337i | 1.12953i | 0.825250 | + | 0.564767i | \(0.191034\pi\) | ||||
−0.825250 | + | 0.564767i | \(0.808966\pi\) | |||||||
\(158\) | −133.234 | −0.843251 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −28.2841 | + | 0.0836112i | −0.176776 | + | 0.000522570i | ||||
\(161\) | 95.5537i | 0.593501i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 42.6651i | 0.261749i | 0.991399 | + | 0.130875i | \(0.0417785\pi\) | ||||
−0.991399 | + | 0.130875i | \(0.958221\pi\) | |||||||
\(164\) | 5.44215i | 0.0331838i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −133.845 | −0.806294 | ||||||||
\(167\) | −73.9872 | −0.443037 | −0.221519 | − | 0.975156i | \(-0.571101\pi\) | ||||
−0.221519 | + | 0.975156i | \(0.571101\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −325.152 | −1.92397 | ||||||||
\(170\) | 8.51430 | − | 0.0251693i | 0.0500841 | − | 0.000148054i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 39.9712i | − | 0.232391i | ||||||
\(173\) | −153.745 | −0.888701 | −0.444351 | − | 0.895853i | \(-0.646566\pi\) | ||||
−0.444351 | + | 0.895853i | \(0.646566\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.874931 | − | 147.985i | −0.00499961 | − | 0.845630i | ||||
\(176\) | − | 15.2390i | − | 0.0865854i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 187.617i | 1.05403i | ||||||||
\(179\) | 292.469i | 1.63390i | 0.576706 | + | 0.816951i | \(0.304338\pi\) | ||||
−0.576706 | + | 0.816951i | \(0.695662\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 45.0019 | 0.248629 | 0.124315 | − | 0.992243i | \(-0.460327\pi\) | ||||
0.124315 | + | 0.992243i | \(0.460327\pi\) | |||||||
\(182\) | −186.093 | −1.02249 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 45.6569 | 0.248135 | ||||||||
\(185\) | −0.715658 | − | 242.094i | −0.00386842 | − | 1.30862i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.58736i | 0.0245314i | ||||||||
\(188\) | −48.5970 | −0.258495 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −207.610 | + | 0.613719i | −1.09268 | + | 0.00323010i | ||||
\(191\) | − | 188.716i | − | 0.988040i | −0.869451 | − | 0.494020i | \(-0.835527\pi\) | ||
0.869451 | − | 0.494020i | \(-0.164473\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 90.8810i | − | 0.470886i | −0.971888 | − | 0.235443i | \(-0.924346\pi\) | ||
0.971888 | − | 0.235443i | \(-0.0756541\pi\) | |||||||
\(194\) | 168.304i | 0.867545i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 27.9187 | 0.142442 | ||||||||
\(197\) | −321.126 | −1.63008 | −0.815040 | − | 0.579405i | \(-0.803285\pi\) | ||||
−0.815040 | + | 0.579405i | \(0.803285\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.7423 | −0.114283 | −0.0571414 | − | 0.998366i | \(-0.518199\pi\) | ||||
−0.0571414 | + | 0.998366i | \(0.518199\pi\) | |||||||
\(200\) | −70.7094 | + | 0.418054i | −0.353547 | + | 0.00209027i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 33.6589i | − | 0.166628i | ||||||
\(203\) | 268.077 | 1.32057 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0402189 | + | 13.6053i | 0.000196190 | + | 0.0663674i | ||||
\(206\) | − | 5.83879i | − | 0.0283437i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 88.9181i | 0.427491i | ||||||||
\(209\) | − | 111.857i | − | 0.535200i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −79.9216 | −0.378776 | −0.189388 | − | 0.981902i | \(-0.560650\pi\) | ||||
−0.189388 | + | 0.981902i | \(0.560650\pi\) | |||||||
\(212\) | −21.6851 | −0.102288 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −165.474 | −0.773242 | ||||||||
\(215\) | −0.295398 | − | 99.9276i | −0.00137394 | − | 0.464779i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 259.131i | − | 1.19415i | ||||||
\(218\) | 119.277 | 0.547141 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.112620 | − | 38.0974i | −0.000511911 | − | 0.173170i | ||||
\(221\) | − | 26.7668i | − | 0.121117i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 65.6593i | 0.294436i | 0.989104 | + | 0.147218i | \(0.0470319\pi\) | ||||
−0.989104 | + | 0.147218i | \(0.952968\pi\) | |||||||
\(224\) | 33.4858i | 0.149490i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −113.343 | −0.501516 | ||||||||
\(227\) | −367.704 | −1.61984 | −0.809921 | − | 0.586538i | \(-0.800490\pi\) | ||||
−0.809921 | + | 0.586538i | \(0.800490\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −299.641 | −1.30848 | −0.654238 | − | 0.756288i | \(-0.727011\pi\) | ||||
−0.654238 | + | 0.756288i | \(0.727011\pi\) | |||||||
\(230\) | 114.142 | − | 0.337416i | 0.496268 | − | 0.00146703i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 128.091i | − | 0.552115i | ||||||
\(233\) | 227.228 | 0.975229 | 0.487614 | − | 0.873059i | \(-0.337867\pi\) | ||||
0.487614 | + | 0.873059i | \(0.337867\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −121.492 | + | 0.359144i | −0.516987 | + | 0.00152827i | ||||
\(236\) | − | 38.7779i | − | 0.164313i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 10.0801i | − | 0.0423536i | ||||||
\(239\) | − | 189.818i | − | 0.794218i | −0.917772 | − | 0.397109i | \(-0.870014\pi\) | ||
0.917772 | − | 0.397109i | \(-0.129986\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 90.9556 | 0.377409 | 0.188705 | − | 0.982034i | \(-0.439571\pi\) | ||||
0.188705 | + | 0.982034i | \(0.439571\pi\) | |||||||
\(242\) | −150.594 | −0.622287 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 36.7982 | 0.150812 | ||||||||
\(245\) | 69.7964 | − | 0.206326i | 0.284883 | − | 0.000842149i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 652.672i | 2.64240i | ||||||||
\(248\) | −123.816 | −0.499259 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −176.770 | + | 1.56769i | −0.707079 | + | 0.00627077i | ||||
\(251\) | 386.041i | 1.53801i | 0.639242 | + | 0.769005i | \(0.279248\pi\) | ||||
−0.639242 | + | 0.769005i | \(0.720752\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 61.4977i | 0.243074i | ||||||||
\(254\) | 129.158i | 0.508496i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −346.316 | −1.34753 | −0.673766 | − | 0.738945i | \(-0.735325\pi\) | ||||
−0.673766 | + | 0.738945i | \(0.735325\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −286.617 | −1.10663 | ||||||||
\(260\) | 0.657128 | + | 222.294i | 0.00252741 | + | 0.854978i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 322.368i | − | 1.23041i | ||||||
\(263\) | 433.471 | 1.64818 | 0.824090 | − | 0.566459i | \(-0.191687\pi\) | ||||
0.824090 | + | 0.566459i | \(0.191687\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −54.2124 | + | 0.160258i | −0.204575 | + | 0.000604748i | ||||
\(266\) | 245.791i | 0.924026i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 166.258i | 0.620365i | ||||||||
\(269\) | 456.780i | 1.69807i | 0.528340 | + | 0.849033i | \(0.322815\pi\) | ||||
−0.528340 | + | 0.849033i | \(0.677185\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −321.543 | −1.18651 | −0.593253 | − | 0.805016i | \(-0.702156\pi\) | ||||
−0.593253 | + | 0.805016i | \(0.702156\pi\) | |||||||
\(272\) | −4.81644 | −0.0177075 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −173.551 | −0.633396 | ||||||||
\(275\) | −0.563100 | − | 95.2423i | −0.00204763 | − | 0.346336i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 331.446i | − | 1.19656i | −0.801288 | − | 0.598278i | \(-0.795852\pi\) | ||
0.801288 | − | 0.598278i | \(-0.204148\pi\) | |||||||
\(278\) | 54.4193 | 0.195753 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.247469 | + | 83.7142i | 0.000883818 | + | 0.298979i | ||||
\(281\) | − | 473.198i | − | 1.68398i | −0.539495 | − | 0.841989i | \(-0.681385\pi\) | ||
0.539495 | − | 0.841989i | \(-0.318615\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.3931i | 0.107396i | 0.998557 | + | 0.0536980i | \(0.0171008\pi\) | ||||
−0.998557 | + | 0.0536980i | \(0.982899\pi\) | |||||||
\(284\) | − | 243.568i | − | 0.857635i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −119.768 | −0.418771 | ||||||||
\(287\) | 16.1074 | 0.0561235 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −287.550 | −0.994983 | ||||||||
\(290\) | −0.946624 | − | 320.225i | −0.00326422 | − | 1.10423i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 210.232i | 0.719972i | ||||||||
\(293\) | 25.0162 | 0.0853796 | 0.0426898 | − | 0.999088i | \(-0.486407\pi\) | ||||
0.0426898 | + | 0.999088i | \(0.486407\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.286579 | − | 96.9444i | −0.000971454 | − | 0.328625i | ||||
\(296\) | 136.950i | 0.462668i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.5991i | 0.0355674i | ||||||||
\(299\) | − | 358.832i | − | 1.20011i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −118.305 | −0.393040 | ||||||||
\(302\) | −307.214 | −1.01726 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 117.442 | 0.386324 | ||||||||
\(305\) | 91.9950 | − | 0.271948i | 0.301623 | − | 0.000891633i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 596.302i | − | 1.94235i | −0.238365 | − | 0.971176i | \(-0.576611\pi\) | ||
0.238365 | − | 0.971176i | \(-0.423389\pi\) | |||||||
\(308\) | −45.1038 | −0.146441 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −309.539 | + | 0.915034i | −0.998514 | + | 0.00295172i | ||||
\(311\) | 54.3049i | 0.174614i | 0.996181 | + | 0.0873070i | \(0.0278261\pi\) | ||||
−0.996181 | + | 0.0873070i | \(0.972174\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 161.429i | − | 0.515748i | −0.966179 | − | 0.257874i | \(-0.916978\pi\) | ||
0.966179 | − | 0.257874i | \(-0.0830219\pi\) | |||||||
\(314\) | − | 250.792i | − | 0.798702i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 188.421 | 0.596269 | ||||||||
\(317\) | −272.583 | −0.859884 | −0.429942 | − | 0.902856i | \(-0.641466\pi\) | ||||
−0.429942 | + | 0.902856i | \(0.641466\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 172.532 | 0.540853 | ||||||||
\(320\) | 39.9998 | − | 0.118244i | 0.124999 | − | 0.000369513i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 135.133i | − | 0.419669i | ||||||
\(323\) | −35.3533 | −0.109453 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.28562 | + | 555.728i | 0.0101096 | + | 1.70993i | ||||
\(326\) | − | 60.3376i | − | 0.185085i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 7.69636i | − | 0.0234645i | ||||||
\(329\) | 143.835i | 0.437189i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −528.713 | −1.59732 | −0.798660 | − | 0.601783i | \(-0.794457\pi\) | ||||
−0.798660 | + | 0.601783i | \(0.794457\pi\) | |||||||
\(332\) | 189.285 | 0.570136 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 104.634 | 0.313274 | ||||||||
\(335\) | 1.22869 | + | 415.643i | 0.00366773 | + | 1.24072i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 389.857i | 1.15685i | 0.815737 | + | 0.578423i | \(0.196332\pi\) | ||||
−0.815737 | + | 0.578423i | \(0.803668\pi\) | |||||||
\(338\) | 459.834 | 1.36046 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.0410 | + | 0.0355947i | −0.0354148 | + | 0.000104690i | ||||
\(341\) | − | 166.775i | − | 0.489075i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 372.689i | − | 1.08656i | ||||||
\(344\) | 56.5278i | 0.164325i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 217.429 | 0.628407 | ||||||||
\(347\) | 120.402 | 0.346980 | 0.173490 | − | 0.984836i | \(-0.444496\pi\) | ||||
0.173490 | + | 0.984836i | \(0.444496\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 548.275 | 1.57099 | 0.785494 | − | 0.618870i | \(-0.212409\pi\) | ||||
0.785494 | + | 0.618870i | \(0.212409\pi\) | |||||||
\(350\) | 1.23734 | + | 209.283i | 0.00353525 | + | 0.597951i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 21.5513i | 0.0612251i | ||||||||
\(353\) | −293.335 | −0.830978 | −0.415489 | − | 0.909598i | \(-0.636390\pi\) | ||||
−0.415489 | + | 0.909598i | \(0.636390\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.80003 | − | 608.918i | −0.00507052 | − | 1.71526i | ||||
\(356\) | − | 265.330i | − | 0.745310i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 413.613i | − | 1.15534i | ||||||
\(359\) | − | 15.8718i | − | 0.0442110i | −0.999756 | − | 0.0221055i | \(-0.992963\pi\) | ||
0.999756 | − | 0.0221055i | \(-0.00703698\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 501.044 | 1.38793 | ||||||||
\(362\) | −63.6423 | −0.175807 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 263.176 | 0.723011 | ||||||||
\(365\) | 1.55367 | + | 525.577i | 0.00425662 | + | 1.43994i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 592.583i | 1.61467i | 0.590094 | + | 0.807334i | \(0.299091\pi\) | ||||
−0.590094 | + | 0.807334i | \(0.700909\pi\) | |||||||
\(368\) | −64.5686 | −0.175458 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.01209 | + | 342.373i | 0.00273539 | + | 0.925331i | ||||
\(371\) | 64.1825i | 0.172999i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 379.589i | − | 1.01766i | −0.860866 | − | 0.508832i | \(-0.830077\pi\) | ||
0.860866 | − | 0.508832i | \(-0.169923\pi\) | |||||||
\(374\) | − | 6.48751i | − | 0.0173463i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 68.7265 | 0.182783 | ||||||||
\(377\) | −1006.71 | −2.67031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −493.432 | −1.30193 | −0.650966 | − | 0.759107i | \(-0.725636\pi\) | ||||
−0.650966 | + | 0.759107i | \(0.725636\pi\) | |||||||
\(380\) | 293.605 | − | 0.867929i | 0.772644 | − | 0.00228402i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 266.884i | 0.698650i | ||||||||
\(383\) | −304.303 | −0.794524 | −0.397262 | − | 0.917705i | \(-0.630040\pi\) | ||||
−0.397262 | + | 0.917705i | \(0.630040\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −112.759 | + | 0.333329i | −0.292881 | + | 0.000865790i | ||||
\(386\) | 128.525i | 0.332967i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 238.017i | − | 0.613447i | ||||||
\(389\) | − | 451.981i | − | 1.16190i | −0.813938 | − | 0.580952i | \(-0.802680\pi\) | ||
0.813938 | − | 0.580952i | \(-0.197320\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.4369 | 0.0497107 | ||||||||
\(392\) | −39.4830 | −0.100722 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 454.140 | 1.15264 | ||||||||
\(395\) | 471.050 | − | 1.39248i | 1.19253 | − | 0.00352526i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 316.160i | 0.796373i | 0.917304 | + | 0.398187i | \(0.130360\pi\) | ||||
−0.917304 | + | 0.398187i | \(0.869640\pi\) | |||||||
\(398\) | 32.1624 | 0.0808101 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 99.9983 | − | 0.591218i | 0.249996 | − | 0.00147805i | ||||
\(401\) | 76.3843i | 0.190485i | 0.995454 | + | 0.0952423i | \(0.0303626\pi\) | ||||
−0.995454 | + | 0.0952423i | \(0.969637\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 973.112i | 2.41467i | ||||||||
\(404\) | 47.6009i | 0.117824i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −379.117 | −0.933787 | ||||||||
\(407\) | −184.465 | −0.453230 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −433.545 | −1.06001 | −0.530006 | − | 0.847994i | \(-0.677810\pi\) | ||||
−0.530006 | + | 0.847994i | \(0.677810\pi\) | |||||||
\(410\) | −0.0568781 | − | 19.2408i | −0.000138727 | − | 0.0469288i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.25730i | 0.0200420i | ||||||||
\(413\) | −114.773 | −0.277901 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 473.211 | − | 1.39887i | 1.14027 | − | 0.00337076i | ||||
\(416\) | − | 125.749i | − | 0.302282i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 158.189i | 0.378443i | ||||||||
\(419\) | − | 158.961i | − | 0.379383i | −0.981844 | − | 0.189691i | \(-0.939251\pi\) | ||
0.981844 | − | 0.189691i | \(-0.0607488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.0663 | −0.0761669 | −0.0380834 | − | 0.999275i | \(-0.512125\pi\) | ||||
−0.0380834 | + | 0.999275i | \(0.512125\pi\) | |||||||
\(422\) | 113.026 | 0.267835 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 30.6673 | 0.0723285 | ||||||||
\(425\) | −30.1022 | + | 0.177973i | −0.0708287 | + | 0.000418759i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 108.914i | − | 0.255067i | ||||||
\(428\) | 234.015 | 0.546765 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.417755 | + | 141.319i | 0.000971524 | + | 0.328649i | ||||
\(431\) | − | 636.866i | − | 1.47765i | −0.673898 | − | 0.738824i | \(-0.735381\pi\) | ||
0.673898 | − | 0.738824i | \(-0.264619\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 594.793i | 1.37366i | 0.726820 | + | 0.686828i | \(0.240997\pi\) | ||||
−0.726820 | + | 0.686828i | \(0.759003\pi\) | |||||||
\(434\) | 366.466i | 0.844392i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −168.683 | −0.386887 | ||||||||
\(437\) | −473.943 | −1.08454 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −507.720 | −1.15654 | −0.578269 | − | 0.815846i | \(-0.696272\pi\) | ||||
−0.578269 | + | 0.815846i | \(0.696272\pi\) | |||||||
\(440\) | 0.159269 | + | 53.8779i | 0.000361976 | + | 0.122450i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 37.8539i | 0.0856423i | ||||||||
\(443\) | 681.009 | 1.53727 | 0.768633 | − | 0.639689i | \(-0.220937\pi\) | ||||
0.768633 | + | 0.639689i | \(0.220937\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.96086 | − | 663.323i | −0.00440643 | − | 1.49061i | ||||
\(446\) | − | 92.8563i | − | 0.208198i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 47.3561i | − | 0.105706i | ||||||
\(449\) | 273.889i | 0.609998i | 0.952353 | + | 0.304999i | \(0.0986561\pi\) | ||||
−0.952353 | + | 0.304999i | \(0.901344\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.3666 | 0.0229859 | ||||||||
\(452\) | 160.291 | 0.354626 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 520.012 | 1.14540 | ||||||||
\(455\) | 657.937 | − | 1.94494i | 1.44602 | − | 0.00427459i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 203.470i | − | 0.445229i | −0.974907 | − | 0.222615i | \(-0.928541\pi\) | ||
0.974907 | − | 0.222615i | \(-0.0714591\pi\) | |||||||
\(458\) | 423.757 | 0.925233 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −161.421 | + | 0.477178i | −0.350915 | + | 0.00103734i | ||||
\(461\) | 846.093i | 1.83534i | 0.397341 | + | 0.917671i | \(0.369933\pi\) | ||||
−0.397341 | + | 0.917671i | \(0.630067\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 439.677i | − | 0.949626i | −0.880087 | − | 0.474813i | \(-0.842516\pi\) | ||
0.880087 | − | 0.474813i | \(-0.157484\pi\) | |||||||
\(464\) | 181.148i | 0.390404i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −321.349 | −0.689591 | ||||||||
\(467\) | 14.0853 | 0.0301612 | 0.0150806 | − | 0.999886i | \(-0.495200\pi\) | ||||
0.0150806 | + | 0.999886i | \(0.495200\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 492.083 | 1.04922 | ||||||||
\(470\) | 171.816 | − | 0.507907i | 0.365565 | − | 0.00108065i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 54.8403i | 0.116187i | ||||||||
\(473\) | −76.1403 | −0.160973 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 734.002 | − | 4.33963i | 1.54527 | − | 0.00913606i | ||||
\(476\) | 14.2555i | 0.0299485i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 268.443i | 0.561597i | ||||||||
\(479\) | 391.596i | 0.817529i | 0.912640 | + | 0.408765i | \(0.134040\pi\) | ||||
−0.912640 | + | 0.408765i | \(0.865960\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1076.33 | 2.23769 | ||||||||
\(482\) | −128.631 | −0.266869 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 212.971 | 0.440024 | ||||||||
\(485\) | −1.75901 | − | 595.041i | −0.00362682 | − | 1.22689i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 881.169i | − | 1.80938i | −0.426069 | − | 0.904691i | \(-0.640102\pi\) | ||
0.426069 | − | 0.904691i | \(-0.359898\pi\) | |||||||
\(488\) | −52.0405 | −0.106640 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −98.7071 | + | 0.291790i | −0.201443 | + | 0.000595489i | ||||
\(491\) | − | 351.635i | − | 0.716161i | −0.933691 | − | 0.358081i | \(-0.883431\pi\) | ||
0.933691 | − | 0.358081i | \(-0.116569\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 54.5304i | − | 0.110609i | ||||||
\(494\) | − | 923.017i | − | 1.86846i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 175.103 | 0.353029 | ||||||||
\(497\) | −720.903 | −1.45051 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −481.852 | −0.965635 | −0.482817 | − | 0.875721i | \(-0.660387\pi\) | ||||
−0.482817 | + | 0.875721i | \(0.660387\pi\) | |||||||
\(500\) | 249.990 | − | 2.21705i | 0.499980 | − | 0.00443410i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 545.944i | − | 1.08754i | ||||||
\(503\) | 670.477 | 1.33296 | 0.666478 | − | 0.745525i | \(-0.267801\pi\) | ||||
0.666478 | + | 0.745525i | \(0.267801\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.351783 | + | 119.002i | 0.000696600 | + | 0.235647i | ||||
\(506\) | − | 86.9708i | − | 0.171879i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 182.657i | − | 0.359561i | ||||||
\(509\) | − | 11.0518i | − | 0.0217128i | −0.999941 | − | 0.0108564i | \(-0.996544\pi\) | ||
0.999941 | − | 0.0108564i | \(-0.00345577\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 622.235 | 1.21768 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 489.765 | 0.952849 | ||||||||
\(515\) | 0.0610236 | + | 20.6432i | 0.000118492 | + | 0.0400838i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 92.5714i | 0.179055i | ||||||||
\(518\) | 405.338 | 0.782505 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.929319 | − | 314.372i | −0.00178715 | − | 0.604561i | ||||
\(521\) | − | 534.980i | − | 1.02683i | −0.858140 | − | 0.513416i | \(-0.828380\pi\) | ||
0.858140 | − | 0.513416i | \(-0.171620\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 615.393i | 1.17666i | 0.808621 | + | 0.588330i | \(0.200214\pi\) | ||||
−0.808621 | + | 0.588330i | \(0.799786\pi\) | |||||||
\(524\) | 455.898i | 0.870034i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −613.021 | −1.16544 | ||||||||
\(527\) | −52.7106 | −0.100020 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −268.431 | −0.507431 | ||||||||
\(530\) | 76.6679 | − | 0.226639i | 0.144656 | − | 0.000427621i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 347.601i | − | 0.653385i | ||||||
\(533\) | −60.4882 | −0.113486 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 585.036 | − | 1.72943i | 1.09352 | − | 0.00323259i | ||||
\(536\) | − | 235.124i | − | 0.438664i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 645.984i | − | 1.20071i | ||||||
\(539\) | − | 53.1818i | − | 0.0986675i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −479.872 | −0.887010 | −0.443505 | − | 0.896272i | \(-0.646265\pi\) | ||||
−0.443505 | + | 0.896272i | \(0.646265\pi\) | |||||||
\(542\) | 454.730 | 0.838986 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.81147 | 0.0125211 | ||||||||
\(545\) | −421.705 | + | 1.24661i | −0.773770 | + | 0.00228735i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 355.636i | 0.650158i | 0.945687 | + | 0.325079i | \(0.105391\pi\) | ||||
−0.945687 | + | 0.325079i | \(0.894609\pi\) | |||||||
\(548\) | 245.438 | 0.447879 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.796343 | + | 134.693i | 0.00144790 | + | 0.244896i | ||||
\(551\) | 1329.65i | 2.41316i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 557.680i | − | 1.00846i | ||||||
\(554\) | 468.736i | 0.846093i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −76.9606 | −0.138418 | ||||||||
\(557\) | 267.691 | 0.480595 | 0.240297 | − | 0.970699i | \(-0.422755\pi\) | ||||
0.240297 | + | 0.970699i | \(0.422755\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 444.270 | 0.794759 | ||||||||
\(560\) | −0.349974 | − | 118.390i | −0.000624953 | − | 0.211410i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 669.203i | 1.19075i | ||||||||
\(563\) | 241.022 | 0.428104 | 0.214052 | − | 0.976822i | \(-0.431334\pi\) | ||||
0.214052 | + | 0.976822i | \(0.431334\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 400.725 | − | 1.18459i | 0.709248 | − | 0.00209662i | ||||
\(566\) | − | 42.9823i | − | 0.0759404i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 344.458i | 0.606440i | ||||||||
\(569\) | 56.2891i | 0.0989263i | 0.998776 | + | 0.0494632i | \(0.0157510\pi\) | ||||
−0.998776 | + | 0.0494632i | \(0.984249\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −382.848 | −0.670486 | −0.335243 | − | 0.942132i | \(-0.608818\pi\) | ||||
−0.335243 | + | 0.942132i | \(0.608818\pi\) | |||||||
\(572\) | 169.378 | 0.296116 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −22.7794 | −0.0396853 | ||||||||
\(575\) | −403.547 | + | 2.38588i | −0.701820 | + | 0.00414936i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 114.953i | 0.199225i | 0.995026 | + | 0.0996126i | \(0.0317603\pi\) | ||||
−0.995026 | + | 0.0996126i | \(0.968240\pi\) | |||||||
\(578\) | 406.657 | 0.703559 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.33873 | + | 452.867i | 0.00230815 | + | 0.780805i | ||||
\(581\) | − | 560.238i | − | 0.964266i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 41.3074i | 0.0708532i | ||||||||
\(584\) | − | 297.313i | − | 0.509097i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −35.3783 | −0.0603725 | ||||||||
\(587\) | 487.696 | 0.830828 | 0.415414 | − | 0.909632i | \(-0.363637\pi\) | ||||
0.415414 | + | 0.909632i | \(0.363637\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1285.28 | 2.18214 | ||||||||
\(590\) | 0.405284 | + | 137.100i | 0.000686921 | + | 0.232373i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 193.676i | − | 0.327155i | ||||||
\(593\) | −631.323 | −1.06463 | −0.532313 | − | 0.846548i | \(-0.678677\pi\) | ||||
−0.532313 | + | 0.846548i | \(0.678677\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.105352 | + | 35.6385i | 0.000177062 | + | 0.0598967i | ||||
\(596\) | − | 14.9894i | − | 0.0251499i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 507.465i | 0.848604i | ||||||||
\(599\) | 701.491i | 1.17110i | 0.810635 | + | 0.585552i | \(0.199122\pi\) | ||||
−0.810635 | + | 0.585552i | \(0.800878\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 400.330 | 0.666106 | 0.333053 | − | 0.942908i | \(-0.391921\pi\) | ||||
0.333053 | + | 0.942908i | \(0.391921\pi\) | |||||||
\(602\) | 167.309 | 0.277921 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 434.466 | 0.719315 | ||||||||
\(605\) | 532.426 | − | 1.57391i | 0.880044 | − | 0.00260151i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 290.432i | 0.478472i | 0.970962 | + | 0.239236i | \(0.0768969\pi\) | ||||
−0.970962 | + | 0.239236i | \(0.923103\pi\) | |||||||
\(608\) | −166.089 | −0.273172 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −130.101 | + | 0.384593i | −0.213280 | + | 0.000630480i | ||||
\(611\) | − | 540.144i | − | 0.884033i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 177.921i | 0.290247i | 0.989414 | + | 0.145123i | \(0.0463579\pi\) | ||||
−0.989414 | + | 0.145123i | \(0.953642\pi\) | |||||||
\(614\) | 843.298i | 1.37345i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 63.7865 | 0.103549 | ||||||||
\(617\) | −465.432 | −0.754347 | −0.377173 | − | 0.926143i | \(-0.623104\pi\) | ||||
−0.377173 | + | 0.926143i | \(0.623104\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 564.501 | 0.911957 | 0.455978 | − | 0.889991i | \(-0.349289\pi\) | ||||
0.455978 | + | 0.889991i | \(0.349289\pi\) | |||||||
\(620\) | 437.755 | − | 1.29405i | 0.706056 | − | 0.00208718i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 76.7988i | − | 0.123471i | ||||||
\(623\) | −785.313 | −1.26053 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 624.956 | − | 7.39010i | 0.999930 | − | 0.0118242i | ||||
\(626\) | 228.295i | 0.364689i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 354.674i | 0.564767i | ||||||||
\(629\) | 58.3017i | 0.0926896i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 696.074 | 1.10313 | 0.551564 | − | 0.834133i | \(-0.314031\pi\) | ||||
0.551564 | + | 0.834133i | \(0.314031\pi\) | |||||||
\(632\) | −266.467 | −0.421626 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 385.491 | 0.608030 | ||||||||
\(635\) | −1.34988 | − | 456.641i | −0.00212580 | − | 0.719119i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 310.310i | 0.487142i | ||||||||
\(638\) | −243.997 | −0.382441 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −56.5683 | + | 0.167222i | −0.0883880 | + | 0.000261285i | ||||
\(641\) | 325.853i | 0.508352i | 0.967158 | + | 0.254176i | \(0.0818042\pi\) | ||||
−0.967158 | + | 0.254176i | \(0.918196\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 108.531i | 0.168789i | 0.996432 | + | 0.0843944i | \(0.0268956\pi\) | ||||
−0.996432 | + | 0.0843944i | \(0.973104\pi\) | |||||||
\(644\) | 191.107i | 0.296750i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 49.9972 | 0.0773950 | ||||||||
\(647\) | −895.382 | −1.38390 | −0.691949 | − | 0.721946i | \(-0.743248\pi\) | ||||
−0.691949 | + | 0.721946i | \(0.743248\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −73.8673 | −0.113817 | ||||||||
\(650\) | −4.64657 | − | 785.919i | −0.00714857 | − | 1.20911i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 85.3302i | 0.130875i | ||||||||
\(653\) | 93.3534 | 0.142961 | 0.0714804 | − | 0.997442i | \(-0.477228\pi\) | ||||
0.0714804 | + | 0.997442i | \(0.477228\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.36920 | + | 1139.74i | 0.00514382 | + | 1.74006i | ||||
\(656\) | 10.8843i | 0.0165919i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 203.414i | − | 0.309140i | ||||||
\(659\) | − | 1031.59i | − | 1.56539i | −0.622407 | − | 0.782694i | \(-0.713845\pi\) | ||
0.622407 | − | 0.782694i | \(-0.286155\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −865.519 | −1.30941 | −0.654704 | − | 0.755885i | \(-0.727207\pi\) | ||||
−0.654704 | + | 0.755885i | \(0.727207\pi\) | |||||||
\(662\) | 747.713 | 1.12948 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −267.690 | −0.403147 | ||||||||
\(665\) | −2.56886 | − | 868.998i | −0.00386295 | − | 1.30676i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 731.028i | − | 1.09599i | ||||||
\(668\) | −147.974 | −0.221519 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.73763 | − | 587.808i | −0.00259347 | − | 0.877325i | ||||
\(671\) | − | 70.0961i | − | 0.104465i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 686.828i | − | 1.02055i | −0.860012 | − | 0.510273i | \(-0.829544\pi\) | ||
0.860012 | − | 0.510273i | \(-0.170456\pi\) | |||||||
\(674\) | − | 551.342i | − | 0.818014i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −650.303 | −0.961987 | ||||||||
\(677\) | −780.080 | −1.15226 | −0.576130 | − | 0.817358i | \(-0.695438\pi\) | ||||
−0.576130 | + | 0.817358i | \(0.695438\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −704.474 | −1.03752 | ||||||||
\(680\) | 17.0286 | − | 0.0503385i | 0.0250421 | − | 7.40272e-5i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 235.855i | 0.345828i | ||||||||
\(683\) | −285.666 | −0.418252 | −0.209126 | − | 0.977889i | \(-0.567062\pi\) | ||||
−0.209126 | + | 0.977889i | \(0.567062\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 613.591 | − | 1.81385i | 0.895754 | − | 0.00264795i | ||||
\(686\) | 527.062i | 0.768311i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 79.9424i | − | 0.116195i | ||||||
\(689\) | − | 241.024i | − | 0.349817i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 65.7949 | 0.0952170 | 0.0476085 | − | 0.998866i | \(-0.484840\pi\) | ||||
0.0476085 | + | 0.998866i | \(0.484840\pi\) | |||||||
\(692\) | −307.491 | −0.444351 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −170.274 | −0.245352 | ||||||||
\(695\) | −192.401 | + | 0.568758i | −0.276835 | + | 0.000818357i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.27647i | − | 0.00470082i | ||||||
\(698\) | −775.377 | −1.11086 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.74986 | − | 295.971i | −0.00249980 | − | 0.422815i | ||||
\(701\) | 736.516i | 1.05067i | 0.850897 | + | 0.525333i | \(0.176059\pi\) | ||||
−0.850897 | + | 0.525333i | \(0.823941\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1421.61i | − | 2.02221i | ||||||
\(704\) | − | 30.4781i | − | 0.0432927i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 414.839 | 0.587590 | ||||||||
\(707\) | 140.887 | 0.199275 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −582.252 | −0.821231 | −0.410615 | − | 0.911809i | \(-0.634686\pi\) | ||||
−0.410615 | + | 0.911809i | \(0.634686\pi\) | |||||||
\(710\) | 2.54563 | + | 861.141i | 0.00358540 | + | 1.21287i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 375.234i | 0.527014i | ||||||||
\(713\) | −706.633 | −0.991070 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 423.444 | − | 1.25175i | 0.592229 | − | 0.00175070i | ||||
\(716\) | 584.937i | 0.816951i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22.4461i | 0.0312619i | ||||||||
\(719\) | 256.052i | 0.356123i | 0.984019 | + | 0.178061i | \(0.0569826\pi\) | ||||
−0.984019 | + | 0.178061i | \(0.943017\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.4396 | 0.0338968 | ||||||||
\(722\) | −708.583 | −0.981417 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 90.0038 | 0.124315 | ||||||||
\(725\) | 6.69361 | + | 1132.15i | 0.00923257 | + | 1.56159i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 74.1018i | 0.101928i | 0.998700 | + | 0.0509641i | \(0.0162294\pi\) | ||||
−0.998700 | + | 0.0509641i | \(0.983771\pi\) | |||||||
\(728\) | −372.187 | −0.511246 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.19722 | − | 743.278i | −0.00300989 | − | 1.01819i | ||||
\(731\) | 24.0648i | 0.0329204i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 233.383i | 0.318395i | 0.987247 | + | 0.159197i | \(0.0508906\pi\) | ||||
−0.987247 | + | 0.159197i | \(0.949109\pi\) | |||||||
\(734\) | − | 838.039i | − | 1.14174i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 91.3138 | 0.124068 | ||||||||
\(737\) | 316.701 | 0.429717 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −541.648 | −0.732948 | −0.366474 | − | 0.930428i | \(-0.619435\pi\) | ||||
−0.366474 | + | 0.930428i | \(0.619435\pi\) | |||||||
\(740\) | −1.43132 | − | 484.188i | −0.00193421 | − | 0.654308i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 90.7678i | − | 0.122329i | ||||||
\(743\) | −843.929 | −1.13584 | −0.567920 | − | 0.823084i | \(-0.692252\pi\) | ||||
−0.567920 | + | 0.823084i | \(0.692252\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.110775 | − | 37.4732i | −0.000148692 | − | 0.0502996i | ||||
\(746\) | 536.820i | 0.719597i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.17473i | 0.0122657i | ||||||||
\(749\) | − | 692.629i | − | 0.924738i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 101.631 | 0.135327 | 0.0676635 | − | 0.997708i | \(-0.478446\pi\) | ||||
0.0676635 | + | 0.997708i | \(0.478446\pi\) | |||||||
\(752\) | −97.1940 | −0.129247 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1423.70 | 1.88819 | ||||||||
\(755\) | 1086.16 | − | 3.21082i | 1.43862 | − | 0.00425274i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 456.777i | 0.603404i | 0.953402 | + | 0.301702i | \(0.0975547\pi\) | ||||
−0.953402 | + | 0.301702i | \(0.902445\pi\) | |||||||
\(758\) | 697.818 | 0.920605 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −415.220 | + | 1.22744i | −0.546342 | + | 0.00161505i | ||||
\(761\) | − | 44.5068i | − | 0.0584846i | −0.999572 | − | 0.0292423i | \(-0.990691\pi\) | ||
0.999572 | − | 0.0292423i | \(-0.00930945\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 499.260i | 0.654338i | ||||||||
\(764\) | − | 377.431i | − | 0.494020i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 430.349 | 0.561813 | ||||||||
\(767\) | 431.007 | 0.561939 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −250.150 | −0.325293 | −0.162647 | − | 0.986684i | \(-0.552003\pi\) | ||||
−0.162647 | + | 0.986684i | \(0.552003\pi\) | |||||||
\(770\) | 159.465 | − | 0.471398i | 0.207098 | − | 0.000612206i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 181.762i | − | 0.235443i | ||||||
\(773\) | −1059.49 | −1.37063 | −0.685313 | − | 0.728249i | \(-0.740334\pi\) | ||||
−0.685313 | + | 0.728249i | \(0.740334\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1094.37 | − | 6.47024i | 1.41209 | − | 0.00834869i | ||||
\(776\) | 336.607i | 0.433772i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 639.198i | 0.821591i | ||||||||
\(779\) | 79.8924i | 0.102558i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −463.969 | −0.594070 | ||||||||
\(782\) | −27.4879 | −0.0351508 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 55.8374 | 0.0712212 | ||||||||
\(785\) | 2.62113 | + | 886.681i | 0.00333902 | + | 1.12953i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 817.246i | − | 1.03843i | −0.854643 | − | 0.519216i | \(-0.826224\pi\) | ||
0.854643 | − | 0.519216i | \(-0.173776\pi\) | |||||||
\(788\) | −642.251 | −0.815040 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −666.166 | + | 1.96926i | −0.843248 | + | 0.00249274i | ||||
\(791\) | − | 474.422i | − | 0.599775i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 409.003i | 0.515767i | ||||||||
\(794\) | − | 447.118i | − | 0.563121i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −45.4845 | −0.0571414 | ||||||||
\(797\) | −1064.96 | −1.33621 | −0.668107 | − | 0.744065i | \(-0.732895\pi\) | ||||
−0.668107 | + | 0.744065i | \(0.732895\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.2580 | 0.0366183 | ||||||||
\(800\) | −141.419 | + | 0.836109i | −0.176774 | + | 0.00104514i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 108.024i | − | 0.134693i | ||||||
\(803\) | 400.466 | 0.498712 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.41233 | + | 477.766i | 0.00175445 | + | 0.593498i | ||||
\(806\) | − | 1376.19i | − | 1.70743i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 67.3178i | − | 0.0833142i | ||||||
\(809\) | 417.926i | 0.516595i | 0.966065 | + | 0.258298i | \(0.0831615\pi\) | ||||
−0.966065 | + | 0.258298i | \(0.916838\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −993.633 | −1.22519 | −0.612597 | − | 0.790395i | \(-0.709875\pi\) | ||||
−0.612597 | + | 0.790395i | \(0.709875\pi\) | |||||||
\(812\) | 536.153 | 0.660287 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 260.872 | 0.320482 | ||||||||
\(815\) | 0.630612 | + | 213.325i | 0.000773758 | + | 0.261748i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 586.789i | − | 0.718224i | ||||||
\(818\) | 613.125 | 0.749541 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0804378 | + | 27.2106i | 9.80949e−5 | + | 0.0331837i | ||||
\(821\) | 671.048i | 0.817354i | 0.912679 | + | 0.408677i | \(0.134010\pi\) | ||||
−0.912679 | + | 0.408677i | \(0.865990\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 688.146i | 0.836144i | 0.908414 | + | 0.418072i | \(0.137294\pi\) | ||||
−0.908414 | + | 0.418072i | \(0.862706\pi\) | |||||||
\(824\) | − | 11.6776i | − | 0.0141718i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 162.314 | 0.196506 | ||||||||
\(827\) | 904.043 | 1.09316 | 0.546580 | − | 0.837407i | \(-0.315930\pi\) | ||||
0.546580 | + | 0.837407i | \(0.315930\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1539.16 | −1.85664 | −0.928321 | − | 0.371779i | \(-0.878748\pi\) | ||||
−0.928321 | + | 0.371779i | \(0.878748\pi\) | |||||||
\(830\) | −669.221 | + | 1.97830i | −0.806291 | + | 0.00238349i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 177.836i | 0.213745i | ||||||||
\(833\) | −16.8086 | −0.0201784 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −369.934 | + | 1.09357i | −0.443035 | + | 0.00130966i | ||||
\(836\) | − | 223.714i | − | 0.267600i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 224.805i | 0.268264i | ||||||||
\(839\) | − | 886.324i | − | 1.05641i | −0.849118 | − | 0.528203i | \(-0.822866\pi\) | ||
0.849118 | − | 0.528203i | \(-0.177134\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1209.90 | −1.43865 | ||||||||
\(842\) | 45.3485 | 0.0538581 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −159.843 | −0.189388 | ||||||||
\(845\) | −1625.75 | + | 4.80591i | −1.92397 | + | 0.00568747i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 630.344i | − | 0.744208i | ||||||
\(848\) | −43.3701 | −0.0511440 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 42.5709 | − | 0.251691i | 0.0500834 | − | 0.000296108i | ||||
\(851\) | 781.586i | 0.918433i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1031.36i | − | 1.20909i | −0.796570 | − | 0.604547i | \(-0.793354\pi\) | ||
0.796570 | − | 0.604547i | \(-0.206646\pi\) | |||||||
\(854\) | 154.027i | 0.180360i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −330.948 | −0.386621 | ||||||||
\(857\) | 543.529 | 0.634222 | 0.317111 | − | 0.948388i | \(-0.397287\pi\) | ||||
0.317111 | + | 0.948388i | \(0.397287\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 363.363 | 0.423007 | 0.211504 | − | 0.977377i | \(-0.432164\pi\) | ||||
0.211504 | + | 0.977377i | \(0.432164\pi\) | |||||||
\(860\) | −0.590795 | − | 199.855i | −0.000686971 | − | 0.232390i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 900.665i | 1.04485i | ||||||||
\(863\) | 693.976 | 0.804144 | 0.402072 | − | 0.915608i | \(-0.368290\pi\) | ||||
0.402072 | + | 0.915608i | \(0.368290\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −768.723 | + | 2.27244i | −0.888697 | + | 0.00262709i | ||||
\(866\) | − | 841.164i | − | 0.971321i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 518.261i | − | 0.597075i | ||||||
\(869\) | − | 358.919i | − | 0.413025i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1847.92 | −2.12160 | ||||||||
\(872\) | 238.553 | 0.273570 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 670.256 | 0.766884 | ||||||||
\(875\) | −6.56193 | − | 739.910i | −0.00749935 | − | 0.845612i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 442.700i | 0.504790i | 0.967624 | + | 0.252395i | \(0.0812182\pi\) | ||||
−0.967624 | + | 0.252395i | \(0.918782\pi\) | |||||||
\(878\) | 718.025 | 0.817796 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.225241 | − | 76.1948i | −0.000255955 | − | 0.0865850i | ||||
\(881\) | 1448.18i | 1.64379i | 0.569642 | + | 0.821893i | \(0.307082\pi\) | ||||
−0.569642 | + | 0.821893i | \(0.692918\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 672.798i | 0.761946i | 0.924586 | + | 0.380973i | \(0.124411\pi\) | ||||
−0.924586 | + | 0.380973i | \(0.875589\pi\) | |||||||
\(884\) | − | 53.5335i | − | 0.0605583i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −963.092 | −1.08701 | ||||||||
\(887\) | 889.935 | 1.00331 | 0.501655 | − | 0.865068i | \(-0.332725\pi\) | ||||
0.501655 | + | 0.865068i | \(0.332725\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −540.620 | −0.608122 | ||||||||
\(890\) | 2.77307 | + | 938.080i | 0.00311581 | + | 1.05402i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 131.319i | 0.147218i | ||||||||
\(893\) | −713.418 | −0.798901 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.32284 | + | 1462.34i | 0.00482999 | + | 1.63390i | ||||
\(896\) | 66.9717i | 0.0747452i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 387.337i | − | 0.431333i | ||||||
\(899\) | 1982.46i | 2.20519i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.0556 | 0.0144901 | ||||||||
\(902\) | −14.6606 | −0.0162535 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −226.685 | −0.250758 | ||||||||
\(905\) | 225.008 | − | 0.665151i | 0.248628 | − | 0.000734974i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 301.835i | − | 0.332783i | −0.986060 | − | 0.166392i | \(-0.946788\pi\) | ||
0.986060 | − | 0.166392i | \(-0.0532116\pi\) | |||||||
\(908\) | −735.409 | −0.809921 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −930.463 | + | 2.75056i | −1.02249 | + | 0.00302259i | ||||
\(911\) | − | 1370.11i | − | 1.50396i | −0.659187 | − | 0.751979i | \(-0.729099\pi\) | ||
0.659187 | − | 0.751979i | \(-0.270901\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 360.566i | − | 0.394924i | ||||||
\(914\) | 287.750i | 0.314824i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −599.282 | −0.654238 | ||||||||
\(917\) | 1349.35 | 1.47148 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −228.522 | −0.248664 | −0.124332 | − | 0.992241i | \(-0.539679\pi\) | ||||
−0.124332 | + | 0.992241i | \(0.539679\pi\) | |||||||
\(920\) | 228.283 | − | 0.674832i | 0.248134 | − | 0.000733513i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 1196.56i | − | 1.29778i | ||||||
\(923\) | 2707.21 | 2.93305 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.15655 | − | 1210.45i | −0.00773681 | − | 1.30860i | ||||
\(926\) | 621.797i | 0.671487i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 256.181i | − | 0.276058i | ||||||
\(929\) | − | 316.260i | − | 0.340430i | −0.985407 | − | 0.170215i | \(-0.945554\pi\) | ||
0.985407 | − | 0.170215i | \(-0.0544462\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 409.855 | 0.440231 | ||||||||
\(932\) | 454.457 | 0.487614 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19.9196 | −0.0213272 | ||||||||
\(935\) | 0.0678036 | + | 22.9367i | 7.25172e−5 | + | 0.0245313i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1277.28i | 1.36315i | 0.731746 | + | 0.681577i | \(0.238706\pi\) | ||||
−0.731746 | + | 0.681577i | \(0.761294\pi\) | |||||||
\(938\) | −695.910 | −0.741908 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −242.984 | + | 0.718289i | −0.258494 | + | 0.000764137i | ||||
\(941\) | − | 1608.79i | − | 1.70966i | −0.518905 | − | 0.854832i | \(-0.673660\pi\) | ||
0.518905 | − | 0.854832i | \(-0.326340\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 43.9240i | − | 0.0465790i | ||||||
\(944\) | − | 77.5558i | − | 0.0821566i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 107.679 | 0.113825 | ||||||||
\(947\) | 1586.42 | 1.67521 | 0.837605 | − | 0.546276i | \(-0.183955\pi\) | ||||
0.837605 | + | 0.546276i | \(0.183955\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2336.68 | −2.46225 | ||||||||
\(950\) | −1038.04 | + | 6.13716i | −1.09267 | + | 0.00646017i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 20.1603i | − | 0.0211768i | ||||||
\(953\) | 985.215 | 1.03380 | 0.516902 | − | 0.856045i | \(-0.327085\pi\) | ||||
0.516902 | + | 0.856045i | \(0.327085\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.78931 | − | 943.574i | −0.00292075 | − | 0.988035i | ||||
\(956\) | − | 379.636i | − | 0.397109i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 553.801i | − | 0.578080i | ||||||
\(959\) | − | 726.436i | − | 0.757493i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 955.307 | 0.994076 | ||||||||
\(962\) | −1522.16 | −1.58229 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 181.911 | 0.188705 | ||||||||
\(965\) | −1.34327 | − | 454.403i | −0.00139199 | − | 0.470884i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 417.957i | − | 0.432220i | −0.976369 | − | 0.216110i | \(-0.930663\pi\) | ||
0.976369 | − | 0.216110i | \(-0.0693370\pi\) | |||||||
\(968\) | −301.187 | −0.311144 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.48762 | + | 841.515i | 0.00256455 | + | 0.867541i | ||||
\(971\) | − | 685.151i | − | 0.705613i | −0.935696 | − | 0.352807i | \(-0.885227\pi\) | ||
0.935696 | − | 0.352807i | \(-0.114773\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 227.785i | 0.234105i | ||||||||
\(974\) | 1246.16i | 1.27943i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 73.5964 | 0.0754061 | ||||||||
\(977\) | 1461.86 | 1.49627 | 0.748137 | − | 0.663544i | \(-0.230949\pi\) | ||||
0.748137 | + | 0.663544i | \(0.230949\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −505.422 | −0.516264 | ||||||||
\(980\) | 139.593 | − | 0.412653i | 0.142442 | − | 0.000421074i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 497.287i | 0.506402i | ||||||||
\(983\) | 814.417 | 0.828501 | 0.414251 | − | 0.910163i | \(-0.364044\pi\) | ||||
0.414251 | + | 0.910163i | \(0.364044\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1605.62 | + | 4.74640i | −1.63007 | + | 0.00481868i | ||||
\(986\) | 77.1176i | 0.0782126i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1305.34i | 1.32120i | ||||||||
\(989\) | 322.610i | 0.326199i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −594.842 | −0.600244 | −0.300122 | − | 0.953901i | \(-0.597027\pi\) | ||||
−0.300122 | + | 0.953901i | \(0.597027\pi\) | |||||||
\(992\) | −247.632 | −0.249629 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1019.51 | 1.02567 | ||||||||
\(995\) | −113.711 | + | 0.336142i | −0.114282 | + | 0.000337832i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 343.098i | 0.344130i | 0.985086 | + | 0.172065i | \(0.0550439\pi\) | ||||
−0.985086 | + | 0.172065i | \(0.944956\pi\) | |||||||
\(998\) | 681.441 | 0.682807 | ||||||||
\(999\) | 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 | 810.3.b.c.809.11 | ✓ | 24 | |
3.2 | odd | 2 | inner | 810.3.b.c.809.14 | yes | 24 | |
5.4 | even | 2 | inner | 810.3.b.c.809.13 | yes | 24 | |
9.2 | odd | 6 | 810.3.j.h.539.2 | 24 | |||
9.4 | even | 3 | 810.3.j.g.269.9 | 24 | |||
9.5 | odd | 6 | 810.3.j.g.269.2 | 24 | |||
9.7 | even | 3 | 810.3.j.h.539.8 | 24 | |||
15.14 | odd | 2 | inner | 810.3.b.c.809.12 | yes | 24 | |
45.4 | even | 6 | 810.3.j.h.269.2 | 24 | |||
45.14 | odd | 6 | 810.3.j.h.269.9 | 24 | |||
45.29 | odd | 6 | 810.3.j.g.539.8 | 24 | |||
45.34 | even | 6 | 810.3.j.g.539.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
810.3.b.c.809.11 | ✓ | 24 | 1.1 | even | 1 | trivial | |
810.3.b.c.809.12 | yes | 24 | 15.14 | odd | 2 | inner | |
810.3.b.c.809.13 | yes | 24 | 5.4 | even | 2 | inner | |
810.3.b.c.809.14 | yes | 24 | 3.2 | odd | 2 | inner | |
810.3.j.g.269.2 | 24 | 9.5 | odd | 6 | |||
810.3.j.g.269.9 | 24 | 9.4 | even | 3 | |||
810.3.j.g.539.2 | 24 | 45.34 | even | 6 | |||
810.3.j.g.539.8 | 24 | 45.29 | odd | 6 | |||
810.3.j.h.269.2 | 24 | 45.4 | even | 6 | |||
810.3.j.h.269.9 | 24 | 45.14 | odd | 6 | |||
810.3.j.h.539.2 | 24 | 9.2 | odd | 6 | |||
810.3.j.h.539.8 | 24 | 9.7 | even | 3 |