Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,10,Mod(36,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.36");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.b (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: | \(19.0563259381\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 36.17 | ||
Character | \(\chi\) | \(=\) | 37.36 |
Dual form | 37.10.b.a.36.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.6764i | 0.471834i | 0.971773 | + | 0.235917i | \(0.0758094\pi\) | ||||
−0.971773 | + | 0.235917i | \(0.924191\pi\) | |||||||
\(3\) | 115.620 | 0.824113 | 0.412057 | − | 0.911158i | \(-0.364811\pi\) | ||||
0.412057 | + | 0.911158i | \(0.364811\pi\) | |||||||
\(4\) | 398.015 | 0.777372 | ||||||||
\(5\) | 1685.85i | 1.20629i | 0.797631 | + | 0.603146i | \(0.206086\pi\) | ||||
−0.797631 | + | 0.603146i | \(0.793914\pi\) | |||||||
\(6\) | 1234.40i | 0.388845i | ||||||||
\(7\) | −9624.92 | −1.51515 | −0.757576 | − | 0.652747i | \(-0.773616\pi\) | ||||
−0.757576 | + | 0.652747i | \(0.773616\pi\) | |||||||
\(8\) | 9715.67i | 0.838625i | ||||||||
\(9\) | −6315.04 | −0.320837 | ||||||||
\(10\) | −17998.7 | −0.569170 | ||||||||
\(11\) | −16164.1 | −0.332878 | −0.166439 | − | 0.986052i | \(-0.553227\pi\) | ||||
−0.166439 | + | 0.986052i | \(0.553227\pi\) | |||||||
\(12\) | 46018.4 | 0.640643 | ||||||||
\(13\) | 24672.3i | 0.239588i | 0.992799 | + | 0.119794i | \(0.0382234\pi\) | ||||
−0.992799 | + | 0.119794i | \(0.961777\pi\) | |||||||
\(14\) | − | 102759.i | − | 0.714900i | ||||||
\(15\) | 194917.i | 0.994122i | ||||||||
\(16\) | 100055. | 0.381680 | ||||||||
\(17\) | 147281.i | 0.427686i | 0.976868 | + | 0.213843i | \(0.0685982\pi\) | ||||
−0.976868 | + | 0.213843i | \(0.931402\pi\) | |||||||
\(18\) | − | 67421.8i | − | 0.151382i | ||||||
\(19\) | 230280.i | 0.405383i | 0.979243 | + | 0.202691i | \(0.0649688\pi\) | ||||
−0.979243 | + | 0.202691i | \(0.935031\pi\) | |||||||
\(20\) | 670991.i | 0.937739i | ||||||||
\(21\) | −1.11283e6 | −1.24866 | ||||||||
\(22\) | − | 172575.i | − | 0.157063i | ||||||
\(23\) | − | 1.76570e6i | − | 1.31565i | −0.753169 | − | 0.657827i | \(-0.771476\pi\) | ||
0.753169 | − | 0.657827i | \(-0.228524\pi\) | |||||||
\(24\) | 1.12332e6i | 0.691122i | ||||||||
\(25\) | −888949. | −0.455142 | ||||||||
\(26\) | −263411. | −0.113046 | ||||||||
\(27\) | −3.00589e6 | −1.08852 | ||||||||
\(28\) | −3.83086e6 | −1.17784 | ||||||||
\(29\) | − | 890190.i | − | 0.233718i | −0.993149 | − | 0.116859i | \(-0.962717\pi\) | ||
0.993149 | − | 0.116859i | \(-0.0372825\pi\) | |||||||
\(30\) | −2.08101e6 | −0.469061 | ||||||||
\(31\) | 8.56024e6i | 1.66479i | 0.554186 | + | 0.832393i | \(0.313030\pi\) | ||||
−0.554186 | + | 0.832393i | \(0.686970\pi\) | |||||||
\(32\) | 6.04265e6i | 1.01872i | ||||||||
\(33\) | −1.86890e6 | −0.274330 | ||||||||
\(34\) | −1.57242e6 | −0.201797 | ||||||||
\(35\) | − | 1.62261e7i | − | 1.82772i | ||||||
\(36\) | −2.51348e6 | −0.249410 | ||||||||
\(37\) | 1.01662e7 | + | 5.15847e6i | 0.891767 | + | 0.452495i | ||||
\(38\) | −2.45856e6 | −0.191273 | ||||||||
\(39\) | 2.85261e6i | 0.197448i | ||||||||
\(40\) | −1.63791e7 | −1.01163 | ||||||||
\(41\) | 1.71308e6 | 0.0946781 | 0.0473391 | − | 0.998879i | \(-0.484926\pi\) | ||||
0.0473391 | + | 0.998879i | \(0.484926\pi\) | |||||||
\(42\) | − | 1.18810e7i | − | 0.589159i | ||||||
\(43\) | 3.12746e7i | 1.39503i | 0.716571 | + | 0.697514i | \(0.245711\pi\) | ||||
−0.716571 | + | 0.697514i | \(0.754289\pi\) | |||||||
\(44\) | −6.43357e6 | −0.258771 | ||||||||
\(45\) | − | 1.06462e7i | − | 0.387024i | ||||||
\(46\) | 1.88513e7 | 0.620771 | ||||||||
\(47\) | −364635. | −0.0108998 | −0.00544990 | − | 0.999985i | \(-0.501735\pi\) | ||||
−0.00544990 | + | 0.999985i | \(0.501735\pi\) | |||||||
\(48\) | 1.15684e7 | 0.314548 | ||||||||
\(49\) | 5.22855e7 | 1.29568 | ||||||||
\(50\) | − | 9.49077e6i | − | 0.214751i | ||||||
\(51\) | 1.70286e7i | 0.352462i | ||||||||
\(52\) | 9.81995e6i | 0.186249i | ||||||||
\(53\) | 3.78264e7 | 0.658498 | 0.329249 | − | 0.944243i | \(-0.393205\pi\) | ||||
0.329249 | + | 0.944243i | \(0.393205\pi\) | |||||||
\(54\) | − | 3.20921e7i | − | 0.513601i | ||||||
\(55\) | − | 2.72502e7i | − | 0.401549i | ||||||
\(56\) | − | 9.35126e7i | − | 1.27064i | ||||||
\(57\) | 2.66250e7i | 0.334081i | ||||||||
\(58\) | 9.50401e6 | 0.110276 | ||||||||
\(59\) | 5.36210e7i | 0.576104i | 0.957615 | + | 0.288052i | \(0.0930076\pi\) | ||||
−0.957615 | + | 0.288052i | \(0.906992\pi\) | |||||||
\(60\) | 7.75799e7i | 0.772803i | ||||||||
\(61\) | − | 1.73097e8i | − | 1.60068i | −0.599545 | − | 0.800341i | \(-0.704652\pi\) | ||
0.599545 | − | 0.800341i | \(-0.295348\pi\) | |||||||
\(62\) | −9.13925e7 | −0.785503 | ||||||||
\(63\) | 6.07818e7 | 0.486117 | ||||||||
\(64\) | −1.32854e7 | −0.0989841 | ||||||||
\(65\) | −4.15937e7 | −0.289013 | ||||||||
\(66\) | − | 1.99531e7i | − | 0.129438i | ||||||
\(67\) | 2.21851e8 | 1.34501 | 0.672504 | − | 0.740094i | \(-0.265219\pi\) | ||||
0.672504 | + | 0.740094i | \(0.265219\pi\) | |||||||
\(68\) | 5.86198e7i | 0.332472i | ||||||||
\(69\) | − | 2.04150e8i | − | 1.08425i | ||||||
\(70\) | 1.73236e8 | 0.862379 | ||||||||
\(71\) | −2.59349e7 | −0.121122 | −0.0605608 | − | 0.998165i | \(-0.519289\pi\) | ||||
−0.0605608 | + | 0.998165i | \(0.519289\pi\) | |||||||
\(72\) | − | 6.13548e7i | − | 0.269062i | ||||||
\(73\) | 8.14841e7 | 0.335830 | 0.167915 | − | 0.985801i | \(-0.446297\pi\) | ||||
0.167915 | + | 0.985801i | \(0.446297\pi\) | |||||||
\(74\) | −5.50739e7 | + | 1.08538e8i | −0.213502 | + | 0.420766i | ||||
\(75\) | −1.02780e8 | −0.375088 | ||||||||
\(76\) | 9.16549e7i | 0.315133i | ||||||||
\(77\) | 1.55579e8 | 0.504361 | ||||||||
\(78\) | −3.04556e7 | −0.0931626 | ||||||||
\(79\) | 5.33481e8i | 1.54098i | 0.637452 | + | 0.770490i | \(0.279988\pi\) | ||||
−0.637452 | + | 0.770490i | \(0.720012\pi\) | |||||||
\(80\) | 1.68678e8i | 0.460418i | ||||||||
\(81\) | −2.23242e8 | −0.576226 | ||||||||
\(82\) | 1.82895e7i | 0.0446724i | ||||||||
\(83\) | −4.93765e8 | −1.14201 | −0.571004 | − | 0.820947i | \(-0.693446\pi\) | ||||
−0.571004 | + | 0.820947i | \(0.693446\pi\) | |||||||
\(84\) | −4.42924e8 | −0.970671 | ||||||||
\(85\) | −2.48292e8 | −0.515915 | ||||||||
\(86\) | −3.33899e8 | −0.658222 | ||||||||
\(87\) | − | 1.02924e8i | − | 0.192610i | ||||||
\(88\) | − | 1.57046e8i | − | 0.279160i | ||||||
\(89\) | 2.88383e8i | 0.487208i | 0.969875 | + | 0.243604i | \(0.0783296\pi\) | ||||
−0.969875 | + | 0.243604i | \(0.921670\pi\) | |||||||
\(90\) | 1.13663e8 | 0.182611 | ||||||||
\(91\) | − | 2.37469e8i | − | 0.363012i | ||||||
\(92\) | − | 7.02775e8i | − | 1.02275i | ||||||
\(93\) | 9.89734e8i | 1.37197i | ||||||||
\(94\) | − | 3.89299e6i | − | 0.00514290i | ||||||
\(95\) | −3.88217e8 | −0.489010 | ||||||||
\(96\) | 6.98651e8i | 0.839537i | ||||||||
\(97\) | − | 7.11545e8i | − | 0.816074i | −0.912965 | − | 0.408037i | \(-0.866213\pi\) | ||
0.912965 | − | 0.408037i | \(-0.133787\pi\) | |||||||
\(98\) | 5.58221e8i | 0.611348i | ||||||||
\(99\) | 1.02077e8 | 0.106800 | ||||||||
\(100\) | −3.53815e8 | −0.353815 | ||||||||
\(101\) | 6.50117e8 | 0.621649 | 0.310824 | − | 0.950467i | \(-0.399395\pi\) | ||||
0.310824 | + | 0.950467i | \(0.399395\pi\) | |||||||
\(102\) | −1.81804e8 | −0.166304 | ||||||||
\(103\) | 4.95305e8i | 0.433616i | 0.976214 | + | 0.216808i | \(0.0695645\pi\) | ||||
−0.976214 | + | 0.216808i | \(0.930435\pi\) | |||||||
\(104\) | −2.39708e8 | −0.200925 | ||||||||
\(105\) | − | 1.87606e9i | − | 1.50625i | ||||||
\(106\) | 4.03850e8i | 0.310702i | ||||||||
\(107\) | 2.43701e9 | 1.79734 | 0.898671 | − | 0.438624i | \(-0.144534\pi\) | ||||
0.898671 | + | 0.438624i | \(0.144534\pi\) | |||||||
\(108\) | −1.19639e9 | −0.846185 | ||||||||
\(109\) | − | 1.19477e9i | − | 0.810707i | −0.914160 | − | 0.405353i | \(-0.867148\pi\) | ||
0.914160 | − | 0.405353i | \(-0.132852\pi\) | |||||||
\(110\) | 2.90934e8 | 0.189464 | ||||||||
\(111\) | 1.17542e9 | + | 5.96422e8i | 0.734917 | + | 0.372907i | ||||
\(112\) | −9.63024e8 | −0.578304 | ||||||||
\(113\) | − | 1.89525e9i | − | 1.09349i | −0.837300 | − | 0.546744i | \(-0.815867\pi\) | ||
0.837300 | − | 0.546744i | \(-0.184133\pi\) | |||||||
\(114\) | −2.84259e8 | −0.157631 | ||||||||
\(115\) | 2.97670e9 | 1.58706 | ||||||||
\(116\) | − | 3.54309e8i | − | 0.181686i | ||||||
\(117\) | − | 1.55807e8i | − | 0.0768688i | ||||||
\(118\) | −5.72479e8 | −0.271826 | ||||||||
\(119\) | − | 1.41756e9i | − | 0.648010i | ||||||
\(120\) | −1.89375e9 | −0.833696 | ||||||||
\(121\) | −2.09667e9 | −0.889192 | ||||||||
\(122\) | 1.84805e9 | 0.755257 | ||||||||
\(123\) | 1.98066e8 | 0.0780255 | ||||||||
\(124\) | 3.40710e9i | 1.29416i | ||||||||
\(125\) | 1.79404e9i | 0.657258i | ||||||||
\(126\) | 6.48930e8i | 0.229367i | ||||||||
\(127\) | 4.73617e9 | 1.61551 | 0.807756 | − | 0.589517i | \(-0.200682\pi\) | ||||
0.807756 | + | 0.589517i | \(0.200682\pi\) | |||||||
\(128\) | 2.95200e9i | 0.972011i | ||||||||
\(129\) | 3.61596e9i | 1.14966i | ||||||||
\(130\) | − | 4.44071e8i | − | 0.136366i | ||||||
\(131\) | − | 3.94559e9i | − | 1.17055i | −0.810834 | − | 0.585277i | \(-0.800986\pi\) | ||
0.810834 | − | 0.585277i | \(-0.199014\pi\) | |||||||
\(132\) | −7.43848e8 | −0.213256 | ||||||||
\(133\) | − | 2.21643e9i | − | 0.614216i | ||||||
\(134\) | 2.36857e9i | 0.634620i | ||||||||
\(135\) | − | 5.06747e9i | − | 1.31307i | ||||||
\(136\) | −1.43093e9 | −0.358669 | ||||||||
\(137\) | 4.10595e9 | 0.995799 | 0.497899 | − | 0.867235i | \(-0.334105\pi\) | ||||
0.497899 | + | 0.867235i | \(0.334105\pi\) | |||||||
\(138\) | 2.17959e9 | 0.511585 | ||||||||
\(139\) | 8.60144e8 | 0.195436 | 0.0977179 | − | 0.995214i | \(-0.468846\pi\) | ||||
0.0977179 | + | 0.995214i | \(0.468846\pi\) | |||||||
\(140\) | − | 6.45824e9i | − | 1.42082i | ||||||
\(141\) | −4.21591e7 | −0.00898267 | ||||||||
\(142\) | − | 2.76891e8i | − | 0.0571493i | ||||||
\(143\) | − | 3.98807e8i | − | 0.0797537i | ||||||
\(144\) | −6.31853e8 | −0.122457 | ||||||||
\(145\) | 1.50072e9 | 0.281932 | ||||||||
\(146\) | 8.69956e8i | 0.158456i | ||||||||
\(147\) | 6.04525e9 | 1.06779 | ||||||||
\(148\) | 4.04630e9 | + | 2.05315e9i | 0.693235 | + | 0.351757i | ||||
\(149\) | −1.09266e10 | −1.81613 | −0.908065 | − | 0.418829i | \(-0.862441\pi\) | ||||
−0.908065 | + | 0.418829i | \(0.862441\pi\) | |||||||
\(150\) | − | 1.09732e9i | − | 0.176980i | ||||||
\(151\) | −2.86959e9 | −0.449184 | −0.224592 | − | 0.974453i | \(-0.572105\pi\) | ||||
−0.224592 | + | 0.974453i | \(0.572105\pi\) | |||||||
\(152\) | −2.23733e9 | −0.339964 | ||||||||
\(153\) | − | 9.30083e8i | − | 0.137218i | ||||||
\(154\) | 1.66102e9i | 0.237975i | ||||||||
\(155\) | −1.44312e10 | −2.00822 | ||||||||
\(156\) | 1.13538e9i | 0.153490i | ||||||||
\(157\) | −4.96979e9 | −0.652815 | −0.326407 | − | 0.945229i | \(-0.605838\pi\) | ||||
−0.326407 | + | 0.945229i | \(0.605838\pi\) | |||||||
\(158\) | −5.69565e9 | −0.727087 | ||||||||
\(159\) | 4.37349e9 | 0.542677 | ||||||||
\(160\) | −1.01870e10 | −1.22887 | ||||||||
\(161\) | 1.69947e10i | 1.99342i | ||||||||
\(162\) | − | 2.38342e9i | − | 0.271883i | ||||||
\(163\) | 1.66773e10i | 1.85047i | 0.379392 | + | 0.925236i | \(0.376133\pi\) | ||||
−0.379392 | + | 0.925236i | \(0.623867\pi\) | |||||||
\(164\) | 6.81830e8 | 0.0736002 | ||||||||
\(165\) | − | 3.15067e9i | − | 0.330922i | ||||||
\(166\) | − | 5.27163e9i | − | 0.538838i | ||||||
\(167\) | 4.95826e8i | 0.0493293i | 0.999696 | + | 0.0246646i | \(0.00785180\pi\) | ||||
−0.999696 | + | 0.0246646i | \(0.992148\pi\) | |||||||
\(168\) | − | 1.08119e10i | − | 1.04715i | ||||||
\(169\) | 9.99578e9 | 0.942598 | ||||||||
\(170\) | − | 2.65087e9i | − | 0.243426i | ||||||
\(171\) | − | 1.45423e9i | − | 0.130062i | ||||||
\(172\) | 1.24477e10i | 1.08446i | ||||||||
\(173\) | −1.57436e10 | −1.33628 | −0.668138 | − | 0.744038i | \(-0.732908\pi\) | ||||
−0.668138 | + | 0.744038i | \(0.732908\pi\) | |||||||
\(174\) | 1.09885e9 | 0.0908799 | ||||||||
\(175\) | 8.55607e9 | 0.689609 | ||||||||
\(176\) | −1.61731e9 | −0.127053 | ||||||||
\(177\) | 6.19966e9i | 0.474775i | ||||||||
\(178\) | −3.07888e9 | −0.229881 | ||||||||
\(179\) | − | 1.17479e10i | − | 0.855307i | −0.903943 | − | 0.427654i | \(-0.859340\pi\) | ||
0.903943 | − | 0.427654i | \(-0.140660\pi\) | |||||||
\(180\) | − | 4.23734e9i | − | 0.300861i | ||||||
\(181\) | 2.78914e9 | 0.193160 | 0.0965799 | − | 0.995325i | \(-0.469210\pi\) | ||||
0.0965799 | + | 0.995325i | \(0.469210\pi\) | |||||||
\(182\) | 2.53532e9 | 0.171282 | ||||||||
\(183\) | − | 2.00135e10i | − | 1.31914i | ||||||
\(184\) | 1.71550e10 | 1.10334 | ||||||||
\(185\) | −8.69639e9 | + | 1.71387e10i | −0.545841 | + | 1.07573i | ||||
\(186\) | −1.05668e10 | −0.647344 | ||||||||
\(187\) | − | 2.38067e9i | − | 0.142368i | ||||||
\(188\) | −1.45130e8 | −0.00847320 | ||||||||
\(189\) | 2.89315e10 | 1.64927 | ||||||||
\(190\) | − | 4.14475e9i | − | 0.230732i | ||||||
\(191\) | 1.59119e10i | 0.865113i | 0.901607 | + | 0.432557i | \(0.142388\pi\) | ||||
−0.901607 | + | 0.432557i | \(0.857612\pi\) | |||||||
\(192\) | −1.53606e9 | −0.0815741 | ||||||||
\(193\) | 2.37920e9i | 0.123431i | 0.998094 | + | 0.0617154i | \(0.0196571\pi\) | ||||
−0.998094 | + | 0.0617154i | \(0.980343\pi\) | |||||||
\(194\) | 7.59673e9 | 0.385051 | ||||||||
\(195\) | −4.80906e9 | −0.238180 | ||||||||
\(196\) | 2.08104e10 | 1.00723 | ||||||||
\(197\) | −4.09579e9 | −0.193749 | −0.0968745 | − | 0.995297i | \(-0.530885\pi\) | ||||
−0.0968745 | + | 0.995297i | \(0.530885\pi\) | |||||||
\(198\) | 1.08982e9i | 0.0503918i | ||||||||
\(199\) | − | 3.64147e10i | − | 1.64603i | −0.568021 | − | 0.823014i | \(-0.692291\pi\) | ||
0.568021 | − | 0.823014i | \(-0.307709\pi\) | |||||||
\(200\) | − | 8.63674e9i | − | 0.381693i | ||||||
\(201\) | 2.56504e10 | 1.10844 | ||||||||
\(202\) | 6.94090e9i | 0.293315i | ||||||||
\(203\) | 8.56801e9i | 0.354118i | ||||||||
\(204\) | 6.77762e9i | 0.273994i | ||||||||
\(205\) | 2.88798e9i | 0.114210i | ||||||||
\(206\) | −5.28807e9 | −0.204595 | ||||||||
\(207\) | 1.11505e10i | 0.422111i | ||||||||
\(208\) | 2.46860e9i | 0.0914461i | ||||||||
\(209\) | − | 3.72228e9i | − | 0.134943i | ||||||
\(210\) | 2.00296e10 | 0.710698 | ||||||||
\(211\) | −2.30030e10 | −0.798937 | −0.399469 | − | 0.916747i | \(-0.630805\pi\) | ||||
−0.399469 | + | 0.916747i | \(0.630805\pi\) | |||||||
\(212\) | 1.50555e10 | 0.511898 | ||||||||
\(213\) | −2.99859e9 | −0.0998179 | ||||||||
\(214\) | 2.60185e10i | 0.848047i | ||||||||
\(215\) | −5.27241e10 | −1.68281 | ||||||||
\(216\) | − | 2.92042e10i | − | 0.912860i | ||||||
\(217\) | − | 8.23917e10i | − | 2.52240i | ||||||
\(218\) | 1.27558e10 | 0.382519 | ||||||||
\(219\) | 9.42118e9 | 0.276762 | ||||||||
\(220\) | − | 1.08460e10i | − | 0.312153i | ||||||
\(221\) | −3.63376e9 | −0.102469 | ||||||||
\(222\) | −6.36764e9 | + | 1.25492e10i | −0.175950 | + | 0.346759i | ||||
\(223\) | −1.22759e10 | −0.332416 | −0.166208 | − | 0.986091i | \(-0.553152\pi\) | ||||
−0.166208 | + | 0.986091i | \(0.553152\pi\) | |||||||
\(224\) | − | 5.81601e10i | − | 1.54351i | ||||||
\(225\) | 5.61375e9 | 0.146026 | ||||||||
\(226\) | 2.02345e10 | 0.515945 | ||||||||
\(227\) | 4.46746e10i | 1.11672i | 0.829599 | + | 0.558360i | \(0.188569\pi\) | ||||
−0.829599 | + | 0.558360i | \(0.811431\pi\) | |||||||
\(228\) | 1.05971e10i | 0.259706i | ||||||||
\(229\) | −6.91514e9 | −0.166166 | −0.0830828 | − | 0.996543i | \(-0.526477\pi\) | ||||
−0.0830828 | + | 0.996543i | \(0.526477\pi\) | |||||||
\(230\) | 3.17804e10i | 0.748831i | ||||||||
\(231\) | 1.79880e10 | 0.415651 | ||||||||
\(232\) | 8.64879e9 | 0.196001 | ||||||||
\(233\) | 1.97668e10 | 0.439374 | 0.219687 | − | 0.975570i | \(-0.429496\pi\) | ||||
0.219687 | + | 0.975570i | \(0.429496\pi\) | |||||||
\(234\) | 1.66345e9 | 0.0362693 | ||||||||
\(235\) | − | 6.14719e8i | − | 0.0131483i | ||||||
\(236\) | 2.13420e10i | 0.447847i | ||||||||
\(237\) | 6.16810e10i | 1.26994i | ||||||||
\(238\) | 1.51345e10 | 0.305753 | ||||||||
\(239\) | 3.96171e10i | 0.785402i | 0.919666 | + | 0.392701i | \(0.128459\pi\) | ||||
−0.919666 | + | 0.392701i | \(0.871541\pi\) | |||||||
\(240\) | 1.95025e10i | 0.379437i | ||||||||
\(241\) | − | 5.37515e10i | − | 1.02639i | −0.858271 | − | 0.513197i | \(-0.828461\pi\) | ||
0.858271 | − | 0.513197i | \(-0.171539\pi\) | |||||||
\(242\) | − | 2.23848e10i | − | 0.419551i | ||||||
\(243\) | 3.33537e10 | 0.613644 | ||||||||
\(244\) | − | 6.88951e10i | − | 1.24433i | ||||||
\(245\) | 8.81453e10i | 1.56297i | ||||||||
\(246\) | 2.11463e9i | 0.0368151i | ||||||||
\(247\) | −5.68155e9 | −0.0971249 | ||||||||
\(248\) | −8.31685e10 | −1.39613 | ||||||||
\(249\) | −5.70891e10 | −0.941144 | ||||||||
\(250\) | −1.91538e10 | −0.310117 | ||||||||
\(251\) | 5.46783e10i | 0.869528i | 0.900544 | + | 0.434764i | \(0.143168\pi\) | ||||
−0.900544 | + | 0.434764i | \(0.856832\pi\) | |||||||
\(252\) | 2.41920e10 | 0.377894 | ||||||||
\(253\) | 2.85410e10i | 0.437953i | ||||||||
\(254\) | 5.05652e10i | 0.762254i | ||||||||
\(255\) | −2.87075e10 | −0.425172 | ||||||||
\(256\) | −3.83188e10 | −0.557612 | ||||||||
\(257\) | − | 1.00641e11i | − | 1.43904i | −0.694470 | − | 0.719522i | \(-0.744361\pi\) | ||
0.694470 | − | 0.719522i | \(-0.255639\pi\) | |||||||
\(258\) | −3.86054e10 | −0.542450 | ||||||||
\(259\) | −9.78490e10 | − | 4.96499e10i | −1.35116 | − | 0.685598i | ||||
\(260\) | −1.65549e10 | −0.224671 | ||||||||
\(261\) | 5.62158e9i | 0.0749853i | ||||||||
\(262\) | 4.21247e10 | 0.552307 | ||||||||
\(263\) | −1.22367e11 | −1.57711 | −0.788556 | − | 0.614963i | \(-0.789171\pi\) | ||||
−0.788556 | + | 0.614963i | \(0.789171\pi\) | |||||||
\(264\) | − | 1.81576e10i | − | 0.230060i | ||||||
\(265\) | 6.37695e10i | 0.794341i | ||||||||
\(266\) | 2.36635e10 | 0.289808 | ||||||||
\(267\) | 3.33428e10i | 0.401514i | ||||||||
\(268\) | 8.82999e10 | 1.04557 | ||||||||
\(269\) | −1.07814e11 | −1.25542 | −0.627712 | − | 0.778445i | \(-0.716009\pi\) | ||||
−0.627712 | + | 0.778445i | \(0.716009\pi\) | |||||||
\(270\) | 5.41022e10 | 0.619553 | ||||||||
\(271\) | 1.00479e11 | 1.13166 | 0.565829 | − | 0.824522i | \(-0.308556\pi\) | ||||
0.565829 | + | 0.824522i | \(0.308556\pi\) | |||||||
\(272\) | 1.47362e10i | 0.163240i | ||||||||
\(273\) | − | 2.74562e10i | − | 0.299163i | ||||||
\(274\) | 4.38368e10i | 0.469852i | ||||||||
\(275\) | 1.43691e10 | 0.151507 | ||||||||
\(276\) | − | 8.12547e10i | − | 0.842865i | ||||||
\(277\) | 2.90794e10i | 0.296774i | 0.988929 | + | 0.148387i | \(0.0474081\pi\) | ||||
−0.988929 | + | 0.148387i | \(0.952592\pi\) | |||||||
\(278\) | 9.18323e9i | 0.0922133i | ||||||||
\(279\) | − | 5.40583e10i | − | 0.534125i | ||||||
\(280\) | 1.57648e11 | 1.53277 | ||||||||
\(281\) | − | 1.02968e11i | − | 0.985203i | −0.870255 | − | 0.492602i | \(-0.836046\pi\) | ||
0.870255 | − | 0.492602i | \(-0.163954\pi\) | |||||||
\(282\) | − | 4.50107e8i | − | 0.00423833i | ||||||
\(283\) | 1.60431e11i | 1.48679i | 0.668853 | + | 0.743395i | \(0.266786\pi\) | ||||
−0.668853 | + | 0.743395i | \(0.733214\pi\) | |||||||
\(284\) | −1.03225e10 | −0.0941566 | ||||||||
\(285\) | −4.48856e10 | −0.403000 | ||||||||
\(286\) | 4.25782e9 | 0.0376305 | ||||||||
\(287\) | −1.64882e10 | −0.143452 | ||||||||
\(288\) | − | 3.81596e10i | − | 0.326842i | ||||||
\(289\) | 9.68963e10 | 0.817084 | ||||||||
\(290\) | 1.60223e10i | 0.133025i | ||||||||
\(291\) | − | 8.22687e10i | − | 0.672537i | ||||||
\(292\) | 3.24319e10 | 0.261065 | ||||||||
\(293\) | −1.84405e11 | −1.46173 | −0.730866 | − | 0.682520i | \(-0.760884\pi\) | ||||
−0.730866 | + | 0.682520i | \(0.760884\pi\) | |||||||
\(294\) | 6.45414e10i | 0.503820i | ||||||||
\(295\) | −9.03967e10 | −0.694950 | ||||||||
\(296\) | −5.01180e10 | + | 9.87716e10i | −0.379473 | + | 0.747858i | ||||
\(297\) | 4.85877e10 | 0.362345 | ||||||||
\(298\) | − | 1.16657e11i | − | 0.856912i | ||||||
\(299\) | 4.35640e10 | 0.315215 | ||||||||
\(300\) | −4.09080e10 | −0.291583 | ||||||||
\(301\) | − | 3.01015e11i | − | 2.11368i | ||||||
\(302\) | − | 3.06369e10i | − | 0.211940i | ||||||
\(303\) | 7.51664e10 | 0.512309 | ||||||||
\(304\) | 2.30407e10i | 0.154727i | ||||||||
\(305\) | 2.91815e11 | 1.93089 | ||||||||
\(306\) | 9.92992e9 | 0.0647440 | ||||||||
\(307\) | 1.71467e11 | 1.10169 | 0.550844 | − | 0.834608i | \(-0.314306\pi\) | ||||
0.550844 | + | 0.834608i | \(0.314306\pi\) | |||||||
\(308\) | 6.19226e10 | 0.392077 | ||||||||
\(309\) | 5.72671e10i | 0.357349i | ||||||||
\(310\) | − | 1.54074e11i | − | 0.947546i | ||||||
\(311\) | − | 1.07057e11i | − | 0.648925i | −0.945898 | − | 0.324463i | \(-0.894817\pi\) | ||
0.945898 | − | 0.324463i | \(-0.105183\pi\) | |||||||
\(312\) | −2.77151e10 | −0.165585 | ||||||||
\(313\) | 6.35488e10i | 0.374247i | 0.982336 | + | 0.187123i | \(0.0599164\pi\) | ||||
−0.982336 | + | 0.187123i | \(0.940084\pi\) | |||||||
\(314\) | − | 5.30594e10i | − | 0.308020i | ||||||
\(315\) | 1.02469e11i | 0.586399i | ||||||||
\(316\) | 2.12333e11i | 1.19792i | ||||||||
\(317\) | 2.89454e11 | 1.60995 | 0.804975 | − | 0.593309i | \(-0.202179\pi\) | ||||
0.804975 | + | 0.593309i | \(0.202179\pi\) | |||||||
\(318\) | 4.66931e10i | 0.256053i | ||||||||
\(319\) | 1.43892e10i | 0.0777996i | ||||||||
\(320\) | − | 2.23972e10i | − | 0.119404i | ||||||
\(321\) | 2.81767e11 | 1.48121 | ||||||||
\(322\) | −1.81442e11 | −0.940562 | ||||||||
\(323\) | −3.39158e10 | −0.173377 | ||||||||
\(324\) | −8.88535e10 | −0.447942 | ||||||||
\(325\) | − | 2.19325e10i | − | 0.109047i | ||||||
\(326\) | −1.78054e11 | −0.873116 | ||||||||
\(327\) | − | 1.38139e11i | − | 0.668114i | ||||||
\(328\) | 1.66437e10i | 0.0793995i | ||||||||
\(329\) | 3.50959e9 | 0.0165148 | ||||||||
\(330\) | 3.36378e10 | 0.156140 | ||||||||
\(331\) | 2.57773e11i | 1.18035i | 0.807275 | + | 0.590176i | \(0.200941\pi\) | ||||
−0.807275 | + | 0.590176i | \(0.799059\pi\) | |||||||
\(332\) | −1.96526e11 | −0.887765 | ||||||||
\(333\) | −6.42000e10 | − | 3.25760e10i | −0.286112 | − | 0.145177i | ||||
\(334\) | −5.29363e9 | −0.0232752 | ||||||||
\(335\) | 3.74006e11i | 1.62247i | ||||||||
\(336\) | −1.11345e11 | −0.476588 | ||||||||
\(337\) | 1.45260e11 | 0.613495 | 0.306747 | − | 0.951791i | \(-0.400759\pi\) | ||||
0.306747 | + | 0.951791i | \(0.400759\pi\) | |||||||
\(338\) | 1.06719e11i | 0.444750i | ||||||||
\(339\) | − | 2.19129e11i | − | 0.901158i | ||||||
\(340\) | −9.88240e10 | −0.401058 | ||||||||
\(341\) | − | 1.38369e11i | − | 0.554171i | ||||||
\(342\) | 1.55259e10 | 0.0613676 | ||||||||
\(343\) | −1.14844e11 | −0.448007 | ||||||||
\(344\) | −3.03853e11 | −1.16991 | ||||||||
\(345\) | 3.44165e11 | 1.30792 | ||||||||
\(346\) | − | 1.68085e11i | − | 0.630500i | ||||||
\(347\) | 3.87660e11i | 1.43538i | 0.696361 | + | 0.717692i | \(0.254801\pi\) | ||||
−0.696361 | + | 0.717692i | \(0.745199\pi\) | |||||||
\(348\) | − | 4.09651e10i | − | 0.149730i | ||||||
\(349\) | −2.14206e11 | −0.772888 | −0.386444 | − | 0.922313i | \(-0.626297\pi\) | ||||
−0.386444 | + | 0.922313i | \(0.626297\pi\) | |||||||
\(350\) | 9.13479e10i | 0.325381i | ||||||||
\(351\) | − | 7.41624e10i | − | 0.260796i | ||||||
\(352\) | − | 9.76743e10i | − | 0.339108i | ||||||
\(353\) | − | 3.23659e11i | − | 1.10943i | −0.832039 | − | 0.554717i | \(-0.812827\pi\) | ||
0.832039 | − | 0.554717i | \(-0.187173\pi\) | |||||||
\(354\) | −6.61899e10 | −0.224015 | ||||||||
\(355\) | − | 4.37222e10i | − | 0.146108i | ||||||
\(356\) | 1.14781e11i | 0.378742i | ||||||||
\(357\) | − | 1.63899e11i | − | 0.534033i | ||||||
\(358\) | 1.25425e11 | 0.403563 | ||||||||
\(359\) | −4.30563e11 | −1.36808 | −0.684040 | − | 0.729444i | \(-0.739779\pi\) | ||||
−0.684040 | + | 0.729444i | \(0.739779\pi\) | |||||||
\(360\) | 1.03435e11 | 0.324568 | ||||||||
\(361\) | 2.69659e11 | 0.835665 | ||||||||
\(362\) | 2.97779e10i | 0.0911394i | ||||||||
\(363\) | −2.42417e11 | −0.732795 | ||||||||
\(364\) | − | 9.45163e10i | − | 0.282196i | ||||||
\(365\) | 1.37370e11i | 0.405110i | ||||||||
\(366\) | 2.13671e11 | 0.622417 | ||||||||
\(367\) | −5.01163e11 | −1.44206 | −0.721028 | − | 0.692906i | \(-0.756330\pi\) | ||||
−0.721028 | + | 0.692906i | \(0.756330\pi\) | |||||||
\(368\) | − | 1.76668e11i | − | 0.502160i | ||||||
\(369\) | −1.08182e10 | −0.0303763 | ||||||||
\(370\) | −1.82979e11 | − | 9.28460e10i | −0.507567 | − | 0.257546i | ||||
\(371\) | −3.64077e11 | −0.997724 | ||||||||
\(372\) | 3.93929e11i | 1.06653i | ||||||||
\(373\) | 3.31574e10 | 0.0886933 | 0.0443466 | − | 0.999016i | \(-0.485879\pi\) | ||||
0.0443466 | + | 0.999016i | \(0.485879\pi\) | |||||||
\(374\) | 2.54169e10 | 0.0671739 | ||||||||
\(375\) | 2.07426e11i | 0.541655i | ||||||||
\(376\) | − | 3.54268e9i | − | 0.00914085i | ||||||
\(377\) | 2.19631e10 | 0.0559960 | ||||||||
\(378\) | 3.08884e11i | 0.778183i | ||||||||
\(379\) | 2.61045e11 | 0.649888 | 0.324944 | − | 0.945733i | \(-0.394654\pi\) | ||||
0.324944 | + | 0.945733i | \(0.394654\pi\) | |||||||
\(380\) | −1.54516e11 | −0.380143 | ||||||||
\(381\) | 5.47595e11 | 1.33136 | ||||||||
\(382\) | −1.69882e11 | −0.408190 | ||||||||
\(383\) | − | 4.44790e11i | − | 1.05624i | −0.849171 | − | 0.528118i | \(-0.822898\pi\) | ||
0.849171 | − | 0.528118i | \(-0.177102\pi\) | |||||||
\(384\) | 3.41310e11i | 0.801047i | ||||||||
\(385\) | 2.62282e11i | 0.608407i | ||||||||
\(386\) | −2.54013e10 | −0.0582388 | ||||||||
\(387\) | − | 1.97500e11i | − | 0.447577i | ||||||
\(388\) | − | 2.83205e11i | − | 0.634393i | ||||||
\(389\) | 3.81235e11i | 0.844150i | 0.906561 | + | 0.422075i | \(0.138698\pi\) | ||||
−0.906561 | + | 0.422075i | \(0.861302\pi\) | |||||||
\(390\) | − | 5.13434e10i | − | 0.112381i | ||||||
\(391\) | 2.60053e11 | 0.562687 | ||||||||
\(392\) | 5.07989e11i | 1.08659i | ||||||||
\(393\) | − | 4.56189e11i | − | 0.964669i | ||||||
\(394\) | − | 4.37282e10i | − | 0.0914174i | ||||||
\(395\) | −8.99366e11 | −1.85887 | ||||||||
\(396\) | 4.06282e10 | 0.0830232 | ||||||||
\(397\) | 6.93446e11 | 1.40106 | 0.700528 | − | 0.713625i | \(-0.252948\pi\) | ||||
0.700528 | + | 0.713625i | \(0.252948\pi\) | |||||||
\(398\) | 3.88777e11 | 0.776652 | ||||||||
\(399\) | − | 2.56263e11i | − | 0.506184i | ||||||
\(400\) | −8.89440e10 | −0.173719 | ||||||||
\(401\) | 5.41091e11i | 1.04501i | 0.852636 | + | 0.522506i | \(0.175003\pi\) | ||||
−0.852636 | + | 0.522506i | \(0.824997\pi\) | |||||||
\(402\) | 2.73853e11i | 0.522999i | ||||||||
\(403\) | −2.11201e11 | −0.398863 | ||||||||
\(404\) | 2.58756e11 | 0.483253 | ||||||||
\(405\) | − | 3.76351e11i | − | 0.695097i | ||||||
\(406\) | −9.14754e10 | −0.167085 | ||||||||
\(407\) | −1.64328e11 | − | 8.33823e10i | −0.296850 | − | 0.150626i | ||||
\(408\) | −1.65444e11 | −0.295584 | ||||||||
\(409\) | 1.15251e8i | 0.000203652i | 1.00000 | 0.000101826i | \(3.24122e-5\pi\) | |||||
−1.00000 | 0.000101826i | \(0.999968\pi\) | ||||||||
\(410\) | −3.08332e10 | −0.0538880 | ||||||||
\(411\) | 4.74730e11 | 0.820651 | ||||||||
\(412\) | 1.97139e11i | 0.337081i | ||||||||
\(413\) | − | 5.16098e11i | − | 0.872885i | ||||||
\(414\) | −1.19047e11 | −0.199166 | ||||||||
\(415\) | − | 8.32412e11i | − | 1.37760i | ||||||
\(416\) | −1.49086e11 | −0.244072 | ||||||||
\(417\) | 9.94497e10 | 0.161061 | ||||||||
\(418\) | 3.97405e10 | 0.0636708 | ||||||||
\(419\) | −1.10931e11 | −0.175829 | −0.0879146 | − | 0.996128i | \(-0.528020\pi\) | ||||
−0.0879146 | + | 0.996128i | \(0.528020\pi\) | |||||||
\(420\) | − | 7.46701e11i | − | 1.17091i | ||||||
\(421\) | 9.56394e11i | 1.48377i | 0.670526 | + | 0.741886i | \(0.266069\pi\) | ||||
−0.670526 | + | 0.741886i | \(0.733931\pi\) | |||||||
\(422\) | − | 2.45589e11i | − | 0.376966i | ||||||
\(423\) | 2.30269e9 | 0.00349706 | ||||||||
\(424\) | 3.67509e11i | 0.552233i | ||||||||
\(425\) | − | 1.30925e11i | − | 0.194658i | ||||||
\(426\) | − | 3.20141e10i | − | 0.0470975i | ||||||
\(427\) | 1.66605e12i | 2.42528i | ||||||||
\(428\) | 9.69966e11 | 1.39720 | ||||||||
\(429\) | − | 4.61101e10i | − | 0.0657261i | ||||||
\(430\) | − | 5.62903e11i | − | 0.794009i | ||||||
\(431\) | − | 1.07470e12i | − | 1.50017i | −0.661340 | − | 0.750086i | \(-0.730012\pi\) | ||
0.661340 | − | 0.750086i | \(-0.269988\pi\) | |||||||
\(432\) | −3.00755e11 | −0.415467 | ||||||||
\(433\) | 1.02600e12 | 1.40266 | 0.701330 | − | 0.712836i | \(-0.252590\pi\) | ||||
0.701330 | + | 0.712836i | \(0.252590\pi\) | |||||||
\(434\) | 8.79646e11 | 1.19016 | ||||||||
\(435\) | 1.73513e11 | 0.232344 | ||||||||
\(436\) | − | 4.75535e11i | − | 0.630221i | ||||||
\(437\) | 4.06606e11 | 0.533344 | ||||||||
\(438\) | 1.00584e11i | 0.130586i | ||||||||
\(439\) | 1.52864e11i | 0.196433i | 0.995165 | + | 0.0982164i | \(0.0313137\pi\) | ||||
−0.995165 | + | 0.0982164i | \(0.968686\pi\) | |||||||
\(440\) | 2.64754e11 | 0.336749 | ||||||||
\(441\) | −3.30185e11 | −0.415704 | ||||||||
\(442\) | − | 3.87954e10i | − | 0.0483482i | ||||||
\(443\) | 1.42971e12 | 1.76373 | 0.881865 | − | 0.471502i | \(-0.156288\pi\) | ||||
0.881865 | + | 0.471502i | \(0.156288\pi\) | |||||||
\(444\) | 4.67833e11 | + | 2.37385e11i | 0.571304 | + | 0.289888i | ||||
\(445\) | −4.86168e11 | −0.587715 | ||||||||
\(446\) | − | 1.31062e11i | − | 0.156845i | ||||||
\(447\) | −1.26333e12 | −1.49670 | ||||||||
\(448\) | 1.27871e11 | 0.149976 | ||||||||
\(449\) | − | 1.20619e12i | − | 1.40058i | −0.713857 | − | 0.700291i | \(-0.753053\pi\) | ||
0.713857 | − | 0.700291i | \(-0.246947\pi\) | |||||||
\(450\) | 5.99346e10i | 0.0689003i | ||||||||
\(451\) | −2.76904e10 | −0.0315163 | ||||||||
\(452\) | − | 7.54339e11i | − | 0.850048i | ||||||
\(453\) | −3.31782e11 | −0.370178 | ||||||||
\(454\) | −4.76964e11 | −0.526907 | ||||||||
\(455\) | 4.00337e11 | 0.437899 | ||||||||
\(456\) | −2.58679e11 | −0.280169 | ||||||||
\(457\) | 2.85197e9i | 0.00305860i | 0.999999 | + | 0.00152930i | \(0.000486791\pi\) | ||||
−0.999999 | + | 0.00152930i | \(0.999513\pi\) | |||||||
\(458\) | − | 7.38287e10i | − | 0.0784026i | ||||||
\(459\) | − | 4.42709e11i | − | 0.465545i | ||||||
\(460\) | 1.18477e12 | 1.23374 | ||||||||
\(461\) | − | 3.33099e11i | − | 0.343494i | −0.985141 | − | 0.171747i | \(-0.945059\pi\) | ||
0.985141 | − | 0.171747i | \(-0.0549411\pi\) | |||||||
\(462\) | 1.92047e11i | 0.196118i | ||||||||
\(463\) | 1.47908e12i | 1.49581i | 0.663806 | + | 0.747905i | \(0.268940\pi\) | ||||
−0.663806 | + | 0.747905i | \(0.731060\pi\) | |||||||
\(464\) | − | 8.90681e10i | − | 0.0892055i | ||||||
\(465\) | −1.66854e12 | −1.65500 | ||||||||
\(466\) | 2.11038e11i | 0.207312i | ||||||||
\(467\) | 8.68555e11i | 0.845028i | 0.906356 | + | 0.422514i | \(0.138852\pi\) | ||||
−0.906356 | + | 0.422514i | \(0.861148\pi\) | |||||||
\(468\) | − | 6.20134e10i | − | 0.0597557i | ||||||
\(469\) | −2.13530e12 | −2.03789 | ||||||||
\(470\) | 6.56298e9 | 0.00620384 | ||||||||
\(471\) | −5.74607e11 | −0.537993 | ||||||||
\(472\) | −5.20964e11 | −0.483135 | ||||||||
\(473\) | − | 5.05527e11i | − | 0.464375i | ||||||
\(474\) | −6.58531e11 | −0.599202 | ||||||||
\(475\) | − | 2.04707e11i | − | 0.184507i | ||||||
\(476\) | − | 5.64212e11i | − | 0.503745i | ||||||
\(477\) | −2.38876e11 | −0.211271 | ||||||||
\(478\) | −4.22968e11 | −0.370580 | ||||||||
\(479\) | 1.66206e12i | 1.44257i | 0.692638 | + | 0.721286i | \(0.256449\pi\) | ||||
−0.692638 | + | 0.721286i | \(0.743551\pi\) | |||||||
\(480\) | −1.17782e12 | −1.01273 | ||||||||
\(481\) | −1.27272e11 | + | 2.50824e11i | −0.108412 | + | 0.213657i | ||||
\(482\) | 5.73872e11 | 0.484287 | ||||||||
\(483\) | 1.96493e12i | 1.64280i | ||||||||
\(484\) | −8.34505e11 | −0.691233 | ||||||||
\(485\) | 1.19955e12 | 0.984424 | ||||||||
\(486\) | 3.56098e11i | 0.289538i | ||||||||
\(487\) | − | 7.94277e11i | − | 0.639870i | −0.947440 | − | 0.319935i | \(-0.896339\pi\) | ||
0.947440 | − | 0.319935i | \(-0.103661\pi\) | |||||||
\(488\) | 1.68175e12 | 1.34237 | ||||||||
\(489\) | 1.92823e12i | 1.52500i | ||||||||
\(490\) | −9.41074e11 | −0.737465 | ||||||||
\(491\) | −4.56186e11 | −0.354222 | −0.177111 | − | 0.984191i | \(-0.556675\pi\) | ||||
−0.177111 | + | 0.984191i | \(0.556675\pi\) | |||||||
\(492\) | 7.88331e10 | 0.0606549 | ||||||||
\(493\) | 1.31108e11 | 0.0999578 | ||||||||
\(494\) | − | 6.06584e10i | − | 0.0458268i | ||||||
\(495\) | 1.72086e11i | 0.128832i | ||||||||
\(496\) | 8.56497e11i | 0.635416i | ||||||||
\(497\) | 2.49621e11 | 0.183518 | ||||||||
\(498\) | − | 6.09505e11i | − | 0.444064i | ||||||
\(499\) | − | 2.21578e12i | − | 1.59983i | −0.600114 | − | 0.799914i | \(-0.704878\pi\) | ||
0.600114 | − | 0.799914i | \(-0.295122\pi\) | |||||||
\(500\) | 7.14053e11i | 0.510935i | ||||||||
\(501\) | 5.73273e10i | 0.0406529i | ||||||||
\(502\) | −5.83767e11 | −0.410273 | ||||||||
\(503\) | − | 2.03088e12i | − | 1.41458i | −0.706922 | − | 0.707291i | \(-0.749917\pi\) | ||
0.706922 | − | 0.707291i | \(-0.250083\pi\) | |||||||
\(504\) | 5.90536e11i | 0.407670i | ||||||||
\(505\) | 1.09600e12i | 0.749890i | ||||||||
\(506\) | −3.04715e11 | −0.206641 | ||||||||
\(507\) | 1.15571e12 | 0.776807 | ||||||||
\(508\) | 1.88506e12 | 1.25585 | ||||||||
\(509\) | 8.83617e11 | 0.583491 | 0.291746 | − | 0.956496i | \(-0.405764\pi\) | ||||
0.291746 | + | 0.956496i | \(0.405764\pi\) | |||||||
\(510\) | − | 3.06493e11i | − | 0.200611i | ||||||
\(511\) | −7.84278e11 | −0.508834 | ||||||||
\(512\) | 1.10232e12i | 0.708910i | ||||||||
\(513\) | − | 6.92197e11i | − | 0.441267i | ||||||
\(514\) | 1.07448e12 | 0.678990 | ||||||||
\(515\) | −8.35007e11 | −0.523067 | ||||||||
\(516\) | 1.43921e12i | 0.893716i | ||||||||
\(517\) | 5.89402e9 | 0.00362831 | ||||||||
\(518\) | 5.30082e11 | − | 1.04467e12i | 0.323489 | − | 0.637525i | ||||
\(519\) | −1.82027e12 | −1.10124 | ||||||||
\(520\) | − | 4.04111e11i | − | 0.242374i | ||||||
\(521\) | 2.98537e11 | 0.177512 | 0.0887560 | − | 0.996053i | \(-0.471711\pi\) | ||||
0.0887560 | + | 0.996053i | \(0.471711\pi\) | |||||||
\(522\) | −6.00182e10 | −0.0353806 | ||||||||
\(523\) | 6.23136e11i | 0.364188i | 0.983281 | + | 0.182094i | \(0.0582875\pi\) | ||||
−0.983281 | + | 0.182094i | \(0.941713\pi\) | |||||||
\(524\) | − | 1.57040e12i | − | 0.909956i | ||||||
\(525\) | 9.89251e11 | 0.568316 | ||||||||
\(526\) | − | 1.30643e12i | − | 0.744135i | ||||||
\(527\) | −1.26076e12 | −0.712006 | ||||||||
\(528\) | −1.86993e11 | −0.104706 | ||||||||
\(529\) | −1.31655e12 | −0.730946 | ||||||||
\(530\) | −6.80828e11 | −0.374797 | ||||||||
\(531\) | − | 3.38619e11i | − | 0.184836i | ||||||
\(532\) | − | 8.82171e11i | − | 0.477475i | ||||||
\(533\) | 4.22656e10i | 0.0226838i | ||||||||
\(534\) | −3.55980e11 | −0.189448 | ||||||||
\(535\) | 4.10842e12i | 2.16812i | ||||||||
\(536\) | 2.15543e12i | 1.12796i | ||||||||
\(537\) | − | 1.35829e12i | − | 0.704870i | ||||||
\(538\) | − | 1.15107e12i | − | 0.592352i | ||||||
\(539\) | −8.45151e11 | −0.431305 | ||||||||
\(540\) | − | 2.01693e12i | − | 1.02075i | ||||||
\(541\) | − | 1.22542e12i | − | 0.615033i | −0.951543 | − | 0.307517i | \(-0.900502\pi\) | ||
0.951543 | − | 0.307517i | \(-0.0994980\pi\) | |||||||
\(542\) | 1.07276e12i | 0.533955i | ||||||||
\(543\) | 3.22480e11 | 0.159186 | ||||||||
\(544\) | −8.89965e11 | −0.435691 | ||||||||
\(545\) | 2.01419e12 | 0.977950 | ||||||||
\(546\) | 2.93133e11 | 0.141155 | ||||||||
\(547\) | − | 7.03370e11i | − | 0.335924i | −0.985793 | − | 0.167962i | \(-0.946281\pi\) | ||
0.985793 | − | 0.167962i | \(-0.0537186\pi\) | |||||||
\(548\) | 1.63423e12 | 0.774106 | ||||||||
\(549\) | 1.09311e12i | 0.513559i | ||||||||
\(550\) | 1.53410e11i | 0.0714861i | ||||||||
\(551\) | 2.04993e11 | 0.0947451 | ||||||||
\(552\) | 1.98346e12 | 0.909278 | ||||||||
\(553\) | − | 5.13471e12i | − | 2.33482i | ||||||
\(554\) | −3.10463e11 | −0.140028 | ||||||||
\(555\) | −1.00548e12 | + | 1.98157e12i | −0.449835 | + | 0.886525i | ||||
\(556\) | 3.42350e11 | 0.151926 | ||||||||
\(557\) | − | 1.53756e12i | − | 0.676835i | −0.940996 | − | 0.338418i | \(-0.890108\pi\) | ||
0.940996 | − | 0.338418i | \(-0.109892\pi\) | |||||||
\(558\) | 5.77147e11 | 0.252019 | ||||||||
\(559\) | −7.71617e11 | −0.334232 | ||||||||
\(560\) | − | 1.62351e12i | − | 0.697604i | ||||||
\(561\) | − | 2.75252e11i | − | 0.117327i | ||||||
\(562\) | 1.09933e12 | 0.464853 | ||||||||
\(563\) | 3.44352e12i | 1.44449i | 0.691637 | + | 0.722245i | \(0.256890\pi\) | ||||
−0.691637 | + | 0.722245i | \(0.743110\pi\) | |||||||
\(564\) | −1.67799e10 | −0.00698288 | ||||||||
\(565\) | 3.19510e12 | 1.31907 | ||||||||
\(566\) | −1.71283e12 | −0.701518 | ||||||||
\(567\) | 2.14869e12 | 0.873070 | ||||||||
\(568\) | − | 2.51975e11i | − | 0.101576i | ||||||
\(569\) | 6.66708e11i | 0.266643i | 0.991073 | + | 0.133321i | \(0.0425643\pi\) | ||||
−0.991073 | + | 0.133321i | \(0.957436\pi\) | |||||||
\(570\) | − | 4.79216e11i | − | 0.190149i | ||||||
\(571\) | −3.30011e12 | −1.29917 | −0.649586 | − | 0.760289i | \(-0.725058\pi\) | ||||
−0.649586 | + | 0.760289i | \(0.725058\pi\) | |||||||
\(572\) | − | 1.58731e11i | − | 0.0619983i | ||||||
\(573\) | 1.83974e12i | 0.712951i | ||||||||
\(574\) | − | 1.76035e11i | − | 0.0676854i | ||||||
\(575\) | 1.56962e12i | 0.598809i | ||||||||
\(576\) | 8.38979e10 | 0.0317578 | ||||||||
\(577\) | 3.34404e11i | 0.125597i | 0.998026 | + | 0.0627987i | \(0.0200026\pi\) | ||||
−0.998026 | + | 0.0627987i | \(0.979997\pi\) | |||||||
\(578\) | 1.03450e12i | 0.385528i | ||||||||
\(579\) | 2.75083e11i | 0.101721i | ||||||||
\(580\) | 5.97309e11 | 0.219166 | ||||||||
\(581\) | 4.75245e12 | 1.73032 | ||||||||
\(582\) | 8.78333e11 | 0.317326 | ||||||||
\(583\) | −6.11432e11 | −0.219200 | ||||||||
\(584\) | 7.91673e11i | 0.281636i | ||||||||
\(585\) | 2.62666e11 | 0.0927262 | ||||||||
\(586\) | − | 1.96878e12i | − | 0.689696i | ||||||
\(587\) | − | 4.93550e12i | − | 1.71577i | −0.513841 | − | 0.857885i | \(-0.671778\pi\) | ||
0.513841 | − | 0.857885i | \(-0.328222\pi\) | |||||||
\(588\) | 2.40610e12 | 0.830071 | ||||||||
\(589\) | −1.97125e12 | −0.674876 | ||||||||
\(590\) | − | 9.65111e11i | − | 0.327901i | ||||||
\(591\) | −4.73555e11 | −0.159671 | ||||||||
\(592\) | 1.01718e12 | + | 5.16132e11i | 0.340370 | + | 0.172708i | ||||
\(593\) | 3.44361e12 | 1.14358 | 0.571791 | − | 0.820399i | \(-0.306249\pi\) | ||||
0.571791 | + | 0.820399i | \(0.306249\pi\) | |||||||
\(594\) | 5.18741e11i | 0.170967i | ||||||||
\(595\) | 2.38979e12 | 0.781689 | ||||||||
\(596\) | −4.34895e12 | −1.41181 | ||||||||
\(597\) | − | 4.21026e12i | − | 1.35651i | ||||||
\(598\) | 4.65106e11i | 0.148729i | ||||||||
\(599\) | −6.66166e10 | −0.0211428 | −0.0105714 | − | 0.999944i | \(-0.503365\pi\) | ||||
−0.0105714 | + | 0.999944i | \(0.503365\pi\) | |||||||
\(600\) | − | 9.98579e11i | − | 0.314559i | ||||||
\(601\) | 3.97296e11 | 0.124217 | 0.0621083 | − | 0.998069i | \(-0.480218\pi\) | ||||
0.0621083 | + | 0.998069i | \(0.480218\pi\) | |||||||
\(602\) | 3.21376e12 | 0.997307 | ||||||||
\(603\) | −1.40100e12 | −0.431528 | ||||||||
\(604\) | −1.14214e12 | −0.349183 | ||||||||
\(605\) | − | 3.53466e12i | − | 1.07263i | ||||||
\(606\) | 8.02506e11i | 0.241725i | ||||||||
\(607\) | 2.65373e12i | 0.793429i | 0.917942 | + | 0.396715i | \(0.129850\pi\) | ||||
−0.917942 | + | 0.396715i | \(0.870150\pi\) | |||||||
\(608\) | −1.39150e12 | −0.412970 | ||||||||
\(609\) | 9.90632e11i | 0.291833i | ||||||||
\(610\) | 3.11553e12i | 0.911061i | ||||||||
\(611\) | − | 8.99641e9i | − | 0.00261146i | ||||||
\(612\) | − | 3.70187e11i | − | 0.106669i | ||||||
\(613\) | 1.43446e12 | 0.410314 | 0.205157 | − | 0.978729i | \(-0.434230\pi\) | ||||
0.205157 | + | 0.978729i | \(0.434230\pi\) | |||||||
\(614\) | 1.83065e12i | 0.519814i | ||||||||
\(615\) | 3.33908e11i | 0.0941216i | ||||||||
\(616\) | 1.51155e12i | 0.422970i | ||||||||
\(617\) | 4.38127e12 | 1.21707 | 0.608537 | − | 0.793525i | \(-0.291757\pi\) | ||||
0.608537 | + | 0.793525i | \(0.291757\pi\) | |||||||
\(618\) | −6.11406e11 | −0.168609 | ||||||||
\(619\) | −5.95175e12 | −1.62943 | −0.814717 | − | 0.579859i | \(-0.803107\pi\) | ||||
−0.814717 | + | 0.579859i | \(0.803107\pi\) | |||||||
\(620\) | −5.74385e12 | −1.56113 | ||||||||
\(621\) | 5.30750e12i | 1.43212i | ||||||||
\(622\) | 1.14299e12 | 0.306185 | ||||||||
\(623\) | − | 2.77566e12i | − | 0.738193i | ||||||
\(624\) | 2.85419e11i | 0.0753620i | ||||||||
\(625\) | −4.76070e12 | −1.24799 | ||||||||
\(626\) | −6.78472e11 | −0.176582 | ||||||||
\(627\) | − | 4.30370e11i | − | 0.111208i | ||||||
\(628\) | −1.97805e12 | −0.507480 | ||||||||
\(629\) | −7.59743e11 | + | 1.49729e12i | −0.193526 | + | 0.381397i | ||||
\(630\) | −1.09400e12 | −0.276683 | ||||||||
\(631\) | − | 7.20462e11i | − | 0.180917i | −0.995900 | − | 0.0904584i | \(-0.971167\pi\) | ||
0.995900 | − | 0.0904584i | \(-0.0288332\pi\) | |||||||
\(632\) | −5.18313e12 | −1.29230 | ||||||||
\(633\) | −2.65960e12 | −0.658415 | ||||||||
\(634\) | 3.09032e12i | 0.759629i | ||||||||
\(635\) | 7.98444e12i | 1.94878i | ||||||||
\(636\) | 1.74071e12 | 0.421862 | ||||||||
\(637\) | 1.29001e12i | 0.310431i | ||||||||
\(638\) | −1.53624e11 | −0.0367085 | ||||||||
\(639\) | 1.63780e11 | 0.0388603 | ||||||||
\(640\) | −4.97661e12 | −1.17253 | ||||||||
\(641\) | 6.90851e12 | 1.61630 | 0.808152 | − | 0.588974i | \(-0.200468\pi\) | ||||
0.808152 | + | 0.588974i | \(0.200468\pi\) | |||||||
\(642\) | 3.00825e12i | 0.698887i | ||||||||
\(643\) | − | 2.16123e12i | − | 0.498600i | −0.968426 | − | 0.249300i | \(-0.919799\pi\) | ||
0.968426 | − | 0.249300i | \(-0.0802006\pi\) | |||||||
\(644\) | 6.76415e12i | 1.54963i | ||||||||
\(645\) | −6.09595e12 | −1.38683 | ||||||||
\(646\) | − | 3.62098e11i | − | 0.0818050i | ||||||
\(647\) | − | 7.44236e12i | − | 1.66971i | −0.550468 | − | 0.834856i | \(-0.685551\pi\) | ||
0.550468 | − | 0.834856i | \(-0.314449\pi\) | |||||||
\(648\) | − | 2.16894e12i | − | 0.483238i | ||||||
\(649\) | − | 8.66738e11i | − | 0.191773i | ||||||
\(650\) | 2.34159e11 | 0.0514519 | ||||||||
\(651\) | − | 9.52612e12i | − | 2.07875i | ||||||
\(652\) | 6.63783e12i | 1.43851i | ||||||||
\(653\) | − | 3.51296e12i | − | 0.756074i | −0.925791 | − | 0.378037i | \(-0.876599\pi\) | ||
0.925791 | − | 0.378037i | \(-0.123401\pi\) | |||||||
\(654\) | 1.47482e12 | 0.315239 | ||||||||
\(655\) | 6.65165e12 | 1.41203 | ||||||||
\(656\) | 1.71402e11 | 0.0361368 | ||||||||
\(657\) | −5.14575e11 | −0.107747 | ||||||||
\(658\) | 3.74697e10i | 0.00779227i | ||||||||
\(659\) | −7.33215e12 | −1.51442 | −0.757211 | − | 0.653170i | \(-0.773439\pi\) | ||||
−0.757211 | + | 0.653170i | \(0.773439\pi\) | |||||||
\(660\) | − | 1.25401e12i | − | 0.257249i | ||||||
\(661\) | − | 5.89973e12i | − | 1.20206i | −0.799227 | − | 0.601029i | \(-0.794758\pi\) | ||
0.799227 | − | 0.601029i | \(-0.205242\pi\) | |||||||
\(662\) | −2.75208e12 | −0.556930 | ||||||||
\(663\) | −4.20135e11 | −0.0844457 | ||||||||
\(664\) | − | 4.79726e12i | − | 0.957716i | ||||||
\(665\) | 3.73656e12 | 0.740925 | ||||||||
\(666\) | 3.47794e11 | − | 6.85424e11i | 0.0684995 | − | 0.134997i | ||||
\(667\) | −1.57181e12 | −0.307492 | ||||||||
\(668\) | 1.97346e11i | 0.0383472i | ||||||||
\(669\) | −1.41934e12 | −0.273948 | ||||||||
\(670\) | −3.99304e12 | −0.765538 | ||||||||
\(671\) | 2.79796e12i | 0.532833i | ||||||||
\(672\) | − | 6.72446e12i | − | 1.27203i | ||||||
\(673\) | 4.51059e12 | 0.847550 | 0.423775 | − | 0.905768i | \(-0.360705\pi\) | ||||
0.423775 | + | 0.905768i | \(0.360705\pi\) | |||||||
\(674\) | 1.55085e12i | 0.289468i | ||||||||
\(675\) | 2.67208e12 | 0.495431 | ||||||||
\(676\) | 3.97847e12 | 0.732749 | ||||||||
\(677\) | 3.07670e12 | 0.562906 | 0.281453 | − | 0.959575i | \(-0.409184\pi\) | ||||
0.281453 | + | 0.959575i | \(0.409184\pi\) | |||||||
\(678\) | 2.33951e12 | 0.425197 | ||||||||
\(679\) | 6.84856e12i | 1.23648i | ||||||||
\(680\) | − | 2.41233e12i | − | 0.432659i | ||||||
\(681\) | 5.16527e12i | 0.920304i | ||||||||
\(682\) | 1.47728e12 | 0.261477 | ||||||||
\(683\) | − | 6.31154e12i | − | 1.10979i | −0.831919 | − | 0.554897i | \(-0.812758\pi\) | ||
0.831919 | − | 0.554897i | \(-0.187242\pi\) | |||||||
\(684\) | − | 5.78804e11i | − | 0.101107i | ||||||
\(685\) | 6.92200e12i | 1.20122i | ||||||||
\(686\) | − | 1.22612e12i | − | 0.211385i | ||||||
\(687\) | −7.99527e11 | −0.136939 | ||||||||
\(688\) | 3.12918e12i | 0.532455i | ||||||||
\(689\) | 9.33267e11i | 0.157768i | ||||||||
\(690\) | 3.67444e12i | 0.617122i | ||||||||
\(691\) | 9.99594e12 | 1.66791 | 0.833955 | − | 0.551833i | \(-0.186071\pi\) | ||||
0.833955 | + | 0.551833i | \(0.186071\pi\) | |||||||
\(692\) | −6.26618e12 | −1.03878 | ||||||||
\(693\) | −9.82485e11 | −0.161818 | ||||||||
\(694\) | −4.13881e12 | −0.677263 | ||||||||
\(695\) | 1.45007e12i | 0.235753i | ||||||||
\(696\) | 9.99972e11 | 0.161527 | ||||||||
\(697\) | 2.52303e11i | 0.0404925i | ||||||||
\(698\) | − | 2.28694e12i | − | 0.364675i | ||||||
\(699\) | 2.28543e12 | 0.362094 | ||||||||
\(700\) | 3.40544e12 | 0.536083 | ||||||||
\(701\) | 2.05074e12i | 0.320760i | 0.987055 | + | 0.160380i | \(0.0512719\pi\) | ||||
−0.987055 | + | 0.160380i | \(0.948728\pi\) | |||||||
\(702\) | 7.91786e11 | 0.123053 | ||||||||
\(703\) | −1.18789e12 | + | 2.34108e12i | −0.183434 | + | 0.361507i | ||||
\(704\) | 2.14747e11 | 0.0329497 | ||||||||
\(705\) | − | 7.10737e10i | − | 0.0108357i | ||||||
\(706\) | 3.45551e12 | 0.523469 | ||||||||
\(707\) | −6.25732e12 | −0.941892 | ||||||||
\(708\) | 2.46755e12i | 0.369077i | ||||||||
\(709\) | 2.76523e12i | 0.410983i | 0.978659 | + | 0.205491i | \(0.0658793\pi\) | ||||
−0.978659 | + | 0.205491i | \(0.934121\pi\) | |||||||
\(710\) | 4.66795e11 | 0.0689388 | ||||||||
\(711\) | − | 3.36895e12i | − | 0.494404i | ||||||
\(712\) | −2.80183e12 | −0.408584 | ||||||||
\(713\) | 1.51148e13 | 2.19028 | ||||||||
\(714\) | 1.74985e12 | 0.251975 | ||||||||
\(715\) | 6.72327e11 | 0.0962063 | ||||||||
\(716\) | − | 4.67584e12i | − | 0.664893i | ||||||
\(717\) | 4.58053e12i | 0.647261i | ||||||||
\(718\) | − | 4.59686e12i | − | 0.645507i | ||||||
\(719\) | −2.70430e12 | −0.377376 | −0.188688 | − | 0.982037i | \(-0.560423\pi\) | ||||
−0.188688 | + | 0.982037i | \(0.560423\pi\) | |||||||
\(720\) | − | 1.06521e12i | − | 0.147719i | ||||||
\(721\) | − | 4.76727e12i | − | 0.656994i | ||||||
\(722\) | 2.87898e12i | 0.394295i | ||||||||
\(723\) | − | 6.21474e12i | − | 0.845864i | ||||||
\(724\) | 1.11012e12 | 0.150157 | ||||||||
\(725\) | 7.91333e11i | 0.106375i | ||||||||
\(726\) | − | 2.58813e12i | − | 0.345758i | ||||||
\(727\) | − | 3.11123e12i | − | 0.413074i | −0.978439 | − | 0.206537i | \(-0.933781\pi\) | ||
0.978439 | − | 0.206537i | \(-0.0662194\pi\) | |||||||
\(728\) | 2.30717e12 | 0.304431 | ||||||||
\(729\) | 8.25043e12 | 1.08194 | ||||||||
\(730\) | −1.46661e12 | −0.191145 | ||||||||
\(731\) | −4.60614e12 | −0.596635 | ||||||||
\(732\) | − | 7.96565e12i | − | 1.02547i | ||||||
\(733\) | −5.41565e12 | −0.692920 | −0.346460 | − | 0.938065i | \(-0.612616\pi\) | ||||
−0.346460 | + | 0.938065i | \(0.612616\pi\) | |||||||
\(734\) | − | 5.35061e12i | − | 0.680411i | ||||||
\(735\) | 1.01914e13i | 1.28807i | ||||||||
\(736\) | 1.06695e13 | 1.34028 | ||||||||
\(737\) | −3.58603e12 | −0.447724 | ||||||||
\(738\) | − | 1.15499e11i | − | 0.0143326i | ||||||
\(739\) | 1.03962e13 | 1.28225 | 0.641127 | − | 0.767435i | \(-0.278467\pi\) | ||||
0.641127 | + | 0.767435i | \(0.278467\pi\) | |||||||
\(740\) | −3.46129e12 | + | 6.82144e12i | −0.424322 | + | 0.836245i | ||||
\(741\) | −6.56900e11 | −0.0800419 | ||||||||
\(742\) | − | 3.88702e12i | − | 0.470760i | ||||||
\(743\) | 1.24097e13 | 1.49387 | 0.746935 | − | 0.664898i | \(-0.231525\pi\) | ||||
0.746935 | + | 0.664898i | \(0.231525\pi\) | |||||||
\(744\) | −9.61593e12 | −1.15057 | ||||||||
\(745\) | − | 1.84206e13i | − | 2.19078i | ||||||
\(746\) | 3.54001e11i | 0.0418485i | ||||||||
\(747\) | 3.11815e12 | 0.366399 | ||||||||
\(748\) | − | 9.47540e11i | − | 0.110673i | ||||||
\(749\) | −2.34560e13 | −2.72324 | ||||||||
\(750\) | −2.21456e12 | −0.255572 | ||||||||
\(751\) | 1.80317e12 | 0.206851 | 0.103425 | − | 0.994637i | \(-0.467020\pi\) | ||||
0.103425 | + | 0.994637i | \(0.467020\pi\) | |||||||
\(752\) | −3.64837e10 | −0.00416024 | ||||||||
\(753\) | 6.32190e12i | 0.716589i | ||||||||
\(754\) | 2.34486e11i | 0.0264208i | ||||||||
\(755\) | − | 4.83769e12i | − | 0.541847i | ||||||
\(756\) | 1.15151e13 | 1.28210 | ||||||||
\(757\) | 8.21800e12i | 0.909568i | 0.890602 | + | 0.454784i | \(0.150283\pi\) | ||||
−0.890602 | + | 0.454784i | \(0.849717\pi\) | |||||||
\(758\) | 2.78702e12i | 0.306640i | ||||||||
\(759\) | 3.29991e12i | 0.360923i | ||||||||
\(760\) | − | 3.77179e12i | − | 0.410096i | ||||||
\(761\) | −5.36207e12 | −0.579565 | −0.289782 | − | 0.957093i | \(-0.593583\pi\) | ||||
−0.289782 | + | 0.957093i | \(0.593583\pi\) | |||||||
\(762\) | 5.84634e12i | 0.628183i | ||||||||
\(763\) | 1.14995e13i | 1.22834i | ||||||||
\(764\) | 6.33319e12i | 0.672515i | ||||||||
\(765\) | 1.56798e12 | 0.165525 | ||||||||
\(766\) | 4.74875e12 | 0.498368 | ||||||||
\(767\) | −1.32296e12 | −0.138028 | ||||||||
\(768\) | −4.43042e12 | −0.459536 | ||||||||
\(769\) | 2.61553e12i | 0.269706i | 0.990866 | + | 0.134853i | \(0.0430563\pi\) | ||||
−0.990866 | + | 0.134853i | \(0.956944\pi\) | |||||||
\(770\) | −2.80022e12 | −0.287067 | ||||||||
\(771\) | − | 1.16361e13i | − | 1.18594i | ||||||
\(772\) | 9.46957e11i | 0.0959517i | ||||||||
\(773\) | 2.50175e11 | 0.0252021 | 0.0126010 | − | 0.999921i | \(-0.495989\pi\) | ||||
0.0126010 | + | 0.999921i | \(0.495989\pi\) | |||||||
\(774\) | 2.10859e12 | 0.211182 | ||||||||
\(775\) | − | 7.60962e12i | − | 0.757714i | ||||||
\(776\) | 6.91313e12 | 0.684380 | ||||||||
\(777\) | −1.13133e13 | − | 5.74052e12i | −1.11351 | − | 0.565011i | ||||
\(778\) | −4.07021e12 | −0.398299 | ||||||||
\(779\) | 3.94488e11i | 0.0383809i | ||||||||
\(780\) | −1.91408e12 | −0.185154 | ||||||||
\(781\) | 4.19215e11 | 0.0403188 | ||||||||
\(782\) | 2.77643e12i | 0.265495i | ||||||||
\(783\) | 2.67581e12i | 0.254406i | ||||||||
\(784\) | 5.23144e12 | 0.494538 | ||||||||
\(785\) | − | 8.37830e12i | − | 0.787486i | ||||||
\(786\) | 4.87045e12 | 0.455164 | ||||||||
\(787\) | 6.45966e12 | 0.600238 | 0.300119 | − | 0.953902i | \(-0.402974\pi\) | ||||
0.300119 | + | 0.953902i | \(0.402974\pi\) | |||||||
\(788\) | −1.63018e12 | −0.150615 | ||||||||
\(789\) | −1.41480e13 | −1.29972 | ||||||||
\(790\) | − | 9.60199e12i | − | 0.877080i | ||||||
\(791\) | 1.82417e13i | 1.65680i | ||||||||
\(792\) | 9.91749e11i | 0.0895650i | ||||||||
\(793\) | 4.27071e12 | 0.383504 | ||||||||
\(794\) | 7.40350e12i | 0.661066i | ||||||||
\(795\) | 7.37303e12i | 0.654627i | ||||||||
\(796\) | − | 1.44936e13i | − | 1.27958i | ||||||
\(797\) | 1.75688e12i | 0.154234i | 0.997022 | + | 0.0771168i | \(0.0245714\pi\) | ||||
−0.997022 | + | 0.0771168i | \(0.975429\pi\) | |||||||
\(798\) | 2.73597e12 | 0.238835 | ||||||||
\(799\) | − | 5.37037e10i | − | 0.00466170i | ||||||
\(800\) | − | 5.37161e12i | − | 0.463660i | ||||||
\(801\) | − | 1.82115e12i | − | 0.156314i | ||||||
\(802\) | −5.77690e12 | −0.493072 | ||||||||
\(803\) | −1.31712e12 | −0.111791 | ||||||||
\(804\) | 1.02092e13 | 0.861669 | ||||||||
\(805\) | −2.86505e13 | −2.40464 | ||||||||
\(806\) | − | 2.25487e12i | − | 0.188197i | ||||||
\(807\) | −1.24655e13 | −1.03461 | ||||||||
\(808\) | 6.31632e12i | 0.521330i | ||||||||
\(809\) | 1.36499e13i | 1.12037i | 0.828368 | + | 0.560184i | \(0.189270\pi\) | ||||
−0.828368 | + | 0.560184i | \(0.810730\pi\) | |||||||
\(810\) | 4.01807e12 | 0.327971 | ||||||||
\(811\) | −2.56854e12 | −0.208493 | −0.104247 | − | 0.994551i | \(-0.533243\pi\) | ||||
−0.104247 | + | 0.994551i | \(0.533243\pi\) | |||||||
\(812\) | 3.41019e12i | 0.275281i | ||||||||
\(813\) | 1.16174e13 | 0.932615 | ||||||||
\(814\) | 8.90222e11 | − | 1.75443e12i | 0.0710704 | − | 0.140064i | ||||
\(815\) | −2.81154e13 | −2.23221 | ||||||||
\(816\) | 1.70380e12i | 0.134528i | ||||||||
\(817\) | −7.20191e12 | −0.565521 | ||||||||
\(818\) | −1.23046e9 | −9.60900e−5 | ||||||||
\(819\) | 1.49963e12i | 0.116468i | ||||||||
\(820\) | 1.14946e12i | 0.0887834i | ||||||||
\(821\) | −9.62363e12 | −0.739256 | −0.369628 | − | 0.929180i | \(-0.620515\pi\) | ||||
−0.369628 | + | 0.929180i | \(0.620515\pi\) | |||||||
\(822\) | 5.06840e12i | 0.387211i | ||||||||
\(823\) | 1.12898e12 | 0.0857803 | 0.0428901 | − | 0.999080i | \(-0.486343\pi\) | ||||
0.0428901 | + | 0.999080i | \(0.486343\pi\) | |||||||
\(824\) | −4.81222e12 | −0.363641 | ||||||||
\(825\) | 1.66135e12 | 0.124859 | ||||||||
\(826\) | 5.51006e12 | 0.411857 | ||||||||
\(827\) | 7.83837e12i | 0.582708i | 0.956615 | + | 0.291354i | \(0.0941057\pi\) | ||||
−0.956615 | + | 0.291354i | \(0.905894\pi\) | |||||||
\(828\) | 4.43805e12i | 0.328137i | ||||||||
\(829\) | − | 3.00307e12i | − | 0.220836i | −0.993885 | − | 0.110418i | \(-0.964781\pi\) | ||
0.993885 | − | 0.110418i | \(-0.0352190\pi\) | |||||||
\(830\) | 8.88715e12 | 0.649997 | ||||||||
\(831\) | 3.36215e12i | 0.244575i | ||||||||
\(832\) | − | 3.27782e11i | − | 0.0237154i | ||||||
\(833\) | 7.70065e12i | 0.554147i | ||||||||
\(834\) | 1.06176e12i | 0.0759942i | ||||||||
\(835\) | −8.35885e11 | −0.0595056 | ||||||||
\(836\) | − | 1.48152e12i | − | 0.104901i | ||||||
\(837\) | − | 2.57312e13i | − | 1.81215i | ||||||
\(838\) | − | 1.18435e12i | − | 0.0829622i | ||||||
\(839\) | −4.45665e12 | −0.310513 | −0.155256 | − | 0.987874i | \(-0.549620\pi\) | ||||
−0.155256 | + | 0.987874i | \(0.549620\pi\) | |||||||
\(840\) | 1.82272e13 | 1.26318 | ||||||||
\(841\) | 1.37147e13 | 0.945376 | ||||||||
\(842\) | −1.02108e13 | −0.700095 | ||||||||
\(843\) | − | 1.19052e13i | − | 0.811919i | ||||||
\(844\) | −9.15552e12 | −0.621072 | ||||||||
\(845\) | 1.68513e13i | 1.13705i | ||||||||
\(846\) | 2.45844e10i | 0.00165003i | ||||||||
\(847\) | 2.01803e13 | 1.34726 | ||||||||
\(848\) | 3.78473e12 | 0.251336 | ||||||||
\(849\) | 1.85490e13i | 1.22528i | ||||||||
\(850\) | 1.39781e12 | 0.0918463 | ||||||||
\(851\) | 9.10832e12 | − | 1.79505e13i | 0.595327 | − | 1.17326i | ||||
\(852\) | −1.19348e12 | −0.0775957 | ||||||||
\(853\) | 2.86713e13i | 1.85429i | 0.374705 | + | 0.927144i | \(0.377744\pi\) | ||||
−0.374705 | + | 0.927144i | \(0.622256\pi\) | |||||||
\(854\) | −1.77873e13 | −1.14433 | ||||||||
\(855\) | 2.45160e12 | 0.156893 | ||||||||
\(856\) | 2.36772e13i | 1.50730i | ||||||||
\(857\) | − | 1.59528e13i | − | 1.01024i | −0.863050 | − | 0.505118i | \(-0.831449\pi\) | ||
0.863050 | − | 0.505118i | \(-0.168551\pi\) | |||||||
\(858\) | 4.92289e11 | 0.0310118 | ||||||||
\(859\) | 2.23959e13i | 1.40346i | 0.712445 | + | 0.701728i | \(0.247588\pi\) | ||||
−0.712445 | + | 0.701728i | \(0.752412\pi\) | |||||||
\(860\) | −2.09850e13 | −1.30817 | ||||||||
\(861\) | −1.90637e12 | −0.118220 | ||||||||
\(862\) | 1.14740e13 | 0.707833 | ||||||||
\(863\) | 2.39027e13 | 1.46690 | 0.733448 | − | 0.679746i | \(-0.237910\pi\) | ||||
0.733448 | + | 0.679746i | \(0.237910\pi\) | |||||||
\(864\) | − | 1.81636e13i | − | 1.10889i | ||||||
\(865\) | − | 2.65412e13i | − | 1.61194i | ||||||
\(866\) | 1.09540e13i | 0.661823i | ||||||||
\(867\) | 1.12031e13 | 0.673370 | ||||||||
\(868\) | − | 3.27931e13i | − | 1.96085i | ||||||
\(869\) | − | 8.62327e12i | − | 0.512959i | ||||||
\(870\) | 1.85250e12i | 0.109628i | ||||||||
\(871\) | 5.47358e12i | 0.322248i | ||||||||
\(872\) | 1.16080e13 | 0.679879 | ||||||||
\(873\) | 4.49343e12i | 0.261827i | ||||||||
\(874\) | 4.34108e12i | 0.251650i | ||||||||
\(875\) | − | 1.72675e13i | − | 0.995846i | ||||||
\(876\) | 3.74977e12 | 0.215147 | ||||||||
\(877\) | 2.13329e13 | 1.21773 | 0.608866 | − | 0.793273i | \(-0.291625\pi\) | ||||
0.608866 | + | 0.793273i | \(0.291625\pi\) | |||||||
\(878\) | −1.63203e12 | −0.0926837 | ||||||||
\(879\) | −2.13209e13 | −1.20463 | ||||||||
\(880\) | − | 2.72653e12i | − | 0.153263i | ||||||
\(881\) | −7.25536e12 | −0.405758 | −0.202879 | − | 0.979204i | \(-0.565030\pi\) | ||||
−0.202879 | + | 0.979204i | \(0.565030\pi\) | |||||||
\(882\) | − | 3.52519e12i | − | 0.196143i | ||||||
\(883\) | − | 2.52446e13i | − | 1.39748i | −0.715377 | − | 0.698739i | \(-0.753745\pi\) | ||
0.715377 | − | 0.698739i | \(-0.246255\pi\) | |||||||
\(884\) | −1.44629e12 | −0.0796562 | ||||||||
\(885\) | −1.04517e13 | −0.572718 | ||||||||
\(886\) | 1.52642e13i | 0.832188i | ||||||||
\(887\) | 2.64882e13 | 1.43680 | 0.718400 | − | 0.695631i | \(-0.244875\pi\) | ||||
0.718400 | + | 0.695631i | \(0.244875\pi\) | |||||||
\(888\) | −5.79464e12 | + | 1.14200e13i | −0.312729 | + | 0.616320i | ||||
\(889\) | −4.55852e13 | −2.44775 | ||||||||
\(890\) | − | 5.19052e12i | − | 0.277304i | ||||||
\(891\) | 3.60851e12 | 0.191813 | ||||||||
\(892\) | −4.88599e12 | −0.258411 | ||||||||
\(893\) | − | 8.39683e10i | − | 0.00441859i | ||||||
\(894\) | − | 1.34878e13i | − | 0.706193i | ||||||
\(895\) | 1.98052e13 | 1.03175 | ||||||||
\(896\) | − | 2.84128e13i | − | 1.47274i | ||||||
\(897\) | 5.03686e12 | 0.259773 | ||||||||
\(898\) | 1.28778e13 | 0.660843 | ||||||||
\(899\) | 7.62024e12 | 0.389090 | ||||||||
\(900\) | 2.23435e12 | 0.113517 | ||||||||
\(901\) | 5.57110e12i | 0.281630i | ||||||||
\(902\) | − | 2.95634e11i | − | 0.0148705i | ||||||
\(903\) | − | 3.48034e13i | − | 1.74191i | ||||||
\(904\) | 1.84137e13 | 0.917027 | ||||||||
\(905\) | 4.70206e12i | 0.233007i | ||||||||
\(906\) | − | 3.54223e12i | − | 0.174663i | ||||||
\(907\) | − | 2.02945e13i | − | 0.995737i | −0.867252 | − | 0.497869i | \(-0.834116\pi\) | ||
0.867252 | − | 0.497869i | \(-0.165884\pi\) | |||||||
\(908\) | 1.77812e13i | 0.868108i | ||||||||
\(909\) | −4.10551e12 | −0.199448 | ||||||||
\(910\) | 4.27415e12i | 0.206616i | ||||||||
\(911\) | − | 2.04758e13i | − | 0.984936i | −0.870331 | − | 0.492468i | \(-0.836095\pi\) | ||
0.870331 | − | 0.492468i | \(-0.163905\pi\) | |||||||
\(912\) | 2.66397e12i | 0.127512i | ||||||||
\(913\) | 7.98129e12 | 0.380150 | ||||||||
\(914\) | −3.04488e10 | −0.00144315 | ||||||||
\(915\) | 3.37396e13 | 1.59127 | ||||||||
\(916\) | −2.75233e12 | −0.129173 | ||||||||
\(917\) | 3.79760e13i | 1.77357i | ||||||||
\(918\) | 4.72654e12 | 0.219660 | ||||||||
\(919\) | 2.34202e13i | 1.08311i | 0.840667 | + | 0.541553i | \(0.182163\pi\) | ||||
−0.840667 | + | 0.541553i | \(0.817837\pi\) | |||||||
\(920\) | 2.89206e13i | 1.33095i | ||||||||
\(921\) | 1.98250e13 | 0.907915 | ||||||||
\(922\) | 3.55629e12 | 0.162072 | ||||||||
\(923\) | − | 6.39874e11i | − | 0.0290193i | ||||||
\(924\) | 7.15948e12 | 0.323116 | ||||||||
\(925\) | −9.03724e12 | − | 4.58562e12i | −0.405881 | − | 0.205949i | ||||
\(926\) | −1.57912e13 | −0.705774 | ||||||||
\(927\) | − | 3.12787e12i | − | 0.139120i | ||||||
\(928\) | 5.37911e12 | 0.238092 | ||||||||
\(929\) | −9.52404e12 | −0.419518 | −0.209759 | − | 0.977753i | \(-0.567268\pi\) | ||||
−0.209759 | + | 0.977753i | \(0.567268\pi\) | |||||||
\(930\) | − | 1.78140e13i | − | 0.780886i | ||||||
\(931\) | 1.20403e13i | 0.525248i | ||||||||
\(932\) | 7.86746e12 | 0.341557 | ||||||||
\(933\) | − | 1.23780e13i | − | 0.534788i | ||||||
\(934\) | −9.27303e12 | −0.398713 | ||||||||
\(935\) | 4.01343e12 | 0.171737 | ||||||||
\(936\) | 1.51377e12 | 0.0644641 | ||||||||
\(937\) | −2.17483e12 | −0.0921716 | −0.0460858 | − | 0.998937i | \(-0.514675\pi\) | ||||
−0.0460858 | + | 0.998937i | \(0.514675\pi\) | |||||||
\(938\) | − | 2.27973e13i | − | 0.961546i | ||||||
\(939\) | 7.34751e12i | 0.308422i | ||||||||
\(940\) | − | 2.44667e11i | − | 0.0102212i | ||||||
\(941\) | −3.97025e13 | −1.65069 | −0.825344 | − | 0.564630i | \(-0.809019\pi\) | ||||
−0.825344 | + | 0.564630i | \(0.809019\pi\) | |||||||
\(942\) | − | 6.13473e12i | − | 0.253844i | ||||||
\(943\) | − | 3.02478e12i | − | 0.124564i | ||||||
\(944\) | 5.36506e12i | 0.219888i | ||||||||
\(945\) | 4.87740e13i | 1.98950i | ||||||||
\(946\) | 5.39720e12 | 0.219108 | ||||||||
\(947\) | 1.85795e13i | 0.750685i | 0.926886 | + | 0.375343i | \(0.122475\pi\) | ||||
−0.926886 | + | 0.375343i | \(0.877525\pi\) | |||||||
\(948\) | 2.45500e13i | 0.987218i | ||||||||
\(949\) | 2.01040e12i | 0.0804610i | ||||||||
\(950\) | 2.18553e12 | 0.0870566 | ||||||||
\(951\) | 3.34666e13 | 1.32678 | ||||||||
\(952\) | 1.37726e13 | 0.543437 | ||||||||
\(953\) | 2.18023e12 | 0.0856217 | 0.0428108 | − | 0.999083i | \(-0.486369\pi\) | ||||
0.0428108 | + | 0.999083i | \(0.486369\pi\) | |||||||
\(954\) | − | 2.55033e12i | − | 0.0996847i | ||||||
\(955\) | −2.68251e13 | −1.04358 | ||||||||
\(956\) | 1.57682e13i | 0.610550i | ||||||||
\(957\) | 1.66367e12i | 0.0641157i | ||||||||
\(958\) | −1.77448e13 | −0.680655 | ||||||||
\(959\) | −3.95195e13 | −1.50879 | ||||||||
\(960\) | − | 2.58956e12i | − | 0.0984022i | ||||||
\(961\) | −4.68381e13 | −1.77151 | ||||||||
\(962\) | −2.67790e12 | − | 1.35880e12i | −0.100811 | − | 0.0511526i | ||||
\(963\) | −1.53898e13 | −0.576654 | ||||||||
\(964\) | − | 2.13939e13i | − | 0.797890i | ||||||
\(965\) | −4.01097e12 | −0.148894 | ||||||||
\(966\) | −2.09783e13 | −0.775129 | ||||||||
\(967\) | 1.41452e12i | 0.0520225i | 0.999662 | + | 0.0260113i | \(0.00828058\pi\) | ||||
−0.999662 | + | 0.0260113i | \(0.991719\pi\) | |||||||
\(968\) | − | 2.03705e13i | − | 0.745699i | ||||||
\(969\) | −3.92134e12 | −0.142882 | ||||||||
\(970\) | 1.28069e13i | 0.464485i | ||||||||
\(971\) | −7.66184e12 | −0.276596 | −0.138298 | − | 0.990391i | \(-0.544163\pi\) | ||||
−0.138298 | + | 0.990391i | \(0.544163\pi\) | |||||||
\(972\) | 1.32753e13 | 0.477030 | ||||||||
\(973\) | −8.27882e12 | −0.296115 | ||||||||
\(974\) | 8.48001e12 | 0.301912 | ||||||||
\(975\) | − | 2.53583e12i | − | 0.0898667i | ||||||
\(976\) | − | 1.73193e13i | − | 0.610949i | ||||||
\(977\) | − | 4.47513e13i | − | 1.57138i | −0.618623 | − | 0.785688i | \(-0.712309\pi\) | ||
0.618623 | − | 0.785688i | \(-0.287691\pi\) | |||||||
\(978\) | −2.05866e13 | −0.719547 | ||||||||
\(979\) | − | 4.66146e12i | − | 0.162181i | ||||||
\(980\) | 3.50831e13i | 1.21501i | ||||||||
\(981\) | 7.54500e12i | 0.260105i | ||||||||
\(982\) | − | 4.87042e12i | − | 0.167134i | ||||||
\(983\) | 5.21169e13 | 1.78028 | 0.890138 | − | 0.455691i | \(-0.150608\pi\) | ||||
0.890138 | + | 0.455691i | \(0.150608\pi\) | |||||||
\(984\) | 1.92434e12i | 0.0654342i | ||||||||
\(985\) | − | 6.90487e12i | − | 0.233718i | ||||||
\(986\) | 1.39976e12i | 0.0471635i | ||||||||
\(987\) | 4.05778e11 | 0.0136101 | ||||||||
\(988\) | −2.26134e12 | −0.0755022 | ||||||||
\(989\) | 5.52215e13 | 1.83538 | ||||||||
\(990\) | −1.83726e12 | −0.0607872 | ||||||||
\(991\) | − | 1.54987e13i | − | 0.510462i | −0.966880 | − | 0.255231i | \(-0.917848\pi\) | ||
0.966880 | − | 0.255231i | \(-0.0821515\pi\) | |||||||
\(992\) | −5.17266e13 | −1.69594 | ||||||||
\(993\) | 2.98037e13i | 0.972743i | ||||||||
\(994\) | 2.66505e12i | 0.0865899i | ||||||||
\(995\) | 6.13895e13 | 1.98559 | ||||||||
\(996\) | −2.27223e13 | −0.731619 | ||||||||
\(997\) | 8.99091e12i | 0.288188i | 0.989564 | + | 0.144094i | \(0.0460267\pi\) | ||||
−0.989564 | + | 0.144094i | \(0.953973\pi\) | |||||||
\(998\) | 2.36565e13 | 0.754854 | ||||||||
\(999\) | −3.05585e13 | − | 1.55058e13i | −0.970706 | − | 0.492549i |
(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 | 37.10.b.a.36.17 | yes | 28 | |
37.36 | even | 2 | inner | 37.10.b.a.36.12 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.10.b.a.36.12 | ✓ | 28 | 37.36 | even | 2 | inner | |
37.10.b.a.36.17 | yes | 28 | 1.1 | even | 1 | trivial |