Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [138,7,Mod(91,138)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(138, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("138.91");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 138 = 2 \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 138.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: | \(31.7474635395\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.4 | ||
Character | \(\chi\) | \(=\) | 138.91 |
Dual form | 138.7.b.a.91.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(97\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.65685 | −0.707107 | ||||||||
\(3\) | −15.5885 | −0.577350 | ||||||||
\(4\) | 32.0000 | 0.500000 | ||||||||
\(5\) | 33.5442i | 0.268354i | 0.990957 | + | 0.134177i | \(0.0428390\pi\) | ||||
−0.990957 | + | 0.134177i | \(0.957161\pi\) | |||||||
\(6\) | 88.1816 | 0.408248 | ||||||||
\(7\) | 442.137i | 1.28903i | 0.764592 | + | 0.644514i | \(0.222940\pi\) | ||||
−0.764592 | + | 0.644514i | \(0.777060\pi\) | |||||||
\(8\) | −181.019 | −0.353553 | ||||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | − | 189.755i | − | 0.189755i | ||||||
\(11\) | 934.810i | 0.702336i | 0.936312 | + | 0.351168i | \(0.114215\pi\) | ||||
−0.936312 | + | 0.351168i | \(0.885785\pi\) | |||||||
\(12\) | −498.831 | −0.288675 | ||||||||
\(13\) | 905.006 | 0.411928 | 0.205964 | − | 0.978560i | \(-0.433967\pi\) | ||||
0.205964 | + | 0.978560i | \(0.433967\pi\) | |||||||
\(14\) | − | 2501.10i | − | 0.911481i | ||||||
\(15\) | − | 522.902i | − | 0.154934i | ||||||
\(16\) | 1024.00 | 0.250000 | ||||||||
\(17\) | 3778.41i | 0.769064i | 0.923112 | + | 0.384532i | \(0.125637\pi\) | ||||
−0.923112 | + | 0.384532i | \(0.874363\pi\) | |||||||
\(18\) | −1374.62 | −0.235702 | ||||||||
\(19\) | − | 6057.54i | − | 0.883152i | −0.897224 | − | 0.441576i | \(-0.854419\pi\) | ||
0.897224 | − | 0.441576i | \(-0.145581\pi\) | |||||||
\(20\) | 1073.41i | 0.134177i | ||||||||
\(21\) | − | 6892.23i | − | 0.744221i | ||||||
\(22\) | − | 5288.08i | − | 0.496627i | ||||||
\(23\) | 11276.3 | + | 4569.58i | 0.926793 | + | 0.375572i | ||||
\(24\) | 2821.81 | 0.204124 | ||||||||
\(25\) | 14499.8 | 0.927986 | ||||||||
\(26\) | −5119.49 | −0.291277 | ||||||||
\(27\) | −3788.00 | −0.192450 | ||||||||
\(28\) | 14148.4i | 0.644514i | ||||||||
\(29\) | 1791.39 | 0.0734507 | 0.0367253 | − | 0.999325i | \(-0.488307\pi\) | ||||
0.0367253 | + | 0.999325i | \(0.488307\pi\) | |||||||
\(30\) | 2957.98i | 0.109555i | ||||||||
\(31\) | −3340.95 | −0.112146 | −0.0560731 | − | 0.998427i | \(-0.517858\pi\) | ||||
−0.0560731 | + | 0.998427i | \(0.517858\pi\) | |||||||
\(32\) | −5792.62 | −0.176777 | ||||||||
\(33\) | − | 14572.2i | − | 0.405494i | ||||||
\(34\) | − | 21373.9i | − | 0.543810i | ||||||
\(35\) | −14831.1 | −0.345915 | ||||||||
\(36\) | 7776.00 | 0.166667 | ||||||||
\(37\) | 40653.3i | 0.802585i | 0.915950 | + | 0.401293i | \(0.131439\pi\) | ||||
−0.915950 | + | 0.401293i | \(0.868561\pi\) | |||||||
\(38\) | 34266.6i | 0.624483i | ||||||||
\(39\) | −14107.6 | −0.237827 | ||||||||
\(40\) | − | 6072.15i | − | 0.0948774i | ||||||
\(41\) | −44522.2 | −0.645989 | −0.322995 | − | 0.946401i | \(-0.604690\pi\) | ||||
−0.322995 | + | 0.946401i | \(0.604690\pi\) | |||||||
\(42\) | 38988.3i | 0.526244i | ||||||||
\(43\) | − | 10473.0i | − | 0.131724i | −0.997829 | − | 0.0658622i | \(-0.979020\pi\) | ||
0.997829 | − | 0.0658622i | \(-0.0209798\pi\) | |||||||
\(44\) | 29913.9i | 0.351168i | ||||||||
\(45\) | 8151.24i | 0.0894512i | ||||||||
\(46\) | −63788.4 | − | 25849.4i | −0.655342 | − | 0.265569i | ||||
\(47\) | −185357. | −1.78532 | −0.892658 | − | 0.450734i | \(-0.851162\pi\) | ||||
−0.892658 | + | 0.450734i | \(0.851162\pi\) | |||||||
\(48\) | −15962.6 | −0.144338 | ||||||||
\(49\) | −77835.8 | −0.661593 | ||||||||
\(50\) | −82023.2 | −0.656185 | ||||||||
\(51\) | − | 58899.6i | − | 0.444019i | ||||||
\(52\) | 28960.2 | 0.205964 | ||||||||
\(53\) | 58071.1i | 0.390061i | 0.980797 | + | 0.195030i | \(0.0624806\pi\) | ||||
−0.980797 | + | 0.195030i | \(0.937519\pi\) | |||||||
\(54\) | 21428.1 | 0.136083 | ||||||||
\(55\) | −31357.5 | −0.188475 | ||||||||
\(56\) | − | 80035.3i | − | 0.455740i | ||||||
\(57\) | 94427.7i | 0.509888i | ||||||||
\(58\) | −10133.6 | −0.0519375 | ||||||||
\(59\) | −362036. | −1.76277 | −0.881385 | − | 0.472398i | \(-0.843389\pi\) | ||||
−0.881385 | + | 0.472398i | \(0.843389\pi\) | |||||||
\(60\) | − | 16732.9i | − | 0.0774670i | ||||||
\(61\) | 380449.i | 1.67613i | 0.545574 | + | 0.838063i | \(0.316312\pi\) | ||||
−0.545574 | + | 0.838063i | \(0.683688\pi\) | |||||||
\(62\) | 18899.2 | 0.0792993 | ||||||||
\(63\) | 107439.i | 0.429676i | ||||||||
\(64\) | 32768.0 | 0.125000 | ||||||||
\(65\) | 30357.7i | 0.110542i | ||||||||
\(66\) | 82433.1i | 0.286728i | ||||||||
\(67\) | 131214.i | 0.436271i | 0.975919 | + | 0.218135i | \(0.0699974\pi\) | ||||
−0.975919 | + | 0.218135i | \(0.930003\pi\) | |||||||
\(68\) | 120909.i | 0.384532i | ||||||||
\(69\) | −175780. | − | 71232.7i | −0.535084 | − | 0.216836i | ||||
\(70\) | 83897.5 | 0.244599 | ||||||||
\(71\) | −218978. | −0.611823 | −0.305911 | − | 0.952060i | \(-0.598961\pi\) | ||||
−0.305911 | + | 0.952060i | \(0.598961\pi\) | |||||||
\(72\) | −43987.7 | −0.117851 | ||||||||
\(73\) | −6020.53 | −0.0154763 | −0.00773813 | − | 0.999970i | \(-0.502463\pi\) | ||||
−0.00773813 | + | 0.999970i | \(0.502463\pi\) | |||||||
\(74\) | − | 229970.i | − | 0.567513i | ||||||
\(75\) | −226029. | −0.535773 | ||||||||
\(76\) | − | 193841.i | − | 0.441576i | ||||||
\(77\) | −413314. | −0.905331 | ||||||||
\(78\) | 79804.9 | 0.168169 | ||||||||
\(79\) | − | 899926.i | − | 1.82526i | −0.408782 | − | 0.912632i | \(-0.634046\pi\) | ||
0.408782 | − | 0.912632i | \(-0.365954\pi\) | |||||||
\(80\) | 34349.3i | 0.0670884i | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 251856. | 0.456783 | ||||||||
\(83\) | 564276.i | 0.986864i | 0.869784 | + | 0.493432i | \(0.164258\pi\) | ||||
−0.869784 | + | 0.493432i | \(0.835742\pi\) | |||||||
\(84\) | − | 220551.i | − | 0.372110i | ||||||
\(85\) | −126744. | −0.206381 | ||||||||
\(86\) | 59244.3i | 0.0931432i | ||||||||
\(87\) | −27925.0 | −0.0424068 | ||||||||
\(88\) | − | 169219.i | − | 0.248313i | ||||||
\(89\) | 770356.i | 1.09275i | 0.837540 | + | 0.546376i | \(0.183993\pi\) | ||||
−0.837540 | + | 0.546376i | \(0.816007\pi\) | |||||||
\(90\) | − | 46110.4i | − | 0.0632516i | ||||||
\(91\) | 400136.i | 0.530987i | ||||||||
\(92\) | 360841. | + | 146227.i | 0.463397 | + | 0.187786i | ||||
\(93\) | 52080.2 | 0.0647476 | ||||||||
\(94\) | 1.04854e6 | 1.26241 | ||||||||
\(95\) | 203195. | 0.236997 | ||||||||
\(96\) | 90298.0 | 0.102062 | ||||||||
\(97\) | − | 1.70896e6i | − | 1.87247i | −0.351369 | − | 0.936237i | \(-0.614284\pi\) | ||
0.351369 | − | 0.936237i | \(-0.385716\pi\) | |||||||
\(98\) | 440306. | 0.467817 | ||||||||
\(99\) | 227159.i | 0.234112i | ||||||||
\(100\) | 463993. | 0.463993 | ||||||||
\(101\) | −553006. | −0.536742 | −0.268371 | − | 0.963316i | \(-0.586485\pi\) | ||||
−0.268371 | + | 0.963316i | \(0.586485\pi\) | |||||||
\(102\) | 333187.i | 0.313969i | ||||||||
\(103\) | 1.07926e6i | 0.987672i | 0.869555 | + | 0.493836i | \(0.164406\pi\) | ||||
−0.869555 | + | 0.493836i | \(0.835594\pi\) | |||||||
\(104\) | −163824. | −0.145639 | ||||||||
\(105\) | 231194. | 0.199714 | ||||||||
\(106\) | − | 328500.i | − | 0.275815i | ||||||
\(107\) | 391614.i | 0.319674i | 0.987143 | + | 0.159837i | \(0.0510968\pi\) | ||||
−0.987143 | + | 0.159837i | \(0.948903\pi\) | |||||||
\(108\) | −121216. | −0.0962250 | ||||||||
\(109\) | − | 358043.i | − | 0.276475i | −0.990399 | − | 0.138238i | \(-0.955856\pi\) | ||
0.990399 | − | 0.138238i | \(-0.0441437\pi\) | |||||||
\(110\) | 177385. | 0.133272 | ||||||||
\(111\) | − | 633723.i | − | 0.463373i | ||||||
\(112\) | 452748.i | 0.322257i | ||||||||
\(113\) | − | 844463.i | − | 0.585255i | −0.956227 | − | 0.292627i | \(-0.905470\pi\) | ||
0.956227 | − | 0.292627i | \(-0.0945296\pi\) | |||||||
\(114\) | − | 534164.i | − | 0.360545i | ||||||
\(115\) | −153283. | + | 378254.i | −0.100786 | + | 0.248708i | ||||
\(116\) | 57324.4 | 0.0367253 | ||||||||
\(117\) | 219916. | 0.137309 | ||||||||
\(118\) | 2.04799e6 | 1.24647 | ||||||||
\(119\) | −1.67057e6 | −0.991345 | ||||||||
\(120\) | 94655.5i | 0.0547775i | ||||||||
\(121\) | 897692. | 0.506723 | ||||||||
\(122\) | − | 2.15214e6i | − | 1.18520i | ||||||
\(123\) | 694033. | 0.372962 | ||||||||
\(124\) | −106910. | −0.0560731 | ||||||||
\(125\) | 1.01051e6i | 0.517382i | ||||||||
\(126\) | − | 607768.i | − | 0.303827i | ||||||
\(127\) | 1.38363e6 | 0.675475 | 0.337738 | − | 0.941240i | \(-0.390338\pi\) | ||||
0.337738 | + | 0.941240i | \(0.390338\pi\) | |||||||
\(128\) | −185364. | −0.0883883 | ||||||||
\(129\) | 163258.i | 0.0760511i | ||||||||
\(130\) | − | 171729.i | − | 0.0781653i | ||||||
\(131\) | −258442. | −0.114961 | −0.0574804 | − | 0.998347i | \(-0.518307\pi\) | ||||
−0.0574804 | + | 0.998347i | \(0.518307\pi\) | |||||||
\(132\) | − | 466312.i | − | 0.202747i | ||||||
\(133\) | 2.67826e6 | 1.13841 | ||||||||
\(134\) | − | 742259.i | − | 0.308490i | ||||||
\(135\) | − | 127065.i | − | 0.0516447i | ||||||
\(136\) | − | 683966.i | − | 0.271905i | ||||||
\(137\) | − | 2.73504e6i | − | 1.06366i | −0.846851 | − | 0.531830i | \(-0.821505\pi\) | ||
0.846851 | − | 0.531830i | \(-0.178495\pi\) | |||||||
\(138\) | 994362. | + | 402953.i | 0.378362 | + | 0.153326i | ||||
\(139\) | 816705. | 0.304103 | 0.152051 | − | 0.988373i | \(-0.451412\pi\) | ||||
0.152051 | + | 0.988373i | \(0.451412\pi\) | |||||||
\(140\) | −474596. | −0.172958 | ||||||||
\(141\) | 2.88943e6 | 1.03075 | ||||||||
\(142\) | 1.23873e6 | 0.432624 | ||||||||
\(143\) | 846008.i | 0.289312i | ||||||||
\(144\) | 248832. | 0.0833333 | ||||||||
\(145\) | 60090.7i | 0.0197108i | ||||||||
\(146\) | 34057.2 | 0.0109434 | ||||||||
\(147\) | 1.21334e6 | 0.381971 | ||||||||
\(148\) | 1.30091e6i | 0.401293i | ||||||||
\(149\) | − | 355203.i | − | 0.107379i | −0.998558 | − | 0.0536893i | \(-0.982902\pi\) | ||
0.998558 | − | 0.0536893i | \(-0.0170980\pi\) | |||||||
\(150\) | 1.27861e6 | 0.378849 | ||||||||
\(151\) | −2.10126e6 | −0.610308 | −0.305154 | − | 0.952303i | \(-0.598708\pi\) | ||||
−0.305154 | + | 0.952303i | \(0.598708\pi\) | |||||||
\(152\) | 1.09653e6i | 0.312242i | ||||||||
\(153\) | 918154.i | 0.256355i | ||||||||
\(154\) | 2.33806e6 | 0.640166 | ||||||||
\(155\) | − | 112069.i | − | 0.0300948i | ||||||
\(156\) | −451445. | −0.118913 | ||||||||
\(157\) | − | 4.24779e6i | − | 1.09765i | −0.835938 | − | 0.548825i | \(-0.815075\pi\) | ||
0.835938 | − | 0.548825i | \(-0.184925\pi\) | |||||||
\(158\) | 5.09075e6i | 1.29066i | ||||||||
\(159\) | − | 905239.i | − | 0.225202i | ||||||
\(160\) | − | 194309.i | − | 0.0474387i | ||||||
\(161\) | −2.02038e6 | + | 4.98566e6i | −0.484122 | + | 1.19466i | ||||
\(162\) | −334032. | −0.0785674 | ||||||||
\(163\) | 878525. | 0.202858 | 0.101429 | − | 0.994843i | \(-0.467659\pi\) | ||||
0.101429 | + | 0.994843i | \(0.467659\pi\) | |||||||
\(164\) | −1.42471e6 | −0.322995 | ||||||||
\(165\) | 488814. | 0.108816 | ||||||||
\(166\) | − | 3.19203e6i | − | 0.697818i | ||||||
\(167\) | −5.95043e6 | −1.27761 | −0.638806 | − | 0.769368i | \(-0.720571\pi\) | ||||
−0.638806 | + | 0.769368i | \(0.720571\pi\) | |||||||
\(168\) | 1.24763e6i | 0.263122i | ||||||||
\(169\) | −4.00777e6 | −0.830315 | ||||||||
\(170\) | 716971. | 0.145934 | ||||||||
\(171\) | − | 1.47198e6i | − | 0.294384i | ||||||
\(172\) | − | 335136.i | − | 0.0658622i | ||||||
\(173\) | −2.66904e6 | −0.515486 | −0.257743 | − | 0.966214i | \(-0.582979\pi\) | ||||
−0.257743 | + | 0.966214i | \(0.582979\pi\) | |||||||
\(174\) | 157968. | 0.0299861 | ||||||||
\(175\) | 6.41089e6i | 1.19620i | ||||||||
\(176\) | 957245.i | 0.175584i | ||||||||
\(177\) | 5.64358e6 | 1.01774 | ||||||||
\(178\) | − | 4.35779e6i | − | 0.772692i | ||||||
\(179\) | −6.73227e6 | −1.17382 | −0.586911 | − | 0.809651i | \(-0.699656\pi\) | ||||
−0.586911 | + | 0.809651i | \(0.699656\pi\) | |||||||
\(180\) | 260840.i | 0.0447256i | ||||||||
\(181\) | 1.03632e6i | 0.174766i | 0.996175 | + | 0.0873829i | \(0.0278503\pi\) | ||||
−0.996175 | + | 0.0873829i | \(0.972150\pi\) | |||||||
\(182\) | − | 2.26351e6i | − | 0.375464i | ||||||
\(183\) | − | 5.93061e6i | − | 0.967712i | ||||||
\(184\) | −2.04123e6 | − | 827182.i | −0.327671 | − | 0.132785i | ||||
\(185\) | −1.36368e6 | −0.215377 | ||||||||
\(186\) | −294610. | −0.0457835 | ||||||||
\(187\) | −3.53210e6 | −0.540142 | ||||||||
\(188\) | −5.93142e6 | −0.892658 | ||||||||
\(189\) | − | 1.67481e6i | − | 0.248074i | ||||||
\(190\) | −1.14945e6 | −0.167582 | ||||||||
\(191\) | 2.29492e6i | 0.329357i | 0.986347 | + | 0.164679i | \(0.0526587\pi\) | ||||
−0.986347 | + | 0.164679i | \(0.947341\pi\) | |||||||
\(192\) | −510803. | −0.0721688 | ||||||||
\(193\) | −2.79873e6 | −0.389305 | −0.194652 | − | 0.980872i | \(-0.562358\pi\) | ||||
−0.194652 | + | 0.980872i | \(0.562358\pi\) | |||||||
\(194\) | 9.66732e6i | 1.32404i | ||||||||
\(195\) | − | 473230.i | − | 0.0638217i | ||||||
\(196\) | −2.49075e6 | −0.330797 | ||||||||
\(197\) | 234382. | 0.0306566 | 0.0153283 | − | 0.999883i | \(-0.495121\pi\) | ||||
0.0153283 | + | 0.999883i | \(0.495121\pi\) | |||||||
\(198\) | − | 1.28500e6i | − | 0.165542i | ||||||
\(199\) | 1.20699e7i | 1.53159i | 0.643084 | + | 0.765796i | \(0.277655\pi\) | ||||
−0.643084 | + | 0.765796i | \(0.722345\pi\) | |||||||
\(200\) | −2.62474e6 | −0.328093 | ||||||||
\(201\) | − | 2.04542e6i | − | 0.251881i | ||||||
\(202\) | 3.12827e6 | 0.379534 | ||||||||
\(203\) | 792039.i | 0.0946800i | ||||||||
\(204\) | − | 1.88479e6i | − | 0.222010i | ||||||
\(205\) | − | 1.49346e6i | − | 0.173354i | ||||||
\(206\) | − | 6.10519e6i | − | 0.698390i | ||||||
\(207\) | 2.74014e6 | + | 1.11041e6i | 0.308931 | + | 0.125191i | ||||
\(208\) | 926726. | 0.102982 | ||||||||
\(209\) | 5.66265e6 | 0.620270 | ||||||||
\(210\) | −1.30783e6 | −0.141219 | ||||||||
\(211\) | −9.75965e6 | −1.03893 | −0.519466 | − | 0.854491i | \(-0.673869\pi\) | ||||
−0.519466 | + | 0.854491i | \(0.673869\pi\) | |||||||
\(212\) | 1.85827e6i | 0.195030i | ||||||||
\(213\) | 3.41353e6 | 0.353236 | ||||||||
\(214\) | − | 2.21530e6i | − | 0.226044i | ||||||
\(215\) | 351309. | 0.0353487 | ||||||||
\(216\) | 685700. | 0.0680414 | ||||||||
\(217\) | − | 1.47715e6i | − | 0.144560i | ||||||
\(218\) | 2.02540e6i | 0.195497i | ||||||||
\(219\) | 93850.7 | 0.00893522 | ||||||||
\(220\) | −1.00344e6 | −0.0942373 | ||||||||
\(221\) | 3.41949e6i | 0.316799i | ||||||||
\(222\) | 3.58488e6i | 0.327654i | ||||||||
\(223\) | 4.34029e6 | 0.391385 | 0.195692 | − | 0.980665i | \(-0.437305\pi\) | ||||
0.195692 | + | 0.980665i | \(0.437305\pi\) | |||||||
\(224\) | − | 2.56113e6i | − | 0.227870i | ||||||
\(225\) | 3.52345e6 | 0.309329 | ||||||||
\(226\) | 4.77700e6i | 0.413838i | ||||||||
\(227\) | 3.60786e6i | 0.308441i | 0.988036 | + | 0.154221i | \(0.0492867\pi\) | ||||
−0.988036 | + | 0.154221i | \(0.950713\pi\) | |||||||
\(228\) | 3.02169e6i | 0.254944i | ||||||||
\(229\) | 3.02966e6i | 0.252283i | 0.992012 | + | 0.126141i | \(0.0402593\pi\) | ||||
−0.992012 | + | 0.126141i | \(0.959741\pi\) | |||||||
\(230\) | 867099. | − | 2.13973e6i | 0.0712665 | − | 0.175863i | ||||
\(231\) | 6.44292e6 | 0.522693 | ||||||||
\(232\) | −324276. | −0.0259687 | ||||||||
\(233\) | 8.26090e6 | 0.653070 | 0.326535 | − | 0.945185i | \(-0.394119\pi\) | ||||
0.326535 | + | 0.945185i | \(0.394119\pi\) | |||||||
\(234\) | −1.24404e6 | −0.0970924 | ||||||||
\(235\) | − | 6.21765e6i | − | 0.479096i | ||||||
\(236\) | −1.15852e7 | −0.881385 | ||||||||
\(237\) | 1.40285e7i | 1.05382i | ||||||||
\(238\) | 9.45020e6 | 0.700987 | ||||||||
\(239\) | −1.15513e7 | −0.846133 | −0.423067 | − | 0.906099i | \(-0.639046\pi\) | ||||
−0.423067 | + | 0.906099i | \(0.639046\pi\) | |||||||
\(240\) | − | 535452.i | − | 0.0387335i | ||||||
\(241\) | − | 1.58670e7i | − | 1.13356i | −0.823870 | − | 0.566779i | \(-0.808189\pi\) | ||
0.823870 | − | 0.566779i | \(-0.191811\pi\) | |||||||
\(242\) | −5.07811e6 | −0.358308 | ||||||||
\(243\) | −920483. | −0.0641500 | ||||||||
\(244\) | 1.21744e7i | 0.838063i | ||||||||
\(245\) | − | 2.61094e6i | − | 0.177541i | ||||||
\(246\) | −3.92604e6 | −0.263724 | ||||||||
\(247\) | − | 5.48211e6i | − | 0.363795i | ||||||
\(248\) | 604776. | 0.0396497 | ||||||||
\(249\) | − | 8.79619e6i | − | 0.569766i | ||||||
\(250\) | − | 5.71632e6i | − | 0.365844i | ||||||
\(251\) | − | 2.91662e7i | − | 1.84441i | −0.386698 | − | 0.922206i | \(-0.626385\pi\) | ||
0.386698 | − | 0.922206i | \(-0.373615\pi\) | |||||||
\(252\) | 3.43805e6i | 0.214838i | ||||||||
\(253\) | −4.27169e6 | + | 1.05412e7i | −0.263778 | + | 0.650921i | ||||
\(254\) | −7.82701e6 | −0.477633 | ||||||||
\(255\) | 1.97574e6 | 0.119154 | ||||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | 1.38551e7 | 0.816225 | 0.408112 | − | 0.912932i | \(-0.366187\pi\) | ||||
0.408112 | + | 0.912932i | \(0.366187\pi\) | |||||||
\(258\) | − | 923527.i | − | 0.0537762i | ||||||
\(259\) | −1.79743e7 | −1.03455 | ||||||||
\(260\) | 971447.i | 0.0552712i | ||||||||
\(261\) | 435307. | 0.0244836 | ||||||||
\(262\) | 1.46197e6 | 0.0812895 | ||||||||
\(263\) | − | 2.31379e6i | − | 0.127191i | −0.997976 | − | 0.0635954i | \(-0.979743\pi\) | ||
0.997976 | − | 0.0635954i | \(-0.0202567\pi\) | |||||||
\(264\) | 2.63786e6i | 0.143364i | ||||||||
\(265\) | −1.94795e6 | −0.104674 | ||||||||
\(266\) | −1.51505e7 | −0.804976 | ||||||||
\(267\) | − | 1.20087e7i | − | 0.630901i | ||||||
\(268\) | 4.19885e6i | 0.218135i | ||||||||
\(269\) | 1.36375e7 | 0.700611 | 0.350305 | − | 0.936636i | \(-0.386078\pi\) | ||||
0.350305 | + | 0.936636i | \(0.386078\pi\) | |||||||
\(270\) | 718790.i | 0.0365183i | ||||||||
\(271\) | 8.01260e6 | 0.402593 | 0.201296 | − | 0.979530i | \(-0.435485\pi\) | ||||
0.201296 | + | 0.979530i | \(0.435485\pi\) | |||||||
\(272\) | 3.86909e6i | 0.192266i | ||||||||
\(273\) | − | 6.23751e6i | − | 0.306565i | ||||||
\(274\) | 1.54717e7i | 0.752121i | ||||||||
\(275\) | 1.35545e7i | 0.651759i | ||||||||
\(276\) | −5.62496e6 | − | 2.27945e6i | −0.267542 | − | 0.108418i | ||||
\(277\) | 1.52540e7 | 0.717701 | 0.358851 | − | 0.933395i | \(-0.383169\pi\) | ||||
0.358851 | + | 0.933395i | \(0.383169\pi\) | |||||||
\(278\) | −4.61998e6 | −0.215033 | ||||||||
\(279\) | −811850. | −0.0373821 | ||||||||
\(280\) | 2.68472e6 | 0.122300 | ||||||||
\(281\) | 1.91616e7i | 0.863602i | 0.901969 | + | 0.431801i | \(0.142122\pi\) | ||||
−0.901969 | + | 0.431801i | \(0.857878\pi\) | |||||||
\(282\) | −1.63451e7 | −0.728853 | ||||||||
\(283\) | 1.35387e7i | 0.597336i | 0.954357 | + | 0.298668i | \(0.0965424\pi\) | ||||
−0.954357 | + | 0.298668i | \(0.903458\pi\) | |||||||
\(284\) | −7.00730e6 | −0.305911 | ||||||||
\(285\) | −3.16750e6 | −0.136830 | ||||||||
\(286\) | − | 4.78575e6i | − | 0.204575i | ||||||
\(287\) | − | 1.96849e7i | − | 0.832698i | ||||||
\(288\) | −1.40761e6 | −0.0589256 | ||||||||
\(289\) | 9.86117e6 | 0.408540 | ||||||||
\(290\) | − | 339924.i | − | 0.0139376i | ||||||
\(291\) | 2.66400e7i | 1.08107i | ||||||||
\(292\) | −192657. | −0.00773813 | ||||||||
\(293\) | 2.43156e7i | 0.966678i | 0.875433 | + | 0.483339i | \(0.160576\pi\) | ||||
−0.875433 | + | 0.483339i | \(0.839424\pi\) | |||||||
\(294\) | −6.86369e6 | −0.270094 | ||||||||
\(295\) | − | 1.21442e7i | − | 0.473046i | ||||||
\(296\) | − | 7.35904e6i | − | 0.283757i | ||||||
\(297\) | − | 3.54106e6i | − | 0.135165i | ||||||
\(298\) | 2.00933e6i | 0.0759281i | ||||||||
\(299\) | 1.02051e7 | + | 4.13550e6i | 0.381772 | + | 0.154708i | ||||
\(300\) | −7.23294e6 | −0.267887 | ||||||||
\(301\) | 4.63050e6 | 0.169796 | ||||||||
\(302\) | 1.18865e7 | 0.431553 | ||||||||
\(303\) | 8.62051e6 | 0.309888 | ||||||||
\(304\) | − | 6.20292e6i | − | 0.220788i | ||||||
\(305\) | −1.27618e7 | −0.449794 | ||||||||
\(306\) | − | 5.19386e6i | − | 0.181270i | ||||||
\(307\) | 1.80406e7 | 0.623499 | 0.311749 | − | 0.950164i | \(-0.399085\pi\) | ||||
0.311749 | + | 0.950164i | \(0.399085\pi\) | |||||||
\(308\) | −1.32260e7 | −0.452666 | ||||||||
\(309\) | − | 1.68239e7i | − | 0.570233i | ||||||
\(310\) | 633960.i | 0.0212803i | ||||||||
\(311\) | 2.01821e7 | 0.670941 | 0.335471 | − | 0.942051i | \(-0.391105\pi\) | ||||
0.335471 | + | 0.942051i | \(0.391105\pi\) | |||||||
\(312\) | 2.55376e6 | 0.0840845 | ||||||||
\(313\) | − | 2.18089e6i | − | 0.0711216i | −0.999368 | − | 0.0355608i | \(-0.988678\pi\) | ||
0.999368 | − | 0.0355608i | \(-0.0113217\pi\) | |||||||
\(314\) | 2.40291e7i | 0.776155i | ||||||||
\(315\) | −3.60396e6 | −0.115305 | ||||||||
\(316\) | − | 2.87976e7i | − | 0.912632i | ||||||
\(317\) | 4.95925e7 | 1.55682 | 0.778409 | − | 0.627757i | \(-0.216027\pi\) | ||||
0.778409 | + | 0.627757i | \(0.216027\pi\) | |||||||
\(318\) | 5.12080e6i | 0.159242i | ||||||||
\(319\) | 1.67461e6i | 0.0515871i | ||||||||
\(320\) | 1.09918e6i | 0.0335442i | ||||||||
\(321\) | − | 6.10466e6i | − | 0.184564i | ||||||
\(322\) | 1.14290e7 | − | 2.82032e7i | 0.342326 | − | 0.844754i | ||||
\(323\) | 2.28879e7 | 0.679201 | ||||||||
\(324\) | 1.88957e6 | 0.0555556 | ||||||||
\(325\) | 1.31224e7 | 0.382264 | ||||||||
\(326\) | −4.96969e6 | −0.143442 | ||||||||
\(327\) | 5.58134e6i | 0.159623i | ||||||||
\(328\) | 8.05938e6 | 0.228392 | ||||||||
\(329\) | − | 8.19531e7i | − | 2.30132i | ||||||
\(330\) | −2.76515e6 | −0.0769444 | ||||||||
\(331\) | −4.39198e7 | −1.21109 | −0.605545 | − | 0.795811i | \(-0.707045\pi\) | ||||
−0.605545 | + | 0.795811i | \(0.707045\pi\) | |||||||
\(332\) | 1.80568e7i | 0.493432i | ||||||||
\(333\) | 9.87876e6i | 0.267528i | ||||||||
\(334\) | 3.36607e7 | 0.903408 | ||||||||
\(335\) | −4.40147e6 | −0.117075 | ||||||||
\(336\) | − | 7.05764e6i | − | 0.186055i | ||||||
\(337\) | − | 5.83063e7i | − | 1.52344i | −0.647906 | − | 0.761720i | \(-0.724355\pi\) | ||
0.647906 | − | 0.761720i | \(-0.275645\pi\) | |||||||
\(338\) | 2.26714e7 | 0.587122 | ||||||||
\(339\) | 1.31639e7i | 0.337897i | ||||||||
\(340\) | −4.05580e6 | −0.103191 | ||||||||
\(341\) | − | 3.12315e6i | − | 0.0787643i | ||||||
\(342\) | 8.32679e6i | 0.208161i | ||||||||
\(343\) | 1.76029e7i | 0.436216i | ||||||||
\(344\) | 1.89582e6i | 0.0465716i | ||||||||
\(345\) | 2.38944e6 | − | 5.89640e6i | 0.0581888 | − | 0.143592i | ||||
\(346\) | 1.50984e7 | 0.364504 | ||||||||
\(347\) | 2.74516e7 | 0.657022 | 0.328511 | − | 0.944500i | \(-0.393453\pi\) | ||||
0.328511 | + | 0.944500i | \(0.393453\pi\) | |||||||
\(348\) | −893600. | −0.0212034 | ||||||||
\(349\) | −2.13234e7 | −0.501627 | −0.250814 | − | 0.968035i | \(-0.580698\pi\) | ||||
−0.250814 | + | 0.968035i | \(0.580698\pi\) | |||||||
\(350\) | − | 3.62655e7i | − | 0.845841i | ||||||
\(351\) | −3.42816e6 | −0.0792756 | ||||||||
\(352\) | − | 5.41500e6i | − | 0.124157i | ||||||
\(353\) | 5.14945e7 | 1.17068 | 0.585338 | − | 0.810789i | \(-0.300962\pi\) | ||||
0.585338 | + | 0.810789i | \(0.300962\pi\) | |||||||
\(354\) | −3.19249e7 | −0.719648 | ||||||||
\(355\) | − | 7.34545e6i | − | 0.164185i | ||||||
\(356\) | 2.46514e7i | 0.546376i | ||||||||
\(357\) | 2.60417e7 | 0.572353 | ||||||||
\(358\) | 3.80835e7 | 0.830018 | ||||||||
\(359\) | 1.63451e7i | 0.353267i | 0.984277 | + | 0.176633i | \(0.0565207\pi\) | ||||
−0.984277 | + | 0.176633i | \(0.943479\pi\) | |||||||
\(360\) | − | 1.47553e6i | − | 0.0316258i | ||||||
\(361\) | 1.03521e7 | 0.220042 | ||||||||
\(362\) | − | 5.86229e6i | − | 0.123578i | ||||||
\(363\) | −1.39936e7 | −0.292557 | ||||||||
\(364\) | 1.28044e7i | 0.265493i | ||||||||
\(365\) | − | 201954.i | − | 0.00415311i | ||||||
\(366\) | 3.35486e7i | 0.684275i | ||||||||
\(367\) | 9.15308e7i | 1.85169i | 0.377899 | + | 0.925847i | \(0.376647\pi\) | ||||
−0.377899 | + | 0.925847i | \(0.623353\pi\) | |||||||
\(368\) | 1.15469e7 | + | 4.67925e6i | 0.231698 | + | 0.0938929i | ||||
\(369\) | −1.08189e7 | −0.215330 | ||||||||
\(370\) | 7.71416e6 | 0.152294 | ||||||||
\(371\) | −2.56754e7 | −0.502799 | ||||||||
\(372\) | 1.66657e6 | 0.0323738 | ||||||||
\(373\) | 4.32183e7i | 0.832802i | 0.909181 | + | 0.416401i | \(0.136709\pi\) | ||||
−0.909181 | + | 0.416401i | \(0.863291\pi\) | |||||||
\(374\) | 1.99806e7 | 0.381938 | ||||||||
\(375\) | − | 1.57523e7i | − | 0.298711i | ||||||
\(376\) | 3.35532e7 | 0.631205 | ||||||||
\(377\) | 1.62122e6 | 0.0302564 | ||||||||
\(378\) | 9.47416e6i | 0.175415i | ||||||||
\(379\) | − | 3.38091e7i | − | 0.621036i | −0.950568 | − | 0.310518i | \(-0.899498\pi\) | ||
0.950568 | − | 0.310518i | \(-0.100502\pi\) | |||||||
\(380\) | 6.50225e6 | 0.118499 | ||||||||
\(381\) | −2.15687e7 | −0.389986 | ||||||||
\(382\) | − | 1.29820e7i | − | 0.232891i | ||||||
\(383\) | − | 9.68623e7i | − | 1.72408i | −0.506837 | − | 0.862042i | \(-0.669185\pi\) | ||
0.506837 | − | 0.862042i | \(-0.330815\pi\) | |||||||
\(384\) | 2.88954e6 | 0.0510310 | ||||||||
\(385\) | − | 1.38643e7i | − | 0.242949i | ||||||
\(386\) | 1.58320e7 | 0.275280 | ||||||||
\(387\) | − | 2.54494e6i | − | 0.0439081i | ||||||
\(388\) | − | 5.46866e7i | − | 0.936237i | ||||||
\(389\) | 7.26653e7i | 1.23446i | 0.786781 | + | 0.617232i | \(0.211746\pi\) | ||||
−0.786781 | + | 0.617232i | \(0.788254\pi\) | |||||||
\(390\) | 2.67699e6i | 0.0451287i | ||||||||
\(391\) | −1.72658e7 | + | 4.26065e7i | −0.288839 | + | 0.712764i | ||||
\(392\) | 1.40898e7 | 0.233909 | ||||||||
\(393\) | 4.02872e6 | 0.0663726 | ||||||||
\(394\) | −1.32586e6 | −0.0216775 | ||||||||
\(395\) | 3.01873e7 | 0.489816 | ||||||||
\(396\) | 7.26908e6i | 0.117056i | ||||||||
\(397\) | −1.07291e8 | −1.71472 | −0.857359 | − | 0.514719i | \(-0.827896\pi\) | ||||
−0.857359 | + | 0.514719i | \(0.827896\pi\) | |||||||
\(398\) | − | 6.82774e7i | − | 1.08300i | ||||||
\(399\) | −4.17500e7 | −0.657260 | ||||||||
\(400\) | 1.48478e7 | 0.231997 | ||||||||
\(401\) | − | 5.88999e7i | − | 0.913443i | −0.889610 | − | 0.456721i | \(-0.849024\pi\) | ||
0.889610 | − | 0.456721i | \(-0.150976\pi\) | |||||||
\(402\) | 1.15707e7i | 0.178107i | ||||||||
\(403\) | −3.02358e6 | −0.0461962 | ||||||||
\(404\) | −1.76962e7 | −0.268371 | ||||||||
\(405\) | 1.98075e6i | 0.0298171i | ||||||||
\(406\) | − | 4.48045e6i | − | 0.0669489i | ||||||
\(407\) | −3.80031e7 | −0.563685 | ||||||||
\(408\) | 1.06620e7i | 0.156985i | ||||||||
\(409\) | −4.04025e7 | −0.590525 | −0.295263 | − | 0.955416i | \(-0.595407\pi\) | ||||
−0.295263 | + | 0.955416i | \(0.595407\pi\) | |||||||
\(410\) | 8.44830e6i | 0.122579i | ||||||||
\(411\) | 4.26351e7i | 0.614104i | ||||||||
\(412\) | 3.45362e7i | 0.493836i | ||||||||
\(413\) | − | 1.60069e8i | − | 2.27226i | ||||||
\(414\) | −1.55006e7 | − | 6.28142e6i | −0.218447 | − | 0.0885231i | ||||
\(415\) | −1.89282e7 | −0.264829 | ||||||||
\(416\) | −5.24235e6 | −0.0728193 | ||||||||
\(417\) | −1.27312e7 | −0.175574 | ||||||||
\(418\) | −3.20328e7 | −0.438597 | ||||||||
\(419\) | 1.08968e8i | 1.48135i | 0.671864 | + | 0.740674i | \(0.265494\pi\) | ||||
−0.671864 | + | 0.740674i | \(0.734506\pi\) | |||||||
\(420\) | 7.39822e6 | 0.0998572 | ||||||||
\(421\) | 1.28899e8i | 1.72745i | 0.503967 | + | 0.863723i | \(0.331873\pi\) | ||||
−0.503967 | + | 0.863723i | \(0.668127\pi\) | |||||||
\(422\) | 5.52089e7 | 0.734636 | ||||||||
\(423\) | −4.50417e7 | −0.595106 | ||||||||
\(424\) | − | 1.05120e7i | − | 0.137907i | ||||||
\(425\) | 5.47862e7i | 0.713681i | ||||||||
\(426\) | −1.93098e7 | −0.249776 | ||||||||
\(427\) | −1.68210e8 | −2.16057 | ||||||||
\(428\) | 1.25317e7i | 0.159837i | ||||||||
\(429\) | − | 1.31880e7i | − | 0.167034i | ||||||
\(430\) | −1.98730e6 | −0.0249953 | ||||||||
\(431\) | 1.24171e8i | 1.55092i | 0.631399 | + | 0.775458i | \(0.282481\pi\) | ||||
−0.631399 | + | 0.775458i | \(0.717519\pi\) | |||||||
\(432\) | −3.87891e6 | −0.0481125 | ||||||||
\(433\) | 9.57857e7i | 1.17988i | 0.807448 | + | 0.589939i | \(0.200848\pi\) | ||||
−0.807448 | + | 0.589939i | \(0.799152\pi\) | |||||||
\(434\) | 8.35605e6i | 0.102219i | ||||||||
\(435\) | − | 936722.i | − | 0.0113800i | ||||||
\(436\) | − | 1.14574e7i | − | 0.138238i | ||||||
\(437\) | 2.76804e7 | − | 6.83066e7i | 0.331687 | − | 0.818500i | ||||
\(438\) | −530900. | −0.00631815 | ||||||||
\(439\) | −1.34328e8 | −1.58772 | −0.793859 | − | 0.608102i | \(-0.791931\pi\) | ||||
−0.793859 | + | 0.608102i | \(0.791931\pi\) | |||||||
\(440\) | 5.67631e6 | 0.0666358 | ||||||||
\(441\) | −1.89141e7 | −0.220531 | ||||||||
\(442\) | − | 1.93435e7i | − | 0.224011i | ||||||
\(443\) | −1.27436e8 | −1.46582 | −0.732909 | − | 0.680327i | \(-0.761838\pi\) | ||||
−0.732909 | + | 0.680327i | \(0.761838\pi\) | |||||||
\(444\) | − | 2.02791e7i | − | 0.231686i | ||||||
\(445\) | −2.58410e7 | −0.293244 | ||||||||
\(446\) | −2.45524e7 | −0.276751 | ||||||||
\(447\) | 5.53706e6i | 0.0619950i | ||||||||
\(448\) | 1.44879e7i | 0.161129i | ||||||||
\(449\) | 1.09130e8 | 1.20560 | 0.602801 | − | 0.797891i | \(-0.294051\pi\) | ||||
0.602801 | + | 0.797891i | \(0.294051\pi\) | |||||||
\(450\) | −1.99316e7 | −0.218728 | ||||||||
\(451\) | − | 4.16198e7i | − | 0.453702i | ||||||
\(452\) | − | 2.70228e7i | − | 0.292627i | ||||||
\(453\) | 3.27554e7 | 0.352362 | ||||||||
\(454\) | − | 2.04092e7i | − | 0.218101i | ||||||
\(455\) | −1.34223e7 | −0.142492 | ||||||||
\(456\) | − | 1.70932e7i | − | 0.180273i | ||||||
\(457\) | 2.47924e7i | 0.259759i | 0.991530 | + | 0.129879i | \(0.0414590\pi\) | ||||
−0.991530 | + | 0.129879i | \(0.958541\pi\) | |||||||
\(458\) | − | 1.71384e7i | − | 0.178391i | ||||||
\(459\) | − | 1.43126e7i | − | 0.148006i | ||||||
\(460\) | −4.90505e6 | + | 1.21041e7i | −0.0503930 | + | 0.124354i | ||||
\(461\) | 1.30389e7 | 0.133088 | 0.0665440 | − | 0.997783i | \(-0.478803\pi\) | ||||
0.0665440 | + | 0.997783i | \(0.478803\pi\) | |||||||
\(462\) | −3.64467e7 | −0.369600 | ||||||||
\(463\) | −5.04368e7 | −0.508165 | −0.254083 | − | 0.967183i | \(-0.581773\pi\) | ||||
−0.254083 | + | 0.967183i | \(0.581773\pi\) | |||||||
\(464\) | 1.83438e6 | 0.0183627 | ||||||||
\(465\) | 1.74699e6i | 0.0173753i | ||||||||
\(466\) | −4.67307e7 | −0.461790 | ||||||||
\(467\) | 1.41528e8i | 1.38961i | 0.719199 | + | 0.694804i | \(0.244509\pi\) | ||||
−0.719199 | + | 0.694804i | \(0.755491\pi\) | |||||||
\(468\) | 7.03733e6 | 0.0686547 | ||||||||
\(469\) | −5.80145e7 | −0.562365 | ||||||||
\(470\) | 3.51724e7i | 0.338772i | ||||||||
\(471\) | 6.62164e7i | 0.633728i | ||||||||
\(472\) | 6.55355e7 | 0.623234 | ||||||||
\(473\) | 9.79027e6 | 0.0925148 | ||||||||
\(474\) | − | 7.93570e7i | − | 0.745161i | ||||||
\(475\) | − | 8.78331e7i | − | 0.819553i | ||||||
\(476\) | −5.34584e7 | −0.495673 | ||||||||
\(477\) | 1.41113e7i | 0.130020i | ||||||||
\(478\) | 6.53443e7 | 0.598306 | ||||||||
\(479\) | 1.16403e7i | 0.105915i | 0.998597 | + | 0.0529575i | \(0.0168648\pi\) | ||||
−0.998597 | + | 0.0529575i | \(0.983135\pi\) | |||||||
\(480\) | 3.02897e6i | 0.0273887i | ||||||||
\(481\) | 3.67915e7i | 0.330607i | ||||||||
\(482\) | 8.97573e7i | 0.801546i | ||||||||
\(483\) | 3.14946e7 | − | 7.77188e7i | 0.279508 | − | 0.689739i | ||||
\(484\) | 2.87261e7 | 0.253362 | ||||||||
\(485\) | 5.73256e7 | 0.502485 | ||||||||
\(486\) | 5.20704e6 | 0.0453609 | ||||||||
\(487\) | −3.71781e7 | −0.321885 | −0.160942 | − | 0.986964i | \(-0.551453\pi\) | ||||
−0.160942 | + | 0.986964i | \(0.551453\pi\) | |||||||
\(488\) | − | 6.88686e7i | − | 0.592600i | ||||||
\(489\) | −1.36949e7 | −0.117120 | ||||||||
\(490\) | 1.47697e7i | 0.125540i | ||||||||
\(491\) | 1.93343e7 | 0.163337 | 0.0816685 | − | 0.996660i | \(-0.473975\pi\) | ||||
0.0816685 | + | 0.996660i | \(0.473975\pi\) | |||||||
\(492\) | 2.22090e7 | 0.186481 | ||||||||
\(493\) | 6.76861e6i | 0.0564883i | ||||||||
\(494\) | 3.10115e7i | 0.257242i | ||||||||
\(495\) | −7.61986e6 | −0.0628249 | ||||||||
\(496\) | −3.42113e6 | −0.0280365 | ||||||||
\(497\) | − | 9.68182e7i | − | 0.788657i | ||||||
\(498\) | 4.97588e7i | 0.402886i | ||||||||
\(499\) | −1.16003e8 | −0.933611 | −0.466805 | − | 0.884360i | \(-0.654595\pi\) | ||||
−0.466805 | + | 0.884360i | \(0.654595\pi\) | |||||||
\(500\) | 3.23364e7i | 0.258691i | ||||||||
\(501\) | 9.27581e7 | 0.737630 | ||||||||
\(502\) | 1.64989e8i | 1.30420i | ||||||||
\(503\) | − | 1.79808e8i | − | 1.41288i | −0.707774 | − | 0.706439i | \(-0.750301\pi\) | ||
0.707774 | − | 0.706439i | \(-0.249699\pi\) | |||||||
\(504\) | − | 1.94486e7i | − | 0.151913i | ||||||
\(505\) | − | 1.85501e7i | − | 0.144037i | ||||||
\(506\) | 2.41643e7 | − | 5.96300e7i | 0.186519 | − | 0.460271i | ||||
\(507\) | 6.24750e7 | 0.479383 | ||||||||
\(508\) | 4.42762e7 | 0.337738 | ||||||||
\(509\) | 8.87698e7 | 0.673150 | 0.336575 | − | 0.941657i | \(-0.390731\pi\) | ||||
0.336575 | + | 0.941657i | \(0.390731\pi\) | |||||||
\(510\) | −1.11765e7 | −0.0842548 | ||||||||
\(511\) | − | 2.66190e6i | − | 0.0199493i | ||||||
\(512\) | −5.93164e6 | −0.0441942 | ||||||||
\(513\) | 2.29459e7i | 0.169963i | ||||||||
\(514\) | −7.83762e7 | −0.577158 | ||||||||
\(515\) | −3.62028e7 | −0.265045 | ||||||||
\(516\) | 5.22426e6i | 0.0380255i | ||||||||
\(517\) | − | 1.73274e8i | − | 1.25389i | ||||||
\(518\) | 1.01678e8 | 0.731541 | ||||||||
\(519\) | 4.16062e7 | 0.297616 | ||||||||
\(520\) | − | 5.49533e6i | − | 0.0390826i | ||||||
\(521\) | 1.45342e8i | 1.02773i | 0.857872 | + | 0.513863i | \(0.171786\pi\) | ||||
−0.857872 | + | 0.513863i | \(0.828214\pi\) | |||||||
\(522\) | −2.46247e6 | −0.0173125 | ||||||||
\(523\) | − | 1.34862e8i | − | 0.942723i | −0.881940 | − | 0.471361i | \(-0.843763\pi\) | ||
0.881940 | − | 0.471361i | \(-0.156237\pi\) | |||||||
\(524\) | −8.27015e6 | −0.0574804 | ||||||||
\(525\) | − | 9.99358e7i | − | 0.690627i | ||||||
\(526\) | 1.30888e7i | 0.0899375i | ||||||||
\(527\) | − | 1.26235e7i | − | 0.0862476i | ||||||
\(528\) | − | 1.49220e7i | − | 0.101374i | ||||||
\(529\) | 1.06274e8 | + | 1.03056e8i | 0.717892 | + | 0.696155i | ||||
\(530\) | 1.10193e7 | 0.0740159 | ||||||||
\(531\) | −8.79748e7 | −0.587590 | ||||||||
\(532\) | 8.57044e7 | 0.569204 | ||||||||
\(533\) | −4.02929e7 | −0.266101 | ||||||||
\(534\) | 6.79313e7i | 0.446114i | ||||||||
\(535\) | −1.31364e7 | −0.0857856 | ||||||||
\(536\) | − | 2.37523e7i | − | 0.154245i | ||||||
\(537\) | 1.04946e8 | 0.677707 | ||||||||
\(538\) | −7.71452e7 | −0.495407 | ||||||||
\(539\) | − | 7.27617e7i | − | 0.464661i | ||||||
\(540\) | − | 4.06609e6i | − | 0.0258223i | ||||||
\(541\) | 1.11207e8 | 0.702328 | 0.351164 | − | 0.936314i | \(-0.385786\pi\) | ||||
0.351164 | + | 0.936314i | \(0.385786\pi\) | |||||||
\(542\) | −4.53261e7 | −0.284676 | ||||||||
\(543\) | − | 1.61546e7i | − | 0.100901i | ||||||
\(544\) | − | 2.18869e7i | − | 0.135953i | ||||||
\(545\) | 1.20103e7 | 0.0741931 | ||||||||
\(546\) | 3.52847e7i | 0.216774i | ||||||||
\(547\) | 1.80007e8 | 1.09983 | 0.549916 | − | 0.835220i | \(-0.314660\pi\) | ||||
0.549916 | + | 0.835220i | \(0.314660\pi\) | |||||||
\(548\) | − | 8.75214e7i | − | 0.531830i | ||||||
\(549\) | 9.24490e7i | 0.558709i | ||||||||
\(550\) | − | 7.66761e7i | − | 0.460863i | ||||||
\(551\) | − | 1.08514e7i | − | 0.0648681i | ||||||
\(552\) | 3.18196e7 | + | 1.28945e7i | 0.189181 | + | 0.0766632i | ||||
\(553\) | 3.97890e8 | 2.35282 | ||||||||
\(554\) | −8.62895e7 | −0.507491 | ||||||||
\(555\) | 2.12577e7 | 0.124348 | ||||||||
\(556\) | 2.61346e7 | 0.152051 | ||||||||
\(557\) | − | 7.76980e7i | − | 0.449619i | −0.974403 | − | 0.224809i | \(-0.927824\pi\) | ||
0.974403 | − | 0.224809i | \(-0.0721759\pi\) | |||||||
\(558\) | 4.59252e6 | 0.0264331 | ||||||||
\(559\) | − | 9.47813e6i | − | 0.0542609i | ||||||
\(560\) | −1.51871e7 | −0.0864789 | ||||||||
\(561\) | 5.50599e7 | 0.311851 | ||||||||
\(562\) | − | 1.08395e8i | − | 0.610659i | ||||||
\(563\) | 1.00614e8i | 0.563808i | 0.959443 | + | 0.281904i | \(0.0909660\pi\) | ||||
−0.959443 | + | 0.281904i | \(0.909034\pi\) | |||||||
\(564\) | 9.24617e7 | 0.515377 | ||||||||
\(565\) | 2.83268e7 | 0.157055 | ||||||||
\(566\) | − | 7.65867e7i | − | 0.422380i | ||||||
\(567\) | 2.61077e7i | 0.143225i | ||||||||
\(568\) | 3.96393e7 | 0.216312 | ||||||||
\(569\) | 6.69611e7i | 0.363485i | 0.983346 | + | 0.181742i | \(0.0581737\pi\) | ||||
−0.983346 | + | 0.181742i | \(0.941826\pi\) | |||||||
\(570\) | 1.79181e7 | 0.0967537 | ||||||||
\(571\) | 8.57505e7i | 0.460605i | 0.973119 | + | 0.230302i | \(0.0739715\pi\) | ||||
−0.973119 | + | 0.230302i | \(0.926028\pi\) | |||||||
\(572\) | 2.70723e7i | 0.144656i | ||||||||
\(573\) | − | 3.57742e7i | − | 0.190154i | ||||||
\(574\) | 1.11355e8i | 0.588807i | ||||||||
\(575\) | 1.63504e8 | + | 6.62579e7i | 0.860052 | + | 0.348525i | ||||
\(576\) | 7.96262e6 | 0.0416667 | ||||||||
\(577\) | 2.24145e8 | 1.16681 | 0.583406 | − | 0.812181i | \(-0.301720\pi\) | ||||
0.583406 | + | 0.812181i | \(0.301720\pi\) | |||||||
\(578\) | −5.57832e7 | −0.288882 | ||||||||
\(579\) | 4.36279e7 | 0.224765 | ||||||||
\(580\) | 1.92290e6i | 0.00985538i | ||||||||
\(581\) | −2.49487e8 | −1.27210 | ||||||||
\(582\) | − | 1.50699e8i | − | 0.764434i | ||||||
\(583\) | −5.42854e7 | −0.273954 | ||||||||
\(584\) | 1.08983e6 | 0.00547168 | ||||||||
\(585\) | 7.37692e6i | 0.0368475i | ||||||||
\(586\) | − | 1.37550e8i | − | 0.683544i | ||||||
\(587\) | −1.67841e8 | −0.829821 | −0.414910 | − | 0.909862i | \(-0.636187\pi\) | ||||
−0.414910 | + | 0.909862i | \(0.636187\pi\) | |||||||
\(588\) | 3.88269e7 | 0.190986 | ||||||||
\(589\) | 2.02379e7i | 0.0990421i | ||||||||
\(590\) | 6.86980e7i | 0.334494i | ||||||||
\(591\) | −3.65365e6 | −0.0176996 | ||||||||
\(592\) | 4.16290e7i | 0.200646i | ||||||||
\(593\) | 3.19387e8 | 1.53163 | 0.765813 | − | 0.643064i | \(-0.222337\pi\) | ||||
0.765813 | + | 0.643064i | \(0.222337\pi\) | |||||||
\(594\) | 2.00312e7i | 0.0955759i | ||||||||
\(595\) | − | 5.60381e7i | − | 0.266031i | ||||||
\(596\) | − | 1.13665e7i | − | 0.0536893i | ||||||
\(597\) | − | 1.88150e8i | − | 0.884265i | ||||||
\(598\) | −5.77288e7 | − | 2.33939e7i | −0.269954 | − | 0.109395i | ||||
\(599\) | −1.64679e7 | −0.0766229 | −0.0383114 | − | 0.999266i | \(-0.512198\pi\) | ||||
−0.0383114 | + | 0.999266i | \(0.512198\pi\) | |||||||
\(600\) | 4.09157e7 | 0.189424 | ||||||||
\(601\) | −4.28796e7 | −0.197527 | −0.0987636 | − | 0.995111i | \(-0.531489\pi\) | ||||
−0.0987636 | + | 0.995111i | \(0.531489\pi\) | |||||||
\(602\) | −2.61941e7 | −0.120064 | ||||||||
\(603\) | 3.18850e7i | 0.145424i | ||||||||
\(604\) | −6.72404e7 | −0.305154 | ||||||||
\(605\) | 3.01124e7i | 0.135981i | ||||||||
\(606\) | −4.87650e7 | −0.219124 | ||||||||
\(607\) | 3.76005e8 | 1.68123 | 0.840616 | − | 0.541632i | \(-0.182193\pi\) | ||||
0.840616 | + | 0.541632i | \(0.182193\pi\) | |||||||
\(608\) | 3.50890e7i | 0.156121i | ||||||||
\(609\) | − | 1.23467e7i | − | 0.0546635i | ||||||
\(610\) | 7.21919e7 | 0.318053 | ||||||||
\(611\) | −1.67749e8 | −0.735422 | ||||||||
\(612\) | 2.93809e7i | 0.128177i | ||||||||
\(613\) | − | 2.00965e8i | − | 0.872448i | −0.899838 | − | 0.436224i | \(-0.856315\pi\) | ||
0.899838 | − | 0.436224i | \(-0.143685\pi\) | |||||||
\(614\) | −1.02053e8 | −0.440880 | ||||||||
\(615\) | 2.32808e7i | 0.100086i | ||||||||
\(616\) | 7.48178e7 | 0.320083 | ||||||||
\(617\) | − | 2.35132e8i | − | 1.00105i | −0.865721 | − | 0.500526i | \(-0.833140\pi\) | ||
0.865721 | − | 0.500526i | \(-0.166860\pi\) | |||||||
\(618\) | 9.51705e7i | 0.403215i | ||||||||
\(619\) | − | 3.57033e8i | − | 1.50535i | −0.658394 | − | 0.752674i | \(-0.728764\pi\) | ||
0.658394 | − | 0.752674i | \(-0.271236\pi\) | |||||||
\(620\) | − | 3.58622e6i | − | 0.0150474i | ||||||
\(621\) | −4.27146e7 | − | 1.73095e7i | −0.178361 | − | 0.0722788i | ||||
\(622\) | −1.14167e8 | −0.474427 | ||||||||
\(623\) | −3.40603e8 | −1.40859 | ||||||||
\(624\) | −1.44462e7 | −0.0594567 | ||||||||
\(625\) | 1.92662e8 | 0.789145 | ||||||||
\(626\) | 1.23370e7i | 0.0502906i | ||||||||
\(627\) | −8.82720e7 | −0.358113 | ||||||||
\(628\) | − | 1.35929e8i | − | 0.548825i | ||||||
\(629\) | −1.53605e8 | −0.617239 | ||||||||
\(630\) | 2.03871e7 | 0.0815330 | ||||||||
\(631\) | 3.29998e8i | 1.31348i | 0.754118 | + | 0.656739i | \(0.228065\pi\) | ||||
−0.754118 | + | 0.656739i | \(0.771935\pi\) | |||||||
\(632\) | 1.62904e8i | 0.645328i | ||||||||
\(633\) | 1.52138e8 | 0.599828 | ||||||||
\(634\) | −2.80537e8 | −1.10084 | ||||||||
\(635\) | 4.64128e7i | 0.181266i | ||||||||
\(636\) | − | 2.89676e7i | − | 0.112601i | ||||||
\(637\) | −7.04419e7 | −0.272529 | ||||||||
\(638\) | − | 9.47301e6i | − | 0.0364776i | ||||||
\(639\) | −5.32117e7 | −0.203941 | ||||||||
\(640\) | − | 6.21788e6i | − | 0.0237193i | ||||||
\(641\) | 7.09804e7i | 0.269503i | 0.990879 | + | 0.134752i | \(0.0430237\pi\) | ||||
−0.990879 | + | 0.134752i | \(0.956976\pi\) | |||||||
\(642\) | 3.45332e7i | 0.130506i | ||||||||
\(643\) | 4.40900e8i | 1.65847i | 0.558901 | + | 0.829234i | \(0.311223\pi\) | ||||
−0.558901 | + | 0.829234i | \(0.688777\pi\) | |||||||
\(644\) | −6.46521e7 | + | 1.59541e8i | −0.242061 | + | 0.597331i | ||||
\(645\) | −5.47636e6 | −0.0204086 | ||||||||
\(646\) | −1.29473e8 | −0.480267 | ||||||||
\(647\) | −5.91668e7 | −0.218457 | −0.109228 | − | 0.994017i | \(-0.534838\pi\) | ||||
−0.109228 | + | 0.994017i | \(0.534838\pi\) | |||||||
\(648\) | −1.06890e7 | −0.0392837 | ||||||||
\(649\) | − | 3.38435e8i | − | 1.23806i | ||||||
\(650\) | −7.42315e7 | −0.270301 | ||||||||
\(651\) | 2.30266e7i | 0.0834615i | ||||||||
\(652\) | 2.81128e7 | 0.101429 | ||||||||
\(653\) | 9.12786e7 | 0.327816 | 0.163908 | − | 0.986476i | \(-0.447590\pi\) | ||||
0.163908 | + | 0.986476i | \(0.447590\pi\) | |||||||
\(654\) | − | 3.15728e7i | − | 0.112870i | ||||||
\(655\) | − | 8.66924e6i | − | 0.0308501i | ||||||
\(656\) | −4.55908e7 | −0.161497 | ||||||||
\(657\) | −1.46299e6 | −0.00515875 | ||||||||
\(658\) | 4.63597e8i | 1.62728i | ||||||||
\(659\) | 4.35911e8i | 1.52315i | 0.648079 | + | 0.761573i | \(0.275572\pi\) | ||||
−0.648079 | + | 0.761573i | \(0.724428\pi\) | |||||||
\(660\) | 1.56421e7 | 0.0544079 | ||||||||
\(661\) | − | 3.14795e8i | − | 1.08999i | −0.838438 | − | 0.544997i | \(-0.816531\pi\) | ||
0.838438 | − | 0.544997i | \(-0.183469\pi\) | |||||||
\(662\) | 2.48448e8 | 0.856370 | ||||||||
\(663\) | − | 5.33045e7i | − | 0.182904i | ||||||
\(664\) | − | 1.02145e8i | − | 0.348909i | ||||||
\(665\) | 8.98402e7i | 0.305496i | ||||||||
\(666\) | − | 5.58827e7i | − | 0.189171i | ||||||
\(667\) | 2.02002e7 | + | 8.18589e6i | 0.0680736 | + | 0.0275860i | ||||
\(668\) | −1.90414e8 | −0.638806 | ||||||||
\(669\) | −6.76584e7 | −0.225966 | ||||||||
\(670\) | 2.48985e7 | 0.0827844 | ||||||||
\(671\) | −3.55647e8 | −1.17720 | ||||||||
\(672\) | 3.99240e7i | 0.131561i | ||||||||
\(673\) | −1.37241e8 | −0.450235 | −0.225118 | − | 0.974332i | \(-0.572277\pi\) | ||||
−0.225118 | + | 0.974332i | \(0.572277\pi\) | |||||||
\(674\) | 3.29830e8i | 1.07724i | ||||||||
\(675\) | −5.49251e7 | −0.178591 | ||||||||
\(676\) | −1.28249e8 | −0.415158 | ||||||||
\(677\) | 7.80267e7i | 0.251465i | 0.992064 | + | 0.125732i | \(0.0401281\pi\) | ||||
−0.992064 | + | 0.125732i | \(0.959872\pi\) | |||||||
\(678\) | − | 7.44661e7i | − | 0.238929i | ||||||
\(679\) | 7.55592e8 | 2.41367 | ||||||||
\(680\) | 2.29431e7 | 0.0729668 | ||||||||
\(681\) | − | 5.62410e7i | − | 0.178079i | ||||||
\(682\) | 1.76672e7i | 0.0556948i | ||||||||
\(683\) | 1.03635e7 | 0.0325269 | 0.0162635 | − | 0.999868i | \(-0.494823\pi\) | ||||
0.0162635 | + | 0.999868i | \(0.494823\pi\) | |||||||
\(684\) | − | 4.71034e7i | − | 0.147192i | ||||||
\(685\) | 9.17449e7 | 0.285437 | ||||||||
\(686\) | − | 9.95769e7i | − | 0.308451i | ||||||
\(687\) | − | 4.72277e7i | − | 0.145656i | ||||||
\(688\) | − | 1.07244e7i | − | 0.0329311i | ||||||
\(689\) | 5.25547e7i | 0.160677i | ||||||||
\(690\) | −1.35167e7 | + | 3.33551e7i | −0.0411457 | + | 0.101535i | ||||
\(691\) | −3.56193e7 | −0.107957 | −0.0539786 | − | 0.998542i | \(-0.517190\pi\) | ||||
−0.0539786 | + | 0.998542i | \(0.517190\pi\) | |||||||
\(692\) | −8.54093e7 | −0.257743 | ||||||||
\(693\) | −1.00435e8 | −0.301777 | ||||||||
\(694\) | −1.55290e8 | −0.464585 | ||||||||
\(695\) | 2.73957e7i | 0.0816071i | ||||||||
\(696\) | 5.05496e6 | 0.0149931 | ||||||||
\(697\) | − | 1.68223e8i | − | 0.496807i | ||||||
\(698\) | 1.20624e8 | 0.354704 | ||||||||
\(699\) | −1.28775e8 | −0.377050 | ||||||||
\(700\) | 2.05148e8i | 0.598100i | ||||||||
\(701\) | − | 8.06295e7i | − | 0.234067i | −0.993128 | − | 0.117033i | \(-0.962662\pi\) | ||
0.993128 | − | 0.117033i | \(-0.0373385\pi\) | |||||||
\(702\) | 1.93926e7 | 0.0560563 | ||||||||
\(703\) | 2.46259e8 | 0.708805 | ||||||||
\(704\) | 3.06318e7i | 0.0877921i | ||||||||
\(705\) | 9.69236e7i | 0.276606i | ||||||||
\(706\) | −2.91297e8 | −0.827793 | ||||||||
\(707\) | − | 2.44504e8i | − | 0.691876i | ||||||
\(708\) | 1.80595e8 | 0.508868 | ||||||||
\(709\) | − | 1.38794e8i | − | 0.389432i | −0.980860 | − | 0.194716i | \(-0.937621\pi\) | ||
0.980860 | − | 0.194716i | \(-0.0623785\pi\) | |||||||
\(710\) | 4.15521e7i | 0.116096i | ||||||||
\(711\) | − | 2.18682e8i | − | 0.608421i | ||||||
\(712\) | − | 1.39449e8i | − | 0.386346i | ||||||
\(713\) | −3.76735e7 | − | 1.52667e7i | −0.103936 | − | 0.0421189i | ||||
\(714\) | −1.47314e8 | −0.404715 | ||||||||
\(715\) | −2.83787e7 | −0.0776380 | ||||||||
\(716\) | −2.15433e8 | −0.586911 | ||||||||
\(717\) | 1.80068e8 | 0.488515 | ||||||||
\(718\) | − | 9.24616e7i | − | 0.249797i | ||||||
\(719\) | −3.57049e8 | −0.960597 | −0.480299 | − | 0.877105i | \(-0.659472\pi\) | ||||
−0.480299 | + | 0.877105i | \(0.659472\pi\) | |||||||
\(720\) | 8.34687e6i | 0.0223628i | ||||||||
\(721\) | −4.77179e8 | −1.27314 | ||||||||
\(722\) | −5.85601e7 | −0.155593 | ||||||||
\(723\) | 2.47342e8i | 0.654460i | ||||||||
\(724\) | 3.31621e7i | 0.0873829i | ||||||||
\(725\) | 2.59748e7 | 0.0681612 | ||||||||
\(726\) | 7.91599e7 | 0.206869 | ||||||||
\(727\) | 3.59873e8i | 0.936584i | 0.883574 | + | 0.468292i | \(0.155130\pi\) | ||||
−0.883574 | + | 0.468292i | \(0.844870\pi\) | |||||||
\(728\) | − | 7.24324e7i | − | 0.187732i | ||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 1.14242e6i | 0.00293669i | ||||||||
\(731\) | 3.95713e7 | 0.101304 | ||||||||
\(732\) | − | 1.89779e8i | − | 0.483856i | ||||||
\(733\) | 1.46603e8i | 0.372247i | 0.982526 | + | 0.186124i | \(0.0595925\pi\) | ||||
−0.982526 | + | 0.186124i | \(0.940408\pi\) | |||||||
\(734\) | − | 5.17776e8i | − | 1.30934i | ||||||
\(735\) | 4.07005e7i | 0.102503i | ||||||||
\(736\) | −6.53193e7 | − | 2.64698e7i | −0.163835 | − | 0.0663923i | ||||
\(737\) | −1.22660e8 | −0.306409 | ||||||||
\(738\) | 6.12009e7 | 0.152261 | ||||||||
\(739\) | 4.58201e8 | 1.13533 | 0.567665 | − | 0.823259i | \(-0.307847\pi\) | ||||
0.567665 | + | 0.823259i | \(0.307847\pi\) | |||||||
\(740\) | −4.36379e7 | −0.107688 | ||||||||
\(741\) | 8.54577e7i | 0.210037i | ||||||||
\(742\) | 1.45242e8 | 0.355533 | ||||||||
\(743\) | − | 2.69220e8i | − | 0.656359i | −0.944615 | − | 0.328179i | \(-0.893565\pi\) | ||
0.944615 | − | 0.328179i | \(-0.106435\pi\) | |||||||
\(744\) | −9.42752e6 | −0.0228917 | ||||||||
\(745\) | 1.19150e7 | 0.0288154 | ||||||||
\(746\) | − | 2.44480e8i | − | 0.588880i | ||||||
\(747\) | 1.37119e8i | 0.328955i | ||||||||
\(748\) | −1.13027e8 | −0.270071 | ||||||||
\(749\) | −1.73147e8 | −0.412069 | ||||||||
\(750\) | 8.91086e7i | 0.211220i | ||||||||
\(751\) | − | 3.67021e8i | − | 0.866505i | −0.901273 | − | 0.433252i | \(-0.857366\pi\) | ||
0.901273 | − | 0.433252i | \(-0.142634\pi\) | |||||||
\(752\) | −1.89806e8 | −0.446329 | ||||||||
\(753\) | 4.54655e8i | 1.06487i | ||||||||
\(754\) | −9.17099e6 | −0.0213945 | ||||||||
\(755\) | − | 7.04852e7i | − | 0.163779i | ||||||
\(756\) | − | 5.35940e7i | − | 0.124037i | ||||||
\(757\) | 3.77306e8i | 0.869774i | 0.900485 | + | 0.434887i | \(0.143212\pi\) | ||||
−0.900485 | + | 0.434887i | \(0.856788\pi\) | |||||||
\(758\) | 1.91253e8i | 0.439138i | ||||||||
\(759\) | 6.65890e7 | − | 1.64321e8i | 0.152292 | − | 0.375809i | ||||
\(760\) | −3.67823e7 | −0.0837912 | ||||||||
\(761\) | −7.71458e8 | −1.75049 | −0.875243 | − | 0.483684i | \(-0.839298\pi\) | ||||
−0.875243 | + | 0.483684i | \(0.839298\pi\) | |||||||
\(762\) | 1.22011e8 | 0.275762 | ||||||||
\(763\) | 1.58304e8 | 0.356384 | ||||||||
\(764\) | 7.34374e7i | 0.164679i | ||||||||
\(765\) | −3.07988e7 | −0.0687937 | ||||||||
\(766\) | 5.47936e8i | 1.21911i | ||||||||
\(767\) | −3.27645e8 | −0.726135 | ||||||||
\(768\) | −1.63457e7 | −0.0360844 | ||||||||
\(769\) | 9.35216e7i | 0.205652i | 0.994699 | + | 0.102826i | \(0.0327885\pi\) | ||||
−0.994699 | + | 0.102826i | \(0.967212\pi\) | |||||||
\(770\) | 7.84282e7i | 0.171791i | ||||||||
\(771\) | −2.15979e8 | −0.471248 | ||||||||
\(772\) | −8.95595e7 | −0.194652 | ||||||||
\(773\) | 2.30059e8i | 0.498082i | 0.968493 | + | 0.249041i | \(0.0801153\pi\) | ||||
−0.968493 | + | 0.249041i | \(0.919885\pi\) | |||||||
\(774\) | 1.43964e7i | 0.0310477i | ||||||||
\(775\) | −4.84430e7 | −0.104070 | ||||||||
\(776\) | 3.09354e8i | 0.662019i | ||||||||
\(777\) | 2.80192e8 | 0.597300 | ||||||||
\(778\) | − | 4.11057e8i | − | 0.872898i | ||||||
\(779\) | 2.69695e8i | 0.570507i | ||||||||
\(780\) | − | 1.51434e7i | − | 0.0319108i | ||||||
\(781\) | − | 2.04703e8i | − | 0.429705i | ||||||
\(782\) | 9.76699e7 | − | 2.41019e8i | 0.204240 | − | 0.504000i | ||||
\(783\) | −6.78577e6 | −0.0141356 | ||||||||
\(784\) | −7.97039e7 | −0.165398 | ||||||||
\(785\) | 1.42489e8 | 0.294558 | ||||||||
\(786\) | −2.27899e7 | −0.0469325 | ||||||||
\(787\) | − | 3.93660e8i | − | 0.807602i | −0.914847 | − | 0.403801i | \(-0.867689\pi\) | ||
0.914847 | − | 0.403801i | \(-0.132311\pi\) | |||||||
\(788\) | 7.50021e6 | 0.0153283 | ||||||||
\(789\) | 3.60684e7i | 0.0734337i | ||||||||
\(790\) | −1.70765e8 | −0.346352 | ||||||||
\(791\) | 3.73368e8 | 0.754410 | ||||||||
\(792\) | − | 4.11201e7i | − | 0.0827711i | ||||||
\(793\) | 3.44308e8i | 0.690443i | ||||||||
\(794\) | 6.06931e8 | 1.21249 | ||||||||
\(795\) | 3.03655e7 | 0.0604337 | ||||||||
\(796\) | 3.86235e8i | 0.765796i | ||||||||
\(797\) | 8.21907e8i | 1.62348i | 0.584017 | + | 0.811741i | \(0.301480\pi\) | ||||
−0.584017 | + | 0.811741i | \(0.698520\pi\) | |||||||
\(798\) | 2.36173e8 | 0.464753 | ||||||||
\(799\) | − | 7.00355e8i | − | 1.37302i | ||||||
\(800\) | −8.39917e7 | −0.164046 | ||||||||
\(801\) | 1.87197e8i | 0.364251i | ||||||||
\(802\) | 3.33188e8i | 0.645902i | ||||||||
\(803\) | − | 5.62805e6i | − | 0.0108695i | ||||||
\(804\) | − | 6.54536e7i | − | 0.125940i | ||||||
\(805\) | −1.67240e8 | − | 6.77720e7i | −0.320592 | − | 0.129916i | ||||
\(806\) | 1.71039e7 | 0.0326656 | ||||||||
\(807\) | −2.12587e8 | −0.404498 | ||||||||
\(808\) | 1.00105e8 | 0.189767 | ||||||||
\(809\) | 8.40293e8 | 1.58703 | 0.793516 | − | 0.608550i | \(-0.208249\pi\) | ||||
0.793516 | + | 0.608550i | \(0.208249\pi\) | |||||||
\(810\) | − | 1.12048e7i | − | 0.0210839i | ||||||
\(811\) | −1.05882e9 | −1.98499 | −0.992497 | − | 0.122266i | \(-0.960984\pi\) | ||||
−0.992497 | + | 0.122266i | \(0.960984\pi\) | |||||||
\(812\) | 2.53452e7i | 0.0473400i | ||||||||
\(813\) | −1.24904e8 | −0.232437 | ||||||||
\(814\) | 2.14978e8 | 0.398585 | ||||||||
\(815\) | 2.94694e7i | 0.0544376i | ||||||||
\(816\) | − | 6.03132e7i | − | 0.111005i | ||||||
\(817\) | −6.34407e7 | −0.116333 | ||||||||
\(818\) | 2.28551e8 | 0.417564 | ||||||||
\(819\) | 9.72331e7i | 0.176996i | ||||||||
\(820\) | − | 4.77908e7i | − | 0.0866768i | ||||||
\(821\) | −3.91303e8 | −0.707106 | −0.353553 | − | 0.935415i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935415i | \(0.615027\pi\) | |||||||
\(822\) | − | 2.41181e8i | − | 0.434237i | ||||||
\(823\) | 8.78390e8 | 1.57575 | 0.787876 | − | 0.615834i | \(-0.211181\pi\) | ||||
0.787876 | + | 0.615834i | \(0.211181\pi\) | |||||||
\(824\) | − | 1.95366e8i | − | 0.349195i | ||||||
\(825\) | − | 2.11294e8i | − | 0.376293i | ||||||
\(826\) | 9.05489e8i | 1.60673i | ||||||||
\(827\) | − | 1.02440e8i | − | 0.181114i | −0.995891 | − | 0.0905571i | \(-0.971135\pi\) | ||
0.995891 | − | 0.0905571i | \(-0.0288648\pi\) | |||||||
\(828\) | 8.76845e7 | + | 3.55330e7i | 0.154466 | + | 0.0625953i | ||||
\(829\) | −2.80924e8 | −0.493090 | −0.246545 | − | 0.969131i | \(-0.579295\pi\) | ||||
−0.246545 | + | 0.969131i | \(0.579295\pi\) | |||||||
\(830\) | 1.07074e8 | 0.187262 | ||||||||
\(831\) | −2.37786e8 | −0.414365 | ||||||||
\(832\) | 2.96552e7 | 0.0514910 | ||||||||
\(833\) | − | 2.94096e8i | − | 0.508808i | ||||||
\(834\) | 7.20184e7 | 0.124150 | ||||||||
\(835\) | − | 1.99603e8i | − | 0.342852i | ||||||
\(836\) | 1.81205e8 | 0.310135 | ||||||||
\(837\) | 1.26555e7 | 0.0215825 | ||||||||
\(838\) | − | 6.16417e8i | − | 1.04747i | ||||||
\(839\) | − | 3.69035e8i | − | 0.624859i | −0.949941 | − | 0.312429i | \(-0.898857\pi\) | ||
0.949941 | − | 0.312429i | \(-0.101143\pi\) | |||||||
\(840\) | −4.18506e7 | −0.0706097 | ||||||||
\(841\) | −5.91614e8 | −0.994605 | ||||||||
\(842\) | − | 7.29165e8i | − | 1.22149i | ||||||
\(843\) | − | 2.98700e8i | − | 0.498601i | ||||||
\(844\) | −3.12309e8 | −0.519466 | ||||||||
\(845\) | − | 1.34438e8i | − | 0.222818i | ||||||
\(846\) | 2.54795e8 | 0.420803 | ||||||||
\(847\) | 3.96902e8i | 0.653181i | ||||||||
\(848\) | 5.94648e7i | 0.0975152i | ||||||||
\(849\) | − | 2.11048e8i | − | 0.344872i | ||||||
\(850\) | − | 3.09917e8i | − | 0.504649i | ||||||
\(851\) | −1.85769e8 | + | 4.58419e8i | −0.301428 | + | 0.743831i | ||||
\(852\) | 1.09233e8 | 0.176618 | ||||||||
\(853\) | −8.81446e8 | −1.42020 | −0.710098 | − | 0.704103i | \(-0.751349\pi\) | ||||
−0.710098 | + | 0.704103i | \(0.751349\pi\) | |||||||
\(854\) | 9.51541e8 | 1.52776 | ||||||||
\(855\) | 4.93765e7 | 0.0789991 | ||||||||
\(856\) | − | 7.08897e7i | − | 0.113022i | ||||||
\(857\) | −7.62975e8 | −1.21218 | −0.606091 | − | 0.795395i | \(-0.707263\pi\) | ||||
−0.606091 | + | 0.795395i | \(0.707263\pi\) | |||||||
\(858\) | 7.46024e7i | 0.118111i | ||||||||
\(859\) | 4.04509e8 | 0.638188 | 0.319094 | − | 0.947723i | \(-0.396622\pi\) | ||||
0.319094 | + | 0.947723i | \(0.396622\pi\) | |||||||
\(860\) | 1.12419e7 | 0.0176744 | ||||||||
\(861\) | 3.06857e8i | 0.480759i | ||||||||
\(862\) | − | 7.02418e8i | − | 1.09666i | ||||||
\(863\) | 9.09614e8 | 1.41522 | 0.707612 | − | 0.706602i | \(-0.249773\pi\) | ||||
0.707612 | + | 0.706602i | \(0.249773\pi\) | |||||||
\(864\) | 2.19424e7 | 0.0340207 | ||||||||
\(865\) | − | 8.95309e7i | − | 0.138333i | ||||||
\(866\) | − | 5.41846e8i | − | 0.834299i | ||||||
\(867\) | −1.53720e8 | −0.235871 | ||||||||
\(868\) | − | 4.72690e7i | − | 0.0722798i | ||||||
\(869\) | 8.41260e8 | 1.28195 | ||||||||
\(870\) | 5.29890e6i | 0.00804688i | ||||||||
\(871\) | 1.18750e8i | 0.179712i | ||||||||
\(872\) | 6.48127e7i | 0.0977487i | ||||||||
\(873\) | − | 4.15276e8i | − | 0.624158i | ||||||
\(874\) | −1.56584e8 | + | 3.86401e8i | −0.234538 | + | 0.578767i | ||||
\(875\) | −4.46784e8 | −0.666920 | ||||||||
\(876\) | 3.00322e6 | 0.00446761 | ||||||||
\(877\) | 1.51423e8 | 0.224487 | 0.112244 | − | 0.993681i | \(-0.464196\pi\) | ||||
0.112244 | + | 0.993681i | \(0.464196\pi\) | |||||||
\(878\) | 7.59874e8 | 1.12269 | ||||||||
\(879\) | − | 3.79042e8i | − | 0.558112i | ||||||
\(880\) | −3.21100e7 | −0.0471186 | ||||||||
\(881\) | − | 3.76759e8i | − | 0.550980i | −0.961304 | − | 0.275490i | \(-0.911160\pi\) | ||
0.961304 | − | 0.275490i | \(-0.0888401\pi\) | |||||||
\(882\) | 1.06994e8 | 0.155939 | ||||||||
\(883\) | 1.10173e9 | 1.60027 | 0.800137 | − | 0.599817i | \(-0.204760\pi\) | ||||
0.800137 | + | 0.599817i | \(0.204760\pi\) | |||||||
\(884\) | 1.09424e8i | 0.158400i | ||||||||
\(885\) | 1.89310e8i | 0.273113i | ||||||||
\(886\) | 7.20885e8 | 1.03649 | ||||||||
\(887\) | 8.28677e8 | 1.18745 | 0.593724 | − | 0.804669i | \(-0.297657\pi\) | ||||
0.593724 | + | 0.804669i | \(0.297657\pi\) | |||||||
\(888\) | 1.14716e8i | 0.163827i | ||||||||
\(889\) | 6.11754e8i | 0.870707i | ||||||||
\(890\) | 1.46179e8 | 0.207355 | ||||||||
\(891\) | 5.51996e7i | 0.0780374i | ||||||||
\(892\) | 1.38889e8 | 0.195692 | ||||||||
\(893\) | 1.12281e9i | 1.57671i | ||||||||
\(894\) | − | 3.13223e7i | − | 0.0438371i | ||||||
\(895\) | − | 2.25829e8i | − | 0.315000i | ||||||
\(896\) | − | 8.19561e7i | − | 0.113935i | ||||||
\(897\) | −1.59082e8 | − | 6.44660e7i | −0.220416 | − | 0.0893210i | ||||
\(898\) | −6.17331e8 | −0.852490 | ||||||||
\(899\) | −5.98493e6 | −0.00823721 | ||||||||
\(900\) | 1.12750e8 | 0.154664 | ||||||||
\(901\) | −2.19417e8 | −0.299982 | ||||||||
\(902\) | 2.35437e8i | 0.320816i | ||||||||
\(903\) | −7.21823e7 | −0.0980320 | ||||||||
\(904\) | 1.52864e8i | 0.206919i | ||||||||
\(905\) | −3.47624e7 | −0.0468990 | ||||||||
\(906\) | −1.85293e8 | −0.249157 | ||||||||
\(907\) | − | 4.23862e8i | − | 0.568071i | −0.958814 | − | 0.284036i | \(-0.908327\pi\) | ||
0.958814 | − | 0.284036i | \(-0.0916734\pi\) | |||||||
\(908\) | 1.15452e8i | 0.154221i | ||||||||
\(909\) | −1.34380e8 | −0.178914 | ||||||||
\(910\) | 7.59277e7 | 0.100757 | ||||||||
\(911\) | − | 8.76974e8i | − | 1.15993i | −0.814641 | − | 0.579965i | \(-0.803066\pi\) | ||
0.814641 | − | 0.579965i | \(-0.196934\pi\) | |||||||
\(912\) | 9.66940e7i | 0.127472i | ||||||||
\(913\) | −5.27491e8 | −0.693111 | ||||||||
\(914\) | − | 1.40247e8i | − | 0.183677i | ||||||
\(915\) | 1.98938e8 | 0.259689 | ||||||||
\(916\) | 9.69492e7i | 0.126141i | ||||||||
\(917\) | − | 1.14267e8i | − | 0.148188i | ||||||
\(918\) | 8.09643e7i | 0.104656i | ||||||||
\(919\) | 3.15963e8i | 0.407089i | 0.979066 | + | 0.203544i | \(0.0652461\pi\) | ||||
−0.979066 | + | 0.203544i | \(0.934754\pi\) | |||||||
\(920\) | 2.77472e7 | − | 6.84714e7i | 0.0356332 | − | 0.0879317i | ||||
\(921\) | −2.81225e8 | −0.359977 | ||||||||
\(922\) | −7.37592e7 | −0.0941074 | ||||||||
\(923\) | −1.98176e8 | −0.252027 | ||||||||
\(924\) | 2.06174e8 | 0.261347 | ||||||||
\(925\) | 5.89465e8i | 0.744788i | ||||||||
\(926\) | 2.85314e8 | 0.359327 | ||||||||
\(927\) | 2.62259e8i | 0.329224i | ||||||||
\(928\) | −1.03768e7 | −0.0129844 | ||||||||
\(929\) | 9.46020e8 | 1.17992 | 0.589961 | − | 0.807432i | \(-0.299143\pi\) | ||||
0.589961 | + | 0.807432i | \(0.299143\pi\) | |||||||
\(930\) | − | 9.88246e6i | − | 0.0122862i | ||||||
\(931\) | 4.71494e8i | 0.584288i | ||||||||
\(932\) | 2.64349e8 | 0.326535 | ||||||||
\(933\) | −3.14607e8 | −0.387368 | ||||||||
\(934\) | − | 8.00604e8i | − | 0.982601i | ||||||
\(935\) | − | 1.18481e8i | − | 0.144949i | ||||||
\(936\) | −3.98091e7 | −0.0485462 | ||||||||
\(937\) | 1.35792e9i | 1.65066i | 0.564653 | + | 0.825328i | \(0.309010\pi\) | ||||
−0.564653 | + | 0.825328i | \(0.690990\pi\) | |||||||
\(938\) | 3.28180e8 | 0.397652 | ||||||||
\(939\) | 3.39968e7i | 0.0410621i | ||||||||
\(940\) | − | 1.98965e8i | − | 0.239548i | ||||||
\(941\) | − | 3.71001e8i | − | 0.445253i | −0.974904 | − | 0.222626i | \(-0.928537\pi\) | ||
0.974904 | − | 0.222626i | \(-0.0714630\pi\) | |||||||
\(942\) | − | 3.74577e8i | − | 0.448113i | ||||||
\(943\) | −5.02046e8 | − | 2.03448e8i | −0.598698 | − | 0.242615i | ||||
\(944\) | −3.70725e8 | −0.440693 | ||||||||
\(945\) | 5.61802e7 | 0.0665715 | ||||||||
\(946\) | −5.53821e7 | −0.0654178 | ||||||||
\(947\) | 7.04611e8 | 0.829658 | 0.414829 | − | 0.909899i | \(-0.363841\pi\) | ||||
0.414829 | + | 0.909899i | \(0.363841\pi\) | |||||||
\(948\) | 4.48911e8i | 0.526908i | ||||||||
\(949\) | −5.44861e6 | −0.00637510 | ||||||||
\(950\) | 4.96859e8i | 0.579512i | ||||||||
\(951\) | −7.73070e8 | −0.898830 | ||||||||
\(952\) | 3.02406e8 | 0.350493 | ||||||||
\(953\) | − | 1.26599e9i | − | 1.46269i | −0.682008 | − | 0.731345i | \(-0.738893\pi\) | ||
0.682008 | − | 0.731345i | \(-0.261107\pi\) | |||||||
\(954\) | − | 7.98254e7i | − | 0.0919382i | ||||||
\(955\) | −7.69812e7 | −0.0883842 | ||||||||
\(956\) | −3.69643e8 | −0.423067 | ||||||||
\(957\) | − | 2.61046e7i | − | 0.0297838i | ||||||
\(958\) | − | 6.58474e7i | − | 0.0748932i | ||||||
\(959\) | 1.20926e9 | 1.37109 | ||||||||
\(960\) | − | 1.71345e7i | − | 0.0193668i | ||||||
\(961\) | −8.76342e8 | −0.987423 | ||||||||
\(962\) | − | 2.08124e8i | − | 0.233775i | ||||||
\(963\) | 9.51623e7i | 0.106558i | ||||||||
\(964\) | − | 5.07744e8i | − | 0.566779i | ||||||
\(965\) | − | 9.38813e7i | − | 0.104471i | ||||||
\(966\) | −1.78160e8 | + | 4.39644e8i | −0.197642 | + | 0.487719i | ||||
\(967\) | 1.26507e9 | 1.39906 | 0.699529 | − | 0.714604i | \(-0.253393\pi\) | ||||
0.699529 | + | 0.714604i | \(0.253393\pi\) | |||||||
\(968\) | −1.62500e8 | −0.179154 | ||||||||
\(969\) | −3.56787e8 | −0.392137 | ||||||||
\(970\) | −3.24282e8 | −0.355311 | ||||||||
\(971\) | 5.63224e8i | 0.615211i | 0.951514 | + | 0.307605i | \(0.0995276\pi\) | ||||
−0.951514 | + | 0.307605i | \(0.900472\pi\) | |||||||
\(972\) | −2.94555e7 | −0.0320750 | ||||||||
\(973\) | 3.61095e8i | 0.391997i | ||||||||
\(974\) | 2.10311e8 | 0.227607 | ||||||||
\(975\) | −2.04558e8 | −0.220700 | ||||||||
\(976\) | 3.89579e8i | 0.419031i | ||||||||
\(977\) | − | 1.08993e9i | − | 1.16873i | −0.811490 | − | 0.584366i | \(-0.801343\pi\) | ||
0.811490 | − | 0.584366i | \(-0.198657\pi\) | |||||||
\(978\) | 7.74698e7 | 0.0828163 | ||||||||
\(979\) | −7.20137e8 | −0.767480 | ||||||||
\(980\) | − | 8.35501e7i | − | 0.0887705i | ||||||
\(981\) | − | 8.70045e7i | − | 0.0921584i | ||||||
\(982\) | −1.09372e8 | −0.115497 | ||||||||
\(983\) | − | 2.78908e8i | − | 0.293630i | −0.989164 | − | 0.146815i | \(-0.953098\pi\) | ||
0.989164 | − | 0.146815i | \(-0.0469023\pi\) | |||||||
\(984\) | −1.25633e8 | −0.131862 | ||||||||
\(985\) | 7.86214e6i | 0.00822682i | ||||||||
\(986\) | − | 3.82890e7i | − | 0.0399433i | ||||||
\(987\) | 1.27752e9i | 1.32867i | ||||||||
\(988\) | − | 1.75428e8i | − | 0.181898i | ||||||
\(989\) | 4.78572e7 | − | 1.18097e8i | 0.0494719 | − | 0.122081i | ||||
\(990\) | 4.31044e7 | 0.0444239 | ||||||||
\(991\) | 2.66809e8 | 0.274145 | 0.137072 | − | 0.990561i | \(-0.456231\pi\) | ||||
0.137072 | + | 0.990561i | \(0.456231\pi\) | |||||||
\(992\) | 1.93528e7 | 0.0198248 | ||||||||
\(993\) | 6.84642e8 | 0.699223 | ||||||||
\(994\) | 5.47687e8i | 0.557665i | ||||||||
\(995\) | −4.04874e8 | −0.411008 | ||||||||
\(996\) | − | 2.81478e8i | − | 0.284883i | ||||||
\(997\) | −3.10128e8 | −0.312936 | −0.156468 | − | 0.987683i | \(-0.550011\pi\) | ||||
−0.156468 | + | 0.987683i | \(0.550011\pi\) | |||||||
\(998\) | 6.56209e8 | 0.660162 | ||||||||
\(999\) | − | 1.53995e8i | − | 0.154458i |
(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 | 138.7.b.a.91.4 | yes | 24 | |
3.2 | odd | 2 | 414.7.b.c.91.17 | 24 | |||
23.22 | odd | 2 | inner | 138.7.b.a.91.3 | ✓ | 24 | |
69.68 | even | 2 | 414.7.b.c.91.20 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.7.b.a.91.3 | ✓ | 24 | 23.22 | odd | 2 | inner | |
138.7.b.a.91.4 | yes | 24 | 1.1 | even | 1 | trivial | |
414.7.b.c.91.17 | 24 | 3.2 | odd | 2 | |||
414.7.b.c.91.20 | 24 | 69.68 | even | 2 |