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 | 107.13 | ||
Root | \(-1.73205 + 0.353400i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.107 |
Dual form | 108.6.b.b.107.14 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.08799 | − | 2.47231i | 0.899439 | − | 0.437047i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 19.7753 | − | 25.1582i | 0.617979 | − | 0.786194i | ||||
\(5\) | − | 33.1536i | − | 0.593069i | −0.955022 | − | 0.296535i | \(-0.904169\pi\) | ||
0.955022 | − | 0.296535i | \(-0.0958310\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 59.4073i | − | 0.458242i | −0.973398 | − | 0.229121i | \(-0.926415\pi\) | ||
0.973398 | − | 0.229121i | \(-0.0735851\pi\) | |||||||
\(8\) | 38.4178 | − | 176.896i | 0.212231 | − | 0.977220i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −81.9660 | − | 168.685i | −0.259199 | − | 0.533430i | ||||
\(11\) | −179.135 | −0.446374 | −0.223187 | − | 0.974776i | \(-0.571646\pi\) | ||||
−0.223187 | + | 0.974776i | \(0.571646\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −143.222 | −0.235045 | −0.117522 | − | 0.993070i | \(-0.537495\pi\) | ||||
−0.117522 | + | 0.993070i | \(0.537495\pi\) | |||||||
\(14\) | −146.873 | − | 302.264i | −0.200273 | − | 0.412160i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −241.872 | − | 995.025i | −0.236203 | − | 0.971704i | ||||
\(17\) | 93.8221i | 0.0787377i | 0.999225 | + | 0.0393689i | \(0.0125347\pi\) | ||||
−0.999225 | + | 0.0393689i | \(0.987465\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1617.39i | − | 1.02785i | −0.857835 | − | 0.513925i | \(-0.828191\pi\) | ||
0.857835 | − | 0.513925i | \(-0.171809\pi\) | |||||||
\(20\) | −834.085 | − | 655.624i | −0.466268 | − | 0.366505i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −911.438 | + | 442.878i | −0.401486 | + | 0.195087i | ||||
\(23\) | −2414.48 | −0.951708 | −0.475854 | − | 0.879524i | \(-0.657861\pi\) | ||||
−0.475854 | + | 0.879524i | \(0.657861\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2025.84 | 0.648269 | ||||||||
\(26\) | −728.711 | + | 354.089i | −0.211408 | + | 0.102726i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1494.58 | − | 1174.80i | −0.360267 | − | 0.283184i | ||||
\(29\) | − | 7910.14i | − | 1.74658i | −0.487198 | − | 0.873291i | \(-0.661981\pi\) | ||
0.487198 | − | 0.873291i | \(-0.338019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4726.80i | 0.883412i | 0.897160 | + | 0.441706i | \(0.145627\pi\) | ||||
−0.897160 | + | 0.441706i | \(0.854373\pi\) | |||||||
\(32\) | −3690.65 | − | 4464.70i | −0.637130 | − | 0.770756i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 231.958 | + | 477.366i | 0.0344121 | + | 0.0708198i | ||||
\(35\) | −1969.56 | −0.271769 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9387.10 | 1.12727 | 0.563634 | − | 0.826025i | \(-0.309403\pi\) | ||||
0.563634 | + | 0.826025i | \(0.309403\pi\) | |||||||
\(38\) | −3998.68 | − | 8229.25i | −0.449219 | − | 0.924488i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5864.73 | − | 1273.69i | −0.579559 | − | 0.125867i | ||||
\(41\) | − | 11838.5i | − | 1.09986i | −0.835212 | − | 0.549928i | \(-0.814655\pi\) | ||
0.835212 | − | 0.549928i | \(-0.185345\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19531.8i | 1.61091i | 0.592659 | + | 0.805454i | \(0.298078\pi\) | ||||
−0.592659 | + | 0.805454i | \(0.701922\pi\) | |||||||
\(44\) | −3542.46 | + | 4506.72i | −0.275850 | + | 0.350937i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12284.8 | + | 5969.34i | −0.856003 | + | 0.415941i | ||||
\(47\) | −7373.21 | −0.486869 | −0.243435 | − | 0.969917i | \(-0.578274\pi\) | ||||
−0.243435 | + | 0.969917i | \(0.578274\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13277.8 | 0.790015 | ||||||||
\(50\) | 10307.5 | − | 5008.51i | 0.583078 | − | 0.283324i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2832.26 | + | 3603.20i | −0.145253 | + | 0.184791i | ||||
\(53\) | 26895.4i | 1.31519i | 0.753372 | + | 0.657594i | \(0.228426\pi\) | ||||
−0.753372 | + | 0.657594i | \(0.771574\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5938.97i | 0.264731i | ||||||||
\(56\) | −10508.9 | − | 2282.30i | −0.447803 | − | 0.0972529i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −19556.3 | − | 40246.7i | −0.763339 | − | 1.57094i | ||||
\(59\) | −6144.64 | −0.229809 | −0.114904 | − | 0.993377i | \(-0.536656\pi\) | ||||
−0.114904 | + | 0.993377i | \(0.536656\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 55252.3 | 1.90119 | 0.950596 | − | 0.310430i | \(-0.100473\pi\) | ||||
0.950596 | + | 0.310430i | \(0.100473\pi\) | |||||||
\(62\) | 11686.1 | + | 24049.9i | 0.386093 | + | 0.794575i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −29816.1 | − | 13591.9i | −0.909916 | − | 0.414792i | ||||
\(65\) | 4748.31i | 0.139398i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 38888.6i | − | 1.05836i | −0.848509 | − | 0.529182i | \(-0.822499\pi\) | ||
0.848509 | − | 0.529182i | \(-0.177501\pi\) | |||||||
\(68\) | 2360.40 | + | 1855.36i | 0.0619032 | + | 0.0486583i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −10021.1 | + | 4869.38i | −0.244440 | + | 0.118776i | ||||
\(71\) | 45277.6 | 1.06595 | 0.532976 | − | 0.846131i | \(-0.321074\pi\) | ||||
0.532976 | + | 0.846131i | \(0.321074\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 21000.4 | 0.461233 | 0.230617 | − | 0.973045i | \(-0.425926\pi\) | ||||
0.230617 | + | 0.973045i | \(0.425926\pi\) | |||||||
\(74\) | 47761.5 | − | 23207.8i | 1.01391 | − | 0.492669i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −40690.5 | − | 31984.4i | −0.808090 | − | 0.635190i | ||||
\(77\) | 10641.9i | 0.204547i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 76460.5i | 1.37838i | 0.724580 | + | 0.689191i | \(0.242034\pi\) | ||||
−0.724580 | + | 0.689191i | \(0.757966\pi\) | |||||||
\(80\) | −32988.6 | + | 8018.91i | −0.576288 | + | 0.140085i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −29268.4 | − | 60234.0i | −0.480689 | − | 0.989253i | ||||
\(83\) | 58515.8 | 0.932347 | 0.466174 | − | 0.884693i | \(-0.345632\pi\) | ||||
0.466174 | + | 0.884693i | \(0.345632\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3110.54 | 0.0466969 | ||||||||
\(86\) | 48288.6 | + | 99377.5i | 0.704042 | + | 1.44891i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6881.99 | + | 31688.2i | −0.0947343 | + | 0.436206i | ||||
\(89\) | 18558.5i | 0.248352i | 0.992260 | + | 0.124176i | \(0.0396287\pi\) | ||||
−0.992260 | + | 0.124176i | \(0.960371\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8508.41i | 0.107707i | ||||||||
\(92\) | −47747.1 | + | 60744.0i | −0.588136 | + | 0.748227i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −37514.9 | + | 18228.9i | −0.437909 | + | 0.212785i | ||||
\(95\) | −53622.2 | −0.609586 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 137248. | 1.48107 | 0.740536 | − | 0.672017i | \(-0.234572\pi\) | ||||
0.740536 | + | 0.672017i | \(0.234572\pi\) | |||||||
\(98\) | 67557.2 | − | 32826.8i | 0.710570 | − | 0.345274i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 40061.7 | − | 50966.5i | 0.400617 | − | 0.509665i | ||||
\(101\) | 97319.1i | 0.949280i | 0.880180 | + | 0.474640i | \(0.157422\pi\) | ||||
−0.880180 | + | 0.474640i | \(0.842578\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 38694.4i | 0.359381i | 0.983723 | + | 0.179690i | \(0.0575096\pi\) | ||||
−0.983723 | + | 0.179690i | \(0.942490\pi\) | |||||||
\(104\) | −5502.27 | + | 25335.3i | −0.0498837 | + | 0.229690i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 66493.8 | + | 136844.i | 0.574799 | + | 1.18293i | ||||
\(107\) | 42882.4 | 0.362093 | 0.181046 | − | 0.983475i | \(-0.442052\pi\) | ||||
0.181046 | + | 0.983475i | \(0.442052\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −41832.7 | −0.337248 | −0.168624 | − | 0.985680i | \(-0.553932\pi\) | ||||
−0.168624 | + | 0.985680i | \(0.553932\pi\) | |||||||
\(110\) | 14683.0 | + | 30217.5i | 0.115700 | + | 0.238109i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −59111.7 | + | 14368.9i | −0.445275 | + | 0.108238i | ||||
\(113\) | − | 30797.2i | − | 0.226890i | −0.993544 | − | 0.113445i | \(-0.963811\pi\) | ||
0.993544 | − | 0.113445i | \(-0.0361885\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 80048.6i | 0.564429i | ||||||||
\(116\) | −199005. | − | 156426.i | −1.37315 | − | 1.07935i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −31263.9 | + | 15191.5i | −0.206699 | + | 0.100437i | ||||
\(119\) | 5573.72 | 0.0360809 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −128962. | −0.800750 | ||||||||
\(122\) | 281123. | − | 136601.i | 1.71001 | − | 0.830911i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 118918. | + | 93474.2i | 0.694534 | + | 0.545931i | ||||
\(125\) | − | 170769.i | − | 0.977538i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 77161.9i | − | 0.424515i | −0.977214 | − | 0.212258i | \(-0.931918\pi\) | ||
0.977214 | − | 0.212258i | \(-0.0680816\pi\) | |||||||
\(128\) | −185308. | + | 4559.32i | −0.999697 | + | 0.0245966i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11739.3 | + | 24159.4i | 0.0609234 | + | 0.125380i | ||||
\(131\) | −309317. | −1.57480 | −0.787401 | − | 0.616441i | \(-0.788574\pi\) | ||||
−0.787401 | + | 0.616441i | \(0.788574\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −96084.5 | −0.471004 | ||||||||
\(134\) | −96144.6 | − | 197865.i | −0.462555 | − | 0.951933i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16596.7 | + | 3604.44i | 0.0769441 | + | 0.0167106i | ||||
\(137\) | − | 69310.1i | − | 0.315497i | −0.987479 | − | 0.157749i | \(-0.949576\pi\) | ||
0.987479 | − | 0.157749i | \(-0.0504236\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 327514.i | − | 1.43778i | −0.695122 | − | 0.718891i | \(-0.744650\pi\) | ||
0.695122 | − | 0.718891i | \(-0.255350\pi\) | |||||||
\(140\) | −38948.8 | + | 49550.7i | −0.167948 | + | 0.213663i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 230372. | − | 111940.i | 0.958758 | − | 0.465871i | ||||
\(143\) | 25656.0 | 0.104918 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −262250. | −1.03584 | ||||||||
\(146\) | 106850. | − | 51919.6i | 0.414851 | − | 0.201581i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 185633. | − | 236163.i | 0.696628 | − | 0.886251i | ||||
\(149\) | − | 317624.i | − | 1.17205i | −0.810292 | − | 0.586026i | \(-0.800692\pi\) | ||
0.810292 | − | 0.586026i | \(-0.199308\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 32871.2i | − | 0.117320i | −0.998278 | − | 0.0586602i | \(-0.981317\pi\) | ||
0.998278 | − | 0.0586602i | \(-0.0186829\pi\) | |||||||
\(152\) | −286109. | − | 62136.5i | −1.00444 | − | 0.218141i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 26310.2 | + | 54146.1i | 0.0893968 | + | 0.183978i | ||||
\(155\) | 156711. | 0.523925 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −292389. | −0.946700 | −0.473350 | − | 0.880874i | \(-0.656955\pi\) | ||||
−0.473350 | + | 0.880874i | \(0.656955\pi\) | |||||||
\(158\) | 189034. | + | 389031.i | 0.602418 | + | 1.23977i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −148021. | + | 122358.i | −0.457112 | + | 0.377862i | ||||
\(161\) | 143438.i | 0.436112i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 324860.i | − | 0.957695i | −0.877898 | − | 0.478848i | \(-0.841055\pi\) | ||
0.877898 | − | 0.478848i | \(-0.158945\pi\) | |||||||
\(164\) | −297835. | − | 234110.i | −0.864701 | − | 0.679689i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 297728. | − | 144669.i | 0.838589 | − | 0.407480i | ||||
\(167\) | −563689. | −1.56404 | −0.782021 | − | 0.623251i | \(-0.785811\pi\) | ||||
−0.782021 | + | 0.623251i | \(0.785811\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −350781. | −0.944754 | ||||||||
\(170\) | 15826.4 | − | 7690.23i | 0.0420010 | − | 0.0204088i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 491384. | + | 386247.i | 1.26649 | + | 0.995508i | ||||
\(173\) | 126447.i | 0.321214i | 0.987018 | + | 0.160607i | \(0.0513452\pi\) | ||||
−0.987018 | + | 0.160607i | \(0.948655\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 120350.i | − | 0.297064i | ||||||
\(176\) | 43327.7 | + | 178244.i | 0.105435 | + | 0.433744i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 45882.4 | + | 94425.4i | 0.108541 | + | 0.223377i | ||||
\(179\) | 719928. | 1.67941 | 0.839705 | − | 0.543043i | \(-0.182728\pi\) | ||||
0.839705 | + | 0.543043i | \(0.182728\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −51023.8 | −0.115765 | −0.0578823 | − | 0.998323i | \(-0.518435\pi\) | ||||
−0.0578823 | + | 0.998323i | \(0.518435\pi\) | |||||||
\(182\) | 21035.5 | + | 43290.7i | 0.0470732 | + | 0.0968761i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −92759.1 | + | 427111.i | −0.201982 | + | 0.930028i | ||||
\(185\) | − | 311216.i | − | 0.668548i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 16806.8i | − | 0.0351465i | ||||||
\(188\) | −145808. | + | 185497.i | −0.300875 | + | 0.382774i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −272829. | + | 132571.i | −0.548285 | + | 0.266418i | ||||
\(191\) | 94246.4 | 0.186931 | 0.0934655 | − | 0.995623i | \(-0.470206\pi\) | ||||
0.0934655 | + | 0.995623i | \(0.470206\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17335.4 | −0.0334997 | −0.0167498 | − | 0.999860i | \(-0.505332\pi\) | ||||
−0.0167498 | + | 0.999860i | \(0.505332\pi\) | |||||||
\(194\) | 698316. | − | 339319.i | 1.33213 | − | 0.647298i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 262573. | − | 334045.i | 0.488213 | − | 0.621105i | ||||
\(197\) | 680902.i | 1.25003i | 0.780614 | + | 0.625013i | \(0.214906\pi\) | ||||
−0.780614 | + | 0.625013i | \(0.785094\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 320286.i | 0.573331i | 0.958031 | + | 0.286665i | \(0.0925468\pi\) | ||||
−0.958031 | + | 0.286665i | \(0.907453\pi\) | |||||||
\(200\) | 77828.4 | − | 358362.i | 0.137582 | − | 0.633501i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 240603. | + | 495159.i | 0.414880 | + | 0.853819i | ||||
\(203\) | −469920. | −0.800357 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −392488. | −0.652291 | ||||||||
\(206\) | 95664.5 | + | 196877.i | 0.157066 | + | 0.323241i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 34641.3 | + | 142509.i | 0.0555182 | + | 0.228394i | ||||
\(209\) | 289731.i | 0.458806i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.09747e6i | 1.69702i | 0.529178 | + | 0.848511i | \(0.322500\pi\) | ||||
−0.529178 | + | 0.848511i | \(0.677500\pi\) | |||||||
\(212\) | 676640. | + | 531865.i | 1.03399 | + | 0.812760i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 218186. | − | 106019.i | 0.325680 | − | 0.158252i | ||||
\(215\) | 647548. | 0.955380 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 280807. | 0.404816 | ||||||||
\(218\) | −212845. | + | 103424.i | −0.303334 | + | 0.147393i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 149414. | + | 117445.i | 0.208130 | + | 0.163598i | ||||
\(221\) | − | 13437.4i | − | 0.0185069i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.14571e6i | − | 1.54281i | −0.636344 | − | 0.771406i | \(-0.719554\pi\) | ||
0.636344 | − | 0.771406i | \(-0.280446\pi\) | |||||||
\(224\) | −265235. | + | 219252.i | −0.353193 | + | 0.291960i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −76140.3 | − | 156696.i | −0.0991615 | − | 0.204073i | ||||
\(227\) | 827252. | 1.06555 | 0.532774 | − | 0.846257i | \(-0.321149\pi\) | ||||
0.532774 | + | 0.846257i | \(0.321149\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 800776. | 1.00907 | 0.504536 | − | 0.863390i | \(-0.331663\pi\) | ||||
0.504536 | + | 0.863390i | \(0.331663\pi\) | |||||||
\(230\) | 197905. | + | 407287.i | 0.246682 | + | 0.507669i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.39927e6 | − | 303891.i | −1.70680 | − | 0.370678i | ||||
\(233\) | 1.65496e6i | 1.99709i | 0.0539626 | + | 0.998543i | \(0.482815\pi\) | ||||
−0.0539626 | + | 0.998543i | \(0.517185\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 244449.i | 0.288747i | ||||||||
\(236\) | −121512. | + | 154588.i | −0.142017 | + | 0.180674i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 28359.0 | − | 13780.0i | 0.0324526 | − | 0.0157691i | ||||
\(239\) | −924466. | −1.04688 | −0.523439 | − | 0.852063i | \(-0.675351\pi\) | ||||
−0.523439 | + | 0.852063i | \(0.675351\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −108394. | −0.120216 | −0.0601082 | − | 0.998192i | \(-0.519145\pi\) | ||||
−0.0601082 | + | 0.998192i | \(0.519145\pi\) | |||||||
\(242\) | −656156. | + | 318833.i | −0.720225 | + | 0.349966i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.09263e6 | − | 1.39005e6i | 1.17490 | − | 1.49471i | ||||
\(245\) | − | 440206.i | − | 0.468533i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 231645.i | 0.241591i | ||||||||
\(248\) | 836151. | + | 181594.i | 0.863288 | + | 0.187487i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −422194. | − | 868871.i | −0.427230 | − | 0.879235i | ||||
\(251\) | 665770. | 0.667022 | 0.333511 | − | 0.942746i | \(-0.391767\pi\) | ||||
0.333511 | + | 0.942746i | \(0.391767\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 432518. | 0.424818 | ||||||||
\(254\) | −190768. | − | 392599.i | −0.185533 | − | 0.381826i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −931572. | + | 481336.i | −0.888417 | + | 0.459038i | ||||
\(257\) | − | 1.17372e6i | − | 1.10849i | −0.832354 | − | 0.554244i | \(-0.813007\pi\) | ||
0.832354 | − | 0.554244i | \(-0.186993\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 557662.i | − | 0.516561i | ||||||
\(260\) | 119459. | + | 93899.5i | 0.109594 | + | 0.0861450i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.57381e6 | + | 764729.i | −1.41644 | + | 0.688263i | ||||
\(263\) | −307275. | −0.273929 | −0.136965 | − | 0.990576i | \(-0.543735\pi\) | ||||
−0.136965 | + | 0.990576i | \(0.543735\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 891678. | 0.779998 | ||||||||
\(266\) | −488877. | + | 237551.i | −0.423639 | + | 0.205851i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −978366. | − | 769034.i | −0.832079 | − | 0.654047i | ||||
\(269\) | − | 1.40037e6i | − | 1.17994i | −0.807424 | − | 0.589972i | \(-0.799139\pi\) | ||
0.807424 | − | 0.589972i | \(-0.200861\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 637013.i | 0.526896i | 0.964674 | + | 0.263448i | \(0.0848598\pi\) | ||||
−0.964674 | + | 0.263448i | \(0.915140\pi\) | |||||||
\(272\) | 93355.3 | − | 22692.9i | 0.0765098 | − | 0.0185981i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −171356. | − | 352650.i | −0.137887 | − | 0.283770i | ||||
\(275\) | −362899. | −0.289370 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 820888. | 0.642813 | 0.321406 | − | 0.946941i | \(-0.395844\pi\) | ||||
0.321406 | + | 0.946941i | \(0.395844\pi\) | |||||||
\(278\) | −809718. | − | 1.66639e6i | −0.628379 | − | 1.29320i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −75666.4 | + | 348407.i | −0.0576777 | + | 0.265578i | ||||
\(281\) | − | 446685.i | − | 0.337470i | −0.985661 | − | 0.168735i | \(-0.946032\pi\) | ||
0.985661 | − | 0.168735i | \(-0.0539683\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 270685.i | − | 0.200908i | −0.994942 | − | 0.100454i | \(-0.967970\pi\) | ||
0.994942 | − | 0.100454i | \(-0.0320296\pi\) | |||||||
\(284\) | 895380. | − | 1.13910e6i | 0.658736 | − | 0.838045i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 130538. | − | 63429.8i | 0.0943672 | − | 0.0458541i | ||||
\(287\) | −703291. | −0.504000 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.41105e6 | 0.993800 | ||||||||
\(290\) | −1.33432e6 | + | 648363.i | −0.931679 | + | 0.452713i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 415290. | − | 528333.i | 0.285033 | − | 0.362619i | ||||
\(293\) | 384363.i | 0.261561i | 0.991411 | + | 0.130781i | \(0.0417483\pi\) | ||||
−0.991411 | + | 0.130781i | \(0.958252\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 203717.i | 0.136293i | ||||||||
\(296\) | 360632. | − | 1.66054e6i | 0.239241 | − | 1.10159i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −785265. | − | 1.61607e6i | −0.512242 | − | 1.05419i | ||||
\(299\) | 345806. | 0.223694 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.16033e6 | 0.738185 | ||||||||
\(302\) | −81268.0 | − | 167249.i | −0.0512746 | − | 0.105523i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.60934e6 | + | 391200.i | −0.998766 | + | 0.242781i | ||||
\(305\) | − | 1.83181e6i | − | 1.12754i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.20012e6i | 1.33229i | 0.745820 | + | 0.666147i | \(0.232058\pi\) | ||||
−0.745820 | + | 0.666147i | \(0.767942\pi\) | |||||||
\(308\) | 267732. | + | 210448.i | 0.160814 | + | 0.126406i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 797342. | − | 387437.i | 0.471238 | − | 0.228980i | ||||
\(311\) | −2.43025e6 | −1.42479 | −0.712395 | − | 0.701779i | \(-0.752389\pi\) | ||||
−0.712395 | + | 0.701779i | \(0.752389\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 406568. | 0.234570 | 0.117285 | − | 0.993098i | \(-0.462581\pi\) | ||||
0.117285 | + | 0.993098i | \(0.462581\pi\) | |||||||
\(314\) | −1.48767e6 | + | 722878.i | −0.851498 | + | 0.413753i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.92361e6 | + | 1.51203e6i | 1.08368 | + | 0.851812i | ||||
\(317\) | 2.49960e6i | 1.39709i | 0.715568 | + | 0.698543i | \(0.246168\pi\) | ||||
−0.715568 | + | 0.698543i | \(0.753832\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.41698e6i | 0.779630i | ||||||||
\(320\) | −450620. | + | 988512.i | −0.246000 | + | 0.539644i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 354623. | + | 729809.i | 0.190602 | + | 0.392256i | ||||
\(323\) | 151747. | 0.0809306 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −290144. | −0.152372 | ||||||||
\(326\) | −803155. | − | 1.65289e6i | −0.418558 | − | 0.861388i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.09417e6 | − | 454809.i | −1.07480 | − | 0.233423i | ||||
\(329\) | 438023.i | 0.223104i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.55857e6i | 1.28359i | 0.766875 | + | 0.641797i | \(0.221811\pi\) | ||||
−0.766875 | + | 0.641797i | \(0.778189\pi\) | |||||||
\(332\) | 1.15717e6 | − | 1.47215e6i | 0.576171 | − | 0.733006i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.86805e6 | + | 1.39362e6i | −1.40676 | + | 0.683561i | ||||
\(335\) | −1.28929e6 | −0.627683 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 320043. | 0.153509 | 0.0767544 | − | 0.997050i | \(-0.475544\pi\) | ||||
0.0767544 | + | 0.997050i | \(0.475544\pi\) | |||||||
\(338\) | −1.78477e6 | + | 867239.i | −0.849748 | + | 0.412902i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 61512.0 | − | 78255.6i | 0.0288578 | − | 0.0367129i | ||||
\(341\) | − | 846737.i | − | 0.394332i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.78725e6i | − | 0.820259i | ||||||
\(344\) | 3.45509e6 | + | 750369.i | 1.57421 | + | 0.341884i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 312617. | + | 643363.i | 0.140386 | + | 0.288912i | ||||
\(347\) | 3.56951e6 | 1.59142 | 0.795710 | − | 0.605678i | \(-0.207098\pi\) | ||||
0.795710 | + | 0.605678i | \(0.207098\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −319652. | −0.140480 | −0.0702400 | − | 0.997530i | \(-0.522377\pi\) | ||||
−0.0702400 | + | 0.997530i | \(0.522377\pi\) | |||||||
\(350\) | −297542. | − | 612338.i | −0.129831 | − | 0.267191i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 661126. | + | 799784.i | 0.284399 | + | 0.344046i | ||||
\(353\) | − | 1.78942e6i | − | 0.764320i | −0.924096 | − | 0.382160i | \(-0.875180\pi\) | ||
0.924096 | − | 0.382160i | \(-0.124820\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1.50111e6i | − | 0.632183i | ||||||
\(356\) | 466898. | + | 367000.i | 0.195253 | + | 0.153476i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.66299e6 | − | 1.77989e6i | 1.51053 | − | 0.733981i | ||||
\(359\) | −1.91480e6 | −0.784130 | −0.392065 | − | 0.919937i | \(-0.628239\pi\) | ||||
−0.392065 | + | 0.919937i | \(0.628239\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −139839. | −0.0564754 | ||||||||
\(362\) | −259609. | + | 126147.i | −0.104123 | + | 0.0505946i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 214056. | + | 168257.i | 0.0846788 | + | 0.0665609i | ||||
\(365\) | − | 696239.i | − | 0.273543i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 882321.i | − | 0.341949i | −0.985275 | − | 0.170974i | \(-0.945308\pi\) | ||
0.985275 | − | 0.170974i | \(-0.0546916\pi\) | |||||||
\(368\) | 583994. | + | 2.40247e6i | 0.224796 | + | 0.924778i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −769423. | − | 1.58346e6i | −0.292187 | − | 0.601318i | ||||
\(371\) | 1.59778e6 | 0.602674 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.86790e6 | −1.06731 | −0.533657 | − | 0.845701i | \(-0.679183\pi\) | ||||
−0.533657 | + | 0.845701i | \(0.679183\pi\) | |||||||
\(374\) | −41551.8 | − | 85513.1i | −0.0153607 | − | 0.0316121i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −283263. | + | 1.30429e6i | −0.103329 | + | 0.475778i | ||||
\(377\) | 1.13290e6i | 0.410525i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 4.53351e6i | − | 1.62120i | −0.585602 | − | 0.810599i | \(-0.699142\pi\) | ||
0.585602 | − | 0.810599i | \(-0.300858\pi\) | |||||||
\(380\) | −1.06040e6 | + | 1.34904e6i | −0.376712 | + | 0.479253i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 479525. | − | 233007.i | 0.168133 | − | 0.0816977i | ||||
\(383\) | 1.75464e6 | 0.611210 | 0.305605 | − | 0.952158i | \(-0.401141\pi\) | ||||
0.305605 | + | 0.952158i | \(0.401141\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 352818. | 0.121311 | ||||||||
\(386\) | −88202.4 | + | 42858.5i | −0.0301309 | + | 0.0146409i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.71412e6 | − | 3.45291e6i | 0.915272 | − | 1.16441i | ||||
\(389\) | 1.84834e6i | 0.619311i | 0.950849 | + | 0.309656i | \(0.100214\pi\) | ||||
−0.950849 | + | 0.309656i | \(0.899786\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 226531.i | − | 0.0749353i | ||||||
\(392\) | 510104. | − | 2.34878e6i | 0.167665 | − | 0.772018i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.68340e6 | + | 3.46443e6i | 0.546321 | + | 1.12432i | ||||
\(395\) | 2.53494e6 | 0.817476 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.30700e6 | −0.416198 | −0.208099 | − | 0.978108i | \(-0.566728\pi\) | ||||
−0.208099 | + | 0.978108i | \(0.566728\pi\) | |||||||
\(398\) | 791847. | + | 1.62961e6i | 0.250573 | + | 0.515676i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −489993. | − | 2.01576e6i | −0.153123 | − | 0.629925i | ||||
\(401\) | 3.45140e6i | 1.07185i | 0.844265 | + | 0.535925i | \(0.180037\pi\) | ||||
−0.844265 | + | 0.535925i | \(0.819963\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 676981.i | − | 0.207641i | ||||||
\(404\) | 2.44837e6 | + | 1.92452e6i | 0.746319 | + | 0.586636i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.39095e6 | + | 1.16179e6i | −0.719872 | + | 0.349794i | ||||
\(407\) | −1.68156e6 | −0.503183 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.83836e6 | −1.72577 | −0.862884 | − | 0.505402i | \(-0.831344\pi\) | ||||
−0.862884 | + | 0.505402i | \(0.831344\pi\) | |||||||
\(410\) | −1.99697e6 | + | 970352.i | −0.586696 | + | 0.285082i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 973481. | + | 765194.i | 0.282543 | + | 0.222090i | ||||
\(413\) | 365036.i | 0.105308i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.94001e6i | − | 0.552947i | ||||||
\(416\) | 528582. | + | 639442.i | 0.149754 | + | 0.181162i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 716305. | + | 1.47415e6i | 0.200520 | + | 0.412668i | ||||
\(419\) | 5.29746e6 | 1.47412 | 0.737060 | − | 0.675827i | \(-0.236214\pi\) | ||||
0.737060 | + | 0.675827i | \(0.236214\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −631619. | −0.173680 | −0.0868400 | − | 0.996222i | \(-0.527677\pi\) | ||||
−0.0868400 | + | 0.996222i | \(0.527677\pi\) | |||||||
\(422\) | 2.71329e6 | + | 5.58393e6i | 0.741679 | + | 1.52637i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.75768e6 | + | 1.03326e6i | 1.28523 | + | 0.279123i | ||||
\(425\) | 190069.i | 0.0510432i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3.28239e6i | − | 0.871205i | ||||||
\(428\) | 848015. | − | 1.07885e6i | 0.223766 | − | 0.284675i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.29472e6 | − | 1.60094e6i | 0.859305 | − | 0.417546i | ||||
\(431\) | −6.01340e6 | −1.55929 | −0.779645 | − | 0.626222i | \(-0.784600\pi\) | ||||
−0.779645 | + | 0.626222i | \(0.784600\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.60717e6 | −1.43722 | −0.718611 | − | 0.695412i | \(-0.755222\pi\) | ||||
−0.718611 | + | 0.695412i | \(0.755222\pi\) | |||||||
\(434\) | 1.42874e6 | − | 694242.i | 0.364107 | − | 0.176924i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −827256. | + | 1.05244e6i | −0.208413 | + | 0.265143i | ||||
\(437\) | 3.90514e6i | 0.978213i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.08822e6i | 1.75540i | 0.479211 | + | 0.877700i | \(0.340923\pi\) | ||||
−0.479211 | + | 0.877700i | \(0.659077\pi\) | |||||||
\(440\) | 1.05058e6 | + | 228163.i | 0.258700 | + | 0.0561840i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −33221.4 | − | 68369.2i | −0.00808838 | − | 0.0166458i | ||||
\(443\) | −405533. | −0.0981786 | −0.0490893 | − | 0.998794i | \(-0.515632\pi\) | ||||
−0.0490893 | + | 0.998794i | \(0.515632\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 615280. | 0.147290 | ||||||||
\(446\) | −2.83255e6 | − | 5.82937e6i | −0.674281 | − | 1.38766i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −807458. | + | 1.77130e6i | −0.190075 | + | 0.416962i | ||||
\(449\) | 5.81570e6i | 1.36140i | 0.732561 | + | 0.680701i | \(0.238325\pi\) | ||||
−0.732561 | + | 0.680701i | \(0.761675\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.12069e6i | 0.490947i | ||||||||
\(452\) | −774802. | − | 609025.i | −0.178379 | − | 0.140213i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.20905e6 | − | 2.04523e6i | 0.958395 | − | 0.465695i | ||||
\(455\) | 282084. | 0.0638779 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.51155e6 | 0.338558 | 0.169279 | − | 0.985568i | \(-0.445856\pi\) | ||||
0.169279 | + | 0.985568i | \(0.445856\pi\) | |||||||
\(458\) | 4.07434e6 | − | 1.97977e6i | 0.907599 | − | 0.441012i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.01388e6 | + | 1.58299e6i | 0.443751 | + | 0.348805i | ||||
\(461\) | − | 8.52192e6i | − | 1.86761i | −0.357787 | − | 0.933803i | \(-0.616469\pi\) | ||
0.357787 | − | 0.933803i | \(-0.383531\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 5.84253e6i | − | 1.26663i | −0.773896 | − | 0.633313i | \(-0.781695\pi\) | ||
0.773896 | − | 0.633313i | \(-0.218305\pi\) | |||||||
\(464\) | −7.87079e6 | + | 1.91324e6i | −1.69716 | + | 0.412548i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.09157e6 | + | 8.42041e6i | 0.872821 | + | 1.79626i | ||||
\(467\) | 1.60988e6 | 0.341586 | 0.170793 | − | 0.985307i | \(-0.445367\pi\) | ||||
0.170793 | + | 0.985307i | \(0.445367\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.31026e6 | −0.484986 | ||||||||
\(470\) | 604353. | + | 1.24375e6i | 0.126196 | + | 0.259710i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −236064. | + | 1.08696e6i | −0.0487724 | + | 0.224574i | ||||
\(473\) | − | 3.49883e6i | − | 0.719067i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3.27656e6i | − | 0.666323i | ||||||
\(476\) | 110222. | − | 140225.i | 0.0222973 | − | 0.0283666i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.70367e6 | + | 2.28557e6i | −0.941602 | + | 0.457535i | ||||
\(479\) | −4.03682e6 | −0.803898 | −0.401949 | − | 0.915662i | \(-0.631667\pi\) | ||||
−0.401949 | + | 0.915662i | \(0.631667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.34444e6 | −0.264958 | ||||||||
\(482\) | −551509. | + | 267984.i | −0.108127 | + | 0.0525402i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.55026e6 | + | 3.24444e6i | −0.494847 | + | 0.629545i | ||||
\(485\) | − | 4.55026e6i | − | 0.878378i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.28957e6i | 1.20171i | 0.799359 | + | 0.600854i | \(0.205173\pi\) | ||||
−0.799359 | + | 0.600854i | \(0.794827\pi\) | |||||||
\(488\) | 2.12268e6 | − | 9.77390e6i | 0.403491 | − | 1.85788i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.08833e6 | − | 2.23976e6i | −0.204771 | − | 0.421417i | ||||
\(491\) | 5.26683e6 | 0.985928 | 0.492964 | − | 0.870050i | \(-0.335913\pi\) | ||||
0.492964 | + | 0.870050i | \(0.335913\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 742146. | 0.137522 | ||||||||
\(494\) | 572698. | + | 1.17861e6i | 0.105587 | + | 0.217296i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.70329e6 | − | 1.14328e6i | 0.858415 | − | 0.208664i | ||||
\(497\) | − | 2.68982e6i | − | 0.488463i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.24696e6i | 0.403966i | 0.979389 | + | 0.201983i | \(0.0647385\pi\) | ||||
−0.979389 | + | 0.201983i | \(0.935261\pi\) | |||||||
\(500\) | −4.29624e6 | − | 3.37701e6i | −0.768535 | − | 0.604098i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.38744e6 | − | 1.64599e6i | 0.599945 | − | 0.291520i | ||||
\(503\) | −7.96470e6 | −1.40362 | −0.701809 | − | 0.712365i | \(-0.747624\pi\) | ||||
−0.701809 | + | 0.712365i | \(0.747624\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.22648e6 | 0.562989 | ||||||||
\(506\) | 2.20065e6 | − | 1.06932e6i | 0.382098 | − | 0.185665i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.94125e6 | − | 1.52590e6i | −0.333752 | − | 0.262342i | ||||
\(509\) | 2.49761e6i | 0.427297i | 0.976911 | + | 0.213648i | \(0.0685347\pi\) | ||||
−0.976911 | + | 0.213648i | \(0.931465\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1.24758e6i | − | 0.211356i | ||||||
\(512\) | −3.54982e6 | + | 4.75217e6i | −0.598455 | + | 0.801157i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.90180e6 | − | 5.97187e6i | −0.484462 | − | 0.997017i | ||||
\(515\) | 1.28286e6 | 0.213138 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.32080e6 | 0.217326 | ||||||||
\(518\) | −1.37871e6 | − | 2.83738e6i | −0.225761 | − | 0.464615i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 839956. | + | 182420.i | 0.136222 | + | 0.0295845i | ||||
\(521\) | − | 9.44582e6i | − | 1.52456i | −0.647246 | − | 0.762281i | \(-0.724079\pi\) | ||
0.647246 | − | 0.762281i | \(-0.275921\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 3.14550e6i | − | 0.502846i | −0.967877 | − | 0.251423i | \(-0.919101\pi\) | ||
0.967877 | − | 0.251423i | \(-0.0808986\pi\) | |||||||
\(524\) | −6.11686e6 | + | 7.78188e6i | −0.973196 | + | 1.23810i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.56341e6 | + | 759680.i | −0.246382 | + | 0.119720i | ||||
\(527\) | −443479. | −0.0695579 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −606637. | −0.0942519 | ||||||||
\(530\) | 4.53685e6 | − | 2.20451e6i | 0.701560 | − | 0.340896i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.90010e6 | + | 2.41731e6i | −0.291071 | + | 0.370300i | ||||
\(533\) | 1.69553e6i | 0.258515i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.42171e6i | − | 0.214746i | ||||||
\(536\) | −6.87922e6 | − | 1.49401e6i | −1.03425 | − | 0.224617i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.46215e6 | − | 7.12506e6i | −0.515691 | − | 1.06129i | ||||
\(539\) | −2.37852e6 | −0.352642 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.17569e6 | −0.172703 | −0.0863515 | − | 0.996265i | \(-0.527521\pi\) | ||||
−0.0863515 | + | 0.996265i | \(0.527521\pi\) | |||||||
\(542\) | 1.57490e6 | + | 3.24112e6i | 0.230279 | + | 0.473911i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 418887. | − | 346265.i | 0.0606876 | − | 0.0501662i | ||||
\(545\) | 1.38690e6i | 0.200012i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.69619e6i | 0.242386i | 0.992629 | + | 0.121193i | \(0.0386719\pi\) | ||||
−0.992629 | + | 0.121193i | \(0.961328\pi\) | |||||||
\(548\) | −1.74372e6 | − | 1.37063e6i | −0.248042 | − | 0.194971i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.84643e6 | + | 897200.i | −0.260271 | + | 0.126469i | ||||
\(551\) | −1.27938e7 | −1.79523 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.54231e6 | 0.631632 | ||||||||
\(554\) | 4.17667e6 | − | 2.02949e6i | 0.578171 | − | 0.280939i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.23968e6 | − | 6.47671e6i | −1.13038 | − | 0.888520i | ||||
\(557\) | 713498.i | 0.0974440i | 0.998812 | + | 0.0487220i | \(0.0155148\pi\) | ||||
−0.998812 | + | 0.0487220i | \(0.984485\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.79737e6i | − | 0.378635i | ||||||
\(560\) | 476382. | + | 1.95977e6i | 0.0641926 | + | 0.264079i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.10435e6 | − | 2.27273e6i | −0.147491 | − | 0.303534i | ||||
\(563\) | 1.28328e7 | 1.70627 | 0.853137 | − | 0.521687i | \(-0.174697\pi\) | ||||
0.853137 | + | 0.521687i | \(0.174697\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.02104e6 | −0.134561 | ||||||||
\(566\) | −669217. | − | 1.37724e6i | −0.0878064 | − | 0.180705i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.73947e6 | − | 8.00941e6i | 0.226227 | − | 1.04167i | ||||
\(569\) | 7.48951e6i | 0.969779i | 0.874575 | + | 0.484890i | \(0.161140\pi\) | ||||
−0.874575 | + | 0.484890i | \(0.838860\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.20920e6i | 1.05368i | 0.849963 | + | 0.526842i | \(0.176624\pi\) | ||||
−0.849963 | + | 0.526842i | \(0.823376\pi\) | |||||||
\(572\) | 507357. | − | 645460.i | 0.0648371 | − | 0.0824859i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.57834e6 | + | 1.73876e6i | −0.453317 | + | 0.220272i | ||||
\(575\) | −4.89135e6 | −0.616962 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.12522e7 | 1.40701 | 0.703505 | − | 0.710691i | \(-0.251617\pi\) | ||||
0.703505 | + | 0.710691i | \(0.251617\pi\) | |||||||
\(578\) | 7.17943e6 | − | 3.48857e6i | 0.893862 | − | 0.434338i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.18607e6 | + | 6.59773e6i | −0.640131 | + | 0.814375i | ||||
\(581\) | − | 3.47626e6i | − | 0.427240i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.81791e6i | − | 0.587066i | ||||||
\(584\) | 806791. | − | 3.71488e6i | 0.0978879 | − | 0.450726i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 950266. | + | 1.95564e6i | 0.114315 | + | 0.235258i | ||||
\(587\) | 8.39201e6 | 1.00524 | 0.502621 | − | 0.864507i | \(-0.332369\pi\) | ||||
0.502621 | + | 0.864507i | \(0.332369\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.64507e6 | 0.908015 | ||||||||
\(590\) | 503652. | + | 1.03651e6i | 0.0595663 | + | 0.122587i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.27047e6 | − | 9.34039e6i | −0.266264 | − | 1.09537i | ||||
\(593\) | − | 5.97649e6i | − | 0.697926i | −0.937137 | − | 0.348963i | \(-0.886534\pi\) | ||
0.937137 | − | 0.348963i | \(-0.113466\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 184789.i | − | 0.0213985i | ||||||
\(596\) | −7.99084e6 | − | 6.28112e6i | −0.921461 | − | 0.724305i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.75946e6 | − | 854940.i | 0.201199 | − | 0.0977648i | ||||
\(599\) | 2.33722e6 | 0.266153 | 0.133077 | − | 0.991106i | \(-0.457514\pi\) | ||||
0.133077 | + | 0.991106i | \(0.457514\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.95099e6 | 0.672052 | 0.336026 | − | 0.941853i | \(-0.390917\pi\) | ||||
0.336026 | + | 0.941853i | \(0.390917\pi\) | |||||||
\(602\) | 5.90375e6 | − | 2.86870e6i | 0.663952 | − | 0.322622i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −826982. | − | 650040.i | −0.0922367 | − | 0.0725016i | ||||
\(605\) | 4.27554e6i | 0.474900i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.38582e7i | 1.52663i | 0.646026 | + | 0.763316i | \(0.276430\pi\) | ||||
−0.646026 | + | 0.763316i | \(0.723570\pi\) | |||||||
\(608\) | −7.22114e6 | + | 5.96921e6i | −0.792222 | + | 0.654874i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.52881e6 | − | 9.32025e6i | −0.492788 | − | 1.01415i | ||||
\(611\) | 1.05600e6 | 0.114436 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.69155e6 | 0.934214 | 0.467107 | − | 0.884201i | \(-0.345296\pi\) | ||||
0.467107 | + | 0.884201i | \(0.345296\pi\) | |||||||
\(614\) | 5.43938e6 | + | 1.11942e7i | 0.582276 | + | 1.19832i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.88251e6 | + | 408840.i | 0.199888 | + | 0.0434112i | ||||
\(617\) | 1.37669e7i | 1.45587i | 0.685646 | + | 0.727936i | \(0.259520\pi\) | ||||
−0.685646 | + | 0.727936i | \(0.740480\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 5.73601e6i | − | 0.601704i | −0.953671 | − | 0.300852i | \(-0.902729\pi\) | ||
0.953671 | − | 0.300852i | \(-0.0972710\pi\) | |||||||
\(620\) | 3.09900e6 | − | 3.94256e6i | 0.323775 | − | 0.411907i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.23651e7 | + | 6.00834e6i | −1.28151 | + | 0.622700i | ||||
\(623\) | 1.10251e6 | 0.113805 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 669150. | 0.0685209 | ||||||||
\(626\) | 2.06862e6 | − | 1.00516e6i | 0.210981 | − | 0.102518i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.78210e6 | + | 7.35599e6i | −0.585041 | + | 0.744290i | ||||
\(629\) | 880717.i | 0.0887585i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.53427e6i | 0.353368i | 0.984268 | + | 0.176684i | \(0.0565370\pi\) | ||||
−0.984268 | + | 0.176684i | \(0.943463\pi\) | |||||||
\(632\) | 1.35255e7 | + | 2.93745e6i | 1.34698 | + | 0.292535i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.17980e6 | + | 1.27180e7i | 0.610592 | + | 1.25659i | ||||
\(635\) | −2.55819e6 | −0.251767 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.90167e6 | −0.185689 | ||||||||
\(638\) | 3.50323e6 | + | 7.20961e6i | 0.340735 | + | 0.701229i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 151158. | + | 6.14362e6i | 0.0145875 | + | 0.592890i | ||||
\(641\) | − | 717761.i | − | 0.0689978i | −0.999405 | − | 0.0344989i | \(-0.989016\pi\) | ||
0.999405 | − | 0.0344989i | \(-0.0109835\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.19240e6i | 0.686035i | 0.939329 | + | 0.343017i | \(0.111449\pi\) | ||||
−0.939329 | + | 0.343017i | \(0.888551\pi\) | |||||||
\(644\) | 3.60863e6 | + | 2.83653e6i | 0.342869 | + | 0.269508i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 772086. | − | 375165.i | 0.0727921 | − | 0.0353705i | ||||
\(647\) | 1.35541e6 | 0.127294 | 0.0636472 | − | 0.997972i | \(-0.479727\pi\) | ||||
0.0636472 | + | 0.997972i | \(0.479727\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.10072e6 | 0.102581 | ||||||||
\(650\) | −1.47625e6 | + | 717327.i | −0.137049 | + | 0.0665938i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.17290e6 | − | 6.42422e6i | −0.752934 | − | 0.591836i | ||||
\(653\) | 7.90801e6i | 0.725745i | 0.931839 | + | 0.362873i | \(0.118204\pi\) | ||||
−0.931839 | + | 0.362873i | \(0.881796\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.02550e7i | 0.933967i | ||||||||
\(656\) | −1.17796e7 | + | 2.86339e6i | −1.06873 | + | 0.259789i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.08293e6 | + | 2.22866e6i | 0.0975068 | + | 0.200668i | ||||
\(659\) | 1.60268e7 | 1.43758 | 0.718792 | − | 0.695226i | \(-0.244696\pi\) | ||||
0.718792 | + | 0.695226i | \(0.244696\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.22510e7 | 1.09061 | 0.545303 | − | 0.838239i | \(-0.316415\pi\) | ||||
0.545303 | + | 0.838239i | \(0.316415\pi\) | |||||||
\(662\) | 6.32558e6 | + | 1.30180e7i | 0.560991 | + | 1.15451i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.24805e6 | − | 1.03512e7i | 0.197873 | − | 0.911108i | ||||
\(665\) | 3.18555e6i | 0.279338i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.90989e7i | 1.66224i | ||||||||
\(668\) | −1.11472e7 | + | 1.41814e7i | −0.966546 | + | 1.22964i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.55992e6 | + | 3.18754e6i | −0.564562 | + | 0.274327i | ||||
\(671\) | −9.89764e6 | −0.848643 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.62568e6 | −0.734101 | −0.367051 | − | 0.930201i | \(-0.619632\pi\) | ||||
−0.367051 | + | 0.930201i | \(0.619632\pi\) | |||||||
\(674\) | 1.62838e6 | − | 791246.i | 0.138072 | − | 0.0670906i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.93681e6 | + | 8.82501e6i | −0.583839 | + | 0.742760i | ||||
\(677\) | 3.13206e6i | 0.262638i | 0.991340 | + | 0.131319i | \(0.0419213\pi\) | ||||
−0.991340 | + | 0.131319i | \(0.958079\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 8.15352e6i | − | 0.678689i | ||||||
\(680\) | 119500. | − | 550241.i | 0.00991052 | − | 0.0456332i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.09340e6 | − | 4.30819e6i | −0.172342 | − | 0.354678i | ||||
\(683\) | 1.42490e7 | 1.16878 | 0.584389 | − | 0.811473i | \(-0.301334\pi\) | ||||
0.584389 | + | 0.811473i | \(0.301334\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.29788e6 | −0.187112 | ||||||||
\(686\) | −4.41865e6 | − | 9.09354e6i | −0.358492 | − | 0.737773i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.94346e7 | − | 4.72418e6i | 1.56532 | − | 0.380501i | ||||
\(689\) | − | 3.85200e6i | − | 0.309128i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 6.95060e6i | − | 0.553767i | −0.960904 | − | 0.276883i | \(-0.910698\pi\) | ||
0.960904 | − | 0.276883i | \(-0.0893016\pi\) | |||||||
\(692\) | 3.18119e6 | + | 2.50054e6i | 0.252537 | + | 0.198504i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.81616e7 | − | 8.82494e6i | 1.43138 | − | 0.695526i | ||||
\(695\) | −1.08583e7 | −0.852705 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.11071e6 | 0.0866002 | ||||||||
\(698\) | −1.62639e6 | + | 790281.i | −0.126353 | + | 0.0613964i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.02778e6 | − | 2.37996e6i | −0.233550 | − | 0.183579i | ||||
\(701\) | 4.21552e6i | 0.324008i | 0.986790 | + | 0.162004i | \(0.0517958\pi\) | ||||
−0.986790 | + | 0.162004i | \(0.948204\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.51826e7i | − | 1.15866i | ||||||
\(704\) | 5.34112e6 | + | 2.43479e6i | 0.406163 | + | 0.185152i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.42400e6 | − | 9.10455e6i | −0.334044 | − | 0.687459i | ||||
\(707\) | 5.78146e6 | 0.435000 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.08494e6 | −0.379901 | −0.189950 | − | 0.981794i | \(-0.560833\pi\) | ||||
−0.189950 | + | 0.981794i | \(0.560833\pi\) | |||||||
\(710\) | −3.71122e6 | − | 7.63766e6i | −0.276294 | − | 0.568610i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.28291e6 | + | 712977.i | 0.242694 | + | 0.0527079i | ||||
\(713\) | − | 1.14128e7i | − | 0.840750i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 850590.i | − | 0.0622236i | ||||||
\(716\) | 1.42368e7 | − | 1.81121e7i | 1.03784 | − | 1.32034i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.74251e6 | + | 4.73399e6i | −0.705277 | + | 0.342702i | ||||
\(719\) | 2.52087e6 | 0.181856 | 0.0909281 | − | 0.995857i | \(-0.471017\pi\) | ||||
0.0909281 | + | 0.995857i | \(0.471017\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.29873e6 | 0.164683 | ||||||||
\(722\) | −711498. | + | 345725.i | −0.0507962 | + | 0.0246824i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.00901e6 | + | 1.28367e6i | −0.0715402 | + | 0.0910135i | ||||
\(725\) | − | 1.60247e7i | − | 1.13225i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.28089e7i | − | 1.60054i | −0.599637 | − | 0.800272i | \(-0.704688\pi\) | ||
0.599637 | − | 0.800272i | \(-0.295312\pi\) | |||||||
\(728\) | 1.50510e6 | + | 326875.i | 0.105254 | + | 0.0228588i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.72132e6 | − | 3.54246e6i | −0.119551 | − | 0.246036i | ||||
\(731\) | −1.83251e6 | −0.126839 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.13592e6 | −0.284323 | −0.142161 | − | 0.989843i | \(-0.545405\pi\) | ||||
−0.142161 | + | 0.989843i | \(0.545405\pi\) | |||||||
\(734\) | −2.18137e6 | − | 4.48924e6i | −0.149448 | − | 0.307562i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.91100e6 | + | 1.07799e7i | 0.606362 | + | 0.733535i | ||||
\(737\) | 6.96631e6i | 0.472426i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.06353e6i | 0.138995i | 0.997582 | + | 0.0694974i | \(0.0221396\pi\) | ||||
−0.997582 | + | 0.0694974i | \(0.977860\pi\) | |||||||
\(740\) | −7.82964e6 | − | 6.15440e6i | −0.525608 | − | 0.413149i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.12950e6 | − | 3.95021e6i | 0.542068 | − | 0.263397i | ||||
\(743\) | −2.14217e7 | −1.42358 | −0.711789 | − | 0.702393i | \(-0.752115\pi\) | ||||
−0.711789 | + | 0.702393i | \(0.752115\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.05304e7 | −0.695109 | ||||||||
\(746\) | −1.45919e7 | + | 7.09035e6i | −0.959984 | + | 0.466467i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −422830. | − | 332361.i | −0.0276320 | − | 0.0217198i | ||||
\(749\) | − | 2.54753e6i | − | 0.165926i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.18689e7i | − | 0.767910i | −0.923352 | − | 0.383955i | \(-0.874562\pi\) | ||
0.923352 | − | 0.383955i | \(-0.125438\pi\) | |||||||
\(752\) | 1.78337e6 | + | 7.33653e6i | 0.115000 | + | 0.473093i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.80089e6 | + | 5.76421e6i | 0.179419 | + | 0.369242i | ||||
\(755\) | −1.08980e6 | −0.0695792 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.89960e7 | −1.20482 | −0.602412 | − | 0.798186i | \(-0.705793\pi\) | ||||
−0.602412 | + | 0.798186i | \(0.705793\pi\) | |||||||
\(758\) | −1.12082e7 | − | 2.30664e7i | −0.708540 | − | 1.45817i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.06005e6 | + | 9.48553e6i | −0.129373 | + | 0.595700i | ||||
\(761\) | − | 2.59190e7i | − | 1.62240i | −0.584771 | − | 0.811198i | \(-0.698816\pi\) | ||
0.584771 | − | 0.811198i | \(-0.301184\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.48517e6i | 0.154541i | ||||||||
\(764\) | 1.86375e6 | − | 2.37107e6i | 0.115520 | − | 0.146964i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.92758e6 | − | 4.33801e6i | 0.549746 | − | 0.267128i | ||||
\(767\) | 880046. | 0.0540153 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.19627e7 | −1.33927 | −0.669637 | − | 0.742689i | \(-0.733550\pi\) | ||||
−0.669637 | + | 0.742689i | \(0.733550\pi\) | |||||||
\(770\) | 1.79514e6 | − | 872277.i | 0.109112 | − | 0.0530185i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −342814. | + | 436128.i | −0.0207021 | + | 0.0263373i | ||||
\(773\) | 1.80022e7i | 1.08362i | 0.840501 | + | 0.541810i | \(0.182261\pi\) | ||||
−0.840501 | + | 0.541810i | \(0.817739\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.57575e6i | 0.572688i | ||||||||
\(776\) | 5.27276e6 | − | 2.42785e7i | 0.314329 | − | 1.44733i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.56969e6 | + | 9.40436e6i | 0.270668 | + | 0.557032i | ||||
\(779\) | −1.91474e7 | −1.13049 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.11081e6 | −0.475813 | ||||||||
\(782\) | −560057. | − | 1.15259e6i | −0.0327503 | − | 0.0673997i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.21152e6 | − | 1.32117e7i | −0.186604 | − | 0.767660i | ||||
\(785\) | 9.69375e6i | 0.561459i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 2.05610e7i | − | 1.18333i | −0.806182 | − | 0.591667i | \(-0.798470\pi\) | ||
0.806182 | − | 0.591667i | \(-0.201530\pi\) | |||||||
\(788\) | 1.71303e7 | + | 1.34651e7i | 0.982764 | + | 0.772491i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.28978e7 | − | 6.26717e6i | 0.735270 | − | 0.357276i | ||||
\(791\) | −1.82958e6 | −0.103970 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.91333e6 | −0.446865 | ||||||||
\(794\) | −6.65002e6 | + | 3.23132e6i | −0.374345 | + | 0.181898i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.05782e6 | + | 6.33376e6i | 0.450749 | + | 0.354307i | ||||
\(797\) | − | 6.25656e6i | − | 0.348891i | −0.984667 | − | 0.174446i | \(-0.944187\pi\) | ||
0.984667 | − | 0.174446i | \(-0.0558133\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 691771.i | − | 0.0383350i | ||||||
\(800\) | −7.47667e6 | − | 9.04476e6i | −0.413032 | − | 0.499657i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.53294e6 | + | 1.75607e7i | 0.468449 | + | 0.964064i | ||||
\(803\) | −3.76191e6 | −0.205883 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.75547e6 | 0.258645 | ||||||||
\(806\) | −1.67371e6 | − | 3.44447e6i | −0.0907491 | − | 0.186761i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.72153e7 | + | 3.73879e6i | 0.927655 | + | 0.201466i | ||||
\(809\) | − | 774632.i | − | 0.0416125i | −0.999784 | − | 0.0208063i | \(-0.993377\pi\) | ||
0.999784 | − | 0.0208063i | \(-0.00662332\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.83962e7i | − | 1.51603i | −0.652238 | − | 0.758014i | \(-0.726170\pi\) | ||
0.652238 | − | 0.758014i | \(-0.273830\pi\) | |||||||
\(812\) | −9.29283e6 | + | 1.18223e7i | −0.494604 | + | 0.629236i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.55576e6 | + | 4.15734e6i | −0.452582 | + | 0.219915i | ||||
\(815\) | −1.07703e7 | −0.567980 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.15904e7 | 1.65577 | ||||||||
\(818\) | −2.97055e7 | + | 1.44342e7i | −1.55222 | + | 0.754242i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.76158e6 | + | 9.87429e6i | −0.403103 | + | 0.512827i | ||||
\(821\) | − | 2.55262e7i | − | 1.32169i | −0.750524 | − | 0.660843i | \(-0.770199\pi\) | ||
0.750524 | − | 0.660843i | \(-0.229801\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.87596e7i | 1.48007i | 0.672566 | + | 0.740037i | \(0.265192\pi\) | ||||
−0.672566 | + | 0.740037i | \(0.734808\pi\) | |||||||
\(824\) | 6.84486e6 | + | 1.48655e6i | 0.351194 | + | 0.0762716i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 902484. | + | 1.85730e6i | 0.0460245 | + | 0.0947180i | ||||
\(827\) | 2.19785e7 | 1.11747 | 0.558733 | − | 0.829348i | \(-0.311288\pi\) | ||||
0.558733 | + | 0.829348i | \(0.311288\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.87554e7 | −0.947852 | −0.473926 | − | 0.880565i | \(-0.657164\pi\) | ||||
−0.473926 | + | 0.880565i | \(0.657164\pi\) | |||||||
\(830\) | −4.79630e6 | − | 9.87074e6i | −0.241664 | − | 0.497341i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.27032e6 | + | 1.94666e6i | 0.213871 | + | 0.0974946i | ||||
\(833\) | 1.24575e6i | 0.0622040i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.86883e7i | 0.927586i | ||||||||
\(836\) | 7.28911e6 | + | 5.72952e6i | 0.360710 | + | 0.283533i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.69534e7 | − | 1.30970e7i | 1.32588 | − | 0.644260i | ||||
\(839\) | 2.04395e7 | 1.00246 | 0.501228 | − | 0.865315i | \(-0.332882\pi\) | ||||
0.501228 | + | 0.865315i | \(0.332882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.20592e7 | −2.05055 | ||||||||
\(842\) | −3.21367e6 | + | 1.56156e6i | −0.156215 | + | 0.0759064i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.76104e7 | + | 2.17029e7i | 1.33419 | + | 1.04872i | ||||
\(845\) | 1.16296e7i | 0.560305i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.66126e6i | 0.366937i | ||||||||
\(848\) | 2.67616e7 | − | 6.50523e6i | 1.27797 | − | 0.310651i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 469909. | + | 967068.i | 0.0223083 | + | 0.0459102i | ||||
\(851\) | −2.26649e7 | −1.07283 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.27007e7 | −0.597663 | −0.298831 | − | 0.954306i | \(-0.596597\pi\) | ||||
−0.298831 | + | 0.954306i | \(0.596597\pi\) | |||||||
\(854\) | −8.11509e6 | − | 1.67008e7i | −0.380758 | − | 0.783596i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.64745e6 | − | 7.58572e6i | 0.0768472 | − | 0.353844i | ||||
\(857\) | 1.16731e7i | 0.542917i | 0.962450 | + | 0.271459i | \(0.0875060\pi\) | ||||
−0.962450 | + | 0.271459i | \(0.912494\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27093.7i | 0.00125281i | 1.00000 | 0.000626405i | \(0.000199391\pi\) | |||||
−1.00000 | 0.000626405i | \(0.999801\pi\) | ||||||||
\(860\) | 1.28055e7 | − | 1.62912e7i | 0.590405 | − | 0.751114i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.05961e7 | + | 1.48670e7i | −1.40249 | + | 0.681483i | ||||
\(863\) | 9.03157e6 | 0.412797 | 0.206398 | − | 0.978468i | \(-0.433826\pi\) | ||||
0.206398 | + | 0.978468i | \(0.433826\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.19218e6 | 0.190502 | ||||||||
\(866\) | −2.85293e7 | + | 1.38627e7i | −1.29269 | + | 0.628134i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.55305e6 | − | 7.06459e6i | 0.250168 | − | 0.318264i | ||||
\(869\) | − | 1.36968e7i | − | 0.615274i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.56969e6i | 0.248763i | ||||||||
\(872\) | −1.60712e6 | + | 7.40003e6i | −0.0715744 | + | 0.329566i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.65473e6 | + | 1.98693e7i | 0.427525 | + | 0.879842i | ||||
\(875\) | −1.01449e7 | −0.447948 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.19962e7 | 0.965713 | 0.482856 | − | 0.875700i | \(-0.339599\pi\) | ||||
0.482856 | + | 0.875700i | \(0.339599\pi\) | |||||||
\(878\) | 1.75243e7 | + | 3.60648e7i | 0.767192 | + | 1.57887i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.90943e6 | − | 1.43647e6i | 0.257240 | − | 0.0625301i | ||||
\(881\) | − | 3.05186e7i | − | 1.32472i | −0.749184 | − | 0.662362i | \(-0.769554\pi\) | ||
0.749184 | − | 0.662362i | \(-0.230446\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.64489e6i | 0.0709962i | 0.999370 | + | 0.0354981i | \(0.0113018\pi\) | ||||
−0.999370 | + | 0.0354981i | \(0.988698\pi\) | |||||||
\(884\) | −338060. | − | 265729.i | −0.0145500 | − | 0.0114369i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.06335e6 | + | 1.00260e6i | −0.0883056 | + | 0.0429087i | ||||
\(887\) | −9.31338e6 | −0.397464 | −0.198732 | − | 0.980054i | \(-0.563682\pi\) | ||||
−0.198732 | + | 0.980054i | \(0.563682\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.58398e6 | −0.194531 | ||||||||
\(890\) | 3.13054e6 | − | 1.52116e6i | 0.132478 | − | 0.0643726i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.88240e7 | − | 2.26568e7i | −1.21295 | − | 0.953426i | ||||
\(893\) | 1.19253e7i | 0.500428i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2.38682e7i | − | 0.996006i | ||||||
\(896\) | 270857. | + | 1.10086e7i | 0.0112712 | + | 0.458103i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.43782e7 | + | 2.95903e7i | 0.594997 | + | 1.22450i | ||||
\(899\) | 3.73897e7 | 1.54295 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.52338e6 | −0.103555 | ||||||||
\(902\) | 5.24300e6 | + | 1.07900e7i | 0.214567 | + | 0.441577i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.44789e6 | − | 1.18316e6i | −0.221721 | − | 0.0481530i | ||||
\(905\) | 1.69162e6i | 0.0686565i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.85183e7i | 0.747452i | 0.927539 | + | 0.373726i | \(0.121920\pi\) | ||||
−0.927539 | + | 0.373726i | \(0.878080\pi\) | |||||||
\(908\) | 1.63592e7 | − | 2.08122e7i | 0.658487 | − | 0.837728i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.43524e6 | − | 697401.i | 0.0574542 | − | 0.0279177i | ||||
\(911\) | 1.72695e7 | 0.689419 | 0.344710 | − | 0.938709i | \(-0.387977\pi\) | ||||
0.344710 | + | 0.938709i | \(0.387977\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.04822e7 | −0.416176 | ||||||||
\(914\) | 7.69077e6 | − | 3.73703e6i | 0.304512 | − | 0.147966i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.58356e7 | − | 2.01461e7i | 0.623586 | − | 0.793327i | ||||
\(917\) | 1.83757e7i | 0.721640i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3.54182e7i | − | 1.38337i | −0.722200 | − | 0.691684i | \(-0.756869\pi\) | ||
0.722200 | − | 0.691684i | \(-0.243131\pi\) | |||||||
\(920\) | 1.41603e7 | + | 3.07530e6i | 0.551571 | + | 0.119789i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.10689e7 | − | 4.33595e7i | −0.816232 | − | 1.67980i | ||||
\(923\) | −6.48473e6 | −0.250546 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.90168e7 | 0.730772 | ||||||||
\(926\) | −1.44446e7 | − | 2.97267e7i | −0.553575 | − | 1.13925i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.53164e7 | + | 2.91936e7i | −1.34619 | + | 1.11280i | ||||
\(929\) | 4.08533e7i | 1.55306i | 0.630080 | + | 0.776530i | \(0.283022\pi\) | ||||
−0.630080 | + | 0.776530i | \(0.716978\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.14753e7i | − | 0.812016i | ||||||
\(932\) | 4.16357e7 | + | 3.27273e7i | 1.57010 | + | 1.23416i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.19105e6 | − | 3.98012e6i | 0.307236 | − | 0.149289i | ||||
\(935\) | −557207. | −0.0208443 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.49763e7 | 1.30144 | 0.650721 | − | 0.759317i | \(-0.274467\pi\) | ||||
0.650721 | + | 0.759317i | \(0.274467\pi\) | |||||||
\(938\) | −1.17546e7 | + | 5.71169e6i | −0.436215 | + | 0.211962i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.14989e6 | + | 4.83405e6i | 0.227011 | + | 0.178440i | ||||
\(941\) | 1.01395e7i | 0.373285i | 0.982428 | + | 0.186642i | \(0.0597606\pi\) | ||||
−0.982428 | + | 0.186642i | \(0.940239\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.85837e7i | 1.04674i | ||||||||
\(944\) | 1.48621e6 | + | 6.11407e6i | 0.0542814 | + | 0.223306i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.65019e6 | − | 1.78020e7i | −0.314266 | − | 0.646757i | ||||
\(947\) | 3.64042e7 | 1.31910 | 0.659549 | − | 0.751662i | \(-0.270747\pi\) | ||||
0.659549 | + | 0.751662i | \(0.270747\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.00772e6 | −0.108410 | ||||||||
\(950\) | −8.10069e6 | − | 1.66711e7i | −0.291215 | − | 0.599317i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 214130. | − | 985966.i | 0.00765747 | − | 0.0352590i | ||||
\(953\) | 3.96453e7i | 1.41403i | 0.707198 | + | 0.707016i | \(0.249959\pi\) | ||||
−0.707198 | + | 0.707016i | \(0.750041\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 3.12461e6i | − | 0.110863i | ||||||
\(956\) | −1.82816e7 | + | 2.32579e7i | −0.646949 | + | 0.823049i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.05393e7 | + | 9.98029e6i | −0.723057 | + | 0.351341i | ||||
\(959\) | −4.11753e6 | −0.144574 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.28647e6 | 0.219583 | ||||||||
\(962\) | −6.84048e6 | + | 3.32387e6i | −0.238314 | + | 0.115799i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.14353e6 | + | 2.72700e6i | −0.0742912 | + | 0.0945134i | ||||
\(965\) | 574731.i | 0.0198676i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.14182e7i | − | 0.392675i | −0.980536 | − | 0.196337i | \(-0.937095\pi\) | ||
0.980536 | − | 0.196337i | \(-0.0629048\pi\) | |||||||
\(968\) | −4.95443e6 | + | 2.28127e7i | −0.169944 | + | 0.782509i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.12497e7 | − | 2.31517e7i | −0.383893 | − | 0.790047i | ||||
\(971\) | −4.35838e7 | −1.48346 | −0.741732 | − | 0.670697i | \(-0.765995\pi\) | ||||
−0.741732 | + | 0.670697i | \(0.765995\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.94567e7 | −0.658852 | ||||||||
\(974\) | 1.55498e7 | + | 3.20013e7i | 0.525203 | + | 1.08086i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.33640e7 | − | 5.49774e7i | −0.449067 | − | 1.84740i | ||||
\(977\) | 4.35775e7i | 1.46058i | 0.683136 | + | 0.730291i | \(0.260616\pi\) | ||||
−0.683136 | + | 0.730291i | \(0.739384\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3.32448e6i | − | 0.110858i | ||||||
\(980\) | −1.10748e7 | − | 8.70522e6i | −0.368358 | − | 0.289544i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.67976e7 | − | 1.30212e7i | 0.886782 | − | 0.430897i | ||||
\(983\) | −7.18955e6 | −0.237311 | −0.118656 | − | 0.992935i | \(-0.537858\pi\) | ||||
−0.118656 | + | 0.992935i | \(0.537858\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.25744e7 | 0.741352 | ||||||||
\(986\) | 3.77603e6 | − | 1.83482e6i | 0.123693 | − | 0.0601036i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.82777e6 | + | 4.58086e6i | 0.189937 | + | 0.149298i | ||||
\(989\) | − | 4.71590e7i | − | 1.53311i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.64691e7i | 1.17962i | 0.807543 | + | 0.589808i | \(0.200797\pi\) | ||||
−0.807543 | + | 0.589808i | \(0.799203\pi\) | |||||||
\(992\) | 2.11037e7 | − | 1.74450e7i | 0.680895 | − | 0.562849i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.65007e6 | − | 1.36858e7i | −0.213481 | − | 0.439343i | ||||
\(995\) | 1.06186e7 | 0.340025 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.18842e7 | 1.01587 | 0.507934 | − | 0.861396i | \(-0.330409\pi\) | ||||
0.507934 | + | 0.861396i | \(0.330409\pi\) | |||||||
\(998\) | 5.55519e6 | + | 1.14325e7i | 0.176552 | + | 0.363342i | ||||
\(999\) | 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.107.13 | yes | 16 | |
3.2 | odd | 2 | inner | 108.6.b.b.107.4 | yes | 16 | |
4.3 | odd | 2 | inner | 108.6.b.b.107.3 | ✓ | 16 | |
12.11 | even | 2 | inner | 108.6.b.b.107.14 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.6.b.b.107.3 | ✓ | 16 | 4.3 | odd | 2 | inner | |
108.6.b.b.107.4 | yes | 16 | 3.2 | odd | 2 | inner | |
108.6.b.b.107.13 | yes | 16 | 1.1 | even | 1 | trivial | |
108.6.b.b.107.14 | yes | 16 | 12.11 | even | 2 | inner |