Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.29 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.5.c.a.58.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.05068i | 1.01267i | 0.862337 | + | 0.506335i | \(0.169000\pi\) | ||||
−0.862337 | + | 0.506335i | \(0.831000\pi\) | |||||||
\(3\) | −5.19615 | −0.577350 | ||||||||
\(4\) | −0.408022 | −0.0255014 | ||||||||
\(5\) | −16.4107 | −0.656426 | −0.328213 | − | 0.944604i | \(-0.606446\pi\) | ||||
−0.328213 | + | 0.944604i | \(0.606446\pi\) | |||||||
\(6\) | − | 21.0480i | − | 0.584666i | ||||||
\(7\) | 47.3137 | 0.965586 | 0.482793 | − | 0.875735i | \(-0.339622\pi\) | ||||
0.482793 | + | 0.875735i | \(0.339622\pi\) | |||||||
\(8\) | 63.1581i | 0.986846i | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | − | 66.4744i | − | 0.664744i | ||||||
\(11\) | 25.6339i | 0.211850i | 0.994374 | + | 0.105925i | \(0.0337804\pi\) | ||||
−0.994374 | + | 0.105925i | \(0.966220\pi\) | |||||||
\(12\) | 2.12014 | 0.0147232 | ||||||||
\(13\) | 105.588i | 0.624780i | 0.949954 | + | 0.312390i | \(0.101130\pi\) | ||||
−0.949954 | + | 0.312390i | \(0.898870\pi\) | |||||||
\(14\) | 191.653i | 0.977820i | ||||||||
\(15\) | 85.2723 | 0.378988 | ||||||||
\(16\) | −262.362 | −1.02485 | ||||||||
\(17\) | 441.346 | 1.52715 | 0.763575 | − | 0.645719i | \(-0.223442\pi\) | ||||
0.763575 | + | 0.645719i | \(0.223442\pi\) | |||||||
\(18\) | 109.368i | 0.337557i | ||||||||
\(19\) | −560.726 | −1.55326 | −0.776629 | − | 0.629959i | \(-0.783072\pi\) | ||||
−0.776629 | + | 0.629959i | \(0.783072\pi\) | |||||||
\(20\) | 6.69591 | 0.0167398 | ||||||||
\(21\) | −245.849 | −0.557481 | ||||||||
\(22\) | −103.835 | −0.214535 | ||||||||
\(23\) | 764.114i | 1.44445i | 0.691658 | + | 0.722225i | \(0.256880\pi\) | ||||
−0.691658 | + | 0.722225i | \(0.743120\pi\) | |||||||
\(24\) | − | 328.179i | − | 0.569756i | ||||||
\(25\) | −355.690 | −0.569104 | ||||||||
\(26\) | −427.703 | −0.632696 | ||||||||
\(27\) | −140.296 | −0.192450 | ||||||||
\(28\) | −19.3050 | −0.0246238 | ||||||||
\(29\) | −1381.28 | −1.64243 | −0.821216 | − | 0.570618i | \(-0.806704\pi\) | ||||
−0.821216 | + | 0.570618i | \(0.806704\pi\) | |||||||
\(30\) | 345.411i | 0.383790i | ||||||||
\(31\) | − | 950.873i | − | 0.989462i | −0.869046 | − | 0.494731i | \(-0.835267\pi\) | ||
0.869046 | − | 0.494731i | \(-0.164733\pi\) | |||||||
\(32\) | − | 52.2142i | − | 0.0509904i | ||||||
\(33\) | − | 133.198i | − | 0.122312i | ||||||
\(34\) | 1787.75i | 1.54650i | ||||||||
\(35\) | −776.449 | −0.633836 | ||||||||
\(36\) | −11.0166 | −0.00850046 | ||||||||
\(37\) | 632.407i | 0.461948i | 0.972960 | + | 0.230974i | \(0.0741913\pi\) | ||||
−0.972960 | + | 0.230974i | \(0.925809\pi\) | |||||||
\(38\) | − | 2271.32i | − | 1.57294i | ||||||
\(39\) | − | 548.650i | − | 0.360717i | ||||||
\(40\) | − | 1036.47i | − | 0.647792i | ||||||
\(41\) | 1029.59 | 0.612489 | 0.306245 | − | 0.951953i | \(-0.400927\pi\) | ||||
0.306245 | + | 0.951953i | \(0.400927\pi\) | |||||||
\(42\) | − | 995.857i | − | 0.564545i | ||||||
\(43\) | − | 2959.97i | − | 1.60085i | −0.599434 | − | 0.800424i | \(-0.704608\pi\) | ||
0.599434 | − | 0.800424i | \(-0.295392\pi\) | |||||||
\(44\) | − | 10.4592i | − | 0.00540248i | ||||||
\(45\) | −443.088 | −0.218809 | ||||||||
\(46\) | −3095.18 | −1.46275 | ||||||||
\(47\) | 4322.20i | 1.95663i | 0.207119 | + | 0.978316i | \(0.433591\pi\) | ||||
−0.207119 | + | 0.978316i | \(0.566409\pi\) | |||||||
\(48\) | 1363.27 | 0.591698 | ||||||||
\(49\) | −162.413 | −0.0676439 | ||||||||
\(50\) | − | 1440.79i | − | 0.576315i | ||||||
\(51\) | −2293.30 | −0.881700 | ||||||||
\(52\) | − | 43.0822i | − | 0.0159327i | ||||||
\(53\) | −2110.03 | −0.751168 | −0.375584 | − | 0.926788i | \(-0.622558\pi\) | ||||
−0.375584 | + | 0.926788i | \(0.622558\pi\) | |||||||
\(54\) | − | 568.295i | − | 0.194889i | ||||||
\(55\) | − | 420.669i | − | 0.139064i | ||||||
\(56\) | 2988.25i | 0.952884i | ||||||||
\(57\) | 2913.62 | 0.896773 | ||||||||
\(58\) | − | 5595.14i | − | 1.66324i | ||||||
\(59\) | −3445.38 | + | 496.740i | −0.989766 | + | 0.142700i | ||||
\(60\) | −34.7930 | −0.00966471 | ||||||||
\(61\) | 4274.01i | 1.14862i | 0.818638 | + | 0.574309i | \(0.194729\pi\) | ||||
−0.818638 | + | 0.574309i | \(0.805271\pi\) | |||||||
\(62\) | 3851.68 | 1.00200 | ||||||||
\(63\) | 1277.47 | 0.321862 | ||||||||
\(64\) | −3986.29 | −0.973215 | ||||||||
\(65\) | − | 1732.77i | − | 0.410122i | ||||||
\(66\) | 539.541 | 0.123862 | ||||||||
\(67\) | − | 867.430i | − | 0.193234i | −0.995322 | − | 0.0966172i | \(-0.969198\pi\) | ||
0.995322 | − | 0.0966172i | \(-0.0308023\pi\) | |||||||
\(68\) | −180.079 | −0.0389444 | ||||||||
\(69\) | − | 3970.45i | − | 0.833953i | ||||||
\(70\) | − | 3145.15i | − | 0.641867i | ||||||
\(71\) | −236.548 | −0.0469249 | −0.0234624 | − | 0.999725i | \(-0.507469\pi\) | ||||
−0.0234624 | + | 0.999725i | \(0.507469\pi\) | |||||||
\(72\) | 1705.27i | 0.328949i | ||||||||
\(73\) | − | 6211.26i | − | 1.16556i | −0.812631 | − | 0.582779i | \(-0.801965\pi\) | ||
0.812631 | − | 0.582779i | \(-0.198035\pi\) | |||||||
\(74\) | −2561.68 | −0.467801 | ||||||||
\(75\) | 1848.22 | 0.328573 | ||||||||
\(76\) | 228.788 | 0.0396102 | ||||||||
\(77\) | 1212.84i | 0.204560i | ||||||||
\(78\) | 2222.41 | 0.365287 | ||||||||
\(79\) | 8916.22 | 1.42865 | 0.714326 | − | 0.699813i | \(-0.246733\pi\) | ||||
0.714326 | + | 0.699813i | \(0.246733\pi\) | |||||||
\(80\) | 4305.53 | 0.672739 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 4170.56i | 0.620250i | ||||||||
\(83\) | 10864.4i | 1.57706i | 0.614994 | + | 0.788532i | \(0.289158\pi\) | ||||
−0.614994 | + | 0.788532i | \(0.710842\pi\) | |||||||
\(84\) | 100.312 | 0.0142165 | ||||||||
\(85\) | −7242.78 | −1.00246 | ||||||||
\(86\) | 11989.9 | 1.62113 | ||||||||
\(87\) | 7177.37 | 0.948258 | ||||||||
\(88\) | −1618.99 | −0.209064 | ||||||||
\(89\) | 6262.72i | 0.790647i | 0.918542 | + | 0.395324i | \(0.129368\pi\) | ||||
−0.918542 | + | 0.395324i | \(0.870632\pi\) | |||||||
\(90\) | − | 1794.81i | − | 0.221581i | ||||||
\(91\) | 4995.75i | 0.603279i | ||||||||
\(92\) | − | 311.775i | − | 0.0368355i | ||||||
\(93\) | 4940.88i | 0.571266i | ||||||||
\(94\) | −17507.9 | −1.98142 | ||||||||
\(95\) | 9201.88 | 1.01960 | ||||||||
\(96\) | 271.313i | 0.0294393i | ||||||||
\(97\) | 7894.97i | 0.839087i | 0.907735 | + | 0.419543i | \(0.137810\pi\) | ||||
−0.907735 | + | 0.419543i | \(0.862190\pi\) | |||||||
\(98\) | − | 657.884i | − | 0.0685010i | ||||||
\(99\) | 692.115i | 0.0706168i | ||||||||
\(100\) | 145.129 | 0.0145129 | ||||||||
\(101\) | 6756.86i | 0.662372i | 0.943566 | + | 0.331186i | \(0.107449\pi\) | ||||
−0.943566 | + | 0.331186i | \(0.892551\pi\) | |||||||
\(102\) | − | 9289.44i | − | 0.892872i | ||||||
\(103\) | 19989.4i | 1.88420i | 0.335338 | + | 0.942098i | \(0.391149\pi\) | ||||
−0.335338 | + | 0.942098i | \(0.608851\pi\) | |||||||
\(104\) | −6668.73 | −0.616562 | ||||||||
\(105\) | 4034.55 | 0.365945 | ||||||||
\(106\) | − | 8547.07i | − | 0.760686i | ||||||
\(107\) | 14259.8 | 1.24550 | 0.622751 | − | 0.782420i | \(-0.286015\pi\) | ||||
0.622751 | + | 0.782420i | \(0.286015\pi\) | |||||||
\(108\) | 57.2439 | 0.00490774 | ||||||||
\(109\) | 219.395i | 0.0184660i | 0.999957 | + | 0.00923302i | \(0.00293900\pi\) | ||||
−0.999957 | + | 0.00923302i | \(0.997061\pi\) | |||||||
\(110\) | 1704.00 | 0.140826 | ||||||||
\(111\) | − | 3286.08i | − | 0.266706i | ||||||
\(112\) | −12413.3 | −0.989582 | ||||||||
\(113\) | − | 12616.9i | − | 0.988089i | −0.869437 | − | 0.494044i | \(-0.835518\pi\) | ||
0.869437 | − | 0.494044i | \(-0.164482\pi\) | |||||||
\(114\) | 11802.1i | 0.908136i | ||||||||
\(115\) | − | 12539.6i | − | 0.948175i | ||||||
\(116\) | 563.595 | 0.0418843 | ||||||||
\(117\) | 2850.87i | 0.208260i | ||||||||
\(118\) | −2012.14 | − | 13956.1i | −0.144508 | − | 1.00231i | ||||
\(119\) | 20881.7 | 1.47459 | ||||||||
\(120\) | 5385.64i | 0.374003i | ||||||||
\(121\) | 13983.9 | 0.955119 | ||||||||
\(122\) | −17312.7 | −1.16317 | ||||||||
\(123\) | −5349.93 | −0.353621 | ||||||||
\(124\) | 387.977i | 0.0252326i | ||||||||
\(125\) | 16093.8 | 1.03000 | ||||||||
\(126\) | 5174.62i | 0.325940i | ||||||||
\(127\) | 3740.54 | 0.231914 | 0.115957 | − | 0.993254i | \(-0.463007\pi\) | ||||
0.115957 | + | 0.993254i | \(0.463007\pi\) | |||||||
\(128\) | − | 16982.6i | − | 1.03654i | ||||||
\(129\) | 15380.4i | 0.924250i | ||||||||
\(130\) | 7018.88 | 0.415318 | ||||||||
\(131\) | − | 21977.1i | − | 1.28064i | −0.768108 | − | 0.640320i | \(-0.778802\pi\) | ||
0.768108 | − | 0.640320i | \(-0.221198\pi\) | |||||||
\(132\) | 54.3476i | 0.00311912i | ||||||||
\(133\) | −26530.0 | −1.49980 | ||||||||
\(134\) | 3513.68 | 0.195683 | ||||||||
\(135\) | 2302.35 | 0.126329 | ||||||||
\(136\) | 27874.6i | 1.50706i | ||||||||
\(137\) | −8143.37 | −0.433873 | −0.216937 | − | 0.976186i | \(-0.569606\pi\) | ||||
−0.216937 | + | 0.976186i | \(0.569606\pi\) | |||||||
\(138\) | 16083.0 | 0.844520 | ||||||||
\(139\) | 13508.7 | 0.699172 | 0.349586 | − | 0.936904i | \(-0.386322\pi\) | ||||
0.349586 | + | 0.936904i | \(0.386322\pi\) | |||||||
\(140\) | 316.808 | 0.0161637 | ||||||||
\(141\) | − | 22458.8i | − | 1.12966i | ||||||
\(142\) | − | 958.182i | − | 0.0475194i | ||||||
\(143\) | −2706.63 | −0.132360 | ||||||||
\(144\) | −7083.77 | −0.341617 | ||||||||
\(145\) | 22667.8 | 1.07814 | ||||||||
\(146\) | 25159.8 | 1.18033 | ||||||||
\(147\) | 843.923 | 0.0390542 | ||||||||
\(148\) | − | 258.036i | − | 0.0117803i | ||||||
\(149\) | 5748.17i | 0.258915i | 0.991585 | + | 0.129457i | \(0.0413235\pi\) | ||||
−0.991585 | + | 0.129457i | \(0.958676\pi\) | |||||||
\(150\) | 7486.55i | 0.332736i | ||||||||
\(151\) | − | 39105.9i | − | 1.71510i | −0.514404 | − | 0.857548i | \(-0.671987\pi\) | ||
0.514404 | − | 0.857548i | \(-0.328013\pi\) | |||||||
\(152\) | − | 35414.4i | − | 1.53283i | ||||||
\(153\) | 11916.3 | 0.509050 | ||||||||
\(154\) | −4912.81 | −0.207152 | ||||||||
\(155\) | 15604.5i | 0.649509i | ||||||||
\(156\) | 223.861i | 0.00919878i | ||||||||
\(157\) | 995.408i | 0.0403833i | 0.999796 | + | 0.0201917i | \(0.00642764\pi\) | ||||
−0.999796 | + | 0.0201917i | \(0.993572\pi\) | |||||||
\(158\) | 36116.8i | 1.44675i | ||||||||
\(159\) | 10964.0 | 0.433687 | ||||||||
\(160\) | 856.869i | 0.0334715i | ||||||||
\(161\) | 36153.1i | 1.39474i | ||||||||
\(162\) | 2952.95i | 0.112519i | ||||||||
\(163\) | −51373.5 | −1.93359 | −0.966794 | − | 0.255559i | \(-0.917741\pi\) | ||||
−0.966794 | + | 0.255559i | \(0.917741\pi\) | |||||||
\(164\) | −420.097 | −0.0156193 | ||||||||
\(165\) | 2185.86i | 0.0802888i | ||||||||
\(166\) | −44008.2 | −1.59705 | ||||||||
\(167\) | −17563.4 | −0.629760 | −0.314880 | − | 0.949132i | \(-0.601964\pi\) | ||||
−0.314880 | + | 0.949132i | \(0.601964\pi\) | |||||||
\(168\) | − | 15527.4i | − | 0.550148i | ||||||
\(169\) | 17412.2 | 0.609650 | ||||||||
\(170\) | − | 29338.2i | − | 1.01516i | ||||||
\(171\) | −15139.6 | −0.517752 | ||||||||
\(172\) | 1207.73i | 0.0408238i | ||||||||
\(173\) | − | 59732.1i | − | 1.99579i | −0.0648356 | − | 0.997896i | \(-0.520652\pi\) | ||
0.0648356 | − | 0.997896i | \(-0.479348\pi\) | |||||||
\(174\) | 29073.2i | 0.960273i | ||||||||
\(175\) | −16829.0 | −0.549519 | ||||||||
\(176\) | − | 6725.36i | − | 0.217115i | ||||||
\(177\) | 17902.7 | − | 2581.14i | 0.571442 | − | 0.0823881i | ||||
\(178\) | −25368.3 | −0.800665 | ||||||||
\(179\) | − | 52499.1i | − | 1.63850i | −0.573439 | − | 0.819248i | \(-0.694391\pi\) | ||
0.573439 | − | 0.819248i | \(-0.305609\pi\) | |||||||
\(180\) | 180.790 | 0.00557993 | ||||||||
\(181\) | −1001.39 | −0.0305665 | −0.0152832 | − | 0.999883i | \(-0.504865\pi\) | ||||
−0.0152832 | + | 0.999883i | \(0.504865\pi\) | |||||||
\(182\) | −20236.2 | −0.610923 | ||||||||
\(183\) | − | 22208.4i | − | 0.663155i | ||||||
\(184\) | −48260.0 | −1.42545 | ||||||||
\(185\) | − | 10378.2i | − | 0.303235i | ||||||
\(186\) | −20013.9 | −0.578504 | ||||||||
\(187\) | 11313.4i | 0.323527i | ||||||||
\(188\) | − | 1763.55i | − | 0.0498968i | ||||||
\(189\) | −6637.93 | −0.185827 | ||||||||
\(190\) | 37273.9i | 1.03252i | ||||||||
\(191\) | 65871.0i | 1.80563i | 0.430034 | + | 0.902813i | \(0.358502\pi\) | ||||
−0.430034 | + | 0.902813i | \(0.641498\pi\) | |||||||
\(192\) | 20713.4 | 0.561886 | ||||||||
\(193\) | 46752.7 | 1.25514 | 0.627570 | − | 0.778560i | \(-0.284050\pi\) | ||||
0.627570 | + | 0.778560i | \(0.284050\pi\) | |||||||
\(194\) | −31980.0 | −0.849718 | ||||||||
\(195\) | 9003.72i | 0.236784i | ||||||||
\(196\) | 66.2681 | 0.00172501 | ||||||||
\(197\) | 56429.6 | 1.45403 | 0.727017 | − | 0.686619i | \(-0.240906\pi\) | ||||
0.727017 | + | 0.686619i | \(0.240906\pi\) | |||||||
\(198\) | −2803.54 | −0.0715116 | ||||||||
\(199\) | 4451.64 | 0.112412 | 0.0562061 | − | 0.998419i | \(-0.482100\pi\) | ||||
0.0562061 | + | 0.998419i | \(0.482100\pi\) | |||||||
\(200\) | − | 22464.7i | − | 0.561618i | ||||||
\(201\) | 4507.30i | 0.111564i | ||||||||
\(202\) | −27369.9 | −0.670764 | ||||||||
\(203\) | −65353.7 | −1.58591 | ||||||||
\(204\) | 935.718 | 0.0224846 | ||||||||
\(205\) | −16896.3 | −0.402054 | ||||||||
\(206\) | −80970.8 | −1.90807 | ||||||||
\(207\) | 20631.1i | 0.481483i | ||||||||
\(208\) | − | 27702.2i | − | 0.640306i | ||||||
\(209\) | − | 14373.6i | − | 0.329058i | ||||||
\(210\) | 16342.7i | 0.370582i | ||||||||
\(211\) | 42832.4i | 0.962071i | 0.876701 | + | 0.481036i | \(0.159739\pi\) | ||||
−0.876701 | + | 0.481036i | \(0.840261\pi\) | |||||||
\(212\) | 860.939 | 0.0191558 | ||||||||
\(213\) | 1229.14 | 0.0270921 | ||||||||
\(214\) | 57761.7i | 1.26128i | ||||||||
\(215\) | 48575.0i | 1.05084i | ||||||||
\(216\) | − | 8860.84i | − | 0.189919i | ||||||
\(217\) | − | 44989.3i | − | 0.955411i | ||||||
\(218\) | −888.699 | −0.0187000 | ||||||||
\(219\) | 32274.6i | 0.672935i | ||||||||
\(220\) | 171.642i | 0.00354633i | ||||||||
\(221\) | 46600.8i | 0.954132i | ||||||||
\(222\) | 13310.9 | 0.270085 | ||||||||
\(223\) | −14776.1 | −0.297132 | −0.148566 | − | 0.988902i | \(-0.547466\pi\) | ||||
−0.148566 | + | 0.988902i | \(0.547466\pi\) | |||||||
\(224\) | − | 2470.45i | − | 0.0492356i | ||||||
\(225\) | −9603.64 | −0.189701 | ||||||||
\(226\) | 51107.1 | 1.00061 | ||||||||
\(227\) | − | 37257.5i | − | 0.723040i | −0.932364 | − | 0.361520i | \(-0.882258\pi\) | ||
0.932364 | − | 0.361520i | \(-0.117742\pi\) | |||||||
\(228\) | −1188.82 | −0.0228690 | ||||||||
\(229\) | 36389.1i | 0.693906i | 0.937883 | + | 0.346953i | \(0.112784\pi\) | ||||
−0.937883 | + | 0.346953i | \(0.887216\pi\) | |||||||
\(230\) | 50794.0 | 0.960189 | ||||||||
\(231\) | − | 6302.08i | − | 0.118103i | ||||||
\(232\) | − | 87239.4i | − | 1.62083i | ||||||
\(233\) | 20634.6i | 0.380088i | 0.981776 | + | 0.190044i | \(0.0608630\pi\) | ||||
−0.981776 | + | 0.190044i | \(0.939137\pi\) | |||||||
\(234\) | −11548.0 | −0.210899 | ||||||||
\(235\) | − | 70930.1i | − | 1.28438i | ||||||
\(236\) | 1405.79 | − | 202.681i | 0.0252404 | − | 0.00363906i | ||||
\(237\) | −46330.0 | −0.824833 | ||||||||
\(238\) | 84585.2i | 1.49328i | ||||||||
\(239\) | −18302.2 | −0.320411 | −0.160205 | − | 0.987084i | \(-0.551216\pi\) | ||||
−0.160205 | + | 0.987084i | \(0.551216\pi\) | |||||||
\(240\) | −22372.2 | −0.388406 | ||||||||
\(241\) | 73211.9 | 1.26051 | 0.630257 | − | 0.776386i | \(-0.282949\pi\) | ||||
0.630257 | + | 0.776386i | \(0.282949\pi\) | |||||||
\(242\) | 56644.3i | 0.967221i | ||||||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | − | 1743.89i | − | 0.0292914i | ||||||
\(245\) | 2665.31 | 0.0444033 | ||||||||
\(246\) | − | 21670.9i | − | 0.358101i | ||||||
\(247\) | − | 59205.8i | − | 0.970444i | ||||||
\(248\) | 60055.4 | 0.976447 | ||||||||
\(249\) | − | 56453.0i | − | 0.910518i | ||||||
\(250\) | 65190.8i | 1.04305i | ||||||||
\(251\) | 66492.8 | 1.05542 | 0.527712 | − | 0.849423i | \(-0.323050\pi\) | ||||
0.527712 | + | 0.849423i | \(0.323050\pi\) | |||||||
\(252\) | −521.236 | −0.00820792 | ||||||||
\(253\) | −19587.2 | −0.306007 | ||||||||
\(254\) | 15151.7i | 0.234852i | ||||||||
\(255\) | 37634.6 | 0.578771 | ||||||||
\(256\) | 5010.54 | 0.0764548 | ||||||||
\(257\) | −48002.7 | −0.726774 | −0.363387 | − | 0.931638i | \(-0.618380\pi\) | ||||
−0.363387 | + | 0.931638i | \(0.618380\pi\) | |||||||
\(258\) | −62301.3 | −0.935961 | ||||||||
\(259\) | 29921.5i | 0.446051i | ||||||||
\(260\) | 707.007i | 0.0104587i | ||||||||
\(261\) | −37294.7 | −0.547477 | ||||||||
\(262\) | 89022.1 | 1.29687 | ||||||||
\(263\) | 23476.9 | 0.339413 | 0.169707 | − | 0.985495i | \(-0.445718\pi\) | ||||
0.169707 | + | 0.985495i | \(0.445718\pi\) | |||||||
\(264\) | 8412.52 | 0.120703 | ||||||||
\(265\) | 34627.0 | 0.493087 | ||||||||
\(266\) | − | 107465.i | − | 1.51881i | ||||||
\(267\) | − | 32542.0i | − | 0.456480i | ||||||
\(268\) | 353.930i | 0.00492775i | ||||||||
\(269\) | 86186.2i | 1.19106i | 0.803334 | + | 0.595529i | \(0.203058\pi\) | ||||
−0.803334 | + | 0.595529i | \(0.796942\pi\) | |||||||
\(270\) | 9326.09i | 0.127930i | ||||||||
\(271\) | −18673.8 | −0.254270 | −0.127135 | − | 0.991885i | \(-0.540578\pi\) | ||||
−0.127135 | + | 0.991885i | \(0.540578\pi\) | |||||||
\(272\) | −115792. | −1.56510 | ||||||||
\(273\) | − | 25958.7i | − | 0.348303i | ||||||
\(274\) | − | 32986.2i | − | 0.439371i | ||||||
\(275\) | − | 9117.73i | − | 0.120565i | ||||||
\(276\) | 1620.03i | 0.0212670i | ||||||||
\(277\) | 132710. | 1.72959 | 0.864797 | − | 0.502122i | \(-0.167447\pi\) | ||||
0.864797 | + | 0.502122i | \(0.167447\pi\) | |||||||
\(278\) | 54719.4i | 0.708030i | ||||||||
\(279\) | − | 25673.6i | − | 0.329821i | ||||||
\(280\) | − | 49039.1i | − | 0.625499i | ||||||
\(281\) | 42447.9 | 0.537581 | 0.268790 | − | 0.963199i | \(-0.413376\pi\) | ||||
0.268790 | + | 0.963199i | \(0.413376\pi\) | |||||||
\(282\) | 90973.5 | 1.14398 | ||||||||
\(283\) | − | 1417.90i | − | 0.0177041i | −0.999961 | − | 0.00885205i | \(-0.997182\pi\) | ||
0.999961 | − | 0.00885205i | \(-0.00281773\pi\) | |||||||
\(284\) | 96.5169 | 0.00119665 | ||||||||
\(285\) | −47814.4 | −0.588666 | ||||||||
\(286\) | − | 10963.7i | − | 0.134037i | ||||||
\(287\) | 48713.9 | 0.591411 | ||||||||
\(288\) | − | 1409.78i | − | 0.0169968i | ||||||
\(289\) | 111265. | 1.33219 | ||||||||
\(290\) | 91820.0i | 1.09180i | ||||||||
\(291\) | − | 41023.5i | − | 0.484447i | ||||||
\(292\) | 2534.33i | 0.0297233i | ||||||||
\(293\) | 44835.8 | 0.522264 | 0.261132 | − | 0.965303i | \(-0.415904\pi\) | ||||
0.261132 | + | 0.965303i | \(0.415904\pi\) | |||||||
\(294\) | 3418.46i | 0.0395491i | ||||||||
\(295\) | 56540.9 | − | 8151.83i | 0.649708 | − | 0.0936723i | ||||
\(296\) | −39941.7 | −0.455872 | ||||||||
\(297\) | − | 3596.34i | − | 0.0407706i | ||||||
\(298\) | −23284.0 | −0.262195 | ||||||||
\(299\) | −80681.1 | −0.902463 | ||||||||
\(300\) | −754.115 | −0.00837905 | ||||||||
\(301\) | − | 140047.i | − | 1.54576i | ||||||
\(302\) | 158406. | 1.73683 | ||||||||
\(303\) | − | 35109.7i | − | 0.382421i | ||||||
\(304\) | 147113. | 1.59186 | ||||||||
\(305\) | − | 70139.3i | − | 0.753984i | ||||||
\(306\) | 48269.3i | 0.515500i | ||||||||
\(307\) | −15561.6 | −0.165112 | −0.0825559 | − | 0.996586i | \(-0.526308\pi\) | ||||
−0.0825559 | + | 0.996586i | \(0.526308\pi\) | |||||||
\(308\) | − | 494.863i | − | 0.00521656i | ||||||
\(309\) | − | 103868.i | − | 1.08784i | ||||||
\(310\) | −63208.7 | −0.657739 | ||||||||
\(311\) | −160952. | −1.66409 | −0.832043 | − | 0.554711i | \(-0.812829\pi\) | ||||
−0.832043 | + | 0.554711i | \(0.812829\pi\) | |||||||
\(312\) | 34651.7 | 0.355972 | ||||||||
\(313\) | 79828.7i | 0.814836i | 0.913242 | + | 0.407418i | \(0.133571\pi\) | ||||
−0.913242 | + | 0.407418i | \(0.866429\pi\) | |||||||
\(314\) | −4032.08 | −0.0408950 | ||||||||
\(315\) | −20964.1 | −0.211279 | ||||||||
\(316\) | −3638.01 | −0.0364326 | ||||||||
\(317\) | 108281. | 1.07754 | 0.538770 | − | 0.842453i | \(-0.318889\pi\) | ||||
0.538770 | + | 0.842453i | \(0.318889\pi\) | |||||||
\(318\) | 44411.9i | 0.439182i | ||||||||
\(319\) | − | 35407.7i | − | 0.347950i | ||||||
\(320\) | 65417.6 | 0.638844 | ||||||||
\(321\) | −74095.9 | −0.719091 | ||||||||
\(322\) | −146445. | −1.41241 | ||||||||
\(323\) | −247474. | −2.37206 | ||||||||
\(324\) | −297.448 | −0.00283349 | ||||||||
\(325\) | − | 37556.6i | − | 0.355565i | ||||||
\(326\) | − | 208098.i | − | 1.95809i | ||||||
\(327\) | − | 1140.01i | − | 0.0106614i | ||||||
\(328\) | 65027.2i | 0.604432i | ||||||||
\(329\) | 204499.i | 1.88930i | ||||||||
\(330\) | −8854.23 | −0.0813061 | ||||||||
\(331\) | 124431. | 1.13573 | 0.567864 | − | 0.823123i | \(-0.307770\pi\) | ||||
0.567864 | + | 0.823123i | \(0.307770\pi\) | |||||||
\(332\) | − | 4432.91i | − | 0.0402173i | ||||||
\(333\) | 17075.0i | 0.153983i | ||||||||
\(334\) | − | 71143.6i | − | 0.637739i | ||||||
\(335\) | 14235.1i | 0.126844i | ||||||||
\(336\) | 64501.5 | 0.571335 | ||||||||
\(337\) | 88676.9i | 0.780820i | 0.920641 | + | 0.390410i | \(0.127667\pi\) | ||||
−0.920641 | + | 0.390410i | \(0.872333\pi\) | |||||||
\(338\) | 70531.3i | 0.617374i | ||||||||
\(339\) | 65559.4i | 0.570473i | ||||||||
\(340\) | 2955.21 | 0.0255641 | ||||||||
\(341\) | 24374.6 | 0.209618 | ||||||||
\(342\) | − | 61325.7i | − | 0.524313i | ||||||
\(343\) | −121285. | −1.03090 | ||||||||
\(344\) | 186946. | 1.57979 | ||||||||
\(345\) | 65157.7i | 0.547429i | ||||||||
\(346\) | 241956. | 2.02108 | ||||||||
\(347\) | 55831.8i | 0.463685i | 0.972753 | + | 0.231842i | \(0.0744754\pi\) | ||||
−0.972753 | + | 0.231842i | \(0.925525\pi\) | |||||||
\(348\) | −2928.52 | −0.0241819 | ||||||||
\(349\) | 66212.9i | 0.543616i | 0.962352 | + | 0.271808i | \(0.0876215\pi\) | ||||
−0.962352 | + | 0.271808i | \(0.912378\pi\) | |||||||
\(350\) | − | 68169.0i | − | 0.556482i | ||||||
\(351\) | − | 14813.6i | − | 0.120239i | ||||||
\(352\) | 1338.45 | 0.0108023 | ||||||||
\(353\) | 119306.i | 0.957439i | 0.877968 | + | 0.478719i | \(0.158899\pi\) | ||||
−0.877968 | + | 0.478719i | \(0.841101\pi\) | |||||||
\(354\) | 10455.4 | + | 72518.1i | 0.0834320 | + | 0.578682i | ||||
\(355\) | 3881.91 | 0.0308027 | ||||||||
\(356\) | − | 2555.33i | − | 0.0201626i | ||||||
\(357\) | −108505. | −0.851357 | ||||||||
\(358\) | 212657. | 1.65926 | ||||||||
\(359\) | −164492. | −1.27631 | −0.638155 | − | 0.769908i | \(-0.720302\pi\) | ||||
−0.638155 | + | 0.769908i | \(0.720302\pi\) | |||||||
\(360\) | − | 27984.6i | − | 0.215931i | ||||||
\(361\) | 184092. | 1.41261 | ||||||||
\(362\) | − | 4056.30i | − | 0.0309538i | ||||||
\(363\) | −72662.5 | −0.551438 | ||||||||
\(364\) | − | 2038.38i | − | 0.0153844i | ||||||
\(365\) | 101931.i | 0.765103i | ||||||||
\(366\) | 89959.2 | 0.671558 | ||||||||
\(367\) | − | 10621.8i | − | 0.0788613i | −0.999222 | − | 0.0394307i | \(-0.987446\pi\) | ||
0.999222 | − | 0.0394307i | \(-0.0125544\pi\) | |||||||
\(368\) | − | 200474.i | − | 1.48035i | ||||||
\(369\) | 27799.0 | 0.204163 | ||||||||
\(370\) | 42038.9 | 0.307077 | ||||||||
\(371\) | −99833.4 | −0.725318 | ||||||||
\(372\) | − | 2015.99i | − | 0.0145681i | ||||||
\(373\) | 49988.6 | 0.359297 | 0.179648 | − | 0.983731i | \(-0.442504\pi\) | ||||
0.179648 | + | 0.983731i | \(0.442504\pi\) | |||||||
\(374\) | −45827.1 | −0.327627 | ||||||||
\(375\) | −83625.7 | −0.594672 | ||||||||
\(376\) | −272982. | −1.93089 | ||||||||
\(377\) | − | 145847.i | − | 1.02616i | ||||||
\(378\) | − | 26888.1i | − | 0.188182i | ||||||
\(379\) | −23033.2 | −0.160352 | −0.0801762 | − | 0.996781i | \(-0.525548\pi\) | ||||
−0.0801762 | + | 0.996781i | \(0.525548\pi\) | |||||||
\(380\) | −3754.57 | −0.0260012 | ||||||||
\(381\) | −19436.4 | −0.133895 | ||||||||
\(382\) | −266823. | −1.82850 | ||||||||
\(383\) | −35518.2 | −0.242133 | −0.121067 | − | 0.992644i | \(-0.538631\pi\) | ||||
−0.121067 | + | 0.992644i | \(0.538631\pi\) | |||||||
\(384\) | 88244.2i | 0.598444i | ||||||||
\(385\) | − | 19903.4i | − | 0.134278i | ||||||
\(386\) | 189380.i | 1.27104i | ||||||||
\(387\) | − | 79919.1i | − | 0.533616i | ||||||
\(388\) | − | 3221.32i | − | 0.0213979i | ||||||
\(389\) | 157436. | 1.04041 | 0.520206 | − | 0.854041i | \(-0.325855\pi\) | ||||
0.520206 | + | 0.854041i | \(0.325855\pi\) | |||||||
\(390\) | −36471.2 | −0.239784 | ||||||||
\(391\) | 337239.i | 2.20589i | ||||||||
\(392\) | − | 10257.7i | − | 0.0667541i | ||||||
\(393\) | 114196.i | 0.739378i | ||||||||
\(394\) | 228578.i | 1.47246i | ||||||||
\(395\) | −146321. | −0.937805 | ||||||||
\(396\) | − | 282.398i | − | 0.00180083i | ||||||
\(397\) | − | 163490.i | − | 1.03731i | −0.854983 | − | 0.518656i | \(-0.826432\pi\) | ||
0.854983 | − | 0.518656i | \(-0.173568\pi\) | |||||||
\(398\) | 18032.2i | 0.113837i | ||||||||
\(399\) | 137854. | 0.865912 | ||||||||
\(400\) | 93319.6 | 0.583247 | ||||||||
\(401\) | − | 74973.1i | − | 0.466248i | −0.972447 | − | 0.233124i | \(-0.925105\pi\) | ||
0.972447 | − | 0.233124i | \(-0.0748948\pi\) | |||||||
\(402\) | −18257.6 | −0.112978 | ||||||||
\(403\) | 100401. | 0.618196 | ||||||||
\(404\) | − | 2756.95i | − | 0.0168914i | ||||||
\(405\) | −11963.4 | −0.0729363 | ||||||||
\(406\) | − | 264727.i | − | 1.60600i | ||||||
\(407\) | −16211.1 | −0.0978640 | ||||||||
\(408\) | − | 144841.i | − | 0.870102i | ||||||
\(409\) | 216548.i | 1.29452i | 0.762271 | + | 0.647258i | \(0.224084\pi\) | ||||
−0.762271 | + | 0.647258i | \(0.775916\pi\) | |||||||
\(410\) | − | 68441.6i | − | 0.407148i | ||||||
\(411\) | 42314.2 | 0.250497 | ||||||||
\(412\) | − | 8156.13i | − | 0.0480496i | ||||||
\(413\) | −163013. | + | 23502.6i | −0.955704 | + | 0.137789i | ||||
\(414\) | −83569.9 | −0.487584 | ||||||||
\(415\) | − | 178292.i | − | 1.03523i | ||||||
\(416\) | 5513.18 | 0.0318578 | ||||||||
\(417\) | −70193.2 | −0.403667 | ||||||||
\(418\) | 58222.8 | 0.333228 | ||||||||
\(419\) | − | 221474.i | − | 1.26152i | −0.775977 | − | 0.630761i | \(-0.782743\pi\) | ||
0.775977 | − | 0.630761i | \(-0.217257\pi\) | |||||||
\(420\) | −1646.18 | −0.00933211 | ||||||||
\(421\) | 315604.i | 1.78065i | 0.455329 | + | 0.890323i | \(0.349522\pi\) | ||||
−0.455329 | + | 0.890323i | \(0.650478\pi\) | |||||||
\(422\) | −173500. | −0.974261 | ||||||||
\(423\) | 116699.i | 0.652211i | ||||||||
\(424\) | − | 133266.i | − | 0.741287i | ||||||
\(425\) | −156983. | −0.869107 | ||||||||
\(426\) | 4978.86i | 0.0274353i | ||||||||
\(427\) | 202219.i | 1.10909i | ||||||||
\(428\) | −5818.29 | −0.0317620 | ||||||||
\(429\) | 14064.1 | 0.0764180 | ||||||||
\(430\) | −196762. | −1.06415 | ||||||||
\(431\) | 37329.5i | 0.200954i | 0.994939 | + | 0.100477i | \(0.0320369\pi\) | ||||
−0.994939 | + | 0.100477i | \(0.967963\pi\) | |||||||
\(432\) | 36808.4 | 0.197233 | ||||||||
\(433\) | 60211.0 | 0.321144 | 0.160572 | − | 0.987024i | \(-0.448666\pi\) | ||||
0.160572 | + | 0.987024i | \(0.448666\pi\) | |||||||
\(434\) | 182237. | 0.967516 | ||||||||
\(435\) | −117785. | −0.622462 | ||||||||
\(436\) | − | 89.5180i | − | 0.000470909i | ||||||
\(437\) | − | 428458.i | − | 2.24360i | ||||||
\(438\) | −130734. | −0.681461 | ||||||||
\(439\) | −185108. | −0.960495 | −0.480248 | − | 0.877133i | \(-0.659453\pi\) | ||||
−0.480248 | + | 0.877133i | \(0.659453\pi\) | |||||||
\(440\) | 26568.7 | 0.137235 | ||||||||
\(441\) | −4385.15 | −0.0225480 | ||||||||
\(442\) | −188765. | −0.966222 | ||||||||
\(443\) | 234937.i | 1.19714i | 0.801071 | + | 0.598569i | \(0.204264\pi\) | ||||
−0.801071 | + | 0.598569i | \(0.795736\pi\) | |||||||
\(444\) | 1340.79i | 0.00680137i | ||||||||
\(445\) | − | 102775.i | − | 0.519002i | ||||||
\(446\) | − | 59853.3i | − | 0.300897i | ||||||
\(447\) | − | 29868.3i | − | 0.149484i | ||||||
\(448\) | −188606. | −0.939722 | ||||||||
\(449\) | −69120.8 | −0.342859 | −0.171430 | − | 0.985196i | \(-0.554839\pi\) | ||||
−0.171430 | + | 0.985196i | \(0.554839\pi\) | |||||||
\(450\) | − | 38901.3i | − | 0.192105i | ||||||
\(451\) | 26392.5i | 0.129756i | ||||||||
\(452\) | 5147.98i | 0.0251976i | ||||||||
\(453\) | 203200.i | 0.990211i | ||||||||
\(454\) | 150918. | 0.732201 | ||||||||
\(455\) | − | 81983.6i | − | 0.396008i | ||||||
\(456\) | 184019.i | 0.884977i | ||||||||
\(457\) | − | 307630.i | − | 1.47298i | −0.676449 | − | 0.736489i | \(-0.736482\pi\) | ||
0.676449 | − | 0.736489i | \(-0.263518\pi\) | |||||||
\(458\) | −147401. | −0.702698 | ||||||||
\(459\) | −61919.2 | −0.293900 | ||||||||
\(460\) | 5116.44i | 0.0241798i | ||||||||
\(461\) | 20386.5 | 0.0959272 | 0.0479636 | − | 0.998849i | \(-0.484727\pi\) | ||||
0.0479636 | + | 0.998849i | \(0.484727\pi\) | |||||||
\(462\) | 25527.7 | 0.119599 | ||||||||
\(463\) | − | 50749.8i | − | 0.236740i | −0.992970 | − | 0.118370i | \(-0.962233\pi\) | ||
0.992970 | − | 0.118370i | \(-0.0377669\pi\) | |||||||
\(464\) | 362396. | 1.68325 | ||||||||
\(465\) | − | 81083.1i | − | 0.374994i | ||||||
\(466\) | −83584.1 | −0.384904 | ||||||||
\(467\) | 9160.46i | 0.0420033i | 0.999779 | + | 0.0210017i | \(0.00668553\pi\) | ||||
−0.999779 | + | 0.0210017i | \(0.993314\pi\) | |||||||
\(468\) | − | 1163.22i | − | 0.00531092i | ||||||
\(469\) | − | 41041.3i | − | 0.186584i | ||||||
\(470\) | 287315. | 1.30066 | ||||||||
\(471\) | − | 5172.29i | − | 0.0233153i | ||||||
\(472\) | −31373.2 | − | 217603.i | −0.140823 | − | 0.976746i | ||||
\(473\) | 75875.5 | 0.339140 | ||||||||
\(474\) | − | 187668.i | − | 0.835284i | ||||||
\(475\) | 199445. | 0.883965 | ||||||||
\(476\) | −8520.20 | −0.0376042 | ||||||||
\(477\) | −56970.9 | −0.250389 | ||||||||
\(478\) | − | 74136.3i | − | 0.324471i | ||||||
\(479\) | 281255. | 1.22583 | 0.612913 | − | 0.790150i | \(-0.289997\pi\) | ||||
0.612913 | + | 0.790150i | \(0.289997\pi\) | |||||||
\(480\) | − | 4452.42i | − | 0.0193248i | ||||||
\(481\) | −66774.5 | −0.288616 | ||||||||
\(482\) | 296558.i | 1.27649i | ||||||||
\(483\) | − | 187857.i | − | 0.805254i | ||||||
\(484\) | −5705.74 | −0.0243569 | ||||||||
\(485\) | − | 129562.i | − | 0.550799i | ||||||
\(486\) | − | 15344.0i | − | 0.0649628i | ||||||
\(487\) | −12464.0 | −0.0525534 | −0.0262767 | − | 0.999655i | \(-0.508365\pi\) | ||||
−0.0262767 | + | 0.999655i | \(0.508365\pi\) | |||||||
\(488\) | −269939. | −1.13351 | ||||||||
\(489\) | 266944. | 1.11636 | ||||||||
\(490\) | 10796.3i | 0.0449659i | ||||||||
\(491\) | −267488. | −1.10954 | −0.554768 | − | 0.832005i | \(-0.687193\pi\) | ||||
−0.554768 | + | 0.832005i | \(0.687193\pi\) | |||||||
\(492\) | 2182.89 | 0.00901781 | ||||||||
\(493\) | −609625. | −2.50824 | ||||||||
\(494\) | 239824. | 0.982740 | ||||||||
\(495\) | − | 11358.1i | − | 0.0463547i | ||||||
\(496\) | 249473.i | 1.01405i | ||||||||
\(497\) | −11192.0 | −0.0453100 | ||||||||
\(498\) | 228673. | 0.922054 | ||||||||
\(499\) | −211721. | −0.850283 | −0.425142 | − | 0.905127i | \(-0.639776\pi\) | ||||
−0.425142 | + | 0.905127i | \(0.639776\pi\) | |||||||
\(500\) | −6566.61 | −0.0262665 | ||||||||
\(501\) | 91261.9 | 0.363592 | ||||||||
\(502\) | 269341.i | 1.06880i | ||||||||
\(503\) | 46231.2i | 0.182725i | 0.995818 | + | 0.0913627i | \(0.0291223\pi\) | ||||
−0.995818 | + | 0.0913627i | \(0.970878\pi\) | |||||||
\(504\) | 80682.6i | 0.317628i | ||||||||
\(505\) | − | 110884.i | − | 0.434798i | ||||||
\(506\) | − | 79341.6i | − | 0.309885i | ||||||
\(507\) | −90476.5 | −0.351982 | ||||||||
\(508\) | −1526.22 | −0.00591412 | ||||||||
\(509\) | − | 118612.i | − | 0.457819i | −0.973448 | − | 0.228909i | \(-0.926484\pi\) | ||
0.973448 | − | 0.228909i | \(-0.0735159\pi\) | |||||||
\(510\) | 152446.i | 0.586105i | ||||||||
\(511\) | − | 293878.i | − | 1.12545i | ||||||
\(512\) | − | 251426.i | − | 0.959113i | ||||||
\(513\) | 78667.7 | 0.298924 | ||||||||
\(514\) | − | 194444.i | − | 0.735982i | ||||||
\(515\) | − | 328040.i | − | 1.23684i | ||||||
\(516\) | − | 6275.56i | − | 0.0235696i | ||||||
\(517\) | −110795. | −0.414513 | ||||||||
\(518\) | −121203. | −0.451702 | ||||||||
\(519\) | 310377.i | 1.15227i | ||||||||
\(520\) | 109438. | 0.404727 | ||||||||
\(521\) | −20361.9 | −0.0750140 | −0.0375070 | − | 0.999296i | \(-0.511942\pi\) | ||||
−0.0375070 | + | 0.999296i | \(0.511942\pi\) | |||||||
\(522\) | − | 151069.i | − | 0.554414i | ||||||
\(523\) | 36769.4 | 0.134426 | 0.0672130 | − | 0.997739i | \(-0.478589\pi\) | ||||
0.0672130 | + | 0.997739i | \(0.478589\pi\) | |||||||
\(524\) | 8967.13i | 0.0326581i | ||||||||
\(525\) | 87446.2 | 0.317265 | ||||||||
\(526\) | 95097.4i | 0.343714i | ||||||||
\(527\) | − | 419664.i | − | 1.51106i | ||||||
\(528\) | 34946.0i | 0.125351i | ||||||||
\(529\) | −304029. | −1.08643 | ||||||||
\(530\) | 140263.i | 0.499334i | ||||||||
\(531\) | −93025.1 | + | 13412.0i | −0.329922 | + | 0.0475668i | ||||
\(532\) | 10824.8 | 0.0382470 | ||||||||
\(533\) | 108713.i | 0.382671i | ||||||||
\(534\) | 131817. | 0.462264 | ||||||||
\(535\) | −234012. | −0.817581 | ||||||||
\(536\) | 54785.2 | 0.190693 | ||||||||
\(537\) | 272793.i | 0.945986i | ||||||||
\(538\) | −349113. | −1.20615 | ||||||||
\(539\) | − | 4163.28i | − | 0.0143304i | ||||||
\(540\) | −939.410 | −0.00322157 | ||||||||
\(541\) | 136111.i | 0.465049i | 0.972590 | + | 0.232525i | \(0.0746986\pi\) | ||||
−0.972590 | + | 0.232525i | \(0.925301\pi\) | |||||||
\(542\) | − | 75641.7i | − | 0.257491i | ||||||
\(543\) | 5203.37 | 0.0176476 | ||||||||
\(544\) | − | 23044.5i | − | 0.0778700i | ||||||
\(545\) | − | 3600.42i | − | 0.0121216i | ||||||
\(546\) | 105150. | 0.352716 | ||||||||
\(547\) | 532541. | 1.77983 | 0.889915 | − | 0.456125i | \(-0.150763\pi\) | ||||
0.889915 | + | 0.456125i | \(0.150763\pi\) | |||||||
\(548\) | 3322.67 | 0.0110644 | ||||||||
\(549\) | 115398.i | 0.382873i | ||||||||
\(550\) | 36933.0 | 0.122093 | ||||||||
\(551\) | 774522. | 2.55112 | ||||||||
\(552\) | 250766. | 0.822983 | ||||||||
\(553\) | 421859. | 1.37949 | ||||||||
\(554\) | 537566.i | 1.75151i | ||||||||
\(555\) | 53926.8i | 0.175073i | ||||||||
\(556\) | −5511.84 | −0.0178298 | ||||||||
\(557\) | −166657. | −0.537172 | −0.268586 | − | 0.963256i | \(-0.586556\pi\) | ||||
−0.268586 | + | 0.963256i | \(0.586556\pi\) | |||||||
\(558\) | 103995. | 0.334000 | ||||||||
\(559\) | 312537. | 1.00018 | ||||||||
\(560\) | 203711. | 0.649588 | ||||||||
\(561\) | − | 58786.3i | − | 0.186789i | ||||||
\(562\) | 171943.i | 0.544392i | ||||||||
\(563\) | 111610.i | 0.352116i | 0.984380 | + | 0.176058i | \(0.0563347\pi\) | ||||
−0.984380 | + | 0.176058i | \(0.943665\pi\) | |||||||
\(564\) | 9163.69i | 0.0288079i | ||||||||
\(565\) | 207052.i | 0.648608i | ||||||||
\(566\) | 5743.47 | 0.0179284 | ||||||||
\(567\) | 34491.7 | 0.107287 | ||||||||
\(568\) | − | 14939.9i | − | 0.0463076i | ||||||
\(569\) | − | 112850.i | − | 0.348560i | −0.984696 | − | 0.174280i | \(-0.944240\pi\) | ||
0.984696 | − | 0.174280i | \(-0.0557598\pi\) | |||||||
\(570\) | − | 193681.i | − | 0.596124i | ||||||
\(571\) | 441479.i | 1.35406i | 0.735956 | + | 0.677029i | \(0.236733\pi\) | ||||
−0.735956 | + | 0.677029i | \(0.763267\pi\) | |||||||
\(572\) | 1104.36 | 0.00337536 | ||||||||
\(573\) | − | 342276.i | − | 1.04248i | ||||||
\(574\) | 197325.i | 0.598904i | ||||||||
\(575\) | − | 271788.i | − | 0.822043i | ||||||
\(576\) | −107630. | −0.324405 | ||||||||
\(577\) | 214151. | 0.643234 | 0.321617 | − | 0.946870i | \(-0.395774\pi\) | ||||
0.321617 | + | 0.946870i | \(0.395774\pi\) | |||||||
\(578\) | 450701.i | 1.34906i | ||||||||
\(579\) | −242934. | −0.724655 | ||||||||
\(580\) | −9248.96 | −0.0274939 | ||||||||
\(581\) | 514034.i | 1.52279i | ||||||||
\(582\) | 166173. | 0.490585 | ||||||||
\(583\) | − | 54088.4i | − | 0.159135i | ||||||
\(584\) | 392291. | 1.15023 | ||||||||
\(585\) | − | 46784.7i | − | 0.136707i | ||||||
\(586\) | 181616.i | 0.528881i | ||||||||
\(587\) | 229548.i | 0.666189i | 0.942893 | + | 0.333094i | \(0.108093\pi\) | ||||
−0.942893 | + | 0.333094i | \(0.891907\pi\) | |||||||
\(588\) | −344.339 | −0.000995937 | ||||||||
\(589\) | 533179.i | 1.53689i | ||||||||
\(590\) | 33020.5 | + | 229029.i | 0.0948592 | + | 0.657941i | ||||
\(591\) | −293217. | −0.839487 | ||||||||
\(592\) | − | 165920.i | − | 0.473428i | ||||||
\(593\) | 161537. | 0.459371 | 0.229686 | − | 0.973265i | \(-0.426230\pi\) | ||||
0.229686 | + | 0.973265i | \(0.426230\pi\) | |||||||
\(594\) | 14567.6 | 0.0412872 | ||||||||
\(595\) | −342683. | −0.967962 | ||||||||
\(596\) | − | 2345.38i | − | 0.00660268i | ||||||
\(597\) | −23131.4 | −0.0649012 | ||||||||
\(598\) | − | 326813.i | − | 0.913898i | ||||||
\(599\) | −259778. | −0.724017 | −0.362008 | − | 0.932175i | \(-0.617909\pi\) | ||||
−0.362008 | + | 0.932175i | \(0.617909\pi\) | |||||||
\(600\) | 116730.i | 0.324251i | ||||||||
\(601\) | − | 609538.i | − | 1.68753i | −0.536713 | − | 0.843765i | \(-0.680334\pi\) | ||
0.536713 | − | 0.843765i | \(-0.319666\pi\) | |||||||
\(602\) | 567286. | 1.56534 | ||||||||
\(603\) | − | 23420.6i | − | 0.0644115i | ||||||
\(604\) | 15956.1i | 0.0437373i | ||||||||
\(605\) | −229485. | −0.626966 | ||||||||
\(606\) | 142218. | 0.387266 | ||||||||
\(607\) | 123432. | 0.335005 | 0.167502 | − | 0.985872i | \(-0.446430\pi\) | ||||
0.167502 | + | 0.985872i | \(0.446430\pi\) | |||||||
\(608\) | 29277.8i | 0.0792012i | ||||||||
\(609\) | 339588. | 0.915625 | ||||||||
\(610\) | 284112. | 0.763537 | ||||||||
\(611\) | −456372. | −1.22246 | ||||||||
\(612\) | −4862.13 | −0.0129815 | ||||||||
\(613\) | − | 182402.i | − | 0.485409i | −0.970100 | − | 0.242705i | \(-0.921965\pi\) | ||
0.970100 | − | 0.242705i | \(-0.0780346\pi\) | |||||||
\(614\) | − | 63035.2i | − | 0.167204i | ||||||
\(615\) | 87795.8 | 0.232126 | ||||||||
\(616\) | −76600.4 | −0.201869 | ||||||||
\(617\) | 550891. | 1.44709 | 0.723544 | − | 0.690278i | \(-0.242512\pi\) | ||||
0.723544 | + | 0.690278i | \(0.242512\pi\) | |||||||
\(618\) | 420737. | 1.10162 | ||||||||
\(619\) | 172751. | 0.450856 | 0.225428 | − | 0.974260i | \(-0.427622\pi\) | ||||
0.225428 | + | 0.974260i | \(0.427622\pi\) | |||||||
\(620\) | − | 6366.96i | − | 0.0165634i | ||||||
\(621\) | − | 107202.i | − | 0.277984i | ||||||
\(622\) | − | 651966.i | − | 1.68517i | ||||||
\(623\) | 296312.i | 0.763438i | ||||||||
\(624\) | 143945.i | 0.369681i | ||||||||
\(625\) | −41803.1 | −0.107016 | ||||||||
\(626\) | −323361. | −0.825160 | ||||||||
\(627\) | 74687.4i | 0.189982i | ||||||||
\(628\) | − | 406.149i | − | 0.00102983i | ||||||
\(629\) | 279111.i | 0.705464i | ||||||||
\(630\) | − | 84919.0i | − | 0.213956i | ||||||
\(631\) | −6939.21 | −0.0174282 | −0.00871408 | − | 0.999962i | \(-0.502774\pi\) | ||||
−0.00871408 | + | 0.999962i | \(0.502774\pi\) | |||||||
\(632\) | 563132.i | 1.40986i | ||||||||
\(633\) | − | 222563.i | − | 0.555452i | ||||||
\(634\) | 438611.i | 1.09119i | ||||||||
\(635\) | −61384.7 | −0.152234 | ||||||||
\(636\) | −4473.57 | −0.0110596 | ||||||||
\(637\) | − | 17148.8i | − | 0.0422626i | ||||||
\(638\) | 143425. | 0.352358 | ||||||||
\(639\) | −6386.80 | −0.0156416 | ||||||||
\(640\) | 278696.i | 0.680410i | ||||||||
\(641\) | −213083. | −0.518601 | −0.259300 | − | 0.965797i | \(-0.583492\pi\) | ||||
−0.259300 | + | 0.965797i | \(0.583492\pi\) | |||||||
\(642\) | − | 300139.i | − | 0.728202i | ||||||
\(643\) | −323868. | −0.783333 | −0.391666 | − | 0.920107i | \(-0.628101\pi\) | ||||
−0.391666 | + | 0.920107i | \(0.628101\pi\) | |||||||
\(644\) | − | 14751.2i | − | 0.0355678i | ||||||
\(645\) | − | 252403.i | − | 0.606702i | ||||||
\(646\) | − | 1.00244e6i | − | 2.40211i | ||||||
\(647\) | −268558. | −0.641548 | −0.320774 | − | 0.947156i | \(-0.603943\pi\) | ||||
−0.320774 | + | 0.947156i | \(0.603943\pi\) | |||||||
\(648\) | 46042.3i | 0.109650i | ||||||||
\(649\) | −12733.4 | − | 88318.4i | −0.0302311 | − | 0.209682i | ||||
\(650\) | 152130. | 0.360070 | ||||||||
\(651\) | 233771.i | 0.551607i | ||||||||
\(652\) | 20961.5 | 0.0493091 | ||||||||
\(653\) | −43918.8 | −0.102997 | −0.0514985 | − | 0.998673i | \(-0.516400\pi\) | ||||
−0.0514985 | + | 0.998673i | \(0.516400\pi\) | |||||||
\(654\) | 4617.82 | 0.0107965 | ||||||||
\(655\) | 360658.i | 0.840646i | ||||||||
\(656\) | −270126. | −0.627710 | ||||||||
\(657\) | − | 167704.i | − | 0.388519i | ||||||
\(658\) | −828361. | −1.91323 | ||||||||
\(659\) | − | 246753.i | − | 0.568187i | −0.958797 | − | 0.284093i | \(-0.908307\pi\) | ||
0.958797 | − | 0.284093i | \(-0.0916925\pi\) | |||||||
\(660\) | − | 891.880i | − | 0.00204747i | ||||||
\(661\) | 91190.3 | 0.208711 | 0.104356 | − | 0.994540i | \(-0.466722\pi\) | ||||
0.104356 | + | 0.994540i | \(0.466722\pi\) | |||||||
\(662\) | 504032.i | 1.15012i | ||||||||
\(663\) | − | 242145.i | − | 0.550869i | ||||||
\(664\) | −686175. | −1.55632 | ||||||||
\(665\) | 435375. | 0.984510 | ||||||||
\(666\) | −69165.4 | −0.155934 | ||||||||
\(667\) | − | 1.05546e6i | − | 2.37241i | ||||||
\(668\) | 7166.24 | 0.0160597 | ||||||||
\(669\) | 76778.8 | 0.171549 | ||||||||
\(670\) | −57661.8 | −0.128451 | ||||||||
\(671\) | −109560. | −0.243335 | ||||||||
\(672\) | 12836.8i | 0.0284262i | ||||||||
\(673\) | − | 377278.i | − | 0.832973i | −0.909142 | − | 0.416486i | \(-0.863261\pi\) | ||
0.909142 | − | 0.416486i | \(-0.136739\pi\) | |||||||
\(674\) | −359202. | −0.790713 | ||||||||
\(675\) | 49902.0 | 0.109524 | ||||||||
\(676\) | −7104.57 | −0.0155469 | ||||||||
\(677\) | 301726. | 0.658317 | 0.329159 | − | 0.944275i | \(-0.393235\pi\) | ||||
0.329159 | + | 0.944275i | \(0.393235\pi\) | |||||||
\(678\) | −265560. | −0.577701 | ||||||||
\(679\) | 373540.i | 0.810210i | ||||||||
\(680\) | − | 457441.i | − | 0.989275i | ||||||
\(681\) | 193596.i | 0.417447i | ||||||||
\(682\) | 98733.7i | 0.212274i | ||||||||
\(683\) | 44408.5i | 0.0951974i | 0.998867 | + | 0.0475987i | \(0.0151569\pi\) | ||||
−0.998867 | + | 0.0475987i | \(0.984843\pi\) | |||||||
\(684\) | 6177.29 | 0.0132034 | ||||||||
\(685\) | 133638. | 0.284806 | ||||||||
\(686\) | − | 491285.i | − | 1.04396i | ||||||
\(687\) | − | 189083.i | − | 0.400627i | ||||||
\(688\) | 776583.i | 1.64063i | ||||||||
\(689\) | − | 222794.i | − | 0.469315i | ||||||
\(690\) | −263933. | −0.554365 | ||||||||
\(691\) | 428913.i | 0.898284i | 0.893460 | + | 0.449142i | \(0.148270\pi\) | ||||
−0.893460 | + | 0.449142i | \(0.851730\pi\) | |||||||
\(692\) | 24372.0i | 0.0508954i | ||||||||
\(693\) | 32746.5i | 0.0681866i | ||||||||
\(694\) | −226157. | −0.469560 | ||||||||
\(695\) | −221687. | −0.458955 | ||||||||
\(696\) | 453309.i | 0.935785i | ||||||||
\(697\) | 454407. | 0.935362 | ||||||||
\(698\) | −268208. | −0.550504 | ||||||||
\(699\) | − | 107220.i | − | 0.219444i | ||||||
\(700\) | 6866.61 | 0.0140135 | ||||||||
\(701\) | − | 142828.i | − | 0.290654i | −0.989384 | − | 0.145327i | \(-0.953577\pi\) | ||
0.989384 | − | 0.145327i | \(-0.0464234\pi\) | |||||||
\(702\) | 60005.0 | 0.121762 | ||||||||
\(703\) | − | 354607.i | − | 0.717525i | ||||||
\(704\) | − | 102184.i | − | 0.206176i | ||||||
\(705\) | 368564.i | 0.741540i | ||||||||
\(706\) | −483269. | −0.969570 | ||||||||
\(707\) | 319692.i | 0.639577i | ||||||||
\(708\) | −7304.69 | + | 1053.16i | −0.0145725 | + | 0.00210101i | ||||
\(709\) | 361262. | 0.718670 | 0.359335 | − | 0.933209i | \(-0.383004\pi\) | ||||
0.359335 | + | 0.933209i | \(0.383004\pi\) | |||||||
\(710\) | 15724.4i | 0.0311930i | ||||||||
\(711\) | 240738. | 0.476217 | ||||||||
\(712\) | −395542. | −0.780247 | ||||||||
\(713\) | 726575. | 1.42923 | ||||||||
\(714\) | − | 439518.i | − | 0.862144i | ||||||
\(715\) | 44417.6 | 0.0868845 | ||||||||
\(716\) | 21420.8i | 0.0417839i | ||||||||
\(717\) | 95101.0 | 0.184989 | ||||||||
\(718\) | − | 666305.i | − | 1.29248i | ||||||
\(719\) | 364020.i | 0.704154i | 0.935971 | + | 0.352077i | \(0.114525\pi\) | ||||
−0.935971 | + | 0.352077i | \(0.885475\pi\) | |||||||
\(720\) | 116249. | 0.224246 | ||||||||
\(721\) | 945774.i | 1.81935i | ||||||||
\(722\) | 745700.i | 1.43051i | ||||||||
\(723\) | −380420. | −0.727758 | ||||||||
\(724\) | 408.588 | 0.000779487 | ||||||||
\(725\) | 491309. | 0.934715 | ||||||||
\(726\) | − | 294333.i | − | 0.558425i | ||||||
\(727\) | 295247. | 0.558619 | 0.279310 | − | 0.960201i | \(-0.409894\pi\) | ||||
0.279310 | + | 0.960201i | \(0.409894\pi\) | |||||||
\(728\) | −315522. | −0.595343 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | −412889. | −0.774797 | ||||||||
\(731\) | − | 1.30637e6i | − | 2.44473i | ||||||
\(732\) | 9061.52i | 0.0169114i | ||||||||
\(733\) | 203200. | 0.378195 | 0.189097 | − | 0.981958i | \(-0.439444\pi\) | ||||
0.189097 | + | 0.981958i | \(0.439444\pi\) | |||||||
\(734\) | 43025.3 | 0.0798605 | ||||||||
\(735\) | −13849.3 | −0.0256362 | ||||||||
\(736\) | 39897.6 | 0.0736531 | ||||||||
\(737\) | 22235.6 | 0.0409368 | ||||||||
\(738\) | 112605.i | 0.206750i | ||||||||
\(739\) | − | 1.00932e6i | − | 1.84816i | −0.382195 | − | 0.924082i | \(-0.624832\pi\) | ||
0.382195 | − | 0.924082i | \(-0.375168\pi\) | |||||||
\(740\) | 4234.54i | 0.00773291i | ||||||||
\(741\) | 307642.i | 0.560286i | ||||||||
\(742\) | − | 404393.i | − | 0.734508i | ||||||
\(743\) | −535342. | −0.969737 | −0.484869 | − | 0.874587i | \(-0.661133\pi\) | ||||
−0.484869 | + | 0.874587i | \(0.661133\pi\) | |||||||
\(744\) | −312057. | −0.563752 | ||||||||
\(745\) | − | 94331.2i | − | 0.169958i | ||||||
\(746\) | 202488.i | 0.363849i | ||||||||
\(747\) | 293338.i | 0.525688i | ||||||||
\(748\) | − | 4616.13i | − | 0.00825039i | ||||||
\(749\) | 674682. | 1.20264 | ||||||||
\(750\) | − | 338741.i | − | 0.602206i | ||||||
\(751\) | − | 808120.i | − | 1.43283i | −0.697672 | − | 0.716417i | \(-0.745781\pi\) | ||
0.697672 | − | 0.716417i | \(-0.254219\pi\) | |||||||
\(752\) | − | 1.13398e6i | − | 2.00526i | ||||||
\(753\) | −345507. | −0.609350 | ||||||||
\(754\) | 590779. | 1.03916 | ||||||||
\(755\) | 641754.i | 1.12583i | ||||||||
\(756\) | 2708.42 | 0.00473885 | ||||||||
\(757\) | −597248. | −1.04223 | −0.521114 | − | 0.853487i | \(-0.674483\pi\) | ||||
−0.521114 | + | 0.853487i | \(0.674483\pi\) | |||||||
\(758\) | − | 93300.0i | − | 0.162384i | ||||||
\(759\) | 101778. | 0.176673 | ||||||||
\(760\) | 581174.i | 1.00619i | ||||||||
\(761\) | 337522. | 0.582818 | 0.291409 | − | 0.956599i | \(-0.405876\pi\) | ||||
0.291409 | + | 0.956599i | \(0.405876\pi\) | |||||||
\(762\) | − | 78730.7i | − | 0.135592i | ||||||
\(763\) | 10380.4i | 0.0178305i | ||||||||
\(764\) | − | 26876.8i | − | 0.0460459i | ||||||
\(765\) | −195555. | −0.334154 | ||||||||
\(766\) | − | 143873.i | − | 0.245201i | ||||||
\(767\) | −52449.7 | − | 363790.i | −0.0891564 | − | 0.618386i | ||||
\(768\) | −26035.5 | −0.0441412 | ||||||||
\(769\) | − | 135631.i | − | 0.229354i | −0.993403 | − | 0.114677i | \(-0.963417\pi\) | ||
0.993403 | − | 0.114677i | \(-0.0365833\pi\) | |||||||
\(770\) | 80622.4 | 0.135980 | ||||||||
\(771\) | 249429. | 0.419603 | ||||||||
\(772\) | −19076.1 | −0.0320078 | ||||||||
\(773\) | − | 320257.i | − | 0.535969i | −0.963423 | − | 0.267985i | \(-0.913642\pi\) | ||
0.963423 | − | 0.267985i | \(-0.0863576\pi\) | |||||||
\(774\) | 323727. | 0.540377 | ||||||||
\(775\) | 338216.i | 0.563107i | ||||||||
\(776\) | −498631. | −0.828049 | ||||||||
\(777\) | − | 155477.i | − | 0.257528i | ||||||
\(778\) | 637723.i | 1.05359i | ||||||||
\(779\) | −577320. | −0.951353 | ||||||||
\(780\) | − | 3673.71i | − | 0.00603832i | ||||||
\(781\) | − | 6063.65i | − | 0.00994105i | ||||||
\(782\) | −1.36605e6 | −2.23384 | ||||||||
\(783\) | 193789. | 0.316086 | ||||||||
\(784\) | 42611.0 | 0.0693249 | ||||||||
\(785\) | − | 16335.3i | − | 0.0265087i | ||||||
\(786\) | −462573. | −0.748746 | ||||||||
\(787\) | −584994. | −0.944500 | −0.472250 | − | 0.881465i | \(-0.656558\pi\) | ||||
−0.472250 | + | 0.881465i | \(0.656558\pi\) | |||||||
\(788\) | −23024.5 | −0.0370799 | ||||||||
\(789\) | −121989. | −0.195960 | ||||||||
\(790\) | − | 592700.i | − | 0.949687i | ||||||
\(791\) | − | 596953.i | − | 0.954085i | ||||||
\(792\) | −43712.7 | −0.0696879 | ||||||||
\(793\) | −451283. | −0.717634 | ||||||||
\(794\) | 662245. | 1.05046 | ||||||||
\(795\) | −179927. | −0.284684 | ||||||||
\(796\) | −1816.37 | −0.00286667 | ||||||||
\(797\) | 3812.61i | 0.00600213i | 0.999995 | + | 0.00300107i | \(0.000955270\pi\) | ||||
−0.999995 | + | 0.00300107i | \(0.999045\pi\) | |||||||
\(798\) | 558403.i | 0.876883i | ||||||||
\(799\) | 1.90759e6i | 2.98807i | ||||||||
\(800\) | 18572.1i | 0.0290189i | ||||||||
\(801\) | 169093.i | 0.263549i | ||||||||
\(802\) | 303692. | 0.472155 | ||||||||
\(803\) | 159219. | 0.246924 | ||||||||
\(804\) | − | 1839.08i | − | 0.00284504i | ||||||
\(805\) | − | 593296.i | − | 0.915544i | ||||||
\(806\) | 406691.i | 0.626029i | ||||||||
\(807\) | − | 447837.i | − | 0.687658i | ||||||
\(808\) | −426750. | −0.653659 | ||||||||
\(809\) | 316184.i | 0.483106i | 0.970388 | + | 0.241553i | \(0.0776567\pi\) | ||||
−0.970388 | + | 0.241553i | \(0.922343\pi\) | |||||||
\(810\) | − | 48459.8i | − | 0.0738604i | ||||||
\(811\) | 924126.i | 1.40504i | 0.711663 | + | 0.702521i | \(0.247942\pi\) | ||||
−0.711663 | + | 0.702521i | \(0.752058\pi\) | |||||||
\(812\) | 26665.7 | 0.0404428 | ||||||||
\(813\) | 97032.0 | 0.146803 | ||||||||
\(814\) | − | 65665.9i | − | 0.0991039i | ||||||
\(815\) | 843073. | 1.26926 | ||||||||
\(816\) | 601675. | 0.903611 | ||||||||
\(817\) | 1.65973e6i | 2.48653i | ||||||||
\(818\) | −877167. | −1.31092 | ||||||||
\(819\) | 134885.i | 0.201093i | ||||||||
\(820\) | 6894.07 | 0.0102529 | ||||||||
\(821\) | 298283.i | 0.442530i | 0.975214 | + | 0.221265i | \(0.0710185\pi\) | ||||
−0.975214 | + | 0.221265i | \(0.928981\pi\) | |||||||
\(822\) | 171401.i | 0.253671i | ||||||||
\(823\) | − | 237822.i | − | 0.351117i | −0.984469 | − | 0.175559i | \(-0.943827\pi\) | ||
0.984469 | − | 0.175559i | \(-0.0561732\pi\) | |||||||
\(824\) | −1.26250e6 | −1.85941 | ||||||||
\(825\) | 47377.1i | 0.0696082i | ||||||||
\(826\) | −95201.6 | − | 660316.i | −0.139535 | − | 0.967813i | ||||
\(827\) | −1.27223e6 | −1.86017 | −0.930087 | − | 0.367340i | \(-0.880269\pi\) | ||||
−0.930087 | + | 0.367340i | \(0.880269\pi\) | |||||||
\(828\) | − | 8417.93i | − | 0.0122785i | ||||||
\(829\) | 1.17715e6 | 1.71287 | 0.856435 | − | 0.516255i | \(-0.172674\pi\) | ||||
0.856435 | + | 0.516255i | \(0.172674\pi\) | |||||||
\(830\) | 722203. | 1.04834 | ||||||||
\(831\) | −689581. | −0.998581 | ||||||||
\(832\) | − | 420903.i | − | 0.608045i | ||||||
\(833\) | −71680.4 | −0.103302 | ||||||||
\(834\) | − | 284330.i | − | 0.408782i | ||||||
\(835\) | 288226. | 0.413391 | ||||||||
\(836\) | 5864.74i | 0.00839144i | ||||||||
\(837\) | 133404.i | 0.190422i | ||||||||
\(838\) | 897121. | 1.27751 | ||||||||
\(839\) | 1.11954e6i | 1.59043i | 0.606328 | + | 0.795215i | \(0.292642\pi\) | ||||
−0.606328 | + | 0.795215i | \(0.707358\pi\) | |||||||
\(840\) | 254815.i | 0.361132i | ||||||||
\(841\) | 1.20067e6 | 1.69758 | ||||||||
\(842\) | −1.27841e6 | −1.80321 | ||||||||
\(843\) | −220566. | −0.310372 | ||||||||
\(844\) | − | 17476.5i | − | 0.0245341i | ||||||
\(845\) | −285746. | −0.400190 | ||||||||
\(846\) | −472712. | −0.660474 | ||||||||
\(847\) | 661630. | 0.922250 | ||||||||
\(848\) | 553592. | 0.769836 | ||||||||
\(849\) | 7367.64i | 0.0102215i | ||||||||
\(850\) | − | 635886.i | − | 0.880119i | ||||||
\(851\) | −483231. | −0.667261 | ||||||||
\(852\) | −501.516 | −0.000690885 | ||||||||
\(853\) | −1.32601e6 | −1.82243 | −0.911213 | − | 0.411936i | \(-0.864853\pi\) | ||||
−0.911213 | + | 0.411936i | \(0.864853\pi\) | |||||||
\(854\) | −819126. | −1.12314 | ||||||||
\(855\) | 248451. | 0.339866 | ||||||||
\(856\) | 900620.i | 1.22912i | ||||||||
\(857\) | 925531.i | 1.26017i | 0.776526 | + | 0.630086i | \(0.216980\pi\) | ||||
−0.776526 | + | 0.630086i | \(0.783020\pi\) | |||||||
\(858\) | 56969.0i | 0.0773863i | ||||||||
\(859\) | − | 610215.i | − | 0.826984i | −0.910508 | − | 0.413492i | \(-0.864309\pi\) | ||
0.910508 | − | 0.413492i | \(-0.135691\pi\) | |||||||
\(860\) | − | 19819.7i | − | 0.0267978i | ||||||
\(861\) | −253125. | −0.341451 | ||||||||
\(862\) | −151210. | −0.203501 | ||||||||
\(863\) | − | 680555.i | − | 0.913780i | −0.889523 | − | 0.456890i | \(-0.848963\pi\) | ||
0.889523 | − | 0.456890i | \(-0.151037\pi\) | |||||||
\(864\) | 7325.45i | 0.00981311i | ||||||||
\(865\) | 980242.i | 1.31009i | ||||||||
\(866\) | 243896.i | 0.325213i | ||||||||
\(867\) | −578152. | −0.769138 | ||||||||
\(868\) | 18356.6i | 0.0243643i | ||||||||
\(869\) | 228557.i | 0.302661i | ||||||||
\(870\) | − | 477111.i | − | 0.630348i | ||||||
\(871\) | 91590.0 | 0.120729 | ||||||||
\(872\) | −13856.6 | −0.0182231 | ||||||||
\(873\) | 213164.i | 0.279696i | ||||||||
\(874\) | 1.73555e6 | 2.27203 | ||||||||
\(875\) | 761456. | 0.994555 | ||||||||
\(876\) | − | 13168.8i | − | 0.0171608i | ||||||
\(877\) | 682360. | 0.887186 | 0.443593 | − | 0.896228i | \(-0.353704\pi\) | ||||
0.443593 | + | 0.896228i | \(0.353704\pi\) | |||||||
\(878\) | − | 749812.i | − | 0.972665i | ||||||
\(879\) | −232974. | −0.301529 | ||||||||
\(880\) | 110368.i | 0.142520i | ||||||||
\(881\) | − | 596457.i | − | 0.768471i | −0.923235 | − | 0.384236i | \(-0.874465\pi\) | ||
0.923235 | − | 0.384236i | \(-0.125535\pi\) | |||||||
\(882\) | − | 17762.9i | − | 0.0228337i | ||||||
\(883\) | 909216. | 1.16613 | 0.583063 | − | 0.812427i | \(-0.301854\pi\) | ||||
0.583063 | + | 0.812427i | \(0.301854\pi\) | |||||||
\(884\) | − | 19014.1i | − | 0.0243317i | ||||||
\(885\) | −293795. | + | 42358.2i | −0.375109 | + | 0.0540817i | ||||
\(886\) | −951656. | −1.21231 | ||||||||
\(887\) | − | 176633.i | − | 0.224505i | −0.993680 | − | 0.112252i | \(-0.964193\pi\) | ||
0.993680 | − | 0.112252i | \(-0.0358065\pi\) | |||||||
\(888\) | 207543. | 0.263198 | ||||||||
\(889\) | 176979. | 0.223933 | ||||||||
\(890\) | 416310. | 0.525578 | ||||||||
\(891\) | 18687.1i | 0.0235389i | ||||||||
\(892\) | 6028.97 | 0.00757728 | ||||||||
\(893\) | − | 2.42357e6i | − | 3.03915i | ||||||
\(894\) | 120987. | 0.151378 | ||||||||
\(895\) | 861544.i | 1.07555i | ||||||||
\(896\) | − | 803510.i | − | 1.00086i | ||||||
\(897\) | 419231. | 0.521037 | ||||||||
\(898\) | − | 279986.i | − | 0.347204i | ||||||
\(899\) | 1.31343e6i | 1.62512i | ||||||||
\(900\) | 3918.50 | 0.00483765 | ||||||||
\(901\) | −931254. | −1.14715 | ||||||||
\(902\) | −106908. | −0.131400 | ||||||||
\(903\) | 727706.i | 0.892443i | ||||||||
\(904\) | 796860. | 0.975091 | ||||||||
\(905\) | 16433.4 | 0.0200646 | ||||||||
\(906\) | −823100. | −1.00276 | ||||||||
\(907\) | 805251. | 0.978852 | 0.489426 | − | 0.872045i | \(-0.337206\pi\) | ||||
0.489426 | + | 0.872045i | \(0.337206\pi\) | |||||||
\(908\) | 15201.9i | 0.0184385i | ||||||||
\(909\) | 182435.i | 0.220791i | ||||||||
\(910\) | 332089. | 0.401026 | ||||||||
\(911\) | 947445. | 1.14161 | 0.570804 | − | 0.821086i | \(-0.306632\pi\) | ||||
0.570804 | + | 0.821086i | \(0.306632\pi\) | |||||||
\(912\) | −764422. | −0.919059 | ||||||||
\(913\) | −278497. | −0.334102 | ||||||||
\(914\) | 1.24611e6 | 1.49164 | ||||||||
\(915\) | 364455.i | 0.435313i | ||||||||
\(916\) | − | 14847.6i | − | 0.0176956i | ||||||
\(917\) | − | 1.03982e6i | − | 1.23657i | ||||||
\(918\) | − | 250815.i | − | 0.297624i | ||||||
\(919\) | − | 702262.i | − | 0.831512i | −0.909476 | − | 0.415756i | \(-0.863517\pi\) | ||
0.909476 | − | 0.415756i | \(-0.136483\pi\) | |||||||
\(920\) | 791979. | 0.935702 | ||||||||
\(921\) | 80860.5 | 0.0953273 | ||||||||
\(922\) | 82579.4i | 0.0971426i | ||||||||
\(923\) | − | 24976.6i | − | 0.0293177i | ||||||
\(924\) | 2571.39i | 0.00301178i | ||||||||
\(925\) | − | 224941.i | − | 0.262897i | ||||||
\(926\) | 205571. | 0.239740 | ||||||||
\(927\) | 539715.i | 0.628065i | ||||||||
\(928\) | 72122.7i | 0.0837483i | ||||||||
\(929\) | 489302.i | 0.566951i | 0.958979 | + | 0.283476i | \(0.0914875\pi\) | ||||
−0.958979 | + | 0.283476i | \(0.908512\pi\) | |||||||
\(930\) | 328442. | 0.379746 | ||||||||
\(931\) | 91069.2 | 0.105068 | ||||||||
\(932\) | − | 8419.37i | − | 0.00969276i | ||||||
\(933\) | 836332. | 0.960761 | ||||||||
\(934\) | −37106.1 | −0.0425355 | ||||||||
\(935\) | − | 185661.i | − | 0.212372i | ||||||
\(936\) | −180056. | −0.205521 | ||||||||
\(937\) | − | 534102.i | − | 0.608338i | −0.952618 | − | 0.304169i | \(-0.901621\pi\) | ||
0.952618 | − | 0.304169i | \(-0.0983787\pi\) | |||||||
\(938\) | 166245. | 0.188949 | ||||||||
\(939\) | − | 414802.i | − | 0.470446i | ||||||
\(940\) | 28941.1i | 0.0327536i | ||||||||
\(941\) | − | 553753.i | − | 0.625370i | −0.949857 | − | 0.312685i | \(-0.898772\pi\) | ||
0.949857 | − | 0.312685i | \(-0.101228\pi\) | |||||||
\(942\) | 20951.3 | 0.0236107 | ||||||||
\(943\) | 786727.i | 0.884709i | ||||||||
\(944\) | 903935. | − | 130326.i | 1.01436 | − | 0.146247i | ||||
\(945\) | 108933. | 0.121982 | ||||||||
\(946\) | 307348.i | 0.343437i | ||||||||
\(947\) | −134884. | −0.150404 | −0.0752020 | − | 0.997168i | \(-0.523960\pi\) | ||||
−0.0752020 | + | 0.997168i | \(0.523960\pi\) | |||||||
\(948\) | 18903.7 | 0.0210344 | ||||||||
\(949\) | 655833. | 0.728217 | ||||||||
\(950\) | 807887.i | 0.895166i | ||||||||
\(951\) | −562644. | −0.622118 | ||||||||
\(952\) | 1.31885e6i | 1.45520i | ||||||||
\(953\) | −573042. | −0.630959 | −0.315479 | − | 0.948932i | \(-0.602165\pi\) | ||||
−0.315479 | + | 0.948932i | \(0.602165\pi\) | |||||||
\(954\) | − | 230771.i | − | 0.253562i | ||||||
\(955\) | − | 1.08099e6i | − | 1.18526i | ||||||
\(956\) | 7467.70 | 0.00817092 | ||||||||
\(957\) | 183984.i | 0.200889i | ||||||||
\(958\) | 1.13927e6i | 1.24136i | ||||||||
\(959\) | −385293. | −0.418942 | ||||||||
\(960\) | −339920. | −0.368837 | ||||||||
\(961\) | 19361.1 | 0.0209644 | ||||||||
\(962\) | − | 270482.i | − | 0.292273i | ||||||
\(963\) | 385013. | 0.415167 | ||||||||
\(964\) | −29872.1 | −0.0321449 | ||||||||
\(965\) | −767243. | −0.823907 | ||||||||
\(966\) | 760948. | 0.815456 | ||||||||
\(967\) | − | 554410.i | − | 0.592896i | −0.955049 | − | 0.296448i | \(-0.904198\pi\) | ||
0.955049 | − | 0.296448i | \(-0.0958021\pi\) | |||||||
\(968\) | 883197.i | 0.942556i | ||||||||
\(969\) | 1.28591e6 | 1.36951 | ||||||||
\(970\) | 524813. | 0.557778 | ||||||||
\(971\) | −1.44834e6 | −1.53614 | −0.768072 | − | 0.640364i | \(-0.778784\pi\) | ||||
−0.768072 | + | 0.640364i | \(0.778784\pi\) | |||||||
\(972\) | 1545.59 | 0.00163591 | ||||||||
\(973\) | 639146. | 0.675110 | ||||||||
\(974\) | − | 50487.8i | − | 0.0532193i | ||||||
\(975\) | 195150.i | 0.205286i | ||||||||
\(976\) | − | 1.12134e6i | − | 1.17716i | ||||||
\(977\) | 405137.i | 0.424437i | 0.977222 | + | 0.212218i | \(0.0680688\pi\) | ||||
−0.977222 | + | 0.212218i | \(0.931931\pi\) | |||||||
\(978\) | 1.08131e6i | 1.13050i | ||||||||
\(979\) | −160538. | −0.167499 | ||||||||
\(980\) | −1087.50 | −0.00113234 | ||||||||
\(981\) | 5923.66i | 0.00615535i | ||||||||
\(982\) | − | 1.08351e6i | − | 1.12359i | ||||||
\(983\) | 361647.i | 0.374264i | 0.982335 | + | 0.187132i | \(0.0599192\pi\) | ||||
−0.982335 | + | 0.187132i | \(0.940081\pi\) | |||||||
\(984\) | − | 337891.i | − | 0.348969i | ||||||
\(985\) | −926047. | −0.954466 | ||||||||
\(986\) | − | 2.46940e6i | − | 2.54002i | ||||||
\(987\) | − | 1.06261e6i | − | 1.09079i | ||||||
\(988\) | 24157.3i | 0.0247477i | ||||||||
\(989\) | 2.26175e6 | 2.31234 | ||||||||
\(990\) | 46007.9 | 0.0469421 | ||||||||
\(991\) | − | 613858.i | − | 0.625058i | −0.949908 | − | 0.312529i | \(-0.898824\pi\) | ||
0.949908 | − | 0.312529i | \(-0.101176\pi\) | |||||||
\(992\) | −49649.1 | −0.0504531 | ||||||||
\(993\) | −646565. | −0.655712 | ||||||||
\(994\) | − | 45335.1i | − | 0.0458841i | ||||||
\(995\) | −73054.3 | −0.0737904 | ||||||||
\(996\) | 23034.1i | 0.0232195i | ||||||||
\(997\) | 1.15654e6 | 1.16351 | 0.581753 | − | 0.813366i | \(-0.302367\pi\) | ||||
0.581753 | + | 0.813366i | \(0.302367\pi\) | |||||||
\(998\) | − | 857616.i | − | 0.861057i | ||||||
\(999\) | − | 88724.3i | − | 0.0889020i |
(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 | 177.5.c.a.58.29 | yes | 40 | |
3.2 | odd | 2 | 531.5.c.d.235.12 | 40 | |||
59.58 | odd | 2 | inner | 177.5.c.a.58.12 | ✓ | 40 | |
177.176 | even | 2 | 531.5.c.d.235.29 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.12 | ✓ | 40 | 59.58 | odd | 2 | inner | |
177.5.c.a.58.29 | yes | 40 | 1.1 | even | 1 | trivial | |
531.5.c.d.235.12 | 40 | 3.2 | odd | 2 | |||
531.5.c.d.235.29 | 40 | 177.176 | even | 2 |