Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,7,Mod(19,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.19");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.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: | \(16.5638940206\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 78x^{10} + 3408x^{8} + 73216x^{6} + 13959168x^{4} + 1308622848x^{2} + 68719476736 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{30}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.3 | ||
Root | \(4.24448 - 6.78118i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 72.19 |
Dual form | 72.7.b.d.19.4 |
$q$-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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.24448 | − | 6.78118i | −0.530560 | − | 0.847648i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −27.9688 | + | 57.5651i | −0.437013 | + | 0.899455i | ||||
\(5\) | 206.098i | 1.64878i | 0.566019 | + | 0.824392i | \(0.308483\pi\) | ||||
−0.566019 | + | 0.824392i | \(0.691517\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 210.403i | 0.613419i | 0.951803 | + | 0.306710i | \(0.0992280\pi\) | ||||
−0.951803 | + | 0.306710i | \(0.900772\pi\) | |||||||
\(8\) | 509.073 | − | 54.6722i | 0.994283 | − | 0.106782i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1397.59 | − | 874.779i | 1.39759 | − | 0.874779i | ||||
\(11\) | −2261.83 | −1.69935 | −0.849673 | − | 0.527310i | \(-0.823201\pi\) | ||||
−0.849673 | + | 0.527310i | \(0.823201\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3538.83i | − | 1.61076i | −0.592762 | − | 0.805378i | \(-0.701962\pi\) | ||
0.592762 | − | 0.805378i | \(-0.298038\pi\) | |||||||
\(14\) | 1426.78 | − | 893.050i | 0.519963 | − | 0.325455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2531.49 | − | 3220.06i | −0.618039 | − | 0.786147i | ||||
\(17\) | −3485.68 | −0.709481 | −0.354740 | − | 0.934965i | \(-0.615431\pi\) | ||||
−0.354740 | + | 0.934965i | \(0.615431\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9846.20 | 1.43552 | 0.717758 | − | 0.696293i | \(-0.245168\pi\) | ||||
0.717758 | + | 0.696293i | \(0.245168\pi\) | |||||||
\(20\) | −11864.1 | − | 5764.32i | −1.48301 | − | 0.720540i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9600.28 | + | 15337.9i | 0.901605 | + | 1.44045i | ||||
\(23\) | − | 2096.31i | − | 0.172294i | −0.996282 | − | 0.0861472i | \(-0.972544\pi\) | ||
0.996282 | − | 0.0861472i | \(-0.0274556\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −26851.4 | −1.71849 | ||||||||
\(26\) | −23997.4 | + | 15020.5i | −1.36535 | + | 0.854602i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −12111.9 | − | 5884.72i | −0.551743 | − | 0.268072i | ||||
\(29\) | − | 10106.1i | − | 0.414369i | −0.978302 | − | 0.207185i | \(-0.933570\pi\) | ||
0.978302 | − | 0.207185i | \(-0.0664301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1373.11i | − | 0.0460914i | −0.999734 | − | 0.0230457i | \(-0.992664\pi\) | ||
0.999734 | − | 0.0230457i | \(-0.00733632\pi\) | |||||||
\(32\) | −11091.0 | + | 30834.0i | −0.338469 | + | 0.940977i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 14794.9 | + | 23637.0i | 0.376422 | + | 0.601390i | ||||
\(35\) | −43363.6 | −1.01140 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 55063.1i | − | 1.08706i | −0.839388 | − | 0.543532i | \(-0.817087\pi\) | ||
0.839388 | − | 0.543532i | \(-0.182913\pi\) | |||||||
\(38\) | −41792.0 | − | 66768.9i | −0.761627 | − | 1.21681i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 11267.8 | + | 104919.i | 0.176060 | + | 1.63936i | ||||
\(41\) | −58478.9 | −0.848491 | −0.424246 | − | 0.905547i | \(-0.639461\pi\) | ||||
−0.424246 | + | 0.905547i | \(0.639461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −106639. | −1.34126 | −0.670628 | − | 0.741794i | \(-0.733975\pi\) | ||||
−0.670628 | + | 0.741794i | \(0.733975\pi\) | |||||||
\(44\) | 63260.7 | − | 130203.i | 0.742636 | − | 1.52849i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14215.4 | + | 8897.73i | −0.146045 | + | 0.0914125i | ||||
\(47\) | 84028.3i | 0.809342i | 0.914462 | + | 0.404671i | \(0.132614\pi\) | ||||
−0.914462 | + | 0.404671i | \(0.867386\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 73379.7 | 0.623717 | ||||||||
\(50\) | 113970. | + | 182084.i | 0.911762 | + | 1.45668i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 203713. | + | 98976.9i | 1.44880 | + | 0.703921i | ||||
\(53\) | − | 80372.5i | − | 0.539859i | −0.962880 | − | 0.269929i | \(-0.913000\pi\) | ||
0.962880 | − | 0.269929i | \(-0.0870003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 466159.i | − | 2.80186i | ||||||
\(56\) | 11503.2 | + | 107110.i | 0.0655019 | + | 0.609912i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −68531.0 | + | 42894.9i | −0.351239 | + | 0.219848i | ||||
\(59\) | 84520.5 | 0.411534 | 0.205767 | − | 0.978601i | \(-0.434031\pi\) | ||||
0.205767 | + | 0.978601i | \(0.434031\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 160512.i | − | 0.707159i | −0.935405 | − | 0.353579i | \(-0.884964\pi\) | ||
0.935405 | − | 0.353579i | \(-0.115036\pi\) | |||||||
\(62\) | −9311.30 | + | 5828.13i | −0.0390693 | + | 0.0244542i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 256166. | − | 55664.2i | 0.977195 | − | 0.212342i | ||||
\(65\) | 729346. | 2.65579 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −229254. | −0.762240 | −0.381120 | − | 0.924525i | \(-0.624462\pi\) | ||||
−0.381120 | + | 0.924525i | \(0.624462\pi\) | |||||||
\(68\) | 97490.4 | − | 200654.i | 0.310052 | − | 0.638146i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 184056. | + | 294057.i | 0.536606 | + | 0.857308i | ||||
\(71\) | 184976.i | 0.516821i | 0.966035 | + | 0.258411i | \(0.0831987\pi\) | ||||
−0.966035 | + | 0.258411i | \(0.916801\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −356258. | −0.915791 | −0.457895 | − | 0.889006i | \(-0.651397\pi\) | ||||
−0.457895 | + | 0.889006i | \(0.651397\pi\) | |||||||
\(74\) | −373393. | + | 233714.i | −0.921448 | + | 0.576753i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −275387. | + | 566798.i | −0.627339 | + | 1.29118i | ||||
\(77\) | − | 475895.i | − | 1.04241i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 443857.i | 0.900247i | 0.892966 | + | 0.450124i | \(0.148620\pi\) | ||||
−0.892966 | + | 0.450124i | \(0.851380\pi\) | |||||||
\(80\) | 663648. | − | 521735.i | 1.29619 | − | 1.01901i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 248212. | + | 396556.i | 0.450175 | + | 0.719222i | ||||
\(83\) | −356957. | −0.624284 | −0.312142 | − | 0.950035i | \(-0.601046\pi\) | ||||
−0.312142 | + | 0.950035i | \(0.601046\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 718392.i | − | 1.16978i | ||||||
\(86\) | 452628. | + | 723140.i | 0.711616 | + | 1.13691i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.15144e6 | + | 123659.i | −1.68963 | + | 0.181459i | ||||
\(89\) | −593976. | −0.842556 | −0.421278 | − | 0.906932i | \(-0.638418\pi\) | ||||
−0.421278 | + | 0.906932i | \(0.638418\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 744580. | 0.988068 | ||||||||
\(92\) | 120674. | + | 58631.3i | 0.154971 | + | 0.0752949i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 569811. | − | 356656.i | 0.686037 | − | 0.429404i | ||||
\(95\) | 2.02928e6i | 2.36686i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −783783. | −0.858778 | −0.429389 | − | 0.903120i | \(-0.641271\pi\) | ||||
−0.429389 | + | 0.903120i | \(0.641271\pi\) | |||||||
\(98\) | −311458. | − | 497601.i | −0.330919 | − | 0.528692i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 751003. | − | 1.54571e6i | 0.751003 | − | 1.54571i | ||||
\(101\) | − | 1.57046e6i | − | 1.52428i | −0.647415 | − | 0.762138i | \(-0.724150\pi\) | ||
0.647415 | − | 0.762138i | \(-0.275850\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 79752.8i | 0.0729851i | 0.999334 | + | 0.0364925i | \(0.0116185\pi\) | ||||
−0.999334 | + | 0.0364925i | \(0.988381\pi\) | |||||||
\(104\) | −193475. | − | 1.80152e6i | −0.171999 | − | 1.60155i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −545021. | + | 341139.i | −0.457610 | + | 0.286427i | ||||
\(107\) | −2.07013e6 | −1.68984 | −0.844922 | − | 0.534890i | \(-0.820353\pi\) | ||||
−0.844922 | + | 0.534890i | \(0.820353\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.62532e6i | 1.25505i | 0.778598 | + | 0.627523i | \(0.215931\pi\) | ||||
−0.778598 | + | 0.627523i | \(0.784069\pi\) | |||||||
\(110\) | −3.16111e6 | + | 1.97860e6i | −2.37499 | + | 1.48655i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 677509. | − | 532632.i | 0.482238 | − | 0.379117i | ||||
\(113\) | 1.61000e6 | 1.11581 | 0.557904 | − | 0.829905i | \(-0.311606\pi\) | ||||
0.557904 | + | 0.829905i | \(0.311606\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 432045. | 0.284077 | ||||||||
\(116\) | 581756. | + | 282655.i | 0.372707 | + | 0.181085i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −358745. | − | 573149.i | −0.218344 | − | 0.348836i | ||||
\(119\) | − | 733397.i | − | 0.435209i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.34431e6 | 1.88778 | ||||||||
\(122\) | −1.08846e6 | + | 681288.i | −0.599421 | + | 0.375190i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 79043.2 | + | 38404.3i | 0.0414572 | + | 0.0201425i | ||||
\(125\) | − | 2.31375e6i | − | 1.18464i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 499189.i | 0.243699i | 0.992549 | + | 0.121849i | \(0.0388825\pi\) | ||||
−0.992549 | + | 0.121849i | \(0.961117\pi\) | |||||||
\(128\) | −1.46476e6 | − | 1.50084e6i | −0.698452 | − | 0.715657i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.09569e6 | − | 4.94583e6i | −1.40905 | − | 2.25117i | ||||
\(131\) | −1.65837e6 | −0.737680 | −0.368840 | − | 0.929493i | \(-0.620245\pi\) | ||||
−0.368840 | + | 0.929493i | \(0.620245\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.07167e6i | 0.880573i | ||||||||
\(134\) | 973062. | + | 1.55461e6i | 0.404414 | + | 0.646111i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.77446e6 | + | 190570.i | −0.705424 | + | 0.0757595i | ||||
\(137\) | 1.62443e6 | 0.631742 | 0.315871 | − | 0.948802i | \(-0.397703\pi\) | ||||
0.315871 | + | 0.948802i | \(0.397703\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.94535e6 | −1.09671 | −0.548355 | − | 0.836246i | \(-0.684746\pi\) | ||||
−0.548355 | + | 0.836246i | \(0.684746\pi\) | |||||||
\(140\) | 1.21283e6 | − | 2.49623e6i | 0.441993 | − | 0.909706i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.25436e6 | − | 785126.i | 0.438082 | − | 0.274204i | ||||
\(143\) | 8.00423e6i | 2.73723i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.08284e6 | 0.683206 | ||||||||
\(146\) | 1.51213e6 | + | 2.41585e6i | 0.485882 | + | 0.776268i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.16971e6 | + | 1.54005e6i | 0.977766 | + | 0.475061i | ||||
\(149\) | − | 1.59888e6i | − | 0.483346i | −0.970358 | − | 0.241673i | \(-0.922304\pi\) | ||
0.970358 | − | 0.241673i | \(-0.0776961\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.58054e6i | 1.62086i | 0.585836 | + | 0.810429i | \(0.300766\pi\) | ||||
−0.585836 | + | 0.810429i | \(0.699234\pi\) | |||||||
\(152\) | 5.01243e6 | − | 538313.i | 1.42731 | − | 0.153287i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.22713e6 | + | 2.01993e6i | −0.883598 | + | 0.553061i | ||||
\(155\) | 282995. | 0.0759948 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.58044e6i | 1.18361i | 0.806082 | + | 0.591804i | \(0.201584\pi\) | ||||
−0.806082 | + | 0.591804i | \(0.798416\pi\) | |||||||
\(158\) | 3.00987e6 | − | 1.88394e6i | 0.763093 | − | 0.477635i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.35482e6 | − | 2.28583e6i | −1.55147 | − | 0.558063i | ||||
\(161\) | 441069. | 0.105689 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.50036e6 | 1.03917 | 0.519583 | − | 0.854420i | \(-0.326087\pi\) | ||||
0.519583 | + | 0.854420i | \(0.326087\pi\) | |||||||
\(164\) | 1.63559e6 | − | 3.36634e6i | 0.370802 | − | 0.763180i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.51510e6 | + | 2.42059e6i | 0.331220 | + | 0.529173i | ||||
\(167\) | − | 6.07108e6i | − | 1.30352i | −0.758427 | − | 0.651758i | \(-0.774032\pi\) | ||
0.758427 | − | 0.651758i | \(-0.225968\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.69651e6 | −1.59453 | ||||||||
\(170\) | −4.87155e6 | + | 3.04920e6i | −0.991562 | + | 0.620639i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.98257e6 | − | 6.13870e6i | 0.586146 | − | 1.20640i | ||||
\(173\) | − | 1.67216e6i | − | 0.322954i | −0.986877 | − | 0.161477i | \(-0.948374\pi\) | ||
0.986877 | − | 0.161477i | \(-0.0516257\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 5.64962e6i | − | 1.05416i | ||||||
\(176\) | 5.72580e6 | + | 7.28323e6i | 1.05026 | + | 1.33594i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.52112e6 | + | 4.02786e6i | 0.447026 | + | 0.714191i | ||||
\(179\) | 4.71439e6 | 0.821990 | 0.410995 | − | 0.911638i | \(-0.365181\pi\) | ||||
0.410995 | + | 0.911638i | \(0.365181\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.41548e6i | − | 1.58784i | −0.608022 | − | 0.793920i | \(-0.708037\pi\) | ||
0.608022 | − | 0.793920i | \(-0.291963\pi\) | |||||||
\(182\) | −3.16035e6 | − | 5.04913e6i | −0.524229 | − | 0.837534i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −114610. | − | 1.06717e6i | −0.0183979 | − | 0.171309i | ||||
\(185\) | 1.13484e7 | 1.79234 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.88401e6 | 1.20565 | ||||||||
\(188\) | −4.83710e6 | − | 2.35017e6i | −0.727967 | − | 0.353693i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.37609e7 | − | 8.61325e6i | 2.00626 | − | 1.25576i | ||||
\(191\) | 9.01454e6i | 1.29373i | 0.762604 | + | 0.646865i | \(0.223920\pi\) | ||||
−0.762604 | + | 0.646865i | \(0.776080\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 803577. | 0.111778 | 0.0558889 | − | 0.998437i | \(-0.482201\pi\) | ||||
0.0558889 | + | 0.998437i | \(0.482201\pi\) | |||||||
\(194\) | 3.32675e6 | + | 5.31497e6i | 0.455633 | + | 0.727941i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.05234e6 | + | 4.22411e6i | −0.272572 | + | 0.561005i | ||||
\(197\) | 1.11135e6i | 0.145362i | 0.997355 | + | 0.0726812i | \(0.0231556\pi\) | ||||
−0.997355 | + | 0.0726812i | \(0.976844\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.01000e6i | 0.128163i | 0.997945 | + | 0.0640814i | \(0.0204117\pi\) | ||||
−0.997945 | + | 0.0640814i | \(0.979588\pi\) | |||||||
\(200\) | −1.36693e7 | + | 1.46803e6i | −1.70867 | + | 0.183503i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.06496e7 | + | 6.66579e6i | −1.29205 | + | 0.808719i | ||||
\(203\) | 2.12634e6 | 0.254182 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1.20524e7i | − | 1.39898i | ||||||
\(206\) | 540818. | − | 338509.i | 0.0618656 | − | 0.0387229i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.13952e7 | + | 8.95851e6i | −1.26629 | + | 0.995510i | ||||
\(209\) | −2.22704e7 | −2.43944 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.52288e7 | −1.62113 | −0.810565 | − | 0.585648i | \(-0.800840\pi\) | ||||
−0.810565 | + | 0.585648i | \(0.800840\pi\) | |||||||
\(212\) | 4.62665e6 | + | 2.24793e6i | 0.485579 | + | 0.235925i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.78662e6 | + | 1.40379e7i | 0.896563 | + | 1.43239i | ||||
\(215\) | − | 2.19781e7i | − | 2.21144i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 288906. | 0.0282734 | ||||||||
\(218\) | 1.10216e7 | − | 6.89864e6i | 1.06384 | − | 0.665877i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.68345e7 | + | 1.30379e7i | 2.52014 | + | 1.22445i | ||||
\(221\) | 1.23352e7i | 1.14280i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 7.55064e6i | − | 0.680877i | −0.940267 | − | 0.340439i | \(-0.889424\pi\) | ||
0.940267 | − | 0.340439i | \(-0.110576\pi\) | |||||||
\(224\) | −6.48755e6 | − | 2.33357e6i | −0.577214 | − | 0.207623i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.83360e6 | − | 1.09177e7i | −0.592003 | − | 0.945813i | ||||
\(227\) | −1.93352e7 | −1.65299 | −0.826497 | − | 0.562941i | \(-0.809670\pi\) | ||||
−0.826497 | + | 0.562941i | \(0.809670\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.03537e7i | 0.862159i | 0.902314 | + | 0.431079i | \(0.141867\pi\) | ||||
−0.902314 | + | 0.431079i | \(0.858133\pi\) | |||||||
\(230\) | −1.83380e6 | − | 2.92977e6i | −0.150720 | − | 0.240797i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −552520. | − | 5.14472e6i | −0.0442470 | − | 0.412000i | ||||
\(233\) | −1.04567e7 | −0.826663 | −0.413331 | − | 0.910581i | \(-0.635635\pi\) | ||||
−0.413331 | + | 0.910581i | \(0.635635\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.73181e7 | −1.33443 | ||||||||
\(236\) | −2.36394e6 | + | 4.86544e6i | −0.179846 | + | 0.370157i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.97329e6 | + | 3.11288e6i | −0.368904 | + | 0.230904i | ||||
\(239\) | 2.58738e6i | 0.189525i | 0.995500 | + | 0.0947626i | \(0.0302092\pi\) | ||||
−0.995500 | + | 0.0947626i | \(0.969791\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.98127e6 | −0.355868 | −0.177934 | − | 0.984042i | \(-0.556941\pi\) | ||||
−0.177934 | + | 0.984042i | \(0.556941\pi\) | |||||||
\(242\) | −1.41949e7 | − | 2.26784e7i | −1.00158 | − | 1.60017i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.23987e6 | + | 4.48932e6i | 0.636058 | + | 0.309038i | ||||
\(245\) | 1.51234e7i | 1.02838i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.48440e7i | − | 2.31227i | ||||||
\(248\) | −75070.8 | − | 699012.i | −0.00492171 | − | 0.0458279i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.56899e7 | + | 9.82064e6i | −1.00416 | + | 0.628521i | ||||
\(251\) | 1.36281e7 | 0.861816 | 0.430908 | − | 0.902396i | \(-0.358193\pi\) | ||||
0.430908 | + | 0.902396i | \(0.358193\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.74149e6i | 0.292788i | ||||||||
\(254\) | 3.38509e6 | − | 2.11879e6i | 0.206571 | − | 0.129297i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.96034e6 | + | 1.63031e7i | −0.236055 | + | 0.971740i | ||||
\(257\) | 5.80282e6 | 0.341853 | 0.170927 | − | 0.985284i | \(-0.445324\pi\) | ||||
0.170927 | + | 0.985284i | \(0.445324\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.15854e7 | 0.666826 | ||||||||
\(260\) | −2.03990e7 | + | 4.19849e7i | −1.16061 | + | 2.38876i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.03892e6 | + | 1.12457e7i | 0.391383 | + | 0.625292i | ||||
\(263\) | − | 2.82908e7i | − | 1.55517i | −0.628778 | − | 0.777585i | \(-0.716445\pi\) | ||
0.628778 | − | 0.777585i | \(-0.283555\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.65646e7 | 0.890111 | ||||||||
\(266\) | 1.40484e7 | − | 8.79315e6i | 0.746416 | − | 0.467196i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.41196e6 | − | 1.31970e7i | 0.333109 | − | 0.685601i | ||||
\(269\) | 5.02831e6i | 0.258324i | 0.991624 | + | 0.129162i | \(0.0412287\pi\) | ||||
−0.991624 | + | 0.129162i | \(0.958771\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.34374e7i | 1.68006i | 0.542541 | + | 0.840029i | \(0.317462\pi\) | ||||
−0.542541 | + | 0.840029i | \(0.682538\pi\) | |||||||
\(272\) | 8.82396e6 | + | 1.12241e7i | 0.438487 | + | 0.557756i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.89487e6 | − | 1.10156e7i | −0.335177 | − | 0.535495i | ||||
\(275\) | 6.07334e7 | 2.92031 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1.94246e7i | − | 0.913929i | −0.889485 | − | 0.456965i | \(-0.848937\pi\) | ||
0.889485 | − | 0.456965i | \(-0.151063\pi\) | |||||||
\(278\) | 1.25014e7 | + | 1.99729e7i | 0.581870 | + | 0.929624i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.20752e7 | + | 2.37078e6i | −1.00561 | + | 0.107998i | ||||
\(281\) | −2.59526e7 | −1.16967 | −0.584833 | − | 0.811154i | \(-0.698840\pi\) | ||||
−0.584833 | + | 0.811154i | \(0.698840\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −336420. | −0.0148430 | −0.00742152 | − | 0.999972i | \(-0.502362\pi\) | ||||
−0.00742152 | + | 0.999972i | \(0.502362\pi\) | |||||||
\(284\) | −1.06482e7 | − | 5.17356e6i | −0.464857 | − | 0.225858i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.42781e7 | − | 3.39738e7i | 2.32021 | − | 1.45226i | ||||
\(287\) | − | 1.23041e7i | − | 0.520481i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.19876e7 | −0.496637 | ||||||||
\(290\) | −8.84056e6 | − | 1.41241e7i | −0.362481 | − | 0.579118i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.96413e6 | − | 2.05081e7i | 0.400213 | − | 0.823713i | ||||
\(293\) | 1.59063e7i | 0.632364i | 0.948699 | + | 0.316182i | \(0.102401\pi\) | ||||
−0.948699 | + | 0.316182i | \(0.897599\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.74195e7i | 0.678532i | ||||||||
\(296\) | −3.01042e6 | − | 2.80311e7i | −0.116078 | − | 1.08085i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.08423e7 | + | 6.78642e6i | −0.409707 | + | 0.256444i | ||||
\(299\) | −7.41847e6 | −0.277524 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 2.24372e7i | − | 0.822752i | ||||||
\(302\) | 3.78426e7 | − | 2.36865e7i | 1.37392 | − | 0.859962i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.49256e7 | − | 3.17054e7i | −0.887205 | − | 1.12853i | ||||
\(305\) | 3.30811e7 | 1.16595 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.19952e7 | 1.79700 | 0.898500 | − | 0.438974i | \(-0.144658\pi\) | ||||
0.898500 | + | 0.438974i | \(0.144658\pi\) | |||||||
\(308\) | 2.73950e7 | + | 1.33102e7i | 0.937602 | + | 0.455547i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.20117e6 | − | 1.91904e6i | −0.0403198 | − | 0.0644168i | ||||
\(311\) | 6.97946e6i | 0.232028i | 0.993248 | + | 0.116014i | \(0.0370118\pi\) | ||||
−0.993248 | + | 0.116014i | \(0.962988\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.81265e7 | −0.591127 | −0.295564 | − | 0.955323i | \(-0.595507\pi\) | ||||
−0.295564 | + | 0.955323i | \(0.595507\pi\) | |||||||
\(314\) | 3.10608e7 | − | 1.94416e7i | 1.00328 | − | 0.627974i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.55507e7 | − | 1.24142e7i | −0.809732 | − | 0.393420i | ||||
\(317\) | 3.82943e7i | 1.20214i | 0.799195 | + | 0.601072i | \(0.205260\pi\) | ||||
−0.799195 | + | 0.601072i | \(0.794740\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.28582e7i | 0.704157i | ||||||||
\(320\) | 1.14723e7 | + | 5.27953e7i | 0.350106 | + | 1.61118i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.87211e6 | − | 2.99097e6i | −0.0560742 | − | 0.0895868i | ||||
\(323\) | −3.43207e7 | −1.01847 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.50227e7i | 2.76807i | ||||||||
\(326\) | −1.91017e7 | − | 3.05178e7i | −0.551339 | − | 0.880846i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.97700e7 | + | 3.19717e6i | −0.843640 | + | 0.0906032i | ||||
\(329\) | −1.76798e7 | −0.496466 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.87879e6 | 0.134533 | 0.0672664 | − | 0.997735i | \(-0.478572\pi\) | ||||
0.0672664 | + | 0.997735i | \(0.478572\pi\) | |||||||
\(332\) | 9.98368e6 | − | 2.05483e7i | 0.272820 | − | 0.561515i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.11691e7 | + | 2.57686e7i | −1.10492 | + | 0.691593i | ||||
\(335\) | − | 4.72488e7i | − | 1.25677i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.80289e6 | 0.151619 | 0.0758097 | − | 0.997122i | \(-0.475846\pi\) | ||||
0.0758097 | + | 0.997122i | \(0.475846\pi\) | |||||||
\(338\) | 3.26677e7 | + | 5.21914e7i | 0.845995 | + | 1.35160i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.13543e7 | + | 2.00926e7i | 1.05217 | + | 0.511210i | ||||
\(341\) | 3.10574e6i | 0.0783253i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.01930e7i | 0.996019i | ||||||||
\(344\) | −5.42871e7 | + | 5.83019e6i | −1.33359 | + | 0.143221i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.13392e7 | + | 7.09746e6i | −0.273751 | + | 0.171346i | ||||
\(347\) | 2.11799e7 | 0.506916 | 0.253458 | − | 0.967346i | \(-0.418432\pi\) | ||||
0.253458 | + | 0.967346i | \(0.418432\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.02066e7i | 0.710600i | 0.934752 | + | 0.355300i | \(0.115621\pi\) | ||||
−0.934752 | + | 0.355300i | \(0.884379\pi\) | |||||||
\(350\) | −3.83111e7 | + | 2.39797e7i | −0.893552 | + | 0.559292i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.50859e7 | − | 6.97412e7i | 0.575176 | − | 1.59905i | ||||
\(353\) | 5.47613e6 | 0.124494 | 0.0622472 | − | 0.998061i | \(-0.480173\pi\) | ||||
0.0622472 | + | 0.998061i | \(0.480173\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.81232e7 | −0.852127 | ||||||||
\(356\) | 1.66128e7 | − | 3.41923e7i | 0.368208 | − | 0.757841i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.00101e7 | − | 3.19692e7i | −0.436115 | − | 0.696758i | ||||
\(359\) | 6.76347e7i | 1.46179i | 0.682487 | + | 0.730897i | \(0.260898\pi\) | ||||
−0.682487 | + | 0.730897i | \(0.739102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.99019e7 | 1.06071 | ||||||||
\(362\) | −6.38481e7 | + | 3.99638e7i | −1.34593 | + | 0.842444i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.08250e7 | + | 4.28618e7i | −0.431799 | + | 0.888723i | ||||
\(365\) | − | 7.34241e7i | − | 1.50994i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4.80835e7i | − | 0.972743i | −0.873752 | − | 0.486371i | \(-0.838320\pi\) | ||
0.873752 | − | 0.486371i | \(-0.161680\pi\) | |||||||
\(368\) | −6.75023e6 | + | 5.30678e6i | −0.135449 | + | 0.106485i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.81680e7 | − | 7.69556e7i | −0.950941 | − | 1.51927i | ||||
\(371\) | 1.69106e7 | 0.331160 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 5.09422e7i | − | 0.981637i | −0.871262 | − | 0.490819i | \(-0.836698\pi\) | ||
0.871262 | − | 0.490819i | \(-0.163302\pi\) | |||||||
\(374\) | −3.34635e7 | − | 5.34629e7i | −0.639671 | − | 1.02197i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.59401e6 | + | 4.27765e7i | 0.0864228 | + | 0.804714i | ||||
\(377\) | −3.57636e7 | −0.667448 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.01401e7 | −0.737329 | −0.368665 | − | 0.929563i | \(-0.620185\pi\) | ||||
−0.368665 | + | 0.929563i | \(0.620185\pi\) | |||||||
\(380\) | −1.16816e8 | − | 5.67567e7i | −2.12888 | − | 1.03435i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.11293e7 | − | 3.82620e7i | 1.09663 | − | 0.686401i | ||||
\(383\) | − | 2.67862e7i | − | 0.476777i | −0.971170 | − | 0.238388i | \(-0.923381\pi\) | ||
0.971170 | − | 0.238388i | \(-0.0766191\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.80811e7 | 1.71871 | ||||||||
\(386\) | −3.41076e6 | − | 5.44920e6i | −0.0593048 | − | 0.0947482i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.19215e7 | − | 4.51186e7i | 0.375297 | − | 0.772432i | ||||
\(389\) | − | 5.82424e7i | − | 0.989442i | −0.869052 | − | 0.494721i | \(-0.835270\pi\) | ||
0.869052 | − | 0.494721i | \(-0.164730\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.30705e6i | 0.122240i | ||||||||
\(392\) | 3.73556e7 | − | 4.01183e6i | 0.620151 | − | 0.0666015i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.53626e6 | − | 4.71710e6i | 0.123216 | − | 0.0771234i | ||||
\(395\) | −9.14781e7 | −1.48431 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.92002e7i | 0.306856i | 0.988160 | + | 0.153428i | \(0.0490312\pi\) | ||||
−0.988160 | + | 0.153428i | \(0.950969\pi\) | |||||||
\(398\) | 6.84899e6 | − | 4.28692e6i | 0.108637 | − | 0.0679980i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.79741e7 | + | 8.64632e7i | 1.06210 | + | 1.35099i | ||||
\(401\) | −4.53461e6 | −0.0703245 | −0.0351623 | − | 0.999382i | \(-0.511195\pi\) | ||||
−0.0351623 | + | 0.999382i | \(0.511195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.85920e6 | −0.0742420 | ||||||||
\(404\) | 9.04039e7 | + | 4.39240e7i | 1.37102 | + | 0.666128i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.02521e6 | − | 1.44191e7i | −0.134859 | − | 0.215457i | ||||
\(407\) | 1.24543e8i | 1.84730i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.02088e8 | −1.49213 | −0.746063 | − | 0.665876i | \(-0.768058\pi\) | ||||
−0.746063 | + | 0.665876i | \(0.768058\pi\) | |||||||
\(410\) | −8.17294e7 | + | 5.11561e7i | −1.18584 | + | 0.742242i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.59098e6 | − | 2.23059e6i | −0.0656468 | − | 0.0318954i | ||||
\(413\) | 1.77834e7i | 0.252443i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 7.35682e7i | − | 1.02931i | ||||||
\(416\) | 1.09116e8 | + | 3.92490e7i | 1.51568 | + | 0.545191i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.45264e7 | + | 1.51020e8i | 1.29427 | + | 2.06778i | ||||
\(419\) | −1.36648e8 | −1.85764 | −0.928820 | − | 0.370531i | \(-0.879176\pi\) | ||||
−0.928820 | + | 0.370531i | \(0.879176\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 3.78060e7i | − | 0.506657i | −0.967380 | − | 0.253329i | \(-0.918475\pi\) | ||
0.967380 | − | 0.253329i | \(-0.0815254\pi\) | |||||||
\(422\) | 6.46383e7 | + | 1.03269e8i | 0.860107 | + | 1.37415i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.39414e6 | − | 4.09154e7i | −0.0576469 | − | 0.536772i | ||||
\(425\) | 9.35955e7 | 1.21924 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.37721e7 | 0.433785 | ||||||||
\(428\) | 5.78991e7 | − | 1.19167e8i | 0.738484 | − | 1.51994i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.49038e8 | + | 9.32857e7i | −1.87452 | + | 1.17330i | ||||
\(431\) | − | 3.82526e6i | − | 0.0477781i | −0.999715 | − | 0.0238891i | \(-0.992395\pi\) | ||
0.999715 | − | 0.0238891i | \(-0.00760485\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.51604e7 | −0.925818 | −0.462909 | − | 0.886406i | \(-0.653194\pi\) | ||||
−0.462909 | + | 0.886406i | \(0.653194\pi\) | |||||||
\(434\) | −1.22625e6 | − | 1.95912e6i | −0.0150007 | − | 0.0239658i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.35618e7 | − | 4.54583e7i | −1.12886 | − | 0.548472i | ||||
\(437\) | − | 2.06407e7i | − | 0.247332i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.64865e7i | − | 0.313063i | −0.987673 | − | 0.156531i | \(-0.949969\pi\) | ||
0.987673 | − | 0.156531i | \(-0.0500312\pi\) | |||||||
\(440\) | −2.54859e7 | − | 2.37309e8i | −0.299187 | − | 2.78584i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.36474e7 | − | 5.23566e7i | 0.968692 | − | 0.606324i | ||||
\(443\) | 8.65074e7 | 0.995044 | 0.497522 | − | 0.867451i | \(-0.334243\pi\) | ||||
0.497522 | + | 0.867451i | \(0.334243\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 1.22417e8i | − | 1.38919i | ||||||
\(446\) | −5.12022e7 | + | 3.20485e7i | −0.577144 | + | 0.361246i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.17119e7 | + | 5.38980e7i | 0.130255 | + | 0.599430i | ||||
\(449\) | 2.98909e7 | 0.330217 | 0.165109 | − | 0.986275i | \(-0.447203\pi\) | ||||
0.165109 | + | 0.986275i | \(0.447203\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.32269e8 | 1.44188 | ||||||||
\(452\) | −4.50297e7 | + | 9.26797e7i | −0.487623 | + | 1.00362i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.20679e7 | + | 1.31116e8i | 0.877012 | + | 1.40116i | ||||
\(455\) | 1.53456e8i | 1.62911i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.17316e7 | −0.751557 | −0.375779 | − | 0.926709i | \(-0.622625\pi\) | ||||
−0.375779 | + | 0.926709i | \(0.622625\pi\) | |||||||
\(458\) | 7.02100e7 | − | 4.39459e7i | 0.730807 | − | 0.457427i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.20838e7 | + | 2.48707e7i | −0.124145 | + | 0.255514i | ||||
\(461\) | − | 1.44580e8i | − | 1.47572i | −0.674952 | − | 0.737861i | \(-0.735836\pi\) | ||
0.674952 | − | 0.737861i | \(-0.264164\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.06977e6i | − | 0.0813052i | −0.999173 | − | 0.0406526i | \(-0.987056\pi\) | ||
0.999173 | − | 0.0406526i | \(-0.0129437\pi\) | |||||||
\(464\) | −3.25421e7 | + | 2.55834e7i | −0.325755 | + | 0.256097i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.43834e7 | + | 7.09090e7i | 0.438594 | + | 0.700719i | ||||
\(467\) | 8.38502e7 | 0.823291 | 0.411646 | − | 0.911344i | \(-0.364954\pi\) | ||||
0.411646 | + | 0.911344i | \(0.364954\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 4.82356e7i | − | 0.467573i | ||||||
\(470\) | 7.35062e7 | + | 1.17437e8i | 0.707995 | + | 1.13113i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.30271e7 | − | 4.62092e6i | 0.409181 | − | 0.0439443i | ||||
\(473\) | 2.41200e8 | 2.27926 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.64385e8 | −2.46692 | ||||||||
\(476\) | 4.22181e7 | + | 2.05122e7i | 0.391451 | + | 0.190192i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.75455e7 | − | 1.09821e7i | 0.160651 | − | 0.100554i | ||||
\(479\) | − | 9.09446e7i | − | 0.827505i | −0.910389 | − | 0.413752i | \(-0.864218\pi\) | ||
0.910389 | − | 0.413752i | \(-0.135782\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.94859e8 | −1.75100 | ||||||||
\(482\) | 2.11429e7 | + | 3.37789e7i | 0.188809 | + | 0.301651i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.35365e7 | + | 1.92516e8i | −0.824983 | + | 1.69797i | ||||
\(485\) | − | 1.61536e8i | − | 1.41594i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.12400e8i | 0.973151i | 0.873639 | + | 0.486575i | \(0.161754\pi\) | ||||
−0.873639 | + | 0.486575i | \(0.838246\pi\) | |||||||
\(488\) | −8.77551e6 | − | 8.17121e7i | −0.0755115 | − | 0.703116i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.02555e8 | − | 6.41910e7i | 0.871700 | − | 0.545614i | ||||
\(491\) | −4.04565e7 | −0.341777 | −0.170889 | − | 0.985290i | \(-0.554664\pi\) | ||||
−0.170889 | + | 0.985290i | \(0.554664\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.52265e7i | 0.293987i | ||||||||
\(494\) | −2.36284e8 | + | 1.47895e8i | −1.95999 | + | 1.22679i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.42149e6 | + | 3.47601e6i | −0.0362346 | + | 0.0284863i | ||||
\(497\) | −3.89194e7 | −0.317028 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.36162e8 | 1.09586 | 0.547931 | − | 0.836524i | \(-0.315416\pi\) | ||||
0.547931 | + | 0.836524i | \(0.315416\pi\) | |||||||
\(500\) | 1.33191e8 | + | 6.47128e7i | 1.06553 | + | 0.517702i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.78442e7 | − | 9.24147e7i | −0.457245 | − | 0.730516i | ||||
\(503\) | 1.62786e8i | 1.27912i | 0.768739 | + | 0.639562i | \(0.220884\pi\) | ||||
−0.768739 | + | 0.639562i | \(0.779116\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.23669e8 | 2.51320 | ||||||||
\(506\) | 3.21529e7 | − | 2.01251e7i | 0.248181 | − | 0.155341i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.87359e7 | − | 1.39617e7i | −0.219196 | − | 0.106500i | ||||
\(509\) | 1.23236e8i | 0.934511i | 0.884122 | + | 0.467255i | \(0.154757\pi\) | ||||
−0.884122 | + | 0.467255i | \(0.845243\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 7.49577e7i | − | 0.561764i | ||||||
\(512\) | 1.27364e8 | − | 4.23423e7i | 0.948934 | − | 0.315474i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.46299e7 | − | 3.93500e7i | −0.181374 | − | 0.289771i | ||||
\(515\) | −1.64369e7 | −0.120337 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.90058e8i | − | 1.37535i | ||||||
\(518\) | −4.91741e7 | − | 7.85629e7i | −0.353791 | − | 0.565234i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.71290e8 | − | 3.98749e7i | 2.64061 | − | 0.283589i | ||||
\(521\) | 2.46388e7 | 0.174223 | 0.0871115 | − | 0.996199i | \(-0.472236\pi\) | ||||
0.0871115 | + | 0.996199i | \(0.472236\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.82039e7 | −0.616571 | −0.308285 | − | 0.951294i | \(-0.599755\pi\) | ||||
−0.308285 | + | 0.951294i | \(0.599755\pi\) | |||||||
\(524\) | 4.63827e7 | − | 9.54644e7i | 0.322376 | − | 0.663510i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.91845e8 | + | 1.20080e8i | −1.31824 | + | 0.825110i | ||||
\(527\) | 4.78622e6i | 0.0327010i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.43641e8 | 0.970315 | ||||||||
\(530\) | −7.03082e7 | − | 1.12328e8i | −0.472257 | − | 0.754500i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.19256e8 | − | 5.79422e7i | −0.792036 | − | 0.384822i | ||||
\(533\) | 2.06947e8i | 1.36671i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 4.26650e8i | − | 2.78619i | ||||||
\(536\) | −1.16707e8 | + | 1.25338e7i | −0.757882 | + | 0.0813932i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.40979e7 | − | 2.13425e7i | 0.218968 | − | 0.137056i | ||||
\(539\) | −1.65972e8 | −1.05991 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.02964e8i | 1.91337i | 0.291128 | + | 0.956684i | \(0.405969\pi\) | ||||
−0.291128 | + | 0.956684i | \(0.594031\pi\) | |||||||
\(542\) | 2.26745e8 | − | 1.41924e8i | 1.42410 | − | 0.891371i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.86595e7 | − | 1.07477e8i | 0.240137 | − | 0.667605i | ||||
\(545\) | −3.34976e8 | −2.06930 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.88974e6 | 0.0604258 | 0.0302129 | − | 0.999543i | \(-0.490381\pi\) | ||||
0.0302129 | + | 0.999543i | \(0.490381\pi\) | |||||||
\(548\) | −4.54335e7 | + | 9.35107e7i | −0.276080 | + | 0.568224i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.57781e8 | − | 4.11844e8i | −1.54940 | − | 2.47540i | ||||
\(551\) | − | 9.95063e7i | − | 0.594834i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.33887e7 | −0.552229 | ||||||||
\(554\) | −1.31722e8 | + | 8.24472e7i | −0.774690 | + | 0.484894i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.23779e7 | − | 1.69549e8i | 0.479277 | − | 0.986441i | ||||
\(557\) | − | 3.10741e8i | − | 1.79818i | −0.437763 | − | 0.899090i | \(-0.644229\pi\) | ||
0.437763 | − | 0.899090i | \(-0.355771\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.77378e8i | 2.16043i | ||||||||
\(560\) | 1.09774e8 | + | 1.39633e8i | 0.625083 | + | 0.795106i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.10155e8 | + | 1.75989e8i | 0.620577 | + | 0.991464i | ||||
\(563\) | −1.02595e8 | −0.574913 | −0.287457 | − | 0.957794i | \(-0.592810\pi\) | ||||
−0.287457 | + | 0.957794i | \(0.592810\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.31817e8i | 1.83973i | ||||||||
\(566\) | 1.42793e6 | + | 2.28133e6i | 0.00787512 | + | 0.0125817i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.01130e7 | + | 9.41662e7i | 0.0551870 | + | 0.513866i | ||||
\(569\) | −2.40381e8 | −1.30486 | −0.652428 | − | 0.757851i | \(-0.726249\pi\) | ||||
−0.652428 | + | 0.757851i | \(0.726249\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.46256e7 | −0.239704 | −0.119852 | − | 0.992792i | \(-0.538242\pi\) | ||||
−0.119852 | + | 0.992792i | \(0.538242\pi\) | |||||||
\(572\) | −4.60765e8 | − | 2.23869e8i | −2.46202 | − | 1.19621i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.34364e7 | + | 5.22245e7i | −0.441184 | + | 0.276146i | ||||
\(575\) | 5.62888e7i | 0.296087i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.24361e8 | 0.647377 | 0.323689 | − | 0.946164i | \(-0.395077\pi\) | ||||
0.323689 | + | 0.946164i | \(0.395077\pi\) | |||||||
\(578\) | 5.08811e7 | + | 8.12902e7i | 0.263496 | + | 0.420973i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.82546e7 | + | 1.19899e8i | −0.298570 | + | 0.614513i | ||||
\(581\) | − | 7.51048e7i | − | 0.382948i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.81789e8i | 0.917407i | ||||||||
\(584\) | −1.81361e8 | + | 1.94774e7i | −0.910555 | + | 0.0977896i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.07864e8 | − | 6.75140e7i | 0.536022 | − | 0.335507i | ||||
\(587\) | 1.65460e8 | 0.818046 | 0.409023 | − | 0.912524i | \(-0.365870\pi\) | ||||
0.409023 | + | 0.912524i | \(0.365870\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.35199e7i | − | 0.0661650i | ||||||
\(590\) | 1.18125e8 | − | 7.39368e7i | 0.575156 | − | 0.360002i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.77306e8 | + | 1.39392e8i | −0.854593 | + | 0.671849i | ||||
\(593\) | 3.64689e8 | 1.74887 | 0.874437 | − | 0.485139i | \(-0.161231\pi\) | ||||
0.874437 | + | 0.485139i | \(0.161231\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.51152e8 | 0.717566 | ||||||||
\(596\) | 9.20399e7 | + | 4.47189e7i | 0.434748 | + | 0.211228i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.14875e7 | + | 5.03060e7i | 0.147243 | + | 0.235243i | ||||
\(599\) | − | 4.13919e8i | − | 1.92590i | −0.269672 | − | 0.962952i | \(-0.586915\pi\) | ||
0.269672 | − | 0.962952i | \(-0.413085\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.49949e8 | −0.690747 | −0.345373 | − | 0.938465i | \(-0.612248\pi\) | ||||
−0.345373 | + | 0.938465i | \(0.612248\pi\) | |||||||
\(602\) | −1.52151e8 | + | 9.52341e7i | −0.697404 | + | 0.436519i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.21244e8 | − | 1.56081e8i | −1.45789 | − | 0.708336i | ||||
\(605\) | 6.89257e8i | 3.11254i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.28292e8i | 1.46789i | 0.679207 | + | 0.733946i | \(0.262324\pi\) | ||||
−0.679207 | + | 0.733946i | \(0.737676\pi\) | |||||||
\(608\) | −1.09204e8 | + | 3.03597e8i | −0.485878 | + | 1.35079i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.40412e8 | − | 2.24329e8i | −0.618607 | − | 0.988317i | ||||
\(611\) | 2.97362e8 | 1.30365 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 9.28329e7i | − | 0.403014i | −0.979487 | − | 0.201507i | \(-0.935416\pi\) | ||
0.979487 | − | 0.201507i | \(-0.0645839\pi\) | |||||||
\(614\) | −2.20692e8 | − | 3.52589e8i | −0.953416 | − | 1.52322i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.60182e7 | − | 2.42265e8i | −0.111310 | − | 1.03645i | ||||
\(617\) | −1.94762e8 | −0.829178 | −0.414589 | − | 0.910009i | \(-0.636075\pi\) | ||||
−0.414589 | + | 0.910009i | \(0.636075\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.23439e6 | 0.0220696 | 0.0110348 | − | 0.999939i | \(-0.496487\pi\) | ||||
0.0110348 | + | 0.999939i | \(0.496487\pi\) | |||||||
\(620\) | −7.91505e6 | + | 1.62907e7i | −0.0332107 | + | 0.0683539i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.73290e7 | − | 2.96242e7i | 0.196678 | − | 0.123105i | ||||
\(623\) | − | 1.24974e8i | − | 0.516840i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.73051e7 | 0.234722 | ||||||||
\(626\) | 7.69375e7 | + | 1.22919e8i | 0.313628 | + | 0.501067i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.63673e8 | − | 1.28109e8i | −1.06460 | − | 0.517252i | ||||
\(629\) | 1.91932e8i | 0.771252i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.99018e8i | 1.19017i | 0.803662 | + | 0.595086i | \(0.202882\pi\) | ||||
−0.803662 | + | 0.595086i | \(0.797118\pi\) | |||||||
\(632\) | 2.42666e7 | + | 2.25955e8i | 0.0961298 | + | 0.895100i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.59681e8 | − | 1.62539e8i | 1.01900 | − | 0.637810i | ||||
\(635\) | −1.02882e8 | −0.401807 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.59678e8i | − | 1.00466i | ||||||
\(638\) | 1.55005e8 | − | 9.70210e7i | 0.596877 | − | 0.373597i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.09321e8 | − | 3.01884e8i | 1.17996 | − | 1.15160i | ||||
\(641\) | 2.26180e8 | 0.858777 | 0.429389 | − | 0.903120i | \(-0.358729\pi\) | ||||
0.429389 | + | 0.903120i | \(0.358729\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.23603e8 | 1.59341 | 0.796703 | − | 0.604371i | \(-0.206575\pi\) | ||||
0.796703 | + | 0.604371i | \(0.206575\pi\) | |||||||
\(644\) | −1.23362e7 | + | 2.53902e7i | −0.0461874 | + | 0.0950623i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.45673e8 | + | 2.32735e8i | 0.540360 | + | 0.863305i | ||||
\(647\) | − | 2.69306e8i | − | 0.994337i | −0.867654 | − | 0.497168i | \(-0.834373\pi\) | ||
0.867654 | − | 0.497168i | \(-0.165627\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.91171e8 | −0.699340 | ||||||||
\(650\) | 6.44366e8 | − | 4.03321e8i | 2.34635 | − | 1.46863i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.25870e8 | + | 2.59064e8i | −0.454129 | + | 0.934683i | ||||
\(653\) | − | 2.66960e8i | − | 0.958754i | −0.877609 | − | 0.479377i | \(-0.840863\pi\) | ||
0.877609 | − | 0.479377i | \(-0.159137\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 3.41787e8i | − | 1.21628i | ||||||
\(656\) | 1.48039e8 | + | 1.88305e8i | 0.524401 | + | 0.667039i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.50414e7 | + | 1.19890e8i | 0.263405 | + | 0.420828i | ||||
\(659\) | 7.64400e7 | 0.267094 | 0.133547 | − | 0.991042i | \(-0.457363\pi\) | ||||
0.133547 | + | 0.991042i | \(0.457363\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.85402e8i | 0.641963i | 0.947085 | + | 0.320981i | \(0.104013\pi\) | ||||
−0.947085 | + | 0.320981i | \(0.895987\pi\) | |||||||
\(662\) | −2.07079e7 | − | 3.30840e7i | −0.0713777 | − | 0.114036i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.81717e8 | + | 1.95156e7i | −0.620714 | + | 0.0666620i | ||||
\(665\) | −4.26967e8 | −1.45188 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.11854e7 | −0.0713936 | ||||||||
\(668\) | 3.49483e8 | + | 1.69801e8i | 1.17245 | + | 0.569654i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.20402e8 | + | 2.00546e8i | −1.06530 | + | 0.666792i | ||||
\(671\) | 3.63050e8i | 1.20171i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.60309e7 | −0.151009 | −0.0755047 | − | 0.997145i | \(-0.524057\pi\) | ||||
−0.0755047 | + | 0.997145i | \(0.524057\pi\) | |||||||
\(674\) | −2.46302e7 | − | 3.93504e7i | −0.0804431 | − | 0.128520i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.15262e8 | − | 4.43051e8i | 0.696832 | − | 1.43421i | ||||
\(677\) | 2.19932e8i | 0.708797i | 0.935095 | + | 0.354398i | \(0.115314\pi\) | ||||
−0.935095 | + | 0.354398i | \(0.884686\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.64910e8i | − | 0.526791i | ||||||
\(680\) | −3.92760e7 | − | 3.65714e8i | −0.124911 | − | 1.16309i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.10606e7 | − | 1.31822e7i | 0.0663922 | − | 0.0415562i | ||||
\(683\) | 5.36350e8 | 1.68339 | 0.841697 | − | 0.539950i | \(-0.181557\pi\) | ||||
0.841697 | + | 0.539950i | \(0.181557\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.34792e8i | 1.04161i | ||||||||
\(686\) | 2.72556e8 | − | 1.70598e8i | 0.844273 | − | 0.528447i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.69956e8 | + | 3.43384e8i | 0.828949 | + | 1.05442i | ||||
\(689\) | −2.84425e8 | −0.869580 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.81630e8 | 1.45975 | 0.729877 | − | 0.683579i | \(-0.239577\pi\) | ||||
0.729877 | + | 0.683579i | \(0.239577\pi\) | |||||||
\(692\) | 9.62583e7 | + | 4.67684e7i | 0.290482 | + | 0.141135i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.98978e7 | − | 1.43625e8i | −0.268949 | − | 0.429686i | ||||
\(695\) | − | 6.07030e8i | − | 1.80824i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.03839e8 | 0.601988 | ||||||||
\(698\) | 2.04836e8 | − | 1.28211e8i | 0.602338 | − | 0.377016i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.25221e8 | + | 1.58013e8i | 0.948166 | + | 0.460680i | ||||
\(701\) | 4.69995e8i | 1.36439i | 0.731169 | + | 0.682196i | \(0.238975\pi\) | ||||
−0.731169 | + | 0.682196i | \(0.761025\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5.42162e8i | − | 1.56050i | ||||||
\(704\) | −5.79404e8 | + | 1.25903e8i | −1.66059 | + | 0.360843i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.32433e7 | − | 3.71347e7i | −0.0660517 | − | 0.105527i | ||||
\(707\) | 3.30430e8 | 0.935020 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 4.05087e8i | − | 1.13660i | −0.822820 | − | 0.568302i | \(-0.807600\pi\) | ||
0.822820 | − | 0.568302i | \(-0.192400\pi\) | |||||||
\(710\) | 1.61813e8 | + | 2.58520e8i | 0.452104 | + | 0.722303i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.02377e8 | + | 3.24739e7i | −0.837739 | + | 0.0899694i | ||||
\(713\) | −2.87846e6 | −0.00794130 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.64966e9 | −4.51311 | ||||||||
\(716\) | −1.31856e8 | + | 2.71385e8i | −0.359220 | + | 0.739343i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.58643e8 | − | 2.87074e8i | 1.23909 | − | 0.775569i | ||||
\(719\) | 3.74151e8i | 1.00661i | 0.864109 | + | 0.503304i | \(0.167882\pi\) | ||||
−0.864109 | + | 0.503304i | \(0.832118\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.67802e7 | −0.0447704 | ||||||||
\(722\) | −2.11807e8 | − | 3.38394e8i | −0.562768 | − | 0.899105i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.42003e8 | + | 2.63340e8i | 1.42819 | + | 0.693907i | ||||
\(725\) | 2.71362e8i | 0.712090i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.13805e8i | 0.556435i | 0.960518 | + | 0.278218i | \(0.0897436\pi\) | ||||
−0.960518 | + | 0.278218i | \(0.910256\pi\) | |||||||
\(728\) | 3.79045e8 | − | 4.07078e7i | 0.982419 | − | 0.105507i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.97902e8 | + | 3.11647e8i | −1.27990 | + | 0.801114i | ||||
\(731\) | 3.71710e8 | 0.951595 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 5.56686e8i | − | 1.41351i | −0.707459 | − | 0.706754i | \(-0.750159\pi\) | ||
0.707459 | − | 0.706754i | \(-0.249841\pi\) | |||||||
\(734\) | −3.26063e8 | + | 2.04089e8i | −0.824543 | + | 0.516098i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.46374e7 | + | 2.32501e7i | 0.162125 | + | 0.0583164i | ||||
\(737\) | 5.18533e8 | 1.29531 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.10164e8 | 0.520744 | 0.260372 | − | 0.965508i | \(-0.416155\pi\) | ||||
0.260372 | + | 0.965508i | \(0.416155\pi\) | |||||||
\(740\) | −3.17401e8 | + | 6.53272e8i | −0.783274 | + | 1.61213i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.17766e7 | − | 1.14674e8i | −0.175700 | − | 0.280707i | ||||
\(743\) | − | 5.71643e8i | − | 1.39367i | −0.717234 | − | 0.696833i | \(-0.754592\pi\) | ||
0.717234 | − | 0.696833i | \(-0.245408\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.29527e8 | 0.796933 | ||||||||
\(746\) | −3.45448e8 | + | 2.16223e8i | −0.832082 | + | 0.520817i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.20507e8 | + | 4.53844e8i | −0.526886 | + | 1.08443i | ||||
\(749\) | − | 4.35561e8i | − | 1.03658i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 2.96917e8i | − | 0.700996i | −0.936564 | − | 0.350498i | \(-0.886012\pi\) | ||
0.936564 | − | 0.350498i | \(-0.113988\pi\) | |||||||
\(752\) | 2.70576e8 | − | 2.12717e8i | 0.636262 | − | 0.500205i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.51798e8 | + | 2.42519e8i | 0.354121 | + | 0.565760i | ||||
\(755\) | −1.15014e9 | −2.67245 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.06152e8i | 1.16679i | 0.812188 | + | 0.583396i | \(0.198276\pi\) | ||||
−0.812188 | + | 0.583396i | \(0.801724\pi\) | |||||||
\(758\) | 1.70374e8 | + | 2.72198e8i | 0.391197 | + | 0.624995i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.10945e8 | + | 1.03305e9i | 0.252737 | + | 2.35332i | ||||
\(761\) | 3.88935e8 | 0.882518 | 0.441259 | − | 0.897380i | \(-0.354532\pi\) | ||||
0.441259 | + | 0.897380i | \(0.354532\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.41972e8 | −0.769869 | ||||||||
\(764\) | −5.18923e8 | − | 2.52126e8i | −1.16365 | − | 0.565377i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.81642e8 | + | 1.13693e8i | −0.404138 | + | 0.252958i | ||||
\(767\) | − | 2.99104e8i | − | 0.662881i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.96129e7 | 0.0871079 | 0.0435540 | − | 0.999051i | \(-0.486132\pi\) | ||||
0.0435540 | + | 0.999051i | \(0.486132\pi\) | |||||||
\(770\) | −4.16303e8 | − | 6.65106e8i | −0.911879 | − | 1.45686i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.24751e7 | + | 4.62580e7i | −0.0488483 | + | 0.100539i | ||||
\(773\) | − | 5.41418e8i | − | 1.17218i | −0.810246 | − | 0.586090i | \(-0.800666\pi\) | ||
0.810246 | − | 0.586090i | \(-0.199334\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.68699e7i | 0.0792077i | ||||||||
\(776\) | −3.99003e8 | + | 4.28511e7i | −0.853867 | + | 0.0917016i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.94952e8 | + | 2.47208e8i | −0.838698 | + | 0.524958i | ||||
\(779\) | −5.75795e8 | −1.21802 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 4.18384e8i | − | 0.878258i | ||||||
\(782\) | 4.95505e7 | − | 3.10146e7i | 0.103616 | − | 0.0648554i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.85760e8 | − | 2.36287e8i | −0.385482 | − | 0.490333i | ||||
\(785\) | −9.44019e8 | −1.95151 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.10149e8 | 0.431126 | 0.215563 | − | 0.976490i | \(-0.430841\pi\) | ||||
0.215563 | + | 0.976490i | \(0.430841\pi\) | |||||||
\(788\) | −6.39750e7 | − | 3.10832e7i | −0.130747 | − | 0.0635252i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.88277e8 | + | 6.20330e8i | 0.787517 | + | 1.25818i | ||||
\(791\) | 3.38748e8i | 0.684459i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.68023e8 | −1.13906 | ||||||||
\(794\) | 1.30200e8 | − | 8.14948e7i | 0.260105 | − | 0.162805i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.81407e7 | − | 2.82485e7i | −0.115277 | − | 0.0560088i | ||||
\(797\) | 6.44520e8i | 1.27310i | 0.771237 | + | 0.636548i | \(0.219638\pi\) | ||||
−0.771237 | + | 0.636548i | \(0.780362\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.92896e8i | − | 0.574213i | ||||||
\(800\) | 2.97808e8 | − | 8.27936e8i | 0.581656 | − | 1.61706i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.92471e7 | + | 3.07500e7i | 0.0373114 | + | 0.0596104i | ||||
\(803\) | 8.05795e8 | 1.55625 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.09034e7i | 0.174258i | ||||||||
\(806\) | 2.06248e7 | + | 3.29511e7i | 0.0393898 | + | 0.0629311i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.58606e7 | − | 7.99480e8i | −0.162765 | − | 1.51556i | ||||
\(809\) | −4.12527e8 | −0.779125 | −0.389562 | − | 0.921000i | \(-0.627374\pi\) | ||||
−0.389562 | + | 0.921000i | \(0.627374\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.60499e8 | 0.300891 | 0.150446 | − | 0.988618i | \(-0.451929\pi\) | ||||
0.150446 | + | 0.988618i | \(0.451929\pi\) | |||||||
\(812\) | −5.94713e7 | + | 1.22403e8i | −0.111081 | + | 0.228625i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.44551e8 | − | 5.28621e8i | 1.56586 | − | 0.980103i | ||||
\(815\) | 9.27516e8i | 1.71336i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.04999e9 | −1.92539 | ||||||||
\(818\) | 4.33311e8 | + | 6.92278e8i | 0.791661 | + | 1.26480i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.93797e8 | + | 3.37091e8i | 1.25832 | + | 0.611372i | ||||
\(821\) | 3.60585e8i | 0.651596i | 0.945439 | + | 0.325798i | \(0.105633\pi\) | ||||
−0.945439 | + | 0.325798i | \(0.894367\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 6.90554e8i | − | 1.23879i | −0.785079 | − | 0.619396i | \(-0.787378\pi\) | ||
0.785079 | − | 0.619396i | \(-0.212622\pi\) | |||||||
\(824\) | 4.36026e6 | + | 4.05999e7i | 0.00779346 | + | 0.0725678i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.20592e8 | − | 7.54810e7i | 0.213983 | − | 0.133936i | ||||
\(827\) | −1.02908e9 | −1.81941 | −0.909706 | − | 0.415252i | \(-0.863693\pi\) | ||||
−0.909706 | + | 0.415252i | \(0.863693\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.71431e8i | − | 0.651950i | −0.945378 | − | 0.325975i | \(-0.894307\pi\) | ||
0.945378 | − | 0.325975i | \(-0.105693\pi\) | |||||||
\(830\) | −4.98879e8 | + | 3.12259e8i | −0.872492 | + | 0.546110i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.96986e8 | − | 9.06528e8i | −0.342031 | − | 1.57402i | ||||
\(833\) | −2.55778e8 | −0.442515 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.25124e9 | 2.14922 | ||||||||
\(836\) | 6.22878e8 | − | 1.28200e9i | 1.06607 | − | 2.19417i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.80000e8 | + | 9.26636e8i | 0.985589 | + | 1.57462i | ||||
\(839\) | 1.45962e7i | 0.0247145i | 0.999924 | + | 0.0123573i | \(0.00393354\pi\) | ||||
−0.999924 | + | 0.0123573i | \(0.996066\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.92691e8 | 0.828298 | ||||||||
\(842\) | −2.56369e8 | + | 1.60467e8i | −0.429467 | + | 0.268812i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.25932e8 | − | 8.76647e8i | 0.708455 | − | 1.45813i | ||||
\(845\) | − | 1.58624e9i | − | 2.62904i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.03653e8i | 1.15800i | ||||||||
\(848\) | −2.58804e8 | + | 2.03462e8i | −0.424408 | + | 0.333654i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.97264e8 | − | 6.34688e8i | −0.646878 | − | 1.03348i | ||||
\(851\) | −1.15429e8 | −0.187295 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 7.71644e8i | − | 1.24328i | −0.783302 | − | 0.621641i | \(-0.786466\pi\) | ||
0.783302 | − | 0.621641i | \(-0.213534\pi\) | |||||||
\(854\) | −1.43345e8 | − | 2.29015e8i | −0.230149 | − | 0.367697i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.05385e9 | + | 1.13179e8i | −1.68018 | + | 0.180444i | ||||
\(857\) | 7.73106e8 | 1.22828 | 0.614139 | − | 0.789198i | \(-0.289504\pi\) | ||||
0.614139 | + | 0.789198i | \(0.289504\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.50724e8 | −0.395563 | −0.197782 | − | 0.980246i | \(-0.563374\pi\) | ||||
−0.197782 | + | 0.980246i | \(0.563374\pi\) | |||||||
\(860\) | 1.26517e9 | + | 6.14703e8i | 1.98909 | + | 0.966429i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.59398e7 | + | 1.62362e7i | −0.0404990 | + | 0.0253492i | ||||
\(863\) | 7.52441e8i | 1.17068i | 0.810786 | + | 0.585342i | \(0.199040\pi\) | ||||
−0.810786 | + | 0.585342i | \(0.800960\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.44630e8 | 0.532481 | ||||||||
\(866\) | 3.19017e8 | + | 5.09677e8i | 0.491202 | + | 0.784768i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.08036e6 | + | 1.66309e7i | −0.0123558 | + | 0.0254306i | ||||
\(869\) | − | 1.00393e9i | − | 1.52983i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.11290e8i | 1.22778i | ||||||||
\(872\) | 8.88598e7 | + | 8.27407e8i | 0.134016 | + | 1.24787i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.39968e8 | + | 8.76088e7i | −0.209650 | + | 0.131224i | ||||
\(875\) | 4.86819e8 | 0.726680 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.37458e8i | 0.945046i | 0.881318 | + | 0.472523i | \(0.156657\pi\) | ||||
−0.881318 | + | 0.472523i | \(0.843343\pi\) | |||||||
\(878\) | −1.79610e8 | + | 1.12421e8i | −0.265367 | + | 0.166098i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.50106e9 | + | 1.18008e9i | −2.20267 | + | 1.73166i | ||||
\(881\) | 1.02174e9 | 1.49421 | 0.747107 | − | 0.664704i | \(-0.231442\pi\) | ||||
0.747107 | + | 0.664704i | \(0.231442\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.63930e8 | 0.383360 | 0.191680 | − | 0.981457i | \(-0.438606\pi\) | ||||
0.191680 | + | 0.981457i | \(0.438606\pi\) | |||||||
\(884\) | −7.10079e8 | − | 3.45002e8i | −1.02790 | − | 0.499419i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.67179e8 | − | 5.86622e8i | −0.527930 | − | 0.843446i | ||||
\(887\) | 3.72432e8i | 0.533674i | 0.963742 | + | 0.266837i | \(0.0859785\pi\) | ||||
−0.963742 | + | 0.266837i | \(0.914022\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.05031e8 | −0.149490 | ||||||||
\(890\) | −8.30134e8 | + | 5.19597e8i | −1.17755 | + | 0.737050i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.34653e8 | + | 2.11182e8i | 0.612419 | + | 0.297552i | ||||
\(893\) | 8.27360e8i | 1.16182i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.71627e8i | 1.35529i | ||||||||
\(896\) | 3.15781e8 | − | 3.08189e8i | 0.438998 | − | 0.428444i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.26871e8 | − | 2.02696e8i | −0.175200 | − | 0.279908i | ||||
\(899\) | −1.38767e7 | −0.0190989 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.80153e8i | 0.383019i | ||||||||
\(902\) | −5.61414e8 | − | 8.96942e8i | −0.765003 | − | 1.22221i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.19606e8 | − | 8.80220e7i | 1.10943 | − | 0.119148i | ||||
\(905\) | 1.94051e9 | 2.61801 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.13146e8 | −1.22382 | −0.611911 | − | 0.790927i | \(-0.709599\pi\) | ||||
−0.611911 | + | 0.790927i | \(0.709599\pi\) | |||||||
\(908\) | 5.40783e8 | − | 1.11303e9i | 0.722380 | − | 1.48679i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.04062e9 | − | 6.51342e8i | 1.38091 | − | 0.864341i | ||||
\(911\) | − | 9.98295e8i | − | 1.32039i | −0.751092 | − | 0.660197i | \(-0.770473\pi\) | ||
0.751092 | − | 0.660197i | \(-0.229527\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.07377e8 | 1.06087 | ||||||||
\(914\) | 3.04463e8 | + | 4.86425e8i | 0.398746 | + | 0.637056i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.96010e8 | − | 2.89580e8i | −0.775473 | − | 0.376775i | ||||
\(917\) | − | 3.48926e8i | − | 0.452507i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.77108e8i | − | 0.357029i | −0.983937 | − | 0.178514i | \(-0.942871\pi\) | ||
0.983937 | − | 0.178514i | \(-0.0571291\pi\) | |||||||
\(920\) | 2.19942e8 | − | 2.36208e7i | 0.282452 | − | 0.0303341i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9.80422e8 | + | 6.13666e8i | −1.25089 | + | 0.782959i | ||||
\(923\) | 6.54598e8 | 0.832472 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.47852e9i | 1.86811i | ||||||||
\(926\) | −5.47226e7 | + | 3.42519e7i | −0.0689181 | + | 0.0431372i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.11610e8 | + | 1.12086e8i | 0.389912 | + | 0.140251i | ||||
\(929\) | −8.71196e8 | −1.08660 | −0.543299 | − | 0.839539i | \(-0.682825\pi\) | ||||
−0.543299 | + | 0.839539i | \(0.682825\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.22511e8 | 0.895356 | ||||||||
\(932\) | 2.92463e8 | − | 6.01943e8i | 0.361262 | − | 0.743546i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.55900e8 | − | 5.68603e8i | −0.436805 | − | 0.697861i | ||||
\(935\) | 1.62488e9i | 1.98786i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.53726e7 | 0.0186865 | 0.00934324 | − | 0.999956i | \(-0.497026\pi\) | ||||
0.00934324 | + | 0.999956i | \(0.497026\pi\) | |||||||
\(938\) | −3.27094e8 | + | 2.04735e8i | −0.396337 | + | 0.248075i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.84366e8 | − | 9.96917e8i | 0.583164 | − | 1.20026i | ||||
\(941\) | − | 1.32198e9i | − | 1.58656i | −0.608856 | − | 0.793281i | \(-0.708371\pi\) | ||
0.608856 | − | 0.793281i | \(-0.291629\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.22590e8i | 0.146190i | ||||||||
\(944\) | −2.13963e8 | − | 2.72161e8i | −0.254344 | − | 0.323527i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.02377e9 | − | 1.63562e9i | −1.20928 | − | 1.93201i | ||||
\(947\) | −5.85382e8 | −0.689270 | −0.344635 | − | 0.938737i | \(-0.611997\pi\) | ||||
−0.344635 | + | 0.938737i | \(0.611997\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.26074e9i | 1.47512i | ||||||||
\(950\) | 1.12217e9 | + | 1.79284e9i | 1.30885 | + | 2.09108i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.00964e7 | − | 3.73352e8i | −0.0464723 | − | 0.432721i | ||||
\(953\) | 3.94470e8 | 0.455759 | 0.227880 | − | 0.973689i | \(-0.426821\pi\) | ||||
0.227880 | + | 0.973689i | \(0.426821\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.85788e9 | −2.13308 | ||||||||
\(956\) | −1.48943e8 | − | 7.23661e7i | −0.170469 | − | 0.0828250i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.16712e8 | + | 3.86012e8i | −0.701432 | + | 0.439041i | ||||
\(959\) | 3.41785e8i | 0.387523i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.85618e8 | 0.997876 | ||||||||
\(962\) | 8.27074e8 | + | 1.32137e9i | 0.929008 | + | 1.48423i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.39320e8 | − | 2.86747e8i | 0.155519 | − | 0.320087i | ||||
\(965\) | 1.65616e8i | 0.184297i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 8.33074e8i | − | 0.921306i | −0.887580 | − | 0.460653i | \(-0.847615\pi\) | ||
0.887580 | − | 0.460653i | \(-0.152385\pi\) | |||||||
\(968\) | 1.70250e9 | − | 1.82841e8i | 1.87698 | − | 0.201580i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.09541e9 | + | 6.85637e8i | −1.20022 | + | 0.751240i | ||||
\(971\) | −1.01281e9 | −1.10630 | −0.553148 | − | 0.833083i | \(-0.686574\pi\) | ||||
−0.553148 | + | 0.833083i | \(0.686574\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 6.19709e8i | − | 0.672743i | ||||||
\(974\) | 7.62206e8 | − | 4.77080e8i | 0.824889 | − | 0.516314i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.16857e8 | + | 4.06333e8i | −0.555931 | + | 0.437052i | ||||
\(977\) | −7.78748e6 | −0.00835051 | −0.00417526 | − | 0.999991i | \(-0.501329\pi\) | ||||
−0.00417526 | + | 0.999991i | \(0.501329\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.34347e9 | 1.43179 | ||||||||
\(980\) | −8.70581e8 | − | 4.22984e8i | −0.924977 | − | 0.449413i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.71717e8 | + | 2.74343e8i | 0.181333 | + | 0.289707i | ||||
\(983\) | 1.06247e9i | 1.11856i | 0.828980 | + | 0.559278i | \(0.188921\pi\) | ||||
−0.828980 | + | 0.559278i | \(0.811079\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.29047e8 | −0.239671 | ||||||||
\(986\) | 2.38877e8 | − | 1.49518e8i | 0.249197 | − | 0.155978i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.00580e9 | + | 9.74547e8i | 2.07978 | + | 1.01049i | ||||
\(989\) | 2.23549e8i | 0.231091i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.44802e8i | 0.354281i | 0.984186 | + | 0.177141i | \(0.0566848\pi\) | ||||
−0.984186 | + | 0.177141i | \(0.943315\pi\) | |||||||
\(992\) | 4.23384e7 | + | 1.52291e7i | 0.0433710 | + | 0.0156005i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.65193e8 | + | 2.63920e8i | 0.168202 | + | 0.268728i | ||||
\(995\) | −2.08159e8 | −0.211313 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.24019e9i | 1.25142i | 0.780056 | + | 0.625709i | \(0.215190\pi\) | ||||
−0.780056 | + | 0.625709i | \(0.784810\pi\) | |||||||
\(998\) | −5.77938e8 | − | 9.23342e8i | −0.581420 | − | 0.928904i | ||||
\(999\) | 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 | 72.7.b.d.19.3 | ✓ | 12 | |
3.2 | odd | 2 | inner | 72.7.b.d.19.10 | yes | 12 | |
4.3 | odd | 2 | 288.7.b.c.271.11 | 12 | |||
8.3 | odd | 2 | inner | 72.7.b.d.19.4 | yes | 12 | |
8.5 | even | 2 | 288.7.b.c.271.2 | 12 | |||
12.11 | even | 2 | 288.7.b.c.271.1 | 12 | |||
24.5 | odd | 2 | 288.7.b.c.271.12 | 12 | |||
24.11 | even | 2 | inner | 72.7.b.d.19.9 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.7.b.d.19.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
72.7.b.d.19.4 | yes | 12 | 8.3 | odd | 2 | inner | |
72.7.b.d.19.9 | yes | 12 | 24.11 | even | 2 | inner | |
72.7.b.d.19.10 | yes | 12 | 3.2 | odd | 2 | inner | |
288.7.b.c.271.1 | 12 | 12.11 | even | 2 | |||
288.7.b.c.271.2 | 12 | 8.5 | even | 2 | |||
288.7.b.c.271.11 | 12 | 4.3 | odd | 2 | |||
288.7.b.c.271.12 | 12 | 24.5 | odd | 2 |