Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,9,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(72.1060139808\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.62 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.9.c.a.58.19 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 19.3849i | 1.21156i | 0.795634 | + | 0.605778i | \(0.207138\pi\) | ||||
−0.795634 | + | 0.605778i | \(0.792862\pi\) | |||||||
\(3\) | 46.7654 | 0.577350 | ||||||||
\(4\) | −119.774 | −0.467866 | ||||||||
\(5\) | 778.298 | 1.24528 | 0.622638 | − | 0.782510i | \(-0.286061\pi\) | ||||
0.622638 | + | 0.782510i | \(0.286061\pi\) | |||||||
\(6\) | 906.541i | 0.699492i | ||||||||
\(7\) | 1420.14 | 0.591476 | 0.295738 | − | 0.955269i | \(-0.404434\pi\) | ||||
0.295738 | + | 0.955269i | \(0.404434\pi\) | |||||||
\(8\) | 2640.73i | 0.644710i | ||||||||
\(9\) | 2187.00 | 0.333333 | ||||||||
\(10\) | 15087.2i | 1.50872i | ||||||||
\(11\) | 18287.8i | 1.24908i | 0.780992 | + | 0.624541i | \(0.214714\pi\) | ||||
−0.780992 | + | 0.624541i | \(0.785286\pi\) | |||||||
\(12\) | −5601.26 | −0.270122 | ||||||||
\(13\) | 10397.2i | 0.364034i | 0.983295 | + | 0.182017i | \(0.0582626\pi\) | ||||
−0.983295 | + | 0.182017i | \(0.941737\pi\) | |||||||
\(14\) | 27529.1i | 0.716606i | ||||||||
\(15\) | 36397.4 | 0.718961 | ||||||||
\(16\) | −81852.3 | −1.24897 | ||||||||
\(17\) | −79909.4 | −0.956758 | −0.478379 | − | 0.878153i | \(-0.658775\pi\) | ||||
−0.478379 | + | 0.878153i | \(0.658775\pi\) | |||||||
\(18\) | 42394.7i | 0.403852i | ||||||||
\(19\) | 126623. | 0.971620 | 0.485810 | − | 0.874064i | \(-0.338525\pi\) | ||||
0.485810 | + | 0.874064i | \(0.338525\pi\) | |||||||
\(20\) | −93219.5 | −0.582622 | ||||||||
\(21\) | 66413.1 | 0.341489 | ||||||||
\(22\) | −354507. | −1.51333 | ||||||||
\(23\) | − | 166838.i | − | 0.596190i | −0.954536 | − | 0.298095i | \(-0.903649\pi\) | ||
0.954536 | − | 0.298095i | \(-0.0963512\pi\) | |||||||
\(24\) | 123495.i | 0.372224i | ||||||||
\(25\) | 215122. | 0.550713 | ||||||||
\(26\) | −201548. | −0.441047 | ||||||||
\(27\) | 102276. | 0.192450 | ||||||||
\(28\) | −170095. | −0.276732 | ||||||||
\(29\) | −83511.6 | −0.118074 | −0.0590371 | − | 0.998256i | \(-0.518803\pi\) | ||||
−0.0590371 | + | 0.998256i | \(0.518803\pi\) | |||||||
\(30\) | 705559.i | 0.871060i | ||||||||
\(31\) | 892019.i | 0.965889i | 0.875651 | + | 0.482944i | \(0.160433\pi\) | ||||
−0.875651 | + | 0.482944i | \(0.839567\pi\) | |||||||
\(32\) | − | 910670.i | − | 0.868483i | ||||||
\(33\) | 855236.i | 0.721157i | ||||||||
\(34\) | − | 1.54903e6i | − | 1.15917i | ||||||
\(35\) | 1.10529e6 | 0.736552 | ||||||||
\(36\) | −261945. | −0.155955 | ||||||||
\(37\) | 612380.i | 0.326749i | 0.986564 | + | 0.163374i | \(0.0522378\pi\) | ||||
−0.986564 | + | 0.163374i | \(0.947762\pi\) | |||||||
\(38\) | 2.45456e6i | 1.17717i | ||||||||
\(39\) | 486228.i | 0.210175i | ||||||||
\(40\) | 2.05528e6i | 0.802842i | ||||||||
\(41\) | 889825. | 0.314897 | 0.157449 | − | 0.987527i | \(-0.449673\pi\) | ||||
0.157449 | + | 0.987527i | \(0.449673\pi\) | |||||||
\(42\) | 1.28741e6i | 0.413733i | ||||||||
\(43\) | − | 1.51063e6i | − | 0.441859i | −0.975290 | − | 0.220929i | \(-0.929091\pi\) | ||
0.975290 | − | 0.220929i | \(-0.0709090\pi\) | |||||||
\(44\) | − | 2.19040e6i | − | 0.584402i | ||||||
\(45\) | 1.70214e6 | 0.415092 | ||||||||
\(46\) | 3.23414e6 | 0.722317 | ||||||||
\(47\) | − | 514948.i | − | 0.105529i | −0.998607 | − | 0.0527645i | \(-0.983197\pi\) | ||
0.998607 | − | 0.0527645i | \(-0.0168033\pi\) | |||||||
\(48\) | −3.82785e6 | −0.721092 | ||||||||
\(49\) | −3.74802e6 | −0.650156 | ||||||||
\(50\) | 4.17012e6i | 0.667219i | ||||||||
\(51\) | −3.73699e6 | −0.552385 | ||||||||
\(52\) | − | 1.24531e6i | − | 0.170319i | ||||||
\(53\) | 2.99146e6 | 0.379123 | 0.189562 | − | 0.981869i | \(-0.439293\pi\) | ||||
0.189562 | + | 0.981869i | \(0.439293\pi\) | |||||||
\(54\) | 1.98261e6i | 0.233164i | ||||||||
\(55\) | 1.42333e7i | 1.55545i | ||||||||
\(56\) | 3.75020e6i | 0.381331i | ||||||||
\(57\) | 5.92155e6 | 0.560965 | ||||||||
\(58\) | − | 1.61886e6i | − | 0.143053i | ||||||
\(59\) | 1.09695e7 | + | 5.14778e6i | 0.905275 | + | 0.424826i | ||||
\(60\) | −4.35945e6 | −0.336377 | ||||||||
\(61\) | 1.64754e7i | 1.18992i | 0.803756 | + | 0.594959i | \(0.202832\pi\) | ||||
−0.803756 | + | 0.594959i | \(0.797168\pi\) | |||||||
\(62\) | −1.72917e7 | −1.17023 | ||||||||
\(63\) | 3.10584e6 | 0.197159 | ||||||||
\(64\) | −3.30096e6 | −0.196753 | ||||||||
\(65\) | 8.09210e6i | 0.453323i | ||||||||
\(66\) | −1.65786e7 | −0.873722 | ||||||||
\(67\) | 6.55053e6i | 0.325070i | 0.986703 | + | 0.162535i | \(0.0519671\pi\) | ||||
−0.986703 | + | 0.162535i | \(0.948033\pi\) | |||||||
\(68\) | 9.57104e6 | 0.447634 | ||||||||
\(69\) | − | 7.80226e6i | − | 0.344211i | ||||||
\(70\) | 2.14259e7i | 0.892373i | ||||||||
\(71\) | 4.70095e7 | 1.84992 | 0.924959 | − | 0.380067i | \(-0.124099\pi\) | ||||
0.924959 | + | 0.380067i | \(0.124099\pi\) | |||||||
\(72\) | 5.77528e6i | 0.214903i | ||||||||
\(73\) | 1.51356e7i | 0.532978i | 0.963838 | + | 0.266489i | \(0.0858637\pi\) | ||||
−0.963838 | + | 0.266489i | \(0.914136\pi\) | |||||||
\(74\) | −1.18709e7 | −0.395874 | ||||||||
\(75\) | 1.00603e7 | 0.317954 | ||||||||
\(76\) | −1.51660e7 | −0.454588 | ||||||||
\(77\) | 2.59711e7i | 0.738802i | ||||||||
\(78\) | −9.42547e6 | −0.254639 | ||||||||
\(79\) | −1.57239e7 | −0.403692 | −0.201846 | − | 0.979417i | \(-0.564694\pi\) | ||||
−0.201846 | + | 0.979417i | \(0.564694\pi\) | |||||||
\(80\) | −6.37055e7 | −1.55531 | ||||||||
\(81\) | 4.78297e6 | 0.111111 | ||||||||
\(82\) | 1.72491e7i | 0.381515i | ||||||||
\(83\) | − | 4.55852e7i | − | 0.960532i | −0.877123 | − | 0.480266i | \(-0.840540\pi\) | ||
0.877123 | − | 0.480266i | \(-0.159460\pi\) | |||||||
\(84\) | −7.95454e6 | −0.159771 | ||||||||
\(85\) | −6.21933e7 | −1.19143 | ||||||||
\(86\) | 2.92833e7 | 0.535336 | ||||||||
\(87\) | −3.90545e6 | −0.0681701 | ||||||||
\(88\) | −4.82932e7 | −0.805295 | ||||||||
\(89\) | − | 1.04577e8i | − | 1.66678i | −0.552688 | − | 0.833388i | \(-0.686398\pi\) | ||
0.552688 | − | 0.833388i | \(-0.313602\pi\) | |||||||
\(90\) | 3.29957e7i | 0.502907i | ||||||||
\(91\) | 1.47654e7i | 0.215318i | ||||||||
\(92\) | 1.99828e7i | 0.278937i | ||||||||
\(93\) | 4.17156e7i | 0.557656i | ||||||||
\(94\) | 9.98221e6 | 0.127854 | ||||||||
\(95\) | 9.85500e7 | 1.20994 | ||||||||
\(96\) | − | 4.25878e7i | − | 0.501419i | ||||||
\(97\) | 7.35443e6i | 0.0830735i | 0.999137 | + | 0.0415367i | \(0.0132254\pi\) | ||||
−0.999137 | + | 0.0415367i | \(0.986775\pi\) | |||||||
\(98\) | − | 7.26549e7i | − | 0.787699i | ||||||
\(99\) | 3.99954e7i | 0.416360i | ||||||||
\(100\) | −2.57660e7 | −0.257660 | ||||||||
\(101\) | 1.26697e7i | 0.121753i | 0.998145 | + | 0.0608767i | \(0.0193896\pi\) | ||||
−0.998145 | + | 0.0608767i | \(0.980610\pi\) | |||||||
\(102\) | − | 7.24412e7i | − | 0.669244i | ||||||
\(103\) | − | 1.08434e8i | − | 0.963422i | −0.876330 | − | 0.481711i | \(-0.840015\pi\) | ||
0.876330 | − | 0.481711i | \(-0.159985\pi\) | |||||||
\(104\) | −2.74562e7 | −0.234696 | ||||||||
\(105\) | 5.16892e7 | 0.425248 | ||||||||
\(106\) | 5.79892e7i | 0.459328i | ||||||||
\(107\) | −7.77276e7 | −0.592980 | −0.296490 | − | 0.955036i | \(-0.595816\pi\) | ||||
−0.296490 | + | 0.955036i | \(0.595816\pi\) | |||||||
\(108\) | −1.22499e7 | −0.0900408 | ||||||||
\(109\) | − | 2.41281e7i | − | 0.170929i | −0.996341 | − | 0.0854647i | \(-0.972763\pi\) | ||
0.996341 | − | 0.0854647i | \(-0.0272375\pi\) | |||||||
\(110\) | −2.75912e8 | −1.88451 | ||||||||
\(111\) | 2.86382e7i | 0.188648i | ||||||||
\(112\) | −1.16241e8 | −0.738735 | ||||||||
\(113\) | 1.55132e8i | 0.951455i | 0.879593 | + | 0.475728i | \(0.157815\pi\) | ||||
−0.879593 | + | 0.475728i | \(0.842185\pi\) | |||||||
\(114\) | 1.14789e8i | 0.679640i | ||||||||
\(115\) | − | 1.29850e8i | − | 0.742421i | ||||||
\(116\) | 1.00025e7 | 0.0552428 | ||||||||
\(117\) | 2.27386e7i | 0.121345i | ||||||||
\(118\) | −9.97890e7 | + | 2.12643e8i | −0.514701 | + | 1.09679i | ||||
\(119\) | −1.13482e8 | −0.565900 | ||||||||
\(120\) | 9.61157e7i | 0.463521i | ||||||||
\(121\) | −1.20085e8 | −0.560204 | ||||||||
\(122\) | −3.19374e8 | −1.44165 | ||||||||
\(123\) | 4.16130e7 | 0.181806 | ||||||||
\(124\) | − | 1.06840e8i | − | 0.451906i | ||||||
\(125\) | −1.36593e8 | −0.559487 | ||||||||
\(126\) | 6.02062e7i | 0.238869i | ||||||||
\(127\) | −5.37223e7 | −0.206509 | −0.103255 | − | 0.994655i | \(-0.532926\pi\) | ||||
−0.103255 | + | 0.994655i | \(0.532926\pi\) | |||||||
\(128\) | − | 2.97120e8i | − | 1.10686i | ||||||
\(129\) | − | 7.06450e7i | − | 0.255107i | ||||||
\(130\) | −1.56864e8 | −0.549226 | ||||||||
\(131\) | − | 3.29311e8i | − | 1.11820i | −0.829099 | − | 0.559101i | \(-0.811146\pi\) | ||
0.829099 | − | 0.559101i | \(-0.188854\pi\) | |||||||
\(132\) | − | 1.02435e8i | − | 0.337405i | ||||||
\(133\) | 1.79821e8 | 0.574691 | ||||||||
\(134\) | −1.26981e8 | −0.393840 | ||||||||
\(135\) | 7.96011e7 | 0.239654 | ||||||||
\(136\) | − | 2.11019e8i | − | 0.616832i | ||||||
\(137\) | −5.67910e8 | −1.61212 | −0.806059 | − | 0.591835i | \(-0.798404\pi\) | ||||
−0.806059 | + | 0.591835i | \(0.798404\pi\) | |||||||
\(138\) | 1.51246e8 | 0.417030 | ||||||||
\(139\) | −1.08782e7 | −0.0291405 | −0.0145702 | − | 0.999894i | \(-0.504638\pi\) | ||||
−0.0145702 | + | 0.999894i | \(0.504638\pi\) | |||||||
\(140\) | −1.32384e8 | −0.344607 | ||||||||
\(141\) | − | 2.40817e7i | − | 0.0609272i | ||||||
\(142\) | 9.11274e8i | 2.24128i | ||||||||
\(143\) | −1.90141e8 | −0.454708 | ||||||||
\(144\) | −1.79011e8 | −0.416322 | ||||||||
\(145\) | −6.49969e7 | −0.147035 | ||||||||
\(146\) | −2.93403e8 | −0.645733 | ||||||||
\(147\) | −1.75277e8 | −0.375367 | ||||||||
\(148\) | − | 7.33469e7i | − | 0.152875i | ||||||
\(149\) | − | 1.46320e8i | − | 0.296865i | −0.988923 | − | 0.148432i | \(-0.952577\pi\) | ||
0.988923 | − | 0.148432i | \(-0.0474228\pi\) | |||||||
\(150\) | 1.95017e8i | 0.385219i | ||||||||
\(151\) | 1.73523e8i | 0.333771i | 0.985976 | + | 0.166885i | \(0.0533710\pi\) | ||||
−0.985976 | + | 0.166885i | \(0.946629\pi\) | |||||||
\(152\) | 3.34376e8i | 0.626413i | ||||||||
\(153\) | −1.74762e8 | −0.318919 | ||||||||
\(154\) | −5.03448e8 | −0.895100 | ||||||||
\(155\) | 6.94256e8i | 1.20280i | ||||||||
\(156\) | − | 5.82372e7i | − | 0.0983337i | ||||||
\(157\) | 7.72308e8i | 1.27114i | 0.772045 | + | 0.635568i | \(0.219234\pi\) | ||||
−0.772045 | + | 0.635568i | \(0.780766\pi\) | |||||||
\(158\) | − | 3.04805e8i | − | 0.489096i | ||||||
\(159\) | 1.39897e8 | 0.218887 | ||||||||
\(160\) | − | 7.08772e8i | − | 1.08150i | ||||||
\(161\) | − | 2.36933e8i | − | 0.352632i | ||||||
\(162\) | 9.27173e7i | 0.134617i | ||||||||
\(163\) | 1.04794e9 | 1.48452 | 0.742261 | − | 0.670111i | \(-0.233754\pi\) | ||||
0.742261 | + | 0.670111i | \(0.233754\pi\) | |||||||
\(164\) | −1.06578e8 | −0.147330 | ||||||||
\(165\) | 6.65628e8i | 0.898040i | ||||||||
\(166\) | 8.83664e8 | 1.16374 | ||||||||
\(167\) | −3.62072e8 | −0.465510 | −0.232755 | − | 0.972535i | \(-0.574774\pi\) | ||||
−0.232755 | + | 0.972535i | \(0.574774\pi\) | |||||||
\(168\) | 1.75379e8i | 0.220161i | ||||||||
\(169\) | 7.07629e8 | 0.867479 | ||||||||
\(170\) | − | 1.20561e9i | − | 1.44348i | ||||||
\(171\) | 2.76923e8 | 0.323873 | ||||||||
\(172\) | 1.80933e8i | 0.206731i | ||||||||
\(173\) | 5.60602e8i | 0.625850i | 0.949778 | + | 0.312925i | \(0.101309\pi\) | ||||
−0.949778 | + | 0.312925i | \(0.898691\pi\) | |||||||
\(174\) | − | 7.57067e7i | − | 0.0825919i | ||||||
\(175\) | 3.05503e8 | 0.325734 | ||||||||
\(176\) | − | 1.49690e9i | − | 1.56006i | ||||||
\(177\) | 5.12995e8 | + | 2.40738e8i | 0.522661 | + | 0.245274i | ||||
\(178\) | 2.02722e9 | 2.01939 | ||||||||
\(179\) | 1.26287e8i | 0.123011i | 0.998107 | + | 0.0615056i | \(0.0195902\pi\) | ||||
−0.998107 | + | 0.0615056i | \(0.980410\pi\) | |||||||
\(180\) | −2.03871e8 | −0.194207 | ||||||||
\(181\) | 1.21141e9 | 1.12869 | 0.564346 | − | 0.825539i | \(-0.309129\pi\) | ||||
0.564346 | + | 0.825539i | \(0.309129\pi\) | |||||||
\(182\) | −2.86225e8 | −0.260869 | ||||||||
\(183\) | 7.70479e8i | 0.687000i | ||||||||
\(184\) | 4.40576e8 | 0.384370 | ||||||||
\(185\) | 4.76614e8i | 0.406892i | ||||||||
\(186\) | −8.08651e8 | −0.675631 | ||||||||
\(187\) | − | 1.46137e9i | − | 1.19507i | ||||||
\(188\) | 6.16772e7i | 0.0493734i | ||||||||
\(189\) | 1.45246e8 | 0.113830 | ||||||||
\(190\) | 1.91038e9i | 1.46590i | ||||||||
\(191\) | − | 7.94897e8i | − | 0.597279i | −0.954366 | − | 0.298640i | \(-0.903467\pi\) | ||
0.954366 | − | 0.298640i | \(-0.0965329\pi\) | |||||||
\(192\) | −1.54371e8 | −0.113595 | ||||||||
\(193\) | −4.07982e8 | −0.294043 | −0.147022 | − | 0.989133i | \(-0.546969\pi\) | ||||
−0.147022 | + | 0.989133i | \(0.546969\pi\) | |||||||
\(194\) | −1.42565e8 | −0.100648 | ||||||||
\(195\) | 3.78430e8i | 0.261726i | ||||||||
\(196\) | 4.48914e8 | 0.304185 | ||||||||
\(197\) | 1.98553e9 | 1.31829 | 0.659145 | − | 0.752015i | \(-0.270918\pi\) | ||||
0.659145 | + | 0.752015i | \(0.270918\pi\) | |||||||
\(198\) | −7.75306e8 | −0.504444 | ||||||||
\(199\) | 8.20394e7 | 0.0523130 | 0.0261565 | − | 0.999658i | \(-0.491673\pi\) | ||||
0.0261565 | + | 0.999658i | \(0.491673\pi\) | |||||||
\(200\) | 5.68080e8i | 0.355050i | ||||||||
\(201\) | 3.06338e8i | 0.187679i | ||||||||
\(202\) | −2.45601e8 | −0.147511 | ||||||||
\(203\) | −1.18598e8 | −0.0698381 | ||||||||
\(204\) | 4.47593e8 | 0.258442 | ||||||||
\(205\) | 6.92548e8 | 0.392134 | ||||||||
\(206\) | 2.10198e9 | 1.16724 | ||||||||
\(207\) | − | 3.64876e8i | − | 0.198730i | ||||||
\(208\) | − | 8.51033e8i | − | 0.454667i | ||||||
\(209\) | 2.31565e9i | 1.21363i | ||||||||
\(210\) | 1.00199e9i | 0.515212i | ||||||||
\(211\) | 3.26356e9i | 1.64650i | 0.567679 | + | 0.823250i | \(0.307841\pi\) | ||||
−0.567679 | + | 0.823250i | \(0.692159\pi\) | |||||||
\(212\) | −3.58298e8 | −0.177379 | ||||||||
\(213\) | 2.19842e9 | 1.06805 | ||||||||
\(214\) | − | 1.50674e9i | − | 0.718428i | ||||||
\(215\) | − | 1.17572e9i | − | 0.550236i | ||||||
\(216\) | 2.70083e8i | 0.124075i | ||||||||
\(217\) | 1.26679e9i | 0.571300i | ||||||||
\(218\) | 4.67720e8 | 0.207090 | ||||||||
\(219\) | 7.07824e8i | 0.307715i | ||||||||
\(220\) | − | 1.70478e9i | − | 0.727742i | ||||||
\(221\) | − | 8.30832e8i | − | 0.348292i | ||||||
\(222\) | −5.55147e8 | −0.228558 | ||||||||
\(223\) | −4.17801e9 | −1.68947 | −0.844735 | − | 0.535186i | \(-0.820242\pi\) | ||||
−0.844735 | + | 0.535186i | \(0.820242\pi\) | |||||||
\(224\) | − | 1.29327e9i | − | 0.513687i | ||||||
\(225\) | 4.70472e8 | 0.183571 | ||||||||
\(226\) | −3.00722e9 | −1.15274 | ||||||||
\(227\) | − | 4.74441e8i | − | 0.178681i | −0.996001 | − | 0.0893406i | \(-0.971524\pi\) | ||
0.996001 | − | 0.0893406i | \(-0.0284760\pi\) | |||||||
\(228\) | −7.09245e8 | −0.262456 | ||||||||
\(229\) | − | 3.53819e8i | − | 0.128659i | −0.997929 | − | 0.0643293i | \(-0.979509\pi\) | ||
0.997929 | − | 0.0643293i | \(-0.0204908\pi\) | |||||||
\(230\) | 2.51713e9 | 0.899484 | ||||||||
\(231\) | 1.21455e9i | 0.426548i | ||||||||
\(232\) | − | 2.20532e8i | − | 0.0761236i | ||||||
\(233\) | − | 4.54456e9i | − | 1.54194i | −0.636871 | − | 0.770971i | \(-0.719771\pi\) | ||
0.636871 | − | 0.770971i | \(-0.280229\pi\) | |||||||
\(234\) | −4.40785e8 | −0.147016 | ||||||||
\(235\) | − | 4.00783e8i | − | 0.131413i | ||||||
\(236\) | −1.31386e9 | − | 6.16568e8i | −0.423547 | − | 0.198762i | ||||
\(237\) | −7.35332e8 | −0.233072 | ||||||||
\(238\) | − | 2.19984e9i | − | 0.685619i | ||||||
\(239\) | −3.88537e8 | −0.119080 | −0.0595402 | − | 0.998226i | \(-0.518963\pi\) | ||||
−0.0595402 | + | 0.998226i | \(0.518963\pi\) | |||||||
\(240\) | −2.97921e9 | −0.897958 | ||||||||
\(241\) | 4.20396e9 | 1.24621 | 0.623104 | − | 0.782139i | \(-0.285871\pi\) | ||||
0.623104 | + | 0.782139i | \(0.285871\pi\) | |||||||
\(242\) | − | 2.32783e9i | − | 0.678718i | ||||||
\(243\) | 2.23677e8 | 0.0641500 | ||||||||
\(244\) | − | 1.97332e9i | − | 0.556722i | ||||||
\(245\) | −2.91707e9 | −0.809623 | ||||||||
\(246\) | 8.06663e8i | 0.220268i | ||||||||
\(247\) | 1.31652e9i | 0.353703i | ||||||||
\(248\) | −2.35558e9 | −0.622718 | ||||||||
\(249\) | − | 2.13181e9i | − | 0.554563i | ||||||
\(250\) | − | 2.64785e9i | − | 0.677849i | ||||||
\(251\) | −3.15846e9 | −0.795758 | −0.397879 | − | 0.917438i | \(-0.630254\pi\) | ||||
−0.397879 | + | 0.917438i | \(0.630254\pi\) | |||||||
\(252\) | −3.71997e8 | −0.0922438 | ||||||||
\(253\) | 3.05111e9 | 0.744690 | ||||||||
\(254\) | − | 1.04140e9i | − | 0.250197i | ||||||
\(255\) | −2.90849e9 | −0.687871 | ||||||||
\(256\) | 4.91460e9 | 1.14427 | ||||||||
\(257\) | 2.22549e8 | 0.0510144 | 0.0255072 | − | 0.999675i | \(-0.491880\pi\) | ||||
0.0255072 | + | 0.999675i | \(0.491880\pi\) | |||||||
\(258\) | 1.36945e9 | 0.309076 | ||||||||
\(259\) | 8.69662e8i | 0.193264i | ||||||||
\(260\) | − | 9.69220e8i | − | 0.212094i | ||||||
\(261\) | −1.82640e8 | −0.0393581 | ||||||||
\(262\) | 6.38365e9 | 1.35476 | ||||||||
\(263\) | 6.28171e9 | 1.31297 | 0.656485 | − | 0.754339i | \(-0.272043\pi\) | ||||
0.656485 | + | 0.754339i | \(0.272043\pi\) | |||||||
\(264\) | −2.25845e9 | −0.464937 | ||||||||
\(265\) | 2.32825e9 | 0.472113 | ||||||||
\(266\) | 3.48581e9i | 0.696269i | ||||||||
\(267\) | − | 4.89059e9i | − | 0.962314i | ||||||
\(268\) | − | 7.84580e8i | − | 0.152089i | ||||||
\(269\) | − | 5.04341e9i | − | 0.963198i | −0.876392 | − | 0.481599i | \(-0.840056\pi\) | ||
0.876392 | − | 0.481599i | \(-0.159944\pi\) | |||||||
\(270\) | 1.54306e9i | 0.290353i | ||||||||
\(271\) | 8.39347e9 | 1.55620 | 0.778098 | − | 0.628143i | \(-0.216185\pi\) | ||||
0.778098 | + | 0.628143i | \(0.216185\pi\) | |||||||
\(272\) | 6.54077e9 | 1.19496 | ||||||||
\(273\) | 6.90509e8i | 0.124314i | ||||||||
\(274\) | − | 1.10089e10i | − | 1.95317i | ||||||
\(275\) | 3.93411e9i | 0.687885i | ||||||||
\(276\) | 9.34505e8i | 0.161044i | ||||||||
\(277\) | 3.66227e9 | 0.622058 | 0.311029 | − | 0.950400i | \(-0.399326\pi\) | ||||
0.311029 | + | 0.950400i | \(0.399326\pi\) | |||||||
\(278\) | − | 2.10872e8i | − | 0.0353053i | ||||||
\(279\) | 1.95084e9i | 0.321963i | ||||||||
\(280\) | 2.91877e9i | 0.474862i | ||||||||
\(281\) | −1.53163e8 | −0.0245656 | −0.0122828 | − | 0.999925i | \(-0.503910\pi\) | ||||
−0.0122828 | + | 0.999925i | \(0.503910\pi\) | |||||||
\(282\) | 4.66822e8 | 0.0738167 | ||||||||
\(283\) | − | 1.25501e9i | − | 0.195660i | −0.995203 | − | 0.0978298i | \(-0.968810\pi\) | ||
0.995203 | − | 0.0978298i | \(-0.0311901\pi\) | |||||||
\(284\) | −5.63050e9 | −0.865513 | ||||||||
\(285\) | 4.60873e9 | 0.698557 | ||||||||
\(286\) | − | 3.68587e9i | − | 0.550904i | ||||||
\(287\) | 1.26367e9 | 0.186254 | ||||||||
\(288\) | − | 1.99164e9i | − | 0.289494i | ||||||
\(289\) | −5.90246e8 | −0.0846139 | ||||||||
\(290\) | − | 1.25996e9i | − | 0.178141i | ||||||
\(291\) | 3.43933e8i | 0.0479625i | ||||||||
\(292\) | − | 1.81285e9i | − | 0.249362i | ||||||
\(293\) | −4.99360e8 | −0.0677553 | −0.0338777 | − | 0.999426i | \(-0.510786\pi\) | ||||
−0.0338777 | + | 0.999426i | \(0.510786\pi\) | |||||||
\(294\) | − | 3.39773e9i | − | 0.454778i | ||||||
\(295\) | 8.53757e9 | + | 4.00650e9i | 1.12732 | + | 0.529026i | ||||
\(296\) | −1.61713e9 | −0.210658 | ||||||||
\(297\) | 1.87040e9i | 0.240386i | ||||||||
\(298\) | 2.83640e9 | 0.359668 | ||||||||
\(299\) | 1.73465e9 | 0.217033 | ||||||||
\(300\) | −1.20495e9 | −0.148760 | ||||||||
\(301\) | − | 2.14529e9i | − | 0.261349i | ||||||
\(302\) | −3.36371e9 | −0.404382 | ||||||||
\(303\) | 5.92504e8i | 0.0702944i | ||||||||
\(304\) | −1.03643e10 | −1.21352 | ||||||||
\(305\) | 1.28228e10i | 1.48178i | ||||||||
\(306\) | − | 3.38774e9i | − | 0.386388i | ||||||
\(307\) | −2.09107e9 | −0.235404 | −0.117702 | − | 0.993049i | \(-0.537553\pi\) | ||||
−0.117702 | + | 0.993049i | \(0.537553\pi\) | |||||||
\(308\) | − | 3.11066e9i | − | 0.345660i | ||||||
\(309\) | − | 5.07096e9i | − | 0.556232i | ||||||
\(310\) | −1.34581e10 | −1.45726 | ||||||||
\(311\) | −4.28031e9 | −0.457545 | −0.228773 | − | 0.973480i | \(-0.573471\pi\) | ||||
−0.228773 | + | 0.973480i | \(0.573471\pi\) | |||||||
\(312\) | −1.28400e9 | −0.135502 | ||||||||
\(313\) | − | 9.82280e8i | − | 0.102343i | −0.998690 | − | 0.0511715i | \(-0.983704\pi\) | ||
0.998690 | − | 0.0511715i | \(-0.0162955\pi\) | |||||||
\(314\) | −1.49711e10 | −1.54005 | ||||||||
\(315\) | 2.41726e9 | 0.245517 | ||||||||
\(316\) | 1.88330e9 | 0.188874 | ||||||||
\(317\) | 6.67356e9 | 0.660877 | 0.330438 | − | 0.943828i | \(-0.392803\pi\) | ||||
0.330438 | + | 0.943828i | \(0.392803\pi\) | |||||||
\(318\) | 2.71188e9i | 0.265193i | ||||||||
\(319\) | − | 1.52724e9i | − | 0.147484i | ||||||
\(320\) | −2.56913e9 | −0.245012 | ||||||||
\(321\) | −3.63496e9 | −0.342357 | ||||||||
\(322\) | 4.59292e9 | 0.427234 | ||||||||
\(323\) | −1.01183e10 | −0.929606 | ||||||||
\(324\) | −5.72873e8 | −0.0519851 | ||||||||
\(325\) | 2.23666e9i | 0.200478i | ||||||||
\(326\) | 2.03142e10i | 1.79858i | ||||||||
\(327\) | − | 1.12836e9i | − | 0.0986862i | ||||||
\(328\) | 2.34979e9i | 0.203017i | ||||||||
\(329\) | − | 7.31296e8i | − | 0.0624180i | ||||||
\(330\) | −1.29031e10 | −1.08803 | ||||||||
\(331\) | 1.51469e10 | 1.26186 | 0.630932 | − | 0.775838i | \(-0.282673\pi\) | ||||
0.630932 | + | 0.775838i | \(0.282673\pi\) | |||||||
\(332\) | 5.45991e9i | 0.449400i | ||||||||
\(333\) | 1.33927e9i | 0.108916i | ||||||||
\(334\) | − | 7.01873e9i | − | 0.563991i | ||||||
\(335\) | 5.09826e9i | 0.404802i | ||||||||
\(336\) | −5.43607e9 | −0.426509 | ||||||||
\(337\) | − | 1.33007e10i | − | 1.03123i | −0.856821 | − | 0.515613i | \(-0.827564\pi\) | ||
0.856821 | − | 0.515613i | \(-0.172436\pi\) | |||||||
\(338\) | 1.37173e10i | 1.05100i | ||||||||
\(339\) | 7.25482e9i | 0.549323i | ||||||||
\(340\) | 7.44911e9 | 0.557428 | ||||||||
\(341\) | −1.63131e10 | −1.20647 | ||||||||
\(342\) | 5.36813e9i | 0.392390i | ||||||||
\(343\) | −1.35095e10 | −0.976028 | ||||||||
\(344\) | 3.98916e9 | 0.284871 | ||||||||
\(345\) | − | 6.07248e9i | − | 0.428637i | ||||||
\(346\) | −1.08672e10 | −0.758252 | ||||||||
\(347\) | 5.23308e9i | 0.360943i | 0.983580 | + | 0.180472i | \(0.0577624\pi\) | ||||
−0.983580 | + | 0.180472i | \(0.942238\pi\) | |||||||
\(348\) | 4.67770e8 | 0.0318945 | ||||||||
\(349\) | − | 4.17787e9i | − | 0.281613i | −0.990037 | − | 0.140807i | \(-0.955030\pi\) | ||
0.990037 | − | 0.140807i | \(-0.0449696\pi\) | |||||||
\(350\) | 5.92213e9i | 0.394644i | ||||||||
\(351\) | 1.06338e9i | 0.0700584i | ||||||||
\(352\) | 1.66542e10 | 1.08481 | ||||||||
\(353\) | 3.00966e10i | 1.93829i | 0.246496 | + | 0.969144i | \(0.420721\pi\) | ||||
−0.246496 | + | 0.969144i | \(0.579279\pi\) | |||||||
\(354\) | −4.66667e9 | + | 9.94434e9i | −0.297163 | + | 0.633232i | ||||
\(355\) | 3.65874e10 | 2.30366 | ||||||||
\(356\) | 1.25256e10i | 0.779827i | ||||||||
\(357\) | −5.30703e9 | −0.326722 | ||||||||
\(358\) | −2.44805e9 | −0.149035 | ||||||||
\(359\) | −2.38260e10 | −1.43441 | −0.717204 | − | 0.696863i | \(-0.754578\pi\) | ||||
−0.717204 | + | 0.696863i | \(0.754578\pi\) | |||||||
\(360\) | 4.49489e9i | 0.267614i | ||||||||
\(361\) | −9.50298e8 | −0.0559540 | ||||||||
\(362\) | 2.34829e10i | 1.36747i | ||||||||
\(363\) | −5.61580e9 | −0.323434 | ||||||||
\(364\) | − | 1.76850e9i | − | 0.100740i | ||||||
\(365\) | 1.17800e10i | 0.663705i | ||||||||
\(366\) | −1.49356e10 | −0.832338 | ||||||||
\(367\) | − | 1.87371e10i | − | 1.03285i | −0.856333 | − | 0.516425i | \(-0.827263\pi\) | ||
0.856333 | − | 0.516425i | \(-0.172737\pi\) | |||||||
\(368\) | 1.36561e10i | 0.744622i | ||||||||
\(369\) | 1.94605e9 | 0.104966 | ||||||||
\(370\) | −9.23910e9 | −0.492973 | ||||||||
\(371\) | 4.24828e9 | 0.224242 | ||||||||
\(372\) | − | 4.99642e9i | − | 0.260908i | ||||||
\(373\) | −1.85649e10 | −0.959083 | −0.479541 | − | 0.877519i | \(-0.659197\pi\) | ||||
−0.479541 | + | 0.877519i | \(0.659197\pi\) | |||||||
\(374\) | 2.83284e10 | 1.44789 | ||||||||
\(375\) | −6.38784e9 | −0.323020 | ||||||||
\(376\) | 1.35984e9 | 0.0680357 | ||||||||
\(377\) | − | 8.68285e8i | − | 0.0429830i | ||||||
\(378\) | 2.81557e9i | 0.137911i | ||||||||
\(379\) | 6.06903e9 | 0.294146 | 0.147073 | − | 0.989126i | \(-0.453015\pi\) | ||||
0.147073 | + | 0.989126i | \(0.453015\pi\) | |||||||
\(380\) | −1.18037e10 | −0.566087 | ||||||||
\(381\) | −2.51234e9 | −0.119228 | ||||||||
\(382\) | 1.54090e10 | 0.723637 | ||||||||
\(383\) | 2.33300e10 | 1.08423 | 0.542113 | − | 0.840305i | \(-0.317624\pi\) | ||||
0.542113 | + | 0.840305i | \(0.317624\pi\) | |||||||
\(384\) | − | 1.38949e10i | − | 0.639046i | ||||||
\(385\) | 2.02133e10i | 0.920013i | ||||||||
\(386\) | − | 7.90868e9i | − | 0.356250i | ||||||
\(387\) | − | 3.30374e9i | − | 0.147286i | ||||||
\(388\) | − | 8.80867e8i | − | 0.0388672i | ||||||
\(389\) | 1.13812e10 | 0.497037 | 0.248518 | − | 0.968627i | \(-0.420056\pi\) | ||||
0.248518 | + | 0.968627i | \(0.420056\pi\) | |||||||
\(390\) | −7.33582e9 | −0.317096 | ||||||||
\(391\) | 1.33320e10i | 0.570410i | ||||||||
\(392\) | − | 9.89751e9i | − | 0.419162i | ||||||
\(393\) | − | 1.54003e10i | − | 0.645595i | ||||||
\(394\) | 3.84892e10i | 1.59718i | ||||||||
\(395\) | −1.22378e10 | −0.502709 | ||||||||
\(396\) | − | 4.79039e9i | − | 0.194801i | ||||||
\(397\) | − | 2.41950e10i | − | 0.974009i | −0.873399 | − | 0.487005i | \(-0.838089\pi\) | ||
0.873399 | − | 0.487005i | \(-0.161911\pi\) | |||||||
\(398\) | 1.59032e9i | 0.0633801i | ||||||||
\(399\) | 8.40940e9 | 0.331798 | ||||||||
\(400\) | −1.76083e10 | −0.687822 | ||||||||
\(401\) | − | 3.34160e10i | − | 1.29234i | −0.763194 | − | 0.646170i | \(-0.776370\pi\) | ||
0.763194 | − | 0.646170i | \(-0.223630\pi\) | |||||||
\(402\) | −5.93832e9 | −0.227384 | ||||||||
\(403\) | −9.27447e9 | −0.351616 | ||||||||
\(404\) | − | 1.51750e9i | − | 0.0569642i | ||||||
\(405\) | 3.72257e9 | 0.138364 | ||||||||
\(406\) | − | 2.29900e9i | − | 0.0846127i | ||||||
\(407\) | −1.11991e10 | −0.408136 | ||||||||
\(408\) | − | 9.86840e9i | − | 0.356128i | ||||||
\(409\) | − | 1.77855e8i | − | 0.00635583i | −0.999995 | − | 0.00317791i | \(-0.998988\pi\) | ||
0.999995 | − | 0.00317791i | \(-0.00101156\pi\) | |||||||
\(410\) | 1.34250e10i | 0.475092i | ||||||||
\(411\) | −2.65585e10 | −0.930757 | ||||||||
\(412\) | 1.29875e10i | 0.450752i | ||||||||
\(413\) | 1.55782e10 | + | 7.31054e9i | 0.535449 | + | 0.251275i | ||||
\(414\) | 7.07307e9 | 0.240772 | ||||||||
\(415\) | − | 3.54789e10i | − | 1.19613i | ||||||
\(416\) | 9.46840e9 | 0.316157 | ||||||||
\(417\) | −5.08721e8 | −0.0168243 | ||||||||
\(418\) | −4.48885e10 | −1.47038 | ||||||||
\(419\) | − | 5.25728e10i | − | 1.70571i | −0.522148 | − | 0.852855i | \(-0.674869\pi\) | ||
0.522148 | − | 0.852855i | \(-0.325131\pi\) | |||||||
\(420\) | −6.19100e9 | −0.198959 | ||||||||
\(421\) | − | 3.56037e10i | − | 1.13336i | −0.823939 | − | 0.566679i | \(-0.808228\pi\) | ||
0.823939 | − | 0.566679i | \(-0.191772\pi\) | |||||||
\(422\) | −6.32637e10 | −1.99483 | ||||||||
\(423\) | − | 1.12619e9i | − | 0.0351764i | ||||||
\(424\) | 7.89965e9i | 0.244424i | ||||||||
\(425\) | −1.71903e10 | −0.526899 | ||||||||
\(426\) | 4.26161e10i | 1.29400i | ||||||||
\(427\) | 2.33973e10i | 0.703809i | ||||||||
\(428\) | 9.30971e9 | 0.277435 | ||||||||
\(429\) | −8.89204e9 | −0.262526 | ||||||||
\(430\) | 2.27911e10 | 0.666641 | ||||||||
\(431\) | 6.55302e10i | 1.89903i | 0.313716 | + | 0.949517i | \(0.398426\pi\) | ||||
−0.313716 | + | 0.949517i | \(0.601574\pi\) | |||||||
\(432\) | −8.37152e9 | −0.240364 | ||||||||
\(433\) | 4.06255e10 | 1.15571 | 0.577853 | − | 0.816141i | \(-0.303891\pi\) | ||||
0.577853 | + | 0.816141i | \(0.303891\pi\) | |||||||
\(434\) | −2.45565e10 | −0.692162 | ||||||||
\(435\) | −3.03960e9 | −0.0848907 | ||||||||
\(436\) | 2.88991e9i | 0.0799720i | ||||||||
\(437\) | − | 2.11255e10i | − | 0.579270i | ||||||
\(438\) | −1.37211e10 | −0.372814 | ||||||||
\(439\) | 1.20990e10 | 0.325757 | 0.162878 | − | 0.986646i | \(-0.447922\pi\) | ||||
0.162878 | + | 0.986646i | \(0.447922\pi\) | |||||||
\(440\) | −3.75865e10 | −1.00282 | ||||||||
\(441\) | −8.19691e9 | −0.216719 | ||||||||
\(442\) | 1.61056e10 | 0.421976 | ||||||||
\(443\) | − | 2.49302e10i | − | 0.647307i | −0.946176 | − | 0.323654i | \(-0.895089\pi\) | ||
0.946176 | − | 0.323654i | \(-0.104911\pi\) | |||||||
\(444\) | − | 3.43010e9i | − | 0.0882621i | ||||||
\(445\) | − | 8.13922e10i | − | 2.07560i | ||||||
\(446\) | − | 8.09903e10i | − | 2.04688i | ||||||
\(447\) | − | 6.84271e9i | − | 0.171395i | ||||||
\(448\) | −4.68782e9 | −0.116375 | ||||||||
\(449\) | 4.83662e10 | 1.19003 | 0.595013 | − | 0.803716i | \(-0.297147\pi\) | ||||
0.595013 | + | 0.803716i | \(0.297147\pi\) | |||||||
\(450\) | 9.12005e9i | 0.222406i | ||||||||
\(451\) | 1.62729e10i | 0.393332i | ||||||||
\(452\) | − | 1.85807e10i | − | 0.445153i | ||||||
\(453\) | 8.11485e9i | 0.192703i | ||||||||
\(454\) | 9.19698e9 | 0.216482 | ||||||||
\(455\) | 1.14919e10i | 0.268130i | ||||||||
\(456\) | 1.56372e10i | 0.361660i | ||||||||
\(457\) | − | 1.22137e10i | − | 0.280017i | −0.990150 | − | 0.140008i | \(-0.955287\pi\) | ||
0.990150 | − | 0.140008i | \(-0.0447129\pi\) | |||||||
\(458\) | 6.85873e9 | 0.155877 | ||||||||
\(459\) | −8.17280e9 | −0.184128 | ||||||||
\(460\) | 1.55526e10i | 0.347353i | ||||||||
\(461\) | 1.05023e10 | 0.232530 | 0.116265 | − | 0.993218i | \(-0.462908\pi\) | ||||
0.116265 | + | 0.993218i | \(0.462908\pi\) | |||||||
\(462\) | −2.35439e10 | −0.516786 | ||||||||
\(463\) | − | 1.84192e10i | − | 0.400817i | −0.979712 | − | 0.200408i | \(-0.935773\pi\) | ||
0.979712 | − | 0.200408i | \(-0.0642269\pi\) | |||||||
\(464\) | 6.83562e9 | 0.147471 | ||||||||
\(465\) | 3.24671e10i | 0.694436i | ||||||||
\(466\) | 8.80957e10 | 1.86815 | ||||||||
\(467\) | − | 5.99569e10i | − | 1.26058i | −0.776358 | − | 0.630292i | \(-0.782935\pi\) | ||
0.776358 | − | 0.630292i | \(-0.217065\pi\) | |||||||
\(468\) | − | 2.72349e9i | − | 0.0567730i | ||||||
\(469\) | 9.30263e9i | 0.192271i | ||||||||
\(470\) | 7.76913e9 | 0.159214 | ||||||||
\(471\) | 3.61173e10i | 0.733891i | ||||||||
\(472\) | −1.35939e10 | + | 2.89676e10i | −0.273890 | + | 0.583640i | ||||
\(473\) | 2.76260e10 | 0.551917 | ||||||||
\(474\) | − | 1.42543e10i | − | 0.282379i | ||||||
\(475\) | 2.72393e10 | 0.535084 | ||||||||
\(476\) | 1.35922e10 | 0.264765 | ||||||||
\(477\) | 6.54233e9 | 0.126374 | ||||||||
\(478\) | − | 7.53173e9i | − | 0.144272i | ||||||
\(479\) | −7.23437e10 | −1.37423 | −0.687114 | − | 0.726550i | \(-0.741123\pi\) | ||||
−0.687114 | + | 0.726550i | \(0.741123\pi\) | |||||||
\(480\) | − | 3.31460e10i | − | 0.624405i | ||||||
\(481\) | −6.36702e9 | −0.118948 | ||||||||
\(482\) | 8.14933e10i | 1.50985i | ||||||||
\(483\) | − | 1.10803e10i | − | 0.203592i | ||||||
\(484\) | 1.43830e10 | 0.262100 | ||||||||
\(485\) | 5.72394e9i | 0.103449i | ||||||||
\(486\) | 4.33596e9i | 0.0777213i | ||||||||
\(487\) | 1.33799e10 | 0.237869 | 0.118934 | − | 0.992902i | \(-0.462052\pi\) | ||||
0.118934 | + | 0.992902i | \(0.462052\pi\) | |||||||
\(488\) | −4.35072e10 | −0.767152 | ||||||||
\(489\) | 4.90074e10 | 0.857089 | ||||||||
\(490\) | − | 5.65471e10i | − | 0.980903i | ||||||
\(491\) | 7.07239e10 | 1.21686 | 0.608429 | − | 0.793608i | \(-0.291800\pi\) | ||||
0.608429 | + | 0.793608i | \(0.291800\pi\) | |||||||
\(492\) | −4.98414e9 | −0.0850608 | ||||||||
\(493\) | 6.67336e9 | 0.112968 | ||||||||
\(494\) | −2.55205e10 | −0.428530 | ||||||||
\(495\) | 3.11283e10i | 0.518484i | ||||||||
\(496\) | − | 7.30138e10i | − | 1.20636i | ||||||
\(497\) | 6.67599e10 | 1.09418 | ||||||||
\(498\) | 4.13249e10 | 0.671884 | ||||||||
\(499\) | −6.14004e10 | −0.990305 | −0.495152 | − | 0.868806i | \(-0.664888\pi\) | ||||
−0.495152 | + | 0.868806i | \(0.664888\pi\) | |||||||
\(500\) | 1.63603e10 | 0.261765 | ||||||||
\(501\) | −1.69324e10 | −0.268762 | ||||||||
\(502\) | − | 6.12265e10i | − | 0.964105i | ||||||
\(503\) | − | 4.03520e10i | − | 0.630367i | −0.949031 | − | 0.315184i | \(-0.897934\pi\) | ||
0.949031 | − | 0.315184i | \(-0.102066\pi\) | |||||||
\(504\) | 8.20168e9i | 0.127110i | ||||||||
\(505\) | 9.86080e9i | 0.151617i | ||||||||
\(506\) | 5.91454e10i | 0.902233i | ||||||||
\(507\) | 3.30926e10 | 0.500839 | ||||||||
\(508\) | 6.43451e9 | 0.0966186 | ||||||||
\(509\) | − | 2.92932e10i | − | 0.436412i | −0.975903 | − | 0.218206i | \(-0.929980\pi\) | ||
0.975903 | − | 0.218206i | \(-0.0700204\pi\) | |||||||
\(510\) | − | 5.63808e10i | − | 0.833394i | ||||||
\(511\) | 2.14947e10i | 0.315244i | ||||||||
\(512\) | 1.92060e10i | 0.279485i | ||||||||
\(513\) | 1.29504e10 | 0.186988 | ||||||||
\(514\) | 4.31408e9i | 0.0618067i | ||||||||
\(515\) | − | 8.43939e10i | − | 1.19973i | ||||||
\(516\) | 8.46141e9i | 0.119356i | ||||||||
\(517\) | 9.41727e9 | 0.131814 | ||||||||
\(518\) | −1.68583e10 | −0.234150 | ||||||||
\(519\) | 2.62168e10i | 0.361335i | ||||||||
\(520\) | −2.13691e10 | −0.292262 | ||||||||
\(521\) | −2.11690e10 | −0.287309 | −0.143655 | − | 0.989628i | \(-0.545885\pi\) | ||||
−0.143655 | + | 0.989628i | \(0.545885\pi\) | |||||||
\(522\) | − | 3.54045e9i | − | 0.0476844i | ||||||
\(523\) | 4.96188e10 | 0.663193 | 0.331596 | − | 0.943421i | \(-0.392413\pi\) | ||||
0.331596 | + | 0.943421i | \(0.392413\pi\) | |||||||
\(524\) | 3.94427e10i | 0.523169i | ||||||||
\(525\) | 1.42869e10 | 0.188062 | ||||||||
\(526\) | 1.21770e11i | 1.59074i | ||||||||
\(527\) | − | 7.12807e10i | − | 0.924122i | ||||||
\(528\) | − | 7.00030e10i | − | 0.900702i | ||||||
\(529\) | 5.04759e10 | 0.644557 | ||||||||
\(530\) | 4.51328e10i | 0.571991i | ||||||||
\(531\) | 2.39904e10 | + | 1.12582e10i | 0.301758 | + | 0.141609i | ||||
\(532\) | −2.15378e10 | −0.268878 | ||||||||
\(533\) | 9.25166e9i | 0.114633i | ||||||||
\(534\) | 9.48036e10 | 1.16590 | ||||||||
\(535\) | −6.04952e10 | −0.738424 | ||||||||
\(536\) | −1.72982e10 | −0.209576 | ||||||||
\(537\) | 5.90584e9i | 0.0710206i | ||||||||
\(538\) | 9.77660e10 | 1.16697 | ||||||||
\(539\) | − | 6.85430e10i | − | 0.812097i | ||||||
\(540\) | −9.53411e9 | −0.112126 | ||||||||
\(541\) | − | 9.36324e10i | − | 1.09304i | −0.837445 | − | 0.546521i | \(-0.815952\pi\) | ||
0.837445 | − | 0.546521i | \(-0.184048\pi\) | |||||||
\(542\) | 1.62706e11i | 1.88542i | ||||||||
\(543\) | 5.66518e10 | 0.651650 | ||||||||
\(544\) | 7.27711e10i | 0.830928i | ||||||||
\(545\) | − | 1.87788e10i | − | 0.212854i | ||||||
\(546\) | −1.33854e10 | −0.150613 | ||||||||
\(547\) | 1.06216e11 | 1.18643 | 0.593214 | − | 0.805045i | \(-0.297859\pi\) | ||||
0.593214 | + | 0.805045i | \(0.297859\pi\) | |||||||
\(548\) | 6.80206e10 | 0.754255 | ||||||||
\(549\) | 3.60317e10i | 0.396639i | ||||||||
\(550\) | −7.62623e10 | −0.833411 | ||||||||
\(551\) | −1.05745e10 | −0.114723 | ||||||||
\(552\) | 2.06037e10 | 0.221916 | ||||||||
\(553\) | −2.23300e10 | −0.238775 | ||||||||
\(554\) | 7.09926e10i | 0.753658i | ||||||||
\(555\) | 2.22890e10i | 0.234919i | ||||||||
\(556\) | 1.30292e9 | 0.0136338 | ||||||||
\(557\) | 8.42642e10 | 0.875432 | 0.437716 | − | 0.899113i | \(-0.355787\pi\) | ||||
0.437716 | + | 0.899113i | \(0.355787\pi\) | |||||||
\(558\) | −3.78169e10 | −0.390076 | ||||||||
\(559\) | 1.57063e10 | 0.160852 | ||||||||
\(560\) | −9.04704e10 | −0.919929 | ||||||||
\(561\) | − | 6.83414e10i | − | 0.689973i | ||||||
\(562\) | − | 2.96904e9i | − | 0.0297626i | ||||||
\(563\) | − | 6.64019e10i | − | 0.660917i | −0.943820 | − | 0.330459i | \(-0.892797\pi\) | ||
0.943820 | − | 0.330459i | \(-0.107203\pi\) | |||||||
\(564\) | 2.88436e9i | 0.0285058i | ||||||||
\(565\) | 1.20739e11i | 1.18482i | ||||||||
\(566\) | 2.43282e10 | 0.237052 | ||||||||
\(567\) | 6.79246e9 | 0.0657196 | ||||||||
\(568\) | 1.24140e11i | 1.19266i | ||||||||
\(569\) | − | 1.72792e11i | − | 1.64845i | −0.566262 | − | 0.824225i | \(-0.691611\pi\) | ||
0.566262 | − | 0.824225i | \(-0.308389\pi\) | |||||||
\(570\) | 8.93396e10i | 0.846340i | ||||||||
\(571\) | 1.22882e11i | 1.15597i | 0.816049 | + | 0.577983i | \(0.196160\pi\) | ||||
−0.816049 | + | 0.577983i | \(0.803840\pi\) | |||||||
\(572\) | 2.27739e10 | 0.212742 | ||||||||
\(573\) | − | 3.71737e10i | − | 0.344839i | ||||||
\(574\) | 2.44961e10i | 0.225657i | ||||||||
\(575\) | − | 3.58907e10i | − | 0.328330i | ||||||
\(576\) | −7.21921e9 | −0.0655843 | ||||||||
\(577\) | 1.51928e11 | 1.37068 | 0.685338 | − | 0.728225i | \(-0.259655\pi\) | ||||
0.685338 | + | 0.728225i | \(0.259655\pi\) | |||||||
\(578\) | − | 1.14418e10i | − | 0.102514i | ||||||
\(579\) | −1.90794e10 | −0.169766 | ||||||||
\(580\) | 7.78491e9 | 0.0687926 | ||||||||
\(581\) | − | 6.47372e10i | − | 0.568132i | ||||||
\(582\) | −6.66710e9 | −0.0581092 | ||||||||
\(583\) | 5.47073e10i | 0.473555i | ||||||||
\(584\) | −3.99692e10 | −0.343617 | ||||||||
\(585\) | 1.76974e10i | 0.151108i | ||||||||
\(586\) | − | 9.68004e9i | − | 0.0820893i | ||||||
\(587\) | − | 1.86857e11i | − | 1.57382i | −0.617065 | − | 0.786912i | \(-0.711678\pi\) | ||
0.617065 | − | 0.786912i | \(-0.288322\pi\) | |||||||
\(588\) | 2.09936e10 | 0.175622 | ||||||||
\(589\) | 1.12950e11i | 0.938477i | ||||||||
\(590\) | −7.76655e10 | + | 1.65500e11i | −0.640944 | + | 1.36581i | ||||
\(591\) | 9.28540e10 | 0.761116 | ||||||||
\(592\) | − | 5.01247e10i | − | 0.408099i | ||||||
\(593\) | 9.07280e9 | 0.0733707 | 0.0366853 | − | 0.999327i | \(-0.488320\pi\) | ||||
0.0366853 | + | 0.999327i | \(0.488320\pi\) | |||||||
\(594\) | −3.62575e10 | −0.291241 | ||||||||
\(595\) | −8.83229e10 | −0.704702 | ||||||||
\(596\) | 1.75253e10i | 0.138893i | ||||||||
\(597\) | 3.83660e9 | 0.0302029 | ||||||||
\(598\) | 3.36260e10i | 0.262948i | ||||||||
\(599\) | 1.34106e10 | 0.104169 | 0.0520847 | − | 0.998643i | \(-0.483413\pi\) | ||||
0.0520847 | + | 0.998643i | \(0.483413\pi\) | |||||||
\(600\) | 2.65665e10i | 0.204988i | ||||||||
\(601\) | 2.00866e11i | 1.53960i | 0.638286 | + | 0.769799i | \(0.279644\pi\) | ||||
−0.638286 | + | 0.769799i | \(0.720356\pi\) | |||||||
\(602\) | 4.15863e10 | 0.316639 | ||||||||
\(603\) | 1.43260e10i | 0.108357i | ||||||||
\(604\) | − | 2.07834e10i | − | 0.156160i | ||||||
\(605\) | −9.34616e10 | −0.697609 | ||||||||
\(606\) | −1.14856e10 | −0.0851655 | ||||||||
\(607\) | 8.10048e10 | 0.596700 | 0.298350 | − | 0.954457i | \(-0.403564\pi\) | ||||
0.298350 | + | 0.954457i | \(0.403564\pi\) | |||||||
\(608\) | − | 1.15311e11i | − | 0.843835i | ||||||
\(609\) | −5.54627e9 | −0.0403210 | ||||||||
\(610\) | −2.48568e11 | −1.79525 | ||||||||
\(611\) | 5.35401e9 | 0.0384162 | ||||||||
\(612\) | 2.09319e10 | 0.149211 | ||||||||
\(613\) | 7.91202e10i | 0.560332i | 0.959952 | + | 0.280166i | \(0.0903895\pi\) | ||||
−0.959952 | + | 0.280166i | \(0.909611\pi\) | |||||||
\(614\) | − | 4.05351e10i | − | 0.285205i | ||||||
\(615\) | 3.23873e10 | 0.226399 | ||||||||
\(616\) | −6.85828e10 | −0.476313 | ||||||||
\(617\) | −1.16447e10 | −0.0803504 | −0.0401752 | − | 0.999193i | \(-0.512792\pi\) | ||||
−0.0401752 | + | 0.999193i | \(0.512792\pi\) | |||||||
\(618\) | 9.82999e10 | 0.673906 | ||||||||
\(619\) | 6.18871e10 | 0.421539 | 0.210769 | − | 0.977536i | \(-0.432403\pi\) | ||||
0.210769 | + | 0.977536i | \(0.432403\pi\) | |||||||
\(620\) | − | 8.31535e10i | − | 0.562748i | ||||||
\(621\) | − | 1.70635e10i | − | 0.114737i | ||||||
\(622\) | − | 8.29734e10i | − | 0.554341i | ||||||
\(623\) | − | 1.48514e11i | − | 0.985859i | ||||||
\(624\) | − | 3.97989e10i | − | 0.262502i | ||||||
\(625\) | −1.90342e11 | −1.24743 | ||||||||
\(626\) | 1.90414e10 | 0.123994 | ||||||||
\(627\) | 1.08292e11i | 0.700691i | ||||||||
\(628\) | − | 9.25021e10i | − | 0.594721i | ||||||
\(629\) | − | 4.89349e10i | − | 0.312620i | ||||||
\(630\) | 4.68584e10i | 0.297458i | ||||||||
\(631\) | −1.05029e11 | −0.662506 | −0.331253 | − | 0.943542i | \(-0.607471\pi\) | ||||
−0.331253 | + | 0.943542i | \(0.607471\pi\) | |||||||
\(632\) | − | 4.15225e10i | − | 0.260265i | ||||||
\(633\) | 1.52622e11i | 0.950607i | ||||||||
\(634\) | 1.29366e11i | 0.800688i | ||||||||
\(635\) | −4.18119e10 | −0.257161 | ||||||||
\(636\) | −1.67560e10 | −0.102410 | ||||||||
\(637\) | − | 3.89688e10i | − | 0.236679i | ||||||
\(638\) | 2.96054e10 | 0.178685 | ||||||||
\(639\) | 1.02810e11 | 0.616639 | ||||||||
\(640\) | − | 2.31248e11i | − | 1.37835i | ||||||
\(641\) | 1.28978e11 | 0.763982 | 0.381991 | − | 0.924166i | \(-0.375239\pi\) | ||||
0.381991 | + | 0.924166i | \(0.375239\pi\) | |||||||
\(642\) | − | 7.04633e10i | − | 0.414785i | ||||||
\(643\) | 1.03531e11 | 0.605657 | 0.302829 | − | 0.953045i | \(-0.402069\pi\) | ||||
0.302829 | + | 0.953045i | \(0.402069\pi\) | |||||||
\(644\) | 2.83783e10i | 0.164985i | ||||||||
\(645\) | − | 5.49829e10i | − | 0.317679i | ||||||
\(646\) | − | 1.96143e11i | − | 1.12627i | ||||||
\(647\) | 7.53363e10 | 0.429920 | 0.214960 | − | 0.976623i | \(-0.431038\pi\) | ||||
0.214960 | + | 0.976623i | \(0.431038\pi\) | |||||||
\(648\) | 1.26305e10i | 0.0716345i | ||||||||
\(649\) | −9.41415e10 | + | 2.00609e11i | −0.530643 | + | 1.13076i | ||||
\(650\) | −4.33574e10 | −0.242890 | ||||||||
\(651\) | 5.92418e10i | 0.329840i | ||||||||
\(652\) | −1.25516e11 | −0.694556 | ||||||||
\(653\) | 1.58411e11 | 0.871228 | 0.435614 | − | 0.900134i | \(-0.356531\pi\) | ||||
0.435614 | + | 0.900134i | \(0.356531\pi\) | |||||||
\(654\) | 2.18731e10 | 0.119564 | ||||||||
\(655\) | − | 2.56302e11i | − | 1.39247i | ||||||
\(656\) | −7.28342e10 | −0.393297 | ||||||||
\(657\) | 3.31017e10i | 0.177659i | ||||||||
\(658\) | 1.41761e10 | 0.0756228 | ||||||||
\(659\) | − | 9.20311e10i | − | 0.487970i | −0.969779 | − | 0.243985i | \(-0.921545\pi\) | ||
0.969779 | − | 0.243985i | \(-0.0784548\pi\) | |||||||
\(660\) | − | 7.97247e10i | − | 0.420162i | ||||||
\(661\) | −4.18994e10 | −0.219484 | −0.109742 | − | 0.993960i | \(-0.535002\pi\) | ||||
−0.109742 | + | 0.993960i | \(0.535002\pi\) | |||||||
\(662\) | 2.93621e11i | 1.52882i | ||||||||
\(663\) | − | 3.88542e10i | − | 0.201087i | ||||||
\(664\) | 1.20378e11 | 0.619265 | ||||||||
\(665\) | 1.39954e11 | 0.715648 | ||||||||
\(666\) | −2.59617e10 | −0.131958 | ||||||||
\(667\) | 1.39329e10i | 0.0703947i | ||||||||
\(668\) | 4.33667e10 | 0.217796 | ||||||||
\(669\) | −1.95386e11 | −0.975415 | ||||||||
\(670\) | −9.88291e10 | −0.490440 | ||||||||
\(671\) | −3.01299e11 | −1.48630 | ||||||||
\(672\) | − | 6.04805e10i | − | 0.296577i | ||||||
\(673\) | 2.42999e11i | 1.18453i | 0.805745 | + | 0.592263i | \(0.201765\pi\) | ||||
−0.805745 | + | 0.592263i | \(0.798235\pi\) | |||||||
\(674\) | 2.57832e11 | 1.24939 | ||||||||
\(675\) | 2.20018e10 | 0.105985 | ||||||||
\(676\) | −8.47553e10 | −0.405864 | ||||||||
\(677\) | −2.40852e11 | −1.14655 | −0.573277 | − | 0.819361i | \(-0.694328\pi\) | ||||
−0.573277 | + | 0.819361i | \(0.694328\pi\) | |||||||
\(678\) | −1.40634e11 | −0.665535 | ||||||||
\(679\) | 1.04443e10i | 0.0491360i | ||||||||
\(680\) | − | 1.64236e11i | − | 0.768126i | ||||||
\(681\) | − | 2.21874e10i | − | 0.103162i | ||||||
\(682\) | − | 3.16227e11i | − | 1.46171i | ||||||
\(683\) | 2.86451e11i | 1.31634i | 0.752870 | + | 0.658169i | \(0.228669\pi\) | ||||
−0.752870 | + | 0.658169i | \(0.771331\pi\) | |||||||
\(684\) | −3.31681e10 | −0.151529 | ||||||||
\(685\) | −4.42003e11 | −2.00753 | ||||||||
\(686\) | − | 2.61880e11i | − | 1.18251i | ||||||
\(687\) | − | 1.65465e10i | − | 0.0742811i | ||||||
\(688\) | 1.23648e11i | 0.551867i | ||||||||
\(689\) | 3.11028e10i | 0.138014i | ||||||||
\(690\) | 1.17714e11 | 0.519318 | ||||||||
\(691\) | − | 1.05033e11i | − | 0.460694i | −0.973109 | − | 0.230347i | \(-0.926014\pi\) | ||
0.973109 | − | 0.230347i | \(-0.0739861\pi\) | |||||||
\(692\) | − | 6.71453e10i | − | 0.292814i | ||||||
\(693\) | 5.67989e10i | 0.246267i | ||||||||
\(694\) | −1.01443e11 | −0.437303 | ||||||||
\(695\) | −8.46645e9 | −0.0362879 | ||||||||
\(696\) | − | 1.03133e10i | − | 0.0439500i | ||||||
\(697\) | −7.11054e10 | −0.301281 | ||||||||
\(698\) | 8.09875e10 | 0.341190 | ||||||||
\(699\) | − | 2.12528e11i | − | 0.890240i | ||||||
\(700\) | −3.65911e10 | −0.152400 | ||||||||
\(701\) | − | 8.98668e10i | − | 0.372158i | −0.982535 | − | 0.186079i | \(-0.940422\pi\) | ||
0.982535 | − | 0.186079i | \(-0.0595780\pi\) | |||||||
\(702\) | −2.06135e10 | −0.0848796 | ||||||||
\(703\) | 7.75411e10i | 0.317476i | ||||||||
\(704\) | − | 6.03674e10i | − | 0.245760i | ||||||
\(705\) | − | 1.87428e10i | − | 0.0758713i | ||||||
\(706\) | −5.83419e11 | −2.34834 | ||||||||
\(707\) | 1.79927e10i | 0.0720143i | ||||||||
\(708\) | −6.14432e10 | − | 2.88340e10i | −0.244535 | − | 0.114755i | ||||
\(709\) | −1.33687e11 | −0.529060 | −0.264530 | − | 0.964377i | \(-0.585217\pi\) | ||||
−0.264530 | + | 0.964377i | \(0.585217\pi\) | |||||||
\(710\) | 7.09242e11i | 2.79101i | ||||||||
\(711\) | −3.43881e10 | −0.134564 | ||||||||
\(712\) | 2.76161e11 | 1.07459 | ||||||||
\(713\) | 1.48823e11 | 0.575853 | ||||||||
\(714\) | − | 1.02876e11i | − | 0.395842i | ||||||
\(715\) | −1.47987e11 | −0.566237 | ||||||||
\(716\) | − | 1.51258e10i | − | 0.0575527i | ||||||
\(717\) | −1.81701e10 | −0.0687511 | ||||||||
\(718\) | − | 4.61864e11i | − | 1.73786i | ||||||
\(719\) | 3.90817e11i | 1.46237i | 0.682177 | + | 0.731187i | \(0.261033\pi\) | ||||
−0.682177 | + | 0.731187i | \(0.738967\pi\) | |||||||
\(720\) | −1.39324e11 | −0.518436 | ||||||||
\(721\) | − | 1.53991e11i | − | 0.569841i | ||||||
\(722\) | − | 1.84214e10i | − | 0.0677914i | ||||||
\(723\) | 1.96600e11 | 0.719499 | ||||||||
\(724\) | −1.45094e11 | −0.528076 | ||||||||
\(725\) | −1.79652e10 | −0.0650250 | ||||||||
\(726\) | − | 1.08862e11i | − | 0.391858i | ||||||
\(727\) | 2.67882e11 | 0.958973 | 0.479486 | − | 0.877549i | \(-0.340823\pi\) | ||||
0.479486 | + | 0.877549i | \(0.340823\pi\) | |||||||
\(728\) | −3.89915e10 | −0.138817 | ||||||||
\(729\) | 1.04604e10 | 0.0370370 | ||||||||
\(730\) | −2.28355e11 | −0.804116 | ||||||||
\(731\) | 1.20713e11i | 0.422752i | ||||||||
\(732\) | − | 9.22831e10i | − | 0.321424i | ||||||
\(733\) | −1.00091e11 | −0.346722 | −0.173361 | − | 0.984858i | \(-0.555463\pi\) | ||||
−0.173361 | + | 0.984858i | \(0.555463\pi\) | |||||||
\(734\) | 3.63216e11 | 1.25135 | ||||||||
\(735\) | −1.36418e11 | −0.467436 | ||||||||
\(736\) | −1.51935e11 | −0.517781 | ||||||||
\(737\) | −1.19795e11 | −0.406039 | ||||||||
\(738\) | 3.77239e10i | 0.127172i | ||||||||
\(739\) | 3.87711e11i | 1.29996i | 0.759951 | + | 0.649980i | \(0.225223\pi\) | ||||
−0.759951 | + | 0.649980i | \(0.774777\pi\) | |||||||
\(740\) | − | 5.70857e10i | − | 0.190371i | ||||||
\(741\) | 6.15674e10i | 0.204210i | ||||||||
\(742\) | 8.23524e10i | 0.271682i | ||||||||
\(743\) | 3.02109e11 | 0.991308 | 0.495654 | − | 0.868520i | \(-0.334928\pi\) | ||||
0.495654 | + | 0.868520i | \(0.334928\pi\) | |||||||
\(744\) | −1.10160e11 | −0.359527 | ||||||||
\(745\) | − | 1.13881e11i | − | 0.369679i | ||||||
\(746\) | − | 3.59877e11i | − | 1.16198i | ||||||
\(747\) | − | 9.96949e10i | − | 0.320177i | ||||||
\(748\) | 1.75033e11i | 0.559132i | ||||||||
\(749\) | −1.10384e11 | −0.350734 | ||||||||
\(750\) | − | 1.23828e11i | − | 0.391356i | ||||||
\(751\) | 2.88819e11i | 0.907959i | 0.891012 | + | 0.453979i | \(0.149996\pi\) | ||||
−0.891012 | + | 0.453979i | \(0.850004\pi\) | |||||||
\(752\) | 4.21497e10i | 0.131802i | ||||||||
\(753\) | −1.47707e11 | −0.459431 | ||||||||
\(754\) | 1.68316e10 | 0.0520763 | ||||||||
\(755\) | 1.35052e11i | 0.415637i | ||||||||
\(756\) | −1.73966e10 | −0.0532570 | ||||||||
\(757\) | −5.13648e11 | −1.56416 | −0.782082 | − | 0.623176i | \(-0.785842\pi\) | ||||
−0.782082 | + | 0.623176i | \(0.785842\pi\) | |||||||
\(758\) | 1.17647e11i | 0.356374i | ||||||||
\(759\) | 1.42686e11 | 0.429947 | ||||||||
\(760\) | 2.60244e11i | 0.780058i | ||||||||
\(761\) | −3.41151e11 | −1.01720 | −0.508601 | − | 0.861002i | \(-0.669837\pi\) | ||||
−0.508601 | + | 0.861002i | \(0.669837\pi\) | |||||||
\(762\) | − | 4.87015e10i | − | 0.144451i | ||||||
\(763\) | − | 3.42651e10i | − | 0.101101i | ||||||
\(764\) | 9.52077e10i | 0.279446i | ||||||||
\(765\) | −1.36017e11 | −0.397143 | ||||||||
\(766\) | 4.52250e11i | 1.31360i | ||||||||
\(767\) | −5.35223e10 | + | 1.14052e11i | −0.154651 | + | 0.329551i | ||||
\(768\) | 2.29833e11 | 0.660644 | ||||||||
\(769\) | − | 3.32287e11i | − | 0.950183i | −0.879936 | − | 0.475092i | \(-0.842415\pi\) | ||
0.879936 | − | 0.475092i | \(-0.157585\pi\) | |||||||
\(770\) | −3.91832e11 | −1.11465 | ||||||||
\(771\) | 1.04076e10 | 0.0294532 | ||||||||
\(772\) | 4.88654e10 | 0.137573 | ||||||||
\(773\) | − | 3.98928e11i | − | 1.11732i | −0.829397 | − | 0.558659i | \(-0.811316\pi\) | ||
0.829397 | − | 0.558659i | \(-0.188684\pi\) | |||||||
\(774\) | 6.40426e10 | 0.178445 | ||||||||
\(775\) | 1.91893e11i | 0.531927i | ||||||||
\(776\) | −1.94211e10 | −0.0535583 | ||||||||
\(777\) | 4.06701e10i | 0.111581i | ||||||||
\(778\) | 2.20623e11i | 0.602187i | ||||||||
\(779\) | 1.12672e11 | 0.305961 | ||||||||
\(780\) | − | 4.53259e10i | − | 0.122453i | ||||||
\(781\) | 8.59701e11i | 2.31070i | ||||||||
\(782\) | −2.58438e11 | −0.691083 | ||||||||
\(783\) | −8.54122e9 | −0.0227234 | ||||||||
\(784\) | 3.06784e11 | 0.812023 | ||||||||
\(785\) | 6.01086e11i | 1.58292i | ||||||||
\(786\) | 2.98534e11 | 0.782173 | ||||||||
\(787\) | 1.14010e11 | 0.297197 | 0.148599 | − | 0.988898i | \(-0.452524\pi\) | ||||
0.148599 | + | 0.988898i | \(0.452524\pi\) | |||||||
\(788\) | −2.37814e11 | −0.616783 | ||||||||
\(789\) | 2.93766e11 | 0.758044 | ||||||||
\(790\) | − | 2.37229e11i | − | 0.609059i | ||||||
\(791\) | 2.20309e11i | 0.562763i | ||||||||
\(792\) | −1.05617e11 | −0.268432 | ||||||||
\(793\) | −1.71298e11 | −0.433171 | ||||||||
\(794\) | 4.69017e11 | 1.18007 | ||||||||
\(795\) | 1.08881e11 | 0.272575 | ||||||||
\(796\) | −9.82615e9 | −0.0244755 | ||||||||
\(797\) | 3.05898e11i | 0.758129i | 0.925370 | + | 0.379064i | \(0.123754\pi\) | ||||
−0.925370 | + | 0.379064i | \(0.876246\pi\) | |||||||
\(798\) | 1.63015e11i | 0.401991i | ||||||||
\(799\) | 4.11492e10i | 0.100966i | ||||||||
\(800\) | − | 1.95905e11i | − | 0.478285i | ||||||
\(801\) | − | 2.28710e11i | − | 0.555592i | ||||||
\(802\) | 6.47765e11 | 1.56574 | ||||||||
\(803\) | −2.76798e11 | −0.665733 | ||||||||
\(804\) | − | 3.66912e10i | − | 0.0878087i | ||||||
\(805\) | − | 1.84404e11i | − | 0.439125i | ||||||
\(806\) | − | 1.79785e11i | − | 0.426003i | ||||||
\(807\) | − | 2.35857e11i | − | 0.556103i | ||||||
\(808\) | −3.34573e10 | −0.0784957 | ||||||||
\(809\) | 3.86187e10i | 0.0901577i | 0.998983 | + | 0.0450789i | \(0.0143539\pi\) | ||||
−0.998983 | + | 0.0450789i | \(0.985646\pi\) | |||||||
\(810\) | 7.21616e10i | 0.167636i | ||||||||
\(811\) | 2.90483e11i | 0.671486i | 0.941954 | + | 0.335743i | \(0.108987\pi\) | ||||
−0.941954 | + | 0.335743i | \(0.891013\pi\) | |||||||
\(812\) | 1.42049e10 | 0.0326748 | ||||||||
\(813\) | 3.92524e11 | 0.898470 | ||||||||
\(814\) | − | 2.17093e11i | − | 0.494479i | ||||||
\(815\) | 8.15610e11 | 1.84864 | ||||||||
\(816\) | 3.05882e11 | 0.689910 | ||||||||
\(817\) | − | 1.91279e11i | − | 0.429319i | ||||||
\(818\) | 3.44769e9 | 0.00770044 | ||||||||
\(819\) | 3.22919e10i | 0.0717725i | ||||||||
\(820\) | −8.29490e10 | −0.183466 | ||||||||
\(821\) | 5.22423e10i | 0.114987i | 0.998346 | + | 0.0574936i | \(0.0183109\pi\) | ||||
−0.998346 | + | 0.0574936i | \(0.981689\pi\) | |||||||
\(822\) | − | 5.14834e11i | − | 1.12766i | ||||||
\(823\) | − | 3.58392e11i | − | 0.781194i | −0.920562 | − | 0.390597i | \(-0.872269\pi\) | ||
0.920562 | − | 0.390597i | \(-0.127731\pi\) | |||||||
\(824\) | 2.86345e11 | 0.621128 | ||||||||
\(825\) | 1.83980e11i | 0.397151i | ||||||||
\(826\) | −1.41714e11 | + | 3.01982e11i | −0.304433 | + | 0.648726i | ||||
\(827\) | −6.11608e11 | −1.30753 | −0.653765 | − | 0.756698i | \(-0.726811\pi\) | ||||
−0.653765 | + | 0.756698i | \(0.726811\pi\) | |||||||
\(828\) | 4.37025e10i | 0.0929790i | ||||||||
\(829\) | 5.97260e11 | 1.26458 | 0.632288 | − | 0.774733i | \(-0.282116\pi\) | ||||
0.632288 | + | 0.774733i | \(0.282116\pi\) | |||||||
\(830\) | 6.87754e11 | 1.44917 | ||||||||
\(831\) | 1.71267e11 | 0.359146 | ||||||||
\(832\) | − | 3.43207e10i | − | 0.0716247i | ||||||
\(833\) | 2.99502e11 | 0.622042 | ||||||||
\(834\) | − | 9.86150e9i | − | 0.0203835i | ||||||
\(835\) | −2.81800e11 | −0.579689 | ||||||||
\(836\) | − | 2.77353e11i | − | 0.567817i | ||||||
\(837\) | 9.12320e10i | 0.185885i | ||||||||
\(838\) | 1.01912e12 | 2.06656 | ||||||||
\(839\) | − | 4.51558e10i | − | 0.0911310i | −0.998961 | − | 0.0455655i | \(-0.985491\pi\) | ||
0.998961 | − | 0.0455655i | \(-0.0145090\pi\) | |||||||
\(840\) | 1.36497e11i | 0.274162i | ||||||||
\(841\) | −4.93272e11 | −0.986058 | ||||||||
\(842\) | 6.90174e11 | 1.37312 | ||||||||
\(843\) | −7.16272e9 | −0.0141830 | ||||||||
\(844\) | − | 3.90888e11i | − | 0.770341i | ||||||
\(845\) | 5.50746e11 | 1.08025 | ||||||||
\(846\) | 2.18311e10 | 0.0426181 | ||||||||
\(847\) | −1.70536e11 | −0.331347 | ||||||||
\(848\) | −2.44858e11 | −0.473512 | ||||||||
\(849\) | − | 5.86910e10i | − | 0.112964i | ||||||
\(850\) | − | 3.33232e11i | − | 0.638367i | ||||||
\(851\) | 1.02168e11 | 0.194804 | ||||||||
\(852\) | −2.63312e11 | −0.499704 | ||||||||
\(853\) | −5.44852e11 | −1.02916 | −0.514580 | − | 0.857442i | \(-0.672052\pi\) | ||||
−0.514580 | + | 0.857442i | \(0.672052\pi\) | |||||||
\(854\) | −4.53554e11 | −0.852703 | ||||||||
\(855\) | 2.15529e11 | 0.403312 | ||||||||
\(856\) | − | 2.05258e11i | − | 0.382300i | ||||||
\(857\) | 3.54415e11i | 0.657035i | 0.944498 | + | 0.328517i | \(0.106549\pi\) | ||||
−0.944498 | + | 0.328517i | \(0.893451\pi\) | |||||||
\(858\) | − | 1.72371e11i | − | 0.318064i | ||||||
\(859\) | − | 9.31168e11i | − | 1.71023i | −0.518436 | − | 0.855116i | \(-0.673486\pi\) | ||
0.518436 | − | 0.855116i | \(-0.326514\pi\) | |||||||
\(860\) | 1.40820e11i | 0.257437i | ||||||||
\(861\) | 5.90961e10 | 0.107534 | ||||||||
\(862\) | −1.27030e12 | −2.30078 | ||||||||
\(863\) | 7.96802e11i | 1.43651i | 0.695782 | + | 0.718253i | \(0.255058\pi\) | ||||
−0.695782 | + | 0.718253i | \(0.744942\pi\) | |||||||
\(864\) | − | 9.31396e10i | − | 0.167140i | ||||||
\(865\) | 4.36315e11i | 0.779356i | ||||||||
\(866\) | 7.87521e11i | 1.40020i | ||||||||
\(867\) | −2.76031e10 | −0.0488518 | ||||||||
\(868\) | − | 1.51728e11i | − | 0.267292i | ||||||
\(869\) | − | 2.87555e11i | − | 0.504245i | ||||||
\(870\) | − | 5.89224e10i | − | 0.102850i | ||||||
\(871\) | −6.81070e10 | −0.118337 | ||||||||
\(872\) | 6.37158e10 | 0.110200 | ||||||||
\(873\) | 1.60841e10i | 0.0276912i | ||||||||
\(874\) | 4.09515e11 | 0.701818 | ||||||||
\(875\) | −1.93981e11 | −0.330923 | ||||||||
\(876\) | − | 8.47787e10i | − | 0.143969i | ||||||
\(877\) | −8.36090e11 | −1.41337 | −0.706683 | − | 0.707530i | \(-0.749809\pi\) | ||||
−0.706683 | + | 0.707530i | \(0.749809\pi\) | |||||||
\(878\) | 2.34539e11i | 0.394672i | ||||||||
\(879\) | −2.33528e10 | −0.0391185 | ||||||||
\(880\) | − | 1.16503e12i | − | 1.94271i | ||||||
\(881\) | − | 3.67142e11i | − | 0.609440i | −0.952442 | − | 0.304720i | \(-0.901437\pi\) | ||
0.952442 | − | 0.304720i | \(-0.0985629\pi\) | |||||||
\(882\) | − | 1.58896e11i | − | 0.262566i | ||||||
\(883\) | 7.40515e11 | 1.21812 | 0.609062 | − | 0.793123i | \(-0.291546\pi\) | ||||
0.609062 | + | 0.793123i | \(0.291546\pi\) | |||||||
\(884\) | 9.95117e10i | 0.162954i | ||||||||
\(885\) | 3.99263e11 | + | 1.87366e11i | 0.650857 | + | 0.305433i | ||||
\(886\) | 4.83269e11 | 0.784248 | ||||||||
\(887\) | − | 5.36816e11i | − | 0.867223i | −0.901100 | − | 0.433611i | \(-0.857239\pi\) | ||
0.901100 | − | 0.433611i | \(-0.142761\pi\) | |||||||
\(888\) | −7.56257e10 | −0.121624 | ||||||||
\(889\) | −7.62929e10 | −0.122145 | ||||||||
\(890\) | 1.57778e12 | 2.51470 | ||||||||
\(891\) | 8.74700e10i | 0.138787i | ||||||||
\(892\) | 5.00416e11 | 0.790444 | ||||||||
\(893\) | − | 6.52041e10i | − | 0.102534i | ||||||
\(894\) | 1.32645e11 | 0.207655 | ||||||||
\(895\) | 9.82885e10i | 0.153183i | ||||||||
\(896\) | − | 4.21951e11i | − | 0.654681i | ||||||
\(897\) | 8.11215e10 | 0.125304 | ||||||||
\(898\) | 9.37573e11i | 1.44178i | ||||||||
\(899\) | − | 7.44939e10i | − | 0.114046i | ||||||
\(900\) | −5.63502e10 | −0.0858865 | ||||||||
\(901\) | −2.39046e11 | −0.362729 | ||||||||
\(902\) | −3.15449e11 | −0.476544 | ||||||||
\(903\) | − | 1.00325e11i | − | 0.150890i | ||||||
\(904\) | −4.09663e11 | −0.613413 | ||||||||
\(905\) | 9.42834e11 | 1.40553 | ||||||||
\(906\) | −1.57305e11 | −0.233470 | ||||||||
\(907\) | 9.73005e11 | 1.43776 | 0.718879 | − | 0.695135i | \(-0.244655\pi\) | ||||
0.718879 | + | 0.695135i | \(0.244655\pi\) | |||||||
\(908\) | 5.68255e10i | 0.0835988i | ||||||||
\(909\) | 2.77087e10i | 0.0405845i | ||||||||
\(910\) | −2.22769e11 | −0.324854 | ||||||||
\(911\) | −5.88576e11 | −0.854533 | −0.427266 | − | 0.904126i | \(-0.640523\pi\) | ||||
−0.427266 | + | 0.904126i | \(0.640523\pi\) | |||||||
\(912\) | −4.84693e11 | −0.700627 | ||||||||
\(913\) | 8.33654e11 | 1.19978 | ||||||||
\(914\) | 2.36762e11 | 0.339256 | ||||||||
\(915\) | 5.99662e11i | 0.855504i | ||||||||
\(916\) | 4.23781e10i | 0.0601949i | ||||||||
\(917\) | − | 4.67666e11i | − | 0.661391i | ||||||
\(918\) | − | 1.58429e11i | − | 0.223081i | ||||||
\(919\) | 2.59564e11i | 0.363900i | 0.983308 | + | 0.181950i | \(0.0582409\pi\) | ||||
−0.983308 | + | 0.181950i | \(0.941759\pi\) | |||||||
\(920\) | 3.42899e11 | 0.478647 | ||||||||
\(921\) | −9.77895e10 | −0.135911 | ||||||||
\(922\) | 2.03585e11i | 0.281723i | ||||||||
\(923\) | 4.88766e11i | 0.673433i | ||||||||
\(924\) | − | 1.45471e11i | − | 0.199567i | ||||||
\(925\) | 1.31736e11i | 0.179945i | ||||||||
\(926\) | 3.57053e11 | 0.485611 | ||||||||
\(927\) | − | 2.37145e11i | − | 0.321141i | ||||||
\(928\) | 7.60515e10i | 0.102545i | ||||||||
\(929\) | − | 3.64709e10i | − | 0.0489647i | −0.999700 | − | 0.0244824i | \(-0.992206\pi\) | ||
0.999700 | − | 0.0244824i | \(-0.00779375\pi\) | |||||||
\(930\) | −6.29372e11 | −0.841347 | ||||||||
\(931\) | −4.74583e11 | −0.631704 | ||||||||
\(932\) | 5.44318e11i | 0.721421i | ||||||||
\(933\) | −2.00170e11 | −0.264164 | ||||||||
\(934\) | 1.16226e12 | 1.52727 | ||||||||
\(935\) | − | 1.13738e12i | − | 1.48819i | ||||||
\(936\) | −6.00466e10 | −0.0782321 | ||||||||
\(937\) | − | 3.56507e11i | − | 0.462498i | −0.972895 | − | 0.231249i | \(-0.925719\pi\) | ||
0.972895 | − | 0.231249i | \(-0.0742813\pi\) | |||||||
\(938\) | −1.80330e11 | −0.232947 | ||||||||
\(939\) | − | 4.59367e10i | − | 0.0590877i | ||||||
\(940\) | 4.80032e10i | 0.0614836i | ||||||||
\(941\) | − | 6.01164e11i | − | 0.766715i | −0.923600 | − | 0.383358i | \(-0.874768\pi\) | ||
0.923600 | − | 0.383358i | \(-0.125232\pi\) | |||||||
\(942\) | −7.00129e11 | −0.889149 | ||||||||
\(943\) | − | 1.48457e11i | − | 0.187739i | ||||||
\(944\) | −8.97883e11 | − | 4.21357e11i | −1.13066 | − | 0.530594i | ||||
\(945\) | 1.13044e11 | 0.141749 | ||||||||
\(946\) | 5.35528e11i | 0.668678i | ||||||||
\(947\) | −1.20108e12 | −1.49339 | −0.746695 | − | 0.665166i | \(-0.768361\pi\) | ||||
−0.746695 | + | 0.665166i | \(0.768361\pi\) | |||||||
\(948\) | 8.80733e10 | 0.109046 | ||||||||
\(949\) | −1.57368e11 | −0.194022 | ||||||||
\(950\) | 5.28031e11i | 0.648283i | ||||||||
\(951\) | 3.12091e11 | 0.381557 | ||||||||
\(952\) | − | 2.99676e11i | − | 0.364841i | ||||||
\(953\) | −1.02787e12 | −1.24614 | −0.623069 | − | 0.782167i | \(-0.714114\pi\) | ||||
−0.623069 | + | 0.782167i | \(0.714114\pi\) | |||||||
\(954\) | 1.26822e11i | 0.153109i | ||||||||
\(955\) | − | 6.18667e11i | − | 0.743778i | ||||||
\(956\) | 4.65364e10 | 0.0557136 | ||||||||
\(957\) | − | 7.14221e10i | − | 0.0851501i | ||||||
\(958\) | − | 1.40237e12i | − | 1.66495i | ||||||
\(959\) | −8.06509e11 | −0.953530 | ||||||||
\(960\) | −1.20146e11 | −0.141458 | ||||||||
\(961\) | 5.71940e10 | 0.0670590 | ||||||||
\(962\) | − | 1.23424e11i | − | 0.144112i | ||||||
\(963\) | −1.69990e11 | −0.197660 | ||||||||
\(964\) | −5.03524e11 | −0.583058 | ||||||||
\(965\) | −3.17531e11 | −0.366165 | ||||||||
\(966\) | 2.14790e11 | 0.246663 | ||||||||
\(967\) | − | 1.12223e12i | − | 1.28344i | −0.766938 | − | 0.641721i | \(-0.778221\pi\) | ||
0.766938 | − | 0.641721i | \(-0.221779\pi\) | |||||||
\(968\) | − | 3.17112e11i | − | 0.361169i | ||||||
\(969\) | −4.73187e11 | −0.536708 | ||||||||
\(970\) | −1.10958e11 | −0.125335 | ||||||||
\(971\) | 5.95508e11 | 0.669901 | 0.334951 | − | 0.942236i | \(-0.391280\pi\) | ||||
0.334951 | + | 0.942236i | \(0.391280\pi\) | |||||||
\(972\) | −2.67906e10 | −0.0300136 | ||||||||
\(973\) | −1.54485e10 | −0.0172359 | ||||||||
\(974\) | 2.59368e11i | 0.288191i | ||||||||
\(975\) | 1.04598e11i | 0.115746i | ||||||||
\(976\) | − | 1.34855e12i | − | 1.48617i | ||||||
\(977\) | − | 1.58558e12i | − | 1.74024i | −0.492836 | − | 0.870122i | \(-0.664040\pi\) | ||
0.492836 | − | 0.870122i | \(-0.335960\pi\) | |||||||
\(978\) | 9.50002e11i | 1.03841i | ||||||||
\(979\) | 1.91249e12 | 2.08194 | ||||||||
\(980\) | 3.49388e11 | 0.378795 | ||||||||
\(981\) | − | 5.27681e10i | − | 0.0569765i | ||||||
\(982\) | 1.37097e12i | 1.47429i | ||||||||
\(983\) | − | 1.00115e12i | − | 1.07223i | −0.844146 | − | 0.536114i | \(-0.819892\pi\) | ||
0.844146 | − | 0.536114i | \(-0.180108\pi\) | |||||||
\(984\) | 1.09889e11i | 0.117212i | ||||||||
\(985\) | 1.54533e12 | 1.64164 | ||||||||
\(986\) | 1.29362e11i | 0.136867i | ||||||||
\(987\) | − | 3.41993e10i | − | 0.0360370i | ||||||
\(988\) | − | 1.57684e11i | − | 0.165485i | ||||||
\(989\) | −2.52031e11 | −0.263432 | ||||||||
\(990\) | −6.03419e11 | −0.628172 | ||||||||
\(991\) | 5.23823e11i | 0.543113i | 0.962422 | + | 0.271557i | \(0.0875384\pi\) | ||||
−0.962422 | + | 0.271557i | \(0.912462\pi\) | |||||||
\(992\) | 8.12335e11 | 0.838858 | ||||||||
\(993\) | 7.08352e11 | 0.728538 | ||||||||
\(994\) | 1.29413e12i | 1.32566i | ||||||||
\(995\) | 6.38510e10 | 0.0651442 | ||||||||
\(996\) | 2.55335e11i | 0.259461i | ||||||||
\(997\) | −8.96073e11 | −0.906907 | −0.453454 | − | 0.891280i | \(-0.649808\pi\) | ||||
−0.453454 | + | 0.891280i | \(0.649808\pi\) | |||||||
\(998\) | − | 1.19024e12i | − | 1.19981i | ||||||
\(999\) | 6.26317e10i | 0.0628828i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.9.c.a.58.62 | yes | 80 | |
59.58 | odd | 2 | inner | 177.9.c.a.58.19 | ✓ | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.9.c.a.58.19 | ✓ | 80 | 59.58 | odd | 2 | inner | |
177.9.c.a.58.62 | yes | 80 | 1.1 | even | 1 | trivial |