Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,3,Mod(1149,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.1149");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.c (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: | \(31.3352304014\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1149.18 | ||
Character | \(\chi\) | \(=\) | 1150.1149 |
Dual form | 1150.3.c.c.1149.17 |
$q$-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 \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | 3.36596i | 1.12199i | 0.827820 | + | 0.560993i | \(0.189581\pi\) | ||||
−0.827820 | + | 0.560993i | \(0.810419\pi\) | |||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.76019 | −0.793364 | ||||||||
\(7\) | −1.16919 | −0.167026 | −0.0835132 | − | 0.996507i | \(-0.526614\pi\) | ||||
−0.0835132 | + | 0.996507i | \(0.526614\pi\) | |||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −2.32968 | −0.258853 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.6148i | 0.964981i | 0.875901 | + | 0.482490i | \(0.160268\pi\) | ||||
−0.875901 | + | 0.482490i | \(0.839732\pi\) | |||||||
\(12\) | − | 6.73192i | − | 0.560993i | ||||||
\(13\) | 15.0913i | 1.16087i | 0.814306 | + | 0.580436i | \(0.197118\pi\) | ||||
−0.814306 | + | 0.580436i | \(0.802882\pi\) | |||||||
\(14\) | − | 1.65348i | − | 0.118106i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −20.0887 | −1.18169 | −0.590843 | − | 0.806787i | \(-0.701205\pi\) | ||||
−0.590843 | + | 0.806787i | \(0.701205\pi\) | |||||||
\(18\) | − | 3.29467i | − | 0.183037i | ||||||
\(19\) | − | 22.5221i | − | 1.18537i | −0.805434 | − | 0.592686i | \(-0.798068\pi\) | ||
0.805434 | − | 0.592686i | \(-0.201932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 3.93543i | − | 0.187401i | ||||||
\(22\) | −15.0116 | −0.682344 | ||||||||
\(23\) | 9.45142 | + | 20.9683i | 0.410931 | + | 0.911666i | ||||
\(24\) | 9.52037 | 0.396682 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −21.3424 | −0.820860 | ||||||||
\(27\) | 22.4520i | 0.831556i | ||||||||
\(28\) | 2.33837 | 0.0835132 | ||||||||
\(29\) | −32.5993 | −1.12411 | −0.562056 | − | 0.827099i | \(-0.689990\pi\) | ||||
−0.562056 | + | 0.827099i | \(0.689990\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −27.0975 | −0.874113 | −0.437056 | − | 0.899434i | \(-0.643979\pi\) | ||||
−0.437056 | + | 0.899434i | \(0.643979\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | −35.7289 | −1.08270 | ||||||||
\(34\) | − | 28.4097i | − | 0.835578i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.65936 | 0.129427 | ||||||||
\(37\) | 53.0568 | 1.43397 | 0.716984 | − | 0.697089i | \(-0.245522\pi\) | ||||
0.716984 | + | 0.697089i | \(0.245522\pi\) | |||||||
\(38\) | 31.8510 | 0.838184 | ||||||||
\(39\) | −50.7968 | −1.30248 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.43720 | 0.230176 | 0.115088 | − | 0.993355i | \(-0.463285\pi\) | ||||
0.115088 | + | 0.993355i | \(0.463285\pi\) | |||||||
\(42\) | 5.56554 | 0.132513 | ||||||||
\(43\) | 36.4382 | 0.847400 | 0.423700 | − | 0.905802i | \(-0.360731\pi\) | ||||
0.423700 | + | 0.905802i | \(0.360731\pi\) | |||||||
\(44\) | − | 21.2296i | − | 0.482490i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −29.6537 | + | 13.3663i | −0.644645 | + | 0.290572i | ||||
\(47\) | − | 49.1365i | − | 1.04546i | −0.852499 | − | 0.522728i | \(-0.824914\pi\) | ||
0.852499 | − | 0.522728i | \(-0.175086\pi\) | |||||||
\(48\) | 13.4638i | 0.280497i | ||||||||
\(49\) | −47.6330 | −0.972102 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 67.6176i | − | 1.32584i | ||||||
\(52\) | − | 30.1827i | − | 0.580436i | ||||||
\(53\) | −104.253 | −1.96703 | −0.983517 | − | 0.180815i | \(-0.942126\pi\) | ||||
−0.983517 | + | 0.180815i | \(0.942126\pi\) | |||||||
\(54\) | −31.7520 | −0.587999 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.30696i | 0.0590528i | ||||||||
\(57\) | 75.8083 | 1.32997 | ||||||||
\(58\) | − | 46.1023i | − | 0.794868i | ||||||
\(59\) | −53.5457 | −0.907554 | −0.453777 | − | 0.891115i | \(-0.649924\pi\) | ||||
−0.453777 | + | 0.891115i | \(0.649924\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 23.5166i | − | 0.385518i | −0.981246 | − | 0.192759i | \(-0.938257\pi\) | ||
0.981246 | − | 0.192759i | \(-0.0617435\pi\) | |||||||
\(62\) | − | 38.3217i | − | 0.618091i | ||||||
\(63\) | 2.72383 | 0.0432354 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 50.5284i | − | 0.765581i | ||||||
\(67\) | −59.4754 | −0.887692 | −0.443846 | − | 0.896103i | \(-0.646386\pi\) | ||||
−0.443846 | + | 0.896103i | \(0.646386\pi\) | |||||||
\(68\) | 40.1773 | 0.590843 | ||||||||
\(69\) | −70.5785 | + | 31.8131i | −1.02288 | + | 0.461060i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 55.2130 | 0.777648 | 0.388824 | − | 0.921312i | \(-0.372881\pi\) | ||||
0.388824 | + | 0.921312i | \(0.372881\pi\) | |||||||
\(72\) | 6.58933i | 0.0915185i | ||||||||
\(73\) | 8.77305i | 0.120179i | 0.998193 | + | 0.0600894i | \(0.0191386\pi\) | ||||
−0.998193 | + | 0.0600894i | \(0.980861\pi\) | |||||||
\(74\) | 75.0337i | 1.01397i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 45.0441i | 0.592686i | ||||||||
\(77\) | − | 12.4107i | − | 0.161177i | ||||||
\(78\) | − | 71.8376i | − | 0.920994i | ||||||
\(79\) | − | 57.0848i | − | 0.722592i | −0.932451 | − | 0.361296i | \(-0.882334\pi\) | ||
0.932451 | − | 0.361296i | \(-0.117666\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −96.5397 | −1.19185 | ||||||||
\(82\) | 13.3462i | 0.162759i | ||||||||
\(83\) | −55.1788 | −0.664805 | −0.332403 | − | 0.943138i | \(-0.607859\pi\) | ||||
−0.332403 | + | 0.943138i | \(0.607859\pi\) | |||||||
\(84\) | 7.87086i | 0.0937007i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 51.5314i | 0.599203i | ||||||||
\(87\) | − | 109.728i | − | 1.26124i | ||||||
\(88\) | 30.0232 | 0.341172 | ||||||||
\(89\) | − | 139.825i | − | 1.57107i | −0.618815 | − | 0.785536i | \(-0.712387\pi\) | ||
0.618815 | − | 0.785536i | \(-0.287613\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 17.6446i | − | 0.193896i | ||||||
\(92\) | −18.9028 | − | 41.9366i | −0.205466 | − | 0.455833i | ||||
\(93\) | − | 91.2091i | − | 0.980743i | ||||||
\(94\) | 69.4894 | 0.739249 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −19.0407 | −0.198341 | ||||||||
\(97\) | 19.8635 | 0.204778 | 0.102389 | − | 0.994744i | \(-0.467351\pi\) | ||||
0.102389 | + | 0.994744i | \(0.467351\pi\) | |||||||
\(98\) | − | 67.3632i | − | 0.687380i | ||||||
\(99\) | − | 24.7291i | − | 0.249789i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 86.5639 | 0.857068 | 0.428534 | − | 0.903526i | \(-0.359030\pi\) | ||||
0.428534 | + | 0.903526i | \(0.359030\pi\) | |||||||
\(102\) | 95.6258 | 0.937507 | ||||||||
\(103\) | 144.118 | 1.39920 | 0.699600 | − | 0.714535i | \(-0.253361\pi\) | ||||
0.699600 | + | 0.714535i | \(0.253361\pi\) | |||||||
\(104\) | 42.6847 | 0.410430 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 147.436i | − | 1.39090i | ||||||
\(107\) | 10.4544 | 0.0977050 | 0.0488525 | − | 0.998806i | \(-0.484444\pi\) | ||||
0.0488525 | + | 0.998806i | \(0.484444\pi\) | |||||||
\(108\) | − | 44.9040i | − | 0.415778i | ||||||
\(109\) | 69.1221i | 0.634148i | 0.948401 | + | 0.317074i | \(0.102700\pi\) | ||||
−0.948401 | + | 0.317074i | \(0.897300\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 178.587i | 1.60889i | ||||||||
\(112\) | −4.67674 | −0.0417566 | ||||||||
\(113\) | 137.264 | 1.21473 | 0.607364 | − | 0.794423i | \(-0.292227\pi\) | ||||
0.607364 | + | 0.794423i | \(0.292227\pi\) | |||||||
\(114\) | 107.209i | 0.940431i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 65.1985 | 0.562056 | ||||||||
\(117\) | − | 35.1580i | − | 0.300496i | ||||||
\(118\) | − | 75.7250i | − | 0.641738i | ||||||
\(119\) | 23.4874 | 0.197373 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.32629 | 0.0688123 | ||||||||
\(122\) | 33.2575 | 0.272602 | ||||||||
\(123\) | 31.7652i | 0.258254i | ||||||||
\(124\) | 54.1950 | 0.437056 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.85208i | 0.0305720i | ||||||||
\(127\) | 57.9697i | 0.456455i | 0.973608 | + | 0.228227i | \(0.0732929\pi\) | ||||
−0.973608 | + | 0.228227i | \(0.926707\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | 122.650i | 0.950772i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −95.0810 | −0.725809 | −0.362905 | − | 0.931826i | \(-0.618215\pi\) | ||||
−0.362905 | + | 0.931826i | \(0.618215\pi\) | |||||||
\(132\) | 71.4579 | 0.541348 | ||||||||
\(133\) | 26.3325i | 0.197988i | ||||||||
\(134\) | − | 84.1109i | − | 0.627693i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 56.8193i | 0.417789i | ||||||||
\(137\) | 198.711 | 1.45045 | 0.725223 | − | 0.688514i | \(-0.241737\pi\) | ||||
0.725223 | + | 0.688514i | \(0.241737\pi\) | |||||||
\(138\) | −44.9905 | − | 99.8131i | −0.326018 | − | 0.723283i | ||||
\(139\) | 0.129480 | 0.000931508 | 0.000465754 | − | 1.00000i | \(-0.499852\pi\) | ||||
0.000465754 | 1.00000i | \(0.499852\pi\) | ||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 165.391 | 1.17299 | ||||||||
\(142\) | 78.0830i | 0.549880i | ||||||||
\(143\) | −160.191 | −1.12022 | ||||||||
\(144\) | −9.31873 | −0.0647134 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12.4070 | −0.0849792 | ||||||||
\(147\) | − | 160.331i | − | 1.09069i | ||||||
\(148\) | −106.114 | −0.716984 | ||||||||
\(149\) | 63.8745i | 0.428688i | 0.976758 | + | 0.214344i | \(0.0687613\pi\) | ||||
−0.976758 | + | 0.214344i | \(0.931239\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −35.2673 | −0.233558 | −0.116779 | − | 0.993158i | \(-0.537257\pi\) | ||||
−0.116779 | + | 0.993158i | \(0.537257\pi\) | |||||||
\(152\) | −63.7020 | −0.419092 | ||||||||
\(153\) | 46.8002 | 0.305884 | ||||||||
\(154\) | 17.5513 | 0.113970 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 101.594 | 0.651241 | ||||||||
\(157\) | −289.136 | −1.84163 | −0.920814 | − | 0.390002i | \(-0.872474\pi\) | ||||
−0.920814 | + | 0.390002i | \(0.872474\pi\) | |||||||
\(158\) | 80.7300 | 0.510950 | ||||||||
\(159\) | − | 350.911i | − | 2.20699i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.0505 | − | 24.5159i | −0.0686364 | − | 0.152272i | ||||
\(162\) | − | 136.528i | − | 0.842764i | ||||||
\(163\) | 46.2536i | 0.283764i | 0.989884 | + | 0.141882i | \(0.0453154\pi\) | ||||
−0.989884 | + | 0.141882i | \(0.954685\pi\) | |||||||
\(164\) | −18.8744 | −0.115088 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 78.0346i | − | 0.470088i | ||||||
\(167\) | − | 90.8735i | − | 0.544153i | −0.962276 | − | 0.272076i | \(-0.912290\pi\) | ||
0.962276 | − | 0.272076i | \(-0.0877103\pi\) | |||||||
\(168\) | −11.1311 | −0.0662564 | ||||||||
\(169\) | −58.7484 | −0.347624 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 52.4692i | 0.306837i | ||||||||
\(172\) | −72.8764 | −0.423700 | ||||||||
\(173\) | 90.7893i | 0.524794i | 0.964960 | + | 0.262397i | \(0.0845129\pi\) | ||||
−0.964960 | + | 0.262397i | \(0.915487\pi\) | |||||||
\(174\) | 155.179 | 0.891831 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 42.4591i | 0.241245i | ||||||||
\(177\) | − | 180.233i | − | 1.01826i | ||||||
\(178\) | 197.743 | 1.11092 | ||||||||
\(179\) | −301.636 | −1.68511 | −0.842557 | − | 0.538607i | \(-0.818951\pi\) | ||||
−0.842557 | + | 0.538607i | \(0.818951\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 248.547i | 1.37319i | 0.727040 | + | 0.686595i | \(0.240895\pi\) | ||||
−0.727040 | + | 0.686595i | \(0.759105\pi\) | |||||||
\(182\) | 24.9532 | 0.137105 | ||||||||
\(183\) | 79.1558 | 0.432546 | ||||||||
\(184\) | 59.3074 | − | 26.7327i | 0.322323 | − | 0.145286i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 128.989 | 0.693490 | ||||||||
\(187\) | − | 213.237i | − | 1.14030i | ||||||
\(188\) | 98.2729i | 0.522728i | ||||||||
\(189\) | − | 26.2506i | − | 0.138892i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 146.382i | 0.766397i | 0.923666 | + | 0.383199i | \(0.125178\pi\) | ||||
−0.923666 | + | 0.383199i | \(0.874822\pi\) | |||||||
\(192\) | − | 26.9277i | − | 0.140248i | ||||||
\(193\) | 120.648i | 0.625120i | 0.949898 | + | 0.312560i | \(0.101187\pi\) | ||||
−0.949898 | + | 0.312560i | \(0.898813\pi\) | |||||||
\(194\) | 28.0912i | 0.144800i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 95.2660 | 0.486051 | ||||||||
\(197\) | 31.6502i | 0.160661i | 0.996768 | + | 0.0803305i | \(0.0255976\pi\) | ||||
−0.996768 | + | 0.0803305i | \(0.974402\pi\) | |||||||
\(198\) | 34.9722 | 0.176627 | ||||||||
\(199\) | − | 37.4496i | − | 0.188189i | −0.995563 | − | 0.0940944i | \(-0.970004\pi\) | ||
0.995563 | − | 0.0940944i | \(-0.0299955\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 200.192i | − | 0.995979i | ||||||
\(202\) | 122.420i | 0.606039i | ||||||||
\(203\) | 38.1146 | 0.187757 | ||||||||
\(204\) | 135.235i | 0.662918i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 203.813i | 0.989384i | ||||||||
\(207\) | −22.0188 | − | 48.8495i | −0.106371 | − | 0.235988i | ||||
\(208\) | 60.3653i | 0.290218i | ||||||||
\(209\) | 239.067 | 1.14386 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −43.6572 | −0.206906 | −0.103453 | − | 0.994634i | \(-0.532989\pi\) | ||||
−0.103453 | + | 0.994634i | \(0.532989\pi\) | |||||||
\(212\) | 208.506 | 0.983517 | ||||||||
\(213\) | 185.845i | 0.872510i | ||||||||
\(214\) | 14.7848i | 0.0690879i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 63.5039 | 0.294000 | ||||||||
\(217\) | 31.6820 | 0.146000 | ||||||||
\(218\) | −97.7535 | −0.448410 | ||||||||
\(219\) | −29.5297 | −0.134839 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 303.165i | − | 1.37179i | ||||||
\(222\) | −252.560 | −1.13766 | ||||||||
\(223\) | − | 348.623i | − | 1.56333i | −0.623697 | − | 0.781666i | \(-0.714370\pi\) | ||
0.623697 | − | 0.781666i | \(-0.285630\pi\) | |||||||
\(224\) | − | 6.61391i | − | 0.0295264i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 194.121i | 0.858943i | ||||||||
\(227\) | −175.793 | −0.774421 | −0.387210 | − | 0.921991i | \(-0.626561\pi\) | ||||
−0.387210 | + | 0.921991i | \(0.626561\pi\) | |||||||
\(228\) | −151.617 | −0.664985 | ||||||||
\(229\) | − | 1.44148i | − | 0.00629466i | −0.999995 | − | 0.00314733i | \(-0.998998\pi\) | ||
0.999995 | − | 0.00314733i | \(-0.00100183\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 41.7738 | 0.180839 | ||||||||
\(232\) | 92.2047i | 0.397434i | ||||||||
\(233\) | 113.416i | 0.486763i | 0.969931 | + | 0.243381i | \(0.0782567\pi\) | ||||
−0.969931 | + | 0.243381i | \(0.921743\pi\) | |||||||
\(234\) | 49.7209 | 0.212483 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 107.091 | 0.453777 | ||||||||
\(237\) | 192.145 | 0.810738 | ||||||||
\(238\) | 33.2162i | 0.139564i | ||||||||
\(239\) | −367.260 | −1.53665 | −0.768326 | − | 0.640059i | \(-0.778910\pi\) | ||||
−0.768326 | + | 0.640059i | \(0.778910\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 220.365i | 0.914378i | 0.889370 | + | 0.457189i | \(0.151144\pi\) | ||||
−0.889370 | + | 0.457189i | \(0.848856\pi\) | |||||||
\(242\) | 11.7752i | 0.0486577i | ||||||||
\(243\) | − | 122.881i | − | 0.505681i | ||||||
\(244\) | 47.0332i | 0.192759i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −44.9228 | −0.182613 | ||||||||
\(247\) | 339.888 | 1.37606 | ||||||||
\(248\) | 76.6433i | 0.309046i | ||||||||
\(249\) | − | 185.730i | − | 0.745902i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 440.210i | − | 1.75382i | −0.480650 | − | 0.876912i | \(-0.659599\pi\) | ||
0.480650 | − | 0.876912i | \(-0.340401\pi\) | |||||||
\(252\) | −5.44766 | −0.0216177 | ||||||||
\(253\) | −222.574 | + | 100.325i | −0.879740 | + | 0.396541i | ||||
\(254\) | −81.9816 | −0.322762 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 491.519i | 1.91252i | 0.292512 | + | 0.956262i | \(0.405509\pi\) | ||||
−0.292512 | + | 0.956262i | \(0.594491\pi\) | |||||||
\(258\) | −173.453 | −0.672297 | ||||||||
\(259\) | −62.0333 | −0.239511 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 75.9459 | 0.290980 | ||||||||
\(262\) | − | 134.465i | − | 0.513225i | ||||||
\(263\) | −267.833 | −1.01838 | −0.509189 | − | 0.860655i | \(-0.670054\pi\) | ||||
−0.509189 | + | 0.860655i | \(0.670054\pi\) | |||||||
\(264\) | 101.057i | 0.382791i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −37.2397 | −0.139999 | ||||||||
\(267\) | 470.647 | 1.76272 | ||||||||
\(268\) | 118.951 | 0.443846 | ||||||||
\(269\) | −95.6985 | −0.355756 | −0.177878 | − | 0.984053i | \(-0.556923\pi\) | ||||
−0.177878 | + | 0.984053i | \(0.556923\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −452.255 | −1.66884 | −0.834419 | − | 0.551131i | \(-0.814197\pi\) | ||||
−0.834419 | + | 0.551131i | \(0.814197\pi\) | |||||||
\(272\) | −80.3547 | −0.295422 | ||||||||
\(273\) | 59.3909 | 0.217549 | ||||||||
\(274\) | 281.020i | 1.02562i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 141.157 | − | 63.6262i | 0.511439 | − | 0.230530i | ||||
\(277\) | − | 87.4783i | − | 0.315806i | −0.987455 | − | 0.157903i | \(-0.949527\pi\) | ||
0.987455 | − | 0.157903i | \(-0.0504734\pi\) | |||||||
\(278\) | 0.183112i | 0.000658676i | ||||||||
\(279\) | 63.1285 | 0.226267 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 232.157i | − | 0.826183i | −0.910690 | − | 0.413091i | \(-0.864449\pi\) | ||
0.910690 | − | 0.413091i | \(-0.135551\pi\) | |||||||
\(282\) | 233.899i | 0.829428i | ||||||||
\(283\) | 239.367 | 0.845820 | 0.422910 | − | 0.906172i | \(-0.361009\pi\) | ||||
0.422910 | + | 0.906172i | \(0.361009\pi\) | |||||||
\(284\) | −110.426 | −0.388824 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 226.545i | − | 0.792114i | ||||||
\(287\) | −11.0338 | −0.0384454 | ||||||||
\(288\) | − | 13.1787i | − | 0.0457593i | ||||||
\(289\) | 114.554 | 0.396382 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 66.8597i | 0.229758i | ||||||||
\(292\) | − | 17.5461i | − | 0.0600894i | ||||||
\(293\) | −581.830 | −1.98577 | −0.992883 | − | 0.119092i | \(-0.962002\pi\) | ||||
−0.992883 | + | 0.119092i | \(0.962002\pi\) | |||||||
\(294\) | 226.742 | 0.771231 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 150.067i | − | 0.506984i | ||||||
\(297\) | −238.323 | −0.802436 | ||||||||
\(298\) | −90.3322 | −0.303128 | ||||||||
\(299\) | −316.440 | + | 142.635i | −1.05833 | + | 0.477039i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −42.6030 | −0.141538 | ||||||||
\(302\) | − | 49.8755i | − | 0.165151i | ||||||
\(303\) | 291.370i | 0.961619i | ||||||||
\(304\) | − | 90.0882i | − | 0.296343i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 66.1855i | 0.216292i | ||||||||
\(307\) | 110.134i | 0.358742i | 0.983782 | + | 0.179371i | \(0.0574062\pi\) | ||||
−0.983782 | + | 0.179371i | \(0.942594\pi\) | |||||||
\(308\) | 24.8213i | 0.0805887i | ||||||||
\(309\) | 485.094i | 1.56988i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −298.100 | −0.958520 | −0.479260 | − | 0.877673i | \(-0.659095\pi\) | ||||
−0.479260 | + | 0.877673i | \(0.659095\pi\) | |||||||
\(312\) | 143.675i | 0.460497i | ||||||||
\(313\) | −109.474 | −0.349758 | −0.174879 | − | 0.984590i | \(-0.555953\pi\) | ||||
−0.174879 | + | 0.984590i | \(0.555953\pi\) | |||||||
\(314\) | − | 408.900i | − | 1.30223i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 114.170i | 0.361296i | ||||||||
\(317\) | 474.434i | 1.49664i | 0.663340 | + | 0.748318i | \(0.269138\pi\) | ||||
−0.663340 | + | 0.748318i | \(0.730862\pi\) | |||||||
\(318\) | 496.263 | 1.56057 | ||||||||
\(319\) | − | 346.034i | − | 1.08475i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 35.1892i | 0.109624i | ||||||||
\(322\) | 34.6707 | − | 15.6277i | 0.107673 | − | 0.0485333i | ||||
\(323\) | 452.438i | 1.40074i | ||||||||
\(324\) | 193.079 | 0.595924 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −65.4124 | −0.200652 | ||||||||
\(327\) | −232.662 | −0.711506 | ||||||||
\(328\) | − | 26.6924i | − | 0.0813794i | ||||||
\(329\) | 57.4496i | 0.174619i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 255.367 | 0.771503 | 0.385751 | − | 0.922603i | \(-0.373942\pi\) | ||||
0.385751 | + | 0.922603i | \(0.373942\pi\) | |||||||
\(332\) | 110.358 | 0.332403 | ||||||||
\(333\) | −123.606 | −0.371188 | ||||||||
\(334\) | 128.515 | 0.384774 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 15.7417i | − | 0.0468504i | ||||||
\(337\) | −458.486 | −1.36049 | −0.680247 | − | 0.732983i | \(-0.738127\pi\) | ||||
−0.680247 | + | 0.732983i | \(0.738127\pi\) | |||||||
\(338\) | − | 83.0828i | − | 0.245807i | ||||||
\(339\) | 462.026i | 1.36291i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 287.634i | − | 0.843502i | ||||||
\(342\) | −74.2027 | −0.216967 | ||||||||
\(343\) | 112.982 | 0.329393 | ||||||||
\(344\) | − | 103.063i | − | 0.299601i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −128.395 | −0.371085 | ||||||||
\(347\) | 510.676i | 1.47169i | 0.677151 | + | 0.735845i | \(0.263215\pi\) | ||||
−0.677151 | + | 0.735845i | \(0.736785\pi\) | |||||||
\(348\) | 219.456i | 0.630620i | ||||||||
\(349\) | 591.870 | 1.69590 | 0.847951 | − | 0.530075i | \(-0.177836\pi\) | ||||
0.847951 | + | 0.530075i | \(0.177836\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −338.831 | −0.965330 | ||||||||
\(352\) | −60.0463 | −0.170586 | ||||||||
\(353\) | − | 168.334i | − | 0.476866i | −0.971159 | − | 0.238433i | \(-0.923366\pi\) | ||
0.971159 | − | 0.238433i | \(-0.0766337\pi\) | |||||||
\(354\) | 254.887 | 0.720021 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 279.651i | 0.785536i | ||||||||
\(357\) | 79.0575i | 0.221450i | ||||||||
\(358\) | − | 426.577i | − | 1.19156i | ||||||
\(359\) | − | 37.5719i | − | 0.104657i | −0.998630 | − | 0.0523285i | \(-0.983336\pi\) | ||
0.998630 | − | 0.0523285i | \(-0.0166643\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −146.243 | −0.405105 | ||||||||
\(362\) | −351.499 | −0.970992 | ||||||||
\(363\) | 28.0260i | 0.0772065i | ||||||||
\(364\) | 35.2891i | 0.0969482i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 111.943i | 0.305856i | ||||||||
\(367\) | −427.036 | −1.16359 | −0.581793 | − | 0.813337i | \(-0.697649\pi\) | ||||
−0.581793 | + | 0.813337i | \(0.697649\pi\) | |||||||
\(368\) | 37.8057 | + | 83.8733i | 0.102733 | + | 0.227917i | ||||
\(369\) | −21.9857 | −0.0595818 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 121.891 | 0.328547 | ||||||||
\(372\) | 182.418i | 0.490371i | ||||||||
\(373\) | 369.980 | 0.991904 | 0.495952 | − | 0.868350i | \(-0.334819\pi\) | ||||
0.495952 | + | 0.868350i | \(0.334819\pi\) | |||||||
\(374\) | 301.563 | 0.806317 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −138.979 | −0.369625 | ||||||||
\(377\) | − | 491.966i | − | 1.30495i | ||||||
\(378\) | 37.1239 | 0.0982114 | ||||||||
\(379\) | − | 78.8009i | − | 0.207918i | −0.994582 | − | 0.103959i | \(-0.966849\pi\) | ||
0.994582 | − | 0.103959i | \(-0.0331511\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −195.124 | −0.512136 | ||||||||
\(382\) | −207.015 | −0.541925 | ||||||||
\(383\) | 254.083 | 0.663403 | 0.331702 | − | 0.943384i | \(-0.392377\pi\) | ||||
0.331702 | + | 0.943384i | \(0.392377\pi\) | |||||||
\(384\) | 38.0815 | 0.0991705 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −170.622 | −0.442027 | ||||||||
\(387\) | −84.8894 | −0.219353 | ||||||||
\(388\) | −39.7270 | −0.102389 | ||||||||
\(389\) | 322.363i | 0.828698i | 0.910118 | + | 0.414349i | \(0.135991\pi\) | ||||
−0.910118 | + | 0.414349i | \(0.864009\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −189.866 | − | 421.226i | −0.485592 | − | 1.07730i | ||||
\(392\) | 134.726i | 0.343690i | ||||||||
\(393\) | − | 320.039i | − | 0.814348i | ||||||
\(394\) | −44.7602 | −0.113605 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 49.4581i | 0.124894i | ||||||||
\(397\) | 715.832i | 1.80310i | 0.432671 | + | 0.901552i | \(0.357571\pi\) | ||||
−0.432671 | + | 0.901552i | \(0.642429\pi\) | |||||||
\(398\) | 52.9617 | 0.133070 | ||||||||
\(399\) | −88.6340 | −0.222140 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 441.435i | 1.10083i | 0.834890 | + | 0.550417i | \(0.185531\pi\) | ||||
−0.834890 | + | 0.550417i | \(0.814469\pi\) | |||||||
\(402\) | 283.114 | 0.704263 | ||||||||
\(403\) | − | 408.937i | − | 1.01473i | ||||||
\(404\) | −173.128 | −0.428534 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 53.9022i | 0.132764i | ||||||||
\(407\) | 563.187i | 1.38375i | ||||||||
\(408\) | −191.252 | −0.468754 | ||||||||
\(409\) | 608.727 | 1.48833 | 0.744164 | − | 0.667996i | \(-0.232848\pi\) | ||||
0.744164 | + | 0.667996i | \(0.232848\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 668.853i | 1.62738i | ||||||||
\(412\) | −288.235 | −0.699600 | ||||||||
\(413\) | 62.6048 | 0.151586 | ||||||||
\(414\) | 69.0836 | − | 31.1393i | 0.166869 | − | 0.0752157i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −85.3695 | −0.205215 | ||||||||
\(417\) | 0.435823i | 0.00104514i | ||||||||
\(418\) | 338.091i | 0.808831i | ||||||||
\(419\) | 287.454i | 0.686047i | 0.939327 | + | 0.343023i | \(0.111451\pi\) | ||||
−0.939327 | + | 0.343023i | \(0.888549\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 130.848i | − | 0.310803i | −0.987851 | − | 0.155402i | \(-0.950333\pi\) | ||
0.987851 | − | 0.155402i | \(-0.0496672\pi\) | |||||||
\(422\) | − | 61.7406i | − | 0.146305i | ||||||
\(423\) | 114.472i | 0.270620i | ||||||||
\(424\) | 294.871i | 0.695452i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −262.824 | −0.616958 | ||||||||
\(427\) | 27.4952i | 0.0643917i | ||||||||
\(428\) | −20.9089 | −0.0488525 | ||||||||
\(429\) | − | 539.197i | − | 1.25687i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 239.816i | − | 0.556417i | −0.960521 | − | 0.278209i | \(-0.910259\pi\) | ||
0.960521 | − | 0.278209i | \(-0.0897406\pi\) | |||||||
\(432\) | 89.8081i | 0.207889i | ||||||||
\(433\) | −305.542 | −0.705640 | −0.352820 | − | 0.935691i | \(-0.614777\pi\) | ||||
−0.352820 | + | 0.935691i | \(0.614777\pi\) | |||||||
\(434\) | 44.8051i | 0.103238i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 138.244i | − | 0.317074i | ||||||
\(437\) | 472.250 | − | 212.865i | 1.08066 | − | 0.487106i | ||||
\(438\) | − | 41.7613i | − | 0.0953455i | ||||||
\(439\) | 579.018 | 1.31895 | 0.659474 | − | 0.751727i | \(-0.270779\pi\) | ||||
0.659474 | + | 0.751727i | \(0.270779\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 110.970 | 0.251632 | ||||||||
\(442\) | 428.740 | 0.969999 | ||||||||
\(443\) | 606.274i | 1.36856i | 0.729217 | + | 0.684282i | \(0.239884\pi\) | ||||
−0.729217 | + | 0.684282i | \(0.760116\pi\) | |||||||
\(444\) | − | 357.174i | − | 0.804446i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 493.028 | 1.10544 | ||||||||
\(447\) | −214.999 | −0.480982 | ||||||||
\(448\) | 9.35348 | 0.0208783 | ||||||||
\(449\) | 202.580 | 0.451181 | 0.225590 | − | 0.974222i | \(-0.427569\pi\) | ||||
0.225590 | + | 0.974222i | \(0.427569\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 100.174i | 0.222115i | ||||||||
\(452\) | −274.529 | −0.607364 | ||||||||
\(453\) | − | 118.708i | − | 0.262049i | ||||||
\(454\) | − | 248.609i | − | 0.547598i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | − | 214.418i | − | 0.470215i | ||||||
\(457\) | −373.760 | −0.817857 | −0.408928 | − | 0.912567i | \(-0.634097\pi\) | ||||
−0.408928 | + | 0.912567i | \(0.634097\pi\) | |||||||
\(458\) | 2.03856 | 0.00445100 | ||||||||
\(459\) | − | 451.031i | − | 0.982639i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 709.377 | 1.53878 | 0.769390 | − | 0.638780i | \(-0.220561\pi\) | ||||
0.769390 | + | 0.638780i | \(0.220561\pi\) | |||||||
\(462\) | 59.0770i | 0.127872i | ||||||||
\(463\) | − | 266.488i | − | 0.575569i | −0.957695 | − | 0.287785i | \(-0.907081\pi\) | ||
0.957695 | − | 0.287785i | \(-0.0929187\pi\) | |||||||
\(464\) | −130.397 | −0.281028 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −160.394 | −0.344193 | ||||||||
\(467\) | −686.135 | −1.46924 | −0.734620 | − | 0.678479i | \(-0.762639\pi\) | ||||
−0.734620 | + | 0.678479i | \(0.762639\pi\) | |||||||
\(468\) | 70.3160i | 0.150248i | ||||||||
\(469\) | 69.5378 | 0.148268 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 973.219i | − | 2.06628i | ||||||
\(472\) | 151.450i | 0.320869i | ||||||||
\(473\) | 386.784i | 0.817725i | ||||||||
\(474\) | 271.734i | 0.573279i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −46.9747 | −0.0986864 | ||||||||
\(477\) | 242.876 | 0.509174 | ||||||||
\(478\) | − | 519.384i | − | 1.08658i | ||||||
\(479\) | 176.517i | 0.368511i | 0.982878 | + | 0.184256i | \(0.0589874\pi\) | ||||
−0.982878 | + | 0.184256i | \(0.941013\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 800.698i | 1.66465i | ||||||||
\(482\) | −311.643 | −0.646563 | ||||||||
\(483\) | 82.5194 | − | 37.1954i | 0.170848 | − | 0.0770091i | ||||
\(484\) | −16.6526 | −0.0344062 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 173.779 | 0.357571 | ||||||||
\(487\) | 524.802i | 1.07762i | 0.842427 | + | 0.538811i | \(0.181126\pi\) | ||||
−0.842427 | + | 0.538811i | \(0.818874\pi\) | |||||||
\(488\) | −66.5149 | −0.136301 | ||||||||
\(489\) | −155.688 | −0.318380 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −551.047 | −1.12229 | −0.561147 | − | 0.827716i | \(-0.689640\pi\) | ||||
−0.561147 | + | 0.827716i | \(0.689640\pi\) | |||||||
\(492\) | − | 63.5304i | − | 0.129127i | ||||||
\(493\) | 654.876 | 1.32835 | ||||||||
\(494\) | 480.674i | 0.973024i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −108.390 | −0.218528 | ||||||||
\(497\) | −64.5542 | −0.129888 | ||||||||
\(498\) | 262.661 | 0.527433 | ||||||||
\(499\) | 736.739 | 1.47643 | 0.738216 | − | 0.674565i | \(-0.235669\pi\) | ||||
0.738216 | + | 0.674565i | \(0.235669\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 305.876 | 0.610532 | ||||||||
\(502\) | 622.551 | 1.24014 | ||||||||
\(503\) | 699.308 | 1.39027 | 0.695137 | − | 0.718877i | \(-0.255344\pi\) | ||||
0.695137 | + | 0.718877i | \(0.255344\pi\) | |||||||
\(504\) | − | 7.70415i | − | 0.0152860i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −141.881 | − | 314.768i | −0.280397 | − | 0.622070i | ||||
\(507\) | − | 197.745i | − | 0.390029i | ||||||
\(508\) | − | 115.939i | − | 0.228227i | ||||||
\(509\) | 316.428 | 0.621666 | 0.310833 | − | 0.950464i | \(-0.399392\pi\) | ||||
0.310833 | + | 0.950464i | \(0.399392\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 10.2573i | − | 0.0200730i | ||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 505.666 | 0.985703 | ||||||||
\(514\) | −695.112 | −1.35236 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 245.299i | − | 0.475386i | ||||||
\(517\) | 521.573 | 1.00885 | ||||||||
\(518\) | − | 87.7283i | − | 0.169360i | ||||||
\(519\) | −305.593 | −0.588811 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 798.875i | 1.53335i | 0.642035 | + | 0.766675i | \(0.278090\pi\) | ||||
−0.642035 | + | 0.766675i | \(0.721910\pi\) | |||||||
\(522\) | 107.404i | 0.205754i | ||||||||
\(523\) | −819.091 | −1.56614 | −0.783070 | − | 0.621934i | \(-0.786347\pi\) | ||||
−0.783070 | + | 0.621934i | \(0.786347\pi\) | |||||||
\(524\) | 190.162 | 0.362905 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 378.773i | − | 0.720101i | ||||||
\(527\) | 544.353 | 1.03293 | ||||||||
\(528\) | −142.916 | −0.270674 | ||||||||
\(529\) | −350.341 | + | 396.361i | −0.662271 | + | 0.749265i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 124.744 | 0.234924 | ||||||||
\(532\) | − | 52.6649i | − | 0.0989942i | ||||||
\(533\) | 142.420i | 0.267204i | ||||||||
\(534\) | 665.595i | 1.24643i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 168.222i | 0.313847i | ||||||||
\(537\) | − | 1015.29i | − | 1.89068i | ||||||
\(538\) | − | 135.338i | − | 0.251558i | ||||||
\(539\) | − | 505.614i | − | 0.938060i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 289.616 | 0.535335 | 0.267668 | − | 0.963511i | \(-0.413747\pi\) | ||||
0.267668 | + | 0.963511i | \(0.413747\pi\) | |||||||
\(542\) | − | 639.585i | − | 1.18005i | ||||||
\(543\) | −836.600 | −1.54070 | ||||||||
\(544\) | − | 113.639i | − | 0.208895i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 83.9914i | 0.153830i | ||||||||
\(547\) | 996.117i | 1.82106i | 0.413448 | + | 0.910528i | \(0.364324\pi\) | ||||
−0.413448 | + | 0.910528i | \(0.635676\pi\) | |||||||
\(548\) | −397.422 | −0.725223 | ||||||||
\(549\) | 54.7861i | 0.0997926i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 734.202i | 1.33249i | ||||||||
\(552\) | 89.9811 | + | 199.626i | 0.163009 | + | 0.361642i | ||||
\(553\) | 66.7427i | 0.120692i | ||||||||
\(554\) | 123.713 | 0.223309 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.258959 | −0.000465754 | ||||||||
\(557\) | −937.756 | −1.68358 | −0.841792 | − | 0.539802i | \(-0.818499\pi\) | ||||
−0.841792 | + | 0.539802i | \(0.818499\pi\) | |||||||
\(558\) | 89.2772i | 0.159995i | ||||||||
\(559\) | 549.901i | 0.983723i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 717.747 | 1.27941 | ||||||||
\(562\) | 328.320 | 0.584200 | ||||||||
\(563\) | −785.252 | −1.39476 | −0.697382 | − | 0.716700i | \(-0.745652\pi\) | ||||
−0.697382 | + | 0.716700i | \(0.745652\pi\) | |||||||
\(564\) | −330.783 | −0.586494 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 338.516i | 0.598085i | ||||||||
\(567\) | 112.873 | 0.199070 | ||||||||
\(568\) | − | 156.166i | − | 0.274940i | ||||||
\(569\) | − | 403.851i | − | 0.709755i | −0.934913 | − | 0.354877i | \(-0.884523\pi\) | ||
0.934913 | − | 0.354877i | \(-0.115477\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 335.474i | − | 0.587519i | −0.955879 | − | 0.293760i | \(-0.905093\pi\) | ||
0.955879 | − | 0.293760i | \(-0.0949065\pi\) | |||||||
\(572\) | 320.383 | 0.560110 | ||||||||
\(573\) | −492.715 | −0.859887 | ||||||||
\(574\) | − | 15.6042i | − | 0.0271850i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 18.6375 | 0.0323567 | ||||||||
\(577\) | − | 152.703i | − | 0.264649i | −0.991206 | − | 0.132325i | \(-0.957756\pi\) | ||
0.991206 | − | 0.132325i | \(-0.0422441\pi\) | |||||||
\(578\) | 162.004i | 0.280284i | ||||||||
\(579\) | −406.097 | −0.701376 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 64.5143 | 0.111040 | ||||||||
\(582\) | −94.5538 | −0.162464 | ||||||||
\(583\) | − | 1106.62i | − | 1.89815i | ||||||
\(584\) | 24.8139 | 0.0424896 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 822.831i | − | 1.40415i | ||||||
\(587\) | 129.262i | 0.220207i | 0.993920 | + | 0.110104i | \(0.0351183\pi\) | ||||
−0.993920 | + | 0.110104i | \(0.964882\pi\) | |||||||
\(588\) | 320.662i | 0.545343i | ||||||||
\(589\) | 610.291i | 1.03615i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −106.533 | −0.180260 | ||||||||
\(592\) | 212.227 | 0.358492 | ||||||||
\(593\) | 879.853i | 1.48373i | 0.670548 | + | 0.741866i | \(0.266059\pi\) | ||||
−0.670548 | + | 0.741866i | \(0.733941\pi\) | |||||||
\(594\) | − | 337.040i | − | 0.567408i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 127.749i | − | 0.214344i | ||||||
\(597\) | 126.054 | 0.211145 | ||||||||
\(598\) | −201.716 | − | 447.514i | −0.337317 | − | 0.748351i | ||||
\(599\) | 709.708 | 1.18482 | 0.592411 | − | 0.805636i | \(-0.298176\pi\) | ||||
0.592411 | + | 0.805636i | \(0.298176\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 238.861 | 0.397439 | 0.198719 | − | 0.980056i | \(-0.436322\pi\) | ||||
0.198719 | + | 0.980056i | \(0.436322\pi\) | |||||||
\(602\) | − | 60.2498i | − | 0.100083i | ||||||
\(603\) | 138.559 | 0.229782 | ||||||||
\(604\) | 70.5346 | 0.116779 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −412.060 | −0.679967 | ||||||||
\(607\) | − | 1082.53i | − | 1.78341i | −0.452621 | − | 0.891703i | \(-0.649511\pi\) | ||
0.452621 | − | 0.891703i | \(-0.350489\pi\) | |||||||
\(608\) | 127.404 | 0.209546 | ||||||||
\(609\) | 128.292i | 0.210660i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 741.535 | 1.21364 | ||||||||
\(612\) | −93.6004 | −0.152942 | ||||||||
\(613\) | 54.0902 | 0.0882384 | 0.0441192 | − | 0.999026i | \(-0.485952\pi\) | ||||
0.0441192 | + | 0.999026i | \(0.485952\pi\) | |||||||
\(614\) | −155.753 | −0.253669 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −35.1026 | −0.0569848 | ||||||||
\(617\) | 454.342 | 0.736373 | 0.368186 | − | 0.929752i | \(-0.379979\pi\) | ||||
0.368186 | + | 0.929752i | \(0.379979\pi\) | |||||||
\(618\) | −686.027 | −1.11008 | ||||||||
\(619\) | 153.676i | 0.248264i | 0.992266 | + | 0.124132i | \(0.0396147\pi\) | ||||
−0.992266 | + | 0.124132i | \(0.960385\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −470.781 | + | 212.204i | −0.758102 | + | 0.341713i | ||||
\(622\) | − | 421.577i | − | 0.677776i | ||||||
\(623\) | 163.482i | 0.262411i | ||||||||
\(624\) | −203.187 | −0.325621 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 154.820i | − | 0.247316i | ||||||
\(627\) | 804.689i | 1.28340i | ||||||||
\(628\) | 578.271 | 0.920814 | ||||||||
\(629\) | −1065.84 | −1.69450 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1241.15i | − | 1.96696i | −0.181027 | − | 0.983478i | \(-0.557942\pi\) | ||
0.181027 | − | 0.983478i | \(-0.442058\pi\) | |||||||
\(632\) | −161.460 | −0.255475 | ||||||||
\(633\) | − | 146.948i | − | 0.232146i | ||||||
\(634\) | −670.950 | −1.05828 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 701.821i | 1.10349i | ||||||||
\(637\) | − | 718.846i | − | 1.12849i | ||||||
\(638\) | 489.366 | 0.767032 | ||||||||
\(639\) | −128.629 | −0.201297 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 545.978i | 0.851759i | 0.904780 | + | 0.425880i | \(0.140035\pi\) | ||||
−0.904780 | + | 0.425880i | \(0.859965\pi\) | |||||||
\(642\) | −49.7651 | −0.0775157 | ||||||||
\(643\) | 539.118 | 0.838441 | 0.419221 | − | 0.907884i | \(-0.362303\pi\) | ||||
0.419221 | + | 0.907884i | \(0.362303\pi\) | |||||||
\(644\) | 22.1009 | + | 49.0317i | 0.0343182 | + | 0.0761362i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −639.844 | −0.990470 | ||||||||
\(647\) | 652.715i | 1.00883i | 0.863460 | + | 0.504417i | \(0.168292\pi\) | ||||
−0.863460 | + | 0.504417i | \(0.831708\pi\) | |||||||
\(648\) | 273.056i | 0.421382i | ||||||||
\(649\) | − | 568.376i | − | 0.875772i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 106.640i | 0.163810i | ||||||||
\(652\) | − | 92.5071i | − | 0.141882i | ||||||
\(653\) | − | 374.815i | − | 0.573989i | −0.957932 | − | 0.286995i | \(-0.907344\pi\) | ||
0.957932 | − | 0.286995i | \(-0.0926562\pi\) | |||||||
\(654\) | − | 329.034i | − | 0.503110i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 37.7488 | 0.0575439 | ||||||||
\(657\) | − | 20.4384i | − | 0.0311087i | ||||||
\(658\) | −81.2460 | −0.123474 | ||||||||
\(659\) | 440.090i | 0.667815i | 0.942606 | + | 0.333907i | \(0.108367\pi\) | ||||
−0.942606 | + | 0.333907i | \(0.891633\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 72.6725i | − | 0.109943i | −0.998488 | − | 0.0549716i | \(-0.982493\pi\) | ||
0.998488 | − | 0.0549716i | \(-0.0175068\pi\) | |||||||
\(662\) | 361.144i | 0.545535i | ||||||||
\(663\) | 1020.44 | 1.53913 | ||||||||
\(664\) | 156.069i | 0.235044i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 174.805i | − | 0.262469i | ||||||
\(667\) | −308.110 | − | 683.552i | −0.461933 | − | 1.02482i | ||||
\(668\) | 181.747i | 0.272076i | ||||||||
\(669\) | 1173.45 | 1.75404 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 249.623 | 0.372017 | ||||||||
\(672\) | 22.2622 | 0.0331282 | ||||||||
\(673\) | 1052.88i | 1.56445i | 0.622993 | + | 0.782227i | \(0.285916\pi\) | ||||
−0.622993 | + | 0.782227i | \(0.714084\pi\) | |||||||
\(674\) | − | 648.398i | − | 0.962014i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 117.497 | 0.173812 | ||||||||
\(677\) | 393.587 | 0.581369 | 0.290684 | − | 0.956819i | \(-0.406117\pi\) | ||||
0.290684 | + | 0.956819i | \(0.406117\pi\) | |||||||
\(678\) | −653.404 | −0.963722 | ||||||||
\(679\) | −23.2241 | −0.0342034 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 591.714i | − | 0.868889i | ||||||
\(682\) | 406.776 | 0.596446 | ||||||||
\(683\) | 645.240i | 0.944714i | 0.881407 | + | 0.472357i | \(0.156597\pi\) | ||||
−0.881407 | + | 0.472357i | \(0.843403\pi\) | |||||||
\(684\) | − | 104.938i | − | 0.153419i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 159.781i | 0.232916i | ||||||||
\(687\) | 4.85195 | 0.00706252 | ||||||||
\(688\) | 145.753 | 0.211850 | ||||||||
\(689\) | − | 1573.31i | − | 2.28347i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 548.216 | 0.793366 | 0.396683 | − | 0.917956i | \(-0.370161\pi\) | ||||
0.396683 | + | 0.917956i | \(0.370161\pi\) | |||||||
\(692\) | − | 181.579i | − | 0.262397i | ||||||
\(693\) | 28.9129i | 0.0417213i | ||||||||
\(694\) | −722.205 | −1.04064 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −310.357 | −0.445915 | ||||||||
\(697\) | −189.581 | −0.271995 | ||||||||
\(698\) | 837.030i | 1.19918i | ||||||||
\(699\) | −381.753 | −0.546141 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 92.2064i | − | 0.131536i | −0.997835 | − | 0.0657678i | \(-0.979050\pi\) | ||
0.997835 | − | 0.0657678i | \(-0.0209496\pi\) | |||||||
\(702\) | − | 479.179i | − | 0.682592i | ||||||
\(703\) | − | 1194.95i | − | 1.69978i | ||||||
\(704\) | − | 84.9183i | − | 0.120623i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 238.060 | 0.337195 | ||||||||
\(707\) | −101.209 | −0.143153 | ||||||||
\(708\) | 360.465i | 0.509132i | ||||||||
\(709\) | 922.612i | 1.30129i | 0.759384 | + | 0.650643i | \(0.225501\pi\) | ||||
−0.759384 | + | 0.650643i | \(0.774499\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 132.989i | 0.187045i | ||||||||
\(712\) | −395.486 | −0.555458 | ||||||||
\(713\) | −256.110 | − | 568.189i | −0.359201 | − | 0.796899i | ||||
\(714\) | −111.804 | −0.156589 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 603.271 | 0.842557 | ||||||||
\(717\) | − | 1236.18i | − | 1.72410i | ||||||
\(718\) | 53.1347 | 0.0740037 | ||||||||
\(719\) | −606.887 | −0.844071 | −0.422035 | − | 0.906579i | \(-0.638684\pi\) | ||||
−0.422035 | + | 0.906579i | \(0.638684\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −168.500 | −0.233704 | ||||||||
\(722\) | − | 206.819i | − | 0.286452i | ||||||
\(723\) | −741.740 | −1.02592 | ||||||||
\(724\) | − | 497.095i | − | 0.686595i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −39.6347 | −0.0545932 | ||||||||
\(727\) | 787.544 | 1.08328 | 0.541640 | − | 0.840611i | \(-0.317804\pi\) | ||||
0.541640 | + | 0.840611i | \(0.317804\pi\) | |||||||
\(728\) | −49.9064 | −0.0685527 | ||||||||
\(729\) | −455.246 | −0.624481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −731.995 | −1.00136 | ||||||||
\(732\) | −158.312 | −0.216273 | ||||||||
\(733\) | 415.085 | 0.566282 | 0.283141 | − | 0.959078i | \(-0.408624\pi\) | ||||
0.283141 | + | 0.959078i | \(0.408624\pi\) | |||||||
\(734\) | − | 603.921i | − | 0.822780i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −118.615 | + | 53.4653i | −0.161161 | + | 0.0726431i | ||||
\(737\) | − | 631.319i | − | 0.856606i | ||||||
\(738\) | − | 31.0924i | − | 0.0421307i | ||||||
\(739\) | −639.964 | −0.865987 | −0.432993 | − | 0.901397i | \(-0.642543\pi\) | ||||
−0.432993 | + | 0.901397i | \(0.642543\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1144.05i | 1.54393i | ||||||||
\(742\) | 172.380i | 0.232318i | ||||||||
\(743\) | −743.739 | −1.00099 | −0.500497 | − | 0.865738i | \(-0.666849\pi\) | ||||
−0.500497 | + | 0.865738i | \(0.666849\pi\) | |||||||
\(744\) | −257.978 | −0.346745 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 523.231i | 0.701382i | ||||||||
\(747\) | 128.549 | 0.172087 | ||||||||
\(748\) | 426.474i | 0.570152i | ||||||||
\(749\) | −12.2232 | −0.0163193 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 517.047i | − | 0.688478i | −0.938882 | − | 0.344239i | \(-0.888137\pi\) | ||
0.938882 | − | 0.344239i | \(-0.111863\pi\) | |||||||
\(752\) | − | 196.546i | − | 0.261364i | ||||||
\(753\) | 1481.73 | 1.96777 | ||||||||
\(754\) | 695.746 | 0.922740 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 52.5011i | 0.0694460i | ||||||||
\(757\) | 911.823 | 1.20452 | 0.602261 | − | 0.798299i | \(-0.294267\pi\) | ||||
0.602261 | + | 0.798299i | \(0.294267\pi\) | |||||||
\(758\) | 111.441 | 0.147020 | ||||||||
\(759\) | −337.689 | − | 749.176i | −0.444914 | − | 0.987057i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 954.073 | 1.25371 | 0.626855 | − | 0.779136i | \(-0.284342\pi\) | ||||
0.626855 | + | 0.779136i | \(0.284342\pi\) | |||||||
\(762\) | − | 275.947i | − | 0.362135i | ||||||
\(763\) | − | 80.8166i | − | 0.105920i | ||||||
\(764\) | − | 292.764i | − | 0.383199i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 359.328i | 0.469097i | ||||||||
\(767\) | − | 808.076i | − | 1.05355i | ||||||
\(768\) | 53.8553i | 0.0701242i | ||||||||
\(769\) | 276.277i | 0.359268i | 0.983734 | + | 0.179634i | \(0.0574913\pi\) | ||||
−0.983734 | + | 0.179634i | \(0.942509\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1654.43 | −2.14583 | ||||||||
\(772\) | − | 241.296i | − | 0.312560i | ||||||
\(773\) | −40.8440 | −0.0528383 | −0.0264192 | − | 0.999651i | \(-0.508410\pi\) | ||||
−0.0264192 | + | 0.999651i | \(0.508410\pi\) | |||||||
\(774\) | − | 120.052i | − | 0.155106i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 56.1824i | − | 0.0724000i | ||||||
\(777\) | − | 208.801i | − | 0.268728i | ||||||
\(778\) | −455.891 | −0.585978 | ||||||||
\(779\) | − | 212.545i | − | 0.272843i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 586.074i | 0.750415i | ||||||||
\(782\) | 595.703 | − | 268.512i | 0.761768 | − | 0.343365i | ||||
\(783\) | − | 731.919i | − | 0.934763i | ||||||
\(784\) | −190.532 | −0.243026 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 452.603 | 0.575831 | ||||||||
\(787\) | 1364.69 | 1.73404 | 0.867019 | − | 0.498274i | \(-0.166033\pi\) | ||||
0.867019 | + | 0.498274i | \(0.166033\pi\) | |||||||
\(788\) | − | 63.3005i | − | 0.0803305i | ||||||
\(789\) | − | 901.515i | − | 1.14261i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −160.487 | −0.202892 | ||||||||
\(792\) | −69.9444 | −0.0883136 | ||||||||
\(793\) | 354.897 | 0.447537 | ||||||||
\(794\) | −1012.34 | −1.27499 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 74.8991i | 0.0940944i | ||||||||
\(797\) | −20.2192 | −0.0253692 | −0.0126846 | − | 0.999920i | \(-0.504038\pi\) | ||||
−0.0126846 | + | 0.999920i | \(0.504038\pi\) | |||||||
\(798\) | − | 125.347i | − | 0.157077i | ||||||
\(799\) | 987.086i | 1.23540i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 325.749i | 0.406678i | ||||||||
\(802\) | −624.283 | −0.778407 | ||||||||
\(803\) | −93.1240 | −0.115970 | ||||||||
\(804\) | 400.384i | 0.497989i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 578.325 | 0.717525 | ||||||||
\(807\) | − | 322.117i | − | 0.399154i | ||||||
\(808\) | − | 244.840i | − | 0.303019i | ||||||
\(809\) | 1032.11 | 1.27579 | 0.637894 | − | 0.770124i | \(-0.279806\pi\) | ||||
0.637894 | + | 0.770124i | \(0.279806\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −70.2781 | −0.0866561 | −0.0433281 | − | 0.999061i | \(-0.513796\pi\) | ||||
−0.0433281 | + | 0.999061i | \(0.513796\pi\) | |||||||
\(812\) | −76.2292 | −0.0938783 | ||||||||
\(813\) | − | 1522.27i | − | 1.87241i | ||||||
\(814\) | −796.467 | −0.978460 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 270.470i | − | 0.331459i | ||||||
\(817\) | − | 820.663i | − | 1.00448i | ||||||
\(818\) | 860.869i | 1.05241i | ||||||||
\(819\) | 41.1062i | 0.0501907i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 84.7400 | 0.103216 | 0.0516078 | − | 0.998667i | \(-0.483565\pi\) | ||||
0.0516078 | + | 0.998667i | \(0.483565\pi\) | |||||||
\(822\) | −945.901 | −1.15073 | ||||||||
\(823\) | − | 46.0292i | − | 0.0559286i | −0.999609 | − | 0.0279643i | \(-0.991098\pi\) | ||
0.999609 | − | 0.0279643i | \(-0.00890247\pi\) | |||||||
\(824\) | − | 407.626i | − | 0.494692i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 88.5366i | 0.107187i | ||||||||
\(827\) | −1283.77 | −1.55232 | −0.776160 | − | 0.630536i | \(-0.782835\pi\) | ||||
−0.776160 | + | 0.630536i | \(0.782835\pi\) | |||||||
\(828\) | 44.0376 | + | 97.6990i | 0.0531855 | + | 0.117994i | ||||
\(829\) | 483.453 | 0.583177 | 0.291588 | − | 0.956544i | \(-0.405816\pi\) | ||||
0.291588 | + | 0.956544i | \(0.405816\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 294.449 | 0.354330 | ||||||||
\(832\) | − | 120.731i | − | 0.145109i | ||||||
\(833\) | 956.883 | 1.14872 | ||||||||
\(834\) | −0.616347 | −0.000739025 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −478.134 | −0.571930 | ||||||||
\(837\) | − | 608.394i | − | 0.726874i | ||||||
\(838\) | −406.521 | −0.485108 | ||||||||
\(839\) | 1060.74i | 1.26429i | 0.774852 | + | 0.632143i | \(0.217824\pi\) | ||||
−0.774852 | + | 0.632143i | \(0.782176\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 221.712 | 0.263629 | ||||||||
\(842\) | 185.047 | 0.219771 | ||||||||
\(843\) | 781.432 | 0.926966 | ||||||||
\(844\) | 87.3144 | 0.103453 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −161.888 | −0.191357 | ||||||||
\(847\) | −9.73498 | −0.0114935 | ||||||||
\(848\) | −417.011 | −0.491759 | ||||||||
\(849\) | 805.700i | 0.948999i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 501.463 | + | 1112.51i | 0.589263 | + | 1.30730i | ||||
\(852\) | − | 371.689i | − | 0.436255i | ||||||
\(853\) | − | 1653.13i | − | 1.93802i | −0.247023 | − | 0.969010i | \(-0.579452\pi\) | ||
0.247023 | − | 0.969010i | \(-0.420548\pi\) | |||||||
\(854\) | −38.8841 | −0.0455318 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 29.5696i | − | 0.0345439i | ||||||
\(857\) | 1453.42i | 1.69593i | 0.530048 | + | 0.847967i | \(0.322174\pi\) | ||||
−0.530048 | + | 0.847967i | \(0.677826\pi\) | |||||||
\(858\) | 762.540 | 0.888742 | ||||||||
\(859\) | −936.399 | −1.09010 | −0.545052 | − | 0.838402i | \(-0.683490\pi\) | ||||
−0.545052 | + | 0.838402i | \(0.683490\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 37.1394i | − | 0.0431352i | ||||||
\(862\) | 339.151 | 0.393446 | ||||||||
\(863\) | − | 961.830i | − | 1.11452i | −0.830339 | − | 0.557259i | \(-0.811853\pi\) | ||
0.830339 | − | 0.557259i | \(-0.188147\pi\) | |||||||
\(864\) | −127.008 | −0.147000 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 432.102i | − | 0.498963i | ||||||
\(867\) | 385.585i | 0.444735i | ||||||||
\(868\) | −63.3640 | −0.0730000 | ||||||||
\(869\) | 605.943 | 0.697287 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 897.563i | − | 1.03050i | ||||||
\(872\) | 195.507 | 0.224205 | ||||||||
\(873\) | −46.2756 | −0.0530075 | ||||||||
\(874\) | 301.037 | + | 667.862i | 0.344436 | + | 0.764144i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 59.0594 | 0.0674194 | ||||||||
\(877\) | − | 1244.55i | − | 1.41910i | −0.704657 | − | 0.709549i | \(-0.748899\pi\) | ||
0.704657 | − | 0.709549i | \(-0.251101\pi\) | |||||||
\(878\) | 818.855i | 0.932637i | ||||||||
\(879\) | − | 1958.41i | − | 2.22800i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 961.719i | − | 1.09162i | −0.837908 | − | 0.545811i | \(-0.816222\pi\) | ||
0.837908 | − | 0.545811i | \(-0.183778\pi\) | |||||||
\(882\) | 156.935i | 0.177931i | ||||||||
\(883\) | − | 42.4945i | − | 0.0481251i | −0.999710 | − | 0.0240626i | \(-0.992340\pi\) | ||
0.999710 | − | 0.0240626i | \(-0.00766009\pi\) | |||||||
\(884\) | 606.330i | 0.685893i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −857.401 | −0.967722 | ||||||||
\(887\) | − | 551.962i | − | 0.622279i | −0.950364 | − | 0.311140i | \(-0.899289\pi\) | ||
0.950364 | − | 0.311140i | \(-0.100711\pi\) | |||||||
\(888\) | 505.121 | 0.568830 | ||||||||
\(889\) | − | 67.7774i | − | 0.0762400i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1024.75i | − | 1.15011i | ||||||
\(892\) | 697.246i | 0.781666i | ||||||||
\(893\) | −1106.65 | −1.23925 | ||||||||
\(894\) | − | 304.054i | − | 0.340106i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13.2278i | 0.0147632i | ||||||||
\(897\) | −480.102 | − | 1065.12i | −0.535231 | − | 1.18743i | ||||
\(898\) | 286.492i | 0.319033i | ||||||||
\(899\) | 883.359 | 0.982601 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2094.30 | 2.32442 | ||||||||
\(902\) | −141.667 | −0.157059 | ||||||||
\(903\) | − | 143.400i | − | 0.158804i | ||||||
\(904\) | − | 388.242i | − | 0.429472i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 167.879 | 0.185297 | ||||||||
\(907\) | −237.524 | −0.261878 | −0.130939 | − | 0.991390i | \(-0.541799\pi\) | ||||
−0.130939 | + | 0.991390i | \(0.541799\pi\) | |||||||
\(908\) | 351.587 | 0.387210 | ||||||||
\(909\) | −201.666 | −0.221855 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 402.885i | − | 0.442245i | −0.975246 | − | 0.221122i | \(-0.929028\pi\) | ||
0.975246 | − | 0.221122i | \(-0.0709720\pi\) | |||||||
\(912\) | 303.233 | 0.332493 | ||||||||
\(913\) | − | 585.712i | − | 0.641524i | ||||||
\(914\) | − | 528.577i | − | 0.578312i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.88295i | 0.00314733i | ||||||||
\(917\) | 111.167 | 0.121229 | ||||||||
\(918\) | 637.854 | 0.694830 | ||||||||
\(919\) | 1338.53i | 1.45650i | 0.685310 | + | 0.728251i | \(0.259667\pi\) | ||||
−0.685310 | + | 0.728251i | \(0.740333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −370.706 | −0.402503 | ||||||||
\(922\) | 1003.21i | 1.08808i | ||||||||
\(923\) | 833.238i | 0.902750i | ||||||||
\(924\) | −83.5475 | −0.0904194 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 376.872 | 0.406989 | ||||||||
\(927\) | −335.748 | −0.362188 | ||||||||
\(928\) | − | 184.409i | − | 0.198717i | ||||||
\(929\) | −621.771 | −0.669291 | −0.334646 | − | 0.942344i | \(-0.608617\pi\) | ||||
−0.334646 | + | 0.942344i | \(0.608617\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1072.79i | 1.15230i | ||||||||
\(932\) | − | 226.831i | − | 0.243381i | ||||||
\(933\) | − | 1003.39i | − | 1.07545i | ||||||
\(934\) | − | 970.341i | − | 1.03891i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −99.4419 | −0.106241 | ||||||||
\(937\) | 915.580 | 0.977140 | 0.488570 | − | 0.872525i | \(-0.337519\pi\) | ||||
0.488570 | + | 0.872525i | \(0.337519\pi\) | |||||||
\(938\) | 98.3412i | 0.104841i | ||||||||
\(939\) | − | 368.486i | − | 0.392424i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 834.255i | − | 0.886563i | −0.896383 | − | 0.443281i | \(-0.853814\pi\) | ||
0.896383 | − | 0.443281i | \(-0.146186\pi\) | |||||||
\(942\) | 1376.34 | 1.46108 | ||||||||
\(943\) | 89.1950 | + | 197.882i | 0.0945864 | + | 0.209843i | ||||
\(944\) | −214.183 | −0.226889 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −546.995 | −0.578219 | ||||||||
\(947\) | 918.683i | 0.970099i | 0.874487 | + | 0.485049i | \(0.161198\pi\) | ||||
−0.874487 | + | 0.485049i | \(0.838802\pi\) | |||||||
\(948\) | −384.290 | −0.405369 | ||||||||
\(949\) | −132.397 | −0.139512 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1596.92 | −1.67921 | ||||||||
\(952\) | − | 66.4323i | − | 0.0697818i | ||||||
\(953\) | −789.341 | −0.828270 | −0.414135 | − | 0.910215i | \(-0.635916\pi\) | ||||
−0.414135 | + | 0.910215i | \(0.635916\pi\) | |||||||
\(954\) | 343.478i | 0.360040i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 734.519 | 0.768326 | ||||||||
\(957\) | 1164.74 | 1.21707 | ||||||||
\(958\) | −249.632 | −0.260577 | ||||||||
\(959\) | −232.330 | −0.242263 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −226.725 | −0.235927 | ||||||||
\(962\) | −1132.36 | −1.17709 | ||||||||
\(963\) | −24.3555 | −0.0252913 | ||||||||
\(964\) | − | 440.730i | − | 0.457189i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 52.6023 | + | 116.700i | 0.0544537 | + | 0.120807i | ||||
\(967\) | 875.476i | 0.905353i | 0.891675 | + | 0.452677i | \(0.149531\pi\) | ||||
−0.891675 | + | 0.452677i | \(0.850469\pi\) | |||||||
\(968\) | − | 23.5503i | − | 0.0243288i | ||||||
\(969\) | −1522.89 | −1.57161 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1232.49i | 1.26930i | 0.772801 | + | 0.634648i | \(0.218855\pi\) | ||||
−0.772801 | + | 0.634648i | \(0.781145\pi\) | |||||||
\(972\) | 245.761i | 0.252841i | ||||||||
\(973\) | −0.151386 | −0.000155587 | ||||||||
\(974\) | −742.182 | −0.761994 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 94.0663i | − | 0.0963794i | ||||||
\(977\) | −879.183 | −0.899880 | −0.449940 | − | 0.893059i | \(-0.648555\pi\) | ||||
−0.449940 | + | 0.893059i | \(0.648555\pi\) | |||||||
\(978\) | − | 220.176i | − | 0.225128i | ||||||
\(979\) | 1484.22 | 1.51606 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 161.033i | − | 0.164151i | ||||||
\(982\) | − | 779.298i | − | 0.793582i | ||||||
\(983\) | 247.090 | 0.251363 | 0.125682 | − | 0.992071i | \(-0.459888\pi\) | ||||
0.125682 | + | 0.992071i | \(0.459888\pi\) | |||||||
\(984\) | 89.8456 | 0.0913065 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 926.134i | 0.939284i | ||||||||
\(987\) | −193.373 | −0.195920 | ||||||||
\(988\) | −679.776 | −0.688032 | ||||||||
\(989\) | 344.393 | + | 764.048i | 0.348223 | + | 0.772546i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1750.79 | −1.76669 | −0.883347 | − | 0.468721i | \(-0.844715\pi\) | ||||
−0.883347 | + | 0.468721i | \(0.844715\pi\) | |||||||
\(992\) | − | 153.287i | − | 0.154523i | ||||||
\(993\) | 859.556i | 0.865615i | ||||||||
\(994\) | − | 91.2935i | − | 0.0918445i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 371.459i | 0.372951i | ||||||||
\(997\) | − | 456.156i | − | 0.457529i | −0.973482 | − | 0.228765i | \(-0.926531\pi\) | ||
0.973482 | − | 0.228765i | \(-0.0734686\pi\) | |||||||
\(998\) | 1041.91i | 1.04399i | ||||||||
\(999\) | 1191.23i | 1.19243i |
(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 | 1150.3.c.c.1149.18 | 32 | ||
5.2 | odd | 4 | 1150.3.d.b.551.5 | 16 | |||
5.3 | odd | 4 | 230.3.d.a.91.12 | yes | 16 | ||
5.4 | even | 2 | inner | 1150.3.c.c.1149.15 | 32 | ||
15.8 | even | 4 | 2070.3.c.a.91.3 | 16 | |||
20.3 | even | 4 | 1840.3.k.d.321.12 | 16 | |||
23.22 | odd | 2 | inner | 1150.3.c.c.1149.16 | 32 | ||
115.22 | even | 4 | 1150.3.d.b.551.6 | 16 | |||
115.68 | even | 4 | 230.3.d.a.91.11 | ✓ | 16 | ||
115.114 | odd | 2 | inner | 1150.3.c.c.1149.17 | 32 | ||
345.68 | odd | 4 | 2070.3.c.a.91.6 | 16 | |||
460.183 | odd | 4 | 1840.3.k.d.321.11 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.d.a.91.11 | ✓ | 16 | 115.68 | even | 4 | ||
230.3.d.a.91.12 | yes | 16 | 5.3 | odd | 4 | ||
1150.3.c.c.1149.15 | 32 | 5.4 | even | 2 | inner | ||
1150.3.c.c.1149.16 | 32 | 23.22 | odd | 2 | inner | ||
1150.3.c.c.1149.17 | 32 | 115.114 | odd | 2 | inner | ||
1150.3.c.c.1149.18 | 32 | 1.1 | even | 1 | trivial | ||
1150.3.d.b.551.5 | 16 | 5.2 | odd | 4 | |||
1150.3.d.b.551.6 | 16 | 115.22 | even | 4 | |||
1840.3.k.d.321.11 | 16 | 460.183 | odd | 4 | |||
1840.3.k.d.321.12 | 16 | 20.3 | even | 4 | |||
2070.3.c.a.91.3 | 16 | 15.8 | even | 4 | |||
2070.3.c.a.91.6 | 16 | 345.68 | odd | 4 |