Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(5,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.k (of order \(18\), degree \(6\), 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: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 29.3 | ||
Character | \(\chi\) | \(=\) | 108.29 |
Dual form | 108.5.k.a.41.3 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{18}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −6.90497 | − | 5.77247i | −0.767219 | − | 0.641385i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 11.0592 | + | 13.1798i | 0.442368 | + | 0.527193i | 0.940448 | − | 0.339938i | \(-0.110406\pi\) |
−0.498080 | + | 0.867131i | \(0.665962\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.77764 | − | 2.83083i | 0.158727 | − | 0.0577720i | −0.261434 | − | 0.965221i | \(-0.584196\pi\) |
0.420162 | + | 0.907449i | \(0.361973\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 14.3573 | + | 79.7174i | 0.177250 | + | 0.984166i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 44.3220 | − | 52.8209i | 0.366298 | − | 0.436537i | −0.551142 | − | 0.834411i | \(-0.685808\pi\) |
0.917440 | + | 0.397875i | \(0.130252\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.19703 | − | 23.8025i | −0.0248345 | − | 0.140843i | 0.969869 | − | 0.243625i | \(-0.0783367\pi\) |
−0.994704 | + | 0.102782i | \(0.967226\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.283269 | − | 154.845i | −0.00125898 | − | 0.688201i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 213.549 | − | 123.293i | 0.738925 | − | 0.426619i | −0.0827531 | − | 0.996570i | \(-0.526371\pi\) |
0.821678 | + | 0.569951i | \(0.193038\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 175.684 | − | 304.294i | 0.486660 | − | 0.842920i | −0.513222 | − | 0.858256i | \(-0.671548\pi\) |
0.999882 | + | 0.0153357i | \(0.00488168\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −70.0452 | − | 25.3494i | −0.158833 | − | 0.0574815i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 275.524 | − | 756.995i | 0.520839 | − | 1.43099i | −0.348750 | − | 0.937216i | \(-0.613394\pi\) |
0.869589 | − | 0.493777i | \(-0.164384\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 57.1279 | − | 323.988i | 0.0914047 | − | 0.518382i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 361.030 | − | 633.323i | 0.495240 | − | 0.868756i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −348.016 | − | 61.3646i | −0.413812 | − | 0.0729662i | −0.0371335 | − | 0.999310i | \(-0.511823\pi\) |
−0.376678 | + | 0.926344i | \(0.622934\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 634.917 | + | 231.091i | 0.660684 | + | 0.240469i | 0.650531 | − | 0.759479i | \(-0.274546\pi\) |
0.0101521 | + | 0.999948i | \(0.496768\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −610.949 | + | 108.880i | −0.561019 | + | 0.0999813i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 123.324 | + | 71.2013i | 0.100673 | + | 0.0581235i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 870.013 | + | 1506.91i | 0.635510 | + | 1.10073i | 0.986407 | + | 0.164321i | \(0.0525432\pi\) |
−0.350897 | + | 0.936414i | \(0.614123\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −108.419 | + | 188.583i | −0.0712814 | + | 0.123986i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 629.967 | − | 111.080i | 0.374757 | − | 0.0660798i | 0.0169027 | − | 0.999857i | \(-0.494619\pi\) |
0.357855 | + | 0.933777i | \(0.383508\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1149.85 | + | 964.841i | 0.621878 | + | 0.521818i | 0.898393 | − | 0.439192i | \(-0.144735\pi\) |
−0.276515 | + | 0.961010i | \(0.589180\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −891.882 | + | 1070.84i | −0.440436 | + | 0.528808i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −649.053 | − | 1783.26i | −0.293822 | − | 0.807270i | −0.995499 | − | 0.0947744i | \(-0.969787\pi\) |
0.701676 | − | 0.712496i | \(-0.252435\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1786.79 | + | 1499.30i | −0.744188 | + | 0.624448i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2186.26 | − | 381.374i | −0.840545 | − | 0.146626i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1728.31i | − | 0.615278i | −0.951503 | − | 0.307639i | \(-0.900461\pi\) | ||
0.951503 | − | 0.307639i | \(-0.0995388\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1186.34 | 0.392177 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2969.62 | + | 1087.01i | −0.914011 | + | 0.334568i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −442.288 | − | 527.098i | −0.127058 | − | 0.151421i | 0.698765 | − | 0.715351i | \(-0.253733\pi\) |
−0.825823 | + | 0.563930i | \(0.809289\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 995.692 | − | 362.402i | 0.267587 | − | 0.0973938i | −0.204742 | − | 0.978816i | \(-0.565636\pi\) |
0.472329 | + | 0.881422i | \(0.343413\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 337.332 | + | 579.370i | 0.0849917 | + | 0.145974i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 267.298 | − | 318.553i | 0.0632657 | − | 0.0753971i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1019.70 | + | 5783.02i | 0.227156 | + | 1.28826i | 0.858521 | + | 0.512778i | \(0.171384\pi\) |
−0.631365 | + | 0.775486i | \(0.717505\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6272.21 | + | 3636.58i | −1.31741 | + | 0.763826i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3889.70 | − | 2245.72i | 0.771612 | − | 0.445491i | −0.0618371 | − | 0.998086i | \(-0.519696\pi\) |
0.833450 | + | 0.552596i | \(0.186363\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −725.679 | + | 1256.91i | −0.136176 | + | 0.235863i | −0.926046 | − | 0.377411i | \(-0.876814\pi\) |
0.789870 | + | 0.613274i | \(0.210148\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2264.68 | + | 1907.36i | −0.402610 | + | 0.339087i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 195.194 | − | 536.290i | 0.0329219 | − | 0.0904520i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −173.955 | + | 986.547i | −0.0278729 | + | 0.158075i | −0.995567 | − | 0.0940505i | \(-0.970018\pi\) |
0.967695 | + | 0.252126i | \(0.0811296\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6148.74 | + | 2289.05i | −0.937165 | + | 0.348887i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1712.04 | − | 301.879i | −0.248518 | − | 0.0438204i | 0.0480014 | − | 0.998847i | \(-0.484715\pi\) |
−0.296519 | + | 0.955027i | \(0.595826\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3986.66 | + | 1451.03i | 0.551787 | + | 0.200834i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2048.81 | + | 2432.63i | 0.270685 | + | 0.321394i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1131.82 | − | 653.456i | −0.142888 | − | 0.0824966i | 0.426851 | − | 0.904322i | \(-0.359623\pi\) |
−0.569740 | + | 0.821825i | \(0.692956\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −100.024 | − | 173.246i | −0.0120787 | − | 0.0209210i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3050.12 | − | 5260.71i | −0.352656 | − | 0.608245i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5953.47 | − | 1049.76i | 0.659664 | − | 0.116317i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10494.3 | + | 8805.79i | 1.11535 | + | 0.935890i | 0.998360 | − | 0.0572434i | \(-0.0182311\pi\) |
0.116990 | + | 0.993133i | \(0.462676\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4847.09 | + | 2774.87i | 0.494551 | + | 0.283122i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3163.83 | − | 8692.56i | −0.310149 | − | 0.852129i | −0.992626 | − | 0.121221i | \(-0.961319\pi\) |
0.682476 | − | 0.730908i | \(-0.260903\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3788.01 | − | 3178.52i | 0.357057 | − | 0.299606i | −0.446560 | − | 0.894754i | \(-0.647351\pi\) |
0.803616 | + | 0.595148i | \(0.202906\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −440.543 | − | 1203.53i | −0.0399586 | − | 0.109163i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 15110.5i | − | 1.31981i | −0.751350 | − | 0.659904i | \(-0.770597\pi\) | ||
0.751350 | − | 0.659904i | \(-0.229403\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15250.4 | −1.28360 | −0.641798 | − | 0.766873i | \(-0.721811\pi\) | ||||
−0.641798 | + | 0.766873i | \(0.721811\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2691.15 | − | 15427.3i | 0.218420 | − | 1.25211i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1774.06 | + | 2114.24i | 0.138935 | + | 0.165576i | 0.831025 | − | 0.556235i | \(-0.187754\pi\) |
−0.692090 | + | 0.721811i | \(0.743310\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13024.1 | − | 4740.40i | 0.984811 | − | 0.358442i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1837.22 | − | 676.316i | 0.134211 | − | 0.0494058i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1311.89 | − | 1563.45i | 0.0926410 | − | 0.110405i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1716.77 | + | 9736.31i | 0.117258 | + | 0.665003i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4991.11 | − | 2869.46i | −0.329904 | − | 0.189666i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 14214.4 | − | 8206.69i | 0.909722 | − | 0.525228i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13768.7 | − | 23848.0i | 0.853659 | − | 1.47858i | −0.0242240 | − | 0.999707i | \(-0.507711\pi\) |
0.877883 | − | 0.478875i | \(-0.158955\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2370.19 | − | 13299.7i | −0.142431 | − | 0.799212i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8139.98 | + | 22364.4i | −0.474330 | + | 1.30321i | 0.439911 | + | 0.898041i | \(0.355010\pi\) |
−0.914241 | + | 0.405170i | \(0.867212\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 505.004 | − | 2864.02i | 0.0285491 | − | 0.161910i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12339.8 | − | 2245.73i | 0.677080 | − | 0.123223i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9749.91 | − | 1719.17i | −0.519469 | − | 0.0915964i | −0.0922346 | − | 0.995737i | \(-0.529401\pi\) |
−0.427234 | + | 0.904141i | \(0.640512\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5846.34 | − | 2127.89i | −0.302590 | − | 0.110134i | 0.186263 | − | 0.982500i | \(-0.440362\pi\) |
−0.488853 | + | 0.872366i | \(0.662585\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5812.11 | + | 16060.0i | −0.292345 | + | 0.807806i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1443.29 | − | 833.286i | −0.0705801 | − | 0.0407495i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3040.00 | − | 5265.43i | −0.144590 | − | 0.250437i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 20992.4 | − | 38.4030i | 0.971466 | − | 0.00177717i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 722.838 | − | 127.456i | 0.0325588 | − | 0.00574100i | −0.157345 | − | 0.987544i | \(-0.550293\pi\) |
0.189904 | + | 0.981803i | \(0.439182\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12154.9 | − | 10199.2i | −0.533086 | − | 0.447312i | 0.336080 | − | 0.941834i | \(-0.390899\pi\) |
−0.869165 | + | 0.494521i | \(0.835343\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12894.6 | + | 15253.5i | 0.550838 | + | 0.651607i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3975.93 | + | 10923.8i | 0.165491 | + | 0.454684i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −26195.4 | + | 21980.5i | −1.06274 | + | 0.891741i | −0.994375 | − | 0.105919i | \(-0.966222\pi\) |
−0.0683613 | + | 0.997661i | \(0.521777\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9976.64 | + | 11934.0i | −0.394630 | + | 0.472053i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6667.59i | − | 0.257227i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −45253.0 | −1.70322 | −0.851612 | − | 0.524172i | \(-0.824375\pi\) | ||||
−0.851612 | + | 0.524172i | \(0.824375\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8191.62 | − | 6848.09i | −0.300886 | − | 0.251537i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 31781.8 | + | 37876.1i | 1.13958 | + | 1.35810i | 0.924353 | + | 0.381539i | \(0.124606\pi\) |
0.215230 | + | 0.976563i | \(0.430950\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26289.6 | − | 9568.64i | 0.920473 | − | 0.335025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 26779.9 | + | 9636.27i | 0.915834 | + | 0.329547i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −30120.6 | + | 35896.3i | −1.00640 | + | 1.19938i | −0.0265522 | + | 0.999647i | \(0.508453\pi\) |
−0.979850 | + | 0.199736i | \(0.935992\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −472.836 | − | 2681.58i | −0.0154395 | − | 0.0875619i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.3287 | + | 6192.69i | 0.000361605 | + | 0.197666i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12684.8 | + | 7323.59i | −0.395894 | + | 0.228569i | −0.684711 | − | 0.728815i | \(-0.740071\pi\) |
0.288817 | + | 0.957384i | \(0.406738\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3216.57 | + | 5571.27i | −0.0981830 | + | 0.170058i | −0.910933 | − | 0.412555i | \(-0.864636\pi\) |
0.812750 | + | 0.582613i | \(0.197970\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8967.18 | − | 3245.22i | −0.267765 | − | 0.0969041i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10239.1 | + | 28131.8i | −0.299171 | + | 0.821965i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2952.50 | − | 16744.5i | 0.0844320 | − | 0.478837i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1015.13 | − | 5947.77i | 0.0284182 | − | 0.166506i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −61078.9 | − | 10769.9i | −1.67427 | − | 0.295218i | −0.745671 | − | 0.666314i | \(-0.767871\pi\) |
−0.928594 | + | 0.371096i | \(0.878982\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9223.47 | − | 3357.07i | −0.247617 | − | 0.0901251i | 0.215230 | − | 0.976563i | \(-0.430950\pi\) |
−0.462847 | + | 0.886438i | \(0.653172\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3684.52 | + | 656.632i | −0.0968972 | + | 0.0172684i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 30005.4 | + | 17323.6i | 0.773156 | + | 0.446382i | 0.833999 | − | 0.551766i | \(-0.186046\pi\) |
−0.0608435 | + | 0.998147i | \(0.519379\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −35471.9 | − | 61439.1i | −0.895733 | − | 1.55145i | −0.832895 | − | 0.553431i | \(-0.813318\pi\) |
−0.0628372 | − | 0.998024i | \(-0.520015\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 26341.3 | − | 45817.8i | 0.651995 | − | 1.13407i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2880.45 | + | 507.902i | −0.0698987 | + | 0.0123250i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8430.94 | + | 7074.40i | 0.200617 | + | 0.168338i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 64301.5 | + | 11095.7i | 1.50065 | + | 0.258948i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8286.42 | − | 22766.7i | −0.189703 | − | 0.521205i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −48385.5 | + | 40600.2i | −1.08680 | + | 0.911934i | −0.996468 | − | 0.0839772i | \(-0.973238\pi\) |
−0.0903334 | + | 0.995912i | \(0.528793\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −39821.6 | − | 6946.53i | −0.877727 | − | 0.153112i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25825.2i | 0.558685i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5592.33 | 0.118761 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12266.3 | − | 4489.99i | 0.255755 | − | 0.0936176i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3830.96 | − | 4565.55i | −0.0784373 | − | 0.0934779i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14199.5 | − | 5168.20i | 0.285538 | − | 0.103927i | −0.195281 | − | 0.980747i | \(-0.562562\pi\) |
0.480819 | + | 0.876820i | \(0.340340\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 26647.7 | − | 97.4976i | 0.526375 | − | 0.00192588i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −40600.0 | + | 48385.2i | −0.787905 | + | 0.938989i | −0.999262 | − | 0.0384200i | \(-0.987768\pi\) |
0.211356 | + | 0.977409i | \(0.432212\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11889.2 | + | 67427.2i | 0.226716 | + | 1.28577i | 0.859377 | + | 0.511343i | \(0.170852\pi\) |
−0.632660 | + | 0.774430i | \(0.718037\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4443.52 | + | 2576.32i | −0.0832729 | + | 0.0482809i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 81880.6 | − | 47273.8i | 1.50824 | − | 0.870780i | 0.508282 | − | 0.861191i | \(-0.330281\pi\) |
0.999954 | − | 0.00958931i | \(-0.00305242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16325.0 | − | 28275.8i | 0.295610 | − | 0.512011i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6895.96 | − | 5807.93i | 0.122772 | − | 0.103401i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −33160.0 | + | 91106.3i | −0.580522 | + | 1.59497i | 0.206769 | + | 0.978390i | \(0.433705\pi\) |
−0.787291 | + | 0.616581i | \(0.788517\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11435.1 | − | 64851.9i | 0.196883 | − | 1.11658i | −0.712830 | − | 0.701337i | \(-0.752587\pi\) |
0.909712 | − | 0.415239i | \(-0.136302\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 55670.3 | + | 19687.6i | 0.942782 | + | 0.333411i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −39521.0 | − | 6968.62i | −0.658409 | − | 0.116095i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7980.33 | − | 2904.60i | −0.130806 | − | 0.0476094i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10079.0 | + | 11967.2i | 0.162562 | + | 0.193016i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21936.7 | − | 12665.2i | −0.348196 | − | 0.201031i | 0.315694 | − | 0.948861i | \(-0.397763\pi\) |
−0.663891 | + | 0.747830i | \(0.731096\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27773.4 | − | 48105.0i | −0.433899 | − | 0.751534i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19151.8 | − | 33032.2i | −0.294530 | − | 0.507992i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 124203. | − | 21900.3i | 1.88046 | − | 0.331576i | 0.888579 | − | 0.458724i | \(-0.151693\pi\) |
0.991884 | + | 0.127148i | \(0.0405823\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11032.4 | + | 9257.31i | 0.164464 | + | 0.138002i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −104.728 | − | 28624.0i | −0.00153738 | − | 0.420193i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 895.943 | + | 2461.58i | 0.0129530 | + | 0.0355880i | 0.946001 | − | 0.324165i | \(-0.105083\pi\) |
−0.933048 | + | 0.359753i | \(0.882861\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22778.9 | − | 19113.8i | 0.324370 | − | 0.272179i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4043.12 | + | 11045.5i | 0.0567146 | + | 0.154939i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 101027.i | − | 1.39616i | −0.716021 | − | 0.698078i | \(-0.754039\pi\) | ||
0.716021 | − | 0.698078i | \(-0.245961\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29168.0 | −0.397162 | −0.198581 | − | 0.980084i | \(-0.563633\pi\) | ||||
−0.198581 | + | 0.980084i | \(0.563633\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −309.397 | + | 1773.65i | −0.00415137 | + | 0.0237981i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14581.3 | − | 17377.4i | −0.192811 | − | 0.229783i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 79476.1 | − | 28926.9i | 1.03580 | − | 0.377001i | 0.232515 | − | 0.972593i | \(-0.425305\pi\) |
0.803287 | + | 0.595592i | \(0.203082\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9306.30 | + | 53931.8i | −0.119555 | + | 0.692845i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 83010.4 | − | 98928.0i | 1.05128 | − | 1.25287i | 0.0847312 | − | 0.996404i | \(-0.472997\pi\) |
0.966553 | − | 0.256468i | \(-0.0825587\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3459.59 | − | 19620.3i | −0.0431968 | − | 0.244981i | 0.955562 | − | 0.294790i | \(-0.0952498\pi\) |
−0.998759 | + | 0.0498092i | \(0.984139\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −47168.2 | − | 27117.7i | −0.580711 | − | 0.333859i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4585.21 | − | 2647.27i | 0.0556667 | − | 0.0321392i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11358.3 | + | 19673.1i | −0.135993 | + | 0.235547i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21631.9 | − | 121382.i | −0.255452 | − | 1.43340i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14958.8 | + | 41099.0i | −0.174245 | + | 0.478735i | −0.995817 | − | 0.0913700i | \(-0.970875\pi\) |
0.821572 | + | 0.570105i | \(0.193098\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2055.72 | − | 11658.6i | 0.0236222 | − | 0.133968i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −17451.2 | − | 47140.1i | −0.197839 | − | 0.534414i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19174.8 | − | 3381.03i | −0.214481 | − | 0.0378187i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11674.4 | + | 4249.15i | 0.128855 | + | 0.0468996i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −28331.3 | + | 78285.0i | −0.308590 | + | 0.852695i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15787.9 | + | 9115.17i | 0.169717 | + | 0.0979863i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3347.53 | + | 5798.10i | 0.0355180 | + | 0.0615189i | 0.883238 | − | 0.468925i | \(-0.155359\pi\) |
−0.847720 | + | 0.530444i | \(0.822025\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −44504.0 | + | 81.4145i | −0.466104 | + | 0.000852677i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26470.7 | − | 4667.50i | 0.273681 | − | 0.0482574i | −0.0351230 | − | 0.999383i | \(-0.511182\pi\) |
0.308804 | + | 0.951126i | \(0.400071\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 119813. | + | 100535.i | 1.22296 | + | 1.02619i | 0.998664 | + | 0.0516685i | \(0.0164539\pi\) |
0.224300 | + | 0.974520i | \(0.427991\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3905.38 | + | 10853.3i | −0.0393589 | + | 0.109381i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19067.4 | − | 52387.3i | −0.189746 | − | 0.521323i | 0.807943 | − | 0.589260i | \(-0.200581\pi\) |
−0.997690 | + | 0.0679366i | \(0.978358\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18666.1 | + | 15662.7i | −0.183431 | + | 0.153917i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −87224.8 | + | 104337.i | −0.846505 | + | 1.01258i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 86642.5i | − | 0.830473i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7951.52 | −0.0752806 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 105304. | + | 88032.5i | 0.984800 | + | 0.823280i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10096.2 | − | 12032.2i | −0.0932752 | − | 0.111161i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −37852.5 | + | 13777.2i | −0.345493 | + | 0.125749i | −0.508938 | − | 0.860803i | \(-0.669962\pi\) |
0.163445 | + | 0.986552i | \(0.447739\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −107636. | + | 90990.2i | −0.970661 | + | 0.820552i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −64942.1 | + | 77395.0i | −0.578678 | + | 0.689641i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 36939.7 | + | 209496.i | 0.325262 | + | 1.84465i | 0.507826 | + | 0.861460i | \(0.330449\pi\) |
−0.182563 | + | 0.983194i | \(0.558439\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −45.4407 | − | 24839.5i | −0.000395408 | − | 0.216144i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 40347.2 | − | 23294.5i | 0.346980 | − | 0.200329i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19589.1 | + | 33929.3i | −0.166504 | + | 0.288394i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −117295. | − | 42449.1i | −0.985465 | − | 0.356640i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12450.0 | + | 34206.2i | −0.103398 | + | 0.284083i | −0.980594 | − | 0.196049i | \(-0.937189\pi\) |
0.877196 | + | 0.480132i | \(0.159411\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29968.9 | + | 169962.i | −0.246048 | + | 1.39541i | 0.571997 | + | 0.820256i | \(0.306169\pi\) |
−0.818045 | + | 0.575154i | \(0.804942\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16590.0 | − | 5935.35i | −0.134658 | − | 0.0481761i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10299.5 | + | 1816.08i | 0.0826543 | + | 0.0145742i | 0.214822 | − | 0.976653i | \(-0.431083\pi\) |
−0.132168 | + | 0.991227i | \(0.542194\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 72615.1 | + | 26429.7i | 0.576196 | + | 0.209718i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18083.5 | + | 3222.73i | −0.141888 | + | 0.0252864i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −65698.6 | − | 37931.1i | −0.509762 | − | 0.294311i | 0.222974 | − | 0.974824i | \(-0.428423\pi\) |
−0.732736 | + | 0.680513i | \(0.761757\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3430.55 | + | 5941.89i | 0.0263238 | + | 0.0455942i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 44348.2 | − | 77139.0i | 0.336560 | − | 0.585410i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −24591.3 | + | 4336.11i | −0.184585 | + | 0.0325473i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22828.4 | + | 19155.3i | 0.169490 | + | 0.142219i | 0.723587 | − | 0.690233i | \(-0.242492\pi\) |
−0.554097 | + | 0.832452i | \(0.686936\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17899.6 | + | 48624.6i | 0.131459 | + | 0.357111i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4892.56 | − | 13442.2i | −0.0355458 | − | 0.0976614i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5382.98 | − | 4516.86i | 0.0386906 | − | 0.0324653i | −0.623237 | − | 0.782033i | \(-0.714183\pi\) |
0.661928 | + | 0.749568i | \(0.269738\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −145523. | − | 25385.2i | −1.03483 | − | 0.180517i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8541.21i | 0.0600948i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 145934. | 1.01596 | 0.507980 | − | 0.861369i | \(-0.330392\pi\) | ||||
0.507980 | + | 0.861369i | \(0.330392\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −232734. | + | 85190.8i | −1.60328 | + | 0.586871i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −96300.0 | − | 114766.i | −0.656491 | − | 0.782375i | 0.330387 | − | 0.943846i | \(-0.392821\pi\) |
−0.986878 | + | 0.161470i | \(0.948376\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9226.89 | − | 3358.31i | 0.0622492 | − | 0.0226569i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −60405.9 | + | 105516.i | −0.403327 | + | 0.704523i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 63115.2 | − | 75217.7i | 0.417095 | − | 0.497074i | −0.516058 | − | 0.856553i | \(-0.672601\pi\) |
0.933153 | + | 0.359479i | \(0.117046\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −34494.1 | − | 195626.i | −0.225627 | − | 1.27960i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 185304. | − | 107438.i | 1.19978 | − | 0.695620i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14926.3 | + | 8617.71i | −0.0956662 | + | 0.0552329i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −89376.0 | + | 154804.i | −0.567074 | + | 0.982201i | 0.429779 | + | 0.902934i | \(0.358591\pi\) |
−0.996853 | + | 0.0792673i | \(0.974742\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20019.5 | + | 16860.9i | −0.125750 | + | 0.105909i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15740.3 | + | 43246.2i | −0.0978871 | + | 0.268943i | −0.978965 | − | 0.204029i | \(-0.934596\pi\) |
0.881078 | + | 0.472971i | \(0.156819\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2835.78 | − | 16082.5i | 0.0174608 | − | 0.0990249i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −98169.3 | − | 55724.3i | −0.598502 | − | 0.339730i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 118157. | + | 20834.2i | 0.713297 | + | 0.125773i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 99480.0 | + | 36207.8i | 0.594688 | + | 0.216449i | 0.621790 | − | 0.783184i | \(-0.286406\pi\) |
−0.0271021 | + | 0.999633i | \(0.508628\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 57399.0 | + | 68151.9i | 0.339798 | + | 0.403454i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4932.08 | − | 2847.54i | −0.0289155 | − | 0.0166943i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14955.1 | − | 25902.9i | −0.0868345 | − | 0.150402i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 28085.6 | + | 48440.9i | 0.161515 | + | 0.278573i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 342282. | − | 60353.5i | 1.94965 | − | 0.343775i | 0.950159 | − | 0.311767i | \(-0.100921\pi\) |
0.999488 | − | 0.0320086i | \(-0.0101904\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −124187. | − | 104205.i | −0.700668 | − | 0.587930i | 0.221296 | − | 0.975207i | \(-0.428971\pi\) |
−0.921964 | + | 0.387277i | \(0.873416\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 132838. | − | 77343.6i | 0.742408 | − | 0.432259i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −27745.8 | − | 76231.0i | −0.153610 | − | 0.422040i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6718.23 | − | 5637.27i | 0.0368468 | − | 0.0309181i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5155.78 | + | 14085.2i | 0.0280143 | + | 0.0765328i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 68099.8i | 0.366599i | 0.983057 | + | 0.183300i | \(0.0586778\pi\) | ||||
−0.983057 | + | 0.183300i | \(0.941322\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 115590. | 0.616515 | 0.308257 | − | 0.951303i | \(-0.400254\pi\) | ||||
0.308257 | + | 0.951303i | \(0.400254\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9403.42 | + | 53905.9i | −0.0496944 | + | 0.284877i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −181944. | − | 216832.i | −0.952741 | − | 1.13543i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −419.769 | + | 152.783i | −0.00217812 | + | 0.000792770i | −0.343109 | − | 0.939296i | \(-0.611480\pi\) |
0.340931 | + | 0.940088i | \(0.389258\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −145174. | − | 120913.i | −0.746467 | − | 0.621721i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20484.1 | − | 24412.0i | 0.104378 | − | 0.124393i | −0.711326 | − | 0.702862i | \(-0.751905\pi\) |
0.815704 | + | 0.578469i | \(0.196350\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3904.56 | − | 22143.9i | −0.0197175 | − | 0.111824i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5726.91 | − | 3292.48i | −0.0286619 | − | 0.0164781i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6386.03 | + | 3686.98i | −0.0316766 | + | 0.0182885i | −0.515755 | − | 0.856736i | \(-0.672488\pi\) |
0.484078 | + | 0.875025i | \(0.339155\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22054.1 | − | 38198.8i | 0.108427 | − | 0.187800i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25054.8 | + | 140589.i | 0.122094 | + | 0.685100i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1177.18 | − | 3234.26i | 0.00568615 | − | 0.0156226i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16663.8 | − | 94505.3i | 0.0797889 | − | 0.452505i | −0.918571 | − | 0.395256i | \(-0.870656\pi\) |
0.998360 | − | 0.0572493i | \(-0.0182330\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −986.543 | − | 179758.i | −0.00468264 | − | 0.853225i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7688.93 | + | 1355.77i | 0.0361796 | + | 0.00637944i | 0.191709 | − | 0.981452i | \(-0.438597\pi\) |
−0.155529 | + | 0.987831i | \(0.549708\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −140479. | − | 51130.3i | −0.655315 | − | 0.238515i | −0.00710280 | − | 0.999975i | \(-0.502261\pi\) |
−0.648212 | + | 0.761460i | \(0.724483\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 35603.4 | − | 98379.2i | 0.164659 | − | 0.454986i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 174259. | + | 100609.i | 0.799029 | + | 0.461319i | 0.843131 | − | 0.537708i | \(-0.180710\pi\) |
−0.0441027 | + | 0.999027i | \(0.514043\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24301.6 | + | 42091.6i | 0.110481 | + | 0.191359i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 307760. | − | 563.008i | 1.38730 | − | 0.00253789i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 101928. | − | 17972.6i | 0.455585 | − | 0.0803319i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −88551.3 | − | 74303.4i | −0.392471 | − | 0.329322i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 137777. | − | 24813.9i | 0.605535 | − | 0.109058i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 78432.5 | + | 215492.i | 0.341842 | + | 0.939203i | 0.984860 | + | 0.173352i | \(0.0554597\pi\) |
−0.643018 | + | 0.765851i | \(0.722318\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32216.7 | − | 27033.0i | 0.139249 | − | 0.116844i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −38488.5 | + | 46039.5i | −0.164982 | + | 0.197350i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 235698.i | 1.00201i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 225927. | 0.952600 | 0.476300 | − | 0.879283i | \(-0.341978\pi\) | ||||
0.476300 | + | 0.879283i | \(0.341978\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 312470. | + | 261221.i | 1.30675 | + | 1.09242i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −259155. | − | 308848.i | −1.07497 | − | 1.28110i | −0.957628 | − | 0.288007i | \(-0.907008\pi\) |
−0.117341 | − | 0.993092i | \(-0.537437\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −81884.4 | + | 29803.5i | −0.336905 | + | 0.122623i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17032.5 | + | 94571.7i | 0.0695135 | + | 0.385967i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23895.4 | − | 28477.5i | 0.0967391 | − | 0.115289i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −52018.8 | − | 295013.i | −0.208910 | − | 1.18479i | −0.891167 | − | 0.453675i | \(-0.850113\pi\) |
0.682257 | − | 0.731112i | \(-0.260999\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −814.058 | − | 444993.i | −0.00324325 | − | 1.77287i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −275570. | + | 159100.i | −1.08917 | + | 0.628833i | −0.933356 | − | 0.358953i | \(-0.883134\pi\) |
−0.155815 | + | 0.987786i | \(0.549800\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 79577.0 | − | 137831.i | 0.312036 | − | 0.540463i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −236764. | − | 85684.8i | −0.921084 | − | 0.333340i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −149917. | + | 411893.i | −0.578648 | + | 1.58982i | 0.211814 | + | 0.977310i | \(0.432063\pi\) |
−0.790461 | + | 0.612512i | \(0.790159\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2085.96 | + | 11830.1i | −0.00798850 | + | 0.0453050i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −129289. | − | 221124.i | −0.491279 | − | 0.840237i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 83784.7 | + | 14773.5i | 0.315901 | + | 0.0557018i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −122961. | − | 44754.1i | −0.460029 | − | 0.167437i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 415192. | − | 73993.0i | 1.54140 | − | 0.274698i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −76314.7 | − | 44060.3i | −0.281146 | − | 0.162320i | 0.352796 | − | 0.935700i | \(-0.385231\pi\) |
−0.633942 | + | 0.773380i | \(0.718564\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 205191. | + | 355401.i | 0.750162 | + | 1.29932i | 0.947744 | + | 0.319033i | \(0.103358\pi\) |
−0.197581 | + | 0.980286i | \(0.563309\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12214.4 | + | 21245.7i | −0.0443154 | + | 0.0770819i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 164078. | − | 28931.4i | 0.590785 | − | 0.104171i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −282757. | − | 237262.i | −1.01042 | − | 0.847845i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 35668.9 | − | 42825.7i | 0.126503 | − | 0.151885i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5287.98 | − | 14528.6i | −0.0186138 | − | 0.0511411i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 199154. | − | 167110.i | 0.695794 | − | 0.583840i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 129864. | + | 22653.6i | 0.450338 | + | 0.0785576i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 160832.i | 0.553599i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −492919. | −1.68415 | −0.842075 | − | 0.539361i | \(-0.818666\pi\) | ||||
−0.842075 | + | 0.539361i | \(0.818666\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 54370.3 | − | 19901.9i | 0.184400 | − | 0.0674986i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −168657. | − | 200998.i | −0.567821 | − | 0.676703i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −371903. | + | 135361.i | −1.24295 | + | 0.452398i | −0.878014 | − | 0.478634i | \(-0.841132\pi\) |
−0.364938 | + | 0.931032i | \(0.618910\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 43185.2 | + | 74170.9i | 0.143282 | + | 0.246087i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −79813.8 | + | 95118.4i | −0.262890 | + | 0.313301i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1439.79 | + | 8165.44i | 0.00470813 | + | 0.0267011i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 233091. | − | 135144.i | 0.756726 | − | 0.438744i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −359117. | + | 207336.i | −1.15751 | + | 0.668291i | −0.950707 | − | 0.310091i | \(-0.899640\pi\) |
−0.206806 | + | 0.978382i | \(0.566307\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18139.7 | − | 31418.9i | 0.0580505 | − | 0.100546i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −117044. | + | 98576.9i | −0.371897 | + | 0.313220i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16738.4 | + | 45988.4i | −0.0528077 | + | 0.145088i | −0.963292 | − | 0.268455i | \(-0.913487\pi\) |
0.910484 | + | 0.413543i | \(0.135709\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8245.69 | + | 46763.6i | −0.0258303 | + | 0.146491i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −41342.8 | + | 35209.4i | −0.128598 | + | 0.109520i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 415714. | + | 73301.6i | 1.28401 | + | 0.226406i | 0.773684 | − | 0.633572i | \(-0.218412\pi\) |
0.510331 | + | 0.859978i | \(0.329523\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −238847. | − | 86933.2i | −0.732567 | − | 0.266633i | −0.0513161 | − | 0.998682i | \(-0.516342\pi\) |
−0.681251 | + | 0.732050i | \(0.738564\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 359579. | + | 426941.i | 1.09518 | + | 1.30035i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −229518. | − | 132512.i | −0.694193 | − | 0.400793i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 72698.7 | + | 125918.i | 0.218361 | + | 0.378212i | 0.954307 | − | 0.298828i | \(-0.0965957\pi\) |
−0.735946 | + | 0.677040i | \(0.763262\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 44309.2 | + | 76422.6i | 0.132171 | + | 0.227963i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14170.2 | + | 2498.59i | −0.0419782 | + | 0.00740189i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −91291.2 | − | 76602.4i | −0.268591 | − | 0.225375i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 29231.9 | + | 16734.7i | 0.0854171 | + | 0.0488998i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 201839. | + | 554549.i | 0.585773 | + | 1.60940i | 0.778151 | + | 0.628077i | \(0.216158\pi\) |
−0.192378 | + | 0.981321i | \(0.561620\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 181865. | − | 152602.i | 0.524225 | − | 0.439877i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −107186. | − | 292824.i | −0.306877 | − | 0.838363i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 632321.i | 1.79816i | 0.437786 | + | 0.899079i | \(0.355763\pi\) | ||||
−0.437786 | + | 0.899079i | \(0.644237\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 35114.4 | 0.0991863 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −109723. | + | 628996.i | −0.307857 | + | 1.76481i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −258279. | − | 307805.i | −0.719840 | − | 0.857872i | 0.274775 | − | 0.961509i | \(-0.411397\pi\) |
−0.994615 | + | 0.103636i | \(0.966952\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −338819. | + | 123320.i | −0.938034 | + | 0.341417i | −0.765389 | − | 0.643568i | \(-0.777454\pi\) |
−0.172645 | + | 0.984984i | \(0.555231\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −446367. | + | 164316.i | −1.22760 | + | 0.451904i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −109337. | + | 130302.i | −0.298714 | + | 0.355993i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −63002.8 | − | 357306.i | −0.170995 | − | 0.969758i | −0.942666 | − | 0.333737i | \(-0.891690\pi\) |
0.771672 | − | 0.636021i | \(-0.219421\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22821.3 | + | 13120.3i | 0.0615327 | + | 0.0353760i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39722.0 | + | 22933.5i | −0.106402 | + | 0.0614311i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 51114.3 | − | 88532.6i | 0.136026 | − | 0.235604i | −0.789963 | − | 0.613155i | \(-0.789900\pi\) |
0.925989 | + | 0.377551i | \(0.123234\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17378.7 | − | 97515.9i | −0.0459480 | − | 0.257825i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −174957. | + | 480690.i | −0.459580 | + | 1.26268i | 0.466220 | + | 0.884669i | \(0.345616\pi\) |
−0.925799 | + | 0.378015i | \(0.876607\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −92539.8 | + | 524819.i | −0.241517 | + | 1.36971i | 0.586929 | + | 0.809639i | \(0.300337\pi\) |
−0.828445 | + | 0.560070i | \(0.810774\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −379950. | − | 447793.i | −0.985244 | − | 1.16117i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10652.7 | − | 1878.36i | −0.0274463 | − | 0.00483952i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 72146.1 | + | 26259.0i | 0.184694 | + | 0.0672231i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −74202.8 | + | 205037.i | −0.188749 | + | 0.521551i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 371581. | + | 214533.i | 0.939188 | + | 0.542241i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 54673.1 | + | 94696.5i | 0.137314 | + | 0.237835i | 0.926479 | − | 0.376346i | \(-0.122820\pi\) |
−0.789165 | + | 0.614181i | \(0.789486\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 568464. | − | 1039.93i | 1.41872 | − | 0.00259536i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 466583. | − | 82271.2i | 1.15713 | − | 0.204033i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 43186.3 | + | 36237.6i | 0.106431 | + | 0.0893061i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 234868. | + | 277834.i | 0.575205 | + | 0.680431i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −56474.2 | − | 155162.i | −0.137447 | − | 0.377631i | 0.851804 | − | 0.523860i | \(-0.175509\pi\) |
−0.989251 | + | 0.146229i | \(0.953286\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 174635. | − | 146536.i | 0.422386 | − | 0.354424i | −0.406684 | − | 0.913569i | \(-0.633315\pi\) |
0.829070 | + | 0.559145i | \(0.188871\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 149075. | − | 178322.i | 0.358332 | − | 0.428634i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 167904.i | − | 0.401101i | −0.979683 | − | 0.200550i | \(-0.935727\pi\) | ||
0.979683 | − | 0.200550i | \(-0.0642730\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −47444.9 | −0.112642 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38614.9 | − | 32281.6i | −0.0911156 | − | 0.0761715i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −381636. | − | 454816.i | −0.894999 | − | 1.06662i | −0.997414 | − | 0.0718765i | \(-0.977101\pi\) |
0.102415 | − | 0.994742i | \(-0.467343\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −384780. | + | 140049.i | −0.896872 | + | 0.326435i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −110617. | − | 39803.5i | −0.256265 | − | 0.0922125i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 346989. | − | 413526.i | 0.798997 | − | 0.952207i | −0.200626 | − | 0.979668i | \(-0.564298\pi\) |
0.999623 | + | 0.0274604i | \(0.00874203\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −63023.7 | − | 357425.i | −0.144245 | − | 0.818054i | −0.967970 | − | 0.251065i | \(-0.919219\pi\) |
0.823725 | − | 0.566989i | \(-0.191892\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 98.1259 | + | 53639.1i | 0.000223232 | + | 0.122027i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 43332.2 | − | 25017.9i | 0.0979869 | − | 0.0565728i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −142339. | + | 246539.i | −0.319943 | + | 0.554158i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −127880. | − | 46279.9i | −0.285727 | − | 0.103405i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24988.7 | − | 68655.8i | 0.0555006 | − | 0.152487i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 139117. | − | 788974.i | 0.307151 | − | 1.74194i | −0.306054 | − | 0.952014i | \(-0.599009\pi\) |
0.613205 | − | 0.789924i | \(-0.289880\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −184565. | − | 153150.i | −0.405080 | − | 0.336132i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 318018. | + | 56075.2i | 0.693865 | + | 0.122347i | 0.509448 | − | 0.860501i | \(-0.329849\pi\) |
0.184416 | + | 0.982848i | \(0.440961\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 106549. | + | 38780.6i | 0.231105 | + | 0.0841152i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 559643. | − | 99736.2i | 1.20675 | − | 0.215060i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −638191. | − | 368460.i | −1.36807 | − | 0.789858i | −0.377392 | − | 0.926054i | \(-0.623179\pi\) |
−0.990682 | + | 0.136196i | \(0.956512\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −85167.7 | − | 147515.i | −0.181507 | − | 0.314380i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 307126. | − | 534213.i | 0.650734 | − | 1.13188i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −41138.3 | + | 7253.79i | −0.0866578 | + | 0.0152801i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 320796. | + | 269180.i | 0.671852 | + | 0.563751i | 0.913613 | − | 0.406585i | \(-0.133281\pi\) |
−0.241761 | + | 0.970336i | \(0.577725\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 45554.1 | + | 7860.68i | 0.0948552 | + | 0.0163679i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −36610.5 | − | 100587.i | −0.0757942 | − | 0.208243i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 120834. | − | 101392.i | 0.248727 | − | 0.208707i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −838270. | − | 146229.i | −1.71565 | − | 0.299281i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 396026.i | − | 0.805911i | −0.915220 | − | 0.402956i | \(-0.867983\pi\) | ||
0.915220 | − | 0.402956i | \(-0.132017\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 611390. | 1.23711 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −275945. | + | 101008.i | −0.555194 | + | 0.203225i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −49214.3 | − | 58651.3i | −0.0984584 | − | 0.117338i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 471516. | − | 171618.i | 0.938002 | − | 0.341405i | 0.172625 | − | 0.984988i | \(-0.444775\pi\) |
0.765376 | + | 0.643583i | \(0.222553\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −81142.5 | + | 296.881i | −0.160513 | + | 0.000587277i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 349869. | − | 416958.i | 0.688219 | − | 0.820188i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4979.09 | − | 28237.8i | −0.00973953 | − | 0.0552356i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 754877. | − | 437672.i | 1.46838 | − | 0.851354i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −397408. | + | 229444.i | −0.768739 | + | 0.443832i | −0.832425 | − | 0.554138i | \(-0.813048\pi\) |
0.0636853 | + | 0.997970i | \(0.479715\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20464.0 | − | 35444.6i | 0.0393658 | − | 0.0681836i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −453314. | + | 381791.i | −0.867207 | + | 0.730381i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −39762.8 | + | 109247.i | −0.0756487 | + | 0.207843i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −103524. | + | 587115.i | −0.195872 | + | 1.11085i | 0.715299 | + | 0.698819i | \(0.246291\pi\) |
−0.911171 | + | 0.412028i | \(0.864821\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −270756. | − | 457297.i | −0.509475 | − | 0.860485i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 364508. | + | 64272.6i | 0.682139 | + | 0.120279i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 321783. | + | 117119.i | 0.598901 | + | 0.217982i | 0.623640 | − | 0.781712i | \(-0.285653\pi\) |
−0.0247390 | + | 0.999694i | \(0.507875\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 232665. | + | 276252.i | 0.430682 | + | 0.511364i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 350660. | + | 202453.i | 0.645581 | + | 0.372726i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 467974. | + | 810555.i | 0.856905 | + | 1.48420i | 0.874866 | + | 0.484365i | \(0.160949\pi\) |
−0.0179608 | + | 0.999839i | \(0.505717\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 38337.2 | + | 66122.3i | 0.0698207 | + | 0.120424i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 630777. | − | 111223.i | 1.14261 | − | 0.201473i | 0.429864 | − | 0.902894i | \(-0.358562\pi\) |
0.712747 | + | 0.701421i | \(0.247451\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9673.85 | + | 8117.32i | 0.0174296 | + | 0.0146252i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −515.203 | − | 140814.i | −0.000923288 | − | 0.252350i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −42775.2 | − | 117524.i | −0.0762480 | − | 0.209490i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −280016. | + | 234962.i | −0.496482 | + | 0.416598i | −0.856342 | − | 0.516408i | \(-0.827269\pi\) |
0.359861 | + | 0.933006i | \(0.382824\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 78363.2 | + | 214082.i | 0.138204 | + | 0.377563i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 272994.i | − | 0.478915i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24716.3 | −0.0431312 | −0.0215656 | − | 0.999767i | \(-0.506865\pi\) | ||||
−0.0215656 | + | 0.999767i | \(0.506865\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −85909.7 | + | 492485.i | −0.149128 | + | 0.854888i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −492900. | − | 587416.i | −0.851118 | − | 1.01432i | −0.999677 | − | 0.0254195i | \(-0.991908\pi\) |
0.148559 | − | 0.988904i | \(-0.452537\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −118612. | + | 43171.3i | −0.203742 | + | 0.0741560i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −58434.5 | + | 338639.i | −0.0998497 | + | 0.578648i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10690.0 | + | 12739.8i | −0.0181713 | + | 0.0216557i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 116072. | + | 658279.i | 0.196280 | + | 1.11316i | 0.910584 | + | 0.413324i | \(0.135632\pi\) |
−0.714304 | + | 0.699836i | \(0.753257\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −984034. | − | 565735.i | −1.65539 | − | 0.951709i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 542163. | − | 313018.i | 0.907342 | − | 0.523854i | 0.0277668 | − | 0.999614i | \(-0.491160\pi\) |
0.879575 | + | 0.475760i | \(0.157827\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 111142. | − | 192504.i | 0.185044 | − | 0.320506i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22741.1 | − | 127606.i | −0.0376678 | − | 0.211363i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 76874.3 | − | 211210.i | 0.126679 | − | 0.348049i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 53778.4 | − | 304992.i | 0.0881669 | − | 0.500019i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −164508. | + | 198252.i | −0.268326 | + | 0.323366i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −579399. | − | 102164.i | −0.940240 | − | 0.165790i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 590795. | + | 215032.i | 0.953866 | + | 0.347179i | 0.771627 | − | 0.636075i | \(-0.219443\pi\) |
0.182239 | + | 0.983254i | \(0.441665\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8022.95 | − | 22169.0i | 0.0128878 | − | 0.0356116i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19783.1 | + | 11421.8i | 0.0316185 | + | 0.0182549i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12805.0 | − | 22179.0i | −0.0203627 | − | 0.0352692i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −267621. | + | 489.579i | −0.423434 | + | 0.000774619i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 423476. | − | 74670.3i | 0.666672 | − | 0.117552i | 0.169938 | − | 0.985455i | \(-0.445643\pi\) |
0.496734 | + | 0.867903i | \(0.334532\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −358468. | − | 300790.i | −0.561509 | − | 0.471162i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 35842.0 | − | 99607.5i | 0.0558634 | − | 0.155248i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34227.8 | + | 94040.0i | 0.0530820 | + | 0.145842i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 87877.7 | − | 73738.2i | 0.135609 | − | 0.113789i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −583177. | + | 697591.i | −0.895474 | + | 1.07116i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 256726.i | 0.392258i | 0.980578 | + | 0.196129i | \(0.0628372\pi\) | ||||
−0.980578 | + | 0.196129i | \(0.937163\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 126232. | 0.191924 | 0.0959618 | − | 0.995385i | \(-0.469407\pi\) | ||||
0.0959618 | + | 0.995385i | \(0.469407\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 201404. | + | 168371.i | 0.304711 | + | 0.254734i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −500461. | − | 596426.i | −0.753451 | − | 0.897928i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 495606. | − | 180386.i | 0.742494 | − | 0.270246i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12374.7 | − | 10461.0i | 0.0184487 | − | 0.0155957i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −222431. | + | 265083.i | −0.329996 | + | 0.393274i | −0.905375 | − | 0.424613i | \(-0.860410\pi\) |
0.575379 | + | 0.817887i | \(0.304855\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11974.4 | − | 67910.2i | −0.0176789 | − | 0.100262i | 0.974692 | − | 0.223554i | \(-0.0717659\pi\) |
−0.992370 | + | 0.123292i | \(0.960655\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 373.486 | + | 204161.i | 0.000548740 | + | 0.299961i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 622211. | − | 359234.i | 0.909760 | − | 0.525250i | 0.0294062 | − | 0.999568i | \(-0.490638\pi\) |
0.880354 | + | 0.474317i | \(0.157305\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45069.7 | + | 78063.0i | −0.0655806 | + | 0.113589i | −0.896951 | − | 0.442129i | \(-0.854223\pi\) |
0.831371 | + | 0.555718i | \(0.187557\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −715760. | − | 259033.i | −1.03649 | − | 0.375106i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −196716. | + | 540473.i | −0.283498 | + | 0.778905i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −147719. | + | 837758.i | −0.211868 | + | 1.20156i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 375579. | − | 318677.i | 0.536106 | − | 0.454883i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −514240. | − | 90674.4i | −0.730536 | − | 0.128813i | −0.204006 | − | 0.978970i | \(-0.565396\pi\) |
−0.526530 | + | 0.850156i | \(0.676507\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −547277. | − | 199193.i | −0.773776 | − | 0.281632i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.14424e6 | + | 203920.i | −1.61014 | + | 0.286949i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 416855. | + | 240671.i | 0.583810 | + | 0.337063i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 40914.3 | + | 70865.6i | 0.0570306 | + | 0.0987799i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −89369.1 | + | 155448.i | −0.123986 | + | 0.215660i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.38043e6 | − | 243407.i | 1.90614 | − | 0.336104i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 359641. | + | 301774.i | 0.494277 | + | 0.414748i | 0.855556 | − | 0.517710i | \(-0.173215\pi\) |
−0.361279 | + | 0.932458i | \(0.617660\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 169159. | + | 459524.i | 0.231400 | + | 0.628602i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −340030. | − | 934226.i | −0.462974 | − | 1.27201i | −0.923238 | − | 0.384228i | \(-0.874468\pi\) |
0.460265 | − | 0.887782i | \(-0.347754\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −609585. | + | 511502.i | −0.826128 | + | 0.693204i | −0.954399 | − | 0.298535i | \(-0.903502\pi\) |
0.128270 | + | 0.991739i | \(0.459058\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −46942.0 | − | 8188.63i | −0.0633221 | − | 0.0110460i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 260591.i | − | 0.349894i | −0.984578 | − | 0.174947i | \(-0.944025\pi\) | ||
0.984578 | − | 0.174947i | \(-0.0559755\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −806217. | −1.07751 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 191991. | − | 70276.9i | 0.255412 | − | 0.0934920i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 44400.3 | + | 52914.2i | 0.0587958 | + | 0.0700701i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 133371. | − | 48543.0i | 0.175802 | − | 0.0639868i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −551305. | + | 963008.i | −0.723375 | + | 1.26358i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 87322.7 | − | 104067.i | 0.114054 | − | 0.135924i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 108616. | + | 615990.i | 0.141219 | + | 0.800893i | 0.970325 | + | 0.241803i | \(0.0777386\pi\) |
−0.829106 | + | 0.559091i | \(0.811150\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 340532. | − | 197438.i | 0.440738 | − | 0.255536i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −491616. | + | 283835.i | −0.633394 | + | 0.365690i | −0.782065 | − | 0.623196i | \(-0.785834\pi\) |
0.148671 | + | 0.988887i | \(0.452500\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 154303. | − | 267260.i | 0.197903 | − | 0.342778i | −0.749945 | − | 0.661500i | \(-0.769920\pi\) |
0.947848 | + | 0.318722i | \(0.103254\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −81493.3 | + | 68635.4i | −0.104048 | + | 0.0876318i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −324902. | + | 892660.i | −0.412957 | + | 1.13459i | 0.542653 | + | 0.839957i | \(0.317420\pi\) |
−0.955610 | + | 0.294633i | \(0.904803\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 39578.0 | − | 224458.i | 0.0500784 | − | 0.284009i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −151615. | + | 426237.i | −0.190979 | + | 0.536903i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −656664. | − | 115788.i | −0.823456 | − | 0.145197i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −236808. | − | 86190.9i | −0.295631 | − | 0.107601i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 112884. | + | 134032.i | 0.140297 | + | 0.166580i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −206780. | − | 119385.i | −0.255853 | − | 0.147717i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −213089. | − | 369081.i | −0.262489 | − | 0.454644i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −56083.6 | − | 96730.5i | −0.0687797 | − | 0.118628i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −109001. | + | 19219.8i | −0.133086 | + | 0.0234667i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 452630. | + | 379801.i | 0.550210 | + | 0.461681i | 0.875012 | − | 0.484101i | \(-0.160853\pi\) |
−0.324802 | + | 0.945782i | \(0.605298\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 647525. | − | 377014.i | 0.783662 | − | 0.456278i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 219349. | + | 602656.i | 0.264301 | + | 0.726160i | 0.998865 | + | 0.0476217i | \(0.0151642\pi\) |
−0.734565 | + | 0.678539i | \(0.762614\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −91826.6 | + | 77051.7i | −0.110161 | + | 0.0924359i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −56398.3 | − | 154075.i | −0.0673633 | − | 0.184031i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 196985.i | 0.234258i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 715806. | 0.847548 | 0.423774 | − | 0.905768i | \(-0.360705\pi\) | ||||
0.423774 | + | 0.905768i | \(0.360705\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10354.7 | − | 59359.2i | 0.0122073 | − | 0.0699792i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −69779.0 | − | 83159.3i | −0.0819070 | − | 0.0976130i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 537922. | − | 195788.i | 0.628689 | − | 0.228824i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 307769. | + | 256336.i | 0.358151 | + | 0.298298i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −495286. | + | 590259.i | −0.573885 | + | 0.683929i | −0.972423 | − | 0.233222i | \(-0.925073\pi\) |
0.398539 | + | 0.917152i | \(0.369517\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 142316. | + | 807114.i | 0.164193 | + | 0.931184i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −209723. | − | 120572.i | −0.240925 | − | 0.138511i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 253341. | − | 146267.i | 0.289790 | − | 0.167310i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −536614. | + | 929442.i | −0.611199 | + | 1.05863i | 0.379840 | + | 0.925052i | \(0.375979\pi\) |
−0.991039 | + | 0.133575i | \(0.957354\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −246969. | − | 1.38580e6i | −0.280099 | − | 1.57170i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −416989. | + | 1.14567e6i | −0.470918 | + | 1.29384i | 0.446097 | + | 0.894985i | \(0.352814\pi\) |
−0.917015 | + | 0.398852i | \(0.869409\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 89483.7 | − | 507487.i | 0.100628 | − | 0.570692i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 89617.1 | − | 52398.3i | 0.100352 | − | 0.0586751i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 509671. | + | 89868.8i | 0.568316 | + | 0.100209i | 0.450421 | − | 0.892817i | \(-0.351274\pi\) |
0.117896 | + | 0.993026i | \(0.462385\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32963.4 | + | 11997.7i | 0.0366016 | + | 0.0133219i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −170744. | + | 471799.i | −0.188792 | + | 0.521670i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −347753. | − | 200775.i | −0.382900 | − | 0.221067i | 0.296179 | − | 0.955132i | \(-0.404287\pi\) |
−0.679079 | + | 0.734065i | \(0.737621\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −533538. | − | 924115.i | −0.585004 | − | 1.01326i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 219301. | − | 401.184i | 0.239451 | − | 0.000438046i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −80698.0 | + | 14229.2i | −0.0877456 | + | 0.0154719i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −357742. | − | 300181.i | −0.387367 | − | 0.325040i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.20457e6 | − | 216945.i | 1.29891 | − | 0.233936i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −57758.5 | − | 158690.i | −0.0620242 | − | 0.170410i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 340877. | − | 286030.i | 0.364540 | − | 0.305885i | −0.442057 | − | 0.896987i | \(-0.645751\pi\) |
0.806597 | + | 0.591102i | \(0.201307\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −500141. | + | 598264.i | −0.532653 | + | 0.637155i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.11262e6i | − | 1.18007i | −0.807377 | − | 0.590036i | \(-0.799113\pi\) | ||
0.807377 | − | 0.590036i | \(-0.200887\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −51494.4 | −0.0543919 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 54905.0 | + | 45899.9i | 0.0577567 | + | 0.0482839i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 771833. | + | 919835.i | 0.808601 | + | 0.963653i | 0.999840 | − | 0.0178902i | \(-0.00569492\pi\) |
−0.191239 | + | 0.981544i | \(0.561250\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −84680.6 | + | 30821.2i | −0.0883525 | + | 0.0321577i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −218954. | − | 1.21572e6i | −0.227518 | − | 1.26327i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −570006. | + | 679307.i | −0.589892 | + | 0.703006i | −0.975585 | − | 0.219621i | \(-0.929518\pi\) |
0.385693 | + | 0.922627i | \(0.373962\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 103513. | + | 587051.i | 0.106690 | + | 0.605067i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 258.604 | + | 141362.i | 0.000265461 | + | 0.145110i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.04719e6 | − | 604596.i | 1.07061 | − | 0.618120i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 123747. | − | 214336.i | 0.126005 | − | 0.218247i | −0.796120 | − | 0.605138i | \(-0.793118\pi\) |
0.922125 | + | 0.386891i | \(0.126451\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 340899. | + | 123371.i | 0.345722 | + | 0.125117i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 417467. | − | 1.14698e6i | 0.421673 | − | 1.15854i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 126217. | − | 715814.i | 0.126978 | − | 0.720129i | −0.853135 | − | 0.521690i | \(-0.825302\pi\) |
0.980113 | − | 0.198439i | \(-0.0635871\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.26846e6 | − | 6961.52i | 1.27100 | − | 0.00697546i |
(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 | 108.5.k.a.29.3 | ✓ | 72 | |
3.2 | odd | 2 | 324.5.k.a.89.4 | 72 | |||
27.13 | even | 9 | 324.5.k.a.233.4 | 72 | |||
27.14 | odd | 18 | inner | 108.5.k.a.41.3 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.k.a.29.3 | ✓ | 72 | 1.1 | even | 1 | trivial | |
108.5.k.a.41.3 | yes | 72 | 27.14 | odd | 18 | inner | |
324.5.k.a.89.4 | 72 | 3.2 | odd | 2 | |||
324.5.k.a.233.4 | 72 | 27.13 | even | 9 |