Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(55,108)]
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, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.55");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.d (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: | \(11.1639560131\) |
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: | \( x^{16} + 38x^{14} + 1016x^{12} + 13512x^{10} + 130640x^{8} + 569472x^{6} + 1783808x^{4} + 352256x^{2} + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{24} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.4 | ||
Root | \(-1.12787 + 1.95353i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.55 |
Dual form | 108.5.d.b.55.3 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.49052 | + | 1.95353i | −0.872630 | + | 0.488382i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 8.36746 | − | 13.6377i | 0.522967 | − | 0.852353i | ||||
\(5\) | −47.1174 | −1.88470 | −0.942348 | − | 0.334634i | \(-0.891387\pi\) | ||||
−0.942348 | + | 0.334634i | \(0.891387\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 67.4003i | 1.37552i | 0.725940 | + | 0.687758i | \(0.241405\pi\) | ||||
−0.725940 | + | 0.687758i | \(0.758595\pi\) | |||||||
\(8\) | −2.56528 | + | 63.9486i | −0.0400825 | + | 0.999196i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 164.464 | − | 92.0451i | 1.64464 | − | 0.920451i | ||||
\(11\) | − | 69.3981i | − | 0.573538i | −0.958000 | − | 0.286769i | \(-0.907419\pi\) | ||
0.958000 | − | 0.286769i | \(-0.0925813\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.28838 | 0.0194579 | 0.00972893 | − | 0.999953i | \(-0.496903\pi\) | ||||
0.00972893 | + | 0.999953i | \(0.496903\pi\) | |||||||
\(14\) | −131.668 | − | 235.262i | −0.671777 | − | 1.20032i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −115.971 | − | 228.225i | −0.453012 | − | 0.891504i | ||||
\(17\) | 116.780 | 0.404083 | 0.202041 | − | 0.979377i | \(-0.435242\pi\) | ||||
0.202041 | + | 0.979377i | \(0.435242\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 513.525i | − | 1.42251i | −0.702935 | − | 0.711254i | \(-0.748128\pi\) | ||
0.702935 | − | 0.711254i | \(-0.251872\pi\) | |||||||
\(20\) | −394.253 | + | 642.571i | −0.985633 | + | 1.60643i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 135.571 | + | 242.236i | 0.280106 | + | 0.500487i | ||||
\(23\) | − | 134.254i | − | 0.253789i | −0.991916 | − | 0.126895i | \(-0.959499\pi\) | ||
0.991916 | − | 0.126895i | \(-0.0405010\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1595.05 | 2.55208 | ||||||||
\(26\) | −11.4782 | + | 6.42394i | −0.0169795 | + | 0.00950287i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 919.182 | + | 563.970i | 1.17243 | + | 0.719349i | ||||
\(29\) | 772.602 | 0.918671 | 0.459335 | − | 0.888263i | \(-0.348088\pi\) | ||||
0.459335 | + | 0.888263i | \(0.348088\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1069.97i | − | 1.11339i | −0.830717 | − | 0.556695i | \(-0.812069\pi\) | ||
0.830717 | − | 0.556695i | \(-0.187931\pi\) | |||||||
\(32\) | 850.643 | + | 570.072i | 0.830706 | + | 0.556711i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −407.623 | + | 228.133i | −0.352615 | + | 0.197347i | ||||
\(35\) | − | 3175.73i | − | 2.59243i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1034.09 | −0.755362 | −0.377681 | − | 0.925936i | \(-0.623278\pi\) | ||||
−0.377681 | + | 0.925936i | \(0.623278\pi\) | |||||||
\(38\) | 1003.19 | + | 1792.47i | 0.694727 | + | 1.24132i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 120.869 | − | 3013.09i | 0.0755434 | − | 1.88318i | ||||
\(41\) | 2272.62 | 1.35195 | 0.675973 | − | 0.736927i | \(-0.263724\pi\) | ||||
0.675973 | + | 0.736927i | \(0.263724\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2523.25i | 1.36466i | 0.731046 | + | 0.682328i | \(0.239033\pi\) | ||||
−0.731046 | + | 0.682328i | \(0.760967\pi\) | |||||||
\(44\) | −946.428 | − | 580.686i | −0.488857 | − | 0.299941i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 262.270 | + | 468.618i | 0.123946 | + | 0.221464i | ||||
\(47\) | 694.871i | 0.314564i | 0.987554 | + | 0.157282i | \(0.0502731\pi\) | ||||
−0.987554 | + | 0.157282i | \(0.949727\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2141.80 | −0.892045 | ||||||||
\(50\) | −5567.55 | + | 3115.97i | −2.22702 | + | 1.24639i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 27.5154 | − | 44.8458i | 0.0101758 | − | 0.0165850i | ||||
\(53\) | −1166.03 | −0.415106 | −0.207553 | − | 0.978224i | \(-0.566550\pi\) | ||||
−0.207553 | + | 0.978224i | \(0.566550\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3269.86i | 1.08095i | ||||||||
\(56\) | −4310.15 | − | 172.901i | −1.37441 | − | 0.0551342i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2696.78 | + | 1509.30i | −0.801660 | + | 0.448662i | ||||
\(59\) | − | 5539.90i | − | 1.59147i | −0.605647 | − | 0.795733i | \(-0.707086\pi\) | ||
0.605647 | − | 0.795733i | \(-0.292914\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3204.11 | −0.861089 | −0.430544 | − | 0.902569i | \(-0.641678\pi\) | ||||
−0.430544 | + | 0.902569i | \(0.641678\pi\) | |||||||
\(62\) | 2090.21 | + | 3734.75i | 0.543760 | + | 0.971578i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4082.84 | − | 328.092i | −0.996787 | − | 0.0801006i | ||||
\(65\) | −154.940 | −0.0366722 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5366.14i | − | 1.19540i | −0.801721 | − | 0.597699i | \(-0.796082\pi\) | ||
0.801721 | − | 0.597699i | \(-0.203918\pi\) | |||||||
\(68\) | 977.152 | − | 1592.60i | 0.211322 | − | 0.344421i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6203.87 | + | 11084.9i | 1.26610 | + | 2.26223i | ||||
\(71\) | 166.225i | 0.0329746i | 0.999864 | + | 0.0164873i | \(0.00524832\pi\) | ||||
−0.999864 | + | 0.0164873i | \(0.994752\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5085.51 | 0.954309 | 0.477154 | − | 0.878819i | \(-0.341668\pi\) | ||||
0.477154 | + | 0.878819i | \(0.341668\pi\) | |||||||
\(74\) | 3609.51 | − | 2020.12i | 0.659151 | − | 0.368905i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7003.28 | − | 4296.90i | −1.21248 | − | 0.743924i | ||||
\(77\) | 4677.46 | 0.788911 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 724.474i | 0.116083i | 0.998314 | + | 0.0580415i | \(0.0184856\pi\) | ||||
−0.998314 | + | 0.0580415i | \(0.981514\pi\) | |||||||
\(80\) | 5464.26 | + | 10753.4i | 0.853790 | + | 1.68021i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7932.63 | + | 4439.62i | −1.17975 | + | 0.660265i | ||||
\(83\) | − | 8153.13i | − | 1.18350i | −0.806121 | − | 0.591750i | \(-0.798437\pi\) | ||
0.806121 | − | 0.591750i | \(-0.201563\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5502.37 | −0.761573 | ||||||||
\(86\) | −4929.24 | − | 8807.46i | −0.666473 | − | 1.19084i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4437.91 | + | 178.026i | 0.573077 | + | 0.0229889i | ||||
\(89\) | −6963.40 | −0.879107 | −0.439553 | − | 0.898217i | \(-0.644863\pi\) | ||||
−0.439553 | + | 0.898217i | \(0.644863\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 221.638i | 0.0267646i | ||||||||
\(92\) | −1830.92 | − | 1123.37i | −0.216318 | − | 0.132723i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1357.45 | − | 2425.46i | −0.153627 | − | 0.274498i | ||||
\(95\) | 24196.0i | 2.68099i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −278.895 | −0.0296413 | −0.0148207 | − | 0.999890i | \(-0.504718\pi\) | ||||
−0.0148207 | + | 0.999890i | \(0.504718\pi\) | |||||||
\(98\) | 7476.00 | − | 4184.07i | 0.778426 | − | 0.435659i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 13346.5 | − | 21752.7i | 1.33465 | − | 2.17527i | ||||
\(101\) | 9308.10 | 0.912469 | 0.456235 | − | 0.889860i | \(-0.349198\pi\) | ||||
0.456235 | + | 0.889860i | \(0.349198\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3271.88i | 0.308406i | 0.988039 | + | 0.154203i | \(0.0492810\pi\) | ||||
−0.988039 | + | 0.154203i | \(0.950719\pi\) | |||||||
\(104\) | −8.43562 | + | 210.287i | −0.000779921 | + | 0.0194422i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4070.06 | − | 2277.88i | 0.362234 | − | 0.202730i | ||||
\(107\) | − | 1845.07i | − | 0.161156i | −0.996748 | − | 0.0805778i | \(-0.974323\pi\) | ||
0.996748 | − | 0.0805778i | \(-0.0256765\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6021.20 | 0.506793 | 0.253396 | − | 0.967363i | \(-0.418452\pi\) | ||||
0.253396 | + | 0.967363i | \(0.418452\pi\) | |||||||
\(110\) | −6387.76 | − | 11413.5i | −0.527914 | − | 0.943266i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 15382.4 | − | 7816.49i | 1.22628 | − | 0.623126i | ||||
\(113\) | 8841.22 | 0.692398 | 0.346199 | − | 0.938161i | \(-0.387472\pi\) | ||||
0.346199 | + | 0.938161i | \(0.387472\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6325.72i | 0.478315i | ||||||||
\(116\) | 6464.72 | − | 10536.5i | 0.480434 | − | 0.783032i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10822.3 | + | 19337.1i | 0.777243 | + | 1.38876i | ||||
\(119\) | 7871.00i | 0.555822i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9824.90 | 0.671054 | ||||||||
\(122\) | 11184.0 | − | 6259.32i | 0.751412 | − | 0.420540i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14591.9 | − | 8952.92i | −0.949002 | − | 0.582266i | ||||
\(125\) | −45706.2 | −2.92520 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9165.05i | − | 0.568234i | −0.958790 | − | 0.284117i | \(-0.908300\pi\) | ||
0.958790 | − | 0.284117i | \(-0.0917004\pi\) | |||||||
\(128\) | 14892.2 | − | 6830.72i | 0.908946 | − | 0.416914i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 540.821 | − | 302.679i | 0.0320012 | − | 0.0179100i | ||||
\(131\) | 16239.9i | 0.946325i | 0.880975 | + | 0.473162i | \(0.156888\pi\) | ||||
−0.880975 | + | 0.473162i | \(0.843112\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 34611.7 | 1.95668 | ||||||||
\(134\) | 10482.9 | + | 18730.6i | 0.583810 | + | 1.04314i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −299.573 | + | 7467.91i | −0.0161967 | + | 0.403758i | ||||
\(137\) | −30410.5 | −1.62025 | −0.810125 | − | 0.586257i | \(-0.800601\pi\) | ||||
−0.810125 | + | 0.586257i | \(0.800601\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 32689.0i | − | 1.69189i | −0.533269 | − | 0.845946i | \(-0.679037\pi\) | ||
0.533269 | − | 0.845946i | \(-0.320963\pi\) | |||||||
\(140\) | −43309.5 | − | 26572.8i | −2.20967 | − | 1.35575i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −324.725 | − | 580.212i | −0.0161042 | − | 0.0287747i | ||||
\(143\) | − | 228.207i | − | 0.0111598i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −36403.0 | −1.73141 | ||||||||
\(146\) | −17751.1 | + | 9934.68i | −0.832759 | + | 0.466067i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8652.71 | + | 14102.6i | −0.395029 | + | 0.643835i | ||||
\(149\) | 13388.8 | 0.603073 | 0.301536 | − | 0.953455i | \(-0.402501\pi\) | ||||
0.301536 | + | 0.953455i | \(0.402501\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 9106.99i | − | 0.399412i | −0.979856 | − | 0.199706i | \(-0.936001\pi\) | ||
0.979856 | − | 0.199706i | \(-0.0639987\pi\) | |||||||
\(152\) | 32839.2 | + | 1317.34i | 1.42136 | + | 0.0570177i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −16326.8 | + | 9137.54i | −0.688428 | + | 0.385290i | ||||
\(155\) | 50414.1i | 2.09840i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4555.18 | 0.184802 | 0.0924009 | − | 0.995722i | \(-0.470546\pi\) | ||||
0.0924009 | + | 0.995722i | \(0.470546\pi\) | |||||||
\(158\) | −1415.28 | − | 2528.79i | −0.0566928 | − | 0.101298i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −40080.1 | − | 26860.3i | −1.56563 | − | 1.04923i | ||||
\(161\) | 9048.79 | 0.349091 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 466.424i | − | 0.0175552i | −0.999961 | − | 0.00877760i | \(-0.997206\pi\) | ||
0.999961 | − | 0.00877760i | \(-0.00279403\pi\) | |||||||
\(164\) | 19016.1 | − | 30993.2i | 0.707022 | − | 1.15233i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15927.4 | + | 28458.7i | 0.578000 | + | 1.03276i | ||||
\(167\) | − | 30165.9i | − | 1.08164i | −0.841138 | − | 0.540821i | \(-0.818114\pi\) | ||
0.841138 | − | 0.540821i | \(-0.181886\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −28550.2 | −0.999621 | ||||||||
\(170\) | 19206.1 | − | 10749.0i | 0.664572 | − | 0.371938i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 34411.2 | + | 21113.2i | 1.16317 | + | 0.713670i | ||||
\(173\) | 51017.1 | 1.70460 | 0.852302 | − | 0.523051i | \(-0.175206\pi\) | ||||
0.852302 | + | 0.523051i | \(0.175206\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 107507.i | 3.51043i | ||||||||
\(176\) | −15838.4 | + | 8048.18i | −0.511312 | + | 0.259820i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 24305.9 | − | 13603.2i | 0.767135 | − | 0.429340i | ||||
\(179\) | − | 26293.5i | − | 0.820622i | −0.911946 | − | 0.410311i | \(-0.865420\pi\) | ||
0.911946 | − | 0.410311i | \(-0.134580\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3132.04 | 0.0956026 | 0.0478013 | − | 0.998857i | \(-0.484779\pi\) | ||||
0.0478013 | + | 0.998857i | \(0.484779\pi\) | |||||||
\(182\) | −432.975 | − | 773.631i | −0.0130713 | − | 0.0233556i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8585.38 | + | 344.401i | 0.253585 | + | 0.0101725i | ||||
\(185\) | 48723.6 | 1.42363 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 8104.31i | − | 0.231757i | ||||||
\(188\) | 9476.41 | + | 5814.31i | 0.268119 | + | 0.164506i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −47267.5 | − | 84456.5i | −1.30935 | − | 2.33952i | ||||
\(191\) | − | 17160.1i | − | 0.470384i | −0.971949 | − | 0.235192i | \(-0.924428\pi\) | ||
0.971949 | − | 0.235192i | \(-0.0755718\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16841.7 | −0.452139 | −0.226070 | − | 0.974111i | \(-0.572588\pi\) | ||||
−0.226070 | + | 0.974111i | \(0.572588\pi\) | |||||||
\(194\) | 973.490 | − | 544.829i | 0.0258659 | − | 0.0144763i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −17921.4 | + | 29209.1i | −0.466510 | + | 0.760338i | ||||
\(197\) | −67293.3 | −1.73396 | −0.866981 | − | 0.498342i | \(-0.833942\pi\) | ||||
−0.866981 | + | 0.498342i | \(0.833942\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13276.3i | 0.335253i | 0.985851 | + | 0.167626i | \(0.0536102\pi\) | ||||
−0.985851 | + | 0.167626i | \(0.946390\pi\) | |||||||
\(200\) | −4091.75 | + | 102001.i | −0.102294 | + | 2.55003i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −32490.1 | + | 18183.6i | −0.796248 | + | 0.445633i | ||||
\(203\) | 52073.6i | 1.26365i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −107080. | −2.54801 | ||||||||
\(206\) | −6391.71 | − | 11420.6i | −0.150620 | − | 0.269124i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −381.357 | − | 750.491i | −0.00881465 | − | 0.0173468i | ||||
\(209\) | −35637.7 | −0.815863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17830.2i | − | 0.400489i | −0.979746 | − | 0.200245i | \(-0.935826\pi\) | ||
0.979746 | − | 0.200245i | \(-0.0641737\pi\) | |||||||
\(212\) | −9756.73 | + | 15901.9i | −0.217086 | + | 0.353817i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3604.39 | + | 6440.26i | 0.0787055 | + | 0.140629i | ||||
\(215\) | − | 118889.i | − | 2.57196i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 72116.2 | 1.53149 | ||||||||
\(218\) | −21017.1 | + | 11762.6i | −0.442242 | + | 0.247508i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 44593.2 | + | 27360.4i | 0.921347 | + | 0.565298i | ||||
\(221\) | 384.017 | 0.00786259 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 68248.8i | − | 1.37241i | −0.727406 | − | 0.686207i | \(-0.759274\pi\) | ||
0.727406 | − | 0.686207i | \(-0.240726\pi\) | |||||||
\(224\) | −38423.0 | + | 57333.6i | −0.765765 | + | 1.14265i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −30860.5 | + | 17271.6i | −0.604207 | + | 0.338154i | ||||
\(227\) | − | 56672.7i | − | 1.09982i | −0.835223 | − | 0.549911i | \(-0.814662\pi\) | ||
0.835223 | − | 0.549911i | \(-0.185338\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 65653.5 | 1.25195 | 0.625975 | − | 0.779843i | \(-0.284701\pi\) | ||||
0.625975 | + | 0.779843i | \(0.284701\pi\) | |||||||
\(230\) | −12357.5 | − | 22080.1i | −0.233601 | − | 0.417392i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1981.94 | + | 49406.8i | −0.0368226 | + | 0.917932i | ||||
\(233\) | 55652.7 | 1.02512 | 0.512559 | − | 0.858652i | \(-0.328697\pi\) | ||||
0.512559 | + | 0.858652i | \(0.328697\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 32740.5i | − | 0.592857i | ||||||
\(236\) | −75551.2 | − | 46354.9i | −1.35649 | − | 0.832284i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −15376.2 | − | 27473.9i | −0.271454 | − | 0.485027i | ||||
\(239\) | − | 13031.8i | − | 0.228144i | −0.993472 | − | 0.114072i | \(-0.963611\pi\) | ||
0.993472 | − | 0.114072i | \(-0.0363895\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 57972.1 | 0.998124 | 0.499062 | − | 0.866566i | \(-0.333678\pi\) | ||||
0.499062 | + | 0.866566i | \(0.333678\pi\) | |||||||
\(242\) | −34294.0 | + | 19193.2i | −0.585582 | + | 0.327730i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −26810.3 | + | 43696.5i | −0.450321 | + | 0.733952i | ||||
\(245\) | 100916. | 1.68123 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1688.67i | − | 0.0276790i | ||||||
\(248\) | 68422.9 | + | 2744.77i | 1.11250 | + | 0.0446275i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 159538. | − | 89288.3i | 2.55262 | − | 1.42861i | ||||
\(251\) | 81292.8i | 1.29034i | 0.764038 | + | 0.645171i | \(0.223214\pi\) | ||||
−0.764038 | + | 0.645171i | \(0.776786\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9317.01 | −0.145558 | ||||||||
\(254\) | 17904.2 | + | 31990.8i | 0.277515 | + | 0.495858i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −38637.4 | + | 52935.0i | −0.589560 | + | 0.807724i | ||||
\(257\) | −18818.7 | −0.284920 | −0.142460 | − | 0.989801i | \(-0.545501\pi\) | ||||
−0.142460 | + | 0.989801i | \(0.545501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 69698.0i | − | 1.03901i | ||||||
\(260\) | −1296.45 | + | 2113.02i | −0.0191783 | + | 0.0312576i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −31725.0 | − | 56685.6i | −0.462168 | − | 0.825791i | ||||
\(263\) | − | 96169.6i | − | 1.39036i | −0.718837 | − | 0.695179i | \(-0.755325\pi\) | ||
0.718837 | − | 0.695179i | \(-0.244675\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 54940.4 | 0.782348 | ||||||||
\(266\) | −120813. | + | 67615.0i | −1.70746 | + | 0.955608i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −73181.5 | − | 44901.0i | −1.01890 | − | 0.625153i | ||||
\(269\) | 20853.4 | 0.288186 | 0.144093 | − | 0.989564i | \(-0.453974\pi\) | ||||
0.144093 | + | 0.989564i | \(0.453974\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 101517.i | 1.38230i | 0.722712 | + | 0.691149i | \(0.242895\pi\) | ||||
−0.722712 | + | 0.691149i | \(0.757105\pi\) | |||||||
\(272\) | −13543.1 | − | 26652.1i | −0.183054 | − | 0.360242i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 106148. | − | 59407.7i | 1.41388 | − | 0.791301i | ||||
\(275\) | − | 110693.i | − | 1.46372i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 53726.5 | 0.700212 | 0.350106 | − | 0.936710i | \(-0.386146\pi\) | ||||
0.350106 | + | 0.936710i | \(0.386146\pi\) | |||||||
\(278\) | 63858.9 | + | 114102.i | 0.826289 | + | 1.47640i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 203083. | + | 8146.64i | 2.59035 | + | 0.103911i | ||||
\(281\) | −99500.6 | −1.26012 | −0.630061 | − | 0.776545i | \(-0.716970\pi\) | ||||
−0.630061 | + | 0.776545i | \(0.716970\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 69719.8i | − | 0.870529i | −0.900303 | − | 0.435265i | \(-0.856655\pi\) | ||
0.900303 | − | 0.435265i | \(-0.143345\pi\) | |||||||
\(284\) | 2266.92 | + | 1390.88i | 0.0281060 | + | 0.0172446i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 445.809 | + | 796.563i | 0.00545026 | + | 0.00973840i | ||||
\(287\) | 153175.i | 1.85962i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −69883.5 | −0.836717 | ||||||||
\(290\) | 127065. | − | 71114.2i | 1.51088 | − | 0.845592i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 42552.8 | − | 69354.4i | 0.499072 | − | 0.813408i | ||||
\(293\) | −12440.0 | −0.144905 | −0.0724526 | − | 0.997372i | \(-0.523083\pi\) | ||||
−0.0724526 | + | 0.997372i | \(0.523083\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 261025.i | 2.99943i | ||||||||
\(296\) | 2652.73 | − | 66128.6i | 0.0302768 | − | 0.754755i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −46733.9 | + | 26155.4i | −0.526259 | + | 0.294530i | ||||
\(299\) | − | 441.480i | − | 0.00493819i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −170068. | −1.87711 | ||||||||
\(302\) | 17790.8 | + | 31788.1i | 0.195065 | + | 0.348539i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −117199. | + | 59554.1i | −1.26817 | + | 0.644413i | ||||
\(305\) | 150969. | 1.62289 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 151986.i | − | 1.61260i | −0.591504 | − | 0.806302i | \(-0.701466\pi\) | ||
0.591504 | − | 0.806302i | \(-0.298534\pi\) | |||||||
\(308\) | 39138.4 | − | 63789.5i | 0.412574 | − | 0.672431i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −98485.4 | − | 175972.i | −1.02482 | − | 1.83113i | ||||
\(311\) | − | 50086.5i | − | 0.517845i | −0.965898 | − | 0.258923i | \(-0.916633\pi\) | ||
0.965898 | − | 0.258923i | \(-0.0833675\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 61969.9 | 0.632546 | 0.316273 | − | 0.948668i | \(-0.397568\pi\) | ||||
0.316273 | + | 0.948668i | \(0.397568\pi\) | |||||||
\(314\) | −15900.0 | + | 8898.67i | −0.161264 | + | 0.0902539i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9880.12 | + | 6062.01i | 0.0989437 | + | 0.0607075i | ||||
\(317\) | −80.9272 | −0.000805334 | −0.000402667 | − | 1.00000i | \(-0.500128\pi\) | ||||
−0.000402667 | 1.00000i | \(0.500128\pi\) | ||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 53617.1i | − | 0.526893i | ||||||
\(320\) | 192373. | + | 15458.9i | 1.87864 | + | 0.150965i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −31585.0 | + | 17677.1i | −0.304627 | + | 0.170490i | ||||
\(323\) | − | 59969.4i | − | 0.574811i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5245.13 | 0.0496580 | ||||||||
\(326\) | 911.172 | + | 1628.06i | 0.00857364 | + | 0.0153192i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5829.91 | + | 145331.i | −0.0541894 | + | 1.35086i | ||||
\(329\) | −46834.5 | −0.432687 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 31123.5i | − | 0.284074i | −0.989861 | − | 0.142037i | \(-0.954635\pi\) | ||
0.989861 | − | 0.142037i | \(-0.0453652\pi\) | |||||||
\(332\) | −111190. | − | 68221.0i | −1.00876 | − | 0.618931i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 58929.9 | + | 105295.i | 0.528254 | + | 0.943873i | ||||
\(335\) | 252839.i | 2.25296i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5863.61 | 0.0516304 | 0.0258152 | − | 0.999667i | \(-0.491782\pi\) | ||||
0.0258152 | + | 0.999667i | \(0.491782\pi\) | |||||||
\(338\) | 99655.0 | − | 55773.6i | 0.872300 | − | 0.488197i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −46040.9 | + | 75039.4i | −0.398277 | + | 0.649129i | ||||
\(341\) | −74253.8 | −0.638572 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17470.1i | 0.148493i | ||||||||
\(344\) | −161358. | − | 6472.85i | −1.36356 | − | 0.0546989i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −178076. | + | 99663.2i | −1.48749 | + | 0.832497i | ||||
\(347\) | 138155.i | 1.14738i | 0.819073 | + | 0.573689i | \(0.194488\pi\) | ||||
−0.819073 | + | 0.573689i | \(0.805512\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 180947. | 1.48559 | 0.742797 | − | 0.669517i | \(-0.233499\pi\) | ||||
0.742797 | + | 0.669517i | \(0.233499\pi\) | |||||||
\(350\) | −210018. | − | 375255.i | −1.71443 | − | 3.06330i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 39561.9 | − | 59033.1i | 0.319295 | − | 0.476442i | ||||
\(353\) | −98784.9 | −0.792759 | −0.396380 | − | 0.918087i | \(-0.629734\pi\) | ||||
−0.396380 | + | 0.918087i | \(0.629734\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 7832.10i | − | 0.0621472i | ||||||
\(356\) | −58266.0 | + | 94964.5i | −0.459743 | + | 0.749309i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 51365.2 | + | 91778.2i | 0.400777 | + | 0.716099i | ||||
\(359\) | 151427.i | 1.17493i | 0.809248 | + | 0.587467i | \(0.199875\pi\) | ||||
−0.809248 | + | 0.587467i | \(0.800125\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −133387. | −1.02353 | ||||||||
\(362\) | −10932.4 | + | 6118.52i | −0.0834257 | + | 0.0466906i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3022.62 | + | 1854.55i | 0.0228129 | + | 0.0139970i | ||||
\(365\) | −239616. | −1.79858 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 101304.i | 0.752132i | 0.926593 | + | 0.376066i | \(0.122723\pi\) | ||||
−0.926593 | + | 0.376066i | \(0.877277\pi\) | |||||||
\(368\) | −30640.2 | + | 15569.6i | −0.226254 | + | 0.114970i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −170071. | + | 95182.9i | −1.24230 | + | 0.695273i | ||||
\(371\) | − | 78590.9i | − | 0.570985i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −181796. | −1.30667 | −0.653336 | − | 0.757068i | \(-0.726631\pi\) | ||||
−0.653336 | + | 0.757068i | \(0.726631\pi\) | |||||||
\(374\) | 15832.0 | + | 28288.3i | 0.113186 | + | 0.202238i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −44436.0 | − | 1782.54i | −0.314311 | − | 0.0126085i | ||||
\(377\) | 2540.61 | 0.0178754 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2324.09i | − | 0.0161798i | −0.999967 | − | 0.00808991i | \(-0.997425\pi\) | ||
0.999967 | − | 0.00808991i | \(-0.00257513\pi\) | |||||||
\(380\) | 329976. | + | 202459.i | 2.28515 | + | 1.40207i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 33522.7 | + | 59897.6i | 0.229727 | + | 0.410471i | ||||
\(383\) | 129732.i | 0.884402i | 0.896916 | + | 0.442201i | \(0.145802\pi\) | ||||
−0.896916 | + | 0.442201i | \(0.854198\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −220390. | −1.48686 | ||||||||
\(386\) | 58786.4 | − | 32900.8i | 0.394550 | − | 0.220817i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2333.65 | + | 3803.48i | −0.0155014 | + | 0.0252649i | ||||
\(389\) | −53603.2 | −0.354235 | −0.177118 | − | 0.984190i | \(-0.556677\pi\) | ||||
−0.177118 | + | 0.984190i | \(0.556677\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 15678.2i | − | 0.102552i | ||||||
\(392\) | 5494.32 | − | 136965.i | 0.0357554 | − | 0.891329i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 234889. | − | 131459.i | 1.51311 | − | 0.846835i | ||||
\(395\) | − | 34135.3i | − | 0.218781i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 156598. | 0.993584 | 0.496792 | − | 0.867870i | \(-0.334511\pi\) | ||||
0.496792 | + | 0.867870i | \(0.334511\pi\) | |||||||
\(398\) | −25935.7 | − | 46341.3i | −0.163731 | − | 0.292551i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −184980. | − | 364030.i | −1.15612 | − | 2.27519i | ||||
\(401\) | −207347. | −1.28946 | −0.644731 | − | 0.764410i | \(-0.723031\pi\) | ||||
−0.644731 | + | 0.764410i | \(0.723031\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 3518.46i | − | 0.0216642i | ||||||
\(404\) | 77885.2 | − | 126941.i | 0.477191 | − | 0.777746i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −101727. | − | 181764.i | −0.617142 | − | 1.10270i | ||||
\(407\) | 71763.9i | 0.433229i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35322.3 | 0.211156 | 0.105578 | − | 0.994411i | \(-0.466331\pi\) | ||||
0.105578 | + | 0.994411i | \(0.466331\pi\) | |||||||
\(410\) | 373765. | − | 209184.i | 2.22347 | − | 1.24440i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 44620.8 | + | 27377.3i | 0.262871 | + | 0.161286i | ||||
\(413\) | 373391. | 2.18909 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 384154.i | 2.23054i | ||||||||
\(416\) | 2797.24 | + | 1874.61i | 0.0161638 | + | 0.0108324i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 124394. | − | 69619.2i | 0.711946 | − | 0.398452i | ||||
\(419\) | − | 272874.i | − | 1.55430i | −0.629318 | − | 0.777148i | \(-0.716666\pi\) | ||
0.629318 | − | 0.777148i | \(-0.283334\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −223490. | −1.26094 | −0.630468 | − | 0.776215i | \(-0.717137\pi\) | ||||
−0.630468 | + | 0.776215i | \(0.717137\pi\) | |||||||
\(422\) | 34831.8 | + | 62236.6i | 0.195592 | + | 0.349479i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2991.20 | − | 74566.1i | 0.0166385 | − | 0.414772i | ||||
\(425\) | 186270. | 1.03125 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 215958.i | − | 1.18444i | ||||||
\(428\) | −25162.4 | − | 15438.6i | −0.137361 | − | 0.0842790i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 232253. | + | 414984.i | 1.25610 | + | 2.24437i | ||||
\(431\) | 158123.i | 0.851216i | 0.904908 | + | 0.425608i | \(0.139940\pi\) | ||||
−0.904908 | + | 0.425608i | \(0.860060\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 135143. | 0.720803 | 0.360401 | − | 0.932797i | \(-0.382640\pi\) | ||||
0.360401 | + | 0.932797i | \(0.382640\pi\) | |||||||
\(434\) | −251723. | + | 140881.i | −1.33642 | + | 0.747950i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 50382.2 | − | 82115.1i | 0.265036 | − | 0.431966i | ||||
\(437\) | −68943.0 | −0.361017 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 75873.6i | 0.393697i | 0.980434 | + | 0.196848i | \(0.0630707\pi\) | ||||
−0.980434 | + | 0.196848i | \(0.936929\pi\) | |||||||
\(440\) | −209103. | − | 8388.11i | −1.08008 | − | 0.0433270i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1340.42 | + | 750.187i | −0.00686113 | + | 0.00383994i | ||||
\(443\) | 99747.7i | 0.508271i | 0.967169 | + | 0.254135i | \(0.0817909\pi\) | ||||
−0.967169 | + | 0.254135i | \(0.918209\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 328097. | 1.65685 | ||||||||
\(446\) | 133326. | + | 238224.i | 0.670262 | + | 1.19761i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 22113.5 | − | 275185.i | 0.110180 | − | 1.37110i | ||||
\(449\) | 156931. | 0.778424 | 0.389212 | − | 0.921148i | \(-0.372747\pi\) | ||||
0.389212 | + | 0.921148i | \(0.372747\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 157716.i | − | 0.775392i | ||||||
\(452\) | 73978.6 | − | 120574.i | 0.362101 | − | 0.590167i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 110712. | + | 197817.i | 0.537133 | + | 0.959737i | ||||
\(455\) | − | 10443.0i | − | 0.0504432i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 109830. | 0.525882 | 0.262941 | − | 0.964812i | \(-0.415308\pi\) | ||||
0.262941 | + | 0.964812i | \(0.415308\pi\) | |||||||
\(458\) | −229165. | + | 128256.i | −1.09249 | + | 0.611430i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 86268.0 | + | 52930.2i | 0.407694 | + | 0.250143i | ||||
\(461\) | −172802. | −0.813104 | −0.406552 | − | 0.913628i | \(-0.633269\pi\) | ||||
−0.406552 | + | 0.913628i | \(0.633269\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 159146.i | 0.742395i | 0.928554 | + | 0.371198i | \(0.121053\pi\) | ||||
−0.928554 | + | 0.371198i | \(0.878947\pi\) | |||||||
\(464\) | −89599.5 | − | 176327.i | −0.416169 | − | 0.818999i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −194257. | + | 108719.i | −0.894549 | + | 0.500649i | ||||
\(467\) | 153806.i | 0.705246i | 0.935765 | + | 0.352623i | \(0.114710\pi\) | ||||
−0.935765 | + | 0.352623i | \(0.885290\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 361679. | 1.64429 | ||||||||
\(470\) | 63959.5 | + | 114281.i | 0.289540 | + | 0.517345i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 354268. | + | 14211.4i | 1.59019 | + | 0.0637900i | ||||
\(473\) | 175109. | 0.782683 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 819098.i | − | 3.63035i | ||||||
\(476\) | 107342. | + | 65860.3i | 0.473757 | + | 0.290677i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25458.0 | + | 45487.8i | 0.111421 | + | 0.199085i | ||||
\(479\) | − | 246496.i | − | 1.07433i | −0.843477 | − | 0.537166i | \(-0.819495\pi\) | ||
0.843477 | − | 0.537166i | \(-0.180505\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3400.48 | −0.0146977 | ||||||||
\(482\) | −202353. | + | 113250.i | −0.870993 | + | 0.487466i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 82209.5 | − | 133989.i | 0.350939 | − | 0.571975i | ||||
\(485\) | 13140.8 | 0.0558649 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 341810.i | − | 1.44121i | −0.693347 | − | 0.720603i | \(-0.743865\pi\) | ||
0.693347 | − | 0.720603i | \(-0.256135\pi\) | |||||||
\(488\) | 8219.45 | − | 204898.i | 0.0345146 | − | 0.860397i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −352250. | + | 197142.i | −1.46710 | + | 0.821084i | ||||
\(491\) | − | 302270.i | − | 1.25381i | −0.779095 | − | 0.626906i | \(-0.784321\pi\) | ||
0.779095 | − | 0.626906i | \(-0.215679\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 90224.4 | 0.371219 | ||||||||
\(494\) | 3298.85 | + | 5894.32i | 0.0135179 | + | 0.0241535i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −244194. | + | 124085.i | −0.992592 | + | 0.504379i | ||||
\(497\) | −11203.6 | −0.0453572 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 193507.i | 0.777132i | 0.921421 | + | 0.388566i | \(0.127029\pi\) | ||||
−0.921421 | + | 0.388566i | \(0.872971\pi\) | |||||||
\(500\) | −382445. | + | 623325.i | −1.52978 | + | 2.49330i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −158808. | − | 283754.i | −0.630179 | − | 1.12599i | ||||
\(503\) | − | 452328.i | − | 1.78779i | −0.448273 | − | 0.893897i | \(-0.647961\pi\) | ||
0.448273 | − | 0.893897i | \(-0.352039\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −438573. | −1.71973 | ||||||||
\(506\) | 32521.2 | − | 18201.0i | 0.127018 | − | 0.0710878i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −124990. | − | 76688.2i | −0.484336 | − | 0.297167i | ||||
\(509\) | 232364. | 0.896876 | 0.448438 | − | 0.893814i | \(-0.351980\pi\) | ||||
0.448438 | + | 0.893814i | \(0.351980\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 342765.i | 1.31267i | ||||||||
\(512\) | 31454.7 | − | 260250.i | 0.119990 | − | 0.992775i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 65687.0 | − | 36762.8i | 0.248630 | − | 0.139150i | ||||
\(515\) | − | 154163.i | − | 0.581252i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 48222.8 | 0.180414 | ||||||||
\(518\) | 136157. | + | 243282.i | 0.507435 | + | 0.906673i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 397.465 | − | 9908.18i | 0.00146991 | − | 0.0366427i | ||||
\(521\) | −425181. | −1.56638 | −0.783192 | − | 0.621780i | \(-0.786410\pi\) | ||||
−0.783192 | + | 0.621780i | \(0.786410\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 91819.6i | 0.335685i | 0.985814 | + | 0.167842i | \(0.0536800\pi\) | ||||
−0.985814 | + | 0.167842i | \(0.946320\pi\) | |||||||
\(524\) | 221474. | + | 135887.i | 0.806603 | + | 0.494896i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 187870. | + | 335682.i | 0.679025 | + | 1.21327i | ||||
\(527\) | − | 124951.i | − | 0.449902i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 261817. | 0.935591 | ||||||||
\(530\) | −191771. | + | 107328.i | −0.682701 | + | 0.382085i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 289613. | − | 472023.i | 1.02328 | − | 1.66778i | ||||
\(533\) | 7473.24 | 0.0263060 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 86934.9i | 0.303729i | ||||||||
\(536\) | 343157. | + | 13765.7i | 1.19444 | + | 0.0479146i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −72789.3 | + | 40737.7i | −0.251480 | + | 0.140745i | ||||
\(539\) | 148637.i | 0.511622i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −419310. | −1.43265 | −0.716326 | − | 0.697766i | \(-0.754178\pi\) | ||||
−0.716326 | + | 0.697766i | \(0.754178\pi\) | |||||||
\(542\) | −198317. | − | 354349.i | −0.675090 | − | 1.20624i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 99338.1 | + | 66572.9i | 0.335674 | + | 0.224957i | ||||
\(545\) | −283703. | −0.955150 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 372884.i | 1.24623i | 0.782129 | + | 0.623116i | \(0.214134\pi\) | ||||
−0.782129 | + | 0.623116i | \(0.785866\pi\) | |||||||
\(548\) | −254459. | + | 414727.i | −0.847337 | + | 1.38103i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 216243. | + | 386378.i | 0.714852 | + | 1.27728i | ||||
\(551\) | − | 396751.i | − | 1.30682i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −48829.8 | −0.159674 | ||||||||
\(554\) | −187534. | + | 104956.i | −0.611026 | + | 0.341971i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −445802. | − | 273524.i | −1.44209 | − | 0.884803i | ||||
\(557\) | 249244. | 0.803369 | 0.401685 | − | 0.915778i | \(-0.368425\pi\) | ||||
0.401685 | + | 0.915778i | \(0.368425\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8297.40i | 0.0265533i | ||||||||
\(560\) | −724781. | + | 368293.i | −2.31116 | + | 1.17440i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 347309. | − | 194377.i | 1.09962 | − | 0.615421i | ||||
\(563\) | 469821.i | 1.48223i | 0.671377 | + | 0.741116i | \(0.265703\pi\) | ||||
−0.671377 | + | 0.741116i | \(0.734297\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −416575. | −1.30496 | ||||||||
\(566\) | 136200. | + | 243358.i | 0.425151 | + | 0.759650i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10629.9 | − | 426.415i | −0.0329482 | − | 0.00132171i | ||||
\(569\) | 501734. | 1.54971 | 0.774853 | − | 0.632142i | \(-0.217824\pi\) | ||||
0.774853 | + | 0.632142i | \(0.217824\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 514877.i | 1.57918i | 0.613636 | + | 0.789589i | \(0.289706\pi\) | ||||
−0.613636 | + | 0.789589i | \(0.710294\pi\) | |||||||
\(572\) | −3112.21 | − | 1909.52i | −0.00951212 | − | 0.00583622i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −299232. | − | 534661.i | −0.908206 | − | 1.62276i | ||||
\(575\) | − | 214143.i | − | 0.647690i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 55168.5 | 0.165707 | 0.0828533 | − | 0.996562i | \(-0.473597\pi\) | ||||
0.0828533 | + | 0.996562i | \(0.473597\pi\) | |||||||
\(578\) | 243930. | − | 136519.i | 0.730145 | − | 0.408637i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −304601. | + | 496451.i | −0.905472 | + | 1.47578i | ||||
\(581\) | 549524. | 1.62792 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 80920.5i | 0.238079i | ||||||||
\(584\) | −13045.8 | + | 325211.i | −0.0382511 | + | 0.953542i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 43421.9 | − | 24301.8i | 0.126449 | − | 0.0707690i | ||||
\(587\) | 221207.i | 0.641980i | 0.947083 | + | 0.320990i | \(0.104016\pi\) | ||||
−0.947083 | + | 0.320990i | \(0.895984\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −549456. | −1.58381 | ||||||||
\(590\) | −509920. | − | 911115.i | −1.46487 | − | 2.61739i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 119925. | + | 236005.i | 0.342188 | + | 0.673408i | ||||
\(593\) | 167379. | 0.475982 | 0.237991 | − | 0.971267i | \(-0.423511\pi\) | ||||
0.237991 | + | 0.971267i | \(0.423511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 370861.i | − | 1.04756i | ||||||
\(596\) | 112030. | − | 182592.i | 0.315387 | − | 0.514031i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 862.442 | + | 1540.99i | 0.00241172 | + | 0.00430922i | ||||
\(599\) | − | 285002.i | − | 0.794319i | −0.917750 | − | 0.397160i | \(-0.869996\pi\) | ||
0.917750 | − | 0.397160i | \(-0.130004\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30586.9 | 0.0846810 | 0.0423405 | − | 0.999103i | \(-0.486519\pi\) | ||||
0.0423405 | + | 0.999103i | \(0.486519\pi\) | |||||||
\(602\) | 593625. | − | 332232.i | 1.63802 | − | 0.916745i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −124198. | − | 76202.4i | −0.340440 | − | 0.208879i | ||||
\(605\) | −462924. | −1.26473 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 165312.i | 0.448670i | 0.974512 | + | 0.224335i | \(0.0720209\pi\) | ||||
−0.974512 | + | 0.224335i | \(0.927979\pi\) | |||||||
\(608\) | 292746. | − | 436827.i | 0.791925 | − | 1.18169i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −526962. | + | 294923.i | −1.41618 | + | 0.792590i | ||||
\(611\) | 2285.00i | 0.00612074i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −64752.4 | −0.172320 | −0.0861599 | − | 0.996281i | \(-0.527460\pi\) | ||||
−0.0861599 | + | 0.996281i | \(0.527460\pi\) | |||||||
\(614\) | 296909. | + | 530511.i | 0.787566 | + | 1.40721i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11999.0 | + | 299117.i | −0.0316216 | + | 0.788277i | ||||
\(617\) | 321272. | 0.843923 | 0.421961 | − | 0.906614i | \(-0.361342\pi\) | ||||
0.421961 | + | 0.906614i | \(0.361342\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 409948.i | − | 1.06991i | −0.844880 | − | 0.534956i | \(-0.820328\pi\) | ||
0.844880 | − | 0.534956i | \(-0.179672\pi\) | |||||||
\(620\) | 687530. | + | 421838.i | 1.78858 | + | 1.09739i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 97845.4 | + | 174828.i | 0.252906 | + | 0.451887i | ||||
\(623\) | − | 469335.i | − | 1.20923i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.15665e6 | 2.96103 | ||||||||
\(626\) | −216307. | + | 121060.i | −0.551979 | + | 0.308924i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 38115.3 | − | 62122.0i | 0.0966452 | − | 0.157516i | ||||
\(629\) | −120761. | −0.305229 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 453263.i | 1.13839i | 0.822202 | + | 0.569195i | \(0.192745\pi\) | ||||
−0.822202 | + | 0.569195i | \(0.807255\pi\) | |||||||
\(632\) | −46329.1 | − | 1858.48i | −0.115990 | − | 0.00465290i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 282.478 | − | 158.093i | 0.000702758 | − | 0.000393310i | ||||
\(635\) | 431833.i | 1.07095i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7043.05 | −0.0173573 | ||||||||
\(638\) | 104743. | + | 187152.i | 0.257325 | + | 0.459783i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −701680. | + | 321846.i | −1.71309 | + | 0.785757i | ||||
\(641\) | 764363. | 1.86030 | 0.930152 | − | 0.367175i | \(-0.119675\pi\) | ||||
0.930152 | + | 0.367175i | \(0.119675\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 674655.i | − | 1.63177i | −0.578211 | − | 0.815887i | \(-0.696249\pi\) | ||
0.578211 | − | 0.815887i | \(-0.303751\pi\) | |||||||
\(644\) | 75715.4 | − | 123404.i | 0.182563 | − | 0.297549i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 117152. | + | 209324.i | 0.280727 | + | 0.501597i | ||||
\(647\) | 372446.i | 0.889723i | 0.895599 | + | 0.444861i | \(0.146747\pi\) | ||||
−0.895599 | + | 0.444861i | \(0.853253\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −384458. | −0.912767 | ||||||||
\(650\) | −18308.2 | + | 10246.5i | −0.0433331 | + | 0.0242521i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6360.93 | − | 3902.79i | −0.0149632 | − | 0.00918078i | ||||
\(653\) | −620680. | −1.45560 | −0.727799 | − | 0.685791i | \(-0.759457\pi\) | ||||
−0.727799 | + | 0.685791i | \(0.759457\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 765181.i | − | 1.78353i | ||||||
\(656\) | −263558. | − | 518669.i | −0.612447 | − | 1.20527i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 163477. | − | 91492.5i | 0.377576 | − | 0.211317i | ||||
\(659\) | 416907.i | 0.959993i | 0.877271 | + | 0.479996i | \(0.159362\pi\) | ||||
−0.877271 | + | 0.479996i | \(0.840638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −724690. | −1.65863 | −0.829315 | − | 0.558782i | \(-0.811269\pi\) | ||||
−0.829315 | + | 0.558782i | \(0.811269\pi\) | |||||||
\(662\) | 60800.5 | + | 108637.i | 0.138737 | + | 0.247892i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 521381. | + | 20915.1i | 1.18255 | + | 0.0474377i | ||||
\(665\) | −1.63082e6 | −3.68775 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 103725.i | − | 0.233149i | ||||||
\(668\) | −411392. | − | 252412.i | −0.921941 | − | 0.565662i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −493927. | − | 882538.i | −1.10030 | − | 1.96600i | ||||
\(671\) | 222359.i | 0.493867i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −239394. | −0.528546 | −0.264273 | − | 0.964448i | \(-0.585132\pi\) | ||||
−0.264273 | + | 0.964448i | \(0.585132\pi\) | |||||||
\(674\) | −20467.0 | + | 11454.7i | −0.0450542 | + | 0.0252153i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −238893. | + | 389357.i | −0.522769 | + | 0.852031i | ||||
\(677\) | −731049. | −1.59503 | −0.797515 | − | 0.603299i | \(-0.793853\pi\) | ||||
−0.797515 | + | 0.603299i | \(0.793853\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 18797.6i | − | 0.0407721i | ||||||
\(680\) | 14115.1 | − | 351868.i | 0.0305258 | − | 0.760961i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 259184. | − | 145057.i | 0.557237 | − | 0.311867i | ||||
\(683\) | − | 804575.i | − | 1.72475i | −0.506273 | − | 0.862373i | \(-0.668977\pi\) | ||
0.506273 | − | 0.862373i | \(-0.331023\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.43286e6 | 3.05368 | ||||||||
\(686\) | −34128.3 | − | 60979.7i | −0.0725214 | − | 0.129580i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 575869. | − | 292624.i | 1.21660 | − | 0.618206i | ||||
\(689\) | −3834.36 | −0.00807707 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 734097.i | 1.53744i | 0.639587 | + | 0.768719i | \(0.279105\pi\) | ||||
−0.639587 | + | 0.768719i | \(0.720895\pi\) | |||||||
\(692\) | 426883. | − | 695753.i | 0.891450 | − | 1.45292i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −269889. | − | 482232.i | −0.560359 | − | 1.00124i | ||||
\(695\) | 1.54022e6i | 3.18870i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 265396. | 0.546298 | ||||||||
\(698\) | −631598. | + | 353484.i | −1.29637 | + | 0.725537i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.46614e6 | + | 899560.i | 2.99212 | + | 1.83584i | ||||
\(701\) | 158522. | 0.322592 | 0.161296 | − | 0.986906i | \(-0.448433\pi\) | ||||
0.161296 | + | 0.986906i | \(0.448433\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 531031.i | 1.07451i | ||||||||
\(704\) | −22769.0 | + | 283341.i | −0.0459408 | + | 0.571695i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 344811. | − | 192979.i | 0.691785 | − | 0.387169i | ||||
\(707\) | 627369.i | 1.25512i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 365334. | 0.726770 | 0.363385 | − | 0.931639i | \(-0.381621\pi\) | ||||
0.363385 | + | 0.931639i | \(0.381621\pi\) | |||||||
\(710\) | 15300.2 | + | 27338.1i | 0.0303516 | + | 0.0542315i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17863.1 | − | 445300.i | 0.0352368 | − | 0.878400i | ||||
\(713\) | −143648. | −0.282566 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10752.5i | 0.0210329i | ||||||||
\(716\) | −358582. | − | 220010.i | −0.699460 | − | 0.429158i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −295816. | − | 528558.i | −0.573817 | − | 1.02528i | ||||
\(719\) | − | 801198.i | − | 1.54982i | −0.632070 | − | 0.774911i | \(-0.717795\pi\) | ||
0.632070 | − | 0.774911i | \(-0.282205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −220526. | −0.424218 | ||||||||
\(722\) | 465590. | − | 260575.i | 0.893160 | − | 0.499872i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 26207.2 | − | 42713.6i | 0.0499970 | − | 0.0814872i | ||||
\(725\) | 1.23234e6 | 2.34452 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 207794.i | − | 0.393155i | −0.980488 | − | 0.196577i | \(-0.937017\pi\) | ||
0.980488 | − | 0.196577i | \(-0.0629827\pi\) | |||||||
\(728\) | −14173.4 | − | 568.563i | −0.0267431 | − | 0.00107279i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 836385. | − | 468097.i | 1.56950 | − | 0.878395i | ||||
\(731\) | 294665.i | 0.551434i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 177976. | 0.331248 | 0.165624 | − | 0.986189i | \(-0.447036\pi\) | ||||
0.165624 | + | 0.986189i | \(0.447036\pi\) | |||||||
\(734\) | −197900. | − | 353603.i | −0.367328 | − | 0.656333i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 76534.7 | − | 114203.i | 0.141287 | − | 0.210824i | ||||
\(737\) | −372400. | −0.685606 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 587913.i | 1.07653i | 0.842777 | + | 0.538263i | \(0.180919\pi\) | ||||
−0.842777 | + | 0.538263i | \(0.819081\pi\) | |||||||
\(740\) | 407693. | − | 664476.i | 0.744509 | − | 1.21343i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 153530. | + | 274323.i | 0.278859 | + | 0.498259i | ||||
\(743\) | 675642.i | 1.22388i | 0.790904 | + | 0.611940i | \(0.209611\pi\) | ||||
−0.790904 | + | 0.611940i | \(0.790389\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −630846. | −1.13661 | ||||||||
\(746\) | 634562. | − | 355143.i | 1.14024 | − | 0.638155i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −110524. | − | 67812.5i | −0.197539 | − | 0.121201i | ||||
\(749\) | 124358. | 0.221672 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 267589.i | − | 0.474447i | −0.971455 | − | 0.237224i | \(-0.923763\pi\) | ||
0.971455 | − | 0.237224i | \(-0.0762374\pi\) | |||||||
\(752\) | 158587. | − | 80584.9i | 0.280435 | − | 0.142501i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8868.04 | + | 4963.15i | −0.0155986 | + | 0.00873000i | ||||
\(755\) | 429098.i | 0.752770i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 400491. | 0.698878 | 0.349439 | − | 0.936959i | \(-0.386372\pi\) | ||||
0.349439 | + | 0.936959i | \(0.386372\pi\) | |||||||
\(758\) | 4540.17 | + | 8112.27i | 0.00790193 | + | 0.0141190i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.54730e6 | − | 62069.5i | −2.67884 | − | 0.107461i | ||||
\(761\) | 755370. | 1.30434 | 0.652170 | − | 0.758073i | \(-0.273859\pi\) | ||||
0.652170 | + | 0.758073i | \(0.273859\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 405831.i | 0.697101i | ||||||||
\(764\) | −234023. | − | 143586.i | −0.400933 | − | 0.245995i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −253435. | − | 452832.i | −0.431926 | − | 0.771756i | ||||
\(767\) | − | 18217.3i | − | 0.0309665i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −482211. | −0.815427 | −0.407713 | − | 0.913110i | \(-0.633674\pi\) | ||||
−0.407713 | + | 0.913110i | \(0.633674\pi\) | |||||||
\(770\) | 769274. | − | 430537.i | 1.29748 | − | 0.726155i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −140923. | + | 229682.i | −0.236454 | + | 0.385382i | ||||
\(773\) | −1.06175e6 | −1.77691 | −0.888454 | − | 0.458965i | \(-0.848220\pi\) | ||||
−0.888454 | + | 0.458965i | \(0.848220\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.70665e6i | − | 2.84146i | ||||||
\(776\) | 715.445 | − | 17835.0i | 0.00118810 | − | 0.0296175i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 187103. | − | 104715.i | 0.309116 | − | 0.173002i | ||||
\(779\) | − | 1.16705e6i | − | 1.92315i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11535.7 | 0.0189122 | ||||||||
\(782\) | 30627.8 | + | 54725.2i | 0.0500844 | + | 0.0894898i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 248387. | + | 488813.i | 0.404107 | + | 0.795262i | ||||
\(785\) | −214628. | −0.348295 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 313747.i | − | 0.506559i | −0.967393 | − | 0.253280i | \(-0.918491\pi\) | ||
0.967393 | − | 0.253280i | \(-0.0815093\pi\) | |||||||
\(788\) | −563074. | + | 917723.i | −0.906804 | + | 1.47795i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 66684.3 | + | 119150.i | 0.106849 | + | 0.190915i | ||||
\(791\) | 595901.i | 0.952404i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10536.3 | −0.0167549 | ||||||||
\(794\) | −546608. | + | 305918.i | −0.867031 | + | 0.485248i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 181058. | + | 111089.i | 0.285754 | + | 0.175326i | ||||
\(797\) | −756561. | −1.19104 | −0.595522 | − | 0.803339i | \(-0.703055\pi\) | ||||
−0.595522 | + | 0.803339i | \(0.703055\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 81147.0i | 0.127110i | ||||||||
\(800\) | 1.35682e6 | + | 909293.i | 2.12003 | + | 1.42077i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 723748. | − | 405058.i | 1.12522 | − | 0.629750i | ||||
\(803\) | − | 352925.i | − | 0.547333i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −426356. | −0.657931 | ||||||||
\(806\) | 6873.41 | + | 12281.3i | 0.0105804 | + | 0.0189048i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −23877.9 | + | 595240.i | −0.0365741 | + | 0.911736i | ||||
\(809\) | 259808. | 0.396968 | 0.198484 | − | 0.980104i | \(-0.436398\pi\) | ||||
0.198484 | + | 0.980104i | \(0.436398\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 108740.i | − | 0.165329i | −0.996577 | − | 0.0826644i | \(-0.973657\pi\) | ||
0.996577 | − | 0.0826644i | \(-0.0263430\pi\) | |||||||
\(812\) | 710162. | + | 435724.i | 1.07707 | + | 0.660845i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −140193. | − | 250493.i | −0.211581 | − | 0.378049i | ||||
\(815\) | 21976.7i | 0.0330862i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.29575e6 | 1.94123 | ||||||||
\(818\) | −123293. | + | 69003.1i | −0.184261 | + | 0.103125i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −895988. | + | 1.46032e6i | −1.33252 | + | 2.17180i | ||||
\(821\) | 468489. | 0.695045 | 0.347523 | − | 0.937672i | \(-0.387023\pi\) | ||||
0.347523 | + | 0.937672i | \(0.387023\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 487197.i | − | 0.719291i | −0.933089 | − | 0.359646i | \(-0.882898\pi\) | ||
0.933089 | − | 0.359646i | \(-0.117102\pi\) | |||||||
\(824\) | −209232. | − | 8393.30i | −0.308158 | − | 0.0123617i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.30333e6 | + | 729429.i | −1.91026 | + | 1.06911i | ||||
\(827\) | 161820.i | 0.236603i | 0.992978 | + | 0.118301i | \(0.0377449\pi\) | ||||
−0.992978 | + | 0.118301i | \(0.962255\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −77603.0 | −0.112920 | −0.0564598 | − | 0.998405i | \(-0.517981\pi\) | ||||
−0.0564598 | + | 0.998405i | \(0.517981\pi\) | |||||||
\(830\) | −750456. | − | 1.34090e6i | −1.08935 | − | 1.94643i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −13425.9 | − | 1078.89i | −0.0193953 | − | 0.00155859i | ||||
\(833\) | −250119. | −0.360460 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.42134e6i | 2.03857i | ||||||||
\(836\) | −298197. | + | 486014.i | −0.426669 | + | 0.695403i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 533066. | + | 952471.i | 0.759089 | + | 1.35632i | ||||
\(839\) | − | 33592.5i | − | 0.0477220i | −0.999715 | − | 0.0238610i | \(-0.992404\pi\) | ||
0.999715 | − | 0.0238610i | \(-0.00759591\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −110367. | −0.156044 | ||||||||
\(842\) | 780095. | − | 436593.i | 1.10033 | − | 0.615818i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −243162. | − | 149193.i | −0.341358 | − | 0.209443i | ||||
\(845\) | 1.34521e6 | 1.88398 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 662201.i | 0.923045i | ||||||||
\(848\) | 135226. | + | 266118.i | 0.188048 | + | 0.370069i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −650178. | + | 363883.i | −0.899901 | + | 0.503644i | ||||
\(851\) | 138831.i | 0.191703i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 713456. | 0.980549 | 0.490274 | − | 0.871568i | \(-0.336897\pi\) | ||||
0.490274 | + | 0.871568i | \(0.336897\pi\) | |||||||
\(854\) | 421880. | + | 753806.i | 0.578460 | + | 1.03358i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 117990. | + | 4733.13i | 0.161026 | + | 0.00645952i | ||||
\(857\) | 345801. | 0.470830 | 0.235415 | − | 0.971895i | \(-0.424355\pi\) | ||||
0.235415 | + | 0.971895i | \(0.424355\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 942252.i | − | 1.27697i | −0.769634 | − | 0.638485i | \(-0.779561\pi\) | ||
0.769634 | − | 0.638485i | \(-0.220439\pi\) | |||||||
\(860\) | −1.62137e6 | − | 994799.i | −2.19222 | − | 1.34505i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −308897. | − | 551931.i | −0.415719 | − | 0.742797i | ||||
\(863\) | 110905.i | 0.148912i | 0.997224 | + | 0.0744561i | \(0.0237221\pi\) | ||||
−0.997224 | + | 0.0744561i | \(0.976278\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.40379e6 | −3.21266 | ||||||||
\(866\) | −471718. | + | 264005.i | −0.628994 | + | 0.352027i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 603430. | − | 983495.i | 0.800916 | − | 1.30537i | ||||
\(869\) | 50277.1 | 0.0665780 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 17645.9i | − | 0.0232599i | ||||||
\(872\) | −15446.1 | + | 385047.i | −0.0203135 | + | 0.506385i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 240647. | − | 134682.i | 0.315034 | − | 0.176314i | ||||
\(875\) | − | 3.08061e6i | − | 4.02366i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −573424. | −0.745550 | −0.372775 | − | 0.927922i | \(-0.621594\pi\) | ||||
−0.372775 | + | 0.927922i | \(0.621594\pi\) | |||||||
\(878\) | −148221. | − | 264838.i | −0.192274 | − | 0.343552i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 746264. | − | 379209.i | 0.963668 | − | 0.489681i | ||||
\(881\) | 446113. | 0.574768 | 0.287384 | − | 0.957815i | \(-0.407214\pi\) | ||||
0.287384 | + | 0.957815i | \(0.407214\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.28083e6i | 1.64274i | 0.570393 | + | 0.821372i | \(0.306791\pi\) | ||||
−0.570393 | + | 0.821372i | \(0.693209\pi\) | |||||||
\(884\) | 3213.25 | − | 5237.09i | 0.00411187 | − | 0.00670170i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −194860. | − | 348171.i | −0.248230 | − | 0.443532i | ||||
\(887\) | 901749.i | 1.14614i | 0.819506 | + | 0.573071i | \(0.194248\pi\) | ||||
−0.819506 | + | 0.573071i | \(0.805752\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 617727. | 0.781615 | ||||||||
\(890\) | −1.14523e6 | + | 640947.i | −1.44582 | + | 0.809175i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −930753. | − | 571069.i | −1.16978 | − | 0.717727i | ||||
\(893\) | 356834. | 0.447469 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.23888e6i | 1.54662i | ||||||||
\(896\) | 460393. | + | 1.00374e6i | 0.573472 | + | 1.25027i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −547771. | + | 306569.i | −0.679276 | + | 0.380168i | ||||
\(899\) | − | 826660.i | − | 1.02284i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −136169. | −0.167737 | ||||||||
\(902\) | 308102. | + | 550510.i | 0.378688 | + | 0.676631i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22680.2 | + | 565384.i | −0.0277530 | + | 0.691841i | ||||
\(905\) | −147573. | −0.180182 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 181413.i | − | 0.220523i | −0.993903 | − | 0.110261i | \(-0.964831\pi\) | ||
0.993903 | − | 0.110261i | \(-0.0351688\pi\) | |||||||
\(908\) | −772883. | − | 474207.i | −0.937436 | − | 0.575170i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 20400.7 | + | 36451.5i | 0.0246355 | + | 0.0440182i | ||||
\(911\) | 47687.4i | 0.0574602i | 0.999587 | + | 0.0287301i | \(0.00914634\pi\) | ||||
−0.999587 | + | 0.0287301i | \(0.990854\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −565812. | −0.678783 | ||||||||
\(914\) | −383364. | + | 214556.i | −0.458900 | + | 0.256831i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 549354. | − | 895360.i | 0.654728 | − | 1.06710i | ||||
\(917\) | −1.09457e6 | −1.30169 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.10248e6i | − | 1.30539i | −0.757622 | − | 0.652694i | \(-0.773639\pi\) | ||
0.757622 | − | 0.652694i | \(-0.226361\pi\) | |||||||
\(920\) | −404521. | − | 16227.3i | −0.477931 | − | 0.0191721i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 603168. | − | 337573.i | 0.709539 | − | 0.397105i | ||||
\(923\) | 546.611i | 0.000641616i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.64942e6 | −1.92774 | ||||||||
\(926\) | −310897. | − | 555504.i | −0.362572 | − | 0.647836i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 657209. | + | 440439.i | 0.763146 | + | 0.511434i | ||||
\(929\) | −924812. | −1.07157 | −0.535787 | − | 0.844353i | \(-0.679985\pi\) | ||||
−0.535787 | + | 0.844353i | \(0.679985\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.09987e6i | 1.26894i | ||||||||
\(932\) | 465672. | − | 758972.i | 0.536103 | − | 0.873763i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −300465. | − | 536865.i | −0.344429 | − | 0.615419i | ||||
\(935\) | 381854.i | 0.436791i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35819.1 | −0.0407977 | −0.0203988 | − | 0.999792i | \(-0.506494\pi\) | ||||
−0.0203988 | + | 0.999792i | \(0.506494\pi\) | |||||||
\(938\) | −1.26245e6 | + | 706550.i | −1.43486 | + | 0.803041i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −446504. | − | 273955.i | −0.505323 | − | 0.310044i | ||||
\(941\) | 434924. | 0.491172 | 0.245586 | − | 0.969375i | \(-0.421020\pi\) | ||||
0.245586 | + | 0.969375i | \(0.421020\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 305109.i | − | 0.343109i | ||||||
\(944\) | −1.26434e6 | + | 642468.i | −1.41880 | + | 0.720954i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −611221. | + | 342080.i | −0.682993 | + | 0.382248i | ||||
\(947\) | 1.40078e6i | 1.56196i | 0.624553 | + | 0.780982i | \(0.285281\pi\) | ||||
−0.624553 | + | 0.780982i | \(0.714719\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16723.1 | 0.0185688 | ||||||||
\(950\) | 1.60013e6 | + | 2.85908e6i | 1.77300 | + | 3.16795i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −503339. | − | 20191.3i | −0.555376 | − | 0.0222788i | ||||
\(953\) | 320073. | 0.352422 | 0.176211 | − | 0.984352i | \(-0.443616\pi\) | ||||
0.176211 | + | 0.984352i | \(0.443616\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 808538.i | 0.886530i | ||||||||
\(956\) | −177723. | − | 109043.i | −0.194459 | − | 0.119312i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 481536. | + | 860398.i | 0.524684 | + | 0.937494i | ||||
\(959\) | − | 2.04968e6i | − | 2.22868i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −221311. | −0.239638 | ||||||||
\(962\) | 11869.4 | − | 6642.93i | 0.0128257 | − | 0.00717810i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 485079. | − | 790603.i | 0.521986 | − | 0.850754i | ||||
\(965\) | 793539. | 0.852145 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.06890e6i | − | 1.14310i | −0.820568 | − | 0.571549i | \(-0.806343\pi\) | ||
0.820568 | − | 0.571549i | \(-0.193657\pi\) | |||||||
\(968\) | −25203.6 | + | 628288.i | −0.0268975 | + | 0.670514i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −45868.3 | + | 25670.9i | −0.0487494 | + | 0.0272834i | ||||
\(971\) | − | 1.25688e6i | − | 1.33308i | −0.745471 | − | 0.666538i | \(-0.767775\pi\) | ||
0.745471 | − | 0.666538i | \(-0.232225\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.20325e6 | 2.32722 | ||||||||
\(974\) | 667734. | + | 1.19309e6i | 0.703859 | + | 1.25764i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 371584. | + | 731259.i | 0.390084 | + | 0.767664i | ||||
\(977\) | −748167. | −0.783807 | −0.391903 | − | 0.920006i | \(-0.628183\pi\) | ||||
−0.391903 | + | 0.920006i | \(0.628183\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 483247.i | 0.504201i | ||||||||
\(980\) | 844412. | − | 1.37626e6i | 0.879229 | − | 1.43301i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 590493. | + | 1.05508e6i | 0.612339 | + | 1.09411i | ||||
\(983\) | − | 1.53724e6i | − | 1.59087i | −0.606038 | − | 0.795436i | \(-0.707242\pi\) | ||
0.606038 | − | 0.795436i | \(-0.292758\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.17069e6 | 3.26799 | ||||||||
\(986\) | −314930. | + | 176256.i | −0.323937 | + | 0.181297i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −23029.4 | − | 14129.8i | −0.0235922 | − | 0.0144752i | ||||
\(989\) | 338758. | 0.346335 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.36196e6i | − | 1.38682i | −0.720546 | − | 0.693408i | \(-0.756109\pi\) | ||
0.720546 | − | 0.693408i | \(-0.243891\pi\) | |||||||
\(992\) | 609959. | − | 910161.i | 0.619836 | − | 0.924901i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 39106.5 | − | 21886.6i | 0.0395800 | − | 0.0221516i | ||||
\(995\) | − | 625547.i | − | 0.631849i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2016.78 | 0.00202893 | 0.00101447 | − | 0.999999i | \(-0.499677\pi\) | ||||
0.00101447 | + | 0.999999i | \(0.499677\pi\) | |||||||
\(998\) | −378020. | − | 675439.i | −0.379537 | − | 0.678148i | ||||
\(999\) | 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 | 108.5.d.b.55.4 | yes | 16 | |
3.2 | odd | 2 | inner | 108.5.d.b.55.13 | yes | 16 | |
4.3 | odd | 2 | inner | 108.5.d.b.55.3 | ✓ | 16 | |
12.11 | even | 2 | inner | 108.5.d.b.55.14 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.d.b.55.3 | ✓ | 16 | 4.3 | odd | 2 | inner | |
108.5.d.b.55.4 | yes | 16 | 1.1 | even | 1 | trivial | |
108.5.d.b.55.13 | yes | 16 | 3.2 | odd | 2 | inner | |
108.5.d.b.55.14 | yes | 16 | 12.11 | even | 2 | inner |