Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(34,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.34");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.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: | \(26.4633302691\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 34.9 | ||
Character | \(\chi\) | \(=\) | 165.34 |
Dual form | 165.6.c.b.34.18 |
$q$-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 \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(67\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.97394i | − | 0.879277i | −0.898175 | − | 0.439639i | \(-0.855107\pi\) | ||
0.898175 | − | 0.439639i | \(-0.144893\pi\) | |||||||
\(3\) | 9.00000i | 0.577350i | ||||||||
\(4\) | 7.25990 | 0.226872 | ||||||||
\(5\) | 47.6857 | − | 29.1732i | 0.853028 | − | 0.521866i | ||||
\(6\) | 44.7655 | 0.507651 | ||||||||
\(7\) | 155.412i | 1.19878i | 0.800459 | + | 0.599388i | \(0.204589\pi\) | ||||
−0.800459 | + | 0.599388i | \(0.795411\pi\) | |||||||
\(8\) | − | 195.276i | − | 1.07876i | ||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | −145.106 | − | 237.186i | −0.458864 | − | 0.750048i | ||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 65.3391i | 0.130985i | ||||||||
\(13\) | − | 1173.30i | − | 1.92554i | −0.270323 | − | 0.962770i | \(-0.587131\pi\) | ||
0.270323 | − | 0.962770i | \(-0.412869\pi\) | |||||||
\(14\) | 773.008 | 1.05406 | ||||||||
\(15\) | 262.559 | + | 429.171i | 0.301299 | + | 0.492496i | ||||
\(16\) | −738.977 | −0.721657 | ||||||||
\(17\) | 898.118i | 0.753721i | 0.926270 | + | 0.376861i | \(0.122996\pi\) | ||||
−0.926270 | + | 0.376861i | \(0.877004\pi\) | |||||||
\(18\) | 402.889i | 0.293092i | ||||||||
\(19\) | 2407.95 | 1.53026 | 0.765128 | − | 0.643879i | \(-0.222676\pi\) | ||||
0.765128 | + | 0.643879i | \(0.222676\pi\) | |||||||
\(20\) | 346.193 | − | 211.794i | 0.193528 | − | 0.118397i | ||||
\(21\) | −1398.70 | −0.692114 | ||||||||
\(22\) | − | 601.847i | − | 0.265112i | ||||||
\(23\) | 4121.12i | 1.62441i | 0.583372 | + | 0.812205i | \(0.301733\pi\) | ||||
−0.583372 | + | 0.812205i | \(0.698267\pi\) | |||||||
\(24\) | 1757.49 | 0.622823 | ||||||||
\(25\) | 1422.85 | − | 2782.29i | 0.455313 | − | 0.890332i | ||||
\(26\) | −5835.95 | −1.69308 | ||||||||
\(27\) | − | 729.000i | − | 0.192450i | ||||||
\(28\) | 1128.27i | 0.271969i | ||||||||
\(29\) | −75.4479 | −0.0166591 | −0.00832957 | − | 0.999965i | \(-0.502651\pi\) | ||||
−0.00832957 | + | 0.999965i | \(0.502651\pi\) | |||||||
\(30\) | 2134.67 | − | 1305.95i | 0.433040 | − | 0.264925i | ||||
\(31\) | 3595.47 | 0.671972 | 0.335986 | − | 0.941867i | \(-0.390931\pi\) | ||||
0.335986 | + | 0.941867i | \(0.390931\pi\) | |||||||
\(32\) | − | 2573.22i | − | 0.444224i | ||||||
\(33\) | 1089.00i | 0.174078i | ||||||||
\(34\) | 4467.18 | 0.662730 | ||||||||
\(35\) | 4533.85 | + | 7410.91i | 0.625600 | + | 1.02259i | ||||
\(36\) | −588.052 | −0.0756240 | ||||||||
\(37\) | − | 16063.1i | − | 1.92897i | −0.264145 | − | 0.964483i | \(-0.585090\pi\) | ||
0.264145 | − | 0.964483i | \(-0.414910\pi\) | |||||||
\(38\) | − | 11977.0i | − | 1.34552i | ||||||
\(39\) | 10559.7 | 1.11171 | ||||||||
\(40\) | −5696.83 | − | 9311.90i | −0.562968 | − | 0.920212i | ||||
\(41\) | 15062.8 | 1.39941 | 0.699705 | − | 0.714432i | \(-0.253315\pi\) | ||||
0.699705 | + | 0.714432i | \(0.253315\pi\) | |||||||
\(42\) | 6957.07i | 0.608560i | ||||||||
\(43\) | 12867.8i | 1.06129i | 0.847595 | + | 0.530643i | \(0.178050\pi\) | ||||
−0.847595 | + | 0.530643i | \(0.821950\pi\) | |||||||
\(44\) | 878.448 | 0.0684045 | ||||||||
\(45\) | −3862.54 | + | 2363.03i | −0.284343 | + | 0.173955i | ||||
\(46\) | 20498.2 | 1.42831 | ||||||||
\(47\) | − | 6698.84i | − | 0.442339i | −0.975235 | − | 0.221169i | \(-0.929013\pi\) | ||
0.975235 | − | 0.221169i | \(-0.0709873\pi\) | |||||||
\(48\) | − | 6650.79i | − | 0.416649i | ||||||
\(49\) | −7345.75 | −0.437065 | ||||||||
\(50\) | −13838.9 | − | 7077.18i | −0.782848 | − | 0.400346i | ||||
\(51\) | −8083.06 | −0.435161 | ||||||||
\(52\) | − | 8518.07i | − | 0.436851i | ||||||
\(53\) | − | 22850.8i | − | 1.11741i | −0.829367 | − | 0.558705i | \(-0.811298\pi\) | ||
0.829367 | − | 0.558705i | \(-0.188702\pi\) | |||||||
\(54\) | −3626.00 | −0.169217 | ||||||||
\(55\) | 5769.97 | − | 3529.95i | 0.257198 | − | 0.157348i | ||||
\(56\) | 30348.2 | 1.29319 | ||||||||
\(57\) | 21671.6i | 0.883493i | ||||||||
\(58\) | 375.274i | 0.0146480i | ||||||||
\(59\) | 13021.3 | 0.486995 | 0.243498 | − | 0.969901i | \(-0.421705\pi\) | ||||
0.243498 | + | 0.969901i | \(0.421705\pi\) | |||||||
\(60\) | 1906.15 | + | 3115.74i | 0.0683563 | + | 0.111733i | ||||
\(61\) | 882.310 | 0.0303596 | 0.0151798 | − | 0.999885i | \(-0.495168\pi\) | ||||
0.0151798 | + | 0.999885i | \(0.495168\pi\) | |||||||
\(62\) | − | 17883.6i | − | 0.590849i | ||||||
\(63\) | − | 12588.3i | − | 0.399592i | ||||||
\(64\) | −36446.3 | −1.11225 | ||||||||
\(65\) | −34229.0 | − | 55949.8i | −1.00487 | − | 1.64254i | ||||
\(66\) | 5416.62 | 0.153062 | ||||||||
\(67\) | − | 14191.7i | − | 0.386231i | −0.981176 | − | 0.193115i | \(-0.938141\pi\) | ||
0.981176 | − | 0.193115i | \(-0.0618591\pi\) | |||||||
\(68\) | 6520.24i | 0.170998i | ||||||||
\(69\) | −37090.1 | −0.937854 | ||||||||
\(70\) | 36861.4 | − | 22551.1i | 0.899139 | − | 0.550076i | ||||
\(71\) | −78746.0 | −1.85388 | −0.926942 | − | 0.375205i | \(-0.877572\pi\) | ||||
−0.926942 | + | 0.375205i | \(0.877572\pi\) | |||||||
\(72\) | 15817.4i | 0.359587i | ||||||||
\(73\) | − | 34227.3i | − | 0.751736i | −0.926673 | − | 0.375868i | \(-0.877345\pi\) | ||
0.926673 | − | 0.375868i | \(-0.122655\pi\) | |||||||
\(74\) | −79896.8 | −1.69610 | ||||||||
\(75\) | 25040.6 | + | 12805.7i | 0.514033 | + | 0.262875i | ||||
\(76\) | 17481.5 | 0.347172 | ||||||||
\(77\) | 18804.8i | 0.361445i | ||||||||
\(78\) | − | 52523.5i | − | 0.977502i | ||||||
\(79\) | 48694.6 | 0.877835 | 0.438917 | − | 0.898527i | \(-0.355362\pi\) | ||||
0.438917 | + | 0.898527i | \(0.355362\pi\) | |||||||
\(80\) | −35238.6 | + | 21558.3i | −0.615594 | + | 0.376608i | ||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | − | 74921.3i | − | 1.23047i | ||||||
\(83\) | 95905.3i | 1.52809i | 0.645166 | + | 0.764043i | \(0.276788\pi\) | ||||
−0.645166 | + | 0.764043i | \(0.723212\pi\) | |||||||
\(84\) | −10154.5 | −0.157021 | ||||||||
\(85\) | 26200.9 | + | 42827.4i | 0.393341 | + | 0.642945i | ||||
\(86\) | 64003.6 | 0.933165 | ||||||||
\(87\) | − | 679.031i | − | 0.00961815i | ||||||
\(88\) | − | 23628.5i | − | 0.325258i | ||||||
\(89\) | −1342.55 | −0.0179662 | −0.00898308 | − | 0.999960i | \(-0.502859\pi\) | ||||
−0.00898308 | + | 0.999960i | \(0.502859\pi\) | |||||||
\(90\) | 11753.6 | + | 19212.1i | 0.152955 | + | 0.250016i | ||||
\(91\) | 182345. | 2.30829 | ||||||||
\(92\) | 29918.9i | 0.368533i | ||||||||
\(93\) | 32359.2i | 0.387963i | ||||||||
\(94\) | −33319.6 | −0.388938 | ||||||||
\(95\) | 114825. | − | 70247.6i | 1.30535 | − | 0.798587i | ||||
\(96\) | 23159.0 | 0.256473 | ||||||||
\(97\) | 80938.9i | 0.873430i | 0.899600 | + | 0.436715i | \(0.143858\pi\) | ||||
−0.899600 | + | 0.436715i | \(0.856142\pi\) | |||||||
\(98\) | 36537.3i | 0.384301i | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 10329.8 | − | 20199.1i | 0.103298 | − | 0.201991i | ||||
\(101\) | 19225.2 | 0.187529 | 0.0937644 | − | 0.995594i | \(-0.470110\pi\) | ||||
0.0937644 | + | 0.995594i | \(0.470110\pi\) | |||||||
\(102\) | 40204.7i | 0.382627i | ||||||||
\(103\) | 126651.i | 1.17630i | 0.808753 | + | 0.588148i | \(0.200143\pi\) | ||||
−0.808753 | + | 0.588148i | \(0.799857\pi\) | |||||||
\(104\) | −229119. | −2.07720 | ||||||||
\(105\) | −66698.2 | + | 40804.6i | −0.590392 | + | 0.361190i | ||||
\(106\) | −113659. | −0.982513 | ||||||||
\(107\) | 77773.3i | 0.656706i | 0.944555 | + | 0.328353i | \(0.106494\pi\) | ||||
−0.944555 | + | 0.328353i | \(0.893506\pi\) | |||||||
\(108\) | − | 5292.47i | − | 0.0436615i | ||||||
\(109\) | −68872.6 | −0.555240 | −0.277620 | − | 0.960691i | \(-0.589546\pi\) | ||||
−0.277620 | + | 0.960691i | \(0.589546\pi\) | |||||||
\(110\) | −17557.8 | − | 28699.5i | −0.138353 | − | 0.226148i | ||||
\(111\) | 144568. | 1.11369 | ||||||||
\(112\) | − | 114846.i | − | 0.865106i | ||||||
\(113\) | 43794.9i | 0.322647i | 0.986902 | + | 0.161323i | \(0.0515762\pi\) | ||||
−0.986902 | + | 0.161323i | \(0.948424\pi\) | |||||||
\(114\) | 107793. | 0.776835 | ||||||||
\(115\) | 120226. | + | 196518.i | 0.847724 | + | 1.38567i | ||||
\(116\) | −547.745 | −0.00377949 | ||||||||
\(117\) | 95037.7i | 0.641846i | ||||||||
\(118\) | − | 64767.3i | − | 0.428204i | ||||||
\(119\) | −139578. | −0.903543 | ||||||||
\(120\) | 83807.1 | − | 51271.5i | 0.531285 | − | 0.325030i | ||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | − | 4388.56i | − | 0.0266945i | ||||||
\(123\) | 135565.i | 0.807949i | ||||||||
\(124\) | 26102.7 | 0.152452 | ||||||||
\(125\) | −13318.4 | − | 174184.i | −0.0762390 | − | 0.997090i | ||||
\(126\) | −62613.6 | −0.351352 | ||||||||
\(127\) | − | 209089.i | − | 1.15033i | −0.818037 | − | 0.575165i | \(-0.804938\pi\) | ||
0.818037 | − | 0.575165i | \(-0.195062\pi\) | |||||||
\(128\) | 98938.8i | 0.533755i | ||||||||
\(129\) | −115810. | −0.612734 | ||||||||
\(130\) | −278291. | + | 170253.i | −1.44425 | + | 0.883561i | ||||
\(131\) | −85677.3 | −0.436202 | −0.218101 | − | 0.975926i | \(-0.569986\pi\) | ||||
−0.218101 | + | 0.975926i | \(0.569986\pi\) | |||||||
\(132\) | 7906.03i | 0.0394933i | ||||||||
\(133\) | 374224.i | 1.83443i | ||||||||
\(134\) | −70588.6 | −0.339604 | ||||||||
\(135\) | −21267.2 | − | 34762.9i | −0.100433 | − | 0.164165i | ||||
\(136\) | 175381. | 0.813085 | ||||||||
\(137\) | 115510.i | 0.525795i | 0.964824 | + | 0.262898i | \(0.0846782\pi\) | ||||
−0.964824 | + | 0.262898i | \(0.915322\pi\) | |||||||
\(138\) | 184484.i | 0.824633i | ||||||||
\(139\) | 120621. | 0.529523 | 0.264761 | − | 0.964314i | \(-0.414707\pi\) | ||||
0.264761 | + | 0.964314i | \(0.414707\pi\) | |||||||
\(140\) | 32915.3 | + | 53802.5i | 0.141931 | + | 0.231997i | ||||
\(141\) | 60289.5 | 0.255384 | ||||||||
\(142\) | 391678.i | 1.63008i | ||||||||
\(143\) | − | 141970.i | − | 0.580572i | ||||||
\(144\) | 59857.1 | 0.240552 | ||||||||
\(145\) | −3597.79 | + | 2201.06i | −0.0142107 | + | 0.00869383i | ||||
\(146\) | −170245. | −0.660984 | ||||||||
\(147\) | − | 66111.7i | − | 0.252339i | ||||||
\(148\) | − | 116616.i | − | 0.437628i | ||||||
\(149\) | −49190.8 | −0.181517 | −0.0907587 | − | 0.995873i | \(-0.528929\pi\) | ||||
−0.0907587 | + | 0.995873i | \(0.528929\pi\) | |||||||
\(150\) | 63694.7 | − | 124550.i | 0.231140 | − | 0.451978i | ||||
\(151\) | −490808. | −1.75174 | −0.875870 | − | 0.482547i | \(-0.839712\pi\) | ||||
−0.875870 | + | 0.482547i | \(0.839712\pi\) | |||||||
\(152\) | − | 470216.i | − | 1.65078i | ||||||
\(153\) | − | 72747.5i | − | 0.251240i | ||||||
\(154\) | 93534.0 | 0.317810 | ||||||||
\(155\) | 171452. | − | 104891.i | 0.573211 | − | 0.350679i | ||||
\(156\) | 76662.7 | 0.252216 | ||||||||
\(157\) | − | 273703.i | − | 0.886199i | −0.896473 | − | 0.443099i | \(-0.853879\pi\) | ||
0.896473 | − | 0.443099i | \(-0.146121\pi\) | |||||||
\(158\) | − | 242204.i | − | 0.771860i | ||||||
\(159\) | 205657. | 0.645137 | ||||||||
\(160\) | −75068.9 | − | 122706.i | −0.231825 | − | 0.378935i | ||||
\(161\) | −640470. | −1.94730 | ||||||||
\(162\) | − | 32634.0i | − | 0.0976974i | ||||||
\(163\) | − | 64881.0i | − | 0.191271i | −0.995416 | − | 0.0956354i | \(-0.969512\pi\) | ||
0.995416 | − | 0.0956354i | \(-0.0304883\pi\) | |||||||
\(164\) | 109354. | 0.317487 | ||||||||
\(165\) | 31769.6 | + | 51929.7i | 0.0908451 | + | 0.148493i | ||||
\(166\) | 477028. | 1.34361 | ||||||||
\(167\) | 379513.i | 1.05302i | 0.850170 | + | 0.526508i | \(0.176499\pi\) | ||||
−0.850170 | + | 0.526508i | \(0.823501\pi\) | |||||||
\(168\) | 273134.i | 0.746625i | ||||||||
\(169\) | −1.00535e6 | −2.70770 | ||||||||
\(170\) | 213021. | − | 130322.i | 0.565327 | − | 0.345856i | ||||
\(171\) | −195044. | −0.510085 | ||||||||
\(172\) | 93418.8i | 0.240776i | ||||||||
\(173\) | 509354.i | 1.29391i | 0.762528 | + | 0.646955i | \(0.223958\pi\) | ||||
−0.762528 | + | 0.646955i | \(0.776042\pi\) | |||||||
\(174\) | −3377.46 | −0.00845702 | ||||||||
\(175\) | 432399. | + | 221128.i | 1.06731 | + | 0.545818i | ||||
\(176\) | −89416.2 | −0.217588 | ||||||||
\(177\) | 117192.i | 0.281167i | ||||||||
\(178\) | 6677.76i | 0.0157972i | ||||||||
\(179\) | −706267. | −1.64754 | −0.823771 | − | 0.566923i | \(-0.808134\pi\) | ||||
−0.823771 | + | 0.566923i | \(0.808134\pi\) | |||||||
\(180\) | −28041.7 | + | 17155.3i | −0.0645093 | + | 0.0394655i | ||||
\(181\) | 250646. | 0.568674 | 0.284337 | − | 0.958724i | \(-0.408227\pi\) | ||||
0.284337 | + | 0.958724i | \(0.408227\pi\) | |||||||
\(182\) | − | 906974.i | − | 2.02963i | ||||||
\(183\) | 7940.79i | 0.0175281i | ||||||||
\(184\) | 804758. | 1.75235 | ||||||||
\(185\) | −468611. | − | 765979.i | −1.00666 | − | 1.64546i | ||||
\(186\) | 160953. | 0.341127 | ||||||||
\(187\) | 108672.i | 0.227256i | ||||||||
\(188\) | − | 48632.9i | − | 0.100354i | ||||||
\(189\) | 113295. | 0.230705 | ||||||||
\(190\) | −349407. | − | 571132.i | −0.702180 | − | 1.14776i | ||||
\(191\) | −592850. | −1.17588 | −0.587938 | − | 0.808906i | \(-0.700060\pi\) | ||||
−0.587938 | + | 0.808906i | \(0.700060\pi\) | |||||||
\(192\) | − | 328017.i | − | 0.642160i | ||||||
\(193\) | 965415.i | 1.86561i | 0.360383 | + | 0.932804i | \(0.382646\pi\) | ||||
−0.360383 | + | 0.932804i | \(0.617354\pi\) | |||||||
\(194\) | 402585. | 0.767986 | ||||||||
\(195\) | 503549. | − | 308061.i | 0.948320 | − | 0.580163i | ||||
\(196\) | −53329.4 | −0.0991577 | ||||||||
\(197\) | − | 175247.i | − | 0.321725i | −0.986977 | − | 0.160862i | \(-0.948573\pi\) | ||
0.986977 | − | 0.160862i | \(-0.0514275\pi\) | |||||||
\(198\) | 48749.6i | 0.0883707i | ||||||||
\(199\) | 48708.5 | 0.0871911 | 0.0435955 | − | 0.999049i | \(-0.486119\pi\) | ||||
0.0435955 | + | 0.999049i | \(0.486119\pi\) | |||||||
\(200\) | −543315. | − | 277850.i | −0.960454 | − | 0.491173i | ||||
\(201\) | 127725. | 0.222990 | ||||||||
\(202\) | − | 95625.1i | − | 0.164890i | ||||||
\(203\) | − | 11725.5i | − | 0.0199706i | ||||||
\(204\) | −58682.2 | −0.0987259 | ||||||||
\(205\) | 718278. | − | 439428.i | 1.19373 | − | 0.730303i | ||||
\(206\) | 629956. | 1.03429 | ||||||||
\(207\) | − | 333811.i | − | 0.541470i | ||||||
\(208\) | 867045.i | 1.38958i | ||||||||
\(209\) | 291362. | 0.461389 | ||||||||
\(210\) | 202960. | + | 331753.i | 0.317586 | + | 0.519118i | ||||
\(211\) | 662206. | 1.02397 | 0.511985 | − | 0.858995i | \(-0.328910\pi\) | ||||
0.511985 | + | 0.858995i | \(0.328910\pi\) | |||||||
\(212\) | − | 165895.i | − | 0.253509i | ||||||
\(213\) | − | 708714.i | − | 1.07034i | ||||||
\(214\) | 386840. | 0.577427 | ||||||||
\(215\) | 375394. | + | 613609.i | 0.553849 | + | 0.905307i | ||||
\(216\) | −142357. | −0.207608 | ||||||||
\(217\) | 558777.i | 0.805544i | ||||||||
\(218\) | 342568.i | 0.488209i | ||||||||
\(219\) | 308046. | 0.434015 | ||||||||
\(220\) | 41889.4 | − | 25627.1i | 0.0583509 | − | 0.0356979i | ||||
\(221\) | 1.05377e6 | 1.45132 | ||||||||
\(222\) | − | 719071.i | − | 0.979241i | ||||||
\(223\) | 44174.7i | 0.0594855i | 0.999558 | + | 0.0297428i | \(0.00946881\pi\) | ||||
−0.999558 | + | 0.0297428i | \(0.990531\pi\) | |||||||
\(224\) | 399908. | 0.532525 | ||||||||
\(225\) | −115251. | + | 225365.i | −0.151771 | + | 0.296777i | ||||
\(226\) | 217833. | 0.283696 | ||||||||
\(227\) | 585184.i | 0.753750i | 0.926264 | + | 0.376875i | \(0.123001\pi\) | ||||
−0.926264 | + | 0.376875i | \(0.876999\pi\) | |||||||
\(228\) | 157333.i | 0.200440i | ||||||||
\(229\) | −914300. | −1.15213 | −0.576063 | − | 0.817405i | \(-0.695412\pi\) | ||||
−0.576063 | + | 0.817405i | \(0.695412\pi\) | |||||||
\(230\) | 977472. | − | 597998.i | 1.21839 | − | 0.745384i | ||||
\(231\) | −169243. | −0.208680 | ||||||||
\(232\) | 14733.2i | 0.0179712i | ||||||||
\(233\) | − | 702641.i | − | 0.847898i | −0.905686 | − | 0.423949i | \(-0.860644\pi\) | ||
0.905686 | − | 0.423949i | \(-0.139356\pi\) | |||||||
\(234\) | 472712. | 0.564361 | ||||||||
\(235\) | −195426. | − | 319439.i | −0.230841 | − | 0.377327i | ||||
\(236\) | 94533.5 | 0.110486 | ||||||||
\(237\) | 438251.i | 0.506818i | ||||||||
\(238\) | 694252.i | 0.794465i | ||||||||
\(239\) | −572014. | −0.647757 | −0.323879 | − | 0.946099i | \(-0.604987\pi\) | ||||
−0.323879 | + | 0.946099i | \(0.604987\pi\) | |||||||
\(240\) | −194025. | − | 317148.i | −0.217435 | − | 0.355413i | ||||
\(241\) | −485324. | −0.538256 | −0.269128 | − | 0.963104i | \(-0.586736\pi\) | ||||
−0.269128 | + | 0.963104i | \(0.586736\pi\) | |||||||
\(242\) | − | 72823.5i | − | 0.0799343i | ||||||
\(243\) | 59049.0i | 0.0641500i | ||||||||
\(244\) | 6405.48 | 0.00688775 | ||||||||
\(245\) | −350287. | + | 214299.i | −0.372828 | + | 0.228089i | ||||
\(246\) | 674291. | 0.710411 | ||||||||
\(247\) | − | 2.82526e6i | − | 2.94657i | ||||||
\(248\) | − | 702110.i | − | 0.724897i | ||||||
\(249\) | −863148. | −0.882240 | ||||||||
\(250\) | −866383. | + | 66245.0i | −0.876718 | + | 0.0670352i | ||||
\(251\) | 25755.4 | 0.0258039 | 0.0129019 | − | 0.999917i | \(-0.495893\pi\) | ||||
0.0129019 | + | 0.999917i | \(0.495893\pi\) | |||||||
\(252\) | − | 91390.1i | − | 0.0906562i | ||||||
\(253\) | 498656.i | 0.489778i | ||||||||
\(254\) | −1.04000e6 | −1.01146 | ||||||||
\(255\) | −385446. | + | 235808.i | −0.371205 | + | 0.227096i | ||||
\(256\) | −674166. | −0.642935 | ||||||||
\(257\) | 243229.i | 0.229711i | 0.993382 | + | 0.114856i | \(0.0366405\pi\) | ||||
−0.993382 | + | 0.114856i | \(0.963359\pi\) | |||||||
\(258\) | 576032.i | 0.538763i | ||||||||
\(259\) | 2.49639e6 | 2.31240 | ||||||||
\(260\) | −248499. | − | 406190.i | −0.227977 | − | 0.372646i | ||||
\(261\) | 6111.28 | 0.00555304 | ||||||||
\(262\) | 426154.i | 0.383542i | ||||||||
\(263\) | − | 46278.0i | − | 0.0412558i | −0.999787 | − | 0.0206279i | \(-0.993433\pi\) | ||
0.999787 | − | 0.0206279i | \(-0.00656653\pi\) | |||||||
\(264\) | 212656. | 0.187788 | ||||||||
\(265\) | −666631. | − | 1.08966e6i | −0.583138 | − | 0.953181i | ||||
\(266\) | 1.86137e6 | 1.61298 | ||||||||
\(267\) | − | 12082.9i | − | 0.0103728i | ||||||
\(268\) | − | 103030.i | − | 0.0876249i | ||||||
\(269\) | −174634. | −0.147146 | −0.0735729 | − | 0.997290i | \(-0.523440\pi\) | ||||
−0.0735729 | + | 0.997290i | \(0.523440\pi\) | |||||||
\(270\) | −172909. | + | 105782.i | −0.144347 | + | 0.0883085i | ||||
\(271\) | −1.78096e6 | −1.47309 | −0.736546 | − | 0.676387i | \(-0.763545\pi\) | ||||
−0.736546 | + | 0.676387i | \(0.763545\pi\) | |||||||
\(272\) | − | 663688.i | − | 0.543929i | ||||||
\(273\) | 1.64111e6i | 1.33269i | ||||||||
\(274\) | 574538. | 0.462320 | ||||||||
\(275\) | 172165. | − | 336657.i | 0.137282 | − | 0.268445i | ||||
\(276\) | −269270. | −0.212773 | ||||||||
\(277\) | 545088.i | 0.426842i | 0.976960 | + | 0.213421i | \(0.0684607\pi\) | ||||
−0.976960 | + | 0.213421i | \(0.931539\pi\) | |||||||
\(278\) | − | 599960.i | − | 0.465597i | ||||||
\(279\) | −291233. | −0.223991 | ||||||||
\(280\) | 1.44718e6 | − | 885354.i | 1.10313 | − | 0.674873i | ||||
\(281\) | 85469.5 | 0.0645722 | 0.0322861 | − | 0.999479i | \(-0.489721\pi\) | ||||
0.0322861 | + | 0.999479i | \(0.489721\pi\) | |||||||
\(282\) | − | 299877.i | − | 0.224554i | ||||||
\(283\) | 1.51069e6i | 1.12127i | 0.828064 | + | 0.560634i | \(0.189442\pi\) | ||||
−0.828064 | + | 0.560634i | \(0.810558\pi\) | |||||||
\(284\) | −571688. | −0.420594 | ||||||||
\(285\) | 632228. | + | 1.03342e6i | 0.461065 | + | 0.753644i | ||||
\(286\) | −706150. | −0.510484 | ||||||||
\(287\) | 2.34093e6i | 1.67758i | ||||||||
\(288\) | 208431.i | 0.148075i | ||||||||
\(289\) | 613242. | 0.431904 | ||||||||
\(290\) | 10947.9 | + | 17895.2i | 0.00764428 | + | 0.0124951i | ||||
\(291\) | −728450. | −0.504275 | ||||||||
\(292\) | − | 248487.i | − | 0.170548i | ||||||
\(293\) | 1.05179e6i | 0.715746i | 0.933770 | + | 0.357873i | \(0.116498\pi\) | ||||
−0.933770 | + | 0.357873i | \(0.883502\pi\) | |||||||
\(294\) | −328836. | −0.221876 | ||||||||
\(295\) | 620931. | − | 379873.i | 0.415421 | − | 0.254146i | ||||
\(296\) | −3.13674e6 | −2.08089 | ||||||||
\(297\) | − | 88209.0i | − | 0.0580259i | ||||||
\(298\) | 244672.i | 0.159604i | ||||||||
\(299\) | 4.83533e6 | 3.12787 | ||||||||
\(300\) | 181792. | + | 92967.9i | 0.116620 | + | 0.0596389i | ||||
\(301\) | −1.99980e6 | −1.27224 | ||||||||
\(302\) | 2.44125e6i | 1.54026i | ||||||||
\(303\) | 173027.i | 0.108270i | ||||||||
\(304\) | −1.77942e6 | −1.10432 | ||||||||
\(305\) | 42073.6 | − | 25739.8i | 0.0258976 | − | 0.0158436i | ||||
\(306\) | −361842. | −0.220910 | ||||||||
\(307\) | − | 1.68373e6i | − | 1.01959i | −0.860295 | − | 0.509796i | \(-0.829721\pi\) | ||
0.860295 | − | 0.509796i | \(-0.170279\pi\) | |||||||
\(308\) | 136521.i | 0.0820016i | ||||||||
\(309\) | −1.13986e6 | −0.679135 | ||||||||
\(310\) | −521723. | − | 852794.i | −0.308344 | − | 0.504011i | ||||
\(311\) | −2.72412e6 | −1.59707 | −0.798536 | − | 0.601947i | \(-0.794392\pi\) | ||||
−0.798536 | + | 0.601947i | \(0.794392\pi\) | |||||||
\(312\) | − | 2.06207e6i | − | 1.19927i | ||||||
\(313\) | − | 1.69158e6i | − | 0.975959i | −0.872855 | − | 0.487979i | \(-0.837734\pi\) | ||
0.872855 | − | 0.487979i | \(-0.162266\pi\) | |||||||
\(314\) | −1.36138e6 | −0.779214 | ||||||||
\(315\) | −367242. | − | 600284.i | −0.208533 | − | 0.340863i | ||||
\(316\) | 353518. | 0.199156 | ||||||||
\(317\) | − | 371370.i | − | 0.207567i | −0.994600 | − | 0.103784i | \(-0.966905\pi\) | ||
0.994600 | − | 0.103784i | \(-0.0330949\pi\) | |||||||
\(318\) | − | 1.02293e6i | − | 0.567254i | ||||||
\(319\) | −9129.20 | −0.00502292 | ||||||||
\(320\) | −1.73797e6 | + | 1.06325e6i | −0.948783 | + | 0.580446i | ||||
\(321\) | −699960. | −0.379149 | ||||||||
\(322\) | 3.18566e6i | 1.71222i | ||||||||
\(323\) | 2.16262e6i | 1.15339i | ||||||||
\(324\) | 47632.2 | 0.0252080 | ||||||||
\(325\) | −3.26447e6 | − | 1.66944e6i | −1.71437 | − | 0.876722i | ||||
\(326\) | −322714. | −0.168180 | ||||||||
\(327\) | − | 619854.i | − | 0.320568i | ||||||
\(328\) | − | 2.94140e6i | − | 1.50963i | ||||||
\(329\) | 1.04108e6 | 0.530265 | ||||||||
\(330\) | 258295. | − | 158020.i | 0.130567 | − | 0.0798780i | ||||
\(331\) | 1.54525e6 | 0.775229 | 0.387614 | − | 0.921822i | \(-0.373299\pi\) | ||||
0.387614 | + | 0.921822i | \(0.373299\pi\) | |||||||
\(332\) | 696263.i | 0.346680i | ||||||||
\(333\) | 1.30111e6i | 0.642989i | ||||||||
\(334\) | 1.88767e6 | 0.925893 | ||||||||
\(335\) | −414016. | − | 676740.i | −0.201560 | − | 0.329465i | ||||
\(336\) | 1.03361e6 | 0.499469 | ||||||||
\(337\) | − | 1.56563e6i | − | 0.750956i | −0.926831 | − | 0.375478i | \(-0.877479\pi\) | ||
0.926831 | − | 0.375478i | \(-0.122521\pi\) | |||||||
\(338\) | 5.00055e6i | 2.38082i | ||||||||
\(339\) | −394154. | −0.186280 | ||||||||
\(340\) | 190216. | + | 310922.i | 0.0892381 | + | 0.145866i | ||||
\(341\) | 435052. | 0.202607 | ||||||||
\(342\) | 970138.i | 0.448506i | ||||||||
\(343\) | 1.47039e6i | 0.674833i | ||||||||
\(344\) | 2.51277e6 | 1.14487 | ||||||||
\(345\) | −1.76867e6 | + | 1.08204e6i | −0.800015 | + | 0.489433i | ||||
\(346\) | 2.53350e6 | 1.13771 | ||||||||
\(347\) | 2.21769e6i | 0.988727i | 0.869255 | + | 0.494364i | \(0.164599\pi\) | ||||
−0.869255 | + | 0.494364i | \(0.835401\pi\) | |||||||
\(348\) | − | 4929.70i | − | 0.00218209i | ||||||
\(349\) | 3.10101e6 | 1.36283 | 0.681413 | − | 0.731899i | \(-0.261366\pi\) | ||||
0.681413 | + | 0.731899i | \(0.261366\pi\) | |||||||
\(350\) | 1.09988e6 | − | 2.15073e6i | 0.479925 | − | 0.938460i | ||||
\(351\) | −855339. | −0.370570 | ||||||||
\(352\) | − | 311359.i | − | 0.133938i | ||||||
\(353\) | 2.34837e6i | 1.00307i | 0.865138 | + | 0.501534i | \(0.167231\pi\) | ||||
−0.865138 | + | 0.501534i | \(0.832769\pi\) | |||||||
\(354\) | 582905. | 0.247224 | ||||||||
\(355\) | −3.75506e6 | + | 2.29727e6i | −1.58141 | + | 0.967478i | ||||
\(356\) | −9746.77 | −0.00407602 | ||||||||
\(357\) | − | 1.25620e6i | − | 0.521661i | ||||||
\(358\) | 3.51293e6i | 1.44865i | ||||||||
\(359\) | −1.76347e6 | −0.722158 | −0.361079 | − | 0.932535i | \(-0.617592\pi\) | ||||
−0.361079 | + | 0.932535i | \(0.617592\pi\) | |||||||
\(360\) | 461444. | + | 754264.i | 0.187656 | + | 0.306737i | ||||
\(361\) | 3.32213e6 | 1.34168 | ||||||||
\(362\) | − | 1.24670e6i | − | 0.500022i | ||||||
\(363\) | 131769.i | 0.0524864i | ||||||||
\(364\) | 1.32381e6 | 0.523686 | ||||||||
\(365\) | −998519. | − | 1.63215e6i | −0.392305 | − | 0.641252i | ||||
\(366\) | 39497.0 | 0.0154121 | ||||||||
\(367\) | − | 2.99827e6i | − | 1.16200i | −0.813904 | − | 0.580999i | \(-0.802662\pi\) | ||
0.813904 | − | 0.580999i | \(-0.197338\pi\) | |||||||
\(368\) | − | 3.04541e6i | − | 1.17227i | ||||||
\(369\) | −1.22008e6 | −0.466470 | ||||||||
\(370\) | −3.80994e6 | + | 2.33084e6i | −1.44682 | + | 0.885134i | ||||
\(371\) | 3.55128e6 | 1.33952 | ||||||||
\(372\) | 234925.i | 0.0880179i | ||||||||
\(373\) | 2.01705e6i | 0.750663i | 0.926891 | + | 0.375331i | \(0.122471\pi\) | ||||
−0.926891 | + | 0.375331i | \(0.877529\pi\) | |||||||
\(374\) | 540529. | 0.199821 | ||||||||
\(375\) | 1.56766e6 | − | 119866.i | 0.575670 | − | 0.0440166i | ||||
\(376\) | −1.30813e6 | −0.477177 | ||||||||
\(377\) | 88523.4i | 0.0320778i | ||||||||
\(378\) | − | 563523.i | − | 0.202853i | ||||||
\(379\) | −3.78909e6 | −1.35499 | −0.677497 | − | 0.735526i | \(-0.736935\pi\) | ||||
−0.677497 | + | 0.735526i | \(0.736935\pi\) | |||||||
\(380\) | 833617. | − | 509991.i | 0.296147 | − | 0.181177i | ||||
\(381\) | 1.88180e6 | 0.664144 | ||||||||
\(382\) | 2.94880e6i | 1.03392i | ||||||||
\(383\) | 2.72827e6i | 0.950366i | 0.879887 | + | 0.475183i | \(0.157618\pi\) | ||||
−0.879887 | + | 0.475183i | \(0.842382\pi\) | |||||||
\(384\) | −890449. | −0.308163 | ||||||||
\(385\) | 548596. | + | 896720.i | 0.188626 | + | 0.308322i | ||||
\(386\) | 4.80192e6 | 1.64039 | ||||||||
\(387\) | − | 1.04229e6i | − | 0.353762i | ||||||
\(388\) | 587608.i | 0.198157i | ||||||||
\(389\) | −432266. | −0.144836 | −0.0724181 | − | 0.997374i | \(-0.523072\pi\) | ||||
−0.0724181 | + | 0.997374i | \(0.523072\pi\) | |||||||
\(390\) | −1.53228e6 | − | 2.50462e6i | −0.510124 | − | 0.833836i | ||||
\(391\) | −3.70125e6 | −1.22435 | ||||||||
\(392\) | 1.43445e6i | 0.471488i | ||||||||
\(393\) | − | 771095.i | − | 0.251841i | ||||||
\(394\) | −871667. | −0.282885 | ||||||||
\(395\) | 2.32203e6 | − | 1.42057e6i | 0.748817 | − | 0.458112i | ||||
\(396\) | −71154.3 | −0.0228015 | ||||||||
\(397\) | − | 3.90462e6i | − | 1.24338i | −0.783265 | − | 0.621688i | \(-0.786447\pi\) | ||
0.783265 | − | 0.621688i | \(-0.213553\pi\) | |||||||
\(398\) | − | 242273.i | − | 0.0766651i | ||||||
\(399\) | −3.36801e6 | −1.05911 | ||||||||
\(400\) | −1.05146e6 | + | 2.05605e6i | −0.328580 | + | 0.642514i | ||||
\(401\) | 4.60863e6 | 1.43124 | 0.715618 | − | 0.698492i | \(-0.246145\pi\) | ||||
0.715618 | + | 0.698492i | \(0.246145\pi\) | |||||||
\(402\) | − | 635297.i | − | 0.196070i | ||||||
\(403\) | − | 4.21858e6i | − | 1.29391i | ||||||
\(404\) | 139573. | 0.0425450 | ||||||||
\(405\) | 312866. | − | 191405.i | 0.0947809 | − | 0.0579851i | ||||
\(406\) | −58321.9 | −0.0175597 | ||||||||
\(407\) | − | 1.94363e6i | − | 0.581605i | ||||||
\(408\) | 1.57843e6i | 0.469435i | ||||||||
\(409\) | 3.86604e6 | 1.14277 | 0.571384 | − | 0.820683i | \(-0.306407\pi\) | ||||
0.571384 | + | 0.820683i | \(0.306407\pi\) | |||||||
\(410\) | −2.18569e6 | − | 3.57267e6i | −0.642139 | − | 1.04962i | ||||
\(411\) | −1.03959e6 | −0.303568 | ||||||||
\(412\) | 919476.i | 0.266868i | ||||||||
\(413\) | 2.02366e6i | 0.583799i | ||||||||
\(414\) | −1.66036e6 | −0.476102 | ||||||||
\(415\) | 2.79786e6 | + | 4.57331e6i | 0.797455 | + | 1.30350i | ||||
\(416\) | −3.01917e6 | −0.855370 | ||||||||
\(417\) | 1.08559e6i | 0.305720i | ||||||||
\(418\) | − | 1.44922e6i | − | 0.405689i | ||||||
\(419\) | −3.60488e6 | −1.00313 | −0.501563 | − | 0.865121i | \(-0.667241\pi\) | ||||
−0.501563 | + | 0.865121i | \(0.667241\pi\) | |||||||
\(420\) | −484222. | + | 296238.i | −0.133943 | + | 0.0819440i | ||||
\(421\) | 2.69664e6 | 0.741510 | 0.370755 | − | 0.928731i | \(-0.379099\pi\) | ||||
0.370755 | + | 0.928731i | \(0.379099\pi\) | |||||||
\(422\) | − | 3.29377e6i | − | 0.900353i | ||||||
\(423\) | 542606.i | 0.147446i | ||||||||
\(424\) | −4.46223e6 | −1.20542 | ||||||||
\(425\) | 2.49882e6 | + | 1.27789e6i | 0.671062 | + | 0.343179i | ||||
\(426\) | −3.52510e6 | −0.941126 | ||||||||
\(427\) | 137121.i | 0.0363944i | ||||||||
\(428\) | 564626.i | 0.148988i | ||||||||
\(429\) | 1.27773e6 | 0.335193 | ||||||||
\(430\) | 3.05206e6 | − | 1.86719e6i | 0.796015 | − | 0.486986i | ||||
\(431\) | −337978. | −0.0876385 | −0.0438193 | − | 0.999039i | \(-0.513953\pi\) | ||||
−0.0438193 | + | 0.999039i | \(0.513953\pi\) | |||||||
\(432\) | 538714.i | 0.138883i | ||||||||
\(433\) | − | 5.43565e6i | − | 1.39326i | −0.717431 | − | 0.696629i | \(-0.754682\pi\) | ||
0.717431 | − | 0.696629i | \(-0.245318\pi\) | |||||||
\(434\) | 2.77932e6 | 0.708296 | ||||||||
\(435\) | −19809.5 | − | 32380.1i | −0.00501938 | − | 0.00820455i | ||||
\(436\) | −500008. | −0.125968 | ||||||||
\(437\) | 9.92346e6i | 2.48576i | ||||||||
\(438\) | − | 1.53220e6i | − | 0.381620i | ||||||
\(439\) | 170878. | 0.0423180 | 0.0211590 | − | 0.999776i | \(-0.493264\pi\) | ||||
0.0211590 | + | 0.999776i | \(0.493264\pi\) | |||||||
\(440\) | −689317. | − | 1.12674e6i | −0.169741 | − | 0.277454i | ||||
\(441\) | 595006. | 0.145688 | ||||||||
\(442\) | − | 5.24137e6i | − | 1.27611i | ||||||
\(443\) | − | 6.94673e6i | − | 1.68179i | −0.541201 | − | 0.840893i | \(-0.682030\pi\) | ||
0.541201 | − | 0.840893i | \(-0.317970\pi\) | |||||||
\(444\) | 1.04955e6 | 0.252665 | ||||||||
\(445\) | −64020.4 | + | 39166.4i | −0.0153256 | + | 0.00937592i | ||||
\(446\) | 219722. | 0.0523043 | ||||||||
\(447\) | − | 442717.i | − | 0.104799i | ||||||
\(448\) | − | 5.66418e6i | − | 1.33334i | ||||||
\(449\) | 1.91825e6 | 0.449045 | 0.224522 | − | 0.974469i | \(-0.427918\pi\) | ||||
0.224522 | + | 0.974469i | \(0.427918\pi\) | |||||||
\(450\) | 1.12095e6 | + | 573252.i | 0.260949 | + | 0.133449i | ||||
\(451\) | 1.82259e6 | 0.421938 | ||||||||
\(452\) | 317946.i | 0.0731995i | ||||||||
\(453\) | − | 4.41728e6i | − | 1.01137i | ||||||
\(454\) | 2.91067e6 | 0.662755 | ||||||||
\(455\) | 8.69525e6 | − | 5.31958e6i | 1.96904 | − | 1.20462i | ||||
\(456\) | 4.23195e6 | 0.953077 | ||||||||
\(457\) | − | 1.14248e6i | − | 0.255892i | −0.991781 | − | 0.127946i | \(-0.959162\pi\) | ||
0.991781 | − | 0.127946i | \(-0.0408385\pi\) | |||||||
\(458\) | 4.54768e6i | 1.01304i | ||||||||
\(459\) | 654728. | 0.145054 | ||||||||
\(460\) | 872830. | + | 1.42670e6i | 0.192325 | + | 0.314369i | ||||
\(461\) | 3.63295e6 | 0.796172 | 0.398086 | − | 0.917348i | \(-0.369675\pi\) | ||||
0.398086 | + | 0.917348i | \(0.369675\pi\) | |||||||
\(462\) | 841806.i | 0.183488i | ||||||||
\(463\) | 6.29651e6i | 1.36505i | 0.730864 | + | 0.682523i | \(0.239117\pi\) | ||||
−0.730864 | + | 0.682523i | \(0.760883\pi\) | |||||||
\(464\) | 55754.3 | 0.0120222 | ||||||||
\(465\) | 944021. | + | 1.54307e6i | 0.202465 | + | 0.330943i | ||||
\(466\) | −3.49490e6 | −0.745537 | ||||||||
\(467\) | 46216.3i | 0.00980624i | 0.999988 | + | 0.00490312i | \(0.00156072\pi\) | ||||
−0.999988 | + | 0.00490312i | \(0.998439\pi\) | |||||||
\(468\) | 689964.i | 0.145617i | ||||||||
\(469\) | 2.20555e6 | 0.463004 | ||||||||
\(470\) | −1.58887e6 | + | 972039.i | −0.331775 | + | 0.202973i | ||||
\(471\) | 2.46333e6 | 0.511647 | ||||||||
\(472\) | − | 2.54276e6i | − | 0.525351i | ||||||
\(473\) | 1.55700e6i | 0.319990i | ||||||||
\(474\) | 2.17983e6 | 0.445633 | ||||||||
\(475\) | 3.42616e6 | − | 6.69961e6i | 0.696745 | − | 1.36243i | ||||
\(476\) | −1.01332e6 | −0.204989 | ||||||||
\(477\) | 1.85092e6i | 0.372470i | ||||||||
\(478\) | 2.84517e6i | 0.569558i | ||||||||
\(479\) | −1.87454e6 | −0.373299 | −0.186649 | − | 0.982427i | \(-0.559763\pi\) | ||||
−0.186649 | + | 0.982427i | \(0.559763\pi\) | |||||||
\(480\) | 1.10435e6 | − | 675620.i | 0.218778 | − | 0.133844i | ||||
\(481\) | −1.88469e7 | −3.71430 | ||||||||
\(482\) | 2.41397e6i | 0.473276i | ||||||||
\(483\) | − | 5.76423e6i | − | 1.12428i | ||||||
\(484\) | 106292. | 0.0206247 | ||||||||
\(485\) | 2.36124e6 | + | 3.85963e6i | 0.455813 | + | 0.745060i | ||||
\(486\) | 293706. | 0.0564056 | ||||||||
\(487\) | − | 2.93849e6i | − | 0.561439i | −0.959790 | − | 0.280719i | \(-0.909427\pi\) | ||
0.959790 | − | 0.280719i | \(-0.0905730\pi\) | |||||||
\(488\) | − | 172294.i | − | 0.0327508i | ||||||
\(489\) | 583929. | 0.110430 | ||||||||
\(490\) | 1.06591e6 | + | 1.74231e6i | 0.200553 | + | 0.327819i | ||||
\(491\) | 7.56455e6 | 1.41605 | 0.708026 | − | 0.706186i | \(-0.249586\pi\) | ||||
0.708026 | + | 0.706186i | \(0.249586\pi\) | |||||||
\(492\) | 984187.i | 0.183301i | ||||||||
\(493\) | − | 67761.1i | − | 0.0125563i | ||||||
\(494\) | −1.40527e7 | −2.59085 | ||||||||
\(495\) | −467368. | + | 285926.i | −0.0857325 | + | 0.0524495i | ||||
\(496\) | −2.65697e6 | −0.484933 | ||||||||
\(497\) | − | 1.22380e7i | − | 2.22239i | ||||||
\(498\) | 4.29325e6i | 0.775734i | ||||||||
\(499\) | 3.96894e6 | 0.713548 | 0.356774 | − | 0.934191i | \(-0.383877\pi\) | ||||
0.356774 | + | 0.934191i | \(0.383877\pi\) | |||||||
\(500\) | −96690.3 | − | 1.26456e6i | −0.0172965 | − | 0.226212i | ||||
\(501\) | −3.41561e6 | −0.607959 | ||||||||
\(502\) | − | 128106.i | − | 0.0226887i | ||||||
\(503\) | − | 7.67415e6i | − | 1.35242i | −0.736711 | − | 0.676208i | \(-0.763622\pi\) | ||
0.736711 | − | 0.676208i | \(-0.236378\pi\) | |||||||
\(504\) | −2.45821e6 | −0.431064 | ||||||||
\(505\) | 916768. | − | 560860.i | 0.159967 | − | 0.0978648i | ||||
\(506\) | 2.48028e6 | 0.430651 | ||||||||
\(507\) | − | 9.04815e6i | − | 1.56329i | ||||||
\(508\) | − | 1.51797e6i | − | 0.260978i | ||||||
\(509\) | 2.34465e6 | 0.401129 | 0.200564 | − | 0.979681i | \(-0.435722\pi\) | ||||
0.200564 | + | 0.979681i | \(0.435722\pi\) | |||||||
\(510\) | 1.17290e6 | + | 1.91719e6i | 0.199680 | + | 0.326392i | ||||
\(511\) | 5.31932e6 | 0.901164 | ||||||||
\(512\) | 6.51930e6i | 1.09907i | ||||||||
\(513\) | − | 1.75540e6i | − | 0.294498i | ||||||
\(514\) | 1.20981e6 | 0.201980 | ||||||||
\(515\) | 3.69482e6 | + | 6.03945e6i | 0.613868 | + | 1.00341i | ||||
\(516\) | −840769. | −0.139012 | ||||||||
\(517\) | − | 810559.i | − | 0.133370i | ||||||
\(518\) | − | 1.24169e7i | − | 2.03324i | ||||||
\(519\) | −4.58418e6 | −0.747040 | ||||||||
\(520\) | −1.09257e7 | + | 6.68412e6i | −1.77191 | + | 1.08402i | ||||
\(521\) | −4.60694e6 | −0.743563 | −0.371782 | − | 0.928320i | \(-0.621253\pi\) | ||||
−0.371782 | + | 0.928320i | \(0.621253\pi\) | |||||||
\(522\) | − | 30397.2i | − | 0.00488266i | ||||||
\(523\) | 3.79276e6i | 0.606319i | 0.952940 | + | 0.303159i | \(0.0980415\pi\) | ||||
−0.952940 | + | 0.303159i | \(0.901959\pi\) | |||||||
\(524\) | −622008. | −0.0989619 | ||||||||
\(525\) | −1.99015e6 | + | 3.89159e6i | −0.315128 | + | 0.616211i | ||||
\(526\) | −230184. | −0.0362753 | ||||||||
\(527\) | 3.22915e6i | 0.506480i | ||||||||
\(528\) | − | 804746.i | − | 0.125624i | ||||||
\(529\) | −1.05473e7 | −1.63871 | ||||||||
\(530\) | −5.41990e6 | + | 3.31579e6i | −0.838110 | + | 0.512739i | ||||
\(531\) | −1.05473e6 | −0.162332 | ||||||||
\(532\) | 2.71683e6i | 0.416181i | ||||||||
\(533\) | − | 1.76732e7i | − | 2.69462i | ||||||
\(534\) | −60099.9 | −0.00912053 | ||||||||
\(535\) | 2.26889e6 | + | 3.70867e6i | 0.342712 | + | 0.560189i | ||||
\(536\) | −2.77130e6 | −0.416650 | ||||||||
\(537\) | − | 6.35640e6i | − | 0.951208i | ||||||
\(538\) | 868619.i | 0.129382i | ||||||||
\(539\) | −888835. | −0.131780 | ||||||||
\(540\) | −154398. | − | 252375.i | −0.0227854 | − | 0.0372445i | ||||
\(541\) | −8.95976e6 | −1.31614 | −0.658072 | − | 0.752955i | \(-0.728628\pi\) | ||||
−0.658072 | + | 0.752955i | \(0.728628\pi\) | |||||||
\(542\) | 8.85837e6i | 1.29526i | ||||||||
\(543\) | 2.25581e6i | 0.328324i | ||||||||
\(544\) | 2.31105e6 | 0.334821 | ||||||||
\(545\) | −3.28424e6 | + | 2.00923e6i | −0.473635 | + | 0.289760i | ||||
\(546\) | 8.16276e6 | 1.17181 | ||||||||
\(547\) | 2.79065e6i | 0.398783i | 0.979920 | + | 0.199391i | \(0.0638965\pi\) | ||||
−0.979920 | + | 0.199391i | \(0.936104\pi\) | |||||||
\(548\) | 838588.i | 0.119288i | ||||||||
\(549\) | −71467.1 | −0.0101199 | ||||||||
\(550\) | −1.67451e6 | − | 856339.i | −0.236038 | − | 0.120709i | ||||
\(551\) | −181675. | −0.0254927 | ||||||||
\(552\) | 7.24282e6i | 1.01172i | ||||||||
\(553\) | 7.56770e6i | 1.05233i | ||||||||
\(554\) | 2.71124e6 | 0.375313 | ||||||||
\(555\) | 6.89381e6 | − | 4.21750e6i | 0.950008 | − | 0.581196i | ||||
\(556\) | 875694. | 0.120134 | ||||||||
\(557\) | 1.22903e7i | 1.67851i | 0.543736 | + | 0.839256i | \(0.317009\pi\) | ||||
−0.543736 | + | 0.839256i | \(0.682991\pi\) | |||||||
\(558\) | 1.44858e6i | 0.196950i | ||||||||
\(559\) | 1.50978e7 | 2.04355 | ||||||||
\(560\) | −3.35041e6 | − | 5.47649e6i | −0.451469 | − | 0.737959i | ||||
\(561\) | −978050. | −0.131206 | ||||||||
\(562\) | − | 425120.i | − | 0.0567768i | ||||||
\(563\) | − | 1.13900e7i | − | 1.51444i | −0.653160 | − | 0.757220i | \(-0.726557\pi\) | ||
0.653160 | − | 0.757220i | \(-0.273443\pi\) | |||||||
\(564\) | 437696. | 0.0579395 | ||||||||
\(565\) | 1.27764e6 | + | 2.08839e6i | 0.168378 | + | 0.275227i | ||||
\(566\) | 7.51408e6 | 0.985905 | ||||||||
\(567\) | 1.01966e6i | 0.133197i | ||||||||
\(568\) | 1.53772e7i | 1.99990i | ||||||||
\(569\) | −4.71367e6 | −0.610350 | −0.305175 | − | 0.952296i | \(-0.598715\pi\) | ||||
−0.305175 | + | 0.952296i | \(0.598715\pi\) | |||||||
\(570\) | 5.14019e6 | − | 3.14467e6i | 0.662662 | − | 0.405404i | ||||
\(571\) | 7.49421e6 | 0.961913 | 0.480957 | − | 0.876744i | \(-0.340289\pi\) | ||||
0.480957 | + | 0.876744i | \(0.340289\pi\) | |||||||
\(572\) | − | 1.03069e6i | − | 0.131715i | ||||||
\(573\) | − | 5.33565e6i | − | 0.678893i | ||||||
\(574\) | 1.16436e7 | 1.47506 | ||||||||
\(575\) | 1.14661e7 | + | 5.86374e6i | 1.44626 | + | 0.739615i | ||||
\(576\) | 2.95215e6 | 0.370751 | ||||||||
\(577\) | − | 5.77654e6i | − | 0.722318i | −0.932504 | − | 0.361159i | \(-0.882381\pi\) | ||
0.932504 | − | 0.361159i | \(-0.117619\pi\) | |||||||
\(578\) | − | 3.05023e6i | − | 0.379763i | ||||||
\(579\) | −8.68873e6 | −1.07711 | ||||||||
\(580\) | −26119.6 | + | 15979.4i | −0.00322401 | + | 0.00197239i | ||||
\(581\) | −1.49048e7 | −1.83183 | ||||||||
\(582\) | 3.62327e6i | 0.443397i | ||||||||
\(583\) | − | 2.76495e6i | − | 0.336912i | ||||||
\(584\) | −6.68379e6 | −0.810943 | ||||||||
\(585\) | 2.77255e6 | + | 4.53194e6i | 0.334958 | + | 0.547513i | ||||
\(586\) | 5.23153e6 | 0.629339 | ||||||||
\(587\) | − | 1.19273e6i | − | 0.142872i | −0.997445 | − | 0.0714358i | \(-0.977242\pi\) | ||
0.997445 | − | 0.0714358i | \(-0.0227581\pi\) | |||||||
\(588\) | − | 479965.i | − | 0.0572487i | ||||||
\(589\) | 8.65771e6 | 1.02829 | ||||||||
\(590\) | −1.88947e6 | − | 3.08847e6i | −0.223465 | − | 0.365270i | ||||
\(591\) | 1.57722e6 | 0.185748 | ||||||||
\(592\) | 1.18702e7i | 1.39205i | ||||||||
\(593\) | 1.14801e7i | 1.34064i | 0.742074 | + | 0.670318i | \(0.233842\pi\) | ||||
−0.742074 | + | 0.670318i | \(0.766158\pi\) | |||||||
\(594\) | −438746. | −0.0510208 | ||||||||
\(595\) | −6.65587e6 | + | 4.07193e6i | −0.770748 | + | 0.471528i | ||||
\(596\) | −357120. | −0.0411812 | ||||||||
\(597\) | 438376.i | 0.0503398i | ||||||||
\(598\) | − | 2.40506e7i | − | 2.75026i | ||||||
\(599\) | −1.07989e7 | −1.22974 | −0.614869 | − | 0.788630i | \(-0.710791\pi\) | ||||
−0.614869 | + | 0.788630i | \(0.710791\pi\) | |||||||
\(600\) | 2.50065e6 | − | 4.88984e6i | 0.283579 | − | 0.554519i | ||||
\(601\) | 6.43742e6 | 0.726986 | 0.363493 | − | 0.931597i | \(-0.381584\pi\) | ||||
0.363493 | + | 0.931597i | \(0.381584\pi\) | |||||||
\(602\) | 9.94690e6i | 1.11866i | ||||||||
\(603\) | 1.14953e6i | 0.128744i | ||||||||
\(604\) | −3.56322e6 | −0.397421 | ||||||||
\(605\) | 698166. | − | 427124.i | 0.0775480 | − | 0.0474423i | ||||
\(606\) | 860626. | 0.0951991 | ||||||||
\(607\) | 2.78009e6i | 0.306258i | 0.988206 | + | 0.153129i | \(0.0489350\pi\) | ||||
−0.988206 | + | 0.153129i | \(0.951065\pi\) | |||||||
\(608\) | − | 6.19619e6i | − | 0.679776i | ||||||
\(609\) | 105529. | 0.0115300 | ||||||||
\(610\) | −128028. | − | 209271.i | −0.0139310 | − | 0.0227712i | ||||
\(611\) | −7.85978e6 | −0.851740 | ||||||||
\(612\) | − | 528140.i | − | 0.0569994i | ||||||
\(613\) | 1.25907e7i | 1.35331i | 0.736299 | + | 0.676657i | \(0.236572\pi\) | ||||
−0.736299 | + | 0.676657i | \(0.763428\pi\) | |||||||
\(614\) | −8.37477e6 | −0.896504 | ||||||||
\(615\) | 3.95485e6 | + | 6.46450e6i | 0.421641 | + | 0.689203i | ||||
\(616\) | 3.67213e6 | 0.389912 | ||||||||
\(617\) | 1.20724e6i | 0.127668i | 0.997961 | + | 0.0638339i | \(0.0203328\pi\) | ||||
−0.997961 | + | 0.0638339i | \(0.979667\pi\) | |||||||
\(618\) | 5.66960e6i | 0.597147i | ||||||||
\(619\) | −1.03935e7 | −1.09028 | −0.545138 | − | 0.838346i | \(-0.683523\pi\) | ||||
−0.545138 | + | 0.838346i | \(0.683523\pi\) | |||||||
\(620\) | 1.24473e6 | − | 761500.i | 0.130045 | − | 0.0795592i | ||||
\(621\) | 3.00430e6 | 0.312618 | ||||||||
\(622\) | 1.35496e7i | 1.40427i | ||||||||
\(623\) | − | 208648.i | − | 0.0215374i | ||||||
\(624\) | −7.80341e6 | −0.802274 | ||||||||
\(625\) | −5.71661e6 | − | 7.91756e6i | −0.585381 | − | 0.810759i | ||||
\(626\) | −8.41381e6 | −0.858138 | ||||||||
\(627\) | 2.62226e6i | 0.266383i | ||||||||
\(628\) | − | 1.98706e6i | − | 0.201054i | ||||||
\(629\) | 1.44265e7 | 1.45390 | ||||||||
\(630\) | −2.98578e6 | + | 1.82664e6i | −0.299713 | + | 0.183359i | ||||
\(631\) | 389320. | 0.0389254 | 0.0194627 | − | 0.999811i | \(-0.493804\pi\) | ||||
0.0194627 | + | 0.999811i | \(0.493804\pi\) | |||||||
\(632\) | − | 9.50890e6i | − | 0.946973i | ||||||
\(633\) | 5.95985e6i | 0.591189i | ||||||||
\(634\) | −1.84717e6 | −0.182509 | ||||||||
\(635\) | −6.09980e6 | − | 9.97057e6i | −0.600318 | − | 0.981264i | ||||
\(636\) | 1.49305e6 | 0.146363 | ||||||||
\(637\) | 8.61880e6i | 0.841585i | ||||||||
\(638\) | 45408.1i | 0.00441654i | ||||||||
\(639\) | 6.37843e6 | 0.617961 | ||||||||
\(640\) | 2.88636e6 | + | 4.71797e6i | 0.278548 | + | 0.455308i | ||||
\(641\) | 9.85176e6 | 0.947041 | 0.473520 | − | 0.880783i | \(-0.342983\pi\) | ||||
0.473520 | + | 0.880783i | \(0.342983\pi\) | |||||||
\(642\) | 3.48156e6i | 0.333377i | ||||||||
\(643\) | − | 9.41361e6i | − | 0.897901i | −0.893557 | − | 0.448951i | \(-0.851798\pi\) | ||
0.893557 | − | 0.448951i | \(-0.148202\pi\) | |||||||
\(644\) | −4.64975e6 | −0.441789 | ||||||||
\(645\) | −5.52248e6 | + | 3.37855e6i | −0.522679 | + | 0.319765i | ||||
\(646\) | 1.07568e7 | 1.01415 | ||||||||
\(647\) | − | 8.37846e6i | − | 0.786871i | −0.919352 | − | 0.393435i | \(-0.871287\pi\) | ||
0.919352 | − | 0.393435i | \(-0.128713\pi\) | |||||||
\(648\) | − | 1.28121e6i | − | 0.119862i | ||||||
\(649\) | 1.57558e6 | 0.146835 | ||||||||
\(650\) | −8.30369e6 | + | 1.62373e7i | −0.770882 | + | 1.50740i | ||||
\(651\) | −5.02899e6 | −0.465081 | ||||||||
\(652\) | − | 471030.i | − | 0.0433940i | ||||||
\(653\) | 1.87196e7i | 1.71796i | 0.512011 | + | 0.858979i | \(0.328901\pi\) | ||||
−0.512011 | + | 0.858979i | \(0.671099\pi\) | |||||||
\(654\) | −3.08312e6 | −0.281868 | ||||||||
\(655\) | −4.08558e6 | + | 2.49948e6i | −0.372092 | + | 0.227639i | ||||
\(656\) | −1.11310e7 | −1.00989 | ||||||||
\(657\) | 2.77241e6i | 0.250579i | ||||||||
\(658\) | − | 5.17826e6i | − | 0.466250i | ||||||
\(659\) | 7.53086e6 | 0.675509 | 0.337755 | − | 0.941234i | \(-0.390333\pi\) | ||||
0.337755 | + | 0.941234i | \(0.390333\pi\) | |||||||
\(660\) | 230644. | + | 377005.i | 0.0206102 | + | 0.0336889i | ||||
\(661\) | −1.12673e7 | −1.00304 | −0.501518 | − | 0.865147i | \(-0.667225\pi\) | ||||
−0.501518 | + | 0.865147i | \(0.667225\pi\) | |||||||
\(662\) | − | 7.68600e6i | − | 0.681641i | ||||||
\(663\) | 9.48389e6i | 0.837920i | ||||||||
\(664\) | 1.87281e7 | 1.64844 | ||||||||
\(665\) | 1.09173e7 | + | 1.78451e7i | 0.957328 | + | 1.56482i | ||||
\(666\) | 6.47164e6 | 0.565365 | ||||||||
\(667\) | − | 310930.i | − | 0.0270613i | ||||||
\(668\) | 2.75522e6i | 0.238900i | ||||||||
\(669\) | −397572. | −0.0343440 | ||||||||
\(670\) | −3.36607e6 | + | 2.05929e6i | −0.289691 | + | 0.177227i | ||||
\(671\) | 106759. | 0.00915377 | ||||||||
\(672\) | 3.59917e6i | 0.307453i | ||||||||
\(673\) | − | 747965.i | − | 0.0636566i | −0.999493 | − | 0.0318283i | \(-0.989867\pi\) | ||
0.999493 | − | 0.0318283i | \(-0.0101330\pi\) | |||||||
\(674\) | −7.78735e6 | −0.660298 | ||||||||
\(675\) | −2.02829e6 | − | 1.03726e6i | −0.171344 | − | 0.0876250i | ||||
\(676\) | −7.29874e6 | −0.614301 | ||||||||
\(677\) | − | 1.52419e7i | − | 1.27811i | −0.769160 | − | 0.639056i | \(-0.779325\pi\) | ||
0.769160 | − | 0.639056i | \(-0.220675\pi\) | |||||||
\(678\) | 1.96050e6i | 0.163792i | ||||||||
\(679\) | −1.25788e7 | −1.04705 | ||||||||
\(680\) | 8.36318e6 | − | 5.11643e6i | 0.693584 | − | 0.424321i | ||||
\(681\) | −5.26665e6 | −0.435178 | ||||||||
\(682\) | − | 2.16392e6i | − | 0.178148i | ||||||
\(683\) | − | 891262.i | − | 0.0731061i | −0.999332 | − | 0.0365531i | \(-0.988362\pi\) | ||
0.999332 | − | 0.0365531i | \(-0.0116378\pi\) | |||||||
\(684\) | −1.41600e6 | −0.115724 | ||||||||
\(685\) | 3.36978e6 | + | 5.50816e6i | 0.274394 | + | 0.448518i | ||||
\(686\) | 7.31362e6 | 0.593366 | ||||||||
\(687\) | − | 8.22870e6i | − | 0.665180i | ||||||
\(688\) | − | 9.50899e6i | − | 0.765885i | ||||||
\(689\) | −2.68110e7 | −2.15162 | ||||||||
\(690\) | 5.38198e6 | + | 8.79724e6i | 0.430348 | + | 0.703435i | ||||
\(691\) | −2.23692e6 | −0.178220 | −0.0891100 | − | 0.996022i | \(-0.528402\pi\) | ||||
−0.0891100 | + | 0.996022i | \(0.528402\pi\) | |||||||
\(692\) | 3.69786e6i | 0.293552i | ||||||||
\(693\) | − | 1.52319e6i | − | 0.120482i | ||||||
\(694\) | 1.10306e7 | 0.869365 | ||||||||
\(695\) | 5.75188e6 | − | 3.51889e6i | 0.451698 | − | 0.276340i | ||||
\(696\) | −132599. | −0.0103757 | ||||||||
\(697\) | 1.35281e7i | 1.05476i | ||||||||
\(698\) | − | 1.54243e7i | − | 1.19830i | ||||||
\(699\) | 6.32377e6 | 0.489534 | ||||||||
\(700\) | 3.13918e6 | + | 1.60536e6i | 0.242142 | + | 0.123831i | ||||
\(701\) | −9.23251e6 | −0.709618 | −0.354809 | − | 0.934939i | \(-0.615454\pi\) | ||||
−0.354809 | + | 0.934939i | \(0.615454\pi\) | |||||||
\(702\) | 4.25441e6i | 0.325834i | ||||||||
\(703\) | − | 3.86791e7i | − | 2.95181i | ||||||
\(704\) | −4.41000e6 | −0.335357 | ||||||||
\(705\) | 2.87495e6 | − | 1.75884e6i | 0.217850 | − | 0.133276i | ||||
\(706\) | 1.16807e7 | 0.881975 | ||||||||
\(707\) | 2.98782e6i | 0.224805i | ||||||||
\(708\) | 850801.i | 0.0637889i | ||||||||
\(709\) | 1.91122e7 | 1.42789 | 0.713945 | − | 0.700201i | \(-0.246906\pi\) | ||||
0.713945 | + | 0.700201i | \(0.246906\pi\) | |||||||
\(710\) | 1.14265e7 | + | 1.86774e7i | 0.850681 | + | 1.39050i | ||||
\(711\) | −3.94426e6 | −0.292612 | ||||||||
\(712\) | 262168.i | 0.0193812i | ||||||||
\(713\) | 1.48174e7i | 1.09156i | ||||||||
\(714\) | −6.24827e6 | −0.458685 | ||||||||
\(715\) | −4.14171e6 | − | 6.76993e6i | −0.302980 | − | 0.495244i | ||||
\(716\) | −5.12743e6 | −0.373781 | ||||||||
\(717\) | − | 5.14813e6i | − | 0.373983i | ||||||
\(718\) | 8.77140e6i | 0.634977i | ||||||||
\(719\) | −3.98132e6 | −0.287213 | −0.143607 | − | 0.989635i | \(-0.545870\pi\) | ||||
−0.143607 | + | 0.989635i | \(0.545870\pi\) | |||||||
\(720\) | 2.85433e6 | − | 1.74622e6i | 0.205198 | − | 0.125536i | ||||
\(721\) | −1.96831e7 | −1.41012 | ||||||||
\(722\) | − | 1.65241e7i | − | 1.17971i | ||||||
\(723\) | − | 4.36792e6i | − | 0.310762i | ||||||
\(724\) | 1.81966e6 | 0.129016 | ||||||||
\(725\) | −107351. | + | 209918.i | −0.00758511 | + | 0.0148322i | ||||
\(726\) | 655411. | 0.0461501 | ||||||||
\(727\) | − | 2.31098e6i | − | 0.162166i | −0.996707 | − | 0.0810832i | \(-0.974162\pi\) | ||
0.996707 | − | 0.0810832i | \(-0.0258380\pi\) | |||||||
\(728\) | − | 3.56077e7i | − | 2.49009i | ||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | −8.11823e6 | + | 4.96657e6i | −0.563838 | + | 0.344945i | ||||
\(731\) | −1.15568e7 | −0.799914 | ||||||||
\(732\) | 57649.3i | 0.00397664i | ||||||||
\(733\) | − | 1.76034e7i | − | 1.21015i | −0.796170 | − | 0.605073i | \(-0.793144\pi\) | ||
0.796170 | − | 0.605073i | \(-0.206856\pi\) | |||||||
\(734\) | −1.49132e7 | −1.02172 | ||||||||
\(735\) | −1.92869e6 | − | 3.15258e6i | −0.131687 | − | 0.215253i | ||||
\(736\) | 1.06045e7 | 0.721601 | ||||||||
\(737\) | − | 1.71719e6i | − | 0.116453i | ||||||
\(738\) | 6.06862e6i | 0.410156i | ||||||||
\(739\) | 8.91956e6 | 0.600803 | 0.300402 | − | 0.953813i | \(-0.402879\pi\) | ||||
0.300402 | + | 0.953813i | \(0.402879\pi\) | |||||||
\(740\) | −3.40207e6 | − | 5.56093e6i | −0.228383 | − | 0.373309i | ||||
\(741\) | 2.54273e7 | 1.70120 | ||||||||
\(742\) | − | 1.76639e7i | − | 1.17781i | ||||||
\(743\) | − | 3.22802e6i | − | 0.214519i | −0.994231 | − | 0.107259i | \(-0.965793\pi\) | ||
0.994231 | − | 0.107259i | \(-0.0342075\pi\) | |||||||
\(744\) | 6.31899e6 | 0.418519 | ||||||||
\(745\) | −2.34570e6 | + | 1.43505e6i | −0.154839 | + | 0.0947277i | ||||
\(746\) | 1.00327e7 | 0.660040 | ||||||||
\(747\) | − | 7.76833e6i | − | 0.509362i | ||||||
\(748\) | 788950.i | 0.0515579i | ||||||||
\(749\) | −1.20869e7 | −0.787244 | ||||||||
\(750\) | −596205. | − | 7.79745e6i | −0.0387028 | − | 0.506173i | ||||
\(751\) | −2.04930e6 | −0.132588 | −0.0662942 | − | 0.997800i | \(-0.521118\pi\) | ||||
−0.0662942 | + | 0.997800i | \(0.521118\pi\) | |||||||
\(752\) | 4.95029e6i | 0.319217i | ||||||||
\(753\) | 231799.i | 0.0148979i | ||||||||
\(754\) | 440310. | 0.0282053 | ||||||||
\(755\) | −2.34045e7 | + | 1.43184e7i | −1.49428 | + | 0.914173i | ||||
\(756\) | 822511. | 0.0523404 | ||||||||
\(757\) | 2.62464e6i | 0.166468i | 0.996530 | + | 0.0832340i | \(0.0265249\pi\) | ||||
−0.996530 | + | 0.0832340i | \(0.973475\pi\) | |||||||
\(758\) | 1.88467e7i | 1.19141i | ||||||||
\(759\) | −4.48790e6 | −0.282773 | ||||||||
\(760\) | −1.37177e7 | − | 2.24226e7i | −0.861484 | − | 1.40816i | ||||
\(761\) | 1.90240e7 | 1.19080 | 0.595401 | − | 0.803428i | \(-0.296993\pi\) | ||||
0.595401 | + | 0.803428i | \(0.296993\pi\) | |||||||
\(762\) | − | 9.35999e6i | − | 0.583966i | ||||||
\(763\) | − | 1.07036e7i | − | 0.665608i | ||||||
\(764\) | −4.30404e6 | −0.266773 | ||||||||
\(765\) | −2.12228e6 | − | 3.46902e6i | −0.131114 | − | 0.214315i | ||||
\(766\) | 1.35703e7 | 0.835635 | ||||||||
\(767\) | − | 1.52780e7i | − | 0.937729i | ||||||
\(768\) | − | 6.06749e6i | − | 0.371198i | ||||||
\(769\) | 1.84565e7 | 1.12547 | 0.562735 | − | 0.826637i | \(-0.309749\pi\) | ||||
0.562735 | + | 0.826637i | \(0.309749\pi\) | |||||||
\(770\) | 4.46023e6 | − | 2.72868e6i | 0.271101 | − | 0.165854i | ||||
\(771\) | −2.18906e6 | −0.132624 | ||||||||
\(772\) | 7.00881e6i | 0.423254i | ||||||||
\(773\) | 6.98835e6i | 0.420655i | 0.977631 | + | 0.210327i | \(0.0674530\pi\) | ||||
−0.977631 | + | 0.210327i | \(0.932547\pi\) | |||||||
\(774\) | −5.18429e6 | −0.311055 | ||||||||
\(775\) | 5.11582e6 | − | 1.00036e7i | 0.305957 | − | 0.598278i | ||||
\(776\) | 1.58055e7 | 0.942221 | ||||||||
\(777\) | 2.24675e7i | 1.33506i | ||||||||
\(778\) | 2.15007e6i | 0.127351i | ||||||||
\(779\) | 3.62704e7 | 2.14145 | ||||||||
\(780\) | 3.65571e6 | − | 2.23649e6i | 0.215147 | − | 0.131623i | ||||
\(781\) | −9.52826e6 | −0.558967 | ||||||||
\(782\) | 1.84098e7i | 1.07655i | ||||||||
\(783\) | 55001.5i | 0.00320605i | ||||||||
\(784\) | 5.42834e6 | 0.315411 | ||||||||
\(785\) | −7.98480e6 | − | 1.30517e7i | −0.462477 | − | 0.755952i | ||||
\(786\) | −3.83538e6 | −0.221438 | ||||||||
\(787\) | − | 1.02434e7i | − | 0.589533i | −0.955569 | − | 0.294766i | \(-0.904758\pi\) | ||
0.955569 | − | 0.294766i | \(-0.0952419\pi\) | |||||||
\(788\) | − | 1.27227e6i | − | 0.0729903i | ||||||
\(789\) | 416502. | 0.0238190 | ||||||||
\(790\) | −7.06586e6 | − | 1.15497e7i | −0.402807 | − | 0.658418i | ||||
\(791\) | −6.80623e6 | −0.386781 | ||||||||
\(792\) | 1.91390e6i | 0.108419i | ||||||||
\(793\) | − | 1.03522e6i | − | 0.0584587i | ||||||
\(794\) | −1.94213e7 | −1.09327 | ||||||||
\(795\) | 9.80692e6 | − | 5.99968e6i | 0.550319 | − | 0.336675i | ||||
\(796\) | 353619. | 0.0197812 | ||||||||
\(797\) | 1.36372e7i | 0.760466i | 0.924891 | + | 0.380233i | \(0.124156\pi\) | ||||
−0.924891 | + | 0.380233i | \(0.875844\pi\) | |||||||
\(798\) | 1.67523e7i | 0.931252i | ||||||||
\(799\) | 6.01634e6 | 0.333400 | ||||||||
\(800\) | −7.15943e6 | − | 3.66131e6i | −0.395506 | − | 0.202261i | ||||
\(801\) | 108746. | 0.00598872 | ||||||||
\(802\) | − | 2.29231e7i | − | 1.25845i | ||||||
\(803\) | − | 4.14150e6i | − | 0.226657i | ||||||
\(804\) | 927271. | 0.0505902 | ||||||||
\(805\) | −3.05412e7 | + | 1.86845e7i | −1.66110 | + | 1.01623i | ||||
\(806\) | −2.09830e7 | −1.13770 | ||||||||
\(807\) | − | 1.57171e6i | − | 0.0849547i | ||||||
\(808\) | − | 3.75423e6i | − | 0.202299i | ||||||
\(809\) | 2.94019e7 | 1.57944 | 0.789722 | − | 0.613465i | \(-0.210225\pi\) | ||||
0.789722 | + | 0.613465i | \(0.210225\pi\) | |||||||
\(810\) | −952038. | − | 1.55618e6i | −0.0509849 | − | 0.0833386i | ||||
\(811\) | −1.42304e7 | −0.759737 | −0.379869 | − | 0.925040i | \(-0.624031\pi\) | ||||
−0.379869 | + | 0.925040i | \(0.624031\pi\) | |||||||
\(812\) | − | 85125.8i | − | 0.00453076i | ||||||
\(813\) | − | 1.60286e7i | − | 0.850490i | ||||||
\(814\) | −9.66752e6 | −0.511392 | ||||||||
\(815\) | −1.89278e6 | − | 3.09390e6i | −0.0998176 | − | 0.163159i | ||||
\(816\) | 5.97319e6 | 0.314037 | ||||||||
\(817\) | 3.09850e7i | 1.62404i | ||||||||
\(818\) | − | 1.92294e7i | − | 1.00481i | ||||||
\(819\) | −1.47699e7 | −0.769430 | ||||||||
\(820\) | 5.21463e6 | − | 3.19021e6i | 0.270825 | − | 0.165685i | ||||
\(821\) | 2.28257e7 | 1.18186 | 0.590931 | − | 0.806722i | \(-0.298761\pi\) | ||||
0.590931 | + | 0.806722i | \(0.298761\pi\) | |||||||
\(822\) | 5.17084e6i | 0.266920i | ||||||||
\(823\) | 1.12391e6i | 0.0578405i | 0.999582 | + | 0.0289202i | \(0.00920688\pi\) | ||||
−0.999582 | + | 0.0289202i | \(0.990793\pi\) | |||||||
\(824\) | 2.47320e7 | 1.26894 | ||||||||
\(825\) | 3.02991e6 | + | 1.54949e6i | 0.154987 | + | 0.0792598i | ||||
\(826\) | 1.00656e7 | 0.513321 | ||||||||
\(827\) | − | 2.69107e7i | − | 1.36824i | −0.729370 | − | 0.684119i | \(-0.760187\pi\) | ||
0.729370 | − | 0.684119i | \(-0.239813\pi\) | |||||||
\(828\) | − | 2.42343e6i | − | 0.122844i | ||||||
\(829\) | 6.83042e6 | 0.345192 | 0.172596 | − | 0.984993i | \(-0.444784\pi\) | ||||
0.172596 | + | 0.984993i | \(0.444784\pi\) | |||||||
\(830\) | 2.27474e7 | − | 1.39164e7i | 1.14614 | − | 0.701184i | ||||
\(831\) | −4.90580e6 | −0.246438 | ||||||||
\(832\) | 4.27626e7i | 2.14169i | ||||||||
\(833\) | − | 6.59734e6i | − | 0.329425i | ||||||
\(834\) | 5.39964e6 | 0.268813 | ||||||||
\(835\) | 1.10716e7 | + | 1.80973e7i | 0.549533 | + | 0.898252i | ||||
\(836\) | 2.11526e6 | 0.104676 | ||||||||
\(837\) | − | 2.62110e6i | − | 0.129321i | ||||||
\(838\) | 1.79305e7i | 0.882026i | ||||||||
\(839\) | 1.37641e7 | 0.675061 | 0.337531 | − | 0.941315i | \(-0.390408\pi\) | ||||
0.337531 | + | 0.941315i | \(0.390408\pi\) | |||||||
\(840\) | 7.96818e6 | + | 1.30246e7i | 0.389638 | + | 0.636892i | ||||
\(841\) | −2.05055e7 | −0.999722 | ||||||||
\(842\) | − | 1.34129e7i | − | 0.651993i | ||||||
\(843\) | 769225.i | 0.0372808i | ||||||||
\(844\) | 4.80755e6 | 0.232310 | ||||||||
\(845\) | −4.79408e7 | + | 2.93293e7i | −2.30974 | + | 1.41306i | ||||
\(846\) | 2.69889e6 | 0.129646 | ||||||||
\(847\) | 2.27538e6i | 0.108980i | ||||||||
\(848\) | 1.68862e7i | 0.806387i | ||||||||
\(849\) | −1.35962e7 | −0.647364 | ||||||||
\(850\) | 6.35614e6 | − | 1.24290e7i | 0.301749 | − | 0.590049i | ||||
\(851\) | 6.61979e7 | 3.13343 | ||||||||
\(852\) | − | 5.14519e6i | − | 0.242830i | ||||||
\(853\) | 2.38141e7i | 1.12063i | 0.828281 | + | 0.560313i | \(0.189319\pi\) | ||||
−0.828281 | + | 0.560313i | \(0.810681\pi\) | |||||||
\(854\) | 682032. | 0.0320008 | ||||||||
\(855\) | −9.30082e6 | + | 5.69006e6i | −0.435117 | + | 0.266196i | ||||
\(856\) | 1.51873e7 | 0.708428 | ||||||||
\(857\) | − | 1.96463e7i | − | 0.913751i | −0.889531 | − | 0.456875i | \(-0.848969\pi\) | ||
0.889531 | − | 0.456875i | \(-0.151031\pi\) | |||||||
\(858\) | − | 6.35535e6i | − | 0.294728i | ||||||
\(859\) | 4.10315e7 | 1.89729 | 0.948646 | − | 0.316339i | \(-0.102454\pi\) | ||||
0.948646 | + | 0.316339i | \(0.102454\pi\) | |||||||
\(860\) | 2.72532e6 | + | 4.45474e6i | 0.125653 | + | 0.205389i | ||||
\(861\) | −2.10683e7 | −0.968550 | ||||||||
\(862\) | 1.68108e6i | 0.0770585i | ||||||||
\(863\) | 1.10401e7i | 0.504599i | 0.967649 | + | 0.252300i | \(0.0811869\pi\) | ||||
−0.967649 | + | 0.252300i | \(0.918813\pi\) | |||||||
\(864\) | −1.87588e6 | −0.0854909 | ||||||||
\(865\) | 1.48595e7 | + | 2.42889e7i | 0.675247 | + | 1.10374i | ||||
\(866\) | −2.70366e7 | −1.22506 | ||||||||
\(867\) | 5.51918e6i | 0.249360i | ||||||||
\(868\) | 4.05667e6i | 0.182755i | ||||||||
\(869\) | 5.89204e6 | 0.264677 | ||||||||
\(870\) | −161057. | + | 98531.3i | −0.00721407 | + | 0.00441343i | ||||
\(871\) | −1.66512e7 | −0.743702 | ||||||||
\(872\) | 1.34492e7i | 0.598970i | ||||||||
\(873\) | − | 6.55605e6i | − | 0.291143i | ||||||
\(874\) | 4.93587e7 | 2.18567 | ||||||||
\(875\) | 2.70703e7 | − | 2.06983e6i | 1.19529 | − | 0.0913935i | ||||
\(876\) | 2.23638e6 | 0.0984658 | ||||||||
\(877\) | − | 2.06101e7i | − | 0.904861i | −0.891800 | − | 0.452430i | \(-0.850557\pi\) | ||
0.891800 | − | 0.452430i | \(-0.149443\pi\) | |||||||
\(878\) | − | 849937.i | − | 0.0372092i | ||||||
\(879\) | −9.46608e6 | −0.413236 | ||||||||
\(880\) | −4.26387e6 | + | 2.60855e6i | −0.185608 | + | 0.113552i | ||||
\(881\) | −7.17874e6 | −0.311608 | −0.155804 | − | 0.987788i | \(-0.549797\pi\) | ||||
−0.155804 | + | 0.987788i | \(0.549797\pi\) | |||||||
\(882\) | − | 2.95952e6i | − | 0.128100i | ||||||
\(883\) | − | 1.55190e6i | − | 0.0669824i | −0.999439 | − | 0.0334912i | \(-0.989337\pi\) | ||
0.999439 | − | 0.0334912i | \(-0.0106626\pi\) | |||||||
\(884\) | 7.65023e6 | 0.329264 | ||||||||
\(885\) | 3.41886e6 | + | 5.58837e6i | 0.146731 | + | 0.239843i | ||||
\(886\) | −3.45526e7 | −1.47876 | ||||||||
\(887\) | − | 3.39646e7i | − | 1.44950i | −0.689014 | − | 0.724748i | \(-0.741956\pi\) | ||
0.689014 | − | 0.724748i | \(-0.258044\pi\) | |||||||
\(888\) | − | 2.82307e7i | − | 1.20140i | ||||||
\(889\) | 3.24949e7 | 1.37899 | ||||||||
\(890\) | 194811. | + | 318434.i | 0.00824403 | + | 0.0134755i | ||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 320704.i | 0.0134956i | ||||||||
\(893\) | − | 1.61305e7i | − | 0.676891i | ||||||
\(894\) | −2.20205e6 | −0.0921474 | ||||||||
\(895\) | −3.36788e7 | + | 2.06040e7i | −1.40540 | + | 0.859795i | ||||
\(896\) | −1.53762e7 | −0.639853 | ||||||||
\(897\) | 4.35180e7i | 1.80587i | ||||||||
\(898\) | − | 9.54127e6i | − | 0.394835i | ||||||
\(899\) | −271271. | −0.0111945 | ||||||||
\(900\) | −836711. | + | 1.63613e6i | −0.0344326 | + | 0.0673304i | ||||
\(901\) | 2.05227e7 | 0.842216 | ||||||||
\(902\) | − | 9.06547e6i | − | 0.371000i | ||||||
\(903\) | − | 1.79982e7i | − | 0.734531i | ||||||
\(904\) | 8.55211e6 | 0.348058 | ||||||||
\(905\) | 1.19522e7 | − | 7.31212e6i | 0.485095 | − | 0.296771i | ||||
\(906\) | −2.19713e7 | −0.889272 | ||||||||
\(907\) | − | 2.58319e7i | − | 1.04265i | −0.853359 | − | 0.521324i | \(-0.825438\pi\) | ||
0.853359 | − | 0.521324i | \(-0.174562\pi\) | |||||||
\(908\) | 4.24837e6i | 0.171005i | ||||||||
\(909\) | −1.55724e6 | −0.0625096 | ||||||||
\(910\) | −2.64593e7 | − | 4.32497e7i | −1.05919 | − | 1.73133i | ||||
\(911\) | 549431. | 0.0219340 | 0.0109670 | − | 0.999940i | \(-0.496509\pi\) | ||||
0.0109670 | + | 0.999940i | \(0.496509\pi\) | |||||||
\(912\) | − | 1.60148e7i | − | 0.637579i | ||||||
\(913\) | 1.16045e7i | 0.460735i | ||||||||
\(914\) | −5.68262e6 | −0.225000 | ||||||||
\(915\) | 231658. | + | 378662.i | 0.00914733 | + | 0.0149520i | ||||
\(916\) | −6.63773e6 | −0.261385 | ||||||||
\(917\) | − | 1.33152e7i | − | 0.522908i | ||||||
\(918\) | − | 3.25658e6i | − | 0.127542i | ||||||
\(919\) | −3.84177e7 | −1.50052 | −0.750261 | − | 0.661142i | \(-0.770072\pi\) | ||||
−0.750261 | + | 0.661142i | \(0.770072\pi\) | |||||||
\(920\) | 3.83754e7 | − | 2.34773e7i | 1.49480 | − | 0.914491i | ||||
\(921\) | 1.51536e7 | 0.588662 | ||||||||
\(922\) | − | 1.80701e7i | − | 0.700055i | ||||||
\(923\) | 9.23930e7i | 3.56973i | ||||||||
\(924\) | −1.22869e6 | −0.0473437 | ||||||||
\(925\) | −4.46921e7 | − | 2.28554e7i | −1.71742 | − | 0.878283i | ||||
\(926\) | 3.13185e7 | 1.20025 | ||||||||
\(927\) | − | 1.02588e7i | − | 0.392099i | ||||||
\(928\) | 194144.i | 0.00740038i | ||||||||
\(929\) | −1.50560e7 | −0.572360 | −0.286180 | − | 0.958176i | \(-0.592386\pi\) | ||||
−0.286180 | + | 0.958176i | \(0.592386\pi\) | |||||||
\(930\) | 7.67515e6 | − | 4.69550e6i | 0.290991 | − | 0.178022i | ||||
\(931\) | −1.76882e7 | −0.668821 | ||||||||
\(932\) | − | 5.10110e6i | − | 0.192364i | ||||||
\(933\) | − | 2.45170e7i | − | 0.922070i | ||||||
\(934\) | 229877. | 0.00862240 | ||||||||
\(935\) | 3.17031e6 | + | 5.18211e6i | 0.118597 | + | 0.193855i | ||||
\(936\) | 1.85586e7 | 0.692398 | ||||||||
\(937\) | 1.83320e7i | 0.682119i | 0.940042 | + | 0.341059i | \(0.110786\pi\) | ||||
−0.940042 | + | 0.341059i | \(0.889214\pi\) | |||||||
\(938\) | − | 1.09703e7i | − | 0.407109i | ||||||
\(939\) | 1.52242e7 | 0.563470 | ||||||||
\(940\) | −1.41878e6 | − | 2.31909e6i | −0.0523714 | − | 0.0856049i | ||||
\(941\) | −3.82211e7 | −1.40711 | −0.703557 | − | 0.710639i | \(-0.748406\pi\) | ||||
−0.703557 | + | 0.710639i | \(0.748406\pi\) | |||||||
\(942\) | − | 1.22525e7i | − | 0.449879i | ||||||
\(943\) | 6.20754e7i | 2.27321i | ||||||||
\(944\) | −9.62245e6 | −0.351444 | ||||||||
\(945\) | 5.40255e6 | − | 3.30517e6i | 0.196797 | − | 0.120397i | ||||
\(946\) | 7.74444e6 | 0.281360 | ||||||||
\(947\) | 3.35057e7i | 1.21407i | 0.794675 | + | 0.607035i | \(0.207641\pi\) | ||||
−0.794675 | + | 0.607035i | \(0.792359\pi\) | |||||||
\(948\) | 3.18166e6i | 0.114983i | ||||||||
\(949\) | −4.01590e7 | −1.44750 | ||||||||
\(950\) | −3.33235e7 | − | 1.70415e7i | −1.19796 | − | 0.612632i | ||||
\(951\) | 3.34233e6 | 0.119839 | ||||||||
\(952\) | 2.72563e7i | 0.974707i | ||||||||
\(953\) | 3.29329e7i | 1.17462i | 0.809362 | + | 0.587310i | \(0.199813\pi\) | ||||
−0.809362 | + | 0.587310i | \(0.800187\pi\) | |||||||
\(954\) | 9.20636e6 | 0.327504 | ||||||||
\(955\) | −2.82705e7 | + | 1.72953e7i | −1.00306 | + | 0.613649i | ||||
\(956\) | −4.15277e6 | −0.146958 | ||||||||
\(957\) | − | 82162.8i | − | 0.00289998i | ||||||
\(958\) | 9.32386e6i | 0.328233i | ||||||||
\(959\) | −1.79515e7 | −0.630311 | ||||||||
\(960\) | −9.56929e6 | − | 1.56417e7i | −0.335121 | − | 0.547780i | ||||
\(961\) | −1.57018e7 | −0.548454 | ||||||||
\(962\) | 9.37433e7i | 3.26590i | ||||||||
\(963\) | − | 6.29964e6i | − | 0.218902i | ||||||
\(964\) | −3.52340e6 | −0.122115 | ||||||||
\(965\) | 2.81642e7 | + | 4.60365e7i | 0.973597 | + | 1.59142i | ||||
\(966\) | −2.86709e7 | −0.988551 | ||||||||
\(967\) | 2.24586e7i | 0.772353i | 0.922425 | + | 0.386177i | \(0.126204\pi\) | ||||
−0.922425 | + | 0.386177i | \(0.873796\pi\) | |||||||
\(968\) | − | 2.85904e6i | − | 0.0980691i | ||||||
\(969\) | −1.94636e7 | −0.665908 | ||||||||
\(970\) | 1.91976e7 | − | 1.17447e7i | 0.655114 | − | 0.400786i | ||||
\(971\) | 3.76102e7 | 1.28014 | 0.640069 | − | 0.768317i | \(-0.278906\pi\) | ||||
0.640069 | + | 0.768317i | \(0.278906\pi\) | |||||||
\(972\) | 428690.i | 0.0145538i | ||||||||
\(973\) | 1.87458e7i | 0.634780i | ||||||||
\(974\) | −1.46159e7 | −0.493660 | ||||||||
\(975\) | 1.50250e7 | − | 2.93802e7i | 0.506176 | − | 0.989791i | ||||
\(976\) | −652007. | −0.0219092 | ||||||||
\(977\) | − | 1.90408e7i | − | 0.638187i | −0.947723 | − | 0.319094i | \(-0.896622\pi\) | ||
0.947723 | − | 0.319094i | \(-0.103378\pi\) | |||||||
\(978\) | − | 2.90443e6i | − | 0.0970987i | ||||||
\(979\) | −162448. | −0.00541700 | ||||||||
\(980\) | −2.54305e6 | + | 1.55579e6i | −0.0845843 | + | 0.0517470i | ||||
\(981\) | 5.57868e6 | 0.185080 | ||||||||
\(982\) | − | 3.76256e7i | − | 1.24510i | ||||||
\(983\) | 3.59407e7i | 1.18632i | 0.805083 | + | 0.593162i | \(0.202120\pi\) | ||||
−0.805083 | + | 0.593162i | \(0.797880\pi\) | |||||||
\(984\) | 2.64726e7 | 0.871584 | ||||||||
\(985\) | −5.11250e6 | − | 8.35676e6i | −0.167897 | − | 0.274440i | ||||
\(986\) | −337040. | −0.0110405 | ||||||||
\(987\) | 9.36969e6i | 0.306149i | ||||||||
\(988\) | − | 2.05111e7i | − | 0.668493i | ||||||
\(989\) | −5.30297e7 | −1.72396 | ||||||||
\(990\) | 1.42218e6 | + | 2.32466e6i | 0.0461176 | + | 0.0753826i | ||||
\(991\) | 2.52119e7 | 0.815495 | 0.407748 | − | 0.913095i | \(-0.366314\pi\) | ||||
0.407748 | + | 0.913095i | \(0.366314\pi\) | |||||||
\(992\) | − | 9.25192e6i | − | 0.298506i | ||||||
\(993\) | 1.39073e7i | 0.447578i | ||||||||
\(994\) | −6.08713e7 | −1.95410 | ||||||||
\(995\) | 2.32270e6 | − | 1.42098e6i | 0.0743764 | − | 0.0455020i | ||||
\(996\) | −6.26637e6 | −0.200156 | ||||||||
\(997\) | 4.86935e6i | 0.155143i | 0.996987 | + | 0.0775716i | \(0.0247166\pi\) | ||||
−0.996987 | + | 0.0775716i | \(0.975283\pi\) | |||||||
\(998\) | − | 1.97413e7i | − | 0.627406i | ||||||
\(999\) | −1.17100e7 | −0.371230 |
(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 | 165.6.c.b.34.9 | ✓ | 26 | |
5.2 | odd | 4 | 825.6.a.y.1.8 | 13 | |||
5.3 | odd | 4 | 825.6.a.v.1.6 | 13 | |||
5.4 | even | 2 | inner | 165.6.c.b.34.18 | yes | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.c.b.34.9 | ✓ | 26 | 1.1 | even | 1 | trivial | |
165.6.c.b.34.18 | yes | 26 | 5.4 | even | 2 | inner | |
825.6.a.v.1.6 | 13 | 5.3 | odd | 4 | |||
825.6.a.y.1.8 | 13 | 5.2 | odd | 4 |