Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,6,Mod(17,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.17");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.1041806482\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 26.10 | ||
Character | \(\chi\) | \(=\) | 63.26 |
Dual form | 63.6.p.b.17.10 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.73742 | + | 3.88985i | 1.19102 | + | 0.687635i | 0.958538 | − | 0.284966i | \(-0.0919823\pi\) |
0.232481 | + | 0.972601i | \(0.425316\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 14.2619 | + | 24.7023i | 0.445684 | + | 0.771947i | ||||
\(5\) | 46.8267 | − | 81.1063i | 0.837662 | − | 1.45087i | −0.0541826 | − | 0.998531i | \(-0.517255\pi\) |
0.891845 | − | 0.452342i | \(-0.149411\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 58.7189 | − | 115.582i | 0.452932 | − | 0.891545i | ||||
\(8\) | − | 27.0441i | − | 0.149399i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 630.983 | − | 364.298i | 1.99534 | − | 1.15201i | ||||
\(11\) | −212.927 | + | 122.934i | −0.530579 | + | 0.306330i | −0.741252 | − | 0.671227i | \(-0.765768\pi\) |
0.210673 | + | 0.977557i | \(0.432434\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 592.325i | 0.972080i | 0.873937 | + | 0.486040i | \(0.161559\pi\) | ||||
−0.873937 | + | 0.486040i | \(0.838441\pi\) | |||||||
\(14\) | 845.209 | − | 550.314i | 1.15251 | − | 0.750396i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 561.578 | − | 972.681i | 0.548416 | − | 0.949884i | ||||
\(17\) | 1015.44 | + | 1758.79i | 0.852180 | + | 1.47602i | 0.879236 | + | 0.476386i | \(0.158053\pi\) |
−0.0270560 | + | 0.999634i | \(0.508613\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −703.867 | − | 406.378i | −0.447308 | − | 0.258253i | 0.259385 | − | 0.965774i | \(-0.416480\pi\) |
−0.706693 | + | 0.707521i | \(0.749814\pi\) | |||||||
\(20\) | 2671.35 | 1.49333 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1912.78 | −0.842572 | ||||||||
\(23\) | 35.1283 | + | 20.2814i | 0.0138464 | + | 0.00799424i | 0.506907 | − | 0.862001i | \(-0.330789\pi\) |
−0.493061 | + | 0.869995i | \(0.664122\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2822.98 | − | 4889.55i | −0.903355 | − | 1.56466i | ||||
\(26\) | −2304.06 | + | 3990.74i | −0.668436 | + | 1.15777i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3692.57 | − | 197.919i | 0.890090 | − | 0.0477081i | ||||
\(29\) | 5893.18i | 1.30123i | 0.759407 | + | 0.650616i | \(0.225489\pi\) | ||||
−0.759407 | + | 0.650616i | \(0.774511\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −152.886 | + | 88.2690i | −0.0285736 | + | 0.0164970i | −0.514219 | − | 0.857659i | \(-0.671918\pi\) |
0.485645 | + | 0.874156i | \(0.338585\pi\) | |||||||
\(32\) | 6817.70 | − | 3936.20i | 1.17696 | − | 0.679520i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 15799.6i | 2.34396i | ||||||||
\(35\) | −6624.78 | − | 10174.8i | −0.914115 | − | 1.40396i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2839.10 | − | 4917.47i | 0.340939 | − | 0.590524i | −0.643668 | − | 0.765305i | \(-0.722588\pi\) |
0.984607 | + | 0.174781i | \(0.0559216\pi\) | |||||||
\(38\) | −3161.50 | − | 5475.88i | −0.355168 | − | 0.615169i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2193.44 | − | 1266.38i | −0.216759 | − | 0.125146i | ||||
\(41\) | −2309.21 | −0.214538 | −0.107269 | − | 0.994230i | \(-0.534211\pi\) | ||||
−0.107269 | + | 0.994230i | \(0.534211\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 18360.2 | 1.51428 | 0.757140 | − | 0.653252i | \(-0.226596\pi\) | ||||
0.757140 | + | 0.653252i | \(0.226596\pi\) | |||||||
\(44\) | −6073.49 | − | 3506.53i | −0.472941 | − | 0.273052i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 157.783 | + | 273.288i | 0.0109942 | + | 0.0190426i | ||||
\(47\) | −5134.85 | + | 8893.82i | −0.339065 | + | 0.587278i | −0.984257 | − | 0.176743i | \(-0.943444\pi\) |
0.645192 | + | 0.764020i | \(0.276777\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9911.19 | − | 13573.6i | −0.589706 | − | 0.807618i | ||||
\(50\) | − | 43924.0i | − | 2.48471i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −14631.8 | + | 8447.67i | −0.750394 | + | 0.433240i | ||||
\(53\) | −34105.8 | + | 19691.0i | −1.66778 | + | 0.962893i | −0.698949 | + | 0.715171i | \(0.746349\pi\) |
−0.968831 | + | 0.247722i | \(0.920318\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 23026.3i | 1.02640i | ||||||||
\(56\) | −3125.79 | − | 1588.00i | −0.133196 | − | 0.0676674i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −22923.6 | + | 39704.8i | −0.894772 | + | 1.54979i | ||||
\(59\) | 17836.4 | + | 30893.5i | 0.667078 | + | 1.15541i | 0.978717 | + | 0.205213i | \(0.0657887\pi\) |
−0.311639 | + | 0.950201i | \(0.600878\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −19552.1 | − | 11288.4i | −0.672775 | − | 0.388427i | 0.124352 | − | 0.992238i | \(-0.460315\pi\) |
−0.797127 | + | 0.603811i | \(0.793648\pi\) | |||||||
\(62\) | −1373.41 | −0.0453755 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 25304.0 | 0.772216 | ||||||||
\(65\) | 48041.3 | + | 27736.7i | 1.41036 | + | 0.814274i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5727.31 | + | 9919.99i | 0.155870 | + | 0.269975i | 0.933376 | − | 0.358901i | \(-0.116848\pi\) |
−0.777505 | + | 0.628876i | \(0.783515\pi\) | |||||||
\(68\) | −28964.1 | + | 50167.4i | −0.759606 | + | 1.31568i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5055.54 | − | 94321.1i | −0.123317 | − | 2.30072i | ||||
\(71\) | − | 47986.7i | − | 1.12973i | −0.825183 | − | 0.564865i | \(-0.808928\pi\) | ||
0.825183 | − | 0.564865i | \(-0.191072\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −51691.9 | + | 29844.4i | −1.13531 | + | 0.655473i | −0.945266 | − | 0.326302i | \(-0.894197\pi\) |
−0.190047 | + | 0.981775i | \(0.560864\pi\) | |||||||
\(74\) | 38256.5 | − | 22087.4i | 0.812130 | − | 0.468883i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 23182.9i | − | 0.460397i | ||||||
\(77\) | 1706.01 | + | 31829.0i | 0.0327910 | + | 0.611781i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 37220.8 | − | 64468.4i | 0.670994 | − | 1.16220i | −0.306629 | − | 0.951829i | \(-0.599201\pi\) |
0.977623 | − | 0.210366i | \(-0.0674656\pi\) | |||||||
\(80\) | −52593.7 | − | 91094.9i | −0.918774 | − | 1.59136i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −15558.1 | − | 8982.50i | −0.255519 | − | 0.147524i | ||||
\(83\) | 87877.8 | 1.40018 | 0.700090 | − | 0.714054i | \(-0.253143\pi\) | ||||
0.700090 | + | 0.714054i | \(0.253143\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 190199. | 2.85536 | ||||||||
\(86\) | 123700. | + | 71418.4i | 1.80354 | + | 1.04127i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3324.63 | + | 5758.42i | 0.0457653 | + | 0.0792678i | ||||
\(89\) | −16626.9 | + | 28798.6i | −0.222503 | + | 0.385386i | −0.955567 | − | 0.294773i | \(-0.904756\pi\) |
0.733064 | + | 0.680159i | \(0.238089\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 68461.9 | + | 34780.7i | 0.866653 | + | 0.440286i | ||||
\(92\) | 1157.00i | 0.0142516i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −69191.2 | + | 39947.6i | −0.807665 | + | 0.466306i | ||||
\(95\) | −65919.6 | + | 38058.7i | −0.749386 | + | 0.432658i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 96672.7i | 1.04322i | 0.853185 | + | 0.521608i | \(0.174668\pi\) | ||||
−0.853185 | + | 0.521608i | \(0.825332\pi\) | |||||||
\(98\) | −13976.4 | − | 130004.i | −0.147004 | − | 1.36739i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 80522.2 | − | 139468.i | 0.805222 | − | 1.39468i | ||||
\(101\) | −9686.45 | − | 16777.4i | −0.0944846 | − | 0.163652i | 0.814909 | − | 0.579589i | \(-0.196787\pi\) |
−0.909393 | + | 0.415937i | \(0.863454\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 85999.1 | + | 49651.6i | 0.798731 | + | 0.461148i | 0.843027 | − | 0.537871i | \(-0.180771\pi\) |
−0.0442961 | + | 0.999018i | \(0.514104\pi\) | |||||||
\(104\) | 16018.9 | 0.145227 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −306380. | −2.64848 | ||||||||
\(107\) | −7121.68 | − | 4111.70i | −0.0601344 | − | 0.0347186i | 0.469631 | − | 0.882863i | \(-0.344387\pi\) |
−0.529766 | + | 0.848144i | \(0.677720\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −71076.3 | − | 123108.i | −0.573005 | − | 0.992474i | −0.996255 | − | 0.0864612i | \(-0.972444\pi\) |
0.423250 | − | 0.906013i | \(-0.360889\pi\) | |||||||
\(110\) | −89569.0 | + | 155138.i | −0.705791 | + | 1.22247i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −79448.8 | − | 122023.i | −0.598470 | − | 0.919170i | ||||
\(113\) | − | 42730.4i | − | 0.314804i | −0.987535 | − | 0.157402i | \(-0.949688\pi\) | ||
0.987535 | − | 0.157402i | \(-0.0503119\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3289.89 | − | 1899.42i | 0.0231973 | − | 0.0133929i | ||||
\(116\) | −145575. | + | 84047.8i | −1.00448 | + | 0.579938i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 277524.i | 1.83483i | ||||||||
\(119\) | 262909. | − | 14091.7i | 1.70192 | − | 0.0912214i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −50300.1 | + | 87122.3i | −0.312324 | + | 0.540961i | ||||
\(122\) | −87820.7 | − | 152110.i | −0.534192 | − | 0.925247i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4360.89 | − | 2517.76i | −0.0254696 | − | 0.0147049i | ||||
\(125\) | −236098. | −1.35150 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −308027. | −1.69465 | −0.847324 | − | 0.531076i | \(-0.821788\pi\) | ||||
−0.847324 | + | 0.531076i | \(0.821788\pi\) | |||||||
\(128\) | −47682.9 | − | 27529.7i | −0.257239 | − | 0.148517i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 215783. | + | 373747.i | 1.11985 | + | 1.93963i | ||||
\(131\) | −77775.3 | + | 134711.i | −0.395971 | + | 0.685842i | −0.993225 | − | 0.116210i | \(-0.962925\pi\) |
0.597254 | + | 0.802053i | \(0.296259\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −88300.1 | + | 57492.0i | −0.432844 | + | 0.281824i | ||||
\(134\) | 89113.5i | 0.428728i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 47564.9 | − | 27461.6i | 0.220515 | − | 0.127315i | ||||
\(137\) | 60915.0 | − | 35169.3i | 0.277283 | − | 0.160089i | −0.354910 | − | 0.934900i | \(-0.615489\pi\) |
0.632193 | + | 0.774811i | \(0.282155\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 63588.8i | − | 0.279154i | −0.990211 | − | 0.139577i | \(-0.955426\pi\) | ||
0.990211 | − | 0.139577i | \(-0.0445742\pi\) | |||||||
\(140\) | 156859. | − | 308759.i | 0.676376 | − | 1.33137i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 186661. | − | 323306.i | 0.776842 | − | 1.34553i | ||||
\(143\) | −72816.7 | − | 126122.i | −0.297777 | − | 0.515765i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 477974. | + | 275958.i | 1.88792 | + | 1.08999i | ||||
\(146\) | −464360. | −1.80291 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 161964. | 0.607804 | ||||||||
\(149\) | 31985.6 | + | 18466.9i | 0.118029 | + | 0.0681440i | 0.557852 | − | 0.829940i | \(-0.311626\pi\) |
−0.439823 | + | 0.898084i | \(0.644959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −269005. | − | 465931.i | −0.960105 | − | 1.66295i | −0.722228 | − | 0.691656i | \(-0.756882\pi\) |
−0.237877 | − | 0.971295i | \(-0.576452\pi\) | |||||||
\(152\) | −10990.1 | + | 19035.4i | −0.0385827 | + | 0.0668272i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −112316. | + | 221082.i | −0.381628 | + | 0.751191i | ||||
\(155\) | 16533.4i | 0.0552755i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −42906.0 | + | 24771.8i | −0.138921 | + | 0.0802064i | −0.567850 | − | 0.823132i | \(-0.692225\pi\) |
0.428928 | + | 0.903338i | \(0.358891\pi\) | |||||||
\(158\) | 501545. | − | 289567.i | 1.59833 | − | 0.922797i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 737278.i | − | 2.27683i | ||||||
\(161\) | 4406.85 | − | 2869.29i | 0.0133987 | − | 0.00872388i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 80462.1 | − | 139364.i | 0.237204 | − | 0.410849i | −0.722707 | − | 0.691155i | \(-0.757102\pi\) |
0.959911 | + | 0.280305i | \(0.0904357\pi\) | |||||||
\(164\) | −32933.7 | − | 57042.9i | −0.0956162 | − | 0.165612i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 592070. | + | 341832.i | 1.66764 | + | 0.962813i | ||||
\(167\) | −151029. | −0.419054 | −0.209527 | − | 0.977803i | \(-0.567192\pi\) | ||||
−0.209527 | + | 0.977803i | \(0.567192\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20443.7 | 0.0550608 | ||||||||
\(170\) | 1.28145e6 | + | 739845.i | 3.40078 | + | 1.96344i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 261851. | + | 453539.i | 0.674890 | + | 1.16894i | ||||
\(173\) | 48380.1 | − | 83796.9i | 0.122900 | − | 0.212869i | −0.798010 | − | 0.602644i | \(-0.794114\pi\) |
0.920910 | + | 0.389775i | \(0.127447\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −730905. | + | 39175.9i | −1.80412 | + | 0.0966994i | ||||
\(176\) | 276147.i | 0.671984i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −224044. | + | 129352.i | −0.530010 | + | 0.306002i | ||||
\(179\) | −55696.7 | + | 32156.5i | −0.129926 | + | 0.0750130i | −0.563554 | − | 0.826079i | \(-0.690566\pi\) |
0.433628 | + | 0.901092i | \(0.357233\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 465762.i | − | 1.05674i | −0.849015 | − | 0.528369i | \(-0.822804\pi\) | ||
0.849015 | − | 0.528369i | \(-0.177196\pi\) | |||||||
\(182\) | 325965. | + | 500639.i | 0.729444 | + | 1.12033i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 548.490 | − | 950.013i | 0.00119433 | − | 0.00206864i | ||||
\(185\) | −265892. | − | 460538.i | −0.571184 | − | 0.989319i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −432430. | − | 249663.i | −0.904298 | − | 0.522096i | ||||
\(188\) | −292930. | −0.604463 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −592171. | −1.19004 | ||||||||
\(191\) | −317171. | − | 183119.i | −0.629086 | − | 0.363203i | 0.151312 | − | 0.988486i | \(-0.451650\pi\) |
−0.780398 | + | 0.625283i | \(0.784984\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 107364. | + | 185960.i | 0.207475 | + | 0.359357i | 0.950918 | − | 0.309442i | \(-0.100142\pi\) |
−0.743444 | + | 0.668799i | \(0.766809\pi\) | |||||||
\(194\) | −376042. | + | 651325.i | −0.717352 | + | 1.24249i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 193948. | − | 438415.i | 0.360616 | − | 0.815164i | ||||
\(197\) | 194807.i | 0.357633i | 0.983882 | + | 0.178817i | \(0.0572269\pi\) | ||||
−0.983882 | + | 0.178817i | \(0.942773\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 481226. | − | 277836.i | 0.861423 | − | 0.497343i | −0.00306524 | − | 0.999995i | \(-0.500976\pi\) |
0.864489 | + | 0.502652i | \(0.167642\pi\) | |||||||
\(200\) | −132233. | + | 76345.0i | −0.233758 | + | 0.134960i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 150715.i | − | 0.259884i | ||||||
\(203\) | 681143. | + | 346041.i | 1.16011 | + | 0.589369i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −108133. | + | 187292.i | −0.179710 | + | 0.311268i | ||||
\(206\) | 386275. | + | 669047.i | 0.634203 | + | 1.09847i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 576144. | + | 332637.i | 0.923363 | + | 0.533104i | ||||
\(209\) | 199830. | 0.316443 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −236704. | −0.366016 | −0.183008 | − | 0.983111i | \(-0.558583\pi\) | ||||
−0.183008 | + | 0.983111i | \(0.558583\pi\) | |||||||
\(212\) | −972826. | − | 561662.i | −1.48661 | − | 0.858292i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −31987.8 | − | 55404.6i | −0.0477475 | − | 0.0827011i | ||||
\(215\) | 859748. | − | 1.48913e6i | 1.26845 | − | 2.19703i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1224.95 | + | 22853.9i | 0.00176591 | + | 0.0329466i | ||||
\(218\) | − | 1.10590e6i | − | 1.57607i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −568804. | + | 328399.i | −0.792329 | + | 0.457451i | ||||
\(221\) | −1.04178e6 | + | 601470.i | −1.43481 | + | 0.828387i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.15994e6i | 1.56197i | 0.624547 | + | 0.780987i | \(0.285284\pi\) | ||||
−0.624547 | + | 0.780987i | \(0.714716\pi\) | |||||||
\(224\) | −54624.5 | − | 1.01913e6i | −0.0727391 | − | 1.35709i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 166215. | − | 287892.i | 0.216470 | − | 0.374938i | ||||
\(227\) | −649781. | − | 1.12545e6i | −0.836956 | − | 1.44965i | −0.892428 | − | 0.451189i | \(-0.851000\pi\) |
0.0554727 | − | 0.998460i | \(-0.482333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11455.0 | − | 6613.53i | −0.0144346 | − | 0.00833383i | 0.492765 | − | 0.870162i | \(-0.335986\pi\) |
−0.507200 | + | 0.861828i | \(0.669319\pi\) | |||||||
\(230\) | 29553.8 | 0.0368378 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 159375. | 0.194402 | ||||||||
\(233\) | 852543. | + | 492216.i | 1.02879 | + | 0.593972i | 0.916637 | − | 0.399720i | \(-0.130892\pi\) |
0.112151 | + | 0.993691i | \(0.464226\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 480896. | + | 832937.i | 0.568044 | + | 0.983880i | ||||
\(236\) | −508761. | + | 881200.i | −0.594612 | + | 1.02990i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.82615e6 | + | 927736.i | 2.08974 | + | 1.06165i | ||||
\(239\) | − | 84518.9i | − | 0.0957104i | −0.998854 | − | 0.0478552i | \(-0.984761\pi\) | ||
0.998854 | − | 0.0478552i | \(-0.0152386\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 93542.5 | − | 54006.8i | 0.103745 | − | 0.0598971i | −0.447230 | − | 0.894419i | \(-0.647589\pi\) |
0.550975 | + | 0.834522i | \(0.314256\pi\) | |||||||
\(242\) | −677786. | + | 391320.i | −0.743968 | + | 0.429530i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 643977.i | − | 0.692462i | ||||||
\(245\) | −1.56502e6 | + | 168250.i | −1.66573 | + | 0.179078i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 240708. | − | 416918.i | 0.251043 | − | 0.434819i | ||||
\(248\) | 2387.15 | + | 4134.67i | 0.00246462 | + | 0.00426885i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.59069e6 | − | 918384.i | −1.60966 | − | 0.929339i | ||||
\(251\) | 957846. | 0.959646 | 0.479823 | − | 0.877365i | \(-0.340701\pi\) | ||||
0.479823 | + | 0.877365i | \(0.340701\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9973.05 | −0.00979550 | ||||||||
\(254\) | −2.07531e6 | − | 1.19818e6i | −2.01836 | − | 1.16530i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −619037. | − | 1.07220e6i | −0.590359 | − | 1.02253i | ||||
\(257\) | −300830. | + | 521054.i | −0.284112 | + | 0.492096i | −0.972393 | − | 0.233348i | \(-0.925032\pi\) |
0.688282 | + | 0.725443i | \(0.258365\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −401660. | − | 616896.i | −0.372057 | − | 0.571430i | ||||
\(260\) | 1.58231e6i | 1.45164i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.04801e6 | + | 605069.i | −0.943218 | + | 0.544567i | ||||
\(263\) | 1.63833e6 | − | 945888.i | 1.46053 | − | 0.843239i | 0.461496 | − | 0.887142i | \(-0.347313\pi\) |
0.999036 | + | 0.0439037i | \(0.0139795\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.68826e6i | 3.22632i | ||||||||
\(266\) | −818550. | + | 43873.6i | −0.709318 | + | 0.0380189i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −163364. | + | 282955.i | −0.138938 | + | 0.240647i | ||||
\(269\) | −131399. | − | 227590.i | −0.110716 | − | 0.191766i | 0.805343 | − | 0.592809i | \(-0.201981\pi\) |
−0.916059 | + | 0.401043i | \(0.868648\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −967784. | − | 558750.i | −0.800489 | − | 0.462162i | 0.0431532 | − | 0.999068i | \(-0.486260\pi\) |
−0.843642 | + | 0.536906i | \(0.819593\pi\) | |||||||
\(272\) | 2.28099e6 | 1.86940 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 547213. | 0.440332 | ||||||||
\(275\) | 1.20218e6 | + | 694080.i | 0.958602 | + | 0.553449i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.13495e6 | − | 1.96579e6i | −0.888745 | − | 1.53935i | −0.841360 | − | 0.540475i | \(-0.818244\pi\) |
−0.0473855 | − | 0.998877i | \(-0.515089\pi\) | |||||||
\(278\) | 247351. | − | 428424.i | 0.191956 | − | 0.332477i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −275167. | + | 179161.i | −0.209750 | + | 0.136568i | ||||
\(281\) | 1.32116e6i | 0.998137i | 0.866563 | + | 0.499068i | \(0.166324\pi\) | ||||
−0.866563 | + | 0.499068i | \(0.833676\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.91757e6 | − | 1.10711e6i | 1.42326 | − | 0.821720i | 0.426684 | − | 0.904401i | \(-0.359682\pi\) |
0.996576 | + | 0.0826808i | \(0.0263482\pi\) | |||||||
\(284\) | 1.18538e6 | − | 684380.i | 0.872092 | − | 0.503502i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 1.13299e6i | − | 0.819048i | ||||||
\(287\) | −135594. | + | 266903.i | −0.0971711 | + | 0.191271i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.35230e6 | + | 2.34226e6i | −0.952423 | + | 1.64964i | ||||
\(290\) | 2.14687e6 | + | 3.71849e6i | 1.49903 | + | 2.59640i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.47445e6 | − | 851273.i | −1.01198 | − | 0.584268i | ||||
\(293\) | −185273. | −0.126079 | −0.0630394 | − | 0.998011i | \(-0.520079\pi\) | ||||
−0.0630394 | + | 0.998011i | \(0.520079\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.34088e6 | 2.23514 | ||||||||
\(296\) | −132988. | − | 76780.9i | −0.0882235 | − | 0.0509359i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 143667. | + | 248838.i | 0.0937164 | + | 0.162322i | ||||
\(299\) | −12013.2 | + | 20807.4i | −0.00777104 | + | 0.0134598i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.07809e6 | − | 2.12210e6i | 0.685865 | − | 1.35005i | ||||
\(302\) | − | 4.18556e6i | − | 2.64081i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −790552. | + | 456425.i | −0.490621 | + | 0.283260i | ||||
\(305\) | −1.83113e6 | + | 1.05720e6i | −1.12712 | + | 0.650741i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.57311e6i | − | 0.952603i | −0.879282 | − | 0.476302i | \(-0.841977\pi\) | ||
0.879282 | − | 0.476302i | \(-0.158023\pi\) | |||||||
\(308\) | −761919. | + | 496084.i | −0.457648 | + | 0.297974i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −64312.4 | + | 111392.i | −0.0380094 | + | 0.0658341i | ||||
\(311\) | 1.05000e6 | + | 1.81865e6i | 0.615585 | + | 1.06623i | 0.990281 | + | 0.139078i | \(0.0444137\pi\) |
−0.374696 | + | 0.927148i | \(0.622253\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.34949e6 | + | 779129.i | 0.778591 | + | 0.449519i | 0.835931 | − | 0.548835i | \(-0.184929\pi\) |
−0.0573400 | + | 0.998355i | \(0.518262\pi\) | |||||||
\(314\) | −385435. | −0.220611 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.12336e6 | 1.19620 | ||||||||
\(317\) | −2.08730e6 | − | 1.20510e6i | −1.16664 | − | 0.673559i | −0.213753 | − | 0.976888i | \(-0.568569\pi\) |
−0.952886 | + | 0.303328i | \(0.901902\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −724470. | − | 1.25482e6i | −0.398606 | − | 0.690406i | ||||
\(320\) | 1.18490e6 | − | 2.05231e6i | 0.646856 | − | 1.12039i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 40851.9 | − | 2189.63i | 0.0219570 | − | 0.00117688i | ||||
\(323\) | − | 1.65061e6i | − | 0.880314i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.89621e6 | − | 1.67213e6i | 1.52097 | − | 0.878133i | ||||
\(326\) | 1.08421e6 | − | 625971.i | 0.565029 | − | 0.326220i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 62450.5i | 0.0320517i | ||||||||
\(329\) | 726449. | + | 1.11573e6i | 0.370011 | + | 0.568288i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −579027. | + | 1.00290e6i | −0.290488 | + | 0.503141i | −0.973925 | − | 0.226869i | \(-0.927151\pi\) |
0.683437 | + | 0.730010i | \(0.260484\pi\) | |||||||
\(332\) | 1.25330e6 | + | 2.17079e6i | 0.624038 | + | 1.08087i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.01755e6 | − | 587481.i | −0.499101 | − | 0.288156i | ||||
\(335\) | 1.07276e6 | 0.522267 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 585639. | 0.280902 | 0.140451 | − | 0.990088i | \(-0.455145\pi\) | ||||
0.140451 | + | 0.990088i | \(0.455145\pi\) | |||||||
\(338\) | 137738. | + | 79522.9i | 0.0655785 | + | 0.0378618i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.71259e6 | + | 4.69835e6i | 1.27259 | + | 2.20418i | ||||
\(341\) | 21702.5 | − | 37589.8i | 0.0101070 | − | 0.0175059i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.15084e6 | + | 348522.i | −0.987125 | + | 0.159954i | ||||
\(344\) | − | 496534.i | − | 0.226232i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 651915. | − | 376383.i | 0.292752 | − | 0.169021i | ||||
\(347\) | 1.57841e6 | − | 911294.i | 0.703713 | − | 0.406289i | −0.105016 | − | 0.994471i | \(-0.533489\pi\) |
0.808729 | + | 0.588182i | \(0.200156\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.25184e6i | 0.550155i | 0.961422 | + | 0.275077i | \(0.0887035\pi\) | ||||
−0.961422 | + | 0.275077i | \(0.911296\pi\) | |||||||
\(350\) | −5.07680e6 | − | 2.57917e6i | −2.21524 | − | 1.12541i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −967784. | + | 1.67625e6i | −0.416315 | + | 0.721078i | ||||
\(353\) | 331320. | + | 573862.i | 0.141518 | + | 0.245116i | 0.928068 | − | 0.372410i | \(-0.121468\pi\) |
−0.786551 | + | 0.617526i | \(0.788135\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.89202e6 | − | 2.24706e6i | −1.63909 | − | 0.946332i | ||||
\(356\) | −948522. | −0.396664 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −500336. | −0.206326 | ||||||||
\(359\) | −1.68613e6 | − | 973487.i | −0.690486 | − | 0.398652i | 0.113308 | − | 0.993560i | \(-0.463855\pi\) |
−0.803794 | + | 0.594908i | \(0.797189\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −907764. | − | 1.57229e6i | −0.366610 | − | 0.634988i | ||||
\(362\) | 1.81175e6 | − | 3.13803e6i | 0.726651 | − | 1.25860i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 117232. | + | 2.18720e6i | 0.0463761 | + | 0.865239i | ||||
\(365\) | 5.59005e6i | 2.19626i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.99252e6 | + | 1.72773e6i | −1.15977 | + | 0.669593i | −0.951249 | − | 0.308425i | \(-0.900198\pi\) |
−0.208521 | + | 0.978018i | \(0.566865\pi\) | |||||||
\(368\) | 39454.6 | − | 22779.1i | 0.0151872 | − | 0.00876834i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 4.13712e6i | − | 1.57106i | ||||||
\(371\) | 273261. | + | 5.09824e6i | 0.103073 | + | 1.92303i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.16752e6 | + | 2.02220e6i | −0.434502 | + | 0.752580i | −0.997255 | − | 0.0740452i | \(-0.976409\pi\) |
0.562752 | + | 0.826625i | \(0.309742\pi\) | |||||||
\(374\) | −1.94231e6 | − | 3.36417e6i | −0.718024 | − | 1.24365i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 240525. | + | 138867.i | 0.0877385 | + | 0.0506559i | ||||
\(377\) | −3.49068e6 | −1.26490 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.01660e6 | −0.363541 | −0.181771 | − | 0.983341i | \(-0.558183\pi\) | ||||
−0.181771 | + | 0.983341i | \(0.558183\pi\) | |||||||
\(380\) | −1.88027e6 | − | 1.08558e6i | −0.667978 | − | 0.385657i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.42461e6 | − | 2.46750e6i | −0.499502 | − | 0.865164i | ||||
\(383\) | −1.17345e6 | + | 2.03247e6i | −0.408759 | + | 0.707991i | −0.994751 | − | 0.102326i | \(-0.967372\pi\) |
0.585992 | + | 0.810317i | \(0.300705\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.66142e6 | + | 1.35208e6i | 0.915085 | + | 0.464890i | ||||
\(386\) | 1.67052e6i | 0.570668i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.38804e6 | + | 1.37873e6i | −0.805308 | + | 0.464945i | ||||
\(389\) | −1.90457e6 | + | 1.09960e6i | −0.638149 | + | 0.368436i | −0.783901 | − | 0.620886i | \(-0.786773\pi\) |
0.145752 | + | 0.989321i | \(0.453440\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 82377.9i | 0.0272501i | ||||||||
\(392\) | −367086. | + | 268039.i | −0.120657 | + | 0.0881013i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −757769. | + | 1.31249e6i | −0.245921 | + | 0.425948i | ||||
\(395\) | −3.48586e6 | − | 6.03769e6i | −1.12413 | − | 1.94705i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.09064e6 | + | 2.36173e6i | 1.30261 | + | 0.752063i | 0.980851 | − | 0.194758i | \(-0.0623922\pi\) |
0.321760 | + | 0.946821i | \(0.395726\pi\) | |||||||
\(398\) | 4.32297e6 | 1.36796 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.34130e6 | −1.98166 | ||||||||
\(401\) | −369827. | − | 213520.i | −0.114852 | − | 0.0663096i | 0.441474 | − | 0.897274i | \(-0.354456\pi\) |
−0.556325 | + | 0.830965i | \(0.687789\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −52283.9 | − | 90558.4i | −0.0160364 | − | 0.0277758i | ||||
\(404\) | 276294. | − | 478555.i | 0.0842206 | − | 0.145874i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.24310e6 | + | 4.98096e6i | 0.976438 | + | 1.49968i | ||||
\(407\) | 1.39609e6i | 0.417759i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 153620. | − | 88692.4i | 0.0454087 | − | 0.0262167i | −0.477124 | − | 0.878836i | \(-0.658321\pi\) |
0.522532 | + | 0.852619i | \(0.324987\pi\) | |||||||
\(410\) | −1.45707e6 | + | 841242.i | −0.428077 | + | 0.247150i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.83250e6i | 0.822104i | ||||||||
\(413\) | 4.61805e6 | − | 247524.i | 1.33224 | − | 0.0714072i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.11503e6 | − | 7.12744e6i | 1.17288 | − | 2.03148i | ||||
\(416\) | 2.33151e6 | + | 4.03830e6i | 0.660548 | + | 1.14410i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.34634e6 | + | 777309.i | 0.376889 | + | 0.217597i | ||||
\(419\) | 2.88404e6 | 0.802539 | 0.401269 | − | 0.915960i | \(-0.368569\pi\) | ||||
0.401269 | + | 0.915960i | \(0.368569\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 779255. | 0.214276 | 0.107138 | − | 0.994244i | \(-0.465831\pi\) | ||||
0.107138 | + | 0.994244i | \(0.465831\pi\) | |||||||
\(422\) | −1.59478e6 | − | 920744.i | −0.435932 | − | 0.251685i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 532525. | + | 922360.i | 0.143855 | + | 0.249164i | ||||
\(425\) | 5.73314e6 | − | 9.93009e6i | 1.53964 | − | 2.66674i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.45281e6 | + | 1.59702e6i | −0.651021 | + | 0.423879i | ||||
\(428\) | − | 234563.i | − | 0.0618941i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.15850e7 | − | 6.68858e6i | 3.02151 | − | 1.74447i | ||||
\(431\) | 746695. | − | 431105.i | 0.193620 | − | 0.111787i | −0.400056 | − | 0.916491i | \(-0.631009\pi\) |
0.593676 | + | 0.804704i | \(0.297676\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.90119e6i | − | 0.743629i | −0.928307 | − | 0.371815i | \(-0.878736\pi\) | ||
0.928307 | − | 0.371815i | \(-0.121264\pi\) | |||||||
\(434\) | −80645.2 | + | 158741.i | −0.0205520 | + | 0.0404543i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.02736e6 | − | 3.51150e6i | 0.510758 | − | 0.884659i | ||||
\(437\) | −16483.8 | − | 28550.8i | −0.00412908 | − | 0.00715178i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −886538. | − | 511843.i | −0.219551 | − | 0.126758i | 0.386191 | − | 0.922419i | \(-0.373791\pi\) |
−0.605743 | + | 0.795661i | \(0.707124\pi\) | |||||||
\(440\) | 622725. | 0.153343 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.35852e6 | −2.27851 | ||||||||
\(443\) | −3.25534e6 | − | 1.87947e6i | −0.788111 | − | 0.455016i | 0.0511864 | − | 0.998689i | \(-0.483700\pi\) |
−0.839297 | + | 0.543673i | \(0.817033\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.55716e6 | + | 2.69709e6i | 0.372764 | + | 0.645647i | ||||
\(446\) | −4.51200e6 | + | 7.81501e6i | −1.07407 | + | 1.86034i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.48582e6 | − | 2.92467e6i | 0.349761 | − | 0.688466i | ||||
\(449\) | − | 741230.i | − | 0.173515i | −0.996229 | − | 0.0867575i | \(-0.972349\pi\) | ||
0.996229 | − | 0.0867575i | \(-0.0276505\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 491695. | − | 283880.i | 0.113829 | − | 0.0657194i | ||||
\(452\) | 1.05554e6 | − | 609415.i | 0.243012 | − | 0.140303i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 1.01102e7i | − | 2.30208i | ||||||
\(455\) | 6.02678e6 | − | 3.92402e6i | 1.36476 | − | 0.888593i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.19819e6 | + | 2.07533e6i | −0.268372 | + | 0.464833i | −0.968441 | − | 0.249241i | \(-0.919819\pi\) |
0.700070 | + | 0.714074i | \(0.253152\pi\) | |||||||
\(458\) | −51451.3 | − | 89116.3i | −0.0114613 | − | 0.0198515i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 93840.1 | + | 54178.6i | 0.0206773 | + | 0.0119380i | ||||
\(461\) | −5.93969e6 | −1.30170 | −0.650851 | − | 0.759206i | \(-0.725588\pi\) | ||||
−0.650851 | + | 0.759206i | \(0.725588\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.06910e6 | 0.448569 | 0.224284 | − | 0.974524i | \(-0.427996\pi\) | ||||
0.224284 | + | 0.974524i | \(0.427996\pi\) | |||||||
\(464\) | 5.73218e6 | + | 3.30948e6i | 1.23602 | + | 0.713616i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.82929e6 | + | 6.63253e6i | 0.816871 | + | 1.41486i | ||||
\(467\) | 2.21202e6 | − | 3.83133e6i | 0.469350 | − | 0.812938i | −0.530036 | − | 0.847975i | \(-0.677822\pi\) |
0.999386 | + | 0.0350370i | \(0.0111549\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.48287e6 | − | 79480.6i | 0.311294 | − | 0.0166851i | ||||
\(470\) | 7.48246e6i | 1.56243i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 835486. | − | 482368.i | 0.172617 | − | 0.0996606i | ||||
\(473\) | −3.90939e6 | + | 2.25709e6i | −0.803445 | + | 0.463869i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.58879e6i | 0.933178i | ||||||||
\(476\) | 4.09768e6 | + | 6.29349e6i | 0.828935 | + | 1.27313i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 328766. | − | 569439.i | 0.0658138 | − | 0.113993i | ||||
\(479\) | 2.78502e6 | + | 4.82379e6i | 0.554612 | + | 0.960617i | 0.997934 | + | 0.0642538i | \(0.0204667\pi\) |
−0.443321 | + | 0.896363i | \(0.646200\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.91274e6 | + | 1.68167e6i | 0.574036 | + | 0.331420i | ||||
\(482\) | 840314. | 0.164749 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.86950e6 | −0.556791 | ||||||||
\(485\) | 7.84076e6 | + | 4.52687e6i | 1.51358 | + | 0.873863i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.77489e6 | − | 3.07420e6i | −0.339116 | − | 0.587367i | 0.645150 | − | 0.764056i | \(-0.276795\pi\) |
−0.984267 | + | 0.176689i | \(0.943461\pi\) | |||||||
\(488\) | −305285. | + | 528769.i | −0.0580305 | + | 0.100512i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.11986e7 | − | 4.95410e6i | −2.10705 | − | 0.932126i | ||||
\(491\) | 2.35429e6i | 0.440713i | 0.975419 | + | 0.220356i | \(0.0707221\pi\) | ||||
−0.975419 | + | 0.220356i | \(0.929278\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.03649e7 | + | 5.98416e6i | −1.92064 | + | 1.10888i | ||||
\(494\) | 3.24350e6 | − | 1.87264e6i | 0.597994 | − | 0.345252i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 198279.i | 0.0361888i | ||||||||
\(497\) | −5.54637e6 | − | 2.81772e6i | −1.00721 | − | 0.511690i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −389036. | + | 673830.i | −0.0699420 | + | 0.121143i | −0.898876 | − | 0.438204i | \(-0.855615\pi\) |
0.828934 | + | 0.559347i | \(0.188948\pi\) | |||||||
\(500\) | −3.36720e6 | − | 5.83215e6i | −0.602342 | − | 1.04329i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.45341e6 | + | 3.72588e6i | 1.14296 | + | 0.659886i | ||||
\(503\) | −8.32976e6 | −1.46795 | −0.733977 | − | 0.679175i | \(-0.762338\pi\) | ||||
−0.733977 | + | 0.679175i | \(0.762338\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.81434e6 | −0.316585 | ||||||||
\(506\) | −67192.6 | − | 38793.7i | −0.0116666 | − | 0.00673573i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.39304e6 | − | 7.60898e6i | −0.755277 | − | 1.30818i | ||||
\(509\) | 1.24589e6 | − | 2.15794e6i | 0.213150 | − | 0.369186i | −0.739549 | − | 0.673103i | \(-0.764961\pi\) |
0.952699 | + | 0.303917i | \(0.0982944\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 414164. | + | 7.72706e6i | 0.0701650 | + | 1.30907i | ||||
\(512\) | − | 7.86994e6i | − | 1.32677i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.05364e6 | + | 2.34037e6i | −0.676764 | + | 0.390730i | ||||
\(515\) | 8.05411e6 | − | 4.65004e6i | 1.33813 | − | 0.772572i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.52498e6i | − | 0.415463i | ||||||
\(518\) | −306517. | − | 5.71869e6i | −0.0501915 | − | 0.936423i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 750112. | − | 1.29923e6i | 0.121652 | − | 0.210707i | ||||
\(521\) | 590637. | + | 1.02301e6i | 0.0953294 | + | 0.165115i | 0.909746 | − | 0.415165i | \(-0.136276\pi\) |
−0.814417 | + | 0.580281i | \(0.802943\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.16423e6 | − | 2.98157e6i | −0.825565 | − | 0.476640i | 0.0267669 | − | 0.999642i | \(-0.491479\pi\) |
−0.852332 | + | 0.523002i | \(0.824812\pi\) | |||||||
\(524\) | −4.43689e6 | −0.705912 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.47175e7 | 2.31936 | ||||||||
\(527\) | −310493. | − | 179263.i | −0.0486997 | − | 0.0281168i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.21735e6 | − | 5.57261e6i | −0.499872 | − | 0.865804i | ||||
\(530\) | −1.43468e7 | + | 2.48494e7i | −2.21853 | + | 3.84260i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.67951e6 | − | 1.36127e6i | −0.410465 | − | 0.208529i | ||||
\(533\) | − | 1.36781e6i | − | 0.208548i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −666970. | + | 385075.i | −0.100745 | + | 0.0581649i | ||||
\(536\) | 268277. | − | 154890.i | 0.0403340 | − | 0.0232868i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 2.04449e6i | − | 0.304530i | ||||||
\(539\) | 3.77902e6 | + | 1.67178e6i | 0.560283 | + | 0.247860i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −771540. | + | 1.33635e6i | −0.113335 | + | 0.196303i | −0.917113 | − | 0.398627i | \(-0.869487\pi\) |
0.803778 | + | 0.594930i | \(0.202820\pi\) | |||||||
\(542\) | −4.34691e6 | − | 7.52907e6i | −0.635598 | − | 1.10089i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.38459e7 | + | 7.99395e6i | 2.00597 | + | 1.15815i | ||||
\(545\) | −1.33131e7 | −1.91994 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.77667e6 | 1.11129 | 0.555643 | − | 0.831421i | \(-0.312472\pi\) | ||||
0.555643 | + | 0.831421i | \(0.312472\pi\) | |||||||
\(548\) | 1.73752e6 | + | 1.00316e6i | 0.247161 | + | 0.142698i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.39974e6 | + | 9.35262e6i | 0.761142 | + | 1.31834i | ||||
\(551\) | 2.39486e6 | − | 4.14801e6i | 0.336047 | − | 0.582051i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.26579e6 | − | 8.08755e6i | −0.732235 | − | 1.12462i | ||||
\(554\) | − | 1.76591e7i | − | 2.44453i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.57079e6 | − | 906896.i | 0.215492 | − | 0.124414i | ||||
\(557\) | 6.40208e6 | − | 3.69624e6i | 0.874346 | − | 0.504804i | 0.00555602 | − | 0.999985i | \(-0.498231\pi\) |
0.868790 | + | 0.495181i | \(0.164898\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.08752e7i | 1.47200i | ||||||||
\(560\) | −1.36171e7 | + | 729867.i | −1.83491 | + | 0.0983499i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.13912e6 | + | 8.90122e6i | −0.686354 | + | 1.18880i | ||||
\(563\) | −5.22242e6 | − | 9.04550e6i | −0.694386 | − | 1.20271i | −0.970387 | − | 0.241555i | \(-0.922343\pi\) |
0.276001 | − | 0.961157i | \(-0.410991\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.46570e6 | − | 2.00092e6i | −0.456741 | − | 0.263699i | ||||
\(566\) | 1.72259e7 | 2.26017 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.29775e6 | −0.168780 | ||||||||
\(569\) | −4.16431e6 | − | 2.40427e6i | −0.539216 | − | 0.311316i | 0.205545 | − | 0.978648i | \(-0.434103\pi\) |
−0.744761 | + | 0.667331i | \(0.767437\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.34054e6 | + | 9.25008e6i | 0.685480 | + | 1.18729i | 0.973286 | + | 0.229597i | \(0.0737408\pi\) |
−0.287806 | + | 0.957689i | \(0.592926\pi\) | |||||||
\(572\) | 2.07701e6 | − | 3.59748e6i | 0.265429 | − | 0.459736i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.95177e6 | + | 1.27079e6i | −0.247257 | + | 0.160989i | ||||
\(575\) | − | 229016.i | − | 0.0288866i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.00975e6 | + | 582981.i | −0.126263 | + | 0.0728979i | −0.561801 | − | 0.827272i | \(-0.689891\pi\) |
0.435538 | + | 0.900170i | \(0.356558\pi\) | |||||||
\(578\) | −1.82221e7 | + | 1.05205e7i | −2.26871 | + | 1.30984i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.57427e7i | 1.94317i | ||||||||
\(581\) | 5.16009e6 | − | 1.01571e7i | 0.634186 | − | 1.24832i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.84138e6 | − | 8.38551e6i | 0.589926 | − | 1.02178i | ||||
\(584\) | 807112. | + | 1.39796e6i | 0.0979269 | + | 0.169614i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.24826e6 | − | 720683.i | −0.150162 | − | 0.0866962i | ||||
\(587\) | −90616.7 | −0.0108546 | −0.00542729 | − | 0.999985i | \(-0.501728\pi\) | ||||
−0.00542729 | + | 0.999985i | \(0.501728\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 143482. | 0.0170416 | ||||||||
\(590\) | 2.25089e7 | + | 1.29955e7i | 2.66210 | + | 1.53696i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.18875e6 | − | 5.52308e6i | −0.373953 | − | 0.647705i | ||||
\(593\) | −7.73816e6 | + | 1.34029e7i | −0.903651 | + | 1.56517i | −0.0809342 | + | 0.996719i | \(0.525790\pi\) |
−0.822717 | + | 0.568451i | \(0.807543\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.11683e7 | − | 2.19835e7i | 1.29328 | − | 2.54568i | ||||
\(596\) | 1.05349e6i | 0.121483i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −161875. | + | 93458.8i | −0.0185109 | + | 0.0106873i | ||||
\(599\) | −1.01493e7 | + | 5.85973e6i | −1.15577 | + | 0.667284i | −0.950286 | − | 0.311377i | \(-0.899210\pi\) |
−0.205483 | + | 0.978661i | \(0.565876\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.43153e6i | − | 0.387527i | −0.981048 | − | 0.193764i | \(-0.937931\pi\) | ||
0.981048 | − | 0.193764i | \(-0.0620695\pi\) | |||||||
\(602\) | 1.55182e7 | − | 1.01039e7i | 1.74522 | − | 1.13631i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.67305e6 | − | 1.32901e7i | 0.855807 | − | 1.48230i | ||||
\(605\) | 4.71078e6 | + | 8.15931e6i | 0.523244 | + | 0.906285i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.39375e7 | − | 8.04681e6i | −1.53537 | − | 0.886446i | −0.999101 | − | 0.0423977i | \(-0.986500\pi\) |
−0.536268 | − | 0.844048i | \(-0.680166\pi\) | |||||||
\(608\) | −6.39834e6 | −0.701954 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.64494e7 | −1.78989 | ||||||||
\(611\) | −5.26803e6 | − | 3.04150e6i | −0.570881 | − | 0.329598i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.15527e6 | − | 2.00099e6i | −0.124175 | − | 0.215077i | 0.797235 | − | 0.603669i | \(-0.206295\pi\) |
−0.921410 | + | 0.388592i | \(0.872962\pi\) | |||||||
\(614\) | 6.11915e6 | − | 1.05987e7i | 0.655043 | − | 1.13457i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 860785. | − | 46137.4i | 0.0913994 | − | 0.00489893i | ||||
\(617\) | 3.72656e6i | 0.394090i | 0.980394 | + | 0.197045i | \(0.0631345\pi\) | ||||
−0.980394 | + | 0.197045i | \(0.936866\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.19584e7 | + | 6.90416e6i | −1.25443 | + | 0.724243i | −0.971985 | − | 0.235042i | \(-0.924477\pi\) |
−0.282440 | + | 0.959285i | \(0.591144\pi\) | |||||||
\(620\) | −408413. | + | 235797.i | −0.0426697 | + | 0.0246354i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.63374e7i | 1.69319i | ||||||||
\(623\) | 2.35227e6 | + | 3.61278e6i | 0.242811 | + | 0.372925i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.23385e6 | + | 3.86913e6i | −0.228746 | + | 0.396199i | ||||
\(626\) | 6.06139e6 | + | 1.04986e7i | 0.618211 | + | 1.07077i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.22384e6 | − | 706586.i | −0.123830 | − | 0.0714934i | ||||
\(629\) | 1.15317e7 | 1.16217 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.04954e6 | 0.904801 | 0.452401 | − | 0.891815i | \(-0.350568\pi\) | ||||
0.452401 | + | 0.891815i | \(0.350568\pi\) | |||||||
\(632\) | −1.74349e6 | − | 1.00660e6i | −0.173630 | − | 0.100246i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.37534e6 | − | 1.62386e7i | −0.926326 | − | 1.60444i | ||||
\(635\) | −1.44239e7 | + | 2.49829e7i | −1.41954 | + | 2.45872i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.04001e6 | − | 5.87065e6i | 0.785069 | − | 0.573241i | ||||
\(638\) | − | 1.12723e7i | − | 1.09638i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.46566e6 | + | 2.57825e6i | −0.430959 | + | 0.248814i | ||||
\(641\) | 5.32452e6 | − | 3.07412e6i | 0.511842 | − | 0.295512i | −0.221749 | − | 0.975104i | \(-0.571176\pi\) |
0.733590 | + | 0.679592i | \(0.237843\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.13071e6i | 0.489384i | 0.969601 | + | 0.244692i | \(0.0786869\pi\) | ||||
−0.969601 | + | 0.244692i | \(0.921313\pi\) | |||||||
\(644\) | 133728. | + | 67937.8i | 0.0127060 | + | 0.00645501i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.42062e6 | − | 1.11208e7i | 0.605335 | − | 1.04847i | ||||
\(647\) | −3.78852e6 | − | 6.56190e6i | −0.355802 | − | 0.616267i | 0.631453 | − | 0.775414i | \(-0.282459\pi\) |
−0.987255 | + | 0.159147i | \(0.949126\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.59571e6 | − | 4.38539e6i | −0.707875 | − | 0.408692i | ||||
\(650\) | 2.60173e7 | 2.41534 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.59016e6 | 0.422872 | ||||||||
\(653\) | 1.08612e7 | + | 6.27074e6i | 0.996773 | + | 0.575487i | 0.907292 | − | 0.420501i | \(-0.138146\pi\) |
0.0894813 | + | 0.995988i | \(0.471479\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.28393e6 | + | 1.26161e7i | 0.663380 | + | 1.14901i | ||||
\(656\) | −1.29680e6 | + | 2.24613e6i | −0.117656 | + | 0.203786i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 554372. | + | 1.03429e7i | 0.0499156 | + | 0.931275i | ||||
\(659\) | 8.97219e6i | 0.804795i | 0.915465 | + | 0.402397i | \(0.131823\pi\) | ||||
−0.915465 | + | 0.402397i | \(0.868177\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15373.7 | + | 8876.02i | −0.00136860 | + | 0.000790159i | −0.500684 | − | 0.865630i | \(-0.666918\pi\) |
0.499316 | + | 0.866420i | \(0.333585\pi\) | |||||||
\(662\) | −7.80230e6 | + | 4.50466e6i | −0.691954 | + | 0.399500i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 2.37657e6i | − | 0.209185i | ||||||
\(665\) | 528158. | + | 9.85385e6i | 0.0463138 | + | 0.864076i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −119522. | + | 207018.i | −0.0104024 | + | 0.0180174i | ||||
\(668\) | −2.15396e6 | − | 3.73077e6i | −0.186765 | − | 0.323487i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.22767e6 | + | 4.17289e6i | 0.622030 | + | 0.359129i | ||||
\(671\) | 5.55092e6 | 0.475947 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −235445. | −0.0200379 | −0.0100189 | − | 0.999950i | \(-0.503189\pi\) | ||||
−0.0100189 | + | 0.999950i | \(0.503189\pi\) | |||||||
\(674\) | 3.94570e6 | + | 2.27805e6i | 0.334560 | + | 0.193158i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 291566. | + | 505007.i | 0.0245397 | + | 0.0425040i | ||||
\(677\) | 6.31071e6 | − | 1.09305e7i | 0.529184 | − | 0.916573i | −0.470237 | − | 0.882540i | \(-0.655832\pi\) |
0.999421 | − | 0.0340329i | \(-0.0108351\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.11736e7 | + | 5.67651e6i | 0.930075 | + | 0.472506i | ||||
\(680\) | − | 5.14375e6i | − | 0.426587i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 292437. | − | 168839.i | 0.0240753 | − | 0.0138999i | ||||
\(683\) | 6.84555e6 | − | 3.95228e6i | 0.561509 | − | 0.324187i | −0.192242 | − | 0.981348i | \(-0.561576\pi\) |
0.753751 | + | 0.657160i | \(0.228243\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 6.58745e6i | − | 0.536402i | ||||||
\(686\) | −1.58468e7 | − | 6.01829e6i | −1.28567 | − | 0.488273i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.03107e7 | − | 1.78586e7i | 0.830455 | − | 1.43839i | ||||
\(689\) | −1.16635e7 | − | 2.02017e7i | −0.936009 | − | 1.62122i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.05423e7 | + | 6.08661e6i | 0.839925 | + | 0.484931i | 0.857239 | − | 0.514919i | \(-0.172178\pi\) |
−0.0173134 | + | 0.999850i | \(0.505511\pi\) | |||||||
\(692\) | 2.75997e6 | 0.219098 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.41792e7 | 1.11751 | ||||||||
\(695\) | −5.15745e6 | − | 2.97765e6i | −0.405017 | − | 0.233836i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.34487e6 | − | 4.06143e6i | −0.182825 | − | 0.316663i | ||||
\(698\) | −4.86947e6 | + | 8.43417e6i | −0.378306 | + | 0.655245i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.13918e7 | − | 1.74963e7i | −0.878714 | − | 1.34959i | ||||
\(701\) | 1.11324e7i | 0.855643i | 0.903863 | + | 0.427821i | \(0.140719\pi\) | ||||
−0.903863 | + | 0.427821i | \(0.859281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.99670e6 | + | 2.30750e6i | −0.305010 | + | 0.176097i | ||||
\(704\) | −5.38791e6 | + | 3.11071e6i | −0.409722 | + | 0.236553i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.15514e6i | 0.389250i | ||||||||
\(707\) | −2.50794e6 | + | 134423.i | −0.188698 | + | 0.0101141i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −275013. | + | 476337.i | −0.0205465 | + | 0.0355876i | −0.876116 | − | 0.482101i | \(-0.839874\pi\) |
0.855569 | + | 0.517688i | \(0.173207\pi\) | |||||||
\(710\) | −1.74814e7 | − | 3.02788e7i | −1.30146 | − | 2.25420i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 778831. | + | 449658.i | 0.0575762 | + | 0.0332416i | ||||
\(713\) | −7160.86 | −0.000527523 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.36391e7 | −0.997746 | ||||||||
\(716\) | −1.58868e6 | − | 917225.i | −0.115812 | − | 0.0668641i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.57344e6 | − | 1.31176e7i | −0.548254 | − | 0.949604i | ||||
\(719\) | 1.86659e6 | − | 3.23302e6i | 0.134656 | − | 0.233231i | −0.790810 | − | 0.612062i | \(-0.790340\pi\) |
0.925466 | + | 0.378831i | \(0.123674\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.07886e7 | − | 7.02442e6i | 0.772905 | − | 0.503237i | ||||
\(722\) | − | 1.41243e7i | − | 1.00838i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.15054e7 | − | 6.64264e6i | 0.815746 | − | 0.470971i | ||||
\(725\) | 2.88150e7 | − | 1.66364e7i | 2.03598 | − | 1.17547i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.07995e7i | − | 0.757825i | −0.925433 | − | 0.378913i | \(-0.876298\pi\) | ||
0.925433 | − | 0.378913i | \(-0.123702\pi\) | |||||||
\(728\) | 940611. | − | 1.85149e6i | 0.0657781 | − | 0.129477i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.17445e7 | + | 3.76625e7i | −1.51023 | + | 2.61579i | ||||
\(731\) | 1.86437e7 | + | 3.22918e7i | 1.29044 | + | 2.23511i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.12726e7 | + | 6.50822e6i | 0.774931 | + | 0.447406i | 0.834631 | − | 0.550810i | \(-0.185681\pi\) |
−0.0597000 | + | 0.998216i | \(0.519014\pi\) | |||||||
\(734\) | −2.68825e7 | −1.84174 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 319326. | 0.0217290 | ||||||||
\(737\) | −2.43900e6 | − | 1.40816e6i | −0.165403 | − | 0.0954955i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.40330e7 | + | 2.43058e7i | 0.945232 | + | 1.63719i | 0.755285 | + | 0.655396i | \(0.227498\pi\) |
0.189947 | + | 0.981794i | \(0.439168\pi\) | |||||||
\(740\) | 7.58424e6 | − | 1.31363e7i | 0.509135 | − | 0.881847i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.79903e7 | + | 3.54119e7i | −1.19958 | + | 2.36124i | ||||
\(743\) | 1.08931e7i | 0.723901i | 0.932197 | + | 0.361951i | \(0.117889\pi\) | ||||
−0.932197 | + | 0.361951i | \(0.882111\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.99556e6 | − | 1.72949e6i | 0.197737 | − | 0.114163i | ||||
\(746\) | −1.57321e7 | + | 9.08296e6i | −1.03500 | + | 0.597558i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1.42427e7i | − | 0.930760i | ||||||
\(749\) | −893414. | + | 581700.i | −0.0581900 | + | 0.0378874i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.92719e6 | + | 1.37303e7i | −0.512884 | + | 0.888341i | 0.487004 | + | 0.873400i | \(0.338090\pi\) |
−0.999888 | + | 0.0149418i | \(0.995244\pi\) | |||||||
\(752\) | 5.76723e6 | + | 9.98914e6i | 0.371897 | + | 0.644145i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.35182e7 | − | 1.35782e7i | −1.50652 | − | 0.869790i | ||||
\(755\) | −5.03866e7 | −3.21697 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.74726e7 | 1.10820 | 0.554100 | − | 0.832450i | \(-0.313063\pi\) | ||||
0.554100 | + | 0.832450i | \(0.313063\pi\) | |||||||
\(758\) | −6.84929e6 | − | 3.95444e6i | −0.432985 | − | 0.249984i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.02926e6 | + | 1.78273e6i | 0.0646386 | + | 0.111957i | ||||
\(761\) | 1.03862e7 | − | 1.79894e7i | 0.650122 | − | 1.12604i | −0.332971 | − | 0.942937i | \(-0.608051\pi\) |
0.983093 | − | 0.183107i | \(-0.0586155\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.84025e7 | + | 986359.i | −1.14437 | + | 0.0613372i | ||||
\(764\) | − | 1.04465e7i | − | 0.647495i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.58120e7 | + | 9.12908e6i | −0.973679 | + | 0.562154i | ||||
\(767\) | −1.82990e7 | + | 1.05649e7i | −1.12315 | + | 0.648453i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.69450e7i | 1.64309i | 0.570141 | + | 0.821547i | \(0.306889\pi\) | ||||
−0.570141 | + | 0.821547i | \(0.693111\pi\) | |||||||
\(770\) | 1.26717e7 | + | 1.94621e7i | 0.770208 | + | 1.18294i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.06242e6 | + | 5.30428e6i | −0.184936 | + | 0.320319i | ||||
\(773\) | 8.34621e6 | + | 1.44561e7i | 0.502390 | + | 0.870165i | 0.999996 | + | 0.00276163i | \(0.000879055\pi\) |
−0.497606 | + | 0.867403i | \(0.665788\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 863192. | + | 498364.i | 0.0516241 | + | 0.0298052i | ||||
\(776\) | 2.61442e6 | 0.155855 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.71092e7 | −1.01340 | ||||||||
\(779\) | 1.62538e6 | + | 938414.i | 0.0959646 | + | 0.0554052i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.89918e6 | + | 1.02177e7i | 0.346070 | + | 0.599411i | ||||
\(782\) | −320438. | + | 555015.i | −0.0187382 | + | 0.0324554i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.87687e7 | + | 2.01777e6i | −1.09055 | + | 0.117242i | ||||
\(785\) | 4.63993e6i | 0.268743i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.26325e7 | − | 1.30669e7i | 1.30255 | − | 0.752028i | 0.321710 | − | 0.946838i | \(-0.395742\pi\) |
0.980841 | + | 0.194810i | \(0.0624090\pi\) | |||||||
\(788\) | −4.81217e6 | + | 2.77831e6i | −0.276074 | + | 0.159391i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 5.42379e7i | − | 3.09197i | ||||||
\(791\) | −4.93884e6 | − | 2.50908e6i | −0.280662 | − | 0.142585i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.68643e6 | − | 1.15812e7i | 0.377582 | − | 0.653991i | ||||
\(794\) | 1.83736e7 | + | 3.18240e7i | 1.03429 | + | 1.79144i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.37264e7 | + | 7.92493e6i | 0.767845 | + | 0.443316i | ||||
\(797\) | 3.57013e6 | 0.199085 | 0.0995423 | − | 0.995033i | \(-0.468262\pi\) | ||||
0.0995423 | + | 0.995033i | \(0.468262\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.08565e7 | −1.15578 | ||||||||
\(800\) | −3.84925e7 | − | 2.22237e7i | −2.12643 | − | 1.22770i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.66112e6 | − | 2.87714e6i | −0.0911937 | − | 0.157952i | ||||
\(803\) | 7.33775e6 | − | 1.27094e7i | 0.401582 | − | 0.695560i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −26359.1 | − | 491782.i | −0.00143364 | − | 0.0267475i | ||||
\(806\) | − | 813507.i | − | 0.0441086i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −453730. | + | 261961.i | −0.0244494 | + | 0.0141159i | ||||
\(809\) | 1.54161e7 | − | 8.90052e6i | 0.828141 | − | 0.478128i | −0.0250745 | − | 0.999686i | \(-0.507982\pi\) |
0.853216 | + | 0.521558i | \(0.174649\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3.44374e7i | − | 1.83856i | −0.393604 | − | 0.919280i | \(-0.628772\pi\) | ||
0.393604 | − | 0.919280i | \(-0.371228\pi\) | |||||||
\(812\) | 1.16637e6 | + | 2.17610e7i | 0.0620793 | + | 1.15821i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.43057e6 | + | 9.40602e6i | −0.287266 | + | 0.497559i | ||||
\(815\) | −7.53555e6 | − | 1.30520e7i | −0.397394 | − | 0.688306i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.29231e7 | − | 7.46118e6i | −0.677350 | − | 0.391068i | ||||
\(818\) | 1.38000e6 | 0.0721101 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.16872e6 | −0.320376 | ||||||||
\(821\) | −9.54659e6 | − | 5.51173e6i | −0.494300 | − | 0.285384i | 0.232057 | − | 0.972702i | \(-0.425455\pi\) |
−0.726357 | + | 0.687318i | \(0.758788\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.13845e6 | − | 1.97185e6i | −0.0585886 | − | 0.101478i | 0.835243 | − | 0.549880i | \(-0.185327\pi\) |
−0.893832 | + | 0.448402i | \(0.851993\pi\) | |||||||
\(824\) | 1.34278e6 | − | 2.32576e6i | 0.0688949 | − | 0.119329i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.20766e7 | + | 1.62959e7i | 1.63583 | + | 0.831050i | ||||
\(827\) | 8.44456e6i | 0.429352i | 0.976685 | + | 0.214676i | \(0.0688695\pi\) | ||||
−0.976685 | + | 0.214676i | \(0.931130\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.63761e6 | − | 2.10018e6i | 0.183836 | − | 0.106138i | −0.405258 | − | 0.914202i | \(-0.632818\pi\) |
0.589094 | + | 0.808065i | \(0.299485\pi\) | |||||||
\(830\) | 5.54494e7 | − | 3.20137e7i | 2.79384 | − | 1.61302i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.49882e7i | 0.750656i | ||||||||
\(833\) | 1.38090e7 | − | 3.12149e7i | 0.689524 | − | 1.55865i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.07220e6 | + | 1.22494e7i | −0.351025 | + | 0.607994i | ||||
\(836\) | 2.84995e6 | + | 4.93627e6i | 0.141033 | + | 0.244277i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.94310e7 | + | 1.12185e7i | 0.955839 | + | 0.551854i | ||||
\(839\) | −308450. | −0.0151279 | −0.00756397 | − | 0.999971i | \(-0.502408\pi\) | ||||
−0.00756397 | + | 0.999971i | \(0.502408\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.42184e7 | −0.693203 | ||||||||
\(842\) | 5.25016e6 | + | 3.03118e6i | 0.255207 | + | 0.147344i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.37585e6 | − | 5.84714e6i | −0.163127 | − | 0.282545i | ||||
\(845\) | 957312. | − | 1.65811e6i | 0.0461224 | − | 0.0798863i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.11617e6 | + | 1.09295e7i | 0.340830 | + | 0.523470i | ||||
\(848\) | 4.42321e7i | 2.11226i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.72531e7 | − | 4.46021e7i | 3.66749 | − | 2.11742i | ||||
\(851\) | 199466. | − | 115162.i | 0.00944158 | − | 0.00545110i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 5.93710e6i | − | 0.279384i | −0.990195 | − | 0.139692i | \(-0.955389\pi\) | ||
0.990195 | − | 0.139692i | \(-0.0446113\pi\) | |||||||
\(854\) | −2.27378e7 | + | 1.21873e6i | −1.06685 | + | 0.0571824i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −111197. | + | 192599.i | −0.00518692 | + | 0.00898400i | ||||
\(857\) | −4.12425e6 | − | 7.14341e6i | −0.191820 | − | 0.332241i | 0.754034 | − | 0.656836i | \(-0.228106\pi\) |
−0.945853 | + | 0.324594i | \(0.894772\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.27857e7 | + | 1.31553e7i | 1.05361 | + | 0.608300i | 0.923657 | − | 0.383220i | \(-0.125185\pi\) |
0.129950 | + | 0.991521i | \(0.458518\pi\) | |||||||
\(860\) | 4.90465e7 | 2.26132 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.70773e6 | 0.307473 | ||||||||
\(863\) | 3.11798e7 | + | 1.80017e7i | 1.42510 | + | 0.822784i | 0.996729 | − | 0.0808178i | \(-0.0257532\pi\) |
0.428374 | + | 0.903601i | \(0.359087\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.53097e6 | − | 7.84786e6i | −0.205897 | − | 0.356625i | ||||
\(866\) | 1.12852e7 | − | 1.95465e7i | 0.511346 | − | 0.885677i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −547074. | + | 356199.i | −0.0246460 | + | 0.0160470i | ||||
\(869\) | 1.83028e7i | 0.822181i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.87586e6 | + | 3.39243e6i | −0.262438 | + | 0.151518i | ||||
\(872\) | −3.32933e6 | + | 1.92219e6i | −0.148274 | + | 0.0856062i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 256478.i | − | 0.0113572i | ||||||
\(875\) | −1.38634e7 | + | 2.72885e7i | −0.612137 | + | 1.20492i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.03213e7 | − | 3.51975e7i | 0.892179 | − | 1.54530i | 0.0549211 | − | 0.998491i | \(-0.482509\pi\) |
0.837258 | − | 0.546808i | \(-0.184157\pi\) | |||||||
\(878\) | −3.98199e6 | − | 6.89701e6i | −0.174327 | − | 0.301943i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.23973e7 | + | 1.29311e7i | 0.974964 | + | 0.562896i | ||||
\(881\) | −1.74116e7 | −0.755787 | −0.377894 | − | 0.925849i | \(-0.623351\pi\) | ||||
−0.377894 | + | 0.925849i | \(0.623351\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.31051e7 | 0.997255 | 0.498628 | − | 0.866816i | \(-0.333838\pi\) | ||||
0.498628 | + | 0.866816i | \(0.333838\pi\) | |||||||
\(884\) | −2.97154e7 | − | 1.71562e7i | −1.27894 | − | 0.738398i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.46217e7 | − | 2.53256e7i | −0.625770 | − | 1.08386i | ||||
\(887\) | 1.32420e7 | − | 2.29359e7i | 0.565126 | − | 0.978828i | −0.431911 | − | 0.901916i | \(-0.642161\pi\) |
0.997038 | − | 0.0769117i | \(-0.0245060\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.80870e7 | + | 3.56022e7i | −0.767560 | + | 1.51086i | ||||
\(890\) | 2.42285e7i | 1.02530i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.86532e7 | + | 1.65429e7i | −1.20576 | + | 0.696147i | ||||
\(893\) | 7.22850e6 | − | 4.17338e6i | 0.303333 | − | 0.175129i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.02314e6i | 0.251342i | ||||||||
\(896\) | −5.98181e6 | + | 3.89474e6i | −0.248922 | + | 0.162072i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.88327e6 | − | 4.99398e6i | 0.119315 | − | 0.206660i | ||||
\(899\) | −520185. | − | 900986.i | −0.0214664 | − | 0.0371808i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.92648e7 | − | 3.99900e7i | −2.84250 | − | 1.64112i | ||||
\(902\) | 4.41701e6 | 0.180764 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.15560e6 | −0.0470313 | ||||||||
\(905\) | −3.77762e7 | − | 2.18101e7i | −1.53319 | − | 0.885190i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.08942e7 | − | 1.88692e7i | −0.439719 | − | 0.761616i | 0.557948 | − | 0.829876i | \(-0.311589\pi\) |
−0.997668 | + | 0.0682597i | \(0.978255\pi\) | |||||||
\(908\) | 1.85342e7 | − | 3.21022e7i | 0.746035 | − | 1.29217i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.58688e7 | − | 2.99452e6i | 2.23648 | − | 0.119874i | ||||
\(911\) | 560911.i | 0.0223923i | 0.999937 | + | 0.0111961i | \(0.00356391\pi\) | ||||
−0.999937 | + | 0.0111961i | \(0.996436\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.87116e7 | + | 1.08031e7i | −0.742906 | + | 0.428917i | ||||
\(914\) | −1.61455e7 | + | 9.32159e6i | −0.639271 | + | 0.369083i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 377286.i | − | 0.0148570i | ||||||
\(917\) | 1.10032e7 | + | 1.68995e7i | 0.432111 | + | 0.663666i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.84712e6 | − | 1.35916e7i | 0.306494 | − | 0.530863i | −0.671099 | − | 0.741368i | \(-0.734178\pi\) |
0.977593 | + | 0.210505i | \(0.0675109\pi\) | |||||||
\(920\) | −51368.0 | − | 88972.0i | −0.00200089 | − | 0.00346564i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.00182e7 | − | 2.31045e7i | −1.55035 | − | 0.895095i | ||||
\(923\) | 2.84237e7 | 1.09819 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.20590e7 | −1.23196 | ||||||||
\(926\) | 1.39404e7 | + | 8.04850e6i | 0.534254 | + | 0.308452i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.31967e7 | + | 4.01779e7i | 0.884213 | + | 1.53150i | ||||
\(929\) | −8.68727e6 | + | 1.50468e7i | −0.330251 | + | 0.572012i | −0.982561 | − | 0.185941i | \(-0.940467\pi\) |
0.652310 | + | 0.757952i | \(0.273800\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.46013e6 | + | 1.35817e7i | 0.0552101 | + | 0.513548i | ||||
\(932\) | 2.80797e7i | 1.05889i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.98066e7 | − | 1.72089e7i | 1.11801 | − | 0.645483i | ||||
\(935\) | −4.04985e7 | + | 2.33818e7i | −1.51499 | + | 0.874681i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 276622.i | 0.0102929i | 0.999987 | + | 0.00514646i | \(0.00163818\pi\) | ||||
−0.999987 | + | 0.00514646i | \(0.998362\pi\) | |||||||
\(938\) | 1.02999e7 | + | 5.23265e6i | 0.382230 | + | 0.194184i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.37170e7 | + | 2.37585e7i | −0.506336 | + | 0.876999i | ||||
\(941\) | 1.43311e7 | + | 2.48222e7i | 0.527601 | + | 0.913831i | 0.999482 | + | 0.0321695i | \(0.0102416\pi\) |
−0.471882 | + | 0.881662i | \(0.656425\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −81118.9 | − | 46834.0i | −0.00297059 | − | 0.00171507i | ||||
\(944\) | 4.00661e7 | 1.46334 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.51189e7 | −1.27589 | ||||||||
\(947\) | −2.43615e7 | − | 1.40651e7i | −0.882733 | − | 0.509646i | −0.0111747 | − | 0.999938i | \(-0.503557\pi\) |
−0.871559 | + | 0.490291i | \(0.836890\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.76776e7 | − | 3.06184e7i | −0.637172 | − | 1.10361i | ||||
\(950\) | −1.78497e7 | + | 3.09166e7i | −0.641686 | + | 1.11143i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −381097. | − | 7.11013e6i | −0.0136284 | − | 0.254264i | ||||
\(953\) | − | 4.83932e7i | − | 1.72604i | −0.505166 | − | 0.863022i | \(-0.668569\pi\) | ||
0.505166 | − | 0.863022i | \(-0.331431\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.97042e7 | + | 1.71497e7i | −1.05392 | + | 0.608483i | ||||
\(956\) | 2.08781e6 | − | 1.20540e6i | 0.0738834 | − | 0.0426566i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.33332e7i | 1.52548i | ||||||||
\(959\) | −488061. | − | 9.10574e6i | −0.0171367 | − | 0.319719i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.42990e7 | + | 2.47666e7i | −0.499456 | + | 0.865083i | ||||
\(962\) | 1.30829e7 | + | 2.26603e7i | 0.455792 | + | 0.789455i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.66819e6 | + | 1.54048e6i | 0.0924748 | + | 0.0533904i | ||||
\(965\) | 2.01100e7 | 0.695175 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.31731e7 | 0.453023 | 0.226512 | − | 0.974008i | \(-0.427268\pi\) | ||||
0.226512 | + | 0.974008i | \(0.427268\pi\) | |||||||
\(968\) | 2.35614e6 | + | 1.36032e6i | 0.0808189 | + | 0.0466608i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.52177e7 | + | 6.09988e7i | 1.20180 | + | 2.08157i | ||||
\(971\) | 1.74045e7 | − | 3.01455e7i | 0.592397 | − | 1.02606i | −0.401511 | − | 0.915854i | \(-0.631515\pi\) |
0.993909 | − | 0.110208i | \(-0.0351518\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.34969e6 | − | 3.73386e6i | −0.248878 | − | 0.126438i | ||||
\(974\) | − | 2.76162e7i | − | 0.932753i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.19601e7 | + | 1.26787e7i | −0.737921 | + | 0.426039i | ||||
\(977\) | −3.91689e7 | + | 2.26142e7i | −1.31282 | + | 0.757956i | −0.982562 | − | 0.185935i | \(-0.940468\pi\) |
−0.330256 | + | 0.943891i | \(0.607135\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 8.17601e6i | − | 0.272637i | ||||||
\(980\) | −2.64762e7 | − | 3.62599e7i | −0.880625 | − | 1.20604i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.15783e6 | + | 1.58618e7i | −0.303050 | + | 0.524897i | ||||
\(983\) | −2.18408e7 | − | 3.78293e7i | −0.720915 | − | 1.24866i | −0.960633 | − | 0.277819i | \(-0.910388\pi\) |
0.239718 | − | 0.970842i | \(-0.422945\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.58000e7 | + | 9.12216e6i | 0.518881 | + | 0.299576i | ||||
\(986\) | −9.31100e7 | −3.05003 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.37318e7 | 0.447543 | ||||||||
\(989\) | 644963. | + | 372370.i | 0.0209674 | + | 0.0121055i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.58972e6 | − | 4.48552e6i | −0.0837661 | − | 0.145087i | 0.821099 | − | 0.570786i | \(-0.193362\pi\) |
−0.904865 | + | 0.425699i | \(0.860028\pi\) | |||||||
\(992\) | −694889. | + | 1.20358e6i | −0.0224200 | + | 0.0388326i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.64077e7 | − | 4.05587e7i | −0.847744 | − | 1.30202i | ||||
\(995\) | − | 5.20406e7i | − | 1.66642i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.66534e7 | − | 2.11619e7i | 1.16782 | − | 0.674242i | 0.214656 | − | 0.976690i | \(-0.431137\pi\) |
0.953166 | + | 0.302447i | \(0.0978037\pi\) | |||||||
\(998\) | −5.24219e6 | + | 3.02658e6i | −0.166605 | + | 0.0961892i | ||||
\(999\) | 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 | 63.6.p.b.26.10 | yes | 24 | |
3.2 | odd | 2 | inner | 63.6.p.b.26.3 | yes | 24 | |
7.2 | even | 3 | 441.6.c.b.440.1 | 24 | |||
7.3 | odd | 6 | inner | 63.6.p.b.17.3 | ✓ | 24 | |
7.5 | odd | 6 | 441.6.c.b.440.23 | 24 | |||
21.2 | odd | 6 | 441.6.c.b.440.24 | 24 | |||
21.5 | even | 6 | 441.6.c.b.440.2 | 24 | |||
21.17 | even | 6 | inner | 63.6.p.b.17.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.6.p.b.17.3 | ✓ | 24 | 7.3 | odd | 6 | inner | |
63.6.p.b.17.10 | yes | 24 | 21.17 | even | 6 | inner | |
63.6.p.b.26.3 | yes | 24 | 3.2 | odd | 2 | inner | |
63.6.p.b.26.10 | yes | 24 | 1.1 | even | 1 | trivial | |
441.6.c.b.440.1 | 24 | 7.2 | even | 3 | |||
441.6.c.b.440.2 | 24 | 21.5 | even | 6 | |||
441.6.c.b.440.23 | 24 | 7.5 | odd | 6 | |||
441.6.c.b.440.24 | 24 | 21.2 | odd | 6 |