Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(107,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.107");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.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: | \(17.3214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 30x^{14} + 619x^{12} + 5604x^{10} + 40971x^{8} - 4866x^{6} + 568069x^{4} - 7909632x^{2} + 20340100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{30}\cdot 3^{32}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 107.10 | ||
Root | \(-1.73205 + 1.98106i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.107 |
Dual form | 108.6.b.b.107.9 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.79734 | + | 5.36373i | 0.317727 | + | 0.948182i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −25.5392 | + | 19.2809i | −0.798099 | + | 0.602527i | ||||
\(5\) | − | 44.9719i | − | 0.804482i | −0.915534 | − | 0.402241i | \(-0.868231\pi\) | ||
0.915534 | − | 0.402241i | \(-0.131769\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 28.5094i | − | 0.219909i | −0.993937 | − | 0.109955i | \(-0.964929\pi\) | ||
0.993937 | − | 0.109955i | \(-0.0350706\pi\) | |||||||
\(8\) | −149.320 | − | 102.331i | −0.824883 | − | 0.565303i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 241.217 | − | 80.8297i | 0.762796 | − | 0.255606i | ||||
\(11\) | 411.905 | 1.02640 | 0.513198 | − | 0.858270i | \(-0.328461\pi\) | ||||
0.513198 | + | 0.858270i | \(0.328461\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 684.385 | 1.12316 | 0.561580 | − | 0.827422i | \(-0.310194\pi\) | ||||
0.561580 | + | 0.827422i | \(0.310194\pi\) | |||||||
\(14\) | 152.917 | − | 51.2411i | 0.208514 | − | 0.0698712i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 280.497 | − | 984.834i | 0.273923 | − | 0.961752i | ||||
\(17\) | 1516.97i | 1.27308i | 0.771245 | + | 0.636538i | \(0.219634\pi\) | ||||
−0.771245 | + | 0.636538i | \(0.780366\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2045.09i | − | 1.29966i | −0.760082 | − | 0.649828i | \(-0.774841\pi\) | ||
0.760082 | − | 0.649828i | \(-0.225159\pi\) | |||||||
\(20\) | 867.098 | + | 1148.55i | 0.484722 | + | 0.642056i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 740.332 | + | 2209.34i | 0.326114 | + | 0.973211i | ||||
\(23\) | 3070.67 | 1.21036 | 0.605178 | − | 0.796090i | \(-0.293102\pi\) | ||||
0.605178 | + | 0.796090i | \(0.293102\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1102.53 | 0.352808 | ||||||||
\(26\) | 1230.07 | + | 3670.85i | 0.356859 | + | 1.06496i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 549.686 | + | 728.107i | 0.132501 | + | 0.175509i | ||||
\(29\) | 643.596i | 0.142108i | 0.997472 | + | 0.0710539i | \(0.0226362\pi\) | ||||
−0.997472 | + | 0.0710539i | \(0.977364\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 731.030i | 0.136625i | 0.997664 | + | 0.0683126i | \(0.0217615\pi\) | ||||
−0.997664 | + | 0.0683126i | \(0.978238\pi\) | |||||||
\(32\) | 5786.53 | − | 265.570i | 0.998949 | − | 0.0458464i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8136.61 | + | 2726.51i | −1.20711 | + | 0.404491i | ||||
\(35\) | −1282.12 | −0.176913 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5461.90 | −0.655902 | −0.327951 | − | 0.944695i | \(-0.606358\pi\) | ||||
−0.327951 | + | 0.944695i | \(0.606358\pi\) | |||||||
\(38\) | 10969.3 | − | 3675.71i | 1.23231 | − | 0.412936i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4602.02 | + | 6715.20i | −0.454777 | + | 0.663604i | ||||
\(41\) | 6382.62i | 0.592979i | 0.955036 | + | 0.296490i | \(0.0958160\pi\) | ||||
−0.955036 | + | 0.296490i | \(0.904184\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 17907.2i | − | 1.47692i | −0.674297 | − | 0.738460i | \(-0.735553\pi\) | ||
0.674297 | − | 0.738460i | \(-0.264447\pi\) | |||||||
\(44\) | −10519.7 | + | 7941.88i | −0.819165 | + | 0.618431i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5519.03 | + | 16470.2i | 0.384564 | + | 1.14764i | ||||
\(47\) | 19287.6 | 1.27360 | 0.636801 | − | 0.771029i | \(-0.280257\pi\) | ||||
0.636801 | + | 0.771029i | \(0.280257\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15994.2 | 0.951640 | ||||||||
\(50\) | 1981.61 | + | 5913.65i | 0.112097 | + | 0.334526i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −17478.6 | + | 13195.5i | −0.896393 | + | 0.676734i | ||||
\(53\) | 11400.4i | 0.557483i | 0.960366 | + | 0.278741i | \(0.0899172\pi\) | ||||
−0.960366 | + | 0.278741i | \(0.910083\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 18524.2i | − | 0.825718i | ||||||
\(56\) | −2917.39 | + | 4257.02i | −0.124315 | + | 0.181399i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3452.07 | + | 1156.76i | −0.134744 | + | 0.0451516i | ||||
\(59\) | −424.395 | −0.0158723 | −0.00793616 | − | 0.999969i | \(-0.502526\pi\) | ||||
−0.00793616 | + | 0.999969i | \(0.502526\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6907.86 | −0.237695 | −0.118847 | − | 0.992913i | \(-0.537920\pi\) | ||||
−0.118847 | + | 0.992913i | \(0.537920\pi\) | |||||||
\(62\) | −3921.05 | + | 1313.91i | −0.129546 | + | 0.0434096i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 11824.8 | + | 30560.0i | 0.360864 | + | 0.932618i | ||||
\(65\) | − | 30778.1i | − | 0.903563i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 58593.9i | − | 1.59465i | −0.603549 | − | 0.797326i | \(-0.706247\pi\) | ||
0.603549 | − | 0.797326i | \(-0.293753\pi\) | |||||||
\(68\) | −29248.5 | − | 38742.1i | −0.767063 | − | 1.01604i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2304.41 | − | 6876.97i | −0.0562101 | − | 0.167746i | ||||
\(71\) | −49133.0 | −1.15672 | −0.578359 | − | 0.815782i | \(-0.696307\pi\) | ||||
−0.578359 | + | 0.815782i | \(0.696307\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 70200.7 | 1.54182 | 0.770911 | − | 0.636943i | \(-0.219801\pi\) | ||||
0.770911 | + | 0.636943i | \(0.219801\pi\) | |||||||
\(74\) | −9816.87 | − | 29296.1i | −0.208398 | − | 0.621915i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 39431.1 | + | 52229.8i | 0.783077 | + | 1.03725i | ||||
\(77\) | − | 11743.2i | − | 0.225714i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 95223.5i | − | 1.71663i | −0.513124 | − | 0.858315i | \(-0.671512\pi\) | ||
0.513124 | − | 0.858315i | \(-0.328488\pi\) | |||||||
\(80\) | −44289.9 | − | 12614.5i | −0.773712 | − | 0.220366i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −34234.6 | + | 11471.7i | −0.562252 | + | 0.188406i | ||||
\(83\) | −55856.8 | −0.889981 | −0.444990 | − | 0.895535i | \(-0.646793\pi\) | ||||
−0.444990 | + | 0.895535i | \(0.646793\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 68221.1 | 1.02417 | ||||||||
\(86\) | 96049.4 | − | 32185.3i | 1.40039 | − | 0.469258i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −61505.5 | − | 42150.6i | −0.846657 | − | 0.580225i | ||||
\(89\) | − | 93780.9i | − | 1.25499i | −0.778622 | − | 0.627493i | \(-0.784081\pi\) | ||
0.778622 | − | 0.627493i | \(-0.215919\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 19511.4i | − | 0.246993i | ||||||
\(92\) | −78422.3 | + | 59205.1i | −0.965984 | + | 0.729273i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 34666.3 | + | 103453.i | 0.404658 | + | 1.20761i | ||||
\(95\) | −91971.6 | −1.04555 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −182666. | −1.97119 | −0.985594 | − | 0.169129i | \(-0.945905\pi\) | ||||
−0.985594 | + | 0.169129i | \(0.945905\pi\) | |||||||
\(98\) | 28747.0 | + | 85788.6i | 0.302362 | + | 0.902328i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −28157.6 | + | 21257.6i | −0.281576 | + | 0.212576i | ||||
\(101\) | 13318.9i | 0.129916i | 0.997888 | + | 0.0649582i | \(0.0206914\pi\) | ||||
−0.997888 | + | 0.0649582i | \(0.979309\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 173353.i | 1.61005i | 0.593242 | + | 0.805024i | \(0.297848\pi\) | ||||
−0.593242 | + | 0.805024i | \(0.702152\pi\) | |||||||
\(104\) | −102192. | − | 70033.7i | −0.926476 | − | 0.634927i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −61148.8 | + | 20490.4i | −0.528595 | + | 0.177128i | ||||
\(107\) | 167439. | 1.41383 | 0.706916 | − | 0.707298i | \(-0.250086\pi\) | ||||
0.706916 | + | 0.707298i | \(0.250086\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 23854.1 | 0.192308 | 0.0961539 | − | 0.995366i | \(-0.469346\pi\) | ||||
0.0961539 | + | 0.995366i | \(0.469346\pi\) | |||||||
\(110\) | 99358.5 | − | 33294.2i | 0.782931 | − | 0.262353i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −28077.1 | − | 7996.80i | −0.211498 | − | 0.0602381i | ||||
\(113\) | 257760.i | 1.89897i | 0.313807 | + | 0.949487i | \(0.398395\pi\) | ||||
−0.313807 | + | 0.949487i | \(0.601605\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 138094.i | − | 0.973711i | ||||||
\(116\) | −12409.1 | − | 16436.9i | −0.0856238 | − | 0.113416i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −762.781 | − | 2276.34i | −0.00504307 | − | 0.0150498i | ||||
\(119\) | 43247.9 | 0.279961 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8614.52 | 0.0534894 | ||||||||
\(122\) | −12415.8 | − | 37051.9i | −0.0755221 | − | 0.225378i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14094.9 | − | 18669.9i | −0.0823204 | − | 0.109040i | ||||
\(125\) | − | 190120.i | − | 1.08831i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 172491.i | 0.948978i | 0.880261 | + | 0.474489i | \(0.157367\pi\) | ||||
−0.880261 | + | 0.474489i | \(0.842633\pi\) | |||||||
\(128\) | −142663. | + | 118352.i | −0.769636 | + | 0.638483i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 165085. | − | 55318.6i | 0.856742 | − | 0.287087i | ||||
\(131\) | 50777.3 | 0.258518 | 0.129259 | − | 0.991611i | \(-0.458740\pi\) | ||||
0.129259 | + | 0.991611i | \(0.458740\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −58304.3 | −0.285806 | ||||||||
\(134\) | 314282. | − | 105313.i | 1.51202 | − | 0.506664i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 155233. | − | 226514.i | 0.719675 | − | 1.05014i | ||||
\(137\) | − | 57768.8i | − | 0.262961i | −0.991319 | − | 0.131481i | \(-0.958027\pi\) | ||
0.991319 | − | 0.131481i | \(-0.0419731\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 84989.7i | 0.373103i | 0.982445 | + | 0.186552i | \(0.0597312\pi\) | ||||
−0.982445 | + | 0.186552i | \(0.940269\pi\) | |||||||
\(140\) | 32744.4 | − | 24720.5i | 0.141194 | − | 0.106595i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −88308.6 | − | 263536.i | −0.367521 | − | 1.09678i | ||||
\(143\) | 281901. | 1.15281 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 28943.7 | 0.114323 | ||||||||
\(146\) | 126174. | + | 376538.i | 0.489879 | + | 1.46193i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 139492. | − | 105310.i | 0.523475 | − | 0.395199i | ||||
\(149\) | 492003.i | 1.81552i | 0.419487 | + | 0.907761i | \(0.362210\pi\) | ||||
−0.419487 | + | 0.907761i | \(0.637790\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 368120.i | 1.31385i | 0.753954 | + | 0.656927i | \(0.228144\pi\) | ||||
−0.753954 | + | 0.656927i | \(0.771856\pi\) | |||||||
\(152\) | −209276. | + | 305372.i | −0.734699 | + | 1.07206i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 62987.2 | − | 21106.4i | 0.214018 | − | 0.0717155i | ||||
\(155\) | 32875.8 | 0.109913 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 82795.9 | 0.268077 | 0.134039 | − | 0.990976i | \(-0.457205\pi\) | ||||
0.134039 | + | 0.990976i | \(0.457205\pi\) | |||||||
\(158\) | 510753. | − | 171149.i | 1.62768 | − | 0.545420i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −11943.2 | − | 260231.i | −0.0368826 | − | 0.803636i | ||||
\(161\) | − | 87543.0i | − | 0.266169i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 191541.i | 0.564668i | 0.959316 | + | 0.282334i | \(0.0911086\pi\) | ||||
−0.959316 | + | 0.282334i | \(0.908891\pi\) | |||||||
\(164\) | −123062. | − | 163007.i | −0.357286 | − | 0.473256i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −100394. | − | 299601.i | −0.282771 | − | 0.843864i | ||||
\(167\) | −318616. | −0.884048 | −0.442024 | − | 0.897003i | \(-0.645739\pi\) | ||||
−0.442024 | + | 0.897003i | \(0.645739\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 97089.3 | 0.261490 | ||||||||
\(170\) | 122616. | + | 365919.i | 0.325406 | + | 0.971098i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 345267. | + | 457335.i | 0.889884 | + | 1.17873i | ||||
\(173\) | − | 87741.7i | − | 0.222890i | −0.993771 | − | 0.111445i | \(-0.964452\pi\) | ||
0.993771 | − | 0.111445i | \(-0.0355479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 31432.4i | − | 0.0775858i | ||||||
\(176\) | 115538. | − | 405658.i | 0.281153 | − | 0.987138i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 503015. | − | 168556.i | 1.18996 | − | 0.398744i | ||||
\(179\) | −197646. | −0.461057 | −0.230528 | − | 0.973066i | \(-0.574045\pi\) | ||||
−0.230528 | + | 0.973066i | \(0.574045\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −638617. | −1.44892 | −0.724459 | − | 0.689318i | \(-0.757910\pi\) | ||||
−0.724459 | + | 0.689318i | \(0.757910\pi\) | |||||||
\(182\) | 104654. | − | 35068.6i | 0.234195 | − | 0.0784766i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −458512. | − | 314224.i | −0.998403 | − | 0.684219i | ||||
\(185\) | 245632.i | 0.527662i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 624847.i | 1.30668i | ||||||||
\(188\) | −492589. | + | 371881.i | −1.01646 | + | 0.767379i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −165304. | − | 493311.i | −0.332200 | − | 0.991371i | ||||
\(191\) | 280543. | 0.556438 | 0.278219 | − | 0.960518i | \(-0.410256\pi\) | ||||
0.278219 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −366016. | −0.707305 | −0.353652 | − | 0.935377i | \(-0.615060\pi\) | ||||
−0.353652 | + | 0.935377i | \(0.615060\pi\) | |||||||
\(194\) | −328312. | − | 979770.i | −0.626300 | − | 1.86905i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −408479. | + | 308382.i | −0.759502 | + | 0.573389i | ||||
\(197\) | − | 876478.i | − | 1.60907i | −0.593904 | − | 0.804536i | \(-0.702414\pi\) | ||
0.593904 | − | 0.804536i | \(-0.297586\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 146658.i | 0.262527i | 0.991348 | + | 0.131263i | \(0.0419034\pi\) | ||||
−0.991348 | + | 0.131263i | \(0.958097\pi\) | |||||||
\(200\) | −164629. | − | 112822.i | −0.291025 | − | 0.199444i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −71438.8 | + | 23938.5i | −0.123184 | + | 0.0412780i | ||||
\(203\) | 18348.5 | 0.0312508 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 287039. | 0.477041 | ||||||||
\(206\) | −929820. | + | 311574.i | −1.52662 | + | 0.511556i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 191968. | − | 674005.i | 0.307659 | − | 1.08020i | ||||
\(209\) | − | 842382.i | − | 1.33396i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 616213.i | 0.952850i | 0.879215 | + | 0.476425i | \(0.158068\pi\) | ||||
−0.879215 | + | 0.476425i | \(0.841932\pi\) | |||||||
\(212\) | −219810. | − | 291157.i | −0.335898 | − | 0.444926i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 300945. | + | 898099.i | 0.449213 | + | 1.34057i | ||||
\(215\) | −805322. | −1.18816 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20841.3 | 0.0300452 | ||||||||
\(218\) | 42873.9 | + | 127947.i | 0.0611014 | + | 0.182343i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 357162. | + | 473091.i | 0.497517 | + | 0.659004i | ||||
\(221\) | 1.03819e6i | 1.42987i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 541567.i | − | 0.729273i | −0.931150 | − | 0.364636i | \(-0.881193\pi\) | ||
0.931150 | − | 0.364636i | \(-0.118807\pi\) | |||||||
\(224\) | −7571.26 | − | 164971.i | −0.0100820 | − | 0.219678i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.38255e6 | + | 463281.i | −1.80057 | + | 0.603356i | ||||
\(227\) | 164616. | 0.212035 | 0.106017 | − | 0.994364i | \(-0.466190\pi\) | ||||
0.106017 | + | 0.994364i | \(0.466190\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −624301. | −0.786693 | −0.393346 | − | 0.919390i | \(-0.628683\pi\) | ||||
−0.393346 | + | 0.919390i | \(0.628683\pi\) | |||||||
\(230\) | 740698. | − | 248201.i | 0.923255 | − | 0.309375i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 65859.7 | − | 96101.6i | 0.0803341 | − | 0.117222i | ||||
\(233\) | 400393.i | 0.483166i | 0.970380 | + | 0.241583i | \(0.0776666\pi\) | ||||
−0.970380 | + | 0.241583i | \(0.922333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 867400.i | − | 1.02459i | ||||||
\(236\) | 10838.7 | − | 8182.70i | 0.0126677 | − | 0.00956350i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 77731.2 | + | 231970.i | 0.0889514 | + | 0.265454i | ||||
\(239\) | −1.04899e6 | −1.18789 | −0.593945 | − | 0.804505i | \(-0.702430\pi\) | ||||
−0.593945 | + | 0.804505i | \(0.702430\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 937726. | 1.04000 | 0.520000 | − | 0.854166i | \(-0.325932\pi\) | ||||
0.520000 | + | 0.854166i | \(0.325932\pi\) | |||||||
\(242\) | 15483.2 | + | 46206.0i | 0.0169951 | + | 0.0507177i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 176421. | − | 133190.i | 0.189704 | − | 0.143217i | ||||
\(245\) | − | 719291.i | − | 0.765578i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.39963e6i | − | 1.45972i | ||||||
\(248\) | 74806.9 | − | 109157.i | 0.0772347 | − | 0.112700i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.01975e6 | − | 341710.i | 1.03192 | − | 0.345786i | ||||
\(251\) | 998062. | 0.999938 | 0.499969 | − | 0.866043i | \(-0.333345\pi\) | ||||
0.499969 | + | 0.866043i | \(0.333345\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.26482e6 | 1.24231 | ||||||||
\(254\) | −925193. | + | 310024.i | −0.899804 | + | 0.301516i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −891219. | − | 552485.i | −0.849933 | − | 0.526891i | ||||
\(257\) | 428916.i | 0.405079i | 0.979274 | + | 0.202539i | \(0.0649194\pi\) | ||||
−0.979274 | + | 0.202539i | \(0.935081\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 155716.i | 0.144239i | ||||||||
\(260\) | 593428. | + | 786047.i | 0.544421 | + | 0.721132i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 91264.0 | + | 272356.i | 0.0821384 | + | 0.245122i | ||||
\(263\) | −769512. | −0.686003 | −0.343001 | − | 0.939335i | \(-0.611444\pi\) | ||||
−0.343001 | + | 0.939335i | \(0.611444\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 512699. | 0.448485 | ||||||||
\(266\) | −104793. | − | 312728.i | −0.0908084 | − | 0.270996i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.12974e6 | + | 1.49644e6i | 0.960820 | + | 1.27269i | ||||
\(269\) | − | 1.64167e6i | − | 1.38326i | −0.722251 | − | 0.691631i | \(-0.756892\pi\) | ||
0.722251 | − | 0.691631i | \(-0.243108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.16025e6i | − | 0.959680i | −0.877356 | − | 0.479840i | \(-0.840695\pi\) | ||
0.877356 | − | 0.479840i | \(-0.159305\pi\) | |||||||
\(272\) | 1.49396e6 | + | 425505.i | 1.22438 | + | 0.348725i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 309856. | − | 103830.i | 0.249335 | − | 0.0835500i | ||||
\(275\) | 454135. | 0.362121 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 422037. | 0.330484 | 0.165242 | − | 0.986253i | \(-0.447159\pi\) | ||||
0.165242 | + | 0.986253i | \(0.447159\pi\) | |||||||
\(278\) | −455862. | + | 152755.i | −0.353770 | + | 0.118545i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 191447. | + | 131201.i | 0.145933 | + | 0.100010i | ||||
\(281\) | 545437.i | 0.412077i | 0.978544 | + | 0.206039i | \(0.0660573\pi\) | ||||
−0.978544 | + | 0.206039i | \(0.933943\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.52288e6i | − | 1.87253i | −0.351289 | − | 0.936267i | \(-0.614256\pi\) | ||
0.351289 | − | 0.936267i | \(-0.385744\pi\) | |||||||
\(284\) | 1.25482e6 | − | 947327.i | 0.923175 | − | 0.696954i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 506672. | + | 1.51204e6i | 0.366279 | + | 1.09307i | ||||
\(287\) | 181965. | 0.130402 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −881340. | −0.620725 | ||||||||
\(290\) | 52021.7 | + | 155246.i | 0.0363236 | + | 0.108399i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.79287e6 | + | 1.35353e6i | −1.23053 | + | 0.928990i | ||||
\(293\) | 1.91422e6i | 1.30263i | 0.758806 | + | 0.651317i | \(0.225783\pi\) | ||||
−0.758806 | + | 0.651317i | \(0.774217\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19085.9i | 0.0127690i | ||||||||
\(296\) | 815569. | + | 558921.i | 0.541043 | + | 0.370784i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.63897e6 | + | 884295.i | −1.72145 | + | 0.576841i | ||||
\(299\) | 2.10152e6 | 1.35942 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −510525. | −0.324788 | ||||||||
\(302\) | −1.97449e6 | + | 661636.i | −1.24577 | + | 0.417447i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.01407e6 | − | 573641.i | −1.24995 | − | 0.356005i | ||||
\(305\) | 310660.i | 0.191221i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 759821.i | 0.460114i | 0.973177 | + | 0.230057i | \(0.0738913\pi\) | ||||
−0.973177 | + | 0.230057i | \(0.926109\pi\) | |||||||
\(308\) | 226418. | + | 299911.i | 0.135999 | + | 0.180142i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 59089.0 | + | 176337.i | 0.0349223 | + | 0.104217i | ||||
\(311\) | 1.14702e6 | 0.672464 | 0.336232 | − | 0.941779i | \(-0.390847\pi\) | ||||
0.336232 | + | 0.941779i | \(0.390847\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 358045. | 0.206575 | 0.103287 | − | 0.994652i | \(-0.467064\pi\) | ||||
0.103287 | + | 0.994652i | \(0.467064\pi\) | |||||||
\(314\) | 148812. | + | 444095.i | 0.0851754 | + | 0.254186i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.83599e6 | + | 2.43193e6i | 1.03432 | + | 1.37004i | ||||
\(317\) | 2.80135e6i | 1.56574i | 0.622186 | + | 0.782870i | \(0.286245\pi\) | ||||
−0.622186 | + | 0.782870i | \(0.713755\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 265100.i | 0.145859i | ||||||||
\(320\) | 1.37434e6 | − | 531784.i | 0.750275 | − | 0.290309i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 469557. | − | 157344.i | 0.252376 | − | 0.0845691i | ||||
\(323\) | 3.10234e6 | 1.65456 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 754551. | 0.396260 | ||||||||
\(326\) | −1.02737e6 | + | 344264.i | −0.535408 | + | 0.179410i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 653139. | − | 953051.i | 0.335213 | − | 0.489138i | ||||
\(329\) | − | 549878.i | − | 0.280077i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 465048.i | − | 0.233307i | −0.993173 | − | 0.116654i | \(-0.962783\pi\) | ||
0.993173 | − | 0.116654i | \(-0.0372167\pi\) | |||||||
\(332\) | 1.42653e6 | − | 1.07697e6i | 0.710292 | − | 0.536237i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −572660. | − | 1.70897e6i | −0.280886 | − | 0.838239i | ||||
\(335\) | −2.63508e6 | −1.28287 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.16600e6 | −0.559274 | −0.279637 | − | 0.960106i | \(-0.590214\pi\) | ||||
−0.279637 | + | 0.960106i | \(0.590214\pi\) | |||||||
\(338\) | 174502. | + | 520761.i | 0.0830825 | + | 0.247940i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.74231e6 | + | 1.31536e6i | −0.817387 | + | 0.617089i | ||||
\(341\) | 301115.i | 0.140232i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 935144.i | − | 0.429184i | ||||||
\(344\) | −1.83246e6 | + | 2.67390e6i | −0.834908 | + | 1.21829i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 470623. | − | 157702.i | 0.211341 | − | 0.0708183i | ||||
\(347\) | −1.11960e6 | −0.499160 | −0.249580 | − | 0.968354i | \(-0.580293\pi\) | ||||
−0.249580 | + | 0.968354i | \(0.580293\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −514671. | −0.226186 | −0.113093 | − | 0.993584i | \(-0.536076\pi\) | ||||
−0.113093 | + | 0.993584i | \(0.536076\pi\) | |||||||
\(350\) | 168595. | − | 56494.6i | 0.0735654 | − | 0.0246511i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.38350e6 | − | 109390.i | 1.02532 | − | 0.0470565i | ||||
\(353\) | − | 2.78955e6i | − | 1.19151i | −0.803167 | − | 0.595754i | \(-0.796853\pi\) | ||
0.803167 | − | 0.595754i | \(-0.203147\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.20961e6i | 0.930559i | ||||||||
\(356\) | 1.80818e6 | + | 2.39508e6i | 0.756163 | + | 1.00160i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −355236. | − | 1.06012e6i | −0.146490 | − | 0.437166i | ||||
\(359\) | −1.28814e6 | −0.527504 | −0.263752 | − | 0.964590i | \(-0.584960\pi\) | ||||
−0.263752 | + | 0.964590i | \(0.584960\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.70629e6 | −0.689103 | ||||||||
\(362\) | −1.14781e6 | − | 3.42537e6i | −0.460361 | − | 1.37384i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 376197. | + | 498305.i | 0.148820 | + | 0.197125i | ||||
\(365\) | − | 3.15706e6i | − | 1.24037i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.88011e6i | − | 0.728648i | −0.931272 | − | 0.364324i | \(-0.881300\pi\) | ||
0.931272 | − | 0.364324i | \(-0.118700\pi\) | |||||||
\(368\) | 861313. | − | 3.02410e6i | 0.331544 | − | 1.16406i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.31750e6 | + | 441484.i | −0.500320 | + | 0.167653i | ||||
\(371\) | 325020. | 0.122596 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.22175e6 | 1.57116 | 0.785580 | − | 0.618761i | \(-0.212365\pi\) | ||||
0.785580 | + | 0.618761i | \(0.212365\pi\) | |||||||
\(374\) | −3.35151e6 | + | 1.12306e6i | −1.23897 | + | 0.415169i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.88002e6 | − | 1.97372e6i | −1.05057 | − | 0.719971i | ||||
\(377\) | 440467.i | 0.159610i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 770147.i | 0.275407i | 0.990473 | + | 0.137704i | \(0.0439722\pi\) | ||||
−0.990473 | + | 0.137704i | \(0.956028\pi\) | |||||||
\(380\) | 2.34888e6 | − | 1.77329e6i | 0.834452 | − | 0.629972i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 504231. | + | 1.50476e6i | 0.176796 | + | 0.527604i | ||||
\(383\) | −2.69430e6 | −0.938532 | −0.469266 | − | 0.883057i | \(-0.655482\pi\) | ||||
−0.469266 | + | 0.883057i | \(0.655482\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −528113. | −0.181583 | ||||||||
\(386\) | −657854. | − | 1.96321e6i | −0.224730 | − | 0.670654i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.66513e6 | − | 3.52195e6i | 1.57320 | − | 1.18769i | ||||
\(389\) | 220210.i | 0.0737843i | 0.999319 | + | 0.0368922i | \(0.0117458\pi\) | ||||
−0.999319 | + | 0.0368922i | \(0.988254\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.65811e6i | 1.54088i | ||||||||
\(392\) | −2.38825e6 | − | 1.63670e6i | −0.784992 | − | 0.537965i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.70119e6 | − | 1.57533e6i | 1.52569 | − | 0.511246i | ||||
\(395\) | −4.28239e6 | −1.38100 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.28702e6 | −0.728271 | −0.364135 | − | 0.931346i | \(-0.618635\pi\) | ||||
−0.364135 | + | 0.931346i | \(0.618635\pi\) | |||||||
\(398\) | −786635. | + | 263594.i | −0.248923 | + | 0.0834120i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 309255. | − | 1.08580e6i | 0.0966421 | − | 0.339314i | ||||
\(401\) | − | 640352.i | − | 0.198865i | −0.995044 | − | 0.0994324i | \(-0.968297\pi\) | ||
0.995044 | − | 0.0994324i | \(-0.0317027\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 500306.i | 0.153452i | ||||||||
\(404\) | −256799. | − | 340153.i | −0.0782781 | − | 0.103686i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 32978.5 | + | 98416.6i | 0.00992925 | + | 0.0296315i | ||||
\(407\) | −2.24978e6 | −0.673216 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.58655e6 | 0.764562 | 0.382281 | − | 0.924046i | \(-0.375139\pi\) | ||||
0.382281 | + | 0.924046i | \(0.375139\pi\) | |||||||
\(410\) | 515906. | + | 1.53960e6i | 0.151569 | + | 0.452322i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.34240e6 | − | 4.42730e6i | −0.970097 | − | 1.28498i | ||||
\(413\) | 12099.3i | 0.00349047i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.51199e6i | 0.715974i | ||||||||
\(416\) | 3.96021e6 | − | 181752.i | 1.12198 | − | 0.0514928i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.51831e6 | − | 1.51404e6i | 1.26484 | − | 0.423836i | ||||
\(419\) | 5.31201e6 | 1.47817 | 0.739084 | − | 0.673614i | \(-0.235259\pi\) | ||||
0.739084 | + | 0.673614i | \(0.235259\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.16990e6 | −1.42160 | −0.710799 | − | 0.703395i | \(-0.751666\pi\) | ||||
−0.710799 | + | 0.703395i | \(0.751666\pi\) | |||||||
\(422\) | −3.30520e6 | + | 1.10754e6i | −0.903476 | + | 0.302747i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.16662e6 | − | 1.70231e6i | 0.315147 | − | 0.459858i | ||||
\(425\) | 1.67250e6i | 0.449152i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 196939.i | 0.0522712i | ||||||||
\(428\) | −4.27626e6 | + | 3.22837e6i | −1.12838 | + | 0.851872i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.44744e6 | − | 4.31953e6i | −0.377510 | − | 1.12659i | ||||
\(431\) | −2.70546e6 | −0.701534 | −0.350767 | − | 0.936463i | \(-0.614079\pi\) | ||||
−0.350767 | + | 0.936463i | \(0.614079\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.62153e6 | 1.69722 | 0.848611 | − | 0.529018i | \(-0.177439\pi\) | ||||
0.848611 | + | 0.529018i | \(0.177439\pi\) | |||||||
\(434\) | 37458.8 | + | 111787.i | 0.00954617 | + | 0.0284883i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −609213. | + | 459927.i | −0.153481 | + | 0.115871i | ||||
\(437\) | − | 6.27979e6i | − | 1.57305i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.18212e6i | 1.03570i | 0.855470 | + | 0.517852i | \(0.173268\pi\) | ||||
−0.855470 | + | 0.517852i | \(0.826732\pi\) | |||||||
\(440\) | −1.89559e6 | + | 2.76602e6i | −0.466781 | + | 0.681121i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.56857e6 | + | 1.86598e6i | −1.35578 | + | 0.454309i | ||||
\(443\) | 5.45464e6 | 1.32056 | 0.660278 | − | 0.751021i | \(-0.270438\pi\) | ||||
0.660278 | + | 0.751021i | \(0.270438\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.21751e6 | −1.00961 | ||||||||
\(446\) | 2.90482e6 | − | 973379.i | 0.691484 | − | 0.231710i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 871249. | − | 337118.i | 0.205091 | − | 0.0793573i | ||||
\(449\) | 6.49269e6i | 1.51988i | 0.649994 | + | 0.759939i | \(0.274771\pi\) | ||||
−0.649994 | + | 0.759939i | \(0.725229\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.62903e6i | 0.608631i | ||||||||
\(452\) | −4.96983e6 | − | 6.58296e6i | −1.14418 | − | 1.51557i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 295870. | + | 882955.i | 0.0673693 | + | 0.201048i | ||||
\(455\) | −877466. | −0.198702 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.42147e6 | −1.21430 | −0.607151 | − | 0.794586i | \(-0.707688\pi\) | ||||
−0.607151 | + | 0.794586i | \(0.707688\pi\) | |||||||
\(458\) | −1.12208e6 | − | 3.34858e6i | −0.249954 | − | 0.745928i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.66257e6 | + | 3.52680e6i | 0.586687 | + | 0.777117i | ||||
\(461\) | 585086.i | 0.128223i | 0.997943 | + | 0.0641117i | \(0.0204214\pi\) | ||||
−0.997943 | + | 0.0641117i | \(0.979579\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.73814e6i | 0.593613i | 0.954938 | + | 0.296806i | \(0.0959216\pi\) | ||||
−0.954938 | + | 0.296806i | \(0.904078\pi\) | |||||||
\(464\) | 633835. | + | 180527.i | 0.136673 | + | 0.0389266i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.14760e6 | + | 719641.i | −0.458129 | + | 0.153515i | ||||
\(467\) | 3.07143e6 | 0.651701 | 0.325850 | − | 0.945421i | \(-0.394349\pi\) | ||||
0.325850 | + | 0.945421i | \(0.394349\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.67048e6 | −0.350679 | ||||||||
\(470\) | 4.65250e6 | − | 1.55901e6i | 0.971498 | − | 0.325540i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 63370.6 | + | 43428.7i | 0.0130928 | + | 0.00897267i | ||||
\(473\) | − | 7.37607e6i | − | 1.51591i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.25476e6i | − | 0.458529i | ||||||
\(476\) | −1.10452e6 | + | 833858.i | −0.223437 | + | 0.168684i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.88539e6 | − | 5.62649e6i | −0.377425 | − | 1.12634i | ||||
\(479\) | −6.67442e6 | −1.32915 | −0.664576 | − | 0.747221i | \(-0.731388\pi\) | ||||
−0.664576 | + | 0.747221i | \(0.731388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.73804e6 | −0.736684 | ||||||||
\(482\) | 1.68541e6 | + | 5.02971e6i | 0.330437 | + | 0.986110i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −220008. | + | 166095.i | −0.0426898 | + | 0.0322288i | ||||
\(485\) | 8.21484e6i | 1.58579i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.75720e6i | 1.86425i | 0.362143 | + | 0.932123i | \(0.382045\pi\) | ||||
−0.362143 | + | 0.932123i | \(0.617955\pi\) | |||||||
\(488\) | 1.03148e6 | + | 706888.i | 0.196070 | + | 0.134370i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.85808e6 | − | 1.29281e6i | 0.725907 | − | 0.243245i | ||||
\(491\) | 9.36580e6 | 1.75324 | 0.876619 | − | 0.481185i | \(-0.159793\pi\) | ||||
0.876619 | + | 0.481185i | \(0.159793\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −976315. | −0.180914 | ||||||||
\(494\) | 7.50722e6 | − | 2.51560e6i | 1.38408 | − | 0.463793i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 719943. | + | 205052.i | 0.131400 | + | 0.0374248i | ||||
\(497\) | 1.40075e6i | 0.254373i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3930.38i | − | 0.000706615i | −1.00000 | 0.000353307i | \(-0.999888\pi\) | |||
1.00000 | 0.000353307i | \(-0.000112461\pi\) | ||||||||
\(500\) | 3.66568e6 | + | 4.85550e6i | 0.655736 | + | 0.868579i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.79385e6 | + | 5.35333e6i | 0.317708 | + | 0.948123i | ||||
\(503\) | −8.81634e6 | −1.55371 | −0.776853 | − | 0.629683i | \(-0.783185\pi\) | ||||
−0.776853 | + | 0.629683i | \(0.783185\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 598975. | 0.104515 | ||||||||
\(506\) | 2.27331e6 | + | 6.78417e6i | 0.394715 | + | 1.17793i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.32577e6 | − | 4.40527e6i | −0.571785 | − | 0.757378i | ||||
\(509\) | − | 1.95674e6i | − | 0.334764i | −0.985892 | − | 0.167382i | \(-0.946469\pi\) | ||
0.985892 | − | 0.167382i | \(-0.0535313\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 2.00138e6i | − | 0.339061i | ||||||
\(512\) | 1.36156e6 | − | 5.77326e6i | 0.229542 | − | 0.973299i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.30059e6 | + | 770907.i | −0.384089 | + | 0.128705i | ||||
\(515\) | 7.79603e6 | 1.29526 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.94465e6 | 1.30722 | ||||||||
\(518\) | −835216. | + | 279873.i | −0.136765 | + | 0.0458287i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.14955e6 | + | 4.59578e6i | −0.510787 | + | 0.745334i | ||||
\(521\) | 3.57120e6i | 0.576394i | 0.957571 | + | 0.288197i | \(0.0930558\pi\) | ||||
−0.957571 | + | 0.288197i | \(0.906944\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 7.38907e6i | − | 1.18123i | −0.806953 | − | 0.590616i | \(-0.798885\pi\) | ||
0.806953 | − | 0.590616i | \(-0.201115\pi\) | |||||||
\(524\) | −1.29681e6 | + | 979030.i | −0.206323 | + | 0.155764i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.38307e6 | − | 4.12745e6i | −0.217962 | − | 0.650456i | ||||
\(527\) | −1.10895e6 | −0.173934 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.99266e6 | 0.464963 | ||||||||
\(530\) | 921494. | + | 2.74998e6i | 0.142496 | + | 0.425246i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.48904e6 | − | 1.12416e6i | 0.228101 | − | 0.172206i | ||||
\(533\) | 4.36817e6i | 0.666011i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 7.53007e6i | − | 1.13740i | ||||||
\(536\) | −5.99597e6 | + | 8.74923e6i | −0.901462 | + | 1.31540i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.80546e6 | − | 2.95063e6i | 1.31158 | − | 0.439500i | ||||
\(539\) | 6.58809e6 | 0.976760 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.71204e6 | 0.398385 | 0.199192 | − | 0.979960i | \(-0.436168\pi\) | ||||
0.199192 | + | 0.979960i | \(0.436168\pi\) | |||||||
\(542\) | 6.22324e6 | − | 2.08535e6i | 0.909952 | − | 0.304917i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 402862. | + | 8.77799e6i | 0.0583659 | + | 1.27174i | ||||
\(545\) | − | 1.07276e6i | − | 0.154708i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 6.90947e6i | − | 0.987362i | −0.869643 | − | 0.493681i | \(-0.835651\pi\) | ||
0.869643 | − | 0.493681i | \(-0.164349\pi\) | |||||||
\(548\) | 1.11383e6 | + | 1.47537e6i | 0.158441 | + | 0.209869i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 816235. | + | 2.43586e6i | 0.115056 | + | 0.343357i | ||||
\(551\) | 1.31621e6 | 0.184691 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.71477e6 | −0.377503 | ||||||||
\(554\) | 758542. | + | 2.26369e6i | 0.105004 | + | 0.313359i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.63867e6 | − | 2.17057e6i | −0.224805 | − | 0.297773i | ||||
\(557\) | − | 2.31133e6i | − | 0.315664i | −0.987466 | − | 0.157832i | \(-0.949550\pi\) | ||
0.987466 | − | 0.157832i | \(-0.0504504\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.22554e7i | − | 1.65882i | ||||||
\(560\) | −359632. | + | 1.26268e6i | −0.0484605 | + | 0.170146i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.92558e6 | + | 980335.i | −0.390724 | + | 0.130928i | ||||
\(563\) | 579007. | 0.0769862 | 0.0384931 | − | 0.999259i | \(-0.487744\pi\) | ||||
0.0384931 | + | 0.999259i | \(0.487744\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.15920e7 | 1.52769 | ||||||||
\(566\) | 1.35320e7 | − | 4.53446e6i | 1.77550 | − | 0.594955i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.33653e6 | + | 5.02782e6i | 0.954157 | + | 0.653897i | ||||
\(569\) | 4.15072e6i | 0.537456i | 0.963216 | + | 0.268728i | \(0.0866033\pi\) | ||||
−0.963216 | + | 0.268728i | \(0.913397\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.30846e6i | 0.553009i | 0.961013 | + | 0.276504i | \(0.0891760\pi\) | ||||
−0.961013 | + | 0.276504i | \(0.910824\pi\) | |||||||
\(572\) | −7.19952e6 | + | 5.43530e6i | −0.920054 | + | 0.694598i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 327052. | + | 976010.i | 0.0414322 | + | 0.123644i | ||||
\(575\) | 3.38549e6 | 0.427024 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.61480e6 | 0.201921 | 0.100960 | − | 0.994890i | \(-0.467809\pi\) | ||||
0.100960 | + | 0.994890i | \(0.467809\pi\) | |||||||
\(578\) | −1.58407e6 | − | 4.72727e6i | −0.197221 | − | 0.588560i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −739199. | + | 558060.i | −0.0912413 | + | 0.0688829i | ||||
\(581\) | 1.59245e6i | 0.195715i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.69589e6i | 0.572198i | ||||||||
\(584\) | −1.04824e7 | − | 7.18370e6i | −1.27182 | − | 0.871598i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.02673e7 | + | 3.44050e6i | −1.23513 | + | 0.413882i | ||||
\(587\) | −9.37987e6 | −1.12357 | −0.561787 | − | 0.827282i | \(-0.689886\pi\) | ||||
−0.561787 | + | 0.827282i | \(0.689886\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.49502e6 | 0.177566 | ||||||||
\(590\) | −102371. | + | 34303.7i | −0.0121073 | + | 0.00405706i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.53204e6 | + | 5.37906e6i | −0.179667 | + | 0.630815i | ||||
\(593\) | − | 4.50800e6i | − | 0.526438i | −0.964736 | − | 0.263219i | \(-0.915216\pi\) | ||
0.964736 | − | 0.263219i | \(-0.0847842\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1.94494e6i | − | 0.225224i | ||||||
\(596\) | −9.48623e6 | − | 1.25653e7i | −1.09390 | − | 1.44897i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.77714e6 | + | 1.12720e7i | 0.431927 | + | 1.28898i | ||||
\(599\) | −1.18281e7 | −1.34694 | −0.673469 | − | 0.739215i | \(-0.735197\pi\) | ||||
−0.673469 | + | 0.739215i | \(0.735197\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 501339. | 0.0566168 | 0.0283084 | − | 0.999599i | \(-0.490988\pi\) | ||||
0.0283084 | + | 0.999599i | \(0.490988\pi\) | |||||||
\(602\) | −917585. | − | 2.73832e6i | −0.103194 | − | 0.307958i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.09767e6 | − | 9.40147e6i | −0.791632 | − | 1.04858i | ||||
\(605\) | − | 387412.i | − | 0.0430313i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.52223e7i | − | 1.67691i | −0.544972 | − | 0.838454i | \(-0.683460\pi\) | ||
0.544972 | − | 0.838454i | \(-0.316540\pi\) | |||||||
\(608\) | −543115. | − | 1.18340e7i | −0.0595844 | − | 1.29829i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.66630e6 | + | 558361.i | −0.181312 | + | 0.0607562i | ||||
\(611\) | 1.32001e7 | 1.43046 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.50361e7 | −1.61616 | −0.808080 | − | 0.589073i | \(-0.799493\pi\) | ||||
−0.808080 | + | 0.589073i | \(0.799493\pi\) | |||||||
\(614\) | −4.07547e6 | + | 1.36566e6i | −0.436272 | + | 0.146191i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.20169e6 | + | 1.75349e6i | −0.127597 | + | 0.186188i | ||||
\(617\) | − | 1.04780e7i | − | 1.10807i | −0.832495 | − | 0.554033i | \(-0.813088\pi\) | ||
0.832495 | − | 0.554033i | \(-0.186912\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.04678e6i | 0.529404i | 0.964330 | + | 0.264702i | \(0.0852737\pi\) | ||||
−0.964330 | + | 0.264702i | \(0.914726\pi\) | |||||||
\(620\) | −839621. | + | 633875.i | −0.0877211 | + | 0.0662253i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.06158e6 | + | 6.15229e6i | 0.213660 | + | 0.637618i | ||||
\(623\) | −2.67364e6 | −0.275983 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.10467e6 | −0.522718 | ||||||||
\(626\) | 643528. | + | 1.92046e6i | 0.0656344 | + | 0.195870i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.11454e6 | + | 1.59638e6i | −0.213952 | + | 0.161524i | ||||
\(629\) | − | 8.28553e6i | − | 0.835014i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.24449e7i | − | 1.24428i | −0.782907 | − | 0.622139i | \(-0.786264\pi\) | ||
0.782907 | − | 0.622139i | \(-0.213736\pi\) | |||||||
\(632\) | −9.74431e6 | + | 1.42188e7i | −0.970417 | + | 1.41602i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.50257e7 | + | 5.03497e6i | −1.48461 | + | 0.497478i | ||||
\(635\) | 7.75724e6 | 0.763436 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.09462e7 | 1.06884 | ||||||||
\(638\) | −1.42193e6 | + | 476474.i | −0.138301 | + | 0.0463434i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.32250e6 | + | 6.41581e6i | 0.513649 | + | 0.619158i | ||||
\(641\) | 2.36665e6i | 0.227504i | 0.993509 | + | 0.113752i | \(0.0362870\pi\) | ||||
−0.993509 | + | 0.113752i | \(0.963713\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 4.58591e6i | − | 0.437419i | −0.975790 | − | 0.218710i | \(-0.929815\pi\) | ||
0.975790 | − | 0.218710i | \(-0.0701847\pi\) | |||||||
\(644\) | 1.68790e6 | + | 2.23577e6i | 0.160374 | + | 0.212429i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.57595e6 | + | 1.66401e7i | 0.525699 | + | 1.56882i | ||||
\(647\) | −1.96170e7 | −1.84235 | −0.921175 | − | 0.389149i | \(-0.872769\pi\) | ||||
−0.921175 | + | 0.389149i | \(0.872769\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −174810. | −0.0162913 | ||||||||
\(650\) | 1.35618e6 | + | 4.04721e6i | 0.125903 | + | 0.375727i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.69308e6 | − | 4.89180e6i | −0.340227 | − | 0.450660i | ||||
\(653\) | 1.11892e6i | 0.102687i | 0.998681 | + | 0.0513435i | \(0.0163503\pi\) | ||||
−0.998681 | + | 0.0513435i | \(0.983650\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2.28355e6i | − | 0.207973i | ||||||
\(656\) | 6.28582e6 | + | 1.79030e6i | 0.570299 | + | 0.162430i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.94940e6 | − | 988317.i | 0.265564 | − | 0.0889880i | ||||
\(659\) | −1.42425e7 | −1.27753 | −0.638766 | − | 0.769401i | \(-0.720555\pi\) | ||||
−0.638766 | + | 0.769401i | \(0.720555\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.50585e6 | −0.134053 | −0.0670267 | − | 0.997751i | \(-0.521351\pi\) | ||||
−0.0670267 | + | 0.997751i | \(0.521351\pi\) | |||||||
\(662\) | 2.49439e6 | − | 835849.i | 0.221218 | − | 0.0741281i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.34052e6 | + | 5.71587e6i | 0.734130 | + | 0.503109i | ||||
\(665\) | 2.62206e6i | 0.229926i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.97627e6i | 0.172001i | ||||||||
\(668\) | 8.13717e6 | − | 6.14318e6i | 0.705558 | − | 0.532663i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.73613e6 | − | 1.41339e7i | −0.407603 | − | 1.21639i | ||||
\(671\) | −2.84538e6 | −0.243969 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.34440e7 | 1.14417 | 0.572084 | − | 0.820195i | \(-0.306135\pi\) | ||||
0.572084 | + | 0.820195i | \(0.306135\pi\) | |||||||
\(674\) | −2.09570e6 | − | 6.25412e6i | −0.177697 | − | 0.530294i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.47958e6 | + | 1.87197e6i | −0.208695 | + | 0.157555i | ||||
\(677\) | − | 1.49438e7i | − | 1.25311i | −0.779378 | − | 0.626554i | \(-0.784465\pi\) | ||
0.779378 | − | 0.626554i | \(-0.215535\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.20770e6i | 0.433482i | ||||||||
\(680\) | −1.01868e7 | − | 6.98112e6i | −0.844819 | − | 0.578966i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.61510e6 | + | 541205.i | −0.132965 | + | 0.0445555i | ||||
\(683\) | −3.84256e6 | −0.315187 | −0.157594 | − | 0.987504i | \(-0.550374\pi\) | ||||
−0.157594 | + | 0.987504i | \(0.550374\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.59797e6 | −0.211548 | ||||||||
\(686\) | 5.01586e6 | − | 1.68077e6i | 0.406944 | − | 0.136363i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.76356e7 | − | 5.02292e6i | −1.42043 | − | 0.404562i | ||||
\(689\) | 7.80228e6i | 0.626143i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.36756e7i | 1.08956i | 0.838578 | + | 0.544781i | \(0.183387\pi\) | ||||
−0.838578 | + | 0.544781i | \(0.816613\pi\) | |||||||
\(692\) | 1.69174e6 | + | 2.24085e6i | 0.134297 | + | 0.177888i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.01230e6 | − | 6.00523e6i | −0.158597 | − | 0.473294i | ||||
\(695\) | 3.82215e6 | 0.300155 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.68224e6 | −0.754908 | ||||||||
\(698\) | −925038. | − | 2.76056e6i | −0.0718656 | − | 0.214466i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 606043. | + | 802756.i | 0.0467475 | + | 0.0619211i | ||||
\(701\) | 1.32451e7i | 1.01803i | 0.860758 | + | 0.509015i | \(0.169990\pi\) | ||||
−0.860758 | + | 0.509015i | \(0.830010\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.11701e7i | 0.852447i | ||||||||
\(704\) | 4.87069e6 | + | 1.25878e7i | 0.370390 | + | 0.957236i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.49624e7 | − | 5.01376e6i | 1.12977 | − | 0.378575i | ||||
\(707\) | 379713. | 0.0285698 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.82356e7 | −1.36240 | −0.681200 | − | 0.732098i | \(-0.738541\pi\) | ||||
−0.681200 | + | 0.732098i | \(0.738541\pi\) | |||||||
\(710\) | −1.18517e7 | + | 3.97141e6i | −0.882340 | + | 0.295664i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.59668e6 | + | 1.40033e7i | −0.709448 | + | 1.03522i | ||||
\(713\) | 2.24475e6i | 0.165365i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1.26776e7i | − | 0.927414i | ||||||
\(716\) | 5.04770e6 | − | 3.81078e6i | 0.367969 | − | 0.277799i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.31522e6 | − | 6.90922e6i | −0.167603 | − | 0.500170i | ||||
\(719\) | 555013. | 0.0400388 | 0.0200194 | − | 0.999800i | \(-0.493627\pi\) | ||||
0.0200194 | + | 0.999800i | \(0.493627\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.94220e6 | 0.354064 | ||||||||
\(722\) | −3.06678e6 | − | 9.15206e6i | −0.218947 | − | 0.653395i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.63097e7 | − | 1.23131e7i | 1.15638 | − | 0.873012i | ||||
\(725\) | 709581.i | 0.0501368i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.12242e7i | − | 0.787625i | −0.919191 | − | 0.393813i | \(-0.871156\pi\) | ||
0.919191 | − | 0.393813i | \(-0.128844\pi\) | |||||||
\(728\) | −1.99662e6 | + | 2.91344e6i | −0.139626 | + | 0.203741i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.69336e7 | − | 5.67431e6i | 1.17610 | − | 0.394099i | ||||
\(731\) | 2.71647e7 | 1.88023 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.30346e6 | 0.502075 | 0.251038 | − | 0.967977i | \(-0.419228\pi\) | ||||
0.251038 | + | 0.967977i | \(0.419228\pi\) | |||||||
\(734\) | 1.00844e7 | − | 3.37919e6i | 0.690891 | − | 0.231511i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.77685e7 | − | 815479.i | 1.20908 | − | 0.0554904i | ||||
\(737\) | − | 2.41351e7i | − | 1.63674i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.03409e7i | 0.696543i | 0.937394 | + | 0.348271i | \(0.113231\pi\) | ||||
−0.937394 | + | 0.348271i | \(0.886769\pi\) | |||||||
\(740\) | −4.73600e6 | − | 6.27324e6i | −0.317930 | − | 0.421126i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 584170. | + | 1.74332e6i | 0.0389520 | + | 0.116243i | ||||
\(743\) | −1.25176e7 | −0.831858 | −0.415929 | − | 0.909397i | \(-0.636543\pi\) | ||||
−0.415929 | + | 0.909397i | \(0.636543\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.21263e7 | 1.46056 | ||||||||
\(746\) | 7.58791e6 | + | 2.26443e7i | 0.499200 | + | 1.48975i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.20476e7 | − | 1.59581e7i | −0.787311 | − | 1.04286i | ||||
\(749\) | − | 4.77360e6i | − | 0.310915i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.04022e7i | 0.673015i | 0.941681 | + | 0.336508i | \(0.109246\pi\) | ||||
−0.941681 | + | 0.336508i | \(0.890754\pi\) | |||||||
\(752\) | 5.41011e6 | − | 1.89951e7i | 0.348868 | − | 1.22489i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.36255e6 | + | 791668.i | −0.151339 | + | 0.0507125i | ||||
\(755\) | 1.65551e7 | 1.05697 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.77986e7 | 1.12888 | 0.564438 | − | 0.825475i | \(-0.309093\pi\) | ||||
0.564438 | + | 0.825475i | \(0.309093\pi\) | |||||||
\(758\) | −4.13086e6 | + | 1.38421e6i | −0.261136 | + | 0.0875045i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.37332e7 | + | 9.41153e6i | 0.862456 | + | 0.591053i | ||||
\(761\) | 2.42339e7i | 1.51691i | 0.651723 | + | 0.758457i | \(0.274047\pi\) | ||||
−0.651723 | + | 0.758457i | \(0.725953\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 680067.i | − | 0.0422902i | ||||||
\(764\) | −7.16484e6 | + | 5.40912e6i | −0.444092 | + | 0.335269i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.84257e6 | − | 1.44515e7i | −0.298197 | − | 0.889900i | ||||
\(767\) | −290449. | −0.0178272 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.26552e7 | −0.771708 | −0.385854 | − | 0.922560i | \(-0.626093\pi\) | ||||
−0.385854 | + | 0.922560i | \(0.626093\pi\) | |||||||
\(770\) | −949198. | − | 2.83265e6i | −0.0576939 | − | 0.172174i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.34774e6 | − | 7.05710e6i | 0.564499 | − | 0.426170i | ||||
\(773\) | 9.16670e6i | 0.551778i | 0.961190 | + | 0.275889i | \(0.0889722\pi\) | ||||
−0.961190 | + | 0.275889i | \(0.911028\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 805979.i | 0.0482025i | ||||||||
\(776\) | 2.72756e7 | + | 1.86924e7i | 1.62600 | + | 1.11432i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.18115e6 | + | 395793.i | −0.0699610 | + | 0.0234433i | ||||
\(779\) | 1.30530e7 | 0.770668 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.02381e7 | −1.18725 | ||||||||
\(782\) | −2.49848e7 | + | 8.37220e6i | −1.46103 | + | 0.489579i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.48633e6 | − | 1.57516e7i | 0.260676 | − | 0.915241i | ||||
\(785\) | − | 3.72349e6i | − | 0.215663i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.49494e6i | 0.488904i | 0.969661 | + | 0.244452i | \(0.0786080\pi\) | ||||
−0.969661 | + | 0.244452i | \(0.921392\pi\) | |||||||
\(788\) | 1.68992e7 | + | 2.23845e7i | 0.969509 | + | 1.28420i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.69689e6 | − | 2.29696e7i | −0.438781 | − | 1.30944i | ||||
\(791\) | 7.34858e6 | 0.417602 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.72764e6 | −0.266969 | ||||||||
\(794\) | −4.11054e6 | − | 1.22669e7i | −0.231392 | − | 0.690533i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.82770e6 | − | 3.74553e6i | −0.158179 | − | 0.209522i | ||||
\(797\) | 3.28175e7i | 1.83004i | 0.403410 | + | 0.915019i | \(0.367825\pi\) | ||||
−0.403410 | + | 0.915019i | \(0.632175\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.92587e7i | 1.62139i | ||||||||
\(800\) | 6.37979e6 | − | 292798.i | 0.352437 | − | 0.0161750i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.43467e6 | − | 1.15093e6i | 0.188560 | − | 0.0631848i | ||||
\(803\) | 2.89160e7 | 1.58252 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.93698e6 | −0.214128 | ||||||||
\(806\) | −2.68350e6 | + | 899219.i | −0.145501 | + | 0.0487560i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.36293e6 | − | 1.98877e6i | 0.0734421 | − | 0.107166i | ||||
\(809\) | − | 1.20827e7i | − | 0.649073i | −0.945873 | − | 0.324536i | \(-0.894792\pi\) | ||
0.945873 | − | 0.324536i | \(-0.105208\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.34126e7i | 0.716080i | 0.933706 | + | 0.358040i | \(0.116555\pi\) | ||||
−0.933706 | + | 0.358040i | \(0.883445\pi\) | |||||||
\(812\) | −468606. | + | 353776.i | −0.0249412 | + | 0.0188295i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.04362e6 | − | 1.20672e7i | −0.213899 | − | 0.638331i | ||||
\(815\) | 8.61397e6 | 0.454265 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.66218e7 | −1.91949 | ||||||||
\(818\) | 4.64890e6 | + | 1.38735e7i | 0.242922 | + | 0.724944i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.33073e6 | + | 5.53435e6i | −0.380726 | + | 0.287430i | ||||
\(821\) | 1.22879e7i | 0.636238i | 0.948051 | + | 0.318119i | \(0.103051\pi\) | ||||
−0.948051 | + | 0.318119i | \(0.896949\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.19120e7i | 1.12767i | 0.825887 | + | 0.563836i | \(0.190675\pi\) | ||||
−0.825887 | + | 0.563836i | \(0.809325\pi\) | |||||||
\(824\) | 1.77394e7 | − | 2.58851e7i | 0.910166 | − | 1.32810i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −64897.1 | + | 21746.5i | −0.00330960 | + | 0.00110902i | ||||
\(827\) | −2.06837e7 | −1.05163 | −0.525816 | − | 0.850598i | \(-0.676240\pi\) | ||||
−0.525816 | + | 0.850598i | \(0.676240\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.09815e6 | −0.358723 | −0.179361 | − | 0.983783i | \(-0.557403\pi\) | ||||
−0.179361 | + | 0.983783i | \(0.557403\pi\) | |||||||
\(830\) | −1.34736e7 | + | 4.51489e6i | −0.678874 | + | 0.227485i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.09271e6 | + | 2.09148e7i | 0.405308 | + | 1.04748i | ||||
\(833\) | 2.42627e7i | 1.21151i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.43288e7i | 0.711201i | ||||||||
\(836\) | 1.62418e7 | + | 2.15137e7i | 0.803747 | + | 1.06463i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.54747e6 | + | 2.84922e7i | 0.469654 | + | 1.40157i | ||||
\(839\) | −2.57457e7 | −1.26270 | −0.631350 | − | 0.775498i | \(-0.717499\pi\) | ||||
−0.631350 | + | 0.775498i | \(0.717499\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00969e7 | 0.979805 | ||||||||
\(842\) | −9.29205e6 | − | 2.77299e7i | −0.451681 | − | 1.34793i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.18811e7 | − | 1.57376e7i | −0.574118 | − | 0.760469i | ||||
\(845\) | − | 4.36629e6i | − | 0.210364i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 245595.i | − | 0.0117628i | ||||||
\(848\) | 1.12275e7 | + | 3.19778e6i | 0.536160 | + | 0.152707i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.97082e6 | + | 3.00604e6i | −0.425878 | + | 0.142708i | ||||
\(851\) | −1.67717e7 | −0.793876 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.11214e7 | −0.523342 | −0.261671 | − | 0.965157i | \(-0.584274\pi\) | ||||
−0.261671 | + | 0.965157i | \(0.584274\pi\) | |||||||
\(854\) | −1.05633e6 | + | 353966.i | −0.0495626 | + | 0.0166080i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.50020e7 | − | 1.71342e7i | −1.16625 | − | 0.799244i | ||||
\(857\) | − | 2.05795e7i | − | 0.957158i | −0.878044 | − | 0.478579i | \(-0.841152\pi\) | ||
0.878044 | − | 0.478579i | \(-0.158848\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.38288e7i | 1.56424i | 0.623126 | + | 0.782121i | \(0.285862\pi\) | ||||
−0.623126 | + | 0.782121i | \(0.714138\pi\) | |||||||
\(860\) | 2.05672e7 | − | 1.55273e7i | 0.948266 | − | 0.715896i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.86263e6 | − | 1.45114e7i | −0.222897 | − | 0.665182i | ||||
\(863\) | 3.87801e6 | 0.177248 | 0.0886241 | − | 0.996065i | \(-0.471753\pi\) | ||||
0.0886241 | + | 0.996065i | \(0.471753\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.94592e6 | −0.179311 | ||||||||
\(866\) | 1.19011e7 | + | 3.55161e7i | 0.539254 | + | 1.60928i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −532268. | + | 401837.i | −0.0239790 | + | 0.0181030i | ||||
\(869\) | − | 3.92230e7i | − | 1.76194i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 4.01008e7i | − | 1.79105i | ||||||
\(872\) | −3.56189e6 | − | 2.44101e6i | −0.158631 | − | 0.108712i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.36831e7 | − | 1.12869e7i | 1.49153 | − | 0.499800i | ||||
\(875\) | −5.42021e6 | −0.239329 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.05430e7 | 0.901914 | 0.450957 | − | 0.892546i | \(-0.351083\pi\) | ||||
0.450957 | + | 0.892546i | \(0.351083\pi\) | |||||||
\(878\) | −2.24318e7 | + | 7.51669e6i | −0.982036 | + | 0.329072i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.82432e7 | − | 5.19597e6i | −0.794135 | − | 0.226183i | ||||
\(881\) | − | 1.83153e7i | − | 0.795012i | −0.917600 | − | 0.397506i | \(-0.869876\pi\) | ||
0.917600 | − | 0.397506i | \(-0.130124\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 484318.i | − | 0.0209040i | −0.999945 | − | 0.0104520i | \(-0.996673\pi\) | ||
0.999945 | − | 0.0104520i | \(-0.00332703\pi\) | |||||||
\(884\) | −2.00172e7 | − | 2.65145e7i | −0.861535 | − | 1.14118i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.80383e6 | + | 2.92572e7i | 0.419577 | + | 1.25213i | ||||
\(887\) | −1.01816e7 | −0.434519 | −0.217259 | − | 0.976114i | \(-0.569712\pi\) | ||||
−0.217259 | + | 0.976114i | \(0.569712\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.91761e6 | 0.208689 | ||||||||
\(890\) | −7.58028e6 | − | 2.26216e7i | −0.320782 | − | 0.957299i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.04419e7 | + | 1.38312e7i | 0.439407 | + | 0.582032i | ||||
\(893\) | − | 3.94448e7i | − | 1.65524i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.88850e6i | 0.370912i | ||||||||
\(896\) | 3.37414e6 | + | 4.06723e6i | 0.140408 | + | 0.169250i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.48250e7 | + | 1.16696e7i | −1.44112 | + | 0.482907i | ||||
\(899\) | −470488. | −0.0194155 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.72941e7 | −0.709719 | ||||||||
\(902\) | −1.41014e7 | + | 4.72526e6i | −0.577093 | + | 0.193379i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.63768e7 | − | 3.84886e7i | 1.07350 | − | 1.56643i | ||||
\(905\) | 2.87198e7i | 1.16563i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 3.22924e7i | − | 1.30341i | −0.758471 | − | 0.651707i | \(-0.774053\pi\) | ||
0.758471 | − | 0.651707i | \(-0.225947\pi\) | |||||||
\(908\) | −4.20415e6 | + | 3.17394e6i | −0.169225 | + | 0.127757i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.57710e6 | − | 4.70649e6i | −0.0631330 | − | 0.188406i | ||||
\(911\) | 6.89661e6 | 0.275321 | 0.137661 | − | 0.990479i | \(-0.456042\pi\) | ||||
0.137661 | + | 0.990479i | \(0.456042\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.30077e7 | −0.913473 | ||||||||
\(914\) | −9.74422e6 | − | 2.90793e7i | −0.385817 | − | 1.15138i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.59441e7 | − | 1.20371e7i | 0.627858 | − | 0.474003i | ||||
\(917\) | − | 1.44763e6i | − | 0.0568506i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.92298e7i | 0.751078i | 0.926807 | + | 0.375539i | \(0.122542\pi\) | ||||
−0.926807 | + | 0.375539i | \(0.877458\pi\) | |||||||
\(920\) | −1.41313e7 | + | 2.06202e7i | −0.550442 | + | 0.803197i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.13824e6 | + | 1.05160e6i | −0.121579 | + | 0.0407401i | ||||
\(923\) | −3.36259e7 | −1.29918 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.02188e6 | −0.231408 | ||||||||
\(926\) | −1.46866e7 | + | 4.92136e6i | −0.562853 | + | 0.188607i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 170920. | + | 3.72418e6i | 0.00651513 | + | 0.141958i | ||||
\(929\) | 2.70174e7i | 1.02708i | 0.858066 | + | 0.513540i | \(0.171666\pi\) | ||||
−0.858066 | + | 0.513540i | \(0.828334\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 3.27096e7i | − | 1.23680i | ||||||
\(932\) | −7.71991e6 | − | 1.02257e7i | −0.291120 | − | 0.385614i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.52040e6 | + | 1.64743e7i | 0.207063 | + | 0.617931i | ||||
\(935\) | 2.81006e7 | 1.05120 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.17247e7 | 1.18045 | 0.590227 | − | 0.807238i | \(-0.299038\pi\) | ||||
0.590227 | + | 0.807238i | \(0.299038\pi\) | |||||||
\(938\) | −3.00242e6 | − | 8.96000e6i | −0.111420 | − | 0.332507i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.67242e7 | + | 2.21527e7i | 0.617343 | + | 0.817724i | ||||
\(941\) | 2.17844e7i | 0.801994i | 0.916079 | + | 0.400997i | \(0.131336\pi\) | ||||
−0.916079 | + | 0.400997i | \(0.868664\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.95989e7i | 0.717716i | ||||||||
\(944\) | −119041. | + | 417959.i | −0.00434779 | + | 0.0152652i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.95632e7 | − | 1.32573e7i | 1.43735 | − | 0.481645i | ||||
\(947\) | −1.96765e7 | −0.712974 | −0.356487 | − | 0.934300i | \(-0.616026\pi\) | ||||
−0.356487 | + | 0.934300i | \(0.616026\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.80443e7 | 1.73171 | ||||||||
\(950\) | 1.20939e7 | − | 4.05257e6i | 0.434769 | − | 0.145687i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.45777e6 | − | 4.42560e6i | −0.230935 | − | 0.158263i | ||||
\(953\) | − | 2.78664e7i | − | 0.993912i | −0.867776 | − | 0.496956i | \(-0.834451\pi\) | ||
0.867776 | − | 0.496956i | \(-0.165549\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.26166e7i | − | 0.447644i | ||||||
\(956\) | 2.67903e7 | − | 2.02254e7i | 0.948054 | − | 0.715736i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.19962e7 | − | 3.57998e7i | −0.422308 | − | 1.26028i | ||||
\(959\) | −1.64696e6 | −0.0578276 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.80947e7 | 0.981334 | ||||||||
\(962\) | −6.71852e6 | − | 2.00498e7i | −0.234065 | − | 0.698510i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.39487e7 | + | 1.80802e7i | −0.830023 | + | 0.626628i | ||||
\(965\) | 1.64604e7i | 0.569014i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.89285e7i | − | 1.33876i | −0.742922 | − | 0.669378i | \(-0.766561\pi\) | ||
0.742922 | − | 0.669378i | \(-0.233439\pi\) | |||||||
\(968\) | −1.28632e6 | − | 881531.i | −0.0441225 | − | 0.0302377i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.40621e7 | + | 1.47648e7i | −1.50361 | + | 0.503848i | ||||
\(971\) | 468345. | 0.0159411 | 0.00797054 | − | 0.999968i | \(-0.497463\pi\) | ||||
0.00797054 | + | 0.999968i | \(0.497463\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.42301e6 | 0.0820489 | ||||||||
\(974\) | −5.23350e7 | + | 1.75370e7i | −1.76764 | + | 0.592322i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.93763e6 | + | 6.80310e6i | −0.0651099 | + | 0.228603i | ||||
\(977\) | 8.75275e6i | 0.293365i | 0.989184 | + | 0.146682i | \(0.0468595\pi\) | ||||
−0.989184 | + | 0.146682i | \(0.953140\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3.86288e7i | − | 1.28811i | ||||||
\(980\) | 1.38685e7 | + | 1.83701e7i | 0.461281 | + | 0.611006i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.68335e7 | + | 5.02356e7i | 0.557052 | + | 1.66239i | ||||
\(983\) | −9.57574e6 | −0.316074 | −0.158037 | − | 0.987433i | \(-0.550517\pi\) | ||||
−0.158037 | + | 0.987433i | \(0.550517\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.94169e7 | −1.29447 | ||||||||
\(986\) | −1.75477e6 | − | 5.23669e6i | −0.0574814 | − | 0.171540i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.69860e7 | + | 3.57453e7i | 0.879521 | + | 1.16500i | ||||
\(989\) | − | 5.49871e7i | − | 1.78760i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.16300e7i | − | 0.376179i | −0.982152 | − | 0.188090i | \(-0.939770\pi\) | ||
0.982152 | − | 0.188090i | \(-0.0602296\pi\) | |||||||
\(992\) | 194140. | + | 4.23013e6i | 0.00626377 | + | 0.136482i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.51326e6 | + | 2.51763e6i | −0.241192 | + | 0.0808213i | ||||
\(995\) | 6.59550e6 | 0.211198 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.59698e7 | 0.508817 | 0.254409 | − | 0.967097i | \(-0.418119\pi\) | ||||
0.254409 | + | 0.967097i | \(0.418119\pi\) | |||||||
\(998\) | 21081.5 | − | 7064.21i | 0.000669999 | − | 0.000224511i | ||||
\(999\) | 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 | 108.6.b.b.107.10 | yes | 16 | |
3.2 | odd | 2 | inner | 108.6.b.b.107.7 | ✓ | 16 | |
4.3 | odd | 2 | inner | 108.6.b.b.107.8 | yes | 16 | |
12.11 | even | 2 | inner | 108.6.b.b.107.9 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.6.b.b.107.7 | ✓ | 16 | 3.2 | odd | 2 | inner | |
108.6.b.b.107.8 | yes | 16 | 4.3 | odd | 2 | inner | |
108.6.b.b.107.9 | yes | 16 | 12.11 | even | 2 | inner | |
108.6.b.b.107.10 | yes | 16 | 1.1 | even | 1 | trivial |