Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [180,8,Mod(71,180)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(180, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("180.71");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 180.e (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: | \(56.2293045871\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 71.2 | ||
Character | \(\chi\) | \(=\) | 180.71 |
Dual form | 180.8.e.a.71.1 |
$q$-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 \(\left(\mathbb{Z}/180\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(91\) | \(101\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −11.3101 | + | 0.285532i | −0.999681 | + | 0.0252377i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 127.837 | − | 6.45880i | 0.998726 | − | 0.0504594i | ||||
\(5\) | 125.000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1017.66i | 1.12139i | 0.828021 | + | 0.560696i | \(0.189467\pi\) | ||||
−0.828021 | + | 0.560696i | \(0.810533\pi\) | |||||||
\(8\) | −1444.01 | + | 109.551i | −0.997135 | + | 0.0756489i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −35.6915 | − | 1413.76i | −0.0112867 | − | 0.447071i | ||||
\(11\) | −4949.52 | −1.12121 | −0.560607 | − | 0.828082i | \(-0.689432\pi\) | ||||
−0.560607 | + | 0.828082i | \(0.689432\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5267.74 | −0.665001 | −0.332500 | − | 0.943103i | \(-0.607892\pi\) | ||||
−0.332500 | + | 0.943103i | \(0.607892\pi\) | |||||||
\(14\) | −290.573 | − | 11509.8i | −0.0283014 | − | 1.12104i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16300.6 | − | 1651.35i | 0.994908 | − | 0.100790i | ||||
\(17\) | − | 21159.8i | − | 1.04458i | −0.852769 | − | 0.522288i | \(-0.825079\pi\) | ||
0.852769 | − | 0.522288i | \(-0.174921\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 12122.1i | − | 0.405454i | −0.979235 | − | 0.202727i | \(-0.935020\pi\) | ||
0.979235 | − | 0.202727i | \(-0.0649804\pi\) | |||||||
\(20\) | 807.350 | + | 15979.6i | 0.0225661 | + | 0.446644i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 55979.5 | − | 1413.25i | 1.12086 | − | 0.0282969i | ||||
\(23\) | −10926.7 | −0.187258 | −0.0936290 | − | 0.995607i | \(-0.529847\pi\) | ||||
−0.0936290 | + | 0.995607i | \(0.529847\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −15625.0 | −0.200000 | ||||||||
\(26\) | 59578.6 | − | 1504.11i | 0.664789 | − | 0.0167831i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6572.83 | + | 130094.i | 0.0565848 | + | 1.11996i | ||||
\(29\) | − | 175111.i | − | 1.33328i | −0.745381 | − | 0.666639i | \(-0.767732\pi\) | ||
0.745381 | − | 0.666639i | \(-0.232268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 70706.1i | 0.426276i | 0.977022 | + | 0.213138i | \(0.0683684\pi\) | ||||
−0.977022 | + | 0.213138i | \(0.931632\pi\) | |||||||
\(32\) | −183890. | + | 23331.2i | −0.992047 | + | 0.125867i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6041.80 | + | 239319.i | 0.0263627 | + | 1.04424i | ||||
\(35\) | −127207. | −0.501502 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 272479. | 0.884355 | 0.442178 | − | 0.896928i | \(-0.354206\pi\) | ||||
0.442178 | + | 0.896928i | \(0.354206\pi\) | |||||||
\(38\) | 3461.26 | + | 137103.i | 0.0102327 | + | 0.405325i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −13693.9 | − | 180501.i | −0.0338312 | − | 0.445932i | ||||
\(41\) | − | 23618.7i | − | 0.0535195i | −0.999642 | − | 0.0267598i | \(-0.991481\pi\) | ||
0.999642 | − | 0.0267598i | \(-0.00851891\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 175131.i | 0.335910i | 0.985795 | + | 0.167955i | \(0.0537163\pi\) | ||||
−0.985795 | + | 0.167955i | \(0.946284\pi\) | |||||||
\(44\) | −632731. | + | 31967.9i | −1.11979 | + | 0.0565757i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 123582. | − | 3119.92i | 0.187198 | − | 0.00472596i | ||||
\(47\) | −1.14576e6 | −1.60973 | −0.804863 | − | 0.593461i | \(-0.797761\pi\) | ||||
−0.804863 | + | 0.593461i | \(0.797761\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −212080. | −0.257522 | ||||||||
\(50\) | 176720. | − | 4461.44i | 0.199936 | − | 0.00504754i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −673411. | + | 34023.2i | −0.664154 | + | 0.0335555i | ||||
\(53\) | 921020.i | 0.849774i | 0.905246 | + | 0.424887i | \(0.139686\pi\) | ||||
−0.905246 | + | 0.424887i | \(0.860314\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 618689.i | − | 0.501422i | ||||||
\(56\) | −111485. | − | 1.46950e6i | −0.0848321 | − | 1.11818i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 49999.8 | + | 1.98052e6i | 0.0336489 | + | 1.33285i | ||||
\(59\) | −312509. | −0.198098 | −0.0990491 | − | 0.995083i | \(-0.531580\pi\) | ||||
−0.0990491 | + | 0.995083i | \(0.531580\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 581361. | 0.327938 | 0.163969 | − | 0.986466i | \(-0.447570\pi\) | ||||
0.163969 | + | 0.986466i | \(0.447570\pi\) | |||||||
\(62\) | −20188.9 | − | 799693.i | −0.0107582 | − | 0.426140i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.07315e6 | − | 316385.i | 0.988555 | − | 0.150864i | ||||
\(65\) | − | 658467.i | − | 0.297397i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.05251e6i | 1.23993i | 0.784631 | + | 0.619963i | \(0.212852\pi\) | ||||
−0.784631 | + | 0.619963i | \(0.787148\pi\) | |||||||
\(68\) | −136667. | − | 2.70500e6i | −0.0527086 | − | 1.04325i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.43872e6 | − | 36321.7i | 0.501342 | − | 0.0126568i | ||||
\(71\) | 4.72551e6 | 1.56691 | 0.783455 | − | 0.621448i | \(-0.213455\pi\) | ||||
0.783455 | + | 0.621448i | \(0.213455\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.46716e6 | 1.64487 | 0.822435 | − | 0.568860i | \(-0.192615\pi\) | ||||
0.822435 | + | 0.568860i | \(0.192615\pi\) | |||||||
\(74\) | −3.08176e6 | + | 77801.5i | −0.884073 | + | 0.0223191i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −78294.5 | − | 1.54966e6i | −0.0204590 | − | 0.404938i | ||||
\(77\) | − | 5.03690e6i | − | 1.25732i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.07098e6i | − | 0.472586i | −0.971682 | − | 0.236293i | \(-0.924068\pi\) | ||
0.971682 | − | 0.236293i | \(-0.0759325\pi\) | |||||||
\(80\) | 206418. | + | 2.03757e6i | 0.0450747 | + | 0.444936i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6743.89 | + | 267130.i | 0.00135071 | + | 0.0535025i | ||||
\(83\) | 854102. | 0.163959 | 0.0819797 | − | 0.996634i | \(-0.473876\pi\) | ||||
0.0819797 | + | 0.996634i | \(0.473876\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.64497e6 | 0.467149 | ||||||||
\(86\) | −50005.4 | − | 1.98075e6i | −0.00847759 | − | 0.335803i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.14713e6 | − | 542226.i | 1.11800 | − | 0.0848185i | ||||
\(89\) | − | 7.69685e6i | − | 1.15731i | −0.815574 | − | 0.578653i | \(-0.803579\pi\) | ||
0.815574 | − | 0.578653i | \(-0.196421\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 5.36074e6i | − | 0.745727i | ||||||
\(92\) | −1.39683e6 | + | 70573.2i | −0.187019 | + | 0.00944892i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.29587e7 | − | 327152.i | 1.60921 | − | 0.0406258i | ||||
\(95\) | 1.51527e6 | 0.181325 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.44110e7 | 1.60322 | 0.801611 | − | 0.597846i | \(-0.203977\pi\) | ||||
0.801611 | + | 0.597846i | \(0.203977\pi\) | |||||||
\(98\) | 2.39865e6 | − | 60555.7i | 0.257440 | − | 0.00649926i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.99745e6 | + | 100919.i | −0.199745 | + | 0.0100919i | ||||
\(101\) | − | 1.16399e7i | − | 1.12415i | −0.827086 | − | 0.562075i | \(-0.810003\pi\) | ||
0.827086 | − | 0.562075i | \(-0.189997\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.09312e6i | − | 0.819941i | −0.912099 | − | 0.409970i | \(-0.865539\pi\) | ||
0.912099 | − | 0.409970i | \(-0.134461\pi\) | |||||||
\(104\) | 7.60664e6 | − | 577087.i | 0.663095 | − | 0.0503066i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −262981. | − | 1.04168e7i | −0.0214464 | − | 0.849503i | ||||
\(107\) | 2.38832e7 | 1.88473 | 0.942367 | − | 0.334581i | \(-0.108595\pi\) | ||||
0.942367 | + | 0.334581i | \(0.108595\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.35844e7 | −1.00472 | −0.502362 | − | 0.864658i | \(-0.667535\pi\) | ||||
−0.502362 | + | 0.864658i | \(0.667535\pi\) | |||||||
\(110\) | 176656. | + | 6.99744e6i | 0.0126547 | + | 0.501262i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.68050e6 | + | 1.65884e7i | 0.113025 | + | 1.11568i | ||||
\(113\) | 2.42115e7i | 1.57851i | 0.614067 | + | 0.789254i | \(0.289533\pi\) | ||||
−0.614067 | + | 0.789254i | \(0.710467\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.36583e6i | − | 0.0837443i | ||||||
\(116\) | −1.13101e6 | − | 2.23857e7i | −0.0672763 | − | 1.33158i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.53451e6 | − | 89231.4i | 0.198035 | − | 0.00499955i | ||||
\(119\) | 2.15334e7 | 1.17138 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.01054e6 | 0.257120 | ||||||||
\(122\) | −6.57525e6 | + | 165997.i | −0.327833 | + | 0.00827640i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 456676. | + | 9.03885e6i | 0.0215096 | + | 0.425733i | ||||
\(125\) | − | 1.95312e6i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.70653e7i | − | 1.17246i | −0.810143 | − | 0.586232i | \(-0.800611\pi\) | ||
0.810143 | − | 0.586232i | \(-0.199389\pi\) | |||||||
\(128\) | −2.33572e7 | + | 4.17030e6i | −0.984432 | + | 0.175765i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 188014. | + | 7.44733e6i | 0.00750563 | + | 0.297303i | ||||
\(131\) | −1.83771e7 | −0.714212 | −0.357106 | − | 0.934064i | \(-0.616236\pi\) | ||||
−0.357106 | + | 0.934064i | \(0.616236\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.23362e7 | 0.454673 | ||||||||
\(134\) | −871591. | − | 3.45242e7i | −0.0312929 | − | 1.23953i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.31808e6 | + | 3.05548e7i | 0.0790210 | + | 1.04158i | ||||
\(137\) | − | 3.21259e7i | − | 1.06742i | −0.845669 | − | 0.533708i | \(-0.820798\pi\) | ||
0.845669 | − | 0.533708i | \(-0.179202\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.31297e7i | 0.414670i | 0.978270 | + | 0.207335i | \(0.0664790\pi\) | ||||
−0.978270 | + | 0.207335i | \(0.933521\pi\) | |||||||
\(140\) | −1.62617e7 | + | 821604.i | −0.500863 | + | 0.0253055i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.34460e7 | + | 1.34928e6i | −1.56641 | + | 0.0395452i | ||||
\(143\) | 2.60727e7 | 0.745608 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.18889e7 | 0.596260 | ||||||||
\(146\) | −6.18341e7 | + | 1.56105e6i | −1.64435 | + | 0.0415127i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.48329e7 | − | 1.75989e6i | 0.883229 | − | 0.0446240i | ||||
\(149\) | 4.50153e7i | 1.11483i | 0.830234 | + | 0.557415i | \(0.188207\pi\) | ||||
−0.830234 | + | 0.557415i | \(0.811793\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.23691e7i | − | 1.47418i | −0.675795 | − | 0.737089i | \(-0.736200\pi\) | ||
0.675795 | − | 0.737089i | \(-0.263800\pi\) | |||||||
\(152\) | 1.32800e6 | + | 1.75044e7i | 0.0306721 | + | 0.404292i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.43820e6 | + | 5.69679e7i | 0.0317319 | + | 1.25692i | ||||
\(155\) | −8.83826e6 | −0.190636 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.23174e7 | 0.666481 | 0.333241 | − | 0.942842i | \(-0.391858\pi\) | ||||
0.333241 | + | 0.942842i | \(0.391858\pi\) | |||||||
\(158\) | 591331. | + | 2.34230e7i | 0.0119270 | + | 0.472435i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.91640e6 | − | 2.29862e7i | −0.0562895 | − | 0.443657i | ||||
\(161\) | − | 1.11196e7i | − | 0.209990i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.79963e6i | 0.177237i | 0.996066 | + | 0.0886183i | \(0.0282451\pi\) | ||||
−0.996066 | + | 0.0886183i | \(0.971755\pi\) | |||||||
\(164\) | −152548. | − | 3.01934e6i | −0.00270056 | − | 0.0534513i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.65998e6 | + | 243874.i | −0.163907 | + | 0.00413796i | ||||
\(167\) | 4.86412e7 | 0.808159 | 0.404080 | − | 0.914724i | \(-0.367592\pi\) | ||||
0.404080 | + | 0.914724i | \(0.367592\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.49995e7 | −0.557774 | ||||||||
\(170\) | −2.99149e7 | + | 755225.i | −0.467000 | + | 0.0117898i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.13113e6 | + | 2.23882e7i | 0.0169498 | + | 0.335482i | ||||
\(173\) | − | 3.88286e7i | − | 0.570152i | −0.958505 | − | 0.285076i | \(-0.907981\pi\) | ||
0.958505 | − | 0.285076i | \(-0.0920188\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.59009e7i | − | 0.224279i | ||||||
\(176\) | −8.06799e7 | + | 8.17336e6i | −1.11550 | + | 0.113007i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.19770e6 | + | 8.70522e7i | 0.0292077 | + | 1.15694i | ||||
\(179\) | 8.56178e7 | 1.11578 | 0.557890 | − | 0.829915i | \(-0.311611\pi\) | ||||
0.557890 | + | 0.829915i | \(0.311611\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.20518e8 | −1.51070 | −0.755350 | − | 0.655322i | \(-0.772533\pi\) | ||||
−0.755350 | + | 0.655322i | \(0.772533\pi\) | |||||||
\(182\) | 1.53066e6 | + | 6.06305e7i | 0.0188205 | + | 0.745490i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.57782e7 | − | 1.19703e6i | 0.186721 | − | 0.0141659i | ||||
\(185\) | 3.40599e7i | 0.395496i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.04731e8i | 1.17119i | ||||||||
\(188\) | −1.46471e8 | + | 7.40025e6i | −1.60768 | + | 0.0812257i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.71378e7 | + | 432658.i | −0.181267 | + | 0.00457622i | ||||
\(191\) | 3.09145e7 | 0.321029 | 0.160515 | − | 0.987033i | \(-0.448685\pi\) | ||||
0.160515 | + | 0.987033i | \(0.448685\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.78880e8 | −1.79106 | −0.895531 | − | 0.444998i | \(-0.853204\pi\) | ||||
−0.895531 | + | 0.444998i | \(0.853204\pi\) | |||||||
\(194\) | −1.62990e8 | + | 4.11481e6i | −1.60271 | + | 0.0404616i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.71117e7 | + | 1.36978e6i | −0.257194 | + | 0.0129944i | ||||
\(197\) | 9.89610e7i | 0.922216i | 0.887344 | + | 0.461108i | \(0.152548\pi\) | ||||
−0.887344 | + | 0.461108i | \(0.847452\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.34679e8i | − | 1.21147i | −0.795665 | − | 0.605736i | \(-0.792879\pi\) | ||
0.795665 | − | 0.605736i | \(-0.207121\pi\) | |||||||
\(200\) | 2.25626e7 | − | 1.71174e6i | 0.199427 | − | 0.0151298i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.32356e6 | + | 1.31648e8i | 0.0283710 | + | 1.12379i | ||||
\(203\) | 1.78203e8 | 1.49513 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.95234e6 | 0.0239347 | ||||||||
\(206\) | 2.59638e6 | + | 1.02844e8i | 0.0206934 | + | 0.819680i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.58671e7 | + | 8.69885e6i | −0.661615 | + | 0.0670255i | ||||
\(209\) | 5.99987e7i | 0.454601i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2.29710e8i | − | 1.68342i | −0.539933 | − | 0.841708i | \(-0.681550\pi\) | ||
0.539933 | − | 0.841708i | \(-0.318450\pi\) | |||||||
\(212\) | 5.94868e6 | + | 1.17740e8i | 0.0428791 | + | 0.848692i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.70122e8 | + | 6.81944e6i | −1.88413 | + | 0.0475664i | ||||
\(215\) | −2.18913e7 | −0.150223 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.19545e7 | −0.478023 | ||||||||
\(218\) | 1.53641e8 | − | 3.87877e6i | 1.00440 | − | 0.0253569i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.99599e6 | − | 7.90914e7i | −0.0253014 | − | 0.500783i | ||||
\(221\) | 1.11464e8i | 0.694644i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.62401e8i | − | 0.980670i | −0.871534 | − | 0.490335i | \(-0.836875\pi\) | ||
0.871534 | − | 0.490335i | \(-0.163125\pi\) | |||||||
\(224\) | −2.37432e7 | − | 1.87136e8i | −0.141147 | − | 1.11247i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.91316e6 | − | 2.73834e8i | −0.0398380 | − | 1.57801i | ||||
\(227\) | 2.61737e8 | 1.48516 | 0.742582 | − | 0.669755i | \(-0.233601\pi\) | ||||
0.742582 | + | 0.669755i | \(0.233601\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.45757e7 | −0.135233 | −0.0676164 | − | 0.997711i | \(-0.521539\pi\) | ||||
−0.0676164 | + | 0.997711i | \(0.521539\pi\) | |||||||
\(230\) | 389990. | + | 1.54477e7i | 0.00211352 | + | 0.0837177i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.91836e7 | + | 2.52861e8i | 0.100861 | + | 1.32946i | ||||
\(233\) | − | 3.76804e7i | − | 0.195151i | −0.995228 | − | 0.0975754i | \(-0.968891\pi\) | ||
0.995228 | − | 0.0975754i | \(-0.0311087\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1.43220e8i | − | 0.719891i | ||||||
\(236\) | −3.99502e7 | + | 2.01843e6i | −0.197846 | + | 0.00999591i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.43545e8 | + | 6.14847e6i | −1.17101 | + | 0.0295630i | ||||
\(239\) | 1.58923e8 | 0.752999 | 0.376500 | − | 0.926417i | \(-0.377128\pi\) | ||||
0.376500 | + | 0.926417i | \(0.377128\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.45238e8 | 1.58876 | 0.794381 | − | 0.607420i | \(-0.207796\pi\) | ||||
0.794381 | + | 0.607420i | \(0.207796\pi\) | |||||||
\(242\) | −5.66697e7 | + | 1.43067e6i | −0.257038 | + | 0.00648912i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.43194e7 | − | 3.75489e6i | 0.327520 | − | 0.0165475i | ||||
\(245\) | − | 2.65100e7i | − | 0.115167i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.38562e7i | 0.269627i | ||||||||
\(248\) | −7.74594e6 | − | 1.02100e8i | −0.0322473 | − | 0.425055i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 557680. | + | 2.20900e7i | 0.00225733 | + | 0.0894142i | ||||
\(251\) | 1.30430e8 | 0.520617 | 0.260309 | − | 0.965525i | \(-0.416176\pi\) | ||||
0.260309 | + | 0.965525i | \(0.416176\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.40817e7 | 0.209956 | ||||||||
\(254\) | 7.72801e6 | + | 3.06111e8i | 0.0295903 | + | 1.17209i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.62982e8 | − | 5.38358e7i | 0.979683 | − | 0.200554i | ||||
\(257\) | 4.75395e8i | 1.74698i | 0.486838 | + | 0.873492i | \(0.338150\pi\) | ||||
−0.486838 | + | 0.873492i | \(0.661850\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.77290e8i | 0.991709i | ||||||||
\(260\) | −4.25291e6 | − | 8.41764e7i | −0.0150065 | − | 0.297019i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.07847e8 | − | 5.24725e6i | 0.713984 | − | 0.0180251i | ||||
\(263\) | −1.50093e8 | −0.508763 | −0.254382 | − | 0.967104i | \(-0.581872\pi\) | ||||
−0.254382 | + | 0.967104i | \(0.581872\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.15127e8 | −0.380031 | ||||||||
\(266\) | −1.39523e8 | + | 3.52237e6i | −0.454528 | + | 0.0114749i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.97156e7 | + | 3.90224e8i | 0.0625659 | + | 1.23835i | ||||
\(269\) | − | 5.82841e8i | − | 1.82565i | −0.408351 | − | 0.912825i | \(-0.633896\pi\) | ||
0.408351 | − | 0.912825i | \(-0.366104\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.19542e8i | − | 1.28051i | −0.768162 | − | 0.640256i | \(-0.778828\pi\) | ||
0.768162 | − | 0.640256i | \(-0.221172\pi\) | |||||||
\(272\) | −3.49421e7 | − | 3.44917e8i | −0.105283 | − | 1.03926i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.17298e6 | + | 3.63347e8i | 0.0269391 | + | 1.06708i | ||||
\(275\) | 7.73362e7 | 0.224243 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.76239e7 | 0.106361 | 0.0531807 | − | 0.998585i | \(-0.483064\pi\) | ||||
0.0531807 | + | 0.998585i | \(0.483064\pi\) | |||||||
\(278\) | −3.74895e6 | − | 1.48498e8i | −0.0104653 | − | 0.414538i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.83687e8 | − | 1.39357e7i | 0.500065 | − | 0.0379381i | ||||
\(281\) | 3.71855e7i | 0.0999774i | 0.998750 | + | 0.0499887i | \(0.0159185\pi\) | ||||
−0.998750 | + | 0.0499887i | \(0.984081\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 9.73301e7i | − | 0.255267i | −0.991821 | − | 0.127633i | \(-0.959262\pi\) | ||
0.991821 | − | 0.127633i | \(-0.0407381\pi\) | |||||||
\(284\) | 6.04094e8 | − | 3.05211e7i | 1.56491 | − | 0.0790653i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.94885e8 | + | 7.44461e6i | −0.745371 | + | 0.0188174i | ||||
\(287\) | 2.40357e7 | 0.0600164 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.73978e7 | −0.0911389 | ||||||||
\(290\) | −2.47565e8 | + | 6.24998e6i | −0.596070 | + | 0.0150482i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.98904e8 | − | 3.53113e7i | 1.64277 | − | 0.0829991i | ||||
\(293\) | − | 6.46069e8i | − | 1.50052i | −0.661142 | − | 0.750261i | \(-0.729928\pi\) | ||
0.661142 | − | 0.750261i | \(-0.270072\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3.90636e7i | − | 0.0885922i | ||||||
\(296\) | −3.93461e8 | + | 2.98504e7i | −0.881821 | + | 0.0669005i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.28533e7 | − | 5.09128e8i | −0.0281358 | − | 1.11447i | ||||
\(299\) | 5.75588e7 | 0.124527 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.78223e8 | −0.376687 | ||||||||
\(302\) | 1.78084e7 | + | 7.05401e8i | 0.0372049 | + | 1.47371i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.00178e7 | − | 1.97598e8i | −0.0408658 | − | 0.403389i | ||||
\(305\) | 7.26701e7i | 0.146658i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.77114e8i | 0.349357i | 0.984626 | + | 0.174678i | \(0.0558885\pi\) | ||||
−0.984626 | + | 0.174678i | \(0.944111\pi\) | |||||||
\(308\) | −3.25323e7 | − | 6.43902e8i | −0.0634436 | − | 1.25572i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.99617e7 | − | 2.52361e6i | 0.190576 | − | 0.00481123i | ||||
\(311\) | −9.69334e8 | −1.82731 | −0.913655 | − | 0.406490i | \(-0.866753\pi\) | ||||
−0.913655 | + | 0.406490i | \(0.866753\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.07689e8 | 0.751491 | 0.375746 | − | 0.926723i | \(-0.377387\pi\) | ||||
0.375746 | + | 0.926723i | \(0.377387\pi\) | |||||||
\(314\) | −3.65513e8 | + | 9.22766e6i | −0.666269 | + | 0.0168205i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.33760e7 | − | 2.64747e8i | −0.0238464 | − | 0.471984i | ||||
\(317\) | 4.14374e8i | 0.730609i | 0.930888 | + | 0.365304i | \(0.119035\pi\) | ||||
−0.930888 | + | 0.365304i | \(0.880965\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.66715e8i | 1.49489i | ||||||||
\(320\) | 3.95481e7 | + | 2.59144e8i | 0.0674685 | + | 0.442095i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.17500e6 | + | 1.25764e8i | 0.00529966 | + | 0.209923i | ||||
\(323\) | −2.56502e8 | −0.423528 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.23084e7 | 0.133000 | ||||||||
\(326\) | −2.79811e6 | − | 1.10835e8i | −0.00447305 | − | 0.177180i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.58746e6 | + | 3.41055e7i | 0.00404869 | + | 0.0533662i | ||||
\(329\) | − | 1.16599e9i | − | 1.80514i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.42363e8i | 0.822038i | 0.911627 | + | 0.411019i | \(0.134827\pi\) | ||||
−0.911627 | + | 0.411019i | \(0.865173\pi\) | |||||||
\(332\) | 1.09186e8 | − | 5.51647e6i | 0.163751 | − | 0.00827329i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.50138e8 | + | 1.38886e7i | −0.807902 | + | 0.0203961i | ||||
\(335\) | −3.81564e8 | −0.554512 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.68411e8 | 0.951347 | 0.475674 | − | 0.879622i | \(-0.342204\pi\) | ||||
0.475674 | + | 0.879622i | \(0.342204\pi\) | |||||||
\(338\) | 3.95848e8 | − | 9.99348e6i | 0.557596 | − | 0.0140769i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.38125e8 | − | 1.70833e7i | 0.466553 | − | 0.0235720i | ||||
\(341\) | − | 3.49961e8i | − | 0.477946i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.22259e8i | 0.832610i | ||||||||
\(344\) | −1.91858e7 | − | 2.52889e8i | −0.0254112 | − | 0.334947i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.10868e7 | + | 4.39156e8i | 0.0143893 | + | 0.569970i | ||||
\(347\) | −2.60027e8 | −0.334091 | −0.167045 | − | 0.985949i | \(-0.553423\pi\) | ||||
−0.167045 | + | 0.985949i | \(0.553423\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.22935e8 | 0.280731 | 0.140365 | − | 0.990100i | \(-0.455172\pi\) | ||||
0.140365 | + | 0.990100i | \(0.455172\pi\) | |||||||
\(350\) | 4.54021e6 | + | 1.79841e8i | 0.00566028 | + | 0.224207i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.10165e8 | − | 1.15478e8i | 1.11230 | − | 0.141124i | ||||
\(353\) | 4.51937e8i | 0.546848i | 0.961894 | + | 0.273424i | \(0.0881561\pi\) | ||||
−0.961894 | + | 0.273424i | \(0.911844\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.90688e8i | 0.700744i | ||||||||
\(356\) | −4.97124e7 | − | 9.83942e8i | −0.0583969 | − | 1.15583i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.68346e8 | + | 2.44466e7i | −1.11542 | + | 0.0281597i | ||||
\(359\) | 1.68222e8 | 0.191890 | 0.0959451 | − | 0.995387i | \(-0.469413\pi\) | ||||
0.0959451 | + | 0.995387i | \(0.469413\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.46925e8 | 0.835607 | ||||||||
\(362\) | 1.36307e9 | − | 3.44119e7i | 1.51022 | − | 0.0381266i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.46239e7 | − | 6.85301e8i | −0.0376289 | − | 0.744777i | ||||
\(365\) | 6.83394e8i | 0.735608i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.78483e8i | 0.399682i | 0.979828 | + | 0.199841i | \(0.0640426\pi\) | ||||
−0.979828 | + | 0.199841i | \(0.935957\pi\) | |||||||
\(368\) | −1.78111e8 | + | 1.80437e7i | −0.186304 | + | 0.0188738i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.72518e6 | − | 3.85220e8i | −0.00998141 | − | 0.395370i | ||||
\(371\) | −9.37281e8 | −0.952931 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.71049e8 | −0.170663 | −0.0853314 | − | 0.996353i | \(-0.527195\pi\) | ||||
−0.0853314 | + | 0.996353i | \(0.527195\pi\) | |||||||
\(374\) | −2.99040e7 | − | 1.18452e9i | −0.0295582 | − | 1.17082i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.65449e9 | − | 1.25520e8i | 1.60511 | − | 0.121774i | ||||
\(377\) | 9.22439e8i | 0.886631i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.39453e9i | − | 1.31580i | −0.753106 | − | 0.657899i | \(-0.771445\pi\) | ||
0.753106 | − | 0.657899i | \(-0.228555\pi\) | |||||||
\(380\) | 1.93707e8 | − | 9.78681e6i | 0.181094 | − | 0.00914952i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.49646e8 | + | 8.82707e6i | −0.320927 | + | 0.00810205i | ||||
\(383\) | −2.07864e8 | −0.189053 | −0.0945266 | − | 0.995522i | \(-0.530134\pi\) | ||||
−0.0945266 | + | 0.995522i | \(0.530134\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.29613e8 | 0.562291 | ||||||||
\(386\) | 2.02315e9 | − | 5.10760e7i | 1.79049 | − | 0.0452023i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.84226e9 | − | 9.30778e7i | 1.60118 | − | 0.0808975i | ||||
\(389\) | − | 1.61926e7i | − | 0.0139474i | −0.999976 | − | 0.00697370i | \(-0.997780\pi\) | ||
0.999976 | − | 0.00697370i | \(-0.00221982\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.31206e8i | 0.195605i | ||||||||
\(392\) | 3.06245e8 | − | 2.32336e7i | 0.256784 | − | 0.0194812i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.82566e7 | − | 1.11926e9i | −0.0232746 | − | 0.921922i | ||||
\(395\) | 2.58872e8 | 0.211347 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.11223e9 | 0.892127 | 0.446063 | − | 0.895001i | \(-0.352826\pi\) | ||||
0.446063 | + | 0.895001i | \(0.352826\pi\) | |||||||
\(398\) | 3.84551e7 | + | 1.52323e9i | 0.0305748 | + | 1.21109i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.54696e8 | + | 2.58023e7i | −0.198982 | + | 0.0201580i | ||||
\(401\) | − | 1.62678e9i | − | 1.25986i | −0.776651 | − | 0.629931i | \(-0.783083\pi\) | ||
0.776651 | − | 0.629931i | \(-0.216917\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 3.72461e8i | − | 0.283474i | ||||||
\(404\) | −7.51797e7 | − | 1.48801e9i | −0.0567239 | − | 1.12272i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.01549e9 | + | 5.08826e7i | −1.49465 | + | 0.0377336i | ||||
\(407\) | −1.34864e9 | −0.991551 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.90820e9 | −1.37909 | −0.689543 | − | 0.724245i | \(-0.742189\pi\) | ||||
−0.689543 | + | 0.724245i | \(0.742189\pi\) | |||||||
\(410\) | −3.33912e7 | + | 842987.i | −0.0239270 | + | 0.000604056i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.87306e7 | − | 1.16244e9i | −0.0413737 | − | 0.818896i | ||||
\(413\) | − | 3.18027e8i | − | 0.222146i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.06763e8i | 0.0733249i | ||||||||
\(416\) | 9.68682e8 | − | 1.22903e8i | 0.659712 | − | 0.0837018i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.71316e7 | − | 6.78592e8i | −0.0114731 | − | 0.454456i | ||||
\(419\) | −1.79661e9 | −1.19318 | −0.596589 | − | 0.802547i | \(-0.703478\pi\) | ||||
−0.596589 | + | 0.802547i | \(0.703478\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.68101e9 | −1.75110 | −0.875551 | − | 0.483126i | \(-0.839501\pi\) | ||||
−0.875551 | + | 0.483126i | \(0.839501\pi\) | |||||||
\(422\) | 6.55896e7 | + | 2.59805e9i | 0.0424856 | + | 1.68288i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.00899e8 | − | 1.32996e9i | −0.0642844 | − | 0.847339i | ||||
\(425\) | 3.30622e8i | 0.208915i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.91625e8i | 0.367747i | ||||||||
\(428\) | 3.05316e9 | − | 1.54257e8i | 1.88233 | − | 0.0951025i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.47593e8 | − | 6.25068e6i | 0.150175 | − | 0.00379129i | ||||
\(431\) | 2.39915e9 | 1.44340 | 0.721699 | − | 0.692207i | \(-0.243361\pi\) | ||||
0.721699 | + | 0.692207i | \(0.243361\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.23124e9 | −0.728844 | −0.364422 | − | 0.931234i | \(-0.618733\pi\) | ||||
−0.364422 | + | 0.931234i | \(0.618733\pi\) | |||||||
\(434\) | 8.13812e8 | − | 2.05453e7i | 0.477871 | − | 0.0120642i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.73658e9 | + | 8.77387e7i | −1.00344 | + | 0.0506977i | ||||
\(437\) | 1.32455e8i | 0.0759245i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.36789e9i | 1.33578i | 0.744258 | + | 0.667892i | \(0.232803\pi\) | ||||
−0.744258 | + | 0.667892i | \(0.767197\pi\) | |||||||
\(440\) | 6.77782e7 | + | 8.93391e8i | 0.0379320 | + | 0.499985i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.18266e7 | − | 1.26067e9i | −0.0175312 | − | 0.694423i | ||||
\(443\) | −1.98826e9 | −1.08657 | −0.543287 | − | 0.839547i | \(-0.682821\pi\) | ||||
−0.543287 | + | 0.839547i | \(0.682821\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.62106e8 | 0.517563 | ||||||||
\(446\) | 4.63708e7 | + | 1.83678e9i | 0.0247499 | + | 0.980357i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.21971e8 | + | 2.10975e9i | 0.169178 | + | 1.10856i | ||||
\(449\) | 2.58417e8i | 0.134729i | 0.997728 | + | 0.0673643i | \(0.0214590\pi\) | ||||
−0.997728 | + | 0.0673643i | \(0.978541\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.16901e8i | 0.0600068i | ||||||||
\(452\) | 1.56377e8 | + | 3.09512e9i | 0.0796505 | + | 1.57650i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.96027e9 | + | 7.47344e7i | −1.48469 | + | 0.0374822i | ||||
\(455\) | 6.70093e8 | 0.333499 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.02477e9 | 0.502252 | 0.251126 | − | 0.967954i | \(-0.419199\pi\) | ||||
0.251126 | + | 0.967954i | \(0.419199\pi\) | |||||||
\(458\) | 2.77954e8 | − | 7.01716e6i | 0.135190 | − | 0.00341297i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.82164e6 | − | 1.74604e8i | −0.00422569 | − | 0.0836376i | ||||
\(461\) | 1.66082e9i | 0.789531i | 0.918782 | + | 0.394765i | \(0.129174\pi\) | ||||
−0.918782 | + | 0.394765i | \(0.870826\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.33523e8i | − | 0.0625205i | −0.999511 | − | 0.0312602i | \(-0.990048\pi\) | ||
0.999511 | − | 0.0312602i | \(-0.00995206\pi\) | |||||||
\(464\) | −2.89169e8 | − | 2.85441e9i | −0.134381 | − | 1.32649i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.07590e7 | + | 4.26170e8i | 0.00492516 | + | 0.195089i | ||||
\(467\) | −3.45042e9 | −1.56770 | −0.783851 | − | 0.620949i | \(-0.786747\pi\) | ||||
−0.783851 | + | 0.620949i | \(0.786747\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.10641e9 | −1.39044 | ||||||||
\(470\) | 4.08940e7 | + | 1.61984e9i | 0.0181684 | + | 0.719662i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.51265e8 | − | 3.42357e7i | 0.197531 | − | 0.0149859i | ||||
\(473\) | − | 8.66812e8i | − | 0.376626i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.89408e8i | 0.0810908i | ||||||||
\(476\) | 2.75276e9 | − | 1.39080e8i | 1.16989 | − | 0.0591071i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.79744e9 | + | 4.53777e7i | −0.752759 | + | 0.0190040i | ||||
\(479\) | 1.18595e9 | 0.493052 | 0.246526 | − | 0.969136i | \(-0.420711\pi\) | ||||
0.246526 | + | 0.969136i | \(0.420711\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.43535e9 | −0.588097 | ||||||||
\(482\) | −3.90468e9 | + | 9.85765e7i | −1.58826 | + | 0.0400967i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.40532e8 | − | 3.23620e7i | 0.256792 | − | 0.0129741i | ||||
\(485\) | 1.80138e9i | 0.716982i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.27332e9i | − | 1.67654i | −0.545256 | − | 0.838270i | \(-0.683568\pi\) | ||
0.545256 | − | 0.838270i | \(-0.316432\pi\) | |||||||
\(488\) | −8.39488e8 | + | 6.36888e7i | −0.326998 | + | 0.0248081i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.56946e6 | + | 2.99831e8i | 0.00290656 | + | 0.115131i | ||||
\(491\) | −2.38152e8 | −0.0907965 | −0.0453982 | − | 0.998969i | \(-0.514456\pi\) | ||||
−0.0453982 | + | 0.998969i | \(0.514456\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.70531e9 | −1.39271 | ||||||||
\(494\) | −1.82330e7 | − | 7.22221e8i | −0.00680478 | − | 0.269541i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.16760e8 | + | 1.15255e9i | 0.0429644 | + | 0.424105i | ||||
\(497\) | 4.80894e9i | 1.75712i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.03075e9i | 1.45222i | 0.687577 | + | 0.726112i | \(0.258675\pi\) | ||||
−0.687577 | + | 0.726112i | \(0.741325\pi\) | |||||||
\(500\) | −1.26148e7 | − | 2.49682e8i | −0.00451322 | − | 0.0893288i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.47517e9 | + | 3.72419e7i | −0.520452 | + | 0.0131392i | ||||
\(503\) | −2.94575e9 | −1.03207 | −0.516033 | − | 0.856569i | \(-0.672592\pi\) | ||||
−0.516033 | + | 0.856569i | \(0.672592\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.45499e9 | 0.502735 | ||||||||
\(506\) | −6.11670e8 | + | 1.54421e7i | −0.209889 | + | 0.00529882i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.74809e8 | − | 3.45994e9i | −0.0591618 | − | 1.17097i | ||||
\(509\) | − | 1.01634e9i | − | 0.341607i | −0.985305 | − | 0.170804i | \(-0.945364\pi\) | ||
0.985305 | − | 0.170804i | \(-0.0546364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.56368e9i | 1.84454i | ||||||||
\(512\) | −2.95898e9 | + | 6.83978e8i | −0.974309 | + | 0.225215i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.35741e8 | − | 5.37677e9i | −0.0440899 | − | 1.74643i | ||||
\(515\) | 1.13664e9 | 0.366689 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.67097e9 | 1.80485 | ||||||||
\(518\) | −7.91751e7 | − | 3.13617e9i | −0.0250285 | − | 0.991394i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.21359e7 | + | 9.50830e8i | 0.0224978 | + | 0.296545i | ||||
\(521\) | 6.78205e7i | 0.0210101i | 0.999945 | + | 0.0105051i | \(0.00334393\pi\) | ||||
−0.999945 | + | 0.0105051i | \(0.996656\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 4.64218e9i | − | 1.41895i | −0.704732 | − | 0.709473i | \(-0.748933\pi\) | ||
0.704732 | − | 0.709473i | \(-0.251067\pi\) | |||||||
\(524\) | −2.34927e9 | + | 1.18694e8i | −0.713302 | + | 0.0360387i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.69757e9 | − | 4.28564e7i | 0.508601 | − | 0.0128400i | ||||
\(527\) | 1.49613e9 | 0.445278 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.28543e9 | −0.964934 | ||||||||
\(530\) | 1.30210e9 | − | 3.28726e7i | 0.379909 | − | 0.00959110i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.57702e9 | − | 7.96768e7i | 0.454094 | − | 0.0229425i | ||||
\(533\) | 1.24417e8i | 0.0355905i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.98541e9i | 0.842879i | ||||||||
\(536\) | −3.34407e8 | − | 4.40784e9i | −0.0937990 | − | 1.23637i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.66420e8 | + | 6.59200e9i | 0.0460752 | + | 1.82507i | ||||
\(539\) | 1.04969e9 | 0.288737 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.11789e9 | 0.846585 | 0.423293 | − | 0.905993i | \(-0.360874\pi\) | ||||
0.423293 | + | 0.905993i | \(0.360874\pi\) | |||||||
\(542\) | 1.19793e8 | + | 4.74507e9i | 0.0323172 | + | 1.28010i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.93684e8 | + | 3.89106e9i | 0.131478 | + | 1.03627i | ||||
\(545\) | − | 1.69805e9i | − | 0.449326i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.06605e9i | 0.539741i | 0.962897 | + | 0.269870i | \(0.0869808\pi\) | ||||
−0.962897 | + | 0.269870i | \(0.913019\pi\) | |||||||
\(548\) | −2.07495e8 | − | 4.10688e9i | −0.0538611 | − | 1.06606i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.74680e8 | + | 2.20820e7i | −0.224171 | + | 0.00565937i | ||||
\(551\) | −2.12272e9 | −0.540583 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.10754e9 | 0.529954 | ||||||||
\(554\) | −4.25530e8 | + | 1.07428e7i | −0.106328 | + | 0.00268432i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.48020e7 | + | 1.67846e9i | 0.0209240 | + | 0.414142i | ||||
\(557\) | 1.35591e9i | 0.332458i | 0.986087 | + | 0.166229i | \(0.0531591\pi\) | ||||
−0.986087 | + | 0.166229i | \(0.946841\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.22542e8i | − | 0.223380i | ||||||
\(560\) | −2.07355e9 | + | 2.10063e8i | −0.498948 | + | 0.0505465i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.06177e7 | − | 4.20572e8i | −0.00252320 | − | 0.0999456i | ||||
\(563\) | −1.03728e9 | −0.244973 | −0.122486 | − | 0.992470i | \(-0.539087\pi\) | ||||
−0.122486 | + | 0.992470i | \(0.539087\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.02644e9 | −0.705930 | ||||||||
\(566\) | 2.77909e7 | + | 1.10081e9i | 0.00644235 | + | 0.255186i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.82365e9 | + | 5.17685e8i | −1.56242 | + | 0.118535i | ||||
\(569\) | − | 7.80253e9i | − | 1.77559i | −0.460239 | − | 0.887795i | \(-0.652236\pi\) | ||
0.460239 | − | 0.887795i | \(-0.347764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 3.86907e9i | − | 0.869721i | −0.900498 | − | 0.434860i | \(-0.856798\pi\) | ||
0.900498 | − | 0.434860i | \(-0.143202\pi\) | |||||||
\(572\) | 3.33306e9 | − | 1.68399e8i | 0.744658 | − | 0.0376229i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.71846e8 | + | 6.86296e6i | −0.0599973 | + | 0.00151468i | ||||
\(575\) | 1.70729e8 | 0.0374516 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.91115e8 | 0.128102 | 0.0640511 | − | 0.997947i | \(-0.479598\pi\) | ||||
0.0640511 | + | 0.997947i | \(0.479598\pi\) | |||||||
\(578\) | 4.22973e8 | − | 1.06783e7i | 0.0911099 | − | 0.00230014i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.79821e9 | − | 1.41376e8i | 0.595500 | − | 0.0300869i | ||||
\(581\) | 8.69182e8i | 0.183863i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.55860e9i | − | 0.952778i | ||||||
\(584\) | −7.89460e9 | + | 5.98934e8i | −1.64016 | + | 0.124432i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.84474e8 | + | 7.30711e9i | 0.0378698 | + | 1.50004i | ||||
\(587\) | 2.86809e9 | 0.585274 | 0.292637 | − | 0.956224i | \(-0.405467\pi\) | ||||
0.292637 | + | 0.956224i | \(0.405467\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.57109e8 | 0.172835 | ||||||||
\(590\) | 1.11539e7 | + | 4.41814e8i | 0.00223586 | + | 0.0885640i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.44156e9 | − | 4.49957e8i | 0.879852 | − | 0.0891343i | ||||
\(593\) | − | 3.55302e9i | − | 0.699692i | −0.936807 | − | 0.349846i | \(-0.886234\pi\) | ||
0.936807 | − | 0.349846i | \(-0.113766\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.69167e9i | 0.523857i | ||||||||
\(596\) | 2.90745e8 | + | 5.75462e9i | 0.0562536 | + | 1.11341i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.50996e8 | + | 1.64349e7i | −0.124487 | + | 0.00314277i | ||||
\(599\) | 9.03993e9 | 1.71859 | 0.859293 | − | 0.511484i | \(-0.170904\pi\) | ||||
0.859293 | + | 0.511484i | \(0.170904\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.36563e9 | 0.444515 | 0.222257 | − | 0.974988i | \(-0.428657\pi\) | ||||
0.222257 | + | 0.974988i | \(0.428657\pi\) | |||||||
\(602\) | 2.01572e9 | − | 5.08883e7i | 0.376567 | − | 0.00950671i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.02829e8 | − | 7.97307e9i | −0.0743861 | − | 1.47230i | ||||
\(605\) | 6.26317e8i | 0.114987i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 8.45762e9i | − | 1.53493i | −0.641092 | − | 0.767464i | \(-0.721518\pi\) | ||
0.641092 | − | 0.767464i | \(-0.278482\pi\) | |||||||
\(608\) | 2.82824e8 | + | 2.22914e9i | 0.0510334 | + | 0.402230i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.07496e7 | − | 8.21906e8i | −0.00370132 | − | 0.146611i | ||||
\(611\) | 6.03557e9 | 1.07047 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.25354e8 | −0.109652 | −0.0548258 | − | 0.998496i | \(-0.517460\pi\) | ||||
−0.0548258 | + | 0.998496i | \(0.517460\pi\) | |||||||
\(614\) | −5.05718e7 | − | 2.00318e9i | −0.00881696 | − | 0.349245i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.51799e8 | + | 7.27331e9i | 0.0951149 | + | 1.25372i | ||||
\(617\) | 3.02077e9i | 0.517749i | 0.965911 | + | 0.258874i | \(0.0833516\pi\) | ||||
−0.965911 | + | 0.258874i | \(0.916648\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 6.17230e9i | − | 1.04600i | −0.852334 | − | 0.522998i | \(-0.824814\pi\) | ||
0.852334 | − | 0.522998i | \(-0.175186\pi\) | |||||||
\(620\) | −1.12986e9 | + | 5.70845e7i | −0.190394 | + | 0.00961939i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.09633e10 | − | 2.76776e8i | 1.82673 | − | 0.0461171i | ||||
\(623\) | 7.83274e9 | 1.29779 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.44141e8 | 0.0400000 | ||||||||
\(626\) | −4.61101e9 | + | 1.16408e8i | −0.751252 | + | 0.0189659i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.13136e9 | − | 2.08732e8i | 0.665632 | − | 0.0336302i | ||||
\(629\) | − | 5.76559e9i | − | 0.923776i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4.87433e9i | − | 0.772346i | −0.922426 | − | 0.386173i | \(-0.873797\pi\) | ||
0.922426 | − | 0.386173i | \(-0.126203\pi\) | |||||||
\(632\) | 2.26878e8 | + | 2.99050e9i | 0.0357506 | + | 0.471232i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.18317e8 | − | 4.68661e9i | −0.0184389 | − | 0.730376i | ||||
\(635\) | 3.38316e9 | 0.524342 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.11718e9 | 0.171252 | ||||||||
\(638\) | −2.47475e8 | − | 9.80263e9i | −0.0377276 | − | 1.49441i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.21287e8 | − | 2.91965e9i | −0.0786045 | − | 0.440251i | ||||
\(641\) | 4.89061e9i | 0.733433i | 0.930333 | + | 0.366716i | \(0.119518\pi\) | ||||
−0.930333 | + | 0.366716i | \(0.880482\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 6.10990e9i | − | 0.906349i | −0.891422 | − | 0.453175i | \(-0.850291\pi\) | ||
0.891422 | − | 0.453175i | \(-0.149709\pi\) | |||||||
\(644\) | −7.18192e7 | − | 1.42149e9i | −0.0105959 | − | 0.209722i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.90106e9 | − | 7.32395e7i | 0.423393 | − | 0.0106889i | ||||
\(647\) | −3.73607e9 | −0.542313 | −0.271156 | − | 0.962535i | \(-0.587406\pi\) | ||||
−0.271156 | + | 0.962535i | \(0.587406\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.54677e9 | 0.222110 | ||||||||
\(650\) | −9.30916e8 | + | 2.35017e7i | −0.132958 | + | 0.00335662i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.32939e7 | + | 1.25276e9i | 0.00894324 | + | 0.177011i | ||||
\(653\) | − | 8.74159e9i | − | 1.22855i | −0.789090 | − | 0.614277i | \(-0.789448\pi\) | ||
0.789090 | − | 0.614277i | \(-0.210552\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2.29714e9i | − | 0.319405i | ||||||
\(656\) | −3.90026e7 | − | 3.84998e8i | −0.00539424 | − | 0.0532470i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.32928e8 | + | 1.31875e10i | 0.0455575 | + | 1.80456i | ||||
\(659\) | 9.06167e9 | 1.23342 | 0.616708 | − | 0.787192i | \(-0.288466\pi\) | ||||
0.616708 | + | 0.787192i | \(0.288466\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.60960e8 | 0.0755486 | 0.0377743 | − | 0.999286i | \(-0.487973\pi\) | ||||
0.0377743 | + | 0.999286i | \(0.487973\pi\) | |||||||
\(662\) | −1.54862e8 | − | 6.13418e9i | −0.0207464 | − | 0.821776i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.23333e9 | + | 9.35679e7i | −0.163490 | + | 0.0124033i | ||||
\(665\) | 1.54202e9i | 0.203336i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.91338e9i | 0.249667i | ||||||||
\(668\) | 6.21815e9 | − | 3.14164e8i | 0.807130 | − | 0.0407792i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.31553e9 | − | 1.08949e8i | 0.554335 | − | 0.0139946i | ||||
\(671\) | −2.87745e9 | −0.367688 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.09503e9 | 1.02368 | 0.511842 | − | 0.859080i | \(-0.328963\pi\) | ||||
0.511842 | + | 0.859080i | \(0.328963\pi\) | |||||||
\(674\) | −7.55980e9 | + | 1.90853e8i | −0.951044 | + | 0.0240098i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.47423e9 | + | 2.26055e8i | −0.557063 | + | 0.0281449i | ||||
\(677\) | 1.44490e10i | 1.78968i | 0.446382 | + | 0.894842i | \(0.352712\pi\) | ||||
−0.446382 | + | 0.894842i | \(0.647288\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.46655e10i | 1.79784i | ||||||||
\(680\) | −3.81935e9 | + | 2.89760e8i | −0.465810 | + | 0.0353393i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.99251e7 | + | 3.95809e9i | 0.0120623 | + | 0.477794i | ||||
\(683\) | 2.15387e9 | 0.258671 | 0.129336 | − | 0.991601i | \(-0.458716\pi\) | ||||
0.129336 | + | 0.991601i | \(0.458716\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.01574e9 | 0.477363 | ||||||||
\(686\) | −1.77675e8 | − | 7.03781e9i | −0.0210132 | − | 0.832345i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.89201e8 | + | 2.85473e9i | 0.0338564 | + | 0.334199i | ||||
\(689\) | − | 4.85169e9i | − | 0.565101i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.09453e10i | − | 1.26199i | −0.775788 | − | 0.630993i | \(-0.782647\pi\) | ||
0.775788 | − | 0.630993i | \(-0.217353\pi\) | |||||||
\(692\) | −2.50786e8 | − | 4.96373e9i | −0.0287695 | − | 0.569426i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.94093e9 | − | 7.42460e7i | 0.333985 | − | 0.00843169i | ||||
\(695\) | −1.64121e9 | −0.185446 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.99766e8 | −0.0559052 | ||||||||
\(698\) | −2.52142e9 | + | 6.36552e7i | −0.280641 | + | 0.00708500i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.02701e8 | − | 2.03272e9i | −0.0113170 | − | 0.223993i | ||||
\(701\) | − | 1.28742e10i | − | 1.41159i | −0.708418 | − | 0.705794i | \(-0.750591\pi\) | ||
0.708418 | − | 0.705794i | \(-0.249409\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.30303e9i | − | 0.358565i | ||||||
\(704\) | −1.02611e10 | + | 1.56595e9i | −1.10838 | + | 0.169151i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.29043e8 | − | 5.11145e9i | −0.0138012 | − | 0.546673i | ||||
\(707\) | 1.18454e10 | 1.26061 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.58274e10 | 1.66782 | 0.833909 | − | 0.551901i | \(-0.186097\pi\) | ||||
0.833909 | + | 0.551901i | \(0.186097\pi\) | |||||||
\(710\) | −1.68661e8 | − | 6.68075e9i | −0.0176852 | − | 0.700520i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.43199e8 | + | 1.11143e10i | 0.0875488 | + | 1.15399i | ||||
\(713\) | − | 7.72582e8i | − | 0.0798236i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.25909e9i | 0.333446i | ||||||||
\(716\) | 1.09451e10 | − | 5.52988e8i | 1.11436 | − | 0.0563015i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.90261e9 | + | 4.80328e7i | −0.191829 | + | 0.00484287i | ||||
\(719\) | 9.93738e9 | 0.997059 | 0.498529 | − | 0.866873i | \(-0.333874\pi\) | ||||
0.498529 | + | 0.866873i | \(0.333874\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.25366e9 | 0.919476 | ||||||||
\(722\) | −8.44781e9 | + | 2.13271e8i | −0.835341 | + | 0.0210888i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.54067e10 | + | 7.78403e8i | −1.50877 | + | 0.0762289i | ||||
\(725\) | 2.73611e9i | 0.266655i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8.00923e9i | − | 0.773073i | −0.922274 | − | 0.386536i | \(-0.873671\pi\) | ||
0.922274 | − | 0.386536i | \(-0.126329\pi\) | |||||||
\(728\) | 5.87276e8 | + | 7.74094e9i | 0.0564134 | + | 0.743590i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.95131e8 | − | 7.72926e9i | −0.0185651 | − | 0.735374i | ||||
\(731\) | 3.70573e9 | 0.350883 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.14827e9 | −0.670405 | −0.335202 | − | 0.942146i | \(-0.608805\pi\) | ||||
−0.335202 | + | 0.942146i | \(0.608805\pi\) | |||||||
\(734\) | −1.08069e8 | − | 4.28068e9i | −0.0100871 | − | 0.399555i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.00930e9 | − | 2.54933e8i | 0.185769 | − | 0.0235697i | ||||
\(737\) | − | 1.51085e10i | − | 1.39022i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.96524e10i | 1.79126i | 0.444796 | + | 0.895632i | \(0.353276\pi\) | ||||
−0.444796 | + | 0.895632i | \(0.646724\pi\) | |||||||
\(740\) | 2.19986e8 | + | 4.35411e9i | 0.0199565 | + | 0.394992i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.06007e10 | − | 2.67624e8i | 0.952627 | − | 0.0240498i | ||||
\(743\) | −1.75981e10 | −1.57400 | −0.787001 | − | 0.616952i | \(-0.788367\pi\) | ||||
−0.787001 | + | 0.616952i | \(0.788367\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.62692e9 | −0.498567 | ||||||||
\(746\) | 1.93458e9 | − | 4.88399e7i | 0.170608 | − | 0.00430714i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.76434e8 | + | 1.33885e10i | 0.0590976 | + | 1.16970i | ||||
\(749\) | 2.43049e10i | 2.11353i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 9.47530e9i | − | 0.816306i | −0.912913 | − | 0.408153i | \(-0.866173\pi\) | ||
0.912913 | − | 0.408153i | \(-0.133827\pi\) | |||||||
\(752\) | −1.86766e10 | + | 1.89205e9i | −1.60153 | + | 0.162245i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.63386e8 | − | 1.04329e10i | −0.0223765 | − | 0.886348i | ||||
\(755\) | 7.79614e9 | 0.659273 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.01517e10 | −1.68840 | −0.844202 | − | 0.536025i | \(-0.819925\pi\) | ||||
−0.844202 | + | 0.536025i | \(0.819925\pi\) | |||||||
\(758\) | 3.98182e8 | + | 1.57722e10i | 0.0332078 | + | 1.31538i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.18805e9 | + | 1.65999e8i | −0.180805 | + | 0.0137170i | ||||
\(761\) | − | 7.69576e9i | − | 0.633002i | −0.948592 | − | 0.316501i | \(-0.897492\pi\) | ||
0.948592 | − | 0.316501i | \(-0.102508\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.38242e10i | − | 1.12669i | ||||||
\(764\) | 3.95201e9 | − | 1.99670e8i | 0.320621 | − | 0.0161989i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.35097e9 | − | 5.93519e7i | 0.188993 | − | 0.00477127i | ||||
\(767\) | 1.64621e9 | 0.131735 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.27670e9 | −0.339131 | −0.169565 | − | 0.985519i | \(-0.554236\pi\) | ||||
−0.169565 | + | 0.985519i | \(0.554236\pi\) | |||||||
\(770\) | −7.12099e9 | + | 1.79775e8i | −0.562112 | + | 0.0141909i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.28675e10 | + | 1.15535e9i | −1.78878 | + | 0.0903759i | ||||
\(773\) | 1.72300e10i | 1.34171i | 0.741590 | + | 0.670854i | \(0.234072\pi\) | ||||
−0.741590 | + | 0.670854i | \(0.765928\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.10478e9i | − | 0.0852552i | ||||||
\(776\) | −2.08096e10 | + | 1.57874e9i | −1.59863 | + | 0.121282i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.62351e6 | + | 1.83140e8i | 0.000352001 | + | 0.0139430i | ||||
\(779\) | −2.86309e8 | −0.0216997 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.33890e10 | −1.75684 | ||||||||
\(782\) | −6.60168e7 | − | 2.61496e9i | −0.00493663 | − | 0.195543i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.45703e9 | + | 3.50218e8i | −0.256210 | + | 0.0259557i | ||||
\(785\) | 4.03968e9i | 0.298059i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.68815e10i | 1.96581i | 0.184113 | + | 0.982905i | \(0.441059\pi\) | ||||
−0.184113 | + | 0.982905i | \(0.558941\pi\) | |||||||
\(788\) | 6.39169e8 | + | 1.26509e10i | 0.0465344 | + | 0.921041i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.92787e9 | + | 7.39163e7i | −0.211279 | + | 0.00533391i | ||||
\(791\) | −2.46390e10 | −1.77013 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.06245e9 | −0.218079 | ||||||||
\(794\) | −1.25794e10 | + | 3.17577e8i | −0.891843 | + | 0.0225152i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.69863e8 | − | 1.72169e10i | −0.0611301 | − | 1.20993i | ||||
\(797\) | − | 1.01705e10i | − | 0.711601i | −0.934562 | − | 0.355800i | \(-0.884208\pi\) | ||
0.934562 | − | 0.355800i | \(-0.115792\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.42441e10i | 1.68148i | ||||||||
\(800\) | 2.87328e9 | − | 3.64551e8i | 0.198409 | − | 0.0251735i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.64497e8 | + | 1.83990e10i | 0.0317960 | + | 1.25946i | ||||
\(803\) | −2.70598e10 | −1.84425 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.38995e9 | 0.0939103 | ||||||||
\(806\) | 1.06350e8 | + | 4.21257e9i | 0.00715424 | + | 0.283384i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.27516e9 | + | 1.68081e10i | 0.0850406 | + | 1.12093i | ||||
\(809\) | − | 2.85965e9i | − | 0.189886i | −0.995483 | − | 0.0949430i | \(-0.969733\pi\) | ||
0.995483 | − | 0.0949430i | \(-0.0302669\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.65794e10i | − | 1.09143i | −0.837971 | − | 0.545714i | \(-0.816258\pi\) | ||
0.837971 | − | 0.545714i | \(-0.183742\pi\) | |||||||
\(812\) | 2.27809e10 | − | 1.15098e9i | 1.49322 | − | 0.0754432i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.52532e10 | − | 3.85080e8i | 0.991235 | − | 0.0250245i | ||||
\(815\) | −1.22495e9 | −0.0792626 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.12296e9 | 0.136196 | ||||||||
\(818\) | 2.15819e10 | − | 5.44851e8i | 1.37865 | − | 0.0348050i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.77417e8 | − | 1.90685e7i | 0.0239042 | − | 0.00120773i | ||||
\(821\) | 1.96549e10i | 1.23956i | 0.784774 | + | 0.619782i | \(0.212779\pi\) | ||||
−0.784774 | + | 0.619782i | \(0.787221\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.62922e10i | − | 1.64410i | −0.569419 | − | 0.822048i | \(-0.692832\pi\) | ||
0.569419 | − | 0.822048i | \(-0.307168\pi\) | |||||||
\(824\) | 9.96162e8 | + | 1.31305e10i | 0.0620276 | + | 0.817591i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.08068e7 | + | 3.59691e9i | 0.00560645 | + | 0.222075i | ||||
\(827\) | −7.90370e9 | −0.485916 | −0.242958 | − | 0.970037i | \(-0.578118\pi\) | ||||
−0.242958 | + | 0.970037i | \(0.578118\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.79874e10 | −1.70617 | −0.853085 | − | 0.521772i | \(-0.825271\pi\) | ||||
−0.853085 | + | 0.521772i | \(0.825271\pi\) | |||||||
\(830\) | −3.04842e7 | − | 1.20750e9i | −0.00185055 | − | 0.0733015i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.09208e10 | + | 1.66663e9i | −0.657390 | + | 0.100325i | ||||
\(833\) | 4.48757e9i | 0.269001i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.08016e9i | 0.361420i | ||||||||
\(836\) | 3.87520e8 | + | 7.67005e9i | 0.0229389 | + | 0.454022i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.03199e10 | − | 5.12990e8i | 1.19280 | − | 0.0301131i | ||||
\(839\) | 2.18716e10 | 1.27854 | 0.639269 | − | 0.768983i | \(-0.279237\pi\) | ||||
0.639269 | + | 0.768983i | \(0.279237\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.34140e10 | −0.777628 | ||||||||
\(842\) | 3.03225e10 | − | 7.65515e8i | 1.75054 | − | 0.0441938i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.48365e9 | − | 2.93654e10i | −0.0849441 | − | 1.68127i | ||||
\(845\) | − | 4.37493e9i | − | 0.249444i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.09900e9i | 0.288332i | ||||||||
\(848\) | 1.52092e9 | + | 1.50131e10i | 0.0856489 | + | 0.845447i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.44031e7 | − | 3.73937e9i | −0.00527254 | − | 0.208849i | ||||
\(851\) | −2.97729e9 | −0.165603 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.59600e10 | 0.880465 | 0.440232 | − | 0.897884i | \(-0.354896\pi\) | ||||
0.440232 | + | 0.897884i | \(0.354896\pi\) | |||||||
\(854\) | −1.68928e8 | − | 6.69134e9i | −0.00928109 | − | 0.367630i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.44875e10 | + | 2.61644e9i | −1.87933 | + | 0.142578i | ||||
\(857\) | − | 4.74214e9i | − | 0.257360i | −0.991686 | − | 0.128680i | \(-0.958926\pi\) | ||
0.991686 | − | 0.128680i | \(-0.0410741\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.57684e10i | 1.38711i | 0.720402 | + | 0.693557i | \(0.243957\pi\) | ||||
−0.720402 | + | 0.693557i | \(0.756043\pi\) | |||||||
\(860\) | −2.79852e9 | + | 1.41392e8i | −0.150032 | + | 0.00758017i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.71346e10 | + | 6.85033e8i | −1.44294 | + | 0.0364281i | ||||
\(863\) | 1.98251e9 | 0.104997 | 0.0524986 | − | 0.998621i | \(-0.483281\pi\) | ||||
0.0524986 | + | 0.998621i | \(0.483281\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.85358e9 | 0.254980 | ||||||||
\(866\) | 1.39254e10 | − | 3.51558e8i | 0.728612 | − | 0.0183944i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.19844e9 | + | 4.64739e8i | −0.477414 | + | 0.0241207i | ||||
\(869\) | 1.02503e10i | 0.529869i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.60798e10i | − | 0.824552i | ||||||
\(872\) | 1.96159e10 | − | 1.48818e9i | 1.00184 | − | 0.0760062i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.78201e7 | − | 1.49808e9i | −0.00191616 | − | 0.0759003i | ||||
\(875\) | 1.98761e9 | 0.100300 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.89235e9 | −0.144795 | −0.0723973 | − | 0.997376i | \(-0.523065\pi\) | ||||
−0.0723973 | + | 0.997376i | \(0.523065\pi\) | |||||||
\(878\) | −6.76110e8 | − | 2.67811e10i | −0.0337122 | − | 1.33536i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.02167e9 | − | 1.00850e10i | −0.0505384 | − | 0.498869i | ||||
\(881\) | − | 1.17827e10i | − | 0.580538i | −0.956945 | − | 0.290269i | \(-0.906255\pi\) | ||
0.956945 | − | 0.290269i | \(-0.0937448\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 5.83580e9i | − | 0.285258i | −0.989776 | − | 0.142629i | \(-0.954444\pi\) | ||
0.989776 | − | 0.142629i | \(-0.0455556\pi\) | |||||||
\(884\) | 7.19924e8 | + | 1.42492e10i | 0.0350513 | + | 0.693759i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.24874e10 | − | 5.67712e8i | 1.08623 | − | 0.0274227i | ||||
\(887\) | 8.23689e9 | 0.396306 | 0.198153 | − | 0.980171i | \(-0.436506\pi\) | ||||
0.198153 | + | 0.980171i | \(0.436506\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.75431e10 | 1.31479 | ||||||||
\(890\) | −1.08815e10 | + | 2.74712e8i | −0.517398 | + | 0.0130621i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.04892e9 | − | 2.07609e10i | −0.0494840 | − | 0.979420i | ||||
\(893\) | 1.38891e10i | 0.652670i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.07022e10i | 0.498992i | ||||||||
\(896\) | −4.24393e9 | − | 2.37696e10i | −0.197102 | − | 1.10394i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.37865e7 | − | 2.92273e9i | −0.00340024 | − | 0.134686i | ||||
\(899\) | 1.23814e10 | 0.568344 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.94886e10 | 0.887654 | ||||||||
\(902\) | −3.33790e7 | − | 1.32216e9i | −0.00151443 | − | 0.0599877i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.65240e9 | − | 3.49615e10i | −0.119412 | − | 1.57399i | ||||
\(905\) | − | 1.50648e10i | − | 0.675605i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 3.33720e9i | − | 0.148510i | −0.997239 | − | 0.0742552i | \(-0.976342\pi\) | ||
0.997239 | − | 0.0742552i | \(-0.0236579\pi\) | |||||||
\(908\) | 3.34597e10 | − | 1.69051e9i | 1.48327 | − | 0.0749405i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.57882e9 | + | 1.91333e8i | −0.333393 | + | 0.00841676i | ||||
\(911\) | −4.07441e10 | −1.78546 | −0.892731 | − | 0.450589i | \(-0.851214\pi\) | ||||
−0.892731 | + | 0.450589i | \(0.851214\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.22739e9 | −0.183834 | ||||||||
\(914\) | −1.15903e10 | + | 2.92606e8i | −0.502092 | + | 0.0126757i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.14168e9 | + | 1.58730e8i | −0.135060 | + | 0.00682376i | ||||
\(917\) | − | 1.87015e10i | − | 0.800912i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.03514e10i | 0.439943i | 0.975506 | + | 0.219972i | \(0.0705965\pi\) | ||||
−0.975506 | + | 0.219972i | \(0.929404\pi\) | |||||||
\(920\) | 1.49629e8 | + | 1.97227e9i | 0.00633516 | + | 0.0835044i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.74217e8 | − | 1.87840e10i | −0.0199260 | − | 0.789279i | ||||
\(923\) | −2.48927e10 | −1.04200 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.25748e9 | −0.176871 | ||||||||
\(926\) | 3.81251e7 | + | 1.51016e9i | 0.00157787 | + | 0.0625005i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.08556e9 | + | 3.22011e10i | 0.167816 | + | 1.32267i | ||||
\(929\) | 3.99110e10i | 1.63319i | 0.577210 | + | 0.816596i | \(0.304141\pi\) | ||||
−0.577210 | + | 0.816596i | \(0.695859\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.57087e9i | 0.104413i | ||||||||
\(932\) | −2.43370e8 | − | 4.81695e9i | −0.00984718 | − | 0.194902i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.90247e10 | − | 9.85207e8i | 1.56720 | − | 0.0395652i | ||||
\(935\) | −1.30913e10 | −0.523773 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.42043e10 | 0.564069 | 0.282034 | − | 0.959404i | \(-0.408991\pi\) | ||||
0.282034 | + | 0.959404i | \(0.408991\pi\) | |||||||
\(938\) | 3.51338e10 | − | 8.86979e8i | 1.39000 | − | 0.0350916i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.25031e8 | − | 1.83088e10i | −0.0363253 | − | 0.718974i | ||||
\(941\) | 9.73811e9i | 0.380988i | 0.981688 | + | 0.190494i | \(0.0610089\pi\) | ||||
−0.981688 | + | 0.190494i | \(0.938991\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.58074e8i | 0.0100220i | ||||||||
\(944\) | −5.09407e9 | + | 5.16060e8i | −0.197089 | + | 0.0199663i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.47503e8 | + | 9.80373e9i | 0.00950519 | + | 0.376506i | ||||
\(947\) | −2.30378e10 | −0.881486 | −0.440743 | − | 0.897633i | \(-0.645285\pi\) | ||||
−0.440743 | + | 0.897633i | \(0.645285\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.87995e10 | −1.09384 | ||||||||
\(950\) | −5.40822e7 | − | 2.14223e9i | −0.00204655 | − | 0.0810650i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.10943e10 | + | 2.35901e9i | −1.16802 | + | 0.0886135i | ||||
\(953\) | 3.13419e10i | 1.17300i | 0.809948 | + | 0.586502i | \(0.199495\pi\) | ||||
−0.809948 | + | 0.586502i | \(0.800505\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.86431e9i | 0.143569i | ||||||||
\(956\) | 2.03162e10 | − | 1.02645e9i | 0.752040 | − | 0.0379958i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.34132e10 | + | 3.38628e8i | −0.492895 | + | 0.0124435i | ||||
\(959\) | 3.26931e10 | 1.19699 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.25133e10 | 0.818289 | ||||||||
\(962\) | 1.62339e10 | − | 4.09838e8i | 0.587910 | − | 0.0148422i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.41341e10 | − | 2.22982e9i | 1.58674 | − | 0.0801679i | ||||
\(965\) | − | 2.23600e10i | − | 0.800988i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 9.68193e9i | − | 0.344325i | −0.985069 | − | 0.172163i | \(-0.944925\pi\) | ||
0.985069 | − | 0.172163i | \(-0.0550755\pi\) | |||||||
\(968\) | −7.23524e9 | + | 5.48911e8i | −0.256383 | + | 0.0194508i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.14351e8 | − | 2.03738e10i | −0.0180950 | − | 0.716754i | ||||
\(971\) | −2.27423e10 | −0.797200 | −0.398600 | − | 0.917125i | \(-0.630504\pi\) | ||||
−0.398600 | + | 0.917125i | \(0.630504\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.33615e10 | −0.465008 | ||||||||
\(974\) | 1.22017e9 | + | 4.83317e10i | 0.0423120 | + | 1.67601i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.47651e9 | − | 9.60028e8i | 0.326268 | − | 0.0330529i | ||||
\(977\) | − | 5.49219e10i | − | 1.88414i | −0.335410 | − | 0.942072i | \(-0.608875\pi\) | ||
0.335410 | − | 0.942072i | \(-0.391125\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.80957e10i | 1.29759i | ||||||||
\(980\) | −1.71223e8 | − | 3.38896e9i | −0.00581126 | − | 0.115020i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.69352e9 | − | 6.80001e7i | 0.0907676 | − | 0.00229150i | ||||
\(983\) | −2.85112e9 | −0.0957365 | −0.0478683 | − | 0.998854i | \(-0.515243\pi\) | ||||
−0.0478683 | + | 0.998854i | \(0.515243\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.23701e10 | −0.412427 | ||||||||
\(986\) | 4.19075e10 | − | 1.05799e9i | 1.39227 | − | 0.0351488i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.12434e8 | + | 8.16319e9i | 0.0136052 | + | 0.269284i | ||||
\(989\) | − | 1.91359e9i | − | 0.0629018i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.09672e10i | 1.33714i | 0.743647 | + | 0.668572i | \(0.233094\pi\) | ||||
−0.743647 | + | 0.668572i | \(0.766906\pi\) | |||||||
\(992\) | −1.64966e9 | − | 1.30021e10i | −0.0536542 | − | 0.422886i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.37311e9 | − | 5.43896e10i | −0.0443457 | − | 1.75656i | ||||
\(995\) | 1.68349e10 | 0.541787 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.90949e10 | −1.56893 | −0.784465 | − | 0.620173i | \(-0.787062\pi\) | ||||
−0.784465 | + | 0.620173i | \(0.787062\pi\) | |||||||
\(998\) | −1.15091e9 | − | 4.55882e10i | −0.0366508 | − | 1.45176i | ||||
\(999\) | 0 | 0 |
(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 | 180.8.e.a.71.2 | yes | 56 | |
3.2 | odd | 2 | inner | 180.8.e.a.71.55 | yes | 56 | |
4.3 | odd | 2 | inner | 180.8.e.a.71.56 | yes | 56 | |
12.11 | even | 2 | inner | 180.8.e.a.71.1 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.8.e.a.71.1 | ✓ | 56 | 12.11 | even | 2 | inner | |
180.8.e.a.71.2 | yes | 56 | 1.1 | even | 1 | trivial | |
180.8.e.a.71.55 | yes | 56 | 3.2 | odd | 2 | inner | |
180.8.e.a.71.56 | yes | 56 | 4.3 | odd | 2 | inner |