Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [338,4,Mod(337,338)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(338, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("338.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 338 = 2 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 338.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.9426455819\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.5 | ||
Root | \(-0.445042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 338.337 |
Dual form | 338.4.b.f.337.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/338\mathbb{Z}\right)^\times\).
\(n\) | \(171\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 0.707107i | ||||||||
\(3\) | −3.66487 | −0.705305 | −0.352653 | − | 0.935754i | \(-0.614720\pi\) | ||||
−0.352653 | + | 0.935754i | \(0.614720\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 8.53079i | 0.763017i | 0.924365 | + | 0.381509i | \(0.124595\pi\) | ||||
−0.924365 | + | 0.381509i | \(0.875405\pi\) | |||||||
\(6\) | − 7.32975i | − 0.498726i | ||||||||
\(7\) | 4.20105i | 0.226835i | 0.993547 | + | 0.113418i | \(0.0361798\pi\) | ||||
−0.993547 | + | 0.113418i | \(0.963820\pi\) | |||||||
\(8\) | − 8.00000i | − 0.353553i | ||||||||
\(9\) | −13.5687 | −0.502544 | ||||||||
\(10\) | −17.0616 | −0.539535 | ||||||||
\(11\) | 65.3726i | 1.79187i | 0.444186 | + | 0.895935i | \(0.353493\pi\) | ||||
−0.444186 | + | 0.895935i | \(0.646507\pi\) | |||||||
\(12\) | 14.6595 | 0.352653 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −8.40209 | −0.160397 | ||||||||
\(15\) | − 31.2643i | − 0.538160i | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 26.9019 | 0.383804 | 0.191902 | − | 0.981414i | \(-0.438534\pi\) | ||||
0.191902 | + | 0.981414i | \(0.438534\pi\) | |||||||
\(18\) | − 27.1374i | − 0.355352i | ||||||||
\(19\) | − 13.3730i | − 0.161472i | −0.996736 | − | 0.0807360i | \(-0.974273\pi\) | ||||
0.996736 | − | 0.0807360i | \(-0.0257271\pi\) | |||||||
\(20\) | − 34.1232i | − 0.381509i | ||||||||
\(21\) | − 15.3963i | − 0.159988i | ||||||||
\(22\) | −130.745 | −1.26704 | ||||||||
\(23\) | −159.929 | −1.44989 | −0.724946 | − | 0.688806i | \(-0.758135\pi\) | ||||
−0.724946 | + | 0.688806i | \(0.758135\pi\) | |||||||
\(24\) | 29.3190i | 0.249363i | ||||||||
\(25\) | 52.2255 | 0.417804 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 148.679 | 1.05975 | ||||||||
\(28\) | − 16.8042i | − 0.113418i | ||||||||
\(29\) | −301.288 | −1.92923 | −0.964616 | − | 0.263658i | \(-0.915071\pi\) | ||||
−0.964616 | + | 0.263658i | \(0.915071\pi\) | |||||||
\(30\) | 62.5286 | 0.380537 | ||||||||
\(31\) | − 73.0232i | − 0.423076i | −0.977370 | − | 0.211538i | \(-0.932153\pi\) | ||||
0.977370 | − | 0.211538i | \(-0.0678472\pi\) | |||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | − 239.582i | − 1.26382i | ||||||||
\(34\) | 53.8038i | 0.271390i | ||||||||
\(35\) | −35.8383 | −0.173079 | ||||||||
\(36\) | 54.2748 | 0.251272 | ||||||||
\(37\) | 118.781i | 0.527769i | 0.964554 | + | 0.263885i | \(0.0850038\pi\) | ||||
−0.964554 | + | 0.263885i | \(0.914996\pi\) | |||||||
\(38\) | 26.7459 | 0.114178 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 68.2464 | 0.269767 | ||||||||
\(41\) | − 432.901i | − 1.64897i | −0.565883 | − | 0.824486i | \(-0.691465\pi\) | ||||
0.565883 | − | 0.824486i | \(-0.308535\pi\) | |||||||
\(42\) | 30.7926 | 0.113129 | ||||||||
\(43\) | 356.508 | 1.26435 | 0.632174 | − | 0.774827i | \(-0.282163\pi\) | ||||
0.632174 | + | 0.774827i | \(0.282163\pi\) | |||||||
\(44\) | − 261.490i | − 0.895935i | ||||||||
\(45\) | − 115.752i | − 0.383450i | ||||||||
\(46\) | − 319.858i | − 1.02523i | ||||||||
\(47\) | − 588.614i | − 1.82677i | −0.407096 | − | 0.913385i | \(-0.633459\pi\) | ||||
0.407096 | − | 0.913385i | \(-0.366541\pi\) | |||||||
\(48\) | −58.6380 | −0.176326 | ||||||||
\(49\) | 325.351 | 0.948546 | ||||||||
\(50\) | 104.451i | 0.295432i | ||||||||
\(51\) | −98.5921 | −0.270699 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −269.462 | −0.698366 | −0.349183 | − | 0.937054i | \(-0.613541\pi\) | ||||
−0.349183 | + | 0.937054i | \(0.613541\pi\) | |||||||
\(54\) | 297.358i | 0.749358i | ||||||||
\(55\) | −557.680 | −1.36723 | ||||||||
\(56\) | 33.6084 | 0.0801983 | ||||||||
\(57\) | 49.0102i | 0.113887i | ||||||||
\(58\) | − 602.576i | − 1.36417i | ||||||||
\(59\) | − 230.340i | − 0.508265i | −0.967169 | − | 0.254133i | \(-0.918210\pi\) | ||||
0.967169 | − | 0.254133i | \(-0.0817900\pi\) | |||||||
\(60\) | 125.057i | 0.269080i | ||||||||
\(61\) | −380.816 | −0.799319 | −0.399659 | − | 0.916664i | \(-0.630872\pi\) | ||||
−0.399659 | + | 0.916664i | \(0.630872\pi\) | |||||||
\(62\) | 146.046 | 0.299160 | ||||||||
\(63\) | − 57.0027i | − 0.113995i | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 479.164 | 0.893652 | ||||||||
\(67\) | 435.848i | 0.794736i | 0.917659 | + | 0.397368i | \(0.130076\pi\) | ||||
−0.917659 | + | 0.397368i | \(0.869924\pi\) | |||||||
\(68\) | −107.608 | −0.191902 | ||||||||
\(69\) | 586.120 | 1.02262 | ||||||||
\(70\) | − 71.6765i | − 0.122385i | ||||||||
\(71\) | 65.9622i | 0.110257i | 0.998479 | + | 0.0551287i | \(0.0175569\pi\) | ||||
−0.998479 | + | 0.0551287i | \(0.982443\pi\) | |||||||
\(72\) | 108.550i | 0.177676i | ||||||||
\(73\) | − 885.517i | − 1.41975i | −0.704326 | − | 0.709876i | \(-0.748751\pi\) | ||||
0.704326 | − | 0.709876i | \(-0.251249\pi\) | |||||||
\(74\) | −237.562 | −0.373189 | ||||||||
\(75\) | −191.400 | −0.294680 | ||||||||
\(76\) | 53.4918i | 0.0807360i | ||||||||
\(77\) | −274.633 | −0.406459 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −385.463 | −0.548962 | −0.274481 | − | 0.961592i | \(-0.588506\pi\) | ||||
−0.274481 | + | 0.961592i | \(0.588506\pi\) | |||||||
\(80\) | 136.493i | 0.190754i | ||||||||
\(81\) | −178.536 | −0.244905 | ||||||||
\(82\) | 865.803 | 1.16600 | ||||||||
\(83\) | − 254.207i | − 0.336179i | −0.985772 | − | 0.168089i | \(-0.946240\pi\) | ||||
0.985772 | − | 0.168089i | \(-0.0537597\pi\) | |||||||
\(84\) | 61.5852i | 0.0799940i | ||||||||
\(85\) | 229.495i | 0.292849i | ||||||||
\(86\) | 713.016i | 0.894029i | ||||||||
\(87\) | 1104.18 | 1.36070 | ||||||||
\(88\) | 522.980 | 0.633522 | ||||||||
\(89\) | 372.612i | 0.443785i | 0.975071 | + | 0.221892i | \(0.0712234\pi\) | ||||
−0.975071 | + | 0.221892i | \(0.928777\pi\) | |||||||
\(90\) | 231.504 | 0.271140 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 639.716 | 0.724946 | ||||||||
\(93\) | 267.621i | 0.298398i | ||||||||
\(94\) | 1177.23 | 1.29172 | ||||||||
\(95\) | 114.082 | 0.123206 | ||||||||
\(96\) | − 117.276i | − 0.124682i | ||||||||
\(97\) | 1313.88i | 1.37531i | 0.726039 | + | 0.687653i | \(0.241359\pi\) | ||||
−0.726039 | + | 0.687653i | \(0.758641\pi\) | |||||||
\(98\) | 650.702i | 0.670723i | ||||||||
\(99\) | − 887.020i | − 0.900494i | ||||||||
\(100\) | −208.902 | −0.208902 | ||||||||
\(101\) | −1463.72 | −1.44204 | −0.721019 | − | 0.692915i | \(-0.756326\pi\) | ||||
−0.721019 | + | 0.692915i | \(0.756326\pi\) | |||||||
\(102\) | − 197.184i | − 0.191413i | ||||||||
\(103\) | −210.886 | −0.201740 | −0.100870 | − | 0.994900i | \(-0.532163\pi\) | ||||
−0.100870 | + | 0.994900i | \(0.532163\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 131.343 | 0.122074 | ||||||||
\(106\) | − 538.924i | − 0.493820i | ||||||||
\(107\) | 391.061 | 0.353321 | 0.176660 | − | 0.984272i | \(-0.443471\pi\) | ||||
0.176660 | + | 0.984272i | \(0.443471\pi\) | |||||||
\(108\) | −594.717 | −0.529876 | ||||||||
\(109\) | 1331.40i | 1.16996i | 0.811049 | + | 0.584978i | \(0.198897\pi\) | ||||
−0.811049 | + | 0.584978i | \(0.801103\pi\) | |||||||
\(110\) | − 1115.36i | − 0.966776i | ||||||||
\(111\) | − 435.317i | − 0.372238i | ||||||||
\(112\) | 67.2167i | 0.0567088i | ||||||||
\(113\) | −711.912 | −0.592665 | −0.296332 | − | 0.955085i | \(-0.595764\pi\) | ||||
−0.296332 | + | 0.955085i | \(0.595764\pi\) | |||||||
\(114\) | −98.0204 | −0.0805303 | ||||||||
\(115\) | − 1364.32i | − 1.10629i | ||||||||
\(116\) | 1205.15 | 0.964616 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 460.679 | 0.359398 | ||||||||
\(119\) | 113.016i | 0.0870603i | ||||||||
\(120\) | −250.114 | −0.190268 | ||||||||
\(121\) | −2942.57 | −2.21080 | ||||||||
\(122\) | − 761.631i | − 0.565204i | ||||||||
\(123\) | 1586.53i | 1.16303i | ||||||||
\(124\) | 292.093i | 0.211538i | ||||||||
\(125\) | 1511.87i | 1.08181i | ||||||||
\(126\) | 114.005 | 0.0806064 | ||||||||
\(127\) | 1171.70 | 0.818677 | 0.409338 | − | 0.912383i | \(-0.365760\pi\) | ||||
0.409338 | + | 0.912383i | \(0.365760\pi\) | |||||||
\(128\) | − 128.000i | − 0.0883883i | ||||||||
\(129\) | −1306.56 | −0.891751 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1128.61 | −0.752726 | −0.376363 | − | 0.926472i | \(-0.622825\pi\) | ||||
−0.376363 | + | 0.926472i | \(0.622825\pi\) | |||||||
\(132\) | 958.329i | 0.631908i | ||||||||
\(133\) | 56.1804 | 0.0366275 | ||||||||
\(134\) | −871.696 | −0.561963 | ||||||||
\(135\) | 1268.35i | 0.808610i | ||||||||
\(136\) | − 215.215i | − 0.135695i | ||||||||
\(137\) | 1747.93i | 1.09004i | 0.838422 | + | 0.545022i | \(0.183479\pi\) | ||||
−0.838422 | + | 0.545022i | \(0.816521\pi\) | |||||||
\(138\) | 1172.24i | 0.723099i | ||||||||
\(139\) | 1676.54 | 1.02304 | 0.511518 | − | 0.859273i | \(-0.329083\pi\) | ||||
0.511518 | + | 0.859273i | \(0.329083\pi\) | |||||||
\(140\) | 143.353 | 0.0865396 | ||||||||
\(141\) | 2157.20i | 1.28843i | ||||||||
\(142\) | −131.924 | −0.0779637 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −217.099 | −0.125636 | ||||||||
\(145\) | − 2570.22i | − 1.47204i | ||||||||
\(146\) | 1771.03 | 1.00392 | ||||||||
\(147\) | −1192.37 | −0.669014 | ||||||||
\(148\) | − 475.124i | − 0.263885i | ||||||||
\(149\) | − 896.961i | − 0.493167i | −0.969122 | − | 0.246584i | \(-0.920692\pi\) | ||||
0.969122 | − | 0.246584i | \(-0.0793080\pi\) | |||||||
\(150\) | − 382.800i | − 0.208370i | ||||||||
\(151\) | 2078.28i | 1.12005i | 0.828475 | + | 0.560027i | \(0.189209\pi\) | ||||
−0.828475 | + | 0.560027i | \(0.810791\pi\) | |||||||
\(152\) | −106.984 | −0.0570890 | ||||||||
\(153\) | −365.024 | −0.192879 | ||||||||
\(154\) | − 549.266i | − 0.287410i | ||||||||
\(155\) | 622.946 | 0.322814 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3494.75 | −1.77650 | −0.888252 | − | 0.459357i | \(-0.848080\pi\) | ||||
−0.888252 | + | 0.459357i | \(0.848080\pi\) | |||||||
\(158\) | − 770.927i | − 0.388175i | ||||||||
\(159\) | 987.544 | 0.492562 | ||||||||
\(160\) | −272.985 | −0.134884 | ||||||||
\(161\) | − 671.869i | − 0.328887i | ||||||||
\(162\) | − 357.071i | − 0.173174i | ||||||||
\(163\) | 451.254i | 0.216840i | 0.994105 | + | 0.108420i | \(0.0345792\pi\) | ||||
−0.994105 | + | 0.108420i | \(0.965421\pi\) | |||||||
\(164\) | 1731.61i | 0.824486i | ||||||||
\(165\) | 2043.83 | 0.964313 | ||||||||
\(166\) | 508.414 | 0.237714 | ||||||||
\(167\) | − 3203.35i | − 1.48433i | −0.670218 | − | 0.742164i | \(-0.733800\pi\) | ||||
0.670218 | − | 0.742164i | \(-0.266200\pi\) | |||||||
\(168\) | −123.170 | −0.0565643 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −458.989 | −0.207076 | ||||||||
\(171\) | 181.454i | 0.0811468i | ||||||||
\(172\) | −1426.03 | −0.632174 | ||||||||
\(173\) | −1899.38 | −0.834725 | −0.417362 | − | 0.908740i | \(-0.637045\pi\) | ||||
−0.417362 | + | 0.908740i | \(0.637045\pi\) | |||||||
\(174\) | 2208.36i | 0.962159i | ||||||||
\(175\) | 219.402i | 0.0947727i | ||||||||
\(176\) | 1045.96i | 0.447967i | ||||||||
\(177\) | 844.165i | 0.358482i | ||||||||
\(178\) | −745.225 | −0.313803 | ||||||||
\(179\) | −2650.89 | −1.10691 | −0.553455 | − | 0.832879i | \(-0.686691\pi\) | ||||
−0.553455 | + | 0.832879i | \(0.686691\pi\) | |||||||
\(180\) | 463.007i | 0.191725i | ||||||||
\(181\) | 2289.94 | 0.940387 | 0.470194 | − | 0.882563i | \(-0.344184\pi\) | ||||
0.470194 | + | 0.882563i | \(0.344184\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1395.64 | 0.563764 | ||||||||
\(184\) | 1279.43i | 0.512614i | ||||||||
\(185\) | −1013.30 | −0.402697 | ||||||||
\(186\) | −535.242 | −0.210999 | ||||||||
\(187\) | 1758.65i | 0.687727i | ||||||||
\(188\) | 2354.46i | 0.913385i | ||||||||
\(189\) | 624.608i | 0.240389i | ||||||||
\(190\) | 228.164i | 0.0871198i | ||||||||
\(191\) | −338.313 | −0.128165 | −0.0640825 | − | 0.997945i | \(-0.520412\pi\) | ||||
−0.0640825 | + | 0.997945i | \(0.520412\pi\) | |||||||
\(192\) | 234.552 | 0.0881632 | ||||||||
\(193\) | − 2684.05i | − 1.00105i | −0.865723 | − | 0.500524i | \(-0.833141\pi\) | ||||
0.865723 | − | 0.500524i | \(-0.166859\pi\) | |||||||
\(194\) | −2627.77 | −0.972489 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1301.40 | −0.474273 | ||||||||
\(197\) | 1897.24i | 0.686156i | 0.939307 | + | 0.343078i | \(0.111470\pi\) | ||||
−0.939307 | + | 0.343078i | \(0.888530\pi\) | |||||||
\(198\) | 1774.04 | 0.636745 | ||||||||
\(199\) | 2415.60 | 0.860491 | 0.430245 | − | 0.902712i | \(-0.358427\pi\) | ||||
0.430245 | + | 0.902712i | \(0.358427\pi\) | |||||||
\(200\) | − 417.804i | − 0.147716i | ||||||||
\(201\) | − 1597.33i | − 0.560532i | ||||||||
\(202\) | − 2927.44i | − 1.01967i | ||||||||
\(203\) | − 1265.72i | − 0.437618i | ||||||||
\(204\) | 394.368 | 0.135350 | ||||||||
\(205\) | 3692.99 | 1.25819 | ||||||||
\(206\) | − 421.772i | − 0.142652i | ||||||||
\(207\) | 2170.03 | 0.728635 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 874.225 | 0.289337 | ||||||||
\(210\) | 262.685i | 0.0863191i | ||||||||
\(211\) | 2668.42 | 0.870623 | 0.435312 | − | 0.900280i | \(-0.356638\pi\) | ||||
0.435312 | + | 0.900280i | \(0.356638\pi\) | |||||||
\(212\) | 1077.85 | 0.349183 | ||||||||
\(213\) | − 241.743i | − 0.0777651i | ||||||||
\(214\) | 782.122i | 0.249835i | ||||||||
\(215\) | 3041.30i | 0.964719i | ||||||||
\(216\) | − 1189.43i | − 0.374679i | ||||||||
\(217\) | 306.774 | 0.0959685 | ||||||||
\(218\) | −2662.81 | −0.827284 | ||||||||
\(219\) | 3245.31i | 1.00136i | ||||||||
\(220\) | 2230.72 | 0.683614 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 870.634 | 0.263212 | ||||||||
\(223\) | − 286.358i | − 0.0859907i | −0.999075 | − | 0.0429953i | \(-0.986310\pi\) | ||||
0.999075 | − | 0.0429953i | \(-0.0136901\pi\) | |||||||
\(224\) | −134.433 | −0.0400992 | ||||||||
\(225\) | −708.632 | −0.209965 | ||||||||
\(226\) | − 1423.82i | − 0.419077i | ||||||||
\(227\) | 5201.24i | 1.52079i | 0.649463 | + | 0.760393i | \(0.274994\pi\) | ||||
−0.649463 | + | 0.760393i | \(0.725006\pi\) | |||||||
\(228\) | − 196.041i | − 0.0569435i | ||||||||
\(229\) | − 890.458i | − 0.256957i | −0.991712 | − | 0.128478i | \(-0.958991\pi\) | ||||
0.991712 | − | 0.128478i | \(-0.0410093\pi\) | |||||||
\(230\) | 2728.64 | 0.782267 | ||||||||
\(231\) | 1006.50 | 0.286678 | ||||||||
\(232\) | 2410.30i | 0.682087i | ||||||||
\(233\) | −4753.11 | −1.33642 | −0.668212 | − | 0.743971i | \(-0.732940\pi\) | ||||
−0.668212 | + | 0.743971i | \(0.732940\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5021.35 | 1.39386 | ||||||||
\(236\) | 921.358i | 0.254133i | ||||||||
\(237\) | 1412.67 | 0.387186 | ||||||||
\(238\) | −226.032 | −0.0615609 | ||||||||
\(239\) | − 2292.62i | − 0.620491i | −0.950656 | − | 0.310245i | \(-0.899589\pi\) | ||||
0.950656 | − | 0.310245i | \(-0.100411\pi\) | |||||||
\(240\) | − 500.229i | − 0.134540i | ||||||||
\(241\) | − 1975.21i | − 0.527943i | −0.964530 | − | 0.263972i | \(-0.914967\pi\) | ||||
0.964530 | − | 0.263972i | \(-0.0850325\pi\) | |||||||
\(242\) | − 5885.14i | − 1.56327i | ||||||||
\(243\) | −3360.03 | −0.887020 | ||||||||
\(244\) | 1523.26 | 0.399659 | ||||||||
\(245\) | 2775.50i | 0.723757i | ||||||||
\(246\) | −3173.06 | −0.822385 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −584.186 | −0.149580 | ||||||||
\(249\) | 931.637i | 0.237109i | ||||||||
\(250\) | −3023.75 | −0.764955 | ||||||||
\(251\) | 7465.74 | 1.87742 | 0.938711 | − | 0.344705i | \(-0.112021\pi\) | ||||
0.938711 | + | 0.344705i | \(0.112021\pi\) | |||||||
\(252\) | 228.011i | 0.0569974i | ||||||||
\(253\) | − 10455.0i | − 2.59802i | ||||||||
\(254\) | 2343.41i | 0.578892i | ||||||||
\(255\) | − 841.069i | − 0.206548i | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 554.966 | 0.134700 | 0.0673499 | − | 0.997729i | \(-0.478546\pi\) | ||||
0.0673499 | + | 0.997729i | \(0.478546\pi\) | |||||||
\(258\) | − 2613.11i | − 0.630563i | ||||||||
\(259\) | −499.004 | −0.119717 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4088.08 | 0.969525 | ||||||||
\(262\) | − 2257.22i | − 0.532258i | ||||||||
\(263\) | −1993.07 | −0.467292 | −0.233646 | − | 0.972322i | \(-0.575066\pi\) | ||||
−0.233646 | + | 0.972322i | \(0.575066\pi\) | |||||||
\(264\) | −1916.66 | −0.446826 | ||||||||
\(265\) | − 2298.72i | − 0.532866i | ||||||||
\(266\) | 112.361i | 0.0258996i | ||||||||
\(267\) | − 1365.58i | − 0.313004i | ||||||||
\(268\) | − 1743.39i | − 0.397368i | ||||||||
\(269\) | −5207.76 | −1.18038 | −0.590191 | − | 0.807263i | \(-0.700948\pi\) | ||||
−0.590191 | + | 0.807263i | \(0.700948\pi\) | |||||||
\(270\) | −2536.70 | −0.571773 | ||||||||
\(271\) | − 4084.90i | − 0.915646i | −0.889043 | − | 0.457823i | \(-0.848629\pi\) | ||||
0.889043 | − | 0.457823i | \(-0.151371\pi\) | |||||||
\(272\) | 430.430 | 0.0959510 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3495.87 | −0.770778 | ||||||||
\(275\) | 3414.12i | 0.748651i | ||||||||
\(276\) | −2344.48 | −0.511308 | ||||||||
\(277\) | −437.993 | −0.0950051 | −0.0475026 | − | 0.998871i | \(-0.515126\pi\) | ||||
−0.0475026 | + | 0.998871i | \(0.515126\pi\) | |||||||
\(278\) | 3353.07i | 0.723395i | ||||||||
\(279\) | 990.829i | 0.212614i | ||||||||
\(280\) | 286.706i | 0.0611927i | ||||||||
\(281\) | − 5462.34i | − 1.15963i | −0.814748 | − | 0.579815i | \(-0.803125\pi\) | ||||
0.814748 | − | 0.579815i | \(-0.196875\pi\) | |||||||
\(282\) | −4314.40 | −0.911058 | ||||||||
\(283\) | 796.676 | 0.167341 | 0.0836704 | − | 0.996493i | \(-0.473336\pi\) | ||||
0.0836704 | + | 0.996493i | \(0.473336\pi\) | |||||||
\(284\) | − 263.849i | − 0.0551287i | ||||||||
\(285\) | −418.096 | −0.0868978 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1818.64 | 0.374045 | ||||||||
\(288\) | − 434.198i | − 0.0888381i | ||||||||
\(289\) | −4189.29 | −0.852694 | ||||||||
\(290\) | 5140.45 | 1.04089 | ||||||||
\(291\) | − 4815.22i | − 0.970011i | ||||||||
\(292\) | 3542.07i | 0.709876i | ||||||||
\(293\) | − 1697.32i | − 0.338426i | −0.985580 | − | 0.169213i | \(-0.945877\pi\) | ||||
0.985580 | − | 0.169213i | \(-0.0541225\pi\) | |||||||
\(294\) | − 2384.74i | − 0.473065i | ||||||||
\(295\) | 1964.98 | 0.387815 | ||||||||
\(296\) | 950.247 | 0.186595 | ||||||||
\(297\) | 9719.54i | 1.89894i | ||||||||
\(298\) | 1793.92 | 0.348722 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 765.600 | 0.147340 | ||||||||
\(301\) | 1497.71i | 0.286798i | ||||||||
\(302\) | −4156.56 | −0.791997 | ||||||||
\(303\) | 5364.36 | 1.01708 | ||||||||
\(304\) | − 213.967i | − 0.0403680i | ||||||||
\(305\) | − 3248.66i | − 0.609894i | ||||||||
\(306\) | − 730.047i | − 0.136386i | ||||||||
\(307\) | 9385.86i | 1.74488i | 0.488718 | + | 0.872442i | \(0.337465\pi\) | ||||
−0.488718 | + | 0.872442i | \(0.662535\pi\) | |||||||
\(308\) | 1098.53 | 0.203230 | ||||||||
\(309\) | 772.870 | 0.142288 | ||||||||
\(310\) | 1245.89i | 0.228264i | ||||||||
\(311\) | 3282.65 | 0.598527 | 0.299264 | − | 0.954170i | \(-0.403259\pi\) | ||||
0.299264 | + | 0.954170i | \(0.403259\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5924.67 | −1.06991 | −0.534955 | − | 0.844880i | \(-0.679672\pi\) | ||||
−0.534955 | + | 0.844880i | \(0.679672\pi\) | |||||||
\(314\) | − 6989.49i | − 1.25618i | ||||||||
\(315\) | 486.278 | 0.0869800 | ||||||||
\(316\) | 1541.85 | 0.274481 | ||||||||
\(317\) | − 6467.88i | − 1.14597i | −0.819566 | − | 0.572985i | \(-0.805785\pi\) | ||||
0.819566 | − | 0.572985i | \(-0.194215\pi\) | |||||||
\(318\) | 1975.09i | 0.348294i | ||||||||
\(319\) | − 19696.0i | − 3.45693i | ||||||||
\(320\) | − 545.971i | − 0.0953772i | ||||||||
\(321\) | −1433.19 | −0.249199 | ||||||||
\(322\) | 1343.74 | 0.232558 | ||||||||
\(323\) | − 359.758i | − 0.0619736i | ||||||||
\(324\) | 714.143 | 0.122452 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −902.508 | −0.153329 | ||||||||
\(327\) | − 4879.42i | − 0.825177i | ||||||||
\(328\) | −3463.21 | −0.582999 | ||||||||
\(329\) | 2472.80 | 0.414376 | ||||||||
\(330\) | 4087.65i | 0.681872i | ||||||||
\(331\) | − 3509.24i | − 0.582735i | −0.956611 | − | 0.291368i | \(-0.905890\pi\) | ||||
0.956611 | − | 0.291368i | \(-0.0941103\pi\) | |||||||
\(332\) | 1016.83i | 0.168089i | ||||||||
\(333\) | − 1611.70i | − 0.265227i | ||||||||
\(334\) | 6406.70 | 1.04958 | ||||||||
\(335\) | −3718.13 | −0.606398 | ||||||||
\(336\) | − 246.341i | − 0.0399970i | ||||||||
\(337\) | 1834.82 | 0.296584 | 0.148292 | − | 0.988944i | \(-0.452622\pi\) | ||||
0.148292 | + | 0.988944i | \(0.452622\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2609.07 | 0.418010 | ||||||||
\(340\) | − 917.978i | − 0.146425i | ||||||||
\(341\) | 4773.71 | 0.758097 | ||||||||
\(342\) | −362.907 | −0.0573795 | ||||||||
\(343\) | 2807.77i | 0.441999i | ||||||||
\(344\) | − 2852.06i | − 0.447014i | ||||||||
\(345\) | 5000.07i | 0.780274i | ||||||||
\(346\) | − 3798.76i | − 0.590239i | ||||||||
\(347\) | −7259.30 | −1.12305 | −0.561527 | − | 0.827459i | \(-0.689786\pi\) | ||||
−0.561527 | + | 0.827459i | \(0.689786\pi\) | |||||||
\(348\) | −4416.73 | −0.680349 | ||||||||
\(349\) | − 1795.24i | − 0.275349i | −0.990478 | − | 0.137674i | \(-0.956037\pi\) | ||||
0.990478 | − | 0.137674i | \(-0.0439628\pi\) | |||||||
\(350\) | −438.804 | −0.0670144 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2091.92 | −0.316761 | ||||||||
\(353\) | 4552.38i | 0.686398i | 0.939263 | + | 0.343199i | \(0.111511\pi\) | ||||
−0.939263 | + | 0.343199i | \(0.888489\pi\) | |||||||
\(354\) | −1688.33 | −0.253485 | ||||||||
\(355\) | −562.710 | −0.0841283 | ||||||||
\(356\) | − 1490.45i | − 0.221892i | ||||||||
\(357\) | − 414.190i | − 0.0614041i | ||||||||
\(358\) | − 5301.78i | − 0.782703i | ||||||||
\(359\) | 10165.4i | 1.49445i | 0.664569 | + | 0.747227i | \(0.268615\pi\) | ||||
−0.664569 | + | 0.747227i | \(0.731385\pi\) | |||||||
\(360\) | −926.014 | −0.135570 | ||||||||
\(361\) | 6680.16 | 0.973927 | ||||||||
\(362\) | 4579.88i | 0.664954i | ||||||||
\(363\) | 10784.2 | 1.55929 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7554.16 | 1.08330 | ||||||||
\(366\) | 2791.28i | 0.398641i | ||||||||
\(367\) | −10401.6 | −1.47945 | −0.739723 | − | 0.672911i | \(-0.765044\pi\) | ||||
−0.739723 | + | 0.672911i | \(0.765044\pi\) | |||||||
\(368\) | −2558.87 | −0.362473 | ||||||||
\(369\) | 5873.91i | 0.828681i | ||||||||
\(370\) | − 2026.59i | − 0.284750i | ||||||||
\(371\) | − 1132.02i | − 0.158414i | ||||||||
\(372\) | − 1070.48i | − 0.149199i | ||||||||
\(373\) | −7953.41 | −1.10405 | −0.552027 | − | 0.833826i | \(-0.686145\pi\) | ||||
−0.552027 | + | 0.833826i | \(0.686145\pi\) | |||||||
\(374\) | −3517.29 | −0.486296 | ||||||||
\(375\) | − 5540.83i | − 0.763006i | ||||||||
\(376\) | −4708.91 | −0.645861 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1249.22 | −0.169981 | ||||||||
\(379\) | − 9014.81i | − 1.22179i | −0.791710 | − | 0.610897i | \(-0.790809\pi\) | ||||
0.791710 | − | 0.610897i | \(-0.209191\pi\) | |||||||
\(380\) | −456.328 | −0.0616030 | ||||||||
\(381\) | −4294.15 | −0.577417 | ||||||||
\(382\) | − 676.627i | − 0.0906263i | ||||||||
\(383\) | 2496.24i | 0.333034i | 0.986039 | + | 0.166517i | \(0.0532520\pi\) | ||||
−0.986039 | + | 0.166517i | \(0.946748\pi\) | |||||||
\(384\) | 469.104i | 0.0623408i | ||||||||
\(385\) | − 2342.84i | − 0.310135i | ||||||||
\(386\) | 5368.10 | 0.707848 | ||||||||
\(387\) | −4837.35 | −0.635391 | ||||||||
\(388\) | − 5255.54i | − 0.687653i | ||||||||
\(389\) | −10896.9 | −1.42029 | −0.710145 | − | 0.704056i | \(-0.751371\pi\) | ||||
−0.710145 | + | 0.704056i | \(0.751371\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4302.40 | −0.556475 | ||||||||
\(392\) | − 2602.81i | − 0.335362i | ||||||||
\(393\) | 4136.21 | 0.530902 | ||||||||
\(394\) | −3794.48 | −0.485186 | ||||||||
\(395\) | − 3288.31i | − 0.418868i | ||||||||
\(396\) | 3548.08i | 0.450247i | ||||||||
\(397\) | 10887.1i | 1.37635i | 0.725546 | + | 0.688174i | \(0.241587\pi\) | ||||
−0.725546 | + | 0.688174i | \(0.758413\pi\) | |||||||
\(398\) | 4831.21i | 0.608459i | ||||||||
\(399\) | −205.894 | −0.0258336 | ||||||||
\(400\) | 835.609 | 0.104451 | ||||||||
\(401\) | 9968.76i | 1.24144i | 0.784034 | + | 0.620718i | \(0.213159\pi\) | ||||
−0.784034 | + | 0.620718i | \(0.786841\pi\) | |||||||
\(402\) | 3194.66 | 0.396356 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5854.89 | 0.721019 | ||||||||
\(405\) | − 1523.05i | − 0.186867i | ||||||||
\(406\) | 2531.45 | 0.309442 | ||||||||
\(407\) | −7765.01 | −0.945693 | ||||||||
\(408\) | 788.737i | 0.0957066i | ||||||||
\(409\) | − 4036.32i | − 0.487979i | −0.969778 | − | 0.243989i | \(-0.921544\pi\) | ||||
0.969778 | − | 0.243989i | \(-0.0784562\pi\) | |||||||
\(410\) | 7385.98i | 0.889677i | ||||||||
\(411\) | − 6405.96i | − 0.768814i | ||||||||
\(412\) | 843.543 | 0.100870 | ||||||||
\(413\) | 967.667 | 0.115292 | ||||||||
\(414\) | 4340.06i | 0.515223i | ||||||||
\(415\) | 2168.59 | 0.256510 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6144.29 | −0.721552 | ||||||||
\(418\) | 1748.45i | 0.204592i | ||||||||
\(419\) | 15194.9 | 1.77164 | 0.885821 | − | 0.464028i | \(-0.153596\pi\) | ||||
0.885821 | + | 0.464028i | \(0.153596\pi\) | |||||||
\(420\) | −525.371 | −0.0610368 | ||||||||
\(421\) | − 10154.8i | − 1.17556i | −0.809019 | − | 0.587782i | \(-0.800001\pi\) | ||||
0.809019 | − | 0.587782i | \(-0.199999\pi\) | |||||||
\(422\) | 5336.84i | 0.615624i | ||||||||
\(423\) | 7986.73i | 0.918033i | ||||||||
\(424\) | 2155.69i | 0.246910i | ||||||||
\(425\) | 1404.97 | 0.160355 | ||||||||
\(426\) | 483.486 | 0.0549882 | ||||||||
\(427\) | − 1599.82i | − 0.181314i | ||||||||
\(428\) | −1564.24 | −0.176660 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6082.59 | −0.682159 | ||||||||
\(431\) | 6616.84i | 0.739494i | 0.929133 | + | 0.369747i | \(0.120556\pi\) | ||||
−0.929133 | + | 0.369747i | \(0.879444\pi\) | |||||||
\(432\) | 2378.87 | 0.264938 | ||||||||
\(433\) | −5697.60 | −0.632354 | −0.316177 | − | 0.948700i | \(-0.602399\pi\) | ||||
−0.316177 | + | 0.948700i | \(0.602399\pi\) | |||||||
\(434\) | 613.548i | 0.0678600i | ||||||||
\(435\) | 9419.55i | 1.03824i | ||||||||
\(436\) | − 5325.61i | − 0.584978i | ||||||||
\(437\) | 2138.73i | 0.234117i | ||||||||
\(438\) | −6490.62 | −0.708068 | ||||||||
\(439\) | −436.007 | −0.0474020 | −0.0237010 | − | 0.999719i | \(-0.507545\pi\) | ||||
−0.0237010 | + | 0.999719i | \(0.507545\pi\) | |||||||
\(440\) | 4461.44i | 0.483388i | ||||||||
\(441\) | −4414.59 | −0.476686 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6609.58 | 0.708873 | 0.354436 | − | 0.935080i | \(-0.384673\pi\) | ||||
0.354436 | + | 0.935080i | \(0.384673\pi\) | |||||||
\(444\) | 1741.27i | 0.186119i | ||||||||
\(445\) | −3178.68 | −0.338616 | ||||||||
\(446\) | 572.715 | 0.0608046 | ||||||||
\(447\) | 3287.25i | 0.347833i | ||||||||
\(448\) | − 268.867i | − 0.0283544i | ||||||||
\(449\) | 8015.31i | 0.842463i | 0.906953 | + | 0.421231i | \(0.138402\pi\) | ||||
−0.906953 | + | 0.421231i | \(0.861598\pi\) | |||||||
\(450\) | − 1417.26i | − 0.148468i | ||||||||
\(451\) | 28299.9 | 2.95474 | ||||||||
\(452\) | 2847.65 | 0.296332 | ||||||||
\(453\) | − 7616.64i | − 0.789980i | ||||||||
\(454\) | −10402.5 | −1.07536 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 392.082 | 0.0402652 | ||||||||
\(457\) | 4507.03i | 0.461335i | 0.973033 | + | 0.230668i | \(0.0740910\pi\) | ||||
−0.973033 | + | 0.230668i | \(0.925909\pi\) | |||||||
\(458\) | 1780.92 | 0.181696 | ||||||||
\(459\) | 3999.75 | 0.406737 | ||||||||
\(460\) | 5457.29i | 0.553146i | ||||||||
\(461\) | − 2103.55i | − 0.212521i | −0.994338 | − | 0.106260i | \(-0.966112\pi\) | ||||
0.994338 | − | 0.106260i | \(-0.0338877\pi\) | |||||||
\(462\) | 2012.99i | 0.202712i | ||||||||
\(463\) | 5468.28i | 0.548883i | 0.961604 | + | 0.274441i | \(0.0884929\pi\) | ||||
−0.961604 | + | 0.274441i | \(0.911507\pi\) | |||||||
\(464\) | −4820.60 | −0.482308 | ||||||||
\(465\) | −2283.02 | −0.227683 | ||||||||
\(466\) | − 9506.22i | − 0.944994i | ||||||||
\(467\) | 6043.79 | 0.598872 | 0.299436 | − | 0.954116i | \(-0.403201\pi\) | ||||
0.299436 | + | 0.954116i | \(0.403201\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1831.02 | −0.180274 | ||||||||
\(470\) | 10042.7i | 0.985606i | ||||||||
\(471\) | 12807.8 | 1.25298 | ||||||||
\(472\) | −1842.72 | −0.179699 | ||||||||
\(473\) | 23305.8i | 2.26555i | ||||||||
\(474\) | 2825.35i | 0.273782i | ||||||||
\(475\) | − 698.410i | − 0.0674637i | ||||||||
\(476\) | − 452.065i | − 0.0435301i | ||||||||
\(477\) | 3656.25 | 0.350960 | ||||||||
\(478\) | 4585.24 | 0.438753 | ||||||||
\(479\) | − 8481.30i | − 0.809020i | −0.914534 | − | 0.404510i | \(-0.867442\pi\) | ||||
0.914534 | − | 0.404510i | \(-0.132558\pi\) | |||||||
\(480\) | 1000.46 | 0.0951342 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3950.42 | 0.373312 | ||||||||
\(483\) | 2462.32i | 0.231965i | ||||||||
\(484\) | 11770.3 | 1.10540 | ||||||||
\(485\) | −11208.5 | −1.04938 | ||||||||
\(486\) | − 6720.05i | − 0.627218i | ||||||||
\(487\) | 6623.36i | 0.616289i | 0.951340 | + | 0.308145i | \(0.0997081\pi\) | ||||
−0.951340 | + | 0.308145i | \(0.900292\pi\) | |||||||
\(488\) | 3046.53i | 0.282602i | ||||||||
\(489\) | − 1653.79i | − 0.152939i | ||||||||
\(490\) | −5551.01 | −0.511774 | ||||||||
\(491\) | −16379.4 | −1.50548 | −0.752739 | − | 0.658319i | \(-0.771268\pi\) | ||||
−0.752739 | + | 0.658319i | \(0.771268\pi\) | |||||||
\(492\) | − 6346.12i | − 0.581514i | ||||||||
\(493\) | −8105.21 | −0.740447 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7566.99 | 0.687093 | ||||||||
\(496\) | − 1168.37i | − 0.105769i | ||||||||
\(497\) | −277.110 | −0.0250102 | ||||||||
\(498\) | −1863.27 | −0.167661 | ||||||||
\(499\) | 7915.70i | 0.710131i | 0.934841 | + | 0.355065i | \(0.115541\pi\) | ||||
−0.934841 | + | 0.355065i | \(0.884459\pi\) | |||||||
\(500\) | − 6047.50i | − 0.540905i | ||||||||
\(501\) | 11739.9i | 1.04690i | ||||||||
\(502\) | 14931.5i | 1.32754i | ||||||||
\(503\) | −479.511 | −0.0425056 | −0.0212528 | − | 0.999774i | \(-0.506765\pi\) | ||||
−0.0212528 | + | 0.999774i | \(0.506765\pi\) | |||||||
\(504\) | −456.022 | −0.0403032 | ||||||||
\(505\) | − 12486.7i | − 1.10030i | ||||||||
\(506\) | 20909.9 | 1.83708 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4686.82 | −0.409338 | ||||||||
\(509\) | − 1192.33i | − 0.103829i | −0.998652 | − | 0.0519145i | \(-0.983468\pi\) | ||||
0.998652 | − | 0.0519145i | \(-0.0165323\pi\) | |||||||
\(510\) | 1682.14 | 0.146052 | ||||||||
\(511\) | 3720.10 | 0.322050 | ||||||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | − 1988.28i | − 0.171120i | ||||||||
\(514\) | 1109.93i | 0.0952471i | ||||||||
\(515\) | − 1799.02i | − 0.153931i | ||||||||
\(516\) | 5226.23 | 0.445876 | ||||||||
\(517\) | 38479.2 | 3.27333 | ||||||||
\(518\) | − 998.008i | − 0.0846524i | ||||||||
\(519\) | 6961.00 | 0.588736 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23238.5 | −1.95412 | −0.977062 | − | 0.212955i | \(-0.931691\pi\) | ||||
−0.977062 | + | 0.212955i | \(0.931691\pi\) | |||||||
\(522\) | 8176.16i | 0.685557i | ||||||||
\(523\) | −11026.3 | −0.921884 | −0.460942 | − | 0.887430i | \(-0.652488\pi\) | ||||
−0.460942 | + | 0.887430i | \(0.652488\pi\) | |||||||
\(524\) | 4514.44 | 0.376363 | ||||||||
\(525\) | − 804.080i | − 0.0668437i | ||||||||
\(526\) | − 3986.14i | − 0.330425i | ||||||||
\(527\) | − 1964.46i | − 0.162378i | ||||||||
\(528\) | − 3833.32i | − 0.315954i | ||||||||
\(529\) | 13410.3 | 1.10219 | ||||||||
\(530\) | 4597.45 | 0.376793 | ||||||||
\(531\) | 3125.41i | 0.255426i | ||||||||
\(532\) | −224.722 | −0.0183138 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2731.16 | 0.221327 | ||||||||
\(535\) | 3336.06i | 0.269590i | ||||||||
\(536\) | 3486.79 | 0.280982 | ||||||||
\(537\) | 9715.18 | 0.780709 | ||||||||
\(538\) | − 10415.5i | − 0.834657i | ||||||||
\(539\) | 21269.0i | 1.69967i | ||||||||
\(540\) | − 5073.41i | − 0.404305i | ||||||||
\(541\) | 8987.70i | 0.714254i | 0.934056 | + | 0.357127i | \(0.116244\pi\) | ||||
−0.934056 | + | 0.357127i | \(0.883756\pi\) | |||||||
\(542\) | 8169.80 | 0.647459 | ||||||||
\(543\) | −8392.35 | −0.663260 | ||||||||
\(544\) | 860.861i | 0.0678476i | ||||||||
\(545\) | −11357.9 | −0.892697 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10734.8 | −0.839101 | −0.419550 | − | 0.907732i | \(-0.637812\pi\) | ||||
−0.419550 | + | 0.907732i | \(0.637812\pi\) | |||||||
\(548\) | − 6991.74i | − 0.545022i | ||||||||
\(549\) | 5167.17 | 0.401693 | ||||||||
\(550\) | −6828.23 | −0.529376 | ||||||||
\(551\) | 4029.11i | 0.311517i | ||||||||
\(552\) | − 4688.96i | − 0.361550i | ||||||||
\(553\) | − 1619.35i | − 0.124524i | ||||||||
\(554\) | − 875.985i | − 0.0671788i | ||||||||
\(555\) | 3713.60 | 0.284024 | ||||||||
\(556\) | −6706.14 | −0.511518 | ||||||||
\(557\) | 13228.3i | 1.00628i | 0.864204 | + | 0.503141i | \(0.167822\pi\) | ||||
−0.864204 | + | 0.503141i | \(0.832178\pi\) | |||||||
\(558\) | −1981.66 | −0.150341 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −573.412 | −0.0432698 | ||||||||
\(561\) | − 6445.22i | − 0.485058i | ||||||||
\(562\) | 10924.7 | 0.819983 | ||||||||
\(563\) | −10734.0 | −0.803522 | −0.401761 | − | 0.915745i | \(-0.631602\pi\) | ||||
−0.401761 | + | 0.915745i | \(0.631602\pi\) | |||||||
\(564\) | − 8628.79i | − 0.644216i | ||||||||
\(565\) | − 6073.18i | − 0.452213i | ||||||||
\(566\) | 1593.35i | 0.118328i | ||||||||
\(567\) | − 750.037i | − 0.0555531i | ||||||||
\(568\) | 527.698 | 0.0389819 | ||||||||
\(569\) | −5313.45 | −0.391479 | −0.195739 | − | 0.980656i | \(-0.562711\pi\) | ||||
−0.195739 | + | 0.980656i | \(0.562711\pi\) | |||||||
\(570\) | − 836.192i | − 0.0614460i | ||||||||
\(571\) | −4629.37 | −0.339287 | −0.169644 | − | 0.985505i | \(-0.554262\pi\) | ||||
−0.169644 | + | 0.985505i | \(0.554262\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1239.88 | 0.0903954 | ||||||||
\(574\) | 3637.28i | 0.264490i | ||||||||
\(575\) | −8352.38 | −0.605771 | ||||||||
\(576\) | 868.397 | 0.0628180 | ||||||||
\(577\) | 504.750i | 0.0364177i | 0.999834 | + | 0.0182088i | \(0.00579638\pi\) | ||||
−0.999834 | + | 0.0182088i | \(0.994204\pi\) | |||||||
\(578\) | − 8378.58i | − 0.602946i | ||||||||
\(579\) | 9836.71i | 0.706045i | ||||||||
\(580\) | 10280.9i | 0.736019i | ||||||||
\(581\) | 1067.94 | 0.0762572 | ||||||||
\(582\) | 9630.44 | 0.685901 | ||||||||
\(583\) | − 17615.4i | − 1.25138i | ||||||||
\(584\) | −7084.14 | −0.501958 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3394.65 | 0.239303 | ||||||||
\(587\) | − 5532.93i | − 0.389044i | −0.980898 | − | 0.194522i | \(-0.937684\pi\) | ||||
0.980898 | − | 0.194522i | \(-0.0623155\pi\) | |||||||
\(588\) | 4769.49 | 0.334507 | ||||||||
\(589\) | −976.536 | −0.0683149 | ||||||||
\(590\) | 3929.96i | 0.274227i | ||||||||
\(591\) | − 6953.15i | − 0.483950i | ||||||||
\(592\) | 1900.49i | 0.131942i | ||||||||
\(593\) | − 18079.8i | − 1.25202i | −0.779816 | − | 0.626009i | \(-0.784687\pi\) | ||||
0.779816 | − | 0.626009i | \(-0.215313\pi\) | |||||||
\(594\) | −19439.1 | −1.34275 | ||||||||
\(595\) | −964.117 | −0.0664285 | ||||||||
\(596\) | 3587.84i | 0.246584i | ||||||||
\(597\) | −8852.88 | −0.606909 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1837.55 | −0.125342 | −0.0626712 | − | 0.998034i | \(-0.519962\pi\) | ||||
−0.0626712 | + | 0.998034i | \(0.519962\pi\) | |||||||
\(600\) | 1531.20i | 0.104185i | ||||||||
\(601\) | −23487.3 | −1.59412 | −0.797060 | − | 0.603901i | \(-0.793612\pi\) | ||||
−0.797060 | + | 0.603901i | \(0.793612\pi\) | |||||||
\(602\) | −2995.41 | −0.202797 | ||||||||
\(603\) | − 5913.89i | − 0.399390i | ||||||||
\(604\) | − 8313.12i | − 0.560027i | ||||||||
\(605\) | − 25102.5i | − 1.68688i | ||||||||
\(606\) | 10728.7i | 0.719182i | ||||||||
\(607\) | −16310.8 | −1.09067 | −0.545335 | − | 0.838218i | \(-0.683598\pi\) | ||||
−0.545335 | + | 0.838218i | \(0.683598\pi\) | |||||||
\(608\) | 427.935 | 0.0285445 | ||||||||
\(609\) | 4638.72i | 0.308654i | ||||||||
\(610\) | 6497.32 | 0.431260 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1460.09 | 0.0964393 | ||||||||
\(613\) | − 8453.11i | − 0.556962i | −0.960442 | − | 0.278481i | \(-0.910169\pi\) | ||||
0.960442 | − | 0.278481i | \(-0.0898310\pi\) | |||||||
\(614\) | −18771.7 | −1.23382 | ||||||||
\(615\) | −13534.4 | −0.887411 | ||||||||
\(616\) | 2197.06i | 0.143705i | ||||||||
\(617\) | 13410.3i | 0.875008i | 0.899216 | + | 0.437504i | \(0.144137\pi\) | ||||
−0.899216 | + | 0.437504i | \(0.855863\pi\) | |||||||
\(618\) | 1545.74i | 0.100613i | ||||||||
\(619\) | − 890.135i | − 0.0577990i | −0.999582 | − | 0.0288995i | \(-0.990800\pi\) | ||||
0.999582 | − | 0.0288995i | \(-0.00920027\pi\) | |||||||
\(620\) | −2491.78 | −0.161407 | ||||||||
\(621\) | −23778.1 | −1.53653 | ||||||||
\(622\) | 6565.30i | 0.423223i | ||||||||
\(623\) | −1565.36 | −0.100666 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6369.30 | −0.407635 | ||||||||
\(626\) | − 11849.3i | − 0.756541i | ||||||||
\(627\) | −3203.92 | −0.204071 | ||||||||
\(628\) | 13979.0 | 0.888252 | ||||||||
\(629\) | 3195.43i | 0.202560i | ||||||||
\(630\) | 972.557i | 0.0615041i | ||||||||
\(631\) | − 10582.4i | − 0.667639i | −0.942637 | − | 0.333819i | \(-0.891662\pi\) | ||||
0.942637 | − | 0.333819i | \(-0.108338\pi\) | |||||||
\(632\) | 3083.71i | 0.194087i | ||||||||
\(633\) | −9779.42 | −0.614055 | ||||||||
\(634\) | 12935.8 | 0.810323 | ||||||||
\(635\) | 9995.57i | 0.624665i | ||||||||
\(636\) | −3950.17 | −0.246281 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 39391.9 | 2.44442 | ||||||||
\(639\) | − 895.021i | − 0.0554092i | ||||||||
\(640\) | 1091.94 | 0.0674419 | ||||||||
\(641\) | −26884.2 | −1.65657 | −0.828286 | − | 0.560305i | \(-0.810684\pi\) | ||||
−0.828286 | + | 0.560305i | \(0.810684\pi\) | |||||||
\(642\) | − 2866.38i | − 0.176210i | ||||||||
\(643\) | − 5691.12i | − 0.349045i | −0.984653 | − | 0.174523i | \(-0.944162\pi\) | ||||
0.984653 | − | 0.174523i | \(-0.0558382\pi\) | |||||||
\(644\) | 2687.48i | 0.164443i | ||||||||
\(645\) | − 11146.0i | − 0.680422i | ||||||||
\(646\) | 719.516 | 0.0438220 | ||||||||
\(647\) | −1809.79 | −0.109969 | −0.0549847 | − | 0.998487i | \(-0.517511\pi\) | ||||
−0.0549847 | + | 0.998487i | \(0.517511\pi\) | |||||||
\(648\) | 1428.29i | 0.0865870i | ||||||||
\(649\) | 15057.9 | 0.910745 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1124.29 | −0.0676871 | ||||||||
\(652\) | − 1805.02i | − 0.108420i | ||||||||
\(653\) | 9459.16 | 0.566869 | 0.283435 | − | 0.958992i | \(-0.408526\pi\) | ||||
0.283435 | + | 0.958992i | \(0.408526\pi\) | |||||||
\(654\) | 9758.85 | 0.583488 | ||||||||
\(655\) | − 9627.94i | − 0.574343i | ||||||||
\(656\) | − 6926.42i | − 0.412243i | ||||||||
\(657\) | 12015.3i | 0.713488i | ||||||||
\(658\) | 4945.59i | 0.293008i | ||||||||
\(659\) | 1015.32 | 0.0600171 | 0.0300085 | − | 0.999550i | \(-0.490447\pi\) | ||||
0.0300085 | + | 0.999550i | \(0.490447\pi\) | |||||||
\(660\) | −8175.31 | −0.482157 | ||||||||
\(661\) | 23648.4i | 1.39156i | 0.718257 | + | 0.695778i | \(0.244940\pi\) | ||||
−0.718257 | + | 0.695778i | \(0.755060\pi\) | |||||||
\(662\) | 7018.49 | 0.412056 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2033.66 | −0.118857 | ||||||||
\(665\) | 479.264i | 0.0279474i | ||||||||
\(666\) | 3223.40 | 0.187544 | ||||||||
\(667\) | 48184.7 | 2.79718 | ||||||||
\(668\) | 12813.4i | 0.742164i | ||||||||
\(669\) | 1049.46i | 0.0606497i | ||||||||
\(670\) | − 7436.26i | − 0.428788i | ||||||||
\(671\) | − 24894.9i | − 1.43228i | ||||||||
\(672\) | 492.682 | 0.0282822 | ||||||||
\(673\) | −17747.0 | −1.01649 | −0.508243 | − | 0.861214i | \(-0.669705\pi\) | ||||
−0.508243 | + | 0.861214i | \(0.669705\pi\) | |||||||
\(674\) | 3669.63i | 0.209717i | ||||||||
\(675\) | 7764.85 | 0.442769 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10754.2 | 0.610511 | 0.305256 | − | 0.952270i | \(-0.401258\pi\) | ||||
0.305256 | + | 0.952270i | \(0.401258\pi\) | |||||||
\(678\) | 5218.14i | 0.295577i | ||||||||
\(679\) | −5519.69 | −0.311968 | ||||||||
\(680\) | 1835.96 | 0.103538 | ||||||||
\(681\) | − 19061.9i | − 1.07262i | ||||||||
\(682\) | 9547.42i | 0.536055i | ||||||||
\(683\) | − 23981.7i | − 1.34354i | −0.740762 | − | 0.671768i | \(-0.765535\pi\) | ||||
0.740762 | − | 0.671768i | \(-0.234465\pi\) | |||||||
\(684\) | − 725.815i | − 0.0405734i | ||||||||
\(685\) | −14911.3 | −0.831723 | ||||||||
\(686\) | −5615.55 | −0.312540 | ||||||||
\(687\) | 3263.42i | 0.181233i | ||||||||
\(688\) | 5704.13 | 0.316087 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −10000.1 | −0.551737 | ||||||||
\(691\) | − 29001.4i | − 1.59662i | −0.602244 | − | 0.798312i | \(-0.705727\pi\) | ||||
0.602244 | − | 0.798312i | \(-0.294273\pi\) | |||||||
\(692\) | 7597.53 | 0.417362 | ||||||||
\(693\) | 3726.41 | 0.204264 | ||||||||
\(694\) | − 14518.6i | − 0.794119i | ||||||||
\(695\) | 14302.2i | 0.780594i | ||||||||
\(696\) | − 8833.46i | − 0.481079i | ||||||||
\(697\) | − 11645.9i | − 0.632882i | ||||||||
\(698\) | 3590.47 | 0.194701 | ||||||||
\(699\) | 17419.6 | 0.942587 | ||||||||
\(700\) | − 877.608i | − 0.0473864i | ||||||||
\(701\) | 31031.5 | 1.67196 | 0.835979 | − | 0.548761i | \(-0.184900\pi\) | ||||
0.835979 | + | 0.548761i | \(0.184900\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1588.45 | 0.0852199 | ||||||||
\(704\) | − 4183.84i | − 0.223984i | ||||||||
\(705\) | −18402.6 | −0.983096 | ||||||||
\(706\) | −9104.75 | −0.485357 | ||||||||
\(707\) | − 6149.16i | − 0.327105i | ||||||||
\(708\) | − 3376.66i | − 0.179241i | ||||||||
\(709\) | − 4382.59i | − 0.232146i | −0.993241 | − | 0.116073i | \(-0.962969\pi\) | ||||
0.993241 | − | 0.116073i | \(-0.0370307\pi\) | |||||||
\(710\) | − 1125.42i | − 0.0594877i | ||||||||
\(711\) | 5230.23 | 0.275878 | ||||||||
\(712\) | 2980.90 | 0.156902 | ||||||||
\(713\) | 11678.5i | 0.613414i | ||||||||
\(714\) | 828.380 | 0.0434192 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10603.6 | 0.553455 | ||||||||
\(717\) | 8402.17i | 0.437636i | ||||||||
\(718\) | −20330.8 | −1.05674 | ||||||||
\(719\) | 28764.6 | 1.49199 | 0.745994 | − | 0.665953i | \(-0.231975\pi\) | ||||
0.745994 | + | 0.665953i | \(0.231975\pi\) | |||||||
\(720\) | − 1852.03i | − 0.0958625i | ||||||||
\(721\) | − 885.941i | − 0.0457617i | ||||||||
\(722\) | 13360.3i | 0.688670i | ||||||||
\(723\) | 7238.89i | 0.372361i | ||||||||
\(724\) | −9159.77 | −0.470194 | ||||||||
\(725\) | −15734.9 | −0.806042 | ||||||||
\(726\) | 21568.3i | 1.10258i | ||||||||
\(727\) | −25408.5 | −1.29621 | −0.648107 | − | 0.761549i | \(-0.724439\pi\) | ||||
−0.648107 | + | 0.761549i | \(0.724439\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17134.5 | 0.870525 | ||||||||
\(730\) | 15108.3i | 0.766006i | ||||||||
\(731\) | 9590.74 | 0.485262 | ||||||||
\(732\) | −5582.57 | −0.281882 | ||||||||
\(733\) | 22341.8i | 1.12580i | 0.826524 | + | 0.562902i | \(0.190315\pi\) | ||||
−0.826524 | + | 0.562902i | \(0.809685\pi\) | |||||||
\(734\) | − 20803.1i | − 1.04613i | ||||||||
\(735\) | − 10171.9i | − 0.510470i | ||||||||
\(736\) | − 5117.73i | − 0.256307i | ||||||||
\(737\) | −28492.5 | −1.42406 | ||||||||
\(738\) | −11747.8 | −0.585966 | ||||||||
\(739\) | − 8210.90i | − 0.408718i | −0.978896 | − | 0.204359i | \(-0.934489\pi\) | ||||
0.978896 | − | 0.204359i | \(-0.0655110\pi\) | |||||||
\(740\) | 4053.18 | 0.201349 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2264.04 | 0.112016 | ||||||||
\(743\) | 32752.3i | 1.61718i | 0.588373 | + | 0.808590i | \(0.299769\pi\) | ||||
−0.588373 | + | 0.808590i | \(0.700231\pi\) | |||||||
\(744\) | 2140.97 | 0.105500 | ||||||||
\(745\) | 7651.79 | 0.376295 | ||||||||
\(746\) | − 15906.8i | − 0.780684i | ||||||||
\(747\) | 3449.26i | 0.168945i | ||||||||
\(748\) | − 7034.58i | − 0.343863i | ||||||||
\(749\) | 1642.87i | 0.0801455i | ||||||||
\(750\) | 11081.7 | 0.539527 | ||||||||
\(751\) | −8907.41 | −0.432804 | −0.216402 | − | 0.976304i | \(-0.569432\pi\) | ||||
−0.216402 | + | 0.976304i | \(0.569432\pi\) | |||||||
\(752\) | − 9417.83i | − 0.456693i | ||||||||
\(753\) | −27361.0 | −1.32416 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17729.4 | −0.854620 | ||||||||
\(756\) | − 2498.43i | − 0.120195i | ||||||||
\(757\) | −10744.6 | −0.515879 | −0.257940 | − | 0.966161i | \(-0.583044\pi\) | ||||
−0.257940 | + | 0.966161i | \(0.583044\pi\) | |||||||
\(758\) | 18029.6 | 0.863938 | ||||||||
\(759\) | 38316.2i | 1.83240i | ||||||||
\(760\) | − 912.656i | − 0.0435599i | ||||||||
\(761\) | − 16997.8i | − 0.809683i | −0.914387 | − | 0.404841i | \(-0.867327\pi\) | ||||
0.914387 | − | 0.404841i | \(-0.132673\pi\) | |||||||
\(762\) | − 8588.30i | − 0.408296i | ||||||||
\(763\) | −5593.28 | −0.265387 | ||||||||
\(764\) | 1353.25 | 0.0640825 | ||||||||
\(765\) | − 3113.94i | − 0.147170i | ||||||||
\(766\) | −4992.48 | −0.235490 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −938.208 | −0.0440816 | ||||||||
\(769\) | − 19032.4i | − 0.892492i | −0.894910 | − | 0.446246i | \(-0.852761\pi\) | ||||
0.894910 | − | 0.446246i | \(-0.147239\pi\) | |||||||
\(770\) | 4685.68 | 0.219299 | ||||||||
\(771\) | −2033.88 | −0.0950045 | ||||||||
\(772\) | 10736.2i | 0.500524i | ||||||||
\(773\) | − 23750.6i | − 1.10511i | −0.833477 | − | 0.552555i | \(-0.813653\pi\) | ||||
0.833477 | − | 0.552555i | \(-0.186347\pi\) | |||||||
\(774\) | − 9674.69i | − 0.449289i | ||||||||
\(775\) | − 3813.68i | − 0.176763i | ||||||||
\(776\) | 10511.1 | 0.486244 | ||||||||
\(777\) | 1828.79 | 0.0844368 | ||||||||
\(778\) | − 21793.7i | − 1.00430i | ||||||||
\(779\) | −5789.17 | −0.266263 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4312.12 | −0.197567 | ||||||||
\(782\) | − 8604.79i | − 0.393487i | ||||||||
\(783\) | −44795.2 | −2.04451 | ||||||||
\(784\) | 5205.62 | 0.237136 | ||||||||
\(785\) | − 29813.0i | − 1.35550i | ||||||||
\(786\) | 8272.42i | 0.375404i | ||||||||
\(787\) | 17825.9i | 0.807403i | 0.914891 | + | 0.403702i | \(0.132277\pi\) | ||||
−0.914891 | + | 0.403702i | \(0.867723\pi\) | |||||||
\(788\) | − 7588.96i | − 0.343078i | ||||||||
\(789\) | 7304.34 | 0.329584 | ||||||||
\(790\) | 6576.62 | 0.296184 | ||||||||
\(791\) | − 2990.78i | − 0.134437i | ||||||||
\(792\) | −7096.16 | −0.318373 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −21774.3 | −0.973225 | ||||||||
\(795\) | 8424.53i | 0.375833i | ||||||||
\(796\) | −9662.42 | −0.430245 | ||||||||
\(797\) | 26461.2 | 1.17604 | 0.588020 | − | 0.808846i | \(-0.299908\pi\) | ||||
0.588020 | + | 0.808846i | \(0.299908\pi\) | |||||||
\(798\) | − 411.788i | − 0.0182671i | ||||||||
\(799\) | − 15834.8i | − 0.701122i | ||||||||
\(800\) | 1671.22i | 0.0738581i | ||||||||
\(801\) | − 5055.87i | − 0.223021i | ||||||||
\(802\) | −19937.5 | −0.877828 | ||||||||
\(803\) | 57888.5 | 2.54401 | ||||||||
\(804\) | 6389.32i | 0.280266i | ||||||||
\(805\) | 5731.58 | 0.250946 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19085.8 | 0.832530 | ||||||||
\(808\) | 11709.8i | 0.509837i | ||||||||
\(809\) | 21873.3 | 0.950588 | 0.475294 | − | 0.879827i | \(-0.342342\pi\) | ||||
0.475294 | + | 0.879827i | \(0.342342\pi\) | |||||||
\(810\) | 3046.10 | 0.132135 | ||||||||
\(811\) | − 39113.8i | − 1.69355i | −0.531949 | − | 0.846776i | \(-0.678540\pi\) | ||||
0.531949 | − | 0.846776i | \(-0.321460\pi\) | |||||||
\(812\) | 5062.90i | 0.218809i | ||||||||
\(813\) | 14970.6i | 0.645810i | ||||||||
\(814\) | − 15530.0i | − 0.668706i | ||||||||
\(815\) | −3849.56 | −0.165453 | ||||||||
\(816\) | −1577.47 | −0.0676748 | ||||||||
\(817\) | − 4767.57i | − 0.204157i | ||||||||
\(818\) | 8072.65 | 0.345053 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14772.0 | −0.629097 | ||||||||
\(821\) | 26296.8i | 1.11786i | 0.829214 | + | 0.558931i | \(0.188788\pi\) | ||||
−0.829214 | + | 0.558931i | \(0.811212\pi\) | |||||||
\(822\) | 12811.9 | 0.543634 | ||||||||
\(823\) | −24681.1 | −1.04536 | −0.522678 | − | 0.852530i | \(-0.675067\pi\) | ||||
−0.522678 | + | 0.852530i | \(0.675067\pi\) | |||||||
\(824\) | 1687.09i | 0.0713258i | ||||||||
\(825\) | − 12512.3i | − 0.528027i | ||||||||
\(826\) | 1935.33i | 0.0815241i | ||||||||
\(827\) | − 3081.68i | − 0.129578i | −0.997899 | − | 0.0647888i | \(-0.979363\pi\) | ||||
0.997899 | − | 0.0647888i | \(-0.0206374\pi\) | |||||||
\(828\) | −8680.12 | −0.364317 | ||||||||
\(829\) | 8498.53 | 0.356051 | 0.178026 | − | 0.984026i | \(-0.443029\pi\) | ||||
0.178026 | + | 0.984026i | \(0.443029\pi\) | |||||||
\(830\) | 4337.18i | 0.181380i | ||||||||
\(831\) | 1605.19 | 0.0670076 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8752.57 | 0.364056 | ||||||||
\(834\) | − 12288.6i | − 0.510215i | ||||||||
\(835\) | 27327.1 | 1.13257 | ||||||||
\(836\) | −3496.90 | −0.144668 | ||||||||
\(837\) | − 10857.0i | − 0.448356i | ||||||||
\(838\) | 30389.7i | 1.25274i | ||||||||
\(839\) | 18680.1i | 0.768664i | 0.923195 | + | 0.384332i | \(0.125568\pi\) | ||||
−0.923195 | + | 0.384332i | \(0.874432\pi\) | |||||||
\(840\) | − 1050.74i | − 0.0431596i | ||||||||
\(841\) | 66385.3 | 2.72194 | ||||||||
\(842\) | 20309.5 | 0.831249 | ||||||||
\(843\) | 20018.8i | 0.817894i | ||||||||
\(844\) | −10673.7 | −0.435312 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −15973.5 | −0.649147 | ||||||||
\(847\) | − 12361.9i | − 0.501486i | ||||||||
\(848\) | −4311.39 | −0.174592 | ||||||||
\(849\) | −2919.72 | −0.118026 | ||||||||
\(850\) | 2809.93i | 0.113388i | ||||||||
\(851\) | − 18996.5i | − 0.765208i | ||||||||
\(852\) | 966.973i | 0.0388826i | ||||||||
\(853\) | 24129.9i | 0.968574i | 0.874909 | + | 0.484287i | \(0.160921\pi\) | ||||
−0.874909 | + | 0.484287i | \(0.839079\pi\) | |||||||
\(854\) | 3199.65 | 0.128208 | ||||||||
\(855\) | −1547.94 | −0.0619164 | ||||||||
\(856\) | − 3128.49i | − 0.124918i | ||||||||
\(857\) | 7739.30 | 0.308482 | 0.154241 | − | 0.988033i | \(-0.450707\pi\) | ||||
0.154241 | + | 0.988033i | \(0.450707\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4302.59 | 0.170899 | 0.0854496 | − | 0.996342i | \(-0.472767\pi\) | ||||
0.0854496 | + | 0.996342i | \(0.472767\pi\) | |||||||
\(860\) | − 12165.2i | − 0.482360i | ||||||||
\(861\) | −6665.08 | −0.263816 | ||||||||
\(862\) | −13233.7 | −0.522901 | ||||||||
\(863\) | 16253.2i | 0.641096i | 0.947232 | + | 0.320548i | \(0.103867\pi\) | ||||
−0.947232 | + | 0.320548i | \(0.896133\pi\) | |||||||
\(864\) | 4757.73i | 0.187340i | ||||||||
\(865\) | − 16203.2i | − 0.636910i | ||||||||
\(866\) | − 11395.2i | − 0.447142i | ||||||||
\(867\) | 15353.2 | 0.601410 | ||||||||
\(868\) | −1227.10 | −0.0479842 | ||||||||
\(869\) | − 25198.7i | − 0.983669i | ||||||||
\(870\) | −18839.1 | −0.734144 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10651.2 | 0.413642 | ||||||||
\(873\) | − 17827.7i | − 0.691152i | ||||||||
\(874\) | −4277.45 | −0.165546 | ||||||||
\(875\) | −6351.46 | −0.245392 | ||||||||
\(876\) | − 12981.2i | − 0.500680i | ||||||||
\(877\) | 9441.33i | 0.363525i | 0.983342 | + | 0.181762i | \(0.0581802\pi\) | ||||
−0.983342 | + | 0.181762i | \(0.941820\pi\) | |||||||
\(878\) | − 872.014i | − 0.0335183i | ||||||||
\(879\) | 6220.48i | 0.238693i | ||||||||
\(880\) | −8922.88 | −0.341807 | ||||||||
\(881\) | 11872.4 | 0.454021 | 0.227011 | − | 0.973892i | \(-0.427105\pi\) | ||||
0.227011 | + | 0.973892i | \(0.427105\pi\) | |||||||
\(882\) | − 8829.18i | − 0.337068i | ||||||||
\(883\) | 493.891 | 0.0188231 | 0.00941153 | − | 0.999956i | \(-0.497004\pi\) | ||||
0.00941153 | + | 0.999956i | \(0.497004\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7201.40 | −0.273528 | ||||||||
\(886\) | 13219.2i | 0.501249i | ||||||||
\(887\) | 20543.6 | 0.777664 | 0.388832 | − | 0.921309i | \(-0.372879\pi\) | ||||
0.388832 | + | 0.921309i | \(0.372879\pi\) | |||||||
\(888\) | −3482.54 | −0.131606 | ||||||||
\(889\) | 4922.38i | 0.185705i | ||||||||
\(890\) | − 6357.36i | − 0.239437i | ||||||||
\(891\) | − 11671.3i | − 0.438838i | ||||||||
\(892\) | 1145.43i | 0.0429953i | ||||||||
\(893\) | −7871.52 | −0.294972 | ||||||||
\(894\) | −6574.50 | −0.245955 | ||||||||
\(895\) | − 22614.2i | − 0.844592i | ||||||||
\(896\) | 537.734 | 0.0200496 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16030.6 | −0.595711 | ||||||||
\(899\) | 22001.0i | 0.816212i | ||||||||
\(900\) | 2834.53 | 0.104983 | ||||||||
\(901\) | −7249.03 | −0.268036 | ||||||||
\(902\) | 56599.7i | 2.08932i | ||||||||
\(903\) | − 5488.90i | − 0.202280i | ||||||||
\(904\) | 5695.30i | 0.209539i | ||||||||
\(905\) | 19535.0i | 0.717532i | ||||||||
\(906\) | 15233.3 | 0.558600 | ||||||||
\(907\) | 5386.61 | 0.197199 | 0.0985994 | − | 0.995127i | \(-0.468564\pi\) | ||||
0.0985994 | + | 0.995127i | \(0.468564\pi\) | |||||||
\(908\) | − 20805.0i | − 0.760393i | ||||||||
\(909\) | 19860.8 | 0.724688 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31793.5 | 1.15627 | 0.578137 | − | 0.815940i | \(-0.303780\pi\) | ||||
0.578137 | + | 0.815940i | \(0.303780\pi\) | |||||||
\(912\) | 784.164i | 0.0284718i | ||||||||
\(913\) | 16618.2 | 0.602389 | ||||||||
\(914\) | −9014.07 | −0.326213 | ||||||||
\(915\) | 11905.9i | 0.430162i | ||||||||
\(916\) | 3561.83i | 0.128478i | ||||||||
\(917\) | − 4741.34i | − 0.170745i | ||||||||
\(918\) | 7999.51i | 0.287607i | ||||||||
\(919\) | −42991.4 | −1.54315 | −0.771575 | − | 0.636139i | \(-0.780531\pi\) | ||||
−0.771575 | + | 0.636139i | \(0.780531\pi\) | |||||||
\(920\) | −10914.6 | −0.391134 | ||||||||
\(921\) | − 34398.0i | − 1.23068i | ||||||||
\(922\) | 4207.10 | 0.150275 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −4025.98 | −0.143339 | ||||||||
\(925\) | 6203.40i | 0.220504i | ||||||||
\(926\) | −10936.6 | −0.388119 | ||||||||
\(927\) | 2861.45 | 0.101383 | ||||||||
\(928\) | − 9641.21i | − 0.341043i | ||||||||
\(929\) | 40676.7i | 1.43655i | 0.695757 | + | 0.718277i | \(0.255069\pi\) | ||||
−0.695757 | + | 0.718277i | \(0.744931\pi\) | |||||||
\(930\) | − 4566.04i | − 0.160996i | ||||||||
\(931\) | − 4350.91i | − 0.153164i | ||||||||
\(932\) | 19012.4 | 0.668212 | ||||||||
\(933\) | −12030.5 | −0.422145 | ||||||||
\(934\) | 12087.6i | 0.423467i | ||||||||
\(935\) | −15002.6 | −0.524748 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21008.3 | 0.732456 | 0.366228 | − | 0.930525i | \(-0.380649\pi\) | ||||
0.366228 | + | 0.930525i | \(0.380649\pi\) | |||||||
\(938\) | − 3662.04i | − 0.127473i | ||||||||
\(939\) | 21713.2 | 0.754614 | ||||||||
\(940\) | −20085.4 | −0.696929 | ||||||||
\(941\) | − 4525.50i | − 0.156777i | −0.996923 | − | 0.0783885i | \(-0.975023\pi\) | ||||
0.996923 | − | 0.0783885i | \(-0.0249775\pi\) | |||||||
\(942\) | 25615.6i | 0.885989i | ||||||||
\(943\) | 69233.5i | 2.39083i | ||||||||
\(944\) | − 3685.43i | − 0.127066i | ||||||||
\(945\) | −5328.40 | −0.183421 | ||||||||
\(946\) | −46611.7 | −1.60198 | ||||||||
\(947\) | 27401.6i | 0.940267i | 0.882595 | + | 0.470134i | \(0.155794\pi\) | ||||
−0.882595 | + | 0.470134i | \(0.844206\pi\) | |||||||
\(948\) | −5650.70 | −0.193593 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1396.82 | 0.0477040 | ||||||||
\(951\) | 23704.0i | 0.808259i | ||||||||
\(952\) | 904.129 | 0.0307805 | ||||||||
\(953\) | −26226.2 | −0.891449 | −0.445725 | − | 0.895170i | \(-0.647054\pi\) | ||||
−0.445725 | + | 0.895170i | \(0.647054\pi\) | |||||||
\(954\) | 7312.49i | 0.248166i | ||||||||
\(955\) | − 2886.08i | − 0.0977921i | ||||||||
\(956\) | 9170.48i | 0.310245i | ||||||||
\(957\) | 72183.2i | 2.43819i | ||||||||
\(958\) | 16962.6 | 0.572063 | ||||||||
\(959\) | −7343.15 | −0.247260 | ||||||||
\(960\) | 2000.91i | 0.0672700i | ||||||||
\(961\) | 24458.6 | 0.821007 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5306.19 | −0.177559 | ||||||||
\(964\) | 7900.83i | 0.263972i | ||||||||
\(965\) | 22897.1 | 0.763817 | ||||||||
\(966\) | −4924.63 | −0.164024 | ||||||||
\(967\) | 20843.6i | 0.693158i | 0.938021 | + | 0.346579i | \(0.112657\pi\) | ||||
−0.938021 | + | 0.346579i | \(0.887343\pi\) | |||||||
\(968\) | 23540.6i | 0.781635i | ||||||||
\(969\) | 1318.47i | 0.0437103i | ||||||||
\(970\) | − 22417.0i | − 0.742026i | ||||||||
\(971\) | 32577.3 | 1.07668 | 0.538339 | − | 0.842729i | \(-0.319052\pi\) | ||||
0.538339 | + | 0.842729i | \(0.319052\pi\) | |||||||
\(972\) | 13440.1 | 0.443510 | ||||||||
\(973\) | 7043.20i | 0.232060i | ||||||||
\(974\) | −13246.7 | −0.435782 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6093.05 | −0.199830 | ||||||||
\(977\) | − 43864.1i | − 1.43637i | −0.695851 | − | 0.718186i | \(-0.744973\pi\) | ||||
0.695851 | − | 0.718186i | \(-0.255027\pi\) | |||||||
\(978\) | 3307.58 | 0.108144 | ||||||||
\(979\) | −24358.6 | −0.795204 | ||||||||
\(980\) | − 11102.0i | − 0.361879i | ||||||||
\(981\) | − 18065.4i | − 0.587955i | ||||||||
\(982\) | − 32758.7i | − 1.06453i | ||||||||
\(983\) | 14758.8i | 0.478875i | 0.970912 | + | 0.239437i | \(0.0769630\pi\) | ||||
−0.970912 | + | 0.239437i | \(0.923037\pi\) | |||||||
\(984\) | 12692.2 | 0.411193 | ||||||||
\(985\) | −16185.0 | −0.523549 | ||||||||
\(986\) | − 16210.4i | − 0.523575i | ||||||||
\(987\) | −9062.49 | −0.292262 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −57016.0 | −1.83317 | ||||||||
\(990\) | 15134.0i | 0.485848i | ||||||||
\(991\) | 48622.4 | 1.55857 | 0.779284 | − | 0.626671i | \(-0.215583\pi\) | ||||
0.779284 | + | 0.626671i | \(0.215583\pi\) | |||||||
\(992\) | 2336.74 | 0.0747900 | ||||||||
\(993\) | 12860.9i | 0.411006i | ||||||||
\(994\) | − 554.220i | − 0.0176849i | ||||||||
\(995\) | 20607.0i | 0.656569i | ||||||||
\(996\) | − 3726.55i | − 0.118554i | ||||||||
\(997\) | −18812.3 | −0.597586 | −0.298793 | − | 0.954318i | \(-0.596584\pi\) | ||||
−0.298793 | + | 0.954318i | \(0.596584\pi\) | |||||||
\(998\) | −15831.4 | −0.502138 | ||||||||
\(999\) | 17660.2i | 0.559305i |
(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 | 338.4.b.f.337.5 | 6 | ||
13.2 | odd | 12 | 338.4.c.k.191.2 | 6 | |||
13.3 | even | 3 | 338.4.e.h.147.2 | 12 | |||
13.4 | even | 6 | 338.4.e.h.23.2 | 12 | |||
13.5 | odd | 4 | 338.4.a.k.1.2 | yes | 3 | ||
13.6 | odd | 12 | 338.4.c.k.315.2 | 6 | |||
13.7 | odd | 12 | 338.4.c.l.315.2 | 6 | |||
13.8 | odd | 4 | 338.4.a.j.1.2 | ✓ | 3 | ||
13.9 | even | 3 | 338.4.e.h.23.5 | 12 | |||
13.10 | even | 6 | 338.4.e.h.147.5 | 12 | |||
13.11 | odd | 12 | 338.4.c.l.191.2 | 6 | |||
13.12 | even | 2 | inner | 338.4.b.f.337.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
338.4.a.j.1.2 | ✓ | 3 | 13.8 | odd | 4 | ||
338.4.a.k.1.2 | yes | 3 | 13.5 | odd | 4 | ||
338.4.b.f.337.2 | 6 | 13.12 | even | 2 | inner | ||
338.4.b.f.337.5 | 6 | 1.1 | even | 1 | trivial | ||
338.4.c.k.191.2 | 6 | 13.2 | odd | 12 | |||
338.4.c.k.315.2 | 6 | 13.6 | odd | 12 | |||
338.4.c.l.191.2 | 6 | 13.11 | odd | 12 | |||
338.4.c.l.315.2 | 6 | 13.7 | odd | 12 | |||
338.4.e.h.23.2 | 12 | 13.4 | even | 6 | |||
338.4.e.h.23.5 | 12 | 13.9 | even | 3 | |||
338.4.e.h.147.2 | 12 | 13.3 | even | 3 | |||
338.4.e.h.147.5 | 12 | 13.10 | even | 6 |