Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,6,Mod(121,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.121");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.i (of order \(3\), degree \(2\), 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: | \(33.6806021607\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{151})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 151x^{2} + 22801 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(-6.14410 + 10.6419i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.121 |
Dual form | 210.6.i.b.151.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | + | 3.46410i | −0.353553 | + | 0.612372i | ||||
\(3\) | 4.50000 | + | 7.79423i | 0.288675 | + | 0.500000i | ||||
\(4\) | −8.00000 | − | 13.8564i | −0.250000 | − | 0.433013i | ||||
\(5\) | 12.5000 | − | 21.6506i | 0.223607 | − | 0.387298i | ||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | −127.009 | + | 25.9959i | −0.979689 | + | 0.200521i | ||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | −40.5000 | + | 70.1481i | −0.166667 | + | 0.288675i | ||||
\(10\) | 50.0000 | + | 86.6025i | 0.158114 | + | 0.273861i | ||||
\(11\) | 188.085 | + | 325.773i | 0.468676 | + | 0.811771i | 0.999359 | − | 0.0357997i | \(-0.0113978\pi\) |
−0.530683 | + | 0.847570i | \(0.678065\pi\) | |||||||
\(12\) | 72.0000 | − | 124.708i | 0.144338 | − | 0.250000i | ||||
\(13\) | −444.087 | −0.728803 | −0.364401 | − | 0.931242i | \(-0.618726\pi\) | ||||
−0.364401 | + | 0.931242i | \(0.618726\pi\) | |||||||
\(14\) | 163.965 | − | 491.963i | 0.223579 | − | 0.670830i | ||||
\(15\) | 225.000 | 0.258199 | ||||||||
\(16\) | −128.000 | + | 221.703i | −0.125000 | + | 0.216506i | ||||
\(17\) | 435.207 | + | 753.801i | 0.365236 | + | 0.632608i | 0.988814 | − | 0.149154i | \(-0.0476549\pi\) |
−0.623578 | + | 0.781761i | \(0.714322\pi\) | |||||||
\(18\) | −162.000 | − | 280.592i | −0.117851 | − | 0.204124i | ||||
\(19\) | −131.701 | + | 228.113i | −0.0836961 | + | 0.144966i | −0.904835 | − | 0.425763i | \(-0.860006\pi\) |
0.821139 | + | 0.570729i | \(0.193339\pi\) | |||||||
\(20\) | −400.000 | −0.223607 | ||||||||
\(21\) | −774.157 | − | 872.954i | −0.383072 | − | 0.431959i | ||||
\(22\) | −1504.68 | −0.662808 | ||||||||
\(23\) | 2112.67 | − | 3659.26i | 0.832747 | − | 1.44236i | −0.0631053 | − | 0.998007i | \(-0.520100\pi\) |
0.895852 | − | 0.444353i | \(-0.146566\pi\) | |||||||
\(24\) | 288.000 | + | 498.831i | 0.102062 | + | 0.176777i | ||||
\(25\) | −312.500 | − | 541.266i | −0.100000 | − | 0.173205i | ||||
\(26\) | 888.174 | − | 1538.36i | 0.257671 | − | 0.446299i | ||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 1376.28 | + | 1551.92i | 0.331750 | + | 0.374088i | ||||
\(29\) | −7291.74 | −1.61004 | −0.805019 | − | 0.593249i | \(-0.797845\pi\) | ||||
−0.805019 | + | 0.593249i | \(0.797845\pi\) | |||||||
\(30\) | −450.000 | + | 779.423i | −0.0912871 | + | 0.158114i | ||||
\(31\) | −4352.32 | − | 7538.43i | −0.813422 | − | 1.40889i | −0.910455 | − | 0.413608i | \(-0.864268\pi\) |
0.0970327 | − | 0.995281i | \(-0.469065\pi\) | |||||||
\(32\) | −512.000 | − | 886.810i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −1692.77 | + | 2931.96i | −0.270590 | + | 0.468676i | ||||
\(34\) | −3481.66 | −0.516522 | ||||||||
\(35\) | −1024.78 | + | 3074.77i | −0.141404 | + | 0.424270i | ||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 1384.32 | − | 2397.71i | 0.166239 | − | 0.287934i | −0.770856 | − | 0.637010i | \(-0.780171\pi\) |
0.937094 | + | 0.349076i | \(0.113504\pi\) | |||||||
\(38\) | −526.804 | − | 912.451i | −0.0591821 | − | 0.102506i | ||||
\(39\) | −1998.39 | − | 3461.32i | −0.210387 | − | 0.364401i | ||||
\(40\) | 800.000 | − | 1385.64i | 0.0790569 | − | 0.136931i | ||||
\(41\) | 10698.1 | 0.993906 | 0.496953 | − | 0.867778i | \(-0.334452\pi\) | ||||
0.496953 | + | 0.867778i | \(0.334452\pi\) | |||||||
\(42\) | 4572.31 | − | 935.851i | 0.399957 | − | 0.0818622i | ||||
\(43\) | −15869.1 | −1.30882 | −0.654411 | − | 0.756139i | \(-0.727083\pi\) | ||||
−0.654411 | + | 0.756139i | \(0.727083\pi\) | |||||||
\(44\) | 3009.36 | − | 5212.37i | 0.234338 | − | 0.405885i | ||||
\(45\) | 1012.50 | + | 1753.70i | 0.0745356 | + | 0.129099i | ||||
\(46\) | 8450.70 | + | 14637.0i | 0.588841 | + | 1.01990i | ||||
\(47\) | −579.008 | + | 1002.87i | −0.0382332 | + | 0.0662218i | −0.884509 | − | 0.466524i | \(-0.845506\pi\) |
0.846276 | + | 0.532745i | \(0.178840\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | 15455.4 | − | 6603.40i | 0.919583 | − | 0.392896i | ||||
\(50\) | 2500.00 | 0.141421 | ||||||||
\(51\) | −3916.86 | + | 6784.21i | −0.210869 | + | 0.365236i | ||||
\(52\) | 3552.70 | + | 6153.45i | 0.182201 | + | 0.315581i | ||||
\(53\) | −16139.7 | − | 27954.8i | −0.789233 | − | 1.36699i | −0.926437 | − | 0.376449i | \(-0.877145\pi\) |
0.137204 | − | 0.990543i | \(-0.456188\pi\) | |||||||
\(54\) | 1458.00 | − | 2525.33i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 9404.26 | 0.419197 | ||||||||
\(56\) | −8128.56 | + | 1663.74i | −0.346373 | + | 0.0708948i | ||||
\(57\) | −2370.62 | −0.0966439 | ||||||||
\(58\) | 14583.5 | − | 25259.3i | 0.569235 | − | 0.985943i | ||||
\(59\) | −18252.4 | − | 31614.1i | −0.682638 | − | 1.18236i | −0.974173 | − | 0.225803i | \(-0.927499\pi\) |
0.291535 | − | 0.956560i | \(-0.405834\pi\) | |||||||
\(60\) | −1800.00 | − | 3117.69i | −0.0645497 | − | 0.111803i | ||||
\(61\) | 20727.4 | − | 35900.9i | 0.713214 | − | 1.23532i | −0.250431 | − | 0.968135i | \(-0.580572\pi\) |
0.963644 | − | 0.267188i | \(-0.0860945\pi\) | |||||||
\(62\) | 34818.5 | 1.15035 | ||||||||
\(63\) | 3320.29 | − | 9962.25i | 0.105396 | − | 0.316232i | ||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −5551.09 | + | 9614.77i | −0.162965 | + | 0.282264i | ||||
\(66\) | −6771.06 | − | 11727.8i | −0.191336 | − | 0.331404i | ||||
\(67\) | 15020.1 | + | 26015.5i | 0.408776 | + | 0.708021i | 0.994753 | − | 0.102307i | \(-0.0326224\pi\) |
−0.585977 | + | 0.810328i | \(0.699289\pi\) | |||||||
\(68\) | 6963.32 | − | 12060.8i | 0.182618 | − | 0.316304i | ||||
\(69\) | 38028.1 | 0.961573 | ||||||||
\(70\) | −8601.74 | − | 9699.48i | −0.209817 | − | 0.236594i | ||||
\(71\) | 37623.3 | 0.885749 | 0.442874 | − | 0.896584i | \(-0.353959\pi\) | ||||
0.442874 | + | 0.896584i | \(0.353959\pi\) | |||||||
\(72\) | −2592.00 | + | 4489.48i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 16199.3 | + | 28058.0i | 0.355787 | + | 0.616241i | 0.987252 | − | 0.159163i | \(-0.0508797\pi\) |
−0.631466 | + | 0.775404i | \(0.717546\pi\) | |||||||
\(74\) | 5537.27 | + | 9590.84i | 0.117548 | + | 0.203600i | ||||
\(75\) | 2812.50 | − | 4871.39i | 0.0577350 | − | 0.100000i | ||||
\(76\) | 4214.43 | 0.0836961 | ||||||||
\(77\) | −32357.2 | − | 36486.6i | −0.621934 | − | 0.701304i | ||||
\(78\) | 15987.1 | 0.297532 | ||||||||
\(79\) | 32339.0 | − | 56012.9i | 0.582988 | − | 1.00976i | −0.412135 | − | 0.911123i | \(-0.635217\pi\) |
0.995123 | − | 0.0986416i | \(-0.0314497\pi\) | |||||||
\(80\) | 3200.00 | + | 5542.56i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | −3280.50 | − | 5681.99i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −21396.1 | + | 37059.1i | −0.351399 | + | 0.608640i | ||||
\(83\) | −105250. | −1.67698 | −0.838490 | − | 0.544917i | \(-0.816561\pi\) | ||||
−0.838490 | + | 0.544917i | \(0.816561\pi\) | |||||||
\(84\) | −5902.74 | + | 17710.7i | −0.0912758 | + | 0.273865i | ||||
\(85\) | 21760.4 | 0.326677 | ||||||||
\(86\) | 31738.2 | − | 54972.1i | 0.462739 | − | 0.801487i | ||||
\(87\) | −32812.8 | − | 56833.5i | −0.464778 | − | 0.805019i | ||||
\(88\) | 12037.4 | + | 20849.5i | 0.165702 | + | 0.287004i | ||||
\(89\) | 11195.7 | − | 19391.5i | 0.149822 | − | 0.259499i | −0.781340 | − | 0.624106i | \(-0.785463\pi\) |
0.931162 | + | 0.364607i | \(0.118797\pi\) | |||||||
\(90\) | −8100.00 | −0.105409 | ||||||||
\(91\) | 56402.9 | − | 11544.4i | 0.714000 | − | 0.146140i | ||||
\(92\) | −67605.6 | −0.832747 | ||||||||
\(93\) | 39170.8 | − | 67845.9i | 0.469630 | − | 0.813422i | ||||
\(94\) | −2316.03 | − | 4011.49i | −0.0270349 | − | 0.0468259i | ||||
\(95\) | 3292.53 | + | 5702.82i | 0.0374300 | + | 0.0648307i | ||||
\(96\) | 4608.00 | − | 7981.29i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 37203.1 | 0.401467 | 0.200734 | − | 0.979646i | \(-0.435667\pi\) | ||||
0.200734 | + | 0.979646i | \(0.435667\pi\) | |||||||
\(98\) | −8036.00 | + | 66746.0i | −0.0845230 | + | 0.702037i | ||||
\(99\) | −30469.8 | −0.312451 | ||||||||
\(100\) | −5000.00 | + | 8660.25i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −82301.6 | − | 142551.i | −0.802795 | − | 1.39048i | −0.917769 | − | 0.397114i | \(-0.870012\pi\) |
0.114974 | − | 0.993368i | \(-0.463321\pi\) | |||||||
\(102\) | −15667.5 | − | 27136.8i | −0.149107 | − | 0.258261i | ||||
\(103\) | −42553.2 | + | 73704.3i | −0.395220 | + | 0.684541i | −0.993129 | − | 0.117023i | \(-0.962665\pi\) |
0.597909 | + | 0.801564i | \(0.295998\pi\) | |||||||
\(104\) | −28421.6 | −0.257671 | ||||||||
\(105\) | −28577.0 | + | 5849.07i | −0.252955 | + | 0.0517742i | ||||
\(106\) | 129117. | 1.11614 | ||||||||
\(107\) | −25535.0 | + | 44227.9i | −0.215614 | + | 0.373454i | −0.953462 | − | 0.301512i | \(-0.902509\pi\) |
0.737849 | + | 0.674966i | \(0.235842\pi\) | |||||||
\(108\) | 5832.00 | + | 10101.3i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | −12926.5 | − | 22389.4i | −0.104212 | − | 0.180500i | 0.809204 | − | 0.587527i | \(-0.199899\pi\) |
−0.913416 | + | 0.407028i | \(0.866565\pi\) | |||||||
\(110\) | −18808.5 | + | 32577.3i | −0.148208 | + | 0.256704i | ||||
\(111\) | 24917.7 | 0.191956 | ||||||||
\(112\) | 10493.8 | − | 31485.6i | 0.0790472 | − | 0.237174i | ||||
\(113\) | 38424.1 | 0.283079 | 0.141540 | − | 0.989933i | \(-0.454795\pi\) | ||||
0.141540 | + | 0.989933i | \(0.454795\pi\) | |||||||
\(114\) | 4741.24 | − | 8212.06i | 0.0341688 | − | 0.0591821i | ||||
\(115\) | −52816.8 | − | 91481.5i | −0.372416 | − | 0.645043i | ||||
\(116\) | 58333.9 | + | 101037.i | 0.402510 | + | 0.697167i | ||||
\(117\) | 17985.5 | − | 31151.9i | 0.121467 | − | 0.210387i | ||||
\(118\) | 146019. | 0.965396 | ||||||||
\(119\) | −74870.8 | − | 84425.7i | −0.484669 | − | 0.546522i | ||||
\(120\) | 14400.0 | 0.0912871 | ||||||||
\(121\) | 9773.47 | − | 16928.1i | 0.0606855 | − | 0.105110i | ||||
\(122\) | 82909.5 | + | 143603.i | 0.504318 | + | 0.873505i | ||||
\(123\) | 48141.2 | + | 83383.1i | 0.286916 | + | 0.496953i | ||||
\(124\) | −69637.0 | + | 120615.i | −0.406711 | + | 0.704444i | ||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 27869.7 | + | 31426.3i | 0.156389 | + | 0.176347i | ||||
\(127\) | −179221. | −0.986004 | −0.493002 | − | 0.870028i | \(-0.664101\pi\) | ||||
−0.493002 | + | 0.870028i | \(0.664101\pi\) | |||||||
\(128\) | −8192.00 | + | 14189.0i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −71410.9 | − | 123687.i | −0.377824 | − | 0.654411i | ||||
\(130\) | −22204.4 | − | 38459.1i | −0.115234 | − | 0.199591i | ||||
\(131\) | −117943. | + | 204283.i | −0.600473 | + | 1.04005i | 0.392277 | + | 0.919847i | \(0.371688\pi\) |
−0.992749 | + | 0.120202i | \(0.961646\pi\) | |||||||
\(132\) | 54168.5 | 0.270590 | ||||||||
\(133\) | 10797.2 | − | 32396.0i | 0.0529275 | − | 0.158804i | ||||
\(134\) | −120161. | −0.578097 | ||||||||
\(135\) | −9112.50 | + | 15783.3i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | 27853.3 | + | 48243.3i | 0.129130 | + | 0.223661i | ||||
\(137\) | 60250.2 | + | 104356.i | 0.274256 | + | 0.475026i | 0.969947 | − | 0.243315i | \(-0.0782349\pi\) |
−0.695691 | + | 0.718341i | \(0.744902\pi\) | |||||||
\(138\) | −76056.3 | + | 131733.i | −0.339967 | + | 0.588841i | ||||
\(139\) | 78689.4 | 0.345445 | 0.172723 | − | 0.984970i | \(-0.444744\pi\) | ||||
0.172723 | + | 0.984970i | \(0.444744\pi\) | |||||||
\(140\) | 50803.5 | − | 10398.3i | 0.219065 | − | 0.0448378i | ||||
\(141\) | −10422.1 | −0.0441478 | ||||||||
\(142\) | −75246.5 | + | 130331.i | −0.313159 | + | 0.542408i | ||||
\(143\) | −83526.2 | − | 144672.i | −0.341572 | − | 0.591621i | ||||
\(144\) | −10368.0 | − | 17957.9i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −91146.8 | + | 157871.i | −0.360016 | + | 0.623565i | ||||
\(146\) | −129595. | −0.503158 | ||||||||
\(147\) | 121018. | + | 90747.8i | 0.461909 | + | 0.346372i | ||||
\(148\) | −44298.2 | −0.166239 | ||||||||
\(149\) | −129970. | + | 225116.i | −0.479600 | + | 0.830691i | −0.999726 | − | 0.0233979i | \(-0.992552\pi\) |
0.520126 | + | 0.854089i | \(0.325885\pi\) | |||||||
\(150\) | 11250.0 | + | 19485.6i | 0.0408248 | + | 0.0707107i | ||||
\(151\) | 146790. | + | 254248.i | 0.523907 | + | 0.907434i | 0.999613 | + | 0.0278292i | \(0.00885947\pi\) |
−0.475706 | + | 0.879605i | \(0.657807\pi\) | |||||||
\(152\) | −8428.86 | + | 14599.2i | −0.0295910 | + | 0.0512532i | ||||
\(153\) | −70503.6 | −0.243491 | ||||||||
\(154\) | 191108. | − | 39115.5i | 0.649346 | − | 0.132907i | ||||
\(155\) | −217616. | −0.727547 | ||||||||
\(156\) | −31974.3 | + | 55381.1i | −0.105194 | + | 0.182201i | ||||
\(157\) | 194783. | + | 337374.i | 0.630669 | + | 1.09235i | 0.987415 | + | 0.158149i | \(0.0505526\pi\) |
−0.356747 | + | 0.934201i | \(0.616114\pi\) | |||||||
\(158\) | 129356. | + | 224051.i | 0.412235 | + | 0.714011i | ||||
\(159\) | 145257. | − | 251593.i | 0.455664 | − | 0.789233i | ||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | −173202. | + | 519679.i | −0.526610 | + | 1.58005i | ||||
\(162\) | 26244.0 | 0.0785674 | ||||||||
\(163\) | −116066. | + | 201033.i | −0.342166 | + | 0.592649i | −0.984835 | − | 0.173495i | \(-0.944494\pi\) |
0.642669 | + | 0.766144i | \(0.277827\pi\) | |||||||
\(164\) | −85584.4 | − | 148237.i | −0.248476 | − | 0.430374i | ||||
\(165\) | 42319.2 | + | 73298.9i | 0.121012 | + | 0.209598i | ||||
\(166\) | 210501. | − | 364598.i | 0.592902 | − | 1.02694i | ||||
\(167\) | −619069. | −1.71770 | −0.858851 | − | 0.512226i | \(-0.828821\pi\) | ||||
−0.858851 | + | 0.512226i | \(0.828821\pi\) | |||||||
\(168\) | −49546.0 | − | 55869.0i | −0.135437 | − | 0.152721i | ||||
\(169\) | −174080. | −0.468847 | ||||||||
\(170\) | −43520.7 | + | 75380.1i | −0.115498 | + | 0.200048i | ||||
\(171\) | −10667.8 | − | 18477.1i | −0.0278987 | − | 0.0483220i | ||||
\(172\) | 126953. | + | 219888.i | 0.327206 | + | 0.566737i | ||||
\(173\) | −188434. | + | 326377.i | −0.478678 | + | 0.829095i | −0.999701 | − | 0.0244478i | \(-0.992217\pi\) |
0.521023 | + | 0.853543i | \(0.325551\pi\) | |||||||
\(174\) | 262503. | 0.657295 | ||||||||
\(175\) | 53760.9 | + | 60621.8i | 0.132700 | + | 0.149635i | ||||
\(176\) | −96299.6 | −0.234338 | ||||||||
\(177\) | 164272. | − | 284527.i | 0.394121 | − | 0.682638i | ||||
\(178\) | 44782.8 | + | 77566.0i | 0.105940 | + | 0.183494i | ||||
\(179\) | −334997. | − | 580232.i | −0.781463 | − | 1.35353i | −0.931089 | − | 0.364792i | \(-0.881140\pi\) |
0.149626 | − | 0.988743i | \(-0.452193\pi\) | |||||||
\(180\) | 16200.0 | − | 28059.2i | 0.0372678 | − | 0.0645497i | ||||
\(181\) | 260652. | 0.591377 | 0.295689 | − | 0.955284i | \(-0.404451\pi\) | ||||
0.295689 | + | 0.955284i | \(0.404451\pi\) | |||||||
\(182\) | −72814.8 | + | 218474.i | −0.162945 | + | 0.488902i | ||||
\(183\) | 373093. | 0.823548 | ||||||||
\(184\) | 135211. | − | 234193.i | 0.294420 | − | 0.509951i | ||||
\(185\) | −34608.0 | − | 59942.7i | −0.0743441 | − | 0.128768i | ||||
\(186\) | 156683. | + | 271384.i | 0.332078 | + | 0.575177i | ||||
\(187\) | −163712. | + | 283558.i | −0.342355 | + | 0.592976i | ||||
\(188\) | 18528.3 | 0.0382332 | ||||||||
\(189\) | 92589.4 | − | 18951.0i | 0.188541 | − | 0.0385902i | ||||
\(190\) | −26340.2 | −0.0529340 | ||||||||
\(191\) | 120941. | − | 209476.i | 0.239878 | − | 0.415481i | −0.720801 | − | 0.693142i | \(-0.756226\pi\) |
0.960679 | + | 0.277661i | \(0.0895592\pi\) | |||||||
\(192\) | 18432.0 | + | 31925.2i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −432764. | − | 749569.i | −0.836292 | − | 1.44850i | −0.892974 | − | 0.450107i | \(-0.851386\pi\) |
0.0566827 | − | 0.998392i | \(-0.481948\pi\) | |||||||
\(194\) | −74406.3 | + | 128875.i | −0.141940 | + | 0.245847i | ||||
\(195\) | −99919.6 | −0.188176 | ||||||||
\(196\) | −215143. | − | 161329.i | −0.400025 | − | 0.299967i | ||||
\(197\) | 59334.4 | 0.108928 | 0.0544642 | − | 0.998516i | \(-0.482655\pi\) | ||||
0.0544642 | + | 0.998516i | \(0.482655\pi\) | |||||||
\(198\) | 60939.6 | − | 105550.i | 0.110468 | − | 0.191336i | ||||
\(199\) | −454112. | − | 786545.i | −0.812887 | − | 1.40796i | −0.910835 | − | 0.412770i | \(-0.864561\pi\) |
0.0979483 | − | 0.995192i | \(-0.468772\pi\) | |||||||
\(200\) | −20000.0 | − | 34641.0i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | −135181. | + | 234140.i | −0.236007 | + | 0.408776i | ||||
\(202\) | 658413. | 1.13532 | ||||||||
\(203\) | 926115. | − | 189555.i | 1.57734 | − | 0.322846i | ||||
\(204\) | 125340. | 0.210869 | ||||||||
\(205\) | 133726. | − | 231620.i | 0.222244 | − | 0.384938i | ||||
\(206\) | −170213. | − | 294817.i | −0.279463 | − | 0.484044i | ||||
\(207\) | 171127. | + | 296400.i | 0.277582 | + | 0.480786i | ||||
\(208\) | 56843.2 | − | 98455.2i | 0.0911003 | − | 0.157790i | ||||
\(209\) | −99084.0 | −0.156905 | ||||||||
\(210\) | 36892.2 | − | 110692.i | 0.0577279 | − | 0.173207i | ||||
\(211\) | −389916. | −0.602927 | −0.301463 | − | 0.953478i | \(-0.597475\pi\) | ||||
−0.301463 | + | 0.953478i | \(0.597475\pi\) | |||||||
\(212\) | −258235. | + | 447276.i | −0.394617 | + | 0.683496i | ||||
\(213\) | 169305. | + | 293244.i | 0.255694 | + | 0.442874i | ||||
\(214\) | −102140. | − | 176912.i | −0.152462 | − | 0.264072i | ||||
\(215\) | −198364. | + | 343576.i | −0.292662 | + | 0.506905i | ||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 748750. | + | 844304.i | 1.07941 | + | 1.21717i | ||||
\(218\) | 103412. | 0.147377 | ||||||||
\(219\) | −145794. | + | 252522.i | −0.205414 | + | 0.355787i | ||||
\(220\) | −75234.1 | − | 130309.i | −0.104799 | − | 0.181517i | ||||
\(221\) | −193270. | − | 334753.i | −0.266185 | − | 0.461046i | ||||
\(222\) | −49835.5 | + | 86317.6i | −0.0678666 | + | 0.117548i | ||||
\(223\) | 432482. | 0.582379 | 0.291189 | − | 0.956665i | \(-0.405949\pi\) | ||||
0.291189 | + | 0.956665i | \(0.405949\pi\) | |||||||
\(224\) | 88081.9 | + | 99322.7i | 0.117291 | + | 0.132260i | ||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | −76848.3 | + | 133105.i | −0.100084 | + | 0.173350i | ||||
\(227\) | −382198. | − | 661987.i | −0.492294 | − | 0.852678i | 0.507667 | − | 0.861553i | \(-0.330508\pi\) |
−0.999961 | + | 0.00887574i | \(0.997175\pi\) | |||||||
\(228\) | 18964.9 | + | 32848.2i | 0.0241610 | + | 0.0418480i | ||||
\(229\) | 354080. | − | 613284.i | 0.446183 | − | 0.772811i | −0.551951 | − | 0.833876i | \(-0.686117\pi\) |
0.998134 | + | 0.0610656i | \(0.0194499\pi\) | |||||||
\(230\) | 422535. | 0.526675 | ||||||||
\(231\) | 138777. | − | 416389.i | 0.171115 | − | 0.513416i | ||||
\(232\) | −466671. | −0.569235 | ||||||||
\(233\) | −635878. | + | 1.10137e6i | −0.767333 | + | 1.32906i | 0.171671 | + | 0.985154i | \(0.445083\pi\) |
−0.939004 | + | 0.343906i | \(0.888250\pi\) | |||||||
\(234\) | 71942.1 | + | 124607.i | 0.0858902 | + | 0.148766i | ||||
\(235\) | 14475.2 | + | 25071.8i | 0.0170984 | + | 0.0296153i | ||||
\(236\) | −292039. | + | 505826.i | −0.341319 | + | 0.591182i | ||||
\(237\) | 582103. | 0.673176 | ||||||||
\(238\) | 442201. | − | 90508.7i | 0.506031 | − | 0.103573i | ||||
\(239\) | −300010. | −0.339735 | −0.169868 | − | 0.985467i | \(-0.554334\pi\) | ||||
−0.169868 | + | 0.985467i | \(0.554334\pi\) | |||||||
\(240\) | −28800.0 | + | 49883.1i | −0.0322749 | + | 0.0559017i | ||||
\(241\) | 28293.5 | + | 49005.9i | 0.0313794 | + | 0.0543507i | 0.881289 | − | 0.472578i | \(-0.156677\pi\) |
−0.849909 | + | 0.526929i | \(0.823343\pi\) | |||||||
\(242\) | 39093.9 | + | 67712.6i | 0.0429112 | + | 0.0743243i | ||||
\(243\) | 29524.5 | − | 51137.9i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −663276. | −0.713214 | ||||||||
\(245\) | 50225.0 | − | 417162.i | 0.0534570 | − | 0.444007i | ||||
\(246\) | −385130. | −0.405760 | ||||||||
\(247\) | 58486.7 | − | 101302.i | 0.0609979 | − | 0.105651i | ||||
\(248\) | −278548. | − | 482460.i | −0.287588 | − | 0.498117i | ||||
\(249\) | −473626. | − | 820345.i | −0.484102 | − | 0.838490i | ||||
\(250\) | 31250.0 | − | 54126.6i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | 1.66302e6 | 1.66614 | 0.833071 | − | 0.553166i | \(-0.186580\pi\) | ||||
0.833071 | + | 0.553166i | \(0.186580\pi\) | |||||||
\(252\) | −164603. | + | 33690.6i | −0.163282 | + | 0.0334201i | ||||
\(253\) | 1.58945e6 | 1.56115 | ||||||||
\(254\) | 358441. | − | 620839.i | 0.348605 | − | 0.603802i | ||||
\(255\) | 97921.6 | + | 169605.i | 0.0943036 | + | 0.163339i | ||||
\(256\) | −32768.0 | − | 56755.8i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 487587. | − | 844525.i | 0.460489 | − | 0.797590i | −0.538496 | − | 0.842628i | \(-0.681007\pi\) |
0.998985 | + | 0.0450375i | \(0.0143407\pi\) | |||||||
\(258\) | 571287. | 0.534324 | ||||||||
\(259\) | −113490. | + | 340517.i | −0.105126 | + | 0.315420i | ||||
\(260\) | 177635. | 0.162965 | ||||||||
\(261\) | 295316. | − | 511502.i | 0.268340 | − | 0.464778i | ||||
\(262\) | −471771. | − | 817132.i | −0.424598 | − | 0.735426i | ||||
\(263\) | 537984. | + | 931815.i | 0.479601 | + | 0.830693i | 0.999726 | − | 0.0233970i | \(-0.00744819\pi\) |
−0.520126 | + | 0.854090i | \(0.674115\pi\) | |||||||
\(264\) | −108337. | + | 187645.i | −0.0956681 | + | 0.165702i | ||||
\(265\) | −806984. | −0.705912 | ||||||||
\(266\) | 90628.7 | + | 102195.i | 0.0785347 | + | 0.0885572i | ||||
\(267\) | 201522. | 0.173000 | ||||||||
\(268\) | 240321. | − | 416249.i | 0.204388 | − | 0.354010i | ||||
\(269\) | −738079. | − | 1.27839e6i | −0.621902 | − | 1.07717i | −0.989131 | − | 0.147036i | \(-0.953027\pi\) |
0.367229 | − | 0.930131i | \(-0.380307\pi\) | |||||||
\(270\) | −36450.0 | − | 63133.3i | −0.0304290 | − | 0.0527046i | ||||
\(271\) | −663286. | + | 1.14884e6i | −0.548627 | + | 0.950250i | 0.449742 | + | 0.893159i | \(0.351516\pi\) |
−0.998369 | + | 0.0570916i | \(0.981817\pi\) | |||||||
\(272\) | −222826. | −0.182618 | ||||||||
\(273\) | 343793. | + | 387668.i | 0.279184 | + | 0.314813i | ||||
\(274\) | −482001. | −0.387857 | ||||||||
\(275\) | 117553. | − | 203608.i | 0.0937352 | − | 0.162354i | ||||
\(276\) | −304225. | − | 526933.i | −0.240393 | − | 0.416373i | ||||
\(277\) | −745269. | − | 1.29084e6i | −0.583598 | − | 1.01082i | −0.995049 | − | 0.0993891i | \(-0.968311\pi\) |
0.411451 | − | 0.911432i | \(-0.365022\pi\) | |||||||
\(278\) | −157379. | + | 272588.i | −0.122133 | + | 0.211541i | ||||
\(279\) | 705075. | 0.542282 | ||||||||
\(280\) | −65586.0 | + | 196785.i | −0.0499938 | + | 0.150002i | ||||
\(281\) | −1.00956e6 | −0.762719 | −0.381360 | − | 0.924427i | \(-0.624544\pi\) | ||||
−0.381360 | + | 0.924427i | \(0.624544\pi\) | |||||||
\(282\) | 20844.3 | − | 36103.4i | 0.0156086 | − | 0.0270349i | ||||
\(283\) | 497080. | + | 860968.i | 0.368944 | + | 0.639030i | 0.989401 | − | 0.145211i | \(-0.0463861\pi\) |
−0.620457 | + | 0.784241i | \(0.713053\pi\) | |||||||
\(284\) | −300986. | − | 521323.i | −0.221437 | − | 0.383540i | ||||
\(285\) | −29632.7 | + | 51325.4i | −0.0216102 | + | 0.0374300i | ||||
\(286\) | 668210. | 0.483056 | ||||||||
\(287\) | −1.35875e6 | + | 278105.i | −0.973719 | + | 0.199299i | ||||
\(288\) | 82944.0 | 0.0589256 | ||||||||
\(289\) | 331118. | − | 573513.i | 0.233205 | − | 0.403923i | ||||
\(290\) | −364587. | − | 631483.i | −0.254569 | − | 0.440927i | ||||
\(291\) | 167414. | + | 289970.i | 0.115894 | + | 0.200734i | ||||
\(292\) | 259189. | − | 448929.i | 0.177893 | − | 0.308120i | ||||
\(293\) | 1.69742e6 | 1.15510 | 0.577549 | − | 0.816356i | \(-0.304009\pi\) | ||||
0.577549 | + | 0.816356i | \(0.304009\pi\) | |||||||
\(294\) | −556395. | + | 237723.i | −0.375418 | + | 0.160399i | ||||
\(295\) | −912621. | −0.610570 | ||||||||
\(296\) | 88596.4 | − | 153453.i | 0.0587742 | − | 0.101800i | ||||
\(297\) | −137114. | − | 237489.i | −0.0901967 | − | 0.156225i | ||||
\(298\) | −519882. | − | 900462.i | −0.339128 | − | 0.587388i | ||||
\(299\) | −938211. | + | 1.62503e6i | −0.606908 | + | 1.05120i | ||||
\(300\) | −90000.0 | −0.0577350 | ||||||||
\(301\) | 2.01551e6 | − | 412531.i | 1.28224 | − | 0.262446i | ||||
\(302\) | −1.17432e6 | −0.740917 | ||||||||
\(303\) | 740714. | − | 1.28295e6i | 0.463494 | − | 0.802795i | ||||
\(304\) | −33715.5 | − | 58396.9i | −0.0209240 | − | 0.0362415i | ||||
\(305\) | −518184. | − | 897522.i | −0.318959 | − | 0.552453i | ||||
\(306\) | 141007. | − | 244232.i | 0.0860870 | − | 0.149107i | ||||
\(307\) | 2.95303e6 | 1.78822 | 0.894111 | − | 0.447846i | \(-0.147809\pi\) | ||||
0.894111 | + | 0.447846i | \(0.147809\pi\) | |||||||
\(308\) | −246715. | + | 740247.i | −0.148190 | + | 0.444631i | ||||
\(309\) | −765957. | −0.456361 | ||||||||
\(310\) | 435232. | − | 753843.i | 0.257227 | − | 0.445530i | ||||
\(311\) | 1.06071e6 | + | 1.83721e6i | 0.621866 | + | 1.07710i | 0.989138 | + | 0.146990i | \(0.0469584\pi\) |
−0.367272 | + | 0.930114i | \(0.619708\pi\) | |||||||
\(312\) | −127897. | − | 221524.i | −0.0743831 | − | 0.128835i | ||||
\(313\) | −192508. | + | 333434.i | −0.111068 | + | 0.192375i | −0.916201 | − | 0.400719i | \(-0.868760\pi\) |
0.805133 | + | 0.593094i | \(0.202094\pi\) | |||||||
\(314\) | −1.55826e6 | −0.891900 | ||||||||
\(315\) | −174185. | − | 196415.i | −0.0989089 | − | 0.111531i | ||||
\(316\) | −1.03485e6 | −0.582988 | ||||||||
\(317\) | −505089. | + | 874840.i | −0.282306 | + | 0.488968i | −0.971952 | − | 0.235178i | \(-0.924433\pi\) |
0.689646 | + | 0.724146i | \(0.257766\pi\) | |||||||
\(318\) | 581029. | + | 1.00637e6i | 0.322203 | + | 0.558072i | ||||
\(319\) | −1.37147e6 | − | 2.37545e6i | −0.754586 | − | 1.30698i | ||||
\(320\) | 51200.0 | − | 88681.0i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | −459630. | −0.248969 | ||||||||
\(322\) | −1.45381e6 | − | 1.63935e6i | −0.781393 | − | 0.881113i | ||||
\(323\) | −229269. | −0.122275 | ||||||||
\(324\) | −52488.0 | + | 90911.9i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 138777. | + | 240369.i | 0.0728803 | + | 0.126232i | ||||
\(326\) | −464265. | − | 804131.i | −0.241948 | − | 0.419066i | ||||
\(327\) | 116339. | − | 201505.i | 0.0601666 | − | 0.104212i | ||||
\(328\) | 684675. | 0.351399 | ||||||||
\(329\) | 47468.6 | − | 142425.i | 0.0241778 | − | 0.0725433i | ||||
\(330\) | −338553. | −0.171136 | ||||||||
\(331\) | −1.78311e6 | + | 3.08844e6i | −0.894558 | + | 1.54942i | −0.0602084 | + | 0.998186i | \(0.519177\pi\) |
−0.834350 | + | 0.551235i | \(0.814157\pi\) | |||||||
\(332\) | 842002. | + | 1.45839e6i | 0.419245 | + | 0.726154i | ||||
\(333\) | 112130. | + | 194215.i | 0.0554128 | + | 0.0959779i | ||||
\(334\) | 1.23814e6 | − | 2.14452e6i | 0.607299 | − | 1.05187i | ||||
\(335\) | 751004. | 0.365620 | ||||||||
\(336\) | 292628. | − | 59894.5i | 0.141406 | − | 0.0289427i | ||||
\(337\) | −1.16658e6 | −0.559551 | −0.279776 | − | 0.960065i | \(-0.590260\pi\) | ||||
−0.279776 | + | 0.960065i | \(0.590260\pi\) | |||||||
\(338\) | 348159. | − | 603029.i | 0.165762 | − | 0.287109i | ||||
\(339\) | 172909. | + | 299487.i | 0.0817180 | + | 0.141540i | ||||
\(340\) | −174083. | − | 301520.i | −0.0816693 | − | 0.141455i | ||||
\(341\) | 1.63721e6 | − | 2.83573e6i | 0.762463 | − | 1.32063i | ||||
\(342\) | 85342.3 | 0.0394547 | ||||||||
\(343\) | −1.79131e6 | + | 1.24047e6i | −0.822122 | + | 0.569311i | ||||
\(344\) | −1.01562e6 | −0.462739 | ||||||||
\(345\) | 475352. | − | 823333.i | 0.215014 | − | 0.372416i | ||||
\(346\) | −753735. | − | 1.30551e6i | −0.338477 | − | 0.586259i | ||||
\(347\) | −1.09312e6 | − | 1.89333e6i | −0.487351 | − | 0.844117i | 0.512543 | − | 0.858662i | \(-0.328704\pi\) |
−0.999894 | + | 0.0145443i | \(0.995370\pi\) | |||||||
\(348\) | −525005. | + | 909336.i | −0.232389 | + | 0.402510i | ||||
\(349\) | 488943. | 0.214880 | 0.107440 | − | 0.994212i | \(-0.465735\pi\) | ||||
0.107440 | + | 0.994212i | \(0.465735\pi\) | |||||||
\(350\) | −317522. | + | 64989.7i | −0.138549 | + | 0.0283579i | ||||
\(351\) | 323740. | 0.140258 | ||||||||
\(352\) | 192599. | − | 333592.i | 0.0828510 | − | 0.143502i | ||||
\(353\) | −462447. | − | 800981.i | −0.197526 | − | 0.342125i | 0.750200 | − | 0.661212i | \(-0.229957\pi\) |
−0.947726 | + | 0.319086i | \(0.896624\pi\) | |||||||
\(354\) | 657087. | + | 1.13811e6i | 0.278686 | + | 0.482698i | ||||
\(355\) | 470291. | − | 814568.i | 0.198059 | − | 0.343049i | ||||
\(356\) | −358262. | −0.149822 | ||||||||
\(357\) | 321115. | − | 963476.i | 0.133349 | − | 0.400102i | ||||
\(358\) | 2.67998e6 | 1.10516 | ||||||||
\(359\) | −157198. | + | 272274.i | −0.0643739 | + | 0.111499i | −0.896416 | − | 0.443214i | \(-0.853838\pi\) |
0.832042 | + | 0.554712i | \(0.187172\pi\) | |||||||
\(360\) | 64800.0 | + | 112237.i | 0.0263523 | + | 0.0456435i | ||||
\(361\) | 1.20336e6 | + | 2.08428e6i | 0.485990 | + | 0.841759i | ||||
\(362\) | −521304. | + | 902925.i | −0.209083 | + | 0.362143i | ||||
\(363\) | 175922. | 0.0700736 | ||||||||
\(364\) | −611188. | − | 689187.i | −0.241781 | − | 0.272636i | ||||
\(365\) | 809966. | 0.318225 | ||||||||
\(366\) | −746186. | + | 1.29243e6i | −0.291168 | + | 0.504318i | ||||
\(367\) | 1.48827e6 | + | 2.57775e6i | 0.576787 | + | 0.999024i | 0.995845 | + | 0.0910644i | \(0.0290269\pi\) |
−0.419058 | + | 0.907959i | \(0.637640\pi\) | |||||||
\(368\) | 540845. | + | 936770.i | 0.208187 | + | 0.360590i | ||||
\(369\) | −433271. | + | 750448.i | −0.165651 | + | 0.286916i | ||||
\(370\) | 276864. | 0.105138 | ||||||||
\(371\) | 2.77659e6 | + | 3.13093e6i | 1.04731 | + | 1.18097i | ||||
\(372\) | −1.25347e6 | −0.469630 | ||||||||
\(373\) | −1.77167e6 | + | 3.06862e6i | −0.659341 | + | 1.14201i | 0.321445 | + | 0.946928i | \(0.395831\pi\) |
−0.980787 | + | 0.195084i | \(0.937502\pi\) | |||||||
\(374\) | −654848. | − | 1.13423e6i | −0.242081 | − | 0.419297i | ||||
\(375\) | −70312.5 | − | 121785.i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | −37056.5 | + | 64183.8i | −0.0135175 | + | 0.0234129i | ||||
\(377\) | 3.23817e6 | 1.17340 | ||||||||
\(378\) | −119531. | + | 358641.i | −0.0430278 | + | 0.129101i | ||||
\(379\) | −2.68890e6 | −0.961559 | −0.480780 | − | 0.876842i | \(-0.659646\pi\) | ||||
−0.480780 | + | 0.876842i | \(0.659646\pi\) | |||||||
\(380\) | 52680.4 | − | 91245.1i | 0.0187150 | − | 0.0324154i | ||||
\(381\) | −806493. | − | 1.39689e6i | −0.284635 | − | 0.493002i | ||||
\(382\) | 483764. | + | 837905.i | 0.169619 | + | 0.293789i | ||||
\(383\) | −2.30505e6 | + | 3.99246e6i | −0.802940 | + | 1.39073i | 0.114734 | + | 0.993396i | \(0.463399\pi\) |
−0.917673 | + | 0.397336i | \(0.869935\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | −1.19442e6 | + | 244472.i | −0.410682 | + | 0.0840576i | ||||
\(386\) | 3.46211e6 | 1.18270 | ||||||||
\(387\) | 642698. | − | 1.11319e6i | 0.218137 | − | 0.377824i | ||||
\(388\) | −297625. | − | 515502.i | −0.100367 | − | 0.173840i | ||||
\(389\) | −1.41964e6 | − | 2.45889e6i | −0.475669 | − | 0.823883i | 0.523942 | − | 0.851754i | \(-0.324461\pi\) |
−0.999612 | + | 0.0278705i | \(0.991127\pi\) | |||||||
\(390\) | 199839. | − | 346132.i | 0.0665303 | − | 0.115234i | ||||
\(391\) | 3.67780e6 | 1.21660 | ||||||||
\(392\) | 989148. | − | 422618.i | 0.325122 | − | 0.138910i | ||||
\(393\) | −2.12297e6 | −0.693366 | ||||||||
\(394\) | −118669. | + | 205540.i | −0.0385120 | + | 0.0667047i | ||||
\(395\) | −808476. | − | 1.40032e6i | −0.260720 | − | 0.451580i | ||||
\(396\) | 243758. | + | 422202.i | 0.0781127 | + | 0.135295i | ||||
\(397\) | −148862. | + | 257837.i | −0.0474033 | + | 0.0821049i | −0.888753 | − | 0.458385i | \(-0.848428\pi\) |
0.841350 | + | 0.540490i | \(0.181761\pi\) | |||||||
\(398\) | 3.63290e6 | 1.14960 | ||||||||
\(399\) | 301089. | − | 61626.3i | 0.0946810 | − | 0.0193791i | ||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | 2.28859e6 | − | 3.96396e6i | 0.710734 | − | 1.23103i | −0.253847 | − | 0.967244i | \(-0.581696\pi\) |
0.964582 | − | 0.263784i | \(-0.0849705\pi\) | |||||||
\(402\) | −540723. | − | 936560.i | −0.166882 | − | 0.289048i | ||||
\(403\) | 1.93281e6 | + | 3.34772e6i | 0.592824 | + | 1.02680i | ||||
\(404\) | −1.31683e6 | + | 2.28081e6i | −0.401398 | + | 0.695241i | ||||
\(405\) | −164025. | −0.0496904 | ||||||||
\(406\) | −1.19559e6 | + | 3.58727e6i | −0.359971 | + | 1.08006i | ||||
\(407\) | 1.04148e6 | 0.311648 | ||||||||
\(408\) | −250679. | + | 434189.i | −0.0745535 | + | 0.129130i | ||||
\(409\) | 1.84079e6 | + | 3.18833e6i | 0.544120 | + | 0.942444i | 0.998662 | + | 0.0517185i | \(0.0164699\pi\) |
−0.454541 | + | 0.890726i | \(0.650197\pi\) | |||||||
\(410\) | 534903. | + | 926479.i | 0.157150 | + | 0.272192i | ||||
\(411\) | −542252. | + | 939207.i | −0.158342 | + | 0.274256i | ||||
\(412\) | 1.36170e6 | 0.395220 | ||||||||
\(413\) | 3.14005e6 | + | 3.54078e6i | 0.905861 | + | 1.02147i | ||||
\(414\) | −1.36901e6 | −0.392561 | ||||||||
\(415\) | −1.31563e6 | + | 2.27873e6i | −0.374984 | + | 0.649492i | ||||
\(416\) | 227373. | + | 393821.i | 0.0644177 | + | 0.111575i | ||||
\(417\) | 354103. | + | 613324.i | 0.0997215 | + | 0.172723i | ||||
\(418\) | 198168. | − | 343237.i | 0.0554744 | − | 0.0960845i | ||||
\(419\) | −1.50062e6 | −0.417576 | −0.208788 | − | 0.977961i | \(-0.566952\pi\) | ||||
−0.208788 | + | 0.977961i | \(0.566952\pi\) | |||||||
\(420\) | 309663. | + | 349181.i | 0.0856576 | + | 0.0965891i | ||||
\(421\) | −2.98818e6 | −0.821679 | −0.410839 | − | 0.911708i | \(-0.634764\pi\) | ||||
−0.410839 | + | 0.911708i | \(0.634764\pi\) | |||||||
\(422\) | 779832. | − | 1.35071e6i | 0.213167 | − | 0.369216i | ||||
\(423\) | −46899.7 | − | 81232.6i | −0.0127444 | − | 0.0220739i | ||||
\(424\) | −1.03294e6 | − | 1.78910e6i | −0.279036 | − | 0.483305i | ||||
\(425\) | 272005. | − | 471126.i | 0.0730472 | − | 0.126522i | ||||
\(426\) | −1.35444e6 | −0.361605 | ||||||||
\(427\) | −1.69928e6 | + | 5.09855e6i | −0.451020 | + | 1.35325i | ||||
\(428\) | 817120. | 0.215614 | ||||||||
\(429\) | 751736. | − | 1.30204e6i | 0.197207 | − | 0.341572i | ||||
\(430\) | −793454. | − | 1.37430e6i | −0.206943 | − | 0.358436i | ||||
\(431\) | −1.51519e6 | − | 2.62438e6i | −0.392892 | − | 0.680509i | 0.599938 | − | 0.800047i | \(-0.295192\pi\) |
−0.992830 | + | 0.119538i | \(0.961859\pi\) | |||||||
\(432\) | 93312.0 | − | 161621.i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 1.41809e6 | 0.363483 | 0.181742 | − | 0.983346i | \(-0.441827\pi\) | ||||
0.181742 | + | 0.983346i | \(0.441827\pi\) | |||||||
\(434\) | −4.42226e6 | + | 905138.i | −1.12699 | + | 0.230670i | ||||
\(435\) | −1.64064e6 | −0.415710 | ||||||||
\(436\) | −206825. | + | 358231.i | −0.0521058 | + | 0.0902499i | ||||
\(437\) | 556483. | + | 963856.i | 0.139395 | + | 0.241440i | ||||
\(438\) | −583176. | − | 1.01009e6i | −0.145249 | − | 0.251579i | ||||
\(439\) | −1.86019e6 | + | 3.22194e6i | −0.460676 | + | 0.797914i | −0.998995 | − | 0.0448275i | \(-0.985726\pi\) |
0.538319 | + | 0.842741i | \(0.319060\pi\) | |||||||
\(440\) | 601872. | 0.148208 | ||||||||
\(441\) | −162729. | + | 1.35161e6i | −0.0398445 | + | 0.330943i | ||||
\(442\) | 1.54616e6 | 0.376443 | ||||||||
\(443\) | 400436. | − | 693575.i | 0.0969446 | − | 0.167913i | −0.813474 | − | 0.581601i | \(-0.802426\pi\) |
0.910419 | + | 0.413688i | \(0.135760\pi\) | |||||||
\(444\) | −199342. | − | 345270.i | −0.0479889 | − | 0.0831193i | ||||
\(445\) | −279892. | − | 484788.i | −0.0670025 | − | 0.116052i | ||||
\(446\) | −864964. | + | 1.49816e6i | −0.205902 | + | 0.356633i | ||||
\(447\) | −2.33947e6 | −0.553794 | ||||||||
\(448\) | −520228. | + | 106479.i | −0.122461 | + | 0.0250651i | ||||
\(449\) | 3.89383e6 | 0.911510 | 0.455755 | − | 0.890105i | \(-0.349369\pi\) | ||||
0.455755 | + | 0.890105i | \(0.349369\pi\) | |||||||
\(450\) | −101250. | + | 175370.i | −0.0235702 | + | 0.0408248i | ||||
\(451\) | 2.01214e6 | + | 3.48514e6i | 0.465820 | + | 0.806823i | ||||
\(452\) | −307393. | − | 532421.i | −0.0707698 | − | 0.122577i | ||||
\(453\) | −1.32111e6 | + | 2.28823e6i | −0.302478 | + | 0.523907i | ||||
\(454\) | 3.05759e6 | 0.696208 | ||||||||
\(455\) | 455093. | − | 1.36547e6i | 0.103056 | − | 0.309209i | ||||
\(456\) | −151720. | −0.0341688 | ||||||||
\(457\) | 1.61339e6 | − | 2.79447e6i | 0.361367 | − | 0.625906i | −0.626819 | − | 0.779165i | \(-0.715644\pi\) |
0.988186 | + | 0.153259i | \(0.0489768\pi\) | |||||||
\(458\) | 1.41632e6 | + | 2.45314e6i | 0.315499 | + | 0.546460i | ||||
\(459\) | −317266. | − | 549521.i | −0.0702897 | − | 0.121745i | ||||
\(460\) | −845070. | + | 1.46370e6i | −0.186208 | + | 0.322521i | ||||
\(461\) | 4.10832e6 | 0.900351 | 0.450176 | − | 0.892940i | \(-0.351361\pi\) | ||||
0.450176 | + | 0.892940i | \(0.351361\pi\) | |||||||
\(462\) | 1.16486e6 | + | 1.31352e6i | 0.253903 | + | 0.286306i | ||||
\(463\) | −1.48281e6 | −0.321465 | −0.160733 | − | 0.986998i | \(-0.551386\pi\) | ||||
−0.160733 | + | 0.986998i | \(0.551386\pi\) | |||||||
\(464\) | 933343. | − | 1.61660e6i | 0.201255 | − | 0.348584i | ||||
\(465\) | −979271. | − | 1.69615e6i | −0.210025 | − | 0.363774i | ||||
\(466\) | −2.54351e6 | − | 4.40549e6i | −0.542587 | − | 0.939787i | ||||
\(467\) | 1.14431e6 | − | 1.98201e6i | 0.242803 | − | 0.420546i | −0.718709 | − | 0.695311i | \(-0.755267\pi\) |
0.961511 | + | 0.274765i | \(0.0886000\pi\) | |||||||
\(468\) | −575537. | −0.121467 | ||||||||
\(469\) | −2.58398e6 | − | 2.91374e6i | −0.542446 | − | 0.611672i | ||||
\(470\) | −115802. | −0.0241808 | ||||||||
\(471\) | −1.75304e6 | + | 3.03636e6i | −0.364117 | + | 0.630669i | ||||
\(472\) | −1.16815e6 | − | 2.02330e6i | −0.241349 | − | 0.418029i | ||||
\(473\) | −2.98474e6 | − | 5.16972e6i | −0.613414 | − | 1.06246i | ||||
\(474\) | −1.16421e6 | + | 2.01646e6i | −0.238004 | + | 0.412235i | ||||
\(475\) | 164626. | 0.0334784 | ||||||||
\(476\) | −570870. | + | 1.71285e6i | −0.115484 | + | 0.346498i | ||||
\(477\) | 2.61463e6 | 0.526156 | ||||||||
\(478\) | 600020. | − | 1.03926e6i | 0.120115 | − | 0.208045i | ||||
\(479\) | −252312. | − | 437018.i | −0.0502458 | − | 0.0870283i | 0.839809 | − | 0.542883i | \(-0.182667\pi\) |
−0.890054 | + | 0.455854i | \(0.849334\pi\) | |||||||
\(480\) | −115200. | − | 199532.i | −0.0228218 | − | 0.0395285i | ||||
\(481\) | −614758. | + | 1.06479e6i | −0.121155 | + | 0.209847i | ||||
\(482\) | −226348. | −0.0443772 | ||||||||
\(483\) | −4.82990e6 | + | 988574.i | −0.942043 | + | 0.192815i | ||||
\(484\) | −312751. | −0.0606855 | ||||||||
\(485\) | 465039. | − | 805471.i | 0.0897708 | − | 0.155488i | ||||
\(486\) | 118098. | + | 204552.i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 739529. | + | 1.28090e6i | 0.141297 | + | 0.244733i | 0.927985 | − | 0.372617i | \(-0.121539\pi\) |
−0.786688 | + | 0.617350i | \(0.788206\pi\) | |||||||
\(488\) | 1.32655e6 | − | 2.29766e6i | 0.252159 | − | 0.436752i | ||||
\(489\) | −2.08919e6 | −0.395100 | ||||||||
\(490\) | 1.34464e6 | + | 1.00831e6i | 0.252998 | + | 0.189716i | ||||
\(491\) | 7.51661e6 | 1.40708 | 0.703539 | − | 0.710657i | \(-0.251602\pi\) | ||||
0.703539 | + | 0.710657i | \(0.251602\pi\) | |||||||
\(492\) | 770260. | − | 1.33413e6i | 0.143458 | − | 0.248476i | ||||
\(493\) | −3.17342e6 | − | 5.49652e6i | −0.588044 | − | 1.01852i | ||||
\(494\) | 233947. | + | 405208.i | 0.0431320 | + | 0.0747069i | ||||
\(495\) | −380872. | + | 659690.i | −0.0698661 | + | 0.121012i | ||||
\(496\) | 2.22839e6 | 0.406711 | ||||||||
\(497\) | −4.77848e6 | + | 978049.i | −0.867759 | + | 0.177611i | ||||
\(498\) | 3.78901e6 | 0.684624 | ||||||||
\(499\) | −1.21517e6 | + | 2.10474e6i | −0.218468 | + | 0.378397i | −0.954340 | − | 0.298723i | \(-0.903439\pi\) |
0.735872 | + | 0.677121i | \(0.236773\pi\) | |||||||
\(500\) | 125000. | + | 216506.i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | −2.78581e6 | − | 4.82516e6i | −0.495858 | − | 0.858851i | ||||
\(502\) | −3.32603e6 | + | 5.76086e6i | −0.589070 | + | 1.02030i | ||||
\(503\) | −5.24665e6 | −0.924617 | −0.462309 | − | 0.886719i | \(-0.652979\pi\) | ||||
−0.462309 | + | 0.886719i | \(0.652979\pi\) | |||||||
\(504\) | 212499. | − | 637584.i | 0.0372632 | − | 0.111805i | ||||
\(505\) | −4.11508e6 | −0.718042 | ||||||||
\(506\) | −3.17890e6 | + | 5.50602e6i | −0.551951 | + | 0.956007i | ||||
\(507\) | −783358. | − | 1.35682e6i | −0.135344 | − | 0.234423i | ||||
\(508\) | 1.43377e6 | + | 2.48335e6i | 0.246501 | + | 0.426952i | ||||
\(509\) | −2.54111e6 | + | 4.40134e6i | −0.434740 | + | 0.752992i | −0.997274 | − | 0.0737822i | \(-0.976493\pi\) |
0.562534 | + | 0.826774i | \(0.309826\pi\) | |||||||
\(510\) | −783373. | −0.133365 | ||||||||
\(511\) | −2.78685e6 | − | 3.14250e6i | −0.472129 | − | 0.532382i | ||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 96010.0 | − | 166294.i | 0.0161073 | − | 0.0278987i | ||||
\(514\) | 1.95035e6 | + | 3.37810e6i | 0.325615 | + | 0.563982i | ||||
\(515\) | 1.06383e6 | + | 1.84261e6i | 0.176748 | + | 0.306136i | ||||
\(516\) | −1.14257e6 | + | 1.97900e6i | −0.188912 | + | 0.327206i | ||||
\(517\) | −435611. | −0.0716759 | ||||||||
\(518\) | −952604. | − | 1.07417e6i | −0.155987 | − | 0.175894i | ||||
\(519\) | −3.39181e6 | −0.552730 | ||||||||
\(520\) | −355270. | + | 615345.i | −0.0576169 | + | 0.0997954i | ||||
\(521\) | −1.16985e6 | − | 2.02623e6i | −0.188814 | − | 0.327036i | 0.756041 | − | 0.654524i | \(-0.227131\pi\) |
−0.944855 | + | 0.327488i | \(0.893798\pi\) | |||||||
\(522\) | 1.18126e6 | + | 2.04601e6i | 0.189745 | + | 0.328648i | ||||
\(523\) | −3.29946e6 | + | 5.71483e6i | −0.527459 | + | 0.913586i | 0.472029 | + | 0.881583i | \(0.343522\pi\) |
−0.999488 | + | 0.0320025i | \(0.989812\pi\) | |||||||
\(524\) | 3.77417e6 | 0.600473 | ||||||||
\(525\) | −230576. | + | 691823.i | −0.0365103 | + | 0.109546i | ||||
\(526\) | −4.30387e6 | −0.678258 | ||||||||
\(527\) | 3.78832e6 | − | 6.56156e6i | 0.594183 | − | 1.02915i | ||||
\(528\) | −433348. | − | 750581.i | −0.0676476 | − | 0.117169i | ||||
\(529\) | −5.70861e6 | − | 9.88760e6i | −0.886934 | − | 1.53621i | ||||
\(530\) | 1.61397e6 | − | 2.79548e6i | 0.249577 | − | 0.432281i | ||||
\(531\) | 2.95689e6 | 0.455092 | ||||||||
\(532\) | −535270. | + | 109558.i | −0.0819962 | + | 0.0167828i | ||||
\(533\) | −4.75087e6 | −0.724361 | ||||||||
\(534\) | −403045. | + | 698094.i | −0.0611646 | + | 0.105940i | ||||
\(535\) | 638375. | + | 1.10570e6i | 0.0964254 | + | 0.167014i | ||||
\(536\) | 961285. | + | 1.66500e6i | 0.144524 | + | 0.250323i | ||||
\(537\) | 3.01498e6 | − | 5.22209e6i | 0.451178 | − | 0.781463i | ||||
\(538\) | 5.90463e6 | 0.879502 | ||||||||
\(539\) | 5.05815e6 | + | 3.79296e6i | 0.749928 | + | 0.562350i | ||||
\(540\) | 291600. | 0.0430331 | ||||||||
\(541\) | 4.18341e6 | − | 7.24587e6i | 0.614521 | − | 1.06438i | −0.375947 | − | 0.926641i | \(-0.622683\pi\) |
0.990468 | − | 0.137741i | \(-0.0439841\pi\) | |||||||
\(542\) | −2.65314e6 | − | 4.59538e6i | −0.387938 | − | 0.671928i | ||||
\(543\) | 1.17293e6 | + | 2.03158e6i | 0.170716 | + | 0.295689i | ||||
\(544\) | 445652. | − | 771892.i | 0.0645652 | − | 0.111830i | ||||
\(545\) | −646327. | −0.0932097 | ||||||||
\(546\) | −2.03051e6 | + | 415600.i | −0.291489 | + | 0.0596614i | ||||
\(547\) | −1.01705e6 | −0.145337 | −0.0726684 | − | 0.997356i | \(-0.523151\pi\) | ||||
−0.0726684 | + | 0.997356i | \(0.523151\pi\) | |||||||
\(548\) | 964003. | − | 1.66970e6i | 0.137128 | − | 0.237513i | ||||
\(549\) | 1.67892e6 | + | 2.90797e6i | 0.237738 | + | 0.411774i | ||||
\(550\) | 470213. | + | 814433.i | 0.0662808 | + | 0.114802i | ||||
\(551\) | 960330. | − | 1.66334e6i | 0.134754 | − | 0.233401i | ||||
\(552\) | 2.43380e6 | 0.339967 | ||||||||
\(553\) | −2.65124e6 | + | 7.95480e6i | −0.368668 | + | 1.10616i | ||||
\(554\) | 5.96215e6 | 0.825332 | ||||||||
\(555\) | 311472. | − | 539485.i | 0.0429226 | − | 0.0743441i | ||||
\(556\) | −629516. | − | 1.09035e6i | −0.0863614 | − | 0.149582i | ||||
\(557\) | −4.56175e6 | − | 7.90117e6i | −0.623007 | − | 1.07908i | −0.988923 | − | 0.148432i | \(-0.952577\pi\) |
0.365915 | − | 0.930648i | \(-0.380756\pi\) | |||||||
\(558\) | −1.41015e6 | + | 2.44245e6i | −0.191726 | + | 0.332078i | ||||
\(559\) | 7.04726e6 | 0.953873 | ||||||||
\(560\) | −550512. | − | 620767.i | −0.0741816 | − | 0.0836486i | ||||
\(561\) | −2.94682e6 | −0.395317 | ||||||||
\(562\) | 2.01911e6 | − | 3.49721e6i | 0.269662 | − | 0.467068i | ||||
\(563\) | 3.19124e6 | + | 5.52739e6i | 0.424315 | + | 0.734935i | 0.996356 | − | 0.0852900i | \(-0.0271817\pi\) |
−0.572041 | + | 0.820225i | \(0.693848\pi\) | |||||||
\(564\) | 83377.2 | + | 144414.i | 0.0110370 | + | 0.0191166i | ||||
\(565\) | 480302. | − | 831907.i | 0.0632985 | − | 0.109636i | ||||
\(566\) | −3.97664e6 | −0.521765 | ||||||||
\(567\) | 564360. | + | 636383.i | 0.0737223 | + | 0.0831306i | ||||
\(568\) | 2.40789e6 | 0.313159 | ||||||||
\(569\) | 4.51774e6 | − | 7.82496e6i | 0.584980 | − | 1.01321i | −0.409898 | − | 0.912131i | \(-0.634436\pi\) |
0.994878 | − | 0.101083i | \(-0.0322309\pi\) | |||||||
\(570\) | −118531. | − | 205302.i | −0.0152807 | − | 0.0264670i | ||||
\(571\) | −7.13771e6 | − | 1.23629e7i | −0.916154 | − | 1.58682i | −0.805203 | − | 0.592999i | \(-0.797944\pi\) |
−0.110950 | − | 0.993826i | \(-0.535389\pi\) | |||||||
\(572\) | −1.33642e6 | + | 2.31475e6i | −0.170786 | + | 0.295810i | ||||
\(573\) | 2.17694e6 | 0.276987 | ||||||||
\(574\) | 1.75411e6 | − | 5.26304e6i | 0.222217 | − | 0.666741i | ||||
\(575\) | −2.64084e6 | −0.333099 | ||||||||
\(576\) | −165888. | + | 287326.i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 3.94911e6 | + | 6.84005e6i | 0.493809 | + | 0.855303i | 0.999975 | − | 0.00713385i | \(-0.00227079\pi\) |
−0.506165 | + | 0.862436i | \(0.668937\pi\) | |||||||
\(578\) | 1.32447e6 | + | 2.29405e6i | 0.164901 | + | 0.285617i | ||||
\(579\) | 3.89488e6 | − | 6.74612e6i | 0.482833 | − | 0.836292i | ||||
\(580\) | 2.91670e6 | 0.360016 | ||||||||
\(581\) | 1.33677e7 | − | 2.73607e6i | 1.64292 | − | 0.336269i | ||||
\(582\) | −1.33931e6 | −0.163898 | ||||||||
\(583\) | 6.07127e6 | − | 1.05157e7i | 0.739789 | − | 1.28135i | ||||
\(584\) | 1.03676e6 | + | 1.79571e6i | 0.125790 | + | 0.217874i | ||||
\(585\) | −449638. | − | 778796.i | −0.0543217 | − | 0.0940880i | ||||
\(586\) | −3.39483e6 | + | 5.88002e6i | −0.408389 | + | 0.707351i | ||||
\(587\) | −480037. | −0.0575016 | −0.0287508 | − | 0.999587i | \(-0.509153\pi\) | ||||
−0.0287508 | + | 0.999587i | \(0.509153\pi\) | |||||||
\(588\) | 289296. | − | 2.40286e6i | 0.0345064 | − | 0.286605i | ||||
\(589\) | 2.29282e6 | 0.272321 | ||||||||
\(590\) | 1.82524e6 | − | 3.16141e6i | 0.215869 | − | 0.373896i | ||||
\(591\) | 267005. | + | 462466.i | 0.0314449 | + | 0.0544642i | ||||
\(592\) | 354386. | + | 613814.i | 0.0415596 | + | 0.0719834i | ||||
\(593\) | 5.03687e6 | − | 8.72412e6i | 0.588199 | − | 1.01879i | −0.406269 | − | 0.913753i | \(-0.633170\pi\) |
0.994468 | − | 0.105037i | \(-0.0334962\pi\) | |||||||
\(594\) | 1.09691e6 | 0.127557 | ||||||||
\(595\) | −2.76376e6 | + | 565679.i | −0.320042 | + | 0.0655055i | ||||
\(596\) | 4.15906e6 | 0.479600 | ||||||||
\(597\) | 4.08701e6 | − | 7.07890e6i | 0.469321 | − | 0.812887i | ||||
\(598\) | −3.75285e6 | − | 6.50012e6i | −0.429149 | − | 0.743307i | ||||
\(599\) | 1.47865e6 | + | 2.56110e6i | 0.168383 | + | 0.291649i | 0.937852 | − | 0.347036i | \(-0.112812\pi\) |
−0.769468 | + | 0.638685i | \(0.779479\pi\) | |||||||
\(600\) | 180000. | − | 311769.i | 0.0204124 | − | 0.0353553i | ||||
\(601\) | −1.95113e6 | −0.220344 | −0.110172 | − | 0.993913i | \(-0.535140\pi\) | ||||
−0.110172 | + | 0.993913i | \(0.535140\pi\) | |||||||
\(602\) | −2.60198e6 | + | 7.80700e6i | −0.292625 | + | 0.877997i | ||||
\(603\) | −2.43325e6 | −0.272517 | ||||||||
\(604\) | 2.34864e6 | − | 4.06797e6i | 0.261954 | − | 0.453717i | ||||
\(605\) | −244337. | − | 423204.i | −0.0271394 | − | 0.0470068i | ||||
\(606\) | 2.96286e6 | + | 5.13182e6i | 0.327740 | + | 0.567662i | ||||
\(607\) | 1.00418e6 | − | 1.73930e6i | 0.110622 | − | 0.191603i | −0.805399 | − | 0.592733i | \(-0.798049\pi\) |
0.916021 | + | 0.401130i | \(0.131382\pi\) | |||||||
\(608\) | 269724. | 0.0295910 | ||||||||
\(609\) | 5.64495e6 | + | 6.36535e6i | 0.616761 | + | 0.695471i | ||||
\(610\) | 4.14548e6 | 0.451076 | ||||||||
\(611\) | 257130. | − | 445363.i | 0.0278644 | − | 0.0482626i | ||||
\(612\) | 564029. | + | 976926.i | 0.0608727 | + | 0.105435i | ||||
\(613\) | −6.88619e6 | − | 1.19272e7i | −0.740164 | − | 1.28200i | −0.952420 | − | 0.304787i | \(-0.901415\pi\) |
0.212257 | − | 0.977214i | \(-0.431919\pi\) | |||||||
\(614\) | −5.90605e6 | + | 1.02296e7i | −0.632232 | + | 1.09506i | ||||
\(615\) | 2.40706e6 | 0.256625 | ||||||||
\(616\) | −2.07086e6 | − | 2.33514e6i | −0.219887 | − | 0.247948i | ||||
\(617\) | 5.75202e6 | 0.608286 | 0.304143 | − | 0.952626i | \(-0.401630\pi\) | ||||
0.304143 | + | 0.952626i | \(0.401630\pi\) | |||||||
\(618\) | 1.53191e6 | − | 2.65335e6i | 0.161348 | − | 0.279463i | ||||
\(619\) | −1.63386e6 | − | 2.82994e6i | −0.171392 | − | 0.296859i | 0.767515 | − | 0.641031i | \(-0.221493\pi\) |
−0.938907 | + | 0.344172i | \(0.888160\pi\) | |||||||
\(620\) | 1.74093e6 | + | 3.01537e6i | 0.181887 | + | 0.315037i | ||||
\(621\) | −1.54014e6 | + | 2.66760e6i | −0.160262 | + | 0.277582i | ||||
\(622\) | −8.48570e6 | −0.879451 | ||||||||
\(623\) | −917851. | + | 2.75393e6i | −0.0947441 | + | 0.284271i | ||||
\(624\) | 1.02318e6 | 0.105194 | ||||||||
\(625\) | −195312. | + | 338291.i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −770032. | − | 1.33374e6i | −0.0785368 | − | 0.136030i | ||||
\(627\) | −445878. | − | 772283.i | −0.0452947 | − | 0.0784527i | ||||
\(628\) | 3.11652e6 | − | 5.39798e6i | 0.315334 | − | 0.546175i | ||||
\(629\) | 2.40986e6 | 0.242865 | ||||||||
\(630\) | 1.02877e6 | − | 210567.i | 0.103268 | − | 0.0211367i | ||||
\(631\) | −4.01563e6 | −0.401495 | −0.200748 | − | 0.979643i | \(-0.564337\pi\) | ||||
−0.200748 | + | 0.979643i | \(0.564337\pi\) | |||||||
\(632\) | 2.06970e6 | − | 3.58482e6i | 0.206117 | − | 0.357006i | ||||
\(633\) | −1.75462e6 | − | 3.03909e6i | −0.174050 | − | 0.301463i | ||||
\(634\) | −2.02036e6 | − | 3.49936e6i | −0.199620 | − | 0.345753i | ||||
\(635\) | −2.24026e6 | + | 3.88024e6i | −0.220477 | + | 0.381878i | ||||
\(636\) | −4.64823e6 | −0.455664 | ||||||||
\(637\) | −6.86356e6 | + | 2.93249e6i | −0.670194 | + | 0.286344i | ||||
\(638\) | 1.09717e7 | 1.06715 | ||||||||
\(639\) | −1.52374e6 | + | 2.63920e6i | −0.147625 | + | 0.255694i | ||||
\(640\) | 204800. | + | 354724.i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | 1.62418e6 | + | 2.81316e6i | 0.156131 | + | 0.270427i | 0.933470 | − | 0.358655i | \(-0.116764\pi\) |
−0.777339 | + | 0.629082i | \(0.783431\pi\) | |||||||
\(642\) | 919260. | − | 1.59220e6i | 0.0880239 | − | 0.152462i | ||||
\(643\) | −4.88701e6 | −0.466140 | −0.233070 | − | 0.972460i | \(-0.574877\pi\) | ||||
−0.233070 | + | 0.972460i | \(0.574877\pi\) | |||||||
\(644\) | 8.58650e6 | − | 1.75747e6i | 0.815833 | − | 0.166983i | ||||
\(645\) | −3.57054e6 | −0.337936 | ||||||||
\(646\) | 458538. | − | 794211.i | 0.0432309 | − | 0.0748780i | ||||
\(647\) | −504818. | − | 874370.i | −0.0474104 | − | 0.0821173i | 0.841346 | − | 0.540496i | \(-0.181764\pi\) |
−0.888757 | + | 0.458379i | \(0.848430\pi\) | |||||||
\(648\) | −209952. | − | 363648.i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 6.86602e6 | − | 1.18923e7i | 0.639872 | − | 1.10829i | ||||
\(650\) | −1.11022e6 | −0.103068 | ||||||||
\(651\) | −3.21133e6 | + | 9.63530e6i | −0.296983 | + | 0.891072i | ||||
\(652\) | 3.71412e6 | 0.342166 | ||||||||
\(653\) | 2.59693e6 | − | 4.49802e6i | 0.238330 | − | 0.412799i | −0.721906 | − | 0.691992i | \(-0.756733\pi\) |
0.960235 | + | 0.279193i | \(0.0900668\pi\) | |||||||
\(654\) | 465356. | + | 806019.i | 0.0425442 | + | 0.0736887i | ||||
\(655\) | 2.94857e6 | + | 5.10707e6i | 0.268540 | + | 0.465124i | ||||
\(656\) | −1.36935e6 | + | 2.37179e6i | −0.124238 | + | 0.215187i | ||||
\(657\) | −2.62429e6 | −0.237191 | ||||||||
\(658\) | 398438. | + | 449287.i | 0.0358754 | + | 0.0404537i | ||||
\(659\) | −2.06522e7 | −1.85248 | −0.926240 | − | 0.376934i | \(-0.876978\pi\) | ||||
−0.926240 | + | 0.376934i | \(0.876978\pi\) | |||||||
\(660\) | 677106. | − | 1.17278e6i | 0.0605058 | − | 0.104799i | ||||
\(661\) | −219603. | − | 380364.i | −0.0195495 | − | 0.0338607i | 0.856085 | − | 0.516835i | \(-0.172890\pi\) |
−0.875635 | + | 0.482974i | \(0.839557\pi\) | |||||||
\(662\) | −7.13245e6 | − | 1.23538e7i | −0.632548 | − | 1.09561i | ||||
\(663\) | 1.73943e6 | − | 3.01278e6i | 0.153682 | − | 0.266185i | ||||
\(664\) | −6.73602e6 | −0.592902 | ||||||||
\(665\) | −566429. | − | 638716.i | −0.0496697 | − | 0.0560085i | ||||
\(666\) | −897038. | −0.0783656 | ||||||||
\(667\) | −1.54051e7 | + | 2.66824e7i | −1.34075 | + | 2.32225i | ||||
\(668\) | 4.95255e6 | + | 8.57807e6i | 0.429425 | + | 0.743787i | ||||
\(669\) | 1.94617e6 | + | 3.37086e6i | 0.168118 | + | 0.291189i | ||||
\(670\) | −1.50201e6 | + | 2.60155e6i | −0.129266 | + | 0.223896i | ||||
\(671\) | 1.55940e7 | 1.33706 | ||||||||
\(672\) | −377776. | + | 1.13348e6i | −0.0322709 | + | 0.0968259i | ||||
\(673\) | 5.73639e6 | 0.488204 | 0.244102 | − | 0.969750i | \(-0.421507\pi\) | ||||
0.244102 | + | 0.969750i | \(0.421507\pi\) | |||||||
\(674\) | 2.33316e6 | − | 4.04115e6i | 0.197831 | − | 0.342654i | ||||
\(675\) | 227812. | + | 394583.i | 0.0192450 | + | 0.0333333i | ||||
\(676\) | 1.39264e6 | + | 2.41212e6i | 0.117212 | + | 0.203017i | ||||
\(677\) | −223788. | + | 387612.i | −0.0187657 | + | 0.0325031i | −0.875256 | − | 0.483660i | \(-0.839307\pi\) |
0.856490 | + | 0.516164i | \(0.172640\pi\) | |||||||
\(678\) | −1.38327e6 | −0.115567 | ||||||||
\(679\) | −4.72512e6 | + | 967127.i | −0.393313 | + | 0.0805025i | ||||
\(680\) | 1.39266e6 | 0.115498 | ||||||||
\(681\) | 3.43979e6 | − | 5.95788e6i | 0.284226 | − | 0.492294i | ||||
\(682\) | 6.54885e6 | + | 1.13429e7i | 0.539143 | + | 0.933823i | ||||
\(683\) | −8.57813e6 | − | 1.48578e7i | −0.703624 | − | 1.21871i | −0.967186 | − | 0.254071i | \(-0.918230\pi\) |
0.263561 | − | 0.964643i | \(-0.415103\pi\) | |||||||
\(684\) | −170685. | + | 295634.i | −0.0139493 | + | 0.0241610i | ||||
\(685\) | 3.01251e6 | 0.245302 | ||||||||
\(686\) | −714478. | − | 8.68623e6i | −0.0579667 | − | 0.704727i | ||||
\(687\) | 6.37344e6 | 0.515207 | ||||||||
\(688\) | 2.03124e6 | − | 3.51822e6i | 0.163603 | − | 0.283368i | ||||
\(689\) | 7.16743e6 | + | 1.24143e7i | 0.575195 | + | 0.996267i | ||||
\(690\) | 1.90141e6 | + | 3.29333e6i | 0.152038 | + | 0.263338i | ||||
\(691\) | 9.83358e6 | − | 1.70323e7i | 0.783460 | − | 1.35699i | −0.146455 | − | 0.989217i | \(-0.546786\pi\) |
0.929915 | − | 0.367775i | \(-0.119880\pi\) | |||||||
\(692\) | 6.02988e6 | 0.478678 | ||||||||
\(693\) | 3.86993e6 | − | 792089.i | 0.306105 | − | 0.0626528i | ||||
\(694\) | 8.74492e6 | 0.689219 | ||||||||
\(695\) | 983618. | − | 1.70368e6i | 0.0772440 | − | 0.133790i | ||||
\(696\) | −2.10002e6 | − | 3.63734e6i | −0.164324 | − | 0.284617i | ||||
\(697\) | 4.65587e6 | + | 8.06420e6i | 0.363010 | + | 0.628752i | ||||
\(698\) | −977887. | + | 1.69375e6i | −0.0759714 | + | 0.131586i | ||||
\(699\) | −1.14458e7 | −0.886040 | ||||||||
\(700\) | 409913. | − | 1.22991e6i | 0.0316189 | − | 0.0948696i | ||||
\(701\) | −1.37912e7 | −1.06000 | −0.530001 | − | 0.847997i | \(-0.677809\pi\) | ||||
−0.530001 | + | 0.847997i | \(0.677809\pi\) | |||||||
\(702\) | −647479. | + | 1.12147e6i | −0.0495887 | + | 0.0858902i | ||||
\(703\) | 364632. | + | 631562.i | 0.0278270 | + | 0.0481978i | ||||
\(704\) | 770397. | + | 1.33437e6i | 0.0585845 | + | 0.101471i | ||||
\(705\) | −130277. | + | 225646.i | −0.00987176 | + | 0.0170984i | ||||
\(706\) | 3.69957e6 | 0.279344 | ||||||||
\(707\) | 1.41587e7 | + | 1.59657e7i | 1.06531 | + | 1.20126i | ||||
\(708\) | −5.25670e6 | −0.394121 | ||||||||
\(709\) | 1.17884e7 | − | 2.04181e7i | 0.880722 | − | 1.52546i | 0.0301832 | − | 0.999544i | \(-0.490391\pi\) |
0.850539 | − | 0.525912i | \(-0.176276\pi\) | |||||||
\(710\) | 1.88116e6 | + | 3.25827e6i | 0.140049 | + | 0.242572i | ||||
\(711\) | 2.61946e6 | + | 4.53704e6i | 0.194329 | + | 0.336588i | ||||
\(712\) | 716524. | − | 1.24106e6i | 0.0529701 | − | 0.0917469i | ||||
\(713\) | −3.67801e7 | −2.70950 | ||||||||
\(714\) | 2.69535e6 | + | 3.03933e6i | 0.197865 | + | 0.223117i | ||||
\(715\) | −4.17631e6 | −0.305512 | ||||||||
\(716\) | −5.35996e6 | + | 9.28372e6i | −0.390732 | + | 0.676767i | ||||
\(717\) | −1.35004e6 | − | 2.33835e6i | −0.0980732 | − | 0.169868i | ||||
\(718\) | −628790. | − | 1.08910e6i | −0.0455192 | − | 0.0788415i | ||||
\(719\) | −8.38687e6 | + | 1.45265e7i | −0.605031 | + | 1.04794i | 0.387015 | + | 0.922073i | \(0.373506\pi\) |
−0.992047 | + | 0.125872i | \(0.959827\pi\) | |||||||
\(720\) | −518400. | −0.0372678 | ||||||||
\(721\) | 3.48862e6 | − | 1.04673e7i | 0.249928 | − | 0.749888i | ||||
\(722\) | −9.62687e6 | −0.687294 | ||||||||
\(723\) | −254642. | + | 441053.i | −0.0181169 | + | 0.0313794i | ||||
\(724\) | −2.08522e6 | − | 3.61170e6i | −0.147844 | − | 0.256074i | ||||
\(725\) | 2.27867e6 | + | 3.94677e6i | 0.161004 | + | 0.278867i | ||||
\(726\) | −351845. | + | 609413.i | −0.0247748 | + | 0.0429112i | ||||
\(727\) | 58043.8 | 0.00407305 | 0.00203653 | − | 0.999998i | \(-0.499352\pi\) | ||||
0.00203653 | + | 0.999998i | \(0.499352\pi\) | |||||||
\(728\) | 3.60979e6 | − | 738844.i | 0.252437 | − | 0.0516683i | ||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −1.61993e6 | + | 2.80580e6i | −0.112510 | + | 0.194872i | ||||
\(731\) | −6.90634e6 | − | 1.19621e7i | −0.478029 | − | 0.827971i | ||||
\(732\) | −2.98474e6 | − | 5.16973e6i | −0.205887 | − | 0.356607i | ||||
\(733\) | 2.00069e6 | − | 3.46530e6i | 0.137537 | − | 0.238222i | −0.789026 | − | 0.614359i | \(-0.789415\pi\) |
0.926564 | + | 0.376137i | \(0.122748\pi\) | |||||||
\(734\) | −1.19061e7 | −0.815699 | ||||||||
\(735\) | 3.47747e6 | − | 1.48577e6i | 0.237435 | − | 0.101445i | ||||
\(736\) | −4.32676e6 | −0.294420 | ||||||||
\(737\) | −5.65011e6 | + | 9.78628e6i | −0.383167 | + | 0.663665i | ||||
\(738\) | −1.73308e6 | − | 3.00179e6i | −0.117133 | − | 0.202880i | ||||
\(739\) | 5.24156e6 | + | 9.07865e6i | 0.353061 | + | 0.611519i | 0.986784 | − | 0.162041i | \(-0.0518076\pi\) |
−0.633723 | + | 0.773560i | \(0.718474\pi\) | |||||||
\(740\) | −553727. | + | 959084.i | −0.0371721 | + | 0.0643839i | ||||
\(741\) | 1.05276e6 | 0.0704343 | ||||||||
\(742\) | −1.63990e7 | + | 3.35652e6i | −1.09347 | + | 0.223810i | ||||
\(743\) | −1.19520e7 | −0.794269 | −0.397134 | − | 0.917761i | \(-0.629995\pi\) | ||||
−0.397134 | + | 0.917761i | \(0.629995\pi\) | |||||||
\(744\) | 2.50693e6 | − | 4.34214e6i | 0.166039 | − | 0.287588i | ||||
\(745\) | 3.24926e6 | + | 5.62789e6i | 0.214484 | + | 0.371497i | ||||
\(746\) | −7.08667e6 | − | 1.22745e7i | −0.466225 | − | 0.807525i | ||||
\(747\) | 4.26264e6 | − | 7.38310e6i | 0.279497 | − | 0.484102i | ||||
\(748\) | 5.23878e6 | 0.342355 | ||||||||
\(749\) | 2.09342e6 | − | 6.28114e6i | 0.136349 | − | 0.409104i | ||||
\(750\) | 562500. | 0.0365148 | ||||||||
\(751\) | −1.38281e7 | + | 2.39510e7i | −0.894669 | + | 1.54961i | −0.0604551 | + | 0.998171i | \(0.519255\pi\) |
−0.834214 | + | 0.551441i | \(0.814078\pi\) | |||||||
\(752\) | −148226. | − | 256735.i | −0.00955829 | − | 0.0165554i | ||||
\(753\) | 7.48357e6 | + | 1.29619e7i | 0.480974 | + | 0.833071i | ||||
\(754\) | −6.47634e6 | + | 1.12173e7i | −0.414860 | + | 0.718558i | ||||
\(755\) | 7.33950e6 | 0.468597 | ||||||||
\(756\) | −1.00331e6 | − | 1.13135e6i | −0.0638454 | − | 0.0719932i | ||||
\(757\) | −1.38554e7 | −0.878780 | −0.439390 | − | 0.898296i | \(-0.644805\pi\) | ||||
−0.439390 | + | 0.898296i | \(0.644805\pi\) | |||||||
\(758\) | 5.37779e6 | − | 9.31461e6i | 0.339962 | − | 0.588832i | ||||
\(759\) | 7.15253e6 | + | 1.23885e7i | 0.450666 | + | 0.780577i | ||||
\(760\) | 210722. | + | 364981.i | 0.0132335 | + | 0.0229211i | ||||
\(761\) | −6.29999e6 | + | 1.09119e7i | −0.394347 | + | 0.683029i | −0.993018 | − | 0.117967i | \(-0.962362\pi\) |
0.598671 | + | 0.800995i | \(0.295696\pi\) | |||||||
\(762\) | 6.45195e6 | 0.402535 | ||||||||
\(763\) | 2.22382e6 | + | 2.50762e6i | 0.138289 | + | 0.155937i | ||||
\(764\) | −3.87012e6 | −0.239878 | ||||||||
\(765\) | −881295. | + | 1.52645e6i | −0.0544462 | + | 0.0943036i | ||||
\(766\) | −9.22019e6 | − | 1.59698e7i | −0.567764 | − | 0.983396i | ||||
\(767\) | 8.10566e6 | + | 1.40394e7i | 0.497508 | + | 0.861709i | ||||
\(768\) | 294912. | − | 510803.i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | 2.90665e7 | 1.77246 | 0.886230 | − | 0.463245i | \(-0.153315\pi\) | ||||
0.886230 | + | 0.463245i | \(0.153315\pi\) | |||||||
\(770\) | 1.54197e6 | − | 4.62654e6i | 0.0937236 | − | 0.281209i | ||||
\(771\) | 8.77657e6 | 0.531727 | ||||||||
\(772\) | −6.92422e6 | + | 1.19931e7i | −0.418146 | + | 0.724250i | ||||
\(773\) | −8.03098e6 | − | 1.39101e7i | −0.483415 | − | 0.837299i | 0.516404 | − | 0.856345i | \(-0.327270\pi\) |
−0.999819 | + | 0.0190465i | \(0.993937\pi\) | |||||||
\(774\) | 2.57079e6 | + | 4.45274e6i | 0.154246 | + | 0.267162i | ||||
\(775\) | −2.72020e6 | + | 4.71152e6i | −0.162684 | + | 0.281778i | ||||
\(776\) | 2.38100e6 | 0.141940 | ||||||||
\(777\) | −3.16477e6 | + | 647758.i | −0.188057 | + | 0.0384911i | ||||
\(778\) | 1.13571e7 | 0.672698 | ||||||||
\(779\) | −1.40894e6 | + | 2.44036e6i | −0.0831860 | + | 0.144082i | ||||
\(780\) | 799357. | + | 1.38453e6i | 0.0470440 | + | 0.0814826i | ||||
\(781\) | 7.07638e6 | + | 1.22566e7i | 0.415129 | + | 0.719025i | ||||
\(782\) | −7.35561e6 | + | 1.27403e7i | −0.430132 | + | 0.745010i | ||||
\(783\) | 5.31568e6 | 0.309852 | ||||||||
\(784\) | −514304. | + | 4.27174e6i | −0.0298834 | + | 0.248208i | ||||
\(785\) | 9.73913e6 | 0.564087 | ||||||||
\(786\) | 4.24594e6 | − | 7.35419e6i | 0.245142 | − | 0.424598i | ||||
\(787\) | 1.83559e6 | + | 3.17933e6i | 0.105642 | + | 0.182978i | 0.914000 | − | 0.405713i | \(-0.132977\pi\) |
−0.808358 | + | 0.588691i | \(0.799643\pi\) | |||||||
\(788\) | −474675. | − | 822161.i | −0.0272321 | − | 0.0471674i | ||||
\(789\) | −4.84185e6 | + | 8.38634e6i | −0.276898 | + | 0.479601i | ||||
\(790\) | 6.46781e6 | 0.368714 | ||||||||
\(791\) | −4.88020e6 | + | 998869.i | −0.277330 | + | 0.0567633i | ||||
\(792\) | −1.95007e6 | −0.110468 | ||||||||
\(793\) | −9.20476e6 | + | 1.59431e7i | −0.519792 | + | 0.900306i | ||||
\(794\) | −595449. | − | 1.03135e6i | −0.0335192 | − | 0.0580569i | ||||
\(795\) | −3.63143e6 | − | 6.28982e6i | −0.203779 | − | 0.352956i | ||||
\(796\) | −7.26579e6 | + | 1.25847e7i | −0.406443 | + | 0.703981i | ||||
\(797\) | −2.53970e7 | −1.41624 | −0.708121 | − | 0.706092i | \(-0.750457\pi\) | ||||
−0.708121 | + | 0.706092i | \(0.750457\pi\) | |||||||
\(798\) | −388699. | + | 1.16626e6i | −0.0216076 | + | 0.0648316i | ||||
\(799\) | −1.00795e6 | −0.0558565 | ||||||||
\(800\) | −320000. | + | 554256.i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | 906851. | + | 1.57071e6i | 0.0499407 | + | 0.0864998i | ||||
\(802\) | 9.15437e6 | + | 1.58558e7i | 0.502565 | + | 0.870468i | ||||
\(803\) | −6.09370e6 | + | 1.05546e7i | −0.333497 | + | 0.577634i | ||||
\(804\) | 4.32578e6 | 0.236007 | ||||||||
\(805\) | 9.08634e6 | + | 1.02459e7i | 0.494196 | + | 0.557265i | ||||
\(806\) | −1.54625e7 | −0.838380 | ||||||||
\(807\) | 6.64271e6 | − | 1.15055e7i | 0.359055 | − | 0.621902i | ||||
\(808\) | −5.26730e6 | − | 9.12323e6i | −0.283831 | − | 0.491610i | ||||
\(809\) | 4.93977e6 | + | 8.55593e6i | 0.265360 | + | 0.459617i | 0.967658 | − | 0.252266i | \(-0.0811758\pi\) |
−0.702298 | + | 0.711883i | \(0.747843\pi\) | |||||||
\(810\) | 328050. | − | 568199.i | 0.0175682 | − | 0.0304290i | ||||
\(811\) | 1.11209e7 | 0.593726 | 0.296863 | − | 0.954920i | \(-0.404059\pi\) | ||||
0.296863 | + | 0.954920i | \(0.404059\pi\) | |||||||
\(812\) | −1.00355e7 | − | 1.13162e7i | −0.534131 | − | 0.602296i | ||||
\(813\) | −1.19391e7 | −0.633500 | ||||||||
\(814\) | −2.08296e6 | + | 3.60779e6i | −0.110184 | + | 0.190845i | ||||
\(815\) | 2.90166e6 | + | 5.02582e6i | 0.153021 | + | 0.265041i | ||||
\(816\) | −1.00272e6 | − | 1.73676e6i | −0.0527173 | − | 0.0913090i | ||||
\(817\) | 2.08997e6 | − | 3.61994e6i | 0.109543 | − | 0.189735i | ||||
\(818\) | −1.47263e7 | −0.769502 | ||||||||
\(819\) | −1.47450e6 | + | 4.42411e6i | −0.0768130 | + | 0.230471i | ||||
\(820\) | −4.27922e6 | −0.222244 | ||||||||
\(821\) | −1.29397e7 | + | 2.24122e7i | −0.669986 | + | 1.16045i | 0.307922 | + | 0.951412i | \(0.400366\pi\) |
−0.977908 | + | 0.209038i | \(0.932967\pi\) | |||||||
\(822\) | −2.16901e6 | − | 3.75683e6i | −0.111965 | − | 0.193929i | ||||
\(823\) | −1.47239e7 | − | 2.55026e7i | −0.757747 | − | 1.31246i | −0.943997 | − | 0.329953i | \(-0.892967\pi\) |
0.186251 | − | 0.982502i | \(-0.440366\pi\) | |||||||
\(824\) | −2.72340e6 | + | 4.71707e6i | −0.139731 | + | 0.242022i | ||||
\(825\) | 2.11596e6 | 0.108236 | ||||||||
\(826\) | −1.85457e7 | + | 3.79590e6i | −0.945788 | + | 0.193582i | ||||
\(827\) | −2.61824e7 | −1.33121 | −0.665605 | − | 0.746304i | \(-0.731826\pi\) | ||||
−0.665605 | + | 0.746304i | \(0.731826\pi\) | |||||||
\(828\) | 2.73803e6 | − | 4.74240e6i | 0.138791 | − | 0.240393i | ||||
\(829\) | 1.79483e7 | + | 3.10874e7i | 0.907063 | + | 1.57108i | 0.818123 | + | 0.575043i | \(0.195015\pi\) |
0.0889398 | + | 0.996037i | \(0.471652\pi\) | |||||||
\(830\) | −5.26251e6 | − | 9.11494e6i | −0.265154 | − | 0.459260i | ||||
\(831\) | 6.70742e6 | − | 1.16176e7i | 0.336940 | − | 0.583598i | ||||
\(832\) | −1.81898e6 | −0.0911003 | ||||||||
\(833\) | 1.17040e7 | + | 8.77647e6i | 0.584414 | + | 0.438235i | ||||
\(834\) | −2.83282e6 | −0.141028 | ||||||||
\(835\) | −7.73836e6 | + | 1.34032e7i | −0.384090 | + | 0.665263i | ||||
\(836\) | 792672. | + | 1.37295e6i | 0.0392263 | + | 0.0679420i | ||||
\(837\) | 3.17284e6 | + | 5.49552e6i | 0.156543 | + | 0.271141i | ||||
\(838\) | 3.00124e6 | − | 5.19829e6i | 0.147635 | − | 0.255712i | ||||
\(839\) | 1.26587e7 | 0.620845 | 0.310422 | − | 0.950599i | \(-0.399530\pi\) | ||||
0.310422 | + | 0.950599i | \(0.399530\pi\) | |||||||
\(840\) | −1.82893e6 | + | 374340.i | −0.0894330 | + | 0.0183050i | ||||
\(841\) | 3.26583e7 | 1.59222 | ||||||||
\(842\) | 5.97637e6 | − | 1.03514e7i | 0.290507 | − | 0.503173i | ||||
\(843\) | −4.54300e6 | − | 7.86871e6i | −0.220178 | − | 0.381360i | ||||
\(844\) | 3.11933e6 | + | 5.40283e6i | 0.150732 | + | 0.261075i | ||||
\(845\) | −2.17599e6 | + | 3.76893e6i | −0.104837 | + | 0.181584i | ||||
\(846\) | 375197. | 0.0180233 | ||||||||
\(847\) | −801254. | + | 2.40409e6i | −0.0383762 | + | 0.115144i | ||||
\(848\) | 8.26352e6 | 0.394617 | ||||||||
\(849\) | −4.47372e6 | + | 7.74871e6i | −0.213010 | + | 0.368944i | ||||
\(850\) | 1.08802e6 | + | 1.88450e6i | 0.0516522 | + | 0.0894642i | ||||
\(851\) | −5.84923e6 | − | 1.01312e7i | −0.276869 | − | 0.479551i | ||||
\(852\) | 2.70887e6 | − | 4.69191e6i | 0.127847 | − | 0.221437i | ||||
\(853\) | 1.53972e6 | 0.0724552 | 0.0362276 | − | 0.999344i | \(-0.488466\pi\) | ||||
0.0362276 | + | 0.999344i | \(0.488466\pi\) | |||||||
\(854\) | −1.42633e7 | − | 1.60836e7i | −0.669231 | − | 0.754637i | ||||
\(855\) | −533389. | −0.0249533 | ||||||||
\(856\) | −1.63424e6 | + | 2.83059e6i | −0.0762310 | + | 0.132036i | ||||
\(857\) | 6.19178e6 | + | 1.07245e7i | 0.287981 | + | 0.498798i | 0.973328 | − | 0.229419i | \(-0.0736827\pi\) |
−0.685347 | + | 0.728217i | \(0.740349\pi\) | |||||||
\(858\) | 3.00694e6 | + | 5.20818e6i | 0.139446 | + | 0.241528i | ||||
\(859\) | 1.67108e7 | − | 2.89439e7i | 0.772705 | − | 1.33836i | −0.163370 | − | 0.986565i | \(-0.552237\pi\) |
0.936075 | − | 0.351799i | \(-0.114430\pi\) | |||||||
\(860\) | 6.34763e6 | 0.292662 | ||||||||
\(861\) | −8.28197e6 | − | 9.33890e6i | −0.380738 | − | 0.429327i | ||||
\(862\) | 1.21215e7 | 0.555633 | ||||||||
\(863\) | −1.73246e7 | + | 3.00071e7i | −0.791838 | + | 1.37150i | 0.132990 | + | 0.991117i | \(0.457542\pi\) |
−0.924828 | + | 0.380386i | \(0.875791\pi\) | |||||||
\(864\) | 373248. | + | 646484.i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 4.71085e6 | + | 8.15942e6i | 0.214071 | + | 0.370783i | ||||
\(866\) | −2.83618e6 | + | 4.91241e6i | −0.128511 | + | 0.222587i | ||||
\(867\) | 5.96012e6 | 0.269282 | ||||||||
\(868\) | 5.70902e6 | − | 1.71294e7i | 0.257195 | − | 0.771691i | ||||
\(869\) | 2.43300e7 | 1.09293 | ||||||||
\(870\) | 3.28128e6 | − | 5.68335e6i | 0.146976 | − | 0.254569i | ||||
\(871\) | −6.67023e6 | − | 1.15532e7i | −0.297917 | − | 0.516007i | ||||
\(872\) | −827299. | − | 1.43292e6i | −0.0368444 | − | 0.0638163i | ||||
\(873\) | −1.50673e6 | + | 2.60973e6i | −0.0669112 | + | 0.115894i | ||||
\(874\) | −4.45186e6 | −0.197135 | ||||||||
\(875\) | 1.98451e6 | − | 406185.i | 0.0876261 | − | 0.0179351i | ||||
\(876\) | 4.66540e6 | 0.205414 | ||||||||
\(877\) | 1.83963e7 | − | 3.18634e7i | 0.807666 | − | 1.39892i | −0.106810 | − | 0.994279i | \(-0.534064\pi\) |
0.914476 | − | 0.404640i | \(-0.132603\pi\) | |||||||
\(878\) | −7.44075e6 | − | 1.28878e7i | −0.325747 | − | 0.564210i | ||||
\(879\) | 7.63837e6 | + | 1.32300e7i | 0.333448 | + | 0.577549i | ||||
\(880\) | −1.20374e6 | + | 2.08495e6i | −0.0523996 | + | 0.0907587i | ||||
\(881\) | −1.37404e7 | −0.596432 | −0.298216 | − | 0.954498i | \(-0.596392\pi\) | ||||
−0.298216 | + | 0.954498i | \(0.596392\pi\) | |||||||
\(882\) | −4.35664e6 | − | 3.26692e6i | −0.188573 | − | 0.141406i | ||||
\(883\) | −6.26276e6 | −0.270311 | −0.135156 | − | 0.990824i | \(-0.543153\pi\) | ||||
−0.135156 | + | 0.990824i | \(0.543153\pi\) | |||||||
\(884\) | −3.09232e6 | + | 5.35605e6i | −0.133093 | + | 0.230523i | ||||
\(885\) | −4.10679e6 | − | 7.11318e6i | −0.176256 | − | 0.305285i | ||||
\(886\) | 1.60174e6 | + | 2.77430e6i | 0.0685502 | + | 0.118732i | ||||
\(887\) | 2.22623e7 | − | 3.85594e7i | 0.950082 | − | 1.64559i | 0.204841 | − | 0.978795i | \(-0.434332\pi\) |
0.745241 | − | 0.666795i | \(-0.232334\pi\) | |||||||
\(888\) | 1.59473e6 | 0.0678666 | ||||||||
\(889\) | 2.27626e7 | − | 4.65900e6i | 0.965978 | − | 0.197714i | ||||
\(890\) | 2.23914e6 | 0.0947558 | ||||||||
\(891\) | 1.23403e6 | − | 2.13740e6i | 0.0520751 | − | 0.0901967i | ||||
\(892\) | −3.45985e6 | − | 5.99264e6i | −0.145595 | − | 0.252178i | ||||
\(893\) | −152512. | − | 264158.i | −0.00639993 | − | 0.0110850i | ||||
\(894\) | 4.67894e6 | − | 8.10416e6i | 0.195796 | − | 0.339128i | ||||
\(895\) | −1.67499e7 | −0.698962 | ||||||||
\(896\) | 671601. | − | 2.01508e6i | 0.0279474 | − | 0.0838537i | ||||
\(897\) | −1.68878e7 | −0.700797 | ||||||||
\(898\) | −7.78767e6 | + | 1.34886e7i | −0.322268 | + | 0.558184i | ||||
\(899\) | 3.17360e7 | + | 5.49683e7i | 1.30964 | + | 2.26837i | ||||
\(900\) | −405000. | − | 701481.i | −0.0166667 | − | 0.0288675i | ||||
\(901\) | 1.40482e7 | − | 2.43322e7i | 0.576513 | − | 0.998550i | ||||
\(902\) | −1.60972e7 | −0.658769 | ||||||||
\(903\) | 1.22852e7 | + | 1.38530e7i | 0.501374 | + | 0.565358i | ||||
\(904\) | 2.45915e6 | 0.100084 | ||||||||
\(905\) | 3.25815e6 | − | 5.64328e6i | 0.132236 | − | 0.229039i | ||||
\(906\) | −5.28444e6 | − | 9.15292e6i | −0.213884 | − | 0.370458i | ||||
\(907\) | 1.39004e7 | + | 2.40762e7i | 0.561060 | + | 0.971784i | 0.997404 | + | 0.0720046i | \(0.0229396\pi\) |
−0.436344 | + | 0.899780i | \(0.643727\pi\) | |||||||
\(908\) | −6.11518e6 | + | 1.05918e7i | −0.246147 | + | 0.426339i | ||||
\(909\) | 1.33329e7 | 0.535197 | ||||||||
\(910\) | 3.81992e6 | + | 4.30742e6i | 0.152915 | + | 0.172430i | ||||
\(911\) | 1.67045e7 | 0.666864 | 0.333432 | − | 0.942774i | \(-0.391793\pi\) | ||||
0.333432 | + | 0.942774i | \(0.391793\pi\) | |||||||
\(912\) | 303439. | − | 525572.i | 0.0120805 | − | 0.0209240i | ||||
\(913\) | −1.97960e7 | − | 3.42877e7i | −0.785960 | − | 1.36132i | ||||
\(914\) | 6.45355e6 | + | 1.11779e7i | 0.255525 | + | 0.442582i | ||||
\(915\) | 4.66366e6 | − | 8.07770e6i | 0.184151 | − | 0.318959i | ||||
\(916\) | −1.13306e7 | −0.446183 | ||||||||
\(917\) | 9.66925e6 | − | 2.90117e7i | 0.379725 | − | 1.13933i | ||||
\(918\) | 2.53813e6 | 0.0994047 | ||||||||
\(919\) | 1.08291e7 | − | 1.87565e7i | 0.422963 | − | 0.732593i | −0.573265 | − | 0.819370i | \(-0.694323\pi\) |
0.996228 | + | 0.0867770i | \(0.0276568\pi\) | |||||||
\(920\) | −3.38028e6 | − | 5.85481e6i | −0.131669 | − | 0.228057i | ||||
\(921\) | 1.32886e7 | + | 2.30166e7i | 0.516215 | + | 0.894111i | ||||
\(922\) | −8.21664e6 | + | 1.42316e7i | −0.318322 | + | 0.551350i | ||||
\(923\) | −1.67080e7 | −0.645536 | ||||||||
\(924\) | −6.87987e6 | + | 1.40816e6i | −0.265094 | + | 0.0542589i | ||||
\(925\) | −1.73040e6 | −0.0664954 | ||||||||
\(926\) | 2.96563e6 | − | 5.13662e6i | 0.113655 | − | 0.196856i | ||||
\(927\) | −3.44681e6 | − | 5.97005e6i | −0.131740 | − | 0.228180i | ||||
\(928\) | 3.73337e6 | + | 6.46639e6i | 0.142309 | + | 0.246486i | ||||
\(929\) | −1.15385e7 | + | 1.99853e7i | −0.438642 | + | 0.759750i | −0.997585 | − | 0.0694559i | \(-0.977874\pi\) |
0.558943 | + | 0.829206i | \(0.311207\pi\) | |||||||
\(930\) | 7.83417e6 | 0.297020 | ||||||||
\(931\) | −529175. | + | 4.39526e6i | −0.0200090 | + | 0.166192i | ||||
\(932\) | 2.03481e7 | 0.767333 | ||||||||
\(933\) | −9.54641e6 | + | 1.65349e7i | −0.359034 | + | 0.621866i | ||||
\(934\) | 4.57726e6 | + | 7.92804e6i | 0.171687 | + | 0.297371i | ||||
\(935\) | 4.09280e6 | + | 7.08894e6i | 0.153106 | + | 0.265187i | ||||
\(936\) | 1.15107e6 | − | 1.99372e6i | 0.0429451 | − | 0.0743831i | ||||
\(937\) | 2.57761e7 | 0.959110 | 0.479555 | − | 0.877512i | \(-0.340798\pi\) | ||||
0.479555 | + | 0.877512i | \(0.340798\pi\) | |||||||
\(938\) | 1.52615e7 | − | 3.12368e6i | 0.566355 | − | 0.115920i | ||||
\(939\) | −3.46515e6 | −0.128250 | ||||||||
\(940\) | 231603. | − | 401149.i | 0.00854919 | − | 0.0148076i | ||||
\(941\) | −1.53396e7 | − | 2.65690e7i | −0.564729 | − | 0.978139i | −0.997075 | − | 0.0764314i | \(-0.975647\pi\) |
0.432346 | − | 0.901708i | \(-0.357686\pi\) | |||||||
\(942\) | −7.01218e6 | − | 1.21454e7i | −0.257469 | − | 0.445950i | ||||
\(943\) | 2.26015e7 | − | 3.91469e7i | 0.827672 | − | 1.43357i | ||||
\(944\) | 9.34524e6 | 0.341319 | ||||||||
\(945\) | 747066. | − | 2.24151e6i | 0.0272132 | − | 0.0816508i | ||||
\(946\) | 2.38779e7 | 0.867498 | ||||||||
\(947\) | 1.42412e7 | − | 2.46666e7i | 0.516028 | − | 0.893786i | −0.483799 | − | 0.875179i | \(-0.660743\pi\) |
0.999827 | − | 0.0186072i | \(-0.00592319\pi\) | |||||||
\(948\) | −4.65682e6 | − | 8.06585e6i | −0.168294 | − | 0.291494i | ||||
\(949\) | −7.19391e6 | − | 1.24602e7i | −0.259298 | − | 0.449118i | ||||
\(950\) | −329253. | + | 570282.i | −0.0118364 | + | 0.0205013i | ||||
\(951\) | −9.09161e6 | −0.325979 | ||||||||
\(952\) | −4.79173e6 | − | 5.40325e6i | −0.171356 | − | 0.193225i | ||||
\(953\) | −2.00240e7 | −0.714199 | −0.357100 | − | 0.934066i | \(-0.616234\pi\) | ||||
−0.357100 | + | 0.934066i | \(0.616234\pi\) | |||||||
\(954\) | −5.22926e6 | + | 9.05734e6i | −0.186024 | + | 0.322203i | ||||
\(955\) | −3.02353e6 | − | 5.23690e6i | −0.107277 | − | 0.185809i | ||||
\(956\) | 2.40008e6 | + | 4.15706e6i | 0.0849339 | + | 0.147110i | ||||
\(957\) | 1.23432e7 | − | 2.13791e7i | 0.435661 | − | 0.754586i | ||||
\(958\) | 2.01850e6 | 0.0710583 | ||||||||
\(959\) | −1.03651e7 | − | 1.16879e7i | −0.363939 | − | 0.410384i | ||||
\(960\) | 921600. | 0.0322749 | ||||||||
\(961\) | −2.35707e7 | + | 4.08257e7i | −0.823312 | + | 1.42602i | ||||
\(962\) | −2.45903e6 | − | 4.25917e6i | −0.0856696 | − | 0.148384i | ||||
\(963\) | −2.06833e6 | − | 3.58246e6i | −0.0718712 | − | 0.124485i | ||||
\(964\) | 452697. | − | 784094.i | 0.0156897 | − | 0.0271754i | ||||
\(965\) | −2.16382e7 | −0.748002 | ||||||||
\(966\) | 6.23529e6 | − | 1.87084e7i | 0.214988 | − | 0.645052i | ||||
\(967\) | 1.74233e7 | 0.599189 | 0.299595 | − | 0.954067i | \(-0.403149\pi\) | ||||
0.299595 | + | 0.954067i | \(0.403149\pi\) | |||||||
\(968\) | 625502. | − | 1.08340e6i | 0.0214556 | − | 0.0371622i | ||||
\(969\) | −1.03171e6 | − | 1.78697e6i | −0.0352978 | − | 0.0611377i | ||||
\(970\) | 1.86016e6 | + | 3.22189e6i | 0.0634775 | + | 0.109946i | ||||
\(971\) | 5.62603e6 | − | 9.74456e6i | 0.191493 | − | 0.331676i | −0.754252 | − | 0.656585i | \(-0.772000\pi\) |
0.945745 | + | 0.324909i | \(0.105334\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | −9.99425e6 | + | 2.04560e6i | −0.338429 | + | 0.0692690i | ||||
\(974\) | −5.91623e6 | −0.199824 | ||||||||
\(975\) | −1.24900e6 | + | 2.16332e6i | −0.0420774 | + | 0.0728803i | ||||
\(976\) | 5.30621e6 | + | 9.19062e6i | 0.178303 | + | 0.308831i | ||||
\(977\) | −2.22637e7 | − | 3.85618e7i | −0.746208 | − | 1.29247i | −0.949628 | − | 0.313379i | \(-0.898539\pi\) |
0.203420 | − | 0.979092i | \(-0.434794\pi\) | |||||||
\(978\) | 4.17839e6 | − | 7.23718e6i | 0.139689 | − | 0.241948i | ||||
\(979\) | 8.42297e6 | 0.280872 | ||||||||
\(980\) | −6.18217e6 | + | 2.64136e6i | −0.205625 | + | 0.0878542i | ||||
\(981\) | 2.09410e6 | 0.0694744 | ||||||||
\(982\) | −1.50332e7 | + | 2.60383e7i | −0.497477 | + | 0.861656i | ||||
\(983\) | 9.94307e6 | + | 1.72219e7i | 0.328199 | + | 0.568457i | 0.982154 | − | 0.188076i | \(-0.0602251\pi\) |
−0.653956 | + | 0.756533i | \(0.726892\pi\) | |||||||
\(984\) | 3.08104e6 | + | 5.33652e6i | 0.101440 | + | 0.175699i | ||||
\(985\) | 741680. | − | 1.28463e6i | 0.0243571 | − | 0.0421878i | ||||
\(986\) | 2.53873e7 | 0.831620 | ||||||||
\(987\) | 1.32370e6 | − | 270933.i | 0.0432512 | − | 0.00885256i | ||||
\(988\) | −1.87158e6 | −0.0609979 | ||||||||
\(989\) | −3.35262e7 | + | 5.80691e7i | −1.08992 | + | 1.88779i | ||||
\(990\) | −1.52349e6 | − | 2.63876e6i | −0.0494028 | − | 0.0855681i | ||||
\(991\) | −2.46286e6 | − | 4.26580e6i | −0.0796628 | − | 0.137980i | 0.823442 | − | 0.567401i | \(-0.192051\pi\) |
−0.903104 | + | 0.429421i | \(0.858718\pi\) | |||||||
\(992\) | −4.45677e6 | + | 7.71935e6i | −0.143794 | + | 0.249059i | ||||
\(993\) | −3.20960e7 | −1.03295 | ||||||||
\(994\) | 6.16890e6 | − | 1.85092e7i | 0.198035 | − | 0.594187i | ||||
\(995\) | −2.27056e7 | −0.727068 | ||||||||
\(996\) | −7.57802e6 | + | 1.31255e7i | −0.242051 | + | 0.419245i | ||||
\(997\) | 5.96238e6 | + | 1.03271e7i | 0.189968 | + | 0.329035i | 0.945239 | − | 0.326378i | \(-0.105828\pi\) |
−0.755271 | + | 0.655413i | \(0.772495\pi\) | |||||||
\(998\) | −4.86070e6 | − | 8.41898e6i | −0.154480 | − | 0.267567i | ||||
\(999\) | −1.00917e6 | + | 1.74793e6i | −0.0319926 | + | 0.0554128i |
(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 | 210.6.i.b.121.1 | ✓ | 4 | |
7.4 | even | 3 | inner | 210.6.i.b.151.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.6.i.b.121.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
210.6.i.b.151.1 | yes | 4 | 7.4 | even | 3 | inner |