Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(288,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, 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("289.288");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 288.22 | ||
Character | \(\chi\) | \(=\) | 289.288 |
Dual form | 289.4.b.f.288.21 |
$q$-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 \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.98104 | 1.76107 | 0.880533 | − | 0.473986i | \(-0.157185\pi\) | ||||
0.880533 | + | 0.473986i | \(0.157185\pi\) | |||||||
\(3\) | 6.26206i | 1.20513i | 0.798068 | + | 0.602567i | \(0.205855\pi\) | ||||
−0.798068 | + | 0.602567i | \(0.794145\pi\) | |||||||
\(4\) | 16.8108 | 2.10135 | ||||||||
\(5\) | 15.7477i | 1.40852i | 0.709943 | + | 0.704259i | \(0.248721\pi\) | ||||
−0.709943 | + | 0.704259i | \(0.751279\pi\) | |||||||
\(6\) | 31.1916i | 2.12232i | ||||||||
\(7\) | − 0.789949i | − 0.0426533i | −0.999773 | − | 0.0213266i | \(-0.993211\pi\) | ||||
0.999773 | − | 0.0213266i | \(-0.00678899\pi\) | |||||||
\(8\) | 43.8870 | 1.93955 | ||||||||
\(9\) | −12.2134 | −0.452347 | ||||||||
\(10\) | 78.4401i | 2.48049i | ||||||||
\(11\) | − 45.3316i | − 1.24254i | −0.783595 | − | 0.621272i | \(-0.786616\pi\) | ||||
0.783595 | − | 0.621272i | \(-0.213384\pi\) | |||||||
\(12\) | 105.270i | 2.53241i | ||||||||
\(13\) | 46.7491 | 0.997374 | 0.498687 | − | 0.866782i | \(-0.333816\pi\) | ||||
0.498687 | + | 0.866782i | \(0.333816\pi\) | |||||||
\(14\) | − 3.93477i | − 0.0751152i | ||||||||
\(15\) | −98.6131 | −1.69745 | ||||||||
\(16\) | 84.1166 | 1.31432 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −60.8354 | −0.796613 | ||||||||
\(19\) | −100.512 | −1.21364 | −0.606819 | − | 0.794840i | \(-0.707555\pi\) | ||||
−0.606819 | + | 0.794840i | \(0.707555\pi\) | |||||||
\(20\) | 264.732i | 2.95979i | ||||||||
\(21\) | 4.94671 | 0.0514029 | ||||||||
\(22\) | − 225.798i | − 2.18820i | ||||||||
\(23\) | 84.1579i | 0.762962i | 0.924377 | + | 0.381481i | \(0.124586\pi\) | ||||
−0.924377 | + | 0.381481i | \(0.875414\pi\) | |||||||
\(24\) | 274.823i | 2.33742i | ||||||||
\(25\) | −122.991 | −0.983925 | ||||||||
\(26\) | 232.859 | 1.75644 | ||||||||
\(27\) | 92.5947i | 0.659995i | ||||||||
\(28\) | − 13.2797i | − 0.0896294i | ||||||||
\(29\) | − 101.693i | − 0.651168i | −0.945513 | − | 0.325584i | \(-0.894439\pi\) | ||||
0.945513 | − | 0.325584i | \(-0.105561\pi\) | |||||||
\(30\) | −491.196 | −2.98933 | ||||||||
\(31\) | 7.36111i | 0.0426482i | 0.999773 | + | 0.0213241i | \(0.00678819\pi\) | ||||
−0.999773 | + | 0.0213241i | \(0.993212\pi\) | |||||||
\(32\) | 67.8926 | 0.375057 | ||||||||
\(33\) | 283.869 | 1.49743 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.4399 | 0.0600779 | ||||||||
\(36\) | −205.317 | −0.950540 | ||||||||
\(37\) | − 251.101i | − 1.11570i | −0.829943 | − | 0.557848i | \(-0.811627\pi\) | ||||
0.829943 | − | 0.557848i | \(-0.188373\pi\) | |||||||
\(38\) | −500.657 | −2.13730 | ||||||||
\(39\) | 292.745i | 1.20197i | ||||||||
\(40\) | 691.120i | 2.73189i | ||||||||
\(41\) | − 260.918i | − 0.993868i | −0.867788 | − | 0.496934i | \(-0.834459\pi\) | ||||
0.867788 | − | 0.496934i | \(-0.165541\pi\) | |||||||
\(42\) | 24.6398 | 0.0905238 | ||||||||
\(43\) | 401.442 | 1.42370 | 0.711852 | − | 0.702329i | \(-0.247856\pi\) | ||||
0.711852 | + | 0.702329i | \(0.247856\pi\) | |||||||
\(44\) | − 762.060i | − 2.61102i | ||||||||
\(45\) | − 192.333i | − 0.637140i | ||||||||
\(46\) | 419.194i | 1.34363i | ||||||||
\(47\) | 304.102 | 0.943785 | 0.471892 | − | 0.881656i | \(-0.343571\pi\) | ||||
0.471892 | + | 0.881656i | \(0.343571\pi\) | |||||||
\(48\) | 526.743i | 1.58393i | ||||||||
\(49\) | 342.376 | 0.998181 | ||||||||
\(50\) | −612.622 | −1.73276 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 785.889 | 2.09583 | ||||||||
\(53\) | −398.236 | −1.03211 | −0.516055 | − | 0.856555i | \(-0.672600\pi\) | ||||
−0.516055 | + | 0.856555i | \(0.672600\pi\) | |||||||
\(54\) | 461.218i | 1.16229i | ||||||||
\(55\) | 713.869 | 1.75015 | ||||||||
\(56\) | − 34.6685i | − 0.0827281i | ||||||||
\(57\) | − 629.414i | − 1.46260i | ||||||||
\(58\) | − 506.536i | − 1.14675i | ||||||||
\(59\) | 577.767 | 1.27490 | 0.637448 | − | 0.770493i | \(-0.279990\pi\) | ||||
0.637448 | + | 0.770493i | \(0.279990\pi\) | |||||||
\(60\) | −1657.77 | −3.56694 | ||||||||
\(61\) | − 126.259i | − 0.265013i | −0.991182 | − | 0.132507i | \(-0.957697\pi\) | ||||
0.991182 | − | 0.132507i | \(-0.0423026\pi\) | |||||||
\(62\) | 36.6660i | 0.0751063i | ||||||||
\(63\) | 9.64795i | 0.0192941i | ||||||||
\(64\) | −334.757 | −0.653822 | ||||||||
\(65\) | 736.191i | 1.40482i | ||||||||
\(66\) | 1413.96 | 2.63707 | ||||||||
\(67\) | −150.923 | −0.275198 | −0.137599 | − | 0.990488i | \(-0.543938\pi\) | ||||
−0.137599 | + | 0.990488i | \(0.543938\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −527.002 | −0.919471 | ||||||||
\(70\) | 61.9637 | 0.105801 | ||||||||
\(71\) | 434.653i | 0.726533i | 0.931685 | + | 0.363267i | \(0.118339\pi\) | ||||
−0.931685 | + | 0.363267i | \(0.881661\pi\) | |||||||
\(72\) | −536.008 | −0.877350 | ||||||||
\(73\) | 493.829i | 0.791757i | 0.918303 | + | 0.395879i | \(0.129560\pi\) | ||||
−0.918303 | + | 0.395879i | \(0.870440\pi\) | |||||||
\(74\) | − 1250.74i | − 1.96481i | ||||||||
\(75\) | − 770.175i | − 1.18576i | ||||||||
\(76\) | −1689.69 | −2.55028 | ||||||||
\(77\) | −35.8096 | −0.0529985 | ||||||||
\(78\) | 1458.18i | 2.11674i | ||||||||
\(79\) | 72.2153i | 0.102846i | 0.998677 | + | 0.0514232i | \(0.0163757\pi\) | ||||
−0.998677 | + | 0.0514232i | \(0.983624\pi\) | |||||||
\(80\) | 1324.64i | 1.85125i | ||||||||
\(81\) | −909.595 | −1.24773 | ||||||||
\(82\) | − 1299.65i | − 1.75027i | ||||||||
\(83\) | −711.089 | −0.940388 | −0.470194 | − | 0.882563i | \(-0.655816\pi\) | ||||
−0.470194 | + | 0.882563i | \(0.655816\pi\) | |||||||
\(84\) | 83.1581 | 0.108015 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1999.60 | 2.50724 | ||||||||
\(87\) | 636.806 | 0.784745 | ||||||||
\(88\) | − 1989.47i | − 2.40997i | ||||||||
\(89\) | 1354.30 | 1.61298 | 0.806489 | − | 0.591250i | \(-0.201365\pi\) | ||||
0.806489 | + | 0.591250i | \(0.201365\pi\) | |||||||
\(90\) | − 958.018i | − 1.12204i | ||||||||
\(91\) | − 36.9294i | − 0.0425412i | ||||||||
\(92\) | 1414.76i | 1.60325i | ||||||||
\(93\) | −46.0957 | −0.0513968 | ||||||||
\(94\) | 1514.75 | 1.66207 | ||||||||
\(95\) | − 1582.84i | − 1.70943i | ||||||||
\(96\) | 425.147i | 0.451994i | ||||||||
\(97\) | − 1402.59i | − 1.46816i | −0.679064 | − | 0.734079i | \(-0.737614\pi\) | ||||
0.679064 | − | 0.734079i | \(-0.262386\pi\) | |||||||
\(98\) | 1705.39 | 1.75786 | ||||||||
\(99\) | 553.651i | 0.562061i | ||||||||
\(100\) | −2067.57 | −2.06757 | ||||||||
\(101\) | 151.252 | 0.149012 | 0.0745058 | − | 0.997221i | \(-0.476262\pi\) | ||||
0.0745058 | + | 0.997221i | \(0.476262\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −687.247 | −0.657441 | −0.328720 | − | 0.944427i | \(-0.606617\pi\) | ||||
−0.328720 | + | 0.944427i | \(0.606617\pi\) | |||||||
\(104\) | 2051.68 | 1.93445 | ||||||||
\(105\) | 77.8994i | 0.0724019i | ||||||||
\(106\) | −1983.63 | −1.81761 | ||||||||
\(107\) | − 456.959i | − 0.412859i | −0.978461 | − | 0.206430i | \(-0.933816\pi\) | ||||
0.978461 | − | 0.206430i | \(-0.0661844\pi\) | |||||||
\(108\) | 1556.59i | 1.38688i | ||||||||
\(109\) | 1281.43i | 1.12605i | 0.826441 | + | 0.563023i | \(0.190362\pi\) | ||||
−0.826441 | + | 0.563023i | \(0.809638\pi\) | |||||||
\(110\) | 3555.81 | 3.08212 | ||||||||
\(111\) | 1572.41 | 1.34456 | ||||||||
\(112\) | − 66.4479i | − 0.0560601i | ||||||||
\(113\) | − 1887.62i | − 1.57143i | −0.618586 | − | 0.785717i | \(-0.712294\pi\) | ||||
0.618586 | − | 0.785717i | \(-0.287706\pi\) | |||||||
\(114\) | − 3135.14i | − 2.57573i | ||||||||
\(115\) | −1325.29 | −1.07465 | ||||||||
\(116\) | − 1709.54i | − 1.36833i | ||||||||
\(117\) | −570.964 | −0.451159 | ||||||||
\(118\) | 2877.88 | 2.24518 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4327.83 | −3.29229 | ||||||||
\(121\) | −723.950 | −0.543914 | ||||||||
\(122\) | − 628.902i | − 0.466706i | ||||||||
\(123\) | 1633.89 | 1.19774 | ||||||||
\(124\) | 123.746i | 0.0896188i | ||||||||
\(125\) | 31.6426i | 0.0226416i | ||||||||
\(126\) | 48.0569i | 0.0339781i | ||||||||
\(127\) | −1920.56 | −1.34190 | −0.670952 | − | 0.741501i | \(-0.734114\pi\) | ||||
−0.670952 | + | 0.741501i | \(0.734114\pi\) | |||||||
\(128\) | −2210.58 | −1.52648 | ||||||||
\(129\) | 2513.85i | 1.71575i | ||||||||
\(130\) | 3667.00i | 2.47398i | ||||||||
\(131\) | 1656.13i | 1.10456i | 0.833660 | + | 0.552279i | \(0.186242\pi\) | ||||
−0.833660 | + | 0.552279i | \(0.813758\pi\) | |||||||
\(132\) | 4772.06 | 3.14663 | ||||||||
\(133\) | 79.3997i | 0.0517656i | ||||||||
\(134\) | −751.757 | −0.484641 | ||||||||
\(135\) | −1458.16 | −0.929615 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2725.42 | −1.69962 | −0.849811 | − | 0.527088i | \(-0.823284\pi\) | ||||
−0.849811 | + | 0.527088i | \(0.823284\pi\) | |||||||
\(138\) | −2625.02 | −1.61925 | ||||||||
\(139\) | 1231.94i | 0.751739i | 0.926673 | + | 0.375870i | \(0.122656\pi\) | ||||
−0.926673 | + | 0.375870i | \(0.877344\pi\) | |||||||
\(140\) | 209.125 | 0.126245 | ||||||||
\(141\) | 1904.31i | 1.13739i | ||||||||
\(142\) | 2165.03i | 1.27947i | ||||||||
\(143\) | − 2119.21i | − 1.23928i | ||||||||
\(144\) | −1027.35 | −0.594530 | ||||||||
\(145\) | 1601.43 | 0.917183 | ||||||||
\(146\) | 2459.78i | 1.39434i | ||||||||
\(147\) | 2143.98i | 1.20294i | ||||||||
\(148\) | − 4221.21i | − 2.34447i | ||||||||
\(149\) | 2317.73 | 1.27434 | 0.637169 | − | 0.770724i | \(-0.280106\pi\) | ||||
0.637169 | + | 0.770724i | \(0.280106\pi\) | |||||||
\(150\) | − 3836.27i | − 2.08820i | ||||||||
\(151\) | −1155.92 | −0.622964 | −0.311482 | − | 0.950252i | \(-0.600825\pi\) | ||||
−0.311482 | + | 0.950252i | \(0.600825\pi\) | |||||||
\(152\) | −4411.19 | −2.35391 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −178.369 | −0.0933339 | ||||||||
\(155\) | −115.921 | −0.0600708 | ||||||||
\(156\) | 4921.28i | 2.52576i | ||||||||
\(157\) | −3226.75 | −1.64027 | −0.820137 | − | 0.572167i | \(-0.806103\pi\) | ||||
−0.820137 | + | 0.572167i | \(0.806103\pi\) | |||||||
\(158\) | 359.708i | 0.181119i | ||||||||
\(159\) | − 2493.77i | − 1.24383i | ||||||||
\(160\) | 1069.15i | 0.528275i | ||||||||
\(161\) | 66.4805 | 0.0325428 | ||||||||
\(162\) | −4530.73 | −2.19733 | ||||||||
\(163\) | − 982.257i | − 0.472002i | −0.971753 | − | 0.236001i | \(-0.924163\pi\) | ||||
0.971753 | − | 0.236001i | \(-0.0758369\pi\) | |||||||
\(164\) | − 4386.25i | − 2.08847i | ||||||||
\(165\) | 4470.29i | 2.10916i | ||||||||
\(166\) | −3541.97 | −1.65608 | ||||||||
\(167\) | 36.6005i | 0.0169595i | 0.999964 | + | 0.00847974i | \(0.00269922\pi\) | ||||
−0.999964 | + | 0.00847974i | \(0.997301\pi\) | |||||||
\(168\) | 217.096 | 0.0996984 | ||||||||
\(169\) | −11.5254 | −0.00524596 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1227.60 | 0.548986 | ||||||||
\(172\) | 6748.56 | 2.99170 | ||||||||
\(173\) | − 2826.57i | − 1.24220i | −0.783732 | − | 0.621099i | \(-0.786686\pi\) | ||||
0.783732 | − | 0.621099i | \(-0.213314\pi\) | |||||||
\(174\) | 3171.96 | 1.38199 | ||||||||
\(175\) | 97.1564i | 0.0419676i | ||||||||
\(176\) | − 3813.14i | − 1.63310i | ||||||||
\(177\) | 3618.01i | 1.53642i | ||||||||
\(178\) | 6745.80 | 2.84056 | ||||||||
\(179\) | 1168.77 | 0.488032 | 0.244016 | − | 0.969771i | \(-0.421535\pi\) | ||||
0.244016 | + | 0.969771i | \(0.421535\pi\) | |||||||
\(180\) | − 3233.27i | − 1.33885i | ||||||||
\(181\) | − 2871.88i | − 1.17936i | −0.807635 | − | 0.589682i | \(-0.799253\pi\) | ||||
0.807635 | − | 0.589682i | \(-0.200747\pi\) | |||||||
\(182\) | − 183.947i | − 0.0749179i | ||||||||
\(183\) | 790.642 | 0.319377 | ||||||||
\(184\) | 3693.44i | 1.47980i | ||||||||
\(185\) | 3954.26 | 1.57148 | ||||||||
\(186\) | −229.605 | −0.0905131 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5112.20 | 1.98322 | ||||||||
\(189\) | 73.1451 | 0.0281509 | ||||||||
\(190\) | − 7884.20i | − 3.01042i | ||||||||
\(191\) | −1626.96 | −0.616350 | −0.308175 | − | 0.951330i | \(-0.599718\pi\) | ||||
−0.308175 | + | 0.951330i | \(0.599718\pi\) | |||||||
\(192\) | − 2096.27i | − 0.787943i | ||||||||
\(193\) | − 796.367i | − 0.297014i | −0.988911 | − | 0.148507i | \(-0.952553\pi\) | ||||
0.988911 | − | 0.148507i | \(-0.0474468\pi\) | |||||||
\(194\) | − 6986.36i | − 2.58552i | ||||||||
\(195\) | −4610.07 | −1.69300 | ||||||||
\(196\) | 5755.61 | 2.09753 | ||||||||
\(197\) | − 977.275i | − 0.353441i | −0.984261 | − | 0.176721i | \(-0.943451\pi\) | ||||
0.984261 | − | 0.176721i | \(-0.0565489\pi\) | |||||||
\(198\) | 2757.76i | 0.989826i | ||||||||
\(199\) | − 711.695i | − 0.253521i | −0.991933 | − | 0.126761i | \(-0.959542\pi\) | ||||
0.991933 | − | 0.126761i | \(-0.0404580\pi\) | |||||||
\(200\) | −5397.69 | −1.90837 | ||||||||
\(201\) | − 945.092i | − 0.331650i | ||||||||
\(202\) | 753.395 | 0.262419 | ||||||||
\(203\) | −80.3322 | −0.0277745 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4108.87 | 1.39988 | ||||||||
\(206\) | −3423.21 | −1.15780 | ||||||||
\(207\) | − 1027.85i | − 0.345124i | ||||||||
\(208\) | 3932.37 | 1.31087 | ||||||||
\(209\) | 4556.38i | 1.50800i | ||||||||
\(210\) | 388.020i | 0.127504i | ||||||||
\(211\) | 3690.17i | 1.20399i | 0.798501 | + | 0.601994i | \(0.205627\pi\) | ||||
−0.798501 | + | 0.601994i | \(0.794373\pi\) | |||||||
\(212\) | −6694.66 | −2.16883 | ||||||||
\(213\) | −2721.82 | −0.875570 | ||||||||
\(214\) | − 2276.13i | − 0.727072i | ||||||||
\(215\) | 6321.79i | 2.00532i | ||||||||
\(216\) | 4063.70i | 1.28009i | ||||||||
\(217\) | 5.81490 | 0.00181909 | ||||||||
\(218\) | 6382.87i | 1.98304i | ||||||||
\(219\) | −3092.38 | −0.954173 | ||||||||
\(220\) | 12000.7 | 3.67767 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 7832.23 | 2.36786 | ||||||||
\(223\) | 1726.16 | 0.518351 | 0.259176 | − | 0.965830i | \(-0.416549\pi\) | ||||
0.259176 | + | 0.965830i | \(0.416549\pi\) | |||||||
\(224\) | − 53.6317i | − 0.0159974i | ||||||||
\(225\) | 1502.13 | 0.445076 | ||||||||
\(226\) | − 9402.31i | − 2.76740i | ||||||||
\(227\) | 2144.75i | 0.627100i | 0.949572 | + | 0.313550i | \(0.101518\pi\) | ||||
−0.949572 | + | 0.313550i | \(0.898482\pi\) | |||||||
\(228\) | − 10581.0i | − 3.07343i | ||||||||
\(229\) | −5082.23 | −1.46656 | −0.733282 | − | 0.679924i | \(-0.762013\pi\) | ||||
−0.733282 | + | 0.679924i | \(0.762013\pi\) | |||||||
\(230\) | −6601.35 | −1.89252 | ||||||||
\(231\) | − 224.242i | − 0.0638703i | ||||||||
\(232\) | − 4462.99i | − 1.26297i | ||||||||
\(233\) | − 3271.12i | − 0.919735i | −0.887987 | − | 0.459868i | \(-0.847897\pi\) | ||||
0.887987 | − | 0.459868i | \(-0.152103\pi\) | |||||||
\(234\) | −2844.00 | −0.794521 | ||||||||
\(235\) | 4788.92i | 1.32934i | ||||||||
\(236\) | 9712.73 | 2.67900 | ||||||||
\(237\) | −452.217 | −0.123944 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4905.70 | −1.32771 | −0.663857 | − | 0.747860i | \(-0.731082\pi\) | ||||
−0.663857 | + | 0.747860i | \(0.731082\pi\) | |||||||
\(240\) | −8295.00 | −2.23100 | ||||||||
\(241\) | 494.108i | 0.132068i | 0.997817 | + | 0.0660338i | \(0.0210345\pi\) | ||||
−0.997817 | + | 0.0660338i | \(0.978965\pi\) | |||||||
\(242\) | −3606.03 | −0.957869 | ||||||||
\(243\) | − 3195.88i | − 0.843686i | ||||||||
\(244\) | − 2122.52i | − 0.556886i | ||||||||
\(245\) | 5391.64i | 1.40596i | ||||||||
\(246\) | 8138.46 | 2.10931 | ||||||||
\(247\) | −4698.86 | −1.21045 | ||||||||
\(248\) | 323.057i | 0.0827183i | ||||||||
\(249\) | − 4452.88i | − 1.13329i | ||||||||
\(250\) | 157.613i | 0.0398734i | ||||||||
\(251\) | −691.360 | −0.173858 | −0.0869288 | − | 0.996215i | \(-0.527705\pi\) | ||||
−0.0869288 | + | 0.996215i | \(0.527705\pi\) | |||||||
\(252\) | 162.190i | 0.0405436i | ||||||||
\(253\) | 3815.01 | 0.948014 | ||||||||
\(254\) | −9566.37 | −2.36318 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8332.94 | −2.03441 | ||||||||
\(257\) | 2900.44 | 0.703986 | 0.351993 | − | 0.936003i | \(-0.385504\pi\) | ||||
0.351993 | + | 0.936003i | \(0.385504\pi\) | |||||||
\(258\) | 12521.6i | 3.02156i | ||||||||
\(259\) | −198.357 | −0.0475880 | ||||||||
\(260\) | 12376.0i | 2.95202i | ||||||||
\(261\) | 1242.01i | 0.294554i | ||||||||
\(262\) | 8249.27i | 1.94520i | ||||||||
\(263\) | 5458.82 | 1.27987 | 0.639934 | − | 0.768430i | \(-0.278962\pi\) | ||||
0.639934 | + | 0.768430i | \(0.278962\pi\) | |||||||
\(264\) | 12458.1 | 2.90434 | ||||||||
\(265\) | − 6271.30i | − 1.45375i | ||||||||
\(266\) | 395.493i | 0.0911626i | ||||||||
\(267\) | 8480.67i | 1.94385i | ||||||||
\(268\) | −2537.14 | −0.578286 | ||||||||
\(269\) | − 1028.77i | − 0.233179i | −0.993180 | − | 0.116590i | \(-0.962804\pi\) | ||||
0.993180 | − | 0.116590i | \(-0.0371962\pi\) | |||||||
\(270\) | −7263.14 | −1.63711 | ||||||||
\(271\) | −4117.13 | −0.922869 | −0.461435 | − | 0.887174i | \(-0.652665\pi\) | ||||
−0.461435 | + | 0.887174i | \(0.652665\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 231.254 | 0.0512679 | ||||||||
\(274\) | −13575.4 | −2.99314 | ||||||||
\(275\) | 5575.36i | 1.22257i | ||||||||
\(276\) | −8859.32 | −1.93213 | ||||||||
\(277\) | − 5787.84i | − 1.25544i | −0.778438 | − | 0.627721i | \(-0.783988\pi\) | ||||
0.778438 | − | 0.627721i | \(-0.216012\pi\) | |||||||
\(278\) | 6136.35i | 1.32386i | ||||||||
\(279\) | − 89.9040i | − 0.0192918i | ||||||||
\(280\) | 545.950 | 0.116524 | ||||||||
\(281\) | −2012.48 | −0.427240 | −0.213620 | − | 0.976917i | \(-0.568525\pi\) | ||||
−0.213620 | + | 0.976917i | \(0.568525\pi\) | |||||||
\(282\) | 9485.43i | 2.00301i | ||||||||
\(283\) | 558.874i | 0.117391i | 0.998276 | + | 0.0586954i | \(0.0186941\pi\) | ||||
−0.998276 | + | 0.0586954i | \(0.981306\pi\) | |||||||
\(284\) | 7306.87i | 1.52670i | ||||||||
\(285\) | 9911.84 | 2.06009 | ||||||||
\(286\) | − 10555.9i | − 2.18245i | ||||||||
\(287\) | −206.112 | −0.0423917 | ||||||||
\(288\) | −829.198 | −0.169656 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 7976.79 | 1.61522 | ||||||||
\(291\) | 8783.10 | 1.76933 | ||||||||
\(292\) | 8301.65i | 1.66376i | ||||||||
\(293\) | 2860.10 | 0.570268 | 0.285134 | − | 0.958488i | \(-0.407962\pi\) | ||||
0.285134 | + | 0.958488i | \(0.407962\pi\) | |||||||
\(294\) | 10679.3i | 2.11846i | ||||||||
\(295\) | 9098.52i | 1.79572i | ||||||||
\(296\) | − 11020.1i | − 2.16395i | ||||||||
\(297\) | 4197.46 | 0.820072 | ||||||||
\(298\) | 11544.7 | 2.24419 | ||||||||
\(299\) | 3934.30i | 0.760958i | ||||||||
\(300\) | − 12947.3i | − 2.49170i | ||||||||
\(301\) | − 317.119i | − 0.0607257i | ||||||||
\(302\) | −5757.70 | −1.09708 | ||||||||
\(303\) | 947.151i | 0.179579i | ||||||||
\(304\) | −8454.76 | −1.59511 | ||||||||
\(305\) | 1988.29 | 0.373276 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4297.16 | −0.798867 | −0.399433 | − | 0.916762i | \(-0.630793\pi\) | ||||
−0.399433 | + | 0.916762i | \(0.630793\pi\) | |||||||
\(308\) | −601.989 | −0.111368 | ||||||||
\(309\) | − 4303.58i | − 0.792304i | ||||||||
\(310\) | −577.406 | −0.105789 | ||||||||
\(311\) | 2989.87i | 0.545145i | 0.962135 | + | 0.272572i | \(0.0878744\pi\) | ||||
−0.962135 | + | 0.272572i | \(0.912126\pi\) | |||||||
\(312\) | 12847.7i | 2.33128i | ||||||||
\(313\) | 3932.78i | 0.710204i | 0.934828 | + | 0.355102i | \(0.115554\pi\) | ||||
−0.934828 | + | 0.355102i | \(0.884446\pi\) | |||||||
\(314\) | −16072.6 | −2.88863 | ||||||||
\(315\) | −151.933 | −0.0271761 | ||||||||
\(316\) | 1214.00i | 0.216116i | ||||||||
\(317\) | 10623.2i | 1.88221i | 0.338120 | + | 0.941103i | \(0.390209\pi\) | ||||
−0.338120 | + | 0.941103i | \(0.609791\pi\) | |||||||
\(318\) | − 12421.6i | − 2.19047i | ||||||||
\(319\) | −4609.89 | −0.809105 | ||||||||
\(320\) | − 5271.65i | − 0.920920i | ||||||||
\(321\) | 2861.51 | 0.497550 | ||||||||
\(322\) | 331.142 | 0.0573100 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −15291.0 | −2.62192 | ||||||||
\(325\) | −5749.70 | −0.981341 | ||||||||
\(326\) | − 4892.67i | − 0.831226i | ||||||||
\(327\) | −8024.41 | −1.35704 | ||||||||
\(328\) | − 11450.9i | − 1.92766i | ||||||||
\(329\) | − 240.225i | − 0.0402555i | ||||||||
\(330\) | 22266.7i | 3.71437i | ||||||||
\(331\) | 7246.73 | 1.20337 | 0.601687 | − | 0.798732i | \(-0.294496\pi\) | ||||
0.601687 | + | 0.798732i | \(0.294496\pi\) | |||||||
\(332\) | −11954.0 | −1.97608 | ||||||||
\(333\) | 3066.79i | 0.504682i | ||||||||
\(334\) | 182.309i | 0.0298667i | ||||||||
\(335\) | − 2376.70i | − 0.387621i | ||||||||
\(336\) | 416.100 | 0.0675599 | ||||||||
\(337\) | 4128.94i | 0.667411i | 0.942677 | + | 0.333706i | \(0.108299\pi\) | ||||
−0.942677 | + | 0.333706i | \(0.891701\pi\) | |||||||
\(338\) | −57.4084 | −0.00923847 | ||||||||
\(339\) | 11820.4 | 1.89379 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 333.691 | 0.0529923 | ||||||||
\(342\) | 6114.71 | 0.966800 | ||||||||
\(343\) | − 541.412i | − 0.0852289i | ||||||||
\(344\) | 17618.1 | 2.76135 | ||||||||
\(345\) | − 8299.07i | − 1.29509i | ||||||||
\(346\) | − 14079.3i | − 2.18759i | ||||||||
\(347\) | − 6293.09i | − 0.973575i | −0.873520 | − | 0.486788i | \(-0.838169\pi\) | ||||
0.873520 | − | 0.486788i | \(-0.161831\pi\) | |||||||
\(348\) | 10705.2 | 1.64902 | ||||||||
\(349\) | 6188.65 | 0.949201 | 0.474600 | − | 0.880201i | \(-0.342593\pi\) | ||||
0.474600 | + | 0.880201i | \(0.342593\pi\) | |||||||
\(350\) | 483.940i | 0.0739077i | ||||||||
\(351\) | 4328.72i | 0.658261i | ||||||||
\(352\) | − 3077.68i | − 0.466025i | ||||||||
\(353\) | −1116.16 | −0.168292 | −0.0841460 | − | 0.996453i | \(-0.526816\pi\) | ||||
−0.0841460 | + | 0.996453i | \(0.526816\pi\) | |||||||
\(354\) | 18021.5i | 2.70574i | ||||||||
\(355\) | −6844.80 | −1.02334 | ||||||||
\(356\) | 22766.8 | 3.38943 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5821.68 | 0.859457 | ||||||||
\(359\) | −78.6313 | −0.0115599 | −0.00577995 | − | 0.999983i | \(-0.501840\pi\) | ||||
−0.00577995 | + | 0.999983i | \(0.501840\pi\) | |||||||
\(360\) | − 8440.91i | − 1.23576i | ||||||||
\(361\) | 3243.74 | 0.472917 | ||||||||
\(362\) | − 14304.9i | − 2.07694i | ||||||||
\(363\) | − 4533.42i | − 0.655490i | ||||||||
\(364\) | − 620.813i | − 0.0893940i | ||||||||
\(365\) | −7776.68 | −1.11520 | ||||||||
\(366\) | 3938.22 | 0.562443 | ||||||||
\(367\) | − 6974.49i | − 0.992004i | −0.868321 | − | 0.496002i | \(-0.834801\pi\) | ||||
0.868321 | − | 0.496002i | \(-0.165199\pi\) | |||||||
\(368\) | 7079.07i | 1.00278i | ||||||||
\(369\) | 3186.69i | 0.449574i | ||||||||
\(370\) | 19696.4 | 2.76747 | ||||||||
\(371\) | 314.586i | 0.0440229i | ||||||||
\(372\) | −774.906 | −0.108003 | ||||||||
\(373\) | 32.5559 | 0.00451925 | 0.00225963 | − | 0.999997i | \(-0.499281\pi\) | ||||
0.00225963 | + | 0.999997i | \(0.499281\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −198.148 | −0.0272862 | ||||||||
\(376\) | 13346.1 | 1.83052 | ||||||||
\(377\) | − 4754.04i | − 0.649458i | ||||||||
\(378\) | 364.339 | 0.0495756 | ||||||||
\(379\) | 5407.85i | 0.732935i | 0.930431 | + | 0.366468i | \(0.119433\pi\) | ||||
−0.930431 | + | 0.366468i | \(0.880567\pi\) | |||||||
\(380\) | − 26608.8i | − 3.59212i | ||||||||
\(381\) | − 12026.6i | − 1.61717i | ||||||||
\(382\) | −8103.97 | −1.08543 | ||||||||
\(383\) | −2705.02 | −0.360889 | −0.180444 | − | 0.983585i | \(-0.557754\pi\) | ||||
−0.180444 | + | 0.983585i | \(0.557754\pi\) | |||||||
\(384\) | − 13842.8i | − 1.83961i | ||||||||
\(385\) | − 563.920i | − 0.0746494i | ||||||||
\(386\) | − 3966.74i | − 0.523061i | ||||||||
\(387\) | −4902.96 | −0.644009 | ||||||||
\(388\) | − 23578.6i | − 3.08511i | ||||||||
\(389\) | 392.912 | 0.0512119 | 0.0256059 | − | 0.999672i | \(-0.491848\pi\) | ||||
0.0256059 | + | 0.999672i | \(0.491848\pi\) | |||||||
\(390\) | −22963.0 | −2.98147 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 15025.8 | 1.93602 | ||||||||
\(393\) | −10370.8 | −1.33114 | ||||||||
\(394\) | − 4867.85i | − 0.622433i | ||||||||
\(395\) | −1137.23 | −0.144861 | ||||||||
\(396\) | 9307.32i | 1.18109i | ||||||||
\(397\) | 11750.1i | 1.48544i | 0.669601 | + | 0.742721i | \(0.266465\pi\) | ||||
−0.669601 | + | 0.742721i | \(0.733535\pi\) | |||||||
\(398\) | − 3544.98i | − 0.446467i | ||||||||
\(399\) | −497.206 | −0.0623845 | ||||||||
\(400\) | −10345.6 | −1.29319 | ||||||||
\(401\) | 2918.07i | 0.363395i | 0.983354 | + | 0.181697i | \(0.0581591\pi\) | ||||
−0.983354 | + | 0.181697i | \(0.941841\pi\) | |||||||
\(402\) | − 4707.54i | − 0.584057i | ||||||||
\(403\) | 344.125i | 0.0425362i | ||||||||
\(404\) | 2542.67 | 0.313125 | ||||||||
\(405\) | − 14324.0i | − 1.75745i | ||||||||
\(406\) | −400.138 | −0.0489126 | ||||||||
\(407\) | −11382.8 | −1.38630 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5650.88 | 0.683174 | 0.341587 | − | 0.939850i | \(-0.389036\pi\) | ||||
0.341587 | + | 0.939850i | \(0.389036\pi\) | |||||||
\(410\) | 20466.5 | 2.46528 | ||||||||
\(411\) | − 17066.7i | − 2.04827i | ||||||||
\(412\) | −11553.2 | −1.38151 | ||||||||
\(413\) | − 456.407i | − 0.0543785i | ||||||||
\(414\) | − 5119.78i | − 0.607786i | ||||||||
\(415\) | − 11198.0i | − 1.32455i | ||||||||
\(416\) | 3173.92 | 0.374072 | ||||||||
\(417\) | −7714.48 | −0.905947 | ||||||||
\(418\) | 22695.5i | 2.65568i | ||||||||
\(419\) | − 14806.3i | − 1.72633i | −0.504920 | − | 0.863166i | \(-0.668478\pi\) | ||||
0.504920 | − | 0.863166i | \(-0.331522\pi\) | |||||||
\(420\) | 1309.55i | 0.152142i | ||||||||
\(421\) | 3314.27 | 0.383676 | 0.191838 | − | 0.981427i | \(-0.438555\pi\) | ||||
0.191838 | + | 0.981427i | \(0.438555\pi\) | |||||||
\(422\) | 18380.9i | 2.12030i | ||||||||
\(423\) | −3714.12 | −0.426918 | ||||||||
\(424\) | −17477.4 | −2.00183 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −13557.5 | −1.54193 | ||||||||
\(427\) | −99.7383 | −0.0113037 | ||||||||
\(428\) | − 7681.85i | − 0.867561i | ||||||||
\(429\) | 13270.6 | 1.49350 | ||||||||
\(430\) | 31489.1i | 3.53149i | ||||||||
\(431\) | − 12204.2i | − 1.36394i | −0.731381 | − | 0.681969i | \(-0.761124\pi\) | ||||
0.731381 | − | 0.681969i | \(-0.238876\pi\) | |||||||
\(432\) | 7788.75i | 0.867446i | ||||||||
\(433\) | −423.908 | −0.0470479 | −0.0235239 | − | 0.999723i | \(-0.507489\pi\) | ||||
−0.0235239 | + | 0.999723i | \(0.507489\pi\) | |||||||
\(434\) | 28.9643 | 0.00320353 | ||||||||
\(435\) | 10028.2i | 1.10533i | ||||||||
\(436\) | 21541.9i | 2.36622i | ||||||||
\(437\) | − 8458.91i | − 0.925960i | ||||||||
\(438\) | −15403.3 | −1.68036 | ||||||||
\(439\) | 14528.7i | 1.57953i | 0.613407 | + | 0.789767i | \(0.289799\pi\) | ||||
−0.613407 | + | 0.789767i | \(0.710201\pi\) | |||||||
\(440\) | 31329.5 | 3.39449 | ||||||||
\(441\) | −4181.57 | −0.451524 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15763.6 | 1.69063 | 0.845317 | − | 0.534265i | \(-0.179411\pi\) | ||||
0.845317 | + | 0.534265i | \(0.179411\pi\) | |||||||
\(444\) | 26433.4 | 2.82539 | ||||||||
\(445\) | 21327.1i | 2.27191i | ||||||||
\(446\) | 8598.09 | 0.912850 | ||||||||
\(447\) | 14513.8i | 1.53575i | ||||||||
\(448\) | 264.441i | 0.0278876i | ||||||||
\(449\) | 5204.32i | 0.547009i | 0.961871 | + | 0.273504i | \(0.0881828\pi\) | ||||
−0.961871 | + | 0.273504i | \(0.911817\pi\) | |||||||
\(450\) | 7482.18 | 0.783808 | ||||||||
\(451\) | −11827.8 | −1.23492 | ||||||||
\(452\) | − 31732.4i | − 3.30213i | ||||||||
\(453\) | − 7238.45i | − 0.750755i | ||||||||
\(454\) | 10683.1i | 1.10436i | ||||||||
\(455\) | 581.554 | 0.0599201 | ||||||||
\(456\) | − 27623.1i | − 2.83678i | ||||||||
\(457\) | 4156.78 | 0.425484 | 0.212742 | − | 0.977108i | \(-0.431761\pi\) | ||||
0.212742 | + | 0.977108i | \(0.431761\pi\) | |||||||
\(458\) | −25314.8 | −2.58272 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −22279.3 | −2.25821 | ||||||||
\(461\) | −6715.13 | −0.678427 | −0.339214 | − | 0.940709i | \(-0.610161\pi\) | ||||
−0.339214 | + | 0.940709i | \(0.610161\pi\) | |||||||
\(462\) | − 1116.96i | − 0.112480i | ||||||||
\(463\) | −14587.2 | −1.46420 | −0.732098 | − | 0.681199i | \(-0.761459\pi\) | ||||
−0.732098 | + | 0.681199i | \(0.761459\pi\) | |||||||
\(464\) | − 8554.05i | − 0.855845i | ||||||||
\(465\) | − 725.902i | − 0.0723933i | ||||||||
\(466\) | − 16293.6i | − 1.61971i | ||||||||
\(467\) | 7011.17 | 0.694729 | 0.347364 | − | 0.937730i | \(-0.387077\pi\) | ||||
0.347364 | + | 0.937730i | \(0.387077\pi\) | |||||||
\(468\) | −9598.36 | −0.948043 | ||||||||
\(469\) | 119.222i | 0.0117381i | ||||||||
\(470\) | 23853.8i | 2.34105i | ||||||||
\(471\) | − 20206.1i | − 1.97675i | ||||||||
\(472\) | 25356.5 | 2.47272 | ||||||||
\(473\) | − 18198.0i | − 1.76902i | ||||||||
\(474\) | −2252.51 | −0.218273 | ||||||||
\(475\) | 12362.1 | 1.19413 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4863.80 | 0.466872 | ||||||||
\(478\) | −24435.5 | −2.33819 | ||||||||
\(479\) | 10914.1i | 1.04108i | 0.853837 | + | 0.520540i | \(0.174269\pi\) | ||||
−0.853837 | + | 0.520540i | \(0.825731\pi\) | |||||||
\(480\) | −6695.10 | −0.636642 | ||||||||
\(481\) | − 11738.7i | − 1.11276i | ||||||||
\(482\) | 2461.18i | 0.232580i | ||||||||
\(483\) | 416.305i | 0.0392185i | ||||||||
\(484\) | −12170.2 | −1.14295 | ||||||||
\(485\) | 22087.6 | 2.06793 | ||||||||
\(486\) | − 15918.8i | − 1.48579i | ||||||||
\(487\) | − 8144.98i | − 0.757873i | −0.925423 | − | 0.378937i | \(-0.876290\pi\) | ||||
0.925423 | − | 0.378937i | \(-0.123710\pi\) | |||||||
\(488\) | − 5541.13i | − 0.514007i | ||||||||
\(489\) | 6150.95 | 0.568826 | ||||||||
\(490\) | 26856.0i | 2.47598i | ||||||||
\(491\) | −3767.66 | −0.346297 | −0.173149 | − | 0.984896i | \(-0.555394\pi\) | ||||
−0.173149 | + | 0.984896i | \(0.555394\pi\) | |||||||
\(492\) | 27466.9 | 2.51688 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −23405.2 | −2.13168 | ||||||||
\(495\) | −8718.75 | −0.791674 | ||||||||
\(496\) | 619.192i | 0.0560535i | ||||||||
\(497\) | 343.354 | 0.0309890 | ||||||||
\(498\) | − 22180.0i | − 1.99580i | ||||||||
\(499\) | − 12922.1i | − 1.15926i | −0.814879 | − | 0.579631i | \(-0.803197\pi\) | ||||
0.814879 | − | 0.579631i | \(-0.196803\pi\) | |||||||
\(500\) | 531.938i | 0.0475780i | ||||||||
\(501\) | −229.194 | −0.0204384 | ||||||||
\(502\) | −3443.70 | −0.306175 | ||||||||
\(503\) | − 2856.34i | − 0.253196i | −0.991954 | − | 0.126598i | \(-0.959594\pi\) | ||||
0.991954 | − | 0.126598i | \(-0.0404059\pi\) | |||||||
\(504\) | 423.419i | 0.0374218i | ||||||||
\(505\) | 2381.88i | 0.209886i | ||||||||
\(506\) | 19002.7 | 1.66951 | ||||||||
\(507\) | − 72.1726i | − 0.00632208i | ||||||||
\(508\) | −32286.1 | −2.81981 | ||||||||
\(509\) | −1841.34 | −0.160346 | −0.0801729 | − | 0.996781i | \(-0.525547\pi\) | ||||
−0.0801729 | + | 0.996781i | \(0.525547\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 390.100 | 0.0337710 | ||||||||
\(512\) | −23822.1 | −2.05625 | ||||||||
\(513\) | − 9306.92i | − 0.800995i | ||||||||
\(514\) | 14447.2 | 1.23976 | ||||||||
\(515\) | − 10822.6i | − 0.926018i | ||||||||
\(516\) | 42259.9i | 3.60540i | ||||||||
\(517\) | − 13785.4i | − 1.17269i | ||||||||
\(518\) | −988.025 | −0.0838056 | ||||||||
\(519\) | 17700.2 | 1.49702 | ||||||||
\(520\) | 32309.2i | 2.72472i | ||||||||
\(521\) | − 15200.3i | − 1.27819i | −0.769127 | − | 0.639096i | \(-0.779309\pi\) | ||||
0.769127 | − | 0.639096i | \(-0.220691\pi\) | |||||||
\(522\) | 6186.52i | 0.518729i | ||||||||
\(523\) | −20391.5 | −1.70489 | −0.852444 | − | 0.522818i | \(-0.824881\pi\) | ||||
−0.852444 | + | 0.522818i | \(0.824881\pi\) | |||||||
\(524\) | 27840.9i | 2.32106i | ||||||||
\(525\) | −608.399 | −0.0505766 | ||||||||
\(526\) | 27190.6 | 2.25393 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 23878.1 | 1.96811 | ||||||||
\(529\) | 5084.45 | 0.417889 | ||||||||
\(530\) | − 31237.6i | − 2.56014i | ||||||||
\(531\) | −7056.49 | −0.576696 | ||||||||
\(532\) | 1334.77i | 0.108778i | ||||||||
\(533\) | − 12197.7i | − 0.991258i | ||||||||
\(534\) | 42242.6i | 3.42325i | ||||||||
\(535\) | 7196.07 | 0.581520 | ||||||||
\(536\) | −6623.58 | −0.533759 | ||||||||
\(537\) | 7318.89i | 0.588144i | ||||||||
\(538\) | − 5124.35i | − 0.410644i | ||||||||
\(539\) | − 15520.4i | − 1.24028i | ||||||||
\(540\) | −24512.8 | −1.95345 | ||||||||
\(541\) | − 14367.0i | − 1.14175i | −0.821038 | − | 0.570874i | \(-0.806604\pi\) | ||||
0.821038 | − | 0.570874i | \(-0.193396\pi\) | |||||||
\(542\) | −20507.6 | −1.62523 | ||||||||
\(543\) | 17983.9 | 1.42129 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20179.6 | −1.58606 | ||||||||
\(546\) | 1151.89 | 0.0902861 | ||||||||
\(547\) | 18943.7i | 1.48076i | 0.672190 | + | 0.740378i | \(0.265354\pi\) | ||||
−0.672190 | + | 0.740378i | \(0.734646\pi\) | |||||||
\(548\) | −45816.4 | −3.57150 | ||||||||
\(549\) | 1542.05i | 0.119878i | ||||||||
\(550\) | 27771.1i | 2.15303i | ||||||||
\(551\) | 10221.4i | 0.790283i | ||||||||
\(552\) | −23128.5 | −1.78336 | ||||||||
\(553\) | 57.0465 | 0.00438673 | ||||||||
\(554\) | − 28829.5i | − 2.21092i | ||||||||
\(555\) | 24761.8i | 1.89384i | ||||||||
\(556\) | 20709.9i | 1.57967i | ||||||||
\(557\) | −23122.6 | −1.75895 | −0.879477 | − | 0.475941i | \(-0.842108\pi\) | ||||
−0.879477 | + | 0.475941i | \(0.842108\pi\) | |||||||
\(558\) | − 447.816i | − 0.0339741i | ||||||||
\(559\) | 18767.0 | 1.41997 | ||||||||
\(560\) | 1046.40 | 0.0789617 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10024.3 | −0.752398 | ||||||||
\(563\) | 13150.5 | 0.984416 | 0.492208 | − | 0.870478i | \(-0.336190\pi\) | ||||
0.492208 | + | 0.870478i | \(0.336190\pi\) | |||||||
\(564\) | 32012.9i | 2.39005i | ||||||||
\(565\) | 29725.7 | 2.21340 | ||||||||
\(566\) | 2783.77i | 0.206733i | ||||||||
\(567\) | 718.534i | 0.0532197i | ||||||||
\(568\) | 19075.6i | 1.40915i | ||||||||
\(569\) | 15690.7 | 1.15605 | 0.578023 | − | 0.816021i | \(-0.303824\pi\) | ||||
0.578023 | + | 0.816021i | \(0.303824\pi\) | |||||||
\(570\) | 49371.3 | 3.62796 | ||||||||
\(571\) | 18135.9i | 1.32918i | 0.747207 | + | 0.664592i | \(0.231394\pi\) | ||||
−0.747207 | + | 0.664592i | \(0.768606\pi\) | |||||||
\(572\) | − 35625.6i | − 2.60416i | ||||||||
\(573\) | − 10188.1i | − 0.742785i | ||||||||
\(574\) | −1026.65 | −0.0746546 | ||||||||
\(575\) | − 10350.6i | − 0.750698i | ||||||||
\(576\) | 4088.51 | 0.295754 | ||||||||
\(577\) | −15740.7 | −1.13569 | −0.567847 | − | 0.823134i | \(-0.692223\pi\) | ||||
−0.567847 | + | 0.823134i | \(0.692223\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4986.89 | 0.357942 | ||||||||
\(580\) | 26921.3 | 1.92732 | ||||||||
\(581\) | 561.724i | 0.0401106i | ||||||||
\(582\) | 43749.0 | 3.11590 | ||||||||
\(583\) | 18052.6i | 1.28244i | ||||||||
\(584\) | 21672.7i | 1.53565i | ||||||||
\(585\) | − 8991.38i | − 0.635466i | ||||||||
\(586\) | 14246.3 | 1.00428 | ||||||||
\(587\) | 9153.33 | 0.643609 | 0.321804 | − | 0.946806i | \(-0.395711\pi\) | ||||
0.321804 | + | 0.946806i | \(0.395711\pi\) | |||||||
\(588\) | 36042.0i | 2.52780i | ||||||||
\(589\) | − 739.883i | − 0.0517595i | ||||||||
\(590\) | 45320.1i | 3.16237i | ||||||||
\(591\) | 6119.75 | 0.425944 | ||||||||
\(592\) | − 21121.7i | − 1.46638i | ||||||||
\(593\) | 3898.87 | 0.269995 | 0.134998 | − | 0.990846i | \(-0.456897\pi\) | ||||
0.134998 | + | 0.990846i | \(0.456897\pi\) | |||||||
\(594\) | 20907.7 | 1.44420 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 38963.0 | 2.67783 | ||||||||
\(597\) | 4456.68 | 0.305527 | ||||||||
\(598\) | 19596.9i | 1.34010i | ||||||||
\(599\) | −11841.6 | −0.807740 | −0.403870 | − | 0.914816i | \(-0.632335\pi\) | ||||
−0.403870 | + | 0.914816i | \(0.632335\pi\) | |||||||
\(600\) | − 33800.6i | − 2.29984i | ||||||||
\(601\) | 17152.8i | 1.16419i | 0.813122 | + | 0.582093i | \(0.197766\pi\) | ||||
−0.813122 | + | 0.582093i | \(0.802234\pi\) | |||||||
\(602\) | − 1579.58i | − 0.106942i | ||||||||
\(603\) | 1843.29 | 0.124485 | ||||||||
\(604\) | −19432.0 | −1.30907 | ||||||||
\(605\) | − 11400.6i | − 0.766114i | ||||||||
\(606\) | 4717.80i | 0.316250i | ||||||||
\(607\) | 10576.6i | 0.707234i | 0.935390 | + | 0.353617i | \(0.115048\pi\) | ||||
−0.935390 | + | 0.353617i | \(0.884952\pi\) | |||||||
\(608\) | −6824.05 | −0.455184 | ||||||||
\(609\) | − 503.045i | − 0.0334719i | ||||||||
\(610\) | 9903.77 | 0.657364 | ||||||||
\(611\) | 14216.5 | 0.941306 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16518.7 | 1.08839 | 0.544196 | − | 0.838958i | \(-0.316835\pi\) | ||||
0.544196 | + | 0.838958i | \(0.316835\pi\) | |||||||
\(614\) | −21404.4 | −1.40686 | ||||||||
\(615\) | 25730.0i | 1.68705i | ||||||||
\(616\) | −1571.58 | −0.102793 | ||||||||
\(617\) | − 14629.4i | − 0.954547i | −0.878755 | − | 0.477274i | \(-0.841625\pi\) | ||||
0.878755 | − | 0.477274i | \(-0.158375\pi\) | |||||||
\(618\) | − 21436.3i | − 1.39530i | ||||||||
\(619\) | 19584.0i | 1.27164i | 0.771836 | + | 0.635822i | \(0.219339\pi\) | ||||
−0.771836 | + | 0.635822i | \(0.780661\pi\) | |||||||
\(620\) | −1948.72 | −0.126230 | ||||||||
\(621\) | −7792.57 | −0.503551 | ||||||||
\(622\) | 14892.7i | 0.960035i | ||||||||
\(623\) | − 1069.82i | − 0.0687987i | ||||||||
\(624\) | 24624.7i | 1.57977i | ||||||||
\(625\) | −15872.1 | −1.01582 | ||||||||
\(626\) | 19589.3i | 1.25072i | ||||||||
\(627\) | −28532.3 | −1.81734 | ||||||||
\(628\) | −54244.3 | −3.44679 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −756.786 | −0.0478588 | ||||||||
\(631\) | −28856.7 | −1.82055 | −0.910276 | − | 0.414002i | \(-0.864131\pi\) | ||||
−0.910276 | + | 0.414002i | \(0.864131\pi\) | |||||||
\(632\) | 3169.31i | 0.199476i | ||||||||
\(633\) | −23108.0 | −1.45097 | ||||||||
\(634\) | 52914.7i | 3.31469i | ||||||||
\(635\) | − 30244.4i | − 1.89010i | ||||||||
\(636\) | − 41922.3i | − 2.61372i | ||||||||
\(637\) | 16005.8 | 0.995559 | ||||||||
\(638\) | −22962.1 | −1.42489 | ||||||||
\(639\) | − 5308.58i | − 0.328645i | ||||||||
\(640\) | − 34811.6i | − 2.15008i | ||||||||
\(641\) | 9419.79i | 0.580436i | 0.956961 | + | 0.290218i | \(0.0937278\pi\) | ||||
−0.956961 | + | 0.290218i | \(0.906272\pi\) | |||||||
\(642\) | 14253.3 | 0.876218 | ||||||||
\(643\) | − 2848.83i | − 0.174723i | −0.996177 | − | 0.0873615i | \(-0.972156\pi\) | ||||
0.996177 | − | 0.0873615i | \(-0.0278435\pi\) | |||||||
\(644\) | 1117.59 | 0.0683839 | ||||||||
\(645\) | −39587.4 | −2.41667 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6881.30 | −0.418132 | −0.209066 | − | 0.977901i | \(-0.567042\pi\) | ||||
−0.209066 | + | 0.977901i | \(0.567042\pi\) | |||||||
\(648\) | −39919.4 | −2.42003 | ||||||||
\(649\) | − 26191.1i | − 1.58411i | ||||||||
\(650\) | −28639.5 | −1.72821 | ||||||||
\(651\) | 36.4133i | 0.00219224i | ||||||||
\(652\) | − 16512.5i | − 0.991841i | ||||||||
\(653\) | − 10521.5i | − 0.630534i | −0.949003 | − | 0.315267i | \(-0.897906\pi\) | ||||
0.949003 | − | 0.315267i | \(-0.102094\pi\) | |||||||
\(654\) | −39969.9 | −2.38983 | ||||||||
\(655\) | −26080.3 | −1.55579 | ||||||||
\(656\) | − 21947.6i | − 1.30626i | ||||||||
\(657\) | − 6031.32i | − 0.358149i | ||||||||
\(658\) | − 1196.57i | − 0.0708925i | ||||||||
\(659\) | 26606.5 | 1.57275 | 0.786374 | − | 0.617751i | \(-0.211956\pi\) | ||||
0.786374 | + | 0.617751i | \(0.211956\pi\) | |||||||
\(660\) | 75149.1i | 4.43208i | ||||||||
\(661\) | 15511.7 | 0.912758 | 0.456379 | − | 0.889785i | \(-0.349146\pi\) | ||||
0.456379 | + | 0.889785i | \(0.349146\pi\) | |||||||
\(662\) | 36096.3 | 2.11922 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −31207.6 | −1.82393 | ||||||||
\(665\) | −1250.36 | −0.0729128 | ||||||||
\(666\) | 15275.8i | 0.888777i | ||||||||
\(667\) | 8558.25 | 0.496817 | ||||||||
\(668\) | 615.284i | 0.0356378i | ||||||||
\(669\) | 10809.3i | 0.624683i | ||||||||
\(670\) | − 11838.5i | − 0.682626i | ||||||||
\(671\) | −5723.52 | −0.329291 | ||||||||
\(672\) | 335.845 | 0.0192790 | ||||||||
\(673\) | 5711.21i | 0.327119i | 0.986533 | + | 0.163559i | \(0.0522975\pi\) | ||||
−0.986533 | + | 0.163559i | \(0.947702\pi\) | |||||||
\(674\) | 20566.4i | 1.17535i | ||||||||
\(675\) | − 11388.3i | − 0.649386i | ||||||||
\(676\) | −193.751 | −0.0110236 | ||||||||
\(677\) | 398.222i | 0.0226070i | 0.999936 | + | 0.0113035i | \(0.00359809\pi\) | ||||
−0.999936 | + | 0.0113035i | \(0.996402\pi\) | |||||||
\(678\) | 58877.8 | 3.33509 | ||||||||
\(679\) | −1107.97 | −0.0626217 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13430.5 | −0.755740 | ||||||||
\(682\) | 1662.13 | 0.0933228 | ||||||||
\(683\) | − 6504.72i | − 0.364416i | −0.983260 | − | 0.182208i | \(-0.941676\pi\) | ||||
0.983260 | − | 0.182208i | \(-0.0583244\pi\) | |||||||
\(684\) | 20636.9 | 1.15361 | ||||||||
\(685\) | − 42919.1i | − 2.39395i | ||||||||
\(686\) | − 2696.80i | − 0.150094i | ||||||||
\(687\) | − 31825.2i | − 1.76741i | ||||||||
\(688\) | 33767.9 | 1.87121 | ||||||||
\(689\) | −18617.1 | −1.02940 | ||||||||
\(690\) | − 41338.0i | − 2.28074i | ||||||||
\(691\) | − 7641.66i | − 0.420698i | −0.977626 | − | 0.210349i | \(-0.932540\pi\) | ||||
0.977626 | − | 0.210349i | \(-0.0674601\pi\) | |||||||
\(692\) | − 47516.9i | − 2.61029i | ||||||||
\(693\) | 437.357 | 0.0239737 | ||||||||
\(694\) | − 31346.1i | − 1.71453i | ||||||||
\(695\) | −19400.2 | −1.05884 | ||||||||
\(696\) | 27947.5 | 1.52205 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 30826.0 | 1.67160 | ||||||||
\(699\) | 20484.0 | 1.10840 | ||||||||
\(700\) | 1633.28i | 0.0881887i | ||||||||
\(701\) | 27948.0 | 1.50582 | 0.752912 | − | 0.658122i | \(-0.228649\pi\) | ||||
0.752912 | + | 0.658122i | \(0.228649\pi\) | |||||||
\(702\) | 21561.5i | 1.15924i | ||||||||
\(703\) | 25238.7i | 1.35405i | ||||||||
\(704\) | 15175.0i | 0.812402i | ||||||||
\(705\) | −29988.5 | −1.60203 | ||||||||
\(706\) | −5559.63 | −0.296373 | ||||||||
\(707\) | − 119.482i | − 0.00635583i | ||||||||
\(708\) | 60821.7i | 3.22856i | ||||||||
\(709\) | 28431.5i | 1.50602i | 0.658009 | + | 0.753010i | \(0.271399\pi\) | ||||
−0.658009 | + | 0.753010i | \(0.728601\pi\) | |||||||
\(710\) | −34094.2 | −1.80216 | ||||||||
\(711\) | − 881.993i | − 0.0465223i | ||||||||
\(712\) | 59435.9 | 3.12845 | ||||||||
\(713\) | −619.495 | −0.0325390 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33372.7 | 1.74555 | ||||||||
\(716\) | 19647.9 | 1.02553 | ||||||||
\(717\) | − 30719.8i | − 1.60007i | ||||||||
\(718\) | −391.666 | −0.0203577 | ||||||||
\(719\) | 21104.4i | 1.09466i | 0.836917 | + | 0.547330i | \(0.184356\pi\) | ||||
−0.836917 | + | 0.547330i | \(0.815644\pi\) | |||||||
\(720\) | − 16178.4i | − 0.837406i | ||||||||
\(721\) | 542.890i | 0.0280420i | ||||||||
\(722\) | 16157.2 | 0.832838 | ||||||||
\(723\) | −3094.13 | −0.159159 | ||||||||
\(724\) | − 48278.5i | − 2.47826i | ||||||||
\(725\) | 12507.3i | 0.640701i | ||||||||
\(726\) | − 22581.2i | − 1.15436i | ||||||||
\(727\) | −7655.66 | −0.390554 | −0.195277 | − | 0.980748i | \(-0.562561\pi\) | ||||
−0.195277 | + | 0.980748i | \(0.562561\pi\) | |||||||
\(728\) | − 1620.72i | − 0.0825108i | ||||||||
\(729\) | −4546.28 | −0.230975 | ||||||||
\(730\) | −38736.0 | −1.96395 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 13291.3 | 0.671122 | ||||||||
\(733\) | −1921.12 | −0.0968052 | −0.0484026 | − | 0.998828i | \(-0.515413\pi\) | ||||
−0.0484026 | + | 0.998828i | \(0.515413\pi\) | |||||||
\(734\) | − 34740.2i | − 1.74698i | ||||||||
\(735\) | −33762.8 | −1.69437 | ||||||||
\(736\) | 5713.70i | 0.286154i | ||||||||
\(737\) | 6841.60i | 0.341945i | ||||||||
\(738\) | 15873.1i | 0.791728i | ||||||||
\(739\) | −24081.6 | −1.19872 | −0.599362 | − | 0.800478i | \(-0.704579\pi\) | ||||
−0.599362 | + | 0.800478i | \(0.704579\pi\) | |||||||
\(740\) | 66474.4 | 3.30222 | ||||||||
\(741\) | − 29424.5i | − 1.45875i | ||||||||
\(742\) | 1566.97i | 0.0775271i | ||||||||
\(743\) | − 17540.0i | − 0.866058i | −0.901380 | − | 0.433029i | \(-0.857445\pi\) | ||||
0.901380 | − | 0.433029i | \(-0.142555\pi\) | |||||||
\(744\) | −2023.00 | −0.0996866 | ||||||||
\(745\) | 36499.0i | 1.79493i | ||||||||
\(746\) | 162.163 | 0.00795870 | ||||||||
\(747\) | 8684.80 | 0.425382 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −360.975 | −0.0176098 | ||||||||
\(750\) | −986.984 | −0.0480528 | ||||||||
\(751\) | 21239.6i | 1.03202i | 0.856583 | + | 0.516009i | \(0.172583\pi\) | ||||
−0.856583 | + | 0.516009i | \(0.827417\pi\) | |||||||
\(752\) | 25580.0 | 1.24044 | ||||||||
\(753\) | − 4329.34i | − 0.209522i | ||||||||
\(754\) | − 23680.1i | − 1.14374i | ||||||||
\(755\) | − 18203.1i | − 0.877457i | ||||||||
\(756\) | 1229.63 | 0.0591550 | ||||||||
\(757\) | 22831.4 | 1.09620 | 0.548098 | − | 0.836414i | \(-0.315352\pi\) | ||||
0.548098 | + | 0.836414i | \(0.315352\pi\) | |||||||
\(758\) | 26936.7i | 1.29075i | ||||||||
\(759\) | 23889.8i | 1.14248i | ||||||||
\(760\) | − 69466.1i | − 3.31553i | ||||||||
\(761\) | −12398.1 | −0.590579 | −0.295289 | − | 0.955408i | \(-0.595416\pi\) | ||||
−0.295289 | + | 0.955408i | \(0.595416\pi\) | |||||||
\(762\) | − 59905.2i | − 2.84795i | ||||||||
\(763\) | 1012.27 | 0.0480295 | ||||||||
\(764\) | −27350.6 | −1.29517 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13473.8 | −0.635548 | ||||||||
\(767\) | 27010.1 | 1.27155 | ||||||||
\(768\) | − 52181.3i | − 2.45173i | ||||||||
\(769\) | −40338.4 | −1.89160 | −0.945800 | − | 0.324751i | \(-0.894720\pi\) | ||||
−0.945800 | + | 0.324751i | \(0.894720\pi\) | |||||||
\(770\) | − 2808.91i | − 0.131462i | ||||||||
\(771\) | 18162.7i | 0.848397i | ||||||||
\(772\) | − 13387.6i | − 0.624131i | ||||||||
\(773\) | 6385.94 | 0.297136 | 0.148568 | − | 0.988902i | \(-0.452534\pi\) | ||||
0.148568 | + | 0.988902i | \(0.452534\pi\) | |||||||
\(774\) | −24421.9 | −1.13414 | ||||||||
\(775\) | − 905.348i | − 0.0419626i | ||||||||
\(776\) | − 61555.4i | − 2.84756i | ||||||||
\(777\) | − 1242.12i | − 0.0573499i | ||||||||
\(778\) | 1957.11 | 0.0901874 | ||||||||
\(779\) | 26225.5i | 1.20620i | ||||||||
\(780\) | −77499.0 | −3.55758 | ||||||||
\(781\) | 19703.5 | 0.902749 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9416.22 | 0.429768 | ||||||||
\(784\) | 28799.5 | 1.31193 | ||||||||
\(785\) | − 50814.0i | − 2.31036i | ||||||||
\(786\) | −51657.4 | −2.34422 | ||||||||
\(787\) | 26132.8i | 1.18365i | 0.806066 | + | 0.591826i | \(0.201593\pi\) | ||||
−0.806066 | + | 0.591826i | \(0.798407\pi\) | |||||||
\(788\) | − 16428.8i | − 0.742704i | ||||||||
\(789\) | 34183.4i | 1.54241i | ||||||||
\(790\) | −5664.58 | −0.255110 | ||||||||
\(791\) | −1491.12 | −0.0670268 | ||||||||
\(792\) | 24298.1i | 1.09015i | ||||||||
\(793\) | − 5902.49i | − 0.264317i | ||||||||
\(794\) | 58527.8i | 2.61596i | ||||||||
\(795\) | 39271.3 | 1.75196 | ||||||||
\(796\) | − 11964.2i | − 0.532737i | ||||||||
\(797\) | −8629.21 | −0.383516 | −0.191758 | − | 0.981442i | \(-0.561419\pi\) | ||||
−0.191758 | + | 0.981442i | \(0.561419\pi\) | |||||||
\(798\) | −2476.60 | −0.109863 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −8350.16 | −0.369028 | ||||||||
\(801\) | −16540.5 | −0.729626 | ||||||||
\(802\) | 14535.0i | 0.639962i | ||||||||
\(803\) | 22386.0 | 0.983793 | ||||||||
\(804\) | − 15887.7i | − 0.696913i | ||||||||
\(805\) | 1046.92i | 0.0458372i | ||||||||
\(806\) | 1714.10i | 0.0749090i | ||||||||
\(807\) | 6442.22 | 0.281012 | ||||||||
\(808\) | 6638.01 | 0.289015 | ||||||||
\(809\) | 42653.7i | 1.85368i | 0.375460 | + | 0.926839i | \(0.377485\pi\) | ||||
−0.375460 | + | 0.926839i | \(0.622515\pi\) | |||||||
\(810\) | − 71348.7i | − 3.09498i | ||||||||
\(811\) | 45388.0i | 1.96521i | 0.185700 | + | 0.982607i | \(0.440545\pi\) | ||||
−0.185700 | + | 0.982607i | \(0.559455\pi\) | |||||||
\(812\) | −1350.45 | −0.0583639 | ||||||||
\(813\) | − 25781.7i | − 1.11218i | ||||||||
\(814\) | −56698.2 | −2.44136 | ||||||||
\(815\) | 15468.3 | 0.664824 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40349.9 | −1.72786 | ||||||||
\(818\) | 28147.3 | 1.20311 | ||||||||
\(819\) | 451.033i | 0.0192434i | ||||||||
\(820\) | 69073.4 | 2.94164 | ||||||||
\(821\) | − 16898.6i | − 0.718349i | −0.933270 | − | 0.359175i | \(-0.883058\pi\) | ||||
0.933270 | − | 0.359175i | \(-0.116942\pi\) | |||||||
\(822\) | − 85010.1i | − 3.60714i | ||||||||
\(823\) | 38258.3i | 1.62042i | 0.586143 | + | 0.810208i | \(0.300646\pi\) | ||||
−0.586143 | + | 0.810208i | \(0.699354\pi\) | |||||||
\(824\) | −30161.2 | −1.27514 | ||||||||
\(825\) | −34913.2 | −1.47336 | ||||||||
\(826\) | − 2273.38i | − 0.0957641i | ||||||||
\(827\) | 30489.3i | 1.28200i | 0.767540 | + | 0.641001i | \(0.221480\pi\) | ||||
−0.767540 | + | 0.641001i | \(0.778520\pi\) | |||||||
\(828\) | − 17279.0i | − 0.725226i | ||||||||
\(829\) | 44358.5 | 1.85843 | 0.929213 | − | 0.369545i | \(-0.120486\pi\) | ||||
0.929213 | + | 0.369545i | \(0.120486\pi\) | |||||||
\(830\) | − 55777.9i | − 2.33263i | ||||||||
\(831\) | 36243.8 | 1.51298 | ||||||||
\(832\) | −15649.6 | −0.652104 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −38426.2 | −1.59543 | ||||||||
\(835\) | −576.374 | −0.0238877 | ||||||||
\(836\) | 76596.4i | 3.16883i | ||||||||
\(837\) | −681.600 | −0.0281476 | ||||||||
\(838\) | − 73750.6i | − 3.04018i | ||||||||
\(839\) | 20819.6i | 0.856702i | 0.903612 | + | 0.428351i | \(0.140905\pi\) | ||||
−0.903612 | + | 0.428351i | \(0.859095\pi\) | |||||||
\(840\) | 3418.77i | 0.140427i | ||||||||
\(841\) | 14047.6 | 0.575980 | ||||||||
\(842\) | 16508.5 | 0.675678 | ||||||||
\(843\) | − 12602.3i | − 0.514882i | ||||||||
\(844\) | 62034.6i | 2.53000i | ||||||||
\(845\) | − 181.498i | − 0.00738903i | ||||||||
\(846\) | −18500.2 | −0.751831 | ||||||||
\(847\) | 571.884i | 0.0231997i | ||||||||
\(848\) | −33498.2 | −1.35653 | ||||||||
\(849\) | −3499.70 | −0.141472 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21132.1 | 0.851233 | ||||||||
\(852\) | −45756.0 | −1.83988 | ||||||||
\(853\) | 43406.9i | 1.74235i | 0.490973 | + | 0.871175i | \(0.336641\pi\) | ||||
−0.490973 | + | 0.871175i | \(0.663359\pi\) | |||||||
\(854\) | −496.801 | −0.0199065 | ||||||||
\(855\) | 19331.8i | 0.773257i | ||||||||
\(856\) | − 20054.6i | − 0.800760i | ||||||||
\(857\) | − 7893.90i | − 0.314645i | −0.987547 | − | 0.157322i | \(-0.949714\pi\) | ||||
0.987547 | − | 0.157322i | \(-0.0502862\pi\) | |||||||
\(858\) | 66101.5 | 2.63015 | ||||||||
\(859\) | 10441.9 | 0.414751 | 0.207376 | − | 0.978261i | \(-0.433508\pi\) | ||||
0.207376 | + | 0.978261i | \(0.433508\pi\) | |||||||
\(860\) | 106274.i | 4.21387i | ||||||||
\(861\) | − 1290.69i | − 0.0510877i | ||||||||
\(862\) | − 60789.9i | − 2.40198i | ||||||||
\(863\) | 39784.6 | 1.56928 | 0.784638 | − | 0.619954i | \(-0.212849\pi\) | ||||
0.784638 | + | 0.619954i | \(0.212849\pi\) | |||||||
\(864\) | 6286.50i | 0.247536i | ||||||||
\(865\) | 44512.1 | 1.74966 | ||||||||
\(866\) | −2111.51 | −0.0828544 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 97.7532 | 0.00382253 | ||||||||
\(869\) | 3273.63 | 0.127791 | ||||||||
\(870\) | 49951.1i | 1.94655i | ||||||||
\(871\) | −7055.53 | −0.274475 | ||||||||
\(872\) | 56238.2i | 2.18402i | ||||||||
\(873\) | 17130.3i | 0.664117i | ||||||||
\(874\) | − 42134.2i | − 1.63068i | ||||||||
\(875\) | 24.9961 | 0.000965739 0 | ||||||||
\(876\) | −51985.4 | −2.00505 | ||||||||
\(877\) | − 11135.4i | − 0.428752i | −0.976751 | − | 0.214376i | \(-0.931228\pi\) | ||||
0.976751 | − | 0.214376i | \(-0.0687717\pi\) | |||||||
\(878\) | 72367.9i | 2.78166i | ||||||||
\(879\) | 17910.1i | 0.687250i | ||||||||
\(880\) | 60048.2 | 2.30025 | ||||||||
\(881\) | − 18890.9i | − 0.722416i | −0.932485 | − | 0.361208i | \(-0.882364\pi\) | ||||
0.932485 | − | 0.361208i | \(-0.117636\pi\) | |||||||
\(882\) | −20828.6 | −0.795164 | ||||||||
\(883\) | 36453.6 | 1.38931 | 0.694656 | − | 0.719342i | \(-0.255557\pi\) | ||||
0.694656 | + | 0.719342i | \(0.255557\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −56975.5 | −2.16408 | ||||||||
\(886\) | 78519.2 | 2.97732 | ||||||||
\(887\) | 23100.3i | 0.874446i | 0.899353 | + | 0.437223i | \(0.144038\pi\) | ||||
−0.899353 | + | 0.437223i | \(0.855962\pi\) | |||||||
\(888\) | 69008.2 | 2.60784 | ||||||||
\(889\) | 1517.14i | 0.0572366i | ||||||||
\(890\) | 106231.i | 4.00098i | ||||||||
\(891\) | 41233.3i | 1.55036i | ||||||||
\(892\) | 29018.2 | 1.08924 | ||||||||
\(893\) | −30566.0 | −1.14541 | ||||||||
\(894\) | 72293.8i | 2.70455i | ||||||||
\(895\) | 18405.4i | 0.687403i | ||||||||
\(896\) | 1746.25i | 0.0651093i | ||||||||
\(897\) | −24636.8 | −0.917057 | ||||||||
\(898\) | 25922.9i | 0.963318i | ||||||||
\(899\) | 748.572 | 0.0277712 | ||||||||
\(900\) | 25252.0 | 0.935260 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −58915.0 | −2.17478 | ||||||||
\(903\) | 1985.82 | 0.0731825 | ||||||||
\(904\) | − 82841.8i | − 3.04787i | ||||||||
\(905\) | 45225.5 | 1.66116 | ||||||||
\(906\) | − 36055.1i | − 1.32213i | ||||||||
\(907\) | − 25240.6i | − 0.924036i | −0.886871 | − | 0.462018i | \(-0.847126\pi\) | ||||
0.886871 | − | 0.462018i | \(-0.152874\pi\) | |||||||
\(908\) | 36054.9i | 1.31776i | ||||||||
\(909\) | −1847.30 | −0.0674050 | ||||||||
\(910\) | 2896.74 | 0.105523 | ||||||||
\(911\) | − 12331.2i | − 0.448465i | −0.974536 | − | 0.224232i | \(-0.928013\pi\) | ||||
0.974536 | − | 0.224232i | \(-0.0719874\pi\) | |||||||
\(912\) | − 52944.2i | − 1.92232i | ||||||||
\(913\) | 32234.8i | 1.16847i | ||||||||
\(914\) | 20705.1 | 0.749304 | ||||||||
\(915\) | 12450.8i | 0.449848i | ||||||||
\(916\) | −85436.4 | −3.08177 | ||||||||
\(917\) | 1308.26 | 0.0471130 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40235.8 | 1.44424 | 0.722121 | − | 0.691767i | \(-0.243168\pi\) | ||||
0.722121 | + | 0.691767i | \(0.243168\pi\) | |||||||
\(920\) | −58163.2 | −2.08433 | ||||||||
\(921\) | − 26909.1i | − 0.962741i | ||||||||
\(922\) | −33448.4 | −1.19475 | ||||||||
\(923\) | 20319.6i | 0.724625i | ||||||||
\(924\) | − 3769.69i | − 0.134214i | ||||||||
\(925\) | 30883.1i | 1.09776i | ||||||||
\(926\) | −72659.3 | −2.57855 | ||||||||
\(927\) | 8393.60 | 0.297392 | ||||||||
\(928\) | − 6904.19i | − 0.244225i | ||||||||
\(929\) | − 45692.0i | − 1.61368i | −0.590772 | − | 0.806838i | \(-0.701177\pi\) | ||||
0.590772 | − | 0.806838i | \(-0.298823\pi\) | |||||||
\(930\) | − 3615.75i | − 0.127489i | ||||||||
\(931\) | −34413.0 | −1.21143 | ||||||||
\(932\) | − 54990.2i | − 1.93269i | ||||||||
\(933\) | −18722.7 | −0.656972 | ||||||||
\(934\) | 34923.0 | 1.22346 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −25057.9 | −0.875045 | ||||||||
\(937\) | 3141.20 | 0.109518 | 0.0547590 | − | 0.998500i | \(-0.482561\pi\) | ||||
0.0547590 | + | 0.998500i | \(0.482561\pi\) | |||||||
\(938\) | 593.850i | 0.0206715i | ||||||||
\(939\) | −24627.3 | −0.855891 | ||||||||
\(940\) | 80505.5i | 2.79341i | ||||||||
\(941\) | 24333.2i | 0.842975i | 0.906834 | + | 0.421487i | \(0.138492\pi\) | ||||
−0.906834 | + | 0.421487i | \(0.861508\pi\) | |||||||
\(942\) | − 100648.i | − 3.48119i | ||||||||
\(943\) | 21958.3 | 0.758284 | ||||||||
\(944\) | 48599.8 | 1.67562 | ||||||||
\(945\) | 1151.87i | 0.0396511i | ||||||||
\(946\) | − 90645.0i | − 3.11535i | ||||||||
\(947\) | − 39879.6i | − 1.36844i | −0.729276 | − | 0.684220i | \(-0.760143\pi\) | ||||
0.729276 | − | 0.684220i | \(-0.239857\pi\) | |||||||
\(948\) | −7602.12 | −0.260449 | ||||||||
\(949\) | 23086.0i | 0.789678i | ||||||||
\(950\) | 61576.1 | 2.10294 | ||||||||
\(951\) | −66523.2 | −2.26831 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26021.7 | −0.884496 | −0.442248 | − | 0.896893i | \(-0.645819\pi\) | ||||
−0.442248 | + | 0.896893i | \(0.645819\pi\) | |||||||
\(954\) | 24226.8 | 0.822193 | ||||||||
\(955\) | − 25621.0i | − 0.868141i | ||||||||
\(956\) | −82468.8 | −2.78999 | ||||||||
\(957\) | − 28867.4i | − 0.975080i | ||||||||
\(958\) | 54363.6i | 1.83341i | ||||||||
\(959\) | 2152.94i | 0.0724944i | ||||||||
\(960\) | 33011.4 | 1.10983 | ||||||||
\(961\) | 29736.8 | 0.998181 | ||||||||
\(962\) | − 58471.1i | − 1.95965i | ||||||||
\(963\) | 5581.01i | 0.186756i | ||||||||
\(964\) | 8306.36i | 0.277520i | ||||||||
\(965\) | 12541.0 | 0.418350 | ||||||||
\(966\) | 2073.63i | 0.0690662i | ||||||||
\(967\) | −42806.0 | −1.42352 | −0.711762 | − | 0.702420i | \(-0.752103\pi\) | ||||
−0.711762 | + | 0.702420i | \(0.752103\pi\) | |||||||
\(968\) | −31772.0 | −1.05495 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 110019. | 3.64176 | ||||||||
\(971\) | 19147.5 | 0.632825 | 0.316413 | − | 0.948622i | \(-0.397522\pi\) | ||||
0.316413 | + | 0.948622i | \(0.397522\pi\) | |||||||
\(972\) | − 53725.3i | − 1.77288i | ||||||||
\(973\) | 973.170 | 0.0320641 | ||||||||
\(974\) | − 40570.5i | − 1.33466i | ||||||||
\(975\) | − 36004.9i | − 1.18265i | ||||||||
\(976\) | − 10620.5i | − 0.348313i | ||||||||
\(977\) | −8209.83 | −0.268839 | −0.134420 | − | 0.990925i | \(-0.542917\pi\) | ||||
−0.134420 | + | 0.990925i | \(0.542917\pi\) | |||||||
\(978\) | 30638.2 | 1.00174 | ||||||||
\(979\) | − 61392.3i | − 2.00419i | ||||||||
\(980\) | 90637.8i | 2.95441i | ||||||||
\(981\) | − 15650.6i | − 0.509364i | ||||||||
\(982\) | −18766.9 | −0.609852 | ||||||||
\(983\) | 35203.4i | 1.14223i | 0.820870 | + | 0.571116i | \(0.193489\pi\) | ||||
−0.820870 | + | 0.571116i | \(0.806511\pi\) | |||||||
\(984\) | 71706.3 | 2.32308 | ||||||||
\(985\) | 15389.9 | 0.497829 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1504.31 | 0.0485132 | ||||||||
\(988\) | −78991.6 | −2.54358 | ||||||||
\(989\) | 33784.5i | 1.08623i | ||||||||
\(990\) | −43428.5 | −1.39419 | ||||||||
\(991\) | − 5669.58i | − 0.181736i | −0.995863 | − | 0.0908678i | \(-0.971036\pi\) | ||||
0.995863 | − | 0.0908678i | \(-0.0289641\pi\) | |||||||
\(992\) | 499.765i | 0.0159955i | ||||||||
\(993\) | 45379.5i | 1.45023i | ||||||||
\(994\) | 1710.26 | 0.0545737 | ||||||||
\(995\) | 11207.6 | 0.357089 | ||||||||
\(996\) | − 74856.5i | − 2.38144i | ||||||||
\(997\) | 27125.7i | 0.861666i | 0.902432 | + | 0.430833i | \(0.141780\pi\) | ||||
−0.902432 | + | 0.430833i | \(0.858220\pi\) | |||||||
\(998\) | − 64365.4i | − 2.04153i | ||||||||
\(999\) | 23250.6 | 0.736353 |
(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 | 289.4.b.f.288.22 | 24 | ||
17.4 | even | 4 | 289.4.a.i.1.2 | yes | 12 | ||
17.13 | even | 4 | 289.4.a.h.1.2 | ✓ | 12 | ||
17.16 | even | 2 | inner | 289.4.b.f.288.21 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.4.a.h.1.2 | ✓ | 12 | 17.13 | even | 4 | ||
289.4.a.i.1.2 | yes | 12 | 17.4 | even | 4 | ||
289.4.b.f.288.21 | 24 | 17.16 | even | 2 | inner | ||
289.4.b.f.288.22 | 24 | 1.1 | even | 1 | trivial |